LMFDB - Embedded newform 273.2.l.c.256.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			256.10
Root			$1.31285 - 2.27393i$ of defining polynomial
Character	$\chi$	$=$	273.256
Dual form			273.2.l.c.16.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.62571 q^{2} +(-0.500000 - 0.866025i) q^{3} +4.89433 q^{4} +(0.734607 + 1.27238i) q^{5} +(-1.31285 - 2.27393i) q^{6} +(-2.15321 + 1.53742i) q^{7} +7.59966 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+2.62571 q^{2} +(-0.500000 - 0.866025i) q^{3} +4.89433 q^{4} +(0.734607 + 1.27238i) q^{5} +(-1.31285 - 2.27393i) q^{6} +(-2.15321 + 1.53742i) q^{7} +7.59966 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.92886 + 3.34089i) q^{10} +(-2.24067 - 3.88095i) 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} +10.1658 q^{16} -3.62878 q^{17} +(-1.31285 + 2.27393i) q^{18} +(1.50693 - 2.61007i) q^{19} +(3.59541 + 6.22743i) q^{20} +(2.40805 + 1.09603i) q^{21} +(-5.88333 - 10.1902i) q^{22} +7.74918 q^{23} +(-3.79983 - 6.58150i) q^{24} +(1.42070 - 2.46073i) q^{25} +(-9.41580 + 0.984334i) q^{26} +1.00000 q^{27} +(-10.5385 + 7.52466i) q^{28} +(-3.98387 + 6.90026i) q^{29} +(1.92886 - 3.34089i) q^{30} +(-0.552624 + 0.957172i) q^{31} +11.4931 q^{32} +(-2.24067 + 3.88095i) q^{33} -9.52812 q^{34} +(-3.53795 - 1.61030i) q^{35} +(-2.44716 + 4.23861i) q^{36} -3.15162 q^{37} +(3.95675 - 6.85329i) q^{38} +(2.11766 + 2.91813i) q^{39} +(5.58276 + 9.66963i) q^{40} +(1.11340 - 1.92847i) q^{41} +(6.32284 + 2.87784i) q^{42} +(2.54662 + 4.41087i) q^{43} +(-10.9666 - 18.9946i) q^{44} -1.46921 q^{45} +20.3471 q^{46} +(1.69770 + 2.94050i) q^{47} +(-5.08290 - 8.80384i) q^{48} +(2.27265 - 6.62080i) q^{49} +(3.73035 - 6.46116i) q^{50} +(1.81439 + 3.14262i) q^{51} +(-17.5511 + 1.83480i) q^{52} +(-4.25619 + 7.37193i) q^{53} +2.62571 q^{54} +(3.29202 - 5.70194i) q^{55} +(-16.3637 + 11.6839i) q^{56} -3.01385 q^{57} +(-10.4605 + 18.1180i) q^{58} +14.4596 q^{59} +(3.59541 - 6.22743i) q^{60} +(-3.81170 + 6.60206i) q^{61} +(-1.45103 + 2.51325i) q^{62} +(-0.254842 - 2.63345i) q^{63} +9.84585 q^{64} +(-3.11130 - 4.28736i) q^{65} +(-5.88333 + 10.1902i) q^{66} +(-2.33539 - 4.04502i) q^{67} -17.7605 q^{68} +(-3.87459 - 6.71099i) q^{69} +(-9.28961 - 4.22816i) q^{70} +(1.24524 + 2.15682i) q^{71} +(-3.79983 + 6.58150i) q^{72} +(3.03070 - 5.24932i) q^{73} -8.27523 q^{74} -2.84141 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} +(7.46787 + 12.9347i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.92347 - 5.06359i) q^{82} +9.30835 q^{83} +(11.7858 + 5.36431i) q^{84} +(-2.66573 - 4.61718i) q^{85} +(6.68667 + 11.5816i) q^{86} +7.96773 q^{87} +(-17.0283 - 29.4939i) q^{88} +6.36075 q^{89} -3.85772 q^{90} +(7.14509 - 6.32042i) q^{91} +37.9270 q^{92} +1.10525 q^{93} +(4.45765 + 7.72088i) q^{94} +4.42800 q^{95} +(-5.74654 - 9.95330i) q^{96} +(-4.02169 - 6.96578i) q^{97} +(5.96732 - 17.3843i) q^{98} +4.48133 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25} + 13 q^{26} + 20 q^{27} - 23 q^{28} - 9 q^{29} - 4 q^{30} - 9 q^{31} - 34 q^{32} - 8 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} - 36 q^{37} + 22 q^{38} + 4 q^{39} - 9 q^{40} - q^{41} + 3 q^{42} - 11 q^{43} + 8 q^{44} + 20 q^{46} + 13 q^{47} - 20 q^{48} - 3 q^{49} + 5 q^{50} - 44 q^{52} - 6 q^{53} - 19 q^{55} - 23 q^{56} - 14 q^{57} + 30 q^{59} + 12 q^{60} + 22 q^{62} + 6 q^{63} + 72 q^{64} - 6 q^{65} - 9 q^{66} - 22 q^{67} - 78 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} + 6 q^{72} + 6 q^{74} + 64 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} + 48 q^{80} - 10 q^{81} - 13 q^{82} + 40 q^{83} + 10 q^{84} - 16 q^{85} + 4 q^{86} + 18 q^{87} - 12 q^{88} - 4 q^{89} + 8 q^{90} + 30 q^{91} + 66 q^{92} + 18 q^{93} - 44 q^{94} + 72 q^{95} + 17 q^{96} + 21 q^{97} - 76 q^{98} + 16 q^{99}+O(q^{100}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	2.62571			1.85665			0.928327	−	0.371765i	$-0.121247\pi$
$2$	2.62571			1.85665			0.928327	+	0.371765i	$0.121247\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	4.89433			2.44716
$5$	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
$7$	−2.15321	+	1.53742i	−0.813838	+	0.581092i
$7$	−2.15321	+	1.53742i	−0.813838	+	0.581092i
$8$	7.59966			2.68688
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.92886	+	3.34089i	0.609960	+	1.05648i
$11$	−2.24067	−	3.88095i	−0.675586	−	1.17015i	−0.976297	−	0.216434i	$-0.930557\pi$
$11$	−2.24067	−	3.88095i	−0.675586	−	1.17015i	0.300711	−	0.953715i	$-0.402776\pi$
$12$	−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
$16$	10.1658			2.54145
$17$	−3.62878			−0.880109			−0.440055	−	0.897971i	$-0.645041\pi$
$17$	−3.62878			−0.880109			−0.440055	+	0.897971i	$0.645041\pi$
$18$	−1.31285	+	2.27393i	−0.309442	+	0.535970i
$19$	1.50693	−	2.61007i	0.345713	−	0.598792i	−0.639770	−	0.768566i	$-0.720971\pi$
$19$	1.50693	−	2.61007i	0.345713	−	0.598792i	0.985483	+	0.169774i	$0.0543038\pi$
$20$	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
$23$	7.74918			1.61582			0.807908	−	0.589309i	$-0.200600\pi$
$23$	7.74918			1.61582			0.807908	+	0.589309i	$0.200600\pi$
$24$	−3.79983	−	6.58150i	−0.775637	−	1.34344i
$25$	1.42070	−	2.46073i	0.284141	−	0.492146i
$26$	−9.41580	+	0.984334i	−1.84659	+	0.193044i
$27$	1.00000			0.192450
$28$	−10.5385	+	7.52466i	−1.99160	+	1.42203i
$29$	−3.98387	+	6.90026i	−0.739785	+	1.28135i	0.212806	+	0.977094i	$0.431740\pi$
$29$	−3.98387	+	6.90026i	−0.739785	+	1.28135i	−0.952592	+	0.304251i	$0.901594\pi$
$30$	1.92886	−	3.34089i	0.352160	−	0.609960i
$31$	−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	$0.198312\pi$
$32$	11.4931			2.03171
$33$	−2.24067	+	3.88095i	−0.390050	+	0.675586i
$34$	−9.52812			−1.63406
$35$	−3.53795	−	1.61030i	−0.598023	−	0.272190i
$36$	−2.44716	+	4.23861i	−0.407861	+	0.706436i
$37$	−3.15162			−0.518123			−0.259062	−	0.965861i	$-0.583413\pi$
$37$	−3.15162			−0.518123			−0.259062	+	0.965861i	$0.583413\pi$
$38$	3.95675	−	6.85329i	0.641869	−	1.11175i
$39$	2.11766	+	2.91813i	0.339098	+	0.467275i
$40$	5.58276	+	9.66963i	0.882712	+	1.52890i
$41$	1.11340	−	1.92847i	0.173884	−	0.301176i	−0.765890	−	0.642971i	$-0.777701\pi$
$41$	1.11340	−	1.92847i	0.173884	−	0.301176i	0.939775	+	0.341795i	$0.111035\pi$
$42$	6.32284	+	2.87784i	0.975636	+	0.444060i
$43$	2.54662	+	4.41087i	0.388355	+	0.672651i	0.992228	−	0.124429i	$-0.0397100\pi$
$43$	2.54662	+	4.41087i	0.388355	+	0.672651i	−0.603873	+	0.797080i	$0.706377\pi$
$44$	−10.9666	−	18.9946i	−1.65327	−	2.86355i
$45$	−1.46921			−0.219018
$46$	20.3471			3.00001
$47$	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
$49$	2.27265	−	6.62080i	0.324665	−	0.945829i
$50$	3.73035	−	6.46116i	0.527551	−	0.913746i
$51$	1.81439	+	3.14262i	0.254066	+	0.440055i
$52$	−17.5511	+	1.83480i	−2.43390	+	0.254441i
$53$	−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	$0.967906\pi$
$54$	2.62571			0.357313
$55$	3.29202	−	5.70194i	0.443896	−	0.768850i
$56$	−16.3637	+	11.6839i	−2.18669	+	1.56133i
$57$	−3.01385			−0.399195
$58$	−10.4605	+	18.1180i	−1.37353	+	2.37902i
$59$	14.4596			1.88248			0.941238	−	0.337744i	$-0.109664\pi$
$59$	14.4596			1.88248			0.941238	+	0.337744i	$0.109664\pi$
$60$	3.59541	−	6.22743i	0.464165	−	0.803958i
$61$	−3.81170	+	6.60206i	−0.488038	+	0.845307i	−0.999905	−	0.0137574i	$-0.995621\pi$
$61$	−3.81170	+	6.60206i	−0.488038	+	0.845307i	0.511867	+	0.859065i	$0.328954\pi$
$62$	−1.45103	+	2.51325i	−0.184281	+	0.319183i
$63$	−0.254842	−	2.63345i	−0.0321070	−	0.331783i
$64$	9.84585			1.23073
$65$	−3.11130	−	4.28736i	−0.385909	−	0.531782i
