LMFDB - Embedded newform 60.2.e.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,2,Mod(11,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("60.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	60.e (of order $2$, degree $1$, 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:	$0.479102412128$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.5
Root			$0.599676 + 1.28078i$ of defining polynomial
Character	$\chi$	$=$	60.11
Dual form			60.2.e.a.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.599676 - 1.28078i) q^{2} +(0.468213 + 1.66757i) q^{3} +(-1.28078 - 1.53610i) q^{4} -1.00000i q^{5} +(2.41656 + 0.400324i) q^{6} +0.936426i q^{7} +(-2.73546 + 0.719224i) q^{8} +(-2.56155 + 1.56155i) q^{9} +O(q^{10})$	\(q+(0.599676 - 1.28078i) q^{2} +(0.468213 + 1.66757i) q^{3} +(-1.28078 - 1.53610i) q^{4} -1.00000i q^{5} +(2.41656 + 0.400324i) q^{6} +0.936426i q^{7} +(-2.73546 + 0.719224i) q^{8} +(-2.56155 + 1.56155i) q^{9} +(-1.28078 - 0.599676i) q^{10} -4.27156 q^{11} +(1.96188 - 2.85500i) q^{12} +3.12311 q^{13} +(1.19935 + 0.561553i) q^{14} +(1.66757 - 0.468213i) q^{15} +(-0.719224 + 3.93481i) q^{16} +2.00000i q^{17} +(0.463897 + 4.21720i) q^{18} -4.27156i q^{19} +(-1.53610 + 1.28078i) q^{20} +(-1.56155 + 0.438447i) q^{21} +(-2.56155 + 5.47091i) q^{22} +7.60669 q^{23} +(-2.48013 - 4.22480i) q^{24} -1.00000 q^{25} +(1.87285 - 4.00000i) q^{26} +(-3.80335 - 3.54042i) q^{27} +(1.43845 - 1.19935i) q^{28} -5.12311i q^{29} +(0.400324 - 2.41656i) q^{30} -2.39871i q^{31} +(4.60831 + 3.28078i) q^{32} +(-2.00000 - 7.12311i) q^{33} +(2.56155 + 1.19935i) q^{34} +0.936426 q^{35} +(5.67948 + 1.93481i) q^{36} -3.12311 q^{37} +(-5.47091 - 2.56155i) q^{38} +(1.46228 + 5.20798i) q^{39} +(0.719224 + 2.73546i) q^{40} +7.12311i q^{41} +(-0.374874 + 2.26293i) q^{42} +1.46228i q^{43} +(5.47091 + 6.56155i) q^{44} +(1.56155 + 2.56155i) q^{45} +(4.56155 - 9.74247i) q^{46} -0.936426 q^{47} +(-6.89830 + 0.642976i) q^{48} +6.12311 q^{49} +(-0.599676 + 1.28078i) q^{50} +(-3.33513 + 0.936426i) q^{51} +(-4.00000 - 4.79741i) q^{52} +4.24621i q^{53} +(-6.81526 + 2.74813i) q^{54} +4.27156i q^{55} +(-0.673500 - 2.56155i) q^{56} +(7.12311 - 2.00000i) q^{57} +(-6.56155 - 3.07221i) q^{58} -7.19612 q^{59} +(-2.85500 - 1.96188i) q^{60} -5.12311 q^{61} +(-3.07221 - 1.43845i) q^{62} +(-1.46228 - 2.39871i) q^{63} +(6.96543 - 3.93481i) q^{64} -3.12311i q^{65} +(-10.3225 - 1.71001i) q^{66} +5.20798i q^{67} +(3.07221 - 2.56155i) q^{68} +(3.56155 + 12.6847i) q^{69} +(0.561553 - 1.19935i) q^{70} +6.67026 q^{71} +(5.88391 - 6.11389i) q^{72} -8.24621 q^{73} +(-1.87285 + 4.00000i) q^{74} +(-0.468213 - 1.66757i) q^{75} +(-6.56155 + 5.47091i) q^{76} -4.00000i q^{77} +(7.54716 + 1.25025i) q^{78} +9.06897i q^{79} +(3.93481 + 0.719224i) q^{80} +(4.12311 - 8.00000i) q^{81} +(9.12311 + 4.27156i) q^{82} -4.68213 q^{83} +(2.67350 + 1.83715i) q^{84} +2.00000 q^{85} +(1.87285 + 0.876894i) q^{86} +(8.54312 - 2.39871i) q^{87} +(11.6847 - 3.07221i) q^{88} -6.24621i q^{89} +(4.21720 - 0.463897i) q^{90} +2.92456i q^{91} +(-9.74247 - 11.6847i) q^{92} +(4.00000 - 1.12311i) q^{93} +(-0.561553 + 1.19935i) q^{94} -4.27156 q^{95} +(-3.31324 + 9.22076i) q^{96} -6.00000 q^{97} +(3.67188 - 7.84233i) q^{98} +(10.9418 - 6.67026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9	$ 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9} - 2 q^{10} + 4 q^{12} - 8 q^{13} - 14 q^{16} + 16 q^{18} + 4 q^{21} - 4 q^{22} - 2 q^{24} - 8 q^{25} + 28 q^{28} + 8 q^{30} - 16 q^{33} + 4 q^{34} + 18 q^{36} + 8 q^{37} + 14 q^{40} - 12 q^{42} - 4 q^{45} + 20 q^{46} - 36 q^{48} + 16 q^{49} - 32 q^{52} - 10 q^{54} + 24 q^{57} - 36 q^{58} - 14 q^{60} - 8 q^{61} - 2 q^{64} - 40 q^{66} + 12 q^{69} - 12 q^{70} + 24 q^{72} - 36 q^{76} + 40 q^{78} + 40 q^{82} + 16 q^{84} + 16 q^{85} + 44 q^{88} + 18 q^{90} + 32 q^{93} + 12 q^{94} + 42 q^{96} - 48 q^{97}+O(q^{100}) $ 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9 - 2 * q^10 + 4 * q^12 - 8 * q^13 - 14 * q^16 + 16 * q^18 + 4 * q^21 - 4 * q^22 - 2 * q^24 - 8 * q^25 + 28 * q^28 + 8 * q^30 - 16 * q^33 + 4 * q^34 + 18 * q^36 + 8 * q^37 + 14 * q^40 - 12 * q^42 - 4 * q^45 + 20 * q^46 - 36 * q^48 + 16 * q^49 - 32 * q^52 - 10 * q^54 + 24 * q^57 - 36 * q^58 - 14 * q^60 - 8 * q^61 - 2 * q^64 - 40 * q^66 + 12 * q^69 - 12 * q^70 + 24 * q^72 - 36 * q^76 + 40 * q^78 + 40 * q^82 + 16 * q^84 + 16 * q^85 + 44 * q^88 + 18 * q^90 + 32 * q^93 + 12 * q^94 + 42 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	0.599676	−	1.28078i	0.424035	−	0.905646i
$2$	0.599676	−	1.28078i	0.424035	−	0.905646i
$3$	0.468213	+	1.66757i	0.270323	+	0.962770i
$3$	0.468213	+	1.66757i	0.270323	+	0.962770i
$4$	−1.28078	−	1.53610i	−0.640388	−	0.768051i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	2.41656	+	0.400324i	0.986555	+	0.163431i
$7$			0.936426i			0.353936i	0.984217	+	0.176968i	$0.0566289\pi$
$7$			0.936426i			0.353936i	−0.984217	+	0.176968i	$0.943371\pi$
$8$	−2.73546	+	0.719224i	−0.967130	+	0.254284i
$9$	−2.56155	+	1.56155i	−0.853851	+	0.520518i
$10$	−1.28078	−	0.599676i	−0.405017	−	0.189634i
$11$	−4.27156			−1.28792			−0.643962	−	0.765058i	$-0.722710\pi$
$11$	−4.27156			−1.28792			−0.643962	+	0.765058i	$0.722710\pi$
$12$	1.96188	−	2.85500i	0.566345	−	0.824168i
$13$	3.12311			0.866194			0.433097	−	0.901347i	$-0.357421\pi$
$13$	3.12311			0.866194			0.433097	+	0.901347i	$0.357421\pi$
$14$	1.19935	+	0.561553i	0.320541	+	0.150081i
$15$	1.66757	−	0.468213i	0.430564	−	0.120892i
$16$	−0.719224	+	3.93481i	−0.179806	+	0.983702i
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$	0.463897	+	4.21720i	0.109342	+	0.994004i
$19$		−	4.27156i		−	0.979963i	−0.871733	−	0.489981i	$-0.837004\pi$
$19$		−	4.27156i		−	0.979963i	0.871733	−	0.489981i	$-0.162996\pi$
$20$	−1.53610	+	1.28078i	−0.343483	+	0.286390i
$21$	−1.56155	+	0.438447i	−0.340759	+	0.0956770i
$22$	−2.56155	+	5.47091i	−0.546125	+	1.16640i
$23$	7.60669			1.58610			0.793052	−	0.609154i	$-0.208491\pi$
$23$	7.60669			1.58610			0.793052	+	0.609154i	$0.208491\pi$
$24$	−2.48013	−	4.22480i	−0.506254	−	0.862384i
$25$	−1.00000			−0.200000
$26$	1.87285	−	4.00000i	0.367297	−	0.784465i
$27$	−3.80335	−	3.54042i	−0.731954	−	0.681354i
$28$	1.43845	−	1.19935i	0.271841	−	0.226656i
$29$		−	5.12311i		−	0.951337i	−0.879625	−	0.475668i	$-0.842206\pi$
$29$		−	5.12311i		−	0.951337i	0.879625	−	0.475668i	$-0.157794\pi$
$30$	0.400324	−	2.41656i	0.0730888	−	0.441201i
$31$		−	2.39871i		−	0.430820i	−0.976524	−	0.215410i	$-0.930891\pi$
$31$		−	2.39871i		−	0.430820i	0.976524	−	0.215410i	$-0.0691088\pi$
$32$	4.60831	+	3.28078i	0.814642	+	0.579965i
$33$	−2.00000	−	7.12311i	−0.348155	−	1.23997i
$34$	2.56155	+	1.19935i	0.439303	+	0.205687i
$35$	0.936426			0.158285
$36$	5.67948	+	1.93481i	0.946580	+	0.322468i
$37$	−3.12311			−0.513435			−0.256718	−	0.966486i	$-0.582641\pi$
$37$	−3.12311			−0.513435			−0.256718	+	0.966486i	$0.582641\pi$
$38$	−5.47091	−	2.56155i	−0.887499	−	0.415539i
$39$	1.46228	+	5.20798i	0.234152	+	0.833945i
$40$	0.719224	+	2.73546i	0.113719	+	0.432514i
$41$			7.12311i			1.11244i	0.831034	+	0.556221i	$0.187749\pi$
$41$			7.12311i			1.11244i	−0.831034	+	0.556221i	$0.812251\pi$
$42$	−0.374874	+	2.26293i	−0.0578442	+	0.349177i
$43$			1.46228i			0.222995i	0.993765	+	0.111498i	$0.0355648\pi$
$43$			1.46228i			0.222995i	−0.993765	+	0.111498i	$0.964435\pi$
$44$	5.47091	+	6.56155i	0.824771	+	0.989191i
$45$	1.56155	+	2.56155i	0.232783	+	0.381854i
$46$	4.56155	−	9.74247i	0.672564	−	1.43645i
$47$	−0.936426			−0.136592			−0.0682959	−	0.997665i	$-0.521756\pi$
$47$	−0.936426			−0.136592			−0.0682959	+	0.997665i	$0.521756\pi$
$48$	−6.89830	+	0.642976i	−0.995684	+	0.0928056i
$49$	6.12311			0.874729
$50$	−0.599676	+	1.28078i	−0.0848071	+	0.181129i
$51$	−3.33513	+	0.936426i	−0.467012	+	0.131126i
$52$	−4.00000	−	4.79741i	−0.554700	−	0.665281i
$53$			4.24621i			0.583262i	0.956531	+	0.291631i	$0.0941979\pi$
$53$			4.24621i			0.583262i	−0.956531	+	0.291631i	$0.905802\pi$
$54$	−6.81526	+	2.74813i	−0.927440	+	0.373973i
$55$			4.27156i			0.575977i
$56$	−0.673500	−	2.56155i	−0.0900002	−	0.342302i
$57$	7.12311	−	2.00000i	0.943478	−	0.264906i
$58$	−6.56155	−	3.07221i	−0.861574	−	0.403400i
$59$	−7.19612			−0.936855			−0.468427	−	0.883502i	$-0.655179\pi$
$59$	−7.19612			−0.936855			−0.468427	+	0.883502i	$0.655179\pi$
$60$	−2.85500	−	1.96188i	−0.368579	−	0.253277i
$61$	−5.12311			−0.655946			−0.327973	−	0.944687i	$-0.606366\pi$
$61$	−5.12311			−0.655946			−0.327973	+	0.944687i	$0.606366\pi$
