LMFDB - Embedded newform 1638.2.bj.d.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (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:	$13.0794958511$
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 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.d.1135.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +2.73205i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +2.73205i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.36603 - 2.36603i) q^{10} +(-0.232051 + 0.133975i) q^{11} +(0.866025 - 3.50000i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.86603 + 3.23205i) q^{17} +(2.13397 + 1.23205i) q^{19} +(2.36603 + 1.36603i) q^{20} +(0.133975 - 0.232051i) q^{22} +(1.73205 + 3.00000i) q^{23} -2.46410 q^{25} +(1.00000 + 3.46410i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(-1.50000 - 2.59808i) q^{29} +9.66025i q^{31} +(0.866025 + 0.500000i) q^{32} -3.73205i q^{34} +(1.36603 - 2.36603i) q^{35} +(-4.09808 + 2.36603i) q^{37} -2.46410 q^{38} -2.73205 q^{40} +(-6.06218 + 3.50000i) q^{41} +(-1.36603 + 2.36603i) q^{43} +0.267949i q^{44} +(-3.00000 - 1.73205i) q^{46} +2.46410i q^{47} +(0.500000 + 0.866025i) q^{49} +(2.13397 - 1.23205i) q^{50} +(-2.59808 - 2.50000i) q^{52} +3.53590 q^{53} +(-0.366025 - 0.633975i) q^{55} +(0.500000 - 0.866025i) q^{56} +(2.59808 + 1.50000i) q^{58} +(-11.1962 - 6.46410i) q^{59} +(4.13397 - 7.16025i) q^{61} +(-4.83013 - 8.36603i) q^{62} -1.00000 q^{64} +(9.56218 + 2.36603i) q^{65} +(-0.803848 + 0.464102i) q^{67} +(1.86603 + 3.23205i) q^{68} +2.73205i q^{70} +(-7.09808 - 4.09808i) q^{71} +13.4641i q^{73} +(2.36603 - 4.09808i) q^{74} +(2.13397 - 1.23205i) q^{76} +0.267949 q^{77} -16.8564 q^{79} +(2.36603 - 1.36603i) q^{80} +(3.50000 - 6.06218i) q^{82} -11.6603i q^{83} +(-8.83013 - 5.09808i) q^{85} -2.73205i q^{86} +(-0.133975 - 0.232051i) q^{88} +(-0.401924 + 0.232051i) q^{89} +(-2.50000 + 2.59808i) q^{91} +3.46410 q^{92} +(-1.23205 - 2.13397i) q^{94} +(-3.36603 + 5.83013i) q^{95} +(2.36603 + 1.36603i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4}+O(q^{10}) $ 4 * q + 2 * q^4	$ 4 q + 2 q^{4} - 2 q^{10} + 6 q^{11} + 4 q^{14} - 2 q^{16} - 4 q^{17} + 12 q^{19} + 6 q^{20} + 4 q^{22} + 4 q^{25} + 4 q^{26} - 6 q^{29} + 2 q^{35} - 6 q^{37} + 4 q^{38} - 4 q^{40} - 2 q^{43} - 12 q^{46} + 2 q^{49} + 12 q^{50} + 28 q^{53} + 2 q^{55} + 2 q^{56} - 24 q^{59} + 20 q^{61} - 2 q^{62} - 4 q^{64} + 14 q^{65} - 24 q^{67} + 4 q^{68} - 18 q^{71} + 6 q^{74} + 12 q^{76} + 8 q^{77} - 12 q^{79} + 6 q^{80} + 14 q^{82} - 18 q^{85} - 4 q^{88} - 12 q^{89} - 10 q^{91} + 2 q^{94} - 10 q^{95} + 6 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^10 + 6 * q^11 + 4 * q^14 - 2 * q^16 - 4 * q^17 + 12 * q^19 + 6 * q^20 + 4 * q^22 + 4 * q^25 + 4 * q^26 - 6 * q^29 + 2 * q^35 - 6 * q^37 + 4 * q^38 - 4 * q^40 - 2 * q^43 - 12 * q^46 + 2 * q^49 + 12 * q^50 + 28 * q^53 + 2 * q^55 + 2 * q^56 - 24 * q^59 + 20 * q^61 - 2 * q^62 - 4 * q^64 + 14 * q^65 - 24 * q^67 + 4 * q^68 - 18 * q^71 + 6 * q^74 + 12 * q^76 + 8 * q^77 - 12 * q^79 + 6 * q^80 + 14 * q^82 - 18 * q^85 - 4 * q^88 - 12 * q^89 - 10 * q^91 + 2 * q^94 - 10 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			2.73205i			1.22181i	0.791704	+	0.610905i	$0.209194\pi$
$5$			2.73205i			1.22181i	−0.791704	+	0.610905i	$0.790806\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.36603	−	2.36603i	−0.431975	−	0.748203i
$11$	−0.232051	+	0.133975i	−0.0699660	+	0.0403949i	−0.534575	−	0.845121i	$-0.679528\pi$
$11$	−0.232051	+	0.133975i	−0.0699660	+	0.0403949i	0.464609	+	0.885516i	$0.346195\pi$
$12$		0			0
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.86603	+	3.23205i	−0.452578	+	0.783887i	−0.998545	−	0.0539188i	$-0.982829\pi$
$17$	−1.86603	+	3.23205i	−0.452578	+	0.783887i	0.545968	+	0.837806i	$0.316162\pi$
$18$		0			0
$19$	2.13397	+	1.23205i	0.489567	+	0.282652i	0.724395	−	0.689385i	$-0.242119\pi$
$19$	2.13397	+	1.23205i	0.489567	+	0.282652i	−0.234828	+	0.972037i	$0.575453\pi$
$20$	2.36603	+	1.36603i	0.529059	+	0.305453i
$21$		0			0
$22$	0.133975	−	0.232051i	0.0285635	−	0.0494734i
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	0.988152	−	0.153481i	$-0.0490483\pi$
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	−0.626994	+	0.779024i	$0.715715\pi$
$24$		0			0
$25$	−2.46410			−0.492820
$26$	1.00000	+	3.46410i	0.196116	+	0.679366i
$27$		0			0
$28$	−0.866025	+	0.500000i	−0.163663	+	0.0944911i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$			9.66025i			1.73503i	0.497409	+	0.867516i	$0.334285\pi$
$31$			9.66025i			1.73503i	−0.497409	+	0.867516i	$0.665715\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	3.73205i		−	0.640041i
$35$	1.36603	−	2.36603i	0.230900	−	0.399931i
$36$		0			0
$37$	−4.09808	+	2.36603i	−0.673720	+	0.388972i	−0.797485	−	0.603339i	$-0.793836\pi$
$37$	−4.09808	+	2.36603i	−0.673720	+	0.388972i	0.123765	+	0.992312i	$0.460503\pi$
$38$	−2.46410			−0.399730
$39$		0			0
$40$	−2.73205			−0.431975
$41$	−6.06218	+	3.50000i	−0.946753	+	0.546608i	−0.892071	−	0.451896i	$-0.850748\pi$
$41$	−6.06218	+	3.50000i	−0.946753	+	0.546608i	−0.0546823	+	0.998504i	$0.517415\pi$
$42$		0			0
$43$	−1.36603	+	2.36603i	−0.208317	+	0.360815i	−0.951184	−	0.308623i	$-0.900132\pi$
$43$	−1.36603	+	2.36603i	−0.208317	+	0.360815i	0.742868	+	0.669438i	$0.233465\pi$
$44$			0.267949i			0.0403949i
$45$		0			0
$46$	−3.00000	−	1.73205i	−0.442326	−	0.255377i
$47$			2.46410i			0.359426i	0.983719	+	0.179713i	$0.0575169\pi$
$47$			2.46410i			0.359426i	−0.983719	+	0.179713i	$0.942483\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	2.13397	−	1.23205i	0.301790	−	0.174238i
$51$		0			0
$52$	−2.59808	−	2.50000i	−0.360288	−	0.346688i
$53$	3.53590			0.485693			0.242846	−	0.970065i	$-0.421919\pi$
$53$	3.53590			0.485693			0.242846	+	0.970065i	$0.421919\pi$
$54$		0			0
$55$	−0.366025	−	0.633975i	−0.0493549	−	0.0854851i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		0			0
$58$	2.59808	+	1.50000i	0.341144	+	0.196960i
$59$	−11.1962	−	6.46410i	−1.45761	−	0.841554i	−0.458721	−	0.888580i	$-0.651692\pi$
$59$	−11.1962	−	6.46410i	−1.45761	−	0.841554i	−0.998894	+	0.0470259i	$0.985026\pi$
$60$		0			0
$61$	4.13397	−	7.16025i	0.529301	−	0.916777i	−0.470115	−	0.882605i	$-0.655787\pi$
$61$	4.13397	−	7.16025i	0.529301	−	0.916777i	0.999416	−	0.0341713i	$-0.0108792\pi$
$62$	−4.83013	−	8.36603i	−0.613427	−	1.06249i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	9.56218	+	2.36603i	1.18604	+	0.293469i
$66$		0			0
$67$	−0.803848	+	0.464102i	−0.0982056	+	0.0566990i	−0.548298	−	0.836283i	$-0.684724\pi$
$67$	−0.803848	+	0.464102i	−0.0982056	+	0.0566990i	0.450093	+	0.892982i	$0.351391\pi$
$68$	1.86603	+	3.23205i	0.226289	+	0.391944i
$69$		0			0
$70$			2.73205i			0.326543i
$71$	−7.09808	−	4.09808i	−0.842387	−	0.486352i	0.0156881	−	0.999877i	$-0.495006\pi$
$71$	−7.09808	−	4.09808i	−0.842387	−	0.486352i	−0.858075	+	0.513525i	$0.828339\pi$
$72$		0			0
$73$			13.4641i			1.57585i	0.615769	+	0.787927i	$0.288846\pi$
$73$			13.4641i			1.57585i	−0.615769	+	0.787927i	$0.711154\pi$
$74$	2.36603	−	4.09808i	0.275045	−	0.476392i
$75$		0			0
$76$	2.13397	−	1.23205i	0.244784	−	0.141326i
