LMFDB - Embedded newform 1110.2.bb.c.1009.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1009,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1110.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.bb (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:	$8.86339462436$
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			1009.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.c.1099.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +1.00000 q^{6} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +1.00000 q^{6} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.00000 + 1.00000i) q^{10} +4.00000 q^{11} +(0.866025 + 0.500000i) q^{12} +(2.59808 - 1.50000i) q^{13} -1.00000 q^{14} +(1.86603 - 1.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-5.19615 - 3.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(1.23205 + 1.86603i) q^{20} +(-0.500000 + 0.866025i) q^{21} +(3.46410 + 2.00000i) q^{22} +4.00000i q^{23} +(0.500000 + 0.866025i) q^{24} +(4.96410 - 0.598076i) q^{25} +3.00000 q^{26} -1.00000i q^{27} +(-0.866025 - 0.500000i) q^{28} +5.00000 q^{29} +(2.23205 - 0.133975i) q^{30} -6.00000 q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.46410 - 2.00000i) q^{33} +(-3.00000 - 5.19615i) q^{34} +(-1.86603 + 1.23205i) q^{35} +1.00000 q^{36} +(-6.06218 + 0.500000i) q^{37} -1.00000i q^{38} +(1.50000 - 2.59808i) q^{39} +(0.133975 + 2.23205i) q^{40} +(4.00000 + 6.92820i) q^{41} +(-0.866025 + 0.500000i) q^{42} +6.00000i q^{43} +(2.00000 + 3.46410i) q^{44} +(1.00000 - 2.00000i) q^{45} +(-2.00000 + 3.46410i) q^{46} -12.0000i q^{47} +1.00000i q^{48} +(-3.00000 + 5.19615i) q^{49} +(4.59808 + 1.96410i) q^{50} -6.00000 q^{51} +(2.59808 + 1.50000i) q^{52} +(3.46410 + 2.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(8.92820 - 0.535898i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-0.866025 - 0.500000i) q^{57} +(4.33013 + 2.50000i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(2.00000 + 1.00000i) q^{60} +(-5.19615 - 3.00000i) q^{62} +1.00000i q^{63} -1.00000 q^{64} +(5.59808 - 3.69615i) q^{65} +4.00000 q^{66} +(6.92820 - 4.00000i) q^{67} -6.00000i q^{68} +(2.00000 + 3.46410i) q^{69} +(-2.23205 + 0.133975i) q^{70} +(1.50000 + 2.59808i) q^{71} +(0.866025 + 0.500000i) q^{72} -16.0000i q^{73} +(-5.50000 - 2.59808i) q^{74} +(4.00000 - 3.00000i) q^{75} +(0.500000 - 0.866025i) q^{76} +(-3.46410 + 2.00000i) q^{77} +(2.59808 - 1.50000i) q^{78} +(5.00000 + 8.66025i) q^{79} +(-1.00000 + 2.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +8.00000i q^{82} +(-14.7224 - 8.50000i) q^{83} -1.00000 q^{84} +(-12.0000 - 6.00000i) q^{85} +(-3.00000 + 5.19615i) q^{86} +(4.33013 - 2.50000i) q^{87} +4.00000i q^{88} +(-2.00000 + 3.46410i) q^{89} +(1.86603 - 1.23205i) q^{90} +(-1.50000 + 2.59808i) q^{91} +(-3.46410 + 2.00000i) q^{92} +(-5.19615 + 3.00000i) q^{93} +(6.00000 - 10.3923i) q^{94} +(-1.23205 - 1.86603i) q^{95} +(-0.500000 + 0.866025i) q^{96} -12.0000i q^{97} +(-5.19615 + 3.00000i) q^{98} +(2.00000 - 3.46410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{5} + 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 2 * q^5 + 4 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} + 2 q^{5} + 4 q^{6} + 2 q^{9} + 8 q^{10} + 16 q^{11} - 4 q^{14} + 4 q^{15} - 2 q^{16} - 2 q^{19} - 2 q^{20} - 2 q^{21} + 2 q^{24} + 6 q^{25} + 12 q^{26} + 20 q^{29} + 2 q^{30} - 24 q^{31} - 12 q^{34} - 4 q^{35} + 4 q^{36} + 6 q^{39} + 4 q^{40} + 16 q^{41} + 8 q^{44} + 4 q^{45} - 8 q^{46} - 12 q^{49} + 8 q^{50} - 24 q^{51} + 2 q^{54} + 8 q^{55} - 2 q^{56} - 8 q^{59} + 8 q^{60} - 4 q^{64} + 12 q^{65} + 16 q^{66} + 8 q^{69} - 2 q^{70} + 6 q^{71} - 22 q^{74} + 16 q^{75} + 2 q^{76} + 20 q^{79} - 4 q^{80} - 2 q^{81} - 4 q^{84} - 48 q^{85} - 12 q^{86} - 8 q^{89} + 4 q^{90} - 6 q^{91} + 24 q^{94} + 2 q^{95} - 2 q^{96} + 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^5 + 4 * q^6 + 2 * q^9 + 8 * q^10 + 16 * q^11 - 4 * q^14 + 4 * q^15 - 2 * q^16 - 2 * q^19 - 2 * q^20 - 2 * q^21 + 2 * q^24 + 6 * q^25 + 12 * q^26 + 20 * q^29 + 2 * q^30 - 24 * q^31 - 12 * q^34 - 4 * q^35 + 4 * q^36 + 6 * q^39 + 4 * q^40 + 16 * q^41 + 8 * q^44 + 4 * q^45 - 8 * q^46 - 12 * q^49 + 8 * q^50 - 24 * q^51 + 2 * q^54 + 8 * q^55 - 2 * q^56 - 8 * q^59 + 8 * q^60 - 4 * q^64 + 12 * q^65 + 16 * q^66 + 8 * q^69 - 2 * q^70 + 6 * q^71 - 22 * q^74 + 16 * q^75 + 2 * q^76 + 20 * q^79 - 4 * q^80 - 2 * q^81 - 4 * q^84 - 48 * q^85 - 12 * q^86 - 8 * q^89 + 4 * q^90 - 6 * q^91 + 24 * q^94 + 2 * q^95 - 2 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.23205	−	0.133975i	0.998203	−	0.0599153i
$5$	2.23205	−	0.133975i	0.998203	−	0.0599153i
$6$	1.00000			0.408248
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i	0.327327	+	0.944911i	$0.393852\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	2.00000	+	1.00000i	0.632456	+	0.316228i
$11$	4.00000			1.20605			0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000			1.20605			0.603023	+	0.797724i	$0.293963\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	2.59808	−	1.50000i	0.720577	−	0.416025i	−0.0943882	−	0.995535i	$-0.530089\pi$
$13$	2.59808	−	1.50000i	0.720577	−	0.416025i	0.814965	+	0.579510i	$0.196756\pi$
$14$	−1.00000			−0.267261
$15$	1.86603	−	1.23205i	0.481806	−	0.318114i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.19615	−	3.00000i	−1.26025	−	0.727607i	−0.287129	−	0.957892i	$-0.592701\pi$
$17$	−5.19615	−	3.00000i	−1.26025	−	0.727607i	−0.973123	+	0.230285i	$0.926034\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	1.23205	+	1.86603i	0.275495	+	0.417256i
$21$	−0.500000	+	0.866025i	−0.109109	+	0.188982i
$22$	3.46410	+	2.00000i	0.738549	+	0.426401i
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	4.96410	−	0.598076i	0.992820	−	0.119615i
$26$	3.00000			0.588348
$27$		−	1.00000i		−	0.192450i
$28$	−0.866025	−	0.500000i	−0.163663	−	0.0944911i
$29$	5.00000			0.928477			0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000			0.928477			0.464238	+	0.885710i	$0.346328\pi$
$30$	2.23205	−	0.133975i	0.407515	−	0.0244603i
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	3.46410	−	2.00000i	0.603023	−	0.348155i
$34$	−3.00000	−	5.19615i	−0.514496	−	0.891133i
$35$	−1.86603	+	1.23205i	−0.315416	+	0.208255i
$36$	1.00000			0.166667
$37$	−6.06218	+	0.500000i	−0.996616	+	0.0821995i
$37$	−6.06218	+	0.500000i	−0.996616	+	0.0821995i
$38$		−	1.00000i		−	0.162221i
$39$	1.50000	−	2.59808i	0.240192	−	0.416025i
$40$	0.133975	+	2.23205i	0.0211832	+	0.352918i
$41$	4.00000	+	6.92820i	0.624695	+	1.08200i	0.988600	+	0.150567i	$0.0481100\pi$
$41$	4.00000	+	6.92820i	0.624695	+	1.08200i	−0.363905	+	0.931436i	$0.618557\pi$
$42$	−0.866025	+	0.500000i	−0.133631	+	0.0771517i
$43$			6.00000i			0.914991i	0.889212	+	0.457496i	$0.151253\pi$
$43$			6.00000i			0.914991i	−0.889212	+	0.457496i	$0.848747\pi$
$44$	2.00000	+	3.46410i	0.301511	+	0.522233i
$45$	1.00000	−	2.00000i	0.149071	−	0.298142i
$46$	−2.00000	+	3.46410i	−0.294884	+	0.510754i
$47$		−	12.0000i		−	1.75038i	−0.483779	−	0.875190i	$-0.660736\pi$
$47$		−	12.0000i		−	1.75038i	0.483779	−	0.875190i	$-0.339264\pi$
$48$			1.00000i			0.144338i
$49$	−3.00000	+	5.19615i	−0.428571	+	0.742307i
$50$	4.59808	+	1.96410i	0.650266	+	0.277766i
$51$	−6.00000			−0.840168
$52$	2.59808	+	1.50000i	0.360288	+	0.208013i
$53$	3.46410	+	2.00000i	0.475831	+	0.274721i	0.718677	−	0.695344i	$-0.244748\pi$
$53$	3.46410	+	2.00000i	0.475831	+	0.274721i	−0.242846	+	0.970065i	$0.578081\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	8.92820	−	0.535898i	1.20388	−	0.0722605i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	−0.866025	−	0.500000i	−0.114708	−	0.0662266i
$58$	4.33013	+	2.50000i	0.568574	+	0.328266i
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$	2.00000	+	1.00000i	0.258199	+	0.129099i
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	−5.19615	−	3.00000i	−0.659912	−	0.381000i
$63$			1.00000i			0.125988i
$64$	−1.00000			−0.125000
$65$	5.59808	−	3.69615i	0.694356	−	0.458451i
$66$	4.00000			0.492366
$67$	6.92820	−	4.00000i	0.846415	−	0.488678i	−0.0130248	−	0.999915i	$-0.504146\pi$
$67$	6.92820	−	4.00000i	0.846415	−	0.488678i	0.859440	+	0.511237i	$0.170813\pi$
$68$		−	6.00000i		−	0.727607i
$69$	2.00000	+	3.46410i	0.240772	+	0.417029i
$70$	−2.23205	+	0.133975i	−0.266781	+	0.0160130i
$71$	1.50000	+	2.59808i	0.178017	+	0.308335i	0.941201	−	0.337846i	$-0.109698\pi$
