LMFDB - Embedded newform 722.2.c.k.429.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(429,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("722.429");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.c (of order $3$, degree $2$, not 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			429.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	722.429
Dual form			722.2.c.k.653.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.766044 + 1.32683i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(-0.766044 - 1.32683i) q^{6} +2.69459 q^{7} +1.00000 q^{8} +(0.326352 + 0.565258i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.766044 + 1.32683i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(-0.766044 - 1.32683i) q^{6} +2.69459 q^{7} +1.00000 q^{8} +(0.326352 + 0.565258i) q^{9} +(-1.00000 - 1.73205i) q^{10} +3.18479 q^{11} +1.53209 q^{12} +(2.87939 + 4.98724i) q^{13} +(-1.34730 + 2.33359i) q^{14} +(-1.53209 - 2.65366i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.25877 - 5.64436i) q^{17} -0.652704 q^{18} +2.00000 q^{20} +(-2.06418 + 3.57526i) q^{21} +(-1.59240 + 2.75811i) q^{22} +(0.347296 + 0.601535i) q^{23} +(-0.766044 + 1.32683i) q^{24} +(0.500000 + 0.866025i) q^{25} -5.75877 q^{26} -5.59627 q^{27} +(-1.34730 - 2.33359i) q^{28} +(1.41147 + 2.44474i) q^{29} +3.06418 q^{30} +2.45336 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.43969 + 4.22567i) q^{33} +(3.25877 + 5.64436i) q^{34} +(-2.69459 + 4.66717i) q^{35} +(0.326352 - 0.565258i) q^{36} -4.36959 q^{37} -8.82295 q^{39} +(-1.00000 + 1.73205i) q^{40} +(0.173648 - 0.300767i) q^{41} +(-2.06418 - 3.57526i) q^{42} +(-3.03209 + 5.25173i) q^{43} +(-1.59240 - 2.75811i) q^{44} -1.30541 q^{45} -0.694593 q^{46} +(-3.94356 - 6.83045i) q^{47} +(-0.766044 - 1.32683i) q^{48} +0.260830 q^{49} -1.00000 q^{50} +(4.99273 + 8.64766i) q^{51} +(2.87939 - 4.98724i) q^{52} +(-4.10607 - 7.11192i) q^{53} +(2.79813 - 4.84651i) q^{54} +(-3.18479 + 5.51622i) q^{55} +2.69459 q^{56} -2.82295 q^{58} +(-0.286989 + 0.497079i) q^{59} +(-1.53209 + 2.65366i) q^{60} +(-1.46791 - 2.54250i) q^{61} +(-1.22668 + 2.12467i) q^{62} +(0.879385 + 1.52314i) q^{63} +1.00000 q^{64} -11.5175 q^{65} +(-2.43969 - 4.22567i) q^{66} +(2.47906 + 4.29385i) q^{67} -6.51754 q^{68} -1.06418 q^{69} +(-2.69459 - 4.66717i) q^{70} +(4.22668 - 7.32083i) q^{71} +(0.326352 + 0.565258i) q^{72} +(-7.88326 + 13.6542i) q^{73} +(2.18479 - 3.78417i) q^{74} -1.53209 q^{75} +8.58172 q^{77} +(4.41147 - 7.64090i) q^{78} +(4.53209 - 7.84981i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(3.30793 - 5.72951i) q^{81} +(0.173648 + 0.300767i) q^{82} +8.47565 q^{83} +4.12836 q^{84} +(6.51754 + 11.2887i) q^{85} +(-3.03209 - 5.25173i) q^{86} -4.32501 q^{87} +3.18479 q^{88} +(-3.86959 - 6.70232i) q^{89} +(0.652704 - 1.13052i) q^{90} +(7.75877 + 13.4386i) q^{91} +(0.347296 - 0.601535i) q^{92} +(-1.87939 + 3.25519i) q^{93} +7.88713 q^{94} +1.53209 q^{96} +(0.173648 - 0.300767i) q^{97} +(-0.130415 + 0.225885i) q^{98} +(1.03936 + 1.80023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 + 6 * q^8 + 3 * q^9	$ 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} + 6 q^{8} + 3 q^{9} - 6 q^{10} + 12 q^{11} + 6 q^{13} - 6 q^{14} - 3 q^{16} - 3 q^{17} - 6 q^{18} + 12 q^{20} + 6 q^{21} - 6 q^{22} + 3 q^{25} - 12 q^{26} - 6 q^{27} - 6 q^{28} - 12 q^{29} - 12 q^{31} - 3 q^{32} - 9 q^{33} - 3 q^{34} - 12 q^{35} + 3 q^{36} - 12 q^{37} - 12 q^{39} - 6 q^{40} + 6 q^{42} - 9 q^{43} - 6 q^{44} - 12 q^{45} + 6 q^{47} + 30 q^{49} - 6 q^{50} + 12 q^{51} + 6 q^{52} + 3 q^{54} - 12 q^{55} + 12 q^{56} + 24 q^{58} + 6 q^{59} - 18 q^{61} + 6 q^{62} - 6 q^{63} + 6 q^{64} - 24 q^{65} - 9 q^{66} + 18 q^{67} + 6 q^{68} + 12 q^{69} - 12 q^{70} + 12 q^{71} + 3 q^{72} - 12 q^{73} + 6 q^{74} - 12 q^{77} + 6 q^{78} + 18 q^{79} - 6 q^{80} + 9 q^{81} + 12 q^{83} - 12 q^{84} - 6 q^{85} - 9 q^{86} - 36 q^{87} + 12 q^{88} - 9 q^{89} + 6 q^{90} + 24 q^{91} - 12 q^{94} - 15 q^{98} + 15 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 + 6 * q^8 + 3 * q^9 - 6 * q^10 + 12 * q^11 + 6 * q^13 - 6 * q^14 - 3 * q^16 - 3 * q^17 - 6 * q^18 + 12 * q^20 + 6 * q^21 - 6 * q^22 + 3 * q^25 - 12 * q^26 - 6 * q^27 - 6 * q^28 - 12 * q^29 - 12 * q^31 - 3 * q^32 - 9 * q^33 - 3 * q^34 - 12 * q^35 + 3 * q^36 - 12 * q^37 - 12 * q^39 - 6 * q^40 + 6 * q^42 - 9 * q^43 - 6 * q^44 - 12 * q^45 + 6 * q^47 + 30 * q^49 - 6 * q^50 + 12 * q^51 + 6 * q^52 + 3 * q^54 - 12 * q^55 + 12 * q^56 + 24 * q^58 + 6 * q^59 - 18 * q^61 + 6 * q^62 - 6 * q^63 + 6 * q^64 - 24 * q^65 - 9 * q^66 + 18 * q^67 + 6 * q^68 + 12 * q^69 - 12 * q^70 + 12 * q^71 + 3 * q^72 - 12 * q^73 + 6 * q^74 - 12 * q^77 + 6 * q^78 + 18 * q^79 - 6 * q^80 + 9 * q^81 + 12 * q^83 - 12 * q^84 - 6 * q^85 - 9 * q^86 - 36 * q^87 + 12 * q^88 - 9 * q^89 + 6 * q^90 + 24 * q^91 - 12 * q^94 - 15 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.766044	+	1.32683i	−0.442276	+	0.766044i	−0.997858	−	0.0654173i	$-0.979162\pi$
$3$	−0.766044	+	1.32683i	−0.442276	+	0.766044i	0.555582	+	0.831462i	$0.312495\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$	−0.766044	−	1.32683i	−0.312736	−	0.541675i
$7$	2.69459			1.01846			0.509230	−	0.860630i	$-0.329930\pi$
$7$	2.69459			1.01846			0.509230	+	0.860630i	$0.329930\pi$
$8$	1.00000			0.353553
$9$	0.326352	+	0.565258i	0.108784	+	0.188419i
$10$	−1.00000	−	1.73205i	−0.316228	−	0.547723i
$11$	3.18479			0.960251			0.480126	−	0.877200i	$-0.340591\pi$
$11$	3.18479			0.960251			0.480126	+	0.877200i	$0.340591\pi$
$12$	1.53209			0.442276
$13$	2.87939	+	4.98724i	0.798598	+	1.38321i	0.920529	+	0.390673i	$0.127758\pi$
$13$	2.87939	+	4.98724i	0.798598	+	1.38321i	−0.121932	+	0.992539i	$0.538909\pi$
$14$	−1.34730	+	2.33359i	−0.360080	+	0.623677i
$15$	−1.53209	−	2.65366i	−0.395584	−	0.685171i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.25877	−	5.64436i	0.790368	−	1.36896i	−0.135371	−	0.990795i	$-0.543223\pi$
$17$	3.25877	−	5.64436i	0.790368	−	1.36896i	0.925739	−	0.378162i	$-0.123444\pi$
$18$	−0.652704			−0.153844
$19$		0			0
$19$		0			0
$20$	2.00000			0.447214
$21$	−2.06418	+	3.57526i	−0.450441	+	0.780186i
$22$	−1.59240	+	2.75811i	−0.339500	+	0.588031i
$23$	0.347296	+	0.601535i	0.0724163	+	0.125429i	0.899960	−	0.435973i	$-0.143596\pi$
$23$	0.347296	+	0.601535i	0.0724163	+	0.125429i	−0.827544	+	0.561402i	$0.810262\pi$
$24$	−0.766044	+	1.32683i	−0.156368	+	0.270838i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−5.75877			−1.12939
$27$	−5.59627			−1.07700
$28$	−1.34730	−	2.33359i	−0.254615	−	0.441006i
$29$	1.41147	+	2.44474i	0.262104	+	0.453978i	0.966801	−	0.255531i	$-0.0822503\pi$
$29$	1.41147	+	2.44474i	0.262104	+	0.453978i	−0.704697	+	0.709509i	$0.748917\pi$
$30$	3.06418			0.559440
$31$	2.45336			0.440637			0.220319	−	0.975428i	$-0.429290\pi$
$31$	2.45336			0.440637			0.220319	+	0.975428i	$0.429290\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.43969	+	4.22567i	−0.424696	+	0.735595i
$34$	3.25877	+	5.64436i	0.558875	+	0.967999i
$35$	−2.69459	+	4.66717i	−0.455469	+	0.788896i
$36$	0.326352	−	0.565258i	0.0543920	−	0.0942097i
$37$	−4.36959			−0.718355			−0.359178	−	0.933269i	$-0.616943\pi$
$37$	−4.36959			−0.718355			−0.359178	+	0.933269i	$0.616943\pi$
$38$		0			0
$39$	−8.82295			−1.41280
$40$	−1.00000	+	1.73205i	−0.158114	+	0.273861i
$41$	0.173648	−	0.300767i	0.0271193	−	0.0469720i	−0.852147	−	0.523302i	$-0.824700\pi$
$41$	0.173648	−	0.300767i	0.0271193	−	0.0469720i	0.879267	+	0.476330i	$0.158033\pi$
$42$	−2.06418	−	3.57526i	−0.318510	−	0.551675i
$43$	−3.03209	+	5.25173i	−0.462389	+	0.800882i	−0.999079	−	0.0428977i	$-0.986341\pi$
$43$	−3.03209	+	5.25173i	−0.462389	+	0.800882i	0.536690	+	0.843779i	$0.319674\pi$
$44$	−1.59240	−	2.75811i	−0.240063	−	0.415801i
$45$	−1.30541			−0.194599
$46$	−0.694593			−0.102412
$47$	−3.94356	−	6.83045i	−0.575228	−	0.996324i	−0.996017	−	0.0891652i	$-0.971580\pi$
$47$	−3.94356	−	6.83045i	−0.575228	−	0.996324i	0.420789	−	0.907159i	$-0.361753\pi$
$48$	−0.766044	−	1.32683i	−0.110569	−	0.191511i
$49$	0.260830			0.0372614
$50$	−1.00000			−0.141421
$51$	4.99273	+	8.64766i	0.699121	+	1.21091i
$52$	2.87939	−	4.98724i	0.399299	−	0.691606i
$53$	−4.10607	−	7.11192i	−0.564012	−	0.976897i	−0.997141	−	0.0755650i	$-0.975924\pi$
$53$	−4.10607	−	7.11192i	−0.564012	−	0.976897i	0.433129	−	0.901332i	$-0.357409\pi$
$54$	2.79813	−	4.84651i	0.380778	−	0.659526i
$55$	−3.18479	+	5.51622i	−0.429437	+	0.743807i
$56$	2.69459			0.360080
$57$		0			0
$58$	−2.82295			−0.370671
$59$	−0.286989	+	0.497079i	−0.0373628	+	0.0647142i	−0.884102	−	0.467294i	$-0.845229\pi$
$59$	−0.286989	+	0.497079i	−0.0373628	+	0.0647142i	0.846739	+	0.532008i	$0.178562\pi$
$60$	−1.53209	+	2.65366i	−0.197792	+	0.342585i
