LMFDB - Embedded newform 231.2.i.e.100.1

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 $ x^8 - 2x^7 + 8x^6 + 21x^4 - 4x^3 + 28x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.1
Root			$1.39083 - 2.40898i$ of defining polynomial
Character	$\chi$	$=$	231.100
Dual form			231.2.i.e.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39083 + 2.40898i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.86880 - 4.96890i) q^{4} +(-0.412855 + 0.715087i) q^{5} +2.78165 q^{6} +(2.63323 - 0.257073i) q^{7} +10.3967 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.39083 + 2.40898i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.86880 - 4.96890i) q^{4} +(-0.412855 + 0.715087i) q^{5} +2.78165 q^{6} +(2.63323 - 0.257073i) q^{7} +10.3967 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.14842 - 1.98912i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-2.86880 + 4.96890i) q^{12} -0.296842 q^{13} +(-3.04309 + 6.70095i) q^{14} +0.825711 q^{15} +(-8.72241 + 15.1077i) q^{16} +(3.34677 + 5.79677i) q^{17} +(-1.39083 - 2.40898i) q^{18} +(1.41669 - 2.45379i) q^{19} +4.73760 q^{20} +(-1.53925 - 2.15191i) q^{21} -2.78165 q^{22} +(1.98481 - 3.43779i) q^{23} +(-5.19835 - 9.00380i) q^{24} +(2.15910 + 3.73967i) q^{25} +(0.412855 - 0.715087i) q^{26} +1.00000 q^{27} +(-8.83158 - 12.3468i) q^{28} -0.484812 q^{29} +(-1.14842 + 1.98912i) q^{30} +(3.66564 + 6.34907i) q^{31} +(-13.8660 - 24.0166i) q^{32} +(0.500000 - 0.866025i) q^{33} -18.6191 q^{34} +(-0.903315 + 1.98912i) q^{35} +5.73760 q^{36} +(2.86880 - 4.96890i) q^{37} +(3.94075 + 6.82559i) q^{38} +(0.148421 + 0.257073i) q^{39} +(-4.29233 + 7.43454i) q^{40} +0.645420 q^{41} +(7.32474 - 0.715087i) q^{42} +6.43308 q^{43} +(2.86880 - 4.96890i) q^{44} +(-0.412855 - 0.715087i) q^{45} +(5.52106 + 9.56275i) q^{46} +(-3.86880 + 6.70095i) q^{47} +17.4448 q^{48} +(6.86783 - 1.35386i) q^{49} -12.0117 q^{50} +(3.34677 - 5.79677i) q^{51} +(0.851579 + 1.47498i) q^{52} +(-3.55677 - 6.16050i) q^{53} +(-1.39083 + 2.40898i) q^{54} -0.825711 q^{55} +(27.3769 - 2.67271i) q^{56} -2.83339 q^{57} +(0.674289 - 1.16790i) q^{58} +(0.578495 + 1.00198i) q^{59} +(-2.36880 - 4.10288i) q^{60} +(-2.63323 + 4.56089i) q^{61} -20.3931 q^{62} +(-1.09398 + 2.40898i) q^{63} +42.2513 q^{64} +(0.122553 - 0.212268i) q^{65} +(1.39083 + 2.40898i) q^{66} +(-1.50865 - 2.61306i) q^{67} +(19.2024 - 33.2595i) q^{68} -3.96962 q^{69} +(-3.53541 - 4.94260i) q^{70} +3.58061 q^{71} +(-5.19835 + 9.00380i) q^{72} +(-8.01625 - 13.8845i) q^{73} +(7.98000 + 13.8218i) q^{74} +(2.15910 - 3.73967i) q^{75} -16.2568 q^{76} +(1.53925 + 2.15191i) q^{77} -0.825711 q^{78} +(2.16210 - 3.74487i) q^{79} +(-7.20219 - 12.4746i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.897667 + 1.55481i) q^{82} +2.37594 q^{83} +(-6.27684 + 13.8218i) q^{84} -5.52693 q^{85} +(-8.94729 + 15.4972i) q^{86} +(0.242406 + 0.419859i) q^{87} +(5.19835 + 9.00380i) q^{88} +(-6.08617 + 10.5416i) q^{89} +2.29684 q^{90} +(-0.781653 + 0.0763099i) q^{91} -22.7761 q^{92} +(3.66564 - 6.34907i) q^{93} +(-10.7617 - 18.6397i) q^{94} +(1.16978 + 2.02612i) q^{95} +(-13.8660 + 24.0166i) q^{96} -10.7680 q^{97} +(-6.29052 + 18.4275i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 24 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 24 q^{8} - 4 q^{9} - 10 q^{10} + 4 q^{11} - 4 q^{12} - 4 q^{13} - 4 q^{14} + 8 q^{15} - 12 q^{16} - 2 q^{17} - 2 q^{18} - 4 q^{21} - 4 q^{22} - 4 q^{23} - 12 q^{24} - 4 q^{25} + 4 q^{26} + 8 q^{27} - 22 q^{28} + 16 q^{29} - 10 q^{30} + 12 q^{31} - 26 q^{32} + 4 q^{33} - 32 q^{34} - 2 q^{35} + 8 q^{36} + 4 q^{37} - 8 q^{38} + 2 q^{39} + 6 q^{40} + 4 q^{41} + 20 q^{42} + 36 q^{43} + 4 q^{44} - 4 q^{45} + 14 q^{46} - 12 q^{47} + 24 q^{48} - 4 q^{49} + 4 q^{50} - 2 q^{51} + 6 q^{52} + 12 q^{53} - 2 q^{54} - 8 q^{55} + 48 q^{56} + 4 q^{58} - 12 q^{59} - 2 q^{61} - 52 q^{62} + 2 q^{63} + 112 q^{64} + 4 q^{65} + 2 q^{66} - 28 q^{67} + 48 q^{68} + 8 q^{69} - 32 q^{70} + 24 q^{71} - 12 q^{72} - 6 q^{73} + 16 q^{74} - 4 q^{75} - 36 q^{76} + 4 q^{77} - 8 q^{78} - 2 q^{79} - 16 q^{80} - 4 q^{81} + 12 q^{82} - 24 q^{83} - 4 q^{84} + 36 q^{85} - 36 q^{86} - 8 q^{87} + 12 q^{88} - 8 q^{89} + 20 q^{90} + 12 q^{91} - 32 q^{92} + 12 q^{93} - 20 q^{94} - 34 q^{95} - 26 q^{96} - 88 q^{97} + 16 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 24 * q^8 - 4 * q^9 - 10 * q^10 + 4 * q^11 - 4 * q^12 - 4 * q^13 - 4 * q^14 + 8 * q^15 - 12 * q^16 - 2 * q^17 - 2 * q^18 - 4 * q^21 - 4 * q^22 - 4 * q^23 - 12 * q^24 - 4 * q^25 + 4 * q^26 + 8 * q^27 - 22 * q^28 + 16 * q^29 - 10 * q^30 + 12 * q^31 - 26 * q^32 + 4 * q^33 - 32 * q^34 - 2 * q^35 + 8 * q^36 + 4 * q^37 - 8 * q^38 + 2 * q^39 + 6 * q^40 + 4 * q^41 + 20 * q^42 + 36 * q^43 + 4 * q^44 - 4 * q^45 + 14 * q^46 - 12 * q^47 + 24 * q^48 - 4 * q^49 + 4 * q^50 - 2 * q^51 + 6 * q^52 + 12 * q^53 - 2 * q^54 - 8 * q^55 + 48 * q^56 + 4 * q^58 - 12 * q^59 - 2 * q^61 - 52 * q^62 + 2 * q^63 + 112 * q^64 + 4 * q^65 + 2 * q^66 - 28 * q^67 + 48 * q^68 + 8 * q^69 - 32 * q^70 + 24 * q^71 - 12 * q^72 - 6 * q^73 + 16 * q^74 - 4 * q^75 - 36 * q^76 + 4 * q^77 - 8 * q^78 - 2 * q^79 - 16 * q^80 - 4 * q^81 + 12 * q^82 - 24 * q^83 - 4 * q^84 + 36 * q^85 - 36 * q^86 - 8 * q^87 + 12 * q^88 - 8 * q^89 + 20 * q^90 + 12 * q^91 - 32 * q^92 + 12 * q^93 - 20 * q^94 - 34 * q^95 - 26 * q^96 - 88 * q^97 + 16 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.39083	+	2.40898i	−0.983463	+	1.70341i	−0.334886	+	0.942259i	$0.608698\pi$
$2$	−1.39083	+	2.40898i	−0.983463	+	1.70341i	−0.648577	+	0.761149i	$0.724635\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−2.86880	−	4.96890i	−1.43440	−	2.48445i
$5$	−0.412855	+	0.715087i	−0.184635	+	0.319796i	−0.943453	−	0.331505i	$-0.892443\pi$
$5$	−0.412855	+	0.715087i	−0.184635	+	0.319796i	0.758819	+	0.651302i	$0.225777\pi$
$6$	2.78165			1.13561
$7$	2.63323	−	0.257073i	0.995268	−	0.0971643i
$7$	2.63323	−	0.257073i	0.995268	−	0.0971643i
$8$	10.3967			3.67579
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.14842	−	1.98912i	−0.363163	−	0.629016i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−2.86880	+	4.96890i	−0.828151	+	1.43440i
$13$	−0.296842			−0.0823291			−0.0411645	−	0.999152i	$-0.513107\pi$
$13$	−0.296842			−0.0823291			−0.0411645	+	0.999152i	$0.513107\pi$
$14$	−3.04309	+	6.70095i	−0.813299	+	1.79091i
$15$	0.825711			0.213198
$16$	−8.72241	+	15.1077i	−2.18060	+	3.77691i
$17$	3.34677	+	5.79677i	0.811711	+	1.40592i	0.911666	+	0.410932i	$0.134797\pi$
$17$	3.34677	+	5.79677i	0.811711	+	1.40592i	−0.0999551	+	0.994992i	$0.531870\pi$
$18$	−1.39083	−	2.40898i	−0.327821	−	0.567803i
$19$	1.41669	−	2.45379i	0.325012	−	0.562937i	−0.656503	−	0.754324i	$-0.727965\pi$
$19$	1.41669	−	2.45379i	0.325012	−	0.562937i	0.981515	+	0.191386i	$0.0612983\pi$
$20$	4.73760			1.05936
$21$	−1.53925	−	2.15191i	−0.335891	−	0.469585i
$22$	−2.78165			−0.593051
$23$	1.98481	−	3.43779i	0.413862	−	0.716830i	−0.581446	−	0.813585i	$-0.697513\pi$
$23$	1.98481	−	3.43779i	0.413862	−	0.716830i	0.995308	+	0.0967550i	$0.0308463\pi$
$24$	−5.19835	−	9.00380i	−1.06111	−	1.83789i
$25$	2.15910	+	3.73967i	0.431820	+	0.747934i
$26$	0.412855	−	0.715087i	0.0809676	−	0.140240i
$27$	1.00000			0.192450
$28$	−8.83158	−	12.3468i	−1.66901	−	2.33332i
$29$	−0.484812			−0.0900273			−0.0450136	−	0.998986i	$-0.514333\pi$
$29$	−0.484812			−0.0900273			−0.0450136	+	0.998986i	$0.514333\pi$
$30$	−1.14842	+	1.98912i	−0.209672	+	0.363163i
$31$	3.66564	+	6.34907i	0.658368	+	1.14033i	0.981038	+	0.193816i	$0.0620864\pi$
$31$	3.66564	+	6.34907i	0.658368	+	1.14033i	−0.322670	+	0.946512i	$0.604580\pi$
$32$	−13.8660	−	24.0166i	−2.45119	−	4.24558i
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$	−18.6191			−3.19315
$35$	−0.903315	+	1.98912i	−0.152688	+	0.336223i
$36$	5.73760			0.956266
$37$	2.86880	−	4.96890i	0.471627	−	0.816883i	−0.527846	−	0.849340i	$-0.677000\pi$
$37$	2.86880	−	4.96890i	0.471627	−	0.816883i	0.999473	+	0.0324576i	$0.0103334\pi$
$38$	3.94075	+	6.82559i	0.639275	+	1.10726i
$39$	0.148421	+	0.257073i	0.0237664	+	0.0411645i
$40$	−4.29233	+	7.43454i	−0.678677	+	1.17550i
$41$	0.645420			0.100798			0.0503988	−	0.998729i	$-0.483951\pi$
$41$	0.645420			0.100798			0.0503988	+	0.998729i	$0.483951\pi$
$42$	7.32474	−	0.715087i	1.13023	−	0.110340i
$43$	6.43308			0.981035			0.490517	−	0.871431i	$-0.336808\pi$
$43$	6.43308			0.981035			0.490517	+	0.871431i	$0.336808\pi$
$44$	2.86880	−	4.96890i	0.432488	−	0.749090i
$45$	−0.412855	−	0.715087i	−0.0615449	−	0.106599i
$46$	5.52106	+	9.56275i	0.814036	+	1.40995i
$47$	−3.86880	+	6.70095i	−0.564322	+	0.977435i	0.432790	+	0.901495i	$0.357529\pi$
$47$	−3.86880	+	6.70095i	−0.564322	+	0.977435i	−0.997112	+	0.0759400i	$0.975804\pi$
$48$	17.4448			2.51794
$49$	6.86783	−	1.35386i	0.981118	−	0.193409i
$50$	−12.0117			−1.69872
$51$	3.34677	−	5.79677i	0.468641	−	0.811711i
$52$	0.851579	+	1.47498i	0.118093	+	0.204543i
$53$	−3.55677	−	6.16050i	−0.488560	−	0.846210i	0.511354	−	0.859370i	$-0.329144\pi$
