LMFDB - Embedded newform 273.2.l.c.16.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(16,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.5
Root			$-0.130586 - 0.226181i$ of defining polynomial
Character	$\chi$	$=$	273.16
Dual form			273.2.l.c.256.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.261171 q^{2} +(-0.500000 + 0.866025i) q^{3} -1.93179 q^{4} +(0.708533 - 1.22721i) q^{5} +(0.130586 - 0.226181i) q^{6} +(2.55312 - 0.693954i) q^{7} +1.02687 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-0.261171 q^{2} +(-0.500000 + 0.866025i) q^{3} -1.93179 q^{4} +(0.708533 - 1.22721i) q^{5} +(0.130586 - 0.226181i) q^{6} +(2.55312 - 0.693954i) q^{7} +1.02687 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.185048 + 0.320513i) q^{10} +(0.422587 - 0.731942i) q^{11} +(0.965895 - 1.67298i) q^{12} +(1.58015 + 3.24085i) q^{13} +(-0.666802 + 0.181241i) q^{14} +(0.708533 + 1.22721i) q^{15} +3.59539 q^{16} +5.09653 q^{17} +(0.130586 + 0.226181i) q^{18} +(-1.73064 - 2.99755i) q^{19} +(-1.36874 + 2.37072i) q^{20} +(-0.675578 + 2.55804i) q^{21} +(-0.110368 + 0.191162i) q^{22} +9.20786 q^{23} +(-0.513436 + 0.889296i) q^{24} +(1.49596 + 2.59108i) q^{25} +(-0.412691 - 0.846417i) q^{26} +1.00000 q^{27} +(-4.93209 + 1.34057i) q^{28} +(-4.02187 - 6.96608i) q^{29} +(-0.185048 - 0.320513i) q^{30} +(2.19517 + 3.80215i) q^{31} -2.99275 q^{32} +(0.422587 + 0.731942i) q^{33} -1.33107 q^{34} +(0.957339 - 3.62492i) q^{35} +(0.965895 + 1.67298i) q^{36} -9.39490 q^{37} +(0.451992 + 0.782874i) q^{38} +(-3.59674 - 0.251971i) q^{39} +(0.727572 - 1.26019i) q^{40} +(-5.16304 - 8.94264i) q^{41} +(0.176442 - 0.668088i) q^{42} +(-5.33350 + 9.23790i) q^{43} +(-0.816348 + 1.41396i) q^{44} -1.41707 q^{45} -2.40483 q^{46} +(1.80540 - 3.12704i) q^{47} +(-1.79769 + 3.11370i) q^{48} +(6.03685 - 3.54350i) q^{49} +(-0.390703 - 0.676717i) q^{50} +(-2.54826 + 4.41372i) q^{51} +(-3.05253 - 6.26064i) q^{52} +(-1.08270 - 1.87530i) q^{53} -0.261171 q^{54} +(-0.598833 - 1.03721i) q^{55} +(2.62173 - 0.712602i) q^{56} +3.46127 q^{57} +(1.05040 + 1.81934i) q^{58} +10.0380 q^{59} +(-1.36874 - 2.37072i) q^{60} +(-1.66982 - 2.89221i) q^{61} +(-0.573316 - 0.993012i) q^{62} +(-1.87754 - 1.86409i) q^{63} -6.40916 q^{64} +(5.09681 + 0.357060i) q^{65} +(-0.110368 - 0.191162i) q^{66} +(1.75301 - 3.03631i) q^{67} -9.84542 q^{68} +(-4.60393 + 7.97424i) q^{69} +(-0.250030 + 0.946725i) q^{70} +(-6.45964 + 11.1884i) q^{71} +(-0.513436 - 0.889296i) q^{72} +(-0.0588842 - 0.101990i) q^{73} +2.45368 q^{74} -2.99193 q^{75} +(3.34322 + 5.79063i) q^{76} +(0.570981 - 2.16199i) q^{77} +(0.939365 + 0.0658076i) q^{78} +(-5.76141 + 9.97906i) q^{79} +(2.54745 - 4.41231i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.34844 + 2.33556i) q^{82} +6.17262 q^{83} +(1.30508 - 4.94160i) q^{84} +(3.61106 - 6.25453i) q^{85} +(1.39296 - 2.41268i) q^{86} +8.04374 q^{87} +(0.433942 - 0.751610i) q^{88} -6.22949 q^{89} +0.370097 q^{90} +(6.28333 + 7.17773i) q^{91} -17.7877 q^{92} -4.39034 q^{93} +(-0.471518 + 0.816694i) q^{94} -4.90485 q^{95} +(1.49638 - 2.59180i) q^{96} +(-0.165103 + 0.285966i) q^{97} +(-1.57665 + 0.925461i) q^{98} -0.845173 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25} + 13 q^{26} + 20 q^{27} - 23 q^{28} - 9 q^{29} - 4 q^{30} - 9 q^{31} - 34 q^{32} - 8 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} - 36 q^{37} + 22 q^{38} + 4 q^{39} - 9 q^{40} - q^{41} + 3 q^{42} - 11 q^{43} + 8 q^{44} + 20 q^{46} + 13 q^{47} - 20 q^{48} - 3 q^{49} + 5 q^{50} - 44 q^{52} - 6 q^{53} - 19 q^{55} - 23 q^{56} - 14 q^{57} + 30 q^{59} + 12 q^{60} + 22 q^{62} + 6 q^{63} + 72 q^{64} - 6 q^{65} - 9 q^{66} - 22 q^{67} - 78 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} + 6 q^{72} + 6 q^{74} + 64 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} + 48 q^{80} - 10 q^{81} - 13 q^{82} + 40 q^{83} + 10 q^{84} - 16 q^{85} + 4 q^{86} + 18 q^{87} - 12 q^{88} - 4 q^{89} + 8 q^{90} + 30 q^{91} + 66 q^{92} + 18 q^{93} - 44 q^{94} + 72 q^{95} + 17 q^{96} + 21 q^{97} - 76 q^{98} + 16 q^{99}+O(q^{100}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.261171			−0.184676			−0.0923380	−	0.995728i	$-0.529434\pi$
$2$	−0.261171			−0.184676			−0.0923380	+	0.995728i	$0.529434\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−1.93179			−0.965895
$5$	0.708533	−	1.22721i	0.316865	−	0.548827i	−0.662967	−	0.748649i	$-0.730703\pi$
$5$	0.708533	−	1.22721i	0.316865	−	0.548827i	0.979832	+	0.199822i	$0.0640363\pi$
$6$	0.130586	−	0.226181i	0.0533114	−	0.0923380i
$7$	2.55312	−	0.693954i	0.964989	−	0.262290i
$7$	2.55312	−	0.693954i	0.964989	−	0.262290i
$8$	1.02687			0.363054
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.185048	+	0.320513i	−0.0585175	+	0.101355i
$11$	0.422587	−	0.731942i	0.127415	−	0.220689i	−0.795260	−	0.606269i	$-0.792665\pi$
$11$	0.422587	−	0.731942i	0.127415	−	0.220689i	0.922674	+	0.385580i	$0.125999\pi$
$12$	0.965895	−	1.67298i	0.278830	−	0.482947i
$13$	1.58015	+	3.24085i	0.438256	+	0.898850i
$13$	1.58015	+	3.24085i	0.438256	+	0.898850i
$14$	−0.666802	+	0.181241i	−0.178210	+	0.0484387i
$15$	0.708533	+	1.22721i	0.182942	+	0.316865i
$16$	3.59539			0.898847
$17$	5.09653			1.23609			0.618045	−	0.786143i	$-0.287925\pi$
$17$	5.09653			1.23609			0.618045	+	0.786143i	$0.287925\pi$
$18$	0.130586	+	0.226181i	0.0307793	+	0.0533114i
$19$	−1.73064	−	2.99755i	−0.397035	−	0.687685i	0.596324	−	0.802744i	$-0.296628\pi$
$19$	−1.73064	−	2.99755i	−0.397035	−	0.687685i	−0.993359	+	0.115059i	$0.963294\pi$
$20$	−1.36874	+	2.37072i	−0.306059	+	0.530109i
$21$	−0.675578	+	2.55804i	−0.147423	+	0.558211i
$22$	−0.110368	+	0.191162i	−0.0235304	+	0.0407559i
$23$	9.20786			1.91997			0.959986	−	0.280047i	$-0.0903501\pi$
$23$	9.20786			1.91997			0.959986	+	0.280047i	$0.0903501\pi$
$24$	−0.513436	+	0.889296i	−0.104805	+	0.181527i
$25$	1.49596	+	2.59108i	0.299193	+	0.518217i
$26$	−0.412691	−	0.846417i	−0.0809354	−	0.165996i
$27$	1.00000			0.192450
$28$	−4.93209	+	1.34057i	−0.932078	+	0.253345i
$29$	−4.02187	−	6.96608i	−0.746843	−	1.29357i	−0.949329	−	0.314284i	$-0.898235\pi$
$29$	−4.02187	−	6.96608i	−0.746843	−	1.29357i	0.202486	−	0.979285i	$-0.435098\pi$
$30$	−0.185048	−	0.320513i	−0.0337851	−	0.0585175i
$31$	2.19517	+	3.80215i	0.394264	+	0.682886i	0.993007	−	0.118056i	$-0.0376661\pi$
$31$	2.19517	+	3.80215i	0.394264	+	0.682886i	−0.598743	+	0.800941i	$0.704333\pi$
$32$	−2.99275			−0.529049
$33$	0.422587	+	0.731942i	0.0735629	+	0.127415i
$34$	−1.33107			−0.228276
$35$	0.957339	−	3.62492i	0.161820	−	0.612723i
$36$	0.965895	+	1.67298i	0.160982	+	0.278830i
$37$	−9.39490			−1.54451			−0.772256	−	0.635312i	$-0.780872\pi$
$37$	−9.39490			−1.54451			−0.772256	+	0.635312i	$0.780872\pi$
$38$	0.451992	+	0.782874i	0.0733229	+	0.126999i
$39$	−3.59674	−	0.251971i	−0.575939	−	0.0403477i
$40$	0.727572	−	1.26019i	0.115039	−	0.199254i
$41$	−5.16304	−	8.94264i	−0.806331	−	1.39661i	−0.915389	−	0.402571i	$-0.868117\pi$
$41$	−5.16304	−	8.94264i	−0.806331	−	1.39661i	0.109058	−	0.994035i	$-0.465217\pi$
$42$	0.176442	−	0.668088i	0.0272256	−	0.103088i
$43$	−5.33350	+	9.23790i	−0.813352	+	1.40877i	0.0971534	+	0.995269i	$0.469026\pi$
$43$	−5.33350	+	9.23790i	−0.813352	+	1.40877i	−0.910505	+	0.413497i	$0.864307\pi$
$44$	−0.816348	+	1.41396i	−0.123069	+	0.213162i
$45$	−1.41707			−0.211244
$46$	−2.40483			−0.354573
$47$	1.80540	−	3.12704i	0.263344	−	0.456126i	−0.703784	−	0.710414i	$-0.748508\pi$
$47$	1.80540	−	3.12704i	0.263344	−	0.456126i	0.967129	+	0.254288i	$0.0818411\pi$
$48$	−1.79769	+	3.11370i	−0.259475	+	0.449424i
$49$	6.03685	−	3.54350i	0.862408	−	0.506214i
$50$	−0.390703	−	0.676717i	−0.0552537	−	0.0957022i
$51$	−2.54826	+	4.41372i	−0.356828	+	0.618045i
$52$	−3.05253	−	6.26064i	−0.423309	−	0.868195i
$53$	−1.08270	−	1.87530i	−0.148721	−	0.257592i	0.782034	−	0.623235i	$-0.214182\pi$
$53$	−1.08270	−	1.87530i	−0.148721	−	0.257592i	−0.930755	+	0.365644i	$0.880849\pi$
$54$	−0.261171			−0.0355409
$55$	−0.598833	−	1.03721i	−0.0807466	−	0.139857i
$56$	2.62173	−	0.712602i	0.350343	−	0.0952254i
$57$	3.46127			0.458457
$58$	1.05040	+	1.81934i	0.137924	+	0.238891i
$59$	10.0380			1.30684			0.653418	−	0.756997i	$-0.273334\pi$
$59$	10.0380			1.30684			0.653418	+	0.756997i	$0.273334\pi$
$60$	−1.36874	−	2.37072i	−0.176703	−	0.306059i
$61$	−1.66982	−	2.89221i	−0.213798	−	0.370309i	0.739102	−	0.673594i	$-0.235250\pi$
$61$	−1.66982	−	2.89221i	−0.213798	−	0.370309i	−0.952900	+	0.303284i	$0.901917\pi$
$62$	−0.573316	−	0.993012i	−0.0728112	−	0.126113i
$63$	−1.87754	−	1.86409i	−0.236548	−	0.234853i
$64$	−6.40916			−0.801145
$65$	5.09681	+	0.357060i	0.632181	+	0.0442878i
$66$	−0.110368	−	0.191162i	−0.0135853	−	0.0235304i
$67$	1.75301	−	3.03631i	0.214164	−	0.370944i	−0.738849	−	0.673871i	$-0.764630\pi$
