LMFDB - Embedded newform 600.2.d.g.349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(349,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("600.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.d (of order $2$, degree $1$, not 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.214798336.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 $ x^8 - 2x^7 - 2x^5 + 9x^4 - 4x^3 - 16*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.3
Root			$1.41216 - 0.0762223i$ of defining polynomial
Character	$\chi$	$=$	600.349
Dual form			600.2.d.g.349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.576222 - 1.29150i) q^{2} -1.00000 q^{3} +(-1.33594 + 1.48838i) q^{4} +(0.576222 + 1.29150i) q^{6} -1.97676i q^{7} +(2.69204 + 0.867721i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.576222 - 1.29150i) q^{2} -1.00000 q^{3} +(-1.33594 + 1.48838i) q^{4} +(0.576222 + 1.29150i) q^{6} -1.97676i q^{7} +(2.69204 + 0.867721i) q^{8} +1.00000 q^{9} +1.43055i q^{11} +(1.33594 - 1.48838i) q^{12} -0.241319 q^{13} +(-2.55298 + 1.13905i) q^{14} +(-0.430552 - 3.97676i) q^{16} -7.38407i q^{17} +(-0.576222 - 1.29150i) q^{18} +3.04033i q^{19} +1.97676i q^{21} +(1.84756 - 0.824316i) q^{22} -0.874337i q^{23} +(-2.69204 - 0.867721i) q^{24} +(0.139054 + 0.311664i) q^{26} -1.00000 q^{27} +(2.94217 + 2.64082i) q^{28} -9.07918i q^{29} -7.44764 q^{31} +(-4.88789 + 2.84756i) q^{32} -1.43055i q^{33} +(-9.53652 + 4.25487i) q^{34} +(-1.33594 + 1.48838i) q^{36} -8.81463 q^{37} +(3.92658 - 1.75191i) q^{38} +0.241319 q^{39} -1.91319 q^{41} +(2.55298 - 1.13905i) q^{42} -11.2452 q^{43} +(-2.12921 - 1.91113i) q^{44} +(-1.12921 + 0.503813i) q^{46} -3.34374i q^{47} +(0.430552 + 3.97676i) q^{48} +3.09242 q^{49} +7.38407i q^{51} +(0.322387 - 0.359175i) q^{52} +9.20632 q^{53} +(0.576222 + 1.29150i) q^{54} +(1.71528 - 5.32151i) q^{56} -3.04033i q^{57} +(-11.7258 + 5.23163i) q^{58} -6.43616i q^{59} -4.57331i q^{61} +(4.29150 + 9.61862i) q^{62} -1.97676i q^{63} +(6.49412 + 4.67187i) q^{64} +(-1.84756 + 0.824316i) q^{66} -4.86671 q^{67} +(10.9903 + 9.86465i) q^{68} +0.874337i q^{69} -8.21808 q^{71} +(2.69204 + 0.867721i) q^{72} +4.12714i q^{73} +(5.07918 + 11.3841i) q^{74} +(-4.52517 - 4.06169i) q^{76} +2.82786 q^{77} +(-0.139054 - 0.311664i) q^{78} +13.6757 q^{79} +1.00000 q^{81} +(1.10242 + 2.47088i) q^{82} -12.3320 q^{83} +(-2.94217 - 2.64082i) q^{84} +(6.47972 + 14.5231i) q^{86} +9.07918i q^{87} +(-1.24132 + 3.85110i) q^{88} +8.08066 q^{89} +0.477031i q^{91} +(1.30135 + 1.16806i) q^{92} +7.44764 q^{93} +(-4.31844 + 1.92674i) q^{94} +(4.88789 - 2.84756i) q^{96} +10.6757i q^{97} +(-1.78192 - 3.99385i) q^{98} +1.43055i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9	$ 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9} + 4 q^{12} + 6 q^{14} + 8 q^{16} - 2 q^{18} + 20 q^{22} + 8 q^{24} - 2 q^{26} - 8 q^{27} + 24 q^{28} + 8 q^{31} - 12 q^{32} - 12 q^{34} - 4 q^{36} + 14 q^{38} - 6 q^{42} - 8 q^{43} + 12 q^{44} + 20 q^{46} - 8 q^{48} + 24 q^{52} + 8 q^{53} + 2 q^{54} + 8 q^{56} - 20 q^{58} + 26 q^{62} + 32 q^{64} - 20 q^{66} + 24 q^{67} + 36 q^{68} - 40 q^{71} - 8 q^{72} - 8 q^{74} - 20 q^{76} - 24 q^{77} + 2 q^{78} + 16 q^{79} + 8 q^{81} - 16 q^{82} - 32 q^{83} - 24 q^{84} - 18 q^{86} - 8 q^{88} + 28 q^{92} - 8 q^{93} + 4 q^{94} + 12 q^{96} - 40 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9 + 4 * q^12 + 6 * q^14 + 8 * q^16 - 2 * q^18 + 20 * q^22 + 8 * q^24 - 2 * q^26 - 8 * q^27 + 24 * q^28 + 8 * q^31 - 12 * q^32 - 12 * q^34 - 4 * q^36 + 14 * q^38 - 6 * q^42 - 8 * q^43 + 12 * q^44 + 20 * q^46 - 8 * q^48 + 24 * q^52 + 8 * q^53 + 2 * q^54 + 8 * q^56 - 20 * q^58 + 26 * q^62 + 32 * q^64 - 20 * q^66 + 24 * q^67 + 36 * q^68 - 40 * q^71 - 8 * q^72 - 8 * q^74 - 20 * q^76 - 24 * q^77 + 2 * q^78 + 16 * q^79 + 8 * q^81 - 16 * q^82 - 32 * q^83 - 24 * q^84 - 18 * q^86 - 8 * q^88 + 28 * q^92 - 8 * q^93 + 4 * q^94 + 12 * q^96 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$	−0.576222	−	1.29150i	−0.407451	−	0.913227i
$2$	−0.576222	−	1.29150i	−0.407451	−	0.913227i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.33594	+	1.48838i	−0.667968	+	0.744190i
$5$		0			0
$5$		0			0
$6$	0.576222	+	1.29150i	0.235242	+	0.527252i
$7$		−	1.97676i		−	0.747145i	−0.927601	−	0.373573i	$-0.878133\pi$
$7$		−	1.97676i		−	0.747145i	0.927601	−	0.373573i	$-0.121867\pi$
$8$	2.69204	+	0.867721i	0.951779	+	0.306786i
$9$	1.00000			0.333333
$10$		0			0
$11$			1.43055i			0.431328i	0.976468	+	0.215664i	$0.0691915\pi$
$11$			1.43055i			0.431328i	−0.976468	+	0.215664i	$0.930808\pi$
$12$	1.33594	−	1.48838i	0.385651	−	0.429658i
$13$	−0.241319			−0.0669300			−0.0334650	−	0.999440i	$-0.510654\pi$
$13$	−0.241319			−0.0669300			−0.0334650	+	0.999440i	$0.510654\pi$
$14$	−2.55298	+	1.13905i	−0.682313	+	0.304425i
$15$		0			0
$16$	−0.430552	−	3.97676i	−0.107638	−	0.994190i
$17$		−	7.38407i		−	1.79090i	−0.445161	−	0.895450i	$-0.646854\pi$
$17$		−	7.38407i		−	1.79090i	0.445161	−	0.895450i	$-0.353146\pi$
$18$	−0.576222	−	1.29150i	−0.135817	−	0.304409i
$19$			3.04033i			0.697500i	0.937216	+	0.348750i	$0.113394\pi$
$19$			3.04033i			0.697500i	−0.937216	+	0.348750i	$0.886606\pi$
$20$		0			0
$21$			1.97676i			0.431365i
$22$	1.84756	−	0.824316i	0.393900	−	0.175745i
$23$		−	0.874337i		−	0.182312i	−0.995837	−	0.0911560i	$-0.970944\pi$
$23$		−	0.874337i		−	0.182312i	0.995837	−	0.0911560i	$-0.0290562\pi$
$24$	−2.69204	−	0.867721i	−0.549510	−	0.177123i
$25$		0			0
$26$	0.139054	+	0.311664i	0.0272707	+	0.0611223i
$27$	−1.00000			−0.192450
$28$	2.94217	+	2.64082i	0.556018	+	0.499069i
$29$		−	9.07918i		−	1.68596i	−0.537943	−	0.842981i	$-0.680799\pi$
$29$		−	9.07918i		−	1.68596i	0.537943	−	0.842981i	$-0.319201\pi$
$30$		0			0
$31$	−7.44764			−1.33764			−0.668818	−	0.743426i	$-0.733200\pi$
$31$	−7.44764			−1.33764			−0.668818	+	0.743426i	$0.733200\pi$
$32$	−4.88789	+	2.84756i	−0.864064	+	0.503381i
$33$		−	1.43055i		−	0.249027i
$34$	−9.53652	+	4.25487i	−1.63550	+	0.729704i
$35$		0			0
$36$	−1.33594	+	1.48838i	−0.222656	+	0.248063i
$37$	−8.81463			−1.44912			−0.724558	−	0.689214i	$-0.757956\pi$
$37$	−8.81463			−1.44912			−0.724558	+	0.689214i	$0.757956\pi$
$38$	3.92658	−	1.75191i	0.636976	−	0.284197i
$39$	0.241319			0.0386420
$40$		0			0
$41$	−1.91319			−0.298790			−0.149395	−	0.988778i	$-0.547733\pi$
$41$	−1.91319			−0.298790			−0.149395	+	0.988778i	$0.547733\pi$
$42$	2.55298	−	1.13905i	0.393934	−	0.175760i
$43$	−11.2452			−1.71487			−0.857437	−	0.514589i	$-0.827944\pi$
$43$	−11.2452			−1.71487			−0.857437	+	0.514589i	$0.827944\pi$
$44$	−2.12921	−	1.91113i	−0.320990	−	0.288113i
$45$		0			0
$46$	−1.12921	+	0.503813i	−0.166492	+	0.0742831i
$47$		−	3.34374i		−	0.487735i	−0.969809	−	0.243867i	$-0.921584\pi$
$47$		−	3.34374i		−	0.487735i	0.969809	−	0.243867i	$-0.0784162\pi$
$48$	0.430552	+	3.97676i	0.0621448	+	0.573996i
$49$	3.09242			0.441774
$50$		0			0
$51$			7.38407i			1.03398i
$52$	0.322387	−	0.359175i	0.0447071	−	0.0498086i
$53$	9.20632			1.26459			0.632293	−	0.774729i	$-0.282114\pi$
$53$	9.20632			1.26459			0.632293	+	0.774729i	$0.282114\pi$
$54$	0.576222	+	1.29150i	0.0784139	+	0.175751i
$55$		0			0
$56$	1.71528	−	5.32151i	0.229213	−	0.711117i
$57$		−	3.04033i		−	0.402702i
$58$	−11.7258	+	5.23163i	−1.53967	+	0.686946i
$59$		−	6.43616i		−	0.837917i	−0.908005	−	0.418958i	$-0.862395\pi$
$59$		−	6.43616i		−	0.837917i	0.908005	−	0.418958i	$-0.137605\pi$
$60$		0			0
$61$		−	4.57331i		−	0.585552i	−0.956181	−	0.292776i	$-0.905421\pi$
