LMFDB - Embedded newform 273.2.j.c.100.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(100,273)]

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, 4]))

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

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

chi := DirichletCharacter("273.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.j (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			100.6
Root			$-0.130586 + 0.226181i$ of defining polynomial
Character	$\chi$	$=$	273.100
Dual form			273.2.j.c.172.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.130586 + 0.226181i) q^{2} +1.00000 q^{3} +(0.965895 - 1.67298i) q^{4} +(0.708533 - 1.22721i) q^{5} +(0.130586 + 0.226181i) q^{6} +(-0.675578 + 2.55804i) q^{7} +1.02687 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.130586 + 0.226181i) q^{2} +1.00000 q^{3} +(0.965895 - 1.67298i) q^{4} +(0.708533 - 1.22721i) q^{5} +(0.130586 + 0.226181i) q^{6} +(-0.675578 + 2.55804i) q^{7} +1.02687 q^{8} +1.00000 q^{9} +0.370097 q^{10} -0.845173 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} +(-1.79769 - 3.11370i) q^{16} +(-2.54826 + 4.41372i) q^{17} +(0.130586 + 0.226181i) q^{18} +3.46127 q^{19} +(-1.36874 - 2.37072i) q^{20} +(-0.675578 + 2.55804i) q^{21} +(-0.110368 - 0.191162i) q^{22} +(-4.60393 - 7.97424i) q^{23} +1.02687 q^{24} +(1.49596 + 2.59108i) q^{25} +(0.939365 - 0.0658076i) q^{26} +1.00000 q^{27} +(3.62702 + 3.60103i) q^{28} +(-4.02187 + 6.96608i) q^{29} +0.370097 q^{30} +(2.19517 + 3.80215i) q^{31} +(1.49638 - 2.59180i) q^{32} -0.845173 q^{33} -1.33107 q^{34} +(2.66060 + 2.64154i) q^{35} +(0.965895 - 1.67298i) q^{36} +(4.69745 + 8.13622i) q^{37} +(0.451992 + 0.782874i) q^{38} +(1.58015 - 3.24085i) q^{39} +(0.727572 - 1.26019i) q^{40} +(-5.16304 + 8.94264i) q^{41} +(-0.666802 + 0.181241i) q^{42} +(-5.33350 - 9.23790i) q^{43} +(-0.816348 + 1.41396i) q^{44} +(0.708533 - 1.22721i) q^{45} +(1.20242 - 2.08264i) q^{46} +(1.80540 - 3.12704i) q^{47} +(-1.79769 - 3.11370i) q^{48} +(-6.08719 - 3.45632i) q^{49} +(-0.390703 + 0.676717i) q^{50} +(-2.54826 + 4.41372i) q^{51} +(-3.89561 - 5.77389i) q^{52} +(-1.08270 - 1.87530i) q^{53} +(0.130586 + 0.226181i) q^{54} +(-0.598833 + 1.03721i) q^{55} +(-0.693732 + 2.62678i) q^{56} +3.46127 q^{57} -2.10080 q^{58} +(-5.01900 + 8.69316i) q^{59} +(-1.36874 - 2.37072i) q^{60} +3.33963 q^{61} +(-0.573316 + 0.993012i) q^{62} +(-0.675578 + 2.55804i) q^{63} -6.40916 q^{64} +(-2.85763 - 4.23544i) q^{65} +(-0.110368 - 0.191162i) q^{66} -3.50602 q^{67} +(4.92271 + 8.52638i) q^{68} +(-4.60393 - 7.97424i) q^{69} +(-0.250030 + 0.946725i) q^{70} +(-6.45964 - 11.1884i) q^{71} +1.02687 q^{72} +(-0.0588842 - 0.101990i) q^{73} +(-1.22684 + 2.12495i) q^{74} +(1.49596 + 2.59108i) 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} -5.09490 q^{80} +1.00000 q^{81} -2.69688 q^{82} +6.17262 q^{83} +(3.62702 + 3.60103i) q^{84} +(3.61106 + 6.25453i) q^{85} +(1.39296 - 2.41268i) q^{86} +(-4.02187 + 6.96608i) q^{87} -0.867884 q^{88} +(3.11475 + 5.39490i) q^{89} +0.370097 q^{90} +(7.22272 + 6.23156i) q^{91} -17.7877 q^{92} +(2.19517 + 3.80215i) q^{93} +0.943037 q^{94} +(2.45242 - 4.24772i) q^{95} +(1.49638 - 2.59180i) q^{96} +(-0.165103 - 0.285966i) q^{97} +(-0.0131454 - 1.82815i) q^{98} -0.845173 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9}+O(q^{10}) $ 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9	$ 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25} + 4 q^{26} + 20 q^{27} + 13 q^{28} - 9 q^{29} + 8 q^{30} - 9 q^{31} + 17 q^{32} + 16 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} + 18 q^{37} + 22 q^{38} - 5 q^{39} - 9 q^{40} - q^{41} - 9 q^{42} - 11 q^{43} + 8 q^{44} - 10 q^{46} + 13 q^{47} - 20 q^{48} - 21 q^{49} + 5 q^{50} - 2 q^{52} - 6 q^{53} - 19 q^{55} - 5 q^{56} - 14 q^{57} - 15 q^{59} + 12 q^{60} + 22 q^{62} - 9 q^{63} + 72 q^{64} - 27 q^{65} - 9 q^{66} + 44 q^{67} + 39 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} - 12 q^{72} - 3 q^{74} - 32 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} - 96 q^{80} + 20 q^{81} + 26 q^{82} + 40 q^{83} + 13 q^{84} - 16 q^{85} + 4 q^{86} - 9 q^{87} + 24 q^{88} + 2 q^{89} + 8 q^{90} + 9 q^{91} + 66 q^{92} - 9 q^{93} + 88 q^{94} - 36 q^{95} + 17 q^{96} + 21 q^{97} - 79 q^{98} + 16 q^{99}+O(q^{100}) $ 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9 + 8 * q^10 + 16 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 - 20 * q^16 - 14 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 - 14 * q^23 - 12 * q^24 - 32 * q^25 + 4 * q^26 + 20 * q^27 + 13 * q^28 - 9 * q^29 + 8 * q^30 - 9 * q^31 + 17 * q^32 + 16 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 + 18 * q^37 + 22 * q^38 - 5 * q^39 - 9 * q^40 - q^41 - 9 * q^42 - 11 * q^43 + 8 * q^44 - 10 * q^46 + 13 * q^47 - 20 * q^48 - 21 * q^49 + 5 * q^50 - 2 * q^52 - 6 * q^53 - 19 * q^55 - 5 * q^56 - 14 * q^57 - 15 * q^59 + 12 * q^60 + 22 * q^62 - 9 * q^63 + 72 * q^64 - 27 * q^65 - 9 * q^66 + 44 * q^67 + 39 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 - 12 * q^72 - 3 * q^74 - 32 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 - 96 * q^80 + 20 * q^81 + 26 * q^82 + 40 * q^83 + 13 * q^84 - 16 * q^85 + 4 * q^86 - 9 * q^87 + 24 * q^88 + 2 * q^89 + 8 * q^90 + 9 * q^91 + 66 * q^92 - 9 * q^93 + 88 * q^94 - 36 * q^95 + 17 * q^96 + 21 * q^97 - 79 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.130586	+	0.226181i	0.0923380	+	0.159934i	0.908495	−	0.417897i	$-0.137233\pi$
$2$	0.130586	+	0.226181i	0.0923380	+	0.159934i	−0.816156	+	0.577831i	$0.803899\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.965895	−	1.67298i	0.482947	−	0.836489i
$5$	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
$7$	−0.675578	+	2.55804i	−0.255345	+	0.966850i
$7$	−0.675578	+	2.55804i	−0.255345	+	0.966850i
$8$	1.02687			0.363054
$9$	1.00000			0.333333
$10$	0.370097			0.117035
$11$	−0.845173			−0.254829			−0.127415	−	0.991850i	$-0.540668\pi$
$11$	−0.845173			−0.254829			−0.127415	+	0.991850i	$0.540668\pi$
$12$	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
$16$	−1.79769	−	3.11370i	−0.449424	−	0.778425i
$17$	−2.54826	+	4.41372i	−0.618045	+	1.07048i	0.371798	+	0.928314i	$0.378742\pi$
$17$	−2.54826	+	4.41372i	−0.618045	+	1.07048i	−0.989842	+	0.142171i	$0.954592\pi$
$18$	0.130586	+	0.226181i	0.0307793	+	0.0533114i
$19$	3.46127			0.794070			0.397035	−	0.917803i	$-0.370039\pi$
$19$	3.46127			0.794070			0.397035	+	0.917803i	$0.370039\pi$
$20$	−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
$23$	−4.60393	−	7.97424i	−0.959986	−	1.66274i	−0.722521	−	0.691349i	$-0.757017\pi$
$23$	−4.60393	−	7.97424i	−0.959986	−	1.66274i	−0.237465	−	0.971396i	$-0.576317\pi$
$24$	1.02687			0.209609
$25$	1.49596	+	2.59108i	0.299193	+	0.518217i
$26$	0.939365	−	0.0658076i	0.184225	−	0.0129059i
$27$	1.00000			0.192450
$28$	3.62702	+	3.60103i	0.685442	+	0.680531i
$29$	−4.02187	+	6.96608i	−0.746843	+	1.29357i	0.202486	+	0.979285i	$0.435098\pi$
$29$	−4.02187	+	6.96608i	−0.746843	+	1.29357i	−0.949329	+	0.314284i	$0.898235\pi$
$30$	0.370097			0.0675702
$31$	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	$0.704333\pi$
$32$	1.49638	−	2.59180i	0.264525	−	0.458170i
$33$	−0.845173			−0.147126
$34$	−1.33107			−0.228276
$35$	2.66060	+	2.64154i	0.449724	+	0.446501i
$36$	0.965895	−	1.67298i	0.160982	−	0.278830i
$37$	4.69745	+	8.13622i	0.772256	+	1.33759i	0.936324	+	0.351137i	$0.114205\pi$
$37$	4.69745	+	8.13622i	0.772256	+	1.33759i	−0.164068	+	0.986449i	$0.552462\pi$
$38$	0.451992	+	0.782874i	0.0733229	+	0.126999i
$39$	1.58015	−	3.24085i	0.253027	−	0.518951i
$40$	0.727572	−	1.26019i	0.115039	−	0.199254i
$41$	−5.16304	+	8.94264i	−0.806331	+	1.39661i	0.109058	+	0.994035i	$0.465217\pi$
$41$	−5.16304	+	8.94264i	−0.806331	+	1.39661i	−0.915389	+	0.402571i	$0.868117\pi$
$42$	−0.666802	+	0.181241i	−0.102890	+	0.0279661i
$43$	−5.33350	−	9.23790i	−0.813352	−	1.40877i	−0.910505	−	0.413497i	$-0.864307\pi$
