LMFDB - Embedded newform 861.2.i.g.739.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(247,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("861.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.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:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			739.10
Character	$\chi$	$=$	861.739
Dual form			861.2.i.g.247.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.605332 + 1.04847i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.267145 - 0.462709i) q^{4} +(-0.413490 - 0.716185i) q^{5} +1.21066 q^{6} +(-2.53279 - 0.764826i) q^{7} +3.06818 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.605332 + 1.04847i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.267145 - 0.462709i) q^{4} +(-0.413490 - 0.716185i) q^{5} +1.21066 q^{6} +(-2.53279 - 0.764826i) q^{7} +3.06818 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500597 - 0.867060i) q^{10} +(0.198481 - 0.343780i) q^{11} +(-0.267145 - 0.462709i) q^{12} +3.17185 q^{13} +(-0.731288 - 3.11852i) q^{14} -0.826979 q^{15} +(1.32298 + 2.29146i) q^{16} +(-0.0795711 + 0.137821i) q^{17} +(0.605332 - 1.04847i) q^{18} +(-1.95747 - 3.39043i) q^{19} -0.441847 q^{20} +(-1.92876 + 1.81105i) q^{21} +0.480588 q^{22} +(-3.56818 - 6.18027i) q^{23} +(1.53409 - 2.65712i) q^{24} +(2.15805 - 3.73786i) q^{25} +(1.92003 + 3.32558i) q^{26} -1.00000 q^{27} +(-1.03052 + 0.967627i) q^{28} +9.77724 q^{29} +(-0.500597 - 0.867060i) q^{30} +(-3.07749 + 5.33036i) q^{31} +(1.46650 - 2.54005i) q^{32} +(-0.198481 - 0.343780i) q^{33} -0.192668 q^{34} +(0.499527 + 2.13020i) q^{35} -0.534291 q^{36} +(-5.04425 - 8.73689i) q^{37} +(2.36984 - 4.10467i) q^{38} +(1.58593 - 2.74691i) q^{39} +(-1.26866 - 2.19738i) q^{40} +1.00000 q^{41} +(-3.06636 - 0.925948i) q^{42} -5.32444 q^{43} +(-0.106047 - 0.183678i) q^{44} +(-0.413490 + 0.716185i) q^{45} +(4.31987 - 7.48223i) q^{46} +(0.655301 + 1.13502i) q^{47} +2.64595 q^{48} +(5.83008 + 3.87429i) q^{49} +5.22536 q^{50} +(0.0795711 + 0.137821i) q^{51} +(0.847346 - 1.46765i) q^{52} +(2.77279 - 4.80261i) q^{53} +(-0.605332 - 1.04847i) q^{54} -0.328280 q^{55} +(-7.77106 - 2.34662i) q^{56} -3.91493 q^{57} +(5.91848 + 10.2511i) q^{58} +(-0.789193 + 1.36692i) q^{59} +(-0.220924 + 0.382651i) q^{60} +(4.28103 + 7.41495i) q^{61} -7.45161 q^{62} +(0.604038 + 2.57588i) q^{63} +8.84277 q^{64} +(-1.31153 - 2.27163i) q^{65} +(0.240294 - 0.416202i) q^{66} +(-6.05857 + 10.4937i) q^{67} +(0.0425141 + 0.0736366i) q^{68} -7.13636 q^{69} +(-1.93106 + 1.81321i) q^{70} -1.25998 q^{71} +(-1.53409 - 2.65712i) q^{72} +(-4.17382 + 7.22927i) q^{73} +(6.10689 - 10.5774i) q^{74} +(-2.15805 - 3.73786i) q^{75} -2.09171 q^{76} +(-0.765643 + 0.718919i) q^{77} +3.84005 q^{78} +(4.56477 + 7.90641i) q^{79} +(1.09407 - 1.89499i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.605332 + 1.04847i) q^{82} +9.77501 q^{83} +(0.322732 + 1.37627i) q^{84} +0.131607 q^{85} +(-3.22305 - 5.58249i) q^{86} +(4.88862 - 8.46734i) q^{87} +(0.608975 - 1.05478i) q^{88} +(-5.90491 - 10.2276i) q^{89} -1.00119 q^{90} +(-8.03365 - 2.42592i) q^{91} -3.81289 q^{92} +(3.07749 + 5.33036i) q^{93} +(-0.793350 + 1.37412i) q^{94} +(-1.61878 + 2.80382i) q^{95} +(-1.46650 - 2.54005i) q^{96} +10.4867 q^{97} +(-0.532926 + 8.45788i) q^{98} -0.396962 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} + 14 q^{3} - 14 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} - 14 q^{9}+O(q^{10}) $ 28 * q + 2 * q^2 + 14 * q^3 - 14 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 - 14 * q^9	\( 28 q + 2 q^{2} + 14 q^{3} - 14 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} - 14 q^{9} - 3 q^{10} + 16 q^{11} + 14 q^{12} + 42 q^{13} - 14 q^{14} - 20 q^{15} - 22 q^{16} - 12 q^{17} + 2 q^{18} - 2 q^{19} + 80 q^{20} + 2 q^{22} + 7 q^{23} - 6 q^{24} - 22 q^{25} - 2 q^{26} - 28 q^{27} - 59 q^{28} - 32 q^{29} + 3 q^{30} - 8 q^{31} + 19 q^{32} - 16 q^{33} + 66 q^{34} - 8 q^{35} + 28 q^{36} - q^{37} - 32 q^{38} + 21 q^{39} + 13 q^{40} + 28 q^{41} - 10 q^{42} + 28 q^{43} + 36 q^{44} - 10 q^{45} + 12 q^{46} - 12 q^{47} - 44 q^{48} + 8 q^{49} - 2 q^{50} + 12 q^{51} - 60 q^{52} + 20 q^{53} - 2 q^{54} - 22 q^{55} + q^{56} - 4 q^{57} - 21 q^{58} - 25 q^{59} + 40 q^{60} - 26 q^{61} - 66 q^{62} + 84 q^{64} + 8 q^{65} + q^{66} + 22 q^{67} - 15 q^{68} + 14 q^{69} - 120 q^{70} - 72 q^{71} + 6 q^{72} - 31 q^{73} + 65 q^{74} + 22 q^{75} - 4 q^{76} - 18 q^{77} - 4 q^{78} - 12 q^{79} - 112 q^{80} - 14 q^{81} + 2 q^{82} + 40 q^{83} - 37 q^{84} + 80 q^{85} + 9 q^{86} - 16 q^{87} + 54 q^{88} - 39 q^{89} + 6 q^{90} - 17 q^{91} + 126 q^{92} + 8 q^{93} - 14 q^{94} + 55 q^{95} - 19 q^{96} + 36 q^{97} - 19 q^{98} - 32 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 + 14 * q^3 - 14 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 - 14 * q^9 - 3 * q^10 + 16 * q^11 + 14 * q^12 + 42 * q^13 - 14 * q^14 - 20 * q^15 - 22 * q^16 - 12 * q^17 + 2 * q^18 - 2 * q^19 + 80 * q^20 + 2 * q^22 + 7 * q^23 - 6 * q^24 - 22 * q^25 - 2 * q^26 - 28 * q^27 - 59 * q^28 - 32 * q^29 + 3 * q^30 - 8 * q^31 + 19 * q^32 - 16 * q^33 + 66 * q^34 - 8 * q^35 + 28 * q^36 - q^37 - 32 * q^38 + 21 * q^39 + 13 * q^40 + 28 * q^41 - 10 * q^42 + 28 * q^43 + 36 * q^44 - 10 * q^45 + 12 * q^46 - 12 * q^47 - 44 * q^48 + 8 * q^49 - 2 * q^50 + 12 * q^51 - 60 * q^52 + 20 * q^53 - 2 * q^54 - 22 * q^55 + q^56 - 4 * q^57 - 21 * q^58 - 25 * q^59 + 40 * q^60 - 26 * q^61 - 66 * q^62 + 84 * q^64 + 8 * q^65 + q^66 + 22 * q^67 - 15 * q^68 + 14 * q^69 - 120 * q^70 - 72 * q^71 + 6 * q^72 - 31 * q^73 + 65 * q^74 + 22 * q^75 - 4 * q^76 - 18 * q^77 - 4 * q^78 - 12 * q^79 - 112 * q^80 - 14 * q^81 + 2 * q^82 + 40 * q^83 - 37 * q^84 + 80 * q^85 + 9 * q^86 - 16 * q^87 + 54 * q^88 - 39 * q^89 + 6 * q^90 - 17 * q^91 + 126 * q^92 + 8 * q^93 - 14 * q^94 + 55 * q^95 - 19 * q^96 + 36 * q^97 - 19 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.605332	+	1.04847i	0.428035	+	0.741378i	0.996698	−	0.0811923i	$-0.0258728\pi$
$2$	0.605332	+	1.04847i	0.428035	+	0.741378i	−0.568664	+	0.822570i	$0.692539\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.267145	−	0.462709i	0.133573	−	0.231355i
$5$	−0.413490	−	0.716185i	−0.184918	−	0.320288i	0.758631	−	0.651521i	$-0.225869\pi$
$5$	−0.413490	−	0.716185i	−0.184918	−	0.320288i	−0.943549	+	0.331233i	$0.892535\pi$
$6$	1.21066			0.494252
$7$	−2.53279	−	0.764826i	−0.957306	−	0.289077i
$7$	−2.53279	−	0.764826i	−0.957306	−	0.289077i
$8$	3.06818			1.08476
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.500597	−	0.867060i	0.158303	−	0.274188i
$11$	0.198481	−	0.343780i	0.0598443	−	0.103653i	−0.834551	−	0.550931i	$-0.814273\pi$
$11$	0.198481	−	0.343780i	0.0598443	−	0.103653i	0.894395	+	0.447277i	$0.147606\pi$
$12$	−0.267145	−	0.462709i	−0.0771182	−	0.133573i
$13$	3.17185			0.879714			0.439857	−	0.898068i	$-0.355029\pi$
$13$	3.17185			0.879714			0.439857	+	0.898068i	$0.355029\pi$
$14$	−0.731288	−	3.11852i	−0.195445	−	0.833460i
$15$	−0.826979			−0.213525
$16$	1.32298	+	2.29146i	0.330744	+	0.572865i
$17$	−0.0795711	+	0.137821i	−0.0192988	+	0.0334266i	−0.875514	−	0.483194i	$-0.839477\pi$
$17$	−0.0795711	+	0.137821i	−0.0192988	+	0.0334266i	0.856215	+	0.516620i	$0.172810\pi$
$18$	0.605332	−	1.04847i	0.142678	−	0.247126i
$19$	−1.95747	−	3.39043i	−0.449073	−	0.777818i	0.549252	−	0.835656i	$-0.314913\pi$
$19$	−1.95747	−	3.39043i	−0.449073	−	0.777818i	−0.998326	+	0.0578384i	$0.981579\pi$
$20$	−0.441847			−0.0988001
$21$	−1.92876	+	1.81105i	−0.420889	+	0.395204i
$22$	0.480588			0.102462
$23$	−3.56818	−	6.18027i	−0.744017	−	1.28867i	−0.950653	−	0.310257i	$-0.899585\pi$
$23$	−3.56818	−	6.18027i	−0.744017	−	1.28867i	0.206636	−	0.978418i	$-0.433748\pi$
$24$	1.53409	−	2.65712i	0.313144	−	0.542382i
$25$	2.15805	−	3.73786i	0.431611	−	0.747571i
$26$	1.92003	+	3.32558i	0.376548	+	0.652200i
$27$	−1.00000			−0.192450
$28$	−1.03052	+	0.967627i	−0.194749	+	0.182864i
$29$	9.77724			1.81559			0.907794	−	0.419416i	$-0.137765\pi$
$29$	9.77724			1.81559			0.907794	+	0.419416i	$0.137765\pi$
$30$	−0.500597	−	0.867060i	−0.0913962	−	0.158303i
$31$	−3.07749	+	5.33036i	−0.552733	+	0.957361i	0.445343	+	0.895360i	$0.353082\pi$
$31$	−3.07749	+	5.33036i	−0.552733	+	0.957361i	−0.998076	+	0.0620013i	$0.980252\pi$
$32$	1.46650	−	2.54005i	0.259242	−	0.449021i
$33$	−0.198481	−	0.343780i	−0.0345511	−	0.0598443i
$34$	−0.192668			−0.0330423
$35$	0.499527	+	2.13020i	0.0844355	+	0.360069i
$36$	−0.534291			−0.0890484
$37$	−5.04425	−	8.73689i	−0.829269	−	1.43634i	−0.898612	−	0.438743i	$-0.855424\pi$
$37$	−5.04425	−	8.73689i	−0.829269	−	1.43634i	0.0693434	−	0.997593i	$-0.477910\pi$
$38$	2.36984	−	4.10467i	0.384438	−	0.665866i
$39$	1.58593	−	2.74691i	0.253952	−	0.439857i
$40$	−1.26866	−	2.19738i	−0.200593	−	0.347437i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−3.06636	−	0.925948i	−0.473150	−	0.142877i
$43$	−5.32444			−0.811969			−0.405985	−	0.913880i	$-0.633071\pi$
$43$	−5.32444			−0.811969			−0.405985	+	0.913880i	$0.633071\pi$
$44$	−0.106047	−	0.183678i	−0.0159871	−	0.0276905i
$45$	−0.413490	+	0.716185i	−0.0616394	+	0.106763i
$46$	4.31987	−	7.48223i	0.636930	−	1.10319i
