LMFDB - Embedded newform 342.2.e.c.229.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(115,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("342.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 8x^{10} + 55x^{8} - 2x^{7} + 70x^{6} - 32x^{5} + 73x^{4} - 18x^{3} + 13x^{2} + 2x + 1 $ x^12 + 8x^10 + 55x^8 - 2x^7 + 70x^6 - 32x^5 + 73x^4 - 18x^3 + 13x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			229.3
Root			$-0.122364 - 0.211941i$ of defining polynomial
Character	$\chi$	$=$	342.229
Dual form			342.2.e.c.115.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.147638 + 1.72575i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.573032 + 0.992520i) q^{5} +(1.42072 - 0.990732i) q^{6} +(0.817447 + 1.41586i) q^{7} +1.00000 q^{8} +(-2.95641 + 0.509572i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.147638 + 1.72575i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.573032 + 0.992520i) q^{5} +(1.42072 - 0.990732i) q^{6} +(0.817447 + 1.41586i) q^{7} +1.00000 q^{8} +(-2.95641 + 0.509572i) q^{9} +1.14606 q^{10} +(-1.10449 - 1.91303i) q^{11} +(-1.56836 - 0.735015i) q^{12} +(-2.18454 + 3.78373i) q^{13} +(0.817447 - 1.41586i) q^{14} +(-1.79744 - 0.842374i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.42591 q^{17} +(1.91951 + 2.30554i) q^{18} -1.00000 q^{19} +(-0.573032 - 0.992520i) q^{20} +(-2.32273 + 1.61974i) q^{21} +(-1.10449 + 1.91303i) q^{22} +(-2.16859 + 3.75611i) q^{23} +(0.147638 + 1.72575i) q^{24} +(1.84327 + 3.19264i) q^{25} +4.36908 q^{26} +(-1.31587 - 5.02678i) q^{27} -1.63489 q^{28} +(-0.700052 - 1.21253i) q^{29} +(0.169203 + 1.97781i) q^{30} +(-3.66575 + 6.34926i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.13835 - 2.18851i) q^{33} +(0.712956 + 1.23488i) q^{34} -1.87369 q^{35} +(1.03690 - 2.81511i) q^{36} +6.94627 q^{37} +(0.500000 + 0.866025i) q^{38} +(-6.85229 - 3.21134i) q^{39} +(-0.573032 + 0.992520i) q^{40} +(2.64018 - 4.57292i) q^{41} +(2.56410 + 1.20167i) q^{42} +(4.37956 + 7.58562i) q^{43} +2.20898 q^{44} +(1.18835 - 3.22629i) q^{45} +4.33718 q^{46} +(-1.53629 - 2.66093i) q^{47} +(1.42072 - 0.990732i) q^{48} +(2.16356 - 3.74740i) q^{49} +(1.84327 - 3.19264i) q^{50} +(-0.210519 - 2.46076i) q^{51} +(-2.18454 - 3.78373i) q^{52} +5.16929 q^{53} +(-3.69538 + 3.65297i) q^{54} +2.53163 q^{55} +(0.817447 + 1.41586i) q^{56} +(-0.147638 - 1.72575i) q^{57} +(-0.700052 + 1.21253i) q^{58} +(-0.653079 + 1.13117i) q^{59} +(1.62824 - 1.13544i) q^{60} +(0.535684 + 0.927832i) q^{61} +7.33149 q^{62} +(-3.13819 - 3.76931i) q^{63} +1.00000 q^{64} +(-2.50362 - 4.33639i) q^{65} +(-3.46448 - 1.62364i) q^{66} +(-3.57079 + 6.18479i) q^{67} +(0.712956 - 1.23488i) q^{68} +(-6.80227 - 3.18790i) q^{69} +(0.936845 + 1.62266i) q^{70} +12.0806 q^{71} +(-2.95641 + 0.509572i) q^{72} +6.78533 q^{73} +(-3.47314 - 6.01565i) q^{74} +(-5.23755 + 3.65237i) q^{75} +(0.500000 - 0.866025i) q^{76} +(1.80573 - 3.12761i) q^{77} +(0.645043 + 7.53992i) q^{78} +(-5.40433 - 9.36057i) q^{79} +1.14606 q^{80} +(8.48067 - 3.01301i) q^{81} -5.28035 q^{82} +(2.59860 + 4.50091i) q^{83} +(-0.241373 - 2.82141i) q^{84} +(0.817092 - 1.41524i) q^{85} +(4.37956 - 7.58562i) q^{86} +(1.98916 - 1.38713i) q^{87} +(-1.10449 - 1.91303i) q^{88} -7.62362 q^{89} +(-3.38823 + 0.584002i) q^{90} -7.14298 q^{91} +(-2.16859 - 3.75611i) q^{92} +(-11.4984 - 5.38876i) q^{93} +(-1.53629 + 2.66093i) q^{94} +(0.573032 - 0.992520i) q^{95} +(-1.56836 - 0.735015i) q^{96} +(-7.77317 - 13.4635i) q^{97} -4.32712 q^{98} +(4.24015 + 5.09289i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 2 q^{3} - 6 q^{4} - 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 + 2 * q^3 - 6 * q^4 - 4 * q^6 - 6 * q^7 + 12 * q^8 + 4 * q^9	\( 12 q - 6 q^{2} + 2 q^{3} - 6 q^{4} - 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9} - 6 q^{11} + 2 q^{12} - 6 q^{13} - 6 q^{14} + 10 q^{15} - 6 q^{16} + 4 q^{18} - 12 q^{19} - 18 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} - 30 q^{25} + 12 q^{26} + 14 q^{27} + 12 q^{28} + 6 q^{29} - 20 q^{30} - 6 q^{31} - 6 q^{32} + 22 q^{33} + 24 q^{35} - 8 q^{36} + 12 q^{37} + 6 q^{38} - 32 q^{39} + 6 q^{41} + 24 q^{42} - 12 q^{43} + 12 q^{44} + 26 q^{45} + 24 q^{46} - 6 q^{47} - 4 q^{48} - 18 q^{49} - 30 q^{50} - 12 q^{51} - 6 q^{52} - 36 q^{53} - 16 q^{54} + 48 q^{55} - 6 q^{56} - 2 q^{57} + 6 q^{58} + 12 q^{59} + 10 q^{60} - 12 q^{61} + 12 q^{62} + 30 q^{63} + 12 q^{64} - 6 q^{65} - 20 q^{66} - 18 q^{67} + 40 q^{69} - 12 q^{70} + 36 q^{71} + 4 q^{72} + 48 q^{73} - 6 q^{74} - 68 q^{75} + 6 q^{76} - 6 q^{77} + 52 q^{78} - 18 q^{79} + 64 q^{81} - 12 q^{82} + 12 q^{83} - 6 q^{84} - 36 q^{85} - 12 q^{86} + 32 q^{87} - 6 q^{88} + 12 q^{89} - 34 q^{90} - 24 q^{91} - 12 q^{92} - 46 q^{93} - 6 q^{94} + 2 q^{96} + 18 q^{97} + 36 q^{98} - 22 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 2 * q^3 - 6 * q^4 - 4 * q^6 - 6 * q^7 + 12 * q^8 + 4 * q^9 - 6 * q^11 + 2 * q^12 - 6 * q^13 - 6 * q^14 + 10 * q^15 - 6 * q^16 + 4 * q^18 - 12 * q^19 - 18 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 - 30 * q^25 + 12 * q^26 + 14 * q^27 + 12 * q^28 + 6 * q^29 - 20 * q^30 - 6 * q^31 - 6 * q^32 + 22 * q^33 + 24 * q^35 - 8 * q^36 + 12 * q^37 + 6 * q^38 - 32 * q^39 + 6 * q^41 + 24 * q^42 - 12 * q^43 + 12 * q^44 + 26 * q^45 + 24 * q^46 - 6 * q^47 - 4 * q^48 - 18 * q^49 - 30 * q^50 - 12 * q^51 - 6 * q^52 - 36 * q^53 - 16 * q^54 + 48 * q^55 - 6 * q^56 - 2 * q^57 + 6 * q^58 + 12 * q^59 + 10 * q^60 - 12 * q^61 + 12 * q^62 + 30 * q^63 + 12 * q^64 - 6 * q^65 - 20 * q^66 - 18 * q^67 + 40 * q^69 - 12 * q^70 + 36 * q^71 + 4 * q^72 + 48 * q^73 - 6 * q^74 - 68 * q^75 + 6 * q^76 - 6 * q^77 + 52 * q^78 - 18 * q^79 + 64 * q^81 - 12 * q^82 + 12 * q^83 - 6 * q^84 - 36 * q^85 - 12 * q^86 + 32 * q^87 - 6 * q^88 + 12 * q^89 - 34 * q^90 - 24 * q^91 - 12 * q^92 - 46 * q^93 - 6 * q^94 + 2 * q^96 + 18 * q^97 + 36 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.147638	+	1.72575i	0.0852390	+	0.996361i
$3$	0.147638	+	1.72575i	0.0852390	+	0.996361i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.573032	+	0.992520i	−0.256267	+	0.443868i	−0.965239	−	0.261369i	$-0.915826\pi$
$5$	−0.573032	+	0.992520i	−0.256267	+	0.443868i	0.708972	+	0.705237i	$0.249159\pi$
$6$	1.42072	−	0.990732i	0.580007	−	0.404465i
$7$	0.817447	+	1.41586i	0.308966	+	0.535144i	0.978136	−	0.207964i	$-0.0666838\pi$
$7$	0.817447	+	1.41586i	0.308966	+	0.535144i	−0.669171	+	0.743109i	$0.733350\pi$
$8$	1.00000			0.353553
$9$	−2.95641	+	0.509572i	−0.985469	+	0.169857i
$10$	1.14606			0.362417
$11$	−1.10449	−	1.91303i	−0.333017	−	0.576802i	0.650085	−	0.759861i	$-0.274733\pi$
$11$	−1.10449	−	1.91303i	−0.333017	−	0.576802i	−0.983102	+	0.183060i	$0.941400\pi$
$12$	−1.56836	−	0.735015i	−0.452747	−	0.212181i
$13$	−2.18454	+	3.78373i	−0.605882	+	1.04942i	0.386029	+	0.922486i	$0.373846\pi$
$13$	−2.18454	+	3.78373i	−0.605882	+	1.04942i	−0.991911	+	0.126932i	$0.959487\pi$
$14$	0.817447	−	1.41586i	0.218472	−	0.378404i
$15$	−1.79744	−	0.842374i	−0.464097	−	0.217500i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.42591			−0.345834			−0.172917	−	0.984936i	$-0.555319\pi$
$17$	−1.42591			−0.345834			−0.172917	+	0.984936i	$0.555319\pi$
$18$	1.91951	+	2.30554i	0.452432	+	0.543420i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−0.573032	−	0.992520i	−0.128134	−	0.221934i
$21$	−2.32273	+	1.61974i	−0.506861	+	0.353457i
$22$	−1.10449	+	1.91303i	−0.235478	+	0.407860i
$23$	−2.16859	+	3.75611i	−0.452183	+	0.783204i	−0.998521	−	0.0543609i	$-0.982688\pi$
$23$	−2.16859	+	3.75611i	−0.452183	+	0.783204i	0.546339	+	0.837564i	$0.316021\pi$
$24$	0.147638	+	1.72575i	0.0301365	+	0.352267i
$25$	1.84327	+	3.19264i	0.368654	+	0.638527i
$26$	4.36908			0.856847
$27$	−1.31587	−	5.02678i	−0.253240	−	0.967404i
$28$	−1.63489			−0.308966
$29$	−0.700052	−	1.21253i	−0.129996	−	0.225160i	0.793679	−	0.608337i	$-0.208163\pi$
$29$	−0.700052	−	1.21253i	−0.129996	−	0.225160i	−0.923675	+	0.383177i	$0.874830\pi$
$30$	0.169203	+	1.97781i	0.0308920	+	0.361098i
$31$	−3.66575	+	6.34926i	−0.658388	+	1.14036i	0.322645	+	0.946520i	$0.395428\pi$
$31$	−3.66575	+	6.34926i	−0.658388	+	1.14036i	−0.981033	+	0.193841i	$0.937905\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.13835	−	2.18851i	0.546316	−	0.380971i
$34$	0.712956	+	1.23488i	0.122271	+	0.211779i
$35$	−1.87369			−0.316712
$36$	1.03690	−	2.81511i	0.172817	−	0.469185i
$37$	6.94627			1.14196			0.570980	−	0.820964i	$-0.306563\pi$
$37$	6.94627			1.14196			0.570980	+	0.820964i	$0.306563\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$	−6.85229	−	3.21134i	−1.09724	−	0.514226i
$40$	−0.573032	+	0.992520i	−0.0906042	+	0.156931i
$41$	2.64018	−	4.57292i	0.412326	−	0.714170i	−0.582818	−	0.812603i	$-0.698050\pi$
$41$	2.64018	−	4.57292i	0.412326	−	0.714170i	0.995144	+	0.0984333i	$0.0313831\pi$
$42$	2.56410	+	1.20167i	0.395649	+	0.185422i
$43$	4.37956	+	7.58562i	0.667877	+	1.15680i	0.978497	+	0.206262i	$0.0661300\pi$
$43$	4.37956	+	7.58562i	0.667877	+	1.15680i	−0.310620	+	0.950534i	$0.600537\pi$
$44$	2.20898			0.333017
$45$	1.18835	−	3.22629i	0.177149	−	0.480947i
$46$	4.33718			0.639483
$47$	−1.53629	−	2.66093i	−0.224091	−	0.388137i	0.731955	−	0.681353i	$-0.238608\pi$
$47$	−1.53629	−	2.66093i	−0.224091	−	0.388137i	−0.956046	+	0.293216i	$0.905275\pi$
