LMFDB - Embedded newform 403.2.k.e.287.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			287.4
Character	$\chi$	$=$	403.287
Dual form			403.2.k.e.66.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.537701 + 1.65487i) q^{2} +(0.587091 + 1.80688i) q^{3} +(-0.831453 - 0.604086i) q^{4} -2.54418 q^{5} -3.30584 q^{6} +(-1.97022 - 1.43145i) q^{7} +(-1.36868 + 0.994405i) q^{8} +(-0.493085 + 0.358248i) q^{9} +O(q^{10})$	\(q+(-0.537701 + 1.65487i) q^{2} +(0.587091 + 1.80688i) q^{3} +(-0.831453 - 0.604086i) q^{4} -2.54418 q^{5} -3.30584 q^{6} +(-1.97022 - 1.43145i) q^{7} +(-1.36868 + 0.994405i) q^{8} +(-0.493085 + 0.358248i) q^{9} +(1.36801 - 4.21030i) q^{10} +(-1.80237 - 1.30950i) q^{11} +(0.603372 - 1.85699i) q^{12} +(0.309017 + 0.951057i) q^{13} +(3.42826 - 2.49077i) q^{14} +(-1.49366 - 4.59702i) q^{15} +(-1.54485 - 4.75455i) q^{16} +(1.72846 - 1.25580i) q^{17} +(-0.327722 - 1.00862i) q^{18} +(-0.879960 + 2.70824i) q^{19} +(2.11536 + 1.53690i) q^{20} +(1.42976 - 4.40034i) q^{21} +(3.13619 - 2.27858i) q^{22} +(-5.08914 + 3.69748i) q^{23} +(-2.60031 - 1.88924i) q^{24} +1.47285 q^{25} -1.74004 q^{26} +(3.67427 + 2.66952i) q^{27} +(0.773426 + 2.38036i) q^{28} +(-1.41478 + 4.35426i) q^{29} +8.41064 q^{30} +(-5.52266 - 0.707300i) q^{31} +5.31528 q^{32} +(1.30795 - 4.02546i) q^{33} +(1.14880 + 3.53564i) q^{34} +(5.01259 + 3.64186i) q^{35} +0.626389 q^{36} +0.890456 q^{37} +(-4.00864 - 2.91245i) q^{38} +(-1.53702 + 1.11671i) q^{39} +(3.48217 - 2.52995i) q^{40} +(-2.80523 + 8.63361i) q^{41} +(6.51322 + 4.73213i) q^{42} +(2.52927 - 7.78429i) q^{43} +(0.707536 + 2.17757i) q^{44} +(1.25450 - 0.911446i) q^{45} +(-3.38243 - 10.4100i) q^{46} +(2.71949 + 8.36973i) q^{47} +(7.68393 - 5.58270i) q^{48} +(-0.330400 - 1.01687i) q^{49} +(-0.791953 + 2.43738i) q^{50} +(3.28385 + 2.38586i) q^{51} +(0.317587 - 0.977431i) q^{52} +(-5.45635 + 3.96427i) q^{53} +(-6.39338 + 4.64506i) q^{54} +(4.58555 + 3.33160i) q^{55} +4.12004 q^{56} -5.41007 q^{57} +(-6.44502 - 4.68258i) q^{58} +(-4.51278 - 13.8889i) q^{59} +(-1.53509 + 4.72451i) q^{60} +4.16615 q^{61} +(4.14003 - 8.75899i) q^{62} +1.48430 q^{63} +(0.231659 - 0.712974i) q^{64} +(-0.786195 - 2.41966i) q^{65} +(5.95834 + 4.32899i) q^{66} +2.93094 q^{67} -2.19575 q^{68} +(-9.66869 - 7.02471i) q^{69} +(-8.72210 + 6.33697i) q^{70} +(-7.12235 + 5.17469i) q^{71} +(0.318634 - 0.980653i) q^{72} +(2.68892 + 1.95362i) q^{73} +(-0.478800 + 1.47359i) q^{74} +(0.864696 + 2.66126i) q^{75} +(2.36765 - 1.72020i) q^{76} +(1.67658 + 5.16000i) q^{77} +(-1.02156 - 3.14404i) q^{78} +(-2.19970 + 1.59818i) q^{79} +(3.93037 + 12.0964i) q^{80} +(-3.23139 + 9.94519i) q^{81} +(-12.7792 - 9.28460i) q^{82} +(1.69794 - 5.22573i) q^{83} +(-3.84695 + 2.79498i) q^{84} +(-4.39752 + 3.19499i) q^{85} +(11.5220 + 8.37124i) q^{86} -8.69823 q^{87} +3.76904 q^{88} +(2.82938 + 2.05567i) q^{89} +(0.833784 + 2.56612i) q^{90} +(0.752557 - 2.31613i) q^{91} +6.46498 q^{92} +(-1.96429 - 10.3940i) q^{93} -15.3131 q^{94} +(2.23878 - 6.89024i) q^{95} +(3.12055 + 9.60408i) q^{96} +(7.05332 + 5.12454i) q^{97} +1.86044 q^{98} +1.35785 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) $ 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.537701	+	1.65487i	−0.380212	+	1.17017i	0.559682	+	0.828707i	$0.310923\pi$
$2$	−0.537701	+	1.65487i	−0.380212	+	1.17017i	−0.939894	+	0.341465i	$0.889077\pi$
$3$	0.587091	+	1.80688i	0.338957	+	1.04320i	0.964740	+	0.263205i	$0.0847795\pi$
$3$	0.587091	+	1.80688i	0.338957	+	1.04320i	−0.625783	+	0.779997i	$0.715220\pi$
$4$	−0.831453	−	0.604086i	−0.415726	−	0.302043i
$5$	−2.54418			−1.13779			−0.568896	−	0.822410i	$-0.692629\pi$
$5$	−2.54418			−1.13779			−0.568896	+	0.822410i	$0.692629\pi$
$6$	−3.30584			−1.34960
$7$	−1.97022	−	1.43145i	−0.744673	−	0.541036i	0.149498	−	0.988762i	$-0.452234\pi$
$7$	−1.97022	−	1.43145i	−0.744673	−	0.541036i	−0.894171	+	0.447726i	$0.852234\pi$
$8$	−1.36868	+	0.994405i	−0.483902	+	0.351575i
$9$	−0.493085	+	0.358248i	−0.164362	+	0.119416i
$10$	1.36801	−	4.21030i	0.432602	−	1.33141i
$11$	−1.80237	−	1.30950i	−0.543435	−	0.394829i	0.281924	−	0.959437i	$-0.409027\pi$
$11$	−1.80237	−	1.30950i	−0.543435	−	0.394829i	−0.825359	+	0.564608i	$0.809027\pi$
$12$	0.603372	−	1.85699i	0.174178	−	0.536066i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$	3.42826	−	2.49077i	0.916240	−	0.665687i
$15$	−1.49366	−	4.59702i	−0.385662	−	1.18695i
$16$	−1.54485	−	4.75455i	−0.386212	−	1.18864i
$17$	1.72846	−	1.25580i	0.419214	−	0.304577i	−0.358107	−	0.933680i	$-0.616578\pi$
$17$	1.72846	−	1.25580i	0.419214	−	0.304577i	0.777322	+	0.629103i	$0.216578\pi$
$18$	−0.327722	−	1.00862i	−0.0772448	−	0.237735i
$19$	−0.879960	+	2.70824i	−0.201877	+	0.621312i	0.797951	+	0.602723i	$0.205918\pi$
$19$	−0.879960	+	2.70824i	−0.201877	+	0.621312i	−0.999827	+	0.0185894i	$0.994082\pi$
$20$	2.11536	+	1.53690i	0.473010	+	0.343662i
$21$	1.42976	−	4.40034i	0.311998	−	0.960232i
$22$	3.13619	−	2.27858i	0.668639	−	0.485794i
$23$	−5.08914	+	3.69748i	−1.06116	+	0.770978i	−0.974303	−	0.225243i	$-0.927682\pi$
$23$	−5.08914	+	3.69748i	−1.06116	+	0.770978i	−0.0868574	+	0.996221i	$0.527682\pi$
$24$	−2.60031	−	1.88924i	−0.530786	−	0.385639i
$25$	1.47285			0.294570
$26$	−1.74004			−0.341250
$27$	3.67427	+	2.66952i	0.707114	+	0.513749i
$28$	0.773426	+	2.38036i	0.146164	+	0.449846i
$29$	−1.41478	+	4.35426i	−0.262719	+	0.808566i	0.729491	+	0.683990i	$0.239757\pi$
$29$	−1.41478	+	4.35426i	−0.262719	+	0.808566i	−0.992210	+	0.124576i	$0.960243\pi$
$30$	8.41064			1.53557
$31$	−5.52266	−	0.707300i	−0.991898	−	0.127035i
$31$	−5.52266	−	0.707300i	−0.991898	−	0.127035i
$32$	5.31528			0.939618
$33$	1.30795	−	4.02546i	0.227685	−	0.700743i
$34$	1.14880	+	3.53564i	0.197017	+	0.606357i
$35$	5.01259	+	3.64186i	0.847282	+	0.615587i
$36$	0.626389			0.104398
$37$	0.890456			0.146390			0.0731951	−	0.997318i	$-0.476680\pi$
$37$	0.890456			0.146390			0.0731951	+	0.997318i	$0.476680\pi$
$38$	−4.00864	−	2.91245i	−0.650287	−	0.472461i
$39$	−1.53702	+	1.11671i	−0.246121	+	0.178817i
$40$	3.48217	−	2.52995i	0.550580	−	0.400020i
$41$	−2.80523	+	8.63361i	−0.438103	+	1.34834i	0.451770	+	0.892135i	$0.350793\pi$
$41$	−2.80523	+	8.63361i	−0.438103	+	1.34834i	−0.889873	+	0.456209i	$0.849207\pi$
$42$	6.51322	+	4.73213i	1.00501	+	0.730184i
$43$	2.52927	−	7.78429i	0.385710	−	1.18709i	−0.550254	−	0.834997i	$-0.685469\pi$
$43$	2.52927	−	7.78429i	0.385710	−	1.18709i	0.935964	−	0.352096i	$-0.114531\pi$
$44$	0.707536	+	2.17757i	0.106665	+	0.328281i
$45$	1.25450	−	0.911446i	0.187009	−	0.135870i
$46$	−3.38243	−	10.4100i	−0.498711	−	1.53488i
$47$	2.71949	+	8.36973i	0.396679	+	1.22085i	0.927647	+	0.373459i	$0.121828\pi$
$47$	2.71949	+	8.36973i	0.396679	+	1.22085i	−0.530968	+	0.847392i	$0.678172\pi$
$48$	7.68393	−	5.58270i	1.10908	−	0.805794i
$49$	−0.330400	−	1.01687i	−0.0472000	−	0.145267i
$50$	−0.791953	+	2.43738i	−0.111999	+	0.344698i
$51$	3.28385	+	2.38586i	0.459831	+	0.334087i
$52$	0.317587	−	0.977431i	0.0440413	−	0.135545i
$53$	−5.45635	+	3.96427i	−0.749488	+	0.544535i	−0.895668	−	0.444723i	$-0.853302\pi$
$53$	−5.45635	+	3.96427i	−0.749488	+	0.544535i	0.146180	+	0.989258i	$0.453302\pi$
$54$	−6.39338	+	4.64506i	−0.870028	+	0.632112i
$55$	4.58555	+	3.33160i	0.618316	+	0.449233i
$56$	4.12004			0.550564
$57$	−5.41007			−0.716582
$58$	−6.44502	−	4.68258i	−0.846273	−	0.614853i
$59$	−4.51278	−	13.8889i	−0.587514	−	1.80818i	−0.588929	−	0.808184i	$-0.700450\pi$
$59$	−4.51278	−	13.8889i	−0.587514	−	1.80818i	0.00141509	−	0.999999i	$-0.499550\pi$
$60$	−1.53509	+	4.72451i	−0.198179	+	0.609931i
$61$	4.16615			0.533420			0.266710	−	0.963777i	$-0.414063\pi$
$61$	4.16615			0.533420			0.266710	+	0.963777i	$0.414063\pi$
$62$	4.14003	−	8.75899i	0.525785	−	1.11239i
$63$	1.48430			0.187004
$64$	0.231659	−	0.712974i	0.0289574	−	0.0891217i
$65$	−0.786195	−	2.41966i	−0.0975155	−	0.300122i
$66$	5.95834	+	4.32899i	0.733421	+	0.532862i
$67$	2.93094			0.358072			0.179036	−	0.983843i	$-0.442702\pi$
$67$	2.93094			0.358072			0.179036	+	0.983843i	$0.442702\pi$
$68$	−2.19575			−0.266274
$69$	−9.66869	−	7.02471i	−1.16397	−	0.845676i
$70$	−8.72210	+	6.33697i	−1.04249	+	0.757413i
$71$	−7.12235	+	5.17469i	−0.845267	+	0.614123i	−0.923837	−	0.382786i	$-0.874965\pi$
$71$	−7.12235	+	5.17469i	−0.845267	+	0.614123i	0.0785698	+	0.996909i	$0.474965\pi$
$72$	0.318634	−	0.980653i	0.0375513	−	0.115571i
$73$	2.68892	+	1.95362i	0.314714	+	0.228653i	0.733917	−	0.679239i	$-0.237690\pi$
$73$	2.68892	+	1.95362i	0.314714	+	0.228653i	−0.419202	+	0.907893i	$0.637690\pi$
$74$	−0.478800	+	1.47359i	−0.0556593	+	0.171302i
$75$	0.864696	+	2.66126i	0.0998465	+	0.307296i
$76$	2.36765	−	1.72020i	0.271588	−	0.197320i