$47$	0.655301	+	1.13502i	0.0955855	+	0.165559i	0.909853	−	0.414931i	$-0.136194\pi$
$47$	0.655301	+	1.13502i	0.0955855	+	0.165559i	−0.814267	+	0.580490i	$0.802861\pi$
$48$	2.64595			0.381910
$49$	5.83008	+	3.87429i	0.832869	+	0.553470i
$50$	5.22536			0.738977
$51$	0.0795711	+	0.137821i	0.0111422	+	0.0192988i
$52$	0.847346	−	1.46765i	0.117506	−	0.203526i
$53$	2.77279	−	4.80261i	0.380872	−	0.659689i	−0.610315	−	0.792159i	$-0.708957\pi$
$53$	2.77279	−	4.80261i	0.380872	−	0.659689i	0.991187	+	0.132469i	$0.0422906\pi$
$54$	−0.605332	−	1.04847i	−0.0823753	−	0.142678i
$55$	−0.328280			−0.0442652
$56$	−7.77106	−	2.34662i	−1.03845	−	0.313580i
$57$	−3.91493			−0.518545
$58$	5.91848	+	10.2511i	0.777135	+	1.34604i
$59$	−0.789193	+	1.36692i	−0.102744	+	0.177958i	−0.912814	−	0.408375i	$-0.866096\pi$
$59$	−0.789193	+	1.36692i	−0.102744	+	0.177958i	0.810070	+	0.586333i	$0.199429\pi$
$60$	−0.220924	+	0.382651i	−0.0285211	+	0.0494000i
$61$	4.28103	+	7.41495i	0.548129	+	0.949388i	0.998403	+	0.0564970i	$0.0179931\pi$
$61$	4.28103	+	7.41495i	0.548129	+	0.949388i	−0.450274	+	0.892891i	$0.648674\pi$
$62$	−7.45161			−0.946355
$63$	0.604038	+	2.57588i	0.0761016	+	0.324530i
$64$	8.84277			1.10535
$65$	−1.31153	−	2.27163i	−0.162675	−	0.281762i
$66$	0.240294	−	0.416202i	0.0295782	−	0.0512309i
$67$	−6.05857	+	10.4937i	−0.740172	+	1.28202i	0.212245	+	0.977216i	$0.431922\pi$
$67$	−6.05857	+	10.4937i	−0.740172	+	1.28202i	−0.952417	+	0.304799i	$0.901411\pi$
$68$	0.0425141	+	0.0736366i	0.00515559	+	0.00892975i
$69$	−7.13636			−0.859117
$70$	−1.93106	+	1.81321i	−0.230806	+	0.216721i
$71$	−1.25998			−0.149532			−0.0747659	−	0.997201i	$-0.523821\pi$
$71$	−1.25998			−0.149532			−0.0747659	+	0.997201i	$0.523821\pi$
$72$	−1.53409	−	2.65712i	−0.180794	−	0.313144i
$73$	−4.17382	+	7.22927i	−0.488509	+	0.846122i	−0.999913	−	0.0132188i	$-0.995792\pi$
$73$	−4.17382	+	7.22927i	−0.488509	+	0.846122i	0.511404	+	0.859340i	$0.329126\pi$
$74$	6.10689	−	10.5774i	0.709912	−	1.22960i
$75$	−2.15805	−	3.73786i	−0.249190	−	0.431611i
$76$	−2.09171			−0.239936
$77$	−0.765643	+	0.718919i	−0.0872532	+	0.0819284i
$78$	3.84005			0.434800
$79$	4.56477	+	7.90641i	0.513577	+	0.889541i	0.999876	+	0.0157488i	$0.00501319\pi$
$79$	4.56477	+	7.90641i	0.513577	+	0.889541i	−0.486299	+	0.873792i	$0.661653\pi$
$80$	1.09407	−	1.89499i	0.122321	−	0.211866i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.605332	+	1.04847i	0.0668478	+	0.115784i
$83$	9.77501			1.07295			0.536473	−	0.843917i	$-0.319756\pi$
$83$	9.77501			1.07295			0.536473	+	0.843917i	$0.319756\pi$
$84$	0.322732	+	1.37627i	0.0352129	+	0.150163i
$85$	0.131607			0.0142748
$86$	−3.22305	−	5.58249i	−0.347551	−	0.601976i
$87$	4.88862	−	8.46734i	0.524115	−	0.907794i
$88$	0.608975	−	1.05478i	0.0649170	−	0.112440i
$89$	−5.90491	−	10.2276i	−0.625919	−	1.08412i	−0.988362	−	0.152117i	$-0.951391\pi$
$89$	−5.90491	−	10.2276i	−0.625919	−	1.08412i	0.362444	−	0.932006i	$-0.381943\pi$
$90$	−1.00119			−0.105535
$91$	−8.03365	−	2.42592i	−0.842155	−	0.254305i
$92$	−3.81289			−0.397521
$93$	3.07749	+	5.33036i	0.319120	+	0.552733i
$94$	−0.793350	+	1.37412i	−0.0818278	+	0.141730i
$95$	−1.61878	+	2.80382i	−0.166084	+	0.287665i
$96$	−1.46650	−	2.54005i	−0.149674	−	0.259242i
$97$	10.4867			1.06476			0.532381	−	0.846505i	$-0.321297\pi$
$97$	10.4867			1.06476			0.532381	+	0.846505i	$0.321297\pi$
$98$	−0.532926	+	8.45788i	−0.0538337	+	0.854375i
$99$	−0.396962			−0.0398962
$100$	−1.15303	−	1.99710i	−0.115303	−	0.199710i
$101$	−5.59782	+	9.69571i	−0.557004	+	0.964760i	0.440740	+	0.897635i	$0.354716\pi$
$101$	−5.59782	+	9.69571i	−0.557004	+	0.964760i	−0.997745	+	0.0671250i	$0.978617\pi$
$102$	−0.0963340	+	0.166855i	−0.00953849	+	0.0165211i
$103$	7.38645	+	12.7937i	0.727809	+	1.26060i	0.957807	+	0.287411i	$0.0927945\pi$
$103$	7.38645	+	12.7937i	0.727809	+	1.26060i	−0.229999	+	0.973191i	$0.573872\pi$
$104$	9.73181			0.954282
$105$	2.09457	+	0.632495i	0.204409	+	0.0617252i
$106$	6.71384			0.652105
$107$	7.70657	+	13.3482i	0.745022	+	1.29042i	0.950184	+	0.311689i	$0.100895\pi$
$107$	7.70657	+	13.3482i	0.745022	+	1.29042i	−0.205162	+	0.978728i	$0.565772\pi$
$108$	−0.267145	+	0.462709i	−0.0257061	+	0.0445242i
$109$	−3.24620	+	5.62258i	−0.310929	+	0.538546i	−0.978564	−	0.205944i	$-0.933974\pi$
$109$	−3.24620	+	5.62258i	−0.310929	+	0.538546i	0.667634	+	0.744489i	$0.267307\pi$
$110$	−0.198718	−	0.344190i	−0.0189471	−	0.0328173i
$111$	−10.0885			−0.957557
$112$	−1.59826	−	6.81565i	−0.151021	−	0.644018i
$113$	7.90856			0.743975			0.371988	−	0.928238i	$-0.378676\pi$
$113$	7.90856			0.743975			0.371988	+	0.928238i	$0.378676\pi$
$114$	−2.36984	−	4.10467i	−0.221955	−	0.384438i
$115$	−2.95081	+	5.11095i	−0.275164	+	0.476599i
$116$	2.61194	−	4.52402i	0.242513	−	0.420045i
$117$	−1.58593	−	2.74691i	−0.146619	−	0.253952i
$118$	−1.91090			−0.175912
$119$	0.306946	−	0.288215i	0.0281377	−	0.0264206i
$120$	−2.53732			−0.231624
$121$	5.42121	+	9.38981i	0.492837	+	0.853619i
$122$	−5.18289	+	8.97702i	−0.469237	+	0.812742i
$123$	0.500000	−	0.866025i	0.0450835	−	0.0780869i
$124$	1.64427	+	2.84796i	0.147660	+	0.255755i
$125$	−7.70423			−0.689087
$126$	−2.33508	+	2.19258i	−0.208025	+	0.195330i
$127$	14.5557			1.29161			0.645806	−	0.763502i	$-0.276522\pi$
$127$	14.5557			1.29161			0.645806	+	0.763502i	$0.276522\pi$
$128$	2.41983	+	4.19126i	0.213884	+	0.370459i
$129$	−2.66222	+	4.61110i	−0.234395	+	0.405985i
$130$	1.58782	−	2.75019i	0.139261	−	0.241207i
$131$	3.03127	+	5.25032i	0.264844	+	0.458722i	0.967523	−	0.252784i	$-0.0813464\pi$
$131$	3.03127	+	5.25032i	0.264844	+	0.458722i	−0.702679	+	0.711507i	$0.748013\pi$
$132$	−0.212093			−0.0184604
$133$	2.36477	+	10.0844i	0.205051	+	0.874427i
$134$	−14.6698			−1.26728
$135$	0.413490	+	0.716185i	0.0355875	+	0.0616394i
$136$	−0.244138	+	0.422860i	−0.0209347	+	0.0362599i
$137$	10.0410	−	17.3915i	0.857861	−	1.48586i	−0.0161037	−	0.999870i	$-0.505126\pi$
$137$	10.0410	−	17.3915i	0.857861	−	1.48586i	0.873965	−	0.485989i	$-0.161540\pi$
$138$	−4.31987	−	7.48223i	−0.367732	−	0.636930i
$139$	−15.7498			−1.33588			−0.667939	−	0.744216i	$-0.732823\pi$
$139$	−15.7498			−1.33588			−0.667939	+	0.744216i	$0.732823\pi$
$140$	1.11911	+	0.337936i	0.0945819	+	0.0285608i
$141$	1.31060			0.110373
$142$	−0.762705	−	1.32104i	−0.0640048	−	0.110859i
$143$	0.629553	−	1.09042i	0.0526459	−	0.0911854i
$144$	1.32298	−	2.29146i	0.110248	−	0.190955i
$145$	−4.04279	−	7.00231i	−0.335735	−	0.581511i
$146$	−10.1062			−0.836394
$147$	6.27028	−	3.11185i	0.517164	−	0.256661i
$148$	−5.39019			−0.443071
$149$	1.87909	+	3.25468i	0.153941	+	0.266634i	0.932673	−	0.360723i	$-0.117470\pi$
$149$	1.87909	+	3.25468i	0.153941	+	0.266634i	−0.778732	+	0.627357i	$0.784137\pi$
$150$	2.61268	−	4.52529i	0.213324	−	0.369489i
$151$	1.94614	−	3.37081i	0.158375	−	0.274313i	−0.775908	−	0.630846i	$-0.782708\pi$
$151$	1.94614	−	3.37081i	0.158375	−	0.274313i	0.934283	+	0.356533i	$0.116041\pi$
$152$	−6.00585	−	10.4024i	−0.487139	−	0.843749i
$153$	0.159142			0.0128659
$154$	−1.21723	−	0.367566i	−0.0980873	−	0.0296194i
$155$	5.09003			0.408841
$156$	−0.847346	−	1.46765i	−0.0678420	−	0.117506i
$157$	−0.510874	+	0.884861i	−0.0407722	+	0.0706196i	−0.885691	−	0.464274i	$-0.846315\pi$
$157$	−0.510874	+	0.884861i	−0.0407722	+	0.0706196i	0.844919	+	0.534894i	$0.179648\pi$
$158$	−5.52641	+	9.57202i	−0.439657	+	0.761509i
$159$	−2.77279	−	4.80261i	−0.219896	−	0.380872i
$160$	−2.42552			−0.191754
$161$	4.31063	+	18.3824i	0.339725	+	1.44873i
$162$	−1.21066			−0.0951188
$163$	2.13396	+	3.69613i	0.167145	+	0.289503i	0.937415	−	0.348215i	$-0.113212\pi$
$163$	2.13396	+	3.69613i	0.167145	+	0.289503i	−0.770270	+	0.637718i	$0.779879\pi$
$164$	0.267145	−	0.462709i	0.0208605	−	0.0361315i
$165$	−0.164140	+	0.284299i	−0.0127783	+	0.0221326i
$166$	5.91713	+	10.2488i	0.459258	+	0.795459i
$167$	0.771033			0.0596643			0.0298322	−	0.999555i	$-0.490503\pi$
$167$	0.771033			0.0596643			0.0298322	+	0.999555i	$0.490503\pi$
$168$	−5.91776	+	5.55662i	−0.456565	+	0.428703i
$169$	−2.93934			−0.226103
$170$	0.0796662	+	0.137986i	0.00611012	+	0.0105830i
$171$	−1.95747	+	3.39043i	−0.149691	+	0.259273i
$172$	−1.42240	+	2.46367i	−0.108457	+	0.187853i
$173$	11.8178	+	20.4689i	0.898487	+	1.55622i	0.829429	+	0.558612i	$0.188666\pi$
$173$	11.8178	+	20.4689i	0.898487	+	1.55622i	0.0690580	+	0.997613i	$0.478001\pi$
$174$	11.8370			0.897358
$175$	−8.32471	+	7.81668i	−0.629289	+	0.590886i
$176$	1.05034			0.0791726
$177$	0.789193	+	1.36692i	0.0593194	+	0.102744i
$178$	7.14886	−	12.3822i	0.535830	−	0.928084i
$179$	7.68018	−	13.3025i	0.574043	−	0.994272i	−0.422101	−	0.906549i	$-0.638707\pi$
$179$	7.68018	−	13.3025i	0.574043	−	0.994272i	0.996145	−	0.0877237i	$-0.0279593\pi$
$180$	0.220924	+	0.382651i	0.0164667	+	0.0285211i
$181$	−11.5190			−0.856197			−0.428099	−	0.903732i	$-0.640816\pi$
$181$	−11.5190			−0.856197			−0.428099	+	0.903732i	$0.640816\pi$
$182$	−2.31954	−	9.89150i	−0.171936	−	0.733207i
$183$	8.56205			0.632925
$184$	−10.9478	−	18.9622i	−0.807083	−	1.39791i
$185$	−4.17149	+	7.22523i	−0.306694	+	0.531209i
$186$	−3.72580	+	6.45328i	−0.273189	+	0.473178i