$66$	−5.88333	+	10.1902i	−0.724188	+	1.25433i
$67$	−2.33539	−	4.04502i	−0.285313	−	0.494177i	0.687372	−	0.726306i	$-0.258764\pi$
$67$	−2.33539	−	4.04502i	−0.285313	−	0.494177i	−0.972685	+	0.232128i	$0.925431\pi$
$68$	−17.7605			−2.15377
$69$	−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	0.930408	−	0.366526i	$-0.119453\pi$
$71$	1.24524	+	2.15682i	0.147783	+	0.255968i	−0.782625	+	0.622494i	$0.786120\pi$
$72$	−3.79983	+	6.58150i	−0.447814	+	0.775637i
$73$	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	$0.0512441\pi$
$74$	−8.27523			−0.961976
$75$	−2.84141			−0.328098
$76$	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	$0.965731\pi$
$80$	7.46787	+	12.9347i	0.834933	+	1.44615i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.92347	−	5.06359i	0.322843	−	0.559180i
$83$	9.30835			1.02172			0.510862	−	0.859663i	$-0.329326\pi$
$83$	9.30835			1.02172			0.510862	+	0.859663i	$0.329326\pi$
$84$	11.7858	+	5.36431i	1.28594	+	0.585294i
$85$	−2.66573	−	4.61718i	−0.289139	−	0.500804i
$86$	6.68667	+	11.5816i	0.721042	+	1.24888i
$87$	7.96773			0.854231
$88$	−17.0283	−	29.4939i	−1.81522	−	3.14406i
$89$	6.36075			0.674238			0.337119	−	0.941462i	$-0.390548\pi$
$89$	6.36075			0.674238			0.337119	+	0.941462i	$0.390548\pi$
$90$	−3.85772			−0.406640
$91$	7.14509	−	6.32042i	0.749009	−	0.662560i
$92$	37.9270			3.95417
$93$	1.10525			0.114609
$94$	4.45765	+	7.72088i	0.459772	+	0.796348i
$95$	4.42800			0.454303
$96$	−5.74654	−	9.95330i	−0.586504	−	1.01585i
$97$	−4.02169	−	6.96578i	−0.408341	−	0.707267i	0.586363	−	0.810048i	$-0.300559\pi$
$97$	−4.02169	−	6.96578i	−0.408341	−	0.707267i	−0.994704	+	0.102781i	$0.967226\pi$
$98$	5.96732	−	17.3843i	0.602790	−	1.75608i
$99$	4.48133			0.450391
$100$	6.95339	−	12.0436i	0.695339	−	1.20436i
$101$	6.95201	+	12.0412i	0.691750	+	1.19815i	0.971264	+	0.238005i	$0.0764935\pi$
$101$	6.95201	+	12.0412i	0.691750	+	1.19815i	−0.279513	+	0.960142i	$0.590173\pi$
$102$	4.76406	+	8.25159i	0.471712	+	0.817029i
$103$	−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
$107$	−10.7266			−1.03698			−0.518488	−	0.855085i	$-0.673505\pi$
$107$	−10.7266			−1.03698			−0.518488	+	0.855085i	$0.673505\pi$
$108$	4.89433			0.470957
$109$	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	$-0.0645636\pi$
$110$	8.64387	−	14.9716i	0.824161	−	1.42749i
$111$	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	0.817255	−	0.576277i	$-0.195495\pi$
$113$	−0.961419	−	1.66523i	−0.0904427	−	0.156651i	−0.907697	+	0.419625i	$0.862162\pi$
$114$	−7.91349			−0.741166
$115$	5.69260	+	9.85988i	0.530838	+	0.919438i
$116$	−19.4984	+	33.7721i	−1.81038	+	3.13566i
$117$	1.46835	−	3.29302i	0.135749	−	0.304440i
$118$	37.9666			3.49511
$119$	7.81355	−	5.57898i	0.716267	−	0.511424i
$120$	5.58276	−	9.66963i	0.509634	−	0.882712i
$121$	−4.54116	+	7.86553i	−0.412833	+	0.715048i
$122$	−10.0084	+	17.3351i	−0.906119	+	1.56944i
$123$	−2.22681			−0.200784
$124$	−2.70472	+	4.68471i	−0.242891	+	0.420700i
$125$	11.5207			1.03044
$126$	−0.669139	−	6.91466i	−0.0596117	−	0.616007i
$127$	−8.60394	+	14.9025i	−0.763476	+	1.32238i	0.177573	+	0.984108i	$0.443175\pi$
$127$	−8.60394	+	14.9025i	−0.763476	+	1.32238i	−0.941049	+	0.338271i	$0.890158\pi$
$128$	2.86615			0.253334
$129$	2.54662	−	4.41087i	0.224217	−	0.388355i
$130$	−8.16936	−	11.2574i	−0.716500	−	0.987335i
$131$	−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
$133$	0.768056	+	7.93683i	0.0665989	+	0.688211i
$134$	−6.13205	−	10.6210i	−0.529728	−	0.917516i
$135$	0.734607	+	1.27238i	0.0632249	+	0.109509i
$136$	−27.5775			−2.36475
$137$	−0.744687			−0.0636229			−0.0318114	−	0.999494i	$-0.510128\pi$
$137$	−0.744687			−0.0636229			−0.0318114	+	0.999494i	$0.510128\pi$
$138$	−10.1735	−	17.6211i	−0.866028	−	1.50001i
$139$	−6.08346	−	10.5369i	−0.515992	−	0.893725i	−0.999828	−	0.0185659i	$-0.994090\pi$
$139$	−6.08346	−	10.5369i	−0.515992	−	0.893725i	0.483835	−	0.875159i	$-0.339243\pi$
$140$	−17.3159	−	7.88132i	−1.46346	−	0.666093i
$141$	1.69770	−	2.94050i	0.142972	−	0.247635i
$142$	3.26964	+	5.66318i	0.274382	+	0.475244i
$143$	9.48995	+	13.0771i	0.793590	+	1.09356i
$144$	−5.08290	+	8.80384i	−0.423575	+	0.733653i
$145$	−11.7063			−0.972156
$146$	7.95772	−	13.7832i	0.658585	−	1.14070i
$147$	−6.87011	+	1.34223i	−0.566637	+	0.110705i
$148$	−15.4251			−1.26793
$149$	−1.30221	+	2.25549i	−0.106681	+	0.184777i	−0.914424	−	0.404758i	$-0.867356\pi$
$149$	−1.30221	+	2.25549i	−0.106681	+	0.184777i	0.807743	+	0.589535i	$0.200689\pi$
$150$	−7.46070			−0.609164
$151$	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	$-0.0230983\pi$
$152$	11.4521	−	19.8357i	0.928890	−	1.60888i
$153$	1.81439	−	3.14262i	0.146685	−	0.254066i
$154$	28.3348	+	12.8966i	2.28328	+	1.03923i
$155$	−1.62385			−0.130430
$156$	10.3645	+	14.2823i	0.829827	+	1.14350i
$157$	−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	$0.172955\pi$
$158$	−9.42962	−	16.3326i	−0.750180	−	1.29935i
$159$	8.51237			0.675075
$160$	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
$163$	−4.63020	+	8.01974i	−0.362665	+	0.628154i	−0.988399	−	0.151883i	$-0.951466\pi$
$163$	−4.63020	+	8.01974i	−0.362665	+	0.628154i	0.625734	+	0.780037i	$0.284800\pi$
$164$	5.44936	−	9.43857i	0.425523	−	0.737028i
$165$	−6.58404			−0.512567
$166$	24.4410			1.89699
$167$	−7.99354	+	13.8452i	−0.618559	+	1.07138i	0.371190	+	0.928557i	$0.378950\pi$
$167$	−7.99354	+	13.8452i	−0.618559	+	1.07138i	−0.989749	+	0.142819i	$0.954383\pi$
$168$	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
$171$	1.50693	+	2.61007i	0.115238	+	0.199597i
$172$	12.4640	+	21.5882i	0.950370	+	1.64609i
$173$	−5.23731	+	9.07128i	−0.398185	+	0.689677i	−0.993502	−	0.113814i	$-0.963693\pi$
$173$	−5.23731	+	9.07128i	−0.398185	+	0.689677i	0.595317	+	0.803491i	$0.297027\pi$
$174$	20.9209			1.58601
$175$	0.724109	+	7.48271i	0.0547375	+	0.565639i
$176$	−22.7782	−	39.4529i	−1.71697	−	2.97388i
$177$	−7.22979	−	12.5224i	−0.543424	−	0.941238i
$178$	16.7015			1.25183
$179$	−5.22181	−	9.04444i	−0.390296	−	0.676013i	0.602192	−	0.798351i	$-0.294294\pi$
$179$	−5.22181	−	9.04444i	−0.390296	−	0.676013i	−0.992488	+	0.122338i	$0.960961\pi$
$180$	−7.19082			−0.535972
$181$	−14.8861			−1.10648			−0.553239	−	0.833023i	$-0.686608\pi$
$181$	−14.8861			−1.10648			−0.553239	+	0.833023i	$0.686608\pi$
$182$	18.7609	−	16.5956i	1.39065	−	1.23015i
$183$	7.62340			0.563538
$184$	58.8911			4.34151
$185$	−2.31520	−	4.01005i	−0.170217	−	0.294825i
$186$	2.90205			0.212789
$187$	8.13089	+	14.0831i	0.594590	+	1.02986i
$188$	8.30909	+	14.3918i	0.606003	+	1.04963i
$189$	−2.15321	+	1.53742i	−0.156623	+	0.111831i
$190$	11.6266			0.843484
$191$	10.3875	−	17.9917i	0.751613	−	1.30183i	−0.195428	−	0.980718i	$-0.562610\pi$
$191$	10.3875	−	17.9917i	0.751613	−	1.30183i	0.947041	−	0.321114i	$-0.104057\pi$
$192$	−4.92293	−	8.52676i	−0.355282	−	0.615366i
$193$	8.52691	+	14.7690i	0.613780	+	1.06310i	0.990597	+	0.136811i	$0.0436853\pi$
$193$	8.52691	+	14.7690i	0.613780	+	1.06310i	−0.376817	+	0.926288i	$0.622981\pi$
$194$	−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	−0.994475	−	0.104977i	$-0.966523\pi$
$197$	−5.70304	+	9.87796i	−0.406325	+	0.703776i	0.588150	+	0.808752i	$0.299857\pi$
$198$	11.7667			0.836220
$199$	−10.4443			−0.740376			−0.370188	−	0.928957i	$-0.620707\pi$
$199$	−10.4443			−0.740376			−0.370188	+	0.928957i	$0.620707\pi$
$200$	10.7969	−	18.7007i	0.763454	−	1.32234i
$201$	−2.33539	+	4.04502i	−0.164726	+	0.285313i
$202$	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
$205$	3.27165			0.228502
