LMFDB - Embedded newform 405.3.n.a.179.26

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(44,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.44"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.n (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			179.26
Character	$\chi$	$=$	405.179
Dual form			405.3.n.a.224.26

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.03789 + 0.741730i) q^{2} +(0.538636 + 0.451970i) q^{4} +(4.99552 - 0.211680i) q^{5} +(2.32404 + 2.76969i) q^{7} +(-3.57490 - 6.19192i) q^{8} +(10.3373 + 3.27394i) q^{10} +(8.70004 - 1.53405i) q^{11} +(3.15234 + 8.66099i) q^{13} +(2.68178 + 7.36812i) q^{14} +(-3.18091 - 18.0399i) q^{16} +(9.89182 - 17.1331i) q^{17} +(12.1652 + 21.0707i) q^{19} +(2.78644 + 2.14380i) q^{20} +(18.8675 + 3.32686i) q^{22} +(-4.74988 - 3.98563i) q^{23} +(24.9104 - 2.11490i) q^{25} +19.9883i q^{26} +2.54225i q^{28} +(5.21445 - 14.3266i) q^{29} +(-9.90161 - 8.30843i) q^{31} +(1.93215 - 10.9578i) q^{32} +(32.8665 - 27.5783i) q^{34} +(12.1961 + 13.3441i) q^{35} +(9.23883 + 5.33404i) q^{37} +(9.16248 + 51.9630i) q^{38} +(-19.1692 - 30.1751i) q^{40} +(23.8792 + 65.6075i) q^{41} +(-58.3296 + 10.2851i) q^{43} +(5.37950 + 3.10586i) q^{44} +(-6.72346 - 11.6454i) q^{46} +(-12.6408 + 10.6069i) q^{47} +(6.23877 - 35.3818i) q^{49} +(52.3332 + 14.1668i) q^{50} +(-2.21654 + 6.08989i) q^{52} -85.3480 q^{53} +(43.1365 - 9.50501i) q^{55} +(8.84144 - 24.2917i) q^{56} +(21.2529 - 25.3282i) q^{58} +(60.9628 + 10.7494i) q^{59} +(55.8155 - 46.8348i) q^{61} +(-14.0157 - 24.2760i) q^{62} +(-24.5711 + 42.5584i) q^{64} +(17.5809 + 42.5988i) q^{65} +(-7.87234 - 21.6291i) q^{67} +(13.0717 - 4.75773i) q^{68} +(14.9565 + 36.2399i) q^{70} +(-49.0653 - 28.3279i) q^{71} +(-101.360 + 58.5204i) q^{73} +(14.8713 + 17.7229i) q^{74} +(-2.97071 + 16.8478i) q^{76} +(24.4681 + 20.5312i) q^{77} +(-7.55144 - 2.74850i) q^{79} +(-19.7090 - 89.4451i) q^{80} +151.413i q^{82} +(-77.8706 - 28.3426i) q^{83} +(45.7880 - 87.6828i) q^{85} +(-126.498 - 22.3050i) q^{86} +(-40.6005 - 48.3858i) q^{88} +(-102.638 + 59.2583i) q^{89} +(-16.6621 + 28.8595i) q^{91} +(-0.757079 - 4.29361i) q^{92} +(-33.6278 + 12.2395i) q^{94} +(65.2316 + 102.684i) q^{95} +(-30.2613 + 5.33588i) q^{97} +(38.9576 - 67.4766i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 12 q^{4} - 3 q^{5} - 3 q^{10} - 6 q^{11} + 48 q^{14} + 12 q^{16} - 6 q^{19} - 63 q^{20} - 15 q^{25} - 96 q^{29} - 102 q^{31} + 12 q^{34} + 252 q^{35} + 117 q^{40} - 96 q^{41} + 666 q^{44} - 6 q^{46}+ \cdots + 543 q^{95}+O(q^{100}) $ 204 * q - 12 * q^4 - 3 * q^5 - 3 * q^10 - 6 * q^11 + 48 * q^14 + 12 * q^16 - 6 * q^19 - 63 * q^20 - 15 * q^25 - 96 * q^29 - 102 * q^31 + 12 * q^34 + 252 * q^35 + 117 * q^40 - 96 * q^41 + 666 * q^44 - 6 * q^46 + 60 * q^49 - 48 * q^50 - 12 * q^55 - 294 * q^56 - 510 * q^59 + 132 * q^61 - 486 * q^64 - 147 * q^65 - 141 * q^70 + 18 * q^71 + 954 * q^74 + 84 * q^76 - 48 * q^79 + 69 * q^85 + 1506 * q^86 - 792 * q^89 - 6 * q^91 + 492 * q^94 + 543 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	2.03789	+	0.741730i	1.01894	+	0.370865i	0.796861	−	0.604163i	$-0.206492\pi$
$2$	2.03789	+	0.741730i	1.01894	+	0.370865i	0.222082	+	0.975028i	$0.428715\pi$
$3$		0			0
$3$		0			0
$4$	0.538636	+	0.451970i	0.134659	+	0.112992i
$5$	4.99552	−	0.211680i	0.999103	−	0.0423360i
$5$	4.99552	−	0.211680i	0.999103	−	0.0423360i
$6$		0			0
$7$	2.32404	+	2.76969i	0.332006	+	0.395670i	0.906061	−	0.423147i	$-0.139075\pi$
$7$	2.32404	+	2.76969i	0.332006	+	0.395670i	−0.574055	+	0.818817i	$0.694630\pi$
$8$	−3.57490	−	6.19192i	−0.446863	−	0.773990i
$9$		0			0
$10$	10.3373	+	3.27394i	1.03373	+	0.327394i
$11$	8.70004	−	1.53405i	0.790913	−	0.139459i	0.236423	−	0.971650i	$-0.424025\pi$
$11$	8.70004	−	1.53405i	0.790913	−	0.139459i	0.554489	+	0.832191i	$0.312914\pi$
$12$		0			0
$13$	3.15234	+	8.66099i	0.242488	+	0.666230i	0.999911	+	0.0133060i	$0.00423556\pi$
$13$	3.15234	+	8.66099i	0.242488	+	0.666230i	−0.757424	+	0.652924i	$0.773542\pi$
$14$	2.68178	+	7.36812i	0.191555	+	0.526294i
$15$		0			0
$16$	−3.18091	−	18.0399i	−0.198807	−	1.12749i
$17$	9.89182	−	17.1331i	0.581872	−	1.00783i	−0.413386	−	0.910556i	$-0.635654\pi$
$17$	9.89182	−	17.1331i	0.581872	−	1.00783i	0.995258	−	0.0972754i	$-0.0310128\pi$
$18$		0			0
$19$	12.1652	+	21.0707i	0.640273	+	1.10899i	0.985372	+	0.170419i	$0.0545121\pi$
$19$	12.1652	+	21.0707i	0.640273	+	1.10899i	−0.345099	+	0.938566i	$0.612155\pi$
$20$	2.78644	+	2.14380i	0.139322	+	0.107190i
$21$		0			0
$22$	18.8675	+	3.32686i	0.857615	+	0.151221i
$23$	−4.74988	−	3.98563i	−0.206517	−	0.173288i	0.533663	−	0.845697i	$-0.320815\pi$
$23$	−4.74988	−	3.98563i	−0.206517	−	0.173288i	−0.740180	+	0.672409i	$0.765260\pi$
$24$		0			0
$25$	24.9104	−	2.11490i	0.996415	−	0.0845961i
$26$			19.9883i			0.768780i
$27$		0			0
$28$			2.54225i			0.0907948i
$29$	5.21445	−	14.3266i	0.179808	−	0.494020i	−0.816743	−	0.577002i	$-0.804222\pi$
$29$	5.21445	−	14.3266i	0.179808	−	0.494020i	0.996551	+	0.0829826i	$0.0264446\pi$
$30$		0			0
$31$	−9.90161	−	8.30843i	−0.319407	−	0.268014i	0.468960	−	0.883219i	$-0.344629\pi$
$31$	−9.90161	−	8.30843i	−0.319407	−	0.268014i	−0.788367	+	0.615205i	$0.789073\pi$
$32$	1.93215	−	10.9578i	0.0603798	−	0.342431i
$33$		0			0
$34$	32.8665	−	27.5783i	0.966663	−	0.811127i
$35$	12.1961	+	13.3441i	0.348460	+	0.381259i
$36$		0			0
$37$	9.23883	+	5.33404i	0.249698	+	0.144163i	0.619626	−	0.784897i	$-0.287284\pi$
$37$	9.23883	+	5.33404i	0.249698	+	0.144163i	−0.369928	+	0.929060i	$0.620618\pi$
$38$	9.16248	+	51.9630i	0.241118	+	1.36745i
$39$		0			0
$40$	−19.1692	−	30.1751i	−0.479230	−	0.754377i
$41$	23.8792	+	65.6075i	0.582419	+	1.60018i	0.784033	+	0.620719i	$0.213159\pi$
$41$	23.8792	+	65.6075i	0.582419	+	1.60018i	−0.201614	+	0.979465i	$0.564619\pi$
$42$		0			0
$43$	−58.3296	+	10.2851i	−1.35650	+	0.239188i	−0.804152	−	0.594424i	$-0.797380\pi$
$43$	−58.3296	+	10.2851i	−1.35650	+	0.239188i	−0.552351	+	0.833612i	$0.686269\pi$
$44$	5.37950	+	3.10586i	0.122261	+	0.0705877i
$45$		0			0
$46$	−6.72346	−	11.6454i	−0.146162	−	0.253160i
$47$	−12.6408	+	10.6069i	−0.268952	+	0.225678i	−0.767282	−	0.641310i	$-0.778391\pi$
$47$	−12.6408	+	10.6069i	−0.268952	+	0.225678i	0.498330	+	0.866988i	$0.333947\pi$
$48$		0			0
$49$	6.23877	−	35.3818i	0.127322	−	0.722078i
$50$	52.3332	+	14.1668i	1.04666	+	0.283337i
$51$		0			0
$52$	−2.21654	+	6.08989i	−0.0426257	+	0.117113i
$53$	−85.3480			−1.61034			−0.805169	−	0.593045i	$-0.797926\pi$
$53$	−85.3480			−1.61034			−0.805169	+	0.593045i	$0.797926\pi$
$54$		0			0
$55$	43.1365	−	9.50501i	0.784299	−	0.172818i
$56$	8.84144	−	24.2917i	0.157883	−	0.433780i
$57$		0			0
$58$	21.2529	−	25.3282i	0.366429	−	0.436693i
$59$	60.9628	+	10.7494i	1.03327	+	0.182193i	0.664469	−	0.747316i	$-0.268658\pi$
$59$	60.9628	+	10.7494i	1.03327	+	0.182193i	0.368799	+	0.929509i	$0.379769\pi$
$60$		0			0
$61$	55.8155	−	46.8348i	0.915009	−	0.767784i	−0.0580564	−	0.998313i	$-0.518490\pi$
$61$	55.8155	−	46.8348i	0.915009	−	0.767784i	0.973065	+	0.230530i	$0.0740459\pi$
$62$	−14.0157	−	24.2760i	−0.226060	−	0.391548i
$63$		0			0
$64$	−24.5711	+	42.5584i	−0.383923	+	0.664974i
$65$	17.5809	+	42.5988i	0.270476	+	0.655366i
$66$		0			0
$67$	−7.87234	−	21.6291i	−0.117498	−	0.322822i	0.866977	−	0.498348i	$-0.166060\pi$
$67$	−7.87234	−	21.6291i	−0.117498	−	0.322822i	−0.984475	+	0.175526i	$0.943837\pi$
$68$	13.0717	−	4.75773i	0.192232	−	0.0699666i
$69$		0			0
$70$	14.9565	+	36.2399i	0.213665	+	0.517713i
$71$	−49.0653	−	28.3279i	−0.691060	−	0.398984i	0.112949	−	0.993601i	$-0.463970\pi$
$71$	−49.0653	−	28.3279i	−0.691060	−	0.398984i	−0.804009	+	0.594617i	$0.797304\pi$
$72$		0			0
