LMFDB - Embedded newform 1638.2.bj.d.1135.1

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			1135.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1638.1135
Dual form			1638.2.bj.d.127.1

$q$-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 $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

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

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	$-0.790806\pi$
$5$		−	2.73205i		−	1.22181i	0.791704	−	0.610905i	$-0.209194\pi$
$6$		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	0.464609	−	0.885516i	$-0.346195\pi$
$11$	−0.232051	−	0.133975i	−0.0699660	−	0.0403949i	−0.534575	+	0.845121i	$0.679528\pi$
$12$		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	0.545968	−	0.837806i	$-0.316162\pi$
$17$	−1.86603	−	3.23205i	−0.452578	−	0.783887i	−0.998545	+	0.0539188i	$0.982829\pi$
$18$		0			0
$19$	2.13397	−	1.23205i	0.489567	−	0.282652i	−0.234828	−	0.972037i	$-0.575453\pi$
$19$	2.13397	−	1.23205i	0.489567	−	0.282652i	0.724395	+	0.689385i	$0.242119\pi$
$20$	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	−0.626994	−	0.779024i	$-0.715715\pi$
$23$	1.73205	−	3.00000i	0.361158	−	0.625543i	0.988152	+	0.153481i	$0.0490483\pi$
$24$		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	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$		−	9.66025i		−	1.73503i	−0.497409	−	0.867516i	$-0.665715\pi$
$31$		−	9.66025i		−	1.73503i	0.497409	−	0.867516i	$-0.334285\pi$
$32$	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	0.123765	−	0.992312i	$-0.460503\pi$
$37$	−4.09808	−	2.36603i	−0.673720	−	0.388972i	−0.797485	+	0.603339i	$0.793836\pi$
$38$	−2.46410			−0.399730
$39$		0			0
$40$	−2.73205			−0.431975
$41$	−6.06218	−	3.50000i	−0.946753	−	0.546608i	−0.0546823	−	0.998504i	$-0.517415\pi$
$41$	−6.06218	−	3.50000i	−0.946753	−	0.546608i	−0.892071	+	0.451896i	$0.850748\pi$
$42$		0			0
$43$	−1.36603	−	2.36603i	−0.208317	−	0.360815i	0.742868	−	0.669438i	$-0.233465\pi$
$43$	−1.36603	−	2.36603i	−0.208317	−	0.360815i	−0.951184	+	0.308623i	$0.900132\pi$
$44$		−	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	$-0.942483\pi$
$47$		−	2.46410i		−	0.359426i	0.983719	−	0.179713i	$-0.0575169\pi$
$48$		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	−0.998894	−	0.0470259i	$-0.985026\pi$
$59$	−11.1962	+	6.46410i	−1.45761	+	0.841554i	−0.458721	+	0.888580i	$0.651692\pi$
$60$		0			0
$61$	4.13397	+	7.16025i	0.529301	+	0.916777i	0.999416	+	0.0341713i	$0.0108792\pi$
$61$	4.13397	+	7.16025i	0.529301	+	0.916777i	−0.470115	+	0.882605i	$0.655787\pi$
$62$	−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	0.450093	−	0.892982i	$-0.351391\pi$
$67$	−0.803848	−	0.464102i	−0.0982056	−	0.0566990i	−0.548298	+	0.836283i	$0.684724\pi$
$68$	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	−0.858075	−	0.513525i	$-0.828339\pi$
$71$	−7.09808	+	4.09808i	−0.842387	+	0.486352i	0.0156881	+	0.999877i	$0.495006\pi$
$72$		0			0
$73$		−	13.4641i		−	1.57585i	−0.615769	−	0.787927i	$-0.711154\pi$
$73$		−	13.4641i		−	1.57585i	0.615769	−	0.787927i	$-0.288846\pi$
$74$	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	$0.221041\pi$