$48$	1.42072	−	0.990732i	0.205064	−	0.143000i
$49$	2.16356	−	3.74740i	0.309080	−	0.535343i
$50$	1.84327	−	3.19264i	0.260678	−	0.451507i
$51$	−0.210519	−	2.46076i	−0.0294786	−	0.344576i
$52$	−2.18454	−	3.78373i	−0.302941	−	0.524709i
$53$	5.16929			0.710056			0.355028	−	0.934856i	$-0.384471\pi$
$53$	5.16929			0.710056			0.355028	+	0.934856i	$0.384471\pi$
$54$	−3.69538	+	3.65297i	−0.502878	+	0.497106i
$55$	2.53163			0.341365
$56$	0.817447	+	1.41586i	0.109236	+	0.189202i
$57$	−0.147638	−	1.72575i	−0.0195552	−	0.228581i
$58$	−0.700052	+	1.21253i	−0.0919213	+	0.159212i
$59$	−0.653079	+	1.13117i	−0.0850236	+	0.147265i	−0.905401	−	0.424557i	$-0.860430\pi$
$59$	−0.653079	+	1.13117i	−0.0850236	+	0.147265i	0.820378	+	0.571822i	$0.193763\pi$
$60$	1.62824	−	1.13544i	0.210204	−	0.146585i
$61$	0.535684	+	0.927832i	0.0685873	+	0.118797i	0.898280	−	0.439424i	$-0.144817\pi$
$61$	0.535684	+	0.927832i	0.0685873	+	0.118797i	−0.829692	+	0.558221i	$0.811484\pi$
$62$	7.33149			0.931101
$63$	−3.13819	−	3.76931i	−0.395374	−	0.474888i
$64$	1.00000			0.125000
$65$	−2.50362	−	4.33639i	−0.310536	−	0.537864i
$66$	−3.46448	−	1.62364i	−0.426448	−	0.199856i
$67$	−3.57079	+	6.18479i	−0.436242	+	0.755593i	−0.997396	−	0.0721184i	$-0.977024\pi$
$67$	−3.57079	+	6.18479i	−0.436242	+	0.755593i	0.561154	+	0.827711i	$0.310357\pi$
$68$	0.712956	−	1.23488i	0.0864586	−	0.149751i
$69$	−6.80227	−	3.18790i	−0.818897	−	0.383778i
$70$	0.936845	+	1.62266i	0.111974	+	0.193945i
$71$	12.0806			1.43370			0.716849	−	0.697228i	$-0.245584\pi$
$71$	12.0806			1.43370			0.716849	+	0.697228i	$0.245584\pi$
$72$	−2.95641	+	0.509572i	−0.348416	+	0.0600537i
$73$	6.78533			0.794163			0.397081	−	0.917783i	$-0.370023\pi$
$73$	6.78533			0.794163			0.397081	+	0.917783i	$0.370023\pi$
$74$	−3.47314	−	6.01565i	−0.403744	−	0.699305i
$75$	−5.23755	+	3.65237i	−0.604780	+	0.421740i
$76$	0.500000	−	0.866025i	0.0573539	−	0.0993399i
$77$	1.80573	−	3.12761i	0.205781	−	0.356424i
$78$	0.645043	+	7.53992i	0.0730367	+	0.853728i
$79$	−5.40433	−	9.36057i	−0.608034	−	1.05315i	−0.991564	−	0.129618i	$-0.958625\pi$
$79$	−5.40433	−	9.36057i	−0.608034	−	1.05315i	0.383530	−	0.923529i	$-0.374708\pi$
$80$	1.14606			0.128134
$81$	8.48067	−	3.01301i	0.942297	−	0.334778i
$82$	−5.28035			−0.583117
$83$	2.59860	+	4.50091i	0.285234	+	0.494039i	0.972666	−	0.232209i	$-0.0745954\pi$
$83$	2.59860	+	4.50091i	0.285234	+	0.494039i	−0.687432	+	0.726249i	$0.741262\pi$
$84$	−0.241373	−	2.82141i	−0.0263359	−	0.307841i
$85$	0.817092	−	1.41524i	0.0886261	−	0.153505i
$86$	4.37956	−	7.58562i	0.472260	−	0.817978i
$87$	1.98916	−	1.38713i	0.213260	−	0.148716i
$88$	−1.10449	−	1.91303i	−0.117739	−	0.203930i
$89$	−7.62362			−0.808102			−0.404051	−	0.914736i	$-0.632398\pi$
$89$	−7.62362			−0.808102			−0.404051	+	0.914736i	$0.632398\pi$
$90$	−3.38823	+	0.584002i	−0.357151	+	0.0615592i
$91$	−7.14298			−0.748787
$92$	−2.16859	−	3.75611i	−0.226091	−	0.391602i
$93$	−11.4984	−	5.38876i	−1.19233	−	0.558788i
$94$	−1.53629	+	2.66093i	−0.158456	+	0.274454i
$95$	0.573032	−	0.992520i	0.0587918	−	0.101830i
$96$	−1.56836	−	0.735015i	−0.160070	−	0.0750172i
$97$	−7.77317	−	13.4635i	−0.789246	−	1.36701i	−0.926429	−	0.376468i	$-0.877138\pi$
$97$	−7.77317	−	13.4635i	−0.789246	−	1.36701i	0.137184	−	0.990546i	$-0.456195\pi$
$98$	−4.32712			−0.437105
$99$	4.24015	+	5.09289i	0.426151	+	0.511855i
$100$	−3.68654			−0.368654
$101$	3.96265	+	6.86352i	0.394299	+	0.682945i	0.993011	−	0.118018i	$-0.0376542\pi$
$101$	3.96265	+	6.86352i	0.394299	+	0.682945i	−0.598713	+	0.800964i	$0.704321\pi$
$102$	−2.02582	+	1.41270i	−0.200586	+	0.139878i
$103$	2.17163	−	3.76138i	0.213978	−	0.370620i	−0.738978	−	0.673729i	$-0.764691\pi$
$103$	2.17163	−	3.76138i	0.213978	−	0.370620i	0.952956	+	0.303109i	$0.0980247\pi$
$104$	−2.18454	+	3.78373i	−0.214212	+	0.371025i
$105$	−0.276628	−	3.23352i	−0.0269962	−	0.315559i
$106$	−2.58464	−	4.47673i	−0.251043	−	0.434819i
$107$	−4.42033			−0.427329			−0.213665	−	0.976907i	$-0.568540\pi$
$107$	−4.42033			−0.427329			−0.213665	+	0.976907i	$0.568540\pi$
$108$	5.01125	+	1.37381i	0.482208	+	0.132195i
$109$	18.5327			1.77511			0.887554	−	0.460704i	$-0.152403\pi$
$109$	18.5327			1.77511			0.887554	+	0.460704i	$0.152403\pi$
$110$	−1.26582	−	2.19246i	−0.120691	−	0.209043i
$111$	1.02553	+	11.9875i	0.0973395	+	1.13780i
$112$	0.817447	−	1.41586i	0.0772415	−	0.133786i
$113$	5.17058	−	8.95570i	0.486407	−	0.842482i	−0.513471	−	0.858107i	$-0.671641\pi$
$113$	5.17058	−	8.95570i	0.486407	−	0.842482i	0.999878	+	0.0156253i	$0.00497390\pi$
$114$	−1.42072	+	0.990732i	−0.133063	+	0.0927906i
$115$	−2.48534	−	4.30474i	−0.231759	−	0.401419i
$116$	1.40010			0.129996
$117$	4.53030	−	12.2994i	0.418826	−	1.13708i
$118$	1.30616			0.120242
$119$	−1.16561	−	2.01889i	−0.106851	−	0.185071i
$120$	−1.79744	−	0.842374i	−0.164083	−	0.0768978i
$121$	3.06020	−	5.30042i	0.278200	−	0.481856i
$122$	0.535684	−	0.927832i	0.0484986	−	0.0840020i
$123$	8.28149	+	3.88114i	0.746717	+	0.349950i
$124$	−3.66575	−	6.34926i	−0.329194	−	0.570180i
$125$	−9.95532			−0.890431
$126$	−1.69522	+	4.60240i	−0.151022	+	0.410015i
$127$	8.15572			0.723703			0.361852	−	0.932236i	$-0.382145\pi$
$127$	8.15572			0.723703			0.361852	+	0.932236i	$0.382145\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−12.4443	+	8.67794i	−1.09566	+	0.764050i
$130$	−2.50362	+	4.33639i	−0.219582	+	0.380327i
$131$	−2.86864	+	4.96864i	−0.250635	+	0.434112i	−0.963701	−	0.266985i	$-0.913973\pi$
$131$	−2.86864	+	4.96864i	−0.250635	+	0.434112i	0.713066	+	0.701097i	$0.247306\pi$
$132$	0.326130	+	3.81214i	0.0283860	+	0.331805i
$133$	−0.817447	−	1.41586i	−0.0708816	−	0.122771i
$134$	7.14158			0.616939
$135$	5.74321	+	1.57447i	0.494297	+	0.135509i
$136$	−1.42591			−0.122271
$137$	10.5788	+	18.3230i	0.903808	+	1.56544i	0.822509	+	0.568752i	$0.192574\pi$
$137$	10.5788	+	18.3230i	0.903808	+	1.56544i	0.0812995	+	0.996690i	$0.474093\pi$
$138$	0.640334	+	7.48488i	0.0545089	+	0.637156i
$139$	−9.18089	+	15.9018i	−0.778713	+	1.34877i	0.153971	+	0.988075i	$0.450794\pi$
$139$	−9.18089	+	15.9018i	−0.778713	+	1.34877i	−0.932684	+	0.360695i	$0.882540\pi$
$140$	0.936845	−	1.62266i	0.0791779	−	0.137140i
$141$	4.36528	−	3.04410i	0.367623	−	0.256360i
$142$	−6.04028	−	10.4621i	−0.506889	−	0.877957i
$143$	9.65121			0.807075
$144$	1.91951	+	2.30554i	0.159959	+	0.192128i
$145$	1.60461			0.133255
$146$	−3.39266	−	5.87627i	−0.280779	−	0.486323i
$147$	6.78649	+	3.18050i	0.559740	+	0.262323i
$148$	−3.47314	+	6.01565i	−0.285490	+	0.494483i
$149$	−10.1991	+	17.6653i	−0.835541	+	1.44720i	0.0580476	+	0.998314i	$0.481512\pi$
$149$	−10.1991	+	17.6653i	−0.835541	+	1.44720i	−0.893589	+	0.448886i	$0.851821\pi$
$150$	5.78182	+	2.70966i	0.472084	+	0.221243i
$151$	7.11165	+	12.3177i	0.578738	+	1.00240i	0.995624	+	0.0934447i	$0.0297878\pi$
$151$	7.11165	+	12.3177i	0.578738	+	1.00240i	−0.416887	+	0.908958i	$0.636879\pi$
$152$	−1.00000			−0.0811107
$153$	4.21557	−	0.726605i	0.340809	−	0.0587425i
$154$	−3.61145			−0.291019
$155$	−4.20118	−	7.27665i	−0.337447	−	0.584475i
$156$	6.20724	−	4.32858i	0.496977	−	0.346564i
$157$	0.979456	−	1.69647i	0.0781691	−	0.135393i	−0.824291	−	0.566166i	$-0.808426\pi$
$157$	0.979456	−	1.69647i	0.0781691	−	0.135393i	0.902460	+	0.430774i	$0.141759\pi$
$158$	−5.40433	+	9.36057i	−0.429945	+	0.744687i
$159$	0.763184	+	8.92088i	0.0605244	+	0.707472i
$160$	−0.573032	−	0.992520i	−0.0453021	−	0.0784656i
$161$	−7.09083			−0.558836
$162$	−6.84968	−	5.83797i	−0.538161	−	0.458675i
$163$	4.31174			0.337722			0.168861	−	0.985640i	$-0.445991\pi$
$163$	4.31174			0.337722			0.168861	+	0.985640i	$0.445991\pi$
$164$	2.64018	+	4.57292i	0.206163	+	0.357085i
$165$	0.373766	+	4.36896i	0.0290976	+	0.340123i
$166$	2.59860	−	4.50091i	0.201691	−	0.349339i
$167$	−2.47885	+	4.29349i	−0.191819	+	0.332241i	−0.945853	−	0.324595i	$-0.894772\pi$
$167$	−2.47885	+	4.29349i	−0.191819	+	0.332241i	0.754034	+	0.656835i	$0.228105\pi$
$168$	−2.32273	+	1.61974i	−0.179202	+	0.124966i
$169$	−3.04442	−	5.27309i	−0.234186	−	0.405622i
$170$	−1.63418			−0.125336
$171$	2.95641	−	0.509572i	0.226082	−	0.0389680i
$172$	−8.75912			−0.667877
$173$	6.55059	+	11.3460i	0.498032	+	0.862617i	0.999997	−	0.00227090i	$-0.000722851\pi$
$173$	6.55059	+	11.3460i	0.498032	+	0.862617i	−0.501965	+	0.864888i	$0.667390\pi$
$174$	−2.19587	−	1.02910i	−0.166468	−	0.0780157i
$175$	−3.01355	+	5.21962i	−0.227803	+	0.394566i
$176$	−1.10449	+	1.91303i	−0.0832541	+	0.144200i
$177$	−2.04853	−	0.960046i	−0.153977	−	0.0721615i
$178$	3.81181	+	6.60225i	0.285707	+	0.494859i
$179$	−12.2984			−0.919224			−0.459612	−	0.888120i	$-0.652012\pi$
$179$	−12.2984			−0.919224			−0.459612	+	0.888120i	$0.652012\pi$
$180$	2.19987	+	2.64229i	0.163969	+	0.196945i
$181$	−1.39563			−0.103736			−0.0518680	−	0.998654i	$-0.516518\pi$
$181$	−1.39563			−0.103736			−0.0518680	+	0.998654i	$0.516518\pi$
$182$	3.57149	+	6.18600i	0.264736	+	0.458537i
$183$	−1.52212	+	1.06144i	−0.112518	+	0.0784638i
$184$	−2.16859	+	3.75611i	−0.159871	+	0.276904i
$185$	−3.98043	+	6.89431i	−0.292647	+	0.506880i
$186$	1.08241	+	12.6523i	0.0793661	+	0.927712i
$187$	1.57491	+	2.72782i	0.115169	+	0.199478i
$188$	3.07258			0.224091
$189$	6.04155	−	5.97221i	0.439458	−	0.434414i
