LMFDB - Embedded newform 546.2.s.d.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(43,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("546.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	546.43
Dual form			546.2.s.d.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.36603 + 2.36603i) q^{10} +(0.232051 + 0.133975i) q^{11} +1.00000 q^{12} +(0.866025 + 3.50000i) q^{13} -1.00000 q^{14} +(2.36603 + 1.36603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.86603 + 3.23205i) q^{17} -1.00000i q^{18} +(2.13397 - 1.23205i) q^{19} +(-2.36603 + 1.36603i) q^{20} +1.00000i q^{21} +(0.133975 + 0.232051i) q^{22} +(-1.73205 + 3.00000i) q^{23} +(0.866025 + 0.500000i) q^{24} -2.46410 q^{25} +(-1.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(-0.866025 - 0.500000i) q^{28} +(1.50000 - 2.59808i) q^{29} +(1.36603 + 2.36603i) q^{30} -9.66025i q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.232051 - 0.133975i) q^{33} +3.73205i q^{34} +(-1.36603 - 2.36603i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-4.09808 - 2.36603i) q^{37} +2.46410 q^{38} +(3.46410 + 1.00000i) q^{39} -2.73205 q^{40} +(6.06218 + 3.50000i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-1.36603 - 2.36603i) q^{43} +0.267949i q^{44} +(2.36603 - 1.36603i) q^{45} +(-3.00000 + 1.73205i) q^{46} +2.46410i q^{47} +(0.500000 + 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-2.13397 - 1.23205i) q^{50} +3.73205 q^{51} +(-2.59808 + 2.50000i) q^{52} -3.53590 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.366025 + 0.633975i) q^{55} +(-0.500000 - 0.866025i) q^{56} -2.46410i q^{57} +(2.59808 - 1.50000i) q^{58} +(11.1962 - 6.46410i) q^{59} +2.73205i q^{60} +(4.13397 + 7.16025i) q^{61} +(4.83013 - 8.36603i) q^{62} +(0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(-9.56218 + 2.36603i) q^{65} +0.267949 q^{66} +(-0.803848 - 0.464102i) q^{67} +(-1.86603 + 3.23205i) q^{68} +(1.73205 + 3.00000i) q^{69} -2.73205i q^{70} +(7.09808 - 4.09808i) q^{71} +(0.866025 - 0.500000i) q^{72} -13.4641i q^{73} +(-2.36603 - 4.09808i) q^{74} +(-1.23205 + 2.13397i) q^{75} +(2.13397 + 1.23205i) q^{76} -0.267949 q^{77} +(2.50000 + 2.59808i) q^{78} -16.8564 q^{79} +(-2.36603 - 1.36603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.50000 + 6.06218i) q^{82} -11.6603i q^{83} +(-0.866025 + 0.500000i) q^{84} +(-8.83013 + 5.09808i) q^{85} -2.73205i q^{86} +(-1.50000 - 2.59808i) q^{87} +(-0.133975 + 0.232051i) q^{88} +(0.401924 + 0.232051i) q^{89} +2.73205 q^{90} +(-2.50000 - 2.59808i) q^{91} -3.46410 q^{92} +(-8.36603 - 4.83013i) q^{93} +(-1.23205 + 2.13397i) q^{94} +(3.36603 + 5.83013i) q^{95} +1.00000i q^{96} +(2.36603 - 1.36603i) q^{97} +(0.866025 - 0.500000i) q^{98} -0.267949i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{14} + 6 q^{15} - 2 q^{16} + 4 q^{17} + 12 q^{19} - 6 q^{20} + 4 q^{22} + 4 q^{25} - 4 q^{26} - 4 q^{27} + 6 q^{29} + 2 q^{30} - 6 q^{33} - 2 q^{35} + 2 q^{36} - 6 q^{37} - 4 q^{38} - 4 q^{40} - 2 q^{42} - 2 q^{43} + 6 q^{45} - 12 q^{46} + 2 q^{48} + 2 q^{49} - 12 q^{50} + 8 q^{51} - 28 q^{53} + 2 q^{55} - 2 q^{56} + 24 q^{59} + 20 q^{61} + 2 q^{62} - 4 q^{64} - 14 q^{65} + 8 q^{66} - 24 q^{67} - 4 q^{68} + 18 q^{71} - 6 q^{74} + 2 q^{75} + 12 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 6 q^{80} - 2 q^{81} + 14 q^{82} - 18 q^{85} - 6 q^{87} - 4 q^{88} + 12 q^{89} + 4 q^{90} - 10 q^{91} - 30 q^{93} + 2 q^{94} + 10 q^{95} + 6 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 - 6 * q^11 + 4 * q^12 - 4 * q^14 + 6 * q^15 - 2 * q^16 + 4 * q^17 + 12 * q^19 - 6 * q^20 + 4 * q^22 + 4 * q^25 - 4 * q^26 - 4 * q^27 + 6 * q^29 + 2 * q^30 - 6 * q^33 - 2 * q^35 + 2 * q^36 - 6 * q^37 - 4 * q^38 - 4 * q^40 - 2 * q^42 - 2 * q^43 + 6 * q^45 - 12 * q^46 + 2 * q^48 + 2 * q^49 - 12 * q^50 + 8 * q^51 - 28 * q^53 + 2 * q^55 - 2 * q^56 + 24 * q^59 + 20 * q^61 + 2 * q^62 - 4 * q^64 - 14 * q^65 + 8 * q^66 - 24 * q^67 - 4 * q^68 + 18 * q^71 - 6 * q^74 + 2 * q^75 + 12 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 6 * q^80 - 2 * q^81 + 14 * q^82 - 18 * q^85 - 6 * q^87 - 4 * q^88 + 12 * q^89 + 4 * q^90 - 10 * q^91 - 30 * q^93 + 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	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	$0.790806\pi$
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.36603	+	2.36603i	−0.431975	+	0.748203i
$11$	0.232051	+	0.133975i	0.0699660	+	0.0403949i	0.534575	−	0.845121i	$-0.320472\pi$
$11$	0.232051	+	0.133975i	0.0699660	+	0.0403949i	−0.464609	+	0.885516i	$0.653805\pi$
$12$	1.00000			0.288675
$13$	0.866025	+	3.50000i	0.240192	+	0.970725i
$13$	0.866025	+	3.50000i	0.240192	+	0.970725i
$14$	−1.00000			−0.267261
$15$	2.36603	+	1.36603i	0.610905	+	0.352706i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.86603	+	3.23205i	0.452578	+	0.783887i	0.998545	−	0.0539188i	$-0.0171712\pi$
$17$	1.86603	+	3.23205i	0.452578	+	0.783887i	−0.545968	+	0.837806i	$0.683838\pi$
$18$		−	1.00000i		−	0.235702i
$19$	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
$21$			1.00000i			0.218218i
$22$	0.133975	+	0.232051i	0.0285635	+	0.0494734i
$23$	−1.73205	+	3.00000i	−0.361158	+	0.625543i	−0.988152	−	0.153481i	$-0.950952\pi$
$23$	−1.73205	+	3.00000i	−0.361158	+	0.625543i	0.626994	+	0.779024i	$0.284285\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−2.46410			−0.492820
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$	−1.00000			−0.192450
$28$	−0.866025	−	0.500000i	−0.163663	−	0.0944911i
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$	1.36603	+	2.36603i	0.249401	+	0.431975i
$31$		−	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
$33$	0.232051	−	0.133975i	0.0403949	−	0.0233220i
$34$			3.73205i			0.640041i
$35$	−1.36603	−	2.36603i	−0.230900	−	0.399931i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−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
$39$	3.46410	+	1.00000i	0.554700	+	0.160128i
$40$	−2.73205			−0.431975
$41$	6.06218	+	3.50000i	0.946753	+	0.546608i	0.892071	−	0.451896i	$-0.149252\pi$
$41$	6.06218	+	3.50000i	0.946753	+	0.546608i	0.0546823	+	0.998504i	$0.482585\pi$
$42$	−0.500000	+	0.866025i	−0.0771517	+	0.133631i
$43$	−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
$45$	2.36603	−	1.36603i	0.352706	−	0.203635i
$46$	−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	$0.942483\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−2.13397	−	1.23205i	−0.301790	−	0.174238i
$51$	3.73205			0.522592
$52$	−2.59808	+	2.50000i	−0.360288	+	0.346688i
$53$	−3.53590			−0.485693			−0.242846	−	0.970065i	$-0.578081\pi$
$53$	−3.53590			−0.485693			−0.242846	+	0.970065i	$0.578081\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−0.366025	+	0.633975i	−0.0493549	+	0.0854851i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		−	2.46410i		−	0.326378i
$58$	2.59808	−	1.50000i	0.341144	−	0.196960i
$59$	11.1962	−	6.46410i	1.45761	−	0.841554i	0.458721	−	0.888580i	$-0.348308\pi$
$59$	11.1962	−	6.46410i	1.45761	−	0.841554i	0.998894	+	0.0470259i	$0.0149743\pi$
$60$			2.73205i			0.352706i
$61$	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
$63$	0.866025	+	0.500000i	0.109109	+	0.0629941i