$187$	0.0315868	+	0.0547099i	0.00230985	+	0.00400078i
$188$	0.700243			0.0510704
$189$	2.53279	+	0.764826i	0.184234	+	0.0556329i
$190$	−3.91961			−0.284358
$191$	−11.1517	−	19.3153i	−0.806908	−	1.39761i	−0.914995	−	0.403465i	$-0.867806\pi$
$191$	−11.1517	−	19.3153i	−0.806908	−	1.39761i	0.108087	−	0.994141i	$-0.465527\pi$
$192$	4.42139	−	7.65807i	0.319086	−	0.552673i
$193$	1.04778	−	1.81481i	0.0754209	−	0.130633i	−0.825848	−	0.563892i	$-0.809303\pi$
$193$	1.04778	−	1.81481i	0.0754209	−	0.130633i	0.901269	+	0.433259i	$0.142637\pi$
$194$	6.34794	+	10.9950i	0.455755	+	0.789392i
$195$	−2.62306			−0.187841
$196$	3.35015	−	1.66263i	0.239296	−	0.118760i
$197$	−13.2692			−0.945390			−0.472695	−	0.881226i	$-0.656719\pi$
$197$	−13.2692			−0.945390			−0.472695	+	0.881226i	$0.656719\pi$
$198$	−0.240294	−	0.416202i	−0.0170770	−	0.0295782i
$199$	−8.09366	+	14.0186i	−0.573744	+	0.993754i	0.422432	+	0.906394i	$0.361176\pi$
$199$	−8.09366	+	14.0186i	−0.573744	+	0.993754i	−0.996177	+	0.0873599i	$0.972157\pi$
$200$	6.62129	−	11.4684i	0.468196	−	0.810939i
$201$	6.05857	+	10.4937i	0.427338	+	0.740172i
$202$	−13.5542			−0.953668
$203$	−24.7637	−	7.47789i	−1.73807	−	0.524845i
$204$	0.0850282			0.00595317
$205$	−0.413490	−	0.716185i	−0.0288794	−	0.0500205i
$206$	−8.94252	+	15.4889i	−0.623055	+	1.07916i
$207$	−3.56818	+	6.18027i	−0.248006	+	0.429558i
$208$	4.19629	+	7.26818i	0.290960	+	0.503958i
$209$	−1.55408			−0.107498
$210$	0.604760	+	2.57895i	0.0417324	+	0.177965i
$211$	9.64598			0.664057			0.332028	−	0.943269i	$-0.392267\pi$
$211$	9.64598			0.664057			0.332028	+	0.943269i	$0.392267\pi$
$212$	−1.48148	−	2.56599i	−0.101748	−	0.176233i
$213$	−0.629988	+	1.09117i	−0.0431661	+	0.0747659i
$214$	−9.33008	+	16.1602i	−0.637791	+	1.10469i
$215$	2.20160	+	3.81328i	0.150148	+	0.260064i
$216$	−3.06818			−0.208763
$217$	11.8714	−	11.1470i	0.805885	−	0.756705i
$218$	−7.86012			−0.532354
$219$	4.17382	+	7.22927i	0.282041	+	0.488509i
$220$	−0.0876984	+	0.151898i	−0.00591262	+	0.0102410i
$221$	−0.252388	+	0.437149i	−0.0169775	+	0.0294058i
$222$	−6.10689	−	10.5774i	−0.409868	−	0.709912i
$223$	−14.1497			−0.947533			−0.473766	−	0.880651i	$-0.657106\pi$
$223$	−14.1497			−0.947533			−0.473766	+	0.880651i	$0.657106\pi$
$224$	−5.65702	+	5.31180i	−0.377976	+	0.354909i
$225$	−4.31611			−0.287740
$226$	4.78731	+	8.29186i	0.318447	+	0.551567i
$227$	10.6771	−	18.4932i	0.708663	−	1.22744i	−0.256691	−	0.966494i	$-0.582632\pi$
$227$	10.6771	−	18.4932i	0.708663	−	1.22744i	0.965353	−	0.260946i	$-0.0840344\pi$
$228$	−1.04586	+	1.81148i	−0.0692635	+	0.119968i
$229$	−13.7574	−	23.8285i	−0.909112	−	1.57463i	−0.815300	−	0.579039i	$-0.803428\pi$
$229$	−13.7574	−	23.8285i	−0.909112	−	1.57463i	−0.0938126	−	0.995590i	$-0.529905\pi$
$230$	−7.14488			−0.471120
$231$	0.239780	+	1.02253i	0.0157764	+	0.0672773i
$232$	29.9983			1.96948
$233$	−2.12147	−	3.67450i	−0.138982	−	0.240724i	0.788129	−	0.615510i	$-0.211050\pi$
$233$	−2.12147	−	3.67450i	−0.138982	−	0.240724i	−0.927112	+	0.374785i	$0.877716\pi$
$234$	1.92003	−	3.32558i	0.125516	−	0.217400i
$235$	0.541921	−	0.938634i	0.0353510	−	0.0612297i
$236$	0.421658	+	0.730334i	0.0274476	+	0.0475407i
$237$	9.12954			0.593027
$238$	0.487988	+	0.147357i	0.0316316	+	0.00955176i
$239$	−19.2763			−1.24688			−0.623441	−	0.781871i	$-0.714266\pi$
$239$	−19.2763			−1.24688			−0.623441	+	0.781871i	$0.714266\pi$
$240$	−1.09407	−	1.89499i	−0.0706222	−	0.122321i
$241$	5.68144	−	9.84054i	0.365974	−	0.633885i	−0.622958	−	0.782255i	$-0.714069\pi$
$241$	5.68144	−	9.84054i	0.365974	−	0.633885i	0.988932	+	0.148370i	$0.0474027\pi$
$242$	−6.56327	+	11.3679i	−0.421903	+	0.730757i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	4.57462			0.292860
$245$	0.364031	−	5.77740i	0.0232571	−	0.369104i
$246$	1.21066			0.0771892
$247$	−6.20880	−	10.7539i	−0.395056	−	0.684257i
$248$	−9.44227	+	16.3545i	−0.599585	+	1.03851i
$249$	4.88750	−	8.46541i	0.309733	−	0.536473i
$250$	−4.66362	−	8.07762i	−0.294953	−	0.510874i
$251$	14.5991			0.921485			0.460743	−	0.887534i	$-0.347583\pi$
$251$	14.5991			0.921485			0.460743	+	0.887534i	$0.347583\pi$
$252$	1.35325	+	0.408639i	0.0852466	+	0.0257419i
$253$	−2.83287			−0.178101
$254$	8.81105	+	15.2612i	0.552854	+	0.957572i
$255$	0.0658037	−	0.113975i	0.00412079	−	0.00713741i
$256$	5.91318	−	10.2419i	0.369574	−	0.640120i
$257$	−6.31396	−	10.9361i	−0.393854	−	0.682175i	0.599100	−	0.800674i	$-0.295525\pi$
$257$	−6.31396	−	10.9361i	−0.393854	−	0.682175i	−0.992954	+	0.118499i	$0.962192\pi$
$258$	−6.44611			−0.401317
$259$	6.09383	+	25.9867i	0.378652	+	1.61474i
$260$	−1.40148			−0.0869158
$261$	−4.88862	−	8.46734i	−0.302598	−	0.524115i
$262$	−3.66986	+	6.35638i	−0.226724	+	0.392698i
$263$	6.95511	−	12.0466i	0.428870	−	0.742825i	−0.567903	−	0.823096i	$-0.692245\pi$
$263$	6.95511	−	12.0466i	0.428870	−	0.742825i	0.996773	+	0.0802705i	$0.0255784\pi$
$264$	−0.608975	−	1.05478i	−0.0374798	−	0.0649170i
$265$	−4.58608			−0.281721
$266$	−9.14166	+	8.58378i	−0.560511	+	0.526305i
$267$	−11.8098			−0.722749
$268$	3.23704	+	5.60671i	0.197733	+	0.342484i
$269$	−8.40538	+	14.5585i	−0.512485	+	0.887650i	0.487410	+	0.873173i	$0.337942\pi$
$269$	−8.40538	+	14.5585i	−0.512485	+	0.887650i	−0.999895	+	0.0144768i	$0.995392\pi$
$270$	−0.500597	+	0.867060i	−0.0304654	+	0.0527676i
$271$	−10.1913	−	17.6518i	−0.619076	−	1.07227i	−0.989655	−	0.143470i	$-0.954174\pi$
$271$	−10.1913	−	17.6518i	−0.619076	−	1.07227i	0.370579	−	0.928801i	$-0.379159\pi$
$272$	−0.421083			−0.0255319
$273$	−6.11773	+	5.74439i	−0.370262	+	0.347666i
$274$	24.3126			1.46878
$275$	−0.856666	−	1.48379i	−0.0516589	−	0.0894758i
$276$	−1.90644	+	3.30206i	−0.114754	+	0.198761i
$277$	−1.20360	+	2.08470i	−0.0723173	+	0.125257i	−0.899917	−	0.436062i	$-0.856373\pi$
$277$	−1.20360	+	2.08470i	−0.0723173	+	0.125257i	0.827599	+	0.561319i	$0.189706\pi$
$278$	−9.53385	−	16.5131i	−0.571802	−	0.990391i
$279$	6.15497			0.368488
$280$	1.53264	+	6.53582i	0.0915926	+	0.390590i
$281$	−4.17078			−0.248808			−0.124404	−	0.992232i	$-0.539702\pi$
$281$	−4.17078			−0.248808			−0.124404	+	0.992232i	$0.539702\pi$
$282$	0.793350	+	1.37412i	0.0472433	+	0.0818278i
$283$	−12.5152	+	21.6770i	−0.743952	+	1.28856i	0.206731	+	0.978398i	$0.433718\pi$
$283$	−12.5152	+	21.6770i	−0.743952	+	1.28856i	−0.950683	+	0.310165i	$0.899616\pi$
$284$	−0.336597	+	0.583003i	−0.0199733	+	0.0345949i
$285$	1.61878	+	2.80382i	0.0958885	+	0.166084i
$286$	1.52436			0.0901371
$287$	−2.53279	−	0.764826i	−0.149506	−	0.0451462i
$288$	−2.93299			−0.172828
$289$	8.48734	+	14.7005i	0.499255	+	0.864735i
$290$	4.89446	−	8.47746i	0.287413	−	0.497813i
$291$	5.24335	−	9.08175i	0.307371	−	0.532381i
$292$	2.23003	+	3.86253i	0.130503	+	0.226037i
$293$	3.54593			0.207156			0.103578	−	0.994621i	$-0.466971\pi$
$293$	3.54593			0.207156			0.103578	+	0.994621i	$0.466971\pi$
$294$	7.05828	+	4.69047i	0.411647	+	0.273554i
$295$	1.30529			0.0759971
$296$	−15.4766	−	26.8063i	−0.899561	−	1.55809i
$297$	−0.198481	+	0.343780i	−0.0115170	+	0.0199481i
$298$	−2.27495	+	3.94033i	−0.131784	+	0.228257i
$299$	−11.3177	−	19.6029i	−0.654522	−	1.13367i
$300$	−2.30605			−0.133140
$301$	13.4857	+	4.07227i	0.777303	+	0.234722i
$302$	4.71225			0.271159
$303$	5.59782	+	9.69571i	0.321587	+	0.557004i
$304$	5.17936	−	8.97092i	0.297057	−	0.514517i
$305$	3.54032	−	6.13201i	0.202718	−	0.351118i
$306$	0.0963340	+	0.166855i	0.00550705	+	0.00953849i
$307$	1.01986			0.0582066			0.0291033	−	0.999576i	$-0.490735\pi$
$307$	1.01986			0.0582066			0.0291033	+	0.999576i	$0.490735\pi$
$308$	0.128112	+	0.546326i	0.00729988	+	0.0311298i
$309$	14.7729			0.840401
$310$	3.08116	+	5.33673i	0.174998	+	0.303106i
$311$	−3.96232	+	6.86294i	−0.224683	+	0.389162i	−0.956224	−	0.292635i	$-0.905468\pi$
$311$	−3.96232	+	6.86294i	−0.224683	+	0.389162i	0.731542	+	0.681797i	$0.238801\pi$
$312$	4.86590	−	8.42799i	0.275478	−	0.477141i
$313$	−11.0931	−	19.2138i	−0.627019	−	1.08603i	−0.988147	−	0.153513i	$-0.950941\pi$
$313$	−11.0931	−	19.2138i	−0.627019	−	1.08603i	0.361128	−	0.932516i	$-0.382392\pi$
$314$	−1.23700			−0.0698077
$315$	1.59504	−	1.49770i	0.0898704	−	0.0843859i
$316$	4.87783			0.274399
$317$	5.02510	+	8.70372i	0.282238	+	0.488850i	0.971936	−	0.235247i	$-0.0755900\pi$
$317$	5.02510	+	8.70372i	0.282238	+	0.488850i	−0.689698	+	0.724097i	$0.742257\pi$
$318$	3.35692	−	5.81435i	0.188247	−	0.326053i
$319$	1.94060	−	3.36122i	0.108653	−	0.188192i
$320$	−3.65640	−	6.33306i	−0.204399	−	0.354029i
$321$	15.4131			0.860278
$322$	−16.6639	+	15.6470i	−0.928645	+	0.871973i
$323$	0.623031			0.0346664
$324$	0.267145	+	0.462709i	0.0148414	+	0.0257061i
$325$	6.84503	−	11.8559i	0.379694	−	0.657649i
$326$	−2.58351	+	4.47477i	−0.143087	+	0.247835i
$327$	3.24620	+	5.62258i	0.179515	+	0.310929i
$328$	3.06818			0.169412
$329$	−0.791654	−	3.37595i	−0.0436453	−	0.186122i
$330$	−0.397437			−0.0218782
$331$	8.84745	+	15.3242i	0.486300	+	0.842296i	0.999876	−	0.0157481i	$-0.00501297\pi$
$331$	8.84745	+	15.3242i	0.486300	+	0.842296i	−0.513576	+	0.858044i	$0.671680\pi$
$332$	2.61135	−	4.52299i	0.143316	−	0.248231i
$333$	−5.04425	+	8.73689i	−0.276423	+	0.478779i
$334$	0.466731	+	0.808402i	0.0255384	+	0.0442338i
