LMFDB - Embedded newform 735.2.d.b.589.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(589,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("735.589");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.d (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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			589.4
Root			$0.403032 + 0.403032i$ of defining polynomial
Character	$\chi$	$=$	735.589
Dual form			735.2.d.b.589.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.193937i q^{2} -1.00000i q^{3} +1.96239 q^{4} +(1.48119 - 1.67513i) q^{5} +0.193937 q^{6} +0.768452i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+0.193937i q^{2} -1.00000i q^{3} +1.96239 q^{4} +(1.48119 - 1.67513i) q^{5} +0.193937 q^{6} +0.768452i q^{8} -1.00000 q^{9} +(0.324869 + 0.287258i) q^{10} +2.00000 q^{11} -1.96239i q^{12} +1.35026i q^{13} +(-1.67513 - 1.48119i) q^{15} +3.77575 q^{16} +3.35026i q^{17} -0.193937i q^{18} +5.35026 q^{19} +(2.90668 - 3.28726i) q^{20} +0.387873i q^{22} -4.96239i q^{23} +0.768452 q^{24} +(-0.612127 - 4.96239i) q^{25} -0.261865 q^{26} +1.00000i q^{27} -7.92478 q^{29} +(0.287258 - 0.324869i) q^{30} -4.57452 q^{31} +2.26916i q^{32} -2.00000i q^{33} -0.649738 q^{34} -1.96239 q^{36} -0.775746i q^{37} +1.03761i q^{38} +1.35026 q^{39} +(1.28726 + 1.13823i) q^{40} -3.73813 q^{41} +12.6253i q^{43} +3.92478 q^{44} +(-1.48119 + 1.67513i) q^{45} +0.962389 q^{46} -9.92478i q^{47} -3.77575i q^{48} +(0.962389 - 0.118714i) q^{50} +3.35026 q^{51} +2.64974i q^{52} -8.57452i q^{53} -0.193937 q^{54} +(2.96239 - 3.35026i) q^{55} -5.35026i q^{57} -1.53690i q^{58} -8.62530 q^{59} +(-3.28726 - 2.90668i) q^{60} +8.70052 q^{61} -0.887166i q^{62} +7.11142 q^{64} +(2.26187 + 2.00000i) q^{65} +0.387873 q^{66} +9.92478i q^{67} +6.57452i q^{68} -4.96239 q^{69} +2.00000 q^{71} -0.768452i q^{72} -9.35026i q^{73} +0.150446 q^{74} +(-4.96239 + 0.612127i) q^{75} +10.4993 q^{76} +0.261865i q^{78} -10.7005 q^{79} +(5.59261 - 6.32487i) q^{80} +1.00000 q^{81} -0.724961i q^{82} +3.22425i q^{83} +(5.61213 + 4.96239i) q^{85} -2.44851 q^{86} +7.92478i q^{87} +1.53690i q^{88} +1.03761 q^{89} +(-0.324869 - 0.287258i) q^{90} -9.73813i q^{92} +4.57452i q^{93} +1.92478 q^{94} +(7.92478 - 8.96239i) q^{95} +2.26916 q^{96} +18.4993i q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} - 2 q^{5} + 2 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 10 * q^4 - 2 * q^5 + 2 * q^6 - 6 * q^9	$ 6 q - 10 q^{4} - 2 q^{5} + 2 q^{6} - 6 q^{9} + 12 q^{10} + 12 q^{11} + 26 q^{16} + 12 q^{19} + 30 q^{20} - 18 q^{24} - 2 q^{25} - 20 q^{26} - 4 q^{29} - 10 q^{30} - 4 q^{31} - 24 q^{34} + 10 q^{36} - 12 q^{39} - 4 q^{40} - 4 q^{41} - 20 q^{44} + 2 q^{45} - 16 q^{46} - 16 q^{50} - 2 q^{54} - 4 q^{55} + 32 q^{59} - 8 q^{60} + 12 q^{61} - 26 q^{64} + 32 q^{65} + 4 q^{66} - 8 q^{69} + 12 q^{71} + 88 q^{74} - 8 q^{75} - 4 q^{76} - 24 q^{79} - 46 q^{80} + 6 q^{81} + 32 q^{85} - 8 q^{86} + 28 q^{89} - 12 q^{90} - 32 q^{94} + 4 q^{95} + 58 q^{96} - 12 q^{99}+O(q^{100}) $ 6 * q - 10 * q^4 - 2 * q^5 + 2 * q^6 - 6 * q^9 + 12 * q^10 + 12 * q^11 + 26 * q^16 + 12 * q^19 + 30 * q^20 - 18 * q^24 - 2 * q^25 - 20 * q^26 - 4 * q^29 - 10 * q^30 - 4 * q^31 - 24 * q^34 + 10 * q^36 - 12 * q^39 - 4 * q^40 - 4 * q^41 - 20 * q^44 + 2 * q^45 - 16 * q^46 - 16 * q^50 - 2 * q^54 - 4 * q^55 + 32 * q^59 - 8 * q^60 + 12 * q^61 - 26 * q^64 + 32 * q^65 + 4 * q^66 - 8 * q^69 + 12 * q^71 + 88 * q^74 - 8 * q^75 - 4 * q^76 - 24 * q^79 - 46 * q^80 + 6 * q^81 + 32 * q^85 - 8 * q^86 + 28 * q^89 - 12 * q^90 - 32 * q^94 + 4 * q^95 + 58 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$			0.193937i			0.137134i	0.997647	+	0.0685669i	$0.0218427\pi$
$2$			0.193937i			0.137134i	−0.997647	+	0.0685669i	$0.978157\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.96239			0.981194
$5$	1.48119	−	1.67513i	0.662410	−	0.749141i
$5$	1.48119	−	1.67513i	0.662410	−	0.749141i
$6$	0.193937			0.0791743
$7$		0			0
$7$		0			0
$8$			0.768452i			0.271689i
$9$	−1.00000			−0.333333
$10$	0.324869	+	0.287258i	0.102733	+	0.0908389i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$		−	1.96239i		−	0.566493i
$13$			1.35026i			0.374495i	0.982313	+	0.187248i	$0.0599567\pi$
$13$			1.35026i			0.374495i	−0.982313	+	0.187248i	$0.940043\pi$
$14$		0			0
$15$	−1.67513	−	1.48119i	−0.432517	−	0.382443i
$16$	3.77575			0.943937
$17$			3.35026i			0.812558i	0.913749	+	0.406279i	$0.133174\pi$
$17$			3.35026i			0.812558i	−0.913749	+	0.406279i	$0.866826\pi$
$18$		−	0.193937i		−	0.0457113i
$19$	5.35026			1.22743			0.613717	−	0.789526i	$-0.289674\pi$
$19$	5.35026			1.22743			0.613717	+	0.789526i	$0.289674\pi$
$20$	2.90668	−	3.28726i	0.649953	−	0.735053i
$21$		0			0
$22$			0.387873i			0.0826948i
$23$		−	4.96239i		−	1.03473i	−0.855765	−	0.517365i	$-0.826913\pi$
$23$		−	4.96239i		−	1.03473i	0.855765	−	0.517365i	$-0.173087\pi$
$24$	0.768452			0.156860
$25$	−0.612127	−	4.96239i	−0.122425	−	0.992478i
$26$	−0.261865			−0.0513560
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−7.92478			−1.47159			−0.735797	−	0.677202i	$-0.763192\pi$
$29$	−7.92478			−1.47159			−0.735797	+	0.677202i	$0.763192\pi$
$30$	0.287258	−	0.324869i	0.0524458	−	0.0593127i
$31$	−4.57452			−0.821607			−0.410804	−	0.911724i	$-0.634752\pi$
$31$	−4.57452			−0.821607			−0.410804	+	0.911724i	$0.634752\pi$
$32$			2.26916i			0.401134i
$33$		−	2.00000i		−	0.348155i
$34$	−0.649738			−0.111429
$35$		0			0
$36$	−1.96239			−0.327065
$37$		−	0.775746i		−	0.127532i	−0.997965	−	0.0637660i	$-0.979689\pi$
$37$		−	0.775746i		−	0.127532i	0.997965	−	0.0637660i	$-0.0203111\pi$
$38$			1.03761i			0.168323i
$39$	1.35026			0.216215
$40$	1.28726	+	1.13823i	0.203533	+	0.179969i
$41$	−3.73813			−0.583799			−0.291899	−	0.956449i	$-0.594287\pi$
$41$	−3.73813			−0.583799			−0.291899	+	0.956449i	$0.594287\pi$
$42$		0			0
$43$			12.6253i			1.92534i	0.270677	+	0.962670i	$0.412752\pi$
$43$			12.6253i			1.92534i	−0.270677	+	0.962670i	$0.587248\pi$
$44$	3.92478			0.591682
$45$	−1.48119	+	1.67513i	−0.220803	+	0.249714i
$46$	0.962389			0.141896
$47$		−	9.92478i		−	1.44768i	−0.689969	−	0.723839i	$-0.742376\pi$
$47$		−	9.92478i		−	1.44768i	0.689969	−	0.723839i	$-0.257624\pi$
$48$		−	3.77575i		−	0.544982i
$49$		0			0
$50$	0.962389	−	0.118714i	0.136102	−	0.0167887i
$51$	3.35026			0.469130
$52$			2.64974i			0.367453i
$53$		−	8.57452i		−	1.17780i	−0.808206	−	0.588900i	$-0.799561\pi$
$53$		−	8.57452i		−	1.17780i	0.808206	−	0.588900i	$-0.200439\pi$
$54$	−0.193937			−0.0263914
$55$	2.96239	−	3.35026i	0.399448	−	0.451749i
$56$		0			0
$57$		−	5.35026i		−	0.708659i
$58$		−	1.53690i		−	0.201805i
$59$	−8.62530			−1.12292			−0.561459	−	0.827504i	$-0.689760\pi$
$59$	−8.62530			−1.12292			−0.561459	+	0.827504i	$0.689760\pi$
$60$	−3.28726	−	2.90668i	−0.424383	−	0.375251i
$61$	8.70052			1.11399			0.556994	−	0.830517i	$-0.311955\pi$
$61$	8.70052			1.11399			0.556994	+	0.830517i	$0.311955\pi$
$62$		−	0.887166i		−	0.112670i