$77$	1.67658	+	5.16000i	0.191065	+	0.588036i
$78$	−1.02156	−	3.14404i	−0.115669	−	0.355992i
$79$	−2.19970	+	1.59818i	−0.247486	+	0.179809i	−0.704612	−	0.709593i	$-0.748879\pi$
$79$	−2.19970	+	1.59818i	−0.247486	+	0.179809i	0.457126	+	0.889402i	$0.348879\pi$
$80$	3.93037	+	12.0964i	0.439429	+	1.35242i
$81$	−3.23139	+	9.94519i	−0.359043	+	1.10502i
$82$	−12.7792	−	9.28460i	−1.41122	−	1.02531i
$83$	1.69794	−	5.22573i	0.186373	−	0.573598i	−0.813596	−	0.581431i	$-0.802493\pi$
$83$	1.69794	−	5.22573i	0.186373	−	0.573598i	0.999969	+	0.00783251i	$0.00249319\pi$
$84$	−3.84695	+	2.79498i	−0.419737	+	0.304957i
$85$	−4.39752	+	3.19499i	−0.476978	+	0.346545i
$86$	11.5220	+	8.37124i	1.24245	+	0.902694i
$87$	−8.69823			−0.932548
$88$	3.76904			0.401781
$89$	2.82938	+	2.05567i	0.299914	+	0.217900i	0.727557	−	0.686048i	$-0.240656\pi$
$89$	2.82938	+	2.05567i	0.299914	+	0.217900i	−0.427643	+	0.903948i	$0.640656\pi$
$90$	0.833784	+	2.56612i	0.0878885	+	0.270493i
$91$	0.752557	−	2.31613i	0.0788894	−	0.242796i
$92$	6.46498			0.674021
$93$	−1.96429	−	10.3940i	−0.203688	−	1.07781i
$94$	−15.3131			−1.57943
$95$	2.23878	−	6.89024i	0.229693	−	0.706924i
$96$	3.12055	+	9.60408i	0.318490	+	0.980212i
$97$	7.05332	+	5.12454i	0.716156	+	0.520318i	0.885154	−	0.465299i	$-0.154053\pi$
$97$	7.05332	+	5.12454i	0.716156	+	0.520318i	−0.168998	+	0.985616i	$0.554053\pi$
$98$	1.86044			0.187933
$99$	1.35785			0.136469
$100$	−1.22460	−	0.889727i	−0.122460	−	0.0889727i
$101$	−14.2953	+	10.3861i	−1.42243	+	1.03346i	−0.431067	+	0.902320i	$0.641863\pi$
$101$	−14.2953	+	10.3861i	−1.42243	+	1.03346i	−0.991364	+	0.131137i	$0.958137\pi$
$102$	−5.71402	+	4.15148i	−0.565773	+	0.411058i
$103$	−4.55436	+	14.0169i	−0.448755	+	1.38112i	0.429559	+	0.903039i	$0.358669\pi$
$103$	−4.55436	+	14.0169i	−0.448755	+	1.38112i	−0.878313	+	0.478086i	$0.841331\pi$
$104$	−1.36868	−	0.994405i	−0.134210	−	0.0975095i
$105$	−3.63756	+	11.1952i	−0.354989	+	1.09254i
$106$	−3.62648	−	11.1612i	−0.352235	−	1.08407i
$107$	−3.02150	+	2.19525i	−0.292099	+	0.212222i	−0.724177	−	0.689614i	$-0.757780\pi$
$107$	−3.02150	+	2.19525i	−0.292099	+	0.212222i	0.432078	+	0.901836i	$0.357780\pi$
$108$	−1.44237	−	4.43915i	−0.138792	−	0.427158i
$109$	1.73399	+	5.33668i	0.166086	+	0.511161i	0.999115	−	0.0420689i	$-0.0133949\pi$
$109$	1.73399	+	5.33668i	0.166086	+	0.511161i	−0.833028	+	0.553230i	$0.813395\pi$
$110$	−7.97904	+	5.79711i	−0.760771	+	0.552733i
$111$	0.522779	+	1.60895i	0.0496199	+	0.152714i
$112$	−3.76220	+	11.5789i	−0.355495	+	1.09410i
$113$	7.46082	+	5.42060i	0.701855	+	0.509927i	0.880536	−	0.473980i	$-0.157183\pi$
$113$	7.46082	+	5.42060i	0.701855	+	0.509927i	−0.178681	+	0.983907i	$0.557183\pi$
$114$	2.90900	−	8.95299i	0.272453	−	0.838524i
$115$	12.9477	−	9.40705i	1.20738	−	0.877212i
$116$	3.80667	−	2.76571i	0.353441	−	0.256790i
$117$	−0.493085	−	0.358248i	−0.0455858	−	0.0331200i
$118$	25.4109			2.33927
$119$	−5.20307			−0.476965
$120$	6.61566	+	4.80655i	0.603924	+	0.438776i
$121$	−1.86543	−	5.74122i	−0.169585	−	0.521929i
$122$	−2.24014	+	6.89445i	−0.202813	+	0.624194i
$123$	−17.2468			−1.55509
$124$	4.16456	+	3.92424i	0.373988	+	0.352407i
$125$	8.97370			0.802633
$126$	−0.798109	+	2.45633i	−0.0711012	+	0.218827i
$127$	4.76106	+	14.6530i	0.422476	+	1.30025i	0.905391	+	0.424580i	$0.139578\pi$
$127$	4.76106	+	14.6530i	0.422476	+	1.30025i	−0.482915	+	0.875667i	$0.660422\pi$
$128$	9.65563	+	7.01523i	0.853445	+	0.620064i
$129$	15.5502			1.36912
$130$	4.42697			0.388271
$131$	−16.1859	−	11.7598i	−1.41417	−	1.02746i	−0.992700	−	0.120614i	$-0.961514\pi$
$131$	−16.1859	−	11.7598i	−1.41417	−	1.02746i	−0.421471	−	0.906842i	$-0.638486\pi$
$132$	−3.51922	+	2.55686i	−0.306309	+	0.222546i
$133$	5.61041	−	4.07620i	0.486484	−	0.353452i
$134$	−1.57597	+	4.85034i	−0.136143	+	0.419006i
$135$	−9.34801	−	6.79173i	−0.804549	−	0.584539i
$136$	−1.11694	+	3.43759i	−0.0957768	+	0.294771i
$137$	1.46491	+	4.50854i	0.125156	+	0.385191i	0.993929	−	0.110019i	$-0.0350912\pi$
$137$	1.46491	+	4.50854i	0.125156	+	0.385191i	−0.868773	+	0.495210i	$0.835091\pi$
$138$	16.8239	−	12.2233i	1.43214	−	1.04051i
$139$	−3.57666	−	11.0078i	−0.303368	−	0.933672i	−0.980281	−	0.197608i	$-0.936683\pi$
$139$	−3.57666	−	11.0078i	−0.303368	−	0.933672i	0.676913	−	0.736063i	$-0.263317\pi$
$140$	−1.96774	−	6.05607i	−0.166304	−	0.511831i
$141$	−13.5265	+	9.82758i	−1.13914	+	0.827632i
$142$	−4.73376	−	14.5690i	−0.397249	−	1.22261i
$143$	0.688444	−	2.11881i	0.0575706	−	0.177184i
$144$	2.46505	+	1.79096i	0.205421	+	0.149247i
$145$	3.59947	−	11.0780i	0.298919	−	0.919979i
$146$	−4.67883	+	3.39937i	−0.387222	+	0.281334i
$147$	1.64338	−	1.19399i	0.135544	−	0.0984782i
$148$	−0.740372	−	0.537912i	−0.0608582	−	0.0442161i
$149$	8.85164			0.725154			0.362577	−	0.931954i	$-0.381897\pi$
$149$	8.85164			0.725154			0.362577	+	0.931954i	$0.381897\pi$
$150$	−4.86900			−0.397552
$151$	−1.93310	−	1.40448i	−0.157314	−	0.114295i	0.506344	−	0.862332i	$-0.330997\pi$
$151$	−1.93310	−	1.40448i	−0.157314	−	0.114295i	−0.663657	+	0.748037i	$0.730997\pi$
$152$	−1.48870	−	4.58175i	−0.120750	−	0.371629i
$153$	−0.402392	+	1.23844i	−0.0325315	+	0.100122i
$154$	−9.44065			−0.760749
$155$	14.0506	+	1.79950i	1.12857	+	0.144539i
$156$	1.95255			0.156329
$157$	−1.98441	+	6.10739i	−0.158373	+	0.487423i	−0.998487	−	0.0549872i	$-0.982488\pi$
$157$	−1.98441	+	6.10739i	−0.158373	+	0.487423i	0.840114	+	0.542410i	$0.182488\pi$
$158$	−1.46200	−	4.49957i	−0.116310	−	0.357967i
$159$	−10.3663	−	7.53158i	−0.822104	−	0.597293i
$160$	−13.5230			−1.06909
$161$	15.3195			1.20734
$162$	−14.7205	−	10.6951i	−1.15655	−	0.840285i
$163$	−4.41849	+	3.21022i	−0.346083	+	0.251444i	−0.747224	−	0.664572i	$-0.768614\pi$
$163$	−4.41849	+	3.21022i	−0.346083	+	0.251444i	0.401141	+	0.916016i	$0.368614\pi$
$164$	7.54785	−	5.48384i	0.589388	−	0.428216i
$165$	−3.32766	+	10.2415i	−0.259058	+	0.797299i
$166$	7.73494	+	5.61976i	0.600348	+	0.436178i
$167$	5.06251	−	15.5808i	0.391749	−	1.20568i	−0.539716	−	0.841847i	$-0.681468\pi$
$167$	5.06251	−	15.5808i	0.391749	−	1.20568i	0.931465	−	0.363832i	$-0.118532\pi$
$168$	2.41884	+	7.44441i	0.186617	+	0.574349i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	−2.92275	−	8.99530i	−0.224165	−	0.689908i
$171$	−0.536324	−	1.65064i	−0.0410137	−	0.126227i
$172$	−6.80534	+	4.94437i	−0.518903	+	0.377005i
$173$	0.0543643	+	0.167316i	0.00413324	+	0.0127208i	0.953102	−	0.302650i	$-0.0978712\pi$
$173$	0.0543643	+	0.167316i	0.00413324	+	0.0127208i	−0.948969	+	0.315370i	$0.897871\pi$
$174$	4.67705	−	14.3945i	0.354566	−	1.09124i
$175$	−2.90183	−	2.10831i	−0.219358	−	0.159373i
$176$	−3.44169	+	10.5924i	−0.259427	+	0.798435i
$177$	22.4462	−	16.3081i	1.68716	−	1.22579i
$178$	−4.92324	+	3.57694i	−0.369012	+	0.268103i
$179$	3.11095	+	2.26024i	0.232523	+	0.168938i	0.697946	−	0.716151i	$-0.254098\pi$
$179$	3.11095	+	2.26024i	0.232523	+	0.168938i	−0.465422	+	0.885089i	$0.654098\pi$
$180$	−1.59365			−0.118783
$181$	10.4515			0.776852			0.388426	−	0.921480i	$-0.373019\pi$
$181$	10.4515			0.776852			0.388426	+	0.921480i	$0.373019\pi$
$182$	3.42826	+	2.49077i	0.254119	+	0.184628i
$183$	2.44590	+	7.52772i	0.180806	+	0.556465i
$184$	3.28862	−	10.1213i	0.242441	−	0.746155i
$185$	−2.26548			−0.166561
$186$	18.2570	+	2.33822i	1.33867	+	0.171446i
$187$	−4.75981			−0.348071
$188$	2.79491	−	8.60184i	0.203840	−	0.627354i
$189$	−3.41785	−	10.5191i	−0.248612	−	0.765149i
$190$	10.1987	+	7.40978i	0.739891	+	0.537562i
$191$	20.8475			1.50847			0.754237	−	0.656602i	$-0.228007\pi$
$191$	20.8475			1.50847			0.754237	+	0.656602i	$0.228007\pi$
$192$	1.42426			0.102787
$193$	−1.82160	−	1.32347i	−0.131121	−	0.0952653i	0.520291	−	0.853989i	$-0.325823\pi$
$193$	−1.82160	−	1.32347i	−0.131121	−	0.0952653i	−0.651413	+	0.758724i	$0.725823\pi$
$194$	−12.2730	+	8.91689i	−0.881153	+	0.640195i
$195$	3.91046	−	2.84112i	0.280034	−	0.203457i
$196$	−0.339563	+	1.04507i	−0.0242545	+	0.0746476i
$197$	6.85950	+	4.98371i	0.488719	+	0.355075i	0.804691	−	0.593693i	$-0.202331\pi$
$197$	6.85950	+	4.98371i	0.488719	+	0.355075i	−0.315973	+	0.948768i	$0.602331\pi$
$198$	−0.730116	+	2.24707i	−0.0518871	+	0.159692i
$199$	−0.476514	−	1.46656i	−0.0337792	−	0.103962i	0.932745	−	0.360536i	$-0.117406\pi$
$199$	−0.476514	−	1.46656i	−0.0337792	−	0.103962i	−0.966525	+	0.256574i	$0.917406\pi$
$200$	−2.01586	+	1.46461i	−0.142543	+	0.103564i
$201$	1.72073	+	5.29586i	0.121371	+	0.373541i
$202$	−9.50113	−	29.2415i	−0.668497	−	2.05742i
$203$	9.02033	−	6.55365i	0.633103	−	0.459976i
$204$	−1.28910	−	3.96745i	−0.0902553	−	0.277777i
$205$	7.13701	−	21.9654i	0.498470	−	1.53413i
$206$	−20.7473	−	15.0738i	−1.44553	−	1.05024i
$207$	1.18477	−	3.64635i	0.0823472	−	0.253439i