$206$	−19.9975	−	34.6367i	−1.39329	−	2.41325i
$207$	−3.87459	+	6.71099i	−0.269303	+	0.466446i
$208$	−36.4547	+	3.81099i	−2.52768	+	0.264245i
$209$	−13.5061			−0.934235
$210$	0.983109	+	10.1591i	0.0678410	+	0.701046i
$211$	−3.06851	+	5.31482i	−0.211245	+	0.365887i	−0.952104	−	0.305773i	$-0.901085\pi$
$211$	−3.06851	+	5.31482i	−0.211245	+	0.365887i	0.740859	+	0.671660i	$0.234418\pi$
$212$	−20.8312	+	36.0807i	−1.43069	+	2.47803i
$213$	1.24524	−	2.15682i	0.0853226	−	0.147783i
$214$	−28.1648			−1.92531
$215$	−3.74153	+	6.48051i	−0.255170	+	0.441967i
$216$	7.59966			0.517091
$217$	−0.281663	−	2.91061i	−0.0191205	−	0.197585i
$218$	18.2080	−	31.5372i	1.23320	−	2.13597i
$219$	−6.06139			−0.409591
$220$	16.1122	−	27.9072i	1.08629	−	1.88150i
$221$	13.0129	−	1.36037i	0.875339	−	0.0915085i
$222$	4.13762	+	7.16656i	0.277699	+	0.480988i
$223$	13.1521	−	22.7802i	0.880733	−	1.52547i	0.0302045	−	0.999544i	$-0.490384\pi$
$223$	13.1521	−	22.7802i	0.880733	−	1.52547i	0.850528	−	0.525930i	$-0.176283\pi$
$224$	−24.7471	+	17.6697i	−1.65348	+	1.18061i
$225$	1.42070	+	2.46073i	0.0947136	+	0.164049i
$226$	−2.52440	−	4.37239i	−0.167921	−	0.290847i
$227$	3.93306			0.261047			0.130523	−	0.991445i	$-0.458334\pi$
$227$	3.93306			0.261047			0.130523	+	0.991445i	$0.458334\pi$
$228$	−14.7508			−0.976895
$229$	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
$231$	−1.14203	−	11.8014i	−0.0751401	−	0.776472i
$232$	−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	$0.770437\pi$
$234$	3.85544	−	8.64649i	0.252038	−	0.565239i
$235$	−2.49428	+	4.32022i	−0.162709	+	0.281820i
$236$	70.7699			4.60673
$237$	−3.59127	+	6.22026i	−0.233278	+	0.404050i
$238$	20.5161	−	14.6488i	1.32986	−	0.949538i
$239$	−8.09328			−0.523511			−0.261755	−	0.965134i	$-0.584301\pi$
$239$	−8.09328			−0.523511			−0.261755	+	0.965134i	$0.584301\pi$
$240$	7.46787	−	12.9347i	0.482049	−	0.834933i
$241$	−15.6065			−1.00531			−0.502653	−	0.864488i	$-0.667643\pi$
$241$	−15.6065			−1.00531			−0.502653	+	0.864488i	$0.667643\pi$
$242$	−11.9238	+	20.6526i	−0.766488	+	1.32760i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−18.6557	+	32.3127i	−1.19431	+	2.06861i
$245$	10.0937	−	1.97202i	0.644861	−	0.125988i
$246$	−5.84693			−0.372787
$247$	−4.42538	+	9.92467i	−0.281580	+	0.631492i
$248$	−4.19975	+	7.27418i	−0.266684	+	0.461911i
$249$	−4.65417	−	8.06126i	−0.294946	−	0.510862i
$250$	30.2500			1.91318
$251$	−4.67520	−	8.09769i	−0.295096	−	0.511122i	0.679911	−	0.733295i	$-0.262018\pi$
$251$	−4.67520	−	8.09769i	−0.295096	−	0.511122i	−0.975007	+	0.222173i	$0.928685\pi$
$252$	−1.24728	−	12.8890i	−0.0785712	−	0.811929i
$253$	−17.3633	−	30.0741i	−1.09162	−	1.89075i
$254$	−22.5914	+	39.1295i	−1.41751	+	2.45520i
$255$	−2.66573	+	4.61718i	−0.166935	+	0.289139i
$256$	−12.1661			−0.760378
$257$	9.72940			0.606903			0.303452	−	0.952847i	$-0.401861\pi$
$257$	9.72940			0.606903			0.303452	+	0.952847i	$0.401861\pi$
$258$	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
$262$	−6.57606	−	11.3901i	−0.406270	−	0.703680i
$263$	7.25776	+	12.5708i	0.447532	+	0.775149i	0.998225	−	0.0595594i	$-0.0189696\pi$
$263$	7.25776	+	12.5708i	0.447532	+	0.775149i	−0.550692	+	0.834708i	$0.685636\pi$
$264$	−17.0283	+	29.4939i	−1.04802	+	1.81522i
$265$	−12.5065			−0.768268
$266$	2.01669	+	20.8398i	0.123651	+	1.27777i
$267$	−3.18037	−	5.50857i	−0.194636	−	0.337119i
$268$	−11.4302	−	19.7976i	−0.698209	−	1.20933i
$269$	−18.4325			−1.12385			−0.561924	−	0.827189i	$-0.689939\pi$
$269$	−18.4325			−1.12385			−0.561924	+	0.827189i	$0.689939\pi$
$270$	1.92886	+	3.34089i	0.117387	+	0.203320i
$271$	4.90428			0.297914			0.148957	−	0.988844i	$-0.452408\pi$
$271$	4.90428			0.297914			0.148957	+	0.988844i	$0.452408\pi$
$272$	−36.8895			−2.23675
$273$	−9.04619	−	3.02762i	−0.547500	−	0.183240i
$274$	−1.95533			−0.118126
$275$	−12.7333			−0.767846
$276$	−18.9635	−	32.8458i	−1.14147	−	1.97708i
$277$	−25.8793			−1.55494			−0.777469	−	0.628921i	$-0.783497\pi$
$277$	−25.8793			−1.55494			−0.777469	+	0.628921i	$0.783497\pi$
$278$	−15.9734	−	27.6667i	−0.958019	−	1.65934i
$279$	−0.552624	−	0.957172i	−0.0330847	−	0.0573044i
$280$	−26.8872	−	12.2377i	−1.60682	−	0.731342i
$281$	4.64246			0.276946			0.138473	−	0.990366i	$-0.455781\pi$
$281$	4.64246			0.276946			0.138473	+	0.990366i	$0.455781\pi$
$282$	4.45765	−	7.72088i	0.265449	−	0.459772i
$283$	12.1426	+	21.0316i	0.721802	+	1.25020i	0.960277	+	0.279049i	$0.0900192\pi$
$283$	12.1426	+	21.0316i	0.721802	+	1.25020i	−0.238475	+	0.971149i	$0.576647\pi$
$284$	6.09462	+	10.5562i	0.361649	+	0.626395i
$285$	−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
$289$	−3.83192			−0.225407
$290$	−30.7373			−1.80496
$291$	−4.02169	+	6.96578i	−0.235756	+	0.408341i
$292$	14.8332	−	25.6919i	0.868049	−	1.50351i
$293$	−10.1171	−	17.5233i	−0.591047	−	1.02372i	−0.994092	−	0.108543i	$-0.965381\pi$
$293$	−10.1171	−	17.5233i	−0.591047	−	1.02372i	0.403045	−	0.915180i	$-0.367952\pi$
$294$	−18.0389	+	3.52429i	−1.05205	+	0.205541i
$295$	10.6221	+	18.3980i	0.618443	+	1.07117i
$296$	−23.9512			−1.39214
$297$	−2.24067	−	3.88095i	−0.130017	−	0.225195i
$298$	−3.41922	+	5.92226i	−0.198070	+	0.343067i
$299$	−27.7886	+	2.90504i	−1.60706	+	0.168003i
$300$	−13.9068			−0.802909
$301$	−12.2648	−	5.58231i	−0.706931	−	0.321759i
$302$	18.1160	−	31.3779i	1.04246	−	1.80559i
$303$	6.95201	−	12.0412i	0.399382	−	0.691750i
$304$	15.3191	−	26.5335i	0.878612	−	1.52180i
$305$	−11.2004			−0.641334
$306$	4.76406	−	8.25159i	0.272343	−	0.471712i
$307$	2.00196			0.114258			0.0571290	−	0.998367i	$-0.481805\pi$
$307$	2.00196			0.114258			0.0571290	+	0.998367i	$0.481805\pi$
$308$	52.8161	+	24.0392i	3.00948	+	1.36976i
$309$	−7.61605	+	13.1914i	−0.433262	+	0.750432i
$310$	−4.26374			−0.242164
$311$	−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	$0.217613\pi$
$312$	16.0935	+	22.1768i	0.911116	+	1.25551i
$313$	−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
$315$	3.16353	−	2.25881i	0.178245	−	0.127269i
$316$	−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	$0.560101\pi$
$318$	22.3510			1.25338
$319$	35.7060			1.99915
$320$	7.23284	+	12.5276i	0.404328	+	0.700316i
$321$	5.36329	+	9.28948i	0.299349	+	0.518488i
$322$	−43.8116	+	31.2821i	−2.44152	+	1.74328i
$323$	−5.46831	+	9.47140i	−0.304265	+	0.527003i
$324$	−2.44716	−	4.23861i	−0.135954	−	0.235479i
$325$	−4.17217	+	9.35681i	−0.231430	+	0.519022i
$326$	−12.1575	+	21.0575i	−0.673343	+	1.16627i
$327$	−13.8690			−0.766959
$328$	8.46148	−	14.6557i	0.467207	−	0.809226i
$329$	−8.17630	−	3.72144i	−0.450774	−	0.205170i
$330$	−17.2877			−0.951659
$331$	−2.28069	+	3.95028i	−0.125358	+	0.217127i	−0.921873	−	0.387492i	$-0.873341\pi$
$331$	−2.28069	+	3.95028i	−0.125358	+	0.217127i	0.796515	+	0.604619i	$0.206675\pi$
$332$	45.5581			2.50033
$333$	1.57581	−	2.72938i	0.0863539	−	0.149569i
$334$	−20.9887	+	36.3535i	−1.14845	+	1.98917i
$335$	3.43119	−	5.94300i	0.187466	−	0.324701i
$336$	24.4798	+	11.1420i	1.33548	+	0.607845i
$337$	25.6864			1.39923			0.699614	−	0.714521i	$-0.253355\pi$
$337$	25.6864			1.39923			0.699614	+	0.714521i	$0.253355\pi$
$338$	33.3961	−	7.05966i	1.81651	−	0.383995i
$339$	−0.961419	+	1.66523i	−0.0522171	+	0.0904427i
$340$	−13.0470	−	22.5980i	−0.707571	−	1.22555i
$341$	4.95298			0.268219
$342$	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
$345$	5.69260	−	9.85988i	0.306479	−	0.530838i
$346$	−13.7516	+	23.8185i	−0.739292	+	1.28049i
$347$	14.5710			0.782210			0.391105	−	0.920346i	$-0.372093\pi$
$347$	14.5710			0.782210			0.391105	+	0.920346i	$0.372093\pi$