$63$		0			0
$64$	7.11142			0.888927
$65$	2.26187	+	2.00000i	0.280550	+	0.248069i
$66$	0.387873			0.0477439
$67$			9.92478i			1.21250i	0.795272	+	0.606252i	$0.207328\pi$
$67$			9.92478i			1.21250i	−0.795272	+	0.606252i	$0.792672\pi$
$68$			6.57452i			0.797277i
$69$	−4.96239			−0.597401
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		−	0.768452i		−	0.0905629i
$73$		−	9.35026i		−	1.09437i	−0.837013	−	0.547183i	$-0.815700\pi$
$73$		−	9.35026i		−	1.09437i	0.837013	−	0.547183i	$-0.184300\pi$
$74$	0.150446			0.0174889
$75$	−4.96239	+	0.612127i	−0.573007	+	0.0706823i
$76$	10.4993			1.20435
$77$		0			0
$78$			0.261865i			0.0296504i
$79$	−10.7005			−1.20390			−0.601951	−	0.798533i	$-0.705610\pi$
$79$	−10.7005			−1.20390			−0.601951	+	0.798533i	$0.705610\pi$
$80$	5.59261	−	6.32487i	0.625273	−	0.707142i
$81$	1.00000			0.111111
$82$		−	0.724961i		−	0.0800586i
$83$			3.22425i			0.353908i	0.984219	+	0.176954i	$0.0566244\pi$
$83$			3.22425i			0.353908i	−0.984219	+	0.176954i	$0.943376\pi$
$84$		0			0
$85$	5.61213	+	4.96239i	0.608721	+	0.538247i
$86$	−2.44851			−0.264029
$87$			7.92478i			0.849625i
$88$			1.53690i			0.163835i
$89$	1.03761			0.109987			0.0549933	−	0.998487i	$-0.482486\pi$
$89$	1.03761			0.109987			0.0549933	+	0.998487i	$0.482486\pi$
$90$	−0.324869	−	0.287258i	−0.0342442	−	0.0302796i
$91$		0			0
$92$		−	9.73813i		−	1.01527i
$93$			4.57452i			0.474355i
$94$	1.92478			0.198526
$95$	7.92478	−	8.96239i	0.813065	−	0.919522i
$96$	2.26916			0.231595
$97$			18.4993i			1.87832i	0.343482	+	0.939159i	$0.388394\pi$
$97$			18.4993i			1.87832i	−0.343482	+	0.939159i	$0.611606\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$	−1.20123	−	9.73813i	−0.120123	−	0.973813i
$101$	17.6629			1.75753			0.878763	−	0.477259i	$-0.158370\pi$
$101$	17.6629			1.75753			0.878763	+	0.477259i	$0.158370\pi$
$102$			0.649738i			0.0643337i
$103$			6.70052i			0.660222i	0.943942	+	0.330111i	$0.107086\pi$
$103$			6.70052i			0.660222i	−0.943942	+	0.330111i	$0.892914\pi$
$104$	−1.03761			−0.101746
$105$		0			0
$106$	1.66291			0.161516
$107$			13.7381i			1.32812i	0.747681	+	0.664058i	$0.231167\pi$
$107$			13.7381i			1.32812i	−0.747681	+	0.664058i	$0.768833\pi$
$108$			1.96239i			0.188831i
$109$	2.77575			0.265868			0.132934	−	0.991125i	$-0.457560\pi$
$109$	2.77575			0.265868			0.132934	+	0.991125i	$0.457560\pi$
$110$	0.649738	+	0.574515i	0.0619501	+	0.0547779i
$111$	−0.775746			−0.0736306
$112$		0			0
$113$		−	12.0508i		−	1.13364i	−0.823841	−	0.566821i	$-0.808173\pi$
$113$		−	12.0508i		−	1.13364i	0.823841	−	0.566821i	$-0.191827\pi$
$114$	1.03761			0.0971812
$115$	−8.31265	−	7.35026i	−0.775159	−	0.685415i
$116$	−15.5515			−1.44392
$117$		−	1.35026i		−	0.124832i
$118$		−	1.67276i		−	0.153990i
$119$		0			0
$120$	1.13823	−	1.28726i	0.103905	−	0.117510i
$121$	−7.00000			−0.636364
$122$			1.68735i			0.152765i
$123$			3.73813i			0.337056i
$124$	−8.97698			−0.806156
$125$	−9.21933	−	6.32487i	−0.824602	−	0.565713i
$126$		0			0
$127$			2.70052i			0.239633i	0.992796	+	0.119816i	$0.0382306\pi$
$127$			2.70052i			0.239633i	−0.992796	+	0.119816i	$0.961769\pi$
$128$			5.91748i			0.523037i
$129$	12.6253			1.11160
$130$	−0.387873	+	0.438658i	−0.0340187	+	0.0384729i
$131$	−20.6253			−1.80204			−0.901020	−	0.433777i	$-0.857181\pi$
$131$	−20.6253			−1.80204			−0.901020	+	0.433777i	$0.857181\pi$
$132$		−	3.92478i		−	0.341608i
$133$		0			0
$134$	−1.92478			−0.166275
$135$	1.67513	+	1.48119i	0.144172	+	0.127481i
$136$	−2.57452			−0.220763
$137$			22.4993i			1.92224i	0.276124	+	0.961122i	$0.410950\pi$
$137$			22.4993i			1.92224i	−0.276124	+	0.961122i	$0.589050\pi$
$138$		−	0.962389i		−	0.0819240i
$139$	−3.27504			−0.277785			−0.138893	−	0.990307i	$-0.544354\pi$
$139$	−3.27504			−0.277785			−0.138893	+	0.990307i	$0.544354\pi$
$140$		0			0
$141$	−9.92478			−0.835817
$142$			0.387873i			0.0325496i
$143$			2.70052i			0.225829i
$144$	−3.77575			−0.314646
$145$	−11.7381	+	13.2750i	−0.974799	+	1.10243i
$146$	1.81336			0.150075
$147$		0			0
$148$		−	1.52232i		−	0.125134i
$149$	4.44851			0.364436			0.182218	−	0.983258i	$-0.441672\pi$
$149$	4.44851			0.364436			0.182218	+	0.983258i	$0.441672\pi$
$150$	−0.118714	−	0.962389i	−0.00969294	−	0.0785787i
$151$	1.29948			0.105750			0.0528749	−	0.998601i	$-0.483162\pi$
$151$	1.29948			0.105750			0.0528749	+	0.998601i	$0.483162\pi$
$152$			4.11142i			0.333480i
$153$		−	3.35026i		−	0.270853i
$154$		0			0
$155$	−6.77575	+	7.66291i	−0.544241	+	0.615500i
$156$	2.64974			0.212149
$157$			2.64974i			0.211472i	0.994394	+	0.105736i	$0.0337199\pi$
$157$			2.64974i			0.211472i	−0.994394	+	0.105736i	$0.966280\pi$
$158$		−	2.07522i		−	0.165096i
$159$	−8.57452			−0.680003
$160$	3.80114	+	3.36107i	0.300506	+	0.265716i
$161$		0			0
$162$			0.193937i			0.0152371i
$163$		−	5.29948i		−	0.415087i	−0.978226	−	0.207544i	$-0.933453\pi$
$163$		−	5.29948i		−	0.415087i	0.978226	−	0.207544i	$-0.0665469\pi$
$164$	−7.33567			−0.572820
$165$	−3.35026	−	2.96239i	−0.260818	−	0.230622i
$166$	−0.625301			−0.0485327
$167$			14.5501i			1.12592i	0.826485	+	0.562959i	$0.190337\pi$
$167$			14.5501i			1.12592i	−0.826485	+	0.562959i	$0.809663\pi$
$168$		0			0
$169$	11.1768			0.859753
$170$	−0.962389	+	1.08840i	−0.0738118	+	0.0834762i
$171$	−5.35026			−0.409145
$172$			24.7757i			1.88913i
$173$		−	4.49929i		−	0.342075i	−0.985265	−	0.171037i	$-0.945288\pi$
$173$		−	4.49929i		−	0.342075i	0.985265	−	0.171037i	$-0.0547119\pi$
$174$	−1.53690			−0.116512
$175$		0			0
$176$	7.55149			0.569215
$177$			8.62530i			0.648317i
$178$			0.201231i			0.0150829i
$179$	−10.0000			−0.747435			−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000			−0.747435			−0.373718	+	0.927543i	$0.621917\pi$
$180$	−2.90668	+	3.28726i	−0.216651	+	0.245018i
$181$	−10.6253			−0.789772			−0.394886	−	0.918730i	$-0.629216\pi$
$181$	−10.6253			−0.789772			−0.394886	+	0.918730i	$0.629216\pi$
$182$		0			0
$183$		−	8.70052i		−	0.643161i
$184$	3.81336			0.281124
$185$	−1.29948	−	1.14903i	−0.0955394	−	0.0844784i
$186$	−0.887166			−0.0650502
$187$			6.70052i			0.489991i
$188$		−	19.4763i		−	1.42045i
$189$		0			0
$190$	1.73813	+	1.53690i	0.126098	+	0.111499i
$191$	−13.8496			−1.00212			−0.501059	−	0.865413i	$-0.667056\pi$
$191$	−13.8496			−1.00212			−0.501059	+	0.865413i	$0.667056\pi$
$192$		−	7.11142i		−	0.513222i
$193$		−	15.3258i		−	1.10318i	−0.834116	−	0.551588i	$-0.814022\pi$
$193$		−	15.3258i		−	1.10318i	0.834116	−	0.551588i	$-0.185978\pi$
$194$	−3.58769			−0.257581
$195$	2.00000	−	2.26187i	0.143223	−	0.161976i
$196$		0			0
$197$		−	0.574515i		−	0.0409325i	−0.999791	−	0.0204663i	$-0.993485\pi$
$197$		−	0.574515i		−	0.0409325i	0.999791	−	0.0204663i	$-0.00651507\pi$
$198$		−	0.387873i		−	0.0275649i
$199$	−0.201231			−0.0142649			−0.00713244	−	0.999975i	$-0.502270\pi$
$199$	−0.201231			−0.0142649			−0.00713244	+	0.999975i	$0.502270\pi$
$200$	3.81336	−	0.470390i	0.269645	−	0.0332616i
$201$	9.92478			0.700040