$67$	1.75301	−	3.03631i	0.214164	−	0.370944i	0.953014	+	0.302927i	$0.0979638\pi$
$68$	−9.84542			−1.19393
$69$	−4.60393	+	7.97424i	−0.554248	+	0.959986i
$70$	−0.250030	+	0.946725i	−0.0298842	+	0.113155i
$71$	−6.45964	+	11.1884i	−0.766619	+	1.32782i	0.172768	+	0.984963i	$0.444729\pi$
$71$	−6.45964	+	11.1884i	−0.766619	+	1.32782i	−0.939387	+	0.342860i	$0.888604\pi$
$72$	−0.513436	−	0.889296i	−0.0605090	−	0.104805i
$73$	−0.0588842	−	0.101990i	−0.00689188	−	0.0119371i	0.862559	−	0.505957i	$-0.168860\pi$
$73$	−0.0588842	−	0.101990i	−0.00689188	−	0.0119371i	−0.869451	+	0.494020i	$0.835527\pi$
$74$	2.45368			0.285234
$75$	−2.99193			−0.345478
$76$	3.34322	+	5.79063i	0.383494	+	0.664231i
$77$	0.570981	−	2.16199i	0.0650693	−	0.246382i
$78$	0.939365	+	0.0658076i	0.106362	+	0.00745125i
$79$	−5.76141	+	9.97906i	−0.648210	+	1.12273i	0.335340	+	0.942097i	$0.391149\pi$
$79$	−5.76141	+	9.97906i	−0.648210	+	1.12273i	−0.983550	+	0.180635i	$0.942185\pi$
$80$	2.54745	−	4.41231i	0.284814	−	0.493312i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.34844	+	2.33556i	0.148910	+	0.257920i
$83$	6.17262			0.677533			0.338766	−	0.940871i	$-0.389990\pi$
$83$	6.17262			0.677533			0.338766	+	0.940871i	$0.389990\pi$
$84$	1.30508	−	4.94160i	0.142395	−	0.539173i
$85$	3.61106	−	6.25453i	0.391674	−	0.678399i
$86$	1.39296	−	2.41268i	0.150207	−	0.260166i
$87$	8.04374			0.862380
$88$	0.433942	−	0.751610i	0.0462584	−	0.0801218i
$89$	−6.22949			−0.660325			−0.330162	−	0.943924i	$-0.607104\pi$
$89$	−6.22949			−0.660325			−0.330162	+	0.943924i	$0.607104\pi$
$90$	0.370097			0.0390116
$91$	6.28333	+	7.17773i	0.658672	+	0.752430i
$92$	−17.7877			−1.85449
$93$	−4.39034			−0.455257
$94$	−0.471518	+	0.816694i	−0.0486334	+	0.0842356i
$95$	−4.90485			−0.503227
$96$	1.49638	−	2.59180i	0.152723	−	0.264525i
$97$	−0.165103	+	0.285966i	−0.0167636	+	0.0290355i	−0.874286	−	0.485412i	$-0.838670\pi$
$97$	−0.165103	+	0.285966i	−0.0167636	+	0.0290355i	0.857522	+	0.514447i	$0.172003\pi$
$98$	−1.57665	+	0.925461i	−0.159266	+	0.0934856i
$99$	−0.845173			−0.0849431
$100$	−2.88989	−	5.00543i	−0.288989	−	0.500543i
$101$	−6.75586	+	11.7015i	−0.672233	+	1.16434i	0.305036	+	0.952341i	$0.401331\pi$
$101$	−6.75586	+	11.7015i	−0.672233	+	1.16434i	−0.977269	+	0.212001i	$0.932002\pi$
$102$	0.665533	−	1.15274i	0.0658976	−	0.114138i
$103$	7.11519	−	12.3239i	0.701080	−	1.21431i	−0.267008	−	0.963694i	$-0.586035\pi$
$103$	7.11519	−	12.3239i	0.701080	−	1.21431i	0.968088	−	0.250612i	$-0.0806318\pi$
$104$	1.62262	+	3.32794i	0.159110	+	0.326331i
$105$	2.66060	+	2.64154i	0.259648	+	0.257788i
$106$	0.282771	+	0.489774i	0.0274651	+	0.0475710i
$107$	−2.07349			−0.200452			−0.100226	−	0.994965i	$-0.531957\pi$
$107$	−2.07349			−0.200452			−0.100226	+	0.994965i	$0.531957\pi$
$108$	−1.93179			−0.185887
$109$	−1.87364	−	3.24524i	−0.179462	−	0.310837i	0.762234	−	0.647301i	$-0.224102\pi$
$109$	−1.87364	−	3.24524i	−0.179462	−	0.310837i	−0.941696	+	0.336464i	$0.890769\pi$
$110$	0.156398	+	0.270889i	0.0149120	+	0.0258283i
$111$	4.69745	−	8.13622i	0.445862	−	0.772256i
$112$	9.17947	−	2.49504i	0.867378	−	0.235759i
$113$	−4.74722	+	8.22242i	−0.446581	+	0.773500i	−0.998161	−	0.0606216i	$-0.980692\pi$
$113$	−4.74722	+	8.22242i	−0.446581	+	0.773500i	0.551580	+	0.834122i	$0.314025\pi$
$114$	−0.903985			−0.0846659
$115$	6.52407	−	11.3000i	0.608373	−	1.05373i
$116$	7.76941	+	13.4570i	0.721371	+	1.24945i
$117$	2.01658	−	2.98888i	0.186433	−	0.276322i
$118$	−2.62164			−0.241341
$119$	13.0120	−	3.53676i	1.19281	−	0.324214i
$120$	0.727572	+	1.26019i	0.0664179	+	0.115039i
$121$	5.14284	+	8.90766i	0.467531	+	0.809787i
$122$	0.436108	+	0.755362i	0.0394834	+	0.0683873i
$123$	10.3261			0.931071
$124$	−4.24061	−	7.34495i	−0.380818	−	0.659596i
$125$	11.3251			1.01295
$126$	0.490360	+	0.486847i	0.0436848	+	0.0433718i
$127$	4.57282	+	7.92035i	0.405772	+	0.702817i	0.994411	−	0.105579i	$-0.0336695\pi$
$127$	4.57282	+	7.92035i	0.405772	+	0.702817i	−0.588639	+	0.808396i	$0.700336\pi$
$128$	7.65940			0.677002
$129$	−5.33350	−	9.23790i	−0.469589	−	0.813352i
$130$	−1.33114	−	0.0932537i	−0.116749	−	0.00817889i
$131$	0.174824	−	0.302804i	0.0152745	−	0.0264561i	−0.858287	−	0.513170i	$-0.828471\pi$
$131$	0.174824	−	0.302804i	0.0152745	−	0.0264561i	0.873562	+	0.486714i	$0.161804\pi$
$132$	−0.816348	−	1.41396i	−0.0710540	−	0.123069i
$133$	−6.49868	−	6.45212i	−0.563507	−	0.559470i
$134$	−0.457837	+	0.792996i	−0.0395511	+	0.0685044i
$135$	0.708533	−	1.22721i	0.0609808	−	0.105622i
$136$	5.23348			0.448767
$137$	−22.7547			−1.94407			−0.972033	−	0.234846i	$-0.924541\pi$
$137$	−22.7547			−1.94407			−0.972033	+	0.234846i	$0.924541\pi$
$138$	1.20242	−	2.08264i	0.102356	−	0.177286i
$139$	4.38169	−	7.58931i	0.371650	−	0.643717i	−0.618169	−	0.786045i	$-0.712125\pi$
$139$	4.38169	−	7.58931i	0.371650	−	0.643717i	0.989820	+	0.142328i	$0.0454588\pi$
$140$	−1.84938	+	7.00258i	−0.156301	+	0.591826i
$141$	1.80540	+	3.12704i	0.152042	+	0.263344i
$142$	1.68707	−	2.92210i	0.141576	−	0.245217i
$143$	3.03987	+	0.212959i	0.254206	+	0.0178085i
$144$	−1.79769	−	3.11370i	−0.149808	−	0.259475i
$145$	−11.3985			−0.946595
$146$	0.0153789	+	0.0266370i	0.00127276	+	0.00220449i
$147$	0.0503326	+	6.99982i	0.00415136	+	0.577335i
$148$	18.1490			1.49184
$149$	−2.65464	−	4.59797i	−0.217476	−	0.376680i	0.736559	−	0.676373i	$-0.236449\pi$
$149$	−2.65464	−	4.59797i	−0.217476	−	0.376680i	−0.954036	+	0.299693i	$0.903116\pi$
$150$	0.781405			0.0638015
$151$	1.94796	+	3.37397i	0.158523	+	0.274570i	0.934336	−	0.356393i	$-0.115994\pi$
$151$	1.94796	+	3.37397i	0.158523	+	0.274570i	−0.775813	+	0.630962i	$0.782660\pi$
$152$	−1.77714	−	3.07810i	−0.144145	−	0.249667i
$153$	−2.54826	−	4.41372i	−0.206015	−	0.356828i
$154$	−0.149124	+	0.564650i	−0.0120167	+	0.0455008i
$155$	6.22140			0.499715
$156$	6.94814	+	0.486755i	0.556296	+	0.0389716i
$157$	−0.537376	−	0.930762i	−0.0428873	−	0.0742829i	0.843785	−	0.536681i	$-0.180322\pi$
$157$	−0.537376	−	0.930762i	−0.0428873	−	0.0742829i	−0.886672	+	0.462399i	$0.846989\pi$
$158$	1.50472	−	2.60625i	0.119709	−	0.207342i
$159$	2.16541			0.171728
$160$	−2.12046	+	3.67275i	−0.167637	+	0.290357i
$161$	23.5088	−	6.38984i	1.85275	−	0.503590i
$162$	0.130586	−	0.226181i	0.0102598	−	0.0177705i
$163$	0.935996	+	1.62119i	0.0733128	+	0.126982i	0.900351	−	0.435164i	$-0.143310\pi$
$163$	0.935996	+	1.62119i	0.0733128	+	0.126982i	−0.827039	+	0.562145i	$0.809976\pi$
$164$	9.97390	+	17.2753i	0.778831	+	1.34897i
$165$	1.19767			0.0932382
$166$	−1.61211			−0.125124
$167$	2.18861	+	3.79078i	0.169360	+	0.293339i	0.938195	−	0.346107i	$-0.112497\pi$
$167$	2.18861	+	3.79078i	0.169360	+	0.293339i	−0.768835	+	0.639447i	$0.779163\pi$
$168$	−0.693732	+	2.62678i	−0.0535226	+	0.202661i
$169$	−8.00622	+	10.2421i	−0.615863	+	0.787853i
$170$	−0.943104	+	1.63350i	−0.0723328	+	0.125284i
$171$	−1.73064	+	2.99755i	−0.132345	+	0.229228i
$172$	10.3032	−	17.8457i	0.785612	−	1.36072i
$173$	−2.09706	−	3.63221i	−0.159436	−	0.276152i	0.775229	−	0.631680i	$-0.217634\pi$
$173$	−2.09706	−	3.63221i	−0.159436	−	0.276152i	−0.934666	+	0.355528i	$0.884301\pi$
$174$	−2.10080			−0.159261
$175$	5.61747	+	5.57722i	0.424641	+	0.421598i
$176$	1.51936	−	2.63161i	0.114526	−	0.198365i
$177$	−5.01900	+	8.69316i	−0.377251	+	0.653418i
$178$	1.62697			0.121946
$179$	2.19908	−	3.80893i	0.164367	−	0.284692i	−0.772063	−	0.635546i	$-0.780775\pi$
$179$	2.19908	−	3.80893i	0.164367	−	0.284692i	0.936430	+	0.350853i	$0.114108\pi$
$180$	2.73747			0.204039
$181$	−8.69733			−0.646468			−0.323234	−	0.946319i	$-0.604770\pi$
$181$	−8.69733			−0.646468			−0.323234	+	0.946319i	$0.604770\pi$
$182$	−1.64103	−	1.87462i	−0.121641	−	0.138956i
$183$	3.33963			0.246873
$184$	9.45529			0.697053
$185$	−6.65659	+	11.5296i	−0.489402	+	0.847670i
$186$	1.14663			0.0840751
$187$	2.15372	−	3.73036i	0.157496	−	0.272791i
$188$	−3.48765	+	6.04079i	−0.254363	+	0.440570i
$189$	2.55312	−	0.693954i	0.185712	−	0.0504777i
$190$	1.28101			0.0929339
$191$	−6.72036	−	11.6400i	−0.486268	−	0.842242i	0.513607	−	0.858026i	$-0.328309\pi$
$191$	−6.72036	−	11.6400i	−0.486268	−	0.842242i	−0.999875	+	0.0157839i	$0.994976\pi$
$192$	3.20458	−	5.55049i	0.231271	−	0.400572i
$193$	−6.94042	+	12.0212i	−0.499583	+	0.865303i	−1.00000		0.000481840i	$-0.999847\pi$
$193$	−6.94042	+	12.0212i	−0.499583	+	0.865303i	0.500417	+	0.865784i	$0.333180\pi$
$194$	0.0431201	−	0.0746862i	0.00309584	−	0.00536216i
$195$	−2.85763	+	4.23544i	−0.204639	+	0.303306i
$196$	−11.6619	+	6.84529i	−0.832995	+	0.488950i
$197$	−7.06487	−	12.2367i	−0.503351	−	0.871829i	−0.999992	−	0.00387354i	$-0.998767\pi$
$197$	−7.06487	−	12.2367i	−0.503351	−	0.871829i	0.496642	−	0.867956i	$-0.334566\pi$
$198$	0.220735			0.0156870
$199$	−15.9124			−1.12800			−0.564002	−	0.825774i	$-0.690739\pi$
$199$	−15.9124			−1.12800			−0.564002	+	0.825774i	$0.690739\pi$