$61$		−	4.57331i		−	0.585552i	0.956181	−	0.292776i	$-0.0945790\pi$
$62$	4.29150	+	9.61862i	0.545021	+	1.22157i
$63$		−	1.97676i		−	0.249048i
$64$	6.49412	+	4.67187i	0.811765	+	0.583984i
$65$		0			0
$66$	−1.84756	+	0.824316i	−0.227418	+	0.101466i
$67$	−4.86671			−0.594563			−0.297282	−	0.954790i	$-0.596080\pi$
$67$	−4.86671			−0.594563			−0.297282	+	0.954790i	$0.596080\pi$
$68$	10.9903	+	9.86465i	1.33277	+	1.19626i
$69$			0.874337i			0.105258i
$70$		0			0
$71$	−8.21808			−0.975307			−0.487653	−	0.873037i	$-0.662147\pi$
$71$	−8.21808			−0.975307			−0.487653	+	0.873037i	$0.662147\pi$
$72$	2.69204	+	0.867721i	0.317260	+	0.102262i
$73$			4.12714i			0.483045i	0.970395	+	0.241523i	$0.0776468\pi$
$73$			4.12714i			0.483045i	−0.970395	+	0.241523i	$0.922353\pi$
$74$	5.07918	+	11.3841i	0.590443	+	1.32337i
$75$		0			0
$76$	−4.52517	−	4.06169i	−0.519072	−	0.465907i
$77$	2.82786			0.322264
$78$	−0.139054	−	0.311664i	−0.0157447	−	0.0352890i
$79$	13.6757			1.53864			0.769320	−	0.638864i	$-0.220595\pi$
$79$	13.6757			1.53864			0.769320	+	0.638864i	$0.220595\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	1.10242	+	2.47088i	0.121742	+	0.272863i
$83$	−12.3320			−1.35361			−0.676806	−	0.736162i	$-0.736636\pi$
$83$	−12.3320			−1.35361			−0.676806	+	0.736162i	$0.736636\pi$
$84$	−2.94217	−	2.64082i	−0.321017	−	0.288138i
$85$		0			0
$86$	6.47972	+	14.5231i	0.698726	+	1.56607i
$87$			9.07918i			0.973391i
$88$	−1.24132	+	3.85110i	−0.132325	+	0.410528i
$89$	8.08066			0.856548			0.428274	−	0.903649i	$-0.359122\pi$
$89$	8.08066			0.856548			0.428274	+	0.903649i	$0.359122\pi$
$90$		0			0
$91$			0.477031i			0.0500064i
$92$	1.30135	+	1.16806i	0.135675	+	0.121779i
$93$	7.44764			0.772285
$94$	−4.31844	+	1.92674i	−0.445413	+	0.198728i
$95$		0			0
$96$	4.88789	−	2.84756i	0.498868	−	0.290627i
$97$			10.6757i			1.08396i	0.840393	+	0.541978i	$0.182324\pi$
$97$			10.6757i			1.08396i	−0.840393	+	0.541978i	$0.817676\pi$
$98$	−1.78192	−	3.99385i	−0.180001	−	0.403440i
$99$			1.43055i			0.143776i
$100$		0			0
$101$		−	13.2063i		−	1.31408i	−0.753856	−	0.657039i	$-0.771809\pi$
$101$		−	13.2063i		−	1.31408i	0.753856	−	0.657039i	$-0.228191\pi$
$102$	9.53652	−	4.25487i	0.944256	−	0.421295i
$103$		−	19.4244i		−	1.91394i	−0.290181	−	0.956972i	$-0.593716\pi$
$103$		−	19.4244i		−	1.91394i	0.290181	−	0.956972i	$-0.406284\pi$
$104$	−0.649641	−	0.209398i	−0.0637025	−	0.0205331i
$105$		0			0
$106$	−5.30489	−	11.8900i	−0.515256	−	1.15485i
$107$	14.8085			1.43159			0.715795	−	0.698311i	$-0.246065\pi$
$107$	14.8085			1.43159			0.715795	+	0.698311i	$0.246065\pi$
$108$	1.33594	−	1.48838i	0.128550	−	0.143219i
$109$		−	15.2296i		−	1.45873i	−0.684126	−	0.729364i	$-0.739816\pi$
$109$		−	15.2296i		−	1.45873i	0.684126	−	0.729364i	$-0.260184\pi$
$110$		0			0
$111$	8.81463			0.836647
$112$	−7.86110	+	0.851098i	−0.742804	+	0.0804212i
$113$			1.13890i			0.107138i	0.998564	+	0.0535692i	$0.0170598\pi$
$113$			1.13890i			0.107138i	−0.998564	+	0.0535692i	$0.982940\pi$
$114$	−3.92658	+	1.75191i	−0.367758	+	0.164081i
$115$		0			0
$116$	13.5133	+	12.1292i	1.25468	+	1.12617i
$117$	−0.241319			−0.0223100
$118$	−8.31229	+	3.70866i	−0.765208	+	0.341410i
$119$	−14.5965			−1.33806
$120$		0			0
$121$	8.95352			0.813956
$122$	−5.90642	+	2.63524i	−0.534742	+	0.238583i
$123$	1.91319			0.172507
$124$	9.94957	−	11.0849i	0.893498	−	0.995456i
$125$		0			0
$126$	−2.55298	+	1.13905i	−0.227438	+	0.101475i
$127$			2.43616i			0.216174i	0.994141	+	0.108087i	$0.0344725\pi$
$127$			2.43616i			0.216174i	−0.994141	+	0.108087i	$0.965527\pi$
$128$	2.29166	−	11.0792i	0.202556	−	0.979271i
$129$	11.2452			0.990083
$130$		0			0
$131$			6.90143i			0.602981i	0.953469	+	0.301491i	$0.0974842\pi$
$131$			6.90143i			0.602981i	−0.953469	+	0.301491i	$0.902516\pi$
$132$	2.12921	+	1.91113i	0.185324	+	0.166342i
$133$	6.01001			0.521134
$134$	2.80431	+	6.28535i	0.242255	+	0.542972i
$135$		0			0
$136$	6.40731	−	19.8782i	0.549423	−	1.70454i
$137$		−	5.39022i		−	0.460518i	−0.973129	−	0.230259i	$-0.926043\pi$
$137$		−	5.39022i		−	0.460518i	0.973129	−	0.230259i	$-0.0739573\pi$
$138$	1.12921	−	0.503813i	0.0961243	−	0.0428874i
$139$			17.4244i			1.47792i	0.673750	+	0.738959i	$0.264682\pi$
$139$			17.4244i			1.47792i	−0.673750	+	0.738959i	$0.735318\pi$
$140$		0			0
$141$			3.34374i			0.281594i
$142$	4.73544	+	10.6136i	0.397389	+	0.890677i
$143$		−	0.345220i		−	0.0288687i
$144$	−0.430552	−	3.97676i	−0.0358793	−	0.331397i
$145$		0			0
$146$	5.33019	−	2.37815i	0.441130	−	0.196817i
$147$	−3.09242			−0.255058
$148$	11.7758	−	13.1195i	0.967962	−	1.07842i
$149$		−	2.28551i		−	0.187236i	−0.995608	−	0.0936180i	$-0.970157\pi$
$149$		−	2.28551i		−	0.187236i	0.995608	−	0.0936180i	$-0.0298432\pi$
$150$		0			0
$151$	6.66425			0.542329			0.271164	−	0.962533i	$-0.412591\pi$
$151$	6.66425			0.542329			0.271164	+	0.962533i	$0.412591\pi$
$152$	−2.63816	+	8.18468i	−0.213983	+	0.663865i
$153$		−	7.38407i		−	0.596967i
$154$	−1.62948	−	3.65217i	−0.131307	−	0.294301i
$155$		0			0
$156$	−0.322387	+	0.359175i	−0.0258116	+	0.0287570i
$157$	−17.4144			−1.38982			−0.694910	−	0.719097i	$-0.744556\pi$
$157$	−17.4144			−1.38982			−0.694910	+	0.719097i	$0.744556\pi$
$158$	−7.88026	−	17.6622i	−0.626920	−	1.40513i
$159$	−9.20632			−0.730109
$160$		0			0
$161$	−1.72836			−0.136214
$162$	−0.576222	−	1.29150i	−0.0452723	−	0.101470i
$163$	4.66187			0.365145			0.182573	−	0.983192i	$-0.441557\pi$
$163$	4.66187			0.365145			0.182573	+	0.983192i	$0.441557\pi$
$164$	2.55590	−	2.84756i	0.199582	−	0.222357i
$165$		0			0
$166$	7.10597	+	15.9267i	0.551530	+	1.23615i
$167$		−	0.137419i		−	0.0106338i	−0.999986	−	0.00531690i	$-0.998308\pi$
$167$		−	0.137419i		−	0.0106338i	0.999986	−	0.00531690i	$-0.00169243\pi$
$168$	−1.71528	+	5.32151i	−0.132336	+	0.410564i
$169$	−12.9418			−0.995520
$170$		0			0
$171$			3.04033i			0.232500i
$172$	15.0228	−	16.7371i	1.14548	−	1.27619i
$173$	−3.96675			−0.301587			−0.150793	−	0.988565i	$-0.548183\pi$
$173$	−3.96675			−0.301587			−0.150793	+	0.988565i	$0.548183\pi$
$174$	11.7258	−	5.23163i	0.888927	−	0.396609i
$175$		0			0
$176$	5.68896	−	0.615927i	0.428822	−	0.0464272i
$177$			6.43616i			0.483771i
$178$	−4.65626	−	10.4362i	−0.349001	−	0.782223i
$179$			4.68749i			0.350359i	0.984537	+	0.175180i	$0.0560506\pi$
$179$			4.68749i			0.350359i	−0.984537	+	0.175180i	$0.943949\pi$
$180$		0			0
$181$		−	9.10242i		−	0.676578i	−0.941042	−	0.338289i	$-0.890152\pi$
$181$		−	9.10242i		−	0.676578i	0.941042	−	0.338289i	$-0.109848\pi$
$182$	0.616084	−	0.274876i	0.0456672	−	0.0203751i
$183$			4.57331i			0.338068i
$184$	0.758681	−	2.35375i	0.0559307	−	0.173521i
$185$		0			0
$186$	−4.29150	−	9.61862i	−0.314668	−	0.705271i
$187$	10.5633			0.772465
$188$	4.97676	+	4.46702i	0.362968	+	0.325791i
$189$			1.97676i			0.143788i
$190$		0			0
$191$	15.2063			1.10029			0.550145	−	0.835069i	$-0.314572\pi$
$191$	15.2063			1.10029			0.550145	+	0.835069i	$0.314572\pi$
$192$	−6.49412	−	4.67187i	−0.468673	−	0.337163i
$193$			20.7564i			1.49408i	0.664780	+	0.747039i	$0.268525\pi$
$193$			20.7564i			1.49408i	−0.664780	+	0.747039i	$0.731475\pi$
$194$	13.7877	−	6.15159i	0.989898	−	0.441659i
$195$		0			0
$196$	−4.13127	+	4.60269i	−0.295091	+	0.328764i
$197$	23.2508			1.65655			0.828275	−	0.560322i	$-0.189323\pi$
$197$	23.2508			1.65655			0.828275	+	0.560322i	$0.189323\pi$
$198$	1.84756	−	0.824316i	0.131300	−	0.0585816i
$199$	7.21633			0.511552			0.255776	−	0.966736i	$-0.417669\pi$
