LMFDB - Embedded newform 231.2.i.e.67.2

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			67.2
Root			$0.643668 + 1.11487i$ of defining polynomial
Character	$\chi$	$=$	231.67
Dual form			231.2.i.e.100.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.643668 - 1.11487i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.171383 - 0.296844i) q^{4} +(-1.95872 - 3.39260i) q^{5} +1.28734 q^{6} +(-0.234193 + 2.63537i) q^{7} -3.01593 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.643668 - 1.11487i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.171383 - 0.296844i) q^{4} +(-1.95872 - 3.39260i) q^{5} +1.28734 q^{6} +(-0.234193 + 2.63537i) q^{7} -3.01593 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.52153 + 4.36742i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.171383 + 0.296844i) q^{12} -3.04306 q^{13} +(3.08882 - 1.43521i) q^{14} +3.91744 q^{15} +(1.59849 + 2.76866i) q^{16} +(-1.98643 + 3.44061i) q^{17} +(-0.643668 + 1.11487i) q^{18} +(-3.79530 - 6.57365i) q^{19} -1.34277 q^{20} +(-2.16520 - 1.52050i) q^{21} -1.28734 q^{22} +(-2.25572 - 3.90703i) q^{23} +(1.50796 - 2.61187i) q^{24} +(-5.17316 + 8.96018i) q^{25} +(1.95872 + 3.39260i) q^{26} +1.00000 q^{27} +(0.742157 + 0.521177i) q^{28} +3.75572 q^{29} +(-2.52153 - 4.36742i) q^{30} +(3.37168 - 5.83991i) q^{31} +(-0.958135 + 1.65954i) q^{32} +(0.500000 + 0.866025i) q^{33} +5.11442 q^{34} +(9.39946 - 4.36742i) q^{35} -0.342766 q^{36} +(-0.171383 - 0.296844i) q^{37} +(-4.88582 + 8.46250i) q^{38} +(1.52153 - 2.63537i) q^{39} +(5.90735 + 10.2318i) q^{40} -2.79182 q^{41} +(-0.301486 + 3.39260i) q^{42} +11.1222 q^{43} +(-0.171383 - 0.296844i) q^{44} +(-1.95872 + 3.39260i) q^{45} +(-2.90387 + 5.02965i) q^{46} +(-0.828617 - 1.43521i) q^{47} -3.19698 q^{48} +(-6.89031 - 1.23437i) q^{49} +13.3192 q^{50} +(-1.98643 - 3.44061i) q^{51} +(-0.521529 + 0.903315i) q^{52} +(6.47016 - 11.2067i) q^{53} +(-0.643668 - 1.11487i) q^{54} -3.91744 q^{55} +(0.706310 - 7.94807i) q^{56} +7.59060 q^{57} +(-2.41744 - 4.18713i) q^{58} +(1.83039 - 3.17034i) q^{59} +(0.671383 - 1.16287i) q^{60} +(0.234193 + 0.405635i) q^{61} -8.68096 q^{62} +(2.39939 - 1.11487i) q^{63} +8.86084 q^{64} +(5.96050 + 10.3239i) q^{65} +(0.643668 - 1.11487i) q^{66} +(1.28911 - 2.23281i) q^{67} +(0.680883 + 1.17932i) q^{68} +4.51145 q^{69} +(-10.9192 - 7.66797i) q^{70} -5.00355 q^{71} +(1.50796 + 2.61187i) q^{72} +(4.36878 - 7.56694i) q^{73} +(-0.220628 + 0.382139i) q^{74} +(-5.17316 - 8.96018i) q^{75} -2.60180 q^{76} +(2.16520 + 1.52050i) q^{77} -3.91744 q^{78} +(-0.359814 - 0.623216i) q^{79} +(6.26198 - 10.8461i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.79700 + 3.11250i) q^{82} -11.5976 q^{83} +(-0.822431 + 0.382139i) q^{84} +15.5635 q^{85} +(-7.15901 - 12.3998i) q^{86} +(-1.87786 + 3.25255i) q^{87} +(-1.50796 + 2.61187i) q^{88} +(6.17764 + 10.7000i) q^{89} +5.04306 q^{90} +(0.712664 - 8.01957i) q^{91} -1.54637 q^{92} +(3.37168 + 5.83991i) q^{93} +(-1.06671 + 1.84759i) q^{94} +(-14.8679 + 25.7519i) q^{95} +(-0.958135 - 1.65954i) q^{96} -13.1687 q^{97} +(3.05891 + 8.47629i) 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 $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.643668	−	1.11487i	−0.455142	−	0.788329i	0.543554	−	0.839374i	$-0.317078\pi$
$2$	−0.643668	−	1.11487i	−0.455142	−	0.788329i	−0.998696	+	0.0510450i	$0.983745\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.171383	−	0.296844i	0.0856916	−	0.148422i
$5$	−1.95872	−	3.39260i	−0.875966	−	1.51722i	−0.855730	−	0.517422i	$-0.826892\pi$
$5$	−1.95872	−	3.39260i	−0.875966	−	1.51722i	−0.0202354	−	0.999795i	$-0.506442\pi$
$6$	1.28734			0.525553
$7$	−0.234193	+	2.63537i	−0.0885168	+	0.996075i
$7$	−0.234193	+	2.63537i	−0.0885168	+	0.996075i
$8$	−3.01593			−1.06629
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−2.52153	+	4.36742i	−0.797378	+	1.38110i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	0.171383	+	0.296844i	0.0494741	+	0.0856916i
$13$	−3.04306			−0.843993			−0.421996	−	0.906598i	$-0.638670\pi$
$13$	−3.04306			−0.843993			−0.421996	+	0.906598i	$0.638670\pi$
$14$	3.08882	−	1.43521i	0.825522	−	0.383575i
$15$	3.91744			1.01148
$16$	1.59849	+	2.76866i	0.399622	+	0.692166i
$17$	−1.98643	+	3.44061i	−0.481781	+	0.834469i	−0.999781	−	0.0209111i	$-0.993343\pi$
$17$	−1.98643	+	3.44061i	−0.481781	+	0.834469i	0.518000	+	0.855380i	$0.326677\pi$
$18$	−0.643668	+	1.11487i	−0.151714	+	0.262776i
$19$	−3.79530	−	6.57365i	−0.870701	−	1.50810i	−0.861272	−	0.508144i	$-0.830332\pi$
$19$	−3.79530	−	6.57365i	−0.870701	−	1.50810i	−0.00942900	−	0.999956i	$-0.503001\pi$
$20$	−1.34277			−0.300252
$21$	−2.16520	−	1.52050i	−0.472485	−	0.331800i
$22$	−1.28734			−0.274461
$23$	−2.25572	−	3.90703i	−0.470351	−	0.814671i	0.529074	−	0.848575i	$-0.322539\pi$
$23$	−2.25572	−	3.90703i	−0.470351	−	0.814671i	−0.999425	+	0.0339042i	$0.989206\pi$
$24$	1.50796	−	2.61187i	0.307812	−	0.533146i
$25$	−5.17316	+	8.96018i	−1.03463	+	1.79204i
$26$	1.95872	+	3.39260i	0.384136	+	0.665344i
$27$	1.00000			0.192450
$28$	0.742157	+	0.521177i	0.140254	+	0.0984931i
$29$	3.75572			0.697420			0.348710	−	0.937231i	$-0.386620\pi$
$29$	3.75572			0.697420			0.348710	+	0.937231i	$0.386620\pi$
$30$	−2.52153	−	4.36742i	−0.460366	−	0.797378i
$31$	3.37168	−	5.83991i	0.605571	−	1.04888i	−0.386390	−	0.922335i	$-0.626278\pi$
$31$	3.37168	−	5.83991i	0.605571	−	1.04888i	0.991961	−	0.126544i	$-0.0403885\pi$
$32$	−0.958135	+	1.65954i	−0.169376	+	0.293368i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	5.11442			0.877115
$35$	9.39946	−	4.36742i	1.58880	−	0.738228i
$36$	−0.342766			−0.0571277
$37$	−0.171383	−	0.296844i	−0.0281752	−	0.0488009i	0.851594	−	0.524202i	$-0.175636\pi$
$37$	−0.171383	−	0.296844i	−0.0281752	−	0.0488009i	−0.879769	+	0.475401i	$0.842303\pi$
$38$	−4.88582	+	8.46250i	−0.792585	+	1.37280i
$39$	1.52153	−	2.63537i	0.243640	−	0.421996i
$40$	5.90735	+	10.2318i	0.934035	+	1.61780i
$41$	−2.79182			−0.436009			−0.218004	−	0.975948i	$-0.569955\pi$
$41$	−2.79182			−0.436009			−0.218004	+	0.975948i	$0.569955\pi$
$42$	−0.301486	+	3.39260i	−0.0465202	+	0.523490i
$43$	11.1222			1.69612			0.848061	−	0.529899i	$-0.177770\pi$
$43$	11.1222			1.69612			0.848061	+	0.529899i	$0.177770\pi$
$44$	−0.171383	−	0.296844i	−0.0258370	−	0.0447510i
$45$	−1.95872	+	3.39260i	−0.291989	+	0.505739i
$46$	−2.90387	+	5.02965i	−0.428153	+	0.741582i
$47$	−0.828617	−	1.43521i	−0.120866	−	0.209346i	0.799243	−	0.601008i	$-0.205234\pi$
$47$	−0.828617	−	1.43521i	−0.120866	−	0.209346i	−0.920109	+	0.391661i	$0.871901\pi$
$48$	−3.19698			−0.461444
$49$	−6.89031	−	1.23437i	−0.984330	−	0.176339i
$50$	13.3192			1.88362
$51$	−1.98643	−	3.44061i	−0.278156	−	0.481781i
$52$	−0.521529	+	0.903315i	−0.0723231	+	0.125267i
$53$	6.47016	−	11.2067i	0.888745	−	1.53935i	0.0473857	−	0.998877i	$-0.484911\pi$
$53$	6.47016	−	11.2067i	0.888745	−	1.53935i	0.841360	−	0.540476i	$-0.181756\pi$
$54$	−0.643668	−	1.11487i	−0.0875921	−	0.151714i
$55$	−3.91744			−0.528227
$56$	0.706310	−	7.94807i	0.0943847	−	1.06211i
$57$	7.59060			1.00540
$58$	−2.41744	−	4.18713i	−0.317425	−	0.549797i
$59$	1.83039	−	3.17034i	0.238297	−	0.412743i	−0.721929	−	0.691967i	$-0.756744\pi$
$59$	1.83039	−	3.17034i	0.238297	−	0.412743i	0.960226	+	0.279225i	$0.0900775\pi$
$60$	0.671383	−	1.16287i	0.0866752	−	0.150126i
$61$	0.234193	+	0.405635i	0.0299854	+	0.0519362i	0.880629	−	0.473807i	$-0.157121\pi$
$61$	0.234193	+	0.405635i	0.0299854	+	0.0519362i	−0.850643	+	0.525743i	$0.823787\pi$
$62$	−8.68096			−1.10248
$63$	2.39939	−	1.11487i	0.302295	−	0.140460i
$64$	8.86084			1.10760
$65$	5.96050	+	10.3239i	0.739309	+	1.28052i
$66$	0.643668	−	1.11487i	0.0792300	−	0.137230i
$67$	1.28911	−	2.23281i	0.157490	−	0.272781i	−0.776473	−	0.630151i	$-0.782993\pi$
$67$	1.28911	−	2.23281i	0.157490	−	0.272781i	0.933963	+	0.357370i	$0.116326\pi$
$68$	0.680883	+	1.17932i	0.0825692	+	0.143014i
$69$	4.51145			0.543114
$70$	−10.9192	−	7.66797i	−1.30510	−	0.916498i
$71$	−5.00355			−0.593813			−0.296906	−	0.954907i	$-0.595955\pi$
$71$	−5.00355			−0.593813			−0.296906	+	0.954907i	$0.595955\pi$
$72$	1.50796	+	2.61187i	0.177715	+	0.307812i
$73$	4.36878	−	7.56694i	0.511327	−	0.885644i	−0.488587	−	0.872515i	$-0.662488\pi$
$73$	4.36878	−	7.56694i	0.511327	−	0.885644i	0.999914	−	0.0131288i	$-0.00417914\pi$
$74$	−0.220628	+	0.382139i	−0.0256475	+	0.0444227i
$75$	−5.17316	−	8.96018i	−0.597345	−	1.03463i
$76$	−2.60180			−0.298447
$77$	2.16520	+	1.52050i	0.246747	+	0.173277i