$77$	0.267949			0.0305356
$78$		0			0
$79$	−16.8564			−1.89649			−0.948247	−	0.317534i	$-0.897145\pi$
$79$	−16.8564			−1.89649			−0.948247	+	0.317534i	$0.897145\pi$
$80$	2.36603	−	1.36603i	0.264530	−	0.152726i
$81$		0			0
$82$	3.50000	−	6.06218i	0.386510	−	0.669456i
$83$		−	11.6603i		−	1.27988i	−0.768425	−	0.639940i	$-0.778959\pi$
$83$		−	11.6603i		−	1.27988i	0.768425	−	0.639940i	$-0.221041\pi$
$84$		0			0
$85$	−8.83013	−	5.09808i	−0.957762	−	0.552964i
$86$		−	2.73205i		−	0.294605i
$87$		0			0
$88$	−0.133975	−	0.232051i	−0.0142817	−	0.0247367i
$89$	−0.401924	+	0.232051i	−0.0426038	+	0.0245973i	−0.521151	−	0.853465i	$-0.674497\pi$
$89$	−0.401924	+	0.232051i	−0.0426038	+	0.0245973i	0.478547	+	0.878062i	$0.341164\pi$
$90$		0			0
$91$	−2.50000	+	2.59808i	−0.262071	+	0.272352i
$92$	3.46410			0.361158
$93$		0			0
$94$	−1.23205	−	2.13397i	−0.127076	−	0.220103i
$95$	−3.36603	+	5.83013i	−0.345347	+	0.598158i
$96$		0			0
$97$	2.36603	+	1.36603i	0.240233	+	0.138699i	0.615284	−	0.788305i	$-0.289041\pi$
$97$	2.36603	+	1.36603i	0.240233	+	0.138699i	−0.375051	+	0.927004i	$0.622375\pi$
$98$	−0.866025	−	0.500000i	−0.0874818	−	0.0505076i
$99$		0			0
$100$	−1.23205	+	2.13397i	−0.123205	+	0.213397i
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$		0			0
$103$	1.80385			0.177738			0.0888692	−	0.996043i	$-0.471675\pi$
$103$	1.80385			0.177738			0.0888692	+	0.996043i	$0.471675\pi$
$104$	3.50000	+	0.866025i	0.343203	+	0.0849208i
$105$		0			0
$106$	−3.06218	+	1.76795i	−0.297425	+	0.171718i
$107$	−4.23205	−	7.33013i	−0.409128	−	0.708630i	0.585664	−	0.810554i	$-0.300834\pi$
$107$	−4.23205	−	7.33013i	−0.409128	−	0.708630i	−0.994792	+	0.101923i	$0.967500\pi$
$108$		0			0
$109$			13.6603i			1.30842i	0.756315	+	0.654208i	$0.226998\pi$
$109$			13.6603i			1.30842i	−0.756315	+	0.654208i	$0.773002\pi$
$110$	0.633975	+	0.366025i	0.0604471	+	0.0348992i
$111$		0			0
$112$			1.00000i			0.0944911i
$113$	0.0980762	−	0.169873i	0.00922623	−	0.0159803i	−0.861375	−	0.507969i	$-0.830396\pi$
$113$	0.0980762	−	0.169873i	0.00922623	−	0.0159803i	0.870602	+	0.491989i	$0.163730\pi$
$114$		0			0
$115$	−8.19615	+	4.73205i	−0.764295	+	0.441266i
$116$	−3.00000			−0.278543
$117$		0			0
$118$	12.9282			1.19014
$119$	3.23205	−	1.86603i	0.296282	−	0.171058i
$120$		0			0
$121$	−5.46410	+	9.46410i	−0.496737	+	0.860373i
$122$			8.26795i			0.748545i
$123$		0			0
$124$	8.36603	+	4.83013i	0.751291	+	0.433758i
$125$			6.92820i			0.619677i
$126$		0			0
$127$	−9.73205	−	16.8564i	−0.863580	−	1.49576i	−0.868450	−	0.495776i	$-0.834884\pi$
$127$	−9.73205	−	16.8564i	−0.863580	−	1.49576i	0.00487054	−	0.999988i	$-0.498450\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−9.46410	+	2.73205i	−0.830057	+	0.239617i
$131$	−5.07180			−0.443125			−0.221562	−	0.975146i	$-0.571116\pi$
$131$	−5.07180			−0.443125			−0.221562	+	0.975146i	$0.571116\pi$
$132$		0			0
$133$	−1.23205	−	2.13397i	−0.106832	−	0.185039i
$134$	0.464102	−	0.803848i	0.0400923	−	0.0694419i
$135$		0			0
$136$	−3.23205	−	1.86603i	−0.277146	−	0.160010i
$137$	7.39230	+	4.26795i	0.631567	+	0.364636i	0.781359	−	0.624082i	$-0.214527\pi$
$137$	7.39230	+	4.26795i	0.631567	+	0.364636i	−0.149792	+	0.988718i	$0.547860\pi$
$138$		0			0
$139$	−3.06218	+	5.30385i	−0.259731	+	0.449866i	−0.966170	−	0.257907i	$-0.916967\pi$
$139$	−3.06218	+	5.30385i	−0.259731	+	0.449866i	0.706439	+	0.707774i	$0.250300\pi$
$140$	−1.36603	−	2.36603i	−0.115450	−	0.199966i
$141$		0			0
$142$	8.19615			0.687806
$143$	0.267949	+	0.928203i	0.0224070	+	0.0776203i
$144$		0			0
$145$	7.09808	−	4.09808i	0.589463	−	0.340327i
$146$	−6.73205	−	11.6603i	−0.557148	−	0.965009i
$147$		0			0
$148$			4.73205i			0.388972i
$149$	−4.39230	−	2.53590i	−0.359832	−	0.207749i	0.309175	−	0.951005i	$-0.399947\pi$
$149$	−4.39230	−	2.53590i	−0.359832	−	0.207749i	−0.669007	+	0.743256i	$0.733280\pi$
$150$		0			0
$151$			2.80385i			0.228174i	0.993471	+	0.114087i	$0.0363942\pi$
$151$			2.80385i			0.228174i	−0.993471	+	0.114087i	$0.963606\pi$
$152$	−1.23205	+	2.13397i	−0.0999325	+	0.173088i
$153$		0			0
$154$	−0.232051	+	0.133975i	−0.0186992	+	0.0107960i
$155$	−26.3923			−2.11988
$156$		0			0
$157$	−8.53590			−0.681239			−0.340619	−	0.940201i	$-0.610637\pi$
$157$	−8.53590			−0.681239			−0.340619	+	0.940201i	$0.610637\pi$
$158$	14.5981	−	8.42820i	1.16136	−	0.670512i
$159$		0			0
$160$	−1.36603	+	2.36603i	−0.107994	+	0.187051i
$161$		−	3.46410i		−	0.273009i
$162$		0			0
$163$	15.7583	+	9.09808i	1.23429	+	0.712616i	0.967921	−	0.251255i	$-0.0808434\pi$
$163$	15.7583	+	9.09808i	1.23429	+	0.712616i	0.266367	+	0.963872i	$0.414177\pi$
$164$			7.00000i			0.546608i
$165$		0			0
$166$	5.83013	+	10.0981i	0.452506	+	0.783763i
$167$	−18.9282	+	10.9282i	−1.46471	+	0.845650i	−0.999223	−	0.0394060i	$-0.987453\pi$
$167$	−18.9282	+	10.9282i	−1.46471	+	0.845650i	−0.465485	+	0.885056i	$0.654120\pi$
$168$		0			0
$169$	−11.5000	−	6.06218i	−0.884615	−	0.466321i
$170$	10.1962			0.782009
$171$		0			0
$172$	1.36603	+	2.36603i	0.104158	+	0.180408i
$173$	−8.63397	+	14.9545i	−0.656429	+	1.13697i	0.325105	+	0.945678i	$0.394600\pi$
$173$	−8.63397	+	14.9545i	−0.656429	+	1.13697i	−0.981534	+	0.191290i	$0.938733\pi$
$174$		0			0
$175$	2.13397	+	1.23205i	0.161313	+	0.0931343i
$176$	0.232051	+	0.133975i	0.0174915	+	0.0100987i
$177$		0			0
$178$	0.232051	−	0.401924i	0.0173929	−	0.0301255i
$179$	−0.803848	−	1.39230i	−0.0600824	−	0.104066i	0.834420	−	0.551130i	$-0.185803\pi$
$179$	−0.803848	−	1.39230i	−0.0600824	−	0.104066i	−0.894502	+	0.447064i	$0.852470\pi$
$180$		0			0
$181$	9.19615			0.683545			0.341772	−	0.939783i	$-0.388973\pi$
$181$	9.19615			0.683545			0.341772	+	0.939783i	$0.388973\pi$
$182$	0.866025	−	3.50000i	0.0641941	−	0.259437i
$183$		0			0
$184$	−3.00000	+	1.73205i	−0.221163	+	0.127688i
$185$	−6.46410	−	11.1962i	−0.475250	−	0.823157i
$186$		0			0
$187$		−	1.00000i		−	0.0731272i
$188$	2.13397	+	1.23205i	0.155636	+	0.0898565i
$189$		0			0
$190$		−	6.73205i		−	0.488394i
$191$	3.09808	−	5.36603i	0.224169	−	0.388272i	−0.731901	−	0.681411i	$-0.761367\pi$
$191$	3.09808	−	5.36603i	0.224169	−	0.388272i	0.956070	+	0.293139i	$0.0946999\pi$
$192$		0			0
$193$	5.89230	−	3.40192i	0.424137	−	0.244876i	−0.272709	−	0.962097i	$-0.587919\pi$
$193$	5.89230	−	3.40192i	0.424137	−	0.244876i	0.696846	+	0.717221i	$0.254586\pi$
$194$	−2.73205			−0.196150
$195$		0			0
$196$	1.00000			0.0714286
$197$	4.96410	−	2.86603i	0.353678	−	0.204196i	−0.312626	−	0.949876i	$-0.601209\pi$
$197$	4.96410	−	2.86603i	0.353678	−	0.204196i	0.666304	+	0.745680i	$0.267875\pi$
$198$		0			0
$199$	3.09808	−	5.36603i	0.219617	−	0.380387i	−0.735074	−	0.677987i	$-0.762853\pi$
$199$	3.09808	−	5.36603i	0.219617	−	0.380387i	0.954691	+	0.297599i	$0.0961860\pi$
$200$		−	2.46410i		−	0.174238i
$201$		0			0
$202$	−8.66025	−	5.00000i	−0.609333	−	0.351799i
$203$			3.00000i			0.210559i
$204$		0			0
$205$	−9.56218	−	16.5622i	−0.667851	−	1.15675i
$206$	−1.56218	+	0.901924i	−0.108842	+	0.0628400i
$207$		0			0
$208$	−3.46410	+	1.00000i	−0.240192	+	0.0693375i
$209$	−0.660254			−0.0456707
$210$		0			0
$211$	−5.92820	−	10.2679i	−0.408114	−	0.706875i	0.586564	−	0.809903i	$-0.300480\pi$