$71$	1.50000	+	2.59808i	0.178017	+	0.308335i	−0.763184	+	0.646181i	$0.776365\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	16.0000i		−	1.87266i	−0.351123	−	0.936329i	$-0.614200\pi$
$73$		−	16.0000i		−	1.87266i	0.351123	−	0.936329i	$-0.385800\pi$
$74$	−5.50000	−	2.59808i	−0.639362	−	0.302020i
$75$	4.00000	−	3.00000i	0.461880	−	0.346410i
$76$	0.500000	−	0.866025i	0.0573539	−	0.0993399i
$77$	−3.46410	+	2.00000i	−0.394771	+	0.227921i
$78$	2.59808	−	1.50000i	0.294174	−	0.169842i
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	−1.00000	+	2.00000i	−0.111803	+	0.223607i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			8.00000i			0.883452i
$83$	−14.7224	−	8.50000i	−1.61600	−	0.932996i	−0.987942	−	0.154828i	$-0.950518\pi$
$83$	−14.7224	−	8.50000i	−1.61600	−	0.932996i	−0.628055	−	0.778169i	$-0.716149\pi$
$84$	−1.00000			−0.109109
$85$	−12.0000	−	6.00000i	−1.30158	−	0.650791i
$86$	−3.00000	+	5.19615i	−0.323498	+	0.560316i
$87$	4.33013	−	2.50000i	0.464238	−	0.268028i
$88$			4.00000i			0.426401i
$89$	−2.00000	+	3.46410i	−0.212000	+	0.367194i	−0.952340	−	0.305038i	$-0.901331\pi$
$89$	−2.00000	+	3.46410i	−0.212000	+	0.367194i	0.740341	+	0.672232i	$0.234664\pi$
$90$	1.86603	−	1.23205i	0.196696	−	0.129870i
$91$	−1.50000	+	2.59808i	−0.157243	+	0.272352i
$92$	−3.46410	+	2.00000i	−0.361158	+	0.208514i
$93$	−5.19615	+	3.00000i	−0.538816	+	0.311086i
$94$	6.00000	−	10.3923i	0.618853	−	1.07188i
$95$	−1.23205	−	1.86603i	−0.126406	−	0.191450i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$		−	12.0000i		−	1.21842i	−0.793011	−	0.609208i	$-0.791488\pi$
$97$		−	12.0000i		−	1.21842i	0.793011	−	0.609208i	$-0.208512\pi$
$98$	−5.19615	+	3.00000i	−0.524891	+	0.303046i
$99$	2.00000	−	3.46410i	0.201008	−	0.348155i
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$	−18.0000			−1.79107			−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000			−1.79107			−0.895533	+	0.444994i	$0.853206\pi$
$102$	−5.19615	−	3.00000i	−0.514496	−	0.297044i
$103$			13.0000i			1.28093i	0.767988	+	0.640464i	$0.221258\pi$
$103$			13.0000i			1.28093i	−0.767988	+	0.640464i	$0.778742\pi$
$104$	1.50000	+	2.59808i	0.147087	+	0.254762i
$105$	−1.00000	+	2.00000i	−0.0975900	+	0.195180i
$106$	2.00000	+	3.46410i	0.194257	+	0.336463i
$107$	−17.3205	+	10.0000i	−1.67444	+	0.966736i	−0.709331	+	0.704875i	$0.751003\pi$
$107$	−17.3205	+	10.0000i	−1.67444	+	0.966736i	−0.965106	+	0.261861i	$0.915664\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	7.00000	−	12.1244i	0.670478	−	1.16130i	−0.307290	−	0.951616i	$-0.599422\pi$
$109$	7.00000	−	12.1244i	0.670478	−	1.16130i	0.977769	−	0.209687i	$-0.0672444\pi$
$110$	8.00000	+	4.00000i	0.762770	+	0.381385i
$111$	−5.00000	+	3.46410i	−0.474579	+	0.328798i
$112$		−	1.00000i		−	0.0944911i
$113$	2.59808	+	1.50000i	0.244406	+	0.141108i	0.617200	−	0.786806i	$-0.288267\pi$
$113$	2.59808	+	1.50000i	0.244406	+	0.141108i	−0.372794	+	0.927914i	$0.621600\pi$
$114$	−0.500000	−	0.866025i	−0.0468293	−	0.0811107i
$115$	0.535898	+	8.92820i	0.0499728	+	0.832559i
$116$	2.50000	+	4.33013i	0.232119	+	0.402042i
$117$		−	3.00000i		−	0.277350i
$118$	−3.46410	+	2.00000i	−0.318896	+	0.184115i
$119$	6.00000			0.550019
$120$	1.23205	+	1.86603i	0.112470	+	0.170344i
$121$	5.00000			0.454545
$122$		0			0
$123$	6.92820	+	4.00000i	0.624695	+	0.360668i
$124$	−3.00000	−	5.19615i	−0.269408	−	0.466628i
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$	−0.500000	+	0.866025i	−0.0445435	+	0.0771517i
$127$	−0.866025	−	0.500000i	−0.0768473	−	0.0443678i	0.461084	−	0.887357i	$-0.347461\pi$
$127$	−0.866025	−	0.500000i	−0.0768473	−	0.0443678i	−0.537931	+	0.842989i	$0.680794\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	3.00000	+	5.19615i	0.264135	+	0.457496i
$130$	6.69615	−	0.401924i	0.587291	−	0.0352510i
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$	3.46410	+	2.00000i	0.301511	+	0.174078i
$133$	0.866025	+	0.500000i	0.0750939	+	0.0433555i
$134$	8.00000			0.691095
$135$	−0.133975	−	2.23205i	−0.0115307	−	0.192104i
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$		−	15.0000i		−	1.28154i	−0.767734	−	0.640768i	$-0.778616\pi$
$137$		−	15.0000i		−	1.28154i	0.767734	−	0.640768i	$-0.221384\pi$
$138$			4.00000i			0.340503i
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$	−2.00000	−	1.00000i	−0.169031	−	0.0845154i
$141$	−6.00000	−	10.3923i	−0.505291	−	0.875190i
$142$			3.00000i			0.251754i
$143$	10.3923	−	6.00000i	0.869048	−	0.501745i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	11.1603	−	0.669873i	0.926809	−	0.0556299i
$146$	8.00000	−	13.8564i	0.662085	−	1.14676i
$147$			6.00000i			0.494872i
$148$	−3.46410	−	5.00000i	−0.284747	−	0.410997i
$149$	−19.0000			−1.55654			−0.778270	−	0.627929i	$-0.783903\pi$
$149$	−19.0000			−1.55654			−0.778270	+	0.627929i	$0.783903\pi$
$150$	4.96410	−	0.598076i	0.405317	−	0.0488327i
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$	0.866025	−	0.500000i	0.0702439	−	0.0405554i
$153$	−5.19615	+	3.00000i	−0.420084	+	0.242536i
$154$	−4.00000			−0.322329
$155$	−13.3923	+	0.803848i	−1.07570	+	0.0645666i
$156$	3.00000			0.240192
$157$	11.2583	+	6.50000i	0.898513	+	0.518756i	0.876717	−	0.481006i	$-0.159728\pi$
$157$	11.2583	+	6.50000i	0.898513	+	0.518756i	0.0217953	+	0.999762i	$0.493062\pi$
$158$			10.0000i			0.795557i
$159$	4.00000			0.317221
$160$	−1.86603	+	1.23205i	−0.147522	+	0.0974022i
$161$	−2.00000	−	3.46410i	−0.157622	−	0.273009i
$162$		−	1.00000i		−	0.0785674i
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	0.629492	−	0.777007i	$-0.283263\pi$
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	−0.358162	+	0.933659i	$0.616597\pi$
$164$	−4.00000	+	6.92820i	−0.312348	+	0.541002i
$165$	7.46410	−	4.92820i	0.581080	−	0.383660i
$166$	−8.50000	−	14.7224i	−0.659728	−	1.14268i
$167$	−13.8564	+	8.00000i	−1.07224	+	0.619059i	−0.928793	−	0.370599i	$-0.879152\pi$
$167$	−13.8564	+	8.00000i	−1.07224	+	0.619059i	−0.143448	+	0.989658i	$0.545819\pi$
$168$	−0.866025	−	0.500000i	−0.0668153	−	0.0385758i
$169$	−2.00000	+	3.46410i	−0.153846	+	0.266469i
$170$	−7.39230	−	11.1962i	−0.566964	−	0.858706i
$171$	−1.00000			−0.0764719
$172$	−5.19615	+	3.00000i	−0.396203	+	0.228748i
$173$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$173$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$174$	5.00000			0.379049
$175$	−4.00000	+	3.00000i	−0.302372	+	0.226779i
$176$	−2.00000	+	3.46410i	−0.150756	+	0.261116i
$177$			4.00000i			0.300658i
$178$	−3.46410	+	2.00000i	−0.259645	+	0.149906i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	2.23205	−	0.133975i	0.166367	−	0.00998588i
$181$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$181$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$182$	−2.59808	+	1.50000i	−0.192582	+	0.111187i
$183$		0			0
$184$	−4.00000			−0.294884
$185$	−13.4641	+	1.92820i	−0.989900	+	0.141764i
$186$	−6.00000			−0.439941
$187$	−20.7846	−	12.0000i	−1.51992	−	0.877527i
$188$	10.3923	−	6.00000i	0.757937	−	0.437595i
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$	−0.133975	−	2.23205i	−0.00971954	−	0.161930i
$191$	−12.0000			−0.868290			−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000			−0.868290			−0.434145	+	0.900843i	$0.642949\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$		−	2.00000i		−	0.143963i	−0.997406	−	0.0719816i	$-0.977068\pi$
$193$		−	2.00000i		−	0.143963i	0.997406	−	0.0719816i	$-0.0229323\pi$
$194$	6.00000	−	10.3923i	0.430775	−	0.746124i
$195$	3.00000	−	6.00000i	0.214834	−	0.429669i
$196$	−6.00000			−0.428571
$197$	−5.19615	−	3.00000i	−0.370211	−	0.213741i	0.303340	−	0.952882i	$-0.401898\pi$
$197$	−5.19615	−	3.00000i	−0.370211	−	0.213741i	−0.673550	+	0.739141i	$0.735232\pi$
$198$	3.46410	−	2.00000i	0.246183	−	0.142134i
$199$	2.00000			0.141776			0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000			0.141776			0.0708881	+	0.997484i	$0.477417\pi$
$200$	0.598076	+	4.96410i	0.0422904	+	0.351015i
$201$	4.00000	−	6.92820i	0.282138	−	0.488678i
$202$	−15.5885	−	9.00000i	−1.09680	−	0.633238i
$203$	−4.33013	+	2.50000i	−0.303915	+	0.175466i
$204$	−3.00000	−	5.19615i	−0.210042	−	0.363803i
$205$	9.85641	+	14.9282i	0.688401	+	1.04263i
$206$	−6.50000	+	11.2583i	−0.452876	+	0.784405i
$207$	3.46410	+	2.00000i	0.240772	+	0.139010i
$208$			3.00000i			0.208013i
$209$	−2.00000	−	3.46410i	−0.138343	−	0.239617i
$210$	−1.86603	+	1.23205i	−0.128768	+	0.0850196i
$211$	15.0000			1.03264			0.516321	−	0.856395i	$-0.327301\pi$
$211$	15.0000			1.03264			0.516321	+	0.856395i	$0.327301\pi$