$62$	−3.07221	−	1.43845i	−0.390171	−	0.182683i
$63$	−1.46228	−	2.39871i	−0.184230	−	0.302209i
$64$	6.96543	−	3.93481i	0.870679	−	0.491851i
$65$		−	3.12311i		−	0.387374i
$66$	−10.3225	−	1.71001i	−1.27061	−	0.210487i
$67$			5.20798i			0.636257i	0.948048	+	0.318128i	$0.103054\pi$
$67$			5.20798i			0.636257i	−0.948048	+	0.318128i	$0.896946\pi$
$68$	3.07221	−	2.56155i	0.372560	−	0.310634i
$69$	3.56155	+	12.6847i	0.428761	+	1.52705i
$70$	0.561553	−	1.19935i	0.0671184	−	0.143350i
$71$	6.67026			0.791615			0.395807	−	0.918334i	$-0.370465\pi$
$71$	6.67026			0.791615			0.395807	+	0.918334i	$0.370465\pi$
$72$	5.88391	−	6.11389i	0.693425	−	0.720529i
$73$	−8.24621			−0.965146			−0.482573	−	0.875856i	$-0.660298\pi$
$73$	−8.24621			−0.965146			−0.482573	+	0.875856i	$0.660298\pi$
$74$	−1.87285	+	4.00000i	−0.217715	+	0.464991i
$75$	−0.468213	−	1.66757i	−0.0540646	−	0.192554i
$76$	−6.56155	+	5.47091i	−0.752662	+	0.627557i
$77$		−	4.00000i		−	0.455842i
$78$	7.54716	+	1.25025i	0.854547	+	0.141563i
$79$			9.06897i			1.02034i	0.860074	+	0.510169i	$0.170417\pi$
$79$			9.06897i			1.02034i	−0.860074	+	0.510169i	$0.829583\pi$
$80$	3.93481	+	0.719224i	0.439925	+	0.0804116i
$81$	4.12311	−	8.00000i	0.458123	−	0.888889i
$82$	9.12311	+	4.27156i	1.00748	+	0.471715i
$83$	−4.68213			−0.513931			−0.256965	−	0.966421i	$-0.582723\pi$
$83$	−4.68213			−0.513931			−0.256965	+	0.966421i	$0.582723\pi$
$84$	2.67350	+	1.83715i	0.291703	+	0.200450i
$85$	2.00000			0.216930
$86$	1.87285	+	0.876894i	0.201955	+	0.0945580i
$87$	8.54312	−	2.39871i	0.915918	−	0.257168i
$88$	11.6847	−	3.07221i	1.24559	−	0.327498i
$89$		−	6.24621i		−	0.662097i	−0.943614	−	0.331049i	$-0.892598\pi$
$89$		−	6.24621i		−	0.662097i	0.943614	−	0.331049i	$-0.107402\pi$
$90$	4.21720	−	0.463897i	0.444532	−	0.0488991i
$91$			2.92456i			0.306577i
$92$	−9.74247	−	11.6847i	−1.01572	−	1.21821i
$93$	4.00000	−	1.12311i	0.414781	−	0.116461i
$94$	−0.561553	+	1.19935i	−0.0579198	+	0.123704i
$95$	−4.27156			−0.438253
$96$	−3.31324	+	9.22076i	−0.338156	+	0.941090i
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$	3.67188	−	7.84233i	0.370916	−	0.792195i
$99$	10.9418	−	6.67026i	1.09969	−	0.670387i
$100$	1.28078	+	1.53610i	0.128078	+	0.153610i
$101$		−	9.12311i		−	0.907783i	−0.891057	−	0.453891i	$-0.850035\pi$
$101$		−	9.12311i		−	0.907783i	0.891057	−	0.453891i	$-0.149965\pi$
$102$	−0.800647	+	4.83311i	−0.0792759	+	0.478549i
$103$		−	12.4041i		−	1.22221i	−0.791549	−	0.611106i	$-0.790725\pi$
$103$		−	12.4041i		−	1.22221i	0.791549	−	0.611106i	$-0.209275\pi$
$104$	−8.54312	+	2.24621i	−0.837722	+	0.220259i
$105$	0.438447	+	1.56155i	0.0427881	+	0.152392i
$106$	5.43845	+	2.54635i	0.528229	+	0.247324i
$107$	0.936426			0.0905278			0.0452639	−	0.998975i	$-0.485587\pi$
$107$	0.936426			0.0905278			0.0452639	+	0.998975i	$0.485587\pi$
$108$	−0.567212	+	10.3768i	−0.0545800	+	0.998509i
$109$	−9.12311			−0.873835			−0.436918	−	0.899502i	$-0.643930\pi$
$109$	−9.12311			−0.873835			−0.436918	+	0.899502i	$0.643930\pi$
$110$	5.47091	+	2.56155i	0.521631	+	0.244234i
$111$	−1.46228	−	5.20798i	−0.138793	−	0.494320i
$112$	−3.68466	−	0.673500i	−0.348167	−	0.0636398i
$113$			14.0000i			1.31701i	0.752577	+	0.658505i	$0.228811\pi$
$113$			14.0000i			1.31701i	−0.752577	+	0.658505i	$0.771189\pi$
$114$	1.71001	−	10.3225i	0.160157	−	0.966787i
$115$		−	7.60669i		−	0.709328i
$116$	−7.86962	+	6.56155i	−0.730676	+	0.609225i
$117$	−8.00000	+	4.87689i	−0.739600	+	0.450869i
$118$	−4.31534	+	9.21662i	−0.397259	+	0.848458i
$119$	−1.87285			−0.171684
$120$	−4.22480	+	2.48013i	−0.385670	+	0.226404i
$121$	7.24621			0.658746
$122$	−3.07221	+	6.56155i	−0.278144	+	0.594055i
$123$	−11.8782	+	3.33513i	−1.07103	+	0.300719i
$124$	−3.68466	+	3.07221i	−0.330892	+	0.275892i
$125$			1.00000i			0.0894427i
$126$	−3.94910	+	0.434406i	−0.351814	+	0.0386999i
$127$		−	4.68213i		−	0.415472i	−0.978185	−	0.207736i	$-0.933391\pi$
$127$		−	4.68213i		−	0.415472i	0.978185	−	0.207736i	$-0.0666095\pi$
$128$	−0.862603	−	11.2808i	−0.0762440	−	0.997089i
$129$	−2.43845	+	0.684658i	−0.214693	+	0.0602808i
$130$	−4.00000	−	1.87285i	−0.350823	−	0.164260i
$131$	17.6121			1.53878			0.769388	−	0.638782i	$-0.220562\pi$
$131$	17.6121			1.53878			0.769388	+	0.638782i	$0.220562\pi$
$132$	−8.38027	+	12.1953i	−0.729409	+	1.06147i
$133$	4.00000			0.346844
$134$	6.67026	+	3.12311i	0.576223	+	0.269795i
$135$	−3.54042	+	3.80335i	−0.304711	+	0.327340i
$136$	−1.43845	−	5.47091i	−0.123346	−	0.469127i
$137$			8.24621i			0.704521i	0.935902	+	0.352261i	$0.114587\pi$
$137$			8.24621i			0.704521i	−0.935902	+	0.352261i	$0.885413\pi$
$138$	18.3820	+	3.04514i	1.56478	+	0.259219i
$139$		−	13.8664i		−	1.17613i	−0.808813	−	0.588066i	$-0.799890\pi$
$139$		−	13.8664i		−	1.17613i	0.808813	−	0.588066i	$-0.200110\pi$
$140$	−1.19935	−	1.43845i	−0.101364	−	0.121571i
$141$	−0.438447	−	1.56155i	−0.0369239	−	0.131506i
$142$	4.00000	−	8.54312i	0.335673	−	0.716922i
$143$	−13.3405			−1.11559
$144$	−4.30208	−	11.2023i	−0.358507	−	0.933527i
$145$	−5.12311			−0.425451
$146$	−4.94506	+	10.5616i	−0.409256	+	0.874080i
$147$	2.86692	+	10.2107i	0.236459	+	0.842163i
$148$	4.00000	+	4.79741i	0.328798	+	0.394345i
$149$		−	14.0000i		−	1.14692i	−0.819232	−	0.573462i	$-0.805600\pi$
$149$		−	14.0000i		−	1.14692i	0.819232	−	0.573462i	$-0.194400\pi$
$150$	−2.41656	−	0.400324i	−0.197311	−	0.0326863i
$151$			6.14441i			0.500025i	0.968243	+	0.250013i	$0.0804347\pi$
$151$			6.14441i			0.500025i	−0.968243	+	0.250013i	$0.919565\pi$
$152$	3.07221	+	11.6847i	0.249189	+	0.947751i
$153$	−3.12311	−	5.12311i	−0.252488	−	0.414179i
$154$	−5.12311	−	2.39871i	−0.412832	−	0.193293i
$155$	−2.39871			−0.192669
$156$	6.12715	−	8.91648i	0.490564	−	0.713889i
$157$	21.3693			1.70546			0.852729	−	0.522354i	$-0.174946\pi$
$157$	21.3693			1.70546			0.852729	+	0.522354i	$0.174946\pi$
$158$	11.6153	+	5.43845i	0.924065	+	0.432660i
$159$	−7.08084	+	1.98813i	−0.561547	+	0.157669i
$160$	3.28078	−	4.60831i	0.259368	−	0.364319i
$161$			7.12311i			0.561379i
$162$	−7.77368	−	10.0782i	−0.610758	−	0.791817i
$163$			24.1671i			1.89291i	0.322834	+	0.946456i	$0.395364\pi$
$163$			24.1671i			1.89291i	−0.322834	+	0.946456i	$0.604636\pi$
$164$	10.9418	−	9.12311i	0.854413	−	0.712395i
$165$	−7.12311	+	2.00000i	−0.554533	+	0.155700i
$166$	−2.80776	+	5.99676i	−0.217925	+	0.465439i
$167$	2.80928			0.217389			0.108694	−	0.994075i	$-0.465333\pi$
$167$	2.80928			0.217389			0.108694	+	0.994075i	$0.465333\pi$
$168$	3.95622	−	2.32246i	0.305229	−	0.179182i
$169$	−3.24621			−0.249709
$170$	1.19935	−	2.56155i	0.0919862	−	0.196462i
$171$	6.67026	+	10.9418i	0.510088	+	0.836742i
$172$	2.24621	−	1.87285i	0.171272	−	0.142804i
$173$			2.00000i			0.152057i	0.997106	+	0.0760286i	$0.0242240\pi$
$173$			2.00000i			0.152057i	−0.997106	+	0.0760286i	$0.975776\pi$
$174$	2.05090	−	12.3803i	0.155478	−	0.938546i
$175$		−	0.936426i		−	0.0707872i
$176$	3.07221	−	16.8078i	0.231576	−	1.26693i
$177$	−3.36932	−	12.0000i	−0.253253	−	0.901975i
$178$	−8.00000	−	3.74571i	−0.599625	−	0.280752i
$179$	14.6875			1.09780			0.548899	−	0.835889i	$-0.315047\pi$
$179$	14.6875			1.09780			0.548899	+	0.835889i	$0.315047\pi$
$180$	1.93481	−	5.67948i	0.144212	−	0.423324i
$181$	4.24621			0.315618			0.157809	−	0.987470i	$-0.449557\pi$
$181$	4.24621			0.315618			0.157809	+	0.987470i	$0.449557\pi$
$182$	3.74571	+	1.75379i	0.277650	+	0.129999i
$183$	−2.39871	−	8.54312i	−0.177317	−	0.631525i
$184$	−20.8078	+	5.47091i	−1.53397	+	0.403321i
$185$			3.12311i			0.229615i
$186$	0.960258	−	5.79661i	0.0704096	−	0.425028i
$187$		−	8.54312i		−	0.624735i
$188$	1.19935	+	1.43845i	0.0874718	+	0.104910i
$189$	3.31534	−	3.56155i	0.241156	−	0.259065i
$190$	−2.56155	+	5.47091i	−0.185835	+	0.396902i
$191$	−7.72197			−0.558742			−0.279371	−	0.960183i	$-0.590126\pi$
$191$	−7.72197			−0.558742			−0.279371	+	0.960183i	$0.590126\pi$
$192$	9.82286	+	9.77299i	0.708904	+	0.705305i
$193$	16.2462			1.16943			0.584714	−	0.811240i	$-0.301207\pi$
$193$	16.2462			1.16943			0.584714	+	0.811240i	$0.301207\pi$
$194$	−3.59806	+	7.68466i	−0.258326	+	0.551726i
$195$	5.20798	−	1.46228i	0.372952	−	0.104716i
$196$	−7.84233	−	9.40572i	−0.560166	−	0.671837i
$197$		−	12.2462i		−	0.872506i	−0.899824	−	0.436253i	$-0.856305\pi$
$197$		−	12.2462i		−	0.872506i	0.899824	−	0.436253i	$-0.143695\pi$
$198$	−1.98156	−	18.0140i	−0.140824	−	1.28020i
$199$			17.6121i			1.24849i	0.781230	+	0.624244i	$0.214593\pi$
$199$			17.6121i			1.24849i	−0.781230	+	0.624244i	$0.785407\pi$
$200$	2.73546	−	0.719224i	0.193426	−	0.0508568i
$201$	−8.68466	+	2.43845i	−0.612569	+	0.171995i