$61$	−1.46791	−	2.54250i	−0.187947	−	0.325533i	0.756619	−	0.653856i	$-0.226850\pi$
$61$	−1.46791	−	2.54250i	−0.187947	−	0.325533i	−0.944566	+	0.328323i	$0.893517\pi$
$62$	−1.22668	+	2.12467i	−0.155789	+	0.269834i
$63$	0.879385	+	1.52314i	0.110792	+	0.191898i
$64$	1.00000			0.125000
$65$	−11.5175			−1.42858
$66$	−2.43969	−	4.22567i	−0.300305	−	0.520144i
$67$	2.47906	+	4.29385i	0.302865	+	0.524577i	0.976784	−	0.214228i	$-0.0687236\pi$
$67$	2.47906	+	4.29385i	0.302865	+	0.524577i	−0.673919	+	0.738805i	$0.735390\pi$
$68$	−6.51754			−0.790368
$69$	−1.06418			−0.128112
$70$	−2.69459	−	4.66717i	−0.322065	−	0.557834i
$71$	4.22668	−	7.32083i	0.501615	−	0.868822i	−0.498383	−	0.866957i	$-0.666073\pi$
$71$	4.22668	−	7.32083i	0.501615	−	0.868822i	0.999998	−	0.00186564i	$-0.000593851\pi$
$72$	0.326352	+	0.565258i	0.0384609	+	0.0666163i
$73$	−7.88326	+	13.6542i	−0.922665	+	1.59810i	−0.127392	+	0.991852i	$0.540661\pi$
$73$	−7.88326	+	13.6542i	−0.922665	+	1.59810i	−0.795274	+	0.606251i	$0.792673\pi$
$74$	2.18479	−	3.78417i	0.253977	−	0.439901i
$75$	−1.53209			−0.176910
$76$		0			0
$77$	8.58172			0.977978
$78$	4.41147	−	7.64090i	0.499501	−	0.865161i
$79$	4.53209	−	7.84981i	0.509900	−	0.883172i	−0.490034	−	0.871703i	$-0.663016\pi$
$79$	4.53209	−	7.84981i	0.509900	−	0.883172i	0.999934	−	0.0114693i	$-0.00365088\pi$
$80$	−1.00000	−	1.73205i	−0.111803	−	0.193649i
$81$	3.30793	−	5.72951i	0.367548	−	0.636612i
$82$	0.173648	+	0.300767i	0.0191762	+	0.0332142i
$83$	8.47565			0.930324			0.465162	−	0.885226i	$-0.345996\pi$
$83$	8.47565			0.930324			0.465162	+	0.885226i	$0.345996\pi$
$84$	4.12836			0.450441
$85$	6.51754	+	11.2887i	0.706927	+	1.22443i
$86$	−3.03209	−	5.25173i	−0.326959	−	0.566309i
$87$	−4.32501			−0.463689
$88$	3.18479			0.339500
$89$	−3.86959	−	6.70232i	−0.410175	−	0.710444i	0.584733	−	0.811226i	$-0.301199\pi$
$89$	−3.86959	−	6.70232i	−0.410175	−	0.710444i	−0.994909	+	0.100781i	$0.967866\pi$
$90$	0.652704	−	1.13052i	0.0688010	−	0.119167i
$91$	7.75877	+	13.4386i	0.813340	+	1.40875i
$92$	0.347296	−	0.601535i	0.0362081	−	0.0627144i
$93$	−1.87939	+	3.25519i	−0.194883	+	0.337548i
$94$	7.88713			0.813495
$95$		0			0
$96$	1.53209			0.156368
$97$	0.173648	−	0.300767i	0.0176313	−	0.0305383i	−0.857075	−	0.515191i	$-0.827721\pi$
$97$	0.173648	−	0.300767i	0.0176313	−	0.0305383i	0.874706	+	0.484653i	$0.161054\pi$
$98$	−0.130415	+	0.225885i	−0.0131739	+	0.0228179i
$99$	1.03936	+	1.80023i	0.104460	+	0.180930i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	0.184793	+	0.320070i	0.0183875	+	0.0318482i	0.875073	−	0.483991i	$-0.160813\pi$
$101$	0.184793	+	0.320070i	0.0183875	+	0.0318482i	−0.856685	+	0.515840i	$0.827480\pi$
$102$	−9.98545			−0.988707
$103$	8.58172			0.845582			0.422791	−	0.906227i	$-0.361050\pi$
$103$	8.58172			0.845582			0.422791	+	0.906227i	$0.361050\pi$
$104$	2.87939	+	4.98724i	0.282347	+	0.489039i
$105$	−4.12836	−	7.15052i	−0.402886	−	0.697819i
$106$	8.21213			0.797633
$107$	−11.4534			−1.10724			−0.553619	−	0.832770i	$-0.686754\pi$
$107$	−11.4534			−1.10724			−0.553619	+	0.832770i	$0.686754\pi$
$108$	2.79813	+	4.84651i	0.269251	+	0.466356i
$109$	−4.34730	+	7.52974i	−0.416395	+	0.721218i	−0.995574	−	0.0939827i	$-0.970040\pi$
$109$	−4.34730	+	7.52974i	−0.416395	+	0.721218i	0.579178	+	0.815201i	$0.303373\pi$
$110$	−3.18479	−	5.51622i	−0.303658	−	0.525951i
$111$	3.34730	−	5.79769i	0.317711	−	0.550292i
$112$	−1.34730	+	2.33359i	−0.127308	+	0.220503i
$113$	2.85978			0.269026			0.134513	−	0.990912i	$-0.457053\pi$
$113$	2.85978			0.269026			0.134513	+	0.990912i	$0.457053\pi$
$114$		0			0
$115$	−1.38919			−0.129542
$116$	1.41147	−	2.44474i	0.131052	−	0.226989i
$117$	−1.87939	+	3.25519i	−0.173749	+	0.300942i
$118$	−0.286989	−	0.497079i	−0.0264195	−	0.0457599i
$119$	8.78106	−	15.2092i	0.804958	−	1.39423i
$120$	−1.53209	−	2.65366i	−0.139860	−	0.242245i
$121$	−0.857097			−0.0779179
$122$	2.93582			0.265797
$123$	0.266044	+	0.460802i	0.0239884	+	0.0415492i
$124$	−1.22668	−	2.12467i	−0.110159	−	0.190801i
$125$	−12.0000			−1.07331
$126$	−1.75877			−0.156684
$127$	−4.86484	−	8.42615i	−0.431685	−	0.747699i	0.565334	−	0.824862i	$-0.308747\pi$
$127$	−4.86484	−	8.42615i	−0.431685	−	0.747699i	−0.997019	+	0.0771626i	$0.975414\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−4.64543	−	8.04612i	−0.409007	−	0.708421i
$130$	5.75877	−	9.97448i	0.505078	−	0.874820i
$131$	3.23396	−	5.60138i	0.282552	−	0.489394i	−0.689461	−	0.724323i	$-0.742152\pi$
$131$	3.23396	−	5.60138i	0.282552	−	0.489394i	0.972013	+	0.234929i	$0.0754857\pi$
$132$	4.87939			0.424696
$133$		0			0
$134$	−4.95811			−0.428316
$135$	5.59627	−	9.69302i	0.481650	−	0.834242i
$136$	3.25877	−	5.64436i	0.279437	−	0.484000i
$137$	5.83022	+	10.0982i	0.498109	+	0.862751i	0.999998	−	0.00218159i	$-0.000694422\pi$
$137$	5.83022	+	10.0982i	0.498109	+	0.862751i	−0.501888	+	0.864933i	$0.667361\pi$
$138$	0.532089	−	0.921605i	0.0452944	−	0.0784522i
$139$	4.13176	+	7.15642i	0.350451	+	0.606999i	0.986329	−	0.164791i	$-0.0526949\pi$
$139$	4.13176	+	7.15642i	0.350451	+	0.606999i	−0.635877	+	0.771790i	$0.719362\pi$
$140$	5.38919			0.455469
$141$	12.0838			1.01764
$142$	4.22668	+	7.32083i	0.354695	+	0.614350i
$143$	9.17024	+	15.8833i	0.766854	+	1.32823i
$144$	−0.652704			−0.0543920
$145$	−5.64590			−0.468866
$146$	−7.88326	−	13.6542i	−0.652423	−	1.13003i
$147$	−0.199807	+	0.346076i	−0.0164798	+	0.0285439i
$148$	2.18479	+	3.78417i	0.179589	+	0.311057i
$149$	8.22668	−	14.2490i	0.673956	−	1.16733i	−0.302817	−	0.953049i	$-0.597927\pi$
$149$	8.22668	−	14.2490i	0.673956	−	1.16733i	0.976773	−	0.214277i	$-0.0687396\pi$
$150$	0.766044	−	1.32683i	0.0625473	−	0.108335i
$151$	4.65539			0.378850			0.189425	−	0.981895i	$-0.439338\pi$
$151$	4.65539			0.378850			0.189425	+	0.981895i	$0.439338\pi$
$152$		0			0
$153$	4.25402			0.343917
$154$	−4.29086	+	7.43199i	−0.345767	+	0.598887i
$155$	−2.45336	+	4.24935i	−0.197059	+	0.341316i
$156$	4.41147	+	7.64090i	0.353201	+	0.611761i
$157$	−4.22668	+	7.32083i	−0.337326	+	0.584266i	−0.983929	−	0.178561i	$-0.942856\pi$
$157$	−4.22668	+	7.32083i	−0.337326	+	0.584266i	0.646603	+	0.762827i	$0.276189\pi$
$158$	4.53209	+	7.84981i	0.360554	+	0.624497i
$159$	12.5817			0.997795
$160$	2.00000			0.158114
$161$	0.935822	+	1.62089i	0.0737531	+	0.127744i
$162$	3.30793	+	5.72951i	0.259896	+	0.450153i
$163$	17.0496			1.33543			0.667715	−	0.744417i	$-0.267272\pi$
$163$	17.0496			1.33543			0.667715	+	0.744417i	$0.267272\pi$
$164$	−0.347296			−0.0271193
$165$	−4.87939	−	8.45134i	−0.379860	−	0.657936i
$166$	−4.23783	+	7.34013i	−0.328919	+	0.569705i
$167$	1.59627	+	2.76481i	0.123523	+	0.213948i	0.921155	−	0.389197i	$-0.127247\pi$
$167$	1.59627	+	2.76481i	0.123523	+	0.213948i	−0.797632	+	0.603145i	$0.793914\pi$
$168$	−2.06418	+	3.57526i	−0.159255	+	0.275837i
$169$	−10.0817	+	17.4620i	−0.775517	+	1.34323i
$170$	−13.0351			−0.999745
$171$		0			0
$172$	6.06418			0.462389
$173$	−4.81521	+	8.34018i	−0.366093	+	0.634092i	−0.988951	−	0.148243i	$-0.952638\pi$
$173$	−4.81521	+	8.34018i	−0.366093	+	0.634092i	0.622858	+	0.782335i	$0.285972\pi$
$174$	2.16250	−	3.74557i	0.163939	−	0.283951i
$175$	1.34730	+	2.33359i	0.101846	+	0.176403i
$176$	−1.59240	+	2.75811i	−0.120031	+	0.207900i
$177$	−0.439693	−	0.761570i	−0.0330493	−	0.0572431i
$178$	7.73917			0.580075
$179$	18.8161			1.40638			0.703192	−	0.711000i	$-0.251757\pi$
$179$	18.8161			1.40638			0.703192	+	0.711000i	$0.251757\pi$
$180$	0.652704	+	1.13052i	0.0486497	+	0.0842637i
$181$	−1.38919	−	2.40614i	−0.103257	−	0.178847i	0.809768	−	0.586751i	$-0.199593\pi$
$181$	−1.38919	−	2.40614i	−0.103257	−	0.178847i	−0.913025	+	0.407904i	$0.866260\pi$
$182$	−15.5175			−1.15024
$183$	4.49794			0.332497
$184$	0.347296	+	0.601535i	0.0256030	+	0.0443457i
$185$	4.36959	−	7.56834i	0.321258	−	0.556436i
$186$	−1.87939	−	3.25519i	−0.137803	−	0.238682i
$187$	10.3785	−	17.9761i	0.758952	−	1.31454i
$188$	−3.94356	+	6.83045i	−0.287614	+	0.498162i
$189$	−15.0797			−1.09688
$190$		0			0
$191$	9.56212			0.691891			0.345945	−	0.938255i	$-0.387558\pi$
$191$	9.56212			0.691891			0.345945	+	0.938255i	$0.387558\pi$
$192$	−0.766044	+	1.32683i	−0.0552845	+	0.0957556i
$193$	11.8405	−	20.5083i	0.852297	−	1.47622i	−0.0268330	−	0.999640i	$-0.508542\pi$
$193$	11.8405	−	20.5083i	0.852297	−	1.47622i	0.879130	−	0.476582i	$-0.158124\pi$
$194$	0.173648	+	0.300767i	0.0124672	+	0.0215938i
$195$	8.82295	−	15.2818i	0.631824	−	1.09435i
$196$	−0.130415	−	0.225885i	−0.00931535	−	0.0161347i
$197$	−22.9222			−1.63314			−0.816570	−	0.577247i	$-0.804127\pi$
$197$	−22.9222			−1.63314			−0.816570	+	0.577247i	$0.804127\pi$
$198$	−2.07873			−0.147729
$199$	−5.04189	−	8.73281i	−0.357410	−	0.619052i	0.630117	−	0.776500i	$-0.283007\pi$