$200$	1.53616	+	2.66071i	0.108623	+	0.188141i
$201$	1.75301	+	3.03631i	0.123648	+	0.214164i
$202$	1.76444	−	3.05609i	0.124145	−	0.215026i
$203$	−15.1025	−	14.9943i	−1.05999	−	1.05239i
$204$	4.92271	−	8.52638i	0.344658	−	0.596966i
$205$	−14.6327			−1.02199
$206$	−1.85828	+	3.21864i	−0.129473	+	0.224253i
$207$	−4.60393	−	7.97424i	−0.319995	−	0.554248i
$208$	5.68127	+	11.6521i	0.393925	+	0.807929i
$209$	−2.92537			−0.202352
$210$	−0.694873	−	0.689894i	−0.0479508	−	0.0476072i
$211$	3.85014	+	6.66864i	0.265055	+	0.459088i	0.967578	−	0.252572i	$-0.0812766\pi$
$211$	3.85014	+	6.66864i	0.265055	+	0.459088i	−0.702523	+	0.711661i	$0.747943\pi$
$212$	2.09155	+	3.62268i	0.143648	+	0.248806i
$213$	−6.45964	−	11.1884i	−0.442608	−	0.766619i
$214$	0.541536			0.0370186
$215$	7.55793	+	13.0907i	0.515446	+	0.892779i
$216$	1.02687			0.0698697
$217$	8.24305	+	8.18399i	0.559575	+	0.555566i
$218$	0.489341	+	0.847563i	0.0331424	+	0.0574042i
$219$	0.117768			0.00795805
$220$	1.15682	+	2.00367i	0.0779927	+	0.135087i
$221$	8.05330	+	16.5171i	0.541724	+	1.11106i
$222$	−1.22684	+	2.12495i	−0.0823401	+	0.142617i
$223$	−13.6554	−	23.6518i	−0.914430	−	1.58384i	−0.807733	−	0.589549i	$-0.799306\pi$
$223$	−13.6554	−	23.6518i	−0.914430	−	1.58384i	−0.106698	−	0.994292i	$-0.534028\pi$
$224$	−7.64087	+	2.07684i	−0.510527	+	0.138764i
$225$	1.49596	−	2.59108i	0.0997309	−	0.172739i
$226$	1.23984	−	2.14746i	0.0824728	−	0.142847i
$227$	−13.2651			−0.880436			−0.440218	−	0.897891i	$-0.645099\pi$
$227$	−13.2651			−0.880436			−0.440218	+	0.897891i	$0.645099\pi$
$228$	−6.68645			−0.442821
$229$	5.12001	−	8.86812i	0.338340	−	0.586022i	−0.645781	−	0.763523i	$-0.723468\pi$
$229$	5.12001	−	8.86812i	0.338340	−	0.586022i	0.984121	+	0.177501i	$0.0568013\pi$
$230$	−1.70390	+	2.95124i	−0.112352	+	0.194599i
$231$	1.58685	+	1.57548i	0.104407	+	0.103659i
$232$	−4.12994	−	7.15327i	−0.271144	−	0.469635i
$233$	2.14383	−	3.71322i	0.140447	−	0.243261i	−0.787218	−	0.616675i	$-0.788479\pi$
$233$	2.14383	−	3.71322i	0.140447	−	0.243261i	0.927665	+	0.373414i	$0.121813\pi$
$234$	−0.526673	+	0.780610i	−0.0344297	+	0.0510301i
$235$	−2.55837	−	4.43122i	−0.166890	−	0.289061i
$236$	−19.3913			−1.26227
$237$	−5.76141	−	9.97906i	−0.374244	−	0.648210i
$238$	−3.39838	+	0.923700i	−0.220284	+	0.0598746i
$239$	−3.42707			−0.221679			−0.110839	−	0.993838i	$-0.535354\pi$
$239$	−3.42707			−0.221679			−0.110839	+	0.993838i	$0.535354\pi$
$240$	2.54745	+	4.41231i	0.164437	+	0.284814i
$241$	8.16339			0.525850			0.262925	−	0.964816i	$-0.415313\pi$
$241$	8.16339			0.525850			0.262925	+	0.964816i	$0.415313\pi$
$242$	−1.34316	−	2.32643i	−0.0863418	−	0.149548i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	3.22574	+	5.58714i	0.206507	+	0.357680i
$245$	−0.0713246	−	9.91920i	−0.00455676	−	0.633715i
$246$	−2.69688			−0.171946
$247$	6.97993	−	10.3453i	0.444123	−	0.658257i
$248$	2.25416	+	3.90431i	0.143139	+	0.247924i
$249$	−3.08631	+	5.34564i	−0.195587	+	0.338766i
$250$	−2.95779			−0.187067
$251$	−12.9962	+	22.5101i	−0.820315	+	1.42083i	0.0851323	+	0.996370i	$0.472869\pi$
$251$	−12.9962	+	22.5101i	−0.820315	+	1.42083i	−0.905448	+	0.424458i	$0.860465\pi$
$252$	3.62702	+	3.60103i	0.228481	+	0.226844i
$253$	3.89112	−	6.73962i	0.244633	−	0.423716i
$254$	−1.19429	−	2.06857i	−0.0749363	−	0.129794i
$255$	3.61106	+	6.25453i	0.226133	+	0.391674i
$256$	10.8179			0.676119
$257$	5.93319			0.370102			0.185051	−	0.982729i	$-0.440755\pi$
$257$	5.93319			0.370102			0.185051	+	0.982729i	$0.440755\pi$
$258$	1.39296	+	2.41268i	0.0867218	+	0.150207i
$259$	−23.9863	+	6.51963i	−1.49044	+	0.405110i
$260$	−9.84596	−	0.689764i	−0.610621	−	0.0427773i
$261$	−4.02187	+	6.96608i	−0.248948	+	0.431190i
$262$	−0.0456591	+	0.0790838i	−0.00282083	+	0.00488581i
$263$	−2.05176	+	3.55376i	−0.126517	+	0.219134i	−0.922325	−	0.386415i	$-0.873713\pi$
$263$	−2.05176	+	3.55376i	−0.126517	+	0.219134i	0.795808	+	0.605549i	$0.207047\pi$
$264$	0.433942	+	0.751610i	0.0267073	+	0.0462584i
$265$	−3.06852			−0.188498
$266$	1.69727	+	1.68511i	0.104066	+	0.103321i
$267$	3.11475	−	5.39490i	0.190619	−	0.330162i
$268$	−3.38645	+	5.86550i	−0.206860	+	0.358293i
$269$	−10.9327			−0.666578			−0.333289	−	0.942825i	$-0.608159\pi$
$269$	−10.9327			−0.666578			−0.333289	+	0.942825i	$0.608159\pi$
$270$	−0.185048	+	0.320513i	−0.0112617	+	0.0195058i
$271$	18.1101			1.10011			0.550055	−	0.835129i	$-0.314607\pi$
$271$	18.1101			1.10011			0.550055	+	0.835129i	$0.314607\pi$
$272$	18.3240			1.11106
$273$	−9.35776	+	1.85266i	−0.566357	+	0.112128i
$274$	5.94288			0.359022
$275$	2.52870			0.152486
$276$	8.89383	−	15.4046i	0.535346	−	0.927246i
$277$	−7.19110			−0.432071			−0.216036	−	0.976385i	$-0.569313\pi$
$277$	−7.19110			−0.432071			−0.216036	+	0.976385i	$0.569313\pi$
$278$	−1.14437	+	1.98211i	−0.0686349	+	0.118879i
$279$	2.19517	−	3.80215i	0.131421	−	0.227629i
$280$	0.983064	−	3.72232i	0.0587493	−	0.222451i
$281$	−5.53072			−0.329935			−0.164968	−	0.986299i	$-0.552752\pi$
$281$	−5.53072			−0.329935			−0.164968	+	0.986299i	$0.552752\pi$
$282$	−0.471518	−	0.816694i	−0.0280785	−	0.0486334i
$283$	0.249695	−	0.432485i	0.0148429	−	0.0257086i	−0.858509	−	0.512799i	$-0.828609\pi$
$283$	0.249695	−	0.432485i	0.0148429	−	0.0257086i	0.873351	+	0.487091i	$0.161942\pi$
$284$	12.4787	−	21.6137i	0.740473	−	1.28254i
$285$	2.45242	−	4.24772i	0.145269	−	0.251613i
$286$	−0.793926	−	0.0556189i	−0.0469458	−	0.00328881i
$287$	−19.3876	−	19.2487i	−1.14442	−	1.13622i
$288$	1.49638	+	2.59180i	0.0881749	+	0.152723i
$289$	8.97458			0.527917
$290$	2.97696			0.174813
$291$	−0.165103	−	0.285966i	−0.00967849	−	0.0167636i
$292$	0.113752	+	0.197024i	0.00665683	+	0.0115300i
$293$	3.68051	−	6.37484i	0.215018	−	0.372422i	−0.738260	−	0.674516i	$-0.764352\pi$
$293$	3.68051	−	6.37484i	0.215018	−	0.372422i	0.953278	+	0.302094i	$0.0976857\pi$
$294$	−0.0131454	−	1.82815i	−0.000766657	−	0.106620i
$295$	7.11225	−	12.3188i	0.414091	−	0.717227i
$296$	−9.64735			−0.560741
$297$	0.422587	−	0.731942i	0.0245210	−	0.0424716i
$298$	0.693315	+	1.20086i	0.0401627	+	0.0695638i
$299$	14.5499	+	29.8413i	0.841440	+	1.72577i
$300$	5.77977			0.333695
$301$	−7.20640	+	27.2867i	−0.415370	+	1.57278i
$302$	−0.508752	−	0.881184i	−0.0292754	−	0.0507064i
$303$	−6.75586	−	11.7015i	−0.388114	−	0.672233i
$304$	−6.22231	−	10.7774i	−0.356874	−	0.618124i
$305$	−4.73248			−0.270981
$306$	0.665533	+	1.15274i	0.0380460	+	0.0658976i
$307$	−19.1859			−1.09500			−0.547500	−	0.836806i	$-0.684420\pi$
$307$	−19.1859			−1.09500			−0.547500	+	0.836806i	$0.684420\pi$
$308$	−1.10301	+	4.17651i	−0.0628501	+	0.237979i
$309$	7.11519	+	12.3239i	0.404769	+	0.701080i
$310$	−1.62485			−0.0922854
$311$	14.7040	+	25.4682i	0.833790	+	1.44417i	0.895012	+	0.446042i	$0.147167\pi$
$311$	14.7040	+	25.4682i	0.833790	+	1.44417i	−0.0612219	+	0.998124i	$0.519500\pi$
$312$	−3.69338	−	0.258742i	−0.209097	−	0.0146484i
$313$	−7.86048	+	13.6148i	−0.444301	+	0.769551i	−0.998003	−	0.0631631i	$-0.979881\pi$
$313$	−7.86048	+	13.6148i	−0.444301	+	0.769551i	0.553702	+	0.832715i	$0.313214\pi$
$314$	0.140347	+	0.243088i	0.00792025	+	0.0137183i
$315$	−3.61794	+	0.983379i	−0.203848	+	0.0554071i
$316$	11.1298	−	19.2774i	0.626102	−	1.08444i
$317$	4.26514	−	7.38743i	0.239554	−	0.414920i	−0.721032	−	0.692901i	$-0.756332\pi$
$317$	4.26514	−	7.38743i	0.239554	−	0.414920i	0.960586	+	0.277982i	$0.0896655\pi$
$318$	−0.565542			−0.0317140
$319$	−6.79836			−0.380635
$320$	−4.54110	+	7.86541i	−0.253855	+	0.439690i
$321$	1.03674	−	1.79569i	0.0578654	−	0.100226i
$322$	−6.13982	+	1.66884i	−0.342159	+	0.0930010i
$323$	−8.82023	−	15.2771i	−0.490771	−	0.850040i
$324$	0.965895	−	1.67298i	0.0536608	−	0.0929433i
$325$	−6.03346	+	8.94251i	−0.334676	+	0.496041i
$326$	−0.244455	−	0.423409i	−0.0135391	−	0.0234505i
$327$	3.74728			0.207225
$328$	−5.30177	−	9.18294i	−0.292741	−	0.507043i
$329$	2.43938	−	9.23658i	0.134487	−	0.509229i
$330$	−0.312796			−0.0172189
$331$	0.873277	+	1.51256i	0.0479996	+	0.0831378i	0.889027	−	0.457855i	$-0.151382\pi$
$331$	0.873277	+	1.51256i	0.0479996	+	0.0831378i	−0.841027	+	0.540993i	$0.818049\pi$
$332$	−11.9242			−0.654425
$333$	4.69745	+	8.13622i	0.257419	+	0.445862i
$334$	−0.571602	−	0.990044i	−0.0312767	−	0.0541728i
$335$	−2.48413	−	4.30264i	−0.135723	−	0.235079i
$336$	−2.42897	+	9.19717i	−0.132511	+	0.501747i
$337$	−1.36849			−0.0745462			−0.0372731	−	0.999305i	$-0.511867\pi$
$337$	−1.36849			−0.0745462			−0.0372731	+	0.999305i	$0.511867\pi$
$338$	2.09100	−	2.67494i	0.113735	−	0.145498i
$339$	−4.74722	−	8.22242i	−0.257833	−	0.446581i
$340$	−6.97580	+	12.0824i	−0.378316	+	0.655262i
$341$	3.71060			0.200940
$342$	0.451992	−	0.782874i	0.0244410	−	0.0423330i
$343$	12.9538	−	13.2363i	0.699439	−	0.714692i
$344$	−5.47682	+	9.48613i	−0.295290	+	0.511458i
$345$	6.52407	+	11.3000i	0.351244	+	0.608373i