$53$	−3.55677	−	6.16050i	−0.488560	−	0.846210i	−0.999913	+	0.0131602i	$0.995811\pi$
$54$	−1.39083	+	2.40898i	−0.189268	+	0.327821i
$55$	−0.825711			−0.111339
$56$	27.3769	−	2.67271i	3.65839	−	0.357155i
$57$	−2.83339			−0.375292
$58$	0.674289	−	1.16790i	0.0885385	−	0.153353i
$59$	0.578495	+	1.00198i	0.0753137	+	0.130447i	0.901223	−	0.433356i	$-0.142671\pi$
$59$	0.578495	+	1.00198i	0.0753137	+	0.130447i	−0.825909	+	0.563803i	$0.809338\pi$
$60$	−2.36880	−	4.10288i	−0.305811	−	0.529679i
$61$	−2.63323	+	4.56089i	−0.337151	+	0.583962i	−0.983896	−	0.178744i	$-0.942797\pi$
$61$	−2.63323	+	4.56089i	−0.337151	+	0.583962i	0.646745	+	0.762707i	$0.276130\pi$
$62$	−20.3931			−2.58992
$63$	−1.09398	+	2.40898i	−0.137829	+	0.303503i
$64$	42.2513			5.28141
$65$	0.122553	−	0.212268i	0.0152008	−	0.0263286i
$66$	1.39083	+	2.40898i	0.171199	+	0.296525i
$67$	−1.50865	−	2.61306i	−0.184311	−	0.319236i	0.759033	−	0.651052i	$-0.225672\pi$
$67$	−1.50865	−	2.61306i	−0.184311	−	0.319236i	−0.943344	+	0.331816i	$0.892339\pi$
$68$	19.2024	−	33.2595i	2.32863	−	4.03331i
$69$	−3.96962			−0.477886
$70$	−3.53541	−	4.94260i	−0.422562	−	0.590753i
$71$	3.58061			0.424940			0.212470	−	0.977168i	$-0.431849\pi$
$71$	3.58061			0.424940			0.212470	+	0.977168i	$0.431849\pi$
$72$	−5.19835	+	9.00380i	−0.612631	+	1.06111i
$73$	−8.01625	−	13.8845i	−0.938231	−	1.62506i	−0.768769	−	0.639527i	$-0.779130\pi$
$73$	−8.01625	−	13.8845i	−0.938231	−	1.62506i	−0.169462	−	0.985537i	$-0.554203\pi$
$74$	7.98000	+	13.8218i	0.927656	+	1.60675i
$75$	2.15910	−	3.73967i	0.249311	−	0.431820i
$76$	−16.2568			−1.86479
$77$	1.53925	+	2.15191i	0.175414	+	0.245233i
$78$	−0.825711			−0.0934934
$79$	2.16210	−	3.74487i	0.243255	−	0.421331i	−0.718384	−	0.695647i	$-0.755118\pi$
$79$	2.16210	−	3.74487i	0.243255	−	0.421331i	0.961640	+	0.274316i	$0.0884513\pi$
$80$	−7.20219	−	12.4746i	−0.805229	−	1.39470i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.897667	+	1.55481i	−0.0991308	+	0.171700i
$83$	2.37594			0.260793			0.130397	−	0.991462i	$-0.458375\pi$
$83$	2.37594			0.260793			0.130397	+	0.991462i	$0.458375\pi$
$84$	−6.27684	+	13.8218i	−0.684860	+	1.50808i
$85$	−5.52693			−0.599480
$86$	−8.94729	+	15.4972i	−0.964811	+	1.67110i
$87$	0.242406	+	0.419859i	0.0259886	+	0.0450136i
$88$	5.19835	+	9.00380i	0.554146	+	0.959809i
$89$	−6.08617	+	10.5416i	−0.645133	+	1.11740i	0.339138	+	0.940737i	$0.389865\pi$
$89$	−6.08617	+	10.5416i	−0.645133	+	1.11740i	−0.984271	+	0.176667i	$0.943469\pi$
$90$	2.29684			0.242108
$91$	−0.781653	+	0.0763099i	−0.0819395	+	0.00799945i
$92$	−22.7761			−2.37457
$93$	3.66564	−	6.34907i	0.380109	−	0.658368i
$94$	−10.7617	−	18.6397i	−1.10998	−	1.92254i
$95$	1.16978	+	2.02612i	0.120017	+	0.207875i
$96$	−13.8660	+	24.0166i	−1.41519	+	2.45119i
$97$	−10.7680			−1.09332			−0.546661	−	0.837354i	$-0.684101\pi$
$97$	−10.7680			−1.09332			−0.546661	+	0.837354i	$0.684101\pi$
$98$	−6.29052	+	18.4275i	−0.635439	+	1.86146i
$99$	−1.00000			−0.100504
$100$	12.3880	−	21.4567i	1.23880	−	2.14567i
$101$	−7.49519	−	12.9821i	−0.745799	−	1.29176i	−0.949820	−	0.312796i	$-0.898734\pi$
$101$	−7.49519	−	12.9821i	−0.745799	−	1.29176i	0.204021	−	0.978966i	$-0.434599\pi$
$102$	9.30955	+	16.1246i	0.921783	+	1.59658i
$103$	1.23203	−	2.13393i	0.121395	−	0.210263i	−0.798923	−	0.601434i	$-0.794596\pi$
$103$	1.23203	−	2.13393i	0.121395	−	0.210263i	0.920318	+	0.391171i	$0.127930\pi$
$104$	−3.08617			−0.302624
$105$	2.17429	−	0.212268i	0.212189	−	0.0207152i
$106$	19.7874			1.92192
$107$	5.79022	−	10.0290i	0.559762	−	0.969536i	−0.437754	−	0.899095i	$-0.644226\pi$
$107$	5.79022	−	10.0290i	0.559762	−	0.969536i	0.997516	−	0.0704414i	$-0.0224408\pi$
$108$	−2.86880	−	4.96890i	−0.276050	−	0.478133i
$109$	2.71173	+	4.69685i	0.259736	+	0.449877i	0.966171	−	0.257901i	$-0.0830310\pi$
$109$	2.71173	+	4.69685i	0.259736	+	0.449877i	−0.706435	+	0.707778i	$0.749698\pi$
$110$	1.14842	−	1.98912i	0.109498	−	0.189655i
$111$	−5.73760			−0.544589
$112$	−19.0844	+	42.0243i	−1.80330	+	3.97092i
$113$	−17.5156			−1.64773			−0.823866	−	0.566785i	$-0.808187\pi$
$113$	−17.5156			−1.64773			−0.823866	+	0.566785i	$0.808187\pi$
$114$	3.94075	−	6.82559i	0.369085	−	0.639275i
$115$	1.63888	+	2.83862i	0.152826	+	0.264703i
$116$	1.39083	+	2.40898i	0.129135	+	0.223668i
$117$	0.148421	−	0.257073i	0.0137215	−	0.0237664i
$118$	−3.21835			−0.296273
$119$	10.3030	+	14.4039i	0.944476	+	1.32040i
$120$	8.58467			0.783669
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−7.32474	−	12.6868i	−0.663151	−	1.14861i
$123$	−0.322710	−	0.558950i	−0.0290978	−	0.0503988i
$124$	21.0320	−	36.4284i	1.88873	−	3.27137i
$125$	−7.69414			−0.688185
$126$	−4.28165	−	5.98587i	−0.381440	−	0.533264i
$127$	5.97924			0.530572			0.265286	−	0.964170i	$-0.414534\pi$
$127$	5.97924			0.530572			0.265286	+	0.964170i	$0.414534\pi$
$128$	−31.0322	+	53.7493i	−2.74288	+	4.75081i
$129$	−3.21654	−	5.57121i	−0.283200	−	0.490517i
$130$	0.340899	+	0.590455i	0.0298988	+	0.0517863i
$131$	−8.82120	+	15.2788i	−0.770712	+	1.33491i	0.166461	+	0.986048i	$0.446766\pi$
$131$	−8.82120	+	15.2788i	−0.770712	+	1.33491i	−0.937173	+	0.348864i	$0.886567\pi$
$132$	−5.73760			−0.499394
$133$	3.09969	−	6.82559i	0.268777	−	0.591853i
$134$	8.39308			0.725052
$135$	−0.412855	+	0.715087i	−0.0355329	+	0.0615449i
$136$	34.7953	+	60.2673i	2.98368	+	5.16788i
$137$	−4.67986	−	8.10575i	−0.399827	−	0.692521i	0.593877	−	0.804556i	$-0.297597\pi$
$137$	−4.67986	−	8.10575i	−0.399827	−	0.692521i	−0.993704	+	0.112035i	$0.964263\pi$
$138$	5.52106	−	9.56275i	0.469984	−	0.814036i
$139$	7.40270			0.627889			0.313944	−	0.949441i	$-0.398349\pi$
$139$	7.40270			0.627889			0.313944	+	0.949441i	$0.398349\pi$
$140$	12.4752	−	1.21791i	1.05435	−	0.102932i
$141$	7.73760			0.651623
$142$	−4.98000	+	8.62562i	−0.417912	+	0.723846i
$143$	−0.148421	−	0.257073i	−0.0124116	−	0.0214975i
$144$	−8.72241	−	15.1077i	−0.726867	−	1.25897i
$145$	0.200157	−	0.346682i	0.0166221	−	0.0287904i
$146$	44.5968			3.69086
$147$	−4.60639	−	5.27078i	−0.379929	−	0.434727i
$148$	−32.9200			−2.70601
$149$	6.00587	−	10.4025i	0.492020	−	0.852204i	−0.507938	−	0.861394i	$-0.669592\pi$
$149$	6.00587	−	10.4025i	0.492020	−	0.852204i	0.999958	+	0.00919009i	$0.00292534\pi$
$150$	6.00587	+	10.4025i	0.490377	+	0.849358i
$151$	−4.66091	−	8.07293i	−0.379299	−	0.656966i	0.611661	−	0.791120i	$-0.290502\pi$
$151$	−4.66091	−	8.07293i	−0.379299	−	0.656966i	−0.990960	+	0.134154i	$0.957168\pi$
$152$	14.7289	−	25.5113i	1.19468	−	2.06924i
$153$	−6.69354			−0.541141
$154$	−7.32474	+	0.715087i	−0.590244	+	0.0576233i
$155$	−6.05352			−0.486230
$156$	0.851579	−	1.47498i	0.0681809	−	0.118093i
$157$	2.55174	+	4.41974i	0.203651	+	0.352733i	0.949702	−	0.313155i	$-0.101386\pi$
$157$	2.55174	+	4.41974i	0.203651	+	0.352733i	−0.746051	+	0.665889i	$0.768053\pi$
$158$	6.01422	+	10.4169i	0.478465	+	0.828727i
$159$	−3.55677	+	6.16050i	−0.282070	+	0.488560i
$160$	22.8986			1.81030
$161$	4.34271	−	9.56275i	0.342253	−	0.753651i
$162$	2.78165			0.218547
$163$	−4.74413	+	8.21708i	−0.371589	+	0.643612i	−0.989810	−	0.142393i	$-0.954520\pi$
$163$	−4.74413	+	8.21708i	−0.371589	+	0.643612i	0.618221	+	0.786004i	$0.287854\pi$
$164$	−1.85158	−	3.20703i	−0.144584	−	0.250427i
$165$	0.412855	+	0.715087i	0.0321408	+	0.0556694i
$166$	−3.30452	+	5.72360i	−0.256481	+	0.444237i
$167$	−3.03850			−0.235126			−0.117563	−	0.993065i	$-0.537508\pi$
$167$	−3.03850			−0.235126			−0.117563	+	0.993065i	$0.537508\pi$
$168$	−16.0031	−	22.3728i	−1.23467	−	1.72610i
$169$	−12.9119			−0.993222
$170$	7.68700	−	13.3143i	0.589566	−	1.02116i
$171$	1.41669	+	2.45379i	0.108337	+	0.187646i
$172$	−18.4552	−	31.9653i	−1.40720	−	2.43733i
$173$	2.88602	−	4.99873i	0.219420	−	0.380046i	−0.735211	−	0.677838i	$-0.762917\pi$
$173$	2.88602	−	4.99873i	0.219420	−	0.380046i	0.954631	+	0.297792i	$0.0962502\pi$
$174$	−1.34858			−0.102235
$175$	6.64678	+	9.29238i	0.502449	+	0.702438i
$176$	−17.4448			−1.31495
$177$	0.578495	−	1.00198i	0.0434824	−	0.0753137i
$178$	−16.9296	−	29.3230i	−1.26893	−	2.19785i
$179$	1.51422	+	2.62270i	0.113178	+	0.196030i	0.917050	−	0.398772i	$-0.130564\pi$
$179$	1.51422	+	2.62270i	0.113178	+	0.196030i	−0.803872	+	0.594802i	$0.797230\pi$
$180$	−2.36880	+	4.10288i	−0.176560	+	0.305811i
$181$	−9.67878			−0.719418			−0.359709	−	0.933064i	$-0.617124\pi$
$181$	−9.67878			−0.719418			−0.359709	+	0.933064i	$0.617124\pi$
$182$	0.903315	−	1.98912i	0.0669582	−	0.147444i
$183$	5.26647			0.389308
$184$	20.6355	−	35.7417i	1.52127	−	2.63491i
$185$	2.36880	+	4.10288i	0.174157	+	0.301650i
$186$	10.1965	+	17.6609i	0.747647	+	1.29496i
$187$	−3.34677	+	5.79677i	−0.244740	+	0.423902i
$188$	44.3952			3.23785
$189$	2.63323	−	0.257073i	0.191539	−	0.0186993i
$190$	−6.50785			−0.472129
$191$	0.645420	−	1.11790i	0.0467009	−	0.0808884i	−0.841730	−	0.539899i	$-0.818463\pi$
$191$	0.645420	−	1.11790i	0.0467009	−	0.0808884i	0.888431	+	0.459010i	$0.151796\pi$
$192$	−21.1256	−	36.5907i	−1.52461	−	2.64071i