$199$	−5.04189	−	8.73281i	−0.357410	−	0.619052i	−0.987527	+	0.157448i	$0.949673\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−7.59627			−0.535799
$202$	−0.369585			−0.0260039
$203$	3.80335	+	6.58759i	0.266943	+	0.462358i
$204$	4.99273	−	8.64766i	0.349561	−	0.605457i
$205$	0.347296	+	0.601535i	0.0242562	+	0.0420130i
$206$	−4.29086	+	7.43199i	−0.298958	+	0.517811i
$207$	−0.226682	+	0.392624i	−0.0157555	+	0.0272893i
$208$	−5.75877			−0.399299
$209$		0			0
$210$	8.25671			0.569767
$211$	11.1800	−	19.3644i	0.769666	−	1.33310i	−0.168078	−	0.985774i	$-0.553756\pi$
$211$	11.1800	−	19.3644i	0.769666	−	1.33310i	0.937744	−	0.347327i	$-0.112911\pi$
$212$	−4.10607	+	7.11192i	−0.282006	+	0.488448i
$213$	6.47565	+	11.2162i	0.443704	+	0.768518i
$214$	5.72668	−	9.91890i	0.391468	−	0.678042i
$215$	−6.06418	−	10.5035i	−0.413573	−	0.716330i
$216$	−5.59627			−0.380778
$217$	6.61081			0.448771
$218$	−4.34730	−	7.52974i	−0.294436	−	0.509978i
$219$	−12.0778	−	20.9194i	−0.816145	−	1.41361i
$220$	6.36959			0.429437
$221$	37.5330			2.52474
$222$	3.34730	+	5.79769i	0.224656	+	0.389115i
$223$	4.63816	−	8.03352i	0.310594	−	0.537964i	−0.667897	−	0.744254i	$-0.732805\pi$
$223$	4.63816	−	8.03352i	0.310594	−	0.537964i	0.978491	+	0.206289i	$0.0661388\pi$
$224$	−1.34730	−	2.33359i	−0.0900200	−	0.155919i
$225$	−0.326352	+	0.565258i	−0.0217568	+	0.0376839i
$226$	−1.42989	+	2.47665i	−0.0951150	+	0.164744i
$227$	7.73648			0.513488			0.256744	−	0.966479i	$-0.417350\pi$
$227$	7.73648			0.513488			0.256744	+	0.966479i	$0.417350\pi$
$228$		0			0
$229$	−23.0351			−1.52220			−0.761101	−	0.648634i	$-0.775341\pi$
$229$	−23.0351			−1.52220			−0.761101	+	0.648634i	$0.775341\pi$
$230$	0.694593	−	1.20307i	0.0458001	−	0.0793281i
$231$	−6.57398	+	11.3865i	−0.432536	+	0.749174i
$232$	1.41147	+	2.44474i	0.0926678	+	0.160505i
$233$	−4.19981	+	7.27428i	−0.275139	+	0.476554i	−0.970170	−	0.242425i	$-0.922057\pi$
$233$	−4.19981	+	7.27428i	−0.275139	+	0.476554i	0.695032	+	0.718979i	$0.255390\pi$
$234$	−1.87939	−	3.25519i	−0.122859	−	0.212798i
$235$	15.7743			1.02900
$236$	0.573978			0.0373628
$237$	6.94356	+	12.0266i	0.451033	+	0.781212i
$238$	8.78106	+	15.2092i	0.569192	+	0.985869i
$239$	−15.7297			−1.01747			−0.508734	−	0.860924i	$-0.669886\pi$
$239$	−15.7297			−1.01747			−0.508734	+	0.860924i	$0.669886\pi$
$240$	3.06418			0.197792
$241$	−8.75150	−	15.1580i	−0.563733	−	0.976415i	−0.997166	−	0.0752291i	$-0.976031\pi$
$241$	−8.75150	−	15.1580i	−0.563733	−	0.976415i	0.433433	−	0.901186i	$-0.357302\pi$
$242$	0.428548	−	0.742267i	0.0275481	−	0.0477148i
$243$	−3.32635	−	5.76141i	−0.213386	−	0.369595i
$244$	−1.46791	+	2.54250i	−0.0939734	+	0.162767i
$245$	−0.260830	+	0.451771i	−0.0166638	+	0.0288626i
$246$	−0.532089			−0.0339247
$247$		0			0
$248$	2.45336			0.155789
$249$	−6.49273	+	11.2457i	−0.411460	+	0.712669i
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	−4.28359	−	7.41939i	−0.270378	−	0.468308i	0.698581	−	0.715531i	$-0.253815\pi$
$251$	−4.28359	−	7.41939i	−0.270378	−	0.468308i	−0.968959	+	0.247223i	$0.920482\pi$
$252$	0.879385	−	1.52314i	0.0553961	−	0.0959488i
$253$	1.10607	+	1.91576i	0.0695378	+	0.120443i
$254$	9.72967			0.610494
$255$	−19.9709			−1.25063
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.01233	+	6.94955i	0.250282	+	0.433501i	0.963603	−	0.267336i	$-0.0861433\pi$
$257$	4.01233	+	6.94955i	0.250282	+	0.433501i	−0.713321	+	0.700837i	$0.752810\pi$
$258$	9.29086			0.578424
$259$	−11.7743			−0.731616
$260$	5.75877	+	9.97448i	0.357144	+	0.618591i
$261$	−0.921274	+	1.59569i	−0.0570254	+	0.0987710i
$262$	3.23396	+	5.60138i	0.199794	+	0.346054i
$263$	2.98040	−	5.16220i	0.183779	−	0.318315i	−0.759385	−	0.650641i	$-0.774500\pi$
$263$	2.98040	−	5.16220i	0.183779	−	0.318315i	0.943165	+	0.332326i	$0.107833\pi$
$264$	−2.43969	+	4.22567i	−0.150153	+	0.260072i
$265$	16.4243			1.00893
$266$		0			0
$267$	11.8571			0.725643
$268$	2.47906	−	4.29385i	0.151432	−	0.262289i
$269$	0.573978	−	0.994159i	0.0349961	−	0.0606149i	−0.847997	−	0.530001i	$-0.822191\pi$
$269$	0.573978	−	0.994159i	0.0349961	−	0.0606149i	0.882993	+	0.469386i	$0.155525\pi$
$270$	5.59627	+	9.69302i	0.340578	+	0.589898i
$271$	−10.0273	+	17.3679i	−0.609118	+	1.05502i	0.382269	+	0.924051i	$0.375143\pi$
$271$	−10.0273	+	17.3679i	−0.609118	+	1.05502i	−0.991386	+	0.130971i	$0.958190\pi$
$272$	3.25877	+	5.64436i	0.197592	+	0.342239i
$273$	−23.7743			−1.43888
$274$	−11.6604			−0.704433
$275$	1.59240	+	2.75811i	0.0960251	+	0.166320i
$276$	0.532089	+	0.921605i	0.0320280	+	0.0554741i
$277$	17.3601			1.04307			0.521533	−	0.853231i	$-0.325360\pi$
$277$	17.3601			1.04307			0.521533	+	0.853231i	$0.325360\pi$
$278$	−8.26352			−0.495613
$279$	0.800660	+	1.38678i	0.0479342	+	0.0830245i
$280$	−2.69459	+	4.66717i	−0.161033	+	0.278917i
$281$	−1.46064	−	2.52990i	−0.0871343	−	0.150921i	0.819164	−	0.573559i	$-0.194438\pi$
$281$	−1.46064	−	2.52990i	−0.0871343	−	0.150921i	−0.906299	+	0.422638i	$0.861104\pi$
$282$	−6.04189	+	10.4649i	−0.359789	+	0.623173i
$283$	4.74035	−	8.21053i	0.281785	−	0.488065i	−0.690040	−	0.723772i	$-0.742407\pi$
$283$	4.74035	−	8.21053i	0.281785	−	0.488065i	0.971824	+	0.235706i	$0.0757403\pi$
$284$	−8.45336			−0.501615
$285$		0			0
$286$	−18.3405			−1.08450
$287$	0.467911	−	0.810446i	0.0276199	−	0.0478391i
$288$	0.326352	−	0.565258i	0.0192305	−	0.0333081i
$289$	−12.7392	−	22.0649i	−0.749363	−	1.29793i
$290$	2.82295	−	4.88949i	0.165769	−	0.287121i
$291$	0.266044	+	0.460802i	0.0155958	+	0.0270127i
$292$	15.7665			0.922665
$293$	−27.2918			−1.59440			−0.797202	−	0.603713i	$-0.793687\pi$
$293$	−27.2918			−1.59440			−0.797202	+	0.603713i	$0.793687\pi$
$294$	−0.199807	−	0.346076i	−0.0116530	−	0.0201836i
$295$	−0.573978	−	0.994159i	−0.0334183	−	0.0578822i
$296$	−4.36959			−0.253977
$297$	−17.8229			−1.03419
$298$	8.22668	+	14.2490i	0.476559	+	0.825424i
$299$	−2.00000	+	3.46410i	−0.115663	+	0.200334i
$300$	0.766044	+	1.32683i	0.0442276	+	0.0766044i
$301$	−8.17024	+	14.1513i	−0.470925	+	0.815666i
$302$	−2.32770	+	4.03169i	−0.133944	+	0.231998i
$303$	−0.566237			−0.0325295
$304$		0			0
$305$	5.87164			0.336209
$306$	−2.12701	+	3.68409i	−0.121593	+	0.210606i
$307$	−10.6643	+	18.4711i	−0.608645	+	1.05420i	0.382819	+	0.923823i	$0.374953\pi$
$307$	−10.6643	+	18.4711i	−0.608645	+	1.05420i	−0.991464	+	0.130380i	$0.958380\pi$
$308$	−4.29086	−	7.43199i	−0.244494	−	0.423477i
$309$	−6.57398	+	11.3865i	−0.373981	+	0.647753i
$310$	−2.45336	−	4.24935i	−0.139342	−	0.241347i
$311$	−29.2918			−1.66099			−0.830493	−	0.557030i	$-0.811941\pi$
$311$	−29.2918			−1.66099			−0.830493	+	0.557030i	$0.811941\pi$
$312$	−8.82295			−0.499501
$313$	−2.78059	−	4.81613i	−0.157168	−	0.272224i	0.776678	−	0.629898i	$-0.216903\pi$
$313$	−2.78059	−	4.81613i	−0.157168	−	0.272224i	−0.933846	+	0.357674i	$0.883570\pi$
$314$	−4.22668	−	7.32083i	−0.238525	−	0.413138i
$315$	−3.51754			−0.198191
$316$	−9.06418			−0.509900
$317$	−1.90167	−	3.29380i	−0.106809	−	0.184998i	0.807667	−	0.589639i	$-0.200730\pi$
$317$	−1.90167	−	3.29380i	−0.106809	−	0.184998i	−0.914476	+	0.404641i	$0.867397\pi$
$318$	−6.29086	+	10.8961i	−0.352774	+	0.611022i
$319$	4.49525	+	7.78601i	0.251686	+	0.435933i
$320$	−1.00000	+	1.73205i	−0.0559017	+	0.0968246i
$321$	8.77379	−	15.1966i	0.489705	−	0.848194i
$322$	−1.87164			−0.104303
$323$		0			0
$324$	−6.61587			−0.367548
$325$	−2.87939	+	4.98724i	−0.159720	+	0.276642i
$326$	−8.52481	+	14.7654i	−0.472146	+	0.817781i
$327$	−6.66044	−	11.5362i	−0.368323	−	0.637955i
$328$	0.173648	−	0.300767i	0.00958812	−	0.0166071i
$329$	−10.6263	−	18.4053i	−0.585847	−	1.01472i
$330$	9.75877			0.537203
$331$	20.4219			1.12249			0.561245	−	0.827650i	$-0.310323\pi$
$331$	20.4219			1.12249			0.561245	+	0.827650i	$0.310323\pi$
$332$	−4.23783	−	7.34013i	−0.232581	−	0.402842i
$333$	−1.42602	−	2.46994i	−0.0781455	−	0.135352i
$334$	−3.19253			−0.174688
$335$	−9.91622			−0.541781
$336$	−2.06418	−	3.57526i	−0.112610	−	0.195046i
$337$	−10.1552	+	17.5894i	−0.553191	+	0.958154i	0.444851	+	0.895604i	$0.353257\pi$
$337$	−10.1552	+	17.5894i	−0.553191	+	0.958154i	−0.998042	+	0.0625498i	$0.980077\pi$
$338$	−10.0817	−	17.4620i	−0.548373	−	0.949810i
$339$	−2.19072	+	3.79444i	−0.118984	+	0.206086i
$340$	6.51754	−	11.2887i	0.353463	−	0.612216i
$341$	7.81345			0.423122
$342$		0			0
$343$	−18.1593			−0.980511
$344$	−3.03209	+	5.25173i	−0.163479	+	0.283154i
$345$	1.06418	−	1.84321i	0.0572934	−	0.0992351i
$346$	−4.81521	−	8.34018i	−0.258867	−	0.448371i
$347$	−2.60741	+	4.51617i	−0.139973	+	0.242441i	−0.927486	−	0.373857i	$-0.878035\pi$
$347$	−2.60741	+	4.51617i	−0.139973	+	0.242441i	0.787513	+	0.616298i	$0.211368\pi$
$348$	2.16250	+	3.74557i	0.115922	+	0.200783i
$349$	14.3405			0.767629			0.383814	−	0.923410i	$-0.374610\pi$
$349$	14.3405			0.767629			0.383814	+	0.923410i	$0.374610\pi$
