LMFDB - Embedded newform 406.2.e.a.233.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [406,2,Mod(233,406)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(406, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("406.233");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 406 = 2 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	406.e (of order $3$, 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:	$3.24192632206$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.3118758597603.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{8} - 16x^{6} - 34x^{5} + 43x^{4} + 155x^{3} + 199x^{2} + 124x + 43 $ x^10 - 4x^8 - 16x^6 - 34x^5 + 43x^4 + 155x^3 + 199x^2 + 124*x + 43
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			233.2
Root			$0.522109 + 2.12798i$ of defining polynomial
Character	$\chi$	$=$	406.233
Dual form			406.2.e.a.291.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.20348 - 2.08450i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.10394 - 1.91209i) q^{5} +2.40697 q^{6} +(-1.36646 - 2.26557i) q^{7} +1.00000 q^{8} +(-1.39675 + 2.41924i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.20348 - 2.08450i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.10394 - 1.91209i) q^{5} +2.40697 q^{6} +(-1.36646 - 2.26557i) q^{7} +1.00000 q^{8} +(-1.39675 + 2.41924i) q^{9} +(1.10394 + 1.91209i) q^{10} +(0.593725 + 1.02836i) q^{11} +(-1.20348 + 2.08450i) q^{12} +1.24330 q^{13} +(2.64527 - 0.0506055i) q^{14} -5.31432 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.98229 - 5.16548i) q^{17} +(-1.39675 - 2.41924i) q^{18} +(-1.09743 + 1.90081i) q^{19} -2.20789 q^{20} +(-3.07805 + 5.57495i) q^{21} -1.18745 q^{22} +(-3.87086 + 6.70453i) q^{23} +(-1.20348 - 2.08450i) q^{24} +(0.0626190 + 0.108459i) q^{25} +(-0.621650 + 1.07673i) q^{26} -0.497031 q^{27} +(-1.27881 + 2.31617i) q^{28} -1.00000 q^{29} +(2.65716 - 4.60233i) q^{30} +(-4.65549 - 8.06354i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.42908 - 2.47524i) q^{33} +5.96459 q^{34} +(-5.84045 + 0.111731i) q^{35} +2.79350 q^{36} +(3.45200 - 5.97904i) q^{37} +(-1.09743 - 1.90081i) q^{38} +(-1.49629 - 2.59166i) q^{39} +(1.10394 - 1.91209i) q^{40} +10.1520 q^{41} +(-3.28903 - 5.45315i) q^{42} -5.76077 q^{43} +(0.593725 - 1.02836i) q^{44} +(3.08387 + 5.34142i) q^{45} +(-3.87086 - 6.70453i) q^{46} +(2.91137 - 5.04264i) q^{47} +2.40697 q^{48} +(-3.26558 + 6.19161i) q^{49} -0.125238 q^{50} +(-7.17829 + 12.4332i) q^{51} +(-0.621650 - 1.07673i) q^{52} +(-0.840732 - 1.45619i) q^{53} +(0.248516 - 0.430442i) q^{54} +2.62175 q^{55} +(-1.36646 - 2.26557i) q^{56} +5.28297 q^{57} +(0.500000 - 0.866025i) q^{58} +(3.98880 + 6.90881i) q^{59} +(2.65716 + 4.60233i) q^{60} +(-4.05762 + 7.02800i) q^{61} +9.31097 q^{62} +(7.38956 - 0.141367i) q^{63} +1.00000 q^{64} +(1.37253 - 2.37730i) q^{65} +(1.42908 + 2.47524i) q^{66} +(-6.07224 - 10.5174i) q^{67} +(-2.98229 + 5.16548i) q^{68} +18.6341 q^{69} +(2.82346 - 5.11384i) q^{70} +4.61064 q^{71} +(-1.39675 + 2.41924i) q^{72} +(-0.0197414 - 0.0341930i) q^{73} +(3.45200 + 5.97904i) q^{74} +(0.150722 - 0.261058i) q^{75} +2.19486 q^{76} +(1.51852 - 2.75034i) q^{77} +2.99259 q^{78} +(1.21167 - 2.09867i) q^{79} +(1.10394 + 1.91209i) q^{80} +(4.78842 + 8.29379i) q^{81} +(-5.07602 + 8.79192i) q^{82} +5.46282 q^{83} +(6.36708 - 0.121806i) q^{84} -13.1691 q^{85} +(2.88038 - 4.98897i) q^{86} +(1.20348 + 2.08450i) q^{87} +(0.593725 + 1.02836i) q^{88} +(3.63416 - 6.29455i) q^{89} -6.16774 q^{90} +(-1.69892 - 2.81678i) q^{91} +7.74172 q^{92} +(-11.2056 + 19.4087i) q^{93} +(2.91137 + 5.04264i) q^{94} +(2.42300 + 4.19677i) q^{95} +(-1.20348 + 2.08450i) q^{96} +3.23923 q^{97} +(-3.72930 - 5.92388i) q^{98} -3.31715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9} - 7 q^{10} - 3 q^{12} + 20 q^{13} + 3 q^{14} - 20 q^{15} - 5 q^{16} - 8 q^{17} - 8 q^{18} - 2 q^{19} + 14 q^{20} + 19 q^{21} - q^{23} - 3 q^{24} - 12 q^{25} - 10 q^{26} + 30 q^{27} - 10 q^{29} + 10 q^{30} - 11 q^{31} - 5 q^{32} - 9 q^{33} + 16 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 2 q^{38} - 18 q^{39} - 7 q^{40} + 46 q^{41} - 8 q^{42} - 6 q^{43} - 4 q^{45} - q^{46} - 16 q^{47} + 6 q^{48} - 11 q^{49} + 24 q^{50} - 7 q^{51} - 10 q^{52} - 7 q^{53} - 15 q^{54} + 12 q^{55} - 3 q^{56} - 68 q^{57} + 5 q^{58} + 9 q^{59} + 10 q^{60} - 15 q^{61} + 22 q^{62} - 3 q^{63} + 10 q^{64} - 5 q^{65} - 9 q^{66} + 4 q^{67} - 8 q^{68} + 28 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 8 q^{74} + 34 q^{75} + 4 q^{76} + 39 q^{77} + 36 q^{78} + 13 q^{79} - 7 q^{80} - 17 q^{81} - 23 q^{82} + 56 q^{83} - 11 q^{84} - 14 q^{85} + 3 q^{86} + 3 q^{87} - 17 q^{89} + 8 q^{90} + 6 q^{91} + 2 q^{92} - 17 q^{93} - 16 q^{94} + 9 q^{95} - 3 q^{96} + 84 q^{97} - 20 q^{98} - 84 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9 - 7 * q^10 - 3 * q^12 + 20 * q^13 + 3 * q^14 - 20 * q^15 - 5 * q^16 - 8 * q^17 - 8 * q^18 - 2 * q^19 + 14 * q^20 + 19 * q^21 - q^23 - 3 * q^24 - 12 * q^25 - 10 * q^26 + 30 * q^27 - 10 * q^29 + 10 * q^30 - 11 * q^31 - 5 * q^32 - 9 * q^33 + 16 * q^34 + 10 * q^35 + 16 * q^36 + 8 * q^37 - 2 * q^38 - 18 * q^39 - 7 * q^40 + 46 * q^41 - 8 * q^42 - 6 * q^43 - 4 * q^45 - q^46 - 16 * q^47 + 6 * q^48 - 11 * q^49 + 24 * q^50 - 7 * q^51 - 10 * q^52 - 7 * q^53 - 15 * q^54 + 12 * q^55 - 3 * q^56 - 68 * q^57 + 5 * q^58 + 9 * q^59 + 10 * q^60 - 15 * q^61 + 22 * q^62 - 3 * q^63 + 10 * q^64 - 5 * q^65 - 9 * q^66 + 4 * q^67 - 8 * q^68 + 28 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 8 * q^74 + 34 * q^75 + 4 * q^76 + 39 * q^77 + 36 * q^78 + 13 * q^79 - 7 * q^80 - 17 * q^81 - 23 * q^82 + 56 * q^83 - 11 * q^84 - 14 * q^85 + 3 * q^86 + 3 * q^87 - 17 * q^89 + 8 * q^90 + 6 * q^91 + 2 * q^92 - 17 * q^93 - 16 * q^94 + 9 * q^95 - 3 * q^96 + 84 * q^97 - 20 * q^98 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/406\mathbb{Z}\right)^\times$.

$n$	$59$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.20348	−	2.08450i	−0.694832	−	1.20348i	−0.970237	−	0.242157i	$-0.922145\pi$
$3$	−1.20348	−	2.08450i	−0.694832	−	1.20348i	0.275405	−	0.961328i	$-0.411188\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.10394	−	1.91209i	0.493698	−	0.855111i	−0.506275	−	0.862372i	$-0.668978\pi$
$5$	1.10394	−	1.91209i	0.493698	−	0.855111i	0.999974	+	0.00726125i	$0.00231135\pi$
$6$	2.40697			0.982641
$7$	−1.36646	−	2.26557i	−0.516473	−	0.856303i
$7$	−1.36646	−	2.26557i	−0.516473	−	0.856303i
$8$	1.00000			0.353553
$9$	−1.39675	+	2.41924i	−0.465584	+	0.806415i
$10$	1.10394	+	1.91209i	0.349097	+	0.604655i
$11$	0.593725	+	1.02836i	0.179015	+	0.310063i	0.941543	−	0.336892i	$-0.109376\pi$
$11$	0.593725	+	1.02836i	0.179015	+	0.310063i	−0.762529	+	0.646955i	$0.776042\pi$
$12$	−1.20348	+	2.08450i	−0.347416	+	0.601742i
$13$	1.24330			0.344830			0.172415	−	0.985024i	$-0.444843\pi$
$13$	1.24330			0.344830			0.172415	+	0.985024i	$0.444843\pi$
$14$	2.64527	−	0.0506055i	0.706977	−	0.0135249i
$15$	−5.31432			−1.37215
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.98229	−	5.16548i	−0.723312	−	1.25281i	−0.959665	−	0.281146i	$-0.909285\pi$
$17$	−2.98229	−	5.16548i	−0.723312	−	1.25281i	0.236353	−	0.971667i	$-0.424048\pi$
$18$	−1.39675	−	2.41924i	−0.329218	−	0.570221i
$19$	−1.09743	+	1.90081i	−0.251768	+	0.436075i	−0.964013	−	0.265856i	$-0.914345\pi$
$19$	−1.09743	+	1.90081i	−0.251768	+	0.436075i	0.712245	+	0.701931i	$0.247679\pi$
$20$	−2.20789			−0.493698
$21$	−3.07805	+	5.57495i	−0.671686	+	1.21655i
$22$	−1.18745			−0.253165
$23$	−3.87086	+	6.70453i	−0.807130	+	1.39799i	0.107713	+	0.994182i	$0.465647\pi$
$23$	−3.87086	+	6.70453i	−0.807130	+	1.39799i	−0.914843	+	0.403809i	$0.867686\pi$
$24$	−1.20348	−	2.08450i	−0.245660	−	0.425496i
$25$	0.0626190	+	0.108459i	0.0125238	+	0.0216919i
$26$	−0.621650	+	1.07673i	−0.121916	+	0.211164i
$27$	−0.497031			−0.0956537
$28$	−1.27881	+	2.31617i	−0.241672	+	0.437715i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$	2.65716	−	4.60233i	0.485128	−	0.840267i
$31$	−4.65549	−	8.06354i	−0.836150	−	1.44825i	−0.893091	−	0.449876i	$-0.851468\pi$
$31$	−4.65549	−	8.06354i	−0.836150	−	1.44825i	0.0569409	−	0.998378i	$-0.481865\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.42908	−	2.47524i	0.248771	−	0.430883i
$34$	5.96459			1.02292
$35$	−5.84045	+	0.111731i	−0.987216	+	0.0188860i
$36$	2.79350			0.465584
$37$	3.45200	−	5.97904i	0.567505	−	0.982948i	−0.429306	−	0.903159i	$-0.641242\pi$
$37$	3.45200	−	5.97904i	0.567505	−	0.982948i	0.996812	−	0.0797892i	$-0.0254247\pi$
$38$	−1.09743	−	1.90081i	−0.178027	−	0.308352i
$39$	−1.49629	−	2.59166i	−0.239599	−	0.414997i
$40$	1.10394	−	1.91209i	0.174549	−	0.302327i
$41$	10.1520			1.58548			0.792741	−	0.609559i	$-0.208653\pi$
$41$	10.1520			1.58548			0.792741	+	0.609559i	$0.208653\pi$
$42$	−3.28903	−	5.45315i	−0.507508	−	0.841439i
$43$	−5.76077			−0.878509			−0.439254	−	0.898363i	$-0.644757\pi$
$43$	−5.76077			−0.878509			−0.439254	+	0.898363i	$0.644757\pi$
$44$	0.593725	−	1.02836i	0.0895074	−	0.155031i
$45$	3.08387	+	5.34142i	0.459716	+	0.796252i