$64$	−1.00000			−0.125000
$65$	−9.56218	+	2.36603i	−1.18604	+	0.293469i
$66$	0.267949			0.0329823
$67$	−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
$69$	1.73205	+	3.00000i	0.208514	+	0.361158i
$70$		−	2.73205i		−	0.326543i
$71$	7.09808	−	4.09808i	0.842387	−	0.486352i	−0.0156881	−	0.999877i	$-0.504994\pi$
$71$	7.09808	−	4.09808i	0.842387	−	0.486352i	0.858075	+	0.513525i	$0.171661\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$		−	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
$75$	−1.23205	+	2.13397i	−0.142265	+	0.246410i
$76$	2.13397	+	1.23205i	0.244784	+	0.141326i
$77$	−0.267949			−0.0305356
$78$	2.50000	+	2.59808i	0.283069	+	0.294174i
$79$	−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
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	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	$-0.221041\pi$
$84$	−0.866025	+	0.500000i	−0.0944911	+	0.0545545i
$85$	−8.83013	+	5.09808i	−0.957762	+	0.552964i
$86$		−	2.73205i		−	0.294605i
$87$	−1.50000	−	2.59808i	−0.160817	−	0.278543i
$88$	−0.133975	+	0.232051i	−0.0142817	+	0.0247367i
$89$	0.401924	+	0.232051i	0.0426038	+	0.0245973i	0.521151	−	0.853465i	$-0.325503\pi$
$89$	0.401924	+	0.232051i	0.0426038	+	0.0245973i	−0.478547	+	0.878062i	$0.658836\pi$
$90$	2.73205			0.287983
$91$	−2.50000	−	2.59808i	−0.262071	−	0.272352i
$92$	−3.46410			−0.361158
$93$	−8.36603	−	4.83013i	−0.867516	−	0.500861i
$94$	−1.23205	+	2.13397i	−0.127076	+	0.220103i
$95$	3.36603	+	5.83013i	0.345347	+	0.598158i
$96$			1.00000i			0.102062i
$97$	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
$99$		−	0.267949i		−	0.0269299i
$100$	−1.23205	−	2.13397i	−0.123205	−	0.213397i
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$	3.23205	+	1.86603i	0.320021	+	0.184764i
$103$	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
$105$	−2.73205			−0.266621
$106$	−3.06218	−	1.76795i	−0.297425	−	0.171718i
$107$	4.23205	−	7.33013i	0.409128	−	0.708630i	−0.585664	−	0.810554i	$-0.699166\pi$
$107$	4.23205	−	7.33013i	0.409128	−	0.708630i	0.994792	+	0.101923i	$0.0324997\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$		−	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
$111$	−4.09808	+	2.36603i	−0.388972	+	0.224573i
$112$		−	1.00000i		−	0.0944911i
$113$	−0.0980762	−	0.169873i	−0.00922623	−	0.0159803i	0.861375	−	0.507969i	$-0.169604\pi$
$113$	−0.0980762	−	0.169873i	−0.00922623	−	0.0159803i	−0.870602	+	0.491989i	$0.836270\pi$
$114$	1.23205	−	2.13397i	0.115392	−	0.199865i
$115$	−8.19615	−	4.73205i	−0.764295	−	0.441266i
$116$	3.00000			0.278543
$117$	2.59808	−	2.50000i	0.240192	−	0.231125i
$118$	12.9282			1.19014
$119$	−3.23205	−	1.86603i	−0.296282	−	0.171058i
$120$	−1.36603	+	2.36603i	−0.124700	+	0.215988i
$121$	−5.46410	−	9.46410i	−0.496737	−	0.860373i
$122$			8.26795i			0.748545i
$123$	6.06218	−	3.50000i	0.546608	−	0.315584i
$124$	8.36603	−	4.83013i	0.751291	−	0.433758i
$125$			6.92820i			0.619677i
$126$	0.500000	+	0.866025i	0.0445435	+	0.0771517i
$127$	−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
$129$	−2.73205			−0.240544
$130$	−9.46410	−	2.73205i	−0.830057	−	0.239617i
$131$	5.07180			0.443125			0.221562	−	0.975146i	$-0.428884\pi$
$131$	5.07180			0.443125			0.221562	+	0.975146i	$0.428884\pi$
$132$	0.232051	+	0.133975i	0.0201974	+	0.0116610i
$133$	−1.23205	+	2.13397i	−0.106832	+	0.185039i
$134$	−0.464102	−	0.803848i	−0.0400923	−	0.0694419i
$135$		−	2.73205i		−	0.235137i
$136$	−3.23205	+	1.86603i	−0.277146	+	0.160010i
$137$	−7.39230	+	4.26795i	−0.631567	+	0.364636i	−0.781359	−	0.624082i	$-0.785473\pi$
$137$	−7.39230	+	4.26795i	−0.631567	+	0.364636i	0.149792	+	0.988718i	$0.452140\pi$
$138$			3.46410i			0.294884i
$139$	−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
$141$	2.13397	+	1.23205i	0.179713	+	0.103757i
$142$	8.19615			0.687806
$143$	−0.267949	+	0.928203i	−0.0224070	+	0.0776203i
$144$	1.00000			0.0833333
$145$	7.09808	+	4.09808i	0.589463	+	0.340327i
$146$	6.73205	−	11.6603i	0.557148	−	0.965009i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$		−	4.73205i		−	0.388972i
$149$	4.39230	−	2.53590i	0.359832	−	0.207749i	−0.309175	−	0.951005i	$-0.600053\pi$
$149$	4.39230	−	2.53590i	0.359832	−	0.207749i	0.669007	+	0.743256i	$0.266720\pi$
$150$	−2.13397	+	1.23205i	−0.174238	+	0.100597i
$151$		−	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
$153$	1.86603	−	3.23205i	0.150859	−	0.261296i
$154$	−0.232051	−	0.133975i	−0.0186992	−	0.0107960i
$155$	26.3923			2.11988
$156$	0.866025	+	3.50000i	0.0693375	+	0.280224i
$157$	−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
$159$	−1.76795	+	3.06218i	−0.140207	+	0.242846i
$160$	−1.36603	−	2.36603i	−0.107994	−	0.187051i
$161$		−	3.46410i		−	0.273009i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	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
$165$	0.366025	+	0.633975i	0.0284950	+	0.0493549i
$166$	5.83013	−	10.0981i	0.452506	−	0.783763i
$167$	18.9282	+	10.9282i	1.46471	+	0.845650i	0.999223	−	0.0394060i	$-0.0125466\pi$
$167$	18.9282	+	10.9282i	1.46471	+	0.845650i	0.465485	+	0.885056i	$0.345880\pi$
$168$	−1.00000			−0.0771517
$169$	−11.5000	+	6.06218i	−0.884615	+	0.466321i
$170$	−10.1962			−0.782009
$171$	−2.13397	−	1.23205i	−0.163189	−	0.0942173i
$172$	1.36603	−	2.36603i	0.104158	−	0.180408i
$173$	8.63397	+	14.9545i	0.656429	+	1.13697i	0.981534	+	0.191290i	$0.0612672\pi$
$173$	8.63397	+	14.9545i	0.656429	+	1.13697i	−0.325105	+	0.945678i	$0.605400\pi$
$174$		−	3.00000i		−	0.227429i
$175$	2.13397	−	1.23205i	0.161313	−	0.0931343i
$176$	−0.232051	+	0.133975i	−0.0174915	+	0.0100987i
$177$		−	12.9282i		−	0.971743i
$178$	0.232051	+	0.401924i	0.0173929	+	0.0301255i
$179$	0.803848	−	1.39230i	0.0600824	−	0.104066i	−0.834420	−	0.551130i	$-0.814197\pi$
$179$	0.803848	−	1.39230i	0.0600824	−	0.104066i	0.894502	+	0.447064i	$0.147530\pi$
$180$	2.36603	+	1.36603i	0.176353	+	0.101818i
$181$	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
$183$	8.26795			0.611184
$184$	−3.00000	−	1.73205i	−0.221163	−	0.127688i
$185$	6.46410	−	11.1962i	0.475250	−	0.823157i
$186$	−4.83013	−	8.36603i	−0.354162	−	0.613427i
$187$			1.00000i			0.0731272i
$188$	−2.13397	+	1.23205i	−0.155636	+	0.0898565i
$189$	0.866025	−	0.500000i	0.0629941	−	0.0363696i
$190$			6.73205i			0.488394i
$191$	−3.09808	−	5.36603i	−0.224169	−	0.388272i	0.731901	−	0.681411i	$-0.238633\pi$
$191$	−3.09808	−	5.36603i	−0.224169	−	0.388272i	−0.956070	+	0.293139i	$0.905300\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	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
$195$	−2.73205	+	9.46410i	−0.195646	+	0.677738i
$196$	1.00000			0.0714286
$197$	−4.96410	−	2.86603i	−0.353678	−	0.204196i	0.312626	−	0.949876i	$-0.398791\pi$
$197$	−4.96410	−	2.86603i	−0.353678	−	0.204196i	−0.666304	+	0.745680i	$0.732125\pi$
$198$	0.133975	−	0.232051i	0.00952116	−	0.0164911i
$199$	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
$201$	−0.803848	+	0.464102i	−0.0566990	+	0.0327352i
$202$	−8.66025	+	5.00000i	−0.609333	+	0.351799i
$203$			3.00000i			0.210559i
$204$	1.86603	+	3.23205i	0.130648	+	0.226289i
$205$	−9.56218	+	16.5622i	−0.667851	+	1.15675i