$190$	−1.14606			−0.0831441
$191$	0.0522362	+	0.0904757i	0.00377968	+	0.00654659i	0.867909	−	0.496723i	$-0.165464\pi$
$191$	0.0522362	+	0.0904757i	0.00377968	+	0.00654659i	−0.864129	+	0.503270i	$0.832130\pi$
$192$	0.147638	+	1.72575i	0.0106549	+	0.124545i
$193$	10.4870	−	18.1640i	0.754870	−	1.30747i	−0.190570	−	0.981674i	$-0.561033\pi$
$193$	10.4870	−	18.1640i	0.754870	−	1.30747i	0.945439	−	0.325799i	$-0.105633\pi$
$194$	−7.77317	+	13.4635i	−0.558081	+	0.966625i
$195$	7.11389	−	4.96083i	0.509436	−	0.355252i
$196$	2.16356	+	3.74740i	0.154540	+	0.267671i
$197$	21.4751			1.53004			0.765018	−	0.644009i	$-0.222730\pi$
$197$	21.4751			1.53004			0.765018	+	0.644009i	$0.222730\pi$
$198$	2.29049	−	6.21853i	0.162778	−	0.441931i
$199$	6.38880			0.452890			0.226445	−	0.974024i	$-0.427290\pi$
$199$	6.38880			0.452890			0.226445	+	0.974024i	$0.427290\pi$
$200$	1.84327	+	3.19264i	0.130339	+	0.225754i
$201$	−11.2006	−	5.24917i	−0.790028	−	0.370248i
$202$	3.96265	−	6.86352i	0.278811	−	0.482915i
$203$	1.14451	−	1.98235i	0.0803289	−	0.139134i
$204$	2.23634	+	1.04807i	0.156575	+	0.0733793i
$205$	3.02581	+	5.24085i	0.211332	+	0.366037i
$206$	−4.34327			−0.302610
$207$	4.49723	−	12.2096i	0.312579	−	0.848629i
$208$	4.36908			0.302941
$209$	1.10449	+	1.91303i	0.0763992	+	0.132327i
$210$	−2.66199	+	1.85633i	−0.183695	+	0.128099i
$211$	0.151291	−	0.262044i	0.0104153	−	0.0180398i	−0.860771	−	0.508993i	$-0.830018\pi$
$211$	0.151291	−	0.262044i	0.0104153	−	0.0180398i	0.871186	+	0.490953i	$0.163351\pi$
$212$	−2.58464	+	4.47673i	−0.177514	+	0.307463i
$213$	1.78355	+	20.8480i	0.122207	+	1.42848i
$214$	2.21016	+	3.82812i	0.151084	+	0.261685i
$215$	−10.0385			−0.684620
$216$	−1.31587	−	5.02678i	−0.0895337	−	0.342029i
$217$	−11.9862			−0.813677
$218$	−9.26634	−	16.0498i	−0.627595	−	1.08703i
$219$	1.00177	+	11.7098i	0.0676936	+	0.791272i
$220$	−1.26582	+	2.19246i	−0.0853413	+	0.147816i
$221$	3.11496	−	5.39527i	0.209535	−	0.362925i
$222$	9.86872	−	6.88189i	0.662345	−	0.461882i
$223$	−10.8305	−	18.7590i	−0.725263	−	1.25619i	−0.958866	−	0.283860i	$-0.908385\pi$
$223$	−10.8305	−	18.7590i	−0.725263	−	1.25619i	0.233602	−	0.972332i	$-0.424949\pi$
$224$	−1.63489			−0.109236
$225$	−7.07633	−	8.49945i	−0.471756	−	0.566630i
$226$	−10.3412			−0.687883
$227$	−3.75429	−	6.50262i	−0.249181	−	0.431594i	0.714118	−	0.700026i	$-0.246828\pi$
$227$	−3.75429	−	6.50262i	−0.249181	−	0.431594i	−0.963299	+	0.268431i	$0.913495\pi$
$228$	1.56836	+	0.735015i	0.103867	+	0.0486776i
$229$	3.05764	−	5.29598i	0.202054	−	0.349968i	−0.747136	−	0.664671i	$-0.768572\pi$
$229$	3.05764	−	5.29598i	0.202054	−	0.349968i	0.949190	+	0.314703i	$0.101905\pi$
$230$	−2.48534	+	4.30474i	−0.163879	+	0.283846i
$231$	5.66405	+	2.65447i	0.372667	+	0.174651i
$232$	−0.700052	−	1.21253i	−0.0459607	−	0.0796062i
$233$	−25.3810			−1.66277			−0.831383	−	0.555700i	$-0.812450\pi$
$233$	−25.3810			−1.66277			−0.831383	+	0.555700i	$0.812450\pi$
$234$	−12.9168	+	2.22636i	−0.844395	+	0.145542i
$235$	3.52137			0.229709
$236$	−0.653079	−	1.13117i	−0.0425118	−	0.0736326i
$237$	15.3561	−	10.7085i	0.997485	−	0.695591i
$238$	−1.16561	+	2.01889i	−0.0755550	+	0.130865i
$239$	−3.08704	+	5.34692i	−0.199684	+	0.345863i	−0.948426	−	0.316999i	$-0.897325\pi$
$239$	−3.08704	+	5.34692i	−0.199684	+	0.345863i	0.748742	+	0.662862i	$0.230658\pi$
$240$	0.169203	+	1.97781i	0.0109220	+	0.127667i
$241$	−5.91630	−	10.2473i	−0.381102	−	0.660089i	0.610118	−	0.792311i	$-0.291122\pi$
$241$	−5.91630	−	10.2473i	−0.381102	−	0.660089i	−0.991220	+	0.132222i	$0.957789\pi$
$242$	−6.12040			−0.393434
$243$	6.45176	+	14.1907i	0.413880	+	0.910331i
$244$	−1.07137			−0.0685873
$245$	2.47958	+	4.29476i	0.158414	+	0.274382i
$246$	−0.779581	−	9.11255i	−0.0497043	−	0.580995i
$247$	2.18454	−	3.78373i	0.138999	−	0.240753i
$248$	−3.66575	+	6.34926i	−0.232775	+	0.403178i
$249$	−7.38378	+	5.14904i	−0.467928	+	0.326307i
$250$	4.97766	+	8.62156i	0.314815	+	0.545275i
$251$	−29.5694			−1.86640			−0.933201	−	0.359354i	$-0.882997\pi$
$251$	−29.5694			−1.86640			−0.933201	+	0.359354i	$0.882997\pi$
$252$	4.83341	−	0.833097i	0.304476	−	0.0524802i
$253$	9.58076			0.602337
$254$	−4.07786	−	7.06306i	−0.255868	−	0.443176i
$255$	2.56299	+	1.20115i	0.160501	+	0.0752189i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.1387	−	24.4889i	0.881948	−	1.52758i	0.0327753	−	0.999463i	$-0.489565\pi$
$257$	14.1387	−	24.4889i	0.881948	−	1.52758i	0.849172	−	0.528116i	$-0.177101\pi$
$258$	13.7375	+	6.43809i	0.855256	+	0.400818i
$259$	5.67821	+	9.83494i	0.352827	+	0.611114i
$260$	5.00724			0.310536
$261$	2.68751	+	3.22799i	0.166353	+	0.199808i
$262$	5.73729			0.354451
$263$	7.44756	+	12.8996i	0.459236	+	0.795421i	0.998921	−	0.0464466i	$-0.0147897\pi$
$263$	7.44756	+	12.8996i	0.459236	+	0.795421i	−0.539684	+	0.841867i	$0.681456\pi$
$264$	3.13835	−	2.18851i	0.193152	−	0.134693i
$265$	−2.96216	+	5.13062i	−0.181964	+	0.315171i
$266$	−0.817447	+	1.41586i	−0.0501209	+	0.0868119i
$267$	−1.12554	−	13.1564i	−0.0688818	−	0.805161i
$268$	−3.57079	−	6.18479i	−0.218121	−	0.377796i
$269$	−28.5720			−1.74206			−0.871032	−	0.491227i	$-0.836549\pi$
$269$	−28.5720			−1.74206			−0.871032	+	0.491227i	$0.836549\pi$
$270$	−1.50807	−	5.76100i	−0.0917783	−	0.350603i
$271$	−17.7114			−1.07589			−0.537947	−	0.842979i	$-0.680800\pi$
$271$	−17.7114			−1.07589			−0.537947	+	0.842979i	$0.680800\pi$
$272$	0.712956	+	1.23488i	0.0432293	+	0.0748753i
$273$	−1.05458	−	12.3270i	−0.0638258	−	0.746062i
$274$	10.5788	−	18.3230i	0.639089	−	1.10693i
$275$	4.07175	−	7.05248i	0.245536	−	0.425280i
$276$	6.16193	−	4.29699i	0.370905	−	0.258648i
$277$	−8.37956	−	14.5138i	−0.503479	−	0.872051i	−0.999992	−	0.00402182i	$-0.998720\pi$
$277$	−8.37956	−	14.5138i	−0.503479	−	0.872051i	0.496513	−	0.868029i	$-0.334614\pi$
$278$	18.3618			1.10127
$279$	7.60203	−	20.6390i	0.455122	−	1.23562i
$280$	−1.87369			−0.111974
$281$	2.02850	+	3.51347i	0.121010	+	0.209596i	0.920166	−	0.391528i	$-0.128053\pi$
$281$	2.02850	+	3.51347i	0.121010	+	0.209596i	−0.799156	+	0.601124i	$0.794720\pi$
$282$	−4.81891	−	2.25839i	−0.286962	−	0.134485i
$283$	−9.69303	+	16.7888i	−0.576191	+	0.997992i	0.419720	+	0.907654i	$0.362128\pi$
$283$	−9.69303	+	16.7888i	−0.576191	+	0.997992i	−0.995911	+	0.0903385i	$0.971205\pi$
$284$	−6.04028	+	10.4621i	−0.358425	+	0.620810i
$285$	1.79744	+	0.842374i	0.106471	+	0.0498979i
$286$	−4.82561	−	8.35820i	−0.285344	−	0.494230i
$287$	8.63281			0.509579
$288$	1.03690	−	2.81511i	0.0610999	−	0.165882i
$289$	−14.9668			−0.880399
$290$	−0.802304	−	1.38963i	−0.0471129	−	0.0816019i
$291$	22.0870	−	15.4023i	1.29476	−	0.902896i
$292$	−3.39266	+	5.87627i	−0.198541	+	0.343882i
$293$	0.515513	−	0.892896i	0.0301166	−	0.0521635i	−0.850574	−	0.525855i	$-0.823745\pi$
$293$	0.515513	−	0.892896i	0.0301166	−	0.0521635i	0.880691	+	0.473691i	$0.157079\pi$
$294$	−0.638849	−	7.46752i	−0.0372584	−	0.435515i
$295$	−0.748470	−	1.29639i	−0.0435776	−	0.0754786i
$296$	6.94627			0.403744
$297$	−8.16303	+	8.06934i	−0.473667	+	0.468230i
$298$	20.3982			1.18163
$299$	−9.47475	−	16.4107i	−0.547939	−	0.949058i
$300$	−0.544274	−	6.36203i	−0.0314237	−	0.367312i
$301$	−7.16011	+	12.4017i	−0.412702	+	0.714821i
$302$	7.11165	−	12.3177i	0.409229	−	0.708806i
$303$	−11.2597	+	7.85185i	−0.646850	+	0.451077i
$304$	0.500000	+	0.866025i	0.0286770	+	0.0496700i
$305$	−1.22786			−0.0703068
$306$	−2.73704	−	3.28749i	−0.156466	−	0.187933i
$307$	−8.79051			−0.501701			−0.250850	−	0.968026i	$-0.580710\pi$
$307$	−8.79051			−0.501701			−0.250850	+	0.968026i	$0.580710\pi$
$308$	1.80573	+	3.12761i	0.102891	+	0.178212i
$309$	6.81181	+	3.19237i	0.387510	+	0.181608i
$310$	−4.20118	+	7.27665i	−0.238611	+	0.413286i
$311$	15.1997	−	26.3266i	0.861895	−	1.49285i	−0.00820248	−	0.999966i	$-0.502611\pi$
$311$	15.1997	−	26.3266i	0.861895	−	1.49285i	0.870098	−	0.492880i	$-0.164056\pi$
$312$	−6.85229	−	3.21134i	−0.387934	−	0.181806i
$313$	−0.531531	−	0.920638i	−0.0300439	−	0.0520375i	0.850613	−	0.525793i	$-0.176231\pi$
$313$	−0.531531	−	0.920638i	−0.0300439	−	0.0520375i	−0.880656	+	0.473756i	$0.842898\pi$
$314$	−1.95891			−0.110548
$315$	5.53939	−	0.954781i	0.312109	−	0.0537958i
$316$	10.8087			0.608034
$317$	8.30479	+	14.3843i	0.466444	+	0.807904i	0.999265	−	0.0383233i	$-0.0122017\pi$
$317$	8.30479	+	14.3843i	0.466444	+	0.807904i	−0.532822	+	0.846228i	$0.678868\pi$
$318$	7.34412	−	5.12138i	0.411838	−	0.287193i
$319$	−1.54640	+	2.67845i	−0.0865819	+	0.149964i
$320$	−0.573032	+	0.992520i	−0.0320334	+	0.0554835i
$321$	−0.652609	−	7.62837i	−0.0364251	−	0.425774i
$322$	3.54542	+	6.14084i	0.197578	+	0.342216i
$323$	1.42591			0.0793398
$324$	−1.63100	+	8.85098i	−0.0906109	+	0.491721i
$325$	−16.1068			−0.893443
$326$	−2.15587	−	3.73408i	−0.119403	−	0.206811i
$327$	2.73613	+	31.9827i	0.151308	+	1.76865i
$328$	2.64018	−	4.57292i	0.145779	−	0.252497i
$329$	2.51167	−	4.35034i	0.138473	−	0.239842i
$330$	3.59675	−	2.50817i	0.197994	−	0.138070i
$331$	−8.36543	−	14.4893i	−0.459805	−	0.796406i	0.539145	−	0.842213i	$-0.318748\pi$
$331$	−8.36543	−	14.4893i	−0.459805	−	0.796406i	−0.998950	+	0.0458067i	$0.985414\pi$
$332$	−5.19721			−0.285234
$333$	−20.5360	+	3.53963i	−1.12537	+	0.193970i
$334$	4.95770			0.271273
$335$	−4.09235	−	7.08816i	−0.223589	−	0.387268i