$46$	−3.87086	−	6.70453i	−0.570727	−	0.988529i
$47$	2.91137	−	5.04264i	0.424667	−	0.735545i	−0.571722	−	0.820447i	$-0.693724\pi$
$47$	2.91137	−	5.04264i	0.424667	−	0.735545i	0.996389	+	0.0849023i	$0.0270578\pi$
$48$	2.40697			0.347416
$49$	−3.26558	+	6.19161i	−0.466511	+	0.884515i
$50$	−0.125238			−0.0177113
$51$	−7.17829	+	12.4332i	−1.00516	+	1.74099i
$52$	−0.621650	−	1.07673i	−0.0862074	−	0.149316i
$53$	−0.840732	−	1.45619i	−0.115483	−	0.200023i	0.802489	−	0.596666i	$-0.203508\pi$
$53$	−0.840732	−	1.45619i	−0.115483	−	0.200023i	−0.917973	+	0.396643i	$0.870175\pi$
$54$	0.248516	−	0.430442i	0.0338187	−	0.0585757i
$55$	2.62175			0.353517
$56$	−1.36646	−	2.26557i	−0.182601	−	0.302749i
$57$	5.28297			0.699746
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$	3.98880	+	6.90881i	0.519298	+	0.899451i	0.999748	+	0.0224288i	$0.00713989\pi$
$59$	3.98880	+	6.90881i	0.519298	+	0.899451i	−0.480450	+	0.877022i	$0.659527\pi$
$60$	2.65716	+	4.60233i	0.343038	+	0.594159i
$61$	−4.05762	+	7.02800i	−0.519524	+	0.899843i	0.480218	+	0.877149i	$0.340558\pi$
$61$	−4.05762	+	7.02800i	−0.519524	+	0.899843i	−0.999742	+	0.0226936i	$0.992776\pi$
$62$	9.31097			1.18249
$63$	7.38956	−	0.141367i	0.930997	−	0.0178105i
$64$	1.00000			0.125000
$65$	1.37253	−	2.37730i	0.170242	−	0.294867i
$66$	1.42908	+	2.47524i	0.175907	+	0.304681i
$67$	−6.07224	−	10.5174i	−0.741842	−	1.28491i	−0.951656	−	0.307166i	$-0.900619\pi$
$67$	−6.07224	−	10.5174i	−0.741842	−	1.28491i	0.209814	−	0.977741i	$-0.432714\pi$
$68$	−2.98229	+	5.16548i	−0.361656	+	0.626407i
$69$	18.6341			2.24328
$70$	2.82346	−	5.11384i	0.337468	−	0.611221i
$71$	4.61064			0.547182			0.273591	−	0.961846i	$-0.411789\pi$
$71$	4.61064			0.547182			0.273591	+	0.961846i	$0.411789\pi$
$72$	−1.39675	+	2.41924i	−0.164609	+	0.285111i
$73$	−0.0197414	−	0.0341930i	−0.00231055	−	0.00400199i	0.864868	−	0.502000i	$-0.167402\pi$
$73$	−0.0197414	−	0.0341930i	−0.00231055	−	0.00400199i	−0.867178	+	0.497998i	$0.834069\pi$
$74$	3.45200	+	5.97904i	0.401287	+	0.695049i
$75$	0.150722	−	0.261058i	0.0174039	−	0.0301444i
$76$	2.19486			0.251768
$77$	1.51852	−	2.75034i	0.173052	−	0.313430i
$78$	2.99259			0.338844
$79$	1.21167	−	2.09867i	0.136323	−	0.236119i	−0.789779	−	0.613392i	$-0.789805\pi$
$79$	1.21167	−	2.09867i	0.136323	−	0.236119i	0.926102	+	0.377273i	$0.123138\pi$
$80$	1.10394	+	1.91209i	0.123425	+	0.213778i
$81$	4.78842	+	8.29379i	0.532047	+	0.921533i
$82$	−5.07602	+	8.79192i	−0.560552	+	0.970905i
$83$	5.46282			0.599622			0.299811	−	0.953999i	$-0.403076\pi$
$83$	5.46282			0.599622			0.299811	+	0.953999i	$0.403076\pi$
$84$	6.36708	−	0.121806i	0.694705	−	0.0132901i
$85$	−13.1691			−1.42839
$86$	2.88038	−	4.98897i	0.310600	−	0.537975i
$87$	1.20348	+	2.08450i	0.129027	+	0.223482i
$88$	0.593725	+	1.02836i	0.0632913	+	0.109624i
$89$	3.63416	−	6.29455i	0.385220	−	0.667221i	−0.606580	−	0.795023i	$-0.707459\pi$
$89$	3.63416	−	6.29455i	0.385220	−	0.667221i	0.991800	+	0.127802i	$0.0407922\pi$
$90$	−6.16774			−0.650137
$91$	−1.69892	−	2.81678i	−0.178095	−	0.295279i
$92$	7.74172			0.807130
$93$	−11.2056	+	19.4087i	−1.16197	+	2.01259i
$94$	2.91137	+	5.04264i	0.300285	+	0.520109i
$95$	2.42300	+	4.19677i	0.248595	+	0.430579i
$96$	−1.20348	+	2.08450i	−0.122830	+	0.212748i
$97$	3.23923			0.328894			0.164447	−	0.986386i	$-0.447416\pi$
$97$	3.23923			0.328894			0.164447	+	0.986386i	$0.447416\pi$
$98$	−3.72930	−	5.92388i	−0.376716	−	0.598402i
$99$	−3.31715			−0.333386
$100$	0.0626190	−	0.108459i	0.00626190	−	0.0108459i
$101$	−4.50359	−	7.80044i	−0.448124	−	0.776173i	0.550140	−	0.835072i	$-0.314574\pi$
$101$	−4.50359	−	7.80044i	−0.448124	−	0.776173i	−0.998264	+	0.0588992i	$0.981241\pi$
$102$	−7.17829	−	12.4332i	−0.710756	−	1.23107i
$103$	−3.11486	+	5.39509i	−0.306916	+	0.531594i	−0.977686	−	0.210071i	$-0.932630\pi$
$103$	−3.11486	+	5.39509i	−0.306916	+	0.531594i	0.670770	+	0.741665i	$0.265964\pi$
$104$	1.24330			0.121916
$105$	7.26180	+	12.0399i	0.708679	+	1.17498i
$106$	1.68146			0.163318
$107$	8.13240	−	14.0857i	0.786189	−	1.36172i	−0.142098	−	0.989853i	$-0.545385\pi$
$107$	8.13240	−	14.0857i	0.786189	−	1.36172i	0.928286	−	0.371866i	$-0.121282\pi$
$108$	0.248516	+	0.430442i	0.0239134	+	0.0414193i
$109$	1.43640	+	2.48792i	0.137582	+	0.238300i	0.926581	−	0.376095i	$-0.122733\pi$
$109$	1.43640	+	2.48792i	0.137582	+	0.238300i	−0.788999	+	0.614395i	$0.789400\pi$
$110$	−1.31088	+	2.27051i	−0.124987	+	0.216484i
$111$	−16.6177			−1.57728
$112$	2.64527	−	0.0506055i	0.249954	−	0.00478177i
$113$	−1.01001			−0.0950134			−0.0475067	−	0.998871i	$-0.515128\pi$
$113$	−1.01001			−0.0950134			−0.0475067	+	0.998871i	$0.515128\pi$
$114$	−2.64148	+	4.57519i	−0.247398	+	0.428505i
$115$	8.54642	+	14.8028i	0.796958	+	1.38037i
$116$	0.500000	+	0.866025i	0.0464238	+	0.0804084i
$117$	−1.73658	+	3.00785i	−0.160547	+	0.278076i
$118$	−7.97761			−0.734398
$119$	−7.62756	+	13.8150i	−0.699217	+	1.26642i
$120$	−5.31432			−0.485128
$121$	4.79498	−	8.30515i	0.435907	−	0.755014i
$122$	−4.05762	−	7.02800i	−0.367359	−	0.636285i
$123$	−12.2178	−	21.1619i	−1.10164	−	1.90810i
$124$	−4.65549	+	8.06354i	−0.418075	+	0.724127i
$125$	11.3159			1.01213
$126$	−3.57235	+	6.47023i	−0.318251	+	0.576414i
$127$	4.78015			0.424170			0.212085	−	0.977251i	$-0.431975\pi$
$127$	4.78015			0.424170			0.212085	+	0.977251i	$0.431975\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	6.93300	+	12.0083i	0.610416	+	1.05727i
$130$	1.37253	+	2.37730i	0.120379	+	0.208503i
$131$	5.42248	−	9.39201i	0.473764	−	0.820584i	−0.525785	−	0.850618i	$-0.676228\pi$
$131$	5.42248	−	9.39201i	0.473764	−	0.820584i	0.999549	+	0.0300341i	$0.00956158\pi$
$132$	−2.85816			−0.248771
$133$	5.80600	−	0.111072i	0.503444	−	0.00963117i
$134$	12.1445			1.04912
$135$	−0.548694	+	0.950366i	−0.0472241	+	0.0817945i
$136$	−2.98229	−	5.16548i	−0.255730	−	0.442936i
$137$	0.310233	+	0.537339i	0.0265050	+	0.0459080i	0.878974	−	0.476870i	$-0.158229\pi$
$137$	0.310233	+	0.537339i	0.0265050	+	0.0459080i	−0.852469	+	0.522778i	$0.824896\pi$
$138$	−9.31704	+	16.1376i	−0.793120	+	1.37372i
$139$	−10.8612			−0.921233			−0.460616	−	0.887599i	$-0.652372\pi$
$139$	−10.8612			−0.921233			−0.460616	+	0.887599i	$0.652372\pi$
$140$	3.01699	+	5.00211i	0.254982	+	0.422756i
$141$	−14.0152			−1.18029
$142$	−2.30532	+	3.99293i	−0.193458	+	0.335079i
$143$	0.738179	+	1.27856i	0.0617296	+	0.106919i
$144$	−1.39675	−	2.41924i	−0.116396	−	0.201604i
$145$	−1.10394	+	1.91209i	−0.0916775	+	0.158790i
$146$	0.0394827			0.00326761
$147$	16.8365	−	0.644418i	1.38865	−	0.0531507i
$148$	−6.90400			−0.567505
$149$	3.49332	−	6.05062i	0.286184	−	0.495686i	−0.686711	−	0.726930i	$-0.740946\pi$
$149$	3.49332	−	6.05062i	0.286184	−	0.495686i	0.972896	+	0.231244i	$0.0742797\pi$
$150$	0.150722	+	0.261058i	0.0123064	+	0.0213153i
$151$	−3.42248	−	5.92791i	−0.278517	−	0.482406i	0.692499	−	0.721419i	$-0.256510\pi$
$151$	−3.42248	−	5.92791i	−0.278517	−	0.482406i	−0.971016	+	0.239012i	$0.923176\pi$
$152$	−1.09743	+	1.90081i	−0.0890135	+	0.154176i
$153$	16.6621			1.34705
$154$	1.62260	+	2.69025i	0.130753	+	0.216786i
$155$	−20.5576			−1.65122
$156$	−1.49629	+	2.59166i	−0.119799	+	0.207499i
$157$	−9.16217	−	15.8693i	−0.731220	−	1.26651i	−0.956362	−	0.292185i	$-0.905618\pi$
$157$	−9.16217	−	15.8693i	−0.731220	−	1.26651i	0.225141	−	0.974326i	$-0.427716\pi$
$158$	1.21167	+	2.09867i	0.0963952	+	0.166961i
$159$	−2.02362	+	3.50501i	−0.160483	+	0.277965i
$160$	−2.20789			−0.174549
$161$	20.4789	−	0.391773i	1.61397	−	0.0308761i
$162$	−9.57685			−0.752428
$163$	10.3326	−	17.8967i	0.809315	−	1.40177i	−0.104024	−	0.994575i	$-0.533172\pi$
$163$	10.3326	−	17.8967i	0.809315	−	1.40177i	0.913339	−	0.407200i	$-0.133495\pi$
$164$	−5.07602	−	8.79192i	−0.396370	−	0.686534i
$165$	−3.15524	−	5.46504i	−0.245635	−	0.425453i
$166$	−2.73141	+	4.73094i	−0.211999	+	0.367192i
$167$	21.9158			1.69590			0.847949	−	0.530079i	$-0.177838\pi$
$167$	21.9158			1.69590			0.847949	+	0.530079i	$0.177838\pi$
$168$	−3.07805	+	5.57495i	−0.237477	+	0.430117i
$169$	−11.4542			−0.881093
$170$	6.58456	−	11.4048i	0.505013	−	0.874708i
$171$	−3.06568	−	5.30991i	−0.234438	−	0.406059i
$172$	2.88038	+	4.98897i	0.219627	+	0.380406i
$173$	7.08633	−	12.2739i	0.538764	−	0.933166i	−0.460207	−	0.887811i	$-0.652225\pi$
$173$	7.08633	−	12.2739i	0.538764	−	0.933166i	0.998971	−	0.0453545i	$-0.0144417\pi$
$174$	−2.40697			−0.182472
$175$	0.160155	−	0.290073i	0.0121066	−	0.0219274i
$176$	−1.18745			−0.0895074
$177$	9.60093	−	16.6293i	0.721650	−	1.24993i
$178$	3.63416	+	6.29455i	0.272392	+	0.471796i
$179$	11.1900	+	19.3817i	0.836381	+	1.44865i	0.892901	+	0.450253i	$0.148666\pi$
$179$	11.1900	+	19.3817i	0.836381	+	1.44865i	−0.0565200	+	0.998401i	$0.518000\pi$
$180$	3.08387	−	5.34142i	0.229858	−	0.398126i
$181$	−15.5160			−1.15330			−0.576649	−	0.816992i	$-0.695640\pi$
$181$	−15.5160			−1.15330			−0.576649	+	0.816992i	$0.695640\pi$
$182$	3.28886	−	0.0629178i	0.243787	−	0.00466378i
$183$	19.5331			1.44393
$184$	−3.87086	+	6.70453i	−0.285364	+	0.494264i
$185$	−7.62162	−	13.2010i	−0.560353	−	0.970560i
