LMFDB - Embedded newform 109.2.c.a.63.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [109,2,Mod(45,109)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(109, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("109.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	109.c (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:	$0.870369382032$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 11 x^{12} - 10 x^{11} + 61 x^{10} - 52 x^{9} + 198 x^{8} - 81 x^{7} + 339 x^{6} + \cdots + 1 $ x^14 - 2x^13 + 11x^12 - 10x^11 + 61x^10 - 52x^9 + 198x^8 - 81x^7 + 339x^6 - 223x^5 + 232x^4 - 40x^3 + 17x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			63.2
Root			$1.04608 - 1.81187i$ of defining polynomial
Character	$\chi$	$=$	109.63
Dual form			109.2.c.a.45.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.09216 q^{2} +(-0.555057 - 0.961388i) q^{3} +2.37715 q^{4} +(1.29404 + 2.24135i) q^{5} +(1.16127 + 2.01138i) q^{6} +(-2.02108 - 3.50062i) q^{7} -0.789063 q^{8} +(0.883822 - 1.53083i) q^{9} +O(q^{10})$	\(q-2.09216 q^{2} +(-0.555057 - 0.961388i) q^{3} +2.37715 q^{4} +(1.29404 + 2.24135i) q^{5} +(1.16127 + 2.01138i) q^{6} +(-2.02108 - 3.50062i) q^{7} -0.789063 q^{8} +(0.883822 - 1.53083i) q^{9} +(-2.70735 - 4.68927i) q^{10} +(1.87859 - 3.25381i) q^{11} +(-1.31946 - 2.28536i) q^{12} +(-1.16127 - 2.01138i) q^{13} +(4.22844 + 7.32386i) q^{14} +(1.43654 - 2.48816i) q^{15} -3.10345 q^{16} +4.05031 q^{17} +(-1.84910 + 3.20274i) q^{18} +3.63891 q^{19} +(3.07614 + 5.32803i) q^{20} +(-2.24363 + 3.88609i) q^{21} +(-3.93032 + 6.80751i) q^{22} -6.02421 q^{23} +(0.437975 + 0.758595i) q^{24} +(-0.849102 + 1.47069i) q^{25} +(2.42957 + 4.20814i) q^{26} -5.29263 q^{27} +(-4.80442 - 8.32150i) q^{28} +(4.46071 + 7.72617i) q^{29} +(-3.00547 + 5.20563i) q^{30} +(0.519926 - 0.900538i) q^{31} +8.07106 q^{32} -4.17090 q^{33} -8.47392 q^{34} +(5.23074 - 9.05991i) q^{35} +(2.10098 - 3.63900i) q^{36} +(-0.380278 + 0.658660i) q^{37} -7.61320 q^{38} +(-1.28914 + 2.23286i) q^{39} +(-1.02108 - 1.76857i) q^{40} -4.66898 q^{41} +(4.69405 - 8.13033i) q^{42} +9.70367 q^{43} +(4.46569 - 7.73480i) q^{44} +4.57482 q^{45} +12.6036 q^{46} +(-3.31353 + 5.73920i) q^{47} +(1.72260 + 2.98362i) q^{48} +(-4.66954 + 8.08789i) q^{49} +(1.77646 - 3.07692i) q^{50} +(-2.24816 - 3.89392i) q^{51} +(-2.76052 - 4.78136i) q^{52} +(-4.62824 - 8.01636i) q^{53} +11.0731 q^{54} +9.72391 q^{55} +(1.59476 + 2.76221i) q^{56} +(-2.01980 - 3.49840i) q^{57} +(-9.33253 - 16.1644i) q^{58} +(-4.77568 + 8.27171i) q^{59} +(3.41487 - 5.91472i) q^{60} +(-2.77172 - 4.80076i) q^{61} +(-1.08777 + 1.88407i) q^{62} -7.14511 q^{63} -10.6791 q^{64} +(3.00547 - 5.20563i) q^{65} +8.72620 q^{66} +(-0.490362 + 0.849331i) q^{67} +9.62821 q^{68} +(3.34378 + 5.79160i) q^{69} +(-10.9436 + 18.9548i) q^{70} +2.83591 q^{71} +(-0.697391 + 1.20792i) q^{72} +(0.254715 - 0.441180i) q^{73} +(0.795603 - 1.37803i) q^{74} +1.88520 q^{75} +8.65024 q^{76} -15.1871 q^{77} +(2.69710 - 4.67152i) q^{78} +(1.49074 - 2.58204i) q^{79} +(-4.01601 - 6.95593i) q^{80} +(0.286248 + 0.495796i) q^{81} +9.76828 q^{82} +(6.95539 + 12.0471i) q^{83} +(-5.33346 + 9.23782i) q^{84} +(5.24129 + 9.07818i) q^{85} -20.3017 q^{86} +(4.95190 - 8.57694i) q^{87} +(-1.48232 + 2.56746i) q^{88} +(5.84208 + 10.1188i) q^{89} -9.57128 q^{90} +(-4.69405 + 8.13033i) q^{91} -14.3205 q^{92} -1.15435 q^{93} +(6.93245 - 12.0074i) q^{94} +(4.70891 + 8.15608i) q^{95} +(-4.47990 - 7.75942i) q^{96} +(8.19391 + 14.1923i) q^{97} +(9.76945 - 16.9212i) q^{98} +(-3.32068 - 5.75158i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 2 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) $ 14 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 2 * q^7 - 12 * q^8 - 6 * q^9	\( 14 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 2 q^{7} - 12 q^{8} - 6 q^{9} - 2 q^{10} + 7 q^{13} - 3 q^{14} + 7 q^{15} + 4 q^{16} + 6 q^{17} - 4 q^{18} + 14 q^{19} + 8 q^{20} - 10 q^{21} - 5 q^{22} - 24 q^{23} - 8 q^{24} + 10 q^{25} - 2 q^{26} - 32 q^{27} - 9 q^{28} - 5 q^{29} + 6 q^{30} + 14 q^{31} - 28 q^{32} - 6 q^{33} - 62 q^{34} + 8 q^{35} + 7 q^{36} + 40 q^{38} - 2 q^{39} + 12 q^{40} + 10 q^{41} + 5 q^{42} + 16 q^{43} - 19 q^{44} + 2 q^{45} + 48 q^{46} - 7 q^{47} + 23 q^{48} + 5 q^{49} - 9 q^{50} + 19 q^{51} + 22 q^{52} - 5 q^{53} + 26 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} - 9 q^{58} + q^{59} + 36 q^{60} - 3 q^{61} - 29 q^{62} + 40 q^{63} - 48 q^{64} - 6 q^{65} + 50 q^{66} + 34 q^{68} - 25 q^{69} - 4 q^{70} - 40 q^{71} - 7 q^{73} + 9 q^{74} + 72 q^{75} - 46 q^{76} - 64 q^{77} + 59 q^{78} - 15 q^{79} - 23 q^{80} + q^{81} + 20 q^{82} + 39 q^{83} - 42 q^{84} - 33 q^{85} - 70 q^{86} + 23 q^{87} + 21 q^{88} + 12 q^{89} - 64 q^{90} - 5 q^{91} - 46 q^{92} - 54 q^{93} + 7 q^{94} + 41 q^{95} - 19 q^{96} - q^{97} + 32 q^{98} + 23 q^{99}+O(q^{100}) \) 14 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 2 * q^7 - 12 * q^8 - 6 * q^9 - 2 * q^10 + 7 * q^13 - 3 * q^14 + 7 * q^15 + 4 * q^16 + 6 * q^17 - 4 * q^18 + 14 * q^19 + 8 * q^20 - 10 * q^21 - 5 * q^22 - 24 * q^23 - 8 * q^24 + 10 * q^25 - 2 * q^26 - 32 * q^27 - 9 * q^28 - 5 * q^29 + 6 * q^30 + 14 * q^31 - 28 * q^32 - 6 * q^33 - 62 * q^34 + 8 * q^35 + 7 * q^36 + 40 * q^38 - 2 * q^39 + 12 * q^40 + 10 * q^41 + 5 * q^42 + 16 * q^43 - 19 * q^44 + 2 * q^45 + 48 * q^46 - 7 * q^47 + 23 * q^48 + 5 * q^49 - 9 * q^50 + 19 * q^51 + 22 * q^52 - 5 * q^53 + 26 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 - 9 * q^58 + q^59 + 36 * q^60 - 3 * q^61 - 29 * q^62 + 40 * q^63 - 48 * q^64 - 6 * q^65 + 50 * q^66 + 34 * q^68 - 25 * q^69 - 4 * q^70 - 40 * q^71 - 7 * q^73 + 9 * q^74 + 72 * q^75 - 46 * q^76 - 64 * q^77 + 59 * q^78 - 15 * q^79 - 23 * q^80 + q^81 + 20 * q^82 + 39 * q^83 - 42 * q^84 - 33 * q^85 - 70 * q^86 + 23 * q^87 + 21 * q^88 + 12 * q^89 - 64 * q^90 - 5 * q^91 - 46 * q^92 - 54 * q^93 + 7 * q^94 + 41 * q^95 - 19 * q^96 - q^97 + 32 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/109\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.09216			−1.47938			−0.739692	−	0.672946i	$-0.765029\pi$
$2$	−2.09216			−1.47938			−0.739692	+	0.672946i	$0.765029\pi$
$3$	−0.555057	−	0.961388i	−0.320463	−	0.555057i	0.660121	−	0.751159i	$-0.270505\pi$
$3$	−0.555057	−	0.961388i	−0.320463	−	0.555057i	−0.980584	+	0.196102i	$0.937172\pi$
$4$	2.37715			1.18858
$5$	1.29404	+	2.24135i	0.578714	+	1.00236i	0.995627	+	0.0934160i	$0.0297787\pi$
$5$	1.29404	+	2.24135i	0.578714	+	1.00236i	−0.416913	+	0.908946i	$0.636888\pi$
$6$	1.16127	+	2.01138i	0.474087	+	0.821143i
$7$	−2.02108	−	3.50062i	−0.763897	−	1.32311i	−0.940828	−	0.338885i	$-0.889950\pi$
$7$	−2.02108	−	3.50062i	−0.763897	−	1.32311i	0.176931	−	0.984223i	$-0.443383\pi$
$8$	−0.789063			−0.278976
$9$	0.883822	−	1.53083i	0.294607	−	0.510275i
$10$	−2.70735	−	4.68927i	−0.856140	−	1.48288i
$11$	1.87859	−	3.25381i	0.566416	−	0.981061i	−0.430501	−	0.902590i	$-0.641663\pi$
$11$	1.87859	−	3.25381i	0.566416	−	0.981061i	0.996916	−	0.0784706i	$-0.0250037\pi$
$12$	−1.31946	−	2.28536i	−0.380894	−	0.659728i
$13$	−1.16127	−	2.01138i	−0.322079	−	0.557857i	0.658838	−	0.752285i	$-0.271048\pi$
$13$	−1.16127	−	2.01138i	−0.322079	−	0.557857i	−0.980917	+	0.194428i	$0.937715\pi$
$14$	4.22844	+	7.32386i	1.13010	+	1.95739i
$15$	1.43654	−	2.48816i	0.370912	−	0.642439i
$16$	−3.10345			−0.775864
$17$	4.05031			0.982346			0.491173	−	0.871062i	$-0.336568\pi$
$17$	4.05031			0.982346			0.491173	+	0.871062i	$0.336568\pi$
$18$	−1.84910	+	3.20274i	−0.435837	+	0.754893i
$19$	3.63891			0.834823			0.417412	−	0.908717i	$-0.362937\pi$
$19$	3.63891			0.834823			0.417412	+	0.908717i	$0.362937\pi$
$20$	3.07614	+	5.32803i	0.687846	+	1.19138i
$21$	−2.24363	+	3.88609i	−0.489601	+	0.848014i
$22$	−3.93032	+	6.80751i	−0.837946	+	1.45137i
$23$	−6.02421			−1.25614			−0.628068	−	0.778159i	$-0.716154\pi$
$23$	−6.02421			−1.25614			−0.628068	+	0.778159i	$0.716154\pi$
$24$	0.437975	+	0.758595i	0.0894013	+	0.154848i
$25$	−0.849102	+	1.47069i	−0.169820	+	0.294138i
$26$	2.42957	+	4.20814i	0.476478	+	0.825284i
$27$	−5.29263			−1.01857
$28$	−4.80442	−	8.32150i	−0.907950	−	1.57261i
$29$	4.46071	+	7.72617i	0.828332	+	1.43471i	0.899346	+	0.437239i	$0.144043\pi$
$29$	4.46071	+	7.72617i	0.828332	+	1.43471i	−0.0710131	+	0.997475i	$0.522623\pi$
$30$	−3.00547	+	5.20563i	−0.548722	+	0.950414i
$31$	0.519926	−	0.900538i	0.0933814	−	0.161741i	−0.815551	−	0.578686i	$-0.803566\pi$
$31$	0.519926	−	0.900538i	0.0933814	−	0.161741i	0.908932	+	0.416944i	$0.136899\pi$
$32$	8.07106			1.42678
$33$	−4.17090			−0.726060
$34$	−8.47392			−1.45327
$35$	5.23074	−	9.05991i	0.884156	−	1.53140i
$36$	2.10098	−	3.63900i	0.350163	−	0.606501i
$37$	−0.380278	+	0.658660i	−0.0625173	+	0.108283i	−0.895590	−	0.444880i	$-0.853246\pi$
$37$	−0.380278	+	0.658660i	−0.0625173	+	0.108283i	0.833073	+	0.553163i	$0.186580\pi$
$38$	−7.61320			−1.23502
$39$	−1.28914	+	2.23286i	−0.206428	+	0.357544i