$202$			3.42548i			0.241016i
$203$		0			0
$204$	6.57452			0.460308
$205$	−5.53690	+	6.26187i	−0.386714	+	0.437348i
$206$	−1.29948			−0.0905388
$207$			4.96239i			0.344910i
$208$			5.09825i			0.353500i
$209$	10.7005			0.740171
$210$		0			0
$211$	6.44851			0.443934			0.221967	−	0.975054i	$-0.428752\pi$
$211$	6.44851			0.443934			0.221967	+	0.975054i	$0.428752\pi$
$212$		−	16.8265i		−	1.15565i
$213$		−	2.00000i		−	0.137038i
$214$	−2.66433			−0.182130
$215$	21.1490	+	18.7005i	1.44235	+	1.27537i
$216$	−0.768452			−0.0522865
$217$		0			0
$218$			0.538319i			0.0364595i
$219$	−9.35026			−0.631832
$220$	5.81336	−	6.57452i	0.391936	−	0.443254i
$221$	−4.52373			−0.304299
$222$		−	0.150446i		−	0.0100972i
$223$			1.55149i			0.103896i	0.998650	+	0.0519478i	$0.0165429\pi$
$223$			1.55149i			0.103896i	−0.998650	+	0.0519478i	$0.983457\pi$
$224$		0			0
$225$	0.612127	+	4.96239i	0.0408085	+	0.330826i
$226$	2.33709			0.155461
$227$			13.1490i			0.872732i	0.899769	+	0.436366i	$0.143735\pi$
$227$			13.1490i			0.872732i	−0.899769	+	0.436366i	$0.856265\pi$
$228$		−	10.4993i		−	0.695333i
$229$	2.77575			0.183426			0.0917132	−	0.995785i	$-0.470766\pi$
$229$	2.77575			0.183426			0.0917132	+	0.995785i	$0.470766\pi$
$230$	1.42548	−	1.61213i	0.0939937	−	0.106300i
$231$		0			0
$232$		−	6.08981i		−	0.399816i
$233$			0.0507852i			0.00332705i	0.999999	+	0.00166353i	$0.000529517\pi$
$233$			0.0507852i			0.00332705i	−0.999999	+	0.00166353i	$0.999470\pi$
$234$	0.261865			0.0171187
$235$	−16.6253	−	14.7005i	−1.08452	−	0.958956i
$236$	−16.9262			−1.10180
$237$			10.7005i			0.695074i
$238$		0			0
$239$	−5.84955			−0.378376			−0.189188	−	0.981941i	$-0.560586\pi$
$239$	−5.84955			−0.378376			−0.189188	+	0.981941i	$0.560586\pi$
$240$	−6.32487	−	5.59261i	−0.408269	−	0.361002i
$241$	0.0752228			0.00484553			0.00242276	−	0.999997i	$-0.499229\pi$
$241$	0.0752228			0.00484553			0.00242276	+	0.999997i	$0.499229\pi$
$242$		−	1.35756i		−	0.0872670i
$243$		−	1.00000i		−	0.0641500i
$244$	17.0738			1.09304
$245$		0			0
$246$	−0.724961			−0.0462218
$247$			7.22425i			0.459668i
$248$		−	3.51530i		−	0.223222i
$249$	3.22425			0.204329
$250$	1.22662	−	1.78797i	0.0775785	−	0.113081i
$251$	−19.2243			−1.21342			−0.606712	−	0.794922i	$-0.707512\pi$
$251$	−19.2243			−1.21342			−0.606712	+	0.794922i	$0.707512\pi$
$252$		0			0
$253$		−	9.92478i		−	0.623965i
$254$	−0.523730			−0.0328618
$255$	4.96239	−	5.61213i	0.310757	−	0.351445i
$256$	13.0752			0.817201
$257$		−	7.35026i		−	0.458497i	−0.973368	−	0.229248i	$-0.926373\pi$
$257$		−	7.35026i		−	0.458497i	0.973368	−	0.229248i	$-0.0736268\pi$
$258$			2.44851i			0.152437i
$259$		0			0
$260$	4.43866	+	3.92478i	0.275274	+	0.243404i
$261$	7.92478			0.490531
$262$		−	4.00000i		−	0.247121i
$263$			12.9624i			0.799295i	0.916669	+	0.399648i	$0.130867\pi$
$263$			12.9624i			0.799295i	−0.916669	+	0.399648i	$0.869133\pi$
$264$	1.53690			0.0945899
$265$	−14.3634	−	12.7005i	−0.882339	−	0.780187i
$266$		0			0
$267$		−	1.03761i		−	0.0635008i
$268$			19.4763i			1.18970i
$269$	4.11142			0.250678			0.125339	−	0.992114i	$-0.459998\pi$
$269$	4.11142			0.250678			0.125339	+	0.992114i	$0.459998\pi$
$270$	−0.287258	+	0.324869i	−0.0174819	+	0.0197709i
$271$	16.4241			0.997691			0.498846	−	0.866691i	$-0.333757\pi$
$271$	16.4241			0.997691			0.498846	+	0.866691i	$0.333757\pi$
$272$			12.6497i			0.767003i
$273$		0			0
$274$	−4.36344			−0.263605
$275$	−1.22425	−	9.92478i	−0.0738253	−	0.598487i
$276$	−9.73813			−0.586167
$277$		−	11.0738i		−	0.665361i	−0.943040	−	0.332680i	$-0.892047\pi$
$277$		−	11.0738i		−	0.665361i	0.943040	−	0.332680i	$-0.107953\pi$
$278$		−	0.635150i		−	0.0380938i
$279$	4.57452			0.273869
$280$		0			0
$281$	14.3733			0.857438			0.428719	−	0.903438i	$-0.358965\pi$
$281$	14.3733			0.857438			0.428719	+	0.903438i	$0.358965\pi$
$282$		−	1.92478i		−	0.114619i
$283$			1.14903i			0.0683028i	0.999417	+	0.0341514i	$0.0108728\pi$
$283$			1.14903i			0.0683028i	−0.999417	+	0.0341514i	$0.989127\pi$
$284$	3.92478			0.232893
$285$	−8.96239	−	7.92478i	−0.530886	−	0.469423i
$286$	−0.523730			−0.0309688
$287$		0			0
$288$		−	2.26916i		−	0.133711i
$289$	5.77575			0.339750
$290$	−2.57452	−	2.27645i	−0.151181	−	0.133678i
$291$	18.4993			1.08445
$292$		−	18.3488i		−	1.07379i
$293$			0.649738i			0.0379581i	0.999820	+	0.0189791i	$0.00604158\pi$
$293$			0.649738i			0.0379581i	−0.999820	+	0.0189791i	$0.993958\pi$
$294$		0			0
$295$	−12.7757	+	14.4485i	−0.743833	+	0.841225i
$296$	0.596124			0.0346490
$297$			2.00000i			0.116052i
$298$			0.862728i			0.0499765i
$299$	6.70052			0.387501
$300$	−9.73813	+	1.20123i	−0.562231	+	0.0693531i
$301$		0			0
$302$			0.252016i			0.0145019i
$303$		−	17.6629i		−	1.01471i
$304$	20.2012			1.15862
$305$	12.8872	−	14.5745i	0.737917	−	0.834534i
$306$	0.649738			0.0371431
$307$		−	24.1016i		−	1.37555i	−0.725924	−	0.687775i	$-0.758588\pi$
$307$		−	24.1016i		−	1.37555i	0.725924	−	0.687775i	$-0.241412\pi$
$308$		0			0
$309$	6.70052			0.381179
$310$	−1.48612	−	1.31406i	−0.0844059	−	0.0746339i
$311$	−8.25202			−0.467929			−0.233964	−	0.972245i	$-0.575170\pi$
$311$	−8.25202			−0.467929			−0.233964	+	0.972245i	$0.575170\pi$
$312$			1.03761i			0.0587432i
$313$		−	14.9018i		−	0.842297i	−0.906992	−	0.421148i	$-0.861627\pi$
$313$		−	14.9018i		−	0.842297i	0.906992	−	0.421148i	$-0.138373\pi$
$314$	−0.513881			−0.0290000
$315$		0			0
$316$	−20.9986			−1.18126
$317$			10.1260i			0.568733i	0.958716	+	0.284367i	$0.0917833\pi$
$317$			10.1260i			0.568733i	−0.958716	+	0.284367i	$0.908217\pi$
$318$		−	1.66291i		−	0.0932515i
$319$	−15.8496			−0.887405
$320$	10.5334	−	11.9126i	0.588835	−	0.665932i
$321$	13.7381			0.766788
$322$		0			0
$323$			17.9248i			0.997361i
$324$	1.96239			0.109022
$325$	6.70052	−	0.826531i	0.371678	−	0.0458477i
$326$	1.02776			0.0569225
$327$		−	2.77575i		−	0.153499i
$328$		−	2.87258i		−	0.158612i
$329$		0			0
$330$	0.574515	−	0.649738i	0.0316260	−	0.0357669i
$331$	27.8496			1.53075			0.765375	−	0.643585i	$-0.222554\pi$
$331$	27.8496			1.53075			0.765375	+	0.643585i	$0.222554\pi$
$332$			6.32724i			0.347252i
$333$			0.775746i			0.0425106i
$334$	−2.82179			−0.154402
$335$	16.6253	+	14.7005i	0.908337	+	0.803175i
$336$		0			0
$337$		−	3.84955i		−	0.209699i	−0.994488	−	0.104849i	$-0.966564\pi$
$337$		−	3.84955i		−	0.209699i	0.994488	−	0.104849i	$-0.0334360\pi$
$338$			2.16759i			0.117901i
$339$	−12.0508			−0.654509
$340$	11.0132	+	9.73813i	0.597273	+	0.528125i
$341$	−9.14903			−0.495448
$342$		−	1.03761i		−	0.0561076i
$343$		0			0
$344$	−9.70194			−0.523093
$345$	−7.35026	+	8.31265i	−0.395725	+	0.447538i
$346$	0.872577			0.0469101
$347$			9.58769i			0.514694i	0.966319	+	0.257347i	$0.0828484\pi$
$347$			9.58769i			0.514694i	−0.966319	+	0.257347i	$0.917152\pi$
$348$			15.5515i			0.833648i
$349$	−15.1490			−0.810909			−0.405455	−	0.914115i	$-0.632887\pi$
$349$	−15.1490			−0.810909			−0.405455	+	0.914115i	$0.632887\pi$
$350$		0			0