$186$	−11.2056	−	19.4087i	−0.821635	−	1.42311i
$187$	3.54132	−	6.13375i	0.258967	−	0.448544i
$188$	−5.82274			−0.424667
$189$	0.679173	+	1.12606i	0.0494026	+	0.0819086i
$190$	−4.84601			−0.351566
$191$	−3.97566	+	6.88605i	−0.287669	+	0.498257i	−0.973253	−	0.229736i	$-0.926214\pi$
$191$	−3.97566	+	6.88605i	−0.287669	+	0.498257i	0.685584	+	0.727993i	$0.259547\pi$
$192$	−1.20348	−	2.08450i	−0.0868540	−	0.150436i
$193$	1.69025	+	2.92761i	0.121667	+	0.210734i	0.920425	−	0.390919i	$-0.127843\pi$
$193$	1.69025	+	2.92761i	0.121667	+	0.210734i	−0.798758	+	0.601652i	$0.794509\pi$
$194$	−1.61962	+	2.80526i	−0.116282	+	0.201406i
$195$	−6.60729			−0.473158
$196$	6.99488	−	0.267730i	0.499634	−	0.0191236i
$197$	0.885106			0.0630612			0.0315306	−	0.999503i	$-0.489962\pi$
$197$	0.885106			0.0630612			0.0315306	+	0.999503i	$0.489962\pi$
$198$	1.65857	−	2.87273i	0.117870	−	0.204156i
$199$	−5.80690	−	10.0578i	−0.411640	−	0.712982i	0.583429	−	0.812164i	$-0.301711\pi$
$199$	−5.80690	−	10.0578i	−0.411640	−	0.712982i	−0.995069	+	0.0991821i	$0.968377\pi$
$200$	0.0626190	+	0.108459i	0.00442783	+	0.00766923i
$201$	−14.6157	+	25.3151i	−1.03091	+	1.78559i
$202$	9.00718			0.633743
$203$	1.36646	+	2.26557i	0.0959066	+	0.159012i
$204$	14.3566			1.00516
$205$	11.2073	−	19.4116i	0.782750	−	1.35576i
$206$	−3.11486	−	5.39509i	−0.217022	−	0.375894i
$207$	−10.8133	−	18.7291i	−0.751574	−	1.30176i
$208$	−0.621650	+	1.07673i	−0.0431037	+	0.0746578i
$209$	−2.60629			−0.180281
$210$	−14.0578	+	0.268933i	−0.970079	+	0.0185582i
$211$	−24.0646			−1.65668			−0.828338	−	0.560229i	$-0.810713\pi$
$211$	−24.0646			−1.65668			−0.828338	+	0.560229i	$0.810713\pi$
$212$	−0.840732	+	1.45619i	−0.0577417	+	0.100012i
$213$	−5.54883	−	9.61086i	−0.380200	−	0.658525i
$214$	8.13240	+	14.0857i	0.555919	+	0.962881i
$215$	−6.35956	+	11.0151i	−0.433718	+	0.751222i
$216$	−0.497031			−0.0338187
$217$	−11.9069	+	21.5658i	−0.808296	+	1.46398i
$218$	−2.87281			−0.194571
$219$	−0.0475168	+	0.0823016i	−0.00321089	+	0.00556143i
$220$	−1.31088	−	2.27051i	−0.0883793	−	0.153078i
$221$	−3.70789	−	6.42225i	−0.249419	−	0.432007i
$222$	8.30886	−	14.3914i	0.557654	−	0.965885i
$223$	3.62968			0.243062			0.121531	−	0.992588i	$-0.461220\pi$
$223$	3.62968			0.243062			0.121531	+	0.992588i	$0.461220\pi$
$224$	−1.27881	+	2.31617i	−0.0854440	+	0.154756i
$225$	−0.349853			−0.0233235
$226$	0.505003	−	0.874691i	0.0335923	−	0.0581836i
$227$	−6.34036	−	10.9818i	−0.420825	−	0.728890i	0.575196	−	0.818016i	$-0.304926\pi$
$227$	−6.34036	−	10.9818i	−0.420825	−	0.728890i	−0.996020	+	0.0891263i	$0.971593\pi$
$228$	−2.64148	−	4.57519i	−0.174937	−	0.302999i
$229$	9.96072	−	17.2525i	0.658223	−	1.14007i	−0.322853	−	0.946449i	$-0.604642\pi$
$229$	9.96072	−	17.2525i	0.658223	−	1.14007i	0.981075	−	0.193626i	$-0.0620248\pi$
$230$	−17.0928			−1.12707
$231$	−7.56059	+	0.144638i	−0.497450	+	0.00951650i
$232$	−1.00000			−0.0656532
$233$	6.84794	−	11.8610i	0.448623	−	0.777038i	−0.549673	−	0.835380i	$-0.685248\pi$
$233$	6.84794	−	11.8610i	0.448623	−	0.777038i	0.998297	+	0.0583412i	$0.0185811\pi$
$234$	−1.73658	−	3.00785i	−0.113524	−	0.196629i
$235$	−6.42798	−	11.1336i	−0.419315	−	0.726275i
$236$	3.98880	−	6.90881i	0.259649	−	0.449725i
$237$	−5.83290			−0.378888
$238$	−8.15036	−	13.5132i	−0.528310	−	0.875928i
$239$	16.6929			1.07977			0.539886	−	0.841738i	$-0.318467\pi$
$239$	16.6929			1.07977			0.539886	+	0.841738i	$0.318467\pi$
$240$	2.65716	−	4.60233i	0.171519	−	0.297079i
$241$	8.40495	+	14.5578i	0.541411	+	0.937751i	0.998823	+	0.0484962i	$0.0154429\pi$
$241$	8.40495	+	14.5578i	0.541411	+	0.937751i	−0.457413	+	0.889255i	$0.651224\pi$
$242$	4.79498	+	8.30515i	0.308233	+	0.533875i
$243$	10.7800	−	18.6716i	0.691540	−	1.19778i
$244$	8.11523			0.519524
$245$	8.23387	+	13.0792i	0.526043	+	0.835602i
$246$	24.4356			1.55796
$247$	−1.36444	+	2.36327i	−0.0868171	+	0.150372i
$248$	−4.65549	−	8.06354i	−0.295624	−	0.512035i
$249$	−6.57442	−	11.3872i	−0.416637	−	0.721636i
$250$	−5.65797	+	9.79989i	−0.357842	+	0.619800i
$251$	−3.73348			−0.235655			−0.117828	−	0.993034i	$-0.537593\pi$
$251$	−3.73348			−0.235655			−0.117828	+	0.993034i	$0.537593\pi$
$252$	−3.81721	−	6.32887i	−0.240462	−	0.398681i
$253$	−9.19291			−0.577953
$254$	−2.39008	+	4.13973i	−0.149967	+	0.259750i
$255$	15.8488	+	27.4510i	0.992493	+	1.71905i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.2718	+	26.4516i	−0.952630	+	1.65000i	−0.212929	+	0.977068i	$0.568300\pi$
$257$	−15.2718	+	26.4516i	−0.952630	+	1.65000i	−0.739701	+	0.672936i	$0.765033\pi$
$258$	−13.8660			−0.863259
$259$	−18.2629	+	0.349380i	−1.13480	+	0.0217094i
$260$	−2.74507			−0.170242
$261$	1.39675	−	2.41924i	0.0864568	−	0.149747i
$262$	5.42248	+	9.39201i	0.335002	+	0.580240i
$263$	8.30910	+	14.3918i	0.512361	+	0.887435i	0.999897	+	0.0143327i	$0.00456238\pi$
$263$	8.30910	+	14.3918i	0.512361	+	0.887435i	−0.487536	+	0.873103i	$0.662104\pi$
$264$	1.42908	−	2.47524i	0.0879537	−	0.152340i
$265$	−3.71248			−0.228056
$266$	−2.80681	+	5.08368i	−0.172096	+	0.311700i
$267$	−17.4946			−1.07065
$268$	−6.07224	+	10.5174i	−0.370921	+	0.642454i
$269$	7.69470	+	13.3276i	0.469154	+	0.812599i	0.999378	−	0.0352588i	$-0.0112255\pi$
$269$	7.69470	+	13.3276i	0.469154	+	0.812599i	−0.530224	+	0.847858i	$0.677892\pi$
$270$	−0.548694	−	0.950366i	−0.0333925	−	0.0578375i
$271$	11.4607	−	19.8505i	0.696187	−	1.20583i	−0.273592	−	0.961846i	$-0.588212\pi$
$271$	11.4607	−	19.8505i	0.696187	−	1.20583i	0.969779	−	0.243985i	$-0.0784549\pi$
$272$	5.96459			0.361656
$273$	−3.82694	+	6.93134i	−0.231617	+	0.419504i
$274$	−0.620466			−0.0374837
$275$	−0.0743570	+	0.128790i	−0.00448389	+	0.00776633i
$276$	−9.31704	−	16.1376i	−0.560820	−	0.971369i
$277$	12.0264	+	20.8303i	0.722596	+	1.25157i	0.959956	+	0.280151i	$0.0903847\pi$
$277$	12.0264	+	20.8303i	0.722596	+	1.25157i	−0.237360	+	0.971422i	$0.576282\pi$
$278$	5.43059	−	9.40605i	0.325705	−	0.564138i
$279$	26.0102			1.55719
$280$	−5.84045	+	0.111731i	−0.349034	+	0.00667721i
$281$	1.73325			0.103397			0.0516984	−	0.998663i	$-0.483537\pi$
$281$	1.73325			0.103397			0.0516984	+	0.998663i	$0.483537\pi$
$282$	7.00758	−	12.1375i	0.417295	−	0.722777i
$283$	8.84699	+	15.3234i	0.525899	+	0.910884i	0.999545	+	0.0301685i	$0.00960438\pi$
$283$	8.84699	+	15.3234i	0.525899	+	0.910884i	−0.473646	+	0.880715i	$0.657062\pi$
$284$	−2.30532	−	3.99293i	−0.136795	−	0.236937i
$285$	5.83210	−	10.1015i	0.345464	−	0.598361i
$286$	−1.47636			−0.0872988
$287$	−13.8723	−	23.0001i	−0.818859	−	1.35765i
$288$	2.79350			0.164609
$289$	−9.28814	+	16.0875i	−0.546361	+	0.946326i
$290$	−1.10394	−	1.91209i	−0.0648258	−	0.112282i
$291$	−3.89837	−	6.75217i	−0.228526	−	0.395819i
$292$	−0.0197414	+	0.0341930i	−0.00115528	+	0.00200100i
$293$	−26.8620			−1.56929			−0.784647	−	0.619942i	$-0.787156\pi$
$293$	−26.8620			−1.56929			−0.784647	+	0.619942i	$0.787156\pi$
$294$	−7.86015	+	14.9030i	−0.458413	+	0.869161i
$295$	17.6137			1.02551
$296$	3.45200	−	5.97904i	0.200643	−	0.347525i
$297$	−0.295100	−	0.511128i	−0.0171234	−	0.0296587i
$298$	3.49332	+	6.05062i	0.202363	+	0.350503i
$299$	−4.81264	+	8.33574i	−0.278322	+	0.482068i
$300$	−0.301444			−0.0174039
$301$	7.87185	+	13.0514i	0.453726	+	0.752270i
$302$	6.84496			0.393883
$303$	−10.8400	+	18.7754i	−0.622742	+	1.07862i
$304$	−1.09743	−	1.90081i	−0.0629420	−	0.109019i
$305$	8.95875	+	15.5170i	0.512977	+	0.888502i
$306$	−8.33105	+	14.4298i	−0.476254	+	0.824896i
$307$	−14.3480			−0.818881			−0.409440	−	0.912337i	$-0.634276\pi$
$307$	−14.3480			−0.818881			−0.409440	+	0.912337i	$0.634276\pi$
$308$	−3.14112	+	0.0600915i	−0.178982	+	0.00342403i
$309$	14.9947			0.853020
$310$	10.2788	−	17.8034i	0.583796	−	1.01116i
$311$	−0.818005	−	1.41683i	−0.0463848	−	0.0803408i	0.841901	−	0.539632i	$-0.181437\pi$
$311$	−0.818005	−	1.41683i	−0.0463848	−	0.0803408i	−0.888286	+	0.459291i	$0.848103\pi$
$312$	−1.49629	−	2.59166i	−0.0847109	−	0.146724i
$313$	−0.366038	+	0.633997i	−0.0206897	+	0.0358356i	−0.876185	−	0.481975i	$-0.839920\pi$
$313$	−0.366038	+	0.633997i	−0.0206897	+	0.0358356i	0.855495	+	0.517811i	$0.173253\pi$
$314$	18.3243			1.03410
$315$	7.88735	−	14.2855i	0.444402	−	0.804899i
$316$	−2.42334			−0.136323
$317$	−9.86355	+	17.0842i	−0.553992	+	0.959543i	0.443989	+	0.896032i	$0.353563\pi$
$317$	−9.86355	+	17.0842i	−0.553992	+	0.959543i	−0.997981	+	0.0635106i	$0.979770\pi$
$318$	−2.02362	−	3.50501i	−0.113479	−	0.196551i
$319$	−0.593725	−	1.02836i	−0.0332422	−	0.0575772i
$320$	1.10394	−	1.91209i	0.0617123	−	0.106889i
$321$	−39.1489			−2.18508
$322$	−9.90018	+	17.9312i	−0.551715	+	0.999264i
$323$	13.0915			0.728428
$324$	4.78842	−	8.29379i	0.266024	−	0.460766i
$325$	0.0778543	+	0.134848i	0.00431858	+	0.00747999i
$326$	10.3326	+	17.8967i	0.572272	+	0.991204i
$327$	3.45738	−	5.98836i	0.191194	−	0.331157i
$328$	10.1520			0.560552
$329$	−15.4027	+	0.294663i	−0.849179	+	0.0162453i
$330$	6.31048			0.347381
$331$	−16.6975	+	28.9209i	−0.917776	+	1.58964i	−0.114992	+	0.993366i	$0.536684\pi$
