LMFDB - Embedded newform 735.2.g.b.734.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(734,735)]

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([1, 1, 1]))

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

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

chi := DirichletCharacter("735.734");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			734.3
Character	$\chi$	$=$	735.734
Dual form			735.2.g.b.734.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.50798 q^{2} +(1.47954 - 0.900534i) q^{3} +4.28995 q^{4} +(1.94085 - 1.11045i) q^{5} +(-3.71065 + 2.25852i) q^{6} -5.74313 q^{8} +(1.37808 - 2.66475i) q^{9} +(-4.86760 + 2.78499i) q^{10} +1.71869i q^{11} +(6.34714 - 3.86324i) q^{12} -0.360784 q^{13} +(1.87156 - 3.39076i) q^{15} +5.82374 q^{16} -2.54287i q^{17} +(-3.45618 + 6.68314i) q^{18} -5.69835i q^{19} +(8.32614 - 4.76378i) q^{20} -4.31044i q^{22} +2.50798 q^{23} +(-8.49719 + 5.17188i) q^{24} +(2.53379 - 4.31044i) q^{25} +0.904837 q^{26} +(-0.360784 - 5.18361i) q^{27} +3.76228i q^{29} +(-4.69384 + 8.50394i) q^{30} -2.78499i q^{31} -3.11954 q^{32} +(1.54774 + 2.54287i) q^{33} +6.37747i q^{34} +(5.91187 - 11.4316i) q^{36} -3.30566i q^{37} +14.2913i q^{38} +(-0.533794 + 0.324898i) q^{39} +(-11.1465 + 6.37747i) q^{40} -2.63477 q^{41} +10.0606i q^{43} +7.37310i q^{44} +(-0.284442 - 6.70217i) q^{45} -6.28995 q^{46} +5.82304i q^{47} +(8.61645 - 5.24448i) q^{48} +(-6.35469 + 10.8105i) q^{50} +(-2.28995 - 3.76228i) q^{51} -1.54774 q^{52} -1.45435 q^{53} +(0.904837 + 13.0004i) q^{54} +(1.90853 + 3.33572i) q^{55} +(-5.13156 - 8.43094i) q^{57} -9.43572i q^{58} +6.85856 q^{59} +(8.02891 - 14.5462i) q^{60} -1.60367i q^{61} +6.98468i q^{62} -3.82374 q^{64} +(-0.700227 + 0.400633i) q^{65} +(-3.88170 - 6.37747i) q^{66} -2.49083i q^{67} -10.9088i q^{68} +(3.71065 - 2.25852i) q^{69} -13.1790i q^{71} +(-7.91447 + 15.3040i) q^{72} +11.6437 q^{73} +8.29052i q^{74} +(-0.132851 - 8.65923i) q^{75} -24.4456i q^{76} +(1.33874 - 0.814836i) q^{78} -13.8698 q^{79} +(11.3030 - 6.46698i) q^{80} +(-5.20181 - 7.34446i) q^{81} +6.60793 q^{82} +3.50427i q^{83} +(-2.82374 - 4.93534i) q^{85} -25.2318i q^{86} +(3.38806 + 5.56645i) q^{87} -9.87067i q^{88} +12.2078 q^{89} +(0.713373 + 16.8089i) q^{90} +10.7591 q^{92} +(-2.50798 - 4.12050i) q^{93} -14.6040i q^{94} +(-6.32775 - 11.0596i) q^{95} +(-4.61549 + 2.80926i) q^{96} +8.18747 q^{97} +(4.57989 + 2.36849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} + 12 q^{9} - 24 q^{15} + 24 q^{16} + 24 q^{25} - 36 q^{30} + 84 q^{36} + 24 q^{39} - 72 q^{46} + 24 q^{51} - 24 q^{60} + 24 q^{64} - 96 q^{79} + 12 q^{81} + 48 q^{85} - 48 q^{99}+O(q^{100}) $ 24 * q + 24 * q^4 + 12 * q^9 - 24 * q^15 + 24 * q^16 + 24 * q^25 - 36 * q^30 + 84 * q^36 + 24 * q^39 - 72 * q^46 + 24 * q^51 - 24 * q^60 + 24 * q^64 - 96 * q^79 + 12 * q^81 + 48 * q^85 - 48 * q^99

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 $

$2$	−2.50798			−1.77341			−0.886704	−	0.462338i	$-0.847011\pi$
$2$	−2.50798			−1.77341			−0.886704	+	0.462338i	$0.847011\pi$
$3$	1.47954	−	0.900534i	0.854213	−	0.519924i
$3$	1.47954	−	0.900534i	0.854213	−	0.519924i
$4$	4.28995			2.14497
$5$	1.94085	−	1.11045i	0.867974	−	0.496609i
$5$	1.94085	−	1.11045i	0.867974	−	0.496609i
$6$	−3.71065	+	2.25852i	−1.51487	+	0.922036i
$7$		0			0
$7$		0			0
$8$	−5.74313			−2.03050
$9$	1.37808	−	2.66475i	0.459359	−	0.888251i
$10$	−4.86760	+	2.78499i	−1.53927	+	0.880690i
$11$			1.71869i			0.518205i	0.965850	+	0.259103i	$0.0834268\pi$
$11$			1.71869i			0.518205i	−0.965850	+	0.259103i	$0.916573\pi$
$12$	6.34714	−	3.86324i	1.83226	−	1.11522i
$13$	−0.360784			−0.100063			−0.0500317	−	0.998748i	$-0.515932\pi$
$13$	−0.360784			−0.100063			−0.0500317	+	0.998748i	$0.515932\pi$
$14$		0			0
$15$	1.87156	−	3.39076i	0.483236	−	0.875490i
$16$	5.82374			1.45593
$17$		−	2.54287i		−	0.616737i	−0.951267	−	0.308369i	$-0.900217\pi$
$17$		−	2.54287i		−	0.616737i	0.951267	−	0.308369i	$-0.0997831\pi$
$18$	−3.45618	+	6.68314i	−0.814630	+	1.57523i
$19$		−	5.69835i		−	1.30729i	−0.756801	−	0.653646i	$-0.773239\pi$
$19$		−	5.69835i		−	1.30729i	0.756801	−	0.653646i	$-0.226761\pi$
$20$	8.32614	−	4.76378i	1.86178	−	1.06521i
$21$		0			0
$22$		−	4.31044i		−	0.918989i
$23$	2.50798			0.522949			0.261475	−	0.965210i	$-0.415791\pi$
$23$	2.50798			0.522949			0.261475	+	0.965210i	$0.415791\pi$
$24$	−8.49719	+	5.17188i	−1.73448	+	1.05571i
$25$	2.53379	−	4.31044i	0.506759	−	0.862088i
$26$	0.904837			0.177453
$27$	−0.360784	−	5.18361i	−0.0694328	−	0.997587i
$28$		0			0
$29$			3.76228i			0.698638i	0.937004	+	0.349319i	$0.113587\pi$
$29$			3.76228i			0.698638i	−0.937004	+	0.349319i	$0.886413\pi$
$30$	−4.69384	+	8.50394i	−0.856974	+	1.55260i
$31$		−	2.78499i		−	0.500198i	−0.968220	−	0.250099i	$-0.919537\pi$
$31$		−	2.78499i		−	0.500198i	0.968220	−	0.250099i	$-0.0804632\pi$
$32$	−3.11954			−0.551462
$33$	1.54774	+	2.54287i	0.269427	+	0.442657i
$34$			6.37747i			1.09373i
$35$		0			0
$36$	5.91187	−	11.4316i	0.985312	−	1.90527i
$37$		−	3.30566i		−	0.543448i	−0.962375	−	0.271724i	$-0.912406\pi$
$37$		−	3.30566i		−	0.543448i	0.962375	−	0.271724i	$-0.0875937\pi$
$38$			14.2913i			2.31836i
$39$	−0.533794	+	0.324898i	−0.0854754	+	0.0520253i
$40$	−11.1465	+	6.37747i	−1.76242	+	1.00837i
$41$	−2.63477			−0.411481			−0.205741	−	0.978607i	$-0.565960\pi$
$41$	−2.63477			−0.411481			−0.205741	+	0.978607i	$0.565960\pi$
$42$		0			0
$43$			10.0606i			1.53423i	0.641510	+	0.767114i	$0.278308\pi$
$43$			10.0606i			1.53423i	−0.641510	+	0.767114i	$0.721692\pi$
$44$			7.37310i			1.11154i
$45$	−0.284442	−	6.70217i	−0.0424021	−	0.999101i
$46$	−6.28995			−0.927402
$47$			5.82304i			0.849378i	0.905339	+	0.424689i	$0.139617\pi$
$47$			5.82304i			0.849378i	−0.905339	+	0.424689i	$0.860383\pi$
$48$	8.61645	−	5.24448i	1.24368	−	0.756975i
$49$		0			0
$50$	−6.35469	+	10.8105i	−0.898689	+	1.52883i
$51$	−2.28995	−	3.76228i	−0.320656	−	0.526825i
$52$	−1.54774			−0.214633
$53$	−1.45435			−0.199770			−0.0998852	−	0.994999i	$-0.531848\pi$
$53$	−1.45435			−0.199770			−0.0998852	+	0.994999i	$0.531848\pi$
$54$	0.904837	+	13.0004i	0.123133	+	1.76913i
$55$	1.90853	+	3.33572i	0.257345	+	0.449789i
$56$		0			0
$57$	−5.13156	−	8.43094i	−0.679692	−	1.11671i
$58$		−	9.43572i		−	1.23897i
$59$	6.85856			0.892909			0.446454	−	0.894806i	$-0.352687\pi$
$59$	6.85856			0.892909			0.446454	+	0.894806i	$0.352687\pi$
$60$	8.02891	−	14.5462i	1.03653	−	1.87790i
$61$		−	1.60367i		−	0.205329i	−0.994716	−	0.102665i	$-0.967263\pi$
$61$		−	1.60367i		−	0.205329i	0.994716	−	0.102665i	$-0.0327368\pi$
$62$			6.98468i			0.887055i
$63$		0			0
$64$	−3.82374			−0.477967
$65$	−0.700227	+	0.400633i	−0.0868524	+	0.0496924i
$66$	−3.88170	−	6.37747i	−0.477804	−	0.785012i
$67$		−	2.49083i		−	0.304303i	−0.988357	−	0.152151i	$-0.951380\pi$
$67$		−	2.49083i		−	0.304303i	0.988357	−	0.152151i	$-0.0486201\pi$
$68$		−	10.9088i		−	1.32288i
$69$	3.71065	−	2.25852i	0.446710	−	0.271894i
$70$		0			0
$71$		−	13.1790i		−	1.56406i	−0.623243	−	0.782028i	$-0.714185\pi$
$71$		−	13.1790i		−	1.56406i	0.623243	−	0.782028i	$-0.285815\pi$
$72$	−7.91447	+	15.3040i	−0.932729	+	1.80360i
$73$	11.6437			1.36280			0.681398	−	0.731913i	$-0.261372\pi$
$73$	11.6437			1.36280			0.681398	+	0.731913i	$0.261372\pi$
$74$			8.29052i			0.963754i
$75$	−0.132851	−	8.65923i	−0.0153403	−	0.999882i