$351$	−1.35026			−0.0720716
$352$			4.53832i			0.241893i
$353$		−	20.3488i		−	1.08306i	−0.840681	−	0.541530i	$-0.817845\pi$
$353$		−	20.3488i		−	1.08306i	0.840681	−	0.541530i	$-0.182155\pi$
$354$	−1.67276			−0.0889063
$355$	2.96239	−	3.35026i	0.157227	−	0.177813i
$356$	2.03620			0.107918
$357$		0			0
$358$		−	1.93937i		−	0.102499i
$359$	31.4010			1.65728			0.828642	−	0.559779i	$-0.189114\pi$
$359$	31.4010			1.65728			0.828642	+	0.559779i	$0.189114\pi$
$360$	−1.28726	−	1.13823i	−0.0678444	−	0.0599898i
$361$	9.62530			0.506595
$362$		−	2.06063i		−	0.108305i
$363$			7.00000i			0.367405i
$364$		0			0
$365$	−15.6629	−	13.8496i	−0.819834	−	0.724919i
$366$	1.68735			0.0881992
$367$			29.4010i			1.53472i	0.641215	+	0.767361i	$0.278431\pi$
$367$			29.4010i			1.53472i	−0.641215	+	0.767361i	$0.721569\pi$
$368$		−	18.7367i		−	0.976719i
$369$	3.73813			0.194600
$370$	0.222839	−	0.252016i	0.0115849	−	0.0131017i
$371$		0			0
$372$			8.97698i			0.465435i
$373$		−	16.0000i		−	0.828449i	−0.910175	−	0.414224i	$-0.864053\pi$
$373$		−	16.0000i		−	0.828449i	0.910175	−	0.414224i	$-0.135947\pi$
$374$	−1.29948			−0.0671943
$375$	−6.32487	+	9.21933i	−0.326615	+	0.476084i
$376$	7.62672			0.393318
$377$		−	10.7005i		−	0.551105i
$378$		0			0
$379$	−10.7005			−0.549649			−0.274824	−	0.961494i	$-0.588620\pi$
$379$	−10.7005			−0.549649			−0.274824	+	0.961494i	$0.588620\pi$
$380$	15.5515	−	17.5877i	0.797775	−	0.902229i
$381$	2.70052			0.138352
$382$		−	2.68594i		−	0.137424i
$383$		−	16.7757i		−	0.857201i	−0.903494	−	0.428600i	$-0.859007\pi$
$383$		−	16.7757i		−	0.857201i	0.903494	−	0.428600i	$-0.140993\pi$
$384$	5.91748			0.301975
$385$		0			0
$386$	2.97224			0.151283
$387$		−	12.6253i		−	0.641780i
$388$			36.3028i			1.84300i
$389$	29.3258			1.48688			0.743439	−	0.668804i	$-0.233193\pi$
$389$	29.3258			1.48688			0.743439	+	0.668804i	$0.233193\pi$
$390$	0.438658	+	0.387873i	0.0222123	+	0.0196407i
$391$	16.6253			0.840778
$392$		0			0
$393$			20.6253i			1.04041i
$394$	0.111420			0.00561324
$395$	−15.8496	+	17.9248i	−0.797478	+	0.901893i
$396$	−3.92478			−0.197227
$397$		−	18.3488i		−	0.920902i	−0.887685	−	0.460451i	$-0.847688\pi$
$397$		−	18.3488i		−	0.920902i	0.887685	−	0.460451i	$-0.152312\pi$
$398$		−	0.0390260i		−	0.00195620i
$399$		0			0
$400$	−2.31124	−	18.7367i	−0.115562	−	0.936836i
$401$	−37.3258			−1.86396			−0.931981	−	0.362506i	$-0.881921\pi$
$401$	−37.3258			−1.86396			−0.931981	+	0.362506i	$0.881921\pi$
$402$			1.92478i			0.0959992i
$403$		−	6.17679i		−	0.307688i
$404$	34.6615			1.72447
$405$	1.48119	−	1.67513i	0.0736011	−	0.0832379i
$406$		0			0
$407$		−	1.55149i		−	0.0769046i
$408$			2.57452i			0.127458i
$409$	−22.3733			−1.10629			−0.553144	−	0.833086i	$-0.686572\pi$
$409$	−22.3733			−1.10629			−0.553144	+	0.833086i	$0.686572\pi$
$410$	−1.21440	−	1.07381i	−0.0599752	−	0.0530316i
$411$	22.4993			1.10981
$412$			13.1490i			0.647806i
$413$		0			0
$414$	−0.962389			−0.0472988
$415$	5.40105	+	4.77575i	0.265127	+	0.234432i
$416$	−3.06396			−0.150223
$417$			3.27504i			0.160379i
$418$			2.07522i			0.101502i
$419$	23.4763			1.14689			0.573445	−	0.819244i	$-0.305606\pi$
$419$	23.4763			1.14689			0.573445	+	0.819244i	$0.305606\pi$
$420$		0			0
$421$	−25.2243			−1.22935			−0.614677	−	0.788779i	$-0.710714\pi$
$421$	−25.2243			−1.22935			−0.614677	+	0.788779i	$0.710714\pi$
$422$			1.25060i			0.0608783i
$423$			9.92478i			0.482559i
$424$	6.58910			0.319995
$425$	16.6253	−	2.05079i	0.806446	−	0.0994777i
$426$	0.387873			0.0187925
$427$		0			0
$428$			26.9596i			1.30314i
$429$	2.70052			0.130383
$430$	−3.62672	+	4.10157i	−0.174896	+	0.197795i
$431$	−19.4010			−0.934516			−0.467258	−	0.884121i	$-0.654758\pi$
$431$	−19.4010			−0.934516			−0.467258	+	0.884121i	$0.654758\pi$
$432$			3.77575i			0.181661i
$433$			6.49929i			0.312336i	0.987731	+	0.156168i	$0.0499141\pi$
$433$			6.49929i			0.312336i	−0.987731	+	0.156168i	$0.950086\pi$
$434$		0			0
$435$	13.2750	+	11.7381i	0.636489	+	0.562800i
$436$	5.44709			0.260868
$437$		−	26.5501i		−	1.27006i
$438$		−	1.81336i		−	0.0866456i
$439$	−14.6497			−0.699194			−0.349597	−	0.936900i	$-0.613681\pi$
$439$	−14.6497			−0.699194			−0.349597	+	0.936900i	$0.613681\pi$
$440$	2.57452	+	2.27645i	0.122735	+	0.108526i
$441$		0			0
$442$		−	0.877317i		−	0.0417297i
$443$		−	19.1392i		−	0.909330i	−0.890663	−	0.454665i	$-0.849759\pi$
$443$		−	19.1392i		−	0.909330i	0.890663	−	0.454665i	$-0.150241\pi$
$444$	−1.52232			−0.0722459
$445$	1.53690	−	1.73813i	0.0728562	−	0.0823955i
$446$	−0.300891			−0.0142476
$447$		−	4.44851i		−	0.210407i
$448$		0			0
$449$	32.8021			1.54803			0.774013	−	0.633169i	$-0.218246\pi$
$449$	32.8021			1.54803			0.774013	+	0.633169i	$0.218246\pi$
$450$	−0.962389	+	0.118714i	−0.0453674	+	0.00559622i
$451$	−7.47627			−0.352044
$452$		−	23.6483i		−	1.11232i
$453$		−	1.29948i		−	0.0610547i
$454$	−2.55008			−0.119681
$455$		0			0
$456$	4.11142			0.192535
$457$		−	18.7005i		−	0.874774i	−0.899273	−	0.437387i	$-0.855904\pi$
$457$		−	18.7005i		−	0.874774i	0.899273	−	0.437387i	$-0.144096\pi$
$458$			0.538319i			0.0251540i
$459$	−3.35026			−0.156377
$460$	−16.3127	−	14.4241i	−0.760581	−	0.672526i
$461$	6.96239			0.324271			0.162135	−	0.986769i	$-0.448162\pi$
$461$	6.96239			0.324271			0.162135	+	0.986769i	$0.448162\pi$
$462$		0			0
$463$		−	5.29948i		−	0.246288i	−0.992389	−	0.123144i	$-0.960702\pi$
$463$		−	5.29948i		−	0.246288i	0.992389	−	0.123144i	$-0.0392976\pi$
$464$	−29.9219			−1.38909
$465$	7.66291	+	6.77575i	0.355359	+	0.314218i
$466$	−0.00984911			−0.000456251
$467$			13.1490i			0.608465i	0.952598	+	0.304232i	$0.0983999\pi$
$467$			13.1490i			0.608465i	−0.952598	+	0.304232i	$0.901600\pi$
$468$		−	2.64974i		−	0.122484i
$469$		0			0
$470$	2.85097	−	3.22425i	0.131505	−	0.148724i
$471$	2.64974			0.122093
$472$		−	6.62813i		−	0.305084i
$473$			25.2506i			1.16102i
$474$	−2.07522			−0.0953181
$475$	−3.27504	−	26.5501i	−0.150269	−	1.21820i
$476$		0			0
$477$			8.57452i			0.392600i
$478$		−	1.13444i		−	0.0518882i
$479$	5.14903			0.235265			0.117633	−	0.993057i	$-0.462469\pi$
$479$	5.14903			0.235265			0.117633	+	0.993057i	$0.462469\pi$
$480$	3.36107	−	3.80114i	0.153411	−	0.173497i
$481$	1.04746			0.0477601
$482$			0.0145884i			0.000664486i
$483$		0			0
$484$	−13.7367			−0.624396
$485$	30.9887	+	27.4010i	1.40713	+	1.24422i
$486$	0.193937			0.00879714
$487$		−	22.1768i		−	1.00493i	−0.864599	−	0.502463i	$-0.832427\pi$
$487$		−	22.1768i		−	1.00493i	0.864599	−	0.502463i	$-0.167573\pi$
$488$			6.68594i			0.302658i
$489$	−5.29948			−0.239651
$490$		0			0
$491$	2.00000			0.0902587			0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000			0.0902587			0.0451294	+	0.998981i	$0.485630\pi$
$492$			7.33567i			0.330718i
$493$		−	26.5501i		−	1.19576i
$494$	−1.40105			−0.0630361
$495$	−2.96239	+	3.35026i	−0.133149	+	0.150583i
$496$	−17.2722			−0.775545
$497$		0			0
$498$			0.625301i			0.0280204i