$335$	10.0206			0.547485
$336$	−6.70165	−	2.02369i	−0.365605	−	0.110401i
$337$	17.6666			0.962363			0.481182	−	0.876621i	$-0.340208\pi$
$337$	17.6666			0.962363			0.481182	+	0.876621i	$0.340208\pi$
$338$	−1.77928	−	3.08180i	−0.0967801	−	0.167628i
$339$	3.95428	−	6.84902i	0.214767	−	0.371988i
$340$	0.0351583	−	0.0608960i	0.00190673	−	0.00330255i
$341$	1.22165	+	2.11595i	0.0661559	+	0.114585i
$342$	−4.73967			−0.256292
$343$	−11.8032	−	14.2718i	−0.637315	−	0.770603i
$344$	−16.3363			−0.880795
$345$	2.95081	+	5.11095i	0.158866	+	0.275164i
$346$	−14.3073	+	24.7810i	−0.769167	+	1.33224i
$347$	−0.891173	+	1.54356i	−0.0478407	+	0.0828625i	−0.888954	−	0.457996i	$-0.848567\pi$
$347$	−0.891173	+	1.54356i	−0.0478407	+	0.0828625i	0.841113	+	0.540859i	$0.181901\pi$
$348$	−2.61194	−	4.52402i	−0.140015	−	0.242513i
$349$	15.5672			0.833292			0.416646	−	0.909069i	$-0.363205\pi$
$349$	15.5672			0.833292			0.416646	+	0.909069i	$0.363205\pi$
$350$	−13.2347	−	3.99649i	−0.707427	−	0.213621i
$351$	−3.17185			−0.169301
$352$	−0.582144	−	1.00830i	−0.0310284	−	0.0537427i
$353$	12.4278	−	21.5256i	0.661465	−	1.14569i	−0.318766	−	0.947833i	$-0.603269\pi$
$353$	12.4278	−	21.5256i	0.661465	−	1.14569i	0.980231	−	0.197857i	$-0.0633981\pi$
$354$	−0.955448	+	1.65488i	−0.0507815	+	0.0879561i
$355$	0.520987	+	0.902376i	0.0276511	+	0.0478932i
$356$	−6.30987			−0.334423
$357$	−0.0961280	−	0.409931i	−0.00508763	−	0.0216958i
$358$	18.5962			0.982842
$359$	15.9591	+	27.6419i	0.842287	+	1.45888i	0.887957	+	0.459927i	$0.152124\pi$
$359$	15.9591	+	27.6419i	0.842287	+	1.45888i	−0.0456701	+	0.998957i	$0.514542\pi$
$360$	−1.26866	+	2.19738i	−0.0668642	+	0.115812i
$361$	1.83665	−	3.18118i	0.0966660	−	0.167430i
$362$	−6.97280	−	12.0772i	−0.366482	−	0.634766i
$363$	10.8424			0.569080
$364$	−3.26865	+	3.06917i	−0.171324	+	0.160868i
$365$	6.90332			0.361336
$366$	5.18289	+	8.97702i	0.270914	+	0.469237i
$367$	−17.2593	+	29.8940i	−0.900928	+	1.56045i	−0.0746360	+	0.997211i	$0.523779\pi$
$367$	−17.2593	+	29.8940i	−0.900928	+	1.56045i	−0.826292	+	0.563242i	$0.809554\pi$
$368$	9.44123	−	16.3527i	0.492158	−	0.852443i
$369$	−0.500000	−	0.866025i	−0.0260290	−	0.0450835i
$370$	−10.1005			−0.525102
$371$	−10.6961	+	10.0433i	−0.555312	+	0.521423i
$372$	3.28854			0.170503
$373$	−11.2569	−	19.4975i	−0.582860	−	1.00954i	−0.995139	−	0.0984853i	$-0.968600\pi$
$373$	−11.2569	−	19.4975i	−0.582860	−	1.00954i	0.412278	−	0.911058i	$-0.364733\pi$
$374$	−0.0382410	+	0.0662353i	−0.00197739	+	0.00342495i
$375$	−3.85211	+	6.67206i	−0.198922	+	0.344543i
$376$	2.01058	+	3.48243i	0.103688	+	0.179592i
$377$	31.0120			1.59720
$378$	0.731288	+	3.11852i	0.0376134	+	0.160400i
$379$	15.8824			0.815824			0.407912	−	0.913021i	$-0.366257\pi$
$379$	15.8824			0.815824			0.407912	+	0.913021i	$0.366257\pi$
$380$	0.864901	+	1.49805i	0.0443685	+	0.0768485i
$381$	7.27786	−	12.6056i	0.372856	−	0.645806i
$382$	13.5010	−	23.3844i	0.690769	−	1.19645i
$383$	−3.39583	−	5.88175i	−0.173519	−	0.300543i	0.766129	−	0.642687i	$-0.222180\pi$
$383$	−3.39583	−	5.88175i	−0.173519	−	0.300543i	−0.939648	+	0.342144i	$0.888847\pi$
$384$	4.83965			0.246972
$385$	0.831465	+	0.251077i	0.0423754	+	0.0127961i
$386$	2.53702			0.129131
$387$	2.66222	+	4.61110i	0.135328	+	0.234395i
$388$	2.80147	−	4.85229i	0.142223	−	0.246338i
$389$	−9.79949	+	16.9732i	−0.496854	+	0.860576i	−0.999993	−	0.00362908i	$-0.998845\pi$
$389$	−9.79949	+	16.9732i	−0.496854	+	0.860576i	0.503140	+	0.864205i	$0.332178\pi$
$390$	−1.58782	−	2.75019i	−0.0804025	−	0.139261i
$391$	1.13570			0.0574346
$392$	17.8877	+	11.8870i	0.903467	+	0.600385i
$393$	6.06255			0.305815
$394$	−8.03226	−	13.9123i	−0.404660	−	0.700891i
$395$	3.77497	−	6.53844i	0.189939	−	0.328985i
$396$	−0.106047	+	0.183678i	−0.00532905	+	0.00923018i
$397$	−11.2827	−	19.5422i	−0.566263	−	0.980796i	−0.996931	−	0.0782855i	$-0.975055\pi$
$397$	−11.2827	−	19.5422i	−0.566263	−	0.980796i	0.430668	−	0.902510i	$-0.358278\pi$
$398$	−19.5974			−0.982330
$399$	9.91571	+	2.99424i	0.496407	+	0.149900i
$400$	11.4202			0.571010
$401$	14.7652	+	25.5741i	0.737340	+	1.27711i	0.953689	+	0.300794i	$0.0972516\pi$
$401$	14.7652	+	25.5741i	0.737340	+	1.27711i	−0.216349	+	0.976316i	$0.569415\pi$
$402$	−7.33489	+	12.7044i	−0.365831	+	0.633638i
$403$	−9.76133	+	16.9071i	−0.486247	+	0.842204i
$404$	2.99086	+	5.18033i	0.148801	+	0.257731i
$405$	0.826979			0.0410929
$406$	−7.14997	−	30.4905i	−0.354847	−	1.51322i
$407$	−4.00475			−0.198508
$408$	0.244138	+	0.422860i	0.0120866	+	0.0209347i
$409$	−4.76162	+	8.24737i	−0.235447	+	0.407806i	−0.959402	−	0.282041i	$-0.908989\pi$
$409$	−4.76162	+	8.24737i	−0.235447	+	0.407806i	0.723956	+	0.689847i	$0.242322\pi$
$410$	0.500597	−	0.867060i	0.0247227	−	0.0428210i
$411$	−10.0410	−	17.3915i	−0.495286	−	0.857861i
$412$	7.89302			0.388861
$413$	3.04432	−	2.85854i	0.149801	−	0.140659i
$414$	−8.63974			−0.424620
$415$	−4.04187	−	7.00072i	−0.198407	−	0.343652i
$416$	4.65151	−	8.05665i	0.228059	−	0.395010i
$417$	−7.87489	+	13.6397i	−0.385635	+	0.667939i
$418$	−0.940736	−	1.62940i	−0.0460129	−	0.0796966i
$419$	11.1971			0.547013			0.273506	−	0.961870i	$-0.411817\pi$
$419$	11.1971			0.547013			0.273506	+	0.961870i	$0.411817\pi$
$420$	0.852215	−	0.800208i	0.0415838	−	0.0390461i
$421$	−7.98853			−0.389337			−0.194668	−	0.980869i	$-0.562363\pi$
$421$	−7.98853			−0.389337			−0.194668	+	0.980869i	$0.562363\pi$
$422$	5.83902	+	10.1135i	0.284239	+	0.492317i
$423$	0.655301	−	1.13502i	0.0318618	−	0.0551863i
$424$	8.50741	−	14.7353i	0.413156	−	0.715607i
$425$	0.343437	+	0.594851i	0.0166592	+	0.0288545i
$426$	−1.52541			−0.0739063
$427$	−5.17181	−	22.0548i	−0.250281	−	1.06731i
$428$	8.23510			0.398059
$429$	−0.629553	−	1.09042i	−0.0303951	−	0.0526459i
$430$	−2.66540	+	4.61661i	−0.128537	+	0.222633i
$431$	−2.85862	+	4.95128i	−0.137695	+	0.238495i	−0.926624	−	0.375990i	$-0.877303\pi$
$431$	−2.85862	+	4.95128i	−0.137695	+	0.238495i	0.788929	+	0.614485i	$0.210636\pi$
$432$	−1.32298	−	2.29146i	−0.0636517	−	0.110248i
$433$	18.7297			0.900090			0.450045	−	0.893006i	$-0.351408\pi$
$433$	18.7297			0.900090			0.450045	+	0.893006i	$0.351408\pi$
$434$	18.8734	+	5.69918i	0.905951	+	0.273569i
$435$	−8.08558			−0.387674
$436$	1.73441	+	3.00409i	0.0830633	+	0.143870i
$437$	−13.9692	+	24.1953i	−0.668236	+	1.15742i
$438$	−5.05310	+	8.75222i	−0.241446	+	0.418197i
$439$	14.3470	+	24.8497i	0.684744	+	1.18601i	0.973517	+	0.228614i	$0.0734192\pi$
$439$	14.3470	+	24.8497i	0.684744	+	1.18601i	−0.288774	+	0.957397i	$0.593247\pi$
$440$	−1.00722			−0.0480173
$441$	0.440193	−	6.98615i	0.0209616	−	0.332674i
$442$	−0.611115			−0.0290678
$443$	10.4067	+	18.0249i	0.494437	+	0.856390i	0.999979	−	0.00641200i	$-0.00204102\pi$
$443$	10.4067	+	18.0249i	0.494437	+	0.856390i	−0.505543	+	0.862802i	$0.668708\pi$
$444$	−2.69509	+	4.66804i	−0.127903	+	0.221535i
$445$	−4.88323	+	8.45801i	−0.231488	+	0.400948i
$446$	−8.56526	−	14.8355i	−0.405577	−	0.702480i
$447$	3.75818			0.177756
$448$	−22.3969	−	6.76318i	−1.05815	−	0.319530i
$449$	31.0640			1.46600			0.733001	−	0.680227i	$-0.238119\pi$
$449$	31.0640			1.46600			0.733001	+	0.680227i	$0.238119\pi$
$450$	−2.61268	−	4.52529i	−0.123163	−	0.213324i
$451$	0.198481	−	0.343780i	0.00934612	−	0.0161879i
$452$	2.11274	−	3.65937i	0.0993747	−	0.172122i
$453$	−1.94614	−	3.37081i	−0.0914377	−	0.158375i
$454$	25.8527			1.21333
$455$	1.58443	+	6.75667i	0.0742791	+	0.316758i
$456$	−12.0117			−0.562499
$457$	−13.0628	−	22.6255i	−0.611053	−	1.05837i	−0.991063	−	0.133392i	$-0.957413\pi$
$457$	−13.0628	−	22.6255i	−0.611053	−	1.05837i	0.380011	−	0.924982i	$-0.375920\pi$
$458$	16.6556	−	28.8483i	0.778263	−	1.34799i
$459$	0.0795711	−	0.137821i	0.00371406	−	0.00643295i
$460$	1.57659	+	2.73073i	0.0735089	+	0.127321i
$461$	17.3348			0.807364			0.403682	−	0.914899i	$-0.367730\pi$
$461$	17.3348			0.807364			0.403682	+	0.914899i	$0.367730\pi$
$462$	−0.926938	+	0.870370i	−0.0431250	+	0.0404933i
$463$	0.550182			0.0255691			0.0127846	−	0.999918i	$-0.495930\pi$
$463$	0.550182			0.0255691			0.0127846	+	0.999918i	$0.495930\pi$
$464$	12.9351	+	22.4042i	0.600495	+	1.04009i
$465$	2.54502	−	4.40810i	0.118022	−	0.204421i
$466$	2.56839	−	4.44858i	0.118978	−	0.206077i
$467$	−8.54106	−	14.7935i	−0.395233	−	0.684564i	0.597898	−	0.801572i	$-0.296003\pi$
$467$	−8.54106	−	14.7935i	−0.395233	−	0.684564i	−0.993131	+	0.117009i	$0.962669\pi$
$468$	−1.69469			−0.0783372
$469$	23.3710	−	21.9447i	1.07917	−	1.01331i
$470$	1.31217			0.0605258
$471$	0.510874	+	0.884861i	0.0235399	+	0.0407722i
$472$	−2.42138	+	4.19396i	−0.111453	+	0.193043i
$473$	−1.05680	+	1.83043i	−0.0485918	+	0.0841634i
$474$	5.52641	+	9.57202i	0.253836	+	0.439657i
$475$	−16.8973			−0.775299
$476$	−0.0513603	−	0.219022i	−0.00235409	−	0.0100389i
$477$	−5.54558			−0.253915
$478$	−11.6686	−	20.2106i	−0.533708	−	0.924410i
$479$	−5.41579	+	9.38042i	−0.247454	+	0.428602i	−0.962819	−	0.270149i	$-0.912927\pi$
$479$	−5.41579	+	9.38042i	−0.247454	+	0.428602i	0.715365	+	0.698751i	$0.246260\pi$
$480$	−1.21276	+	2.10057i	−0.0553548	+	0.0958772i
$481$	−15.9996	−	27.7121i	−0.729520	−	1.26356i
$482$	13.7566			0.626597