$348$	38.9967			2.09044
$349$	8.87949	−	15.3797i	0.475308	−	0.823258i	−0.524292	−	0.851539i	$-0.675670\pi$
$349$	8.87949	−	15.3797i	0.475308	−	0.823258i	0.999600	+	0.0282805i	$0.00900317\pi$
$350$	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
$353$	−3.34866	−	5.80004i	−0.178231	−	0.308705i	0.763044	−	0.646347i	$-0.223704\pi$
$353$	−3.34866	−	5.80004i	−0.178231	−	0.308705i	−0.941275	+	0.337642i	$0.890371\pi$
$354$	−18.9833	−	32.8800i	−1.00895	−	1.74755i
$355$	−1.82953	+	3.16883i	−0.0971013	+	0.168184i
$356$	31.1316			1.64997
$357$	−8.73831	−	3.97724i	−0.462481	−	0.210498i
$358$	−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	$-0.516166\pi$
$360$	−11.1655			−0.588475
$361$	4.95834	+	8.58810i	0.260965	+	0.452005i
$362$	−39.0866			−2.05435
$363$	9.08233			0.476699
$364$	34.9704	−	30.9342i	1.83295	−	1.62139i
$365$	8.90549			0.466135
$366$	20.0168			1.04630
$367$	11.3762	+	19.7042i	0.593835	+	1.02855i	0.993710	+	0.111983i	$0.0357201\pi$
$367$	11.3762	+	19.7042i	0.593835	+	1.02855i	−0.399875	+	0.916570i	$0.630947\pi$
$368$	78.7766			4.10651
$369$	1.11340	+	1.92847i	0.0579614	+	0.100392i
$370$	−6.07905	−	10.5292i	−0.316035	−	0.547388i
$371$	−2.16931	−	22.4169i	−0.112625	−	1.16383i
$372$	5.40944			0.280467
$373$	−8.59000	+	14.8783i	−0.444774	+	0.770370i	−0.998036	−	0.0626364i	$-0.980049\pi$
$373$	−8.59000	+	14.8783i	−0.444774	+	0.770370i	0.553263	+	0.833007i	$0.313383\pi$
$374$	21.3493	+	36.9781i	1.10395	+	1.91209i
$375$	−5.76036	−	9.97723i	−0.297463	−	0.515222i
$376$	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	−0.432498	−	0.901635i	$-0.642368\pi$
$379$	10.9914	−	19.0377i	0.564590	−	0.977899i	0.997088	−	0.0762637i	$-0.0242991\pi$
$380$	21.6721			1.11175
$381$	17.2079			0.881586
$382$	27.2745	−	47.2408i	1.39549	−	2.41705i
$383$	−1.52458	+	2.64065i	−0.0779023	+	0.134931i	−0.902345	−	0.431015i	$-0.858156\pi$
$383$	−1.52458	+	2.64065i	−0.0779023	+	0.134931i	0.824442	+	0.565946i	$0.191489\pi$
$384$	−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
$387$	−5.09323			−0.258904
$388$	−19.6835	−	34.0928i	−0.999278	−	1.73080i
$389$	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	$0.0461474\pi$
$390$	−5.66447	+	12.7036i	−0.286832	+	0.643269i
$391$	−28.1201			−1.42209
$392$	17.2714	−	50.3158i	0.872337	−	2.54133i
$393$	−2.50449	+	4.33791i	−0.126335	+	0.218818i
$394$	−14.9745	+	25.9366i	−0.754405	+	1.30667i
$395$	5.27635	−	9.13890i	0.265482	−	0.459828i
$396$	21.9331			1.10218
$397$	3.51106	−	6.08133i	0.176215	−	0.305213i	−0.764366	−	0.644782i	$-0.776948\pi$
$397$	3.51106	−	6.08133i	0.176215	−	0.305213i	0.940581	+	0.339569i	$0.110281\pi$
$398$	−27.4236			−1.37462
$399$	6.48947	−	4.63357i	0.324880	−	0.231969i
$400$	14.4426	−	25.0153i	0.722130	−	1.25077i
$401$	8.89389			0.444140			0.222070	−	0.975031i	$-0.428719\pi$
$401$	8.89389			0.444140			0.222070	+	0.975031i	$0.428719\pi$
$402$	−6.13205	+	10.6210i	−0.305839	+	0.529728i
$403$	1.62289	−	3.63960i	0.0808417	−	0.181301i
$404$	34.0254	+	58.9337i	1.69283	+	2.93206i
$405$	0.734607	−	1.27238i	0.0365029	−	0.0632249i
$406$	−5.33152	−	55.0942i	−0.264599	−	2.73428i
$407$	7.06173	+	12.2313i	0.350037	+	0.606282i
$408$	13.7888	+	23.8828i	0.682645	+	1.18238i
$409$	−0.547463			−0.0270703			−0.0135352	−	0.999908i	$-0.504309\pi$
$409$	−0.547463			−0.0270703			−0.0135352	+	0.999908i	$0.504309\pi$
$410$	8.59040			0.424250
$411$	0.372343	+	0.644917i	0.0183663	+	0.0318114i
$412$	−37.2755	−	64.5630i	−1.83643	−	3.18079i
$413$	−31.1345	+	22.2305i	−1.53203	+	1.09389i
$414$	−10.1735	+	17.6211i	−0.500002	+	0.866028i
$415$	6.83798	+	11.8437i	0.335663	+	0.581386i
$416$	−41.2143	+	4.30857i	−2.02070	+	0.211245i
$417$	−6.08346	+	10.5369i	−0.297908	+	0.515992i
$418$	−35.4630			−1.73455
$419$	−15.9631	+	27.6488i	−0.779847	+	1.35073i	0.152183	+	0.988352i	$0.451370\pi$
$419$	−15.9631	+	27.6488i	−0.779847	+	1.35073i	−0.932030	+	0.362382i	$0.881964\pi$
$420$	1.83252	+	18.9367i	0.0894179	+	0.924014i
$421$	−25.4622			−1.24095			−0.620476	−	0.784226i	$-0.713060\pi$
$421$	−25.4622			−1.24095			−0.620476	+	0.784226i	$0.713060\pi$
$422$	−8.05700	+	13.9551i	−0.392209	+	0.679326i
$423$	−3.39540			−0.165090
$424$	−32.3455	+	56.0241i	−1.57084	+	2.72077i
$425$	−5.15543	+	8.92947i	−0.250075	+	0.433143i
$426$	3.26964	−	5.66318i	0.158415	−	0.274382i
$427$	−1.94276	−	20.0758i	−0.0940168	−	0.971538i
$428$	−52.4994			−2.53765
$429$	6.58014	−	14.7571i	0.317692	−	0.712479i
$430$	−9.82415	+	17.0159i	−0.473762	+	0.820581i
$431$	−7.77555	−	13.4676i	−0.374535	−	0.648714i	0.615722	−	0.787963i	$-0.288864\pi$
$431$	−7.77555	−	13.4676i	−0.374535	−	0.648714i	−0.990257	+	0.139249i	$0.955531\pi$
$432$	10.1658			0.489102
$433$	15.1163	+	26.1822i	0.726443	+	1.25824i	0.958377	+	0.285505i	$0.0921612\pi$
$433$	15.1163	+	26.1822i	0.726443	+	1.25824i	−0.231934	+	0.972731i	$0.574505\pi$
$434$	−0.739564	−	7.64241i	−0.0355002	−	0.366847i
$435$	5.85315	+	10.1380i	0.280637	+	0.486078i
$436$	33.9398	−	58.7855i	1.62542	−	2.81531i
$437$	11.6774	−	20.2259i	0.558608	−	0.967537i
$438$	−15.9154			−0.760469
$439$	35.6103			1.69959			0.849793	−	0.527116i	$-0.176727\pi$
$439$	35.6103			1.69959			0.849793	+	0.527116i	$0.176727\pi$
$440$	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	$0.895788\pi$
$444$	7.71254	+	13.3585i	0.366021	+	0.633967i
$445$	4.67265	+	8.09327i	0.221505	+	0.383658i
$446$	34.5336	−	59.8140i	1.63522	−	2.83228i
$447$	2.60442			0.123185
$448$	−21.2002	+	15.1373i	−1.00162	+	0.715168i
$449$	−5.74953	−	9.95847i	−0.271337	−	0.469969i	0.697868	−	0.716227i	$-0.254132\pi$
$449$	−5.74953	−	9.95847i	−0.271337	−	0.469969i	−0.969204	+	0.246258i	$0.920799\pi$
$450$	3.73035	+	6.46116i	0.175850	+	0.304582i
$451$	−9.97905			−0.469895
$452$	−4.70550	−	8.15017i	−0.221328	−	0.383352i
$453$	−13.7990			−0.648333
$454$	10.3271			0.484673
$455$	13.2908	+	4.44822i	0.623082	+	0.208536i
$456$	−22.9043			−1.07259
$457$	−8.91472			−0.417013			−0.208506	−	0.978021i	$-0.566860\pi$
$457$	−8.91472			−0.417013			−0.208506	+	0.978021i	$0.566860\pi$
$458$	14.9361	+	25.8701i	0.697919	+	1.20883i
$459$	−3.62878			−0.169377
$460$	27.8615	+	48.2575i	1.29905	+	2.25002i
$461$	6.22417	+	10.7806i	0.289888	+	0.502101i	0.973783	−	0.227480i	$-0.0730485\pi$
$461$	6.22417	+	10.7806i	0.289888	+	0.502101i	−0.683895	+	0.729581i	$0.739715\pi$
$462$	−2.99863	−	30.9869i	−0.139509	−	1.44164i
$463$	22.4118			1.04156			0.520782	−	0.853690i	$-0.325640\pi$
$463$	22.4118			1.04156			0.520782	+	0.853690i	$0.325640\pi$
$464$	−40.4992	+	70.1466i	−1.88013	+	3.25648i
$465$	0.811923	+	1.40629i	0.0376520	+	0.0652152i
$466$	7.86811	+	13.6280i	0.364483	+	0.631303i
$467$	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
$471$	0.495034			0.0228099
$472$	109.888			5.05800
$473$	11.4122	−	19.7666i	0.524735	−	0.908868i
$474$	−9.42962	+	16.3326i	−0.433117	+	0.750180i
$475$	−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
$478$	−21.2506			−0.971979
$479$	4.65459	+	8.06199i	0.212674	+	0.368362i	0.952550	−	0.304381i	$-0.0984495\pi$
$479$	4.65459	+	8.06199i	0.212674	+	0.368362i	−0.739877	+	0.672743i	$0.765116\pi$
$480$	8.44290	−	14.6235i	0.385364	−	0.667470i
$481$	11.3017	−	1.18149i	0.515315	−	0.0538714i
$482$	−40.9782			−1.86651
$483$	18.6604	+	8.49330i	0.849080	+	0.386458i
$484$	−22.2260	+	38.4965i	−1.01027	+	1.74984i
$485$	5.90873	−	10.2342i	0.268302	−	0.464712i
$486$	−1.31285	+	2.27393i	−0.0595522	+	0.103147i
$487$	−9.48493			−0.429803			−0.214902	−	0.976636i	$-0.568943\pi$
$487$	−9.48493			−0.429803			−0.214902	+	0.976636i	$0.568943\pi$