$499$	6.55008			0.293222			0.146611	−	0.989194i	$-0.453163\pi$
$499$	6.55008			0.293222			0.146611	+	0.989194i	$0.453163\pi$
$500$	−18.0919	−	12.4119i	−0.809095	−	0.555075i
$501$	14.5501			0.650050
$502$		−	3.72829i		−	0.166402i
$503$			8.77575i			0.391291i	0.980675	+	0.195646i	$0.0626802\pi$
$503$			8.77575i			0.391291i	−0.980675	+	0.195646i	$0.937320\pi$
$504$		0			0
$505$	26.1622	−	29.5877i	1.16420	−	1.31663i
$506$	1.92478			0.0855668
$507$		−	11.1768i		−	0.496379i
$508$			5.29948i			0.235126i
$509$	13.1392			0.582384			0.291192	−	0.956665i	$-0.405948\pi$
$509$	13.1392			0.582384			0.291192	+	0.956665i	$0.405948\pi$
$510$	1.08840	+	0.962389i	0.0481950	+	0.0426153i
$511$		0			0
$512$			14.3707i			0.635103i
$513$			5.35026i			0.236220i
$514$	1.42548			0.0628754
$515$	11.2243	+	9.92478i	0.494600	+	0.437338i
$516$	24.7757			1.09069
$517$		−	19.8496i		−	0.872982i
$518$		0			0
$519$	−4.49929			−0.197497
$520$	−1.53690	+	1.73813i	−0.0673977	+	0.0762223i
$521$	37.6629			1.65004			0.825021	−	0.565102i	$-0.191163\pi$
$521$	37.6629			1.65004			0.825021	+	0.565102i	$0.191163\pi$
$522$			1.53690i			0.0672685i
$523$		−	4.00000i		−	0.174908i	−0.996169	−	0.0874539i	$-0.972127\pi$
$523$		−	4.00000i		−	0.174908i	0.996169	−	0.0874539i	$-0.0278730\pi$
$524$	−40.4749			−1.76815
$525$		0			0
$526$	−2.51388			−0.109610
$527$		−	15.3258i		−	0.667603i
$528$		−	7.55149i		−	0.328637i
$529$	−1.62530			−0.0706652
$530$	2.46310	−	2.78560i	0.106990	−	0.120999i
$531$	8.62530			0.374306
$532$		0			0
$533$		−	5.04746i		−	0.218630i
$534$	0.201231			0.00870811
$535$	23.0132	+	20.3488i	0.994946	+	0.879757i
$536$	−7.62672			−0.329424
$537$			10.0000i			0.431532i
$538$			0.797355i			0.0343764i
$539$		0			0
$540$	3.28726	+	2.90668i	0.141461	+	0.125084i
$541$	−22.4749			−0.966269			−0.483135	−	0.875546i	$-0.660502\pi$
$541$	−22.4749			−0.966269			−0.483135	+	0.875546i	$0.660502\pi$
$542$			3.18523i			0.136817i
$543$			10.6253i			0.455975i
$544$	−7.60228			−0.325945
$545$	4.11142	−	4.64974i	0.176114	−	0.199173i
$546$		0			0
$547$		−	25.9248i		−	1.10846i	−0.832362	−	0.554232i	$-0.813012\pi$
$547$		−	25.9248i		−	1.10846i	0.832362	−	0.554232i	$-0.186988\pi$
$548$			44.1524i			1.88610i
$549$	−8.70052			−0.371329
$550$	1.92478	−	0.237428i	0.0820728	−	0.0101239i
$551$	−42.3996			−1.80629
$552$		−	3.81336i		−	0.162307i
$553$		0			0
$554$	2.14762			0.0912435
$555$	−1.14903	+	1.29948i	−0.0487736	+	0.0551597i
$556$	−6.42690			−0.272561
$557$		−	28.5256i		−	1.20867i	−0.796730	−	0.604335i	$-0.793439\pi$
$557$		−	28.5256i		−	1.20867i	0.796730	−	0.604335i	$-0.206561\pi$
$558$			0.887166i			0.0375567i
$559$	−17.0475			−0.721031
$560$		0			0
$561$	6.70052			0.282896
$562$			2.78751i			0.117584i
$563$		−	11.6267i		−	0.490008i	−0.969522	−	0.245004i	$-0.921211\pi$
$563$		−	11.6267i		−	0.490008i	0.969522	−	0.245004i	$-0.0787892\pi$
$564$	−19.4763			−0.820099
$565$	−20.1866	−	17.8496i	−0.849258	−	0.750936i
$566$	−0.222839			−0.00936663
$567$		0			0
$568$			1.53690i			0.0644871i
$569$	−9.32582			−0.390959			−0.195479	−	0.980708i	$-0.562626\pi$
$569$	−9.32582			−0.390959			−0.195479	+	0.980708i	$0.562626\pi$
$570$	1.53690	−	1.73813i	0.0643738	−	0.0728025i
$571$	−19.6991			−0.824382			−0.412191	−	0.911097i	$-0.635236\pi$
$571$	−19.6991			−0.824382			−0.412191	+	0.911097i	$0.635236\pi$
$572$			5.29948i			0.221582i
$573$			13.8496i			0.578573i
$574$		0			0
$575$	−24.6253	+	3.03761i	−1.02695	+	0.126677i
$576$	−7.11142			−0.296309
$577$		−	32.7974i		−	1.36537i	−0.730712	−	0.682686i	$-0.760812\pi$
$577$		−	32.7974i		−	1.36537i	0.730712	−	0.682686i	$-0.239188\pi$
$578$			1.12013i			0.0465912i
$579$	−15.3258			−0.636920
$580$	−23.0348	+	26.0508i	−0.956467	+	1.08170i
$581$		0			0
$582$			3.58769i			0.148715i
$583$		−	17.1490i		−	0.710240i
$584$	7.18523			0.297327
$585$	−2.26187	−	2.00000i	−0.0935166	−	0.0826898i
$586$	−0.126008			−0.00520534
$587$		−	18.8218i		−	0.776859i	−0.921479	−	0.388429i	$-0.873018\pi$
$587$		−	18.8218i		−	0.776859i	0.921479	−	0.388429i	$-0.126982\pi$
$588$		0			0
$589$	−24.4749			−1.00847
$590$	−2.80209	−	2.47768i	−0.115360	−	0.102005i
$591$	−0.574515			−0.0236324
$592$		−	2.92902i		−	0.120382i
$593$			33.7499i			1.38594i	0.720965	+	0.692971i	$0.243699\pi$
$593$			33.7499i			1.38594i	−0.720965	+	0.692971i	$0.756301\pi$
$594$	−0.387873			−0.0159146
$595$		0			0
$596$	8.72970			0.357582
$597$			0.201231i			0.00823583i
$598$			1.29948i			0.0531395i
$599$	20.2981			0.829356			0.414678	−	0.909968i	$-0.363894\pi$
$599$	20.2981			0.829356			0.414678	+	0.909968i	$0.363894\pi$
$600$	−0.470390	−	3.81336i	−0.0192036	−	0.155680i
$601$	13.8496			0.564935			0.282468	−	0.959277i	$-0.408847\pi$
$601$	13.8496			0.564935			0.282468	+	0.959277i	$0.408847\pi$
$602$		0			0
$603$		−	9.92478i		−	0.404168i
$604$	2.55008			0.103761
$605$	−10.3684	+	11.7259i	−0.421534	+	0.476726i
$606$	3.42548			0.139151
$607$			25.2506i			1.02489i	0.858720	+	0.512445i	$0.171260\pi$
$607$			25.2506i			1.02489i	−0.858720	+	0.512445i	$0.828740\pi$
$608$			12.1406i			0.492366i
$609$		0			0
$610$	2.82653	+	2.49929i	0.114443	+	0.101193i
$611$	13.4010			0.542148
$612$		−	6.57452i		−	0.265759i
$613$			9.14903i			0.369526i	0.982783	+	0.184763i	$0.0591517\pi$
$613$			9.14903i			0.369526i	−0.982783	+	0.184763i	$0.940848\pi$
$614$	4.67418			0.188634
$615$	6.26187	+	5.53690i	0.252503	+	0.223270i
$616$		0			0
$617$			15.9492i			0.642091i	0.947064	+	0.321046i	$0.104034\pi$
$617$			15.9492i			0.642091i	−0.947064	+	0.321046i	$0.895966\pi$
$618$			1.29948i			0.0522726i
$619$	11.1735			0.449100			0.224550	−	0.974463i	$-0.427909\pi$
$619$	11.1735			0.449100			0.224550	+	0.974463i	$0.427909\pi$
$620$	−13.2966	+	15.0376i	−0.534006	+	0.603925i
$621$	4.96239			0.199134
$622$		−	1.60037i		−	0.0641689i
$623$		0			0
$624$	5.09825			0.204093
$625$	−24.2506	+	6.07522i	−0.970024	+	0.243009i
$626$	2.89000			0.115507
$627$		−	10.7005i		−	0.427338i
$628$			5.19982i			0.207495i
$629$	2.59895			0.103627
$630$		0			0
$631$	−14.5501			−0.579229			−0.289615	−	0.957143i	$-0.593527\pi$
$631$	−14.5501			−0.579229			−0.289615	+	0.957143i	$0.593527\pi$
$632$		−	8.22284i		−	0.327087i
$633$		−	6.44851i		−	0.256305i
$634$	−1.96380			−0.0779926
$635$	4.52373	+	4.00000i	0.179519	+	0.158735i
$636$	−16.8265			−0.667215
$637$		0			0
$638$		−	3.07381i		−	0.121693i
$639$	−2.00000			−0.0791188
$640$	9.91256	+	8.76494i	0.391828	+	0.346465i
$641$	−38.7269			−1.52962			−0.764810	−	0.644256i	$-0.777167\pi$
$641$	−38.7269			−1.52962			−0.764810	+	0.644256i	$0.777167\pi$
$642$			2.66433i			0.105153i
$643$		−	11.9511i		−	0.471306i	−0.971837	−	0.235653i	$-0.924277\pi$
$643$		−	11.9511i		−	0.471306i	0.971837	−	0.235653i	$-0.0757229\pi$
$644$		0			0
$645$	18.7005	−	21.1490i	0.736332	−	0.832742i
$646$	−3.47627			−0.136772
$647$			14.5501i			0.572023i	0.958226	+	0.286011i	$0.0923295\pi$
$647$			14.5501i			0.572023i	−0.958226	+	0.286011i	$0.907671\pi$
$648$			0.768452i			0.0301876i