$193$	10.4889	+	18.1673i	0.755006	+	1.30771i	0.945372	+	0.325995i	$0.105699\pi$
$193$	10.4889	+	18.1673i	0.755006	+	1.30771i	−0.190366	+	0.981713i	$0.560967\pi$
$194$	14.9764	−	25.9399i	1.07524	−	1.86237i
$195$	−0.245106			−0.0175524
$196$	−26.4296	−	30.2416i	−1.88783	−	2.16012i
$197$	15.0836			1.07466			0.537332	−	0.843371i	$-0.319432\pi$
$197$	15.0836			1.07466			0.537332	+	0.843371i	$0.319432\pi$
$198$	1.39083	−	2.40898i	0.0988418	−	0.171199i
$199$	12.8601	+	22.2744i	0.911632	+	1.57899i	0.811759	+	0.583992i	$0.198510\pi$
$199$	12.8601	+	22.2744i	0.911632	+	1.57899i	0.0998726	+	0.995000i	$0.468156\pi$
$200$	22.4475	+	38.8802i	1.58728	+	2.74925i
$201$	−1.50865	+	2.61306i	−0.106412	+	0.184311i
$202$	41.6980			2.93386
$203$	−1.27662	+	0.124632i	−0.0896013	+	0.00874743i
$204$	−38.4048			−2.68888
$205$	−0.266465	+	0.461531i	−0.0186107	+	0.0322347i
$206$	3.42707	+	5.93587i	0.238776	+	0.413571i
$207$	1.98481	+	3.43779i	0.137954	+	0.238943i
$208$	2.58918	−	4.48458i	0.179527	−	0.310950i
$209$	2.83339			0.195990
$210$	−2.51271	+	5.53305i	−0.173393	+	0.381817i
$211$	1.84814			0.127232			0.0636158	−	0.997974i	$-0.479737\pi$
$211$	1.84814			0.127232			0.0636158	+	0.997974i	$0.479737\pi$
$212$	−20.4073	+	35.3465i	−1.40158	+	2.42761i
$213$	−1.79030	−	3.10090i	−0.122670	−	0.212470i
$214$	16.1064	+	27.8971i	1.10101	+	1.90701i
$215$	−2.65593	+	4.60021i	−0.181133	+	0.313731i
$216$	10.3967			0.707406
$217$	11.2847	+	15.7763i	0.766052	+	1.07096i
$218$	−15.0862			−1.02176
$219$	−8.01625	+	13.8845i	−0.541688	+	0.938231i
$220$	2.36880	+	4.10288i	0.159704	+	0.276616i
$221$	−0.993461	−	1.72072i	−0.0668274	−	0.115748i
$222$	7.98000	−	13.8218i	0.535583	−	0.927656i
$223$	−6.17851			−0.413744			−0.206872	−	0.978368i	$-0.566328\pi$
$223$	−6.17851			−0.413744			−0.206872	+	0.978368i	$0.566328\pi$
$224$	−42.6865	−	59.6768i	−2.85211	−	3.98733i
$225$	−4.31820			−0.287880
$226$	24.3612	−	42.1949i	1.62048	−	2.80676i
$227$	−2.50557	−	4.33977i	−0.166300	−	0.288041i	0.770816	−	0.637058i	$-0.219849\pi$
$227$	−2.50557	−	4.33977i	−0.166300	−	0.288041i	−0.937116	+	0.349017i	$0.886515\pi$
$228$	8.12842	+	14.0788i	0.538318	+	0.932394i
$229$	−11.2164	+	19.4274i	−0.741201	+	1.28380i	0.210748	+	0.977540i	$0.432410\pi$
$229$	−11.2164	+	19.4274i	−0.741201	+	1.28380i	−0.951949	+	0.306257i	$0.900923\pi$
$230$	−9.11760			−0.601197
$231$	1.09398	−	2.40898i	0.0719789	−	0.158499i
$232$	−5.04044			−0.330921
$233$	−2.41669	+	4.18584i	−0.158323	+	0.274223i	−0.934264	−	0.356582i	$-0.883942\pi$
$233$	−2.41669	+	4.18584i	−0.158323	+	0.274223i	0.775941	+	0.630805i	$0.217275\pi$
$234$	0.412855	+	0.715087i	0.0269892	+	0.0467467i
$235$	−3.19451	−	5.53305i	−0.208387	−	0.360937i
$236$	3.31917	−	5.74897i	0.216060	−	0.374226i
$237$	−4.32420			−0.280887
$238$	−49.0284	+	4.78646i	−3.17804	+	0.310260i
$239$	−2.58467			−0.167188			−0.0835941	−	0.996500i	$-0.526640\pi$
$239$	−2.58467			−0.167188			−0.0835941	+	0.996500i	$0.526640\pi$
$240$	−7.20219	+	12.4746i	−0.464899	+	0.805229i
$241$	−1.38902	−	2.40585i	−0.0894745	−	0.154974i	0.817815	−	0.575482i	$-0.195185\pi$
$241$	−1.38902	−	2.40585i	−0.0894745	−	0.154974i	−0.907289	+	0.420507i	$0.861852\pi$
$242$	−1.39083	−	2.40898i	−0.0894057	−	0.154855i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	30.2168			1.93444
$245$	−1.86729	+	5.47004i	−0.119297	+	0.349468i
$246$	1.79533			0.114466
$247$	−0.420534	+	0.728387i	−0.0267580	+	0.0463461i
$248$	38.1105	+	66.0094i	2.42002	+	4.19160i
$249$	−1.18797	−	2.05762i	−0.0752845	−	0.130397i
$250$	10.7012	−	18.5351i	0.676804	−	1.17226i
$251$	0.936967			0.0591409			0.0295704	−	0.999563i	$-0.490586\pi$
$251$	0.936967			0.0591409			0.0295704	+	0.999563i	$0.490586\pi$
$252$	15.1084	−	1.47498i	0.951741	−	0.0929149i
$253$	3.96962			0.249568
$254$	−8.31609	+	14.4039i	−0.521798	+	0.903781i
$255$	2.76346	+	4.78646i	0.173055	+	0.299740i
$256$	−44.0695	−	76.3306i	−2.75434	−	4.77066i
$257$	9.01714	−	15.6181i	0.562474	−	0.974233i	−0.434806	−	0.900524i	$-0.643183\pi$
$257$	9.01714	−	15.6181i	0.562474	−	0.974233i	0.997280	−	0.0737089i	$-0.0234836\pi$
$258$	17.8946			1.11407
$259$	6.27684	−	13.8218i	0.390024	−	0.858843i
$260$	−1.40632			−0.0872160
$261$	0.242406	−	0.419859i	0.0150045	−	0.0259886i
$262$	−24.5375	−	42.5002i	−1.51593	−	2.62567i
$263$	−3.94826	−	6.83859i	−0.243460	−	0.421686i	0.718237	−	0.695798i	$-0.244949\pi$
$263$	−3.94826	−	6.83859i	−0.243460	−	0.421686i	−0.961698	+	0.274113i	$0.911616\pi$
$264$	5.19835	−	9.00380i	0.319936	−	0.554146i
$265$	5.87372			0.360820
$266$	12.1316	+	16.9603i	0.743836	+	1.03990i
$267$	12.1723			0.744936
$268$	−8.65602	+	14.9927i	−0.528751	+	0.915823i
$269$	−8.60850	−	14.9104i	−0.524870	−	0.909101i	−0.999581	−	0.0289593i	$-0.990781\pi$
$269$	−8.60850	−	14.9104i	−0.524870	−	0.909101i	0.474711	−	0.880142i	$-0.342553\pi$
$270$	−1.14842	−	1.98912i	−0.0698907	−	0.121054i
$271$	4.66767	−	8.08464i	0.283541	−	0.491107i	−0.688713	−	0.725034i	$-0.741824\pi$
$271$	4.66767	−	8.08464i	0.283541	−	0.491107i	0.972254	+	0.233927i	$0.0751575\pi$
$272$	−116.768			−7.08007
$273$	0.456913	+	0.638777i	0.0276536	+	0.0386605i
$274$	26.0355			1.57286
$275$	−2.15910	+	3.73967i	−0.130199	+	0.225511i
$276$	11.3880	+	19.7247i	0.685480	+	1.18729i
$277$	−2.73760	−	4.74166i	−0.164486	−	0.284898i	0.771987	−	0.635639i	$-0.219263\pi$
$277$	−2.73760	−	4.74166i	−0.164486	−	0.284898i	−0.936473	+	0.350740i	$0.885930\pi$
$278$	−10.2959	+	17.8330i	−0.617505	+	1.06955i
$279$	−7.33128			−0.438912
$280$	−9.39150	+	20.6803i	−0.561249	+	1.23589i
$281$	−18.3501			−1.09467			−0.547337	−	0.836912i	$-0.684359\pi$
$281$	−18.3501			−1.09467			−0.547337	+	0.836912i	$0.684359\pi$
$282$	−10.7617	+	18.6397i	−0.640847	+	1.10998i
$283$	−13.0203	−	22.5518i	−0.773977	−	1.34057i	−0.935368	−	0.353677i	$-0.884931\pi$
$283$	−13.0203	−	22.5518i	−0.773977	−	1.34057i	0.161391	−	0.986891i	$-0.448402\pi$
$284$	−10.2720	−	17.7917i	−0.609533	−	1.05574i
$285$	1.16978	−	2.02612i	0.0692918	−	0.120017i
$286$	0.825711			0.0488253
$287$	1.69954	−	0.165920i	0.100321	−	0.00979393i
$288$	27.7320			1.63413
$289$	−13.9017	+	24.0785i	−0.817749	+	1.41638i
$290$	0.556768	+	0.964350i	0.0326945	+	0.0566286i
$291$	5.38399	+	9.32534i	0.315615	+	0.546661i
$292$	−45.9940	+	79.6639i	−2.69159	+	4.66198i
$293$	21.3317			1.24621			0.623106	−	0.782137i	$-0.285870\pi$
$293$	21.3317			1.24621			0.623106	+	0.782137i	$0.285870\pi$
$294$	19.1039	−	3.76598i	1.11416	−	0.219636i
$295$	−0.955340			−0.0556220
$296$	29.8260	−	51.6602i	1.73360	−	3.00269i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	16.7062	+	28.9361i	0.967767	+	1.67622i
$299$	−0.589175	+	1.02048i	−0.0340729	+	0.0590159i
$300$	−24.7761			−1.43045
$301$	16.9398	−	1.65377i	0.976393	−	0.0953215i
$302$	25.9301			1.49211
$303$	−7.49519	+	12.9821i	−0.430587	+	0.745799i
$304$	24.7140	+	42.8059i	1.41744	+	2.45508i
$305$	−2.17429	−	3.76598i	−0.124499	−	0.215639i
$306$	9.30955	−	16.1246i	0.532192	−	0.921783i
$307$	−6.88329			−0.392850			−0.196425	−	0.980519i	$-0.562933\pi$
$307$	−6.88329			−0.392850			−0.196425	+	0.980519i	$0.562933\pi$
$308$	6.27684	−	13.8218i	0.357656	−	0.787568i
$309$	−2.46405			−0.140175
$310$	8.41939	−	14.5828i	0.478189	−	0.828248i
$311$	1.89864	+	3.28854i	0.107662	+	0.186476i	0.914823	−	0.403856i	$-0.132330\pi$
$311$	1.89864	+	3.28854i	0.107662	+	0.186476i	−0.807161	+	0.590332i	$0.798997\pi$
$312$	1.54309	+	2.67271i	0.0873601	+	0.151312i
$313$	−1.30955	+	2.26821i	−0.0740203	+	0.128207i	−0.900660	−	0.434525i	$-0.856916\pi$
$313$	−1.30955	+	2.26821i	−0.0740203	+	0.128207i	0.826640	+	0.562732i	$0.190250\pi$
$314$	−14.1961			−0.801132
$315$	−1.27097	−	1.77686i	−0.0716113	−	0.100114i
$316$	−24.8105			−1.39570
$317$	13.9321	−	24.1311i	0.782505	−	1.35534i	−0.147973	−	0.988991i	$-0.547275\pi$
$317$	13.9321	−	24.1311i	0.782505	−	1.35534i	0.930478	−	0.366347i	$-0.119392\pi$
$318$	−9.89370	−	17.1364i	−0.554811	−	0.960961i
$319$	−0.242406	−	0.419859i	−0.0135721	−	0.0235076i
$320$	−17.4437	+	30.2133i	−0.975131	+	1.68898i
$321$	−11.5804			−0.646357
$322$	16.9966	+	23.7616i	0.947181	+	1.32418i
$323$	18.9654			1.05526
$324$	−2.86880	+	4.96890i	−0.159378	+	0.276050i
$325$	−0.640911	−	1.11009i	−0.0355514	−	0.0615768i
$326$	−13.1965	−	22.8571i	−0.730889	−	1.26594i
$327$	2.71173	−	4.69685i	0.149959	−	0.259736i
$328$	6.71023			0.370511
$329$	−8.46481	+	18.6397i	−0.466680	+	1.02764i
$330$	−2.29684			−0.126437
$331$	4.02076	−	6.96416i	0.221001	−	0.382785i	−0.734111	−	0.679029i	$-0.762401\pi$
$331$	4.02076	−	6.96416i	0.221001	−	0.382785i	0.955112	+	0.296245i	$0.0957343\pi$
$332$	−6.81609	−	11.8058i	−0.374082	−	0.647928i
$333$	2.86880	+	4.96890i	0.157209	+	0.272294i
$334$	4.22603	−	7.31969i	0.231238	−	0.400516i
$335$	2.49142			0.136121
$336$	45.9363	−	4.48458i	2.50603	−	0.244654i
$337$	26.2686			1.43094			0.715471	−	0.698643i	$-0.246212\pi$
$337$	26.2686			1.43094			0.715471	+	0.698643i	$0.246212\pi$
$338$	17.9582	−	31.1045i	0.976797	−	1.69186i
$339$	8.75782	+	15.1690i	0.475659	+	0.823866i