$43$	−5.33350	−	9.23790i	−0.813352	−	1.40877i	0.0971534	−	0.995269i	$-0.469026\pi$
$44$	−0.816348	+	1.41396i	−0.123069	+	0.213162i
$45$	0.708533	−	1.22721i	0.105622	−	0.182942i
$46$	1.20242	−	2.08264i	0.177286	−	0.307069i
$47$	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
$49$	−6.08719	−	3.45632i	−0.869598	−	0.493760i
$50$	−0.390703	+	0.676717i	−0.0552537	+	0.0957022i
$51$	−2.54826	+	4.41372i	−0.356828	+	0.618045i
$52$	−3.89561	−	5.77389i	−0.540224	−	0.800694i
$53$	−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	$0.880849\pi$
$54$	0.130586	+	0.226181i	0.0177705	+	0.0307793i
$55$	−0.598833	+	1.03721i	−0.0807466	+	0.139857i
$56$	−0.693732	+	2.62678i	−0.0927038	+	0.351019i
$57$	3.46127			0.458457
$58$	−2.10080			−0.275848
$59$	−5.01900	+	8.69316i	−0.653418	+	1.13175i	0.328870	+	0.944375i	$0.393332\pi$
$59$	−5.01900	+	8.69316i	−0.653418	+	1.13175i	−0.982288	+	0.187378i	$0.940001\pi$
$60$	−1.36874	−	2.37072i	−0.176703	−	0.306059i
$61$	3.33963			0.427596			0.213798	−	0.976878i	$-0.431417\pi$
$61$	3.33963			0.427596			0.213798	+	0.976878i	$0.431417\pi$
$62$	−0.573316	+	0.993012i	−0.0728112	+	0.126113i
$63$	−0.675578	+	2.55804i	−0.0851149	+	0.322283i
$64$	−6.40916			−0.801145
$65$	−2.85763	−	4.23544i	−0.354445	−	0.525341i
$66$	−0.110368	−	0.191162i	−0.0135853	−	0.0235304i
$67$	−3.50602			−0.428329			−0.214164	−	0.976798i	$-0.568703\pi$
$67$	−3.50602			−0.428329			−0.214164	+	0.976798i	$0.568703\pi$
$68$	4.92271	+	8.52638i	0.596966	+	1.03398i
$69$	−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	−0.939387	−	0.342860i	$-0.888604\pi$
$71$	−6.45964	−	11.1884i	−0.766619	−	1.32782i	0.172768	−	0.984963i	$-0.444729\pi$
$72$	1.02687			0.121018
$73$	−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	$0.835527\pi$
$74$	−1.22684	+	2.12495i	−0.142617	+	0.247020i
$75$	1.49596	+	2.59108i	0.172739	+	0.299193i
$76$	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	$0.942185\pi$
$80$	−5.09490			−0.569627
$81$	1.00000			0.111111
$82$	−2.69688			−0.297820
$83$	6.17262			0.677533			0.338766	−	0.940871i	$-0.389990\pi$
$83$	6.17262			0.677533			0.338766	+	0.940871i	$0.389990\pi$
$84$	3.62702	+	3.60103i	0.395740	+	0.392905i
$85$	3.61106	+	6.25453i	0.391674	+	0.678399i
$86$	1.39296	−	2.41268i	0.150207	−	0.260166i
$87$	−4.02187	+	6.96608i	−0.431190	+	0.746843i
$88$	−0.867884			−0.0925167
$89$	3.11475	+	5.39490i	0.330162	+	0.571858i	0.982544	−	0.186033i	$-0.0595631\pi$
$89$	3.11475	+	5.39490i	0.330162	+	0.571858i	−0.652381	+	0.757891i	$0.726230\pi$
$90$	0.370097			0.0390116
$91$	7.22272	+	6.23156i	0.757147	+	0.653245i
$92$	−17.7877			−1.85449
$93$	2.19517	+	3.80215i	0.227629	+	0.394264i
$94$	0.943037			0.0972668
$95$	2.45242	−	4.24772i	0.251613	−	0.435807i
$96$	1.49638	−	2.59180i	0.152723	−	0.264525i
$97$	−0.165103	−	0.285966i	−0.0167636	−	0.0290355i	0.857522	−	0.514447i	$-0.172003\pi$
$97$	−0.165103	−	0.285966i	−0.0167636	−	0.0290355i	−0.874286	+	0.485412i	$0.838670\pi$
$98$	−0.0131454	−	1.82815i	−0.00132789	−	0.184671i
$99$	−0.845173			−0.0849431
$100$	5.77977			0.577977
$101$	13.5117			1.34447			0.672233	−	0.740340i	$-0.265335\pi$
$101$	13.5117			1.34447			0.672233	+	0.740340i	$0.265335\pi$
$102$	−1.33107			−0.131795
$103$	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
$107$	1.03674	+	1.79569i	0.100226	+	0.173596i	0.911778	−	0.410684i	$-0.134710\pi$
$107$	1.03674	+	1.79569i	0.100226	+	0.173596i	−0.811552	+	0.584281i	$0.801377\pi$
$108$	0.965895	−	1.67298i	0.0929433	−	0.160982i
$109$	−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	$0.890769\pi$
$110$	−0.312796			−0.0298239
$111$	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	0.551580	−	0.834122i	$-0.314025\pi$
$113$	−4.74722	−	8.22242i	−0.446581	−	0.773500i	−0.998161	+	0.0606216i	$0.980692\pi$
$114$	0.451992	+	0.782874i	0.0423330	+	0.0733229i
$115$	−13.0481			−1.21675
$116$	7.76941	+	13.4570i	0.721371	+	1.24945i
$117$	1.58015	−	3.24085i	0.146085	−	0.299617i
$118$	−2.62164			−0.241341
$119$	−9.56895	−	9.50039i	−0.877184	−	0.870899i
$120$	0.727572	−	1.26019i	0.0664179	−	0.115039i
$121$	−10.2857			−0.935062
$122$	0.436108	+	0.755362i	0.0394834	+	0.0683873i
$123$	−5.16304	+	8.94264i	−0.465535	+	0.806331i
$124$	8.48121			0.761636
$125$	11.3251			1.01295
$126$	−0.666802	+	0.181241i	−0.0594035	+	0.0161462i
$127$	4.57282	−	7.92035i	0.405772	−	0.702817i	−0.588639	−	0.808396i	$-0.700336\pi$
$127$	4.57282	−	7.92035i	0.405772	−	0.702817i	0.994411	+	0.105579i	$0.0336695\pi$
$128$	−3.82970	−	6.63323i	−0.338501	−	0.586301i
$129$	−5.33350	−	9.23790i	−0.469589	−	0.813352i
$130$	0.584810	−	1.19943i	0.0512913	−	0.105197i
$131$	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
$133$	−2.33836	+	8.85409i	−0.202762	+	0.767747i
$134$	−0.457837	−	0.792996i	−0.0395511	−	0.0685044i
$135$	0.708533	−	1.22721i	0.0609808	−	0.105622i
$136$	−2.61674	+	4.53232i	−0.224383	+	0.388643i
$137$	11.3773	−	19.7061i	0.972033	−	1.68361i	0.282634	−	0.959228i	$-0.408792\pi$
$137$	11.3773	−	19.7061i	0.972033	−	1.68361i	0.689399	−	0.724382i	$-0.257875\pi$
$138$	1.20242	−	2.08264i	0.102356	−	0.177286i
$139$	4.38169	+	7.58931i	0.371650	+	0.643717i	0.989820	−	0.142328i	$-0.0454588\pi$
$139$	4.38169	+	7.58931i	0.371650	+	0.643717i	−0.618169	+	0.786045i	$0.712125\pi$
$140$	6.98910	−	1.89968i	0.590687	−	0.160552i
$141$	1.80540	−	3.12704i	0.152042	−	0.263344i
$142$	1.68707	−	2.92210i	0.141576	−	0.245217i
$143$	−1.33550	+	2.73908i	−0.111680	+	0.229053i
$144$	−1.79769	−	3.11370i	−0.149808	−	0.259475i
$145$	5.69925	+	9.87140i	0.473297	+	0.819775i
$146$	0.0153789	−	0.0266370i	0.00127276	−	0.00220449i
$147$	−6.08719	−	3.45632i	−0.502063	−	0.285072i
$148$	18.1490			1.49184
$149$	5.30927			0.434953			0.217476	−	0.976066i	$-0.430218\pi$
$149$	5.30927			0.434953			0.217476	+	0.976066i	$0.430218\pi$
$150$	−0.390703	+	0.676717i	−0.0319007	+	0.0552537i
$151$	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	$0.782660\pi$
$152$	3.55428			0.288290
$153$	−2.54826	+	4.41372i	−0.206015	+	0.356828i
$154$	0.563563	−	0.153180i	0.0454132	−	0.0123436i
$155$	6.22140			0.499715
$156$	−3.89561	−	5.77389i	−0.311898	−	0.462281i
$157$	−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	$0.846989\pi$
$158$	−3.00943			−0.239418
$159$	−1.08270	−	1.87530i	−0.0858639	−	0.148721i
$160$	−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
$163$	−1.87199			−0.146626			−0.0733128	−	0.997309i	$-0.523357\pi$
$163$	−1.87199			−0.146626			−0.0733128	+	0.997309i	$0.523357\pi$
$164$	9.97390	+	17.2753i	0.778831	+	1.34897i
$165$	−0.598833	+	1.03721i	−0.0466191	+	0.0807466i
$166$	0.806055	+	1.39613i	0.0625620	+	0.108361i
$167$	2.18861	−	3.79078i	0.169360	−	0.293339i	−0.768835	−	0.639447i	$-0.779163\pi$
$167$	2.18861	−	3.79078i	0.169360	−	0.293339i	0.938195	+	0.346107i	$0.112497\pi$
$168$	−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
$171$	3.46127			0.264690
$172$	−20.6064			−1.57122
$173$	4.19411			0.318872			0.159436	−	0.987208i	$-0.449032\pi$
$173$	4.19411			0.318872			0.159436	+	0.987208i	$0.449032\pi$
$174$	−2.10080			−0.159261
$175$	−7.63875	+	2.07626i	−0.577435	+	0.156950i
$176$	1.51936	+	2.63161i	0.114526	+	0.198365i
$177$	−5.01900	+	8.69316i	−0.377251	+	0.653418i
$178$	−0.813483	+	1.40899i	−0.0609731	+	0.105609i
$179$	−4.39817			−0.328735			−0.164367	−	0.986399i	$-0.552558\pi$
$179$	−4.39817			−0.328735			−0.164367	+	0.986399i	$0.552558\pi$
$180$	−1.36874	−	2.37072i	−0.102020	−	0.176703i
$181$	−8.69733			−0.646468			−0.323234	−	0.946319i	$-0.604770\pi$
$181$	−8.69733			−0.646468			−0.323234	+	0.946319i	$0.604770\pi$
$182$	−0.466276	+	2.44740i	−0.0345626	+	0.181413i
$183$	3.33963			0.246873
$184$	−4.72764	−	8.18852i	−0.348527	−	0.603666i
$185$	13.3132			0.978805
$186$	−0.573316	+	0.993012i	−0.0420376	+	0.0728112i
$187$	2.15372	−	3.73036i	0.157496	−	0.272791i
$188$	−3.48765	−	6.04079i	−0.254363	−	0.440570i
$189$	−0.675578	+	2.55804i	−0.0491411	+	0.186070i
$190$	1.28101			0.0929339
$191$	13.4407			0.972537			0.486268	−	0.873809i	$-0.338358\pi$