$649$	−17.2506			−0.677145
$650$	0.160295	+	1.29948i	0.00628727	+	0.0509697i
$651$		0			0
$652$		−	10.3996i		−	0.407281i
$653$		−	49.9756i		−	1.95569i	−0.209319	−	0.977847i	$-0.567125\pi$
$653$		−	49.9756i		−	1.95569i	0.209319	−	0.977847i	$-0.432875\pi$
$654$	0.538319			0.0210499
$655$	−30.5501	+	34.5501i	−1.19369	+	1.34998i
$656$	−14.1142			−0.551069
$657$			9.35026i			0.364788i
$658$		0			0
$659$	16.9525			0.660377			0.330189	−	0.943915i	$-0.392888\pi$
$659$	16.9525			0.660377			0.330189	+	0.943915i	$0.392888\pi$
$660$	−6.57452	−	5.81336i	−0.255913	−	0.226285i
$661$	15.6531			0.608834			0.304417	−	0.952539i	$-0.401538\pi$
$661$	15.6531			0.608834			0.304417	+	0.952539i	$0.401538\pi$
$662$			5.40105i			0.209918i
$663$			4.52373i			0.175687i
$664$	−2.47768			−0.0961528
$665$		0			0
$666$	−0.150446			−0.00582965
$667$			39.3258i			1.52270i
$668$			28.5529i			1.10475i
$669$	1.55149			0.0599842
$670$	−2.85097	+	3.22425i	−0.110143	+	0.124564i
$671$	17.4010			0.671760
$672$		0			0
$673$		−	26.0263i		−	1.00324i	−0.865088	−	0.501621i	$-0.832737\pi$
$673$		−	26.0263i		−	1.00324i	0.865088	−	0.501621i	$-0.167263\pi$
$674$	0.746569			0.0287568
$675$	4.96239	−	0.612127i	0.191002	−	0.0235608i
$676$	21.9332			0.843585
$677$			35.4518i			1.36252i	0.732039	+	0.681262i	$0.238569\pi$
$677$			35.4518i			1.36252i	−0.732039	+	0.681262i	$0.761431\pi$
$678$		−	2.33709i		−	0.0897553i
$679$		0			0
$680$	−3.81336	+	4.31265i	−0.146236	+	0.165383i
$681$	13.1490			0.503872
$682$		−	1.77433i		−	0.0679427i
$683$			23.6629i			0.905436i	0.891654	+	0.452718i	$0.149546\pi$
$683$			23.6629i			0.905436i	−0.891654	+	0.452718i	$0.850454\pi$
$684$	−10.4993			−0.401450
$685$	37.6893	+	33.3258i	1.44003	+	1.27331i
$686$		0			0
$687$		−	2.77575i		−	0.105901i
$688$			47.6699i			1.81740i
$689$	11.5778			0.441081
$690$	−1.61213	−	1.42548i	−0.0613726	−	0.0542673i
$691$	0.574515			0.0218556			0.0109278	−	0.999940i	$-0.496522\pi$
$691$	0.574515			0.0218556			0.0109278	+	0.999940i	$0.496522\pi$
$692$		−	8.82936i		−	0.335642i
$693$		0			0
$694$	−1.85940			−0.0705820
$695$	−4.85097	+	5.48612i	−0.184008	+	0.208100i
$696$	−6.08981			−0.230834
$697$		−	12.5237i		−	0.474370i
$698$		−	2.93795i		−	0.111203i
$699$	0.0507852			0.00192087
$700$		0			0
$701$	42.7269			1.61377			0.806886	−	0.590707i	$-0.201151\pi$
$701$	42.7269			1.61377			0.806886	+	0.590707i	$0.201151\pi$
$702$		−	0.261865i		−	0.00988346i
$703$		−	4.15045i		−	0.156537i
$704$	14.2228			0.536043
$705$	−14.7005	+	16.6253i	−0.553654	+	0.626145i
$706$	3.94639			0.148524
$707$		0			0
$708$			16.9262i			0.636125i
$709$	−27.2506			−1.02342			−0.511709	−	0.859159i	$-0.670987\pi$
$709$	−27.2506			−1.02342			−0.511709	+	0.859159i	$0.670987\pi$
$710$	0.649738	+	0.574515i	0.0243842	+	0.0215612i
$711$	10.7005			0.401301
$712$			0.797355i			0.0298821i
$713$			22.7005i			0.850141i
$714$		0			0
$715$	4.52373	+	4.00000i	0.169178	+	0.149592i
$716$	−19.6239			−0.733379
$717$			5.84955i			0.218456i
$718$			6.08981i			0.227270i
$719$	−10.7005			−0.399062			−0.199531	−	0.979891i	$-0.563942\pi$
$719$	−10.7005			−0.399062			−0.199531	+	0.979891i	$0.563942\pi$
$720$	−5.59261	+	6.32487i	−0.208424	+	0.235714i
$721$		0			0
$722$			1.86670i			0.0694713i
$723$		−	0.0752228i		−	0.00279757i
$724$	−20.8510			−0.774920
$725$	4.85097	+	39.3258i	0.180160	+	1.46052i
$726$	−1.35756			−0.0503836
$727$		−	39.9511i		−	1.48171i	−0.671668	−	0.740853i	$-0.734422\pi$
$727$		−	39.9511i		−	1.48171i	0.671668	−	0.740853i	$-0.265578\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	2.68594	−	3.03761i	0.0994109	−	0.112427i
$731$	−42.2981			−1.56445
$732$		−	17.0738i		−	0.631066i
$733$		−	30.3488i		−	1.12096i	−0.828168	−	0.560480i	$-0.810617\pi$
$733$		−	30.3488i		−	1.12096i	0.828168	−	0.560480i	$-0.189383\pi$
$734$	−5.70194			−0.210462
$735$		0			0
$736$	11.2605			0.415066
$737$			19.8496i			0.731168i
$738$			0.724961i			0.0266862i
$739$	−37.2506			−1.37029			−0.685143	−	0.728409i	$-0.740260\pi$
$739$	−37.2506			−1.37029			−0.685143	+	0.728409i	$0.740260\pi$
$740$	−2.55008	−	2.25485i	−0.0937427	−	0.0828898i
$741$	7.22425			0.265390
$742$		0			0
$743$		−	26.3634i		−	0.967181i	−0.875294	−	0.483590i	$-0.839332\pi$
$743$		−	26.3634i		−	0.967181i	0.875294	−	0.483590i	$-0.160668\pi$
$744$	−3.51530			−0.128877
$745$	6.58910	−	7.45183i	0.241406	−	0.273014i
$746$	3.10299			0.113608
$747$		−	3.22425i		−	0.117969i
$748$			13.1490i			0.480776i
$749$		0			0
$750$	−1.78797	−	1.22662i	−0.0652873	−	0.0447900i
$751$	50.6516			1.84830			0.924152	−	0.382024i	$-0.124773\pi$
$751$	50.6516			1.84830			0.924152	+	0.382024i	$0.124773\pi$
$752$		−	37.4734i		−	1.36652i
$753$			19.2243i			0.700571i
$754$	2.07522			0.0755752
$755$	1.92478	−	2.17679i	0.0700498	−	0.0792216i
$756$		0			0
$757$			38.9525i			1.41575i	0.706336	+	0.707877i	$0.250347\pi$
$757$			38.9525i			1.41575i	−0.706336	+	0.707877i	$0.749653\pi$
$758$		−	2.07522i		−	0.0753755i
$759$	−9.92478			−0.360247
$760$	6.88717	+	6.08981i	0.249824	+	0.220901i
$761$	−48.2130			−1.74772			−0.873860	−	0.486178i	$-0.838391\pi$
$761$	−48.2130			−1.74772			−0.873860	+	0.486178i	$0.838391\pi$
$762$			0.523730i			0.0189727i
$763$		0			0
$764$	−27.1782			−0.983273
$765$	−5.61213	−	4.96239i	−0.202907	−	0.179416i
$766$	3.25343			0.117551
$767$		−	11.6464i		−	0.420528i
$768$		−	13.0752i		−	0.471811i
$769$	4.44851			0.160417			0.0802086	−	0.996778i	$-0.474441\pi$
$769$	4.44851			0.160417			0.0802086	+	0.996778i	$0.474441\pi$
$770$		0			0
$771$	−7.35026			−0.264713
$772$		−	30.0752i		−	1.08243i
$773$			39.3014i			1.41357i	0.707427	+	0.706786i	$0.249856\pi$
$773$			39.3014i			1.41357i	−0.707427	+	0.706786i	$0.750144\pi$
$774$	2.44851			0.0880098
$775$	2.80018	+	22.7005i	0.100586	+	0.815427i
$776$	−14.2158			−0.510318
$777$		0			0
$778$			5.68735i			0.203901i
$779$	−20.0000			−0.716574
$780$	3.92478	−	4.43866i	0.140530	−	0.158929i
$781$	4.00000			0.143131
$782$			3.22425i			0.115299i
$783$		−	7.92478i		−	0.283208i
$784$		0			0
$785$	4.43866	+	3.92478i	0.158423	+	0.140081i
$786$	−4.00000			−0.142675
$787$		−	0.897015i		−	0.0319751i	−0.999872	−	0.0159876i	$-0.994911\pi$
$787$		−	0.897015i		−	0.0319751i	0.999872	−	0.0159876i	$-0.00508922\pi$
$788$		−	1.12742i		−	0.0401628i
$789$	12.9624			0.461473
$790$	−3.47627	−	3.07381i	−0.123680	−	0.109361i
$791$		0			0
$792$		−	1.53690i		−	0.0546115i
$793$			11.7480i			0.417183i
$794$	3.55851			0.126287
$795$	−12.7005	+	14.3634i	−0.450441	+	0.509419i
$796$	−0.394893			−0.0139966
$797$		−	3.19982i		−	0.113343i	−0.998393	−	0.0566717i	$-0.981951\pi$
$797$		−	3.19982i		−	0.113343i	0.998393	−	0.0566717i	$-0.0180488\pi$
$798$		0			0
$799$	33.2506			1.17632
$800$	11.2605	−	1.38901i	0.398117	−	0.0491090i
$801$	−1.03761			−0.0366622
$802$		−	7.23884i		−	0.255612i
$803$		−	18.7005i		−	0.659927i
$804$	19.4763			0.686875
$805$		0			0
$806$	1.19791			0.0421944
$807$		−	4.11142i		−	0.144729i
$808$			13.5731i			0.477500i