$78$	−3.91744			−0.443563
$79$	−0.359814	−	0.623216i	−0.0404822	−	0.0701172i	0.845074	−	0.534649i	$-0.179556\pi$
$79$	−0.359814	−	0.623216i	−0.0404822	−	0.0701172i	−0.885557	+	0.464532i	$0.846223\pi$
$80$	6.26198	−	10.8461i	0.700111	−	1.21263i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.79700	+	3.11250i	0.198446	+	0.343718i
$83$	−11.5976			−1.27300			−0.636499	−	0.771278i	$-0.719618\pi$
$83$	−11.5976			−1.27300			−0.636499	+	0.771278i	$0.719618\pi$
$84$	−0.822431	+	0.382139i	−0.0897345	+	0.0416947i
$85$	15.5635			1.68810
$86$	−7.15901	−	12.3998i	−0.771976	−	1.33710i
$87$	−1.87786	+	3.25255i	−0.201328	+	0.348710i
$88$	−1.50796	+	2.61187i	−0.160749	+	0.278426i
$89$	6.17764	+	10.7000i	0.654829	+	1.13420i	0.981937	+	0.189210i	$0.0605926\pi$
$89$	6.17764	+	10.7000i	0.654829	+	1.13420i	−0.327108	+	0.944987i	$0.606074\pi$
$90$	5.04306			0.531585
$91$	0.712664	−	8.01957i	0.0747075	−	0.840680i
$92$	−1.54637			−0.161220
$93$	3.37168	+	5.83991i	0.349626	+	0.605571i
$94$	−1.06671	+	1.84759i	−0.110023	+	0.190565i
$95$	−14.8679	+	25.7519i	−1.52541	+	2.64209i
$96$	−0.958135	−	1.65954i	−0.0977892	−	0.169376i
$97$	−13.1687			−1.33708			−0.668538	−	0.743678i	$-0.733080\pi$
$97$	−13.1687			−1.33708			−0.668538	+	0.743678i	$0.733080\pi$
$98$	3.05891	+	8.47629i	0.308997	+	0.856235i
$99$	−1.00000			−0.100504
$100$	1.77319	+	3.07125i	0.177319	+	0.307125i
$101$	−3.53509	+	6.12296i	−0.351755	+	0.609258i	−0.986557	−	0.163417i	$-0.947748\pi$
$101$	−3.53509	+	6.12296i	−0.351755	+	0.609258i	0.634802	+	0.772675i	$0.281082\pi$
$102$	−2.55721	+	4.42921i	−0.253201	+	0.438558i
$103$	−1.16868	−	2.02421i	−0.115153	−	0.199451i	0.802688	−	0.596400i	$-0.203403\pi$
$103$	−1.16868	−	2.02421i	−0.115153	−	0.199451i	−0.917841	+	0.396948i	$0.870069\pi$
$104$	9.17764			0.899942
$105$	−0.917438	+	10.3239i	−0.0895328	+	1.00751i
$106$	−16.6585			−1.61802
$107$	5.42660	+	9.39914i	0.524609	+	0.908649i	0.999589	+	0.0286528i	$0.00912171\pi$
$107$	5.42660	+	9.39914i	0.524609	+	0.908649i	−0.474981	+	0.879996i	$0.657545\pi$
$108$	0.171383	−	0.296844i	0.0164914	−	0.0285639i
$109$	1.09620	−	1.89868i	0.104997	−	0.181860i	−0.808740	−	0.588166i	$-0.799850\pi$
$109$	1.09620	−	1.89868i	0.104997	−	0.181860i	0.913737	+	0.406306i	$0.133183\pi$
$110$	2.52153	+	4.36742i	0.240418	+	0.416417i
$111$	0.342766			0.0325340
$112$	−7.67080	+	3.56420i	−0.724822	+	0.336785i
$113$	−11.6415			−1.09514			−0.547568	−	0.836761i	$-0.684446\pi$
$113$	−11.6415			−1.09514			−0.547568	+	0.836761i	$0.684446\pi$
$114$	−4.88582	−	8.46250i	−0.457599	−	0.792585i
$115$	−8.83665	+	15.3055i	−0.824022	+	1.42725i
$116$	0.643668	−	1.11487i	0.0597631	−	0.103513i
$117$	1.52153	+	2.63537i	0.140665	+	0.243640i
$118$	−4.71266			−0.433836
$119$	−8.60204	−	6.04075i	−0.788548	−	0.553755i
$120$	−11.8147			−1.07853
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	0.301486	−	0.522188i	0.0272952	−	0.0472767i
$123$	1.39591	−	2.41779i	0.125865	−	0.218004i
$124$	−1.15570	−	2.00173i	−0.103785	−	0.179760i
$125$	20.9439			1.87328
$126$	−2.78734	−	1.95739i	−0.248316	−	0.174379i
$127$	5.41837			0.480802			0.240401	−	0.970674i	$-0.422721\pi$
$127$	5.41837			0.480802			0.240401	+	0.970674i	$0.422721\pi$
$128$	−3.78717	−	6.55957i	−0.334742	−	0.579789i
$129$	−5.56111	+	9.63212i	−0.489628	+	0.848061i
$130$	7.67316	−	13.2903i	0.672981	−	1.16564i
$131$	1.03297	+	1.78916i	0.0902514	+	0.156320i	0.907617	−	0.419800i	$-0.137900\pi$
$131$	1.03297	+	1.78916i	0.0902514	+	0.156320i	−0.817365	+	0.576120i	$0.804566\pi$
$132$	0.342766			0.0298340
$133$	18.2128	−	8.46250i	1.57925	−	0.733792i
$134$	−3.31904			−0.286722
$135$	−1.95872	−	3.39260i	−0.168580	−	0.291989i
$136$	5.99094	−	10.3766i	0.513719	−	0.889787i
$137$	2.09153	−	3.62263i	0.178691	−	0.309502i	−0.762741	−	0.646704i	$-0.776147\pi$
$137$	2.09153	−	3.62263i	0.178691	−	0.309502i	0.941432	+	0.337202i	$0.109480\pi$
$138$	−2.90387	−	5.02965i	−0.247194	−	0.428153i
$139$	3.61077			0.306261			0.153131	−	0.988206i	$-0.451064\pi$
$139$	3.61077			0.306261			0.153131	+	0.988206i	$0.451064\pi$
$140$	0.314467	−	3.53868i	0.0265773	−	0.299073i
$141$	1.65723			0.139564
$142$	3.22063	+	5.57829i	0.270269	+	0.468120i
$143$	−1.52153	+	2.63537i	−0.127237	+	0.220380i
$144$	1.59849	−	2.76866i	0.133207	−	0.230722i
$145$	−7.35641	−	12.7417i	−0.610916	−	1.05814i
$146$	−11.2482			−0.930905
$147$	4.51415	−	5.35000i	0.372321	−	0.441260i
$148$	−0.117489			−0.00965752
$149$	−6.65960	−	11.5348i	−0.545575	−	0.944964i	−0.998570	−	0.0534512i	$-0.982978\pi$
$149$	−6.65960	−	11.5348i	−0.545575	−	0.944964i	0.452995	−	0.891513i	$-0.350355\pi$
$150$	−6.65960	+	11.5348i	−0.543754	+	0.941809i
$151$	3.52160	−	6.09959i	0.286584	−	0.496378i	−0.686408	−	0.727217i	$-0.740814\pi$
$151$	3.52160	−	6.09959i	0.286584	−	0.496378i	0.972992	+	0.230839i	$0.0741469\pi$
$152$	11.4463	+	19.8257i	0.928421	+	1.60807i
$153$	3.97287			0.321187
$154$	0.301486	−	3.39260i	0.0242944	−	0.273384i
$155$	−26.4167			−2.12184
$156$	−0.521529	−	0.903315i	−0.0417558	−	0.0723231i
$157$	−6.37793	+	11.0469i	−0.509015	+	0.881639i	0.490931	+	0.871199i	$0.336657\pi$
$157$	−6.37793	+	11.0469i	−0.509015	+	0.881639i	−0.999945	+	0.0104406i	$0.996677\pi$
$158$	−0.463201	+	0.802288i	−0.0368503	+	0.0638266i
$159$	6.47016	+	11.2067i	0.513117	+	0.888745i
$160$	7.50687			0.593470
$161$	10.8247	−	5.02965i	0.853107	−	0.396392i
$162$	1.28734			0.101143
$163$	−5.70207	−	9.87627i	−0.446621	−	0.773569i	0.551543	−	0.834146i	$-0.314039\pi$
$163$	−5.70207	−	9.87627i	−0.446621	−	0.773569i	−0.998164	+	0.0605770i	$0.980706\pi$
$164$	−0.478471	+	0.828736i	−0.0373623	+	0.0647134i
$165$	1.95872	−	3.39260i	0.152486	−	0.264114i
$166$	7.46498	+	12.9297i	0.579395	+	1.00354i
$167$	12.1109			0.937167			0.468583	−	0.883419i	$-0.344765\pi$
$167$	12.1109			0.937167			0.468583	+	0.883419i	$0.344765\pi$
$168$	6.53008	+	4.58572i	0.503806	+	0.353796i
$169$	−3.73980			−0.287677
$170$	−10.0177	−	17.3512i	−0.768323	−	1.33077i
$171$	−3.79530	+	6.57365i	−0.290234	+	0.502700i
$172$	1.90616	−	3.30157i	0.145343	−	0.251742i
$173$	−1.82124	−	3.15448i	−0.138466	−	0.239830i	0.788450	−	0.615099i	$-0.210884\pi$
$173$	−1.82124	−	3.15448i	−0.138466	−	0.239830i	−0.926916	+	0.375268i	$0.877551\pi$
$174$	4.83488			0.366531
$175$	−22.4018	−	15.7316i	−1.69342	−	1.18920i
$176$	3.19698			0.240981
$177$	1.83039	+	3.17034i	0.137581	+	0.238297i
$178$	7.95270	−	13.7745i	0.596080	−	1.03244i
$179$	−4.96320	+	8.59652i	−0.370967	+	0.642534i	−0.989715	−	0.143056i	$-0.954307\pi$
$179$	−4.96320	+	8.59652i	−0.370967	+	0.642534i	0.618748	+	0.785590i	$0.287640\pi$
$180$	0.671383	+	1.16287i	0.0500420	+	0.0866752i
$181$	−8.07219			−0.600001			−0.300001	−	0.953939i	$-0.596987\pi$
$181$	−8.07219			−0.600001			−0.300001	+	0.953939i	$0.596987\pi$
$182$	−9.39946	+	4.36742i	−0.696735	+	0.323734i
$183$	−0.468387			−0.0346241
$184$	6.80310	+	11.7833i	0.501531	+	0.868677i
$185$	−0.671383	+	1.16287i	−0.0493611	+	0.0854959i
$186$	4.34048	−	7.51793i	0.318259	−	0.551241i
$187$	1.98643	+	3.44061i	0.145262	+	0.251602i
$188$	−0.568044			−0.0414289
$189$	−0.234193	+	2.63537i	−0.0170351	+	0.191695i
$190$	38.2798			2.77711
$191$	−2.79182	−	4.83557i	−0.202009	−	0.349890i	0.747167	−	0.664637i	$-0.231414\pi$
$191$	−2.79182	−	4.83557i	−0.202009	−	0.349890i	−0.949176	+	0.314747i	$0.898080\pi$
$192$	−4.43042	+	7.67371i	−0.319738	+	0.553802i
$193$	−5.56688	+	9.64211i	−0.400712	+	0.694054i	−0.993812	−	0.111075i	$-0.964571\pi$
$193$	−5.56688	+	9.64211i	−0.400712	+	0.694054i	0.593100	+	0.805129i	$0.297904\pi$
$194$	8.47626	+	14.6813i	0.608560	+	1.05406i
$195$	−11.9210			−0.853680
$196$	−1.54730	+	1.83380i	−0.110521	+	0.130986i
$197$	−0.644475			−0.0459170			−0.0229585	−	0.999736i	$-0.507309\pi$
$197$	−0.644475			−0.0459170			−0.0229585	+	0.999736i	$0.507309\pi$
$198$	0.643668	+	1.11487i	0.0457435	+	0.0792300i
$199$	12.6177	−	21.8545i	0.894447	−	1.54923i	0.0599599	−	0.998201i	$-0.480903\pi$
$199$	12.6177	−	21.8545i	0.894447	−	1.54923i	0.834487	−	0.551027i	$-0.185764\pi$
$200$	15.6019	−	27.0232i	1.10322	−	1.91083i
$201$	1.28911	+	2.23281i	0.0909270	+	0.157490i
$202$	9.10171			0.640394
$203$	−0.879565	+	9.89770i	−0.0617334	+	0.694683i
$204$	−1.36177			−0.0953427
$205$	5.46839	+	9.47152i	0.381929	+	0.661520i
$206$	−1.50448	+	2.60584i	−0.104822	+	0.181557i
$207$	−2.25572	+	3.90703i	−0.156784	+	0.271557i
$208$	−4.86430	−	8.42521i	−0.337278	−	0.584183i
$209$	−7.59060			−0.525053
$210$	12.1003	−	5.62233i	0.834998	−	0.387978i
