LMFDB - Embedded newform 588.3.g.e.295.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,3,Mod(295,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("588.295");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	588.g (of order $2$, degree $1$, 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:	$16.0218395444$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 8 x^{10} - 15 x^{9} + 37 x^{8} - 14 x^{7} - 38 x^{6} + 112 x^{5} + 67 x^{4} + \cdots + 4 $ x^12 - 3x^11 + 8x^10 - 15x^9 + 37x^8 - 14x^7 - 38x^6 + 112x^5 + 67x^4 - 105x^3 + 187x^2 - 52*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{18}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			295.1
Root			$-0.774016 - 2.30803i$ of defining polynomial
Character	$\chi$	$=$	588.295
Dual form			588.3.g.e.295.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.84208 - 0.778937i) q^{2} -1.73205i q^{3} +(2.78651 + 2.86973i) q^{4} +4.44722 q^{5} +(-1.34916 + 3.19058i) q^{6} +(-2.89764 - 7.45679i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-1.84208 - 0.778937i) q^{2} -1.73205i q^{3} +(2.78651 + 2.86973i) q^{4} +4.44722 q^{5} +(-1.34916 + 3.19058i) q^{6} +(-2.89764 - 7.45679i) q^{8} -3.00000 q^{9} +(-8.19213 - 3.46410i) q^{10} -6.89185i q^{11} +(4.97051 - 4.82638i) q^{12} +6.99560 q^{13} -7.70281i q^{15} +(-0.470674 + 15.9931i) q^{16} -29.7259 q^{17} +(5.52624 + 2.33681i) q^{18} +0.384966i q^{19} +(12.3922 + 12.7623i) q^{20} +(-5.36832 + 12.6953i) q^{22} -27.7180i q^{23} +(-12.9155 + 5.01887i) q^{24} -5.22226 q^{25} +(-12.8865 - 5.44913i) q^{26} +5.19615i q^{27} +31.2510 q^{29} +(-6.00000 + 14.1892i) q^{30} -57.5924i q^{31} +(13.3246 - 29.0939i) q^{32} -11.9370 q^{33} +(54.7575 + 23.1546i) q^{34} +(-8.35954 - 8.60918i) q^{36} +23.6955 q^{37} +(0.299864 - 0.709138i) q^{38} -12.1167i q^{39} +(-12.8865 - 33.1619i) q^{40} +40.9079 q^{41} +35.0746i q^{43} +(19.7777 - 19.2042i) q^{44} -13.3417 q^{45} +(-21.5906 + 51.0588i) q^{46} -26.9429i q^{47} +(27.7008 + 0.815231i) q^{48} +(9.61982 + 4.06781i) q^{50} +51.4868i q^{51} +(19.4933 + 20.0755i) q^{52} -22.8065 q^{53} +(4.04748 - 9.57173i) q^{54} -30.6496i q^{55} +0.666781 q^{57} +(-57.5669 - 24.3426i) q^{58} -108.257i q^{59} +(22.1050 - 21.4640i) q^{60} -59.8405 q^{61} +(-44.8609 + 106.090i) q^{62} +(-47.2073 + 43.2142i) q^{64} +31.1110 q^{65} +(21.9890 + 9.29820i) q^{66} +85.5547i q^{67} +(-82.8317 - 85.3053i) q^{68} -48.0090 q^{69} -94.9245i q^{71} +(8.69293 + 22.3704i) q^{72} -84.8360 q^{73} +(-43.6491 - 18.4573i) q^{74} +9.04522i q^{75} +(-1.10475 + 1.07271i) q^{76} +(-9.43817 + 22.3200i) q^{78} -31.1124i q^{79} +(-2.09319 + 71.1247i) q^{80} +9.00000 q^{81} +(-75.3556 - 31.8647i) q^{82} -137.509i q^{83} -132.198 q^{85} +(27.3209 - 64.6101i) q^{86} -54.1283i q^{87} +(-51.3911 + 19.9701i) q^{88} +5.54117 q^{89} +(24.5764 + 10.3923i) q^{90} +(79.5431 - 77.2366i) q^{92} -99.7530 q^{93} +(-20.9868 + 49.6309i) q^{94} +1.71203i q^{95} +(-50.3921 - 23.0789i) q^{96} -152.194 q^{97} +20.6756i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 10 q^{4} - 10 q^{8} - 36 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + 10 * q^4 - 10 * q^8 - 36 * q^9	$ 12 q + 2 q^{2} + 10 q^{4} - 10 q^{8} - 36 q^{9} + 66 q^{16} - 6 q^{18} + 32 q^{22} - 60 q^{25} - 8 q^{29} - 72 q^{30} + 182 q^{32} - 30 q^{36} - 104 q^{37} + 240 q^{44} - 160 q^{46} + 94 q^{50} + 104 q^{53} - 356 q^{58} - 24 q^{60} - 302 q^{64} + 384 q^{65} + 30 q^{72} - 580 q^{74} + 168 q^{78} + 108 q^{81} - 432 q^{85} - 240 q^{86} + 160 q^{88} + 384 q^{92} - 48 q^{93}+O(q^{100}) $ 12 * q + 2 * q^2 + 10 * q^4 - 10 * q^8 - 36 * q^9 + 66 * q^16 - 6 * q^18 + 32 * q^22 - 60 * q^25 - 8 * q^29 - 72 * q^30 + 182 * q^32 - 30 * q^36 - 104 * q^37 + 240 * q^44 - 160 * q^46 + 94 * q^50 + 104 * q^53 - 356 * q^58 - 24 * q^60 - 302 * q^64 + 384 * q^65 + 30 * q^72 - 580 * q^74 + 168 * q^78 + 108 * q^81 - 432 * q^85 - 240 * q^86 + 160 * q^88 + 384 * q^92 - 48 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.84208	−	0.778937i	−0.921040	−	0.389468i
$2$	−1.84208	−	0.778937i	−0.921040	−	0.389468i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	2.78651	+	2.86973i	0.696629	+	0.717432i
$5$	4.44722			0.889443			0.444722	−	0.895669i	$-0.353303\pi$
$5$	4.44722			0.889443			0.444722	+	0.895669i	$0.353303\pi$
$6$	−1.34916	+	3.19058i	−0.224860	+	0.531763i
$7$		0			0
$7$		0			0
$8$	−2.89764	−	7.45679i	−0.362206	−	0.932098i
$9$	−3.00000			−0.333333
$10$	−8.19213	−	3.46410i	−0.819213	−	0.346410i
$11$		−	6.89185i		−	0.626532i	−0.949665	−	0.313266i	$-0.898577\pi$
$11$		−	6.89185i		−	0.626532i	0.949665	−	0.313266i	$-0.101423\pi$
$12$	4.97051	−	4.82638i	0.414210	−	0.402199i
$13$	6.99560			0.538123			0.269062	−	0.963123i	$-0.413286\pi$
$13$	6.99560			0.538123			0.269062	+	0.963123i	$0.413286\pi$
$14$		0			0
$15$		−	7.70281i		−	0.513520i
$16$	−0.470674	+	15.9931i	−0.0294171	+	0.999567i
$17$	−29.7259			−1.74858			−0.874291	−	0.485401i	$-0.838673\pi$
$17$	−29.7259			−1.74858			−0.874291	+	0.485401i	$0.838673\pi$
$18$	5.52624	+	2.33681i	0.307013	+	0.129823i
$19$			0.384966i			0.0202614i	0.999949	+	0.0101307i	$0.00322475\pi$
$19$			0.384966i			0.0202614i	−0.999949	+	0.0101307i	$0.996775\pi$
$20$	12.3922	+	12.7623i	0.619612	+	0.638115i
$21$		0			0
$22$	−5.36832	+	12.6953i	−0.244014	+	0.577061i
$23$		−	27.7180i		−	1.20513i	−0.798070	−	0.602565i	$-0.794145\pi$
$23$		−	27.7180i		−	1.20513i	0.798070	−	0.602565i	$-0.205855\pi$
$24$	−12.9155	+	5.01887i	−0.538147	+	0.209119i
$25$	−5.22226			−0.208890
$26$	−12.8865	−	5.44913i	−0.495633	−	0.209582i
$27$			5.19615i			0.192450i
$28$		0			0
$29$	31.2510			1.07762			0.538811	−	0.842427i	$-0.318874\pi$
$29$	31.2510			1.07762			0.538811	+	0.842427i	$0.318874\pi$
$30$	−6.00000	+	14.1892i	−0.200000	+	0.472973i
$31$		−	57.5924i		−	1.85782i	−0.370305	−	0.928910i	$-0.620747\pi$
$31$		−	57.5924i		−	1.85782i	0.370305	−	0.928910i	$-0.379253\pi$
$32$	13.3246	−	29.0939i	0.416394	−	0.909184i
$33$	−11.9370			−0.361728
$34$	54.7575	+	23.1546i	1.61051	+	0.681018i
$35$		0			0
$36$	−8.35954	−	8.60918i	−0.232210	−	0.239144i
$37$	23.6955			0.640420			0.320210	−	0.947347i	$-0.396247\pi$
$37$	23.6955			0.640420			0.320210	+	0.947347i	$0.396247\pi$
$38$	0.299864	−	0.709138i	0.00789117	−	0.0186615i
$39$		−	12.1167i		−	0.310686i
$40$	−12.8865	−	33.1619i	−0.322161	−	0.829049i
$41$	40.9079			0.997753			0.498877	−	0.866673i	$-0.333746\pi$
$41$	40.9079			0.997753			0.498877	+	0.866673i	$0.333746\pi$
$42$		0			0
$43$			35.0746i			0.815687i	0.913052	+	0.407844i	$0.133719\pi$
$43$			35.0746i			0.815687i	−0.913052	+	0.407844i	$0.866281\pi$
$44$	19.7777	−	19.2042i	0.449494	−	0.436460i
$45$	−13.3417			−0.296481
$46$	−21.5906	+	51.0588i	−0.469360	+	1.10997i
$47$		−	26.9429i		−	0.573253i	−0.958042	−	0.286626i	$-0.907466\pi$
$47$		−	26.9429i		−	0.573253i	0.958042	−	0.286626i	$-0.0925338\pi$
$48$	27.7008	+	0.815231i	0.577100	+	0.0169840i
$49$		0			0
$50$	9.61982	+	4.06781i	0.192396	+	0.0813562i
$51$			51.4868i			1.00954i
$52$	19.4933	+	20.0755i	0.374872	+	0.386067i
$53$	−22.8065			−0.430311			−0.215156	−	0.976580i	$-0.569026\pi$
$53$	−22.8065			−0.430311			−0.215156	+	0.976580i	$0.569026\pi$
$54$	4.04748	−	9.57173i	0.0749532	−	0.177254i
$55$		−	30.6496i		−	0.557265i
$56$		0			0
$57$	0.666781			0.0116979
$58$	−57.5669	−	24.3426i	−0.992532	−	0.419699i
$59$		−	108.257i		−	1.83486i	−0.397898	−	0.917430i	$-0.630260\pi$