$83$			11.6603i			1.27988i	−0.768425	+	0.639940i	$0.778959\pi$
$84$		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	0.478547	−	0.878062i	$-0.341164\pi$
$89$	−0.401924	−	0.232051i	−0.0426038	−	0.0245973i	−0.521151	+	0.853465i	$0.674497\pi$
$90$		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	−0.375051	−	0.927004i	$-0.622375\pi$
$97$	2.36603	−	1.36603i	0.240233	−	0.138699i	0.615284	+	0.788305i	$0.289041\pi$
$98$	−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	−0.502477	−	0.864590i	$-0.667578\pi$
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	0.999996	+	0.00286291i	$0.000911295\pi$
$102$		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	−0.994792	−	0.101923i	$-0.967500\pi$
$107$	−4.23205	+	7.33013i	−0.409128	+	0.708630i	0.585664	+	0.810554i	$0.300834\pi$
$108$		0			0
$109$		−	13.6603i		−	1.30842i	−0.756315	−	0.654208i	$-0.773002\pi$
$109$		−	13.6603i		−	1.30842i	0.756315	−	0.654208i	$-0.226998\pi$
$110$	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	0.870602	−	0.491989i	$-0.163730\pi$
$113$	0.0980762	+	0.169873i	0.00922623	+	0.0159803i	−0.861375	+	0.507969i	$0.830396\pi$
$114$		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	0.00487054	+	0.999988i	$0.498450\pi$
$127$	−9.73205	+	16.8564i	−0.863580	+	1.49576i	−0.868450	+	0.495776i	$0.834884\pi$
$128$	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	−0.149792	−	0.988718i	$-0.547860\pi$
$137$	7.39230	−	4.26795i	0.631567	−	0.364636i	0.781359	+	0.624082i	$0.214527\pi$
$138$		0			0
$139$	−3.06218	−	5.30385i	−0.259731	−	0.449866i	0.706439	−	0.707774i	$-0.250300\pi$
$139$	−3.06218	−	5.30385i	−0.259731	−	0.449866i	−0.966170	+	0.257907i	$0.916967\pi$
$140$	−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	−0.669007	−	0.743256i	$-0.733280\pi$
$149$	−4.39230	+	2.53590i	−0.359832	+	0.207749i	0.309175	+	0.951005i	$0.399947\pi$
$150$		0			0
$151$		−	2.80385i		−	0.228174i	−0.993471	−	0.114087i	$-0.963606\pi$
$151$		−	2.80385i		−	0.228174i	0.993471	−	0.114087i	$-0.0363942\pi$
$152$	−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	0.266367	−	0.963872i	$-0.414177\pi$
$163$	15.7583	−	9.09808i	1.23429	−	0.712616i	0.967921	+	0.251255i	$0.0808434\pi$
$164$		−	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	−0.465485	−	0.885056i	$-0.654120\pi$
$167$	−18.9282	−	10.9282i	−1.46471	−	0.845650i	−0.999223	+	0.0394060i	$0.987453\pi$
$168$		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	−0.981534	−	0.191290i	$-0.938733\pi$
$173$	−8.63397	−	14.9545i	−0.656429	−	1.13697i	0.325105	−	0.945678i	$-0.394600\pi$
$174$		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	−0.894502	−	0.447064i	$-0.852470\pi$
$179$	−0.803848	+	1.39230i	−0.0600824	+	0.104066i	0.834420	+	0.551130i	$0.185803\pi$
$180$		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	0.956070	−	0.293139i	$-0.0946999\pi$
$191$	3.09808	+	5.36603i	0.224169	+	0.388272i	−0.731901	+	0.681411i	$0.761367\pi$
$192$		0			0
$193$	5.89230	+	3.40192i	0.424137	+	0.244876i	0.696846	−	0.717221i	$-0.254586\pi$
$193$	5.89230	+	3.40192i	0.424137	+	0.244876i	−0.272709	+	0.962097i	$0.587919\pi$
$194$	−2.73205			−0.196150
$195$		0			0
$196$	1.00000			0.0714286