$211$	−17.6357			−1.21409			−0.607044	−	0.794668i	$-0.707645\pi$
$211$	−17.6357			−1.21409			−0.607044	+	0.794668i	$0.707645\pi$
$212$	−2.21776	−	3.84127i	−0.152316	−	0.263819i
$213$	2.50178	−	4.33321i	0.171419	−	0.296906i
$214$	6.98585	−	12.0998i	0.477543	−	0.827129i
$215$	−21.7853	−	37.7332i	−1.48574	−	2.57338i
$216$	−3.01593			−0.205208
$217$	14.6007	+	10.2533i	0.991159	+	0.696037i
$218$	−2.82236			−0.191154
$219$	4.36878	+	7.56694i	0.295215	+	0.511327i
$220$	−0.671383	+	1.16287i	−0.0452646	+	0.0784007i
$221$	6.04484	−	10.4700i	0.406620	−	0.704286i
$222$	−0.220628	−	0.382139i	−0.0148076	−	0.0256475i
$223$	16.5853			1.11064			0.555318	−	0.831638i	$-0.312596\pi$
$223$	16.5853			1.11064			0.555318	+	0.831638i	$0.312596\pi$
$224$	−4.14910	−	2.91369i	−0.277224	−	0.194679i
$225$	10.3463			0.689755
$226$	7.49323	+	12.9787i	0.498442	+	0.863327i
$227$	1.17409	−	2.03358i	0.0779269	−	0.134973i	−0.824428	−	0.565966i	$-0.808503\pi$
$227$	1.17409	−	2.03358i	0.0779269	−	0.134973i	0.902355	+	0.430993i	$0.141837\pi$
$228$	1.30090	−	2.25323i	0.0861543	−	0.149224i
$229$	8.72518	+	15.1125i	0.576576	+	0.998660i	0.995868	+	0.0908081i	$0.0289450\pi$
$229$	8.72518	+	15.1125i	0.576576	+	0.998660i	−0.419292	+	0.907851i	$0.637722\pi$
$230$	22.7515			1.50019
$231$	−2.39939	+	1.11487i	−0.157868	+	0.0733528i
$232$	−11.3270			−0.743653
$233$	2.79530	+	4.84160i	0.183126	+	0.317184i	0.942943	−	0.332953i	$-0.108045\pi$
$233$	2.79530	+	4.84160i	0.183126	+	0.317184i	−0.759817	+	0.650137i	$0.774712\pi$
$234$	1.95872	−	3.39260i	0.128045	−	0.221781i
$235$	−3.24605	+	5.62233i	−0.211749	+	0.366760i
$236$	−0.627398	−	1.08668i	−0.0408401	−	0.0707372i
$237$	0.719627			0.0467448
$238$	−1.19776	+	13.4784i	−0.0776394	+	0.873672i
$239$	17.8147			1.15234			0.576169	−	0.817331i	$-0.304547\pi$
$239$	17.8147			1.15234			0.576169	+	0.817331i	$0.304547\pi$
$240$	6.26198	+	10.8461i	0.404209	+	0.700111i
$241$	−1.49211	+	2.58441i	−0.0961152	+	0.166476i	−0.910074	−	0.414447i	$-0.863975\pi$
$241$	−1.49211	+	2.58441i	−0.0961152	+	0.166476i	0.813958	+	0.580923i	$0.197308\pi$
$242$	−0.643668	+	1.11487i	−0.0413765	+	0.0716663i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	0.160547			0.0102780
$245$	9.30845	+	25.7938i	0.594695	+	1.64791i
$246$	−3.59401			−0.229146
$247$	11.5493	+	20.0040i	0.734866	+	1.27282i
$248$	−10.1687	+	17.6128i	−0.645715	+	1.11841i
$249$	5.79878	−	10.0438i	0.367483	−	0.636499i
$250$	−13.4809	−	23.3496i	−0.852607	−	1.47676i
$251$	25.0829			1.58322			0.791608	−	0.611029i	$-0.209244\pi$
$251$	25.0829			1.58322			0.791608	+	0.611029i	$0.209244\pi$
$252$	0.0802736	−	0.903315i	0.00505676	−	0.0569035i
$253$	−4.51145			−0.283632
$254$	−3.48763	−	6.04075i	−0.218833	−	0.379030i
$255$	−7.78173	+	13.4784i	−0.487311	+	0.844048i
$256$	3.98548	−	6.90306i	0.249093	−	0.431441i
$257$	11.2785	+	19.5350i	0.703535	+	1.21856i	0.967218	+	0.253948i	$0.0817293\pi$
$257$	11.2785	+	19.5350i	0.703535	+	1.21856i	−0.263683	+	0.964609i	$0.584937\pi$
$258$	14.3180			0.891401
$259$	0.822431	−	0.382139i	0.0511034	−	0.0237449i
$260$	4.08612			0.253410
$261$	−1.87786	−	3.25255i	−0.116237	−	0.201328i
$262$	1.32978	−	2.30326i	0.0821544	−	0.142296i
$263$	−12.8779	+	22.3052i	−0.794087	+	1.37540i	0.129330	+	0.991602i	$0.458717\pi$
$263$	−12.8779	+	22.3052i	−0.794087	+	1.37540i	−0.923417	+	0.383798i	$0.874616\pi$
$264$	−1.50796	−	2.61187i	−0.0928087	−	0.160749i
$265$	−50.6929			−3.11404
$266$	−21.1575	−	14.8578i	−1.29725	−	0.910990i
$267$	−12.3553			−0.756131
$268$	−0.441865	−	0.765332i	−0.0269912	−	0.0467501i
$269$	10.3481	−	17.9234i	0.630935	−	1.09281i	−0.356426	−	0.934323i	$-0.616005\pi$
$269$	10.3481	−	17.9234i	0.630935	−	1.09281i	0.987361	−	0.158488i	$-0.0506618\pi$
$270$	−2.52153	+	4.36742i	−0.153455	+	0.265793i
$271$	−1.53390	−	2.65680i	−0.0931779	−	0.161389i	0.815669	−	0.578519i	$-0.196369\pi$
$271$	−1.53390	−	2.65680i	−0.0931779	−	0.161389i	−0.908847	+	0.417130i	$0.863036\pi$
$272$	−12.7012			−0.770122
$273$	6.58882	+	4.62697i	0.398774	+	0.280037i
$274$	−5.38499			−0.325319
$275$	5.17316	+	8.96018i	0.311953	+	0.540319i
$276$	0.773186	−	1.33920i	0.0465403	−	0.0806102i
$277$	3.34277	−	5.78984i	0.200847	−	0.347878i	−0.747954	−	0.663750i	$-0.768964\pi$
$277$	3.34277	−	5.78984i	0.200847	−	0.347878i	0.948802	+	0.315872i	$0.102297\pi$
$278$	−2.32413	−	4.02552i	−0.139392	−	0.241435i
$279$	−6.74335			−0.403714
$280$	−28.3481	+	13.1718i	−1.69412	+	0.787166i
$281$	3.11286			0.185698			0.0928489	−	0.995680i	$-0.470403\pi$
$281$	3.11286			0.185698			0.0928489	+	0.995680i	$0.470403\pi$
$282$	−1.06671	−	1.84759i	−0.0635215	−	0.110023i
$283$	11.1799	−	19.3642i	0.664578	−	1.15108i	−0.314822	−	0.949151i	$-0.601945\pi$
$283$	11.1799	−	19.3642i	0.664578	−	1.15108i	0.979400	−	0.201932i	$-0.0647220\pi$
$284$	−0.857525	+	1.48528i	−0.0508848	+	0.0881350i
$285$	−14.8679	−	25.7519i	−0.880695	−	1.52541i
$286$	3.91744			0.231643
$287$	0.653825	−	7.35746i	0.0385941	−	0.434297i
$288$	1.91627			0.112917
$289$	0.608157	+	1.05336i	0.0357739	+	0.0619623i
$290$	−9.47016	+	16.4028i	−0.556107	+	0.963206i
$291$	6.58434	−	11.4044i	0.385981	−	0.668538i
$292$	−1.49747	−	2.59370i	−0.0876328	−	0.151785i
$293$	10.6291			0.620958			0.310479	−	0.950580i	$-0.399511\pi$
$293$	10.6291			0.620958			0.310479	+	0.950580i	$0.399511\pi$
$294$	−8.87014	−	1.58905i	−0.517317	−	0.0926752i
$295$	−14.3409			−0.834960
$296$	0.516879	+	0.895261i	0.0300430	+	0.0520360i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	−8.57314	+	14.8491i	−0.496628	+	0.860186i
$299$	6.86430	+	11.8893i	0.396972	+	0.687576i
$300$	−3.54637			−0.204750
$301$	−2.60475	+	29.3111i	−0.150135	+	1.68946i
$302$	−9.06697			−0.521746
$303$	−3.53509	−	6.12296i	−0.203086	−	0.351755i
$304$	12.1335	−	21.0158i	0.695903	−	1.20534i
$305$	0.917438	−	1.58905i	0.0525324	−	0.0909887i
$306$	−2.55721	−	4.42921i	−0.146186	−	0.253201i
$307$	−18.5229			−1.05716			−0.528580	−	0.848883i	$-0.677275\pi$
$307$	−18.5229			−1.05716			−0.528580	+	0.848883i	$0.677275\pi$
$308$	0.822431	−	0.382139i	0.0468623	−	0.0217744i
$309$	2.33736			0.132968
$310$	17.0036	+	29.4510i	0.965737	+	1.67271i
$311$	9.92192	−	17.1853i	0.562620	−	0.974487i	−0.434646	−	0.900601i	$-0.643127\pi$
$311$	9.92192	−	17.1853i	0.562620	−	0.974487i	0.997267	−	0.0738860i	$-0.0235401\pi$
$312$	−4.58882	+	7.94807i	−0.259791	+	0.449971i
$313$	10.5572	+	18.2856i	0.596729	+	1.03356i	0.993300	+	0.115561i	$0.0368665\pi$
$313$	10.5572	+	18.2856i	0.596729	+	1.03356i	−0.396572	+	0.918004i	$0.629800\pi$
$314$	16.4211			0.926696
$315$	−8.48203	−	5.95647i	−0.477908	−	0.335609i
$316$	−0.246664			−0.0138759
$317$	7.90329	+	13.6889i	0.443893	+	0.768845i	0.997974	−	0.0636174i	$-0.0202637\pi$
$317$	7.90329	+	13.6889i	0.443893	+	0.768845i	−0.554081	+	0.832462i	$0.686930\pi$
$318$	8.32927	−	14.4267i	0.467083	−	0.809011i
$319$	1.87786	−	3.25255i	0.105140	−	0.182108i
$320$	−17.3559	−	30.0613i	−0.970224	−	1.68048i
$321$	−10.8532			−0.605766
$322$	−12.5749	−	8.83068i	−0.700772	−	0.492114i
$323$	30.1565			1.67795
$324$	0.171383	+	0.296844i	0.00952129	+	0.0164914i
$325$	15.7422	−	27.2663i	0.873222	−	1.51246i
$326$	−7.34048	+	12.7141i	−0.406551	+	0.704168i
$327$	1.09620	+	1.89868i	0.0606200	+	0.104997i
$328$	8.41992			0.464912
$329$	3.97635	−	1.84759i	0.219223	−	0.101861i
$330$	−5.04306			−0.277611
$331$	4.58163	+	7.93562i	0.251829	+	0.436181i	0.964030	−	0.265795i	$-0.0856345\pi$
$331$	4.58163	+	7.93562i	0.251829	+	0.436181i	−0.712200	+	0.701976i	$0.752301\pi$
$332$	−1.98763	+	3.44267i	−0.109085	+	0.188941i
$333$	−0.171383	+	0.296844i	−0.00939174	+	0.0162670i
$334$	−7.79537	−	13.5020i	−0.426544	−	0.738796i
$335$	−10.1000			−0.551824
$336$	0.748711	−	8.42521i	0.0408455	−	0.459633i
$337$	−12.7174			−0.692760			−0.346380	−	0.938094i	$-0.612589\pi$
$337$	−12.7174			−0.692760			−0.346380	+	0.938094i	$0.612589\pi$
$338$	2.40719	+	4.16937i	0.130934	+	0.226784i
$339$	5.82073	−	10.0818i	0.316138	−	0.547568i
$340$	2.66732	−	4.61993i	0.144656	−	0.250551i
$341$	−3.37168	−	5.83991i	−0.182586	−	0.316249i
$342$	9.77165			0.528390
$343$	4.86668	−	17.8694i	0.262776	−	0.964857i
$344$	−33.5438			−1.80856
$345$	−8.83665	−	15.3055i	−0.475749	−	0.824022i
$346$	−2.34454	+	4.06087i	−0.126043	+	0.218314i
$347$	−1.27370	+	2.20611i	−0.0683756	+	0.118430i	−0.898186	−	0.439615i	$-0.855115\pi$
$347$	−1.27370	+	2.20611i	−0.0683756	+	0.118430i	0.829811	+	0.558045i	$0.188448\pi$
$348$	0.643668	+	1.11487i	0.0345042	+	0.0597631i