$40$	−1.02108	−	1.76857i	−0.161447	−	0.279635i
$41$	−4.66898			−0.729173			−0.364586	−	0.931170i	$-0.618790\pi$
$41$	−4.66898			−0.729173			−0.364586	+	0.931170i	$0.618790\pi$
$42$	4.69405	−	8.13033i	0.724307	−	1.25454i
$43$	9.70367			1.47980			0.739898	−	0.672720i	$-0.234874\pi$
$43$	9.70367			1.47980			0.739898	+	0.672720i	$0.234874\pi$
$44$	4.46569	−	7.73480i	0.673228	−	1.16606i
$45$	4.57482			0.681974
$46$	12.6036			1.85831
$47$	−3.31353	+	5.73920i	−0.483328	+	0.837149i	−0.999817	−	0.0191454i	$-0.993905\pi$
$47$	−3.31353	+	5.73920i	−0.483328	+	0.837149i	0.516489	+	0.856294i	$0.327239\pi$
$48$	1.72260	+	2.98362i	0.248635	+	0.430649i
$49$	−4.66954	+	8.08789i	−0.667078	+	1.15541i
$50$	1.77646	−	3.07692i	0.251229	−	0.435142i
$51$	−2.24816	−	3.89392i	−0.314805	−	0.545258i
$52$	−2.76052	−	4.78136i	−0.382815	−	0.663055i
$53$	−4.62824	−	8.01636i	−0.635738	−	1.10113i	−0.986358	−	0.164613i	$-0.947362\pi$
$53$	−4.62824	−	8.01636i	−0.635738	−	1.10113i	0.350620	−	0.936518i	$-0.385971\pi$
$54$	11.0731			1.50685
$55$	9.72391			1.31117
$56$	1.59476	+	2.76221i	0.213109	+	0.369115i
$57$	−2.01980	−	3.49840i	−0.267530	−	0.463375i
$58$	−9.33253	−	16.1644i	−1.22542	−	2.12249i
$59$	−4.77568	+	8.27171i	−0.621740	+	1.07689i	0.367422	+	0.930055i	$0.380241\pi$
$59$	−4.77568	+	8.27171i	−0.621740	+	1.07689i	−0.989162	+	0.146831i	$0.953093\pi$
$60$	3.41487	−	5.91472i	0.440858	−	0.763588i
$61$	−2.77172	−	4.80076i	−0.354882	−	0.614674i	0.632215	−	0.774793i	$-0.282146\pi$
$61$	−2.77172	−	4.80076i	−0.354882	−	0.614674i	−0.987098	+	0.160118i	$0.948812\pi$
$62$	−1.08777	+	1.88407i	−0.138147	+	0.239278i
$63$	−7.14511			−0.900199
$64$	−10.6791			−1.33488
$65$	3.00547	−	5.20563i	0.372783	−	0.645679i
$66$	8.72620			1.07412
$67$	−0.490362	+	0.849331i	−0.0599072	+	0.103762i	−0.894424	−	0.447221i	$-0.852414\pi$
$67$	−0.490362	+	0.849331i	−0.0599072	+	0.103762i	0.834516	+	0.550983i	$0.185747\pi$
$68$	9.62821			1.16759
$69$	3.34378	+	5.79160i	0.402544	+	0.697227i
$70$	−10.9436	+	18.9548i	−1.30801	+	2.26553i
$71$	2.83591			0.336561			0.168280	−	0.985739i	$-0.446179\pi$
$71$	2.83591			0.336561			0.168280	+	0.985739i	$0.446179\pi$
$72$	−0.697391	+	1.20792i	−0.0821883	+	0.142354i
$73$	0.254715	−	0.441180i	0.0298122	−	0.0516362i	−0.850734	−	0.525596i	$-0.823842\pi$
$73$	0.254715	−	0.441180i	0.0298122	−	0.0516362i	0.880547	+	0.473960i	$0.157176\pi$
$74$	0.795603	−	1.37803i	0.0924870	−	0.160192i
$75$	1.88520			0.217684
$76$	8.65024			0.992251
$77$	−15.1871			−1.73073
$78$	2.69710	−	4.67152i	0.305387	−	0.528945i
$79$	1.49074	−	2.58204i	0.167722	−	0.290503i	−0.769897	−	0.638168i	$-0.779692\pi$
$79$	1.49074	−	2.58204i	0.167722	−	0.290503i	0.937618	+	0.347666i	$0.113026\pi$
$80$	−4.01601	−	6.95593i	−0.449003	−	0.777697i
$81$	0.286248	+	0.495796i	0.0318053	+	0.0550885i
$82$	9.76828			1.07873
$83$	6.95539	+	12.0471i	0.763453	+	1.32234i	0.941060	+	0.338238i	$0.109831\pi$
$83$	6.95539	+	12.0471i	0.763453	+	1.32234i	−0.177607	+	0.984101i	$0.556836\pi$
$84$	−5.33346	+	9.23782i	−0.581928	+	1.00793i
$85$	5.24129	+	9.07818i	0.568497	+	0.984666i
$86$	−20.3017			−2.18918
$87$	4.95190	−	8.57694i	0.530899	−	0.919544i
$88$	−1.48232	+	2.56746i	−0.158016	+	0.273692i
$89$	5.84208	+	10.1188i	0.619260	+	1.07259i	0.989621	+	0.143702i	$0.0459005\pi$
$89$	5.84208	+	10.1188i	0.619260	+	1.07259i	−0.370361	+	0.928888i	$0.620766\pi$
$90$	−9.57128			−1.00890
$91$	−4.69405	+	8.13033i	−0.492070	+	0.852290i
$92$	−14.3205			−1.49301
$93$	−1.15435			−0.119701
$94$	6.93245	−	12.0074i	0.715027	−	1.23846i
$95$	4.70891	+	8.15608i	0.483124	+	0.836796i
$96$	−4.47990	−	7.75942i	−0.457228	−	0.791942i
$97$	8.19391	+	14.1923i	0.831965	+	1.44101i	0.896477	+	0.443090i	$0.146118\pi$
$97$	8.19391	+	14.1923i	0.831965	+	1.44101i	−0.0645119	+	0.997917i	$0.520549\pi$
$98$	9.76945	−	16.9212i	0.986864	−	1.70930i
$99$	−3.32068	−	5.75158i	−0.333741	−	0.578056i
$100$	−2.01844	+	3.49605i	−0.201844	+	0.349605i
$101$	−15.2806			−1.52047			−0.760236	−	0.649647i	$-0.774917\pi$
$101$	−15.2806			−1.52047			−0.760236	+	0.649647i	$0.774917\pi$
$102$	4.70351	+	8.14673i	0.465717	+	0.806646i
$103$	−1.73227	−	3.00038i	−0.170686	−	0.295636i	0.767974	−	0.640481i	$-0.221265\pi$
$103$	−1.73227	−	3.00038i	−0.170686	−	0.295636i	−0.938660	+	0.344845i	$0.887932\pi$
$104$	0.916316	+	1.58711i	0.0898521	+	0.155628i
$105$	−11.6134			−1.13336
$106$	9.68305	+	16.7715i	0.940501	+	1.62900i
$107$	14.7322			1.42421			0.712107	−	0.702071i	$-0.247741\pi$
$107$	14.7322			1.42421			0.712107	+	0.702071i	$0.247741\pi$
$108$	−12.5814			−1.21064
$109$	9.56791	−	4.17792i	0.916440	−	0.400173i
$109$	9.56791	−	4.17792i	0.916440	−	0.400173i
$110$	−20.3440			−1.93973
$111$	0.844304			0.0801378
$112$	6.27234	+	10.8640i	0.592680	+	1.02655i
$113$	7.14505			0.672150			0.336075	−	0.941835i	$-0.390900\pi$
$113$	7.14505			0.672150			0.336075	+	0.941835i	$0.390900\pi$
$114$	4.22576	+	7.31924i	0.395779	+	0.685509i
$115$	−7.79560	−	13.5024i	−0.726943	−	1.25910i
$116$	10.6038	+	18.3663i	0.984536	+	1.70527i
$117$	−4.10543			−0.379547
$118$	9.99150	−	17.3058i	0.919792	−	1.59313i
$119$	−8.18602	−	14.1786i	−0.750411	−	1.29975i
$120$	−1.13352	+	1.96331i	−0.103476	+	0.179225i
$121$	−1.55819	−	2.69886i	−0.141654	−	0.245351i
$122$	5.79889	+	10.0440i	0.525007	+	0.909339i
$123$	2.59155	+	4.48870i	0.233673	+	0.404733i
$124$	1.23594	−	2.14072i	0.110991	−	0.192242i
$125$	8.54534			0.764319
$126$	14.9487			1.33174
$127$	−2.38895	+	4.13779i	−0.211985	+	0.367169i	−0.952336	−	0.305052i	$-0.901326\pi$
$127$	−2.38895	+	4.13779i	−0.211985	+	0.367169i	0.740350	+	0.672221i	$0.234660\pi$
$128$	6.20026			0.548031
$129$	−5.38609	−	9.32898i	−0.474219	−	0.821371i
$130$	−6.28794	+	10.8910i	−0.551489	+	0.955207i
$131$	10.3663	−	17.9550i	0.905709	−	1.56873i	0.0857453	−	0.996317i	$-0.472673\pi$
$131$	10.3663	−	17.9550i	0.905709	−	1.56873i	0.819963	−	0.572416i	$-0.193994\pi$
$132$	−9.91486			−0.862977
$133$	−7.35454	−	12.7384i	−0.637719	−	1.10456i
$134$	1.02592	−	1.77694i	0.0886257	−	0.153504i
$135$	−6.84890	−	11.8626i	−0.589460	−	1.02097i
$136$	−3.19595			−0.274051
$137$	−5.88899	−	10.2000i	−0.503130	−	0.871447i	−0.999993	−	0.00361831i	$-0.998848\pi$
$137$	−5.88899	−	10.2000i	−0.503130	−	0.871447i	0.496863	−	0.867829i	$-0.334485\pi$
$138$	−6.99575	−	12.1170i	−0.595517	−	1.03147i
$139$	0.523698	−	0.907072i	0.0444195	−	0.0769368i	−0.842961	−	0.537975i	$-0.819190\pi$
$139$	0.523698	−	0.907072i	0.0444195	−	0.0769368i	0.887380	+	0.461038i	$0.152523\pi$
$140$	12.4343	−	21.5368i	1.05089	−	1.82019i
$141$	7.35680			0.619554
$142$	−5.93319			−0.497902
$143$	−8.72620			−0.729722
$144$	−2.74290	+	4.75085i	−0.228575	+	0.395904i
$145$	−11.5447	+	19.9960i	−0.958736	+	1.66058i
$146$	−0.532907	+	0.923021i	−0.0441037	+	0.0763898i
$147$	10.3675			0.855094
$148$	−0.903978	+	1.56574i	−0.0743065	+	0.128703i
$149$	1.18438	+	2.05140i	0.0970281	+	0.168058i	0.910453	−	0.413612i	$-0.135733\pi$
$149$	1.18438	+	2.05140i	0.0970281	+	0.168058i	−0.813425	+	0.581670i	$0.802400\pi$
$150$	−3.94415			−0.322039
$151$	−5.42653	+	9.39902i	−0.441605	+	0.764882i	−0.997809	−	0.0661641i	$-0.978924\pi$
$151$	−5.42653	+	9.39902i	−0.441605	+	0.764882i	0.556204	+	0.831046i	$0.312257\pi$
$152$	−2.87133			−0.232895
$153$	3.57976	−	6.20032i	0.289406	−	0.501267i
$154$	31.7740			2.56042
$155$	2.69123			0.216165
$156$	−3.06449	+	5.30786i	−0.245356	+	0.424969i
$157$	6.45561	+	11.1814i	0.515214	+	0.892377i	0.999844	+	0.0176574i	$0.00562083\pi$
$157$	6.45561	+	11.1814i	0.515214	+	0.892377i	−0.484630	+	0.874719i	$0.661046\pi$
$158$	−3.11888	+	5.40206i	−0.248125	+	0.429765i
$159$	−5.13788	+	8.89908i	−0.407461	+	0.705743i
$160$	10.4443	+	18.0901i	0.825695	+	1.43015i
$161$	12.1754	+	21.0885i	0.959558	+	1.66200i
$162$	−0.598878	−	1.03729i	−0.0470523	−	0.0814970i
$163$	−20.0098			−1.56729			−0.783645	−	0.621209i	$-0.786642\pi$
$163$	−20.0098			−1.56729			−0.783645	+	0.621209i	$0.786642\pi$
$164$	−11.0989			−0.866677
$165$	−5.39733	−	9.34844i	−0.420181	−	0.727775i
$166$	−14.5518	−	25.2045i	−1.12944	−	1.95625i
$167$	4.83955	+	8.38234i	0.374496	+	0.648645i	0.990251	−	0.139292i	$-0.0444826\pi$
$167$	4.83955	+	8.38234i	0.374496	+	0.648645i	−0.615756	+	0.787937i	$0.711149\pi$
$168$	1.77037	−	3.06637i	0.136587	−	0.236575i
$169$	3.80290	−	6.58681i	0.292531	−	0.506678i
$170$	−10.9656	−	18.9930i	−0.841026	−	1.45670i
$171$	3.21615	−	5.57054i	0.245945	−	0.425990i
$172$	23.0671			1.75885
$173$	−6.09384			−0.463306			−0.231653	−	0.972798i	$-0.574413\pi$
$173$	−6.09384			−0.463306			−0.231653	+	0.972798i	$0.574413\pi$
$174$	−10.3602	+	17.9444i	−0.785403	+	1.36036i
$175$	6.86442			0.518901
$176$	−5.83011	+	10.0981i	−0.439461	+	0.761169i
$177$	10.6031			0.796978
$178$	−12.2226	−	21.1702i	−0.916123	−	1.58677i
$179$	−4.64937	+	8.05295i	−0.347510	+	0.601906i	−0.985807	−	0.167885i	$-0.946306\pi$
$179$	−4.64937	+	8.05295i	−0.347510	+	0.601906i	0.638296	+	0.769791i	$0.279640\pi$
$180$	10.8750			0.810578