$488$	−28.9676	+	50.1734i	−1.31130	+	2.27124i
$489$	9.26039			0.418769
$490$	26.5030	−	5.17794i	1.19728	−	0.233915i
$491$	−7.76607	+	13.4512i	−0.350478	+	0.607046i	−0.986333	−	0.164763i	$-0.947314\pi$
$491$	−7.76607	+	13.4512i	−0.350478	+	0.607046i	0.635855	+	0.771808i	$0.280647\pi$
$492$	−10.8987			−0.491352
$493$	14.4566	−	25.0395i	0.651092	−	1.12772i
$494$	−11.6197	+	26.0593i	−0.522797	+	1.17246i
$495$	3.29202	+	5.70194i	0.147965	+	0.256283i
$496$	−5.61786	+	9.73042i	−0.252249	+	0.436909i
$497$	−5.99722	−	2.72963i	−0.269012	−	0.122441i
$498$	−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	$0.977929\pi$
$500$	56.3862			2.52167
$501$	15.9871			0.714250
$502$	−12.2757	−	21.2622i	−0.547892	−	0.948976i
$503$	−16.8374	−	29.1632i	−0.750741	−	1.30032i	−0.947464	−	0.319862i	$-0.896363\pi$
$503$	−16.8374	−	29.1632i	−0.750741	−	1.30032i	0.196723	−	0.980459i	$-0.436970\pi$
$504$	−1.93671	−	20.0133i	−0.0862679	−	0.891464i
$505$	−10.2140	+	17.6911i	−0.454517	+	0.787246i
$506$	−45.5910	−	78.9659i	−2.02677	−	3.51046i
$507$	−8.68792	−	9.67058i	−0.385844	−	0.429485i
$508$	−42.1105	+	72.9375i	−1.86835	+	3.23608i
$509$	18.6952			0.828652			0.414326	−	0.910129i	$-0.364017\pi$
$509$	18.6952			0.828652			0.414326	+	0.910129i	$0.364017\pi$
$510$	−6.99943	+	12.1234i	−0.309940	+	0.536831i
$511$	1.54470	+	15.9624i	0.0683333	+	0.706134i
$512$	−37.6768			−1.66509
$513$	1.50693	−	2.61007i	0.0665324	−	0.115238i
$514$	25.5465			1.12681
$515$	11.1896	−	19.3810i	0.493073	−	0.854028i
$516$	12.4640	−	21.5882i	0.548696	−	0.950370i
$517$	7.60795	−	13.1774i	0.334597	−	0.579539i
$518$	17.8183	−	12.7225i	0.782893	−	0.558996i
$519$	10.4746			0.459785
$520$	−23.6448	−	32.5825i	−1.03689	−	1.42884i
$521$	−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	$0.330651\pi$
$522$	−10.4605	−	18.1180i	−0.457842	−	0.793005i
$523$	−38.0949			−1.66577			−0.832886	−	0.553445i	$-0.813313\pi$
$523$	−38.0949			−1.66577			−0.832886	+	0.553445i	$0.813313\pi$
$524$	−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
$527$	2.00535	−	3.47337i	0.0873545	−	0.151302i
$528$	−22.7782	+	39.4529i	−0.991292	+	1.71697i
$529$	37.0498			1.61086
$530$	−32.8384			−1.42641
$531$	−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
$535$	−7.87982	−	13.6482i	−0.340674	−	0.590065i
$536$	−17.7482	−	30.7407i	−0.766604	−	1.32780i
$537$	−5.22181	+	9.04444i	−0.225338	+	0.390296i
$538$	−48.3983			−2.08660
$539$	−30.7872	+	6.01496i	−1.32610	+	0.259083i
$540$	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	$0.681363\pi$
$542$	12.8772			0.553123
$543$	7.44306	+	12.8918i	0.319412	+	0.553239i
$544$	−41.7059			−1.78813
$545$	20.3766			0.872837
$546$	−23.7526	−	7.94963i	−1.01652	−	0.340213i
$547$	21.9105			0.936827			0.468414	−	0.883509i	$-0.344826\pi$
$547$	21.9105			0.936827			0.468414	+	0.883509i	$0.344826\pi$
$548$	−3.64474			−0.155696
$549$	−3.81170	−	6.60206i	−0.162679	−	0.281769i
$550$	−33.4339			−1.42563
$551$	12.0068	+	20.7964i	0.511506	+	0.885955i
$552$	−29.4455	−	51.0012i	−1.25329	−	2.17075i
$553$	17.2960	+	7.87225i	0.735499	+	0.334762i
$554$	−67.9515			−2.88698
$555$	−2.31520	+	4.01005i	−0.0982750	+	0.170217i
$556$	−29.7745	−	51.5709i	−1.26272	−	2.18709i
$557$	−3.55577	−	6.15877i	−0.150663	−	0.260956i	0.780809	−	0.624770i	$-0.214807\pi$
$557$	−3.55577	−	6.15877i	−0.150663	−	0.260956i	−0.931471	+	0.363815i	$0.881474\pi$
$558$	−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
$562$	12.1897			0.514193
$563$	25.2362			1.06358			0.531789	−	0.846877i	$-0.321520\pi$
$563$	25.2362			1.06358			0.531789	+	0.846877i	$0.321520\pi$
$564$	8.30909	−	14.3918i	0.349876	−	0.606003i
$565$	1.41253	−	2.44658i	0.0594256	−	0.102928i
$566$	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
$569$	15.9583			0.669007			0.334504	−	0.942394i	$-0.391431\pi$
$569$	15.9583			0.669007			0.334504	+	0.942394i	$0.391431\pi$
$570$	−5.81331	−	10.0689i	−0.243493	−	0.421742i
$571$	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	$0.151637\pi$
$572$	46.4469	+	64.0037i	1.94204	+	2.67613i
$573$	−20.7750			−0.867888
$574$	1.49004	+	15.3976i	0.0621932	+	0.642684i
$575$	11.0093	−	19.0687i	0.459119	−	0.795218i
$576$	−4.92293	+	8.52676i	−0.205122	+	0.355282i
$577$	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	$0.0774488\pi$
$578$	−10.0615			−0.418503
$579$	8.52691	−	14.7690i	0.354366	−	0.613780i
$580$	−57.2945			−2.37903
$581$	−20.0429	+	14.3109i	−0.831518	+	0.593715i
$582$	−10.5598	+	18.2901i	−0.437717	+	0.758148i
$583$	38.1468			1.57988
$584$	23.0323	−	39.8930i	0.953082	−	1.65079i
$585$	5.26862	−	0.550784i	0.217831	−	0.0227721i
$586$	−26.5645	−	46.0111i	−1.09737	−	1.90070i
$587$	1.24993	−	2.16495i	0.0515903	−	0.0893570i	−0.839077	−	0.544013i	$-0.816904\pi$
$587$	1.24993	−	2.16495i	0.0515903	−	0.0893570i	0.890667	+	0.454656i	$0.150238\pi$
$588$	−33.6246	+	6.56929i	−1.38665	+	0.270913i
$589$	1.66553	+	2.88478i	0.0686268	+	0.118865i
$590$	27.8905	+	48.3078i	1.14823	+	1.98880i
$591$	11.4061			0.469184
$592$	−32.0388			−1.31678
$593$	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
$595$	12.8385	+	5.84342i	0.526325	+	0.239557i
$596$	−6.37344	+	11.0391i	−0.261066	+	0.452180i
$597$	5.22215	+	9.04502i	0.213728	+	0.370188i
$598$	−72.9648	+	7.62778i	−2.98375	+	0.311923i
$599$	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	$-0.0163288\pi$
$600$	−21.5937			−0.881560
$601$	−6.02647	+	10.4381i	−0.245825	+	0.425781i	−0.962363	−	0.271767i	$-0.912392\pi$
$601$	−6.02647	+	10.4381i	−0.245825	+	0.425781i	0.716538	+	0.697548i	$0.245725\pi$
$602$	−32.2037	−	14.6575i	−1.31253	−	0.597395i
$603$	4.67078			0.190209
$604$	33.7684	−	58.4885i	1.37402	−	2.37987i
$605$	−13.3439			−0.542506
$606$	18.2539	−	31.6167i	0.741515	−	1.28434i
$607$	2.17000	−	3.75855i	0.0880776	−	0.152555i	−0.818621	−	0.574334i	$-0.805261\pi$
$607$	2.17000	−	3.75855i	0.0880776	−	0.152555i	0.906698	+	0.421779i	$0.138594\pi$
$608$	17.3192	−	29.9978i	0.702388	−	1.21657i
$609$	−17.1562	+	12.2498i	−0.695205	+	0.496386i
$610$	−29.4090			−1.19074
$611$	−7.19031	−	9.90822i	−0.290889	−	0.400844i
$612$	8.88023	−	15.3810i	0.358962	−	0.621741i
$613$	23.9659	+	41.5101i	0.967972	+	1.67658i	0.701409	+	0.712759i	$0.252555\pi$
$613$	23.9659	+	41.5101i	0.967972	+	1.67658i	0.266563	+	0.963817i	$0.414112\pi$
$614$	5.25656			0.212137
$615$	−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	0.842458	−	0.538762i	$-0.181108\pi$
$617$	−1.12653	−	1.95120i	−0.0453523	−	0.0785524i	−0.887810	+	0.460209i	$0.847774\pi$
$618$	−19.9975	+	34.6367i	−0.804418	+	1.39329i
$619$	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	$0.109755\pi$
$620$	−7.94763			−0.319185
$621$	7.74918			0.310964
$622$	−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
$626$	−29.2851	−	50.7232i	−1.17047	−	2.02731i
$627$	6.75304	+	11.6966i	0.269690	+	0.467117i
$628$	−1.21143	+	2.09826i	−0.0483413	+	0.0837296i
$629$	11.4366			0.456005
$630$	8.30650	−	5.93096i	0.330939	−	0.236295i
$631$	−19.9790	−	34.6047i	−0.795352	−	1.37759i	−0.922615	−	0.385721i	$-0.873953\pi$
$631$	−19.9790	−	34.6047i	−0.795352	−	1.37759i	0.127264	−	0.991869i	$-0.459381\pi$
$632$	−27.2924	−	47.2719i	−1.08563	−	1.88037i
$633$	6.13702			0.243925
$634$	35.3793	+	61.2787i	1.40509	+	2.43369i
$635$	−25.2821			−1.00329
$636$	41.6623			1.65202
$637$	−5.66773	+	24.5942i	−0.224564	+	0.974459i
$638$	93.7536			3.71174
$639$	−2.49048			−0.0985220
$640$	2.10549	+	3.64682i	0.0832269	+	0.144153i
$641$	11.6665			0.460800			0.230400	−	0.973096i	$-0.425997\pi$
$641$	11.6665			0.460800			0.230400	+	0.973096i	$0.425997\pi$