$199$	7.21633			0.511552			0.255776	+	0.966736i	$0.417669\pi$
$200$		0			0
$201$	4.86671			0.343271
$202$	−17.0559	+	7.60978i	−1.20005	+	0.535422i
$203$	−17.9474			−1.25966
$204$	−10.9903	−	9.86465i	−0.769476	−	0.690663i
$205$		0			0
$206$	−25.0866	+	11.1928i	−1.74787	+	0.779838i
$207$		−	0.874337i		−	0.0607707i
$208$	0.103901	+	0.959669i	0.00720420	+	0.0665411i
$209$	−4.34935			−0.300851
$210$		0			0
$211$			4.38407i			0.301812i	0.988548	+	0.150906i	$0.0482191\pi$
$211$			4.38407i			0.301812i	−0.988548	+	0.150906i	$0.951781\pi$
$212$	−12.2991	+	13.7025i	−0.844703	+	0.941092i
$213$	8.21808			0.563094
$214$	−8.53298	−	19.1251i	−0.583302	−	1.30737i
$215$		0			0
$216$	−2.69204	−	0.867721i	−0.183170	−	0.0590409i
$217$			14.7222i			0.999409i
$218$	−19.6690	+	8.77561i	−1.33215	+	0.594360i
$219$		−	4.12714i		−	0.278886i
$220$		0			0
$221$			1.78192i			0.119865i
$222$	−5.07918	−	11.3841i	−0.340892	−	0.764049i
$223$			4.98852i			0.334056i	0.985952	+	0.167028i	$0.0534170\pi$
$223$			4.98852i			0.334056i	−0.985952	+	0.167028i	$0.946583\pi$
$224$	5.62894	+	9.66218i	0.376099	+	0.645582i
$225$		0			0
$226$	1.47088	−	0.656257i	0.0978416	−	0.0436536i
$227$	11.2569			0.747149			0.373574	−	0.927600i	$-0.378132\pi$
$227$	11.2569			0.747149			0.373574	+	0.927600i	$0.378132\pi$
$228$	4.52517	+	4.06169i	0.299687	+	0.268992i
$229$			15.8364i			1.04650i	0.852180	+	0.523249i	$0.175280\pi$
$229$			15.8364i			1.04650i	−0.852180	+	0.523249i	$0.824720\pi$
$230$		0			0
$231$	−2.82786			−0.186059
$232$	7.87820	−	24.4415i	0.517229	−	1.60466i
$233$			10.9591i			0.717956i	0.933346	+	0.358978i	$0.116875\pi$
$233$			10.9591i			0.717956i	−0.933346	+	0.358978i	$0.883125\pi$
$234$	0.139054	+	0.311664i	0.00909022	+	0.0203741i
$235$		0			0
$236$	9.57945	+	8.59830i	0.623569	+	0.559701i
$237$	−13.6757			−0.888334
$238$	8.41086	+	18.8514i	0.545195	+	1.22196i
$239$	−17.3182			−1.12022			−0.560111	−	0.828418i	$-0.689242\pi$
$239$	−17.3182			−1.12022			−0.560111	+	0.828418i	$0.689242\pi$
$240$		0			0
$241$	4.76869			0.307178			0.153589	−	0.988135i	$-0.450917\pi$
$241$	4.76869			0.307178			0.153589	+	0.988135i	$0.450917\pi$
$242$	−5.15922	−	11.5635i	−0.331647	−	0.743327i
$243$	−1.00000			−0.0641500
$244$	6.80682	+	6.10964i	0.435762	+	0.391130i
$245$		0			0
$246$	−1.10242	−	2.47088i	−0.0702879	−	0.157538i
$247$		−	0.733691i		−	0.0466836i
$248$	−20.0493	−	6.46247i	−1.27313	−	0.410367i
$249$	12.3320			0.781508
$250$		0			0
$251$		−	6.15837i		−	0.388713i	−0.980931	−	0.194356i	$-0.937738\pi$
$251$		−	6.15837i		−	0.388713i	0.980931	−	0.194356i	$-0.0622618\pi$
$252$	2.94217	+	2.64082i	0.185339	+	0.166356i
$253$	1.25079			0.0786362
$254$	3.14630	−	1.40377i	0.197416	−	0.0880804i
$255$		0			0
$256$	−15.6293	+	3.42440i	−0.976828	+	0.214025i
$257$		−	14.1584i		−	0.883175i	−0.897218	−	0.441587i	$-0.854416\pi$
$257$		−	14.1584i		−	0.883175i	0.897218	−	0.441587i	$-0.145584\pi$
$258$	−6.47972	−	14.5231i	−0.403410	−	0.904170i
$259$			17.4244i			1.08270i
$260$		0			0
$261$		−	9.07918i		−	0.561987i
$262$	8.91319	−	3.97676i	0.550659	−	0.245685i
$263$			15.5960i			0.961691i	0.876805	+	0.480845i	$0.159670\pi$
$263$			15.5960i			0.961691i	−0.876805	+	0.480845i	$0.840330\pi$
$264$	1.24132	−	3.85110i	0.0763979	−	0.237019i
$265$		0			0
$266$	−3.46310	−	7.76191i	−0.212336	−	0.475913i
$267$	−8.08066			−0.494528
$268$	6.50161	−	7.24352i	0.397149	−	0.442468i
$269$			11.3182i			0.690084i	0.938587	+	0.345042i	$0.112135\pi$
$269$			11.3182i			0.690084i	−0.938587	+	0.345042i	$0.887865\pi$
$270$		0			0
$271$	−6.20485			−0.376918			−0.188459	−	0.982081i	$-0.560349\pi$
$271$	−6.20485			−0.376918			−0.188459	+	0.982081i	$0.560349\pi$
$272$	−29.3647	+	3.17923i	−1.78050	+	0.192769i
$273$		−	0.477031i		−	0.0288712i
$274$	−6.96146	+	3.10597i	−0.420557	+	0.187638i
$275$		0			0
$276$	−1.30135	−	1.16806i	−0.0783319	−	0.0703089i
$277$	18.9288			1.13732			0.568661	−	0.822572i	$-0.307462\pi$
$277$	18.9288			1.13732			0.568661	+	0.822572i	$0.307462\pi$
$278$	22.5036	−	10.0403i	1.34968	−	0.602179i
$279$	−7.44764			−0.445879
$280$		0			0
$281$	−21.6231			−1.28993			−0.644963	−	0.764214i	$-0.723127\pi$
$281$	−21.6231			−1.28993			−0.644963	+	0.764214i	$0.723127\pi$
$282$	4.31844	−	1.92674i	0.257159	−	0.114736i
$283$	29.1522			1.73292			0.866460	−	0.499247i	$-0.166390\pi$
$283$	29.1522			1.73292			0.866460	+	0.499247i	$0.166390\pi$
$284$	10.9788	−	12.2316i	0.651473	−	0.725814i
$285$		0			0
$286$	−0.445851	+	0.198923i	−0.0263637	+	0.0117626i
$287$			3.78192i			0.223240i
$288$	−4.88789	+	2.84756i	−0.288021	+	0.167794i
$289$	−37.5245			−2.20733
$290$		0			0
$291$		−	10.6757i		−	0.625822i
$292$	−6.14275	−	5.51359i	−0.359477	−	0.322659i
$293$	2.32427			0.135785			0.0678927	−	0.997693i	$-0.478372\pi$
$293$	2.32427			0.135785			0.0678927	+	0.997693i	$0.478372\pi$
$294$	1.78192	+	3.99385i	0.103924	+	0.232926i
$295$		0			0
$296$	−23.7293	−	7.64863i	−1.37924	−	0.444568i
$297$		−	1.43055i		−	0.0830090i
$298$	−2.95173	+	1.31696i	−0.170989	+	0.0762895i
$299$			0.210995i			0.0122021i
$300$		0			0
$301$			22.2290i			1.28126i
$302$	−3.84009	−	8.60686i	−0.220972	−	0.495269i
$303$			13.2063i			0.758683i
$304$	12.0907	−	1.30902i	0.693447	−	0.0750775i
$305$		0			0
$306$	−9.53652	+	4.25487i	−0.545166	+	0.243235i
$307$	3.52297			0.201066			0.100533	−	0.994934i	$-0.467945\pi$
$307$	3.52297			0.201066			0.100533	+	0.994934i	$0.467945\pi$
$308$	−3.77784	+	4.20893i	−0.215262	+	0.239826i
$309$			19.4244i			1.10502i
$310$		0			0
$311$	−21.6757			−1.22912			−0.614559	−	0.788871i	$-0.710666\pi$
$311$	−21.6757			−1.22912			−0.614559	+	0.788871i	$0.710666\pi$
$312$	0.649641	+	0.209398i	0.0367787	+	0.0118548i
$313$			12.5486i			0.709288i	0.935001	+	0.354644i	$0.115398\pi$
$313$			12.5486i			0.709288i	−0.935001	+	0.354644i	$0.884602\pi$
$314$	10.0346	+	22.4907i	0.566283	+	1.26922i
$315$		0			0
$316$	−18.2699	+	20.3547i	−1.02776	+	1.14504i
$317$	−10.8611			−0.610020			−0.305010	−	0.952349i	$-0.598660\pi$
$317$	−10.8611			−0.610020			−0.305010	+	0.952349i	$0.598660\pi$
$318$	5.30489	+	11.8900i	0.297483	+	0.666755i
$319$	12.9882			0.727202
$320$		0			0
$321$	−14.8085			−0.826529
$322$	0.995917	+	2.23217i	0.0555003	+	0.124394i
$323$	22.4500			1.24915
$324$	−1.33594	+	1.48838i	−0.0742186	+	0.0826878i
$325$		0			0
$326$	−2.68627	−	6.02079i	−0.148779	−	0.333461i
$327$			15.2296i			0.842197i
$328$	−5.15038	−	1.66011i	−0.284382	−	0.0916645i
$329$	−6.60978			−0.364409
$330$		0			0
$331$		−	1.23185i		−	0.0677088i	−0.999427	−	0.0338544i	$-0.989222\pi$
$331$		−	1.23185i		−	0.0677088i	0.999427	−	0.0338544i	$-0.0107783\pi$
$332$	16.4747	−	18.3547i	0.904169	−	1.00734i
$333$	−8.81463			−0.483038
$334$	−0.177476	+	0.0791838i	−0.00971107	+	0.00433275i
$335$		0			0
$336$	7.86110	−	0.851098i	0.428858	−	0.0464312i
$337$			4.13890i			0.225460i	0.993626	+	0.112730i	$0.0359595\pi$
$337$			4.13890i			0.225460i	−0.993626	+	0.112730i	$0.964040\pi$
$338$	7.45733	+	16.7143i	0.405625	+	0.909136i
$339$		−	1.13890i		−	0.0618564i
$340$		0			0
$341$		−	10.6542i		−	0.576959i
$342$	3.92658	−	1.75191i	0.212325	−	0.0947322i
$343$		−	19.9503i		−	1.07721i
$344$	−30.2724	−	9.75767i	−1.63218	−	0.526098i
$345$		0			0
$346$	2.28573	+	5.12306i	0.122882	+	0.275417i
$347$	−17.4586			−0.937226			−0.468613	−	0.883404i	$-0.655246\pi$
$347$	−17.4586			−0.937226			−0.468613	+	0.883404i	$0.655246\pi$
$348$	−13.5133	−	12.1292i	−0.724388	−	0.650194i
$349$		−	21.2196i		−	1.13586i	−0.823078	−	0.567928i	$-0.807745\pi$