$346$	0.547691	+	0.948629i	0.0294440	+	0.0509986i
$347$	−7.10377			−0.381350			−0.190675	−	0.981653i	$-0.561068\pi$
$347$	−7.10377			−0.381350			−0.190675	+	0.981653i	$0.561068\pi$
$348$	−15.5388			−0.832968
$349$	7.07469	+	12.2537i	0.378699	+	0.655927i	0.990873	−	0.134797i	$-0.0430381\pi$
$349$	7.07469	+	12.2537i	0.378699	+	0.655927i	−0.612174	+	0.790723i	$0.709705\pi$
$350$	−1.46712	−	1.45661i	−0.0784210	−	0.0778591i
$351$	1.58015	+	3.24085i	0.0843424	+	0.172984i
$352$	−1.26470	+	2.19052i	−0.0674086	+	0.116755i
$353$	14.7323	−	25.5171i	0.784123	−	1.35814i	−0.145399	−	0.989373i	$-0.546447\pi$
$353$	14.7323	−	25.5171i	0.784123	−	1.35814i	0.929522	−	0.368767i	$-0.120220\pi$
$354$	1.31082	−	2.27041i	0.0696693	−	0.120671i
$355$	9.15374	+	15.8547i	0.485830	+	0.841482i
$356$	12.0341			0.637804
$357$	−3.44310	+	13.0371i	−0.182228	+	0.689999i
$358$	−0.574338	+	0.994782i	−0.0303547	+	0.0525759i
$359$	8.62856	−	14.9451i	0.455398	−	0.788773i	−0.543313	−	0.839530i	$-0.682830\pi$
$359$	8.62856	−	14.9451i	0.455398	−	0.788773i	0.998711	+	0.0507577i	$0.0161636\pi$
$360$	−1.45514			−0.0766928
$361$	3.50980	−	6.07916i	0.184726	−	0.319956i
$362$	2.27149			0.119387
$363$	−10.2857			−0.539858
$364$	−12.1381	−	13.8659i	−0.636208	−	0.726769i
$365$	−0.166886			−0.00873519
$366$	−0.872217			−0.0455915
$367$	−1.30606	+	2.26217i	−0.0681760	+	0.118084i	−0.898098	−	0.439795i	$-0.855051\pi$
$367$	−1.30606	+	2.26217i	−0.0681760	+	0.118084i	0.829922	+	0.557879i	$0.188385\pi$
$368$	33.1059			1.72576
$369$	−5.16304	+	8.94264i	−0.268777	+	0.465535i
$370$	1.73851	−	3.01119i	0.0903809	−	0.156544i
$371$	−4.06564	−	4.03651i	−0.211078	−	0.209565i
$372$	8.48121			0.439730
$373$	−11.1498	−	19.3121i	−0.577317	−	0.999942i	−0.995786	−	0.0917109i	$-0.970766\pi$
$373$	−11.1498	−	19.3121i	−0.577317	−	0.999942i	0.418469	−	0.908231i	$-0.362567\pi$
$374$	−0.562491	+	0.974263i	−0.0290857	+	0.0503779i
$375$	−5.66254	+	9.80781i	−0.292412	+	0.506473i
$376$	1.85391	−	3.21107i	0.0956082	−	0.165598i
$377$	16.2209	−	24.0418i	0.835417	−	1.23821i
$378$	−0.666802	+	0.181241i	−0.0342966	+	0.00932203i
$379$	3.28264	+	5.68571i	0.168618	+	0.292055i	0.937934	−	0.346813i	$-0.112736\pi$
$379$	3.28264	+	5.68571i	0.168618	+	0.292055i	−0.769316	+	0.638868i	$0.779403\pi$
$380$	9.47513			0.486064
$381$	−9.14563			−0.468545
$382$	1.75517	+	3.04004i	0.0898022	+	0.155542i
$383$	3.16746	+	5.48621i	0.161850	+	0.280332i	0.935532	−	0.353242i	$-0.114921\pi$
$383$	3.16746	+	5.48621i	0.161850	+	0.280332i	−0.773682	+	0.633574i	$0.781587\pi$
$384$	−3.82970	+	6.63323i	−0.195434	+	0.338501i
$385$	−2.24867	−	2.23256i	−0.114603	−	0.113782i
$386$	1.81264	−	3.13959i	0.0922610	−	0.159801i
$387$	10.6670			0.542235
$388$	0.318944	−	0.552426i	0.0161919	−	0.0280452i
$389$	8.33868	+	14.4430i	0.422788	+	0.732290i	0.996211	−	0.0869695i	$-0.0277183\pi$
$389$	8.33868	+	14.4430i	0.422788	+	0.732290i	−0.573423	+	0.819259i	$0.694385\pi$
$390$	0.746331	−	1.10618i	0.0377919	−	0.0560134i
$391$	46.9281			2.37326
$392$	6.19907	−	3.63872i	0.313100	−	0.183783i
$393$	0.174824	+	0.302804i	0.00881871	+	0.0152745i
$394$	1.84514	+	3.19588i	0.0929569	+	0.161006i
$395$	8.16430	+	14.1410i	0.410790	+	0.711510i
$396$	1.63270			0.0820461
$397$	12.8024	+	22.1745i	0.642536	+	1.11290i	0.984865	+	0.173324i	$0.0554508\pi$
$397$	12.8024	+	22.1745i	0.642536	+	1.11290i	−0.342329	+	0.939580i	$0.611216\pi$
$398$	4.15588			0.208315
$399$	8.83704	−	2.40196i	0.442406	−	0.120249i
$400$	5.37857	+	9.31596i	0.268928	+	0.465798i
$401$	−26.6301			−1.32984			−0.664921	−	0.746914i	$-0.731535\pi$
$401$	−26.6301			−1.32984			−0.664921	+	0.746914i	$0.731535\pi$
$402$	−0.457837	−	0.792996i	−0.0228348	−	0.0395511i
$403$	−8.85348	+	13.1222i	−0.441023	+	0.653663i
$404$	13.0509	−	22.6048i	0.649306	−	1.12463i
$405$	0.708533	+	1.22721i	0.0352073	+	0.0609808i
$406$	3.94433	+	3.91607i	0.195754	+	0.194351i
$407$	−3.97016	+	6.87652i	−0.196793	+	0.340856i
$408$	−2.61674	+	4.53232i	−0.129548	+	0.224383i
$409$	−4.62905			−0.228892			−0.114446	−	0.993429i	$-0.536509\pi$
$409$	−4.62905			−0.228892			−0.114446	+	0.993429i	$0.536509\pi$
$410$	3.82165			0.188738
$411$	11.3773	−	19.7061i	0.561203	−	0.972033i
$412$	−13.7450	+	23.8071i	−0.677170	+	1.17289i
$413$	25.6282	−	6.96591i	1.26108	−	0.342770i
$414$	1.20242	+	2.08264i	0.0590955	+	0.102356i
$415$	4.37350	−	7.57512i	0.214687	−	0.371848i
$416$	−4.72902	−	9.69907i	−0.231859	−	0.475536i
$417$	4.38169	+	7.58931i	0.214572	+	0.371650i
$418$	0.764024			0.0373696
$419$	8.64392	+	14.9717i	0.422283	+	0.731416i	0.996162	−	0.0875239i	$-0.0278954\pi$
$419$	8.64392	+	14.9717i	0.422283	+	0.731416i	−0.573879	+	0.818940i	$0.694562\pi$
$420$	−5.13972	−	5.10290i	−0.250793	−	0.248996i
$421$	−7.92499			−0.386241			−0.193120	−	0.981175i	$-0.561861\pi$
$421$	−7.92499			−0.386241			−0.193120	+	0.981175i	$0.561861\pi$
$422$	−1.00555	−	1.74166i	−0.0489493	−	0.0847826i
$423$	−3.61080			−0.175563
$424$	−1.11180	−	1.92569i	−0.0539936	−	0.0935196i
$425$	7.62421	+	13.2055i	0.369829	+	0.640562i
$426$	1.68707	+	2.92210i	0.0817390	+	0.141576i
$427$	−6.27031	−	6.22538i	−0.303441	−	0.301267i
$428$	4.00554			0.193615
$429$	−1.70436	+	2.52612i	−0.0822873	+	0.121962i
$430$	−1.97391	−	3.41892i	−0.0951906	−	0.164875i
$431$	2.52893	−	4.38023i	0.121814	−	0.210988i	−0.798669	−	0.601771i	$-0.794462\pi$
$431$	2.52893	−	4.38023i	0.121814	−	0.210988i	0.920483	+	0.390782i	$0.127795\pi$
$432$	3.59539			0.172983
$433$	−0.0476082	+	0.0824598i	−0.00228790	+	0.00396277i	−0.867167	−	0.498017i	$-0.834062\pi$
$433$	−0.0476082	+	0.0824598i	−0.00228790	+	0.00396277i	0.864879	+	0.501980i	$0.167395\pi$
$434$	−2.15285	−	2.13742i	−0.103340	−	0.102600i
$435$	5.69925	−	9.87140i	0.273258	−	0.473297i
$436$	3.61948	+	6.26912i	0.173341	+	0.300236i
$437$	−15.9355	−	27.6010i	−0.762296	−	1.32034i
$438$	−0.0307577			−0.00146966
$439$	10.1425			0.484077			0.242038	−	0.970267i	$-0.422184\pi$
$439$	10.1425			0.484077			0.242038	+	0.970267i	$0.422184\pi$
$440$	−0.614924	−	1.06508i	−0.0293154	−	0.0507757i
$441$	−6.08719	−	3.45632i	−0.289866	−	0.164587i
$442$	−2.10329	−	4.31379i	−0.100043	−	0.205186i
$443$	−0.312119	+	0.540607i	−0.0148292	+	0.0256850i	−0.873345	−	0.487103i	$-0.838054\pi$
$443$	−0.312119	+	0.540607i	−0.0148292	+	0.0256850i	0.858516	+	0.512788i	$0.171387\pi$
$444$	−9.07448	+	15.7175i	−0.430656	+	0.745918i
$445$	−4.41380	+	7.64492i	−0.209234	+	0.362404i
$446$	3.56639	+	6.17717i	0.168873	+	0.292497i
$447$	5.30927			0.251120
$448$	−16.3634	+	4.44766i	−0.773096	+	0.210132i
$449$	17.3597	−	30.0678i	0.819254	−	1.41899i	−0.0869792	−	0.996210i	$-0.527721\pi$
$449$	17.3597	−	30.0678i	0.819254	−	1.41899i	0.906233	−	0.422779i	$-0.138945\pi$
$450$	−0.390703	+	0.676717i	−0.0184179	+	0.0319007i
$451$	−8.72732			−0.410954
$452$	9.17062	−	15.8840i	0.431350	−	0.747120i
$453$	−3.89592			−0.183046
$454$	3.46447			0.162595
$455$	13.2606	−	2.62534i	0.621664	−	0.123078i
$456$	3.55428			0.166444
$457$	2.82464			0.132131			0.0660655	−	0.997815i	$-0.478955\pi$
$457$	2.82464			0.132131			0.0660655	+	0.997815i	$0.478955\pi$
$458$	−1.33720	+	2.31610i	−0.0624833	+	0.108224i
$459$	5.09653			0.237885
$460$	−12.6031	+	21.8293i	−0.587624	+	1.01779i
$461$	12.3630	−	21.4134i	0.575804	−	0.997321i	−0.420150	−	0.907455i	$-0.638023\pi$
$461$	12.3630	−	21.4134i	0.575804	−	0.997321i	0.995954	−	0.0898666i	$-0.0286441\pi$
$462$	−0.414440	−	0.411470i	−0.0192815	−	0.0191433i
$463$	37.8124			1.75729			0.878646	−	0.477473i	$-0.158447\pi$
$463$	37.8124			1.75729			0.878646	+	0.477473i	$0.158447\pi$
$464$	−14.4602	−	25.0458i	−0.671298	−	1.16272i
$465$	−3.11070	+	5.38789i	−0.144255	+	0.249857i
$466$	−0.559906	+	0.969786i	−0.0259372	+	0.0449245i
$467$	−9.66701	+	16.7437i	−0.447336	+	0.774808i	−0.998212	−	0.0597790i	$-0.980960\pi$
$467$	−9.66701	+	16.7437i	−0.447336	+	0.774808i	0.550876	+	0.834587i	$0.314294\pi$
$468$	−3.89561	+	5.77389i	−0.180075	+	0.266898i
$469$	2.36859	−	8.96857i	0.109372	−	0.414130i
$470$	0.668173	+	1.15731i	0.0308205	+	0.0533827i
$471$	1.07475			0.0495219
$472$	10.3077			0.474452
$473$	4.50774	+	7.80763i	0.207266	+	0.358995i
$474$	1.50472	+	2.60625i	0.0691139	+	0.119709i
$475$	5.17793	−	8.96844i	0.237580	−	0.411500i
$476$	−25.1365	+	6.83227i	−1.15213	+	0.313157i
$477$	−1.08270	+	1.87530i	−0.0495735	+	0.0858639i
$478$	0.895052			0.0409387
$479$	3.20910	−	5.55832i	0.146627	−	0.253966i	−0.783352	−	0.621579i	$-0.786491\pi$
$479$	3.20910	−	5.55832i	0.146627	−	0.253966i	0.929979	+	0.367613i	$0.119825\pi$
$480$	−2.12046	−	3.67275i	−0.0967855	−	0.167637i
$481$	−14.8454	−	30.4475i	−0.676892	−	1.38828i
$482$	−2.13205			−0.0971120
$483$	−6.22064	+	23.5541i	−0.283049	+	1.07175i
$484$	−9.93489	−	17.2077i	−0.451586	−	0.782169i
$485$	0.233961	+	0.405233i	0.0106236	+	0.0184007i
$486$	0.130586	+	0.226181i	0.00592349	+	0.0102598i