$340$	15.8556	+	27.4628i	0.859893	+	1.48938i
$341$	−3.66564	+	6.34907i	−0.198506	+	0.343822i
$342$	−7.88151			−0.426183
$343$	17.7365	−	5.33057i	0.957683	−	0.287824i
$344$	66.8827			3.60608
$345$	1.63888	−	2.83862i	0.0882344	−	0.152826i
$346$	8.02790	+	13.9047i	0.431583	+	0.747523i
$347$	−4.24421	−	7.35120i	−0.227841	−	0.394633i	0.729327	−	0.684166i	$-0.239833\pi$
$347$	−4.24421	−	7.35120i	−0.227841	−	0.394633i	−0.957168	+	0.289533i	$0.906500\pi$
$348$	1.39083	−	2.40898i	0.0745561	−	0.129135i
$349$	−31.9290			−1.70912			−0.854561	−	0.519351i	$-0.826174\pi$
$349$	−31.9290			−1.70912			−0.854561	+	0.519351i	$0.826174\pi$
$350$	−31.6297	+	3.08789i	−1.69068	+	0.165055i
$351$	−0.296842			−0.0158442
$352$	13.8660	−	24.0166i	0.739061	−	1.28009i
$353$	−0.0719562	−	0.124632i	−0.00382984	−	0.00663348i	0.864104	−	0.503313i	$-0.167886\pi$
$353$	−0.0719562	−	0.124632i	−0.00382984	−	0.00663348i	−0.867934	+	0.496680i	$0.834552\pi$
$354$	1.60917	+	2.78717i	0.0855266	+	0.148136i
$355$	−1.47827	+	2.56044i	−0.0784586	+	0.135894i
$356$	69.8400			3.70151
$357$	7.32263	−	16.1246i	0.387555	−	0.853405i
$358$	−8.42406			−0.445225
$359$	−4.11744	+	7.13162i	−0.217310	+	0.376392i	−0.953985	−	0.299855i	$-0.903062\pi$
$359$	−4.11744	+	7.13162i	−0.217310	+	0.376392i	0.736675	+	0.676247i	$0.236395\pi$
$360$	−4.29233	−	7.43454i	−0.226226	−	0.391835i
$361$	5.48595	+	9.50195i	0.288734	+	0.500102i
$362$	13.4615	−	23.3160i	0.707521	−	1.22546i
$363$	1.00000			0.0524864
$364$	2.62158	+	3.66504i	0.137408	+	0.192100i
$365$	13.2382			0.692919
$366$	−7.32474	+	12.6868i	−0.382870	+	0.663151i
$367$	−8.31512	−	14.4022i	−0.434046	−	0.751789i	0.563171	−	0.826340i	$-0.309581\pi$
$367$	−8.31512	−	14.4022i	−0.434046	−	0.751789i	−0.997217	+	0.0745508i	$0.976248\pi$
$368$	34.6247	+	59.9717i	1.80494	+	3.12624i
$369$	−0.322710	+	0.558950i	−0.0167996	+	0.0290978i
$370$	−13.1784			−0.685110
$371$	−10.9495	−	15.3077i	−0.568469	−	0.794736i
$372$	−42.0639			−2.18091
$373$	2.56242	−	4.43823i	0.132677	−	0.229803i	−0.792031	−	0.610481i	$-0.790976\pi$
$373$	2.56242	−	4.43823i	0.132677	−	0.229803i	0.924708	+	0.380678i	$0.124309\pi$
$374$	−9.30955	−	16.1246i	−0.481385	−	0.833784i
$375$	3.84707	+	6.66332i	0.198662	+	0.344092i
$376$	−40.2227	+	69.6678i	−2.07433	+	3.59284i
$377$	0.143912			0.00741186
$378$	−3.04309	+	6.70095i	−0.156520	+	0.344660i
$379$	−19.6383			−1.00875			−0.504377	−	0.863484i	$-0.668278\pi$
$379$	−19.6383			−1.00875			−0.504377	+	0.863484i	$0.668278\pi$
$380$	6.71173	−	11.6251i	0.344304	−	0.596353i
$381$	−2.98962	−	5.17818i	−0.153163	−	0.265286i
$382$	1.79533	+	3.10961i	0.0918573	+	0.159102i
$383$	5.38513	−	9.32731i	0.275167	−	0.476603i	−0.695010	−	0.719000i	$-0.744600\pi$
$383$	5.38513	−	9.32731i	0.275167	−	0.476603i	0.970177	+	0.242397i	$0.0779335\pi$
$384$	62.0644			3.16721
$385$	−2.17429	+	0.212268i	−0.110812	+	0.0108182i
$386$	−58.3528			−2.97008
$387$	−3.21654	+	5.57121i	−0.163506	+	0.283200i
$388$	30.8911	+	53.5050i	1.56826	+	2.71631i
$389$	−16.3394	−	28.3007i	−0.828441	−	1.43490i	−0.899261	−	0.437412i	$-0.855895\pi$
$389$	−16.3394	−	28.3007i	−0.828441	−	1.43490i	0.0708206	−	0.997489i	$-0.477438\pi$
$390$	0.340899	−	0.590455i	0.0172621	−	0.0298988i
$391$	26.5708			1.34374
$392$	71.4027	−	14.0757i	3.60638	−	0.710931i
$393$	17.6424			0.889942
$394$	−20.9787	+	36.3362i	−1.05689	+	1.83059i
$395$	1.78527	+	3.09218i	0.0898267	+	0.155584i
$396$	2.86880	+	4.96890i	0.144163	+	0.249697i
$397$	16.4742	−	28.5342i	0.826817	−	1.43209i	−0.0737049	−	0.997280i	$-0.523482\pi$
$397$	16.4742	−	28.5342i	0.826817	−	1.43209i	0.900522	−	0.434810i	$-0.143184\pi$
$398$	−71.5450			−3.58622
$399$	−7.46097	+	0.728387i	−0.373516	+	0.0364649i
$400$	−75.3302			−3.76651
$401$	9.67932	−	16.7651i	0.483362	−	0.837208i	−0.516455	−	0.856314i	$-0.672749\pi$
$401$	9.67932	−	16.7651i	0.483362	−	0.837208i	0.999817	+	0.0191063i	$0.00608209\pi$
$402$	−4.19654	−	7.26862i	−0.209304	−	0.362526i
$403$	−1.08812	−	1.88467i	−0.0542029	−	0.0938821i
$404$	−43.0044	+	74.4858i	−2.13955	+	3.70580i
$405$	0.825711			0.0410299
$406$	1.47532	−	3.24870i	0.0732191	−	0.161230i
$407$	5.73760			0.284402
$408$	34.7953	−	60.2673i	1.72263	−	2.98368i
$409$	15.0573	+	26.0800i	0.744535	+	1.28957i	0.950412	+	0.310995i	$0.100662\pi$
$409$	15.0573	+	26.0800i	0.744535	+	1.28957i	−0.205877	+	0.978578i	$0.566005\pi$
$410$	−0.741214	−	1.28382i	−0.0366059	−	0.0634033i
$411$	−4.67986	+	8.10575i	−0.230840	+	0.399827i
$412$	−14.1378			−0.696517
$413$	1.78089	+	2.48974i	0.0876321	+	0.122512i
$414$	−11.0421			−0.542690
$415$	−0.980920	+	1.69900i	−0.0481515	+	0.0834008i
$416$	4.11601	+	7.12914i	0.201804	+	0.349535i
$417$	−3.70135	−	6.41093i	−0.181256	−	0.313944i
$418$	−3.94075	+	6.82559i	−0.192749	+	0.333850i
$419$	−2.70722			−0.132256			−0.0661282	−	0.997811i	$-0.521065\pi$
$419$	−2.70722			−0.132256			−0.0661282	+	0.997811i	$0.521065\pi$
$420$	−7.29233	−	10.1949i	−0.355829	−	0.497459i
$421$	−30.1501			−1.46943			−0.734713	−	0.678378i	$-0.762683\pi$
$421$	−30.1501			−1.46943			−0.734713	+	0.678378i	$0.762683\pi$
$422$	−2.57045	+	4.45215i	−0.125127	+	0.216727i
$423$	−3.86880	−	6.70095i	−0.188107	−	0.325812i
$424$	−36.9786	−	64.0489i	−1.79584	−	3.11049i
$425$	−14.4520	+	25.0316i	−0.701026	+	1.21421i
$426$	9.96000			0.482564
$427$	−5.76143	+	12.6868i	−0.278815	+	0.613958i
$428$	−66.4439			−3.21169
$429$	−0.148421	+	0.257073i	−0.00716583	+	0.0124116i
$430$	−7.38788	−	12.7962i	−0.356275	−	0.617087i
$431$	−16.3405	−	28.3025i	−0.787092	−	1.36328i	−0.927741	−	0.373224i	$-0.878252\pi$
$431$	−16.3405	−	28.3025i	−0.787092	−	1.36328i	0.140650	−	0.990059i	$-0.455081\pi$
$432$	−8.72241	+	15.1077i	−0.419657	+	0.726867i
$433$	−26.2432			−1.26117			−0.630583	−	0.776122i	$-0.717184\pi$
$433$	−26.2432			−1.26117			−0.630583	+	0.776122i	$0.717184\pi$
$434$	−53.6997	+	5.24250i	−2.57767	+	0.251648i
$435$	−0.400314			−0.0191936
$436$	15.5588	−	26.9486i	0.745131	−	1.29061i
$437$	−5.62374	−	9.74061i	−0.269020	−	0.465957i
$438$	−22.2984	−	38.6220i	−1.06546	−	1.84543i
$439$	13.8453	−	23.9807i	0.660798	−	1.14454i	−0.319608	−	0.947550i	$-0.603551\pi$
$439$	13.8453	−	23.9807i	0.660798	−	1.14454i	0.980406	−	0.196986i	$-0.0631155\pi$
$440$	−8.58467			−0.409258
$441$	−2.26143	+	6.62464i	−0.107687	+	0.315459i
$442$	5.52693			0.262889
$443$	10.4469	−	18.0946i	0.496348	−	0.859701i	−0.503643	−	0.863912i	$-0.668007\pi$
$443$	10.4469	−	18.0946i	0.496348	−	0.859701i	0.999991	+	0.00421138i	$0.00134053\pi$
$444$	16.4600	+	28.5096i	0.781157	+	1.35300i
$445$	−5.02542	−	8.70428i	−0.238228	−	0.412623i
$446$	8.59324	−	14.8839i	0.406902	−	0.704774i
$447$	−12.0117			−0.568136
$448$	111.257	−	10.8616i	5.25642	−	0.513164i
$449$	23.9615			1.13081			0.565407	−	0.824812i	$-0.308719\pi$
$449$	23.9615			1.13081			0.565407	+	0.824812i	$0.308719\pi$
$450$	6.00587	−	10.4025i	0.283119	−	0.490377i
$451$	0.322710	+	0.558950i	0.0151958	+	0.0263199i
$452$	50.2488	+	87.0335i	2.36351	+	4.09371i
$453$	−4.66091	+	8.07293i	−0.218989	+	0.379299i
$454$	13.9392			0.654201
$455$	0.268142	−	0.590455i	0.0125707	−	0.0276810i
$456$	−29.4579			−1.37949
$457$	−9.30541	+	16.1174i	−0.435289	+	0.753942i	−0.997319	−	0.0731743i	$-0.976687\pi$
$457$	−9.30541	+	16.1174i	−0.435289	+	0.753942i	0.562030	+	0.827117i	$0.310020\pi$
$458$	−31.2002	−	54.0403i	−1.45789	−	2.52514i
$459$	3.34677	+	5.79677i	0.156214	+	0.270570i
$460$	9.40324	−	16.2869i	0.438428	−	0.759380i
$461$	−6.88513			−0.320672			−0.160336	−	0.987062i	$-0.551258\pi$
$461$	−6.88513			−0.320672			−0.160336	+	0.987062i	$0.551258\pi$
$462$	4.28165	+	5.98587i	0.199201	+	0.278488i
$463$	2.73532			0.127121			0.0635605	−	0.997978i	$-0.479754\pi$
$463$	2.73532			0.127121			0.0635605	+	0.997978i	$0.479754\pi$
$464$	4.22872	−	7.32437i	0.196314	−	0.340025i
$465$	3.02676	+	5.24250i	0.140363	+	0.243115i
$466$	−6.72241	−	11.6436i	−0.311410	−	0.539377i
$467$	−17.8180	+	30.8618i	−0.824521	+	1.42811i	0.0777644	+	0.996972i	$0.475222\pi$
$467$	−17.8180	+	30.8618i	−0.824521	+	1.42811i	−0.902285	+	0.431140i	$0.858112\pi$
$468$	−1.70316			−0.0787285
$469$	−4.64437	−	6.49296i	−0.214457	−	0.299817i
$470$	17.7720			0.819763
$471$	2.55174	−	4.41974i	0.117578	−	0.203651i
$472$	6.01444	+	10.4173i	0.276837	+	0.479496i
$473$	3.21654	+	5.57121i	0.147897	+	0.256164i
$474$	6.01422	−	10.4169i	0.276242	−	0.478465i
$475$	12.2351			0.561387
$476$	42.0143	−	92.5165i	1.92572	−	4.24049i
$477$	7.11354			0.325706
$478$	3.59482	−	6.22642i	0.164423	−	0.284790i
$479$	13.6899	+	23.7116i	0.625508	+	1.08341i	0.988442	+	0.151598i	$0.0484418\pi$
$479$	13.6899	+	23.7116i	0.625508	+	1.08341i	−0.362934	+	0.931815i	$0.618225\pi$
$480$	−11.4493	−	19.8308i	−0.522588	−	0.905149i
$481$	−0.851579	+	1.47498i	−0.0388287	+	0.0672532i
$482$	7.72753			0.351979
$483$	−10.4529	+	1.02048i	−0.475625	+	0.0464335i
$484$	5.73760			0.260800
$485$	4.44562	−	7.70003i	0.201865	−	0.349641i
$486$	−1.39083	−	2.40898i	−0.0630892	−	0.109274i