$349$		−	21.2196i		−	1.13586i	0.823078	−	0.567928i	$-0.192255\pi$
$350$		0			0
$351$	0.241319			0.0128807
$352$	−4.07358	−	6.99237i	−0.217122	−	0.372695i
$353$		−	21.0398i		−	1.11984i	−0.828548	−	0.559918i	$-0.810833\pi$
$353$		−	21.0398i		−	1.11984i	0.828548	−	0.559918i	$-0.189167\pi$
$354$	8.31229	−	3.70866i	0.441793	−	0.197113i
$355$		0			0
$356$	−10.7952	+	12.0271i	−0.572147	+	0.637435i
$357$	14.5965			0.772531
$358$	6.05388	−	2.70103i	0.319957	−	0.142754i
$359$	−23.5153			−1.24109			−0.620546	−	0.784170i	$-0.713089\pi$
$359$	−23.5153			−1.24109			−0.620546	+	0.784170i	$0.713089\pi$
$360$		0			0
$361$	9.75639			0.513494
$362$	−11.7558	+	5.24502i	−0.617869	+	0.275672i
$363$	−8.95352			−0.469938
$364$	−0.710003	−	0.637282i	−0.0372143	−	0.0334027i
$365$		0			0
$366$	5.90642	−	2.63524i	0.308733	−	0.137746i
$367$		−	25.4012i		−	1.32593i	−0.748650	−	0.662965i	$-0.769298\pi$
$367$		−	25.4012i		−	1.32593i	0.748650	−	0.662965i	$-0.230702\pi$
$368$	−3.47703	+	0.376448i	−0.181253	+	0.0196237i
$369$	−1.91319			−0.0995967
$370$		0			0
$371$		−	18.1987i		−	0.944829i
$372$	−9.94957	+	11.0849i	−0.515861	+	0.574727i
$373$	10.0677			0.521286			0.260643	−	0.965435i	$-0.416065\pi$
$373$	10.0677			0.521286			0.260643	+	0.965435i	$0.416065\pi$
$374$	−6.08681	−	13.6425i	−0.314741	−	0.705436i
$375$		0			0
$376$	2.90143	−	9.00148i	0.149630	−	0.464216i
$377$			2.19098i			0.112841i
$378$	2.55298	−	1.13905i	0.131311	−	0.0585866i
$379$		−	18.9674i		−	0.974289i	−0.873321	−	0.487145i	$-0.838038\pi$
$379$		−	18.9674i		−	0.974289i	0.873321	−	0.487145i	$-0.161962\pi$
$380$		0			0
$381$		−	2.43616i		−	0.124808i
$382$	−8.76222	−	19.6389i	−0.448314	−	1.00482i
$383$			28.7446i			1.46878i	0.678727	+	0.734391i	$0.262532\pi$
$383$			28.7446i			1.46878i	−0.678727	+	0.734391i	$0.737468\pi$
$384$	−2.29166	+	11.0792i	−0.116946	+	0.565382i
$385$		0			0
$386$	26.8068	−	11.9603i	1.36443	−	0.608763i
$387$	−11.2452			−0.571624
$388$	−15.8895	−	14.2621i	−0.806669	−	0.724048i
$389$			29.8161i			1.51174i	0.654724	+	0.755868i	$0.272785\pi$
$389$			29.8161i			1.51174i	−0.654724	+	0.755868i	$0.727215\pi$
$390$		0			0
$391$	−6.45617			−0.326503
$392$	8.32490	+	2.68335i	0.420471	+	0.135530i
$393$		−	6.90143i		−	0.348131i
$394$	−13.3976	−	30.0283i	−0.674962	−	1.51281i
$395$		0			0
$396$	−2.12921	−	1.91113i	−0.106997	−	0.0960377i
$397$	2.73167			0.137099			0.0685494	−	0.997648i	$-0.478163\pi$
$397$	2.73167			0.137099			0.0685494	+	0.997648i	$0.478163\pi$
$398$	−4.15821	−	9.31988i	−0.208432	−	0.467163i
$399$	−6.01001			−0.300877
$400$		0			0
$401$	25.8744			1.29211			0.646054	−	0.763292i	$-0.276418\pi$
$401$	25.8744			1.29211			0.646054	+	0.763292i	$0.276418\pi$
$402$	−2.80431	−	6.28535i	−0.139866	−	0.313485i
$403$	1.79726			0.0895279
$404$	19.6560	+	17.6428i	0.977924	+	0.877762i
$405$		0			0
$406$	10.3417	+	23.1790i	0.513249	+	1.15035i
$407$		−	12.6098i		−	0.625044i
$408$	−6.40731	+	19.8782i	−0.317209	+	0.984117i
$409$	−22.4786			−1.11150			−0.555748	−	0.831351i	$-0.687568\pi$
$409$	−22.4786			−1.11150			−0.555748	+	0.831351i	$0.687568\pi$
$410$		0			0
$411$			5.39022i			0.265880i
$412$	28.9109	+	25.9498i	1.42434	+	1.27845i
$413$	−12.7227			−0.626045
$414$	−1.12921	+	0.503813i	−0.0554974	+	0.0247610i
$415$		0			0
$416$	1.17954	−	0.687170i	0.0578318	−	0.0336913i
$417$		−	17.4244i		−	0.853277i
$418$	2.50619	+	5.61718i	0.122582	+	0.274745i
$419$		−	24.5307i		−	1.19840i	−0.800598	−	0.599201i	$-0.795485\pi$
$419$		−	24.5307i		−	1.19840i	0.800598	−	0.599201i	$-0.204515\pi$
$420$		0			0
$421$			33.3856i			1.62712i	0.581483	+	0.813558i	$0.302473\pi$
$421$			33.3856i			1.62712i	−0.581483	+	0.813558i	$0.697527\pi$
$422$	5.66202	−	2.52620i	0.275623	−	0.122974i
$423$		−	3.34374i		−	0.162578i
$424$	24.7838	+	7.98852i	1.20361	+	0.387957i
$425$		0			0
$426$	−4.73544	−	10.6136i	−0.229433	−	0.514232i
$427$	−9.04033			−0.437492
$428$	−19.7832	+	22.0406i	−0.956256	+	1.06537i
$429$			0.345220i			0.0166674i
$430$		0			0
$431$	11.6548			0.561391			0.280696	−	0.959797i	$-0.409435\pi$
$431$	11.6548			0.561391			0.280696	+	0.959797i	$0.409435\pi$
$432$	0.430552	+	3.97676i	0.0207149	+	0.191332i
$433$		−	19.7681i		−	0.949996i	−0.879987	−	0.474998i	$-0.842449\pi$
$433$		−	19.7681i		−	0.949996i	0.879987	−	0.474998i	$-0.157551\pi$
$434$	19.0137	−	8.48326i	0.912687	−	0.407210i
$435$		0			0
$436$	22.6674	+	20.3457i	1.08557	+	0.974383i
$437$	2.65827			0.127163
$438$	−5.33019	+	2.37815i	−0.254687	+	0.113632i
$439$	25.1699			1.20129			0.600646	−	0.799515i	$-0.294910\pi$
$439$	25.1699			1.20129			0.600646	+	0.799515i	$0.294910\pi$
$440$		0			0
$441$	3.09242			0.147258
$442$	2.30135	−	1.02678i	0.109464	−	0.0488390i
$443$	19.5515			0.928922			0.464461	−	0.885594i	$-0.346248\pi$
$443$	19.5515			0.928922			0.464461	+	0.885594i	$0.346248\pi$
$444$	−11.7758	+	13.1195i	−0.558853	+	0.622625i
$445$		0			0
$446$	6.44266	−	2.87449i	0.305069	−	0.136111i
$447$			2.28551i			0.108101i
$448$	9.23517	−	12.8373i	0.436321	−	0.606507i
$449$	19.9612			0.942029			0.471014	−	0.882125i	$-0.343888\pi$
$449$	19.9612			0.942029			0.471014	+	0.882125i	$0.343888\pi$
$450$		0			0
$451$		−	2.73692i		−	0.128876i
$452$	−1.69511	−	1.52149i	−0.0797313	−	0.0715650i
$453$	−6.66425			−0.313114
$454$	−6.48650	−	14.5383i	−0.304426	−	0.682317i
$455$		0			0
$456$	2.63816	−	8.18468i	0.123543	−	0.383283i
$457$		−	5.01176i		−	0.234440i	−0.993106	−	0.117220i	$-0.962602\pi$
$457$		−	5.01176i		−	0.234440i	0.993106	−	0.117220i	$-0.0373983\pi$
$458$	20.4527	−	9.12528i	0.955690	−	0.426396i
$459$			7.38407i			0.344659i
$460$		0			0
$461$			5.12566i			0.238726i	0.992851	+	0.119363i	$0.0380852\pi$
$461$			5.12566i			0.238726i	−0.992851	+	0.119363i	$0.961915\pi$
$462$	1.62948	+	3.65217i	0.0758101	+	0.169915i
$463$			5.79515i			0.269324i	0.990892	+	0.134662i	$0.0429948\pi$
$463$			5.79515i			0.269324i	−0.990892	+	0.134662i	$0.957005\pi$
$464$	−36.1057	+	3.90906i	−1.67617	+	0.181474i
$465$		0			0
$466$	14.1537	−	6.31490i	0.655657	−	0.292532i
$467$	−16.8208			−0.778373			−0.389186	−	0.921159i	$-0.627244\pi$
$467$	−16.8208			−0.778373			−0.389186	+	0.921159i	$0.627244\pi$
$468$	0.322387	−	0.359175i	0.0149024	−	0.0166029i
$469$			9.62032i			0.444225i
$470$		0			0
$471$	17.4144			0.802413
$472$	5.58479	−	17.3264i	0.257061	−	0.797511i
$473$		−	16.0868i		−	0.739672i
$474$	7.88026	+	17.6622i	0.361952	+	0.811251i
$475$		0			0
$476$	19.5000	−	21.7252i	0.893783	−	0.995773i
$477$	9.20632			0.421529
$478$	9.97914	+	22.3664i	0.456435	+	1.02302i
$479$	36.9065			1.68630			0.843151	−	0.537678i	$-0.180698\pi$
$479$	36.9065			1.68630			0.843151	+	0.537678i	$0.180698\pi$
$480$		0			0
$481$	2.12714			0.0969892
$482$	−2.74782	−	6.15875i	−0.125160	−	0.280523i
$483$	1.72836			0.0786429
$484$	−11.9613	+	13.3262i	−0.543697	+	0.605738i
$485$		0			0
$486$	0.576222	+	1.29150i	0.0261380	+	0.0585836i
$487$		−	5.14984i		−	0.233361i	−0.993169	−	0.116681i	$-0.962775\pi$
$487$		−	5.14984i		−	0.233361i	0.993169	−	0.116681i	$-0.0372254\pi$
$488$	3.96835	−	12.3115i	0.179639	−	0.557316i
$489$	−4.66187			−0.210817
$490$		0			0
$491$		−	23.1154i		−	1.04318i	−0.853195	−	0.521591i	$-0.825339\pi$
$491$		−	23.1154i		−	1.04318i	0.853195	−	0.521591i	$-0.174661\pi$
$492$	−2.55590	+	2.84756i	−0.115229	+	0.128378i
$493$	−67.0414			−3.01939
$494$	−0.947560	+	0.422769i	−0.0426328	+	0.0190213i
$495$		0			0
$496$	3.20660	+	29.6175i	0.143980	+	1.32986i
$497$			16.2452i			0.728696i
$498$	−7.10597	−	15.9267i	−0.318426	−	0.713694i