$59$		−	108.257i		−	1.83486i	0.397898	−	0.917430i	$-0.369740\pi$
$60$	22.1050	−	21.4640i	0.368416	−	0.357733i
$61$	−59.8405			−0.980992			−0.490496	−	0.871443i	$-0.663184\pi$
$61$	−59.8405			−0.980992			−0.490496	+	0.871443i	$0.663184\pi$
$62$	−44.8609	+	106.090i	−0.723563	+	1.71113i
$63$		0			0
$64$	−47.2073	+	43.2142i	−0.737614	+	0.675222i
$65$	31.1110			0.478630
$66$	21.9890	+	9.29820i	0.333166	+	0.140882i
$67$			85.5547i			1.27694i	0.769648	+	0.638468i	$0.220432\pi$
$67$			85.5547i			1.27694i	−0.769648	+	0.638468i	$0.779568\pi$
$68$	−82.8317	−	85.3053i	−1.21811	−	1.25449i
$69$	−48.0090			−0.695783
$70$		0			0
$71$		−	94.9245i		−	1.33696i	−0.743728	−	0.668482i	$-0.766944\pi$
$71$		−	94.9245i		−	1.33696i	0.743728	−	0.668482i	$-0.233056\pi$
$72$	8.69293	+	22.3704i	0.120735	+	0.310699i
$73$	−84.8360			−1.16214			−0.581069	−	0.813855i	$-0.697365\pi$
$73$	−84.8360			−1.16214			−0.581069	+	0.813855i	$0.697365\pi$
$74$	−43.6491	−	18.4573i	−0.589852	−	0.249423i
$75$			9.04522i			0.120603i
$76$	−1.10475	+	1.07271i	−0.0145362	+	0.0141147i
$77$		0			0
$78$	−9.43817	+	22.3200i	−0.121002	+	0.286154i
$79$		−	31.1124i		−	0.393828i	−0.980421	−	0.196914i	$-0.936908\pi$
$79$		−	31.1124i		−	0.393828i	0.980421	−	0.196914i	$-0.0630920\pi$
$80$	−2.09319	+	71.1247i	−0.0261649	+	0.889058i
$81$	9.00000			0.111111
$82$	−75.3556	−	31.8647i	−0.918970	−	0.388593i
$83$		−	137.509i		−	1.65674i	−0.560182	−	0.828370i	$-0.689269\pi$
$83$		−	137.509i		−	1.65674i	0.560182	−	0.828370i	$-0.310731\pi$
$84$		0			0
$85$	−132.198			−1.55527
$86$	27.3209	−	64.6101i	0.317685	−	0.751281i
$87$		−	54.1283i		−	0.622165i
$88$	−51.3911	+	19.9701i	−0.583989	+	0.226933i
$89$	5.54117			0.0622603			0.0311301	−	0.999515i	$-0.490089\pi$
$89$	5.54117			0.0622603			0.0311301	+	0.999515i	$0.490089\pi$
$90$	24.5764	+	10.3923i	0.273071	+	0.115470i
$91$		0			0
$92$	79.5431	−	77.2366i	0.864599	−	0.839529i
$93$	−99.7530			−1.07261
$94$	−20.9868	+	49.6309i	−0.223264	+	0.527989i
$95$			1.71203i			0.0180214i
$96$	−50.3921	−	23.0789i	−0.524918	−	0.240405i
$97$	−152.194			−1.56901			−0.784504	−	0.620123i	$-0.787082\pi$
$97$	−152.194			−1.56901			−0.784504	+	0.620123i	$0.787082\pi$
$98$		0			0
$99$			20.6756i			0.208844i
$100$	−14.5519	−	14.9865i	−0.145519	−	0.149865i
$101$	−70.1953			−0.695003			−0.347501	−	0.937680i	$-0.612970\pi$
$101$	−70.1953			−0.695003			−0.347501	+	0.937680i	$0.612970\pi$
$102$	40.1050	−	94.8427i	0.393186	−	0.929831i
$103$			29.8796i			0.290094i	0.989425	+	0.145047i	$0.0463333\pi$
$103$			29.8796i			0.290094i	−0.989425	+	0.145047i	$0.953667\pi$
$104$	−20.2708	−	52.1647i	−0.194911	−	0.501584i
$105$		0			0
$106$	42.0114	+	17.7648i	0.396334	+	0.167593i
$107$			57.0450i			0.533131i	0.963817	+	0.266565i	$0.0858889\pi$
$107$			57.0450i			0.533131i	−0.963817	+	0.266565i	$0.914111\pi$
$108$	−14.9115	+	14.4792i	−0.138070	+	0.134066i
$109$	130.560			1.19779			0.598897	−	0.800826i	$-0.295606\pi$
$109$	130.560			1.19779			0.598897	+	0.800826i	$0.295606\pi$
$110$	−23.8741	+	56.4589i	−0.217037	+	0.513263i
$111$		−	41.0419i		−	0.369747i
$112$		0			0
$113$	130.724			1.15685			0.578425	−	0.815736i	$-0.303668\pi$
$113$	130.724			1.15685			0.578425	+	0.815736i	$0.303668\pi$
$114$	−1.22826	−	0.519380i	−0.0107742	−	0.00455597i
$115$		−	123.268i		−	1.07190i
$116$	87.0814	+	89.6819i	0.750702	+	0.773120i
$117$	−20.9868			−0.179374
$118$	−84.3251	+	199.417i	−0.714620	+	1.68998i
$119$		0			0
$120$	−57.4382	+	22.3200i	−0.478651	+	0.186000i
$121$	73.5024			0.607458
$122$	110.231	+	46.6120i	0.903533	+	0.382066i
$123$		−	70.8545i		−	0.576053i
$124$	165.275	−	160.482i	1.33286	−	1.29421i
$125$	−134.405			−1.07524
$126$		0			0
$127$			237.060i			1.86661i	0.359084	+	0.933305i	$0.383089\pi$
$127$			237.060i			1.86661i	−0.359084	+	0.933305i	$0.616911\pi$
$128$	120.621	−	42.8325i	0.942350	−	0.334629i
$129$	60.7509			0.470937
$130$	−57.3089	−	24.2335i	−0.440837	−	0.186411i
$131$			135.200i			1.03206i	0.856571	+	0.516029i	$0.172590\pi$
$131$			135.200i			1.03206i	−0.856571	+	0.516029i	$0.827410\pi$
$132$	−33.2627	−	34.2560i	−0.251990	−	0.259516i
$133$		0			0
$134$	66.6417	−	157.599i	0.497326	−	1.17611i
$135$			23.1084i			0.171173i
$136$	86.1351	+	221.660i	0.633346	+	1.62985i
$137$	−108.058			−0.788741			−0.394370	−	0.918952i	$-0.629037\pi$
$137$	−108.058			−0.788741			−0.394370	+	0.918952i	$0.629037\pi$
$138$	88.4364	+	37.3960i	0.640843	+	0.270985i
$139$		−	149.826i		−	1.07788i	−0.842343	−	0.538942i	$-0.818824\pi$
$139$		−	149.826i		−	1.07788i	0.842343	−	0.538942i	$-0.181176\pi$
$140$		0			0
$141$	−46.6664			−0.330968
$142$	−73.9402	+	174.858i	−0.520706	+	1.23140i
$143$		−	48.2127i		−	0.337151i
$144$	1.41202	−	47.9792i	0.00980570	−	0.333189i
$145$	138.980			0.958483
$146$	156.275	+	66.0819i	1.07037	+	0.452616i
$147$		0			0
$148$	66.0279	+	67.9997i	0.446135	+	0.459458i
$149$	−90.3627			−0.606461			−0.303230	−	0.952917i	$-0.598065\pi$
$149$	−90.3627			−0.606461			−0.303230	+	0.952917i	$0.598065\pi$
$150$	7.04566	−	16.6620i	0.0469710	−	0.111080i
$151$		−	271.596i		−	1.79865i	−0.437282	−	0.899325i	$-0.644059\pi$
$151$		−	271.596i		−	1.79865i	0.437282	−	0.899325i	$-0.355941\pi$
$152$	2.87061	−	1.11550i	0.0188856	−	0.00733878i
$153$	89.1777			0.582861
$154$		0			0
$155$		−	256.126i		−	1.65243i
$156$	34.7717	−	33.7635i	0.222896	−	0.216432i
$157$	72.0109			0.458668			0.229334	−	0.973348i	$-0.426345\pi$
$157$	72.0109			0.458668			0.229334	+	0.973348i	$0.426345\pi$
$158$	−24.2346	+	57.3115i	−0.153384	+	0.362731i
$159$			39.5020i			0.248440i
$160$	59.2575	−	129.387i	0.370359	−	0.808668i
$161$		0			0
$162$	−16.5787	−	7.01043i	−0.102338	−	0.0432743i
$163$		−	71.9254i		−	0.441260i	−0.975358	−	0.220630i	$-0.929189\pi$
$163$		−	71.9254i		−	0.441260i	0.975358	−	0.220630i	$-0.0708114\pi$
$164$	113.990	+	117.394i	0.695064	+	0.715820i
$165$	−53.0866			−0.321737
$166$	−107.111	+	253.303i	−0.645248	+	1.52592i
$167$		−	16.6502i		−	0.0997017i	−0.998757	−	0.0498508i	$-0.984125\pi$
$167$		−	16.6502i		−	0.0997017i	0.998757	−	0.0498508i	$-0.0158746\pi$
$168$		0			0
$169$	−120.062			−0.710423
$170$	243.518	+	102.974i	1.43246	+	0.605727i
$171$		−	1.15490i		−	0.00675379i
$172$	−100.654	+	97.7358i	−0.585200	+	0.568231i
$173$	133.855			0.773729			0.386864	−	0.922137i	$-0.373558\pi$
$173$	133.855			0.773729			0.386864	+	0.922137i	$0.373558\pi$
$174$	−42.1626	+	99.7087i	−0.242314	+	0.573039i
$175$		0			0
$176$	110.222	+	3.24381i	0.626261	+	0.0184308i
$177$	−187.506			−1.05936
$178$	−10.2073	−	4.31622i	−0.0573442	−	0.0242484i
$179$			244.253i			1.36454i	0.731100	+	0.682270i	$0.239007\pi$
$179$			244.253i			1.36454i	−0.731100	+	0.682270i	$0.760993\pi$
$180$	−37.1767	−	38.2869i	−0.206537	−	0.212705i
$181$	207.248			1.14502			0.572509	−	0.819898i	$-0.305970\pi$
$181$	207.248			1.14502			0.572509	+	0.819898i	$0.305970\pi$
$182$		0			0
$183$			103.647i			0.566376i
$184$	−206.687	+	80.3169i	−1.12330	+	0.436505i
$185$	105.379			0.569617
$186$	183.753	+	77.7013i	0.987920	+	0.417749i
$187$			204.867i			1.09554i
$188$	77.3187	−	75.0767i	0.411270	−	0.399344i
$189$		0			0
$190$	1.33356	−	3.15369i	0.00701875	−	0.0165984i
$191$		−	193.570i		−	1.01346i	−0.862105	−	0.506729i	$-0.830855\pi$
$191$		−	193.570i		−	1.01346i	0.862105	−	0.506729i	$-0.169145\pi$
$192$	74.8492	+	81.7655i	0.389840	+	0.425862i
$193$	210.453			1.09043			0.545215	−	0.838296i	$-0.316448\pi$
$193$	210.453			1.09043			0.545215	+	0.838296i	$0.316448\pi$