$349$	−25.0183			−1.33920			−0.669600	−	0.742722i	$-0.733534\pi$
$349$	−25.0183			−1.33920			−0.669600	+	0.742722i	$0.733534\pi$
$350$	−3.11927	+	35.1009i	−0.166732	+	1.87622i
$351$	−3.04306			−0.162426
$352$	0.958135	+	1.65954i	0.0510688	+	0.0884537i
$353$	5.71444	−	9.89770i	0.304149	−	0.526802i	−0.672922	−	0.739713i	$-0.734961\pi$
$353$	5.71444	−	9.89770i	0.304149	−	0.526802i	0.977072	+	0.212911i	$0.0682946\pi$
$354$	2.35633	−	4.08129i	0.125238	−	0.216918i
$355$	9.80056	+	16.9751i	0.520160	+	0.900943i
$356$	4.23498			0.224453
$357$	9.53246	−	4.42921i	0.504511	−	0.234419i
$358$	12.7786			0.675371
$359$	−14.9811	−	25.9480i	−0.790672	−	1.36948i	−0.925551	−	0.378622i	$-0.876398\pi$
$359$	−14.9811	−	25.9480i	−0.790672	−	1.36948i	0.134879	−	0.990862i	$-0.456935\pi$
$360$	5.90735	−	10.2318i	0.311345	−	0.539265i
$361$	−19.3086	+	33.4435i	−1.01624	+	1.76018i
$362$	5.19581	+	8.99941i	0.273086	+	0.472998i
$363$	1.00000			0.0524864
$364$	−2.25843	−	1.58597i	−0.118374	−	0.0831275i
$365$	−34.2288			−1.79162
$366$	0.301486	+	0.522188i	0.0157589	+	0.0272952i
$367$	7.23130	−	12.5250i	0.377471	−	0.653798i	−0.613223	−	0.789910i	$-0.710127\pi$
$367$	7.23130	−	12.5250i	0.377471	−	0.653798i	0.990693	+	0.136112i	$0.0434606\pi$
$368$	7.21150	−	12.4907i	0.375925	−	0.651122i
$369$	1.39591	+	2.41779i	0.0726681	+	0.125865i
$370$	1.72859			0.0898652
$371$	28.0184	+	19.6758i	1.45464	+	1.02152i
$372$	2.31139			0.119840
$373$	−15.0726	−	26.1066i	−0.780431	−	1.35175i	−0.931691	−	0.363252i	$-0.881666\pi$
$373$	−15.0726	−	26.1066i	−0.780431	−	1.35175i	0.151260	−	0.988494i	$-0.451667\pi$
$374$	2.55721	−	4.42921i	0.132230	−	0.229029i
$375$	−10.4719	+	18.1379i	−0.540769	+	0.936639i
$376$	2.49905	+	4.32848i	0.128879	+	0.223224i
$377$	−11.4289			−0.588617
$378$	3.08882	−	1.43521i	0.158872	−	0.0738190i
$379$	−11.7452			−0.603311			−0.301655	−	0.953417i	$-0.597539\pi$
$379$	−11.7452			−0.603311			−0.301655	+	0.953417i	$0.597539\pi$
$380$	5.09620	+	8.82688i	0.261430	+	0.452809i
$381$	−2.70918	+	4.69244i	−0.138796	+	0.240401i
$382$	−3.59401	+	6.22500i	−0.183885	+	0.318499i
$383$	−13.9685	−	24.1942i	−0.713759	−	1.23627i	−0.963436	−	0.267937i	$-0.913658\pi$
$383$	−13.9685	−	24.1942i	−0.713759	−	1.23627i	0.249678	−	0.968329i	$-0.419675\pi$
$384$	7.57434			0.386526
$385$	0.917438	−	10.3239i	0.0467570	−	0.526154i
$386$	14.3329			0.729524
$387$	−5.56111	−	9.63212i	−0.282687	−	0.489628i
$388$	−2.25689	+	3.90905i	−0.114576	+	0.198452i
$389$	7.87896	−	13.6468i	0.399479	−	0.691918i	−0.594183	−	0.804330i	$-0.702524\pi$
$389$	7.87896	−	13.6468i	0.399479	−	0.691918i	0.993662	+	0.112412i	$0.0358577\pi$
$390$	7.67316	+	13.2903i	0.388546	+	0.672981i
$391$	17.9234			0.906424
$392$	20.7807	+	3.72277i	1.04958	+	0.188028i
$393$	−2.06595			−0.104213
$394$	0.414828	+	0.718503i	0.0208987	+	0.0361977i
$395$	−1.40955	+	2.44141i	−0.0709221	+	0.122841i
$396$	−0.171383	+	0.296844i	−0.00861233	+	0.0149170i
$397$	−6.40446	−	11.0928i	−0.321430	−	0.556734i	0.659353	−	0.751834i	$-0.270830\pi$
$397$	−6.40446	−	11.0928i	−0.321430	−	0.556734i	−0.980783	+	0.195100i	$0.937497\pi$
$398$	−32.4865			−1.62840
$399$	−1.77767	+	20.0040i	−0.0889947	+	1.00145i
$400$	−33.0770			−1.65385
$401$	5.49033	+	9.50953i	0.274174	+	0.474883i	0.969926	−	0.243398i	$-0.0782622\pi$
$401$	5.49033	+	9.50953i	0.274174	+	0.474883i	−0.695752	+	0.718282i	$0.744929\pi$
$402$	1.65952	−	2.87438i	0.0827694	−	0.143361i
$403$	−10.2602	+	17.7712i	−0.511097	+	0.885246i
$404$	1.21171	+	2.09875i	0.0602849	+	0.104417i
$405$	3.91744			0.194659
$406$	11.6008	−	5.39024i	0.575736	−	0.267513i
$407$	−0.342766			−0.0169903
$408$	5.99094	+	10.3766i	0.296596	+	0.513719i
$409$	−9.01281	+	15.6106i	−0.445655	+	0.771896i	−0.998098	−	0.0616543i	$-0.980362\pi$
$409$	−9.01281	+	15.6106i	−0.445655	+	0.771896i	0.552443	+	0.833551i	$0.313696\pi$
$410$	7.03965	−	12.1930i	0.347664	−	0.602171i
$411$	2.09153	+	3.62263i	0.103167	+	0.178691i
$412$	−0.801168			−0.0394707
$413$	7.92633	+	5.56623i	0.390029	+	0.273896i
$414$	5.80775			0.285435
$415$	22.7164	+	39.3459i	1.11510	+	1.93141i
$416$	2.91566	−	5.05007i	0.142952	−	0.247600i
$417$	−1.80538	+	3.12702i	−0.0884100	+	0.153131i
$418$	4.88582	+	8.46250i	0.238974	+	0.413914i
$419$	11.8542			0.579116			0.289558	−	0.957160i	$-0.406492\pi$
$419$	11.8542			0.579116			0.289558	+	0.957160i	$0.406492\pi$
$420$	2.90735	+	2.04168i	0.141864	+	0.0996236i
$421$	26.4890			1.29100			0.645498	−	0.763762i	$-0.276650\pi$
$421$	26.4890			1.29100			0.645498	+	0.763762i	$0.276650\pi$
$422$	11.3515	+	19.6614i	0.552583	+	0.957101i
$423$	−0.828617	+	1.43521i	−0.0402887	+	0.0697821i
$424$	−19.5135	+	33.7985i	−0.947661	+	1.64140i
$425$	−20.5523	−	35.5976i	−0.996932	−	1.72674i
$426$	−6.44126			−0.312080
$427$	−1.12384	+	0.522188i	−0.0543866	+	0.0252705i
$428$	3.72011			0.179818
$429$	−1.52153	−	2.63537i	−0.0734601	−	0.127237i
$430$	−28.0450	+	48.5753i	−1.35245	+	2.34251i
$431$	1.08841	−	1.88517i	0.0524266	−	0.0908056i	−0.838621	−	0.544715i	$-0.816638\pi$
$431$	1.08841	−	1.88517i	0.0524266	−	0.0908056i	0.891048	+	0.453910i	$0.149971\pi$
$432$	1.59849	+	2.76866i	0.0769073	+	0.133207i
$433$	−16.4831			−0.792129			−0.396065	−	0.918223i	$-0.629624\pi$
$433$	−16.4831			−0.792129			−0.396065	+	0.918223i	$0.629624\pi$
$434$	2.03302	−	22.8775i	0.0975882	−	1.09815i
$435$	14.7128			0.705425
$436$	−0.375741	−	0.650802i	−0.0179947	−	0.0311678i
$437$	−17.1223	+	29.6567i	−0.819070	+	1.41867i
$438$	5.62408	−	9.74120i	0.268729	−	0.465453i
$439$	0.376500	+	0.652117i	0.0179694	+	0.0311239i	0.874870	−	0.484357i	$-0.160947\pi$
$439$	0.376500	+	0.652117i	0.0179694	+	0.0311239i	−0.856901	+	0.515481i	$0.827613\pi$
$440$	11.8147			0.563244
$441$	2.37616	+	6.58437i	0.113150	+	0.313541i
$442$	−15.5635			−0.740279
$443$	−20.0309	−	34.6946i	−0.951698	−	1.64839i	−0.741750	−	0.670677i	$-0.766004\pi$
$443$	−20.0309	−	34.6946i	−0.951698	−	1.64839i	−0.209949	−	0.977712i	$-0.567330\pi$
$444$	0.0587444	−	0.101748i	0.00278789	−	0.00482876i
$445$	24.2005	−	41.9166i	1.14722	−	1.98704i
$446$	−10.6754	−	18.4904i	−0.505497	−	0.875547i
$447$	13.3192			0.629976
$448$	−2.07515	+	23.3516i	−0.0980416	+	1.10326i
$449$	−7.71924			−0.364294			−0.182147	−	0.983271i	$-0.558305\pi$
$449$	−7.71924			−0.364294			−0.182147	+	0.983271i	$0.558305\pi$
$450$	−6.65960	−	11.5348i	−0.313936	−	0.543754i
$451$	−1.39591	+	2.41779i	−0.0657308	+	0.113849i
$452$	−1.99515	+	3.45570i	−0.0938440	+	0.162543i
$453$	3.52160	+	6.09959i	0.165459	+	0.286584i
$454$	−3.02289			−0.141871
$455$	−28.6031	+	13.2903i	−1.34093	+	0.623059i
$456$	−22.8927			−1.07205
$457$	−13.1823	−	22.8324i	−0.616643	−	1.06806i	−0.990094	−	0.140407i	$-0.955159\pi$
$457$	−13.1823	−	22.8324i	−0.616643	−	1.06806i	0.373451	−	0.927650i	$-0.378174\pi$
$458$	11.2322	−	19.4548i	0.524848	−	0.909064i
$459$	−1.98643	+	3.44061i	−0.0927188	+	0.160594i
$460$	3.02891	+	5.24622i	0.141224	+	0.244606i
$461$	12.4685			0.580718			0.290359	−	0.956918i	$-0.406225\pi$
$461$	12.4685			0.580718			0.290359	+	0.956918i	$0.406225\pi$
$462$	2.78734	+	1.95739i	0.129679	+	0.0910662i
$463$	37.7630			1.75499			0.877497	−	0.479582i	$-0.159212\pi$
$463$	37.7630			1.75499			0.877497	+	0.479582i	$0.159212\pi$
$464$	6.00348	+	10.3983i	0.278705	+	0.482731i
$465$	13.2083	−	22.8775i	0.612522	−	1.06092i
$466$	3.59849	−	6.23277i	0.166697	−	0.288727i
$467$	−11.0104	−	19.0706i	−0.509502	−	0.882483i	−0.999939	−	0.0110065i	$-0.996496\pi$
$467$	−11.0104	−	19.0706i	−0.509502	−	0.882483i	0.490438	−	0.871476i	$-0.336837\pi$
$468$	1.04306			0.0482154
$469$	5.58237	+	3.92019i	0.257770	+	0.181018i
$470$	8.35753			0.385504
$471$	−6.37793	−	11.0469i	−0.293880	−	0.509015i
$472$	−5.52034	+	9.56150i	−0.254094	+	0.440104i
$473$	5.56111	−	9.63212i	0.255700	−	0.442885i
$474$	−0.463201	−	0.802288i	−0.0212755	−	0.0368503i
$475$	78.5348			3.60342
$476$	−3.26741	+	1.51819i	−0.149761	+	0.0695860i
$477$	−12.9403			−0.592497
$478$	−11.4668	−	19.8610i	−0.524477	−	0.908421i
$479$	4.72401	−	8.18223i	0.215846	−	0.373856i	−0.737688	−	0.675142i	$-0.764082\pi$
$479$	4.72401	−	8.18223i	0.215846	−	0.373856i	0.953534	+	0.301286i	$0.0974158\pi$
$480$	−3.75343	+	6.50114i	−0.171320	+	0.296735i
$481$	0.521529	+	0.903315i	0.0237797	+	0.0411876i
$482$	3.84169			0.174984
$483$	−1.05655	+	11.8893i	−0.0480747	+	0.540982i
$484$	−0.342766			−0.0155803
$485$	25.7937	+	44.6761i	1.17123	+	2.02864i
$486$	−0.643668	+	1.11487i	−0.0291974	+	0.0505713i
$487$	−20.1170	+	34.8437i	−0.911589	+	1.57892i	−0.0997702	+	0.995011i	$0.531811\pi$