$350$	−2.69459			−0.144032
$351$	−16.1138	−	27.9099i	−0.860091	−	1.48972i
$352$	−1.59240	−	2.75811i	−0.0848750	−	0.147008i
$353$	26.2499			1.39714			0.698571	−	0.715541i	$-0.253820\pi$
$353$	26.2499			1.39714			0.698571	+	0.715541i	$0.253820\pi$
$354$	0.879385			0.0467388
$355$	8.45336	+	14.6417i	0.448658	+	0.777098i
$356$	−3.86959	+	6.70232i	−0.205088	+	0.355222i
$357$	13.4534	+	23.3019i	0.712027	+	1.23327i
$358$	−9.40807	+	16.2953i	−0.497232	+	0.861231i
$359$	16.8452	−	29.1768i	0.889058	−	1.53989i	0.0480664	−	0.998844i	$-0.484694\pi$
$359$	16.8452	−	29.1768i	0.889058	−	1.53989i	0.840991	−	0.541049i	$-0.181973\pi$
$360$	−1.30541			−0.0688010
$361$		0			0
$362$	2.77837			0.146028
$363$	0.656574	−	1.13722i	0.0344612	−	0.0596885i
$364$	7.75877	−	13.4386i	0.406670	−	0.704373i
$365$	−15.7665	−	27.3084i	−0.825257	−	1.42939i
$366$	−2.24897	+	3.89533i	−0.117556	+	0.203612i
$367$	5.23442	+	9.06629i	0.273235	+	0.473256i	0.969688	−	0.244346i	$-0.0785731\pi$
$367$	5.23442	+	9.06629i	0.273235	+	0.473256i	−0.696454	+	0.717602i	$0.745240\pi$
$368$	−0.694593			−0.0362081
$369$	0.226682			0.0118006
$370$	4.36959	+	7.56834i	0.227164	+	0.393459i
$371$	−11.0642	−	19.1637i	−0.574423	−	0.994931i
$372$	3.75877			0.194883
$373$	23.9026			1.23763			0.618815	−	0.785537i	$-0.287613\pi$
$373$	23.9026			1.23763			0.618815	+	0.785537i	$0.287613\pi$
$374$	10.3785	+	17.9761i	0.536660	+	0.929522i
$375$	9.19253	−	15.9219i	0.474700	−	0.822205i
$376$	−3.94356	−	6.83045i	−0.203374	−	0.352254i
$377$	−8.12836	+	14.0787i	−0.418632	+	0.725091i
$378$	7.53983	−	13.0594i	0.387807	−	0.671701i
$379$	17.8135			0.915016			0.457508	−	0.889206i	$-0.348742\pi$
$379$	17.8135			0.915016			0.457508	+	0.889206i	$0.348742\pi$
$380$		0			0
$381$	14.9067			0.763695
$382$	−4.78106	+	8.28104i	−0.244620	+	0.423695i
$383$	−12.5398	+	21.7196i	−0.640755	+	1.10982i	0.344509	+	0.938783i	$0.388045\pi$
$383$	−12.5398	+	21.7196i	−0.640755	+	1.10982i	−0.985264	+	0.171038i	$0.945288\pi$
$384$	−0.766044	−	1.32683i	−0.0390920	−	0.0677094i
$385$	−8.58172	+	14.8640i	−0.437365	+	0.757538i
$386$	11.8405	+	20.5083i	0.602665	+	1.04385i
$387$	−3.95811			−0.201202
$388$	−0.347296			−0.0176313
$389$	4.70914	+	8.15647i	0.238763	+	0.413549i	0.960360	−	0.278764i	$-0.0899248\pi$
$389$	4.70914	+	8.15647i	0.238763	+	0.413549i	−0.721597	+	0.692314i	$0.756591\pi$
$390$	8.82295	+	15.2818i	0.446767	+	0.773824i
$391$	4.52704			0.228942
$392$	0.260830			0.0131739
$393$	4.95471	+	8.58180i	0.249932	+	0.432895i
$394$	11.4611	−	19.8512i	0.577402	−	1.00009i
$395$	9.06418	+	15.6996i	0.456068	+	0.789933i
$396$	1.03936	−	1.80023i	0.0522299	−	0.0904649i
$397$	−3.42602	+	5.93404i	−0.171947	+	0.297821i	−0.939101	−	0.343643i	$-0.888339\pi$
$397$	−3.42602	+	5.93404i	−0.171947	+	0.297821i	0.767153	+	0.641464i	$0.221672\pi$
$398$	10.0838			0.505454
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−2.37346	+	4.11095i	−0.118525	+	0.205291i	−0.919183	−	0.393830i	$-0.871150\pi$
$401$	−2.37346	+	4.11095i	−0.118525	+	0.205291i	0.800659	+	0.599121i	$0.204483\pi$
$402$	3.79813	−	6.57856i	0.189434	−	0.328109i
$403$	7.06418	+	12.2355i	0.351892	+	0.609494i
$404$	0.184793	−	0.320070i	0.00919377	−	0.0159241i
$405$	6.61587	+	11.4590i	0.328745	+	0.569403i
$406$	−7.60670			−0.377514
$407$	−13.9162			−0.689802
$408$	4.99273	+	8.64766i	0.247177	+	0.428123i
$409$	−15.8464	−	27.4468i	−0.783555	−	1.35716i	−0.929859	−	0.367917i	$-0.880071\pi$
$409$	−15.8464	−	27.4468i	−0.783555	−	1.35716i	0.146304	−	0.989240i	$-0.453262\pi$
$410$	−0.694593			−0.0343035
$411$	−17.8648			−0.881207
$412$	−4.29086	−	7.43199i	−0.211395	−	0.366148i
$413$	−0.773318	+	1.33943i	−0.0380525	+	0.0659089i
$414$	−0.226682	−	0.392624i	−0.0111408	−	0.0192964i
$415$	−8.47565	+	14.6803i	−0.416053	+	0.720626i
$416$	2.87939	−	4.98724i	0.141173	−	0.244520i
$417$	−12.6604			−0.619985
$418$		0			0
$419$	−11.0101			−0.537879			−0.268939	−	0.963157i	$-0.586673\pi$
$419$	−11.0101			−0.537879			−0.268939	+	0.963157i	$0.586673\pi$
$420$	−4.12836	+	7.15052i	−0.201443	+	0.348910i
$421$	4.33275	−	7.50454i	0.211165	−	0.365749i	−0.740914	−	0.671600i	$-0.765608\pi$
$421$	4.33275	−	7.50454i	0.211165	−	0.365749i	0.952079	+	0.305851i	$0.0989409\pi$
$422$	11.1800	+	19.3644i	0.544236	+	0.942645i
$423$	2.57398	−	4.45826i	0.125151	−	0.216768i
$424$	−4.10607	−	7.11192i	−0.199408	−	0.345385i
$425$	6.51754			0.316147
$426$	−12.9513			−0.627493
$427$	−3.95542	−	6.85099i	−0.191416	−	0.331543i
$428$	5.72668	+	9.91890i	0.276810	+	0.479448i
$429$	−28.0993			−1.35665
$430$	12.1284			0.584881
$431$	14.9436	+	25.8830i	0.719806	+	1.24674i	0.961076	+	0.276283i	$0.0891026\pi$
$431$	14.9436	+	25.8830i	0.719806	+	1.24674i	−0.241270	+	0.970458i	$0.577564\pi$
$432$	2.79813	−	4.84651i	0.134625	−	0.233178i
$433$	−4.63041	−	8.02011i	−0.222524	−	0.385422i	0.733050	−	0.680175i	$-0.238096\pi$
$433$	−4.63041	−	8.02011i	−0.222524	−	0.385422i	−0.955574	+	0.294753i	$0.904763\pi$
$434$	−3.30541	+	5.72513i	−0.158665	+	0.274815i
$435$	4.32501	−	7.49113i	0.207368	−	0.359172i
$436$	8.69459			0.416395
$437$		0			0
$438$	24.1557			1.15420
$439$	−10.4311	+	18.0672i	−0.497848	+	0.862298i	−0.999997	−	0.00248311i	$-0.999210\pi$
$439$	−10.4311	+	18.0672i	−0.497848	+	0.862298i	0.502149	+	0.864781i	$0.332543\pi$
$440$	−3.18479	+	5.51622i	−0.151829	+	0.262976i
$441$	0.0851223	+	0.147436i	0.00405344	+	0.00702077i
$442$	−18.7665	+	32.5046i	−0.892632	+	1.54608i
$443$	−11.9140	−	20.6357i	−0.566051	−	0.980430i	−0.996951	−	0.0780297i	$-0.975137\pi$
$443$	−11.9140	−	20.6357i	−0.566051	−	0.980430i	0.430900	−	0.902400i	$-0.358196\pi$
$444$	−6.69459			−0.317711
$445$	15.4783			0.733744
$446$	4.63816	+	8.03352i	0.219623	+	0.380398i
$447$	12.6040	+	21.8308i	0.596149	+	1.03256i
$448$	2.69459			0.127308
$449$	−2.18210			−0.102980			−0.0514899	−	0.998674i	$-0.516397\pi$
$449$	−2.18210			−0.102980			−0.0514899	+	0.998674i	$0.516397\pi$
$450$	−0.326352	−	0.565258i	−0.0153844	−	0.0266465i
$451$	0.553033	−	0.957882i	0.0260413	−	0.0451049i
$452$	−1.42989	−	2.47665i	−0.0672565	−	0.116492i
$453$	−3.56624	+	6.17690i	−0.167556	+	0.290216i
$454$	−3.86824	+	6.69999i	−0.181546	+	0.314446i
$455$	−31.0351			−1.45495
$456$		0			0
$457$	1.78106			0.0833144			0.0416572	−	0.999132i	$-0.486736\pi$
$457$	1.78106			0.0833144			0.0416572	+	0.999132i	$0.486736\pi$
$458$	11.5175	−	19.9490i	0.538179	−	0.932154i
$459$	−18.2369	+	31.5873i	−0.851228	+	1.47437i
$460$	0.694593	+	1.20307i	0.0323856	+	0.0560934i
$461$	7.74422	−	13.4134i	0.360684	−	0.624724i	−0.627389	−	0.778706i	$-0.715876\pi$
$461$	7.74422	−	13.4134i	0.360684	−	0.624724i	0.988074	+	0.153982i	$0.0492098\pi$
$462$	−6.57398	−	11.3865i	−0.305849	−	0.529746i
$463$	−2.71007			−0.125948			−0.0629739	−	0.998015i	$-0.520058\pi$
$463$	−2.71007			−0.125948			−0.0629739	+	0.998015i	$0.520058\pi$
$464$	−2.82295			−0.131052
$465$	−3.75877	−	6.51038i	−0.174309	−	0.301912i
$466$	−4.19981	−	7.27428i	−0.194552	−	0.336974i
$467$	12.9135			0.597567			0.298784	−	0.954321i	$-0.403419\pi$
$467$	12.9135			0.597567			0.298784	+	0.954321i	$0.403419\pi$
$468$	3.75877			0.173749
$469$	6.68004	+	11.5702i	0.308456	+	0.534261i
$470$	−7.88713	+	13.6609i	−0.363806	+	0.630130i
$471$	−6.47565	−	11.2162i	−0.298382	−	0.516813i
$472$	−0.286989	+	0.497079i	−0.0132097	+	0.0228799i
$473$	−9.65657	+	16.7257i	−0.444010	+	0.769047i
$474$	−13.8871			−0.637857
$475$		0			0
$476$	−17.5621			−0.804958
$477$	2.68004	−	4.64197i	0.122711	−	0.212541i
$478$	7.86484	−	13.6223i	0.359729	−	0.623069i
$479$	9.27631	+	16.0670i	0.423845	+	0.734122i	0.996312	−	0.0858063i	$-0.0273466\pi$
$479$	9.27631	+	16.0670i	0.423845	+	0.734122i	−0.572466	+	0.819928i	$0.694013\pi$
$480$	−1.53209	+	2.65366i	−0.0699300	+	0.121122i
$481$	−12.5817	−	21.7922i	−0.573677	−	0.993638i
$482$	17.5030			0.797239
$483$	−2.86753			−0.130477
$484$	0.428548	+	0.742267i	0.0194795	+	0.0337394i
$485$	0.347296	+	0.601535i	0.0157699	+	0.0273143i
$486$	6.65270			0.301773
$487$	41.1735			1.86575			0.932876	−	0.360199i	$-0.117291\pi$
$487$	41.1735			1.86575			0.932876	+	0.360199i	$0.117291\pi$
$488$	−1.46791	−	2.54250i	−0.0664492	−	0.115093i
$489$	−13.0608	+	22.6219i	−0.590629	+	1.02300i
$490$	−0.260830	−	0.451771i	−0.0117831	−	0.0204089i
$491$	11.2888	−	19.5528i	0.509456	−	0.882404i	−0.490484	−	0.871450i	$-0.663180\pi$
$491$	11.2888	−	19.5528i	0.509456	−	0.882404i	0.999940	−	0.0109540i	$-0.00348682\pi$
$492$	0.266044	−	0.460802i	0.0119942	−	0.0207746i
$493$	18.3987			0.828635
$494$		0			0
$495$	−4.15745			−0.186864
$496$	−1.22668	+	2.12467i	−0.0550796	+	0.0954007i
$497$	11.3892	−	19.7266i	0.510875	−	0.884861i
$498$	−6.49273	−	11.2457i	−0.290946	−	0.503933i
$499$	14.6643	−	25.3993i	0.656465	−	1.13703i	−0.325060	−	0.945694i	$-0.605384\pi$