$202$	−11.6847	−	5.47091i	−0.822130	−	0.384932i
$203$	4.79741			0.336712
$204$	5.71001	+	3.92375i	0.399780	+	0.274718i
$205$	7.12311			0.497499
$206$	−15.8869	−	7.43845i	−1.10689	−	0.518261i
$207$	−19.4849	+	11.8782i	−1.35430	+	0.825595i
$208$	−2.24621	+	12.2888i	−0.155747	+	0.852077i
$209$			18.2462i			1.26212i
$210$	2.26293	+	0.374874i	0.156157	+	0.0258687i
$211$			1.34700i			0.0927313i	0.998925	+	0.0463656i	$0.0147639\pi$
$211$			1.34700i			0.0927313i	−0.998925	+	0.0463656i	$0.985236\pi$
$212$	6.52262	−	5.43845i	0.447975	−	0.373514i
$213$	3.12311	+	11.1231i	0.213992	+	0.762143i
$214$	0.561553	−	1.19935i	0.0383870	−	0.0819861i
$215$	1.46228			0.0997266
$216$	12.9502	+	6.94920i	0.881152	+	0.472833i
$217$	2.24621			0.152483
$218$	−5.47091	+	11.6847i	−0.370537	+	0.791385i
$219$	−3.86098	−	13.7511i	−0.260901	−	0.929213i
$220$	6.56155	−	5.47091i	0.442380	−	0.368849i
$221$			6.24621i			0.420166i
$222$	−7.54716	−	1.25025i	−0.506532	−	0.0839115i
$223$		−	18.0227i		−	1.20689i	−0.797406	−	0.603443i	$-0.793795\pi$
$223$		−	18.0227i		−	1.20689i	0.797406	−	0.603443i	$-0.206205\pi$
$224$	−3.07221	+	4.31534i	−0.205270	+	0.288331i
$225$	2.56155	−	1.56155i	0.170770	−	0.104104i
$226$	17.9309	+	8.39547i	1.19274	+	0.558458i
$227$	8.65840			0.574678			0.287339	−	0.957829i	$-0.407229\pi$
$227$	8.65840			0.574678			0.287339	+	0.957829i	$0.407229\pi$
$228$	−12.1953	−	8.38027i	−0.807654	−	0.554997i
$229$	0.246211			0.0162701			0.00813505	−	0.999967i	$-0.497411\pi$
$229$	0.246211			0.0162701			0.00813505	+	0.999967i	$0.497411\pi$
$230$	−9.74247	−	4.56155i	−0.642399	−	0.300780i
$231$	6.67026	−	1.87285i	0.438871	−	0.123225i
$232$	3.68466	+	14.0140i	0.241910	+	0.920066i
$233$		−	10.0000i		−	0.655122i	−0.944830	−	0.327561i	$-0.893773\pi$
$233$		−	10.0000i		−	0.655122i	0.944830	−	0.327561i	$-0.106227\pi$
$234$	1.44880	+	13.1708i	0.0947110	+	0.861000i
$235$			0.936426i			0.0610857i
$236$	9.21662	+	11.0540i	0.599951	+	0.719553i
$237$	−15.1231	+	4.24621i	−0.982351	+	0.275821i
$238$	−1.12311	+	2.39871i	−0.0728001	+	0.155485i
$239$	−20.8319			−1.34751			−0.673753	−	0.738957i	$-0.735319\pi$
$239$	−20.8319			−1.34751			−0.673753	+	0.738957i	$0.735319\pi$
$240$	0.642976	+	6.89830i	0.0415039	+	0.445284i
$241$	−11.3693			−0.732362			−0.366181	−	0.930544i	$-0.619335\pi$
$241$	−11.3693			−0.732362			−0.366181	+	0.930544i	$0.619335\pi$
$242$	4.34538	−	9.28078i	0.279332	−	0.596591i
$243$	15.2710	+	3.12985i	0.979636	+	0.200780i
$244$	6.56155	+	7.86962i	0.420060	+	0.503801i
$245$		−	6.12311i		−	0.391191i
$246$	−2.85155	+	17.2134i	−0.181808	+	1.09749i
$247$		−	13.3405i		−	0.848837i
$248$	1.72521	+	6.56155i	0.109551	+	0.416659i
$249$	−2.19224	−	7.80776i	−0.138927	−	0.494797i
$250$	1.28078	+	0.599676i	0.0810034	+	0.0379269i
$251$	−25.1035			−1.58452			−0.792259	−	0.610184i	$-0.791095\pi$
$251$	−25.1035			−1.58452			−0.792259	+	0.610184i	$0.791095\pi$
$252$	−1.81181	+	5.31842i	−0.114133	+	0.335029i
$253$	−32.4924			−2.04278
$254$	−5.99676	−	2.80776i	−0.376270	−	0.176175i
$255$	0.936426	+	3.33513i	0.0586413	+	0.208854i
$256$	−14.9654	−	5.66001i	−0.935340	−	0.353751i
$257$		−	2.49242i		−	0.155473i	−0.996974	−	0.0777365i	$-0.975231\pi$
$257$		−	2.49242i		−	0.155473i	0.996974	−	0.0777365i	$-0.0247693\pi$
$258$	−0.585385	+	3.53368i	−0.0364445	+	0.219997i
$259$		−	2.92456i		−	0.181723i
$260$	−4.79741	+	4.00000i	−0.297523	+	0.248069i
$261$	8.00000	+	13.1231i	0.495188	+	0.812300i
$262$	10.5616	−	22.5571i	0.652495	−	1.39359i
$263$	15.0981			0.930989			0.465494	−	0.885051i	$-0.345877\pi$
$263$	15.0981			0.930989			0.465494	+	0.885051i	$0.345877\pi$
$264$	10.5940	+	18.0465i	0.652017	+	1.11068i
$265$	4.24621			0.260843
$266$	2.39871	−	5.12311i	0.147074	−	0.314118i
$267$	10.4160	−	2.92456i	0.637447	−	0.178980i
$268$	8.00000	−	6.67026i	0.488678	−	0.407451i
$269$			14.0000i			0.853595i	0.904347	+	0.426798i	$0.140358\pi$
$269$			14.0000i			0.853595i	−0.904347	+	0.426798i	$0.859642\pi$
$270$	2.74813	+	6.81526i	0.167246	+	0.414764i
$271$		−	31.7738i		−	1.93012i	−0.262032	−	0.965059i	$-0.584392\pi$
$271$		−	31.7738i		−	1.93012i	0.262032	−	0.965059i	$-0.415608\pi$
$272$	−7.86962	−	1.43845i	−0.477166	−	0.0872187i
$273$	−4.87689	+	1.36932i	−0.295163	+	0.0828748i
$274$	10.5616	+	4.94506i	0.638047	+	0.298742i
$275$	4.27156			0.257585
$276$	14.9234	−	21.7171i	0.898282	−	1.30722i
$277$	−1.36932			−0.0822743			−0.0411371	−	0.999154i	$-0.513098\pi$
$277$	−1.36932			−0.0822743			−0.0411371	+	0.999154i	$0.513098\pi$
$278$	−17.7597	−	8.31534i	−1.06516	−	0.498721i
$279$	3.74571	+	6.14441i	0.224250	+	0.367856i
$280$	−2.56155	+	0.673500i	−0.153082	+	0.0402493i
$281$		−	27.6155i		−	1.64740i	−0.567023	−	0.823702i	$-0.691905\pi$
$281$		−	27.6155i		−	1.64740i	0.567023	−	0.823702i	$-0.308095\pi$
$282$	−2.26293	−	0.374874i	−0.134755	−	0.0223234i
$283$			4.38684i			0.260770i	0.991463	+	0.130385i	$0.0416214\pi$
$283$			4.38684i			0.260770i	−0.991463	+	0.130385i	$0.958379\pi$
$284$	−8.54312	−	10.2462i	−0.506941	−	0.608001i
$285$	−2.00000	−	7.12311i	−0.118470	−	0.421936i
$286$	−8.00000	+	17.0862i	−0.473050	+	1.01033i
$287$	−6.67026			−0.393733
$288$	−16.9275	−	1.20777i	−0.997464	−	0.0711682i
$289$	13.0000			0.764706
$290$	−3.07221	+	6.56155i	−0.180406	+	0.385308i
$291$	−2.80928	−	10.0054i	−0.164683	−	0.586527i
$292$	10.5616	+	12.6670i	0.618068	+	0.741282i
$293$		−	30.4924i		−	1.78139i	−0.454605	−	0.890693i	$-0.650220\pi$
$293$		−	30.4924i		−	1.78139i	0.454605	−	0.890693i	$-0.349780\pi$
$294$	14.7968	+	2.45122i	0.862968	+	0.142958i
$295$			7.19612i			0.418974i
$296$	8.54312	−	2.24621i	0.496559	−	0.130558i
$297$	16.2462	+	15.1231i	0.942701	+	0.877532i
$298$	−17.9309	−	8.39547i	−1.03871	−	0.486337i
$299$	23.7565			1.37387
$300$	−1.96188	+	2.85500i	−0.113269	+	0.164834i
$301$	−1.36932			−0.0789261
$302$	7.86962	+	3.68466i	0.452846	+	0.212028i
$303$	15.2134	−	4.27156i	0.873986	−	0.245395i
$304$	16.8078	+	3.07221i	0.963991	+	0.176203i
$305$			5.12311i			0.293348i
$306$	−8.43441	+	0.927794i	−0.482163	+	0.0530385i
$307$			8.13254i			0.464149i	0.972698	+	0.232074i	$0.0745513\pi$
$307$			8.13254i			0.464149i	−0.972698	+	0.232074i	$0.925449\pi$
$308$	−6.14441	+	5.12311i	−0.350110	+	0.291916i
$309$	20.6847	−	5.80776i	1.17671	−	0.330392i
$310$	−1.43845	+	3.07221i	−0.0816983	+	0.174490i
$311$	−14.1617			−0.803035			−0.401517	−	0.915851i	$-0.631517\pi$
$311$	−14.1617			−0.803035			−0.401517	+	0.915851i	$0.631517\pi$
$312$	−7.74571	−	13.1945i	−0.438514	−	0.746992i
$313$	10.4924			0.593067			0.296533	−	0.955022i	$-0.404169\pi$
$313$	10.4924			0.593067			0.296533	+	0.955022i	$0.404169\pi$
$314$	12.8147	−	27.3693i	0.723174	−	1.54454i
$315$	−2.39871	+	1.46228i	−0.135152	+	0.0823901i
$316$	13.9309	−	11.6153i	0.783673	−	0.653413i
$317$			32.7386i			1.83878i	0.393342	+	0.919392i	$0.371319\pi$
$317$			32.7386i			1.83878i	−0.393342	+	0.919392i	$0.628681\pi$
$318$	−1.69986	+	10.2612i	−0.0953233	+	0.575420i
$319$			21.8836i			1.22525i
$320$	−3.93481	−	6.96543i	−0.219962	−	0.389380i
$321$	0.438447	+	1.56155i	0.0244717	+	0.0871574i
$322$	9.12311	+	4.27156i	0.508411	+	0.238045i
$323$	8.54312			0.475352
$324$	−17.5696	+	3.91270i	−0.976089	+	0.217372i
$325$	−3.12311			−0.173239
$326$	30.9526	+	14.4924i	1.71431	+	0.802661i
$327$	−4.27156	−	15.2134i	−0.236218	−	0.841302i
$328$	−5.12311	−	19.4849i	−0.282876	−	1.07588i
$329$		−	0.876894i		−	0.0483448i
$330$	−1.71001	+	10.3225i	−0.0941327	+	0.568233i
$331$			28.0281i			1.54056i	0.637705	+	0.770281i	$0.279884\pi$
$331$			28.0281i			1.54056i	−0.637705	+	0.770281i	$0.720116\pi$
$332$	5.99676	+	7.19224i	0.329115	+	0.394725i
$333$	8.00000	−	4.87689i	0.438397	−	0.267252i
$334$	1.68466	−	3.59806i	0.0921804	−	0.196877i
$335$	5.20798			0.284543
$336$	−0.602100	−	6.45975i	−0.0328473	−	0.352408i
$337$	−34.4924			−1.87892			−0.939461	−	0.342656i	$-0.888674\pi$
$337$	−34.4924			−1.87892			−0.939461	+	0.342656i	$0.888674\pi$
$338$	−1.94668	+	4.15767i	−0.105885	+	0.226147i
$339$	−23.3459	+	6.55498i	−1.26798	+	0.356018i
$340$	−2.56155	−	3.07221i	−0.138920	−	0.166614i
$341$			10.2462i			0.554863i
$342$	18.0140	−	1.98156i	0.974087	−	0.107151i
$343$			12.2888i			0.663534i
$344$	−1.05171	−	4.00000i	−0.0567042	−	0.215666i
$345$	12.6847	−	3.56155i	0.682919	−	0.191748i
$346$	2.56155	+	1.19935i	0.137710	+	0.0644776i
$347$	−23.8718			−1.28150			−0.640752	−	0.767748i	$-0.721377\pi$
$347$	−23.8718			−1.28150			−0.640752	+	0.767748i	$0.721377\pi$
$348$	−14.6265	−	10.0509i	−0.784062	−	0.538785i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$	−1.19935	−	0.561553i	−0.0641081	−	0.0300163i