$73$	−101.360	+	58.5204i	−1.38850	+	0.801650i	−0.993146	−	0.116880i	$-0.962711\pi$
$73$	−101.360	+	58.5204i	−1.38850	+	0.801650i	−0.395352	+	0.918530i	$0.629377\pi$
$74$	14.8713	+	17.7229i	0.200963	+	0.239498i
$75$		0			0
$76$	−2.97071	+	16.8478i	−0.0390883	+	0.221681i
$77$	24.4681	+	20.5312i	0.317768	+	0.266639i
$78$		0			0
$79$	−7.55144	−	2.74850i	−0.0955879	−	0.0347912i	0.293784	−	0.955872i	$-0.405086\pi$
$79$	−7.55144	−	2.74850i	−0.0955879	−	0.0347912i	−0.389371	+	0.921081i	$0.627308\pi$
$80$	−19.7090	−	89.4451i	−0.246362	−	1.11806i
$81$		0			0
$82$			151.413i			1.84649i
$83$	−77.8706	−	28.3426i	−0.938200	−	0.341477i	−0.172745	−	0.984967i	$-0.555264\pi$
$83$	−77.8706	−	28.3426i	−0.938200	−	0.341477i	−0.765455	+	0.643490i	$0.777486\pi$
$84$		0			0
$85$	45.7880	−	87.6828i	0.538682	−	1.03156i
$86$	−126.498	−	22.3050i	−1.47090	−	0.259360i
$87$		0			0
$88$	−40.6005	−	48.3858i	−0.461370	−	0.549839i
$89$	−102.638	+	59.2583i	−1.15324	+	0.665823i	−0.949675	−	0.313238i	$-0.898586\pi$
$89$	−102.638	+	59.2583i	−1.15324	+	0.665823i	−0.203565	+	0.979061i	$0.565253\pi$
$90$		0			0
$91$	−16.6621	+	28.8595i	−0.183100	+	0.317138i
$92$	−0.757079	−	4.29361i	−0.00822912	−	0.0466696i
$93$		0			0
$94$	−33.6278	+	12.2395i	−0.357743	+	0.130208i
$95$	65.2316	+	102.684i	0.686649	+	1.08088i
$96$		0			0
$97$	−30.2613	+	5.33588i	−0.311972	+	0.0550090i	−0.327442	−	0.944871i	$-0.606187\pi$
$97$	−30.2613	+	5.33588i	−0.311972	+	0.0550090i	0.0154702	+	0.999880i	$0.495075\pi$
$98$	38.9576	−	67.4766i	0.397527	−	0.688537i
$99$		0			0
$100$	14.3735	+	10.1196i	0.143735	+	0.101196i
$101$	−69.5507	−	82.8873i	−0.688621	−	0.820666i	0.302567	−	0.953128i	$-0.402156\pi$
$101$	−69.5507	−	82.8873i	−0.688621	−	0.820666i	−0.991188	+	0.132462i	$0.957712\pi$
$102$		0			0
$103$	32.9784	+	5.81498i	0.320179	+	0.0564561i	0.331428	−	0.943481i	$-0.392470\pi$
$103$	32.9784	+	5.81498i	0.320179	+	0.0564561i	−0.0112492	+	0.999937i	$0.503581\pi$
$104$	42.3588	−	50.4812i	0.407296	−	0.485396i
$105$		0			0
$106$	−173.929	−	63.3051i	−1.64084	−	0.597218i
$107$	−183.486			−1.71482			−0.857411	−	0.514632i	$-0.827928\pi$
$107$	−183.486			−1.71482			−0.857411	+	0.514632i	$0.827928\pi$
$108$		0			0
$109$	−75.0243			−0.688297			−0.344148	−	0.938915i	$-0.611832\pi$
$109$	−75.0243			−0.688297			−0.344148	+	0.938915i	$0.611832\pi$
$110$	94.9573	+	12.6255i	0.863248	+	0.114777i
$111$		0			0
$112$	42.5722	−	50.7356i	0.380109	−	0.452996i
$113$	31.4551	−	178.391i	0.278364	−	1.57868i	−0.449705	−	0.893177i	$-0.648471\pi$
$113$	31.4551	−	178.391i	0.278364	−	1.57868i	0.728069	−	0.685504i	$-0.240418\pi$
$114$		0			0
$115$	−24.5718	−	18.9048i	−0.213668	−	0.164390i
$116$	9.28387	−	5.36004i	0.0800333	−	0.0462073i
$117$		0			0
$118$	116.262	+	67.1239i	0.985272	+	0.568847i
$119$	70.4425	−	12.4209i	0.591954	−	0.104377i
$120$		0			0
$121$	−40.3654	+	14.6918i	−0.333599	+	0.121420i
$122$	148.484	−	54.0439i	1.21709	−	0.442983i
$123$		0			0
$124$	−1.57821	−	8.95045i	−0.0127275	−	0.0721811i
$125$	123.993	−	15.8381i	0.991941	−	0.126704i
$126$		0			0
$127$	107.545	−	62.0910i	0.846809	−	0.488905i	−0.0127639	−	0.999919i	$-0.504063\pi$
$127$	107.545	−	62.0910i	0.846809	−	0.488905i	0.859573	+	0.511013i	$0.170730\pi$
$128$	−115.734	+	97.1127i	−0.904175	+	0.758693i
$129$		0			0
$130$	4.23112	+	99.8518i	0.0325471	+	0.768091i
$131$	−79.4604	+	94.6972i	−0.606568	+	0.722880i	−0.978699	−	0.205301i	$-0.934183\pi$
$131$	−79.4604	+	94.6972i	−0.606568	+	0.722880i	0.372131	+	0.928180i	$0.378627\pi$
$132$		0			0
$133$	−30.0869	+	82.6631i	−0.226217	+	0.621527i
$134$		−	49.9167i		−	0.372513i
$135$		0			0
$136$	−141.449			−1.04007
$137$	178.739	+	65.0558i	1.30467	+	0.474860i	0.898514	−	0.438946i	$-0.144648\pi$
$137$	178.739	+	65.0558i	1.30467	+	0.474860i	0.406153	+	0.913805i	$0.366870\pi$
$138$		0			0
$139$	183.719	+	154.158i	1.32172	+	1.10905i	0.985938	+	0.167110i	$0.0534436\pi$
$139$	183.719	+	154.158i	1.32172	+	1.10905i	0.335778	+	0.941941i	$0.391001\pi$
$140$	0.538144	+	12.6999i	0.00384389	+	0.0907133i
$141$		0			0
$142$	−78.9778	−	94.1221i	−0.556182	−	0.662832i
$143$	40.7119	+	70.5151i	0.284699	+	0.493112i
$144$		0			0
$145$	23.0162	−	72.6724i	0.158732	−	0.501189i
$146$	−249.967	+	44.0759i	−1.71210	+	0.301890i
$147$		0			0
$148$	2.56555	+	7.04878i	0.0173348	+	0.0476269i
$149$	−86.2208	−	236.890i	−0.578663	−	1.58986i	−0.790435	−	0.612545i	$-0.790146\pi$
$149$	−86.2208	−	236.890i	−0.578663	−	1.58986i	0.211772	−	0.977319i	$-0.432077\pi$
$150$		0			0
$151$	32.4942	+	184.284i	0.215194	+	1.22042i	0.880570	+	0.473916i	$0.157160\pi$
$151$	32.4942	+	184.284i	0.215194	+	1.22042i	−0.665377	+	0.746508i	$0.731729\pi$
$152$	86.9788	−	150.652i	0.572229	−	0.991129i
$153$		0			0
$154$	34.6346	+	59.9890i	0.224900	+	0.389539i
$155$	−51.2224	−	39.4090i	−0.330467	−	0.254251i
$156$		0			0
$157$	87.5981	+	15.4459i	0.557949	+	0.0983815i	0.445510	−	0.895277i	$-0.353022\pi$
$157$	87.5981	+	15.4459i	0.557949	+	0.0983815i	0.112440	+	0.993659i	$0.464134\pi$
$158$	−13.3503	−	11.2023i	−0.0844958	−	0.0709004i
$159$		0			0
$160$	7.33257	−	55.1489i	0.0458286	−	0.344680i
$161$		−	22.4185i		−	0.139245i
$162$		0			0
$163$		−	95.4121i		−	0.585350i	−0.956212	−	0.292675i	$-0.905455\pi$
$163$		−	95.4121i		−	0.585350i	0.956212	−	0.292675i	$-0.0945454\pi$
$164$	−16.7904	+	46.1313i	−0.102381	+	0.281288i
$165$		0			0
$166$	−137.669	−	115.518i	−0.829330	−	0.695891i
$167$	−16.2091	+	91.9261i	−0.0970602	+	0.550456i	0.897036	+	0.441957i	$0.145716\pi$
$167$	−16.2091	+	91.9261i	−0.0970602	+	0.550456i	−0.994097	+	0.108499i	$0.965396\pi$
$168$		0			0
$169$	64.3861	−	54.0263i	0.380983	−	0.319682i
$170$	158.348	−	144.725i	0.931457	−	0.851324i
$171$		0			0
$172$	−36.0670	−	20.8233i	−0.209692	−	0.121066i
$173$	9.71927	+	55.1207i	0.0561808	+	0.318617i	0.999927	−	0.0120526i	$-0.00383655\pi$
$173$	9.71927	+	55.1207i	0.0561808	+	0.318617i	−0.943747	+	0.330670i	$0.892725\pi$
$174$		0			0
$175$	63.7505	+	64.0789i	0.364288	+	0.366165i
$176$	−55.3482	−	152.068i	−0.314478	−	0.864022i
$177$		0			0
$178$	−253.119	+	44.6317i	−1.42202	+	0.250740i
$179$	43.6437	+	25.1977i	0.243820	+	0.140769i	0.616931	−	0.787017i	$-0.288376\pi$
$179$	43.6437	+	25.1977i	0.243820	+	0.140769i	−0.373111	+	0.927787i	$0.621709\pi$
$180$		0			0
$181$	−120.436	−	208.601i	−0.665390	−	1.15249i	−0.979179	−	0.202997i	$-0.934932\pi$
$181$	−120.436	−	208.601i	−0.665390	−	1.15249i	0.313789	−	0.949493i	$-0.398402\pi$
$182$	−55.3613	+	46.4537i	−0.304183	+	0.255240i
$183$		0			0
$184$	−7.69828	+	43.6591i	−0.0418385	+	0.237278i
$185$	47.2818	+	24.6906i	0.255577	+	0.133463i
$186$		0			0
$187$	59.7761	−	164.233i	0.319658	−	0.878254i
$188$	−11.6027			−0.0617167
$189$		0			0
$190$	56.7708	+	257.642i	0.298794	+	1.35601i
$191$	−112.920	+	310.246i	−0.591206	+	1.62432i	0.177065	+	0.984199i	$0.443340\pi$
$191$	−112.920	+	310.246i	−0.591206	+	1.62432i	−0.768271	+	0.640125i	$0.778883\pi$
$192$		0			0
$193$	−55.0909	+	65.6548i	−0.285445	+	0.340180i	−0.889645	−	0.456652i	$-0.849048\pi$
$193$	−55.0909	+	65.6548i	−0.285445	+	0.340180i	0.604200	+	0.796833i	$0.293493\pi$
$194$	−65.6268	−	11.5718i	−0.338282	−	0.0596483i
$195$		0			0
$196$	19.3519	−	16.2382i	0.0987344	−	0.0828480i
$197$	81.4582	+	141.090i	0.413493	+	0.716191i	0.995269	−	0.0971578i	$-0.0309752\pi$
$197$	81.4582	+	141.090i	0.413493	+	0.716191i	−0.581776	+	0.813349i	$0.697642\pi$
$198$		0			0
$199$	−90.2959	+	156.397i	−0.453748	+	0.785915i	−0.998615	−	0.0526075i	$-0.983247\pi$
$199$	−90.2959	+	156.397i	−0.453748	+	0.785915i	0.544867	+	0.838522i	$0.316580\pi$
$200$	−102.148	−	146.682i	−0.510738	−	0.733412i
$201$		0			0
$202$	−80.2564	−	220.503i	−0.397309	−	1.09160i