$212$			4.00000i			0.274721i
$213$	2.59808	+	1.50000i	0.178017	+	0.102778i
$214$	−20.0000			−1.36717
$215$	0.803848	+	13.3923i	0.0548219	+	0.913348i
$216$	1.00000			0.0680414
$217$	5.19615	−	3.00000i	0.352738	−	0.203653i
$218$	12.1244	−	7.00000i	0.821165	−	0.474100i
$219$	−8.00000	−	13.8564i	−0.540590	−	0.936329i
$220$	4.92820	+	7.46410i	0.332259	+	0.503230i
$221$	−18.0000			−1.21081
$222$	−6.06218	+	0.500000i	−0.406867	+	0.0335578i
$223$			16.0000i			1.07144i	0.844396	+	0.535720i	$0.179960\pi$
$223$			16.0000i			1.07144i	−0.844396	+	0.535720i	$0.820040\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	1.96410	−	4.59808i	0.130940	−	0.306538i
$226$	1.50000	+	2.59808i	0.0997785	+	0.172821i
$227$	−23.3827	+	13.5000i	−1.55196	+	0.896026i	−0.553981	+	0.832529i	$0.686892\pi$
$227$	−23.3827	+	13.5000i	−1.55196	+	0.896026i	−0.997982	+	0.0634974i	$0.979775\pi$
$228$		−	1.00000i		−	0.0662266i
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	0.231287	−	0.972886i	$-0.425707\pi$
$230$	−4.00000	+	8.00000i	−0.263752	+	0.527504i
$231$	−2.00000	+	3.46410i	−0.131590	+	0.227921i
$232$			5.00000i			0.328266i
$233$		−	21.0000i		−	1.37576i	−0.725826	−	0.687878i	$-0.758542\pi$
$233$		−	21.0000i		−	1.37576i	0.725826	−	0.687878i	$-0.241458\pi$
$234$	1.50000	−	2.59808i	0.0980581	−	0.169842i
$235$	−1.60770	−	26.7846i	−0.104874	−	1.74724i
$236$	−4.00000			−0.260378
$237$	8.66025	+	5.00000i	0.562544	+	0.324785i
$238$	5.19615	+	3.00000i	0.336817	+	0.194461i
$239$	8.50000	−	14.7224i	0.549819	−	0.952315i	−0.448467	−	0.893799i	$-0.648030\pi$
$239$	8.50000	−	14.7224i	0.549819	−	0.952315i	0.998286	−	0.0585157i	$-0.0186368\pi$
$240$	0.133975	+	2.23205i	0.00864802	+	0.144078i
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	4.33013	+	2.50000i	0.278351	+	0.160706i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−6.00000	+	12.0000i	−0.383326	+	0.766652i
$246$	4.00000	+	6.92820i	0.255031	+	0.441726i
$247$	−2.59808	−	1.50000i	−0.165312	−	0.0954427i
$248$		−	6.00000i		−	0.381000i
$249$	−17.0000			−1.07733
$250$	10.5263	+	3.76795i	0.665740	+	0.238306i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$	−0.866025	+	0.500000i	−0.0545545	+	0.0314970i
$253$			16.0000i			1.00591i
$254$	−0.500000	−	0.866025i	−0.0313728	−	0.0543393i
$255$	−13.3923	+	0.803848i	−0.838659	+	0.0503389i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.52628	−	5.50000i	−0.594233	−	0.343081i	0.172536	−	0.985003i	$-0.444804\pi$
$257$	−9.52628	−	5.50000i	−0.594233	−	0.343081i	−0.766769	+	0.641923i	$0.778137\pi$
$258$			6.00000i			0.373544i
$259$	5.00000	−	3.46410i	0.310685	−	0.215249i
$260$	6.00000	+	3.00000i	0.372104	+	0.186052i
$261$	2.50000	−	4.33013i	0.154746	−	0.268028i
$262$		0			0
$263$	22.5167	−	13.0000i	1.38844	−	0.801614i	0.395298	−	0.918553i	$-0.370641\pi$
$263$	22.5167	−	13.0000i	1.38844	−	0.801614i	0.993139	+	0.116939i	$0.0373081\pi$
$264$	2.00000	+	3.46410i	0.123091	+	0.213201i
$265$	8.00000	+	4.00000i	0.491436	+	0.245718i
$266$	0.500000	+	0.866025i	0.0306570	+	0.0530994i
$267$			4.00000i			0.244796i
$268$	6.92820	+	4.00000i	0.423207	+	0.244339i
$269$	−5.00000			−0.304855			−0.152428	−	0.988315i	$-0.548709\pi$
$269$	−5.00000			−0.304855			−0.152428	+	0.988315i	$0.548709\pi$
$270$	1.00000	−	2.00000i	0.0608581	−	0.121716i
$271$	7.00000	−	12.1244i	0.425220	−	0.736502i	−0.571221	−	0.820796i	$-0.693530\pi$
$271$	7.00000	−	12.1244i	0.425220	−	0.736502i	0.996441	+	0.0842940i	$0.0268635\pi$
$272$	5.19615	−	3.00000i	0.315063	−	0.181902i
$273$			3.00000i			0.181568i
$274$	7.50000	−	12.9904i	0.453092	−	0.784778i
$275$	19.8564	−	2.39230i	1.19739	−	0.144261i
$276$	−2.00000	+	3.46410i	−0.120386	+	0.208514i
$277$	−14.7224	+	8.50000i	−0.884585	+	0.510716i	−0.872167	−	0.489207i	$-0.837286\pi$
$277$	−14.7224	+	8.50000i	−0.884585	+	0.510716i	−0.0124177	+	0.999923i	$0.503953\pi$
$278$	−3.46410	+	2.00000i	−0.207763	+	0.119952i
$279$	−3.00000	+	5.19615i	−0.179605	+	0.311086i
$280$	−1.23205	−	1.86603i	−0.0736291	−	0.111516i
$281$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$281$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$282$		−	12.0000i		−	0.714590i
$283$	13.8564	−	8.00000i	0.823678	−	0.475551i	−0.0280052	−	0.999608i	$-0.508916\pi$
$283$	13.8564	−	8.00000i	0.823678	−	0.475551i	0.851683	+	0.524057i	$0.175582\pi$
$284$	−1.50000	+	2.59808i	−0.0890086	+	0.154167i
$285$	−2.00000	−	1.00000i	−0.118470	−	0.0592349i
$286$	12.0000			0.709575
$287$	−6.92820	−	4.00000i	−0.408959	−	0.236113i
$288$			1.00000i			0.0589256i
$289$	9.50000	+	16.4545i	0.558824	+	0.967911i
$290$	10.0000	+	5.00000i	0.587220	+	0.293610i
$291$	−6.00000	−	10.3923i	−0.351726	−	0.609208i
$292$	13.8564	−	8.00000i	0.810885	−	0.468165i
$293$	1.73205	−	1.00000i	0.101187	−	0.0584206i	−0.448552	−	0.893757i	$-0.648060\pi$
$293$	1.73205	−	1.00000i	0.101187	−	0.0584206i	0.549740	+	0.835336i	$0.314727\pi$
$294$	−3.00000	+	5.19615i	−0.174964	+	0.303046i
$295$	−4.00000	+	8.00000i	−0.232889	+	0.465778i
$296$	−0.500000	−	6.06218i	−0.0290619	−	0.352357i
$297$		−	4.00000i		−	0.232104i
$298$	−16.4545	−	9.50000i	−0.953183	−	0.550320i
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$	4.59808	+	1.96410i	0.265470	+	0.113397i
$301$	−3.00000	−	5.19615i	−0.172917	−	0.299501i
$302$			16.0000i			0.920697i
$303$	−15.5885	+	9.00000i	−0.895533	+	0.517036i
$304$	1.00000			0.0573539
$305$		0			0
$306$	−6.00000			−0.342997
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$	−3.46410	−	2.00000i	−0.197386	−	0.113961i
$309$	6.50000	+	11.2583i	0.369772	+	0.640464i
$310$	−12.0000	−	6.00000i	−0.681554	−	0.340777i
$311$	2.00000	−	3.46410i	0.113410	−	0.196431i	−0.803733	−	0.594990i	$-0.797156\pi$
$311$	2.00000	−	3.46410i	0.113410	−	0.196431i	0.917143	+	0.398559i	$0.130489\pi$
$312$	2.59808	+	1.50000i	0.147087	+	0.0849208i
$313$	3.46410	+	2.00000i	0.195803	+	0.113047i	0.594696	−	0.803951i	$-0.297272\pi$
$313$	3.46410	+	2.00000i	0.195803	+	0.113047i	−0.398894	+	0.916997i	$0.630606\pi$
$314$	6.50000	+	11.2583i	0.366816	+	0.635344i
$315$	0.133975	+	2.23205i	0.00754861	+	0.125762i
$316$	−5.00000	+	8.66025i	−0.281272	+	0.487177i
$317$	−6.92820	−	4.00000i	−0.389127	−	0.224662i	0.292655	−	0.956218i	$-0.405461\pi$
$317$	−6.92820	−	4.00000i	−0.389127	−	0.224662i	−0.681782	+	0.731556i	$0.738795\pi$
$318$	3.46410	+	2.00000i	0.194257	+	0.112154i
$319$	20.0000			1.11979
$320$	−2.23205	+	0.133975i	−0.124775	+	0.00748941i
$321$	−10.0000	+	17.3205i	−0.558146	+	0.966736i
$322$		−	4.00000i		−	0.222911i
$323$			6.00000i			0.333849i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	12.0000	−	9.00000i	0.665640	−	0.499230i
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$		−	14.0000i		−	0.774202i
$328$	−6.92820	+	4.00000i	−0.382546	+	0.220863i
$329$	6.00000	+	10.3923i	0.330791	+	0.572946i
$330$	8.92820	−	0.535898i	0.491481	−	0.0295002i
$331$	2.50000	−	4.33013i	0.137412	−	0.238005i	−0.789104	−	0.614260i	$-0.789455\pi$
$331$	2.50000	−	4.33013i	0.137412	−	0.238005i	0.926516	+	0.376254i	$0.122788\pi$
$332$		−	17.0000i		−	0.932996i
$333$	−2.59808	+	5.50000i	−0.142374	+	0.301398i
$334$	−16.0000			−0.875481
$335$	14.9282	−	9.85641i	0.815615	−	0.538513i
$336$	−0.500000	−	0.866025i	−0.0272772	−	0.0472456i
$337$	−19.0526	+	11.0000i	−1.03786	+	0.599208i	−0.919226	−	0.393730i	$-0.871184\pi$
$337$	−19.0526	+	11.0000i	−1.03786	+	0.599208i	−0.118633	+	0.992938i	$0.537851\pi$
$338$	−3.46410	+	2.00000i	−0.188422	+	0.108786i
$339$	3.00000			0.162938
$340$	−0.803848	−	13.3923i	−0.0435948	−	0.726300i
$341$	−24.0000			−1.29967
$342$	−0.866025	−	0.500000i	−0.0468293	−	0.0270369i
$343$		−	13.0000i		−	0.701934i
$344$	−6.00000			−0.323498
$345$	4.92820	+	7.46410i	0.265326	+	0.401854i
$346$		0			0
$347$			19.0000i			1.01997i	0.860182	+	0.509987i	$0.170350\pi$
$347$			19.0000i			1.01997i	−0.860182	+	0.509987i	$0.829650\pi$
$348$	4.33013	+	2.50000i	0.232119	+	0.134014i
$349$	7.00000	−	12.1244i	0.374701	−	0.649002i	−0.615581	−	0.788074i	$-0.711079\pi$
$349$	7.00000	−	12.1244i	0.374701	−	0.649002i	0.990282	+	0.139072i	$0.0444119\pi$
$350$	−4.96410	+	0.598076i	−0.265342	+	0.0319685i
$351$	−1.50000	−	2.59808i	−0.0800641	−	0.138675i
$352$	−3.46410	+	2.00000i	−0.184637	+	0.106600i
$353$	21.6506	+	12.5000i	1.15235	+	0.665308i	0.949458	−	0.313894i	$-0.101634\pi$
$353$	21.6506	+	12.5000i	1.15235	+	0.665308i	0.202889	+	0.979202i	$0.434967\pi$
$354$	−2.00000	+	3.46410i	−0.106299	+	0.184115i
$355$	3.69615	+	5.59808i	0.196171	+	0.297115i
$356$	−4.00000			−0.212000
