LMFDB - Embedded newform 273.2.j.c.172.1

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			172.1
Root			$1.31285 + 2.27393i$ of defining polynomial
Character	$\chi$	$=$	273.172
Dual form			273.2.j.c.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31285 + 2.27393i) q^{2} +1.00000 q^{3} +(-2.44716 - 4.23861i) q^{4} +(0.734607 + 1.27238i) q^{5} +(-1.31285 + 2.27393i) q^{6} +(2.40805 + 1.09603i) q^{7} +7.59966 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.31285 + 2.27393i) q^{2} +1.00000 q^{3} +(-2.44716 - 4.23861i) q^{4} +(0.734607 + 1.27238i) q^{5} +(-1.31285 + 2.27393i) q^{6} +(2.40805 + 1.09603i) q^{7} +7.59966 q^{8} +1.00000 q^{9} -3.85772 q^{10} +4.48133 q^{11} +(-2.44716 - 4.23861i) q^{12} +(-3.58601 - 0.374884i) q^{13} +(-5.65370 + 4.03682i) q^{14} +(0.734607 + 1.27238i) q^{15} +(-5.08290 + 8.80384i) q^{16} +(1.81439 + 3.14262i) q^{17} +(-1.31285 + 2.27393i) q^{18} -3.01385 q^{19} +(3.59541 - 6.22743i) q^{20} +(2.40805 + 1.09603i) q^{21} +(-5.88333 + 10.1902i) q^{22} +(-3.87459 + 6.71099i) q^{23} +7.59966 q^{24} +(1.42070 - 2.46073i) q^{25} +(5.56036 - 7.66216i) q^{26} +1.00000 q^{27} +(-1.24728 - 12.8890i) q^{28} +(-3.98387 - 6.90026i) q^{29} -3.85772 q^{30} +(-0.552624 + 0.957172i) q^{31} +(-5.74654 - 9.95330i) q^{32} +4.48133 q^{33} -9.52812 q^{34} +(0.374417 + 3.86910i) q^{35} +(-2.44716 - 4.23861i) q^{36} +(1.57581 - 2.72938i) q^{37} +(3.95675 - 6.85329i) q^{38} +(-3.58601 - 0.374884i) q^{39} +(5.58276 + 9.66963i) q^{40} +(1.11340 + 1.92847i) q^{41} +(-5.65370 + 4.03682i) q^{42} +(2.54662 - 4.41087i) q^{43} +(-10.9666 - 18.9946i) q^{44} +(0.734607 + 1.27238i) q^{45} +(-10.1735 - 17.6211i) q^{46} +(1.69770 + 2.94050i) q^{47} +(-5.08290 + 8.80384i) q^{48} +(4.59746 + 5.27858i) q^{49} +(3.73035 + 6.46116i) q^{50} +(1.81439 + 3.14262i) q^{51} +(7.18657 + 16.1171i) q^{52} +(-4.25619 + 7.37193i) q^{53} +(-1.31285 + 2.27393i) q^{54} +(3.29202 + 5.70194i) q^{55} +(18.3004 + 8.32942i) q^{56} -3.01385 q^{57} +20.9209 q^{58} +(-7.22979 - 12.5224i) q^{59} +(3.59541 - 6.22743i) q^{60} +7.62340 q^{61} +(-1.45103 - 2.51325i) q^{62} +(2.40805 + 1.09603i) q^{63} +9.84585 q^{64} +(-2.15732 - 4.83815i) q^{65} +(-5.88333 + 10.1902i) q^{66} +4.67078 q^{67} +(8.88023 - 15.3810i) q^{68} +(-3.87459 + 6.71099i) q^{69} +(-9.28961 - 4.22816i) q^{70} +(1.24524 - 2.15682i) q^{71} +7.59966 q^{72} +(3.03070 - 5.24932i) q^{73} +(4.13762 + 7.16656i) q^{74} +(1.42070 - 2.46073i) q^{75} +(7.37540 + 12.7746i) q^{76} +(10.7913 + 4.91165i) q^{77} +(5.56036 - 7.66216i) q^{78} +(-3.59127 - 6.22026i) q^{79} -14.9357 q^{80} +1.00000 q^{81} -5.84693 q^{82} +9.30835 q^{83} +(-1.24728 - 12.8890i) q^{84} +(-2.66573 + 4.61718i) q^{85} +(6.68667 + 11.5816i) q^{86} +(-3.98387 - 6.90026i) q^{87} +34.0566 q^{88} +(-3.18037 + 5.50857i) q^{89} -3.85772 q^{90} +(-8.22443 - 4.83310i) q^{91} +37.9270 q^{92} +(-0.552624 + 0.957172i) q^{93} -8.91531 q^{94} +(-2.21400 - 3.83476i) q^{95} +(-5.74654 - 9.95330i) q^{96} +(-4.02169 + 6.96578i) q^{97} +(-18.0389 + 3.52429i) q^{98} +4.48133 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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.31285	+	2.27393i	−0.928327	+	1.60791i	−0.142206	+	0.989837i	$0.545420\pi$
$2$	−1.31285	+	2.27393i	−0.928327	+	1.60791i	−0.786121	+	0.618073i	$0.787914\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−2.44716	−	4.23861i	−1.22358	−	2.11931i
$5$	0.734607	+	1.27238i	0.328526	+	0.569024i	0.982220	−	0.187735i	$-0.0601147\pi$
$5$	0.734607	+	1.27238i	0.328526	+	0.569024i	−0.653693	+	0.756760i	$0.726781\pi$
$6$	−1.31285	+	2.27393i	−0.535970	+	0.928327i
$7$	2.40805	+	1.09603i	0.910159	+	0.414259i
$7$	2.40805	+	1.09603i	0.910159	+	0.414259i
$8$	7.59966			2.68688
$9$	1.00000			0.333333
$10$	−3.85772			−1.21992
$11$	4.48133			1.35117			0.675586	−	0.737281i	$-0.263891\pi$
$11$	4.48133			1.35117			0.675586	+	0.737281i	$0.263891\pi$
$12$	−2.44716	−	4.23861i	−0.706436	−	1.22358i
$13$	−3.58601	−	0.374884i	−0.994580	−	0.103974i
$13$	−3.58601	−	0.374884i	−0.994580	−	0.103974i
$14$	−5.65370	+	4.03682i	−1.51102	+	1.07889i
$15$	0.734607	+	1.27238i	0.189675	+	0.328526i
$16$	−5.08290	+	8.80384i	−1.27072	+	2.20096i
$17$	1.81439	+	3.14262i	0.440055	+	0.762197i	0.997693	−	0.0678869i	$-0.0216257\pi$
$17$	1.81439	+	3.14262i	0.440055	+	0.762197i	−0.557638	+	0.830084i	$0.688292\pi$
$18$	−1.31285	+	2.27393i	−0.309442	+	0.535970i
$19$	−3.01385			−0.691425			−0.345713	−	0.938340i	$-0.612363\pi$
$19$	−3.01385			−0.691425			−0.345713	+	0.938340i	$0.612363\pi$
$20$	3.59541	−	6.22743i	0.803958	−	1.39250i
$21$	2.40805	+	1.09603i	0.525481	+	0.239172i
$22$	−5.88333	+	10.1902i	−1.25433	+	2.17256i
$23$	−3.87459	+	6.71099i	−0.807908	+	1.39934i	0.106403	+	0.994323i	$0.466067\pi$
$23$	−3.87459	+	6.71099i	−0.807908	+	1.39934i	−0.914310	+	0.405014i	$0.867267\pi$
$24$	7.59966			1.55127
$25$	1.42070	−	2.46073i	0.284141	−	0.492146i
$26$	5.56036	−	7.66216i	1.09048	−	1.50267i
$27$	1.00000			0.192450
$28$	−1.24728	−	12.8890i	−0.235714	−	2.43579i
$29$	−3.98387	−	6.90026i	−0.739785	−	1.28135i	−0.952592	−	0.304251i	$-0.901594\pi$
$29$	−3.98387	−	6.90026i	−0.739785	−	1.28135i	0.212806	−	0.977094i	$-0.431740\pi$
$30$	−3.85772			−0.704321
$31$	−0.552624	+	0.957172i	−0.0992541	+	0.171913i	−0.911376	−	0.411574i	$-0.864979\pi$
$31$	−0.552624	+	0.957172i	−0.0992541	+	0.171913i	0.812122	+	0.583488i	$0.198312\pi$
$32$	−5.74654	−	9.95330i	−1.01585	−	1.75951i
$33$	4.48133			0.780100
$34$	−9.52812			−1.63406
$35$	0.374417	+	3.86910i	0.0632881	+	0.653998i
$36$	−2.44716	−	4.23861i	−0.407861	−	0.706436i
$37$	1.57581	−	2.72938i	0.259062	−	0.448708i	−0.706929	−	0.707284i	$-0.749920\pi$
$37$	1.57581	−	2.72938i	0.259062	−	0.448708i	0.965991	+	0.258576i	$0.0832534\pi$
$38$	3.95675	−	6.85329i	0.641869	−	1.11175i
$39$	−3.58601	−	0.374884i	−0.574221	−	0.0600294i
$40$	5.58276	+	9.66963i	0.882712	+	1.52890i
$41$	1.11340	+	1.92847i	0.173884	+	0.301176i	0.939775	−	0.341795i	$-0.111035\pi$
$41$	1.11340	+	1.92847i	0.173884	+	0.301176i	−0.765890	+	0.642971i	$0.777701\pi$
$42$	−5.65370	+	4.03682i	−0.872385	+	0.622895i
$43$	2.54662	−	4.41087i	0.388355	−	0.672651i	−0.603873	−	0.797080i	$-0.706377\pi$
$43$	2.54662	−	4.41087i	0.388355	−	0.672651i	0.992228	+	0.124429i	$0.0397100\pi$
$44$	−10.9666	−	18.9946i	−1.65327	−	2.86355i
$45$	0.734607	+	1.27238i	0.109509	+	0.189675i
$46$	−10.1735	−	17.6211i	−1.50001	−	2.59809i
$47$	1.69770	+	2.94050i	0.247635	+	0.428916i	0.962869	−	0.269969i	$-0.0870134\pi$
$47$	1.69770	+	2.94050i	0.247635	+	0.428916i	−0.715234	+	0.698885i	$0.753680\pi$
$48$	−5.08290	+	8.80384i	−0.733653	+	1.27072i
$49$	4.59746	+	5.27858i	0.656780	+	0.754083i
$50$	3.73035	+	6.46116i	0.527551	+	0.913746i
$51$	1.81439	+	3.14262i	0.254066	+	0.440055i
$52$	7.18657	+	16.1171i	0.996598	+	2.23504i
$53$	−4.25619	+	7.37193i	−0.584632	+	1.01261i	0.410289	+	0.911955i	$0.365428\pi$
$53$	−4.25619	+	7.37193i	−0.584632	+	1.01261i	−0.994921	+	0.100657i	$0.967906\pi$
$54$	−1.31285	+	2.27393i	−0.178657	+	0.309442i
$55$	3.29202	+	5.70194i	0.443896	+	0.768850i
$56$	18.3004	+	8.32942i	2.44549	+	1.11306i
$57$	−3.01385			−0.399195
$58$	20.9209			2.74705
$59$	−7.22979	−	12.5224i	−0.941238	−	1.63027i	−0.763114	−	0.646264i	$-0.776330\pi$
$59$	−7.22979	−	12.5224i	−0.941238	−	1.63027i	−0.178124	−	0.984008i	$-0.557003\pi$
$60$	3.59541	−	6.22743i	0.464165	−	0.803958i
$61$	7.62340			0.976077			0.488038	−	0.872822i	$-0.337713\pi$
$61$	7.62340			0.976077			0.488038	+	0.872822i	$0.337713\pi$
$62$	−1.45103	−	2.51325i	−0.184281	−	0.319183i
$63$	2.40805	+	1.09603i	0.303386	+	0.138086i
$64$	9.84585			1.23073
$65$	−2.15732	−	4.83815i	−0.267582	−	0.600098i
$66$	−5.88333	+	10.1902i	−0.724188	+	1.25433i
$67$	4.67078			0.570627			0.285313	−	0.958434i	$-0.407902\pi$
$67$	4.67078			0.570627			0.285313	+	0.958434i	$0.407902\pi$
$68$	8.88023	−	15.3810i	1.07689	−	1.86522i
$69$	−3.87459	+	6.71099i	−0.466446	+	0.807908i
$70$	−9.28961	−	4.22816i	−1.11032	−	0.505362i
$71$	1.24524	−	2.15682i	0.147783	−	0.255968i	−0.782625	−	0.622494i	$-0.786120\pi$
$71$	1.24524	−	2.15682i	0.147783	−	0.255968i	0.930408	+	0.366526i	$0.119453\pi$
$72$	7.59966			0.895628
$73$	3.03070	−	5.24932i	0.354716	−	0.614387i	−0.632353	−	0.774680i	$-0.717911\pi$
$73$	3.03070	−	5.24932i	0.354716	−	0.614387i	0.987069	+	0.160294i	$0.0512441\pi$
$74$	4.13762	+	7.16656i	0.480988	+	0.833096i
$75$	1.42070	−	2.46073i	0.164049	−	0.284141i
$76$	7.37540	+	12.7746i	0.846016	+	1.46534i
