LMFDB - Embedded newform 966.2.l.c.47.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.12
Character	$\chi$	$=$	966.47
Dual form			966.2.l.c.185.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.55959 - 0.753450i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.416548 - 0.721483i) q^{5} +(-1.72737 - 0.127287i) q^{6} +(-0.928188 + 2.47759i) q^{7} -1.00000i q^{8} +(1.86463 - 2.35014i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.55959 - 0.753450i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.416548 - 0.721483i) q^{5} +(-1.72737 - 0.127287i) q^{6} +(-0.928188 + 2.47759i) q^{7} -1.00000i q^{8} +(1.86463 - 2.35014i) q^{9} +(-0.721483 + 0.416548i) q^{10} +(-4.71420 + 2.72174i) q^{11} +(1.43230 + 0.973918i) q^{12} +4.31686i q^{13} +(2.04263 - 1.68156i) q^{14} +(0.106043 - 1.43906i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.06776 + 3.58147i) q^{17} +(-2.78989 + 1.10297i) q^{18} +(4.06048 + 2.34432i) q^{19} +0.833097 q^{20} +(0.419150 + 4.56337i) q^{21} +5.44349 q^{22} +(0.866025 + 0.500000i) q^{23} +(-0.753450 - 1.55959i) q^{24} +(2.15297 + 3.72906i) q^{25} +(2.15843 - 3.73851i) q^{26} +(1.13734 - 5.07015i) q^{27} +(-2.60975 + 0.434962i) q^{28} -2.38358i q^{29} +(-0.811368 + 1.19324i) q^{30} +(6.27845 - 3.62487i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.30151 + 7.79671i) q^{33} -4.13553i q^{34} +(1.40091 + 1.70171i) q^{35} +(2.96760 + 0.439744i) q^{36} +(-4.03836 + 6.99465i) q^{37} +(-2.34432 - 4.06048i) q^{38} +(3.25254 + 6.73252i) q^{39} +(-0.721483 - 0.416548i) q^{40} +3.22165 q^{41} +(1.91869 - 4.16157i) q^{42} +0.00771499 q^{43} +(-4.71420 - 2.72174i) q^{44} +(-0.918880 - 2.32424i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(4.25083 - 7.36265i) q^{47} +(-0.127287 + 1.72737i) q^{48} +(-5.27693 - 4.59935i) q^{49} -4.30595i q^{50} +(5.92332 + 4.02766i) q^{51} +(-3.73851 + 2.15843i) q^{52} +(-9.26638 + 5.34995i) q^{53} +(-3.52004 + 3.82221i) q^{54} +4.53495i q^{55} +(2.47759 + 0.928188i) q^{56} +(8.09900 + 0.596804i) q^{57} +(-1.19179 + 2.06424i) q^{58} +(1.67536 + 2.90180i) q^{59} +(1.29929 - 0.627696i) q^{60} +(-4.11439 - 2.37545i) q^{61} -7.24973 q^{62} +(4.09197 + 6.80116i) q^{63} -1.00000 q^{64} +(3.11454 + 1.79818i) q^{65} +(8.48959 - 4.10139i) q^{66} +(-5.26796 - 9.12438i) q^{67} +(-2.06776 + 3.58147i) q^{68} +(1.72737 + 0.127287i) q^{69} +(-0.362365 - 2.17418i) q^{70} +8.50698i q^{71} +(-2.35014 - 1.86463i) q^{72} +(-2.30198 + 1.32905i) q^{73} +(6.99465 - 4.03836i) q^{74} +(6.16741 + 4.19364i) q^{75} +4.68864i q^{76} +(-2.36771 - 14.2062i) q^{77} +(0.549482 - 7.45681i) q^{78} +(7.52635 - 13.0360i) q^{79} +(0.416548 + 0.721483i) q^{80} +(-2.04633 - 8.76428i) q^{81} +(-2.79003 - 1.61082i) q^{82} +16.0290 q^{83} +(-3.74242 + 2.64468i) q^{84} +3.44529 q^{85} +(-0.00668138 - 0.00385749i) q^{86} +(-1.79591 - 3.71740i) q^{87} +(2.72174 + 4.71420i) q^{88} +(-6.89501 + 11.9425i) q^{89} +(-0.366349 + 2.47229i) q^{90} +(-10.6954 - 4.00686i) q^{91} +1.00000i q^{92} +(7.06064 - 10.3838i) q^{93} +(-7.36265 + 4.25083i) q^{94} +(3.38277 - 1.95304i) q^{95} +(0.973918 - 1.43230i) q^{96} +5.96192i q^{97} +(2.27029 + 6.62162i) q^{98} +(-2.39374 + 16.1541i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.55959	−	0.753450i	0.900428	−	0.435004i
$3$	1.55959	−	0.753450i	0.900428	−	0.435004i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.416548	−	0.721483i	0.186286	−	0.322657i	−0.757723	−	0.652576i	$-0.773688\pi$
$5$	0.416548	−	0.721483i	0.186286	−	0.322657i	0.944009	+	0.329919i	$0.107022\pi$
$6$	−1.72737	−	0.127287i	−0.705195	−	0.0519648i
$7$	−0.928188	+	2.47759i	−0.350822	+	0.936442i
$7$	−0.928188	+	2.47759i	−0.350822	+	0.936442i
$8$		−	1.00000i		−	0.353553i
$9$	1.86463	−	2.35014i	0.621542	−	0.783380i
$10$	−0.721483	+	0.416548i	−0.228153	+	0.131724i
$11$	−4.71420	+	2.72174i	−1.42138	+	0.820636i	−0.996417	−	0.0845726i	$-0.973047\pi$
$11$	−4.71420	+	2.72174i	−1.42138	+	0.820636i	−0.424967	+	0.905209i	$0.639714\pi$
$12$	1.43230	+	0.973918i	0.413469	+	0.281146i
$13$			4.31686i			1.19728i	0.801017	+	0.598641i	$0.204292\pi$
$13$			4.31686i			1.19728i	−0.801017	+	0.598641i	$0.795708\pi$
$14$	2.04263	−	1.68156i	0.545916	−	0.449417i
$15$	0.106043	−	1.43906i	0.0273801	−	0.371565i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.06776	+	3.58147i	0.501506	+	0.868634i	0.999998	+	0.00174009i	$0.000553888\pi$
$17$	2.06776	+	3.58147i	0.501506	+	0.868634i	−0.498492	+	0.866894i	$0.666113\pi$
$18$	−2.78989	+	1.10297i	−0.657582	+	0.259972i
$19$	4.06048	+	2.34432i	0.931538	+	0.537824i	0.887298	−	0.461197i	$-0.152580\pi$
$19$	4.06048	+	2.34432i	0.931538	+	0.537824i	0.0442401	+	0.999021i	$0.485913\pi$
$20$	0.833097			0.186286
$21$	0.419150	+	4.56337i	0.0914661	+	0.995808i
$22$	5.44349			1.16056
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$24$	−0.753450	−	1.55959i	−0.153797	−	0.318349i
$25$	2.15297	+	3.72906i	0.430595	+	0.745812i
$26$	2.15843	−	3.73851i	0.423303	−	0.733183i
$27$	1.13734	−	5.07015i	0.218881	−	0.975752i
$28$	−2.60975	+	0.434962i	−0.493197	+	0.0822000i
$29$		−	2.38358i		−	0.442619i	−0.975204	−	0.221310i	$-0.928967\pi$
$29$		−	2.38358i		−	0.442619i	0.975204	−	0.221310i	$-0.0710331\pi$
$30$	−0.811368	+	1.19324i	−0.148135	+	0.217856i
$31$	6.27845	−	3.62487i	1.12764	−	0.651045i	0.184302	−	0.982870i	$-0.440998\pi$
$31$	6.27845	−	3.62487i	1.12764	−	0.651045i	0.943341	+	0.331825i	$0.107664\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−5.30151	+	7.79671i	−0.922874	+	1.35723i
$34$		−	4.13553i		−	0.709237i
$35$	1.40091	+	1.70171i	0.236796	+	0.287641i
$36$	2.96760	+	0.439744i	0.494599	+	0.0732907i
$37$	−4.03836	+	6.99465i	−0.663903	+	1.14991i	0.315678	+	0.948866i	$0.397768\pi$
$37$	−4.03836	+	6.99465i	−0.663903	+	1.14991i	−0.979581	+	0.201048i	$0.935565\pi$
$38$	−2.34432	−	4.06048i	−0.380299	−	0.658697i
$39$	3.25254	+	6.73252i	0.520823	+	1.07807i
$40$	−0.721483	−	0.416548i	−0.114076	−	0.0658621i
$41$	3.22165			0.503137			0.251569	−	0.967839i	$-0.419054\pi$
$41$	3.22165			0.503137			0.251569	+	0.967839i	$0.419054\pi$
$42$	1.91869	−	4.16157i	0.296060	−	0.642144i
$43$	0.00771499			0.00117652			0.000588262	−	1.00000i	$-0.499813\pi$
$43$	0.00771499			0.00117652			0.000588262		1.00000i	$0.499813\pi$
$44$	−4.71420	−	2.72174i	−0.710692	−	0.410318i
$45$	−0.918880	−	2.32424i	−0.136978	−	0.346478i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	4.25083	−	7.36265i	0.620047	−	1.07395i	−0.369430	−	0.929259i	$-0.620447\pi$
$47$	4.25083	−	7.36265i	0.620047	−	1.07395i	0.989476	−	0.144694i	$-0.0462197\pi$
$48$	−0.127287	+	1.72737i	−0.0183723	+	0.249324i
$49$	−5.27693	−	4.59935i	−0.753848	−	0.657049i
$50$		−	4.30595i		−	0.608953i
$51$	5.92332	+	4.02766i	0.829430	+	0.563986i
$52$	−3.73851	+	2.15843i	−0.518438	+	0.299321i
$53$	−9.26638	+	5.34995i	−1.27284	+	0.734872i	−0.975521	−	0.219907i	$-0.929424\pi$
$53$	−9.26638	+	5.34995i	−1.27284	+	0.734872i	−0.297315	+	0.954779i	$0.596091\pi$
$54$	−3.52004	+	3.82221i	−0.479017	+	0.520137i
$55$			4.53495i			0.611493i
$56$	2.47759	+	0.928188i	0.331082	+	0.124034i
$57$	8.09900	+	0.596804i	1.07274	+	0.0790486i
$58$	−1.19179	+	2.06424i	−0.156490	+	0.271048i
$59$	1.67536	+	2.90180i	0.218113	+	0.377783i	0.954231	−	0.299070i	$-0.0966765\pi$
$59$	1.67536	+	2.90180i	0.218113	+	0.377783i	−0.736118	+	0.676853i	$0.763343\pi$
$60$	1.29929	−	0.627696i	0.167737	−	0.0810353i
$61$	−4.11439	−	2.37545i	−0.526794	−	0.304145i	0.212916	−	0.977071i	$-0.431704\pi$
$61$	−4.11439	−	2.37545i	−0.526794	−	0.304145i	−0.739710	+	0.672926i	$0.765037\pi$
$62$	−7.24973			−0.920717
$63$	4.09197	+	6.80116i	0.515540	+	0.856866i
$64$	−1.00000			−0.125000
$65$	3.11454	+	1.79818i	0.386311	+	0.223037i
$66$	8.48959	−	4.10139i	1.04500	−	0.504847i
$67$	−5.26796	−	9.12438i	−0.643584	−	1.11472i	−0.984627	−	0.174672i	$-0.944113\pi$
$67$	−5.26796	−	9.12438i	−0.643584	−	1.11472i	0.341043	−	0.940048i	$-0.389220\pi$
$68$	−2.06776	+	3.58147i	−0.250753	+	0.434317i
$69$	1.72737	+	0.127287i	0.207951	+	0.0153236i
$70$	−0.362365	−	2.17418i	−0.0433109	−	0.259864i
$71$			8.50698i			1.00959i	0.863239	+	0.504796i	$0.168432\pi$
$71$			8.50698i			1.00959i	−0.863239	+	0.504796i	$0.831568\pi$
$72$	−2.35014	−	1.86463i	−0.276967	−	0.219748i
$73$	−2.30198	+	1.32905i	−0.269426	+	0.155553i	−0.628627	−	0.777707i	$-0.716383\pi$
$73$	−2.30198	+	1.32905i	−0.269426	+	0.155553i	0.359201	+	0.933260i	$0.383049\pi$
$74$	6.99465	−	4.03836i	0.813112	−	0.469450i
$75$	6.16741	+	4.19364i	0.712152	+	0.484240i
$76$			4.68864i			0.537824i
$77$	−2.36771	−	14.2062i	−0.269825	−	1.61894i
$78$	0.549482	−	7.45681i	0.0622166	−	0.844317i
$79$	7.52635	−	13.0360i	0.846781	−	1.46667i	−0.0372851	−	0.999305i	$-0.511871\pi$
$79$	7.52635	−	13.0360i	0.846781	−	1.46667i	0.884066	−	0.467362i	$-0.154796\pi$