$351$	−11.8782	−	11.0571i	−0.634014	−	0.590184i
$352$	−19.6847	−	14.0140i	−1.04920	−	0.746950i
$353$		−	3.75379i		−	0.199794i	−0.994998	−	0.0998970i	$-0.968149\pi$
$353$		−	3.75379i		−	0.199794i	0.994998	−	0.0998970i	$-0.0318513\pi$
$354$	−17.3898	−	2.88078i	−0.924258	−	0.153111i
$355$		−	6.67026i		−	0.354021i
$356$	−9.59482	+	8.00000i	−0.508525	+	0.423999i
$357$	−0.876894	−	3.12311i	−0.0464102	−	0.165292i
$358$	8.80776	−	18.8114i	0.465505	−	0.994215i
$359$	1.05171			0.0555069			0.0277535	−	0.999615i	$-0.491165\pi$
$359$	1.05171			0.0555069			0.0277535	+	0.999615i	$0.491165\pi$
$360$	−6.11389	−	5.88391i	−0.322230	−	0.310109i
$361$	0.753789			0.0396731
$362$	2.54635	−	5.43845i	0.133833	−	0.285838i
$363$	3.39277	+	12.0835i	0.178074	+	0.634221i
$364$	4.49242	−	3.74571i	0.235467	−	0.196328i
$365$			8.24621i			0.431626i
$366$	−12.3803	−	2.05090i	−0.647127	−	0.107202i
$367$			26.5658i			1.38672i	0.720590	+	0.693361i	$0.243871\pi$
$367$			26.5658i			1.38672i	−0.720590	+	0.693361i	$0.756129\pi$
$368$	−5.47091	+	29.9309i	−0.285191	+	1.56025i
$369$	−11.1231	−	18.2462i	−0.579046	−	0.949860i
$370$	4.00000	+	1.87285i	0.207950	+	0.0973650i
$371$	−3.97626			−0.206437
$372$	−6.84831	−	4.70596i	−0.355068	−	0.243993i
$373$	−0.876894			−0.0454039			−0.0227019	−	0.999742i	$-0.507227\pi$
$373$	−0.876894			−0.0454039			−0.0227019	+	0.999742i	$0.507227\pi$
$374$	−10.9418	−	5.12311i	−0.565788	−	0.264909i
$375$	−1.66757	+	0.468213i	−0.0861127	+	0.0241784i
$376$	2.56155	−	0.673500i	0.132102	−	0.0347331i
$377$		−	16.0000i		−	0.824042i
$378$	−2.57342	−	6.38199i	−0.132362	−	0.328254i
$379$		−	25.1035i		−	1.28948i	−0.764402	−	0.644740i	$-0.776966\pi$
$379$		−	25.1035i		−	1.28948i	0.764402	−	0.644740i	$-0.223034\pi$
$380$	5.47091	+	6.56155i	0.280652	+	0.336601i
$381$	7.80776	−	2.19224i	0.400004	−	0.112312i
$382$	−4.63068	+	9.89012i	−0.236926	+	0.506022i
$383$	4.68213			0.239246			0.119623	−	0.992819i	$-0.461831\pi$
$383$	4.68213			0.239246			0.119623	+	0.992819i	$0.461831\pi$
$384$	18.4076	−	6.72026i	0.939357	−	0.342942i
$385$	−4.00000			−0.203859
$386$	9.74247	−	20.8078i	0.495879	−	1.05909i
$387$	−2.28343	−	3.74571i	−0.116073	−	0.190405i
$388$	7.68466	+	9.21662i	0.390129	+	0.467903i
$389$			28.7386i			1.45711i	0.684989	+	0.728553i	$0.259807\pi$
$389$			28.7386i			1.45711i	−0.684989	+	0.728553i	$0.740193\pi$
$390$	1.25025	−	7.54716i	0.0633090	−	0.382165i
$391$			15.2134i			0.769374i
$392$	−16.7495	+	4.40388i	−0.845977	+	0.222430i
$393$	8.24621	+	29.3693i	0.415966	+	1.48149i
$394$	−15.6847	−	7.34376i	−0.790182	−	0.369973i
$395$	9.06897			0.456309
$396$	−24.2602	−	8.26465i	−1.21912	−	0.415314i
$397$	23.1231			1.16052			0.580258	−	0.814433i	$-0.302952\pi$
$397$	23.1231			1.16052			0.580258	+	0.814433i	$0.302952\pi$
$398$	22.5571	+	10.5616i	1.13069	+	0.529403i
$399$	1.87285	+	6.67026i	0.0937599	+	0.333931i
$400$	0.719224	−	3.93481i	0.0359612	−	0.196740i
$401$			24.0000i			1.19850i	0.800561	+	0.599251i	$0.204535\pi$
$401$			24.0000i			1.19850i	−0.800561	+	0.599251i	$0.795465\pi$
$402$	−2.08488	+	12.5854i	−0.103984	+	0.627702i
$403$		−	7.49141i		−	0.373174i
$404$	−14.0140	+	11.6847i	−0.697224	+	0.581333i
$405$	−8.00000	−	4.12311i	−0.397523	−	0.204879i
$406$	2.87689	−	6.14441i	0.142778	−	0.304942i
$407$	13.3405			0.661265
$408$	8.44961	−	4.96026i	0.418318	−	0.245569i
$409$	0.630683			0.0311853			0.0155926	−	0.999878i	$-0.495037\pi$
$409$	0.630683			0.0311853			0.0155926	+	0.999878i	$0.495037\pi$
$410$	4.27156	−	9.12311i	0.210957	−	0.450558i
$411$	−13.7511	+	3.86098i	−0.678292	+	0.190448i
$412$	−19.0540	+	15.8869i	−0.938722	+	0.782690i
$413$		−	6.73863i		−	0.331586i
$414$	3.52872	+	32.0790i	0.173427	+	1.57659i
$415$			4.68213i			0.229837i
$416$	14.3922	+	10.2462i	0.705637	+	0.502362i
$417$	23.1231	−	6.49242i	1.13234	−	0.317935i
$418$	23.3693	+	10.9418i	1.14303	+	0.535182i
$419$	−6.14441			−0.300174			−0.150087	−	0.988673i	$-0.547955\pi$
$419$	−6.14441			−0.300174			−0.150087	+	0.988673i	$0.547955\pi$
$420$	1.83715	−	2.67350i	0.0896439	−	0.130453i
$421$	−0.630683			−0.0307376			−0.0153688	−	0.999882i	$-0.504892\pi$
$421$	−0.630683			−0.0307376			−0.0153688	+	0.999882i	$0.504892\pi$
$422$	1.72521	+	0.807764i	0.0839817	+	0.0393213i
$423$	2.39871	−	1.46228i	0.116629	−	0.0710985i
$424$	−3.05398	−	11.6153i	−0.148314	−	0.564090i
$425$		−	2.00000i		−	0.0970143i
$426$	16.1191	+	2.67026i	0.780971	+	0.129375i
$427$		−	4.79741i		−	0.232163i
$428$	−1.19935	−	1.43845i	−0.0579729	−	0.0695300i
$429$	−6.24621	−	22.2462i	−0.301570	−	1.07406i
$430$	0.876894	−	1.87285i	0.0422876	−	0.0903170i
$431$	36.0453			1.73624			0.868121	−	0.496353i	$-0.165328\pi$
$431$	36.0453			1.73624			0.868121	+	0.496353i	$0.165328\pi$
$432$	16.6663	−	12.4191i	0.801859	−	0.597513i
$433$	18.0000			0.865025			0.432512	−	0.901628i	$-0.357627\pi$
$433$	18.0000			0.865025			0.432512	+	0.901628i	$0.357627\pi$
$434$	1.34700	−	2.87689i	0.0646581	−	0.138095i
$435$	−2.39871	−	8.54312i	−0.115009	−	0.409611i
$436$	11.6847	+	14.0140i	0.559594	+	0.671150i
$437$		−	32.4924i		−	1.55432i
$438$	−19.9274	−	3.30115i	−0.952169	−	0.157735i
$439$		−	29.9009i		−	1.42709i	−0.700608	−	0.713546i	$-0.747088\pi$
$439$		−	29.9009i		−	1.42709i	0.700608	−	0.713546i	$-0.252912\pi$
$440$	−3.07221	−	11.6847i	−0.146462	−	0.557044i
$441$	−15.6847	+	9.56155i	−0.746888	+	0.455312i
$442$	8.00000	+	3.74571i	0.380521	+	0.178165i
$443$	−25.7446			−1.22316			−0.611582	−	0.791181i	$-0.709467\pi$
$443$	−25.7446			−1.22316			−0.611582	+	0.791181i	$0.709467\pi$
$444$	−6.12715	+	8.91648i	−0.290782	+	0.423157i
$445$	−6.24621			−0.296099
$446$	−23.0830	−	10.8078i	−1.09301	−	0.511762i
$447$	23.3459	−	6.55498i	1.10422	−	0.310040i
$448$	3.68466	+	6.52262i	0.174084	+	0.308165i
$449$		−	2.63068i		−	0.124150i	−0.998071	−	0.0620748i	$-0.980228\pi$
$449$		−	2.63068i		−	0.124150i	0.998071	−	0.0620748i	$-0.0197717\pi$
$450$	−0.463897	−	4.21720i	−0.0218683	−	0.198801i
$451$		−	30.4268i		−	1.43274i
$452$	21.5054	−	17.9309i	1.01153	−	0.843397i
$453$	−10.2462	+	2.87689i	−0.481409	+	0.135168i
$454$	5.19224	−	11.0895i	0.243684	−	0.520455i
$455$	2.92456			0.137105
$456$	−18.0465	+	10.5940i	−0.845104	+	0.496110i
$457$	−10.0000			−0.467780			−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000			−0.467780			−0.233890	+	0.972263i	$0.575146\pi$
$458$	0.147647	−	0.315342i	0.00689909	−	0.0147349i
$459$	7.08084	−	7.60669i	0.330505	−	0.355050i
$460$	−11.6847	+	9.74247i	−0.544800	+	0.454245i
$461$		−	15.8617i		−	0.738755i	−0.929279	−	0.369377i	$-0.879571\pi$
$461$		−	15.8617i		−	0.738755i	0.929279	−	0.369377i	$-0.120429\pi$
$462$	1.60129	−	9.66622i	0.0744990	−	0.449713i
$463$		−	0.936426i		−	0.0435194i	−0.999763	−	0.0217597i	$-0.993073\pi$
$463$		−	0.936426i		−	0.0435194i	0.999763	−	0.0217597i	$-0.00692688\pi$
$464$	20.1584	+	3.68466i	0.935832	+	0.171056i
$465$	−1.12311	−	4.00000i	−0.0520828	−	0.185496i
$466$	−12.8078	−	5.99676i	−0.593308	−	0.277795i
$467$	−16.1498			−0.747324			−0.373662	−	0.927565i	$-0.621898\pi$
$467$	−16.1498			−0.747324			−0.373662	+	0.927565i	$0.621898\pi$
$468$	17.7376	+	6.04261i	0.819922	+	0.279320i
$469$	−4.87689			−0.225194
$470$	1.19935	+	0.561553i	0.0553220	+	0.0259025i
$471$	10.0054	+	35.6347i	0.461024	+	1.64196i
$472$	19.6847	−	5.17562i	0.906060	−	0.238227i
$473$		−	6.24621i		−	0.287201i
$474$	−3.63052	+	21.9157i	−0.166755	+	1.00662i
$475$			4.27156i			0.195993i
$476$	2.39871	+	2.87689i	0.109944	+	0.131862i
$477$	−6.63068	−	10.8769i	−0.303598	−	0.498019i
$478$	−12.4924	+	26.6811i	−0.571390	+	1.22036i
$479$	22.9354			1.04794			0.523971	−	0.851736i	$-0.324450\pi$
$479$	22.9354			1.04794			0.523971	+	0.851736i	$0.324450\pi$
$480$	9.22076	+	3.31324i	0.420868	+	0.151228i
$481$	−9.75379			−0.444734
$482$	−6.81791	+	14.5616i	−0.310547	+	0.663261i
$483$	−11.8782	+	3.33513i	−0.540479	+	0.151754i
$484$	−9.28078	−	11.1309i	−0.421853	−	0.505951i
$485$			6.00000i			0.272446i
$486$	13.1663	−	17.6819i	0.597236	−	0.802066i
$487$		−	15.3287i		−	0.694608i	−0.937753	−	0.347304i	$-0.887097\pi$
$487$		−	15.3287i		−	0.694608i	0.937753	−	0.347304i	$-0.112903\pi$
$488$	14.0140	−	3.68466i	0.634385	−	0.166797i
$489$	−40.3002	+	11.3153i	−1.82244	+	0.511697i
$490$	−7.84233	−	3.67188i	−0.354280	−	0.165879i
$491$	18.6638			0.842285			0.421143	−	0.906994i	$-0.361629\pi$
$491$	18.6638			0.842285			0.421143	+	0.906994i	$0.361629\pi$
$492$	20.3365	+	13.9747i	0.916840	+	0.630026i
$493$	10.2462			0.461466
$494$	−17.0862	−	8.00000i	−0.768746	−	0.359937i