$76$		−	24.4456i		−	2.80410i
$77$		0			0
$78$	1.33874	−	0.814836i	0.151583	−	0.0922621i
$79$	−13.8698			−1.56048			−0.780239	−	0.625481i	$-0.784903\pi$
$79$	−13.8698			−1.56048			−0.780239	+	0.625481i	$0.784903\pi$
$80$	11.3030	−	6.46698i	1.26371	−	0.723030i
$81$	−5.20181	−	7.34446i	−0.577979	−	0.816051i
$82$	6.60793			0.729724
$83$			3.50427i			0.384644i	0.981332	+	0.192322i	$0.0616018\pi$
$83$			3.50427i			0.384644i	−0.981332	+	0.192322i	$0.938398\pi$
$84$		0			0
$85$	−2.82374	−	4.93534i	−0.306277	−	0.535312i
$86$		−	25.2318i		−	2.72081i
$87$	3.38806	+	5.56645i	0.363239	+	0.596786i
$88$		−	9.87067i		−	1.05222i
$89$	12.2078			1.29403			0.647014	−	0.762478i	$-0.276017\pi$
$89$	12.2078			1.29403			0.647014	+	0.762478i	$0.276017\pi$
$90$	0.713373	+	16.8089i	0.0751962	+	1.77181i
$91$		0			0
$92$	10.7591			1.12171
$93$	−2.50798	−	4.12050i	−0.260065	−	0.427276i
$94$		−	14.6040i		−	1.50629i
$95$	−6.32775	−	11.0596i	−0.649213	−	1.13470i
$96$	−4.61549	+	2.80926i	−0.471066	+	0.286718i
$97$	8.18747			0.831311			0.415656	−	0.909522i	$-0.363552\pi$
$97$	8.18747			0.831311			0.415656	+	0.909522i	$0.363552\pi$
$98$		0			0
$99$	4.57989	+	2.36849i	0.460296	+	0.238042i
$100$	10.8698	−	18.4915i	1.08698	−	1.84915i
$101$	1.24693			0.124074			0.0620372	−	0.998074i	$-0.480240\pi$
$101$	1.24693			0.124074			0.0620372	+	0.998074i	$0.480240\pi$
$102$	5.74313	+	9.43572i	0.568654	+	0.934275i
$103$	−4.14604			−0.408521			−0.204261	−	0.978917i	$-0.565479\pi$
$103$	−4.14604			−0.408521			−0.204261	+	0.978917i	$0.565479\pi$
$104$	2.07203			0.203179
$105$		0			0
$106$	3.64748			0.354274
$107$	−1.10752			−0.107068			−0.0535342	−	0.998566i	$-0.517049\pi$
$107$	−1.10752			−0.107068			−0.0535342	+	0.998566i	$0.517049\pi$
$108$	−1.54774	−	22.2374i	−0.148931	−	2.13980i
$109$	−9.11368			−0.872933			−0.436466	−	0.899721i	$-0.643770\pi$
$109$	−9.11368			−0.872933			−0.436466	+	0.899721i	$0.643770\pi$
$110$	−4.78654	−	8.36591i	−0.456378	−	0.797659i
$111$	−2.97686	−	4.89086i	−0.282551	−	0.464220i
$112$		0			0
$113$	3.79282			0.356799			0.178399	−	0.983958i	$-0.442908\pi$
$113$	3.79282			0.356799			0.178399	+	0.983958i	$0.442908\pi$
$114$	12.8698	+	21.1446i	1.20537	+	1.98037i
$115$	4.86760	−	2.78499i	0.453906	−	0.259701i
$116$			16.1400i			1.49856i
$117$	−0.497187	+	0.961399i	−0.0459650	+	0.0888814i
$118$	−17.2011			−1.58349
$119$		0			0
$120$	−10.7486	+	19.4736i	−0.981211	+	1.77769i
$121$	8.04610			0.731463
$122$			4.02197i			0.364132i
$123$	−3.89824	+	2.37270i	−0.351493	+	0.213939i
$124$		−	11.9474i		−	1.07291i
$125$	0.131176	−	11.1796i	0.0117328	−	0.999931i
$126$		0			0
$127$			5.98643i			0.531210i	0.964082	+	0.265605i	$0.0855716\pi$
$127$			5.98643i			0.531210i	−0.964082	+	0.265605i	$0.914428\pi$
$128$	15.8289			1.39909
$129$	9.05993	+	14.8851i	0.797682	+	1.31056i
$130$	1.75615	−	1.00478i	0.154025	−	0.0881248i
$131$	−14.5802			−1.27388			−0.636941	−	0.770912i	$-0.719801\pi$
$131$	−14.5802			−1.27388			−0.636941	+	0.770912i	$0.719801\pi$
$132$	6.63973	+	10.9088i	0.577914	+	0.949488i
$133$		0			0
$134$			6.24693i			0.539653i
$135$	−6.45638	−	9.65998i	−0.555677	−	0.831399i
$136$			14.6040i			1.25229i
$137$	−15.7133			−1.34248			−0.671240	−	0.741240i	$-0.734238\pi$
$137$	−15.7133			−1.34248			−0.671240	+	0.741240i	$0.734238\pi$
$138$	−9.30622	+	5.66431i	−0.792198	+	0.482178i
$139$			14.7324i			1.24959i	0.780790	+	0.624794i	$0.214817\pi$
$139$			14.7324i			1.24959i	−0.780790	+	0.624794i	$0.785183\pi$
$140$		0			0
$141$	5.24385	+	8.61542i	0.441612	+	0.725549i
$142$			33.0525i			2.77371i
$143$		−	0.620076i		−	0.0518534i
$144$	8.02555	−	15.5188i	0.668796	−	1.29324i
$145$	4.17783	+	7.30202i	0.346950	+	0.606400i
$146$	−29.2022			−2.41679
$147$		0			0
$148$		−	14.1811i		−	1.16568i
$149$		−	12.7026i		−	1.04064i	−0.853972	−	0.520319i	$-0.825813\pi$
$149$		−	12.7026i		−	1.04064i	0.853972	−	0.520319i	$-0.174187\pi$
$150$	0.333186	+	21.7172i	0.0272046	+	1.77320i
$151$	16.6936			1.35850			0.679252	−	0.733905i	$-0.262304\pi$
$151$	16.6936			1.35850			0.679252	+	0.733905i	$0.262304\pi$
$152$			32.7264i			2.65446i
$153$	−6.77613	−	3.50427i	−0.547818	−	0.283304i
$154$		0			0
$155$	−3.09259	−	5.40524i	−0.248403	−	0.434159i
$156$	−2.28995	+	1.39379i	−0.183342	+	0.111593i
$157$	−1.44313			−0.115175			−0.0575873	−	0.998340i	$-0.518341\pi$
$157$	−1.44313			−0.115175			−0.0575873	+	0.998340i	$0.518341\pi$
$158$	34.7852			2.76736
$159$	−2.15177	+	1.30969i	−0.170646	+	0.103865i
$160$	−6.05456	+	3.46410i	−0.478655	+	0.273861i
$161$		0			0
$162$	13.0460	+	18.4197i	1.02499	+	1.44719i
$163$			16.8619i			1.32072i	0.750947	+	0.660362i	$0.229597\pi$
$163$			16.8619i			1.32072i	−0.750947	+	0.660362i	$0.770403\pi$
$164$	−11.3030			−0.882616
$165$	5.82767	+	3.21664i	0.453684	+	0.250415i
$166$		−	8.78863i		−	0.682130i
$167$		−	7.20879i		−	0.557833i	−0.960315	−	0.278916i	$-0.910025\pi$
$167$		−	7.20879i		−	0.557833i	0.960315	−	0.278916i	$-0.0899752\pi$
$168$		0			0
$169$	−12.8698			−0.989987
$170$	7.08187	+	12.3777i	0.543155	+	0.949327i
$171$	−15.1847	−	7.85276i	−1.16120	−	0.600516i
$172$			43.1595i			3.29088i
$173$			8.98599i			0.683192i	0.939847	+	0.341596i	$0.110967\pi$
$173$			8.98599i			0.683192i	−0.939847	+	0.341596i	$0.889033\pi$
$174$	−8.49719	−	13.9605i	−0.644170	−	1.05834i
$175$		0			0
$176$			10.0092i			0.754473i
$177$	10.1475	−	6.17637i	0.762734	−	0.464244i
$178$	−30.6170			−2.29484
$179$			10.9620i			0.819335i	0.912235	+	0.409667i	$0.134355\pi$
$179$			10.9620i			0.819335i	−0.912235	+	0.409667i	$0.865645\pi$
$180$	−1.22024	−	28.7519i	−0.0909513	−	2.14304i
$181$			5.39306i			0.400863i	0.979708	+	0.200431i	$0.0642344\pi$
$181$			5.39306i			0.400863i	−0.979708	+	0.200431i	$0.935766\pi$
$182$		0			0
$183$	−1.44416	−	2.37270i	−0.106756	−	0.175395i
$184$	−14.4036			−1.06185
$185$	−3.67078	−	6.41579i	−0.269881	−	0.471698i
$186$	6.28995	+	10.3341i	0.461201	+	0.757734i
$187$	4.37042			0.319597
$188$			24.9805i			1.82189i
$189$		0			0
$190$	15.8698	+	27.7373i	1.15132	+	2.01228i
$191$			21.3180i			1.54252i	0.636521	+	0.771259i	$0.280373\pi$
$191$			21.3180i			1.54252i	−0.636521	+	0.771259i	$0.719627\pi$
$192$	−5.65737	+	3.44341i	−0.408286	+	0.248507i
$193$		−	13.9361i		−	1.00314i	−0.865116	−	0.501571i	$-0.832756\pi$
$193$		−	13.9361i		−	1.00314i	0.865116	−	0.501571i	$-0.167244\pi$
$194$	−20.5340			−1.47425
$195$	−0.675229	+	1.22333i	−0.0483542	+	0.0876045i
$196$		0			0
$197$	−2.01202			−0.143350			−0.0716752	−	0.997428i	$-0.522835\pi$
$197$	−2.01202			−0.143350			−0.0716752	+	0.997428i	$0.522835\pi$
$198$	−11.4863	−	5.94011i	−0.816293	−	0.422145i
$199$			7.96983i			0.564966i	0.959272	+	0.282483i	$0.0911581\pi$
$199$			7.96983i			0.564966i	−0.959272	+	0.282483i	$0.908842\pi$
$200$	−14.5519	+	24.7554i	−1.02897	+	1.75047i
$201$	−2.24307	−	3.68528i	−0.158214	−	0.259939i
$202$	−3.12728			−0.220035
$203$		0			0
$204$	−9.82374	−	16.1400i	−0.687799	−	1.13003i
$205$	−5.11368	+	2.92578i	−0.357155	+	0.204345i
$206$	10.3982			0.724474
$207$	3.45618	−	6.68314i	0.240221	−	0.464510i
$208$	−2.10111			−0.145686
$209$	9.79371			0.677445
$210$		0			0
$211$	−4.95390			−0.341041			−0.170520	−	0.985354i	$-0.554545\pi$
$211$	−4.95390			−0.341041			−0.170520	+	0.985354i	$0.554545\pi$
$212$	−6.23909			−0.428502
$213$	−11.8681	−	19.4988i	−0.813190	−	1.33604i
$214$	2.77764			0.189876