$487$	−20.1170	+	34.8437i	−0.911589	+	1.57892i	−0.811819	+	0.583909i	$0.801523\pi$
$488$	−0.706310	−	1.22337i	−0.0319732	−	0.0553791i
$489$	11.4041			0.515713
$490$	22.7651	−	26.9803i	1.02842	−	1.21885i
$491$	20.2964			0.915966			0.457983	−	0.888961i	$-0.348572\pi$
$491$	20.2964			0.915966			0.457983	+	0.888961i	$0.348572\pi$
$492$	−0.478471	−	0.828736i	−0.0215711	−	0.0373623i
$493$	−7.46050	+	12.9220i	−0.336004	+	0.581976i
$494$	14.8679	−	25.7519i	0.668936	−	1.15863i
$495$	1.95872	+	3.39260i	0.0880379	+	0.152486i
$496$	21.5583			0.967998
$497$	1.17180	−	13.1862i	0.0525624	−	0.591482i
$498$	−14.9300			−0.669027
$499$	−18.1477	−	31.4328i	−0.812403	−	1.40712i	−0.911178	−	0.412014i	$-0.864826\pi$
$499$	−18.1477	−	31.4328i	−0.812403	−	1.40712i	0.0987744	−	0.995110i	$-0.468508\pi$
$500$	3.58943	−	6.21708i	0.160524	−	0.278036i
$501$	−6.05543	+	10.4883i	−0.270537	+	0.468583i
$502$	−16.1450	−	27.9640i	−0.720588	−	1.24809i
$503$	−27.6923			−1.23474			−0.617368	−	0.786674i	$-0.711801\pi$
$503$	−27.6923			−1.23474			−0.617368	+	0.786674i	$0.711801\pi$
$504$	−7.23639	+	3.36235i	−0.322334	+	0.149771i
$505$	27.6970			1.23250
$506$	2.90387	+	5.02965i	0.129093	+	0.223595i
$507$	1.86990	−	3.23876i	0.0830451	−	0.143838i
$508$	0.928617	−	1.60841i	0.0412007	−	0.0713617i
$509$	−4.54399	−	7.87041i	−0.201409	−	0.348850i	0.747574	−	0.664179i	$-0.231219\pi$
$509$	−4.54399	−	7.87041i	−0.201409	−	0.348850i	−0.948983	+	0.315329i	$0.897885\pi$
$510$	20.0354			0.887183
$511$	18.9185	+	13.2855i	0.836906	+	0.587714i
$512$	−25.4100			−1.12297
$513$	−3.79530	−	6.57365i	−0.167567	−	0.290234i
$514$	14.5192	−	25.1481i	0.640416	−	1.10923i
$515$	−4.57823	+	7.92972i	−0.201741	+	0.349425i
$516$	1.90616	+	3.30157i	0.0839140	+	0.145343i
$517$	−1.65723			−0.0728850
$518$	−0.955405	−	0.670929i	−0.0419781	−	0.0294789i
$519$	3.64247			0.159887
$520$	−17.9764	−	31.1361i	−0.788318	−	1.36541i
$521$	−19.4255	+	33.6459i	−0.851046	+	1.47405i	0.0292202	+	0.999573i	$0.490698\pi$
$521$	−19.4255	+	33.6459i	−0.851046	+	1.47405i	−0.880266	+	0.474481i	$0.842636\pi$
$522$	−2.41744	+	4.18713i	−0.105808	+	0.183266i
$523$	10.7500	+	18.6196i	0.470066	+	0.814178i	0.999414	−	0.0342267i	$-0.0108968\pi$
$523$	10.7500	+	18.6196i	0.470066	+	0.814178i	−0.529348	+	0.848405i	$0.677564\pi$
$524$	0.708138			0.0309352
$525$	24.8249	−	11.5348i	1.08345	−	0.503418i
$526$	33.1565			1.44569
$527$	13.3952	+	23.2012i	0.583505	+	1.01066i
$528$	−1.59849	+	2.76866i	−0.0695653	+	0.120491i
$529$	1.32343	−	2.29225i	0.0575405	−	0.0996630i
$530$	32.6294	+	56.5158i	1.41733	+	2.45489i
$531$	−3.66079			−0.158865
$532$	0.609325	−	6.85670i	0.0264176	−	0.297276i
$533$	8.49566			0.367988
$534$	7.95270	+	13.7745i	0.344147	+	0.596080i
$535$	21.2584	−	36.8205i	0.919079	−	1.59189i
$536$	−3.88787	+	6.73399i	−0.167930	+	0.290864i
$537$	−4.96320	−	8.59652i	−0.214178	−	0.370967i
$538$	−26.6430			−1.14866
$539$	−4.51415	+	5.35000i	−0.194438	+	0.230441i
$540$	−1.34277			−0.0577835
$541$	14.9470	+	25.8890i	0.642622	+	1.11305i	0.984845	+	0.173435i	$0.0554867\pi$
$541$	14.9470	+	25.8890i	0.642622	+	1.11305i	−0.342223	+	0.939619i	$0.611180\pi$
$542$	−1.97465	+	3.42019i	−0.0848183	+	0.146910i
$543$	4.03610	−	6.99072i	0.173205	−	0.300001i
$544$	−3.80654	−	6.59313i	−0.163204	−	0.282678i
$545$	−8.58860			−0.367895
$546$	0.917438	−	10.3239i	0.0392627	−	0.441821i
$547$	−31.9072			−1.36425			−0.682127	−	0.731234i	$-0.738945\pi$
$547$	−31.9072			−1.36425			−0.682127	+	0.731234i	$0.738945\pi$
$548$	−0.716905	−	1.24172i	−0.0306247	−	0.0530435i
$549$	0.234193	−	0.405635i	0.00999513	−	0.0173121i
$550$	6.65960	−	11.5348i	0.283966	−	0.491844i
$551$	−14.2541	−	24.6888i	−0.607245	−	1.05178i
$552$	−13.6062			−0.579118
$553$	1.72667	−	0.802288i	0.0734254	−	0.0341167i
$554$	−8.60653			−0.365656
$555$	−0.671383	−	1.16287i	−0.0284986	−	0.0493611i
$556$	0.618825	−	1.07184i	0.0262440	−	0.0454560i
$557$	7.30446	−	12.6517i	0.309500	−	0.536069i	−0.668753	−	0.743484i	$-0.733172\pi$
$557$	7.30446	−	12.6517i	0.309500	−	0.536069i	0.978253	+	0.207415i	$0.0665051\pi$
$558$	4.34048	+	7.51793i	0.183747	+	0.318259i
$559$	−33.8455			−1.43151
$560$	27.1169	+	19.0427i	1.14590	+	0.804701i
$561$	−3.97287			−0.167735
$562$	−2.00365	−	3.47042i	−0.0845189	−	0.146391i
$563$	4.24116	−	7.34590i	0.178743	−	0.309593i	−0.762707	−	0.646744i	$-0.776130\pi$
$563$	4.24116	−	7.34590i	0.178743	−	0.309593i	0.941450	+	0.337151i	$0.109463\pi$
$564$	0.284022	−	0.491941i	0.0119595	−	0.0207144i
$565$	22.8023	+	39.4948i	0.959301	+	1.66156i
$566$	−28.7847			−1.20991
$567$	−2.16520	−	1.52050i	−0.0909297	−	0.0638550i
$568$	15.0904			0.633177
$569$	−10.3529	−	17.9318i	−0.434017	−	0.751740i	0.563198	−	0.826322i	$-0.309571\pi$
$569$	−10.3529	−	17.9318i	−0.434017	−	0.751740i	−0.997215	+	0.0745824i	$0.976238\pi$
$570$	−19.1399	+	33.1513i	−0.801683	+	1.38856i
$571$	−0.504409	+	0.873661i	−0.0211088	+	0.0365616i	−0.876387	−	0.481608i	$-0.840053\pi$
$571$	−0.504409	+	0.873661i	−0.0211088	+	0.0365616i	0.855278	+	0.518169i	$0.173386\pi$
$572$	0.521529	+	0.903315i	0.0218062	+	0.0377695i
$573$	5.58364			0.233260
$574$	−8.62343	+	4.00683i	−0.359935	+	0.167242i
$575$	46.6769			1.94656
$576$	−4.43042	−	7.67371i	−0.184601	−	0.319738i
$577$	19.1925	−	33.2425i	0.798996	−	1.38390i	−0.121274	−	0.992619i	$-0.538698\pi$
$577$	19.1925	−	33.2425i	0.798996	−	1.38390i	0.920270	−	0.391283i	$-0.127969\pi$
$578$	0.782902	−	1.35603i	0.0325644	−	0.0564033i
$579$	−5.56688	−	9.64211i	−0.231351	−	0.400712i
$580$	−5.04306			−0.209402
$581$	2.71607	−	30.5638i	0.112682	−	1.26800i
$582$	−16.9525			−0.702704
$583$	−6.47016	−	11.2067i	−0.267967	−	0.464132i
$584$	−13.1759	+	22.8214i	−0.545223	+	0.944354i
$585$	5.96050	−	10.3239i	0.246436	−	0.426840i
$586$	−6.84160	−	11.8500i	−0.282624	−	0.489519i
$587$	3.95733			0.163336			0.0816682	−	0.996660i	$-0.473975\pi$
$587$	3.95733			0.163336			0.0816682	+	0.996660i	$0.473975\pi$
$588$	−0.814467	−	2.25690i	−0.0335881	−	0.0930730i
$589$	−51.1861			−2.10909
$590$	9.23079	+	15.9882i	0.380025	+	0.658223i
$591$	0.322238	−	0.558132i	0.0132551	−	0.0229585i
$592$	0.547908	−	0.949005i	0.0225189	−	0.0390039i
$593$	−4.25131	−	7.36349i	−0.174581	−	0.302382i	0.765435	−	0.643513i	$-0.222524\pi$
$593$	−4.25131	−	7.36349i	−0.174581	−	0.302382i	−0.940016	+	0.341130i	$0.889190\pi$
$594$	−1.28734			−0.0528200
$595$	−3.64486	+	41.0154i	−0.149425	+	1.68147i
$596$	−4.56537			−0.187005
$597$	12.6177	+	21.8545i	0.516409	+	0.894447i
$598$	8.83665	−	15.3055i	0.361358	−	0.625890i
$599$	3.48076	−	6.02885i	0.142220	−	0.246332i	−0.786112	−	0.618084i	$-0.787909\pi$
$599$	3.48076	−	6.02885i	0.142220	−	0.246332i	0.928332	+	0.371751i	$0.121243\pi$
$600$	15.6019	+	27.0232i	0.636944	+	1.10322i
$601$	31.8738			1.30016			0.650081	−	0.759865i	$-0.274735\pi$
$601$	31.8738			1.30016			0.650081	+	0.759865i	$0.274735\pi$
$602$	34.3545	−	15.9627i	1.40019	−	0.650590i
$603$	−2.57823			−0.104994
$604$	−1.20709	−	2.09074i	−0.0491157	−	0.0850709i
$605$	−1.95872	+	3.39260i	−0.0796333	+	0.137929i
$606$	−4.55085	+	7.88231i	−0.184866	+	0.320197i
$607$	−1.67204	−	2.89606i	−0.0678660	−	0.117547i	0.830096	−	0.557621i	$-0.188286\pi$
$607$	−1.67204	−	2.89606i	−0.0678660	−	0.117547i	−0.897962	+	0.440074i	$0.854952\pi$
$608$	14.5456			0.589903
$609$	−8.13188	−	5.71058i	−0.329520	−	0.231404i
$610$	−2.36210			−0.0956387
$611$	2.52153	+	4.36742i	0.102010	+	0.176687i
$612$	0.680883	−	1.17932i	0.0275231	−	0.0476714i
$613$	2.11325	−	3.66025i	0.0853533	−	0.147836i	−0.820188	−	0.572093i	$-0.806131\pi$
$613$	2.11325	−	3.66025i	0.0853533	−	0.147836i	0.905542	+	0.424257i	$0.139465\pi$
$614$	11.9226	+	20.6506i	0.481158	+	0.833390i
$615$	−10.9368			−0.441013
$616$	−6.53008	−	4.58572i	−0.263104	−	0.184764i
$617$	3.91266			0.157518			0.0787590	−	0.996894i	$-0.474904\pi$
$617$	3.91266			0.157518			0.0787590	+	0.996894i	$0.474904\pi$
$618$	−1.50448	−	2.60584i	−0.0605191	−	0.104822i
$619$	−0.869194	+	1.50549i	−0.0349359	+	0.0605107i	−0.882965	−	0.469439i	$-0.844456\pi$
$619$	−0.869194	+	1.50549i	−0.0349359	+	0.0605107i	0.848029	+	0.529950i	$0.177789\pi$
$620$	−4.52737	+	7.84164i	−0.181824	+	0.314928i
$621$	−2.25572	−	3.90703i	−0.0905190	−	0.156784i
$622$	−25.5457			−1.02429
$623$	−29.6452	+	13.7745i	−1.18771	+	0.551863i
$624$	9.72859			0.389455
$625$	−15.1574	−	26.2534i	−0.606295	−	1.05013i
$626$	13.5907	−	23.5397i	0.543193	−	0.940837i
$627$	3.79530	−	6.57365i	0.151570	−	0.262526i