$203$	51.7988	−	18.8532i	0.255166	−	0.0928729i
$204$		0			0
$205$	133.177	+	322.689i	0.649643	+	1.57409i
$206$	62.8930	+	36.3113i	0.305306	+	0.176269i
$207$		0			0
$208$	146.216	−	84.4176i	0.702960	−	0.405854i
$209$	138.161	+	164.654i	0.661058	+	0.787818i
$210$		0			0
$211$	27.1933	−	154.221i	0.128878	−	0.730906i	−0.850050	−	0.526702i	$-0.823428\pi$
$211$	27.1933	−	154.221i	0.128878	−	0.730906i	0.978928	−	0.204204i	$-0.0654605\pi$
$212$	−45.9715	−	38.5747i	−0.216847	−	0.181956i
$213$		0			0
$214$	−373.923	−	136.097i	−1.74731	−	0.635967i
$215$	−289.209	+	63.7265i	−1.34516	+	0.296402i
$216$		0			0
$217$		−	46.7335i		−	0.215362i
$218$	−152.891	−	55.6478i	−0.701335	−	0.255265i
$219$		0			0
$220$	27.5308	+	14.3766i	0.125140	+	0.0653483i
$221$	179.572	+	31.6634i	0.812544	+	0.143273i
$222$		0			0
$223$	7.70503	+	9.18250i	0.0345517	+	0.0411771i	0.783044	−	0.621967i	$-0.213666\pi$
$223$	7.70503	+	9.18250i	0.0345517	+	0.0411771i	−0.748492	+	0.663144i	$0.769222\pi$
$224$	34.8401	−	20.1149i	0.155536	−	0.0897988i
$225$		0			0
$226$	196.420	−	340.209i	0.869114	−	1.50535i
$227$	33.5298	+	190.157i	0.147709	+	0.837697i	0.965152	+	0.261689i	$0.0842793\pi$
$227$	33.5298	+	190.157i	0.147709	+	0.837697i	−0.817444	+	0.576008i	$0.804610\pi$
$228$		0			0
$229$	413.128	−	150.366i	1.80405	−	0.656622i	0.806163	−	0.591694i	$-0.201540\pi$
$229$	413.128	−	150.366i	1.80405	−	0.656622i	0.997890	−	0.0649279i	$-0.0206817\pi$
$230$	−36.0523	−	56.7515i	−0.156749	−	0.246746i
$231$		0			0
$232$	−107.350	+	18.9287i	−0.462716	+	0.0815893i
$233$	79.8540	−	138.311i	0.342721	−	0.593611i	−0.642216	−	0.766524i	$-0.721985\pi$
$233$	79.8540	−	138.311i	0.342721	−	0.593611i	0.984937	+	0.172913i	$0.0553181\pi$
$234$		0			0
$235$	−60.9018	+	55.6625i	−0.259157	+	0.236862i
$236$	27.9784	+	33.3434i	0.118553	+	0.141285i
$237$		0			0
$238$	152.767	+	26.9369i	0.641877	+	0.113180i
$239$	44.1733	−	52.6436i	0.184825	−	0.220266i	−0.665674	−	0.746243i	$-0.731856\pi$
$239$	44.1733	−	52.6436i	0.184825	−	0.220266i	0.850499	+	0.525977i	$0.176300\pi$
$240$		0			0
$241$	−197.027	−	71.7120i	−0.817539	−	0.297560i	−0.100805	−	0.994906i	$-0.532142\pi$
$241$	−197.027	−	71.7120i	−0.817539	−	0.297560i	−0.716734	+	0.697346i	$0.754364\pi$
$242$	−93.1575			−0.384948
$243$		0			0
$244$	51.2322			0.209968
$245$	23.6763	−	178.071i	0.0966378	−	0.726821i
$246$		0			0
$247$	−144.144	+	171.785i	−0.583581	+	0.695484i
$248$	−16.0478	+	91.0118i	−0.0647090	+	0.366983i
$249$		0			0
$250$	264.430	+	59.6928i	1.05772	+	0.238771i
$251$	−89.5394	+	51.6956i	−0.356731	+	0.205959i	−0.667646	−	0.744479i	$-0.732698\pi$
$251$	−89.5394	+	51.6956i	−0.356731	+	0.205959i	0.310915	+	0.950438i	$0.399365\pi$
$252$		0			0
$253$	−47.4383	−	27.3885i	−0.187503	−	0.108255i
$254$	265.219	−	46.7652i	1.04417	−	0.184115i
$255$		0			0
$256$	−123.171	+	44.8305i	−0.481136	+	0.175119i
$257$	−101.124	+	36.8062i	−0.393480	+	0.143215i	−0.531180	−	0.847259i	$-0.678251\pi$
$257$	−101.124	+	36.8062i	−0.393480	+	0.143215i	0.137700	+	0.990474i	$0.456029\pi$
$258$		0			0
$259$	6.69782	+	37.9852i	0.0258603	+	0.146661i
$260$	−9.78364	+	30.8913i	−0.0376294	+	0.118813i
$261$		0			0
$262$	−232.171	+	134.044i	−0.886149	+	0.511618i
$263$	29.1199	−	24.4345i	0.110722	−	0.0929069i	−0.585746	−	0.810495i	$-0.699198\pi$
$263$	29.1199	−	24.4345i	0.110722	−	0.0929069i	0.696468	+	0.717588i	$0.254754\pi$
$264$		0			0
$265$	−426.357	+	18.0664i	−1.60889	+	0.0681753i
$266$	−122.627	+	146.142i	−0.461005	+	0.549404i
$267$		0			0
$268$	5.53535	−	15.2083i	0.0206543	−	0.0567472i
$269$			101.363i			0.376814i	0.982091	+	0.188407i	$0.0603323\pi$
$269$			101.363i			0.376814i	−0.982091	+	0.188407i	$0.939668\pi$
$270$		0			0
$271$	198.243			0.731524			0.365762	−	0.930708i	$-0.380808\pi$
$271$	198.243			0.731524			0.365762	+	0.930708i	$0.380808\pi$
$272$	−340.544	−	123.948i	−1.25200	−	0.455691i
$273$		0			0
$274$	315.996	+	265.152i	1.15327	+	0.967710i
$275$	213.477	−	56.6135i	0.776280	−	0.205867i
$276$		0			0
$277$	242.799	+	289.356i	0.876529	+	1.04461i	0.998642	+	0.0520907i	$0.0165885\pi$
$277$	242.799	+	289.356i	0.876529	+	1.04461i	−0.122113	+	0.992516i	$0.538967\pi$
$278$	260.054	+	450.426i	0.935445	+	1.62024i
$279$		0			0
$280$	39.0255	−	123.221i	0.139377	−	0.440075i
$281$	56.2501	−	9.91841i	0.200178	−	0.0352968i	−0.0726599	−	0.997357i	$-0.523149\pi$
$281$	56.2501	−	9.91841i	0.200178	−	0.0352968i	0.272838	+	0.962060i	$0.412038\pi$
$282$		0			0
$283$	173.966	+	477.966i	0.614719	+	1.68893i	0.719553	+	0.694437i	$0.244347\pi$
$283$	173.966	+	477.966i	0.614719	+	1.68893i	−0.104834	+	0.994490i	$0.533431\pi$
$284$	−13.6250	−	37.4344i	−0.0479754	−	0.131811i
$285$		0			0
$286$	30.6631	+	173.899i	0.107213	+	0.608038i
$287$	−126.216	+	218.613i	−0.439778	+	0.761717i
$288$		0			0
$289$	−51.1962	−	88.6744i	−0.177149	−	0.306832i
$290$	100.808	−	131.026i	0.347613	−	0.451815i
$291$		0			0
$292$	−81.0458	−	14.2906i	−0.277554	−	0.0489403i
$293$	−161.315	−	135.359i	−0.550562	−	0.461976i	0.324569	−	0.945862i	$-0.394781\pi$
$293$	−161.315	−	135.359i	−0.550562	−	0.461976i	−0.875131	+	0.483886i	$0.839225\pi$
$294$		0			0
$295$	306.816	+	40.7942i	1.04005	+	0.138285i
$296$		−	76.2747i		−	0.257685i
$297$		0			0
$298$		−	546.707i		−	1.83459i
$299$	19.5462	−	53.7027i	0.0653719	−	0.179608i
$300$		0			0
$301$	−164.047	−	137.652i	−0.545007	−	0.457315i
$302$	−70.4693	+	399.651i	−0.233342	+	1.32335i
$303$		0			0
$304$	341.416	−	286.482i	1.12308	−	0.942376i
$305$	268.914	−	245.779i	0.881684	−	0.805833i
$306$		0			0
$307$	−46.5102	−	26.8527i	−0.151499	−	0.0874681i	0.422334	−	0.906440i	$-0.361211\pi$
$307$	−46.5102	−	26.8527i	−0.151499	−	0.0874681i	−0.573833	+	0.818972i	$0.694544\pi$
$308$	3.89995	+	22.1177i	0.0126622	+	0.0718107i
$309$		0			0
$310$	−75.1545	−	118.304i	−0.242434	−	0.381626i
$311$	108.295	+	297.537i	0.348215	+	0.956712i	0.982932	+	0.183968i	$0.0588942\pi$
$311$	108.295	+	297.537i	0.348215	+	0.956712i	−0.634718	+	0.772744i	$0.718884\pi$
$312$		0			0
$313$	100.283	−	17.6826i	0.320393	−	0.0564939i	−0.0111389	−	0.999938i	$-0.503546\pi$
$313$	100.283	−	17.6826i	0.320393	−	0.0564939i	0.331532	+	0.943444i	$0.392435\pi$
$314$	167.058	+	96.4511i	0.532032	+	0.307169i
$315$		0			0
$316$	−2.82524	−	4.89347i	−0.00894065	−	0.0154857i
$317$	389.774	−	327.059i	1.22957	−	1.03173i	0.231304	−	0.972881i	$-0.425701\pi$
$317$	389.774	−	327.059i	1.22957	−	1.03173i	0.998267	−	0.0588511i	$-0.0187437\pi$
$318$		0			0
$319$	23.3882	−	132.641i	0.0733172	−	0.415802i
$320$	−113.736	+	217.802i	−0.355427	+	0.680632i
$321$		0			0
$322$	16.6284	−	45.6863i	0.0516411	−	0.141883i
$323$	481.343			1.49023
$324$		0			0
$325$	96.8432	+	209.082i	0.297979	+	0.643328i
$326$	70.7700	−	194.439i	0.217086	−	0.596438i
$327$		0			0
$328$	320.871	−	382.399i	0.978264	−	1.16585i
$329$	−58.7554	−	10.3602i	−0.178588	−	0.0314898i
$330$		0			0
$331$	177.270	−	148.747i	0.535559	−	0.449387i	−0.334457	−	0.942411i	$-0.608553\pi$
$331$	177.270	−	148.747i	0.535559	−	0.449387i	0.870016	+	0.493024i	$0.164109\pi$
$332$	−29.1340	−	50.4615i	−0.0877529	−	0.151992i
$333$		0			0
$334$	−101.217	+	175.312i	−0.303044	+	0.524887i
$335$	−43.9048	−	106.382i	−0.131059	−	0.317558i
$336$		0			0
$337$	−57.8789	−	159.021i	−0.171748	−	0.471873i	0.823718	−	0.567000i	$-0.191896\pi$
$337$	−57.8789	−	159.021i	−0.171748	−	0.471873i	−0.995465	+	0.0951279i	$0.969674\pi$
$338$	171.284	−	62.3424i	0.506759	−	0.184445i
$339$		0			0
$340$	64.2930	−	26.5343i	0.189097	−	0.0780422i
$341$	−98.8899	−	57.0941i	−0.290000	−	0.167431i
$342$		0			0
$343$	265.923	−	153.531i	0.775287	−	0.447612i
$344$	272.207	+	324.404i	0.791300	+	0.943034i
$345$		0			0
$346$	−21.0779	+	119.539i	−0.0609188	+	0.345488i
