LMFDB - Embedded newform 231.2.i.f.67.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(67,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("231.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.i (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 15x^{8} + 72x^{6} + 120x^{4} + 72x^{2} + 12 $ x^10 + 15x^8 + 72x^6 + 120x^4 + 72x^2 + 12
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			67.4
Root			$-2.42024i$ of defining polynomial
Character	$\chi$	$=$	231.67
Dual form			231.2.i.f.100.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.534421 + 0.925645i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.428788 - 0.742682i) q^{4} +(1.34592 + 2.33120i) q^{5} +1.06884 q^{6} +(-0.855706 - 2.50355i) q^{7} +3.05430 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.534421 + 0.925645i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.428788 - 0.742682i) q^{4} +(1.34592 + 2.33120i) q^{5} +1.06884 q^{6} +(-0.855706 - 2.50355i) q^{7} +3.05430 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.43858 + 2.49169i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.428788 - 0.742682i) q^{12} -3.28888 q^{13} +(1.86009 - 2.13003i) q^{14} +2.69184 q^{15} +(0.774707 + 1.34183i) q^{16} +(0.534421 - 0.925645i) q^{17} +(0.534421 - 0.925645i) q^{18} +(3.17886 + 5.50595i) q^{19} +2.30845 q^{20} +(-2.59599 - 0.510712i) q^{21} -1.06884 q^{22} +(0.774707 + 1.34183i) q^{23} +(1.52715 - 2.64510i) q^{24} +(-1.12300 + 1.94508i) q^{25} +(-1.75765 - 3.04433i) q^{26} -1.00000 q^{27} +(-2.22626 - 0.437974i) q^{28} -8.57566 q^{29} +(1.43858 + 2.49169i) q^{30} +(-1.92879 + 3.34076i) q^{31} +(2.22626 - 3.85599i) q^{32} +(0.500000 + 0.866025i) q^{33} +1.14242 q^{34} +(4.68457 - 5.36440i) q^{35} -0.857576 q^{36} +(-3.91476 - 6.78057i) q^{37} +(-3.39770 + 5.88499i) q^{38} +(-1.64444 + 2.84825i) q^{39} +(4.11084 + 7.12018i) q^{40} -6.87715 q^{41} +(-0.914616 - 2.67590i) q^{42} -2.76571 q^{43} +(0.428788 + 0.742682i) q^{44} +(1.34592 - 2.33120i) q^{45} +(-0.828039 + 1.43421i) q^{46} +(4.56647 + 7.90936i) q^{47} +1.54941 q^{48} +(-5.53553 + 4.28461i) q^{49} -2.40061 q^{50} +(-0.534421 - 0.925645i) q^{51} +(-1.41023 + 2.44259i) q^{52} +(1.77722 - 3.07824i) q^{53} +(-0.534421 - 0.925645i) q^{54} -2.69184 q^{55} +(-2.61358 - 7.64659i) q^{56} +6.35772 q^{57} +(-4.58301 - 7.93801i) q^{58} +(0.774707 - 1.34183i) q^{59} +(1.15423 - 1.99918i) q^{60} +(-6.18471 - 10.7122i) q^{61} -4.12314 q^{62} +(-1.74029 + 1.99284i) q^{63} +7.85787 q^{64} +(-4.42656 - 7.66703i) q^{65} +(-0.534421 + 0.925645i) q^{66} +(4.05193 - 7.01815i) q^{67} +(-0.458307 - 0.793810i) q^{68} +1.54941 q^{69} +(7.46906 + 1.46939i) q^{70} +10.4350 q^{71} +(-1.52715 - 2.64510i) q^{72} +(-7.12501 + 12.3409i) q^{73} +(4.18426 - 7.24736i) q^{74} +(1.12300 + 1.94508i) q^{75} +5.45223 q^{76} +(2.59599 + 0.510712i) q^{77} -3.51529 q^{78} +(-4.69371 - 8.12974i) q^{79} +(-2.08538 + 3.61199i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.67530 - 6.36580i) q^{82} +2.46916 q^{83} +(-1.49243 + 1.70901i) q^{84} +2.87715 q^{85} +(-1.47806 - 2.56007i) q^{86} +(-4.28783 + 7.42674i) q^{87} +(-1.52715 + 2.64510i) q^{88} +(5.81498 + 10.0718i) q^{89} +2.87715 q^{90} +(2.81431 + 8.23388i) q^{91} +1.32874 q^{92} +(1.92879 + 3.34076i) q^{93} +(-4.88084 + 8.45386i) q^{94} +(-8.55698 + 14.8211i) q^{95} +(-2.22626 - 3.85599i) q^{96} +12.6644 q^{97} +(-6.92433 - 2.83415i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9} - 2 q^{10} - 5 q^{11} + 10 q^{12} + 10 q^{13} - 10 q^{14} + 8 q^{15} - 16 q^{16} - 2 q^{17} - 2 q^{18} + 3 q^{19} - 16 q^{20} - 2 q^{21} + 4 q^{22} - 16 q^{23} + 6 q^{24} - 7 q^{25} + 10 q^{26} - 10 q^{27} + 4 q^{28} + 2 q^{30} - 5 q^{31} - 4 q^{32} + 5 q^{33} + 40 q^{34} + 26 q^{35} + 20 q^{36} - 15 q^{37} - 6 q^{38} + 5 q^{39} + 6 q^{40} - 44 q^{41} - 14 q^{42} + 6 q^{43} - 10 q^{44} + 4 q^{45} - 16 q^{46} + 2 q^{47} - 32 q^{48} + 31 q^{49} + 68 q^{50} + 2 q^{51} - 40 q^{52} - 6 q^{53} + 2 q^{54} - 8 q^{55} - 12 q^{56} + 6 q^{57} - 12 q^{58} - 16 q^{59} - 8 q^{60} - 12 q^{61} - 8 q^{62} - q^{63} - 8 q^{64} + 28 q^{65} + 2 q^{66} - 7 q^{67} - 10 q^{68} - 32 q^{69} + 32 q^{70} + 48 q^{71} - 6 q^{72} - 17 q^{73} + 36 q^{74} + 7 q^{75} + 60 q^{76} + 2 q^{77} + 20 q^{78} - 7 q^{79} - 16 q^{80} - 5 q^{81} - 8 q^{82} - 24 q^{83} - 28 q^{84} + 4 q^{85} + 18 q^{86} - 6 q^{88} + 6 q^{89} + 4 q^{90} + 11 q^{91} + 136 q^{92} + 5 q^{93} - 82 q^{94} + 18 q^{95} + 4 q^{96} - 28 q^{97} - 38 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9 - 2 * q^10 - 5 * q^11 + 10 * q^12 + 10 * q^13 - 10 * q^14 + 8 * q^15 - 16 * q^16 - 2 * q^17 - 2 * q^18 + 3 * q^19 - 16 * q^20 - 2 * q^21 + 4 * q^22 - 16 * q^23 + 6 * q^24 - 7 * q^25 + 10 * q^26 - 10 * q^27 + 4 * q^28 + 2 * q^30 - 5 * q^31 - 4 * q^32 + 5 * q^33 + 40 * q^34 + 26 * q^35 + 20 * q^36 - 15 * q^37 - 6 * q^38 + 5 * q^39 + 6 * q^40 - 44 * q^41 - 14 * q^42 + 6 * q^43 - 10 * q^44 + 4 * q^45 - 16 * q^46 + 2 * q^47 - 32 * q^48 + 31 * q^49 + 68 * q^50 + 2 * q^51 - 40 * q^52 - 6 * q^53 + 2 * q^54 - 8 * q^55 - 12 * q^56 + 6 * q^57 - 12 * q^58 - 16 * q^59 - 8 * q^60 - 12 * q^61 - 8 * q^62 - q^63 - 8 * q^64 + 28 * q^65 + 2 * q^66 - 7 * q^67 - 10 * q^68 - 32 * q^69 + 32 * q^70 + 48 * q^71 - 6 * q^72 - 17 * q^73 + 36 * q^74 + 7 * q^75 + 60 * q^76 + 2 * q^77 + 20 * q^78 - 7 * q^79 - 16 * q^80 - 5 * q^81 - 8 * q^82 - 24 * q^83 - 28 * q^84 + 4 * q^85 + 18 * q^86 - 6 * q^88 + 6 * q^89 + 4 * q^90 + 11 * q^91 + 136 * q^92 + 5 * q^93 - 82 * q^94 + 18 * q^95 + 4 * q^96 - 28 * q^97 - 38 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.534421	+	0.925645i	0.377893	+	0.654530i	0.990755	−	0.135660i	$-0.0433154\pi$
$2$	0.534421	+	0.925645i	0.377893	+	0.654530i	−0.612863	+	0.790190i	$0.709982\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.428788	−	0.742682i	0.214394	−	0.371341i
$5$	1.34592	+	2.33120i	0.601913	+	1.04254i	0.992531	+	0.121991i	$0.0389280\pi$
$5$	1.34592	+	2.33120i	0.601913	+	1.04254i	−0.390618	+	0.920553i	$0.627739\pi$
$6$	1.06884			0.436353
$7$	−0.855706	−	2.50355i	−0.323427	−	0.946253i
$7$	−0.855706	−	2.50355i	−0.323427	−	0.946253i
$8$	3.05430			1.07986
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.43858	+	2.49169i	−0.454917	+	0.787940i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−0.428788	−	0.742682i	−0.123780	−	0.214394i
$13$	−3.28888			−0.912171			−0.456085	−	0.889936i	$-0.650749\pi$
$13$	−3.28888			−0.912171			−0.456085	+	0.889936i	$0.650749\pi$
$14$	1.86009	−	2.13003i	0.497130	−	0.569275i
$15$	2.69184			0.695030
$16$	0.774707	+	1.34183i	0.193677	+	0.335458i
$17$	0.534421	−	0.925645i	0.129616	−	0.224502i	−0.793912	−	0.608033i	$-0.791959\pi$
$17$	0.534421	−	0.925645i	0.129616	−	0.224502i	0.923528	+	0.383531i	$0.125292\pi$
$18$	0.534421	−	0.925645i	0.125964	−	0.218177i
$19$	3.17886	+	5.50595i	0.729281	+	1.26315i	0.957188	+	0.289468i	$0.0934785\pi$
$19$	3.17886	+	5.50595i	0.729281	+	1.26315i	−0.227907	+	0.973683i	$0.573188\pi$
$20$	2.30845			0.516186
$21$	−2.59599	−	0.510712i	−0.566492	−	0.111446i
$22$	−1.06884			−0.227878
$23$	0.774707	+	1.34183i	0.161537	+	0.279791i	0.935420	−	0.353538i	$-0.115021\pi$
$23$	0.774707	+	1.34183i	0.161537	+	0.279791i	−0.773883	+	0.633329i	$0.781688\pi$
$24$	1.52715	−	2.64510i	0.311728	−	0.539929i
$25$	−1.12300	+	1.94508i	−0.224599	+	0.389017i
$26$	−1.75765	−	3.04433i	−0.344703	−	0.597043i
$27$	−1.00000			−0.192450
$28$	−2.22626	−	0.437974i	−0.420723	−	0.0827693i
$29$	−8.57566			−1.59246			−0.796230	−	0.604994i	$-0.793175\pi$
$29$	−8.57566			−1.59246			−0.796230	+	0.604994i	$0.793175\pi$
$30$	1.43858	+	2.49169i	0.262647	+	0.454917i
$31$	−1.92879	+	3.34076i	−0.346421	+	0.600018i	−0.985611	−	0.169031i	$-0.945936\pi$
$31$	−1.92879	+	3.34076i	−0.346421	+	0.600018i	0.639190	+	0.769049i	$0.279270\pi$
$32$	2.22626	−	3.85599i	0.393551	−	0.681650i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	1.14242			0.195924
$35$	4.68457	−	5.36440i	0.791836	−	0.906749i
$36$	−0.857576			−0.142929
$37$	−3.91476	−	6.78057i	−0.643583	−	1.11472i	−0.984627	−	0.174671i	$-0.944114\pi$
$37$	−3.91476	−	6.78057i	−0.643583	−	1.11472i	0.341044	−	0.940047i	$-0.389219\pi$
$38$	−3.39770	+	5.88499i	−0.551180	+	0.954672i
$39$	−1.64444	+	2.84825i	−0.263321	+	0.456085i
$40$	4.11084	+	7.12018i	0.649981	+	1.12580i
$41$	−6.87715			−1.07403			−0.537015	−	0.843573i	$-0.680448\pi$
$41$	−6.87715			−1.07403			−0.537015	+	0.843573i	$0.680448\pi$
$42$	−0.914616	−	2.67590i	−0.141128	−	0.412901i
$43$	−2.76571			−0.421767			−0.210884	−	0.977511i	$-0.567634\pi$
$43$	−2.76571			−0.421767			−0.210884	+	0.977511i	$0.567634\pi$
$44$	0.428788	+	0.742682i	0.0646422	+	0.111964i
$45$	1.34592	−	2.33120i	0.200638	−	0.347515i
$46$	−0.828039	+	1.43421i	−0.122088	+	0.211462i
$47$	4.56647	+	7.90936i	0.666089	+	1.15370i	0.978989	+	0.203913i	$0.0653661\pi$
$47$	4.56647	+	7.90936i	0.666089	+	1.15370i	−0.312900	+	0.949786i	$0.601301\pi$
$48$	1.54941			0.223639
$49$	−5.53553	+	4.28461i	−0.790790	+	0.612087i
$50$	−2.40061			−0.339498
$51$	−0.534421	−	0.925645i	−0.0748339	−	0.129616i