$357$	5.19615	−	3.00000i	0.275010	−	0.158777i
$358$		0			0
$359$	27.0000			1.42501			0.712503	−	0.701669i	$-0.247562\pi$
$359$	27.0000			1.42501			0.712503	+	0.701669i	$0.247562\pi$
$360$	2.00000	+	1.00000i	0.105409	+	0.0527046i
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$	4.33013	−	2.50000i	0.227273	−	0.131216i
$364$	−3.00000			−0.157243
$365$	−2.14359	−	35.7128i	−0.112201	−	1.86929i
$366$		0			0
$367$	−16.4545	+	9.50000i	−0.858917	+	0.495896i	−0.863649	−	0.504093i	$-0.831827\pi$
$367$	−16.4545	+	9.50000i	−0.858917	+	0.495896i	0.00473247	+	0.999989i	$0.498494\pi$
$368$	−3.46410	−	2.00000i	−0.180579	−	0.104257i
$369$	8.00000			0.416463
$370$	−12.6244	−	5.06218i	−0.656309	−	0.263170i
$371$	−4.00000			−0.207670
$372$	−5.19615	−	3.00000i	−0.269408	−	0.155543i
$373$	25.1147	−	14.5000i	1.30039	−	0.750782i	0.319921	−	0.947444i	$-0.396344\pi$
$373$	25.1147	−	14.5000i	1.30039	−	0.750782i	0.980471	+	0.196663i	$0.0630104\pi$
$374$	−12.0000	−	20.7846i	−0.620505	−	1.07475i
$375$	8.52628	−	7.23205i	0.440295	−	0.373461i
$376$	12.0000			0.618853
$377$	12.9904	−	7.50000i	0.669039	−	0.386270i
$378$			1.00000i			0.0514344i
$379$	−14.5000	+	25.1147i	−0.744815	+	1.29006i	0.205466	+	0.978664i	$0.434129\pi$
$379$	−14.5000	+	25.1147i	−0.744815	+	1.29006i	−0.950281	+	0.311393i	$0.899204\pi$
$380$	1.00000	−	2.00000i	0.0512989	−	0.102598i
$381$	−1.00000			−0.0512316
$382$	−10.3923	−	6.00000i	−0.531717	−	0.306987i
$383$	−5.19615	+	3.00000i	−0.265511	+	0.153293i	−0.626846	−	0.779143i	$-0.715654\pi$
$383$	−5.19615	+	3.00000i	−0.265511	+	0.153293i	0.361335	+	0.932436i	$0.382321\pi$
$384$	−1.00000			−0.0510310
$385$	−7.46410	+	4.92820i	−0.380406	+	0.251164i
$386$	1.00000	−	1.73205i	0.0508987	−	0.0881591i
$387$	5.19615	+	3.00000i	0.264135	+	0.152499i
$388$	10.3923	−	6.00000i	0.527589	−	0.304604i
$389$	13.5000	+	23.3827i	0.684477	+	1.18555i	0.973601	+	0.228257i	$0.0733028\pi$
$389$	13.5000	+	23.3827i	0.684477	+	1.18555i	−0.289124	+	0.957292i	$0.593364\pi$
$390$	5.59808	−	3.69615i	0.283470	−	0.187162i
$391$	12.0000	−	20.7846i	0.606866	−	1.05112i
$392$	−5.19615	−	3.00000i	−0.262445	−	0.151523i
$393$		0			0
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$	12.3205	+	18.6603i	0.619912	+	0.938899i
$396$	4.00000			0.201008
$397$			6.00000i			0.301131i	0.988600	+	0.150566i	$0.0481095\pi$
$397$			6.00000i			0.301131i	−0.988600	+	0.150566i	$0.951890\pi$
$398$	1.73205	+	1.00000i	0.0868199	+	0.0501255i
$399$	1.00000			0.0500626
$400$	−1.96410	+	4.59808i	−0.0982051	+	0.229904i
$401$	2.00000			0.0998752			0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000			0.0998752			0.0499376	+	0.998752i	$0.484098\pi$
$402$	6.92820	−	4.00000i	0.345547	−	0.199502i
$403$	−15.5885	+	9.00000i	−0.776516	+	0.448322i
$404$	−9.00000	−	15.5885i	−0.447767	−	0.775555i
$405$	−1.23205	−	1.86603i	−0.0612211	−	0.0927235i
$406$	−5.00000			−0.248146
$407$	−24.2487	+	2.00000i	−1.20196	+	0.0991363i
$408$		−	6.00000i		−	0.297044i
$409$	5.50000	−	9.52628i	0.271957	−	0.471044i	−0.697406	−	0.716677i	$-0.745662\pi$
$409$	5.50000	−	9.52628i	0.271957	−	0.471044i	0.969363	+	0.245633i	$0.0789957\pi$
$410$	1.07180	+	17.8564i	0.0529323	+	0.881865i
$411$	−7.50000	−	12.9904i	−0.369948	−	0.640768i
$412$	−11.2583	+	6.50000i	−0.554658	+	0.320232i
$413$		−	4.00000i		−	0.196827i
$414$	2.00000	+	3.46410i	0.0982946	+	0.170251i
$415$	−34.0000	−	17.0000i	−1.66899	−	0.834497i
$416$	−1.50000	+	2.59808i	−0.0735436	+	0.127381i
$417$			4.00000i			0.195881i
$418$		−	4.00000i		−	0.195646i
$419$	−12.0000	+	20.7846i	−0.586238	+	1.01539i	0.408481	+	0.912767i	$0.366058\pi$
$419$	−12.0000	+	20.7846i	−0.586238	+	1.01539i	−0.994720	+	0.102628i	$0.967275\pi$
$420$	−2.23205	+	0.133975i	−0.108913	+	0.00653729i
$421$	34.0000			1.65706			0.828529	−	0.559946i	$-0.189178\pi$
$421$	34.0000			1.65706			0.828529	+	0.559946i	$0.189178\pi$
$422$	12.9904	+	7.50000i	0.632362	+	0.365094i
$423$	−10.3923	−	6.00000i	−0.505291	−	0.291730i
$424$	−2.00000	+	3.46410i	−0.0971286	+	0.168232i
$425$	−27.5885	−	11.7846i	−1.33824	−	0.571638i
$426$	1.50000	+	2.59808i	0.0726752	+	0.125877i
$427$		0			0
$428$	−17.3205	−	10.0000i	−0.837218	−	0.483368i
$429$	6.00000	−	10.3923i	0.289683	−	0.501745i
$430$	−6.00000	+	12.0000i	−0.289346	+	0.578691i
$431$	−1.50000	−	2.59808i	−0.0722525	−	0.125145i	0.827636	−	0.561266i	$-0.189685\pi$
$431$	−1.50000	−	2.59808i	−0.0722525	−	0.125145i	−0.899888	+	0.436121i	$0.856352\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$			14.0000i			0.672797i	0.941720	+	0.336399i	$0.109209\pi$
$433$			14.0000i			0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$	6.00000			0.288009
$435$	9.33013	−	6.16025i	0.447345	−	0.295362i
$436$	14.0000			0.670478
$437$	3.46410	−	2.00000i	0.165710	−	0.0956730i
$438$		−	16.0000i		−	0.764510i
$439$	17.0000	+	29.4449i	0.811366	+	1.40533i	0.911908	+	0.410394i	$0.134609\pi$
$439$	17.0000	+	29.4449i	0.811366	+	1.40533i	−0.100543	+	0.994933i	$0.532058\pi$
$440$	0.535898	+	8.92820i	0.0255480	+	0.425635i
$441$	3.00000	+	5.19615i	0.142857	+	0.247436i
$442$	−15.5885	−	9.00000i	−0.741467	−	0.428086i
$443$			7.00000i			0.332580i	0.986077	+	0.166290i	$0.0531788\pi$
$443$			7.00000i			0.332580i	−0.986077	+	0.166290i	$0.946821\pi$
$444$	−5.50000	−	2.59808i	−0.261018	−	0.123299i
$445$	−4.00000	+	8.00000i	−0.189618	+	0.379236i
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$	−16.4545	+	9.50000i	−0.778270	+	0.449335i
$448$	0.866025	−	0.500000i	0.0409159	−	0.0236228i
$449$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$449$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$450$	4.00000	−	3.00000i	0.188562	−	0.141421i
$451$	16.0000	+	27.7128i	0.753411	+	1.30495i
$452$			3.00000i			0.141108i
$453$	13.8564	+	8.00000i	0.651031	+	0.375873i
$454$	−27.0000			−1.26717
$455$	−3.00000	+	6.00000i	−0.140642	+	0.281284i
$456$	0.500000	−	0.866025i	0.0234146	−	0.0405554i
$457$	29.4449	−	17.0000i	1.37737	−	0.795226i	0.385530	−	0.922695i	$-0.374019\pi$
$457$	29.4449	−	17.0000i	1.37737	−	0.795226i	0.991843	+	0.127469i	$0.0406853\pi$
$458$		−	22.0000i		−	1.02799i
$459$	−3.00000	+	5.19615i	−0.140028	+	0.242536i
$460$	−7.46410	+	4.92820i	−0.348016	+	0.229779i
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	−0.741998	−	0.670402i	$-0.766122\pi$
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	0.951584	+	0.307388i	$0.0994551\pi$
$462$	−3.46410	+	2.00000i	−0.161165	+	0.0930484i
$463$	25.1147	−	14.5000i	1.16718	−	0.673872i	0.214166	−	0.976797i	$-0.431297\pi$
$463$	25.1147	−	14.5000i	1.16718	−	0.673872i	0.953014	+	0.302925i	$0.0979632\pi$
$464$	−2.50000	+	4.33013i	−0.116060	+	0.201021i
$465$	−11.1962	+	7.39230i	−0.519209	+	0.342810i
$466$	10.5000	−	18.1865i	0.486403	−	0.842475i
$467$		−	13.0000i		−	0.601568i	−0.953692	−	0.300784i	$-0.902752\pi$
$467$		−	13.0000i		−	0.601568i	0.953692	−	0.300784i	$-0.0972484\pi$
$468$	2.59808	−	1.50000i	0.120096	−	0.0693375i
$469$	−4.00000	+	6.92820i	−0.184703	+	0.319915i
$470$	12.0000	−	24.0000i	0.553519	−	1.10704i
$471$	13.0000			0.599008
$472$	−3.46410	−	2.00000i	−0.159448	−	0.0920575i
$473$			24.0000i			1.10352i
$474$	5.00000	+	8.66025i	0.229658	+	0.397779i
$475$	−3.00000	−	4.00000i	−0.137649	−	0.183533i
$476$	3.00000	+	5.19615i	0.137505	+	0.238165i
$477$	3.46410	−	2.00000i	0.158610	−	0.0915737i
$478$	14.7224	−	8.50000i	0.673388	−	0.388781i
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$	−1.00000	+	2.00000i	−0.0456435	+	0.0912871i
$481$	−15.0000	+	10.3923i	−0.683941	+	0.473848i
$482$		−	14.0000i		−	0.637683i
$483$	−3.46410	−	2.00000i	−0.157622	−	0.0910032i
$484$	2.50000	+	4.33013i	0.113636	+	0.196824i
$485$	−1.60770	−	26.7846i	−0.0730017	−	1.21623i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$			17.0000i			0.770344i	0.922845	+	0.385172i	$0.125858\pi$
$487$			17.0000i			0.770344i	−0.922845	+	0.385172i	$0.874142\pi$
$488$		0			0
$489$	4.00000			0.180886
$490$	−11.1962	+	7.39230i	−0.505791	+	0.333950i
$491$	26.0000			1.17336			0.586682	−	0.809818i	$-0.300434\pi$
$491$	26.0000			1.17336			0.586682	+	0.809818i	$0.300434\pi$
$492$			8.00000i			0.360668i
$493$	−25.9808	−	15.0000i	−1.17011	−	0.675566i
$494$	−1.50000	−	2.59808i	−0.0674882	−	0.116893i
$495$	4.00000	−	8.00000i	0.179787	−	0.359573i
$496$	3.00000	−	5.19615i	0.134704	−	0.233314i
$497$	−2.59808	−	1.50000i	−0.116540	−	0.0672842i
$498$	−14.7224	−	8.50000i	−0.659728	−	0.380894i
$499$	4.50000	+	7.79423i	0.201448	+	0.348918i	0.948995	−	0.315291i	$-0.102102\pi$