$194$	280.353	+	118.549i	1.44512	+	0.611079i
$195$		−	53.8858i		−	0.276337i
$196$		0			0
$197$	134.477			0.682624			0.341312	−	0.939950i	$-0.389129\pi$
$197$	134.477			0.682624			0.341312	+	0.939950i	$0.389129\pi$
$198$	16.1050	−	38.0860i	0.0813382	−	0.192354i
$199$			150.881i			0.758194i	0.925357	+	0.379097i	$0.123765\pi$
$199$			150.881i			0.758194i	−0.925357	+	0.379097i	$0.876235\pi$
$200$	15.1323	+	38.9413i	0.0756613	+	0.194706i
$201$	148.185			0.737239
$202$	129.305	+	54.6777i	0.640125	+	0.270682i
$203$		0			0
$204$	−147.753	+	143.469i	−0.724280	+	0.703278i
$205$	181.926			0.887445
$206$	23.2743	−	55.0407i	0.112982	−	0.267188i
$207$			83.1540i			0.401710i
$208$	−3.29265	+	111.881i	−0.0158300	+	0.537890i
$209$	2.65313			0.0126944
$210$		0			0
$211$		−	62.4617i		−	0.296027i	−0.988985	−	0.148014i	$-0.952712\pi$
$211$		−	62.4617i		−	0.296027i	0.988985	−	0.148014i	$-0.0472879\pi$
$212$	−63.5506	−	65.4484i	−0.299767	−	0.308719i
$213$	−164.414			−0.771897
$214$	44.4345	−	105.081i	0.207638	−	0.491035i
$215$			155.984i			0.725508i
$216$	38.7466	−	15.0566i	0.179382	−	0.0697065i
$217$		0			0
$218$	−240.501	−	101.698i	−1.10322	−	0.466503i
$219$			146.940i			0.670960i
$220$	87.9559	−	85.4055i	0.399800	−	0.388207i
$221$	−207.951			−0.940953
$222$	−31.9690	+	75.6024i	−0.144005	+	0.340551i
$223$			42.3392i			0.189862i	0.995484	+	0.0949308i	$0.0302630\pi$
$223$			42.3392i			0.189862i	−0.995484	+	0.0949308i	$0.969737\pi$
$224$		0			0
$225$	15.6668			0.0696301
$226$	−240.804	−	101.826i	−1.06550	−	0.450556i
$227$			56.3948i			0.248435i	0.992255	+	0.124218i	$0.0396421\pi$
$227$			56.3948i			0.248435i	−0.992255	+	0.124218i	$0.960358\pi$
$228$	1.85800	+	1.91348i	0.00814910	+	0.00839246i
$229$	322.510			1.40834			0.704171	−	0.710030i	$-0.251319\pi$
$229$	322.510			1.40834			0.704171	+	0.710030i	$0.251319\pi$
$230$	−96.0180	+	227.069i	−0.417470	+	0.987258i
$231$		0			0
$232$	−90.5543	−	233.032i	−0.390320	−	1.00445i
$233$	146.164			0.627315			0.313658	−	0.949536i	$-0.398446\pi$
$233$	146.164			0.627315			0.313658	+	0.949536i	$0.398446\pi$
$234$	38.6594	+	16.3474i	0.165211	+	0.0698607i
$235$		−	119.821i		−	0.509876i
$236$	310.667	−	301.659i	1.31639	−	1.27822i
$237$	−53.8883			−0.227377
$238$		0			0
$239$			183.332i			0.767078i	0.923525	+	0.383539i	$0.125295\pi$
$239$			183.332i			0.767078i	−0.923525	+	0.383539i	$0.874705\pi$
$240$	123.192	+	3.62551i	0.513298	+	0.0151063i
$241$	49.1022			0.203743			0.101872	−	0.994798i	$-0.467517\pi$
$241$	49.1022			0.203743			0.101872	+	0.994798i	$0.467517\pi$
$242$	−135.397	−	57.2537i	−0.559493	−	0.236586i
$243$		−	15.5885i		−	0.0641500i
$244$	−166.746	−	171.726i	−0.683387	−	0.703795i
$245$		0			0
$246$	−55.1912	+	130.520i	−0.224355	+	0.530568i
$247$			2.69307i			0.0109031i
$248$	−429.455	+	166.882i	−1.73167	+	0.672913i
$249$	−238.173			−0.956519
$250$	247.585	+	104.693i	0.990338	+	0.418772i
$251$			141.843i			0.565112i	0.959251	+	0.282556i	$0.0911822\pi$
$251$			141.843i			0.565112i	−0.959251	+	0.282556i	$0.908818\pi$
$252$		0			0
$253$	−191.028			−0.755053
$254$	184.654	−	436.683i	0.726986	−	1.71922i
$255$			228.973i			0.897933i
$256$	−255.557	−	15.0550i	−0.998269	−	0.0588088i
$257$	−133.128			−0.518009			−0.259004	−	0.965876i	$-0.583394\pi$
$257$	−133.128			−0.518009			−0.259004	+	0.965876i	$0.583394\pi$
$258$	−111.908	−	47.3211i	−0.433752	−	0.183415i
$259$		0			0
$260$	86.6911	+	89.2800i	0.333427	+	0.343385i
$261$	−93.7530			−0.359207
$262$	105.312	−	249.048i	0.401954	−	0.950566i
$263$			185.044i			0.703588i	0.936077	+	0.351794i	$0.114428\pi$
$263$			185.044i			0.703588i	−0.936077	+	0.351794i	$0.885572\pi$
$264$	34.5893	+	89.0119i	0.131020	+	0.337166i
$265$	−101.425			−0.382737
$266$		0			0
$267$		−	9.59758i		−	0.0359460i
$268$	−245.519	+	238.399i	−0.916115	+	0.889550i
$269$	233.882			0.869449			0.434724	−	0.900564i	$-0.356846\pi$
$269$	233.882			0.869449			0.434724	+	0.900564i	$0.356846\pi$
$270$	18.0000	−	42.5675i	0.0666667	−	0.157658i
$271$		−	156.127i		−	0.576115i	−0.957613	−	0.288057i	$-0.906991\pi$
$271$		−	156.127i		−	0.576115i	0.957613	−	0.288057i	$-0.0930094\pi$
$272$	13.9912	−	475.409i	0.0514382	−	1.74783i
$273$		0			0
$274$	199.051	+	84.1700i	0.726462	+	0.307190i
$275$			35.9910i			0.130877i
$276$	−133.778	−	137.773i	−0.484702	−	0.499177i
$277$	433.704			1.56572			0.782860	−	0.622198i	$-0.213760\pi$
$277$	433.704			1.56572			0.782860	+	0.622198i	$0.213760\pi$
$278$	−116.705	+	275.991i	−0.419802	+	0.992774i
$279$			172.777i			0.619274i
$280$		0			0
$281$	364.288			1.29640			0.648200	−	0.761470i	$-0.275522\pi$
$281$	364.288			1.29640			0.648200	+	0.761470i	$0.275522\pi$
$282$	85.9633	+	36.3502i	0.304834	+	0.128901i
$283$		−	31.7470i		−	0.112180i	−0.998426	−	0.0560902i	$-0.982137\pi$
$283$		−	31.7470i		−	0.112180i	0.998426	−	0.0560902i	$-0.0178634\pi$
$284$	272.407	−	264.509i	0.959181	−	0.931368i
$285$	2.96532			0.0104046
$286$	−37.5546	+	88.8115i	−0.131310	+	0.310530i
$287$		0			0
$288$	−39.9738	+	87.2817i	−0.138798	+	0.303061i
$289$	594.630			2.05754
$290$	−256.012	−	108.257i	−0.882801	−	0.373299i
$291$			263.607i			0.905867i
$292$	−236.397	−	243.456i	−0.809578	−	0.833754i
$293$	−178.116			−0.607905			−0.303953	−	0.952687i	$-0.598306\pi$
$293$	−178.116			−0.607905			−0.303953	+	0.952687i	$0.598306\pi$
$294$		0			0
$295$		−	481.441i		−	1.63200i
$296$	−68.6612	−	176.693i	−0.231964	−	0.596934i
$297$	35.8111			0.120576
$298$	166.455	+	70.3868i	0.558575	+	0.236197i
$299$		−	193.904i		−	0.648509i
$300$	−25.9573	+	25.2046i	−0.0865244	+	0.0840155i
$301$		0			0
$302$	−211.556	+	500.301i	−0.700517	+	1.65663i
$303$			121.582i			0.401260i
$304$	−6.15679	−	0.181193i	−0.0202526	−	0.000596031i
$305$	−266.124			−0.872537
$306$	−164.272	−	69.4638i	−0.536838	−	0.227006i
$307$			23.6786i			0.0771289i	0.999256	+	0.0385645i	$0.0122785\pi$
$307$			23.6786i			0.0771289i	−0.999256	+	0.0385645i	$0.987722\pi$
$308$		0			0
$309$	51.7530			0.167486
$310$	−199.506	+	471.805i	−0.643568	+	1.52195i
$311$			443.605i			1.42638i	0.700969	+	0.713192i	$0.252751\pi$
$311$			443.605i			1.42638i	−0.700969	+	0.713192i	$0.747249\pi$
$312$	−90.3519	+	35.1100i	−0.289589	+	0.112532i
$313$	−605.911			−1.93582			−0.967909	−	0.251300i	$-0.919142\pi$
$313$	−605.911			−1.93582			−0.967909	+	0.251300i	$0.919142\pi$
$314$	−132.650	−	56.0920i	−0.422452	−	0.178637i
$315$		0			0
$316$	89.2842	−	86.6952i	0.282545	−	0.274352i
$317$	−301.424			−0.950863			−0.475431	−	0.879753i	$-0.657708\pi$
$317$	−301.424			−0.950863			−0.475431	+	0.879753i	$0.657708\pi$
$318$	30.7696	−	72.7658i	0.0967597	−	0.228823i
$319$		−	215.377i		−	0.675164i
$320$	−209.941	+	192.183i	−0.656066	+	0.600572i
$321$	98.8049			0.307803
$322$		0			0
$323$		−	11.4435i		−	0.0354287i
$324$	25.0786	+	25.8275i	0.0774032	+	0.0797147i
$325$	−36.5329			−0.112409
$326$	−56.0254	+	132.492i	−0.171857	+	0.406418i
$327$		−	226.136i		−	0.691547i
$328$	−118.537	−	305.041i	−0.361392	−	0.930004i
$329$		0			0
$330$	97.7897	+	41.3511i	0.296333	+	0.125306i
$331$			174.770i			0.528007i	0.964522	+	0.264004i	$0.0850431\pi$
$331$			174.770i			0.528007i	−0.964522	+	0.264004i	$0.914957\pi$
$332$	394.614	−	383.172i	1.18860	−	1.15413i
$333$	−71.0866			−0.213473
$334$	−12.9694	+	30.6710i	−0.0388307	+	0.0918292i
$335$			380.480i			1.13576i
$336$		0			0
$337$	178.164			0.528678			0.264339	−	0.964430i	$-0.414846\pi$