$52$	−1.41023	+	2.44259i	−0.195564	+	0.338727i
$53$	1.77722	−	3.07824i	0.244120	−	0.422829i	−0.717764	−	0.696287i	$-0.754834\pi$
$53$	1.77722	−	3.07824i	0.244120	−	0.422829i	0.961884	+	0.273458i	$0.0881675\pi$
$54$	−0.534421	−	0.925645i	−0.0727255	−	0.125964i
$55$	−2.69184			−0.362967
$56$	−2.61358	−	7.64659i	−0.349255	−	1.02182i
$57$	6.35772			0.842101
$58$	−4.58301	−	7.93801i	−0.601779	−	1.04231i
$59$	0.774707	−	1.34183i	0.100858	−	0.174692i	−0.811180	−	0.584796i	$-0.801174\pi$
$59$	0.774707	−	1.34183i	0.100858	−	0.174692i	0.912038	+	0.410105i	$0.134508\pi$
$60$	1.15423	−	1.99918i	0.149010	−	0.258093i
$61$	−6.18471	−	10.7122i	−0.791871	−	1.37156i	−0.924807	−	0.380436i	$-0.875774\pi$
$61$	−6.18471	−	10.7122i	−0.791871	−	1.37156i	0.132936	−	0.991125i	$-0.457560\pi$
$62$	−4.12314			−0.523639
$63$	−1.74029	+	1.99284i	−0.219255	+	0.251074i
$64$	7.85787			0.982233
$65$	−4.42656	−	7.66703i	−0.549048	−	0.950978i
$66$	−0.534421	+	0.925645i	−0.0657827	+	0.113939i
$67$	4.05193	−	7.01815i	0.495022	−	0.857403i	−0.504962	−	0.863142i	$-0.668493\pi$
$67$	4.05193	−	7.01815i	0.495022	−	0.857403i	0.999984	+	0.00573872i	$0.00182670\pi$
$68$	−0.458307	−	0.793810i	−0.0555778	−	0.0962636i
$69$	1.54941			0.186527
$70$	7.46906	+	1.46939i	0.892723	+	0.175626i
$71$	10.4350			1.23841			0.619206	−	0.785229i	$-0.287455\pi$
$71$	10.4350			1.23841			0.619206	+	0.785229i	$0.287455\pi$
$72$	−1.52715	−	2.64510i	−0.179976	−	0.311728i
$73$	−7.12501	+	12.3409i	−0.833919	+	1.44439i	0.0609879	+	0.998139i	$0.480575\pi$
$73$	−7.12501	+	12.3409i	−0.833919	+	1.44439i	−0.894907	+	0.446252i	$0.852758\pi$
$74$	4.18426	−	7.24736i	0.486411	−	0.842488i
$75$	1.12300	+	1.94508i	0.129672	+	0.224599i
$76$	5.45223			0.625413
$77$	2.59599	+	0.510712i	0.295841	+	0.0582010i
$78$	−3.51529			−0.398029
$79$	−4.69371	−	8.12974i	−0.528083	−	0.914667i	−0.999464	−	0.0327372i	$-0.989578\pi$
$79$	−4.69371	−	8.12974i	−0.528083	−	0.914667i	0.471381	−	0.881930i	$-0.343756\pi$
$80$	−2.08538	+	3.61199i	−0.233153	+	0.403833i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.67530	−	6.36580i	−0.405869	−	0.702985i
$83$	2.46916			0.271026			0.135513	−	0.990776i	$-0.456732\pi$
$83$	2.46916			0.271026			0.135513	+	0.990776i	$0.456732\pi$
$84$	−1.49243	+	1.70901i	−0.162837	+	0.186468i
$85$	2.87715			0.312071
$86$	−1.47806	−	2.56007i	−0.159383	−	0.276059i
$87$	−4.28783	+	7.42674i	−0.459704	+	0.796230i
$88$	−1.52715	+	2.64510i	−0.162795	+	0.281969i
$89$	5.81498	+	10.0718i	0.616387	+	1.06761i	0.990140	+	0.140084i	$0.0447374\pi$
$89$	5.81498	+	10.0718i	0.616387	+	1.06761i	−0.373753	+	0.927528i	$0.621929\pi$
$90$	2.87715			0.303278
$91$	2.81431	+	8.23388i	0.295020	+	0.863145i
$92$	1.32874			0.138531
$93$	1.92879	+	3.34076i	0.200006	+	0.346421i
$94$	−4.88084	+	8.45386i	−0.503420	+	0.871950i
$95$	−8.55698	+	14.8211i	−0.877927	+	1.52061i
$96$	−2.22626	−	3.85599i	−0.227217	−	0.393551i
$97$	12.6644			1.28587			0.642936	−	0.765920i	$-0.277716\pi$
$97$	12.6644			1.28587			0.642936	+	0.765920i	$0.277716\pi$
$98$	−6.92433	−	2.83415i	−0.699463	−	0.286292i
$99$	1.00000			0.100504
$100$	0.963053	+	1.66806i	0.0963053	+	0.166806i
$101$	2.73842	−	4.74308i	0.272483	−	0.471954i	−0.697014	−	0.717057i	$-0.745489\pi$
$101$	2.73842	−	4.74308i	0.272483	−	0.471954i	0.969497	+	0.245103i	$0.0788219\pi$
$102$	0.571212	−	0.989369i	0.0565584	−	0.0979621i
$103$	3.16327	+	5.47894i	0.311686	+	0.539856i	0.978727	−	0.205165i	$-0.0657730\pi$
$103$	3.16327	+	5.47894i	0.311686	+	0.539856i	−0.667042	+	0.745021i	$0.732440\pi$
$104$	−10.0452			−0.985015
$105$	−2.30342	−	6.73915i	−0.224791	−	0.657674i
$106$	3.79914			0.369005
$107$	1.75341	+	3.03699i	0.169508	+	0.293597i	0.938247	−	0.345966i	$-0.112449\pi$
$107$	1.75341	+	3.03699i	0.169508	+	0.293597i	−0.768739	+	0.639563i	$0.779115\pi$
$108$	−0.428788	+	0.742682i	−0.0412601	+	0.0714646i
$109$	−1.90497	+	3.29951i	−0.182463	+	0.316036i	−0.942719	−	0.333588i	$-0.891740\pi$
$109$	−1.90497	+	3.29951i	−0.182463	+	0.316036i	0.760255	+	0.649624i	$0.225074\pi$
$110$	−1.43858	−	2.49169i	−0.137163	−	0.237573i
$111$	−7.82952			−0.743145
$112$	2.69642	−	3.08773i	0.254788	−	0.291763i
$113$	11.1319			1.04720			0.523601	−	0.851964i	$-0.324588\pi$
$113$	11.1319			1.04720			0.523601	+	0.851964i	$0.324588\pi$
$114$	3.39770	+	5.88499i	0.318224	+	0.551180i
$115$	−2.08538	+	3.61199i	−0.194463	+	0.336820i
$116$	−3.67714	+	6.36899i	−0.341414	+	0.591346i
$117$	1.64444	+	2.84825i	0.152028	+	0.263321i
$118$	1.65608			0.152454
$119$	−2.77471	−	0.545871i	−0.254357	−	0.0500399i
$120$	8.22168			0.750533
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	6.61048	−	11.4497i	0.598485	−	1.03661i
$123$	−3.43858	+	5.95579i	−0.310046	+	0.537015i
$124$	1.65408	+	2.86495i	0.148541	+	0.257280i
$125$	7.41335			0.663070
$126$	−2.77471	−	0.545871i	−0.247191	−	0.0486300i
$127$	12.6951			1.12650			0.563252	−	0.826285i	$-0.309550\pi$
$127$	12.6951			1.12650			0.563252	+	0.826285i	$0.309550\pi$
$128$	−0.253106	−	0.438393i	−0.0223717	−	0.0387488i
$129$	−1.38286	+	2.39518i	−0.121754	+	0.210884i
$130$	4.73130	−	8.19485i	0.414962	−	0.718736i
$131$	−3.27284	−	5.66872i	−0.285949	−	0.495278i	0.686890	−	0.726762i	$-0.258976\pi$
$131$	−3.27284	−	5.66872i	−0.285949	−	0.495278i	−0.972839	+	0.231483i	$0.925642\pi$
$132$	0.857576			0.0746424
$133$	11.0642	−	12.6699i	0.959392	−	1.09862i
$134$	8.66175			0.748261
$135$	−1.34592	−	2.33120i	−0.115838	−	0.200638i
$136$	1.63228	−	2.82720i	0.139967	−	0.242430i
$137$	−10.7067	+	18.5445i	−0.914733	+	1.58436i	−0.107441	+	0.994211i	$0.534266\pi$
$137$	−10.7067	+	18.5445i	−0.914733	+	1.58436i	−0.807292	+	0.590152i	$0.799068\pi$
$138$	0.828039	+	1.43421i	0.0704874	+	0.122088i
$139$	0.850905			0.0721728			0.0360864	−	0.999349i	$-0.488511\pi$
$139$	0.850905			0.0721728			0.0360864	+	0.999349i	$0.488511\pi$
$140$	−1.97536	−	5.77933i	−0.166948	−	0.488443i
$141$	9.13295			0.769133
$142$	5.57671	+	9.65914i	0.467987	+	0.810577i
$143$	1.64444	−	2.84825i	0.137515	−	0.238183i
$144$	0.774707	−	1.34183i	0.0645589	−	0.111819i
$145$	−11.5421	−	19.9916i	−0.958523	−	1.66021i
$146$	−15.2310			−1.26053
$147$	0.942814	+	6.93622i	0.0777620	+	0.572090i
$148$	−6.71441			−0.551921
$149$	7.89214	+	13.6696i	0.646550	+	1.11986i	0.983941	+	0.178492i	$0.0571220\pi$
$149$	7.89214	+	13.6696i	0.646550	+	1.11986i	−0.337392	+	0.941364i	$0.609545\pi$
$150$	−1.20031	+	2.07899i	−0.0980045	+	0.169749i
$151$	8.52968	−	14.7738i	0.694136	−	1.20228i	−0.276336	−	0.961061i	$-0.589120\pi$
$151$	8.52968	−	14.7738i	0.694136	−	1.20228i	0.970471	−	0.241217i	$-0.0775466\pi$
$152$	9.70919	+	16.8168i	0.787519	+	1.36402i
$153$	−1.06884			−0.0864108
$154$	0.914616	+	2.67590i	0.0737018	+	0.215630i
$155$	−10.3840			−0.834060
$156$	1.41023	+	2.44259i	0.112909	+	0.195564i
$157$	9.10941	−	15.7780i	0.727010	−	1.25922i	−0.231132	−	0.972922i	$-0.574243\pi$
$157$	9.10941	−	15.7780i	0.727010	−	1.25922i	0.958141	−	0.286295i	$-0.0924239\pi$
$158$	5.01683	−	8.68941i	0.399118	−	0.691292i
$159$	−1.77722	−	3.07824i	−0.140943	−	0.244120i
$160$	11.9855			0.947533
$161$	2.69642	−	3.08773i	0.212508	−	0.243347i
$162$	−1.06884			−0.0839762
$163$	−4.95750	−	8.58665i	−0.388302	−	0.672558i	0.603920	−	0.797045i	$-0.293605\pi$
$163$	−4.95750	−	8.58665i	−0.388302	−	0.672558i	−0.992221	+	0.124487i	$0.960271\pi$
$164$	−2.94884	+	5.10754i	−0.230266	+	0.398832i
$165$	−1.34592	+	2.33120i	−0.104780	+	0.181484i
$166$	1.31957	+	2.28557i	0.102419	+	0.177394i
$167$	−0.193790			−0.0149960			−0.00749798	−	0.999972i	$-0.502387\pi$
$167$	−0.193790			−0.0149960			−0.00749798	+	0.999972i	$0.502387\pi$
$168$	−7.92893	−	1.55987i	−0.611731	−	0.120346i
$169$	−2.18328			−0.167944
$170$	1.53761	+	2.66322i	0.117929	+	0.204260i
$171$	3.17886	−	5.50595i	0.243094	−	0.421050i
$172$	−1.18590	+	2.05404i	−0.0904243	+	0.156619i
$173$	−4.51409	−	7.81863i	−0.343200	−	0.594439i	0.641825	−	0.766851i	$-0.278177\pi$
$173$	−4.51409	−	7.81863i	−0.343200	−	0.594439i	−0.985025	+	0.172411i	$0.944844\pi$
$174$	−9.16603			−0.694875
$175$	5.83057	+	1.14705i	0.440750	+	0.0867091i
$176$	−1.54941			−0.116791
$177$	−0.774707	−	1.34183i	−0.0582305	−	0.100858i
$178$	−6.21530	+	10.7652i	−0.465856	+	0.806887i
$179$	−6.11215	+	10.5866i	−0.456843	+	0.791276i	−0.998792	−	0.0491356i	$-0.984353\pi$
$179$	−6.11215	+	10.5866i	−0.456843	+	0.791276i	0.541949	+	0.840412i	$0.317687\pi$
$180$	−1.15423	−	1.99918i	−0.0860310	−	0.149010i
$181$	−18.5108			−1.37590			−0.687950	−	0.725758i	$-0.741489\pi$
$181$	−18.5108			−1.37590			−0.687950	+	0.725758i	$0.741489\pi$
$182$	−6.11761	+	7.00541i	−0.453468	+	0.519276i
$183$	−12.3694			−0.914374
$184$	2.36619	+	4.09835i	0.174437	+	0.302135i
$185$	10.5379	−	18.2522i	0.774762	−	1.34193i
$186$	−2.06157	+	3.57074i	−0.151162	+	0.261820i
$187$	0.534421	+	0.925645i	0.0390808	+	0.0676899i
$188$	7.83219			0.571221
$189$	0.855706	+	2.50355i	0.0622435	+	0.182107i
$190$	−18.2921			−1.32705
$191$	−9.23277	−	15.9916i	−0.668060	−	1.15711i	−0.978446	−	0.206503i	$-0.933792\pi$