$487$	17.6462			0.799625			0.399812	−	0.916597i	$-0.369075\pi$
$487$	17.6462			0.799625			0.399812	+	0.916597i	$0.369075\pi$
$488$	−1.71469	−	2.96992i	−0.0776202	−	0.134442i
$489$	−1.87199			−0.0846544
$490$	0.0186279	+	2.59061i	0.000841524	+	0.117032i
$491$	−18.1979	−	31.5196i	−0.821258	−	1.42246i	−0.904746	−	0.425952i	$-0.859939\pi$
$491$	−18.1979	−	31.5196i	−0.821258	−	1.42246i	0.0834876	−	0.996509i	$-0.473394\pi$
$492$	−19.9478			−0.899316
$493$	−20.4976	−	35.5028i	−0.923164	−	1.59897i
$494$	−1.82296	+	2.70190i	−0.0820188	+	0.121564i
$495$	−0.598833	+	1.03721i	−0.0269155	+	0.0466191i
$496$	7.89249	+	13.6702i	0.354383	+	0.613810i
$497$	−8.72799	+	33.0481i	−0.391504	+	1.48241i
$498$	0.806055	−	1.39613i	0.0361202	−	0.0625620i
$499$	−10.7163	+	18.5611i	−0.479725	+	0.830909i	−0.999730	−	0.0232550i	$-0.992597\pi$
$499$	−10.7163	+	18.5611i	−0.479725	+	0.830909i	0.520004	+	0.854164i	$0.325930\pi$
$500$	−21.8777			−0.978399
$501$	−4.37722			−0.195560
$502$	3.39425	−	5.87901i	0.151493	−	0.262393i
$503$	−14.3812	+	24.9090i	−0.641226	+	1.11064i	0.343933	+	0.938994i	$0.388241\pi$
$503$	−14.3812	+	24.9090i	−0.641226	+	1.11064i	−0.985159	+	0.171642i	$0.945093\pi$
$504$	−1.92799	−	1.91418i	−0.0858797	−	0.0852644i
$505$	9.57349	+	16.5818i	0.426015	+	0.737879i
$506$	−1.01625	+	1.76020i	−0.0451778	+	0.0782502i
$507$	−4.86680	−	12.0546i	−0.216142	−	0.535365i
$508$	−8.83372	−	15.3004i	−0.391933	−	0.678848i
$509$	5.72879			0.253924			0.126962	−	0.991908i	$-0.459477\pi$
$509$	5.72879			0.253924			0.126962	+	0.991908i	$0.459477\pi$
$510$	−0.943104	−	1.63350i	−0.0417614	−	0.0723328i
$511$	−0.221115	−	0.219531i	−0.00978156	−	0.00971148i
$512$	−18.1441			−0.801865
$513$	−1.73064	−	2.99755i	−0.0764094	−	0.132345i
$514$	−1.54958			−0.0683490
$515$	−10.0827	−	17.4637i	−0.444296	−	0.769543i
$516$	10.3032	+	17.8457i	0.453573	+	0.785612i
$517$	−1.52587	−	2.64289i	−0.0671079	−	0.116234i
$518$	6.26454	−	1.70274i	0.275248	−	0.0748141i
$519$	4.19411			0.184101
$520$	5.23377	+	0.366654i	0.229516	+	0.0160788i
$521$	9.04941	+	15.6740i	0.396462	+	0.686692i	0.993287	−	0.115679i	$-0.0369045\pi$
$521$	9.04941	+	15.6740i	0.396462	+	0.686692i	−0.596825	+	0.802372i	$0.703571\pi$
$522$	1.05040	−	1.81934i	0.0459747	−	0.0796304i
$523$	−19.6991			−0.861380			−0.430690	−	0.902500i	$-0.641730\pi$
$523$	−19.6991			−0.861380			−0.430690	+	0.902500i	$0.641730\pi$
$524$	−0.337723	+	0.584954i	−0.0147535	+	0.0255538i
$525$	−7.63875	+	2.07626i	−0.333382	+	0.0906154i
$526$	0.535862	−	0.928141i	0.0233647	−	0.0404689i
$527$	11.1877	+	19.3777i	0.487346	+	0.844108i
$528$	1.51936	+	2.63161i	0.0661218	+	0.114526i
$529$	61.7848			2.68629
$530$	0.801410			0.0348110
$531$	−5.01900	−	8.69316i	−0.217806	−	0.377251i
$532$	12.5541	+	12.4641i	0.544289	+	0.540389i
$533$	20.8234	−	30.8634i	0.901960	−	1.33684i
$534$	−0.813483	+	1.40899i	−0.0352028	+	0.0609731i
$535$	−1.46913	+	2.54462i	−0.0635162	+	0.110013i
$536$	1.80012	−	3.11789i	0.0777532	−	0.134673i
$537$	2.19908	+	3.80893i	0.0948975	+	0.164367i
$538$	2.85531			0.123101
$539$	−0.0425398	−	5.91606i	−0.00183232	−	0.254823i
$540$	−1.36874	+	2.37072i	−0.0589010	+	0.102020i
$541$	−16.2839	+	28.2045i	−0.700099	+	1.21261i	0.268332	+	0.963326i	$0.413528\pi$
$541$	−16.2839	+	28.2045i	−0.700099	+	1.21261i	−0.968431	+	0.249281i	$0.919806\pi$
$542$	−4.72984			−0.203164
$543$	4.34867	−	7.53211i	0.186619	−	0.323234i
$544$	−15.2527			−0.653952
$545$	−5.31014			−0.227461
$546$	2.44398	−	0.483861i	0.104593	−	0.0207073i
$547$	−21.3915			−0.914635			−0.457318	−	0.889303i	$-0.651190\pi$
$547$	−21.3915			−0.914635			−0.457318	+	0.889303i	$0.651190\pi$
$548$	43.9573			1.87776
$549$	−1.66982	+	2.89221i	−0.0712661	+	0.123436i
$550$	−0.660423			−0.0281605
$551$	−13.9208	+	24.1115i	−0.593045	+	1.02718i
$552$	−4.72764	+	8.18852i	−0.201222	+	0.348527i
$553$	−7.78457	+	29.4759i	−0.331034	+	1.25344i
$554$	1.87811			0.0797932
$555$	−6.65659	−	11.5296i	−0.282557	−	0.489402i
$556$	−8.46450	+	14.6609i	−0.358975	+	0.621763i
$557$	−3.67328	+	6.36230i	−0.155642	+	0.269579i	−0.933292	−	0.359117i	$-0.883078\pi$
$557$	−3.67328	+	6.36230i	−0.155642	+	0.269579i	0.777651	+	0.628696i	$0.216411\pi$
$558$	−0.573316	+	0.993012i	−0.0242704	+	0.0420376i
$559$	−38.3664	−	2.68778i	−1.62273	−	0.113681i
$560$	3.44201	−	13.0330i	0.145451	−	0.550744i
$561$	2.15372	+	3.73036i	0.0909303	+	0.157496i
$562$	1.44447			0.0609312
$563$	15.3321			0.646172			0.323086	−	0.946370i	$-0.395280\pi$
$563$	15.3321			0.646172			0.323086	+	0.946370i	$0.395280\pi$
$564$	−3.48765	−	6.04079i	−0.146857	−	0.254363i
$565$	6.72712	+	11.6517i	0.283012	+	0.490191i
$566$	−0.0652133	+	0.112953i	−0.00274112	+	0.00474776i
$567$	−0.675578	+	2.55804i	−0.0283716	+	0.107428i
$568$	−6.63322	+	11.4891i	−0.278324	+	0.482071i
$569$	−20.8272			−0.873122			−0.436561	−	0.899675i	$-0.643804\pi$
$569$	−20.8272			−0.873122			−0.436561	+	0.899675i	$0.643804\pi$
$570$	−0.640503	+	1.10938i	−0.0268277	+	0.0464670i
$571$	1.20349	+	2.08451i	0.0503646	+	0.0872340i	0.890109	−	0.455748i	$-0.150628\pi$
$571$	1.20349	+	2.08451i	0.0503646	+	0.0872340i	−0.839744	+	0.542982i	$0.817295\pi$
$572$	−5.87238	−	0.411392i	−0.245537	−	0.0172012i
$573$	13.4407			0.561494
$574$	5.06350	+	5.02722i	0.211346	+	0.209832i
$575$	13.7746	+	23.8583i	0.574442	+	0.994962i
$576$	3.20458	+	5.55049i	0.133524	+	0.231271i
$577$	−18.8790	−	32.6993i	−0.785941	−	1.36129i	−0.928435	−	0.371494i	$-0.878846\pi$
$577$	−18.8790	−	32.6993i	−0.785941	−	1.36129i	0.142494	−	0.989796i	$-0.454488\pi$
$578$	−2.34390			−0.0974935
$579$	−6.94042	−	12.0212i	−0.288434	−	0.499583i
$580$	22.0195			0.914311
$581$	15.7594	−	4.28351i	0.653812	−	0.177710i
$582$	0.0431201	+	0.0746862i	0.00178739	+	0.00309584i
$583$	−1.83014			−0.0757968
$584$	−0.0604665	−	0.104731i	−0.00250212	−	0.00433380i
$585$	−2.23918	−	4.59250i	−0.0925788	−	0.189876i
$586$	−0.961245	+	1.66492i	−0.0397087	+	0.0687774i
$587$	−22.6783	−	39.2799i	−0.936032	−	1.62125i	−0.772784	−	0.634669i	$-0.781136\pi$
$587$	−22.6783	−	39.2799i	−0.936032	−	1.62125i	−0.163248	−	0.986585i	$-0.552197\pi$
$588$	−0.0972320	−	13.5222i	−0.00400978	−	0.557645i
$589$	7.59808	−	13.1603i	0.313073	−	0.542259i
$590$	−1.85752	+	3.21731i	−0.0764727	+	0.132455i
$591$	14.1297			0.581219
$592$	−33.7783			−1.38828
$593$	−16.4508	+	28.4936i	−0.675553	+	1.17009i	0.300754	+	0.953702i	$0.402762\pi$
$593$	−16.4508	+	28.4936i	−0.675553	+	1.17009i	−0.976307	+	0.216390i	$0.930572\pi$
$594$	−0.110368	+	0.191162i	−0.00452844	+	0.00784348i
$595$	4.87910	−	18.4745i	0.200024	−	0.757380i
$596$	5.12820	+	8.88230i	0.210059	+	0.363833i
$597$	7.95622	−	13.7806i	0.325626	−	0.564002i
$598$	−3.80000	−	7.79370i	−0.155394	−	0.318708i
$599$	0.183467	+	0.317774i	0.00749626	+	0.0129839i	0.869749	−	0.493494i	$-0.164281\pi$
$599$	0.183467	+	0.317774i	0.00749626	+	0.0129839i	−0.862253	+	0.506478i	$0.830947\pi$
$600$	−3.07232			−0.125427
$601$	−11.9288	−	20.6612i	−0.486584	−	0.842788i	0.513297	−	0.858211i	$-0.328424\pi$
$601$	−11.9288	−	20.6612i	−0.486584	−	0.842788i	−0.999881	+	0.0154227i	$0.995091\pi$
$602$	1.88211	−	7.12650i	0.0767089	−	0.290455i
$603$	−3.50602			−0.142776
$604$	−3.76305	−	6.51780i	−0.153116	−	0.265205i
$605$	14.5755			0.592578
$606$	1.76444	+	3.05609i	0.0716754	+	0.124145i
$607$	2.93429	+	5.08234i	0.119099	+	0.206286i	0.919411	−	0.393298i	$-0.128666\pi$
$607$	2.93429	+	5.08234i	0.119099	+	0.206286i	−0.800312	+	0.599584i	$0.795333\pi$
$608$	5.17937	+	8.97093i	0.210051	+	0.363819i
$609$	20.5366	−	5.58199i	0.832187	−	0.226194i
$610$	1.23599			0.0500437
$611$	12.9871	+	0.909817i	0.525401	+	0.0368072i
$612$	4.92271	+	8.52638i	0.198989	+	0.344658i
$613$	−11.1773	+	19.3597i	−0.451448	+	0.781931i	−0.998476	−	0.0551834i	$-0.982426\pi$
$613$	−11.1773	+	19.3597i	−0.451448	+	0.781931i	0.547028	+	0.837114i	$0.315759\pi$
$614$	5.01082			0.202220
$615$	7.31636	−	12.6723i	0.295024	−	0.510997i
$616$	0.586324	−	2.22009i	0.0236237	−	0.0894498i
$617$	−12.0268	+	20.8310i	−0.484180	+	0.838625i	−0.999835	−	0.0181717i	$-0.994215\pi$
$617$	−12.0268	+	20.8310i	−0.484180	+	0.838625i	0.515655	+	0.856797i	$0.327549\pi$
$618$	−1.85828	−	3.21864i	−0.0747511	−	0.129473i
$619$	12.0016	+	20.7874i	0.482386	+	0.835517i	0.999796	−	0.0202208i	$-0.00643691\pi$
$619$	12.0016	+	20.7874i	0.482386	+	0.835517i	−0.517409	+	0.855738i	$0.673104\pi$
$620$	−12.0184			−0.482672
$621$	9.20786			0.369499
$622$	−3.84028	−	6.65155i	−0.153981	−	0.266703i
$623$	−15.9047	+	4.32298i	−0.637206	+	0.173197i
$624$	−12.9317	−	0.905934i	−0.517681	−	0.0362664i
$625$	0.544375	−	0.942886i	0.0217750	−	0.0377154i
$626$	2.05293	−	3.55578i	0.0820517	−	0.142118i
$627$	1.46269	−	2.53345i	0.0584141	−	0.101176i
$628$	1.03810	+	1.79804i	0.0414246	+	0.0717495i
$629$	−47.8813			−1.90915
$630$	0.944902	−	0.256830i	0.0376458	−	0.0102324i