$499$	4.50000	+	7.79423i	0.201448	+	0.348918i	−0.747547	+	0.664208i	$0.768769\pi$
$500$	7.23205	+	8.52628i	0.323427	+	0.381307i
$501$	−8.00000	+	13.8564i	−0.357414	+	0.619059i
$502$	−10.3923	−	6.00000i	−0.463831	−	0.267793i
$503$	−12.1244	−	7.00000i	−0.540598	−	0.312115i	0.204723	−	0.978820i	$-0.434371\pi$
$503$	−12.1244	−	7.00000i	−0.540598	−	0.312115i	−0.745321	+	0.666705i	$0.767704\pi$
$504$	−1.00000			−0.0445435
$505$	−40.1769	+	2.41154i	−1.78785	+	0.107312i
$506$	−8.00000	+	13.8564i	−0.355643	+	0.615992i
$507$			4.00000i			0.177646i
$508$		−	1.00000i		−	0.0443678i
$509$	19.5000	−	33.7750i	0.864322	−	1.49705i	−0.00339621	−	0.999994i	$-0.501081\pi$
$509$	19.5000	−	33.7750i	0.864322	−	1.49705i	0.867719	−	0.497056i	$-0.165586\pi$
$510$	−12.0000	−	6.00000i	−0.531369	−	0.265684i
$511$	8.00000	+	13.8564i	0.353899	+	0.612971i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.866025	+	0.500000i	−0.0382360	+	0.0220755i
$514$	−5.50000	−	9.52628i	−0.242595	−	0.420186i
$515$	1.74167	+	29.0167i	0.0767471	+	1.27863i
$516$	−3.00000	+	5.19615i	−0.132068	+	0.228748i
$517$		−	48.0000i		−	2.11104i
$518$	6.06218	−	0.500000i	0.266357	−	0.0219687i
$519$		0			0
$520$	3.69615	+	5.59808i	0.162087	+	0.245492i
$521$	15.0000	+	25.9808i	0.657162	+	1.13824i	0.981347	+	0.192244i	$0.0615766\pi$
$521$	15.0000	+	25.9808i	0.657162	+	1.13824i	−0.324185	+	0.945994i	$0.605090\pi$
$522$	4.33013	−	2.50000i	0.189525	−	0.109422i
$523$	−13.8564	+	8.00000i	−0.605898	+	0.349816i	−0.771358	−	0.636401i	$-0.780422\pi$
$523$	−13.8564	+	8.00000i	−0.605898	+	0.349816i	0.165460	+	0.986216i	$0.447089\pi$
$524$		0			0
$525$	−1.96410	+	4.59808i	−0.0857204	+	0.200676i
$526$	26.0000			1.13365
$527$	31.1769	+	18.0000i	1.35809	+	0.784092i
$528$			4.00000i			0.174078i
$529$	7.00000			0.304348
$530$	4.92820	+	7.46410i	0.214067	+	0.324220i
$531$	2.00000	+	3.46410i	0.0867926	+	0.150329i
$532$			1.00000i			0.0433555i
$533$	20.7846	+	12.0000i	0.900281	+	0.519778i
$534$	−2.00000	+	3.46410i	−0.0865485	+	0.149906i
$535$	−37.3205	+	24.6410i	−1.61351	+	1.06532i
$536$	4.00000	+	6.92820i	0.172774	+	0.299253i
$537$		0			0
$538$	−4.33013	−	2.50000i	−0.186685	−	0.107783i
$539$	−12.0000	+	20.7846i	−0.516877	+	0.895257i
$540$	1.86603	−	1.23205i	0.0803009	−	0.0530190i
$541$	46.0000			1.97769			0.988847	−	0.148933i	$-0.0475840\pi$
$541$	46.0000			1.97769			0.988847	+	0.148933i	$0.0475840\pi$
$542$	12.1244	−	7.00000i	0.520786	−	0.300676i
$543$		0			0
$544$	6.00000			0.257248
$545$	14.0000	−	28.0000i	0.599694	−	1.19939i
$546$	−1.50000	+	2.59808i	−0.0641941	+	0.111187i
$547$		−	16.0000i		−	0.684111i	−0.939680	−	0.342055i	$-0.888877\pi$
$547$		−	16.0000i		−	0.684111i	0.939680	−	0.342055i	$-0.111123\pi$
$548$	12.9904	−	7.50000i	0.554922	−	0.320384i
$549$		0			0
$550$	18.3923	+	7.85641i	0.784251	+	0.334998i
$551$	−2.50000	−	4.33013i	−0.106504	−	0.184470i
$552$	−3.46410	+	2.00000i	−0.147442	+	0.0851257i
$553$	−8.66025	−	5.00000i	−0.368271	−	0.212622i
$554$	−17.0000			−0.722261
$555$	−10.6962	+	8.40192i	−0.454026	+	0.356642i
$556$	−4.00000			−0.169638
$557$	27.7128	+	16.0000i	1.17423	+	0.677942i	0.954673	−	0.297658i	$-0.0962055\pi$
$557$	27.7128	+	16.0000i	1.17423	+	0.677942i	0.219557	+	0.975600i	$0.429539\pi$
$558$	−5.19615	+	3.00000i	−0.219971	+	0.127000i
$559$	9.00000	+	15.5885i	0.380659	+	0.659321i
$560$	−0.133975	−	2.23205i	−0.00566146	−	0.0943214i
$561$	−24.0000			−1.01328
$562$		0			0
$563$		−	5.00000i		−	0.210725i	−0.994434	−	0.105362i	$-0.966400\pi$
$563$		−	5.00000i		−	0.210725i	0.994434	−	0.105362i	$-0.0336003\pi$
$564$	6.00000	−	10.3923i	0.252646	−	0.437595i
$565$	6.00000	+	3.00000i	0.252422	+	0.126211i
$566$	16.0000			0.672530
$567$	0.866025	+	0.500000i	0.0363696	+	0.0209980i
$568$	−2.59808	+	1.50000i	−0.109013	+	0.0629386i
$569$	−14.0000			−0.586911			−0.293455	−	0.955973i	$-0.594805\pi$
$569$	−14.0000			−0.586911			−0.293455	+	0.955973i	$0.594805\pi$
$570$	−1.23205	−	1.86603i	−0.0516049	−	0.0781592i
$571$	15.5000	−	26.8468i	0.648655	−	1.12350i	−0.334790	−	0.942293i	$-0.608665\pi$
$571$	15.5000	−	26.8468i	0.648655	−	1.12350i	0.983444	−	0.181210i	$-0.0580014\pi$
$572$	10.3923	+	6.00000i	0.434524	+	0.250873i
$573$	−10.3923	+	6.00000i	−0.434145	+	0.250654i
$574$	−4.00000	−	6.92820i	−0.166957	−	0.289178i
$575$	2.39230	+	19.8564i	0.0997660	+	0.828069i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	17.3205	+	10.0000i	0.721062	+	0.416305i	0.815144	−	0.579259i	$-0.196658\pi$
$577$	17.3205	+	10.0000i	0.721062	+	0.416305i	−0.0940813	+	0.995565i	$0.529991\pi$
$578$			19.0000i			0.790296i
$579$	−1.00000	−	1.73205i	−0.0415586	−	0.0719816i
$580$	6.16025	+	9.33013i	0.255791	+	0.387412i
$581$	17.0000			0.705279
$582$		−	12.0000i		−	0.497416i
$583$	13.8564	+	8.00000i	0.573874	+	0.331326i
$584$	16.0000			0.662085
$585$	−0.401924	−	6.69615i	−0.0166175	−	0.276852i
$586$	2.00000			0.0826192
$587$	−28.5788	+	16.5000i	−1.17957	+	0.681028i	−0.955916	−	0.293640i	$-0.905133\pi$
$587$	−28.5788	+	16.5000i	−1.17957	+	0.681028i	−0.223659	+	0.974668i	$0.571800\pi$
$588$	−5.19615	+	3.00000i	−0.214286	+	0.123718i
$589$	3.00000	+	5.19615i	0.123613	+	0.214104i
$590$	−7.46410	+	4.92820i	−0.307292	+	0.202891i
$591$	−6.00000			−0.246807
$592$	2.59808	−	5.50000i	0.106780	−	0.226049i
$593$			42.0000i			1.72473i	0.506284	+	0.862367i	$0.331019\pi$
$593$			42.0000i			1.72473i	−0.506284	+	0.862367i	$0.668981\pi$
$594$	2.00000	−	3.46410i	0.0820610	−	0.142134i
$595$	13.3923	−	0.803848i	0.549031	−	0.0329545i
$596$	−9.50000	−	16.4545i	−0.389135	−	0.674002i
$597$	1.73205	−	1.00000i	0.0708881	−	0.0409273i
$598$			12.0000i			0.490716i
$599$	11.5000	+	19.9186i	0.469877	+	0.813851i	0.999407	−	0.0344402i	$-0.0109648\pi$
$599$	11.5000	+	19.9186i	0.469877	+	0.813851i	−0.529529	+	0.848292i	$0.677632\pi$
$600$	3.00000	+	4.00000i	0.122474	+	0.163299i
$601$	−5.00000	+	8.66025i	−0.203954	+	0.353259i	−0.949799	−	0.312861i	$-0.898713\pi$
$601$	−5.00000	+	8.66025i	−0.203954	+	0.353259i	0.745845	+	0.666120i	$0.232046\pi$
$602$		−	6.00000i		−	0.244542i
$603$		−	8.00000i		−	0.325785i
$604$	−8.00000	+	13.8564i	−0.325515	+	0.563809i
$605$	11.1603	−	0.669873i	0.453729	−	0.0272342i
$606$	−18.0000			−0.731200
$607$	35.5070	+	20.5000i	1.44119	+	0.832069i	0.997929	−	0.0643251i	$-0.0204895\pi$
$607$	35.5070	+	20.5000i	1.44119	+	0.832069i	0.443257	+	0.896394i	$0.353823\pi$
$608$	0.866025	+	0.500000i	0.0351220	+	0.0202777i
$609$	−2.50000	+	4.33013i	−0.101305	+	0.175466i
$610$		0			0
$611$	−18.0000	−	31.1769i	−0.728202	−	1.26128i
$612$	−5.19615	−	3.00000i	−0.210042	−	0.121268i
$613$	−33.7750	−	19.5000i	−1.36416	−	0.787598i	−0.373985	−	0.927435i	$-0.622009\pi$
$613$	−33.7750	−	19.5000i	−1.36416	−	0.787598i	−0.990174	+	0.139837i	$0.955342\pi$
$614$	2.00000	−	3.46410i	0.0807134	−	0.139800i
$615$	16.0000	+	8.00000i	0.645182	+	0.322591i
$616$	−2.00000	−	3.46410i	−0.0805823	−	0.139573i
$617$	−21.6506	−	12.5000i	−0.871622	−	0.503231i	−0.00373492	−	0.999993i	$-0.501189\pi$
$617$	−21.6506	−	12.5000i	−0.871622	−	0.503231i	−0.867887	+	0.496762i	$0.834522\pi$
$618$			13.0000i			0.522937i
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$	−7.39230	−	11.1962i	−0.296882	−	0.449648i
$621$	4.00000			0.160514
$622$	3.46410	−	2.00000i	0.138898	−	0.0801927i
$623$		−	4.00000i		−	0.160257i
$624$	1.50000	+	2.59808i	0.0600481	+	0.104006i
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	2.00000	+	3.46410i	0.0799361	+	0.138453i
$627$	−3.46410	−	2.00000i	−0.138343	−	0.0798723i
$628$			13.0000i			0.518756i
$629$	33.0000	+	15.5885i	1.31580	+	0.621552i
$630$	−1.00000	+	2.00000i	−0.0398410	+	0.0796819i
$631$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$631$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$632$	−8.66025	+	5.00000i	−0.344486	+	0.198889i
$633$	12.9904	−	7.50000i	0.516321	−	0.298098i
$634$	−4.00000	−	6.92820i	−0.158860	−	0.275154i
$635$	−2.00000	−	1.00000i	−0.0793676	−	0.0396838i
$636$	2.00000	+	3.46410i	0.0793052	+	0.137361i
$637$			18.0000i			0.713186i
$638$	17.3205	+	10.0000i	0.685725	+	0.395904i
$639$	3.00000			0.118678
$640$	−2.00000	−	1.00000i	−0.0790569	−	0.0395285i
$641$	19.0000	−	32.9090i	0.750455	−	1.29983i	−0.197148	−	0.980374i	$-0.563168\pi$
$641$	19.0000	−	32.9090i	0.750455	−	1.29983i	0.947602	−	0.319452i	$-0.103499\pi$
$642$	−17.3205	+	10.0000i	−0.683586	+	0.394669i
$643$			16.0000i			0.630978i	0.948929	+	0.315489i	$0.102169\pi$
$643$			16.0000i			0.630978i	−0.948929	+	0.315489i	$0.897831\pi$