$197$	4.96410	+	2.86603i	0.353678	+	0.204196i	0.666304	−	0.745680i	$-0.267875\pi$
$197$	4.96410	+	2.86603i	0.353678	+	0.204196i	−0.312626	+	0.949876i	$0.601209\pi$
$198$		0			0
$199$	3.09808	+	5.36603i	0.219617	+	0.380387i	0.954691	−	0.297599i	$-0.0961860\pi$
$199$	3.09808	+	5.36603i	0.219617	+	0.380387i	−0.735074	+	0.677987i	$0.762853\pi$
$200$			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	−0.994678	−	0.103028i	$-0.967147\pi$
$211$	−5.92820	+	10.2679i	−0.408114	+	0.706875i	0.586564	+	0.809903i	$0.300480\pi$
$212$	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	0.814263	−	0.580496i	$-0.197141\pi$
$223$	10.7321	+	6.19615i	0.718671	+	0.414925i	−0.0955922	+	0.995421i	$0.530474\pi$
$224$	−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	0.0153030	−	0.999883i	$-0.495129\pi$
$227$	13.3923	−	7.73205i	0.888878	−	0.513194i	0.873575	+	0.486689i	$0.161795\pi$
$228$		0			0
$229$		−	24.3205i		−	1.60714i	−0.595207	−	0.803572i	$-0.702930\pi$
$229$		−	24.3205i		−	1.60714i	0.595207	−	0.803572i	$-0.297070\pi$
$230$	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	$-0.713914\pi$
$239$		−	24.1962i		−	1.56512i	0.622576	−	0.782559i	$-0.286086\pi$
$240$		0			0
$241$	−24.9282	+	14.3923i	−1.60577	+	0.927090i	−0.615464	+	0.788165i	$0.711031\pi$
$241$	−24.9282	+	14.3923i	−1.60577	+	0.927090i	−0.990303	+	0.138925i	$0.955635\pi$
$242$			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	0.716205	−	0.697889i	$-0.245877\pi$
$251$	−3.90192	−	6.75833i	−0.246287	−	0.426582i	−0.962493	+	0.271307i	$0.912544\pi$
$252$		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	−0.0429595	−	0.999077i	$-0.513679\pi$
$257$	13.5263	−	23.4282i	0.843746	−	1.46141i	0.886706	−	0.462334i	$-0.152988\pi$
$258$		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	−0.999440	−	0.0334733i	$-0.989343\pi$
$263$	−7.63397	+	13.2224i	−0.470731	+	0.815330i	0.528709	+	0.848803i	$0.322676\pi$
$264$		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	0.704749	+	0.709457i	$0.251060\pi$
$269$	15.8564	+	27.4641i	0.966782	+	1.67452i	0.262033	+	0.965059i	$0.415607\pi$
$270$		0			0
$271$	20.3660	+	11.7583i	1.23715	+	0.714268i	0.968510	−	0.248974i	$-0.0800932\pi$
$271$	20.3660	+	11.7583i	1.23715	+	0.714268i	0.268638	+	0.963241i	$0.413427\pi$
$272$	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	0.769414	−	0.638750i	$-0.220548\pi$
$277$	−2.80385	−	4.85641i	−0.168467	−	0.291793i	−0.937881	+	0.346957i	$0.887215\pi$
$278$			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	$0.0747787\pi$
$281$			7.80385i			0.465539i	−0.972532	+	0.232769i	$0.925221\pi$
$282$		0			0
$283$	−4.53590	+	7.85641i	−0.269631	+	0.467015i	−0.968767	−	0.247974i	$-0.920235\pi$
$283$	−4.53590	+	7.85641i	−0.269631	+	0.467015i	0.699135	+	0.714989i	$0.253568\pi$
$284$	−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	0.457493	−	0.889213i	$-0.348747\pi$
$293$	24.9282	−	14.3923i	1.45632	−	0.840807i	0.998828	+	0.0484056i	$0.0154140\pi$
$294$		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	$-0.928694\pi$
$307$		−	7.78461i		−	0.444291i	0.975014	−	0.222146i	$-0.0713060\pi$
$308$	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	$-0.831312\pi$
