LMFDB - Embedded newform 930.2.i.n.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(211,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("930.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.3636603.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 4x^{3} + 12x^{2} - 16x + 64 $ x^6 - x^5 + 3x^4 + 4x^3 + 12x^2 - 16x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$-1.55951 - 1.25217i$ of defining polynomial
Character	$\chi$	$=$	930.211
Dual form			930.2.i.n.811.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.695350 - 1.20438i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.695350 - 1.20438i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.61903 + 4.53629i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.390699 + 0.676711i) q^{13} +(0.695350 + 1.20438i) q^{14} -1.00000 q^{15} +1.00000 q^{16} +(-1.80465 - 3.12575i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-3.72833 - 6.45765i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.695350 - 1.20438i) q^{21} +(2.61903 - 4.53629i) q^{22} +2.39070 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.390699 - 0.676711i) q^{26} -1.00000 q^{27} +(-0.695350 - 1.20438i) q^{28} -2.84735 q^{29} +1.00000 q^{30} +(-5.54270 + 0.527670i) q^{31} -1.00000 q^{32} -5.23805 q^{33} +(1.80465 + 3.12575i) q^{34} +1.39070 q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.80465 + 4.85780i) q^{37} +(3.72833 + 6.45765i) q^{38} -0.781399 q^{39} +(0.500000 - 0.866025i) q^{40} +(-5.50973 + 9.54313i) q^{41} +(-0.695350 + 1.20438i) q^{42} +(-3.92368 - 6.79601i) q^{43} +(-2.61903 + 4.53629i) q^{44} +(-0.500000 - 0.866025i) q^{45} -2.39070 q^{46} +1.17210 q^{47} +(0.500000 + 0.866025i) q^{48} +(2.53298 - 4.38725i) q^{49} +(0.500000 + 0.866025i) q^{50} +(1.80465 - 3.12575i) q^{51} +(-0.390699 + 0.676711i) q^{52} +(3.81438 - 6.60669i) q^{53} +1.00000 q^{54} +(-2.61903 - 4.53629i) q^{55} +(0.695350 + 1.20438i) q^{56} +(3.72833 - 6.45765i) q^{57} +2.84735 q^{58} +(-2.08605 - 3.61314i) q^{59} -1.00000 q^{60} -9.45665 q^{61} +(5.54270 - 0.527670i) q^{62} +1.39070 q^{63} +1.00000 q^{64} +(-0.390699 - 0.676711i) q^{65} +5.23805 q^{66} +(-2.80465 + 4.85780i) q^{67} +(-1.80465 - 3.12575i) q^{68} +(1.19535 + 2.07041i) q^{69} -1.39070 q^{70} +(1.60930 - 2.78739i) q^{71} +(0.500000 - 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(-2.80465 - 4.85780i) q^{74} +(0.500000 - 0.866025i) q^{75} +(-3.72833 - 6.45765i) q^{76} +7.28456 q^{77} +0.781399 q^{78} +(-3.92368 - 6.79601i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.50973 - 9.54313i) q^{82} +(-6.93340 + 12.0090i) q^{83} +(0.695350 - 1.20438i) q^{84} +3.60930 q^{85} +(3.92368 + 6.79601i) q^{86} +(-1.42368 - 2.46588i) q^{87} +(2.61903 - 4.53629i) q^{88} -9.21860 q^{89} +(0.500000 + 0.866025i) q^{90} +1.08669 q^{91} +2.39070 q^{92} +(-3.22833 - 4.53629i) q^{93} -1.17210 q^{94} +7.45665 q^{95} +(-0.500000 - 0.866025i) q^{96} +13.2846 q^{97} +(-2.53298 + 4.38725i) q^{98} +(-2.61903 - 4.53629i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 4 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} + 3 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 6 q^{16} - 11 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 14 q^{23} - 3 q^{24} - 3 q^{25} + 2 q^{26} - 6 q^{27} - 4 q^{28} + 24 q^{29} + 6 q^{30} + 8 q^{31} - 6 q^{32} + 10 q^{33} + 11 q^{34} + 8 q^{35} - 3 q^{36} + 17 q^{37} + 2 q^{38} - 4 q^{39} + 3 q^{40} - 12 q^{41} - 4 q^{42} - 3 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} + 6 q^{47} + 3 q^{48} - 5 q^{49} + 3 q^{50} + 11 q^{51} - 2 q^{52} + 2 q^{53} + 6 q^{54} + 5 q^{55} + 4 q^{56} + 2 q^{57} - 24 q^{58} - 12 q^{59} - 6 q^{60} - 16 q^{61} - 8 q^{62} + 8 q^{63} + 6 q^{64} - 2 q^{65} - 10 q^{66} - 17 q^{67} - 11 q^{68} + 7 q^{69} - 8 q^{70} + 10 q^{71} + 3 q^{72} + 6 q^{73} - 17 q^{74} + 3 q^{75} - 2 q^{76} + 4 q^{77} + 4 q^{78} - 3 q^{79} - 3 q^{80} - 3 q^{81} + 12 q^{82} + 4 q^{84} + 22 q^{85} + 3 q^{86} + 12 q^{87} - 5 q^{88} - 56 q^{89} + 3 q^{90} + 88 q^{91} + 14 q^{92} + q^{93} - 6 q^{94} + 4 q^{95} - 3 q^{96} + 40 q^{97} + 5 q^{98} + 5 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 4 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 5 * q^11 + 3 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 + 6 * q^16 - 11 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 + 14 * q^23 - 3 * q^24 - 3 * q^25 + 2 * q^26 - 6 * q^27 - 4 * q^28 + 24 * q^29 + 6 * q^30 + 8 * q^31 - 6 * q^32 + 10 * q^33 + 11 * q^34 + 8 * q^35 - 3 * q^36 + 17 * q^37 + 2 * q^38 - 4 * q^39 + 3 * q^40 - 12 * q^41 - 4 * q^42 - 3 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 + 6 * q^47 + 3 * q^48 - 5 * q^49 + 3 * q^50 + 11 * q^51 - 2 * q^52 + 2 * q^53 + 6 * q^54 + 5 * q^55 + 4 * q^56 + 2 * q^57 - 24 * q^58 - 12 * q^59 - 6 * q^60 - 16 * q^61 - 8 * q^62 + 8 * q^63 + 6 * q^64 - 2 * q^65 - 10 * q^66 - 17 * q^67 - 11 * q^68 + 7 * q^69 - 8 * q^70 + 10 * q^71 + 3 * q^72 + 6 * q^73 - 17 * q^74 + 3 * q^75 - 2 * q^76 + 4 * q^77 + 4 * q^78 - 3 * q^79 - 3 * q^80 - 3 * q^81 + 12 * q^82 + 4 * q^84 + 22 * q^85 + 3 * q^86 + 12 * q^87 - 5 * q^88 - 56 * q^89 + 3 * q^90 + 88 * q^91 + 14 * q^92 + q^93 - 6 * q^94 + 4 * q^95 - 3 * q^96 + 40 * q^97 + 5 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−0.695350	−	1.20438i	−0.262817	−	0.455213i	0.704172	−	0.710029i	$-0.251318\pi$
$7$	−0.695350	−	1.20438i	−0.262817	−	0.455213i	−0.966990	+	0.254816i	$0.917985\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−2.61903	+	4.53629i	−0.789666	+	1.36774i	0.136505	+	0.990639i	$0.456413\pi$
$11$	−2.61903	+	4.53629i	−0.789666	+	1.36774i	−0.926171	+	0.377103i	$0.876920\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−0.390699	+	0.676711i	−0.108360	+	0.187686i	−0.915106	−	0.403213i	$-0.867893\pi$
$13$	−0.390699	+	0.676711i	−0.108360	+	0.187686i	0.806746	+	0.590899i	$0.201227\pi$
$14$	0.695350	+	1.20438i	0.185840	+	0.321884i
$15$	−1.00000			−0.258199
$16$	1.00000			0.250000
$17$	−1.80465	−	3.12575i	−0.437692	−	0.758105i	0.559819	−	0.828615i	$-0.310871\pi$
$17$	−1.80465	−	3.12575i	−0.437692	−	0.758105i	−0.997511	+	0.0705101i	$0.977537\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−3.72833	−	6.45765i	−0.855337	−	1.48149i	−0.876332	−	0.481708i	$-0.840017\pi$
$19$	−3.72833	−	6.45765i	−0.855337	−	1.48149i	0.0209951	−	0.999780i	$-0.493317\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	0.695350	−	1.20438i	0.151738	−	0.262817i
$22$	2.61903	−	4.53629i	0.558378	−	0.967140i
$23$	2.39070			0.498495			0.249248	−	0.968440i	$-0.419817\pi$
$23$	2.39070			0.498495			0.249248	+	0.968440i	$0.419817\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.390699	−	0.676711i	0.0766224	−	0.132714i
$27$	−1.00000			−0.192450
$28$	−0.695350	−	1.20438i	−0.131409	−	0.227607i
$29$	−2.84735			−0.528740			−0.264370	−	0.964421i	$-0.585164\pi$
$29$	−2.84735			−0.528740			−0.264370	+	0.964421i	$0.585164\pi$
$30$	1.00000			0.182574
$31$	−5.54270	+	0.527670i	−0.995499	+	0.0947723i
$31$	−5.54270	+	0.527670i	−0.995499	+	0.0947723i
$32$	−1.00000			−0.176777
$33$	−5.23805			−0.911828
$34$	1.80465	+	3.12575i	0.309495	+	0.536061i
$35$	1.39070			0.235071
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	2.80465	+	4.85780i	0.461082	+	0.798617i	0.999015	−	0.0443704i	$-0.0141282\pi$
$37$	2.80465	+	4.85780i	0.461082	+	0.798617i	−0.537933	+	0.842987i	$0.680795\pi$
$38$	3.72833	+	6.45765i	0.604815	+	1.04757i
$39$	−0.781399			−0.125124
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−5.50973	+	9.54313i	−0.860475	+	1.49039i	0.0109968	+	0.999940i	$0.496500\pi$
$41$	−5.50973	+	9.54313i	−0.860475	+	1.49039i	−0.871471	+	0.490446i	$0.836834\pi$
$42$	−0.695350	+	1.20438i	−0.107295	+	0.185840i
$43$	−3.92368	−	6.79601i	−0.598355	−	1.03638i	−0.993064	−	0.117575i	$-0.962488\pi$
$43$	−3.92368	−	6.79601i	−0.598355	−	1.03638i	0.394709	−	0.918806i	$-0.370845\pi$
$44$	−2.61903	+	4.53629i	−0.394833	+	0.683871i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	−2.39070			−0.352489
$47$	1.17210			0.170968			0.0854840	−	0.996340i	$-0.472756\pi$
$47$	1.17210			0.170968			0.0854840	+	0.996340i	$0.472756\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	2.53298	−	4.38725i	0.361854	−	0.626749i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	1.80465	−	3.12575i	0.252702	−	0.437692i
$52$	−0.390699	+	0.676711i	−0.0541802	+	0.0938429i
$53$	3.81438	−	6.60669i	0.523945	−	0.907499i	−0.475667	−	0.879626i	$-0.657793\pi$
$53$	3.81438	−	6.60669i	0.523945	−	0.907499i	0.999611	−	0.0278735i	$-0.00887356\pi$
$54$	1.00000			0.136083
$55$	−2.61903	−	4.53629i	−0.353149	−	0.611673i
$56$	0.695350	+	1.20438i	0.0929200	+	0.160942i
$57$	3.72833	−	6.45765i	0.493829	−	0.855337i
$58$	2.84735			0.373876