$336$	2.56410	+	1.20167i	0.139883	+	0.0655565i
$337$	15.7918	−	27.3523i	0.860237	−	1.48997i	−0.0114634	−	0.999934i	$-0.503649\pi$
$337$	15.7918	−	27.3523i	0.860237	−	1.48997i	0.871700	−	0.490040i	$-0.163018\pi$
$338$	−3.04442	+	5.27309i	−0.165594	+	0.286818i
$339$	16.2187	+	7.60091i	0.880876	+	0.412825i
$340$	0.817092	+	1.41524i	0.0443130	+	0.0767524i
$341$	16.1951			0.877016
$342$	−1.91951	−	2.30554i	−0.103795	−	0.124669i
$343$	18.5186			0.999913
$344$	4.37956	+	7.58562i	0.236130	+	0.408989i
$345$	7.06196	−	4.92462i	0.380203	−	0.265133i
$346$	6.55059	−	11.3460i	0.352162	−	0.609962i
$347$	−17.2828	+	29.9347i	−0.927789	+	1.60698i	−0.140776	+	0.990042i	$0.544960\pi$
$347$	−17.2828	+	29.9347i	−0.927789	+	1.60698i	−0.787013	+	0.616936i	$0.788374\pi$
$348$	0.206709	+	2.41623i	0.0110808	+	0.129523i
$349$	−2.51645	−	4.35862i	−0.134703	−	0.233312i	0.790781	−	0.612099i	$-0.209675\pi$
$349$	−2.51645	−	4.35862i	−0.134703	−	0.233312i	−0.925484	+	0.378787i	$0.876341\pi$
$350$	6.02710			0.322162
$351$	21.8945	+	6.00228i	1.16864	+	0.320378i
$352$	2.20898			0.117739
$353$	0.814604	+	1.41094i	0.0433570	+	0.0750966i	0.886890	−	0.461982i	$-0.152861\pi$
$353$	0.814604	+	1.41094i	0.0433570	+	0.0750966i	−0.843533	+	0.537078i	$0.819528\pi$
$354$	0.192839	+	2.25410i	0.0102493	+	0.119804i
$355$	−6.92254	+	11.9902i	−0.367410	+	0.636373i
$356$	3.81181	−	6.60225i	0.202026	−	0.349918i
$357$	3.31200	−	2.30961i	0.175290	−	0.122237i
$358$	6.14919	+	10.6507i	0.324995	+	0.562908i
$359$	2.96052			0.156250			0.0781252	−	0.996944i	$-0.475107\pi$
$359$	2.96052			0.156250			0.0781252	+	0.996944i	$0.475107\pi$
$360$	1.18835	−	3.22629i	0.0626317	−	0.170041i
$361$	1.00000			0.0526316
$362$	0.697813	+	1.20865i	0.0366762	+	0.0635251i
$363$	9.59899	+	4.49858i	0.503816	+	0.236114i
$364$	3.57149	−	6.18600i	0.187197	−	0.324234i
$365$	−3.88821	+	6.73457i	−0.203518	+	0.352504i
$366$	1.68029	+	0.787472i	0.0878302	+	0.0411618i
$367$	14.1162	+	24.4500i	0.736862	+	1.27628i	0.953902	+	0.300119i	$0.0970265\pi$
$367$	14.1162	+	24.4500i	0.736862	+	1.27628i	−0.217040	+	0.976163i	$0.569640\pi$
$368$	4.33718			0.226091
$369$	−5.47520	+	14.8648i	−0.285027	+	0.773829i
$370$	7.96086			0.413866
$371$	4.22562	+	7.31898i	0.219383	+	0.379983i
$372$	10.4160	−	7.26355i	0.540045	−	0.376597i
$373$	4.93227	−	8.54294i	0.255383	−	0.442336i	−0.709616	−	0.704588i	$-0.751132\pi$
$373$	4.93227	−	8.54294i	0.255383	−	0.442336i	0.964999	+	0.262252i	$0.0844651\pi$
$374$	1.57491	−	2.72782i	0.0814365	−	0.141052i
$375$	−1.46979	−	17.1804i	−0.0758994	−	0.887190i
$376$	−1.53629	−	2.66093i	−0.0792281	−	0.137227i
$377$	6.11716			0.315050
$378$	−8.19286	−	2.24603i	−0.421395	−	0.115523i
$379$	−4.36079			−0.223999			−0.111999	−	0.993708i	$-0.535725\pi$
$379$	−4.36079			−0.223999			−0.111999	+	0.993708i	$0.535725\pi$
$380$	0.573032	+	0.992520i	0.0293959	+	0.0509152i
$381$	1.20410	+	14.0747i	0.0616877	+	0.721070i
$382$	0.0522362	−	0.0904757i	0.00267263	−	0.00462914i
$383$	16.6855	−	28.9001i	0.852588	−	1.47673i	−0.0262761	−	0.999655i	$-0.508365\pi$
$383$	16.6855	−	28.9001i	0.852588	−	1.47673i	0.878864	−	0.477072i	$-0.158302\pi$
$384$	1.42072	−	0.990732i	0.0725009	−	0.0505581i
$385$	2.06947	+	3.58444i	0.105470	+	0.182680i
$386$	−20.9740			−1.06755
$387$	−16.8132	−	20.1945i	−0.854662	−	1.02654i
$388$	15.5463			0.789246
$389$	6.61771	+	11.4622i	0.335531	+	0.581157i	0.983587	−	0.180436i	$-0.0577509\pi$
$389$	6.61771	+	11.4622i	0.335531	+	0.581157i	−0.648056	+	0.761593i	$0.724418\pi$
$390$	−7.85315	−	3.68040i	−0.397660	−	0.186364i
$391$	3.09222	−	5.35588i	0.156380	−	0.270859i
$392$	2.16356	−	3.74740i	0.109276	−	0.189272i
$393$	−8.99813	−	4.21699i	−0.453896	−	0.212719i
$394$	−10.7375	−	18.5980i	−0.540949	−	0.936952i
$395$	12.3874			0.623278
$396$	−6.53065	+	1.12564i	−0.328177	+	0.0565654i
$397$	27.6615			1.38829			0.694145	−	0.719835i	$-0.255783\pi$
$397$	27.6615			1.38829			0.694145	+	0.719835i	$0.255783\pi$
$398$	−3.19440	−	5.53286i	−0.160121	−	0.277337i
$399$	2.32273	−	1.61974i	0.116282	−	0.0810885i
$400$	1.84327	−	3.19264i	0.0921635	−	0.159632i
$401$	−3.90931	+	6.77112i	−0.195221	+	0.338133i	−0.946973	−	0.321313i	$-0.895876\pi$
$401$	−3.90931	+	6.77112i	−0.195221	+	0.338133i	0.751752	+	0.659446i	$0.229209\pi$
$402$	1.05437	+	12.3246i	0.0525872	+	0.614694i
$403$	−16.0159	−	27.7404i	−0.797810	−	1.38185i
$404$	−7.92531			−0.394299
$405$	−1.86922	+	10.1438i	−0.0928825	+	0.504049i
$406$	−2.28902			−0.113602
$407$	−7.67209	−	13.2885i	−0.380292	−	0.658684i
$408$	−0.210519	−	2.46076i	−0.0104222	−	0.121826i
$409$	−9.80320	+	16.9796i	−0.484737	+	0.839589i	−0.999846	−	0.0175352i	$-0.994418\pi$
$409$	−9.80320	+	16.9796i	−0.484737	+	0.839589i	0.515109	+	0.857125i	$0.327751\pi$
$410$	3.02581	−	5.24085i	0.149434	−	0.258827i
$411$	−30.0591	+	20.9615i	−1.48270	+	1.03396i
$412$	2.17163	+	3.76138i	0.106989	+	0.185310i
$413$	−2.13543			−0.105078
$414$	−12.8225	+	2.21011i	−0.630190	+	0.108621i
$415$	−5.95633			−0.292385
$416$	−2.18454	−	3.78373i	−0.107106	−	0.185513i
$417$	−28.7979	−	13.4962i	−1.41024	−	0.660911i
$418$	1.10449	−	1.91303i	0.0540224	−	0.0935696i
$419$	−6.59852	+	11.4290i	−0.322359	+	0.558342i	−0.980974	−	0.194138i	$-0.937809\pi$
$419$	−6.59852	+	11.4290i	−0.322359	+	0.558342i	0.658615	+	0.752480i	$0.271142\pi$
$420$	2.93862	+	1.37719i	0.143390	+	0.0672000i
$421$	15.1960	+	26.3202i	0.740606	+	1.28277i	0.952220	+	0.305414i	$0.0987949\pi$
$421$	15.1960	+	26.3202i	0.740606	+	1.28277i	−0.211613	+	0.977353i	$0.567872\pi$
$422$	−0.302582			−0.0147295
$423$	5.89783	+	7.08395i	0.286763	+	0.344433i
$424$	5.16929			0.251043
$425$	−2.62834	−	4.55242i	−0.127493	−	0.220825i
$426$	17.1631	−	11.9686i	0.831555	−	0.579880i
$427$	−0.875787	+	1.51691i	−0.0423823	+	0.0734083i
$428$	2.21016	−	3.82812i	0.106832	−	0.185039i
$429$	1.42489	+	16.6556i	0.0687942	+	0.804138i
$430$	5.01925	+	8.69360i	0.242050	+	0.419243i
$431$	−12.2675			−0.590903			−0.295452	−	0.955358i	$-0.595470\pi$
$431$	−12.2675			−0.590903			−0.295452	+	0.955358i	$0.595470\pi$
$432$	−3.69538	+	3.65297i	−0.177794	+	0.175753i
$433$	−3.30259			−0.158712			−0.0793561	−	0.996846i	$-0.525286\pi$
$433$	−3.30259			−0.158712			−0.0793561	+	0.996846i	$0.525286\pi$
$434$	5.99311	+	10.3804i	0.287678	+	0.498273i
$435$	0.236901	+	2.76915i	0.0113586	+	0.132770i
$436$	−9.26634	+	16.0498i	−0.443777	+	0.768644i
$437$	2.16859	−	3.75611i	0.103738	−	0.179679i
$438$	9.64006	−	6.72244i	0.460620	−	0.321211i
$439$	−10.4785	−	18.1493i	−0.500112	−	0.866220i	−1.00000		0.000129598i	$-0.999959\pi$
$439$	−10.4785	−	18.1493i	−0.500112	−	0.866220i	0.499888	−	0.866090i	$-0.333375\pi$
$440$	2.53163			0.120691
$441$	−4.48680	+	12.1813i	−0.213657	+	0.580063i
$442$	−6.22992			−0.296327
$443$	−17.4811	−	30.2782i	−0.830554	−	1.43856i	−0.897599	−	0.440812i	$-0.854690\pi$
$443$	−17.4811	−	30.2782i	−0.830554	−	1.43856i	0.0670450	−	0.997750i	$-0.478643\pi$
$444$	−10.8943	−	5.10561i	−0.517018	−	0.242302i
$445$	4.36857	−	7.56659i	0.207090	−	0.358691i
$446$	−10.8305	+	18.7590i	−0.512838	+	0.888262i
$447$	−31.9917	−	14.9930i	−1.51315	−	0.709143i
$448$	0.817447	+	1.41586i	0.0386207	+	0.0668931i
$449$	12.8844			0.608055			0.304027	−	0.952663i	$-0.401669\pi$
$449$	12.8844			0.608055			0.304027	+	0.952663i	$0.401669\pi$
$450$	−3.82257	+	10.3780i	−0.180198	+	0.489224i
$451$	−11.6642			−0.549246
$452$	5.17058	+	8.95570i	0.243204	+	0.421241i
$453$	−20.2073	+	14.0915i	−0.949424	+	0.662075i
$454$	−3.75429	+	6.50262i	−0.176198	+	0.305183i
$455$	4.09315	−	7.08954i	0.191890	−	0.332363i
$456$	−0.147638	−	1.72575i	−0.00691379	−	0.0808155i
$457$	1.35841	+	2.35284i	0.0635439	+	0.110061i	0.896047	−	0.443959i	$-0.146426\pi$
$457$	1.35841	+	2.35284i	0.0635439	+	0.110061i	−0.832503	+	0.554020i	$0.813093\pi$
$458$	−6.11527			−0.285748
$459$	1.87632	+	7.16774i	0.0875789	+	0.334561i
$460$	4.97069			0.231759
$461$	1.83407	+	3.17670i	0.0854211	+	0.147954i	0.905571	−	0.424196i	$-0.139443\pi$
$461$	1.83407	+	3.17670i	0.0854211	+	0.147954i	−0.820149	+	0.572149i	$0.806110\pi$
$462$	−0.533188	−	6.23245i	−0.0248062	−	0.289960i
$463$	−6.14975	+	10.6517i	−0.285803	+	0.495025i	−0.972804	−	0.231632i	$-0.925594\pi$
$463$	−6.14975	+	10.6517i	−0.285803	+	0.495025i	0.687001	+	0.726657i	$0.258927\pi$
$464$	−0.700052	+	1.21253i	−0.0324991	+	0.0562901i
$465$	11.9374	−	8.32448i	0.553584	−	0.386039i
$466$	12.6905	+	21.9806i	0.587877	+	1.01823i
$467$	17.4976			0.809693			0.404847	−	0.914385i	$-0.367325\pi$
$467$	17.4976			0.809693			0.404847	+	0.914385i	$0.367325\pi$
$468$	8.38647	+	10.0731i	0.387665	+	0.465628i
$469$	−11.6757			−0.539135
$470$	−1.76069	−	3.04960i	−0.0812144	−	0.140667i
$471$	3.07228	+	1.43983i	0.141563	+	0.0663438i
$472$	−0.653079	+	1.13117i	−0.0300604	+	0.0520661i
$473$	9.67437	−	16.7565i	0.444828	−	0.770465i
$474$	−16.9519	−	7.94453i	−0.778625	−	0.364904i
$475$	−1.84327	−	3.19264i	−0.0845750	−	0.146488i
$476$	2.33121			0.106851
$477$	−15.2825	+	2.63412i	−0.699738	+	0.120608i
$478$	6.17409			0.282396
$479$	5.75981	+	9.97628i	0.263172	+	0.455828i	0.967083	−	0.254461i	$-0.0818979\pi$
$479$	5.75981	+	9.97628i	0.263172	+	0.455828i	−0.703911	+	0.710288i	$0.748565\pi$
$480$	1.62824	−	1.13544i	0.0743185	−	0.0518256i
$481$	−15.1744	+	26.2828i	−0.691893	+	1.19839i
$482$	−5.91630	+	10.2473i	−0.269480	+	0.466753i