$331$	−16.6975	+	28.9209i	−0.917776	+	1.58964i	−0.802785	+	0.596269i	$0.796649\pi$
$332$	−2.73141	−	4.73094i	−0.149906	−	0.259644i
$333$	9.64317	+	16.7025i	0.528443	+	0.915290i
$334$	−10.9579	+	18.9797i	−0.599590	+	1.03852i
$335$	−26.8136			−1.46498
$336$	−3.28903	−	5.45315i	−0.179431	−	0.297494i
$337$	−10.5851			−0.576607			−0.288304	−	0.957539i	$-0.593091\pi$
$337$	−10.5851			−0.576607			−0.288304	+	0.957539i	$0.593091\pi$
$338$	5.72710	−	9.91963i	0.311513	−	0.539557i
$339$	1.21553	+	2.10535i	0.0660184	+	0.114347i
$340$	6.58456	+	11.4048i	0.357098	+	0.618512i
$341$	5.52816	−	9.57505i	0.299366	−	0.518518i
$342$	6.13136			0.331546
$343$	18.4898	−	1.06220i	0.998354	−	0.0573532i
$344$	−5.76077			−0.310600
$345$	20.5710	−	35.6300i	1.10750	−	1.91825i
$346$	7.08633	+	12.2739i	0.380963	+	0.659848i
$347$	−11.6732	−	20.2185i	−0.626648	−	1.08539i	−0.988220	−	0.153042i	$-0.951093\pi$
$347$	−11.6732	−	20.2185i	−0.626648	−	1.08539i	0.361571	−	0.932345i	$-0.382240\pi$
$348$	1.20348	−	2.08450i	0.0645136	−	0.111741i
$349$	7.42792			0.397607			0.198804	−	0.980039i	$-0.436294\pi$
$349$	7.42792			0.397607			0.198804	+	0.980039i	$0.436294\pi$
$350$	0.171133	+	0.283735i	0.00914743	+	0.0151663i
$351$	−0.617959			−0.0329842
$352$	0.593725	−	1.02836i	0.0316457	−	0.0548119i
$353$	16.2697	+	28.1799i	0.865946	+	1.49986i	0.866105	+	0.499863i	$0.166616\pi$
$353$	16.2697	+	28.1799i	0.865946	+	1.49986i	−0.000158409		1.00000i	$0.500050\pi$
$354$	9.60093	+	16.6293i	0.510284	+	0.883837i
$355$	5.08988	−	8.81593i	0.270143	−	0.467901i
$356$	−7.26832			−0.385220
$357$	37.9770	−	0.726521i	2.00996	−	0.0384516i
$358$	−22.3800			−1.18282
$359$	−3.62800	+	6.28388i	−0.191478	+	0.331650i	−0.945740	−	0.324923i	$-0.894662\pi$
$359$	−3.62800	+	6.28388i	−0.191478	+	0.331650i	0.754262	+	0.656574i	$0.227995\pi$
$360$	3.08387	+	5.34142i	0.162534	+	0.281517i
$361$	7.09129	+	12.2825i	0.373226	+	0.646446i
$362$	7.75801	−	13.4373i	0.407752	−	0.706247i
$363$	−23.0827			−1.21153
$364$	−1.58994	+	2.87970i	−0.0833356	+	0.150937i
$365$	−0.0871733			−0.00456286
$366$	−9.76656	+	16.9162i	−0.510506	+	0.884223i
$367$	12.0923	+	20.9445i	0.631215	+	1.09330i	0.987304	+	0.158844i	$0.0507768\pi$
$367$	12.0923	+	20.9445i	0.631215	+	1.09330i	−0.356089	+	0.934452i	$0.615890\pi$
$368$	−3.87086	−	6.70453i	−0.201783	−	0.349498i
$369$	−14.1799	+	24.5603i	−0.738175	+	1.27856i
$370$	15.2432			0.792459
$371$	−2.15027	+	3.89456i	−0.111636	+	0.202195i
$372$	22.4112			1.16197
$373$	12.0275	−	20.8322i	0.622759	−	1.07865i	−0.366210	−	0.930532i	$-0.619345\pi$
$373$	12.0275	−	20.8322i	0.622759	−	1.07865i	0.988970	−	0.148119i	$-0.0473217\pi$
$374$	3.54132	+	6.13375i	0.183118	+	0.317169i
$375$	−13.6186	−	23.5880i	−0.703260	−	1.21808i
$376$	2.91137	−	5.04264i	0.150143	−	0.260054i
$377$	−1.24330			−0.0640332
$378$	−1.31478	+	0.0251525i	−0.0676250	+	0.00129371i
$379$	27.4551			1.41027			0.705137	−	0.709071i	$-0.250885\pi$
$379$	27.4551			1.41027			0.705137	+	0.709071i	$0.250885\pi$
$380$	2.42300	−	4.19677i	0.124298	−	0.215290i
$381$	−5.75284	−	9.96421i	−0.294727	−	0.510482i
$382$	−3.97566	−	6.88605i	−0.203413	−	0.352321i
$383$	0.651505	−	1.12844i	0.0332904	−	0.0576606i	−0.848900	−	0.528553i	$-0.822735\pi$
$383$	0.651505	−	1.12844i	0.0332904	−	0.0576606i	0.882191	+	0.470893i	$0.156068\pi$
$384$	2.40697			0.122830
$385$	−3.58252	−	5.93976i	−0.182582	−	0.302718i
$386$	−3.38051			−0.172063
$387$	8.04636	−	13.9367i	0.409020	−	0.708443i
$388$	−1.61962	−	2.80526i	−0.0822235	−	0.142415i
$389$	−8.57411	−	14.8508i	−0.434724	−	0.752965i	0.562549	−	0.826764i	$-0.309821\pi$
$389$	−8.57411	−	14.8508i	−0.434724	−	0.752965i	−0.997273	+	0.0737994i	$0.976488\pi$
$390$	3.30365	−	5.72208i	0.167287	−	0.289749i
$391$	46.1762			2.33523
$392$	−3.26558	+	6.19161i	−0.164937	+	0.312723i
$393$	−26.1035			−1.31675
$394$	−0.442553	+	0.766524i	−0.0222955	+	0.0386169i
$395$	−2.67523	−	4.63363i	−0.134605	−	0.233143i
$396$	1.65857	+	2.87273i	0.0833464	+	0.144360i
$397$	9.67161	−	16.7517i	0.485404	−	0.840745i	−0.514455	−	0.857517i	$-0.672006\pi$
$397$	9.67161	−	16.7517i	0.485404	−	0.840745i	0.999859	+	0.0167724i	$0.00533906\pi$
$398$	11.6138			0.582147
$399$	−7.21896	−	11.9689i	−0.361400	−	0.599195i
$400$	−0.125238			−0.00626190
$401$	−16.3292	+	28.2829i	−0.815440	+	1.41238i	0.0935722	+	0.995612i	$0.470171\pi$
$401$	−16.3292	+	28.2829i	−0.815440	+	1.41238i	−0.909012	+	0.416770i	$0.863162\pi$
$402$	−14.6157	−	25.3151i	−0.728964	−	1.26260i
$403$	−5.78817	−	10.0254i	−0.288329	−	0.499401i
$404$	−4.50359	+	7.80044i	−0.224062	+	0.388087i
$405$	21.1446			1.05068
$406$	−2.64527	+	0.0506055i	−0.131282	+	0.00251151i
$407$	8.19816			0.406368
$408$	−7.17829	+	12.4332i	−0.355378	+	0.615533i
$409$	−2.17454	−	3.76641i	−0.107524	−	0.186237i	0.807243	−	0.590220i	$-0.200959\pi$
$409$	−2.17454	−	3.76641i	−0.107524	−	0.186237i	−0.914767	+	0.403983i	$0.867626\pi$
$410$	11.2073	+	19.4116i	0.553488	+	0.958669i
$411$	0.746721	−	1.29336i	0.0368330	−	0.0637967i
$412$	6.22971			0.306916
$413$	10.2018	−	18.4775i	0.501999	−	0.909219i
$414$	21.6265			1.06289
$415$	6.03064	−	10.4454i	0.296033	−	0.512744i
$416$	−0.621650	−	1.07673i	−0.0304789	−	0.0527910i
$417$	13.0713	+	22.6401i	0.640102	+	1.10869i
$418$	1.30315	−	2.25711i	0.0637389	−	0.110399i
$419$	18.3596			0.896925			0.448462	−	0.893802i	$-0.351972\pi$
$419$	18.3596			0.896925			0.448462	+	0.893802i	$0.351972\pi$
$420$	6.79599	−	12.3089i	0.331610	−	0.600611i
$421$	2.64832			0.129071			0.0645355	−	0.997915i	$-0.479443\pi$
$421$	2.64832			0.129071			0.0645355	+	0.997915i	$0.479443\pi$
$422$	12.0323	−	20.8406i	0.585723	−	1.01450i
$423$	8.13293	+	14.0866i	0.395436	+	0.684916i
$424$	−0.840732	−	1.45619i	−0.0408296	−	0.0707189i
$425$	0.373496	−	0.646915i	0.0181172	−	0.0313800i
$426$	11.0977			0.537683
$427$	21.4670	−	0.410675i	1.03886	−	0.0198740i
$428$	−16.2648			−0.786189
$429$	1.77677	−	3.07746i	0.0857834	−	0.148581i
$430$	−6.35956	−	11.0151i	−0.306685	−	0.531194i
$431$	−0.824327	−	1.42778i	−0.0397064	−	0.0687735i	0.845489	−	0.533992i	$-0.179309\pi$
$431$	−0.824327	−	1.42778i	−0.0397064	−	0.0687735i	−0.885196	+	0.465219i	$0.845976\pi$
$432$	0.248516	−	0.430442i	0.0119567	−	0.0207096i
$433$	6.12954			0.294567			0.147284	−	0.989094i	$-0.452947\pi$
$433$	6.12954			0.294567			0.147284	+	0.989094i	$0.452947\pi$
$434$	−12.7231	−	21.0946i	−0.610727	−	1.01257i
$435$	5.31432			0.254802
$436$	1.43640	−	2.48792i	0.0687912	−	0.119150i
$437$	−8.49601	−	14.7155i	−0.406419	−	0.703939i
$438$	−0.0475168	−	0.0823016i	−0.00227044	−	0.00393252i
$439$	5.15678	−	8.93181i	0.246120	−	0.426292i	−0.716326	−	0.697766i	$-0.754178\pi$
$439$	5.15678	−	8.93181i	0.246120	−	0.426292i	0.962446	+	0.271474i	$0.0875110\pi$
$440$	2.62175			0.124987
$441$	−10.4178	−	16.5484i	−0.496086	−	0.788018i
$442$	7.41577			0.352732
$443$	−4.20069	+	7.27580i	−0.199581	+	0.345684i	−0.948392	−	0.317099i	$-0.897291\pi$
$443$	−4.20069	+	7.27580i	−0.199581	+	0.345684i	0.748812	+	0.662783i	$0.230625\pi$
$444$	8.30886	+	14.3914i	0.394321	+	0.682984i
$445$	−8.02381	−	13.8976i	−0.380365	−	0.658812i
$446$	−1.81484	+	3.14340i	−0.0859352	+	0.148844i
$447$	−16.8167			−0.795400
$448$	−1.36646	−	2.26557i	−0.0645591	−	0.107038i
$449$	9.90897			0.467633			0.233817	−	0.972281i	$-0.424878\pi$
$449$	9.90897			0.467633			0.233817	+	0.972281i	$0.424878\pi$
$450$	0.174926	−	0.302981i	0.00824611	−	0.0142827i
$451$	6.02752	+	10.4400i	0.283825	+	0.491599i
$452$	0.505003	+	0.874691i	0.0237533	+	0.0411420i
$453$	−8.23780	+	14.2683i	−0.387046	+	0.670383i
$454$	12.6807			0.595136
$455$	−7.26143	+	0.138915i	−0.340421	+	0.00651245i
$456$	5.28297			0.247398
$457$	10.7686	−	18.6518i	0.503734	−	0.872493i	−0.496256	−	0.868176i	$-0.665292\pi$
$457$	10.7686	−	18.6518i	0.503734	−	0.872493i	0.999991	−	0.00431728i	$-0.00137424\pi$
$458$	9.96072	+	17.2525i	0.465434	+	0.806155i
$459$	1.48229	+	2.56741i	0.0691875	+	0.119836i
$460$	8.54642	−	14.8028i	0.398479	−	0.690186i
$461$	−22.0453			−1.02675			−0.513376	−	0.858164i	$-0.671605\pi$
$461$	−22.0453			−1.02675			−0.513376	+	0.858164i	$0.671605\pi$
$462$	3.65503	−	6.61998i	0.170048	−	0.307989i
$463$	−18.1202			−0.842116			−0.421058	−	0.907034i	$-0.638341\pi$
$463$	−18.1202			−0.842116			−0.421058	+	0.907034i	$0.638341\pi$
$464$	0.500000	−	0.866025i	0.0232119	−	0.0402042i
$465$	24.7407	+	42.8522i	1.14732	+	1.98722i
$466$	6.84794	+	11.8610i	0.317225	+	0.549449i
$467$	−12.4161	+	21.5053i	−0.574547	+	0.995145i	0.421543	+	0.906808i	$0.361489\pi$
$467$	−12.4161	+	21.5053i	−0.574547	+	0.995145i	−0.996091	+	0.0883369i	$0.971845\pi$
$468$	3.47316			0.160547
$469$	−15.5304	+	28.1287i	−0.717129	+	1.29886i
$470$	12.8560			0.593001
$471$	−22.0531	+	38.1970i	−1.01615	+	1.76003i
$472$	3.98880	+	6.90881i	0.183600	+	0.318004i
$473$	−3.42031	−	5.92415i	−0.157266	−	0.272393i
$474$	2.91645	−	5.05144i	0.133957	−	0.232020i
$475$	−0.274880			−0.0126124
$476$	15.7779	−	0.301841i	0.723180	−	0.0138348i
$477$	4.69718			0.215069
$478$	−8.34644	+	14.4564i	−0.381757	+	0.661223i
$479$	−6.27114	−	10.8619i	−0.286536	−	0.496294i	0.686445	−	0.727182i	$-0.259170\pi$