$191$	13.4407			0.972537			0.486268	+	0.873809i	$0.338358\pi$
$192$	−6.40916			−0.462541
$193$	13.8808			0.999165			0.499583	−	0.866266i	$-0.333487\pi$
$193$	13.8808			0.999165			0.499583	+	0.866266i	$0.333487\pi$
$194$	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	0.496642	+	0.867956i	$0.334566\pi$
$197$	−7.06487	+	12.2367i	−0.503351	+	0.871829i	−0.999992	+	0.00387354i	$0.998767\pi$
$198$	−0.110368	−	0.191162i	−0.00784348	−	0.0135853i
$199$	7.95622	−	13.7806i	0.564002	−	0.976879i	−0.433140	−	0.901327i	$-0.642594\pi$
$199$	7.95622	−	13.7806i	0.564002	−	0.976879i	0.997142	−	0.0755529i	$-0.0240722\pi$
$200$	1.53616	+	2.66071i	0.108623	+	0.188141i
$201$	−3.50602			−0.247296
$202$	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
$205$	7.31636	+	12.6723i	0.510997	+	0.885072i
$206$	3.71657			0.258945
$207$	−4.60393	−	7.97424i	−0.319995	−	0.554248i
$208$	−12.9317	+	0.905934i	−0.896650	+	0.0628152i
$209$	−2.92537			−0.202352
$210$	−0.250030	+	0.946725i	−0.0172537	+	0.0653302i
$211$	3.85014	−	6.66864i	0.265055	−	0.459088i	−0.702523	−	0.711661i	$-0.747943\pi$
$211$	3.85014	−	6.66864i	0.265055	−	0.459088i	0.967578	+	0.252572i	$0.0812766\pi$
$212$	−4.18311			−0.287297
$213$	−6.45964	−	11.1884i	−0.442608	−	0.766619i
$214$	−0.270768	+	0.468984i	−0.0185093	+	0.0320591i
$215$	−15.1159			−1.03089
$216$	1.02687			0.0698697
$217$	−11.2091	+	3.04670i	−0.760921	+	0.206823i
$218$	0.489341	−	0.847563i	0.0331424	−	0.0574042i
$219$	−0.0588842	−	0.101990i	−0.00397903	−	0.00689188i
$220$	1.15682	+	2.00367i	0.0779927	+	0.135087i
$221$	10.2776	+	15.2329i	0.691344	+	1.02468i
$222$	−1.22684	+	2.12495i	−0.0823401	+	0.142617i
$223$	−13.6554	+	23.6518i	−0.914430	+	1.58384i	−0.106698	+	0.994292i	$0.534028\pi$
$223$	−13.6554	+	23.6518i	−0.914430	+	1.58384i	−0.807733	+	0.589549i	$0.799306\pi$
$224$	5.61903	+	5.57877i	0.375437	+	0.372747i
$225$	1.49596	+	2.59108i	0.0997309	+	0.172739i
$226$	1.23984	−	2.14746i	0.0824728	−	0.142847i
$227$	6.63255	−	11.4879i	0.440218	−	0.762480i	−0.557487	−	0.830185i	$-0.688235\pi$
$227$	6.63255	−	11.4879i	0.440218	−	0.762480i	0.997705	+	0.0677055i	$0.0215678\pi$
$228$	3.34322	−	5.79063i	0.221410	−	0.383494i
$229$	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
$231$	0.570981	−	2.16199i	0.0375678	−	0.142249i
$232$	−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	$0.121813\pi$
$234$	0.939365	−	0.0658076i	0.0614082	−	0.00430198i
$235$	−2.55837	−	4.43122i	−0.166890	−	0.289061i
$236$	9.69565	+	16.7934i	0.631133	+	1.09315i
$237$	−5.76141	+	9.97906i	−0.374244	+	0.648210i
$238$	0.899240	−	3.40493i	0.0582891	−	0.220709i
$239$	−3.42707			−0.221679			−0.110839	−	0.993838i	$-0.535354\pi$
$239$	−3.42707			−0.221679			−0.110839	+	0.993838i	$0.535354\pi$
$240$	−5.09490			−0.328875
$241$	−4.08170	+	7.06971i	−0.262925	+	0.455400i	−0.967018	−	0.254708i	$-0.918021\pi$
$241$	−4.08170	+	7.06971i	−0.262925	+	0.455400i	0.704093	+	0.710108i	$0.251354\pi$
$242$	−1.34316	−	2.32643i	−0.0863418	−	0.149548i
$243$	1.00000			0.0641500
$244$	3.22574	−	5.58714i	0.206507	−	0.357680i
$245$	−8.55462	+	5.02137i	−0.546534	+	0.320804i
$246$	−2.69688			−0.171946
$247$	5.46934	−	11.2175i	0.348006	−	0.713750i
$248$	2.25416	+	3.90431i	0.143139	+	0.247924i
$249$	6.17262			0.391174
$250$	1.47889	+	2.56152i	0.0935335	+	0.162005i
$251$	−12.9962	−	22.5101i	−0.820315	−	1.42083i	−0.905448	−	0.424458i	$-0.860465\pi$
$251$	−12.9962	−	22.5101i	−0.820315	−	1.42083i	0.0851323	−	0.996370i	$-0.472869\pi$
$252$	3.62702	+	3.60103i	0.228481	+	0.226844i
$253$	3.89112	+	6.73962i	0.244633	+	0.423716i
$254$	2.38858			0.149873
$255$	3.61106	+	6.25453i	0.226133	+	0.391674i
$256$	−5.40895	+	9.36857i	−0.338059	+	0.585536i
$257$	−2.96659	−	5.13829i	−0.185051	−	0.320518i	0.758543	−	0.651623i	$-0.225912\pi$
$257$	−2.96659	−	5.13829i	−0.185051	−	0.320518i	−0.943594	+	0.331106i	$0.892578\pi$
$258$	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
$262$	0.0913181			0.00564165
$263$	4.10353			0.253034			0.126517	−	0.991964i	$-0.459620\pi$
$263$	4.10353			0.253034			0.126517	+	0.991964i	$0.459620\pi$
$264$	−0.867884			−0.0534146
$265$	−3.06852			−0.188498
$266$	−2.30798	+	0.627324i	−0.141512	+	0.0384637i
$267$	3.11475	+	5.39490i	0.190619	+	0.330162i
$268$	−3.38645	+	5.86550i	−0.206860	+	0.358293i
$269$	5.46635	−	9.46799i	0.333289	−	0.577274i	−0.649866	−	0.760049i	$-0.725175\pi$
$269$	5.46635	−	9.46799i	0.333289	−	0.577274i	0.983155	+	0.182775i	$0.0585081\pi$
$270$	0.370097			0.0225234
$271$	−9.05504	−	15.6838i	−0.550055	−	0.952723i	−0.998270	−	0.0587971i	$-0.981273\pi$
$271$	−9.05504	−	15.6838i	−0.550055	−	0.952723i	0.448215	−	0.893926i	$-0.352060\pi$
$272$	18.3240			1.11106
$273$	7.22272	+	6.23156i	0.437139	+	0.377151i
$274$	5.94288			0.359022
$275$	−1.26435	−	2.18991i	−0.0762430	−	0.132057i
$276$	−17.7877			−1.07069
$277$	3.59555	−	6.22767i	0.216036	−	0.374185i	−0.737557	−	0.675285i	$-0.764021\pi$
$277$	3.59555	−	6.22767i	0.216036	−	0.374185i	0.953592	+	0.301100i	$0.0973540\pi$
$278$	−1.14437	+	1.98211i	−0.0686349	+	0.118879i
$279$	2.19517	+	3.80215i	0.131421	+	0.227629i
$280$	2.73209	+	2.71252i	0.163274	+	0.162104i
$281$	−5.53072			−0.329935			−0.164968	−	0.986299i	$-0.552752\pi$
$281$	−5.53072			−0.329935			−0.164968	+	0.986299i	$0.552752\pi$
$282$	0.943037			0.0561570
$283$	−0.499391			−0.0296857			−0.0148429	−	0.999890i	$-0.504725\pi$
$283$	−0.499391			−0.0296857			−0.0148429	+	0.999890i	$0.504725\pi$
$284$	−24.9573			−1.48095
$285$	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
$289$	−4.48729	−	7.77221i	−0.263958	−	0.457189i
$290$	−1.48848	+	2.57813i	−0.0874067	+	0.151393i
$291$	−0.165103	−	0.285966i	−0.00967849	−	0.0167636i
$292$	−0.227504			−0.0133137
$293$	3.68051	+	6.37484i	0.215018	+	0.372422i	0.953278	−	0.302094i	$-0.0976857\pi$
$293$	3.68051	+	6.37484i	0.215018	+	0.372422i	−0.738260	+	0.674516i	$0.764352\pi$
$294$	−0.0131454	−	1.82815i	−0.000766657	−	0.106620i
$295$	7.11225	+	12.3188i	0.414091	+	0.717227i
$296$	4.82367	+	8.35485i	0.280370	+	0.485616i
$297$	−0.845173			−0.0490419
$298$	0.693315	+	1.20086i	0.0401627	+	0.0695638i
$299$	−33.1183	+	2.32012i	−1.91528	+	0.134176i
$300$	5.77977			0.333695
$301$	27.2342	−	7.40242i	1.56975	−	0.426668i
$302$	−0.508752	+	0.881184i	−0.0292754	+	0.0507064i
$303$	13.5117			0.776228
$304$	−6.22231	−	10.7774i	−0.356874	−	0.618124i
$305$	2.36624	−	4.09845i	0.135491	−	0.234676i
$306$	−1.33107			−0.0760920
$307$	−19.1859			−1.09500			−0.547500	−	0.836806i	$-0.684420\pi$
$307$	−19.1859			−1.09500			−0.547500	+	0.836806i	$0.684420\pi$
$308$	−3.06546	−	3.04349i	−0.174671	−	0.173419i
$309$	7.11519	−	12.3239i	0.404769	−	0.701080i
$310$	0.812426	+	1.40716i	0.0461427	+	0.0799215i
$311$	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	$0.519500\pi$
$312$	1.62262	−	3.32794i	0.0918625	−	0.188407i
$313$	−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
$315$	2.66060	+	2.64154i	0.149908	+	0.148834i
$316$	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	$0.0896655\pi$
$318$	0.282771	−	0.489774i	0.0158570	−	0.0274651i
$319$	3.39918	−	5.88755i	0.190317	−	0.329639i
$320$	−4.54110	+	7.86541i	−0.253855	+	0.439690i
$321$	1.03674	+	1.79569i	0.0578654	+	0.100226i
$322$	4.51517	+	4.48282i	0.251621	+	0.249818i
$323$	−8.82023	+	15.2771i	−0.490771	+	0.850040i
$324$	0.965895	−	1.67298i	0.0536608	−	0.0929433i
$325$	10.7612	−	0.753879i	0.596922	−	0.0418177i
$326$	−0.244455	−	0.423409i	−0.0135391	−	0.0234505i
$327$	−1.87364	−	3.24524i	−0.103612	−	0.179462i
$328$	−5.30177	+	9.18294i	−0.292741	+	0.507043i
$329$	6.77943	+	6.73085i	0.373762	+	0.371084i
$330$	−0.312796			−0.0172189
$331$	−1.74655			−0.0959993			−0.0479996	−	0.998847i	$-0.515285\pi$
$331$	−1.74655			−0.0959993			−0.0479996	+	0.998847i	$0.515285\pi$
$332$	5.96210	−	10.3267i	0.327213	−	0.566749i
$333$	4.69745	+	8.13622i	0.257419	+	0.445862i
$334$	1.14320			0.0625533
$335$	−2.48413	+	4.30264i	−0.135723	+	0.235079i
$336$	9.17947	−	2.49504i	0.500781	−	0.136115i