$483$	−1.04688	−	12.2370i	−0.0476346	−	0.556802i
$484$	3.06020	+	5.30042i	0.139100	+	0.240928i
$485$	17.8171			0.809032
$486$	9.06359	−	12.6827i	0.411133	−	0.575300i
$487$	−31.3219			−1.41933			−0.709666	−	0.704538i	$-0.751154\pi$
$487$	−31.3219			−1.41933			−0.709666	+	0.704538i	$0.751154\pi$
$488$	0.535684	+	0.927832i	0.0242493	+	0.0420010i
$489$	0.636578	+	7.44097i	0.0287870	+	0.336492i
$490$	2.47958	−	4.29476i	0.112016	−	0.194017i
$491$	18.1009	−	31.3517i	0.816883	−	1.41488i	−0.0910845	−	0.995843i	$-0.529033\pi$
$491$	18.1009	−	31.3517i	0.816883	−	1.41488i	0.907968	−	0.419040i	$-0.137633\pi$
$492$	−7.50191	+	5.23141i	−0.338212	+	0.235850i
$493$	0.998212	+	1.72895i	0.0449572	+	0.0778682i
$494$	−4.36908			−0.196574
$495$	−7.48453	+	1.29005i	−0.336405	+	0.0579834i
$496$	7.33149			0.329194
$497$	9.87521	+	17.1044i	0.442964	+	0.767236i
$498$	8.15109	+	3.82003i	0.365259	+	0.171179i
$499$	6.93596	−	12.0134i	0.310496	−	0.537795i	−0.667974	−	0.744185i	$-0.732838\pi$
$499$	6.93596	−	12.0134i	0.310496	−	0.537795i	0.978470	+	0.206390i	$0.0661714\pi$
$500$	4.97766	−	8.62156i	0.222608	−	0.385568i
$501$	−7.77546	−	3.64398i	−0.347382	−	0.162801i
$502$	14.7847	+	25.6078i	0.659873	+	1.14293i
$503$	−1.02490			−0.0456982			−0.0228491	−	0.999739i	$-0.507274\pi$
$503$	−1.02490			−0.0456982			−0.0228491	+	0.999739i	$0.507274\pi$
$504$	−3.13819	−	3.76931i	−0.139786	−	0.167898i
$505$	−9.08290			−0.404184
$506$	−4.79038	−	8.29719i	−0.212958	−	0.368855i
$507$	8.65054	−	6.03240i	0.384184	−	0.267908i
$508$	−4.07786	+	7.06306i	−0.180926	+	0.313373i
$509$	−1.94719	+	3.37264i	−0.0863078	+	0.149490i	−0.905948	−	0.423389i	$-0.860840\pi$
$509$	−1.94719	+	3.37264i	−0.0863078	+	0.149490i	0.819640	+	0.572879i	$0.194174\pi$
$510$	−0.241268	−	2.82019i	−0.0106835	−	0.124880i
$511$	5.54664	+	9.60707i	0.245369	+	0.424992i
$512$	1.00000			0.0441942
$513$	1.31587	+	5.02678i	0.0580971	+	0.221938i
$514$	−28.2774			−1.24726
$515$	2.48883	+	4.31078i	0.109671	+	0.189956i
$516$	−1.29318	−	15.1160i	−0.0569291	−	0.665446i
$517$	−3.39364	+	5.87795i	−0.149252	+	0.258512i
$518$	5.67821	−	9.83494i	0.249486	−	0.432123i
$519$	−18.6131	+	12.9798i	−0.817026	+	0.569748i
$520$	−2.50362	−	4.33639i	−0.109791	−	0.190163i
$521$	30.3308			1.32882			0.664408	−	0.747370i	$-0.268684\pi$
$521$	30.3308			1.32882			0.664408	+	0.747370i	$0.268684\pi$
$522$	1.45177	−	3.94145i	0.0635422	−	0.172512i
$523$	13.5519			0.592582			0.296291	−	0.955098i	$-0.404250\pi$
$523$	13.5519			0.592582			0.296291	+	0.955098i	$0.404250\pi$
$524$	−2.86864	−	4.96864i	−0.125317	−	0.217056i
$525$	−9.45266	−	4.43001i	−0.412548	−	0.193341i
$526$	7.44756	−	12.8996i	0.324729	−	0.562447i
$527$	5.22703	−	9.05348i	0.227693	−	0.394376i
$528$	−3.46448	−	1.62364i	−0.150772	−	0.0706597i
$529$	2.09441	+	3.62763i	0.0910615	+	0.157723i
$530$	5.92433			0.257336
$531$	1.35436	−	3.67698i	0.0587740	−	0.159567i
$532$	1.63489			0.0708816
$533$	11.5351	+	19.9794i	0.499642	+	0.865405i
$534$	−10.8310	+	7.55296i	−0.468705	+	0.326849i
$535$	2.53299	−	4.38726i	0.109511	−	0.189678i
$536$	−3.57079	+	6.18479i	−0.154235	+	0.267142i
$537$	−1.81571	−	21.2239i	−0.0783537	−	0.915879i
$538$	14.2860	+	24.7441i	0.615913	+	1.06679i
$539$	−9.55854			−0.411715
$540$	−4.23514	+	4.18653i	−0.182251	+	0.180160i
$541$	6.78464			0.291694			0.145847	−	0.989307i	$-0.453409\pi$
$541$	6.78464			0.291694			0.145847	+	0.989307i	$0.453409\pi$
$542$	8.85572	+	15.3386i	0.380386	+	0.658848i
$543$	−0.206048	−	2.40850i	−0.00884235	−	0.103358i
$544$	0.712956	−	1.23488i	0.0305677	−	0.0529448i
$545$	−10.6198	+	18.3940i	−0.454902	+	0.787914i
$546$	−10.1482	+	7.07677i	−0.434302	+	0.302858i
$547$	15.5510	+	26.9351i	0.664913	+	1.15166i	0.979309	+	0.202371i	$0.0648648\pi$
$547$	15.5510	+	26.9351i	0.664913	+	1.15166i	−0.314396	+	0.949292i	$0.601802\pi$
$548$	−21.1576			−0.903808
$549$	−2.05650	−	2.47008i	−0.0877692	−	0.105420i
$550$	−8.14350			−0.347240
$551$	0.700052	+	1.21253i	0.0298232	+	0.0516553i
$552$	−6.80227	−	3.18790i	−0.289524	−	0.135686i
$553$	8.83550	−	15.3035i	0.375724	−	0.650773i
$554$	−8.37956	+	14.5138i	−0.356013	+	0.616633i
$555$	−12.4855	−	5.85136i	−0.529980	−	0.248376i
$556$	−9.18089	−	15.9018i	−0.389356	−	0.674385i
$557$	23.6478			1.00199			0.500995	−	0.865450i	$-0.332967\pi$
$557$	23.6478			1.00199			0.500995	+	0.865450i	$0.332967\pi$
$558$	−21.6749	+	3.73593i	−0.917571	+	0.158154i
$559$	−38.2693			−1.61862
$560$	0.936845	+	1.62266i	0.0395889	+	0.0685701i
$561$	−4.47501	+	3.12062i	−0.188935	+	0.131753i
$562$	2.02850	−	3.51347i	0.0855673	−	0.148207i
$563$	16.1173	−	27.9160i	0.679263	−	1.17652i	−0.295940	−	0.955206i	$-0.595633\pi$
$563$	16.1173	−	27.9160i	0.679263	−	1.17652i	0.975203	−	0.221311i	$-0.0710338\pi$
$564$	0.453630	+	5.30250i	0.0191013	+	0.223275i
$565$	5.92581	+	10.2638i	0.249301	+	0.431801i
$566$	19.3861			0.814857
$567$	11.1985	+	9.54447i	0.470292	+	0.400830i
$568$	12.0806			0.506889
$569$	−14.5117	−	25.1350i	−0.608361	−	1.05371i	−0.991511	−	0.130026i	$-0.958494\pi$
$569$	−14.5117	−	25.1350i	−0.608361	−	1.05371i	0.383150	−	0.923686i	$-0.374839\pi$
$570$	−0.169203	−	1.97781i	−0.00708712	−	0.0828415i
$571$	9.28675	−	16.0851i	0.388638	−	0.673141i	−0.603628	−	0.797266i	$-0.706279\pi$
$571$	9.28675	−	16.0851i	0.388638	−	0.673141i	0.992267	+	0.124124i	$0.0396122\pi$
$572$	−4.82561	+	8.35820i	−0.201769	+	0.349474i
$573$	−0.148426	+	0.103504i	−0.00620059	+	0.00432394i
$574$	−4.31641	−	7.47623i	−0.180163	−	0.312052i
$575$	−15.9892			−0.666796
$576$	−2.95641	+	0.509572i	−0.123184	+	0.0212322i
$577$	−9.63391			−0.401065			−0.200533	−	0.979687i	$-0.564267\pi$
$577$	−9.63391			−0.401065			−0.200533	+	0.979687i	$0.564267\pi$
$578$	7.48339	+	12.9616i	0.311268	+	0.539132i
$579$	32.8947	+	15.4162i	1.36706	+	0.640675i
$580$	−0.802304	+	1.38963i	−0.0333138	+	0.0577013i
$581$	−4.24844	+	7.35851i	−0.176255	+	0.305283i
$582$	−24.3823	−	11.4268i	−1.01068	−	0.473656i
$583$	−5.70943	−	9.88902i	−0.236460	−	0.409561i
$584$	6.78533			0.280779
$585$	9.61142	+	11.5444i	0.397383	+	0.477301i
$586$	−1.03103			−0.0425913
$587$	12.8763	+	22.3024i	0.531461	+	0.920518i	0.999326	+	0.0367175i	$0.0116902\pi$
$587$	12.8763	+	22.3024i	0.531461	+	0.920518i	−0.467865	+	0.883800i	$0.654976\pi$
$588$	−6.14764	+	4.28702i	−0.253524	+	0.176794i
$589$	3.66575	−	6.34926i	0.151044	−	0.261617i
$590$	−0.748470	+	1.29639i	−0.0308140	+	0.0533714i
$591$	3.17054	+	37.0605i	0.130419	+	1.52447i
$592$	−3.47314	−	6.01565i	−0.142745	−	0.247242i
$593$	−23.1785			−0.951825			−0.475913	−	0.879493i	$-0.657882\pi$
$593$	−23.1785			−0.951825			−0.475913	+	0.879493i	$0.657882\pi$
$594$	11.0698	+	3.03472i	0.454198	+	0.124516i
$595$	2.67172			0.109530
$596$	−10.1991	−	17.6653i	−0.417771	−	0.723600i
$597$	0.943231	+	11.0255i	0.0386039	+	0.451242i
$598$	−9.47475	+	16.4107i	−0.387451	+	0.671085i
$599$	22.3463	−	38.7049i	0.913045	−	1.58144i	0.103307	−	0.994650i	$-0.467058\pi$
$599$	22.3463	−	38.7049i	0.913045	−	1.58144i	0.809738	−	0.586791i	$-0.199609\pi$
$600$	−5.23755	+	3.65237i	−0.213822	+	0.149107i
$601$	24.1800	+	41.8810i	0.986323	+	1.70836i	0.635901	+	0.771770i	$0.280629\pi$
$601$	24.1800	+	41.8810i	0.986323	+	1.70836i	0.350422	+	0.936592i	$0.386038\pi$
$602$	14.3202			0.583649
$603$	7.40511	−	20.1043i	0.301559	−	0.818712i
$604$	−14.2233			−0.578738
$605$	3.50718	+	6.07462i	0.142587	+	0.246968i
$606$	12.4297	+	5.82522i	0.504923	+	0.236633i
$607$	−13.4826	+	23.3525i	−0.547240	+	0.947848i	0.451222	+	0.892412i	$0.350988\pi$
$607$	−13.4826	+	23.3525i	−0.547240	+	0.947848i	−0.998462	+	0.0554365i	$0.982345\pi$
$608$	0.500000	−	0.866025i	0.0202777	−	0.0351220i
$609$	3.59001	+	1.68246i	0.145474	+	0.0681769i
$610$	0.613928	+	1.06335i	0.0248572	+	0.0430540i
$611$	13.4243			0.543091
$612$	−1.47853	+	4.01410i	−0.0597659	+	0.162260i
$613$	14.7376			0.595248			0.297624	−	0.954683i	$-0.403806\pi$
$613$	14.7376			0.595248			0.297624	+	0.954683i	$0.403806\pi$
$614$	4.39525	+	7.61280i	0.177378	+	0.307228i
$615$	−8.59766	+	5.99553i	−0.346691	+	0.241763i
$616$	1.80573	−	3.12761i	0.0727547	−	0.126015i
$617$	−7.57298	+	13.1168i	−0.304877	+	0.528062i	−0.977234	−	0.212165i	$-0.931949\pi$
$617$	−7.57298	+	13.1168i	−0.304877	+	0.528062i	0.672357	+	0.740227i	$0.265282\pi$
$618$	−0.641233	−	7.49539i	−0.0257942	−	0.301509i
$619$	0.730870	+	1.26590i	0.0293761	+	0.0508810i	0.880340	−	0.474344i	$-0.157315\pi$
$619$	0.730870	+	1.26590i	0.0293761	+	0.0508810i	−0.850964	+	0.525225i	$0.823981\pi$
$620$	8.40235			0.337447
$621$	21.7347	+	5.95847i	0.872185	+	0.239105i
$622$	−30.3994			−1.21890
$623$	−6.23190	−	10.7940i	−0.249676	−	0.432451i
$624$	0.645043	+	7.53992i	0.0258224	+	0.301838i
$625$	−3.51164	+	6.08233i	−0.140465	+	0.243293i
$626$	−0.531531	+	0.920638i	−0.0212442	+	0.0367961i
$627$	−3.13835	+	2.18851i	−0.125334	+	0.0874006i
$628$	0.979456	+	1.69647i	0.0390845	+	0.0676964i
$629$	−9.90477			−0.394929
$630$	−3.59656	−	4.31986i	−0.143290	−	0.172107i
$631$	−8.53126			−0.339624			−0.169812	−	0.985476i	$-0.554316\pi$
$631$	−8.53126			−0.339624			−0.169812	+	0.985476i	$0.554316\pi$
$632$	−5.40433	−	9.36057i	−0.214973	−	0.372344i
$633$	0.474557	+	0.222402i	0.0188620	+	0.00883970i
$634$	8.30479	−	14.3843i	0.329826	−	0.571275i
$635$	−4.67349	+	8.09472i	−0.185462	+	0.321229i