$347$	6.55502	+	5.50032i	0.0188905	+	0.0158511i	0.652184	−	0.758061i	$-0.273853\pi$
$347$	6.55502	+	5.50032i	0.0188905	+	0.0158511i	−0.633293	+	0.773912i	$0.718297\pi$
$348$		0			0
$349$	−397.135	−	144.545i	−1.13792	−	0.414170i	−0.296761	−	0.954952i	$-0.595906\pi$
$349$	−397.135	−	144.545i	−1.13792	−	0.414170i	−0.841163	+	0.540782i	$0.818129\pi$
$350$	82.3869	+	177.871i	0.235391	+	0.508203i
$351$		0			0
$352$		−	98.2973i		−	0.279254i
$353$	349.306	+	127.137i	0.989535	+	0.360161i	0.785540	−	0.618811i	$-0.212385\pi$
$353$	349.306	+	127.137i	0.989535	+	0.360161i	0.203995	+	0.978972i	$0.434607\pi$
$354$		0			0
$355$	−251.103	−	131.126i	−0.707332	−	0.369369i
$356$	−82.0677	−	14.4707i	−0.230527	−	0.0406482i
$357$		0			0
$358$	70.2510	+	83.7219i	0.196232	+	0.233860i
$359$	−615.787	+	355.525i	−1.71528	+	0.990320i	−0.788239	+	0.615369i	$0.789007\pi$
$359$	−615.787	+	355.525i	−1.71528	+	0.990320i	−0.927045	+	0.374950i	$0.877660\pi$
$360$		0			0
$361$	−115.483	+	200.023i	−0.319899	+	0.554081i
$362$	−90.7088	−	514.435i	−0.250577	−	1.42109i
$363$		0			0
$364$	−22.0184	+	8.01405i	−0.0604902	+	0.0220166i
$365$	−493.960	+	313.796i	−1.35331	+	0.859714i
$366$		0			0
$367$	597.597	−	105.372i	1.62833	−	0.287118i	0.716469	−	0.697619i	$-0.245757\pi$
$367$	597.597	−	105.372i	1.62833	−	0.287118i	0.911860	+	0.410501i	$0.134646\pi$
$368$	−56.7912	+	98.3652i	−0.154324	+	0.267297i
$369$		0			0
$370$	78.0412	+	85.3870i	0.210922	+	0.230776i
$371$	−198.352	−	236.387i	−0.534643	−	0.637162i
$372$		0			0
$373$	15.9903	+	2.81952i	0.0428694	+	0.00755902i	0.195042	−	0.980795i	$-0.437516\pi$
$373$	15.9903	+	2.81952i	0.0428694	+	0.00755902i	−0.152172	+	0.988354i	$0.548627\pi$
$374$	243.634	−	290.351i	0.651427	−	0.776340i
$375$		0			0
$376$	110.866	+	40.3520i	0.294857	+	0.107319i
$377$	140.520			0.372732
$378$		0			0
$379$	−202.525			−0.534367			−0.267184	−	0.963646i	$-0.586093\pi$
$379$	−202.525			−0.534367			−0.267184	+	0.963646i	$0.586093\pi$
$380$	−11.2739	+	84.7921i	−0.0296682	+	0.223137i
$381$		0			0
$382$	−460.237	+	548.489i	−1.20481	+	1.43584i
$383$	113.044	−	641.106i	0.295155	−	1.67391i	−0.371417	−	0.928466i	$-0.621128\pi$
$383$	113.044	−	641.106i	0.295155	−	1.67391i	0.666572	−	0.745441i	$-0.267761\pi$
$384$		0			0
$385$	126.577	+	97.3845i	0.328771	+	0.252947i
$386$	−160.967	+	92.9344i	−0.417013	+	0.240763i
$387$		0			0
$388$	−18.7115	−	10.8031i	−0.0482254	−	0.0278430i
$389$	127.502	−	22.4820i	0.327768	−	0.0577943i	−0.00734304	−	0.999973i	$-0.502337\pi$
$389$	127.502	−	22.4820i	0.327768	−	0.0577943i	0.335111	+	0.942179i	$0.391226\pi$
$390$		0			0
$391$	−115.271	+	41.9553i	−0.294811	+	0.107303i
$392$	−241.384	+	87.8567i	−0.615776	+	0.224124i
$393$		0			0
$394$	61.3520	+	347.945i	0.155716	+	0.883108i
$395$	−38.3052	−	12.1317i	−0.0969751	−	0.0307132i
$396$		0			0
$397$	−131.369	+	75.8460i	−0.330904	+	0.191048i	−0.656243	−	0.754550i	$-0.727855\pi$
$397$	−131.369	+	75.8460i	−0.330904	+	0.191048i	0.325338	+	0.945598i	$0.394522\pi$
$398$	−300.017	+	251.744i	−0.753812	+	0.632523i
$399$		0			0
$400$	−117.390	−	442.653i	−0.293476	−	1.10663i
$401$	164.397	−	195.920i	0.409966	−	0.488579i	−0.521065	−	0.853517i	$-0.674465\pi$
$401$	164.397	−	195.920i	0.409966	−	0.488579i	0.931032	+	0.364938i	$0.118910\pi$
$402$		0			0
$403$	40.7460	−	111.949i	0.101107	−	0.277788i
$404$		−	76.0809i		−	0.188319i
$405$		0			0
$406$	119.544			0.294443
$407$	88.5609	+	32.2335i	0.217594	+	0.0791978i
$408$		0			0
$409$	−475.249	−	398.781i	−1.16198	−	0.975015i	−0.162047	−	0.986783i	$-0.551809\pi$
$409$	−475.249	−	398.781i	−1.16198	−	0.975015i	−0.999931	+	0.0117684i	$0.996254\pi$
$410$	32.0510	+	756.384i	0.0781732	+	1.84484i
$411$		0			0
$412$	15.1352	+	18.0374i	0.0367358	+	0.0437801i
$413$	111.908	+	193.830i	0.270963	+	0.469322i
$414$		0			0
$415$	−395.003	−	125.102i	−0.951816	−	0.301451i
$416$	100.996	−	17.8083i	0.242779	−	0.0428085i
$417$		0			0
$418$	159.428	+	438.024i	0.381406	+	1.04791i
$419$	−52.8741	−	145.270i	−0.126191	−	0.346707i	0.860469	−	0.509504i	$-0.170171\pi$
$419$	−52.8741	−	145.270i	−0.126191	−	0.346707i	−0.986660	+	0.162796i	$0.947949\pi$
$420$		0			0
$421$	52.5666	+	298.120i	0.124861	+	0.708124i	0.981390	+	0.192025i	$0.0615053\pi$
$421$	52.5666	+	298.120i	0.124861	+	0.708124i	−0.856529	+	0.516099i	$0.827384\pi$
$422$	169.807	−	294.115i	0.402387	−	0.696955i
$423$		0			0
$424$	305.111	+	528.467i	0.719601	+	1.24639i
$425$	210.174	−	447.713i	0.494527	−	1.05344i
$426$		0			0
$427$	259.436	+	45.7455i	0.607578	+	0.107132i
$428$	−98.8322	−	82.9301i	−0.230916	−	0.193762i
$429$		0			0
$430$	−636.643	−	84.6478i	−1.48057	−	0.196855i
$431$		−	194.130i		−	0.450418i	−0.974311	−	0.225209i	$-0.927694\pi$
$431$		−	194.130i		−	0.450418i	0.974311	−	0.225209i	$-0.0723064\pi$
$432$		0			0
$433$		−	697.839i		−	1.61164i	−0.592162	−	0.805819i	$-0.701725\pi$
$433$		−	697.839i		−	1.61164i	0.592162	−	0.805819i	$-0.298275\pi$
$434$	34.6637	−	95.2376i	0.0798702	−	0.219441i
$435$		0			0
$436$	−40.4108	−	33.9087i	−0.0926854	−	0.0777723i
$437$	26.1968	−	148.569i	0.0599469	−	0.339976i
$438$		0			0
$439$	307.468	−	257.996i	0.700382	−	0.587691i	−0.221500	−	0.975160i	$-0.571095\pi$
$439$	307.468	−	257.996i	0.700382	−	0.587691i	0.921882	+	0.387470i	$0.126651\pi$
$440$	−213.063	−	233.118i	−0.484234	−	0.529813i
$441$		0			0
$442$	342.462	+	197.720i	0.774801	+	0.447331i
$443$	−0.222903	−	1.26415i	−0.000503168	−	0.00285361i	0.984555	−	0.175075i	$-0.0560167\pi$
$443$	−0.222903	−	1.26415i	−0.000503168	−	0.00285361i	−0.985058	+	0.172221i	$0.944906\pi$
$444$		0			0
$445$	−500.188	+	317.752i	−1.12402	+	0.714050i
$446$	8.89104	+	24.4279i	0.0199351	+	0.0547711i
$447$		0			0
$448$	−174.978	+	30.8533i	−0.390575	+	0.0688689i
$449$	−581.893	−	335.956i	−1.29597	−	0.748231i	−0.316268	−	0.948670i	$-0.602430\pi$
$449$	−581.893	−	335.956i	−1.29597	−	0.748231i	−0.979706	+	0.200439i	$0.935763\pi$
$450$		0			0
$451$	308.395	+	534.156i	0.683803	+	1.18438i
$452$	97.5702	−	81.8711i	0.215863	−	0.181131i
$453$		0			0
$454$	−72.7153	+	412.389i	−0.160166	+	0.908345i
$455$	−77.1266	+	147.695i	−0.169509	+	0.324605i
$456$		0			0
$457$	−96.5574	+	265.289i	−0.211285	+	0.580502i	−0.999386	−	0.0350451i	$-0.988843\pi$
$457$	−96.5574	+	265.289i	−0.211285	+	0.580502i	0.788100	+	0.615547i	$0.211065\pi$
$458$	953.439			2.08174
$459$		0			0
$460$	−4.69087	−	21.2885i	−0.0101975	−	0.0462794i
$461$	97.1395	−	266.889i	0.210715	−	0.578934i	−0.788640	−	0.614855i	$-0.789214\pi$
$461$	97.1395	−	266.889i	0.210715	−	0.578934i	0.999355	+	0.0359213i	$0.0114366\pi$
$462$		0			0
$463$	−462.859	+	551.614i	−0.999695	+	1.19139i	−0.0182133	+	0.999834i	$0.505798\pi$
$463$	−462.859	+	551.614i	−0.999695	+	1.19139i	−0.981482	+	0.191556i	$0.938647\pi$
$464$	−275.036	−	48.4963i	−0.592750	−	0.104518i
$465$		0			0
$466$	265.323	−	222.632i	0.569363	−	0.477752i
$467$	−192.068	−	332.672i	−0.411281	−	0.712359i	0.583750	−	0.811934i	$-0.301585\pi$
$467$	−192.068	−	332.672i	−0.411281	−	0.712359i	−0.995030	+	0.0995750i	$0.968252\pi$
$468$		0			0
$469$	41.6101	−	72.0708i	0.0887209	−	0.153669i
$470$	−165.398	+	68.2611i	−0.351910	+	0.145236i
$471$		0			0
$472$	−151.377	−	415.905i	−0.320714	−	0.881154i
$473$	−491.692	+	178.961i	−1.03952	+	0.378354i
$474$		0			0
$475$	347.602	+	499.151i	0.731793	+	1.05085i
$476$	43.5568	+	25.1475i	0.0915058	+	0.0528309i
$477$		0			0
$478$	129.067	−	74.5171i	0.270015	−	0.155894i
$479$	−200.228	−	238.622i	−0.418012	−	0.498167i	0.515412	−	0.856943i	$-0.327639\pi$
$479$	−200.228	−	238.622i	−0.418012	−	0.498167i	−0.933424	+	0.358775i	$0.883194\pi$
$480$		0			0
$481$	−17.0741	+	96.8321i	−0.0354971	+	0.201314i
$482$	−348.328	−	292.282i	−0.722671	−	0.606393i