$628$	2.18614	+	3.78651i	0.0872366	+	0.151098i
$629$	1.36177			0.0542972
$630$	−1.18105	+	13.2903i	−0.0470542	+	0.529498i
$631$	−13.3994			−0.533420			−0.266710	−	0.963777i	$-0.585937\pi$
$631$	−13.3994			−0.533420			−0.266710	+	0.963777i	$0.585937\pi$
$632$	1.08517	+	1.87957i	0.0431658	+	0.0747654i
$633$	8.81783	−	15.2729i	0.350477	−	0.607044i
$634$	10.1742	−	17.6222i	0.404069	−	0.699867i
$635$	−10.6131	−	18.3824i	−0.421166	−	0.729481i
$636$	4.43551			0.175879
$637$	20.9676	+	3.75626i	0.830767	+	0.148829i
$638$	−4.83488			−0.191415
$639$	2.50178	+	4.33321i	0.0989688	+	0.171419i
$640$	−14.8360	+	25.6967i	−0.586444	+	1.01575i
$641$	−5.39101	+	9.33750i	−0.212932	+	0.368809i	−0.952631	−	0.304129i	$-0.901635\pi$
$641$	−5.39101	+	9.33750i	−0.212932	+	0.368809i	0.739699	+	0.672938i	$0.234968\pi$
$642$	6.98585	+	12.0998i	0.275710	+	0.477543i
$643$	30.1180			1.18774			0.593868	−	0.804562i	$-0.297600\pi$
$643$	30.1180			1.18774			0.593868	+	0.804562i	$0.297600\pi$
$644$	0.362150	−	4.07526i	0.0142707	−	0.160588i
$645$	43.5706			1.71559
$646$	−19.4107	−	33.6204i	−0.763705	−	1.32278i
$647$	6.32343	−	10.9525i	0.248600	−	0.430587i	−0.714538	−	0.699597i	$-0.753363\pi$
$647$	6.32343	−	10.9525i	0.248600	−	0.430587i	0.963138	+	0.269009i	$0.0866963\pi$
$648$	1.50796	−	2.61187i	0.0592384	−	0.102604i
$649$	−1.83039	−	3.17034i	−0.0718493	−	0.124447i
$650$	−40.5311			−1.58976
$651$	−16.1799	+	7.51793i	−0.634141	+	0.294651i
$652$	−3.90896			−0.153087
$653$	−0.751146	−	1.30102i	−0.0293946	−	0.0509130i	0.850954	−	0.525240i	$-0.176025\pi$
$653$	−0.751146	−	1.30102i	−0.0293946	−	0.0509130i	−0.880348	+	0.474327i	$0.842691\pi$
$654$	1.41118	−	2.44423i	0.0551815	−	0.0955771i
$655$	4.04661	−	7.00894i	0.158114	−	0.273862i
$656$	−4.46269	−	7.72961i	−0.174239	−	0.301790i
$657$	−8.73756			−0.340885
$658$	−4.61927	−	3.24386i	−0.180078	−	0.126459i
$659$	−14.4079			−0.561251			−0.280626	−	0.959817i	$-0.590542\pi$
$659$	−14.4079			−0.561251			−0.280626	+	0.959817i	$0.590542\pi$
$660$	−0.671383	−	1.16287i	−0.0261336	−	0.0452646i
$661$	8.39269	−	14.5366i	0.326438	−	0.565407i	−0.655364	−	0.755313i	$-0.727485\pi$
$661$	8.39269	−	14.5366i	0.326438	−	0.565407i	0.981802	+	0.189906i	$0.0608182\pi$
$662$	5.89810	−	10.2158i	0.229236	−	0.397049i
$663$	6.04484	+	10.4700i	0.234762	+	0.406620i
$664$	34.9774			1.35739
$665$	−64.3837	−	45.2131i	−2.49669	−	1.75329i
$666$	0.441256			0.0170983
$667$	−8.47187	−	14.6737i	−0.328032	−	0.568168i
$668$	2.07560	−	3.59504i	0.0803073	−	0.139096i
$669$	−8.29267	+	14.3633i	−0.320613	+	0.555318i
$670$	6.50107	+	11.2602i	0.251158	+	0.435019i
$671$	0.468387			0.0180819
$672$	4.59788	−	2.13638i	0.177367	−	0.0824128i
$673$	−48.1663			−1.85667			−0.928337	−	0.371740i	$-0.878761\pi$
$673$	−48.1663			−1.85667			−0.928337	+	0.371740i	$0.878761\pi$
$674$	8.18577	+	14.1782i	0.315304	+	0.546123i
$675$	−5.17316	+	8.96018i	−0.199115	+	0.344877i
$676$	−0.640938	+	1.11014i	−0.0246515	+	0.0426976i
$677$	5.85741	+	10.1453i	0.225118	+	0.389916i	0.956355	−	0.292207i	$-0.0943898\pi$
$677$	5.85741	+	10.1453i	0.225118	+	0.389916i	−0.731237	+	0.682124i	$0.761056\pi$
$678$	−14.9865			−0.575552
$679$	3.08402	−	34.7043i	0.118354	−	1.33183i
$680$	−46.9383			−1.80000
$681$	1.17409	+	2.03358i	0.0449911	+	0.0779269i
$682$	−4.34048	+	7.51793i	−0.166206	+	0.287876i
$683$	−5.70996	+	9.88994i	−0.218486	+	0.378428i	−0.954345	−	0.298706i	$-0.903445\pi$
$683$	−5.70996	+	9.88994i	−0.218486	+	0.378428i	0.735860	+	0.677134i	$0.236778\pi$
$684$	1.30090	+	2.25323i	0.0497412	+	0.0861543i
$685$	−16.3868			−0.626109
$686$	−23.0545	+	6.07626i	−0.880225	+	0.231993i
$687$	−17.4504			−0.665773
$688$	17.7787	+	30.7937i	0.677808	+	1.17400i
$689$	−19.6891	+	34.1025i	−0.750095	+	1.29920i
$690$	−11.3757	+	19.7034i	−0.433067	+	0.750094i
$691$	11.4596	+	19.8486i	0.435943	+	0.755075i	0.997372	−	0.0724499i	$-0.0230817\pi$
$691$	11.4596	+	19.8486i	0.435943	+	0.755075i	−0.561429	+	0.827525i	$0.689748\pi$
$692$	−1.24852			−0.0474615
$693$	0.234193	−	2.63537i	0.00889627	−	0.100109i
$694$	3.27935			0.124482
$695$	−7.07248	−	12.2499i	−0.268274	−	0.464665i
$696$	5.66349	−	9.80946i	0.214674	−	0.371827i
$697$	5.54576	−	9.60554i	0.210061	−	0.363836i
$698$	16.1035	+	27.8921i	0.609526	+	1.05573i
$699$	−5.59060			−0.211456
$700$	−8.50913	+	3.95373i	−0.321615	+	0.149437i
$701$	25.3982			0.959277			0.479638	−	0.877466i	$-0.340768\pi$
$701$	25.3982			0.959277			0.479638	+	0.877466i	$0.340768\pi$
$702$	1.95872	+	3.39260i	0.0739271	+	0.128045i
$703$	−1.30090	+	2.25323i	−0.0490644	+	0.0849821i
$704$	4.43042	−	7.67371i	0.166978	−	0.289214i
$705$	−3.24605	−	5.62233i	−0.122253	−	0.211749i
$706$	−14.7128			−0.553724
$707$	−15.3084	−	10.7502i	−0.575730	−	0.404304i
$708$	1.25480			0.0471581
$709$	8.25054	+	14.2903i	0.309855	+	0.536685i	0.978331	−	0.207049i	$-0.0663860\pi$
$709$	8.25054	+	14.2903i	0.309855	+	0.536685i	−0.668475	+	0.743735i	$0.733053\pi$
$710$	12.6166	−	21.8526i	0.473493	−	0.820114i
$711$	−0.359814	+	0.623216i	−0.0134941	+	0.0233724i
$712$	−18.6313	−	32.2704i	−0.698238	−	1.20938i
$713$	−30.4223			−1.13932
$714$	−11.0737	−	7.77647i	−0.414424	−	0.291027i
$715$	11.9210			0.445820
$716$	1.70122	+	2.94660i	0.0635775	+	0.110120i
$717$	−8.90735	+	15.4280i	−0.332651	+	0.576169i
$718$	−19.2857	+	33.4038i	−0.719736	+	1.24662i
$719$	17.9149	+	31.0295i	0.668112	+	1.15720i	0.978431	+	0.206572i	$0.0662308\pi$
$719$	17.9149	+	31.0295i	0.668112	+	1.15720i	−0.310319	+	0.950632i	$0.600436\pi$
$720$	−12.5240			−0.466741
$721$	5.60823	−	2.60584i	0.208862	−	0.0970465i
$722$	49.7133			1.85014
$723$	−1.49211	−	2.58441i	−0.0554922	−	0.0961152i
$724$	−1.38344	+	2.39619i	−0.0514151	+	0.0890535i
$725$	−19.4290	+	33.6519i	−0.721573	+	1.24980i
$726$	−0.643668	−	1.11487i	−0.0238888	−	0.0413765i
$727$	−18.7401			−0.695031			−0.347516	−	0.937674i	$-0.612975\pi$
$727$	−18.7401			−0.695031			−0.347516	+	0.937674i	$0.612975\pi$
$728$	−2.14934	+	24.1864i	−0.0796600	+	0.896409i
$729$	1.00000			0.0370370
$730$	22.0320	+	38.1605i	0.815441	+	1.41239i
$731$	−22.0935	+	38.2671i	−0.817159	+	1.41536i
$732$	−0.0802736	+	0.139038i	−0.00296700	+	0.00513899i
$733$	−23.9039	−	41.4028i	−0.882912	−	1.52925i	−0.848088	−	0.529856i	$-0.822246\pi$
$733$	−23.9039	−	41.4028i	−0.882912	−	1.52925i	−0.0348246	−	0.999393i	$-0.511087\pi$
$734$	−18.6182			−0.687211
$735$	−26.9924	−	4.83557i	−0.995628	−	0.178363i
$736$	8.64515			0.318664
$737$	−1.28911	−	2.23281i	−0.0474851	−	0.0822466i
$738$	1.79700	−	3.11250i	0.0661486	−	0.114573i
$739$	6.07009	−	10.5137i	0.223292	−	0.386753i	−0.732514	−	0.680752i	$-0.761653\pi$
$739$	6.07009	−	10.5137i	0.223292	−	0.386753i	0.955806	+	0.293999i	$0.0949864\pi$
$740$	0.230128	+	0.398593i	0.00845966	+	0.0146526i
$741$	−23.0986			−0.848550
$742$	3.90132	−	43.9014i	0.143222	−	1.61167i
$743$	30.9615			1.13587			0.567934	−	0.823074i	$-0.307743\pi$
$743$	30.9615			1.13587			0.567934	+	0.823074i	$0.307743\pi$
$744$	−10.1687	−	17.6128i	−0.372804	−	0.645715i
$745$	−26.0886	+	45.1867i	−0.955811	+	1.65551i
$746$	−19.4035	+	33.6079i	−0.710414	+	1.23047i
$747$	5.79878	+	10.0438i	0.212166	+	0.367483i
$748$	1.36177			0.0497911
$749$	−26.0410	+	12.0998i	−0.951519	+	0.442119i
$750$	26.9618			0.984506
$751$	16.0219	+	27.7507i	0.584646	+	1.01264i	0.994919	+	0.100674i	$0.0321000\pi$
$751$	16.0219	+	27.7507i	0.584646	+	1.01264i	−0.410273	+	0.911963i	$0.634567\pi$
$752$	2.64907	−	4.58832i	0.0966016	−	0.167319i
$753$	−12.5414	+	21.7224i	−0.457035	+	0.791608i
$754$	7.35641	+	12.7417i	0.267904	+	0.464024i
$755$	−27.5913			−1.00415
$756$	0.742157	+	0.521177i	0.0269920	+	0.0189550i
$757$	32.5209			1.18199			0.590996	−	0.806675i	$-0.298735\pi$
$757$	32.5209			1.18199			0.590996	+	0.806675i	$0.298735\pi$
$758$	7.56001	+	13.0943i	0.274592	+	0.475607i
$759$	2.25572	−	3.90703i	0.0818775	−	0.141816i
$760$	44.8404	−	77.6658i	1.62653	−	2.81723i
$761$	1.23181	+	2.13355i	0.0446530	+	0.0773412i	0.887488	−	0.460831i	$-0.152448\pi$
$761$	1.23181	+	2.13355i	0.0446530	+	0.0773412i	−0.842835	+	0.538172i	$0.819115\pi$
$762$	6.97526			0.252687
$763$	4.74698	+	3.33355i	0.171852	+	0.120683i
$764$	−1.91388			−0.0692419
$765$	−7.78173	−	13.4784i	−0.281349	−	0.487311i
$766$	−17.9822	+	31.1461i	−0.649723	+	1.12535i
$767$	−5.57000	+	9.64752i	−0.201121	+	0.348352i
$768$	3.98548	+	6.90306i	0.143814	+	0.249093i
$769$	49.0232			1.76782			0.883911	−	0.467656i	$-0.154901\pi$
$769$	49.0232			1.76782			0.883911	+	0.467656i	$0.154901\pi$
$770$	−12.1003	+	5.62233i	−0.436063	+	0.202615i