$337$	178.164			0.528678			0.264339	+	0.964430i	$0.414846\pi$
$338$	221.163	+	93.5204i	0.654328	+	0.276688i
$339$		−	226.421i		−	0.667907i
$340$	−368.370	−	379.371i	−1.08344	−	1.11580i
$341$	−396.919			−1.16398
$342$	−0.899593	+	2.12742i	−0.00263039	+	0.00622051i
$343$		0			0
$344$	261.543	−	101.634i	0.760301	−	0.295447i
$345$	−213.506			−0.618859
$346$	−246.572	−	104.265i	−0.712635	−	0.301343i
$347$		−	257.761i		−	0.742827i	−0.928468	−	0.371413i	$-0.878873\pi$
$347$		−	257.761i		−	0.742827i	0.928468	−	0.371413i	$-0.121127\pi$
$348$	155.334	−	150.829i	0.446361	−	0.433418i
$349$	359.032			1.02874			0.514372	−	0.857567i	$-0.328025\pi$
$349$	359.032			1.02874			0.514372	+	0.857567i	$0.328025\pi$
$350$		0			0
$351$			36.3502i			0.103562i
$352$	−200.511	−	91.8313i	−0.569633	−	0.260884i
$353$	−184.563			−0.522840			−0.261420	−	0.965225i	$-0.584191\pi$
$353$	−184.563			−0.522840			−0.261420	+	0.965225i	$0.584191\pi$
$354$	345.401	+	146.055i	0.975709	+	0.412586i
$355$		−	422.150i		−	1.18915i
$356$	15.4405	+	15.9016i	0.0433723	+	0.0446675i
$357$		0			0
$358$	190.257	−	449.933i	0.531445	−	1.25680i
$359$		−	44.1431i		−	0.122961i	−0.998108	−	0.0614807i	$-0.980418\pi$
$359$		−	44.1431i		−	0.122961i	0.998108	−	0.0614807i	$-0.0195823\pi$
$360$	38.6594	+	99.4858i	0.107387	+	0.276350i
$361$	360.852			0.999589
$362$	−381.768	−	161.433i	−1.05461	−	0.445948i
$363$		−	127.310i		−	0.350716i
$364$		0			0
$365$	−377.284			−1.03366
$366$	80.7343	−	190.926i	0.220586	−	0.521655i
$367$			688.602i			1.87630i	0.346231	+	0.938149i	$0.387461\pi$
$367$			688.602i			1.87630i	−0.346231	+	0.938149i	$0.612539\pi$
$368$	443.296	+	13.0461i	1.20461	+	0.0354515i
$369$	−122.724			−0.332584
$370$	−194.117	−	82.0837i	−0.524640	−	0.221848i
$371$		0			0
$372$	−277.963	−	286.264i	−0.747213	−	0.769527i
$373$	92.6177			0.248305			0.124152	−	0.992263i	$-0.460379\pi$
$373$	92.6177			0.248305			0.124152	+	0.992263i	$0.460379\pi$
$374$	159.578	−	377.381i	0.426680	−	1.00904i
$375$			232.796i			0.620790i
$376$	−200.907	+	78.0709i	−0.534328	+	0.207635i
$377$	218.620			0.579893
$378$		0			0
$379$			557.187i			1.47015i	0.677986	+	0.735075i	$0.262853\pi$
$379$			557.187i			1.47015i	−0.677986	+	0.735075i	$0.737147\pi$
$380$	−4.91305	+	4.77059i	−0.0129291	+	0.0125542i
$381$	410.599			1.07769
$382$	−150.779	+	356.572i	−0.394710	+	0.933435i
$383$		−	621.913i		−	1.62379i	−0.583801	−	0.811897i	$-0.698435\pi$
$383$		−	621.913i		−	1.62379i	0.583801	−	0.811897i	$-0.301565\pi$
$384$	−74.1881	−	208.921i	−0.193198	−	0.544066i
$385$		0			0
$386$	−387.671	−	163.930i	−1.00433	−	0.424688i
$387$		−	105.224i		−	0.271896i
$388$	−424.090	−	436.755i	−1.09302	−	1.12566i
$389$	11.6948			0.0300639			0.0150319	−	0.999887i	$-0.495215\pi$
$389$	11.6948			0.0300639			0.0150319	+	0.999887i	$0.495215\pi$
$390$	−41.9736	+	99.2619i	−0.107625	+	0.254518i
$391$			823.943i			2.10727i
$392$		0			0
$393$	234.173			0.595859
$394$	−247.717	−	104.749i	−0.628724	−	0.265861i
$395$		−	138.364i		−	0.350288i
$396$	−59.3332	+	57.6127i	−0.149831	+	0.145487i
$397$	−294.784			−0.742528			−0.371264	−	0.928527i	$-0.621076\pi$
$397$	−294.784			−0.742528			−0.371264	+	0.928527i	$0.621076\pi$
$398$	117.526	−	277.934i	0.295293	−	0.698327i
$399$		0			0
$400$	2.45798	−	83.5200i	0.00614495	−	0.208800i
$401$	−365.737			−0.912062			−0.456031	−	0.889964i	$-0.650729\pi$
$401$	−365.737			−0.912062			−0.456031	+	0.889964i	$0.650729\pi$
$402$	−272.969	−	115.427i	−0.679027	−	0.287132i
$403$		−	402.894i		−	0.999736i
$404$	−195.600	−	201.441i	−0.484159	−	0.498617i
$405$	40.0250			0.0988270
$406$		0			0
$407$		−	163.306i		−	0.401244i
$408$	383.926	−	149.190i	0.940995	−	0.365663i
$409$	422.359			1.03266			0.516332	−	0.856389i	$-0.327297\pi$
$409$	422.359			1.03266			0.516332	+	0.856389i	$0.327297\pi$
$410$	−335.123	−	141.709i	−0.817372	−	0.345632i
$411$			187.161i			0.455380i
$412$	−85.7464	+	83.2600i	−0.208122	+	0.202087i
$413$		0			0
$414$	64.7717	−	153.176i	0.156453	−	0.369991i
$415$		−	611.534i		−	1.47358i
$416$	93.2137	−	203.529i	0.224071	−	0.489253i
$417$	−259.506			−0.622317
$418$	−4.88728	−	2.06662i	−0.0116921	−	0.00494407i
$419$		−	5.47390i		−	0.0130642i	−0.999979	−	0.00653210i	$-0.997921\pi$
$419$		−	5.47390i		−	0.0130642i	0.999979	−	0.00653210i	$-0.00207925\pi$
$420$		0			0
$421$	−229.260			−0.544560			−0.272280	−	0.962218i	$-0.587778\pi$
$421$	−229.260			−0.544560			−0.272280	+	0.962218i	$0.587778\pi$
$422$	−48.6537	+	115.059i	−0.115293	+	0.272653i
$423$			80.8286i			0.191084i
$424$	66.0851	+	170.063i	0.155861	+	0.401092i
$425$	155.236			0.365262
$426$	302.864	+	128.068i	0.710948	+	0.300630i
$427$		0			0
$428$	−163.704	+	158.957i	−0.382485	+	0.371394i
$429$	−83.5068			−0.194654
$430$	121.502	−	287.335i	0.282562	−	0.668222i
$431$		−	26.9612i		−	0.0625550i	−0.999511	−	0.0312775i	$-0.990042\pi$
$431$		−	26.9612i		−	0.0625550i	0.999511	−	0.0312775i	$-0.00995756\pi$
$432$	−83.1025	−	2.44569i	−0.192367	−	0.00566132i
$433$	−258.038			−0.595931			−0.297966	−	0.954577i	$-0.596308\pi$
$433$	−258.038			−0.595931			−0.297966	+	0.954577i	$0.596308\pi$
$434$		0			0
$435$		−	240.720i		−	0.553380i
$436$	363.806	+	374.670i	0.834418	+	0.859336i
$437$	10.6705			0.0244176
$438$	114.457	−	270.676i	0.261318	−	0.617981i
$439$		−	359.895i		−	0.819806i	−0.912129	−	0.409903i	$-0.865562\pi$
$439$		−	359.895i		−	0.819806i	0.912129	−	0.409903i	$-0.134438\pi$
$440$	−228.547	+	88.8115i	−0.519426	+	0.201844i
$441$		0			0
$442$	383.062	+	161.980i	0.866655	+	0.366471i
$443$			131.375i			0.296558i	0.988946	+	0.148279i	$0.0473733\pi$
$443$			131.375i			0.296558i	−0.988946	+	0.148279i	$0.952627\pi$
$444$	117.779	−	114.364i	0.265268	−	0.257576i
$445$	24.6428			0.0553770
$446$	32.9795	−	77.9921i	0.0739451	−	0.174870i
$447$			156.513i			0.350140i
$448$		0			0
$449$	−445.571			−0.992363			−0.496182	−	0.868219i	$-0.665265\pi$
$449$	−445.571			−0.992363			−0.496182	+	0.868219i	$0.665265\pi$
$450$	−28.8595	−	12.2034i	−0.0641321	−	0.0271187i
$451$		−	281.931i		−	0.625124i
$452$	364.264	+	375.142i	0.805894	+	0.829960i
$453$	−470.418			−1.03845
$454$	43.9280	−	103.884i	0.0967576	−	0.228819i
$455$		0			0
$456$	−1.93209	−	4.97204i	−0.00423705	−	0.0109036i
$457$	252.897			0.553385			0.276693	−	0.960958i	$-0.410762\pi$
$457$	252.897			0.553385			0.276693	+	0.960958i	$0.410762\pi$
$458$	−594.090	−	251.215i	−1.29714	−	0.548505i
$459$		−	154.460i		−	0.336515i
$460$	353.746	−	343.488i	0.769012	−	0.746713i
$461$	761.919			1.65275			0.826376	−	0.563118i	$-0.190398\pi$
$461$	761.919			1.65275			0.826376	+	0.563118i	$0.190398\pi$
$462$		0			0
$463$			35.7412i			0.0771949i	0.999255	+	0.0385975i	$0.0122890\pi$
$463$			35.7412i			0.0771949i	−0.999255	+	0.0385975i	$0.987711\pi$
$464$	−14.7090	+	499.800i	−0.0317005	+	1.07715i
$465$	−443.623			−0.954029
$466$	−269.246	−	113.853i	−0.577782	−	0.244319i
$467$		−	70.0508i		−	0.150002i	−0.997183	−	0.0750008i	$-0.976104\pi$
$467$		−	70.0508i		−	0.150002i	0.997183	−	0.0750008i	$-0.0238959\pi$
$468$	−58.4800	−	60.2264i	−0.124957	−	0.128689i
$469$		0			0
$470$	−93.3329	+	220.720i	−0.198581	+	0.469616i
$471$		−	124.727i		−	0.264812i
$472$	−807.247	+	313.689i	−1.71027	+	0.664596i
$473$	241.729			0.511054
$474$	99.2665	+	41.9756i	0.209423	+	0.0885561i
$475$		−	2.01039i		−	0.00423241i
$476$		0			0
$477$	68.4195			0.143437
$478$	142.804	−	337.712i	0.298753	−	0.706510i
$479$			476.221i			0.994199i	0.867694	+	0.497100i	$0.165602\pi$