$317$		−	18.0000i		−	1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$		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	−0.425105	−	0.905144i	$-0.639763\pi$
$331$	2.66025	−	1.53590i	0.146221	−	0.0844206i	0.571325	+	0.820724i	$0.306429\pi$
$332$	−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	0.793460	−	0.608623i	$-0.208278\pi$
$347$	−2.42820	−	4.20577i	−0.130353	−	0.225778i	−0.923813	+	0.382845i	$0.874944\pi$
$348$		0			0
$349$	27.4641	+	15.8564i	1.47012	+	0.848774i	0.999438	−	0.0335290i	$-0.0106746\pi$
$349$	27.4641	+	15.8564i	1.47012	+	0.848774i	0.470682	+	0.882303i	$0.344008\pi$
$350$	−2.46410			−0.131712
$351$		0			0
$352$	−0.267949			−0.0142817
$353$	4.73205	+	2.73205i	0.251862	+	0.145412i	0.620616	−	0.784114i	$-0.286882\pi$
$353$	4.73205	+	2.73205i	0.251862	+	0.145412i	−0.368755	+	0.929527i	$0.620216\pi$
$354$		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	$0.242957\pi$
$359$			26.1962i			1.38258i	−0.722577	+	0.691290i	$0.757043\pi$
$360$		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	−0.0467851	−	0.998905i	$-0.514898\pi$
$367$	16.1244	−	27.9282i	0.841685	−	1.45784i	0.888470	−	0.458935i	$-0.151769\pi$
$368$	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	0.695789	−	0.718246i	$-0.255055\pi$
$373$	−5.29423	−	9.16987i	−0.274125	−	0.474798i	−0.969914	+	0.243448i	$0.921721\pi$
$374$	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	0.0833842	−	0.996517i	$-0.473427\pi$
$379$	−14.3660	−	8.29423i	−0.737933	−	0.426046i	−0.821317	+	0.570472i	$0.806760\pi$
$380$	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	0.569565	−	0.821946i	$-0.307112\pi$
$383$	30.6506	−	17.6962i	1.56617	−	0.904231i	0.996609	−	0.0822852i	$-0.0262218\pi$
$384$		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	−0.278236	−	0.960513i	$-0.589750\pi$
$397$	8.25833	−	4.76795i	0.414474	−	0.239297i	0.692710	+	0.721216i	$0.256417\pi$
$398$		−	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	0.267927	−	0.963439i	$-0.413661\pi$
$401$	−8.66025	−	5.00000i	−0.432472	−	0.249688i	−0.700399	+	0.713751i	$0.746995\pi$
$402$		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	−0.813464	−	0.581615i	$-0.802421\pi$
$409$	−14.4904	+	8.36603i	−0.716503	+	0.413673i	0.0969611	+	0.995288i	$0.469088\pi$
$410$	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	−0.810215	−	0.586132i	$-0.800650\pi$
$419$	2.09808	−	3.63397i	0.102498	−	0.177531i	0.912713	+	0.408601i	$0.133983\pi$
$420$		0			0
$421$		−	6.39230i		−	0.311542i	−0.987793	−	0.155771i	$-0.950214\pi$
$421$		−	6.39230i		−	0.311542i	0.987793	−	0.155771i	$-0.0497862\pi$
$422$	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	0.433416	−	0.901194i	$-0.357308\pi$
$431$	−2.70577	−	1.56218i	−0.130332	−	0.0752475i	−0.563749	+	0.825946i	$0.690641\pi$
$432$		0			0
$433$	−2.46410	−	4.26795i	−0.118417	−	0.205105i	0.800723	−	0.599034i	$-0.204449\pi$
$433$	−2.46410	−	4.26795i	−0.118417	−	0.205105i	−0.919141	+	0.393930i	$0.871115\pi$
$434$		−	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	−0.808847	−	0.588020i	$-0.799908\pi$
$439$	2.19615	−	3.80385i	0.104817	−	0.181548i	0.913663	+	0.406472i	$0.133241\pi$