$80$	0.416548	+	0.721483i	0.0465715	+	0.0806643i
$81$	−2.04633	−	8.76428i	−0.227370	−	0.973808i
$82$	−2.79003	−	1.61082i	−0.308107	−	0.177886i
$83$	16.0290			1.75941			0.879703	−	0.475523i	$-0.157741\pi$
$83$	16.0290			1.75941			0.879703	+	0.475523i	$0.157741\pi$
$84$	−3.74242	+	2.64468i	−0.408331	+	0.288558i
$85$	3.44529			0.373695
$86$	−0.00668138	−	0.00385749i	−0.000720471	−	0.000415964i
$87$	−1.79591	−	3.71740i	−0.192541	−	0.398547i
$88$	2.72174	+	4.71420i	0.290139	+	0.502535i
$89$	−6.89501	+	11.9425i	−0.730869	+	1.26590i	0.225643	+	0.974210i	$0.427552\pi$
$89$	−6.89501	+	11.9425i	−0.730869	+	1.26590i	−0.956512	+	0.291693i	$0.905782\pi$
$90$	−0.366349	+	2.47229i	−0.0386166	+	0.260603i
$91$	−10.6954	−	4.00686i	−1.12119	−	0.420033i
$92$			1.00000i			0.104257i
$93$	7.06064	−	10.3838i	0.732154	−	1.07675i
$94$	−7.36265	+	4.25083i	−0.759399	+	0.438439i
$95$	3.38277	−	1.95304i	0.347065	−	0.200378i
$96$	0.973918	−	1.43230i	0.0994001	−	0.146184i
$97$			5.96192i			0.605341i	0.953095	+	0.302670i	$0.0978781\pi$
$97$			5.96192i			0.605341i	−0.953095	+	0.302670i	$0.902122\pi$
$98$	2.27029	+	6.62162i	0.229333	+	0.668884i
$99$	−2.39374	+	16.1541i	−0.240580	+	1.62354i
$100$	−2.15297	+	3.72906i	−0.215297	+	0.372906i
$101$	−1.65425	−	2.86525i	−0.164604	−	0.285103i	0.771910	−	0.635731i	$-0.219301\pi$
$101$	−1.65425	−	2.86525i	−0.164604	−	0.285103i	−0.936515	+	0.350628i	$0.885968\pi$
$102$	−3.11591	−	6.44972i	−0.308521	−	0.638617i
$103$	−8.91628	−	5.14782i	−0.878547	−	0.507229i	−0.00836790	−	0.999965i	$-0.502664\pi$
$103$	−8.91628	−	5.14782i	−0.878547	−	0.507229i	−0.870179	+	0.492736i	$0.835997\pi$
$104$	4.31686			0.423303
$105$	3.46699	+	1.59845i	0.338343	+	0.155993i
$106$	10.6999			1.03927
$107$	−4.27409	−	2.46764i	−0.413191	−	0.238556i	0.278969	−	0.960300i	$-0.410007\pi$
$107$	−4.27409	−	2.46764i	−0.413191	−	0.238556i	−0.692160	+	0.721744i	$0.743341\pi$
$108$	4.95955	−	1.55011i	0.477233	−	0.149160i
$109$	−4.90715	−	8.49944i	−0.470020	−	0.814098i	0.529392	−	0.848377i	$-0.322420\pi$
$109$	−4.90715	−	8.49944i	−0.470020	−	0.814098i	−0.999412	+	0.0342788i	$0.989087\pi$
$110$	2.26748	−	3.92738i	0.216195	−	0.374461i
$111$	−1.02807	+	13.9515i	−0.0975796	+	1.32422i
$112$	−1.68156	−	2.04263i	−0.158893	−	0.193010i
$113$			14.2294i			1.33859i	0.742997	+	0.669295i	$0.233404\pi$
$113$			14.2294i			1.33859i	−0.742997	+	0.669295i	$0.766596\pi$
$114$	−6.71554	−	4.56635i	−0.628968	−	0.427678i
$115$	0.721483	−	0.416548i	0.0672786	−	0.0388433i
$116$	2.06424	−	1.19179i	0.191660	−	0.110655i
$117$	10.1452	+	8.04934i	0.937927	+	0.744162i
$118$		−	3.35071i		−	0.308458i
$119$	−10.7927	+	1.79880i	−0.989365	+	0.164895i
$120$	−1.43906	−	0.106043i	−0.131368	−	0.00968033i
$121$	9.31577	−	16.1354i	0.846888	−	1.46685i
$122$	2.37545	+	4.11439i	0.215063	+	0.372500i
$123$	5.02444	−	2.42735i	0.453039	−	0.218867i
$124$	6.27845	+	3.62487i	0.563822	+	0.325523i
$125$	7.75276			0.693428
$126$	−0.143168	−	7.93596i	−0.0127544	−	0.706992i
$127$	6.64084			0.589279			0.294640	−	0.955608i	$-0.404800\pi$
$127$	6.64084			0.589279			0.294640	+	0.955608i	$0.404800\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	0.0120322	−	0.00581286i	0.00105938	−	0.000511793i
$130$	−1.79818	−	3.11454i	−0.157711	−	0.273163i
$131$	7.30697	−	12.6560i	0.638413	−	1.10576i	−0.347368	−	0.937729i	$-0.612925\pi$
$131$	7.30697	−	12.6560i	0.638413	−	1.10576i	0.985781	−	0.168035i	$-0.0537421\pi$
$132$	−9.40290	−	0.692887i	−0.818417	−	0.0603081i
$133$	−9.57716	+	7.88424i	−0.830445	+	0.683651i
$134$			10.5359i			0.910165i
$135$	−3.18427	−	2.93253i	−0.274059	−	0.252392i
$136$	3.58147	−	2.06776i	0.307109	−	0.177309i
$137$	19.3657	−	11.1808i	1.65452	−	0.955240i	0.679346	−	0.733818i	$-0.262264\pi$
$137$	19.3657	−	11.1808i	1.65452	−	0.955240i	0.975178	−	0.221422i	$-0.0710698\pi$
$138$	−1.43230	−	0.973918i	−0.121926	−	0.0829054i
$139$			19.0007i			1.61162i	0.592177	+	0.805808i	$0.298269\pi$
$139$			19.0007i			1.61162i	−0.592177	+	0.805808i	$0.701731\pi$
$140$	−0.773271	+	2.06407i	−0.0653533	+	0.174446i
$141$	1.08215	−	14.6855i	0.0911337	−	1.23674i
$142$	4.25349	−	7.36726i	0.356945	−	0.618246i
$143$	−11.7494	−	20.3505i	−0.982533	−	1.70180i
$144$	1.10297	+	2.78989i	0.0919140	+	0.232490i
$145$	−1.71971	−	0.992875i	−0.142814	−	0.0824538i
$146$	2.65809			0.219985
$147$	−11.6952	−	3.19718i	−0.964605	−	0.263699i
$148$	−8.07673			−0.663903
$149$	14.2183	+	8.20895i	1.16481	+	0.672503i	0.952452	−	0.304689i	$-0.0985524\pi$
$149$	14.2183	+	8.20895i	1.16481	+	0.672503i	0.212358	+	0.977192i	$0.431886\pi$
$150$	−3.24432	−	6.71551i	−0.264897	−	0.548319i
$151$	7.80246	+	13.5143i	0.634955	+	1.09977i	0.986525	+	0.163613i	$0.0523148\pi$
$151$	7.80246	+	13.5143i	0.634955	+	1.09977i	−0.351569	+	0.936162i	$0.614352\pi$
$152$	2.34432	−	4.06048i	0.190149	−	0.329348i
$153$	12.2726	+	1.81857i	0.992178	+	0.147023i
$154$	−5.05258	+	13.4867i	−0.407149	+	1.08679i
$155$		−	6.03973i		−	0.485123i
$156$	−4.20427	+	6.18304i	−0.336611	+	0.495040i
$157$	−10.6703	+	6.16051i	−0.851584	+	0.491662i	−0.861185	−	0.508292i	$-0.830277\pi$
$157$	−10.6703	+	6.16051i	−0.851584	+	0.491662i	0.00960120	+	0.999954i	$0.496944\pi$
$158$	−13.0360	+	7.52635i	−1.03709	+	0.598764i
$159$	−10.4208	+	15.3255i	−0.826425	+	1.21539i
$160$		−	0.833097i		−	0.0658621i
$161$	−2.04263	+	1.68156i	−0.160982	+	0.132526i
$162$	−2.60996	+	8.61325i	−0.205058	+	0.676721i
$163$	−1.55089	+	2.68622i	−0.121475	+	0.210401i	−0.920350	−	0.391097i	$-0.872096\pi$
$163$	−1.55089	+	2.68622i	−0.121475	+	0.210401i	0.798875	+	0.601498i	$0.205429\pi$
$164$	1.61082	+	2.79003i	0.125784	+	0.217865i
$165$	3.41686	+	7.07265i	0.266002	+	0.550605i
$166$	−13.8815	−	8.01448i	−1.07741	−	0.622044i
$167$	18.9451			1.46602			0.733009	−	0.680219i	$-0.238115\pi$
$167$	18.9451			1.46602			0.733009	+	0.680219i	$0.238115\pi$
$168$	4.56337	−	0.419150i	0.352071	−	0.0323381i
$169$	−5.63530			−0.433484
$170$	−2.98371	−	1.72265i	−0.228840	−	0.132121i
$171$	13.0808	−	5.17142i	1.00031	−	0.395468i
$172$	0.00385749	+	0.00668138i	0.000294131	+	0.000509450i
$173$	−6.31075	+	10.9305i	−0.479797	+	0.831033i	−0.999731	−	0.0231732i	$-0.992623\pi$
$173$	−6.31075	+	10.9305i	−0.479797	+	0.831033i	0.519934	+	0.854206i	$0.325956\pi$
$174$	−0.303399	+	4.11731i	−0.0230006	+	0.312133i
$175$	−11.2375	+	1.87292i	−0.849472	+	0.141580i
$176$		−	5.44349i		−	0.410318i
$177$	4.79923	+	3.26332i	0.360732	+	0.245286i
$178$	11.9425	−	6.89501i	0.895128	−	0.516803i
$179$	−10.6193	+	6.13107i	−0.793726	+	0.458258i	−0.841272	−	0.540611i	$-0.818193\pi$
$179$	−10.6193	+	6.13107i	−0.793726	+	0.458258i	0.0475469	+	0.998869i	$0.484860\pi$
$180$	1.55342	−	1.95790i	0.115785	−	0.145933i
$181$		−	6.54888i		−	0.486775i	−0.969929	−	0.243387i	$-0.921741\pi$
$181$		−	6.54888i		−	0.486775i	0.969929	−	0.243387i	$-0.0782586\pi$
$182$	7.25908	+	8.81776i	0.538079	+	0.653616i
$183$	−8.20654	−	0.604729i	−0.606645	−	0.0447028i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	3.36435	+	5.82722i	0.247352	+	0.428426i
$186$	−11.3066	+	5.46231i	−0.829039	+	0.400516i
$187$	−19.4957	−	11.2558i	−1.42567	−	0.823108i
$188$	8.50165			0.620047
$189$	11.5061	+	7.52392i	0.836947	+	0.547284i
$190$	−3.90609			−0.283377
$191$	−19.7238	−	11.3876i	−1.42717	−	0.823975i	−0.430270	−	0.902700i	$-0.641582\pi$
$191$	−19.7238	−	11.3876i	−1.42717	−	0.823975i	−0.996896	+	0.0787255i	$0.974915\pi$
$192$	−1.55959	+	0.753450i	−0.112554	+	0.0543755i
$193$	−3.78643	−	6.55828i	−0.272553	−	0.472076i	0.696962	−	0.717108i	$-0.254535\pi$
$193$	−3.78643	−	6.55828i	−0.272553	−	0.472076i	−0.969515	+	0.245033i	$0.921201\pi$
$194$	2.98096	−	5.16317i	0.214020	−	0.370694i
$195$	6.21224	+	0.457772i	0.444868	+	0.0327817i
$196$	1.34468	−	6.86963i	0.0960488	−	0.490688i
$197$		−	4.75361i		−	0.338680i	−0.985558	−	0.169340i	$-0.945836\pi$
$197$		−	4.75361i		−	0.338680i	0.985558	−	0.169340i	$-0.0541637\pi$
$198$	10.1501	−	12.7930i	0.721334	−	0.909156i
$199$	−3.77576	+	2.17993i	−0.267656	+	0.154531i	−0.627822	−	0.778357i	$-0.716053\pi$
$199$	−3.77576	+	2.17993i	−0.267656	+	0.154531i	0.360166	+	0.932888i	$0.382720\pi$
$200$	3.72906	−	2.15297i	0.263684	−	0.152238i
$201$	−15.0906	−	10.2611i	−1.06441	−	0.723764i
$202$			3.30850i			0.232786i
$203$	5.90554	+	2.21241i	0.414487	+	0.155281i
$204$	−0.526400	+	7.14357i	−0.0368554	+	0.500150i
$205$	1.34197	−	2.32437i	0.0937274	−	0.162341i
$206$	5.14782	+	8.91628i	0.358665	+	0.621226i
$207$	2.78989	−	1.10297i	0.193910	−	0.0766616i
$208$	−3.73851	−	2.15843i	−0.259219	−	0.149660i
$209$	−25.5225			−1.76543
$210$	−2.20327	−	3.11779i	−0.152040	−	0.215148i
$211$	0.969865			0.0667683			0.0333841	−	0.999443i	$-0.489372\pi$
$211$	0.969865			0.0667683			0.0333841	+	0.999443i	$0.489372\pi$
$212$	−9.26638	−	5.34995i	−0.636418	−	0.367436i