$499$		−	14.3111i		−	0.640654i	−0.947307	−	0.320327i	$-0.896207\pi$
$499$		−	14.3111i		−	0.640654i	0.947307	−	0.320327i	$-0.103793\pi$
$500$		0			0
$501$			0.137419i			0.00613942i
$502$	−7.95352	+	3.54859i	−0.354983	+	0.158381i
$503$		−	15.4224i		−	0.687650i	−0.939034	−	0.343825i	$-0.888277\pi$
$503$		−	15.4224i		−	0.687650i	0.939034	−	0.343825i	$-0.111723\pi$
$504$	1.71528	−	5.32151i	0.0764045	−	0.237039i
$505$		0			0
$506$	−0.720730	−	1.61539i	−0.0320404	−	0.0718127i
$507$	12.9418			0.574764
$508$	−3.62593	−	3.25455i	−0.160875	−	0.144397i
$509$		−	43.1578i		−	1.91294i	−0.291835	−	0.956469i	$-0.594266\pi$
$509$		−	43.1578i		−	1.91294i	0.291835	−	0.956469i	$-0.405734\pi$
$510$		0			0
$511$	8.15837			0.360905
$512$	13.4285	+	18.2119i	0.593463	+	0.804861i
$513$		−	3.04033i		−	0.134234i
$514$	−18.2855	+	8.15837i	−0.806539	+	0.359850i
$515$		0			0
$516$	−15.0228	+	16.7371i	−0.661343	+	0.736810i
$517$	4.78340			0.210374
$518$	22.5036	−	10.0403i	0.988751	−	0.441147i
$519$	3.96675			0.174121
$520$		0			0
$521$	−17.8232			−0.780848			−0.390424	−	0.920635i	$-0.627672\pi$
$521$	−17.8232			−0.780848			−0.390424	+	0.920635i	$0.627672\pi$
$522$	−11.7258	+	5.23163i	−0.513222	+	0.228982i
$523$	24.7502			1.08225			0.541126	−	0.840941i	$-0.317998\pi$
$523$	24.7502			1.08225			0.541126	+	0.840941i	$0.317998\pi$
$524$	−10.2720	−	9.21987i	−0.448733	−	0.402772i
$525$		0			0
$526$	20.1422	−	8.98677i	0.878242	−	0.391842i
$527$			54.9939i			2.39557i
$528$	−5.68896	+	0.615927i	−0.247580	+	0.0268048i
$529$	22.2355			0.966762
$530$		0			0
$531$		−	6.43616i		−	0.279306i
$532$	−8.02898	+	8.94517i	−0.348100	+	0.387822i
$533$	0.461690			0.0199980
$534$	4.65626	+	10.4362i	0.201496	+	0.451617i
$535$		0			0
$536$	−13.1014	−	4.22295i	−0.565893	−	0.182403i
$537$		−	4.68749i		−	0.202280i
$538$	14.6175	−	6.52181i	0.630203	−	0.281175i
$539$			4.42386i			0.190549i
$540$		0			0
$541$			16.9982i			0.730812i	0.930848	+	0.365406i	$0.119070\pi$
$541$			16.9982i			0.730812i	−0.930848	+	0.365406i	$0.880930\pi$
$542$	3.57537	+	8.01355i	0.153575	+	0.344211i
$543$			9.10242i			0.390622i
$544$	21.0266	+	36.0925i	0.901506	+	1.54745i
$545$		0			0
$546$	−0.616084	+	0.274876i	−0.0263660	+	0.0117636i
$547$	37.2385			1.59220			0.796101	−	0.605163i	$-0.206892\pi$
$547$	37.2385			1.59220			0.796101	+	0.605163i	$0.206892\pi$
$548$	8.02270	+	7.20099i	0.342713	+	0.307611i
$549$		−	4.57331i		−	0.195184i
$550$		0			0
$551$	27.6037			1.17596
$552$	−0.758681	+	2.35375i	−0.0322916	+	0.100182i
$553$		−	27.0336i		−	1.14959i
$554$	−10.9072	−	24.4465i	−0.463403	−	1.03863i
$555$		0			0
$556$	−25.9341	−	23.2779i	−1.09985	−	0.987202i
$557$	−14.7604			−0.625420			−0.312710	−	0.949849i	$-0.601237\pi$
$557$	−14.7604			−0.625420			−0.312710	+	0.949849i	$0.601237\pi$
$558$	4.29150	+	9.61862i	0.181674	+	0.407189i
$559$	2.71368			0.114776
$560$		0			0
$561$	−10.5633			−0.445983
$562$	12.4597	+	27.9262i	0.525581	+	1.17800i
$563$	−3.00561			−0.126671			−0.0633356	−	0.997992i	$-0.520174\pi$
$563$	−3.00561			−0.126671			−0.0633356	+	0.997992i	$0.520174\pi$
$564$	−4.97676	−	4.46702i	−0.209559	−	0.188096i
$565$		0			0
$566$	−16.7982	−	37.6500i	−0.706079	−	1.58255i
$567$		−	1.97676i		−	0.0830161i
$568$	−22.1234	−	7.13100i	−0.928276	−	0.299210i
$569$	23.1840			0.971923			0.485962	−	0.873980i	$-0.338469\pi$
$569$	23.1840			0.971923			0.485962	+	0.873980i	$0.338469\pi$
$570$		0			0
$571$			0.202739i			0.00848438i	0.999991	+	0.00424219i	$0.00135033\pi$
$571$			0.202739i			0.00848438i	−0.999991	+	0.00424219i	$0.998650\pi$
$572$	0.513819	+	0.461192i	0.0214838	+	0.0192834i
$573$	−15.2063			−0.635253
$574$	4.88434	−	2.17923i	0.203869	−	0.0909592i
$575$		0			0
$576$	6.49412	+	4.67187i	0.270588	+	0.194661i
$577$			21.8023i			0.907643i	0.891093	+	0.453821i	$0.149940\pi$
$577$			21.8023i			0.907643i	−0.891093	+	0.453821i	$0.850060\pi$
$578$	21.6225	+	48.4629i	0.899376	+	2.01579i
$579$		−	20.7564i		−	0.862606i
$580$		0			0
$581$			24.3774i			1.01134i
$582$	−13.7877	+	6.15159i	−0.571518	+	0.254992i
$583$			13.1701i			0.545451i
$584$	−3.58120	+	11.1104i	−0.148191	+	0.459752i
$585$		0			0
$586$	−1.33930	−	3.00179i	−0.0553258	−	0.124003i
$587$	−36.7126			−1.51529			−0.757645	−	0.652667i	$-0.773650\pi$
$587$	−36.7126			−1.51529			−0.757645	+	0.652667i	$0.773650\pi$
$588$	4.13127	−	4.60269i	0.170371	−	0.189812i
$589$		−	22.6433i		−	0.933001i
$590$		0			0
$591$	−23.2508			−0.956409
$592$	3.79515	+	35.0537i	0.155980	+	1.44070i
$593$		−	10.6036i		−	0.435439i	−0.976011	−	0.217719i	$-0.930138\pi$
$593$		−	10.6036i		−	0.435439i	0.976011	−	0.217719i	$-0.0698618\pi$
$594$	−1.84756	+	0.824316i	−0.0758061	+	0.0338221i
$595$		0			0
$596$	3.40170	+	3.05329i	0.139339	+	0.125068i
$597$	−7.21633			−0.295345
$598$	0.272499	−	0.121580i	0.0111433	−	0.00497177i
$599$	25.7988			1.05411			0.527056	−	0.849831i	$-0.323296\pi$
$599$	25.7988			1.05411			0.527056	+	0.849831i	$0.323296\pi$
$600$		0			0
$601$	18.5021			0.754717			0.377358	−	0.926067i	$-0.376832\pi$
$601$	18.5021			0.754717			0.377358	+	0.926067i	$0.376832\pi$
$602$	28.7087	−	12.8089i	1.17008	−	0.522050i
$603$	−4.86671			−0.198188
$604$	−8.90300	+	9.91893i	−0.362258	+	0.403596i
$605$		0			0
$606$	17.0559	−	7.60978i	0.692850	−	0.309126i
$607$		−	37.5828i		−	1.52544i	−0.646730	−	0.762719i	$-0.723864\pi$
$607$		−	37.5828i		−	1.52544i	0.646730	−	0.762719i	$-0.276136\pi$
$608$	−8.65751	−	14.8608i	−0.351108	−	0.602685i
$609$	17.9474			0.727264
$610$		0			0
$611$			0.806910i			0.0326441i
$612$	10.9903	+	9.86465i	0.444257	+	0.398755i
$613$	4.93405			0.199284			0.0996422	−	0.995023i	$-0.468230\pi$
$613$	4.93405			0.199284			0.0996422	+	0.995023i	$0.468230\pi$
$614$	−2.03001	−	4.54991i	−0.0819247	−	0.183619i
$615$		0			0
$616$	7.61270	+	2.45379i	0.306724	+	0.0988661i
$617$		−	6.26043i		−	0.252035i	−0.992028	−	0.126018i	$-0.959780\pi$
$617$		−	6.26043i		−	0.252035i	0.992028	−	0.126018i	$-0.0402196\pi$
$618$	25.0866	−	11.1928i	1.00913	−	0.450239i
$619$		−	8.02562i		−	0.322577i	−0.986907	−	0.161288i	$-0.948435\pi$
$619$		−	8.02562i		−	0.322577i	0.986907	−	0.161288i	$-0.0515649\pi$
$620$		0			0
$621$			0.874337i			0.0350860i
$622$	12.4900	+	27.9942i	0.500805	+	1.12246i
$623$		−	15.9735i		−	0.639966i
$624$	−0.103901	−	0.959669i	−0.00415935	−	0.0384175i
$625$		0			0
$626$	16.2065	−	7.23078i	0.647741	−	0.289000i
$627$	4.34935			0.173696
$628$	23.2645	−	25.9192i	0.928355	−	1.03429i
$629$			65.0878i			2.59522i
$630$		0			0
$631$	−26.5248			−1.05594			−0.527968	−	0.849264i	$-0.677046\pi$
$631$	−26.5248			−1.05594			−0.527968	+	0.849264i	$0.677046\pi$
$632$	36.8156	+	11.8667i	1.46444	+	0.472032i
$633$		−	4.38407i		−	0.174251i
$634$	6.25841	+	14.0271i	0.248553	+	0.557087i
$635$		0			0
$636$	12.2991	−	13.7025i	0.487689	−	0.543340i
$637$	−0.746260			−0.0295679
$638$	−7.48412	−	16.7743i	−0.296299	−	0.664101i
$639$	−8.21808			−0.325102
$640$		0			0
$641$	−26.5863			−1.05009			−0.525047	−	0.851073i	$-0.675952\pi$
$641$	−26.5863			−1.05009			−0.525047	+	0.851073i	$0.675952\pi$
$642$	8.53298	+	19.1251i	0.336770	+	0.754808i
$643$	−2.89233			−0.114062			−0.0570312	−	0.998372i	$-0.518163\pi$
$643$	−2.89233			−0.114062			−0.0570312	+	0.998372i	$0.518163\pi$
$644$	2.30897	−	2.57245i	0.0909862	−	0.101369i
$645$		0			0
$646$	−12.9362	−	28.9942i	−0.508968	−	1.14076i
$647$		−	12.3472i		−	0.485420i	−0.970099	−	0.242710i	$-0.921964\pi$
$647$		−	12.3472i		−	0.485420i	0.970099	−	0.242710i	$-0.0780363\pi$
$648$	2.69204	+	0.867721i	0.105753	+	0.0340873i
$649$	9.20726			0.361417