$208$	4.04446	−	2.93847i	0.280433	−	0.203747i
$209$	5.13245	−	3.72894i	0.355019	−	0.257936i
$210$	−16.5708	−	12.0394i	−1.14349	−	0.830797i
$211$	−14.2248			−0.979273			−0.489637	−	0.871927i	$-0.662871\pi$
$211$	−14.2248			−0.979273			−0.489637	+	0.871927i	$0.662871\pi$
$212$	6.93146			0.476055
$213$	−13.5315	−	9.83121i	−0.927163	−	0.673623i
$214$	−2.00819	−	6.18058i	−0.137277	−	0.422496i
$215$	−6.43491	+	19.8046i	−0.438857	+	1.35066i
$216$	−7.68349			−0.522795
$217$	9.86838	+	9.29893i	0.669909	+	0.631252i
$218$	−9.76391			−0.661295
$219$	−1.95131	+	6.00551i	−0.131857	+	0.405814i
$220$	−1.80010	−	5.54013i	−0.121363	−	0.373516i
$221$	1.72846	+	1.25580i	0.116269	+	0.0844744i
$222$	−2.94370			−0.197568
$223$	24.8972			1.66724			0.833619	−	0.552339i	$-0.186265\pi$
$223$	24.8972			1.66724			0.833619	+	0.552339i	$0.186265\pi$
$224$	−10.4723	−	7.60855i	−0.699708	−	0.508368i
$225$	−0.726240	+	0.527645i	−0.0484160	+	0.0351763i
$226$	−12.9821	+	9.43205i	−0.863557	+	0.627411i
$227$	−0.0133422	+	0.0410632i	−0.000885556	+	0.00272546i	−0.951498	−	0.307654i	$-0.900456\pi$
$227$	−0.0133422	+	0.0410632i	−0.000885556	+	0.00272546i	0.950613	+	0.310379i	$0.100456\pi$
$228$	4.49822	+	3.26815i	0.297902	+	0.216438i
$229$	3.74430	−	11.5238i	0.247430	−	0.761511i	−0.747797	−	0.663927i	$-0.768888\pi$
$229$	3.74430	−	11.5238i	0.247430	−	0.761511i	0.995227	−	0.0975841i	$-0.0311115\pi$
$230$	8.60550	+	26.4850i	0.567430	+	1.74637i
$231$	−8.33918	+	6.05877i	−0.548678	+	0.398638i
$232$	−2.39351	−	7.36646i	−0.157142	−	0.483632i
$233$	−0.903687	−	2.78126i	−0.0592025	−	0.182207i	0.917082	−	0.398699i	$-0.130538\pi$
$233$	−0.903687	−	2.78126i	−0.0592025	−	0.182207i	−0.976284	+	0.216493i	$0.930538\pi$
$234$	0.857987	−	0.623364i	0.0560884	−	0.0407506i
$235$	−6.91887	−	21.2941i	−0.451338	−	1.38907i
$236$	−4.63793	+	14.2741i	−0.301904	+	0.929164i
$237$	−4.17914	−	3.03632i	−0.271464	−	0.197230i
$238$	2.79770	−	8.61043i	0.181348	−	0.558131i
$239$	−11.9428	+	8.67693i	−0.772513	+	0.561264i	−0.902723	−	0.430223i	$-0.858435\pi$
$239$	−11.9428	+	8.67693i	−0.772513	+	0.561264i	0.130210	+	0.991486i	$0.458435\pi$
$240$	−19.5493	+	14.2034i	−1.26190	+	0.916826i
$241$	−9.88166	−	7.17945i	−0.636534	−	0.462469i	0.222124	−	0.975018i	$-0.428701\pi$
$241$	−9.88166	−	7.17945i	−0.636534	−	0.462469i	−0.858658	+	0.512549i	$0.828701\pi$
$242$	10.5040			0.675225
$243$	−6.24191			−0.400419
$244$	−3.46395	−	2.51671i	−0.221757	−	0.161116i
$245$	0.840597	+	2.58709i	0.0537038	+	0.165283i
$246$	9.27363	−	28.5413i	0.591265	−	1.81973i
$247$	−2.84761			−0.181189
$248$	8.26210	−	4.52369i	0.524644	−	0.287255i
$249$	10.4391			0.661551
$250$	−4.82517	+	14.8504i	−0.305171	+	0.939219i
$251$	8.39754	+	25.8450i	0.530048	+	1.63132i	0.754112	+	0.656746i	$0.228067\pi$
$251$	8.39754	+	25.8450i	0.530048	+	1.63132i	−0.224064	+	0.974574i	$0.571933\pi$
$252$	−1.23412	−	0.896643i	−0.0777425	−	0.0564832i
$253$	14.0144			0.881076
$254$	−26.8090			−1.68214
$255$	−8.35470	−	6.07005i	−0.523192	−	0.380121i
$256$	−15.5882	+	11.3255i	−0.974261	+	0.707842i
$257$	17.9886	−	13.0695i	1.12210	−	0.815253i	0.137574	−	0.990492i	$-0.456070\pi$
$257$	17.9886	−	13.0695i	1.12210	−	0.815253i	0.984526	+	0.175238i	$0.0560696\pi$
$258$	−8.36135	+	25.7336i	−0.520555	+	1.60210i
$259$	−1.75439	−	1.27464i	−0.109013	−	0.0792024i
$260$	−0.807997	+	2.48676i	−0.0501099	+	0.154222i
$261$	−0.862293	−	2.65386i	−0.0533746	−	0.164270i
$262$	28.1641	−	20.4624i	1.73999	−	1.26417i
$263$	0.514459	+	1.58334i	0.0317229	+	0.0976330i	0.965664	−	0.259793i	$-0.0836544\pi$
$263$	0.514459	+	1.58334i	0.0317229	+	0.0976330i	−0.933941	+	0.357426i	$0.883654\pi$
$264$	2.21277	+	6.81021i	0.136187	+	0.419139i
$265$	13.8819	−	10.0858i	0.852761	−	0.619567i
$266$	3.72888	+	11.4763i	0.228632	+	0.703658i
$267$	−2.05324	+	6.31922i	−0.125656	+	0.386730i
$268$	−2.43694	−	1.77054i	−0.148860	−	0.108153i
$269$	5.92728	−	18.2423i	0.361393	−	1.11225i	−0.590816	−	0.806806i	$-0.701194\pi$
$269$	5.92728	−	18.2423i	0.361393	−	1.11225i	0.952209	−	0.305447i	$-0.0988058\pi$
$270$	16.2659	−	11.8179i	0.989911	−	0.719212i
$271$	−9.82937	+	7.14146i	−0.597092	+	0.433813i	−0.844845	−	0.535010i	$-0.820308\pi$
$271$	−9.82937	+	7.14146i	−0.597092	+	0.433813i	0.247754	+	0.968823i	$0.420308\pi$
$272$	−8.64099	−	6.27805i	−0.523937	−	0.380663i
$273$	4.62679			0.280026
$274$	−8.24876			−0.498326
$275$	−2.65462	−	1.92869i	−0.160080	−	0.116305i
$276$	3.79553	+	11.6814i	0.228464	+	0.703140i
$277$	−2.89704	+	8.91616i	−0.174066	+	0.535720i	−0.999590	−	0.0286474i	$-0.990880\pi$
$277$	−2.89704	+	8.91616i	−0.174066	+	0.535720i	0.825523	+	0.564368i	$0.190880\pi$
$278$	20.1397			1.20790
$279$	2.97653	−	1.62972i	0.178200	−	0.0975687i
$280$	−10.4821			−0.626427
$281$	−6.08614	+	18.7312i	−0.363069	+	1.11741i	0.588113	+	0.808779i	$0.299871\pi$
$281$	−6.08614	+	18.7312i	−0.363069	+	1.11741i	−0.951182	+	0.308632i	$0.900129\pi$
$282$	−8.99019	−	27.6690i	−0.535358	−	1.64766i
$283$	7.03107	+	5.10837i	0.417954	+	0.303661i	0.776814	−	0.629730i	$-0.216835\pi$
$283$	7.03107	+	5.10837i	0.417954	+	0.303661i	−0.358860	+	0.933391i	$0.616835\pi$
$284$	9.04785			0.536891
$285$	13.7642			0.815321
$286$	3.13619	+	2.27858i	0.185447	+	0.134735i
$287$	17.8855	−	12.9946i	1.05575	−	0.767044i
$288$	−2.62089	+	1.90419i	−0.154437	+	0.112205i
$289$	−3.84274	+	11.8267i	−0.226044	+	0.695691i
$290$	16.3973	+	11.9133i	0.962882	+	0.699575i
$291$	−5.11848	+	15.7531i	−0.300051	+	0.923461i
$292$	−1.05556	−	3.24868i	−0.0617720	−	0.190115i
$293$	19.1755	−	13.9318i	1.12025	−	0.813906i	0.135999	−	0.990709i	$-0.456576\pi$
$293$	19.1755	−	13.9318i	1.12025	−	0.813906i	0.984246	+	0.176803i	$0.0565755\pi$
$294$	1.09225	+	3.36159i	0.0637012	+	0.196052i
$295$	11.4813	+	35.3359i	0.668469	+	2.05734i
$296$	−1.21875	+	0.885474i	−0.0708385	+	0.0514672i
$297$	−3.12667	−	9.62291i	−0.181428	−	0.558378i
$298$	−4.75954	+	14.6483i	−0.275713	+	0.848556i
$299$	−5.08914	−	3.69748i	−0.294313	−	0.213831i
$300$	0.888676	−	2.73506i	0.0513077	−	0.157909i
$301$	−16.1260	+	11.7162i	−0.929488	+	0.675313i
$302$	3.36367	−	2.44385i	0.193558	−	0.140628i
$303$	−27.1591	−	19.7322i	−1.56025	−	1.13359i
$304$	14.2359			0.816482
$305$	−10.5994			−0.606921
$306$	−1.83309	−	1.33182i	−0.104791	−	0.0761349i
$307$	4.58528	+	14.1120i	0.261696	+	0.805417i	0.992436	+	0.122762i	$0.0391750\pi$
$307$	4.58528	+	14.1120i	0.261696	+	0.805417i	−0.730740	+	0.682656i	$0.760825\pi$
$308$	1.72308	−	5.30309i	0.0981816	−	0.302172i
$309$	−28.0006			−1.59290
$310$	−10.5330	+	22.2844i	−0.598233	+	1.26567i
$311$	13.3070			0.754572			0.377286	−	0.926097i	$-0.376857\pi$
$311$	13.3070			0.754572			0.377286	+	0.926097i	$0.376857\pi$
$312$	0.993230	−	3.05685i	0.0562306	−	0.173060i
$313$	0.549117	+	1.69001i	0.0310379	+	0.0955248i	0.965375	−	0.260865i	$-0.0840076\pi$
$313$	0.549117	+	1.69001i	0.0310379	+	0.0955248i	−0.934337	+	0.356389i	$0.884008\pi$
$314$	−9.03995	−	6.56791i	−0.510154	−	0.370648i
$315$	−3.77632			−0.212772
$316$	2.79438			0.157196
$317$	−17.8918	−	12.9992i	−1.00491	−	0.730107i	−0.0417712	−	0.999127i	$-0.513300\pi$
$317$	−17.8918	−	12.9992i	−1.00491	−	0.730107i	−0.963134	+	0.269021i	$0.913300\pi$
$318$	18.0378	−	13.1052i	1.01151	−	0.734905i
$319$	8.25186	−	5.99533i	0.462016	−	0.335674i
$320$	−0.589383	+	1.81393i	−0.0329475	+	0.101402i
$321$	−5.74043	−	4.17067i	−0.320400	−	0.232784i
$322$	−8.23730	+	25.3518i	−0.459047	+	1.41280i
$323$	1.88003	+	5.78615i	0.104608	+	0.321950i
$324$	8.69449	−	6.31692i	0.483027	−	0.350940i
$325$	0.455135	+	1.40076i	0.0252464	+	0.0777003i
$326$	−2.93669	−	9.03819i	−0.162648	−	0.500579i
$327$	−8.62473	+	6.26623i	−0.476949	+	0.346523i
$328$	−4.74584	−	14.6062i	−0.262045	−	0.806492i
$329$	6.62284	−	20.3830i	0.365129	−	1.12375i
$330$	−15.1591	−	11.0137i	−0.834481	−	0.606286i
$331$	−4.89281	+	15.0585i	−0.268933	+	0.827692i	0.721828	+	0.692073i	$0.243302\pi$
$331$	−4.89281	+	15.0585i	−0.268933	+	0.827692i	−0.990761	+	0.135619i	$0.956698\pi$
$332$	−4.56854	+	3.31924i	−0.250731	+	0.182167i
$333$	−0.439071	+	0.319004i	−0.0240609	+	0.0174813i
$334$	23.0622	+	16.7556i	1.26191	+	0.916828i
$335$	−7.45685			−0.407411
$336$	−23.1304			−1.26187
$337$	4.79811	+	3.48603i	0.261370	+	0.189896i	0.710751	−	0.703444i	$-0.248355\pi$
$337$	4.79811	+	3.48603i	0.261370	+	0.189896i	−0.449381	+	0.893340i	$0.648355\pi$
$338$	−0.537701	−	1.65487i	−0.0292471	−	0.0900133i
$339$	−5.41419	+	16.6632i	−0.294059	+	0.905019i
$340$	5.58638			0.302964
$341$	9.02766	+	8.50673i	0.488875	+	0.460665i
$342$	3.01998			0.163302
$343$	−6.07253	+	18.6893i	−0.327886	+	1.00913i
$344$	4.27897	+	13.1693i	0.230707	+	0.710043i
$345$	24.5989	+	17.8721i	1.32436	+	0.962203i
$346$	−0.306119			−0.0164571
$347$	−36.6068			−1.96515			−0.982577	−	0.185857i	$-0.940494\pi$