$213$	6.40958	+	13.2674i	0.439177	+	0.909066i
$214$	2.46764	+	4.27409i	0.168685	+	0.292170i
$215$	0.00321367	−	0.00556623i	0.000219170	−	0.000379614i
$216$	−5.07015	−	1.13734i	−0.344980	−	0.0773860i
$217$	3.15336	+	18.9200i	0.214064	+	1.28437i
$218$			9.81430i			0.664708i
$219$	−2.58876	+	3.80719i	−0.174932	+	0.257266i
$220$	−3.92738	+	2.26748i	−0.264784	+	0.152873i
$221$	−15.4607	+	8.92625i	−1.04000	+	0.600444i
$222$	7.86607	−	11.5683i	0.527936	−	0.776414i
$223$		−	16.1431i		−	1.08102i	−0.841337	−	0.540510i	$-0.818231\pi$
$223$		−	16.1431i		−	1.08102i	0.841337	−	0.540510i	$-0.181769\pi$
$224$	0.434962	+	2.60975i	0.0290621	+	0.174371i
$225$	12.7783	+	1.89352i	0.851888	+	0.126234i
$226$	7.11470	−	12.3230i	0.473263	−	0.819715i
$227$	0.199262	+	0.345132i	0.0132255	+	0.0229072i	0.872562	−	0.488503i	$-0.162457\pi$
$227$	0.199262	+	0.345132i	0.0132255	+	0.0229072i	−0.859337	+	0.511410i	$0.829123\pi$
$228$	3.53265	+	7.31234i	0.233956	+	0.484272i
$229$	−9.20700	−	5.31566i	−0.608415	−	0.351269i	0.163930	−	0.986472i	$-0.447583\pi$
$229$	−9.20700	−	5.31566i	−0.608415	−	0.351269i	−0.772345	+	0.635203i	$0.780916\pi$
$230$	−0.833097			−0.0549328
$231$	−14.3963	−	20.3718i	−0.947205	−	1.34037i
$232$	−2.38358			−0.156490
$233$	−13.2216	−	7.63350i	−0.866177	−	0.500087i	−0.000100834	−	1.00000i	$-0.500032\pi$
$233$	−13.2216	−	7.63350i	−0.866177	−	0.500087i	−0.866076	+	0.499913i	$0.833365\pi$
$234$	−4.76136	−	12.0436i	−0.311260	−	0.787311i
$235$	−3.54135	−	6.13380i	−0.231012	−	0.400125i
$236$	−1.67536	+	2.90180i	−0.109056	+	0.188891i
$237$	1.91602	−	26.0015i	0.124459	−	1.68898i
$238$	10.2462	+	3.83855i	0.664159	+	0.248816i
$239$		−	19.0010i		−	1.22907i	−0.788889	−	0.614536i	$-0.789343\pi$
$239$		−	19.0010i		−	1.22907i	0.788889	−	0.614536i	$-0.210657\pi$
$240$	1.19324	+	0.811368i	0.0770236	+	0.0523736i
$241$	11.5084	−	6.64440i	0.741324	−	0.428004i	−0.0812265	−	0.996696i	$-0.525884\pi$
$241$	11.5084	−	6.64440i	0.741324	−	0.428004i	0.822551	+	0.568692i	$0.192550\pi$
$242$	−16.1354	+	9.31577i	−1.03722	+	0.598840i
$243$	−9.79487	−	12.1269i	−0.628341	−	0.777938i
$244$		−	4.75089i		−	0.304145i
$245$	−5.51645	+	1.89137i	−0.352433	+	0.120835i
$246$	−5.56497	−	0.410075i	−0.354810	−	0.0261454i
$247$	−10.1201	+	17.5285i	−0.643926	+	1.11531i
$248$	−3.62487	−	6.27845i	−0.230179	−	0.398682i
$249$	24.9986	−	12.0770i	1.58422	−	0.765349i
$250$	−6.71408	−	3.87638i	−0.424636	−	0.245164i
$251$	3.75962			0.237305			0.118653	−	0.992936i	$-0.462142\pi$
$251$	3.75962			0.237305			0.118653	+	0.992936i	$0.462142\pi$
$252$	−3.84399	+	6.94433i	−0.242149	+	0.437452i
$253$	−5.44349			−0.342229
$254$	−5.75113	−	3.32042i	−0.360858	−	0.208342i
$255$	5.37324	−	2.59586i	0.336485	−	0.162559i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.91191	+	5.04357i	−0.181640	+	0.314610i	−0.942439	−	0.334378i	$-0.891474\pi$
$257$	−2.91191	+	5.04357i	−0.181640	+	0.314610i	0.760799	+	0.648987i	$0.224807\pi$
$258$	−0.0133266		0.000982020i	−0.000829679		6.11379e-5i
$259$	−13.5815	−	16.4978i	−0.843916	−	1.02512i
$260$			3.59636i			0.223037i
$261$	−5.60174	−	4.44448i	−0.346739	−	0.275107i
$262$	−12.6560	+	7.30697i	−0.781893	+	0.451426i
$263$	−3.60195	+	2.07959i	−0.222106	+	0.128233i	−0.606925	−	0.794759i	$-0.707597\pi$
$263$	−3.60195	+	2.07959i	−0.222106	+	0.128233i	0.384819	+	0.922992i	$0.374264\pi$
$264$	7.79671	+	5.30151i	0.479854	+	0.326285i
$265$			8.91405i			0.547586i
$266$	12.2362	−	2.03938i	0.750248	−	0.125042i
$267$	−1.75529	+	23.8204i	−0.107422	+	1.45779i
$268$	5.26796	−	9.12438i	0.321792	−	0.557360i
$269$	−12.3545	−	21.3986i	−0.753266	−	1.30470i	−0.946232	−	0.323490i	$-0.895144\pi$
$269$	−12.3545	−	21.3986i	−0.753266	−	1.30470i	0.192965	−	0.981206i	$-0.438189\pi$
$270$	1.29140	+	4.13179i	0.0785918	+	0.251452i
$271$	−14.4300	−	8.33114i	−0.876558	−	0.506081i	−0.00703573	−	0.999975i	$-0.502240\pi$
$271$	−14.4300	−	8.33114i	−0.876558	−	0.506081i	−0.869522	+	0.493895i	$0.835573\pi$
$272$	−4.13553			−0.250753
$273$	−19.6994	+	1.80941i	−1.19226	+	0.109511i
$274$	−22.3616			−1.35091
$275$	−20.2991	−	11.7197i	−1.22408	−	0.706724i
$276$	0.753450	+	1.55959i	0.0453523	+	0.0938761i
$277$	−2.01556	−	3.49105i	−0.121103	−	0.209757i	0.799100	−	0.601198i	$-0.205310\pi$
$277$	−2.01556	−	3.49105i	−0.121103	−	0.209757i	−0.920203	+	0.391441i	$0.871977\pi$
$278$	9.50033	−	16.4551i	0.569792	−	0.986909i
$279$	3.18803	−	21.5143i	0.190862	−	1.28803i
$280$	1.70171	−	1.40091i	0.101697	−	0.0837201i
$281$			17.5622i			1.04767i	0.851819	+	0.523835i	$0.175499\pi$
$281$			17.5622i			1.04767i	−0.851819	+	0.523835i	$0.824501\pi$
$282$	−8.27991	+	12.1769i	−0.493061	+	0.725125i
$283$	14.7482	−	8.51489i	0.876691	−	0.506158i	0.00712509	−	0.999975i	$-0.497732\pi$
$283$	14.7482	−	8.51489i	0.876691	−	0.506158i	0.869566	+	0.493817i	$0.164399\pi$
$284$	−7.36726	+	4.25349i	−0.437166	+	0.252398i
$285$	3.80421	−	5.59469i	0.225342	−	0.331401i
$286$			23.4988i			1.38951i
$287$	−2.99030	+	7.98194i	−0.176512	+	0.471159i
$288$	0.439744	−	2.96760i	0.0259122	−	0.174867i
$289$	−0.0512881	+	0.0888336i	−0.00301695	+	0.00522551i
$290$	0.992875	+	1.71971i	0.0583037	+	0.100985i
$291$	4.49200	+	9.29813i	0.263326	+	0.545066i
$292$	−2.30198	−	1.32905i	−0.134713	−	0.0777765i
$293$	−16.4690			−0.962127			−0.481063	−	0.876686i	$-0.659749\pi$
$293$	−16.4690			−0.962127			−0.481063	+	0.876686i	$0.659749\pi$
$294$	8.52976	+	8.61645i	0.497466	+	0.502521i
$295$	2.79147			0.162526
$296$	6.99465	+	4.03836i	0.406556	+	0.234725i
$297$	8.43803	+	26.9972i	0.489624	+	1.56654i
$298$	−8.20895	−	14.2183i	−0.475532	−	0.823645i
$299$	−2.15843	+	3.73851i	−0.124825	+	0.216204i
$300$	−0.548093	+	7.43796i	−0.0316442	+	0.429431i
$301$	−0.00716096	+	0.0191146i	−0.000412751	+	0.00110175i
$302$		−	15.6049i		−	0.897962i
$303$	−4.73877	−	3.22221i	−0.272235	−	0.185111i
$304$	−4.06048	+	2.34432i	−0.232884	+	0.134456i
$305$	−3.42769	+	1.97898i	−0.196269	+	0.113316i
$306$	−9.71907	−	7.71122i	−0.555602	−	0.440821i
$307$			29.4404i			1.68025i	0.542391	+	0.840126i	$0.317519\pi$
$307$			29.4404i			1.68025i	−0.542391	+	0.840126i	$0.682481\pi$
$308$	11.1190	−	9.15357i	0.633566	−	0.521573i
$309$	−17.7843	−	1.31050i	−1.01172	−	0.0745519i
$310$	−3.01986	+	5.23056i	−0.171517	+	0.297076i
$311$	−11.6388	−	20.1590i	−0.659975	−	1.14311i	−0.980621	−	0.195912i	$-0.937233\pi$
$311$	−11.6388	−	20.1590i	−0.659975	−	1.14311i	0.320646	−	0.947199i	$-0.396100\pi$
$312$	6.73252	−	3.25254i	0.381154	−	0.184139i
$313$	10.2417	+	5.91305i	0.578895	+	0.334225i	0.760694	−	0.649110i	$-0.224859\pi$
$313$	10.2417	+	5.91305i	0.578895	+	0.334225i	−0.181799	+	0.983336i	$0.558192\pi$
$314$	12.3210			0.695315
$315$	6.61143	−	0.119273i	0.372512	−	0.00672025i
$316$	15.0527			0.846781
$317$	8.69181	+	5.01822i	0.488181	+	0.281851i	0.723819	−	0.689989i	$-0.242385\pi$
$317$	8.69181	+	5.01822i	0.488181	+	0.281851i	−0.235639	+	0.971841i	$0.575718\pi$
$318$	16.6874	−	8.06183i	0.935785	−	0.452085i
$319$	6.48749	+	11.2367i	0.363229	+	0.629132i
$320$	−0.416548	+	0.721483i	−0.0232858	+	0.0403321i
$321$	−8.52506	−	0.628200i	−0.475822	−	0.0350627i
$322$	2.60975	−	0.434962i	0.145436	−	0.0242395i
$323$			19.3900i			1.07889i
$324$	6.56692	−	6.15431i	0.364829	−	0.341906i
$325$	−16.0978	+	9.29410i	−0.892948	+	0.515544i
$326$	2.68622	−	1.55089i	0.148776	−	0.0858958i
$327$	−14.0570	−	9.55832i	−0.777355	−	0.528576i
$328$		−	3.22165i		−	0.177886i
$329$	14.2961	+	17.3657i	0.788168	+	0.957404i
$330$	0.577242	−	7.83353i	0.0317761	−	0.431221i
$331$	12.1037	−	20.9642i	0.665279	−	1.15230i	−0.313930	−	0.949446i	$-0.601646\pi$
$331$	12.1037	−	20.9642i	0.665279	−	1.15230i	0.979210	−	0.202851i	$-0.0650208\pi$
$332$	8.01448	+	13.8815i	0.439852	+	0.761845i
$333$	8.90838	+	22.5331i	0.488176	+	1.23481i
$334$	−16.4070	−	9.47256i	−0.897749	−	0.518316i
$335$	−8.77744			−0.479563
$336$	−4.16157	−	1.91869i	−0.227032	−	0.104673i
$337$	10.2573			0.558752			0.279376	−	0.960182i	$-0.409872\pi$
$337$	10.2573			0.558752			0.279376	+	0.960182i	$0.409872\pi$
$338$	4.88031	+	2.81765i	0.265454	+	0.153260i
$339$	10.7211	+	22.1920i	0.582292	+	1.20530i
$340$	1.72265	+	2.98371i	0.0934236	+	0.161814i
$341$	−19.7319	+	34.1767i	−1.06854	+	1.85077i
$342$	−13.9140	−	2.06180i	−0.752382	−	0.111489i
$343$	16.2933	−	8.80503i	0.879755	−	0.475427i
$344$		−	0.00771499i		−	0.000415964i
$345$	0.811368	−	1.19324i	0.0436826	−	0.0642421i
$346$	10.9305	−	6.31075i	0.587629	−	0.339268i
$347$	0.420671	−	0.242874i	0.0225828	−	0.0130382i	−0.488666	−	0.872471i	$-0.662516\pi$
$347$	0.420671	−	0.242874i	0.0225828	−	0.0130382i	0.511249	+	0.859433i	$0.329183\pi$
$348$	2.32141	−	3.41400i	0.124441	−	0.183010i
$349$		−	0.588445i		−	0.0314987i	−0.999876	−	0.0157494i	$-0.994987\pi$
$349$		−	0.588445i		−	0.0314987i	0.999876	−	0.0157494i	$-0.00501339\pi$