$650$		0			0
$651$		−	14.7222i		−	0.577009i
$652$	−6.22795	+	6.93863i	−0.243905	+	0.271738i
$653$	−39.0507			−1.52817			−0.764086	−	0.645114i	$-0.776810\pi$
$653$	−39.0507			−1.52817			−0.764086	+	0.645114i	$0.776810\pi$
$654$	19.6690	−	8.77561i	0.769117	−	0.343154i
$655$		0			0
$656$	0.823728	+	7.60830i	0.0321612	+	0.297054i
$657$			4.12714i			0.161015i
$658$	3.80870	+	8.53652i	0.148479	+	0.332788i
$659$		−	23.7738i		−	0.926094i	−0.886334	−	0.463047i	$-0.846756\pi$
$659$		−	23.7738i		−	0.926094i	0.886334	−	0.463047i	$-0.153244\pi$
$660$		0			0
$661$		−	21.5051i		−	0.836450i	−0.908343	−	0.418225i	$-0.862652\pi$
$661$		−	21.5051i		−	0.836450i	0.908343	−	0.418225i	$-0.137348\pi$
$662$	−1.59094	+	0.709822i	−0.0618335	+	0.0275880i
$663$		−	1.78192i		−	0.0692040i
$664$	−33.1982	−	10.7007i	−1.28834	−	0.415268i
$665$		0			0
$666$	5.07918	+	11.3841i	0.196814	+	0.441124i
$667$	−7.93827			−0.307371
$668$	0.204532	+	0.183583i	0.00791356	+	0.00710303i
$669$		−	4.98852i		−	0.192867i
$670$		0			0
$671$	6.54235			0.252565
$672$	−5.62894	−	9.66218i	−0.217141	−	0.372727i
$673$			36.1896i			1.39501i	0.716582	+	0.697503i	$0.245706\pi$
$673$			36.1896i			1.39501i	−0.716582	+	0.697503i	$0.754294\pi$
$674$	5.34538	−	2.38492i	0.205896	−	0.0918639i
$675$		0			0
$676$	17.2894	−	19.2623i	0.664976	−	0.740856i
$677$	9.17214			0.352514			0.176257	−	0.984344i	$-0.443601\pi$
$677$	9.17214			0.352514			0.176257	+	0.984344i	$0.443601\pi$
$678$	−1.47088	+	0.656257i	−0.0564889	+	0.0252034i
$679$	21.1034			0.809873
$680$		0			0
$681$	−11.2569			−0.431367
$682$	−13.7599	+	6.13921i	−0.526895	+	0.235083i
$683$	16.3974			0.627429			0.313714	−	0.949517i	$-0.398427\pi$
$683$	16.3974			0.627429			0.313714	+	0.949517i	$0.398427\pi$
$684$	−4.52517	−	4.06169i	−0.173024	−	0.155302i
$685$		0			0
$686$	−25.7658	+	11.4958i	−0.983742	+	0.438912i
$687$		−	15.8364i		−	0.604196i
$688$	4.84163	+	44.7194i	0.184586	+	1.70491i
$689$	−2.22166			−0.0846387
$690$		0			0
$691$		−	24.4904i		−	0.931657i	−0.884875	−	0.465828i	$-0.845756\pi$
$691$		−	24.4904i		−	0.931657i	0.884875	−	0.465828i	$-0.154244\pi$
$692$	5.29933	−	5.90404i	0.201450	−	0.224438i
$693$	2.82786			0.107421
$694$	10.0600	+	22.5477i	0.381873	+	0.855900i
$695$		0			0
$696$	−7.87820	+	24.4415i	−0.298622	+	0.926452i
$697$			14.1271i			0.535104i
$698$	−27.4050	+	12.2272i	−1.03730	+	0.462806i
$699$		−	10.9591i		−	0.414512i
$700$		0			0
$701$			12.3887i			0.467916i	0.972247	+	0.233958i	$0.0751679\pi$
$701$			12.3887i			0.467916i	−0.972247	+	0.233958i	$0.924832\pi$
$702$	−0.139054	−	0.311664i	−0.00524824	−	0.0117630i
$703$		−	26.7994i		−	1.01076i
$704$	−6.68335	+	9.29018i	−0.251888	+	0.350137i
$705$		0			0
$706$	−27.1729	+	12.1236i	−1.02266	+	0.456278i
$707$	−26.1057			−0.981807
$708$	−9.57945	−	8.59830i	−0.360018	−	0.323144i
$709$			33.4144i			1.25490i	0.778655	+	0.627452i	$0.215902\pi$
$709$			33.4144i			1.25490i	−0.778655	+	0.627452i	$0.784098\pi$
$710$		0			0
$711$	13.6757			0.512880
$712$	21.7534	+	7.01176i	0.815244	+	0.262777i
$713$			6.51175i			0.243867i
$714$	−8.41086	−	18.8514i	−0.314768	−	0.705496i
$715$		0			0
$716$	−6.97676	−	6.26218i	−0.260734	−	0.234029i
$717$	17.3182			0.646761
$718$	13.5501	+	30.3700i	0.505684	+	1.13340i
$719$	33.8938			1.26403			0.632013	−	0.774958i	$-0.282229\pi$
$719$	33.8938			1.26403			0.632013	+	0.774958i	$0.282229\pi$
$720$		0			0
$721$	−38.3974			−1.42999
$722$	−5.62185	−	12.6004i	−0.209224	−	0.468937i
$723$	−4.76869			−0.177349
$724$	13.5479	+	12.1603i	0.503503	+	0.451932i
$725$		0			0
$726$	5.15922	+	11.5635i	0.191477	+	0.429160i
$727$			14.1846i			0.526076i	0.964785	+	0.263038i	$0.0847245\pi$
$727$			14.1846i			0.526076i	−0.964785	+	0.263038i	$0.915275\pi$
$728$	−0.413929	+	1.28418i	−0.0153412	+	0.0475950i
$729$	1.00000			0.0370370
$730$		0			0
$731$			83.0352i			3.07117i
$732$	−6.80682	−	6.10964i	−0.251587	−	0.225819i
$733$	−8.09296			−0.298920			−0.149460	−	0.988768i	$-0.547754\pi$
$733$	−8.09296			−0.298920			−0.149460	+	0.988768i	$0.547754\pi$
$734$	−32.8056	+	14.6367i	−1.21088	+	0.540251i
$735$		0			0
$736$	2.48972	+	4.27366i	0.0917725	+	0.157529i
$737$		−	6.96208i		−	0.256452i
$738$	1.10242	+	2.47088i	0.0405808	+	0.0909544i
$739$		−	22.0919i		−	0.812663i	−0.913726	−	0.406331i	$-0.866808\pi$
$739$		−	22.0919i		−	0.812663i	0.913726	−	0.406331i	$-0.133192\pi$
$740$		0			0
$741$			0.733691i			0.0269528i
$742$	−23.5036	+	10.4865i	−0.862844	+	0.384971i
$743$			8.78340i			0.322232i	0.986936	+	0.161116i	$0.0515093\pi$
$743$			8.78340i			0.322232i	−0.986936	+	0.161116i	$0.948491\pi$
$744$	20.0493	+	6.46247i	0.735044	+	0.236926i
$745$		0			0
$746$	−5.80123	−	13.0024i	−0.212398	−	0.476052i
$747$	−12.3320			−0.451204
$748$	−14.1119	+	15.7222i	−0.515982	+	0.574861i
$749$		−	29.2728i		−	1.06961i
$750$		0			0
$751$	13.3779			0.488167			0.244084	−	0.969754i	$-0.421513\pi$
$751$	13.3779			0.488167			0.244084	+	0.969754i	$0.421513\pi$
$752$	−13.2973	+	1.43965i	−0.484901	+	0.0524988i
$753$			6.15837i			0.224423i
$754$	2.82965	−	1.26249i	0.103050	−	0.0459773i
$755$		0			0
$756$	−2.94217	−	2.64082i	−0.107006	−	0.0960459i
$757$	9.72450			0.353443			0.176721	−	0.984261i	$-0.443451\pi$
$757$	9.72450			0.353443			0.176721	+	0.984261i	$0.443451\pi$
$758$	−24.4963	+	10.9294i	−0.889747	+	0.396975i
$759$	−1.25079			−0.0454006
$760$		0			0
$761$	33.8835			1.22828			0.614138	−	0.789198i	$-0.289504\pi$
$761$	33.8835			1.22828			0.614138	+	0.789198i	$0.289504\pi$
$762$	−3.14630	+	1.40377i	−0.113978	+	0.0508532i
$763$	−30.1052			−1.08988
$764$	−20.3147	+	22.6328i	−0.734959	+	0.818826i
$765$		0			0
$766$	37.1236	−	16.5633i	1.34133	−	0.598456i
$767$			1.55317i			0.0560817i
$768$	15.6293	−	3.42440i	0.563972	−	0.123568i
$769$	−18.7334			−0.675545			−0.337772	−	0.941228i	$-0.609673\pi$
$769$	−18.7334			−0.675545			−0.337772	+	0.941228i	$0.609673\pi$
$770$		0			0
$771$			14.1584i			0.509901i
$772$	−30.8934	−	27.7292i	−1.11188	−	0.997996i
$773$	22.5006			0.809292			0.404646	−	0.914474i	$-0.367395\pi$
$773$	22.5006			0.809292			0.404646	+	0.914474i	$0.367395\pi$
$774$	6.47972	+	14.5231i	0.232909	+	0.522023i
$775$		0			0
$776$	−9.26355	+	28.7395i	−0.332542	+	1.03169i
$777$		−	17.4244i		−	0.625097i
$778$	38.5074	−	17.1807i	1.38056	−	0.615958i
$779$		−	5.81673i		−	0.208406i
$780$		0			0
$781$		−	11.7564i		−	0.420677i
$782$	3.72019	+	8.33813i	0.133034	+	0.298171i
$783$			9.07918i			0.324464i
$784$	−1.33145	−	12.2978i	−0.0475517	−	0.439207i
$785$		0			0
$786$	−8.91319	+	3.97676i	−0.317923	+	0.141846i
$787$	−28.1063			−1.00188			−0.500940	−	0.865482i	$-0.667012\pi$
$787$	−28.1063			−1.00188			−0.500940	+	0.865482i	$0.667012\pi$
$788$	−31.0616	+	34.6060i	−1.10652	+	1.23279i
$789$		−	15.5960i		−	0.555232i
$790$		0			0
$791$	2.25133			0.0800479
$792$	−1.24132	+	3.85110i	−0.0441084	+	0.136843i
$793$			1.10363i			0.0391910i
$794$	−1.57405	−	3.52795i	−0.0558610	−	0.125202i
$795$		0			0
$796$	−9.64055	+	10.7406i	−0.341700	+	0.380692i
$797$	−38.1461			−1.35120			−0.675602	−	0.737267i	$-0.736116\pi$
$797$	−38.1461			−1.35120			−0.675602	+	0.737267i	$0.736116\pi$
$798$	3.46310	+	7.76191i	0.122592	+	0.274769i
$799$	−24.6904			−0.873485
$800$		0			0
$801$	8.08066			0.285516
$802$	−14.9094	−	33.4168i	−0.526470	−	1.17999i
$803$	−5.90409			−0.208351
$804$	−6.50161	+	7.24352i	−0.229294	+	0.255459i
$805$		0			0
$806$	−1.03562	−	2.32116i	−0.0364782	−	0.0817593i
$807$		−	11.3182i		−	0.398420i
$808$	11.4594	−	35.5519i	0.403140	−	1.25071i