$631$	2.22088	−	3.84667i	0.0884117	−	0.153134i	−0.818428	−	0.574609i	$-0.805154\pi$
$631$	2.22088	−	3.84667i	0.0884117	−	0.153134i	0.906840	+	0.421475i	$0.138488\pi$
$632$	−5.91623	+	10.2472i	−0.235335	+	0.407612i
$633$	−7.70029			−0.306059
$634$	−1.11393	+	1.92939i	−0.0442399	+	0.0766257i
$635$	12.9600			0.514300
$636$	−4.18311			−0.165871
$637$	21.0231	+	13.9653i	0.832966	+	0.553324i
$638$	1.77554			0.0702941
$639$	12.9193			0.511079
$640$	5.42693	−	9.39973i	0.214518	−	0.371557i
$641$	−9.55298			−0.377320			−0.188660	−	0.982042i	$-0.560414\pi$
$641$	−9.55298			−0.377320			−0.188660	+	0.982042i	$0.560414\pi$
$642$	−0.270768	+	0.468984i	−0.0106864	+	0.0185093i
$643$	10.6560	−	18.4567i	0.420232	−	0.727863i	−0.575730	−	0.817640i	$-0.695282\pi$
$643$	10.6560	−	18.4567i	0.420232	−	0.727863i	0.995962	+	0.0897769i	$0.0286154\pi$
$644$	−45.4140	+	12.3438i	−1.78956	+	0.486415i
$645$	−15.1159			−0.595186
$646$	2.30359	+	3.98994i	0.0906336	+	0.156982i
$647$	−15.2741	+	26.4555i	−0.600486	+	1.04007i	0.392262	+	0.919854i	$0.371693\pi$
$647$	−15.2741	+	26.4555i	−0.600486	+	1.04007i	−0.992748	+	0.120218i	$0.961641\pi$
$648$	−0.513436	+	0.889296i	−0.0201697	+	0.0349349i
$649$	4.24192	−	7.34723i	0.166510	−	0.288404i
$650$	1.57577	−	2.33553i	0.0618067	−	0.0916069i
$651$	−11.2091	+	3.04670i	−0.439318	+	0.119409i
$652$	−1.80815	−	3.13180i	−0.0708125	−	0.122651i
$653$	34.9351			1.36711			0.683557	−	0.729897i	$-0.260432\pi$
$653$	34.9351			1.36711			0.683557	+	0.729897i	$0.260432\pi$
$654$	−0.978682			−0.0382695
$655$	−0.247737	−	0.429093i	−0.00967989	−	0.0167661i
$656$	−18.5631	−	32.1523i	−0.724768	−	1.25534i
$657$	−0.0588842	+	0.101990i	−0.00229729	+	0.00397903i
$658$	−0.637096	+	2.41233i	−0.0248366	+	0.0940425i
$659$	−12.9552	+	22.4391i	−0.504665	+	0.874105i	0.495321	+	0.868710i	$0.335050\pi$
$659$	−12.9552	+	22.4391i	−0.504665	+	0.874105i	−0.999985	+	0.00539457i	$0.998283\pi$
$660$	−2.31364			−0.0900582
$661$	−9.18554	+	15.9098i	−0.357276	+	0.618820i	−0.987505	−	0.157589i	$-0.949628\pi$
$661$	−9.18554	+	15.9098i	−0.357276	+	0.618820i	0.630229	+	0.776409i	$0.282961\pi$
$662$	−0.228075	−	0.395037i	−0.00886439	−	0.0153536i
$663$	−18.3309	−	1.28418i	−0.711912	−	0.0498733i
$664$	6.33848			0.245981
$665$	−12.5227	+	3.40374i	−0.485608	+	0.131991i
$666$	−1.22684	−	2.12495i	−0.0475391	−	0.0823401i
$667$	−37.0328	−	64.1428i	−1.43392	−	2.48362i
$668$	−4.22793	−	7.32299i	−0.163584	−	0.283335i
$669$	27.3107			1.05589
$670$	0.648784	+	1.12373i	0.0250647	+	0.0434134i
$671$	−2.82257			−0.108964
$672$	2.02184	−	7.65560i	0.0779942	−	0.295321i
$673$	−11.2401	−	19.4684i	−0.433273	−	0.750450i	0.563880	−	0.825857i	$-0.309308\pi$
$673$	−11.2401	−	19.4684i	−0.433273	−	0.750450i	−0.997153	+	0.0754063i	$0.975975\pi$
$674$	0.357409			0.0137669
$675$	1.49596	+	2.59108i	0.0575796	+	0.0997309i
$676$	15.4663	−	19.7856i	0.594859	−	0.760983i
$677$	9.93644	−	17.2104i	0.381888	−	0.661450i	−0.609444	−	0.792829i	$-0.708607\pi$
$677$	9.93644	−	17.2104i	0.381888	−	0.661450i	0.991332	+	0.131379i	$0.0419406\pi$
$678$	1.23984	+	2.14746i	0.0476157	+	0.0824728i
$679$	−0.223080	+	0.844680i	−0.00856101	+	0.0324158i
$680$	3.70809	−	6.42260i	0.142199	−	0.246295i
$681$	6.63255	−	11.4879i	0.254160	−	0.440218i
$682$	−0.969102			−0.0371088
$683$	3.68530			0.141014			0.0705071	−	0.997511i	$-0.477538\pi$
$683$	3.68530			0.141014			0.0705071	+	0.997511i	$0.477538\pi$
$684$	3.34322	−	5.79063i	0.127831	−	0.221410i
$685$	−16.1224	+	27.9249i	−0.616007	+	1.06696i
$686$	−3.38316	+	3.45694i	−0.129170	+	0.131987i
$687$	5.12001	+	8.86812i	0.195341	+	0.338340i
$688$	−19.1760	+	33.2139i	−0.731079	+	1.26627i
$689$	4.36672	−	6.47214i	0.166359	−	0.246569i
$690$	−1.70390	−	2.95124i	−0.0648664	−	0.112352i
$691$	25.1361			0.956221			0.478111	−	0.878300i	$-0.341322\pi$
$691$	25.1361			0.956221			0.478111	+	0.878300i	$0.341322\pi$
$692$	4.05107	+	7.01666i	0.153999	+	0.266733i
$693$	−2.15783	+	0.586512i	−0.0819692	+	0.0222797i
$694$	1.85530			0.0704263
$695$	−6.20914	−	10.7545i	−0.235526	−	0.407943i
$696$	8.25988			0.313090
$697$	−26.3136	−	45.5764i	−0.996697	−	1.72633i
$698$	−1.84771	−	3.20032i	−0.0699367	−	0.121134i
$699$	2.14383	+	3.71322i	0.0810870	+	0.140447i
$700$	−10.8518	−	10.7740i	−0.410158	−	0.407220i
$701$	12.8909			0.486882			0.243441	−	0.969916i	$-0.421724\pi$
$701$	12.8909			0.486882			0.243441	+	0.969916i	$0.421724\pi$
$702$	−0.412691	−	0.846417i	−0.0155760	−	0.0319460i
$703$	16.2591	+	28.1617i	0.613225	+	1.06214i
$704$	−2.70842	+	4.69113i	−0.102078	+	0.176804i
$705$	5.11674			0.192707
$706$	−3.84766	+	6.66435i	−0.144809	+	0.250816i
$707$	−9.12823	+	34.5636i	−0.343302	+	1.29990i
$708$	9.69565	−	16.7934i	0.364385	−	0.631133i
$709$	8.89024	+	15.3984i	0.333880	+	0.578297i	0.983269	−	0.182159i	$-0.0583086\pi$
$709$	8.89024	+	15.3984i	0.333880	+	0.578297i	−0.649389	+	0.760456i	$0.724975\pi$
$710$	−2.39069	−	4.14080i	−0.0897212	−	0.155402i
$711$	11.5228			0.432140
$712$	−6.39689			−0.239733
$713$	20.2128	+	35.0097i	0.756976	+	1.31112i
$714$	0.899240	−	3.40493i	0.0336532	−	0.127426i
$715$	2.41519	−	3.57968i	0.0903230	−	0.133872i
$716$	−4.24817	+	7.35804i	−0.158761	+	0.274983i
$717$	1.71353	−	2.96793i	0.0639931	−	0.110839i
$718$	−2.25353	+	3.90323i	−0.0841011	+	0.145667i
$719$	−23.0380	−	39.9030i	−0.859173	−	1.48813i	−0.872719	−	0.488222i	$-0.837646\pi$
$719$	−23.0380	−	39.9030i	−0.859173	−	1.48813i	0.0135467	−	0.999908i	$-0.495688\pi$
$720$	−5.09490			−0.189876
$721$	9.61373	−	36.4019i	0.358034	−	1.35568i
$722$	−0.916660	+	1.58770i	−0.0341146	+	0.0590881i
$723$	−4.08170	+	7.06971i	−0.151800	+	0.262925i
$724$	16.8014			0.624420
$725$	12.0331	−	20.8420i	0.446900	−	0.774053i
$726$	2.68633			0.0996989
$727$	31.3066			1.16110			0.580548	−	0.814226i	$-0.302838\pi$
$727$	31.3066			1.16110			0.580548	+	0.814226i	$0.302838\pi$
$728$	6.45217	+	7.37060i	0.239133	+	0.273173i
$729$	1.00000			0.0370370
$730$	0.0435857			0.00161318
$731$	−27.1823	+	47.0812i	−1.00538	+	1.74136i
$732$	−6.45147			−0.238453
$733$	−5.25813	+	9.10736i	−0.194214	+	0.336388i	−0.946642	−	0.322286i	$-0.895549\pi$
$733$	−5.25813	+	9.10736i	−0.194214	+	0.336388i	0.752429	+	0.658674i	$0.228882\pi$
$734$	0.341107	−	0.590814i	0.0125905	−	0.0218073i
$735$	8.62594	+	4.89783i	0.318173	+	0.180659i
$736$	−27.5569			−1.01576
$737$	−1.48160	−	2.56620i	−0.0545754	−	0.0945273i
$738$	1.34844	−	2.33556i	0.0496367	−	0.0859732i
$739$	6.13405	−	10.6245i	0.225645	−	0.390828i	−0.730868	−	0.682519i	$-0.760885\pi$
$739$	6.13405	−	10.6245i	0.225645	−	0.390828i	0.956513	+	0.291691i	$0.0942179\pi$
$740$	12.8591	−	22.2727i	0.472711	−	0.818760i
$741$	5.46934	+	11.2175i	0.200921	+	0.412084i
$742$	1.06183	+	1.05422i	0.0389810	+	0.0387017i
$743$	14.6672	+	25.4043i	0.538087	+	0.931994i	0.999007	+	0.0445521i	$0.0141861\pi$
$743$	14.6672	+	25.4043i	0.538087	+	0.931994i	−0.460920	+	0.887442i	$0.652481\pi$
$744$	−4.50831			−0.165283
$745$	−7.52359			−0.275643
$746$	2.91202	+	5.04377i	0.106617	+	0.184665i
$747$	−3.08631	−	5.34564i	−0.112922	−	0.195587i
$748$	−4.16054	+	7.20627i	−0.152124	+	0.263487i
$749$	−5.29387	+	1.43891i	−0.193434	+	0.0525765i
$750$	1.47889	−	2.56152i	0.0540016	−	0.0935335i
$751$	26.6226			0.971472			0.485736	−	0.874105i	$-0.338552\pi$
$751$	26.6226			0.971472			0.485736	+	0.874105i	$0.338552\pi$
$752$	6.49111	−	11.2429i	0.236706	−	0.409988i
$753$	−12.9962	−	22.5101i	−0.473609	−	0.820315i
$754$	−4.23642	+	6.27902i	−0.154281	+	0.228669i
$755$	5.52078			0.200922
$756$	−4.93209	+	1.34057i	−0.179378	+	0.0487562i
$757$	21.2671	+	36.8357i	0.772966	+	1.33882i	0.935931	+	0.352184i	$0.114561\pi$
$757$	21.2671	+	36.8357i	0.772966	+	1.33882i	−0.162965	+	0.986632i	$0.552106\pi$
$758$	−0.857333	−	1.48494i	−0.0311397	−	0.0539356i
$759$	3.89112	+	6.73962i	0.141239	+	0.244633i
$760$	−5.03665			−0.182698
$761$	−18.3261	−	31.7418i	−0.664322	−	1.15064i	−0.979469	−	0.201597i	$-0.935387\pi$
$761$	−18.3261	−	31.7418i	−0.664322	−	1.15064i	0.315146	−	0.949043i	$-0.397946\pi$
$762$	2.38858			0.0865290
$763$	−7.03567	−	6.98527i	−0.254709	−	0.252884i
$764$	12.9823	+	22.4861i	0.469684	+	0.813517i
$765$	−7.22211			−0.261116
$766$	−0.827251	−	1.43284i	−0.0298898	−	0.0517707i
$767$	15.8616	+	32.5317i	0.572729	+	1.17465i
$768$	−5.40895	+	9.36857i	−0.195179	+	0.338059i
$769$	13.7781	+	23.8644i	0.496853	+	0.860574i	0.999993	−	0.00363055i	$-0.00115564\pi$
$769$	13.7781	+	23.8644i	0.496853	+	0.860574i	−0.503141	+	0.864204i	$0.667822\pi$
$770$	0.587288	+	0.583080i	0.0211644	+	0.0210128i
$771$	−2.96659	+	5.13829i	−0.106839	+	0.185051i
$772$	13.4074	−	23.2224i	0.482544	−	0.835791i
$773$	16.0414			0.576969			0.288484	−	0.957485i	$-0.406849\pi$
$773$	16.0414			0.576969			0.288484	+	0.957485i	$0.406849\pi$
$774$	−2.78592			−0.100138
$775$	−6.56779	+	11.3757i	−0.235922	+	0.408629i