$347$	−36.6068			−1.96515			−0.982577	+	0.185857i	$0.940494\pi$
$348$	7.23216	+	5.25447i	0.387685	+	0.281669i
$349$	19.2255	−	13.9681i	1.02911	−	0.747696i	0.0609836	−	0.998139i	$-0.480576\pi$
$349$	19.2255	−	13.9681i	1.02911	−	0.747696i	0.968131	+	0.250443i	$0.0805763\pi$
$350$	5.04930	−	3.66853i	0.269897	−	0.196091i
$351$	−1.40345	+	4.31937i	−0.0749105	+	0.230551i
$352$	−9.58011	−	6.96036i	−0.510622	−	0.370988i
$353$	−0.297859	+	0.916717i	−0.0158535	+	0.0487919i	−0.958670	−	0.284519i	$-0.908166\pi$
$353$	−0.297859	+	0.916717i	−0.0158535	+	0.0487919i	0.942817	+	0.333311i	$0.108166\pi$
$354$	14.9185	+	45.9145i	0.792911	+	2.44033i
$355$	18.1205	−	13.1653i	0.961738	−	0.698744i
$356$	−1.11070	−	3.41838i	−0.0588670	−	0.181174i
$357$	−3.05467	−	9.40132i	−0.161670	−	0.497570i
$358$	−5.41317	+	3.93290i	−0.286095	+	0.207860i
$359$	−8.16786	−	25.1381i	−0.431083	−	1.32674i	−0.897048	−	0.441934i	$-0.854293\pi$
$359$	−8.16786	−	25.1381i	−0.431083	−	1.32674i	0.465965	−	0.884803i	$-0.345707\pi$
$360$	−0.810661	+	2.49496i	−0.0427256	+	0.131496i
$361$	8.81110	+	6.40164i	0.463742	+	0.336928i
$362$	−5.61977	+	17.2959i	−0.295369	+	0.909051i
$363$	9.27851	−	6.74123i	0.486995	−	0.353823i
$364$	−2.02486	+	1.47114i	−0.106131	+	0.0771089i
$365$	−6.84110	−	4.97035i	−0.358080	−	0.260160i
$366$	−13.7726			−0.719905
$367$	−27.9201			−1.45742			−0.728708	−	0.684825i	$-0.759879\pi$
$367$	−27.9201			−1.45742			−0.728708	+	0.684825i	$0.759879\pi$
$368$	25.4418	+	18.4846i	1.32625	+	0.963574i
$369$	−1.70975	−	5.26207i	−0.0890061	−	0.273933i
$370$	1.21815	−	3.74909i	0.0633287	−	0.194906i
$371$	16.4249			0.852736
$372$	−4.64566	+	9.82874i	−0.240866	+	0.509596i
$373$	−28.2962			−1.46512			−0.732561	−	0.680702i	$-0.761675\pi$
$373$	−28.2962			−1.46512			−0.732561	+	0.680702i	$0.761675\pi$
$374$	2.55935	−	7.87688i	0.132341	−	0.407304i
$375$	5.26838	+	16.2144i	0.272058	+	0.837308i
$376$	−12.0450	−	8.75122i	−0.621175	−	0.451310i
$377$	−4.57834			−0.235796
$378$	19.2455			0.989882
$379$	−3.71593	−	2.69978i	−0.190875	−	0.138679i	0.488244	−	0.872707i	$-0.337638\pi$
$379$	−3.71593	−	2.69978i	−0.190875	−	0.138679i	−0.679118	+	0.734029i	$0.737638\pi$
$380$	−6.02373	+	4.37650i	−0.309011	+	0.224510i
$381$	−23.6811	+	17.2053i	−1.21322	+	0.881455i
$382$	−11.2097	+	34.5001i	−0.573541	+	1.76518i
$383$	−30.2006	−	21.9420i	−1.54318	−	1.12119i	−0.948302	−	0.317371i	$-0.897200\pi$
$383$	−30.2006	−	21.9420i	−1.54318	−	1.12119i	−0.594879	−	0.803816i	$-0.702800\pi$
$384$	−7.00693	+	21.5651i	−0.357571	+	1.10049i
$385$	−4.26553	−	13.1280i	−0.217392	−	0.669063i
$386$	3.16965	−	2.30288i	0.161331	−	0.117214i
$387$	1.54156	+	4.74442i	0.0783617	+	0.241173i
$388$	−2.76884	−	8.52162i	−0.140567	−	0.432620i
$389$	−2.53546	+	1.84212i	−0.128553	+	0.0933992i	−0.650204	−	0.759760i	$-0.725316\pi$
$389$	−2.53546	+	1.84212i	−0.128553	+	0.0933992i	0.521651	+	0.853159i	$0.325316\pi$
$390$	2.59903	+	7.99900i	0.131607	+	0.405045i
$391$	−4.15310	+	12.7819i	−0.210031	+	0.646410i
$392$	1.46339	+	1.06321i	0.0739123	+	0.0537005i
$393$	11.7459	−	36.1501i	0.592501	−	1.82353i
$394$	−11.9358	+	8.67185i	−0.601316	+	0.436882i
$395$	5.59644	−	4.06605i	0.281587	−	0.204585i
$396$	−1.12899	−	0.820256i	−0.0567337	−	0.0412194i
$397$	26.5802			1.33402			0.667011	−	0.745048i	$-0.267574\pi$
$397$	26.5802			1.33402			0.667011	+	0.745048i	$0.267574\pi$
$398$	2.68320			0.134496
$399$	10.6590	+	7.74424i	0.533619	+	0.387697i
$400$	−2.27533	−	7.00274i	−0.113766	−	0.350137i
$401$	5.72283	−	17.6131i	0.285785	−	0.879555i	−0.700378	−	0.713772i	$-0.746985\pi$
$401$	5.72283	−	17.6131i	0.285785	−	0.879555i	0.986162	−	0.165782i	$-0.0530149\pi$
$402$	−9.68922			−0.483255
$403$	−1.03391	−	5.47093i	−0.0515028	−	0.272526i
$404$	18.1599			0.903490
$405$	8.22123	−	25.3023i	0.408516	−	1.25728i
$406$	5.99523	+	18.4514i	0.297538	+	0.915729i
$407$	−1.60493	−	1.16605i	−0.0795535	−	0.0577990i
$408$	−6.86705			−0.339970
$409$	6.14910			0.304053			0.152027	−	0.988376i	$-0.451420\pi$
$409$	6.14910			0.304053			0.152027	+	0.988376i	$0.451420\pi$
$410$	32.5125	+	23.6217i	1.60568	+	1.16659i
$411$	−7.28636	+	5.29385i	−0.359409	+	0.261126i
$412$	12.2541	−	8.90315i	0.603718	−	0.438627i
$413$	−10.9901	+	33.8240i	−0.540787	+	1.66437i
$414$	5.39719	+	3.92129i	0.265258	+	0.192721i
$415$	−4.31987	+	13.2952i	−0.212054	+	0.652635i
$416$	1.64251	+	5.05514i	0.0805308	+	0.247848i
$417$	17.7900	−	12.9252i	0.871179	−	0.632949i
$418$	3.41121	+	10.4986i	0.166847	+	0.513504i
$419$	−10.5823	−	32.5688i	−0.516977	−	1.59109i	−0.779656	−	0.626208i	$-0.784606\pi$
$419$	−10.5823	−	32.5688i	−0.516977	−	1.59109i	0.262680	−	0.964883i	$-0.415394\pi$
$420$	9.78734	−	7.11092i	0.477573	−	0.346977i
$421$	0.541696	+	1.66717i	0.0264006	+	0.0812528i	0.963389	−	0.268109i	$-0.0863986\pi$
$421$	0.541696	+	1.66717i	0.0264006	+	0.0812528i	−0.936988	+	0.349361i	$0.886399\pi$
$422$	7.64867	−	23.5402i	0.372332	−	1.14592i
$423$	−4.33938	−	3.15274i	−0.210988	−	0.153292i
$424$	3.52592	−	10.8517i	0.171234	−	0.527003i
$425$	2.54577	−	1.84961i	0.123488	−	0.0897192i
$426$	23.5453	−	17.1067i	1.14077	−	0.828821i
$427$	−8.20822	−	5.96362i	−0.397223	−	0.288600i
$428$	3.83835			0.185534
$429$	4.23262			0.204353
$430$	−29.3141	−	21.2979i	−1.41365	−	1.02708i
$431$	0.800215	+	2.46281i	0.0385450	+	0.118629i	0.968478	−	0.249101i	$-0.0801350\pi$
$431$	0.800215	+	2.46281i	0.0385450	+	0.118629i	−0.929933	+	0.367730i	$0.880135\pi$
$432$	7.01616	−	21.5935i	0.337565	−	1.03892i
$433$	28.0735			1.34913			0.674563	−	0.738217i	$-0.264332\pi$
$433$	28.0735			1.34913			0.674563	+	0.738217i	$0.264332\pi$
$434$	−20.6948	+	11.3309i	−0.993382	+	0.543900i
$435$	22.1299			1.06105
$436$	1.78208	−	5.48468i	0.0853462	−	0.262668i
$437$	−5.53541	−	17.0362i	−0.264795	−	0.814954i
$438$	−8.88914	−	6.45834i	−0.424739	−	0.308591i
$439$	−26.6591			−1.27237			−0.636184	−	0.771538i	$-0.719488\pi$
$439$	−26.6591			−1.27237			−0.636184	+	0.771538i	$0.719488\pi$
$440$	−9.58912			−0.457143
$441$	0.527205	+	0.383037i	0.0251050	+	0.0182399i
$442$	−3.00759	+	2.18514i	−0.143057	+	0.103937i
$443$	27.9114	−	20.2788i	1.32611	−	0.963477i	0.326278	−	0.945274i	$-0.394206\pi$
$443$	27.9114	−	20.2788i	1.32611	−	0.963477i	0.999834	−	0.0182027i	$-0.00579441\pi$
$444$	0.537276	−	1.65357i	0.0254980	−	0.0784748i
$445$	−7.19846	−	5.22999i	−0.341240	−	0.247925i
$446$	−13.3872	+	41.2017i	−0.633905	+	1.95096i
$447$	5.19671	+	15.9938i	0.245796	+	0.756483i
$448$	−1.47700	+	1.07311i	−0.0697819	+	0.0506995i
$449$	11.8100	+	36.3476i	0.557350	+	1.71535i	0.689655	+	0.724138i	$0.257762\pi$
$449$	11.8100	+	36.3476i	0.557350	+	1.71535i	−0.132305	+	0.991209i	$0.542238\pi$
$450$	−0.482685	−	1.48555i	−0.0227540	−	0.0700296i
$451$	16.3618	−	11.8875i	0.770445	−	0.559761i
$452$	−2.92881	−	9.01394i	−0.137760	−	0.423980i
$453$	1.40282	−	4.31744i	0.0659103	−	0.202851i
$454$	−0.0607803	−	0.0441595i	−0.00285256	−	0.00207251i
$455$	−1.91464	+	5.89265i	−0.0897597	+	0.276252i
$456$	7.40467	−	5.37981i	0.346755	−	0.251932i
$457$	−25.1187	+	18.2498i	−1.17500	+	0.853689i	−0.991599	−	0.129348i	$-0.958711\pi$
$457$	−25.1187	+	18.2498i	−1.17500	+	0.853689i	−0.183404	+	0.983038i	$0.558711\pi$
$458$	17.0571	+	12.3927i	0.797024	+	0.579072i
$459$	9.70324			0.452908
$460$	−16.4481			−0.766895
$461$	−2.39261	−	1.73833i	−0.111435	−	0.0809622i	0.530672	−	0.847577i	$-0.321940\pi$
$461$	−2.39261	−	1.73833i	−0.111435	−	0.0809622i	−0.642107	+	0.766615i	$0.721940\pi$
$462$	−5.54252	−	17.0581i	−0.257861	−	0.793615i
$463$	−3.75812	+	11.5663i	−0.174655	+	0.537532i	−0.999618	−	0.0276552i	$-0.991196\pi$
$463$	−3.75812	+	11.5663i	−0.174655	+	0.537532i	0.824963	+	0.565187i	$0.191196\pi$
$464$	22.8882			1.06256
$465$	4.99752	+	26.4443i	0.231754	+	1.22632i
$466$	5.08856			0.235723
$467$	−1.45816	+	4.48776i	−0.0674756	+	0.207669i	−0.979109	−	0.203335i	$-0.934822\pi$
$467$	−1.45816	+	4.48776i	−0.0674756	+	0.207669i	0.911633	+	0.411004i	$0.134822\pi$
$468$	0.193565	+	0.595732i	0.00894754	+	0.0275377i
$469$	−5.77460	−	4.19549i	−0.266646	−	0.193730i
$470$	38.9594			1.79706
$471$	−12.2004			−0.562163
$472$	19.9878	+	14.5220i	0.920012	+	0.668428i
$473$	−14.7522	+	10.7181i	−0.678307	+	0.492819i
$474$	7.27186	−	5.28331i	0.334007	−	0.242671i
$475$	−1.29605	+	3.98883i	−0.0594668	+	0.183020i
$476$	4.32611	+	3.14310i	0.198287	+	0.144064i
$477$	1.27026	−	3.90945i	0.0581611	−	0.179001i
$478$	−7.93758	−	24.4294i	−0.363057	−	1.11737i
$479$	−18.2518	+	13.2607i	−0.833948	+	0.605899i	−0.920673	−	0.390334i	$-0.872360\pi$
$479$	−18.2518	+	13.2607i	−0.833948	+	0.605899i	0.0867255	+	0.996232i	$0.472360\pi$
$480$	−7.93925	−	24.4345i	−0.362375	−	1.11528i
$481$	0.275166	+	0.846874i	0.0125465	+	0.0386141i