$499$	14.6643	−	25.3993i	0.656465	−	1.13703i	0.981524	−	0.191337i	$-0.0612823\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$	−4.89124			−0.218525
$502$	8.56717			0.382372
$503$	−16.8084	−	29.1130i	−0.749450	−	1.29808i	−0.948087	−	0.318012i	$-0.896985\pi$
$503$	−16.8084	−	29.1130i	−0.749450	−	1.29808i	0.198637	−	0.980073i	$-0.436348\pi$
$504$	0.879385	+	1.52314i	0.0391709	+	0.0678460i
$505$	−0.739170			−0.0328926
$506$	−2.21213			−0.0983413
$507$	−15.4461	−	26.7534i	−0.685985	−	1.18816i
$508$	−4.86484	+	8.42615i	−0.215842	+	0.373850i
$509$	−2.01455	−	3.48930i	−0.0892933	−	0.154660i	0.817919	−	0.575333i	$-0.195128\pi$
$509$	−2.01455	−	3.48930i	−0.0892933	−	0.154660i	−0.907213	+	0.420672i	$0.861794\pi$
$510$	9.98545	−	17.2953i	0.442163	−	0.765849i
$511$	−21.2422	+	36.7925i	−0.939698	+	1.62760i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−8.02465			−0.353952
$515$	−8.58172	+	14.8640i	−0.378156	+	0.654985i
$516$	−4.64543	+	8.04612i	−0.204504	+	0.354211i
$517$	−12.5594	−	21.7536i	−0.552363	−	0.956721i
$518$	5.88713	−	10.1968i	0.258665	−	0.448022i
$519$	−7.37733	−	12.7779i	−0.323829	−	0.560888i
$520$	−11.5175			−0.505078
$521$	4.98957			0.218597			0.109299	−	0.994009i	$-0.465140\pi$
$521$	4.98957			0.218597			0.109299	+	0.994009i	$0.465140\pi$
$522$	−0.921274	−	1.59569i	−0.0403231	−	0.0698416i
$523$	13.2763	+	22.9952i	0.580533	+	1.00551i	0.995416	+	0.0956374i	$0.0304889\pi$
$523$	13.2763	+	22.9952i	0.580533	+	1.00551i	−0.414884	+	0.909874i	$0.636178\pi$
$524$	−6.46791			−0.282552
$525$	−4.12836			−0.180176
$526$	2.98040	+	5.16220i	0.129952	+	0.225083i
$527$	7.99495	−	13.8477i	0.348265	−	0.603213i
$528$	−2.43969	−	4.22567i	−0.106174	−	0.183899i
$529$	11.2588	−	19.5008i	0.489512	−	0.847859i
$530$	−8.21213	+	14.2238i	−0.356712	+	0.617844i
$531$	−0.374638			−0.0162579
$532$		0			0
$533$	2.00000			0.0866296
$534$	−5.92855	+	10.2685i	−0.256553	+	0.444363i
$535$	11.4534	−	19.8378i	0.495172	−	0.857663i
$536$	2.47906	+	4.29385i	0.107079	+	0.185466i
$537$	−14.4140	+	24.9658i	−0.622010	+	1.07735i
$538$	0.573978	+	0.994159i	0.0247459	+	0.0428612i
$539$	0.830689			0.0357803
$540$	−11.1925			−0.481650
$541$	5.98545	+	10.3671i	0.257335	+	0.445717i	0.965527	−	0.260303i	$-0.0838224\pi$
$541$	5.98545	+	10.3671i	0.257335	+	0.445717i	−0.708192	+	0.706020i	$0.750489\pi$
$542$	−10.0273	−	17.3679i	−0.430711	−	0.746014i
$543$	4.25671			0.182673
$544$	−6.51754			−0.279437
$545$	−8.69459	−	15.0595i	−0.372435	−	0.645077i
$546$	11.8871	−	20.5891i	0.508722	−	0.881132i
$547$	−1.59833	−	2.76838i	−0.0683395	−	0.118367i	0.829831	−	0.558015i	$-0.188437\pi$
$547$	−1.59833	−	2.76838i	−0.0683395	−	0.118367i	−0.898170	+	0.439647i	$0.855103\pi$
$548$	5.83022	−	10.0982i	0.249055	−	0.431375i
$549$	0.958111	−	1.65950i	0.0408912	−	0.0708256i
$550$	−3.18479			−0.135800
$551$		0			0
$552$	−1.06418			−0.0452944
$553$	12.2121	−	21.1520i	0.519313	−	0.899476i
$554$	−8.68004	+	15.0343i	−0.368780	+	0.638745i
$555$	6.69459	+	11.5954i	0.284170	+	0.492196i
$556$	4.13176	−	7.15642i	0.175226	−	0.303500i
$557$	11.9881	+	20.7641i	0.507954	+	0.879802i	0.999958	+	0.00920875i	$0.00293128\pi$
$557$	11.9881	+	20.7641i	0.507954	+	0.879802i	−0.492004	+	0.870593i	$0.663735\pi$
$558$	−1.60132			−0.0677892
$559$	−34.9222			−1.47705
$560$	−2.69459	−	4.66717i	−0.113867	−	0.197224i
$561$	15.9008	+	27.5410i	0.671332	+	1.16278i
$562$	2.92127			0.123227
$563$	−8.75702			−0.369064			−0.184532	−	0.982826i	$-0.559077\pi$
$563$	−8.75702			−0.369064			−0.184532	+	0.982826i	$0.559077\pi$
$564$	−6.04189	−	10.4649i	−0.254409	−	0.440650i
$565$	−2.85978	+	4.95329i	−0.120312	+	0.208387i
$566$	4.74035	+	8.21053i	0.199252	+	0.345114i
$567$	8.91353	−	15.4387i	0.374333	−	0.648364i
$568$	4.22668	−	7.32083i	0.177348	−	0.307175i
$569$	−36.4201			−1.52681			−0.763406	−	0.645919i	$-0.776474\pi$
$569$	−36.4201			−1.52681			−0.763406	+	0.645919i	$0.776474\pi$
$570$		0			0
$571$	34.2131			1.43177			0.715886	−	0.698217i	$-0.246023\pi$
$571$	34.2131			1.43177			0.715886	+	0.698217i	$0.246023\pi$
$572$	9.17024	−	15.8833i	0.383427	−	0.664115i
$573$	−7.32501	+	12.6873i	−0.306007	+	0.530019i
$574$	0.467911	+	0.810446i	0.0195302	+	0.0338274i
$575$	−0.347296	+	0.601535i	−0.0144833	+	0.0250857i
$576$	0.326352	+	0.565258i	0.0135980	+	0.0235524i
$577$	15.5098			0.645681			0.322841	−	0.946453i	$-0.395362\pi$
$577$	15.5098			0.645681			0.322841	+	0.946453i	$0.395362\pi$
$578$	25.4783			1.05976
$579$	18.1407	+	31.4206i	0.753901	+	1.30579i
$580$	2.82295	+	4.88949i	0.117217	+	0.203025i
$581$	22.8384			0.947498
$582$	−0.532089			−0.0220558
$583$	−13.0770	−	22.6500i	−0.541593	−	0.938066i
$584$	−7.88326	+	13.6542i	−0.326211	+	0.565015i
$585$	−3.75877	−	6.51038i	−0.155406	−	0.269171i
$586$	13.6459	−	23.6354i	0.563707	−	0.976369i
$587$	5.79086	−	10.0301i	0.239014	−	0.413985i	−0.721417	−	0.692501i	$-0.756509\pi$
$587$	5.79086	−	10.0301i	0.239014	−	0.413985i	0.960432	+	0.278516i	$0.0898424\pi$
$588$	0.399615			0.0164798
$589$		0			0
$590$	1.14796			0.0472606
$591$	17.5594	−	30.4138i	0.722298	−	1.25106i
$592$	2.18479	−	3.78417i	0.0897944	−	0.155528i
$593$	23.1964	+	40.1773i	0.952562	+	1.64989i	0.739851	+	0.672771i	$0.234896\pi$
$593$	23.1964	+	40.1773i	0.952562	+	1.64989i	0.212711	+	0.977115i	$0.431771\pi$
$594$	8.91147	−	15.4351i	0.365642	−	0.633311i
$595$	17.5621	+	30.4185i	0.719977	+	1.24704i
$596$	−16.4534			−0.673956
$597$	15.4492			0.632295
$598$	−2.00000	−	3.46410i	−0.0817861	−	0.141658i
$599$	−12.8161	−	22.1982i	−0.523653	−	0.906994i	−0.999621	−	0.0275314i	$-0.991235\pi$
$599$	−12.8161	−	22.1982i	−0.523653	−	0.906994i	0.475968	−	0.879463i	$-0.342098\pi$
$600$	−1.53209			−0.0625473
$601$	7.99226			0.326011			0.163006	−	0.986625i	$-0.447881\pi$
$601$	7.99226			0.326011			0.163006	+	0.986625i	$0.447881\pi$
$602$	−8.17024	−	14.1513i	−0.332994	−	0.576763i
$603$	−1.61809	+	2.80261i	−0.0658937	+	0.114131i
$604$	−2.32770	−	4.03169i	−0.0947126	−	0.164047i
$605$	0.857097	−	1.48453i	0.0348459	−	0.0603549i
$606$	0.283119	−	0.490376i	0.0115009	−	0.0199202i
$607$	−26.9905			−1.09551			−0.547755	−	0.836639i	$-0.684518\pi$
$607$	−26.9905			−1.09551			−0.547755	+	0.836639i	$0.684518\pi$
$608$		0			0
$609$	−11.6541			−0.472249
$610$	−2.93582	+	5.08499i	−0.118868	+	0.205885i
$611$	22.7101	−	39.3350i	0.918751	−	1.59132i
$612$	−2.12701	−	3.68409i	−0.0859793	−	0.148921i
$613$	7.12567	−	12.3420i	0.287803	−	0.498489i	−0.685482	−	0.728090i	$-0.740409\pi$
$613$	7.12567	−	12.3420i	0.287803	−	0.498489i	0.973285	+	0.229600i	$0.0737418\pi$
$614$	−10.6643	−	18.4711i	−0.430377	−	0.745434i
$615$	−1.06418			−0.0429118
$616$	8.58172			0.345767
$617$	15.2802	+	26.4661i	0.615157	+	1.06548i	0.990357	+	0.138539i	$0.0442407\pi$
$617$	15.2802	+	26.4661i	0.615157	+	1.06548i	−0.375200	+	0.926944i	$0.622426\pi$
$618$	−6.57398	−	11.3865i	−0.264444	−	0.458031i
$619$	−28.6750			−1.15255			−0.576273	−	0.817258i	$-0.695493\pi$
$619$	−28.6750			−1.15255			−0.576273	+	0.817258i	$0.695493\pi$
$620$	4.90673			0.197059
$621$	−1.94356	−	3.36635i	−0.0779925	−	0.135087i
$622$	14.6459	−	25.3674i	0.587247	−	1.01714i
$623$	−10.4270	−	18.0600i	−0.417747	−	0.723559i
$624$	4.41147	−	7.64090i	0.176600	−	0.305881i
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	5.56118			0.222270
$627$		0			0
$628$	8.45336			0.337326
$629$	−14.2395	+	24.6635i	−0.567765	+	0.983398i
$630$	1.75877	−	3.04628i	0.0700711	−	0.121367i
$631$	2.24897	+	3.89533i	0.0895301	+	0.155071i	0.907313	−	0.420457i	$-0.138130\pi$
$631$	2.24897	+	3.89533i	0.0895301	+	0.155071i	−0.817783	+	0.575527i	$0.804797\pi$
$632$	4.53209	−	7.84981i	0.180277	−	0.312249i
$633$	17.1288	+	29.6680i	0.680810	+	1.17920i
$634$	3.80335			0.151050
$635$	19.4593			0.772221
$636$	−6.29086	−	10.8961i	−0.249449	−	0.432058i
$637$	0.751030	+	1.30082i	0.0297569	+	0.0515404i
$638$	−8.99050			−0.355937
$639$	5.51754			0.218271
$640$	−1.00000	−	1.73205i	−0.0395285	−	0.0684653i
$641$	5.80406	−	10.0529i	0.229247	−	0.397067i	−0.728338	−	0.685218i	$-0.759707\pi$
$641$	5.80406	−	10.0529i	0.229247	−	0.397067i	0.957585	+	0.288151i	$0.0930404\pi$
$642$	8.77379	+	15.1966i	0.346274	+	0.599764i
$643$	−13.0228	+	22.5561i	−0.513567	+	0.889525i	0.486309	+	0.873787i	$0.338343\pi$
$643$	−13.0228	+	22.5561i	−0.513567	+	0.889525i	−0.999876	+	0.0157377i	$0.994990\pi$
$644$	0.935822	−	1.62089i	0.0368766	−	0.0638721i
$645$	18.5817			0.731654
$646$		0			0
$647$	−2.31490			−0.0910082			−0.0455041	−	0.998964i	$-0.514489\pi$
$647$	−2.31490			−0.0910082			−0.0455041	+	0.998964i	$0.514489\pi$
$648$	3.30793	−	5.72951i	0.129948	−	0.225076i
$649$	−0.914000	+	1.58310i	−0.0358777	+	0.0621419i
$650$	−2.87939	−	4.98724i	−0.112939	−	0.195616i
$651$	−5.06418	+	8.77141i	−0.198481	+	0.343779i