$809$	−4.44851			−0.156401			−0.0782006	−	0.996938i	$-0.524917\pi$
$809$	−4.44851			−0.156401			−0.0782006	+	0.996938i	$0.524917\pi$
$810$	0.324869	+	0.287258i	0.0114147	+	0.0100932i
$811$	−37.6747			−1.32294			−0.661468	−	0.749973i	$-0.730066\pi$
$811$	−37.6747			−1.32294			−0.661468	+	0.749973i	$0.730066\pi$
$812$		0			0
$813$		−	16.4241i		−	0.576017i
$814$	0.300891			0.0105462
$815$	−8.87732	−	7.84955i	−0.310959	−	0.274958i
$816$	12.6497			0.442829
$817$			67.5487i			2.36323i
$818$		−	4.33900i		−	0.151710i
$819$		0			0
$820$	−10.8656	+	12.2882i	−0.379442	+	0.429123i
$821$	−0.749399			−0.0261542			−0.0130771	−	0.999914i	$-0.504163\pi$
$821$	−0.749399			−0.0261542			−0.0130771	+	0.999914i	$0.504163\pi$
$822$			4.36344i			0.152192i
$823$			26.3996i			0.920233i	0.887858	+	0.460117i	$0.152192\pi$
$823$			26.3996i			0.920233i	−0.887858	+	0.460117i	$0.847808\pi$
$824$	−5.14903			−0.179375
$825$	−9.92478	+	1.22425i	−0.345536	+	0.0426230i
$826$		0			0
$827$			5.43724i			0.189071i	0.995521	+	0.0945357i	$0.0301367\pi$
$827$			5.43724i			0.189071i	−0.995521	+	0.0945357i	$0.969863\pi$
$828$			9.73813i			0.338424i
$829$	22.7757			0.791034			0.395517	−	0.918459i	$-0.370565\pi$
$829$	22.7757			0.791034			0.395517	+	0.918459i	$0.370565\pi$
$830$	−0.926192	+	1.04746i	−0.0321486	+	0.0363579i
$831$	−11.0738			−0.384146
$832$			9.60228i			0.332899i
$833$		0			0
$834$	−0.635150			−0.0219934
$835$	24.3733	+	21.5515i	0.843472	+	0.745820i
$836$	20.9986			0.726251
$837$		−	4.57452i		−	0.158118i
$838$			4.55291i			0.157278i
$839$	15.8496			0.547187			0.273594	−	0.961845i	$-0.411788\pi$
$839$	15.8496			0.547187			0.273594	+	0.961845i	$0.411788\pi$
$840$		0			0
$841$	33.8021			1.16559
$842$		−	4.89191i		−	0.168586i
$843$		−	14.3733i		−	0.495042i
$844$	12.6545			0.435585
$845$	16.5550	−	18.7226i	0.569509	−	0.644077i
$846$	−1.92478			−0.0661752
$847$		0			0
$848$		−	32.3752i		−	1.11177i
$849$	1.14903			0.0394346
$850$	0.397722	+	3.22425i	0.0136418	+	0.110591i
$851$	−3.84955			−0.131961
$852$		−	3.92478i		−	0.134461i
$853$		−	21.0494i		−	0.720717i	−0.932814	−	0.360358i	$-0.882654\pi$
$853$		−	21.0494i		−	0.720717i	0.932814	−	0.360358i	$-0.117346\pi$
$854$		0			0
$855$	−7.92478	+	8.96239i	−0.271022	+	0.306507i
$856$	−10.5571			−0.360834
$857$		−	50.1524i		−	1.71317i	−0.516004	−	0.856586i	$-0.672581\pi$
$857$		−	50.1524i		−	1.71317i	0.516004	−	0.856586i	$-0.327419\pi$
$858$			0.523730i			0.0178799i
$859$	−5.35026			−0.182549			−0.0912743	−	0.995826i	$-0.529094\pi$
$859$	−5.35026			−0.182549			−0.0912743	+	0.995826i	$0.529094\pi$
$860$	41.5026	+	36.6977i	1.41523	+	1.25138i
$861$		0			0
$862$		−	3.76257i		−	0.128154i
$863$			33.6893i			1.14680i	0.819277	+	0.573398i	$0.194375\pi$
$863$			33.6893i			1.14680i	−0.819277	+	0.573398i	$0.805625\pi$
$864$	−2.26916			−0.0771984
$865$	−7.53690	−	6.66433i	−0.256262	−	0.226594i
$866$	−1.26045			−0.0428319
$867$		−	5.77575i		−	0.196155i
$868$		0			0
$869$	−21.4010			−0.725981
$870$	−2.27645	+	2.57452i	−0.0771790	+	0.0872842i
$871$	−13.4010			−0.454077
$872$			2.13303i			0.0722334i
$873$		−	18.4993i		−	0.626106i
$874$	5.14903			0.174169
$875$		0			0
$876$	−18.3488			−0.619950
$877$		−	21.5026i		−	0.726092i	−0.931771	−	0.363046i	$-0.881737\pi$
$877$		−	21.5026i		−	0.726092i	0.931771	−	0.363046i	$-0.118263\pi$
$878$		−	2.84112i		−	0.0958832i
$879$	0.649738			0.0219151
$880$	11.1852	−	12.6497i	0.377054	−	0.426423i
$881$	−32.3634			−1.09035			−0.545176	−	0.838322i	$-0.683537\pi$
$881$	−32.3634			−1.09035			−0.545176	+	0.838322i	$0.683537\pi$
$882$		0			0
$883$			2.59895i			0.0874617i	0.999043	+	0.0437309i	$0.0139244\pi$
$883$			2.59895i			0.0874617i	−0.999043	+	0.0437309i	$0.986076\pi$
$884$	−8.87732			−0.298576
$885$	14.4485	+	12.7757i	0.485681	+	0.429452i
$886$	3.71179			0.124700
$887$		−	38.2784i		−	1.28526i	−0.766176	−	0.642631i	$-0.777843\pi$
$887$		−	38.2784i		−	1.28526i	0.766176	−	0.642631i	$-0.222157\pi$
$888$		−	0.596124i		−	0.0200046i
$889$		0			0
$890$	0.337088	+	0.298062i	0.0112992	+	0.00999106i
$891$	2.00000			0.0670025
$892$			3.04463i			0.101942i
$893$		−	53.1002i		−	1.77693i
$894$	0.862728			0.0288539
$895$	−14.8119	+	16.7513i	−0.495109	+	0.559934i
$896$		0			0
$897$		−	6.70052i		−	0.223724i
$898$			6.36153i			0.212287i
$899$	36.2520			1.20907
$900$	1.20123	+	9.73813i	0.0400410	+	0.324604i
$901$	28.7269			0.957031
$902$		−	1.44992i		−	0.0482771i
$903$		0			0
$904$	9.26045			0.307998
$905$	−15.7381	+	17.7988i	−0.523153	+	0.591651i
$906$	0.252016			0.00837267
$907$		−	49.9972i		−	1.66013i	−0.557668	−	0.830064i	$-0.688304\pi$
$907$		−	49.9972i		−	1.66013i	0.557668	−	0.830064i	$-0.311696\pi$
$908$			25.8035i			0.856320i
$909$	−17.6629			−0.585842
$910$		0			0
$911$	−24.9525			−0.826715			−0.413357	−	0.910569i	$-0.635644\pi$
$911$	−24.9525			−0.826715			−0.413357	+	0.910569i	$0.635644\pi$
$912$		−	20.2012i		−	0.668930i
$913$			6.44851i			0.213414i
$914$	3.62672			0.119961
$915$	−14.5745	−	12.8872i	−0.481819	−	0.426037i
$916$	5.44709			0.179977
$917$		0			0
$918$		−	0.649738i		−	0.0214446i
$919$	11.6991			0.385918			0.192959	−	0.981207i	$-0.438192\pi$
$919$	11.6991			0.385918			0.192959	+	0.981207i	$0.438192\pi$
$920$	5.64832	−	6.38787i	0.186220	−	0.210602i
$921$	−24.1016			−0.794174
$922$			1.35026i			0.0444685i
$923$			2.70052i			0.0888888i
$924$		0			0
$925$	−3.84955	+	0.474855i	−0.126573	+	0.0156131i
$926$	1.02776			0.0337744
$927$		−	6.70052i		−	0.220074i
$928$		−	17.9826i		−	0.590307i
$929$	23.7090			0.777866			0.388933	−	0.921266i	$-0.372844\pi$
$929$	23.7090			0.777866			0.388933	+	0.921266i	$0.372844\pi$
$930$	−1.31406	+	1.48612i	−0.0430899	+	0.0487318i
$931$		0			0
$932$			0.0996603i			0.00326448i
$933$			8.25202i			0.270159i
$934$	−2.55008			−0.0834411
$935$	11.2243	+	9.92478i	0.367072	+	0.324575i
$936$	1.03761			0.0339154
$937$			19.9003i			0.650116i	0.945694	+	0.325058i	$0.105384\pi$
$937$			19.9003i			0.650116i	−0.945694	+	0.325058i	$0.894616\pi$
$938$		0			0
$939$	−14.9018			−0.486300
$940$	−32.6253	−	28.8481i	−1.06412	−	0.940923i
$941$	6.28821			0.204990			0.102495	−	0.994734i	$-0.467317\pi$
$941$	6.28821			0.204990			0.102495	+	0.994734i	$0.467317\pi$
$942$			0.513881i			0.0167432i
$943$			18.5501i			0.604074i
$944$	−32.5669			−1.05996
$945$		0			0
$946$	−4.89701			−0.159216
$947$		−	40.0362i		−	1.30100i	−0.759506	−	0.650501i	$-0.774559\pi$
$947$		−	40.0362i		−	1.30100i	0.759506	−	0.650501i	$-0.225441\pi$
$948$			20.9986i			0.682002i
$949$	12.6253			0.409835
$950$	5.14903	−	0.635150i	0.167057	−	0.0206070i
$951$	10.1260			0.328358
$952$		0			0
$953$		−	40.9478i		−	1.32643i	−0.748429	−	0.663215i	$-0.769192\pi$
$953$		−	40.9478i		−	1.32643i	0.748429	−	0.663215i	$-0.230808\pi$
$954$	−1.66291			−0.0538388
$955$	−20.5139	+	23.1998i	−0.663814	+	0.750728i
$956$	−11.4791			−0.371261
$957$			15.8496i			0.512343i
$958$			0.998585i			0.0322628i
$959$		0			0
$960$	−11.9126	−	10.5334i	−0.384476	−	0.339964i