$77$	10.7913	+	4.91165i	1.22978	+	0.559735i
$78$	5.56036	−	7.66216i	0.629587	−	0.867569i
$79$	−3.59127	−	6.22026i	−0.404050	−	0.699834i	0.590161	−	0.807286i	$-0.299064\pi$
$79$	−3.59127	−	6.22026i	−0.404050	−	0.699834i	−0.994210	+	0.107451i	$0.965731\pi$
$80$	−14.9357			−1.66987
$81$	1.00000			0.111111
$82$	−5.84693			−0.645686
$83$	9.30835			1.02172			0.510862	−	0.859663i	$-0.329326\pi$
$83$	9.30835			1.02172			0.510862	+	0.859663i	$0.329326\pi$
$84$	−1.24728	−	12.8890i	−0.136089	−	1.40630i
$85$	−2.66573	+	4.61718i	−0.289139	+	0.500804i
$86$	6.68667	+	11.5816i	0.721042	+	1.24888i
$87$	−3.98387	−	6.90026i	−0.427115	−	0.739785i
$88$	34.0566			3.63044
$89$	−3.18037	+	5.50857i	−0.337119	+	0.583907i	−0.983890	−	0.178777i	$-0.942786\pi$
$89$	−3.18037	+	5.50857i	−0.337119	+	0.583907i	0.646771	+	0.762685i	$0.276119\pi$
$90$	−3.85772			−0.406640
$91$	−8.22443	−	4.83310i	−0.862154	−	0.506646i
$92$	37.9270			3.95417
$93$	−0.552624	+	0.957172i	−0.0573044	+	0.0992541i
$94$	−8.91531			−0.919544
$95$	−2.21400	−	3.83476i	−0.227151	−	0.393438i
$96$	−5.74654	−	9.95330i	−0.586504	−	1.01585i
$97$	−4.02169	+	6.96578i	−0.408341	+	0.707267i	−0.994704	−	0.102781i	$-0.967226\pi$
$97$	−4.02169	+	6.96578i	−0.408341	+	0.707267i	0.586363	+	0.810048i	$0.300559\pi$
$98$	−18.0389	+	3.52429i	−1.82220	+	0.356007i
$99$	4.48133			0.450391
$100$	−13.9068			−1.39068
$101$	−13.9040			−1.38350			−0.691750	−	0.722137i	$-0.743160\pi$
$101$	−13.9040			−1.38350			−0.691750	+	0.722137i	$0.743160\pi$
$102$	−9.52812			−0.943424
$103$	−7.61605	−	13.1914i	−0.750432	−	1.29979i	−0.947613	−	0.319419i	$-0.896512\pi$
$103$	−7.61605	−	13.1914i	−0.750432	−	1.29979i	0.197181	−	0.980367i	$-0.436821\pi$
$104$	−27.2524	−	2.84899i	−2.67232	−	0.279366i
$105$	0.374417	+	3.86910i	0.0365394	+	0.377586i
$106$	−11.1755	−	19.3565i	−1.08546	−	1.88007i
$107$	5.36329	−	9.28948i	0.518488	−	0.898048i	−0.481281	−	0.876566i	$-0.659828\pi$
$107$	5.36329	−	9.28948i	0.518488	−	0.898048i	0.999769	−	0.0214817i	$-0.00683837\pi$
$108$	−2.44716	−	4.23861i	−0.235479	−	0.407861i
$109$	6.93451	−	12.0109i	0.664206	−	1.15044i	−0.315294	−	0.948994i	$-0.602103\pi$
$109$	6.93451	−	12.0109i	0.664206	−	1.15044i	0.979500	−	0.201445i	$-0.0645636\pi$
$110$	−17.2877			−1.64832
$111$	1.57581	−	2.72938i	0.149569	−	0.259062i
$112$	−21.8891	+	15.6291i	−2.06833	+	1.47682i
$113$	−0.961419	+	1.66523i	−0.0904427	+	0.156651i	−0.907697	−	0.419625i	$-0.862162\pi$
$113$	−0.961419	+	1.66523i	−0.0904427	+	0.156651i	0.817255	+	0.576277i	$0.195495\pi$
$114$	3.95675	−	6.85329i	0.370583	−	0.641869i
$115$	−11.3852			−1.06168
$116$	−19.4984	+	33.7721i	−1.81038	+	3.13566i
$117$	−3.58601	−	0.374884i	−0.331527	−	0.0346580i
$118$	37.9666			3.49511
$119$	0.924766	+	9.55622i	0.0847731	+	0.876017i
$120$	5.58276	+	9.66963i	0.509634	+	0.882712i
$121$	9.08233			0.825666
$122$	−10.0084	+	17.3351i	−0.906119	+	1.56944i
$123$	1.11340	+	1.92847i	0.100392	+	0.173884i
$124$	5.40944			0.485782
$125$	11.5207			1.03044
$126$	−5.65370	+	4.03682i	−0.503672	+	0.359629i
$127$	−8.60394	−	14.9025i	−0.763476	−	1.32238i	−0.941049	−	0.338271i	$-0.890158\pi$
$127$	−8.60394	−	14.9025i	−0.763476	−	1.32238i	0.177573	−	0.984108i	$-0.443175\pi$
$128$	−1.43307	+	2.48215i	−0.126667	+	0.219394i
$129$	2.54662	−	4.41087i	0.224217	−	0.388355i
$130$	13.8338	+	1.44620i	1.21331	+	0.126840i
$131$	−2.50449	−	4.33791i	−0.218818	−	0.379005i	0.735629	−	0.677385i	$-0.236887\pi$
$131$	−2.50449	−	4.33791i	−0.218818	−	0.379005i	−0.954447	+	0.298381i	$0.903554\pi$
$132$	−10.9666	−	18.9946i	−0.954516	−	1.65327i
$133$	−7.25753	−	3.30326i	−0.629307	−	0.286429i
$134$	−6.13205	+	10.6210i	−0.529728	+	0.917516i
$135$	0.734607	+	1.27238i	0.0632249	+	0.109509i
$136$	13.7888	+	23.8828i	1.18238	+	2.04794i
$137$	0.372343	+	0.644917i	0.0318114	+	0.0550990i	0.881493	−	0.472197i	$-0.156539\pi$
$137$	0.372343	+	0.644917i	0.0318114	+	0.0550990i	−0.849681	+	0.527296i	$0.823206\pi$
$138$	−10.1735	−	17.6211i	−0.866028	−	1.50001i
$139$	−6.08346	+	10.5369i	−0.515992	+	0.893725i	0.483835	+	0.875159i	$0.339243\pi$
$139$	−6.08346	+	10.5369i	−0.515992	+	0.893725i	−0.999828	+	0.0185659i	$0.994090\pi$
$140$	15.4834	−	11.0553i	1.30858	−	0.934347i
$141$	1.69770	+	2.94050i	0.142972	+	0.247635i
$142$	3.26964	+	5.66318i	0.274382	+	0.475244i
$143$	−16.0701	−	1.67998i	−1.34385	−	0.140487i
$144$	−5.08290	+	8.80384i	−0.423575	+	0.733653i
$145$	5.85315	−	10.1380i	0.486078	−	0.841912i
$146$	7.95772	+	13.7832i	0.658585	+	1.14070i
$147$	4.59746	+	5.27858i	0.379192	+	0.435370i
$148$	−15.4251			−1.26793
$149$	2.60442			0.213362			0.106681	−	0.994293i	$-0.465978\pi$
$149$	2.60442			0.213362			0.106681	+	0.994293i	$0.465978\pi$
$150$	3.73035	+	6.46116i	0.304582	+	0.527551i
$151$	6.89949	−	11.9503i	0.561473	−	0.972499i	−0.435896	−	0.899997i	$-0.643568\pi$
$151$	6.89949	−	11.9503i	0.561473	−	0.972499i	0.997368	−	0.0725019i	$-0.0230983\pi$
$152$	−22.9043			−1.85778
$153$	1.81439	+	3.14262i	0.146685	+	0.254066i
$154$	−25.3361	+	18.0903i	−2.04164	+	1.45776i
$155$	−1.62385			−0.130430
$156$	7.18657	+	16.1171i	0.575386	+	1.29040i
$157$	−0.247517	+	0.428712i	−0.0197540	+	0.0342149i	−0.875733	−	0.482795i	$-0.839622\pi$
$157$	−0.247517	+	0.428712i	−0.0197540	+	0.0342149i	0.855979	+	0.517010i	$0.172955\pi$
$158$	18.8592			1.50036
$159$	−4.25619	+	7.37193i	−0.337537	+	0.584632i
$160$	8.44290	−	14.6235i	0.667470	−	1.15609i
$161$	−16.6856	+	11.9138i	−1.31501	+	0.938937i
$162$	−1.31285	+	2.27393i	−0.103147	+	0.178657i
$163$	9.26039			0.725330			0.362665	−	0.931920i	$-0.381867\pi$
$163$	9.26039			0.725330			0.362665	+	0.931920i	$0.381867\pi$
$164$	5.44936	−	9.43857i	0.425523	−	0.737028i
$165$	3.29202	+	5.70194i	0.256283	+	0.443896i
$166$	−12.2205	+	21.1665i	−0.948494	+	1.64284i
$167$	−7.99354	−	13.8452i	−0.618559	−	1.07138i	−0.989749	−	0.142819i	$-0.954383\pi$
$167$	−7.99354	−	13.8452i	−0.618559	−	1.07138i	0.371190	−	0.928557i	$-0.378950\pi$
$168$	18.3004	+	8.32942i	1.41191	+	0.642628i
$169$	12.7189	+	2.68867i	0.978379	+	0.206821i
$170$	−6.99943	−	12.1234i	−0.536831	−	0.929819i
$171$	−3.01385			−0.230475
$172$	−24.9280			−1.90074
$173$	10.4746			0.796370			0.398185	−	0.917305i	$-0.369640\pi$
$173$	10.4746			0.796370			0.398185	+	0.917305i	$0.369640\pi$
$174$	20.9209			1.58601
$175$	6.11816	−	4.36845i	0.462489	−	0.330224i
$176$	−22.7782	+	39.4529i	−1.71697	+	2.97388i
$177$	−7.22979	−	12.5224i	−0.543424	−	0.941238i
$178$	−8.35073	−	14.4639i	−0.625913	−	1.08411i
$179$	10.4436			0.780592			0.390296	−	0.920689i	$-0.372373\pi$
$179$	10.4436			0.780592			0.390296	+	0.920689i	$0.372373\pi$
$180$	3.59541	−	6.22743i	0.267986	−	0.464165i
$181$	−14.8861			−1.10648			−0.553239	−	0.833023i	$-0.686608\pi$
$181$	−14.8861			−1.10648			−0.553239	+	0.833023i	$0.686608\pi$
$182$	21.7876	−	12.3566i	1.61500	−	0.915932i
$183$	7.62340			0.563538
$184$	−29.4455	+	51.0012i	−2.17075	+	3.75986i
$185$	4.63041			0.340434
$186$	−1.45103	−	2.51325i	−0.106394	−	0.184281i
$187$	8.13089	+	14.0831i	0.594590	+	1.02986i
$188$	8.30909	−	14.3918i	0.606003	−	1.04963i
$189$	2.40805	+	1.09603i	0.175160	+	0.0797241i
$190$	11.6266			0.843484
$191$	−20.7750			−1.50323			−0.751613	−	0.659604i	$-0.770724\pi$
$191$	−20.7750			−1.50323			−0.751613	+	0.659604i	$0.770724\pi$
$192$	9.84585			0.710563
$193$	−17.0538			−1.22756			−0.613780	−	0.789477i	$-0.710352\pi$
$193$	−17.0538			−1.22756			−0.613780	+	0.789477i	$0.710352\pi$
$194$	−10.5598	−	18.2901i	−0.758148	−	1.31315i
$195$	−2.15732	−	4.83815i	−0.154489	−	0.346467i
$196$	11.1231	−	32.4044i	0.794508	−	2.31460i
$197$	−5.70304	−	9.87796i	−0.406325	−	0.703776i	0.588150	−	0.808752i	$-0.299857\pi$
$197$	−5.70304	−	9.87796i	−0.406325	−	0.703776i	−0.994475	+	0.104977i	$0.966523\pi$
$198$	−5.88333	+	10.1902i	−0.418110	+	0.724188i
$199$	5.22215	+	9.04502i	0.370188	+	0.641185i	0.989594	−	0.143886i	$-0.0459599\pi$
$199$	5.22215	+	9.04502i	0.370188	+	0.641185i	−0.619406	+	0.785071i	$0.712627\pi$
$200$	10.7969	−	18.7007i	0.763454	−	1.32234i
$201$	4.67078			0.329452
$202$	18.2539	−	31.6167i	1.28434	−	2.22454i
$203$	−2.03051	−	20.9826i	−0.142514	−	1.47269i
$204$	8.88023	−	15.3810i	0.621741	−	1.07689i
$205$	−1.63583	+	2.83334i	−0.114251	+	0.197889i
$206$	39.9950			2.78659
$207$	−3.87459	+	6.71099i	−0.269303	+	0.466446i
$208$	21.5277	−	29.6652i	1.49268	−	2.05691i
$209$	−13.5061			−0.934235
$210$	−9.28961	−	4.22816i	−0.641044	−	0.291771i
$211$	−3.06851	−	5.31482i	−0.211245	−	0.365887i	0.740859	−	0.671660i	$-0.234418\pi$