$483$	18.0749	+	5.45807i	0.822437	+	0.248351i
$484$	5.79300			0.263318
$485$	−4.33614	−	7.51042i	−0.196894	−	0.341030i
$486$	−0.605332	+	1.04847i	−0.0274584	+	0.0475594i
$487$	10.0446	−	17.3977i	0.455163	−	0.788365i	−0.543535	−	0.839387i	$-0.682914\pi$
$487$	10.0446	−	17.3977i	0.455163	−	0.788365i	0.998698	+	0.0510215i	$0.0162477\pi$
$488$	13.1349	+	22.7504i	0.594591	+	1.02986i
$489$	4.26792			0.193002
$490$	6.27777	−	3.11557i	0.283601	−	0.140747i
$491$	−11.3968			−0.514330			−0.257165	−	0.966368i	$-0.582788\pi$
$491$	−11.3968			−0.514330			−0.257165	+	0.966368i	$0.582788\pi$
$492$	−0.267145	−	0.462709i	−0.0120438	−	0.0208605i
$493$	−0.777986	+	1.34751i	−0.0350387	+	0.0606889i
$494$	7.51677	−	13.0194i	0.338196	−	0.585772i
$495$	0.164140	+	0.284299i	0.00737754	+	0.0127783i
$496$	−16.2858			−0.731252
$497$	3.19126	+	0.963663i	0.143148	+	0.0432262i
$498$	11.8343			0.530306
$499$	−2.88335	−	4.99411i	−0.129076	−	0.223567i	0.794243	−	0.607601i	$-0.207868\pi$
$499$	−2.88335	−	4.99411i	−0.129076	−	0.223567i	−0.923319	+	0.384034i	$0.874535\pi$
$500$	−2.05815	+	3.56482i	−0.0920432	+	0.159423i
$501$	0.385516	−	0.667734i	0.0172236	−	0.0298322i
$502$	8.83729	+	15.3066i	0.394428	+	0.683169i
$503$	27.0330			1.20534			0.602671	−	0.797989i	$-0.294103\pi$
$503$	27.0330			1.20534			0.602671	+	0.797989i	$0.294103\pi$
$504$	1.85330	+	7.90324i	0.0825523	+	0.352038i
$505$	9.25857			0.412001
$506$	−1.71483	−	2.97017i	−0.0762333	−	0.132040i
$507$	−1.46967	+	2.54555i	−0.0652704	+	0.113052i
$508$	3.88849	−	6.73507i	0.172524	−	0.298820i
$509$	11.6931	+	20.2530i	0.518287	+	0.897699i	0.999774	+	0.0212460i	$0.00676333\pi$
$509$	11.6931	+	20.2530i	0.518287	+	0.897699i	−0.481488	+	0.876453i	$0.659903\pi$
$510$	0.159332			0.00705536
$511$	16.1005	−	15.1180i	0.712246	−	0.668781i
$512$	23.9971			1.06053
$513$	1.95747	+	3.39043i	0.0864242	+	0.149691i
$514$	7.64409	−	13.2399i	0.337166	−	0.583989i
$515$	6.10844	−	10.5801i	0.269170	−	0.466216i
$516$	1.42240	+	2.46367i	0.0626176	+	0.108457i
$517$	0.520260			0.0228810
$518$	−23.5574	+	22.1198i	−1.03505	+	0.971887i
$519$	23.6355			1.03748
$520$	−4.02400	−	6.96978i	−0.176464	−	0.305645i
$521$	−11.8713	+	20.5616i	−0.520089	+	0.900821i	0.479638	+	0.877466i	$0.340768\pi$
$521$	−11.8713	+	20.5616i	−0.520089	+	0.900821i	−0.999727	+	0.0233543i	$0.992565\pi$
$522$	5.91848	−	10.2511i	0.259045	−	0.448679i
$523$	−12.5217	−	21.6882i	−0.547534	−	0.948357i	−0.998443	−	0.0557871i	$-0.982233\pi$
$523$	−12.5217	−	21.6882i	−0.547534	−	0.948357i	0.450908	−	0.892570i	$-0.351100\pi$
$524$	3.23916			0.141503
$525$	2.60709	+	11.1178i	0.113783	+	0.485218i
$526$	16.8406			0.734285
$527$	−0.489758	−	0.848286i	−0.0213342	−	0.0369519i
$528$	0.525172	−	0.909624i	0.0228552	−	0.0395863i
$529$	−13.9638	+	24.1860i	−0.607122	+	1.05157i
$530$	−2.77610	−	4.80835i	−0.120586	−	0.208861i
$531$	1.57839			0.0684961
$532$	5.29787	+	1.59979i	0.229692	+	0.0693599i
$533$	3.17185			0.137388
$534$	−7.14886	−	12.3822i	−0.309361	−	0.535830i
$535$	6.37318	−	11.0387i	0.275536	−	0.477243i
$536$	−18.5888	+	32.1967i	−0.802912	+	1.39068i
$537$	−7.68018	−	13.3025i	−0.331424	−	0.574043i
$538$	−20.3522			−0.877445
$539$	2.48906	−	1.23529i	0.107212	−	0.0532077i
$540$	0.441847			0.0190141
$541$	−4.81976	−	8.34808i	−0.207218	−	0.358912i	0.743619	−	0.668603i	$-0.233108\pi$
$541$	−4.81976	−	8.34808i	−0.207218	−	0.358912i	−0.950837	+	0.309691i	$0.899774\pi$
$542$	12.3382	−	21.3704i	0.529972	−	0.917939i
$543$	−5.75948	+	9.97571i	−0.247163	+	0.428099i
$544$	0.233382	+	0.404229i	0.0100061	+	0.0173312i
$545$	5.36908			0.229986
$546$	−9.72606	−	2.93697i	−0.416237	−	0.125691i
$547$	−22.0752			−0.943868			−0.471934	−	0.881634i	$-0.656444\pi$
$547$	−22.0752			−0.943868			−0.471934	+	0.881634i	$0.656444\pi$
$548$	−5.36482	−	9.29214i	−0.229174	−	0.396940i
$549$	4.28103	−	7.41495i	0.182710	−	0.316463i
$550$	1.03714	−	1.79637i	0.0442236	−	0.0765975i
$551$	−19.1386	−	33.1491i	−0.815332	−	1.41220i
$552$	−21.8956			−0.931939
$553$	−5.51459	−	23.5166i	−0.234504	−	1.00003i
$554$	−2.91431			−0.123817
$555$	4.17149	+	7.22523i	0.177070	+	0.306694i
$556$	−4.20748	+	7.28757i	−0.178437	+	0.309062i
$557$	20.5616	−	35.6138i	0.871224	−	1.50901i	0.0104935	−	0.999945i	$-0.496660\pi$
$557$	20.5616	−	35.6138i	0.871224	−	1.50901i	0.860731	−	0.509060i	$-0.170007\pi$
$558$	3.72580	+	6.45328i	0.157726	+	0.273189i
$559$	−16.8883			−0.714301
$560$	−4.22040	+	3.96285i	−0.178345	+	0.167461i
$561$	0.0631735			0.00266719
$562$	−2.52471	−	4.37293i	−0.106498	−	0.184461i
$563$	19.1200	−	33.1167i	0.805810	−	1.39570i	−0.109933	−	0.993939i	$-0.535064\pi$
$563$	19.1200	−	33.1167i	0.805810	−	1.39570i	0.915743	−	0.401765i	$-0.131603\pi$
$564$	0.350121	−	0.606428i	0.0147428	−	0.0255352i
$565$	−3.27011	−	5.66400i	−0.137575	−	0.238286i
$566$	−30.3035			−1.27375
$567$	1.92876	−	1.81105i	0.0810001	−	0.0760570i
$568$	−3.86583			−0.162207
$569$	−17.3013	−	29.9667i	−0.725307	−	1.25627i	−0.958848	−	0.283922i	$-0.908364\pi$
$569$	−17.3013	−	29.9667i	−0.725307	−	1.25627i	0.233540	−	0.972347i	$-0.424969\pi$
$570$	−1.95980	+	3.39448i	−0.0820872	+	0.142179i
$571$	−8.87025	+	15.3637i	−0.371208	+	0.642952i	−0.989752	−	0.142799i	$-0.954390\pi$
$571$	−8.87025	+	15.3637i	−0.371208	+	0.642952i	0.618543	+	0.785751i	$0.287723\pi$
$572$	−0.336365	−	0.582600i	−0.0140641	−	0.0243597i
$573$	−22.3034			−0.931737
$574$	−0.731288	−	3.11852i	−0.0305234	−	0.130165i
$575$	−30.8013			−1.28450
$576$	−4.42139	−	7.65807i	−0.184224	−	0.319086i
$577$	−22.1310	+	38.3321i	−0.921327	+	1.59579i	−0.123963	+	0.992287i	$0.539560\pi$
$577$	−22.1310	+	38.3321i	−0.921327	+	1.59579i	−0.797364	+	0.603499i	$0.793773\pi$
$578$	−10.2753	+	17.7974i	−0.427397	+	0.740273i
$579$	−1.04778	−	1.81481i	−0.0435443	−	0.0754209i
$580$	−4.32005			−0.179380
$581$	−24.7581	−	7.47618i	−1.02714	−	0.310164i
$582$	12.6959			0.526261
$583$	−1.10069	−	1.90646i	−0.0455860	−	0.0789574i
$584$	−12.8060	+	22.1807i	−0.529917	+	0.917842i
$585$	−1.31153	+	2.27163i	−0.0542250	+	0.0939205i
$586$	2.14647	+	3.71779i	0.0886698	+	0.153581i
$587$	23.5641			0.972595			0.486298	−	0.873793i	$-0.338347\pi$
$587$	23.5641			0.972595			0.486298	+	0.873793i	$0.338347\pi$
$588$	0.235191	−	3.73263i	0.00969911	−	0.153931i
$589$	24.0963			0.992870
$590$	0.790136	+	1.36856i	0.0325294	+	0.0563425i
$591$	−6.63459	+	11.4914i	−0.272910	+	0.472695i
$592$	13.3468	−	23.1174i	0.548552	−	0.950119i
$593$	14.8967	+	25.8018i	0.611734	+	1.05955i	0.990948	+	0.134245i	$0.0428608\pi$
$593$	14.8967	+	25.8018i	0.611734	+	1.05955i	−0.379215	+	0.925309i	$0.623806\pi$
$594$	−0.480588			−0.0197188
$595$	−0.333334	−	0.100657i	−0.0136654	−	0.00412652i
$596$	2.00796			0.0822493
$597$	8.09366	+	14.0186i	0.331251	+	0.573744i
$598$	13.7020	−	23.7325i	0.560316	−	0.970496i
$599$	−6.33254	+	10.9683i	−0.258741	+	0.448152i	−0.965905	−	0.258897i	$-0.916641\pi$
$599$	−6.33254	+	10.9683i	−0.258741	+	0.448152i	0.707164	+	0.707049i	$0.249974\pi$
$600$	−6.62129	−	11.4684i	−0.270313	−	0.468196i
$601$	17.6451			0.719757			0.359879	−	0.932999i	$-0.382818\pi$
$601$	17.6451			0.719757			0.359879	+	0.932999i	$0.382818\pi$
$602$	3.89370	+	16.6044i	0.158695	+	0.676744i
$603$	12.1171			0.493448
$604$	−1.03980	−	1.80099i	−0.0423091	−	0.0732814i
$605$	4.48323	−	7.76518i	0.182269	−	0.315699i
$606$	−6.77709	+	11.7383i	−0.275300	+	0.476834i
$607$	−13.5421	−	23.4557i	−0.549658	−	0.952035i	−0.998298	−	0.0583228i	$-0.981425\pi$
$607$	−13.5421	−	23.4557i	−0.549658	−	0.952035i	0.448640	−	0.893713i	$-0.351909\pi$
$608$	−11.4825			−0.465675
$609$	−18.8579	+	17.7071i	−0.764161	+	0.717527i
$610$	8.57228			0.347082
$611$	2.07852	+	3.60010i	0.0840879	+	0.145645i
$612$	0.0425141	−	0.0736366i	0.00171853	−	0.00297658i
$613$	−12.9983	+	22.5138i	−0.524998	+	0.909323i	0.474579	+	0.880213i	$0.342600\pi$
$613$	−12.9983	+	22.5138i	−0.524998	+	0.909323i	−0.999576	+	0.0291095i	$0.990733\pi$
$614$	0.617356	+	1.06929i	0.0249145	+	0.0431531i
$615$	−0.826979			−0.0333470
$616$	−2.34913	+	2.20577i	−0.0946491	+	0.0888730i
$617$	−2.10539			−0.0847596			−0.0423798	−	0.999102i	$-0.513494\pi$
$617$	−2.10539			−0.0847596			−0.0423798	+	0.999102i	$0.513494\pi$
$618$	8.94252	+	15.4889i	0.359721	+	0.623055i
$619$	13.9495	−	24.1612i	0.560677	−	0.971121i	−0.436760	−	0.899578i	$-0.643874\pi$
$619$	13.9495	−	24.1612i	0.560677	−	0.971121i	0.997437	−	0.0715435i	$-0.0227925\pi$
$620$	1.35978	−	2.35521i	0.0546100	−	0.0945873i
$621$	3.56818	+	6.18027i	0.143186	+	0.248006i
$622$	−9.59409			−0.384688
$623$	7.13357	+	30.4206i	0.285801	+	1.21878i
$624$	8.39257			0.335972
$625$	−7.60464	−	13.1716i	−0.304186	−	0.526865i
$626$	13.4300	−	23.2615i	0.536772	−	0.929716i
$627$	−0.777040	+	1.34587i	−0.0310320	+	0.0537490i
$628$	0.272955	+	0.472773i	0.0108921	+	0.0188657i
$629$	1.60551			0.0640157
$630$	2.53582	+	0.765740i	0.101029	+	0.0305078i
$631$	−21.9270			−0.872900			−0.436450	−	0.899728i	$-0.643764\pi$
$631$	−21.9270			−0.872900			−0.436450	+	0.899728i	$0.643764\pi$
$632$	14.0055	+	24.2583i	0.557110	+	0.964942i
$633$	4.82299	−	8.35366i	0.191697	−	0.332028i
$634$	−6.08371	+	10.5373i	−0.241615	+	0.418489i
$635$	−6.01864	−	10.4246i	−0.238842	−	0.413687i