$337$	−1.36849			−0.0745462			−0.0372731	−	0.999305i	$-0.511867\pi$
$337$	−1.36849			−0.0745462			−0.0372731	+	0.999305i	$0.511867\pi$
$338$	1.27107	−	3.14833i	0.0691370	−	0.171246i
$339$	−4.74722	−	8.22242i	−0.257833	−	0.446581i
$340$	13.9516			0.756632
$341$	−1.85530	−	3.21347i	−0.100470	−	0.174019i
$342$	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
$345$	−13.0481			−0.702489
$346$	0.547691	+	0.948629i	0.0294440	+	0.0509986i
$347$	3.55189	−	6.15205i	0.190675	−	0.330259i	−0.754799	−	0.655956i	$-0.772266\pi$
$347$	3.55189	−	6.15205i	0.190675	−	0.330259i	0.945474	+	0.325697i	$0.105599\pi$
$348$	7.76941	+	13.4570i	0.416484	+	0.721371i
$349$	7.07469	−	12.2537i	0.378699	−	0.655927i	−0.612174	−	0.790723i	$-0.709705\pi$
$349$	7.07469	−	12.2537i	0.378699	−	0.655927i	0.990873	+	0.134797i	$0.0430381\pi$
$350$	−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
$353$	−29.4647			−1.56825			−0.784123	−	0.620606i	$-0.786887\pi$
$353$	−29.4647			−1.56825			−0.784123	+	0.620606i	$0.786887\pi$
$354$	−2.62164			−0.139339
$355$	−18.3075			−0.971660
$356$	12.0341			0.637804
$357$	−9.56895	−	9.50039i	−0.506442	−	0.502814i
$358$	−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	$0.0161636\pi$
$360$	0.727572	−	1.26019i	0.0383464	−	0.0664179i
$361$	−7.01960			−0.369453
$362$	−1.13575	−	1.96717i	−0.0596935	−	0.103392i
$363$	−10.2857			−0.539858
$364$	17.4016	−	6.06443i	0.912094	−	0.317863i
$365$	−0.166886			−0.00873519
$366$	0.436108	+	0.755362i	0.0227958	+	0.0394834i
$367$	2.61213			0.136352			0.0681760	−	0.997673i	$-0.478282\pi$
$367$	2.61213			0.136352			0.0681760	+	0.997673i	$0.478282\pi$
$368$	−16.5529	+	28.6705i	−0.862881	+	1.49455i
$369$	−5.16304	+	8.94264i	−0.268777	+	0.465535i
$370$	1.73851	+	3.01119i	0.0903809	+	0.156544i
$371$	5.52854	−	1.50269i	0.287028	−	0.0780159i
$372$	8.48121			0.439730
$373$	22.2997			1.15463			0.577317	−	0.816520i	$-0.304100\pi$
$373$	22.2997			1.15463			0.577317	+	0.816520i	$0.304100\pi$
$374$	1.12498			0.0581714
$375$	11.3251			0.584825
$376$	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	−0.769316	−	0.638868i	$-0.779403\pi$
$379$	3.28264	−	5.68571i	0.168618	−	0.292055i	0.937934	+	0.346813i	$0.112736\pi$
$380$	−4.73757	−	8.20570i	−0.243032	−	0.420944i
$381$	4.57282	−	7.92035i	0.234272	−	0.405772i
$382$	1.75517	+	3.04004i	0.0898022	+	0.155542i
$383$	−6.33493			−0.323700			−0.161850	−	0.986815i	$-0.551746\pi$
$383$	−6.33493			−0.323700			−0.161850	+	0.986815i	$0.551746\pi$
$384$	−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
$387$	−5.33350	−	9.23790i	−0.271117	−	0.469589i
$388$	−0.637887			−0.0323838
$389$	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	$0.694385\pi$
$390$	0.584810	−	1.19943i	0.0296130	−	0.0607354i
$391$	46.9281			2.37326
$392$	−6.25076	−	3.54920i	−0.315711	−	0.179261i
$393$	0.174824	−	0.302804i	0.00881871	−	0.0152745i
$394$	−3.69028			−0.185914
$395$	8.16430	+	14.1410i	0.410790	+	0.711510i
$396$	−0.816348	+	1.41396i	−0.0410231	+	0.0710540i
$397$	−25.6049			−1.28507			−0.642536	−	0.766256i	$-0.722118\pi$
$397$	−25.6049			−1.28507			−0.642536	+	0.766256i	$0.722118\pi$
$398$	4.15588			0.208315
$399$	−2.33836	+	8.85409i	−0.117064	+	0.443259i
$400$	5.37857	−	9.31596i	0.268928	−	0.465798i
$401$	13.3150	+	23.0623i	0.664921	+	1.15168i	0.979307	+	0.202382i	$0.0648682\pi$
$401$	13.3150	+	23.0623i	0.664921	+	1.15168i	−0.314385	+	0.949295i	$0.601798\pi$
$402$	−0.457837	−	0.792996i	−0.0228348	−	0.0395511i
$403$	15.7909	−	1.10624i	0.786601	−	0.0551057i
$404$	13.0509	−	22.6048i	0.649306	−	1.12463i
$405$	0.708533	−	1.22721i	0.0352073	−	0.0609808i
$406$	1.41925	−	5.37393i	0.0704363	−	0.266704i
$407$	−3.97016	−	6.87652i	−0.196793	−	0.340856i
$408$	−2.61674	+	4.53232i	−0.129548	+	0.224383i
$409$	2.31452	−	4.00887i	0.114446	−	0.198226i	−0.803112	−	0.595828i	$-0.796824\pi$
$409$	2.31452	−	4.00887i	0.114446	−	0.198226i	0.917558	+	0.397602i	$0.130157\pi$
$410$	−1.91082	+	3.30964i	−0.0943689	+	0.163452i
$411$	11.3773	−	19.7061i	0.561203	−	0.972033i
$412$	−13.7450	−	23.8071i	−0.677170	−	1.17289i
$413$	−18.8468	−	18.7117i	−0.927389	−	0.920745i
$414$	1.20242	−	2.08264i	0.0590955	−	0.102356i
$415$	4.37350	−	7.57512i	0.214687	−	0.371848i
$416$	−6.03513	−	8.94498i	−0.295897	−	0.438564i
$417$	4.38169	+	7.58931i	0.214572	+	0.371650i
$418$	−0.382012	−	0.661664i	−0.0186848	−	0.0323631i
$419$	8.64392	−	14.9717i	0.422283	−	0.731416i	−0.573879	−	0.818940i	$-0.694562\pi$
$419$	8.64392	−	14.9717i	0.422283	−	0.731416i	0.996162	+	0.0875239i	$0.0278954\pi$
$420$	6.98910	−	1.89968i	0.341033	−	0.0926949i
$421$	−7.92499			−0.386241			−0.193120	−	0.981175i	$-0.561861\pi$
$421$	−7.92499			−0.386241			−0.193120	+	0.981175i	$0.561861\pi$
$422$	2.01109			0.0978986
$423$	1.80540	−	3.12704i	0.0877815	−	0.152042i
$424$	−1.11180	−	1.92569i	−0.0539936	−	0.0935196i
$425$	−15.2484			−0.739657
$426$	1.68707	−	2.92210i	0.0817390	−	0.141576i
$427$	−2.25619	+	8.54293i	−0.109184	+	0.413422i
$428$	4.00554			0.193615
$429$	−1.33550	+	2.73908i	−0.0644788	+	0.132244i
$430$	−1.97391	−	3.41892i	−0.0951906	−	0.164875i
$431$	−5.05786			−0.243628			−0.121814	−	0.992553i	$-0.538871\pi$
$431$	−5.05786			−0.243628			−0.121814	+	0.992553i	$0.538871\pi$
$432$	−1.79769	−	3.11370i	−0.0864916	−	0.149808i
$433$	−0.0476082	−	0.0824598i	−0.00228790	−	0.00396277i	0.864879	−	0.501980i	$-0.167395\pi$
$433$	−0.0476082	−	0.0824598i	−0.00228790	−	0.00396277i	−0.867167	+	0.498017i	$0.834062\pi$
$434$	−2.15285	−	2.13742i	−0.103340	−	0.102600i
$435$	5.69925	+	9.87140i	0.273258	+	0.473297i
$436$	−7.23895			−0.346683
$437$	−15.9355	−	27.6010i	−0.762296	−	1.32034i
$438$	0.0153789	−	0.0266370i	0.000734831	−	0.00127276i
$439$	−5.07127	−	8.78369i	−0.242038	−	0.419223i	0.719256	−	0.694745i	$-0.244483\pi$
$439$	−5.07127	−	8.78369i	−0.242038	−	0.419223i	−0.961295	+	0.275522i	$0.911149\pi$
$440$	−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	$0.171387\pi$
$444$	18.1490			0.861312
$445$	8.82760			0.418468
$446$	−7.13278			−0.337747
$447$	5.30927			0.251120
$448$	4.32989	−	16.3949i	0.204568	−	0.774587i
$449$	17.3597	+	30.0678i	0.819254	+	1.41899i	0.906233	+	0.422779i	$0.138945\pi$
$449$	17.3597	+	30.0678i	0.819254	+	1.41899i	−0.0869792	+	0.996210i	$0.527721\pi$
$450$	−0.390703	+	0.676717i	−0.0184179	+	0.0319007i
$451$	4.36366	−	7.55808i	0.205477	−	0.355896i
$452$	−18.3412			−0.862700
$453$	1.94796	+	3.37397i	0.0915232	+	0.158523i
$454$	3.46447			0.162595
$455$	12.7650	−	4.44857i	0.598432	−	0.208552i
$456$	3.55428			0.166444
$457$	−1.41232	−	2.44621i	−0.0660655	−	0.114429i	0.831101	−	0.556122i	$-0.187711\pi$
$457$	−1.41232	−	2.44621i	−0.0660655	−	0.114429i	−0.897166	+	0.441693i	$0.854378\pi$
$458$	2.67440			0.124967
$459$	−2.54826	+	4.41372i	−0.118943	+	0.206015i
$460$	−12.6031	+	21.8293i	−0.587624	+	1.01779i
$461$	12.3630	+	21.4134i	0.575804	+	0.997321i	0.995954	+	0.0898666i	$0.0286441\pi$
$461$	12.3630	+	21.4134i	0.575804	+	0.997321i	−0.420150	+	0.907455i	$0.638023\pi$
$462$	0.563563	−	0.153180i	0.0262193	−	0.00712658i
$463$	37.8124			1.75729			0.878646	−	0.477473i	$-0.158447\pi$
$463$	37.8124			1.75729			0.878646	+	0.477473i	$0.158447\pi$
$464$	28.9204			1.34260
$465$	6.22140			0.288511
$466$	1.11981			0.0518743
$467$	−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
$471$	−0.537376	−	0.930762i	−0.0247610	−	0.0428873i
$472$	−5.15387	+	8.92676i	−0.237226	+	0.410887i
$473$	4.50774	+	7.80763i	0.207266	+	0.358995i
$474$	−3.00943			−0.138228
$475$	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
$478$	−0.447526	−	0.775138i	−0.0204694	−	0.0354540i
$479$	−6.41820			−0.293255			−0.146627	−	0.989192i	$-0.546842\pi$
$479$	−6.41820			−0.293255			−0.146627	+	0.989192i	$0.546842\pi$
$480$	−2.12046	−	3.67275i	−0.0967855	−	0.167637i
$481$	33.7910	−	2.36724i	1.54074	−	0.107937i
$482$	−2.13205			−0.0971120
$483$	23.5088	−	6.38984i	1.06969	−	0.290748i
$484$	−9.93489	+	17.2077i	−0.451586	+	0.782169i
$485$	−0.467923			−0.0212473