$191$	−9.23277	−	15.9916i	−0.668060	−	1.15711i	0.310386	−	0.950611i	$-0.399542\pi$
$192$	3.92893	−	6.80511i	0.283546	−	0.491117i
$193$	8.52099	−	14.7588i	0.613354	−	1.06236i	−0.377317	−	0.926084i	$-0.623153\pi$
$193$	8.52099	−	14.7588i	0.613354	−	1.06236i	0.990671	−	0.136276i	$-0.0435135\pi$
$194$	6.76811	+	11.7227i	0.485922	+	0.841641i
$195$	−8.85313			−0.633986
$196$	0.808534	+	5.94833i	0.0577524	+	0.424881i
$197$	5.45281			0.388497			0.194248	−	0.980952i	$-0.437773\pi$
$197$	5.45281			0.388497			0.194248	+	0.980952i	$0.437773\pi$
$198$	0.534421	+	0.925645i	0.0379797	+	0.0657827i
$199$	−2.16574	+	3.75117i	−0.153525	+	0.265913i	−0.932521	−	0.361116i	$-0.882396\pi$
$199$	−2.16574	+	3.75117i	−0.153525	+	0.265913i	0.778996	+	0.627029i	$0.215729\pi$
$200$	−3.42996	+	5.94087i	−0.242535	+	0.420083i
$201$	−4.05193	−	7.01815i	−0.285801	−	0.495022i
$202$	5.85387			0.411877
$203$	7.33825	+	21.4696i	0.515044	+	1.50687i
$204$	−0.916613			−0.0641758
$205$	−9.25609	−	16.0320i	−0.646473	−	1.11972i
$206$	−3.38103	+	5.85612i	−0.235568	+	0.408015i
$207$	0.774707	−	1.34183i	0.0538458	−	0.0932637i
$208$	−2.54792	−	4.41312i	−0.176666	−	0.305995i
$209$	−6.35772			−0.439773
$210$	5.00706	−	5.73370i	0.345520	−	0.395663i
$211$	26.0751			1.79508			0.897542	−	0.440929i	$-0.145351\pi$
$211$	26.0751			1.79508			0.897542	+	0.440929i	$0.145351\pi$
$212$	−1.52410	−	2.63982i	−0.104676	−	0.181304i
$213$	5.21752	−	9.03701i	0.357499	−	0.619206i
$214$	−1.87412	+	3.24607i	−0.128112	+	0.221897i
$215$	−3.72242	−	6.44743i	−0.253867	−	0.439711i
$216$	−3.05430			−0.207819
$217$	10.0142	+	1.97011i	0.679811	+	0.133740i
$218$	−4.07223			−0.275807
$219$	7.12501	+	12.3409i	0.481464	+	0.833919i
$220$	−1.15423	+	1.99918i	−0.0778180	+	0.134785i
$221$	−1.75765	+	3.04433i	−0.118232	+	0.204784i
$222$	−4.18426	−	7.24736i	−0.280829	−	0.486411i
$223$	13.3681			0.895196			0.447598	−	0.894235i	$-0.352280\pi$
$223$	13.3681			0.895196			0.447598	+	0.894235i	$0.352280\pi$
$224$	−11.5587	−	2.27395i	−0.772298	−	0.151935i
$225$	2.24599			0.149733
$226$	5.94913	+	10.3042i	0.395730	+	0.685425i
$227$	11.3789	−	19.7089i	0.755247	−	1.30813i	−0.190005	−	0.981783i	$-0.560850\pi$
$227$	11.3789	−	19.7089i	0.755247	−	1.30813i	0.945252	−	0.326342i	$-0.105816\pi$
$228$	2.72611	−	4.72177i	0.180541	−	0.312707i
$229$	−12.7815	−	22.1382i	−0.844627	−	1.46294i	−0.885945	−	0.463791i	$-0.846489\pi$
$229$	−12.7815	−	22.1382i	−0.844627	−	1.46294i	0.0413181	−	0.999146i	$-0.486844\pi$
$230$	−4.45790			−0.293945
$231$	1.74029	−	1.99284i	0.114502	−	0.131119i
$232$	−26.1926			−1.71963
$233$	11.2338	+	19.4576i	0.735952	+	1.27471i	0.954304	+	0.298837i	$0.0965985\pi$
$233$	11.2338	+	19.4576i	0.735952	+	1.27471i	−0.218352	+	0.975870i	$0.570068\pi$
$234$	−1.75765	+	3.04433i	−0.114901	+	0.199014i
$235$	−12.2922	+	21.2907i	−0.801855	+	1.38885i
$236$	−0.664369	−	1.15072i	−0.0432468	−	0.0749056i
$237$	−9.38741			−0.609778
$238$	−0.977580	−	2.86012i	−0.0633671	−	0.185394i
$239$	−13.1701			−0.851900			−0.425950	−	0.904747i	$-0.640060\pi$
$239$	−13.1701			−0.851900			−0.425950	+	0.904747i	$0.640060\pi$
$240$	2.08538	+	3.61199i	0.134611	+	0.233153i
$241$	−7.27537	+	12.6013i	−0.468648	+	0.811722i	−0.999358	−	0.0358316i	$-0.988592\pi$
$241$	−7.27537	+	12.6013i	−0.468648	+	0.811722i	0.530710	+	0.847553i	$0.321925\pi$
$242$	0.534421	−	0.925645i	0.0343539	−	0.0595027i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−10.6077			−0.679089
$245$	−17.4387	−	7.13770i	−1.11412	−	0.456011i
$246$	−7.35059			−0.468657
$247$	−10.4549	−	18.1084i	−0.665229	−	1.15221i
$248$	−5.89109	+	10.2037i	−0.374085	+	0.647934i
$249$	1.23458	−	2.13836i	0.0782384	−	0.135513i
$250$	3.96185	+	6.86213i	0.250569	+	0.433999i
$251$	−5.15996			−0.325694			−0.162847	−	0.986651i	$-0.552068\pi$
$251$	−5.15996			−0.325694			−0.162847	+	0.986651i	$0.552068\pi$
$252$	0.733833	+	2.14698i	0.0462271	+	0.135247i
$253$	−1.54941			−0.0974108
$254$	6.78451	+	11.7511i	0.425698	+	0.737331i
$255$	1.43858	−	2.49169i	0.0900871	−	0.156035i
$256$	8.12840	−	14.0788i	0.508025	−	0.879925i
$257$	−7.41173	−	12.8375i	−0.462331	−	0.800781i	0.536746	−	0.843744i	$-0.319653\pi$
$257$	−7.41173	−	12.8375i	−0.462331	−	0.800781i	−0.999077	+	0.0429634i	$0.986320\pi$
$258$	−2.95611			−0.184039
$259$	−13.6256	+	15.6030i	−0.846654	+	0.969522i
$260$	−7.59223			−0.470850
$261$	4.28783	+	7.42674i	0.265410	+	0.459704i
$262$	3.49815	−	6.05897i	0.216116	−	0.374324i
$263$	−7.73443	+	13.3964i	−0.476926	+	0.826059i	−0.999650	−	0.0264421i	$-0.991582\pi$
$263$	−7.73443	+	13.3964i	−0.476926	+	0.826059i	0.522725	+	0.852502i	$0.324916\pi$
$264$	1.52715	+	2.64510i	0.0939895	+	0.162795i
$265$	9.56799			0.587757
$266$	17.6408	+	3.47049i	1.08163	+	0.212790i
$267$	11.6300			0.711742
$268$	−3.47483	−	6.01859i	−0.212259	−	0.367644i
$269$	2.95721	−	5.12204i	0.180304	−	0.312296i	−0.761680	−	0.647954i	$-0.775625\pi$
$269$	2.95721	−	5.12204i	0.180304	−	0.312296i	0.941984	+	0.335657i	$0.108958\pi$
$270$	1.43858	−	2.49169i	0.0875489	−	0.151639i
$271$	4.64510	+	8.04555i	0.282170	+	0.488733i	0.971919	−	0.235316i	$-0.0756125\pi$
$271$	4.64510	+	8.04555i	0.282170	+	0.488733i	−0.689749	+	0.724049i	$0.742279\pi$
$272$	1.65608			0.100415
$273$	8.53790	+	1.67967i	0.516737	+	0.101658i
$274$	−22.8875			−1.38268
$275$	−1.12300	−	1.94508i	−0.0677192	−	0.117293i
$276$	0.664369	−	1.15072i	0.0399903	−	0.0692653i
$277$	−4.78333	+	8.28497i	−0.287402	+	0.497796i	−0.973189	−	0.230007i	$-0.926125\pi$
$277$	−4.78333	+	8.28497i	−0.287402	+	0.497796i	0.685787	+	0.727803i	$0.259458\pi$
$278$	0.454742	+	0.787636i	0.0272736	+	0.0472393i
$279$	3.85758			0.230947
$280$	14.3081	−	16.3845i	0.855070	−	0.979160i
$281$	−13.0057			−0.775853			−0.387927	−	0.921690i	$-0.626809\pi$
$281$	−13.0057			−0.775853			−0.387927	+	0.921690i	$0.626809\pi$
$282$	4.88084	+	8.45386i	0.290650	+	0.503420i
$283$	−12.1118	+	20.9782i	−0.719971	+	1.24703i	0.241039	+	0.970515i	$0.422512\pi$
$283$	−12.1118	+	20.9782i	−0.719971	+	1.24703i	−0.961011	+	0.276512i	$0.910822\pi$
$284$	4.47442	−	7.74992i	0.265508	−	0.459873i
$285$	8.55698	+	14.8211i	0.506872	+	0.877927i
$286$	3.51529			0.207864
$287$	5.88482	+	17.2173i	0.347370	+	1.01630i
$288$	−4.45252			−0.262367
$289$	7.92879	+	13.7331i	0.466399	+	0.807827i
$290$	12.3367	−	21.3678i	0.724438	−	1.25476i
$291$	6.33218	−	10.9677i	0.371199	−	0.642936i
$292$	6.11023	+	10.5832i	0.357574	+	0.619337i
$293$	3.05010			0.178189			0.0890944	−	0.996023i	$-0.471603\pi$
$293$	3.05010			0.178189			0.0890944	+	0.996023i	$0.471603\pi$
$294$	−5.91661	+	4.57957i	−0.345064	+	0.267086i
$295$	4.17077			0.242832
$296$	−11.9568	−	20.7099i	−0.694978	−	1.20374i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	−8.43546	+	14.6106i	−0.488653	+	0.846372i
$299$	−2.54792	−	4.41312i	−0.147350	−	0.255217i
$300$	1.92611			0.111204
$301$	2.36664	+	6.92410i	0.136411	+	0.399098i
$302$	18.2338			1.04924
$303$	−2.73842	−	4.74308i	−0.157318	−	0.272483i
$304$	−4.92537	+	8.53099i	−0.282489	+	0.489286i
$305$	16.6482	−	28.8356i	0.953275	−	1.65112i
$306$	−0.571212	−	0.989369i	−0.0326540	−	0.0565584i
$307$	20.5254			1.17145			0.585723	−	0.810511i	$-0.300811\pi$
$307$	20.5254			1.17145			0.585723	+	0.810511i	$0.300811\pi$
$308$	1.49243	−	1.70901i	0.0850389	−	0.0973799i
$309$	6.32653			0.359904
$310$	−5.54941	−	9.61187i	−0.315185	−	0.545917i
$311$	−3.99768	+	6.92418i	−0.226687	+	0.392634i	−0.956824	−	0.290667i	$-0.906123\pi$
$311$	−3.99768	+	6.92418i	−0.226687	+	0.392634i	0.730137	+	0.683301i	$0.239456\pi$
$312$	−5.02261	+	8.69941i	−0.284349	+	0.492507i
$313$	−7.95736	−	13.7825i	−0.449776	−	0.779036i	0.548595	−	0.836088i	$-0.315163\pi$
$313$	−7.95736	−	13.7825i	−0.449776	−	0.779036i	−0.998371	+	0.0570527i	$0.981830\pi$
$314$	19.4730			1.09893
$315$	−6.98799	−	1.37475i	−0.393729	−	0.0774586i
$316$	−8.05042			−0.452871
$317$	−13.3958	−	23.2022i	−0.752381	−	1.30316i	−0.946666	−	0.322218i	$-0.895572\pi$
$317$	−13.3958	−	23.2022i	−0.752381	−	1.30316i	0.194284	−	0.980945i	$-0.437762\pi$
$318$	1.89957	−	3.29015i	0.106523	−	0.184503i
$319$	4.28783	−	7.42674i	0.240072	−	0.415818i
$320$	10.5761	+	18.3183i	0.591219	+	1.02402i
$321$	3.50682			0.195731
$322$	4.29917	+	0.845779i	0.239583	+	0.0471334i
$323$	6.79540			0.378106
$324$	0.428788	+	0.742682i	0.0238215	+	0.0412601i
$325$	3.69339	−	6.39715i	0.204873	−	0.354850i
$326$	5.29879	−	9.17778i	0.293473	−	0.508310i
$327$	1.90497	+	3.29951i	0.105345	+	0.182463i
$328$	−21.0049			−1.15980
$329$	15.8939	−	18.2005i	0.876261	−	1.00343i
$330$	−2.87715			−0.158382
$331$	5.06134	+	8.76650i	0.278196	+	0.481850i	0.970937	−	0.239337i	$-0.0769300\pi$
$331$	5.06134	+	8.76650i	0.278196	+	0.481850i	−0.692740	+	0.721187i	$0.743597\pi$
$332$	1.05875	−	1.83380i	0.0581062	−	0.100643i
$333$	−3.91476	+	6.78057i	−0.214528	+	0.371573i
$334$	−0.103566	−	0.179381i	−0.00566686	−	0.00981530i
$335$	21.8143			1.19184
$336$	−1.32584	−	3.87903i	−0.0723307	−	0.211619i
$337$	1.36539			0.0743777			0.0371889	−	0.999308i	$-0.488160\pi$
$337$	1.36539			0.0743777			0.0371889	+	0.999308i	$0.488160\pi$
$338$	−1.16679	−	2.02094i	−0.0634650	−	0.109925i