$487$	−14.6853	−	25.4357i	−0.665455	−	1.15260i	−0.979162	−	0.203083i	$-0.934904\pi$
$487$	−14.6853	−	25.4357i	−0.665455	−	1.15260i	0.313706	−	0.949520i	$-0.398429\pi$
$488$	−27.3769	+	47.4182i	−1.23929	+	2.14652i
$489$	9.48827			0.429074
$490$	−10.5802	−	12.1062i	−0.477963	−	0.546900i
$491$	−1.69115			−0.0763207			−0.0381604	−	0.999272i	$-0.512150\pi$
$491$	−1.69115			−0.0763207			−0.0381604	+	0.999272i	$0.512150\pi$
$492$	−1.85158	+	3.20703i	−0.0834756	+	0.144584i
$493$	−1.62255	−	2.81034i	−0.0730761	−	0.126572i
$494$	−1.16978	−	2.02612i	−0.0526309	−	0.0911594i
$495$	0.412855	−	0.715087i	0.0185565	−	0.0321408i
$496$	−127.893			−5.74256
$497$	9.42857	−	0.920475i	0.422929	−	0.0412890i
$498$	6.60904			0.296158
$499$	−14.7983	+	25.6313i	−0.662461	+	1.14742i	0.317506	+	0.948256i	$0.397155\pi$
$499$	−14.7983	+	25.6313i	−0.662461	+	1.14742i	−0.979967	+	0.199160i	$0.936179\pi$
$500$	22.0729	+	38.2314i	0.987132	+	1.70976i
$501$	1.51925	+	2.63142i	0.0678751	+	0.117563i
$502$	−1.30316	+	2.25714i	−0.0581628	+	0.100741i
$503$	28.2737			1.26066			0.630331	−	0.776326i	$-0.282919\pi$
$503$	28.2737			1.26066			0.630331	+	0.776326i	$0.282919\pi$
$504$	−11.3738	+	25.0455i	−0.506631	+	1.11561i
$505$	12.3777			0.550801
$506$	−5.52106	+	9.56275i	−0.245441	+	0.425116i
$507$	6.45594	+	11.1820i	0.286718	+	0.496611i
$508$	−17.1532	−	29.7103i	−0.761052	−	1.31818i
$509$	−5.45037	+	9.44032i	−0.241584	+	0.418435i	−0.961166	−	0.275972i	$-0.911000\pi$
$509$	−5.45037	+	9.44032i	−0.241584	+	0.418435i	0.719582	+	0.694408i	$0.244333\pi$
$510$	−15.3740			−0.680772
$511$	−24.6780	−	34.5005i	−1.09169	−	1.52621i
$512$	121.043			5.34941
$513$	1.41669	−	2.45379i	0.0625486	−	0.108337i
$514$	25.0826	+	43.4443i	1.10634	+	1.91624i
$515$	1.01730	+	1.76201i	0.0448275	+	0.0776436i
$516$	−18.4552	+	31.9653i	−0.812445	+	1.40720i
$517$	−7.73760			−0.340299
$518$	24.5664	+	34.3445i	1.07939	+	1.50901i
$519$	−5.77203			−0.253364
$520$	1.27414	−	2.20688i	0.0558749	−	0.0967782i
$521$	−2.81803	−	4.88098i	−0.123460	−	0.213839i	0.797670	−	0.603094i	$-0.206066\pi$
$521$	−2.81803	−	4.88098i	−0.123460	−	0.213839i	−0.921130	+	0.389255i	$0.872732\pi$
$522$	0.674289	+	1.16790i	0.0295128	+	0.0511177i
$523$	13.4113	−	23.2290i	0.586434	−	1.01573i	−0.408261	−	0.912865i	$-0.633865\pi$
$523$	13.4113	−	23.2290i	0.586434	−	1.01573i	0.994695	−	0.102868i	$-0.0328019\pi$
$524$	101.225			4.42203
$525$	4.72405	−	10.4025i	0.206174	−	0.454001i
$526$	21.9654			0.957737
$527$	−24.5361	+	42.4978i	−1.06881	+	1.85123i
$528$	8.72241	+	15.1077i	0.379594	+	0.657476i
$529$	3.62105	+	6.27183i	0.157437	+	0.272688i
$530$	−8.16933	+	14.1497i	−0.354853	+	0.614624i
$531$	−1.15699			−0.0502091
$532$	−42.8081	+	4.17919i	−1.85596	+	0.181191i
$533$	−0.191588			−0.00829858
$534$	−16.9296	+	29.3230i	−0.732617	+	1.26893i
$535$	4.78105	+	8.28102i	0.206703	+	0.358020i
$536$	−15.6850	−	27.1672i	−0.677487	−	1.17344i
$537$	1.51422	−	2.62270i	0.0653433	−	0.113178i
$538$	47.8918			2.06476
$539$	4.60639	+	5.27078i	0.198411	+	0.227029i
$540$	4.73760			0.203874
$541$	−3.03355	+	5.25426i	−0.130422	+	0.225898i	−0.923839	−	0.382780i	$-0.874967\pi$
$541$	−3.03355	+	5.25426i	−0.130422	+	0.225898i	0.793417	+	0.608678i	$0.208300\pi$
$542$	12.9838	+	22.4887i	0.557704	+	0.965971i
$543$	4.83939	+	8.38207i	0.207678	+	0.359709i
$544$	92.8127	−	160.756i	3.97931	−	6.89237i
$545$	−4.47821			−0.191825
$546$	−2.17429	+	0.212268i	−0.0930510	+	0.00908421i
$547$	−13.7115			−0.586263			−0.293132	−	0.956072i	$-0.594697\pi$
$547$	−13.7115			−0.586263			−0.293132	+	0.956072i	$0.594697\pi$
$548$	−26.8511	+	46.5075i	−1.14702	+	1.98670i
$549$	−2.63323	−	4.56089i	−0.112384	−	0.194654i
$550$	−6.00587	−	10.4025i	−0.256091	−	0.443563i
$551$	−0.686830	+	1.18962i	−0.0292600	+	0.0506797i
$552$	−41.2710			−1.75661
$553$	4.73061	−	10.4169i	0.201166	−	0.442973i
$554$	15.2301			0.647064
$555$	2.36880	−	4.10288i	0.100550	−	0.174157i
$556$	−21.2368	−	36.7833i	−0.900643	−	1.55996i
$557$	5.54782	+	9.60910i	0.235069	+	0.407151i	0.959293	−	0.282414i	$-0.0911352\pi$
$557$	5.54782	+	9.60910i	0.235069	+	0.407151i	−0.724224	+	0.689565i	$0.757802\pi$
$558$	10.1965	−	17.6609i	0.431654	−	0.747647i
$559$	−1.90961			−0.0807677
$560$	−22.1719	−	30.9969i	−0.936934	−	1.30986i
$561$	6.69354			0.282601
$562$	25.5218	−	44.2051i	1.07657	−	1.86468i
$563$	−2.17578	−	3.76857i	−0.0916983	−	0.158826i	0.816528	−	0.577306i	$-0.195896\pi$
$563$	−2.17578	−	3.76857i	−0.0916983	−	0.158826i	−0.908226	+	0.418480i	$0.862563\pi$
$564$	−22.1976	−	38.4474i	−0.934688	−	1.61893i
$565$	7.23142	−	12.5252i	0.304228	−	0.526939i
$566$	72.4360			3.04471
$567$	−1.53925	−	2.15191i	−0.0646423	−	0.0903717i
$568$	37.2265			1.56199
$569$	−4.57112	+	7.91741i	−0.191631	+	0.331915i	−0.945791	−	0.324776i	$-0.894711\pi$
$569$	−4.57112	+	7.91741i	−0.191631	+	0.331915i	0.754160	+	0.656691i	$0.228044\pi$
$570$	3.25392	+	5.63596i	0.136292	+	0.236064i
$571$	−2.38226	−	4.12619i	−0.0996944	−	0.172676i	0.811864	−	0.583847i	$-0.198453\pi$
$571$	−2.38226	−	4.12619i	−0.0996944	−	0.172676i	−0.911558	+	0.411171i	$0.865120\pi$
$572$	−0.851579	+	1.47498i	−0.0356063	+	0.0616719i
$573$	−1.29084			−0.0539256
$574$	−1.96407	+	4.32493i	−0.0819786	+	0.180519i
$575$	17.1416			0.714856
$576$	−21.1256	+	36.5907i	−0.880235	+	1.52461i
$577$	8.80479	+	15.2504i	0.366548	+	0.634880i	0.989023	−	0.147759i	$-0.0472061\pi$
$577$	8.80479	+	15.2504i	0.366548	+	0.634880i	−0.622475	+	0.782640i	$0.713873\pi$
$578$	−38.6698	−	66.9780i	−1.60845	−	2.78592i
$579$	10.4889	−	18.1673i	0.435903	−	0.755006i
$580$	−2.29684			−0.0953712
$581$	6.25640	−	0.610789i	0.259559	−	0.0253398i
$582$	−29.9528			−1.24158
$583$	3.55677	−	6.16050i	0.147306	−	0.255142i
$584$	−83.3425	−	144.353i	−3.44874	−	5.97339i
$585$	0.122553	+	0.212268i	0.00506693	+	0.00877619i
$586$	−29.6687	+	51.3877i	−1.22560	+	2.12281i
$587$	33.3405			1.37611			0.688054	−	0.725659i	$-0.258465\pi$
$587$	33.3405			1.37611			0.688054	+	0.725659i	$0.258465\pi$
$588$	−12.9752	+	38.0095i	−0.535088	+	1.56749i
$589$	20.7724			0.855911
$590$	1.32871	−	2.30140i	0.0547022	−	0.0947470i
$591$	−7.54182	−	13.0628i	−0.310229	−	0.537332i
$592$	50.0457	+	86.6816i	2.05686	+	3.56259i
$593$	1.86707	−	3.23386i	0.0766713	−	0.132799i	−0.825141	−	0.564928i	$-0.808904\pi$
$593$	1.86707	−	3.23386i	0.0766713	−	0.132799i	0.901812	+	0.432129i	$0.142237\pi$
$594$	−2.78165			−0.114133
$595$	−14.5537	+	1.42082i	−0.596643	+	0.0582480i
$596$	−68.9185			−2.82301
$597$	12.8601	−	22.2744i	0.526331	−	0.911632i
$598$	−1.63888	−	2.83862i	−0.0670188	−	0.116080i
$599$	−7.08256	−	12.2673i	−0.289385	−	0.501230i	0.684278	−	0.729221i	$-0.260118\pi$
$599$	−7.08256	−	12.2673i	−0.289385	−	0.501230i	−0.973663	+	0.227991i	$0.926784\pi$
$600$	22.4475	−	38.8802i	0.916416	−	1.58728i
$601$	−18.3032			−0.746602			−0.373301	−	0.927710i	$-0.621774\pi$
$601$	−18.3032			−0.746602			−0.373301	+	0.927710i	$0.621774\pi$
$602$	−19.5764	+	43.1077i	−0.797875	+	1.75694i
$603$	3.01730			0.122874
$604$	−26.7424	+	46.3192i	−1.08813	+	1.88470i
$605$	−0.412855	−	0.715087i	−0.0167850	−	0.0290724i
$606$	−20.8490	−	36.1116i	−0.846934	−	1.46693i
$607$	22.6313	−	39.1985i	0.918576	−	1.59102i	0.116996	−	0.993132i	$-0.462674\pi$
$607$	22.6313	−	39.1985i	0.918576	−	1.59102i	0.801580	−	0.597888i	$-0.203993\pi$
$608$	−78.5757			−3.18666
$609$	0.746245	+	1.04327i	0.0302394	+	0.0422755i
$610$	12.0962			0.489762
$611$	1.14842	−	1.98912i	0.0464601	−	0.0804713i
$612$	19.2024	+	33.2595i	0.776211	+	1.34444i
$613$	7.28722	+	12.6218i	0.294328	+	0.509791i	0.974828	−	0.222957i	$-0.0715708\pi$
$613$	7.28722	+	12.6218i	0.294328	+	0.509791i	−0.680500	+	0.732748i	$0.738237\pi$
$614$	9.57346	−	16.5817i	0.386354	−	0.669184i
$615$	0.532930			0.0214898
$616$	16.0031	+	22.3728i	0.644783	+	0.901424i
$617$	−39.8257			−1.60332			−0.801662	−	0.597778i	$-0.796050\pi$
$617$	−39.8257			−1.60332			−0.801662	+	0.597778i	$0.796050\pi$
$618$	3.42707	−	5.93587i	0.137857	−	0.238776i
$619$	0.218883	+	0.379117i	0.00879767	+	0.0152380i	0.870391	−	0.492362i	$-0.163866\pi$
$619$	0.218883	+	0.379117i	0.00879767	+	0.0152380i	−0.861593	+	0.507600i	$0.830533\pi$
$620$	17.3663	+	30.0793i	0.697448	+	1.20802i
$621$	1.98481	−	3.43779i	0.0796477	−	0.137954i
$622$	−10.5627			−0.423526
$623$	−13.3164	+	29.3230i	−0.533509	+	1.17480i
$624$	−5.17835			−0.207300
$625$	−7.61894	+	13.1964i	−0.304757	+	0.527855i
$626$	−3.64272	−	6.30938i	−0.145592	−	0.252173i
$627$	−1.41669	−	2.45379i	−0.0565773	−	0.0979948i
$628$	14.6408	−	25.3587i	0.584233	−	1.01192i
$629$	38.4048			1.53130
$630$	6.04812	−	0.590455i	0.240963	−	0.0235243i
$631$	29.1632			1.16097			0.580484	−	0.814272i	$-0.302863\pi$
$631$	29.1632			1.16097			0.580484	+	0.814272i	$0.302863\pi$
$632$	22.4787	−	38.9343i	0.894155	−	1.54872i
$633$	−0.924072	−	1.60054i	−0.0367286	−	0.0636158i
$634$	38.7543	+	67.1244i	1.53913	+	2.66585i
$635$	−2.46856	+	4.27568i	−0.0979619	+	0.169675i
$636$	40.8146			1.61840
$637$	−2.03866	+	0.401883i	−0.0807746	+	0.0159232i
$638$	1.34858			0.0533907