$206$	1.56218	+	0.901924i	0.108842	+	0.0628400i
$207$	3.46410			0.240772
$208$	−3.46410	−	1.00000i	−0.240192	−	0.0693375i
$209$	0.660254			0.0456707
$210$	−2.36603	−	1.36603i	−0.163271	−	0.0942647i
$211$	−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
$213$		−	8.19615i		−	0.561591i
$214$	7.33013	−	4.23205i	0.501077	−	0.289297i
$215$	6.46410	−	3.73205i	0.440848	−	0.254524i
$216$		−	1.00000i		−	0.0680414i
$217$	4.83013	+	8.36603i	0.327890	+	0.567923i
$218$	6.83013	−	11.8301i	0.462595	−	0.801237i
$219$	−11.6603	−	6.73205i	−0.787927	−	0.454910i
$220$	−0.732051			−0.0493549
$221$	−9.69615	+	9.33013i	−0.652234	+	0.627612i
$222$	−4.73205			−0.317594
$223$	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
$225$	1.23205	+	2.13397i	0.0821367	+	0.142265i
$226$		−	0.196152i		−	0.0130479i
$227$	−13.3923	+	7.73205i	−0.888878	+	0.513194i	−0.873575	−	0.486689i	$-0.838205\pi$
$227$	−13.3923	+	7.73205i	−0.888878	+	0.513194i	−0.0153030	+	0.999883i	$0.504871\pi$
$228$	2.13397	−	1.23205i	0.141326	−	0.0815946i
$229$		−	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
$231$	−0.133975	+	0.232051i	−0.00881488	+	0.0152678i
$232$	2.59808	+	1.50000i	0.170572	+	0.0984798i
$233$	8.19615			0.536948			0.268474	−	0.963287i	$-0.413481\pi$
$233$	8.19615			0.536948			0.268474	+	0.963287i	$0.413481\pi$
$234$	3.50000	−	0.866025i	0.228802	−	0.0566139i
$235$	−6.73205			−0.439151
$236$	11.1962	+	6.46410i	0.728807	+	0.420777i
$237$	−8.42820	+	14.5981i	−0.547471	+	0.948247i
$238$	−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	$0.713914\pi$
$240$	−2.36603	+	1.36603i	−0.152726	+	0.0881766i
$241$	−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
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−4.13397	+	7.16025i	−0.264651	+	0.458388i
$245$	2.36603	+	1.36603i	0.151160	+	0.0872722i
$246$	7.00000			0.446304
$247$	6.16025	+	6.40192i	0.391968	+	0.407345i
$248$	9.66025			0.613427
$249$	−10.0981	−	5.83013i	−0.639940	−	0.369469i
$250$	−3.46410	+	6.00000i	−0.219089	+	0.379473i
$251$	3.90192	+	6.75833i	0.246287	+	0.426582i	0.962493	−	0.271307i	$-0.0874560\pi$
$251$	3.90192	+	6.75833i	0.246287	+	0.426582i	−0.716205	+	0.697889i	$0.754123\pi$
$252$			1.00000i			0.0629941i
$253$	−0.803848	+	0.464102i	−0.0505375	+	0.0291778i
$254$	−16.8564	+	9.73205i	−1.05767	+	0.610643i
$255$			10.1962i			0.638508i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.5263	+	23.4282i	−0.843746	+	1.46141i	0.0429595	+	0.999077i	$0.486321\pi$
$257$	−13.5263	+	23.4282i	−0.843746	+	1.46141i	−0.886706	+	0.462334i	$0.847012\pi$
$258$	−2.36603	−	1.36603i	−0.147302	−	0.0850450i
$259$	4.73205			0.294035
$260$	−6.83013	−	7.09808i	−0.423586	−	0.440204i
$261$	−3.00000			−0.185695
$262$	4.39230	+	2.53590i	0.271357	+	0.156668i
$263$	7.63397	−	13.2224i	0.470731	−	0.815330i	−0.528709	−	0.848803i	$-0.677324\pi$
$263$	7.63397	−	13.2224i	0.470731	−	0.815330i	0.999440	+	0.0334733i	$0.0106569\pi$
$264$	0.133975	+	0.232051i	0.00824557	+	0.0142817i
$265$		−	9.66025i		−	0.593425i
$266$	−2.13397	+	1.23205i	−0.130842	+	0.0755419i
$267$	0.401924	−	0.232051i	0.0245973	−	0.0142013i
$268$		−	0.928203i		−	0.0566990i
$269$	−15.8564	−	27.4641i	−0.966782	−	1.67452i	−0.704749	−	0.709457i	$-0.748940\pi$
$269$	−15.8564	−	27.4641i	−0.966782	−	1.67452i	−0.262033	−	0.965059i	$-0.584393\pi$
$270$	1.36603	−	2.36603i	0.0831337	−	0.143992i
$271$	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
$273$	−3.50000	+	0.866025i	−0.211830	+	0.0524142i
$274$	−8.53590			−0.515672
$275$	−0.571797	−	0.330127i	−0.0344806	−	0.0199074i
$276$	−1.73205	+	3.00000i	−0.104257	+	0.180579i
$277$	−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
$279$	−8.36603	+	4.83013i	−0.500861	+	0.289172i
$280$	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	$-0.0747787\pi$
$282$	1.23205	+	2.13397i	0.0733676	+	0.127076i
$283$	−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
$285$	6.73205			0.398772
$286$	−0.696152	+	0.669873i	−0.0411644	+	0.0396104i
$287$	−7.00000			−0.413197
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	1.53590	−	2.66025i	0.0903470	−	0.156486i
$290$	4.09808	+	7.09808i	0.240647	+	0.416813i
$291$		−	2.73205i		−	0.160156i
$292$	11.6603	−	6.73205i	0.682365	−	0.393963i
$293$	−24.9282	+	14.3923i	−1.45632	+	0.840807i	−0.998828	−	0.0484056i	$-0.984586\pi$
$293$	−24.9282	+	14.3923i	−1.45632	+	0.840807i	−0.457493	+	0.889213i	$0.651253\pi$
$294$		−	1.00000i		−	0.0583212i
$295$	17.6603	+	30.5885i	1.02822	+	1.78093i
$296$	2.36603	−	4.09808i	0.137522	−	0.238196i
$297$	−0.232051	−	0.133975i	−0.0134650	−	0.00777399i
$298$	5.07180			0.293801
$299$	−12.0000	−	3.46410i	−0.693978	−	0.200334i
$300$	−2.46410			−0.142265
$301$	2.36603	+	1.36603i	0.136375	+	0.0787364i
$302$	1.40192	−	2.42820i	0.0806716	−	0.139727i
$303$	5.00000	+	8.66025i	0.287242	+	0.497519i
$304$			2.46410i			0.141326i
$305$	−19.5622	+	11.2942i	−1.12013	+	0.646706i
$306$	3.23205	−	1.86603i	0.184764	−	0.106674i
$307$		−	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
$309$	0.901924	−	1.56218i	0.0513087	−	0.0888692i
$310$	22.8564	+	13.1962i	1.29816	+	0.749491i
$311$	8.80385			0.499220			0.249610	−	0.968346i	$-0.419698\pi$
$311$	8.80385			0.499220			0.249610	+	0.968346i	$0.419698\pi$
$312$	−1.00000	+	3.46410i	−0.0566139	+	0.196116i
$313$	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
$315$	−1.36603	+	2.36603i	−0.0769668	+	0.133310i
$316$	−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	$0.831312\pi$
$318$	−3.06218	+	1.76795i	−0.171718	+	0.0991417i
$319$	0.696152	−	0.401924i	0.0389771	−	0.0225034i
$320$		−	2.73205i		−	0.152726i
$321$	−4.23205	−	7.33013i	−0.236210	−	0.409128i
$322$	1.73205	−	3.00000i	0.0965234	−	0.167183i
$323$	7.96410	+	4.59808i	0.443134	+	0.255844i
$324$	−1.00000			−0.0555556
$325$	−2.13397	−	8.62436i	−0.118372	−	0.478393i
$326$	18.1962			1.00779
$327$	−11.8301	−	6.83013i	−0.654208	−	0.377707i
$328$	−3.50000	+	6.06218i	−0.193255	+	0.334728i
$329$	−1.23205	−	2.13397i	−0.0679252	−	0.117650i
$330$			0.732051i			0.0402981i
$331$	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
$333$			4.73205i			0.259315i
$334$	10.9282	+	18.9282i	0.597965	+	1.03571i
$335$	1.26795	−	2.19615i	0.0692755	−	0.119989i
$336$	−0.866025	−	0.500000i	−0.0472456	−	0.0272772i
$337$	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
$339$	−0.196152			−0.0106535
$340$	−8.83013	−	5.09808i	−0.478881	−	0.276482i
$341$	1.29423	−	2.24167i	0.0700864	−	0.121393i
$342$	−1.23205	−	2.13397i	−0.0666217	−	0.115392i
$343$			1.00000i			0.0539949i
$344$	2.36603	−	1.36603i	0.127568	−	0.0736512i
$345$	−8.19615	+	4.73205i	−0.441266	+	0.254765i
$346$			17.2679i			0.928331i
$347$	2.42820	+	4.20577i	0.130353	+	0.225778i	0.923813	−	0.382845i	$-0.125056\pi$
$347$	2.42820	+	4.20577i	0.130353	+	0.225778i	−0.793460	+	0.608623i	$0.791722\pi$
$348$	1.50000	−	2.59808i	0.0804084	−	0.139272i
$349$	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
$351$	−0.866025	−	3.50000i	−0.0462250	−	0.186816i
$352$	−0.267949			−0.0142817
$353$	−4.73205	−	2.73205i	−0.251862	−	0.145412i	0.368755	−	0.929527i	$-0.379784\pi$
$353$	−4.73205	−	2.73205i	−0.251862	−	0.145412i	−0.620616	+	0.784114i	$0.713118\pi$