$211$	−3.06851	−	5.31482i	−0.211245	−	0.365887i	−0.952104	+	0.305773i	$0.901085\pi$
$212$	41.6623			2.86138
$213$	1.24524	−	2.15682i	0.0853226	−	0.147783i
$214$	14.0824	+	24.3914i	0.962654	+	1.66736i
$215$	7.48305			0.510340
$216$	7.59966			0.517091
$217$	−2.37983	+	1.69923i	−0.161554	+	0.115351i
$218$	18.2080	+	31.5372i	1.23320	+	2.13597i
$219$	3.03070	−	5.24932i	0.204796	−	0.354716i
$220$	16.1122	−	27.9072i	1.08629	−	1.88150i
$221$	−5.32831	−	11.9496i	−0.358421	−	0.803820i
$222$	4.13762	+	7.16656i	0.277699	+	0.480988i
$223$	13.1521	+	22.7802i	0.880733	+	1.52547i	0.850528	+	0.525930i	$0.176283\pi$
$223$	13.1521	+	22.7802i	0.880733	+	1.52547i	0.0302045	+	0.999544i	$0.490384\pi$
$224$	−2.92892	−	30.2665i	−0.195697	−	2.02226i
$225$	1.42070	−	2.46073i	0.0947136	−	0.164049i
$226$	−2.52440	−	4.37239i	−0.167921	−	0.290847i
$227$	−1.96653	−	3.40613i	−0.130523	−	0.226073i	0.793355	−	0.608759i	$-0.208332\pi$
$227$	−1.96653	−	3.40613i	−0.130523	−	0.226073i	−0.923878	+	0.382686i	$0.874999\pi$
$228$	7.37540	+	12.7746i	0.488448	+	0.846016i
$229$	5.68842	+	9.85263i	0.375901	+	0.651080i	0.990461	−	0.137790i	$-0.0439999\pi$
$229$	5.68842	+	9.85263i	0.375901	+	0.651080i	−0.614560	+	0.788870i	$0.710667\pi$
$230$	14.9471	−	25.8891i	0.985583	−	1.70708i
$231$	10.7913	+	4.91165i	0.710015	+	0.323163i
$232$	−30.2760	−	52.4396i	−1.98772	−	3.44283i
$233$	2.99657	+	5.19021i	0.196312	+	0.340022i	0.947330	−	0.320260i	$-0.103770\pi$
$233$	2.99657	+	5.19021i	0.196312	+	0.340022i	−0.751018	+	0.660282i	$0.770437\pi$
$234$	5.56036	−	7.66216i	0.363492	−	0.500891i
$235$	−2.49428	+	4.32022i	−0.162709	+	0.281820i
$236$	−35.3850	+	61.2885i	−2.30336	+	3.98954i
$237$	−3.59127	−	6.22026i	−0.233278	−	0.404050i
$238$	−22.9442	−	10.4431i	−1.48725	−	0.676923i
$239$	−8.09328			−0.523511			−0.261755	−	0.965134i	$-0.584301\pi$
$239$	−8.09328			−0.523511			−0.261755	+	0.965134i	$0.584301\pi$
$240$	−14.9357			−0.964098
$241$	7.80327	+	13.5157i	0.502653	+	0.870620i	0.999995	+	0.00306601i	$0.000975944\pi$
$241$	7.80327	+	13.5157i	0.502653	+	0.870620i	−0.497342	+	0.867554i	$0.665691\pi$
$242$	−11.9238	+	20.6526i	−0.766488	+	1.32760i
$243$	1.00000			0.0641500
$244$	−18.6557	−	32.3127i	−1.19431	−	2.06861i
$245$	−3.33902	+	9.72738i	−0.213322	+	0.621460i
$246$	−5.84693			−0.372787
$247$	10.8077	+	1.12984i	0.687678	+	0.0718903i
$248$	−4.19975	+	7.27418i	−0.266684	+	0.461911i
$249$	9.30835			0.589892
$250$	−15.1250	+	26.1973i	−0.956589	+	1.65686i
$251$	−4.67520	+	8.09769i	−0.295096	+	0.511122i	−0.975007	−	0.222173i	$-0.928685\pi$
$251$	−4.67520	+	8.09769i	−0.295096	+	0.511122i	0.679911	+	0.733295i	$0.262018\pi$
$252$	−1.24728	−	12.8890i	−0.0785712	−	0.811929i
$253$	−17.3633	+	30.0741i	−1.09162	+	1.89075i
$254$	45.1828			2.83502
$255$	−2.66573	+	4.61718i	−0.166935	+	0.289139i
$256$	6.08303	+	10.5361i	0.380189	+	0.658507i
$257$	−4.86470	+	8.42591i	−0.303452	+	0.525594i	−0.976915	−	0.213627i	$-0.931472\pi$
$257$	−4.86470	+	8.42591i	−0.303452	+	0.525594i	0.673464	+	0.739220i	$0.264806\pi$
$258$	6.68667	+	11.5816i	0.416294	+	0.721042i
$259$	6.78611	−	4.84538i	0.421669	−	0.301077i
$260$	−15.2277	+	20.9838i	−0.944384	+	1.30136i
$261$	−3.98387	−	6.90026i	−0.246595	−	0.427115i
$262$	13.1521			0.812540
$263$	−14.5155			−0.895065			−0.447532	−	0.894268i	$-0.647697\pi$
$263$	−14.5155			−0.895065			−0.447532	+	0.894268i	$0.647697\pi$
$264$	34.0566			2.09604
$265$	−12.5065			−0.768268
$266$	17.0394	−	12.1664i	1.04475	−	0.745969i
$267$	−3.18037	+	5.50857i	−0.194636	+	0.337119i
$268$	−11.4302	−	19.7976i	−0.698209	−	1.20933i
$269$	9.21624	+	15.9630i	0.561924	+	0.973281i	0.997329	+	0.0730463i	$0.0232721\pi$
$269$	9.21624	+	15.9630i	0.561924	+	0.973281i	−0.435404	+	0.900235i	$0.643395\pi$
$270$	−3.85772			−0.234774
$271$	−2.45214	+	4.24723i	−0.148957	+	0.258001i	−0.930842	−	0.365421i	$-0.880925\pi$
$271$	−2.45214	+	4.24723i	−0.148957	+	0.258001i	0.781885	+	0.623422i	$0.214258\pi$
$272$	−36.8895			−2.23675
$273$	−8.22443	−	4.83310i	−0.497765	−	0.292512i
$274$	−1.95533			−0.118126
$275$	6.36665	−	11.0274i	0.383923	−	0.664975i
$276$	37.9270			2.28294
$277$	12.9397	+	22.4122i	0.777469	+	1.34662i	0.933396	+	0.358848i	$0.116830\pi$
$277$	12.9397	+	22.4122i	0.777469	+	1.34662i	−0.155927	+	0.987769i	$0.549836\pi$
$278$	−15.9734	−	27.6667i	−0.958019	−	1.65934i
$279$	−0.552624	+	0.957172i	−0.0330847	+	0.0573044i
$280$	2.84544	+	29.4038i	0.170048	+	1.75722i
$281$	4.64246			0.276946			0.138473	−	0.990366i	$-0.455781\pi$
$281$	4.64246			0.276946			0.138473	+	0.990366i	$0.455781\pi$
$282$	−8.91531			−0.530899
$283$	−24.2852			−1.44360			−0.721802	−	0.692100i	$-0.756686\pi$
$283$	−24.2852			−1.44360			−0.721802	+	0.692100i	$0.756686\pi$
$284$	−12.1892			−0.723299
$285$	−2.21400	−	3.83476i	−0.131146	−	0.227151i
$286$	24.9178	−	34.3367i	1.47342	−	2.03037i
$287$	0.567483	+	5.86418i	0.0334975	+	0.346152i
$288$	−5.74654	−	9.95330i	−0.338618	−	0.586504i
$289$	1.91596	−	3.31854i	0.112704	−	0.195208i
$290$	15.3687	+	26.6193i	0.902479	+	1.56314i
$291$	−4.02169	+	6.96578i	−0.235756	+	0.408341i
$292$	−29.6665			−1.73610
$293$	−10.1171	+	17.5233i	−0.591047	+	1.02372i	0.403045	+	0.915180i	$0.367952\pi$
$293$	−10.1171	+	17.5233i	−0.591047	+	1.02372i	−0.994092	+	0.108543i	$0.965381\pi$
$294$	−18.0389	+	3.52429i	−1.05205	+	0.205541i
$295$	10.6221	−	18.3980i	0.618443	−	1.07117i
$296$	11.9756	−	20.7424i	0.696069	−	1.20563i
$297$	4.48133			0.260033
$298$	−3.41922	+	5.92226i	−0.198070	+	0.343067i
$299$	16.4102	−	22.6131i	0.949024	−	1.30775i
$300$	−13.9068			−0.802909
$301$	10.9668	−	7.83046i	0.632117	−	0.451340i
$302$	18.1160	+	31.3779i	1.04246	+	1.80559i
$303$	−13.9040			−0.798765
$304$	15.3191	−	26.5335i	0.878612	−	1.52180i
$305$	5.60021	+	9.69984i	0.320667	+	0.555411i
$306$	−9.52812			−0.544686
$307$	2.00196			0.114258			0.0571290	−	0.998367i	$-0.481805\pi$
$307$	2.00196			0.114258			0.0571290	+	0.998367i	$0.481805\pi$
$308$	−5.58947	−	57.7597i	−0.318490	−	3.29117i
$309$	−7.61605	−	13.1914i	−0.433262	−	0.750432i
$310$	2.13187	−	3.69251i	0.121082	−	0.209720i
$311$	−2.81050	+	4.86793i	−0.159369	+	0.276035i	−0.934641	−	0.355592i	$-0.884279\pi$
$311$	−2.81050	+	4.86793i	−0.159369	+	0.276035i	0.775272	+	0.631627i	$0.217613\pi$
$312$	−27.2524	−	2.84899i	−1.54287	−	0.161292i
$313$	−11.1532	−	19.3179i	−0.630417	−	1.09192i	−0.987466	−	0.157829i	$-0.949550\pi$
$313$	−11.1532	−	19.3179i	−0.630417	−	1.09192i	0.357049	−	0.934086i	$-0.383783\pi$
$314$	−0.649906	−	1.12567i	−0.0366763	−	0.0635253i
$315$	0.374417	+	3.86910i	0.0210960	+	0.217999i
$316$	−17.5769	+	30.4440i	−0.988776	+	1.71261i
$317$	13.4742	+	23.3380i	0.756787	+	1.31079i	0.944481	+	0.328566i	$0.106565\pi$
$317$	13.4742	+	23.3380i	0.756787	+	1.31079i	−0.187694	+	0.982227i	$0.560101\pi$
$318$	−11.1755	−	19.3565i	−0.626690	−	1.08546i
$319$	−17.8530	−	30.9223i	−0.999577	−	1.73132i
$320$	7.23284	+	12.5276i	0.404328	+	0.700316i
$321$	5.36329	−	9.28948i	0.299349	−	0.518488i
$322$	−5.18528	−	53.5830i	−0.288964	−	2.98606i
$323$	−5.46831	−	9.47140i	−0.304265	−	0.527003i
$324$	−2.44716	−	4.23861i	−0.135954	−	0.235479i
$325$	−6.01715	+	8.29161i	−0.333771	+	0.459936i
$326$	−12.1575	+	21.0575i	−0.673343	+	1.16627i
$327$	6.93451	−	12.0109i	0.383480	−	0.664206i
$328$	8.46148	+	14.6557i	0.467207	+	0.809226i
$329$	0.865289	+	8.94160i	0.0477049	+	0.492967i
$330$	−17.2877			−0.951659
$331$	4.56139			0.250716			0.125358	−	0.992112i	$-0.459992\pi$
$331$	4.56139			0.250716			0.125358	+	0.992112i	$0.459992\pi$
$332$	−22.7791	−	39.4545i	−1.25016	−	2.16535i
$333$	1.57581	−	2.72938i	0.0863539	−	0.149569i
$334$	41.9774			2.29690
$335$	3.43119	+	5.94300i	0.187466	+	0.324701i
$336$	−21.8891	+	15.6291i	−1.19415	+	0.852640i
$337$	25.6864			1.39923			0.699614	−	0.714521i	$-0.253355\pi$
$337$	25.6864			1.39923			0.699614	+	0.714521i	$0.253355\pi$
$338$	−22.8119	+	25.3921i	−1.24080	+	1.38115i
$339$	−0.961419	+	1.66523i	−0.0522171	+	0.0904427i
$340$	26.0939			1.41514
$341$	−2.47649	+	4.28940i	−0.134109	+	0.232284i
$342$	3.95675	−	6.85329i	0.213956	−	0.370583i
$343$	5.28547	+	17.7500i	0.285389	+	0.958412i
$344$	19.3534	−	33.5211i	1.04347	−	1.80734i
$345$	−11.3852			−0.612959
$346$	−13.7516	+	23.8185i	−0.739292	+	1.28049i
$347$	−7.28548	−	12.6188i	−0.391105	−	0.677414i	0.601490	−	0.798880i	$-0.294574\pi$
$347$	−7.28548	−	12.6188i	−0.391105	−	0.677414i	−0.992596	+	0.121466i	$0.961240\pi$
$348$	−19.4984	+	33.7721i	−1.04522	+	1.81038i