$483$		0			0
$484$	−28.3826	−	10.3304i	−0.0586416	−	0.0213438i
$485$	−150.041	+	33.0612i	−0.309363	+	0.0681673i
$486$		0			0
$487$		−	144.089i		−	0.295871i	−0.988997	−	0.147936i	$-0.952737\pi$
$487$		−	144.089i		−	0.295871i	0.988997	−	0.147936i	$-0.0472629\pi$
$488$	−489.532	−	178.175i	−1.00314	−	0.365113i
$489$		0			0
$490$	180.330	−	345.327i	0.368021	−	0.704749i
$491$	−135.820	−	23.9487i	−0.276618	−	0.0487753i	0.0336179	−	0.999435i	$-0.489297\pi$
$491$	−135.820	−	23.9487i	−0.276618	−	0.0487753i	−0.310236	+	0.950659i	$0.600408\pi$
$492$		0			0
$493$	−193.879	−	231.056i	−0.393263	−	0.468673i
$494$	−421.167	+	243.161i	−0.852566	+	0.492229i
$495$		0			0
$496$	−118.387	+	205.052i	−0.238683	+	0.413411i
$497$	−35.5706	−	201.731i	−0.0715706	−	0.405897i
$498$		0			0
$499$	−449.216	+	163.501i	−0.900232	+	0.327658i	−0.750346	−	0.661045i	$-0.770113\pi$
$499$	−449.216	+	163.501i	−0.900232	+	0.327658i	−0.149886	+	0.988703i	$0.547891\pi$
$500$	73.9452	+	47.5099i	0.147890	+	0.0950198i
$501$		0			0
$502$	−220.815	+	38.9357i	−0.439871	+	0.0775611i
$503$	−293.589	+	508.511i	−0.583676	+	1.01096i	0.411363	+	0.911472i	$0.365053\pi$
$503$	−293.589	+	508.511i	−0.583676	+	1.01096i	−0.995039	+	0.0994853i	$0.968280\pi$
$504$		0			0
$505$	−364.987	−	399.342i	−0.722747	−	0.790777i
$506$	−76.3590	−	91.0011i	−0.150907	−	0.179844i
$507$		0			0
$508$	85.9908	+	15.1625i	0.169273	+	0.0298474i
$509$	76.4269	−	91.0820i	0.150151	−	0.178943i	−0.685726	−	0.727860i	$-0.740515\pi$
$509$	76.4269	−	91.0820i	0.150151	−	0.178943i	0.835877	+	0.548917i	$0.184960\pi$
$510$		0			0
$511$	−397.649	−	144.733i	−0.778179	−	0.283234i
$512$	320.062			0.625121
$513$		0			0
$514$	−233.380			−0.454047
$515$	165.975	+	22.0680i	0.322282	+	0.0428504i
$516$		0			0
$517$	−93.7036	+	111.672i	−0.181245	+	0.215999i
$518$	−14.5254	+	82.3775i	−0.0280413	+	0.159030i
$519$		0			0
$520$	200.918	−	261.146i	0.386381	−	0.502205i
$521$	617.263	−	356.377i	1.18477	−	0.684025i	0.227654	−	0.973742i	$-0.426895\pi$
$521$	617.263	−	356.377i	1.18477	−	0.684025i	0.957112	+	0.289717i	$0.0935613\pi$
$522$		0			0
$523$	−632.955	−	365.437i	−1.21024	−	0.698731i	−0.247427	−	0.968906i	$-0.579585\pi$
$523$	−632.955	−	365.437i	−1.21024	−	0.698731i	−0.962811	+	0.270175i	$0.912918\pi$
$524$	−85.6005	+	15.0937i	−0.163360	+	0.0288047i
$525$		0			0
$526$	77.4668	−	28.1956i	0.147275	−	0.0536038i
$527$	−240.294	+	87.4600i	−0.455967	+	0.165958i
$528$		0			0
$529$	−85.1837	−	483.101i	−0.161028	−	0.913234i
$530$	−882.267	−	279.424i	−1.66466	−	0.527216i
$531$		0			0
$532$	−53.5671	+	30.9270i	−0.100690	+	0.0581334i
$533$	−492.951	+	413.635i	−0.924861	+	0.776050i
$534$		0			0
$535$	−916.607	+	38.8403i	−1.71328	+	0.0725987i
$536$	−105.783	+	126.067i	−0.197355	+	0.235199i
$537$		0			0
$538$	−75.1838	+	206.566i	−0.139747	+	0.383951i
$539$		−	317.394i		−	0.588857i
$540$		0			0
$541$	−163.171			−0.301610			−0.150805	−	0.988564i	$-0.548187\pi$
$541$	−163.171			−0.301610			−0.150805	+	0.988564i	$0.548187\pi$
$542$	403.996	+	147.043i	0.745381	+	0.271296i
$543$		0			0
$544$	−168.629	−	141.496i	−0.309979	−	0.260104i
$545$	−374.785	+	15.8811i	−0.687679	+	0.0291397i
$546$		0			0
$547$	429.435	+	511.781i	0.785074	+	0.935615i	0.999151	−	0.0412022i	$-0.0131188\pi$
$547$	429.435	+	511.781i	0.785074	+	0.935615i	−0.214077	+	0.976817i	$0.568674\pi$
$548$	66.8723	+	115.826i	0.122030	+	0.211362i
$549$		0			0
$550$	477.033	+	42.9703i	0.867334	+	0.0781278i
$551$	365.306	−	64.4133i	0.662987	−	0.116903i
$552$		0			0
$553$	−9.93740	−	27.3028i	−0.0179700	−	0.0493721i
$554$	280.172	+	769.765i	0.505725	+	1.38947i
$555$		0			0
$556$	29.2827	+	166.070i	0.0526667	+	0.298688i
$557$	−429.574	+	744.043i	−0.771227	+	1.33581i	0.165663	+	0.986182i	$0.447024\pi$
$557$	−429.574	+	744.043i	−0.771227	+	1.33581i	−0.936891	+	0.349623i	$0.886310\pi$
$558$		0			0
$559$	−272.954	−	472.770i	−0.488289	−	0.845742i
$560$	201.931	−	262.462i	0.360590	−	0.468682i
$561$		0			0
$562$	121.988	+	21.5098i	0.217061	+	0.0382736i
$563$	−51.6792	−	43.3640i	−0.0917926	−	0.0770232i	0.595737	−	0.803180i	$-0.296860\pi$
$563$	−51.6792	−	43.3640i	−0.0917926	−	0.0770232i	−0.687529	+	0.726157i	$0.741305\pi$
$564$		0			0
$565$	119.373	−	897.813i	0.211279	−	1.58905i
$566$			1103.08i			1.94890i
$567$		0			0
$568$			405.078i			0.713165i
$569$	−16.2220	+	44.5695i	−0.0285096	+	0.0783295i	−0.953131	−	0.302558i	$-0.902159\pi$
$569$	−16.2220	+	44.5695i	−0.0285096	+	0.0783295i	0.924621	+	0.380888i	$0.124382\pi$
$570$		0			0
$571$	595.231	+	499.458i	1.04244	+	0.874707i	0.992278	−	0.124034i	$-0.0395832\pi$
$571$	595.231	+	499.458i	1.04244	+	0.874707i	0.0501575	+	0.998741i	$0.484028\pi$
$572$	−9.94176	+	56.3825i	−0.0173807	+	0.0985708i
$573$		0			0
$574$	−419.366	+	351.890i	−0.730602	+	0.613048i
$575$	−126.751	−	89.2379i	−0.220436	−	0.155196i
$576$		0			0
$577$	−675.220	−	389.839i	−1.17023	−	0.675630i	−0.216492	−	0.976284i	$-0.569462\pi$
$577$	−675.220	−	389.839i	−1.17023	−	0.675630i	−0.953733	+	0.300654i	$0.902795\pi$
$578$	−38.5595	−	218.682i	−0.0667120	−	0.378342i
$579$		0			0
$580$	45.2431	−	28.7414i	0.0780053	−	0.0495541i
$581$	−102.475	−	281.547i	−0.176376	−	0.484590i
$582$		0			0
$583$	−742.531	+	130.928i	−1.27364	+	0.224577i
$584$	724.707	+	418.410i	1.24094	+	0.716455i
$585$		0			0
$586$	−228.341	−	395.498i	−0.389660	−	0.674912i
$587$	−80.5262	+	67.5695i	−0.137183	+	0.115110i	−0.708797	−	0.705412i	$-0.750762\pi$
$587$	−80.5262	+	67.5695i	−0.137183	+	0.115110i	0.571614	+	0.820522i	$0.306317\pi$
$588$		0			0
$589$	54.6098	−	309.708i	0.0927161	−	0.525819i
$590$	594.998	+	310.708i	1.00847	+	0.526625i
$591$		0			0
$592$	66.8374	−	183.634i	0.112901	−	0.310193i
$593$	56.8607			0.0958864			0.0479432	−	0.998850i	$-0.484733\pi$
$593$	56.8607			0.0958864			0.0479432	+	0.998850i	$0.484733\pi$
$594$		0			0
$595$	349.267	−	76.9601i	0.587004	−	0.129345i
$596$	60.6253	−	166.567i	0.101720	−	0.279474i
$597$		0			0
$598$	79.6658	−	94.9420i	0.133220	−	0.158766i
$599$	−356.770	−	62.9081i	−0.595609	−	0.105022i	−0.132286	−	0.991212i	$-0.542232\pi$
$599$	−356.770	−	62.9081i	−0.595609	−	0.105022i	−0.463323	+	0.886190i	$0.653343\pi$
$600$		0			0
$601$	−189.072	+	158.650i	−0.314596	+	0.263977i	−0.786389	−	0.617732i	$-0.788052\pi$
$601$	−189.072	+	158.650i	−0.314596	+	0.263977i	0.471792	+	0.881710i	$0.343607\pi$
$602$	−232.209	−	402.197i	−0.385729	−	0.668102i
$603$		0			0
$604$	−65.7882	+	113.948i	−0.108921	+	0.188656i
$605$	−198.536	+	81.9378i	−0.328159	+	0.135434i
$606$		0			0
$607$	−237.324	−	652.041i	−0.390978	−	1.07420i	−0.966556	−	0.256456i	$-0.917445\pi$
$607$	−237.324	−	652.041i	−0.390978	−	1.07420i	0.575578	−	0.817747i	$-0.304777\pi$
$608$	254.394	−	92.5917i	0.418411	−	0.152289i
$609$		0			0
$610$	730.317	−	301.408i	1.19724	−	0.494112i
$611$	−131.714	−	76.0450i	−0.215571	−	0.124460i
$612$		0			0
$613$	820.457	−	473.691i	1.33843	−	0.772742i	0.351855	−	0.936055i	$-0.385551\pi$
$613$	820.457	−	473.691i	1.33843	−	0.772742i	0.986574	+	0.163312i	$0.0522178\pi$
$614$	−74.8651	−	89.2207i	−0.121930	−	0.145311i
$615$		0			0
$616$	39.6562	−	224.902i	0.0643770	−	0.365100i
$617$	752.232	+	631.198i	1.21918	+	1.02301i	0.998867	+	0.0475809i	$0.0151512\pi$
$617$	752.232	+	631.198i	1.21918	+	1.02301i	0.220310	+	0.975430i	$0.429293\pi$
$618$		0			0
$619$	25.3213	+	9.21619i	0.0409067	+	0.0148888i	0.362392	−	0.932026i	$-0.381960\pi$
$619$	25.3213	+	9.21619i	0.0409067	+	0.0148888i	−0.321486	+	0.946914i	$0.604182\pi$
$620$	−9.77859	−	44.3781i	−0.0157719	−	0.0715775i
$621$		0			0
$622$			686.673i			1.10398i
$623$	−402.663	−	146.557i	−0.646329	−	0.235245i
$624$		0			0
$625$	616.054	−	105.366i	0.985687	−	0.168586i