$354$	6.46410	−	11.1962i	0.343563	−	0.595069i
$355$	11.1962	+	19.3923i	0.594230	+	1.02924i
$356$			0.464102i			0.0245973i
$357$	−3.23205	+	1.86603i	−0.171058	+	0.0987605i
$358$	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	$-0.242957\pi$
$360$	1.36603	+	2.36603i	0.0719959	+	0.124700i
$361$	−6.46410	+	11.1962i	−0.340216	+	0.589271i
$362$	7.96410	+	4.59808i	0.418584	+	0.241670i
$363$	−10.9282			−0.573582
$364$	1.00000	−	3.46410i	0.0524142	−	0.181568i
$365$	36.7846			1.92539
$366$	7.16025	+	4.13397i	0.374272	+	0.216086i
$367$	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
$369$		−	7.00000i		−	0.364405i
$370$	11.1962	−	6.46410i	0.582060	−	0.336053i
$371$	3.06218	−	1.76795i	0.158980	−	0.0917873i
$372$		−	9.66025i		−	0.500861i
$373$	−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
$375$	6.00000	+	3.46410i	0.309839	+	0.178885i
$376$	−2.46410			−0.127076
$377$	10.3923	+	3.00000i	0.535231	+	0.154508i
$378$	1.00000			0.0514344
$379$	−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
$381$	9.73205	+	16.8564i	0.498588	+	0.863580i
$382$		−	6.19615i		−	0.317023i
$383$	−30.6506	+	17.6962i	−1.56617	+	0.904231i	−0.569565	+	0.821946i	$0.692888\pi$
$383$	−30.6506	+	17.6962i	−1.56617	+	0.904231i	−0.996609	+	0.0822852i	$0.973778\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		−	0.732051i		−	0.0373088i
$386$	3.40192	+	5.89230i	0.173153	+	0.299910i
$387$	−1.36603	+	2.36603i	−0.0694390	+	0.120272i
$388$	2.36603	+	1.36603i	0.120117	+	0.0693494i
$389$	−29.1769			−1.47933			−0.739664	−	0.672976i	$-0.765016\pi$
$389$	−29.1769			−1.47933			−0.739664	+	0.672976i	$0.765016\pi$
$390$	−7.09808	+	6.83013i	−0.359425	+	0.345857i
$391$	−12.9282			−0.653807
$392$	0.866025	+	0.500000i	0.0437409	+	0.0252538i
$393$	2.53590	−	4.39230i	0.127919	−	0.221562i
$394$	−2.86603	−	4.96410i	−0.144388	−	0.250088i
$395$		−	46.0526i		−	2.31716i
$396$	0.232051	−	0.133975i	0.0116610	−	0.00673248i
$397$	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
$399$	1.23205	+	2.13397i	0.0616797	+	0.106832i
$400$	1.23205	−	2.13397i	0.0616025	−	0.106699i
$401$	8.66025	+	5.00000i	0.432472	+	0.249688i	0.700399	−	0.713751i	$-0.253005\pi$
$401$	8.66025	+	5.00000i	0.432472	+	0.249688i	−0.267927	+	0.963439i	$0.586339\pi$
$402$	−0.928203			−0.0462946
$403$	33.8109	−	8.36603i	1.68424	−	0.416741i
$404$	−10.0000			−0.497519
$405$	−2.36603	−	1.36603i	−0.117569	−	0.0678783i
$406$	−1.50000	+	2.59808i	−0.0744438	+	0.128940i
$407$	−0.633975	−	1.09808i	−0.0314250	−	0.0544296i
$408$			3.73205i			0.184764i
$409$	−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
$411$			8.53590i			0.421045i
$412$	0.901924	+	1.56218i	0.0444346	+	0.0769630i
$413$	−6.46410	+	11.1962i	−0.318078	+	0.550927i
$414$	3.00000	+	1.73205i	0.147442	+	0.0851257i
$415$	31.8564			1.56377
$416$	−2.50000	−	2.59808i	−0.122573	−	0.127381i
$417$	−6.12436			−0.299911
$418$	0.571797	+	0.330127i	0.0279675	+	0.0161470i
$419$	−2.09808	+	3.63397i	−0.102498	+	0.177531i	−0.912713	−	0.408601i	$-0.866017\pi$
$419$	−2.09808	+	3.63397i	−0.102498	+	0.177531i	0.810215	+	0.586132i	$0.199350\pi$
$420$	−1.36603	−	2.36603i	−0.0666552	−	0.115450i
$421$		−	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
$423$	2.13397	−	1.23205i	0.103757	−	0.0599044i
$424$		−	3.53590i		−	0.171718i
$425$	−4.59808	−	7.96410i	−0.223039	−	0.386316i
$426$	4.09808	−	7.09808i	0.198552	−	0.343903i
$427$	−7.16025	−	4.13397i	−0.346509	−	0.200057i
$428$	8.46410			0.409128
$429$	0.669873	+	0.696152i	0.0323418	+	0.0336106i
$430$	7.46410			0.359951
$431$	2.70577	+	1.56218i	0.130332	+	0.0752475i	0.563749	−	0.825946i	$-0.309359\pi$
$431$	2.70577	+	1.56218i	0.130332	+	0.0752475i	−0.433416	+	0.901194i	$0.642692\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−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
$435$	7.09808	−	4.09808i	0.340327	−	0.196488i
$436$	11.8301	−	6.83013i	0.566560	−	0.327104i
$437$			8.53590i			0.408327i
$438$	−6.73205	−	11.6603i	−0.321670	−	0.557148i
$439$	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
$441$	−1.00000			−0.0476190
$442$	−13.0622	+	3.23205i	−0.621304	+	0.153733i
$443$	−10.6077			−0.503987			−0.251993	−	0.967729i	$-0.581086\pi$
$443$	−10.6077			−0.503987			−0.251993	+	0.967729i	$0.581086\pi$
$444$	−4.09808	−	2.36603i	−0.194486	−	0.112287i
$445$	−0.633975	+	1.09808i	−0.0300533	+	0.0520538i
$446$	6.19615	+	10.7321i	0.293396	+	0.508177i
$447$		−	5.07180i		−	0.239888i
$448$	0.866025	−	0.500000i	0.0409159	−	0.0236228i
$449$	6.29423	−	3.63397i	0.297043	−	0.171498i	−0.344071	−	0.938944i	$-0.611806\pi$
$449$	6.29423	−	3.63397i	0.297043	−	0.171498i	0.641114	+	0.767446i	$0.278473\pi$
$450$			2.46410i			0.116159i
$451$	0.937822	+	1.62436i	0.0441603	+	0.0764879i
$452$	0.0980762	−	0.169873i	0.00461312	−	0.00799015i
$453$	−2.42820	−	1.40192i	−0.114087	−	0.0658681i
$454$	−15.4641			−0.725766
$455$	7.09808	−	6.83013i	0.332763	−	0.320201i
$456$	2.46410			0.115392
$457$	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
$459$	−1.86603	−	3.23205i	−0.0870986	−	0.150859i
$460$		−	9.46410i		−	0.441266i
$461$	−24.0000	+	13.8564i	−1.11779	+	0.645357i	−0.940836	−	0.338862i	$-0.889958\pi$
$461$	−24.0000	+	13.8564i	−1.11779	+	0.645357i	−0.176955	+	0.984219i	$0.556625\pi$
$462$	−0.232051	+	0.133975i	−0.0107960	+	0.00623306i
$463$		−	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
$465$	13.1962	−	22.8564i	0.611957	−	1.05994i
$466$	7.09808	+	4.09808i	0.328812	+	0.189840i
$467$	−17.8564			−0.826296			−0.413148	−	0.910664i	$-0.635571\pi$
$467$	−17.8564			−0.826296			−0.413148	+	0.910664i	$0.635571\pi$
$468$	3.46410	+	1.00000i	0.160128	+	0.0462250i
$469$	0.928203			0.0428604
$470$	−5.83013	−	3.36603i	−0.268924	−	0.155263i
$471$	−4.26795	+	7.39230i	−0.196657	+	0.340619i
$472$	6.46410	+	11.1962i	0.297534	+	0.515345i
$473$		−	0.732051i		−	0.0336597i
$474$	−14.5981	+	8.42820i	−0.670512	+	0.387120i
$475$	−5.25833	+	3.03590i	−0.241269	+	0.139297i
$476$		−	3.73205i		−	0.171058i
$477$	1.76795	+	3.06218i	0.0809488	+	0.140207i
$478$	−12.0981	+	20.9545i	−0.553353	+	0.958436i
$479$	−9.18653	−	5.30385i	−0.419743	−	0.242339i	0.275224	−	0.961380i	$-0.411248\pi$
$479$	−9.18653	−	5.30385i	−0.419743	−	0.242339i	−0.694968	+	0.719041i	$0.744581\pi$
$480$	−2.73205			−0.124700
$481$	4.73205	−	16.3923i	0.215763	−	0.747425i
$482$	−28.7846			−1.31110
$483$	−3.00000	−	1.73205i	−0.136505	−	0.0788110i
$484$	5.46410	−	9.46410i	0.248368	−	0.430186i
$485$	3.73205	+	6.46410i	0.169464	+	0.293520i
$486$			1.00000i			0.0453609i
$487$	−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
$489$		−	18.1962i		−	0.822858i
$490$	1.36603	+	2.36603i	0.0617107	+	0.106886i
$491$	−6.12436	+	10.6077i	−0.276388	+	0.478719i	−0.970484	−	0.241164i	$-0.922471\pi$
$491$	−6.12436	+	10.6077i	−0.276388	+	0.478719i	0.694096	+	0.719882i	$0.255804\pi$
$492$	6.06218	+	3.50000i	0.273304	+	0.157792i
$493$	11.1962			0.504249
$494$	2.13397	+	8.62436i	0.0960121	+	0.388028i
$495$	0.732051			0.0329032
$496$	8.36603	+	4.83013i	0.375646	+	0.216879i
$497$	−4.09808	+	7.09808i	−0.183824	+	0.318392i
$498$	−5.83013	−	10.0981i	−0.261254	−	0.452506i