$59$	−2.08605	−	3.61314i	−0.271580	−	0.470391i	0.697686	−	0.716403i	$-0.254213\pi$
$59$	−2.08605	−	3.61314i	−0.271580	−	0.470391i	−0.969267	+	0.246012i	$0.920880\pi$
$60$	−1.00000			−0.129099
$61$	−9.45665			−1.21080			−0.605400	−	0.795921i	$-0.706987\pi$
$61$	−9.45665			−1.21080			−0.605400	+	0.795921i	$0.706987\pi$
$62$	5.54270	−	0.527670i	0.703924	−	0.0670141i
$63$	1.39070			0.175212
$64$	1.00000			0.125000
$65$	−0.390699	−	0.676711i	−0.0484603	−	0.0839357i
$66$	5.23805			0.644760
$67$	−2.80465	+	4.85780i	−0.342643	+	0.593474i	−0.984923	−	0.172996i	$-0.944655\pi$
$67$	−2.80465	+	4.85780i	−0.342643	+	0.593474i	0.642280	+	0.766470i	$0.277989\pi$
$68$	−1.80465	−	3.12575i	−0.218846	−	0.379052i
$69$	1.19535	+	2.07041i	0.143903	+	0.249248i
$70$	−1.39070			−0.166220
$71$	1.60930	−	2.78739i	0.190989	−	0.330802i	−0.754589	−	0.656197i	$-0.772164\pi$
$71$	1.60930	−	2.78739i	0.190989	−	0.330802i	0.945578	+	0.325395i	$0.105497\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$	−2.80465	−	4.85780i	−0.326034	−	0.564707i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	−3.72833	−	6.45765i	−0.427668	−	0.740744i
$77$	7.28456			0.830152
$78$	0.781399			0.0884760
$79$	−3.92368	−	6.79601i	−0.441448	−	0.764611i	0.556349	−	0.830949i	$-0.312202\pi$
$79$	−3.92368	−	6.79601i	−0.441448	−	0.764611i	−0.997797	+	0.0663381i	$0.978868\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.50973	−	9.54313i	0.608447	−	1.05386i
$83$	−6.93340	+	12.0090i	−0.761040	+	1.31816i	0.181275	+	0.983432i	$0.441978\pi$
$83$	−6.93340	+	12.0090i	−0.761040	+	1.31816i	−0.942315	+	0.334727i	$0.891356\pi$
$84$	0.695350	−	1.20438i	0.0758689	−	0.131409i
$85$	3.60930			0.391484
$86$	3.92368	+	6.79601i	0.423101	+	0.732832i
$87$	−1.42368	−	2.46588i	−0.152634	−	0.264370i
$88$	2.61903	−	4.53629i	0.279189	−	0.483570i
$89$	−9.21860			−0.977170			−0.488585	−	0.872516i	$-0.662487\pi$
$89$	−9.21860			−0.977170			−0.488585	+	0.872516i	$0.662487\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	1.08669			0.113916
$92$	2.39070			0.249248
$93$	−3.22833	−	4.53629i	−0.334762	−	0.470391i
$94$	−1.17210			−0.120893
$95$	7.45665			0.765037
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	13.2846			1.34884			0.674421	−	0.738347i	$-0.264393\pi$
$97$	13.2846			1.34884			0.674421	+	0.738347i	$0.264393\pi$
$98$	−2.53298	+	4.38725i	−0.255869	+	0.443179i
$99$	−2.61903	−	4.53629i	−0.263222	−	0.455914i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−14.6947			−1.46218			−0.731089	−	0.682282i	$-0.760988\pi$
$101$	−14.6947			−1.46218			−0.731089	+	0.682282i	$0.760988\pi$
$102$	−1.80465	+	3.12575i	−0.178687	+	0.309495i
$103$	−3.08605	+	5.34519i	−0.304077	+	0.526678i	−0.977055	−	0.212985i	$-0.931681\pi$
$103$	−3.08605	+	5.34519i	−0.304077	+	0.526678i	0.672978	+	0.739662i	$0.265015\pi$
$104$	0.390699	−	0.676711i	0.0383112	−	0.0663570i
$105$	0.695350	+	1.20438i	0.0678592	+	0.117536i
$106$	−3.81438	+	6.60669i	−0.370485	+	0.641699i
$107$	−0.695350	−	1.20438i	−0.0672220	−	0.116432i	0.830455	−	0.557085i	$-0.188080\pi$
$107$	−0.695350	−	1.20438i	−0.0672220	−	0.116432i	−0.897677	+	0.440653i	$0.854747\pi$
$108$	−1.00000			−0.0962250
$109$	−7.45665			−0.714218			−0.357109	−	0.934063i	$-0.616238\pi$
$109$	−7.45665			−0.714218			−0.357109	+	0.934063i	$0.616238\pi$
$110$	2.61903	+	4.53629i	0.249714	+	0.432518i
$111$	−2.80465	+	4.85780i	−0.266206	+	0.461082i
$112$	−0.695350	−	1.20438i	−0.0657044	−	0.113803i
$113$	−5.53298	+	9.58340i	−0.520499	+	0.901530i	0.479217	+	0.877696i	$0.340921\pi$
$113$	−5.53298	+	9.58340i	−0.520499	+	0.901530i	−0.999716	+	0.0238339i	$0.992413\pi$
$114$	−3.72833	+	6.45765i	−0.349190	+	0.604815i
$115$	−1.19535	+	2.07041i	−0.111467	+	0.193066i
$116$	−2.84735			−0.264370
$117$	−0.390699	−	0.676711i	−0.0361202	−	0.0625620i
$118$	2.08605	+	3.61314i	0.192036	+	0.332617i
$119$	−2.50973	+	4.34697i	−0.230066	+	0.398486i
$120$	1.00000			0.0912871
$121$	−8.21860	−	14.2350i	−0.747146	−	1.29409i
$122$	9.45665			0.856165
$123$	−11.0195			−0.993591
$124$	−5.54270	+	0.527670i	−0.497749	+	0.0473862i
$125$	1.00000			0.0894427
$126$	−1.39070			−0.123893
$127$	−5.93340	−	10.2770i	−0.526504	−	0.911932i	−0.999523	−	0.0308800i	$-0.990169\pi$
$127$	−5.93340	−	10.2770i	−0.526504	−	0.911932i	0.473019	−	0.881052i	$-0.343164\pi$
$128$	−1.00000			−0.0883883
$129$	3.92368	−	6.79601i	0.345461	−	0.598355i
$130$	0.390699	+	0.676711i	0.0342666	+	0.0593515i
$131$	6.31438	+	10.9368i	0.551690	+	0.955554i	0.998153	+	0.0607525i	$0.0193500\pi$
$131$	6.31438	+	10.9368i	0.551690	+	0.955554i	−0.446463	+	0.894802i	$0.647317\pi$
$132$	−5.23805			−0.455914
$133$	−5.18498	+	8.98065i	−0.449595	+	0.778721i
$134$	2.80465	−	4.85780i	0.242285	−	0.419650i
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	1.80465	+	3.12575i	0.154747	+	0.268031i
$137$	6.82410	−	11.8197i	0.583022	−	1.00982i	−0.412096	−	0.911140i	$-0.635203\pi$
$137$	6.82410	−	11.8197i	0.583022	−	1.00982i	0.995119	−	0.0986842i	$-0.0314634\pi$
$138$	−1.19535	−	2.07041i	−0.101755	−	0.176245i
$139$	−0.238053			−0.0201914			−0.0100957	−	0.999949i	$-0.503214\pi$
$139$	−0.238053			−0.0201914			−0.0100957	+	0.999949i	$0.503214\pi$
$140$	1.39070			0.117536
$141$	0.586049	+	1.01507i	0.0493542	+	0.0854840i
$142$	−1.60930	+	2.78739i	−0.135050	+	0.233913i
$143$	−2.04650	−	3.54465i	−0.171137	−	0.296418i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.42368	−	2.46588i	0.118230	−	0.204780i
$146$	−1.00000	+	1.73205i	−0.0827606	+	0.143346i
$147$	5.06596			0.417833
$148$	2.80465	+	4.85780i	0.230541	+	0.399308i
$149$	10.8144	+	18.7310i	0.885948	+	1.53451i	0.844623	+	0.535362i	$0.179825\pi$
$149$	10.8144	+	18.7310i	0.885948	+	1.53451i	0.0413253	+	0.999146i	$0.486842\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	0.456655			0.0371620			0.0185810	−	0.999827i	$-0.494085\pi$
$151$	0.456655			0.0371620			0.0185810	+	0.999827i	$0.494085\pi$
$152$	3.72833	+	6.45765i	0.302407	+	0.523785i
$153$	3.60930			0.291795
$154$	−7.28456			−0.587006
$155$	2.31438	−	5.06396i	0.185895	−	0.406747i
$156$	−0.781399			−0.0625620
$157$	23.4956			1.87515			0.937575	−	0.347784i	$-0.113066\pi$
$157$	23.4956			1.87515			0.937575	+	0.347784i	$0.113066\pi$
$158$	3.92368	+	6.79601i	0.312151	+	0.540661i
$159$	7.62875			0.604999
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−1.66237	−	2.87931i	−0.131013	−	0.226922i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	12.5226			0.980847			0.490423	−	0.871484i	$-0.336842\pi$
$163$	12.5226			0.980847			0.490423	+	0.871484i	$0.336842\pi$
$164$	−5.50973	+	9.54313i	−0.430237	+	0.745193i
$165$	2.61903	−	4.53629i	0.203891	−	0.353149i
$166$	6.93340	−	12.0090i	0.538136	−	0.932080i
$167$	−9.35708	−	16.2069i	−0.724073	−	1.25413i	−0.959355	−	0.282203i	$-0.908935\pi$
$167$	−9.35708	−	16.2069i	−0.724073	−	1.25413i	0.235282	−	0.971927i	$-0.424399\pi$
$168$	−0.695350	+	1.20438i	−0.0536474	+	0.0929200i
$169$	6.19471	+	10.7295i	0.476516	+	0.825350i
$170$	−3.60930			−0.276821
$171$	7.45665			0.570225
$172$	−3.92368	−	6.79601i	−0.299178	−	0.518191i
$173$	−3.42368	+	5.92998i	−0.260297	+	0.450848i	−0.966321	−	0.257340i	$-0.917154\pi$
$173$	−3.42368	+	5.92998i	−0.260297	+	0.450848i	0.706024	+	0.708188i	$0.250487\pi$
$174$	1.42368	+	2.46588i	0.107929	+	0.186938i
$175$	−0.695350	+	1.20438i	−0.0525635	+	0.0910426i
$176$	−2.61903	+	4.53629i	−0.197417	+	0.341936i
$177$	2.08605	−	3.61314i	0.156797	−	0.271580i
$178$	9.21860			0.690963
$179$	−4.40043	−	7.62176i	−0.328903	−	0.569677i	0.653391	−	0.757020i	$-0.273346\pi$
$179$	−4.40043	−	7.62176i	−0.328903	−	0.569677i	−0.982295	+	0.187343i	$0.940012\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−6.84735	+	11.8600i	−0.508960	+	0.881544i	0.490986	+	0.871167i	$0.336636\pi$
$181$	−6.84735	+	11.8600i	−0.508960	+	0.881544i	−0.999946	+	0.0103770i	$0.996697\pi$
$182$	−1.08669			−0.0805509
$183$	−4.72833	−	8.18970i	−0.349528	−	0.605400i
$184$	−2.39070			−0.176245
$185$	−5.60930			−0.412404
$186$	3.22833	+	4.53629i	0.236712	+	0.332617i
$187$	18.9057			1.38252
$188$	1.17210			0.0854840
$189$	0.695350	+	1.20438i	0.0505792	+	0.0876058i
$190$	−7.45665			−0.540963
$191$	2.72833	−	4.72560i	0.197415	−	0.341933i	−0.750275	−	0.661126i	$-0.770079\pi$
$191$	2.72833	−	4.72560i	0.197415	−	0.341933i	0.947689	+	0.319194i	$0.103412\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−4.57632	−	7.92642i	−0.329411	−	0.570556i	0.652984	−	0.757372i	$-0.273517\pi$
$193$	−4.57632	−	7.92642i	−0.329411	−	0.570556i	−0.982395	+	0.186815i	$0.940183\pi$
$194$	−13.2846			−0.953776
$195$	0.390699	−	0.676711i	0.0279786	−	0.0484603i
$196$	2.53298	−	4.38725i	0.180927	−	0.313375i
$197$	−9.62875	+	16.6775i	−0.686020	+	1.18822i	0.287095	+	0.957902i	$0.407311\pi$