$771$	−22.5570			−0.812372
$772$	1.90814	+	3.30499i	0.0686754	+	0.118949i
$773$	−0.208182	+	0.360582i	−0.00748779	+	0.0129692i	−0.869745	−	0.493501i	$-0.835717\pi$
$773$	−0.208182	+	0.360582i	−0.00748779	+	0.0129692i	0.862257	+	0.506471i	$0.169050\pi$
$774$	−7.15901	+	12.3998i	−0.257325	+	0.445701i
$775$	34.8844	+	60.4216i	1.25309	+	2.17041i
$776$	39.7158			1.42571
$777$	−0.0802736	+	0.903315i	−0.00287980	+	0.0324062i
$778$	−20.2857			−0.727278
$779$	10.5958	+	18.3524i	0.379633	+	0.657544i
$780$	−2.04306	+	3.53868i	−0.0731532	+	0.126705i
$781$	−2.50178	+	4.33321i	−0.0895206	+	0.155054i
$782$	−11.5367	−	19.9822i	−0.412552	−	0.714561i
$783$	3.75572			0.134219
$784$	−7.59652	−	21.0501i	−0.271304	−	0.751788i
$785$	49.9703			1.78352
$786$	1.32978	+	2.30326i	0.0474319	+	0.0821544i
$787$	−2.41532	+	4.18345i	−0.0860968	+	0.149124i	−0.905858	−	0.423581i	$-0.860773\pi$
$787$	−2.41532	+	4.18345i	−0.0860968	+	0.149124i	0.819761	+	0.572705i	$0.194106\pi$
$788$	−0.110452	+	0.191309i	−0.00393470	+	0.00681510i
$789$	−12.8779	−	22.3052i	−0.458467	−	0.794087i
$790$	3.62912			0.129118
$791$	2.72635	−	30.6795i	0.0969379	−	1.09084i
$792$	3.01593			0.107166
$793$	−0.712664	−	1.23437i	−0.0253074	−	0.0438338i
$794$	−8.24469	+	14.2802i	−0.292593	+	0.506786i
$795$	25.3465	−	43.9014i	0.898947	−	1.55702i
$796$	−4.32493	−	7.49101i	−0.153293	−	0.265512i
$797$	43.5752			1.54351			0.771756	−	0.635919i	$-0.219379\pi$
$797$	43.5752			1.54351			0.771756	+	0.635919i	$0.219379\pi$
$798$	23.4460	−	10.8941i	0.829980	−	0.385646i
$799$	6.58397			0.232924
$800$	−9.91317	−	17.1701i	−0.350484	−	0.607055i
$801$	6.17764	−	10.7000i	0.218276	−	0.378066i
$802$	7.06790	−	12.2420i	0.249576	−	0.432279i
$803$	−4.36878	−	7.56694i	−0.154171	−	0.267032i
$804$	0.883730			0.0311667
$805$	−38.2662	−	26.8723i	−1.34871	−	0.947123i
$806$	26.4167			0.930487
$807$	10.3481	+	17.9234i	0.364270	+	0.630935i
$808$	10.6616	−	18.4664i	0.375073	−	0.649646i
$809$	9.36761	−	16.2252i	0.329348	−	0.570447i	−0.653035	−	0.757328i	$-0.726505\pi$
$809$	9.36761	−	16.2252i	0.329348	−	0.570447i	0.982383	+	0.186881i	$0.0598379\pi$
$810$	−2.52153	−	4.36742i	−0.0885975	−	0.153455i
$811$	−4.64229			−0.163013			−0.0815063	−	0.996673i	$-0.525973\pi$
$811$	−4.64229			−0.163013			−0.0815063	+	0.996673i	$0.525973\pi$
$812$	2.78734	+	1.95739i	0.0978163	+	0.0686911i
$813$	3.06780			0.107593
$814$	0.220628	+	0.382139i	0.00773300	+	0.0133939i
$815$	−22.3375	+	38.6897i	−0.782449	+	1.35524i
$816$	6.35059	−	10.9995i	0.222315	−	0.385061i
$817$	−42.2121	−	73.1135i	−1.47682	−	2.55792i
$818$	23.2050			0.811344
$819$	−7.30149	+	3.39260i	−0.255135	+	0.118547i
$820$	3.74876			0.130912
$821$	−8.95582	−	15.5119i	−0.312560	−	0.541370i	0.666356	−	0.745634i	$-0.267853\pi$
$821$	−8.95582	−	15.5119i	−0.312560	−	0.541370i	−0.978916	+	0.204264i	$0.934520\pi$
$822$	2.69250	−	4.66354i	0.0939116	−	0.162660i
$823$	13.7972	−	23.8974i	0.480938	−	0.833010i	−0.518822	−	0.854882i	$-0.673629\pi$
$823$	13.7972	−	23.8974i	0.480938	−	0.833010i	0.999761	+	0.0218723i	$0.00696272\pi$
$824$	3.52465	+	6.10487i	0.122787	+	0.212673i
$825$	−10.3463			−0.360213
$826$	1.10367	−	12.4196i	0.0384018	−	0.432133i
$827$	27.2202			0.946538			0.473269	−	0.880918i	$-0.343074\pi$
$827$	27.2202			0.946538			0.473269	+	0.880918i	$0.343074\pi$
$828$	0.773186	+	1.33920i	0.0268701	+	0.0465403i
$829$	−9.70996	+	16.8181i	−0.337241	+	0.584118i	−0.983913	−	0.178650i	$-0.942827\pi$
$829$	−9.70996	+	16.8181i	−0.337241	+	0.584118i	0.646672	+	0.762768i	$0.276160\pi$
$830$	29.2436	−	50.6514i	1.01506	−	1.75814i
$831$	3.34277	+	5.78984i	0.115959	+	0.200847i
$832$	−26.9641			−0.934810
$833$	17.9341	−	21.2548i	0.621381	−	0.736436i
$834$	4.64827			0.160956
$835$	−23.7218	−	41.0873i	−0.820926	−	1.42189i
$836$	−1.30090	+	2.25323i	−0.0449926	+	0.0779295i
$837$	3.37168	−	5.83991i	0.116542	−	0.201857i
$838$	−7.63018	−	13.2159i	−0.263580	−	0.456534i
$839$	42.1143			1.45395			0.726973	−	0.686666i	$-0.240927\pi$
$839$	42.1143			1.45395			0.726973	+	0.686666i	$0.240927\pi$
$840$	2.76693	−	31.1361i	0.0954680	−	1.07430i
$841$	−14.8945			−0.513605
$842$	−17.0501	−	29.5317i	−0.587587	−	1.01773i
$843$	−1.55643	+	2.69582i	−0.0536063	+	0.0928489i
$844$	−3.02246	+	5.23505i	−0.104037	+	0.180198i
$845$	7.32521	+	12.6876i	0.251995	+	0.436468i
$846$	2.13342			0.0733484
$847$	2.39939	−	1.11487i	0.0824440	−	0.0383072i
$848$	41.3699			1.42065
$849$	11.1799	+	19.3642i	0.383694	+	0.664578i
$850$	−26.4577	+	45.8261i	−0.907492	+	1.57182i
$851$	−0.773186	+	1.33920i	−0.0265045	+	0.0459071i
$852$	−0.857525	−	1.48528i	−0.0293783	−	0.0508848i
$853$	−53.7179			−1.83926			−0.919632	−	0.392780i	$-0.871513\pi$
$853$	−53.7179			−1.83926			−0.919632	+	0.392780i	$0.871513\pi$
$854$	1.30555	+	0.916818i	0.0446750	+	0.0313729i
$855$	29.7357			1.01694
$856$	−16.3662	−	28.3471i	−0.559386	−	0.968885i
$857$	3.48424	−	6.03488i	0.119019	−	0.206148i	−0.800360	−	0.599520i	$-0.795358\pi$
$857$	3.48424	−	6.03488i	0.119019	−	0.206148i	0.919379	+	0.393372i	$0.128692\pi$
$858$	−1.95872	+	3.39260i	−0.0668696	+	0.115821i
$859$	16.8147	+	29.1239i	0.573710	+	0.993696i	0.996180	+	0.0873187i	$0.0278299\pi$
$859$	16.8147	+	29.1239i	0.573710	+	0.993696i	−0.422470	+	0.906377i	$0.638837\pi$
$860$	−14.9345			−0.509263
$861$	6.04484	+	4.24496i	0.206007	+	0.144668i
$862$	−2.80229			−0.0954462
$863$	−22.0486	−	38.1893i	−0.750544	−	1.29998i	−0.947560	−	0.319579i	$-0.896458\pi$
$863$	−22.0486	−	38.1893i	−0.750544	−	1.29998i	0.197016	−	0.980400i	$-0.436875\pi$
$864$	−0.958135	+	1.65954i	−0.0325964	+	0.0564586i
$865$	−7.13458	+	12.3575i	−0.242583	+	0.420166i
$866$	10.6097	+	18.3765i	0.360531	+	0.624459i
$867$	−1.21631			−0.0413082
$868$	5.54594	−	2.57689i	0.188241	−	0.0874655i
$869$	−0.719627			−0.0244117
$870$	−9.47016	−	16.4028i	−0.321069	−	0.556107i
$871$	−3.92285	+	6.79457i	−0.132921	+	0.230225i
$872$	−3.30606	+	5.72627i	−0.111957	+	0.193916i
$873$	6.58434	+	11.4044i	0.222846	+	0.385981i
$874$	44.0843			1.49117
$875$	−4.90492	+	55.1948i	−0.165817	+	1.86592i
$876$	2.99494			0.101190
$877$	−5.07248	−	8.78579i	−0.171285	−	0.296675i	0.767584	−	0.640948i	$-0.221459\pi$
$877$	−5.07248	−	8.78579i	−0.171285	−	0.296675i	−0.938870	+	0.344273i	$0.888125\pi$
$878$	0.484682	−	0.839494i	0.0163572	−	0.0283315i
$879$	−5.31454	+	9.20505i	−0.179255	+	0.310479i
$880$	−6.26198	−	10.8461i	−0.211091	−	0.365621i
$881$	32.4394			1.09291			0.546455	−	0.837489i	$-0.315977\pi$
$881$	32.4394			1.09291			0.546455	+	0.837489i	$0.315977\pi$
$882$	5.81123	−	6.88724i	0.195674	−	0.231905i
$883$	25.0795			0.843992			0.421996	−	0.906598i	$-0.361330\pi$
$883$	25.0795			0.843992			0.421996	+	0.906598i	$0.361330\pi$
$884$	−2.07197	−	3.58875i	−0.0696878	−	0.120703i
$885$	7.17046	−	12.4196i	0.241032	−	0.417480i
$886$	−25.7865	+	44.6636i	−0.866315	+	1.50050i
$887$	26.3127	+	45.5749i	0.883493	+	1.53025i	0.847432	+	0.530905i	$0.178148\pi$
$887$	26.3127	+	45.5749i	0.883493	+	1.53025i	0.0360611	+	0.999350i	$0.488519\pi$
$888$	−1.03376			−0.0346907
$889$	−1.26895	+	14.2794i	−0.0425591	+	0.478915i
$890$	−62.3084			−2.08858
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	2.84245	−	4.92327i	0.0951722	−	0.164843i
$893$	−6.28970	+	10.8941i	−0.210477	+	0.364556i
$894$	−8.57314	−	14.8491i	−0.286729	−	0.496628i
$895$	38.8861			1.29982
$896$	18.1738	−	8.44437i	0.607144	−	0.282106i
$897$	−13.7286			−0.458384
$898$	4.96863	+	8.60592i	0.165805	+	0.287183i
$899$	12.6631	−	21.9331i	0.422337	−	0.731510i
$900$	1.77319	−	3.07125i	0.0591062	−	0.102375i
$901$	25.7051	+	44.5226i	0.856361	+	1.48326i
$902$	3.59401			0.119667
$903$	−24.0818	−	16.9113i	−0.801392	−	0.562774i
$904$	35.1098			1.16773
$905$	15.8112	+	27.3857i	0.525581	+	0.910332i
$906$	4.53349	−	7.85223i	0.150615	−	0.260873i
$907$	18.1814	−	31.4911i	0.603704	−	1.04565i	−0.388551	−	0.921427i	$-0.627024\pi$
$907$	18.1814	−	31.4911i	0.603704	−	1.04565i	0.992255	−	0.124219i	$-0.0396425\pi$
$908$	−0.402438	−	0.697043i	−0.0133554	−	0.0231322i
$909$	7.07019			0.234503
$910$	33.2278	+	23.3341i	1.10149	+	0.773517i
$911$	−14.4516			−0.478802			−0.239401	−	0.970921i	$-0.576951\pi$
$911$	−14.4516			−0.478802			−0.239401	+	0.970921i	$0.576951\pi$
$912$	12.1335	+	21.0158i	0.401780	+	0.695903i
$913$	−5.79878	+	10.0438i	−0.191912	+	0.332401i
$914$	−16.9701	+	29.3930i	−0.561320	+	0.972235i
$915$	0.917438	+	1.58905i	0.0303296	+	0.0525324i
$916$	5.98140			0.197631
$917$	−4.95702	+	2.30326i	−0.163695	+	0.0760602i