$349$	8.87949	+	15.3797i	0.475308	+	0.823258i	0.999600	−	0.0282805i	$-0.00900317\pi$
$349$	8.87949	+	15.3797i	0.475308	+	0.823258i	−0.524292	+	0.851539i	$0.675670\pi$
$350$	1.90130	+	19.6474i	0.101629	+	1.05020i
$351$	−3.58601	−	0.374884i	−0.191407	−	0.0200098i
$352$	−25.7522	−	44.6040i	−1.37259	−	2.37740i
$353$	6.69731			0.356462			0.178231	−	0.983989i	$-0.442963\pi$
$353$	6.69731			0.356462			0.178231	+	0.983989i	$0.442963\pi$
$354$	37.9666			2.01790
$355$	3.65906			0.194203
$356$	31.1316			1.64997
$357$	0.924766	+	9.55622i	0.0489438	+	0.505769i
$358$	−13.7109	+	23.7480i	−0.724645	+	1.25512i
$359$	−16.8686	−	29.2173i	−0.890292	−	1.54203i	−0.839526	−	0.543320i	$-0.817167\pi$
$359$	−16.8686	−	29.2173i	−0.890292	−	1.54203i	−0.0507658	−	0.998711i	$-0.516166\pi$
$360$	5.58276	+	9.66963i	0.294237	+	0.509634i
$361$	−9.91669			−0.521931
$362$	19.5433	−	33.8500i	1.02717	−	1.77912i
$363$	9.08233			0.476699
$364$	−0.359107	+	46.6875i	−0.0188223	+	2.44709i
$365$	8.90549			0.466135
$366$	−10.0084	+	17.3351i	−0.523148	+	0.906119i
$367$	−22.7525			−1.18767			−0.593835	−	0.804587i	$-0.702387\pi$
$367$	−22.7525			−1.18767			−0.593835	+	0.804587i	$0.702387\pi$
$368$	−39.3883	−	68.2225i	−2.05326	−	3.55635i
$369$	1.11340	+	1.92847i	0.0579614	+	0.100392i
$370$	−6.07905	+	10.5292i	−0.316035	+	0.547388i
$371$	−18.3289	+	13.0871i	−0.951592	+	0.679450i
$372$	5.40944			0.280467
$373$	17.1800			0.889547			0.444774	−	0.895643i	$-0.353284\pi$
$373$	17.1800			0.889547			0.444774	+	0.895643i	$0.353284\pi$
$374$	−42.6987			−2.20789
$375$	11.5207			0.594927
$376$	12.9019	+	22.3468i	0.665366	+	1.15245i
$377$	11.6994	+	26.2379i	0.602549	+	1.35132i
$378$	−5.65370	+	4.03682i	−0.290795	+	0.207632i
$379$	10.9914	+	19.0377i	0.564590	+	0.977899i	0.997088	+	0.0762637i	$0.0242991\pi$
$379$	10.9914	+	19.0377i	0.564590	+	0.977899i	−0.432498	+	0.901635i	$0.642368\pi$
$380$	−10.8360	+	18.7686i	−0.555877	+	0.962807i
$381$	−8.60394	−	14.9025i	−0.440793	−	0.763476i
$382$	27.2745	−	47.2408i	1.39549	−	2.41705i
$383$	3.04916			0.155805			0.0779023	−	0.996961i	$-0.475178\pi$
$383$	3.04916			0.155805			0.0779023	+	0.996961i	$0.475178\pi$
$384$	−1.43307	+	2.48215i	−0.0731312	+	0.126667i
$385$	1.67789	+	17.3387i	0.0855131	+	0.883663i
$386$	22.3892	−	38.7792i	1.13958	−	1.97381i
$387$	2.54662	−	4.41087i	0.129452	−	0.224217i
$388$	39.3670			1.99856
$389$	7.29046	−	12.6274i	0.369641	−	0.640237i	−0.619868	−	0.784706i	$-0.712814\pi$
$389$	7.29046	−	12.6274i	0.369641	−	0.640237i	0.989509	+	0.144469i	$0.0461474\pi$
$390$	13.8338	+	1.44620i	0.700504	+	0.0732311i
$391$	−28.1201			−1.42209
$392$	34.9391	+	40.1154i	1.76469	+	2.02613i
$393$	−2.50449	−	4.33791i	−0.126335	−	0.218818i
$394$	29.9490			1.50881
$395$	5.27635	−	9.13890i	0.265482	−	0.459828i
$396$	−10.9666	−	18.9946i	−0.551090	−	0.954516i
$397$	−7.02211			−0.352430			−0.176215	−	0.984352i	$-0.556385\pi$
$397$	−7.02211			−0.352430			−0.176215	+	0.984352i	$0.556385\pi$
$398$	−27.4236			−1.37462
$399$	−7.25753	−	3.30326i	−0.363331	−	0.165370i
$400$	14.4426	+	25.0153i	0.722130	+	1.25077i
$401$	−4.44694	+	7.70233i	−0.222070	+	0.384636i	−0.955436	−	0.295197i	$-0.904615\pi$
$401$	−4.44694	+	7.70233i	−0.222070	+	0.384636i	0.733367	+	0.679833i	$0.237948\pi$
$402$	−6.13205	+	10.6210i	−0.305839	+	0.529728i
$403$	2.34054	−	3.22526i	0.116591	−	0.160662i
$404$	34.0254	+	58.9337i	1.69283	+	2.93206i
$405$	0.734607	+	1.27238i	0.0365029	+	0.0632249i
$406$	50.3787	+	22.9299i	2.50025	+	1.13799i
$407$	7.06173	−	12.2313i	0.350037	−	0.606282i
$408$	13.7888	+	23.8828i	0.682645	+	1.18238i
$409$	0.273732	+	0.474117i	0.0135352	+	0.0234436i	0.872714	−	0.488232i	$-0.162358\pi$
$409$	0.273732	+	0.474117i	0.0135352	+	0.0234436i	−0.859178	+	0.511676i	$0.829025\pi$
$410$	−4.29520	−	7.43951i	−0.212125	−	0.367411i
$411$	0.372343	+	0.644917i	0.0183663	+	0.0318114i
$412$	−37.2755	+	64.5630i	−1.83643	+	3.18079i
$413$	−3.68490	−	38.0786i	−0.181322	−	1.87372i
$414$	−10.1735	−	17.6211i	−0.500002	−	0.866028i
$415$	6.83798	+	11.8437i	0.335663	+	0.581386i
$416$	16.8758	+	37.8469i	0.827405	+	1.85560i
$417$	−6.08346	+	10.5369i	−0.297908	+	0.515992i
$418$	17.7315	−	30.7118i	0.867276	−	1.50217i
$419$	−15.9631	−	27.6488i	−0.779847	−	1.35073i	−0.932030	−	0.362382i	$-0.881964\pi$
$419$	−15.9631	−	27.6488i	−0.779847	−	1.35073i	0.152183	−	0.988352i	$-0.451370\pi$
$420$	15.4834	−	11.0553i	0.755511	−	0.539445i
$421$	−25.4622			−1.24095			−0.620476	−	0.784226i	$-0.713060\pi$
$421$	−25.4622			−1.24095			−0.620476	+	0.784226i	$0.713060\pi$
$422$	16.1140			0.784418
$423$	1.69770	+	2.94050i	0.0825449	+	0.142972i
$424$	−32.3455	+	56.0241i	−1.57084	+	2.72077i
$425$	10.3109			0.500150
$426$	3.26964	+	5.66318i	0.158415	+	0.274382i
$427$	18.3576	+	8.35544i	0.888385	+	0.404348i
$428$	−52.4994			−2.53765
$429$	−16.0701	−	1.67998i	−0.775871	−	0.0811101i
$430$	−9.82415	+	17.0159i	−0.473762	+	0.820581i
$431$	15.5511			0.749070			0.374535	−	0.927213i	$-0.377802\pi$
$431$	15.5511			0.749070			0.374535	+	0.927213i	$0.377802\pi$
$432$	−5.08290	+	8.80384i	−0.244551	+	0.423575i
$433$	15.1163	−	26.1822i	0.726443	−	1.25824i	−0.231934	−	0.972731i	$-0.574505\pi$
$433$	15.1163	−	26.1822i	0.726443	−	1.25824i	0.958377	−	0.285505i	$-0.0921612\pi$
$434$	−0.739564	−	7.64241i	−0.0355002	−	0.366847i
$435$	5.85315	−	10.1380i	0.280637	−	0.486078i
$436$	−67.8796			−3.25084
$437$	11.6774	−	20.2259i	0.558608	−	0.967537i
$438$	7.95772	+	13.7832i	0.380234	+	0.658585i
$439$	−17.8051	+	30.8394i	−0.849793	+	1.47188i	0.0315997	+	0.999501i	$0.489940\pi$
$439$	−17.8051	+	30.8394i	−0.849793	+	1.47188i	−0.881393	+	0.472384i	$0.843394\pi$
$440$	25.0182	+	43.3328i	1.19270	+	2.06581i
$441$	4.59746	+	5.27858i	0.218927	+	0.251361i
$442$	34.1679	+	3.57193i	1.62520	+	0.169900i
$443$	−4.10324	−	7.10702i	−0.194951	−	0.337665i	0.751934	−	0.659239i	$-0.229121\pi$
$443$	−4.10324	−	7.10702i	−0.194951	−	0.337665i	−0.946884	+	0.321574i	$0.895788\pi$
$444$	−15.4251			−0.732042
$445$	−9.34531			−0.443010
$446$	−69.0673			−3.27043
$447$	2.60442			0.123185
$448$	23.7094	+	10.7913i	1.12016	+	0.509841i
$449$	−5.74953	+	9.95847i	−0.271337	+	0.469969i	−0.969204	−	0.246258i	$-0.920799\pi$
$449$	−5.74953	+	9.95847i	−0.271337	+	0.469969i	0.697868	+	0.716227i	$0.254132\pi$
$450$	3.73035	+	6.46116i	0.175850	+	0.304582i
$451$	4.98953	+	8.64211i	0.234948	+	0.406941i
$452$	9.41100			0.442656
$453$	6.89949	−	11.9503i	0.324166	−	0.561473i
$454$	10.3271			0.484673
$455$	0.107799	−	14.0150i	0.00505371	−	0.657033i
$456$	−22.9043			−1.07259
$457$	4.45736	−	7.72037i	0.208506	−	0.361144i	−0.742738	−	0.669582i	$-0.766473\pi$
$457$	4.45736	−	7.72037i	0.208506	−	0.361144i	0.951244	+	0.308439i	$0.0998064\pi$
$458$	−29.8722			−1.39584
$459$	1.81439	+	3.14262i	0.0846886	+	0.146685i
$460$	27.8615	+	48.2575i	1.29905	+	2.25002i
$461$	6.22417	−	10.7806i	0.289888	−	0.502101i	−0.683895	−	0.729581i	$-0.739715\pi$
$461$	6.22417	−	10.7806i	0.289888	−	0.502101i	0.973783	+	0.227480i	$0.0730485\pi$
$462$	−25.3361	+	18.0903i	−1.17874	+	0.841639i
$463$	22.4118			1.04156			0.520782	−	0.853690i	$-0.325640\pi$
$463$	22.4118			1.04156			0.520782	+	0.853690i	$0.325640\pi$
$464$	80.9984			3.76025
$465$	−1.62385			−0.0753040
$466$	−15.7362			−0.728966
$467$	13.2868	+	23.0134i	0.614839	+	1.06493i	0.990413	+	0.138140i	$0.0441125\pi$
$467$	13.2868	+	23.0134i	0.614839	+	1.06493i	−0.375573	+	0.926793i	$0.622554\pi$
$468$	7.18657	+	16.1171i	0.332199	+	0.745014i
$469$	11.2475	+	5.11930i	0.519361	+	0.236387i
$470$	−6.54925	−	11.3436i	−0.302094	−	0.523243i
$471$	−0.247517	+	0.428712i	−0.0114050	+	0.0197540i
$472$	−54.9439	−	95.1656i	−2.52900	−	4.38035i
$473$	11.4122	−	19.7666i	0.524735	−	0.908868i
$474$	18.8592			0.866234
$475$	−4.28179	+	7.41629i	−0.196462	+	0.340283i
$476$	38.2421	−	27.3054i	1.75282	−	1.25154i
$477$	−4.25619	+	7.37193i	−0.194877	+	0.337537i
$478$	10.6253	−	18.4035i	0.485989	−	0.841758i
$479$	−9.30919			−0.425348			−0.212674	−	0.977123i	$-0.568217\pi$
$479$	−9.30919			−0.425348			−0.212674	+	0.977123i	$0.568217\pi$
$480$	8.44290	−	14.6235i	0.385364	−	0.667470i
$481$	−6.67407	+	9.19685i	−0.304312	+	0.419340i
$482$	−40.9782			−1.86651
$483$	−16.6856	+	11.9138i	−0.759223	+	0.542096i
$484$	−22.2260	−	38.4965i	−1.01027	−	1.74984i
$485$	−11.8175			−0.536603
$486$	−1.31285	+	2.27393i	−0.0595522	+	0.103147i
$487$	4.74247	+	8.21419i	0.214902	+	0.372221i	0.953242	−	0.302208i	$-0.0977236\pi$