$197$	−9.62875	+	16.6775i	−0.686020	+	1.18822i	−0.973115	+	0.230320i	$0.926023\pi$
$198$	2.61903	+	4.53629i	0.186126	+	0.322380i
$199$	−8.93340	+	15.4731i	−0.633272	+	1.09686i	0.353606	+	0.935394i	$0.384955\pi$
$199$	−8.93340	+	15.4731i	−0.633272	+	1.09686i	−0.986878	+	0.161465i	$0.948378\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−5.60930			−0.395650
$202$	14.6947			1.03392
$203$	1.97991	+	3.42930i	0.138962	+	0.240690i
$204$	1.80465	−	3.12575i	0.126351	−	0.218846i
$205$	−5.50973	−	9.54313i	−0.384816	−	0.666521i
$206$	3.08605	−	5.34519i	0.215015	−	0.372417i
$207$	−1.19535	+	2.07041i	−0.0830825	+	0.143903i
$208$	−0.390699	+	0.676711i	−0.0270901	+	0.0469215i
$209$	39.0584			2.70172
$210$	−0.695350	−	1.20438i	−0.0479837	−	0.0831102i
$211$	7.72833	+	13.3859i	0.532040	+	0.921520i	0.999300	+	0.0374005i	$0.0119077\pi$
$211$	7.72833	+	13.3859i	0.532040	+	0.921520i	−0.467260	+	0.884120i	$0.654759\pi$
$212$	3.81438	−	6.60669i	0.261972	−	0.453750i
$213$	3.21860			0.220535
$214$	0.695350	+	1.20438i	0.0475331	+	0.0823298i
$215$	7.84735			0.535185
$216$	1.00000			0.0680414
$217$	4.48963	+	6.30861i	0.304776	+	0.428256i
$218$	7.45665			0.505028
$219$	2.00000			0.135147
$220$	−2.61903	−	4.53629i	−0.176575	−	0.305836i
$221$	2.82030			0.189714
$222$	2.80465	−	4.85780i	0.188236	−	0.326034i
$223$	−2.54270	−	4.40409i	−0.170272	−	0.294920i	0.768243	−	0.640158i	$-0.221131\pi$
$223$	−2.54270	−	4.40409i	−0.170272	−	0.294920i	−0.938515	+	0.345239i	$0.887798\pi$
$224$	0.695350	+	1.20438i	0.0464600	+	0.0804711i
$225$	1.00000			0.0666667
$226$	5.53298	−	9.58340i	0.368048	−	0.637478i
$227$	−8.15200	+	14.1197i	−0.541068	+	0.937156i	0.457776	+	0.889068i	$0.348646\pi$
$227$	−8.15200	+	14.1197i	−0.541068	+	0.937156i	−0.998843	+	0.0480887i	$0.984687\pi$
$228$	3.72833	−	6.45765i	0.246915	−	0.427668i
$229$	14.5757	+	25.2458i	0.963188	+	1.66829i	0.714406	+	0.699731i	$0.246697\pi$
$229$	14.5757	+	25.2458i	0.963188	+	1.66829i	0.248782	+	0.968559i	$0.419970\pi$
$230$	1.19535	−	2.07041i	0.0788190	−	0.136519i
$231$	3.64228	+	6.30861i	0.239644	+	0.415076i
$232$	2.84735			0.186938
$233$	9.60930			0.629526			0.314763	−	0.949170i	$-0.398075\pi$
$233$	9.60930			0.629526			0.314763	+	0.949170i	$0.398075\pi$
$234$	0.390699	+	0.676711i	0.0255408	+	0.0442380i
$235$	−0.586049	+	1.01507i	−0.0382296	+	0.0662156i
$236$	−2.08605	−	3.61314i	−0.135790	−	0.235196i
$237$	3.92368	−	6.79601i	0.254870	−	0.441448i
$238$	2.50973	−	4.34697i	0.162681	−	0.281772i
$239$	−1.84735	+	3.19971i	−0.119495	+	0.206972i	−0.919568	−	0.392931i	$-0.871461\pi$
$239$	−1.84735	+	3.19971i	−0.119495	+	0.206972i	0.800072	+	0.599903i	$0.204794\pi$
$240$	−1.00000			−0.0645497
$241$	12.8144	+	22.1952i	0.825447	+	1.42972i	0.901578	+	0.432618i	$0.142410\pi$
$241$	12.8144	+	22.1952i	0.825447	+	1.42972i	−0.0761310	+	0.997098i	$0.524257\pi$
$242$	8.21860	+	14.2350i	0.528312	+	0.915063i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−9.45665			−0.605400
$245$	2.53298	+	4.38725i	0.161826	+	0.280291i
$246$	11.0195			0.702575
$247$	5.82662			0.370739
$248$	5.54270	−	0.527670i	0.351962	−	0.0335071i
$249$	−13.8668			−0.878773
$250$	−1.00000			−0.0632456
$251$	−5.92368	−	10.2601i	−0.373899	−	0.647612i	0.616262	−	0.787541i	$-0.288646\pi$
$251$	−5.92368	−	10.2601i	−0.373899	−	0.647612i	−0.990162	+	0.139928i	$0.955313\pi$
$252$	1.39070			0.0876058
$253$	−6.26131	+	10.8449i	−0.393645	+	0.681813i
$254$	5.93340	+	10.2770i	0.372295	+	0.644834i
$255$	1.80465	+	3.12575i	0.113012	+	0.195742i
$256$	1.00000			0.0625000
$257$	9.28076	−	16.0747i	0.578918	−	1.00271i	−0.416686	−	0.909050i	$-0.636809\pi$
$257$	9.28076	−	16.0747i	0.578918	−	1.00271i	0.995604	−	0.0936645i	$-0.0298581\pi$
$258$	−3.92368	+	6.79601i	−0.244277	+	0.423101i
$259$	3.90043	−	6.75573i	0.242361	−	0.419781i
$260$	−0.390699	−	0.676711i	−0.0242301	−	0.0419678i
$261$	1.42368	−	2.46588i	0.0881234	−	0.152634i
$262$	−6.31438	−	10.9368i	−0.390103	−	0.675679i
$263$	−9.84735			−0.607214			−0.303607	−	0.952797i	$-0.598191\pi$
$263$	−9.84735			−0.607214			−0.303607	+	0.952797i	$0.598191\pi$
$264$	5.23805			0.322380
$265$	3.81438	+	6.60669i	0.234315	+	0.405846i
$266$	5.18498	−	8.98065i	0.317912	−	0.550639i
$267$	−4.60930	−	7.98354i	−0.282085	−	0.488585i
$268$	−2.80465	+	4.85780i	−0.171321	+	0.296737i
$269$	−6.09577	+	10.5582i	−0.371666	+	0.643744i	−0.989822	−	0.142311i	$-0.954547\pi$
$269$	−6.09577	+	10.5582i	−0.371666	+	0.643744i	0.618156	+	0.786055i	$0.287880\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	−16.6482			−1.01131			−0.505653	−	0.862737i	$-0.668748\pi$
$271$	−16.6482			−1.01131			−0.505653	+	0.862737i	$0.668748\pi$
$272$	−1.80465	−	3.12575i	−0.109423	−	0.189526i
$273$	0.543345	+	0.941101i	0.0328847	+	0.0569581i
$274$	−6.82410	+	11.8197i	−0.412259	+	0.714054i
$275$	5.23805			0.315867
$276$	1.19535	+	2.07041i	0.0719516	+	0.124624i
$277$	0.866806			0.0520813			0.0260407	−	0.999661i	$-0.491710\pi$
$277$	0.866806			0.0520813			0.0260407	+	0.999661i	$0.491710\pi$
$278$	0.238053			0.0142775
$279$	2.31438	−	5.06396i	0.138558	−	0.303171i
$280$	−1.39070			−0.0831102
$281$	28.5150			1.70106			0.850531	−	0.525924i	$-0.176280\pi$
$281$	28.5150			1.70106			0.850531	+	0.525924i	$0.176280\pi$
$282$	−0.586049	−	1.01507i	−0.0348987	−	0.0604463i
$283$	−5.50316			−0.327129			−0.163564	−	0.986533i	$-0.552299\pi$
$283$	−5.50316			−0.327129			−0.163564	+	0.986533i	$0.552299\pi$
$284$	1.60930	−	2.78739i	0.0954944	−	0.165401i
$285$	3.72833	+	6.45765i	0.220847	+	0.382518i
$286$	2.04650	+	3.54465i	0.121012	+	0.209599i
$287$	15.3247			0.904591
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	1.98647	−	3.44067i	0.116851	−	0.202393i
$290$	−1.42368	+	2.46588i	−0.0836012	+	0.144802i
$291$	6.64228	+	11.5048i	0.389377	+	0.674421i
$292$	1.00000	−	1.73205i	0.0585206	−	0.101361i
$293$	0.595775	+	1.03191i	0.0348055	+	0.0602850i	0.882903	−	0.469555i	$-0.155585\pi$
$293$	0.595775	+	1.03191i	0.0348055	+	0.0602850i	−0.848098	+	0.529840i	$0.822252\pi$
$294$	−5.06596			−0.295453
$295$	4.17210			0.242909
$296$	−2.80465	−	4.85780i	−0.163017	−	0.282354i
$297$	2.61903	−	4.53629i	0.151971	−	0.263222i
$298$	−10.8144	−	18.7310i	−0.626460	−	1.08506i
$299$	−0.934044	+	1.61781i	−0.0540172	+	0.0935605i
$300$	0.500000	−	0.866025i	0.0288675	−	0.0500000i
$301$	−5.45665	+	9.45120i	−0.314516	+	0.544758i
$302$	−0.456655			−0.0262775
$303$	−7.34735	−	12.7260i	−0.422094	−	0.731089i
$304$	−3.72833	−	6.45765i	−0.213834	−	0.370372i
$305$	4.72833	−	8.18970i	0.270743	−	0.468941i
$306$	−3.60930			−0.206330
$307$	10.7478	+	18.6157i	0.613408	+	1.06245i	0.990662	+	0.136344i	$0.0435353\pi$
$307$	10.7478	+	18.6157i	0.613408	+	1.06245i	−0.377253	+	0.926110i	$0.623131\pi$
$308$	7.28456			0.415076
$309$	−6.17210			−0.351118
$310$	−2.31438	+	5.06396i	−0.131448	+	0.287613i
$311$	−5.25751			−0.298126			−0.149063	−	0.988828i	$-0.547626\pi$
$311$	−5.25751			−0.298126			−0.149063	+	0.988828i	$0.547626\pi$
$312$	0.781399			0.0442380
$313$	10.4431	+	18.0880i	0.590281	+	1.02240i	0.994194	+	0.107599i	$0.0343162\pi$
$313$	10.4431	+	18.0880i	0.590281	+	1.02240i	−0.403914	+	0.914797i	$0.632350\pi$
$314$	−23.4956			−1.32593
$315$	−0.695350	+	1.20438i	−0.0391785	+	0.0678592i
$316$	−3.92368	−	6.79601i	−0.220724	−	0.382305i
$317$	−3.20508	−	5.55135i	−0.180015	−	0.311795i	0.761870	−	0.647729i	$-0.224281\pi$
$317$	−3.20508	−	5.55135i	−0.180015	−	0.311795i	−0.941885	+	0.335934i	$0.890948\pi$
$318$	−7.62875			−0.427799
$319$	7.45730	−	12.9164i	0.417528	−	0.723180i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	0.695350	−	1.20438i	0.0388106	−	0.0672220i
$322$	1.66237	+	2.87931i	0.0926404	+	0.160458i
$323$	−13.4567	+	23.3076i	−0.748748	+	1.29687i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	0.781399			0.0433442
$326$	−12.5226			−0.693563
$327$	−3.72833	−	6.45765i	−0.206177	−	0.357109i
$328$	5.50973	−	9.54313i	0.304224	−	0.526931i
$329$	−0.815018	−	1.41165i	−0.0449334	−	0.0778269i
$330$	−2.61903	+	4.53629i	−0.144173	+	0.249714i
$331$	17.3571	−	30.0633i	0.954031	−	1.65243i	0.217462	−	0.976069i	$-0.430222\pi$
$331$	17.3571	−	30.0633i	0.954031	−	1.65243i	0.736569	−	0.676362i	$-0.236445\pi$
$332$	−6.93340	+	12.0090i	−0.380520	+	0.659080i
$333$	−5.60930			−0.307388
$334$	9.35708	+	16.2069i	0.511997	+	0.886804i
$335$	−2.80465	−	4.85780i	−0.153234	−	0.265410i
$336$	0.695350	−	1.20438i	0.0379344	−	0.0657044i
$337$	−3.15265			−0.171736			−0.0858678	−	0.996307i	$-0.527366\pi$
$337$	−3.15265			−0.171736			−0.0858678	+	0.996307i	$0.527366\pi$
$338$	−6.19471	−	10.7295i	−0.336948	−	0.583611i
$339$	−11.0660			−0.601020
$340$	3.60930			0.195742
$341$	12.1228	−	26.5253i	0.656488	−	1.43642i
$342$	−7.45665			−0.403210
$343$	−16.7801			−0.906041
$344$	3.92368	+	6.79601i	0.211550	+	0.366416i