$479$			476.221i			0.994199i	−0.867694	+	0.497100i	$0.834398\pi$
$480$	−224.105	−	102.637i	−0.466885	−	0.213827i
$481$	165.765			0.344625
$482$	−90.4501	−	38.2475i	−0.187656	−	0.0793517i
$483$		0			0
$484$	204.815	+	210.932i	0.423172	+	0.435809i
$485$	−676.839			−1.39554
$486$	−12.1424	+	28.7152i	−0.0249844	+	0.0590847i
$487$			324.563i			0.666454i	0.942847	+	0.333227i	$0.108138\pi$
$487$			324.563i			0.666454i	−0.942847	+	0.333227i	$0.891862\pi$
$488$	173.397	+	446.218i	0.355321	+	0.914381i
$489$	−124.579			−0.254762
$490$		0			0
$491$			836.859i			1.70440i	0.523218	+	0.852199i	$0.324731\pi$
$491$			836.859i			1.70440i	−0.523218	+	0.852199i	$0.675269\pi$
$492$	203.333	−	197.437i	0.413279	−	0.401295i
$493$	−928.965			−1.88431
$494$	2.09773	−	4.96085i	0.00424642	−	0.0100422i
$495$			91.9487i			0.185755i
$496$	921.080	+	27.1072i	1.85702	+	0.0546517i
$497$		0			0
$498$	438.734	+	185.522i	0.880992	+	0.372534i
$499$		−	518.925i		−	1.03993i	−0.854188	−	0.519965i	$-0.825945\pi$
$499$		−	518.925i		−	1.03993i	0.854188	−	0.519965i	$-0.174055\pi$
$500$	−374.521	−	385.706i	−0.749043	−	0.771411i
$501$	−28.8390			−0.0575628
$502$	110.487	−	261.286i	0.220093	−	0.520490i
$503$			438.986i			0.872735i	0.899768	+	0.436368i	$0.143735\pi$
$503$			438.986i			0.872735i	−0.899768	+	0.436368i	$0.856265\pi$
$504$		0			0
$505$	−312.174			−0.618165
$506$	351.890	+	148.799i	0.695434	+	0.294069i
$507$			207.953i			0.410163i
$508$	−680.296	+	660.570i	−1.33917	+	1.30033i
$509$	46.3659			0.0910921			0.0455461	−	0.998962i	$-0.485497\pi$
$509$	46.3659			0.0910921			0.0455461	+	0.998962i	$0.485497\pi$
$510$	178.355	−	421.786i	0.349717	−	0.827032i
$511$		0			0
$512$	459.029	+	226.795i	0.896542	+	0.442960i
$513$	−2.00034			−0.00389930
$514$	245.233	+	103.698i	0.477107	+	0.201748i
$515$			132.881i			0.258022i
$516$	169.283	+	174.339i	0.328068	+	0.337865i
$517$	−185.686			−0.359161
$518$		0			0
$519$		−	231.844i		−	0.446712i
$520$	−90.1485	−	231.988i	−0.173363	−	0.446130i
$521$	−231.334			−0.444019			−0.222010	−	0.975044i	$-0.571262\pi$
$521$	−231.334			−0.444019			−0.222010	+	0.975044i	$0.571262\pi$
$522$	172.701	+	73.0277i	0.330844	+	0.139900i
$523$			451.873i			0.864002i	0.901873	+	0.432001i	$0.142192\pi$
$523$			451.873i			0.864002i	−0.901873	+	0.432001i	$0.857808\pi$
$524$	−387.986	+	376.736i	−0.740431	+	0.718961i
$525$		0			0
$526$	144.137	−	340.865i	0.274026	−	0.648033i
$527$			1711.99i			3.24855i
$528$	5.61845	−	190.910i	0.0106410	−	0.361572i
$529$	−239.288			−0.452340
$530$	186.834	+	79.0040i	0.352516	+	0.149064i
$531$			324.770i			0.611620i
$532$		0			0
$533$	286.175			0.536914
$534$	−7.47591	+	17.6795i	−0.0139998	+	0.0331077i
$535$			253.692i			0.474190i
$536$	637.963	−	247.907i	1.19023	−	0.462513i
$537$	423.058			0.787817
$538$	−430.829	−	182.179i	−0.800797	−	0.338623i
$539$		0			0
$540$	−66.3149	+	64.3919i	−0.122805	+	0.119244i
$541$	854.097			1.57874			0.789369	−	0.613919i	$-0.210408\pi$
$541$	854.097			1.57874			0.789369	+	0.613919i	$0.210408\pi$
$542$	−121.613	+	287.599i	−0.224379	+	0.530625i
$543$		−	358.964i		−	0.661076i
$544$	−396.086	+	864.842i	−0.728100	+	1.58978i
$545$	580.627			1.06537
$546$		0			0
$547$		−	259.614i		−	0.474615i	−0.971435	−	0.237308i	$-0.923735\pi$
$547$		−	259.614i		−	0.474615i	0.971435	−	0.237308i	$-0.0762649\pi$
$548$	−301.104	−	310.096i	−0.549460	−	0.565868i
$549$	179.522			0.326997
$550$	28.0348	−	66.2984i	0.0509723	−	0.120543i
$551$			12.0306i			0.0218341i
$552$	139.113	+	357.993i	0.252016	+	0.648538i
$553$		0			0
$554$	−798.918	−	337.828i	−1.44209	−	0.609798i
$555$		−	182.522i		−	0.328869i
$556$	429.960	−	417.492i	0.773309	−	0.750885i
$557$	−330.363			−0.593111			−0.296555	−	0.955016i	$-0.595838\pi$
$557$	−330.363			−0.593111			−0.296555	+	0.955016i	$0.595838\pi$
$558$	134.583	−	318.270i	0.241188	−	0.570376i
$559$			245.368i			0.438940i
$560$		0			0
$561$	354.839			0.632512
$562$	−671.048	−	283.758i	−1.19404	−	0.504907i
$563$		−	628.643i		−	1.11660i	−0.829641	−	0.558298i	$-0.811455\pi$
$563$		−	628.643i		−	1.11660i	0.829641	−	0.558298i	$-0.188545\pi$
$564$	−130.037	−	133.920i	−0.230562	−	0.237447i
$565$	581.358			1.02895
$566$	−24.7289	+	58.4806i	−0.0436907	+	0.103323i
$567$		0			0
$568$	−707.832	+	275.057i	−1.24618	+	0.484256i
$569$	81.7707			0.143709			0.0718547	−	0.997415i	$-0.477108\pi$
$569$	81.7707			0.143709			0.0718547	+	0.997415i	$0.477108\pi$
$570$	−5.46236	−	2.30980i	−0.00958308	−	0.00405228i
$571$			671.252i			1.17557i	0.809017	+	0.587786i	$0.200000\pi$
$571$			671.252i			1.17557i	−0.809017	+	0.587786i	$0.800000\pi$
$572$	138.357	−	134.345i	0.241883	−	0.234869i
$573$	−335.274			−0.585120
$574$		0			0
$575$			144.751i			0.251740i
$576$	141.622	−	129.643i	0.245871	−	0.225074i
$577$	716.020			1.24094			0.620468	−	0.784232i	$-0.286943\pi$
$577$	716.020			1.24094			0.620468	+	0.784232i	$0.286943\pi$
$578$	−1095.35	−	463.179i	−1.89508	−	0.801348i
$579$		−	364.515i		−	0.629560i
$580$	387.270	+	398.835i	0.667707	+	0.687646i
$581$		0			0
$582$	205.334	−	485.586i	0.352807	−	0.834340i
$583$			157.179i			0.269604i
$584$	245.825	+	632.604i	0.420933	+	1.08323i
$585$	−93.3329			−0.159543
$586$	328.104	+	138.741i	0.559905	+	0.236760i
$587$		−	945.713i		−	1.61109i	−0.592531	−	0.805547i	$-0.701871\pi$
$587$		−	945.713i		−	1.61109i	0.592531	−	0.805547i	$-0.298129\pi$
$588$		0			0
$589$	22.1711			0.0376420
$590$	−375.012	+	886.853i	−0.635614	+	1.50314i
$591$		−	232.921i		−	0.394113i
$592$	−11.1529	+	378.964i	−0.0188393	+	0.640143i
$593$	760.458			1.28239			0.641196	−	0.767377i	$-0.278439\pi$
$593$	760.458			1.28239			0.641196	+	0.767377i	$0.278439\pi$
$594$	−65.9669	−	27.8946i	−0.111055	−	0.0469606i
$595$		0			0
$596$	−251.797	−	259.316i	−0.422478	−	0.435094i
$597$	261.333			0.437744
$598$	−151.039	+	357.187i	−0.252574	+	0.597302i
$599$		−	40.4954i		−	0.0676049i	−0.999429	−	0.0338025i	$-0.989238\pi$
$599$		−	40.4954i		−	0.0676049i	0.999429	−	0.0338025i	$-0.0107617\pi$
$600$	67.4483	−	26.2098i	0.112414	−	0.0436831i
$601$	694.789			1.15605			0.578027	−	0.816017i	$-0.303823\pi$
$601$	694.789			1.15605			0.578027	+	0.816017i	$0.303823\pi$
$602$		0			0
$603$		−	256.664i		−	0.425645i
$604$	779.407	−	756.806i	1.29041	−	1.25299i
$605$	326.881			0.540299
$606$	94.7045	−	223.963i	0.156278	−	0.369576i
$607$			11.3755i			0.0187405i	0.999956	+	0.00937025i	$0.00298269\pi$
$607$			11.3755i			0.0187405i	−0.999956	+	0.00937025i	$0.997017\pi$
$608$	11.2002	+	5.12953i	0.0184213	+	0.00843672i
$609$		0			0
$610$	490.221	+	207.294i	0.803641	+	0.339826i
$611$		−	188.482i		−	0.308481i
$612$	248.495	+	255.916i	0.406038	+	0.418163i
$613$	442.393			0.721685			0.360843	−	0.932627i	$-0.382489\pi$
$613$	442.393			0.721685			0.360843	+	0.932627i	$0.382489\pi$
$614$	18.4441	−	43.6178i	0.0300393	−	0.0710388i
$615$		−	315.105i		−	0.512367i
$616$		0			0
$617$	−725.342			−1.17559			−0.587797	−	0.809008i	$-0.700005\pi$
$617$	−725.342			−1.17559			−0.587797	+	0.809008i	$0.700005\pi$
$618$	−95.3332	−	40.3124i	−0.154261	−	0.0652303i
$619$		−	515.682i		−	0.833089i	−0.909115	−	0.416545i	$-0.863241\pi$
$619$		−	515.682i		−	0.833089i	0.909115	−	0.416545i	$-0.136759\pi$
$620$	735.012	−	713.699i	1.18550	−	1.15113i
$621$	144.027			0.231928
$622$	345.541	−	817.156i	0.555532	−	1.31376i
$623$		0			0
$624$	193.784	+	5.70303i	0.310551	+	0.00913947i
$625$	−467.171			−0.747474