$642$	14.0824	+	24.3914i	0.555788	+	0.962654i
$643$	−3.24846	−	5.62650i	−0.128107	−	0.221888i	0.794836	−	0.606824i	$-0.207557\pi$
$643$	−3.24846	−	5.62650i	−0.128107	−	0.221888i	−0.922943	+	0.384936i	$0.874223\pi$
$644$	−81.6650	+	58.3099i	−3.21805	+	2.29773i
$645$	7.48305			0.294645
$646$	−14.3582	+	24.8691i	−0.564915	+	0.978461i
$647$	−7.49768	−	12.9864i	−0.294764	−	0.510546i	0.680166	−	0.733058i	$-0.261908\pi$
$647$	−7.49768	−	12.9864i	−0.294764	−	0.510546i	−0.974930	+	0.222512i	$0.928574\pi$
$648$	−3.79983	−	6.58150i	−0.149271	−	0.258546i
$649$	−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
$653$	36.9795			1.44712			0.723560	−	0.690262i	$-0.242505\pi$
$653$	36.9795			1.44712			0.723560	+	0.690262i	$0.242505\pi$
$654$	−36.4160			−1.42398
$655$	3.67963	−	6.37331i	0.143775	−	0.249026i
$656$	11.3186	−	19.6044i	0.441918	−	0.765425i
$657$	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	0.825503	−	0.564398i	$-0.190892\pi$
$659$	−1.95181	−	3.38064i	−0.0760319	−	0.131691i	−0.901535	+	0.432707i	$0.857558\pi$
$660$	−32.2244			−1.25433
$661$	−19.7061	−	34.1320i	−0.766479	−	1.32758i	−0.939461	−	0.342655i	$-0.888674\pi$
$661$	−19.7061	−	34.1320i	−0.766479	−	1.32758i	0.172983	−	0.984925i	$-0.444660\pi$
$662$	−5.98843	+	10.3723i	−0.232747	+	0.403129i
$663$	−7.68454	−	10.5893i	−0.298443	−	0.411253i
$664$	70.7402			2.74525
$665$	−9.53442	+	6.80771i	−0.369729	+	0.263992i
$666$	4.13762	−	7.16656i	0.160329	−	0.277699i
$667$	−30.8717	+	53.4713i	−1.19536	+	2.07042i
$668$	−39.1230	+	67.7631i	−1.51372	+	2.62183i
$669$	−26.3043			−1.01698
$670$	9.00930	−	15.6046i	0.348059	−	0.602857i
$671$	34.1630			1.31885
$672$	27.6760	+	12.5967i	1.06762	+	0.485929i
$673$	17.4150	−	30.1637i	0.671301	−	1.16273i	−0.306235	−	0.951956i	$-0.599069\pi$
$673$	17.4150	−	30.1637i	0.671301	−	1.16273i	0.977535	−	0.210771i	$-0.0675974\pi$
$674$	67.4450			2.59788
$675$	1.42070	−	2.46073i	0.0546829	−	0.0947136i
$676$	62.2506	−	13.1592i	2.39425	−	0.506125i
$677$	−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
$679$	19.3689	+	8.81575i	0.743311	+	0.338318i
$680$	−20.2586	−	35.0890i	−0.776883	−	1.34560i
$681$	−1.96653	−	3.40613i	−0.0753577	−	0.130523i
$682$	13.0051			0.497990
$683$	−22.1728			−0.848421			−0.424210	−	0.905564i	$-0.639448\pi$
$683$	−22.1728			−0.848421			−0.424210	+	0.905564i	$0.639448\pi$
$684$	7.37540	+	12.7746i	0.282005	+	0.488448i
$685$	−0.547052	−	0.947522i	−0.0209018	−	0.0362030i
$686$	13.8781	+	46.6064i	0.529868	+	1.77944i
$687$	5.68842	−	9.85263i	0.217027	−	0.375901i
$688$	25.8884	+	44.8400i	0.986986	+	1.70951i
$689$	12.4991	−	28.0314i	0.476178	−	1.06791i
$690$	14.9471	−	25.8891i	0.569026	−	0.985583i
$691$	−17.6675			−0.672104			−0.336052	−	0.941843i	$-0.609092\pi$
$691$	−17.6675			−0.672104			−0.336052	+	0.941843i	$0.609092\pi$
$692$	−25.6331	+	44.3978i	−0.974425	+	1.68775i
$693$	−9.64926	+	6.88971i	−0.366545	+	0.261718i
$694$	38.2591			1.45229
$695$	8.93791	−	15.4809i	0.339034	−	0.587224i
$696$	60.5520			2.29522
$697$	−4.04030	+	6.99800i	−0.153037	+	0.265068i
$698$	23.3149	−	40.3826i	0.882483	−	1.52851i
$699$	2.99657	−	5.19021i	0.113341	−	0.196312i
$700$	3.54403	+	36.6228i	0.133952	+	1.38421i
$701$	7.13063			0.269320			0.134660	−	0.990892i	$-0.457006\pi$
$701$	7.13063			0.269320			0.134660	+	0.990892i	$0.457006\pi$
$702$	−9.41580	+	0.984334i	−0.355377	+	0.0371513i
$703$	−4.74926	+	8.22597i	−0.179122	+	0.310248i
$704$	−22.0613	−	38.2112i	−0.831465	−	1.44014i
$705$	4.98857			0.187880
$706$	−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
$709$	−1.16524	+	2.01826i	−0.0437615	+	0.0757972i	−0.887077	−	0.461622i	$-0.847268\pi$
$709$	−1.16524	+	2.01826i	−0.0437615	+	0.0757972i	0.843315	+	0.537420i	$0.180601\pi$
$710$	−4.80380	+	8.32043i	−0.180283	+	0.312260i
$711$	7.18254			0.269366
$712$	48.3395			1.81160
$713$	−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
$717$	4.04664	+	7.00899i	0.151125	+	0.261755i
$718$	−44.2920	−	76.7160i	−1.65296	−	2.86302i
$719$	21.2152	−	36.7457i	0.791192	−	1.37038i	−0.134037	−	0.990976i	$-0.542794\pi$
$719$	21.2152	−	36.7457i	0.791192	−	1.37038i	0.925229	−	0.379409i	$-0.123873\pi$
$720$	−14.9357			−0.556622
$721$	36.6798	+	16.6948i	1.36603	+	0.621746i
$722$	13.0191	+	22.5498i	0.484523	+	0.839218i
$723$	7.80327	+	13.5157i	0.290207	+	0.502653i
$724$	−72.8576			−2.70773
$725$	11.3198	+	19.6065i	0.420406	+	0.728165i
$726$	23.8475			0.885064
$727$	4.46010			0.165416			0.0827080	−	0.996574i	$-0.473643\pi$
$727$	4.46010			0.165416			0.0827080	+	0.996574i	$0.473643\pi$
$728$	54.3002	−	48.0330i	2.01250	−	1.78022i
$729$	1.00000			0.0370370
$730$	23.3832			0.865451
$731$	−9.24112	−	16.0061i	−0.341795	−	0.592007i
$732$	37.3114			1.37907
$733$	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
$735$	−6.75465	−	7.75536i	−0.249149	−	0.286061i
$736$	89.0620			3.28287
$737$	−10.4657	+	18.1271i	−0.385508	+	0.667719i
$738$	2.92347	+	5.06359i	0.107614	+	0.186393i
$739$	5.62287	+	9.73909i	0.206841	+	0.358258i	0.950718	−	0.310058i	$-0.100349\pi$
$739$	5.62287	+	9.73909i	0.206841	+	0.358258i	−0.743877	+	0.668316i	$0.767015\pi$
$740$	−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	−0.545137	−	0.838347i	$-0.683523\pi$
$743$	12.3604	−	21.4089i	0.453461	−	0.785417i	0.998598	+	0.0529295i	$0.0168559\pi$
$744$	8.39950			0.307941
$745$	−3.82645			−0.140190
$746$	−22.5548	+	39.0661i	−0.825791	+	1.43031i
$747$	−4.65417	+	8.06126i	−0.170287	+	0.294946i
$748$	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
$751$	−4.17908			−0.152497			−0.0762485	−	0.997089i	$-0.524294\pi$
$751$	−4.17908			−0.152497			−0.0762485	+	0.997089i	$0.524294\pi$
$752$	17.2585	+	29.8925i	0.629351	+	1.09007i
$753$	−4.67520	+	8.09769i	−0.170374	+	0.295096i
$754$	30.7191	−	68.8929i	1.11873	−	2.50893i
$755$	20.2737			0.737834
$756$	−10.5385	+	7.52466i	−0.383283	+	0.273669i
$757$	−17.9530	+	31.0955i	−0.652512	+	1.13018i	0.329999	+	0.943981i	$0.392951\pi$
$757$	−17.9530	+	31.0955i	−0.652512	+	1.13018i	−0.982511	+	0.186203i	$0.940382\pi$
$758$	28.8602	−	49.9873i	1.04825	−	1.81562i
$759$	−17.3633	+	30.0741i	−0.630249	+	1.09162i
$760$	33.6513			1.22066
$761$	−8.92075	+	15.4512i	−0.323377	+	0.560106i	−0.981183	−	0.193082i	$-0.938152\pi$
$761$	−8.92075	+	15.4512i	−0.323377	+	0.560106i	0.657805	+	0.753188i	$0.271485\pi$
$762$	45.1828			1.63680
$763$	3.53441	+	36.5234i	0.127954	+	1.32224i
$764$	50.8398	−	88.0572i	1.83932	−	3.18580i
$765$	5.33146			0.192759
$766$	−4.00309	+	6.93356i	−0.144638	+	0.250520i
$767$	−51.8522	+	5.42066i	−1.87227	+	0.195729i
$768$	6.08303	+	10.5361i	0.219502	+	0.380189i
$769$	−9.41573	+	16.3085i	−0.339540	+	0.588100i	−0.984346	−	0.176246i	$-0.943605\pi$
$769$	−9.41573	+	16.3085i	−0.339540	+	0.588100i	0.644806	+	0.764346i	$0.276938\pi$
$770$	4.40564	+	45.5264i	0.158768	+	1.64066i
$771$	−4.86470	−	8.42591i	−0.175198	−	0.303452i
$772$	41.7335	+	72.2845i	1.50202	+	2.60158i
$773$	−45.2210			−1.62649			−0.813243	−	0.581925i	$-0.802300\pi$
$773$	−45.2210			−1.62649			−0.813243	+	0.581925i	$0.802300\pi$
$774$	−13.3733			−0.480694
$775$	1.57023	+	2.71972i	0.0564043	+	0.0976951i
$776$	−30.5635	−	52.9375i	−1.09717	−	1.90035i
$777$	−7.58928	−	3.45426i	−0.272264	−	0.123921i
$778$	19.1426	−	33.1559i	0.686295	−	1.18870i
$779$	−3.35563	−	5.81213i	−0.120228	−	0.208241i
$780$	−10.5586	+	23.6795i	−0.378059	+	0.847862i
$781$	5.58034	−	9.66544i	0.199680	−	0.345856i
$782$	−73.8351			−2.64034
$783$	−3.98387	+	6.90026i	−0.142372	+	0.246595i
$784$	23.1033	−	67.3058i	0.825120	−	2.40378i
$785$	−0.727311			−0.0259588