$487$	4.74247	+	8.21419i	0.214902	+	0.372221i	−0.738340	+	0.674428i	$0.764390\pi$
$488$	57.9352			2.62261
$489$	9.26039			0.418769
$490$	−17.7357	−	20.3633i	−0.801218	−	0.919920i
$491$	−7.76607	−	13.4512i	−0.350478	−	0.607046i	0.635855	−	0.771808i	$-0.280647\pi$
$491$	−7.76607	−	13.4512i	−0.350478	−	0.607046i	−0.986333	+	0.164763i	$0.947314\pi$
$492$	5.44936	−	9.43857i	0.245676	−	0.425523i
$493$	14.4566	−	25.0395i	0.651092	−	1.12772i
$494$	−16.7581	+	23.0926i	−0.753983	+	1.03899i
$495$	3.29202	+	5.70194i	0.147965	+	0.256283i
$496$	−5.61786	−	9.73042i	−0.252249	−	0.436909i
$497$	5.36254	−	3.82893i	0.240543	−	0.171751i
$498$	−12.2205	+	21.1665i	−0.547613	+	0.948494i
$499$	−9.80198	−	16.9775i	−0.438797	−	0.760019i	0.558800	−	0.829302i	$-0.311262\pi$
$499$	−9.80198	−	16.9775i	−0.438797	−	0.760019i	−0.997597	+	0.0692837i	$0.977929\pi$
$500$	−28.1931	−	48.8318i	−1.26083	−	2.18383i
$501$	−7.99354	−	13.8452i	−0.357125	−	0.618559i
$502$	−12.2757	−	21.2622i	−0.547892	−	0.948976i
$503$	−16.8374	+	29.1632i	−0.750741	+	1.30032i	0.196723	+	0.980459i	$0.436970\pi$
$503$	−16.8374	+	29.1632i	−0.750741	+	1.30032i	−0.947464	+	0.319862i	$0.896363\pi$
$504$	18.3004	+	8.32942i	0.815164	+	0.371022i
$505$	−10.2140	−	17.6911i	−0.454517	−	0.787246i
$506$	−45.5910	−	78.9659i	−2.02677	−	3.51046i
$507$	12.7189	+	2.68867i	0.564867	+	0.119408i
$508$	−42.1105	+	72.9375i	−1.86835	+	3.23608i
$509$	−9.34762	+	16.1906i	−0.414326	+	0.717634i	−0.995357	−	0.0962474i	$-0.969316\pi$
$509$	−9.34762	+	16.1906i	−0.414326	+	0.717634i	0.581031	+	0.813881i	$0.302649\pi$
$510$	−6.99943	−	12.1234i	−0.309940	−	0.536831i
$511$	13.0515	−	9.31893i	0.577363	−	0.412245i
$512$	−37.6768			−1.66509
$513$	−3.01385			−0.133065
$514$	−12.7733	−	22.1239i	−0.563405	−	0.975846i
$515$	11.1896	−	19.3810i	0.493073	−	0.854028i
$516$	−24.9280			−1.09739
$517$	7.60795	+	13.1774i	0.334597	+	0.579539i
$518$	2.10887	+	21.7924i	0.0926586	+	0.957503i
$519$	10.4746			0.459785
$520$	−16.3949	−	36.7683i	−0.718962	−	1.61240i
$521$	−11.2457	+	19.4782i	−0.492684	+	0.853355i	−0.999964	−	0.00842674i	$-0.997318\pi$
$521$	−11.2457	+	19.4782i	−0.492684	+	0.853355i	0.507280	+	0.861781i	$0.330651\pi$
$522$	20.9209			0.915684
$523$	19.0474	−	32.9911i	0.832886	−	1.44260i	−0.0628541	−	0.998023i	$-0.520020\pi$
$523$	19.0474	−	32.9911i	0.832886	−	1.44260i	0.895740	−	0.444578i	$-0.146646\pi$
$524$	−12.2578	+	21.2311i	−0.535485	+	0.927487i
$525$	6.11816	−	4.36845i	0.267018	−	0.190655i
$526$	19.0567	−	33.0072i	0.830913	−	1.43918i
$527$	−4.01070			−0.174709
$528$	−22.7782	+	39.4529i	−0.991292	+	1.71697i
$529$	−18.5249	−	32.0860i	−0.805430	−	1.39505i
$530$	16.4192	−	28.4389i	0.713204	−	1.23531i
$531$	−7.22979	−	12.5224i	−0.313746	−	0.543424i
$532$	3.75912	+	38.8455i	0.162978	+	1.68416i
$533$	−3.26972	−	7.33291i	−0.141627	−	0.317623i
$534$	−8.35073	−	14.4639i	−0.361371	−	0.625913i
$535$	15.7596			0.681348
$536$	35.4963			1.53321
$537$	10.4436			0.450675
$538$	−48.3983			−2.08660
$539$	20.6027	+	23.6551i	0.887422	+	1.01890i
$540$	3.59541	−	6.22743i	0.154722	−	0.267986i
$541$	10.6876	+	18.5115i	0.459496	+	0.795870i	0.998934	−	0.0461548i	$-0.0146968\pi$
$541$	10.6876	+	18.5115i	0.459496	+	0.795870i	−0.539438	+	0.842025i	$0.681363\pi$
$542$	−6.43860	−	11.1520i	−0.276562	−	0.479019i
$543$	−14.8861			−0.638825
$544$	20.8530	−	36.1184i	0.894063	−	1.54856i
$545$	20.3766			0.872837
$546$	21.7876	−	12.3566i	0.932422	−	0.528814i
$547$	21.9105			0.936827			0.468414	−	0.883509i	$-0.344826\pi$
$547$	21.9105			0.936827			0.468414	+	0.883509i	$0.344826\pi$
$548$	1.82237	−	3.15644i	0.0778478	−	0.134836i
$549$	7.62340			0.325359
$550$	16.7169	+	28.9546i	0.712813	+	1.23463i
$551$	12.0068	+	20.7964i	0.511506	+	0.885955i
$552$	−29.4455	+	51.0012i	−1.25329	+	2.17075i
$553$	−1.83041	−	18.9149i	−0.0778370	−	0.804342i
$554$	−67.9515			−2.88698
$555$	4.63041			0.196550
$556$	59.5489			2.52544
$557$	7.11154			0.301326			0.150663	−	0.988585i	$-0.451859\pi$
$557$	7.11154			0.301326			0.150663	+	0.988585i	$0.451859\pi$
$558$	−1.45103	−	2.51325i	−0.0614269	−	0.106394i
$559$	−10.7858	+	14.8627i	−0.456189	+	0.628627i
$560$	−35.9661	−	16.3700i	−1.51984	−	0.691757i
$561$	8.13089	+	14.0831i	0.343287	+	0.594590i
$562$	−6.09486	+	10.5566i	−0.257096	+	0.445304i
$563$	−12.6181	−	21.8552i	−0.531789	−	0.921086i	−0.999311	−	0.0371048i	$-0.988186\pi$
$563$	−12.6181	−	21.8552i	−0.531789	−	0.921086i	0.467522	−	0.883981i	$-0.345147\pi$
$564$	8.30909	−	14.3918i	0.349876	−	0.606003i
$565$	−2.82506			−0.118851
$566$	31.8829	−	55.2227i	1.34014	−	2.32119i
$567$	2.40805	+	1.09603i	0.101129	+	0.0460287i
$568$	9.46341	−	16.3911i	0.397076	−	0.687756i
$569$	−7.97916	+	13.8203i	−0.334504	+	0.579377i	−0.983389	−	0.181509i	$-0.941902\pi$
$569$	−7.97916	+	13.8203i	−0.334504	+	0.579377i	0.648886	+	0.760886i	$0.275235\pi$
$570$	11.6266			0.486985
$571$	1.12785	−	1.95350i	0.0471992	−	0.0817514i	−0.841461	−	0.540318i	$-0.818304\pi$
$571$	1.12785	−	1.95350i	0.0471992	−	0.0817514i	0.888660	+	0.458567i	$0.151637\pi$
$572$	32.2054	+	72.2261i	1.34658	+	3.01992i
$573$	−20.7750			−0.867888
$574$	−14.0797	−	6.40839i	−0.587677	−	0.267481i
$575$	11.0093	+	19.0687i	0.459119	+	0.795218i
$576$	9.84585			0.410244
$577$	6.64490	−	11.5093i	0.276631	−	0.479138i	−0.693915	−	0.720057i	$-0.744115\pi$
$577$	6.64490	−	11.5093i	0.276631	−	0.479138i	0.970545	+	0.240919i	$0.0774488\pi$
$578$	5.03075	+	8.71352i	0.209252	+	0.362435i
$579$	−17.0538			−0.708733
$580$	−57.2945			−2.37903
$581$	22.4150	+	10.2022i	0.929931	+	0.423258i
$582$	−10.5598	−	18.2901i	−0.437717	−	0.758148i
$583$	−19.0734	+	33.0361i	−0.789939	+	1.36821i
$584$	23.0323	−	39.8930i	0.953082	−	1.65079i
$585$	−2.15732	−	4.83815i	−0.0891940	−	0.200033i
$586$	−26.5645	−	46.0111i	−1.09737	−	1.90070i
$587$	1.24993	+	2.16495i	0.0515903	+	0.0893570i	0.890667	−	0.454656i	$-0.150238\pi$
$587$	1.24993	+	2.16495i	0.0515903	+	0.0893570i	−0.839077	+	0.544013i	$0.816904\pi$
$588$	11.1231	−	32.4044i	0.458710	−	1.33633i
$589$	1.66553	−	2.88478i	0.0686268	−	0.118865i
$590$	27.8905	+	48.3078i	1.14823	+	1.98880i
$591$	−5.70304	−	9.87796i	−0.234592	−	0.406325i
$592$	16.0194	+	27.7464i	0.658392	+	1.14037i
$593$	18.7712	+	32.5127i	0.770841	+	1.33514i	0.937102	+	0.349054i	$0.113497\pi$
$593$	18.7712	+	32.5127i	0.770841	+	1.33514i	−0.166261	+	0.986082i	$0.553170\pi$
$594$	−5.88333	+	10.1902i	−0.241396	+	0.418110i
$595$	−11.4798	+	8.19672i	−0.470625	+	0.336033i
$596$	−6.37344	−	11.0391i	−0.261066	−	0.452180i
$597$	5.22215	+	9.04502i	0.213728	+	0.370188i
$598$	29.8765	+	67.0032i	1.22174	+	2.73997i
$599$	13.3080	−	23.0501i	0.543749	−	0.941800i	−0.454936	−	0.890524i	$-0.650338\pi$
$599$	13.3080	−	23.0501i	0.543749	−	0.941800i	0.998685	−	0.0512760i	$-0.0163288\pi$
$600$	10.7969	−	18.7007i	0.440780	−	0.763454i
$601$	−6.02647	−	10.4381i	−0.245825	−	0.425781i	0.716538	−	0.697548i	$-0.245725\pi$
$601$	−6.02647	−	10.4381i	−0.245825	−	0.425781i	−0.962363	+	0.271767i	$0.912392\pi$
$602$	3.40808	+	35.2180i	0.138903	+	1.43538i
$603$	4.67078			0.190209
$604$	−67.5368			−2.74803
$605$	6.67194	+	11.5561i	0.271253	+	0.469824i
$606$	18.2539	−	31.6167i	0.741515	−	1.28434i
$607$	−4.34000			−0.176155			−0.0880776	−	0.996114i	$-0.528072\pi$
$607$	−4.34000			−0.176155			−0.0880776	+	0.996114i	$0.528072\pi$
$608$	17.3192	+	29.9978i	0.702388	+	1.21657i
$609$	−2.03051	−	20.9826i	−0.0822804	−	0.850259i
$610$	−29.4090			−1.19074
$611$	−4.98562	−	11.1811i	−0.201696	−	0.452339i
$612$	8.88023	−	15.3810i	0.358962	−	0.621741i
$613$	−47.9317			−1.93594			−0.967972	−	0.251058i	$-0.919221\pi$
$613$	−47.9317			−1.93594			−0.967972	+	0.251058i	$0.919221\pi$
$614$	−2.62828	+	4.55231i	−0.106069	+	0.183716i
$615$	−1.63583	+	2.83334i	−0.0659629	+	0.114251i
$616$	82.0101	+	37.3269i	3.30428	+	1.50394i
$617$	−1.12653	+	1.95120i	−0.0453523	+	0.0785524i	−0.887810	−	0.460209i	$-0.847774\pi$
$617$	−1.12653	+	1.95120i	−0.0453523	+	0.0785524i	0.842458	+	0.538762i	$0.181108\pi$
$618$	39.9950			1.60884
$619$	4.42465	−	7.66373i	0.177842	−	0.308031i	−0.763299	−	0.646045i	$-0.776422\pi$
$619$	4.42465	−	7.66373i	0.177842	−	0.308031i	0.941141	+	0.338014i	$0.109755\pi$
$620$	3.97382	+	6.88285i	0.159592	+	0.276422i
$621$	−3.87459	+	6.71099i	−0.155482	+	0.269303i
$622$	−7.37955	−	12.7818i	−0.295893	−	0.512502i
$623$	−13.6960	+	9.77917i	−0.548721	+	0.391794i
$624$	21.5277	−	29.6652i	0.861799	−	1.18756i
$625$	1.35968	+	2.35503i	0.0543871	+	0.0942012i
$626$	58.5702			2.34093
$627$	−13.5061			−0.539381