$636$	−8.10730	−	3.79950i	−0.321475	−	0.150660i
$637$	9.45277	+	16.3727i	0.374532	+	0.648709i
$638$	3.09280			0.122445
$639$	−35.7150	+	6.15592i	−1.41286	+	0.243524i
$640$	1.14606			0.0453021
$641$	4.52036	+	7.82949i	0.178543	+	0.309246i	0.941382	−	0.337343i	$-0.109528\pi$
$641$	4.52036	+	7.82949i	0.178543	+	0.309246i	−0.762838	+	0.646589i	$0.776195\pi$
$642$	−6.28006	+	4.37936i	−0.247854	+	0.172840i
$643$	9.39572	−	16.2739i	0.370531	−	0.641779i	−0.619116	−	0.785299i	$-0.712509\pi$
$643$	9.39572	−	16.2739i	0.370531	−	0.641779i	0.989647	+	0.143521i	$0.0458424\pi$
$644$	3.54542	−	6.14084i	0.139709	−	0.241983i
$645$	−1.48207	−	17.3239i	−0.0583563	−	0.682129i
$646$	−0.712956	−	1.23488i	−0.0280509	−	0.0485855i
$647$	28.8633			1.13473			0.567367	−	0.823465i	$-0.307962\pi$
$647$	28.8633			1.13473			0.567367	+	0.823465i	$0.307962\pi$
$648$	8.48067	−	3.01301i	0.333152	−	0.118362i
$649$	2.88528			0.113257
$650$	8.05339	+	13.9489i	0.315880	+	0.547120i
$651$	−1.76962	−	20.6852i	−0.0693570	−	0.810716i
$652$	−2.15587	+	3.73408i	−0.0844304	+	0.146238i
$653$	23.8280	−	41.2713i	0.932461	−	1.61507i	0.153361	−	0.988170i	$-0.450990\pi$
$653$	23.8280	−	41.2713i	0.932461	−	1.61507i	0.779100	−	0.626900i	$-0.215676\pi$
$654$	26.3298	−	18.3609i	1.02958	−	0.717968i
$655$	−3.28765	−	5.69437i	−0.128459	−	0.222498i
$656$	−5.28035			−0.206163
$657$	−20.0602	+	3.45762i	−0.782622	+	0.134894i
$658$	−5.02334			−0.195830
$659$	−24.8385	−	43.0216i	−0.967571	−	1.67588i	−0.702544	−	0.711641i	$-0.747952\pi$
$659$	−24.8385	−	43.0216i	−0.967571	−	1.67588i	−0.265027	−	0.964241i	$-0.585381\pi$
$660$	−3.97051	−	1.86079i	−0.154552	−	0.0724311i
$661$	9.00134	−	15.5908i	0.350111	−	0.606411i	−0.636157	−	0.771559i	$-0.719477\pi$
$661$	9.00134	−	15.5908i	0.350111	−	0.606411i	0.986269	+	0.165149i	$0.0528104\pi$
$662$	−8.36543	+	14.4893i	−0.325132	+	0.563144i
$663$	9.77075	+	4.57908i	0.379465	+	0.177837i
$664$	2.59860	+	4.50091i	0.100845	+	0.174669i
$665$	1.87369			0.0726586
$666$	13.3334	+	16.0149i	0.516659	+	0.620564i
$667$	6.07251			0.235129
$668$	−2.47885	−	4.29349i	−0.0959096	−	0.166120i
$669$	30.7742	−	21.4602i	1.18980	−	0.829700i
$670$	−4.09235	+	7.08816i	−0.158101	+	0.273840i
$671$	1.18332	−	2.04956i	0.0456814	−	0.0791226i
$672$	−0.241373	−	2.82141i	−0.00931116	−	0.108838i
$673$	−8.33566	−	14.4378i	−0.321316	−	0.556536i	0.659444	−	0.751754i	$-0.270792\pi$
$673$	−8.33566	−	14.4378i	−0.321316	−	0.556536i	−0.980760	+	0.195218i	$0.937458\pi$
$674$	−31.5837			−1.21656
$675$	13.6232	−	13.4668i	0.524356	−	0.518338i
$676$	6.08883			0.234186
$677$	21.8921	+	37.9182i	0.841380	+	1.45731i	0.888728	+	0.458435i	$0.151590\pi$
$677$	21.8921	+	37.9182i	0.841380	+	1.45731i	−0.0473478	+	0.998878i	$0.515077\pi$
$678$	−1.52675	−	17.8462i	−0.0586345	−	0.685380i
$679$	12.7083	−	22.0114i	0.487700	−	0.844721i
$680$	0.817092	−	1.41524i	0.0313341	−	0.0542722i
$681$	10.6676	−	7.43899i	0.408784	−	0.285063i
$682$	−8.09757	−	14.0254i	−0.310072	−	0.537060i
$683$	33.3197			1.27494			0.637472	−	0.770474i	$-0.279980\pi$
$683$	33.3197			1.27494			0.637472	+	0.770474i	$0.279980\pi$
$684$	−1.03690	+	2.81511i	−0.0396469	+	0.107638i
$685$	−24.2480			−0.926467
$686$	−9.25932	−	16.0376i	−0.353522	−	0.612319i
$687$	9.59095	+	4.49482i	0.365918	+	0.171488i
$688$	4.37956	−	7.58562i	0.166969	−	0.289199i
$689$	−11.2925	+	19.5592i	−0.430210	+	0.745146i
$690$	−7.79583	−	3.65353i	−0.296782	−	0.139088i
$691$	25.0713	+	43.4248i	0.953757	+	1.65196i	0.737187	+	0.675689i	$0.236154\pi$
$691$	25.0713	+	43.4248i	0.953757	+	1.65196i	0.216570	+	0.976267i	$0.430513\pi$
$692$	−13.1012			−0.498032
$693$	−3.74471	+	10.1666i	−0.142250	+	0.386198i
$694$	34.5656			1.31209
$695$	−10.5219	−	18.2244i	−0.399117	−	0.691292i
$696$	1.98916	−	1.38713i	0.0753988	−	0.0525789i
$697$	−3.76466	+	6.52057i	−0.142597	+	0.246984i
$698$	−2.51645	+	4.35862i	−0.0952491	+	0.164976i
$699$	−3.74721	−	43.8012i	−0.141732	−	1.65671i
$700$	−3.01355	−	5.21962i	−0.113901	−	0.197283i
$701$	−38.8954			−1.46906			−0.734529	−	0.678578i	$-0.762597\pi$
$701$	−38.8954			−1.46906			−0.734529	+	0.678578i	$0.762597\pi$
$702$	−5.74914	−	21.9624i	−0.216987	−	0.828916i
$703$	−6.94627			−0.261984
$704$	−1.10449	−	1.91303i	−0.0416271	−	0.0721002i
$705$	0.519889	+	6.07699i	0.0195801	+	0.228873i
$706$	0.814604	−	1.41094i	0.0306580	−	0.0531013i
$707$	−6.47851	+	11.2211i	−0.243650	+	0.422014i
$708$	1.85569	−	1.29405i	0.0697410	−	0.0486335i
$709$	20.2895	+	35.1425i	0.761989	+	1.31980i	0.941824	+	0.336107i	$0.109110\pi$
$709$	20.2895	+	35.1425i	0.761989	+	1.31980i	−0.179835	+	0.983697i	$0.557556\pi$
$710$	13.8451			0.519597
$711$	20.7473	+	24.9198i	0.778084	+	0.934564i
$712$	−7.62362			−0.285707
$713$	−15.8990	−	27.5379i	−0.595423	−	1.03130i
$714$	−3.65618	−	1.71348i	−0.136829	−	0.0641253i
$715$	−5.53045	+	9.57902i	−0.206827	+	0.358235i
$716$	6.14919	−	10.6507i	0.229806	−	0.398036i
$717$	−9.68319	−	4.53805i	−0.361625	−	0.169476i
$718$	−1.48026	−	2.56389i	−0.0552429	−	0.0956835i
$719$	31.4899			1.17437			0.587187	−	0.809451i	$-0.300235\pi$
$719$	31.4899			1.17437			0.587187	+	0.809451i	$0.300235\pi$
$720$	−3.38823	+	0.584002i	−0.126272	+	0.0217645i
$721$	7.10078			0.264447
$722$	−0.500000	−	0.866025i	−0.0186081	−	0.0322301i
$723$	16.8108	−	11.7229i	0.625202	−	0.435981i
$724$	0.697813	−	1.20865i	0.0259340	−	0.0449190i
$725$	2.58077	−	4.47002i	0.0958474	−	0.166013i
$726$	−0.903605	−	10.5623i	−0.0335359	−	0.392002i
$727$	1.31306	+	2.27429i	0.0486987	+	0.0843487i	0.889347	−	0.457232i	$-0.151159\pi$
$727$	1.31306	+	2.27429i	0.0486987	+	0.0843487i	−0.840649	+	0.541581i	$0.817826\pi$
$728$	−7.14298			−0.264736
$729$	−23.5370	+	13.2292i	−0.871739	+	0.489970i
$730$	7.77641			0.287818
$731$	−6.24486	−	10.8164i	−0.230975	−	0.400060i
$732$	−0.158175	−	1.84891i	−0.00584631	−	0.0683377i
$733$	4.04043	−	6.99824i	0.149237	−	0.258486i	−0.781709	−	0.623644i	$-0.785652\pi$
$733$	4.04043	−	6.99824i	0.149237	−	0.258486i	0.930946	+	0.365158i	$0.118985\pi$
$734$	14.1162	−	24.4500i	0.521040	−	0.902468i
$735$	−7.04558	+	4.91319i	−0.259880	+	0.181226i
$736$	−2.16859	−	3.75611i	−0.0799354	−	0.138452i
$737$	15.7756			0.581103
$738$	15.6109	−	2.69072i	0.574644	−	0.0990468i
$739$	46.0684			1.69465			0.847326	−	0.531073i	$-0.178211\pi$
$739$	46.0684			1.69465			0.847326	+	0.531073i	$0.178211\pi$
$740$	−3.98043	−	6.89431i	−0.146324	−	0.253440i
$741$	6.85229	+	3.21134i	0.251725	+	0.117971i
$742$	4.22562	−	7.31898i	0.155127	−	0.268688i
$743$	−18.0871	+	31.3277i	−0.663550	+	1.14930i	0.316126	+	0.948717i	$0.397618\pi$
$743$	−18.0871	+	31.3277i	−0.663550	+	1.14930i	−0.979676	+	0.200585i	$0.935716\pi$
$744$	−11.4984	−	5.38876i	−0.421553	−	0.197561i
$745$	−11.6888	−	20.2456i	−0.428244	−	0.741741i
$746$	−9.86453			−0.361166
$747$	−9.97607	−	11.9823i	−0.365005	−	0.438411i
$748$	−3.14981			−0.115169
$749$	−3.61338	−	6.25856i	−0.132030	−	0.228683i
$750$	−14.1437	+	9.86306i	−0.516456	+	0.360148i
$751$	11.3308	−	19.6256i	0.413468	−	0.716148i	−0.581798	−	0.813333i	$-0.697651\pi$
$751$	11.3308	−	19.6256i	0.413468	−	0.716148i	0.995266	+	0.0971851i	$0.0309839\pi$
$752$	−1.53629	+	2.66093i	−0.0560227	+	0.0970342i
$753$	−4.36557	−	51.0293i	−0.159090	−	1.85961i
$754$	−3.05858	−	5.29762i	−0.111387	−	0.192928i
$755$	−16.3008			−0.593247
$756$	2.15131	+	8.21824i	0.0782424	+	0.298895i
$757$	6.45466			0.234599			0.117299	−	0.993097i	$-0.462576\pi$
$757$	6.45466			0.234599			0.117299	+	0.993097i	$0.462576\pi$
$758$	2.18039	+	3.77655i	0.0791955	+	0.137171i
$759$	1.41449	+	16.5340i	0.0513426	+	0.600145i
$760$	0.573032	−	0.992520i	0.0207860	−	0.0360025i
$761$	−3.73318	+	6.46606i	−0.135328	+	0.234394i	−0.925723	−	0.378203i	$-0.876542\pi$
$761$	−3.73318	+	6.46606i	−0.135328	+	0.234394i	0.790395	+	0.612598i	$0.209875\pi$
$762$	11.5870	−	8.08014i	0.419753	−	0.292712i
$763$	15.1495	+	26.2397i	0.548448	+	0.949939i
$764$	−0.104472			−0.00377968
$765$	−1.69449	+	4.60041i	−0.0612643	+	0.166328i
$766$	−33.3710			−1.20574
$767$	−2.85335	−	4.94215i	−0.103029	−	0.178451i
$768$	−1.56836	−	0.735015i	−0.0565933	−	0.0265226i
$769$	12.4774	−	21.6115i	0.449947	−	0.779331i	−0.548435	−	0.836193i	$-0.684776\pi$
$769$	12.4774	−	21.6115i	0.449947	−	0.779331i	0.998382	+	0.0568620i	$0.0181095\pi$
$770$	2.06947	−	3.58444i	0.0745787	−	0.129174i
$771$	44.3491	+	20.7843i	1.59720	+	0.748529i
$772$	10.4870	+	18.1640i	0.377435	+	0.653736i
$773$	−52.8951			−1.90250			−0.951252	−	0.308414i	$-0.900202\pi$
$773$	−52.8951			−1.90250			−0.951252	+	0.308414i	$0.900202\pi$
$774$	−9.08233	+	24.6579i	−0.326458	+	0.886309i
$775$	−27.0278			−0.970869
$776$	−7.77317	−	13.4635i	−0.279041	−	0.483312i
$777$	−16.1343	+	11.2512i	−0.578815	+	0.403633i
$778$	6.61771	−	11.4622i	0.237256	−	0.410940i
$779$	−2.64018	+	4.57292i	−0.0945941	+	0.163842i
$780$	0.739260	+	8.64123i	0.0264697	+	0.309406i
$781$	−13.3429	−	23.1105i	−0.477445	−	0.826960i
$782$	−6.18444			−0.221155
$783$	−5.17392	+	5.11453i	−0.184901	+	0.182778i
$784$	−4.32712			−0.154540
$785$	1.12252	+	1.94426i	0.0400644	+	0.0693936i
$786$	0.847043	+	9.90111i	0.0302130	+	0.353161i
$787$	−18.3515	+	31.7858i	−0.654161	+	1.13304i	0.327942	+	0.944698i	$0.393645\pi$
$787$	−18.3515	+	31.7858i	−0.654161	+	1.13304i	−0.982103	+	0.188343i	$0.939688\pi$