$626$	217.481	+	38.3478i	0.347414	+	0.0612584i
$627$		0			0
$628$	40.2024	+	47.9114i	0.0640166	+	0.0762920i
$629$	182.778	−	105.527i	0.290584	−	0.167769i
$630$		0			0
$631$	−127.491	+	220.821i	−0.202046	+	0.349955i	−0.949188	−	0.314711i	$-0.898093\pi$
$631$	−127.491	+	220.821i	−0.202046	+	0.349955i	0.747141	+	0.664665i	$0.231426\pi$
$632$	9.97721	+	56.5835i	0.0157867	+	0.0895309i
$633$		0			0
$634$	1036.90	−	377.402i	1.63550	−	0.595272i
$635$	524.098	−	332.942i	0.825352	−	0.524318i
$636$		0			0
$637$	326.108	−	57.5017i	0.511944	−	0.0902695i
$638$	146.046	−	252.959i	0.228912	−	0.396488i
$639$		0			0
$640$	−557.597	+	509.627i	−0.871245	+	0.796292i
$641$	425.457	+	507.040i	0.663739	+	0.791014i	0.987917	−	0.154983i	$-0.0495321\pi$
$641$	425.457	+	507.040i	0.663739	+	0.791014i	−0.324178	+	0.945996i	$0.605088\pi$
$642$		0			0
$643$	110.331	+	19.4543i	0.171587	+	0.0302555i	0.258782	−	0.965936i	$-0.416679\pi$
$643$	110.331	+	19.4543i	0.171587	+	0.0302555i	−0.0871943	+	0.996191i	$0.527790\pi$
$644$	10.1325	−	12.0754i	0.0157336	−	0.0187506i
$645$		0			0
$646$	980.922	+	357.027i	1.51846	+	0.552673i
$647$	10.7396			0.0165990			0.00829952	−	0.999966i	$-0.497358\pi$
$647$	10.7396			0.0165990			0.00829952	+	0.999966i	$0.497358\pi$
$648$		0			0
$649$	546.869			0.842633
$650$	42.2732	+	497.916i	0.0650358	+	0.766024i
$651$		0			0
$652$	43.1234	−	51.3924i	0.0661401	−	0.0788227i
$653$	135.331	−	767.498i	0.207244	−	1.17534i	−0.686624	−	0.727013i	$-0.740908\pi$
$653$	135.331	−	767.498i	0.207244	−	1.17534i	0.893869	−	0.448329i	$-0.147981\pi$
$654$		0			0
$655$	−376.900	+	489.882i	−0.575420	+	0.747911i
$656$	1107.59	−	639.469i	1.68840	−	0.974801i
$657$		0			0
$658$	−112.052	−	64.6934i	−0.170292	−	0.0983182i
$659$	−735.143	+	129.626i	−1.11554	+	0.196700i	−0.700883	−	0.713276i	$-0.747211\pi$
$659$	−735.143	+	129.626i	−1.11554	+	0.196700i	−0.414660	+	0.909976i	$0.636099\pi$
$660$		0			0
$661$	509.948	−	185.606i	0.771480	−	0.280796i	0.0738649	−	0.997268i	$-0.476467\pi$
$661$	509.948	−	185.606i	0.771480	−	0.280796i	0.697615	+	0.716472i	$0.254244\pi$
$662$	471.586	−	171.643i	0.712365	−	0.259280i
$663$		0			0
$664$	102.885	+	583.490i	0.154947	+	0.878750i
$665$	−132.801	+	419.314i	−0.199702	+	0.630547i
$666$		0			0
$667$	−81.8684	+	47.2667i	−0.122741	+	0.0708647i
$668$	−50.2786	+	42.1888i	−0.0752674	+	0.0631568i
$669$		0			0
$670$	−10.5664	−	249.360i	−0.0157707	−	0.372179i
$671$	413.750	−	493.089i	0.616618	−	0.734856i
$672$		0			0
$673$	−256.931	+	705.911i	−0.381769	+	1.04890i	0.588842	+	0.808248i	$0.299584\pi$
$673$	−256.931	+	705.911i	−0.381769	+	1.04890i	−0.970611	+	0.240654i	$0.922638\pi$
$674$		−	366.997i		−	0.544506i
$675$		0			0
$676$	59.0990			0.0874245
$677$	89.4060	+	32.5411i	0.132062	+	0.0480667i	0.407206	−	0.913336i	$-0.366503\pi$
$677$	89.4060	+	32.5411i	0.132062	+	0.0480667i	−0.275144	+	0.961403i	$0.588725\pi$
$678$		0			0
$679$	−85.1072	−	71.4135i	−0.125342	−	0.105174i
$680$	−706.612	+	29.9420i	−1.03914	+	0.0440323i
$681$		0			0
$682$	−159.178	−	189.701i	−0.233399	−	0.278154i
$683$	−207.041	−	358.606i	−0.303135	−	0.525045i	0.673709	−	0.738996i	$-0.264700\pi$
$683$	−207.041	−	358.606i	−0.303135	−	0.525045i	−0.976844	+	0.213951i	$0.931367\pi$
$684$		0			0
$685$	906.666	+	287.152i	1.32360	+	0.419200i
$686$	655.800	−	115.635i	0.955977	−	0.168565i
$687$		0			0
$688$	371.083	+	1019.54i	0.539365	+	1.48189i
$689$	−269.046	−	739.197i	−0.390487	−	1.07286i
$690$		0			0
$691$	−36.2485	−	205.575i	−0.0524580	−	0.297504i	0.947280	−	0.320408i	$-0.103820\pi$
$691$	−36.2485	−	205.575i	−0.0524580	−	0.297504i	−0.999738	+	0.0229038i	$0.992709\pi$
$692$	−19.6777	+	34.0829i	−0.0284360	+	0.0492527i
$693$		0			0
$694$	9.27863	+	16.0711i	0.0133698	+	0.0231572i
$695$	950.401	+	731.210i	1.36748	+	1.05210i
$696$		0			0
$697$	1360.27	+	239.853i	1.95161	+	0.344121i
$698$	−702.103	−	589.134i	−1.00588	−	0.844032i
$699$		0			0
$700$	5.37661	+	63.3285i	0.00768088	+	0.0904693i
$701$		−	128.633i		−	0.183499i	−0.995782	−	0.0917494i	$-0.970754\pi$
$701$		−	128.633i		−	0.183499i	0.995782	−	0.0917494i	$-0.0292459\pi$
$702$		0			0
$703$			259.558i			0.369215i
$704$	−148.483	+	407.953i	−0.210913	+	0.579478i
$705$		0			0
$706$	617.544	+	518.181i	0.874708	+	0.733967i
$707$	67.9331	−	385.268i	0.0960864	−	0.544933i
$708$		0			0
$709$	−30.2527	+	25.3851i	−0.0426696	+	0.0358040i	−0.663873	−	0.747845i	$-0.731088\pi$
$709$	−30.2527	+	25.3851i	−0.0426696	+	0.0358040i	0.621203	+	0.783649i	$0.286644\pi$
$710$	−414.459	−	453.471i	−0.583745	−	0.638691i
$711$		0			0
$712$	733.845	+	423.685i	1.03068	+	0.595064i
$713$	13.9172	+	78.9282i	0.0195192	+	0.110699i
$714$		0			0
$715$	218.304	+	343.641i	0.305320	+	0.480617i
$716$	12.1195	+	33.2981i	0.0169267	+	0.0465057i
$717$		0			0
$718$	−1518.61	+	267.771i	−2.11505	+	0.372941i
$719$	1187.82	+	685.786i	1.65204	+	0.953806i	0.976232	+	0.216728i	$0.0695386\pi$
$719$	1187.82	+	685.786i	1.65204	+	0.953806i	0.675808	+	0.737077i	$0.263795\pi$
$720$		0			0
$721$	60.5376	+	104.854i	0.0839633	+	0.145429i
$722$	−383.705	+	321.967i	−0.531448	+	0.445937i
$723$		0			0
$724$	29.4101	−	166.793i	0.0406217	−	0.230377i
$725$	99.5946	−	367.908i	0.137372	−	0.507460i
$726$		0			0
$727$	290.996	−	799.505i	0.400270	−	1.09973i	−0.561882	−	0.827217i	$-0.689922\pi$
$727$	290.996	−	799.505i	0.400270	−	1.09973i	0.962152	−	0.272515i	$-0.0878553\pi$
$728$	238.261			0.327282
$729$		0			0
$730$	−1239.38	+	273.095i	−1.69779	+	0.374103i
$731$	−400.770	+	1101.11i	−0.548249	+	1.50630i
$732$		0			0
$733$	440.220	−	524.633i	0.600573	−	0.715735i	−0.377028	−	0.926202i	$-0.623054\pi$
$733$	440.220	−	524.633i	0.600573	−	0.715735i	0.977601	+	0.210467i	$0.0674985\pi$
$734$	1295.99	+	228.518i	1.76566	+	0.311333i
$735$		0			0
$736$	−52.8512	+	44.3474i	−0.0718087	+	0.0602546i
$737$	−101.670	−	176.097i	−0.137951	−	0.238938i
$738$		0			0
$739$	439.434	−	761.121i	0.594633	−	1.02993i	−0.398966	−	0.916966i	$-0.630631\pi$
$739$	439.434	−	761.121i	0.594633	−	1.02993i	0.993599	−	0.112968i	$-0.0360359\pi$
$740$	14.3083	+	34.6692i	0.0193356	+	0.0468503i
$741$		0			0
$742$	−228.884	−	628.854i	−0.308469	−	0.847512i
$743$	403.184	−	146.747i	0.542643	−	0.197506i	−0.0561318	−	0.998423i	$-0.517877\pi$
$743$	403.184	−	146.747i	0.542643	−	0.197506i	0.598775	+	0.800918i	$0.295654\pi$
$744$		0			0
$745$	−480.862	−	1165.14i	−0.645453	−	1.56394i
$746$	30.4950	+	17.6063i	0.0408780	+	0.0236009i
$747$		0			0
$748$	106.426	−	61.4452i	0.142281	−	0.0821459i
$749$	−426.430	−	508.199i	−0.569332	−	0.678503i
$750$		0			0
$751$	−75.6930	+	429.277i	−0.100790	+	0.571607i	0.892029	+	0.451978i	$0.149281\pi$
$751$	−75.6930	+	429.277i	−0.100790	+	0.571607i	−0.992819	+	0.119629i	$0.961830\pi$
$752$	231.555	+	194.298i	0.307919	+	0.258375i
$753$		0			0
$754$	286.364	+	104.228i	0.379793	+	0.138233i
$755$	201.335	+	913.715i	0.266668	+	1.21022i
$756$		0			0
$757$			387.406i			0.511765i	0.966708	+	0.255883i	$0.0823660\pi$
$757$			387.406i			0.511765i	−0.966708	+	0.255883i	$0.917634\pi$
$758$	−412.723	−	150.219i	−0.544490	−	0.198178i
$759$		0			0
$760$	402.614	−	770.994i	0.529755	−	1.01447i
$761$	819.711	+	144.537i	1.07715	+	0.189931i	0.683955	−	0.729524i	$-0.260259\pi$
$761$	819.711	+	144.537i	1.07715	+	0.189931i	0.393195	+	0.919455i	$0.371370\pi$
$762$		0			0
$763$	−174.360	−	207.794i	−0.228519	−	0.272338i
$764$	−201.045	+	116.073i	−0.263148	+	0.151928i
$765$		0			0
$766$	705.899	−	1222.65i	0.921539	−	1.59615i
$767$	99.0753	+	561.884i	0.129172	+	0.732573i
$768$		0			0
$769$	−527.601	+	192.031i	−0.686087	+	0.249715i	−0.661459	−	0.749981i	$-0.730062\pi$
$769$	−527.601	+	192.031i	−0.686087	+	0.249715i	−0.0246284	+	0.999697i	$0.507840\pi$