$440$	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	−0.641114	−	0.767446i	$-0.721527\pi$
$449$	−6.29423	+	3.63397i	−0.297043	+	0.171498i	0.344071	+	0.938944i	$0.388194\pi$
$450$		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	0.995307	−	0.0967670i	$-0.0308502\pi$
$457$	30.1244	+	17.3923i	1.40916	+	0.813578i	0.413851	+	0.910345i	$0.364183\pi$
$458$	−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	0.176955	−	0.984219i	$-0.443375\pi$
$461$	24.0000	−	13.8564i	1.11779	−	0.645357i	0.940836	+	0.338862i	$0.110042\pi$
$462$		0			0
$463$		−	9.19615i		−	0.427381i	−0.976901	−	0.213691i	$-0.931452\pi$
$463$		−	9.19615i		−	0.427381i	0.976901	−	0.213691i	$-0.0685485\pi$
$464$	−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	0.694968	−	0.719041i	$-0.255419\pi$
$479$	9.18653	+	5.30385i	0.419743	+	0.242339i	−0.275224	+	0.961380i	$0.588752\pi$
$480$		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	−0.696778	−	0.717286i	$-0.745384\pi$
$487$	−9.35641	+	5.40192i	−0.423979	+	0.244785i	0.272799	+	0.962071i	$0.412051\pi$
$488$	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	−0.694096	−	0.719882i	$-0.744196\pi$
$491$	6.12436	−	10.6077i	0.276388	−	0.478719i	0.970484	+	0.241164i	$0.0775291\pi$
$492$		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	$-0.662491\pi$
$499$		−	38.9808i		−	1.74502i	0.488598	−	0.872509i	$-0.337509\pi$
$500$	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	0.965964	+	0.258676i	$0.0832863\pi$
$503$	15.8564	+	27.4641i	0.707002	+	1.22456i	−0.258962	+	0.965888i	$0.583380\pi$
$504$		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	0.713157	−	0.701004i	$-0.247265\pi$
$509$	10.4378	+	6.02628i	0.462648	+	0.267110i	−0.250509	+	0.968114i	$0.580598\pi$
$510$		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	−0.347470	−	0.937691i	$-0.612959\pi$
$523$	14.5981	−	25.2846i	0.638329	−	1.10562i	0.985799	−	0.167928i	$-0.0537075\pi$
$524$	−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	$-0.860022\pi$
$541$		−	19.8038i		−	0.851434i	0.904856	−	0.425717i	$-0.139978\pi$
$542$	−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	0.810937	−	0.585133i	$-0.198958\pi$
$557$	16.7487	+	9.66987i	0.709666	+	0.409726i	−0.101272	+	0.994859i	$0.532291\pi$
$558$		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	0.935335	+	0.353764i	$0.115098\pi$
$563$	18.3660	+	31.8109i	0.774036	+	1.34067i	−0.161299	+	0.986906i	$0.551568\pi$
$564$		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	−0.994190	−	0.107639i	$-0.965671\pi$
$569$	−9.63397	+	16.6865i	−0.403877	+	0.699536i	0.590313	+	0.807175i	$0.299004\pi$
$570$		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	$0.113235\pi$
$577$			16.7321i			0.696564i	−0.937390	+	0.348282i	$0.886765\pi$
$578$	−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	0.999714	−	0.0239066i	$-0.00761042\pi$
$587$	35.8301	+	20.6865i	1.47887	+	0.853825i	0.479153	+	0.877731i	$0.340944\pi$
$588$		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	$0.460071\pi$
$593$			48.3205i			1.98429i	−0.125111	+	0.992143i	$0.539929\pi$
$594$		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	−0.187123	−	0.982337i	$-0.559916\pi$