$479$	−6.27114	−	10.8619i	−0.286536	−	0.496294i	−0.972980	+	0.230888i	$0.925837\pi$
$480$	2.65716	+	4.60233i	0.121282	+	0.210067i
$481$	4.29187	−	7.43374i	0.195693	−	0.338950i
$482$	−16.8099			−0.765670
$483$	−25.4627	−	42.2168i	−1.15859	−	1.92093i
$484$	−9.58996			−0.435907
$485$	3.57593	−	6.19369i	0.162375	−	0.281241i
$486$	10.7800	+	18.6716i	0.488993	+	0.846960i
$487$	7.64343	+	13.2388i	0.346357	+	0.599908i	0.985599	−	0.169098i	$-0.0540853\pi$
$487$	7.64343	+	13.2388i	0.346357	+	0.599908i	−0.639242	+	0.769005i	$0.720752\pi$
$488$	−4.05762	+	7.02800i	−0.183680	+	0.318142i
$489$	−49.7407			−2.24935
$490$	−15.4439	+	0.591117i	−0.697684	+	0.0267040i
$491$	29.0450			1.31078			0.655391	−	0.755290i	$-0.272504\pi$
$491$	29.0450			1.31078			0.655391	+	0.755290i	$0.272504\pi$
$492$	−12.2178	+	21.1619i	−0.550822	+	0.954052i
$493$	2.98229	+	5.16548i	0.134316	+	0.232642i
$494$	−1.36444	−	2.36327i	−0.0613889	−	0.106329i
$495$	−3.66194	+	6.34267i	−0.164592	+	0.285082i
$496$	9.31097			0.418075
$497$	−6.30025	−	10.4457i	−0.282605	−	0.468554i
$498$	13.1488			0.589214
$499$	−8.35320	+	14.4682i	−0.373941	+	0.647684i	−0.990168	−	0.139884i	$-0.955327\pi$
$499$	−8.35320	+	14.4682i	−0.373941	+	0.647684i	0.616227	+	0.787568i	$0.288660\pi$
$500$	−5.65797	−	9.79989i	−0.253032	−	0.438265i
$501$	−26.3754	−	45.6835i	−1.17836	−	2.04099i
$502$	1.86674	−	3.23329i	0.0833168	−	0.144309i
$503$	43.1520			1.92405			0.962026	−	0.272959i	$-0.0880025\pi$
$503$	43.1520			1.92405			0.962026	+	0.272959i	$0.0880025\pi$
$504$	7.38956	−	0.141367i	0.329157	−	0.00629697i
$505$	−19.8868			−0.884952
$506$	4.59645	−	7.96129i	0.204337	−	0.353923i
$507$	13.7850	+	23.8763i	0.612212	+	1.06038i
$508$	−2.39008	−	4.13973i	−0.106042	−	0.183671i
$509$	4.48820	−	7.77379i	0.198936	−	0.344567i	−0.749248	−	0.662290i	$-0.769585\pi$
$509$	4.48820	−	7.77379i	0.198936	−	0.344567i	0.948184	+	0.317723i	$0.102918\pi$
$510$	−31.6977			−1.40360
$511$	−0.0504908	+	0.0914487i	−0.00223358	+	0.00404545i
$512$	1.00000			0.0441942
$513$	0.545458	−	0.944761i	0.0240826	−	0.0417122i
$514$	−15.2718	−	26.4516i	−0.673611	−	1.16673i
$515$	6.87725	+	11.9117i	0.303048	+	0.524894i
$516$	6.93300	−	12.0083i	0.305208	−	0.528636i
$517$	6.91422			0.304087
$518$	8.82889	−	15.9908i	0.387919	−	0.702598i
$519$	−34.1132			−1.49740
$520$	1.37253	−	2.37730i	0.0601896	−	0.104251i
$521$	−10.0074	−	17.3334i	−0.438433	−	0.759388i	0.559136	−	0.829076i	$-0.311133\pi$
$521$	−10.0074	−	17.3334i	−0.438433	−	0.759388i	−0.997569	+	0.0696879i	$0.977800\pi$
$522$	1.39675	+	2.41924i	0.0611342	+	0.105887i
$523$	−16.9443	+	29.3484i	−0.740923	+	1.28332i	0.211152	+	0.977453i	$0.432279\pi$
$523$	−16.9443	+	29.3484i	−0.740923	+	1.28332i	−0.952075	+	0.305864i	$0.901055\pi$
$524$	−10.8450			−0.473764
$525$	−0.797400	+	0.0152547i	−0.0348014	+	0.000665771i
$526$	−16.6182			−0.724588
$527$	−27.7680	+	48.0957i	−1.20959	+	2.09508i
$528$	1.42908	+	2.47524i	0.0621926	+	0.107721i
$529$	−18.4671	−	31.9860i	−0.802918	−	1.39070i
$530$	1.85624	−	3.21510i	0.0806300	−	0.139655i
$531$	−22.2855			−0.967107
$532$	−2.99919	−	4.97261i	−0.130031	−	0.215590i
$533$	12.6220			0.546721
$534$	8.74731	−	15.1508i	0.378533	−	0.655639i
$535$	−17.9554	−	31.0997i	−0.776280	−	1.34456i
$536$	−6.07224	−	10.5174i	−0.262281	−	0.454283i
$537$	26.9340	−	46.6511i	1.16229	−	2.01314i
$538$	−15.3894			−0.663484
$539$	−8.30607	+	0.317916i	−0.357768	+	0.0136936i
$540$	1.09739			0.0472241
$541$	−10.8908	+	18.8633i	−0.468230	+	0.810999i	−0.999341	−	0.0363040i	$-0.988442\pi$
$541$	−10.8908	+	18.8633i	−0.468230	+	0.810999i	0.531111	+	0.847303i	$0.321775\pi$
$542$	11.4607	+	19.8505i	0.492279	+	0.852651i
$543$	18.6733	+	32.3431i	0.801348	+	1.38798i
$544$	−2.98229	+	5.16548i	−0.127865	+	0.221468i
$545$	6.34283			0.271697
$546$	−4.08925	−	6.77990i	−0.175004	−	0.290153i
$547$	−10.7968			−0.461639			−0.230819	−	0.972997i	$-0.574141\pi$
$547$	−10.7968			−0.461639			−0.230819	+	0.972997i	$0.574141\pi$
$548$	0.310233	−	0.537339i	0.0132525	−	0.0229540i
$549$	−11.3350	−	19.6327i	−0.483764	−	0.837905i
$550$	−0.0743570	−	0.128790i	−0.00317059	−	0.00549163i
$551$	1.09743	−	1.90081i	0.0467522	−	0.0809771i
$552$	18.6341			0.793120
$553$	−6.41038	+	0.122634i	−0.272597	+	0.00521493i
$554$	−24.0528			−1.02191
$555$	−18.3450	+	31.7745i	−0.778703	+	1.34875i
$556$	5.43059	+	9.40605i	0.230308	+	0.398905i
$557$	−13.2676	−	22.9802i	−0.562166	−	0.973701i	−0.997307	−	0.0733383i	$-0.976635\pi$
$557$	−13.2676	−	22.9802i	−0.562166	−	0.973701i	0.435141	−	0.900362i	$-0.356699\pi$
$558$	−13.0051	+	22.5255i	−0.550550	+	0.953581i
$559$	−7.16237			−0.302936
$560$	2.82346	−	5.11384i	0.119313	−	0.216099i
$561$	−17.0477			−0.719755
$562$	−0.866623	+	1.50104i	−0.0365563	+	0.0633174i
$563$	−10.4272	−	18.0605i	−0.439455	−	0.761158i	0.558193	−	0.829711i	$-0.311495\pi$
$563$	−10.4272	−	18.0605i	−0.439455	−	0.761158i	−0.997647	+	0.0685535i	$0.978162\pi$
$564$	7.00758	+	12.1375i	0.295072	+	0.511080i
$565$	−1.11499	+	1.93122i	−0.0469079	+	0.0812469i
$566$	−17.6940			−0.743734
$567$	12.2470	−	22.1816i	0.514324	−	0.931541i
$568$	4.61064			0.193458
$569$	−6.78151	+	11.7459i	−0.284296	+	0.492415i	−0.972438	−	0.233161i	$-0.925093\pi$
$569$	−6.78151	+	11.7459i	−0.284296	+	0.492415i	0.688142	+	0.725576i	$0.258426\pi$
$570$	5.83210	+	10.1015i	0.244280	+	0.423105i
$571$	11.0204	+	19.0879i	0.461190	+	0.798804i	0.999021	−	0.0442486i	$-0.0140894\pi$
$571$	11.0204	+	19.0879i	0.461190	+	0.798804i	−0.537831	+	0.843053i	$0.680756\pi$
$572$	0.738179	−	1.27856i	0.0308648	−	0.0534594i
$573$	19.1386			0.799526
$574$	26.8548	−	0.513749i	1.12090	−	0.0214434i
$575$	−0.969558			−0.0404334
$576$	−1.39675	+	2.41924i	−0.0581980	+	0.100802i
$577$	2.98000	+	5.16151i	0.124059	+	0.214877i	0.921365	−	0.388699i	$-0.127075\pi$
$577$	2.98000	+	5.16151i	0.124059	+	0.214877i	−0.797306	+	0.603576i	$0.793742\pi$
$578$	−9.28814	−	16.0875i	−0.386336	−	0.669153i
$579$	4.06839	−	7.04666i	0.169077	−	0.292849i
$580$	2.20789			0.0916775
$581$	−7.46472	−	12.3764i	−0.309689	−	0.513459i
$582$	7.79673			0.323185
$583$	0.998328	−	1.72915i	0.0413465	−	0.0716142i
$584$	−0.0197414	−	0.0341930i	−0.000816903	−	0.00141492i
$585$	3.83418	+	6.64099i	0.158524	+	0.274571i
$586$	13.4310	−	23.2632i	0.554829	−	0.960993i
$587$	−17.1038			−0.705949			−0.352974	−	0.935633i	$-0.614830\pi$
$587$	−17.1038			−0.705949			−0.352974	+	0.935633i	$0.614830\pi$
$588$	−8.97631	−	14.2586i	−0.370177	−	0.588014i
$589$	20.4363			0.842063
$590$	−8.80683	+	15.2539i	−0.362571	+	0.627992i
$591$	−1.06521	−	1.84500i	−0.0438170	−	0.0758932i
$592$	3.45200	+	5.97904i	0.141876	+	0.245737i
$593$	−21.7398	+	37.6545i	−0.892747	+	1.54628i	−0.0561785	+	0.998421i	$0.517892\pi$
$593$	−21.7398	+	37.6545i	−0.892747	+	1.54628i	−0.836568	+	0.547862i	$0.815442\pi$
$594$	0.590200			0.0242162
$595$	17.9951	+	29.8355i	0.737726	+	1.22314i
$596$	−6.98665			−0.286184
$597$	−13.9770	+	24.2089i	−0.572042	+	0.990806i
$598$	−4.81264	−	8.33574i	−0.196804	−	0.340874i
$599$	19.0524	+	32.9998i	0.778461	+	1.34833i	0.932829	+	0.360320i	$0.117333\pi$
$599$	19.0524	+	32.9998i	0.778461	+	1.34833i	−0.154368	+	0.988013i	$0.549334\pi$
$600$	0.150722	−	0.261058i	0.00615320	−	0.0106577i
$601$	48.5105			1.97878			0.989391	−	0.145275i	$-0.0464067\pi$
$601$	48.5105			1.97878			0.989391	+	0.145275i	$0.0464067\pi$
$602$	−15.2388	+	0.291526i	−0.621086	+	0.0118817i
$603$	33.9256			1.38156
$604$	−3.42248	+	5.92791i	−0.139259	+	0.241203i
$605$	−10.5868	−	18.3368i	−0.430414	−	0.745498i
$606$	−10.8400	−	18.7754i	−0.440345	−	0.762700i
$607$	24.2511	−	42.0041i	0.984322	−	1.70490i	0.339409	−	0.940639i	$-0.389773\pi$
$607$	24.2511	−	42.0041i	0.984322	−	1.70490i	0.644913	−	0.764256i	$-0.276894\pi$
$608$	2.19486			0.0890135
$609$	3.07805	−	5.57495i	0.124729	−	0.225909i
$610$	−17.9175			−0.725459
$611$	3.61971	−	6.26952i	0.146438	−	0.253638i
$612$	−8.33105	−	14.4298i	−0.336763	−	0.583290i
$613$	−2.83156	−	4.90440i	−0.114366	−	0.198087i	0.803160	−	0.595763i	$-0.203150\pi$
$613$	−2.83156	−	4.90440i	−0.114366	−	0.198087i	−0.917526	+	0.397676i	$0.869817\pi$
$614$	7.17398	−	12.4257i	0.289518	−	0.501460i
$615$	−53.9511			−2.17552
$616$	1.51852	−	2.75034i	0.0611829	−	0.110814i
$617$	24.7525			0.996496			0.498248	−	0.867034i	$-0.333977\pi$
$617$	24.7525			0.996496			0.498248	+	0.867034i	$0.333977\pi$
$618$	−7.49736	+	12.9858i	−0.301588	+	0.522366i
$619$	3.87717	+	6.71546i	0.155837	+	0.269917i	0.933363	−	0.358933i	$-0.116859\pi$
$619$	3.87717	+	6.71546i	0.155837	+	0.269917i	−0.777527	+	0.628850i	$0.783526\pi$
$620$	10.2788	+	17.8034i	0.412806	+	0.715001i
$621$	1.92394	−	3.33236i	0.0772050	−	0.133723i
$622$	1.63601			0.0655980
$623$	−19.2266	+	0.367817i	−0.770299	+	0.0147363i
$624$	2.99259			0.119799
$625$	12.1791	−	21.0948i	0.487163	−	0.843790i
$626$	−0.366038	−	0.633997i	−0.0146298	−	0.0253396i
$627$	3.13663	+	5.43281i	0.125265	+	0.216965i
$628$	−9.16217	+	15.8693i	−0.365610	+	0.633255i
$629$	−41.1795			−1.64193
$630$	8.42796	+	13.9734i	0.335778	+	0.556714i
$631$	39.3718			1.56737			0.783684	−	0.621160i	$-0.213338\pi$