$350$	10.6684	+	3.99673i	0.570249	+	0.213634i
$351$	21.8872	+	4.90973i	1.16825	+	0.262062i
$352$	−2.72174	+	4.71420i	−0.145069	+	0.251268i
$353$	0.953586	+	1.65166i	0.0507542	+	0.0879089i	0.890286	−	0.455401i	$-0.150504\pi$
$353$	0.953586	+	1.65166i	0.0507542	+	0.0879089i	−0.839532	+	0.543310i	$0.817171\pi$
$354$	−2.52459	−	5.22573i	−0.134181	−	0.277745i
$355$	6.13764	+	3.54357i	0.325752	+	0.188073i
$356$	−13.7900			−0.730869
$357$	−15.4769	+	10.9371i	−0.819122	+	0.578855i
$358$	12.2621			0.648074
$359$	18.8384	+	10.8764i	0.994253	+	0.574032i	0.906543	−	0.422114i	$-0.138712\pi$
$359$	18.8384	+	10.8764i	0.994253	+	0.574032i	0.0877100	+	0.996146i	$0.472045\pi$
$360$	−2.32424	+	0.918880i	−0.122498	+	0.0484292i
$361$	1.49166	+	2.58363i	0.0785083	+	0.135980i
$362$	−3.27444	+	5.67150i	−0.172101	+	0.298087i
$363$	2.37156	−	32.1835i	0.124475	−	1.68920i
$364$	−1.87767	−	11.2659i	−0.0984166	−	0.590496i
$365$			2.21445i			0.115910i
$366$	6.80471	+	4.62698i	0.355688	+	0.241856i
$367$	−13.8367	+	7.98860i	−0.722267	+	0.417001i	−0.815587	−	0.578635i	$-0.803586\pi$
$367$	−13.8367	+	7.98860i	−0.722267	+	0.417001i	0.0933192	+	0.995636i	$0.470252\pi$
$368$	−0.866025	+	0.500000i	−0.0451447	+	0.0260643i
$369$	6.00718	−	7.57133i	0.312721	−	0.394148i
$370$		−	6.72870i		−	0.349808i
$371$	−4.65405	−	27.9241i	−0.241626	−	1.44975i
$372$	12.5229	+	0.922799i	0.649285	+	0.0478449i
$373$	10.0856	−	17.4689i	0.522215	−	0.904503i	−0.477451	−	0.878658i	$-0.658439\pi$
$373$	10.0856	−	17.4689i	0.522215	−	0.904503i	0.999666	−	0.0258447i	$-0.00822753\pi$
$374$	11.2558	+	19.4957i	0.582026	+	1.00810i
$375$	12.0911	−	5.84131i	0.624382	−	0.301644i
$376$	−7.36265	−	4.25083i	−0.379700	−	0.219220i
$377$	10.2896			0.529940
$378$	−6.20263	−	12.2690i	−0.319029	−	0.631047i
$379$	19.4282			0.997960			0.498980	−	0.866613i	$-0.333708\pi$
$379$	19.4282			0.997960			0.498980	+	0.866613i	$0.333708\pi$
$380$	3.38277	+	1.95304i	0.173533	+	0.100189i
$381$	10.3570	−	5.00354i	0.530604	−	0.256339i
$382$	11.3876	+	19.7238i	0.582638	+	1.00916i
$383$	14.0747	−	24.3781i	0.719184	−	1.24566i	−0.242139	−	0.970242i	$-0.577849\pi$
$383$	14.0747	−	24.3781i	0.719184	−	1.24566i	0.961323	−	0.275422i	$-0.0888177\pi$
$384$	1.72737	+	0.127287i	0.0881493	+	0.00649560i
$385$	−11.2358	−	4.20929i	−0.572627	−	0.214525i
$386$			7.57286i			0.385448i
$387$	0.0143856	−	0.0181313i	0.000731260	−	0.000921667i
$388$	−5.16317	+	2.98096i	−0.262120	+	0.151335i
$389$	5.13287	−	2.96347i	0.260247	−	0.150254i	−0.364200	−	0.931321i	$-0.618658\pi$
$389$	5.13287	−	2.96347i	0.260247	−	0.150254i	0.624447	+	0.781067i	$0.285324\pi$
$390$	−5.15107	−	3.50256i	−0.260835	−	0.177359i
$391$			4.13553i			0.209143i
$392$	−4.59935	+	5.27693i	−0.232302	+	0.266525i
$393$	1.86017	−	25.2436i	0.0938331	−	1.27337i
$394$	−2.37680	+	4.11674i	−0.119742	+	0.207399i
$395$	−6.27018	−	10.8603i	−0.315487	−	0.546439i
$396$	−15.1867	+	6.00399i	−0.763160	+	0.301712i
$397$	4.49012	+	2.59237i	0.225352	+	0.130107i	0.608426	−	0.793610i	$-0.291801\pi$
$397$	4.49012	+	2.59237i	0.225352	+	0.130107i	−0.383074	+	0.923718i	$0.625134\pi$
$398$	4.35987			0.218540
$399$	−8.99603	+	19.5121i	−0.450365	+	0.976825i
$400$	−4.30595			−0.215297
$401$	−2.57744	−	1.48809i	−0.128711	−	0.0743114i	0.434262	−	0.900787i	$-0.357009\pi$
$401$	−2.57744	−	1.48809i	−0.128711	−	0.0743114i	−0.562973	+	0.826475i	$0.690343\pi$
$402$	7.93829	+	16.4317i	0.395926	+	0.819539i
$403$	15.6480	+	27.1032i	0.779485	+	1.35011i
$404$	1.65425	−	2.86525i	0.0823021	−	0.142551i
$405$	−7.17567	−	2.17435i	−0.356562	−	0.108044i
$406$	−4.00814	−	4.86877i	−0.198921	−	0.241633i
$407$		−	43.9656i		−	2.17929i
$408$	4.02766	−	5.92332i	0.199399	−	0.293248i
$409$	−3.60686	+	2.08242i	−0.178348	+	0.102969i	−0.586516	−	0.809937i	$-0.699501\pi$
$409$	−3.60686	+	2.08242i	−0.178348	+	0.102969i	0.408168	+	0.912907i	$0.366168\pi$
$410$	−2.32437	+	1.34197i	−0.114792	+	0.0662753i
$411$	21.7784	−	32.0285i	1.07425	−	1.57985i
$412$		−	10.2956i		−	0.507229i
$413$	−8.74454	+	1.45743i	−0.430291	+	0.0717156i
$414$	−2.96760	−	0.439744i	−0.145849	−	0.0216122i
$415$	6.67684	−	11.5646i	0.327753	−	0.567685i
$416$	2.15843	+	3.73851i	0.105826	+	0.183296i
$417$	14.3160	+	29.6332i	0.701060	+	1.45114i
$418$	22.1032	+	12.7613i	1.08110	+	0.624174i
$419$	5.26380			0.257154			0.128577	−	0.991700i	$-0.458959\pi$
$419$	5.26380			0.257154			0.128577	+	0.991700i	$0.458959\pi$
$420$	0.349193	+	3.80173i	0.0170389	+	0.185505i
$421$	6.95886			0.339154			0.169577	−	0.985517i	$-0.445760\pi$
$421$	6.95886			0.339154			0.169577	+	0.985517i	$0.445760\pi$
$422$	−0.839928	−	0.484933i	−0.0408871	−	0.0236062i
$423$	−9.37705	−	23.7186i	−0.455928	−	1.15324i
$424$	5.34995	+	9.26638i	0.259816	+	0.450015i
$425$	−8.90368	+	15.4216i	−0.431892	+	0.748059i
$426$	1.08283	−	14.6947i	0.0524633	−	0.711959i
$427$	9.70432	−	7.98893i	0.469625	−	0.386612i
$428$		−	4.93529i		−	0.238556i
$429$	−33.6573	−	22.8859i	−1.62499	−	1.10494i
$430$	−0.00556623	+	0.00321367i	−0.000268428	+	0.000154977i
$431$	24.9257	−	14.3908i	1.20063	−	0.693182i	0.239932	−	0.970790i	$-0.422875\pi$
$431$	24.9257	−	14.3908i	1.20063	−	0.693182i	0.960695	+	0.277608i	$0.0895415\pi$
$432$	3.82221	+	3.52004i	0.183896	+	0.169358i
$433$		−	26.2233i		−	1.26021i	−0.776509	−	0.630106i	$-0.783011\pi$
$433$		−	26.2233i		−	1.26021i	0.776509	−	0.630106i	$-0.216989\pi$
$434$	6.72912	−	17.9619i	0.323008	−	0.862198i
$435$	−3.43012	−	0.252761i	−0.164462	−	0.0121190i
$436$	4.90715	−	8.49944i	0.235010	−	0.407049i
$437$	2.34432	+	4.06048i	0.112144	+	0.194239i
$438$	4.14553	−	2.00274i	0.198081	−	0.0956946i
$439$	−19.2316	−	11.1034i	−0.917873	−	0.529934i	−0.0349174	−	0.999390i	$-0.511117\pi$
$439$	−19.2316	−	11.1034i	−0.917873	−	0.529934i	−0.882956	+	0.469456i	$0.844450\pi$
$440$	4.53495			0.216195
$441$	−20.6486	+	3.82547i	−0.983268	+	0.182165i
$442$	17.8525			0.849157
$443$	33.9255	+	19.5869i	1.61185	+	0.930602i	0.988941	+	0.148307i	$0.0473825\pi$
$443$	33.9255	+	19.5869i	1.61185	+	0.930602i	0.622909	+	0.782295i	$0.285951\pi$
$444$	−12.5964	+	6.08541i	−0.597797	+	0.288801i
$445$	5.74421	+	9.94926i	0.272302	+	0.471640i
$446$	−8.07154	+	13.9803i	−0.382198	+	0.661987i
$447$	28.3597	+	2.08979i	1.34137	+	0.0988437i
$448$	0.928188	−	2.47759i	0.0438528	−	0.117055i
$449$		−	9.16628i		−	0.432584i	−0.976329	−	0.216292i	$-0.930604\pi$
$449$		−	9.16628i		−	0.432584i	0.976329	−	0.216292i	$-0.0693963\pi$
$450$	−10.1196	−	8.02899i	−0.477042	−	0.378490i
$451$	−15.1875	+	8.76850i	−0.715151	+	0.412893i
$452$	−12.3230	+	7.11470i	−0.579626	+	0.334647i
$453$	22.3509	+	15.1979i	1.05014	+	0.714060i
$454$		−	0.398524i		−	0.0187036i
$455$	−7.34604	+	6.04752i	−0.344388	+	0.283512i
$456$	0.596804	−	8.09900i	0.0279479	−	0.379270i
$457$	3.69530	−	6.40045i	0.172859	−	0.299400i	−0.766559	−	0.642173i	$-0.778033\pi$
$457$	3.69530	−	6.40045i	0.172859	−	0.299400i	0.939418	+	0.342773i	$0.111366\pi$
$458$	5.31566	+	9.20700i	0.248385	+	0.430215i
$459$	20.5104	−	6.41054i	0.957341	−	0.299218i
$460$	0.721483	+	0.416548i	0.0336393	+	0.0194217i
$461$	−3.08009			−0.143454			−0.0717271	−	0.997424i	$-0.522851\pi$
$461$	−3.08009			−0.143454			−0.0717271	+	0.997424i	$0.522851\pi$
$462$	2.28164	+	24.8406i	0.106151	+	1.15569i
$463$	−3.29336			−0.153055			−0.0765276	−	0.997067i	$-0.524383\pi$
$463$	−3.29336			−0.153055			−0.0765276	+	0.997067i	$0.524383\pi$
$464$	2.06424	+	1.19179i	0.0958299	+	0.0553274i
$465$	−4.55063	−	9.41948i	−0.211030	−	0.436818i
$466$	7.63350	+	13.2216i	0.353615	+	0.612479i
$467$	−1.69381	+	2.93376i	−0.0783801	+	0.135758i	−0.902551	−	0.430583i	$-0.858308\pi$
$467$	−1.69381	+	2.93376i	−0.0783801	+	0.135758i	0.824171	+	0.566341i	$0.191641\pi$
$468$	−1.89831	+	12.8107i	−0.0877496	+	0.592175i
$469$	27.4962	−	4.58272i	1.26965	−	0.211611i
$470$			7.08270i			0.326701i
$471$	−11.9997	+	17.6474i	−0.552915	+	0.813149i
$472$	2.90180	−	1.67536i	0.133566	−	0.0771146i
$473$	−0.0363700	+	0.0209982i	−0.00167229	+	0.000965499i
$474$	−14.6601	+	21.5600i	−0.673360	+	0.990283i
$475$			20.1890i			0.926336i
$476$	−6.95415	−	8.44735i	−0.318743	−	0.387184i
$477$	−4.70522	+	31.7530i	−0.215437	+	1.45387i
$478$	−9.50049	+	16.4553i	−0.434542	+	0.752649i
$479$	−4.47302	−	7.74750i	−0.204377	−	0.353992i	0.745557	−	0.666442i	$-0.232184\pi$
$479$	−4.47302	−	7.74750i	−0.204377	−	0.353992i	−0.949934	+	0.312450i	$0.898850\pi$
$480$	−0.627696	−	1.29929i	−0.0286503	−	0.0593041i
$481$	−30.1950	−	17.4331i	−1.37677	−	0.794879i
$482$	−13.2888			−0.605289
$483$	−1.91869	+	4.16157i	−0.0873033	+	0.189358i
$484$	18.6315			0.846888
$485$	4.30142	+	2.48343i	0.195317	+	0.112767i
$486$	2.41918	+	15.3996i	0.109736	+	0.698540i
$487$	17.4869	+	30.2881i	0.792405	+	1.37249i	0.924474	+	0.381245i	$0.124505\pi$