$601$	18.5622	−	32.1506i	0.757167	−	1.31145i	0.944290	−	0.329115i	$-0.106750\pi$
$602$	−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	0.999548	+	0.0300594i	$0.00956963\pi$
$607$	12.9545	+	22.4378i	0.525806	+	0.910723i	−0.473742	+	0.880664i	$0.657097\pi$
$608$	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	0.231810	−	0.972761i	$-0.425535\pi$
$613$	−12.2487	−	7.07180i	−0.494721	−	0.285627i	−0.726531	+	0.687134i	$0.758869\pi$
$614$	−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	−0.560050	−	0.828459i	$-0.689218\pi$
$617$	−3.04552	+	1.75833i	−0.122608	+	0.0707877i	0.437442	+	0.899247i	$0.355885\pi$
$618$		0			0
$619$			32.3205i			1.29907i	0.760331	+	0.649535i	$0.225037\pi$
$619$			32.3205i			1.29907i	−0.760331	+	0.649535i	$0.774963\pi$
$620$	−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	−0.969190	−	0.246315i	$-0.920780\pi$
$631$	−31.1603	+	17.9904i	−1.24047	+	0.716186i	−0.271280	+	0.962500i	$0.587447\pi$
$632$			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	−0.986115	−	0.166065i	$-0.946894\pi$
$641$	−16.1244	−	27.9282i	−0.636874	−	1.10310i	0.349241	−	0.937033i	$-0.386439\pi$
$642$		0			0
$643$	−31.4545	+	18.1603i	−1.24044	+	0.716171i	−0.969185	−	0.246336i	$-0.920773\pi$
$643$	−31.4545	+	18.1603i	−1.24044	+	0.716171i	−0.271259	+	0.962506i	$0.587440\pi$
$644$	−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	−0.848500	−	0.529196i	$-0.822494\pi$
$647$	0.866025	−	1.50000i	0.0340470	−	0.0589711i	0.882547	+	0.470225i	$0.155827\pi$
$648$		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	0.0872099	−	0.996190i	$-0.472205\pi$
$653$	23.1603	−	40.1147i	0.906331	−	1.56981i	0.819121	−	0.573621i	$-0.194462\pi$
$654$		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	0.992574	−	0.121641i	$-0.0388156\pi$
$659$	10.0359	+	17.3827i	0.390943	+	0.677133i	−0.601631	+	0.798774i	$0.705482\pi$
$660$		0			0
$661$	−41.9090	−	24.1962i	−1.63007	−	0.941121i	−0.984070	−	0.177784i	$-0.943107\pi$
$661$	−41.9090	−	24.1962i	−1.63007	−	0.941121i	−0.646000	−	0.763337i	$-0.723560\pi$
$662$	−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	0.324783	+	0.945789i	$0.394709\pi$
$673$	−17.0359	+	29.5070i	−0.656686	+	1.13741i	−0.981468	+	0.191624i	$0.938625\pi$
$674$	−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	−0.590027	−	0.807384i	$-0.700883\pi$
$683$	−4.85641	+	2.80385i	−0.185825	+	0.107286i	0.404201	+	0.914670i	$0.367549\pi$
$684$		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	0.512869	−	0.858467i	$-0.328583\pi$
$691$	0.679492	+	0.392305i	0.0258491	+	0.0149240i	−0.487020	+	0.873391i	$0.661916\pi$
$692$	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	−0.253754	−	0.967269i	$-0.581665\pi$
$709$	12.1699	−	7.02628i	0.457049	−	0.263877i	0.710803	+	0.703391i	$0.248332\pi$
$710$		−	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	0.982238	+	0.187640i	$0.0600838\pi$
$719$	17.5263	+	30.3564i	0.653620	+	1.13210i	−0.328618	+	0.944463i	$0.606583\pi$
$720$		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	$-0.874141\pi$
$733$		−	20.8564i		−	0.770349i	0.922844	−	0.385174i	$-0.125859\pi$
$734$	−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	0.711413	−	0.702774i	$-0.248056\pi$