$631$	39.3718			1.56737			0.783684	+	0.621160i	$0.213338\pi$
$632$	1.21167	−	2.09867i	0.0481976	−	0.0834807i
$633$	28.9614	+	50.1626i	1.15111	+	1.99378i
$634$	−9.86355	−	17.0842i	−0.391732	−	0.678499i
$635$	5.27702	−	9.14006i	0.209412	−	0.362712i
$636$	4.04723			0.160483
$637$	−4.06009	+	7.69803i	−0.160867	+	0.305007i
$638$	1.18745			0.0470116
$639$	−6.43991	+	11.1543i	−0.254759	+	0.441256i
$640$	1.10394	+	1.91209i	0.0436372	+	0.0755818i
$641$	6.23774	+	10.8041i	0.246376	+	0.426736i	0.962518	−	0.271219i	$-0.0874269\pi$
$641$	6.23774	+	10.8041i	0.246376	+	0.426736i	−0.716142	+	0.697955i	$0.754094\pi$
$642$	19.5744	−	33.9039i	0.772541	−	1.33808i
$643$	−17.0296			−0.671581			−0.335790	−	0.941937i	$-0.609003\pi$
$643$	−17.0296			−0.671581			−0.335790	+	0.941937i	$0.609003\pi$
$644$	−10.5787	−	17.5394i	−0.416861	−	0.691148i
$645$	30.6145			1.20545
$646$	−6.54573	+	11.3375i	−0.257538	+	0.446069i
$647$	−16.0448	−	27.7903i	−0.630785	−	1.09255i	−0.987392	−	0.158297i	$-0.949400\pi$
$647$	−16.0448	−	27.7903i	−0.630785	−	1.09255i	0.356607	−	0.934254i	$-0.383934\pi$
$648$	4.78842	+	8.29379i	0.188107	+	0.325811i
$649$	−4.73651	+	8.20387i	−0.185924	+	0.322030i
$650$	−0.155709			−0.00610739
$651$	59.2837	−	1.13413i	2.32351	−	0.0444501i
$652$	−20.6653			−0.809315
$653$	18.6417	−	32.2884i	0.729506	−	1.26354i	−0.227587	−	0.973758i	$-0.573083\pi$
$653$	18.6417	−	32.2884i	0.729506	−	1.26354i	0.957092	−	0.289783i	$-0.0935832\pi$
$654$	3.45738	+	5.98836i	0.135194	+	0.234163i
$655$	−11.9722	−	20.7365i	−0.467793	−	0.810242i
$656$	−5.07602	+	8.79192i	−0.198185	+	0.343267i
$657$	0.110295			0.00430302
$658$	7.44617	−	13.4865i	0.290282	−	0.525757i
$659$	−18.0912			−0.704734			−0.352367	−	0.935862i	$-0.614623\pi$
$659$	−18.0912			−0.704734			−0.352367	+	0.935862i	$0.614623\pi$
$660$	−3.15524	+	5.46504i	−0.122818	+	0.212726i
$661$	−13.6050	−	23.5645i	−0.529172	−	0.916553i	−0.999421	−	0.0340193i	$-0.989169\pi$
$661$	−13.6050	−	23.5645i	−0.529172	−	0.916553i	0.470249	−	0.882534i	$-0.344164\pi$
$662$	−16.6975	−	28.9209i	−0.648966	−	1.12404i
$663$	−8.92477	+	15.4582i	−0.346609	+	0.600345i
$664$	5.46282			0.211999
$665$	6.19712	−	11.2242i	0.240314	−	0.435255i
$666$	−19.2863			−0.747331
$667$	3.87086	−	6.70453i	0.149880	−	0.259600i
$668$	−10.9579	−	18.9797i	−0.423974	−	0.734345i
$669$	−4.36827	−	7.56606i	−0.168887	−	0.292521i
$670$	13.4068	−	23.2213i	0.517950	−	0.897116i
$671$	−9.63643			−0.372010
$672$	6.36708	−	0.121806i	0.245615	−	0.00469876i
$673$	−26.8539			−1.03514			−0.517572	−	0.855640i	$-0.673164\pi$
$673$	−26.8539			−1.03514			−0.517572	+	0.855640i	$0.673164\pi$
$674$	5.29255	−	9.16697i	0.203861	−	0.353098i
$675$	−0.0311236	−	0.0539077i	−0.00119795	−	0.00207491i
$676$	5.72710	+	9.91963i	0.220273	+	0.381524i
$677$	9.25884	−	16.0368i	0.355846	−	0.616344i	−0.631416	−	0.775444i	$-0.717526\pi$
$677$	9.25884	−	16.0368i	0.355846	−	0.616344i	0.987262	+	0.159100i	$0.0508593\pi$
$678$	−2.43105			−0.0933641
$679$	−4.42628	−	7.33869i	−0.169865	−	0.281633i
$680$	−13.1691			−0.505013
$681$	−15.2611	+	26.4329i	−0.584805	+	1.01291i
$682$	5.52816	+	9.57505i	0.211684	+	0.366648i
$683$	20.6331	+	35.7375i	0.789502	+	1.36746i	0.926272	+	0.376855i	$0.122995\pi$
$683$	20.6331	+	35.7375i	0.789502	+	1.36746i	−0.136770	+	0.990603i	$0.543672\pi$
$684$	−3.06568	+	5.30991i	−0.117219	+	0.203030i
$685$	1.36992			0.0523419
$686$	−8.32500	+	16.5437i	−0.317850	+	0.631642i
$687$	−47.9503			−1.82942
$688$	2.88038	−	4.98897i	0.109814	−	0.190203i
$689$	−1.04528	−	1.81048i	−0.0398221	−	0.0689739i
$690$	20.5710	+	35.6300i	0.783124	+	1.35641i
$691$	18.8654	−	32.6758i	0.717674	−	1.24305i	−0.244245	−	0.969713i	$-0.578540\pi$
$691$	18.8654	−	32.6758i	0.717674	−	1.24305i	0.961919	−	0.273334i	$-0.0881265\pi$
$692$	−14.1727			−0.538764
$693$	4.53274	+	7.51521i	0.172185	+	0.285479i
$694$	23.3463			0.886215
$695$	−11.9901	+	20.7675i	−0.454811	+	0.787756i
$696$	1.20348	+	2.08450i	0.0456180	+	0.0790127i
$697$	−30.2763	−	52.4402i	−1.14680	−	1.98631i
$698$	−3.71396	+	6.43277i	−0.140575	+	0.243484i
$699$	−32.9656			−1.24687
$700$	−0.331288	+	0.00633773i	−0.0125215	+	0.000239544i
$701$	48.1772			1.81963			0.909814	−	0.415017i	$-0.136224\pi$
$701$	48.1772			1.81963			0.909814	+	0.415017i	$0.136224\pi$
$702$	0.308980	−	0.535168i	0.0116617	−	0.0201986i
$703$	7.57667	+	13.1232i	0.285760	+	0.494950i
$704$	0.593725	+	1.02836i	0.0223769	+	0.0387579i
$705$	−15.4719	+	26.7982i	−0.582707	+	1.00928i
$706$	−32.5393			−1.22463
$707$	−11.5184	+	20.8622i	−0.433196	+	0.784602i
$708$	−19.2019			−0.721650
$709$	5.70674	−	9.88437i	0.214321	−	0.371215i	−0.738741	−	0.673989i	$-0.764579\pi$
$709$	5.70674	−	9.88437i	0.214321	−	0.371215i	0.953062	+	0.302774i	$0.0979127\pi$
$710$	5.08988	+	8.81593i	0.191020	+	0.330856i
$711$	3.38480	+	5.86265i	0.126940	+	0.219866i
$712$	3.63416	−	6.29455i	0.136196	−	0.235898i
$713$	72.0829			2.69953
$714$	−18.3593	+	33.2523i	−0.687080	+	1.24444i
$715$	3.25963			0.121903
$716$	11.1900	−	19.3817i	0.418191	−	0.724327i
$717$	−20.0896	−	34.7962i	−0.750260	−	1.29949i
$718$	−3.62800	−	6.28388i	−0.135396	−	0.234512i
$719$	8.83370	−	15.3004i	0.329441	−	0.570609i	−0.652960	−	0.757393i	$-0.726473\pi$
$719$	8.83370	−	15.3004i	0.329441	−	0.570609i	0.982401	+	0.186783i	$0.0598063\pi$
$720$	−6.16774			−0.229858
$721$	16.4793	−	0.315258i	0.613719	−	0.0117408i
$722$	−14.1826			−0.527821
$723$	20.2305	−	35.0402i	0.752379	−	1.30316i
$724$	7.75801	+	13.4373i	0.288324	+	0.499392i
$725$	−0.0626190	−	0.108459i	−0.00232561	−	0.00402808i
$726$	11.5414	−	19.9902i	0.428341	−	0.741908i
$727$	−24.8691			−0.922342			−0.461171	−	0.887311i	$-0.652571\pi$
$727$	−24.8691			−0.922342			−0.461171	+	0.887311i	$0.652571\pi$
$728$	−1.69892	−	2.81678i	−0.0629661	−	0.104397i
$729$	−23.1639			−0.857924
$730$	0.0435867	−	0.0754943i	0.00161321	−	0.00279417i
$731$	17.1803	+	29.7571i	0.635436	+	1.10061i
$732$	−9.76656	−	16.9162i	−0.360982	−	0.625240i
$733$	−7.19441	+	12.4611i	−0.265732	+	0.460261i	−0.967755	−	0.251893i	$-0.918947\pi$
$733$	−7.19441	+	12.4611i	−0.265732	+	0.460261i	0.702023	+	0.712154i	$0.252280\pi$
$734$	−24.1847			−0.892673
$735$	17.3543	−	32.9042i	0.640123	−	1.21369i
$736$	7.74172			0.285364
$737$	7.21048	−	12.4889i	0.265601	−	0.460035i
$738$	−14.1799	−	24.5603i	−0.521968	−	0.904076i
$739$	2.09010	+	3.62016i	0.0768855	+	0.133170i	0.901905	−	0.431935i	$-0.142169\pi$
$739$	2.09010	+	3.62016i	0.0768855	+	0.133170i	−0.825019	+	0.565105i	$0.808836\pi$
$740$	−7.62162	+	13.2010i	−0.280176	+	0.485280i
$741$	6.56832			0.241293
$742$	−2.29765	−	3.80947i	−0.0843495	−	0.139850i
$743$	45.1899			1.65786			0.828928	−	0.559355i	$-0.188951\pi$
$743$	45.1899			1.65786			0.828928	+	0.559355i	$0.188951\pi$
$744$	−11.2056	+	19.4087i	−0.410818	+	0.711557i
$745$	−7.71286	−	13.3591i	−0.282577	−	0.489439i
$746$	12.0275	+	20.8322i	0.440357	+	0.762721i
$747$	−7.63020	+	13.2159i	−0.279175	+	0.483544i
$748$	−7.08265			−0.258967
$749$	−43.0247	+	0.823088i	−1.57209	+	0.0300750i
$750$	27.2371			0.994559
$751$	−11.6399	+	20.1608i	−0.424744	+	0.735679i	−0.996397	−	0.0848172i	$-0.972969\pi$
$751$	−11.6399	+	20.1608i	−0.424744	+	0.735679i	0.571652	+	0.820496i	$0.306303\pi$
$752$	2.91137	+	5.04264i	0.106167	+	0.183886i
$753$	4.49319	+	7.78244i	0.163741	+	0.283608i
$754$	0.621650	−	1.07673i	0.0226392	−	0.0392122i
$755$	−15.1129			−0.550014
$756$	0.635608	−	1.15121i	0.0231168	−	0.0418691i
$757$	30.8864			1.12258			0.561292	−	0.827618i	$-0.310304\pi$
$757$	30.8864			1.12258			0.561292	+	0.827618i	$0.310304\pi$
$758$	−13.7276	+	23.7768i	−0.498607	+	0.863613i
$759$	11.0635	+	19.1626i	0.401581	+	0.695558i
$760$	2.42300	+	4.19677i	0.0878916	+	0.152233i
$761$	13.1679	−	22.8076i	0.477338	−	0.826773i	−0.522325	−	0.852747i	$-0.674935\pi$
$761$	13.1679	−	22.8076i	0.477338	−	0.826773i	0.999663	+	0.0259733i	$0.00826848\pi$
$762$	11.5057			0.416807
$763$	3.67377	−	6.65391i	0.132999	−	0.240888i
$764$	7.95133			0.287669
$765$	18.3940	−	31.8593i	0.665036	−	1.15188i
$766$	0.651505	+	1.12844i	0.0235398	+	0.0407722i
$767$	4.95928	+	8.58973i	0.179069	+	0.310157i
$768$	−1.20348	+	2.08450i	−0.0434270	+	0.0752178i
$769$	−19.8275			−0.714996			−0.357498	−	0.933914i	$-0.616370\pi$
$769$	−19.8275			−0.714996			−0.357498	+	0.933914i	$0.616370\pi$
$770$	6.93524	−	0.132675i	0.249929	−	0.00478128i
$771$	73.5176			2.64767
$772$	1.69025	−	2.92761i	0.0608336	−	0.105367i
$773$	−9.58375	−	16.5995i	−0.344704	−	0.597044i	0.640596	−	0.767878i	$-0.278687\pi$
$773$	−9.58375	−	16.5995i	−0.344704	−	0.597044i	−0.985300	+	0.170834i	$0.945354\pi$
$774$	8.04636	+	13.9367i	0.289221	+	0.500945i
$775$	0.583044	−	1.00986i	0.0209436	−	0.0362753i
$776$	3.23923			0.116282
$777$	22.7074	+	37.6485i	0.814625	+	1.35063i
$778$	17.1482			0.614793
$779$	−11.1412	+	19.2971i	−0.399174	+	0.691389i
$780$	3.30365	+	5.72208i	0.118289	+	0.204883i
$781$	2.73745	+	4.74140i	0.0979537	+	0.169661i
$782$	−23.0881	+	39.9897i	−0.825628	+	1.43003i
$783$	0.497031			0.0177624
$784$	−3.72930	−	5.92388i	−0.133189	−	0.211567i