$211$	−5.92820	−	10.2679i	−0.408114	−	0.706875i	−0.994678	+	0.103028i	$0.967147\pi$
$212$	1.76795	−	3.06218i	0.121423	−	0.210311i
$213$		0			0
$214$	7.33013	+	4.23205i	0.501077	+	0.289297i
$215$	−6.46410	−	3.73205i	−0.440848	−	0.254524i
$216$		0			0
$217$	4.83013	−	8.36603i	0.327890	−	0.567923i
$218$	−6.83013	−	11.8301i	−0.462595	−	0.801237i
$219$		0			0
$220$	−0.732051			−0.0493549
$221$	9.69615	+	9.33013i	0.652234	+	0.627612i
$222$		0			0
$223$	10.7321	−	6.19615i	0.718671	−	0.414925i	−0.0955922	−	0.995421i	$-0.530474\pi$
$223$	10.7321	−	6.19615i	0.718671	−	0.414925i	0.814263	+	0.580496i	$0.197141\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$			0.196152i			0.0130479i
$227$	13.3923	+	7.73205i	0.888878	+	0.513194i	0.873575	−	0.486689i	$-0.161795\pi$
$227$	13.3923	+	7.73205i	0.888878	+	0.513194i	0.0153030	+	0.999883i	$0.495129\pi$
$228$		0			0
$229$			24.3205i			1.60714i	0.595207	+	0.803572i	$0.297070\pi$
$229$			24.3205i			1.60714i	−0.595207	+	0.803572i	$0.702930\pi$
$230$	4.73205	−	8.19615i	0.312022	−	0.540438i
$231$		0			0
$232$	2.59808	−	1.50000i	0.170572	−	0.0984798i
$233$	−8.19615			−0.536948			−0.268474	−	0.963287i	$-0.586519\pi$
$233$	−8.19615			−0.536948			−0.268474	+	0.963287i	$0.586519\pi$
$234$		0			0
$235$	−6.73205			−0.439151
$236$	−11.1962	+	6.46410i	−0.728807	+	0.420777i
$237$		0			0
$238$	−1.86603	+	3.23205i	−0.120956	+	0.209503i
$239$			24.1962i			1.56512i	0.622576	+	0.782559i	$0.286086\pi$
$239$			24.1962i			1.56512i	−0.622576	+	0.782559i	$0.713914\pi$
$240$		0			0
$241$	−24.9282	−	14.3923i	−1.60577	−	0.927090i	−0.990303	−	0.138925i	$-0.955635\pi$
$241$	−24.9282	−	14.3923i	−1.60577	−	0.927090i	−0.615464	−	0.788165i	$-0.711031\pi$
$242$		−	10.9282i		−	0.702492i
$243$		0			0
$244$	−4.13397	−	7.16025i	−0.264651	−	0.458388i
$245$	−2.36603	+	1.36603i	−0.151160	+	0.0872722i
$246$		0			0
$247$	6.16025	−	6.40192i	0.391968	−	0.407345i
$248$	−9.66025			−0.613427
$249$		0			0
$250$	−3.46410	−	6.00000i	−0.219089	−	0.379473i
$251$	−3.90192	+	6.75833i	−0.246287	+	0.426582i	−0.962493	−	0.271307i	$-0.912544\pi$
$251$	−3.90192	+	6.75833i	−0.246287	+	0.426582i	0.716205	+	0.697889i	$0.245877\pi$
$252$		0			0
$253$	−0.803848	−	0.464102i	−0.0505375	−	0.0291778i
$254$	16.8564	+	9.73205i	1.05767	+	0.610643i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	13.5263	+	23.4282i	0.843746	+	1.46141i	0.886706	+	0.462334i	$0.152988\pi$
$257$	13.5263	+	23.4282i	0.843746	+	1.46141i	−0.0429595	+	0.999077i	$0.513679\pi$
$258$		0			0
$259$	4.73205			0.294035
$260$	6.83013	−	7.09808i	0.423586	−	0.440204i
$261$		0			0
$262$	4.39230	−	2.53590i	0.271357	−	0.156668i
$263$	−7.63397	−	13.2224i	−0.470731	−	0.815330i	0.528709	−	0.848803i	$-0.322676\pi$
$263$	−7.63397	−	13.2224i	−0.470731	−	0.815330i	−0.999440	+	0.0334733i	$0.989343\pi$
$264$		0			0
$265$			9.66025i			0.593425i
$266$	2.13397	+	1.23205i	0.130842	+	0.0755419i
$267$		0			0
$268$			0.928203i			0.0566990i
$269$	15.8564	−	27.4641i	0.966782	−	1.67452i	0.262033	−	0.965059i	$-0.415607\pi$
$269$	15.8564	−	27.4641i	0.966782	−	1.67452i	0.704749	−	0.709457i	$-0.251060\pi$
$270$		0			0
$271$	20.3660	−	11.7583i	1.23715	−	0.714268i	0.268638	−	0.963241i	$-0.413427\pi$
$271$	20.3660	−	11.7583i	1.23715	−	0.714268i	0.968510	+	0.248974i	$0.0800932\pi$
$272$	3.73205			0.226289
$273$		0			0
$274$	−8.53590			−0.515672
$275$	0.571797	−	0.330127i	0.0344806	−	0.0199074i
$276$		0			0
$277$	−2.80385	+	4.85641i	−0.168467	+	0.291793i	−0.937881	−	0.346957i	$-0.887215\pi$
$277$	−2.80385	+	4.85641i	−0.168467	+	0.291793i	0.769414	+	0.638750i	$0.220548\pi$
$278$		−	6.12436i		−	0.367314i
$279$		0			0
$280$	2.36603	+	1.36603i	0.141397	+	0.0816356i
$281$		−	7.80385i		−	0.465539i	−0.972532	−	0.232769i	$-0.925221\pi$
$281$		−	7.80385i		−	0.465539i	0.972532	−	0.232769i	$-0.0747787\pi$
$282$		0			0
$283$	−4.53590	−	7.85641i	−0.269631	−	0.467015i	0.699135	−	0.714989i	$-0.253568\pi$
$283$	−4.53590	−	7.85641i	−0.269631	−	0.467015i	−0.968767	+	0.247974i	$0.920235\pi$
$284$	−7.09808	+	4.09808i	−0.421193	+	0.243176i
$285$		0			0
$286$	−0.696152	−	0.669873i	−0.0411644	−	0.0396104i
$287$	7.00000			0.413197
$288$		0			0
$289$	1.53590	+	2.66025i	0.0903470	+	0.156486i
$290$	−4.09808	+	7.09808i	−0.240647	+	0.416813i
$291$		0			0
$292$	11.6603	+	6.73205i	0.682365	+	0.393963i
$293$	24.9282	+	14.3923i	1.45632	+	0.840807i	0.998828	−	0.0484056i	$-0.0154140\pi$
$293$	24.9282	+	14.3923i	1.45632	+	0.840807i	0.457493	+	0.889213i	$0.348747\pi$
$294$		0			0
$295$	17.6603	−	30.5885i	1.02822	−	1.78093i
$296$	−2.36603	−	4.09808i	−0.137522	−	0.238196i
$297$		0			0
$298$	5.07180			0.293801
$299$	12.0000	−	3.46410i	0.693978	−	0.200334i
$300$		0			0
$301$	2.36603	−	1.36603i	0.136375	−	0.0787364i
$302$	−1.40192	−	2.42820i	−0.0806716	−	0.139727i
$303$		0			0
$304$		−	2.46410i		−	0.141326i
$305$	19.5622	+	11.2942i	1.12013	+	0.646706i
$306$		0			0
$307$			7.78461i			0.444291i	0.975014	+	0.222146i	$0.0713060\pi$
$307$			7.78461i			0.444291i	−0.975014	+	0.222146i	$0.928694\pi$
$308$	0.133975	−	0.232051i	0.00763391	−	0.0132223i
$309$		0			0
$310$	22.8564	−	13.1962i	1.29816	−	0.749491i
$311$	−8.80385			−0.499220			−0.249610	−	0.968346i	$-0.580302\pi$
$311$	−8.80385			−0.499220			−0.249610	+	0.968346i	$0.580302\pi$
$312$		0			0
$313$	12.1962			0.689367			0.344684	−	0.938719i	$-0.387986\pi$
$313$	12.1962			0.689367			0.344684	+	0.938719i	$0.387986\pi$
$314$	7.39230	−	4.26795i	0.417172	−	0.240854i
$315$		0			0
$316$	−8.42820	+	14.5981i	−0.474123	+	0.821206i
$317$			18.0000i			1.01098i	0.862832	+	0.505490i	$0.168688\pi$
$317$			18.0000i			1.01098i	−0.862832	+	0.505490i	$0.831312\pi$
$318$		0			0
$319$	0.696152	+	0.401924i	0.0389771	+	0.0225034i
$320$		−	2.73205i		−	0.152726i
$321$		0			0
$322$	1.73205	+	3.00000i	0.0965234	+	0.167183i
$323$	−7.96410	+	4.59808i	−0.443134	+	0.255844i
$324$		0			0
$325$	−2.13397	+	8.62436i	−0.118372	+	0.478393i
$326$	−18.1962			−1.00779
$327$		0			0
$328$	−3.50000	−	6.06218i	−0.193255	−	0.334728i
$329$	1.23205	−	2.13397i	0.0679252	−	0.117650i
$330$		0			0
$331$	2.66025	+	1.53590i	0.146221	+	0.0844206i	0.571325	−	0.820724i	$-0.306429\pi$
$331$	2.66025	+	1.53590i	0.146221	+	0.0844206i	−0.425105	+	0.905144i	$0.639763\pi$
$332$	−10.0981	−	5.83013i	−0.554204	−	0.319970i
$333$		0			0
$334$	10.9282	−	18.9282i	0.597965	−	1.03571i
$335$	−1.26795	−	2.19615i	−0.0692755	−	0.119989i
$336$		0			0
$337$	13.7846			0.750896			0.375448	−	0.926844i	$-0.377489\pi$
$337$	13.7846			0.750896			0.375448	+	0.926844i	$0.377489\pi$
$338$	12.9904	−	0.500000i	0.706584	−	0.0271964i
$339$		0			0
$340$	−8.83013	+	5.09808i	−0.478881	+	0.276482i
$341$	−1.29423	−	2.24167i	−0.0700864	−	0.121393i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−2.36603	−	1.36603i	−0.127568	−	0.0736512i
$345$		0			0
$346$		−	17.2679i		−	0.928331i
$347$	−2.42820	+	4.20577i	−0.130353	+	0.225778i	−0.923813	−	0.382845i	$-0.874944\pi$
$347$	−2.42820	+	4.20577i	−0.130353	+	0.225778i	0.793460	+	0.608623i	$0.208278\pi$
$348$		0			0
$349$	27.4641	−	15.8564i	1.47012	−	0.848774i	0.470682	−	0.882303i	$-0.344008\pi$
$349$	27.4641	−	15.8564i	1.47012	−	0.848774i	0.999438	+	0.0335290i	$0.0106746\pi$