$339$	5.56596	−	9.64052i	0.302301	−	0.523601i
$340$	1.23369	−	2.13681i	0.0669061	−	0.115885i
$341$	−1.92879	−	3.34076i	−0.104450	−	0.180912i
$342$	6.79540			0.367453
$343$	15.4635	+	10.1921i	0.834952	+	0.550323i
$344$	−8.44731			−0.455448
$345$	2.08538	+	3.61199i	0.112273	+	0.194463i
$346$	4.82485	−	8.35689i	0.259386	−	0.449269i
$347$	12.6539	−	21.9171i	0.679295	−	1.17657i	−0.295898	−	0.955220i	$-0.595619\pi$
$347$	12.6539	−	21.9171i	0.679295	−	1.17657i	0.975193	−	0.221355i	$-0.0710478\pi$
$348$	3.67714	+	6.36899i	0.197115	+	0.341414i
$349$	−5.48986			−0.293866			−0.146933	−	0.989146i	$-0.546940\pi$
$349$	−5.48986			−0.293866			−0.146933	+	0.989146i	$0.546940\pi$
$350$	2.05422	+	6.01005i	0.109803	+	0.321251i
$351$	3.28888			0.175547
$352$	2.22626	+	3.85599i	0.118660	+	0.205525i
$353$	−8.67185	+	15.0201i	−0.461556	+	0.799438i	−0.999039	−	0.0438363i	$-0.986042\pi$
$353$	−8.67185	+	15.0201i	−0.461556	+	0.799438i	0.537483	+	0.843275i	$0.319375\pi$
$354$	0.828039	−	1.43421i	0.0440098	−	0.0762272i
$355$	14.0447	+	24.3262i	0.745416	+	1.29110i
$356$	9.97357			0.528598
$357$	−1.86009	+	2.13003i	−0.0984465	+	0.112733i
$358$	−13.0658			−0.690552
$359$	−4.77269	−	8.26654i	−0.251893	−	0.436292i	0.712154	−	0.702023i	$-0.247720\pi$
$359$	−4.77269	−	8.26654i	−0.251893	−	0.436292i	−0.964047	+	0.265732i	$0.914386\pi$
$360$	4.11084	−	7.12018i	0.216660	−	0.375266i
$361$	−10.7103	+	18.5508i	−0.563701	+	0.976358i
$362$	−9.89259	−	17.1345i	−0.519943	−	0.900568i
$363$	−1.00000			−0.0524864
$364$	7.32190	+	1.44044i	0.383772	+	0.0754997i
$365$	−38.3587			−2.00779
$366$	−6.61048	−	11.4497i	−0.345535	−	0.598485i
$367$	−3.30873	+	5.73088i	−0.172714	+	0.299150i	−0.939368	−	0.342911i	$-0.888587\pi$
$367$	−3.30873	+	5.73088i	−0.172714	+	0.299150i	0.766654	+	0.642061i	$0.221920\pi$
$368$	−1.20034	+	2.07905i	−0.0625721	+	0.108378i
$369$	3.43858	+	5.95579i	0.179005	+	0.310046i
$370$	22.5267			1.17111
$371$	−9.22731	−	1.81530i	−0.479058	−	0.0942455i
$372$	3.30816			0.171520
$373$	16.3575	+	28.3320i	0.846959	+	1.46698i	0.883909	+	0.467659i	$0.154902\pi$
$373$	16.3575	+	28.3320i	0.846959	+	1.46698i	−0.0369504	+	0.999317i	$0.511764\pi$
$374$	−0.571212	+	0.989369i	−0.0295367	+	0.0511590i
$375$	3.70667	−	6.42015i	0.191412	−	0.331535i
$376$	13.9474	+	24.1576i	0.719281	+	1.24583i
$377$	28.2043			1.45260
$378$	−1.86009	+	2.13003i	−0.0956728	+	0.109557i
$379$	−7.69346			−0.395186			−0.197593	−	0.980284i	$-0.563312\pi$
$379$	−7.69346			−0.395186			−0.197593	+	0.980284i	$0.563312\pi$
$380$	7.33825	+	12.7102i	0.376444	+	0.652021i
$381$	6.34753	−	10.9942i	0.325194	−	0.563252i
$382$	9.86838	−	17.0925i	0.504910	−	0.874530i
$383$	3.22903	+	5.59285i	0.164996	+	0.285781i	0.936654	−	0.350257i	$-0.113906\pi$
$383$	3.22903	+	5.59285i	0.164996	+	0.285781i	−0.771658	+	0.636038i	$0.780572\pi$
$384$	−0.506213			−0.0258326
$385$	2.30342	+	6.73915i	0.117393	+	0.343459i
$386$	18.2152			0.927129
$387$	1.38286	+	2.39518i	0.0702945	+	0.121754i
$388$	5.43033	−	9.40560i	0.275683	−	0.477497i
$389$	−2.76278	+	4.78527i	−0.140078	+	0.242623i	−0.927526	−	0.373759i	$-0.878069\pi$
$389$	−2.76278	+	4.78527i	−0.140078	+	0.242623i	0.787448	+	0.616382i	$0.211402\pi$
$390$	−4.73130	−	8.19485i	−0.239579	−	0.414962i
$391$	1.65608			0.0837515
$392$	−16.9072	+	13.0865i	−0.853941	+	0.660967i
$393$	−6.54568			−0.330186
$394$	2.91410	+	5.04737i	0.146810	+	0.254283i
$395$	12.6347	−	21.8839i	0.635721	−	1.10110i
$396$	0.428788	−	0.742682i	0.0215474	−	0.0373212i
$397$	−16.2728	−	28.1853i	−0.816707	−	1.41458i	−0.908096	−	0.418763i	$-0.862464\pi$
$397$	−16.2728	−	28.1853i	−0.816707	−	1.41458i	0.0913884	−	0.995815i	$-0.470870\pi$
$398$	−4.62967			−0.232064
$399$	−5.44034	−	15.9169i	−0.272358	−	0.796841i
$400$	−3.47997			−0.173998
$401$	16.0902	+	27.8691i	0.803509	+	1.39172i	0.917293	+	0.398212i	$0.130369\pi$
$401$	16.0902	+	27.8691i	0.803509	+	1.39172i	−0.113785	+	0.993505i	$0.536297\pi$
$402$	4.33087	−	7.50129i	0.216004	−	0.374131i
$403$	6.34355	−	10.9873i	0.315995	−	0.547319i
$404$	−2.34840	−	4.06755i	−0.116837	−	0.202368i
$405$	−2.69184			−0.133758
$406$	−15.9515	+	18.2664i	−0.791660	+	0.906547i
$407$	7.82952			0.388095
$408$	−1.63228	−	2.82720i	−0.0808100	−	0.139967i
$409$	1.09029	−	1.88843i	0.0539112	−	0.0933770i	−0.837810	−	0.545961i	$-0.816165\pi$
$409$	1.09029	−	1.88843i	0.0539112	−	0.0933770i	0.891722	+	0.452584i	$0.149498\pi$
$410$	9.89330	−	17.1357i	0.488595	−	0.846272i
$411$	10.7067	+	18.5445i	0.528121	+	0.914733i
$412$	5.42548			0.267294
$413$	−4.02226	−	0.791304i	−0.197923	−	0.0389375i
$414$	1.65608			0.0813918
$415$	3.32329	+	5.75611i	0.163134	+	0.282556i
$416$	−7.32190	+	12.6819i	−0.358985	+	0.621781i
$417$	0.425452	−	0.736905i	0.0208345	−	0.0360864i
$418$	−3.39770	−	5.88499i	−0.166187	−	0.287844i
$419$	−36.7377			−1.79475			−0.897376	−	0.441266i	$-0.854530\pi$
$419$	−36.7377			−1.79475			−0.897376	+	0.441266i	$0.854530\pi$
$420$	−5.99273	−	1.17895i	−0.292415	−	0.0575271i
$421$	−36.6439			−1.78591			−0.892957	−	0.450142i	$-0.851373\pi$
$421$	−36.6439			−1.78591			−0.892957	+	0.450142i	$0.851373\pi$
$422$	13.9351	+	24.1363i	0.678349	+	1.17494i
$423$	4.56647	−	7.90936i	0.222030	−	0.384566i
$424$	5.42817	−	9.40186i	0.263615	−	0.456595i
$425$	1.20031	+	2.07899i	0.0582233	+	0.100846i
$426$	11.1534			0.540385
$427$	−21.5263	+	24.6503i	−1.04173	+	1.19291i
$428$	3.00736			0.145366
$429$	−1.64444	−	2.84825i	−0.0793943	−	0.137515i
$430$	3.97868	−	6.89128i	0.191869	−	0.332327i
$431$	−12.9141	+	22.3679i	−0.622051	+	1.07742i	0.367052	+	0.930200i	$0.380367\pi$
$431$	−12.9141	+	22.3679i	−0.622051	+	1.07742i	−0.989103	+	0.147224i	$0.952966\pi$
$432$	−0.774707	−	1.34183i	−0.0372731	−	0.0645589i
$433$	−4.81228			−0.231263			−0.115632	−	0.993292i	$-0.536889\pi$
$433$	−4.81228			−0.231263			−0.115632	+	0.993292i	$0.536889\pi$
$434$	3.52820	+	10.3225i	0.169359	+	0.495496i
$435$	−23.0843			−1.10681
$436$	1.63366	+	2.82958i	0.0782381	+	0.135512i
$437$	−4.92537	+	8.53099i	−0.235612	+	0.408093i
$438$	−7.61551	+	13.1905i	−0.363883	+	0.630264i
$439$	−13.6430	−	23.6304i	−0.651146	−	1.12782i	−0.982845	−	0.184432i	$-0.940955\pi$
$439$	−13.6430	−	23.6304i	−0.651146	−	1.12782i	0.331699	−	0.943385i	$-0.392378\pi$
$440$	−8.22168			−0.391953
$441$	6.47835	+	2.65161i	0.308493	+	0.126267i
$442$	−3.75730			−0.178716
$443$	13.5654	+	23.4959i	0.644510	+	1.11632i	0.984414	+	0.175864i	$0.0562720\pi$
$443$	13.5654	+	23.4959i	0.644510	+	1.11632i	−0.339904	+	0.940460i	$0.610395\pi$
$444$	−3.35720	+	5.81485i	−0.159326	+	0.275960i
$445$	−15.6530	+	27.1118i	−0.742022	+	1.28522i
$446$	7.14421	+	12.3741i	0.338288	+	0.585933i
$447$	15.7843			0.746571
$448$	−6.72403	−	19.6726i	−0.317680	−	0.929442i
$449$	4.27537			0.201767			0.100884	−	0.994898i	$-0.467833\pi$
$449$	4.27537			0.201767			0.100884	+	0.994898i	$0.467833\pi$
$450$	1.20031	+	2.07899i	0.0565829	+	0.0980045i
$451$	3.43858	−	5.95579i	0.161916	−	0.280447i
$452$	4.77323	−	8.26747i	0.224514	−	0.388869i
$453$	−8.52968	−	14.7738i	−0.400759	−	0.694136i
$454$	24.3246			1.14161
$455$	−15.4070	+	17.6429i	−0.722290	+	0.827110i
$456$	19.4184			0.909349
$457$	−14.5498	−	25.2009i	−0.680609	−	1.17885i	−0.974795	−	0.223102i	$-0.928382\pi$
$457$	−14.5498	−	25.2009i	−0.680609	−	1.17885i	0.294186	−	0.955748i	$-0.404952\pi$
$458$	13.6614	−	23.6623i	0.638357	−	1.10567i
$459$	−0.534421	+	0.925645i	−0.0249446	+	0.0432054i
$460$	1.78837	+	3.09756i	0.0833834	+	0.144424i
$461$	−2.96972			−0.138314			−0.0691569	−	0.997606i	$-0.522031\pi$
$461$	−2.96972			−0.138314			−0.0691569	+	0.997606i	$0.522031\pi$
$462$	2.77471	+	0.545871i	0.129091	+	0.0253962i
$463$	−20.3076			−0.943773			−0.471887	−	0.881659i	$-0.656427\pi$
$463$	−20.3076			−0.943773			−0.471887	+	0.881659i	$0.656427\pi$
$464$	−6.64362	−	11.5071i	−0.308422	−	0.534203i
$465$	−5.19198	+	8.99278i	−0.240772	+	0.417030i
$466$	−12.0072	+	20.7971i	−0.556222	+	0.963405i
$467$	−18.5675	−	32.1598i	−0.859200	−	1.48818i	−0.872693	−	0.488269i	$-0.837628\pi$
$467$	−18.5675	−	32.1598i	−0.859200	−	1.48818i	0.0134931	−	0.999909i	$-0.495705\pi$
$468$	2.82046			0.130376
$469$	−21.0375	−	4.13874i	−0.971424	−	0.191109i
$470$	−26.2769			−1.21206
$471$	−9.10941	−	15.7780i	−0.419739	−	0.727010i
$472$	2.36619	−	4.09835i	0.108913	−	0.188642i
$473$	1.38286	−	2.39518i	0.0635838	−	0.110130i
$474$	−5.01683	−	8.68941i	−0.230431	−	0.399118i
$475$	−14.2794			−0.655183
$476$	−1.59517	+	1.82666i	−0.0731144	+	0.0837249i
$477$	−3.55444			−0.162747
$478$	−7.03836	−	12.1908i	−0.321927	−	0.557594i
$479$	−9.18431	+	15.9077i	−0.419642	+	0.726841i	−0.995903	−	0.0904243i	$-0.971178\pi$
$479$	−9.18431	+	15.9077i	−0.419642	+	0.726841i	0.576261	+	0.817265i	$0.304511\pi$
$480$	5.99273	−	10.3797i	0.273529	−	0.473767i
$481$	12.8752	+	22.3005i	0.587057	+	1.01681i
$482$	−15.5525			−0.708395
$483$	−1.32584	−	3.87903i	−0.0603279	−	0.176502i
$484$	−0.857576			−0.0389807
$485$	17.0452	+	29.5232i	0.773983	+	1.34058i
$486$	−0.534421	+	0.925645i	−0.0242418	+	0.0419881i