$636$	−2.96295			−0.117489
$637$	18.4922	+	12.2887i	0.732687	+	0.486895i
$638$	4.69883			0.186028
$639$	0.629988	+	1.09117i	0.0249220	+	0.0431661i
$640$	2.00115	−	3.46609i	0.0791023	−	0.137009i
$641$	−17.4442	+	30.2142i	−0.689003	+	1.19339i	0.283157	+	0.959074i	$0.408618\pi$
$641$	−17.4442	+	30.2142i	−0.689003	+	1.19339i	−0.972161	+	0.234315i	$0.924715\pi$
$642$	9.33008	+	16.1602i	0.368229	+	0.637791i
$643$	−38.0533			−1.50067			−0.750337	−	0.661055i	$-0.770109\pi$
$643$	−38.0533			−1.50067			−0.750337	+	0.661055i	$0.770109\pi$
$644$	9.65726	+	2.91620i	0.380549	+	0.114914i
$645$	4.40320			0.173376
$646$	0.377141	+	0.653227i	0.0148384	+	0.0257009i
$647$	0.280021	−	0.485011i	0.0110088	−	0.0190677i	−0.860469	−	0.509504i	$-0.829829\pi$
$647$	0.280021	−	0.485011i	0.0110088	−	0.0190677i	0.871477	+	0.490436i	$0.163162\pi$
$648$	−1.53409	+	2.65712i	−0.0602647	+	0.104381i
$649$	0.313280	+	0.542617i	0.0122973	+	0.0212996i
$650$	16.5741			0.650088
$651$	−3.71784	−	15.8544i	−0.145714	−	0.621385i
$652$	2.28031			0.0893038
$653$	12.5821	+	21.7928i	0.492375	+	0.852819i	0.999961	−	0.00878198i	$-0.00279543\pi$
$653$	12.5821	+	21.7928i	0.492375	+	0.852819i	−0.507586	+	0.861601i	$0.669462\pi$
$654$	−3.93006	+	6.80706i	−0.153677	+	0.266177i
$655$	2.50680	−	4.34190i	0.0979488	−	0.169652i
$656$	1.32298	+	2.29146i	0.0516535	+	0.0894666i
$657$	8.34764			0.325672
$658$	3.06036	−	2.87359i	0.119305	−	0.112024i
$659$	−45.6924			−1.77992			−0.889962	−	0.456035i	$-0.849269\pi$
$659$	−45.6924			−1.77992			−0.889962	+	0.456035i	$0.849269\pi$
$660$	0.0876984	+	0.151898i	0.00341366	+	0.00591262i
$661$	−6.79106	+	11.7625i	−0.264141	+	0.457506i	−0.967338	−	0.253489i	$-0.918422\pi$
$661$	−6.79106	+	11.7625i	−0.264141	+	0.457506i	0.703197	+	0.710995i	$0.251755\pi$
$662$	−10.7113	+	18.5525i	−0.416306	+	0.721064i
$663$	0.252388	+	0.437149i	0.00980194	+	0.0169775i
$664$	29.9915			1.16389
$665$	6.24448	−	5.86340i	0.242150	−	0.227373i
$666$	−12.2138			−0.473275
$667$	−34.8869	−	60.4260i	−1.35083	−	2.33970i
$668$	0.205978	−	0.356764i	0.00796952	−	0.0138036i
$669$	−7.07484	+	12.2540i	−0.273529	+	0.473766i
$670$	6.06581	+	10.5063i	0.234343	+	0.405893i
$671$	3.39881			0.131210
$672$	1.77164	+	7.55502i	0.0683424	+	0.291441i
$673$	11.3582			0.437825			0.218913	−	0.975744i	$-0.429749\pi$
$673$	11.3582			0.437825			0.218913	+	0.975744i	$0.429749\pi$
$674$	10.6942	+	18.5229i	0.411925	+	0.713475i
$675$	−2.15805	+	3.73786i	−0.0830635	+	0.143870i
$676$	−0.785232	+	1.36006i	−0.0302012	+	0.0523100i
$677$	−0.166798	−	0.288902i	−0.00641056	−	0.0111034i	0.862802	−	0.505541i	$-0.168707\pi$
$677$	−0.166798	−	0.288902i	−0.00641056	−	0.0111034i	−0.869213	+	0.494438i	$0.835374\pi$
$678$	9.57462			0.367711
$679$	−26.5606	−	8.02050i	−1.01930	−	0.307798i
$680$	0.403795			0.0154848
$681$	−10.6771	−	18.4932i	−0.409146	−	0.708663i
$682$	−1.47900	+	2.56171i	−0.0566340	+	0.0980930i
$683$	21.3356	−	36.9543i	0.816383	−	1.41402i	−0.0919480	−	0.995764i	$-0.529309\pi$
$683$	21.3356	−	36.9543i	0.816383	−	1.41402i	0.908331	−	0.418253i	$-0.137357\pi$
$684$	1.04586	+	1.81148i	0.0399893	+	0.0692635i
$685$	−16.6074			−0.634537
$686$	7.81860	−	21.0145i	0.298515	−	0.802336i
$687$	−27.5147			−1.04975
$688$	−7.04410	−	12.2007i	−0.268554	−	0.465149i
$689$	8.79488	−	15.2332i	0.335058	−	0.580338i
$690$	−3.57244	+	6.18765i	−0.136001	+	0.235560i
$691$	−22.5819	−	39.1131i	−0.859058	−	1.48793i	−0.872829	−	0.488026i	$-0.837717\pi$
$691$	−22.5819	−	39.1131i	−0.859058	−	1.48793i	0.0137712	−	0.999905i	$-0.495616\pi$
$692$	12.6282			0.480053
$693$	1.00542	+	0.303607i	0.0381929	+	0.0115331i
$694$	−2.15782			−0.0819099
$695$	6.51237	+	11.2798i	0.247028	+	0.427866i
$696$	14.9991	−	25.9793i	0.568541	−	0.984742i
$697$	−0.0795711	+	0.137821i	−0.00301397	+	0.00522035i
$698$	9.42332	+	16.3217i	0.356678	+	0.617784i
$699$	−4.24294			−0.160483
$700$	1.39294	+	5.94011i	0.0526484	+	0.224515i
$701$	−40.4169			−1.52653			−0.763263	−	0.646088i	$-0.776404\pi$
$701$	−40.4169			−1.52653			−0.763263	+	0.646088i	$0.776404\pi$
$702$	−1.92003	−	3.32558i	−0.0724667	−	0.125516i
$703$	−19.7479	+	34.2043i	−0.744805	+	1.29004i
$704$	1.75512	−	3.03997i	0.0661488	−	0.114573i
$705$	−0.541921	−	0.938634i	−0.0204099	−	0.0353510i
$706$	30.0918			1.13252
$707$	21.5937	−	20.2759i	0.812113	−	0.762553i
$708$	0.843317			0.0316938
$709$	9.31523	+	16.1345i	0.349841	+	0.605942i	0.986221	−	0.165433i	$-0.0529023\pi$
$709$	9.31523	+	16.1345i	0.349841	+	0.605942i	−0.636380	+	0.771376i	$0.719569\pi$
$710$	−0.630741	+	1.09248i	−0.0236713	+	0.0409999i
$711$	4.56477	−	7.90641i	0.171192	−	0.296514i
$712$	−18.1173	−	31.3801i	−0.678974	−	1.17602i
$713$	43.9241			1.64497
$714$	0.371609	−	0.348931i	0.0139071	−	0.0130584i
$715$	−1.04126			−0.0389407
$716$	−4.10345	−	7.10738i	−0.153353	−	0.265615i
$717$	−9.63816	+	16.6938i	−0.359944	+	0.623441i
$718$	−19.3211	+	33.4651i	−0.721056	+	1.24891i
$719$	17.0530	+	29.5367i	0.635971	+	1.10153i	0.986309	+	0.164910i	$0.0527334\pi$
$719$	17.0530	+	29.5367i	0.635971	+	1.10153i	−0.350338	+	0.936623i	$0.613933\pi$
$720$	−2.18815			−0.0815475
$721$	−8.92340	−	38.0532i	−0.332325	−	1.41717i
$722$	4.44715			0.165506
$723$	−5.68144	−	9.84054i	−0.211295	−	0.365974i
$724$	−3.07723	+	5.32993i	−0.114365	+	0.198085i
$725$	21.0998	−	36.5459i	0.783627	−	1.35728i
$726$	6.56327	+	11.3679i	0.243586	+	0.421903i
$727$	−10.7831			−0.399923			−0.199961	−	0.979804i	$-0.564082\pi$
$727$	−10.7831			−0.399923			−0.199961	+	0.979804i	$0.564082\pi$
$728$	−24.6487	−	7.44314i	−0.913540	−	0.275861i
$729$	1.00000			0.0370370
$730$	4.17881	+	7.23790i	0.154665	+	0.267887i
$731$	0.423672	−	0.733821i	0.0156701	−	0.0271413i
$732$	2.28731	−	3.96174i	0.0845415	−	0.146430i
$733$	17.1415	+	29.6900i	0.633136	+	1.09662i	0.986907	+	0.161291i	$0.0515659\pi$
$733$	17.1415	+	29.6900i	0.633136	+	1.09662i	−0.353771	+	0.935332i	$0.615101\pi$
$734$	−41.7904			−1.54251
$735$	−4.82136	−	3.20396i	−0.177838	−	0.118180i
$736$	−20.9309			−0.771522
$737$	2.40502	+	4.16562i	0.0885902	+	0.153443i
$738$	0.605332	−	1.04847i	0.0222826	−	0.0385946i
$739$	−14.5508	+	25.2028i	−0.535261	+	0.927098i	0.463890	+	0.885893i	$0.346453\pi$
$739$	−14.5508	+	25.2028i	−0.535261	+	0.927098i	−0.999151	+	0.0412057i	$0.986880\pi$
$740$	2.22879	+	3.86037i	0.0819318	+	0.141910i
$741$	−12.4176			−0.456172
$742$	−17.0048	−	5.13491i	−0.624264	−	0.188509i
$743$	−29.1285			−1.06862			−0.534311	−	0.845288i	$-0.679429\pi$
$743$	−29.1285			−1.06862			−0.534311	+	0.845288i	$0.679429\pi$
$744$	9.44227	+	16.3545i	0.346170	+	0.599585i
$745$	1.55397	−	2.69155i	0.0569330	−	0.0986108i
$746$	13.6283	−	23.6050i	0.498969	−	0.864239i
$747$	−4.88750	−	8.46541i	−0.178824	−	0.309733i
$748$	0.0337530			0.00123413
$749$	−9.31013	−	39.7023i	−0.340185	−	1.45069i
$750$	−9.32724			−0.340583
$751$	−16.5317	−	28.6337i	−0.603250	−	1.04486i	−0.992325	−	0.123654i	$-0.960539\pi$
$751$	−16.5317	−	28.6337i	−0.603250	−	1.04486i	0.389075	−	0.921206i	$-0.372795\pi$
$752$	−1.73390	+	3.00320i	−0.0632287	+	0.109515i
$753$	7.29954	−	12.6432i	0.266010	−	0.460743i
$754$	18.7726	+	32.5150i	0.683656	+	1.18413i
$755$	−3.21884			−0.117145
$756$	1.03052	−	0.967627i	0.0374795	−	0.0351923i
$757$	3.40606			0.123795			0.0618977	−	0.998083i	$-0.480285\pi$
$757$	3.40606			0.123795			0.0618977	+	0.998083i	$0.480285\pi$
$758$	9.61413	+	16.6522i	0.349201	+	0.604834i
$759$	−1.41643	+	2.45333i	−0.0514133	+	0.0890504i
$760$	−4.96671	+	8.60260i	−0.180162	+	0.312049i
$761$	−1.68877	−	2.92503i	−0.0612178	−	0.106032i	0.833792	−	0.552078i	$-0.186165\pi$
$761$	−1.68877	−	2.92503i	−0.0612178	−	0.106032i	−0.895010	+	0.446046i	$0.852832\pi$
$762$	17.6221			0.638381
$763$	12.5222	−	11.7581i	0.453336	−	0.425670i
$764$	−11.9165			−0.431124
$765$	−0.0658037	−	0.113975i	−0.00237914	−	0.00412079i
$766$	4.11121	−	7.12083i	0.148544	−	0.257286i
$767$	−2.50320	+	4.33568i	−0.0903855	+	0.156552i
$768$	−5.91318	−	10.2419i	−0.213373	−	0.369574i
$769$	−1.44772			−0.0522063			−0.0261031	−	0.999659i	$-0.508310\pi$
$769$	−1.44772			−0.0522063			−0.0261031	+	0.999659i	$0.508310\pi$
$770$	0.240067	+	1.02375i	0.00865141	+	0.0368933i
$771$	−12.6279			−0.454783
$772$	−0.559819	−	0.969636i	−0.0201483	−	0.0348979i
$773$	2.50532	−	4.33935i	0.0901102	−	0.156075i	−0.817447	−	0.576004i	$-0.804611\pi$
$773$	2.50532	−	4.33935i	0.0901102	−	0.156075i	0.907557	+	0.419928i	$0.137945\pi$
$774$	−3.22305	+	5.58249i	−0.115850	+	0.200659i
$775$	13.2828	+	23.0064i	0.477131	+	0.826414i
$776$	32.1750			1.15502
$777$	25.5521	+	7.71594i	0.916675	+	0.276808i
$778$	−23.7278			−0.850683
$779$	−1.95747	−	3.39043i	−0.0701335	−	0.121475i
$780$	−0.700738	+	1.21371i	−0.0250904	+	0.0434579i
$781$	−0.250082	+	0.433154i	−0.00894863	+	0.0154995i
$782$	0.687474	+	1.19074i	0.0245840	+	0.0425808i
$783$	−9.77724			−0.349410
$784$	−1.16473	+	18.4850i	−0.0415975	+	0.660179i
$785$	0.844965			0.0301581
$786$	3.66986	+	6.35638i	0.130899	+	0.226724i
$787$	24.6847	−	42.7552i	0.879915	−	1.52406i	0.0284814	−	0.999594i	$-0.490933\pi$
$787$	24.6847	−	42.7552i	0.879915	−	1.52406i	0.851433	−	0.524463i	$-0.175734\pi$
$788$	−3.54480	+	6.13977i	−0.126278	+	0.218720i