$499$		−	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
$501$	18.9282	−	10.9282i	0.845650	−	0.488236i
$502$			7.80385i			0.348303i
$503$	−15.8564	−	27.4641i	−0.707002	−	1.22456i	−0.965964	−	0.258676i	$-0.916714\pi$
$503$	−15.8564	−	27.4641i	−0.707002	−	1.22456i	0.258962	−	0.965888i	$-0.416620\pi$
$504$	−0.500000	+	0.866025i	−0.0222718	+	0.0385758i
$505$	−23.6603	−	13.6603i	−1.05287	−	0.607873i
$506$	−0.928203			−0.0412637
$507$	−0.500000	+	12.9904i	−0.0222058	+	0.576923i
$508$	−19.4641			−0.863580
$509$	−10.4378	−	6.02628i	−0.462648	−	0.267110i	0.250509	−	0.968114i	$-0.419402\pi$
$509$	−10.4378	−	6.02628i	−0.462648	−	0.267110i	−0.713157	+	0.701004i	$0.752735\pi$
$510$	−5.09808	+	8.83013i	−0.225747	+	0.391005i
$511$	6.73205	+	11.6603i	0.297808	+	0.515819i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.13397	+	1.23205i	−0.0942173	+	0.0543964i
$514$	−23.4282	+	13.5263i	−1.03337	+	0.596619i
$515$			4.92820i			0.217163i
$516$	−1.36603	−	2.36603i	−0.0601359	−	0.104158i
$517$	−0.330127	+	0.571797i	−0.0145190	+	0.0251476i
$518$	4.09808	+	2.36603i	0.180059	+	0.103957i
$519$	17.2679			0.757979
$520$	−2.36603	−	9.56218i	−0.103757	−	0.419329i
$521$	−5.73205			−0.251126			−0.125563	−	0.992086i	$-0.540074\pi$
$521$	−5.73205			−0.251126			−0.125563	+	0.992086i	$0.540074\pi$
$522$	−2.59808	−	1.50000i	−0.113715	−	0.0656532i
$523$	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
$525$		−	2.46410i		−	0.107542i
$526$	13.2224	−	7.63397i	0.576525	−	0.332857i
$527$	31.2224	−	18.0263i	1.36007	−	0.785237i
$528$			0.267949i			0.0116610i
$529$	5.50000	+	9.52628i	0.239130	+	0.414186i
$530$	4.83013	−	8.36603i	0.209807	−	0.363397i
$531$	−11.1962	−	6.46410i	−0.485872	−	0.280518i
$532$	−2.46410			−0.106832
$533$	−7.00000	+	24.2487i	−0.303204	+	1.05033i
$534$	0.464102			0.0200836
$535$	20.0263	+	11.5622i	0.865812	+	0.499877i
$536$	0.464102	−	0.803848i	0.0200461	−	0.0347209i
$537$	−0.803848	−	1.39230i	−0.0346886	−	0.0600824i
$538$		−	31.7128i		−	1.36724i
$539$	0.232051	−	0.133975i	0.00999514	−	0.00577069i
$540$	2.36603	−	1.36603i	0.101818	−	0.0587844i
$541$		−	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
$543$	4.59808	−	7.96410i	0.197322	−	0.341772i
$544$	−3.23205	−	1.86603i	−0.138573	−	0.0800052i
$545$	37.3205			1.59863
$546$	−3.46410	−	1.00000i	−0.148250	−	0.0427960i
$547$	−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
$549$	4.13397	−	7.16025i	0.176434	−	0.305592i
$550$	−0.330127	−	0.571797i	−0.0140767	−	0.0243815i
$551$		−	7.39230i		−	0.314923i
$552$	−3.00000	+	1.73205i	−0.127688	+	0.0737210i
$553$	14.5981	−	8.42820i	0.620773	−	0.358404i
$554$		−	5.60770i		−	0.238248i
$555$	−6.46410	−	11.1962i	−0.274386	−	0.475250i
$556$	3.06218	−	5.30385i	0.129865	−	0.224933i
$557$	−16.7487	−	9.66987i	−0.709666	−	0.409726i	0.101272	−	0.994859i	$-0.467709\pi$
$557$	−16.7487	−	9.66987i	−0.709666	−	0.409726i	−0.810937	+	0.585133i	$0.801042\pi$
$558$	−9.66025			−0.408951
$559$	7.09808	−	6.83013i	0.300217	−	0.288884i
$560$	2.73205			0.115450
$561$	0.866025	+	0.500000i	0.0365636	+	0.0211100i
$562$	3.90192	−	6.75833i	0.164593	−	0.285083i
$563$	−18.3660	−	31.8109i	−0.774036	−	1.34067i	−0.935335	−	0.353764i	$-0.884902\pi$
$563$	−18.3660	−	31.8109i	−0.774036	−	1.34067i	0.161299	−	0.986906i	$-0.448432\pi$
$564$			2.46410i			0.103757i
$565$	0.464102	−	0.267949i	0.0195249	−	0.0112727i
$566$	−7.85641	+	4.53590i	−0.330229	+	0.190658i
$567$		−	1.00000i		−	0.0419961i
$568$	4.09808	+	7.09808i	0.171951	+	0.297829i
$569$	9.63397	−	16.6865i	0.403877	−	0.699536i	−0.590313	−	0.807175i	$-0.700996\pi$
$569$	9.63397	−	16.6865i	0.403877	−	0.699536i	0.994190	+	0.107639i	$0.0343290\pi$
$570$	5.83013	+	3.36603i	0.244197	+	0.140987i
$571$	−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
$573$	−6.19615			−0.258848
$574$	−6.06218	−	3.50000i	−0.253030	−	0.146087i
$575$	4.26795	−	7.39230i	0.177986	−	0.308280i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$			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
$579$	5.89230	−	3.40192i	0.244876	−	0.141379i
$580$			8.19615i			0.340327i
$581$	5.83013	+	10.0981i	0.241874	+	0.418939i
$582$	1.36603	−	2.36603i	0.0566236	−	0.0980749i
$583$	−0.820508	−	0.473721i	−0.0339820	−	0.0196195i
$584$	13.4641			0.557148
$585$	6.83013	+	7.09808i	0.282391	+	0.293469i
$586$	−28.7846			−1.18908
$587$	−35.8301	−	20.6865i	−1.47887	−	0.853825i	−0.479153	−	0.877731i	$-0.659056\pi$
$587$	−35.8301	−	20.6865i	−1.47887	−	0.853825i	−0.999714	+	0.0239066i	$0.992390\pi$
$588$	0.500000	−	0.866025i	0.0206197	−	0.0357143i
$589$	−11.9019	−	20.6147i	−0.490410	−	0.849415i
$590$			35.3205i			1.45412i
$591$	−4.96410	+	2.86603i	−0.204196	+	0.117893i
$592$	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	$-0.460071\pi$
$594$	−0.133975	−	0.232051i	−0.00549704	−	0.00952116i
$595$	5.09808	−	8.83013i	0.209001	−	0.362000i
$596$	4.39230	+	2.53590i	0.179916	+	0.103874i
$597$	6.19615			0.253592
$598$	−8.66025	−	9.00000i	−0.354144	−	0.368037i
$599$	33.7128			1.37747			0.688734	−	0.725014i	$-0.258167\pi$
$599$	33.7128			1.37747			0.688734	+	0.725014i	$0.258167\pi$
$600$	−2.13397	−	1.23205i	−0.0871191	−	0.0502983i
$601$	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
$603$			0.928203i			0.0377994i
$604$	2.42820	−	1.40192i	0.0988022	−	0.0570435i
$605$	25.8564	−	14.9282i	1.05121	−	0.606918i
$606$			10.0000i			0.406222i
$607$	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
$609$	2.59808	+	1.50000i	0.105279	+	0.0607831i
$610$	−22.5885			−0.914580
$611$	−8.62436	+	2.13397i	−0.348904	+	0.0863314i
$612$	3.73205			0.150859
$613$	−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
$615$	9.56218	+	16.5622i	0.385584	+	0.667851i
$616$		−	0.267949i		−	0.0107960i
$617$	3.04552	−	1.75833i	0.122608	−	0.0707877i	−0.437442	−	0.899247i	$-0.644115\pi$
$617$	3.04552	−	1.75833i	0.122608	−	0.0707877i	0.560050	+	0.828459i	$0.310782\pi$
$618$	1.56218	−	0.901924i	0.0628400	−	0.0362807i
$619$			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
$621$	1.73205	−	3.00000i	0.0695048	−	0.120386i
$622$	7.62436	+	4.40192i	0.305709	+	0.176501i
$623$	−0.464102			−0.0185938
$624$	−2.59808	+	2.50000i	−0.104006	+	0.100080i
$625$	−31.2487			−1.24995
$626$	10.5622	+	6.09808i	0.422150	+	0.243728i
$627$	0.330127	−	0.571797i	0.0131840	−	0.0228354i
$628$	−4.26795	−	7.39230i	−0.170310	−	0.294985i
$629$		−	17.6603i		−	0.704160i
$630$	−2.36603	+	1.36603i	−0.0942647	+	0.0544238i
$631$	−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
$633$	5.92820	+	10.2679i	0.235625	+	0.408114i
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$	−46.0526	−	26.5885i	−1.82754	−	1.05513i
$636$	−3.53590			−0.140207
$637$	3.46410	+	1.00000i	0.137253	+	0.0396214i
$638$	0.803848			0.0318246
$639$	−7.09808	−	4.09808i	−0.280796	−	0.162117i
$640$	1.36603	−	2.36603i	0.0539969	−	0.0935254i
$641$	16.1244	+	27.9282i	0.636874	+	1.10310i	0.986115	+	0.166065i	$0.0531061\pi$
$641$	16.1244	+	27.9282i	0.636874	+	1.10310i	−0.349241	+	0.937033i	$0.613561\pi$
$642$		−	8.46410i		−	0.334051i
$643$	−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
$645$		−	7.46410i		−	0.293899i