$918$	5.11442			0.168801
$919$	−22.8306	−	39.5437i	−0.753111	−	1.30443i	−0.946308	−	0.323266i	$-0.895219\pi$
$919$	−22.8306	−	39.5437i	−0.753111	−	1.30443i	0.193197	−	0.981160i	$-0.438114\pi$
$920$	26.6507	−	46.1604i	0.878648	−	1.52186i
$921$	9.26147	−	16.0413i	0.305176	−	0.528580i
$922$	−8.02559	−	13.9007i	−0.264309	−	0.457796i
$923$	15.2261			0.501174
$924$	−0.0802736	+	0.903315i	−0.00264081	+	0.0297169i
$925$	3.54637			0.116604
$926$	−24.3068	−	42.1006i	−0.798772	−	1.38351i
$927$	−1.16868	+	2.02421i	−0.0383844	+	0.0664838i
$928$	−3.59849	+	6.23277i	−0.118126	+	0.204601i
$929$	22.6831	+	39.2882i	0.744207	+	1.28900i	0.950564	+	0.310528i	$0.100506\pi$
$929$	22.6831	+	39.2882i	0.744207	+	1.28900i	−0.206357	+	0.978477i	$0.566161\pi$
$930$	−34.0071			−1.11514
$931$	18.0365	+	49.9793i	0.591121	+	1.63800i
$932$	1.91627			0.0627695
$933$	9.92192	+	17.1853i	0.324829	+	0.562620i
$934$	−14.1741	+	24.5503i	−0.463791	+	0.803310i
$935$	7.78173	−	13.4784i	0.254490	−	0.440789i
$936$	−4.58882	−	7.94807i	−0.149990	−	0.259791i
$937$	14.7757			0.482699			0.241350	−	0.970438i	$-0.422410\pi$
$937$	14.7757			0.482699			0.241350	+	0.970438i	$0.422410\pi$
$938$	0.777298	−	8.74689i	0.0253797	−	0.285596i
$939$	−21.1144			−0.689043
$940$	1.11264	+	1.92715i	0.0362903	+	0.0628566i
$941$	7.96057	−	13.7881i	0.259507	−	0.449480i	−0.706603	−	0.707610i	$-0.749773\pi$
$941$	7.96057	−	13.7881i	0.259507	−	0.449480i	0.966110	+	0.258131i	$0.0831066\pi$
$942$	−8.21054	+	14.2211i	−0.267514	+	0.463348i
$943$	6.29757	+	10.9077i	0.205077	+	0.355204i
$944$	11.7035			0.380915
$945$	9.39946	−	4.36742i	0.305765	−	0.142072i
$946$	−14.3180			−0.465519
$947$	−12.1792	−	21.0950i	−0.395770	−	0.685494i	0.597429	−	0.801922i	$-0.296189\pi$
$947$	−12.1792	−	21.0950i	−0.395770	−	0.685494i	−0.993199	+	0.116428i	$0.962856\pi$
$948$	0.123332	−	0.213617i	0.00400564	−	0.00693797i
$949$	−13.2944	+	23.0267i	−0.431556	+	0.747477i
$950$	−50.5503	−	87.5557i	−1.64007	−	2.84068i
$951$	−15.8066			−0.512563
$952$	25.9431	+	18.2185i	0.840822	+	0.590464i
$953$	−47.2682			−1.53117			−0.765583	−	0.643337i	$-0.777550\pi$
$953$	−47.2682			−1.53117			−0.765583	+	0.643337i	$0.777550\pi$
$954$	8.32927	+	14.4267i	0.269670	+	0.467083i
$955$	−10.9368	+	18.9430i	−0.353906	+	0.612983i
$956$	3.05314	−	5.28820i	0.0987457	−	0.171033i
$957$	1.87786	+	3.25255i	0.0607026	+	0.105140i
$958$	−12.1628			−0.392962
$959$	9.05713	+	6.36033i	0.292470	+	0.205386i
$960$	34.7118			1.12032
$961$	−7.23639	−	12.5338i	−0.233432	−	0.404316i
$962$	0.671383	−	1.16287i	0.0216463	−	0.0374924i
$963$	5.42660	−	9.39914i	0.174870	−	0.302883i
$964$	0.511445	+	0.885849i	0.0164725	+	0.0285313i
$965$	43.6158			1.40404
$966$	13.9350	−	6.47485i	0.448353	−	0.208325i
$967$	37.7062			1.21255			0.606275	−	0.795255i	$-0.292663\pi$
$967$	37.7062			1.21255			0.606275	+	0.795255i	$0.292663\pi$
$968$	1.50796	+	2.61187i	0.0484678	+	0.0839487i
$969$	−15.0782	+	26.1163i	−0.484382	+	0.838975i
$970$	33.2052	−	57.5131i	1.06615	−	1.84663i
$971$	−0.995759	−	1.72471i	−0.0319554	−	0.0553484i	0.849605	−	0.527419i	$-0.176840\pi$
$971$	−0.995759	−	1.72471i	−0.0319554	−	0.0553484i	−0.881561	+	0.472070i	$0.843507\pi$
$972$	−0.342766			−0.0109942
$973$	−0.845618	+	9.51569i	−0.0271093	+	0.305059i
$974$	51.7947			1.65961
$975$	15.7422	+	27.2663i	0.504155	+	0.873222i
$976$	−0.748711	+	1.29681i	−0.0239657	+	0.0415097i
$977$	13.6300	−	23.6079i	0.436063	−	0.755284i	−0.561319	−	0.827600i	$-0.689706\pi$
$977$	13.6300	−	23.6079i	0.436063	−	0.755284i	0.997382	+	0.0723163i	$0.0230391\pi$
$978$	−7.34048	−	12.7141i	−0.234723	−	0.406551i
$979$	12.3553			0.394877
$980$	9.25207	+	1.65747i	0.295547	+	0.0529460i
$981$	−2.19240			−0.0699980
$982$	−13.0642	−	22.6278i	−0.416894	−	0.722082i
$983$	−5.07112	+	8.78343i	−0.161744	+	0.280148i	−0.935494	−	0.353342i	$-0.885045\pi$
$983$	−5.07112	+	8.78343i	−0.161744	+	0.280148i	0.773751	+	0.633490i	$0.218378\pi$
$984$	−4.20996	+	7.29186i	−0.134209	+	0.232456i
$985$	1.26235	+	2.18645i	0.0402217	+	0.0696660i
$986$	19.2083			0.611718
$987$	−0.388113	+	4.36742i	−0.0123538	+	0.139016i
$988$	7.91744			0.251887
$989$	−25.0886	−	43.4548i	−0.797772	−	1.38178i
$990$	2.52153	−	4.36742i	0.0801395	−	0.138806i
$991$	−11.0702	+	19.1741i	−0.351656	+	0.609086i	−0.986540	−	0.163521i	$-0.947715\pi$
$991$	−11.0702	+	19.1741i	−0.351656	+	0.609086i	0.634884	+	0.772608i	$0.281048\pi$
$992$	6.46104	+	11.1908i	0.205138	+	0.355310i
$993$	−9.16327			−0.290788
$994$	−15.4551	+	7.18113i	−0.490206	+	0.227772i
$995$	−98.8584			−3.13402
$996$	−1.98763	−	3.44267i	−0.0629804	−	0.109085i
$997$	−24.4492	+	42.3473i	−0.774314	+	1.34115i	0.160865	+	0.986976i	$0.448571\pi$
$997$	−24.4492	+	42.3473i	−0.774314	+	1.34115i	−0.935179	+	0.354175i	$0.884762\pi$
$998$	−23.3622	+	40.4645i	−0.739518	+	1.28088i
$999$	−0.171383	−	0.296844i	−0.00542233	−	0.00939174i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.i.e.67.2	✓	8
3.2	odd	2		693.2.i.i.298.3		8
7.2	even	3	inner	231.2.i.e.100.2	yes	8
7.3	odd	6		1617.2.a.x.1.3		4
7.4	even	3		1617.2.a.z.1.3		4
21.2	odd	6		693.2.i.i.100.3		8
21.11	odd	6		4851.2.a.bt.1.2		4
21.17	even	6		4851.2.a.bu.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.e.67.2	✓	8	1.1	even	1	trivial
231.2.i.e.100.2	yes	8	7.2	even	3	inner
693.2.i.i.100.3		8	21.2	odd	6
693.2.i.i.298.3		8	3.2	odd	2
1617.2.a.x.1.3		4	7.3	odd	6
1617.2.a.z.1.3		4	7.4	even	3
4851.2.a.bt.1.2		4	21.11	odd	6
4851.2.a.bu.1.2		4	21.17	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)

\(f(q)\)	\(=\)	\(q+(-0.643668 - 1.11487i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.171383 - 0.296844i) q^{4} +(-1.95872 - 3.39260i) q^{5} +1.28734 q^{6} +(-0.234193 + 2.63537i) q^{7} -3.01593 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.643668 - 1.11487i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.171383 - 0.296844i) q^{4} +(-1.95872 - 3.39260i) q^{5} +1.28734 q^{6} +(-0.234193 + 2.63537i) q^{7} -3.01593 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.52153 + 4.36742i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.171383 + 0.296844i) q^{12} -3.04306 q^{13} +(3.08882 - 1.43521i) q^{14} +3.91744 q^{15} +(1.59849 + 2.76866i) q^{16} +(-1.98643 + 3.44061i) q^{17} +(-0.643668 + 1.11487i) q^{18} +(-3.79530 - 6.57365i) q^{19} -1.34277 q^{20} +(-2.16520 - 1.52050i) q^{21} -1.28734 q^{22} +(-2.25572 - 3.90703i) q^{23} +(1.50796 - 2.61187i) q^{24} +(-5.17316 + 8.96018i) q^{25} +(1.95872 + 3.39260i) q^{26} +1.00000 q^{27} +(0.742157 + 0.521177i) q^{28} +3.75572 q^{29} +(-2.52153 - 4.36742i) q^{30} +(3.37168 - 5.83991i) q^{31} +(-0.958135 + 1.65954i) q^{32} +(0.500000 + 0.866025i) q^{33} +5.11442 q^{34} +(9.39946 - 4.36742i) q^{35} -0.342766 q^{36} +(-0.171383 - 0.296844i) q^{37} +(-4.88582 + 8.46250i) q^{38} +(1.52153 - 2.63537i) q^{39} +(5.90735 + 10.2318i) q^{40} -2.79182 q^{41} +(-0.301486 + 3.39260i) q^{42} +11.1222 q^{43} +(-0.171383 - 0.296844i) q^{44} +(-1.95872 + 3.39260i) q^{45} +(-2.90387 + 5.02965i) q^{46} +(-0.828617 - 1.43521i) q^{47} -3.19698 q^{48} +(-6.89031 - 1.23437i) q^{49} +13.3192 q^{50} +(-1.98643 - 3.44061i) q^{51} +(-0.521529 + 0.903315i) q^{52} +(6.47016 - 11.2067i) q^{53} +(-0.643668 - 1.11487i) q^{54} -3.91744 q^{55} +(0.706310 - 7.94807i) q^{56} +7.59060 q^{57} +(-2.41744 - 4.18713i) q^{58} +(1.83039 - 3.17034i) q^{59} +(0.671383 - 1.16287i) q^{60} +(0.234193 + 0.405635i) q^{61} -8.68096 q^{62} +(2.39939 - 1.11487i) q^{63} +8.86084 q^{64} +(5.96050 + 10.3239i) q^{65} +(0.643668 - 1.11487i) q^{66} +(1.28911 - 2.23281i) q^{67} +(0.680883 + 1.17932i) q^{68} +4.51145 q^{69} +(-10.9192 - 7.66797i) q^{70} -5.00355 q^{71} +(1.50796 + 2.61187i) q^{72} +(4.36878 - 7.56694i) q^{73} +(-0.220628 + 0.382139i) q^{74} +(-5.17316 - 8.96018i) q^{75} -2.60180 q^{76} +(2.16520 + 1.52050i) q^{77} -3.91744 q^{78} +(-0.359814 - 0.623216i) q^{79} +(6.26198 - 10.8461i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.79700 + 3.11250i) q^{82} -11.5976 q^{83} +(-0.822431 + 0.382139i) q^{84} +15.5635 q^{85} +(-7.15901 - 12.3998i) q^{86} +(-1.87786 + 3.25255i) q^{87} +(-1.50796 + 2.61187i) q^{88} +(6.17764 + 10.7000i) q^{89} +5.04306 q^{90} +(0.712664 - 8.01957i) q^{91} -1.54637 q^{92} +(3.37168 + 5.83991i) q^{93} +(-1.06671 + 1.84759i) q^{94} +(-14.8679 + 25.7519i) q^{95} +(-0.958135 - 1.65954i) q^{96} -13.1687 q^{97} +(3.05891 + 8.47629i) 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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