$181$	0.874677	−	1.51498i	0.0650142	−	0.112608i	−0.831686	−	0.555246i	$-0.812624\pi$
$181$	0.874677	−	1.51498i	0.0650142	−	0.112608i	0.896700	+	0.442638i	$0.145957\pi$
$182$	9.82072	−	17.0100i	0.727960	−	1.26086i
$183$	−3.07693	+	5.32940i	−0.227453	+	0.393960i
$184$	4.75348			0.350431
$185$	−1.96838			−0.144719
$186$	2.41510			0.177084
$187$	7.60887	−	13.1790i	0.556416	−	0.963741i
$188$	−7.87676	+	13.6430i	−0.574472	+	0.995014i
$189$	10.6968	+	18.5275i	0.778081	+	1.34768i
$190$	−9.85182	−	17.0638i	−0.714726	−	1.23794i
$191$	6.31594			0.457005			0.228503	−	0.973543i	$-0.426617\pi$
$191$	6.31594			0.457005			0.228503	+	0.973543i	$0.426617\pi$
$192$	5.92750	+	10.2667i	0.427781	+	0.740938i
$193$	−12.6382	+	21.8900i	−0.909718	+	1.57568i	−0.0952626	+	0.995452i	$0.530369\pi$
$193$	−12.6382	+	21.8900i	−0.909718	+	1.57568i	−0.814456	+	0.580226i	$0.802964\pi$
$194$	−17.1430	−	29.6926i	−1.23080	−	2.13180i
$195$	−6.67284			−0.477852
$196$	−11.1002	+	19.2261i	−0.792872	+	1.37330i
$197$	5.08658	−	8.81021i	0.362404	−	0.627702i	−0.625952	−	0.779861i	$-0.715290\pi$
$197$	5.08658	−	8.81021i	0.362404	−	0.627702i	0.988356	+	0.152160i	$0.0486229\pi$
$198$	6.94740	+	12.0333i	0.493730	+	0.855166i
$199$	4.05320			0.287324			0.143662	−	0.989627i	$-0.454112\pi$
$199$	4.05320			0.287324			0.143662	+	0.989627i	$0.454112\pi$
$200$	0.669994	−	1.16046i	0.0473758	−	0.0820572i
$201$	1.08872			0.0767921
$202$	31.9694			2.24936
$203$	18.0309	−	31.2304i	1.26552	−	2.19195i
$204$	−5.34421	−	9.25644i	−0.374170	−	0.648081i
$205$	−6.04187	−	10.4648i	−0.421983	−	0.730895i
$206$	3.62420	+	6.27729i	0.252510	+	0.437360i
$207$	−5.32434	+	9.22202i	−0.370067	+	0.640975i
$208$	3.60395	+	6.24223i	0.249889	+	0.432821i
$209$	6.83602	−	11.8403i	0.472857	−	0.819013i
$210$	24.2972			1.67667
$211$	−11.7379	−	20.3306i	−0.808067	−	1.39961i	−0.914201	−	0.405262i	$-0.867180\pi$
$211$	−11.7379	−	20.3306i	−0.808067	−	1.39961i	0.106134	−	0.994352i	$-0.466153\pi$
$212$	−11.0020	−	19.0561i	−0.755623	−	1.30878i
$213$	−1.57409	−	2.72641i	−0.107855	−	0.186810i
$214$	−30.8222			−2.10696
$215$	12.5570	+	21.7493i	0.856379	+	1.48329i
$216$	4.17622			0.284156
$217$	−4.20325			−0.285335
$218$	−20.0176	+	8.74090i	−1.35577	+	0.592009i
$219$	−0.565527			−0.0382148
$220$	23.1152			1.55843
$221$	−4.70351	−	8.14673i	−0.316393	−	0.548008i
$222$	−1.76642			−0.118555
$223$	9.94141	+	17.2190i	0.665726	+	1.15307i	0.979088	+	0.203438i	$0.0652115\pi$
$223$	9.94141	+	17.2190i	0.665726	+	1.15307i	−0.313362	+	0.949634i	$0.601455\pi$
$224$	−16.3123	−	28.2537i	−1.08991	−	1.88778i
$225$	1.50091	+	2.59965i	0.100061	+	0.173310i
$226$	−14.9486			−0.994367
$227$	−6.84748	+	11.8602i	−0.454483	+	0.787188i	−0.998658	−	0.0517840i	$-0.983509\pi$
$227$	−6.84748	+	11.8602i	−0.454483	+	0.787188i	0.544175	+	0.838971i	$0.316843\pi$
$228$	−4.80138	−	8.31624i	−0.317979	−	0.550756i
$229$	10.6278	−	18.4080i	0.702308	−	1.21643i	−0.265347	−	0.964153i	$-0.585486\pi$
$229$	10.6278	−	18.4080i	0.702308	−	1.21643i	0.967654	−	0.252280i	$-0.0811803\pi$
$230$	16.3097	+	28.2492i	1.07543	+	1.86270i
$231$	8.42973	+	14.6007i	0.554635	+	0.960656i
$232$	−3.51978	−	6.09643i	−0.231085	−	0.400250i
$233$	4.85376	−	8.40696i	0.317980	−	0.550758i	−0.662086	−	0.749428i	$-0.730329\pi$
$233$	4.85376	−	8.40696i	0.317980	−	0.550758i	0.980067	+	0.198670i	$0.0636621\pi$
$234$	8.58924			0.561496
$235$	−17.1514			−1.11884
$236$	−11.3525	+	19.6631i	−0.738985	+	1.27996i
$237$	−3.30979			−0.214994
$238$	17.1265	+	29.6640i	1.11015	+	1.92283i
$239$	−11.2510	+	19.4874i	−0.727769	+	1.26053i	0.230056	+	0.973178i	$0.426109\pi$
$239$	−11.2510	+	19.4874i	−0.727769	+	1.26053i	−0.957824	+	0.287355i	$0.907224\pi$
$240$	−4.45823	+	7.72188i	−0.287777	+	0.498445i
$241$	13.2490			0.853446			0.426723	−	0.904382i	$-0.359668\pi$
$241$	13.2490			0.853446			0.426723	+	0.904382i	$0.359668\pi$
$242$	3.25999	+	5.64646i	0.209560	+	0.362968i
$243$	−7.62118	+	13.2003i	−0.488899	+	0.846798i
$244$	−6.58880	−	11.4121i	−0.421805	−	0.730587i
$245$	−24.1704			−1.54419
$246$	−5.42196	−	9.39111i	−0.345691	−	0.598755i
$247$	−4.22576	−	7.31924i	−0.268879	−	0.465712i
$248$	−0.410254	+	0.710581i	−0.0260512	+	0.0451219i
$249$	7.72128	−	13.3737i	0.489316	−	0.847521i
$250$	−17.8783			−1.13072
$251$	−9.89455			−0.624539			−0.312269	−	0.949994i	$-0.601089\pi$
$251$	−9.89455			−0.624539			−0.312269	+	0.949994i	$0.601089\pi$
$252$	−16.9850			−1.06996
$253$	−11.3170	+	19.6016i	−0.711495	+	1.23235i
$254$	4.99808	−	8.65693i	0.313608	−	0.543184i
$255$	5.81843	−	10.0778i	0.364364	−	0.631097i
$256$	8.38619			0.524137
$257$	−0.485742	+	0.841330i	−0.0302998	+	0.0524808i	−0.880778	−	0.473530i	$-0.842980\pi$
$257$	−0.485742	+	0.841330i	−0.0302998	+	0.0524808i	0.850478	+	0.526011i	$0.176313\pi$
$258$	11.2686	+	19.5178i	0.701552	+	1.21512i
$259$	3.07429			0.191027
$260$	7.14446	−	12.3746i	0.443081	−	0.767439i
$261$	15.7699			0.976132
$262$	−21.6880	+	37.5648i	−1.33989	+	2.32076i
$263$	−11.9833			−0.738922			−0.369461	−	0.929246i	$-0.620458\pi$
$263$	−11.9833			−0.738922			−0.369461	+	0.929246i	$0.620458\pi$
$264$	3.29110			0.202553
$265$	11.9783	−	20.7470i	0.735822	−	1.27448i
$266$	15.3869	+	26.6509i	0.943431	+	1.63407i
$267$	6.48538	−	11.2330i	0.396899	−	0.687449i
$268$	−1.16566	+	2.01899i	−0.0712042	+	0.123329i
$269$	−0.0281534	−	0.0487632i	−0.00171655	−	0.00297314i	0.865166	−	0.501486i	$-0.167213\pi$
$269$	−0.0281534	−	0.0487632i	−0.00171655	−	0.00297314i	−0.866882	+	0.498513i	$0.833880\pi$
$270$	14.3290	+	24.8186i	0.872037	+	1.51041i
$271$	−4.57690	−	7.92742i	−0.278027	−	0.481556i	0.692868	−	0.721065i	$-0.256347\pi$
$271$	−4.57690	−	7.92742i	−0.278027	−	0.481556i	−0.970894	+	0.239509i	$0.923014\pi$
$272$	−12.5700			−0.762166
$273$	10.4219			0.630760
$274$	12.3207	+	21.3401i	0.744323	+	1.28920i
$275$	3.19023	+	5.52563i	0.192378	+	0.333208i
$276$	7.94868	+	13.7675i	0.478454	+	0.828707i
$277$	−3.20849	+	5.55726i	−0.192779	+	0.333904i	−0.946170	−	0.323669i	$-0.895084\pi$
$277$	−3.20849	+	5.55726i	−0.192779	+	0.333904i	0.753391	+	0.657573i	$0.228417\pi$
$278$	−1.09566	+	1.89774i	−0.0657135	+	0.113819i
$279$	−0.919044	−	1.59183i	−0.0550217	−	0.0953005i
$280$	−4.12738	+	7.14883i	−0.246658	+	0.427224i
$281$	−22.8877			−1.36536			−0.682682	−	0.730716i	$-0.739186\pi$
$281$	−22.8877			−1.36536			−0.682682	+	0.730716i	$0.739186\pi$
$282$	−15.3916			−0.916558
$283$	11.4721	−	19.8703i	0.681948	−	1.18117i	−0.292438	−	0.956285i	$-0.594466\pi$
$283$	11.4721	−	19.8703i	0.681948	−	1.18117i	0.974386	−	0.224884i	$-0.0722003\pi$
$284$	6.74139			0.400028
$285$	5.22743	−	9.05418i	0.309646	−	0.536323i
$286$	18.2567			1.07954
$287$	9.43640	+	16.3443i	0.557013	+	0.964775i
$288$	7.13339	−	12.3554i	0.420339	−	0.728048i
$289$	−0.594950			−0.0349971
$290$	24.1534	−	41.8350i	1.41834	−	2.45663i
$291$	9.09618	−	15.7550i	0.533228	−	0.923577i
$292$	0.605497	−	1.04875i	0.0354340	−	0.0613736i
$293$	8.87000			0.518191			0.259096	−	0.965852i	$-0.416576\pi$
$293$	8.87000			0.518191			0.259096	+	0.965852i	$0.416576\pi$
$294$	−21.6904			−1.26501
$295$	−24.7197			−1.43924
$296$	0.300063	−	0.519724i	0.0174408	−	0.0302084i
$297$	−9.94268	+	17.2212i	−0.576933	+	0.999277i
$298$	−2.47791	−	4.29187i	−0.143542	−	0.248622i
$299$	6.99575	+	12.1170i	0.404574	+	0.700743i
$300$	4.48141			0.258734
$301$	−19.6119	−	33.9688i	−1.13041	−	1.95793i
$302$	11.3532	−	19.6643i	0.653303	−	1.13155i
$303$	8.48159	+	14.6905i	0.487255	+	0.843950i
$304$	−11.2932			−0.647709
$305$	7.17346	−	12.4248i	0.410751	−	0.711442i
$306$	−7.48944	+	12.9721i	−0.428143	+	0.741566i
$307$	2.91063	+	5.04136i	0.166118	+	0.287725i	0.937052	−	0.349190i	$-0.113543\pi$
$307$	2.91063	+	5.04136i	0.166118	+	0.287725i	−0.770934	+	0.636916i	$0.780210\pi$
$308$	−36.1021			−2.05711
$309$	−1.92302	+	3.33077i	−0.109397	+	0.189481i
$310$	−5.63049			−0.319790
$311$	−10.4501			−0.592573			−0.296286	−	0.955099i	$-0.595748\pi$
$311$	−10.4501			−0.592573			−0.296286	+	0.955099i	$0.595748\pi$
$312$	1.01722	−	1.76187i	0.0575885	−	0.0997462i
$313$	6.32000	+	10.9466i	0.357227	+	0.618736i	0.987497	−	0.157641i	$-0.0503888\pi$
$313$	6.32000	+	10.9466i	0.357227	+	0.618736i	−0.630269	+	0.776377i	$0.717056\pi$
$314$	−13.5062	−	23.3934i	−0.762199	−	1.32017i
$315$	−9.24609	−	16.0147i	−0.520958	−	0.902326i
$316$	3.54372	−	6.13791i	0.199350	−	0.345284i
$317$	−3.57551	−	6.19297i	−0.200821	−	0.347832i	0.747972	−	0.663730i	$-0.231028\pi$
$317$	−3.57551	−	6.19297i	−0.200821	−	0.347832i	−0.948793	+	0.315898i	$0.897694\pi$
$318$	10.7493	−	18.6183i	0.602791	−	1.04406i
$319$	33.5193			1.87672
$320$	−13.8192	−	23.9356i	−0.772517	−	1.33804i
$321$	−8.17721	−	14.1633i	−0.456408	−	0.790521i
$322$	−25.4730	−	44.1205i	−1.41955	−	2.45874i
$323$	14.7387			0.820085
$324$	0.680455	+	1.17858i	0.0378031	+	0.0654768i
$325$	3.94415			0.218782
$326$	41.8638			2.31862
$327$	−9.32735	−	6.87949i	−0.515803	−	0.380436i
$328$	3.68412			0.203422
$329$	26.7877			1.47685
$330$	11.2921	+	19.5585i	0.621609	+	1.07666i