$646$	4.59808	+	7.96410i	0.180909	+	0.313343i
$647$	−0.866025	+	1.50000i	−0.0340470	+	0.0589711i	−0.882547	−	0.470225i	$-0.844173\pi$
$647$	−0.866025	+	1.50000i	−0.0340470	+	0.0589711i	0.848500	+	0.529196i	$0.177506\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	3.46410			0.135978
$650$	2.46410	−	8.53590i	0.0966500	−	0.334805i
$651$	9.66025			0.378615
$652$	15.7583	+	9.09808i	0.617144	+	0.356308i
$653$	−23.1603	+	40.1147i	−0.906331	+	1.56981i	−0.0872099	+	0.996190i	$0.527795\pi$
$653$	−23.1603	+	40.1147i	−0.906331	+	1.56981i	−0.819121	+	0.573621i	$0.805538\pi$
$654$	−6.83013	−	11.8301i	−0.267079	−	0.462595i
$655$			13.8564i			0.541415i
$656$	−6.06218	+	3.50000i	−0.236688	+	0.136652i
$657$	−11.6603	+	6.73205i	−0.454910	+	0.262642i
$658$		−	2.46410i		−	0.0960607i
$659$	−10.0359	−	17.3827i	−0.390943	−	0.677133i	0.601631	−	0.798774i	$-0.294518\pi$
$659$	−10.0359	−	17.3827i	−0.390943	−	0.677133i	−0.992574	+	0.121641i	$0.961184\pi$
$660$	−0.366025	+	0.633975i	−0.0142475	+	0.0246774i
$661$	−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
$663$	3.23205	+	13.0622i	0.125522	+	0.507293i
$664$	11.6603			0.452506
$665$	−5.83013	−	3.36603i	−0.226083	−	0.130529i
$666$	−2.36603	+	4.09808i	−0.0916816	+	0.158797i
$667$	5.19615	+	9.00000i	0.201196	+	0.348481i
$668$			21.8564i			0.845650i
$669$	10.7321	−	6.19615i	0.414925	−	0.239557i
$670$	2.19615	−	1.26795i	0.0848448	−	0.0489852i
$671$			2.21539i			0.0855242i
$672$	−0.500000	−	0.866025i	−0.0192879	−	0.0334077i
$673$	−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
$675$	2.46410			0.0948433
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	45.7654			1.75891			0.879453	−	0.475986i	$-0.157909\pi$
$677$	45.7654			1.75891			0.879453	+	0.475986i	$0.157909\pi$
$678$	−0.169873	−	0.0980762i	−0.00652393	−	0.00376659i
$679$	−1.36603	+	2.36603i	−0.0524232	+	0.0907997i
$680$	−5.09808	−	8.83013i	−0.195502	−	0.338620i
$681$			15.4641i			0.592586i
$682$	2.24167	−	1.29423i	0.0858380	−	0.0495586i
$683$	4.85641	−	2.80385i	0.185825	−	0.107286i	−0.404201	−	0.914670i	$-0.632451\pi$
$683$	4.85641	−	2.80385i	0.185825	−	0.107286i	0.590027	+	0.807384i	$0.299117\pi$
$684$		−	2.46410i		−	0.0942173i
$685$	−11.6603	−	20.1962i	−0.445515	−	0.771655i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	−21.0622	−	12.1603i	−0.803572	−	0.463943i
$688$	2.73205			0.104158
$689$	−3.06218	−	12.3756i	−0.116660	−	0.471475i
$690$	−9.46410			−0.360292
$691$	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
$693$	0.133975	+	0.232051i	0.00508927	+	0.00881488i
$694$			4.85641i			0.184347i
$695$	14.4904	−	8.36603i	0.549651	−	0.317341i
$696$	2.59808	−	1.50000i	0.0984798	−	0.0568574i
$697$			26.1244i			0.989531i
$698$	15.8564	+	27.4641i	0.600174	+	1.03953i
$699$	4.09808	−	7.09808i	0.155003	−	0.268474i
$700$	2.13397	+	1.23205i	0.0806567	+	0.0465671i
$701$	20.3205			0.767495			0.383747	−	0.923438i	$-0.374633\pi$
$701$	20.3205			0.767495			0.383747	+	0.923438i	$0.374633\pi$
$702$	1.00000	−	3.46410i	0.0377426	−	0.130744i
$703$	−11.6603			−0.439775
$704$	−0.232051	−	0.133975i	−0.00874574	−	0.00504936i
$705$	−3.36603	+	5.83013i	−0.126772	+	0.219575i
$706$	−2.73205	−	4.73205i	−0.102822	−	0.178093i
$707$		−	10.0000i		−	0.376089i
$708$	11.1962	−	6.46410i	0.420777	−	0.242936i
$709$	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
$711$	8.42820	+	14.5981i	0.316082	+	0.547471i
$712$	−0.232051	+	0.401924i	−0.00869647	+	0.0150627i
$713$	28.9808	+	16.7321i	1.08534	+	0.626620i
$714$	−3.73205			−0.139668
$715$	−2.53590	−	0.732051i	−0.0948372	−	0.0273771i
$716$	1.60770			0.0600824
$717$	20.9545	+	12.0981i	0.782559	+	0.451811i
$718$	13.0981	−	22.6865i	0.488816	−	0.846654i
$719$	−17.5263	−	30.3564i	−0.653620	−	1.13210i	−0.982238	−	0.187640i	$-0.939916\pi$
$719$	−17.5263	−	30.3564i	−0.653620	−	1.13210i	0.328618	−	0.944463i	$-0.393417\pi$
$720$			2.73205i			0.101818i
$721$	−1.56218	+	0.901924i	−0.0581785	+	0.0335894i
$722$	−11.1962	+	6.46410i	−0.416678	+	0.240569i
$723$			28.7846i			1.07051i
$724$	4.59808	+	7.96410i	0.170886	+	0.295984i
$725$	−3.69615	+	6.40192i	−0.137272	+	0.237761i
$726$	−9.46410	−	5.46410i	−0.351246	−	0.202792i
$727$	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
$729$	1.00000			0.0370370
$730$	31.8564	+	18.3923i	1.17906	+	0.680730i
$731$	5.09808	−	8.83013i	0.188559	−	0.326594i
$732$	4.13397	+	7.16025i	0.152796	+	0.264651i
$733$		−	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
$735$	2.36603	−	1.36603i	0.0872722	−	0.0503866i
$736$		−	3.46410i		−	0.127688i
$737$	−0.124356	−	0.215390i	−0.00458070	−	0.00793400i
$738$	3.50000	−	6.06218i	0.128837	−	0.223152i
$739$	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
$741$	8.62436	−	2.13397i	0.316824	−	0.0783935i
$742$	3.53590			0.129807
$743$	−22.0981	−	12.7583i	−0.810700	−	0.468058i	0.0364990	−	0.999334i	$-0.488379\pi$
$743$	−22.0981	−	12.7583i	−0.810700	−	0.468058i	−0.847199	+	0.531276i	$0.821713\pi$
$744$	4.83013	−	8.36603i	0.177081	−	0.306713i
$745$	6.92820	+	12.0000i	0.253830	+	0.439646i
$746$		−	10.5885i		−	0.387671i
$747$	−10.0981	+	5.83013i	−0.369469	+	0.213313i
$748$	−0.866025	+	0.500000i	−0.0316650	+	0.0182818i
$749$			8.46410i			0.309272i
$750$	3.46410	+	6.00000i	0.126491	+	0.219089i
$751$	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
$753$	7.80385			0.284388
$754$	7.50000	+	7.79423i	0.273134	+	0.283849i
$755$	7.66025			0.278785
$756$	0.866025	+	0.500000i	0.0314970	+	0.0181848i
$757$	−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
$759$			0.928203i			0.0336916i
$760$	−5.83013	+	3.36603i	−0.211481	+	0.122099i
$761$	30.5885	−	17.6603i	1.10883	−	0.640184i	0.170304	−	0.985391i	$-0.445525\pi$
$761$	30.5885	−	17.6603i	1.10883	−	0.640184i	0.938526	+	0.345208i	$0.112192\pi$
$762$			19.4641i			0.705110i
$763$	6.83013	+	11.8301i	0.247267	+	0.428279i
$764$	3.09808	−	5.36603i	0.112084	−	0.194136i
$765$	8.83013	+	5.09808i	0.319254	+	0.184321i
$766$	−35.3923			−1.27878
$767$	32.3205	+	33.5885i	1.16703	+	1.21281i
$768$	−1.00000			−0.0360844
$769$	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
$771$	13.5263	+	23.4282i	0.487137	+	0.843746i
$772$			6.80385i			0.244876i
$773$	−18.7128	+	10.8038i	−0.673053	+	0.388587i	−0.797232	−	0.603672i	$-0.793704\pi$
$773$	−18.7128	+	10.8038i	−0.673053	+	0.388587i	0.124179	+	0.992260i	$0.460370\pi$
$774$	−2.36603	+	1.36603i	−0.0850450	+	0.0491008i
$775$			23.8038i			0.855059i
$776$	1.36603	+	2.36603i	0.0490375	+	0.0849354i
$777$	2.36603	−	4.09808i	0.0848807	−	0.147018i
$778$	−25.2679	−	14.5885i	−0.905900	−	0.523022i
$779$	17.2487			0.617999
$780$	−9.56218	+	2.36603i	−0.342381	+	0.0847173i
$781$	2.19615			0.0785845
$782$	−11.1962	−	6.46410i	−0.400374	−	0.231156i
$783$	−1.50000	+	2.59808i	−0.0536056	+	0.0928477i
$784$	0.500000	+	0.866025i	0.0178571	+	0.0309295i
$785$		−	23.3205i		−	0.832345i
$786$	4.39230	−	2.53590i	0.156668	−	0.0904525i
$787$	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
$789$	−7.63397	−	13.2224i	−0.271777	−	0.470731i
$790$	23.0263	−	39.8827i	0.819238	−	1.41896i
$791$	0.169873	+	0.0980762i	0.00603999	+	0.00348719i
$792$	0.267949			0.00952116
$793$	−21.4808	+	20.6699i	−0.762804	+	0.734009i