$495$	−6.67026	−	10.9418i	−0.299806	−	0.491798i
$496$	9.43845	+	1.72521i	0.423799	+	0.0774640i
$497$			6.24621i			0.280181i
$498$	−11.3146	−	1.87437i	−0.507021	−	0.0839924i
$499$			1.57756i			0.0706212i	0.999376	+	0.0353106i	$0.0112421\pi$
$499$			1.57756i			0.0706212i	−0.999376	+	0.0353106i	$0.988758\pi$
$500$	1.53610	−	1.28078i	0.0686966	−	0.0572781i
$501$	1.31534	+	4.68466i	0.0587651	+	0.209295i
$502$	−15.0540	+	32.1520i	−0.671892	+	1.43501i
$503$	−19.8955			−0.887097			−0.443549	−	0.896250i	$-0.646281\pi$
$503$	−19.8955			−0.887097			−0.443549	+	0.896250i	$0.646281\pi$
$504$	5.72521	+	5.50985i	0.255021	+	0.245428i
$505$	−9.12311			−0.405973
$506$	−19.4849	+	41.6155i	−0.866211	+	1.85004i
$507$	−1.51992	−	5.41327i	−0.0675020	−	0.240412i
$508$	−7.19224	+	5.99676i	−0.319104	+	0.266063i
$509$			2.87689i			0.127516i	0.997965	+	0.0637581i	$0.0203086\pi$
$509$			2.87689i			0.127516i	−0.997965	+	0.0637581i	$0.979691\pi$
$510$	4.83311	+	0.800647i	0.214014	+	0.0354533i
$511$		−	7.72197i		−	0.341600i
$512$	−16.2236	+	15.7732i	−0.716990	+	0.697083i
$513$	−15.1231	+	16.2462i	−0.667701	+	0.717288i
$514$	−3.19224	−	1.49465i	−0.140803	−	0.0659261i
$515$	−12.4041			−0.546590
$516$	4.17481	+	2.86881i	0.183786	+	0.126292i
$517$	4.00000			0.175920
$518$	−3.74571	−	1.75379i	−0.164577	−	0.0770571i
$519$	−3.33513	+	0.936426i	−0.146396	+	0.0411046i
$520$	2.24621	+	8.54312i	0.0985029	+	0.374640i
$521$		−	21.7538i		−	0.953051i	−0.879161	−	0.476525i	$-0.841896\pi$
$521$		−	21.7538i		−	0.953051i	0.879161	−	0.476525i	$-0.158104\pi$
$522$	21.6052	−	2.37659i	0.945633	−	0.104021i
$523$		−	0.641132i		−	0.0280348i	−0.999902	−	0.0140174i	$-0.995538\pi$
$523$		−	0.641132i		−	0.0280348i	0.999902	−	0.0140174i	$-0.00446202\pi$
$524$	−22.5571	−	27.0540i	−0.985413	−	1.18186i
$525$	1.56155	−	0.438447i	0.0681518	−	0.0191354i
$526$	9.05398	−	19.3373i	0.394772	−	0.843146i
$527$	4.79741			0.208979
$528$	29.4665	−	2.74651i	1.28236	−	0.119527i
$529$	34.8617			1.51573
$530$	2.54635	−	5.43845i	0.110606	−	0.236231i
$531$	18.4332	−	11.2371i	0.799934	−	0.487649i
$532$	−5.12311	−	6.14441i	−0.222115	−	0.266394i
$533$			22.2462i			0.963590i
$534$	2.50051	−	15.0943i	0.108207	−	0.653195i
$535$		−	0.936426i		−	0.0404852i
$536$	−3.74571	−	14.2462i	−0.161790	−	0.615343i
$537$	6.87689	+	24.4924i	0.296760	+	1.05693i
$538$	17.9309	+	8.39547i	0.773055	+	0.361954i
$539$	−26.1552			−1.12658
$540$	10.3768	+	0.567212i	0.446547	+	0.0244089i
$541$	38.9848			1.67609			0.838045	−	0.545602i	$-0.183699\pi$
$541$	38.9848			1.67609			0.838045	+	0.545602i	$0.183699\pi$
$542$	−40.6951	−	19.0540i	−1.74800	−	0.818438i
$543$	1.98813	+	7.08084i	0.0853189	+	0.303868i
$544$	−6.56155	+	9.21662i	−0.281324	+	0.395159i
$545$			9.12311i			0.390791i
$546$	−1.17077	+	7.06736i	−0.0501043	+	0.302455i
$547$			25.2188i			1.07828i	0.842217	+	0.539139i	$0.181250\pi$
$547$			25.2188i			1.07828i	−0.842217	+	0.539139i	$0.818750\pi$
$548$	12.6670	−	10.5616i	0.541109	−	0.451167i
$549$	13.1231	−	8.00000i	0.560080	−	0.341432i
$550$	2.56155	−	5.47091i	0.109225	−	0.233280i
$551$	−21.8836			−0.932275
$552$	−18.8656	−	32.1368i	−0.802972	−	1.36783i
$553$	−8.49242			−0.361135
$554$	−0.821147	+	1.75379i	−0.0348872	+	0.0745113i
$555$	−5.20798	+	1.46228i	−0.221067	+	0.0620703i
$556$	−21.3002	+	17.7597i	−0.903329	+	0.753180i
$557$			19.7538i			0.836995i	0.908218	+	0.418497i	$0.137443\pi$
$557$			19.7538i			0.836995i	−0.908218	+	0.418497i	$0.862557\pi$
$558$	10.1158	−	1.11275i	0.428237	−	0.0471066i
$559$			4.56685i			0.193157i
$560$	−0.673500	+	3.68466i	−0.0284606	+	0.155705i
$561$	14.2462	−	4.00000i	0.601476	−	0.168880i
$562$	−35.3693	−	16.5604i	−1.49196	−	0.698558i
$563$	−36.1606			−1.52399			−0.761994	−	0.647584i	$-0.775779\pi$
$563$	−36.1606			−1.52399			−0.761994	+	0.647584i	$0.775779\pi$
$564$	−1.83715	+	2.67350i	−0.0773581	+	0.112575i
$565$	14.0000			0.588984
$566$	5.61856	+	2.63068i	0.236166	+	0.110576i
$567$	7.49141	+	3.86098i	0.314610	+	0.162146i
$568$	−18.2462	+	4.79741i	−0.765594	+	0.201295i
$569$		−	4.87689i		−	0.204450i	−0.994761	−	0.102225i	$-0.967404\pi$
$569$		−	4.87689i		−	0.204450i	0.994761	−	0.102225i	$-0.0325962\pi$
$570$	−10.3225	−	1.71001i	−0.432360	−	0.0716243i
$571$			16.7909i			0.702679i	0.936248	+	0.351339i	$0.114274\pi$
$571$			16.7909i			0.702679i	−0.936248	+	0.351339i	$0.885726\pi$
$572$	17.0862	+	20.4924i	0.714411	+	0.856831i
$573$	−3.61553	−	12.8769i	−0.151041	−	0.537940i
$574$	−4.00000	+	8.54312i	−0.166957	+	0.356583i
$575$	−7.60669			−0.317221
$576$	−11.6979	+	20.9561i	−0.487413	+	0.873171i
$577$	−15.7538			−0.655839			−0.327919	−	0.944706i	$-0.606347\pi$
$577$	−15.7538			−0.655839			−0.327919	+	0.944706i	$0.606347\pi$
$578$	7.79579	−	16.6501i	0.324262	−	0.692553i
$579$	7.60669	+	27.0916i	0.316123	+	1.12589i
$580$	6.56155	+	7.86962i	0.272454	+	0.326768i
$581$		−	4.38447i		−	0.181899i
$582$	−14.4993	−	2.40194i	−0.601017	−	0.0995637i
$583$		−	18.1379i		−	0.751197i
$584$	22.5571	−	5.93087i	0.933421	−	0.245421i
$585$	4.87689	+	8.00000i	0.201635	+	0.330759i
$586$	−39.0540	−	18.2856i	−1.61330	−	0.755371i
$587$	38.0335			1.56981			0.784904	−	0.619617i	$-0.212712\pi$
$587$	38.0335			1.56981			0.784904	+	0.619617i	$0.212712\pi$
$588$	12.0128	−	17.4815i	0.495399	−	0.720924i
$589$	−10.2462			−0.422188
$590$	9.21662	+	4.31534i	0.379442	+	0.177660i
$591$	20.4214	−	5.73384i	0.840023	−	0.235859i
$592$	2.24621	−	12.2888i	0.0923187	−	0.505067i
$593$		−	8.24621i		−	0.338631i	−0.985562	−	0.169316i	$-0.945844\pi$
$593$		−	8.24621i		−	0.338631i	0.985562	−	0.169316i	$-0.0541557\pi$
$594$	29.1118	−	11.7388i	1.19447	−	0.481649i
$595$			1.87285i			0.0767795i
$596$	−21.5054	+	17.9309i	−0.880897	+	0.734477i
$597$	−29.3693	+	8.24621i	−1.20201	+	0.337495i
$598$	14.2462	−	30.4268i	0.582571	−	1.24424i
$599$	36.8665			1.50632			0.753162	−	0.657836i	$-0.228528\pi$
$599$	36.8665			1.50632			0.753162	+	0.657836i	$0.228528\pi$
$600$	2.48013	+	4.22480i	0.101251	+	0.172477i
$601$	14.8769			0.606841			0.303421	−	0.952857i	$-0.401871\pi$
$601$	14.8769			0.606841			0.303421	+	0.952857i	$0.401871\pi$
$602$	−0.821147	+	1.75379i	−0.0334675	+	0.0714791i
$603$	−8.13254	−	13.3405i	−0.331183	−	0.543268i
$604$	9.43845	−	7.86962i	0.384045	−	0.320210i
$605$		−	7.24621i		−	0.294600i
$606$	3.65219	−	22.0465i	0.148360	−	0.895578i
$607$			29.4903i			1.19698i	0.801132	+	0.598488i	$0.204232\pi$
$607$			29.4903i			1.19698i	−0.801132	+	0.598488i	$0.795768\pi$
$608$	14.0140	−	19.6847i	0.568344	−	0.798318i
$609$	2.24621	+	8.00000i	0.0910211	+	0.324176i
$610$	6.56155	+	3.07221i	0.265670	+	0.124390i
$611$	−2.92456			−0.118315
$612$	−3.86962	+	11.3590i	−0.156420	+	0.459159i
$613$	0.876894			0.0354174			0.0177087	−	0.999843i	$-0.494363\pi$
$613$	0.876894			0.0354174			0.0177087	+	0.999843i	$0.494363\pi$
$614$	10.4160	+	4.87689i	0.420354	+	0.196815i
$615$	3.33513	+	11.8782i	0.134486	+	0.478977i
$616$	2.87689	+	10.9418i	0.115913	+	0.440859i
$617$		−	14.0000i		−	0.563619i	−0.959470	−	0.281809i	$-0.909065\pi$
$617$		−	14.0000i		−	0.563619i	0.959470	−	0.281809i	$-0.0909346\pi$
$618$	4.96565	−	29.9752i	0.199748	−	1.20578i
$619$			20.3061i			0.816171i	0.912944	+	0.408085i	$0.133803\pi$
$619$			20.3061i			0.816171i	−0.912944	+	0.408085i	$0.866197\pi$
$620$	3.07221	+	3.68466i	0.123383	+	0.147979i
$621$	−28.9309	−	26.9309i	−1.16096	−	1.08070i
$622$	−8.49242	+	18.1379i	−0.340515	+	0.727265i
$623$	5.84912			0.234340
$624$	−21.5441	+	2.00808i	−0.862455	+	0.0803877i
$625$	1.00000			0.0400000
$626$	6.29206	−	13.4384i	0.251481	−	0.537108i
$627$	−30.4268	+	8.54312i	−1.21513	+	0.341179i
$628$	−27.3693	−	32.8255i	−1.09215	−	1.30988i
$629$		−	6.24621i		−	0.249053i
$630$	0.434406	+	3.94910i	0.0173071	+	0.157336i
$631$			30.1315i			1.19951i	0.800182	+	0.599757i	$0.204736\pi$
$631$			30.1315i			1.19951i	−0.800182	+	0.599757i	$0.795264\pi$
$632$	−6.52262	−	24.8078i	−0.259456	−	0.986800i
$633$	−2.24621	+	0.630683i	−0.0892789	+	0.0250674i
$634$	41.9309	+	19.6326i	1.66529	+	0.779710i
$635$	−4.68213			−0.185805
$636$	12.1229	+	8.33054i	0.480706	+	0.330327i
$637$	19.1231			0.757685
$638$	28.0281	+	13.1231i	1.10964	+	0.519549i
$639$	−17.0862	+	10.4160i	−0.675921	+	0.412049i
$640$	−11.2808	+	0.862603i	−0.445912	+	0.0340974i
$641$		−	47.6155i		−	1.88070i	−0.340208	−	0.940350i	$-0.610498\pi$
$641$		−	47.6155i		−	1.88070i	0.340208	−	0.940350i	$-0.389502\pi$
$642$	2.26293	+	0.374874i	0.0893106	+	0.0147951i
$643$		−	20.4214i		−	0.805340i	−0.915345	−	0.402670i	$-0.868082\pi$
$643$		−	20.4214i		−	0.805340i	0.915345	−	0.402670i	$-0.131918\pi$