$331$	−3.82239			−0.210098			−0.105049	−	0.994467i	$-0.533500\pi$
$331$	−3.82239			−0.210098			−0.105049	+	0.994467i	$0.533500\pi$
$332$	16.5340	+	28.6378i	0.907422	+	1.57170i
$333$	0.672196	+	1.16428i	0.0368361	+	0.0638020i
$334$	−10.1251	−	17.5372i	−0.554023	−	0.959595i
$335$	−2.53820			−0.138677
$336$	6.96301	−	12.0603i	0.379863	−	0.657943i
$337$	−4.87265	−	8.43967i	−0.265430	−	0.459738i	0.702246	−	0.711934i	$-0.252181\pi$
$337$	−4.87265	−	8.43967i	−0.265430	−	0.459738i	−0.967676	+	0.252196i	$0.918847\pi$
$338$	−7.95629	+	13.7807i	−0.432765	+	0.749571i
$339$	−3.96591	−	6.86916i	−0.215399	−	0.373082i
$340$	12.4593	+	21.5802i	0.675702	+	1.17035i
$341$	−1.95345	−	3.38348i	−0.105785	−	0.183226i
$342$	−6.72872	+	11.6545i	−0.363847	+	0.630202i
$343$	9.45498			0.510521
$344$	−7.65680			−0.412827
$345$	−8.65401	+	14.9892i	−0.465916	+	0.806991i
$346$	12.7493			0.685408
$347$	−12.6832	−	21.9679i	−0.680870	−	1.17930i	−0.974716	−	0.223448i	$-0.928269\pi$
$347$	−12.6832	−	21.9679i	−0.680870	−	1.17930i	0.293846	−	0.955853i	$-0.405065\pi$
$348$	11.7714	−	20.3887i	0.631014	−	1.09295i
$349$	11.6657	−	20.2056i	0.624451	−	1.08158i	−0.364196	−	0.931322i	$-0.618656\pi$
$349$	11.6657	−	20.2056i	0.624451	−	1.08158i	0.988647	−	0.150258i	$-0.0480105\pi$
$350$	−14.3615			−0.767654
$351$	6.14618	+	10.6455i	0.328059	+	0.568215i
$352$	15.1622	−	26.2617i	0.808148	−	1.39975i
$353$	16.0555	+	27.8089i	0.854546	+	1.48012i	0.877066	+	0.480371i	$0.159498\pi$
$353$	16.0555	+	27.8089i	0.854546	+	1.48012i	−0.0225196	+	0.999746i	$0.507169\pi$
$354$	−22.1834			−1.17904
$355$	3.66979	+	6.35627i	0.194772	+	0.337356i
$356$	13.8875	+	24.0539i	0.736037	+	1.27485i
$357$	−9.08742	+	15.7399i	−0.480957	+	0.833042i
$358$	9.72725	−	16.8481i	0.514101	−	0.890450i
$359$	−7.86215			−0.414948			−0.207474	−	0.978240i	$-0.566524\pi$
$359$	−7.86215			−0.414948			−0.207474	+	0.978240i	$0.566524\pi$
$360$	−3.60982			−0.190254
$361$	−5.75833			−0.303070
$362$	−1.82997	+	3.16960i	−0.0961810	+	0.166590i
$363$	−1.72977	+	2.99605i	−0.0907893	+	0.157252i
$364$	−11.1585	+	19.3270i	−0.584862	+	1.01301i
$365$	1.31845			0.0690110
$366$	6.43744	−	11.1500i	0.336490	−	0.582818i
$367$	6.85781	+	11.8781i	0.357975	+	0.620031i	0.987622	−	0.156850i	$-0.0501340\pi$
$367$	6.85781	+	11.8781i	0.357975	+	0.620031i	−0.629648	+	0.776881i	$0.716801\pi$
$368$	18.6959			0.974590
$369$	−4.12655	+	7.14740i	−0.214820	+	0.372079i
$370$	4.11818			0.214094
$371$	−18.7081	+	32.4034i	−0.971277	+	1.68230i
$372$	−2.74408			−0.142274
$373$	29.1938			1.51160			0.755799	−	0.654803i	$-0.227249\pi$
$373$	29.1938			1.51160			0.755799	+	0.654803i	$0.227249\pi$
$374$	−15.9190	+	27.5725i	−0.823153	+	1.42574i
$375$	−4.74316	−	8.21539i	−0.244936	−	0.424241i
$376$	2.61458	−	4.52859i	0.134837	−	0.233544i
$377$	10.3602	−	17.9444i	0.533577	−	0.924182i
$378$	−22.3796	−	38.7625i	−1.15108	−	1.99373i
$379$	−0.675559	−	1.17010i	−0.0347011	−	0.0601041i	0.848153	−	0.529751i	$-0.177715\pi$
$379$	−0.675559	−	1.17010i	−0.0347011	−	0.0601041i	−0.882854	+	0.469647i	$0.844381\pi$
$380$	11.1938	+	19.3882i	0.574230	+	0.994595i
$381$	5.30403			0.271733
$382$	−13.2140			−0.676086
$383$	1.49240	+	2.58491i	0.0762580	+	0.132083i	0.901633	−	0.432503i	$-0.142369\pi$
$383$	1.49240	+	2.58491i	0.0762580	+	0.132083i	−0.825375	+	0.564585i	$0.809036\pi$
$384$	−3.44150	−	5.96085i	−0.175623	−	0.304189i
$385$	−19.6528	−	34.0397i	−1.00160	−	1.73482i
$386$	26.4412	−	45.7975i	1.34582	−	2.33103i
$387$	8.57632	−	14.8546i	0.435959	−	0.755103i
$388$	19.4782	+	33.7372i	0.988854	+	1.71275i
$389$	−7.55747	+	13.0899i	−0.383179	+	0.663686i	−0.991515	−	0.129994i	$-0.958504\pi$
$389$	−7.55747	+	13.0899i	−0.383179	+	0.663686i	0.608336	+	0.793680i	$0.291837\pi$
$390$	13.9607			0.706927
$391$	−24.4000			−1.23396
$392$	3.68456	−	6.38185i	0.186099	−	0.322332i
$393$	−23.0156			−1.16098
$394$	−10.6420	+	18.4324i	−0.536134	+	0.928611i
$395$	7.71635			0.388252
$396$	−7.89375	−	13.6724i	−0.396676	−	0.687063i
$397$	4.32235	−	7.48653i	0.216933	−	0.375738i	−0.736936	−	0.675962i	$-0.763728\pi$
$397$	4.32235	−	7.48653i	0.216933	−	0.375738i	0.953869	+	0.300224i	$0.0970615\pi$
$398$	−8.47996			−0.425062
$399$	−8.16438	+	14.1411i	−0.408730	+	0.707942i
$400$	2.63515	−	4.56421i	0.131757	−	0.228211i
$401$	−7.50680	+	13.0022i	−0.374872	+	0.649297i	−0.990308	−	0.138890i	$-0.955647\pi$
$401$	−7.50680	+	13.0022i	−0.374872	+	0.649297i	0.615436	+	0.788187i	$0.288980\pi$
$402$	−2.27777			−0.113605
$403$	−2.41510			−0.120305
$404$	−36.3242			−1.80720
$405$	−0.740836	+	1.28316i	−0.0368124	+	0.0637610i
$406$	−37.7236	+	65.3392i	−1.87219	+	3.24273i
$407$	1.42877	+	2.47470i	0.0708215	+	0.122666i
$408$	1.77394	+	3.07255i	0.0878230	+	0.152114i
$409$	5.34315			0.264202			0.132101	−	0.991236i	$-0.457828\pi$
$409$	5.34315			0.264202			0.132101	+	0.991236i	$0.457828\pi$
$410$	12.6406	+	21.8941i	0.624274	+	1.08127i
$411$	−6.53745	+	11.3232i	−0.322469	+	0.558532i
$412$	−4.11787	−	7.13236i	−0.202873	−	0.351386i
$413$	38.6081			1.89978
$414$	11.1394	−	19.2940i	0.547471	−	0.948247i
$415$	−18.0012	+	31.1789i	−0.883643	+	1.53051i
$416$	−9.37269	−	16.2340i	−0.459534	−	0.795936i
$417$	−1.16273			−0.0569391
$418$	−14.3021	+	24.7719i	−0.699537	+	1.21163i
$419$	−19.4004			−0.947773			−0.473886	−	0.880586i	$-0.657149\pi$
$419$	−19.4004			−0.947773			−0.473886	+	0.880586i	$0.657149\pi$
$420$	−27.6069			−1.34708
$421$	−2.47562	+	4.28790i	−0.120654	+	0.208980i	−0.920026	−	0.391858i	$-0.871833\pi$
$421$	−2.47562	+	4.28790i	−0.120654	+	0.208980i	0.799372	+	0.600837i	$0.205166\pi$
$422$	24.5575	+	42.5349i	1.19544	+	2.07057i
$423$	5.85714	+	10.1449i	0.284784	+	0.493260i
$424$	3.65197	+	6.32541i	0.177356	+	0.307189i
$425$	−3.43913	+	5.95675i	−0.166822	+	0.288945i
$426$	3.29326	+	5.70410i	0.159559	+	0.276364i
$427$	−11.2037	+	19.4055i	−0.542187	+	0.939096i
$428$	35.0207			1.69279
$429$	4.84354	+	8.38926i	0.233849	+	0.405038i
$430$	−26.2713	−	45.5031i	−1.26691	−	2.19436i
$431$	5.15362	+	8.92634i	0.248241	+	0.429966i	0.963038	−	0.269366i	$-0.0868141\pi$
$431$	5.15362	+	8.92634i	0.248241	+	0.429966i	−0.714797	+	0.699332i	$0.753481\pi$
$432$	16.4254			0.790270
$433$	3.57414	+	6.19059i	0.171762	+	0.297501i	0.939036	−	0.343819i	$-0.111721\pi$
$433$	3.57414	+	6.19059i	0.171762	+	0.297501i	−0.767274	+	0.641320i	$0.778387\pi$
$434$	8.79389			0.422120
$435$	25.6319			1.22896
$436$	22.7444	−	9.93156i	1.08926	−	0.475635i
$437$	−21.9216			−1.04865
$438$	1.18318			0.0565343
$439$	10.4721	+	18.1382i	0.499807	+	0.865691i	1.00000		0.000223217i	$-7.10522e-5\pi$
$439$	10.4721	+	18.1382i	0.499807	+	0.865691i	−0.500193	+	0.865914i	$0.666738\pi$
$440$	−7.67277			−0.365785
$441$	8.25410	+	14.2965i	0.393052	+	0.680786i
$442$	9.84052	+	17.0443i	0.468066	+	0.810714i
$443$	4.30046	+	7.44862i	0.204321	+	0.353895i	0.949916	−	0.312505i	$-0.101168\pi$
$443$	4.30046	+	7.44862i	0.204321	+	0.353895i	−0.745595	+	0.666399i	$0.767835\pi$
$444$	2.00704			0.0952498
$445$	−15.1198	+	26.1883i	−0.716749	+	1.24145i
$446$	−20.7991	−	36.0250i	−0.984864	−	1.70584i
$447$	1.31480	−	2.27729i	0.0621877	−	0.107712i
$448$	21.5833	+	37.3834i	1.01971	+	1.76620i
$449$	−13.4592	−	23.3120i	−0.635177	−	1.10016i	−0.986478	−	0.163897i	$-0.947594\pi$
$449$	−13.4592	−	23.3120i	−0.635177	−	1.10016i	0.351300	−	0.936263i	$-0.385740\pi$
$450$	−3.14015	−	5.43890i	−0.148028	−	0.256392i
$451$	−8.77110	+	15.1920i	−0.413015	+	0.715363i
$452$	16.9849			0.798901
$453$	12.0481			0.566071
$454$	14.3260	−	24.8134i	0.672355	−	1.16455i
$455$	−24.2972			−1.13907
$456$	1.59375	+	2.76046i	0.0746343	+	0.129270i
$457$	19.4287	−	33.6514i	0.908835	−	1.57415i	0.0931490	−	0.995652i	$-0.470307\pi$
$457$	19.4287	−	33.6514i	0.908835	−	1.57415i	0.815686	−	0.578496i	$-0.196360\pi$
$458$	−22.2352	+	38.5125i	−1.03898	+	1.79957i
$459$	−21.4368			−1.00059
$460$	−18.5313	−	32.0972i	−0.864027	−	1.49654i
$461$	1.62825	−	2.82022i	0.0758353	−	0.131351i	−0.825614	−	0.564235i	$-0.809171\pi$
$461$	1.62825	−	2.82022i	0.0758353	−	0.131351i	0.901449	+	0.432885i	$0.142504\pi$
$462$	−17.6364	−	30.5471i	−0.820518	−	1.42118i
$463$	−31.0481			−1.44293			−0.721465	−	0.692451i	$-0.756531\pi$
$463$	−31.0481			−1.44293			−0.721465	+	0.692451i	$0.756531\pi$
$464$	−13.8436	−	23.9778i	−0.642673	−	1.11314i
$465$	−1.49379	−	2.58731i	−0.0692727	−	0.119984i
$466$	−10.1549	+	17.5887i	−0.470415	+	0.814782i
$467$	8.33374	−	14.4345i	0.385639	−	0.667947i	−0.606218	−	0.795298i	$-0.707314\pi$
$467$	8.33374	−	14.4345i	0.385639	−	0.667947i	0.991858	+	0.127351i	$0.0406476\pi$
$468$	−9.75923			−0.451121
$469$	3.96424			0.183052
$470$	35.8836			1.65519
$471$	7.16647	−	12.4127i	0.330213	−	0.571947i
$472$	3.76831	−	6.52690i	0.173450	−	0.300425i
$473$	18.2292	−	31.5739i	0.838179	−	1.45177i
$474$	6.92463			0.318059
$475$	−3.08981	+	5.35170i	−0.141770	+	0.245553i
$476$	−19.4594	−	33.7047i	−0.891920	−	1.54485i
$477$	−16.3622			−0.749173
$478$	23.5390	−	40.7708i	1.07665	−	1.86481i