$794$	9.53590			0.338416
$795$	−8.36603	−	4.83013i	−0.296712	−	0.171307i
$796$	−3.09808	+	5.36603i	−0.109808	+	0.190194i
$797$	1.36603	+	2.36603i	0.0483871	+	0.0838089i	0.889205	−	0.457510i	$-0.151259\pi$
$797$	1.36603	+	2.36603i	0.0483871	+	0.0838089i	−0.840817	+	0.541319i	$0.817925\pi$
$798$			2.46410i			0.0872283i
$799$	−7.96410	+	4.59808i	−0.281750	+	0.162668i
$800$	2.13397	−	1.23205i	0.0754474	−	0.0435596i
$801$		−	0.464102i		−	0.0163982i
$802$	5.00000	+	8.66025i	0.176556	+	0.305804i
$803$	1.80385	−	3.12436i	0.0636564	−	0.110256i
$804$	−0.803848	−	0.464102i	−0.0283495	−	0.0163676i
$805$	9.46410			0.333566
$806$	33.4641	+	9.66025i	1.17872	+	0.340268i
$807$	−31.7128			−1.11634
$808$	−8.66025	−	5.00000i	−0.304667	−	0.175899i
$809$	−5.09808	+	8.83013i	−0.179239	+	0.310451i	−0.941620	−	0.336677i	$-0.890697\pi$
$809$	−5.09808	+	8.83013i	−0.179239	+	0.310451i	0.762381	+	0.647128i	$0.224030\pi$
$810$	−1.36603	−	2.36603i	−0.0479972	−	0.0831337i
$811$			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
$813$	20.3660	−	11.7583i	0.714268	−	0.412383i
$814$		−	1.26795i		−	0.0444416i
$815$	24.8564	+	43.0526i	0.870682	+	1.50807i
$816$	−1.86603	+	3.23205i	−0.0653240	+	0.113144i
$817$	−5.83013	−	3.36603i	−0.203970	−	0.117762i
$818$	−16.7321			−0.585022
$819$	−1.00000	+	3.46410i	−0.0349428	+	0.121046i
$820$	−19.1244			−0.667851
$821$	12.4808	+	7.20577i	0.435582	+	0.251483i	0.701722	−	0.712451i	$-0.252415\pi$
$821$	12.4808	+	7.20577i	0.435582	+	0.251483i	−0.266140	+	0.963934i	$0.585748\pi$
$822$	−4.26795	+	7.39230i	−0.148862	+	0.257836i
$823$	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
$825$	−0.571797	+	0.330127i	−0.0199074	+	0.0114935i
$826$	−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	$0.752161\pi$
$828$	1.73205	+	3.00000i	0.0601929	+	0.104257i
$829$	−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
$831$	−5.60770			−0.194529
$832$	−0.866025	−	3.50000i	−0.0300240	−	0.121341i
$833$	3.73205			0.129308
$834$	−5.30385	−	3.06218i	−0.183657	−	0.106035i
$835$	−29.8564	+	51.7128i	−1.03322	+	1.78960i
$836$	0.330127	+	0.571797i	0.0114177	+	0.0197760i
$837$			9.66025i			0.333907i
$838$	−3.63397	+	2.09808i	−0.125534	+	0.0724768i
$839$	12.4641	−	7.19615i	0.430309	−	0.248439i	−0.269170	−	0.963093i	$-0.586749\pi$
$839$	12.4641	−	7.19615i	0.430309	−	0.248439i	0.699478	+	0.714654i	$0.253416\pi$
$840$		−	2.73205i		−	0.0942647i
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	3.19615	−	5.53590i	0.110147	−	0.190780i
$843$	−6.75833	−	3.90192i	−0.232769	−	0.134389i
$844$	−11.8564			−0.408114
$845$	−16.5622	−	31.4186i	−0.569756	−	1.08083i
$846$	2.46410			0.0847176
$847$	9.46410	+	5.46410i	0.325190	+	0.187749i
$848$	1.76795	−	3.06218i	0.0607116	−	0.105156i
$849$	4.53590	+	7.85641i	0.155672	+	0.269631i
$850$		−	9.19615i		−	0.315425i
$851$	14.1962	−	8.19615i	0.486638	−	0.280960i
$852$	7.09808	−	4.09808i	0.243176	−	0.140398i
$853$		−	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
$855$	3.36603	−	5.83013i	0.115116	−	0.199386i
$856$	7.33013	+	4.23205i	0.250539	+	0.144649i
$857$	21.6077			0.738105			0.369052	−	0.929409i	$-0.379682\pi$
$857$	21.6077			0.738105			0.369052	+	0.929409i	$0.379682\pi$
$858$	0.232051	+	0.937822i	0.00792208	+	0.0320167i
$859$	−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
$861$	−3.50000	+	6.06218i	−0.119280	+	0.206598i
$862$	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	$0.837918\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−40.8564	+	23.5885i	−1.38916	+	0.802032i
$866$		−	4.92820i		−	0.167467i
$867$	−1.53590	−	2.66025i	−0.0521618	−	0.0903470i
$868$	−4.83013	+	8.36603i	−0.163945	+	0.283961i
$869$	−3.91154	−	2.25833i	−0.132690	−	0.0766086i
$870$	8.19615			0.277876
$871$	0.928203	−	3.21539i	0.0314510	−	0.108949i
$872$	13.6603			0.462595
$873$	−2.36603	−	1.36603i	−0.0800778	−	0.0462330i
$874$	−4.26795	+	7.39230i	−0.144366	+	0.250048i
$875$	−3.46410	−	6.00000i	−0.117108	−	0.202837i
$876$		−	13.4641i		−	0.454910i
$877$	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
$879$			28.7846i			0.970881i
$880$	−0.366025	−	0.633975i	−0.0123387	−	0.0213713i
$881$	0.535898	−	0.928203i	0.0180549	−	0.0312720i	−0.856857	−	0.515554i	$-0.827586\pi$
$881$	0.535898	−	0.928203i	0.0180549	−	0.0312720i	0.874912	+	0.484283i	$0.160919\pi$
$882$	−0.866025	−	0.500000i	−0.0291606	−	0.0168359i
$883$	−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
$885$	35.3205			1.18729
$886$	−9.18653	−	5.30385i	−0.308628	−	0.178186i
$887$	−22.5263	+	39.0167i	−0.756358	+	1.31005i	0.188338	+	0.982104i	$0.439690\pi$
$887$	−22.5263	+	39.0167i	−0.756358	+	1.31005i	−0.944696	+	0.327947i	$0.893643\pi$
$888$	−2.36603	−	4.09808i	−0.0793986	−	0.137522i
$889$		−	19.4641i		−	0.652805i
$890$	−1.09808	+	0.633975i	−0.0368076	+	0.0212509i
$891$	−0.232051	+	0.133975i	−0.00777399	+	0.00448832i
$892$			12.3923i			0.414925i
$893$	3.03590	+	5.25833i	0.101592	+	0.175963i
$894$	2.53590	−	4.39230i	0.0848131	−	0.146901i
$895$	3.80385	+	2.19615i	0.127149	+	0.0734093i
$896$	1.00000			0.0334077
$897$	−9.00000	+	8.66025i	−0.300501	+	0.289157i
$898$	7.26795			0.242535
$899$	−25.0981	−	14.4904i	−0.837068	−	0.483281i
$900$	−1.23205	+	2.13397i	−0.0410684	+	0.0711325i
$901$	−6.59808	−	11.4282i	−0.219814	−	0.380729i
$902$			1.87564i			0.0624521i
$903$	2.36603	−	1.36603i	0.0787364	−	0.0454585i
$904$	0.169873	−	0.0980762i	0.00564989	−	0.00326197i
$905$			25.1244i			0.835162i
$906$	−1.40192	−	2.42820i	−0.0465758	−	0.0806716i
$907$	−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
$909$	10.0000			0.331679
$910$	9.56218	−	2.36603i	0.316983	−	0.0784330i
$911$	−0.0525589			−0.00174135			−0.000870677	−	1.00000i	$-0.500277\pi$
$911$	−0.0525589			−0.00174135			−0.000870677		1.00000i	$0.500277\pi$
$912$	2.13397	+	1.23205i	0.0706630	+	0.0407973i
$913$	1.56218	−	2.70577i	0.0517005	−	0.0895480i
$914$	17.3923	+	30.1244i	0.575286	+	0.996425i
$915$			22.5885i			0.746751i
$916$	21.0622	−	12.1603i	0.695914	−	0.401786i
$917$	−4.39230	+	2.53590i	−0.145047	+	0.0837427i
$918$		−	3.73205i		−	0.123176i
$919$	−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
$921$	−6.74167	−	3.89230i	−0.222146	−	0.128256i
$922$	−27.7128			−0.912673
$923$	20.4904	+	21.2942i	0.674449	+	0.700908i
$924$	−0.267949			−0.00881488
$925$	10.0981	+	5.83013i	0.332023	+	0.191693i
$926$	4.59808	−	7.96410i	0.151102	−	0.261717i
$927$	−0.901924	−	1.56218i	−0.0296231	−	0.0513087i
$928$			3.00000i			0.0984798i
$929$	−37.7032	+	21.7679i	−1.23700	+	0.714183i	−0.968480	−	0.249090i	$-0.919868\pi$
$929$	−37.7032	+	21.7679i	−1.23700	+	0.714183i	−0.268521	+	0.963274i	$0.586535\pi$
$930$	22.8564	−	13.1962i	0.749491	−	0.432719i
$931$		−	2.46410i		−	0.0807577i
$932$	4.09808	+	7.09808i	0.134237	+	0.232505i
$933$	4.40192	−	7.62436i	0.144113	−	0.249610i
$934$	−15.4641	−	8.92820i	−0.506001	−	0.292140i
$935$	−2.73205			−0.0893476
$936$	2.50000	+	2.59808i	0.0817151	+	0.0849208i
$937$	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
$939$	6.09808	−	10.5622i	0.199003	−	0.344684i
$940$	−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	$0.704003\pi$