$345$	−2.39070			−0.128711
$346$	3.42368	−	5.92998i	0.184058	−	0.318798i
$347$	−9.15200	−	15.8517i	−0.491305	−	0.850966i	0.508645	−	0.860977i	$-0.330147\pi$
$347$	−9.15200	−	15.8517i	−0.491305	−	0.850966i	−0.999950	+	0.0100108i	$0.996813\pi$
$348$	−1.42368	−	2.46588i	−0.0763171	−	0.132185i
$349$	8.71416			0.466458			0.233229	−	0.972422i	$-0.425071\pi$
$349$	8.71416			0.466458			0.233229	+	0.972422i	$0.425071\pi$
$350$	0.695350	−	1.20438i	0.0371680	−	0.0643769i
$351$	0.390699	−	0.676711i	0.0208540	−	0.0361202i
$352$	2.61903	−	4.53629i	0.139595	−	0.241785i
$353$	5.36088	+	9.28532i	0.285331	+	0.494208i	0.972689	−	0.232111i	$-0.0745632\pi$
$353$	5.36088	+	9.28532i	0.285331	+	0.494208i	−0.687359	+	0.726318i	$0.741230\pi$
$354$	−2.08605	+	3.61314i	−0.110872	+	0.192036i
$355$	1.60930	+	2.78739i	0.0854128	+	0.147939i
$356$	−9.21860			−0.488585
$357$	−5.01945			−0.265658
$358$	4.40043	+	7.62176i	0.232570	+	0.402823i
$359$	−9.11903	+	15.7946i	−0.481284	+	0.833608i	−0.999769	−	0.0214784i	$-0.993163\pi$
$359$	−9.11903	+	15.7946i	−0.481284	+	0.833608i	0.518485	+	0.855086i	$0.326496\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	−18.3009	+	31.6980i	−0.963203	+	1.66832i
$362$	6.84735	−	11.8600i	0.359889	−	0.623346i
$363$	8.21860	−	14.2350i	0.431365	−	0.747146i
$364$	1.08669			0.0569581
$365$	1.00000	+	1.73205i	0.0523424	+	0.0906597i
$366$	4.72833	+	8.18970i	0.247154	+	0.428083i
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	−0.361874	−	0.932227i	$-0.617863\pi$
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	0.988269	−	0.152721i	$-0.0488036\pi$
$368$	2.39070			0.124624
$369$	−5.50973	−	9.54313i	−0.286825	−	0.496795i
$370$	5.60930			0.291614
$371$	−10.6093			−0.550807
$372$	−3.22833	−	4.53629i	−0.167381	−	0.235196i
$373$	−20.9598			−1.08526			−0.542629	−	0.839972i	$-0.682571\pi$
$373$	−20.9598			−1.08526			−0.542629	+	0.839972i	$0.682571\pi$
$374$	−18.9057			−0.977591
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−1.17210			−0.0604463
$377$	1.11246	−	1.92684i	0.0572946	−	0.0992371i
$378$	−0.695350	−	1.20438i	−0.0357649	−	0.0619467i
$379$	−7.67526	−	13.2939i	−0.394251	−	0.682864i	0.598754	−	0.800933i	$-0.295663\pi$
$379$	−7.67526	−	13.2939i	−0.394251	−	0.682864i	−0.993005	+	0.118070i	$0.962329\pi$
$380$	7.45665			0.382518
$381$	5.93340	−	10.2770i	0.303977	−	0.526504i
$382$	−2.72833	+	4.72560i	−0.139593	+	0.241783i
$383$	3.58605	−	6.21122i	0.183239	−	0.317378i	−0.759743	−	0.650223i	$-0.774675\pi$
$383$	3.58605	−	6.21122i	0.183239	−	0.317378i	0.942982	+	0.332845i	$0.108009\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−3.64228	+	6.30861i	−0.185628	+	0.321517i
$386$	4.57632	+	7.92642i	0.232929	+	0.403444i
$387$	7.84735			0.398903
$388$	13.2846			0.674421
$389$	−8.48647	−	14.6990i	−0.430281	−	0.745269i	0.566616	−	0.823982i	$-0.308252\pi$
$389$	−8.48647	−	14.6990i	−0.430281	−	0.745269i	−0.996897	+	0.0787129i	$0.974919\pi$
$390$	−0.390699	+	0.676711i	−0.0197838	+	0.0342666i
$391$	−4.31438	−	7.47272i	−0.218187	−	0.377912i
$392$	−2.53298	+	4.38725i	−0.127935	+	0.221589i
$393$	−6.31438	+	10.9368i	−0.318518	+	0.551690i
$394$	9.62875	−	16.6775i	0.485090	−	0.840200i
$395$	7.84735			0.394843
$396$	−2.61903	−	4.53629i	−0.131611	−	0.227957i
$397$	13.3144	+	23.0612i	0.668229	+	1.15741i	0.978399	+	0.206726i	$0.0662809\pi$
$397$	13.3144	+	23.0612i	0.668229	+	1.15741i	−0.310169	+	0.950681i	$0.600386\pi$
$398$	8.93340	−	15.4731i	0.447791	−	0.775597i
$399$	−10.3700			−0.519148
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	18.1319			0.905464			0.452732	−	0.891647i	$-0.350449\pi$
$401$	18.1319			0.905464			0.452732	+	0.891647i	$0.350449\pi$
$402$	5.60930			0.279766
$403$	1.80845	−	3.95697i	0.0900853	−	0.197111i
$404$	−14.6947			−0.731089
$405$	1.00000			0.0496904
$406$	−1.97991	−	3.42930i	−0.0982611	−	0.170193i
$407$	−29.3818			−1.45640
$408$	−1.80465	+	3.12575i	−0.0893435	+	0.154747i
$409$	−6.51945	−	11.2920i	−0.322366	−	0.558355i	0.658610	−	0.752485i	$-0.271145\pi$
$409$	−6.51945	−	11.2920i	−0.322366	−	0.558355i	−0.980976	+	0.194130i	$0.937812\pi$
$410$	5.50973	+	9.54313i	0.272106	+	0.471301i
$411$	13.6482			0.673216
$412$	−3.08605	+	5.34519i	−0.152039	+	0.263339i
$413$	−2.90107	+	5.02479i	−0.142752	+	0.247254i
$414$	1.19535	−	2.07041i	0.0587482	−	0.101755i
$415$	−6.93340	−	12.0090i	−0.340347	−	0.589499i
$416$	0.390699	−	0.676711i	0.0191556	−	0.0331785i
$417$	−0.119027	−	0.206160i	−0.00582876	−	0.0100957i
$418$	−39.0584			−1.91041
$419$	−2.76195			−0.134930			−0.0674650	−	0.997722i	$-0.521491\pi$
$419$	−2.76195			−0.134930			−0.0674650	+	0.997722i	$0.521491\pi$
$420$	0.695350	+	1.20438i	0.0339296	+	0.0587678i
$421$	−6.96638	+	12.0661i	−0.339521	+	0.588067i	−0.984343	−	0.176266i	$-0.943598\pi$
$421$	−6.96638	+	12.0661i	−0.339521	+	0.588067i	0.644822	+	0.764333i	$0.276932\pi$
$422$	−7.72833	−	13.3859i	−0.376209	−	0.651613i
$423$	−0.586049	+	1.01507i	−0.0284947	+	0.0493542i
$424$	−3.81438	+	6.60669i	−0.185242	+	0.320849i
$425$	−1.80465	+	3.12575i	−0.0875384	+	0.151621i
$426$	−3.21860			−0.155942
$427$	6.57568	+	11.3894i	0.318220	+	0.551172i
$428$	−0.695350	−	1.20438i	−0.0336110	−	0.0582159i
$429$	2.04650	−	3.54465i	0.0988061	−	0.171137i
$430$	−7.84735			−0.378433
$431$	−7.68182	−	13.3053i	−0.370020	−	0.640894i	0.619548	−	0.784959i	$-0.287316\pi$
$431$	−7.68182	−	13.3053i	−0.370020	−	0.640894i	−0.989568	+	0.144065i	$0.953983\pi$
$432$	−1.00000			−0.0481125
$433$	−3.25751			−0.156546			−0.0782729	−	0.996932i	$-0.524941\pi$
$433$	−3.25751			−0.156546			−0.0782729	+	0.996932i	$0.524941\pi$
$434$	−4.48963	−	6.30861i	−0.215509	−	0.302823i
$435$	2.84735			0.136520
$436$	−7.45665			−0.357109
$437$	−8.91331	−	15.4383i	−0.426381	−	0.738514i
$438$	−2.00000			−0.0955637
$439$	−11.7911	+	20.4228i	−0.562760	+	0.974728i	0.434495	+	0.900674i	$0.356927\pi$
$439$	−11.7911	+	20.4228i	−0.562760	+	0.974728i	−0.997254	+	0.0740539i	$0.976406\pi$
$440$	2.61903	+	4.53629i	0.124857	+	0.216259i
$441$	2.53298	+	4.38725i	0.120618	+	0.208916i
$442$	−2.82030			−0.134148
$443$	11.0660	−	19.1668i	0.525759	−	0.910642i	−0.473790	−	0.880638i	$-0.657115\pi$
$443$	11.0660	−	19.1668i	0.525759	−	0.910642i	0.999550	−	0.0300044i	$-0.00955212\pi$
$444$	−2.80465	+	4.85780i	−0.133103	+	0.230541i
$445$	4.60930	−	7.98354i	0.218502	−	0.378456i
$446$	2.54270	+	4.40409i	0.120401	+	0.208540i
$447$	−10.8144	+	18.7310i	−0.511502	+	0.885948i
$448$	−0.695350	−	1.20438i	−0.0328522	−	0.0569016i
$449$	−24.9133			−1.17573			−0.587866	−	0.808958i	$-0.700032\pi$
$449$	−24.9133			−1.17573			−0.587866	+	0.808958i	$0.700032\pi$
$450$	−1.00000			−0.0471405
$451$	−28.8602	−	49.9874i	−1.35898	−	2.35381i
$452$	−5.53298	+	9.58340i	−0.260249	+	0.450765i
$453$	0.228327	+	0.395475i	0.0107278	+	0.0185810i
$454$	8.15200	−	14.1197i	0.382593	−	0.662670i
$455$	−0.543345	+	0.941101i	−0.0254724	+	0.0441195i
$456$	−3.72833	+	6.45765i	−0.174595	+	0.302407i
$457$	28.8203			1.34816			0.674078	−	0.738660i	$-0.264541\pi$
$457$	28.8203			1.34816			0.674078	+	0.738660i	$0.264541\pi$
$458$	−14.5757	−	25.2458i	−0.681077	−	1.17966i
$459$	1.80465	+	3.12575i	0.0842339	+	0.145897i
$460$	−1.19535	+	2.07041i	−0.0557335	+	0.0965332i
$461$	−17.1708			−0.799725			−0.399862	−	0.916575i	$-0.630942\pi$
$461$	−17.1708			−0.799725			−0.399862	+	0.916575i	$0.630942\pi$
$462$	−3.64228	−	6.30861i	−0.169454	−	0.293503i
$463$	−22.7412			−1.05687			−0.528437	−	0.848973i	$-0.677222\pi$
$463$	−22.7412			−1.05687			−0.528437	+	0.848973i	$0.677222\pi$
$464$	−2.84735			−0.132185
$465$	5.54270	−	0.527670i	0.257037	−	0.0244701i
$466$	−9.60930			−0.445142
$467$	−7.56151			−0.349905			−0.174953	−	0.984577i	$-0.555977\pi$
$467$	−7.56151			−0.349905			−0.174953	+	0.984577i	$0.555977\pi$
$468$	−0.390699	−	0.676711i	−0.0180601	−	0.0312810i
$469$	7.80085			0.360210
$470$	0.586049	−	1.01507i	0.0270324	−	0.0468215i
$471$	11.7478	+	20.3478i	0.541309	+	0.937575i
$472$	2.08605	+	3.61314i	0.0960182	+	0.166308i
$473$	41.1049			1.89000
$474$	−3.92368	+	6.79601i	−0.180220	+	0.312151i
$475$	−3.72833	+	6.45765i	−0.171067	+	0.296297i
$476$	−2.50973	+	4.34697i	−0.115033	+	0.199243i
$477$	3.81438	+	6.60669i	0.174648	+	0.302500i
$478$	1.84735	−	3.19971i	0.0844960	−	0.146351i
$479$	−9.57568	−	16.5856i	−0.437524	−	0.757814i	0.559974	−	0.828510i	$-0.310811\pi$
$479$	−9.57568	−	16.5856i	−0.437524	−	0.757814i	−0.997498	+	0.0706964i	$0.977478\pi$
$480$	1.00000			0.0456435
$481$	−4.38310			−0.199852
$482$	−12.8144	−	22.1952i	−0.583679	−	1.01096i
$483$	1.66237	−	2.87931i	0.0756405	−	0.131013i
$484$	−8.21860	−	14.2350i	−0.373573	−	0.647047i
$485$	−6.64228	+	11.5048i	−0.301610	+	0.522404i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−2.15200	+	3.72738i	−0.0975166	+	0.168904i	−0.910656	−	0.413165i	$-0.864423\pi$