$776$	−0.169539	+	0.293650i	−0.00608610	+	0.0105414i
$777$	6.34699	−	24.0326i	0.227697	−	0.862164i
$778$	−2.17782	−	3.77210i	−0.0780788	−	0.135236i
$779$	−17.8707	+	30.9529i	−0.640283	+	1.10900i
$780$	5.52034	−	8.18197i	0.197660	−	0.292962i
$781$	5.45952	+	9.45616i	0.195357	+	0.338368i
$782$	−12.2563			−0.438284
$783$	−4.02187	−	6.96608i	−0.143730	−	0.248948i
$784$	21.7048	−	12.7403i	0.775173	−	0.455009i
$785$	−1.52299			−0.0543580
$786$	−0.0456591	−	0.0790838i	−0.00162860	−	0.00282083i
$787$	47.6101			1.69712			0.848559	−	0.529101i	$-0.177471\pi$
$787$	47.6101			1.69712			0.848559	+	0.529101i	$0.177471\pi$
$788$	13.6478	+	23.6387i	0.486184	+	0.842095i
$789$	−2.05176	−	3.55376i	−0.0730448	−	0.126517i
$790$	−2.13228	−	3.69322i	−0.0758632	−	0.131399i
$791$	−6.41424	+	24.2872i	−0.228064	+	0.863553i
$792$	−0.867884			−0.0308389
$793$	6.73464	−	9.98176i	0.239154	−	0.354463i
$794$	−3.34363	−	5.79134i	−0.118661	−	0.205527i
$795$	1.53426	−	2.65742i	0.0544146	−	0.0942489i
$796$	30.7395			1.08953
$797$	23.0425	−	39.9107i	0.816206	−	1.41371i	−0.0922533	−	0.995736i	$-0.529407\pi$
$797$	23.0425	−	39.9107i	0.816206	−	1.41371i	0.908459	−	0.417974i	$-0.137260\pi$
$798$	−2.30798	+	0.627324i	−0.0817017	+	0.0222070i
$799$	9.20126	−	15.9371i	0.325517	−	0.563812i
$800$	−4.47705	−	7.75448i	−0.158288	−	0.274162i
$801$	3.11475	+	5.39490i	0.110054	+	0.190619i
$802$	6.95501			0.245590
$803$	−0.0995347			−0.00351250
$804$	−3.38645	−	5.86550i	−0.119431	−	0.206860i
$805$	8.81505	−	33.3777i	0.310690	−	1.17641i
$806$	2.31228	−	3.42714i	0.0814464	−	0.120716i
$807$	5.46635	−	9.46799i	0.192425	−	0.333289i
$808$	−6.93740	+	12.0159i	−0.244057	+	0.422719i
$809$	−12.3378	+	21.3696i	−0.433773	+	0.751317i	−0.997195	−	0.0748527i	$-0.976151\pi$
$809$	−12.3378	+	21.3696i	−0.433773	+	0.751317i	0.563422	+	0.826169i	$0.309485\pi$
$810$	−0.185048	−	0.320513i	−0.00650194	−	0.0112617i
$811$	−49.5770			−1.74088			−0.870442	−	0.492270i	$-0.836167\pi$
$811$	−49.5770			−1.74088			−0.870442	+	0.492270i	$0.836167\pi$
$812$	29.1748	+	28.9658i	1.02383	+	1.01650i
$813$	−9.05504	+	15.6838i	−0.317574	+	0.550055i
$814$	1.03689	−	1.79595i	0.0363430	−	0.0629480i
$815$	2.65273			0.0929212
$816$	−9.16200	+	15.8690i	−0.320734	+	0.555528i
$817$	36.9214			1.29172
$818$	1.20897			0.0422708
$819$	3.07443	−	9.03039i	0.107429	−	0.315547i
$820$	28.2673			0.987138
$821$	39.5268			1.37950			0.689748	−	0.724050i	$-0.257722\pi$
$821$	39.5268			1.37950			0.689748	+	0.724050i	$0.257722\pi$
$822$	−2.97144	+	5.14668i	−0.103641	+	0.179511i
$823$	6.79595			0.236892			0.118446	−	0.992961i	$-0.462209\pi$
$823$	6.79595			0.236892			0.118446	+	0.992961i	$0.462209\pi$
$824$	7.30638	−	12.6550i	0.254530	−	0.440858i
$825$	−1.26435	+	2.18991i	−0.0440189	+	0.0762430i
$826$	−6.69336	+	1.81930i	−0.232892	+	0.0633014i
$827$	6.29136			0.218772			0.109386	−	0.993999i	$-0.465112\pi$
$827$	6.29136			0.218772			0.109386	+	0.993999i	$0.465112\pi$
$828$	8.89383	+	15.4046i	0.309082	+	0.535346i
$829$	10.6744	−	18.4886i	0.370737	−	0.642136i	−0.618942	−	0.785437i	$-0.712438\pi$
$829$	10.6744	−	18.4886i	0.370737	−	0.642136i	0.989679	+	0.143301i	$0.0457717\pi$
$830$	−1.14223	+	1.97841i	−0.0396475	+	0.0686715i
$831$	3.59555	−	6.22767i	0.124728	−	0.216036i
$832$	−10.1275	−	20.7711i	−0.351106	−	0.720109i
$833$	30.7670	−	18.0595i	1.06601	−	0.625726i
$834$	−1.14437	−	1.98211i	−0.0396264	−	0.0686349i
$835$	6.20280			0.214657
$836$	5.65121			0.195451
$837$	2.19517	+	3.80215i	0.0758762	+	0.131421i
$838$	−2.25755	−	3.91018i	−0.0779856	−	0.135075i
$839$	−0.123635	+	0.214141i	−0.00426834	+	0.00739299i	−0.868152	−	0.496299i	$-0.834692\pi$
$839$	−0.123635	+	0.214141i	−0.00426834	+	0.00739299i	0.863883	+	0.503692i	$0.168025\pi$
$840$	2.73209	+	2.71252i	0.0942662	+	0.0935908i
$841$	−17.8509	+	30.9186i	−0.615548	+	1.06616i
$842$	2.06978			0.0713294
$843$	2.76536	−	4.78975i	0.0952441	−	0.164968i
$844$	−7.43767	−	12.8824i	−0.256015	−	0.443431i
$845$	6.89657	+	17.0822i	0.237249	+	0.587646i
$846$	0.943037			0.0324223
$847$	19.3118	+	19.1734i	0.663562	+	0.658807i
$848$	−3.89274	−	6.74242i	−0.133677	−	0.231536i
$849$	0.249695	+	0.432485i	0.00856953	+	0.0148429i
$850$	−1.99123	−	3.44891i	−0.0682985	−	0.118296i
$851$	−86.5070			−2.96542
$852$	12.4787	+	21.6137i	0.427512	+	0.740473i
$853$	18.7494			0.641968			0.320984	−	0.947085i	$-0.395986\pi$
$853$	18.7494			0.641968			0.320984	+	0.947085i	$0.395986\pi$
$854$	1.63762	+	1.62589i	0.0560384	+	0.0556369i
$855$	2.45242	+	4.24772i	0.0838711	+	0.145269i
$856$	−2.12921			−0.0727748
$857$	7.57209	+	13.1152i	0.258658	+	0.448008i	0.965883	−	0.258981i	$-0.0833866\pi$
$857$	7.57209	+	13.1152i	0.258658	+	0.448008i	−0.707225	+	0.706989i	$0.750053\pi$
$858$	0.445130	−	0.659751i	0.0151965	−	0.0225235i
$859$	9.21320	−	15.9577i	0.314350	−	0.544471i	−0.664949	−	0.746889i	$-0.731547\pi$
$859$	9.21320	−	15.9577i	0.314350	−	0.544471i	0.979299	+	0.202418i	$0.0648800\pi$
$860$	−14.6003	−	25.2885i	−0.497867	−	0.862331i
$861$	26.3637	−	7.16582i	0.898473	−	0.244211i
$862$	−0.660484	+	1.14399i	−0.0224962	+	0.0389645i
$863$	7.56920	−	13.1102i	0.257658	−	0.446278i	−0.707956	−	0.706257i	$-0.750382\pi$
$863$	7.56920	−	13.1102i	0.257658	−	0.446278i	0.965614	+	0.259979i	$0.0837157\pi$
$864$	−2.99275			−0.101816
$865$	−5.94333			−0.202079
$866$	0.0124339	−	0.0215362i	0.000422521	−	0.000731828i
$867$	−4.48729	+	7.77221i	−0.152396	+	0.263958i
$868$	−15.9238	−	15.8098i	−0.540490	−	0.536618i
$869$	4.86939	+	8.43404i	0.165183	+	0.286105i
$870$	−1.48848	+	2.57813i	−0.0504643	+	0.0874067i
$871$	12.6102	+	0.883417i	0.427282	+	0.0299334i
$872$	−1.92399	−	3.33244i	−0.0651544	−	0.112851i
$873$	0.330205			0.0111758
$874$	4.16189	+	7.20860i	0.140778	+	0.243834i
$875$	28.9143	−	7.85909i	0.977482	−	0.265686i
$876$	−0.227504			−0.00768664
$877$	20.6958	+	35.8462i	0.698847	+	1.21044i	0.968866	+	0.247584i	$0.0796367\pi$
$877$	20.6958	+	35.8462i	0.698847	+	1.21044i	−0.270019	+	0.962855i	$0.587030\pi$
$878$	−2.64894			−0.0893974
$879$	3.68051	+	6.37484i	0.124141	+	0.215018i
$880$	−2.15304	−	3.72917i	−0.0725789	−	0.125710i
$881$	−1.68361	−	2.91610i	−0.0567224	−	0.0982461i	0.836270	−	0.548318i	$-0.184732\pi$
$881$	−1.68361	−	2.91610i	−0.0567224	−	0.0982461i	−0.892992	+	0.450072i	$0.851398\pi$
$882$	1.58980	+	0.902692i	0.0535313	+	0.0303952i
$883$	−31.9217			−1.07425			−0.537125	−	0.843503i	$-0.680490\pi$
$883$	−31.9217			−1.07425			−0.537125	+	0.843503i	$0.680490\pi$
$884$	−15.5573	−	31.9075i	−0.523248	−	1.07317i
$885$	7.11225	+	12.3188i	0.239076	+	0.414091i
$886$	0.0815167	−	0.141191i	0.00273861	−	0.00474340i
$887$	−5.64973			−0.189699			−0.0948497	−	0.995492i	$-0.530237\pi$
$887$	−5.64973			−0.189699			−0.0948497	+	0.995492i	$0.530237\pi$
$888$	4.82367	−	8.35485i	0.161872	−	0.280370i
$889$	17.1713	+	17.0483i	0.575907	+	0.571781i
$890$	1.15276	−	1.99664i	0.0386405	−	0.0669274i
$891$	0.422587	+	0.731942i	0.0141572	+	0.0245210i
$892$	26.3793	+	45.6903i	0.883244	+	1.52982i
$893$	−12.4979			−0.418228
$894$	−1.38663			−0.0463759
$895$	−3.11625	−	5.39750i	−0.104165	−	0.180418i
$896$	19.5554	−	5.31527i	0.653299	−	0.177571i
$897$	−33.1183	−	2.32012i	−1.10579	−	0.0774664i
$898$	−4.53385	+	7.85286i	−0.151297	+	0.262053i
$899$	17.6574	−	30.5835i	0.588907	−	1.02002i
$900$	−2.88989	+	5.00543i	−0.0963295	+	0.166848i
$901$	−5.51802	−	9.55750i	−0.183832	−	0.318406i
$902$	2.27933			0.0758933
$903$	−20.0278	−	19.8843i	−0.666482	−	0.661707i
$904$	−4.87478	+	8.44337i	−0.162133	+	0.280822i
$905$	−6.16234	+	10.6735i	−0.204843	+	0.354799i
$906$	1.01750			0.0338043
$907$	−14.7805	+	25.6005i	−0.490778	+	0.850052i	−0.999944	−	0.0106163i	$-0.996621\pi$
$907$	−14.7805	+	25.6005i	−0.490778	+	0.850052i	0.509166	+	0.860668i	$0.329954\pi$
$908$	25.6254			0.850408
$909$	13.5117			0.448155
$910$	−3.46328	+	0.685663i	−0.114807	+	0.0227295i
$911$	24.1869			0.801347			0.400673	−	0.916221i	$-0.368776\pi$
$911$	24.1869			0.801347			0.400673	+	0.916221i	$0.368776\pi$
$912$	12.4446			0.412082
$913$	2.60847	−	4.51799i	0.0863276	−	0.149524i
$914$	−0.737715			−0.0244015
$915$	2.36624	−	4.09845i	0.0782255	−	0.135491i
$916$	−9.89078	+	17.1313i	−0.326801	+	0.566035i
$917$	0.236215	−	0.894416i	0.00780050	−	0.0295362i
$918$	−1.33107			−0.0439318
$919$	−23.8374	−	41.2876i	−0.786323	−	1.36195i	−0.928206	−	0.372068i	$-0.878649\pi$
$919$	−23.8374	−	41.2876i	−0.786323	−	1.36195i	0.141882	−	0.989884i	$-0.454684\pi$
$920$	6.69938	−	11.6037i	0.220872	−	0.382562i
$921$	9.59297	−	16.6155i	0.316099	−	0.547500i
$922$	−3.22887	+	5.59257i	−0.106337	+	0.184181i
$923$	−46.4673	−	3.25529i	−1.52949	−	0.107149i
$924$	−3.06546	−	3.04349i	−0.100846	−	0.100124i
$925$	−14.0544	−	24.3430i	−0.462106	−	0.800392i
$926$	−9.87552			−0.324530
$927$	−14.2304			−0.467387
$928$	12.0365	+	20.8478i	0.395117	+	0.684362i