$628$	2.42286			0.0966826
$629$	11.4366			0.456005
$630$	−9.28961	−	4.22816i	−0.370107	−	0.168454i
$631$	−19.9790	+	34.6047i	−0.795352	+	1.37759i	0.127264	+	0.991869i	$0.459381\pi$
$631$	−19.9790	+	34.6047i	−0.795352	+	1.37759i	−0.922615	+	0.385721i	$0.873953\pi$
$632$	−27.2924	−	47.2719i	−1.08563	−	1.88037i
$633$	−3.06851	−	5.31482i	−0.121962	−	0.211245i
$634$	−70.7586			−2.81018
$635$	12.6410	−	21.8949i	0.501644	−	0.868873i
$636$	41.6623			1.65202
$637$	−14.5077	−	20.6525i	−0.574815	−	0.818283i
$638$	93.7536			3.71174
$639$	1.24524	−	2.15682i	0.0492610	−	0.0853226i
$640$	−4.21098			−0.166454
$641$	−5.83326	−	10.1035i	−0.230400	−	0.399064i	0.727526	−	0.686080i	$-0.240670\pi$
$641$	−5.83326	−	10.1035i	−0.230400	−	0.399064i	−0.957926	+	0.287016i	$0.907337\pi$
$642$	14.0824	+	24.3914i	0.555788	+	0.962654i
$643$	−3.24846	+	5.62650i	−0.128107	+	0.221888i	−0.922943	−	0.384936i	$-0.874223\pi$
$643$	−3.24846	+	5.62650i	−0.128107	+	0.221888i	0.794836	+	0.606824i	$0.207557\pi$
$644$	91.3304	+	41.5690i	3.59892	+	1.63805i
$645$	7.48305			0.294645
$646$	28.7164			1.12983
$647$	14.9954			0.589528			0.294764	−	0.955570i	$-0.404759\pi$
$647$	14.9954			0.589528			0.294764	+	0.955570i	$0.404759\pi$
$648$	7.59966			0.298543
$649$	−32.3991	−	56.1168i	−1.27177	−	2.20278i
$650$	−10.9549	−	24.5682i	−0.429686	−	0.963645i
$651$	−2.37983	+	1.69923i	−0.0932730	+	0.0665982i
$652$	−22.6617	−	39.2512i	−0.887501	−	1.53720i
$653$	−18.4897	+	32.0252i	−0.723560	+	1.25324i	0.236005	+	0.971752i	$0.424162\pi$
$653$	−18.4897	+	32.0252i	−0.723560	+	1.25324i	−0.959564	+	0.281490i	$0.909171\pi$
$654$	18.2080	+	31.5372i	0.711989	+	1.23320i
$655$	3.67963	−	6.37331i	0.143775	−	0.249026i
$656$	−22.6373			−0.883836
$657$	3.03070	−	5.24932i	0.118239	−	0.204796i
$658$	−21.4686	−	9.77140i	−0.836931	−	0.380929i
$659$	−1.95181	+	3.38064i	−0.0760319	+	0.131691i	−0.901535	−	0.432707i	$-0.857558\pi$
$659$	−1.95181	+	3.38064i	−0.0760319	+	0.131691i	0.825503	+	0.564398i	$0.190892\pi$
$660$	16.1122	−	27.9072i	0.627167	−	1.08629i
$661$	39.4122			1.53296			0.766479	−	0.642270i	$-0.222007\pi$
$661$	39.4122			1.53296			0.766479	+	0.642270i	$0.222007\pi$
$662$	−5.98843	+	10.3723i	−0.232747	+	0.403129i
$663$	−5.32831	−	11.9496i	−0.206934	−	0.464086i
$664$	70.7402			2.74525
$665$	−1.12844	−	11.6609i	−0.0437590	−	0.452191i
$666$	4.13762	+	7.16656i	0.160329	+	0.277699i
$667$	61.7434			2.39071
$668$	−39.1230	+	67.7631i	−1.51372	+	2.62183i
$669$	13.1521	+	22.7802i	0.508491	+	0.880733i
$670$	−18.0186			−0.696119
$671$	34.1630			1.31885
$672$	−2.92892	−	30.2665i	−0.112985	−	1.16755i
$673$	17.4150	+	30.1637i	0.671301	+	1.16273i	0.977535	+	0.210771i	$0.0675974\pi$
$673$	17.4150	+	30.1637i	0.671301	+	1.16273i	−0.306235	+	0.951956i	$0.599069\pi$
$674$	−33.7225	+	58.4091i	−1.29894	+	2.24983i
$675$	1.42070	−	2.46073i	0.0546829	−	0.0947136i
$676$	−19.7291	−	60.4902i	−0.758810	−	2.32655i
$677$	−7.46136	−	12.9235i	−0.286763	−	0.496689i	0.686272	−	0.727345i	$-0.259246\pi$
$677$	−7.46136	−	12.9235i	−0.286763	−	0.496689i	−0.973035	+	0.230656i	$0.925913\pi$
$678$	−2.52440	−	4.37239i	−0.0969491	−	0.167921i
$679$	−17.3191	+	12.3661i	−0.664647	+	0.474567i
$680$	−20.2586	+	35.0890i	−0.776883	+	1.34560i
$681$	−1.96653	−	3.40613i	−0.0753577	−	0.130523i
$682$	−6.50253	−	11.2627i	−0.248995	−	0.431272i
$683$	11.0864	+	19.2023i	0.424210	+	0.734754i	0.996346	−	0.0854050i	$-0.0272184\pi$
$683$	11.0864	+	19.2023i	0.424210	+	0.734754i	−0.572136	+	0.820159i	$0.693885\pi$
$684$	7.37540	+	12.7746i	0.282005	+	0.488448i
$685$	−0.547052	+	0.947522i	−0.0209018	+	0.0362030i
$686$	−47.3013	−	11.2844i	−1.80597	−	0.430840i
$687$	5.68842	+	9.85263i	0.217027	+	0.375901i
$688$	25.8884	+	44.8400i	0.986986	+	1.70951i
$689$	18.0263	−	24.8402i	0.686749	−	0.946338i
$690$	14.9471	−	25.8891i	0.569026	−	0.985583i
$691$	8.83376	−	15.3005i	0.336052	−	0.582060i	−0.647634	−	0.761951i	$-0.724241\pi$
$691$	8.83376	−	15.3005i	0.336052	−	0.582060i	0.983686	+	0.179892i	$0.0575748\pi$
$692$	−25.6331	−	44.3978i	−0.974425	−	1.68775i
$693$	10.7913	+	4.91165i	0.409927	+	0.186578i
$694$	38.2591			1.45229
$695$	−17.8758			−0.678068
$696$	−30.2760	−	52.4396i	−1.14761	−	1.98772i
$697$	−4.04030	+	6.99800i	−0.153037	+	0.265068i
$698$	−46.6299			−1.76497
$699$	2.99657	+	5.19021i	0.113341	+	0.196312i
$700$	−33.4883	−	15.2422i	−1.26574	−	0.576101i
$701$	7.13063			0.269320			0.134660	−	0.990892i	$-0.457006\pi$
$701$	7.13063			0.269320			0.134660	+	0.990892i	$0.457006\pi$
$702$	5.56036	−	7.66216i	0.209862	−	0.289190i
$703$	−4.74926	+	8.22597i	−0.179122	+	0.310248i
$704$	44.1225			1.66293
$705$	−2.49428	+	4.32022i	−0.0939401	+	0.162709i
$706$	−8.79258	+	15.2292i	−0.330913	+	0.573158i
$707$	−33.4816	−	15.2391i	−1.25921	−	0.573127i
$708$	−35.3850	+	61.2885i	−1.32985	+	2.30336i
$709$	2.33048			0.0875231			0.0437615	−	0.999042i	$-0.486066\pi$
$709$	2.33048			0.0875231			0.0437615	+	0.999042i	$0.486066\pi$
$710$	−4.80380	+	8.32043i	−0.180283	+	0.312260i
$711$	−3.59127	−	6.22026i	−0.134683	−	0.233278i
$712$	−24.1698	+	41.8632i	−0.905800	+	1.56889i
$713$	−4.28238	−	7.41730i	−0.160376	−	0.277780i
$714$	−22.9442	−	10.4431i	−0.858666	−	0.390822i
$715$	−9.66764	−	21.6813i	−0.361549	−	0.810836i
$716$	−25.5572	−	44.2664i	−0.955119	−	1.65431i
$717$	−8.09328			−0.302249
$718$	88.5840			3.30593
$719$	−42.4303			−1.58238			−0.791192	−	0.611568i	$-0.790539\pi$
$719$	−42.4303			−1.58238			−0.791192	+	0.611568i	$0.790539\pi$
$720$	−14.9357			−0.556622
$721$	−3.88178	−	40.1130i	−0.144565	−	1.49389i
$722$	13.0191	−	22.5498i	0.484523	−	0.839218i
$723$	7.80327	+	13.5157i	0.290207	+	0.502653i
$724$	36.4288	+	63.0965i	1.35387	+	2.34496i
$725$	−22.6396			−0.840813
$726$	−11.9238	+	20.6526i	−0.442532	+	0.766488i
$727$	4.46010			0.165416			0.0827080	−	0.996574i	$-0.473643\pi$
$727$	4.46010			0.165416			0.0827080	+	0.996574i	$0.473643\pi$
$728$	−62.5028	−	36.7299i	−2.31651	−	1.36130i
$729$	1.00000			0.0370370
$730$	−11.6916	+	20.2504i	−0.432725	+	0.749502i
$731$	18.4822			0.683591
$732$	−18.6557	−	32.3127i	−0.689535	−	1.19431i
$733$	5.54355	+	9.60171i	0.204756	+	0.354647i	0.950055	−	0.312083i	$-0.101027\pi$
$733$	5.54355	+	9.60171i	0.204756	+	0.354647i	−0.745299	+	0.666730i	$0.767693\pi$
$734$	29.8706	−	51.7375i	1.10255	−	1.90967i
$735$	−3.33902	+	9.72738i	−0.123161	+	0.358800i
$736$	89.0620			3.28287
$737$	20.9313			0.771015
$738$	−5.84693			−0.215229
$739$	−11.2457			−0.413681			−0.206841	−	0.978375i	$-0.566318\pi$
$739$	−11.2457			−0.413681			−0.206841	+	0.978375i	$0.566318\pi$
$740$	−11.3314	−	19.6265i	−0.416550	−	0.721485i
$741$	10.8077	+	1.12984i	0.397031	+	0.0415059i
$742$	−5.69596	−	58.8602i	−0.209105	−	2.16082i
$743$	12.3604	+	21.4089i	0.453461	+	0.785417i	0.998598	−	0.0529295i	$-0.0168559\pi$
$743$	12.3604	+	21.4089i	0.453461	+	0.785417i	−0.545137	+	0.838347i	$0.683523\pi$
$744$	−4.19975	+	7.27418i	−0.153970	+	0.266684i
$745$	1.91322	+	3.31380i	0.0700951	+	0.121408i
$746$	−22.5548	+	39.0661i	−0.825791	+	1.43031i
$747$	9.30835			0.340575
$748$	39.7953	−	68.9274i	1.45506	−	2.52024i
$749$	23.0966	−	16.4913i	0.843931	−	0.602579i
$750$	−15.1250	+	26.1973i	−0.552287	+	0.956589i
$751$	2.08954	−	3.61919i	0.0762485	−	0.132066i	−0.825380	−	0.564578i	$-0.809039\pi$
$751$	2.08954	−	3.61919i	0.0762485	−	0.132066i	0.901629	+	0.432511i	$0.142372\pi$
$752$	−34.5169			−1.25870
$753$	−4.67520	+	8.09769i	−0.170374	+	0.295096i
$754$	−75.0226	−	7.84291i	−2.73216	−	0.285622i
$755$	20.2737			0.737834
$756$	−1.24728	−	12.8890i	−0.0453631	−	0.468767i
$757$	−17.9530	−	31.0955i	−0.652512	−	1.13018i	−0.982511	−	0.186203i	$-0.940382\pi$
$757$	−17.9530	−	31.0955i	−0.652512	−	1.13018i	0.329999	−	0.943981i	$-0.392951\pi$
$758$	−57.7203			−2.09650
$759$	−17.3633	+	30.0741i	−0.630249	+	1.09162i
$760$	−16.8256	−	29.1428i	−0.610330	−	1.05712i
$761$	17.8415			0.646754			0.323377	−	0.946270i	$-0.395182\pi$
$761$	17.8415			0.646754			0.323377	+	0.946270i	$0.395182\pi$
$762$	45.1828			1.63680
$763$	29.8630	−	21.3226i	1.08111	−	0.771929i
$764$	50.8398	+	88.0572i	1.83932	+	3.18580i
$765$	−2.66573	+	4.61718i	−0.0963797	+	0.166935i
$766$	−4.00309	+	6.93356i	−0.144638	+	0.250520i
$767$	21.2317	+	47.6156i	0.766631	+	1.71930i
$768$	6.08303	+	10.5361i	0.219502	+	0.380189i
$769$	−9.41573	−	16.3085i	−0.339540	−	0.588100i	0.644806	−	0.764346i	$-0.276938\pi$
$769$	−9.41573	−	16.3085i	−0.339540	−	0.588100i	−0.984346	+	0.176246i	$0.943605\pi$
$770$	−41.6298	−	18.9478i	−1.50023	−	0.682831i