$626$	1116.14	+	471.967i	1.78297	+	0.753940i
$627$		−	4.59536i		−	0.00732912i
$628$	200.660	+	206.652i	0.319522	+	0.329063i
$629$	−704.371			−1.11983
$630$		0			0
$631$			138.190i			0.219001i	0.993987	+	0.109501i	$0.0349252\pi$
$631$			138.190i			0.219001i	−0.993987	+	0.109501i	$0.965075\pi$
$632$	−231.999	+	90.1527i	−0.367086	+	0.142647i
$633$	−108.187			−0.170911
$634$	555.246	+	234.790i	0.875783	+	0.370331i
$635$			1054.26i			1.66024i
$636$	−113.360	+	110.073i	−0.178239	+	0.173071i
$637$		0			0
$638$	−167.765	+	396.742i	−0.262955	+	0.621853i
$639$			284.774i			0.445655i
$640$	536.427	−	190.486i	0.838167	−	0.297634i
$641$	1192.63			1.86058			0.930291	−	0.366822i	$-0.119554\pi$
$641$	1192.63			1.86058			0.930291	+	0.366822i	$0.119554\pi$
$642$	−182.006	−	76.9627i	−0.283499	−	0.119880i
$643$		−	1010.96i		−	1.57226i	−0.618063	−	0.786129i	$-0.712082\pi$
$643$		−	1010.96i		−	1.57226i	0.618063	−	0.786129i	$-0.287918\pi$
$644$		0			0
$645$	270.173			0.418872
$646$	−8.91374	+	21.0798i	−0.0137984	+	0.0326312i
$647$			931.173i			1.43922i	0.694380	+	0.719608i	$0.255679\pi$
$647$			931.173i			1.43922i	−0.694380	+	0.719608i	$0.744321\pi$
$648$	−26.0788	−	67.1111i	−0.0402451	−	0.103566i
$649$	−746.089			−1.14960
$650$	67.2964	+	28.4568i	0.103533	+	0.0437797i
$651$		0			0
$652$	206.406	−	200.421i	0.316574	−	0.307395i
$653$	−368.700			−0.564624			−0.282312	−	0.959323i	$-0.591101\pi$
$653$	−368.700			−0.564624			−0.282312	+	0.959323i	$0.591101\pi$
$654$	−176.145	+	416.560i	−0.269336	+	0.636942i
$655$			601.262i			0.917957i
$656$	−19.2543	+	654.243i	−0.0293510	+	0.997321i
$657$	254.508			0.387379
$658$		0			0
$659$		−	823.325i		−	1.24936i	−0.780883	−	0.624678i	$-0.785230\pi$
$659$		−	823.325i		−	1.24936i	0.780883	−	0.624678i	$-0.214770\pi$
$660$	−147.927	−	152.344i	−0.224131	−	0.230824i
$661$	745.835			1.12834			0.564171	−	0.825658i	$-0.309196\pi$
$661$	745.835			1.12834			0.564171	+	0.825658i	$0.309196\pi$
$662$	136.135	−	321.941i	0.205642	−	0.486316i
$663$			360.181i			0.543259i
$664$	−1025.38	+	398.453i	−1.54424	+	0.600080i
$665$		0			0
$666$	130.947	+	55.3720i	0.196617	+	0.0831411i
$667$		−	866.216i		−	1.29867i
$668$	47.7815	−	46.3960i	0.0715292	−	0.0694550i
$669$	73.3336			0.109617
$670$	296.370	−	700.875i	0.442344	−	1.04608i
$671$			412.412i			0.614623i
$672$		0			0
$673$	748.460			1.11213			0.556063	−	0.831140i	$-0.312311\pi$
$673$	748.460			1.11213			0.556063	+	0.831140i	$0.312311\pi$
$674$	−328.193	−	138.779i	−0.486933	−	0.205903i
$675$		−	27.1357i		−	0.0402010i
$676$	−334.553	−	344.544i	−0.494901	−	0.509680i
$677$	−254.878			−0.376482			−0.188241	−	0.982123i	$-0.560279\pi$
$677$	−254.878			−0.376482			−0.188241	+	0.982123i	$0.560279\pi$
$678$	−176.367	+	417.085i	−0.260129	+	0.615169i
$679$		0			0
$680$	383.062	+	985.769i	0.563326	+	1.44966i
$681$	97.6786			0.143434
$682$	731.156	+	309.175i	1.07208	+	0.453335i
$683$		−	552.718i		−	0.809250i	−0.914483	−	0.404625i	$-0.867402\pi$
$683$		−	552.718i		−	0.809250i	0.914483	−	0.404625i	$-0.132598\pi$
$684$	3.31424	−	3.21814i	0.00484539	−	0.00470489i
$685$	−480.555			−0.701540
$686$		0			0
$687$		−	558.604i		−	0.813107i
$688$	−560.950	−	16.5087i	−0.815334	−	0.0239952i
$689$	−159.545			−0.231560
$690$	393.296	+	166.308i	0.569994	+	0.241026i
$691$			964.387i			1.39564i	0.716274	+	0.697820i	$0.245846\pi$
$691$			964.387i			1.39564i	−0.716274	+	0.697820i	$0.754154\pi$
$692$	372.989	+	384.128i	0.539001	+	0.555098i
$693$		0			0
$694$	−200.779	+	474.816i	−0.289308	+	0.684173i
$695$		−	666.308i		−	0.958717i
$696$	−403.623	+	156.845i	−0.579919	+	0.225352i
$697$	−1216.02			−1.74465
$698$	−661.365	−	279.663i	−0.947514	−	0.400663i
$699$		−	253.164i		−	0.362181i
$700$		0			0
$701$	82.8566			0.118198			0.0590988	−	0.998252i	$-0.481177\pi$
$701$	82.8566			0.118198			0.0590988	+	0.998252i	$0.481177\pi$
$702$	28.3145	−	66.9600i	0.0403341	−	0.0953846i
$703$			9.12198i			0.0129758i
$704$	297.826	+	325.346i	0.423048	+	0.462139i
$705$	−207.536			−0.294377
$706$	339.979	+	143.763i	0.481557	+	0.203630i
$707$		0			0
$708$	−522.488	−	538.091i	−0.737978	−	0.760016i
$709$	342.116			0.482533			0.241266	−	0.970459i	$-0.422437\pi$
$709$	342.116			0.482533			0.241266	+	0.970459i	$0.422437\pi$
$710$	−328.828	+	777.634i	−0.463138	+	1.09526i
$711$			93.3372i			0.131276i
$712$	−16.0563	−	41.3193i	−0.0225510	−	0.0580327i
$713$	−1596.35			−2.23892
$714$		0			0
$715$		−	214.412i		−	0.299877i
$716$	−700.938	+	680.613i	−0.978964	+	0.950577i
$717$	317.540			0.442873
$718$	−34.3847	+	81.3152i	−0.0478896	+	0.113252i
$719$		−	276.644i		−	0.384762i	−0.981320	−	0.192381i	$-0.938379\pi$
$719$		−	276.644i		−	0.384762i	0.981320	−	0.192381i	$-0.0616210\pi$
$720$	6.27956	−	213.374i	0.00872162	−	0.296353i
$721$		0			0
$722$	−664.718	−	281.081i	−0.920662	−	0.389309i
$723$		−	85.0475i		−	0.117631i
$724$	577.500	+	594.746i	0.797652	+	0.821472i
$725$	−163.201			−0.225105
$726$	−99.1663	+	234.515i	−0.136593	+	0.323023i
$727$		−	877.174i		−	1.20657i	−0.797527	−	0.603283i	$-0.793859\pi$
$727$		−	877.174i		−	1.20657i	0.797527	−	0.603283i	$-0.206141\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$	694.987	+	293.881i	0.952038	+	0.402576i
$731$		−	1042.62i		−	1.42630i
$732$	−297.438	+	288.813i	−0.406336	+	0.394554i
$733$	899.396			1.22701			0.613503	−	0.789692i	$-0.289760\pi$
$733$	899.396			1.22701			0.613503	+	0.789692i	$0.289760\pi$
$734$	536.377	−	1268.46i	0.730759	−	1.72815i
$735$		0			0
$736$	−806.425	−	369.332i	−1.09569	−	0.501809i
$737$	589.631			0.800041
$738$	226.067	+	95.5940i	0.306323	+	0.129531i
$739$		−	729.862i		−	0.987635i	−0.869566	−	0.493817i	$-0.835601\pi$
$739$		−	729.862i		−	0.987635i	0.869566	−	0.493817i	$-0.164399\pi$
$740$	293.641	+	302.410i	0.396812	+	0.408662i
$741$	4.66453			0.00629492
$742$		0			0
$743$			677.223i			0.911471i	0.890115	+	0.455736i	$0.150624\pi$
$743$			677.223i			0.911471i	−0.890115	+	0.455736i	$0.849376\pi$
$744$	289.049	+	743.837i	0.388507	+	0.999781i
$745$	−401.862			−0.539413
$746$	−170.609	−	72.1434i	−0.228699	−	0.0967069i
$747$			412.528i			0.552246i
$748$	−587.911	+	570.864i	−0.785978	+	0.763187i
$749$		0			0
$750$	181.334	−	428.829i	0.241778	−	0.571772i
$751$			1266.08i			1.68586i	0.538022	+	0.842931i	$0.319172\pi$
$751$			1266.08i			1.68586i	−0.538022	+	0.842931i	$0.680828\pi$
$752$	430.900	+	12.6813i	0.573005	+	0.0168634i
$753$	245.679			0.326267
$754$	−402.715	−	170.291i	−0.534104	−	0.225850i
$755$		−	1207.85i		−	1.59980i
$756$		0			0
$757$	443.450			0.585799			0.292900	−	0.956143i	$-0.405380\pi$
$757$	443.450			0.585799			0.292900	+	0.956143i	$0.405380\pi$
$758$	434.013	−	1026.38i	0.572577	−	1.35407i
$759$			330.871i			0.435930i
$760$	12.7662	−	4.96085i	0.0167977	−	0.00652743i
$761$	399.651			0.525165			0.262583	−	0.964910i	$-0.415426\pi$
$761$	399.651			0.525165			0.262583	+	0.964910i	$0.415426\pi$
$762$	−756.356	−	319.831i	−0.992594	−	0.419726i
$763$		0			0
$764$	555.494	−	539.387i	0.727087	−	0.706004i
$765$	396.593			0.518422
$766$	−484.431	+	1145.61i	−0.632416	+	1.49558i
$767$		−	757.321i		−	0.987380i
$768$	−26.0761	+	442.638i	−0.0339532	+	0.576351i
$769$	−1095.05			−1.42399			−0.711995	−	0.702184i	$-0.752208\pi$
$769$	−1095.05			−1.42399			−0.711995	+	0.702184i	$0.752208\pi$
$770$		0			0
$771$			230.585i			0.299072i
$772$	586.430	+	603.943i	0.759625	+	0.782309i
$773$	−156.651			−0.202654			−0.101327	−	0.994853i	$-0.532309\pi$