$215$	11.1718	+	19.5261i	0.761912	+	1.33167i
$216$	2.07203	+	29.7701i	0.140984	+	2.02560i
$217$		0			0
$218$	22.8569			1.54806
$219$	17.2274	−	10.4856i	1.16412	−	0.708550i
$220$	8.18747	+	14.3101i	0.551999	+	0.964785i
$221$			0.917427i			0.0617128i
$222$	7.46590	+	12.2662i	0.501078	+	0.823251i
$223$	15.6534			1.04823			0.524114	−	0.851648i	$-0.324397\pi$
$223$	15.6534			1.04823			0.524114	+	0.851648i	$0.324397\pi$
$224$		0			0
$225$	−7.99450	−	12.6920i	−0.532966	−	0.846136i
$226$	−9.51230			−0.632749
$227$		−	12.6120i		−	0.837087i	−0.908197	−	0.418544i	$-0.862541\pi$
$227$		−	12.6120i		−	0.837087i	0.908197	−	0.418544i	$-0.137459\pi$
$228$	−22.0141	−	36.1683i	−1.45792	−	2.39530i
$229$			5.99233i			0.395984i	0.980204	+	0.197992i	$0.0634421\pi$
$229$			5.99233i			0.395984i	−0.980204	+	0.197992i	$0.936558\pi$
$230$	−12.2078	+	6.98468i	−0.804961	+	0.460556i
$231$		0			0
$232$		−	21.6073i		−	1.41859i
$233$	−21.8033			−1.42838			−0.714190	−	0.699952i	$-0.753205\pi$
$233$	−21.8033			−1.42838			−0.714190	+	0.699952i	$0.753205\pi$
$234$	1.24693	−	2.41117i	0.0815146	−	0.157623i
$235$	6.46621	+	11.3016i	0.421809	+	0.737238i
$236$	29.4229			1.91526
$237$	−20.5210	+	12.4903i	−1.33298	+	0.811330i
$238$		0			0
$239$			24.9069i			1.61109i	0.592533	+	0.805546i	$0.298128\pi$
$239$			24.9069i			1.61109i	−0.592533	+	0.805546i	$0.701872\pi$
$240$	10.8995	−	19.7469i	0.703560	−	1.27466i
$241$			17.0265i			1.09678i	0.836224	+	0.548388i	$0.184758\pi$
$241$			17.0265i			1.09678i	−0.836224	+	0.548388i	$0.815242\pi$
$242$	−20.1794			−1.29718
$243$	−14.3102	−	6.18201i	−0.918002	−	0.396576i
$244$		−	6.87967i		−	0.440426i
$245$		0			0
$246$	9.77670	−	5.95067i	0.623339	−	0.379401i
$247$			2.05587i			0.130812i
$248$			15.9945i			1.01565i
$249$	3.15572	+	5.18471i	0.199985	+	0.328568i
$250$	−0.328987	+	28.0381i	−0.0208070	+	1.77328i
$251$	27.3925			1.72900			0.864501	−	0.502631i	$-0.167635\pi$
$251$	27.3925			1.72900			0.864501	+	0.502631i	$0.167635\pi$
$252$		0			0
$253$			4.31044i			0.270995i
$254$		−	15.0138i		−	0.942051i
$255$	−8.62227	−	4.75915i	−0.539948	−	0.298030i
$256$	−32.0511			−2.00319
$257$		−	30.3882i		−	1.89557i	−0.318915	−	0.947783i	$-0.603318\pi$
$257$		−	30.3882i		−	1.89557i	0.318915	−	0.947783i	$-0.396682\pi$
$258$	−22.7221	−	37.3314i	−1.41461	−	2.32415i
$259$		0			0
$260$	−3.00393	+	1.71869i	−0.186296	+	0.106589i
$261$	10.0256	+	5.18471i	0.620566	+	0.320926i
$262$	36.5669			2.25911
$263$	19.3366			1.19235			0.596174	−	0.802855i	$-0.296687\pi$
$263$	19.3366			1.19235			0.596174	+	0.802855i	$0.296687\pi$
$264$	−8.88888	−	14.6040i	−0.547073	−	0.898817i
$265$	−2.82268	+	1.61499i	−0.173396	+	0.0992078i
$266$		0			0
$267$	18.0620	−	10.9936i	1.10538	−	0.672796i
$268$		−	10.6855i		−	0.652721i
$269$	22.0016			1.34146			0.670729	−	0.741702i	$-0.265981\pi$
$269$	22.0016			1.34146			0.670729	+	0.741702i	$0.265981\pi$
$270$	16.1924	+	24.2270i	0.985441	+	1.47441i
$271$			15.0577i			0.914691i	0.889289	+	0.457345i	$0.151200\pi$
$271$			15.0577i			0.914691i	−0.889289	+	0.457345i	$0.848800\pi$
$272$		−	14.8090i		−	0.897929i
$273$		0			0
$274$	39.4086			2.38076
$275$	7.40832	+	4.35481i	0.446738	+	0.262605i
$276$	15.9185	−	9.68892i	0.958180	−	0.583205i
$277$		−	1.67599i		−	0.100700i	−0.998732	−	0.0503502i	$-0.983966\pi$
$277$		−	1.67599i		−	0.100700i	0.998732	−	0.0503502i	$-0.0160338\pi$
$278$		−	36.9486i		−	2.21603i
$279$	−7.42130	−	3.83792i	−0.444302	−	0.229770i
$280$		0			0
$281$			2.10086i			0.125327i	0.998035	+	0.0626633i	$0.0199594\pi$
$281$			2.10086i			0.125327i	−0.998035	+	0.0626633i	$0.980041\pi$
$282$	−13.1514	−	21.6073i	−0.783157	−	1.28669i
$283$	−5.00401			−0.297457			−0.148729	−	0.988878i	$-0.547518\pi$
$283$	−5.00401			−0.297457			−0.148729	+	0.988878i	$0.547518\pi$
$284$		−	56.5371i		−	3.35486i
$285$	−19.3217	−	10.6648i	−1.14452	−	0.631730i
$286$			1.55514i			0.0919571i
$287$		0			0
$288$	−4.29897	+	8.31281i	−0.253319	+	0.489837i
$289$	10.5338			0.619635
$290$	−10.4779	−	18.3133i	−0.615284	−	1.07539i
$291$	12.1137	−	7.37310i	0.710117	−	0.432219i
$292$	49.9510			2.92316
$293$			17.2734i			1.00912i	0.863376	+	0.504561i	$0.168346\pi$
$293$			17.2734i			1.00912i	−0.863376	+	0.504561i	$0.831654\pi$
$294$		0			0
$295$	13.3114	−	7.61610i	0.775022	−	0.443427i
$296$			18.9848i			1.10347i
$297$	8.90903	−	0.620076i	0.516955	−	0.0359805i
$298$			31.8578i			1.84547i
$299$	−0.904837			−0.0523280
$300$	−0.569922	−	37.1476i	−0.0329045	−	2.14472i
$301$		0			0
$302$	−41.8671			−2.40918
$303$	1.84489	−	1.12291i	0.105986	−	0.0645093i
$304$		−	33.1857i		−	1.90333i
$305$	−1.78080	−	3.11249i	−0.101968	−	0.178220i
$306$	16.9944	+	8.78863i	0.971504	+	0.502413i
$307$	10.2324			0.583994			0.291997	−	0.956419i	$-0.405680\pi$
$307$	10.2324			0.583994			0.291997	+	0.956419i	$0.405680\pi$
$308$		0			0
$309$	−6.13423	+	3.73365i	−0.348964	+	0.212400i
$310$	7.75615	+	13.5562i	0.440520	+	0.769941i
$311$	−10.4779			−0.594148			−0.297074	−	0.954855i	$-0.596011\pi$
$311$	−10.4779			−0.594148			−0.297074	+	0.954855i	$0.596011\pi$
$312$	3.06564	−	1.86593i	0.173558	−	0.105638i
$313$	−0.256176			−0.0144799			−0.00723997	−	0.999974i	$-0.502305\pi$
$313$	−0.256176			−0.0144799			−0.00723997	+	0.999974i	$0.502305\pi$
$314$	3.61935			0.204252
$315$		0			0
$316$	−59.5008			−3.34718
$317$	−30.9385			−1.73768			−0.868840	−	0.495094i	$-0.835134\pi$
$317$	−30.9385			−1.73768			−0.868840	+	0.495094i	$0.835134\pi$
$318$	5.39659	−	3.28468i	0.302626	−	0.184196i
$319$	−6.46621			−0.362038
$320$	−7.42130	+	4.24608i	−0.414863	+	0.237363i
$321$	−1.63862	+	0.997363i	−0.0914591	+	0.0556674i
$322$		0			0
$323$	−14.4902			−0.806256
$324$	−22.3155	−	31.5073i	−1.23975	−	1.75041i
$325$	−0.914151	+	1.55514i	−0.0507080	+	0.0862634i
$326$		−	42.2892i		−	2.34218i
$327$	−13.4841	+	8.20719i	−0.745670	+	0.453858i
$328$	15.1318			0.835514
$329$		0			0
$330$	−14.6157	−	8.06726i	−0.804566	−	0.444088i
$331$	−8.37902			−0.460553			−0.230276	−	0.973125i	$-0.573963\pi$
$331$	−8.37902			−0.460553			−0.230276	+	0.973125i	$0.573963\pi$
$332$			15.0331i			0.825051i
$333$	−8.80877	−	4.55545i	−0.482718	−	0.249637i
$334$			18.0795i			0.989264i
$335$	−2.76594	−	4.83432i	−0.151120	−	0.264127i
$336$		0			0
$337$			11.7454i			0.639810i	0.947450	+	0.319905i	$0.103651\pi$
$337$			11.7454i			0.639810i	−0.947450	+	0.319905i	$0.896349\pi$
$338$	32.2772			1.75565
$339$	5.61163	−	3.41556i	0.304782	−	0.185508i
$340$	−12.1137	−	21.1723i	−0.656957	−	1.14823i
$341$	4.78654			0.259205
$342$	38.0829	+	19.6945i	2.05929	+	1.06496i
$343$		0			0
$344$		−	57.7794i		−	3.11526i
$345$	4.69384	−	8.50394i	0.252708	−	0.457837i
$346$		−	22.5367i		−	1.21158i
$347$	−0.442059			−0.0237310			−0.0118655	−	0.999930i	$-0.503777\pi$
$347$	−0.442059			−0.0237310			−0.0118655	+	0.999930i	$0.503777\pi$
$348$	14.5346	+	23.8798i	0.779137	+	1.28009i
$349$		−	21.7405i		−	1.16374i	−0.813282	−	0.581870i	$-0.802321\pi$
$349$		−	21.7405i		−	1.16374i	0.813282	−	0.581870i	$-0.197679\pi$
$350$		0			0
$351$	0.130165	+	1.87016i	0.00694768	+	0.0998219i
$352$		−	5.36153i		−	0.285771i
$353$			22.7835i			1.21264i	0.795220	+	0.606321i	$0.207355\pi$
$353$			22.7835i			1.21264i	−0.795220	+	0.606321i	$0.792645\pi$
$354$	−25.4497	+	15.4902i	−1.35264	+	0.823294i
$355$	−14.6346	−	25.5784i	−0.776724	−	1.35756i
$356$	52.3709			2.77565
$357$		0			0