$479$	1.01570			0.0464084			0.0232042	−	0.999731i	$-0.492613\pi$
$479$	1.01570			0.0464084			0.0232042	+	0.999731i	$0.492613\pi$
$480$	11.5944	−	20.0821i	0.529209	−	0.916617i
$481$	1.76642			0.0805419
$482$	−27.7192			−1.26257
$483$	13.5161	−	23.4106i	0.615005	−	1.06522i
$484$	−3.70405	−	6.41560i	−0.168366	−	0.291618i
$485$	−21.2066	+	36.7309i	−0.962941	+	1.66786i
$486$	15.9448	−	27.6171i	0.723269	−	1.25274i
$487$	−8.91241	−	15.4368i	−0.403860	−	0.699506i	0.590328	−	0.807163i	$-0.298998\pi$
$487$	−8.91241	−	15.4368i	−0.403860	−	0.699506i	−0.994188	+	0.107657i	$0.965665\pi$
$488$	2.18706	+	3.78810i	0.0990036	+	0.171479i
$489$	11.1066	+	19.2372i	0.502258	+	0.869936i
$490$	50.5684			2.28445
$491$	11.0702			0.499591			0.249796	−	0.968299i	$-0.419637\pi$
$491$	11.0702			0.499591			0.249796	+	0.968299i	$0.419637\pi$
$492$	6.16052	+	10.6703i	0.277738	+	0.481056i
$493$	18.0673	+	31.2934i	0.813709	+	1.40938i
$494$	8.84099	+	15.3130i	0.397775	+	0.688966i
$495$	8.59421	−	14.8856i	0.386281	−	0.669058i
$496$	−1.61357	+	2.79478i	−0.0724513	+	0.125489i
$497$	−5.73161	−	9.92743i	−0.257098	−	0.445306i
$498$	−16.1542	+	27.9799i	−0.723887	+	1.25381i
$499$	25.2246			1.12921			0.564604	−	0.825362i	$-0.309029\pi$
$499$	25.2246			1.12921			0.564604	+	0.825362i	$0.309029\pi$
$500$	20.3136			0.908451
$501$	5.37246	−	9.30537i	0.240024	−	0.415733i
$502$	20.7010			0.923932
$503$	−7.94938	+	13.7687i	−0.354445	+	0.613917i	−0.987023	−	0.160580i	$-0.948664\pi$
$503$	−7.94938	+	13.7687i	−0.354445	+	0.613917i	0.632577	+	0.774497i	$0.281997\pi$
$504$	5.63794			0.251134
$505$	−19.7737	−	34.2491i	−0.879919	−	1.52406i
$506$	23.6771	−	41.0099i	1.05257	−	1.82311i
$507$	−8.44331			−0.374980
$508$	−5.67890	+	9.83615i	−0.251961	+	0.436409i
$509$	−3.94523	+	6.83334i	−0.174869	+	0.302882i	−0.940116	−	0.340855i	$-0.889284\pi$
$509$	−3.94523	+	6.83334i	−0.174869	+	0.302882i	0.765247	+	0.643737i	$0.222617\pi$
$510$	−12.1731	+	21.0845i	−0.539035	+	0.933635i
$511$	−2.05920			−0.0910938
$512$	−29.9458			−1.32343
$513$	−19.2594			−0.850324
$514$	1.01625	−	1.76020i	0.0448250	−	0.0776392i
$515$	4.48327	−	7.76526i	0.197557	−	0.342178i
$516$	−12.8036	−	22.1764i	−0.563645	−	0.976262i
$517$	12.4495	+	21.5632i	0.547529	+	0.948348i
$518$	−6.43192			−0.282602
$519$	3.38243	+	5.85855i	0.148472	+	0.257162i
$520$	−2.37151	+	4.10757i	−0.103997	+	0.180129i
$521$	−13.0416	−	22.5888i	−0.571365	−	0.989633i	−0.996426	−	0.0844681i	$-0.973081\pi$
$521$	−13.0416	−	22.5888i	−0.571365	−	0.989633i	0.425062	−	0.905164i	$-0.360252\pi$
$522$	−32.9932			−1.44407
$523$	1.16419	−	2.01643i	0.0509064	−	0.0881724i	−0.839449	−	0.543438i	$-0.817122\pi$
$523$	1.16419	−	2.01643i	0.0509064	−	0.0881724i	0.890356	+	0.455265i	$0.150456\pi$
$524$	24.6423	−	42.6817i	1.07650	−	1.86456i
$525$	−3.81015	−	6.59937i	−0.166288	−	0.288020i
$526$	25.0710			1.09315
$527$	2.10586	−	3.64746i	0.0917329	−	0.158886i
$528$	12.9442			0.563324
$529$	13.2911			0.577876
$530$	−25.0606	+	43.4062i	−1.08856	+	1.88545i
$531$	8.44170	+	14.6215i	0.366339	+	0.634517i
$532$	−17.4828	−	30.2812i	−0.757978	−	1.31286i
$533$	5.42196	+	9.39111i	0.234851	+	0.406774i
$534$	−13.5685	+	23.5013i	−0.587166	+	1.01700i
$535$	19.0641	+	33.0200i	0.824213	+	1.42758i
$536$	0.386926	−	0.670175i	0.0167127	−	0.0289472i
$537$	10.3227			0.445456
$538$	0.0589016	+	0.102021i	0.00253943	+	0.00439842i
$539$	17.5443	+	30.3876i	0.755687	+	1.30889i
$540$	−16.2809	−	28.1993i	−0.700617	−	1.21351i
$541$	9.64318			0.414593			0.207296	−	0.978278i	$-0.433534\pi$
$541$	9.64318			0.414593			0.207296	+	0.978278i	$0.433534\pi$
$542$	9.57562	+	16.5855i	0.411308	+	0.712406i
$543$	−1.94198			−0.0833385
$544$	32.6903			1.40159
$545$	21.7455	+	16.0386i	0.931475	+	0.687019i
$546$	−21.8043			−0.933136
$547$	−14.8601			−0.635373			−0.317687	−	0.948196i	$-0.602906\pi$
$547$	−14.8601			−0.635373			−0.317687	+	0.948196i	$0.602906\pi$
$548$	−13.9990	−	24.2470i	−0.598008	−	1.03578i
$549$	−9.79884			−0.418204
$550$	−6.67448	−	11.5605i	−0.284601	−	0.492943i
$551$	16.2321	+	28.1148i	0.691511	+	1.19773i
$552$	−2.63845	−	4.56994i	−0.112300	−	0.194509i
$553$	−12.0517			−0.512489
$554$	6.71268	−	11.6267i	0.285195	−	0.493972i
$555$	1.09257	+	1.89238i	0.0463769	+	0.0803271i
$556$	1.24491	−	2.15625i	0.0527959	−	0.0914452i
$557$	−1.18243	−	2.04803i	−0.0501012	−	0.0867778i	0.839887	−	0.542761i	$-0.182621\pi$
$557$	−1.18243	−	2.04803i	−0.0501012	−	0.0867778i	−0.889988	+	0.455983i	$0.849288\pi$
$558$	1.92279	+	3.33037i	0.0813983	+	0.140986i
$559$	−11.2686	−	19.5178i	−0.476611	−	0.825514i
$560$	−16.2334	+	28.1170i	−0.685985	+	1.18816i
$561$	−16.8934			−0.713242
$562$	47.8847			2.01990
$563$	4.41396	−	7.64520i	0.186026	−	0.322207i	−0.757896	−	0.652376i	$-0.773772\pi$
$563$	4.41396	−	7.64520i	0.186026	−	0.322207i	0.943922	+	0.330169i	$0.107106\pi$
$564$	17.4882			0.736387
$565$	9.24601	+	16.0146i	0.388983	+	0.673738i
$566$	−24.0016	+	41.5720i	−1.00886	+	1.74740i
$567$	1.15706	−	2.00409i	0.0485920	−	0.0841639i
$568$	−2.23771			−0.0938922
$569$	3.72796	+	6.45702i	0.156284	+	0.270692i	0.933526	−	0.358510i	$-0.116715\pi$
$569$	3.72796	+	6.45702i	0.156284	+	0.270692i	−0.777242	+	0.629202i	$0.783382\pi$
$570$	−10.9366	+	18.9428i	−0.458086	+	0.793428i
$571$	−14.6051	−	25.2968i	−0.611204	−	1.05864i	−0.991038	−	0.133582i	$-0.957352\pi$
$571$	−14.6051	−	25.2968i	−0.611204	−	1.05864i	0.379833	−	0.925055i	$-0.375981\pi$
$572$	−20.7435			−0.867330
$573$	−3.50571	−	6.07206i	−0.146453	−	0.253664i
$574$	−19.7425	−	34.1950i	−0.824036	−	1.42727i
$575$	5.11517	−	8.85974i	0.213317	−	0.369477i
$576$	−9.43841	+	16.3478i	−0.393267	+	0.681158i
$577$	−26.7582			−1.11396			−0.556979	−	0.830527i	$-0.688040\pi$
$577$	−26.7582			−1.11396			−0.556979	+	0.830527i	$0.688040\pi$
$578$	1.24473			0.0517741
$579$	28.0597			1.16612
$580$	−27.4435	+	47.5336i	−1.13953	+	1.97372i
$581$	28.1148	−	48.6963i	1.16640	−	2.02026i
$582$	−19.0307	+	32.9621i	−0.788848	+	1.36632i
$583$	−34.7783			−1.44037
$584$	−0.200986	+	0.348119i	−0.00831688	+	0.0144053i
$585$	−5.31261	−	9.20171i	−0.219649	−	0.380444i
$586$	−18.5575			−0.766603
$587$	3.57304	−	6.18869i	0.147475	−	0.255435i	−0.782818	−	0.622250i	$-0.786219\pi$
$587$	3.57304	−	6.18869i	0.147475	−	0.255435i	0.930294	+	0.366815i	$0.119552\pi$
$588$	24.6450			1.01634
$589$	1.89196	−	3.27698i	0.0779570	−	0.135026i
$590$	51.7178			2.12919
$591$	−11.2934			−0.464547
$592$	1.18017	−	2.04412i	0.0485049	−	0.0840129i
$593$	−15.2773	−	26.4610i	−0.627363	−	1.08662i	−0.988079	−	0.153948i	$-0.950801\pi$
$593$	−15.2773	−	26.4610i	−0.627363	−	1.08662i	0.360716	−	0.932676i	$-0.382532\pi$
$594$	20.8017	−	36.0296i	0.853505	−	1.47831i
$595$	21.1861	−	36.6955i	0.868547	−	1.50437i
$596$	2.81545	+	4.87650i	0.115325	+	0.199749i
$597$	−2.24976	−	3.89670i	−0.0920765	−	0.159481i
$598$	−14.6363	−	25.3507i	−0.598521	−	1.03667i
$599$	−29.0881			−1.18851			−0.594255	−	0.804277i	$-0.702553\pi$
$599$	−29.0881			−1.18851			−0.594255	+	0.804277i	$0.702553\pi$
$600$	−1.48754			−0.0607286
$601$	−16.9859	−	29.4205i	−0.692871	−	1.20009i	−0.970893	−	0.239513i	$-0.923012\pi$
$601$	−16.9859	−	29.4205i	−0.692871	−	1.20009i	0.278022	−	0.960575i	$-0.410321\pi$
$602$	41.0313	+	71.0683i	1.67231	+	2.89653i
$603$	0.866785	+	1.50132i	0.0352982	+	0.0611383i
$604$	−12.8997	+	22.3429i	−0.524880	+	0.909120i
$605$	4.03273	−	6.98489i	0.163954	−	0.283976i
$606$	−17.7449	−	30.7350i	−0.720836	−	1.24853i
$607$	6.18446	−	10.7118i	0.251020	−	0.434779i	−0.712787	−	0.701380i	$-0.752567\pi$
$607$	6.18446	−	10.7118i	0.251020	−	0.434779i	0.963807	+	0.266602i	$0.0859008\pi$
$608$	29.3699			1.19111
$609$	−40.0328			−1.62221
$610$	−15.0081	+	25.9947i	−0.607658	+	1.05250i
$611$	15.3916			0.622679
$612$	8.50963	−	14.7391i	0.343981	−	0.595793i
$613$	−34.6623			−1.40000			−0.699999	−	0.714144i	$-0.746816\pi$
$613$	−34.6623			−1.40000			−0.699999	+	0.714144i	$0.746816\pi$
$614$	−6.08951	−	10.5473i	−0.245753	−	0.425656i
$615$	−6.70717	+	11.6172i	−0.270459	+	0.468449i
$616$	11.9836			0.482833
$617$	4.64449	−	8.04449i	0.186980	−	0.323859i	−0.757262	−	0.653111i	$-0.773463\pi$
$617$	4.64449	−	8.04449i	0.186980	−	0.323859i	0.944242	+	0.329252i	$0.106797\pi$
$618$	4.02327	−	6.96852i	0.161840	−	0.280315i
$619$	−12.2752	+	21.2613i	−0.493384	+	0.854565i	−0.999971	−	0.00762323i	$-0.997573\pi$
$619$	−12.2752	+	21.2613i	−0.493384	+	0.854565i	0.506587	+	0.862189i	$0.330907\pi$
$620$	6.39746			0.256928
$621$	31.8840			1.27946
$622$	21.8634			0.876643
$623$	23.6147	−	40.9018i	0.946101	−	1.63870i
$624$	4.00080	−	6.92959i	0.160160	−	0.277406i
$625$	15.3036	+	26.5065i	0.612142	+	1.06026i
$626$	−13.2225	−	22.9020i	−0.528476	−	0.915348i
$627$	−15.1775			−0.606132
$628$	15.3460	+	26.5800i	0.612371	+	1.06066i
$629$	−1.54024	+	2.66778i	−0.0614136	+	0.106371i
$630$	19.3443	+	33.5054i	0.770697	+	1.33489i
$631$	23.0300			0.916810			0.458405	−	0.888743i	$-0.348421\pi$
$631$	23.0300			0.916810			0.458405	+	0.888743i	$0.348421\pi$