$644$	10.9418	−	9.12311i	0.431168	−	0.359501i
$645$	0.684658	+	2.43845i	0.0269584	+	0.0960138i
$646$	5.12311	−	10.9418i	0.201566	−	0.430500i
$647$	3.63043			0.142727			0.0713634	−	0.997450i	$-0.477265\pi$
$647$	3.63043			0.142727			0.0713634	+	0.997450i	$0.477265\pi$
$648$	−5.52478	+	24.8491i	−0.217034	+	0.976164i
$649$	30.7386			1.20660
$650$	−1.87285	+	4.00000i	−0.0734593	+	0.156893i
$651$	1.05171	+	3.74571i	0.0412196	+	0.146806i
$652$	37.1231	−	30.9526i	1.45385	−	1.21220i
$653$			26.9848i			1.05600i	0.849245	+	0.527999i	$0.177058\pi$
$653$			26.9848i			1.05600i	−0.849245	+	0.527999i	$0.822942\pi$
$654$	−22.0465	−	3.65219i	−0.862086	−	0.142812i
$655$		−	17.6121i		−	0.688161i
$656$	−28.0281	−	5.12311i	−1.09431	−	0.200024i
$657$	21.1231	−	12.8769i	0.824091	−	0.502375i
$658$	−1.12311	−	0.525853i	−0.0437832	−	0.0204999i
$659$	−26.9764			−1.05085			−0.525425	−	0.850840i	$-0.676094\pi$
$659$	−26.9764			−1.05085			−0.525425	+	0.850840i	$0.676094\pi$
$660$	12.1953	+	8.38027i	0.474702	+	0.326202i
$661$	−46.1080			−1.79339			−0.896696	−	0.442647i	$-0.854039\pi$
$661$	−46.1080			−1.79339			−0.896696	+	0.442647i	$0.854039\pi$
$662$	35.8977	+	16.8078i	1.39520	+	0.653252i
$663$	−10.4160	+	2.92456i	−0.404523	+	0.113580i
$664$	12.8078	−	3.36750i	0.497038	−	0.130684i
$665$		−	4.00000i		−	0.155113i
$666$	−1.44880	−	13.1708i	−0.0561399	−	0.510357i
$667$		−	38.9699i		−	1.50892i
$668$	−3.59806	−	4.31534i	−0.139213	−	0.166966i
$669$	30.0540	−	8.43845i	1.16195	−	0.326249i
$670$	3.12311	−	6.67026i	0.120656	−	0.257695i
$671$	21.8836			0.844809
$672$	−8.63456	−	3.10261i	−0.333086	−	0.119686i
$673$	−10.4924			−0.404453			−0.202227	−	0.979339i	$-0.564818\pi$
$673$	−10.4924			−0.404453			−0.202227	+	0.979339i	$0.564818\pi$
$674$	−20.6843	+	44.1771i	−0.796729	+	1.70164i
$675$	3.80335	+	3.54042i	0.146391	+	0.136271i
$676$	4.15767	+	4.98651i	0.159910	+	0.191789i
$677$			34.4924i			1.32565i	0.748774	+	0.662826i	$0.230643\pi$
$677$			34.4924i			1.32565i	−0.748774	+	0.662826i	$0.769357\pi$
$678$	−5.60453	+	33.8318i	−0.215241	+	1.29930i
$679$		−	5.61856i		−	0.215620i
$680$	−5.47091	+	1.43845i	−0.209800	+	0.0551619i
$681$	4.05398	+	14.4384i	0.155349	+	0.553282i
$682$	13.1231	+	6.14441i	0.502510	+	0.235282i
$683$	36.1606			1.38365			0.691823	−	0.722067i	$-0.256808\pi$
$683$	36.1606			1.38365			0.691823	+	0.722067i	$0.256808\pi$
$684$	8.26465	−	24.2602i	0.316007	−	0.927613i
$685$	8.24621			0.315072
$686$	15.7392	+	7.36932i	0.600927	+	0.281362i
$687$	0.115279	+	0.410574i	0.00439818	+	0.0156644i
$688$	−5.75379	−	1.05171i	−0.219361	−	0.0400959i
$689$			13.2614i			0.505218i
$690$	3.04514	−	18.3820i	0.115926	−	0.699790i
$691$		−	29.0798i		−	1.10625i	−0.833100	−	0.553123i	$-0.813436\pi$
$691$		−	29.0798i		−	1.10625i	0.833100	−	0.553123i	$-0.186564\pi$
$692$	3.07221	−	2.56155i	0.116788	−	0.0973756i
$693$	6.24621	+	10.2462i	0.237274	+	0.389221i
$694$	−14.3153	+	30.5744i	−0.543403	+	1.16059i
$695$	−13.8664			−0.525982
$696$	−21.6441	+	12.7060i	−0.820418	+	0.481618i
$697$	−14.2462			−0.539614
$698$	−8.39547	+	17.9309i	−0.317773	+	0.678693i
$699$	16.6757	−	4.68213i	0.630731	−	0.177094i
$700$	−1.43845	+	1.19935i	−0.0543682	+	0.0453313i
$701$			50.4924i			1.90707i	0.301278	+	0.953536i	$0.402587\pi$
$701$			50.4924i			1.90707i	−0.301278	+	0.953536i	$0.597413\pi$
$702$	−21.2848	+	8.58270i	−0.803342	+	0.323933i
$703$			13.3405i			0.503148i
$704$	−29.7533	+	16.8078i	−1.12137	+	0.633466i
$705$	−1.56155	+	0.438447i	−0.0588115	+	0.0165129i
$706$	−4.80776	−	2.25106i	−0.180943	−	0.0847197i
$707$	8.54312			0.321297
$708$	−14.1179	+	20.5449i	−0.530583	+	0.772126i
$709$	−26.4924			−0.994944			−0.497472	−	0.867480i	$-0.665738\pi$
$709$	−26.4924			−0.994944			−0.497472	+	0.867480i	$0.665738\pi$
$710$	−8.54312	−	4.00000i	−0.320617	−	0.150117i
$711$	−14.1617	−	23.2306i	−0.531104	−	0.871217i
$712$	4.49242	+	17.0862i	0.168361	+	0.640334i
$713$		−	18.2462i		−	0.683326i
$714$	−4.52585	−	0.749747i	−0.169376	−	0.0280586i
$715$			13.3405i			0.498907i
$716$	−18.8114	−	22.5616i	−0.703016	−	0.843165i
$717$	−9.75379	−	34.7386i	−0.364262	−	1.29734i
$718$	0.630683	−	1.34700i	0.0235369	−	0.0502696i
$719$	−5.84912			−0.218135			−0.109068	−	0.994034i	$-0.534787\pi$
$719$	−5.84912			−0.218135			−0.109068	+	0.994034i	$0.534787\pi$
$720$	−11.2023	+	4.30208i	−0.417486	+	0.160329i
$721$	11.6155			0.432585
$722$	0.452029	−	0.965435i	0.0168228	−	0.0359298i
$723$	−5.32326	−	18.9591i	−0.197974	−	0.705096i
$724$	−5.43845	−	6.52262i	−0.202118	−	0.242411i
$725$			5.12311i			0.190267i
$726$	17.5109	+	2.90083i	0.649889	+	0.107660i
$727$		−	26.5658i		−	0.985270i	−0.870236	−	0.492635i	$-0.836034\pi$
$727$		−	26.5658i		−	0.985270i	0.870236	−	0.492635i	$-0.163966\pi$
$728$	−2.10341	−	8.00000i	−0.0779576	−	0.296500i
$729$	1.93087	+	26.9309i	0.0715137	+	0.997440i
$730$	10.5616	+	4.94506i	0.390901	+	0.183025i
$731$	−2.92456			−0.108169
$732$	−10.0509	+	14.6265i	−0.371492	+	0.540610i
$733$	−35.1231			−1.29730			−0.648651	−	0.761086i	$-0.724666\pi$
$733$	−35.1231			−1.29730			−0.648651	+	0.761086i	$0.724666\pi$
$734$	34.0248	+	15.9309i	1.25588	+	0.588019i
$735$	10.2107	−	2.86692i	0.376627	−	0.105748i
$736$	35.0540	+	24.9559i	1.29211	+	0.919885i
$737$		−	22.2462i		−	0.819450i
$738$	−30.0396	+	3.30439i	−1.10577	+	0.121636i
$739$			18.6638i			0.686559i	0.939233	+	0.343279i	$0.111538\pi$
$739$			18.6638i			0.686559i	−0.939233	+	0.343279i	$0.888462\pi$
$740$	4.79741	−	4.00000i	0.176356	−	0.147043i
$741$	22.2462	−	6.24621i	0.817235	−	0.229460i
$742$	−2.38447	+	5.09271i	−0.0875367	+	0.186959i
$743$	−12.4041			−0.455062			−0.227531	−	0.973771i	$-0.573065\pi$
$743$	−12.4041			−0.455062			−0.227531	+	0.973771i	$0.573065\pi$
$744$	−10.1341	+	5.94910i	−0.371533	+	0.218105i
$745$	−14.0000			−0.512920
$746$	−0.525853	+	1.12311i	−0.0192528	+	0.0411198i
$747$	11.9935	−	7.31140i	0.438820	−	0.267510i
$748$	−13.1231	+	10.9418i	−0.479828	+	0.400073i
$749$			0.876894i			0.0320410i
$750$	−0.400324	+	2.41656i	−0.0146178	+	0.0882401i
$751$		−	15.7392i		−	0.574333i	−0.957881	−	0.287166i	$-0.907287\pi$
$751$		−	15.7392i		−	0.574333i	0.957881	−	0.287166i	$-0.0927133\pi$
$752$	0.673500	−	3.68466i	0.0245600	−	0.134366i
$753$	−11.7538	−	41.8617i	−0.428332	−	1.52553i
$754$	−20.4924	−	9.59482i	−0.746290	−	0.349423i
$755$	6.14441			0.223618
$756$	−9.71712	−	0.531153i	−0.353408	−	0.0193178i
$757$	19.1231			0.695041			0.347521	−	0.937672i	$-0.387024\pi$
$757$	19.1231			0.695041			0.347521	+	0.937672i	$0.387024\pi$
$758$	−32.1520	−	15.0540i	−1.16781	−	0.546785i
$759$	−15.2134	−	54.1833i	−0.552211	−	1.96673i
$760$	11.6847	−	3.07221i	0.423847	−	0.111441i
$761$			51.2311i			1.85712i	0.371177	+	0.928562i	$0.378954\pi$
$761$			51.2311i			1.85712i	−0.371177	+	0.928562i	$0.621046\pi$
$762$	1.87437	−	11.3146i	0.0679012	−	0.409886i
$763$		−	8.54312i		−	0.309282i
$764$	9.89012	+	11.8617i	0.357812	+	0.429143i
$765$	−5.12311	+	3.12311i	−0.185226	+	0.112916i
$766$	2.80776	−	5.99676i	0.101449	−	0.216672i
$767$	−22.4742			−0.811498
$768$	2.43143	−	27.6059i	0.0877368	−	0.996144i
$769$	−26.9848			−0.973098			−0.486549	−	0.873653i	$-0.661745\pi$
$769$	−26.9848			−0.973098			−0.486549	+	0.873653i	$0.661745\pi$
$770$	−2.39871	+	5.12311i	−0.0864434	+	0.184624i
$771$	4.15628	−	1.16699i	0.149685	−	0.0420279i
$772$	−20.8078	−	24.9559i	−0.748888	−	0.898181i
$773$			16.2462i			0.584336i	0.956367	+	0.292168i	$0.0943766\pi$
$773$			16.2462i			0.584336i	−0.956367	+	0.292168i	$0.905623\pi$
$774$	−6.16673	+	0.678347i	−0.221658	+	0.0243827i
$775$			2.39871i			0.0861641i
$776$	16.4127	−	4.31534i	0.589183	−	0.154912i
$777$	4.87689	−	1.36932i	0.174958	−	0.0491240i
$778$	36.8078	+	17.2339i	1.31962	+	0.617865i
$779$	30.4268			1.09015
$780$	−8.91648	−	6.12715i	−0.319261	−	0.219387i
$781$	−28.4924			−1.01954
$782$	19.4849	+	9.12311i	0.696780	+	0.326242i
$783$	−18.1379	+	19.4849i	−0.648197	+	0.696335i
$784$	−4.40388	+	24.0932i	−0.157282	+	0.860473i
$785$		−	21.3693i		−	0.762704i
$786$	42.5606	+	7.05053i	1.51809	+	0.251484i
$787$			13.9817i			0.498392i	0.968453	+	0.249196i	$0.0801664\pi$
$787$			13.9817i			0.498392i	−0.968453	+	0.249196i	$0.919834\pi$
$788$	−18.8114	+	15.6847i	−0.670130	+	0.558743i
$789$	7.06913	+	25.1771i	0.251668	+	0.896328i
$790$	5.43845	−	11.6153i	0.193491	−	0.413255i
$791$	−13.1100			−0.466137
$792$	−25.1335	+	26.1158i	−0.893079	+	0.927986i
$793$	−16.0000			−0.568177
$794$	13.8664	−	29.6155i	0.492099	−	1.05102i
$795$	1.98813	+	7.08084i	0.0705118	+	0.251131i