$350$	−2.46410			−0.131712
$351$		0			0
$352$	−0.267949			−0.0142817
$353$	4.73205	−	2.73205i	0.251862	−	0.145412i	−0.368755	−	0.929527i	$-0.620216\pi$
$353$	4.73205	−	2.73205i	0.251862	−	0.145412i	0.620616	+	0.784114i	$0.286882\pi$
$354$		0			0
$355$	11.1962	−	19.3923i	0.594230	−	1.02924i
$356$			0.464102i			0.0245973i
$357$		0			0
$358$	1.39230	+	0.803848i	0.0735856	+	0.0424847i
$359$		−	26.1962i		−	1.38258i	−0.722577	−	0.691290i	$-0.757043\pi$
$359$		−	26.1962i		−	1.38258i	0.722577	−	0.691290i	$-0.242957\pi$
$360$		0			0
$361$	−6.46410	−	11.1962i	−0.340216	−	0.589271i
$362$	−7.96410	+	4.59808i	−0.418584	+	0.241670i
$363$		0			0
$364$	1.00000	+	3.46410i	0.0524142	+	0.181568i
$365$	−36.7846			−1.92539
$366$		0			0
$367$	16.1244	+	27.9282i	0.841685	+	1.45784i	0.888470	+	0.458935i	$0.151769\pi$
$367$	16.1244	+	27.9282i	0.841685	+	1.45784i	−0.0467851	+	0.998905i	$0.514898\pi$
$368$	1.73205	−	3.00000i	0.0902894	−	0.156386i
$369$		0			0
$370$	11.1962	+	6.46410i	0.582060	+	0.336053i
$371$	−3.06218	−	1.76795i	−0.158980	−	0.0917873i
$372$		0			0
$373$	−5.29423	+	9.16987i	−0.274125	+	0.474798i	−0.969914	−	0.243448i	$-0.921721\pi$
$373$	−5.29423	+	9.16987i	−0.274125	+	0.474798i	0.695789	+	0.718246i	$0.255055\pi$
$374$	0.500000	+	0.866025i	0.0258544	+	0.0447811i
$375$		0			0
$376$	−2.46410			−0.127076
$377$	−10.3923	+	3.00000i	−0.535231	+	0.154508i
$378$		0			0
$379$	−14.3660	+	8.29423i	−0.737933	+	0.426046i	−0.821317	−	0.570472i	$-0.806760\pi$
$379$	−14.3660	+	8.29423i	−0.737933	+	0.426046i	0.0833842	+	0.996517i	$0.473427\pi$
$380$	3.36603	+	5.83013i	0.172673	+	0.299079i
$381$		0			0
$382$			6.19615i			0.317023i
$383$	30.6506	+	17.6962i	1.56617	+	0.904231i	0.996609	+	0.0822852i	$0.0262218\pi$
$383$	30.6506	+	17.6962i	1.56617	+	0.904231i	0.569565	+	0.821946i	$0.307112\pi$
$384$		0			0
$385$			0.732051i			0.0373088i
$386$	−3.40192	+	5.89230i	−0.173153	+	0.299910i
$387$		0			0
$388$	2.36603	−	1.36603i	0.120117	−	0.0693494i
$389$	29.1769			1.47933			0.739664	−	0.672976i	$-0.234984\pi$
$389$	29.1769			1.47933			0.739664	+	0.672976i	$0.234984\pi$
$390$		0			0
$391$	−12.9282			−0.653807
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$		0			0
$394$	−2.86603	+	4.96410i	−0.144388	+	0.250088i
$395$		−	46.0526i		−	2.31716i
$396$		0			0
$397$	8.25833	+	4.76795i	0.414474	+	0.239297i	0.692710	−	0.721216i	$-0.256417\pi$
$397$	8.25833	+	4.76795i	0.414474	+	0.239297i	−0.278236	+	0.960513i	$0.589750\pi$
$398$			6.19615i			0.310585i
$399$		0			0
$400$	1.23205	+	2.13397i	0.0616025	+	0.106699i
$401$	−8.66025	+	5.00000i	−0.432472	+	0.249688i	−0.700399	−	0.713751i	$-0.746995\pi$
$401$	−8.66025	+	5.00000i	−0.432472	+	0.249688i	0.267927	+	0.963439i	$0.413661\pi$
$402$		0			0
$403$	33.8109	+	8.36603i	1.68424	+	0.416741i
$404$	10.0000			0.497519
$405$		0			0
$406$	−1.50000	−	2.59808i	−0.0744438	−	0.128940i
$407$	0.633975	−	1.09808i	0.0314250	−	0.0544296i
$408$		0			0
$409$	−14.4904	−	8.36603i	−0.716503	−	0.413673i	0.0969611	−	0.995288i	$-0.469088\pi$
$409$	−14.4904	−	8.36603i	−0.716503	−	0.413673i	−0.813464	+	0.581615i	$0.802421\pi$
$410$	16.5622	+	9.56218i	0.817948	+	0.472242i
$411$		0			0
$412$	0.901924	−	1.56218i	0.0444346	−	0.0769630i
$413$	6.46410	+	11.1962i	0.318078	+	0.550927i
$414$		0			0
$415$	31.8564			1.56377
$416$	2.50000	−	2.59808i	0.122573	−	0.127381i
$417$		0			0
$418$	0.571797	−	0.330127i	0.0279675	−	0.0161470i
$419$	2.09808	+	3.63397i	0.102498	+	0.177531i	0.912713	−	0.408601i	$-0.133983\pi$
$419$	2.09808	+	3.63397i	0.102498	+	0.177531i	−0.810215	+	0.586132i	$0.800650\pi$
$420$		0			0
$421$			6.39230i			0.311542i	0.987793	+	0.155771i	$0.0497862\pi$
$421$			6.39230i			0.311542i	−0.987793	+	0.155771i	$0.950214\pi$
$422$	10.2679	+	5.92820i	0.499836	+	0.288580i
$423$		0			0
$424$			3.53590i			0.171718i
$425$	4.59808	−	7.96410i	0.223039	−	0.386316i
$426$		0			0
$427$	−7.16025	+	4.13397i	−0.346509	+	0.200057i
$428$	−8.46410			−0.409128
$429$		0			0
$430$	7.46410			0.359951
$431$	−2.70577	+	1.56218i	−0.130332	+	0.0752475i	−0.563749	−	0.825946i	$-0.690641\pi$
$431$	−2.70577	+	1.56218i	−0.130332	+	0.0752475i	0.433416	+	0.901194i	$0.357308\pi$
$432$		0			0
$433$	−2.46410	+	4.26795i	−0.118417	+	0.205105i	−0.919141	−	0.393930i	$-0.871115\pi$
$433$	−2.46410	+	4.26795i	−0.118417	+	0.205105i	0.800723	+	0.599034i	$0.204449\pi$
$434$			9.66025i			0.463707i
$435$		0			0
$436$	11.8301	+	6.83013i	0.566560	+	0.327104i
$437$			8.53590i			0.408327i
$438$		0			0
$439$	2.19615	+	3.80385i	0.104817	+	0.181548i	0.913663	−	0.406472i	$-0.133241\pi$
$439$	2.19615	+	3.80385i	0.104817	+	0.181548i	−0.808847	+	0.588020i	$0.799908\pi$
$440$	0.633975	−	0.366025i	0.0302236	−	0.0174496i
$441$		0			0
$442$	−13.0622	−	3.23205i	−0.621304	−	0.153733i
$443$	10.6077			0.503987			0.251993	−	0.967729i	$-0.418914\pi$
$443$	10.6077			0.503987			0.251993	+	0.967729i	$0.418914\pi$
$444$		0			0
$445$	−0.633975	−	1.09808i	−0.0300533	−	0.0520538i
$446$	−6.19615	+	10.7321i	−0.293396	+	0.508177i
$447$		0			0
$448$	0.866025	+	0.500000i	0.0409159	+	0.0236228i
$449$	−6.29423	−	3.63397i	−0.297043	−	0.171498i	0.344071	−	0.938944i	$-0.388194\pi$
$449$	−6.29423	−	3.63397i	−0.297043	−	0.171498i	−0.641114	+	0.767446i	$0.721527\pi$
$450$		0			0
$451$	0.937822	−	1.62436i	0.0441603	−	0.0764879i
$452$	−0.0980762	−	0.169873i	−0.00461312	−	0.00799015i
$453$		0			0
$454$	−15.4641			−0.725766
$455$	−7.09808	−	6.83013i	−0.332763	−	0.320201i
$456$		0			0
$457$	30.1244	−	17.3923i	1.40916	−	0.813578i	0.413851	−	0.910345i	$-0.364183\pi$
$457$	30.1244	−	17.3923i	1.40916	−	0.813578i	0.995307	+	0.0967670i	$0.0308502\pi$
$458$	−12.1603	−	21.0622i	−0.568211	−	0.984171i
$459$		0			0
$460$			9.46410i			0.441266i
$461$	24.0000	+	13.8564i	1.11779	+	0.645357i	0.940836	−	0.338862i	$-0.110042\pi$
$461$	24.0000	+	13.8564i	1.11779	+	0.645357i	0.176955	+	0.984219i	$0.443375\pi$
$462$		0			0
$463$			9.19615i			0.427381i	0.976901	+	0.213691i	$0.0685485\pi$
$463$			9.19615i			0.427381i	−0.976901	+	0.213691i	$0.931452\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$		0			0
$466$	7.09808	−	4.09808i	0.328812	−	0.189840i
$467$	17.8564			0.826296			0.413148	−	0.910664i	$-0.364429\pi$
$467$	17.8564			0.826296			0.413148	+	0.910664i	$0.364429\pi$
$468$		0			0
$469$	0.928203			0.0428604
$470$	5.83013	−	3.36603i	0.268924	−	0.155263i
$471$		0			0
$472$	6.46410	−	11.1962i	0.297534	−	0.515345i
$473$		−	0.732051i		−	0.0336597i
$474$		0			0
$475$	−5.25833	−	3.03590i	−0.241269	−	0.139297i
$476$		−	3.73205i		−	0.171058i
$477$		0			0
$478$	−12.0981	−	20.9545i	−0.553353	−	0.958436i
$479$	9.18653	−	5.30385i	0.419743	−	0.242339i	−0.275224	−	0.961380i	$-0.588752\pi$
$479$	9.18653	−	5.30385i	0.419743	−	0.242339i	0.694968	+	0.719041i	$0.255419\pi$
$480$		0			0
$481$	4.73205	+	16.3923i	0.215763	+	0.747425i
$482$	28.7846			1.31110
$483$		0			0
$484$	5.46410	+	9.46410i	0.248368	+	0.430186i
$485$	−3.73205	+	6.46410i	−0.169464	+	0.293520i
$486$		0			0
$487$	−9.35641	−	5.40192i	−0.423979	−	0.244785i	0.272799	−	0.962071i	$-0.412051\pi$
$487$	−9.35641	−	5.40192i	−0.423979	−	0.244785i	−0.696778	+	0.717286i	$0.745384\pi$
$488$	7.16025	+	4.13397i	0.324129	+	0.187136i