$961$	−10.0738			−0.324962
$962$			0.203141i			0.00654953i
$963$		−	13.7381i		−	0.442705i
$964$	0.147616			0.00475440
$965$	−25.6728	−	22.7005i	−0.826435	−	0.730756i
$966$		0			0
$967$			38.2784i			1.23095i	0.788157	+	0.615475i	$0.211036\pi$
$967$			38.2784i			1.23095i	−0.788157	+	0.615475i	$0.788964\pi$
$968$		−	5.37916i		−	0.172893i
$969$	17.9248			0.575827
$970$	−5.31406	+	6.00985i	−0.170624	+	0.192965i
$971$	28.7269			0.921889			0.460945	−	0.887429i	$-0.347511\pi$
$971$	28.7269			0.921889			0.460945	+	0.887429i	$0.347511\pi$
$972$		−	1.96239i		−	0.0629436i
$973$		0			0
$974$	4.30089			0.137809
$975$	−0.826531	−	6.70052i	−0.0264702	−	0.214588i
$976$	32.8510			1.05153
$977$		−	41.3014i		−	1.32135i	−0.750673	−	0.660674i	$-0.770270\pi$
$977$		−	41.3014i		−	1.32135i	0.750673	−	0.660674i	$-0.229730\pi$
$978$		−	1.02776i		−	0.0328642i
$979$	2.07522			0.0663244
$980$		0			0
$981$	−2.77575			−0.0886228
$982$			0.387873i			0.0123775i
$983$		−	24.0000i		−	0.765481i	−0.923856	−	0.382741i	$-0.874980\pi$
$983$		−	24.0000i		−	0.765481i	0.923856	−	0.382741i	$-0.125020\pi$
$984$	−2.87258			−0.0915744
$985$	−0.962389	−	0.850969i	−0.0306643	−	0.0271141i
$986$	5.14903			0.163979
$987$		0			0
$988$			14.1768i			0.451024i
$989$	62.6516			1.99221
$990$	−0.649738	−	0.574515i	−0.0206500	−	0.0182593i
$991$	25.1002			0.797333			0.398666	−	0.917096i	$-0.369473\pi$
$991$	25.1002			0.797333			0.398666	+	0.917096i	$0.369473\pi$
$992$		−	10.3803i		−	0.329575i
$993$		−	27.8496i		−	0.883779i
$994$		0			0
$995$	−0.298062	+	0.337088i	−0.00944920	+	0.0106864i
$996$	6.32724			0.200486
$997$		−	32.7974i		−	1.03870i	−0.854561	−	0.519351i	$-0.826174\pi$
$997$		−	32.7974i		−	1.03870i	0.854561	−	0.519351i	$-0.173826\pi$
$998$			1.27030i			0.0402106i
$999$	0.775746			0.0245435

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.d.b.589.4		6
3.2	odd	2		2205.2.d.l.1324.3		6
5.2	odd	4		3675.2.a.bi.1.2		3
5.3	odd	4		3675.2.a.bj.1.2		3
5.4	even	2	inner	735.2.d.b.589.3		6
7.2	even	3		735.2.q.f.214.4		12
7.3	odd	6		735.2.q.e.79.3		12
7.4	even	3		735.2.q.f.79.3		12
7.5	odd	6		735.2.q.e.214.4		12
7.6	odd	2		105.2.d.b.64.4	yes	6
15.14	odd	2		2205.2.d.l.1324.4		6
21.20	even	2		315.2.d.e.64.3		6
28.27	even	2		1680.2.t.k.1009.1		6
35.4	even	6		735.2.q.f.79.4		12
35.9	even	6		735.2.q.f.214.3		12
35.13	even	4		525.2.a.k.1.2		3
35.19	odd	6		735.2.q.e.214.3		12
35.24	odd	6		735.2.q.e.79.4		12
35.27	even	4		525.2.a.j.1.2		3
35.34	odd	2		105.2.d.b.64.3	✓	6
84.83	odd	2		5040.2.t.v.1009.5		6
105.62	odd	4		1575.2.a.x.1.2		3
105.83	odd	4		1575.2.a.w.1.2		3
105.104	even	2		315.2.d.e.64.4		6
140.27	odd	4		8400.2.a.dg.1.1		3
140.83	odd	4		8400.2.a.dj.1.3		3
140.139	even	2		1680.2.t.k.1009.4		6
420.419	odd	2		5040.2.t.v.1009.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.d.b.64.3	✓	6	35.34	odd	2
105.2.d.b.64.4	yes	6	7.6	odd	2
315.2.d.e.64.3		6	21.20	even	2
315.2.d.e.64.4		6	105.104	even	2
525.2.a.j.1.2		3	35.27	even	4
525.2.a.k.1.2		3	35.13	even	4
735.2.d.b.589.3		6	5.4	even	2	inner
735.2.d.b.589.4		6	1.1	even	1	trivial
735.2.q.e.79.3		12	7.3	odd	6
735.2.q.e.79.4		12	35.24	odd	6
735.2.q.e.214.3		12	35.19	odd	6
735.2.q.e.214.4		12	7.5	odd	6
735.2.q.f.79.3		12	7.4	even	3
735.2.q.f.79.4		12	35.4	even	6
735.2.q.f.214.3		12	35.9	even	6
735.2.q.f.214.4		12	7.2	even	3
1575.2.a.w.1.2		3	105.83	odd	4
1575.2.a.x.1.2		3	105.62	odd	4
1680.2.t.k.1009.1		6	28.27	even	2
1680.2.t.k.1009.4		6	140.139	even	2
2205.2.d.l.1324.3		6	3.2	odd	2
2205.2.d.l.1324.4		6	15.14	odd	2
3675.2.a.bi.1.2		3	5.2	odd	4
3675.2.a.bj.1.2		3	5.3	odd	4
5040.2.t.v.1009.5		6	84.83	odd	2
5040.2.t.v.1009.6		6	420.419	odd	2
8400.2.a.dg.1.1		3	140.27	odd	4
8400.2.a.dj.1.3		3	140.83	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.193937i q^{2} -1.00000i q^{3} +1.96239 q^{4} +(1.48119 - 1.67513i) q^{5} +0.193937 q^{6} +0.768452i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+0.193937i q^{2} -1.00000i q^{3} +1.96239 q^{4} +(1.48119 - 1.67513i) q^{5} +0.193937 q^{6} +0.768452i q^{8} -1.00000 q^{9} +(0.324869 + 0.287258i) q^{10} +2.00000 q^{11} -1.96239i q^{12} +1.35026i q^{13} +(-1.67513 - 1.48119i) q^{15} +3.77575 q^{16} +3.35026i q^{17} -0.193937i q^{18} +5.35026 q^{19} +(2.90668 - 3.28726i) q^{20} +0.387873i q^{22} -4.96239i q^{23} +0.768452 q^{24} +(-0.612127 - 4.96239i) q^{25} -0.261865 q^{26} +1.00000i q^{27} -7.92478 q^{29} +(0.287258 - 0.324869i) q^{30} -4.57452 q^{31} +2.26916i q^{32} -2.00000i q^{33} -0.649738 q^{34} -1.96239 q^{36} -0.775746i q^{37} +1.03761i q^{38} +1.35026 q^{39} +(1.28726 + 1.13823i) q^{40} -3.73813 q^{41} +12.6253i q^{43} +3.92478 q^{44} +(-1.48119 + 1.67513i) q^{45} +0.962389 q^{46} -9.92478i q^{47} -3.77575i q^{48} +(0.962389 - 0.118714i) q^{50} +3.35026 q^{51} +2.64974i q^{52} -8.57452i q^{53} -0.193937 q^{54} +(2.96239 - 3.35026i) q^{55} -5.35026i q^{57} -1.53690i q^{58} -8.62530 q^{59} +(-3.28726 - 2.90668i) q^{60} +8.70052 q^{61} -0.887166i q^{62} +7.11142 q^{64} +(2.26187 + 2.00000i) q^{65} +0.387873 q^{66} +9.92478i q^{67} +6.57452i q^{68} -4.96239 q^{69} +2.00000 q^{71} -0.768452i q^{72} -9.35026i q^{73} +0.150446 q^{74} +(-4.96239 + 0.612127i) q^{75} +10.4993 q^{76} +0.261865i q^{78} -10.7005 q^{79} +(5.59261 - 6.32487i) q^{80} +1.00000 q^{81} -0.724961i q^{82} +3.22425i q^{83} +(5.61213 + 4.96239i) q^{85} -2.44851 q^{86} +7.92478i q^{87} +1.53690i q^{88} +1.03761 q^{89} +(-0.324869 - 0.287258i) q^{90} -9.73813i q^{92} +4.57452i q^{93} +1.92478 q^{94} +(7.92478 - 8.96239i) q^{95} +2.26916 q^{96} +18.4993i q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} - 2 q^{5} + 2 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 10 * q^4 - 2 * q^5 + 2 * q^6 - 6 * q^9	\( 6 q - 10 q^{4} - 2 q^{5} + 2 q^{6} - 6 q^{9} + 12 q^{10} + 12 q^{11} + 26 q^{16} + 12 q^{19} + 30 q^{20} - 18 q^{24} - 2 q^{25} - 20 q^{26} - 4 q^{29} - 10 q^{30} - 4 q^{31} - 24 q^{34} + 10 q^{36} - 12 q^{39} - 4 q^{40} - 4 q^{41} - 20 q^{44} + 2 q^{45} - 16 q^{46} - 16 q^{50} - 2 q^{54} - 4 q^{55} + 32 q^{59} - 8 q^{60} + 12 q^{61} - 26 q^{64} + 32 q^{65} + 4 q^{66} - 8 q^{69} + 12 q^{71} + 88 q^{74} - 8 q^{75} - 4 q^{76} - 24 q^{79} - 46 q^{80} + 6 q^{81} + 32 q^{85} - 8 q^{86} + 28 q^{89} - 12 q^{90} - 32 q^{94} + 4 q^{95} + 58 q^{96} - 12 q^{99}+O(q^{100}) \) 6 * q - 10 * q^4 - 2 * q^5 + 2 * q^6 - 6 * q^9 + 12 * q^10 + 12 * q^11 + 26 * q^16 + 12 * q^19 + 30 * q^20 - 18 * q^24 - 2 * q^25 - 20 * q^26 - 4 * q^29 - 10 * q^30 - 4 * q^31 - 24 * q^34 + 10 * q^36 - 12 * q^39 - 4 * q^40 - 4 * q^41 - 20 * q^44 + 2 * q^45 - 16 * q^46 - 16 * q^50 - 2 * q^54 - 4 * q^55 + 32 * q^59 - 8 * q^60 + 12 * q^61 - 26 * q^64 + 32 * q^65 + 4 * q^66 - 8 * q^69 + 12 * q^71 + 88 * q^74 - 8 * q^75 - 4 * q^76 - 24 * q^79 - 46 * q^80 + 6 * q^81 + 32 * q^85 - 8 * q^86 + 28 * q^89 - 12 * q^90 - 32 * q^94 + 4 * q^95 + 58 * q^96 - 12 * q^99

Introduction

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