$796$	27.0540	−	22.5571i	0.958903	−	0.799517i
$797$		−	36.7386i		−	1.30135i	−0.759357	−	0.650675i	$-0.774486\pi$
$797$		−	36.7386i		−	1.30135i	0.759357	−	0.650675i	$-0.225514\pi$
$798$	9.66622	+	1.60129i	0.342181	+	0.0566852i
$799$		−	1.87285i		−	0.0662568i
$800$	−4.60831	−	3.28078i	−0.162928	−	0.115993i
$801$	9.75379	+	16.0000i	0.344633	+	0.565332i
$802$	30.7386	+	14.3922i	1.08542	+	0.508207i
$803$	35.2242			1.24303
$804$	14.8688	+	10.2174i	0.524383	+	0.360341i
$805$	7.12311			0.251056
$806$	−9.59482	−	4.49242i	−0.337963	−	0.158239i
$807$	−23.3459	+	6.55498i	−0.821815	+	0.230746i
$808$	6.56155	+	24.9559i	0.230835	+	0.877944i
$809$		−	46.2462i		−	1.62593i	−0.582312	−	0.812965i	$-0.697852\pi$
$809$		−	46.2462i		−	1.62593i	0.582312	−	0.812965i	$-0.302148\pi$
$810$	−10.0782	+	7.77368i	−0.354111	+	0.273139i
$811$			25.9246i			0.910337i	0.890405	+	0.455169i	$0.150421\pi$
$811$			25.9246i			0.910337i	−0.890405	+	0.455169i	$0.849579\pi$
$812$	−6.14441	−	7.36932i	−0.215627	−	0.258612i
$813$	52.9848	−	14.8769i	1.85826	−	0.521755i
$814$	8.00000	−	17.0862i	0.280400	−	0.598872i
$815$	24.1671			0.846536
$816$	−1.28595	−	13.7966i	−0.0450174	−	0.482978i
$817$	6.24621			0.218527
$818$	0.378206	−	0.807764i	0.0132237	−	0.0282428i
$819$	−4.56685	−	7.49141i	−0.159579	−	0.261771i
$820$	−9.12311	−	10.9418i	−0.318593	−	0.382105i
$821$		−	29.2311i		−	1.02017i	−0.860124	−	0.510085i	$-0.829614\pi$
$821$		−	29.2311i		−	1.02017i	0.860124	−	0.510085i	$-0.170386\pi$
$822$	−3.30115	+	19.9274i	−0.115141	+	0.695049i
$823$			46.8071i			1.63159i	0.578338	+	0.815797i	$0.303701\pi$
$823$			46.8071i			1.63159i	−0.578338	+	0.815797i	$0.696299\pi$
$824$	8.92132	+	33.9309i	0.310789	+	1.18204i
$825$	2.00000	+	7.12311i	0.0696311	+	0.247995i
$826$	−8.63068	−	4.04100i	−0.300300	−	0.140604i
$827$	13.2252			0.459887			0.229943	−	0.973204i	$-0.426146\pi$
$827$	13.2252			0.459887			0.229943	+	0.973204i	$0.426146\pi$
$828$	43.2021	+	14.7175i	1.50138	+	0.511468i
$829$	−17.1231			−0.594710			−0.297355	−	0.954767i	$-0.596104\pi$
$829$	−17.1231			−0.594710			−0.297355	+	0.954767i	$0.596104\pi$
$830$	5.99676	+	2.80776i	0.208151	+	0.0974589i
$831$	−0.641132	−	2.28343i	−0.0222406	−	0.0792112i
$832$	21.7538	−	12.2888i	0.754177	−	0.426038i
$833$			12.2462i			0.424306i
$834$	5.55104	−	33.5089i	0.192217	−	1.16032i
$835$		−	2.80928i		−	0.0972191i
$836$	28.0281	−	23.3693i	0.969371	−	0.808245i
$837$	−8.49242	+	9.12311i	−0.293541	+	0.315341i
$838$	−3.68466	+	7.86962i	−0.127284	+	0.271851i
$839$	−48.5647			−1.67664			−0.838320	−	0.545179i	$-0.816462\pi$
$839$	−48.5647			−1.67664			−0.838320	+	0.545179i	$0.816462\pi$
$840$	−2.32246	−	3.95622i	−0.0801324	−	0.136502i
$841$	2.75379			0.0949582
$842$	−0.378206	+	0.807764i	−0.0130338	+	0.0278374i
$843$	46.0507	−	12.9300i	1.58607	−	0.445331i
$844$	2.06913	−	1.72521i	0.0712224	−	0.0593840i
$845$			3.24621i			0.111673i
$846$	−0.434406	−	3.94910i	−0.0149352	−	0.135773i
$847$			6.78554i			0.233154i
$848$	−16.7080	−	3.05398i	−0.573756	−	0.104874i
$849$	−7.31534	+	2.05398i	−0.251062	+	0.0704923i
$850$	−2.56155	−	1.19935i	−0.0878605	−	0.0411375i
$851$	−23.7565			−0.814362
$852$	13.0862	−	19.0436i	0.448327	−	0.652424i
$853$	49.8617			1.70723			0.853617	−	0.520902i	$-0.174404\pi$
$853$	49.8617			1.70723			0.853617	+	0.520902i	$0.174404\pi$
$854$	−6.14441	−	2.87689i	−0.210257	−	0.0984453i
$855$	10.9418	−	6.67026i	0.374202	−	0.228118i
$856$	−2.56155	+	0.673500i	−0.0875521	+	0.0230198i
$857$			28.7386i			0.981693i	0.871246	+	0.490847i	$0.163312\pi$
$857$			28.7386i			0.981693i	−0.871246	+	0.490847i	$0.836688\pi$
$858$	−32.2381	−	5.34053i	−1.10059	−	0.182323i
$859$			37.3923i			1.27581i	0.770115	+	0.637905i	$0.220199\pi$
$859$			37.3923i			1.27581i	−0.770115	+	0.637905i	$0.779801\pi$
$860$	−1.87285	−	2.24621i	−0.0638637	−	0.0765952i
$861$	−3.12311	−	11.1231i	−0.106435	−	0.379074i
$862$	21.6155	−	46.1660i	0.736228	−	1.57242i
$863$	27.6175			0.940110			0.470055	−	0.882637i	$-0.344234\pi$
$863$	27.6175			0.940110			0.470055	+	0.882637i	$0.344234\pi$
$864$	−5.91167	−	28.7933i	−0.201119	−	0.979567i
$865$	2.00000			0.0680020
$866$	10.7942	−	23.0540i	0.366801	−	0.783406i
$867$	6.08677	+	21.6784i	0.206718	+	0.736236i
$868$	−2.87689	−	3.45041i	−0.0976482	−	0.117115i
$869$		−	38.7386i		−	1.31412i
$870$	−12.3803	−	2.05090i	−0.419730	−	0.0695320i
$871$			16.2651i			0.551121i
$872$	24.9559	−	6.56155i	0.845112	−	0.222202i
$873$	15.3693	−	9.36932i	0.520173	−	0.317103i
$874$	−41.6155	−	19.4849i	−1.40767	−	0.659088i
$875$	−0.936426			−0.0316570
$876$	−16.1780	+	23.5430i	−0.546606	+	0.795443i
$877$	−3.61553			−0.122088			−0.0610439	−	0.998135i	$-0.519443\pi$
$877$	−3.61553			−0.122088			−0.0610439	+	0.998135i	$0.519443\pi$
$878$	−38.2964	−	17.9309i	−1.29244	−	0.605138i
$879$	50.8481	−	14.2770i	1.71506	−	0.481550i
$880$	−16.8078	−	3.07221i	−0.566590	−	0.103564i
$881$			25.3693i			0.854714i	0.904083	+	0.427357i	$0.140555\pi$
$881$			25.3693i			0.854714i	−0.904083	+	0.427357i	$0.859445\pi$
$882$	2.84049	+	25.8224i	0.0956443	+	0.869485i
$883$			10.8265i			0.364342i	0.983267	+	0.182171i	$0.0583125\pi$
$883$			10.8265i			0.364342i	−0.983267	+	0.182171i	$0.941688\pi$
$884$	9.59482	−	8.00000i	0.322709	−	0.269069i
$885$	−12.0000	+	3.36932i	−0.403376	+	0.113258i
$886$	−15.4384	+	32.9731i	−0.518665	+	1.10775i
$887$	−53.4774			−1.79560			−0.897798	−	0.440408i	$-0.854834\pi$
$887$	−53.4774			−1.79560			−0.897798	+	0.440408i	$0.854834\pi$
$888$	7.74571	+	13.1945i	0.259929	+	0.442779i
$889$	4.38447			0.147050
$890$	−3.74571	+	8.00000i	−0.125556	+	0.268161i
$891$	−17.6121	+	34.1725i	−0.590027	+	1.14482i
$892$	−27.6847	+	23.0830i	−0.926951	+	0.772876i
$893$			4.00000i			0.133855i
$894$	5.60453	−	33.8318i	0.187444	−	1.13150i
$895$		−	14.6875i		−	0.490950i
$896$	10.5636	−	0.807764i	0.352906	−	0.0269855i
$897$	11.1231	+	39.6155i	0.371390	+	1.32272i
$898$	−3.36932	−	1.57756i	−0.112436	−	0.0526438i
$899$	−12.2888			−0.409855
$900$	−5.67948	−	1.93481i	−0.189316	−	0.0644936i
$901$	−8.49242			−0.282924
$902$	−38.9699	−	18.2462i	−1.29756	−	0.607532i
$903$	−0.641132	−	2.28343i	−0.0213355	−	0.0759877i
$904$	−10.0691	−	38.2964i	−0.334894	−	1.27372i
$905$		−	4.24621i		−	0.141149i
$906$	−2.45975	+	14.8483i	−0.0817198	+	0.493302i
$907$		−	35.8653i		−	1.19089i	−0.803397	−	0.595444i	$-0.796976\pi$
$907$		−	35.8653i		−	1.19089i	0.803397	−	0.595444i	$-0.203024\pi$
$908$	−11.0895	−	13.3002i	−0.368017	−	0.441382i
$909$	14.2462	+	23.3693i	0.472517	+	0.775111i
$910$	1.75379	−	3.74571i	0.0581375	−	0.124169i
$911$	−41.8944			−1.38802			−0.694012	−	0.719963i	$-0.744159\pi$
$911$	−41.8944			−1.38802			−0.694012	+	0.719963i	$0.744159\pi$
$912$	2.74651	+	29.4665i	0.0909461	+	0.975733i
$913$	20.0000			0.661903
$914$	−5.99676	+	12.8078i	−0.198355	+	0.423643i
$915$	−8.54312	+	2.39871i	−0.282427	+	0.0792988i
$916$	−0.315342	−	0.378206i	−0.0104192	−	0.0124963i
$917$			16.4924i			0.544628i
$918$	−5.49626	−	13.6305i	−0.181404	−	0.449874i
$919$		−	50.1423i		−	1.65404i	−0.562172	−	0.827020i	$-0.690034\pi$
$919$		−	50.1423i		−	1.65404i	0.562172	−	0.827020i	$-0.309966\pi$
$920$	5.47091	+	20.8078i	0.180371	+	0.686012i
$921$	−13.5616	+	3.80776i	−0.446868	+	0.125470i
$922$	−20.3153	−	9.51191i	−0.669050	−	0.313258i
$923$	20.8319			0.685692
$924$	−11.4200	−	7.84751i	−0.375691	−	0.258164i
$925$	3.12311			0.102687
$926$	−1.19935	−	0.561553i	−0.0394132	−	0.0184538i
$927$	19.3697	+	31.7738i	0.636183	+	1.04359i
$928$	16.8078	−	23.6089i	0.551742	−	0.774998i
$929$		−	24.8769i		−	0.816184i	−0.912941	−	0.408092i	$-0.866194\pi$
$929$		−	24.8769i		−	0.816184i	0.912941	−	0.408092i	$-0.133806\pi$
$930$	−5.79661	−	0.960258i	−0.190078	−	0.0314881i
$931$		−	26.1552i		−	0.857202i
$932$	−15.3610	+	12.8078i	−0.503167	+	0.419532i
$933$	−6.63068	−	23.6155i	−0.217079	−	0.773138i
$934$	−9.68466	+	20.6843i	−0.316892	+	0.676811i
$935$	−8.54312			−0.279390
$936$	18.3761	−	19.0943i	0.600641	−	0.624117i
$937$	10.4924			0.342773			0.171386	−	0.985204i	$-0.445175\pi$
$937$	10.4924			0.342773			0.171386	+	0.985204i	$0.445175\pi$
$938$	−2.92456	+	6.24621i	−0.0954902	+	0.203946i
$939$	4.91269	+	17.4968i	0.160320	+	0.570987i
$940$	1.43845	−	1.19935i	0.0469170	−	0.0391186i
$941$			9.12311i			0.297405i	0.988882	+	0.148702i	$0.0475096\pi$
$941$			9.12311i			0.297405i	−0.988882	+	0.148702i	$0.952490\pi$
$942$	51.6401	+	8.55464i	1.68253	+	0.278725i
$943$			54.1833i			1.76445i
$944$	5.17562	−	28.3153i	0.168452	−	0.921586i
$945$	−3.56155	−	3.31534i	−0.115857	−	0.107848i
$946$	−8.00000	−	3.74571i	−0.260102	−	0.121783i