$788$	−10.7375	+	18.5980i	−0.382509	+	0.662525i
$789$	−21.1618	+	14.7571i	−0.753381	+	0.525366i
$790$	−6.19370	−	10.7278i	−0.220362	−	0.381678i
$791$	16.9067			0.601133
$792$	4.24015	+	5.09289i	0.150667	+	0.180968i
$793$	−4.68089			−0.166223
$794$	−13.8307	−	23.9555i	−0.490835	−	0.850151i
$795$	−9.29148	−	4.35447i	−0.329535	−	0.154437i
$796$	−3.19440	+	5.53286i	−0.113222	+	0.196107i
$797$	6.58912	−	11.4127i	0.233398	−	0.404258i	−0.725408	−	0.688320i	$-0.758349\pi$
$797$	6.58912	−	11.4127i	0.233398	−	0.404258i	0.958806	+	0.284062i	$0.0916820\pi$
$798$	−2.56410	−	1.20167i	−0.0907682	−	0.0425387i
$799$	2.19061	+	3.79425i	0.0774983	+	0.134231i
$800$	−3.68654			−0.130339
$801$	22.5385	−	3.88479i	0.796359	−	0.137262i
$802$	7.81861			0.276085
$803$	−7.49433	−	12.9806i	−0.264469	−	0.458074i
$804$	10.1462	−	7.07540i	0.357829	−	0.249530i
$805$	4.06327	−	7.03779i	0.143212	−	0.248050i
$806$	−16.0159	+	27.7404i	−0.564137	+	0.977114i
$807$	−4.21831	−	49.3080i	−0.148492	−	1.73572i
$808$	3.96265	+	6.86352i	0.139406	+	0.241458i
$809$	−53.7680			−1.89038			−0.945191	−	0.326519i	$-0.894124\pi$
$809$	−53.7680			−1.89038			−0.945191	+	0.326519i	$0.894124\pi$
$810$	9.71938	−	3.45309i	0.341504	−	0.121329i
$811$	−26.3479			−0.925200			−0.462600	−	0.886567i	$-0.653083\pi$
$811$	−26.3479			−0.925200			−0.462600	+	0.886567i	$0.653083\pi$
$812$	1.14451	+	1.98235i	0.0401644	+	0.0695669i
$813$	−2.61489	−	30.5655i	−0.0917080	−	1.07198i
$814$	−7.67209	+	13.2885i	−0.268907	+	0.465760i
$815$	−2.47076	+	4.27949i	−0.0865471	+	0.149904i
$816$	−2.02582	+	1.41270i	−0.0709180	+	0.0494542i
$817$	−4.37956	−	7.58562i	−0.153221	−	0.265387i
$818$	19.6064			0.685522
$819$	21.1175	−	3.63986i	0.737906	−	0.127187i
$820$	−6.05161			−0.211332
$821$	−16.0585	−	27.8142i	−0.560447	−	0.970722i	−0.997457	−	0.0712657i	$-0.977296\pi$
$821$	−16.0585	−	27.8142i	−0.560447	−	0.970722i	0.437011	−	0.899456i	$-0.356037\pi$
$822$	33.1827	+	15.5512i	1.15738	+	0.542409i
$823$	25.8298	−	44.7386i	0.900372	−	1.55949i	0.0733601	−	0.997306i	$-0.476628\pi$
$823$	25.8298	−	44.7386i	0.900372	−	1.55949i	0.827012	−	0.562184i	$-0.190039\pi$
$824$	2.17163	−	3.76138i	0.0756525	−	0.131034i
$825$	12.7719	+	5.98560i	0.444662	+	0.208392i
$826$	1.06771	+	1.84934i	0.0371505	+	0.0643466i
$827$	10.0857			0.350713			0.175357	−	0.984505i	$-0.443892\pi$
$827$	10.0857			0.350713			0.175357	+	0.984505i	$0.443892\pi$
$828$	8.32525	+	9.99954i	0.289322	+	0.347508i
$829$	15.4641			0.537092			0.268546	−	0.963267i	$-0.413457\pi$
$829$	15.4641			0.537092			0.268546	+	0.963267i	$0.413457\pi$
$830$	2.97816	+	5.15833i	0.103374	+	0.179048i
$831$	23.8100	−	16.6038i	0.825961	−	0.575979i
$832$	−2.18454	+	3.78373i	−0.0757352	+	0.131177i
$833$	−3.08505	+	5.34346i	−0.106891	+	0.185140i
$834$	2.71090	+	31.6878i	0.0938708	+	1.09726i
$835$	−2.84092	−	4.92061i	−0.0983140	−	0.170285i
$836$	−2.20898			−0.0763992
$837$	36.7400	+	10.0721i	1.26992	+	0.348142i
$838$	13.1970			0.455884
$839$	12.1835	+	21.1024i	0.420621	+	0.728537i	0.996000	−	0.0893500i	$-0.0284790\pi$
$839$	12.1835	+	21.1024i	0.420621	+	0.728537i	−0.575380	+	0.817887i	$0.695146\pi$
$840$	−0.276628	−	3.23352i	−0.00954459	−	0.111567i
$841$	13.5199	−	23.4171i	0.466202	−	0.807485i
$842$	15.1960	−	26.3202i	0.523688	−	0.907054i
$843$	−5.76388	+	4.01941i	−0.198519	+	0.138436i
$844$	0.151291	+	0.262044i	0.00520765	+	0.00901991i
$845$	6.97819			0.240057
$846$	3.18596	−	8.64965i	0.109536	−	0.297381i
$847$	10.0062			0.343817
$848$	−2.58464	−	4.47673i	−0.0887570	−	0.153732i
$849$	−30.4043	−	14.2491i	−1.04347	−	0.489026i
$850$	−2.62834	+	4.55242i	−0.0901513	+	0.156147i
$851$	−15.0636	+	26.0910i	−0.516375	+	0.894387i
$852$	−18.9467	−	8.87939i	−0.649102	−	0.304203i
$853$	−13.5908	−	23.5400i	−0.465341	−	0.805994i	0.533876	−	0.845563i	$-0.320735\pi$
$853$	−13.5908	−	23.5400i	−0.465341	−	0.805994i	−0.999217	+	0.0395686i	$0.987402\pi$
$854$	1.75157			0.0599376
$855$	−1.18835	+	3.22629i	−0.0406408	+	0.110337i
$856$	−4.42033			−0.151084
$857$	21.9284	+	37.9811i	0.749060	+	1.29741i	0.948274	+	0.317454i	$0.102828\pi$
$857$	21.9284	+	37.9811i	0.749060	+	1.29741i	−0.199214	+	0.979956i	$0.563839\pi$
$858$	13.7117	−	9.56177i	0.468109	−	0.326433i
$859$	26.5531	−	45.9913i	0.905979	−	1.56920i	0.0863825	−	0.996262i	$-0.472469\pi$
$859$	26.5531	−	45.9913i	0.905979	−	1.56920i	0.819597	−	0.572940i	$-0.194197\pi$
$860$	5.01925	−	8.69360i	0.171155	−	0.296449i
$861$	1.27453	+	14.8980i	0.0434360	+	0.507724i
$862$	6.13373	+	10.6239i	0.208916	+	0.361853i
$863$	9.08908			0.309396			0.154698	−	0.987962i	$-0.450560\pi$
$863$	9.08908			0.309396			0.154698	+	0.987962i	$0.450560\pi$
$864$	5.01125	+	1.37381i	0.170486	+	0.0467380i
$865$	−15.0148			−0.510518
$866$	1.65129	+	2.86012i	0.0561133	+	0.0971910i
$867$	−2.20967	−	25.8289i	−0.0750443	−	0.877194i
$868$	5.99311	−	10.3804i	0.203419	−	0.352333i
$869$	−11.9381	+	20.6773i	−0.404971	+	0.701431i
$870$	2.27970	−	1.58974i	0.0772891	−	0.0538971i
$871$	−15.6011	−	27.0218i	−0.528622	−	0.915600i
$872$	18.5327			0.627595
$873$	29.8413	+	35.8427i	1.00997	+	1.21309i
$874$	−4.33718			−0.146707
$875$	−8.13795	−	14.0953i	−0.275113	−	0.476509i
$876$	−10.6418	−	4.98732i	−0.359554	−	0.168506i
$877$	−4.63591	+	8.02963i	−0.156544	+	0.271141i	−0.933620	−	0.358265i	$-0.883369\pi$
$877$	−4.63591	+	8.02963i	−0.156544	+	0.271141i	0.777076	+	0.629406i	$0.216702\pi$
$878$	−10.4785	+	18.1493i	−0.353633	+	0.612510i
$879$	1.61702	+	0.757820i	0.0545408	+	0.0255606i
$880$	−1.26582	−	2.19246i	−0.0426707	−	0.0739078i
$881$	0.681963			0.0229759			0.0114880	−	0.999934i	$-0.496343\pi$
$881$	0.681963			0.0229759			0.0114880	+	0.999934i	$0.496343\pi$
$882$	12.7927	−	2.20498i	0.430754	−	0.0742456i
$883$	−1.29612			−0.0436179			−0.0218090	−	0.999762i	$-0.506943\pi$
$883$	−1.29612			−0.0436179			−0.0218090	+	0.999762i	$0.506943\pi$
$884$	3.11496	+	5.39527i	0.104767	+	0.181462i
$885$	2.12673	−	1.48307i	0.0714894	−	0.0498527i
$886$	−17.4811	+	30.2782i	−0.587291	+	1.01722i
$887$	−10.7287	+	18.5826i	−0.360234	+	0.623943i	−0.987999	−	0.154460i	$-0.950636\pi$
$887$	−10.7287	+	18.5826i	−0.360234	+	0.623943i	0.627765	+	0.778403i	$0.283970\pi$
$888$	1.02553	+	11.9875i	0.0344147	+	0.402274i
$889$	6.66687	+	11.5474i	0.223600	+	0.387286i
$890$	−8.73715			−0.292870
$891$	−15.1308	−	12.8960i	−0.506901	−	0.432032i
$892$	21.6610			0.725263
$893$	1.53629	+	2.66093i	0.0514100	+	0.0890447i
$894$	3.01155	+	35.2021i	0.100721	+	1.17733i
$895$	7.04736	−	12.2064i	0.235567	−	0.408015i
$896$	0.817447	−	1.41586i	0.0273090	−	0.0473005i
$897$	26.9220	−	18.7739i	0.898898	−	0.626841i
$898$	−6.44222	−	11.1583i	−0.214980	−	0.372356i
$899$	10.2649			0.342352
$900$	10.8989	−	1.87856i	0.363297	−	0.0626186i
$901$	−7.37094			−0.245562
$902$	5.83210	+	10.1015i	0.194188	+	0.336343i
$903$	−22.4593	−	10.5256i	−0.747398	−	0.350269i
$904$	5.17058	−	8.95570i	0.171971	−	0.297862i
$905$	0.799737	−	1.38519i	0.0265842	−	0.0460451i
$906$	22.3072	+	10.4543i	0.741109	+	0.347322i
$907$	1.98110	+	3.43137i	0.0657814	+	0.113937i	0.897040	−	0.441949i	$-0.145713\pi$
$907$	1.98110	+	3.43137i	0.0657814	+	0.113937i	−0.831259	+	0.555885i	$0.812379\pi$
$908$	7.50858			0.249181
$909$	−15.2127	−	18.2721i	−0.504572	−	0.606047i
$910$	−8.18630			−0.271373
$911$	8.58261	+	14.8655i	0.284355	+	0.492517i	0.972452	−	0.233101i	$-0.0748874\pi$
$911$	8.58261	+	14.8655i	0.284355	+	0.492517i	−0.688098	+	0.725618i	$0.741554\pi$
$912$	−1.42072	+	0.990732i	−0.0470448	+	0.0328064i
$913$	5.74027	−	9.94244i	0.189975	−	0.329047i
$914$	1.35841	−	2.35284i	0.0449323	−	0.0778250i
$915$	−0.181278	−	2.11897i	−0.00599288	−	0.0700509i
$916$	3.05764	+	5.29598i	0.101027	+	0.174984i
$917$	−9.37986			−0.309750
$918$	5.26928	−	5.20881i	0.173912	−	0.171916i
$919$	−1.23791			−0.0408350			−0.0204175	−	0.999792i	$-0.506500\pi$
$919$	−1.23791			−0.0408350			−0.0204175	+	0.999792i	$0.506500\pi$
$920$	−2.48534	−	4.30474i	−0.0819394	−	0.141923i
$921$	−1.29782	−	15.1702i	−0.0427645	−	0.499875i
$922$	1.83407	−	3.17670i	0.0604018	−	0.104619i
$923$	−26.3904	+	45.7096i	−0.868652	+	1.50455i
$924$	−5.13087	+	3.57798i	−0.168793	+	0.117707i
$925$	12.8039	+	22.1769i	0.420988	+	0.729173i
$926$	12.2995			0.404186
$927$	−4.50354	+	12.2268i	−0.147916	+	0.401580i
$928$	1.40010			0.0459607
$929$	−18.4485	−	31.9538i	−0.605276	−	1.04837i	−0.992008	−	0.126177i	$-0.959729\pi$
$929$	−18.4485	−	31.9538i	−0.605276	−	1.04837i	0.386731	−	0.922192i	$-0.373604\pi$
$930$	−13.1779	−	6.17586i	−0.432121	−	0.202514i
$931$	−2.16356	+	3.74740i	−0.0709079	+	0.122816i
$932$	12.6905	−	21.9806i	0.415691	−	0.719999i
$933$	47.6772	+	22.3440i	1.56088	+	0.731510i
$934$	−8.74881	−	15.1534i	−0.286270	−	0.495834i
$935$	−3.60988			−0.118056
$936$	4.53030	−	12.2994i	0.148077	−	0.402019i
$937$	−29.7583			−0.972162			−0.486081	−	0.873914i	$-0.661574\pi$
$937$	−29.7583			−0.972162			−0.486081	+	0.873914i	$0.661574\pi$
$938$	5.83786	+	10.1115i	0.190613	+	0.330151i
$939$	1.51031	−	1.05321i	0.0492872	−	0.0343702i
$940$	−1.76069	+	3.04960i	−0.0574272	+	0.0994669i
$941$	−14.4325	+	24.9978i	−0.470486	+	0.814905i	−0.999430	−	0.0337510i	$-0.989255\pi$
$941$	−14.4325	+	24.9978i	−0.470486	+	0.814905i	0.528944	+	0.848656i	$0.322588\pi$
$942$	−0.289210	−	3.38059i	−0.00942298	−	0.110145i