$786$	−6.57606	+	11.3901i	−0.234560	+	0.406270i
$787$	−25.8420			−0.921166			−0.460583	−	0.887617i	$-0.652360\pi$
$787$	−25.8420			−0.921166			−0.460583	+	0.887617i	$0.652360\pi$
$788$	−27.9126	+	48.3460i	−0.994344	+	1.72225i
$789$	7.25776	−	12.5708i	0.258383	−	0.447532i
$790$	13.8541	−	23.9961i	0.492908	−	0.853742i
$791$	4.63030	+	2.10748i	0.164635	+	0.0749333i
$792$	34.0566			1.21015
$793$	11.1938	−	25.1040i	0.397503	−	0.891469i
$794$	9.21900	−	15.9678i	0.327170	−	0.566675i
$795$	6.25325	+	10.8309i	0.221780	+	0.384134i
$796$	−51.1178			−1.81182
$797$	6.20361	+	10.7450i	0.219743	+	0.380606i	0.954729	−	0.297476i	$-0.0961448\pi$
$797$	6.20361	+	10.7450i	0.219743	+	0.380606i	−0.734986	+	0.678082i	$0.762811\pi$
$798$	17.0394	−	12.1664i	0.603190	−	0.430686i
$799$	−6.16058	−	10.6704i	−0.217946	−	0.377493i
$800$	16.3283	−	28.2814i	0.577292	−	0.999898i
$801$	−3.18037	+	5.50857i	−0.112373	+	0.194636i
$802$	23.3527			0.824613
$803$	−27.1631			−0.958566
$804$	−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
$808$	52.8329	+	91.5092i	1.85865	+	3.21928i
$809$	−4.78373	−	8.28566i	−0.168187	−	0.291308i	0.769595	−	0.638532i	$-0.220458\pi$
$809$	−4.78373	−	8.28566i	−0.168187	−	0.291308i	−0.937782	+	0.347223i	$0.887125\pi$
$810$	1.92886	−	3.34089i	0.0677733	−	0.117387i
$811$	−50.2886			−1.76587			−0.882936	−	0.469493i	$-0.844437\pi$
$811$	−50.2886			−1.76587			−0.882936	+	0.469493i	$0.844437\pi$
$812$	−9.93799	−	102.696i	−0.348755	−	3.60392i
$813$	−2.45214	−	4.24723i	−0.0860004	−	0.148957i
$814$	18.5420	+	32.1157i	0.649898	+	1.12566i
$815$	−13.6055			−0.476580
$816$	18.4447	+	31.9472i	0.645695	+	1.11838i
$817$	15.3503			0.537038
$818$	−1.43748			−0.0502602
$819$	1.90110	+	9.34804i	0.0664299	+	0.326647i
$820$	16.0126			0.559183
$821$	24.3408			0.849500			0.424750	−	0.905311i	$-0.360362\pi$
$821$	24.3408			0.849500			0.424750	+	0.905311i	$0.360362\pi$
$822$	0.977664	+	1.69336i	0.0340999	+	0.0590628i
$823$	−27.0572			−0.943155			−0.471577	−	0.881825i	$-0.656315\pi$
$823$	−27.0572			−0.943155			−0.471577	+	0.881825i	$0.656315\pi$
$824$	−57.8794	−	100.250i	−2.01632	−	3.49238i
$825$	6.36665	+	11.0274i	0.221658	+	0.383923i
$826$	−81.7501	+	58.3707i	−2.84445	+	2.03098i
$827$	−24.2045			−0.841672			−0.420836	−	0.907137i	$-0.638263\pi$
$827$	−24.2045			−0.841672			−0.420836	+	0.907137i	$0.638263\pi$
$828$	−18.9635	+	32.8458i	−0.659028	+	1.14147i
$829$	−23.6241	−	40.9181i	−0.820499	−	1.42115i	−0.905311	−	0.424748i	$-0.860363\pi$
$829$	−23.6241	−	40.9181i	−0.820499	−	1.42115i	0.0848127	−	0.996397i	$-0.472971\pi$
$830$	17.9545	+	31.0981i	0.623210	+	1.07943i
$831$	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
$835$	−23.4885			−0.812852
$836$	−66.1032			−2.28623
$837$	−0.552624	+	0.957172i	−0.0191015	+	0.0330847i
$838$	−41.9143	+	72.5977i	−1.44791	+	2.50785i
$839$	5.87914	+	10.1830i	0.202970	+	0.351555i	0.949484	−	0.313815i	$-0.101607\pi$
$839$	5.87914	+	10.1830i	0.202970	+	0.351555i	−0.746514	+	0.665370i	$0.768274\pi$
$840$	2.84544	+	29.4038i	0.0981771	+	1.01453i
$841$	−17.2424	−	29.8647i	−0.594565	−	1.02982i
$842$	−66.8562			−2.30402
$843$	−2.32123	−	4.02049i	−0.0799474	−	0.138473i
$844$	−15.0183	+	26.0125i	−0.516951	+	0.895386i
$845$	12.7644	+	14.2082i	0.439109	+	0.488775i
$846$	−8.91531			−0.306515
$847$	−2.31456	−	23.9179i	−0.0795291	−	0.821827i
$848$	−43.2675	+	74.9416i	−1.48581	+	2.57350i
$849$	12.1426	−	21.0316i	0.416733	−	0.721802i
$850$	−13.5366	+	23.4461i	−0.464303	+	0.804196i
$851$	−24.4225			−0.837192
$852$	6.09462	−	10.5562i	0.208798	−	0.361649i
$853$	−36.1551			−1.23793			−0.618963	−	0.785420i	$-0.712447\pi$
$853$	−36.1551			−1.23793			−0.618963	+	0.785420i	$0.712447\pi$
$854$	−5.10112	−	52.7133i	−0.174557	−	1.80381i
$855$	−2.21400	+	3.83476i	−0.0757172	+	0.131146i
$856$	−81.5182			−2.78624
$857$	−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	$0.266265\pi$
$858$	17.2775	−	38.7478i	0.589845	−	1.32283i
$859$	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
$861$	4.79479	−	3.42354i	0.163406	−	0.116674i
$862$	−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	$0.834061\pi$
$864$	11.4931			0.391003
$865$	−15.3895			−0.523257
$866$	39.6909	+	68.7467i	1.34875	+	2.33611i
$867$	1.91596	+	3.31854i	0.0650695	+	0.112704i
$868$	−1.37855	−	14.2455i	−0.0467911	−	0.483524i
$869$	−16.0937	+	27.8751i	−0.545940	+	0.945597i
$870$	15.3687	+	26.6193i	0.521046	+	0.902479i
$871$	9.89114	+	13.6300i	0.335149	+	0.461834i
$872$	52.6999	−	91.2789i	1.78464	−	3.09110i
$873$	8.04339			0.272227
$874$	30.6615	−	53.1073i	1.03714	−	1.79638i
$875$	−24.8065	+	17.7122i	−0.838614	+	0.598782i
$876$	−29.6665			−1.00234
$877$	22.4448	−	38.8755i	0.757907	−	1.31273i	−0.186009	−	0.982548i	$-0.559555\pi$
$877$	22.4448	−	38.8755i	0.757907	−	1.31273i	0.943916	−	0.330186i	$-0.107111\pi$
$878$	93.5021			3.15554
$879$	−10.1171	+	17.5233i	−0.341241	+	0.591047i
$880$	33.4660	−	57.9648i	1.12814	−	1.95399i
$881$	0.618105	−	1.07059i	0.0208245	−	0.0360691i	−0.855425	−	0.517926i	$-0.826704\pi$
$881$	0.618105	−	1.07059i	0.0208245	−	0.0360691i	0.876250	+	0.481857i	$0.160038\pi$
$882$	12.0716	+	13.8600i	0.406471	+	0.466690i
$883$	0.495858			0.0166870			0.00834348	−	0.999965i	$-0.497344\pi$
$883$	0.495858			0.0166870			0.00834348	+	0.999965i	$0.497344\pi$
$884$	63.6892	−	6.65811i	2.14210	−	0.223936i
$885$	10.6221	−	18.3980i	0.357058	−	0.618443i
$886$	−10.7739	−	18.6609i	−0.361956	−	0.626926i
$887$	18.4701			0.620165			0.310082	−	0.950710i	$-0.399643\pi$
$887$	18.4701			0.620165			0.310082	+	0.950710i	$0.399643\pi$
$888$	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
$891$	−2.24067	+	3.88095i	−0.0750651	+	0.130017i
$892$	64.3709	−	111.494i	2.15530	−	3.73308i
$893$	10.2332			0.342442
$894$	6.83843			0.228711
$895$	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
$899$	−4.40316	−	7.62649i	−0.146853	−	0.254358i
$900$	6.95339	+	12.0436i	0.231780	+	0.401454i
$901$	15.4448	−	26.7511i	0.514540	−	0.891210i
$902$	−26.2020			−0.872433
$903$	1.29797	+	13.4128i	0.0431937	+	0.446349i
$904$	−7.30645	−	12.6551i	−0.243009	−	0.420904i
$905$	−10.9355	−	18.9408i	−0.363507	−	0.629613i
$906$	−36.2321			−1.20373
$907$	−19.1799	−	33.2206i	−0.636859	−	1.10307i	−0.986118	−	0.166046i	$-0.946900\pi$
$907$	−19.1799	−	33.2206i	−0.636859	−	1.10307i	0.349259	−	0.937026i	$-0.386433\pi$
$908$	19.2497			0.638824
$909$	−13.9040			−0.461167
$910$	34.8977	+	11.6797i	1.15685	+	0.387179i
$911$	2.03620			0.0674623			0.0337311	−	0.999431i	$-0.489261\pi$
$911$	2.03620			0.0674623			0.0337311	+	0.999431i	$0.489261\pi$
$912$	−30.6382			−1.01453
$913$	−20.8569	−	36.1252i	−0.690262	−	1.19557i
$914$	−23.4074			−0.774249
$915$	5.60021	+	9.69984i	0.185137	+	0.320667i
$916$	27.8410	+	48.2220i	0.919892	+	1.59330i
$917$	12.0619	+	5.48997i	0.398319	+	0.181295i
$918$	−9.52812			−0.314475
$919$	9.88794	−	17.1264i	0.326173	−	0.564948i	−0.655576	−	0.755129i	$-0.727574\pi$
$919$	9.88794	−	17.1264i	0.326173	−	0.564948i	0.981749	+	0.190181i	$0.0609075\pi$
$920$	43.2618	+	74.9317i	1.42630	+	2.47042i
$921$	−1.00098	−	1.73375i	−0.0329834	−	0.0571290i
$922$	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
$926$	58.8467			1.93382
$927$	15.2321			0.500288
$928$	−45.7869	+	79.3052i	−1.50303	+	2.60332i
$929$	20.8276	−	36.0745i	0.683332	−	1.18357i	−0.290625	−	0.956837i	$-0.593863\pi$
$929$	20.8276	−	36.0745i	0.683332	−	1.18357i	0.973958	−	0.226729i	$-0.0728033\pi$
$930$	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
$933$	5.62100			0.184023
$934$	34.8872	+	60.4264i	1.14154	+	1.97721i