$486$	0.130586	+	0.226181i	0.00592349	+	0.0102598i
$487$	−8.82309	+	15.2820i	−0.399812	+	0.692495i	−0.993702	−	0.112051i	$-0.964258\pi$
$487$	−8.82309	+	15.2820i	−0.399812	+	0.692495i	0.593890	+	0.804546i	$0.297591\pi$
$488$	3.42937			0.155240
$489$	−1.87199			−0.0846544
$490$	−2.25285	−	1.27917i	−0.101773	−	0.0577872i
$491$	−18.1979	+	31.5196i	−0.821258	+	1.42246i	0.0834876	+	0.996509i	$0.473394\pi$
$491$	−18.1979	+	31.5196i	−0.821258	+	1.42246i	−0.904746	+	0.425952i	$0.859939\pi$
$492$	9.97390	+	17.2753i	0.449658	+	0.778831i
$493$	−20.4976	−	35.5028i	−0.923164	−	1.59897i
$494$	3.25140	−	0.227778i	0.146287	−	0.0102482i
$495$	−0.598833	+	1.03721i	−0.0269155	+	0.0466191i
$496$	7.89249	−	13.6702i	0.354383	−	0.613810i
$497$	32.9845	−	8.96540i	1.47956	−	0.402153i
$498$	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	$0.325930\pi$
$500$	10.9388	−	18.9466i	0.489200	−	0.847319i
$501$	2.18861	−	3.79078i	0.0977798	−	0.169360i
$502$	3.39425	−	5.87901i	0.151493	−	0.262393i
$503$	−14.3812	−	24.9090i	−0.641226	−	1.11064i	−0.985159	−	0.171642i	$-0.945093\pi$
$503$	−14.3812	−	24.9090i	−0.641226	−	1.11064i	0.343933	−	0.938994i	$-0.388241\pi$
$504$	−0.693732	+	2.62678i	−0.0309013	+	0.117006i
$505$	9.57349	−	16.5818i	0.426015	−	0.737879i
$506$	−1.01625	+	1.76020i	−0.0451778	+	0.0782502i
$507$	−8.00622	−	10.2421i	−0.355569	−	0.454867i
$508$	−8.83372	−	15.3004i	−0.391933	−	0.678848i
$509$	−2.86440	−	4.96128i	−0.126962	−	0.219905i	0.795536	−	0.605906i	$-0.207189\pi$
$509$	−2.86440	−	4.96128i	−0.126962	−	0.219905i	−0.922498	+	0.386001i	$0.873856\pi$
$510$	−0.943104	+	1.63350i	−0.0417614	+	0.0723328i
$511$	0.300677	−	0.0817259i	0.0133012	−	0.00361534i
$512$	−18.1441			−0.801865
$513$	3.46127			0.152819
$514$	0.774789	−	1.34197i	0.0341745	−	0.0591919i
$515$	−10.0827	−	17.4637i	−0.444296	−	0.769543i
$516$	−20.6064			−0.907147
$517$	−1.52587	+	2.64289i	−0.0671079	+	0.116234i
$518$	−4.60689	−	4.57388i	−0.202415	−	0.200965i
$519$	4.19411			0.184101
$520$	−2.93441	−	4.34925i	−0.128683	−	0.190727i
$521$	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	$0.703571\pi$
$522$	−2.10080			−0.0919493
$523$	9.84953	+	17.0599i	0.430690	+	0.745977i	0.996933	−	0.0782615i	$-0.0249369\pi$
$523$	9.84953	+	17.0599i	0.430690	+	0.745977i	−0.566243	+	0.824238i	$0.691604\pi$
$524$	−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
$527$	−22.3755			−0.974692
$528$	1.51936	+	2.63161i	0.0661218	+	0.114526i
$529$	−30.8924	+	53.5072i	−1.34315	+	2.32640i
$530$	−0.400705	−	0.694041i	−0.0174055	−	0.0301472i
$531$	−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
$535$	2.93827			0.127032
$536$	−3.60023			−0.155506
$537$	−4.39817			−0.189795
$538$	2.85531			0.123101
$539$	5.14473	+	2.92119i	0.221599	+	0.125825i
$540$	−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	$0.919806\pi$
$542$	2.36492	−	4.09616i	0.101582	−	0.175945i
$543$	−8.69733			−0.373238
$544$	7.62633	+	13.2092i	0.326976	+	0.566339i
$545$	−5.31014			−0.227461
$546$	−0.466276	+	2.44740i	−0.0199548	+	0.104739i
$547$	−21.3915			−0.914635			−0.457318	−	0.889303i	$-0.651190\pi$
$547$	−21.3915			−0.914635			−0.457318	+	0.889303i	$0.651190\pi$
$548$	−21.9786	−	38.0681i	−0.938881	−	1.62619i
$549$	3.33963			0.142532
$550$	0.330212	−	0.571943i	0.0140803	−	0.0243877i
$551$	−13.9208	+	24.1115i	−0.593045	+	1.02718i
$552$	−4.72764	−	8.18852i	−0.201222	−	0.348527i
$553$	−21.6346	−	21.4796i	−0.919997	−	0.913405i
$554$	1.87811			0.0797932
$555$	13.3132			0.565113
$556$	16.9290			0.717950
$557$	7.34655			0.311283			0.155642	−	0.987814i	$-0.450255\pi$
$557$	7.34655			0.311283			0.155642	+	0.987814i	$0.450255\pi$
$558$	−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
$562$	−0.722233	−	1.25094i	−0.0304656	−	0.0527679i
$563$	−7.66606	+	13.2780i	−0.323086	+	0.559601i	−0.981123	−	0.193384i	$-0.938054\pi$
$563$	−7.66606	+	13.2780i	−0.323086	+	0.559601i	0.658037	+	0.752985i	$0.271387\pi$
$564$	−3.48765	−	6.04079i	−0.146857	−	0.254363i
$565$	−13.4542			−0.566024
$566$	−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
$569$	10.4136	+	18.0369i	0.436561	+	0.756146i	0.997422	−	0.0717646i	$-0.0228630\pi$
$569$	10.4136	+	18.0369i	0.436561	+	0.756146i	−0.560861	+	0.827910i	$0.689530\pi$
$570$	1.28101			0.0536554
$571$	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	$0.817295\pi$
$572$	3.29247	+	4.87993i	0.137665	+	0.204040i
$573$	13.4407			0.561494
$574$	1.82195	−	6.89873i	0.0760468	−	0.287947i
$575$	13.7746	−	23.8583i	0.574442	−	0.994962i
$576$	−6.40916			−0.267048
$577$	−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	$-0.454488\pi$
$578$	1.17195	−	2.02988i	0.0487468	−	0.0844319i
$579$	13.8808			0.576868
$580$	22.0195			0.914311
$581$	−4.17009	+	15.7898i	−0.173004	+	0.655072i
$582$	0.0431201	−	0.0746862i	0.00178739	−	0.00309584i
$583$	0.915071	+	1.58495i	0.0378984	+	0.0656419i
$584$	−0.0604665	−	0.104731i	−0.00250212	−	0.00433380i
$585$	−2.85763	−	4.23544i	−0.118148	−	0.175114i
$586$	−0.961245	+	1.66492i	−0.0397087	+	0.0687774i
$587$	−22.6783	+	39.2799i	−0.936032	+	1.62125i	−0.163248	+	0.986585i	$0.552197\pi$
$587$	−22.6783	+	39.2799i	−0.936032	+	1.62125i	−0.772784	+	0.634669i	$0.781136\pi$
$588$	−11.6619	+	6.84529i	−0.480930	+	0.282295i
$589$	7.59808	+	13.1603i	0.313073	+	0.542259i
$590$	−1.85752	+	3.21731i	−0.0764727	+	0.132455i
$591$	−7.06487	+	12.2367i	−0.290610	+	0.503351i
$592$	16.8892	−	29.2529i	0.694140	−	1.20229i
$593$	−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
$595$	−18.4389	+	5.01181i	−0.755922	+	0.205464i
$596$	5.12820	−	8.88230i	0.210059	−	0.363833i
$597$	7.95622	−	13.7806i	0.325626	−	0.564002i
$598$	−4.84954	−	7.18775i	−0.198312	−	0.293929i
$599$	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	$0.830947\pi$
$600$	1.53616	+	2.66071i	0.0627135	+	0.108623i
$601$	−11.9288	+	20.6612i	−0.486584	+	0.842788i	−0.999881	−	0.0154227i	$-0.995091\pi$
$601$	−11.9288	+	20.6612i	−0.486584	+	0.842788i	0.513297	+	0.858211i	$0.328424\pi$
$602$	5.23068	+	5.19320i	0.213187	+	0.211659i
$603$	−3.50602			−0.142776
$604$	7.52610			0.306233
$605$	−7.28774	+	12.6227i	−0.296289	+	0.513187i
$606$	1.76444	+	3.05609i	0.0716754	+	0.124145i
$607$	−5.86858			−0.238198			−0.119099	−	0.992882i	$-0.538001\pi$
$607$	−5.86858			−0.238198			−0.119099	+	0.992882i	$0.538001\pi$
$608$	5.17937	−	8.97093i	0.210051	−	0.363819i
$609$	−15.1025	−	14.9943i	−0.611983	−	0.607598i
$610$	1.23599			0.0500437
$611$	−7.28147	−	10.7922i	−0.294577	−	0.436607i
$612$	4.92271	+	8.52638i	0.198989	+	0.344658i
$613$	22.3547			0.902896			0.451448	−	0.892297i	$-0.350908\pi$
$613$	22.3547			0.902896			0.451448	+	0.892297i	$0.350908\pi$
$614$	−2.50541	−	4.33950i	−0.101110	−	0.175128i
$615$	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	0.515655	−	0.856797i	$-0.327549\pi$
$617$	−12.0268	−	20.8310i	−0.484180	−	0.838625i	−0.999835	+	0.0181717i	$0.994215\pi$
$618$	3.71657			0.149502
$619$	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	$0.673104\pi$
$620$	6.00922	−	10.4083i	0.241336	−	0.418006i
$621$	−4.60393	−	7.97424i	−0.184749	−	0.319995i
$622$	−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
$626$	−4.10587			−0.164103
$627$	−2.92537			−0.116828
$628$	−2.07619			−0.0828491
$629$	−47.8813			−1.90915
$630$	−0.250030	+	0.946725i	−0.00996142	+	0.0377184i
$631$	2.22088	+	3.84667i	0.0884117	+	0.153134i	0.906840	−	0.421475i	$-0.138488\pi$
$631$	2.22088	+	3.84667i	0.0884117	+	0.153134i	−0.818428	+	0.574609i	$0.805154\pi$
$632$	−5.91623	+	10.2472i	−0.235335	+	0.407612i
$633$	3.85014	−	6.66864i	0.153029	−	0.265055i
$634$	2.22786			0.0884797
$635$	−6.47998	−	11.2237i	−0.257150	−	0.445397i
$636$	−4.18311			−0.165871
$637$	−20.8201	+	14.2661i	−0.824923	+	0.565245i
$638$	1.77554			0.0702941
$639$	−6.45964	−	11.1884i	−0.255540	−	0.442608i
$640$	−10.8539			−0.429037
$641$	4.77649	−	8.27312i	0.188660	−	0.326769i	−0.756144	−	0.654406i	$-0.772919\pi$
$641$	4.77649	−	8.27312i	0.188660	−	0.326769i	0.944804	+	0.327637i	$0.106252\pi$