$644$	2.00000	−	3.46410i	0.0788110	−	0.136505i
$645$	7.39230	+	11.1962i	0.291072	+	0.440848i
$646$	−3.00000	+	5.19615i	−0.118033	+	0.204440i
$647$	−15.5885	+	9.00000i	−0.612845	+	0.353827i	−0.774078	−	0.633090i	$-0.781786\pi$
$647$	−15.5885	+	9.00000i	−0.612845	+	0.353827i	0.161233	+	0.986916i	$0.448453\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−8.00000	+	13.8564i	−0.314027	+	0.543912i
$650$	14.8923	−	1.79423i	0.584124	−	0.0703754i
$651$	3.00000	−	5.19615i	0.117579	−	0.203653i
$652$			4.00000i			0.156652i
$653$	36.3731	−	21.0000i	1.42339	−	0.821794i	0.426801	−	0.904345i	$-0.359640\pi$
$653$	36.3731	−	21.0000i	1.42339	−	0.821794i	0.996587	+	0.0825519i	$0.0263070\pi$
$654$	7.00000	−	12.1244i	0.273722	−	0.474100i
$655$		0			0
$656$	−8.00000			−0.312348
$657$	−13.8564	−	8.00000i	−0.540590	−	0.312110i
$658$			12.0000i			0.467809i
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	0.602844	−	0.797859i	$-0.294034\pi$
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	−0.992388	+	0.123148i	$0.960701\pi$
$660$	8.00000	+	4.00000i	0.311400	+	0.155700i
$661$	13.0000	+	22.5167i	0.505641	+	0.875797i	0.999979	+	0.00652642i	$0.00207744\pi$
$661$	13.0000	+	22.5167i	0.505641	+	0.875797i	−0.494337	+	0.869270i	$0.664589\pi$
$662$	4.33013	−	2.50000i	0.168295	−	0.0971653i
$663$	−15.5885	+	9.00000i	−0.605406	+	0.349531i
$664$	8.50000	−	14.7224i	0.329864	−	0.571341i
$665$	2.00000	+	1.00000i	0.0775567	+	0.0387783i
$666$	−5.00000	+	3.46410i	−0.193746	+	0.134231i
$667$			20.0000i			0.774403i
$668$	−13.8564	−	8.00000i	−0.536120	−	0.309529i
$669$	8.00000	+	13.8564i	0.309298	+	0.535720i
$670$	17.8564	−	1.07180i	0.689853	−	0.0414071i
$671$		0			0
$672$		−	1.00000i		−	0.0385758i
$673$	−13.8564	+	8.00000i	−0.534125	+	0.308377i	−0.742695	−	0.669630i	$-0.766453\pi$
$673$	−13.8564	+	8.00000i	−0.534125	+	0.308377i	0.208569	+	0.978008i	$0.433119\pi$
$674$	−22.0000			−0.847408
$675$	−0.598076	−	4.96410i	−0.0230200	−	0.191068i
$676$	−4.00000			−0.153846
$677$			30.0000i			1.15299i	0.817099	+	0.576497i	$0.195581\pi$
$677$			30.0000i			1.15299i	−0.817099	+	0.576497i	$0.804419\pi$
$678$	2.59808	+	1.50000i	0.0997785	+	0.0576072i
$679$	6.00000	+	10.3923i	0.230259	+	0.398820i
$680$	6.00000	−	12.0000i	0.230089	−	0.460179i
$681$	−13.5000	+	23.3827i	−0.517321	+	0.896026i
$682$	−20.7846	−	12.0000i	−0.795884	−	0.459504i
$683$	−3.46410	−	2.00000i	−0.132550	−	0.0765279i	0.432259	−	0.901750i	$-0.357717\pi$
$683$	−3.46410	−	2.00000i	−0.132550	−	0.0765279i	−0.564809	+	0.825222i	$0.691050\pi$
$684$	−0.500000	−	0.866025i	−0.0191180	−	0.0331133i
$685$	−2.00962	−	33.4808i	−0.0767836	−	1.27923i
$686$	6.50000	−	11.2583i	0.248171	−	0.429845i
$687$	−19.0526	−	11.0000i	−0.726900	−	0.419676i
$688$	−5.19615	−	3.00000i	−0.198101	−	0.114374i
$689$	12.0000			0.457164
$690$	0.535898	+	8.92820i	0.0204013	+	0.339891i
$691$	−1.50000	+	2.59808i	−0.0570627	+	0.0988355i	−0.893146	−	0.449768i	$-0.851507\pi$
$691$	−1.50000	+	2.59808i	−0.0570627	+	0.0988355i	0.836083	+	0.548603i	$0.184840\pi$
$692$		0			0
$693$			4.00000i			0.151947i
$694$	−9.50000	+	16.4545i	−0.360615	+	0.624604i
$695$	−4.00000	+	8.00000i	−0.151729	+	0.303457i
$696$	2.50000	+	4.33013i	0.0947623	+	0.164133i
$697$		−	48.0000i		−	1.81813i
$698$	12.1244	−	7.00000i	0.458914	−	0.264954i
$699$	−10.5000	−	18.1865i	−0.397146	−	0.687878i
$700$	−4.59808	−	1.96410i	−0.173791	−	0.0742361i
$701$	−21.0000	+	36.3731i	−0.793159	+	1.37379i	0.130843	+	0.991403i	$0.458232\pi$
$701$	−21.0000	+	36.3731i	−0.793159	+	1.37379i	−0.924002	+	0.382389i	$0.875102\pi$
$702$		−	3.00000i		−	0.113228i
$703$	3.46410	+	5.00000i	0.130651	+	0.188579i
$704$	−4.00000			−0.150756
$705$	−14.7846	−	22.3923i	−0.556821	−	0.843343i
$706$	12.5000	+	21.6506i	0.470444	+	0.814832i
$707$	15.5885	−	9.00000i	0.586264	−	0.338480i
$708$	−3.46410	+	2.00000i	−0.130189	+	0.0751646i
$709$	−12.0000			−0.450669			−0.225335	−	0.974281i	$-0.572348\pi$
$709$	−12.0000			−0.450669			−0.225335	+	0.974281i	$0.572348\pi$
$710$	0.401924	+	6.69615i	0.0150839	+	0.251302i
$711$	10.0000			0.375029
$712$	−3.46410	−	2.00000i	−0.129823	−	0.0749532i
$713$		−	24.0000i		−	0.898807i
$714$	6.00000			0.224544
$715$	22.3923	−	14.7846i	0.837425	−	0.552913i
$716$		0			0
$717$		−	17.0000i		−	0.634877i
$718$	23.3827	+	13.5000i	0.872634	+	0.503816i
$719$	16.5000	−	28.5788i	0.615346	−	1.06581i	−0.374978	−	0.927034i	$-0.622350\pi$
$719$	16.5000	−	28.5788i	0.615346	−	1.06581i	0.990324	−	0.138777i	$-0.0443171\pi$
$720$	1.23205	+	1.86603i	0.0459158	+	0.0695427i
$721$	−6.50000	−	11.2583i	−0.242073	−	0.419282i
$722$	15.5885	−	9.00000i	0.580142	−	0.334945i
$723$	−12.1244	−	7.00000i	−0.450910	−	0.260333i
$724$		0			0
$725$	24.8205	−	2.99038i	0.921811	−	0.111060i
$726$	5.00000			0.185567
$727$	9.52628	−	5.50000i	0.353310	−	0.203984i	−0.312832	−	0.949808i	$-0.601278\pi$
$727$	9.52628	−	5.50000i	0.353310	−	0.203984i	0.666142	+	0.745825i	$0.267944\pi$
$728$	−2.59808	−	1.50000i	−0.0962911	−	0.0555937i
$729$	−1.00000			−0.0370370
$730$	16.0000	−	32.0000i	0.592187	−	1.18437i
$731$	18.0000	−	31.1769i	0.665754	−	1.15312i
$732$		0			0
$733$	12.1244	−	7.00000i	0.447823	−	0.258551i	−0.259087	−	0.965854i	$-0.583422\pi$
$733$	12.1244	−	7.00000i	0.447823	−	0.258551i	0.706910	+	0.707303i	$0.250088\pi$
$734$	−19.0000			−0.701303
$735$	0.803848	+	13.3923i	0.0296504	+	0.493983i
$736$	−2.00000	−	3.46410i	−0.0737210	−	0.127688i
$737$	27.7128	−	16.0000i	1.02081	−	0.589368i
$738$	6.92820	+	4.00000i	0.255031	+	0.147242i
$739$	7.00000			0.257499			0.128750	−	0.991677i	$-0.458904\pi$
$739$	7.00000			0.257499			0.128750	+	0.991677i	$0.458904\pi$
$740$	−8.40192	−	10.6962i	−0.308861	−	0.393198i
$741$	−3.00000			−0.110208
$742$	−3.46410	−	2.00000i	−0.127171	−	0.0734223i
$743$	1.73205	−	1.00000i	0.0635428	−	0.0366864i	−0.467892	−	0.883786i	$-0.654986\pi$
$743$	1.73205	−	1.00000i	0.0635428	−	0.0366864i	0.531435	+	0.847099i	$0.321653\pi$
$744$	−3.00000	−	5.19615i	−0.109985	−	0.190500i
$745$	−42.4090	+	2.54552i	−1.55374	+	0.0932605i
$746$	29.0000			1.06177
$747$	−14.7224	+	8.50000i	−0.538666	+	0.310999i
$748$		−	24.0000i		−	0.877527i
$749$	10.0000	−	17.3205i	0.365392	−	0.632878i
$750$	11.0000	−	2.00000i	0.401663	−	0.0730297i
$751$	−14.0000			−0.510867			−0.255434	−	0.966827i	$-0.582218\pi$
$751$	−14.0000			−0.510867			−0.255434	+	0.966827i	$0.582218\pi$
$752$	10.3923	+	6.00000i	0.378968	+	0.218797i
$753$	−10.3923	+	6.00000i	−0.378717	+	0.218652i
$754$	15.0000			0.546268
$755$	19.7128	+	29.8564i	0.717423	+	1.08659i
$756$	−0.500000	+	0.866025i	−0.0181848	+	0.0314970i
$757$	32.0429	+	18.5000i	1.16462	+	0.672394i	0.952407	−	0.304829i	$-0.0985994\pi$
$757$	32.0429	+	18.5000i	1.16462	+	0.672394i	0.212213	+	0.977223i	$0.431933\pi$
$758$	−25.1147	+	14.5000i	−0.912208	+	0.526664i
$759$	8.00000	+	13.8564i	0.290382	+	0.502956i
$760$	1.86603	−	1.23205i	0.0676879	−	0.0446912i
$761$	−19.0000	+	32.9090i	−0.688749	+	1.19295i	0.283493	+	0.958974i	$0.408507\pi$
$761$	−19.0000	+	32.9090i	−0.688749	+	1.19295i	−0.972243	+	0.233975i	$0.924827\pi$
$762$	−0.866025	−	0.500000i	−0.0313728	−	0.0181131i
$763$			14.0000i			0.506834i
$764$	−6.00000	−	10.3923i	−0.217072	−	0.375980i
$765$	−11.1962	+	7.39230i	−0.404798	+	0.267269i
$766$	−6.00000			−0.216789
$767$			12.0000i			0.433295i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−23.0000			−0.829401			−0.414701	−	0.909958i	$-0.636114\pi$
$769$	−23.0000			−0.829401			−0.414701	+	0.909958i	$0.636114\pi$
$770$	−8.92820	+	0.535898i	−0.321750	+	0.0193124i
$771$	−11.0000			−0.396155
$772$	1.73205	−	1.00000i	0.0623379	−	0.0359908i
$773$	12.1244	−	7.00000i	0.436083	−	0.251773i	−0.265852	−	0.964014i	$-0.585653\pi$
$773$	12.1244	−	7.00000i	0.436083	−	0.251773i	0.701935	+	0.712241i	$0.252320\pi$
$774$	3.00000	+	5.19615i	0.107833	+	0.186772i
$775$	−29.7846	+	3.58846i	−1.06989	+	0.128901i
$776$	12.0000			0.430775
$777$	2.59808	−	5.50000i	0.0932055	−	0.197311i
$778$			27.0000i			0.967997i
$779$	4.00000	−	6.92820i	0.143315	−	0.248229i
$780$	6.69615	−	0.401924i	0.239761	−	0.0143912i
$781$	6.00000	+	10.3923i	0.214697	+	0.371866i
$782$	20.7846	−	12.0000i	0.743256	−	0.429119i
$783$		−	5.00000i		−	0.178685i
$784$	−3.00000	−	5.19615i	−0.107143	−	0.185577i
$785$	26.0000	+	13.0000i	0.927980	+	0.463990i
$786$		0			0
$787$			10.0000i			0.356462i	0.983989	+	0.178231i	$0.0570374\pi$
$787$			10.0000i			0.356462i	−0.983989	+	0.178231i	$0.942963\pi$
$788$		−	6.00000i		−	0.213741i