$652$	−8.52481	−	14.7654i	−0.333858	−	0.578258i
$653$	3.30541			0.129351			0.0646753	−	0.997906i	$-0.479399\pi$
$653$	3.30541			0.129351			0.0646753	+	0.997906i	$0.479399\pi$
$654$	13.3209			0.520888
$655$	6.46791	+	11.2028i	0.252722	+	0.437728i
$656$	0.173648	+	0.300767i	0.00677982	+	0.0117430i
$657$	−10.2909			−0.401485
$658$	21.2526			0.828512
$659$	6.87464	+	11.9072i	0.267798	+	0.463839i	0.968293	−	0.249818i	$-0.0803707\pi$
$659$	6.87464	+	11.9072i	0.267798	+	0.463839i	−0.700495	+	0.713657i	$0.747037\pi$
$660$	−4.87939	+	8.45134i	−0.189930	+	0.328968i
$661$	1.66725	+	2.88776i	0.0648486	+	0.112321i	0.896627	−	0.442787i	$-0.146010\pi$
$661$	1.66725	+	2.88776i	0.0648486	+	0.112321i	−0.831778	+	0.555108i	$0.812677\pi$
$662$	−10.2110	+	17.6859i	−0.396860	+	0.687382i
$663$	−28.7520	+	49.7999i	−1.11663	+	1.93407i
$664$	8.47565			0.328919
$665$		0			0
$666$	2.85204			0.110514
$667$	−0.980400	+	1.69810i	−0.0379612	+	0.0657508i
$668$	1.59627	−	2.76481i	0.0617614	−	0.106974i
$669$	7.10607	+	12.3081i	0.274736	+	0.475857i
$670$	4.95811	−	8.58770i	0.191549	−	0.331772i
$671$	−4.67499	−	8.09732i	−0.180476	−	0.312594i
$672$	4.12836			0.159255
$673$	38.9810			1.50261			0.751304	−	0.659957i	$-0.229425\pi$
$673$	38.9810			1.50261			0.751304	+	0.659957i	$0.229425\pi$
$674$	−10.1552	−	17.5894i	−0.391165	−	0.677517i
$675$	−2.79813	−	4.84651i	−0.107700	−	0.186542i
$676$	20.1634			0.775517
$677$	−43.5877			−1.67521			−0.837606	−	0.546275i	$-0.816045\pi$
$677$	−43.5877			−1.67521			−0.837606	+	0.546275i	$0.816045\pi$
$678$	−2.19072	−	3.79444i	−0.0841342	−	0.145725i
$679$	0.467911	−	0.810446i	0.0179568	−	0.0311021i
$680$	6.51754	+	11.2887i	0.249936	+	0.432902i
$681$	−5.92649	+	10.2650i	−0.227104	+	0.393355i
$682$	−3.90673	+	6.76665i	−0.149596	+	0.259108i
$683$	32.9317			1.26010			0.630048	−	0.776556i	$-0.283035\pi$
$683$	32.9317			1.26010			0.630048	+	0.776556i	$0.283035\pi$
$684$		0			0
$685$	−23.3209			−0.891045
$686$	9.07966	−	15.7264i	0.346663	−	0.600438i
$687$	17.6459	−	30.5636i	0.673233	−	1.16607i
$688$	−3.03209	−	5.25173i	−0.115597	−	0.200220i
$689$	23.6459	−	40.9559i	0.900837	−	1.56030i
$690$	1.06418	+	1.84321i	0.0405126	+	0.0701698i
$691$	34.3209			1.30563			0.652814	−	0.757518i	$-0.273588\pi$
$691$	34.3209			1.30563			0.652814	+	0.757518i	$0.273588\pi$
$692$	9.63041			0.366093
$693$	2.80066	+	4.85088i	0.106388	+	0.184270i
$694$	−2.60741	−	4.51617i	−0.0989760	−	0.171431i
$695$	−16.5270			−0.626906
$696$	−4.32501			−0.163939
$697$	−1.13176	−	1.96026i	−0.0428684	−	0.0742503i
$698$	−7.17024	+	12.4192i	−0.271398	+	0.470075i
$699$	−6.43448	−	11.1448i	−0.243374	−	0.421537i
$700$	1.34730	−	2.33359i	0.0509230	−	0.0882013i
$701$	−3.22668	+	5.58878i	−0.121870	+	0.211085i	−0.920505	−	0.390730i	$-0.872222\pi$
$701$	−3.22668	+	5.58878i	−0.121870	+	0.211085i	0.798635	+	0.601816i	$0.205556\pi$
$702$	32.2276			1.21635
$703$		0			0
$704$	3.18479			0.120031
$705$	−12.0838	+	20.9297i	−0.455101	+	0.788259i
$706$	−13.1250	+	22.7331i	−0.493964	+	0.855571i
$707$	0.497941	+	0.862458i	0.0187270	+	0.0324361i
$708$	−0.439693	+	0.761570i	−0.0165247	+	0.0286216i
$709$	1.68954	+	2.92637i	0.0634520	+	0.109902i	0.896006	−	0.444041i	$-0.146456\pi$
$709$	1.68954	+	2.92637i	0.0634520	+	0.109902i	−0.832554	+	0.553944i	$0.813122\pi$
$710$	−16.9067			−0.634498
$711$	5.91622			0.221876
$712$	−3.86959	−	6.70232i	−0.145019	−	0.251180i
$713$	0.852044	+	1.47578i	0.0319093	+	0.0552685i
$714$	−26.9067			−1.00696
$715$	−36.6810			−1.37179
$716$	−9.40807	−	16.2953i	−0.351596	−	0.608982i
$717$	12.0496	−	20.8706i	0.450002	−	0.779426i
$718$	16.8452	+	29.1768i	0.628659	+	1.08887i
$719$	15.6013	−	27.0223i	0.581831	−	1.00776i	−0.413431	−	0.910535i	$-0.635670\pi$
$719$	15.6013	−	27.0223i	0.581831	−	1.00776i	0.995262	−	0.0972256i	$-0.0309968\pi$
$720$	0.652704	−	1.13052i	0.0243248	−	0.0421318i
$721$	23.1242			0.861192
$722$		0			0
$723$	26.8161			0.997303
$724$	−1.38919	+	2.40614i	−0.0516287	+	0.0894235i
$725$	−1.41147	+	2.44474i	−0.0524208	+	0.0907955i
$726$	0.656574	+	1.13722i	0.0243677	+	0.0422062i
$727$	12.8307	−	22.2234i	0.475864	−	0.824220i	−0.523754	−	0.851870i	$-0.675469\pi$
$727$	12.8307	−	22.2234i	0.475864	−	0.824220i	0.999618	+	0.0276492i	$0.00880214\pi$
$728$	7.75877	+	13.4386i	0.287559	+	0.498067i
$729$	30.0401			1.11260
$730$	31.5330			1.16709
$731$	19.7618	+	34.2284i	0.730915	+	1.26598i
$732$	−2.24897	−	3.89533i	−0.0831243	−	0.143976i
$733$	−23.8735			−0.881788			−0.440894	−	0.897559i	$-0.645339\pi$
$733$	−23.8735			−0.881788			−0.440894	+	0.897559i	$0.645339\pi$
$734$	−10.4688			−0.386412
$735$	−0.399615	−	0.692153i	−0.0147400	−	0.0255304i
$736$	0.347296	−	0.601535i	0.0128015	−	0.0221729i
$737$	7.89528	+	13.6750i	0.290826	+	0.503726i
$738$	−0.113341	+	0.196312i	−0.00417213	+	0.00722635i
$739$	22.9702	−	39.7855i	0.844972	−	1.46353i	−0.0406734	−	0.999172i	$-0.512950\pi$
$739$	22.9702	−	39.7855i	0.844972	−	1.46353i	0.885645	−	0.464362i	$-0.153716\pi$
$740$	−8.73917			−0.321258
$741$		0			0
$742$	22.1284			0.812357
$743$	25.5057	−	44.1771i	0.935713	−	1.62070i	0.162355	−	0.986732i	$-0.448091\pi$
$743$	25.5057	−	44.1771i	0.935713	−	1.62070i	0.773358	−	0.633969i	$-0.218576\pi$
$744$	−1.87939	+	3.25519i	−0.0689016	+	0.119341i
$745$	16.4534	+	28.4981i	0.602805	+	1.04409i
$746$	−11.9513	+	20.7003i	−0.437568	+	0.757891i
$747$	2.76604	+	4.79093i	0.101204	+	0.175291i
$748$	−20.7570			−0.758952
$749$	−30.8621			−1.12768
$750$	9.19253	+	15.9219i	0.335664	+	0.581387i
$751$	18.1848	+	31.4970i	0.663573	+	1.14934i	0.979670	+	0.200615i	$0.0642939\pi$
$751$	18.1848	+	31.4970i	0.663573	+	1.14934i	−0.316098	+	0.948727i	$0.602373\pi$
$752$	7.88713			0.287614
$753$	13.1257			0.478326
$754$	−8.12836	−	14.0787i	−0.296017	−	0.512717i
$755$	−4.65539	+	8.06338i	−0.169427	+	0.293456i
$756$	7.53983	+	13.0594i	0.274221	+	0.474965i
$757$	2.90167	−	5.02585i	0.105463	−	0.182668i	−0.808464	−	0.588545i	$-0.799701\pi$
$757$	2.90167	−	5.02585i	0.105463	−	0.182668i	0.913927	+	0.405878i	$0.133034\pi$
$758$	−8.90673	+	15.4269i	−0.323507	+	0.560330i
$759$	−3.38919			−0.123020
$760$		0			0
$761$	22.6355			0.820535			0.410268	−	0.911965i	$-0.365435\pi$
$761$	22.6355			0.820535			0.410268	+	0.911965i	$0.365435\pi$
$762$	−7.45336	+	12.9096i	−0.270007	+	0.467666i
$763$	−11.7142	+	20.2896i	−0.424082	+	0.734532i
$764$	−4.78106	−	8.28104i	−0.172973	−	0.299597i
$765$	−4.25402	+	7.36818i	−0.153805	+	0.266397i
$766$	−12.5398	−	21.7196i	−0.453082	−	0.784762i
$767$	−3.30541			−0.119351
$768$	1.53209			0.0552845
$769$	−5.45130	−	9.44194i	−0.196579	−	0.340485i	0.750838	−	0.660486i	$-0.229650\pi$
$769$	−5.45130	−	9.44194i	−0.196579	−	0.340485i	−0.947417	+	0.320002i	$0.896317\pi$
$770$	−8.58172	−	14.8640i	−0.309264	−	0.535660i
$771$	−12.2945			−0.442775
$772$	−23.6810			−0.852297
$773$	2.62536	+	4.54726i	0.0944277	+	0.163554i	0.909370	−	0.415989i	$-0.136565\pi$
$773$	2.62536	+	4.54726i	0.0944277	+	0.163554i	−0.814942	+	0.579543i	$0.803231\pi$
$774$	1.97906	−	3.42782i	0.0711357	−	0.123211i
$775$	1.22668	+	2.12467i	0.0440637	+	0.0763206i
$776$	0.173648	−	0.300767i	0.00623361	−	0.0107969i
$777$	9.01960	−	15.6224i	0.323576	−	0.560451i
$778$	−9.41828			−0.337662
$779$		0			0
$780$	−17.6459			−0.631824
$781$	13.4611	−	23.3153i	0.481676	−	0.834288i
$782$	−2.26352	+	3.92053i	−0.0809432	+	0.140198i
$783$	−7.89899	−	13.6814i	−0.282287	−	0.488935i
$784$	−0.130415	+	0.225885i	−0.00465768	+	0.00806733i
$785$	−8.45336	−	14.6417i	−0.301713	−	0.522583i
$786$	−9.90941			−0.353457
$787$	−2.38743			−0.0851027			−0.0425514	−	0.999094i	$-0.513549\pi$
$787$	−2.38743			−0.0851027			−0.0425514	+	0.999094i	$0.513549\pi$
$788$	11.4611	+	19.8512i	0.408285	+	0.707170i
$789$	4.56624	+	7.90895i	0.162562	+	0.281566i
$790$	−18.1284			−0.644978
$791$	7.70596			0.273992
$792$	1.03936	+	1.80023i	0.0369322	+	0.0639684i
$793$	8.45336	−	14.6417i	0.300188	−	0.519940i
$794$	−3.42602	−	5.93404i	−0.121585	−	0.210591i
$795$	−12.5817	+	21.7922i	−0.446228	+	0.772889i
$796$	−5.04189	+	8.73281i	−0.178705	+	0.309526i
$797$	31.0951			1.10145			0.550723	−	0.834688i	$-0.314352\pi$
$797$	31.0951			1.10145			0.550723	+	0.834688i	$0.314352\pi$
$798$		0			0
$799$	−51.4047			−1.81857
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	2.52569	−	4.37463i	0.0892409	−	0.154570i
$802$	−2.37346	−	4.11095i	−0.0838096	−	0.145163i
$803$	−25.1065	+	43.4858i	−0.885990	+	1.53458i
$804$	3.79813	+	6.57856i	0.133950	+	0.232008i
$805$	−3.74329			−0.131934
$806$	−14.1284			−0.497650
$807$	0.879385	+	1.52314i	0.0309558	+	0.0536171i
$808$	0.184793	+	0.320070i	0.00650098	+	0.0112600i
$809$	22.3037			0.784155			0.392077	−	0.919932i	$-0.371757\pi$
$809$	22.3037			0.784155			0.392077	+	0.919932i	$0.371757\pi$
$810$	−13.2317			−0.464916