$487$	10.0623	−	17.4285i	0.455968	−	0.789760i	−0.542775	−	0.839878i	$-0.682626\pi$
$487$	10.0623	−	17.4285i	0.455968	−	0.789760i	0.998743	+	0.0501182i	$0.0159598\pi$
$488$	−18.8900	−	32.7184i	−0.855108	−	1.48109i
$489$	−9.91501			−0.448372
$490$	−2.71262	−	19.9565i	−0.122544	−	0.901545i
$491$	15.0288			0.678238			0.339119	−	0.940743i	$-0.389871\pi$
$491$	15.0288			0.678238			0.339119	+	0.940743i	$0.389871\pi$
$492$	2.94884	+	5.10754i	0.132944	+	0.230266i
$493$	−4.58301	+	7.93801i	−0.206409	+	0.357510i
$494$	11.1746	−	19.3550i	0.502770	−	0.870824i
$495$	1.34592	+	2.33120i	0.0604946	+	0.104780i
$496$	−5.97698			−0.268374
$497$	−8.92933	−	26.1247i	−0.400535	−	1.17185i
$498$	2.63914			0.118263
$499$	−1.07121	−	1.85539i	−0.0479540	−	0.0830588i	0.841052	−	0.540954i	$-0.181937\pi$
$499$	−1.07121	−	1.85539i	−0.0479540	−	0.0830588i	−0.889006	+	0.457895i	$0.848603\pi$
$500$	3.17875	−	5.50576i	0.142158	−	0.246225i
$501$	−0.0968952	+	0.167827i	−0.00432896	+	0.00749798i
$502$	−2.75759	−	4.77629i	−0.123077	−	0.213176i
$503$	6.30359			0.281063			0.140532	−	0.990076i	$-0.455119\pi$
$503$	6.30359			0.281063			0.140532	+	0.990076i	$0.455119\pi$
$504$	−5.31535	+	6.08672i	−0.236765	+	0.271124i
$505$	14.7427			0.656044
$506$	−0.828039	−	1.43421i	−0.0368108	−	0.0637582i
$507$	−1.09164	+	1.89077i	−0.0484813	+	0.0839722i
$508$	5.44349	−	9.42840i	0.241516	−	0.418317i
$509$	12.3517	+	21.3937i	0.547477	+	0.948259i	0.998446	+	0.0557192i	$0.0177452\pi$
$509$	12.3517	+	21.3937i	0.547477	+	0.948259i	−0.450969	+	0.892540i	$0.648922\pi$
$510$	3.07522			0.136173
$511$	36.9929	+	7.27765i	1.63647	+	0.321944i
$512$	16.3635			0.723173
$513$	−3.17886	−	5.50595i	−0.140350	−	0.243094i
$514$	7.92197	−	13.7213i	0.349423	−	0.605219i
$515$	−8.51500	+	14.7484i	−0.375216	+	0.649893i
$516$	1.18590	+	2.05404i	0.0522065	+	0.0904243i
$517$	−9.13295			−0.401667
$518$	−21.7246	−	4.27391i	−0.954525	−	0.187785i
$519$	−9.02818			−0.396293
$520$	−13.5200	−	23.4174i	−0.592893	−	1.02692i
$521$	−1.82659	+	3.16375i	−0.0800244	+	0.138606i	−0.903260	−	0.429093i	$-0.858833\pi$
$521$	−1.82659	+	3.16375i	−0.0800244	+	0.138606i	0.823236	+	0.567700i	$0.192166\pi$
$522$	−4.58301	+	7.93801i	−0.200593	+	0.347437i
$523$	3.83139	+	6.63617i	0.167535	+	0.290179i	0.937553	−	0.347843i	$-0.113086\pi$
$523$	3.83139	+	6.63617i	0.167535	+	0.290179i	−0.770018	+	0.638023i	$0.779753\pi$
$524$	−5.61341			−0.245223
$525$	3.90866	−	4.47590i	0.170588	−	0.195344i
$526$	−16.5338			−0.720907
$527$	2.06157	+	3.57074i	0.0898034	+	0.155544i
$528$	−0.774707	+	1.34183i	−0.0337148	+	0.0583957i
$529$	10.2997	−	17.8395i	0.447811	−	0.775632i
$530$	5.11334	+	8.85656i	0.222109	+	0.384704i
$531$	−1.54941			−0.0672388
$532$	−4.66551	−	13.6499i	−0.202275	−	0.591799i
$533$	22.6181			0.979699
$534$	6.21530	+	10.7652i	0.268962	+	0.465856i
$535$	−4.71989	+	8.17509i	−0.204059	+	0.353440i
$536$	12.3758	−	21.4355i	0.534553	−	0.925873i
$537$	6.11215	+	10.5866i	0.263759	+	0.456843i
$538$	6.32159			0.272543
$539$	−0.942814	−	6.93622i	−0.0406099	−	0.298764i
$540$	−2.30845			−0.0993400
$541$	7.24283	+	12.5449i	0.311394	+	0.539349i	0.978664	−	0.205466i	$-0.0658709\pi$
$541$	7.24283	+	12.5449i	0.311394	+	0.539349i	−0.667271	+	0.744815i	$0.732538\pi$
$542$	−4.96488	+	8.59943i	−0.213260	+	0.369377i
$543$	−9.25542	+	16.0309i	−0.397188	+	0.687950i
$544$	−2.37952	−	4.12145i	−0.102021	−	0.176706i
$545$	−10.2558			−0.439309
$546$	3.00806	+	8.80072i	0.128733	+	0.376636i
$547$	6.15312			0.263089			0.131544	−	0.991310i	$-0.458006\pi$
$547$	6.15312			0.263089			0.131544	+	0.991310i	$0.458006\pi$
$548$	9.18178	+	15.9033i	0.392226	+	0.679356i
$549$	−6.18471	+	10.7122i	−0.263957	+	0.457187i
$550$	1.20031	−	2.07899i	0.0511812	−	0.0886484i
$551$	−27.2608	−	47.2171i	−1.16135	−	2.01152i
$552$	4.73237			0.201423
$553$	−16.3368	+	18.7076i	−0.694710	+	0.795528i
$554$	−10.2253			−0.434429
$555$	−10.5379	−	18.2522i	−0.447309	−	0.774762i
$556$	0.364858	−	0.631952i	0.0154734	−	0.0268007i
$557$	9.90091	−	17.1489i	0.419515	−	0.726621i	−0.576376	−	0.817185i	$-0.695533\pi$
$557$	9.90091	−	17.1489i	0.419515	−	0.726621i	0.995891	+	0.0905634i	$0.0288668\pi$
$558$	2.06157	+	3.57074i	0.0872732	+	0.151162i
$559$	9.09609			0.384724
$560$	10.8273	+	2.13006i	0.457536	+	0.0900115i
$561$	1.06884			0.0451266
$562$	−6.95051	−	12.0386i	−0.293189	−	0.507819i
$563$	−2.92208	+	5.06119i	−0.123151	+	0.213304i	−0.921009	−	0.389542i	$-0.872633\pi$
$563$	−2.92208	+	5.06119i	−0.123151	+	0.213304i	0.797858	+	0.602846i	$0.205967\pi$
$564$	3.91610	−	6.78288i	0.164897	−	0.285611i
$565$	14.9826	+	25.9507i	0.630325	+	1.09175i
$566$	−25.8912			−1.08829
$567$	2.59599	+	0.510712i	0.109021	+	0.0214479i
$568$	31.8717			1.33731
$569$	17.1742	+	29.7466i	0.719979	+	1.24704i	0.961007	+	0.276522i	$0.0891820\pi$
$569$	17.1742	+	29.7466i	0.719979	+	1.24704i	−0.241028	+	0.970518i	$0.577485\pi$
$570$	−9.14606	+	15.8414i	−0.383086	+	0.663525i
$571$	−4.82810	+	8.36252i	−0.202050	+	0.349960i	−0.949189	−	0.314707i	$-0.898094\pi$
$571$	−4.82810	+	8.36252i	−0.202050	+	0.349960i	0.747139	+	0.664668i	$0.231427\pi$
$572$	−1.41023	−	2.44259i	−0.0589647	−	0.102130i
$573$	−18.4655			−0.771409
$574$	−12.7921	+	14.6485i	−0.533933	+	0.611418i
$575$	−3.47997			−0.145125
$576$	−3.92893	−	6.80511i	−0.163706	−	0.283546i
$577$	17.3262	−	30.0099i	0.721299	−	1.24933i	−0.239180	−	0.970975i	$-0.576879\pi$
$577$	17.3262	−	30.0099i	0.721299	−	1.24933i	0.960479	−	0.278351i	$-0.0897880\pi$
$578$	−8.47463	+	14.6785i	−0.352498	+	0.610544i
$579$	−8.52099	−	14.7588i	−0.354120	−	0.613354i
$580$	−19.7965			−0.822006
$581$	−2.11288	−	6.18167i	−0.0876569	−	0.256459i
$582$	13.5362			0.561094
$583$	1.77722	+	3.07824i	0.0736050	+	0.127488i
$584$	−21.7619	+	37.6927i	−0.900514	+	1.55974i
$585$	−4.42656	+	7.66703i	−0.183016	+	0.316993i
$586$	1.63004	+	2.82331i	0.0673363	+	0.116630i
$587$	−15.4442			−0.637451			−0.318726	−	0.947847i	$-0.603255\pi$
$587$	−15.4442			−0.637451			−0.318726	+	0.947847i	$0.603255\pi$
$588$	5.55567	+	2.27395i	0.229112	+	0.0937763i
$589$	−24.5254			−1.01055
$590$	2.22895	+	3.86065i	0.0917643	+	0.158940i
$591$	2.72640	−	4.72227i	0.112149	−	0.194248i
$592$	6.06558	−	10.5059i	0.249294	−	0.431790i
$593$	2.78395	+	4.82194i	0.114323	+	0.198013i	0.917509	−	0.397715i	$-0.130197\pi$
$593$	2.78395	+	4.82194i	0.114323	+	0.198013i	−0.803186	+	0.595728i	$0.796863\pi$
$594$	1.06884			0.0438551
$595$	−2.46200	−	7.20309i	−0.100932	−	0.295298i
$596$	13.5362			0.554465
$597$	2.16574	+	3.75117i	0.0886377	+	0.153525i
$598$	2.72332	−	4.71693i	0.111365	−	0.192890i
$599$	−13.7745	+	23.8581i	−0.562810	+	0.974816i	0.434440	+	0.900701i	$0.356946\pi$
$599$	−13.7745	+	23.8581i	−0.562810	+	0.974816i	−0.997250	+	0.0741146i	$0.976387\pi$
$600$	3.42996	+	5.94087i	0.140028	+	0.242535i
$601$	15.6408			0.638000			0.319000	−	0.947755i	$-0.396653\pi$
$601$	15.6408			0.638000			0.319000	+	0.947755i	$0.396653\pi$
$602$	−5.14448	+	5.89105i	−0.209673	+	0.240101i
$603$	−8.10386			−0.330015
$604$	−7.31485	−	12.6697i	−0.297637	−	0.515522i
$605$	1.34592	−	2.33120i	0.0547194	−	0.0947768i
$606$	2.92694	−	5.06960i	0.118899	−	0.205938i
$607$	−5.72550	−	9.91685i	−0.232391	−	0.402513i	0.726120	−	0.687568i	$-0.241321\pi$
$607$	−5.72550	−	9.91685i	−0.232391	−	0.402513i	−0.958511	+	0.285055i	$0.907988\pi$
$608$	28.3079			1.14804
$609$	22.2623	+	4.37969i	0.902116	+	0.177474i
$610$	35.5887			1.44094
$611$	−15.0186	−	26.0129i	−0.607587	−	1.05237i
$612$	−0.458307	+	0.793810i	−0.0185259	+	0.0320879i
$613$	−7.45755	+	12.9169i	−0.301208	+	0.521707i	−0.976410	−	0.215926i	$-0.930723\pi$
$613$	−7.45755	+	12.9169i	−0.301208	+	0.521707i	0.675202	+	0.737633i	$0.264056\pi$
$614$	10.9692	+	18.9992i	0.442681	+	0.766746i
$615$	−18.5122			−0.746483
$616$	7.92893	+	1.55987i	0.319466	+	0.0628488i
$617$	27.8601			1.12161			0.560803	−	0.827949i	$-0.310493\pi$
$617$	27.8601			1.12161			0.560803	+	0.827949i	$0.310493\pi$
$618$	3.38103	+	5.85612i	0.136005	+	0.235568i
$619$	−0.648970	+	1.12405i	−0.0260843	+	0.0451793i	−0.878773	−	0.477240i	$-0.841637\pi$
$619$	−0.648970	+	1.12405i	−0.0260843	+	0.0451793i	0.852689	+	0.522420i	$0.174970\pi$
$620$	−4.45252	+	7.71199i	−0.178817	+	0.309721i
$621$	−0.774707	−	1.34183i	−0.0310879	−	0.0538458i
$622$	−8.54577			−0.342654
$623$	20.2394	−	23.1766i	0.810876	−	0.928552i
$624$	−5.09583			−0.203997
$625$	15.5927	+	27.0074i	0.623710	+	1.08030i
$626$	8.50516	−	14.7314i	0.339935	−	0.588784i
$627$	−3.17886	+	5.50595i	−0.126951	+	0.219886i
$628$	−7.81200	−	13.5308i	−0.311733	−	0.539937i
$629$	−8.36853			−0.333675
$630$	−2.46200	−	7.20309i	−0.0980883	−	0.286978i
$631$	45.9952			1.83104			0.915519	−	0.402274i	$-0.131780\pi$
$631$	45.9952			1.83104			0.915519	+	0.402274i	$0.131780\pi$
$632$	−14.3360	−	24.8306i	−0.570255	−	0.987710i
$633$	13.0375	−	22.5817i	0.518196	−	0.897542i
$634$	14.3180	−	24.7995i	0.568639	−	0.984912i
$635$	17.0865	+	29.5947i	0.678058	+	1.17443i
$636$	−3.04820			−0.120869
$637$	18.2057	−	14.0916i	0.721336	−	0.558328i
$638$	9.16603			0.362887
$639$	−5.21752	−	9.03701i	−0.206402	−	0.357499i