$809$	10.0745			0.354201			0.177101	−	0.984193i	$-0.443328\pi$
$809$	10.0745			0.354201			0.177101	+	0.984193i	$0.443328\pi$
$810$		0			0
$811$		−	40.6001i		−	1.42566i	−0.701335	−	0.712832i	$-0.747412\pi$
$811$		−	40.6001i		−	1.42566i	0.701335	−	0.712832i	$-0.252588\pi$
$812$	23.9765	−	26.7125i	0.841411	−	0.937426i
$813$	6.20485			0.217613
$814$	−16.2855	+	7.26604i	−0.570807	+	0.254674i
$815$		0			0
$816$	29.3647	−	3.17923i	1.02797	−	0.111295i
$817$		−	34.1891i		−	1.19612i
$818$	12.9527	+	29.0311i	0.452879	+	1.01505i
$819$			0.477031i			0.0166688i
$820$		0			0
$821$			10.3397i			0.360858i	0.983588	+	0.180429i	$0.0577486\pi$
$821$			10.3397i			0.360858i	−0.983588	+	0.180429i	$0.942251\pi$
$822$	6.96146	−	3.10597i	0.242809	−	0.108333i
$823$			28.5013i			0.993493i	0.867896	+	0.496746i	$0.165472\pi$
$823$			28.5013i			0.993493i	−0.867896	+	0.496746i	$0.834528\pi$
$824$	16.8550	−	52.2912i	0.587170	−	1.82165i
$825$		0			0
$826$	7.33113	+	16.4314i	0.255083	+	0.571722i
$827$	32.1957			1.11956			0.559778	−	0.828643i	$-0.310886\pi$
$827$	32.1957			1.11956			0.559778	+	0.828643i	$0.310886\pi$
$828$	1.30135	+	1.16806i	0.0452249	+	0.0405928i
$829$		−	31.5286i		−	1.09503i	−0.836795	−	0.547516i	$-0.815573\pi$
$829$		−	31.5286i		−	1.09503i	0.836795	−	0.547516i	$-0.184427\pi$
$830$		0			0
$831$	−18.9288			−0.656633
$832$	−1.56716	−	1.12741i	−0.0543314	−	0.0390860i
$833$		−	22.8346i		−	0.791173i
$834$	−22.5036	+	10.0403i	−0.779236	+	0.347668i
$835$		0			0
$836$	5.81045	−	6.47349i	0.200959	−	0.223890i
$837$	7.44764			0.257428
$838$	−31.6813	+	14.1351i	−1.09441	+	0.488290i
$839$	−54.9816			−1.89818			−0.949089	−	0.315009i	$-0.897992\pi$
$839$	−54.9816			−1.89818			−0.949089	+	0.315009i	$0.897992\pi$
$840$		0			0
$841$	−53.4316			−1.84247
$842$	43.1175	−	19.2376i	1.48593	−	0.662970i
$843$	21.6231			0.744739
$844$	−6.52517	−	5.85684i	−0.224606	−	0.201601i
$845$		0			0
$846$	−4.31844	+	1.92674i	−0.148471	+	0.0662427i
$847$		−	17.6990i		−	0.608144i
$848$	−3.96380	−	36.6113i	−0.136117	−	1.25724i
$849$	−29.1522			−1.00050
$850$		0			0
$851$			7.70696i			0.264191i
$852$	−10.9788	+	12.2316i	−0.376128	+	0.419049i
$853$	−4.22607			−0.144698			−0.0723489	−	0.997379i	$-0.523050\pi$
$853$	−4.22607			−0.144698			−0.0723489	+	0.997379i	$0.523050\pi$
$854$	5.20924	+	11.6756i	0.178257	+	0.399530i
$855$		0			0
$856$	39.8650	+	12.8496i	1.36256	+	0.439191i
$857$			54.8223i			1.87270i	0.351074	+	0.936348i	$0.385817\pi$
$857$			54.8223i			1.87270i	−0.351074	+	0.936348i	$0.614183\pi$
$858$	0.445851	−	0.198923i	0.0152211	−	0.00679113i
$859$			14.2126i			0.484926i	0.970161	+	0.242463i	$0.0779554\pi$
$859$			14.2126i			0.484926i	−0.970161	+	0.242463i	$0.922045\pi$
$860$		0			0
$861$		−	3.78192i		−	0.128887i
$862$	−6.71574	−	15.0521i	−0.228739	−	0.512678i
$863$		−	40.7446i		−	1.38696i	−0.720474	−	0.693482i	$-0.756076\pi$
$863$		−	40.7446i		−	1.38696i	0.720474	−	0.693482i	$-0.243924\pi$
$864$	4.88789	−	2.84756i	0.166289	−	0.0968758i
$865$		0			0
$866$	−25.5305	+	11.3908i	−0.867563	+	0.387077i
$867$	37.5245			1.27440
$868$	−21.9122	−	19.6679i	−0.743750	−	0.667573i
$869$			19.5638i			0.663658i
$870$		0			0
$871$	1.17443			0.0397941
$872$	13.2150	−	40.9985i	0.447517	−	1.38839i
$873$			10.6757i			0.361319i
$874$	−1.53176	−	3.43316i	−0.0518125	−	0.116128i
$875$		0			0
$876$	6.14275	+	5.51359i	0.207544	+	0.186287i
$877$	−34.4568			−1.16352			−0.581762	−	0.813359i	$-0.697637\pi$
$877$	−34.4568			−1.16352			−0.581762	+	0.813359i	$0.697637\pi$
$878$	−14.5034	−	32.5068i	−0.489467	−	1.09705i
$879$	−2.32427			−0.0783957
$880$		0			0
$881$	23.8528			0.803623			0.401811	−	0.915722i	$-0.368381\pi$
$881$	23.8528			0.803623			0.401811	+	0.915722i	$0.368381\pi$
$882$	−1.78192	−	3.99385i	−0.0600004	−	0.134480i
$883$	24.2417			0.815798			0.407899	−	0.913027i	$-0.366262\pi$
$883$	24.2417			0.815798			0.407899	+	0.913027i	$0.366262\pi$
$884$	−2.65217	−	2.38053i	−0.0892023	−	0.0800659i
$885$		0			0
$886$	−11.2660	−	25.2508i	−0.378490	−	0.848317i
$887$		−	39.1843i		−	1.31568i	−0.753158	−	0.657840i	$-0.771470\pi$
$887$		−	39.1843i		−	1.31568i	0.753158	−	0.657840i	$-0.228530\pi$
$888$	23.7293	+	7.64863i	0.796303	+	0.256671i
$889$	4.81571			0.161514
$890$		0			0
$891$			1.43055i			0.0479253i
$892$	−7.42481	−	6.66434i	−0.248601	−	0.223139i
$893$	10.1661			0.340195
$894$	2.95173	−	1.31696i	0.0987206	−	0.0440457i
$895$		0			0
$896$	−21.9009	−	4.53005i	−0.731658	−	0.151339i
$897$		−	0.210995i		−	0.00704490i
$898$	−11.5021	−	25.7799i	−0.383830	−	0.860286i
$899$			67.6185i			2.25520i
$900$		0			0
$901$		−	67.9802i		−	2.26475i
$902$	−3.53473	+	1.57707i	−0.117693	+	0.0525108i
$903$		−	22.2290i		−	0.739736i
$904$	−0.988244	+	3.06595i	−0.0328685	+	0.101972i
$905$		0			0
$906$	3.84009	+	8.60686i	0.127578	+	0.285944i
$907$	−18.9418			−0.628951			−0.314475	−	0.949266i	$-0.601829\pi$
$907$	−18.9418			−0.628951			−0.314475	+	0.949266i	$0.601829\pi$
$908$	−15.0385	+	16.7546i	−0.499071	+	0.556021i
$909$		−	13.2063i		−	0.438026i
$910$		0			0
$911$	17.8493			0.591375			0.295688	−	0.955285i	$-0.404451\pi$
$911$	17.8493			0.591375			0.295688	+	0.955285i	$0.404451\pi$
$912$	−12.0907	+	1.30902i	−0.400362	+	0.0433460i
$913$		−	17.6415i		−	0.583850i
$914$	−6.47267	+	2.88789i	−0.214097	+	0.0955228i
$915$		0			0
$916$	−23.5706	−	21.1564i	−0.778793	−	0.699027i
$917$	13.6425			0.450515
$918$	9.53652	−	4.25487i	0.314752	−	0.140432i
$919$	−24.4983			−0.808126			−0.404063	−	0.914731i	$-0.632402\pi$
$919$	−24.4983			−0.808126			−0.404063	+	0.914731i	$0.632402\pi$
$920$		0			0
$921$	−3.52297			−0.116086
$922$	6.61978	−	2.95352i	0.218011	−	0.0972690i
$923$	1.98318			0.0652772
$924$	3.77784	−	4.20893i	0.124282	−	0.138464i
$925$		0			0
$926$	7.48443	−	3.33930i	0.245954	−	0.109736i
$927$		−	19.4244i		−	0.637981i
$928$	25.8535	+	44.3780i	0.848682	+	1.45678i
$929$	−11.5577			−0.379196			−0.189598	−	0.981862i	$-0.560718\pi$
$929$	−11.5577			−0.379196			−0.189598	+	0.981862i	$0.560718\pi$
$930$		0			0
$931$			9.40197i			0.308137i
$932$	−16.3114	−	14.6407i	−0.534296	−	0.479572i
$933$	21.6757			0.709632
$934$	9.69251	+	21.7240i	0.317148	+	0.710831i
$935$		0			0
$936$	−0.649641	−	0.209398i	−0.0212342	−	0.00684438i
$937$		−	59.5587i		−	1.94570i	−0.231440	−	0.972849i	$-0.574344\pi$
$937$		−	59.5587i		−	1.94570i	0.231440	−	0.972849i	$-0.425656\pi$
$938$	12.4246	−	5.54345i	0.405679	−	0.181000i
$939$		−	12.5486i		−	0.409508i
$940$		0			0
$941$			55.9289i			1.82323i	0.411044	+	0.911615i	$0.365164\pi$
$941$			55.9289i			1.82323i	−0.411044	+	0.911615i	$0.634836\pi$
$942$	−10.0346	−	22.4907i	−0.326944	−	0.732785i
$943$			1.67277i			0.0544730i
$944$	−25.5951	+	2.77110i	−0.833048	+	0.0901917i
$945$		0			0
$946$	−20.7761	+	9.26958i	−0.675489	+	0.301380i
$947$	30.0945			0.977941			0.488970	−	0.872300i	$-0.337373\pi$
$947$	30.0945			0.977941			0.488970	+	0.872300i	$0.337373\pi$
$948$	18.2699	−	20.3547i	0.593379	−	0.661089i
$949$		−	0.995959i		−	0.0323302i
$950$		0			0
$951$	10.8611			0.352195
$952$	−39.2944	−	12.6657i	−1.27354	−	0.410498i
$953$		−	12.4097i		−	0.401989i	−0.979592	−	0.200995i	$-0.935583\pi$
$953$		−	12.4097i		−	0.401989i	0.979592	−	0.200995i	$-0.0644174\pi$
$954$	−5.30489	−	11.8900i	−0.171752	−	0.384951i
$955$		0			0
$956$	23.1360	−	25.7761i	0.748272	−	0.833658i
$957$	−12.9882			−0.419850
$958$	−21.2664	−	47.6647i	−0.687085	−	1.53998i
$959$	−10.6552			−0.344074
$960$		0			0
$961$	24.4674			0.789271
$962$	−1.22571	−	2.74720i	−0.0395183	−	0.0885732i