$482$	17.1945	−	12.4925i	0.783187	−	0.569018i
$483$	8.99392	+	27.6804i	0.409238	+	1.25950i
$484$	−1.91717	+	5.90043i	−0.0871440	+	0.268202i
$485$	−17.9449	−	13.0377i	−0.814836	−	0.592013i
$486$	3.35628	−	10.3296i	0.152244	−	0.468559i
$487$	−3.47003	+	2.52113i	−0.157242	+	0.114243i	−0.663624	−	0.748066i	$-0.730983\pi$
$487$	−3.47003	+	2.52113i	−0.157242	+	0.114243i	0.506382	+	0.862309i	$0.330983\pi$
$488$	−5.70213	+	4.14284i	−0.258123	+	0.187537i
$489$	−8.39454	−	6.09899i	−0.379614	−	0.275806i
$490$	−4.73330			−0.213829
$491$	19.5749			0.883401			0.441700	−	0.897163i	$-0.354375\pi$
$491$	19.5749			0.883401			0.441700	+	0.897163i	$0.354375\pi$
$492$	14.3399	+	10.4186i	0.646493	+	0.469705i
$493$	3.02269	+	9.30287i	0.136135	+	0.418980i
$494$	1.53116	−	4.71244i	0.0688903	−	0.212022i
$495$	−3.45461			−0.155273
$496$	5.16877	+	27.3504i	0.232084	+	1.22807i
$497$	21.4399			0.961710
$498$	−5.61312	+	17.2754i	−0.251530	+	0.774129i
$499$	2.21236	+	6.80893i	0.0990386	+	0.304810i	0.988285	−	0.152619i	$-0.0487706\pi$
$499$	2.21236	+	6.80893i	0.0990386	+	0.304810i	−0.889247	+	0.457428i	$0.848771\pi$
$500$	−7.46121	−	5.42089i	−0.333675	−	0.242429i
$501$	31.1248			1.39055
$502$	−47.2855			−2.11046
$503$	−23.8259	−	17.3105i	−1.06235	−	0.771839i	−0.0878244	−	0.996136i	$-0.527991\pi$
$503$	−23.8259	−	17.3105i	−1.06235	−	0.771839i	−0.974521	+	0.224297i	$0.927991\pi$
$504$	−2.03153	+	1.47599i	−0.0904916	+	0.0657460i
$505$	36.3697	−	26.4241i	1.61843	−	1.17586i
$506$	−7.53554	+	23.1920i	−0.334996	+	1.03101i
$507$	−1.53702	−	1.11671i	−0.0682616	−	0.0495949i
$508$	4.89309	−	15.0594i	0.217096	−	0.668153i
$509$	−13.5511	−	41.7061i	−0.600644	−	1.84859i	−0.524343	−	0.851507i	$-0.675689\pi$
$509$	−13.5511	−	41.7061i	−0.600644	−	1.84859i	−0.0763014	−	0.997085i	$-0.524311\pi$
$510$	14.5375	−	10.5621i	0.643731	−	0.467698i
$511$	−2.50126	−	7.69810i	−0.110649	−	0.340544i
$512$	−2.98421	−	9.18445i	−0.131885	−	0.405899i
$513$	−10.4629	+	7.60174i	−0.461948	+	0.335625i
$514$	11.9559	+	36.7964i	0.527351	+	1.62302i
$515$	11.5871	−	35.6615i	0.510589	−	1.57143i
$516$	−12.9292	−	9.39364i	−0.569178	−	0.413532i
$517$	6.05862	−	18.6465i	0.266458	−	0.820073i
$518$	3.05271	−	2.21792i	0.134128	−	0.0974500i
$519$	−0.270403	+	0.196460i	−0.0118694	+	0.00862362i
$520$	3.48217	+	2.52995i	0.152703	+	0.110945i
$521$	27.5319			1.20619			0.603097	−	0.797668i	$-0.293933\pi$
$521$	27.5319			1.20619			0.603097	+	0.797668i	$0.293933\pi$
$522$	4.85547			0.212518
$523$	−35.0777	−	25.4855i	−1.53384	−	1.11440i	−0.954055	−	0.299633i	$-0.903136\pi$
$523$	−35.0777	−	25.4855i	−1.53384	−	1.11440i	−0.579787	−	0.814768i	$-0.696864\pi$
$524$	6.35393	+	19.5554i	0.277573	+	0.854280i
$525$	2.10581	−	6.48103i	0.0919053	−	0.282855i
$526$	−2.89686			−0.126309
$527$	−10.4339	+	5.71282i	−0.454510	+	0.248855i
$528$	−21.1598			−0.920864
$529$	5.12065	−	15.7597i	0.222637	−	0.685205i
$530$	9.22643	+	28.3960i	0.400770	+	1.23344i
$531$	7.20086	+	5.23173i	0.312491	+	0.227038i
$532$	−7.12717			−0.309002
$533$	−9.07791			−0.393208
$534$	−9.35349	−	6.79571i	−0.404765	−	0.294079i
$535$	7.68723	−	5.58510i	0.332348	−	0.241465i
$536$	−4.01153	+	2.91455i	−0.173272	+	0.125889i
$537$	−2.25757	+	6.94808i	−0.0974212	+	0.299832i
$538$	27.0016	+	19.6178i	1.16412	+	0.845784i
$539$	−0.736082	+	2.26543i	−0.0317053	+	0.0975789i
$540$	3.66964	+	11.2940i	0.157916	+	0.486016i
$541$	−4.18731	+	3.04226i	−0.180026	+	0.130797i	−0.674149	−	0.738595i	$-0.735489\pi$
$541$	−4.18731	+	3.04226i	−0.180026	+	0.130797i	0.494123	+	0.869392i	$0.335489\pi$
$542$	−6.53295	−	20.1063i	−0.280614	−	0.863642i
$543$	6.13596	+	18.8845i	0.263319	+	0.810413i
$544$	9.18728	−	6.67495i	0.393901	−	0.286186i
$545$	−4.41159	−	13.5775i	−0.188972	−	0.581595i
$546$	−2.48783	+	7.65675i	−0.106469	+	0.327679i
$547$	5.92507	+	4.30482i	0.253338	+	0.184061i	0.707205	−	0.707009i	$-0.249956\pi$
$547$	5.92507	+	4.30482i	0.253338	+	0.184061i	−0.453867	+	0.891069i	$0.649956\pi$
$548$	1.50554	−	4.63357i	0.0643135	−	0.197937i
$549$	−2.05427	+	1.49251i	−0.0876739	+	0.0636988i
$550$	4.61914	−	3.35600i	0.196961	−	0.143100i
$551$	−10.5474	−	7.66315i	−0.449335	−	0.326461i
$552$	20.2188			0.860568
$553$	6.62160			0.281579
$554$	−13.1974	−	9.58847i	−0.560703	−	0.407375i
$555$	−1.33004	−	4.09345i	−0.0564572	−	0.173757i
$556$	−3.67585	+	11.3131i	−0.155891	+	0.479782i
$557$	−17.5740			−0.744635			−0.372318	−	0.928105i	$-0.621437\pi$
$557$	−17.5740			−0.744635			−0.372318	+	0.928105i	$0.621437\pi$
$558$	1.09650	+	5.80208i	0.0464184	+	0.245622i
$559$	8.18489			0.346184
$560$	9.57172	−	29.4587i	0.404479	−	1.24486i
$561$	−2.79444	−	8.60039i	−0.117981	−	0.363109i
$562$	−27.7253	−	20.1436i	−1.16952	−	0.849707i
$563$	5.08764			0.214419			0.107209	−	0.994236i	$-0.465808\pi$
$563$	5.08764			0.214419			0.107209	+	0.994236i	$0.465808\pi$
$564$	17.1834			0.723550
$565$	−18.9817	−	13.7910i	−0.798564	−	0.580191i
$566$	−12.2343	+	8.88876i	−0.514247	+	0.373622i
$567$	20.6025	−	14.9686i	0.865226	−	0.628623i
$568$	4.60249	−	14.1650i	0.193116	−	0.594350i
$569$	−19.7443	−	14.3451i	−0.827726	−	0.601378i	0.0911892	−	0.995834i	$-0.470933\pi$
$569$	−19.7443	−	14.3451i	−0.827726	−	0.601378i	−0.918915	+	0.394456i	$0.870933\pi$
$570$	−7.40103	+	22.7780i	−0.309995	+	0.954066i
$571$	0.845726	+	2.60288i	0.0353925	+	0.108927i	0.967192	−	0.254046i	$-0.0817616\pi$
$571$	0.845726	+	2.60288i	0.0353925	+	0.108927i	−0.931800	+	0.362973i	$0.881762\pi$
$572$	−1.85235	+	1.34581i	−0.0774508	+	0.0562713i
$573$	12.2394	+	37.6690i	0.511308	+	1.57364i
$574$	11.8873	+	36.5854i	0.496167	+	1.52705i
$575$	−7.49554	+	5.44583i	−0.312586	+	0.227107i
$576$	0.141193	+	0.434548i	0.00588305	+	0.0181062i
$577$	7.65466	−	23.5586i	0.318668	−	0.980759i	−0.655551	−	0.755151i	$-0.727563\pi$
$577$	7.65466	−	23.5586i	0.318668	−	0.980759i	0.974218	−	0.225607i	$-0.0724366\pi$
$578$	−17.5055	−	12.7185i	−0.728134	−	0.529020i
$579$	1.32190	−	4.06840i	0.0549364	−	0.169077i
$580$	−9.68486	+	7.03646i	−0.402142	+	0.292173i
$581$	−10.8257	+	7.86531i	−0.449125	+	0.326308i
$582$	−23.3171	−	16.9409i	−0.966526	−	0.702222i
$583$	15.0256			0.622296
$584$	−5.62296			−0.232680
$585$	1.25450	+	0.911446i	0.0518671	+	0.0376837i
$586$	12.7447	+	39.2242i	0.526480	+	1.62034i
$587$	−8.95189	+	27.5511i	−0.369484	+	1.13715i	0.577641	+	0.816291i	$0.303973\pi$
$587$	−8.95189	+	27.5511i	−0.369484	+	1.13715i	−0.947125	+	0.320864i	$0.896027\pi$
$588$	−2.08766			−0.0860937
$589$	6.77525	−	14.3343i	0.279169	−	0.590633i
$590$	−64.6500			−2.66160
$591$	−4.97782	+	15.3202i	−0.204760	+	0.630188i
$592$	−1.37562	−	4.23372i	−0.0565376	−	0.174005i
$593$	−27.7235	−	20.1423i	−1.13847	−	0.827147i	−0.151564	−	0.988447i	$-0.548431\pi$
$593$	−27.7235	−	20.1423i	−1.13847	−	0.827147i	−0.986905	+	0.161301i	$0.948431\pi$
$594$	17.6059			0.722380
$595$	13.2375			0.542686
$596$	−7.35972	−	5.34715i	−0.301466	−	0.219028i
$597$	2.37014	−	1.72201i	0.0970034	−	0.0704771i
$598$	8.85531	−	6.43376i	0.362120	−	0.263096i
$599$	12.7974	−	39.3862i	0.522886	−	1.60928i	−0.245573	−	0.969378i	$-0.578976\pi$
$599$	12.7974	−	39.3862i	0.522886	−	1.60928i	0.768459	−	0.639899i	$-0.221024\pi$
$600$	−3.82986	−	2.78256i	−0.156354	−	0.113598i
$601$	−3.20304	+	9.85794i	−0.130655	+	0.402114i	−0.994889	−	0.100976i	$-0.967803\pi$
$601$	−3.20304	+	9.85794i	−0.130655	+	0.402114i	0.864234	+	0.503090i	$0.167803\pi$
$602$	−10.7179	−	32.9864i	−0.436830	−	1.34442i
$603$	−1.44521	+	1.05000i	−0.0588533	+	0.0427594i
$604$	0.758857	+	2.33552i	0.0308774	+	0.0950310i
$605$	4.74600	+	14.6067i	0.192952	+	0.593846i
$606$	47.2578	−	34.3348i	1.91972	−	1.39476i
$607$	10.0690	+	30.9891i	0.408687	+	1.25781i	0.917777	+	0.397096i	$0.129982\pi$
$607$	10.0690	+	30.9891i	0.408687	+	1.25781i	−0.509090	+	0.860713i	$0.670018\pi$
$608$	−4.67724	+	14.3951i	−0.189687	+	0.583796i
$609$	17.1374	+	12.4511i	0.694443	+	0.504542i
$610$	5.69932	−	17.5407i	0.230759	−	0.710203i
$611$	−7.11972	+	5.17278i	−0.288033	+	0.209268i
$612$	1.08269	−	0.786622i	0.0437652	−	0.0317973i
$613$	−13.9261	−	10.1179i	−0.562468	−	0.408657i	0.269893	−	0.962890i	$-0.413012\pi$
$613$	−13.9261	−	10.1179i	−0.562468	−	0.408657i	−0.832361	+	0.554233i	$0.813012\pi$
$614$	−25.8192			−1.04198
$615$	43.8790			1.76937
$616$	−7.42584	−	5.39519i	−0.299196	−	0.217378i
$617$	4.70078	+	14.4675i	0.189246	+	0.582441i	0.999996	−	0.00295303i	$-0.000939980\pi$
$617$	4.70078	+	14.4675i	0.189246	+	0.582441i	−0.810749	+	0.585394i	$0.800940\pi$
$618$	15.0560	−	46.3375i	0.605640	−	1.86397i
$619$	−17.2365			−0.692795			−0.346398	−	0.938088i	$-0.612595\pi$
$619$	−17.2365			−0.692795			−0.346398	+	0.938088i	$0.612595\pi$
$620$	−10.5954	−	9.98398i	−0.425521	−	0.400966i
$621$	−28.5694			−1.14645