$640$	0.681321	−	1.18008i	0.0269316	−	0.0466469i
$641$	1.26224	−	2.18626i	0.0498555	−	0.0863522i	−0.840021	−	0.542554i	$-0.817457\pi$
$641$	1.26224	−	2.18626i	0.0498555	−	0.0863522i	0.889876	+	0.456202i	$0.150791\pi$
$642$	1.87412	+	3.24607i	0.0739655	+	0.128112i
$643$	22.1800			0.874692			0.437346	−	0.899293i	$-0.355919\pi$
$643$	22.1800			0.874692			0.437346	+	0.899293i	$0.355919\pi$
$644$	−1.13701	−	3.32657i	−0.0448045	−	0.131085i
$645$	−7.44485			−0.293141
$646$	3.63161	+	6.29013i	0.142884	+	0.247482i
$647$	−11.6482	+	20.1753i	−0.457940	+	0.793175i	−0.998852	−	0.0479044i	$-0.984746\pi$
$647$	−11.6482	+	20.1753i	−0.457940	+	0.793175i	0.540912	+	0.841079i	$0.318079\pi$
$648$	−1.52715	+	2.64510i	−0.0599921	+	0.103909i
$649$	0.774707	+	1.34183i	0.0304099	+	0.0526715i
$650$	7.89532			0.309680
$651$	6.71328	−	7.68753i	0.263114	−	0.301298i
$652$	−8.50287			−0.332998
$653$	−18.6188	−	32.2488i	−0.728611	−	1.26199i	−0.957470	−	0.288532i	$-0.906833\pi$
$653$	−18.6188	−	32.2488i	−0.728611	−	1.26199i	0.228859	−	0.973460i	$-0.426501\pi$
$654$	−2.03612	+	3.52666i	−0.0796185	+	0.137903i
$655$	8.80995	−	15.2593i	0.344233	−	0.596229i
$656$	−5.32777	−	9.22798i	−0.208015	−	0.360292i
$657$	14.2500			0.555946
$658$	25.3412	+	4.98541i	0.987905	+	0.194351i
$659$	−13.8016			−0.537632			−0.268816	−	0.963192i	$-0.586632\pi$
$659$	−13.8016			−0.537632			−0.268816	+	0.963192i	$0.586632\pi$
$660$	1.15423	+	1.99918i	0.0449282	+	0.0778180i
$661$	−13.4675	+	23.3264i	−0.523825	+	0.907292i	0.475790	+	0.879559i	$0.342162\pi$
$661$	−13.4675	+	23.3264i	−0.523825	+	0.907292i	−0.999615	+	0.0277328i	$0.991171\pi$
$662$	−5.40978	+	9.37001i	−0.210257	+	0.364176i
$663$	1.75765	+	3.04433i	0.0682613	+	0.118232i
$664$	7.54155			0.292669
$665$	44.4277	+	8.74030i	1.72283	+	0.338934i
$666$	−8.36853			−0.324274
$667$	−6.64362	−	11.5071i	−0.257242	−	0.445556i
$668$	−0.0830950	+	0.143925i	−0.00321504	+	0.00556861i
$669$	6.68406	−	11.5771i	0.258421	−	0.447598i
$670$	11.6580	+	20.1923i	0.450388	+	0.780095i
$671$	12.3694			0.477516
$672$	−7.74865	+	8.87315i	−0.298911	+	0.342289i
$673$	24.7186			0.952832			0.476416	−	0.879220i	$-0.341936\pi$
$673$	24.7186			0.952832			0.476416	+	0.879220i	$0.341936\pi$
$674$	0.729695	+	1.26387i	0.0281068	+	0.0486824i
$675$	1.12300	−	1.94508i	0.0432241	−	0.0748663i
$676$	−0.936162	+	1.62148i	−0.0360062	+	0.0623646i
$677$	12.4334	+	21.5353i	0.477854	+	0.827667i	0.999678	−	0.0253859i	$-0.00808146\pi$
$677$	12.4334	+	21.5353i	0.477854	+	0.827667i	−0.521824	+	0.853053i	$0.674748\pi$
$678$	11.8983			0.456950
$679$	−10.8370	−	31.7059i	−0.415885	−	1.21676i
$680$	8.78768			0.336992
$681$	−11.3789	−	19.7089i	−0.436042	−	0.755247i
$682$	2.06157	−	3.57074i	0.0789416	−	0.136731i
$683$	−3.06026	+	5.30053i	−0.117098	+	0.202819i	−0.918616	−	0.395151i	$-0.870692\pi$
$683$	−3.06026	+	5.30053i	−0.117098	+	0.202819i	0.801519	+	0.597970i	$0.204026\pi$
$684$	−2.72611	−	4.72177i	−0.104236	−	0.180541i
$685$	−57.6413			−2.20236
$686$	−1.17024	+	19.7606i	−0.0446801	+	0.754464i
$687$	−25.5630			−0.975291
$688$	−2.14261	−	3.71112i	−0.0816864	−	0.141485i
$689$	−5.84507	+	10.1240i	−0.222679	+	0.385692i
$690$	−2.22895	+	3.86065i	−0.0848546	+	0.146972i
$691$	−6.24162	−	10.8108i	−0.237443	−	0.411263i	0.722537	−	0.691332i	$-0.242976\pi$
$691$	−6.24162	−	10.8108i	−0.237443	−	0.411263i	−0.959980	+	0.280070i	$0.909642\pi$
$692$	−7.74234			−0.294320
$693$	−0.855706	−	2.50355i	−0.0325056	−	0.0951020i
$694$	27.0500			1.02680
$695$	1.14525	+	1.98363i	0.0434418	+	0.0752434i
$696$	−13.0963	+	22.6835i	−0.496414	+	0.859815i
$697$	−3.67530	+	6.36580i	−0.139212	+	0.241122i
$698$	−2.93390	−	5.08166i	−0.111050	−	0.192344i
$699$	22.4676			0.849804
$700$	3.35197	−	3.83842i	0.126693	−	0.145079i
$701$	−28.0867			−1.06082			−0.530409	−	0.847742i	$-0.677962\pi$
$701$	−28.0867			−1.06082			−0.530409	+	0.847742i	$0.677962\pi$
$702$	1.75765	+	3.04433i	0.0663381	+	0.114901i
$703$	24.8890	−	43.1089i	0.938705	−	1.62588i
$704$	−3.92893	+	6.80511i	−0.148077	+	0.256477i
$705$	12.2922	+	21.2907i	0.462951	+	0.801855i
$706$	−18.5377			−0.697675
$707$	−14.2178	−	2.79708i	−0.534716	−	0.105195i
$708$	−1.32874			−0.0499371
$709$	6.88131	+	11.9188i	0.258433	+	0.447619i	0.965822	−	0.259205i	$-0.0834606\pi$
$709$	6.88131	+	11.9188i	0.258433	+	0.447619i	−0.707389	+	0.706824i	$0.750127\pi$
$710$	−15.0116	+	26.0008i	−0.563375	+	0.975794i
$711$	−4.69371	+	8.12974i	−0.176028	+	0.304889i
$712$	17.7607	+	30.7624i	0.665610	+	1.15287i
$713$	−5.97698			−0.223840
$714$	−2.96572	−	0.583450i	−0.110989	−	0.0218351i
$715$	8.85313			0.331088
$716$	5.24163	+	9.07877i	0.195889	+	0.339289i
$717$	−6.58503	+	11.4056i	−0.245922	+	0.425950i
$718$	5.10126	−	8.83563i	0.190377	−	0.329743i
$719$	−15.3224	−	26.5392i	−0.571430	−	0.989745i	−0.996419	−	0.0845470i	$-0.973056\pi$
$719$	−15.3224	−	26.5392i	−0.571430	−	0.989745i	0.424990	−	0.905198i	$-0.360278\pi$
$720$	4.17077			0.155435
$721$	11.0100	−	12.6078i	0.410033	−	0.469538i
$722$	−22.8953			−0.852074
$723$	7.27537	+	12.6013i	0.270574	+	0.468648i
$724$	−7.93722	+	13.7477i	−0.294985	+	0.510928i
$725$	9.63042	−	16.6804i	0.357665	−	0.619494i
$726$	−0.534421	−	0.925645i	−0.0198342	−	0.0343539i
$727$	28.8508			1.07002			0.535009	−	0.844846i	$-0.320308\pi$
$727$	28.8508			1.07002			0.535009	+	0.844846i	$0.320308\pi$
$728$	8.59576	+	25.1487i	0.318580	+	0.932073i
$729$	1.00000			0.0370370
$730$	−20.4997	−	35.5066i	−0.758729	−	1.31416i
$731$	−1.47806	+	2.56007i	−0.0546678	+	0.0946875i
$732$	−5.30386	+	9.18655i	−0.196036	+	0.339545i
$733$	−4.02618	−	6.97355i	−0.148710	−	0.257574i	0.782041	−	0.623227i	$-0.214179\pi$
$733$	−4.02618	−	6.97355i	−0.148710	−	0.257574i	−0.930751	+	0.365653i	$0.880846\pi$
$734$	−7.07301			−0.261070
$735$	−14.9008	+	11.5335i	−0.549623	+	0.425419i
$736$	6.89879			0.254293
$737$	4.05193	+	7.01815i	0.149255	+	0.258517i
$738$	−3.67530	+	6.36580i	−0.135290	+	0.234328i
$739$	7.72812	−	13.3855i	0.284283	−	0.492393i	−0.688152	−	0.725567i	$-0.741578\pi$
$739$	7.72812	−	13.3855i	0.284283	−	0.492393i	0.972435	+	0.233173i	$0.0749110\pi$
$740$	−9.03705	−	15.6526i	−0.332208	−	0.575402i
$741$	−20.9098			−0.768140
$742$	−3.25095	−	9.51134i	−0.119346	−	0.349172i
$743$	14.1256			0.518216			0.259108	−	0.965848i	$-0.416571\pi$
$743$	14.1256			0.518216			0.259108	+	0.965848i	$0.416571\pi$
$744$	5.89109	+	10.2037i	0.215978	+	0.374085i
$745$	−21.2444	+	36.7963i	−0.778333	+	1.34811i
$746$	−17.4836	+	30.2825i	−0.640119	+	1.10872i
$747$	−1.23458	−	2.13836i	−0.0451709	−	0.0782384i
$748$	0.916613			0.0335147
$749$	6.10286	−	6.98852i	0.222994	−	0.255355i
$750$	7.92370			0.289333
$751$	−0.935267	−	1.61993i	−0.0341284	−	0.0591121i	0.848457	−	0.529265i	$-0.177532\pi$
$751$	−0.935267	−	1.61993i	−0.0341284	−	0.0591121i	−0.882585	+	0.470153i	$0.844199\pi$
$752$	−7.07535	+	12.2549i	−0.258012	+	0.446889i
$753$	−2.57998	+	4.46866i	−0.0940197	+	0.162847i
$754$	15.0730	+	26.1072i	0.548926	+	0.950767i
$755$	45.9210			1.67124
$756$	2.22626	+	0.437974i	0.0809683	+	0.0159290i
$757$	2.68353			0.0975345			0.0487672	−	0.998810i	$-0.484471\pi$
$757$	2.68353			0.0975345			0.0487672	+	0.998810i	$0.484471\pi$
$758$	−4.11155	−	7.12141i	−0.149338	−	0.258661i
$759$	−0.774707	+	1.34183i	−0.0281201	+	0.0487054i
$760$	−26.1356	+	45.2681i	−0.948036	+	1.64205i
$761$	−13.1029	−	22.6950i	−0.474981	−	0.822692i	0.524608	−	0.851344i	$-0.324212\pi$
$761$	−13.1029	−	22.6950i	−0.474981	−	0.822692i	−0.999589	+	0.0286520i	$0.990879\pi$
$762$	13.5690			0.491554
$763$	9.89059	+	1.94579i	0.358063	+	0.0704422i
$764$	−15.8356			−0.572912
$765$	−1.43858	−	2.49169i	−0.0520118	−	0.0900871i
$766$	−3.45133	+	5.97787i	−0.124701	+	0.215989i
$767$	−2.54792	+	4.41312i	−0.0919999	+	0.159349i
$768$	−8.12840	−	14.0788i	−0.293308	−	0.508025i
$769$	−14.9106			−0.537689			−0.268844	−	0.963184i	$-0.586642\pi$
$769$	−14.9106			−0.537689			−0.268844	+	0.963184i	$0.586642\pi$
$770$	−5.00706	+	5.73370i	−0.180442	+	0.206628i
$771$	−14.8235			−0.533854
$772$	−7.30739	−	12.6568i	−0.262999	−	0.455527i
$773$	−5.50652	+	9.53758i	−0.198056	+	0.343043i	−0.947898	−	0.318574i	$-0.896796\pi$
$773$	−5.50652	+	9.53758i	−0.198056	+	0.343043i	0.749842	+	0.661617i	$0.230129\pi$
$774$	−1.47806	+	2.56007i	−0.0531276	+	0.0920197i
$775$	−4.33204	−	7.50331i	−0.155611	−	0.269527i
$776$	38.6808			1.38856
$777$	6.69977	+	19.6016i	0.240353	+	0.703204i
$778$	−5.90595			−0.211739
$779$	−21.8615	−	37.8652i	−0.783270	−	1.35666i
$780$	−3.79611	+	6.57506i	−0.135923	+	0.235425i
$781$	−5.21752	+	9.03701i	−0.186698	+	0.323370i
$782$	0.885044	+	1.53294i	0.0316491	+	0.0548179i
$783$	8.57566			0.306469
$784$	−10.0376	−	4.10844i	−0.358487	−	0.146730i
$785$	49.0421			1.75039
$786$	−3.49815	−	6.05897i	−0.124775	−	0.216116i
$787$	20.5926	−	35.6674i	0.734046	−	1.27141i	−0.221094	−	0.975252i	$-0.570963\pi$
$787$	20.5926	−	35.6674i	0.734046	−	1.27141i	0.955141	−	0.296153i	$-0.0957038\pi$
$788$	2.33810	−	4.04970i	0.0832913	−	0.144265i
$789$	7.73443	+	13.3964i	0.275353	+	0.476926i
$790$	27.0090			0.960937