$739$	12.4641	+	7.19615i	0.458499	+	0.264715i	−0.252914	+	0.967489i	$0.581389\pi$
$740$	−12.9282			−0.475250
$741$		0			0
$742$	3.53590			0.129807
$743$	22.0981	+	12.7583i	0.810700	+	0.468058i	0.847199	−	0.531276i	$-0.178287\pi$
$743$	22.0981	+	12.7583i	0.810700	+	0.468058i	−0.0364990	+	0.999334i	$0.511621\pi$
$744$		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	−0.610608	−	0.791933i	$-0.709075\pi$
$751$	10.4282	−	18.0622i	0.380531	−	0.659098i	0.991138	+	0.132835i	$0.0424081\pi$
$752$	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	−0.866503	−	0.499173i	$-0.833637\pi$
$757$	−0.0262794	+	0.0455173i	−0.000955143	+	0.00165436i	0.865547	+	0.500827i	$0.166971\pi$
$758$	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	−0.938526	−	0.345208i	$-0.887808\pi$
$761$	−30.5885	+	17.6603i	−1.10883	+	0.640184i	−0.170304	+	0.985391i	$0.554475\pi$
$762$		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	0.929734	−	0.368233i	$-0.120037\pi$
$769$	29.8301	+	17.2224i	1.07570	+	0.621057i	0.145968	+	0.989289i	$0.453370\pi$
$770$	−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	−0.124179	−	0.992260i	$-0.539630\pi$
$773$	18.7128	−	10.8038i	0.673053	−	0.388587i	0.797232	+	0.603672i	$0.206296\pi$
$774$		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	−0.264268	−	0.964449i	$-0.585130\pi$
$787$	12.3109	−	7.10770i	0.438836	−	0.253362i	0.703104	+	0.711087i	$0.251797\pi$
$788$			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	0.840817	−	0.541319i	$-0.182075\pi$
$797$	−1.36603	−	2.36603i	−0.0483871	−	0.0838089i	−0.889205	+	0.457510i	$0.848741\pi$
$798$		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	−0.762381	−	0.647128i	$-0.775970\pi$
$809$	5.09808	−	8.83013i	0.179239	−	0.310451i	0.941620	+	0.336677i	$0.109303\pi$
$810$		0			0
$811$			8.53590i			0.299736i	0.988706	+	0.149868i	$0.0478849\pi$
$811$			8.53590i			0.299736i	−0.988706	+	0.149868i	$0.952115\pi$
$812$	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	0.266140	−	0.963934i	$-0.414252\pi$
$821$	−12.4808	−	7.20577i	−0.435582	−	0.251483i	−0.701722	+	0.712451i	$0.747585\pi$
$822$		0			0
$823$	10.4641	+	18.1244i	0.364756	+	0.631775i	0.988737	−	0.149664i	$-0.0478192\pi$
$823$	10.4641	+	18.1244i	0.364756	+	0.631775i	−0.623981	+	0.781439i	$0.714486\pi$
$824$		−	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	$-0.752161\pi$
$827$		−	40.3923i		−	1.40458i	0.711892	−	0.702289i	$-0.247839\pi$
$828$		0			0
$829$	−0.330127	+	0.571797i	−0.0114658	+	0.0198593i	−0.871701	−	0.490037i	$-0.836983\pi$
$829$	−0.330127	+	0.571797i	−0.0114658	+	0.0198593i	0.860236	+	0.509897i	$0.170316\pi$
$830$	−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	−0.699478	−	0.714654i	$-0.746584\pi$
$839$	−12.4641	+	7.19615i	−0.430309	+	0.248439i	0.269170	+	0.963093i	$0.413251\pi$
$840$		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	$-0.806298\pi$
$853$		−	33.3923i		−	1.14333i	0.820487	−	0.571665i	$-0.193702\pi$
$854$	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	$-0.837918\pi$
$863$		−	28.6410i		−	0.974952i	0.873137	−	0.487476i	$-0.162082\pi$