$771$	−4.86470	+	8.42591i	−0.175198	+	0.303452i
$772$	41.7335	+	72.2845i	1.50202	+	2.60158i
$773$	22.6105	+	39.1625i	0.813243	+	1.40858i	0.910583	+	0.413326i	$0.135633\pi$
$773$	22.6105	+	39.1625i	0.813243	+	1.40858i	−0.0973404	+	0.995251i	$0.531034\pi$
$774$	6.68667	+	11.5816i	0.240347	+	0.416294i
$775$	1.57023	+	2.71972i	0.0564043	+	0.0976951i
$776$	−30.5635	+	52.9375i	−1.09717	+	1.90035i
$777$	6.78611	−	4.84538i	0.243450	−	0.173827i
$778$	19.1426	+	33.1559i	0.686295	+	1.18870i
$779$	−3.35563	−	5.81213i	−0.120228	−	0.208241i
$780$	−15.2277	+	20.9838i	−0.545240	+	0.751340i
$781$	5.58034	−	9.66544i	0.199680	−	0.345856i
$782$	36.9175	−	63.9431i	1.32017	−	2.28660i
$783$	−3.98387	−	6.90026i	−0.142372	−	0.246595i
$784$	−69.8402	+	13.6448i	−2.49429	+	0.487314i
$785$	−0.727311			−0.0259588
$786$	13.1521			0.469120
$787$	12.9210	+	22.3798i	0.460583	+	0.797753i	0.998990	−	0.0449316i	$-0.0143070\pi$
$787$	12.9210	+	22.3798i	0.460583	+	0.797753i	−0.538407	+	0.842685i	$0.680974\pi$
$788$	−27.9126	+	48.3460i	−0.994344	+	1.72225i
$789$	−14.5155			−0.516766
$790$	13.8541	+	23.9961i	0.492908	+	0.853742i
$791$	−4.14028	+	2.95622i	−0.147211	+	0.105111i
$792$	34.0566			1.21015
$793$	−27.3376	−	2.85789i	−0.970787	−	0.101487i
$794$	9.21900	−	15.9678i	0.327170	−	0.566675i
$795$	−12.5065			−0.443560
$796$	25.5589	−	44.2693i	0.905911	−	1.56908i
$797$	6.20361	−	10.7450i	0.219743	−	0.380606i	−0.734986	−	0.678082i	$-0.762811\pi$
$797$	6.20361	−	10.7450i	0.219743	−	0.380606i	0.954729	+	0.297476i	$0.0961448\pi$
$798$	17.0394	−	12.1664i	0.603190	−	0.430686i
$799$	−6.16058	+	10.6704i	−0.217946	+	0.377493i
$800$	−32.6565			−1.15458
$801$	−3.18037	+	5.50857i	−0.112373	+	0.194636i
$802$	−11.6764	−	20.2241i	−0.412307	−	0.714136i
$803$	13.5816	−	23.5239i	0.479283	−	0.830142i
$804$	−11.4302	−	19.7976i	−0.403111	−	0.698209i
$805$	−27.4162	−	12.4785i	−0.966294	−	0.439808i
$806$	4.26122	+	9.55651i	0.150095	+	0.336614i
$807$	9.21624	+	15.9630i	0.324427	+	0.561924i
$808$	−105.666			−3.71731
$809$	9.56746			0.336374			0.168187	−	0.985755i	$-0.446209\pi$
$809$	9.56746			0.336374			0.168187	+	0.985755i	$0.446209\pi$
$810$	−3.85772			−0.135547
$811$	−50.2886			−1.76587			−0.882936	−	0.469493i	$-0.844437\pi$
$811$	−50.2886			−1.76587			−0.882936	+	0.469493i	$0.844437\pi$
$812$	−83.9682	+	59.9545i	−2.94671	+	2.10399i
$813$	−2.45214	+	4.24723i	−0.0860004	+	0.148957i
$814$	18.5420	+	32.1157i	0.649898	+	1.12566i
$815$	6.80275	+	11.7827i	0.238290	+	0.412730i
$816$	−36.8895			−1.29139
$817$	−7.67513	+	13.2937i	−0.268519	+	0.465088i
$818$	−1.43748			−0.0502602
$819$	−8.22443	−	4.83310i	−0.287385	−	0.168882i
$820$	16.0126			0.559183
$821$	−12.1704	+	21.0798i	−0.424750	+	0.735689i	−0.996397	−	0.0848111i	$-0.972971\pi$
$821$	−12.1704	+	21.0798i	−0.424750	+	0.735689i	0.571647	+	0.820500i	$0.306305\pi$
$822$	−1.95533			−0.0681999
$823$	13.5286	+	23.4322i	0.471577	+	0.816796i	0.999471	−	0.0325144i	$-0.0103515\pi$
$823$	13.5286	+	23.4322i	0.471577	+	0.816796i	−0.527894	+	0.849310i	$0.677018\pi$
$824$	−57.8794	−	100.250i	−2.01632	−	3.49238i
$825$	6.36665	−	11.0274i	0.221658	−	0.383923i
$826$	91.4256	+	41.6123i	3.18110	+	1.44788i
$827$	−24.2045			−0.841672			−0.420836	−	0.907137i	$-0.638263\pi$
$827$	−24.2045			−0.841672			−0.420836	+	0.907137i	$0.638263\pi$
$828$	37.9270			1.31806
$829$	47.2482			1.64100			0.820499	−	0.571648i	$-0.193696\pi$
$829$	47.2482			1.64100			0.820499	+	0.571648i	$0.193696\pi$
$830$	−35.9090			−1.24642
$831$	12.9397	+	22.4122i	0.448872	+	0.777469i
$832$	−35.3073	−	3.69105i	−1.22406	−	0.127964i
$833$	−8.24697	+	24.0255i	−0.285741	+	0.832433i
$834$	−15.9734	−	27.6667i	−0.553113	−	0.958019i
$835$	11.7442	−	20.3416i	0.406426	−	0.703950i
$836$	33.0516	+	57.2470i	1.14311	+	1.97993i
$837$	−0.552624	+	0.957172i	−0.0191015	+	0.0330847i
$838$	83.8286			2.89581
$839$	5.87914	−	10.1830i	0.202970	−	0.351555i	−0.746514	−	0.665370i	$-0.768274\pi$
$839$	5.87914	−	10.1830i	0.202970	−	0.351555i	0.949484	+	0.313815i	$0.101607\pi$
$840$	2.84544	+	29.4038i	0.0981771	+	1.01453i
$841$	−17.2424	+	29.8647i	−0.594565	+	1.02982i
$842$	33.4281	−	57.8992i	1.15201	−	1.99534i
$843$	4.64246			0.159895
$844$	−15.0183	+	26.0125i	−0.516951	+	0.895386i
$845$	5.92241	+	18.1584i	0.203737	+	0.624667i
$846$	−8.91531			−0.306515
$847$	21.8707	+	9.95446i	0.751488	+	0.342039i
$848$	−43.2675	−	74.9416i	−1.48581	−	2.57350i
$849$	−24.2852			−0.833465
$850$	−13.5366	+	23.4461i	−0.464303	+	0.804196i
$851$	12.2112	+	21.1505i	0.418596	+	0.725029i
$852$	−12.1892			−0.417597
$853$	−36.1551			−1.23793			−0.618963	−	0.785420i	$-0.712447\pi$
$853$	−36.1551			−1.23793			−0.618963	+	0.785420i	$0.712447\pi$
$854$	−43.1005	+	30.7743i	−1.47487	+	1.05308i
$855$	−2.21400	−	3.83476i	−0.0757172	−	0.131146i
$856$	40.7591	−	70.5969i	1.39312	−	2.41295i
$857$	−9.01116	+	15.6078i	−0.307815	+	0.533152i	−0.977884	−	0.209147i	$-0.932931\pi$
$857$	−9.01116	+	15.6078i	−0.307815	+	0.533152i	0.670069	+	0.742299i	$0.266265\pi$
$858$	24.9178	−	34.3367i	0.850680	−	1.17223i
$859$	21.1610	+	36.6520i	0.722005	+	1.25055i	0.960195	+	0.279330i	$0.0901124\pi$
$859$	21.1610	+	36.6520i	0.722005	+	1.25055i	−0.238191	+	0.971218i	$0.576554\pi$
$860$	−18.3123	−	31.7178i	−0.624443	−	1.08157i
$861$	0.567483	+	5.86418i	0.0193398	+	0.199851i
$862$	−20.4163	+	35.3621i	−0.695382	+	1.20444i
$863$	−0.0671459	−	0.116300i	−0.00228567	−	0.00395890i	0.864880	−	0.501978i	$-0.167394\pi$
$863$	−0.0671459	−	0.116300i	−0.00228567	−	0.00395890i	−0.867166	+	0.498019i	$0.834061\pi$
$864$	−5.74654	−	9.95330i	−0.195501	−	0.338618i
$865$	7.69473	+	13.3277i	0.261629	+	0.453154i
$866$	39.6909	+	68.7467i	1.34875	+	2.33611i
$867$	1.91596	−	3.31854i	0.0650695	−	0.112704i
$868$	13.0262	+	5.92889i	0.442139	+	0.201240i
$869$	−16.0937	−	27.8751i	−0.545940	−	0.945597i
$870$	15.3687	+	26.6193i	0.521046	+	0.902479i
$871$	−16.7495	−	1.75100i	−0.567534	−	0.0593304i
$872$	52.6999	−	91.2789i	1.78464	−	3.09110i
$873$	−4.02169	+	6.96578i	−0.136114	+	0.235756i
$874$	30.6615	+	53.1073i	1.03714	+	1.79638i
$875$	27.7425	+	12.6270i	0.937868	+	0.426870i
$876$	−29.6665			−1.00234
$877$	−44.8896			−1.51581			−0.757907	−	0.652362i	$-0.773778\pi$
$877$	−44.8896			−1.51581			−0.757907	+	0.652362i	$0.773778\pi$
$878$	−46.7511	−	80.9752i	−1.57777	−	2.73278i
$879$	−10.1171	+	17.5233i	−0.341241	+	0.591047i
$880$	−66.9320			−2.25628
$881$	0.618105	+	1.07059i	0.0208245	+	0.0360691i	0.876250	−	0.481857i	$-0.160038\pi$
$881$	0.618105	+	1.07059i	0.0208245	+	0.0360691i	−0.855425	+	0.517926i	$0.826704\pi$
$882$	−18.0389	+	3.52429i	−0.607401	+	0.118669i
$883$	0.495858			0.0166870			0.00834348	−	0.999965i	$-0.497344\pi$
$883$	0.495858			0.0166870			0.00834348	+	0.999965i	$0.497344\pi$
$884$	−37.6107	+	51.8274i	−1.26498	+	1.74314i
$885$	10.6221	−	18.3980i	0.357058	−	0.618443i
$886$	21.5478			0.723912
$887$	−9.23504	+	15.9956i	−0.310082	+	0.537078i	−0.978380	−	0.206816i	$-0.933690\pi$
$887$	−9.23504	+	15.9956i	−0.310082	+	0.537078i	0.668298	+	0.743894i	$0.267023\pi$
$888$	11.9756	−	20.7424i	0.401876	−	0.696069i
$889$	−4.38528	−	45.3161i	−0.147078	−	1.51985i
$890$	12.2690	−	21.2505i	0.411258	−	0.712320i
$891$	4.48133			0.150130
$892$	64.3709	−	111.494i	2.15530	−	3.73308i
$893$	−5.11661	−	8.86223i	−0.171221	−	0.296563i
$894$	−3.41922	+	5.92226i	−0.114356	+	0.198070i
$895$	7.67196	+	13.2882i	0.256445	+	0.444176i
$896$	−6.17142	+	4.40648i	−0.206173	+	0.147210i
$897$	16.4102	−	22.6131i	0.547919	−	0.755031i
$898$	−15.0966	−	26.1480i	−0.503779	−	0.872570i
$899$	8.80631			0.293707
$900$	−13.9068			−0.463560
$901$	−30.8896			−1.02908
$902$	−26.2020			−0.872433
$903$	10.9668	−	7.83046i	0.364953	−	0.260581i
$904$	−7.30645	+	12.6551i	−0.243009	+	0.420904i
$905$	−10.9355	−	18.9408i	−0.363507	−	0.629613i
$906$	18.1160	+	31.3779i	0.601865	+	1.04246i
$907$	38.3599			1.27372			0.636859	−	0.770980i	$-0.280233\pi$
$907$	38.3599			1.27372			0.636859	+	0.770980i	$0.280233\pi$
$908$	−9.62486	+	16.6707i	−0.319412	+	0.553238i
$909$	−13.9040			−0.461167
$910$	31.7276	+	18.6448i	1.05176	+	0.618068i
$911$	2.03620			0.0674623			0.0337311	−	0.999431i	$-0.489261\pi$
$911$	2.03620			0.0674623			0.0337311	+	0.999431i	$0.489261\pi$
$912$	15.3191	−	26.5335i	0.507267	−	0.878612i
$913$	41.7138			1.38052
$914$	11.7037	+	20.2714i	0.387124	+	0.670519i
$915$	5.60021	+	9.69984i	0.185137	+	0.320667i
$916$	27.8410	−	48.2220i	0.919892	−	1.59330i
$917$	−1.27650	−	13.1909i	−0.0421537	−	0.435602i