$489$		0			0
$490$	1.36603	−	2.36603i	0.0617107	−	0.106886i
$491$	6.12436	+	10.6077i	0.276388	+	0.478719i	0.970484	−	0.241164i	$-0.0775291\pi$
$491$	6.12436	+	10.6077i	0.276388	+	0.478719i	−0.694096	+	0.719882i	$0.744196\pi$
$492$		0			0
$493$	11.1962			0.504249
$494$	−2.13397	+	8.62436i	−0.0960121	+	0.388028i
$495$		0			0
$496$	8.36603	−	4.83013i	0.375646	−	0.216879i
$497$	4.09808	+	7.09808i	0.183824	+	0.318392i
$498$		0			0
$499$			38.9808i			1.74502i	0.488598	+	0.872509i	$0.337509\pi$
$499$			38.9808i			1.74502i	−0.488598	+	0.872509i	$0.662491\pi$
$500$	6.00000	+	3.46410i	0.268328	+	0.154919i
$501$		0			0
$502$		−	7.80385i		−	0.348303i
$503$	15.8564	−	27.4641i	0.707002	−	1.22456i	−0.258962	−	0.965888i	$-0.583380\pi$
$503$	15.8564	−	27.4641i	0.707002	−	1.22456i	0.965964	−	0.258676i	$-0.0832863\pi$
$504$		0			0
$505$	−23.6603	+	13.6603i	−1.05287	+	0.607873i
$506$	0.928203			0.0412637
$507$		0			0
$508$	−19.4641			−0.863580
$509$	10.4378	−	6.02628i	0.462648	−	0.267110i	−0.250509	−	0.968114i	$-0.580598\pi$
$509$	10.4378	−	6.02628i	0.462648	−	0.267110i	0.713157	+	0.701004i	$0.247265\pi$
$510$		0			0
$511$	6.73205	−	11.6603i	0.297808	−	0.515819i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−23.4282	−	13.5263i	−1.03337	−	0.596619i
$515$			4.92820i			0.217163i
$516$		0			0
$517$	−0.330127	−	0.571797i	−0.0145190	−	0.0251476i
$518$	−4.09808	+	2.36603i	−0.180059	+	0.103957i
$519$		0			0
$520$	−2.36603	+	9.56218i	−0.103757	+	0.419329i
$521$	5.73205			0.251126			0.125563	−	0.992086i	$-0.459926\pi$
$521$	5.73205			0.251126			0.125563	+	0.992086i	$0.459926\pi$
$522$		0			0
$523$	14.5981	+	25.2846i	0.638329	+	1.10562i	0.985799	+	0.167928i	$0.0537075\pi$
$523$	14.5981	+	25.2846i	0.638329	+	1.10562i	−0.347470	+	0.937691i	$0.612959\pi$
$524$	−2.53590	+	4.39230i	−0.110781	+	0.191879i
$525$		0			0
$526$	13.2224	+	7.63397i	0.576525	+	0.332857i
$527$	−31.2224	−	18.0263i	−1.36007	−	0.785237i
$528$		0			0
$529$	5.50000	−	9.52628i	0.239130	−	0.414186i
$530$	−4.83013	−	8.36603i	−0.209807	−	0.363397i
$531$		0			0
$532$	−2.46410			−0.106832
$533$	7.00000	+	24.2487i	0.303204	+	1.05033i
$534$		0			0
$535$	20.0263	−	11.5622i	0.865812	−	0.499877i
$536$	−0.464102	−	0.803848i	−0.0200461	−	0.0347209i
$537$		0			0
$538$			31.7128i			1.36724i
$539$	−0.232051	−	0.133975i	−0.00999514	−	0.00577069i
$540$		0			0
$541$			19.8038i			0.851434i	0.904856	+	0.425717i	$0.139978\pi$
$541$			19.8038i			0.851434i	−0.904856	+	0.425717i	$0.860022\pi$
$542$	−11.7583	+	20.3660i	−0.505064	+	0.874796i
$543$		0			0
$544$	−3.23205	+	1.86603i	−0.138573	+	0.0800052i
$545$	−37.3205			−1.59863
$546$		0			0
$547$	−37.1244			−1.58732			−0.793661	−	0.608360i	$-0.791828\pi$
$547$	−37.1244			−1.58732			−0.793661	+	0.608360i	$0.791828\pi$
$548$	7.39230	−	4.26795i	0.315784	−	0.182318i
$549$		0			0
$550$	−0.330127	+	0.571797i	−0.0140767	+	0.0243815i
$551$		−	7.39230i		−	0.314923i
$552$		0			0
$553$	14.5981	+	8.42820i	0.620773	+	0.358404i
$554$		−	5.60770i		−	0.238248i
$555$		0			0
$556$	3.06218	+	5.30385i	0.129865	+	0.224933i
$557$	16.7487	−	9.66987i	0.709666	−	0.409726i	−0.101272	−	0.994859i	$-0.532291\pi$
$557$	16.7487	−	9.66987i	0.709666	−	0.409726i	0.810937	+	0.585133i	$0.198958\pi$
$558$		0			0
$559$	7.09808	+	6.83013i	0.300217	+	0.288884i
$560$	−2.73205			−0.115450
$561$		0			0
$562$	3.90192	+	6.75833i	0.164593	+	0.285083i
$563$	18.3660	−	31.8109i	0.774036	−	1.34067i	−0.161299	−	0.986906i	$-0.551568\pi$
$563$	18.3660	−	31.8109i	0.774036	−	1.34067i	0.935335	−	0.353764i	$-0.115098\pi$
$564$		0			0
$565$	0.464102	+	0.267949i	0.0195249	+	0.0112727i
$566$	7.85641	+	4.53590i	0.330229	+	0.190658i
$567$		0			0
$568$	4.09808	−	7.09808i	0.171951	−	0.297829i
$569$	−9.63397	−	16.6865i	−0.403877	−	0.699536i	0.590313	−	0.807175i	$-0.299004\pi$
$569$	−9.63397	−	16.6865i	−0.403877	−	0.699536i	−0.994190	+	0.107639i	$0.965671\pi$
$570$		0			0
$571$	−30.1962			−1.26367			−0.631835	−	0.775103i	$-0.717698\pi$
$571$	−30.1962			−1.26367			−0.631835	+	0.775103i	$0.717698\pi$
$572$	0.937822	+	0.232051i	0.0392123	+	0.00970253i
$573$		0			0
$574$	−6.06218	+	3.50000i	−0.253030	+	0.146087i
$575$	−4.26795	−	7.39230i	−0.177986	−	0.308280i
$576$		0			0
$577$		−	16.7321i		−	0.696564i	−0.937390	−	0.348282i	$-0.886765\pi$
$577$		−	16.7321i		−	0.696564i	0.937390	−	0.348282i	$-0.113235\pi$
$578$	−2.66025	−	1.53590i	−0.110652	−	0.0638850i
$579$		0			0
$580$		−	8.19615i		−	0.340327i
$581$	−5.83013	+	10.0981i	−0.241874	+	0.418939i
$582$		0			0
$583$	−0.820508	+	0.473721i	−0.0339820	+	0.0196195i
$584$	−13.4641			−0.557148
$585$		0			0
$586$	−28.7846			−1.18908
$587$	35.8301	−	20.6865i	1.47887	−	0.853825i	0.479153	−	0.877731i	$-0.340944\pi$
$587$	35.8301	−	20.6865i	1.47887	−	0.853825i	0.999714	+	0.0239066i	$0.00761042\pi$
$588$		0			0
$589$	−11.9019	+	20.6147i	−0.490410	+	0.849415i
$590$			35.3205i			1.45412i
$591$		0			0
$592$	4.09808	+	2.36603i	0.168430	+	0.0972430i
$593$		−	48.3205i		−	1.98429i	−0.125111	−	0.992143i	$-0.539929\pi$
$593$		−	48.3205i		−	1.98429i	0.125111	−	0.992143i	$-0.460071\pi$
$594$		0			0
$595$	5.09808	+	8.83013i	0.209001	+	0.362000i
$596$	−4.39230	+	2.53590i	−0.179916	+	0.103874i
$597$		0			0
$598$	−8.66025	+	9.00000i	−0.354144	+	0.368037i
$599$	−33.7128			−1.37747			−0.688734	−	0.725014i	$-0.741833\pi$
$599$	−33.7128			−1.37747			−0.688734	+	0.725014i	$0.741833\pi$
$600$		0			0
$601$	18.5622	+	32.1506i	0.757167	+	1.31145i	0.944290	+	0.329115i	$0.106750\pi$
$601$	18.5622	+	32.1506i	0.757167	+	1.31145i	−0.187123	+	0.982337i	$0.559916\pi$
$602$	−1.36603	+	2.36603i	−0.0556750	+	0.0964320i
$603$		0			0
$604$	2.42820	+	1.40192i	0.0988022	+	0.0570435i
$605$	−25.8564	−	14.9282i	−1.05121	−	0.606918i
$606$		0			0
$607$	12.9545	−	22.4378i	0.525806	−	0.910723i	−0.473742	−	0.880664i	$-0.657097\pi$
$607$	12.9545	−	22.4378i	0.525806	−	0.910723i	0.999548	−	0.0300594i	$-0.00956963\pi$
$608$	1.23205	+	2.13397i	0.0499663	+	0.0865441i
$609$		0			0
$610$	−22.5885			−0.914580
$611$	8.62436	+	2.13397i	0.348904	+	0.0863314i
$612$		0			0
$613$	−12.2487	+	7.07180i	−0.494721	+	0.285627i	−0.726531	−	0.687134i	$-0.758869\pi$
$613$	−12.2487	+	7.07180i	−0.494721	+	0.285627i	0.231810	+	0.972761i	$0.425535\pi$
$614$	−3.89230	−	6.74167i	−0.157081	−	0.272072i
$615$		0			0
$616$			0.267949i			0.0107960i
$617$	−3.04552	−	1.75833i	−0.122608	−	0.0707877i	0.437442	−	0.899247i	$-0.355885\pi$
$617$	−3.04552	−	1.75833i	−0.122608	−	0.0707877i	−0.560050	+	0.828459i	$0.689218\pi$
$618$		0			0
$619$		−	32.3205i		−	1.29907i	−0.760331	−	0.649535i	$-0.774963\pi$
$619$		−	32.3205i		−	1.29907i	0.760331	−	0.649535i	$-0.225037\pi$
$620$	−13.1962	+	22.8564i	−0.529970	+	0.917935i
$621$		0			0
$622$	7.62436	−	4.40192i	0.305709	−	0.176501i
$623$	0.464102			0.0185938
$624$		0			0
$625$	−31.2487			−1.24995
$626$	−10.5622	+	6.09808i	−0.422150	+	0.243728i
$627$		0			0
$628$	−4.26795	+	7.39230i	−0.170310	+	0.294985i
$629$		−	17.6603i		−	0.704160i
$630$		0			0
$631$	−31.1603	−	17.9904i	−1.24047	−	0.716186i	−0.271280	−	0.962500i	$-0.587447\pi$
$631$	−31.1603	−	17.9904i	−1.24047	−	0.716186i	−0.969190	+	0.246315i	$0.920780\pi$
$632$		−	16.8564i		−	0.670512i