$947$	−25.5141			−0.829096			−0.414548	−	0.910027i	$-0.636060\pi$
$947$	−25.5141			−0.829096			−0.414548	+	0.910027i	$0.636060\pi$
$948$	25.8919	+	17.7922i	0.840931	+	0.577864i
$949$	−25.7538			−0.836003
$950$	5.47091	+	2.56155i	0.177500	+	0.0831077i
$951$	−54.5938	+	15.3287i	−1.77033	+	0.497066i
$952$	5.12311	−	1.34700i	0.166041	−	0.0436565i
$953$			10.4924i			0.339883i	0.985454	+	0.169941i	$0.0543579\pi$
$953$			10.4924i			0.339883i	−0.985454	+	0.169941i	$0.945642\pi$
$954$	−17.9071	+	1.96981i	−0.579765	+	0.0637748i
$955$			7.72197i			0.249877i
$956$	26.6811	+	32.0000i	0.862927	+	1.03495i
$957$	−36.4924	+	10.2462i	−1.17963	+	0.331213i
$958$	13.7538	−	29.3751i	0.444365	−	0.949065i
$959$	−7.72197			−0.249355
$960$	9.77299	−	9.82286i	0.315422	−	0.317031i
$961$	25.2462			0.814394
$962$	−5.84912	+	12.4924i	−0.188583	+	0.402772i
$963$	−2.39871	+	1.46228i	−0.0772972	+	0.0471213i
$964$	14.5616	+	17.4644i	0.468996	+	0.562492i
$965$		−	16.2462i		−	0.522984i
$966$	−2.85155	+	17.2134i	−0.0917470	+	0.553831i
$967$		−	23.6412i		−	0.760250i	−0.924935	−	0.380125i	$-0.875881\pi$
$967$		−	23.6412i		−	0.760250i	0.924935	−	0.380125i	$-0.124119\pi$
$968$	−19.8217	+	5.21165i	−0.637093	+	0.167509i
$969$	4.00000	+	14.2462i	0.128499	+	0.457654i
$970$	7.68466	+	3.59806i	0.246740	+	0.115527i
$971$	41.5991			1.33498			0.667490	−	0.744619i	$-0.267369\pi$
$971$	41.5991			1.33498			0.667490	+	0.744619i	$0.267369\pi$
$972$	−14.7510	−	27.4665i	−0.473139	−	0.880988i
$973$	12.9848			0.416275
$974$	−19.6326	−	9.19224i	−0.629069	−	0.294538i
$975$	−1.46228	−	5.20798i	−0.0468304	−	0.166789i
$976$	3.68466	−	20.1584i	0.117943	−	0.645256i
$977$			48.2462i			1.54353i	0.635906	+	0.771767i	$0.280627\pi$
$977$			48.2462i			1.54353i	−0.635906	+	0.771767i	$0.719373\pi$
$978$	−9.67465	+	58.4011i	−0.309361	+	1.86746i
$979$			26.6811i			0.852730i
$980$	−9.40572	+	7.84233i	−0.300455	+	0.250514i
$981$	23.3693	−	14.2462i	0.746125	−	0.454847i
$982$	11.1922	−	23.9041i	0.357159	−	0.762812i
$983$	3.03984			0.0969558			0.0484779	−	0.998824i	$-0.484563\pi$
$983$	3.03984			0.0969558			0.0484779	+	0.998824i	$0.484563\pi$
$984$	30.0937	−	17.6662i	0.959353	−	0.563179i
$985$	−12.2462			−0.390197
$986$	6.14441	−	13.1231i	0.195678	−	0.417925i
$987$	1.46228	−	0.410574i	0.0465449	−	0.0130687i
$988$	−20.4924	+	17.0862i	−0.651951	+	0.543586i
$989$			11.1231i			0.353694i
$990$	−18.0140	+	1.98156i	−0.572523	+	0.0629782i
$991$		−	16.7909i		−	0.533382i	−0.963782	−	0.266691i	$-0.914070\pi$
$991$		−	16.7909i		−	0.533382i	0.963782	−	0.266691i	$-0.0859303\pi$
$992$	7.86962	−	11.0540i	0.249861	−	0.350964i
$993$	−46.7386	+	13.1231i	−1.48321	+	0.416449i
$994$	8.00000	+	3.74571i	0.253745	+	0.118807i
$995$	17.6121			0.558341
$996$	−9.18576	+	13.3675i	−0.291062	+	0.423565i
$997$	7.61553			0.241186			0.120593	−	0.992702i	$-0.461520\pi$
$997$	7.61553			0.241186			0.120593	+	0.992702i	$0.461520\pi$
$998$	2.02050	+	0.946025i	0.0639578	+	0.0299459i
$999$	11.8782	+	11.0571i	0.375811	+	0.349831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.2.e.a.11.5	yes	8
3.2	odd	2	inner	60.2.e.a.11.4	yes	8
4.3	odd	2	inner	60.2.e.a.11.3	✓	8
5.2	odd	4		300.2.h.b.299.8		8
5.3	odd	4		300.2.h.a.299.1		8
5.4	even	2		300.2.e.c.251.4		8
8.3	odd	2		960.2.h.g.191.6		8
8.5	even	2		960.2.h.g.191.3		8
12.11	even	2	inner	60.2.e.a.11.6	yes	8
15.2	even	4		300.2.h.a.299.2		8
15.8	even	4		300.2.h.b.299.7		8
15.14	odd	2		300.2.e.c.251.5		8
20.3	even	4		300.2.h.a.299.4		8
20.7	even	4		300.2.h.b.299.5		8
20.19	odd	2		300.2.e.c.251.6		8
24.5	odd	2		960.2.h.g.191.5		8
24.11	even	2		960.2.h.g.191.4		8
60.23	odd	4		300.2.h.b.299.6		8
60.47	odd	4		300.2.h.a.299.3		8
60.59	even	2		300.2.e.c.251.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.e.a.11.3	✓	8	4.3	odd	2	inner
60.2.e.a.11.4	yes	8	3.2	odd	2	inner
60.2.e.a.11.5	yes	8	1.1	even	1	trivial
60.2.e.a.11.6	yes	8	12.11	even	2	inner
300.2.e.c.251.3		8	60.59	even	2
300.2.e.c.251.4		8	5.4	even	2
300.2.e.c.251.5		8	15.14	odd	2
300.2.e.c.251.6		8	20.19	odd	2
300.2.h.a.299.1		8	5.3	odd	4
300.2.h.a.299.2		8	15.2	even	4
300.2.h.a.299.3		8	60.47	odd	4
300.2.h.a.299.4		8	20.3	even	4
300.2.h.b.299.5		8	20.7	even	4
300.2.h.b.299.6		8	60.23	odd	4
300.2.h.b.299.7		8	15.8	even	4
300.2.h.b.299.8		8	5.2	odd	4
960.2.h.g.191.3		8	8.5	even	2
960.2.h.g.191.4		8	24.11	even	2
960.2.h.g.191.5		8	24.5	odd	2
960.2.h.g.191.6		8	8.3	odd	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	60.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.599676 - 1.28078i) q^{2} +(0.468213 + 1.66757i) q^{3} +(-1.28078 - 1.53610i) q^{4} -1.00000i q^{5} +(2.41656 + 0.400324i) q^{6} +0.936426i q^{7} +(-2.73546 + 0.719224i) q^{8} +(-2.56155 + 1.56155i) q^{9} +O(q^{10})\)	\(q+(0.599676 - 1.28078i) q^{2} +(0.468213 + 1.66757i) q^{3} +(-1.28078 - 1.53610i) q^{4} -1.00000i q^{5} +(2.41656 + 0.400324i) q^{6} +0.936426i q^{7} +(-2.73546 + 0.719224i) q^{8} +(-2.56155 + 1.56155i) q^{9} +(-1.28078 - 0.599676i) q^{10} -4.27156 q^{11} +(1.96188 - 2.85500i) q^{12} +3.12311 q^{13} +(1.19935 + 0.561553i) q^{14} +(1.66757 - 0.468213i) q^{15} +(-0.719224 + 3.93481i) q^{16} +2.00000i q^{17} +(0.463897 + 4.21720i) q^{18} -4.27156i q^{19} +(-1.53610 + 1.28078i) q^{20} +(-1.56155 + 0.438447i) q^{21} +(-2.56155 + 5.47091i) q^{22} +7.60669 q^{23} +(-2.48013 - 4.22480i) q^{24} -1.00000 q^{25} +(1.87285 - 4.00000i) q^{26} +(-3.80335 - 3.54042i) q^{27} +(1.43845 - 1.19935i) q^{28} -5.12311i q^{29} +(0.400324 - 2.41656i) q^{30} -2.39871i q^{31} +(4.60831 + 3.28078i) q^{32} +(-2.00000 - 7.12311i) q^{33} +(2.56155 + 1.19935i) q^{34} +0.936426 q^{35} +(5.67948 + 1.93481i) q^{36} -3.12311 q^{37} +(-5.47091 - 2.56155i) q^{38} +(1.46228 + 5.20798i) q^{39} +(0.719224 + 2.73546i) q^{40} +7.12311i q^{41} +(-0.374874 + 2.26293i) q^{42} +1.46228i q^{43} +(5.47091 + 6.56155i) q^{44} +(1.56155 + 2.56155i) q^{45} +(4.56155 - 9.74247i) q^{46} -0.936426 q^{47} +(-6.89830 + 0.642976i) q^{48} +6.12311 q^{49} +(-0.599676 + 1.28078i) q^{50} +(-3.33513 + 0.936426i) q^{51} +(-4.00000 - 4.79741i) q^{52} +4.24621i q^{53} +(-6.81526 + 2.74813i) q^{54} +4.27156i q^{55} +(-0.673500 - 2.56155i) q^{56} +(7.12311 - 2.00000i) q^{57} +(-6.56155 - 3.07221i) q^{58} -7.19612 q^{59} +(-2.85500 - 1.96188i) q^{60} -5.12311 q^{61} +(-3.07221 - 1.43845i) q^{62} +(-1.46228 - 2.39871i) q^{63} +(6.96543 - 3.93481i) q^{64} -3.12311i q^{65} +(-10.3225 - 1.71001i) q^{66} +5.20798i q^{67} +(3.07221 - 2.56155i) q^{68} +(3.56155 + 12.6847i) q^{69} +(0.561553 - 1.19935i) q^{70} +6.67026 q^{71} +(5.88391 - 6.11389i) q^{72} -8.24621 q^{73} +(-1.87285 + 4.00000i) q^{74} +(-0.468213 - 1.66757i) q^{75} +(-6.56155 + 5.47091i) q^{76} -4.00000i q^{77} +(7.54716 + 1.25025i) q^{78} +9.06897i q^{79} +(3.93481 + 0.719224i) q^{80} +(4.12311 - 8.00000i) q^{81} +(9.12311 + 4.27156i) q^{82} -4.68213 q^{83} +(2.67350 + 1.83715i) q^{84} +2.00000 q^{85} +(1.87285 + 0.876894i) q^{86} +(8.54312 - 2.39871i) q^{87} +(11.6847 - 3.07221i) q^{88} -6.24621i q^{89} +(4.21720 - 0.463897i) q^{90} +2.92456i q^{91} +(-9.74247 - 11.6847i) q^{92} +(4.00000 - 1.12311i) q^{93} +(-0.561553 + 1.19935i) q^{94} -4.27156 q^{95} +(-3.31324 + 9.22076i) q^{96} -6.00000 q^{97} +(3.67188 - 7.84233i) q^{98} +(10.9418 - 6.67026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9	\( 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9} - 2 q^{10} + 4 q^{12} - 8 q^{13} - 14 q^{16} + 16 q^{18} + 4 q^{21} - 4 q^{22} - 2 q^{24} - 8 q^{25} + 28 q^{28} + 8 q^{30} - 16 q^{33} + 4 q^{34} + 18 q^{36} + 8 q^{37} + 14 q^{40} - 12 q^{42} - 4 q^{45} + 20 q^{46} - 36 q^{48} + 16 q^{49} - 32 q^{52} - 10 q^{54} + 24 q^{57} - 36 q^{58} - 14 q^{60} - 8 q^{61} - 2 q^{64} - 40 q^{66} + 12 q^{69} - 12 q^{70} + 24 q^{72} - 36 q^{76} + 40 q^{78} + 40 q^{82} + 16 q^{84} + 16 q^{85} + 44 q^{88} + 18 q^{90} + 32 q^{93} + 12 q^{94} + 42 q^{96} - 48 q^{97}+O(q^{100}) \) 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9 - 2 * q^10 + 4 * q^12 - 8 * q^13 - 14 * q^16 + 16 * q^18 + 4 * q^21 - 4 * q^22 - 2 * q^24 - 8 * q^25 + 28 * q^28 + 8 * q^30 - 16 * q^33 + 4 * q^34 + 18 * q^36 + 8 * q^37 + 14 * q^40 - 12 * q^42 - 4 * q^45 + 20 * q^46 - 36 * q^48 + 16 * q^49 - 32 * q^52 - 10 * q^54 + 24 * q^57 - 36 * q^58 - 14 * q^60 - 8 * q^61 - 2 * q^64 - 40 * q^66 + 12 * q^69 - 12 * q^70 + 24 * q^72 - 36 * q^76 + 40 * q^78 + 40 * q^82 + 16 * q^84 + 16 * q^85 + 44 * q^88 + 18 * q^90 + 32 * q^93 + 12 * q^94 + 42 * q^96 - 48 * q^97

Introduction

L-functions

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