$791$	−9.52565	−	27.8693i	−0.338693	−	0.990918i
$792$	3.05430			0.108530
$793$	20.3408	+	35.2312i	0.722322	+	1.25110i
$794$	17.3930	−	30.1256i	0.617256	−	1.06912i
$795$	4.78399	−	8.28612i	0.169671	−	0.293878i
$796$	1.85728	+	3.21691i	0.0658297	+	0.114020i
$797$	−21.5389			−0.762947			−0.381473	−	0.924380i	$-0.624583\pi$
$797$	−21.5389			−0.762947			−0.381473	+	0.924380i	$0.624583\pi$
$798$	11.8259	−	13.5421i	0.418634	−	0.479387i
$799$	9.76168			0.345343
$800$	5.00016	+	8.66052i	0.176782	+	0.306196i
$801$	5.81498	−	10.0718i	0.205462	−	0.355871i
$802$	−17.1979	+	29.7877i	−0.607280	+	1.05184i
$803$	−7.12501	−	12.3409i	−0.251436	−	0.435500i
$804$	−6.94967			−0.245096
$805$	10.8273	+	2.13006i	0.381612	+	0.0750748i
$806$	13.5605			0.477649
$807$	−2.95721	−	5.12204i	−0.104099	−	0.180304i
$808$	8.36394	−	14.4868i	0.294242	−	0.509643i
$809$	14.4335	−	24.9996i	0.507456	−	0.878940i	−0.492506	−	0.870309i	$-0.663919\pi$
$809$	14.4335	−	24.9996i	0.507456	−	0.878940i	0.999963	−	0.00863141i	$-0.00274750\pi$
$810$	−1.43858	−	2.49169i	−0.0505464	−	0.0875489i
$811$	−19.7341			−0.692959			−0.346480	−	0.938057i	$-0.612623\pi$
$811$	−19.7341			−0.692959			−0.346480	+	0.938057i	$0.612623\pi$
$812$	19.0916	+	3.75592i	0.669985	+	0.131807i
$813$	9.29021			0.325822
$814$	4.18426	+	7.24736i	0.146658	+	0.254020i
$815$	13.3448	−	23.1139i	0.467448	−	0.809643i
$816$	0.828039	−	1.43421i	0.0289872	−	0.0502073i
$817$	−8.79181	−	15.2279i	−0.307587	−	0.532756i
$818$	2.33069			0.0814907
$819$	5.72359	−	6.55421i	0.199998	−	0.229022i
$820$	−15.8756			−0.554400
$821$	1.16927	+	2.02524i	0.0408079	+	0.0706813i	0.885708	−	0.464243i	$-0.153674\pi$
$821$	1.16927	+	2.02524i	0.0408079	+	0.0706813i	−0.844900	+	0.534924i	$0.820340\pi$
$822$	−11.4437	+	19.8212i	−0.399147	+	0.691342i
$823$	−19.7444	+	34.1984i	−0.688248	+	1.19208i	0.284157	+	0.958778i	$0.408286\pi$
$823$	−19.7444	+	34.1984i	−0.688248	+	1.19208i	−0.972404	+	0.233302i	$0.925047\pi$
$824$	9.66156	+	16.7343i	0.336576	+	0.582968i
$825$	−2.24599			−0.0781953
$826$	−1.41712	−	4.14608i	−0.0493078	−	0.144260i
$827$	−8.04663			−0.279809			−0.139904	−	0.990165i	$-0.544679\pi$
$827$	−8.04663			−0.279809			−0.139904	+	0.990165i	$0.544679\pi$
$828$	−0.664369	−	1.15072i	−0.0230884	−	0.0399903i
$829$	−3.50513	+	6.07107i	−0.121738	+	0.210857i	−0.920453	−	0.390853i	$-0.872180\pi$
$829$	−3.50513	+	6.07107i	−0.121738	+	0.210857i	0.798715	+	0.601710i	$0.205514\pi$
$830$	−3.55207	+	6.15237i	−0.123294	+	0.213552i
$831$	4.78333	+	8.28497i	0.165932	+	0.287402i
$832$	−25.8436			−0.895965
$833$	1.00772	+	7.41372i	0.0349154	+	0.256870i
$834$	0.909484			0.0314928
$835$	−0.260826	−	0.451764i	−0.00902626	−	0.0156339i
$836$	−2.72611	+	4.72177i	−0.0942846	+	0.163306i
$837$	1.92879	−	3.34076i	0.0666687	−	0.115474i
$838$	−19.6334	−	34.0060i	−0.678224	−	1.17472i
$839$	22.4205			0.774043			0.387021	−	0.922071i	$-0.373504\pi$
$839$	22.4205			0.774043			0.387021	+	0.922071i	$0.373504\pi$
$840$	−7.03534	−	20.5834i	−0.242742	−	0.710194i
$841$	44.5419			1.53593
$842$	−19.5833	−	33.9192i	−0.674884	−	1.16893i
$843$	−6.50283	+	11.2632i	−0.223970	+	0.387927i
$844$	11.1807	−	19.3655i	0.384855	−	0.666588i
$845$	−2.93851	−	5.08965i	−0.101088	−	0.175089i
$846$	9.76168			0.335614
$847$	−1.74029	+	1.99284i	−0.0597969	+	0.0684748i
$848$	5.50730			0.189122
$849$	12.1118	+	20.9782i	0.415676	+	0.719971i
$850$	−1.28294	+	2.22211i	−0.0440044	+	0.0762178i
$851$	6.06558	−	10.5059i	0.207926	−	0.360138i
$852$	−4.47442	−	7.74992i	−0.153291	−	0.265508i
$853$	−36.0726			−1.23510			−0.617551	−	0.786531i	$-0.711875\pi$
$853$	−36.0726			−1.23510			−0.617551	+	0.786531i	$0.711875\pi$
$854$	−34.3215	−	6.75210i	−1.17446	−	0.231052i
$855$	17.1140			0.585285
$856$	5.35543	+	9.27588i	0.183045	+	0.317043i
$857$	−14.4568	+	25.0399i	−0.493835	+	0.855347i	−0.999975	−	0.00710463i	$-0.997739\pi$
$857$	−14.4568	+	25.0399i	−0.493835	+	0.855347i	0.506140	+	0.862451i	$0.331072\pi$
$858$	1.75765	−	3.04433i	0.0600051	−	0.103932i
$859$	14.5667	+	25.2302i	0.497008	+	0.860843i	0.999994	−	0.00345141i	$-0.00109862\pi$
$859$	14.5667	+	25.2302i	0.497008	+	0.860843i	−0.502986	+	0.864295i	$0.667765\pi$
$860$	−6.38452			−0.217710
$861$	17.8530	+	3.51224i	0.608430	+	0.119697i
$862$	−27.6063			−0.940275
$863$	−24.3239	−	42.1302i	−0.827995	−	1.43413i	−0.899609	−	0.436697i	$-0.856148\pi$
$863$	−24.3239	−	42.1302i	−0.827995	−	1.43413i	0.0716137	−	0.997432i	$-0.477185\pi$
$864$	−2.22626	+	3.85599i	−0.0757389	+	0.131184i
$865$	12.1512	−	21.0465i	0.413153	−	0.715602i
$866$	−2.57178	−	4.45446i	−0.0873927	−	0.151369i
$867$	15.8576			0.538551
$868$	5.75715	−	6.59263i	0.195410	−	0.223769i
$869$	9.38741			0.318446
$870$	−12.3367	−	21.3678i	−0.418254	−	0.724438i
$871$	−13.3263	+	23.0818i	−0.451545	+	0.782098i
$872$	−5.81836	+	10.0777i	−0.197034	+	0.341274i
$873$	−6.33218	−	10.9677i	−0.214312	−	0.371199i
$874$	−10.5289			−0.356145
$875$	−6.34365	−	18.5597i	−0.214454	−	0.627432i
$876$	12.2205			0.412891
$877$	−5.25459	−	9.10122i	−0.177435	−	0.307326i	0.763566	−	0.645729i	$-0.223447\pi$
$877$	−5.25459	−	9.10122i	−0.177435	−	0.307326i	−0.941001	+	0.338403i	$0.890113\pi$
$878$	14.5822	−	25.2572i	0.492127	−	0.852388i
$879$	1.52505	−	2.64147i	0.0514387	−	0.0890944i
$880$	−2.08538	−	3.61199i	−0.0702983	−	0.121760i
$881$	−18.6650			−0.628841			−0.314420	−	0.949284i	$-0.601810\pi$
$881$	−18.6650			−0.628841			−0.314420	+	0.949284i	$0.601810\pi$
$882$	1.00772	+	7.41372i	0.0339317	+	0.249633i
$883$	26.2974			0.884980			0.442490	−	0.896774i	$-0.354095\pi$
$883$	26.2974			0.884980			0.442490	+	0.896774i	$0.354095\pi$
$884$	1.50731	+	2.61075i	0.0506965	+	0.0878089i
$885$	2.08538	−	3.61199i	0.0700994	−	0.121416i
$886$	−14.4992	+	25.1134i	−0.487112	+	0.843702i
$887$	23.3883	+	40.5097i	0.785302	+	1.36018i	0.928818	+	0.370536i	$0.120826\pi$
$887$	23.3883	+	40.5097i	0.785302	+	1.36018i	−0.143516	+	0.989648i	$0.545841\pi$
$888$	−23.9137			−0.802491
$889$	−10.8632	−	31.7827i	−0.364342	−	1.06596i
$890$	−33.4611			−1.12162
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	5.73209	−	9.92827i	0.191925	−	0.332423i
$893$	−29.0324	+	50.2855i	−0.971531	+	1.68274i
$894$	8.43546	+	14.6106i	0.282124	+	0.488653i
$895$	−32.9058			−1.09992
$896$	−0.880955	+	1.00880i	−0.0294306	+	0.0337017i
$897$	−5.09583			−0.170145
$898$	2.28485	+	3.95747i	0.0762464	+	0.132063i
$899$	16.5406	−	28.6492i	0.551661	−	0.955504i
$900$	0.963053	−	1.66806i	0.0321018	−	0.0556019i
$901$	−1.89957	−	3.29015i	−0.0632839	−	0.109611i
$902$	7.35059			0.244748
$903$	7.17976	+	1.41248i	0.238928	+	0.0470044i
$904$	34.0002			1.13083
$905$	−24.9141	−	43.1525i	−0.828173	−	1.43444i
$906$	9.11689	−	15.7909i	0.302888	−	0.524618i
$907$	−20.3777	+	35.2951i	−0.676629	+	1.17196i	0.299361	+	0.954140i	$0.403227\pi$
$907$	−20.3777	+	35.2951i	−0.676629	+	1.17196i	−0.975990	+	0.217816i	$0.930107\pi$
$908$	−9.75830	−	16.9019i	−0.323840	−	0.560908i
$909$	−5.47683			−0.181655
$910$	−24.5648	−	4.83266i	−0.814316	−	0.160201i
$911$	−14.9736			−0.496099			−0.248050	−	0.968747i	$-0.579790\pi$
$911$	−14.9736			−0.496099			−0.248050	+	0.968747i	$0.579790\pi$
$912$	4.92537	+	8.53099i	0.163095	+	0.282489i
$913$	−1.23458	+	2.13836i	−0.0408586	+	0.0707693i
$914$	15.5514	−	26.9358i	0.514395	−	0.890958i
$915$	−16.6482	−	28.8356i	−0.550374	−	0.953275i
$916$	−21.9222			−0.724331
$917$	−11.3913	+	13.0445i	−0.376175	+	0.430767i
$918$	−1.14242			−0.0377056
$919$	16.9907	+	29.4288i	0.560473	+	0.970767i	0.997455	+	0.0712972i	$0.0227139\pi$
$919$	16.9907	+	29.4288i	0.560473	+	0.970767i	−0.436982	+	0.899470i	$0.643953\pi$
$920$	−6.36939	+	11.0321i	−0.209992	+	0.363718i
$921$	10.2627	−	17.7755i	0.338167	−	0.585723i
$922$	−1.58708	−	2.74891i	−0.0522678	−	0.0905305i
$923$	−34.3196			−1.12964
$924$	−0.733833	−	2.14698i	−0.0241413	−	0.0706306i
$925$	17.5850			0.578192
$926$	−10.8528	−	18.7976i	−0.356645	−	0.617728i
$927$	3.16327	−	5.47894i	0.103895	−	0.179952i
$928$	−19.0916	+	33.0677i	−0.626714	+	1.08550i
$929$	26.0368	+	45.0971i	0.854241	+	1.47959i	0.877348	+	0.479855i	$0.159311\pi$
$929$	26.0368	+	45.0971i	0.854241	+	1.47959i	−0.0231073	+	0.999733i	$0.507356\pi$
$930$	−11.0988			−0.363945
$931$	−41.1875	−	16.8582i	−1.34987	−	0.552505i
$932$	19.2677			0.631135
$933$	3.99768	+	6.92418i	0.130878	+	0.226687i
$934$	19.8457	−	34.3738i	0.649371	−	1.12474i
$935$	−1.43858	+	2.49169i	−0.0470464	+	0.0814868i
$936$	5.02261	+	8.69941i	0.164169	+	0.284349i
$937$	−50.0381			−1.63467			−0.817336	−	0.576161i	$-0.804550\pi$
$937$	−50.0381			−1.63467			−0.817336	+	0.576161i	$0.804550\pi$
$938$	−7.41191	−	21.6851i	−0.242008	−	0.708044i
$939$	−15.9147			−0.519357
$940$	10.5415	+	18.2584i	0.343826	+	0.595523i
$941$	−12.7152	+	22.0234i	−0.414504	+	0.717941i	−0.995376	−	0.0960531i	$-0.969378\pi$
$941$	−12.7152	+	22.0234i	−0.414504	+	0.717941i	0.580873	+	0.813995i	$0.302711\pi$
$942$	9.73652	−	16.8642i	0.317233	−	0.549464i
$943$	−5.32777	−	9.22798i	−0.173496	−	0.300504i
$944$	2.40068			0.0781355
$945$	−4.68457	+	5.36440i	−0.152389	+	0.174504i
$946$	2.95611			0.0961114