$633$		0			0
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	46.0526	−	26.5885i	1.82754	−	1.05513i
$636$		0			0
$637$	3.46410	−	1.00000i	0.137253	−	0.0396214i
$638$	−0.803848			−0.0318246
$639$		0			0
$640$	1.36603	+	2.36603i	0.0539969	+	0.0935254i
$641$	−16.1244	+	27.9282i	−0.636874	+	1.10310i	0.349241	+	0.937033i	$0.386439\pi$
$641$	−16.1244	+	27.9282i	−0.636874	+	1.10310i	−0.986115	+	0.166065i	$0.946894\pi$
$642$		0			0
$643$	−31.4545	−	18.1603i	−1.24044	−	0.716171i	−0.271259	−	0.962506i	$-0.587440\pi$
$643$	−31.4545	−	18.1603i	−1.24044	−	0.716171i	−0.969185	+	0.246336i	$0.920773\pi$
$644$	−3.00000	−	1.73205i	−0.118217	−	0.0682524i
$645$		0			0
$646$	4.59808	−	7.96410i	0.180909	−	0.313343i
$647$	0.866025	+	1.50000i	0.0340470	+	0.0589711i	0.882547	−	0.470225i	$-0.155827\pi$
$647$	0.866025	+	1.50000i	0.0340470	+	0.0589711i	−0.848500	+	0.529196i	$0.822494\pi$
$648$		0			0
$649$	3.46410			0.135978
$650$	−2.46410	−	8.53590i	−0.0966500	−	0.334805i
$651$		0			0
$652$	15.7583	−	9.09808i	0.617144	−	0.356308i
$653$	23.1603	+	40.1147i	0.906331	+	1.56981i	0.819121	+	0.573621i	$0.194462\pi$
$653$	23.1603	+	40.1147i	0.906331	+	1.56981i	0.0872099	+	0.996190i	$0.472205\pi$
$654$		0			0
$655$		−	13.8564i		−	0.541415i
$656$	6.06218	+	3.50000i	0.236688	+	0.136652i
$657$		0			0
$658$			2.46410i			0.0960607i
$659$	10.0359	−	17.3827i	0.390943	−	0.677133i	−0.601631	−	0.798774i	$-0.705482\pi$
$659$	10.0359	−	17.3827i	0.390943	−	0.677133i	0.992574	+	0.121641i	$0.0388156\pi$
$660$		0			0
$661$	−41.9090	+	24.1962i	−1.63007	+	0.941121i	−0.646000	+	0.763337i	$0.723560\pi$
$661$	−41.9090	+	24.1962i	−1.63007	+	0.941121i	−0.984070	+	0.177784i	$0.943107\pi$
$662$	−3.07180			−0.119389
$663$		0			0
$664$	11.6603			0.452506
$665$	5.83013	−	3.36603i	0.226083	−	0.130529i
$666$		0			0
$667$	5.19615	−	9.00000i	0.201196	−	0.348481i
$668$			21.8564i			0.845650i
$669$		0			0
$670$	2.19615	+	1.26795i	0.0848448	+	0.0489852i
$671$			2.21539i			0.0855242i
$672$		0			0
$673$	−17.0359	−	29.5070i	−0.656686	−	1.13741i	−0.981468	−	0.191624i	$-0.938625\pi$
$673$	−17.0359	−	29.5070i	−0.656686	−	1.13741i	0.324783	−	0.945789i	$-0.394709\pi$
$674$	−11.9378	+	6.89230i	−0.459828	+	0.265482i
$675$		0			0
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	−45.7654			−1.75891			−0.879453	−	0.475986i	$-0.842091\pi$
$677$	−45.7654			−1.75891			−0.879453	+	0.475986i	$0.842091\pi$
$678$		0			0
$679$	−1.36603	−	2.36603i	−0.0524232	−	0.0907997i
$680$	5.09808	−	8.83013i	0.195502	−	0.338620i
$681$		0			0
$682$	2.24167	+	1.29423i	0.0858380	+	0.0495586i
$683$	−4.85641	−	2.80385i	−0.185825	−	0.107286i	0.404201	−	0.914670i	$-0.367549\pi$
$683$	−4.85641	−	2.80385i	−0.185825	−	0.107286i	−0.590027	+	0.807384i	$0.700883\pi$
$684$		0			0
$685$	−11.6603	+	20.1962i	−0.445515	+	0.771655i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	2.73205			0.104158
$689$	3.06218	−	12.3756i	0.116660	−	0.471475i
$690$		0			0
$691$	0.679492	−	0.392305i	0.0258491	−	0.0149240i	−0.487020	−	0.873391i	$-0.661916\pi$
$691$	0.679492	−	0.392305i	0.0258491	−	0.0149240i	0.512869	+	0.858467i	$0.328583\pi$
$692$	8.63397	+	14.9545i	0.328214	+	0.568484i
$693$		0			0
$694$		−	4.85641i		−	0.184347i
$695$	−14.4904	−	8.36603i	−0.549651	−	0.317341i
$696$		0			0
$697$		−	26.1244i		−	0.989531i
$698$	−15.8564	+	27.4641i	−0.600174	+	1.03953i
$699$		0			0
$700$	2.13397	−	1.23205i	0.0806567	−	0.0465671i
$701$	−20.3205			−0.767495			−0.383747	−	0.923438i	$-0.625367\pi$
$701$	−20.3205			−0.767495			−0.383747	+	0.923438i	$0.625367\pi$
$702$		0			0
$703$	−11.6603			−0.439775
$704$	0.232051	−	0.133975i	0.00874574	−	0.00504936i
$705$		0			0
$706$	−2.73205	+	4.73205i	−0.102822	+	0.178093i
$707$		−	10.0000i		−	0.376089i
$708$		0			0
$709$	12.1699	+	7.02628i	0.457049	+	0.263877i	0.710803	−	0.703391i	$-0.248332\pi$
$709$	12.1699	+	7.02628i	0.457049	+	0.263877i	−0.253754	+	0.967269i	$0.581665\pi$
$710$			22.3923i			0.840368i
$711$		0			0
$712$	−0.232051	−	0.401924i	−0.00869647	−	0.0150627i
$713$	−28.9808	+	16.7321i	−1.08534	+	0.626620i
$714$		0			0
$715$	−2.53590	+	0.732051i	−0.0948372	+	0.0273771i
$716$	−1.60770			−0.0600824
$717$		0			0
$718$	13.0981	+	22.6865i	0.488816	+	0.846654i
$719$	17.5263	−	30.3564i	0.653620	−	1.13210i	−0.328618	−	0.944463i	$-0.606583\pi$
$719$	17.5263	−	30.3564i	0.653620	−	1.13210i	0.982238	−	0.187640i	$-0.0600838\pi$
$720$		0			0
$721$	−1.56218	−	0.901924i	−0.0581785	−	0.0335894i
$722$	11.1962	+	6.46410i	0.416678	+	0.240569i
$723$		0			0
$724$	4.59808	−	7.96410i	0.170886	−	0.295984i
$725$	3.69615	+	6.40192i	0.137272	+	0.237761i
$726$		0			0
$727$	5.46410			0.202652			0.101326	−	0.994853i	$-0.467691\pi$
$727$	5.46410			0.202652			0.101326	+	0.994853i	$0.467691\pi$
$728$	−2.59808	−	2.50000i	−0.0962911	−	0.0926562i
$729$		0			0
$730$	31.8564	−	18.3923i	1.17906	−	0.680730i
$731$	−5.09808	−	8.83013i	−0.188559	−	0.326594i
$732$		0			0
$733$			20.8564i			0.770349i	0.922844	+	0.385174i	$0.125859\pi$
$733$			20.8564i			0.770349i	−0.922844	+	0.385174i	$0.874141\pi$
$734$	−27.9282	−	16.1244i	−1.03085	−	0.595161i
$735$		0			0
$736$			3.46410i			0.127688i
$737$	0.124356	−	0.215390i	0.00458070	−	0.00793400i
$738$		0			0
$739$	12.4641	−	7.19615i	0.458499	−	0.264715i	−0.252914	−	0.967489i	$-0.581389\pi$
$739$	12.4641	−	7.19615i	0.458499	−	0.264715i	0.711413	+	0.702774i	$0.248056\pi$
$740$	−12.9282			−0.475250
$741$		0			0
$742$	3.53590			0.129807
$743$	22.0981	−	12.7583i	0.810700	−	0.468058i	−0.0364990	−	0.999334i	$-0.511621\pi$
$743$	22.0981	−	12.7583i	0.810700	−	0.468058i	0.847199	+	0.531276i	$0.178287\pi$
$744$		0			0
$745$	6.92820	−	12.0000i	0.253830	−	0.439646i
$746$		−	10.5885i		−	0.387671i
$747$		0			0
$748$	−0.866025	−	0.500000i	−0.0316650	−	0.0182818i
$749$			8.46410i			0.309272i
$750$		0			0
$751$	10.4282	+	18.0622i	0.380531	+	0.659098i	0.991138	−	0.132835i	$-0.0424081\pi$
$751$	10.4282	+	18.0622i	0.380531	+	0.659098i	−0.610608	+	0.791933i	$0.709075\pi$
$752$	2.13397	−	1.23205i	0.0778180	−	0.0449283i
$753$		0			0
$754$	7.50000	−	7.79423i	0.273134	−	0.283849i
$755$	−7.66025			−0.278785
$756$		0			0
$757$	−0.0262794	−	0.0455173i	−0.000955143	−	0.00165436i	0.865547	−	0.500827i	$-0.166971\pi$
$757$	−0.0262794	−	0.0455173i	−0.000955143	−	0.00165436i	−0.866503	+	0.499173i	$0.833637\pi$
$758$	8.29423	−	14.3660i	0.301260	−	0.521798i
$759$		0			0
$760$	−5.83013	−	3.36603i	−0.211481	−	0.122099i
$761$	−30.5885	−	17.6603i	−1.10883	−	0.640184i	−0.170304	−	0.985391i	$-0.554475\pi$
$761$	−30.5885	−	17.6603i	−1.10883	−	0.640184i	−0.938526	+	0.345208i	$0.887808\pi$
$762$		0			0
$763$	6.83013	−	11.8301i	0.247267	−	0.428279i
$764$	−3.09808	−	5.36603i	−0.112084	−	0.194136i
$765$		0			0
$766$	−35.3923			−1.27878
$767$	−32.3205	+	33.5885i	−1.16703	+	1.21281i
$768$		0			0
$769$	29.8301	−	17.2224i	1.07570	−	0.621057i	0.145968	−	0.989289i	$-0.453370\pi$
$769$	29.8301	−	17.2224i	1.07570	−	0.621057i	0.929734	+	0.368233i	$0.120037\pi$
$770$	−0.366025	−	0.633975i	−0.0131906	−	0.0228469i
$771$		0			0
$772$		−	6.80385i		−	0.244876i
$773$	18.7128	+	10.8038i	0.673053	+	0.388587i	0.797232	−	0.603672i	$-0.206296\pi$