$358$		−	27.4923i		−	1.45301i
$359$			25.0230i			1.32067i	0.750973	+	0.660333i	$0.229585\pi$
$359$			25.0230i			1.32067i	−0.750973	+	0.660333i	$0.770415\pi$
$360$	1.63359	+	38.4914i	0.0860975	+	2.02868i
$361$	−13.4712			−0.709011
$362$		−	13.5257i		−	0.710893i
$363$	11.9045	−	7.24579i	0.624825	−	0.380305i
$364$		0			0
$365$	22.5987	−	12.9298i	1.18287	−	0.676777i
$366$	3.62192	+	5.95067i	0.189321	+	0.311046i
$367$	−21.3471			−1.11431			−0.557156	−	0.830408i	$-0.688107\pi$
$367$	−21.3471			−1.11431			−0.557156	+	0.830408i	$0.688107\pi$
$368$	14.6058			0.761380
$369$	−3.63091	+	7.02100i	−0.189017	+	0.365499i
$370$	9.20623	+	16.0907i	0.478609	+	0.836513i
$371$		0			0
$372$	−10.7591	−	17.6767i	−0.557832	−	0.916495i
$373$			14.1348i			0.731872i	0.930640	+	0.365936i	$0.119251\pi$
$373$			14.1348i			0.731872i	−0.930640	+	0.365936i	$0.880749\pi$
$374$	−10.9609			−0.566775
$375$	−9.87351	−	16.6587i	−0.509866	−	0.860254i
$376$		−	33.4425i		−	1.72466i
$377$		−	1.35737i		−	0.0699081i
$378$		0			0
$379$	−9.53880			−0.489975			−0.244988	−	0.969526i	$-0.578784\pi$
$379$	−9.53880			−0.489975			−0.244988	+	0.969526i	$0.578784\pi$
$380$	−27.1457	−	47.4453i	−1.39254	−	2.43389i
$381$	5.39099	+	8.85716i	0.276189	+	0.453766i
$382$		−	53.4651i		−	2.73551i
$383$			15.7704i			0.805831i	0.915237	+	0.402916i	$0.132003\pi$
$383$			15.7704i			0.805831i	−0.915237	+	0.402916i	$0.867997\pi$
$384$	23.4195	−	14.2545i	1.19512	−	0.727422i
$385$		0			0
$386$			34.9514i			1.77898i
$387$	26.8090	+	13.8643i	1.36278	+	0.704761i
$388$	35.1238			1.78314
$389$			34.1501i			1.73148i	0.500494	+	0.865740i	$0.333152\pi$
$389$			34.1501i			1.73148i	−0.500494	+	0.865740i	$0.666848\pi$
$390$	1.69346	−	3.06808i	0.0857517	−	0.155358i
$391$		−	6.37747i		−	0.322522i
$392$		0			0
$393$	−21.5721	+	13.1300i	−1.08817	+	0.662322i
$394$	5.04610			0.254219
$395$	−26.9193	+	15.4018i	−1.35446	+	0.774948i
$396$	19.6475	+	10.1607i	0.987323	+	0.510594i
$397$	4.28244			0.214930			0.107465	−	0.994209i	$-0.465727\pi$
$397$	4.28244			0.214930			0.107465	+	0.994209i	$0.465727\pi$
$398$		−	19.9881i		−	1.00191i
$399$		0			0
$400$	14.7562	−	25.1029i	0.737808	−	1.25514i
$401$			12.5072i			0.624580i	0.949987	+	0.312290i	$0.101096\pi$
$401$			12.5072i			0.624580i	−0.949987	+	0.312290i	$0.898904\pi$
$402$	5.62558	+	9.24258i	0.280578	+	0.460978i
$403$			1.00478i			0.0500515i
$404$	5.34928			0.266136
$405$	−18.2516	−	8.47813i	−0.906930	−	0.421282i
$406$		0			0
$407$	5.68142			0.281617
$408$	13.1514	+	21.6073i	0.651094	+	1.06972i
$409$			6.45731i			0.319293i	0.987174	+	0.159647i	$0.0510355\pi$
$409$			6.45731i			0.319293i	−0.987174	+	0.159647i	$0.948965\pi$
$410$	12.8250	−	7.33779i	0.633381	−	0.362388i
$411$	−23.2485	+	14.1504i	−1.14676	+	0.697987i
$412$	−17.7863			−0.876267
$413$		0			0
$414$	−8.66802	+	16.7611i	−0.426010	+	0.823766i
$415$	3.89133	+	6.80127i	0.191018	+	0.333861i
$416$	1.12548			0.0551812
$417$	13.2671	+	21.7972i	0.649691	+	1.06741i
$418$	−24.5624			−1.20139
$419$	−10.0144			−0.489233			−0.244617	−	0.969620i	$-0.578662\pi$
$419$	−10.0144			−0.489233			−0.244617	+	0.969620i	$0.578662\pi$
$420$		0			0
$421$	17.7858			0.866825			0.433413	−	0.901196i	$-0.357309\pi$
$421$	17.7858			0.866825			0.433413	+	0.901196i	$0.357309\pi$
$422$	12.4243			0.604804
$423$	15.5170	+	8.02459i	0.754461	+	0.390169i
$424$	8.35252			0.405634
$425$	−10.9609	−	6.44312i	−0.531682	−	0.312537i
$426$	29.7649	+	48.9025i	1.44212	+	2.36934i
$427$		0			0
$428$	−4.75121			−0.229659
$429$	−0.558400	−	0.917427i	−0.0269598	−	0.0442938i
$430$	−28.0187	−	48.9711i	−1.35118	−	2.36160i
$431$		−	2.93906i		−	0.141569i	−0.997492	−	0.0707847i	$-0.977450\pi$
$431$		−	2.93906i		−	0.141569i	0.997492	−	0.0707847i	$-0.0225503\pi$
$432$	−2.10111	−	30.1880i	−0.101090	−	1.45242i
$433$	31.6675			1.52184			0.760922	−	0.648843i	$-0.224747\pi$
$433$	31.6675			1.52184			0.760922	+	0.648843i	$0.224747\pi$
$434$		0			0
$435$	12.7570	+	7.04135i	0.611651	+	0.337607i
$436$	−39.0972			−1.87242
$437$		−	14.2913i		−	0.683647i
$438$	−43.2058	+	26.2976i	−2.06445	+	1.25655i
$439$			21.4950i			1.02590i	0.858418	+	0.512951i	$0.171448\pi$
$439$			21.4950i			1.02590i	−0.858418	+	0.512951i	$0.828552\pi$
$440$	−10.9609	−	19.1575i	−0.522541	−	0.913297i
$441$		0			0
$442$		−	2.30088i		−	0.109442i
$443$	26.2694			1.24810			0.624048	−	0.781386i	$-0.285487\pi$
$443$	26.2694			1.24810			0.624048	+	0.781386i	$0.285487\pi$
$444$	−12.7706	−	20.9815i	−0.606065	−	0.995739i
$445$	23.6936	−	13.5562i	1.12318	−	0.642626i
$446$	−39.2583			−1.85893
$447$	−11.4391	−	18.7940i	−0.541052	−	0.888926i
$448$		0			0
$449$		−	36.0069i		−	1.69927i	−0.527369	−	0.849636i	$-0.676821\pi$
$449$		−	36.0069i		−	1.69927i	0.527369	−	0.849636i	$-0.323179\pi$
$450$	20.0500	+	31.8313i	0.945166	+	1.50054i
$451$		−	4.52835i		−	0.213232i
$452$	16.2710			0.765323
$453$	24.6988	−	15.0331i	1.16045	−	0.706318i
$454$			31.6306i			1.48450i
$455$		0			0
$456$	29.4712	+	48.4200i	1.38012	+	2.26747i
$457$		−	18.2465i		−	0.853537i	−0.904361	−	0.426768i	$-0.859652\pi$
$457$		−	18.2465i		−	0.853537i	0.904361	−	0.426768i	$-0.140348\pi$
$458$		−	15.0286i		−	0.702242i
$459$	−13.1813	+	0.917427i	−0.615249	+	0.0428218i
$460$	20.8818	−	11.9474i	0.973617	−	0.557052i
$461$	−22.8072			−1.06224			−0.531119	−	0.847298i	$-0.678228\pi$
$461$	−22.8072			−1.06224			−0.531119	+	0.847298i	$0.678228\pi$
$462$		0			0
$463$			23.3718i			1.08618i	0.839674	+	0.543090i	$0.182746\pi$
$463$			23.3718i			1.08618i	−0.839674	+	0.543090i	$0.817254\pi$
$464$			21.9106i			1.01717i
$465$	−9.44322	−	5.21228i	−0.437919	−	0.241714i
$466$	54.6821			2.53310
$467$			10.8894i			0.503903i	0.967740	+	0.251951i	$0.0810723\pi$
$467$			10.8894i			0.503903i	−0.967740	+	0.251951i	$0.918928\pi$
$468$	−2.13291	+	4.12435i	−0.0985936	+	0.190648i
$469$		0			0
$470$	−16.2171	−	28.3443i	−0.748039	−	1.30742i
$471$	−2.13517	+	1.29959i	−0.0983836	+	0.0598820i
$472$	−39.3896			−1.81305
$473$	−17.2911			−0.795045
$474$	51.4661	−	31.3253i	2.36392	−	1.43882i
$475$	−24.5624	−	14.4384i	−1.12700	−	0.662481i
$476$		0			0
$477$	−2.00421	+	3.87549i	−0.0917663	+	0.177446i
$478$		−	62.4659i		−	2.85712i
$479$	10.2767			0.469555			0.234777	−	0.972049i	$-0.424564\pi$
$479$	10.2767			0.469555			0.234777	+	0.972049i	$0.424564\pi$
$480$	−5.83842	+	10.5776i	−0.266486	+	0.482800i
$481$			1.19263i			0.0543792i
$482$		−	42.7021i		−	1.94503i
$483$		0			0
$484$	34.5173			1.56897
$485$	15.8906	−	9.09179i	0.721557	−	0.412837i
$486$	35.8897	+	15.5043i	1.62799	+	0.703291i
$487$			13.8475i			0.627492i	0.949507	+	0.313746i	$0.101584\pi$
$487$			13.8475i			0.627492i	−0.949507	+	0.313746i	$0.898416\pi$
$488$			9.21010i			0.416921i
$489$	15.1847	+	24.9478i	0.686676	+	1.12818i
$490$		0			0
$491$			13.5981i			0.613672i	0.951762	+	0.306836i	$0.0992704\pi$
$491$			13.5981i			0.613672i	−0.951762	+	0.306836i	$0.900730\pi$
$492$	−16.7232	+	10.1787i	−0.753942	+	0.458893i
$493$	9.56701			0.430876
$494$		−	5.15608i		−	0.231983i
$495$	11.5190	−	0.488868i	0.517739	−	0.0219730i
$496$		−	16.2190i		−	0.728256i
$497$		0			0
$498$	−7.91447	−	13.0031i	−0.354656	−	0.582684i
$499$	36.2109			1.62102			0.810511	−	0.585723i	$-0.199190\pi$
$499$	36.2109			1.62102			0.810511	+	0.585723i	$0.199190\pi$
$500$	0.562740	−	47.9597i	0.0251665	−	2.14482i
$501$	−6.49176	−	10.6657i	−0.290030	−	0.476508i