$487$	17.4869	+	30.2881i	0.792405	+	1.37249i	−0.132069	+	0.991241i	$0.542162\pi$
$488$	−2.37545	+	4.11439i	−0.107531	+	0.186250i
$489$	−0.394817	+	5.35791i	−0.0178542	+	0.242293i
$490$	5.72307	+	1.12025i	0.258542	+	0.0506078i
$491$		−	30.5172i		−	1.37722i	−0.725131	−	0.688611i	$-0.758221\pi$
$491$		−	30.5172i		−	1.37722i	0.725131	−	0.688611i	$-0.241779\pi$
$492$	4.61437	+	3.13762i	0.208032	+	0.141455i
$493$	8.53671	−	4.92867i	0.384474	−	0.221976i
$494$	17.5285	−	10.1201i	0.788646	−	0.455325i
$495$	10.6578	+	8.45599i	0.479031	+	0.380069i
$496$			7.24973i			0.325523i
$497$	−21.0768	−	7.89608i	−0.945425	−	0.354187i
$498$	−27.6879	−	2.04028i	−1.24072	−	0.0914273i
$499$	6.37285	−	11.0381i	0.285288	−	0.494133i	−0.687391	−	0.726288i	$-0.741244\pi$
$499$	6.37285	−	11.0381i	0.285288	−	0.494133i	0.972679	+	0.232154i	$0.0745774\pi$
$500$	3.87638	+	6.71408i	0.173357	+	0.300263i
$501$	29.5466	−	14.2742i	1.32004	−	0.637724i
$502$	−3.25593	−	1.87981i	−0.145319	−	0.0839001i
$503$	1.14489			0.0510480			0.0255240	−	0.999674i	$-0.491875\pi$
$503$	1.14489			0.0510480			0.0255240	+	0.999674i	$0.491875\pi$
$504$	6.80116	−	4.09197i	0.302948	−	0.182271i
$505$	−2.75630			−0.122654
$506$	4.71420	+	2.72174i	0.209572	+	0.120996i
$507$	−8.78874	+	4.24591i	−0.390322	+	0.188568i
$508$	3.32042	+	5.75113i	0.147320	+	0.255165i
$509$	−5.02659	+	8.70631i	−0.222800	+	0.385901i	−0.955657	−	0.294482i	$-0.904853\pi$
$509$	−5.02659	+	8.70631i	−0.222800	+	0.385901i	0.732857	+	0.680382i	$0.238186\pi$
$510$	−5.95129	−	0.438542i	−0.263527	−	0.0194190i
$511$	−1.15617	−	6.93696i	−0.0511459	−	0.306873i
$512$			1.00000i			0.0441942i
$513$	16.5042	−	17.9210i	0.728678	−	0.791230i
$514$	5.04357	−	2.91191i	0.222463	−	0.128439i
$515$	−7.42812	+	4.28863i	−0.327322	+	0.188980i
$516$	0.0110502	+	0.00751376i	0.000486457	+	0.000330775i
$517$			46.2786i			2.03533i
$518$	3.51307	+	21.0783i	0.154355	+	0.926126i
$519$	−1.60656	+	21.8020i	−0.0705200	+	0.956999i
$520$	1.79818	−	3.11454i	0.0788555	−	0.136582i
$521$	−13.6522	−	23.6462i	−0.598112	−	1.03596i	−0.993100	−	0.117274i	$-0.962585\pi$
$521$	−13.6522	−	23.6462i	−0.598112	−	1.03596i	0.394988	−	0.918686i	$-0.370749\pi$
$522$	2.62901	+	6.64991i	0.115069	+	0.291059i
$523$	30.2011	+	17.4366i	1.32060	+	0.762449i	0.983824	−	0.179136i	$-0.0573301\pi$
$523$	30.2011	+	17.4366i	1.32060	+	0.762449i	0.336776	+	0.941585i	$0.390663\pi$
$524$	14.6139			0.638413
$525$	−16.1147	+	11.3879i	−0.703301	+	0.497007i
$526$	4.15917			0.181349
$527$	25.9647	+	14.9907i	1.13104	+	0.653006i
$528$	−4.10139	−	8.48959i	−0.178490	−	0.369462i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	4.45703	−	7.71979i	0.193601	−	0.335326i
$531$	9.94357	+	1.47346i	0.431514	+	0.0639426i
$532$	−11.6165	−	4.35194i	−0.503641	−	0.188680i
$533$			13.9074i			0.602397i
$534$	13.4303	−	19.7514i	0.581188	−	0.854729i
$535$	−3.56073	+	2.05579i	−0.153944	+	0.0888794i
$536$	−9.12438	+	5.26796i	−0.394113	+	0.227541i
$537$	−11.9423	+	17.5631i	−0.515349	+	0.757902i
$538$			24.7090i			1.06528i
$539$	37.3947	+	7.31977i	1.61071	+	0.315285i
$540$	0.947512	−	4.22393i	0.0407744	−	0.181769i
$541$	−17.3133	+	29.9876i	−0.744358	+	1.28927i	0.206136	+	0.978523i	$0.433911\pi$
$541$	−17.3133	+	29.9876i	−0.744358	+	1.28927i	−0.950494	+	0.310742i	$0.899422\pi$
$542$	8.33114	+	14.4300i	0.357853	+	0.619820i
$543$	−4.93425	−	10.2136i	−0.211749	−	0.438306i
$544$	3.58147	+	2.06776i	0.153554	+	0.0886546i
$545$	−8.17626			−0.350233
$546$	17.9649	+	8.28271i	0.768827	+	0.354467i
$547$	40.6583			1.73842			0.869211	−	0.494441i	$-0.164627\pi$
$547$	40.6583			1.73842			0.869211	+	0.494441i	$0.164627\pi$
$548$	19.3657	+	11.1808i	0.827262	+	0.477620i
$549$	−13.2544	+	5.24009i	−0.565686	+	0.223641i
$550$	11.7197	+	20.2991i	0.499729	+	0.865556i
$551$	5.58786	−	9.67847i	0.238051	−	0.412317i
$552$	0.127287	−	1.72737i	0.00541771	−	0.0735216i
$553$	25.3121	+	30.7471i	1.07638	+	1.30750i
$554$			4.03112i			0.171266i
$555$	9.63752	+	6.55320i	0.409090	+	0.278168i
$556$	−16.4551	+	9.50033i	−0.697850	+	0.402904i
$557$	−14.7534	+	8.51786i	−0.625120	+	0.360913i	−0.778860	−	0.627198i	$-0.784202\pi$
$557$	−14.7534	+	8.51786i	−0.625120	+	0.360913i	0.153740	+	0.988111i	$0.450868\pi$
$558$	−13.5180	+	17.0379i	−0.572265	+	0.721271i
$559$			0.0333045i			0.00140863i
$560$	−2.17418	+	0.362365i	−0.0918757	+	0.0153127i
$561$	−38.8859	−	2.86545i	−1.64177	−	0.120979i
$562$	8.78108	−	15.2093i	0.370408	−	0.641565i
$563$	−19.4642	−	33.7129i	−0.820317	−	1.42083i	−0.905447	−	0.424460i	$-0.860464\pi$
$563$	−19.4642	−	33.7129i	−0.820317	−	1.42083i	0.0851299	−	0.996370i	$-0.472869\pi$
$564$	13.2591	−	6.40557i	0.558308	−	0.269723i
$565$	10.2663	+	5.92723i	0.431905	+	0.249361i
$566$	−17.0298			−0.715815
$567$	23.6137	+	3.06493i	0.991682	+	0.128715i
$568$	8.50698			0.356945
$569$	−29.6209	−	17.1016i	−1.24177	−	0.716937i	−0.272317	−	0.962208i	$-0.587790\pi$
$569$	−29.6209	−	17.1016i	−1.24177	−	0.716937i	−0.969455	+	0.245271i	$0.921123\pi$
$570$	−6.09189	+	2.94304i	−0.255161	+	0.123270i
$571$	9.47734	+	16.4152i	0.396614	+	0.686956i	0.993306	−	0.115514i	$-0.0368517\pi$
$571$	9.47734	+	16.4152i	0.396614	+	0.686956i	−0.596691	+	0.802471i	$0.703518\pi$
$572$	11.7494	−	20.3505i	0.491267	−	0.850899i
$573$	−39.3410	−	2.89898i	−1.64349	−	0.121107i
$574$	6.58064	−	5.41741i	0.274671	−	0.226118i
$575$			4.30595i			0.179571i
$576$	−1.86463	+	2.35014i	−0.0776928	+	0.0979226i
$577$	26.9568	−	15.5635i	1.12223	−	0.647918i	0.180258	−	0.983619i	$-0.442307\pi$
$577$	26.9568	−	15.5635i	1.12223	−	0.647918i	0.941968	+	0.335702i	$0.108973\pi$
$578$	0.0888336	−	0.0512881i	0.00369499	−	0.00213330i
$579$	−10.8466	−	7.37534i	−0.450769	−	0.306509i
$580$		−	1.98575i		−	0.0824538i
$581$	−14.8779	+	39.7132i	−0.617239	+	1.64758i
$582$	0.758876	−	10.2984i	0.0314564	−	0.426883i
$583$	29.1224	−	50.4414i	1.20613	−	2.08907i
$584$	1.32905	+	2.30198i	0.0549963	+	0.0952564i
$585$	10.0334	−	3.96668i	0.414832	−	0.164002i
$586$	14.2625	+	8.23448i	0.589180	+	0.340163i
$587$	4.06499			0.167780			0.0838900	−	0.996475i	$-0.473266\pi$
$587$	4.06499			0.167780			0.0838900	+	0.996475i	$0.473266\pi$
$588$	−3.07877	−	11.7269i	−0.126966	−	0.483611i
$589$	33.9914			1.40059
$590$	−2.41748	−	1.39573i	−0.0995262	−	0.0574615i
$591$	−3.58160	−	7.41367i	−0.147327	−	0.304957i
$592$	−4.03836	−	6.99465i	−0.165976	−	0.287478i
$593$	13.4676	−	23.3265i	0.553047	−	0.957906i	−0.445005	−	0.895528i	$-0.646798\pi$
$593$	13.4676	−	23.3265i	0.553047	−	0.957906i	0.998053	−	0.0623780i	$-0.0198684\pi$
$594$	6.19108	−	27.5993i	0.254023	−	1.13241i
$595$	−3.19788	+	8.53603i	−0.131100	+	0.349943i
$596$			16.4179i			0.672503i
$597$	−4.24615	+	6.24464i	−0.173783	+	0.255576i
$598$	3.73851	−	2.15843i	0.152879	−	0.0882648i
$599$	−0.366680	+	0.211703i	−0.0149821	+	0.00864994i	−0.507472	−	0.861668i	$-0.669420\pi$
$599$	−0.366680	+	0.211703i	−0.0149821	+	0.00864994i	0.492490	+	0.870318i	$0.336087\pi$
$600$	4.19364	−	6.16741i	0.171205	−	0.251784i
$601$		−	4.16416i		−	0.169860i	−0.996387	−	0.0849299i	$-0.972933\pi$
$601$		−	4.16416i		−	0.169860i	0.996387	−	0.0849299i	$-0.0270666\pi$
$602$	0.0157589	−	0.0129732i	0.000642284	−	0.000528750i
$603$	−31.2664	−	4.63311i	−1.27326	−	0.188675i
$604$	−7.80246	+	13.5143i	−0.317478	+	0.549887i
$605$	−7.76094	−	13.4423i	−0.315527	−	0.546509i
$606$	2.49279	+	5.15990i	0.101263	+	0.209607i
$607$	−26.9362	−	15.5517i	−1.09331	−	0.631222i	−0.158853	−	0.987302i	$-0.550780\pi$
$607$	−26.9362	−	15.5517i	−1.09331	−	0.631222i	−0.934455	+	0.356080i	$0.884113\pi$
$608$	4.68864			0.190149
$609$	10.8771	−	0.999077i	0.440764	−	0.0404847i
$610$	3.95795			0.160253
$611$	31.7835	+	18.3502i	1.28582	+	0.742371i
$612$	4.56136	+	11.5376i	0.184382	+	0.466382i
$613$	−3.88874	−	6.73549i	−0.157065	−	0.272044i	0.776744	−	0.629816i	$-0.216870\pi$
$613$	−3.88874	−	6.73549i	−0.157065	−	0.272044i	−0.933809	+	0.357772i	$0.883536\pi$
$614$	14.7202	−	25.4961i	0.594059	−	1.02894i
$615$	0.341632	−	4.63616i	0.0137759	−	0.186948i
$616$	−14.2062	+	2.36771i	−0.572382	+	0.0953977i
$617$			21.2783i			0.856631i	0.903629	+	0.428316i	$0.140893\pi$
$617$			21.2783i			0.856631i	−0.903629	+	0.428316i	$0.859107\pi$
$618$	14.7464	+	10.0271i	0.593189	+	0.403349i
$619$	−13.0909	+	7.55804i	−0.526168	+	0.303783i	−0.739454	−	0.673207i	$-0.764916\pi$
$619$	−13.0909	+	7.55804i	−0.526168	+	0.303783i	0.213287	+	0.976990i	$0.431583\pi$
$620$	5.23056	−	3.01986i	0.210064	−	0.121281i
$621$	3.52004	−	3.82221i	0.141254	−	0.153380i
$622$			23.2776i			0.933346i
$623$	−23.1888	−	28.1679i	−0.929039	−	1.12852i
$624$	−7.45681	−	0.549482i	−0.298511	−	0.0219969i
$625$	−7.53548	+	13.0518i	−0.301419	+	0.522073i
$626$	−5.91305	−	10.2417i	−0.236333	−	0.409341i
$627$	−39.8046	+	19.2299i	−1.58964	+	0.767970i
$628$	−10.6703	−	6.16051i	−0.425792	−	0.245831i