$770$	185.716	+	292.344i	0.241190	+	0.379668i
$771$		0			0
$772$	−59.3480	+	10.4646i	−0.0768756	+	0.0135552i
$773$	−189.771	+	328.693i	−0.245499	+	0.425217i	−0.962272	−	0.272090i	$-0.912285\pi$
$773$	−189.771	+	328.693i	−0.245499	+	0.425217i	0.716773	+	0.697307i	$0.245618\pi$
$774$		0			0
$775$	−264.224	−	186.025i	−0.340935	−	0.240033i
$776$	141.220	+	168.300i	0.181985	+	0.216881i
$777$		0			0
$778$	276.509	+	48.7560i	0.355410	+	0.0626684i
$779$	−1091.90	+	1301.28i	−1.40167	+	1.67045i
$780$		0			0
$781$	−470.326	−	171.185i	−0.602210	−	0.219187i
$782$	−266.029			−0.340191
$783$		0			0
$784$	−658.128			−0.839449
$785$	440.867	+	58.6175i	0.561614	+	0.0746720i
$786$		0			0
$787$	−646.804	+	770.831i	−0.821860	+	0.979455i	−0.999990	−	0.00455231i	$-0.998551\pi$
$787$	−646.804	+	770.831i	−0.821860	+	0.979455i	0.178130	+	0.984007i	$0.442995\pi$
$788$	−19.8919	+	112.813i	−0.0252436	+	0.143163i
$789$		0			0
$790$	−69.0631	−	53.1351i	−0.0874217	−	0.0672596i
$791$	567.190	−	327.468i	0.717055	−	0.413992i
$792$		0			0
$793$	581.585	+	335.778i	0.733399	+	0.423428i
$794$	−323.972	+	57.1251i	−0.408026	+	0.0719459i
$795$		0			0
$796$	−119.323	+	43.4302i	−0.149904	+	0.0545605i
$797$	11.4218	−	4.15721i	0.0143310	−	0.00521607i	−0.334845	−	0.942273i	$-0.608684\pi$
$797$	11.4218	−	4.15721i	0.0143310	−	0.00521607i	0.349176	+	0.937057i	$0.386462\pi$
$798$		0			0
$799$	56.6886	+	321.497i	0.0709494	+	0.402374i
$800$	24.9561	−	277.049i	0.0311951	−	0.346311i
$801$		0			0
$802$	480.341	−	277.325i	0.598929	−	0.345792i
$803$	−792.066	+	664.622i	−0.986383	+	0.827674i
$804$		0			0
$805$	−4.74554	−	111.992i	−0.00589508	−	0.139120i
$806$	166.071	−	197.916i	0.206044	−	0.245553i
$807$		0			0
$808$	−264.594	+	726.966i	−0.327468	+	0.899711i
$809$		−	1078.95i		−	1.33368i	−0.745199	−	0.666842i	$-0.767646\pi$
$809$		−	1078.95i		−	1.33368i	0.745199	−	0.666842i	$-0.232354\pi$
$810$		0			0
$811$	1043.57			1.28677			0.643386	−	0.765542i	$-0.277529\pi$
$811$	1043.57			1.28677			0.643386	+	0.765542i	$0.277529\pi$
$812$	36.4218	+	13.2564i	0.0448544	+	0.0163257i
$813$		0			0
$814$	156.568	+	131.376i	0.192344	+	0.161396i
$815$	−20.1968	−	476.633i	−0.0247814	−	0.584825i
$816$		0			0
$817$	−926.304	−	1103.93i	−1.13379	−	1.35120i
$818$	−672.715	−	1165.18i	−0.822390	−	1.42442i
$819$		0			0
$820$	−74.1117	+	234.004i	−0.0903802	+	0.285370i
$821$	−381.096	+	67.1976i	−0.464186	+	0.0818484i	−0.400850	−	0.916144i	$-0.631285\pi$
$821$	−381.096	+	67.1976i	−0.464186	+	0.0818484i	−0.0633359	+	0.997992i	$0.520174\pi$
$822$		0			0
$823$	338.120	+	928.977i	0.410838	+	1.12877i	0.956746	+	0.290924i	$0.0939627\pi$
$823$	338.120	+	928.977i	0.410838	+	1.12877i	−0.545908	+	0.837845i	$0.683815\pi$
$824$	−81.8887	−	224.987i	−0.0993795	−	0.273043i
$825$		0			0
$826$	84.2859	+	478.009i	0.102041	+	0.578703i
$827$	−24.4367	+	42.3257i	−0.0295486	+	0.0511798i	−0.880422	−	0.474192i	$-0.842740\pi$
$827$	−24.4367	+	42.3257i	−0.0295486	+	0.0511798i	0.850873	+	0.525372i	$0.176074\pi$
$828$		0			0
$829$	−546.065	−	945.813i	−0.658704	−	1.14091i	−0.980952	−	0.194253i	$-0.937772\pi$
$829$	−546.065	−	945.813i	−0.658704	−	1.14091i	0.322248	−	0.946655i	$-0.395562\pi$
$830$	−712.180	−	547.930i	−0.858048	−	0.660156i
$831$		0			0
$832$	−446.054	−	78.6513i	−0.536122	−	0.0945328i
$833$	−544.489	−	456.880i	−0.653648	−	0.548476i
$834$		0			0
$835$	−61.5137	+	462.650i	−0.0736691	+	0.554072i
$836$			151.133i			0.180781i
$837$		0			0
$838$		−	335.263i		−	0.400075i
$839$	−34.5885	+	95.0311i	−0.0412259	+	0.113267i	−0.958597	−	0.284765i	$-0.908084\pi$
$839$	−34.5885	+	95.0311i	−0.0412259	+	0.113267i	0.917372	+	0.398032i	$0.130307\pi$
$840$		0			0
$841$	466.183	+	391.174i	0.554320	+	0.465130i
$842$	−114.000	+	646.525i	−0.135392	+	0.767844i
$843$		0			0
$844$	84.3506	−	70.7785i	0.0999414	−	0.0838608i
$845$	310.205	−	283.519i	0.367107	−	0.335525i
$846$		0			0
$847$	−134.503	−	77.6553i	−0.158799	−	0.0916827i
$848$	271.485	+	1539.67i	0.320147	+	1.81564i
$849$		0			0
$850$	760.393	−	756.496i	0.894580	−	0.889995i
$851$	−22.6239	−	62.1586i	−0.0265850	−	0.0730418i
$852$		0			0
$853$	490.805	−	86.5422i	0.575387	−	0.101456i	0.121620	−	0.992577i	$-0.461191\pi$
$853$	490.805	−	86.5422i	0.575387	−	0.101456i	0.453767	+	0.891120i	$0.350080\pi$
$854$	494.769	+	285.655i	0.579355	+	0.334491i
$855$		0			0
$856$	655.945	+	1136.13i	0.766291	+	1.32725i
$857$	599.546	−	503.079i	0.699587	−	0.587024i	−0.222069	−	0.975031i	$-0.571281\pi$
$857$	599.546	−	503.079i	0.699587	−	0.587024i	0.921656	+	0.388007i	$0.126837\pi$
$858$		0			0
$859$	−105.854	+	600.327i	−0.123229	+	0.698867i	0.859115	+	0.511783i	$0.171015\pi$
$859$	−105.854	+	600.327i	−0.123229	+	0.698867i	−0.982344	+	0.187084i	$0.940096\pi$
$860$	−184.581	−	96.3884i	−0.214629	−	0.112080i
$861$		0			0
$862$	143.992	−	395.615i	0.167044	−	0.458950i
$863$	−72.8410			−0.0844044			−0.0422022	−	0.999109i	$-0.513437\pi$
$863$	−72.8410			−0.0844044			−0.0422022	+	0.999109i	$0.513437\pi$
$864$		0			0
$865$	60.2207	+	273.299i	0.0696194	+	0.315953i
$866$	517.608	−	1422.12i	0.597700	−	1.64217i
$867$		0			0
$868$	21.1221	−	25.1724i	0.0243343	−	0.0290004i
$869$	−69.9142	−	12.3278i	−0.0804536	−	0.0141861i
$870$		0			0
$871$	162.513	−	136.364i	0.186582	−	0.156561i
$872$	268.205	+	464.544i	0.307574	+	0.532734i
$873$		0			0
$874$	163.584	−	283.336i	0.187167	−	0.324184i
$875$	332.031	+	306.612i	0.379464	+	0.350414i
$876$		0			0
$877$	−544.678	−	1496.49i	−0.621070	−	1.70638i	−0.704353	−	0.709849i	$-0.748763\pi$
$877$	−544.678	−	1496.49i	−0.621070	−	1.70638i	0.0832836	−	0.996526i	$-0.473459\pi$
$878$	817.948	−	297.709i	0.931603	−	0.339076i
$879$		0			0
$880$	−308.682	−	747.941i	−0.350775	−	0.849933i
$881$	−597.963	−	345.234i	−0.678732	−	0.391866i	0.120645	−	0.992696i	$-0.461504\pi$
$881$	−597.963	−	345.234i	−0.678732	−	0.391866i	−0.799377	+	0.600830i	$0.794837\pi$
$882$		0			0
$883$	−858.918	+	495.896i	−0.972727	+	0.561604i	−0.900066	−	0.435753i	$-0.856482\pi$
$883$	−858.918	+	495.896i	−0.972727	+	0.561604i	−0.0726604	+	0.997357i	$0.523149\pi$
$884$	82.4132	+	98.2163i	0.0932276	+	0.111104i
$885$		0			0
$886$	0.483404	−	2.74152i	0.000545603	−	0.00309427i
$887$	861.700	+	723.052i	0.971477	+	0.815166i	0.982782	−	0.184770i	$-0.0591542\pi$
$887$	861.700	+	723.052i	0.971477	+	0.815166i	−0.0113051	+	0.999936i	$0.503599\pi$
$888$		0			0
$889$	421.912	+	153.563i	0.474591	+	0.172737i
$890$	−1255.01	+	276.538i	−1.41013	+	0.310717i
$891$		0			0
$892$			8.42847i			0.00944895i
$893$	−377.271	−	137.315i	−0.422476	−	0.153769i
$894$		0			0
$895$	223.357	+	116.637i	0.249561	+	0.130321i
$896$	−537.944	−	94.8540i	−0.600384	−	0.105864i
$897$		0			0
$898$	−936.642	−	1116.25i	−1.04303	−	1.24304i
$899$	−170.663	+	98.5322i	−0.189836	+	0.109602i
$900$		0			0
$901$	−844.247	+	1462.28i	−0.937011	+	1.62295i
$902$	232.275	+	1317.30i	0.257511	+	1.46042i
$903$		0			0
$904$	−1217.03	+	442.963i	−1.34627	+	0.490003i
$905$	−645.795	−	1016.57i	−0.713585	−	1.12329i
$906$		0			0
$907$	−784.120	+	138.261i	−0.864520	+	0.152438i	−0.588287	−	0.808652i	$-0.700197\pi$
$907$	−784.120	+	138.261i	−0.864520	+	0.152438i	−0.276233	+	0.961091i	$0.589086\pi$
$908$	−67.8849	+	117.580i	−0.0747631	+	0.129493i
$909$		0			0
$910$	−266.725	+	243.779i	−0.293105	+	0.267889i
$911$	254.988	+	303.883i	0.279899	+	0.333571i	0.887617	−	0.460582i	$-0.152359\pi$
$911$	254.988	+	303.883i	0.279899	+	0.333571i	−0.607718	+	0.794153i	$0.707915\pi$
$912$		0			0
$913$	−720.956	−	127.124i	−0.789656	−	0.139238i
$914$	−393.546	+	469.010i	−0.430575	+	0.513140i
$915$		0			0
$916$	290.487	+	105.729i	0.317125	+	0.115424i
$917$	−446.951			−0.487406
$918$		0			0
$919$	1270.39			1.38236			0.691179	−	0.722684i	$-0.257092\pi$