$789$	−6.95511	−	12.0466i	−0.247608	−	0.428870i
$790$	9.14045			0.325203
$791$	−20.0308	−	6.04867i	−0.712212	−	0.215066i
$792$	−1.21795			−0.0432780
$793$	13.5788	+	23.5192i	0.482197	+	0.835190i
$794$	13.6596	−	23.6591i	0.484760	−	0.839629i
$795$	−2.29304	+	3.97166i	−0.0813257	+	0.140860i
$796$	4.32437	+	7.49002i	0.153273	+	0.265477i
$797$	−12.2118			−0.432565			−0.216283	−	0.976331i	$-0.569393\pi$
$797$	−12.2118			−0.432565			−0.216283	+	0.976331i	$0.569393\pi$
$798$	2.86294	+	12.2088i	0.101347	+	0.432187i
$799$	−0.208572			−0.00737876
$800$	−6.32955	−	10.9631i	−0.223783	−	0.387604i
$801$	−5.90491	+	10.2276i	−0.208640	+	0.361374i
$802$	−17.8757	+	30.9617i	−0.631214	+	1.09329i
$803$	1.65685	+	2.86975i	0.0584689	+	0.101271i
$804$	6.47407			0.228323
$805$	11.3828	−	10.6881i	0.401190	−	0.376707i
$806$	−23.6354			−0.832522
$807$	8.40538	+	14.5585i	0.295883	+	0.512485i
$808$	−17.1751	+	29.7482i	−0.604218	+	1.04654i
$809$	−0.357593	+	0.619370i	−0.0125723	+	0.0217759i	−0.872243	−	0.489073i	$-0.837335\pi$
$809$	−0.357593	+	0.619370i	−0.0125723	+	0.0217759i	0.859671	+	0.510848i	$0.170669\pi$
$810$	0.500597	+	0.867060i	0.0175892	+	0.0304654i
$811$	36.3424			1.27616			0.638078	−	0.769972i	$-0.279730\pi$
$811$	36.3424			1.27616			0.638078	+	0.769972i	$0.279730\pi$
$812$	−10.0756	+	9.46072i	−0.353584	+	0.332006i
$813$	−20.3826			−0.714848
$814$	−2.42421	−	4.19885i	−0.0849684	−	0.147170i
$815$	1.76474	−	3.05662i	0.0618162	−	0.107069i
$816$	−0.210541	+	0.364668i	−0.00737042	+	0.0127659i
$817$	10.4224	+	18.0521i	0.364634	+	0.631564i
$818$	−11.5294			−0.403118
$819$	1.91592	+	8.17030i	0.0669477	+	0.285493i
$820$	−0.441847			−0.0154300
$821$	14.3551	+	24.8637i	0.500995	+	0.867749i	0.999999	+	0.00114945i	$0.000365882\pi$
$821$	14.3551	+	24.8637i	0.500995	+	0.867749i	−0.499004	+	0.866600i	$0.666301\pi$
$822$	12.1563	−	21.0553i	0.424000	−	0.734389i
$823$	−24.9525	+	43.2190i	−0.869790	+	1.50652i	−0.00757852	+	0.999971i	$0.502412\pi$
$823$	−24.9525	+	43.2190i	−0.869790	+	1.50652i	−0.862211	+	0.506549i	$0.830921\pi$
$824$	22.6629	+	39.2534i	0.789501	+	1.36746i
$825$	−1.71333			−0.0596506
$826$	4.83990	+	1.46150i	0.168402	+	0.0508522i
$827$	−19.8378			−0.689829			−0.344914	−	0.938634i	$-0.612092\pi$
$827$	−19.8378			−0.689829			−0.344914	+	0.938634i	$0.612092\pi$
$828$	1.90644	+	3.30206i	0.0662535	+	0.114754i
$829$	8.18210	−	14.1718i	0.284176	−	0.492208i	−0.688233	−	0.725490i	$-0.741613\pi$
$829$	8.18210	−	14.1718i	0.284176	−	0.492208i	0.972409	+	0.233282i	$0.0749466\pi$
$830$	4.89334	−	8.47552i	0.169850	−	0.294190i
$831$	1.20360	+	2.08470i	0.0417524	+	0.0723173i
$832$	28.0480			0.972389
$833$	−0.997866	+	0.495228i	−0.0345740	+	0.0171586i
$834$	−19.0677			−0.660261
$835$	−0.318814	−	0.552202i	−0.0110330	−	0.0191097i
$836$	−0.415165	+	0.719088i	−0.0143588	+	0.0248702i
$837$	3.07749	−	5.33036i	0.106373	−	0.184244i
$838$	6.77795	+	11.7398i	0.234140	+	0.405543i
$839$	−9.07123			−0.313174			−0.156587	−	0.987664i	$-0.550049\pi$
$839$	−9.07123			−0.313174			−0.156587	+	0.987664i	$0.550049\pi$
$840$	6.42650	+	1.94061i	0.221735	+	0.0669573i
$841$	66.5944			2.29636
$842$	−4.83571	−	8.37570i	−0.166650	−	0.288646i
$843$	−2.08539	+	3.61200i	−0.0718247	+	0.124404i
$844$	2.57688	−	4.46328i	0.0886998	−	0.153633i
$845$	1.21539	+	2.10511i	0.0418106	+	0.0724181i
$846$	1.58670			0.0545519
$847$	−6.54923	−	27.9287i	−0.225034	−	0.959643i
$848$	14.6733			0.503884
$849$	12.5152	+	21.6770i	0.429521	+	0.743952i
$850$	−0.415788	+	0.720165i	−0.0142614	+	0.0247015i
$851$	−35.9975	+	62.3496i	−1.23398	+	2.13732i
$852$	0.336597	+	0.583003i	0.0115316	+	0.0199733i
$853$	24.6232			0.843083			0.421542	−	0.906809i	$-0.361489\pi$
$853$	24.6232			0.843083			0.421542	+	0.906809i	$0.361489\pi$
$854$	19.9930	−	18.7729i	0.684148	−	0.642397i
$855$	3.23757			0.110722
$856$	23.6451	+	40.9546i	0.808174	+	1.39980i
$857$	−21.6417	+	37.4845i	−0.739266	+	1.28045i	0.213560	+	0.976930i	$0.431494\pi$
$857$	−21.6417	+	37.4845i	−0.739266	+	1.28045i	−0.952826	+	0.303517i	$0.901839\pi$
$858$	0.762178	−	1.32013i	0.0260203	−	0.0450685i
$859$	−3.94277	−	6.82908i	−0.134526	−	0.233005i	0.790891	−	0.611958i	$-0.209618\pi$
$859$	−3.94277	−	6.82908i	−0.134526	−	0.233005i	−0.925416	+	0.378952i	$0.876284\pi$
$860$	2.35259			0.0802226
$861$	−1.92876	+	1.81105i	−0.0657318	+	0.0617204i
$862$	−6.92167			−0.235753
$863$	−4.80000	−	8.31385i	−0.163394	−	0.283007i	0.772690	−	0.634784i	$-0.218911\pi$
$863$	−4.80000	−	8.31385i	−0.163394	−	0.283007i	−0.936084	+	0.351777i	$0.885578\pi$
$864$	−1.46650	+	2.54005i	−0.0498912	+	0.0864141i
$865$	9.77303	−	16.9274i	0.332293	−	0.575549i
$866$	11.3377	+	19.6374i	0.385270	+	0.667307i
$867$	16.9747			0.576490
$868$	−1.98641	−	8.47088i	−0.0674230	−	0.287520i
$869$	3.62409			0.122939
$870$	−4.89446	−	8.47746i	−0.165938	−	0.287413i
$871$	−19.2169	+	33.2846i	−0.651139	+	1.12781i
$872$	−9.95991	+	17.2511i	−0.337285	+	0.584195i
$873$	−5.24335	−	9.08175i	−0.177460	−	0.307371i
$874$	−33.8240			−1.14411
$875$	19.5132	+	5.89239i	0.659667	+	0.199199i
$876$	4.46006			0.150692
$877$	−21.2929	−	36.8805i	−0.719012	−	1.24536i	−0.961392	−	0.275183i	$-0.911261\pi$
$877$	−21.2929	−	36.8805i	−0.719012	−	1.24536i	0.242380	−	0.970181i	$-0.422072\pi$
$878$	−17.3694	+	30.0846i	−0.586188	+	1.01531i
$879$	1.77297	−	3.07087i	0.0598007	−	0.103578i
$880$	−0.434306	−	0.752241i	−0.0146405	−	0.0253580i
$881$	−21.6986			−0.731043			−0.365521	−	0.930803i	$-0.619109\pi$
$881$	−21.6986			−0.731043			−0.365521	+	0.930803i	$0.619109\pi$
$882$	7.59120	−	3.76741i	0.255609	−	0.126855i
$883$	44.7964			1.50752			0.753759	−	0.657151i	$-0.228239\pi$
$883$	44.7964			1.50752			0.753759	+	0.657151i	$0.228239\pi$
$884$	0.134849	+	0.233565i	0.00453545	+	0.00785563i
$885$	0.652646	−	1.13042i	0.0219385	−	0.0379985i
$886$	−12.5990	+	21.8221i	−0.423272	+	0.733129i
$887$	7.43476	+	12.8774i	0.249635	+	0.432380i	0.963424	−	0.267980i	$-0.0863561\pi$
$887$	7.43476	+	12.8774i	0.249635	+	0.432380i	−0.713790	+	0.700360i	$0.753023\pi$
$888$	−30.9533			−1.03872
$889$	−36.8666	−	11.1326i	−1.23647	−	0.373375i
$890$	−11.8239			−0.396339
$891$	0.198481	+	0.343780i	0.00664937	+	0.0115170i
$892$	−3.78002	+	6.54719i	−0.126564	+	0.219216i
$893$	2.56546	−	4.44351i	0.0858498	−	0.148696i
$894$	2.27495	+	3.94033i	0.0760856	+	0.131784i
$895$	−12.7027			−0.424604
$896$	−2.92333	−	12.4663i	−0.0976617	−	0.416471i
$897$	−22.6355			−0.755777
$898$	18.8041	+	32.5696i	0.627500	+	1.08686i
$899$	−30.0893	+	52.1162i	−1.00353	+	1.73817i
$900$	−1.15303	+	1.99710i	−0.0384342	+	0.0665701i
$901$	0.441268	+	0.764298i	0.0147008	+	0.0254625i
$902$	0.480588			0.0160018
$903$	10.2695	−	9.64283i	0.341749	−	0.320893i
$904$	24.2649			0.807038
$905$	4.76297	+	8.24970i	0.158326	+	0.274229i
$906$	2.35612	−	4.08093i	0.0782770	−	0.135580i
$907$	−19.6449	+	34.0259i	−0.652297	+	1.12981i	0.330267	+	0.943888i	$0.392861\pi$
$907$	−19.6449	+	34.0259i	−0.652297	+	1.12981i	−0.982564	+	0.185924i	$0.940472\pi$
$908$	−5.70466	−	9.88077i	−0.189316	−	0.327905i
$909$	11.1956			0.371336
$910$	−6.12504	+	5.75125i	−0.203043	+	0.190652i
$911$	−20.6834			−0.685270			−0.342635	−	0.939469i	$-0.611319\pi$
$911$	−20.6834			−0.685270			−0.342635	+	0.939469i	$0.611319\pi$
$912$	−5.17936	−	8.97092i	−0.171506	−	0.297057i
$913$	1.94016	−	3.36045i	0.0642098	−	0.111215i
$914$	15.8147	−	27.3918i	0.523103	−	0.906042i
$915$	−3.54032	−	6.13201i	−0.117039	−	0.202718i
$916$	−14.7009			−0.485730
$917$	−3.66201	−	15.6164i	−0.120930	−	0.515698i
$918$	0.192668			0.00635899
$919$	20.8754	+	36.1572i	0.688616	+	1.19272i	0.972286	+	0.233795i	$0.0751146\pi$
$919$	20.8754	+	36.1572i	0.688616	+	1.19272i	−0.283670	+	0.958922i	$0.591552\pi$
$920$	−9.05361	+	15.6813i	−0.298489	+	0.516997i
$921$	0.509931	−	0.883227i	0.0168028	−	0.0291033i
$922$	10.4933	+	18.1750i	0.345580	+	0.598562i
$923$	−3.99646			−0.131545
$924$	0.537189	+	0.162214i	0.0176722	+	0.00533646i
$925$	−43.5430			−1.43168
$926$	0.333043	+	0.576847i	0.0109445	+	0.0189564i
$927$	7.38645	−	12.7937i	0.242603	−	0.420201i
$928$	14.3383	−	24.8346i	0.470677	−	0.815237i
$929$	2.57322	+	4.45694i	0.0844245	+	0.146228i	0.905146	−	0.425101i	$-0.139761\pi$
$929$	2.57322	+	4.45694i	0.0844245	+	0.146228i	−0.820721	+	0.571329i	$0.806428\pi$
$930$	6.16233			0.202071
$931$	1.72333	−	27.3503i	0.0564797	−	0.896369i
$932$	−2.26697			−0.0742569
$933$	3.96232	+	6.86294i	0.129721	+	0.224683i
$934$	10.3404	−	17.9100i	0.338347	−	0.586034i
$935$	0.0261216	−	0.0452439i	0.000854267	−	0.00147963i
$936$	−4.86590	−	8.42799i	−0.159047	−	0.275478i
$937$	2.92520			0.0955623			0.0477811	−	0.998858i	$-0.484785\pi$
$937$	2.92520			0.0955623			0.0477811	+	0.998858i	$0.484785\pi$
$938$	37.1555	+	11.2198i	1.21317	+	0.366340i
$939$	−22.1862			−0.724019
$940$	−0.289543	−	0.501503i	−0.00944385	−	0.0163572i
$941$	−16.6892	+	28.9066i	−0.544053	+	0.942327i	0.454613	+	0.890689i	$0.349778\pi$
$941$	−16.6892	+	28.9066i	−0.544053	+	0.942327i	−0.998666	+	0.0516381i	$0.983556\pi$
$942$	−0.618498	+	1.07127i	−0.0201517	+	0.0349038i
$943$	−3.56818	−	6.18027i	−0.116196	−	0.201257i
$944$	−4.17633			−0.135928
$945$	−0.499527	−	2.13020i	−0.0162496	−	0.0692953i