$502$	−68.6998			−3.06622
$503$			0.513189i			0.0228819i	0.999935	+	0.0114410i	$0.00364185\pi$
$503$			0.513189i			0.0228819i	−0.999935	+	0.0114410i	$0.996358\pi$
$504$		0			0
$505$	2.42011	−	1.38466i	0.107693	−	0.0616165i
$506$		−	10.8105i		−	0.480584i
$507$	−19.0414	+	11.5897i	−0.845660	+	0.514718i
$508$			25.6815i			1.13943i
$509$	18.8040			0.833475			0.416737	−	0.909027i	$-0.363173\pi$
$509$	18.8040			0.833475			0.416737	+	0.909027i	$0.363173\pi$
$510$	21.6245	+	11.9358i	0.957547	+	0.528528i
$511$		0			0
$512$	48.7256			2.15339
$513$	−29.5380	+	2.05587i	−1.30414	+	0.0907689i
$514$			76.2130i			3.36161i
$515$	−8.04683	+	4.60397i	−0.354586	+	0.202875i
$516$	38.8666	+	63.8562i	1.71101	+	2.81111i
$517$	−10.0080			−0.440152
$518$		0			0
$519$	8.09219	+	13.2951i	0.355208	+	0.583591i
$520$	4.02149	−	2.30088i	0.176354	−	0.100900i
$521$	−30.3694			−1.33051			−0.665254	−	0.746617i	$-0.731677\pi$
$521$	−30.3694			−1.33051			−0.665254	+	0.746617i	$0.731677\pi$
$522$	−25.1438	−	13.0031i	−1.10052	−	0.569132i
$523$	39.0288			1.70661			0.853305	−	0.521411i	$-0.174594\pi$
$523$	39.0288			1.70661			0.853305	+	0.521411i	$0.174594\pi$
$524$	−62.5485			−2.73244
$525$		0			0
$526$	−48.4958			−2.11452
$527$	−7.08187			−0.308491
$528$	9.01364	+	14.8090i	0.392268	+	0.644480i
$529$	−16.7101			−0.726524
$530$	7.07920	−	4.05035i	0.307501	−	0.175936i
$531$	9.45162	−	18.2764i	0.410165	−	0.793127i
$532$		0			0
$533$	0.950580			0.0411742
$534$	−45.2990	+	27.5716i	−1.96028	+	1.19314i
$535$	−2.14954	+	1.22985i	−0.0929325	+	0.0531711i
$536$			14.3051i			0.617888i
$537$	9.87161	+	16.2186i	0.425992	+	0.699886i
$538$	−55.1794			−2.37895
$539$		0			0
$540$	−27.6975	−	41.4408i	−1.19191	−	1.78333i
$541$	−10.5123			−0.451959			−0.225980	−	0.974132i	$-0.572558\pi$
$541$	−10.5123			−0.451959			−0.225980	+	0.974132i	$0.572558\pi$
$542$		−	37.7644i		−	1.62212i
$543$	4.85663	+	7.97924i	0.208418	+	0.342422i
$544$			7.93260i			0.340108i
$545$	−17.6883	+	10.1203i	−0.757683	+	0.433506i
$546$		0			0
$547$		−	25.2465i		−	1.07946i	−0.841837	−	0.539731i	$-0.818526\pi$
$547$		−	25.2465i		−	1.07946i	0.841837	−	0.539731i	$-0.181474\pi$
$548$	−67.4093			−2.87958
$549$	−4.27339	−	2.20998i	−0.182384	−	0.0943197i
$550$	−18.5799	−	10.9218i	−0.792249	−	0.465706i
$551$	21.4388			0.913324
$552$	−21.3107	+	12.9710i	−0.907045	+	0.552081i
$553$		0			0
$554$			4.20334i			0.178583i
$555$	−11.2087	−	6.18676i	−0.475783	−	0.262613i
$556$			63.2013i			2.68033i
$557$	20.3489			0.862212			0.431106	−	0.902301i	$-0.358124\pi$
$557$	20.3489			0.862212			0.431106	+	0.902301i	$0.358124\pi$
$558$	18.6124	+	9.62542i	0.787928	+	0.407476i
$559$		−	3.62970i		−	0.153520i
$560$		0			0
$561$	6.46621	−	3.93571i	0.273003	−	0.166166i
$562$		−	5.26890i		−	0.222255i
$563$			35.6652i			1.50311i	0.659671	+	0.751555i	$0.270696\pi$
$563$			35.6652i			1.50311i	−0.659671	+	0.751555i	$0.729304\pi$
$564$	22.4958	+	36.9597i	0.947245	+	1.55628i
$565$	7.36129	−	4.21174i	0.309692	−	0.177189i
$566$	12.5499			0.527513
$567$		0			0
$568$			75.6885i			3.17582i
$569$		−	25.1745i		−	1.05537i	−0.849440	−	0.527685i	$-0.823060\pi$
$569$		−	25.1745i		−	1.05537i	0.849440	−	0.527685i	$-0.176940\pi$
$570$	48.4585	+	26.7471i	2.02970	+	1.12031i
$571$	4.98040			0.208423			0.104212	−	0.994555i	$-0.466768\pi$
$571$	4.98040			0.208423			0.104212	+	0.994555i	$0.466768\pi$
$572$		−	2.66009i		−	0.111224i
$573$	19.1976	+	31.5409i	0.801992	+	1.31764i
$574$		0			0
$575$	6.35469	−	10.8105i	0.265009	−	0.450828i
$576$	−5.26940	+	10.1893i	−0.219558	+	0.424555i
$577$	21.9323			0.913054			0.456527	−	0.889710i	$-0.349093\pi$
$577$	21.9323			0.913054			0.456527	+	0.889710i	$0.349093\pi$
$578$	−26.4185			−1.09886
$579$	−12.5499	−	20.6190i	−0.521557	−	0.856897i
$580$	17.9227	+	31.3253i	0.744199	+	1.30071i
$581$		0			0
$582$	−30.3808	+	18.4915i	−1.25933	+	0.766499i
$583$		−	2.49958i		−	0.103522i
$584$	−66.8715			−2.76716
$585$	0.102622	+	2.41803i	0.00424289	+	0.0999734i
$586$		−	43.3213i		−	1.78958i
$587$			31.8719i			1.31549i	0.753240	+	0.657746i	$0.228490\pi$
$587$			31.8719i			1.31549i	−0.753240	+	0.657746i	$0.771510\pi$
$588$		0			0
$589$	−15.8698			−0.653905
$590$	−33.3848	+	19.1010i	−1.37443	+	0.786376i
$591$	−2.97686	+	1.81189i	−0.122452	+	0.0745313i
$592$		−	19.2513i		−	0.791224i
$593$		−	32.9073i		−	1.35134i	−0.737205	−	0.675669i	$-0.763855\pi$
$593$		−	32.9073i		−	1.35134i	0.737205	−	0.675669i	$-0.236145\pi$
$594$	−22.3436	+	1.55514i	−0.916771	+	0.0638080i
$595$		0			0
$596$		−	54.4935i		−	2.23214i
$597$	7.17710	+	11.7917i	0.293739	+	0.482601i
$598$	2.26931			0.0927989
$599$			21.8163i			0.891392i	0.895184	+	0.445696i	$0.147044\pi$
$599$			21.8163i			0.891392i	−0.895184	+	0.445696i	$0.852956\pi$
$600$	0.762979	+	49.7311i	0.0311485	+	2.03026i
$601$			23.9262i			0.975969i	0.872852	+	0.487985i	$0.162268\pi$
$601$			23.9262i			0.975969i	−0.872852	+	0.487985i	$0.837732\pi$
$602$		0			0
$603$	−6.63744	−	3.43255i	−0.270297	−	0.139784i
$604$	71.6145			2.91395
$605$	15.6163	−	8.93480i	0.634891	−	0.363251i
$606$	−4.62693	+	2.81622i	−0.187956	+	0.114401i
$607$	−44.2982			−1.79801			−0.899005	−	0.437939i	$-0.855708\pi$
$607$	−44.2982			−1.79801			−0.899005	+	0.437939i	$0.855708\pi$
$608$			17.7763i			0.720922i
$609$		0			0
$610$	4.46621	+	7.80604i	0.180831	+	0.316057i
$611$		−	2.10086i		−	0.0849916i
$612$	−29.0692	−	15.0331i	−1.17505	−	0.607679i
$613$			8.04230i			0.324825i	0.986723	+	0.162413i	$0.0519276\pi$
$613$			8.04230i			0.324825i	−0.986723	+	0.162413i	$0.948072\pi$
$614$	−25.6626			−1.03566
$615$	−4.93113	+	8.93386i	−0.198842	+	0.360248i
$616$		0			0
$617$	−13.1311			−0.528637			−0.264318	−	0.964435i	$-0.585147\pi$
$617$	−13.1311			−0.528637			−0.264318	+	0.964435i	$0.585147\pi$
$618$	15.3845	−	9.36390i	0.618855	−	0.376671i
$619$		−	25.1620i		−	1.01134i	−0.862726	−	0.505672i	$-0.831245\pi$
$619$		−	25.1620i		−	1.01134i	0.862726	−	0.505672i	$-0.168755\pi$
$620$	−13.2671	−	23.1882i	−0.532818	−	0.931260i
$621$	−0.904837	−	13.0004i	−0.0363098	−	0.521687i
$622$	26.2783			1.05367
$623$		0			0
$624$	−3.10867	+	1.89212i	−0.124447	+	0.0757455i
$625$	−12.1598	−	21.8435i	−0.486391	−	0.873741i
$626$	0.642484			0.0256788
$627$	14.4902	−	8.81958i	0.578682	−	0.352220i
$628$	−6.19097			−0.247046
$629$	−8.40588			−0.335164
$630$		0			0
$631$	−9.42011			−0.375009			−0.187504	−	0.982264i	$-0.560040\pi$
$631$	−9.42011			−0.375009			−0.187504	+	0.982264i	$0.560040\pi$
$632$	79.6562			3.16856
$633$	−7.32950	+	4.46116i	−0.291321	+	0.177315i
$634$	77.5930			3.08161
$635$	6.64764	+	11.6188i	0.263804	+	0.461076i
$636$	−9.23097	+	5.61851i	−0.366032	+	0.222788i
$637$		0			0
$638$	16.2171			0.642041
$639$	−35.1187	−	18.1616i	−1.38927	−	0.718462i
$640$	30.7216	−	17.5773i	1.21438	−	0.694802i
$641$		−	4.91040i		−	0.193949i	−0.995287	−	0.0969747i	$-0.969083\pi$
$641$		−	4.91040i		−	0.193949i	0.995287	−	0.0969747i	$-0.0309166\pi$
$642$	4.10963	−	2.50136i	0.162194	−	0.0987209i
$643$	−8.98926			−0.354502			−0.177251	−	0.984166i	$-0.556720\pi$
$643$	−8.98926			−0.354502			−0.177251	+	0.984166i	$0.556720\pi$
$644$		0			0
$645$	34.1131	+	18.8291i	1.34320	+	0.741394i
$646$	36.3411			1.42982
$647$		−	0.238947i		−	0.00939397i	−0.999989	−	0.00469699i	$-0.998505\pi$
$647$		−	0.238947i		−	0.00939397i	0.999989	−	0.00469699i	$-0.00149510\pi$