$918$	−9.52812			−0.314475
$919$	−19.7759			−0.652346			−0.326173	−	0.945310i	$-0.605759\pi$
$919$	−19.7759			−0.652346			−0.326173	+	0.945310i	$0.605759\pi$
$920$	−86.5237			−2.85260
$921$	2.00196			0.0659669
$922$	16.3428	+	28.3066i	0.538222	+	0.932229i
$923$	−5.27401	+	7.26756i	−0.173596	+	0.239215i
$924$	−5.58947	−	57.7597i	−0.183880	−	1.90016i
$925$	−4.47752	−	7.75530i	−0.147220	−	0.254993i
$926$	−29.4234	+	50.9628i	−0.966912	+	1.67474i
$927$	−7.61605	−	13.1914i	−0.250144	−	0.433262i
$928$	−45.7869	+	79.3052i	−1.50303	+	2.60332i
$929$	−41.6553			−1.36666			−0.683332	−	0.730107i	$-0.739470\pi$
$929$	−41.6553			−1.36666			−0.683332	+	0.730107i	$0.739470\pi$
$930$	2.13187	−	3.69251i	0.0699068	−	0.121082i
$931$	−13.8561	−	15.9089i	−0.454114	−	0.521392i
$932$	14.6662	−	25.4026i	0.480407	−	0.832090i
$933$	−2.81050	+	4.86793i	−0.0920117	+	0.159369i
$934$	−69.7744			−2.28309
$935$	−11.9460	+	20.6911i	−0.390677	+	0.676672i
$936$	−27.2524	−	2.84899i	−0.890774	−	0.0931220i
$937$	−30.8282			−1.00711			−0.503557	−	0.863962i	$-0.667975\pi$
$937$	−30.8282			−1.00711			−0.503557	+	0.863962i	$0.667975\pi$
$938$	−26.4072	+	18.8551i	−0.862226	+	0.615642i
$939$	−11.1532	−	19.3179i	−0.363972	−	0.630417i
$940$	24.4157			0.796352
$941$	15.3104	−	26.5184i	0.499104	−	0.864474i	−0.500895	−	0.865508i	$-0.666996\pi$
$941$	15.3104	−	26.5184i	0.499104	−	0.864474i	0.999999	+	0.00103413i	$0.000329174\pi$
$942$	−0.649906	−	1.12567i	−0.0211751	−	0.0366763i
$943$	−17.2559			−0.561930
$944$	146.993			4.78422
$945$	0.374417	+	3.86910i	0.0121798	+	0.125862i
$946$	29.9652	+	51.9012i	0.974251	+	1.68745i
$947$	7.29211	−	12.6303i	0.236962	−	0.410430i	−0.722879	−	0.690974i	$-0.757182\pi$
$947$	7.29211	−	12.6303i	0.236962	−	0.410430i	0.959841	+	0.280545i	$0.0905151\pi$
$948$	−17.5769	+	30.4440i	−0.570870	+	0.988776i
$949$	−12.8360	+	17.6880i	−0.416674	+	0.574175i
$950$	−11.2427	−	19.4730i	−0.364762	−	0.631787i
$951$	13.4742	+	23.3380i	0.436931	+	0.756787i
$952$	7.02790	+	72.6240i	0.227776	+	2.35376i
$953$	−3.77371	+	6.53626i	−0.122243	+	0.211730i	−0.920652	−	0.390385i	$-0.872342\pi$
$953$	−3.77371	+	6.53626i	−0.122243	+	0.211730i	0.798409	+	0.602115i	$0.205675\pi$
$954$	−11.1755	−	19.3565i	−0.361820	−	0.626690i
$955$	−15.2615	−	26.4336i	−0.493849	−	0.855372i
$956$	19.8056	+	34.3043i	0.640559	+	1.10948i
$957$	−17.8530	−	30.9223i	−0.577106	−	0.999577i
$958$	12.2216	−	21.1684i	0.394862	−	0.683921i
$959$	0.189777	+	1.96109i	0.00612823	+	0.0633270i
$960$	7.23284	+	12.5276i	0.233439	+	0.404328i
$961$	14.8892	+	25.7889i	0.480297	+	0.831899i
$962$	−12.1509	−	27.2505i	−0.391761	−	0.878591i
$963$	5.36329	−	9.28948i	0.172829	−	0.299349i
$964$	38.1918	−	66.1501i	1.23007	−	2.13055i
$965$	−12.5279	−	21.6989i	−0.403286	−	0.698512i
$966$	−5.18528	−	53.5830i	−0.166834	−	1.72400i
$967$	3.20099			0.102937			0.0514685	−	0.998675i	$-0.483610\pi$
$967$	3.20099			0.102937			0.0514685	+	0.998675i	$0.483610\pi$
$968$	69.0226			2.21847
$969$	−5.46831	−	9.47140i	−0.175668	−	0.304265i
$970$	15.5146	−	26.8720i	0.498143	−	0.862809i
$971$	23.5096			0.754460			0.377230	−	0.926120i	$-0.376877\pi$
$971$	23.5096			0.754460			0.377230	+	0.926120i	$0.376877\pi$
$972$	−2.44716	−	4.23861i	−0.0784928	−	0.135954i
$973$	−26.1980	+	18.7057i	−0.839869	+	0.599678i
$974$	−24.9046			−0.797996
$975$	−6.01715	+	8.29161i	−0.192703	+	0.265544i
$976$	−38.7490	+	67.1152i	−1.24033	+	2.14831i
$977$	−49.6115			−1.58721			−0.793606	−	0.608433i	$-0.791799\pi$
$977$	−49.6115			−1.58721			−0.793606	+	0.608433i	$0.791799\pi$
$978$	−12.1575	+	21.0575i	−0.388755	+	0.673343i
$979$	−14.2523	+	24.6857i	−0.455506	+	0.788959i
$980$	49.4017	−	9.65170i	1.57808	−	0.308312i
$981$	6.93451	−	12.0109i	0.221402	−	0.383480i
$982$	40.7828			1.30143
$983$	−12.9570	+	22.4422i	−0.413265	+	0.715795i	−0.995245	−	0.0974078i	$-0.968945\pi$
$983$	−12.9570	+	22.4422i	−0.413265	+	0.715795i	0.581980	+	0.813203i	$0.302278\pi$
$984$	8.46148	+	14.6557i	0.269742	+	0.467207i
$985$	8.37899	−	14.5128i	0.266977	−	0.462418i
$986$	37.9587	+	65.7465i	1.20885	+	2.09379i
$987$	0.865289	+	8.94160i	0.0275424	+	0.284614i
$988$	−21.6593	−	48.5746i	−0.689073	−	1.54536i
$989$	19.7342	+	34.1806i	0.627511	+	1.08688i
$990$	−17.2877			−0.549440
$991$	−60.5995			−1.92501			−0.962503	−	0.271273i	$-0.912556\pi$
$991$	−60.5995			−1.92501			−0.962503	+	0.271273i	$0.912556\pi$
$992$	12.7027			0.403311
$993$	4.56139			0.144751
$994$	1.66648	+	17.2209i	0.0528576	+	0.546212i
$995$	−7.67245	+	13.2891i	−0.243233	+	0.421292i
$996$	−22.7791	−	39.4545i	−0.721782	−	1.25016i
$997$	0.169889	+	0.294257i	0.00538045	+	0.00931922i	0.868703	−	0.495333i	$-0.164954\pi$
$997$	0.169889	+	0.294257i	0.00538045	+	0.00931922i	−0.863323	+	0.504652i	$0.831621\pi$
$998$	51.4742			1.62939
$999$	1.57581	−	2.72938i	0.0498565	−	0.0863539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.j.c.172.1	yes	20
3.2	odd	2		819.2.n.f.172.10		20
7.2	even	3		273.2.l.c.16.10	yes	20
13.9	even	3		273.2.l.c.256.10	yes	20
21.2	odd	6		819.2.s.f.289.1		20
39.35	odd	6		819.2.s.f.802.1		20
91.9	even	3	inner	273.2.j.c.100.1	✓	20
273.191	odd	6		819.2.n.f.100.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.1	✓	20	91.9	even	3	inner
273.2.j.c.172.1	yes	20	1.1	even	1	trivial
273.2.l.c.16.10	yes	20	7.2	even	3
273.2.l.c.256.10	yes	20	13.9	even	3
819.2.n.f.100.10		20	273.191	odd	6
819.2.n.f.172.10		20	3.2	odd	2
819.2.s.f.289.1		20	21.2	odd	6
819.2.s.f.802.1		20	39.35	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)

\(f(q)\)	\(=\)	\(q+(-1.31285 + 2.27393i) q^{2} +1.00000 q^{3} +(-2.44716 - 4.23861i) q^{4} +(0.734607 + 1.27238i) q^{5} +(-1.31285 + 2.27393i) q^{6} +(2.40805 + 1.09603i) q^{7} +7.59966 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.31285 + 2.27393i) q^{2} +1.00000 q^{3} +(-2.44716 - 4.23861i) q^{4} +(0.734607 + 1.27238i) q^{5} +(-1.31285 + 2.27393i) q^{6} +(2.40805 + 1.09603i) q^{7} +7.59966 q^{8} +1.00000 q^{9} -3.85772 q^{10} +4.48133 q^{11} +(-2.44716 - 4.23861i) q^{12} +(-3.58601 - 0.374884i) q^{13} +(-5.65370 + 4.03682i) q^{14} +(0.734607 + 1.27238i) q^{15} +(-5.08290 + 8.80384i) q^{16} +(1.81439 + 3.14262i) q^{17} +(-1.31285 + 2.27393i) q^{18} -3.01385 q^{19} +(3.59541 - 6.22743i) q^{20} +(2.40805 + 1.09603i) q^{21} +(-5.88333 + 10.1902i) q^{22} +(-3.87459 + 6.71099i) q^{23} +7.59966 q^{24} +(1.42070 - 2.46073i) q^{25} +(5.56036 - 7.66216i) q^{26} +1.00000 q^{27} +(-1.24728 - 12.8890i) q^{28} +(-3.98387 - 6.90026i) q^{29} -3.85772 q^{30} +(-0.552624 + 0.957172i) q^{31} +(-5.74654 - 9.95330i) q^{32} +4.48133 q^{33} -9.52812 q^{34} +(0.374417 + 3.86910i) q^{35} +(-2.44716 - 4.23861i) q^{36} +(1.57581 - 2.72938i) q^{37} +(3.95675 - 6.85329i) q^{38} +(-3.58601 - 0.374884i) q^{39} +(5.58276 + 9.66963i) q^{40} +(1.11340 + 1.92847i) q^{41} +(-5.65370 + 4.03682i) q^{42} +(2.54662 - 4.41087i) q^{43} +(-10.9666 - 18.9946i) q^{44} +(0.734607 + 1.27238i) q^{45} +(-10.1735 - 17.6211i) q^{46} +(1.69770 + 2.94050i) q^{47} +(-5.08290 + 8.80384i) q^{48} +(4.59746 + 5.27858i) q^{49} +(3.73035 + 6.46116i) q^{50} +(1.81439 + 3.14262i) q^{51} +(7.18657 + 16.1171i) q^{52} +(-4.25619 + 7.37193i) q^{53} +(-1.31285 + 2.27393i) q^{54} +(3.29202 + 5.70194i) q^{55} +(18.3004 + 8.32942i) q^{56} -3.01385 q^{57} +20.9209 q^{58} +(-7.22979 - 12.5224i) q^{59} +(3.59541 - 6.22743i) q^{60} +7.62340 q^{61} +(-1.45103 - 2.51325i) q^{62} +(2.40805 + 1.09603i) q^{63} +9.84585 q^{64} +(-2.15732 - 4.83815i) q^{65} +(-5.88333 + 10.1902i) q^{66} +4.67078 q^{67} +(8.88023 - 15.3810i) q^{68} +(-3.87459 + 6.71099i) q^{69} +(-9.28961 - 4.22816i) q^{70} +(1.24524 - 2.15682i) q^{71} +7.59966 q^{72} +(3.03070 - 5.24932i) q^{73} +(4.13762 + 7.16656i) q^{74} +(1.42070 - 2.46073i) q^{75} +(7.37540 + 12.7746i) q^{76} +(10.7913 + 4.91165i) q^{77} +(5.56036 - 7.66216i) q^{78} +(-3.59127 - 6.22026i) q^{79} -14.9357 q^{80} +1.00000 q^{81} -5.84693 q^{82} +9.30835 q^{83} +(-1.24728 - 12.8890i) q^{84} +(-2.66573 + 4.61718i) q^{85} +(6.68667 + 11.5816i) q^{86} +(-3.98387 - 6.90026i) q^{87} +34.0566 q^{88} +(-3.18037 + 5.50857i) q^{89} -3.85772 q^{90} +(-8.22443 - 4.83310i) q^{91} +37.9270 q^{92} +(-0.552624 + 0.957172i) q^{93} -8.91531 q^{94} +(-2.21400 - 3.83476i) q^{95} +(-5.74654 - 9.95330i) q^{96} +(-4.02169 + 6.96578i) q^{97} +(-18.0389 + 3.52429i) q^{98} +4.48133 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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