$946$	−2.55886			−0.0831958
$947$	−12.6633	−	21.9334i	−0.411501	−	0.712741i	0.583553	−	0.812075i	$-0.301662\pi$
$947$	−12.6633	−	21.9334i	−0.411501	−	0.712741i	−0.995054	+	0.0993343i	$0.968329\pi$
$948$	2.43891	−	4.22432i	0.0792123	−	0.137200i
$949$	−13.2387	+	22.9302i	−0.429748	+	0.744345i
$950$	−10.2285	−	17.7162i	−0.331855	−	0.574790i
$951$	10.0502			0.325900
$952$	0.941766	−	0.884294i	0.0305228	−	0.0286601i
$953$	43.0540			1.39466			0.697328	−	0.716752i	$-0.254372\pi$
$953$	43.0540			1.39466			0.697328	+	0.716752i	$0.254372\pi$
$954$	−3.35692	−	5.81435i	−0.108684	−	0.188247i
$955$	−9.22222	+	15.9734i	−0.298424	+	0.516886i
$956$	−5.14958	+	8.91933i	−0.166549	+	0.288472i
$957$	−1.94060	−	3.36122i	−0.0627306	−	0.108653i
$958$	−13.1134			−0.423675
$959$	−38.7333	+	36.3695i	−1.25076	+	1.17443i
$960$	−7.31279			−0.236019
$961$	−3.44184	−	5.96143i	−0.111027	−	0.192304i
$962$	19.3702	−	33.5501i	0.624519	−	1.08170i
$963$	7.70657	−	13.3482i	0.248341	−	0.430139i
$964$	−3.03554	−	5.25771i	−0.0977681	−	0.169339i
$965$	−1.73299			−0.0557868
$966$	5.21873	+	22.2549i	0.167910	+	0.716039i
$967$	−26.3902			−0.848653			−0.424327	−	0.905509i	$-0.639489\pi$
$967$	−26.3902			−0.848653			−0.424327	+	0.905509i	$0.639489\pi$
$968$	16.6332	+	28.8096i	0.534612	+	0.925976i
$969$	0.311516	−	0.539561i	0.0100073	−	0.0173332i
$970$	5.24961	−	9.09260i	0.168555	−	0.291946i
$971$	−3.57841	−	6.19799i	−0.114837	−	0.198903i	0.802878	−	0.596144i	$-0.203301\pi$
$971$	−3.57841	−	6.19799i	−0.114837	−	0.198903i	−0.917714	+	0.397241i	$0.869968\pi$
$972$	0.534291			0.0171374
$973$	39.8909	+	12.0458i	1.27884	+	0.386172i
$974$	24.3212			0.779302
$975$	−6.84503	−	11.8559i	−0.219216	−	0.379694i
$976$	−11.3274	+	19.6196i	−0.362581	+	0.628009i
$977$	−4.96834	+	8.60542i	−0.158951	+	0.275312i	−0.934491	−	0.355987i	$-0.884145\pi$
$977$	−4.96834	+	8.60542i	−0.158951	+	0.275312i	0.775539	+	0.631299i	$0.217478\pi$
$978$	2.58351	+	4.47477i	0.0826115	+	0.143087i
$979$	−4.68805			−0.149831
$980$	−2.57601	−	1.71185i	−0.0822875	−	0.0546829i
$981$	6.49240			0.207286
$982$	−6.89885	−	11.9492i	−0.220151	−	0.381313i
$983$	13.4359	−	23.2716i	0.428538	−	0.742250i	−0.568206	−	0.822887i	$-0.692362\pi$
$983$	13.4359	−	23.2716i	0.428538	−	0.742250i	0.996744	+	0.0806371i	$0.0256955\pi$
$984$	1.53409	−	2.65712i	0.0489049	−	0.0847059i
$985$	5.48667	+	9.50319i	0.174820	+	0.302797i
$986$	−1.88376			−0.0599912
$987$	−3.31949	−	1.00238i	−0.105660	−	0.0319062i
$988$	−6.63460			−0.211075
$989$	18.9985	+	32.9064i	0.604119	+	1.04636i
$990$	−0.198718	+	0.344190i	−0.00631568	+	0.0109391i
$991$	24.6685	−	42.7271i	0.783620	−	1.35727i	−0.146200	−	0.989255i	$-0.546704\pi$
$991$	24.6685	−	42.7271i	0.783620	−	1.35727i	0.929820	−	0.368014i	$-0.119962\pi$
$992$	9.02624	+	15.6339i	0.286583	+	0.496377i
$993$	17.6949			0.561531
$994$	0.921405	+	3.92927i	0.0292252	+	0.124629i
$995$	13.3866			0.424383
$996$	−2.61135	−	4.52299i	−0.0827437	−	0.143316i
$997$	−6.81582	+	11.8053i	−0.215859	+	0.373879i	−0.953538	−	0.301273i	$-0.902589\pi$
$997$	−6.81582	+	11.8053i	−0.215859	+	0.373879i	0.737679	+	0.675152i	$0.235922\pi$
$998$	3.49077	−	6.04619i	0.110498	−	0.191389i
$999$	5.04425	+	8.73689i	0.159593	+	0.276423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.i.g.739.10	yes	28
7.2	even	3	inner	861.2.i.g.247.10	✓	28
7.3	odd	6		6027.2.a.bk.1.5		14
7.4	even	3		6027.2.a.bj.1.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.g.247.10	✓	28	7.2	even	3	inner
861.2.i.g.739.10	yes	28	1.1	even	1	trivial
6027.2.a.bj.1.5		14	7.4	even	3
6027.2.a.bk.1.5		14	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.605332 + 1.04847i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.267145 - 0.462709i) q^{4} +(-0.413490 - 0.716185i) q^{5} +1.21066 q^{6} +(-2.53279 - 0.764826i) q^{7} +3.06818 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.605332 + 1.04847i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.267145 - 0.462709i) q^{4} +(-0.413490 - 0.716185i) q^{5} +1.21066 q^{6} +(-2.53279 - 0.764826i) q^{7} +3.06818 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500597 - 0.867060i) q^{10} +(0.198481 - 0.343780i) q^{11} +(-0.267145 - 0.462709i) q^{12} +3.17185 q^{13} +(-0.731288 - 3.11852i) q^{14} -0.826979 q^{15} +(1.32298 + 2.29146i) q^{16} +(-0.0795711 + 0.137821i) q^{17} +(0.605332 - 1.04847i) q^{18} +(-1.95747 - 3.39043i) q^{19} -0.441847 q^{20} +(-1.92876 + 1.81105i) q^{21} +0.480588 q^{22} +(-3.56818 - 6.18027i) q^{23} +(1.53409 - 2.65712i) q^{24} +(2.15805 - 3.73786i) q^{25} +(1.92003 + 3.32558i) q^{26} -1.00000 q^{27} +(-1.03052 + 0.967627i) q^{28} +9.77724 q^{29} +(-0.500597 - 0.867060i) q^{30} +(-3.07749 + 5.33036i) q^{31} +(1.46650 - 2.54005i) q^{32} +(-0.198481 - 0.343780i) q^{33} -0.192668 q^{34} +(0.499527 + 2.13020i) q^{35} -0.534291 q^{36} +(-5.04425 - 8.73689i) q^{37} +(2.36984 - 4.10467i) q^{38} +(1.58593 - 2.74691i) q^{39} +(-1.26866 - 2.19738i) q^{40} +1.00000 q^{41} +(-3.06636 - 0.925948i) q^{42} -5.32444 q^{43} +(-0.106047 - 0.183678i) q^{44} +(-0.413490 + 0.716185i) q^{45} +(4.31987 - 7.48223i) q^{46} +(0.655301 + 1.13502i) q^{47} +2.64595 q^{48} +(5.83008 + 3.87429i) q^{49} +5.22536 q^{50} +(0.0795711 + 0.137821i) q^{51} +(0.847346 - 1.46765i) q^{52} +(2.77279 - 4.80261i) q^{53} +(-0.605332 - 1.04847i) q^{54} -0.328280 q^{55} +(-7.77106 - 2.34662i) q^{56} -3.91493 q^{57} +(5.91848 + 10.2511i) q^{58} +(-0.789193 + 1.36692i) q^{59} +(-0.220924 + 0.382651i) q^{60} +(4.28103 + 7.41495i) q^{61} -7.45161 q^{62} +(0.604038 + 2.57588i) q^{63} +8.84277 q^{64} +(-1.31153 - 2.27163i) q^{65} +(0.240294 - 0.416202i) q^{66} +(-6.05857 + 10.4937i) q^{67} +(0.0425141 + 0.0736366i) q^{68} -7.13636 q^{69} +(-1.93106 + 1.81321i) q^{70} -1.25998 q^{71} +(-1.53409 - 2.65712i) q^{72} +(-4.17382 + 7.22927i) q^{73} +(6.10689 - 10.5774i) q^{74} +(-2.15805 - 3.73786i) q^{75} -2.09171 q^{76} +(-0.765643 + 0.718919i) q^{77} +3.84005 q^{78} +(4.56477 + 7.90641i) q^{79} +(1.09407 - 1.89499i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.605332 + 1.04847i) q^{82} +9.77501 q^{83} +(0.322732 + 1.37627i) q^{84} +0.131607 q^{85} +(-3.22305 - 5.58249i) q^{86} +(4.88862 - 8.46734i) q^{87} +(0.608975 - 1.05478i) q^{88} +(-5.90491 - 10.2276i) q^{89} -1.00119 q^{90} +(-8.03365 - 2.42592i) q^{91} -3.81289 q^{92} +(3.07749 + 5.33036i) q^{93} +(-0.793350 + 1.37412i) q^{94} +(-1.61878 + 2.80382i) q^{95} +(-1.46650 - 2.54005i) q^{96} +10.4867 q^{97} +(-0.532926 + 8.45788i) q^{98} -0.396962 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} + 14 q^{3} - 14 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} - 14 q^{9}+O(q^{10}) \) 28 * q + 2 * q^2 + 14 * q^3 - 14 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 - 14 * q^9	\( 28 q + 2 q^{2} + 14 q^{3} - 14 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} - 14 q^{9} - 3 q^{10} + 16 q^{11} + 14 q^{12} + 42 q^{13} - 14 q^{14} - 20 q^{15} - 22 q^{16} - 12 q^{17} + 2 q^{18} - 2 q^{19} + 80 q^{20} + 2 q^{22} + 7 q^{23} - 6 q^{24} - 22 q^{25} - 2 q^{26} - 28 q^{27} - 59 q^{28} - 32 q^{29} + 3 q^{30} - 8 q^{31} + 19 q^{32} - 16 q^{33} + 66 q^{34} - 8 q^{35} + 28 q^{36} - q^{37} - 32 q^{38} + 21 q^{39} + 13 q^{40} + 28 q^{41} - 10 q^{42} + 28 q^{43} + 36 q^{44} - 10 q^{45} + 12 q^{46} - 12 q^{47} - 44 q^{48} + 8 q^{49} - 2 q^{50} + 12 q^{51} - 60 q^{52} + 20 q^{53} - 2 q^{54} - 22 q^{55} + q^{56} - 4 q^{57} - 21 q^{58} - 25 q^{59} + 40 q^{60} - 26 q^{61} - 66 q^{62} + 84 q^{64} + 8 q^{65} + q^{66} + 22 q^{67} - 15 q^{68} + 14 q^{69} - 120 q^{70} - 72 q^{71} + 6 q^{72} - 31 q^{73} + 65 q^{74} + 22 q^{75} - 4 q^{76} - 18 q^{77} - 4 q^{78} - 12 q^{79} - 112 q^{80} - 14 q^{81} + 2 q^{82} + 40 q^{83} - 37 q^{84} + 80 q^{85} + 9 q^{86} - 16 q^{87} + 54 q^{88} - 39 q^{89} + 6 q^{90} - 17 q^{91} + 126 q^{92} + 8 q^{93} - 14 q^{94} + 55 q^{95} - 19 q^{96} + 36 q^{97} - 19 q^{98} - 32 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 + 14 * q^3 - 14 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 - 14 * q^9 - 3 * q^10 + 16 * q^11 + 14 * q^12 + 42 * q^13 - 14 * q^14 - 20 * q^15 - 22 * q^16 - 12 * q^17 + 2 * q^18 - 2 * q^19 + 80 * q^20 + 2 * q^22 + 7 * q^23 - 6 * q^24 - 22 * q^25 - 2 * q^26 - 28 * q^27 - 59 * q^28 - 32 * q^29 + 3 * q^30 - 8 * q^31 + 19 * q^32 - 16 * q^33 + 66 * q^34 - 8 * q^35 + 28 * q^36 - q^37 - 32 * q^38 + 21 * q^39 + 13 * q^40 + 28 * q^41 - 10 * q^42 + 28 * q^43 + 36 * q^44 - 10 * q^45 + 12 * q^46 - 12 * q^47 - 44 * q^48 + 8 * q^49 - 2 * q^50 + 12 * q^51 - 60 * q^52 + 20 * q^53 - 2 * q^54 - 22 * q^55 + q^56 - 4 * q^57 - 21 * q^58 - 25 * q^59 + 40 * q^60 - 26 * q^61 - 66 * q^62 + 84 * q^64 + 8 * q^65 + q^66 + 22 * q^67 - 15 * q^68 + 14 * q^69 - 120 * q^70 - 72 * q^71 + 6 * q^72 - 31 * q^73 + 65 * q^74 + 22 * q^75 - 4 * q^76 - 18 * q^77 - 4 * q^78 - 12 * q^79 - 112 * q^80 - 14 * q^81 + 2 * q^82 + 40 * q^83 - 37 * q^84 + 80 * q^85 + 9 * q^86 - 16 * q^87 + 54 * q^88 - 39 * q^89 + 6 * q^90 - 17 * q^91 + 126 * q^92 + 8 * q^93 - 14 * q^94 + 55 * q^95 - 19 * q^96 + 36 * q^97 - 19 * q^98 - 32 * q^99

Introduction

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