$648$	29.8747	+	42.1802i	1.17359	+	1.65699i
$649$			11.7878i			0.462710i
$650$	2.29267	−	3.90024i	0.0899259	−	0.152980i
$651$		0			0
$652$			72.3365i			2.83292i
$653$	1.95812			0.0766272			0.0383136	−	0.999266i	$-0.487801\pi$
$653$	1.95812			0.0766272			0.0383136	+	0.999266i	$0.487801\pi$
$654$	33.8177	−	20.5834i	1.32238	−	0.804876i
$655$	−28.2981	+	16.1907i	−1.10570	+	0.632622i
$656$	−15.3442			−0.599090
$657$	16.0459	−	31.0277i	0.626012	−	1.21050i
$658$		0			0
$659$			31.6741i			1.23385i	0.787023	+	0.616924i	$0.211621\pi$
$659$			31.6741i			1.23385i	−0.787023	+	0.616924i	$0.788379\pi$
$660$	25.0004	+	13.7992i	0.973139	+	0.537134i
$661$		−	28.7000i		−	1.11630i	−0.829740	−	0.558150i	$-0.811511\pi$
$661$		−	28.7000i		−	1.11630i	0.829740	−	0.558150i	$-0.188489\pi$
$662$	21.0144			0.816747
$663$	0.826174	+	1.35737i	0.0320860	+	0.0527159i
$664$		−	20.1255i		−	0.781020i
$665$		0			0
$666$	22.0922	+	11.4250i	0.856055	+	0.442709i
$667$			9.43572i			0.365352i
$668$		−	30.9253i		−	1.19654i
$669$	23.1598	−	14.0964i	0.895409	−	0.544998i
$670$	6.93692	+	12.1244i	0.267996	+	0.468405i
$671$	2.75622			0.106403
$672$		0			0
$673$		−	33.9688i		−	1.30940i	−0.755889	−	0.654700i	$-0.772795\pi$
$673$		−	33.9688i		−	1.30940i	0.755889	−	0.654700i	$-0.227205\pi$
$674$		−	29.4571i		−	1.13464i
$675$	−23.2578	−	11.5791i	−0.895193	−	0.445679i
$676$	−55.2109			−2.12350
$677$			7.18943i			0.276312i	0.990410	+	0.138156i	$0.0441176\pi$
$677$			7.18943i			0.276312i	−0.990410	+	0.138156i	$0.955882\pi$
$678$	−14.0738	+	8.56616i	−0.540502	+	0.328981i
$679$		0			0
$680$	16.2171	+	28.3443i	0.621897	+	1.08695i
$681$	−11.3575	−	18.6599i	−0.435222	−	0.715051i
$682$	−12.0045			−0.459677
$683$	8.04026			0.307652			0.153826	−	0.988098i	$-0.450840\pi$
$683$	8.04026			0.307652			0.153826	+	0.988098i	$0.450840\pi$
$684$	−65.1415	−	33.6879i	−2.49075	−	1.28809i
$685$	−30.4972	+	17.4489i	−1.16524	+	0.666688i
$686$		0			0
$687$	5.39630	+	8.86589i	0.205882	+	0.338255i
$688$			58.5904i			2.23374i
$689$	0.524706			0.0199897
$690$	−11.7720	+	21.3277i	−0.448154	+	0.811931i
$691$		−	44.2571i		−	1.68362i	−0.539773	−	0.841810i	$-0.681490\pi$
$691$		−	44.2571i		−	1.68362i	0.539773	−	0.841810i	$-0.318510\pi$
$692$			38.5494i			1.46543i
$693$		0			0
$694$	1.10867			0.0420847
$695$	16.3597	+	28.5934i	0.620557	+	1.08461i
$696$	−19.4581	−	31.9688i	−0.737557	−	1.21177i
$697$			6.69988i			0.253776i
$698$			54.5246i			2.06379i
$699$	−32.2588	+	19.6346i	−1.22014	+	0.742649i
$700$		0			0
$701$		−	0.779307i		−	0.0294340i	−0.999892	−	0.0147170i	$-0.995315\pi$
$701$		−	0.779307i		−	0.0294340i	0.999892	−	0.0147170i	$-0.00468474\pi$
$702$	−0.326450	−	4.69032i	−0.0123211	−	0.177025i
$703$	−18.8368			−0.710444
$704$		−	6.57183i		−	0.247685i
$705$	19.7445	+	10.8982i	0.743622	+	0.410450i
$706$		−	57.1404i		−	2.15051i
$707$		0			0
$708$	43.5323	−	26.4963i	1.63604	−	0.995792i
$709$	−9.26534			−0.347967			−0.173984	−	0.984749i	$-0.555664\pi$
$709$	−9.26534			−0.347967			−0.173984	+	0.984749i	$0.555664\pi$
$710$	36.7033	+	64.1500i	1.37745	+	2.40751i
$711$	−19.1137	+	36.9597i	−0.716819	+	1.38610i
$712$	−70.1112			−2.62753
$713$		−	6.98468i		−	0.261578i
$714$		0			0
$715$	−0.688564	−	1.20347i	−0.0257508	−	0.0450074i
$716$			47.0262i			1.75745i
$717$	22.4295	+	36.8507i	0.837645	+	1.37622i
$718$		−	62.7572i		−	2.34208i
$719$	−18.1996			−0.678730			−0.339365	−	0.940655i	$-0.610212\pi$
$719$	−18.1996			−0.678730			−0.339365	+	0.940655i	$0.610212\pi$
$720$	−1.65652	−	39.0317i	−0.0617347	−	1.45463i
$721$		0			0
$722$	33.7855			1.25737
$723$	15.3330	+	25.1914i	0.570239	+	0.936879i
$724$			23.1359i			0.859840i
$725$	16.2171	+	9.53285i	0.602288	+	0.354041i
$726$	−29.8563	+	18.1723i	−1.10807	+	0.674436i
$727$	−31.6357			−1.17330			−0.586652	−	0.809839i	$-0.699554\pi$
$727$	−31.6357			−1.17330			−0.586652	+	0.809839i	$0.699554\pi$
$728$		0			0
$729$	−26.7397	+	3.74032i	−0.990358	+	0.138531i
$730$	−56.6771	+	32.4276i	−2.09771	+	1.20020i
$731$	25.5829			0.946216
$732$	−6.19538	−	10.1787i	−0.228988	−	0.376217i
$733$	−17.0085			−0.628224			−0.314112	−	0.949386i	$-0.601707\pi$
$733$	−17.0085			−0.628224			−0.314112	+	0.949386i	$0.601707\pi$
$734$	53.5381			1.97613
$735$		0			0
$736$	−7.82374			−0.288387
$737$	4.28096			0.157691
$738$	9.10623	−	17.6085i	0.335205	−	0.648178i
$739$	−18.9804			−0.698205			−0.349103	−	0.937084i	$-0.613514\pi$
$739$	−18.9804			−0.698205			−0.349103	+	0.937084i	$0.613514\pi$
$740$	−15.7474	−	27.5234i	−0.578887	−	1.01178i
$741$	1.85138	+	3.04174i	0.0680123	+	0.111741i
$742$		0			0
$743$	3.80063			0.139432			0.0697159	−	0.997567i	$-0.477791\pi$
$743$	3.80063			0.139432			0.0697159	+	0.997567i	$0.477791\pi$
$744$	14.4036	+	23.6646i	0.528063	+	0.867585i
$745$	−14.1056	−	24.6538i	−0.516790	−	0.903247i
$746$		−	35.4497i		−	1.29791i
$747$	9.33802	+	4.82915i	0.341660	+	0.176689i
$748$	18.7489			0.685526
$749$		0			0
$750$	24.7625	+	41.7797i	0.904199	+	1.52558i
$751$	−12.6456			−0.461444			−0.230722	−	0.973020i	$-0.574109\pi$
$751$	−12.6456			−0.461444			−0.230722	+	0.973020i	$0.574109\pi$
$752$			33.9119i			1.23664i
$753$	40.5283	−	24.6679i	1.47694	−	0.898949i
$754$			3.40425i			0.123976i
$755$	32.3997	−	18.5374i	1.17915	−	0.674645i
$756$		0			0
$757$			6.50118i			0.236289i	0.992996	+	0.118145i	$0.0376947\pi$
$757$			6.50118i			0.236289i	−0.992996	+	0.118145i	$0.962305\pi$
$758$	23.9231			0.868926
$759$	3.88170	+	6.37747i	0.140897	+	0.231487i
$760$	36.3411	+	63.5169i	1.31823	+	2.30400i
$761$	43.7825			1.58711			0.793556	−	0.608497i	$-0.208227\pi$
$761$	43.7825			1.58711			0.793556	+	0.608497i	$0.208227\pi$
$762$	−13.5205	−	22.2135i	−0.489795	−	0.804712i
$763$		0			0
$764$			91.4531i			3.30866i
$765$	−17.0428	+	0.723300i	−0.616183	+	0.0261510i
$766$		−	39.5519i		−	1.42907i
$767$	−2.47446			−0.0893474
$768$	−47.4209	+	28.8631i	−1.71115	+	1.04151i
$769$		−	33.3141i		−	1.20134i	−0.799498	−	0.600668i	$-0.794901\pi$
$769$		−	33.3141i		−	1.20134i	0.799498	−	0.600668i	$-0.205099\pi$
$770$		0			0
$771$	−27.3657	−	44.9606i	−0.985550	−	1.61922i
$772$		−	59.7851i		−	2.15171i
$773$		−	42.3324i		−	1.52259i	−0.648405	−	0.761296i	$-0.724563\pi$
$773$		−	42.3324i		−	1.52259i	0.648405	−	0.761296i	$-0.275437\pi$
$774$	−67.2364	−	34.7713i	−2.41676	−	1.24983i
$775$	−12.0045	−	7.05658i	−0.431215	−	0.253480i
$776$	−47.0217			−1.68798
$777$		0			0
$778$		−	85.6477i		−	3.07062i
$779$			15.0138i			0.537926i
$780$	−2.89670	+	5.24802i	−0.103718	+	0.187909i
$781$	22.6506			0.810502
$782$			15.9945i			0.571963i
$783$	19.5022	−	1.35737i	0.696952	−	0.0485084i
$784$		0			0
$785$	−2.80091	+	1.60253i	−0.0999686	+	0.0571968i
$786$	54.1022	−	32.9298i	1.92976	−	1.17457i
$787$	−25.9101			−0.923597			−0.461799	−	0.886985i	$-0.652796\pi$
$787$	−25.9101			−0.923597			−0.461799	+	0.886985i	$0.652796\pi$
$788$	−8.63145			−0.307483
$789$	28.6093	−	17.4133i	1.01852	−	0.619930i
$790$	67.5129	−	38.6273i	2.40200	−	1.37430i
$791$		0			0
$792$	−26.3029	−	13.6025i	−0.934633	−	0.483345i
$793$			0.578579i			0.0205459i
$794$	−10.7403			−0.381158
$795$	−2.72191	+	4.93135i	−0.0965362	+	0.174897i
$796$			34.1901i			1.21184i
$797$			27.5780i			0.976865i	0.872602	+	0.488432i	$0.162431\pi$
$797$			27.5780i			0.976865i	−0.872602	+	0.488432i	$0.837569\pi$
$798$		0			0
$799$	14.8073			0.523843
$800$	−7.90428	+	13.4466i	−0.279458	+	0.475409i