$629$	−33.4015			−1.33181
$630$	−5.78530	−	3.20242i	−0.230492	−	0.127587i
$631$	−43.9524			−1.74972			−0.874859	−	0.484378i	$-0.839046\pi$
$631$	−43.9524			−1.74972			−0.874859	+	0.484378i	$0.839046\pi$
$632$	−13.0360	−	7.52635i	−0.518545	−	0.299382i
$633$	1.51259	−	0.730745i	0.0601201	−	0.0290445i
$634$	−5.01822	−	8.69181i	−0.199299	−	0.345196i
$635$	2.76623	−	4.79125i	0.109774	−	0.190135i
$636$	−18.4827	−	1.36196i	−0.732885	−	0.0540053i
$637$	19.8547	−	22.7798i	0.786673	−	0.902568i
$638$		−	12.9750i		−	0.513684i
$639$	19.9926	+	15.8623i	0.790895	+	0.627504i
$640$	0.721483	−	0.416548i	0.0285191	−	0.0164655i
$641$	16.4913	−	9.52125i	0.651367	−	0.376067i	−0.137613	−	0.990486i	$-0.543943\pi$
$641$	16.4913	−	9.52125i	0.651367	−	0.376067i	0.788980	+	0.614419i	$0.210610\pi$
$642$	7.06882	+	4.80656i	0.278984	+	0.189700i
$643$			15.4822i			0.610557i	0.952263	+	0.305278i	$0.0987495\pi$
$643$			15.4822i			0.610557i	−0.952263	+	0.305278i	$0.901250\pi$
$644$	−2.47759	−	0.928188i	−0.0976308	−	0.0365757i
$645$	0.000818118	−	0.0111024i	3.22134e−5	−	0.000437155i
$646$	9.69499	−	16.7922i	0.381444	−	0.660681i
$647$	−0.324901	−	0.562746i	−0.0127732	−	0.0221238i	0.859568	−	0.511021i	$-0.170733\pi$
$647$	−0.324901	−	0.562746i	−0.0127732	−	0.0221238i	−0.872341	+	0.488897i	$0.837399\pi$
$648$	−8.76428	+	2.04633i	−0.344293	+	0.0803874i
$649$	−15.7959	−	9.11978i	−0.620044	−	0.357983i
$650$	18.5882			0.729089
$651$	19.1732	+	27.1315i	0.751457	+	1.06337i
$652$	−3.10178			−0.121475
$653$	−6.71521	−	3.87703i	−0.262787	−	0.151720i	0.362819	−	0.931860i	$-0.381814\pi$
$653$	−6.71521	−	3.87703i	−0.262787	−	0.151720i	−0.625605	+	0.780140i	$0.715148\pi$
$654$	7.39458	+	15.3063i	0.289151	+	0.598522i
$655$	−6.08741	−	10.5437i	−0.237855	−	0.411977i
$656$	−1.61082	+	2.79003i	−0.0628921	+	0.108932i
$657$	−1.16888	+	7.88814i	−0.0456024	+	0.307746i
$658$	−3.69789	−	22.1872i	−0.144159	−	0.864947i
$659$		−	15.0130i		−	0.584823i	−0.956293	−	0.292411i	$-0.905542\pi$
$659$		−	15.0130i		−	0.584823i	0.956293	−	0.292411i	$-0.0944577\pi$
$660$	−4.41667	+	6.49541i	−0.171919	+	0.252834i
$661$	29.6499	−	17.1184i	1.15325	−	0.665828i	0.203571	−	0.979060i	$-0.434745\pi$
$661$	29.6499	−	17.1184i	1.15325	−	0.665828i	0.949677	+	0.313232i	$0.101412\pi$
$662$	−20.9642	+	12.1037i	−0.814797	+	0.470423i
$663$	−17.3869	+	25.5701i	−0.675250	+	0.993062i
$664$		−	16.0290i		−	0.622044i
$665$	1.69900	+	10.1939i	0.0658844	+	0.395303i
$666$	3.55169	−	23.9685i	0.137625	−	0.928759i
$667$	1.19179	−	2.06424i	0.0461462	−	0.0799276i
$668$	9.47256	+	16.4070i	0.366504	+	0.634804i
$669$	−12.1630	−	25.1765i	−0.470249	−	0.973381i
$670$	7.60149	+	4.38872i	0.293671	+	0.169551i
$671$	25.8614			0.998369
$672$	2.64468	+	3.74242i	0.102021	+	0.144367i
$673$	42.2150			1.62727			0.813634	−	0.581378i	$-0.197486\pi$
$673$	42.2150			1.62727			0.813634	+	0.581378i	$0.197486\pi$
$674$	−8.88311	−	5.12866i	−0.342164	−	0.197549i
$675$	21.3556	−	6.67472i	0.821977	−	0.256910i
$676$	−2.81765	−	4.88031i	−0.108371	−	0.187704i
$677$	−15.6323	+	27.0760i	−0.600799	+	1.04061i	0.391902	+	0.920007i	$0.371817\pi$
$677$	−15.6323	+	27.0760i	−0.600799	+	1.04061i	−0.992700	+	0.120607i	$0.961516\pi$
$678$	1.81122	−	24.5794i	0.0695596	−	0.943966i
$679$	−14.7712	−	5.53378i	−0.566867	−	0.212367i
$680$		−	3.44529i		−	0.132121i
$681$	0.570806	+	0.388129i	0.0218733	+	0.0148732i
$682$	34.1767	−	19.7319i	1.30869	−	0.755574i
$683$	0.609454	−	0.351868i	0.0233201	−	0.0134639i	−0.488295	−	0.872679i	$-0.662381\pi$
$683$	0.609454	−	0.351868i	0.0233201	−	0.0134639i	0.511615	+	0.859215i	$0.329048\pi$
$684$	11.0190	+	8.74256i	0.421320	+	0.334280i
$685$		−	18.6294i		−	0.711792i
$686$	−18.5129	−	0.521265i	−0.706827	−	0.0199020i
$687$	−18.3642	−	1.35323i	−0.700638	−	0.0516290i
$688$	−0.00385749	+	0.00668138i	−0.000147066	+	0.000254725i
$689$	−23.0950	−	40.0017i	−0.879849	−	1.52394i
$690$	−1.29929	+	0.627696i	−0.0494630	+	0.0238960i
$691$	−10.4324	−	6.02314i	−0.396867	−	0.229131i	0.288264	−	0.957551i	$-0.406922\pi$
$691$	−10.4324	−	6.02314i	−0.396867	−	0.229131i	−0.685131	+	0.728420i	$0.740255\pi$
$692$	−12.6215			−0.479797
$693$	−37.8014	−	20.9247i	−1.43595	−	0.794865i
$694$	−0.485749			−0.0184388
$695$	13.7087	+	7.91470i	0.519999	+	0.300222i
$696$	−3.71740	+	1.79591i	−0.140908	+	0.0680736i
$697$	6.66161	+	11.5382i	0.252326	+	0.437042i
$698$	−0.294222	+	0.509608i	−0.0111365	+	0.0192890i
$699$	−26.3717	−	1.94330i	−0.997470	−	0.0735022i
$700$	−7.24073	−	8.79547i	−0.273674	−	0.332437i
$701$		−	3.07246i		−	0.116045i	−0.998315	−	0.0580226i	$-0.981520\pi$
$701$		−	3.07246i		−	0.116045i	0.998315	−	0.0580226i	$-0.0184795\pi$
$702$	−16.5000	−	15.1955i	−0.622751	−	0.573518i
$703$	−32.7954	+	18.9344i	−1.23690	+	0.714125i
$704$	4.71420	−	2.72174i	0.177673	−	0.102580i
$705$	−10.1446	−	6.89797i	−0.382066	−	0.259792i
$706$		−	1.90717i		−	0.0717773i
$707$	8.63438	−	1.43907i	0.324729	−	0.0541219i
$708$	−0.426504	+	5.78792i	−0.0160290	+	0.217523i
$709$	−10.5443	+	18.2633i	−0.396000	+	0.685891i	−0.993228	−	0.116180i	$-0.962935\pi$
$709$	−10.5443	+	18.2633i	−0.396000	+	0.685891i	0.597229	+	0.802071i	$0.296268\pi$
$710$	−3.54357	−	6.13764i	−0.132988	−	0.230341i
$711$	−16.6027	−	41.9953i	−0.622648	−	1.57495i
$712$	11.9425	+	6.89501i	0.447564	+	0.258401i
$713$	7.24973			0.271505
$714$	18.8719	−	1.73341i	0.706264	−	0.0648711i
$715$	−19.5768			−0.732129
$716$	−10.6193	−	6.13107i	−0.396863	−	0.229129i
$717$	−14.3163	−	29.6337i	−0.534651	−	1.10669i
$718$	−10.8764	−	18.8384i	−0.405902	−	0.703043i
$719$	−23.4751	+	40.6601i	−0.875475	+	1.51637i	−0.0192193	+	0.999815i	$0.506118\pi$
$719$	−23.4751	+	40.6601i	−0.875475	+	1.51637i	−0.856256	+	0.516552i	$0.827215\pi$
$720$	2.47229	+	0.366349i	0.0921370	+	0.0136530i
$721$	21.0302	−	17.3128i	0.783205	−	0.644761i
$722$		−	2.98331i		−	0.111027i
$723$	12.9422	−	19.0336i	0.481326	−	0.707866i
$724$	5.67150	−	3.27444i	0.210780	−	0.121694i
$725$	8.88851	−	5.13178i	0.330111	−	0.190590i
$726$	−18.1456	+	26.6860i	−0.673446	+	0.990409i
$727$		−	21.6691i		−	0.803662i	−0.915714	−	0.401831i	$-0.868374\pi$
$727$		−	21.6691i		−	0.803662i	0.915714	−	0.401831i	$-0.131626\pi$
$728$	−4.00686	+	10.6954i	−0.148504	+	0.396399i
$729$	−24.4129	−	11.5329i	−0.904183	−	0.427146i
$730$	1.10722	−	1.91777i	0.0409802	−	0.0709798i
$731$	0.0159528	+	0.0276310i	0.000590035	+	0.00102197i
$732$	−3.57956	−	7.40943i	−0.132304	−	0.273861i
$733$	−14.5800	−	8.41778i	−0.538525	−	0.310918i	0.205956	−	0.978561i	$-0.433970\pi$
$733$	−14.5800	−	8.41778i	−0.538525	−	0.310918i	−0.744481	+	0.667644i	$0.767303\pi$
$734$	15.9772			0.589729
$735$	−7.17833	+	7.10612i	−0.264777	+	0.262113i
$736$	1.00000			0.0368605
$737$	49.6684	+	28.6761i	1.82956	+	1.05630i
$738$	−8.98803	+	3.55338i	−0.330854	+	0.130802i
$739$	−2.90882	−	5.03822i	−0.107003	−	0.185334i	0.807552	−	0.589796i	$-0.200792\pi$
$739$	−2.90882	−	5.03822i	−0.107003	−	0.185334i	−0.914555	+	0.404462i	$0.867459\pi$
$740$	−3.36435	+	5.82722i	−0.123676	+	0.214213i
$741$	−2.57632	+	34.9623i	−0.0946435	+	1.28437i
$742$	−9.93152	+	26.5100i	−0.364598	+	0.973212i
$743$		−	19.9536i		−	0.732025i	−0.930610	−	0.366013i	$-0.880723\pi$
$743$		−	19.9536i		−	0.732025i	0.930610	−	0.366013i	$-0.119277\pi$
$744$	−10.3838	−	7.06064i	−0.380688	−	0.258856i
$745$	11.8452	−	6.83885i	0.433976	−	0.250556i
$746$	−17.4689	+	10.0856i	−0.639580	+	0.369262i
$747$	29.8880	−	37.6703i	1.09355	−	1.37828i
$748$		−	22.5117i		−	0.823108i
$749$	10.0810	−	8.29900i	0.368351	−	0.303239i
$750$	−13.3919	−	0.986828i	−0.489002	−	0.0360339i
$751$	−14.7078	+	25.4747i	−0.536696	+	0.929585i	0.462383	+	0.886680i	$0.346995\pi$
$751$	−14.7078	+	25.4747i	−0.536696	+	0.929585i	−0.999079	+	0.0429047i	$0.986339\pi$
$752$	4.25083	+	7.36265i	0.155012	+	0.268488i
$753$	5.86346	−	2.83269i	0.213677	−	0.103229i
$754$	−8.91103	−	5.14479i	−0.324521	−	0.187362i
$755$	13.0004			0.473133
$756$	−0.762844	+	13.7265i	−0.0277444	+	0.499230i
$757$	13.1396			0.477567			0.238784	−	0.971073i	$-0.423251\pi$
$757$	13.1396			0.477567			0.238784	+	0.971073i	$0.423251\pi$
$758$	−16.8253	−	9.71411i	−0.611123	−	0.352832i
$759$	−8.48959	+	4.10139i	−0.308153	+	0.148871i
$760$	−1.95304	−	3.38277i	−0.0708444	−	0.122706i
$761$	1.32366	−	2.29264i	0.0479826	−	0.0831082i	−0.841037	−	0.540978i	$-0.818054\pi$
$761$	1.32366	−	2.29264i	0.0479826	−	0.0831082i	0.889019	+	0.457870i	$0.151387\pi$
$762$	−11.4712	−	0.845294i	−0.415556	−	0.0306218i
$763$	25.6129	−	4.26885i	0.927249	−	0.154543i
$764$		−	22.7751i		−	0.823975i
$765$	6.42419	−	8.09693i	0.232267	−	0.292745i
$766$	−24.3781	+	14.0747i	−0.880817	+	0.508540i
$767$	−12.5267	+	7.23229i	−0.452312	+	0.261143i
$768$	−1.43230	−	0.973918i	−0.0516837	−	0.0351432i
$769$			9.62648i			0.347140i	0.984822	+	0.173570i	$0.0555302\pi$