$639$	−1.79030	+	3.10090i	−0.0708233	+	0.122670i
$640$	−25.6236	−	44.3814i	−1.01286	−	1.75433i
$641$	2.69300	+	4.66442i	0.106367	+	0.184233i	0.914296	−	0.405047i	$-0.132745\pi$
$641$	2.69300	+	4.66442i	0.106367	+	0.184233i	−0.807929	+	0.589280i	$0.799411\pi$
$642$	16.1064	−	27.8971i	0.635669	−	1.10101i
$643$	−2.19971			−0.0867481			−0.0433740	−	0.999059i	$-0.513811\pi$
$643$	−2.19971			−0.0867481			−0.0433740	+	0.999059i	$0.513811\pi$
$644$	−59.9748	+	5.85511i	−2.36334	+	0.230724i
$645$	5.31186			0.209154
$646$	−26.3776	+	45.6873i	−1.03781	+	1.79754i
$647$	8.62105	+	14.9321i	0.338928	+	0.587041i	0.984231	−	0.176886i	$-0.0566023\pi$
$647$	8.62105	+	14.9321i	0.338928	+	0.587041i	−0.645303	+	0.763927i	$0.723269\pi$
$648$	−5.19835	−	9.00380i	−0.204210	−	0.353703i
$649$	−0.578495	+	1.00198i	−0.0227079	+	0.0393313i
$650$	3.56559			0.139854
$651$	8.02031	−	17.6609i	0.314341	−	0.692186i
$652$	54.4399			2.13203
$653$	−20.3835	+	35.3052i	−0.797666	+	1.38160i	0.123466	+	0.992349i	$0.460599\pi$
$653$	−20.3835	+	35.3052i	−0.797666	+	1.38160i	−0.921132	+	0.389250i	$0.872734\pi$
$654$	7.54309	+	13.0650i	0.294958	+	0.510882i
$655$	−7.28376	−	12.6158i	−0.284600	−	0.492942i
$656$	−5.62961	+	9.75078i	−0.219800	+	0.380704i
$657$	16.0325			0.625487
$658$	−33.1297	−	46.3162i	−1.29153	−	1.80559i
$659$	33.9747			1.32347			0.661734	−	0.749739i	$-0.269821\pi$
$659$	33.9747			1.32347			0.661734	+	0.749739i	$0.269821\pi$
$660$	2.36880	−	4.10288i	0.0922053	−	0.159704i
$661$	14.9579	+	25.9078i	0.581795	+	1.00770i	0.995267	+	0.0971811i	$0.0309826\pi$
$661$	14.9579	+	25.9078i	0.581795	+	1.00770i	−0.413472	+	0.910517i	$0.635684\pi$
$662$	11.1844	+	19.3719i	0.434692	+	0.752909i
$663$	−0.993461	+	1.72072i	−0.0385828	+	0.0668274i
$664$	24.7019			0.958621
$665$	3.60116	+	5.03452i	0.139647	+	0.195230i
$666$	−15.9600			−0.618438
$667$	−0.962260	+	1.66668i	−0.0372589	+	0.0645342i
$668$	8.71684	+	15.0980i	0.337265	+	0.584159i
$669$	3.08925	+	5.35075i	0.119437	+	0.206872i
$670$	−3.46513	+	6.00178i	−0.133870	+	0.231869i
$671$	−5.26647			−0.203310
$672$	−30.3384	+	66.8060i	−1.17033	+	2.57710i
$673$	11.3711			0.438325			0.219163	−	0.975688i	$-0.429667\pi$
$673$	11.3711			0.438325			0.219163	+	0.975688i	$0.429667\pi$
$674$	−36.5351	+	63.2806i	−1.40728	+	2.43748i
$675$	2.15910	+	3.73967i	0.0831038	+	0.143940i
$676$	37.0416	+	64.1579i	1.42468	+	2.46761i
$677$	−4.85596	+	8.41076i	−0.186630	+	0.323252i	−0.944124	−	0.329589i	$-0.893090\pi$
$677$	−4.85596	+	8.41076i	−0.186630	+	0.323252i	0.757495	+	0.652841i	$0.226423\pi$
$678$	−48.7224			−1.87117
$679$	−28.3546	+	2.76815i	−1.08815	+	0.106232i
$680$	−57.4618			−2.20356
$681$	−2.50557	+	4.33977i	−0.0960136	+	0.166300i
$682$	−10.1965	−	17.6609i	−0.390446	−	0.676272i
$683$	−4.85512	−	8.40931i	−0.185776	−	0.321773i	0.758062	−	0.652183i	$-0.226147\pi$
$683$	−4.85512	−	8.40931i	−0.185776	−	0.321773i	−0.943838	+	0.330409i	$0.892813\pi$
$684$	8.12842	−	14.0788i	0.310798	−	0.538318i
$685$	7.72842			0.295288
$686$	−11.8272	+	50.1409i	−0.451565	+	1.91439i
$687$	22.4328			0.855865
$688$	−56.1119	+	97.1887i	−2.13925	+	3.70528i
$689$	1.05580	+	1.82869i	0.0402227	+	0.0696677i
$690$	4.55880	+	7.89607i	0.173550	+	0.300598i
$691$	1.96902	−	3.41044i	0.0749051	−	0.129739i	−0.826140	−	0.563465i	$-0.809468\pi$
$691$	1.96902	−	3.41044i	0.0749051	−	0.129739i	0.901045	+	0.433726i	$0.142801\pi$
$692$	−33.1176			−1.25894
$693$	−2.63323	+	0.257073i	−0.100028	+	0.00976538i
$694$	23.6119			0.896294
$695$	−3.05624	+	5.29357i	−0.115930	+	0.200797i
$696$	2.52022	+	4.36515i	0.0955287	+	0.165461i
$697$	2.16007	+	3.74135i	0.0818185	+	0.141714i
$698$	44.4077	−	76.9165i	1.68086	−	2.91133i
$699$	4.83339			0.182816
$700$	27.1047	−	59.6852i	1.02446	−	2.25589i
$701$	11.7432			0.443533			0.221766	−	0.975100i	$-0.428818\pi$
$701$	11.7432			0.443533			0.221766	+	0.975100i	$0.428818\pi$
$702$	0.412855	−	0.715087i	0.0155822	−	0.0269892i
$703$	−8.12842	−	14.0788i	−0.306569	−	0.530994i
$704$	21.1256	+	36.5907i	0.796203	+	1.37906i
$705$	−3.19451	+	5.53305i	−0.120312	+	0.208387i
$706$	0.400314			0.0150660
$707$	−23.0739	−	32.2579i	−0.867784	−	1.21319i
$708$	−6.63834			−0.249484
$709$	3.26744	−	5.65936i	0.122711	−	0.212542i	−0.798125	−	0.602492i	$-0.794174\pi$
$709$	3.26744	−	5.65936i	0.122711	−	0.212542i	0.920836	+	0.389950i	$0.127508\pi$
$710$	−4.11204	−	7.12227i	−0.154322	−	0.267294i
$711$	2.16210	+	3.74487i	0.0810852	+	0.140444i
$712$	−63.2761	+	109.597i	−2.37137	+	4.10734i
$713$	29.1024			1.08989
$714$	28.6594	+	40.0666i	1.07255	+	1.49946i
$715$	0.245106			0.00916643
$716$	8.68797	−	15.0480i	0.324685	−	0.562370i
$717$	1.29233	+	2.23839i	0.0482631	+	0.0835941i
$718$	−11.4533	−	19.8377i	−0.427433	−	0.740336i
$719$	1.84382	−	3.19359i	0.0687629	−	0.119101i	−0.829594	−	0.558367i	$-0.811428\pi$
$719$	1.84382	−	3.19359i	0.0687629	−	0.119101i	0.898357	+	0.439266i	$0.144761\pi$
$720$	14.4044			0.536819
$721$	2.69564	−	5.93587i	0.100391	−	0.221063i
$722$	−30.5200			−1.13584
$723$	−1.38902	+	2.40585i	−0.0516581	+	0.0894745i
$724$	27.7665	+	48.0929i	1.03193	+	1.78736i
$725$	−1.04676	−	1.81304i	−0.0388756	−	0.0673345i
$726$	−1.39083	+	2.40898i	−0.0516184	+	0.0894057i
$727$	−0.674563			−0.0250182			−0.0125091	−	0.999922i	$-0.503982\pi$
$727$	−0.674563			−0.0250182			−0.0125091	+	0.999922i	$0.503982\pi$
$728$	−8.12661	+	0.793371i	−0.301192	+	0.0294043i
$729$	1.00000			0.0370370
$730$	−18.4121	+	31.8906i	−0.681461	+	1.18032i
$731$	21.5300	+	37.2911i	0.796317	+	1.37926i
$732$	−15.1084	−	26.1686i	−0.558423	−	0.967218i
$733$	−8.66961	+	15.0162i	−0.320219	+	0.554636i	−0.980533	−	0.196354i	$-0.937090\pi$
$733$	−8.66961	+	15.0162i	−0.320219	+	0.554636i	0.660314	+	0.750990i	$0.270423\pi$
$734$	46.2596			1.70747
$735$	5.67084	−	1.11790i	0.209172	−	0.0412344i
$736$	−110.086			−4.05781
$737$	1.50865	−	2.61306i	0.0555718	−	0.0962532i
$738$	−0.897667	−	1.55481i	−0.0330436	−	0.0572332i
$739$	−18.2695	−	31.6437i	−0.672054	−	1.16403i	−0.977321	−	0.211764i	$-0.932079\pi$
$739$	−18.2695	−	31.6437i	−0.672054	−	1.16403i	0.305267	−	0.952267i	$-0.401254\pi$
$740$	13.5912	−	23.5407i	0.499623	−	0.865372i
$741$	0.841068			0.0308974
$742$	52.1048	−	5.08679i	1.91283	−	0.186742i
$743$	9.83489			0.360807			0.180404	−	0.983593i	$-0.442260\pi$
$743$	9.83489			0.360807			0.180404	+	0.983593i	$0.442260\pi$
$744$	38.1105	−	66.0094i	1.39720	−	2.42002i
$745$	4.95911	+	8.58944i	0.181688	+	0.314693i
$746$	7.12775	+	12.3456i	0.260966	+	0.452006i
$747$	−1.18797	+	2.05762i	−0.0434655	+	0.0752845i
$748$	38.4048			1.40422
$749$	12.6688	−	27.8971i	0.462909	−	1.01934i
$750$	−21.4024			−0.781506
$751$	14.3484	−	24.8522i	0.523581	−	0.906869i	−0.476042	−	0.879423i	$-0.657929\pi$
$751$	14.3484	−	24.8522i	0.523581	−	0.906869i	0.999623	−	0.0274468i	$-0.00873768\pi$
$752$	−67.4905	−	116.897i	−2.46112	−	4.26279i
$753$	−0.468484	−	0.811437i	−0.0170725	−	0.0295704i
$754$	−0.200157	+	0.346682i	−0.00728929	+	0.0126254i
$755$	7.69713			0.280127
$756$	−8.83158	−	12.3468i	−0.321201	−	0.449048i
$757$	−50.9435			−1.85157			−0.925786	−	0.378047i	$-0.876596\pi$
$757$	−50.9435			−1.85157			−0.925786	+	0.378047i	$0.876596\pi$
$758$	27.3135	−	47.3084i	0.992072	−	1.71832i
$759$	−1.98481	−	3.43779i	−0.0720441	−	0.124784i
$760$	12.1619	+	21.0649i	0.441157	+	0.764106i
$761$	−21.9590	+	38.0340i	−0.796011	+	1.37873i	0.126184	+	0.992007i	$0.459727\pi$
$761$	−21.9590	+	38.0340i	−0.796011	+	1.37873i	−0.922195	+	0.386725i	$0.873606\pi$
$762$	16.6322			0.602520
$763$	8.34804	+	11.6708i	0.302219	+	0.422511i
$764$	−7.40632			−0.267951
$765$	2.76346	−	4.78646i	0.0999133	−	0.173055i
$766$	14.9796	+	25.9453i	0.541233	+	0.937444i
$767$	−0.171722	−	0.297430i	−0.00620051	−	0.0107396i
$768$	−44.0695	+	76.3306i	−1.59022	+	2.75434i
$769$	4.82343			0.173937			0.0869687	−	0.996211i	$-0.472282\pi$
$769$	4.82343			0.173937			0.0869687	+	0.996211i	$0.472282\pi$
$770$	2.51271	−	5.53305i	0.0905518	−	0.199397i
$771$	−18.0343			−0.649489
$772$	60.1809	−	104.236i	2.16596	−	3.75155i
$773$	−3.64542	−	6.31405i	−0.131117	−	0.227101i	0.792991	−	0.609234i	$-0.208523\pi$
$773$	−3.64542	−	6.31405i	−0.131117	−	0.227101i	−0.924107	+	0.382133i	$0.875190\pi$
$774$	−8.94729	−	15.4972i	−0.321604	−	0.557034i
$775$	−15.8290	+	27.4166i	−0.568593	+	0.984833i
$776$	−111.951			−4.01882
$777$	−15.1084	+	1.47498i	−0.542012	+	0.0529146i
$778$	90.9011			3.25896
$779$	0.914363	−	1.58372i	0.0327605	−	0.0567428i
$780$	0.703158	+	1.21791i	0.0251771	+	0.0436080i
$781$	1.79030	+	3.10090i	0.0640621	+	0.110959i
$782$	−36.9554	+	64.0087i	−1.32152	+	2.28894i
$783$	−0.484812			−0.0173258
$784$	−39.4503	+	115.566i	−1.40894	+	4.12735i
$785$	−4.21399			−0.150404
$786$	−24.5375	+	42.5002i	−0.875225	+	1.51593i
$787$	14.4907	+	25.0986i	0.516537	+	0.894668i	0.999816	+	0.0192017i	$0.00611248\pi$
$787$	14.4907	+	25.0986i	0.516537	+	0.894668i	−0.483279	+	0.875467i	$0.660554\pi$
$788$	−43.2719	−	74.9491i	−1.54150	−	2.66995i
$789$	−3.94826	+	6.83859i	−0.140562	+	0.243460i