$487$	−2.15200	+	3.72738i	−0.0975166	+	0.168904i	0.813140	+	0.582069i	$0.197757\pi$
$488$	9.45665			0.428083
$489$	6.26131	+	10.8449i	0.283146	+	0.490423i
$490$	−2.53298	−	4.38725i	−0.114428	−	0.198196i
$491$	−13.2943	+	23.0264i	−0.599963	+	1.03917i	0.392863	+	0.919597i	$0.371485\pi$
$491$	−13.2943	+	23.0264i	−0.599963	+	1.03917i	−0.992826	+	0.119569i	$0.961849\pi$
$492$	−11.0195			−0.496795
$493$	5.13848	+	8.90011i	0.231425	+	0.400841i
$494$	−5.82662			−0.262152
$495$	5.23805			0.235433
$496$	−5.54270	+	0.527670i	−0.248875	+	0.0236931i
$497$	−4.47611			−0.200781
$498$	13.8668			0.621386
$499$	19.7943	+	34.2847i	0.886114	+	1.53479i	0.844432	+	0.535663i	$0.179938\pi$
$499$	19.7943	+	34.2847i	0.886114	+	1.53479i	0.0416821	+	0.999131i	$0.486728\pi$
$500$	1.00000			0.0447214
$501$	9.35708	−	16.2069i	0.418044	−	0.724073i
$502$	5.92368	+	10.2601i	0.264387	+	0.457931i
$503$	−15.5951	−	27.0116i	−0.695353	−	1.20439i	−0.970062	−	0.242859i	$-0.921915\pi$
$503$	−15.5951	−	27.0116i	−0.695353	−	1.20439i	0.274709	−	0.961527i	$-0.411418\pi$
$504$	−1.39070			−0.0619467
$505$	7.34735	−	12.7260i	0.326953	−	0.566299i
$506$	6.26131	−	10.8449i	0.278349	−	0.482115i
$507$	−6.19471	+	10.7295i	−0.275117	+	0.476516i
$508$	−5.93340	−	10.2770i	−0.263252	−	0.455966i
$509$	17.5389	−	30.3783i	0.777398	−	1.34649i	−0.156038	−	0.987751i	$-0.549872\pi$
$509$	17.5389	−	30.3783i	0.777398	−	1.34649i	0.933437	−	0.358742i	$-0.116794\pi$
$510$	−1.80465	−	3.12575i	−0.0799113	−	0.138410i
$511$	−2.78140			−0.123042
$512$	−1.00000			−0.0441942
$513$	3.72833	+	6.45765i	0.164610	+	0.285112i
$514$	−9.28076	+	16.0747i	−0.409357	+	0.709027i
$515$	−3.08605	−	5.34519i	−0.135988	−	0.235537i
$516$	3.92368	−	6.79601i	0.172730	−	0.299178i
$517$	−3.06976	+	5.31697i	−0.135008	+	0.233840i
$518$	−3.90043	+	6.75573i	−0.171375	+	0.296830i
$519$	−6.84735			−0.300565
$520$	0.390699	+	0.676711i	0.0171333	+	0.0296757i
$521$	0.980548	+	1.69836i	0.0429586	+	0.0744065i	0.886705	−	0.462335i	$-0.152988\pi$
$521$	0.980548	+	1.69836i	0.0429586	+	0.0744065i	−0.843747	+	0.536742i	$0.819655\pi$
$522$	−1.42368	+	2.46588i	−0.0623127	+	0.107929i
$523$	−21.1049			−0.922851			−0.461426	−	0.887179i	$-0.652662\pi$
$523$	−21.1049			−0.922851			−0.461426	+	0.887179i	$0.652662\pi$
$524$	6.31438	+	10.9368i	0.275845	+	0.477777i
$525$	−1.39070			−0.0606951
$526$	9.84735			0.429365
$527$	11.6520	+	16.3728i	0.507569	+	0.713211i
$528$	−5.23805			−0.227957
$529$	−17.2846			−0.751502
$530$	−3.81438	−	6.60669i	−0.165686	−	0.286976i
$531$	4.17210			0.181054
$532$	−5.18498	+	8.98065i	−0.224797	+	0.389361i
$533$	−4.30529	−	7.45698i	−0.186483	−	0.322998i
$534$	4.60930	+	7.98354i	0.199464	+	0.345482i
$535$	1.39070			0.0601252
$536$	2.80465	−	4.85780i	0.121142	−	0.209825i
$537$	4.40043	−	7.62176i	0.189892	−	0.328903i
$538$	6.09577	−	10.5582i	0.262808	−	0.455196i
$539$	13.2679	+	22.9806i	0.571488	+	0.989846i
$540$	0.500000	−	0.866025i	0.0215166	−	0.0372678i
$541$	−17.7478	−	30.7401i	−0.763037	−	1.32162i	−0.941278	−	0.337631i	$-0.890374\pi$
$541$	−17.7478	−	30.7401i	−0.763037	−	1.32162i	0.178242	−	0.983987i	$-0.442959\pi$
$542$	16.6482			0.715102
$543$	−13.6947			−0.587696
$544$	1.80465	+	3.12575i	0.0773737	+	0.134015i
$545$	3.72833	−	6.45765i	0.159704	−	0.276615i
$546$	−0.543345	−	0.941101i	−0.0232530	−	0.0402754i
$547$	−17.9431	+	31.0784i	−0.767193	+	1.32882i	0.171887	+	0.985117i	$0.445014\pi$
$547$	−17.9431	+	31.0784i	−0.767193	+	1.32882i	−0.939079	+	0.343700i	$0.888320\pi$
$548$	6.82410	−	11.8197i	0.291511	−	0.504912i
$549$	4.72833	−	8.18970i	0.201800	−	0.349528i
$550$	−5.23805			−0.223351
$551$	10.6159	+	18.3872i	0.452251	+	0.783322i
$552$	−1.19535	−	2.07041i	−0.0508775	−	0.0881223i
$553$	−5.45665	+	9.45120i	−0.232041	+	0.401906i
$554$	−0.866806			−0.0368271
$555$	−2.80465	−	4.85780i	−0.119051	−	0.206202i
$556$	−0.238053			−0.0100957
$557$	−27.7607			−1.17626			−0.588129	−	0.808767i	$-0.700135\pi$
$557$	−27.7607			−1.17626			−0.588129	+	0.808767i	$0.700135\pi$
$558$	−2.31438	+	5.06396i	−0.0979754	+	0.214374i
$559$	6.13191			0.259352
$560$	1.39070			0.0587678
$561$	9.45285	+	16.3728i	0.399100	+	0.691261i
$562$	−28.5150			−1.20283
$563$	−1.35115	+	2.34027i	−0.0569444	+	0.0986305i	−0.893092	−	0.449873i	$-0.851469\pi$
$563$	−1.35115	+	2.34027i	−0.0569444	+	0.0986305i	0.836148	+	0.548504i	$0.184802\pi$
$564$	0.586049	+	1.01507i	0.0246771	+	0.0427420i
$565$	−5.53298	−	9.58340i	−0.232774	−	0.403177i
$566$	5.50316			0.231315
$567$	−0.695350	+	1.20438i	−0.0292019	+	0.0505792i
$568$	−1.60930	+	2.78739i	−0.0675248	+	0.116956i
$569$	20.5615	−	35.6136i	0.861984	−	1.49300i	−0.00802797	−	0.999968i	$-0.502555\pi$
$569$	20.5615	−	35.6136i	0.861984	−	1.49300i	0.870011	−	0.493031i	$-0.164111\pi$
$570$	−3.72833	−	6.45765i	−0.156162	−	0.270481i
$571$	2.84735	−	4.93176i	0.119158	−	0.206388i	−0.800276	−	0.599632i	$-0.795314\pi$
$571$	2.84735	−	4.93176i	0.119158	−	0.206388i	0.919434	+	0.393244i	$0.128647\pi$
$572$	−2.04650	−	3.54465i	−0.0855686	−	0.148209i
$573$	5.45665			0.227955
$574$	−15.3247			−0.639642
$575$	−1.19535	−	2.07041i	−0.0498495	−	0.0863419i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−17.6288	−	30.5339i	−0.733895	−	1.27114i	−0.955207	−	0.295940i	$-0.904367\pi$
$577$	−17.6288	−	30.5339i	−0.733895	−	1.27114i	0.221312	−	0.975203i	$-0.428966\pi$
$578$	−1.98647	+	3.44067i	−0.0826264	+	0.143113i
$579$	4.57632	−	7.92642i	0.190185	−	0.329411i
$580$	1.42368	−	2.46588i	0.0591150	−	0.102390i
$581$	19.2846			0.800058
$582$	−6.64228	−	11.5048i	−0.275331	−	0.476888i
$583$	19.9799	+	34.6062i	0.827483	+	1.43324i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$	0.781399			0.0323069
$586$	−0.595775	−	1.03191i	−0.0246112	−	0.0426279i
$587$	−36.6093			−1.51103			−0.755514	−	0.655133i	$-0.772613\pi$
$587$	−36.6093			−1.51103			−0.755514	+	0.655133i	$0.772613\pi$
$588$	5.06596			0.208916
$589$	24.0725	+	33.8255i	0.991891	+	1.39376i
$590$	−4.17210			−0.171763
$591$	−19.2575			−0.792148
$592$	2.80465	+	4.85780i	0.115270	+	0.199654i
$593$	15.5497			0.638548			0.319274	−	0.947662i	$-0.396561\pi$
$593$	15.5497			0.638548			0.319274	+	0.947662i	$0.396561\pi$
$594$	−2.61903	+	4.53629i	−0.107460	+	0.186126i
$595$	−2.50973	−	4.34697i	−0.102889	−	0.178209i
$596$	10.8144	+	18.7310i	0.442974	+	0.767254i
$597$	−17.8668			−0.731240
$598$	0.934044	−	1.61781i	0.0381959	−	0.0661573i
$599$	8.62875	−	14.9454i	0.352561	−	0.610654i	−0.634136	−	0.773221i	$-0.718644\pi$
$599$	8.62875	−	14.9454i	0.352561	−	0.610654i	0.986697	+	0.162567i	$0.0519775\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	3.85772	+	6.68177i	0.157360	+	0.272555i	0.933916	−	0.357493i	$-0.116368\pi$
$601$	3.85772	+	6.68177i	0.157360	+	0.272555i	−0.776556	+	0.630048i	$0.783035\pi$
$602$	5.45665	−	9.45120i	0.222397	−	0.385202i
$603$	−2.80465	−	4.85780i	−0.114214	−	0.197825i
$604$	0.456655			0.0185810
$605$	16.4372			0.668267
$606$	7.34735	+	12.7260i	0.298466	+	0.516958i
$607$	−11.6947	+	20.2558i	−0.474674	+	0.822159i	−0.999579	−	0.0290016i	$-0.990767\pi$
$607$	−11.6947	+	20.2558i	−0.474674	+	0.822159i	0.524906	+	0.851160i	$0.324101\pi$
$608$	3.72833	+	6.45765i	0.151204	+	0.261892i
$609$	−1.97991	+	3.42930i	−0.0802299	+	0.138962i
$610$	−4.72833	+	8.18970i	−0.191444	+	0.331591i
$611$	−0.457938	+	0.793171i	−0.0185262	+	0.0320883i
$612$	3.60930			0.145897
$613$	13.6482	+	23.6394i	0.551246	+	0.954786i	0.998185	+	0.0602214i	$0.0191807\pi$
$613$	13.6482	+	23.6394i	0.551246	+	0.954786i	−0.446939	+	0.894564i	$0.647486\pi$
$614$	−10.7478	−	18.6157i	−0.433745	−	0.751269i
$615$	5.50973	−	9.54313i	0.222174	−	0.384816i
$616$	−7.28456			−0.293503
$617$	−10.0233	−	17.3608i	−0.403521	−	0.698919i	0.590627	−	0.806945i	$-0.298880\pi$
$617$	−10.0233	−	17.3608i	−0.403521	−	0.698919i	−0.994148	+	0.108026i	$0.965547\pi$
$618$	6.17210			0.248278
$619$	−5.82919			−0.234295			−0.117147	−	0.993115i	$-0.537375\pi$
$619$	−5.82919			−0.234295			−0.117147	+	0.993115i	$0.537375\pi$
$620$	2.31438	−	5.06396i	0.0929476	−	0.203373i
$621$	−2.39070			−0.0959355
$622$	5.25751			0.210807
$623$	6.41015	+	11.1027i	0.256817	+	0.444821i
$624$	−0.781399			−0.0312810
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−10.4431	−	18.0880i	−0.417391	−	0.722943i
$627$	19.5292	+	33.8255i	0.779920	+	1.35086i
$628$	23.4956			0.937575
$629$	10.1228	−	17.5332i	0.403624	−	0.699096i
$630$	0.695350	−	1.20438i	0.0277034	−	0.0479837i
$631$	16.6850	−	28.8992i	0.664219	−	1.15046i	−0.315278	−	0.948999i	$-0.602098\pi$
$631$	16.6850	−	28.8992i	0.664219	−	1.15046i	0.979497	−	0.201461i	$-0.0645689\pi$
$632$	3.92368	+	6.79601i	0.156075	+	0.270331i
$633$	−7.72833	+	13.3859i	−0.307173	+	0.532040i