$622$	−7.15520	+	22.0214i	−0.286897	+	0.882979i
$623$	−2.63193	−	8.10023i	−0.105446	−	0.324529i
$624$	7.68393	+	5.58270i	0.307604	+	0.223487i
$625$	−30.1950			−1.20780
$626$	−3.09201			−0.123582
$627$	9.75096	+	7.08448i	0.389416	+	0.282927i
$628$	5.33933	−	3.87925i	0.213063	−	0.154799i
$629$	1.53912	−	1.11824i	0.0613688	−	0.0445871i
$630$	2.03053	−	6.24934i	0.0808984	−	0.248980i
$631$	−25.7320	−	18.6954i	−1.02438	−	0.744253i	−0.0572006	−	0.998363i	$-0.518217\pi$
$631$	−25.7320	−	18.6954i	−1.02438	−	0.744253i	−0.967175	+	0.254110i	$0.918217\pi$
$632$	1.42146	−	4.37479i	0.0565425	−	0.174020i
$633$	−8.35122	−	25.7024i	−0.331931	−	1.02158i
$634$	31.1325	−	22.6191i	1.23643	−	0.898318i
$635$	−12.1130	−	37.2800i	−0.480689	−	1.47941i
$636$	4.06939	+	12.5243i	0.161362	+	0.496621i
$637$	0.864998	−	0.628458i	0.0342725	−	0.0249004i
$638$	5.48448	+	16.8795i	0.217133	+	0.668266i
$639$	1.65811	−	5.10313i	0.0655937	−	0.201877i
$640$	−24.5657	−	17.8480i	−0.971043	−	0.705504i
$641$	−7.64256	+	23.5214i	−0.301863	+	0.929038i	0.678966	+	0.734169i	$0.262428\pi$
$641$	−7.64256	+	23.5214i	−0.301863	+	0.929038i	−0.980829	+	0.194869i	$0.937572\pi$
$642$	9.98857	−	7.25712i	0.394218	−	0.286416i
$643$	−37.6666	+	27.3664i	−1.48543	+	1.07923i	−0.509669	+	0.860371i	$0.670232\pi$
$643$	−37.6666	+	27.3664i	−1.48543	+	1.07923i	−0.975757	+	0.218855i	$0.929768\pi$
$644$	−12.7374	−	9.25428i	−0.501925	−	0.364670i
$645$	−39.5624			−1.55777
$646$	−10.5862			−0.416510
$647$	−4.38782	−	3.18794i	−0.172503	−	0.125331i	0.498184	−	0.867072i	$-0.334001\pi$
$647$	−4.38782	−	3.18794i	−0.172503	−	0.125331i	−0.670687	+	0.741741i	$0.734001\pi$
$648$	−5.46681	−	16.8251i	−0.214756	−	0.660952i
$649$	−10.0538	+	30.9425i	−0.394647	+	1.21460i
$650$	−2.56281			−0.100522
$651$	−11.0084	+	23.2903i	−0.431453	+	0.912818i
$652$	5.61302			0.219823
$653$	1.90427	−	5.86073i	0.0745197	−	0.229348i	−0.906858	−	0.421436i	$-0.861526\pi$
$653$	1.90427	−	5.86073i	0.0745197	−	0.229348i	0.981378	+	0.192088i	$0.0615260\pi$
$654$	−5.73230	−	17.6422i	−0.224151	−	0.689865i
$655$	41.1799	+	29.9190i	1.60903	+	1.16903i
$656$	45.3826			1.77189
$657$	−2.02575			−0.0790319
$658$	30.1702	+	21.9199i	1.17616	+	0.854528i
$659$	−30.7923	+	22.3719i	−1.19950	+	0.871485i	−0.994235	−	0.107222i	$-0.965804\pi$
$659$	−30.7923	+	22.3719i	−1.19950	+	0.871485i	−0.205261	+	0.978707i	$0.565804\pi$
$660$	8.95353	−	6.50512i	0.348516	−	0.253212i
$661$	6.49941	−	20.0031i	0.252798	−	0.778032i	−0.741458	−	0.671000i	$-0.765865\pi$
$661$	6.49941	−	20.0031i	0.252798	−	0.778032i	0.994256	−	0.107032i	$-0.0341347\pi$
$662$	−22.2891	−	16.1940i	−0.866291	−	0.629397i
$663$	−1.25432	+	3.86040i	−0.0487137	+	0.149925i
$664$	2.87255	+	8.84080i	0.111477	+	0.343090i
$665$	−14.2739	+	10.3706i	−0.553518	+	0.402154i
$666$	−0.291822	−	0.898136i	−0.0113079	−	0.0348021i
$667$	−8.89974	−	27.3906i	−0.344599	−	1.06057i
$668$	−13.6214	+	9.89652i	−0.527027	+	0.382908i
$669$	14.6169	+	44.9862i	0.565122	+	1.73927i
$670$	4.00956	−	12.3401i	0.154903	−	0.476741i
$671$	−7.50894	−	5.45556i	−0.289879	−	0.210610i
$672$	7.59956	−	23.3890i	0.293159	−	0.902252i
$673$	−11.7863	+	8.56324i	−0.454328	+	0.330089i	−0.791302	−	0.611425i	$-0.790596\pi$
$673$	−11.7863	+	8.56324i	−0.454328	+	0.330089i	0.336974	+	0.941514i	$0.390596\pi$
$674$	−8.34889	+	6.06582i	−0.321587	+	0.233647i
$675$	5.41165	+	3.93179i	0.208295	+	0.151335i
$676$	1.02773			0.0395282
$677$	−23.1895			−0.891246			−0.445623	−	0.895221i	$-0.647018\pi$
$677$	−23.1895			−0.891246			−0.445623	+	0.895221i	$0.647018\pi$
$678$	−24.6642	−	17.9196i	−0.947225	−	0.688199i
$679$	−6.56107	−	20.1929i	−0.251791	−	0.774933i
$680$	2.84170	−	8.74584i	0.108974	−	0.335388i
$681$	−0.0820294			−0.00314337
$682$	−18.9318	+	10.3656i	−0.724934	+	0.396918i
$683$	1.01806			0.0389550			0.0194775	−	0.999810i	$-0.493800\pi$
$683$	1.01806			0.0389550			0.0194775	+	0.999810i	$0.493800\pi$
$684$	−0.551197	+	1.69641i	−0.0210756	+	0.0648639i
$685$	−3.72701	−	11.4705i	−0.142402	−	0.438267i
$686$	−27.6633	−	20.0985i	−1.05619	−	0.767366i
$687$	23.0203			0.878278
$688$	−40.9181			−1.55999
$689$	−5.45635	−	3.96427i	−0.207870	−	0.151027i
$690$	−42.8030	+	31.0982i	−1.62948	+	1.18389i
$691$	−12.2866	+	8.92670i	−0.467402	+	0.339588i	−0.796428	−	0.604733i	$-0.793280\pi$
$691$	−12.2866	+	8.92670i	−0.467402	+	0.339588i	0.329026	+	0.944321i	$0.393280\pi$
$692$	0.0558720	−	0.171956i	0.00212393	−	0.00653679i
$693$	−2.67526	−	1.94369i	−0.101625	−	0.0738346i
$694$	19.6835	−	60.5796i	0.747175	−	2.29957i
$695$	9.09966	+	28.0059i	0.345170	+	1.06232i
$696$	11.9051	−	8.64956i	0.451262	−	0.327861i
$697$	5.99337	+	18.4457i	0.227015	+	0.698681i
$698$	12.7779	+	39.3264i	0.483651	+	1.48853i
$699$	4.49486	−	3.26571i	0.170011	−	0.123520i
$700$	1.13914	+	3.50591i	0.0430555	+	0.132511i
$701$	4.25071	−	13.0823i	0.160547	−	0.494113i	−0.838134	−	0.545465i	$-0.816353\pi$
$701$	4.25071	−	13.0823i	0.160547	−	0.494113i	0.998681	+	0.0513522i	$0.0163531\pi$
$702$	−6.39338	−	4.64506i	−0.241302	−	0.175316i
$703$	−0.783566	+	2.41157i	−0.0295527	+	0.0909540i
$704$	−1.35117	+	0.981685i	−0.0509243	+	0.0369987i
$705$	34.4139	−	25.0031i	1.29610	−	0.941673i
$706$	−1.35689	−	0.985840i	−0.0510673	−	0.0371026i
$707$	43.0319			1.61838
$708$	−28.5144			−1.07164
$709$	21.6014	+	15.6943i	0.811257	+	0.589413i	0.914195	−	0.405275i	$-0.132824\pi$
$709$	21.6014	+	15.6943i	0.811257	+	0.589413i	−0.102938	+	0.994688i	$0.532824\pi$
$710$	12.0435	+	37.0662i	0.451986	+	1.39107i
$711$	0.512098	−	1.57608i	0.0192052	−	0.0591074i
$712$	−5.91669			−0.221737
$713$	30.7208	−	16.8204i	1.15050	−	0.629927i
$714$	17.2005			0.643712
$715$	−1.75153	+	5.39064i	−0.0655033	+	0.201599i
$716$	−1.22123	−	3.75856i	−0.0456395	−	0.140464i
$717$	−22.6896	−	16.4850i	−0.847360	−	0.615643i
$718$	45.9922			1.71641
$719$	−11.1907			−0.417342			−0.208671	−	0.977986i	$-0.566914\pi$
$719$	−11.1907			−0.417342			−0.208671	+	0.977986i	$0.566914\pi$
$720$	−6.27152	−	4.55653i	−0.233726	−	0.169812i
$721$	29.0375	−	21.0970i	1.08141	−	0.785693i
$722$	−15.3317	+	11.1391i	−0.570585	+	0.414554i
$723$	7.17096	−	22.0700i	0.266691	−	0.820791i
$724$	−8.68990	−	6.31358i	−0.322958	−	0.234643i
$725$	−2.08376	+	6.41317i	−0.0773891	+	0.238179i
$726$	6.16682	+	18.9795i	0.228872	+	0.704397i
$727$	−11.9698	+	8.69655i	−0.443934	+	0.322537i	−0.787196	−	0.616703i	$-0.788468\pi$
$727$	−11.9698	+	8.69655i	−0.443934	+	0.322537i	0.343262	+	0.939240i	$0.388468\pi$
$728$	1.27316	+	3.91839i	0.0471865	+	0.145225i
$729$	6.02959	+	18.5572i	0.223318	+	0.687303i
$730$	11.9038	−	8.64860i	0.440578	−	0.320099i
$731$	−5.40378	−	16.6311i	−0.199866	−	0.615125i
$732$	2.51373	−	7.73648i	0.0929103	−	0.285948i
$733$	34.7025	+	25.2129i	1.28177	+	0.931258i	0.999605	−	0.0281088i	$-0.00894848\pi$
$733$	34.7025	+	25.2129i	1.28177	+	0.931258i	0.282162	+	0.959367i	$0.408948\pi$
$734$	15.0127	−	46.2042i	0.554127	−	1.70543i
$735$	−4.18105	+	3.03771i	−0.154220	+	0.112048i
$736$	−27.0503	+	19.6532i	−0.997086	+	0.724425i
$737$	−5.28265	−	3.83807i	−0.194589	−	0.141377i
$738$	9.62740			0.354390
$739$	39.8459			1.46575			0.732877	−	0.680361i	$-0.238177\pi$
$739$	39.8459			1.46575			0.732877	+	0.680361i	$0.238177\pi$
$740$	1.88364	+	1.36854i	0.0692440	+	0.0503087i
$741$	−1.67180	−	5.14529i	−0.0614153	−	0.189017i
$742$	−8.83167	+	27.1811i	−0.324221	+	0.997849i
$743$	32.4920			1.19202			0.596009	−	0.802978i	$-0.296752\pi$
$743$	32.4920			1.19202			0.596009	+	0.802978i	$0.296752\pi$
$744$	13.0244	+	12.2728i	0.477496	+	0.449943i
$745$	−22.5202			−0.825075
$746$	15.2149	−	46.8266i	0.557057	−	1.71444i
$747$	1.03487	+	3.18501i	0.0378640	+	0.116534i
$748$	3.95755	+	2.87533i	0.144702	+	0.105132i
$749$	9.09539			0.332338
$750$	−29.6656			−1.08323
$751$	37.8589	+	27.5061i	1.38149	+	1.00371i	0.996739	+	0.0806931i	$0.0257134\pi$
$751$	37.8589	+	27.5061i	1.38149	+	1.00371i	0.384753	+	0.923020i	$0.374287\pi$
$752$	35.5931	−	25.8599i	1.29795	−	0.943014i
$753$	−41.7686	+	30.3467i	−1.52213	+	1.10589i
$754$	2.46178	−	7.57658i	0.0896527	−	0.275923i
$755$	4.91816	+	3.57326i	0.178990	+	0.130044i
$756$	−3.51263	+	10.8108i	−0.127753	+	0.393184i
$757$	−6.44528	−	19.8365i	−0.234258	−	0.720971i	−0.997219	−	0.0745267i	$-0.976255\pi$
$757$	−6.44528	−	19.8365i	−0.234258	−	0.720971i	0.762961	−	0.646444i	$-0.223745\pi$
$758$	6.46587	−	4.69773i	0.234851	−	0.170629i
$759$	8.22770	+	25.3223i	0.298647	+	0.919140i
$760$	3.78752	+	11.6568i	0.137388	+	0.422836i
$761$	−5.01214	+	3.64153i	−0.181690	+	0.132005i	−0.674913	−	0.737898i	$-0.735819\pi$
$761$	−5.01214	+	3.64153i	−0.181690	+	0.132005i	0.493223	+	0.869903i	$0.335819\pi$
$762$	−15.7393	−	48.4406i	−0.570174	−	1.75482i
$763$	4.22284	−	12.9966i	0.152877	−	0.470507i
$764$	−17.3337	−	12.5937i	−0.627113	−	0.455624i