$790$	−9.93201			−0.353365
$791$	−46.1227	+	4.50279i	−1.63994	+	0.160101i
$792$	−10.3967			−0.369431
$793$	0.781653	−	1.35386i	0.0277573	−	0.0480771i
$794$	45.8256	+	79.3722i	1.62629	+	2.81681i
$795$	−2.93686	−	5.08679i	−0.104160	−	0.180410i
$796$	73.7863	−	127.802i	2.61529	−	4.52981i
$797$	−18.5564			−0.657302			−0.328651	−	0.944451i	$-0.606594\pi$
$797$	−18.5564			−0.657302			−0.328651	+	0.944451i	$0.606594\pi$
$798$	8.62225	−	18.9864i	0.305224	−	0.672112i
$799$	−51.7919			−1.83227
$800$	59.8763	−	103.709i	2.11695	−	3.66666i
$801$	−6.08617	−	10.5416i	−0.215044	−	0.372468i
$802$	26.9245	+	46.6346i	0.950738	+	1.64673i
$803$	8.01625	−	13.8845i	0.282887	−	0.489975i
$804$	17.3120			0.610549
$805$	5.04529	+	7.05345i	0.177823	+	0.248601i
$806$	6.05352			0.213226
$807$	−8.60850	+	14.9104i	−0.303034	+	0.524870i
$808$	−77.9252	−	134.970i	−2.74140	−	4.74824i
$809$	25.8901	+	44.8429i	0.910247	+	1.57659i	0.813715	+	0.581264i	$0.197441\pi$
$809$	25.8901	+	44.8429i	0.910247	+	1.57659i	0.0965313	+	0.995330i	$0.469225\pi$
$810$	−1.14842	+	1.98912i	−0.0403514	+	0.0698907i
$811$	−33.1104			−1.16266			−0.581331	−	0.813667i	$-0.697468\pi$
$811$	−33.1104			−1.16266			−0.581331	+	0.813667i	$0.697468\pi$
$812$	4.28165	+	5.98587i	0.150257	+	0.210063i
$813$	−9.33534			−0.327405
$814$	−7.98000	+	13.8218i	−0.279699	+	0.484453i
$815$	−3.91728	−	6.78494i	−0.137216	−	0.237666i
$816$	58.3838	+	101.124i	2.04384	+	3.54004i
$817$	9.11370	−	15.7854i	0.318848	−	0.552261i
$818$	−83.7683			−2.92889
$819$	0.324740	−	0.715087i	0.0113473	−	0.0249872i
$820$	3.05774			0.106781
$821$	5.26903	−	9.12623i	0.183891	−	0.318508i	−0.759312	−	0.650727i	$-0.774464\pi$
$821$	5.26903	−	9.12623i	0.183891	−	0.318508i	0.943202	+	0.332220i	$0.107797\pi$
$822$	−13.0177	−	22.5474i	−0.454046	−	0.786431i
$823$	−2.51633	−	4.35841i	−0.0877137	−	0.151925i	0.818831	−	0.574035i	$-0.194623\pi$
$823$	−2.51633	−	4.35841i	−0.0877137	−	0.151925i	−0.906544	+	0.422111i	$0.861289\pi$
$824$	12.8090	−	22.1859i	0.446223	−	0.772881i
$825$	4.31820			0.150340
$826$	−8.47465	+	0.827348i	−0.294871	+	0.0287871i
$827$	−37.6214			−1.30822			−0.654112	−	0.756398i	$-0.726957\pi$
$827$	−37.6214			−1.30822			−0.654112	+	0.756398i	$0.726957\pi$
$828$	11.3880	−	19.7247i	0.395762	−	0.685480i
$829$	−8.85512	−	15.3375i	−0.307551	−	0.532694i	0.670275	−	0.742113i	$-0.266176\pi$
$829$	−8.85512	−	15.3375i	−0.307551	−	0.532694i	−0.977826	+	0.209419i	$0.932843\pi$
$830$	−2.72858	−	4.72604i	−0.0947104	−	0.164043i
$831$	−2.73760	+	4.74166i	−0.0949662	+	0.164486i
$832$	−12.5419			−0.434814
$833$	30.8331	+	35.2802i	1.06830	+	1.22239i
$834$	20.5917			0.713034
$835$	1.25446	−	2.17279i	0.0434124	−	0.0751925i
$836$	−8.12842	−	14.0788i	−0.281127	−	0.486927i
$837$	3.66564	+	6.34907i	0.126703	+	0.219456i
$838$	3.76527	−	6.52164i	0.130069	−	0.225286i
$839$	−4.81384			−0.166192			−0.0830961	−	0.996542i	$-0.526481\pi$
$839$	−4.81384			−0.166192			−0.0830961	+	0.996542i	$0.526481\pi$
$840$	22.6054	−	2.20688i	0.779961	−	0.0761447i
$841$	−28.7650			−0.991895
$842$	41.9336	−	72.6310i	1.44513	−	2.50303i
$843$	9.17505	+	15.8916i	0.316005	+	0.547337i
$844$	−5.30195	−	9.18325i	−0.182501	−	0.316101i
$845$	5.33074	−	9.23312i	0.183383	−	0.317629i
$846$	21.5233			0.739987
$847$	−1.09398	+	2.40898i	−0.0375898	+	0.0827736i
$848$	124.094			4.26142
$849$	−13.0203	+	22.5518i	−0.446856	+	0.773977i
$850$	−40.2005	−	69.6293i	−1.37887	−	2.38827i
$851$	−11.3880	−	19.7247i	−0.390377	−	0.676153i
$852$	−10.2720	+	17.7917i	−0.351914	+	0.609533i
$853$	50.3883			1.72526			0.862631	−	0.505833i	$-0.168815\pi$
$853$	50.3883			1.72526			0.862631	+	0.505833i	$0.168815\pi$
$854$	−22.5492	−	31.5244i	−0.771617	−	1.07874i
$855$	−2.33956			−0.0800113
$856$	60.1992	−	104.268i	2.05757	−	3.56381i
$857$	−8.85383	−	15.3353i	−0.302441	−	0.523843i	0.674247	−	0.738506i	$-0.264468\pi$
$857$	−8.85383	−	15.3353i	−0.302441	−	0.523843i	−0.976688	+	0.214662i	$0.931135\pi$
$858$	−0.412855	−	0.715087i	−0.0140947	−	0.0244127i
$859$	−3.58467	+	6.20882i	−0.122307	+	0.211842i	−0.920677	−	0.390325i	$-0.872363\pi$
$859$	−3.58467	+	6.20882i	−0.122307	+	0.211842i	0.798370	+	0.602167i	$0.205696\pi$
$860$	30.4773			1.03927
$861$	−0.993461	−	1.38889i	−0.0338571	−	0.0473331i
$862$	90.9069			3.09630
$863$	−4.40464	+	7.62906i	−0.149936	+	0.259696i	−0.931203	−	0.364500i	$-0.881240\pi$
$863$	−4.40464	+	7.62906i	−0.149936	+	0.259696i	0.781268	+	0.624196i	$0.214573\pi$
$864$	−13.8660	−	24.0166i	−0.471732	−	0.817063i
$865$	2.38302	+	4.12750i	0.0810250	+	0.140339i
$866$	36.4997	−	63.2193i	1.24031	−	2.14828i
$867$	27.8035			0.944255
$868$	46.0173	−	101.331i	1.56193	−	3.43941i
$869$	4.32420			0.146689
$870$	0.556768	−	0.964350i	0.0188762	−	0.0326945i
$871$	0.447830	+	0.775665i	0.0151741	+	0.0262824i
$872$	28.1930	+	48.8317i	0.954736	+	1.65365i
$873$	5.38399	−	9.32534i	0.182220	−	0.315615i
$874$	31.2866			1.05829
$875$	−20.2605	+	1.97795i	−0.684929	+	0.0668670i
$876$	91.9880			3.10799
$877$	−1.05624	+	1.82947i	−0.0356669	+	0.0617768i	−0.883308	−	0.468793i	$-0.844689\pi$
$877$	−1.05624	+	1.82947i	−0.0356669	+	0.0617768i	0.847641	+	0.530570i	$0.178022\pi$
$878$	38.5127	+	66.7060i	1.29974	+	2.25122i
$879$	−10.6659	−	18.4738i	−0.359751	−	0.623106i
$880$	7.20219	−	12.4746i	0.242786	−	0.420517i
$881$	32.9967			1.11169			0.555843	−	0.831287i	$-0.312396\pi$
$881$	32.9967			1.11169			0.555843	+	0.831287i	$0.312396\pi$
$882$	−12.8134	−	14.6615i	−0.431449	−	0.493678i
$883$	−28.3648			−0.954552			−0.477276	−	0.878753i	$-0.658376\pi$
$883$	−28.3648			−0.954552			−0.477276	+	0.878753i	$0.658376\pi$
$884$	−5.70008	+	9.87282i	−0.191714	+	0.332059i
$885$	0.477670	+	0.827348i	0.0160567	+	0.0278110i
$886$	29.0597	+	50.3329i	0.976281	+	1.69097i
$887$	−14.7104	+	25.4791i	−0.493927	+	0.855506i	−0.999976	−	0.00699889i	$-0.997772\pi$
$887$	−14.7104	+	25.4791i	−0.493927	+	0.855506i	0.506049	+	0.862505i	$0.331105\pi$
$888$	−59.6520			−2.00179
$889$	15.7447	−	1.53710i	0.528062	−	0.0515527i
$890$	27.9580			0.937153
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	17.7249	+	30.7004i	0.593473	+	1.02793i
$893$	10.9618	+	18.9864i	0.366823	+	0.635356i
$894$	16.7062	−	28.9361i	0.558741	−	0.967767i
$895$	−2.50061			−0.0835863
$896$	−67.8975	+	149.512i	−2.26830	+	4.99484i
$897$	1.17835			0.0393440
$898$	−33.3263	+	57.7229i	−1.11211	+	1.92624i
$899$	−1.77714	−	3.07811i	−0.0592711	−	0.102661i
$900$	12.3880	+	21.4567i	0.412935	+	0.715224i
$901$	23.8074	−	41.2356i	0.793138	−	1.37376i
$902$	−1.79533			−0.0597781
$903$	−9.90210	−	13.8434i	−0.329521	−	0.460679i
$904$	−182.105			−6.05671
$905$	3.99594	−	6.92117i	0.132830	−	0.230067i
$906$	−12.9650	−	22.4561i	−0.430734	−	0.746054i
$907$	−4.68807	−	8.11998i	−0.155665	−	0.269620i	0.777636	−	0.628715i	$-0.216419\pi$
$907$	−4.68807	−	8.11998i	−0.155665	−	0.269620i	−0.933301	+	0.359095i	$0.883085\pi$
$908$	−14.3759	+	24.8999i	−0.477082	+	0.826331i
$909$	14.9904			0.497200
$910$	1.04946	+	1.46717i	0.0347892	+	0.0486362i
$911$	−23.7992			−0.788504			−0.394252	−	0.919002i	$-0.628996\pi$
$911$	−23.7992			−0.788504			−0.394252	+	0.919002i	$0.628996\pi$
$912$	24.7140	−	42.8059i	0.818362	−	1.41744i
$913$	1.18797	+	2.05762i	0.0393161	+	0.0680974i
$914$	−25.8844	−	44.8331i	−0.856181	−	1.48295i
$915$	−2.17429	+	3.76598i	−0.0718798	+	0.124499i
$916$	128.710			4.25271
$917$	−19.3005	+	42.5002i	−0.637359	+	1.40348i
$918$	−18.6191			−0.614522
$919$	4.17203	−	7.22617i	0.137623	−	0.238369i	−0.788974	−	0.614427i	$-0.789387\pi$
$919$	4.17203	−	7.22617i	0.137623	−	0.238369i	0.926596	+	0.376058i	$0.122721\pi$
$920$	17.0389	+	29.5123i	0.561757	+	0.972992i
$921$	3.44164	+	5.96110i	0.113406	+	0.196425i
$922$	9.57602	−	16.5861i	0.315369	−	0.546236i
$923$	−1.06287			−0.0349849
$924$	−15.1084	+	1.47498i	−0.497031	+	0.0485232i
$925$	24.7761			0.814633
$926$	−3.80435	+	6.58933i	−0.125019	+	0.216539i
$927$	1.23203	+	2.13393i	0.0404651	+	0.0700876i
$928$	6.72241	+	11.6436i	0.220674	+	0.382218i
$929$	−21.3983	+	37.0629i	−0.702055	+	1.21599i	0.265689	+	0.964059i	$0.414401\pi$
$929$	−21.3983	+	37.0629i	−0.702055	+	1.21599i	−0.967744	+	0.251936i	$0.918933\pi$
$930$	−16.8388			−0.552166
$931$	6.40752	−	18.7702i	0.209998	−	0.615168i
$932$	27.7320			0.908393
$933$	1.89864	−	3.28854i	0.0621586	−	0.107662i
$934$	−49.5636	−	85.8467i	−1.62177	−	2.80899i
$935$	−2.76346	−	4.78646i	−0.0903749	−	0.156534i
$936$	1.54309	−	2.67271i	0.0504374	−	0.0873601i
$937$	−15.5047			−0.506517			−0.253258	−	0.967399i	$-0.581502\pi$
$937$	−15.5047			−0.506517			−0.253258	+	0.967399i	$0.581502\pi$
$938$	22.1009	−	2.15763i	0.721621	−	0.0704491i
$939$	2.61910			0.0854712
$940$	−18.3288	+	31.7464i	−0.597820	+	1.03545i
$941$	−4.68678	−	8.11774i	−0.152785	−	0.264631i	0.779466	−	0.626445i	$-0.215491\pi$
$941$	−4.68678	−	8.11774i	−0.152785	−	0.264631i	−0.932250	+	0.361814i	$0.882157\pi$
$942$	7.09805	+	12.2942i	0.231267	+	0.400566i
$943$	1.28104	−	2.21882i	0.0417163	−	0.0722547i
$944$	−20.1835			−0.656916