$773$	−156.651			−0.202654			−0.101327	+	0.994853i	$0.532309\pi$
$774$	−81.9626	+	193.830i	−0.105895	+	0.250427i
$775$			300.763i			0.388081i
$776$	441.004	+	1134.88i	0.568304	+	1.46247i
$777$		0			0
$778$	−21.5428	−	9.10955i	−0.0276900	−	0.0117089i
$779$			15.7482i			0.0202159i
$780$	154.637	−	150.153i	0.198253	−	0.192504i
$781$	−654.206			−0.837651
$782$	641.800	−	1517.77i	0.820716	−	1.94088i
$783$			162.385i			0.207388i
$784$		0			0
$785$	320.248			0.407960
$786$	−431.364	−	182.406i	−0.548810	−	0.232068i
$787$		−	968.894i		−	1.23112i	−0.788089	−	0.615561i	$-0.788929\pi$
$787$		−	968.894i		−	1.23112i	0.788089	−	0.615561i	$-0.211071\pi$
$788$	374.722	+	385.912i	0.475536	+	0.489736i
$789$	320.505			0.406217
$790$	−107.777	+	254.877i	−0.136426	+	0.322629i
$791$		0			0
$792$	154.173	−	59.9104i	0.194663	−	0.0756445i
$793$	−418.620			−0.527895
$794$	543.015	+	229.618i	0.683898	+	0.289191i
$795$			175.674i			0.220974i
$796$	−432.986	+	420.431i	−0.543953	+	0.528180i
$797$	−1019.72			−1.27944			−0.639722	−	0.768607i	$-0.720950\pi$
$797$	−1019.72			−1.27944			−0.639722	+	0.768607i	$0.720950\pi$
$798$		0			0
$799$			800.902i			1.00238i
$800$	−69.5846	+	151.936i	−0.0869808	+	0.189920i
$801$	−16.6235			−0.0207534
$802$	673.716	+	284.886i	0.840045	+	0.355219i
$803$			584.677i			0.728116i
$804$	412.920	+	425.251i	0.513582	+	0.528919i
$805$		0			0
$806$	−313.829	+	742.162i	−0.389366	+	0.920797i
$807$		−	405.095i		−	0.501976i
$808$	203.401	+	523.431i	0.251734	+	0.647811i
$809$	−657.474			−0.812700			−0.406350	−	0.913718i	$-0.633199\pi$
$809$	−657.474			−0.812700			−0.406350	+	0.913718i	$0.633199\pi$
$810$	−73.7292	−	31.1769i	−0.0910236	−	0.0384900i
$811$		−	868.536i		−	1.07094i	−0.844553	−	0.535472i	$-0.820134\pi$
$811$		−	868.536i		−	1.07094i	0.844553	−	0.535472i	$-0.179866\pi$
$812$		0			0
$813$	−270.420			−0.332620
$814$	−127.205	+	300.823i	−0.156272	+	0.369561i
$815$		−	319.868i		−	0.392476i
$816$	−823.432	−	24.2335i	−1.00911	−	0.0296979i
$817$	−13.5025			−0.0165270
$818$	−778.019	−	328.991i	−0.951124	−	0.402190i
$819$		0			0
$820$	506.940	+	522.079i	0.618220	+	0.636681i
$821$	−322.361			−0.392645			−0.196322	−	0.980539i	$-0.562900\pi$
$821$	−322.361			−0.392645			−0.196322	+	0.980539i	$0.562900\pi$
$822$	145.787	−	344.766i	0.177356	−	0.419423i
$823$			1093.88i			1.32914i	0.747228	+	0.664568i	$0.231384\pi$
$823$			1093.88i			1.32914i	−0.747228	+	0.664568i	$0.768616\pi$
$824$	222.806	−	86.5806i	0.270396	−	0.105073i
$825$	62.3383			0.0755616
$826$		0			0
$827$			1056.73i			1.27779i	0.769293	+	0.638896i	$0.220609\pi$
$827$			1056.73i			1.27779i	−0.769293	+	0.638896i	$0.779391\pi$
$828$	−238.629	+	231.710i	−0.288200	+	0.279843i
$829$	−1097.85			−1.32430			−0.662152	−	0.749370i	$-0.730357\pi$
$829$	−1097.85			−1.32430			−0.662152	+	0.749370i	$0.730357\pi$
$830$	−476.346	+	1126.49i	−0.573911	+	1.35722i
$831$		−	751.198i		−	0.903969i
$832$	−330.244	+	302.310i	−0.396927	+	0.363353i
$833$		0			0
$834$	478.031	+	202.139i	0.573178	+	0.242373i
$835$		−	74.0470i		−	0.0886790i
$836$	7.39299	+	7.61376i	0.00884328	+	0.00910737i
$837$	299.259			0.357538
$838$	−4.26382	+	10.0834i	−0.00508810	+	0.0120327i
$839$			224.384i			0.267442i	0.991019	+	0.133721i	$0.0426926\pi$
$839$			224.384i			0.267442i	−0.991019	+	0.133721i	$0.957307\pi$
$840$		0			0
$841$	135.626			0.161267
$842$	422.315	+	178.579i	0.501562	+	0.212089i
$843$		−	630.966i		−	0.748477i
$844$	179.248	−	174.051i	0.212379	−	0.206221i
$845$	−533.940			−0.631881
$846$	62.9604	−	148.893i	0.0744213	−	0.175996i
$847$		0			0
$848$	10.7344	−	364.746i	0.0126585	−	0.430125i
$849$	−54.9875			−0.0647674
$850$	−285.958	−	120.919i	−0.336421	−	0.142258i
$851$		−	656.793i		−	0.771790i
$852$	−458.142	−	471.824i	−0.537726	−	0.553784i
$853$	334.159			0.391746			0.195873	−	0.980629i	$-0.437246\pi$
$853$	334.159			0.391746			0.195873	+	0.980629i	$0.437246\pi$
$854$		0			0
$855$		−	5.13608i		−	0.00600712i
$856$	425.372	−	165.296i	0.496930	−	0.193103i
$857$	776.526			0.906098			0.453049	−	0.891486i	$-0.350336\pi$
$857$	776.526			0.906098			0.453049	+	0.891486i	$0.350336\pi$
$858$	153.826	+	65.0465i	0.179285	+	0.0758118i
$859$		−	78.5323i		−	0.0914229i	−0.998955	−	0.0457115i	$-0.985445\pi$
$859$		−	78.5323i		−	0.0914229i	0.998955	−	0.0457115i	$-0.0145555\pi$
$860$	−447.632	+	434.652i	−0.520502	+	0.505409i
$861$		0			0
$862$	−21.0011	+	49.6647i	−0.0243632	+	0.0576156i
$863$		−	958.205i		−	1.11032i	−0.831744	−	0.555160i	$-0.812657\pi$
$863$		−	958.205i		−	1.11032i	0.831744	−	0.555160i	$-0.187343\pi$
$864$	151.176	+	69.2367i	0.174973	+	0.0801351i
$865$	595.282			0.688188
$866$	475.327	+	200.996i	0.548876	+	0.232096i
$867$		−	1029.93i		−	1.18792i
$868$		0			0
$869$	−214.422			−0.246746
$870$	−187.506	+	443.426i	−0.215524	+	0.509685i
$871$			598.507i			0.687149i
$872$	−378.315	−	973.554i	−0.433848	−	1.11646i
$873$	456.581			0.523003
$874$	−19.6559	−	8.31164i	−0.0224896	−	0.00950989i
$875$		0			0
$876$	−421.679	+	409.451i	−0.481368	+	0.467410i
$877$	−1010.54			−1.15227			−0.576136	−	0.817354i	$-0.695440\pi$
$877$	−1010.54			−1.15227			−0.576136	+	0.817354i	$0.695440\pi$
$878$	−280.336	+	662.955i	−0.319289	+	0.755074i
$879$			308.506i			0.350974i
$880$	490.181	+	14.4259i	0.557024	+	0.0163931i
$881$	1028.53			1.16746			0.583731	−	0.811947i	$-0.301592\pi$
$881$	1028.53			1.16746			0.583731	+	0.811947i	$0.301592\pi$
$882$		0			0
$883$		−	1095.21i		−	1.24033i	−0.784472	−	0.620164i	$-0.787066\pi$
$883$		−	1095.21i		−	1.24033i	0.784472	−	0.620164i	$-0.212934\pi$
$884$	−579.457	−	596.762i	−0.655495	−	0.675070i
$885$	−833.880			−0.942238
$886$	102.333	−	242.003i	0.115500	−	0.273141i
$887$			317.844i			0.358336i	0.983818	+	0.179168i	$0.0573406\pi$
$887$			317.844i			0.358336i	−0.983818	+	0.179168i	$0.942659\pi$
$888$	−306.040	+	118.925i	−0.344640	+	0.133924i
$889$		0			0
$890$	−45.3939	−	19.1952i	−0.0510044	−	0.0215676i
$891$		−	62.0267i		−	0.0696147i
$892$	−121.502	+	117.979i	−0.136213	+	0.132263i
$893$	10.3721			0.0116149
$894$	121.914	−	288.309i	0.136369	−	0.322493i
$895$			1086.24i			1.21368i
$896$		0			0
$897$	−335.852			−0.374417
$898$	820.777	+	347.072i	0.914006	+	0.386494i
$899$		−	1799.82i		−	2.00203i
$900$	43.6557	+	44.9594i	0.0485063	+	0.0499549i
$901$	677.944			0.752435
$902$	−219.607	+	519.340i	−0.243466	+	0.575764i
$903$		0			0
$904$	−378.792	−	974.780i	−0.419017	−	1.07830i
$905$	921.678			1.01843
$906$	866.548	+	366.426i	0.956454	+	0.404444i
$907$			195.634i			0.215693i	0.994168	+	0.107847i	$0.0343955\pi$
$907$			195.634i			0.215693i	−0.994168	+	0.107847i	$0.965604\pi$
$908$	−161.838	+	157.145i	−0.178235	+	0.173067i
$909$	210.586			0.231668
$910$		0			0
$911$		−	1081.20i		−	1.18683i	−0.804897	−	0.593414i	$-0.797780\pi$
$911$		−	1081.20i		−	1.18683i	0.804897	−	0.593414i	$-0.202220\pi$
$912$	−0.313836	+	10.6639i	−0.000344119	+	0.0116929i
$913$	−947.694			−1.03800
$914$	−465.857	−	196.991i	−0.509690	−	0.215526i
$915$			460.940i			0.503760i
$916$	898.680	+	925.517i	0.981091	+	1.01039i
$917$		0			0
$918$	−120.315	+	284.528i	−0.131062	+	0.309944i
$919$		−	624.365i		−	0.679396i	−0.940534	−	0.339698i	$-0.889675\pi$
$919$		−	624.365i		−	0.679396i	0.940534	−	0.339698i	$-0.110325\pi$
$920$	−919.183	+	357.187i	−0.999112	+	0.388247i
$921$	41.0125			0.0445304
$922$	−1403.52	−	593.487i	−1.52225	−	0.643695i
$923$		−	664.054i		−	0.719452i
$924$		0			0
$925$	−123.744			−0.133778