$929$	1.14517	+	1.98350i	0.0375719	+	0.0650765i	0.884200	−	0.467109i	$-0.154704\pi$
$929$	1.14517	+	1.98350i	0.0375719	+	0.0650765i	−0.846628	+	0.532185i	$0.821371\pi$
$930$	0.812426	−	1.40716i	0.0266405	−	0.0461427i
$931$	−21.0694	−	11.9633i	−0.690522	−	0.392080i
$932$	−4.14142	+	7.17315i	−0.135657	+	0.234964i
$933$	−29.4081			−0.962778
$934$	2.52475	−	4.37299i	0.0826122	−	0.143089i
$935$	−3.05197	−	5.28616i	−0.0998100	−	0.172876i
$936$	2.07077	−	3.06919i	0.0676852	−	0.100320i
$937$	31.5319			1.03010			0.515050	−	0.857160i	$-0.327773\pi$
$937$	31.5319			1.03010			0.515050	+	0.857160i	$0.327773\pi$
$938$	−0.618609	+	2.34233i	−0.0201983	+	0.0764799i
$939$	−7.86048	−	13.6148i	−0.256517	−	0.444301i
$940$	4.94223	+	8.56019i	0.161198	+	0.279203i
$941$	−14.9605	−	25.9124i	−0.487700	−	0.844721i	0.512200	−	0.858866i	$-0.328831\pi$
$941$	−14.9605	−	25.9124i	−0.487700	−	0.844721i	−0.999900	+	0.0141453i	$0.995497\pi$
$942$	−0.280694			−0.00914552
$943$	−47.5405	−	82.3426i	−1.54813	−	2.68145i
$944$	36.0905			1.17465
$945$	0.957339	−	3.62492i	0.0311422	−	0.117919i
$946$	−1.17729	−	2.03913i	−0.0382771	−	0.0662978i
$947$	−18.0132			−0.585352			−0.292676	−	0.956212i	$-0.594546\pi$
$947$	−18.0132			−0.585352			−0.292676	+	0.956212i	$0.594546\pi$
$948$	11.1298	+	19.2774i	0.361480	+	0.626102i
$949$	0.237490	−	0.351996i	0.00770924	−	0.0114263i
$950$	−1.35233	+	2.34230i	−0.0438753	+	0.0759943i
$951$	4.26514	+	7.38743i	0.138307	+	0.239554i
$952$	13.3617	−	3.63179i	0.433055	−	0.117707i
$953$	−2.30018	+	3.98403i	−0.0745101	+	0.129055i	−0.900873	−	0.434082i	$-0.857073\pi$
$953$	−2.30018	+	3.98403i	−0.0745101	+	0.129055i	0.826363	+	0.563138i	$0.190406\pi$
$954$	0.282771	−	0.489774i	0.00915505	−	0.0158570i
$955$	−19.0464			−0.616327
$956$	6.62038			0.214118
$957$	3.39918	−	5.88755i	0.109880	−	0.190317i
$958$	−0.838125	+	1.45167i	−0.0270786	+	0.0469015i
$959$	−58.0955	+	15.7907i	−1.87600	+	0.509909i
$960$	−4.54110	−	7.86541i	−0.146563	−	0.253855i
$961$	5.86245	−	10.1541i	0.189111	−	0.327551i
$962$	3.87719	+	7.95201i	0.125006	+	0.256383i
$963$	1.03674	+	1.79569i	0.0334086	+	0.0578654i
$964$	−15.7700			−0.507916
$965$	9.83503	+	17.0348i	0.316601	+	0.548369i
$966$	1.62465	−	6.15167i	0.0522723	−	0.197927i
$967$	−35.1105			−1.12908			−0.564539	−	0.825407i	$-0.690946\pi$
$967$	−35.1105			−1.12908			−0.564539	+	0.825407i	$0.690946\pi$
$968$	5.28103	+	9.14702i	0.169739	+	0.293996i
$969$	17.6405			0.566693
$970$	−0.0611040	−	0.105835i	−0.00196193	−	0.00339816i
$971$	17.5404	+	30.3808i	0.562898	+	0.974967i	0.997242	+	0.0742202i	$0.0236468\pi$
$971$	17.5404	+	30.3808i	0.562898	+	0.974967i	−0.434344	+	0.900747i	$0.643020\pi$
$972$	0.965895	+	1.67298i	0.0309811	+	0.0536608i
$973$	5.92035	−	22.4171i	0.189798	−	0.718660i
$974$	−4.60868			−0.147672
$975$	−4.72771	−	9.69638i	−0.151408	−	0.310533i
$976$	−6.00364	−	10.3986i	−0.192172	−	0.332852i
$977$	−30.4620	+	52.7617i	−0.974565	+	1.68800i	−0.293203	+	0.956050i	$0.594721\pi$
$977$	−30.4620	+	52.7617i	−0.974565	+	1.68800i	−0.681362	+	0.731947i	$0.738612\pi$
$978$	0.488911			0.0156336
$979$	−2.63250	+	4.55962i	−0.0841351	+	0.145726i
$980$	0.137784	+	19.1618i	0.00440135	+	0.612102i
$981$	−1.87364	+	3.24524i	−0.0598207	+	0.103612i
$982$	4.75276	+	8.23203i	0.151667	+	0.262694i
$983$	−17.1946	−	29.7819i	−0.548422	−	0.949895i	−0.998383	−	0.0568467i	$-0.981895\pi$
$983$	−17.1946	−	29.7819i	−0.548422	−	0.949895i	0.449961	−	0.893048i	$-0.351438\pi$
$984$	10.6035			0.338029
$985$	−20.0228			−0.637978
$986$	5.35338	+	9.27232i	0.170486	+	0.295291i
$987$	6.77943	+	6.73085i	0.215791	+	0.214245i
$988$	−13.4838	+	19.9850i	−0.428976	+	0.635807i
$989$	−49.1102	+	85.0613i	−1.56161	+	2.70479i
$990$	0.156398	−	0.270889i	0.00497066	−	0.00860943i
$991$	−4.85038	+	8.40110i	−0.154077	+	0.266870i	−0.932723	−	0.360595i	$-0.882574\pi$
$991$	−4.85038	+	8.40110i	−0.154077	+	0.266870i	0.778645	+	0.627464i	$0.215907\pi$
$992$	−6.56961	−	11.3789i	−0.208585	−	0.361280i
$993$	−1.74655			−0.0554252
$994$	2.27950	−	8.63122i	0.0723014	−	0.273766i
$995$	−11.2745	+	19.5280i	−0.357425	+	0.619079i
$996$	5.96210	−	10.3267i	0.188916	−	0.327213i
$997$	−31.2290			−0.989031			−0.494516	−	0.869169i	$-0.664654\pi$
$997$	−31.2290			−0.989031			−0.494516	+	0.869169i	$0.664654\pi$
$998$	2.79878	−	4.84763i	0.0885938	−	0.153449i
$999$	−9.39490			−0.297241

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.c.16.5	yes	20
3.2	odd	2		819.2.s.f.289.6		20
7.4	even	3		273.2.j.c.172.6	yes	20
13.9	even	3		273.2.j.c.100.6	✓	20
21.11	odd	6		819.2.n.f.172.5		20
39.35	odd	6		819.2.n.f.100.5		20
91.74	even	3	inner	273.2.l.c.256.5	yes	20
273.74	odd	6		819.2.s.f.802.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.6	✓	20	13.9	even	3
273.2.j.c.172.6	yes	20	7.4	even	3
273.2.l.c.16.5	yes	20	1.1	even	1	trivial
273.2.l.c.256.5	yes	20	91.74	even	3	inner
819.2.n.f.100.5		20	39.35	odd	6
819.2.n.f.172.5		20	21.11	odd	6
819.2.s.f.289.6		20	3.2	odd	2
819.2.s.f.802.6		20	273.74	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.261171 q^{2} +(-0.500000 + 0.866025i) q^{3} -1.93179 q^{4} +(0.708533 - 1.22721i) q^{5} +(0.130586 - 0.226181i) q^{6} +(2.55312 - 0.693954i) q^{7} +1.02687 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-0.261171 q^{2} +(-0.500000 + 0.866025i) q^{3} -1.93179 q^{4} +(0.708533 - 1.22721i) q^{5} +(0.130586 - 0.226181i) q^{6} +(2.55312 - 0.693954i) q^{7} +1.02687 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.185048 + 0.320513i) q^{10} +(0.422587 - 0.731942i) q^{11} +(0.965895 - 1.67298i) q^{12} +(1.58015 + 3.24085i) q^{13} +(-0.666802 + 0.181241i) q^{14} +(0.708533 + 1.22721i) q^{15} +3.59539 q^{16} +5.09653 q^{17} +(0.130586 + 0.226181i) q^{18} +(-1.73064 - 2.99755i) q^{19} +(-1.36874 + 2.37072i) q^{20} +(-0.675578 + 2.55804i) q^{21} +(-0.110368 + 0.191162i) q^{22} +9.20786 q^{23} +(-0.513436 + 0.889296i) q^{24} +(1.49596 + 2.59108i) q^{25} +(-0.412691 - 0.846417i) q^{26} +1.00000 q^{27} +(-4.93209 + 1.34057i) q^{28} +(-4.02187 - 6.96608i) q^{29} +(-0.185048 - 0.320513i) q^{30} +(2.19517 + 3.80215i) q^{31} -2.99275 q^{32} +(0.422587 + 0.731942i) q^{33} -1.33107 q^{34} +(0.957339 - 3.62492i) q^{35} +(0.965895 + 1.67298i) q^{36} -9.39490 q^{37} +(0.451992 + 0.782874i) q^{38} +(-3.59674 - 0.251971i) q^{39} +(0.727572 - 1.26019i) q^{40} +(-5.16304 - 8.94264i) q^{41} +(0.176442 - 0.668088i) q^{42} +(-5.33350 + 9.23790i) q^{43} +(-0.816348 + 1.41396i) q^{44} -1.41707 q^{45} -2.40483 q^{46} +(1.80540 - 3.12704i) q^{47} +(-1.79769 + 3.11370i) q^{48} +(6.03685 - 3.54350i) q^{49} +(-0.390703 - 0.676717i) q^{50} +(-2.54826 + 4.41372i) q^{51} +(-3.05253 - 6.26064i) q^{52} +(-1.08270 - 1.87530i) q^{53} -0.261171 q^{54} +(-0.598833 - 1.03721i) q^{55} +(2.62173 - 0.712602i) q^{56} +3.46127 q^{57} +(1.05040 + 1.81934i) q^{58} +10.0380 q^{59} +(-1.36874 - 2.37072i) q^{60} +(-1.66982 - 2.89221i) q^{61} +(-0.573316 - 0.993012i) q^{62} +(-1.87754 - 1.86409i) q^{63} -6.40916 q^{64} +(5.09681 + 0.357060i) q^{65} +(-0.110368 - 0.191162i) q^{66} +(1.75301 - 3.03631i) q^{67} -9.84542 q^{68} +(-4.60393 + 7.97424i) q^{69} +(-0.250030 + 0.946725i) q^{70} +(-6.45964 + 11.1884i) q^{71} +(-0.513436 - 0.889296i) q^{72} +(-0.0588842 - 0.101990i) q^{73} +2.45368 q^{74} -2.99193 q^{75} +(3.34322 + 5.79063i) q^{76} +(0.570981 - 2.16199i) q^{77} +(0.939365 + 0.0658076i) q^{78} +(-5.76141 + 9.97906i) q^{79} +(2.54745 - 4.41231i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.34844 + 2.33556i) q^{82} +6.17262 q^{83} +(1.30508 - 4.94160i) q^{84} +(3.61106 - 6.25453i) q^{85} +(1.39296 - 2.41268i) q^{86} +8.04374 q^{87} +(0.433942 - 0.751610i) q^{88} -6.22949 q^{89} +0.370097 q^{90} +(6.28333 + 7.17773i) q^{91} -17.7877 q^{92} -4.39034 q^{93} +(-0.471518 + 0.816694i) q^{94} -4.90485 q^{95} +(1.49638 - 2.59180i) q^{96} +(-0.165103 + 0.285966i) q^{97} +(-1.57665 + 0.925461i) q^{98} -0.845173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25} + 13 q^{26} + 20 q^{27} - 23 q^{28} - 9 q^{29} - 4 q^{30} - 9 q^{31} - 34 q^{32} - 8 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} - 36 q^{37} + 22 q^{38} + 4 q^{39} - 9 q^{40} - q^{41} + 3 q^{42} - 11 q^{43} + 8 q^{44} + 20 q^{46} + 13 q^{47} - 20 q^{48} - 3 q^{49} + 5 q^{50} - 44 q^{52} - 6 q^{53} - 19 q^{55} - 23 q^{56} - 14 q^{57} + 30 q^{59} + 12 q^{60} + 22 q^{62} + 6 q^{63} + 72 q^{64} - 6 q^{65} - 9 q^{66} - 22 q^{67} - 78 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} + 6 q^{72} + 6 q^{74} + 64 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} + 48 q^{80} - 10 q^{81} - 13 q^{82} + 40 q^{83} + 10 q^{84} - 16 q^{85} + 4 q^{86} + 18 q^{87} - 12 q^{88} - 4 q^{89} + 8 q^{90} + 30 q^{91} + 66 q^{92} + 18 q^{93} - 44 q^{94} + 72 q^{95} + 17 q^{96} + 21 q^{97} - 76 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more