$769$			9.62648i			0.347140i	−0.984822	+	0.173570i	$0.944470\pi$
$770$	7.62581	+	9.26323i	0.274815	+	0.333824i
$771$	−0.741298	+	10.0599i	−0.0266972	+	0.362297i
$772$	3.78643	−	6.55828i	0.136277	−	0.236038i
$773$	23.2778	+	40.3183i	0.837244	+	1.45015i	0.892190	+	0.451660i	$0.149168\pi$
$773$	23.2778	+	40.3183i	0.837244	+	1.45015i	−0.0549458	+	0.998489i	$0.517499\pi$
$774$	−0.0215239	+	0.00850939i	−0.000773662	+	0.000305864i
$775$	27.0347	+	15.6085i	0.971115	+	0.560673i
$776$	5.96192			0.214020
$777$	−33.6118	−	15.4967i	−1.20582	−	0.555942i
$778$	−5.92693			−0.212491
$779$	13.0814	+	7.55257i	0.468691	+	0.270599i
$780$	2.70968	+	5.60884i	0.0970221	+	0.200829i
$781$	−23.1538	−	40.1036i	−0.828508	−	1.43502i
$782$	2.06776	−	3.58147i	0.0739431	−	0.128073i
$783$	−12.0851	−	2.71093i	−0.431886	−	0.0968807i
$784$	6.62162	−	2.27029i	0.236486	−	0.0810816i
$785$			10.2646i			0.366359i
$786$	−14.2328	+	20.9315i	−0.507666	+	0.746604i
$787$	−26.1971	+	15.1249i	−0.933825	+	0.539144i	−0.888019	−	0.459807i	$-0.847919\pi$
$787$	−26.1971	+	15.1249i	−0.933825	+	0.539144i	−0.0458054	+	0.998950i	$0.514585\pi$
$788$	4.11674	−	2.37680i	0.146653	−	0.0846701i
$789$	−4.05069	+	5.95719i	−0.144208	+	0.212081i
$790$			12.5404i			0.446166i
$791$	−35.2547	−	13.2076i	−1.25351	−	0.469607i
$792$	16.1541	+	2.39374i	0.574010	+	0.0850578i
$793$	10.2545	−	17.7613i	0.364147	−	0.630721i
$794$	−2.59237	−	4.49012i	−0.0919997	−	0.159348i
$795$	6.71629	+	13.9022i	0.238202	+	0.493062i
$796$	−3.77576	−	2.17993i	−0.133828	−	0.0772657i
$797$	43.4068			1.53755			0.768774	−	0.639521i	$-0.220867\pi$
$797$	43.4068			1.53755			0.768774	+	0.639521i	$0.220867\pi$
$798$	17.5468	−	12.3999i	0.621151	−	0.438953i
$799$	35.1588			1.24383
$800$	3.72906	+	2.15297i	0.131842	+	0.0761192i
$801$	15.2100	+	38.4726i	0.537417	+	1.35936i
$802$	1.48809	+	2.57744i	0.0525461	+	0.0910125i
$803$	7.23464	−	12.5308i	0.255305	−	0.442201i
$804$	1.34109	−	18.1994i	0.0472966	−	0.641844i
$805$	0.362365	+	2.17418i	0.0127717	+	0.0766297i
$806$		−	31.2961i		−	1.10236i
$807$	−35.3907	−	24.0645i	−1.24581	−	0.847111i
$808$	−2.86525	+	1.65425i	−0.100799	+	0.0581964i
$809$	44.9987	−	25.9800i	1.58207	−	0.913409i	0.587513	−	0.809215i	$-0.300107\pi$
$809$	44.9987	−	25.9800i	1.58207	−	0.913409i	0.994557	−	0.104194i	$-0.0332263\pi$
$810$	5.12714	+	5.47088i	0.180149	+	0.192227i
$811$		−	14.6743i		−	0.515284i	−0.966240	−	0.257642i	$-0.917055\pi$
$811$		−	14.6743i		−	0.515284i	0.966240	−	0.257642i	$-0.0829455\pi$
$812$	1.03677	+	6.22055i	0.0363833	+	0.218298i
$813$	−28.7819	−	2.12090i	−1.00942	−	0.0743831i
$814$	−21.9828	+	38.0753i	−0.770496	+	1.33454i
$815$	1.29204	+	2.23788i	0.0452582	+	0.0783895i
$816$	−6.44972	+	3.11591i	−0.225785	+	0.109079i
$817$	0.0313265	+	0.0180864i	0.00109598	+	0.000632763i
$818$	4.16485			0.145620
$819$	−29.3597	+	17.6645i	−1.02591	+	0.617246i
$820$	2.68395			0.0937274
$821$	−33.2346	−	19.1880i	−1.15989	−	0.669665i	−0.208615	−	0.977998i	$-0.566896\pi$
$821$	−33.2346	−	19.1880i	−1.15989	−	0.669665i	−0.951279	+	0.308333i	$0.900229\pi$
$822$	−34.8749	+	16.8483i	−1.21640	+	0.587653i
$823$	−12.4859	−	21.6262i	−0.435230	−	0.753841i	0.562084	−	0.827080i	$-0.310000\pi$
$823$	−12.4859	−	21.6262i	−0.435230	−	0.753841i	−0.997314	+	0.0732389i	$0.976666\pi$
$824$	−5.14782	+	8.91628i	−0.179333	+	0.310613i
$825$	−40.4884	−	2.98354i	−1.40963	−	0.103873i
$826$	8.30171	+	3.11009i	0.288853	+	0.108214i
$827$		−	4.84748i		−	0.168564i	−0.996442	−	0.0842818i	$-0.973140\pi$
$827$		−	4.84748i		−	0.168564i	0.996442	−	0.0842818i	$-0.0268596\pi$
$828$	2.35014	+	1.86463i	0.0816731	+	0.0648003i
$829$	7.51308	−	4.33768i	0.260940	−	0.150654i	−0.363823	−	0.931468i	$-0.618529\pi$
$829$	7.51308	−	4.33768i	0.260940	−	0.150654i	0.624763	+	0.780814i	$0.285195\pi$
$830$	−11.5646	+	6.67684i	−0.401414	+	0.231756i
$831$	−5.77378	−	3.92598i	−0.200290	−	0.136191i
$832$		−	4.31686i		−	0.149660i
$833$	5.56097	−	28.4095i	0.192676	−	0.984332i
$834$	2.41854	−	32.8211i	0.0837473	−	1.13650i
$835$	7.89156	−	13.6686i	0.273099	−	0.473021i
$836$	−12.7613	−	22.1032i	−0.441358	−	0.764454i
$837$	−11.2379	−	35.9554i	−0.388439	−	1.24280i
$838$	−4.55859	−	2.63190i	−0.157474	−	0.0909175i
$839$	−43.3868			−1.49788			−0.748940	−	0.662638i	$-0.769437\pi$
$839$	−43.3868			−1.49788			−0.748940	+	0.662638i	$0.769437\pi$
$840$	1.59845	−	3.46699i	0.0551519	−	0.119622i
$841$	23.3186			0.804088
$842$	−6.02655	−	3.47943i	−0.207689	−	0.119909i
$843$	13.2322	+	27.3897i	0.455741	+	0.943353i
$844$	0.484933	+	0.839928i	0.0166921	+	0.0289115i
$845$	−2.34737	+	4.06577i	−0.0807521	+	0.139867i
$846$	−3.73855	+	25.2295i	−0.128534	+	0.867407i
$847$	31.3301	+	38.0574i	1.07652	+	1.30767i
$848$		−	10.6999i		−	0.367436i
$849$	16.5856	−	24.3918i	0.569217	−	0.837123i
$850$	15.4216	−	8.90368i	0.528958	−	0.305394i
$851$	−6.99465	+	4.03836i	−0.239774	+	0.138433i
$852$	−8.28509	+	12.1845i	−0.283843	+	0.417436i
$853$			27.5374i			0.942862i	0.881903	+	0.471431i	$0.156262\pi$
$853$			27.5374i			0.942862i	−0.881903	+	0.471431i	$0.843738\pi$
$854$	−12.3987	+	2.06646i	−0.424273	+	0.0707127i
$855$	1.71768	−	11.5917i	0.0587434	−	0.396427i
$856$	−2.46764	+	4.27409i	−0.0843423	+	0.146085i
$857$	19.4480	+	33.6849i	0.664330	+	1.15065i	0.979466	+	0.201607i	$0.0646164\pi$
$857$	19.4480	+	33.6849i	0.664330	+	1.15065i	−0.315136	+	0.949046i	$0.602050\pi$
$858$	17.7051	+	36.6484i	0.604444	+	1.25116i
$859$	−28.9655	−	16.7232i	−0.988290	−	0.570589i	−0.0835270	−	0.996506i	$-0.526618\pi$
$859$	−28.9655	−	16.7232i	−0.988290	−	0.570589i	−0.904763	+	0.425916i	$0.859952\pi$
$860$	0.00642733			0.000219170
$861$	1.35036	+	14.7016i	0.0460200	+	0.501028i
$862$	−28.7817			−0.980308
$863$	14.2837	+	8.24669i	0.486222	+	0.280721i	0.723006	−	0.690842i	$-0.242760\pi$
$863$	14.2837	+	8.24669i	0.486222	+	0.280721i	−0.236784	+	0.971562i	$0.576093\pi$
$864$	−1.55011	−	4.95955i	−0.0527360	−	0.168727i
$865$	5.25746	+	9.10619i	0.178759	+	0.309620i
$866$	−13.1117	+	22.7101i	−0.445552	+	0.771720i
$867$	−0.0130567	+	0.177187i	−0.000443427	+	0.00601758i
$868$	−14.8085	+	12.1909i	−0.502634	+	0.413786i
$869$			81.9392i			2.77960i
$870$	2.84419	+	1.93396i	0.0964271	+	0.0655673i
$871$	39.3887	−	22.7411i	1.33463	−	0.770552i
$872$	−8.49944	+	4.90715i	−0.287827	+	0.166177i
$873$	14.0113	+	11.1168i	0.474212	+	0.376245i
$874$		−	4.68864i		−	0.158596i
$875$	−7.19602	+	19.2082i	−0.243270	+	0.649355i
$876$	−4.59150	−	0.338341i	−0.155132	−	0.0114315i
$877$	−13.9837	+	24.2204i	−0.472195	+	0.817866i	−0.999494	−	0.0318139i	$-0.989872\pi$
$877$	−13.9837	+	24.2204i	−0.472195	+	0.817866i	0.527299	+	0.849680i	$0.323205\pi$
$878$	11.1034	+	19.2316i	0.374720	+	0.649034i
$879$	−25.6848	+	12.4085i	−0.866326	+	0.418529i
$880$	−3.92738	−	2.26748i	−0.132392	−	0.0764366i
$881$	−4.60800			−0.155247			−0.0776237	−	0.996983i	$-0.524733\pi$
$881$	−4.60800			−0.155247			−0.0776237	+	0.996983i	$0.524733\pi$
$882$	19.7950	+	7.01136i	0.666531	+	0.236085i
$883$	21.4581			0.722124			0.361062	−	0.932542i	$-0.382414\pi$
$883$	21.4581			0.722124			0.361062	+	0.932542i	$0.382414\pi$
$884$	−15.4607	−	8.92625i	−0.520000	−	0.300222i
$885$	4.35354	−	2.10323i	0.146343	−	0.0706994i
$886$	−19.5869	−	33.9255i	−0.658035	−	1.13975i
$887$	23.2403	−	40.2533i	0.780332	−	1.35157i	−0.151417	−	0.988470i	$-0.548384\pi$
$887$	23.2403	−	40.2533i	0.780332	−	1.35157i	0.931748	−	0.363104i	$-0.118283\pi$
$888$	13.9515	+	1.02807i	0.468181	+	0.0344996i
$889$	−6.16395	+	16.4533i	−0.206732	+	0.551826i
$890$		−	11.4884i		−	0.385093i
$891$	33.5009	+	35.7469i	1.12232	+	1.19757i
$892$	13.9803	−	8.07154i	0.468096	−	0.270255i
$893$	34.5208	−	19.9306i	1.15519	−	0.666951i
$894$	−23.5154	−	15.9897i	−0.786471	−	0.534775i
$895$			10.2156i			0.341468i
$896$	−2.04263	+	1.68156i	−0.0682395	+	0.0561771i
$897$	−0.549482	+	7.45681i	−0.0183467	+	0.248976i
$898$	−4.58314	+	7.93823i	−0.152941	+	0.264902i
$899$	−8.64015	−	14.9652i	−0.288165	−	0.499117i
$900$	4.74933	+	12.0131i	0.158311	+	0.400437i
$901$	−38.3214	−	22.1249i	−1.27667	−	0.737086i
$902$	17.5370			0.583918
$903$	0.00323374	+	0.0352063i	0.000107612	+	0.00117159i
$904$	14.2294			0.473263
$905$	−4.72491	−	2.72793i	−0.157061	−	0.0906793i
$906$	−11.7575	−	24.3372i	−0.390618	−	0.808551i
$907$	−22.9103	−	39.6818i	−0.760724	−	1.31761i	−0.942478	−	0.334269i	$-0.891511\pi$
$907$	−22.9103	−	39.6818i	−0.760724	−	1.31761i	0.181753	−	0.983344i	$-0.441823\pi$
$908$	−0.199262	+	0.345132i	−0.00661274	+	0.0114536i
$909$	−9.81830	−	1.45489i	−0.325653	−	0.0482558i
$910$	9.38562	−	1.56428i	0.311130	−	0.0518554i
$911$		−	42.0103i		−	1.39186i	−0.718109	−	0.695931i	$-0.754992\pi$
$911$		−	42.0103i		−	1.39186i	0.718109	−	0.695931i	$-0.245008\pi$
$912$	−4.56635	+	6.71554i	−0.151207	+	0.222374i
$913$	−75.5637	+	43.6267i	−2.50079	+	1.44383i