$632$	−1.17629	+	2.03739i	−0.0467903	+	0.0810432i
$633$	−13.0304	+	22.5693i	−0.517911	+	0.897047i
$634$	7.48056	+	12.9567i	0.297091	+	0.514577i
$635$	−12.3656			−0.490716
$636$	−12.2135	+	21.1544i	−0.484298	+	0.838828i
$637$	21.6904			0.859406
$638$	−70.1279			−2.77639
$639$	2.50644	−	4.34128i	0.0991533	−	0.171739i
$640$	8.02341	+	13.8970i	0.317153	+	0.549326i
$641$	−13.8262	−	23.9477i	−0.546102	−	0.945876i	−0.998537	−	0.0540787i	$-0.982778\pi$
$641$	−13.8262	−	23.9477i	−0.546102	−	0.945876i	0.452435	−	0.891797i	$-0.350556\pi$
$642$	17.1081	+	29.6321i	0.675202	+	1.16948i
$643$	19.3351	−	33.4894i	0.762503	−	1.32069i	−0.179054	−	0.983839i	$-0.557304\pi$
$643$	19.3351	−	33.4894i	0.762503	−	1.32069i	0.941557	−	0.336855i	$-0.109363\pi$
$644$	28.9428	+	50.1305i	1.14051	+	1.97542i
$645$	13.9397	−	24.1442i	0.548875	−	0.950679i
$646$	−30.8359			−1.21322
$647$	−3.32728	−	5.76301i	−0.130809	−	0.226567i	0.793180	−	0.608987i	$-0.208424\pi$
$647$	−3.32728	−	5.76301i	−0.130809	−	0.226567i	−0.923989	+	0.382420i	$0.875091\pi$
$648$	−0.225868	−	0.391214i	−0.00887292	−	0.0153683i
$649$	17.9431	+	31.0783i	0.704327	+	1.21993i
$650$	−8.25181			−0.323663
$651$	2.33305	+	4.04095i	0.0914393	+	0.158377i
$652$	−47.5664			−1.86284
$653$	−2.29964			−0.0899917			−0.0449959	−	0.998987i	$-0.514327\pi$
$653$	−2.29964			−0.0899917			−0.0449959	+	0.998987i	$0.514327\pi$
$654$	19.5143	+	14.3930i	0.763071	+	0.562811i
$655$	53.6579			2.09659
$656$	14.4900			0.565739
$657$	−0.450247	−	0.779850i	−0.0175658	−	0.0304248i
$658$	−56.0442			−2.18483
$659$	14.1582	+	24.5228i	0.551526	+	0.955271i	0.998165	+	0.0605567i	$0.0192876\pi$
$659$	14.1582	+	24.5228i	0.551526	+	0.955271i	−0.446639	+	0.894714i	$0.647379\pi$
$660$	−12.8303	−	22.2227i	−0.499417	−	0.865016i
$661$	13.5602	+	23.4870i	0.527432	+	0.913540i	0.999489	+	0.0319714i	$0.0101785\pi$
$661$	13.5602	+	23.4870i	0.527432	+	0.913540i	−0.472056	+	0.881568i	$0.656488\pi$
$662$	7.99708			0.310815
$663$	−5.22144	+	9.04380i	−0.202784	+	0.351232i
$664$	−5.48824	−	9.50591i	−0.212985	−	0.368901i
$665$	19.0342	−	32.9682i	0.738114	−	1.27845i
$666$	−1.40634	−	2.43586i	−0.0544947	−	0.0943877i
$667$	−26.8723	−	46.5441i	−1.04050	−	1.80219i
$668$	11.5043	+	19.9261i	0.445116	+	0.770964i
$669$	11.0361	−	19.1151i	0.426681	−	0.739033i
$670$	5.31033			0.205156
$671$	−20.8277			−0.804044
$672$	−18.1085	+	31.3648i	−0.698551	+	1.20993i
$673$	−9.28262			−0.357819			−0.178909	−	0.983866i	$-0.557257\pi$
$673$	−9.28262			−0.357819			−0.178909	+	0.983866i	$0.557257\pi$
$674$	10.1944	+	17.6572i	0.392673	+	0.680129i
$675$	4.49398	−	7.78381i	0.172974	−	0.299599i
$676$	9.04006	−	15.6578i	0.347695	−	0.602225i
$677$	−14.0312			−0.539263			−0.269631	−	0.962964i	$-0.586902\pi$
$677$	−14.0312			−0.539263			−0.269631	+	0.962964i	$0.586902\pi$
$678$	8.29734	+	14.3714i	0.318657	+	0.551931i
$679$	33.1211	−	57.3675i	1.27107	−	2.20156i
$680$	−4.13570	−	7.16325i	−0.158597	−	0.274698i
$681$	15.2030			0.582579
$682$	4.08695	+	7.07880i	0.156497	+	0.271061i
$683$	13.4178	+	23.2404i	0.513419	+	0.889267i	0.999879	+	0.0155646i	$0.00495457\pi$
$683$	13.4178	+	23.2404i	0.513419	+	0.889267i	−0.486460	+	0.873703i	$0.661712\pi$
$684$	7.64528	−	13.2420i	0.292325	−	0.506321i
$685$	15.2412	−	26.3986i	0.582337	−	1.00864i
$686$	−19.7814			−0.755256
$687$	−23.5963			−0.900253
$688$	−30.1149			−1.14812
$689$	−10.7493	+	18.6183i	−0.409516	+	0.709302i
$690$	18.1056	−	31.3598i	0.689269	−	1.19385i
$691$	−21.4596	+	37.1691i	−0.816361	+	1.41398i	0.0919857	+	0.995760i	$0.470679\pi$
$691$	−21.4596	+	37.1691i	−0.816361	+	1.41398i	−0.908347	+	0.418218i	$0.862655\pi$
$692$	−14.4860			−0.550675
$693$	−13.4227	+	23.2488i	−0.509887	+	0.883150i
$694$	26.5353	+	45.9606i	1.00727	+	1.74464i
$695$	2.71075			0.102825
$696$	−3.90736	+	6.76774i	−0.148108	+	0.256531i
$697$	−18.9109			−0.716300
$698$	−24.4066	+	42.2734i	−0.923802	+	1.60007i
$699$	−10.7765			−0.407603
$700$	16.3178			0.616753
$701$	8.14657	−	14.1103i	0.307692	−	0.532937i	−0.670165	−	0.742212i	$-0.733777\pi$
$701$	8.14657	−	14.1103i	0.307692	−	0.532937i	0.977857	+	0.209274i	$0.0671102\pi$
$702$	−12.8588	−	22.2721i	−0.485325	−	0.840608i
$703$	−1.38380	+	2.39681i	−0.0521909	+	0.0903973i
$704$	−20.0616	+	34.7477i	−0.756100	+	1.30960i
$705$	9.52002	+	16.4892i	0.358545	+	0.621018i
$706$	−33.5907	−	58.1807i	−1.26420	−	2.18966i
$707$	30.8833	+	53.4914i	1.16148	+	2.01175i
$708$	25.2052			0.947268
$709$	−29.8993			−1.12289			−0.561446	−	0.827514i	$-0.689755\pi$
$709$	−29.8993			−1.12289			−0.561446	+	0.827514i	$0.689755\pi$
$710$	−7.67781	−	13.2984i	−0.288143	−	0.499079i
$711$	−2.63511	−	4.56414i	−0.0988242	−	0.171169i
$712$	−4.60977	−	7.98436i	−0.172758	−	0.299226i
$713$	−3.13214	+	5.42503i	−0.117300	+	0.203169i
$714$	19.0124	−	32.9304i	0.711520	−	1.23239i
$715$	−11.2921	−	19.5585i	−0.422300	−	0.731446i
$716$	−11.0523	+	19.1431i	−0.413043	+	0.715411i
$717$	24.9799			0.932890
$718$	16.4489			0.613868
$719$	−5.55788	+	9.62653i	−0.207274	+	0.359009i	−0.950855	−	0.309637i	$-0.899792\pi$
$719$	−5.55788	+	9.62653i	−0.207274	+	0.359009i	0.743581	+	0.668646i	$0.233126\pi$
$720$	−14.1978			−0.529119
$721$	−7.00213	+	12.1280i	−0.260773	+	0.451672i
$722$	12.0474			0.448357
$723$	−7.35398	−	12.7375i	−0.273498	−	0.473712i
$724$	2.07924	−	3.60135i	0.0772743	−	0.133843i
$725$	−15.1504			−0.562671
$726$	3.61896	−	6.26822i	0.134312	−	0.232636i
$727$	−5.10311	+	8.83884i	−0.189264	+	0.327815i	−0.945005	−	0.327056i	$-0.893943\pi$
$727$	−5.10311	+	8.83884i	−0.189264	+	0.327815i	0.755741	+	0.654870i	$0.227277\pi$
$728$	3.70390	−	6.41534i	0.137276	−	0.237768i
$729$	18.6383			0.690306
$730$	−2.75842			−0.102094
$731$	39.3029			1.45367
$732$	−7.31432	+	12.6688i	−0.270345	+	0.468252i
$733$	6.28904	−	10.8929i	0.232291	−	0.402340i	−0.726191	−	0.687493i	$-0.758711\pi$
$733$	6.28904	−	10.8929i	0.232291	−	0.402340i	0.958482	+	0.285153i	$0.0920445\pi$
$734$	−14.3477	−	24.8509i	−0.529582	−	0.917263i
$735$	13.4160	+	23.2371i	0.494855	+	0.857114i
$736$	−48.6218			−1.79222
$737$	1.84238	+	3.19109i	0.0678648	+	0.117545i
$738$	8.63343	−	14.9535i	0.317801	−	0.550447i
$739$	−6.76483	−	11.7170i	−0.248848	−	0.431018i	0.714358	−	0.699780i	$-0.246719\pi$
$739$	−6.76483	−	11.7170i	−0.248848	−	0.431018i	−0.963207	+	0.268762i	$0.913385\pi$
$740$	−4.67915			−0.172009
$741$	−4.69108	+	8.12519i	−0.172331	+	0.298486i
$742$	39.1405	−	67.7933i	1.43689	−	2.48877i
$743$	−5.26802	−	9.12448i	−0.193265	−	0.334745i	0.753065	−	0.657946i	$-0.228574\pi$
$743$	−5.26802	−	9.12448i	−0.193265	−	0.334745i	−0.946330	+	0.323201i	$0.895241\pi$
$744$	0.910858			0.0333937
$745$	−3.06528	+	5.30921i	−0.112303	+	0.194515i
$746$	−61.0783			−2.23623
$747$	24.5893			0.899676
$748$	18.0874	−	31.3284i	0.661343	−	1.14548i
$749$	−29.7750	−	51.5718i	−1.08795	−	1.88439i
$750$	9.92346	+	17.1879i	0.362354	+	0.627615i
$751$	−7.55556	−	13.0866i	−0.275706	−	0.477537i	0.694607	−	0.719390i	$-0.255578\pi$
$751$	−7.55556	−	13.0866i	−0.275706	−	0.477537i	−0.970313	+	0.241852i	$0.922245\pi$
$752$	10.2834	−	17.8113i	0.374997	−	0.649513i
$753$	5.49204	+	9.51250i	0.200141	+	0.346655i
$754$	−21.6752	+	37.5426i	−0.789364	+	1.36722i
$755$	−28.0887			−1.02225
$756$	25.4280	+	44.0426i	0.924808	+	1.60181i
$757$	18.9182	+	32.7674i	0.687595	+	1.19095i	0.972614	+	0.232428i	$0.0746670\pi$
$757$	18.9182	+	32.7674i	0.687595	+	1.19095i	−0.285018	+	0.958522i	$0.592000\pi$
$758$	1.41338	+	2.44804i	0.0513363	+	0.0889170i
$759$	25.1264			0.912030
$760$	−3.71563	−	6.43565i	−0.134780	−	0.233446i
$761$	6.73869			0.244277			0.122139	−	0.992513i	$-0.461025\pi$
$761$	6.73869			0.244277			0.122139	+	0.992513i	$0.461025\pi$
$762$	−11.0969			−0.401998
$763$	−33.9628	−	25.0497i	−1.22954	−	0.906859i
$764$	15.0139			0.543185
$765$	18.5295			0.669934
$766$	−3.12234	−	5.40806i	−0.112815	−	0.195401i
$767$	22.1834			0.800997
$768$	−4.65482	−	8.06238i	−0.167966	−	0.290926i
$769$	17.2947	+	29.9553i	0.623663	+	1.08022i	0.988798	+	0.149262i	$0.0476897\pi$
$769$	17.2947	+	29.9553i	0.623663	+	1.08022i	−0.365134	+	0.930955i	$0.618977\pi$
$770$	41.1169	+	71.2166i	1.48175	+	2.56647i
$771$	1.07846			0.0388398
$772$	−30.0429	+	52.0359i	−1.08127	+	1.87281i
$773$	4.95417	+	8.58088i	0.178189	+	0.308633i	0.941260	−	0.337682i	$-0.109643\pi$
$773$	4.95417	+	8.58088i	0.178189	+	0.308633i	−0.763071	+	0.646315i	$0.776309\pi$
$774$	−17.9431	+	31.0783i	−0.644950	+	1.11709i
$775$	0.882940	+	1.52930i	0.0317161	+	0.0549340i
$776$	−6.46551	−	11.1986i	−0.232098	−	0.402006i
$777$	−1.70641	−	2.95558i	−0.0612170	−	0.106031i
$778$	15.8115	−	27.3863i	0.566869	−	0.981846i
$779$	−16.9900			−0.608731
$780$	−15.8624			−0.567963
$781$	5.32751	−	9.22752i	0.190633	−	0.330186i
$782$	51.0487			1.82550
$783$	−23.6089	−	40.8918i	−0.843713	−	1.46135i
$784$	14.4917	−	25.1004i	0.517561	−	0.896443i
$785$	−16.7077	+	28.9386i	−0.596323	+	1.03286i
$786$	48.1524			1.71754
$787$	8.47090	+	14.6720i	0.301955	+	0.523001i	0.976579	−	0.215160i	$-0.0690274\pi$