$785$	−40.4580			−1.44401
$786$	13.0517	−	22.6063i	0.465540	−	0.806339i
$787$	−6.76623	−	11.7195i	−0.241190	−	0.417753i	0.719864	−	0.694116i	$-0.244204\pi$
$787$	−6.76623	−	11.7195i	−0.241190	−	0.417753i	−0.961054	+	0.276362i	$0.910871\pi$
$788$	−0.442553	−	0.766524i	−0.0157653	−	0.0273063i
$789$	19.9998	−	34.6406i	0.712010	−	1.23324i
$790$	5.35045			0.190361
$791$	1.38013	+	2.28824i	0.0490718	+	0.0813603i
$792$	−3.31715			−0.117870
$793$	−5.04484	+	8.73791i	−0.179147	+	0.310292i
$794$	9.67161	+	16.7517i	0.343233	+	0.594497i
$795$	4.46792	+	7.73866i	0.158461	+	0.274462i
$796$	−5.80690	+	10.0578i	−0.205820	+	0.356491i
$797$	21.2360			0.752216			0.376108	−	0.926576i	$-0.377262\pi$
$797$	21.2360			0.752216			0.376108	+	0.926576i	$0.377262\pi$
$798$	13.9749	−	0.267347i	0.494705	−	0.00946399i
$799$	−34.7302			−1.22867
$800$	0.0626190	−	0.108459i	0.00221392	−	0.00383462i
$801$	10.1520	+	17.5838i	0.358705	+	0.621295i
$802$	−16.3292	−	28.2829i	−0.576603	−	0.998705i
$803$	0.0234419	−	0.0406025i	0.000827246	−	0.00143283i
$804$	29.2314			1.03091
$805$	21.8585	−	39.5899i	0.770410	−	1.39536i
$806$	11.5763			0.407759
$807$	18.5209	−	32.0792i	0.651967	−	1.12924i
$808$	−4.50359	−	7.80044i	−0.158436	−	0.274419i
$809$	14.2949	+	24.7595i	0.502582	+	0.870498i	0.999996	+	0.00298434i	$0.000949946\pi$
$809$	14.2949	+	24.7595i	0.502582	+	0.870498i	−0.497413	+	0.867514i	$0.665717\pi$
$810$	−10.5723	+	18.3118i	−0.371473	+	0.643410i
$811$	12.8153			0.450007			0.225004	−	0.974358i	$-0.427761\pi$
$811$	12.8153			0.450007			0.225004	+	0.974358i	$0.427761\pi$
$812$	1.27881	−	2.31617i	0.0448774	−	0.0812817i
$813$	−55.1710			−1.93493
$814$	−4.09908	+	7.09981i	−0.143673	+	0.248848i
$815$	−22.8133	−	39.5138i	−0.799115	−	1.38411i
$816$	−7.17829	−	12.4332i	−0.251290	−	0.435248i
$817$	6.32205	−	10.9501i	0.221181	−	0.383096i
$818$	4.34907			0.152062
$819$	9.18745	−	0.175761i	0.321035	−	0.00614159i
$820$	−22.4145			−0.782750
$821$	−6.65000	+	11.5181i	−0.232087	+	0.401986i	−0.958422	−	0.285355i	$-0.907889\pi$
$821$	−6.65000	+	11.5181i	−0.232087	+	0.401986i	0.726335	+	0.687340i	$0.241222\pi$
$822$	0.746721	+	1.29336i	0.0260449	+	0.0451111i
$823$	19.1329	+	33.1391i	0.666930	+	1.15516i	0.978758	+	0.205019i	$0.0657255\pi$
$823$	19.1329	+	33.1391i	0.666930	+	1.15516i	−0.311828	+	0.950139i	$0.600941\pi$
$824$	−3.11486	+	5.39509i	−0.108511	+	0.187947i
$825$	0.357950			0.0124622
$826$	10.9011	+	18.0738i	0.379297	+	0.628868i
$827$	−47.0423			−1.63582			−0.817910	−	0.575346i	$-0.804868\pi$
$827$	−47.0423			−1.63582			−0.817910	+	0.575346i	$0.804868\pi$
$828$	−10.8133	+	18.7291i	−0.375787	+	0.650882i
$829$	−6.68523	−	11.5792i	−0.232188	−	0.402161i	0.726264	−	0.687416i	$-0.241255\pi$
$829$	−6.68523	−	11.5792i	−0.232188	−	0.402161i	−0.958452	+	0.285255i	$0.907922\pi$
$830$	6.03064	+	10.4454i	0.209327	+	0.362564i
$831$	28.9472	−	50.1380i	1.00417	−	1.73927i
$832$	1.24330			0.0431037
$833$	41.7216	−	1.59690i	1.44557	−	0.0553293i
$834$	−26.1425			−0.905241
$835$	24.1938	−	41.9049i	0.837262	−	1.45018i
$836$	1.30315	+	2.25711i	0.0450702	+	0.0780639i
$837$	2.31392	+	4.00783i	0.0799808	+	0.138531i
$838$	−9.17980	+	15.8999i	−0.317111	+	0.549252i
$839$	−17.0873			−0.589919			−0.294959	−	0.955510i	$-0.595306\pi$
$839$	−17.0873			−0.589919			−0.294959	+	0.955510i	$0.595306\pi$
$840$	7.26180	+	12.0399i	0.250556	+	0.415417i
$841$	1.00000			0.0344828
$842$	−1.32416	+	2.29351i	−0.0456335	+	0.0790395i
$843$	−2.08594	−	3.61295i	−0.0718434	−	0.124436i
$844$	12.0323	+	20.8406i	0.414169	+	0.717362i
$845$	−12.6448	+	21.9014i	−0.434994	+	0.753432i
$846$	−16.2659			−0.559231
$847$	−25.3680	+	0.485305i	−0.871655	+	0.0166753i
$848$	1.68146			0.0577417
$849$	21.2944	−	36.8831i	0.730823	−	1.26582i
$850$	0.373496	+	0.646915i	0.0128108	+	0.0221890i
$851$	26.7244	+	46.2881i	0.916102	+	1.58673i
$852$	−5.54883	+	9.61086i	−0.190100	+	0.329263i
$853$	−44.1225			−1.51073			−0.755363	−	0.655307i	$-0.772539\pi$
$853$	−44.1225			−1.51073			−0.755363	+	0.655307i	$0.772539\pi$
$854$	−10.3778	+	18.7963i	−0.355122	+	0.643195i
$855$	−13.5373			−0.462967
$856$	8.13240	−	14.0857i	0.277960	−	0.481440i
$857$	−8.08485	−	14.0034i	−0.276173	−	0.478346i	0.694257	−	0.719727i	$-0.255733\pi$
$857$	−8.08485	−	14.0034i	−0.276173	−	0.478346i	−0.970430	+	0.241381i	$0.922400\pi$
$858$	1.77677	+	3.07746i	0.0606581	+	0.105063i
$859$	16.5232	−	28.6190i	0.563763	−	0.976466i	−0.433401	−	0.901201i	$-0.642687\pi$
$859$	16.5232	−	28.6190i	0.563763	−	0.976466i	0.997164	−	0.0752647i	$-0.0239802\pi$
$860$	12.7191			0.433718
$861$	−31.2485	+	56.5971i	−1.06495	+	1.92883i
$862$	1.64865			0.0561534
$863$	0.375276	−	0.649998i	0.0127746	−	0.0221262i	−0.859567	−	0.511022i	$-0.829267\pi$
$863$	0.375276	−	0.649998i	0.0127746	−	0.0221262i	0.872342	+	0.488896i	$0.162600\pi$
$864$	0.248516	+	0.430442i	0.00845467	+	0.0146439i
$865$	−15.6458	−	27.0993i	−0.531973	−	0.921405i
$866$	−3.06477	+	5.30834i	−0.104145	+	0.180385i
$867$	44.7126			1.51852
$868$	24.6300	−	0.471186i	0.835997	−	0.0159931i
$869$	2.87759			0.0976156
$870$	−2.65716	+	4.60233i	−0.0900861	+	0.156034i
$871$	−7.54961	−	13.0763i	−0.255809	−	0.443074i
$872$	1.43640	+	2.48792i	0.0486428	+	0.0842517i
$873$	−4.52440	+	7.83650i	−0.153128	+	0.265225i
$874$	16.9920			0.574764
$875$	−15.4628	−	25.6370i	−0.522737	−	0.866689i
$876$	0.0950337			0.00321089
$877$	−21.2668	+	36.8352i	−0.718129	+	1.24384i	0.243611	+	0.969873i	$0.421668\pi$
$877$	−21.2668	+	36.8352i	−0.718129	+	1.24384i	−0.961740	+	0.273963i	$0.911665\pi$
$878$	5.15678	+	8.93181i	0.174033	+	0.301434i
$879$	32.3280	+	55.9938i	1.09040	+	1.88862i
$880$	−1.31088	+	2.27051i	−0.0441897	+	0.0765388i
$881$	−41.6234			−1.40233			−0.701165	−	0.713000i	$-0.747336\pi$
$881$	−41.6234			−1.40233			−0.701165	+	0.713000i	$0.747336\pi$
$882$	19.5402	−	0.747905i	0.657953	−	0.0251833i
$883$	3.11629			0.104872			0.0524358	−	0.998624i	$-0.483302\pi$
$883$	3.11629			0.104872			0.0524358	+	0.998624i	$0.483302\pi$
$884$	−3.70789	+	6.42225i	−0.124710	+	0.216004i
$885$	−21.1978	−	36.7156i	−0.712555	−	1.23418i
$886$	−4.20069	−	7.27580i	−0.141125	−	0.244435i
$887$	7.57565	−	13.1214i	0.254366	−	0.440574i	−0.710357	−	0.703841i	$-0.751467\pi$
$887$	7.57565	−	13.1214i	0.254366	−	0.440574i	0.964723	+	0.263267i	$0.0848000\pi$
$888$	−16.6177			−0.557654
$889$	−6.53188	−	10.8298i	−0.219072	−	0.363218i
$890$	16.0476			0.537918
$891$	−5.68602	+	9.84847i	−0.190489	+	0.329936i
$892$	−1.81484	−	3.14340i	−0.0607654	−	0.105249i
$893$	6.39006	+	11.0679i	0.213835	+	0.370374i
$894$	8.40833	−	14.5636i	0.281217	−	0.487081i
$895$	49.4126			1.65168
$896$	2.64527	−	0.0506055i	0.0883722	−	0.00169061i
$897$	23.1678			0.773549
$898$	−4.95449	+	8.58142i	−0.165333	+	0.286366i
$899$	4.65549	+	8.06354i	0.155269	+	0.268934i
$900$	0.174926	+	0.302981i	0.00583088	+	0.0100994i
$901$	−5.01462	+	8.68558i	−0.167061	+	0.289358i
$902$	−12.0550			−0.401389
$903$	17.7319	−	32.1160i	0.590082	−	1.06875i
$904$	−1.01001			−0.0335923
$905$	−17.1288	+	29.6680i	−0.569381	+	0.986197i
$906$	−8.23780	−	14.2683i	−0.273683	−	0.474032i
$907$	28.0144	+	48.5224i	0.930204	+	1.61116i	0.782970	+	0.622060i	$0.213704\pi$
$907$	28.0144	+	48.5224i	0.930204	+	1.61116i	0.147235	+	0.989102i	$0.452963\pi$
$908$	−6.34036	+	10.9818i	−0.210412	+	0.364445i
$909$	25.1616			0.834557
$910$	3.51041	−	6.35804i	0.116369	−	0.210767i
$911$	25.0412			0.829653			0.414827	−	0.909900i	$-0.363842\pi$
$911$	25.0412			0.829653			0.414827	+	0.909900i	$0.363842\pi$
$912$	−2.64148	+	4.57519i	−0.0874683	+	0.151500i
$913$	3.24341	+	5.61776i	0.107341	+	0.185921i
$914$	10.7686	+	18.6518i	0.356194	+	0.616946i
$915$	21.5635	−	37.3490i	0.712866	−	1.23472i
$916$	−19.9214			−0.658223
$917$	−28.6878	+	0.548814i	−0.947355	+	0.0181234i
$918$	−2.96459			−0.0978459
$919$	22.0458	−	38.1844i	0.727224	−	1.25959i	−0.230828	−	0.972995i	$-0.574144\pi$
$919$	22.0458	−	38.1844i	0.727224	−	1.25959i	0.958052	−	0.286594i	$-0.0925231\pi$
$920$	8.54642	+	14.8028i	0.281767	+	0.488035i
$921$	17.2675	+	29.9083i	0.568985	+	0.985511i
$922$	11.0226	−	19.0918i	0.363011	−	0.628754i
$923$	5.73241			0.188684
$924$	3.90555	+	6.47534i	0.128483	+	0.213023i
$925$	0.864643			0.0284293
$926$	9.06009	−	15.6925i	0.297733	−	0.515689i
$927$	−8.70136	−	15.0712i	−0.285790	−	0.495003i
$928$	0.500000	+	0.866025i	0.0164133	+	0.0284287i
$929$	−24.6413	+	42.6800i	−0.808456	+	1.40029i	0.105478	+	0.994422i	$0.466363\pi$
$929$	−24.6413	+	42.6800i	−0.808456	+	1.40029i	−0.913933	+	0.405864i	$0.866971\pi$
$930$	−49.4814			−1.62256
$931$	−8.18530	−	13.0021i	−0.268263	−	0.426127i
$932$	−13.6959			−0.448623
$933$	−1.96891	+	3.41026i	−0.0644593	+	0.111647i
$934$	−12.4161	−	21.5053i	−0.406266	−	0.703674i
$935$	−7.81884	−	13.5426i	−0.255703	−	0.442891i
$936$	−1.73658	+	3.00785i	−0.0567620	+	0.0983146i
$937$	−38.6362			−1.26219			−0.631094	−	0.775706i	$-0.717394\pi$
$937$	−38.6362			−1.26219			−0.631094	+	0.775706i	$0.717394\pi$
$938$	−16.5949	−	27.5141i	−0.541844	−	0.898367i
$939$	1.76209			0.0575035
$940$	−6.42798	+	11.1336i	−0.209657	+	0.363137i