$789$	13.0000	−	22.5167i	0.462812	−	0.801614i
$790$	1.33975	+	22.3205i	0.0476660	+	0.794128i
$791$	−3.00000			−0.106668
$792$	3.46410	+	2.00000i	0.123091	+	0.0710669i
$793$		0			0
$794$	−3.00000	+	5.19615i	−0.106466	+	0.184405i
$795$	8.92820	−	0.535898i	0.316651	−	0.0190064i
$796$	1.00000	+	1.73205i	0.0354441	+	0.0613909i
$797$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$797$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$798$	0.866025	+	0.500000i	0.0306570	+	0.0176998i
$799$	−36.0000	+	62.3538i	−1.27359	+	2.20592i
$800$	−4.00000	+	3.00000i	−0.141421	+	0.106066i
$801$	2.00000	+	3.46410i	0.0706665	+	0.122398i
$802$	1.73205	+	1.00000i	0.0611608	+	0.0353112i
$803$		−	64.0000i		−	2.25851i
$804$	8.00000			0.282138
$805$	−4.92820	−	7.46410i	−0.173696	−	0.263075i
$806$	−18.0000			−0.634023
$807$	−4.33013	+	2.50000i	−0.152428	+	0.0880042i
$808$		−	18.0000i		−	0.633238i
$809$	−21.0000	−	36.3731i	−0.738321	−	1.27881i	−0.953251	−	0.302180i	$-0.902286\pi$
$809$	−21.0000	−	36.3731i	−0.738321	−	1.27881i	0.214930	−	0.976629i	$-0.431048\pi$
$810$	−0.133975	−	2.23205i	−0.00470739	−	0.0784263i
$811$	−10.0000	−	17.3205i	−0.351147	−	0.608205i	0.635303	−	0.772263i	$-0.280875\pi$
$811$	−10.0000	−	17.3205i	−0.351147	−	0.608205i	−0.986451	+	0.164057i	$0.947542\pi$
$812$	−4.33013	−	2.50000i	−0.151958	−	0.0877328i
$813$		−	14.0000i		−	0.491001i
$814$	−22.0000	−	10.3923i	−0.771100	−	0.364250i
$815$	8.00000	+	4.00000i	0.280228	+	0.140114i
$816$	3.00000	−	5.19615i	0.105021	−	0.181902i
$817$	5.19615	−	3.00000i	0.181790	−	0.104957i
$818$	9.52628	−	5.50000i	0.333079	−	0.192303i
$819$	1.50000	+	2.59808i	0.0524142	+	0.0907841i
$820$	−8.00000	+	16.0000i	−0.279372	+	0.558744i
$821$	−13.5000	−	23.3827i	−0.471153	−	0.816061i	0.528302	−	0.849056i	$-0.322829\pi$
$821$	−13.5000	−	23.3827i	−0.471153	−	0.816061i	−0.999456	+	0.0329950i	$0.989495\pi$
$822$		−	15.0000i		−	0.523185i
$823$	7.79423	+	4.50000i	0.271690	+	0.156860i	0.629655	−	0.776875i	$-0.283196\pi$
$823$	7.79423	+	4.50000i	0.271690	+	0.156860i	−0.357966	+	0.933735i	$0.616529\pi$
$824$	−13.0000			−0.452876
$825$	16.0000	−	12.0000i	0.557048	−	0.417786i
$826$	2.00000	−	3.46410i	0.0695889	−	0.120532i
$827$	16.4545	−	9.50000i	0.572178	−	0.330347i	−0.185841	−	0.982580i	$-0.559501\pi$
$827$	16.4545	−	9.50000i	0.572178	−	0.330347i	0.758019	+	0.652233i	$0.226167\pi$
$828$			4.00000i			0.139010i
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	−0.718481	−	0.695546i	$-0.755162\pi$
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	0.961601	+	0.274450i	$0.0884958\pi$
$830$	−20.9449	−	31.7224i	−0.727007	−	1.10110i
$831$	−8.50000	+	14.7224i	−0.294862	+	0.510716i
$832$	−2.59808	+	1.50000i	−0.0900721	+	0.0520031i
$833$	31.1769	−	18.0000i	1.08022	−	0.623663i
$834$	−2.00000	+	3.46410i	−0.0692543	+	0.119952i
$835$	−29.8564	+	19.7128i	−1.03322	+	0.682190i
$836$	2.00000	−	3.46410i	0.0691714	−	0.119808i
$837$			6.00000i			0.207390i
$838$	−20.7846	+	12.0000i	−0.717992	+	0.414533i
$839$	24.0000	−	41.5692i	0.828572	−	1.43513i	−0.0705865	−	0.997506i	$-0.522487\pi$
$839$	24.0000	−	41.5692i	0.828572	−	1.43513i	0.899158	−	0.437623i	$-0.144180\pi$
$840$	−2.00000	−	1.00000i	−0.0690066	−	0.0345033i
$841$	−4.00000			−0.137931
$842$	29.4449	+	17.0000i	1.01474	+	0.585859i
$843$		0			0
$844$	7.50000	+	12.9904i	0.258161	+	0.447147i
$845$	−4.00000	+	8.00000i	−0.137604	+	0.275208i
$846$	−6.00000	−	10.3923i	−0.206284	−	0.357295i
$847$	−4.33013	+	2.50000i	−0.148785	+	0.0859010i
$848$	−3.46410	+	2.00000i	−0.118958	+	0.0686803i
$849$	8.00000	−	13.8564i	0.274559	−	0.475551i
$850$	−18.0000	−	24.0000i	−0.617395	−	0.823193i
$851$	−2.00000	−	24.2487i	−0.0685591	−	0.831235i
$852$			3.00000i			0.102778i
$853$	−15.5885	−	9.00000i	−0.533739	−	0.308154i	0.208799	−	0.977959i	$-0.433045\pi$
$853$	−15.5885	−	9.00000i	−0.533739	−	0.308154i	−0.742538	+	0.669804i	$0.766378\pi$
$854$		0			0
$855$	−2.23205	+	0.133975i	−0.0763345	+	0.00458183i
$856$	−10.0000	−	17.3205i	−0.341793	−	0.592003i
$857$		−	33.0000i		−	1.12726i	−0.826028	−	0.563629i	$-0.809405\pi$
$857$		−	33.0000i		−	1.12726i	0.826028	−	0.563629i	$-0.190595\pi$
$858$	10.3923	−	6.00000i	0.354787	−	0.204837i
$859$	−9.00000			−0.307076			−0.153538	−	0.988143i	$-0.549067\pi$
$859$	−9.00000			−0.307076			−0.153538	+	0.988143i	$0.549067\pi$
$860$	−11.1962	+	7.39230i	−0.381786	+	0.252076i
$861$	−8.00000			−0.272639
$862$		−	3.00000i		−	0.102180i
$863$	29.4449	+	17.0000i	1.00231	+	0.578687i	0.908932	−	0.416944i	$-0.136899\pi$
$863$	29.4449	+	17.0000i	1.00231	+	0.578687i	0.0933825	+	0.995630i	$0.470232\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	−7.00000	+	12.1244i	−0.237870	+	0.412002i
$867$	16.4545	+	9.50000i	0.558824	+	0.322637i
$868$	5.19615	+	3.00000i	0.176369	+	0.101827i
$869$	20.0000	+	34.6410i	0.678454	+	1.17512i
$870$	11.1603	−	0.669873i	0.378368	−	0.0227108i
$871$	12.0000	−	20.7846i	0.406604	−	0.704260i
$872$	12.1244	+	7.00000i	0.410582	+	0.237050i
$873$	−10.3923	−	6.00000i	−0.351726	−	0.203069i
$874$	4.00000			0.135302
$875$	−8.52628	+	7.23205i	−0.288241	+	0.244488i
$876$	8.00000	−	13.8564i	0.270295	−	0.468165i
$877$		−	5.00000i		−	0.168838i	−0.996430	−	0.0844190i	$-0.973097\pi$
$877$		−	5.00000i		−	0.168838i	0.996430	−	0.0844190i	$-0.0269034\pi$
$878$			34.0000i			1.14744i
$879$	1.00000	−	1.73205i	0.0337292	−	0.0584206i
$880$	−4.00000	+	8.00000i	−0.134840	+	0.269680i
$881$	8.00000	+	13.8564i	0.269527	+	0.466834i	0.968740	−	0.248079i	$-0.0797994\pi$
$881$	8.00000	+	13.8564i	0.269527	+	0.466834i	−0.699213	+	0.714914i	$0.746466\pi$
$882$			6.00000i			0.202031i
$883$	−48.4974	+	28.0000i	−1.63207	+	0.942275i	−0.648614	+	0.761117i	$0.724651\pi$
$883$	−48.4974	+	28.0000i	−1.63207	+	0.942275i	−0.983454	+	0.181158i	$0.942016\pi$
$884$	−9.00000	−	15.5885i	−0.302703	−	0.524297i
$885$	0.535898	+	8.92820i	0.0180140	+	0.300118i
$886$	−3.50000	+	6.06218i	−0.117585	+	0.203663i
$887$		−	12.0000i		−	0.402921i	−0.979497	−	0.201460i	$-0.935431\pi$
$887$		−	12.0000i		−	0.402921i	0.979497	−	0.201460i	$-0.0645687\pi$
$888$	−3.46410	−	5.00000i	−0.116248	−	0.167789i
$889$	1.00000			0.0335389
$890$	−7.46410	+	4.92820i	−0.250197	+	0.165194i
$891$	−2.00000	−	3.46410i	−0.0670025	−	0.116052i
$892$	−13.8564	+	8.00000i	−0.463947	+	0.267860i
$893$	−10.3923	+	6.00000i	−0.347765	+	0.200782i
$894$	−19.0000			−0.635455
$895$		0			0
$896$	1.00000			0.0334077
$897$	10.3923	+	6.00000i	0.346989	+	0.200334i
$898$		0			0
$899$	−30.0000			−1.00056
$900$	4.96410	−	0.598076i	0.165470	−	0.0199359i
$901$	−12.0000	−	20.7846i	−0.399778	−	0.692436i
$902$			32.0000i			1.06548i
$903$	−5.19615	−	3.00000i	−0.172917	−	0.0998337i
$904$	−1.50000	+	2.59808i	−0.0498893	+	0.0864107i
$905$		0			0
$906$	8.00000	+	13.8564i	0.265782	+	0.460348i
$907$	−13.8564	+	8.00000i	−0.460094	+	0.265636i	−0.712084	−	0.702094i	$-0.752248\pi$
$907$	−13.8564	+	8.00000i	−0.460094	+	0.265636i	0.251990	+	0.967730i	$0.418915\pi$
$908$	−23.3827	−	13.5000i	−0.775982	−	0.448013i
$909$	−9.00000	+	15.5885i	−0.298511	+	0.517036i
$910$	−5.59808	+	3.69615i	−0.185574	+	0.122526i
$911$	9.00000			0.298183			0.149092	−	0.988823i	$-0.452365\pi$
$911$	9.00000			0.298183			0.149092	+	0.988823i	$0.452365\pi$
$912$	0.866025	−	0.500000i	0.0286770	−	0.0165567i
$913$	−58.8897	−	34.0000i	−1.94897	−	1.12524i
$914$	34.0000			1.12462
$915$		0			0
$916$	11.0000	−	19.0526i	0.363450	−	0.629514i
$917$		0			0
$918$	−5.19615	+	3.00000i	−0.171499	+	0.0990148i
$919$	−52.0000			−1.71532			−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−52.0000			−1.71532			−0.857661	+	0.514216i	$0.828083\pi$
$920$	−8.92820	+	0.535898i	−0.294354	+	0.0176680i
$921$	−2.00000	−	3.46410i	−0.0659022	−	0.114146i
$922$	7.79423	−	4.50000i	0.256689	−	0.148200i
$923$	7.79423	+	4.50000i	0.256550	+	0.148119i
$924$	−4.00000			−0.131590
$925$	−29.7942	+	6.10770i	−0.979628	+	0.200820i
$926$	29.0000			0.952999
$927$	11.2583	+	6.50000i	0.369772	+	0.213488i
$928$	−4.33013	+	2.50000i	−0.142143	+	0.0820665i
$929$	8.00000	+	13.8564i	0.262471	+	0.454614i	0.966898	−	0.255163i	$-0.0821291\pi$
$929$	8.00000	+	13.8564i	0.262471	+	0.454614i	−0.704427	+	0.709777i	$0.748796\pi$
$930$	−13.3923	+	0.803848i	−0.439151	+	0.0263592i
$931$	6.00000			0.196642
$932$	18.1865	−	10.5000i	0.595720	−	0.343939i
$933$		−	4.00000i		−	0.130954i
$934$	6.50000	−	11.2583i	0.212686	−	0.368384i
$935$	−48.0000	−	24.0000i	−1.56977	−	0.784884i
$936$	3.00000			0.0980581
$937$	41.5692	+	24.0000i	1.35801	+	0.784046i	0.989355	−	0.145522i	$-0.0464860\pi$