$787$	8.47090	+	14.6720i	0.301955	+	0.523001i	−0.674624	+	0.738162i	$0.735694\pi$
$788$	12.0916	−	20.9432i	0.430744	−	0.746071i
$789$	6.65142	+	11.5206i	0.236797	+	0.410144i
$790$	−16.1439			−0.574373
$791$	−14.4407	−	25.0121i	−0.513453	−	0.889327i
$792$	2.62022	+	4.53836i	0.0931055	+	0.161264i
$793$	−6.43744	+	11.1500i	−0.228600	+	0.395947i
$794$	−9.04307	+	15.6630i	−0.320926	+	0.555861i
$795$	−26.5946			−0.943213
$796$	9.63507			0.341506
$797$	−41.9783			−1.48695			−0.743473	−	0.668766i	$-0.766823\pi$
$797$	−41.9783			−1.48695			−0.743473	+	0.668766i	$0.766823\pi$
$798$	17.0812	−	29.5856i	0.604669	−	1.04732i
$799$	−13.4208	+	23.2456i	−0.474795	+	0.822369i
$800$	−6.85315	+	11.8700i	−0.242296	+	0.419668i
$801$	20.6535			0.729754
$802$	15.7055	−	27.2026i	0.554579	−	0.960559i
$803$	−0.957011	−	1.65759i	−0.0337722	−	0.0584951i
$804$	2.58804			0.0912732
$805$	−31.5111	+	54.5788i	−1.11062	+	1.92365i
$806$	5.05279			0.177977
$807$	−0.0312536	+	0.0541327i	−0.00110018	+	0.00190556i
$808$	12.0573			0.424175
$809$	−22.1692			−0.779428			−0.389714	−	0.920936i	$-0.627426\pi$
$809$	−22.1692			−0.779428			−0.389714	+	0.920936i	$0.627426\pi$
$810$	1.54995	−	2.68459i	0.0544597	−	0.0943269i
$811$	0.417167	+	0.722555i	0.0146487	+	0.0253723i	0.873257	−	0.487260i	$-0.162004\pi$
$811$	0.417167	+	0.722555i	0.0146487	+	0.0253723i	−0.858608	+	0.512633i	$0.828670\pi$
$812$	42.8622	−	74.2395i	1.50417	−	2.60530i
$813$	−5.08088	+	8.80034i	−0.178194	+	0.308642i
$814$	−2.98922	−	5.17749i	−0.104772	−	0.181471i
$815$	−25.8936	−	44.8490i	−0.907013	−	1.57099i
$816$	6.97705	+	12.0846i	0.244246	+	0.423046i
$817$	35.3108			1.23537
$818$	−11.1787			−0.390856
$819$	8.29741	+	14.3715i	0.289935	+	0.502182i
$820$	−14.3624	−	24.8765i	−0.501558	−	0.868725i
$821$	26.1016	+	45.2094i	0.910954	+	1.57782i	0.812720	+	0.582655i	$0.197986\pi$
$821$	26.1016	+	45.2094i	0.910954	+	1.57782i	0.0982341	+	0.995163i	$0.468681\pi$
$822$	13.6774	−	23.6900i	0.477055	−	0.826284i
$823$	27.2396	−	47.1804i	0.949513	−	1.64461i	0.203062	−	0.979166i	$-0.434911\pi$
$823$	27.2396	−	47.1804i	0.949513	−	1.64461i	0.746452	−	0.665440i	$-0.231756\pi$
$824$	1.36687	+	2.36749i	0.0476172	+	0.0824754i
$825$	3.54152	−	6.13409i	0.123300	−	0.213562i
$826$	−80.7746			−2.81051
$827$	17.5084			0.608826			0.304413	−	0.952540i	$-0.401540\pi$
$827$	17.5084			0.608826			0.304413	+	0.952540i	$0.401540\pi$
$828$	−12.6568	+	21.9221i	−0.439852	+	0.761847i
$829$	−13.7540			−0.477695			−0.238847	−	0.971057i	$-0.576770\pi$
$829$	−13.7540			−0.477695			−0.238847	+	0.971057i	$0.576770\pi$
$830$	37.6614	−	65.2315i	1.30725	−	2.26422i
$831$	7.12358			0.247114
$832$	12.4013	+	21.4797i	0.429938	+	0.744674i
$833$	−18.9131	+	32.7585i	−0.655301	+	1.13501i
$834$	2.43262			0.0842348
$835$	−12.5252	+	21.6943i	−0.433452	+	0.750761i
$836$	16.2502	−	28.1462i	0.562026	−	0.973458i
$837$	−2.75178	+	4.76622i	−0.0951153	+	0.164745i
$838$	40.5889			1.40212
$839$	5.63795			0.194644			0.0973218	−	0.995253i	$-0.468972\pi$
$839$	5.63795			0.194644			0.0973218	+	0.995253i	$0.468972\pi$
$840$	9.16373			0.316179
$841$	−25.2958	+	43.8136i	−0.872269	+	1.51081i
$842$	5.17941	−	8.97099i	0.178494	−	0.309161i
$843$	12.7040	+	22.0039i	0.437548	+	0.757855i
$844$	−27.9027	−	48.3288i	−0.960449	−	1.66355i
$845$	19.6845			0.677167
$846$	−12.2541	−	21.2247i	−0.421305	−	0.729721i
$847$	−6.29845	+	10.9092i	−0.216417	+	0.374846i
$848$	14.3635	+	24.8784i	0.493246	+	0.854327i
$849$	−25.4708			−0.874155
$850$	7.19522	−	12.4625i	0.246794	−	0.427460i
$851$	2.29087	−	3.96791i	0.0785301	−	0.136018i
$852$	−3.74186	−	6.48109i	−0.128194	−	0.222038i
$853$	45.2880			1.55063			0.775315	−	0.631575i	$-0.217591\pi$
$853$	45.2880			1.55063			0.775315	+	0.631575i	$0.217591\pi$
$854$	23.4401	−	40.5994i	0.802103	−	1.38928i
$855$	16.6474			0.569328
$856$	−11.6246			−0.397321
$857$	18.6387	−	32.2831i	0.636685	−	1.10277i	−0.349470	−	0.936947i	$-0.613638\pi$
$857$	18.6387	−	32.2831i	0.636685	−	1.10277i	0.986155	−	0.165823i	$-0.0530282\pi$
$858$	−10.1335	−	17.5517i	−0.345952	−	0.599206i
$859$	−1.58938	−	2.75289i	−0.0542289	−	0.0939273i	0.837637	−	0.546228i	$-0.183937\pi$
$859$	−1.58938	−	2.75289i	−0.0542289	−	0.0939273i	−0.891866	+	0.452301i	$0.850603\pi$
$860$	29.8498	+	51.7014i	1.01787	+	1.76300i
$861$	10.4755	−	18.1441i	0.357004	−	0.618348i
$862$	−10.7822	−	18.6754i	−0.367244	−	0.636085i
$863$	12.6057	−	21.8337i	0.429103	−	0.743229i	−0.567690	−	0.823242i	$-0.692163\pi$
$863$	12.6057	−	21.8337i	0.429103	−	0.743229i	0.996794	+	0.0800133i	$0.0254963\pi$
$864$	−42.7172			−1.45327
$865$	−7.88570	−	13.6584i	−0.268122	−	0.464401i
$866$	−7.47768	−	12.9517i	−0.254102	−	0.440117i
$867$	0.330232	+	0.571978i	0.0112153	+	0.0194254i
$868$	−9.99176			−0.339143
$869$	−5.60099	−	9.70119i	−0.190000	−	0.329090i
$870$	−53.6261			−1.81810
$871$	2.27777			0.0771793
$872$	−7.54968	+	3.29664i	−0.255664	+	0.111638i
$873$	28.9678			0.980413
$874$	45.8635			1.55136
$875$	−17.2708	−	29.9140i	−0.583861	−	1.01128i
$876$	−1.34434			−0.0454211
$877$	−17.2970	−	29.9593i	−0.584078	−	1.01165i	−0.994990	−	0.0999774i	$-0.968123\pi$
$877$	−17.2970	−	29.9593i	−0.584078	−	1.01165i	0.410912	−	0.911675i	$-0.365210\pi$
$878$	−21.9094	−	37.9482i	−0.739406	−	1.28069i
$879$	−4.92336	−	8.52751i	−0.166061	−	0.287626i
$880$	−30.1777			−1.01729
$881$	6.32640	−	10.9577i	0.213142	−	0.369173i	−0.739554	−	0.673097i	$-0.764964\pi$
$881$	6.32640	−	10.9577i	0.213142	−	0.369173i	0.952696	+	0.303924i	$0.0982970\pi$
$882$	−17.2689	−	29.9107i	−0.581475	−	1.00714i
$883$	−4.99050	+	8.64380i	−0.167944	+	0.290887i	−0.937697	−	0.347455i	$-0.887046\pi$
$883$	−4.99050	+	8.64380i	−0.167944	+	0.290887i	0.769753	+	0.638342i	$0.220379\pi$
$884$	−11.1810	−	19.3660i	−0.376057	−	0.651349i
$885$	13.7209	+	23.7653i	0.461222	+	0.798861i
$886$	−8.99728	−	15.5837i	−0.302269	−	0.523546i
$887$	−21.2721	+	36.8443i	−0.714246	+	1.23711i	0.249004	+	0.968502i	$0.419897\pi$
$887$	−21.2721	+	36.8443i	−0.714246	+	1.23711i	−0.963250	+	0.268607i	$0.913437\pi$
$888$	−0.666208			−0.0223565
$889$	19.3131			0.647740
$890$	31.6332	−	54.7903i	1.06035	−	1.83657i
$891$	2.15097			0.0720602
$892$	23.6322	+	40.9322i	0.791266	+	1.37051i
$893$	−12.0576	+	20.8844i	−0.403494	+	0.698871i
$894$	−2.75077	+	4.76447i	−0.0919995	+	0.159348i
$895$	−24.0660			−0.804437
$896$	−12.5312	−	21.7047i	−0.418639	−	0.725104i
$897$	7.76608	−	13.4512i	0.259302	−	0.449124i
$898$	28.1588	+	48.7725i	0.939671	+	1.62756i
$899$	9.27695			0.309404
$900$	3.56789	+	6.17977i	0.118930	+	0.205992i
$901$	−18.7458	−	32.4688i	−0.624515	−	1.08169i
$902$	18.3506	−	31.7841i	0.611008	−	1.05830i
$903$	−21.7715	+	37.7093i	−0.724509	+	1.25489i
$904$	−5.63789			−0.187513
$905$	4.52748			0.150499
$906$	−25.2067			−0.837436
$907$	1.91404	−	3.31522i	0.0635547	−	0.110080i	−0.832497	−	0.554029i	$-0.813090\pi$
$907$	1.91404	−	3.31522i	0.0635547	−	0.110080i	0.896052	+	0.443949i	$0.146423\pi$
$908$	−16.2775	+	28.1934i	−0.540187	+	0.935632i
$909$	−13.5053	+	23.3919i	−0.447943	+	0.775859i
$910$	50.8338			1.68512
$911$	11.9969	−	20.7793i	0.397476	−	0.688449i	−0.595938	−	0.803031i	$-0.703220\pi$
$911$	11.9969	−	20.7793i	0.397476	−	0.688449i	0.993414	+	0.114582i	$0.0365529\pi$
$912$	6.26837	+	10.8571i	0.207567	+	0.359516i
$913$	52.2653			1.72973
$914$	−40.6480	+	70.4043i	−1.34451	+	2.32877i
$915$	−15.9267			−0.526521
$916$	25.2640	−	43.7585i	0.834746	−	1.44582i
$917$	−83.8046			−2.76747
$918$	44.8494			1.48025
$919$	0.541364	−	0.937670i	0.0178580	−	0.0309309i	−0.856958	−	0.515386i	$-0.827649\pi$
$919$	0.541364	−	0.937670i	0.0178580	−	0.0309309i	0.874816	+	0.484455i	$0.160982\pi$
$920$	6.15122	+	10.6542i	0.202800	+	0.351259i
$921$	3.23113	−	5.59648i	0.106469	−	0.184410i
$922$	−3.40657	+	5.90035i	−0.112189	+	0.194318i
$923$	−3.29326	−	5.70410i	−0.108399	−	0.187753i
$924$	20.0387	+	34.7081i	0.659226	+	1.14181i
$925$	−0.645789	−	1.11854i	−0.0212334	−	0.0367773i
$926$	64.9578			2.13465
$927$	−6.12408			−0.201141
$928$	36.0026	+	62.3584i	1.18184	+	2.04701i
$929$	11.4160	+	19.7731i	0.374546	+	0.648733i	0.990259	−	0.139238i	$-0.0444652\pi$
$929$	11.4160	+	19.7731i	0.374546	+	0.648733i	−0.615713	+	0.787971i	$0.711132\pi$
$930$	3.12525	+	5.41309i	0.102481	+	0.177502i
$931$	−16.9921	+	29.4311i	−0.556892	+	0.964565i
$932$	11.5381	−	19.9846i	0.377944	−	0.654618i
$933$	5.80043	+	10.0466i	0.189897	+	0.328912i
$934$	−17.4355	+	30.1992i	−0.570508	+	0.988150i
$935$	39.3849			1.28802
$936$	3.23944			0.105884
$937$	−9.24301	+	16.0094i	−0.301956	+	0.523003i	−0.976579	−	0.215160i	$-0.930973\pi$
$937$	−9.24301	+	16.0094i	−0.301956	+	0.523003i	0.674623	+	0.738162i	$0.264306\pi$
$938$	−8.29385			−0.270804
$939$	7.01592	−	12.1519i	0.228956	−	0.396563i
$940$	−40.7715			−1.32982
$941$	−5.46623	−	9.46779i	−0.178194	−	0.308641i	0.763068	−	0.646318i	$-0.223692\pi$
$941$	−5.46623	−	9.46779i	−0.178194	−	0.308641i	−0.941262	+	0.337677i	$0.890359\pi$
$942$	−14.9934	+	25.9694i	−0.488512	+	0.846128i