$801$	16.8233	−	32.5309i	0.594423	−	1.14942i
$802$		−	31.3678i		−	1.10764i
$803$			20.0120i			0.706208i
$804$	−9.62267	−	15.8096i	−0.339365	−	0.557563i
$805$		0			0
$806$		−	2.51996i		−	0.0887617i
$807$	32.5522	−	19.8132i	1.14589	−	0.697456i
$808$	−7.16130			−0.251934
$809$		−	31.1891i		−	1.09655i	−0.836298	−	0.548275i	$-0.815285\pi$
$809$		−	31.1891i		−	1.09655i	0.836298	−	0.548275i	$-0.184715\pi$
$810$	45.7746	+	21.2630i	1.60836	+	0.747104i
$811$		−	17.5174i		−	0.615120i	−0.951529	−	0.307560i	$-0.900488\pi$
$811$		−	17.5174i		−	0.615120i	0.951529	−	0.307560i	$-0.0995124\pi$
$812$		0			0
$813$	13.5600	+	22.2785i	0.475569	+	0.781341i
$814$	−14.2489			−0.499422
$815$	18.7243	+	32.7264i	0.655884	+	1.14635i
$816$	−13.3360	−	21.9106i	−0.466855	−	0.767023i
$817$	57.3289			2.00568
$818$		−	16.1948i		−	0.566237i
$819$		0			0
$820$	−21.9374	+	12.5514i	−0.766088	+	0.438315i
$821$		−	35.4867i		−	1.23849i	−0.785197	−	0.619247i	$-0.787438\pi$
$821$		−	35.4867i		−	1.23849i	0.785197	−	0.619247i	$-0.212562\pi$
$822$	58.3066	−	35.4888i	2.03368	−	1.23782i
$823$		−	30.0470i		−	1.04737i	−0.851912	−	0.523686i	$-0.824557\pi$
$823$		−	30.0470i		−	1.04737i	0.851912	−	0.523686i	$-0.175443\pi$
$824$	23.8112			0.829503
$825$	14.8826	−	0.228329i	0.518144	−	0.00794941i
$826$		0			0
$827$	21.6751			0.753717			0.376859	−	0.926271i	$-0.377004\pi$
$827$	21.6751			0.753717			0.376859	+	0.926271i	$0.377004\pi$
$828$	14.8268	−	28.6703i	0.515268	−	0.996361i
$829$		−	9.16245i		−	0.318225i	−0.987260	−	0.159113i	$-0.949137\pi$
$829$		−	9.16245i		−	0.318225i	0.987260	−	0.159113i	$-0.0508633\pi$
$830$	−9.75935	−	17.0574i	−0.338752	−	0.592071i
$831$	−1.50929	−	2.47969i	−0.0523566	−	0.0860196i
$832$	1.37954			0.0478270
$833$		0			0
$834$	−33.2735	−	54.6669i	−1.15217	−	1.89296i
$835$	−8.00501	−	13.9912i	−0.277025	−	0.484184i
$836$	42.0145			1.45310
$837$	−14.4363	+	1.00478i	−0.498991	+	0.0347302i
$838$	25.1158			0.867610
$839$	31.7155			1.09494			0.547471	−	0.836825i	$-0.315591\pi$
$839$	31.7155			1.09494			0.547471	+	0.836825i	$0.315591\pi$
$840$		0			0
$841$	14.8452			0.511904
$842$	−44.6063			−1.53723
$843$	1.89189	+	3.10830i	0.0651603	+	0.107056i
$844$	−21.2520			−0.731523
$845$	−24.9784	+	14.2913i	−0.859284	+	0.491637i
$846$	−38.9162	−	20.1255i	−1.33797	−	0.691928i
$847$		0			0
$848$	−8.46976			−0.290853
$849$	−7.40363	+	4.50628i	−0.254092	+	0.154655i
$850$	27.4897	+	16.1592i	0.942888	+	0.554255i
$851$		−	8.29052i		−	0.284195i
$852$	−50.9136	−	83.6488i	−1.74427	−	2.86576i
$853$	−10.2006			−0.349262			−0.174631	−	0.984634i	$-0.555873\pi$
$853$	−10.2006			−0.349262			−0.174631	+	0.984634i	$0.555873\pi$
$854$		0			0
$855$	−38.1913	+	1.62085i	−1.30612	+	0.0554319i
$856$	6.36065			0.217402
$857$		−	1.80558i		−	0.0616774i	−0.999524	−	0.0308387i	$-0.990182\pi$
$857$		−	1.80558i		−	0.0616774i	0.999524	−	0.0308387i	$-0.00981783\pi$
$858$	1.40045	+	2.30088i	0.0478107	+	0.0785509i
$859$		−	7.71307i		−	0.263166i	−0.991305	−	0.131583i	$-0.957994\pi$
$859$		−	7.71307i		−	0.263166i	0.991305	−	0.131583i	$-0.0420061\pi$
$860$	47.9265	+	83.7660i	1.63428	+	2.85640i
$861$		0			0
$862$			7.37109i			0.251060i
$863$	−22.3531			−0.760909			−0.380455	−	0.924800i	$-0.624233\pi$
$863$	−22.3531			−0.760909			−0.380455	+	0.924800i	$0.624233\pi$
$864$	1.12548	+	16.1705i	0.0382896	+	0.550132i
$865$	9.97851	+	17.4405i	0.339280	+	0.592993i
$866$	−79.4214			−2.69885
$867$	15.5852	−	9.48604i	0.529300	−	0.322163i
$868$		0			0
$869$		−	23.8380i		−	0.808648i
$870$	−31.9942	−	17.6595i	−1.08471	−	0.598715i
$871$			0.898649i			0.0304496i
$872$	52.3411			1.77249
$873$	11.2830	−	21.8176i	0.381870	−	0.738413i
$874$			35.8423i			1.21238i
$875$		0			0
$876$	73.9045	−	44.9826i	2.49700	−	1.51982i
$877$		−	51.7428i		−	1.74723i	−0.486618	−	0.873615i	$-0.661770\pi$
$877$		−	51.7428i		−	1.74723i	0.486618	−	0.873615i	$-0.338230\pi$
$878$		−	53.9090i		−	1.81934i
$879$	15.5553	+	25.5567i	0.524667	+	0.862005i
$880$	11.1148	+	19.4264i	0.374678	+	0.654863i
$881$	−40.9882			−1.38093			−0.690464	−	0.723367i	$-0.742594\pi$
$881$	−40.9882			−1.38093			−0.690464	+	0.723367i	$0.742594\pi$
$882$		0			0
$883$			10.6943i			0.359891i	0.983677	+	0.179945i	$0.0575921\pi$
$883$			10.6943i			0.359891i	−0.983677	+	0.179945i	$0.942408\pi$
$884$			3.93571i			0.132372i
$885$	12.8362	−	23.2557i	0.431485	−	0.781733i
$886$	−65.8830			−2.21338
$887$		−	47.0848i		−	1.58095i	−0.612493	−	0.790476i	$-0.709833\pi$
$887$		−	47.0848i		−	1.58095i	0.612493	−	0.790476i	$-0.290167\pi$
$888$	17.0965	+	28.0888i	0.573721	+	0.942599i
$889$		0			0
$890$	−59.4229	+	33.9987i	−1.99186	+	1.13964i
$891$	12.6229	−	8.94032i	0.422882	−	0.299512i
$892$	67.1521			2.24842
$893$	33.1817			1.11038
$894$	28.6891	+	47.1349i	0.959506	+	1.57643i
$895$	12.1727	+	21.2755i	0.406889	+	0.711161i
$896$		0			0
$897$	−1.33874	+	0.814836i	−0.0446993	+	0.0272066i
$898$			90.3046i			3.01350i
$899$	10.4779			0.349458
$900$	−34.2960	−	54.4482i	−1.14320	−	1.81494i
$901$			3.69823i			0.123206i
$902$			11.3570i			0.378147i
$903$		0			0
$904$	−21.7827			−0.724480
$905$	5.98873	+	10.4671i	0.199072	+	0.347939i
$906$	−61.9440	+	37.7028i	−2.05795	+	1.25259i
$907$		−	8.71819i		−	0.289483i	−0.989470	−	0.144741i	$-0.953765\pi$
$907$		−	8.71819i		−	0.289483i	0.989470	−	0.144741i	$-0.0462350\pi$
$908$		−	54.1048i		−	1.79553i
$909$	1.71837	−	3.32277i	0.0569947	−	0.110209i
$910$		0			0
$911$			4.85314i			0.160792i	0.996763	+	0.0803958i	$0.0256184\pi$
$911$			4.85314i			0.160792i	−0.996763	+	0.0803958i	$0.974382\pi$
$912$	−29.8849	−	49.0996i	−0.989587	−	1.62585i
$913$	−6.02277			−0.199324
$914$			45.7619i			1.51367i
$915$	−5.43767	−	3.00138i	−0.179764	−	0.0992224i
$916$			25.7068i			0.849376i
$917$		0			0
$918$	33.0583	−	2.30088i	1.09109	−	0.0759405i
$919$	−35.8584			−1.18286			−0.591429	−	0.806357i	$-0.701436\pi$
$919$	−35.8584			−1.18286			−0.591429	+	0.806357i	$0.701436\pi$
$920$	−27.9553	+	15.9945i	−0.921658	+	0.527324i
$921$	15.1392	−	9.21462i	0.498855	−	0.303632i
$922$	57.1999			1.88378
$923$			4.75475i			0.156505i
$924$		0			0
$925$	−14.2489	−	8.37587i	−0.468500	−	0.275397i
$926$		−	58.6160i		−	1.92624i
$927$	−5.71355	+	11.0482i	−0.187658	+	0.362869i
$928$		−	11.7366i		−	0.385273i
$929$	25.4003			0.833355			0.416678	−	0.909054i	$-0.363194\pi$
$929$	25.4003			0.833355			0.416678	+	0.909054i	$0.363194\pi$
$930$	23.6834	+	13.0723i	0.776608	+	0.428657i
$931$		0			0
$932$	−93.5349			−3.06384
$933$	−15.5025	+	9.43572i	−0.507528	+	0.308911i
$934$		−	27.3104i		−	0.893625i
$935$	8.48232	−	4.85314i	0.277402	−	0.158715i
$936$	2.85541	−	5.52144i	0.0933320	−	0.180474i
$937$	−40.3037			−1.31667			−0.658333	−	0.752727i	$-0.728738\pi$
$937$	−40.3037			−1.31667			−0.658333	+	0.752727i	$0.728738\pi$
$938$		0			0
$939$	−0.379023	+	0.230695i	−0.0123689	+	0.00752846i
$940$	27.7397	+	48.4834i	0.904768	+	1.58136i
$941$	18.2413			0.594650			0.297325	−	0.954776i	$-0.403906\pi$
$941$	18.2413			0.594650			0.297325	+	0.954776i	$0.403906\pi$
$942$	5.35497	−	3.25935i	0.174474	−	0.106195i
$943$	−6.60793			−0.215184
$944$	39.9425			1.30002
$945$		0			0
$946$	43.3657			1.40994
$947$	−18.8485			−0.612494			−0.306247	−	0.951952i	$-0.599073\pi$
$947$	−18.8485			−0.612494			−0.306247	+	0.951952i	$0.599073\pi$
$948$	−88.0338	+	53.5825i	−2.85921	+	1.74028i
$949$	−4.20087			−0.136366