$642$	−0.270768	+	0.468984i	−0.0106864	+	0.0185093i
$643$	10.6560	+	18.4567i	0.420232	+	0.727863i	0.995962	−	0.0897769i	$-0.0286154\pi$
$643$	10.6560	+	18.4567i	0.420232	+	0.727863i	−0.575730	+	0.817640i	$0.695282\pi$
$644$	12.0170	−	45.5016i	0.473534	−	1.79302i
$645$	−15.1159			−0.595186
$646$	−4.60718			−0.181267
$647$	30.5481			1.20097			0.600486	−	0.799636i	$-0.294974\pi$
$647$	30.5481			1.20097			0.600486	+	0.799636i	$0.294974\pi$
$648$	1.02687			0.0403393
$649$	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
$653$	−17.4675	−	30.2546i	−0.683557	−	1.18396i	−0.973888	−	0.227029i	$-0.927099\pi$
$653$	−17.4675	−	30.2546i	−0.683557	−	1.18396i	0.290331	−	0.956926i	$-0.406235\pi$
$654$	0.489341	−	0.847563i	0.0191347	−	0.0331424i
$655$	−0.247737	−	0.429093i	−0.00967989	−	0.0167661i
$656$	37.1263			1.44954
$657$	−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	−0.999985	−	0.00539457i	$-0.998283\pi$
$659$	−12.9552	−	22.4391i	−0.504665	−	0.874105i	0.495321	−	0.868710i	$-0.335050\pi$
$660$	1.15682	+	2.00367i	0.0450291	+	0.0779927i
$661$	18.3711			0.714552			0.357276	−	0.933999i	$-0.383706\pi$
$661$	18.3711			0.714552			0.357276	+	0.933999i	$0.383706\pi$
$662$	−0.228075	−	0.395037i	−0.00886439	−	0.0153536i
$663$	10.2776	+	15.2329i	0.399147	+	0.591597i
$664$	6.33848			0.245981
$665$	9.20906	+	9.14308i	0.357112	+	0.354553i
$666$	−1.22684	+	2.12495i	−0.0475391	+	0.0823401i
$667$	74.0657			2.86783
$668$	−4.22793	−	7.32299i	−0.163584	−	0.283335i
$669$	−13.6554	+	23.6518i	−0.527947	+	0.914430i
$670$	−1.29757			−0.0501295
$671$	−2.82257			−0.108964
$672$	5.61903	+	5.57877i	0.216759	+	0.215206i
$673$	−11.2401	+	19.4684i	−0.433273	+	0.750450i	−0.997153	−	0.0754063i	$-0.975975\pi$
$673$	−11.2401	+	19.4684i	−0.433273	+	0.750450i	0.563880	+	0.825857i	$0.309308\pi$
$674$	−0.178705	−	0.309526i	−0.00688345	−	0.0119225i
$675$	1.49596	+	2.59108i	0.0575796	+	0.0997309i
$676$	−24.8680	+	3.50146i	−0.956460	+	0.134672i
$677$	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
$679$	0.843054	−	0.229147i	0.0323535	−	0.00879387i
$680$	3.70809	+	6.42260i	0.142199	+	0.246295i
$681$	6.63255	−	11.4879i	0.254160	−	0.440218i
$682$	0.484551	−	0.839267i	0.0185544	−	0.0321372i
$683$	−1.84265	+	3.19156i	−0.0705071	+	0.122122i	−0.899124	−	0.437695i	$-0.855795\pi$
$683$	−1.84265	+	3.19156i	−0.0705071	+	0.122122i	0.828617	+	0.559817i	$0.189128\pi$
$684$	3.34322	−	5.79063i	0.127831	−	0.221410i
$685$	−16.1224	−	27.9249i	−0.616007	−	1.06696i
$686$	4.68538	+	1.20143i	0.178889	+	0.0458710i
$687$	5.12001	−	8.86812i	0.195341	−	0.338340i
$688$	−19.1760	+	33.2139i	−0.731079	+	1.26627i
$689$	−7.78839	+	0.545620i	−0.296714	+	0.0207864i
$690$	−1.70390	−	2.95124i	−0.0648664	−	0.112352i
$691$	−12.5680	−	21.7685i	−0.478111	−	0.828112i	0.521575	−	0.853206i	$-0.325345\pi$
$691$	−12.5680	−	21.7685i	−0.478111	−	0.828112i	−0.999685	+	0.0250939i	$0.992012\pi$
$692$	4.05107	−	7.01666i	0.153999	−	0.266733i
$693$	0.570981	−	2.16199i	0.0216898	−	0.0821273i
$694$	1.85530			0.0704263
$695$	12.4183			0.471052
$696$	−4.12994	+	7.15327i	−0.156545	+	0.271144i
$697$	−26.3136	−	45.5764i	−0.996697	−	1.72633i
$698$	3.69541			0.139873
$699$	2.14383	−	3.71322i	0.0810870	−	0.140447i
$700$	−3.90469	+	14.7849i	−0.147583	+	0.558817i
$701$	12.8909			0.486882			0.243441	−	0.969916i	$-0.421724\pi$
$701$	12.8909			0.486882			0.243441	+	0.969916i	$0.421724\pi$
$702$	0.939365	−	0.0658076i	0.0354540	−	0.00248375i
$703$	16.2591	+	28.1617i	0.613225	+	1.06214i
$704$	5.41685			0.204155
$705$	−2.55837	−	4.43122i	−0.0963537	−	0.166890i
$706$	−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
$709$	−17.7805			−0.667760			−0.333880	−	0.942616i	$-0.608358\pi$
$709$	−17.7805			−0.667760			−0.333880	+	0.942616i	$0.608358\pi$
$710$	−2.39069	−	4.14080i	−0.0897212	−	0.155402i
$711$	−5.76141	+	9.97906i	−0.216070	+	0.374244i
$712$	3.19844	+	5.53987i	0.119867	+	0.207615i
$713$	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
$717$	−3.42707			−0.127986
$718$	4.50707			0.168202
$719$	46.0760			1.71835			0.859173	−	0.511686i	$-0.170979\pi$
$719$	46.0760			1.71835			0.859173	+	0.511686i	$0.170979\pi$
$720$	−5.09490			−0.189876
$721$	26.7181	+	26.5267i	0.995035	+	0.987906i
$722$	−0.916660	−	1.58770i	−0.0341146	−	0.0590881i
$723$	−4.08170	+	7.06971i	−0.151800	+	0.262925i
$724$	−8.40071	+	14.5505i	−0.312210	+	0.540763i
$725$	−24.0663			−0.893799
$726$	−1.34316	−	2.32643i	−0.0498495	−	0.0863418i
$727$	31.3066			1.16110			0.580548	−	0.814226i	$-0.302838\pi$
$727$	31.3066			1.16110			0.580548	+	0.814226i	$0.302838\pi$
$728$	7.41680	+	6.39900i	0.274885	+	0.237163i
$729$	1.00000			0.0370370
$730$	−0.0217929	−	0.0377464i	−0.000806590	−	0.00139706i
$731$	54.3647			2.01075
$732$	3.22574	−	5.58714i	0.119227	−	0.206507i
$733$	−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
$735$	−8.55462	+	5.02137i	−0.315542	+	0.185216i
$736$	−27.5569			−1.01576
$737$	2.96320			0.109151
$738$	−2.69688			−0.0992734
$739$	−12.2681			−0.451289			−0.225645	−	0.974210i	$-0.572449\pi$
$739$	−12.2681			−0.451289			−0.225645	+	0.974210i	$0.572449\pi$
$740$	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	−0.460920	−	0.887442i	$-0.652481\pi$
$743$	14.6672	−	25.4043i	0.538087	−	0.931994i	0.999007	−	0.0445521i	$-0.0141861\pi$
$744$	2.25416	+	3.90431i	0.0826414	+	0.143139i
$745$	3.76179	−	6.51562i	0.137821	−	0.238714i
$746$	2.91202	+	5.04377i	0.106617	+	0.184665i
$747$	6.17262			0.225844
$748$	−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
$751$	−13.3113	−	23.0558i	−0.485736	−	0.841320i	0.514129	−	0.857713i	$-0.328115\pi$
$751$	−13.3113	−	23.0558i	−0.485736	−	0.841320i	−0.999866	+	0.0163929i	$0.994782\pi$
$752$	−12.9822			−0.473413
$753$	−12.9962	−	22.5101i	−0.473609	−	0.820315i
$754$	−3.31958	+	6.80836i	−0.120892	+	0.247946i
$755$	5.52078			0.200922
$756$	3.62702	+	3.60103i	0.131913	+	0.130968i
$757$	21.2671	−	36.8357i	0.772966	−	1.33882i	−0.162965	−	0.986632i	$-0.552106\pi$
$757$	21.2671	−	36.8357i	0.772966	−	1.33882i	0.935931	−	0.352184i	$-0.114561\pi$
$758$	1.71467			0.0622794
$759$	3.89112	+	6.73962i	0.141239	+	0.244633i
$760$	2.51832	−	4.36186i	0.0913492	−	0.158221i
$761$	36.6523			1.32864			0.664322	−	0.747446i	$-0.268720\pi$
$761$	36.6523			1.32864			0.664322	+	0.747446i	$0.268720\pi$
$762$	2.38858			0.0865290
$763$	9.56726	−	2.60044i	0.346358	−	0.0941422i
$764$	12.9823	−	22.4861i	0.469684	−	0.813517i
$765$	3.61106	+	6.25453i	0.130558	+	0.226133i
$766$	−0.827251	−	1.43284i	−0.0298898	−	0.0517707i
$767$	20.2424	+	30.0024i	0.730912	+	1.08332i
$768$	−5.40895	+	9.36857i	−0.195179	+	0.338059i
$769$	13.7781	−	23.8644i	0.496853	−	0.860574i	−0.503141	−	0.864204i	$-0.667822\pi$
$769$	13.7781	−	23.8644i	0.496853	−	0.860574i	0.999993	+	0.00363055i	$0.00115564\pi$
$770$	0.211318	−	0.800146i	0.00761538	−	0.0288353i
$771$	−2.96659	−	5.13829i	−0.106839	−	0.185051i
$772$	13.4074	−	23.2224i	0.482544	−	0.835791i
$773$	−8.02069	+	13.8922i	−0.288484	+	0.499669i	−0.973448	−	0.228908i	$-0.926485\pi$
$773$	−8.02069	+	13.8922i	−0.288484	+	0.499669i	0.684964	+	0.728577i	$0.259818\pi$
$774$	1.39296	−	2.41268i	0.0500689	−	0.0867218i
$775$	−6.56779	+	11.3757i	−0.235922	+	0.408629i
$776$	−0.169539	−	0.293650i	−0.00608610	−	0.0105414i
$777$	−23.9863	+	6.51963i	−0.860504	+	0.233890i
$778$	−2.17782	+	3.77210i	−0.0780788	+	0.135236i
$779$	−17.8707	+	30.9529i	−0.640283	+	1.10900i
$780$	−9.84596	+	0.689764i	−0.352542	+	0.0246975i
$781$	5.45952	+	9.45616i	0.195357	+	0.338368i
$782$	6.12814	+	10.6143i	0.219142	+	0.379565i
$783$	−4.02187	+	6.96608i	−0.143730	+	0.248948i
$784$	0.180965	+	25.1671i	0.00646304	+	0.898824i
$785$	−1.52299			−0.0543580
$786$	0.0913181			0.00325721
$787$	−23.8051	+	41.2316i	−0.848559	+	1.46975i	0.0339358	+	0.999424i	$0.489196\pi$
$787$	−23.8051	+	41.2316i	−0.848559	+	1.46975i	−0.882494	+	0.470323i	$0.844138\pi$
$788$	13.6478	+	23.6387i	0.486184	+	0.842095i
$789$	4.10353			0.146090
$790$	−2.13228	+	3.69322i	−0.0758632	+	0.131399i