$634$	3.20508	+	5.55135i	0.127290	+	0.220472i
$635$	11.8668			0.470920
$636$	7.62875			0.302500
$637$	1.97927	+	3.42819i	0.0784213	+	0.135830i
$638$	−7.45730	+	12.9164i	−0.295237	+	0.511366i
$639$	1.60930	+	2.78739i	0.0636630	+	0.110267i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−7.66237	+	13.2716i	−0.302645	+	0.524197i	−0.976734	−	0.214453i	$-0.931203\pi$
$641$	−7.66237	+	13.2716i	−0.302645	+	0.524197i	0.674089	+	0.738650i	$0.264536\pi$
$642$	−0.695350	+	1.20438i	−0.0274433	+	0.0475331i
$643$	2.63635			0.103968			0.0519838	−	0.998648i	$-0.483446\pi$
$643$	2.63635			0.103968			0.0519838	+	0.998648i	$0.483446\pi$
$644$	−1.66237	−	2.87931i	−0.0655066	−	0.113461i
$645$	3.92368	+	6.79601i	0.154495	+	0.267593i
$646$	13.4567	−	23.3076i	0.529445	−	0.917026i
$647$	−33.9717			−1.33556			−0.667782	−	0.744357i	$-0.732756\pi$
$647$	−33.9717			−1.33556			−0.667782	+	0.744357i	$0.732756\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	21.8537			0.857832
$650$	−0.781399			−0.0306490
$651$	−3.21860	+	7.04244i	−0.126147	+	0.276015i
$652$	12.5226			0.490423
$653$	−13.9340			−0.545281			−0.272641	−	0.962116i	$-0.587897\pi$
$653$	−13.9340			−0.545281			−0.272641	+	0.962116i	$0.587897\pi$
$654$	3.72833	+	6.45765i	0.145789	+	0.252514i
$655$	−12.6288			−0.493446
$656$	−5.50973	+	9.54313i	−0.215119	+	0.372596i
$657$	1.00000	+	1.73205i	0.0390137	+	0.0675737i
$658$	0.815018	+	1.41165i	0.0317727	+	0.0550319i
$659$	−3.58225			−0.139545			−0.0697723	−	0.997563i	$-0.522227\pi$
$659$	−3.58225			−0.139545			−0.0697723	+	0.997563i	$0.522227\pi$
$660$	2.61903	−	4.53629i	0.101945	−	0.176575i
$661$	−4.05307	+	7.02013i	−0.157646	+	0.273051i	−0.934019	−	0.357222i	$-0.883724\pi$
$661$	−4.05307	+	7.02013i	−0.157646	+	0.273051i	0.776373	+	0.630273i	$0.217057\pi$
$662$	−17.3571	+	30.0633i	−0.674602	+	1.16845i
$663$	1.41015	+	2.44245i	0.0547657	+	0.0948570i
$664$	6.93340	−	12.0090i	0.269068	−	0.466040i
$665$	−5.18498	−	8.98065i	−0.201065	−	0.348255i
$666$	5.60930			0.217356
$667$	−6.80717			−0.263575
$668$	−9.35708	−	16.2069i	−0.362036	−	0.627065i
$669$	2.54270	−	4.40409i	0.0983066	−	0.170272i
$670$	2.80465	+	4.85780i	0.108353	+	0.187673i
$671$	24.7672	−	42.8981i	0.956128	−	1.65606i
$672$	−0.695350	+	1.20438i	−0.0268237	+	0.0464600i
$673$	−0.576323	+	0.998221i	−0.0222156	+	0.0384786i	−0.876919	−	0.480637i	$-0.840405\pi$
$673$	−0.576323	+	0.998221i	−0.0222156	+	0.0384786i	0.854704	+	0.519116i	$0.173739\pi$
$674$	3.15265			0.121435
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	6.19471	+	10.7295i	0.238258	+	0.412675i
$677$	23.2905	−	40.3403i	0.895126	−	1.55040i	0.0614774	−	0.998108i	$-0.480419\pi$
$677$	23.2905	−	40.3403i	0.895126	−	1.55040i	0.833649	−	0.552295i	$-0.186248\pi$
$678$	11.0660			0.424985
$679$	−9.23741	−	15.9997i	−0.354499	−	0.614011i
$680$	−3.60930			−0.138410
$681$	−16.3040			−0.624771
$682$	−12.1228	+	26.5253i	−0.464207	+	1.01571i
$683$	44.6482			1.70842			0.854208	−	0.519931i	$-0.174042\pi$
$683$	44.6482			1.70842			0.854208	+	0.519931i	$0.174042\pi$
$684$	7.45665			0.285112
$685$	6.82410	+	11.8197i	0.260736	+	0.451607i
$686$	16.7801			0.640668
$687$	−14.5757	+	25.2458i	−0.556097	+	0.963188i
$688$	−3.92368	−	6.79601i	−0.149589	−	0.259095i
$689$	2.98055	+	5.16246i	0.113550	+	0.196674i
$690$	2.39070			0.0910124
$691$	6.66237	−	11.5396i	0.253449	−	0.438986i	−0.711024	−	0.703167i	$-0.751768\pi$
$691$	6.66237	−	11.5396i	0.253449	−	0.438986i	0.964473	+	0.264182i	$0.0851018\pi$
$692$	−3.42368	+	5.92998i	−0.130149	+	0.225424i
$693$	−3.64228	+	6.30861i	−0.138359	+	0.239644i
$694$	9.15200	+	15.8517i	0.347405	+	0.601724i
$695$	0.119027	−	0.206160i	0.00451494	−	0.00782010i
$696$	1.42368	+	2.46588i	0.0539643	+	0.0934690i
$697$	39.7725			1.50649
$698$	−8.71416			−0.329836
$699$	4.80465	+	8.32190i	0.181729	+	0.314763i
$700$	−0.695350	+	1.20438i	−0.0262817	+	0.0455213i
$701$	−13.2814	−	23.0041i	−0.501631	−	0.868851i	−0.999998	−	0.00188492i	$-0.999400\pi$
$701$	−13.2814	−	23.0041i	−0.501631	−	0.868851i	0.498367	−	0.866966i	$-0.333933\pi$
$702$	−0.390699	+	0.676711i	−0.0147460	+	0.0255408i
$703$	20.9133	−	36.2229i	0.788760	−	1.36617i
$704$	−2.61903	+	4.53629i	−0.0987083	+	0.170968i
$705$	−1.17210			−0.0441438
$706$	−5.36088	−	9.28532i	−0.201759	−	0.349457i
$707$	10.2180	+	17.6980i	0.384286	+	0.665603i
$708$	2.08605	−	3.61314i	0.0783985	−	0.135790i
$709$	37.3222			1.40166			0.700832	−	0.713326i	$-0.252812\pi$
$709$	37.3222			1.40166			0.700832	+	0.713326i	$0.252812\pi$
$710$	−1.60930	−	2.78739i	−0.0603960	−	0.104609i
$711$	7.84735			0.294299
$712$	9.21860			0.345482
$713$	−13.2509	+	1.26150i	−0.496252	+	0.0472435i
$714$	5.01945			0.187848
$715$	4.09301			0.153070
$716$	−4.40043	−	7.62176i	−0.164452	−	0.284839i
$717$	−3.69471			−0.137981
$718$	9.11903	−	15.7946i	0.340319	−	0.589450i
$719$	−19.9664	−	34.5828i	−0.744620	−	1.28972i	−0.950372	−	0.311116i	$-0.899297\pi$
$719$	−19.9664	−	34.5828i	−0.744620	−	1.28972i	0.205752	−	0.978604i	$-0.434036\pi$
$720$	−0.500000	−	0.866025i	−0.0186339	−	0.0322749i
$721$	8.58353			0.319667
$722$	18.3009	−	31.6980i	0.681087	−	1.17968i
$723$	−12.8144	+	22.1952i	−0.476572	+	0.825447i
$724$	−6.84735	+	11.8600i	−0.254480	+	0.440772i
$725$	1.42368	+	2.46588i	0.0528740	+	0.0915805i
$726$	−8.21860	+	14.2350i	−0.305021	+	0.528312i
$727$	−17.8869	−	30.9810i	−0.663388	−	1.14902i	−0.979720	−	0.200374i	$-0.935784\pi$
$727$	−17.8869	−	30.9810i	−0.663388	−	1.14902i	0.316331	−	0.948649i	$-0.397549\pi$
$728$	−1.08669			−0.0402754
$729$	1.00000			0.0370370
$730$	−1.00000	−	1.73205i	−0.0370117	−	0.0641061i
$731$	−14.1617	+	24.5288i	−0.523791	+	0.907232i
$732$	−4.72833	−	8.18970i	−0.174764	−	0.302700i
$733$	11.5059	−	19.9288i	0.424981	−	0.736089i	−0.571438	−	0.820646i	$-0.693614\pi$
$733$	11.5059	−	19.9288i	0.424981	−	0.736089i	0.996419	+	0.0845567i	$0.0269474\pi$
$734$	−12.0000	+	20.7846i	−0.442928	+	0.767174i
$735$	−2.53298	+	4.38725i	−0.0934303	+	0.161826i
$736$	−2.39070			−0.0881223
$737$	−14.6909	−	25.4454i	−0.541147	−	0.937293i
$738$	5.50973	+	9.54313i	0.202816	+	0.351287i
$739$	14.9004	−	25.8083i	0.548121	−	0.949373i	−0.450282	−	0.892886i	$-0.648677\pi$
$739$	14.9004	−	25.8083i	0.548121	−	0.949373i	0.998403	−	0.0564872i	$-0.0179900\pi$
$740$	−5.60930			−0.206202
$741$	2.91331	+	5.04600i	0.107023	+	0.185369i
$742$	10.6093			0.389480
$743$	−13.3712			−0.490543			−0.245272	−	0.969454i	$-0.578877\pi$
$743$	−13.3712			−0.490543			−0.245272	+	0.969454i	$0.578877\pi$
$744$	3.22833	+	4.53629i	0.118356	+	0.166308i
$745$	−21.6288			−0.792416
$746$	20.9598			0.767393
$747$	−6.93340	−	12.0090i	−0.253680	−	0.439387i
$748$	18.9057			0.691261
$749$	−0.967022	+	1.67493i	−0.0353342	+	0.0612007i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	−8.07568	−	13.9875i	−0.294686	−	0.510411i	0.680226	−	0.733002i	$-0.261882\pi$
$751$	−8.07568	−	13.9875i	−0.294686	−	0.510411i	−0.974912	+	0.222592i	$0.928548\pi$
$752$	1.17210			0.0427420
$753$	5.92368	−	10.2601i	0.215871	−	0.373899i
$754$	−1.11246	+	1.92684i	−0.0405134	+	0.0701712i
$755$	−0.228327	+	0.395475i	−0.00830968	+	0.0143928i
$756$	0.695350	+	1.20438i	0.0252896	+	0.0438029i
$757$	6.98963	−	12.1064i	0.254043	−	0.440015i	−0.710592	−	0.703604i	$-0.751573\pi$
$757$	6.98963	−	12.1064i	0.254043	−	0.440015i	0.964635	+	0.263589i	$0.0849063\pi$
$758$	7.67526	+	13.2939i	0.278778	+	0.482857i
$759$	−12.5226			−0.454542
$760$	−7.45665			−0.270481
$761$	8.74778	+	15.1516i	0.317107	+	0.549245i	0.979883	−	0.199572i	$-0.0639553\pi$
$761$	8.74778	+	15.1516i	0.317107	+	0.549245i	−0.662776	+	0.748817i	$0.730622\pi$
$762$	−5.93340	+	10.2770i	−0.214945	+	0.372295i
$763$	5.18498	+	8.98065i	0.187709	+	0.325121i
$764$	2.72833	−	4.72560i	0.0987074	−	0.170966i
$765$	−1.80465	+	3.12575i	−0.0652473	+	0.113012i
$766$	−3.58605	+	6.21122i	−0.129569	+	0.224420i
$767$	3.26007			0.117714
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−2.57632	−	4.46232i	−0.0929046	−	0.160915i	0.815828	−	0.578295i	$-0.196282\pi$
$769$	−2.57632	−	4.46232i	−0.0929046	−	0.160915i	−0.908732	+	0.417380i	$0.862948\pi$
$770$	3.64228	−	6.30861i	0.131259	−	0.227347i
$771$	18.5615			0.668477
$772$	−4.57632	−	7.92642i	−0.164705	−	0.285278i
$773$	−15.5628			−0.559755			−0.279877	−	0.960036i	$-0.590294\pi$
$773$	−15.5628			−0.559755			−0.279877	+	0.960036i	$0.590294\pi$
$774$	−7.84735			−0.282067
$775$	3.22833	+	4.53629i	0.115965	+	0.162948i
$776$	−13.2846			−0.476888
$777$	7.80085			0.279854
$778$	8.48647	+	14.6990i	0.304255	+	0.526985i
$779$	82.1682			2.94398
$780$	0.390699	−	0.676711i	0.0139893	−	0.0242301i
$781$	8.42960	+	14.6005i	0.301635	+	0.522447i
$782$	4.31438	+	7.47272i	0.154282	+	0.267224i
$783$	2.84735			0.101756
$784$	2.53298	−	4.38725i	0.0904635	−	0.156687i