$935$	−11.9460	+	20.6911i	−0.390677	+	0.676672i
$936$	11.1589	−	25.0258i	0.364741	−	0.817994i
$937$	−30.8282			−1.00711			−0.503557	−	0.863962i	$-0.667975\pi$
$937$	−30.8282			−1.00711			−0.503557	+	0.863962i	$0.667975\pi$
$938$	29.5326	+	13.4418i	0.964274	+	0.438889i
$939$	−11.1532	+	19.3179i	−0.363972	+	0.630417i
$940$	−12.2078	+	21.1446i	−0.398176	+	0.689661i
$941$	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	$0.000329174\pi$
$942$	1.29981			0.0423502
$943$	8.62796	−	14.9441i	0.280965	−	0.486645i
$944$	146.993			4.78422
$945$	−3.53795	−	1.61030i	−0.115090	−	0.0523829i
$946$	29.9652	−	51.9012i	0.974251	−	1.68745i
$947$	−14.5842			−0.473924			−0.236962	−	0.971519i	$-0.576152\pi$
$947$	−14.5842			−0.473924			−0.236962	+	0.971519i	$0.576152\pi$
$948$	−17.5769	+	30.4440i	−0.570870	+	0.988776i
$949$	−8.90022	+	19.9603i	−0.288913	+	0.647938i
$950$	−11.2427	−	19.4730i	−0.364762	−	0.631787i
$951$	13.4742	−	23.3380i	0.436931	−	0.756787i
$952$	59.3803	−	42.3983i	1.92453	−	1.37414i
$953$	−3.77371	−	6.53626i	−0.122243	−	0.211730i	0.798409	−	0.602115i	$-0.205675\pi$
$953$	−3.77371	−	6.53626i	−0.122243	−	0.211730i	−0.920652	+	0.390385i	$0.872342\pi$
$954$	−11.1755	−	19.3565i	−0.361820	−	0.626690i
$955$	30.5229			0.987699
$956$	−39.6112			−1.28112
$957$	−17.8530	−	30.9223i	−0.577106	−	0.999577i
$958$	12.2216	+	21.1684i	0.394862	+	0.683921i
$959$	1.60347	−	1.14490i	0.0517787	−	0.0369707i
$960$	7.23284	−	12.5276i	0.233439	−	0.404328i
$961$	14.8892	+	25.7889i	0.480297	+	0.831899i
$962$	29.6751	−	3.10225i	0.956762	−	0.100020i
$963$	5.36329	−	9.28948i	0.172829	−	0.299349i
$964$	−76.3836			−2.46015
$965$	−12.5279	+	21.6989i	−0.403286	+	0.698512i
$966$	48.9968	+	22.3009i	1.57645	+	0.717519i
$967$	3.20099			0.102937			0.0514685	−	0.998675i	$-0.483610\pi$
$967$	3.20099			0.102937			0.0514685	+	0.998675i	$0.483610\pi$
$968$	−34.5113	+	59.7753i	−1.10923	+	1.92125i
$969$	10.9366			0.351335
$970$	15.5146	−	26.8720i	0.498143	−	0.862809i
$971$	−11.7548	+	20.3599i	−0.377230	+	0.653381i	−0.990658	−	0.136369i	$-0.956457\pi$
$971$	−11.7548	+	20.3599i	−0.377230	+	0.653381i	0.613428	+	0.789751i	$0.289790\pi$
$972$	−2.44716	+	4.23861i	−0.0784928	+	0.135954i
$973$	29.2986	+	13.3353i	0.939270	+	0.427509i
$974$	−24.9046			−0.797996
$975$	10.1893	−	1.06520i	0.326319	−	0.0341136i
$976$	−38.7490	+	67.1152i	−1.24033	+	2.14831i
$977$	24.8057	+	42.9648i	0.793606	+	1.37457i	0.923721	+	0.383066i	$0.125132\pi$
$977$	24.8057	+	42.9648i	0.793606	+	1.37457i	−0.130115	+	0.991499i	$0.541535\pi$
$978$	24.3151			0.777510
$979$	−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
$982$	−20.3914	+	35.3190i	−0.650716	+	1.12707i
$983$	−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	$0.302278\pi$
$984$	−16.9230			−0.539484
$985$	−16.7580			−0.533954
$986$	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
$990$	8.64387	+	14.9716i	0.274720	+	0.475829i
$991$	30.2997	+	52.4807i	0.962503	+	1.66710i	0.716180	+	0.697915i	$0.245889\pi$
$991$	30.2997	+	52.4807i	0.962503	+	1.66710i	0.246322	+	0.969188i	$0.420778\pi$
$992$	−6.35135	+	11.0009i	−0.201656	+	0.349278i
$993$	4.56139			0.144751
$994$	−15.7469	−	7.16721i	−0.499463	−	0.227330i
$995$	−7.67245	−	13.2891i	−0.243233	−	0.421292i
$996$	−22.7791	−	39.4545i	−0.721782	−	1.25016i
$997$	−0.339779			−0.0107609			−0.00538045	−	0.999986i	$-0.501713\pi$
$997$	−0.339779			−0.0107609			−0.00538045	+	0.999986i	$0.501713\pi$
$998$	−25.7371	−	44.5780i	−0.814694	−	1.41109i
$999$	−3.15162			−0.0997129

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.1	✓	20	7.2	even	3
273.2.j.c.172.1	yes	20	13.3	even	3
273.2.l.c.16.10	yes	20	91.16	even	3	inner
273.2.l.c.256.10	yes	20	1.1	even	1	trivial
819.2.n.f.100.10		20	21.2	odd	6
819.2.n.f.172.10		20	39.29	odd	6
819.2.s.f.289.1		20	273.107	odd	6
819.2.s.f.802.1		20	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.62571 q^{2} +(-0.500000 - 0.866025i) q^{3} +4.89433 q^{4} +(0.734607 + 1.27238i) q^{5} +(-1.31285 - 2.27393i) q^{6} +(-2.15321 + 1.53742i) q^{7} +7.59966 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+2.62571 q^{2} +(-0.500000 - 0.866025i) q^{3} +4.89433 q^{4} +(0.734607 + 1.27238i) q^{5} +(-1.31285 - 2.27393i) q^{6} +(-2.15321 + 1.53742i) q^{7} +7.59966 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.92886 + 3.34089i) q^{10} +(-2.24067 - 3.88095i) 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} +10.1658 q^{16} -3.62878 q^{17} +(-1.31285 + 2.27393i) q^{18} +(1.50693 - 2.61007i) q^{19} +(3.59541 + 6.22743i) q^{20} +(2.40805 + 1.09603i) q^{21} +(-5.88333 - 10.1902i) q^{22} +7.74918 q^{23} +(-3.79983 - 6.58150i) q^{24} +(1.42070 - 2.46073i) q^{25} +(-9.41580 + 0.984334i) q^{26} +1.00000 q^{27} +(-10.5385 + 7.52466i) q^{28} +(-3.98387 + 6.90026i) q^{29} +(1.92886 - 3.34089i) q^{30} +(-0.552624 + 0.957172i) q^{31} +11.4931 q^{32} +(-2.24067 + 3.88095i) q^{33} -9.52812 q^{34} +(-3.53795 - 1.61030i) q^{35} +(-2.44716 + 4.23861i) q^{36} -3.15162 q^{37} +(3.95675 - 6.85329i) q^{38} +(2.11766 + 2.91813i) q^{39} +(5.58276 + 9.66963i) q^{40} +(1.11340 - 1.92847i) q^{41} +(6.32284 + 2.87784i) q^{42} +(2.54662 + 4.41087i) q^{43} +(-10.9666 - 18.9946i) q^{44} -1.46921 q^{45} +20.3471 q^{46} +(1.69770 + 2.94050i) q^{47} +(-5.08290 - 8.80384i) q^{48} +(2.27265 - 6.62080i) q^{49} +(3.73035 - 6.46116i) q^{50} +(1.81439 + 3.14262i) q^{51} +(-17.5511 + 1.83480i) q^{52} +(-4.25619 + 7.37193i) q^{53} +2.62571 q^{54} +(3.29202 - 5.70194i) q^{55} +(-16.3637 + 11.6839i) q^{56} -3.01385 q^{57} +(-10.4605 + 18.1180i) q^{58} +14.4596 q^{59} +(3.59541 - 6.22743i) q^{60} +(-3.81170 + 6.60206i) q^{61} +(-1.45103 + 2.51325i) q^{62} +(-0.254842 - 2.63345i) q^{63} +9.84585 q^{64} +(-3.11130 - 4.28736i) q^{65} +(-5.88333 + 10.1902i) q^{66} +(-2.33539 - 4.04502i) q^{67} -17.7605 q^{68} +(-3.87459 - 6.71099i) q^{69} +(-9.28961 - 4.22816i) q^{70} +(1.24524 + 2.15682i) q^{71} +(-3.79983 + 6.58150i) q^{72} +(3.03070 - 5.24932i) q^{73} -8.27523 q^{74} -2.84141 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} +(7.46787 + 12.9347i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.92347 - 5.06359i) q^{82} +9.30835 q^{83} +(11.7858 + 5.36431i) q^{84} +(-2.66573 - 4.61718i) q^{85} +(6.68667 + 11.5816i) q^{86} +7.96773 q^{87} +(-17.0283 - 29.4939i) q^{88} +6.36075 q^{89} -3.85772 q^{90} +(7.14509 - 6.32042i) q^{91} +37.9270 q^{92} +1.10525 q^{93} +(4.45765 + 7.72088i) q^{94} +4.42800 q^{95} +(-5.74654 - 9.95330i) q^{96} +(-4.02169 - 6.96578i) q^{97} +(5.96732 - 17.3843i) q^{98} +4.48133 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25} + 13 q^{26} + 20 q^{27} - 23 q^{28} - 9 q^{29} - 4 q^{30} - 9 q^{31} - 34 q^{32} - 8 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} - 36 q^{37} + 22 q^{38} + 4 q^{39} - 9 q^{40} - q^{41} + 3 q^{42} - 11 q^{43} + 8 q^{44} + 20 q^{46} + 13 q^{47} - 20 q^{48} - 3 q^{49} + 5 q^{50} - 44 q^{52} - 6 q^{53} - 19 q^{55} - 23 q^{56} - 14 q^{57} + 30 q^{59} + 12 q^{60} + 22 q^{62} + 6 q^{63} + 72 q^{64} - 6 q^{65} - 9 q^{66} - 22 q^{67} - 78 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} + 6 q^{72} + 6 q^{74} + 64 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} + 48 q^{80} - 10 q^{81} - 13 q^{82} + 40 q^{83} + 10 q^{84} - 16 q^{85} + 4 q^{86} + 18 q^{87} - 12 q^{88} - 4 q^{89} + 8 q^{90} + 30 q^{91} + 66 q^{92} + 18 q^{93} - 44 q^{94} + 72 q^{95} + 17 q^{96} + 21 q^{97} - 76 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Introduction

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