$947$	−10.3518	−	17.9298i	−0.336387	−	0.582639i	0.647363	−	0.762182i	$-0.275872\pi$
$947$	−10.3518	−	17.9298i	−0.336387	−	0.582639i	−0.983750	+	0.179542i	$0.942538\pi$
$948$	−4.02521	+	6.97186i	−0.130733	+	0.226436i
$949$	23.4333	−	40.5877i	0.760677	−	1.31753i
$950$	−7.63120	−	13.2176i	−0.247589	−	0.428837i
$951$	−26.7915			−0.868775
$952$	−8.47478	−	1.66725i	−0.274669	−	0.0540359i
$953$	−4.08220			−0.132235			−0.0661177	−	0.997812i	$-0.521061\pi$
$953$	−4.08220			−0.132235			−0.0661177	+	0.997812i	$0.521061\pi$
$954$	−1.89957	−	3.29015i	−0.0615009	−	0.106523i
$955$	24.8531	−	43.0469i	0.804228	−	1.39296i
$956$	−5.64716	+	9.78117i	−0.182642	+	0.316346i
$957$	−4.28783	−	7.42674i	−0.138606	−	0.240072i
$958$	−19.6332			−0.634319
$959$	55.5889	+	10.9360i	1.79506	+	0.353143i
$960$	21.1521			0.682681
$961$	8.05956	+	13.9596i	0.259986	+	0.450308i
$962$	−13.7615	+	23.8357i	−0.443690	+	0.768493i
$963$	1.75341	−	3.03699i	0.0565028	−	0.0978657i
$964$	6.23918	+	10.8066i	0.200950	+	0.348056i
$965$	45.8742			1.47674
$966$	2.88205	−	3.30030i	0.0927284	−	0.106185i
$967$	−20.6016			−0.662503			−0.331251	−	0.943543i	$-0.607471\pi$
$967$	−20.6016			−0.662503			−0.331251	+	0.943543i	$0.607471\pi$
$968$	−1.52715	−	2.64510i	−0.0490844	−	0.0850167i
$969$	3.39770	−	5.88499i	0.109150	−	0.189053i
$970$	−18.2186	+	31.5556i	−0.584966	+	1.01319i
$971$	13.1401	+	22.7593i	0.421685	+	0.730380i	0.996104	−	0.0881812i	$-0.0281054\pi$
$971$	13.1401	+	22.7593i	0.421685	+	0.730380i	−0.574419	+	0.818561i	$0.694772\pi$
$972$	0.857576			0.0275067
$973$	−0.728125	−	2.13028i	−0.0233426	−	0.0682938i
$974$	21.5101			0.689228
$975$	−3.69339	−	6.39715i	−0.118283	−	0.204873i
$976$	9.58267	−	16.5977i	0.306734	−	0.531279i
$977$	−14.5896	+	25.2699i	−0.466761	+	0.808454i	−0.999279	−	0.0379644i	$-0.987913\pi$
$977$	−14.5896	+	25.2699i	−0.466761	+	0.808454i	0.532518	+	0.846419i	$0.321246\pi$
$978$	−5.29879	−	9.17778i	−0.169437	−	0.293473i
$979$	−11.6300			−0.371695
$980$	−12.7785	+	9.89082i	−0.408195	+	0.315951i
$981$	3.80995			0.121642
$982$	8.03169	+	13.9113i	0.256302	+	0.443927i
$983$	−23.1034	+	40.0162i	−0.736883	+	1.27632i	0.217009	+	0.976170i	$0.430370\pi$
$983$	−23.1034	+	40.0162i	−0.736883	+	1.27632i	−0.953892	+	0.300150i	$0.902963\pi$
$984$	−10.5024	+	18.1908i	−0.334805	+	0.579900i
$985$	7.33904	+	12.7116i	0.233841	+	0.405025i
$986$	−9.79704			−0.312001
$987$	−7.81512	−	22.8648i	−0.248758	−	0.727794i
$988$	−17.9317			−0.570484
$989$	−2.14261	−	3.71112i	−0.0681312	−	0.118007i
$990$	−1.43858	+	2.49169i	−0.0457209	+	0.0791910i
$991$	15.7825	−	27.3361i	0.501348	−	0.868361i	−0.498650	−	0.866803i	$-0.666171\pi$
$991$	15.7825	−	27.3361i	0.501348	−	0.868361i	0.999999	−	0.00155771i	$-0.000495834\pi$
$992$	8.58796	+	14.8748i	0.272668	+	0.472275i
$993$	10.1227			0.321234
$994$	19.4101	−	22.2270i	0.615652	−	0.704996i
$995$	−11.6596			−0.369635
$996$	−1.05875	−	1.83380i	−0.0335476	−	0.0581062i
$997$	−9.04177	+	15.6608i	−0.286356	+	0.495982i	−0.972937	−	0.231070i	$-0.925777\pi$
$997$	−9.04177	+	15.6608i	−0.286356	+	0.495982i	0.686581	+	0.727053i	$0.259111\pi$
$998$	1.14496	−	1.98312i	0.0362430	−	0.0627747i
$999$	3.91476	+	6.78057i	0.123858	+	0.214528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.i.f.67.4	✓	10
3.2	odd	2		693.2.i.j.298.2		10
7.2	even	3	inner	231.2.i.f.100.4	yes	10
7.3	odd	6		1617.2.a.bb.1.2		5
7.4	even	3		1617.2.a.ba.1.2		5
21.2	odd	6		693.2.i.j.100.2		10
21.11	odd	6		4851.2.a.ca.1.4		5
21.17	even	6		4851.2.a.bz.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.f.67.4	✓	10	1.1	even	1	trivial
231.2.i.f.100.4	yes	10	7.2	even	3	inner
693.2.i.j.100.2		10	21.2	odd	6
693.2.i.j.298.2		10	3.2	odd	2
1617.2.a.ba.1.2		5	7.4	even	3
1617.2.a.bb.1.2		5	7.3	odd	6
4851.2.a.bz.1.4		5	21.17	even	6
4851.2.a.ca.1.4		5	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.534421 + 0.925645i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.428788 - 0.742682i) q^{4} +(1.34592 + 2.33120i) q^{5} +1.06884 q^{6} +(-0.855706 - 2.50355i) q^{7} +3.05430 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.534421 + 0.925645i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.428788 - 0.742682i) q^{4} +(1.34592 + 2.33120i) q^{5} +1.06884 q^{6} +(-0.855706 - 2.50355i) q^{7} +3.05430 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.43858 + 2.49169i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.428788 - 0.742682i) q^{12} -3.28888 q^{13} +(1.86009 - 2.13003i) q^{14} +2.69184 q^{15} +(0.774707 + 1.34183i) q^{16} +(0.534421 - 0.925645i) q^{17} +(0.534421 - 0.925645i) q^{18} +(3.17886 + 5.50595i) q^{19} +2.30845 q^{20} +(-2.59599 - 0.510712i) q^{21} -1.06884 q^{22} +(0.774707 + 1.34183i) q^{23} +(1.52715 - 2.64510i) q^{24} +(-1.12300 + 1.94508i) q^{25} +(-1.75765 - 3.04433i) q^{26} -1.00000 q^{27} +(-2.22626 - 0.437974i) q^{28} -8.57566 q^{29} +(1.43858 + 2.49169i) q^{30} +(-1.92879 + 3.34076i) q^{31} +(2.22626 - 3.85599i) q^{32} +(0.500000 + 0.866025i) q^{33} +1.14242 q^{34} +(4.68457 - 5.36440i) q^{35} -0.857576 q^{36} +(-3.91476 - 6.78057i) q^{37} +(-3.39770 + 5.88499i) q^{38} +(-1.64444 + 2.84825i) q^{39} +(4.11084 + 7.12018i) q^{40} -6.87715 q^{41} +(-0.914616 - 2.67590i) q^{42} -2.76571 q^{43} +(0.428788 + 0.742682i) q^{44} +(1.34592 - 2.33120i) q^{45} +(-0.828039 + 1.43421i) q^{46} +(4.56647 + 7.90936i) q^{47} +1.54941 q^{48} +(-5.53553 + 4.28461i) q^{49} -2.40061 q^{50} +(-0.534421 - 0.925645i) q^{51} +(-1.41023 + 2.44259i) q^{52} +(1.77722 - 3.07824i) q^{53} +(-0.534421 - 0.925645i) q^{54} -2.69184 q^{55} +(-2.61358 - 7.64659i) q^{56} +6.35772 q^{57} +(-4.58301 - 7.93801i) q^{58} +(0.774707 - 1.34183i) q^{59} +(1.15423 - 1.99918i) q^{60} +(-6.18471 - 10.7122i) q^{61} -4.12314 q^{62} +(-1.74029 + 1.99284i) q^{63} +7.85787 q^{64} +(-4.42656 - 7.66703i) q^{65} +(-0.534421 + 0.925645i) q^{66} +(4.05193 - 7.01815i) q^{67} +(-0.458307 - 0.793810i) q^{68} +1.54941 q^{69} +(7.46906 + 1.46939i) q^{70} +10.4350 q^{71} +(-1.52715 - 2.64510i) q^{72} +(-7.12501 + 12.3409i) q^{73} +(4.18426 - 7.24736i) q^{74} +(1.12300 + 1.94508i) q^{75} +5.45223 q^{76} +(2.59599 + 0.510712i) q^{77} -3.51529 q^{78} +(-4.69371 - 8.12974i) q^{79} +(-2.08538 + 3.61199i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.67530 - 6.36580i) q^{82} +2.46916 q^{83} +(-1.49243 + 1.70901i) q^{84} +2.87715 q^{85} +(-1.47806 - 2.56007i) q^{86} +(-4.28783 + 7.42674i) q^{87} +(-1.52715 + 2.64510i) q^{88} +(5.81498 + 10.0718i) q^{89} +2.87715 q^{90} +(2.81431 + 8.23388i) q^{91} +1.32874 q^{92} +(1.92879 + 3.34076i) q^{93} +(-4.88084 + 8.45386i) q^{94} +(-8.55698 + 14.8211i) q^{95} +(-2.22626 - 3.85599i) q^{96} +12.6644 q^{97} +(-6.92433 - 2.83415i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} + 5 q^{3} - 10 q^{4} + 4 q^{5} - 4 q^{6} - q^{7} + 12 q^{8} - 5 q^{9} - 2 q^{10} - 5 q^{11} + 10 q^{12} + 10 q^{13} - 10 q^{14} + 8 q^{15} - 16 q^{16} - 2 q^{17} - 2 q^{18} + 3 q^{19} - 16 q^{20} - 2 q^{21} + 4 q^{22} - 16 q^{23} + 6 q^{24} - 7 q^{25} + 10 q^{26} - 10 q^{27} + 4 q^{28} + 2 q^{30} - 5 q^{31} - 4 q^{32} + 5 q^{33} + 40 q^{34} + 26 q^{35} + 20 q^{36} - 15 q^{37} - 6 q^{38} + 5 q^{39} + 6 q^{40} - 44 q^{41} - 14 q^{42} + 6 q^{43} - 10 q^{44} + 4 q^{45} - 16 q^{46} + 2 q^{47} - 32 q^{48} + 31 q^{49} + 68 q^{50} + 2 q^{51} - 40 q^{52} - 6 q^{53} + 2 q^{54} - 8 q^{55} - 12 q^{56} + 6 q^{57} - 12 q^{58} - 16 q^{59} - 8 q^{60} - 12 q^{61} - 8 q^{62} - q^{63} - 8 q^{64} + 28 q^{65} + 2 q^{66} - 7 q^{67} - 10 q^{68} - 32 q^{69} + 32 q^{70} + 48 q^{71} - 6 q^{72} - 17 q^{73} + 36 q^{74} + 7 q^{75} + 60 q^{76} + 2 q^{77} + 20 q^{78} - 7 q^{79} - 16 q^{80} - 5 q^{81} - 8 q^{82} - 24 q^{83} - 28 q^{84} + 4 q^{85} + 18 q^{86} - 6 q^{88} + 6 q^{89} + 4 q^{90} + 11 q^{91} + 136 q^{92} + 5 q^{93} - 82 q^{94} + 18 q^{95} + 4 q^{96} - 28 q^{97} - 38 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 5 * q^3 - 10 * q^4 + 4 * q^5 - 4 * q^6 - q^7 + 12 * q^8 - 5 * q^9 - 2 * q^10 - 5 * q^11 + 10 * q^12 + 10 * q^13 - 10 * q^14 + 8 * q^15 - 16 * q^16 - 2 * q^17 - 2 * q^18 + 3 * q^19 - 16 * q^20 - 2 * q^21 + 4 * q^22 - 16 * q^23 + 6 * q^24 - 7 * q^25 + 10 * q^26 - 10 * q^27 + 4 * q^28 + 2 * q^30 - 5 * q^31 - 4 * q^32 + 5 * q^33 + 40 * q^34 + 26 * q^35 + 20 * q^36 - 15 * q^37 - 6 * q^38 + 5 * q^39 + 6 * q^40 - 44 * q^41 - 14 * q^42 + 6 * q^43 - 10 * q^44 + 4 * q^45 - 16 * q^46 + 2 * q^47 - 32 * q^48 + 31 * q^49 + 68 * q^50 + 2 * q^51 - 40 * q^52 - 6 * q^53 + 2 * q^54 - 8 * q^55 - 12 * q^56 + 6 * q^57 - 12 * q^58 - 16 * q^59 - 8 * q^60 - 12 * q^61 - 8 * q^62 - q^63 - 8 * q^64 + 28 * q^65 + 2 * q^66 - 7 * q^67 - 10 * q^68 - 32 * q^69 + 32 * q^70 + 48 * q^71 - 6 * q^72 - 17 * q^73 + 36 * q^74 + 7 * q^75 + 60 * q^76 + 2 * q^77 + 20 * q^78 - 7 * q^79 - 16 * q^80 - 5 * q^81 - 8 * q^82 - 24 * q^83 - 28 * q^84 + 4 * q^85 + 18 * q^86 - 6 * q^88 + 6 * q^89 + 4 * q^90 + 11 * q^91 + 136 * q^92 + 5 * q^93 - 82 * q^94 + 18 * q^95 + 4 * q^96 - 28 * q^97 - 38 * q^98 + 10 * q^99

Introduction

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