$943$	11.4509	+	19.8336i	0.372894	+	0.645871i
$944$	1.30616			0.0425118
$945$	2.46554	+	9.41863i	0.0802039	+	0.306388i
$946$	−19.3487			−0.629082
$947$	−18.0124	−	31.1983i	−0.585323	−	1.01381i	−0.994835	−	0.101504i	$-0.967634\pi$
$947$	−18.0124	−	31.1983i	−0.585323	−	1.01381i	0.409512	−	0.912305i	$-0.365699\pi$
$948$	1.59577	+	18.6530i	0.0518282	+	0.605822i
$949$	−14.8228	+	25.6739i	−0.481169	+	0.833409i
$950$	−1.84327	+	3.19264i	−0.0598036	+	0.103583i
$951$	−23.5976	+	16.4557i	−0.765205	+	0.533611i
$952$	−1.16561	−	2.01889i	−0.0377775	−	0.0654326i
$953$	−3.29871			−0.106856			−0.0534278	−	0.998572i	$-0.517015\pi$
$953$	−3.29871			−0.106856			−0.0534278	+	0.998572i	$0.517015\pi$
$954$	9.92247	+	11.9180i	0.321252	+	0.385859i
$955$	−0.119732			−0.00387443
$956$	−3.08704	−	5.34692i	−0.0998421	−	0.172932i
$957$	−4.85063	−	2.27326i	−0.156799	−	0.0734840i
$958$	5.75981	−	9.97628i	0.186091	−	0.322319i
$959$	−17.2952	+	29.9562i	−0.558492	+	0.967336i
$960$	−1.79744	−	0.842374i	−0.0580121	−	0.0271875i
$961$	−11.3754	−	19.7028i	−0.366949	−	0.635574i
$962$	30.3488			0.978484
$963$	13.0683	−	2.25248i	0.421120	−	0.0725851i
$964$	11.8326			0.381102
$965$	12.0187	+	20.8171i	0.386897	+	0.670125i
$966$	−10.0741	+	7.02512i	−0.324129	+	0.226029i
$967$	−25.8504	+	44.7743i	−0.831294	+	1.43984i	0.0657191	+	0.997838i	$0.479066\pi$
$967$	−25.8504	+	44.7743i	−0.831294	+	1.43984i	−0.897013	+	0.442005i	$0.854267\pi$
$968$	3.06020	−	5.30042i	0.0983585	−	0.170362i
$969$	0.210519	+	2.46076i	0.00676284	+	0.0790511i
$970$	−8.90854	−	15.4300i	−0.286036	−	0.495429i
$971$	−4.38750			−0.140801			−0.0704007	−	0.997519i	$-0.522428\pi$
$971$	−4.38750			−0.140801			−0.0704007	+	0.997519i	$0.522428\pi$
$972$	−15.5154	−	1.50794i	−0.497655	−	0.0483673i
$973$	−30.0195			−0.962382
$974$	15.6610	+	27.1256i	0.501810	+	0.869160i
$975$	−2.37798	−	27.7962i	−0.0761562	−	0.890191i
$976$	0.535684	−	0.927832i	0.0171468	−	0.0296992i
$977$	−24.6775	+	42.7426i	−0.789502	+	1.36746i	0.136771	+	0.990603i	$0.456328\pi$
$977$	−24.6775	+	42.7426i	−0.789502	+	1.36746i	−0.926273	+	0.376854i	$0.877006\pi$
$978$	6.12578	−	4.27178i	0.195881	−	0.136596i
$979$	8.42022	+	14.5843i	0.269111	+	0.466115i
$980$	−4.95916			−0.158414
$981$	−54.7901	+	9.44374i	−1.74931	+	0.301515i
$982$	−36.2018			−1.15525
$983$	26.2273	+	45.4270i	0.836520	+	1.44890i	0.892787	+	0.450480i	$0.148747\pi$
$983$	26.2273	+	45.4270i	0.836520	+	1.44890i	−0.0562663	+	0.998416i	$0.517920\pi$
$984$	8.28149	+	3.88114i	0.264004	+	0.123726i
$985$	−12.3059	+	21.3144i	−0.392098	+	0.679134i
$986$	0.998212	−	1.72895i	0.0317895	−	0.0550611i
$987$	7.87841	+	3.69223i	0.250772	+	0.117525i
$988$	2.18454	+	3.78373i	0.0694994	+	0.120377i
$989$	−37.9899			−1.20801
$990$	4.85948	+	5.83677i	0.154445	+	0.185505i
$991$	−16.9358			−0.537985			−0.268992	−	0.963142i	$-0.586691\pi$
$991$	−16.9358			−0.537985			−0.268992	+	0.963142i	$0.586691\pi$
$992$	−3.66575	−	6.34926i	−0.116388	−	0.201589i
$993$	23.7699	−	16.5758i	0.754314	−	0.526017i
$994$	9.87521	−	17.1044i	0.313223	−	0.542518i
$995$	−3.66098	+	6.34101i	−0.116061	+	0.201024i
$996$	−0.767306	−	8.96906i	−0.0243130	−	0.284196i
$997$	−29.9924	−	51.9483i	−0.949868	−	1.64522i	−0.745697	−	0.666285i	$-0.767884\pi$
$997$	−29.9924	−	51.9483i	−0.949868	−	1.64522i	−0.204171	−	0.978935i	$-0.565450\pi$
$998$	−13.8719			−0.439108
$999$	−9.14040	−	34.9174i	−0.289189	−	1.10474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.e.c.229.3	yes	12
3.2	odd	2		1026.2.e.d.685.4		12
9.2	odd	6		1026.2.e.d.343.4		12
9.4	even	3		3078.2.a.x.1.4		6
9.5	odd	6		3078.2.a.v.1.3		6
9.7	even	3	inner	342.2.e.c.115.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.e.c.115.3	✓	12	9.7	even	3	inner
342.2.e.c.229.3	yes	12	1.1	even	1	trivial
1026.2.e.d.343.4		12	9.2	odd	6
1026.2.e.d.685.4		12	3.2	odd	2
3078.2.a.v.1.3		6	9.5	odd	6
3078.2.a.x.1.4		6	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.147638 + 1.72575i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.573032 + 0.992520i) q^{5} +(1.42072 - 0.990732i) q^{6} +(0.817447 + 1.41586i) q^{7} +1.00000 q^{8} +(-2.95641 + 0.509572i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.147638 + 1.72575i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.573032 + 0.992520i) q^{5} +(1.42072 - 0.990732i) q^{6} +(0.817447 + 1.41586i) q^{7} +1.00000 q^{8} +(-2.95641 + 0.509572i) q^{9} +1.14606 q^{10} +(-1.10449 - 1.91303i) q^{11} +(-1.56836 - 0.735015i) q^{12} +(-2.18454 + 3.78373i) q^{13} +(0.817447 - 1.41586i) q^{14} +(-1.79744 - 0.842374i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.42591 q^{17} +(1.91951 + 2.30554i) q^{18} -1.00000 q^{19} +(-0.573032 - 0.992520i) q^{20} +(-2.32273 + 1.61974i) q^{21} +(-1.10449 + 1.91303i) q^{22} +(-2.16859 + 3.75611i) q^{23} +(0.147638 + 1.72575i) q^{24} +(1.84327 + 3.19264i) q^{25} +4.36908 q^{26} +(-1.31587 - 5.02678i) q^{27} -1.63489 q^{28} +(-0.700052 - 1.21253i) q^{29} +(0.169203 + 1.97781i) q^{30} +(-3.66575 + 6.34926i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.13835 - 2.18851i) q^{33} +(0.712956 + 1.23488i) q^{34} -1.87369 q^{35} +(1.03690 - 2.81511i) q^{36} +6.94627 q^{37} +(0.500000 + 0.866025i) q^{38} +(-6.85229 - 3.21134i) q^{39} +(-0.573032 + 0.992520i) q^{40} +(2.64018 - 4.57292i) q^{41} +(2.56410 + 1.20167i) q^{42} +(4.37956 + 7.58562i) q^{43} +2.20898 q^{44} +(1.18835 - 3.22629i) q^{45} +4.33718 q^{46} +(-1.53629 - 2.66093i) q^{47} +(1.42072 - 0.990732i) q^{48} +(2.16356 - 3.74740i) q^{49} +(1.84327 - 3.19264i) q^{50} +(-0.210519 - 2.46076i) q^{51} +(-2.18454 - 3.78373i) q^{52} +5.16929 q^{53} +(-3.69538 + 3.65297i) q^{54} +2.53163 q^{55} +(0.817447 + 1.41586i) q^{56} +(-0.147638 - 1.72575i) q^{57} +(-0.700052 + 1.21253i) q^{58} +(-0.653079 + 1.13117i) q^{59} +(1.62824 - 1.13544i) q^{60} +(0.535684 + 0.927832i) q^{61} +7.33149 q^{62} +(-3.13819 - 3.76931i) q^{63} +1.00000 q^{64} +(-2.50362 - 4.33639i) q^{65} +(-3.46448 - 1.62364i) q^{66} +(-3.57079 + 6.18479i) q^{67} +(0.712956 - 1.23488i) q^{68} +(-6.80227 - 3.18790i) q^{69} +(0.936845 + 1.62266i) q^{70} +12.0806 q^{71} +(-2.95641 + 0.509572i) q^{72} +6.78533 q^{73} +(-3.47314 - 6.01565i) q^{74} +(-5.23755 + 3.65237i) q^{75} +(0.500000 - 0.866025i) q^{76} +(1.80573 - 3.12761i) q^{77} +(0.645043 + 7.53992i) q^{78} +(-5.40433 - 9.36057i) q^{79} +1.14606 q^{80} +(8.48067 - 3.01301i) q^{81} -5.28035 q^{82} +(2.59860 + 4.50091i) q^{83} +(-0.241373 - 2.82141i) q^{84} +(0.817092 - 1.41524i) q^{85} +(4.37956 - 7.58562i) q^{86} +(1.98916 - 1.38713i) q^{87} +(-1.10449 - 1.91303i) q^{88} -7.62362 q^{89} +(-3.38823 + 0.584002i) q^{90} -7.14298 q^{91} +(-2.16859 - 3.75611i) q^{92} +(-11.4984 - 5.38876i) q^{93} +(-1.53629 + 2.66093i) q^{94} +(0.573032 - 0.992520i) q^{95} +(-1.56836 - 0.735015i) q^{96} +(-7.77317 - 13.4635i) q^{97} -4.32712 q^{98} +(4.24015 + 5.09289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 2 q^{3} - 6 q^{4} - 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 + 2 * q^3 - 6 * q^4 - 4 * q^6 - 6 * q^7 + 12 * q^8 + 4 * q^9	\( 12 q - 6 q^{2} + 2 q^{3} - 6 q^{4} - 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9} - 6 q^{11} + 2 q^{12} - 6 q^{13} - 6 q^{14} + 10 q^{15} - 6 q^{16} + 4 q^{18} - 12 q^{19} - 18 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} - 30 q^{25} + 12 q^{26} + 14 q^{27} + 12 q^{28} + 6 q^{29} - 20 q^{30} - 6 q^{31} - 6 q^{32} + 22 q^{33} + 24 q^{35} - 8 q^{36} + 12 q^{37} + 6 q^{38} - 32 q^{39} + 6 q^{41} + 24 q^{42} - 12 q^{43} + 12 q^{44} + 26 q^{45} + 24 q^{46} - 6 q^{47} - 4 q^{48} - 18 q^{49} - 30 q^{50} - 12 q^{51} - 6 q^{52} - 36 q^{53} - 16 q^{54} + 48 q^{55} - 6 q^{56} - 2 q^{57} + 6 q^{58} + 12 q^{59} + 10 q^{60} - 12 q^{61} + 12 q^{62} + 30 q^{63} + 12 q^{64} - 6 q^{65} - 20 q^{66} - 18 q^{67} + 40 q^{69} - 12 q^{70} + 36 q^{71} + 4 q^{72} + 48 q^{73} - 6 q^{74} - 68 q^{75} + 6 q^{76} - 6 q^{77} + 52 q^{78} - 18 q^{79} + 64 q^{81} - 12 q^{82} + 12 q^{83} - 6 q^{84} - 36 q^{85} - 12 q^{86} + 32 q^{87} - 6 q^{88} + 12 q^{89} - 34 q^{90} - 24 q^{91} - 12 q^{92} - 46 q^{93} - 6 q^{94} + 2 q^{96} + 18 q^{97} + 36 q^{98} - 22 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 2 * q^3 - 6 * q^4 - 4 * q^6 - 6 * q^7 + 12 * q^8 + 4 * q^9 - 6 * q^11 + 2 * q^12 - 6 * q^13 - 6 * q^14 + 10 * q^15 - 6 * q^16 + 4 * q^18 - 12 * q^19 - 18 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 - 30 * q^25 + 12 * q^26 + 14 * q^27 + 12 * q^28 + 6 * q^29 - 20 * q^30 - 6 * q^31 - 6 * q^32 + 22 * q^33 + 24 * q^35 - 8 * q^36 + 12 * q^37 + 6 * q^38 - 32 * q^39 + 6 * q^41 + 24 * q^42 - 12 * q^43 + 12 * q^44 + 26 * q^45 + 24 * q^46 - 6 * q^47 - 4 * q^48 - 18 * q^49 - 30 * q^50 - 12 * q^51 - 6 * q^52 - 36 * q^53 - 16 * q^54 + 48 * q^55 - 6 * q^56 - 2 * q^57 + 6 * q^58 + 12 * q^59 + 10 * q^60 - 12 * q^61 + 12 * q^62 + 30 * q^63 + 12 * q^64 - 6 * q^65 - 20 * q^66 - 18 * q^67 + 40 * q^69 - 12 * q^70 + 36 * q^71 + 4 * q^72 + 48 * q^73 - 6 * q^74 - 68 * q^75 + 6 * q^76 - 6 * q^77 + 52 * q^78 - 18 * q^79 + 64 * q^81 - 12 * q^82 + 12 * q^83 - 6 * q^84 - 36 * q^85 - 12 * q^86 + 32 * q^87 - 6 * q^88 + 12 * q^89 - 34 * q^90 - 24 * q^91 - 12 * q^92 - 46 * q^93 - 6 * q^94 + 2 * q^96 + 18 * q^97 + 36 * q^98 - 22 * q^99

Introduction

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