$811$	−1.65951	−	2.87436i	−0.0582733	−	0.100932i	0.835417	−	0.549616i	$-0.185226\pi$
$811$	−1.65951	−	2.87436i	−0.0582733	−	0.100932i	−0.893690	+	0.448684i	$0.851893\pi$
$812$	3.80335	−	6.58759i	0.133471	−	0.231179i
$813$	−15.3628	−	26.6091i	−0.538796	−	0.933222i
$814$	6.95811	−	12.0518i	0.243882	−	0.422415i
$815$	−17.0496	+	29.5308i	−0.597222	+	1.03442i
$816$	−9.98545			−0.349561
$817$		0			0
$818$	31.6928			1.10811
$819$	−5.06418	+	8.77141i	−0.176957	+	0.306498i
$820$	0.347296	−	0.601535i	0.0121281	−	0.0210065i
$821$	0.916222	+	1.58694i	0.0319764	+	0.0553847i	0.881571	−	0.472052i	$-0.156487\pi$
$821$	0.916222	+	1.58694i	0.0319764	+	0.0553847i	−0.849594	+	0.527437i	$0.823153\pi$
$822$	8.93242	−	15.4714i	0.311554	−	0.539627i
$823$	17.1189	+	29.6507i	0.596726	+	1.03356i	0.993301	+	0.115557i	$0.0368654\pi$
$823$	17.1189	+	29.6507i	0.596726	+	1.03356i	−0.396575	+	0.918002i	$0.629801\pi$
$824$	8.58172			0.298958
$825$	−4.87939			−0.169878
$826$	−0.773318	−	1.33943i	−0.0269072	−	0.0466046i
$827$	9.93289	+	17.2043i	0.345400	+	0.598251i	0.985426	−	0.170102i	$-0.0544098\pi$
$827$	9.93289	+	17.2043i	0.345400	+	0.598251i	−0.640026	+	0.768353i	$0.721076\pi$
$828$	0.453363			0.0157555
$829$	−35.7351			−1.24113			−0.620565	−	0.784155i	$-0.713097\pi$
$829$	−35.7351			−1.24113			−0.620565	+	0.784155i	$0.713097\pi$
$830$	−8.47565	−	14.6803i	−0.294194	−	0.509559i
$831$	−13.2986	+	23.0339i	−0.461323	+	0.799035i
$832$	2.87939	+	4.98724i	0.0998247	+	0.172901i
$833$	0.849985	−	1.47222i	0.0294502	−	0.0510093i
$834$	6.33022	−	10.9643i	0.219198	−	0.379661i
$835$	−6.38507			−0.220964
$836$		0			0
$837$	−13.7297			−0.474567
$838$	5.50505	−	9.53503i	0.190169	−	0.329382i
$839$	27.1976	−	47.1076i	0.938965	−	1.62633i	0.171559	−	0.985174i	$-0.445120\pi$
$839$	27.1976	−	47.1076i	0.938965	−	1.62633i	0.767406	−	0.641161i	$-0.221547\pi$
$840$	−4.12836	−	7.15052i	−0.142442	−	0.246716i
$841$	10.5155	−	18.2133i	0.362603	−	0.628046i
$842$	4.33275	+	7.50454i	0.149316	+	0.258624i
$843$	4.47565			0.154150
$844$	−22.3601			−0.769666
$845$	−20.1634	−	34.9241i	−0.693643	−	1.20143i
$846$	2.57398	+	4.45826i	0.0884952	+	0.153278i
$847$	−2.30953			−0.0793563
$848$	8.21213			0.282006
$849$	7.26264	+	12.5793i	0.249253	+	0.431719i
$850$	−3.25877	+	5.64436i	−0.111775	+	0.193600i
$851$	−1.51754	−	2.62846i	−0.0520206	−	0.0901024i
$852$	6.47565	−	11.2162i	0.221852	−	0.384259i
$853$	−7.98814	+	13.8359i	−0.273509	+	0.473731i	−0.969758	−	0.244069i	$-0.921518\pi$
$853$	−7.98814	+	13.8359i	−0.273509	+	0.473731i	0.696249	+	0.717800i	$0.254851\pi$
$854$	7.91085			0.270704
$855$		0			0
$856$	−11.4534			−0.391468
$857$	13.0073	−	22.5293i	0.444320	−	0.769585i	−0.553685	−	0.832726i	$-0.686779\pi$
$857$	13.0073	−	22.5293i	0.444320	−	0.769585i	0.998005	+	0.0631417i	$0.0201120\pi$
$858$	14.0496	−	24.3347i	0.479646	−	0.830772i
$859$	−26.6352	−	46.1336i	−0.908782	−	1.57406i	−0.815759	−	0.578393i	$-0.803680\pi$
$859$	−26.6352	−	46.1336i	−0.908782	−	1.57406i	−0.0930234	−	0.995664i	$-0.529653\pi$
$860$	−6.06418	+	10.5035i	−0.206787	+	0.358165i
$861$	0.716881	+	1.24168i	0.0244313	+	0.0423162i
$862$	−29.8871			−1.01796
$863$	3.23173			0.110010			0.0550048	−	0.998486i	$-0.482483\pi$
$863$	3.23173			0.110010			0.0550048	+	0.998486i	$0.482483\pi$
$864$	2.79813	+	4.84651i	0.0951944	+	0.164882i
$865$	−9.63041	−	16.6804i	−0.327444	−	0.567150i
$866$	9.26083			0.314696
$867$	39.0351			1.32570
$868$	−3.30541	−	5.72513i	−0.112193	−	0.194324i
$869$	14.4338	−	25.0000i	0.489632	−	0.848067i
$870$	4.32501	+	7.49113i	0.146631	+	0.253973i
$871$	−14.2763	+	24.7273i	−0.483734	+	0.837852i
$872$	−4.34730	+	7.52974i	−0.147218	+	0.254989i
$873$	0.226682			0.00767201
$874$		0			0
$875$	−32.3351			−1.09313
$876$	−12.0778	+	20.9194i	−0.408073	+	0.706803i
$877$	−5.86215	+	10.1535i	−0.197951	+	0.342861i	−0.947864	−	0.318676i	$-0.896762\pi$
$877$	−5.86215	+	10.1535i	−0.197951	+	0.342861i	0.749913	+	0.661536i	$0.230095\pi$
$878$	−10.4311	−	18.0672i	−0.352032	−	0.609737i
$879$	20.9067	−	36.2115i	0.705166	−	1.22138i
$880$	−3.18479	−	5.51622i	−0.107359	−	0.185952i
$881$	27.0473			0.911246			0.455623	−	0.890173i	$-0.349417\pi$
$881$	27.0473			0.911246			0.455623	+	0.890173i	$0.349417\pi$
$882$	−0.170245			−0.00573243
$883$	−7.24051	−	12.5409i	−0.243663	−	0.422036i	0.718092	−	0.695948i	$-0.245016\pi$
$883$	−7.24051	−	12.5409i	−0.243663	−	0.422036i	−0.961755	+	0.273912i	$0.911682\pi$
$884$	−18.7665	−	32.5046i	−0.631186	−	1.09325i
$885$	1.75877			0.0591204
$886$	23.8280			0.800517
$887$	5.79561	+	10.0383i	0.194597	+	0.337053i	0.946768	−	0.321915i	$-0.104327\pi$
$887$	5.79561	+	10.0383i	0.194597	+	0.337053i	−0.752171	+	0.658968i	$0.770993\pi$
$888$	3.34730	−	5.79769i	0.112328	−	0.194558i
$889$	−13.1088	−	22.7050i	−0.439654	−	0.761502i
$890$	−7.73917	+	13.4046i	−0.259418	+	0.449324i
$891$	10.5351	−	18.2473i	0.352939	−	0.611307i
$892$	−9.27631			−0.310594
$893$		0			0
$894$	−25.2080			−0.843082
$895$	−18.8161	+	32.5905i	−0.628954	+	1.08938i
$896$	−1.34730	+	2.33359i	−0.0450100	+	0.0779596i
$897$	−3.06418	−	5.30731i	−0.102310	−	0.177206i
$898$	1.09105	−	1.88976i	0.0364089	−	0.0630620i
$899$	3.46286	+	5.99785i	0.115493	+	0.200039i
$900$	0.652704			0.0217568
$901$	−53.5229			−1.78311
$902$	0.553033	+	0.957882i	0.0184140	+	0.0318940i
$903$	−12.5175	−	21.6810i	−0.416558	−	0.721499i
$904$	2.85978			0.0951150
$905$	5.55674			0.184712
$906$	−3.56624	−	6.17690i	−0.118480	−	0.205214i
$907$	−20.9893	+	36.3546i	−0.696939	+	1.20713i	0.272584	+	0.962132i	$0.412122\pi$
$907$	−20.9893	+	36.3546i	−0.696939	+	1.20713i	−0.969523	+	0.245002i	$0.921211\pi$
$908$	−3.86824	−	6.69999i	−0.128372	−	0.222347i
$909$	−0.120615	+	0.208911i	−0.00400054	+	0.00692914i
$910$	15.5175	−	26.8772i	0.514401	−	0.890969i
$911$	−44.8675			−1.48653			−0.743264	−	0.668999i	$-0.766723\pi$
$911$	−44.8675			−1.48653			−0.743264	+	0.668999i	$0.766723\pi$
$912$		0			0
$913$	26.9932			0.893344
$914$	−0.890530	+	1.54244i	−0.0294561	+	0.0510195i
$915$	−4.49794	+	7.79066i	−0.148697	+	0.257551i
$916$	11.5175	+	19.9490i	0.380550	+	0.659132i
$917$	8.71419	−	15.0934i	0.287768	−	0.498429i
$918$	−18.2369	−	31.5873i	−0.601909	−	1.04254i
$919$	−32.5270			−1.07297			−0.536484	−	0.843911i	$-0.680248\pi$
$919$	−32.5270			−1.07297			−0.536484	+	0.843911i	$0.680248\pi$
$920$	−1.38919			−0.0458001
$921$	−16.3387	−	28.2994i	−0.538378	−	0.932498i
$922$	7.74422	+	13.4134i	0.255042	+	0.441746i
$923$	48.6810			1.60235
$924$	13.1480			0.432536
$925$	−2.18479	−	3.78417i	−0.0718355	−	0.124423i
$926$	1.35504	−	2.34699i	0.0445293	−	0.0771270i
$927$	2.80066	+	4.85088i	0.0919857	+	0.159324i
$928$	1.41147	−	2.44474i	0.0463339	−	0.0802527i
$929$	−5.92009	+	10.2539i	−0.194232	+	0.336420i	−0.946648	−	0.322268i	$-0.895555\pi$
$929$	−5.92009	+	10.2539i	−0.194232	+	0.336420i	0.752417	+	0.658688i	$0.228888\pi$
$930$	7.51754			0.246510
$931$		0			0
$932$	8.39961			0.275139
$933$	22.4388	−	38.8652i	0.734614	−	1.27239i
$934$	−6.45677	+	11.1834i	−0.211272	+	0.365934i
$935$	20.7570	+	35.9522i	0.678827	+	1.17576i
$936$	−1.87939	+	3.25519i	−0.0614296	+	0.106399i
$937$	0.381911	+	0.661490i	0.0124765	+	0.0216099i	0.872196	−	0.489156i	$-0.162695\pi$
$937$	0.381911	+	0.661490i	0.0124765	+	0.0216099i	−0.859720	+	0.510766i	$0.829362\pi$
$938$	−13.3601			−0.436222
$939$	8.52023			0.278047
$940$	−7.88713	−	13.6609i	−0.257250	−	0.445570i
$941$	10.7469	+	18.6142i	0.350339	+	0.606805i	0.986309	−	0.164909i	$-0.0527330\pi$
$941$	10.7469	+	18.6142i	0.350339	+	0.606805i	−0.635970	+	0.771714i	$0.719400\pi$
$942$	12.9513			0.421976
$943$	0.241230			0.00785551
$944$	−0.286989	−	0.497079i	−0.00934070	−	0.0161786i
$945$	15.0797	−	26.1187i	0.490541	−	0.849643i
$946$	−9.65657	−	16.7257i	−0.313962	−	0.543799i
$947$	−15.8425	+	27.4401i	−0.514814	+	0.891683i	0.485039	+	0.874493i	$0.338806\pi$
$947$	−15.8425	+	27.4401i	−0.514814	+	0.891683i	−0.999852	+	0.0171907i	$0.994528\pi$
$948$	6.94356	−	12.0266i	0.225516	−	0.390606i
$949$	−90.7957			−2.94735
$950$		0			0
$951$	5.82707			0.188956
$952$	8.78106	−	15.2092i	0.284596	−	0.492934i
$953$	−27.9356	+	48.3858i	−0.904922	+	1.56737i	−0.0839001	+	0.996474i	$0.526738\pi$
$953$	−27.9356	+	48.3858i	−0.904922	+	1.56737i	−0.821022	+	0.570897i	$0.806596\pi$
$954$	2.68004	+	4.64197i	0.0867697	+	0.150289i
$955$	−9.56212	+	16.5621i	−0.309423	+	0.535936i
$956$	7.86484	+	13.6223i	0.254367	+	0.440577i
$957$	−13.7743			−0.445258
$958$	−18.5526			−0.599408
$959$	15.7101	+	27.2106i	0.507305	+	0.878678i
$960$	−1.53209	−	2.65366i	−0.0494480	−	0.0856464i
$961$	−24.9810			−0.805839
$962$	25.1634			0.811302
$963$	−3.73783	−	6.47410i	−0.120450	−	0.208625i
$964$	−8.75150	+	15.1580i	−0.281867	+	0.488207i
$965$	23.6810	+	41.0167i	0.762318	+	1.32037i
$966$	1.43376	−	2.48335i	0.0461306	−	0.0799005i