$791$	24.2404	−	6.58870i	0.861891	−	0.234267i
$792$	−0.867884			−0.0308389
$793$	5.27714	−	10.8233i	0.187397	−	0.384345i
$794$	−3.34363	−	5.79134i	−0.118661	−	0.205527i
$795$	−3.06852			−0.108829
$796$	−15.3697	−	26.6212i	−0.544766	−	0.943563i
$797$	23.0425	+	39.9107i	0.816206	+	1.41371i	0.908459	+	0.417974i	$0.137260\pi$
$797$	23.0425	+	39.9107i	0.816206	+	1.41371i	−0.0922533	+	0.995736i	$0.529407\pi$
$798$	−2.30798	+	0.627324i	−0.0817017	+	0.0222070i
$799$	9.20126	+	15.9371i	0.325517	+	0.563812i
$800$	8.95410			0.316575
$801$	3.11475	+	5.39490i	0.110054	+	0.190619i
$802$	−3.47751	+	6.02322i	−0.122795	+	0.212687i
$803$	0.0497674	+	0.0861996i	0.00175625	+	0.00304192i
$804$	−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
$808$	13.8748			0.488113
$809$	24.6755			0.867546			0.433773	−	0.901022i	$-0.357182\pi$
$809$	24.6755			0.867546			0.433773	+	0.901022i	$0.357182\pi$
$810$	0.370097			0.0130039
$811$	−49.5770			−1.74088			−0.870442	−	0.492270i	$-0.836167\pi$
$811$	−49.5770			−1.74088			−0.870442	+	0.492270i	$0.836167\pi$
$812$	−39.6725	+	10.7832i	−1.39223	+	0.378417i
$813$	−9.05504	−	15.6838i	−0.317574	−	0.550055i
$814$	1.03689	−	1.79595i	0.0363430	−	0.0629480i
$815$	−1.32637	+	2.29733i	−0.0464606	+	0.0804721i
$816$	18.3240			0.641468
$817$	−18.4607	−	31.9749i	−0.645858	−	1.11866i
$818$	1.20897			0.0422708
$819$	7.22272	+	6.23156i	0.252382	+	0.217748i
$820$	28.2673			0.987138
$821$	−19.7634	−	34.2312i	−0.689748	−	1.19468i	−0.971919	−	0.235314i	$-0.924388\pi$
$821$	−19.7634	−	34.2312i	−0.689748	−	1.19468i	0.282172	−	0.959364i	$-0.408945\pi$
$822$	5.94288			0.207282
$823$	−3.39797	+	5.88546i	−0.118446	+	0.205154i	−0.919152	−	0.393903i	$-0.871125\pi$
$823$	−3.39797	+	5.88546i	−0.118446	+	0.205154i	0.800706	+	0.599057i	$0.204458\pi$
$824$	7.30638	−	12.6550i	0.254530	−	0.440858i
$825$	−1.26435	−	2.18991i	−0.0440189	−	0.0762430i
$826$	1.77112	−	6.70627i	0.0616252	−	0.233341i
$827$	6.29136			0.218772			0.109386	−	0.993999i	$-0.465112\pi$
$827$	6.29136			0.218772			0.109386	+	0.993999i	$0.465112\pi$
$828$	−17.7877			−0.618164
$829$	−21.3488			−0.741475			−0.370737	−	0.928738i	$-0.620895\pi$
$829$	−21.3488			−0.741475			−0.370737	+	0.928738i	$0.620895\pi$
$830$	2.28447			0.0792950
$831$	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
$835$	−3.10140	−	5.37178i	−0.107328	−	0.185898i
$836$	−2.82560	+	4.89409i	−0.0977255	+	0.169266i
$837$	2.19517	+	3.80215i	0.0758762	+	0.131421i
$838$	4.51509			0.155971
$839$	−0.123635	−	0.214141i	−0.00426834	−	0.00739299i	0.863883	−	0.503692i	$-0.168025\pi$
$839$	−0.123635	−	0.214141i	−0.00426834	−	0.00739299i	−0.868152	+	0.496299i	$0.834692\pi$
$840$	2.73209	+	2.71252i	0.0942662	+	0.0935908i
$841$	−17.8509	−	30.9186i	−0.615548	−	1.06616i
$842$	−1.03489	−	1.79248i	−0.0356647	−	0.0617731i
$843$	−5.53072			−0.190488
$844$	−7.43767	−	12.8824i	−0.256015	−	0.443431i
$845$	−18.2419	+	2.56850i	−0.627541	+	0.0883590i
$846$	0.943037			0.0324223
$847$	6.94879	−	26.3112i	0.238763	−	0.904065i
$848$	−3.89274	+	6.74242i	−0.133677	+	0.231536i
$849$	−0.499391			−0.0171391
$850$	−1.99123	−	3.44891i	−0.0682985	−	0.118296i
$851$	43.2535	−	74.9172i	1.48271	−	2.56813i
$852$	−24.9573			−0.855025
$853$	18.7494			0.641968			0.320984	−	0.947085i	$-0.395986\pi$
$853$	18.7494			0.641968			0.320984	+	0.947085i	$0.395986\pi$
$854$	−2.22688	+	0.605279i	−0.0762021	+	0.0207122i
$855$	2.45242	−	4.24772i	0.0838711	−	0.145269i
$856$	1.06460	+	1.84395i	0.0363874	+	0.0630248i
$857$	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	$0.750053\pi$
$858$	−0.793926	+	0.0556189i	−0.0271042	+	0.00189880i
$859$	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
$861$	−19.3876	−	19.2487i	−0.660729	−	0.655995i
$862$	−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	$0.0837157\pi$
$864$	1.49638	−	2.59180i	0.0509078	−	0.0881749i
$865$	2.97166	−	5.14707i	0.101040	−	0.175006i
$866$	0.0124339	−	0.0215362i	0.000422521	−	0.000731828i
$867$	−4.48729	−	7.77221i	−0.152396	−	0.263958i
$868$	−5.72973	+	21.6953i	−0.194480	+	0.736387i
$869$	4.86939	−	8.43404i	0.165183	−	0.286105i
$870$	−1.48848	+	2.57813i	−0.0504643	+	0.0874067i
$871$	−5.54006	+	11.3625i	−0.187718	+	0.385004i
$872$	−1.92399	−	3.33244i	−0.0651544	−	0.112851i
$873$	−0.165103	−	0.285966i	−0.00558788	−	0.00967849i
$874$	4.16189	−	7.20860i	0.140778	−	0.243834i
$875$	−7.65098	+	28.9701i	−0.258650	+	0.979367i
$876$	−0.227504			−0.00768664
$877$	−41.3916			−1.39769			−0.698847	−	0.715271i	$-0.746303\pi$
$877$	−41.3916			−1.39769			−0.698847	+	0.715271i	$0.746303\pi$
$878$	1.32447	−	2.29405i	0.0446987	−	0.0774204i
$879$	3.68051	+	6.37484i	0.124141	+	0.215018i
$880$	4.30608			0.145158
$881$	−1.68361	+	2.91610i	−0.0567224	+	0.0982461i	−0.892992	−	0.450072i	$-0.851398\pi$
$881$	−1.68361	+	2.91610i	−0.0567224	+	0.0982461i	0.836270	+	0.548318i	$0.184732\pi$
$882$	−0.0131454	−	1.82815i	−0.000442630	−	0.0615571i
$883$	−31.9217			−1.07425			−0.537125	−	0.843503i	$-0.680490\pi$
$883$	−31.9217			−1.07425			−0.537125	+	0.843503i	$0.680490\pi$
$884$	35.4114	−	2.48076i	1.19101	−	0.0834370i
$885$	7.11225	+	12.3188i	0.239076	+	0.414091i
$886$	−0.163033			−0.00547721
$887$	2.82486	+	4.89281i	0.0948497	+	0.164284i	0.909546	−	0.415604i	$-0.136430\pi$
$887$	2.82486	+	4.89281i	0.0948497	+	0.164284i	−0.814696	+	0.579888i	$0.803096\pi$
$888$	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
$891$	−0.845173			−0.0283144
$892$	26.3793	+	45.6903i	0.883244	+	1.52982i
$893$	6.24897	−	10.8235i	0.209114	−	0.362196i
$894$	0.693315	+	1.20086i	0.0231879	+	0.0401627i
$895$	−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
$899$	−35.3148			−1.17781
$900$	5.77977			0.192659
$901$	11.0360			0.367664
$902$	2.27933			0.0758933
$903$	27.2342	−	7.40242i	0.906296	−	0.246337i
$904$	−4.87478	−	8.44337i	−0.162133	−	0.280822i
$905$	−6.16234	+	10.6735i	−0.204843	+	0.354799i
$906$	−0.508752	+	0.881184i	−0.0169021	+	0.0292754i
$907$	29.5610			0.981556			0.490778	−	0.871285i	$-0.336713\pi$
$907$	29.5610			0.981556			0.490778	+	0.871285i	$0.336713\pi$
$908$	−12.8127	−	22.1922i	−0.425204	−	0.736475i
$909$	13.5117			0.448155
$910$	2.67311	+	2.30628i	0.0886127	+	0.0764524i
$911$	24.1869			0.801347			0.400673	−	0.916221i	$-0.368776\pi$
$911$	24.1869			0.801347			0.400673	+	0.916221i	$0.368776\pi$
$912$	−6.22231	−	10.7774i	−0.206041	−	0.356874i
$913$	−5.21693			−0.172655
$914$	0.368858	−	0.638880i	0.0122007	−	0.0211323i
$915$	2.36624	−	4.09845i	0.0782255	−	0.135491i
$916$	−9.89078	−	17.1313i	−0.326801	−	0.566035i
$917$	0.656479	+	0.651776i	0.0216789	+	0.0215235i
$918$	−1.33107			−0.0439318
$919$	47.6748			1.57265			0.786323	−	0.617816i	$-0.211982\pi$
$919$	47.6748			1.57265			0.786323	+	0.617816i	$0.211982\pi$
$920$	−13.3988			−0.441744
$921$	−19.1859			−0.632198
$922$	−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
$926$	4.93776	+	8.55246i	0.162265	+	0.281051i
$927$	7.11519	−	12.3239i	0.233693	−	0.404769i
$928$	12.0365	+	20.8478i	0.395117	+	0.684362i
$929$	−2.29035			−0.0751438			−0.0375719	−	0.999294i	$-0.511962\pi$
$929$	−2.29035			−0.0751438			−0.0375719	+	0.999294i	$0.511962\pi$
$930$	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
$933$	14.7040	+	25.4682i	0.481389	+	0.833790i
$934$	−5.04949			−0.165224
$935$	−3.05197	−	5.28616i	−0.0998100	−	0.172876i
$936$	1.62262	−	3.32794i	0.0530368	−	0.108777i
$937$	31.5319			1.03010			0.515050	−	0.857160i	$-0.327773\pi$
$937$	31.5319			1.03010			0.515050	+	0.857160i	$0.327773\pi$
$938$	2.33782	−	0.635435i	0.0763327	−	0.0207477i
$939$	−7.86048	+	13.6148i	−0.256517	+	0.444301i
$940$	−9.88446			−0.322395
$941$	−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	$0.995497\pi$
$942$	0.140347	−	0.243088i	0.00457276	−	0.00792025i
$943$	95.0811			3.09627
$944$	36.0905			1.17465
$945$	2.66060	+	2.64154i	0.0865493	+	0.0859292i
$946$	−1.17729	+	2.03913i	−0.0382771	+	0.0662978i
$947$	9.00662	+	15.5999i	0.292676	+	0.506929i	0.974442	−	0.224641i	$-0.0721210\pi$