$785$	−11.7478	+	20.3478i	−0.419296	+	0.726242i
$786$	6.31438	−	10.9368i	0.225226	−	0.390103i
$787$	4.12939	+	7.15232i	0.147197	+	0.254953i	0.930190	−	0.367077i	$-0.119642\pi$
$787$	4.12939	+	7.15232i	0.147197	+	0.254953i	−0.782993	+	0.622030i	$0.786308\pi$
$788$	−9.62875	+	16.6775i	−0.343010	+	0.594111i
$789$	−4.92368	−	8.52806i	−0.175288	−	0.303607i
$790$	−7.84735			−0.279196
$791$	15.3894			0.547185
$792$	2.61903	+	4.53629i	0.0930631	+	0.161190i
$793$	3.69471	−	6.39942i	0.131203	−	0.227250i
$794$	−13.3144	−	23.0612i	−0.472510	−	0.818411i
$795$	−3.81438	+	6.60669i	−0.135282	+	0.234315i
$796$	−8.93340	+	15.4731i	−0.316636	+	0.548430i
$797$	1.64228	−	2.84451i	0.0581725	−	0.100758i	−0.835473	−	0.549532i	$-0.814806\pi$
$797$	1.64228	−	2.84451i	0.0581725	−	0.100758i	0.893645	+	0.448774i	$0.148139\pi$
$798$	10.3700			0.367093
$799$	−2.11523	−	3.66368i	−0.0748313	−	0.129612i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	4.60930	−	7.98354i	0.162862	−	0.282085i
$802$	−18.1319			−0.640260
$803$	5.23805	+	9.07257i	0.184847	+	0.320164i
$804$	−5.60930			−0.197825
$805$	3.32474			0.117182
$806$	−1.80845	+	3.95697i	−0.0636999	+	0.139378i
$807$	−12.1915			−0.429163
$808$	14.6947			0.516958
$809$	20.6416	+	35.7524i	0.725721	+	1.25699i	0.958676	+	0.284499i	$0.0918271\pi$
$809$	20.6416	+	35.7524i	0.725721	+	1.25699i	−0.232955	+	0.972487i	$0.574840\pi$
$810$	−1.00000			−0.0351364
$811$	−4.37125	+	7.57122i	−0.153495	+	0.265862i	−0.932510	−	0.361144i	$-0.882386\pi$
$811$	−4.37125	+	7.57122i	−0.153495	+	0.265862i	0.779015	+	0.627005i	$0.215720\pi$
$812$	1.97991	+	3.42930i	0.0694811	+	0.120345i
$813$	−8.32410	−	14.4178i	−0.291939	−	0.505653i
$814$	29.3818			1.02983
$815$	−6.26131	+	10.8449i	−0.219324	+	0.379880i
$816$	1.80465	−	3.12575i	0.0631754	−	0.109423i
$817$	−29.2575	+	50.6755i	−1.02359	+	1.77291i
$818$	6.51945	+	11.2920i	0.227947	+	0.394816i
$819$	−0.543345	+	0.941101i	−0.0189860	+	0.0328847i
$820$	−5.50973	−	9.54313i	−0.192408	−	0.333260i
$821$	7.03890			0.245659			0.122830	−	0.992428i	$-0.460803\pi$
$821$	7.03890			0.245659			0.122830	+	0.992428i	$0.460803\pi$
$822$	−13.6482			−0.476036
$823$	4.74185	+	8.21313i	0.165291	+	0.286292i	0.936758	−	0.349977i	$-0.113810\pi$
$823$	4.74185	+	8.21313i	0.165291	+	0.286292i	−0.771468	+	0.636268i	$0.780477\pi$
$824$	3.08605	−	5.34519i	0.107508	−	0.186209i
$825$	2.61903	+	4.53629i	0.0911828	+	0.157933i
$826$	2.90107	−	5.02479i	0.100941	−	0.174835i
$827$	6.78140	−	11.7457i	0.235812	−	0.408439i	−0.723696	−	0.690119i	$-0.757558\pi$
$827$	6.78140	−	11.7457i	0.235812	−	0.408439i	0.959508	+	0.281680i	$0.0908916\pi$
$828$	−1.19535	+	2.07041i	−0.0415413	+	0.0719516i
$829$	−23.8398			−0.827989			−0.413994	−	0.910279i	$-0.635867\pi$
$829$	−23.8398			−0.827989			−0.413994	+	0.910279i	$0.635867\pi$
$830$	6.93340	+	12.0090i	0.240662	+	0.416839i
$831$	0.433403	+	0.750676i	0.0150346	+	0.0260407i
$832$	−0.390699	+	0.676711i	−0.0135451	+	0.0234607i
$833$	−18.2846			−0.633522
$834$	0.119027	+	0.206160i	0.00412156	+	0.00713875i
$835$	18.7142			0.647630
$836$	39.0584			1.35086
$837$	5.54270	−	0.527670i	0.191584	−	0.0182389i
$838$	2.76195			0.0954099
$839$	−11.8398			−0.408754			−0.204377	−	0.978892i	$-0.565517\pi$
$839$	−11.8398			−0.408754			−0.204377	+	0.978892i	$0.565517\pi$
$840$	−0.695350	−	1.20438i	−0.0239918	−	0.0415551i
$841$	−20.8926			−0.720434
$842$	6.96638	−	12.0661i	0.240077	−	0.415826i
$843$	14.2575	+	24.6947i	0.491055	+	0.850531i
$844$	7.72833	+	13.3859i	0.266020	+	0.460760i
$845$	−12.3894			−0.426209
$846$	0.586049	−	1.01507i	0.0201488	−	0.0348987i
$847$	−11.4296	+	19.7967i	−0.392726	+	0.680221i
$848$	3.81438	−	6.60669i	0.130986	−	0.226875i
$849$	−2.75158	−	4.76588i	−0.0944340	−	0.163564i
$850$	1.80465	−	3.12575i	0.0618990	−	0.107212i
$851$	6.70508	+	11.6135i	0.229847	+	0.398107i
$852$	3.21860			0.110267
$853$	25.0452			0.857532			0.428766	−	0.903416i	$-0.358948\pi$
$853$	25.0452			0.857532			0.428766	+	0.903416i	$0.358948\pi$
$854$	−6.57568	−	11.3894i	−0.225015	−	0.389738i
$855$	−3.72833	+	6.45765i	−0.127506	+	0.220847i
$856$	0.695350	+	1.20438i	0.0237666	+	0.0411649i
$857$	−20.3533	+	35.2529i	−0.695255	+	1.20422i	0.274840	+	0.961490i	$0.411375\pi$
$857$	−20.3533	+	35.2529i	−0.695255	+	1.20422i	−0.970095	+	0.242727i	$0.921958\pi$
$858$	−2.04650	+	3.54465i	−0.0698665	+	0.121012i
$859$	7.11903	−	12.3305i	0.242898	−	0.420712i	−0.718640	−	0.695382i	$-0.755235\pi$
$859$	7.11903	−	12.3305i	0.242898	−	0.420712i	0.961539	+	0.274670i	$0.0885686\pi$
$860$	7.84735			0.267593
$861$	7.66237	+	13.2716i	0.261133	+	0.452296i
$862$	7.68182	+	13.3053i	0.261644	+	0.453181i
$863$	−11.8175	+	20.4686i	−0.402274	+	0.696758i	−0.994000	−	0.109381i	$-0.965113\pi$
$863$	−11.8175	+	20.4686i	−0.402274	+	0.696758i	0.591726	+	0.806139i	$0.298447\pi$
$864$	1.00000			0.0340207
$865$	−3.42368	−	5.92998i	−0.116409	−	0.201625i
$866$	3.25751			0.110695
$867$	3.97295			0.134928
$868$	4.48963	+	6.30861i	0.152388	+	0.214128i
$869$	41.1049			1.39439
$870$	−2.84735			−0.0965343
$871$	−2.19155	−	3.79588i	−0.0742578	−	0.128618i
$872$	7.45665			0.252514
$873$	−6.64228	+	11.5048i	−0.224807	+	0.389377i
$874$	8.91331	+	15.4383i	0.301497	+	0.522208i
$875$	−0.695350	−	1.20438i	−0.0235071	−	0.0407155i
$876$	2.00000			0.0675737
$877$	15.8706	−	27.4887i	0.535912	−	0.928227i	−0.463206	−	0.886250i	$-0.653301\pi$
$877$	15.8706	−	27.4887i	0.535912	−	0.928227i	0.999119	−	0.0419768i	$-0.0133656\pi$
$878$	11.7911	−	20.4228i	0.397931	−	0.689237i
$879$	−0.595775	+	1.03191i	−0.0200950	+	0.0348055i
$880$	−2.61903	−	4.53629i	−0.0882874	−	0.152918i
$881$	−19.5562	+	33.8724i	−0.658866	+	1.14119i	0.322043	+	0.946725i	$0.395630\pi$
$881$	−19.5562	+	33.8724i	−0.658866	+	1.14119i	−0.980910	+	0.194465i	$0.937703\pi$
$882$	−2.53298	−	4.38725i	−0.0852898	−	0.147726i
$883$	−54.6545			−1.83927			−0.919636	−	0.392773i	$-0.871516\pi$
$883$	−54.6545			−1.83927			−0.919636	+	0.392773i	$0.871516\pi$
$884$	2.82030			0.0948570
$885$	2.08605	+	3.61314i	0.0701218	+	0.121454i
$886$	−11.0660	+	19.1668i	−0.371768	+	0.643921i
$887$	19.5059	+	33.7853i	0.654945	+	1.13440i	0.981908	+	0.189361i	$0.0606415\pi$
$887$	19.5059	+	33.7853i	0.654945	+	1.13440i	−0.326963	+	0.945037i	$0.606025\pi$
$888$	2.80465	−	4.85780i	0.0941179	−	0.163017i
$889$	−8.25158	+	14.2922i	−0.276749	+	0.479343i
$890$	−4.60930	+	7.98354i	−0.154504	+	0.267609i
$891$	5.23805			0.175481
$892$	−2.54270	−	4.40409i	−0.0851360	−	0.147460i
$893$	−4.36996	−	7.56900i	−0.146235	−	0.253287i
$894$	10.8144	−	18.7310i	0.361687	−	0.626460i
$895$	8.80085			0.294180
$896$	0.695350	+	1.20438i	0.0232300	+	0.0402355i
$897$	−1.86809			−0.0623737
$898$	24.9133			0.831368
$899$	15.7820	−	1.50246i	0.526361	−	0.0501099i
$900$	1.00000			0.0333333
$901$	−27.5345			−0.917306
$902$	28.8602	+	49.9874i	0.960941	+	1.66440i
$903$	−10.9133			−0.363172
$904$	5.53298	−	9.58340i	0.184024	−	0.318739i
$905$	−6.84735	−	11.8600i	−0.227614	−	0.394239i
$906$	−0.228327	−	0.395475i	−0.00758567	−	0.0131388i
$907$	37.5628			1.24725			0.623626	−	0.781723i	$-0.285659\pi$
$907$	37.5628			1.24725			0.623626	+	0.781723i	$0.285659\pi$
$908$	−8.15200	+	14.1197i	−0.270534	+	0.468578i
$909$	7.34735	−	12.7260i	0.243696	−	0.422094i
$910$	0.543345	−	0.941101i	0.0180117	−	0.0311972i
$911$	7.42304	+	12.8571i	0.245936	+	0.425974i	0.962394	−	0.271656i	$-0.0875713\pi$
$911$	7.42304	+	12.8571i	0.245936	+	0.425974i	−0.716458	+	0.697630i	$0.754238\pi$
$912$	3.72833	−	6.45765i	0.123457	−	0.213834i
$913$	−36.3175	−	62.9038i	−1.20193	−	2.08181i
$914$	−28.8203			−0.953291
$915$	9.45665			0.312627
$916$	14.5757	+	25.2458i	0.481594	+	0.834145i
$917$	8.78140	−	15.2098i	0.289987	−	0.502273i
$918$	−1.80465	−	3.12575i	−0.0595623	−	0.103165i
$919$	18.3137	−	31.7203i	0.604114	−	1.04636i	−0.388076	−	0.921627i	$-0.626860\pi$
$919$	18.3137	−	31.7203i	0.604114	−	1.04636i	0.992191	−	0.124730i	$-0.0398063\pi$
$920$	1.19535	−	2.07041i	0.0394095	−	0.0682593i
$921$	−10.7478	+	18.6157i	−0.354151	+	0.613408i
$922$	17.1708			0.565491
$923$	1.25751	+	2.17806i	0.0413913	+	0.0716918i
$924$	3.64228	+	6.30861i	0.119822	+	0.207538i
$925$	2.80465	−	4.85780i	0.0922163	−	0.159723i
$926$	22.7412			0.747323
$927$	−3.08605	−	5.34519i	−0.101359	−	0.175559i
$928$	2.84735			0.0934690
$929$	−53.0195			−1.73951			−0.869756	−	0.493482i	$-0.835724\pi$
$929$	−53.0195			−1.73951			−0.869756	+	0.493482i	$0.835724\pi$
$930$	−5.54270	+	0.527670i	−0.181752	+	0.0173030i
$931$	−37.7751			−1.23803
$932$	9.60930			0.314763
$933$	−2.62875	−	4.55313i	−0.0860615	−	0.149063i
$934$	7.56151			0.247420
$935$	−9.45285	+	16.3728i	−0.309141	+	0.535449i
$936$	0.390699	+	0.676711i	0.0127704	+	0.0221190i
$937$	21.9133	+	37.9550i	0.715877	+	1.23993i	0.962620	+	0.270854i	$0.0873060\pi$