$914$	−6.40045	+	3.69530i	−0.211708	+	0.122230i
$915$	−3.85472	+	5.66898i	−0.127433	+	0.187411i
$916$		−	10.6313i		−	0.351269i
$917$	24.5743	+	29.8509i	0.811514	+	0.985763i
$918$	−20.9678	−	4.70349i	−0.692039	−	0.155238i
$919$	−2.13331	+	3.69500i	−0.0703713	+	0.121887i	−0.899064	−	0.437817i	$-0.855752\pi$
$919$	−2.13331	+	3.69500i	−0.0703713	+	0.121887i	0.828693	+	0.559704i	$0.189085\pi$
$920$	−0.416548	−	0.721483i	−0.0137332	−	0.0237866i
$921$	22.1819	+	45.9149i	0.730917	+	1.51295i
$922$	2.66744	+	1.54005i	0.0878474	+	0.0507187i
$923$	−36.7234			−1.20877
$924$	10.4444	−	22.6534i	0.343594	−	0.745243i
$925$	−34.7780			−1.14349
$926$	2.85213	+	1.64668i	0.0937268	+	0.0541132i
$927$	−28.7236	+	11.3558i	−0.943408	+	0.372972i
$928$	−1.19179	−	2.06424i	−0.0391224	−	0.0677620i
$929$	−7.54555	+	13.0693i	−0.247561	+	0.428789i	−0.962849	−	0.270042i	$-0.912963\pi$
$929$	−7.54555	+	13.0693i	−0.247561	+	0.428789i	0.715287	+	0.698831i	$0.246296\pi$
$930$	−0.768781	+	10.4328i	−0.0252093	+	0.342106i
$931$	−10.6445	−	31.0464i	−0.348861	−	1.01750i
$932$		−	15.2670i		−	0.500087i
$933$	−33.3405	−	22.6705i	−1.09152	−	0.742197i
$934$	2.93376	−	1.69381i	0.0959956	−	0.0554231i
$935$	−16.2418	+	9.37720i	−0.531163	+	0.306667i
$936$	8.04934	−	10.1452i	0.263101	−	0.331607i
$937$			20.1486i			0.658225i	0.944291	+	0.329113i	$0.106750\pi$
$937$			20.1486i			0.658225i	−0.944291	+	0.329113i	$0.893250\pi$
$938$	−26.1037	−	9.77932i	−0.852317	−	0.319306i
$939$	20.4280	+	1.50531i	0.666643	+	0.0491240i
$940$	3.54135	−	6.13380i	0.115506	−	0.200062i
$941$	12.9192	+	22.3766i	0.421152	+	0.729457i	0.996052	−	0.0887664i	$-0.0282925\pi$
$941$	12.9192	+	22.3766i	0.421152	+	0.729457i	−0.574900	+	0.818224i	$0.694959\pi$
$942$	19.2157	−	9.28326i	0.626081	−	0.302465i
$943$	2.79003	+	1.61082i	0.0908559	+	0.0524557i
$944$	−3.35071			−0.109056
$945$	10.2212	−	5.16739i	0.332497	−	0.168095i
$946$	0.0419964			0.00136542
$947$	−37.1957	−	21.4750i	−1.20870	−	0.697842i	−0.246223	−	0.969213i	$-0.579190\pi$
$947$	−37.1957	−	21.4750i	−1.20870	−	0.697842i	−0.962475	+	0.271371i	$0.912523\pi$
$948$	23.4760	−	11.3415i	0.762465	−	0.368353i
$949$	−5.73731	−	9.93731i	−0.186241	−	0.322579i
$950$	10.0945	−	17.4842i	0.327509	−	0.567263i
$951$	17.3366	+	1.27751i	0.562178	+	0.0414262i
$952$	1.79880	+	10.7927i	0.0582993	+	0.349793i
$953$			18.5368i			0.600464i	0.953866	+	0.300232i	$0.0970642\pi$
$953$			18.5368i			0.600464i	−0.953866	+	0.300232i	$0.902936\pi$
$954$	19.9513	−	25.1463i	0.645948	−	0.814141i
$955$	−16.4319	+	9.48694i	−0.531722	+	0.306990i
$956$	16.4553	−	9.50049i	0.532204	−	0.307268i
$957$	18.5841	+	12.6366i	0.600737	+	0.408482i
$958$			8.94604i			0.289033i
$959$	9.72644	+	58.3582i	0.314083	+	1.88449i
$960$	−0.106043	+	1.43906i	−0.00342251	+	0.0464456i
$961$	10.7793	−	18.6703i	0.347719	−	0.602267i
$962$	17.4331	+	30.1950i	0.562064	+	0.973524i
$963$	−13.7689	+	5.44347i	−0.443696	+	0.175413i
$964$	11.5084	+	6.64440i	0.370662	+	0.214002i
$965$	−6.30892			−0.203091
$966$	3.74242	−	2.64468i	0.120410	−	0.0850911i
$967$	−11.5284			−0.370729			−0.185365	−	0.982670i	$-0.559347\pi$
$967$	−11.5284			−0.370729			−0.185365	+	0.982670i	$0.559347\pi$
$968$	−16.1354	−	9.31577i	−0.518611	−	0.299420i
$969$	14.6094	+	30.2404i	0.469321	+	0.971461i
$970$	−2.48343	−	4.30142i	−0.0797380	−	0.138110i
$971$	16.4703	−	28.5274i	0.528556	−	0.915487i	−0.470889	−	0.882192i	$-0.656067\pi$
$971$	16.4703	−	28.5274i	0.528556	−	0.915487i	0.999446	−	0.0332942i	$-0.0105998\pi$
$972$	5.60473	−	14.5460i	0.179772	−	0.466564i
$973$	−47.0759	−	17.6362i	−1.50918	−	0.565391i
$974$		−	34.9737i		−	1.12063i
$975$	−18.1034	+	26.6239i	−0.579772	+	0.852646i
$976$	4.11439	−	2.37545i	0.131699	−	0.0760362i
$977$	39.7525	−	22.9511i	1.27180	−	0.734272i	0.296470	−	0.955042i	$-0.404190\pi$
$977$	39.7525	−	22.9511i	1.27180	−	0.734272i	0.975326	+	0.220770i	$0.0708572\pi$
$978$	3.02088	−	4.44268i	0.0965970	−	0.142061i
$979$		−	75.0658i		−	2.39911i
$980$	−4.39620	−	3.83170i	−0.140431	−	0.122399i
$981$	−29.1249	−	4.31578i	−0.929886	−	0.137792i
$982$	−15.2586	+	26.4287i	−0.486922	+	0.843373i
$983$	17.3734	+	30.0917i	0.554127	+	0.959776i	0.997971	+	0.0636717i	$0.0202811\pi$
$983$	17.3734	+	30.0917i	0.554127	+	0.959776i	−0.443844	+	0.896104i	$0.646386\pi$
$984$	−2.42735	−	5.02444i	−0.0773811	−	0.160173i
$985$	−3.42965	−	1.98011i	−0.109278	−	0.0630915i
$986$	−9.85735			−0.313922
$987$	35.3802	+	16.3120i	1.12616	+	0.519217i
$988$	−20.2402			−0.643926
$989$	0.00668138	+	0.00385749i	0.000212455	+	0.000122661i
$990$	−5.00191	−	12.6520i	−0.158971	−	0.402107i
$991$	6.92195	+	11.9892i	0.219883	+	0.380848i	0.954772	−	0.297339i	$-0.0960991\pi$
$991$	6.92195	+	11.9892i	0.219883	+	0.380848i	−0.734889	+	0.678187i	$0.762766\pi$
$992$	3.62487	−	6.27845i	0.115090	−	0.199341i
$993$	3.08129	−	41.8150i	0.0977819	−	1.32696i
$994$	14.3050	+	17.3766i	0.453728	+	0.551153i
$995$			3.63219i			0.115148i
$996$	22.9583	+	15.6109i	0.727461	+	0.494650i
$997$	−4.79372	+	2.76765i	−0.151818	+	0.0876525i	−0.573985	−	0.818866i	$-0.694603\pi$
$997$	−4.79372	+	2.76765i	−0.151818	+	0.0876525i	0.422166	+	0.906518i	$0.361270\pi$
$998$	−11.0381	+	6.37285i	−0.349405	+	0.201729i
$999$	30.8710	+	28.4304i	0.976715	+	0.899498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.c.47.12	✓	56
3.2	odd	2	inner	966.2.l.c.47.26	yes	56
7.3	odd	6	inner	966.2.l.c.185.26	yes	56
21.17	even	6	inner	966.2.l.c.185.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.c.47.12	✓	56	1.1	even	1	trivial
966.2.l.c.47.26	yes	56	3.2	odd	2	inner
966.2.l.c.185.12	yes	56	21.17	even	6	inner
966.2.l.c.185.26	yes	56	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.55959 - 0.753450i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.416548 - 0.721483i) q^{5} +(-1.72737 - 0.127287i) q^{6} +(-0.928188 + 2.47759i) q^{7} -1.00000i q^{8} +(1.86463 - 2.35014i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.55959 - 0.753450i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.416548 - 0.721483i) q^{5} +(-1.72737 - 0.127287i) q^{6} +(-0.928188 + 2.47759i) q^{7} -1.00000i q^{8} +(1.86463 - 2.35014i) q^{9} +(-0.721483 + 0.416548i) q^{10} +(-4.71420 + 2.72174i) q^{11} +(1.43230 + 0.973918i) q^{12} +4.31686i q^{13} +(2.04263 - 1.68156i) q^{14} +(0.106043 - 1.43906i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.06776 + 3.58147i) q^{17} +(-2.78989 + 1.10297i) q^{18} +(4.06048 + 2.34432i) q^{19} +0.833097 q^{20} +(0.419150 + 4.56337i) q^{21} +5.44349 q^{22} +(0.866025 + 0.500000i) q^{23} +(-0.753450 - 1.55959i) q^{24} +(2.15297 + 3.72906i) q^{25} +(2.15843 - 3.73851i) q^{26} +(1.13734 - 5.07015i) q^{27} +(-2.60975 + 0.434962i) q^{28} -2.38358i q^{29} +(-0.811368 + 1.19324i) q^{30} +(6.27845 - 3.62487i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.30151 + 7.79671i) q^{33} -4.13553i q^{34} +(1.40091 + 1.70171i) q^{35} +(2.96760 + 0.439744i) q^{36} +(-4.03836 + 6.99465i) q^{37} +(-2.34432 - 4.06048i) q^{38} +(3.25254 + 6.73252i) q^{39} +(-0.721483 - 0.416548i) q^{40} +3.22165 q^{41} +(1.91869 - 4.16157i) q^{42} +0.00771499 q^{43} +(-4.71420 - 2.72174i) q^{44} +(-0.918880 - 2.32424i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(4.25083 - 7.36265i) q^{47} +(-0.127287 + 1.72737i) q^{48} +(-5.27693 - 4.59935i) q^{49} -4.30595i q^{50} +(5.92332 + 4.02766i) q^{51} +(-3.73851 + 2.15843i) q^{52} +(-9.26638 + 5.34995i) q^{53} +(-3.52004 + 3.82221i) q^{54} +4.53495i q^{55} +(2.47759 + 0.928188i) q^{56} +(8.09900 + 0.596804i) q^{57} +(-1.19179 + 2.06424i) q^{58} +(1.67536 + 2.90180i) q^{59} +(1.29929 - 0.627696i) q^{60} +(-4.11439 - 2.37545i) q^{61} -7.24973 q^{62} +(4.09197 + 6.80116i) q^{63} -1.00000 q^{64} +(3.11454 + 1.79818i) q^{65} +(8.48959 - 4.10139i) q^{66} +(-5.26796 - 9.12438i) q^{67} +(-2.06776 + 3.58147i) q^{68} +(1.72737 + 0.127287i) q^{69} +(-0.362365 - 2.17418i) q^{70} +8.50698i q^{71} +(-2.35014 - 1.86463i) q^{72} +(-2.30198 + 1.32905i) q^{73} +(6.99465 - 4.03836i) q^{74} +(6.16741 + 4.19364i) q^{75} +4.68864i q^{76} +(-2.36771 - 14.2062i) q^{77} +(0.549482 - 7.45681i) q^{78} +(7.52635 - 13.0360i) q^{79} +(0.416548 + 0.721483i) q^{80} +(-2.04633 - 8.76428i) q^{81} +(-2.79003 - 1.61082i) q^{82} +16.0290 q^{83} +(-3.74242 + 2.64468i) q^{84} +3.44529 q^{85} +(-0.00668138 - 0.00385749i) q^{86} +(-1.79591 - 3.71740i) q^{87} +(2.72174 + 4.71420i) q^{88} +(-6.89501 + 11.9425i) q^{89} +(-0.366349 + 2.47229i) q^{90} +(-10.6954 - 4.00686i) q^{91} +1.00000i q^{92} +(7.06064 - 10.3838i) q^{93} +(-7.36265 + 4.25083i) q^{94} +(3.38277 - 1.95304i) q^{95} +(0.973918 - 1.43230i) q^{96} +5.96192i q^{97} +(2.27029 + 6.62162i) q^{98} +(-2.39374 + 16.1541i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

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