$943$	28.1270			0.915940
$944$	14.8211	−	25.6709i	0.482385	−	0.835516i
$945$	−27.6844	+	47.9508i	−0.900573	+	1.55984i
$946$	−38.1385	+	66.0578i	−1.23999	+	2.14772i
$947$	−17.0231			−0.553177			−0.276588	−	0.960988i	$-0.589204\pi$
$947$	−17.0231			−0.553177			−0.276588	+	0.960988i	$0.589204\pi$
$948$	−7.86788			−0.255537
$949$	−1.18318			−0.0384075
$950$	6.46438	−	11.1966i	0.209732	−	0.363267i
$951$	−3.96923	+	6.87491i	−0.128711	+	0.222934i
$952$	6.45928	+	11.1878i	0.209346	+	0.362599i
$953$	−15.7584	−	27.2943i	−0.510464	−	0.884150i	−0.999926	−	0.0121255i	$-0.996140\pi$
$953$	−15.7584	−	27.2943i	−0.510464	−	0.884150i	0.489462	−	0.872024i	$-0.337193\pi$
$954$	34.2324			1.10831
$955$	8.17310	+	14.1562i	0.264475	+	0.458085i
$956$	−26.7454	+	46.3244i	−0.865008	+	1.49824i
$957$	−18.6052	−	32.2251i	−0.601419	−	1.04169i
$958$	−2.12500			−0.0686558
$959$	−23.8043	+	41.2302i	−0.768680	+	1.33139i
$960$	−15.3409	+	26.5712i	−0.495125	+	0.857582i
$961$	14.9594	+	25.9104i	0.482560	+	0.835818i
$962$	−3.69565			−0.119152
$963$	13.0206	−	22.5524i	0.419584	−	0.726741i
$964$	31.4950			1.01439
$965$	−65.4176			−2.10587
$966$	−28.2780	+	48.9788i	−0.909828	+	1.57587i
$967$	−3.14338	−	5.44449i	−0.101084	−	0.175083i	0.811047	−	0.584980i	$-0.198898\pi$
$967$	−3.14338	−	5.44449i	−0.101084	−	0.175083i	−0.912132	+	0.409897i	$0.865564\pi$
$968$	1.22951	+	2.12957i	0.0395179	+	0.0684470i
$969$	−8.18084	−	14.1696i	−0.262807	−	0.455194i
$970$	44.3676	−	76.8470i	1.42456	−	2.46741i
$971$	2.78730	+	4.82775i	0.0894489	+	0.154930i	0.907278	−	0.420531i	$-0.138156\pi$
$971$	2.78730	+	4.82775i	0.0894489	+	0.154930i	−0.817829	+	0.575461i	$0.804823\pi$
$972$	−18.1167	+	31.3791i	−0.581094	+	1.00648i
$973$	−4.23375			−0.135728
$974$	18.6462	+	32.2962i	0.597464	+	1.03484i
$975$	−2.18923	−	3.79186i	−0.0701115	−	0.121437i
$976$	8.60191	+	14.8989i	0.275340	+	0.476903i
$977$	−39.1705			−1.25317			−0.626587	−	0.779351i	$-0.715549\pi$
$977$	−39.1705			−1.25317			−0.626587	+	0.779351i	$0.715549\pi$
$978$	−23.2368	−	40.2474i	−0.743032	−	1.28697i
$979$	43.8995			1.40303
$980$	−57.4567			−1.83539
$981$	2.06066	−	18.3393i	0.0657919	−	0.585530i
$982$	−23.1607			−0.739087
$983$	−28.4159			−0.906327			−0.453163	−	0.891428i	$-0.649705\pi$
$983$	−28.4159			−0.906327			−0.453163	+	0.891428i	$0.649705\pi$
$984$	−2.04490	−	3.54187i	−0.0651890	−	0.112911i
$985$	26.3290			0.838913
$986$	−37.7997	−	65.4710i	−1.20379	−	2.08502i
$987$	−14.8687	−	25.7533i	−0.473276	−	0.819737i
$988$	−10.0453	−	17.3989i	−0.319583	−	0.553534i
$989$	−58.4570			−1.85882
$990$	−17.9805	+	31.1431i	−0.571458	+	0.989794i
$991$	23.6610	+	40.9820i	0.751616	+	1.30184i	0.947039	+	0.321118i	$0.104059\pi$
$991$	23.6610	+	40.9820i	0.751616	+	1.30184i	−0.195424	+	0.980719i	$0.562608\pi$
$992$	4.19635	−	7.26830i	0.133234	−	0.230769i
$993$	2.12165	+	3.67480i	0.0673285	+	0.116616i
$994$	11.9915	+	20.7698i	0.380346	+	0.658779i
$995$	5.24502	+	9.08464i	0.166278	+	0.288002i
$996$	18.3547	−	31.7912i	0.581590	−	1.00734i
$997$	−52.2199			−1.65382			−0.826911	−	0.562334i	$-0.809904\pi$
$997$	−52.2199			−1.65382			−0.826911	+	0.562334i	$0.809904\pi$
$998$	−52.7740			−1.67053
$999$	2.01267	−	3.48605i	0.0636781	−	0.110294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	109.2.c.a.63.2	yes	14
3.2	odd	2		981.2.h.d.172.6		14
109.45	even	3	inner	109.2.c.a.45.2	✓	14
327.263	odd	6		981.2.h.d.154.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
109.2.c.a.45.2	✓	14	109.45	even	3	inner
109.2.c.a.63.2	yes	14	1.1	even	1	trivial
981.2.h.d.154.6		14	327.263	odd	6
981.2.h.d.172.6		14	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:	\( N \)	\(=\)	\( 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	109.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.09216 q^{2} +(-0.555057 - 0.961388i) q^{3} +2.37715 q^{4} +(1.29404 + 2.24135i) q^{5} +(1.16127 + 2.01138i) q^{6} +(-2.02108 - 3.50062i) q^{7} -0.789063 q^{8} +(0.883822 - 1.53083i) q^{9} +O(q^{10})\)	\(q-2.09216 q^{2} +(-0.555057 - 0.961388i) q^{3} +2.37715 q^{4} +(1.29404 + 2.24135i) q^{5} +(1.16127 + 2.01138i) q^{6} +(-2.02108 - 3.50062i) q^{7} -0.789063 q^{8} +(0.883822 - 1.53083i) q^{9} +(-2.70735 - 4.68927i) q^{10} +(1.87859 - 3.25381i) q^{11} +(-1.31946 - 2.28536i) q^{12} +(-1.16127 - 2.01138i) q^{13} +(4.22844 + 7.32386i) q^{14} +(1.43654 - 2.48816i) q^{15} -3.10345 q^{16} +4.05031 q^{17} +(-1.84910 + 3.20274i) q^{18} +3.63891 q^{19} +(3.07614 + 5.32803i) q^{20} +(-2.24363 + 3.88609i) q^{21} +(-3.93032 + 6.80751i) q^{22} -6.02421 q^{23} +(0.437975 + 0.758595i) q^{24} +(-0.849102 + 1.47069i) q^{25} +(2.42957 + 4.20814i) q^{26} -5.29263 q^{27} +(-4.80442 - 8.32150i) q^{28} +(4.46071 + 7.72617i) q^{29} +(-3.00547 + 5.20563i) q^{30} +(0.519926 - 0.900538i) q^{31} +8.07106 q^{32} -4.17090 q^{33} -8.47392 q^{34} +(5.23074 - 9.05991i) q^{35} +(2.10098 - 3.63900i) q^{36} +(-0.380278 + 0.658660i) q^{37} -7.61320 q^{38} +(-1.28914 + 2.23286i) q^{39} +(-1.02108 - 1.76857i) q^{40} -4.66898 q^{41} +(4.69405 - 8.13033i) q^{42} +9.70367 q^{43} +(4.46569 - 7.73480i) q^{44} +4.57482 q^{45} +12.6036 q^{46} +(-3.31353 + 5.73920i) q^{47} +(1.72260 + 2.98362i) q^{48} +(-4.66954 + 8.08789i) q^{49} +(1.77646 - 3.07692i) q^{50} +(-2.24816 - 3.89392i) q^{51} +(-2.76052 - 4.78136i) q^{52} +(-4.62824 - 8.01636i) q^{53} +11.0731 q^{54} +9.72391 q^{55} +(1.59476 + 2.76221i) q^{56} +(-2.01980 - 3.49840i) q^{57} +(-9.33253 - 16.1644i) q^{58} +(-4.77568 + 8.27171i) q^{59} +(3.41487 - 5.91472i) q^{60} +(-2.77172 - 4.80076i) q^{61} +(-1.08777 + 1.88407i) q^{62} -7.14511 q^{63} -10.6791 q^{64} +(3.00547 - 5.20563i) q^{65} +8.72620 q^{66} +(-0.490362 + 0.849331i) q^{67} +9.62821 q^{68} +(3.34378 + 5.79160i) q^{69} +(-10.9436 + 18.9548i) q^{70} +2.83591 q^{71} +(-0.697391 + 1.20792i) q^{72} +(0.254715 - 0.441180i) q^{73} +(0.795603 - 1.37803i) q^{74} +1.88520 q^{75} +8.65024 q^{76} -15.1871 q^{77} +(2.69710 - 4.67152i) q^{78} +(1.49074 - 2.58204i) q^{79} +(-4.01601 - 6.95593i) q^{80} +(0.286248 + 0.495796i) q^{81} +9.76828 q^{82} +(6.95539 + 12.0471i) q^{83} +(-5.33346 + 9.23782i) q^{84} +(5.24129 + 9.07818i) q^{85} -20.3017 q^{86} +(4.95190 - 8.57694i) q^{87} +(-1.48232 + 2.56746i) q^{88} +(5.84208 + 10.1188i) q^{89} -9.57128 q^{90} +(-4.69405 + 8.13033i) q^{91} -14.3205 q^{92} -1.15435 q^{93} +(6.93245 - 12.0074i) q^{94} +(4.70891 + 8.15608i) q^{95} +(-4.47990 - 7.75942i) q^{96} +(8.19391 + 14.1923i) q^{97} +(9.76945 - 16.9212i) q^{98} +(-3.32068 - 5.75158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 2 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) \) 14 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 2 * q^7 - 12 * q^8 - 6 * q^9	\( 14 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 2 q^{7} - 12 q^{8} - 6 q^{9} - 2 q^{10} + 7 q^{13} - 3 q^{14} + 7 q^{15} + 4 q^{16} + 6 q^{17} - 4 q^{18} + 14 q^{19} + 8 q^{20} - 10 q^{21} - 5 q^{22} - 24 q^{23} - 8 q^{24} + 10 q^{25} - 2 q^{26} - 32 q^{27} - 9 q^{28} - 5 q^{29} + 6 q^{30} + 14 q^{31} - 28 q^{32} - 6 q^{33} - 62 q^{34} + 8 q^{35} + 7 q^{36} + 40 q^{38} - 2 q^{39} + 12 q^{40} + 10 q^{41} + 5 q^{42} + 16 q^{43} - 19 q^{44} + 2 q^{45} + 48 q^{46} - 7 q^{47} + 23 q^{48} + 5 q^{49} - 9 q^{50} + 19 q^{51} + 22 q^{52} - 5 q^{53} + 26 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} - 9 q^{58} + q^{59} + 36 q^{60} - 3 q^{61} - 29 q^{62} + 40 q^{63} - 48 q^{64} - 6 q^{65} + 50 q^{66} + 34 q^{68} - 25 q^{69} - 4 q^{70} - 40 q^{71} - 7 q^{73} + 9 q^{74} + 72 q^{75} - 46 q^{76} - 64 q^{77} + 59 q^{78} - 15 q^{79} - 23 q^{80} + q^{81} + 20 q^{82} + 39 q^{83} - 42 q^{84} - 33 q^{85} - 70 q^{86} + 23 q^{87} + 21 q^{88} + 12 q^{89} - 64 q^{90} - 5 q^{91} - 46 q^{92} - 54 q^{93} + 7 q^{94} + 41 q^{95} - 19 q^{96} - q^{97} + 32 q^{98} + 23 q^{99}+O(q^{100}) \) 14 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 2 * q^7 - 12 * q^8 - 6 * q^9 - 2 * q^10 + 7 * q^13 - 3 * q^14 + 7 * q^15 + 4 * q^16 + 6 * q^17 - 4 * q^18 + 14 * q^19 + 8 * q^20 - 10 * q^21 - 5 * q^22 - 24 * q^23 - 8 * q^24 + 10 * q^25 - 2 * q^26 - 32 * q^27 - 9 * q^28 - 5 * q^29 + 6 * q^30 + 14 * q^31 - 28 * q^32 - 6 * q^33 - 62 * q^34 + 8 * q^35 + 7 * q^36 + 40 * q^38 - 2 * q^39 + 12 * q^40 + 10 * q^41 + 5 * q^42 + 16 * q^43 - 19 * q^44 + 2 * q^45 + 48 * q^46 - 7 * q^47 + 23 * q^48 + 5 * q^49 - 9 * q^50 + 19 * q^51 + 22 * q^52 - 5 * q^53 + 26 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 - 9 * q^58 + q^59 + 36 * q^60 - 3 * q^61 - 29 * q^62 + 40 * q^63 - 48 * q^64 - 6 * q^65 + 50 * q^66 + 34 * q^68 - 25 * q^69 - 4 * q^70 - 40 * q^71 - 7 * q^73 + 9 * q^74 + 72 * q^75 - 46 * q^76 - 64 * q^77 + 59 * q^78 - 15 * q^79 - 23 * q^80 + q^81 + 20 * q^82 + 39 * q^83 - 42 * q^84 - 33 * q^85 - 70 * q^86 + 23 * q^87 + 21 * q^88 + 12 * q^89 - 64 * q^90 - 5 * q^91 - 46 * q^92 - 54 * q^93 + 7 * q^94 + 41 * q^95 - 19 * q^96 - q^97 + 32 * q^98 + 23 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more