$941$	−0.281802	−	0.488096i	−0.00918649	−	0.0159115i	0.861396	−	0.507935i	$-0.169591\pi$
$941$	−0.281802	−	0.488096i	−0.00918649	−	0.0159115i	−0.870582	+	0.492023i	$0.836258\pi$
$942$	−22.0531	−	38.1970i	−0.718527	−	1.24453i
$943$	−39.2971	+	68.0646i	−1.27969	+	2.21649i
$944$	−7.97761			−0.259649
$945$	2.90289	−	0.0555339i	0.0944309	−	0.00180652i
$946$	6.84062			0.222408
$947$	−3.85983	+	6.68543i	−0.125428	+	0.217247i	−0.921900	−	0.387428i	$-0.873364\pi$
$947$	−3.85983	+	6.68543i	−0.125428	+	0.217247i	0.796472	+	0.604675i	$0.206697\pi$
$948$	2.91645	+	5.05144i	0.0947219	+	0.164063i
$949$	−0.0245444	−	0.0425122i	−0.000796746	−	0.00138000i
$950$	0.137440	−	0.238053i	0.00445915	−	0.00772347i
$951$	47.4825			1.53973
$952$	−7.62756	+	13.8150i	−0.247211	+	0.447747i
$953$	−60.2876			−1.95291			−0.976453	−	0.215729i	$-0.930787\pi$
$953$	−60.2876			−1.95291			−0.976453	+	0.215729i	$0.930787\pi$
$954$	−2.34859	+	4.06787i	−0.0760384	+	0.131702i
$955$	8.77781	+	15.2036i	0.284043	+	0.491977i
$956$	−8.34644	−	14.4564i	−0.269943	−	0.467555i
$957$	−1.42908	+	2.47524i	−0.0461955	+	0.0800130i
$958$	12.5423			0.405223
$959$	0.793456	−	1.43710i	0.0256220	−	0.0464065i
$960$	−5.31432			−0.171519
$961$	−27.8471	+	48.2326i	−0.898293	+	1.55589i
$962$	4.29187	+	7.43374i	0.138376	+	0.239674i
$963$	22.7179	+	39.3485i	0.732074	+	1.26799i
$964$	8.40495	−	14.5578i	0.270705	−	0.468875i
$965$	7.46378			0.240268
$966$	49.2921	−	0.942987i	1.58595	−	0.0303401i
$967$	25.9669			0.835040			0.417520	−	0.908668i	$-0.362899\pi$
$967$	25.9669			0.835040			0.417520	+	0.908668i	$0.362899\pi$
$968$	4.79498	−	8.30515i	0.154117	−	0.266938i
$969$	−15.7554	−	27.2891i	−0.506135	−	0.876652i
$970$	3.57593	+	6.19369i	0.114816	+	0.198867i
$971$	14.2517	−	24.6847i	0.457359	−	0.792169i	−0.541461	−	0.840726i	$-0.682129\pi$
$971$	14.2517	−	24.6847i	0.457359	−	0.792169i	0.998820	+	0.0485565i	$0.0154621\pi$
$972$	−21.5601			−0.691540
$973$	14.8414	+	24.6067i	0.475792	+	0.788855i
$974$	−15.2869			−0.489823
$975$	0.187393	−	0.324574i	0.00600137	−	0.0103947i
$976$	−4.05762	−	7.02800i	−0.129881	−	0.224961i
$977$	25.4411	+	44.0652i	0.813932	+	1.40977i	0.910092	+	0.414406i	$0.136011\pi$
$977$	25.4411	+	44.0652i	0.813932	+	1.40977i	−0.0961602	+	0.995366i	$0.530656\pi$
$978$	24.8704	−	43.0767i	0.795266	−	1.37744i
$979$	8.63077			0.275841
$980$	7.21003	−	13.6704i	0.230316	−	0.436684i
$981$	−8.02520			−0.256225
$982$	−14.5225	+	25.1537i	−0.463431	+	0.802687i
$983$	1.14405	+	1.98155i	0.0364895	+	0.0632017i	0.883693	−	0.468066i	$-0.155049\pi$
$983$	1.14405	+	1.98155i	0.0364895	+	0.0632017i	−0.847204	+	0.531268i	$0.821716\pi$
$984$	−12.2178	−	21.1619i	−0.389490	−	0.674616i
$985$	0.977107	−	1.69240i	0.0311332	−	0.0539243i
$986$	−5.96459			−0.189951
$987$	19.1512	+	31.7523i	0.609588	+	1.01069i
$988$	2.72887			0.0868171
$989$	22.2991	−	38.6232i	0.709071	−	1.22815i
$990$	−3.66194	−	6.34267i	−0.116384	−	0.201583i
$991$	14.0617	+	24.3555i	0.446683	+	0.773678i	0.998168	−	0.0605071i	$-0.0192718\pi$
$991$	14.0617	+	24.3555i	0.446683	+	0.773678i	−0.551485	+	0.834185i	$0.685938\pi$
$992$	−4.65549	+	8.06354i	−0.147812	+	0.256018i
$993$	80.3807			2.55080
$994$	12.1964	−	0.233323i	0.386845	−	0.00740057i
$995$	−25.6420			−0.812905
$996$	−6.57442	+	11.3872i	−0.208319	+	0.360818i
$997$	8.94188	+	15.4878i	0.283192	+	0.490503i	0.972169	−	0.234280i	$-0.0752733\pi$
$997$	8.94188	+	15.4878i	0.283192	+	0.490503i	−0.688977	+	0.724783i	$0.741940\pi$
$998$	−8.35320	−	14.4682i	−0.264416	−	0.457982i
$999$	−1.71575	+	2.97177i	−0.0542840	+	0.0940226i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	406.2.e.a.233.2	✓	10
7.2	even	3		2842.2.a.z.1.4		5
7.4	even	3	inner	406.2.e.a.291.2	yes	10
7.5	odd	6		2842.2.a.x.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.a.233.2	✓	10	1.1	even	1	trivial
406.2.e.a.291.2	yes	10	7.4	even	3	inner
2842.2.a.x.1.2		5	7.5	odd	6
2842.2.a.z.1.4		5	7.2	even	3

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:	\( N \)	\(=\)	\( 406 = 2 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	406.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.20348 - 2.08450i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.10394 - 1.91209i) q^{5} +2.40697 q^{6} +(-1.36646 - 2.26557i) q^{7} +1.00000 q^{8} +(-1.39675 + 2.41924i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.20348 - 2.08450i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.10394 - 1.91209i) q^{5} +2.40697 q^{6} +(-1.36646 - 2.26557i) q^{7} +1.00000 q^{8} +(-1.39675 + 2.41924i) q^{9} +(1.10394 + 1.91209i) q^{10} +(0.593725 + 1.02836i) q^{11} +(-1.20348 + 2.08450i) q^{12} +1.24330 q^{13} +(2.64527 - 0.0506055i) q^{14} -5.31432 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.98229 - 5.16548i) q^{17} +(-1.39675 - 2.41924i) q^{18} +(-1.09743 + 1.90081i) q^{19} -2.20789 q^{20} +(-3.07805 + 5.57495i) q^{21} -1.18745 q^{22} +(-3.87086 + 6.70453i) q^{23} +(-1.20348 - 2.08450i) q^{24} +(0.0626190 + 0.108459i) q^{25} +(-0.621650 + 1.07673i) q^{26} -0.497031 q^{27} +(-1.27881 + 2.31617i) q^{28} -1.00000 q^{29} +(2.65716 - 4.60233i) q^{30} +(-4.65549 - 8.06354i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.42908 - 2.47524i) q^{33} +5.96459 q^{34} +(-5.84045 + 0.111731i) q^{35} +2.79350 q^{36} +(3.45200 - 5.97904i) q^{37} +(-1.09743 - 1.90081i) q^{38} +(-1.49629 - 2.59166i) q^{39} +(1.10394 - 1.91209i) q^{40} +10.1520 q^{41} +(-3.28903 - 5.45315i) q^{42} -5.76077 q^{43} +(0.593725 - 1.02836i) q^{44} +(3.08387 + 5.34142i) q^{45} +(-3.87086 - 6.70453i) q^{46} +(2.91137 - 5.04264i) q^{47} +2.40697 q^{48} +(-3.26558 + 6.19161i) q^{49} -0.125238 q^{50} +(-7.17829 + 12.4332i) q^{51} +(-0.621650 - 1.07673i) q^{52} +(-0.840732 - 1.45619i) q^{53} +(0.248516 - 0.430442i) q^{54} +2.62175 q^{55} +(-1.36646 - 2.26557i) q^{56} +5.28297 q^{57} +(0.500000 - 0.866025i) q^{58} +(3.98880 + 6.90881i) q^{59} +(2.65716 + 4.60233i) q^{60} +(-4.05762 + 7.02800i) q^{61} +9.31097 q^{62} +(7.38956 - 0.141367i) q^{63} +1.00000 q^{64} +(1.37253 - 2.37730i) q^{65} +(1.42908 + 2.47524i) q^{66} +(-6.07224 - 10.5174i) q^{67} +(-2.98229 + 5.16548i) q^{68} +18.6341 q^{69} +(2.82346 - 5.11384i) q^{70} +4.61064 q^{71} +(-1.39675 + 2.41924i) q^{72} +(-0.0197414 - 0.0341930i) q^{73} +(3.45200 + 5.97904i) q^{74} +(0.150722 - 0.261058i) q^{75} +2.19486 q^{76} +(1.51852 - 2.75034i) q^{77} +2.99259 q^{78} +(1.21167 - 2.09867i) q^{79} +(1.10394 + 1.91209i) q^{80} +(4.78842 + 8.29379i) q^{81} +(-5.07602 + 8.79192i) q^{82} +5.46282 q^{83} +(6.36708 - 0.121806i) q^{84} -13.1691 q^{85} +(2.88038 - 4.98897i) q^{86} +(1.20348 + 2.08450i) q^{87} +(0.593725 + 1.02836i) q^{88} +(3.63416 - 6.29455i) q^{89} -6.16774 q^{90} +(-1.69892 - 2.81678i) q^{91} +7.74172 q^{92} +(-11.2056 + 19.4087i) q^{93} +(2.91137 + 5.04264i) q^{94} +(2.42300 + 4.19677i) q^{95} +(-1.20348 + 2.08450i) q^{96} +3.23923 q^{97} +(-3.72930 - 5.92388i) q^{98} -3.31715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9} - 7 q^{10} - 3 q^{12} + 20 q^{13} + 3 q^{14} - 20 q^{15} - 5 q^{16} - 8 q^{17} - 8 q^{18} - 2 q^{19} + 14 q^{20} + 19 q^{21} - q^{23} - 3 q^{24} - 12 q^{25} - 10 q^{26} + 30 q^{27} - 10 q^{29} + 10 q^{30} - 11 q^{31} - 5 q^{32} - 9 q^{33} + 16 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 2 q^{38} - 18 q^{39} - 7 q^{40} + 46 q^{41} - 8 q^{42} - 6 q^{43} - 4 q^{45} - q^{46} - 16 q^{47} + 6 q^{48} - 11 q^{49} + 24 q^{50} - 7 q^{51} - 10 q^{52} - 7 q^{53} - 15 q^{54} + 12 q^{55} - 3 q^{56} - 68 q^{57} + 5 q^{58} + 9 q^{59} + 10 q^{60} - 15 q^{61} + 22 q^{62} - 3 q^{63} + 10 q^{64} - 5 q^{65} - 9 q^{66} + 4 q^{67} - 8 q^{68} + 28 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 8 q^{74} + 34 q^{75} + 4 q^{76} + 39 q^{77} + 36 q^{78} + 13 q^{79} - 7 q^{80} - 17 q^{81} - 23 q^{82} + 56 q^{83} - 11 q^{84} - 14 q^{85} + 3 q^{86} + 3 q^{87} - 17 q^{89} + 8 q^{90} + 6 q^{91} + 2 q^{92} - 17 q^{93} - 16 q^{94} + 9 q^{95} - 3 q^{96} + 84 q^{97} - 20 q^{98} - 84 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9 - 7 * q^10 - 3 * q^12 + 20 * q^13 + 3 * q^14 - 20 * q^15 - 5 * q^16 - 8 * q^17 - 8 * q^18 - 2 * q^19 + 14 * q^20 + 19 * q^21 - q^23 - 3 * q^24 - 12 * q^25 - 10 * q^26 + 30 * q^27 - 10 * q^29 + 10 * q^30 - 11 * q^31 - 5 * q^32 - 9 * q^33 + 16 * q^34 + 10 * q^35 + 16 * q^36 + 8 * q^37 - 2 * q^38 - 18 * q^39 - 7 * q^40 + 46 * q^41 - 8 * q^42 - 6 * q^43 - 4 * q^45 - q^46 - 16 * q^47 + 6 * q^48 - 11 * q^49 + 24 * q^50 - 7 * q^51 - 10 * q^52 - 7 * q^53 - 15 * q^54 + 12 * q^55 - 3 * q^56 - 68 * q^57 + 5 * q^58 + 9 * q^59 + 10 * q^60 - 15 * q^61 + 22 * q^62 - 3 * q^63 + 10 * q^64 - 5 * q^65 - 9 * q^66 + 4 * q^67 - 8 * q^68 + 28 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 8 * q^74 + 34 * q^75 + 4 * q^76 + 39 * q^77 + 36 * q^78 + 13 * q^79 - 7 * q^80 - 17 * q^81 - 23 * q^82 + 56 * q^83 - 11 * q^84 - 14 * q^85 + 3 * q^86 + 3 * q^87 - 17 * q^89 + 8 * q^90 + 6 * q^91 + 2 * q^92 - 17 * q^93 - 16 * q^94 + 9 * q^95 - 3 * q^96 + 84 * q^97 - 20 * q^98 - 84 * q^99

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