$919$	1270.39			1.38236			0.691179	+	0.722684i	$0.257092\pi$
$920$	−29.2151	+	219.729i	−0.0317556	+	0.238836i
$921$		0			0
$922$	395.918	−	471.837i	0.429413	−	0.511754i
$923$	90.6767	−	514.253i	0.0982412	−	0.557154i
$924$		0			0
$925$	241.424	+	113.334i	0.260999	+	0.122523i
$926$	−1352.40	+	780.809i	−1.46048	+	0.843207i
$927$		0			0
$928$	−146.913	−	84.8200i	−0.158311	−	0.0914008i
$929$	−482.079	+	85.0036i	−0.518923	+	0.0915001i	−0.426974	−	0.904264i	$-0.640421\pi$
$929$	−482.079	+	85.0036i	−0.518923	+	0.0915001i	−0.0919483	+	0.995764i	$0.529309\pi$
$930$		0			0
$931$	821.416	−	298.971i	0.882294	−	0.321129i
$932$	105.525	−	38.4079i	0.113224	−	0.0412102i
$933$		0			0
$934$	−144.660	−	820.409i	−0.154882	−	0.878382i
$935$	263.848	−	833.085i	0.282190	−	0.891000i
$936$		0			0
$937$	−417.683	+	241.149i	−0.445766	+	0.257363i	−0.706040	−	0.708172i	$-0.749520\pi$
$937$	−417.683	+	241.149i	−0.445766	+	0.257363i	0.260274	+	0.965535i	$0.416187\pi$
$938$	138.254	−	116.009i	0.147392	−	0.123677i
$939$		0			0
$940$	−57.9617	+	2.45607i	−0.0616614	+	0.00261284i
$941$	167.759	−	199.928i	0.178278	−	0.212463i	−0.669504	−	0.742809i	$-0.733493\pi$
$941$	167.759	−	199.928i	0.178278	−	0.212463i	0.847782	+	0.530345i	$0.177938\pi$
$942$		0			0
$943$	148.064	−	406.802i	0.157014	−	0.431391i
$944$		−	1133.95i		−	1.20122i
$945$		0			0
$946$	−1134.75			−1.19953
$947$	161.848	+	58.9078i	0.170906	+	0.0622046i	0.426056	−	0.904697i	$-0.359903\pi$
$947$	161.848	+	58.9078i	0.170906	+	0.0622046i	−0.255150	+	0.966901i	$0.582125\pi$
$948$		0			0
$949$	−826.367	−	693.404i	−0.870776	−	0.730668i
$950$	338.137	+	1275.04i	0.355934	+	1.34215i
$951$		0			0
$952$	−328.734	−	391.770i	−0.345309	−	0.411524i
$953$	825.741	+	1430.23i	0.866465	+	1.50076i	0.865585	+	0.500761i	$0.166947\pi$
$953$	825.741	+	1430.23i	0.866465	+	1.50076i	0.000879492		1.00000i	$0.499720\pi$
$954$		0			0
$955$	−498.422	+	1573.74i	−0.521908	+	1.64790i
$956$	47.5867	−	8.39081i	0.0497768	−	0.00877700i
$957$		0			0
$958$	−231.048	−	634.800i	−0.241178	−	0.662630i
$959$	235.214	+	646.245i	0.245270	+	0.673874i
$960$		0			0
$961$	−137.864	−	781.867i	−0.143459	−	0.813597i
$962$	−106.618	+	184.668i	−0.110830	+	0.191963i
$963$		0			0
$964$	−73.7143	−	127.677i	−0.0764671	−	0.132445i
$965$	−261.310	+	339.641i	−0.270787	+	0.351960i
$966$		0			0
$967$	1336.23	+	235.614i	1.38183	+	0.243654i	0.814657	−	0.579943i	$-0.196925\pi$
$967$	1336.23	+	235.614i	1.38183	+	0.243654i	0.567175	+	0.823597i	$0.308036\pi$
$968$	235.273	+	197.418i	0.243051	+	0.203944i
$969$		0			0
$970$	−330.289	−	43.9151i	−0.340504	−	0.0452733i
$971$		−	563.556i		−	0.580387i	−0.956968	−	0.290194i	$-0.906280\pi$
$971$		−	563.556i		−	0.580387i	0.956968	−	0.290194i	$-0.0937197\pi$
$972$		0			0
$973$			867.114i			0.891175i
$974$	106.875	−	293.638i	0.109728	−	0.301476i
$975$		0			0
$976$	−1022.44	−	857.927i	−1.04758	−	0.879024i
$977$	−28.6746	+	162.622i	−0.0293497	+	0.166450i	−0.995960	−	0.0898018i	$-0.971377\pi$
$977$	−28.6746	+	162.622i	−0.0293497	+	0.166450i	0.966610	+	0.256252i	$0.0824877\pi$
$978$		0			0
$979$	−802.052	+	673.002i	−0.819257	+	0.687438i
$980$	93.2356	−	85.2146i	0.0951384	−	0.0869537i
$981$		0			0
$982$	−259.021	−	149.546i	−0.263769	−	0.152287i
$983$	72.9652	+	413.806i	0.0742271	+	0.420963i	0.999165	+	0.0408456i	$0.0130052\pi$
$983$	72.9652	+	413.806i	0.0742271	+	0.420963i	−0.924938	+	0.380117i	$0.875884\pi$
$984$		0			0
$985$	436.792	+	687.573i	0.443443	+	0.698044i
$986$	−223.722	−	614.671i	−0.226898	−	0.623398i
$987$		0			0
$988$	−155.283	+	27.3806i	−0.157169	+	0.0277131i
$989$	318.051	+	183.627i	0.321589	+	0.185669i
$990$		0			0
$991$	−402.904	−	697.851i	−0.406564	−	0.704189i	0.587939	−	0.808906i	$-0.299940\pi$
$991$	−402.904	−	697.851i	−0.406564	−	0.704189i	−0.994502	+	0.104717i	$0.966606\pi$
$992$	−110.174	+	92.4466i	−0.111062	+	0.0931921i
$993$		0			0
$994$	77.1409	−	437.488i	0.0776066	−	0.440129i
$995$	−417.969	+	800.398i	−0.420069	+	0.804420i
$996$		0			0
$997$	−667.318	+	1833.44i	−0.669326	+	1.83896i	−0.140804	+	0.990037i	$0.544969\pi$
$997$	−667.318	+	1833.44i	−0.669326	+	1.83896i	−0.528522	+	0.848920i	$0.677253\pi$
$998$	−1036.72			−1.03880
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.n.a.179.26		204
3.2	odd	2		135.3.n.a.104.9	yes	204
5.4	even	2	inner	405.3.n.a.179.9		204
15.14	odd	2		135.3.n.a.104.26	yes	204
27.7	even	9		135.3.n.a.74.26	yes	204
27.20	odd	18	inner	405.3.n.a.224.9		204
135.34	even	18		135.3.n.a.74.9	✓	204
135.74	odd	18	inner	405.3.n.a.224.26		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.n.a.74.9	✓	204	135.34	even	18
135.3.n.a.74.26	yes	204	27.7	even	9
135.3.n.a.104.9	yes	204	3.2	odd	2
135.3.n.a.104.26	yes	204	15.14	odd	2
405.3.n.a.179.9		204	5.4	even	2	inner
405.3.n.a.179.26		204	1.1	even	1	trivial
405.3.n.a.224.9		204	27.20	odd	18	inner
405.3.n.a.224.26		204	135.74	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.n (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.03789 + 0.741730i) q^{2} +(0.538636 + 0.451970i) q^{4} +(4.99552 - 0.211680i) q^{5} +(2.32404 + 2.76969i) q^{7} +(-3.57490 - 6.19192i) q^{8} +(10.3373 + 3.27394i) q^{10} +(8.70004 - 1.53405i) q^{11} +(3.15234 + 8.66099i) q^{13} +(2.68178 + 7.36812i) q^{14} +(-3.18091 - 18.0399i) q^{16} +(9.89182 - 17.1331i) q^{17} +(12.1652 + 21.0707i) q^{19} +(2.78644 + 2.14380i) q^{20} +(18.8675 + 3.32686i) q^{22} +(-4.74988 - 3.98563i) q^{23} +(24.9104 - 2.11490i) q^{25} +19.9883i q^{26} +2.54225i q^{28} +(5.21445 - 14.3266i) q^{29} +(-9.90161 - 8.30843i) q^{31} +(1.93215 - 10.9578i) q^{32} +(32.8665 - 27.5783i) q^{34} +(12.1961 + 13.3441i) q^{35} +(9.23883 + 5.33404i) q^{37} +(9.16248 + 51.9630i) q^{38} +(-19.1692 - 30.1751i) q^{40} +(23.8792 + 65.6075i) q^{41} +(-58.3296 + 10.2851i) q^{43} +(5.37950 + 3.10586i) q^{44} +(-6.72346 - 11.6454i) q^{46} +(-12.6408 + 10.6069i) q^{47} +(6.23877 - 35.3818i) q^{49} +(52.3332 + 14.1668i) q^{50} +(-2.21654 + 6.08989i) q^{52} -85.3480 q^{53} +(43.1365 - 9.50501i) q^{55} +(8.84144 - 24.2917i) q^{56} +(21.2529 - 25.3282i) q^{58} +(60.9628 + 10.7494i) q^{59} +(55.8155 - 46.8348i) q^{61} +(-14.0157 - 24.2760i) q^{62} +(-24.5711 + 42.5584i) q^{64} +(17.5809 + 42.5988i) q^{65} +(-7.87234 - 21.6291i) q^{67} +(13.0717 - 4.75773i) q^{68} +(14.9565 + 36.2399i) q^{70} +(-49.0653 - 28.3279i) q^{71} +(-101.360 + 58.5204i) q^{73} +(14.8713 + 17.7229i) q^{74} +(-2.97071 + 16.8478i) q^{76} +(24.4681 + 20.5312i) q^{77} +(-7.55144 - 2.74850i) q^{79} +(-19.7090 - 89.4451i) q^{80} +151.413i q^{82} +(-77.8706 - 28.3426i) q^{83} +(45.7880 - 87.6828i) q^{85} +(-126.498 - 22.3050i) q^{86} +(-40.6005 - 48.3858i) q^{88} +(-102.638 + 59.2583i) q^{89} +(-16.6621 + 28.8595i) q^{91} +(-0.757079 - 4.29361i) q^{92} +(-33.6278 + 12.2395i) q^{94} +(65.2316 + 102.684i) q^{95} +(-30.2613 + 5.33588i) q^{97} +(38.9576 - 67.4766i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 12 q^{4} - 3 q^{5} - 3 q^{10} - 6 q^{11} + 48 q^{14} + 12 q^{16} - 6 q^{19} - 63 q^{20} - 15 q^{25} - 96 q^{29} - 102 q^{31} + 12 q^{34} + 252 q^{35} + 117 q^{40} - 96 q^{41} + 666 q^{44} - 6 q^{46}+ \cdots + 543 q^{95}+O(q^{100}) \) 204 * q - 12 * q^4 - 3 * q^5 - 3 * q^10 - 6 * q^11 + 48 * q^14 + 12 * q^16 - 6 * q^19 - 63 * q^20 - 15 * q^25 - 96 * q^29 - 102 * q^31 + 12 * q^34 + 252 * q^35 + 117 * q^40 - 96 * q^41 + 666 * q^44 - 6 * q^46 + 60 * q^49 - 48 * q^50 - 12 * q^55 - 294 * q^56 - 510 * q^59 + 132 * q^61 - 486 * q^64 - 147 * q^65 - 141 * q^70 + 18 * q^71 + 954 * q^74 + 84 * q^76 - 48 * q^79 + 69 * q^85 + 1506 * q^86 - 792 * q^89 - 6 * q^91 + 492 * q^94 + 543 * q^95

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