$864$		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	0.135711	−	0.990748i	$-0.456668\pi$
$877$	31.4378	−	18.1506i	1.06158	−	0.612903i	0.925869	+	0.377845i	$0.123335\pi$
$878$	−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	−0.874912	−	0.484283i	$-0.839081\pi$
$881$	−0.535898	+	0.928203i	−0.0180549	+	0.0312720i	0.856857	+	0.515554i	$0.172414\pi$
$882$		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	−0.188338	−	0.982104i	$-0.560310\pi$
$887$	22.5263	−	39.0167i	0.756358	−	1.31005i	0.944696	−	0.327947i	$-0.106357\pi$
$888$		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	−0.998743	−	0.0501213i	$-0.984039\pi$
$907$	−13.7321	+	23.7846i	−0.455965	+	0.789755i	0.542778	+	0.839876i	$0.317373\pi$
$908$	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	−0.972866	−	0.231370i	$-0.925679\pi$
$919$	−20.8205	−	36.0622i	−0.686805	−	1.18958i	0.286061	−	0.958212i	$-0.407654\pi$
$920$	−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	0.268521	−	0.963274i	$-0.413465\pi$
$929$	37.7032	−	21.7679i	1.23700	−	0.714183i	0.968480	+	0.249090i	$0.0801316\pi$
$930$		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	$-0.704003\pi$
$941$		−	49.1769i		−	1.60312i	0.597913	−	0.801561i	$-0.295997\pi$
$942$		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	0.306627	−	0.951830i	$-0.400799\pi$
$947$	−11.2128	−	6.47372i	−0.364367	−	0.210368i	−0.670995	+	0.741462i	$0.734133\pi$
$948$		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	0.985566	−	0.169293i	$-0.0541484\pi$
$953$	10.6865	+	18.5096i	0.346171	+	0.599585i	−0.639395	+	0.768878i	$0.720815\pi$
$954$		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	$-0.803505\pi$
$967$		−	36.0000i		−	1.15768i	0.815440	−	0.578841i	$-0.196495\pi$
$968$	−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	0.829924	−	0.557877i	$-0.188384\pi$
$971$	−2.12436	−	3.67949i	−0.0681738	−	0.118081i	−0.898097	+	0.439796i	$0.855051\pi$
$972$		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	0.0185251	−	0.999828i	$-0.494103\pi$
$977$	−26.1962	−	15.1244i	−0.838089	−	0.483871i	−0.856614	+	0.515957i	$0.827436\pi$
$978$		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	$-0.650165\pi$
$983$		−	55.8564i		−	1.78154i	0.454452	−	0.890771i	$-0.349835\pi$
$984$		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	−0.590816	−	0.806806i	$-0.701194\pi$
$991$	12.6962	−	21.9904i	0.403307	−	0.698547i	0.994123	+	0.108259i	$0.0345275\pi$
$992$	−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	0.796202	+	0.605031i	$0.206839\pi$
$997$	29.1147	+	50.4282i	0.922073	+	1.59708i	0.125871	+	0.992047i	$0.459828\pi$
$998$	−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.1135.1		4
3.2	odd	2		546.2.s.d.43.2	✓	4
13.10	even	6	inner	1638.2.bj.d.127.1		4
39.20	even	12		7098.2.a.bs.1.1		2
39.23	odd	6		546.2.s.d.127.2	yes	4
39.32	even	12		7098.2.a.bj.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.d.43.2	✓	4	3.2	odd	2
546.2.s.d.127.2	yes	4	39.23	odd	6
1638.2.bj.d.127.1		4	13.10	even	6	inner
1638.2.bj.d.1135.1		4	1.1	even	1	trivial
7098.2.a.bj.1.2		2	39.32	even	12
7098.2.a.bs.1.1		2	39.20	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

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