$967$	−10.7784	+	18.6687i	−0.346609	+	0.600344i	−0.985645	−	0.168833i	$-0.946000\pi$
$967$	−10.7784	+	18.6687i	−0.346609	+	0.600344i	0.639036	+	0.769177i	$0.279334\pi$
$968$	−0.857097			−0.0275481
$969$		0			0
$970$	−0.694593			−0.0223020
$971$	−24.3282	+	42.1376i	−0.780728	+	1.35226i	0.150790	+	0.988566i	$0.451818\pi$
$971$	−24.3282	+	42.1376i	−0.780728	+	1.35226i	−0.931518	+	0.363695i	$0.881515\pi$
$972$	−3.32635	+	5.76141i	−0.106693	+	0.184797i
$973$	11.1334	+	19.2836i	0.356921	+	0.618205i
$974$	−20.5868	+	35.6573i	−0.659643	+	1.14253i
$975$	−4.41147	−	7.64090i	−0.141280	−	0.244705i
$976$	2.93582			0.0939734
$977$	−50.5482			−1.61718			−0.808590	−	0.588373i	$-0.799769\pi$
$977$	−50.5482			−1.61718			−0.808590	+	0.588373i	$0.799769\pi$
$978$	−13.0608	−	22.6219i	−0.417638	−	0.723369i
$979$	−12.3238	−	21.3455i	−0.393871	−	0.682205i
$980$	0.521660			0.0166638
$981$	−5.67499			−0.181189
$982$	11.2888	+	19.5528i	0.360240	+	0.623954i
$983$	15.0300	−	26.0328i	0.479383	−	0.830317i	−0.520337	−	0.853961i	$-0.674194\pi$
$983$	15.0300	−	26.0328i	0.479383	−	0.830317i	0.999720	+	0.0236445i	$0.00752697\pi$
$984$	0.266044	+	0.460802i	0.00848119	+	0.0146898i
$985$	22.9222	−	39.7024i	0.730362	−	1.26502i
$986$	−9.19934	+	15.9337i	−0.292967	+	0.507433i
$987$	32.5609			1.03642
$988$		0			0
$989$	−4.21213			−0.133938
$990$	2.07873	−	3.60046i	0.0660662	−	0.114430i
$991$	−1.37639	+	2.38398i	−0.0437225	+	0.0757297i	−0.887059	−	0.461657i	$-0.847255\pi$
$991$	−1.37639	+	2.38398i	−0.0437225	+	0.0757297i	0.843336	+	0.537387i	$0.180588\pi$
$992$	−1.22668	−	2.12467i	−0.0389472	−	0.0674585i
$993$	−15.6441	+	27.0964i	−0.496450	+	0.859877i
$994$	11.3892	+	19.7266i	0.361243	+	0.625691i
$995$	20.1676			0.639355
$996$	12.9855			0.411460
$997$	−4.35235	−	7.53849i	−0.137840	−	0.238746i	0.788839	−	0.614600i	$-0.210683\pi$
$997$	−4.35235	−	7.53849i	−0.137840	−	0.238746i	−0.926679	+	0.375854i	$0.877349\pi$
$998$	14.6643	+	25.3993i	0.464191	+	0.804002i
$999$	24.4534			0.773670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.c.k.429.1		6
19.2	odd	18		722.2.e.k.595.1		6
19.3	odd	18		722.2.e.l.99.1		6
19.4	even	9		722.2.e.b.423.1		6
19.5	even	9		722.2.e.m.389.1		6
19.6	even	9		38.2.e.a.35.1	yes	6
19.7	even	3	inner	722.2.c.k.653.1		6
19.8	odd	6		722.2.a.k.1.1		3
19.9	even	9		722.2.e.m.245.1		6
19.10	odd	18		722.2.e.a.245.1		6
19.11	even	3		722.2.a.l.1.3		3
19.12	odd	6		722.2.c.l.653.3		6
19.13	odd	18		722.2.e.k.415.1		6
19.14	odd	18		722.2.e.a.389.1		6
19.15	odd	18		722.2.e.l.423.1		6
19.16	even	9		722.2.e.b.99.1		6
19.17	even	9		38.2.e.a.25.1	✓	6
19.18	odd	2		722.2.c.l.429.3		6
57.8	even	6		6498.2.a.bq.1.2		3
57.11	odd	6		6498.2.a.bl.1.2		3
57.17	odd	18		342.2.u.c.253.1		6
57.44	odd	18		342.2.u.c.73.1		6
76.11	odd	6		5776.2.a.bn.1.1		3
76.27	even	6		5776.2.a.bo.1.3		3
76.55	odd	18		304.2.u.c.177.1		6
76.63	odd	18		304.2.u.c.225.1		6
95.17	odd	36		950.2.u.b.899.2		12
95.44	even	18		950.2.l.d.301.1		6
95.63	odd	36		950.2.u.b.149.2		12
95.74	even	18		950.2.l.d.101.1		6
95.82	odd	36		950.2.u.b.149.1		12
95.93	odd	36		950.2.u.b.899.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.25.1	✓	6	19.17	even	9
38.2.e.a.35.1	yes	6	19.6	even	9
304.2.u.c.177.1		6	76.55	odd	18
304.2.u.c.225.1		6	76.63	odd	18
342.2.u.c.73.1		6	57.44	odd	18
342.2.u.c.253.1		6	57.17	odd	18
722.2.a.k.1.1		3	19.8	odd	6
722.2.a.l.1.3		3	19.11	even	3
722.2.c.k.429.1		6	1.1	even	1	trivial
722.2.c.k.653.1		6	19.7	even	3	inner
722.2.c.l.429.3		6	19.18	odd	2
722.2.c.l.653.3		6	19.12	odd	6
722.2.e.a.245.1		6	19.10	odd	18
722.2.e.a.389.1		6	19.14	odd	18
722.2.e.b.99.1		6	19.16	even	9
722.2.e.b.423.1		6	19.4	even	9
722.2.e.k.415.1		6	19.13	odd	18
722.2.e.k.595.1		6	19.2	odd	18
722.2.e.l.99.1		6	19.3	odd	18
722.2.e.l.423.1		6	19.15	odd	18
722.2.e.m.245.1		6	19.9	even	9
722.2.e.m.389.1		6	19.5	even	9
950.2.l.d.101.1		6	95.74	even	18
950.2.l.d.301.1		6	95.44	even	18
950.2.u.b.149.1		12	95.82	odd	36
950.2.u.b.149.2		12	95.63	odd	36
950.2.u.b.899.1		12	95.93	odd	36
950.2.u.b.899.2		12	95.17	odd	36
5776.2.a.bn.1.1		3	76.11	odd	6
5776.2.a.bo.1.3		3	76.27	even	6
6498.2.a.bl.1.2		3	57.11	odd	6
6498.2.a.bq.1.2		3	57.8	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.766044 + 1.32683i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(-0.766044 - 1.32683i) q^{6} +2.69459 q^{7} +1.00000 q^{8} +(0.326352 + 0.565258i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.766044 + 1.32683i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(-0.766044 - 1.32683i) q^{6} +2.69459 q^{7} +1.00000 q^{8} +(0.326352 + 0.565258i) q^{9} +(-1.00000 - 1.73205i) q^{10} +3.18479 q^{11} +1.53209 q^{12} +(2.87939 + 4.98724i) q^{13} +(-1.34730 + 2.33359i) q^{14} +(-1.53209 - 2.65366i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.25877 - 5.64436i) q^{17} -0.652704 q^{18} +2.00000 q^{20} +(-2.06418 + 3.57526i) q^{21} +(-1.59240 + 2.75811i) q^{22} +(0.347296 + 0.601535i) q^{23} +(-0.766044 + 1.32683i) q^{24} +(0.500000 + 0.866025i) q^{25} -5.75877 q^{26} -5.59627 q^{27} +(-1.34730 - 2.33359i) q^{28} +(1.41147 + 2.44474i) q^{29} +3.06418 q^{30} +2.45336 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.43969 + 4.22567i) q^{33} +(3.25877 + 5.64436i) q^{34} +(-2.69459 + 4.66717i) q^{35} +(0.326352 - 0.565258i) q^{36} -4.36959 q^{37} -8.82295 q^{39} +(-1.00000 + 1.73205i) q^{40} +(0.173648 - 0.300767i) q^{41} +(-2.06418 - 3.57526i) q^{42} +(-3.03209 + 5.25173i) q^{43} +(-1.59240 - 2.75811i) q^{44} -1.30541 q^{45} -0.694593 q^{46} +(-3.94356 - 6.83045i) q^{47} +(-0.766044 - 1.32683i) q^{48} +0.260830 q^{49} -1.00000 q^{50} +(4.99273 + 8.64766i) q^{51} +(2.87939 - 4.98724i) q^{52} +(-4.10607 - 7.11192i) q^{53} +(2.79813 - 4.84651i) q^{54} +(-3.18479 + 5.51622i) q^{55} +2.69459 q^{56} -2.82295 q^{58} +(-0.286989 + 0.497079i) q^{59} +(-1.53209 + 2.65366i) q^{60} +(-1.46791 - 2.54250i) q^{61} +(-1.22668 + 2.12467i) q^{62} +(0.879385 + 1.52314i) q^{63} +1.00000 q^{64} -11.5175 q^{65} +(-2.43969 - 4.22567i) q^{66} +(2.47906 + 4.29385i) q^{67} -6.51754 q^{68} -1.06418 q^{69} +(-2.69459 - 4.66717i) q^{70} +(4.22668 - 7.32083i) q^{71} +(0.326352 + 0.565258i) q^{72} +(-7.88326 + 13.6542i) q^{73} +(2.18479 - 3.78417i) q^{74} -1.53209 q^{75} +8.58172 q^{77} +(4.41147 - 7.64090i) q^{78} +(4.53209 - 7.84981i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(3.30793 - 5.72951i) q^{81} +(0.173648 + 0.300767i) q^{82} +8.47565 q^{83} +4.12836 q^{84} +(6.51754 + 11.2887i) q^{85} +(-3.03209 - 5.25173i) q^{86} -4.32501 q^{87} +3.18479 q^{88} +(-3.86959 - 6.70232i) q^{89} +(0.652704 - 1.13052i) q^{90} +(7.75877 + 13.4386i) q^{91} +(0.347296 - 0.601535i) q^{92} +(-1.87939 + 3.25519i) q^{93} +7.88713 q^{94} +1.53209 q^{96} +(0.173648 - 0.300767i) q^{97} +(-0.130415 + 0.225885i) q^{98} +(1.03936 + 1.80023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 + 6 * q^8 + 3 * q^9	\( 6 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} + 6 q^{8} + 3 q^{9} - 6 q^{10} + 12 q^{11} + 6 q^{13} - 6 q^{14} - 3 q^{16} - 3 q^{17} - 6 q^{18} + 12 q^{20} + 6 q^{21} - 6 q^{22} + 3 q^{25} - 12 q^{26} - 6 q^{27} - 6 q^{28} - 12 q^{29} - 12 q^{31} - 3 q^{32} - 9 q^{33} - 3 q^{34} - 12 q^{35} + 3 q^{36} - 12 q^{37} - 12 q^{39} - 6 q^{40} + 6 q^{42} - 9 q^{43} - 6 q^{44} - 12 q^{45} + 6 q^{47} + 30 q^{49} - 6 q^{50} + 12 q^{51} + 6 q^{52} + 3 q^{54} - 12 q^{55} + 12 q^{56} + 24 q^{58} + 6 q^{59} - 18 q^{61} + 6 q^{62} - 6 q^{63} + 6 q^{64} - 24 q^{65} - 9 q^{66} + 18 q^{67} + 6 q^{68} + 12 q^{69} - 12 q^{70} + 12 q^{71} + 3 q^{72} - 12 q^{73} + 6 q^{74} - 12 q^{77} + 6 q^{78} + 18 q^{79} - 6 q^{80} + 9 q^{81} + 12 q^{83} - 12 q^{84} - 6 q^{85} - 9 q^{86} - 36 q^{87} + 12 q^{88} - 9 q^{89} + 6 q^{90} + 24 q^{91} - 12 q^{94} - 15 q^{98} + 15 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 + 6 * q^8 + 3 * q^9 - 6 * q^10 + 12 * q^11 + 6 * q^13 - 6 * q^14 - 3 * q^16 - 3 * q^17 - 6 * q^18 + 12 * q^20 + 6 * q^21 - 6 * q^22 + 3 * q^25 - 12 * q^26 - 6 * q^27 - 6 * q^28 - 12 * q^29 - 12 * q^31 - 3 * q^32 - 9 * q^33 - 3 * q^34 - 12 * q^35 + 3 * q^36 - 12 * q^37 - 12 * q^39 - 6 * q^40 + 6 * q^42 - 9 * q^43 - 6 * q^44 - 12 * q^45 + 6 * q^47 + 30 * q^49 - 6 * q^50 + 12 * q^51 + 6 * q^52 + 3 * q^54 - 12 * q^55 + 12 * q^56 + 24 * q^58 + 6 * q^59 - 18 * q^61 + 6 * q^62 - 6 * q^63 + 6 * q^64 - 24 * q^65 - 9 * q^66 + 18 * q^67 + 6 * q^68 + 12 * q^69 - 12 * q^70 + 12 * q^71 + 3 * q^72 - 12 * q^73 + 6 * q^74 - 12 * q^77 + 6 * q^78 + 18 * q^79 - 6 * q^80 + 9 * q^81 + 12 * q^83 - 12 * q^84 - 6 * q^85 - 9 * q^86 - 36 * q^87 + 12 * q^88 - 9 * q^89 + 6 * q^90 + 24 * q^91 - 12 * q^94 - 15 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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