$937$	21.9133	+	37.9550i	0.715877	+	1.23993i	−0.246744	+	0.969081i	$0.579361\pi$
$938$	−7.80085			−0.254707
$939$	−10.4431	+	18.0880i	−0.340799	+	0.590281i
$940$	−0.586049	+	1.01507i	−0.0191148	+	0.0331078i
$941$	−9.89070	+	17.1312i	−0.322428	+	0.558461i	−0.980988	−	0.194067i	$-0.937832\pi$
$941$	−9.89070	+	17.1312i	−0.322428	+	0.558461i	0.658561	+	0.752528i	$0.271166\pi$
$942$	−11.7478	−	20.3478i	−0.382763	−	0.662966i
$943$	−13.1721	+	22.8147i	−0.428943	+	0.742950i
$944$	−2.08605	−	3.61314i	−0.0678951	−	0.117598i
$945$	−1.39070			−0.0452395
$946$	−41.1049			−1.33643
$947$	−14.8279	−	25.6827i	−0.481842	−	0.834575i	0.517941	−	0.855417i	$-0.326699\pi$
$947$	−14.8279	−	25.6827i	−0.481842	−	0.834575i	−0.999783	+	0.0208416i	$0.993365\pi$
$948$	3.92368	−	6.79601i	0.127435	−	0.220724i
$949$	0.781399	+	1.35342i	0.0253653	+	0.0439339i
$950$	3.72833	−	6.45765i	0.120963	−	0.209514i
$951$	3.20508	−	5.55135i	0.103932	−	0.180015i
$952$	2.50973	−	4.34697i	0.0813407	−	0.140886i
$953$	41.4567			1.34291			0.671456	−	0.741044i	$-0.265669\pi$
$953$	41.4567			1.34291			0.671456	+	0.741044i	$0.265669\pi$
$954$	−3.81438	−	6.60669i	−0.123495	−	0.213900i
$955$	2.72833	+	4.72560i	0.0882866	+	0.152917i
$956$	−1.84735	+	3.19971i	−0.0597477	+	0.103486i
$957$	14.9146			0.482120
$958$	9.57568	+	16.5856i	0.309376	+	0.535855i
$959$	−18.9805			−0.612914
$960$	−1.00000			−0.0322749
$961$	30.4431	−	5.84944i	0.982036	−	0.188691i
$962$	4.38310			0.141317
$963$	1.39070			0.0448147
$964$	12.8144	+	22.1952i	0.412723	+	0.714858i
$965$	9.15265			0.294634
$966$	−1.66237	+	2.87931i	−0.0534859	+	0.0926404i
$967$	−2.87441	−	4.97862i	−0.0924347	−	0.160102i	0.816100	−	0.577910i	$-0.196132\pi$
$967$	−2.87441	−	4.97862i	−0.0924347	−	0.160102i	−0.908535	+	0.417809i	$0.862798\pi$
$968$	8.21860	+	14.2350i	0.264156	+	0.457531i
$969$	−26.9133			−0.864580
$970$	6.64228	−	11.5048i	0.213271	−	0.369396i
$971$	7.99027	−	13.8396i	0.256420	−	0.444133i	−0.708860	−	0.705349i	$-0.750790\pi$
$971$	7.99027	−	13.8396i	0.256420	−	0.444133i	0.965280	+	0.261216i	$0.0841236\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	0.165530	+	0.286707i	0.00530666	+	0.00919140i
$974$	2.15200	−	3.72738i	0.0689547	−	0.119433i
$975$	0.390699	+	0.676711i	0.0125124	+	0.0216721i
$976$	−9.45665			−0.302700
$977$	−28.7814			−0.920799			−0.460399	−	0.887712i	$-0.652294\pi$
$977$	−28.7814			−0.920799			−0.460399	+	0.887712i	$0.652294\pi$
$978$	−6.26131	−	10.8449i	−0.200214	−	0.346782i
$979$	24.1438	−	41.8182i	0.771638	−	1.33652i
$980$	2.53298	+	4.38725i	0.0809130	+	0.140145i
$981$	3.72833	−	6.45765i	0.119036	−	0.206177i
$982$	13.2943	−	23.0264i	0.424238	−	0.734801i
$983$	12.8474	−	22.2523i	0.409767	−	0.709737i	−0.585096	−	0.810964i	$-0.698943\pi$
$983$	12.8474	−	22.2523i	0.409767	−	0.709737i	0.994863	+	0.101227i	$0.0322767\pi$
$984$	11.0195			0.351287
$985$	−9.62875	−	16.6775i	−0.306798	−	0.531389i
$986$	−5.13848	−	8.90011i	−0.163642	−	0.283437i
$987$	0.815018	−	1.41165i	0.0259423	−	0.0449334i
$988$	5.82662			0.185369
$989$	−9.38033	−	16.2472i	−0.298277	−	0.516631i
$990$	−5.23805			−0.166476
$991$	−2.03890			−0.0647679			−0.0323840	−	0.999476i	$-0.510310\pi$
$991$	−2.03890			−0.0647679			−0.0323840	+	0.999476i	$0.510310\pi$
$992$	5.54270	−	0.527670i	0.175981	−	0.0167535i
$993$	34.7142			1.10162
$994$	4.47611			0.141973
$995$	−8.93340	−	15.4731i	−0.283208	−	0.490530i
$996$	−13.8668			−0.439387
$997$	−22.8602	+	39.5951i	−0.723991	+	1.25399i	0.235397	+	0.971899i	$0.424361\pi$
$997$	−22.8602	+	39.5951i	−0.723991	+	1.25399i	−0.959388	+	0.282090i	$0.908972\pi$
$998$	−19.7943	−	34.2847i	−0.626577	−	1.08526i
$999$	−2.80465	−	4.85780i	−0.0887352	−	0.153694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.i.n.211.2	✓	6
31.5	even	3	inner	930.2.i.n.811.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.i.n.211.2	✓	6	1.1	even	1	trivial
930.2.i.n.811.2	yes	6	31.5	even	3	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.695350 - 1.20438i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.695350 - 1.20438i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.61903 + 4.53629i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.390699 + 0.676711i) q^{13} +(0.695350 + 1.20438i) q^{14} -1.00000 q^{15} +1.00000 q^{16} +(-1.80465 - 3.12575i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-3.72833 - 6.45765i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.695350 - 1.20438i) q^{21} +(2.61903 - 4.53629i) q^{22} +2.39070 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.390699 - 0.676711i) q^{26} -1.00000 q^{27} +(-0.695350 - 1.20438i) q^{28} -2.84735 q^{29} +1.00000 q^{30} +(-5.54270 + 0.527670i) q^{31} -1.00000 q^{32} -5.23805 q^{33} +(1.80465 + 3.12575i) q^{34} +1.39070 q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.80465 + 4.85780i) q^{37} +(3.72833 + 6.45765i) q^{38} -0.781399 q^{39} +(0.500000 - 0.866025i) q^{40} +(-5.50973 + 9.54313i) q^{41} +(-0.695350 + 1.20438i) q^{42} +(-3.92368 - 6.79601i) q^{43} +(-2.61903 + 4.53629i) q^{44} +(-0.500000 - 0.866025i) q^{45} -2.39070 q^{46} +1.17210 q^{47} +(0.500000 + 0.866025i) q^{48} +(2.53298 - 4.38725i) q^{49} +(0.500000 + 0.866025i) q^{50} +(1.80465 - 3.12575i) q^{51} +(-0.390699 + 0.676711i) q^{52} +(3.81438 - 6.60669i) q^{53} +1.00000 q^{54} +(-2.61903 - 4.53629i) q^{55} +(0.695350 + 1.20438i) q^{56} +(3.72833 - 6.45765i) q^{57} +2.84735 q^{58} +(-2.08605 - 3.61314i) q^{59} -1.00000 q^{60} -9.45665 q^{61} +(5.54270 - 0.527670i) q^{62} +1.39070 q^{63} +1.00000 q^{64} +(-0.390699 - 0.676711i) q^{65} +5.23805 q^{66} +(-2.80465 + 4.85780i) q^{67} +(-1.80465 - 3.12575i) q^{68} +(1.19535 + 2.07041i) q^{69} -1.39070 q^{70} +(1.60930 - 2.78739i) q^{71} +(0.500000 - 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(-2.80465 - 4.85780i) q^{74} +(0.500000 - 0.866025i) q^{75} +(-3.72833 - 6.45765i) q^{76} +7.28456 q^{77} +0.781399 q^{78} +(-3.92368 - 6.79601i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.50973 - 9.54313i) q^{82} +(-6.93340 + 12.0090i) q^{83} +(0.695350 - 1.20438i) q^{84} +3.60930 q^{85} +(3.92368 + 6.79601i) q^{86} +(-1.42368 - 2.46588i) q^{87} +(2.61903 - 4.53629i) q^{88} -9.21860 q^{89} +(0.500000 + 0.866025i) q^{90} +1.08669 q^{91} +2.39070 q^{92} +(-3.22833 - 4.53629i) q^{93} -1.17210 q^{94} +7.45665 q^{95} +(-0.500000 - 0.866025i) q^{96} +13.2846 q^{97} +(-2.53298 + 4.38725i) q^{98} +(-2.61903 - 4.53629i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 4 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} + 3 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 6 q^{16} - 11 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 14 q^{23} - 3 q^{24} - 3 q^{25} + 2 q^{26} - 6 q^{27} - 4 q^{28} + 24 q^{29} + 6 q^{30} + 8 q^{31} - 6 q^{32} + 10 q^{33} + 11 q^{34} + 8 q^{35} - 3 q^{36} + 17 q^{37} + 2 q^{38} - 4 q^{39} + 3 q^{40} - 12 q^{41} - 4 q^{42} - 3 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} + 6 q^{47} + 3 q^{48} - 5 q^{49} + 3 q^{50} + 11 q^{51} - 2 q^{52} + 2 q^{53} + 6 q^{54} + 5 q^{55} + 4 q^{56} + 2 q^{57} - 24 q^{58} - 12 q^{59} - 6 q^{60} - 16 q^{61} - 8 q^{62} + 8 q^{63} + 6 q^{64} - 2 q^{65} - 10 q^{66} - 17 q^{67} - 11 q^{68} + 7 q^{69} - 8 q^{70} + 10 q^{71} + 3 q^{72} + 6 q^{73} - 17 q^{74} + 3 q^{75} - 2 q^{76} + 4 q^{77} + 4 q^{78} - 3 q^{79} - 3 q^{80} - 3 q^{81} + 12 q^{82} + 4 q^{84} + 22 q^{85} + 3 q^{86} + 12 q^{87} - 5 q^{88} - 56 q^{89} + 3 q^{90} + 88 q^{91} + 14 q^{92} + q^{93} - 6 q^{94} + 4 q^{95} - 3 q^{96} + 40 q^{97} + 5 q^{98} + 5 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 4 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 5 * q^11 + 3 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 + 6 * q^16 - 11 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 + 14 * q^23 - 3 * q^24 - 3 * q^25 + 2 * q^26 - 6 * q^27 - 4 * q^28 + 24 * q^29 + 6 * q^30 + 8 * q^31 - 6 * q^32 + 10 * q^33 + 11 * q^34 + 8 * q^35 - 3 * q^36 + 17 * q^37 + 2 * q^38 - 4 * q^39 + 3 * q^40 - 12 * q^41 - 4 * q^42 - 3 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 + 6 * q^47 + 3 * q^48 - 5 * q^49 + 3 * q^50 + 11 * q^51 - 2 * q^52 + 2 * q^53 + 6 * q^54 + 5 * q^55 + 4 * q^56 + 2 * q^57 - 24 * q^58 - 12 * q^59 - 6 * q^60 - 16 * q^61 - 8 * q^62 + 8 * q^63 + 6 * q^64 - 2 * q^65 - 10 * q^66 - 17 * q^67 - 11 * q^68 + 7 * q^69 - 8 * q^70 + 10 * q^71 + 3 * q^72 + 6 * q^73 - 17 * q^74 + 3 * q^75 - 2 * q^76 + 4 * q^77 + 4 * q^78 - 3 * q^79 - 3 * q^80 - 3 * q^81 + 12 * q^82 + 4 * q^84 + 22 * q^85 + 3 * q^86 + 12 * q^87 - 5 * q^88 - 56 * q^89 + 3 * q^90 + 88 * q^91 + 14 * q^92 + q^93 - 6 * q^94 + 4 * q^95 - 3 * q^96 + 40 * q^97 + 5 * q^98 + 5 * q^99

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