$945$	−0.903315	+	1.98912i	−0.0293849	+	0.0647062i
$946$	−17.8946			−0.581803
$947$	−28.1834	+	48.8150i	−0.915837	+	1.58628i	−0.110165	+	0.993913i	$0.535138\pi$
$947$	−28.1834	+	48.8150i	−0.915837	+	1.58628i	−0.805671	+	0.592363i	$0.798195\pi$
$948$	12.4053	+	21.4866i	0.402904	+	0.697851i
$949$	2.37956	+	4.12151i	0.0772437	+	0.133790i
$950$	−17.0170	+	29.4743i	−0.552103	+	0.956271i
$951$	−27.8642			−0.903559
$952$	107.117	+	149.753i	3.47169	+	4.85352i
$953$	17.5555			0.568678			0.284339	−	0.958724i	$-0.408226\pi$
$953$	17.5555			0.568678			0.284339	+	0.958724i	$0.408226\pi$
$954$	−9.89370	+	17.1364i	−0.320320	+	0.554811i
$955$	0.532930	+	0.923062i	0.0172452	+	0.0298696i
$956$	7.41489	+	12.8430i	0.239815	+	0.415371i
$957$	−0.242406	+	0.419859i	−0.00783587	+	0.0135721i
$958$	−76.1612			−2.46066
$959$	−14.4069	−	20.1413i	−0.465224	−	0.650395i
$960$	34.8874			1.12598
$961$	−11.3738	+	19.7001i	−0.366898	+	0.635486i
$962$	−2.36880	−	4.10288i	−0.0763731	−	0.132282i
$963$	5.79022	+	10.0290i	0.186587	+	0.323179i
$964$	−7.96962	+	13.8038i	−0.256684	+	0.444590i
$965$	−17.3216			−0.557601
$966$	12.0799	−	26.6003i	0.388665	−	0.855850i
$967$	52.7796			1.69728			0.848638	−	0.528974i	$-0.177423\pi$
$967$	52.7796			1.69728			0.848638	+	0.528974i	$0.177423\pi$
$968$	−5.19835	+	9.00380i	−0.167081	+	0.289393i
$969$	−9.48270	−	16.4245i	−0.304628	−	0.527632i
$970$	12.3662	+	21.4188i	0.397054	+	0.687717i
$971$	26.6328	−	46.1293i	0.854687	−	1.48036i	−0.0222486	−	0.999752i	$-0.507083\pi$
$971$	26.6328	−	46.1293i	0.854687	−	1.48036i	0.876935	−	0.480608i	$-0.159584\pi$
$972$	5.73760			0.184033
$973$	19.4930	−	1.90303i	0.624918	−	0.0610084i
$974$	81.6990			2.61780
$975$	−0.640911	+	1.11009i	−0.0205256	+	0.0355514i
$976$	−45.9363	−	79.5639i	−1.47038	−	2.54678i
$977$	−2.55331	−	4.42246i	−0.0816876	−	0.141487i	0.822287	−	0.569073i	$-0.192698\pi$
$977$	−2.55331	−	4.42246i	−0.0816876	−	0.141487i	−0.903975	+	0.427585i	$0.859364\pi$
$978$	−13.1965	+	22.8571i	−0.421979	+	0.730889i
$979$	−12.1723			−0.389030
$980$	32.5370	−	6.41406i	1.03936	−	0.204890i
$981$	−5.42346			−0.173158
$982$	2.35210	−	4.07396i	0.0750586	−	0.130005i
$983$	−16.6439	−	28.8281i	−0.530858	−	0.919474i	−0.999352	−	0.0360065i	$-0.988536\pi$
$983$	−16.6439	−	28.8281i	−0.530858	−	0.919474i	0.468493	−	0.883467i	$-0.344797\pi$
$984$	−3.35512	−	5.81123i	−0.106957	−	0.185255i
$985$	−6.22736	+	10.7861i	−0.198420	+	0.343674i
$986$	9.02676			0.287471
$987$	20.3749	−	1.98912i	0.648540	−	0.0633145i
$988$	4.82571			0.153526
$989$	12.7684	−	22.1156i	0.406013	−	0.703235i
$990$	1.14842	+	1.98912i	0.0364992	+	0.0632185i
$991$	−18.9904	−	32.8923i	−0.603249	−	1.04486i	−0.992326	−	0.123653i	$-0.960539\pi$
$991$	−18.9904	−	32.8923i	−0.603249	−	1.04486i	0.389076	−	0.921206i	$-0.372794\pi$
$992$	101.656	−	176.073i	3.22757	−	5.59032i
$993$	−8.04151			−0.255190
$994$	−10.8961	+	23.9935i	−0.345603	+	0.761027i
$995$	−21.2375			−0.673275
$996$	−6.81609	+	11.8058i	−0.215976	+	0.374082i
$997$	−13.4735	−	23.3368i	−0.426711	−	0.739084i	0.569868	−	0.821736i	$-0.306994\pi$
$997$	−13.4735	−	23.3368i	−0.426711	−	0.739084i	−0.996578	+	0.0826520i	$0.973661\pi$
$998$	−41.1636	−	71.2975i	−1.30301	−	2.25688i
$999$	2.86880	−	4.96890i	0.0907648	−	0.157209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.i.e.100.1	yes	8
3.2	odd	2		693.2.i.i.100.4		8
7.2	even	3		1617.2.a.z.1.4		4
7.4	even	3	inner	231.2.i.e.67.1	✓	8
7.5	odd	6		1617.2.a.x.1.4		4
21.2	odd	6		4851.2.a.bt.1.1		4
21.5	even	6		4851.2.a.bu.1.1		4
21.11	odd	6		693.2.i.i.298.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.e.67.1	✓	8	7.4	even	3	inner
231.2.i.e.100.1	yes	8	1.1	even	1	trivial
693.2.i.i.100.4		8	3.2	odd	2
693.2.i.i.298.4		8	21.11	odd	6
1617.2.a.x.1.4		4	7.5	odd	6
1617.2.a.z.1.4		4	7.2	even	3
4851.2.a.bt.1.1		4	21.2	odd	6
4851.2.a.bu.1.1		4	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.39083 + 2.40898i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.86880 - 4.96890i) q^{4} +(-0.412855 + 0.715087i) q^{5} +2.78165 q^{6} +(2.63323 - 0.257073i) q^{7} +10.3967 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.39083 + 2.40898i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.86880 - 4.96890i) q^{4} +(-0.412855 + 0.715087i) q^{5} +2.78165 q^{6} +(2.63323 - 0.257073i) q^{7} +10.3967 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.14842 - 1.98912i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-2.86880 + 4.96890i) q^{12} -0.296842 q^{13} +(-3.04309 + 6.70095i) q^{14} +0.825711 q^{15} +(-8.72241 + 15.1077i) q^{16} +(3.34677 + 5.79677i) q^{17} +(-1.39083 - 2.40898i) q^{18} +(1.41669 - 2.45379i) q^{19} +4.73760 q^{20} +(-1.53925 - 2.15191i) q^{21} -2.78165 q^{22} +(1.98481 - 3.43779i) q^{23} +(-5.19835 - 9.00380i) q^{24} +(2.15910 + 3.73967i) q^{25} +(0.412855 - 0.715087i) q^{26} +1.00000 q^{27} +(-8.83158 - 12.3468i) q^{28} -0.484812 q^{29} +(-1.14842 + 1.98912i) q^{30} +(3.66564 + 6.34907i) q^{31} +(-13.8660 - 24.0166i) q^{32} +(0.500000 - 0.866025i) q^{33} -18.6191 q^{34} +(-0.903315 + 1.98912i) q^{35} +5.73760 q^{36} +(2.86880 - 4.96890i) q^{37} +(3.94075 + 6.82559i) q^{38} +(0.148421 + 0.257073i) q^{39} +(-4.29233 + 7.43454i) q^{40} +0.645420 q^{41} +(7.32474 - 0.715087i) q^{42} +6.43308 q^{43} +(2.86880 - 4.96890i) q^{44} +(-0.412855 - 0.715087i) q^{45} +(5.52106 + 9.56275i) q^{46} +(-3.86880 + 6.70095i) q^{47} +17.4448 q^{48} +(6.86783 - 1.35386i) q^{49} -12.0117 q^{50} +(3.34677 - 5.79677i) q^{51} +(0.851579 + 1.47498i) q^{52} +(-3.55677 - 6.16050i) q^{53} +(-1.39083 + 2.40898i) q^{54} -0.825711 q^{55} +(27.3769 - 2.67271i) q^{56} -2.83339 q^{57} +(0.674289 - 1.16790i) q^{58} +(0.578495 + 1.00198i) q^{59} +(-2.36880 - 4.10288i) q^{60} +(-2.63323 + 4.56089i) q^{61} -20.3931 q^{62} +(-1.09398 + 2.40898i) q^{63} +42.2513 q^{64} +(0.122553 - 0.212268i) q^{65} +(1.39083 + 2.40898i) q^{66} +(-1.50865 - 2.61306i) q^{67} +(19.2024 - 33.2595i) q^{68} -3.96962 q^{69} +(-3.53541 - 4.94260i) q^{70} +3.58061 q^{71} +(-5.19835 + 9.00380i) q^{72} +(-8.01625 - 13.8845i) q^{73} +(7.98000 + 13.8218i) q^{74} +(2.15910 - 3.73967i) q^{75} -16.2568 q^{76} +(1.53925 + 2.15191i) q^{77} -0.825711 q^{78} +(2.16210 - 3.74487i) q^{79} +(-7.20219 - 12.4746i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.897667 + 1.55481i) q^{82} +2.37594 q^{83} +(-6.27684 + 13.8218i) q^{84} -5.52693 q^{85} +(-8.94729 + 15.4972i) q^{86} +(0.242406 + 0.419859i) q^{87} +(5.19835 + 9.00380i) q^{88} +(-6.08617 + 10.5416i) q^{89} +2.29684 q^{90} +(-0.781653 + 0.0763099i) q^{91} -22.7761 q^{92} +(3.66564 - 6.34907i) q^{93} +(-10.7617 - 18.6397i) q^{94} +(1.16978 + 2.02612i) q^{95} +(-13.8660 + 24.0166i) q^{96} -10.7680 q^{97} +(-6.29052 + 18.4275i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 24 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 24 q^{8} - 4 q^{9} - 10 q^{10} + 4 q^{11} - 4 q^{12} - 4 q^{13} - 4 q^{14} + 8 q^{15} - 12 q^{16} - 2 q^{17} - 2 q^{18} - 4 q^{21} - 4 q^{22} - 4 q^{23} - 12 q^{24} - 4 q^{25} + 4 q^{26} + 8 q^{27} - 22 q^{28} + 16 q^{29} - 10 q^{30} + 12 q^{31} - 26 q^{32} + 4 q^{33} - 32 q^{34} - 2 q^{35} + 8 q^{36} + 4 q^{37} - 8 q^{38} + 2 q^{39} + 6 q^{40} + 4 q^{41} + 20 q^{42} + 36 q^{43} + 4 q^{44} - 4 q^{45} + 14 q^{46} - 12 q^{47} + 24 q^{48} - 4 q^{49} + 4 q^{50} - 2 q^{51} + 6 q^{52} + 12 q^{53} - 2 q^{54} - 8 q^{55} + 48 q^{56} + 4 q^{58} - 12 q^{59} - 2 q^{61} - 52 q^{62} + 2 q^{63} + 112 q^{64} + 4 q^{65} + 2 q^{66} - 28 q^{67} + 48 q^{68} + 8 q^{69} - 32 q^{70} + 24 q^{71} - 12 q^{72} - 6 q^{73} + 16 q^{74} - 4 q^{75} - 36 q^{76} + 4 q^{77} - 8 q^{78} - 2 q^{79} - 16 q^{80} - 4 q^{81} + 12 q^{82} - 24 q^{83} - 4 q^{84} + 36 q^{85} - 36 q^{86} - 8 q^{87} + 12 q^{88} - 8 q^{89} + 20 q^{90} + 12 q^{91} - 32 q^{92} + 12 q^{93} - 20 q^{94} - 34 q^{95} - 26 q^{96} - 88 q^{97} + 16 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 24 * q^8 - 4 * q^9 - 10 * q^10 + 4 * q^11 - 4 * q^12 - 4 * q^13 - 4 * q^14 + 8 * q^15 - 12 * q^16 - 2 * q^17 - 2 * q^18 - 4 * q^21 - 4 * q^22 - 4 * q^23 - 12 * q^24 - 4 * q^25 + 4 * q^26 + 8 * q^27 - 22 * q^28 + 16 * q^29 - 10 * q^30 + 12 * q^31 - 26 * q^32 + 4 * q^33 - 32 * q^34 - 2 * q^35 + 8 * q^36 + 4 * q^37 - 8 * q^38 + 2 * q^39 + 6 * q^40 + 4 * q^41 + 20 * q^42 + 36 * q^43 + 4 * q^44 - 4 * q^45 + 14 * q^46 - 12 * q^47 + 24 * q^48 - 4 * q^49 + 4 * q^50 - 2 * q^51 + 6 * q^52 + 12 * q^53 - 2 * q^54 - 8 * q^55 + 48 * q^56 + 4 * q^58 - 12 * q^59 - 2 * q^61 - 52 * q^62 + 2 * q^63 + 112 * q^64 + 4 * q^65 + 2 * q^66 - 28 * q^67 + 48 * q^68 + 8 * q^69 - 32 * q^70 + 24 * q^71 - 12 * q^72 - 6 * q^73 + 16 * q^74 - 4 * q^75 - 36 * q^76 + 4 * q^77 - 8 * q^78 - 2 * q^79 - 16 * q^80 - 4 * q^81 + 12 * q^82 - 24 * q^83 - 4 * q^84 + 36 * q^85 - 36 * q^86 - 8 * q^87 + 12 * q^88 - 8 * q^89 + 20 * q^90 + 12 * q^91 - 32 * q^92 + 12 * q^93 - 20 * q^94 - 34 * q^95 - 26 * q^96 - 88 * q^97 + 16 * q^98 - 8 * q^99

Introduction

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