$937$	41.5692	+	24.0000i	1.35801	+	0.784046i	0.368652	+	0.929567i	$0.379819\pi$
$938$	−6.92820	+	4.00000i	−0.226214	+	0.130605i
$939$	4.00000			0.130535
$940$	22.3923	−	14.7846i	0.730356	−	0.482221i
$941$	−1.50000	+	2.59808i	−0.0488986	+	0.0846949i	−0.889439	−	0.457054i	$-0.848904\pi$
$941$	−1.50000	+	2.59808i	−0.0488986	+	0.0846949i	0.840540	+	0.541749i	$0.182238\pi$
$942$	11.2583	+	6.50000i	0.366816	+	0.211781i
$943$	−27.7128	+	16.0000i	−0.902453	+	0.521032i
$944$	−2.00000	−	3.46410i	−0.0650945	−	0.112747i
$945$	1.23205	+	1.86603i	0.0400786	+	0.0607018i
$946$	−12.0000	+	20.7846i	−0.390154	+	0.675766i
$947$	49.3634	+	28.5000i	1.60410	+	0.926126i	0.990656	+	0.136385i	$0.0435483\pi$
$947$	49.3634	+	28.5000i	1.60410	+	0.926126i	0.613441	+	0.789741i	$0.289785\pi$
$948$			10.0000i			0.324785i
$949$	−24.0000	−	41.5692i	−0.779073	−	1.34939i
$950$	−0.598076	−	4.96410i	−0.0194042	−	0.161057i
$951$	−8.00000			−0.259418
$952$			6.00000i			0.194461i
$953$	−6.06218	−	3.50000i	−0.196373	−	0.113376i	0.398589	−	0.917129i	$-0.369500\pi$
$953$	−6.06218	−	3.50000i	−0.196373	−	0.113376i	−0.594963	+	0.803753i	$0.702833\pi$
$954$	4.00000			0.129505
$955$	−26.7846	+	1.60770i	−0.866730	+	0.0520238i
$956$	17.0000			0.549819
$957$	17.3205	−	10.0000i	0.559893	−	0.323254i
$958$		0			0
$959$	7.50000	+	12.9904i	0.242188	+	0.419481i
$960$	−1.86603	+	1.23205i	−0.0602257	+	0.0397643i
$961$	5.00000			0.161290
$962$	−18.1865	+	1.50000i	−0.586357	+	0.0483619i
$963$			20.0000i			0.644491i
$964$	7.00000	−	12.1244i	0.225455	−	0.390499i
$965$	−0.267949	−	4.46410i	−0.00862559	−	0.143705i
$966$	−2.00000	−	3.46410i	−0.0643489	−	0.111456i
$967$	−6.06218	+	3.50000i	−0.194946	+	0.112552i	−0.594296	−	0.804246i	$-0.702569\pi$
$967$	−6.06218	+	3.50000i	−0.194946	+	0.112552i	0.399350	+	0.916799i	$0.369236\pi$
$968$			5.00000i			0.160706i
$969$	3.00000	+	5.19615i	0.0963739	+	0.166924i
$970$	12.0000	−	24.0000i	0.385297	−	0.770594i
$971$	7.00000	−	12.1244i	0.224641	−	0.389089i	−0.731571	−	0.681765i	$-0.761212\pi$
$971$	7.00000	−	12.1244i	0.224641	−	0.389089i	0.956212	+	0.292676i	$0.0945458\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	4.00000i		−	0.128234i
$974$	−8.50000	+	14.7224i	−0.272358	+	0.471737i
$975$	5.89230	−	13.7942i	0.188705	−	0.441769i
$976$		0			0
$977$	−30.3109	−	17.5000i	−0.969731	−	0.559875i	−0.0705770	−	0.997506i	$-0.522484\pi$
$977$	−30.3109	−	17.5000i	−0.969731	−	0.559875i	−0.899154	+	0.437632i	$0.855817\pi$
$978$	3.46410	+	2.00000i	0.110770	+	0.0639529i
$979$	−8.00000	+	13.8564i	−0.255681	+	0.442853i
$980$	−13.3923	+	0.803848i	−0.427801	+	0.0256780i
$981$	−7.00000	−	12.1244i	−0.223493	−	0.387101i
$982$	22.5167	+	13.0000i	0.718536	+	0.414847i
$983$	15.5885	+	9.00000i	0.497195	+	0.287055i	0.727554	−	0.686050i	$-0.240657\pi$
$983$	15.5885	+	9.00000i	0.497195	+	0.287055i	−0.230360	+	0.973106i	$0.573990\pi$
$984$	−4.00000	+	6.92820i	−0.127515	+	0.220863i
$985$	−12.0000	−	6.00000i	−0.382352	−	0.191176i
$986$	−15.0000	−	25.9808i	−0.477697	−	0.827396i
$987$	10.3923	+	6.00000i	0.330791	+	0.190982i
$988$		−	3.00000i		−	0.0954427i
$989$	−24.0000			−0.763156
$990$	7.46410	−	4.92820i	0.237225	−	0.156629i
$991$	52.0000			1.65183			0.825917	−	0.563791i	$-0.190658\pi$
$991$	52.0000			1.65183			0.825917	+	0.563791i	$0.190658\pi$
$992$	5.19615	−	3.00000i	0.164978	−	0.0952501i
$993$		−	5.00000i		−	0.158670i
$994$	−1.50000	−	2.59808i	−0.0475771	−	0.0824060i
$995$	4.46410	−	0.267949i	0.141522	−	0.00849456i
$996$	−8.50000	−	14.7224i	−0.269333	−	0.466498i
$997$	−2.59808	−	1.50000i	−0.0822819	−	0.0475055i	0.458295	−	0.888800i	$-0.348460\pi$
$997$	−2.59808	−	1.50000i	−0.0822819	−	0.0475055i	−0.540576	+	0.841295i	$0.681794\pi$
$998$			9.00000i			0.284890i
$999$	0.500000	+	6.06218i	0.0158193	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.c.1009.2	yes	4
5.4	even	2	inner	1110.2.bb.c.1009.1	✓	4
37.26	even	3	inner	1110.2.bb.c.1099.1	yes	4
185.174	even	6	inner	1110.2.bb.c.1099.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.c.1009.1	✓	4	5.4	even	2	inner
1110.2.bb.c.1009.2	yes	4	1.1	even	1	trivial
1110.2.bb.c.1099.1	yes	4	37.26	even	3	inner
1110.2.bb.c.1099.2	yes	4	185.174	even	6	inner

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +1.00000 q^{6} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +1.00000 q^{6} +(-0.866025 + 0.500000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.00000 + 1.00000i) q^{10} +4.00000 q^{11} +(0.866025 + 0.500000i) q^{12} +(2.59808 - 1.50000i) q^{13} -1.00000 q^{14} +(1.86603 - 1.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-5.19615 - 3.00000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(1.23205 + 1.86603i) q^{20} +(-0.500000 + 0.866025i) q^{21} +(3.46410 + 2.00000i) q^{22} +4.00000i q^{23} +(0.500000 + 0.866025i) q^{24} +(4.96410 - 0.598076i) q^{25} +3.00000 q^{26} -1.00000i q^{27} +(-0.866025 - 0.500000i) q^{28} +5.00000 q^{29} +(2.23205 - 0.133975i) q^{30} -6.00000 q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.46410 - 2.00000i) q^{33} +(-3.00000 - 5.19615i) q^{34} +(-1.86603 + 1.23205i) q^{35} +1.00000 q^{36} +(-6.06218 + 0.500000i) q^{37} -1.00000i q^{38} +(1.50000 - 2.59808i) q^{39} +(0.133975 + 2.23205i) q^{40} +(4.00000 + 6.92820i) q^{41} +(-0.866025 + 0.500000i) q^{42} +6.00000i q^{43} +(2.00000 + 3.46410i) q^{44} +(1.00000 - 2.00000i) q^{45} +(-2.00000 + 3.46410i) q^{46} -12.0000i q^{47} +1.00000i q^{48} +(-3.00000 + 5.19615i) q^{49} +(4.59808 + 1.96410i) q^{50} -6.00000 q^{51} +(2.59808 + 1.50000i) q^{52} +(3.46410 + 2.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(8.92820 - 0.535898i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-0.866025 - 0.500000i) q^{57} +(4.33013 + 2.50000i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(2.00000 + 1.00000i) q^{60} +(-5.19615 - 3.00000i) q^{62} +1.00000i q^{63} -1.00000 q^{64} +(5.59808 - 3.69615i) q^{65} +4.00000 q^{66} +(6.92820 - 4.00000i) q^{67} -6.00000i q^{68} +(2.00000 + 3.46410i) q^{69} +(-2.23205 + 0.133975i) q^{70} +(1.50000 + 2.59808i) q^{71} +(0.866025 + 0.500000i) q^{72} -16.0000i q^{73} +(-5.50000 - 2.59808i) q^{74} +(4.00000 - 3.00000i) q^{75} +(0.500000 - 0.866025i) q^{76} +(-3.46410 + 2.00000i) q^{77} +(2.59808 - 1.50000i) q^{78} +(5.00000 + 8.66025i) q^{79} +(-1.00000 + 2.00000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +8.00000i q^{82} +(-14.7224 - 8.50000i) q^{83} -1.00000 q^{84} +(-12.0000 - 6.00000i) q^{85} +(-3.00000 + 5.19615i) q^{86} +(4.33013 - 2.50000i) q^{87} +4.00000i q^{88} +(-2.00000 + 3.46410i) q^{89} +(1.86603 - 1.23205i) q^{90} +(-1.50000 + 2.59808i) q^{91} +(-3.46410 + 2.00000i) q^{92} +(-5.19615 + 3.00000i) q^{93} +(6.00000 - 10.3923i) q^{94} +(-1.23205 - 1.86603i) q^{95} +(-0.500000 + 0.866025i) q^{96} -12.0000i q^{97} +(-5.19615 + 3.00000i) q^{98} +(2.00000 - 3.46410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{5} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 2 * q^5 + 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} + 2 q^{5} + 4 q^{6} + 2 q^{9} + 8 q^{10} + 16 q^{11} - 4 q^{14} + 4 q^{15} - 2 q^{16} - 2 q^{19} - 2 q^{20} - 2 q^{21} + 2 q^{24} + 6 q^{25} + 12 q^{26} + 20 q^{29} + 2 q^{30} - 24 q^{31} - 12 q^{34} - 4 q^{35} + 4 q^{36} + 6 q^{39} + 4 q^{40} + 16 q^{41} + 8 q^{44} + 4 q^{45} - 8 q^{46} - 12 q^{49} + 8 q^{50} - 24 q^{51} + 2 q^{54} + 8 q^{55} - 2 q^{56} - 8 q^{59} + 8 q^{60} - 4 q^{64} + 12 q^{65} + 16 q^{66} + 8 q^{69} - 2 q^{70} + 6 q^{71} - 22 q^{74} + 16 q^{75} + 2 q^{76} + 20 q^{79} - 4 q^{80} - 2 q^{81} - 4 q^{84} - 48 q^{85} - 12 q^{86} - 8 q^{89} + 4 q^{90} - 6 q^{91} + 24 q^{94} + 2 q^{95} - 2 q^{96} + 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^5 + 4 * q^6 + 2 * q^9 + 8 * q^10 + 16 * q^11 - 4 * q^14 + 4 * q^15 - 2 * q^16 - 2 * q^19 - 2 * q^20 - 2 * q^21 + 2 * q^24 + 6 * q^25 + 12 * q^26 + 20 * q^29 + 2 * q^30 - 24 * q^31 - 12 * q^34 - 4 * q^35 + 4 * q^36 + 6 * q^39 + 4 * q^40 + 16 * q^41 + 8 * q^44 + 4 * q^45 - 8 * q^46 - 12 * q^49 + 8 * q^50 - 24 * q^51 + 2 * q^54 + 8 * q^55 - 2 * q^56 - 8 * q^59 + 8 * q^60 - 4 * q^64 + 12 * q^65 + 16 * q^66 + 8 * q^69 - 2 * q^70 + 6 * q^71 - 22 * q^74 + 16 * q^75 + 2 * q^76 + 20 * q^79 - 4 * q^80 - 2 * q^81 - 4 * q^84 - 48 * q^85 - 12 * q^86 - 8 * q^89 + 4 * q^90 - 6 * q^91 + 24 * q^94 + 2 * q^95 - 2 * q^96 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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