$963$	14.8085			0.477196
$964$	−6.37066	+	7.09762i	−0.205185	+	0.228599i
$965$		0			0
$966$	−0.995917	−	2.23217i	−0.0320431	−	0.0718188i
$967$			41.8371i			1.34539i	0.739920	+	0.672694i	$0.234863\pi$
$967$			41.8371i			1.34539i	−0.739920	+	0.672694i	$0.765137\pi$
$968$	24.1032	+	7.76916i	0.774706	+	0.249710i
$969$	−22.4500			−0.721199
$970$		0			0
$971$		−	40.6875i		−	1.30572i	−0.757477	−	0.652862i	$-0.773568\pi$
$971$		−	40.6875i		−	1.30572i	0.757477	−	0.652862i	$-0.226432\pi$
$972$	1.33594	−	1.48838i	0.0428502	−	0.0477398i
$973$	34.4439			1.10422
$974$	−6.65101	+	2.96745i	−0.213112	+	0.0950833i
$975$		0			0
$976$	−18.1869	+	1.96905i	−0.582150	+	0.0630276i
$977$			1.67923i			0.0537233i	0.999639	+	0.0268617i	$0.00855136\pi$
$977$			1.67923i			0.0537233i	−0.999639	+	0.0268617i	$0.991449\pi$
$978$	2.68627	+	6.02079i	0.0858975	+	0.192524i
$979$			11.5598i			0.369453i
$980$		0			0
$981$		−	15.2296i		−	0.486243i
$982$	−29.8535	+	13.3196i	−0.952663	+	0.425046i
$983$			13.4944i			0.430404i	0.976570	+	0.215202i	$0.0690411\pi$
$983$			13.4944i			0.430404i	−0.976570	+	0.215202i	$0.930959\pi$
$984$	5.15038	+	1.66011i	0.164188	+	0.0529225i
$985$		0			0
$986$	38.6307	+	86.5838i	1.23025	+	2.75739i
$987$	6.60978			0.210392
$988$	1.09201	+	0.980164i	0.0347415	+	0.0311832i
$989$			9.83208i			0.312642i
$990$		0			0
$991$	−10.8502			−0.344667			−0.172333	−	0.985039i	$-0.555131\pi$
$991$	−10.8502			−0.344667			−0.172333	+	0.985039i	$0.555131\pi$
$992$	36.4032	−	21.2076i	1.15580	−	0.673341i
$993$			1.23185i			0.0390917i
$994$	20.9806	−	9.36083i	0.665465	−	0.296908i
$995$		0			0
$996$	−16.4747	+	18.3547i	−0.522022	+	0.581590i
$997$	39.0972			1.23822			0.619110	−	0.785304i	$-0.287493\pi$
$997$	39.0972			1.23822			0.619110	+	0.785304i	$0.287493\pi$
$998$	−18.4828	+	8.24639i	−0.585063	+	0.261035i
$999$	8.81463			0.278882

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.d.g.349.3		8
3.2	odd	2		1800.2.d.t.1549.6		8
4.3	odd	2		2400.2.d.h.49.7		8
5.2	odd	4		600.2.k.e.301.7	yes	8
5.3	odd	4		600.2.k.d.301.2	yes	8
5.4	even	2		600.2.d.h.349.6		8
8.3	odd	2		2400.2.d.g.49.7		8
8.5	even	2		600.2.d.h.349.5		8
12.11	even	2		7200.2.d.t.2449.7		8
15.2	even	4		1800.2.k.q.901.2		8
15.8	even	4		1800.2.k.t.901.7		8
15.14	odd	2		1800.2.d.s.1549.3		8
20.3	even	4		2400.2.k.d.1201.8		8
20.7	even	4		2400.2.k.e.1201.1		8
20.19	odd	2		2400.2.d.g.49.2		8
24.5	odd	2		1800.2.d.s.1549.4		8
24.11	even	2		7200.2.d.s.2449.7		8
40.3	even	4		2400.2.k.d.1201.4		8
40.13	odd	4		600.2.k.d.301.1	✓	8
40.19	odd	2		2400.2.d.h.49.2		8
40.27	even	4		2400.2.k.e.1201.5		8
40.29	even	2	inner	600.2.d.g.349.4		8
40.37	odd	4		600.2.k.e.301.8	yes	8
60.23	odd	4		7200.2.k.r.3601.8		8
60.47	odd	4		7200.2.k.s.3601.2		8
60.59	even	2		7200.2.d.s.2449.2		8
120.29	odd	2		1800.2.d.t.1549.5		8
120.53	even	4		1800.2.k.t.901.8		8
120.59	even	2		7200.2.d.t.2449.2		8
120.77	even	4		1800.2.k.q.901.1		8
120.83	odd	4		7200.2.k.r.3601.7		8
120.107	odd	4		7200.2.k.s.3601.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.d.g.349.3		8	1.1	even	1	trivial
600.2.d.g.349.4		8	40.29	even	2	inner
600.2.d.h.349.5		8	8.5	even	2
600.2.d.h.349.6		8	5.4	even	2
600.2.k.d.301.1	✓	8	40.13	odd	4
600.2.k.d.301.2	yes	8	5.3	odd	4
600.2.k.e.301.7	yes	8	5.2	odd	4
600.2.k.e.301.8	yes	8	40.37	odd	4
1800.2.d.s.1549.3		8	15.14	odd	2
1800.2.d.s.1549.4		8	24.5	odd	2
1800.2.d.t.1549.5		8	120.29	odd	2
1800.2.d.t.1549.6		8	3.2	odd	2
1800.2.k.q.901.1		8	120.77	even	4
1800.2.k.q.901.2		8	15.2	even	4
1800.2.k.t.901.7		8	15.8	even	4
1800.2.k.t.901.8		8	120.53	even	4
2400.2.d.g.49.2		8	20.19	odd	2
2400.2.d.g.49.7		8	8.3	odd	2
2400.2.d.h.49.2		8	40.19	odd	2
2400.2.d.h.49.7		8	4.3	odd	2
2400.2.k.d.1201.4		8	40.3	even	4
2400.2.k.d.1201.8		8	20.3	even	4
2400.2.k.e.1201.1		8	20.7	even	4
2400.2.k.e.1201.5		8	40.27	even	4
7200.2.d.s.2449.2		8	60.59	even	2
7200.2.d.s.2449.7		8	24.11	even	2
7200.2.d.t.2449.2		8	120.59	even	2
7200.2.d.t.2449.7		8	12.11	even	2
7200.2.k.r.3601.7		8	120.83	odd	4
7200.2.k.r.3601.8		8	60.23	odd	4
7200.2.k.s.3601.1		8	120.107	odd	4
7200.2.k.s.3601.2		8	60.47	odd	4

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.576222 - 1.29150i) q^{2} -1.00000 q^{3} +(-1.33594 + 1.48838i) q^{4} +(0.576222 + 1.29150i) q^{6} -1.97676i q^{7} +(2.69204 + 0.867721i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.576222 - 1.29150i) q^{2} -1.00000 q^{3} +(-1.33594 + 1.48838i) q^{4} +(0.576222 + 1.29150i) q^{6} -1.97676i q^{7} +(2.69204 + 0.867721i) q^{8} +1.00000 q^{9} +1.43055i q^{11} +(1.33594 - 1.48838i) q^{12} -0.241319 q^{13} +(-2.55298 + 1.13905i) q^{14} +(-0.430552 - 3.97676i) q^{16} -7.38407i q^{17} +(-0.576222 - 1.29150i) q^{18} +3.04033i q^{19} +1.97676i q^{21} +(1.84756 - 0.824316i) q^{22} -0.874337i q^{23} +(-2.69204 - 0.867721i) q^{24} +(0.139054 + 0.311664i) q^{26} -1.00000 q^{27} +(2.94217 + 2.64082i) q^{28} -9.07918i q^{29} -7.44764 q^{31} +(-4.88789 + 2.84756i) q^{32} -1.43055i q^{33} +(-9.53652 + 4.25487i) q^{34} +(-1.33594 + 1.48838i) q^{36} -8.81463 q^{37} +(3.92658 - 1.75191i) q^{38} +0.241319 q^{39} -1.91319 q^{41} +(2.55298 - 1.13905i) q^{42} -11.2452 q^{43} +(-2.12921 - 1.91113i) q^{44} +(-1.12921 + 0.503813i) q^{46} -3.34374i q^{47} +(0.430552 + 3.97676i) q^{48} +3.09242 q^{49} +7.38407i q^{51} +(0.322387 - 0.359175i) q^{52} +9.20632 q^{53} +(0.576222 + 1.29150i) q^{54} +(1.71528 - 5.32151i) q^{56} -3.04033i q^{57} +(-11.7258 + 5.23163i) q^{58} -6.43616i q^{59} -4.57331i q^{61} +(4.29150 + 9.61862i) q^{62} -1.97676i q^{63} +(6.49412 + 4.67187i) q^{64} +(-1.84756 + 0.824316i) q^{66} -4.86671 q^{67} +(10.9903 + 9.86465i) q^{68} +0.874337i q^{69} -8.21808 q^{71} +(2.69204 + 0.867721i) q^{72} +4.12714i q^{73} +(5.07918 + 11.3841i) q^{74} +(-4.52517 - 4.06169i) q^{76} +2.82786 q^{77} +(-0.139054 - 0.311664i) q^{78} +13.6757 q^{79} +1.00000 q^{81} +(1.10242 + 2.47088i) q^{82} -12.3320 q^{83} +(-2.94217 - 2.64082i) q^{84} +(6.47972 + 14.5231i) q^{86} +9.07918i q^{87} +(-1.24132 + 3.85110i) q^{88} +8.08066 q^{89} +0.477031i q^{91} +(1.30135 + 1.16806i) q^{92} +7.44764 q^{93} +(-4.31844 + 1.92674i) q^{94} +(4.88789 - 2.84756i) q^{96} +10.6757i q^{97} +(-1.78192 - 3.99385i) q^{98} +1.43055i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{6} - 8 q^{8} + 8 q^{9} + 4 q^{12} + 6 q^{14} + 8 q^{16} - 2 q^{18} + 20 q^{22} + 8 q^{24} - 2 q^{26} - 8 q^{27} + 24 q^{28} + 8 q^{31} - 12 q^{32} - 12 q^{34} - 4 q^{36} + 14 q^{38} - 6 q^{42} - 8 q^{43} + 12 q^{44} + 20 q^{46} - 8 q^{48} + 24 q^{52} + 8 q^{53} + 2 q^{54} + 8 q^{56} - 20 q^{58} + 26 q^{62} + 32 q^{64} - 20 q^{66} + 24 q^{67} + 36 q^{68} - 40 q^{71} - 8 q^{72} - 8 q^{74} - 20 q^{76} - 24 q^{77} + 2 q^{78} + 16 q^{79} + 8 q^{81} - 16 q^{82} - 32 q^{83} - 24 q^{84} - 18 q^{86} - 8 q^{88} + 28 q^{92} - 8 q^{93} + 4 q^{94} + 12 q^{96} - 40 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^6 - 8 * q^8 + 8 * q^9 + 4 * q^12 + 6 * q^14 + 8 * q^16 - 2 * q^18 + 20 * q^22 + 8 * q^24 - 2 * q^26 - 8 * q^27 + 24 * q^28 + 8 * q^31 - 12 * q^32 - 12 * q^34 - 4 * q^36 + 14 * q^38 - 6 * q^42 - 8 * q^43 + 12 * q^44 + 20 * q^46 - 8 * q^48 + 24 * q^52 + 8 * q^53 + 2 * q^54 + 8 * q^56 - 20 * q^58 + 26 * q^62 + 32 * q^64 - 20 * q^66 + 24 * q^67 + 36 * q^68 - 40 * q^71 - 8 * q^72 - 8 * q^74 - 20 * q^76 - 24 * q^77 + 2 * q^78 + 16 * q^79 + 8 * q^81 - 16 * q^82 - 32 * q^83 - 24 * q^84 - 18 * q^86 - 8 * q^88 + 28 * q^92 - 8 * q^93 + 4 * q^94 + 12 * q^96 - 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more