$773$	18.7128	+	10.8038i	0.673053	+	0.388587i	−0.124179	+	0.992260i	$0.539630\pi$
$774$		0			0
$775$		−	23.8038i		−	0.855059i
$776$	−1.36603	+	2.36603i	−0.0490375	+	0.0849354i
$777$		0			0
$778$	−25.2679	+	14.5885i	−0.905900	+	0.523022i
$779$	−17.2487			−0.617999
$780$		0			0
$781$	2.19615			0.0785845
$782$	11.1962	−	6.46410i	0.400374	−	0.231156i
$783$		0			0
$784$	0.500000	−	0.866025i	0.0178571	−	0.0309295i
$785$		−	23.3205i		−	0.832345i
$786$		0			0
$787$	12.3109	+	7.10770i	0.438836	+	0.253362i	0.703104	−	0.711087i	$-0.251797\pi$
$787$	12.3109	+	7.10770i	0.438836	+	0.253362i	−0.264268	+	0.964449i	$0.585130\pi$
$788$		−	5.73205i		−	0.204196i
$789$		0			0
$790$	23.0263	+	39.8827i	0.819238	+	1.41896i
$791$	−0.169873	+	0.0980762i	−0.00603999	+	0.00348719i
$792$		0			0
$793$	−21.4808	−	20.6699i	−0.762804	−	0.734009i
$794$	−9.53590			−0.338416
$795$		0			0
$796$	−3.09808	−	5.36603i	−0.109808	−	0.190194i
$797$	−1.36603	+	2.36603i	−0.0483871	+	0.0838089i	−0.889205	−	0.457510i	$-0.848741\pi$
$797$	−1.36603	+	2.36603i	−0.0483871	+	0.0838089i	0.840817	+	0.541319i	$0.182075\pi$
$798$		0			0
$799$	−7.96410	−	4.59808i	−0.281750	−	0.162668i
$800$	−2.13397	−	1.23205i	−0.0754474	−	0.0435596i
$801$		0			0
$802$	5.00000	−	8.66025i	0.176556	−	0.305804i
$803$	−1.80385	−	3.12436i	−0.0636564	−	0.110256i
$804$		0			0
$805$	9.46410			0.333566
$806$	−33.4641	+	9.66025i	−1.17872	+	0.340268i
$807$		0			0
$808$	−8.66025	+	5.00000i	−0.304667	+	0.175899i
$809$	5.09808	+	8.83013i	0.179239	+	0.310451i	0.941620	−	0.336677i	$-0.109303\pi$
$809$	5.09808	+	8.83013i	0.179239	+	0.310451i	−0.762381	+	0.647128i	$0.775970\pi$
$810$		0			0
$811$		−	8.53590i		−	0.299736i	−0.988706	−	0.149868i	$-0.952115\pi$
$811$		−	8.53590i		−	0.299736i	0.988706	−	0.149868i	$-0.0478849\pi$
$812$	2.59808	+	1.50000i	0.0911746	+	0.0526397i
$813$		0			0
$814$			1.26795i			0.0444416i
$815$	−24.8564	+	43.0526i	−0.870682	+	1.50807i
$816$		0			0
$817$	−5.83013	+	3.36603i	−0.203970	+	0.117762i
$818$	16.7321			0.585022
$819$		0			0
$820$	−19.1244			−0.667851
$821$	−12.4808	+	7.20577i	−0.435582	+	0.251483i	−0.701722	−	0.712451i	$-0.747585\pi$
$821$	−12.4808	+	7.20577i	−0.435582	+	0.251483i	0.266140	+	0.963934i	$0.414252\pi$
$822$		0			0
$823$	10.4641	−	18.1244i	0.364756	−	0.631775i	−0.623981	−	0.781439i	$-0.714486\pi$
$823$	10.4641	−	18.1244i	0.364756	−	0.631775i	0.988737	+	0.149664i	$0.0478192\pi$
$824$			1.80385i			0.0628400i
$825$		0			0
$826$	−11.1962	−	6.46410i	−0.389564	−	0.224915i
$827$			40.3923i			1.40458i	0.711892	+	0.702289i	$0.247839\pi$
$827$			40.3923i			1.40458i	−0.711892	+	0.702289i	$0.752161\pi$
$828$		0			0
$829$	−0.330127	−	0.571797i	−0.0114658	−	0.0198593i	0.860236	−	0.509897i	$-0.170316\pi$
$829$	−0.330127	−	0.571797i	−0.0114658	−	0.0198593i	−0.871701	+	0.490037i	$0.836983\pi$
$830$	−27.5885	+	15.9282i	−0.957609	+	0.552876i
$831$		0			0
$832$	−0.866025	+	3.50000i	−0.0300240	+	0.121341i
$833$	−3.73205			−0.129308
$834$		0			0
$835$	−29.8564	−	51.7128i	−1.03322	−	1.78960i
$836$	−0.330127	+	0.571797i	−0.0114177	+	0.0197760i
$837$		0			0
$838$	−3.63397	−	2.09808i	−0.125534	−	0.0724768i
$839$	−12.4641	−	7.19615i	−0.430309	−	0.248439i	0.269170	−	0.963093i	$-0.413251\pi$
$839$	−12.4641	−	7.19615i	−0.430309	−	0.248439i	−0.699478	+	0.714654i	$0.746584\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−3.19615	−	5.53590i	−0.110147	−	0.190780i
$843$		0			0
$844$	−11.8564			−0.408114
$845$	16.5622	−	31.4186i	0.569756	−	1.08083i
$846$		0			0
$847$	9.46410	−	5.46410i	0.325190	−	0.187749i
$848$	−1.76795	−	3.06218i	−0.0607116	−	0.105156i
$849$		0			0
$850$			9.19615i			0.315425i
$851$	−14.1962	−	8.19615i	−0.486638	−	0.280960i
$852$		0			0
$853$			33.3923i			1.14333i	0.820487	+	0.571665i	$0.193702\pi$
$853$			33.3923i			1.14333i	−0.820487	+	0.571665i	$0.806298\pi$
$854$	4.13397	−	7.16025i	0.141462	−	0.245019i
$855$		0			0
$856$	7.33013	−	4.23205i	0.250539	−	0.144649i
$857$	−21.6077			−0.738105			−0.369052	−	0.929409i	$-0.620318\pi$
$857$	−21.6077			−0.738105			−0.369052	+	0.929409i	$0.620318\pi$
$858$		0			0
$859$	−45.0526			−1.53717			−0.768587	−	0.639746i	$-0.779040\pi$
$859$	−45.0526			−1.53717			−0.768587	+	0.639746i	$0.779040\pi$
$860$	−6.46410	+	3.73205i	−0.220424	+	0.127262i
$861$		0			0
$862$	1.56218	−	2.70577i	0.0532080	−	0.0921589i
$863$			28.6410i			0.974952i	0.873137	+	0.487476i	$0.162082\pi$
$863$			28.6410i			0.974952i	−0.873137	+	0.487476i	$0.837918\pi$
$864$		0			0
$865$	−40.8564	−	23.5885i	−1.38916	−	0.802032i
$866$		−	4.92820i		−	0.167467i
$867$		0			0
$868$	−4.83013	−	8.36603i	−0.163945	−	0.283961i
$869$	3.91154	−	2.25833i	0.132690	−	0.0766086i
$870$		0			0
$871$	0.928203	+	3.21539i	0.0314510	+	0.108949i
$872$	−13.6603			−0.462595
$873$		0			0
$874$	−4.26795	−	7.39230i	−0.144366	−	0.250048i
$875$	3.46410	−	6.00000i	0.117108	−	0.202837i
$876$		0			0
$877$	31.4378	+	18.1506i	1.06158	+	0.612903i	0.925869	−	0.377845i	$-0.123335\pi$
$877$	31.4378	+	18.1506i	1.06158	+	0.612903i	0.135711	+	0.990748i	$0.456668\pi$
$878$	−3.80385	−	2.19615i	−0.128374	−	0.0741166i
$879$		0			0
$880$	−0.366025	+	0.633975i	−0.0123387	+	0.0213713i
$881$	−0.535898	−	0.928203i	−0.0180549	−	0.0312720i	0.856857	−	0.515554i	$-0.172414\pi$
$881$	−0.535898	−	0.928203i	−0.0180549	−	0.0312720i	−0.874912	+	0.484283i	$0.839081\pi$
$882$		0			0
$883$	−34.4449			−1.15916			−0.579581	−	0.814915i	$-0.696784\pi$
$883$	−34.4449			−1.15916			−0.579581	+	0.814915i	$0.696784\pi$
$884$	12.9282	−	3.73205i	0.434823	−	0.125522i
$885$		0			0
$886$	−9.18653	+	5.30385i	−0.308628	+	0.178186i
$887$	22.5263	+	39.0167i	0.756358	+	1.31005i	0.944696	+	0.327947i	$0.106357\pi$
$887$	22.5263	+	39.0167i	0.756358	+	1.31005i	−0.188338	+	0.982104i	$0.560310\pi$
$888$		0			0
$889$			19.4641i			0.652805i
$890$	1.09808	+	0.633975i	0.0368076	+	0.0212509i
$891$		0			0
$892$		−	12.3923i		−	0.414925i
$893$	−3.03590	+	5.25833i	−0.101592	+	0.175963i
$894$		0			0
$895$	3.80385	−	2.19615i	0.127149	−	0.0734093i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	7.26795			0.242535
$899$	25.0981	−	14.4904i	0.837068	−	0.483281i
$900$		0			0
$901$	−6.59808	+	11.4282i	−0.219814	+	0.380729i
$902$			1.87564i			0.0624521i
$903$		0			0
$904$	0.169873	+	0.0980762i	0.00564989	+	0.00326197i
$905$			25.1244i			0.835162i
$906$		0			0
$907$	−13.7321	−	23.7846i	−0.455965	−	0.789755i	0.542778	−	0.839876i	$-0.317373\pi$
$907$	−13.7321	−	23.7846i	−0.455965	−	0.789755i	−0.998743	+	0.0501213i	$0.984039\pi$
$908$	13.3923	−	7.73205i	0.444439	−	0.256597i
$909$		0			0
$910$	9.56218	+	2.36603i	0.316983	+	0.0784330i
$911$	0.0525589			0.00174135			0.000870677	−	1.00000i	$-0.499723\pi$
$911$	0.0525589			0.00174135			0.000870677		1.00000i	$0.499723\pi$
$912$		0			0
$913$	1.56218	+	2.70577i	0.0517005	+	0.0895480i
$914$	−17.3923	+	30.1244i	−0.575286	+	0.996425i
$915$		0			0
$916$	21.0622	+	12.1603i	0.695914	+	0.401786i
$917$	4.39230	+	2.53590i	0.145047	+	0.0837427i
$918$		0			0
$919$	−20.8205	+	36.0622i	−0.686805	+	1.18958i	0.286061	+	0.958212i	$0.407654\pi$
$919$	−20.8205	+	36.0622i	−0.686805	+	1.18958i	−0.972866	+	0.231370i	$0.925679\pi$
$920$	−4.73205	−	8.19615i	−0.156011	−	0.270219i
$921$		0			0