$947$	9.00662	+	15.5999i	0.292676	+	0.506929i	−0.681766	+	0.731571i	$0.738788\pi$
$948$	11.1298	+	19.2774i	0.361480	+	0.626102i
$949$	−0.423582	+	0.0296742i	−0.0137501	+	0.000963267i
$950$	−1.35233	+	2.34230i	−0.0438753	+	0.0759943i
$951$	4.26514	−	7.38743i	0.138307	−	0.239554i
$952$	−9.82607	−	9.75567i	−0.318465	−	0.316183i
$953$	−2.30018	−	3.98403i	−0.0745101	−	0.129055i	0.826363	−	0.563138i	$-0.190406\pi$
$953$	−2.30018	−	3.98403i	−0.0745101	−	0.129055i	−0.900873	+	0.434082i	$0.857073\pi$
$954$	0.282771	−	0.489774i	0.00915505	−	0.0158570i
$955$	9.52320	−	16.4947i	0.308163	−	0.533755i
$956$	−3.31019	+	5.73341i	−0.107059	+	0.185432i
$957$	3.39918	−	5.88755i	0.109880	−	0.190317i
$958$	−0.838125	−	1.45167i	−0.0270786	−	0.0469015i
$959$	42.7229	+	42.4168i	1.37959	+	1.36971i
$960$	−4.54110	+	7.86541i	−0.146563	+	0.253855i
$961$	5.86245	−	10.1541i	0.189111	−	0.327551i
$962$	4.94804	+	7.33375i	0.159531	+	0.236450i
$963$	1.03674	+	1.79569i	0.0334086	+	0.0578654i
$964$	7.88498	+	13.6572i	0.253958	+	0.439868i
$965$	9.83503	−	17.0348i	0.316601	−	0.548369i
$966$	4.51517	+	4.48282i	0.145273	+	0.144232i
$967$	−35.1105			−1.12908			−0.564539	−	0.825407i	$-0.690946\pi$
$967$	−35.1105			−1.12908			−0.564539	+	0.825407i	$0.690946\pi$
$968$	−10.5621			−0.339478
$969$	−8.82023	+	15.2771i	−0.283347	+	0.490771i
$970$	−0.0611040	−	0.105835i	−0.00196193	−	0.00339816i
$971$	−35.0808			−1.12580			−0.562898	−	0.826527i	$-0.690313\pi$
$971$	−35.0808			−1.12580			−0.562898	+	0.826527i	$0.690313\pi$
$972$	0.965895	−	1.67298i	0.0309811	−	0.0536608i
$973$	−22.3740	+	6.08138i	−0.717277	+	0.194960i
$974$	−4.60868			−0.147672
$975$	10.7612	−	0.753879i	0.344633	−	0.0241434i
$976$	−6.00364	−	10.3986i	−0.192172	−	0.332852i
$977$	60.9240			1.94913			0.974565	−	0.224103i	$-0.0719453\pi$
$977$	60.9240			1.94913			0.974565	+	0.224103i	$0.0719453\pi$
$978$	−0.244455	−	0.423409i	−0.00781682	−	0.0135391i
$979$	−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
$982$	−9.50552			−0.303333
$983$	−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	$-0.351438\pi$
$984$	−5.30177	+	9.18294i	−0.169014	+	0.292741i
$985$	10.0114	+	17.3402i	0.318989	+	0.552505i
$986$	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
$990$	−0.312796			−0.00994131
$991$	9.70075			0.308155			0.154077	−	0.988059i	$-0.450760\pi$
$991$	9.70075			0.308155			0.154077	+	0.988059i	$0.450760\pi$
$992$	13.1392			0.417170
$993$	−1.74655			−0.0554252
$994$	6.33511	+	6.28972i	0.200937	+	0.199498i
$995$	−11.2745	−	19.5280i	−0.357425	−	0.619079i
$996$	5.96210	−	10.3267i	0.188916	−	0.327213i
$997$	15.6145	−	27.0451i	0.494516	−	0.856526i	−0.505465	−	0.862847i	$-0.668679\pi$
$997$	15.6145	−	27.0451i	0.494516	−	0.856526i	0.999980	+	0.00632142i	$0.00201218\pi$
$998$	−5.59756			−0.177188
$999$	4.69745	+	8.13622i	0.148621	+	0.257419i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.6	✓	20	1.1	even	1	trivial
273.2.j.c.172.6	yes	20	91.81	even	3	inner
273.2.l.c.16.5	yes	20	13.3	even	3
273.2.l.c.256.5	yes	20	7.4	even	3
819.2.n.f.100.5		20	3.2	odd	2
819.2.n.f.172.5		20	273.263	odd	6
819.2.s.f.289.6		20	39.29	odd	6
819.2.s.f.802.6		20	21.11	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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.130586 + 0.226181i) q^{2} +1.00000 q^{3} +(0.965895 - 1.67298i) q^{4} +(0.708533 - 1.22721i) q^{5} +(0.130586 + 0.226181i) q^{6} +(-0.675578 + 2.55804i) q^{7} +1.02687 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.130586 + 0.226181i) q^{2} +1.00000 q^{3} +(0.965895 - 1.67298i) q^{4} +(0.708533 - 1.22721i) q^{5} +(0.130586 + 0.226181i) q^{6} +(-0.675578 + 2.55804i) q^{7} +1.02687 q^{8} +1.00000 q^{9} +0.370097 q^{10} -0.845173 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} +(-1.79769 - 3.11370i) q^{16} +(-2.54826 + 4.41372i) q^{17} +(0.130586 + 0.226181i) q^{18} +3.46127 q^{19} +(-1.36874 - 2.37072i) q^{20} +(-0.675578 + 2.55804i) q^{21} +(-0.110368 - 0.191162i) q^{22} +(-4.60393 - 7.97424i) q^{23} +1.02687 q^{24} +(1.49596 + 2.59108i) q^{25} +(0.939365 - 0.0658076i) q^{26} +1.00000 q^{27} +(3.62702 + 3.60103i) q^{28} +(-4.02187 + 6.96608i) q^{29} +0.370097 q^{30} +(2.19517 + 3.80215i) q^{31} +(1.49638 - 2.59180i) q^{32} -0.845173 q^{33} -1.33107 q^{34} +(2.66060 + 2.64154i) q^{35} +(0.965895 - 1.67298i) q^{36} +(4.69745 + 8.13622i) q^{37} +(0.451992 + 0.782874i) q^{38} +(1.58015 - 3.24085i) q^{39} +(0.727572 - 1.26019i) q^{40} +(-5.16304 + 8.94264i) q^{41} +(-0.666802 + 0.181241i) q^{42} +(-5.33350 - 9.23790i) q^{43} +(-0.816348 + 1.41396i) q^{44} +(0.708533 - 1.22721i) q^{45} +(1.20242 - 2.08264i) q^{46} +(1.80540 - 3.12704i) q^{47} +(-1.79769 - 3.11370i) q^{48} +(-6.08719 - 3.45632i) q^{49} +(-0.390703 + 0.676717i) q^{50} +(-2.54826 + 4.41372i) q^{51} +(-3.89561 - 5.77389i) q^{52} +(-1.08270 - 1.87530i) q^{53} +(0.130586 + 0.226181i) q^{54} +(-0.598833 + 1.03721i) q^{55} +(-0.693732 + 2.62678i) q^{56} +3.46127 q^{57} -2.10080 q^{58} +(-5.01900 + 8.69316i) q^{59} +(-1.36874 - 2.37072i) q^{60} +3.33963 q^{61} +(-0.573316 + 0.993012i) q^{62} +(-0.675578 + 2.55804i) q^{63} -6.40916 q^{64} +(-2.85763 - 4.23544i) q^{65} +(-0.110368 - 0.191162i) q^{66} -3.50602 q^{67} +(4.92271 + 8.52638i) q^{68} +(-4.60393 - 7.97424i) q^{69} +(-0.250030 + 0.946725i) q^{70} +(-6.45964 - 11.1884i) q^{71} +1.02687 q^{72} +(-0.0588842 - 0.101990i) q^{73} +(-1.22684 + 2.12495i) q^{74} +(1.49596 + 2.59108i) 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} -5.09490 q^{80} +1.00000 q^{81} -2.69688 q^{82} +6.17262 q^{83} +(3.62702 + 3.60103i) q^{84} +(3.61106 + 6.25453i) q^{85} +(1.39296 - 2.41268i) q^{86} +(-4.02187 + 6.96608i) q^{87} -0.867884 q^{88} +(3.11475 + 5.39490i) q^{89} +0.370097 q^{90} +(7.22272 + 6.23156i) q^{91} -17.7877 q^{92} +(2.19517 + 3.80215i) q^{93} +0.943037 q^{94} +(2.45242 - 4.24772i) q^{95} +(1.49638 - 2.59180i) q^{96} +(-0.165103 - 0.285966i) q^{97} +(-0.0131454 - 1.82815i) q^{98} -0.845173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9	\( 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25} + 4 q^{26} + 20 q^{27} + 13 q^{28} - 9 q^{29} + 8 q^{30} - 9 q^{31} + 17 q^{32} + 16 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} + 18 q^{37} + 22 q^{38} - 5 q^{39} - 9 q^{40} - q^{41} - 9 q^{42} - 11 q^{43} + 8 q^{44} - 10 q^{46} + 13 q^{47} - 20 q^{48} - 21 q^{49} + 5 q^{50} - 2 q^{52} - 6 q^{53} - 19 q^{55} - 5 q^{56} - 14 q^{57} - 15 q^{59} + 12 q^{60} + 22 q^{62} - 9 q^{63} + 72 q^{64} - 27 q^{65} - 9 q^{66} + 44 q^{67} + 39 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} - 12 q^{72} - 3 q^{74} - 32 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} - 96 q^{80} + 20 q^{81} + 26 q^{82} + 40 q^{83} + 13 q^{84} - 16 q^{85} + 4 q^{86} - 9 q^{87} + 24 q^{88} + 2 q^{89} + 8 q^{90} + 9 q^{91} + 66 q^{92} - 9 q^{93} + 88 q^{94} - 36 q^{95} + 17 q^{96} + 21 q^{97} - 79 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9 + 8 * q^10 + 16 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 - 20 * q^16 - 14 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 - 14 * q^23 - 12 * q^24 - 32 * q^25 + 4 * q^26 + 20 * q^27 + 13 * q^28 - 9 * q^29 + 8 * q^30 - 9 * q^31 + 17 * q^32 + 16 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 + 18 * q^37 + 22 * q^38 - 5 * q^39 - 9 * q^40 - q^41 - 9 * q^42 - 11 * q^43 + 8 * q^44 - 10 * q^46 + 13 * q^47 - 20 * q^48 - 21 * q^49 + 5 * q^50 - 2 * q^52 - 6 * q^53 - 19 * q^55 - 5 * q^56 - 14 * q^57 - 15 * q^59 + 12 * q^60 + 22 * q^62 - 9 * q^63 + 72 * q^64 - 27 * q^65 - 9 * q^66 + 44 * q^67 + 39 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 - 12 * q^72 - 3 * q^74 - 32 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 - 96 * q^80 + 20 * q^81 + 26 * q^82 + 40 * q^83 + 13 * q^84 - 16 * q^85 + 4 * q^86 - 9 * q^87 + 24 * q^88 + 2 * q^89 + 8 * q^90 + 9 * q^91 + 66 * q^92 - 9 * q^93 + 88 * q^94 - 36 * q^95 + 17 * q^96 + 21 * q^97 - 79 * q^98 + 16 * q^99

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