$926$	27.8402	−	65.8382i	0.0300650	−	0.0710996i
$927$		−	89.6389i		−	0.0966978i
$928$	416.408	−	909.214i	0.448715	−	0.979756i
$929$	−1200.56			−1.29232			−0.646160	−	0.763202i	$-0.723626\pi$
$929$	−1200.56			−1.29232			−0.646160	+	0.763202i	$0.723626\pi$
$930$	817.190	+	345.555i	0.878699	+	0.371564i
$931$		0			0
$932$	407.289	+	419.452i	0.437006	+	0.450056i
$933$	768.347			0.823523
$934$	−54.5651	+	129.039i	−0.0584209	+	0.138158i
$935$			911.086i			0.974424i
$936$	60.8123	+	156.494i	0.0649704	+	0.167195i
$937$	125.964			0.134433			0.0672167	−	0.997738i	$-0.478588\pi$
$937$	125.964			0.134433			0.0672167	+	0.997738i	$0.478588\pi$
$938$		0			0
$939$			1049.47i			1.11765i
$940$	343.853	−	333.883i	0.365801	−	0.355194i
$941$	−605.718			−0.643696			−0.321848	−	0.946791i	$-0.604304\pi$
$941$	−605.718			−0.643696			−0.321848	+	0.946791i	$0.604304\pi$
$942$	−97.1542	+	229.756i	−0.103136	+	0.243903i
$943$		−	1133.89i		−	1.20242i
$944$	1731.36	+	50.9536i	1.83406	+	0.0539762i
$945$		0			0
$946$	−445.283	−	188.291i	−0.470701	−	0.199040i
$947$		−	88.1938i		−	0.0931296i	−0.998915	−	0.0465648i	$-0.985173\pi$
$947$		−	88.1938i		−	0.0931296i	0.998915	−	0.0465648i	$-0.0148274\pi$
$948$	−150.160	−	154.645i	−0.158397	−	0.163127i
$949$	−593.479			−0.625373
$950$	−1.56597	+	3.70331i	−0.00164839	+	0.00389822i
$951$			522.081i			0.548981i
$952$		0			0
$953$	−1596.54			−1.67527			−0.837637	−	0.546227i	$-0.816064\pi$
$953$	−1596.54			−1.67527			−0.837637	+	0.546227i	$0.816064\pi$
$954$	−126.034	−	53.2945i	−0.132111	−	0.0558642i
$955$		−	860.850i		−	0.901413i
$956$	−526.112	+	510.857i	−0.550327	+	0.534369i
$957$	−373.045			−0.389806
$958$	370.946	−	877.238i	0.387209	−	0.915697i
$959$		0			0
$960$	332.871	+	363.629i	0.346740	+	0.378780i
$961$	−2355.89			−2.45150
$962$	−305.351	−	129.120i	−0.317413	−	0.134220i
$963$		−	171.135i		−	0.177710i
$964$	136.824	+	140.910i	0.141934	+	0.146172i
$965$	935.930			0.969876
$966$		0			0
$967$		−	921.626i		−	0.953078i	−0.879153	−	0.476539i	$-0.841891\pi$
$967$		−	921.626i		−	0.953078i	0.879153	−	0.476539i	$-0.158109\pi$
$968$	−212.984	−	548.091i	−0.220025	−	0.566210i
$969$	−19.8207			−0.0204548
$970$	1246.79	+	527.215i	1.28535	+	0.543520i
$971$			450.133i			0.463577i	0.972766	+	0.231788i	$0.0744577\pi$
$971$			450.133i			0.463577i	−0.972766	+	0.231788i	$0.925542\pi$
$972$	44.7346	−	43.4375i	0.0460233	−	0.0446887i
$973$		0			0
$974$	252.814	−	597.871i	0.259563	−	0.613831i
$975$			63.2768i			0.0648992i
$976$	28.1654	−	957.034i	0.0288580	−	0.980568i
$977$	1478.46			1.51327			0.756633	−	0.653839i	$-0.226843\pi$
$977$	1478.46			1.51327			0.756633	+	0.653839i	$0.226843\pi$
$978$	229.484	+	97.0388i	0.234646	+	0.0992217i
$979$		−	38.1889i		−	0.0390081i
$980$		0			0
$981$	−391.679			−0.399265
$982$	651.860	−	1541.56i	0.663809	−	1.56982i
$983$		−	309.402i		−	0.314753i	−0.987539	−	0.157376i	$-0.949696\pi$
$983$		−	309.402i		−	0.314753i	0.987539	−	0.157376i	$-0.0503036\pi$
$984$	−528.347	+	205.311i	−0.536938	+	0.208650i
$985$	598.048			0.607156
$986$	1711.23	+	723.605i	1.73552	+	0.733879i
$987$		0			0
$988$	−7.72838	+	7.50428i	−0.00782225	+	0.00759542i
$989$	972.197			0.983010
$990$	71.6222	−	169.377i	0.0723457	−	0.171088i
$991$		−	1724.92i		−	1.74058i	−0.492536	−	0.870292i	$-0.663930\pi$
$991$		−	1724.92i		−	1.74058i	0.492536	−	0.870292i	$-0.336070\pi$
$992$	−1675.59	−	767.397i	−1.68910	−	0.773586i
$993$	302.711			0.304845
$994$		0			0
$995$			670.999i			0.674371i
$996$	−663.673	−	683.492i	−0.666338	−	0.686237i
$997$	761.581			0.763872			0.381936	−	0.924189i	$-0.375257\pi$
$997$	761.581			0.763872			0.381936	+	0.924189i	$0.375257\pi$
$998$	−404.210	+	955.901i	−0.405020	+	0.957817i
$999$			123.126i			0.123249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.3.g.e.295.1	✓	12
4.3	odd	2	inner	588.3.g.e.295.4	yes	12
7.6	odd	2	inner	588.3.g.e.295.2	yes	12
28.27	even	2	inner	588.3.g.e.295.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.3.g.e.295.1	✓	12	1.1	even	1	trivial
588.3.g.e.295.2	yes	12	7.6	odd	2	inner
588.3.g.e.295.3	yes	12	28.27	even	2	inner
588.3.g.e.295.4	yes	12	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	588.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.84208 - 0.778937i) q^{2} -1.73205i q^{3} +(2.78651 + 2.86973i) q^{4} +4.44722 q^{5} +(-1.34916 + 3.19058i) q^{6} +(-2.89764 - 7.45679i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-1.84208 - 0.778937i) q^{2} -1.73205i q^{3} +(2.78651 + 2.86973i) q^{4} +4.44722 q^{5} +(-1.34916 + 3.19058i) q^{6} +(-2.89764 - 7.45679i) q^{8} -3.00000 q^{9} +(-8.19213 - 3.46410i) q^{10} -6.89185i q^{11} +(4.97051 - 4.82638i) q^{12} +6.99560 q^{13} -7.70281i q^{15} +(-0.470674 + 15.9931i) q^{16} -29.7259 q^{17} +(5.52624 + 2.33681i) q^{18} +0.384966i q^{19} +(12.3922 + 12.7623i) q^{20} +(-5.36832 + 12.6953i) q^{22} -27.7180i q^{23} +(-12.9155 + 5.01887i) q^{24} -5.22226 q^{25} +(-12.8865 - 5.44913i) q^{26} +5.19615i q^{27} +31.2510 q^{29} +(-6.00000 + 14.1892i) q^{30} -57.5924i q^{31} +(13.3246 - 29.0939i) q^{32} -11.9370 q^{33} +(54.7575 + 23.1546i) q^{34} +(-8.35954 - 8.60918i) q^{36} +23.6955 q^{37} +(0.299864 - 0.709138i) q^{38} -12.1167i q^{39} +(-12.8865 - 33.1619i) q^{40} +40.9079 q^{41} +35.0746i q^{43} +(19.7777 - 19.2042i) q^{44} -13.3417 q^{45} +(-21.5906 + 51.0588i) q^{46} -26.9429i q^{47} +(27.7008 + 0.815231i) q^{48} +(9.61982 + 4.06781i) q^{50} +51.4868i q^{51} +(19.4933 + 20.0755i) q^{52} -22.8065 q^{53} +(4.04748 - 9.57173i) q^{54} -30.6496i q^{55} +0.666781 q^{57} +(-57.5669 - 24.3426i) q^{58} -108.257i q^{59} +(22.1050 - 21.4640i) q^{60} -59.8405 q^{61} +(-44.8609 + 106.090i) q^{62} +(-47.2073 + 43.2142i) q^{64} +31.1110 q^{65} +(21.9890 + 9.29820i) q^{66} +85.5547i q^{67} +(-82.8317 - 85.3053i) q^{68} -48.0090 q^{69} -94.9245i q^{71} +(8.69293 + 22.3704i) q^{72} -84.8360 q^{73} +(-43.6491 - 18.4573i) q^{74} +9.04522i q^{75} +(-1.10475 + 1.07271i) q^{76} +(-9.43817 + 22.3200i) q^{78} -31.1124i q^{79} +(-2.09319 + 71.1247i) q^{80} +9.00000 q^{81} +(-75.3556 - 31.8647i) q^{82} -137.509i q^{83} -132.198 q^{85} +(27.3209 - 64.6101i) q^{86} -54.1283i q^{87} +(-51.3911 + 19.9701i) q^{88} +5.54117 q^{89} +(24.5764 + 10.3923i) q^{90} +(79.5431 - 77.2366i) q^{92} -99.7530 q^{93} +(-20.9868 + 49.6309i) q^{94} +1.71203i q^{95} +(-50.3921 - 23.0789i) q^{96} -152.194 q^{97} +20.6756i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 10 q^{4} - 10 q^{8} - 36 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 10 * q^4 - 10 * q^8 - 36 * q^9	\( 12 q + 2 q^{2} + 10 q^{4} - 10 q^{8} - 36 q^{9} + 66 q^{16} - 6 q^{18} + 32 q^{22} - 60 q^{25} - 8 q^{29} - 72 q^{30} + 182 q^{32} - 30 q^{36} - 104 q^{37} + 240 q^{44} - 160 q^{46} + 94 q^{50} + 104 q^{53} - 356 q^{58} - 24 q^{60} - 302 q^{64} + 384 q^{65} + 30 q^{72} - 580 q^{74} + 168 q^{78} + 108 q^{81} - 432 q^{85} - 240 q^{86} + 160 q^{88} + 384 q^{92} - 48 q^{93}+O(q^{100}) \) 12 * q + 2 * q^2 + 10 * q^4 - 10 * q^8 - 36 * q^9 + 66 * q^16 - 6 * q^18 + 32 * q^22 - 60 * q^25 - 8 * q^29 - 72 * q^30 + 182 * q^32 - 30 * q^36 - 104 * q^37 + 240 * q^44 - 160 * q^46 + 94 * q^50 + 104 * q^53 - 356 * q^58 - 24 * q^60 - 302 * q^64 + 384 * q^65 + 30 * q^72 - 580 * q^74 + 168 * q^78 + 108 * q^81 - 432 * q^85 - 240 * q^86 + 160 * q^88 + 384 * q^92 - 48 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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