$765$	1.02376	−	3.15080i	0.0370141	−	0.113918i
$766$	52.5502	−	38.1800i	1.89872	−	1.37950i
$767$	11.8146	−	8.58382i	0.426601	−	0.309944i
$768$	−29.6154	−	21.5169i	−1.06865	−	0.776423i
$769$	33.8696			1.22137			0.610684	−	0.791874i	$-0.290894\pi$
$769$	33.8696			1.22137			0.610684	+	0.791874i	$0.290894\pi$
$770$	24.0187			0.865574
$771$	34.1760	+	24.8303i	1.23082	+	0.894241i
$772$	0.715083	+	2.20080i	0.0257364	+	0.0792085i
$773$	−14.6855	+	45.1973i	−0.528200	+	1.62563i	0.229699	+	0.973262i	$0.426226\pi$
$773$	−14.6855	+	45.1973i	−0.528200	+	1.62563i	−0.757900	+	0.652371i	$0.773774\pi$
$774$	−8.68032			−0.312008
$775$	−8.13404	−	1.04175i	−0.292183	−	0.0374206i
$776$	−14.7496			−0.529480
$777$	1.27314	−	3.91831i	0.0456735	−	0.140568i
$778$	−1.68516	−	5.18638i	−0.0604158	−	0.185941i
$779$	−20.9134	−	15.1945i	−0.749299	−	0.544398i
$780$	−4.96764			−0.177870
$781$	19.6134			0.701821
$782$	−18.9194	−	13.7457i	−0.676555	−	0.491546i
$783$	−16.8221	+	12.2220i	−0.601172	+	0.436777i
$784$	−4.32433	+	3.14181i	−0.154440	+	0.112207i
$785$	5.04870	−	15.5383i	0.180196	−	0.554586i
$786$	53.5080	+	38.8759i	1.90857	+	1.38666i
$787$	−6.80133	+	20.9323i	−0.242441	+	0.746157i	0.753606	+	0.657327i	$0.228313\pi$
$787$	−6.80133	+	20.9323i	−0.242441	+	0.746157i	−0.996047	+	0.0888302i	$0.971687\pi$
$788$	−2.69275	−	8.28745i	−0.0959254	−	0.295228i
$789$	−2.55887	+	1.85913i	−0.0910982	+	0.0661868i
$790$	3.71959	+	11.4477i	0.132337	+	0.407292i
$791$	−6.94013	−	21.3595i	−0.246763	−	0.759458i
$792$	−1.85846	+	1.35025i	−0.0660375	+	0.0479791i
$793$	1.28741	+	3.96224i	0.0457173	+	0.140703i
$794$	−14.2922	+	43.9869i	−0.507211	+	1.56104i
$795$	26.3738	+	19.1617i	0.935383	+	0.679595i
$796$	−0.489729	+	1.50723i	−0.0173580	+	0.0534224i
$797$	−18.8828	+	13.7192i	−0.668864	+	0.485958i	−0.869645	−	0.493678i	$-0.835652\pi$
$797$	−18.8828	+	13.7192i	−0.668864	+	0.485958i	0.200781	+	0.979636i	$0.435652\pi$
$798$	−18.5471	+	13.4753i	−0.656561	+	0.477019i
$799$	15.2113	+	11.0516i	0.538136	+	0.390979i
$800$	7.82861			0.276783
$801$	−2.13157			−0.0753152
$802$	26.0702	+	18.9411i	0.920572	+	0.668835i
$803$	−2.28818	−	7.04228i	−0.0807480	−	0.248517i
$804$	1.76845	−	5.44273i	0.0623684	−	0.191950i
$805$	−38.9755			−1.37371
$806$	9.60963	+	1.23073i	0.338485	+	0.0433506i
$807$	36.4415			1.28280
$808$	9.23765	−	28.4306i	0.324979	−	1.00018i
$809$	11.4497	+	35.2386i	0.402550	+	1.23892i	0.922924	+	0.384983i	$0.125793\pi$
$809$	11.4497	+	35.2386i	0.402550	+	1.23892i	−0.520373	+	0.853939i	$0.674207\pi$
$810$	37.4516	+	27.2102i	1.31592	+	0.956069i
$811$	42.8049			1.50308			0.751541	−	0.659686i	$-0.229311\pi$
$811$	42.8049			1.50308			0.751541	+	0.659686i	$0.229311\pi$
$812$	−11.4589			−0.402130
$813$	−18.6745	−	13.5678i	−0.654943	−	0.475844i
$814$	2.79264	−	2.02897i	0.0978821	−	0.0711155i
$815$	11.2414	−	8.16738i	0.393770	−	0.286091i
$816$	6.27063	−	19.2990i	0.219516	−	0.675601i
$817$	18.8560	+	13.6997i	0.659690	+	0.479293i
$818$	−3.30638	+	10.1760i	−0.115605	+	0.355795i
$819$	0.458673	+	1.41165i	0.0160273	+	0.0493271i
$820$	−19.2031	+	13.9519i	−0.670601	+	0.487220i
$821$	4.50097	+	13.8526i	0.157085	+	0.483458i	0.998366	−	0.0571398i	$-0.0181981\pi$
$821$	4.50097	+	13.8526i	0.157085	+	0.483458i	−0.841281	+	0.540598i	$0.818198\pi$
$822$	−4.84277	−	14.9045i	−0.168911	−	0.519855i
$823$	−11.3483	+	8.24503i	−0.395577	+	0.287404i	−0.767737	−	0.640765i	$-0.778617\pi$
$823$	−11.3483	+	8.24503i	−0.395577	+	0.287404i	0.372160	+	0.928169i	$0.378617\pi$
$824$	−7.70499	−	23.7135i	−0.268416	−	0.826100i
$825$	1.92641	−	5.92889i	0.0670692	−	0.206418i
$826$	−50.0651	−	36.3744i	−1.74199	−	1.26563i
$827$	−0.676082	+	2.08077i	−0.0235097	+	0.0723554i	−0.962123	−	0.272616i	$-0.912111\pi$
$827$	−0.676082	+	2.08077i	−0.0235097	+	0.0723554i	0.938613	+	0.344971i	$0.112111\pi$
$828$	−3.18779	+	2.31606i	−0.110783	+	0.0804887i
$829$	26.9791	−	19.6015i	0.937024	−	0.680788i	−0.0106784	−	0.999943i	$-0.503399\pi$
$829$	26.9791	−	19.6015i	0.937024	−	0.680788i	0.947702	+	0.319155i	$0.103399\pi$
$830$	−19.6791	−	14.2977i	−0.683070	−	0.496280i
$831$	−17.8113			−0.617865
$832$	0.749665			0.0259900
$833$	−1.84807	−	1.34270i	−0.0640318	−	0.0465218i
$834$	11.8239	+	36.3901i	0.409427	+	1.26009i
$835$	−12.8799	+	39.6404i	−0.445729	+	1.37181i
$836$	−6.51999			−0.225498
$837$	−18.4036	−	17.3416i	−0.636121	−	0.599414i
$838$	59.5874			2.05841
$839$	−0.630518	+	1.94053i	−0.0217679	+	0.0669947i	−0.961350	−	0.275328i	$-0.911214\pi$
$839$	−0.630518	+	1.94053i	−0.0217679	+	0.0669947i	0.939582	+	0.342323i	$0.111214\pi$
$840$	−6.15396	−	18.9399i	−0.212332	−	0.653490i
$841$	6.50353	+	4.72509i	0.224260	+	0.162934i
$842$	−3.05023			−0.105118
$843$	−37.4182			−1.28875
$844$	11.8272	+	8.59297i	0.407110	+	0.295782i
$845$	2.05828	−	1.49543i	0.0708071	−	0.0514444i
$846$	7.55068	−	5.48589i	0.259598	−	0.188609i
$847$	−4.54294	+	13.9817i	−0.156097	+	0.480418i
$848$	27.2776	+	19.8183i	0.936716	+	0.680564i
$849$	−5.10233	+	15.7034i	−0.175112	+	0.538938i
$850$	1.69201	+	5.20746i	0.0580354	+	0.178614i
$851$	−4.53166	+	3.29244i	−0.155343	+	0.112864i
$852$	5.31191	+	16.3484i	0.181983	+	0.560086i
$853$	13.6747	+	42.0865i	0.468214	+	1.44101i	0.854895	+	0.518801i	$0.173621\pi$
$853$	13.6747	+	42.0865i	0.468214	+	1.44101i	−0.386681	+	0.922213i	$0.626379\pi$
$854$	14.2826	−	10.3769i	0.488741	−	0.355091i
$855$	1.36450	+	4.19951i	0.0466651	+	0.143620i
$856$	1.95250	−	6.00918i	0.0667351	−	0.205390i
$857$	2.24073	+	1.62798i	0.0765418	+	0.0556108i	0.625398	−	0.780306i	$-0.284937\pi$
$857$	2.24073	+	1.62798i	0.0765418	+	0.0556108i	−0.548856	+	0.835917i	$0.684937\pi$
$858$	−2.27588	+	7.00445i	−0.0776974	+	0.239128i
$859$	−16.8642	+	12.2526i	−0.575399	+	0.418052i	−0.837062	−	0.547107i	$-0.815729\pi$
$859$	−16.8642	+	12.2526i	−0.575399	+	0.418052i	0.261664	+	0.965159i	$0.415729\pi$
$860$	17.3140	−	12.5794i	0.590403	−	0.428953i
$861$	33.9800	+	24.6879i	1.15803	+	0.841362i
$862$	−4.50591			−0.153472
$863$	31.7939			1.08228			0.541138	−	0.840934i	$-0.317993\pi$
$863$	31.7939			1.08228			0.541138	+	0.840934i	$0.317993\pi$
$864$	19.5298	+	14.1892i	0.664418	+	0.482728i
$865$	−0.138313	−	0.425682i	−0.00470277	−	0.0144736i
$866$	−15.0952	+	46.4581i	−0.512954	+	1.57871i
$867$	−23.6255			−0.802365
$868$	−2.58774	−	13.6930i	−0.0878336	−	0.464769i
$869$	6.05749			0.205486
$870$	−11.8992	+	36.6221i	−0.403422	+	1.24161i
$871$	0.905712	+	2.78749i	0.0306889	+	0.0944506i
$872$	−7.68011	−	5.57993i	−0.260081	−	0.188960i
$873$	−5.31374			−0.179843
$874$	31.1692			1.05432
$875$	−17.6802	−	12.8454i	−0.597698	−	0.434253i
$876$	5.25026	−	3.81454i	0.177390	−	0.128881i
$877$	20.1216	−	14.6192i	0.679458	−	0.493655i	−0.193720	−	0.981057i	$-0.562055\pi$
$877$	20.1216	−	14.6192i	0.679458	−	0.493655i	0.873178	+	0.487402i	$0.162055\pi$
$878$	14.3346	−	44.1174i	0.483770	−	1.48889i
$879$	36.4309	+	26.4686i	1.22878	+	0.892763i
$880$	8.75628	−	26.9491i	0.295174	−	0.908453i
$881$	15.4159	+	47.4454i	0.519376	+	1.59847i	0.775176	+	0.631745i	$0.217661\pi$
$881$	15.4159	+	47.4454i	0.519376	+	1.59847i	−0.255801	+	0.966730i	$0.582339\pi$
$882$	−0.917357	+	0.666499i	−0.0308890	+	0.0224422i
$883$	−5.92688	−	18.2411i	−0.199455	−	0.613861i	−0.999896	−	0.0144481i	$-0.995401\pi$
$883$	−5.92688	−	18.2411i	−0.199455	−	0.613861i	0.800440	−	0.599413i	$-0.204599\pi$
$884$	−0.678524	−	2.08828i	−0.0228212	−	0.0702365i
$885$	−57.1071	+	41.4908i	−1.91964	+	1.39470i
$886$	18.5509	+	57.0939i	0.623230	+	1.91811i
$887$	6.36427	−	19.5872i	0.213691	−	0.657675i	−0.785553	−	0.618795i	$-0.787621\pi$
$887$	6.36427	−	19.5872i	0.213691	−	0.657675i	0.999244	−	0.0388795i	$-0.0123789\pi$
$888$	−2.31546	−	1.68228i	−0.0777018	−	0.0564537i
$889$	11.5947	−	35.6849i	0.388875	−	1.19683i
$890$	12.5256	−	9.10038i	0.419859	−	0.305045i
$891$	18.8474	−	13.6934i	0.631410	−	0.458747i
$892$	−20.7008	−	15.0400i	−0.693115	−	0.503577i
$893$	−25.0603			−0.838610
$894$	−29.2621			−0.978670
$895$	−7.91482	−	5.75045i	−0.264563	−	0.192216i
$896$	−8.98177	−	27.6431i	−0.300060	−	0.923490i
$897$	3.69311	−	11.3662i	0.123309	−	0.379507i
$898$	−66.5009			−2.21916
$899$	10.8931	−	23.0464i	0.363306	−	0.768640i
$900$	0.922577			0.0307526
$901$	−4.45277	+	13.7042i	−0.148343	+	0.456553i
$902$	10.8746	+	33.4686i	0.362085	+	1.11438i
$903$	−30.6372	−	22.2593i	−1.01954	−	0.740742i
$904$	−15.6018			−0.518907
$905$	−26.5904			−0.883895
$906$	6.39053	+	4.64299i	0.212311	+	0.154253i
$907$	40.3515	−	29.3171i	1.33985	−	0.973457i	0.340399	−	0.940281i	$-0.389438\pi$
$907$	40.3515	−	29.3171i	1.33985	−	0.973457i	0.999450	−	0.0331763i	$-0.0105623\pi$
$908$	0.0358991	−	0.0260823i	0.00119135	−	0.000865570i
$909$	3.32798	−	10.2425i	0.110382	−	0.339722i