$950$	61.6019	+	36.2113i	1.99863	+	1.17485i
$951$	−45.7747	+	27.8612i	−1.48435	+	0.903461i
$952$		0			0
$953$	−25.3110			−0.819903			−0.409952	−	0.912107i	$-0.634454\pi$
$953$	−25.3110			−0.819903			−0.409952	+	0.912107i	$0.634454\pi$
$954$	5.02650	−	9.71963i	0.162739	−	0.314684i
$955$	23.6726	+	41.3751i	0.766029	+	1.33887i
$956$			106.849i			3.45575i
$957$	−9.56701	+	5.82304i	−0.309257	+	0.188232i
$958$	−25.7737			−0.832712
$959$		0			0
$960$	−7.15637	+	12.9654i	−0.230971	+	0.418456i
$961$	23.2438			0.749802
$962$		−	2.99108i		−	0.0964364i
$963$	−1.52625	+	2.95128i	−0.0491827	+	0.0951035i
$964$			73.0429i			2.35255i
$965$	−15.4754	−	27.0479i	−0.498170	−	0.870702i
$966$		0			0
$967$		−	32.2840i		−	1.03818i	−0.854718	−	0.519092i	$-0.826270\pi$
$967$		−	32.2840i		−	1.03818i	0.854718	−	0.519092i	$-0.173730\pi$
$968$	−46.2098			−1.48524
$969$	−21.4388	+	13.0489i	−0.688714	+	0.419191i
$970$	−39.8534	+	22.8020i	−1.27961	+	0.732128i
$971$	−1.38783			−0.0445377			−0.0222688	−	0.999752i	$-0.507089\pi$
$971$	−1.38783			−0.0445377			−0.0222688	+	0.999752i	$0.507089\pi$
$972$	−61.3901	−	26.5205i	−1.96909	−	0.850645i
$973$		0			0
$974$		−	34.7293i		−	1.11280i
$975$	0.0479303	+	3.12411i	0.00153500	+	0.100052i
$976$		−	9.33937i		−	0.298946i
$977$	−57.8116			−1.84956			−0.924779	−	0.380505i	$-0.875750\pi$
$977$	−57.8116			−1.84956			−0.924779	+	0.380505i	$0.875750\pi$
$978$	−38.0829	−	62.5685i	−1.21776	−	2.00072i
$979$			20.9815i			0.670572i
$980$		0			0
$981$	−12.5593	+	24.2857i	−0.400989	+	0.775383i
$982$		−	34.1036i		−	1.08829i
$983$			26.0114i			0.829635i	0.909905	+	0.414818i	$0.136155\pi$
$983$			26.0114i			0.829635i	−0.909905	+	0.414818i	$0.863845\pi$
$984$	22.3881	−	13.6267i	0.713706	−	0.434403i
$985$	−3.90503	+	2.23425i	−0.124424	+	0.0711891i
$986$	−23.9938			−0.764119
$987$		0			0
$988$			8.81958i			0.280588i
$989$			25.2318i			0.802324i
$990$	−28.8893	+	1.22607i	−0.918162	+	0.0389670i
$991$	−36.2324			−1.15096			−0.575480	−	0.817816i	$-0.695185\pi$
$991$	−36.2324			−1.15096			−0.575480	+	0.817816i	$0.695185\pi$
$992$			8.68788i			0.275841i
$993$	−12.3971	+	7.54560i	−0.393410	+	0.239452i
$994$		0			0
$995$	8.85011	+	15.4682i	0.280567	+	0.490376i
$996$	13.5379	+	22.2421i	0.428963	+	0.704769i
$997$	34.5948			1.09563			0.547814	−	0.836600i	$-0.315460\pi$
$997$	34.5948			1.09563			0.547814	+	0.836600i	$0.315460\pi$
$998$	−90.8160			−2.87473
$999$	−17.1353	+	1.19263i	−0.542136	+	0.0377331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.g.b.734.3		24
3.2	odd	2	inner	735.2.g.b.734.24		24
5.4	even	2	inner	735.2.g.b.734.22		24
7.2	even	3		735.2.p.f.374.11		24
7.3	odd	6		735.2.p.f.509.12		24
7.4	even	3		105.2.p.a.89.11	yes	24
7.5	odd	6		105.2.p.a.59.12	yes	24
7.6	odd	2	inner	735.2.g.b.734.2		24
15.14	odd	2	inner	735.2.g.b.734.1		24
21.2	odd	6		735.2.p.f.374.1		24
21.5	even	6		105.2.p.a.59.2	yes	24
21.11	odd	6		105.2.p.a.89.1	yes	24
21.17	even	6		735.2.p.f.509.2		24
21.20	even	2	inner	735.2.g.b.734.21		24
35.4	even	6		105.2.p.a.89.2	yes	24
35.9	even	6		735.2.p.f.374.2		24
35.12	even	12		525.2.t.j.101.1		24
35.18	odd	12		525.2.t.j.26.2		24
35.19	odd	6		105.2.p.a.59.1	✓	24
35.24	odd	6		735.2.p.f.509.1		24
35.32	odd	12		525.2.t.j.26.11		24
35.33	even	12		525.2.t.j.101.12		24
35.34	odd	2	inner	735.2.g.b.734.23		24
105.32	even	12		525.2.t.j.26.1		24
105.44	odd	6		735.2.p.f.374.12		24
105.47	odd	12		525.2.t.j.101.11		24
105.53	even	12		525.2.t.j.26.12		24
105.59	even	6		735.2.p.f.509.11		24
105.68	odd	12		525.2.t.j.101.2		24
105.74	odd	6		105.2.p.a.89.12	yes	24
105.89	even	6		105.2.p.a.59.11	yes	24
105.104	even	2	inner	735.2.g.b.734.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.1	✓	24	35.19	odd	6
105.2.p.a.59.2	yes	24	21.5	even	6
105.2.p.a.59.11	yes	24	105.89	even	6
105.2.p.a.59.12	yes	24	7.5	odd	6
105.2.p.a.89.1	yes	24	21.11	odd	6
105.2.p.a.89.2	yes	24	35.4	even	6
105.2.p.a.89.11	yes	24	7.4	even	3
105.2.p.a.89.12	yes	24	105.74	odd	6
525.2.t.j.26.1		24	105.32	even	12
525.2.t.j.26.2		24	35.18	odd	12
525.2.t.j.26.11		24	35.32	odd	12
525.2.t.j.26.12		24	105.53	even	12
525.2.t.j.101.1		24	35.12	even	12
525.2.t.j.101.2		24	105.68	odd	12
525.2.t.j.101.11		24	105.47	odd	12
525.2.t.j.101.12		24	35.33	even	12
735.2.g.b.734.1		24	15.14	odd	2	inner
735.2.g.b.734.2		24	7.6	odd	2	inner
735.2.g.b.734.3		24	1.1	even	1	trivial
735.2.g.b.734.4		24	105.104	even	2	inner
735.2.g.b.734.21		24	21.20	even	2	inner
735.2.g.b.734.22		24	5.4	even	2	inner
735.2.g.b.734.23		24	35.34	odd	2	inner
735.2.g.b.734.24		24	3.2	odd	2	inner
735.2.p.f.374.1		24	21.2	odd	6
735.2.p.f.374.2		24	35.9	even	6
735.2.p.f.374.11		24	7.2	even	3
735.2.p.f.374.12		24	105.44	odd	6
735.2.p.f.509.1		24	35.24	odd	6
735.2.p.f.509.2		24	21.17	even	6
735.2.p.f.509.11		24	105.59	even	6
735.2.p.f.509.12		24	7.3	odd	6

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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.50798 q^{2} +(1.47954 - 0.900534i) q^{3} +4.28995 q^{4} +(1.94085 - 1.11045i) q^{5} +(-3.71065 + 2.25852i) q^{6} -5.74313 q^{8} +(1.37808 - 2.66475i) q^{9} +(-4.86760 + 2.78499i) q^{10} +1.71869i q^{11} +(6.34714 - 3.86324i) q^{12} -0.360784 q^{13} +(1.87156 - 3.39076i) q^{15} +5.82374 q^{16} -2.54287i q^{17} +(-3.45618 + 6.68314i) q^{18} -5.69835i q^{19} +(8.32614 - 4.76378i) q^{20} -4.31044i q^{22} +2.50798 q^{23} +(-8.49719 + 5.17188i) q^{24} +(2.53379 - 4.31044i) q^{25} +0.904837 q^{26} +(-0.360784 - 5.18361i) q^{27} +3.76228i q^{29} +(-4.69384 + 8.50394i) q^{30} -2.78499i q^{31} -3.11954 q^{32} +(1.54774 + 2.54287i) q^{33} +6.37747i q^{34} +(5.91187 - 11.4316i) q^{36} -3.30566i q^{37} +14.2913i q^{38} +(-0.533794 + 0.324898i) q^{39} +(-11.1465 + 6.37747i) q^{40} -2.63477 q^{41} +10.0606i q^{43} +7.37310i q^{44} +(-0.284442 - 6.70217i) q^{45} -6.28995 q^{46} +5.82304i q^{47} +(8.61645 - 5.24448i) q^{48} +(-6.35469 + 10.8105i) q^{50} +(-2.28995 - 3.76228i) q^{51} -1.54774 q^{52} -1.45435 q^{53} +(0.904837 + 13.0004i) q^{54} +(1.90853 + 3.33572i) q^{55} +(-5.13156 - 8.43094i) q^{57} -9.43572i q^{58} +6.85856 q^{59} +(8.02891 - 14.5462i) q^{60} -1.60367i q^{61} +6.98468i q^{62} -3.82374 q^{64} +(-0.700227 + 0.400633i) q^{65} +(-3.88170 - 6.37747i) q^{66} -2.49083i q^{67} -10.9088i q^{68} +(3.71065 - 2.25852i) q^{69} -13.1790i q^{71} +(-7.91447 + 15.3040i) q^{72} +11.6437 q^{73} +8.29052i q^{74} +(-0.132851 - 8.65923i) q^{75} -24.4456i q^{76} +(1.33874 - 0.814836i) q^{78} -13.8698 q^{79} +(11.3030 - 6.46698i) q^{80} +(-5.20181 - 7.34446i) q^{81} +6.60793 q^{82} +3.50427i q^{83} +(-2.82374 - 4.93534i) q^{85} -25.2318i q^{86} +(3.38806 + 5.56645i) q^{87} -9.87067i q^{88} +12.2078 q^{89} +(0.713373 + 16.8089i) q^{90} +10.7591 q^{92} +(-2.50798 - 4.12050i) q^{93} -14.6040i q^{94} +(-6.32775 - 11.0596i) q^{95} +(-4.61549 + 2.80926i) q^{96} +8.18747 q^{97} +(4.57989 + 2.36849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 12 q^{9} - 24 q^{15} + 24 q^{16} + 24 q^{25} - 36 q^{30} + 84 q^{36} + 24 q^{39} - 72 q^{46} + 24 q^{51} - 24 q^{60} + 24 q^{64} - 96 q^{79} + 12 q^{81} + 48 q^{85} - 48 q^{99}+O(q^{100}) \) 24 * q + 24 * q^4 + 12 * q^9 - 24 * q^15 + 24 * q^16 + 24 * q^25 - 36 * q^30 + 84 * q^36 + 24 * q^39 - 72 * q^46 + 24 * q^51 - 24 * q^60 + 24 * q^64 - 96 * q^79 + 12 * q^81 + 48 * q^85 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more