$942$	−7.39230	+	4.26795i	−0.240854	+	0.139057i
$943$	−21.0000	+	12.1244i	−0.683854	+	0.394823i
$944$			12.9282i			0.420777i
$945$	1.36603	+	2.36603i	0.0444368	+	0.0769668i
$946$	0.366025	−	0.633975i	0.0119005	−	0.0206123i
$947$	11.2128	+	6.47372i	0.364367	+	0.210368i	0.670995	−	0.741462i	$-0.265867\pi$
$947$	11.2128	+	6.47372i	0.364367	+	0.210368i	−0.306627	+	0.951830i	$0.599201\pi$
$948$	−16.8564			−0.547471
$949$	47.1244	−	11.6603i	1.52972	−	0.378508i
$950$	−6.07180			−0.196995
$951$	15.5885	+	9.00000i	0.505490	+	0.291845i
$952$	1.86603	−	3.23205i	0.0604782	−	0.104751i
$953$	−10.6865	−	18.5096i	−0.346171	−	0.599585i	0.639395	−	0.768878i	$-0.279185\pi$
$953$	−10.6865	−	18.5096i	−0.346171	−	0.599585i	−0.985566	+	0.169293i	$0.945852\pi$
$954$			3.53590i			0.114479i
$955$	14.6603	−	8.46410i	0.474395	−	0.273892i
$956$	−20.9545	+	12.0981i	−0.677716	+	0.391280i
$957$		−	0.803848i		−	0.0259847i
$958$	−5.30385	−	9.18653i	−0.171360	−	0.296803i
$959$	4.26795	−	7.39230i	0.137819	−	0.238710i
$960$	−2.36603	−	1.36603i	−0.0763631	−	0.0440883i
$961$	−62.3205			−2.01034
$962$	12.2942	−	11.8301i	0.396382	−	0.381419i
$963$	−8.46410			−0.272752
$964$	−24.9282	−	14.3923i	−0.802883	−	0.463545i
$965$	−9.29423	+	16.0981i	−0.299192	+	0.518215i
$966$	−1.73205	−	3.00000i	−0.0557278	−	0.0965234i
$967$		−	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
$969$	7.96410	−	4.59808i	0.255844	−	0.147711i
$970$			7.46410i			0.239658i
$971$	2.12436	+	3.67949i	0.0681738	+	0.118081i	0.898097	−	0.439796i	$-0.144949\pi$
$971$	2.12436	+	3.67949i	0.0681738	+	0.118081i	−0.829924	+	0.557877i	$0.811616\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	5.30385	+	3.06218i	0.170034	+	0.0981689i
$974$	−10.8038			−0.346178
$975$	−8.53590	−	2.46410i	−0.273368	−	0.0789144i
$976$	−8.26795			−0.264651
$977$	26.1962	+	15.1244i	0.838089	+	0.483871i	0.856614	−	0.515957i	$-0.172564\pi$
$977$	26.1962	+	15.1244i	0.838089	+	0.483871i	−0.0185251	+	0.999828i	$0.505897\pi$
$978$	9.09808	−	15.7583i	0.290924	−	0.503896i
$979$	0.0621778	+	0.107695i	0.00198721	+	0.00344195i
$980$			2.73205i			0.0872722i
$981$	−11.8301	+	6.83013i	−0.377707	+	0.218069i
$982$	−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	$0.650165\pi$
$984$	3.50000	+	6.06218i	0.111576	+	0.193255i
$985$	7.83013	−	13.5622i	0.249489	−	0.432127i
$986$	9.69615	+	5.59808i	0.308788	+	0.178279i
$987$	−2.46410			−0.0784332
$988$	−2.46410	+	8.53590i	−0.0783935	+	0.271563i
$989$	9.46410			0.300941
$990$	0.633975	+	0.366025i	0.0201490	+	0.0116331i
$991$	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
$993$		−	3.07180i		−	0.0974805i
$994$	−7.09808	+	4.09808i	−0.225137	+	0.129983i
$995$	−14.6603	+	8.46410i	−0.464761	+	0.268330i
$996$		−	11.6603i		−	0.369469i
$997$	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
$999$	4.09808	+	2.36603i	0.129657	+	0.0748577i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.d.43.2	✓	4	1.1	even	1	trivial
546.2.s.d.127.2	yes	4	13.10	even	6	inner
1638.2.bj.d.127.1		4	39.23	odd	6
1638.2.bj.d.1135.1		4	3.2	odd	2
7098.2.a.bj.1.2		2	13.6	odd	12
7098.2.a.bs.1.1		2	13.7	odd	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.36603 + 2.36603i) q^{10} +(0.232051 + 0.133975i) q^{11} +1.00000 q^{12} +(0.866025 + 3.50000i) q^{13} -1.00000 q^{14} +(2.36603 + 1.36603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.86603 + 3.23205i) q^{17} -1.00000i q^{18} +(2.13397 - 1.23205i) q^{19} +(-2.36603 + 1.36603i) q^{20} +1.00000i q^{21} +(0.133975 + 0.232051i) q^{22} +(-1.73205 + 3.00000i) q^{23} +(0.866025 + 0.500000i) q^{24} -2.46410 q^{25} +(-1.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(-0.866025 - 0.500000i) q^{28} +(1.50000 - 2.59808i) q^{29} +(1.36603 + 2.36603i) q^{30} -9.66025i q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.232051 - 0.133975i) q^{33} +3.73205i q^{34} +(-1.36603 - 2.36603i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-4.09808 - 2.36603i) q^{37} +2.46410 q^{38} +(3.46410 + 1.00000i) q^{39} -2.73205 q^{40} +(6.06218 + 3.50000i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-1.36603 - 2.36603i) q^{43} +0.267949i q^{44} +(2.36603 - 1.36603i) q^{45} +(-3.00000 + 1.73205i) q^{46} +2.46410i q^{47} +(0.500000 + 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-2.13397 - 1.23205i) q^{50} +3.73205 q^{51} +(-2.59808 + 2.50000i) q^{52} -3.53590 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.366025 + 0.633975i) q^{55} +(-0.500000 - 0.866025i) q^{56} -2.46410i q^{57} +(2.59808 - 1.50000i) q^{58} +(11.1962 - 6.46410i) q^{59} +2.73205i q^{60} +(4.13397 + 7.16025i) q^{61} +(4.83013 - 8.36603i) q^{62} +(0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(-9.56218 + 2.36603i) q^{65} +0.267949 q^{66} +(-0.803848 - 0.464102i) q^{67} +(-1.86603 + 3.23205i) q^{68} +(1.73205 + 3.00000i) q^{69} -2.73205i q^{70} +(7.09808 - 4.09808i) q^{71} +(0.866025 - 0.500000i) q^{72} -13.4641i q^{73} +(-2.36603 - 4.09808i) q^{74} +(-1.23205 + 2.13397i) q^{75} +(2.13397 + 1.23205i) q^{76} -0.267949 q^{77} +(2.50000 + 2.59808i) q^{78} -16.8564 q^{79} +(-2.36603 - 1.36603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.50000 + 6.06218i) q^{82} -11.6603i q^{83} +(-0.866025 + 0.500000i) q^{84} +(-8.83013 + 5.09808i) q^{85} -2.73205i q^{86} +(-1.50000 - 2.59808i) q^{87} +(-0.133975 + 0.232051i) q^{88} +(0.401924 + 0.232051i) q^{89} +2.73205 q^{90} +(-2.50000 - 2.59808i) q^{91} -3.46410 q^{92} +(-8.36603 - 4.83013i) q^{93} +(-1.23205 + 2.13397i) q^{94} +(3.36603 + 5.83013i) q^{95} +1.00000i q^{96} +(2.36603 - 1.36603i) q^{97} +(0.866025 - 0.500000i) q^{98} -0.267949i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{14} + 6 q^{15} - 2 q^{16} + 4 q^{17} + 12 q^{19} - 6 q^{20} + 4 q^{22} + 4 q^{25} - 4 q^{26} - 4 q^{27} + 6 q^{29} + 2 q^{30} - 6 q^{33} - 2 q^{35} + 2 q^{36} - 6 q^{37} - 4 q^{38} - 4 q^{40} - 2 q^{42} - 2 q^{43} + 6 q^{45} - 12 q^{46} + 2 q^{48} + 2 q^{49} - 12 q^{50} + 8 q^{51} - 28 q^{53} + 2 q^{55} - 2 q^{56} + 24 q^{59} + 20 q^{61} + 2 q^{62} - 4 q^{64} - 14 q^{65} + 8 q^{66} - 24 q^{67} - 4 q^{68} + 18 q^{71} - 6 q^{74} + 2 q^{75} + 12 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 6 q^{80} - 2 q^{81} + 14 q^{82} - 18 q^{85} - 6 q^{87} - 4 q^{88} + 12 q^{89} + 4 q^{90} - 10 q^{91} - 30 q^{93} + 2 q^{94} + 10 q^{95} + 6 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 - 6 * q^11 + 4 * q^12 - 4 * q^14 + 6 * q^15 - 2 * q^16 + 4 * q^17 + 12 * q^19 - 6 * q^20 + 4 * q^22 + 4 * q^25 - 4 * q^26 - 4 * q^27 + 6 * q^29 + 2 * q^30 - 6 * q^33 - 2 * q^35 + 2 * q^36 - 6 * q^37 - 4 * q^38 - 4 * q^40 - 2 * q^42 - 2 * q^43 + 6 * q^45 - 12 * q^46 + 2 * q^48 + 2 * q^49 - 12 * q^50 + 8 * q^51 - 28 * q^53 + 2 * q^55 - 2 * q^56 + 24 * q^59 + 20 * q^61 + 2 * q^62 - 4 * q^64 - 14 * q^65 + 8 * q^66 - 24 * q^67 - 4 * q^68 + 18 * q^71 - 6 * q^74 + 2 * q^75 + 12 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 6 * q^80 - 2 * q^81 + 14 * q^82 - 18 * q^85 - 6 * q^87 - 4 * q^88 + 12 * q^89 + 4 * q^90 - 10 * q^91 - 30 * q^93 + 2 * q^94 + 10 * q^95 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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