$910$	−8.72210	−	6.33697i	−0.289135	−	0.210069i
$911$	−0.406895	+	1.25229i	−0.0134810	+	0.0414903i	−0.957571	−	0.288198i	$-0.906944\pi$
$911$	−0.406895	+	1.25229i	−0.0134810	+	0.0414903i	0.944090	+	0.329689i	$0.106944\pi$
$912$	8.35774	+	25.7225i	0.276752	+	0.851756i
$913$	−9.90340	+	7.19524i	−0.327755	+	0.238128i
$914$	−16.6948	−	51.3812i	−0.552214	−	1.69954i
$915$	−6.22282	−	19.1519i	−0.205720	−	0.633141i
$916$	−10.0745	+	7.31958i	−0.332872	+	0.241846i
$917$	15.0563	+	46.3386i	0.497204	+	1.53024i
$918$	−5.21744	+	16.0576i	−0.172201	+	0.529981i
$919$	22.2185	+	16.1427i	0.732921	+	0.532498i	0.890486	−	0.455011i	$-0.150364\pi$
$919$	22.2185	+	16.1427i	0.732921	+	0.532498i	−0.157565	+	0.987509i	$0.550364\pi$
$920$	−8.36685	+	25.7505i	−0.275847	+	0.848969i
$921$	−22.8068	+	16.5701i	−0.751509	+	0.546003i
$922$	4.16323	−	3.02476i	0.137109	−	0.0996152i
$923$	−7.12235	−	5.17469i	−0.234435	−	0.170327i
$924$	10.5937			0.348506
$925$	1.31151			0.0431221
$926$	−17.1200	−	12.4384i	−0.562599	−	0.408752i
$927$	−2.77582	−	8.54311i	−0.0911700	−	0.280593i
$928$	−7.51998	+	23.1441i	−0.246856	+	0.759743i
$929$	28.5822			0.937753			0.468876	−	0.883264i	$-0.344659\pi$
$929$	28.5822			0.937753			0.468876	+	0.883264i	$0.344659\pi$
$930$	−46.4491	−	5.94885i	−1.52313	−	0.195070i
$931$	3.04465			0.0997845
$932$	−0.928748	+	2.85839i	−0.0304222	+	0.0936298i
$933$	7.81242	+	24.0442i	0.255767	+	0.787171i
$934$	−6.64262	−	4.82615i	−0.217353	−	0.157916i
$935$	12.1098			0.396033
$936$	1.03112			0.0337032
$937$	8.34161	+	6.06053i	0.272508	+	0.197989i	0.715643	−	0.698466i	$-0.246134\pi$
$937$	8.34161	+	6.06053i	0.272508	+	0.197989i	−0.443135	+	0.896455i	$0.646134\pi$
$938$	10.0480	−	7.30032i	0.328080	−	0.238364i
$939$	−2.73126	+	1.98437i	−0.0891312	+	0.0647576i
$940$	−7.11075	+	21.8846i	−0.231927	+	0.713798i
$941$	22.6167	+	16.4320i	0.737283	+	0.535667i	0.891859	−	0.452314i	$-0.149401\pi$
$941$	22.6167	+	16.4320i	0.737283	+	0.535667i	−0.154576	+	0.987981i	$0.549401\pi$
$942$	6.56015	−	20.1901i	0.213741	−	0.657827i
$943$	−17.6464	−	54.3100i	−0.574645	−	1.76858i
$944$	−59.0640	+	42.9125i	−1.92237	+	1.39668i
$945$	8.69562	+	26.7624i	0.282869	+	0.870580i
$946$	−9.80483	−	30.1762i	−0.318783	−	0.981112i
$947$	−46.8171	+	34.0146i	−1.52135	+	1.10533i	−0.560539	+	0.828128i	$0.689406\pi$
$947$	−46.8171	+	34.0146i	−1.52135	+	1.10533i	−0.960813	+	0.277199i	$0.910594\pi$
$948$	1.64056	+	5.04911i	0.0532828	+	0.163988i
$949$	−1.02708	+	3.16102i	−0.0333403	+	0.102611i
$950$	−5.90412	−	4.28959i	−0.191555	−	0.139173i
$951$	12.9838	−	39.9601i	0.421029	−	1.29579i
$952$	7.12134	−	5.17396i	0.230804	−	0.167689i
$953$	−16.4035	+	11.9179i	−0.531363	+	0.386058i	−0.820867	−	0.571119i	$-0.806509\pi$
$953$	−16.4035	+	11.9179i	−0.531363	+	0.386058i	0.289504	+	0.957177i	$0.406509\pi$
$954$	5.78663	+	4.20423i	0.187349	+	0.136117i
$955$	−53.0399			−1.71633
$956$	15.1714			0.490680
$957$	15.6774	+	11.3903i	0.506779	+	0.368197i
$958$	−12.1308	−	37.3348i	−0.391929	−	1.20623i
$959$	3.56754	−	10.9798i	0.115202	−	0.354555i
$960$	−3.62358			−0.116951
$961$	29.9995	+	7.81235i	0.967724	+	0.252011i
$962$	−1.54943			−0.0499556
$963$	0.703414	−	2.16489i	0.0226672	−	0.0697625i
$964$	3.87913	+	11.9387i	0.124938	+	0.384521i
$965$	4.63447	+	3.36714i	0.149189	+	0.108392i
$966$	−50.6437			−1.62943
$967$	−40.9969			−1.31837			−0.659185	−	0.751980i	$-0.729099\pi$
$967$	−40.9969			−1.31837			−0.659185	+	0.751980i	$0.729099\pi$
$968$	8.26228	+	6.00290i	0.265560	+	0.192941i
$969$	−9.35112	+	6.79399i	−0.300401	+	0.218254i
$970$	31.2248	−	22.6862i	1.00257	−	0.728409i
$971$	14.9450	−	45.9961i	0.479609	−	1.47608i	−0.360030	−	0.932941i	$-0.617234\pi$
$971$	14.9450	−	45.9961i	0.479609	−	1.47608i	0.839639	−	0.543144i	$-0.182766\pi$
$972$	5.18985	+	3.77065i	0.166465	+	0.120944i
$973$	−8.71032	+	26.8076i	−0.279240	+	0.859413i
$974$	−2.30631	−	7.09808i	−0.0738988	−	0.227437i
$975$	−2.26380	+	1.64475i	−0.0724997	+	0.0526741i
$976$	−6.43606	−	19.8082i	−0.206013	−	0.634043i
$977$	9.05328	+	27.8631i	0.289640	+	0.891420i	0.984969	+	0.172729i	$0.0552585\pi$
$977$	9.05328	+	27.8631i	0.289640	+	0.891420i	−0.695329	+	0.718691i	$0.744742\pi$
$978$	14.6068	−	10.6125i	0.467075	−	0.339350i
$979$	−2.40770	−	7.41015i	−0.0769506	−	0.236829i
$980$	0.863908	−	2.65884i	0.0275965	−	0.0849334i
$981$	−2.76686	−	2.01024i	−0.0883390	−	0.0641821i
$982$	−10.5254	+	32.3939i	−0.335880	+	1.03373i
$983$	42.2600	−	30.7037i	1.34788	−	0.979295i	0.348771	−	0.937208i	$-0.386599\pi$
$983$	42.2600	−	30.7037i	1.34788	−	0.979295i	0.999114	−	0.0420873i	$-0.0134008\pi$
$984$	23.6054	−	17.1503i	0.752512	−	0.546732i
$985$	−17.4518	−	12.6795i	−0.556060	−	0.404001i
$986$	−17.0204			−0.542040
$987$	40.7178			1.29606
$988$	2.36765	+	1.72020i	0.0753250	+	0.0547268i
$989$	15.9104	+	48.9673i	0.505922	+	1.55707i
$990$	1.85755	−	5.71694i	0.0590367	−	0.181696i
$991$	−60.3002			−1.91550			−0.957750	−	0.287601i	$-0.907142\pi$
$991$	−60.3002			−1.91550			−0.957750	+	0.287601i	$0.907142\pi$
$992$	−29.3545	−	3.75950i	−0.932006	−	0.119364i
$993$	−30.0815			−0.954607
$994$	−11.5282	+	35.4803i	−0.365654	+	1.12537i
$995$	1.21234	+	3.73119i	0.0384337	+	0.118287i
$996$	−8.67962	−	6.30611i	−0.275024	−	0.199817i
$997$	−10.5163			−0.333056			−0.166528	−	0.986037i	$-0.553256\pi$
$997$	−10.5163			−0.333056			−0.166528	+	0.986037i	$0.553256\pi$
$998$	−12.4575			−0.394336
$999$	3.27178	+	2.37709i	0.103515	+	0.0752077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.e.287.4	yes	68
31.4	even	5	inner	403.2.k.e.66.4	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.e.66.4	✓	68	31.4	even	5	inner
403.2.k.e.287.4	yes	68	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.537701 + 1.65487i) q^{2} +(0.587091 + 1.80688i) q^{3} +(-0.831453 - 0.604086i) q^{4} -2.54418 q^{5} -3.30584 q^{6} +(-1.97022 - 1.43145i) q^{7} +(-1.36868 + 0.994405i) q^{8} +(-0.493085 + 0.358248i) q^{9} +O(q^{10})\)	\(q+(-0.537701 + 1.65487i) q^{2} +(0.587091 + 1.80688i) q^{3} +(-0.831453 - 0.604086i) q^{4} -2.54418 q^{5} -3.30584 q^{6} +(-1.97022 - 1.43145i) q^{7} +(-1.36868 + 0.994405i) q^{8} +(-0.493085 + 0.358248i) q^{9} +(1.36801 - 4.21030i) q^{10} +(-1.80237 - 1.30950i) q^{11} +(0.603372 - 1.85699i) q^{12} +(0.309017 + 0.951057i) q^{13} +(3.42826 - 2.49077i) q^{14} +(-1.49366 - 4.59702i) q^{15} +(-1.54485 - 4.75455i) q^{16} +(1.72846 - 1.25580i) q^{17} +(-0.327722 - 1.00862i) q^{18} +(-0.879960 + 2.70824i) q^{19} +(2.11536 + 1.53690i) q^{20} +(1.42976 - 4.40034i) q^{21} +(3.13619 - 2.27858i) q^{22} +(-5.08914 + 3.69748i) q^{23} +(-2.60031 - 1.88924i) q^{24} +1.47285 q^{25} -1.74004 q^{26} +(3.67427 + 2.66952i) q^{27} +(0.773426 + 2.38036i) q^{28} +(-1.41478 + 4.35426i) q^{29} +8.41064 q^{30} +(-5.52266 - 0.707300i) q^{31} +5.31528 q^{32} +(1.30795 - 4.02546i) q^{33} +(1.14880 + 3.53564i) q^{34} +(5.01259 + 3.64186i) q^{35} +0.626389 q^{36} +0.890456 q^{37} +(-4.00864 - 2.91245i) q^{38} +(-1.53702 + 1.11671i) q^{39} +(3.48217 - 2.52995i) q^{40} +(-2.80523 + 8.63361i) q^{41} +(6.51322 + 4.73213i) q^{42} +(2.52927 - 7.78429i) q^{43} +(0.707536 + 2.17757i) q^{44} +(1.25450 - 0.911446i) q^{45} +(-3.38243 - 10.4100i) q^{46} +(2.71949 + 8.36973i) q^{47} +(7.68393 - 5.58270i) q^{48} +(-0.330400 - 1.01687i) q^{49} +(-0.791953 + 2.43738i) q^{50} +(3.28385 + 2.38586i) q^{51} +(0.317587 - 0.977431i) q^{52} +(-5.45635 + 3.96427i) q^{53} +(-6.39338 + 4.64506i) q^{54} +(4.58555 + 3.33160i) q^{55} +4.12004 q^{56} -5.41007 q^{57} +(-6.44502 - 4.68258i) q^{58} +(-4.51278 - 13.8889i) q^{59} +(-1.53509 + 4.72451i) q^{60} +4.16615 q^{61} +(4.14003 - 8.75899i) q^{62} +1.48430 q^{63} +(0.231659 - 0.712974i) q^{64} +(-0.786195 - 2.41966i) q^{65} +(5.95834 + 4.32899i) q^{66} +2.93094 q^{67} -2.19575 q^{68} +(-9.66869 - 7.02471i) q^{69} +(-8.72210 + 6.33697i) q^{70} +(-7.12235 + 5.17469i) q^{71} +(0.318634 - 0.980653i) q^{72} +(2.68892 + 1.95362i) q^{73} +(-0.478800 + 1.47359i) q^{74} +(0.864696 + 2.66126i) q^{75} +(2.36765 - 1.72020i) q^{76} +(1.67658 + 5.16000i) q^{77} +(-1.02156 - 3.14404i) q^{78} +(-2.19970 + 1.59818i) q^{79} +(3.93037 + 12.0964i) q^{80} +(-3.23139 + 9.94519i) q^{81} +(-12.7792 - 9.28460i) q^{82} +(1.69794 - 5.22573i) q^{83} +(-3.84695 + 2.79498i) q^{84} +(-4.39752 + 3.19499i) q^{85} +(11.5220 + 8.37124i) q^{86} -8.69823 q^{87} +3.76904 q^{88} +(2.82938 + 2.05567i) q^{89} +(0.833784 + 2.56612i) q^{90} +(0.752557 - 2.31613i) q^{91} +6.46498 q^{92} +(-1.96429 - 10.3940i) q^{93} -15.3131 q^{94} +(2.23878 - 6.89024i) q^{95} +(3.12055 + 9.60408i) q^{96} +(7.05332 + 5.12454i) q^{97} +1.86044 q^{98} +1.35785 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

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