$922$	−27.7128			−0.912673
$923$	−20.4904	+	21.2942i	−0.674449	+	0.700908i
$924$		0			0
$925$	10.0981	−	5.83013i	0.332023	−	0.191693i
$926$	−4.59808	−	7.96410i	−0.151102	−	0.261717i
$927$		0			0
$928$		−	3.00000i		−	0.0984798i
$929$	37.7032	+	21.7679i	1.23700	+	0.714183i	0.968480	−	0.249090i	$-0.0801316\pi$
$929$	37.7032	+	21.7679i	1.23700	+	0.714183i	0.268521	+	0.963274i	$0.413465\pi$
$930$		0			0
$931$			2.46410i			0.0807577i
$932$	−4.09808	+	7.09808i	−0.134237	+	0.232505i
$933$		0			0
$934$	−15.4641	+	8.92820i	−0.506001	+	0.292140i
$935$	2.73205			0.0893476
$936$		0			0
$937$	45.5692			1.48868			0.744341	−	0.667800i	$-0.232764\pi$
$937$	45.5692			1.48868			0.744341	+	0.667800i	$0.232764\pi$
$938$	−0.803848	+	0.464102i	−0.0262466	+	0.0151535i
$939$		0			0
$940$	−3.36603	+	5.83013i	−0.109788	+	0.190158i
$941$			49.1769i			1.60312i	0.597913	+	0.801561i	$0.295997\pi$
$941$			49.1769i			1.60312i	−0.597913	+	0.801561i	$0.704003\pi$
$942$		0			0
$943$	−21.0000	−	12.1244i	−0.683854	−	0.394823i
$944$			12.9282i			0.420777i
$945$		0			0
$946$	0.366025	+	0.633975i	0.0119005	+	0.0206123i
$947$	−11.2128	+	6.47372i	−0.364367	+	0.210368i	−0.670995	−	0.741462i	$-0.734133\pi$
$947$	−11.2128	+	6.47372i	−0.364367	+	0.210368i	0.306627	+	0.951830i	$0.400799\pi$
$948$		0			0
$949$	47.1244	+	11.6603i	1.52972	+	0.378508i
$950$	6.07180			0.196995
$951$		0			0
$952$	1.86603	+	3.23205i	0.0604782	+	0.104751i
$953$	10.6865	−	18.5096i	0.346171	−	0.599585i	−0.639395	−	0.768878i	$-0.720815\pi$
$953$	10.6865	−	18.5096i	0.346171	−	0.599585i	0.985566	+	0.169293i	$0.0541484\pi$
$954$		0			0
$955$	14.6603	+	8.46410i	0.474395	+	0.273892i
$956$	20.9545	+	12.0981i	0.677716	+	0.391280i
$957$		0			0
$958$	−5.30385	+	9.18653i	−0.171360	+	0.296803i
$959$	−4.26795	−	7.39230i	−0.137819	−	0.238710i
$960$		0			0
$961$	−62.3205			−2.01034
$962$	−12.2942	−	11.8301i	−0.396382	−	0.381419i
$963$		0			0
$964$	−24.9282	+	14.3923i	−0.802883	+	0.463545i
$965$	9.29423	+	16.0981i	0.299192	+	0.518215i
$966$		0			0
$967$			36.0000i			1.15768i	0.815440	+	0.578841i	$0.196495\pi$
$967$			36.0000i			1.15768i	−0.815440	+	0.578841i	$0.803505\pi$
$968$	−9.46410	−	5.46410i	−0.304188	−	0.175623i
$969$		0			0
$970$		−	7.46410i		−	0.239658i
$971$	−2.12436	+	3.67949i	−0.0681738	+	0.118081i	−0.898097	−	0.439796i	$-0.855051\pi$
$971$	−2.12436	+	3.67949i	−0.0681738	+	0.118081i	0.829924	+	0.557877i	$0.188384\pi$
$972$		0			0
$973$	5.30385	−	3.06218i	0.170034	−	0.0981689i
$974$	10.8038			0.346178
$975$		0			0
$976$	−8.26795			−0.264651
$977$	−26.1962	+	15.1244i	−0.838089	+	0.483871i	−0.856614	−	0.515957i	$-0.827436\pi$
$977$	−26.1962	+	15.1244i	−0.838089	+	0.483871i	0.0185251	+	0.999828i	$0.494103\pi$
$978$		0			0
$979$	0.0621778	−	0.107695i	0.00198721	−	0.00344195i
$980$			2.73205i			0.0872722i
$981$		0			0
$982$	−10.6077	−	6.12436i	−0.338505	−	0.195436i
$983$			55.8564i			1.78154i	0.454452	+	0.890771i	$0.349835\pi$
$983$			55.8564i			1.78154i	−0.454452	+	0.890771i	$0.650165\pi$
$984$		0			0
$985$	7.83013	+	13.5622i	0.249489	+	0.432127i
$986$	−9.69615	+	5.59808i	−0.308788	+	0.178279i
$987$		0			0
$988$	−2.46410	−	8.53590i	−0.0783935	−	0.271563i
$989$	−9.46410			−0.300941
$990$		0			0
$991$	12.6962	+	21.9904i	0.403307	+	0.698547i	0.994123	−	0.108259i	$-0.0345275\pi$
$991$	12.6962	+	21.9904i	0.403307	+	0.698547i	−0.590816	+	0.806806i	$0.701194\pi$
$992$	−4.83013	+	8.36603i	−0.153357	+	0.265622i
$993$		0			0
$994$	−7.09808	−	4.09808i	−0.225137	−	0.129983i
$995$	14.6603	+	8.46410i	0.464761	+	0.268330i
$996$		0			0
$997$	29.1147	−	50.4282i	0.922073	−	1.59708i	0.125871	−	0.992047i	$-0.459828\pi$
$997$	29.1147	−	50.4282i	0.922073	−	1.59708i	0.796202	−	0.605031i	$-0.206839\pi$
$998$	−19.4904	−	33.7583i	−0.616957	−	1.06860i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.d.127.1		4
3.2	odd	2		546.2.s.d.127.2	yes	4
13.4	even	6	inner	1638.2.bj.d.1135.1		4
39.2	even	12		7098.2.a.bs.1.1		2
39.11	even	12		7098.2.a.bj.1.2		2
39.17	odd	6		546.2.s.d.43.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.d.43.2	✓	4	39.17	odd	6
546.2.s.d.127.2	yes	4	3.2	odd	2
1638.2.bj.d.127.1		4	1.1	even	1	trivial
1638.2.bj.d.1135.1		4	13.4	even	6	inner
7098.2.a.bj.1.2		2	39.11	even	12
7098.2.a.bs.1.1		2	39.2	even	12

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +2.73205i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +2.73205i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.36603 - 2.36603i) q^{10} +(-0.232051 + 0.133975i) q^{11} +(0.866025 - 3.50000i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.86603 + 3.23205i) q^{17} +(2.13397 + 1.23205i) q^{19} +(2.36603 + 1.36603i) q^{20} +(0.133975 - 0.232051i) q^{22} +(1.73205 + 3.00000i) q^{23} -2.46410 q^{25} +(1.00000 + 3.46410i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(-1.50000 - 2.59808i) q^{29} +9.66025i q^{31} +(0.866025 + 0.500000i) q^{32} -3.73205i q^{34} +(1.36603 - 2.36603i) q^{35} +(-4.09808 + 2.36603i) q^{37} -2.46410 q^{38} -2.73205 q^{40} +(-6.06218 + 3.50000i) q^{41} +(-1.36603 + 2.36603i) q^{43} +0.267949i q^{44} +(-3.00000 - 1.73205i) q^{46} +2.46410i q^{47} +(0.500000 + 0.866025i) q^{49} +(2.13397 - 1.23205i) q^{50} +(-2.59808 - 2.50000i) q^{52} +3.53590 q^{53} +(-0.366025 - 0.633975i) q^{55} +(0.500000 - 0.866025i) q^{56} +(2.59808 + 1.50000i) q^{58} +(-11.1962 - 6.46410i) q^{59} +(4.13397 - 7.16025i) q^{61} +(-4.83013 - 8.36603i) q^{62} -1.00000 q^{64} +(9.56218 + 2.36603i) q^{65} +(-0.803848 + 0.464102i) q^{67} +(1.86603 + 3.23205i) q^{68} +2.73205i q^{70} +(-7.09808 - 4.09808i) q^{71} +13.4641i q^{73} +(2.36603 - 4.09808i) q^{74} +(2.13397 - 1.23205i) q^{76} +0.267949 q^{77} -16.8564 q^{79} +(2.36603 - 1.36603i) q^{80} +(3.50000 - 6.06218i) q^{82} -11.6603i q^{83} +(-8.83013 - 5.09808i) q^{85} -2.73205i q^{86} +(-0.133975 - 0.232051i) q^{88} +(-0.401924 + 0.232051i) q^{89} +(-2.50000 + 2.59808i) q^{91} +3.46410 q^{92} +(-1.23205 - 2.13397i) q^{94} +(-3.36603 + 5.83013i) q^{95} +(2.36603 + 1.36603i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 4 * q + 2 * q^4	\( 4 q + 2 q^{4} - 2 q^{10} + 6 q^{11} + 4 q^{14} - 2 q^{16} - 4 q^{17} + 12 q^{19} + 6 q^{20} + 4 q^{22} + 4 q^{25} + 4 q^{26} - 6 q^{29} + 2 q^{35} - 6 q^{37} + 4 q^{38} - 4 q^{40} - 2 q^{43} - 12 q^{46} + 2 q^{49} + 12 q^{50} + 28 q^{53} + 2 q^{55} + 2 q^{56} - 24 q^{59} + 20 q^{61} - 2 q^{62} - 4 q^{64} + 14 q^{65} - 24 q^{67} + 4 q^{68} - 18 q^{71} + 6 q^{74} + 12 q^{76} + 8 q^{77} - 12 q^{79} + 6 q^{80} + 14 q^{82} - 18 q^{85} - 4 q^{88} - 12 q^{89} - 10 q^{91} + 2 q^{94} - 10 q^{95} + 6 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^10 + 6 * q^11 + 4 * q^14 - 2 * q^16 - 4 * q^17 + 12 * q^19 + 6 * q^20 + 4 * q^22 + 4 * q^25 + 4 * q^26 - 6 * q^29 + 2 * q^35 - 6 * q^37 + 4 * q^38 - 4 * q^40 - 2 * q^43 - 12 * q^46 + 2 * q^49 + 12 * q^50 + 28 * q^53 + 2 * q^55 + 2 * q^56 - 24 * q^59 + 20 * q^61 - 2 * q^62 - 4 * q^64 + 14 * q^65 - 24 * q^67 + 4 * q^68 - 18 * q^71 + 6 * q^74 + 12 * q^76 + 8 * q^77 - 12 * q^79 + 6 * q^80 + 14 * q^82 - 18 * q^85 - 4 * q^88 - 12 * q^89 - 10 * q^91 + 2 * q^94 - 10 * q^95 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more