LMFDB - Embedded newform 405.3.n.a.179.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(44,405)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			179.9
Character	$\chi$	$=$	405.179
Dual form			405.3.n.a.224.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.03789 - 0.741730i) q^{2} +(0.538636 + 0.451970i) q^{4} +(4.62185 + 1.90748i) q^{5} +(-2.32404 - 2.76969i) q^{7} +(3.57490 + 6.19192i) q^{8} +(-8.00397 - 7.31539i) q^{10} +(8.70004 - 1.53405i) q^{11} +(-3.15234 - 8.66099i) q^{13} +(2.68178 + 7.36812i) q^{14} +(-3.18091 - 18.0399i) q^{16} +(-9.89182 + 17.1331i) q^{17} +(12.1652 + 21.0707i) q^{19} +(1.62737 + 3.11638i) q^{20} +(-18.8675 - 3.32686i) q^{22} +(4.74988 + 3.98563i) q^{23} +(17.7230 + 17.6322i) q^{25} +19.9883i q^{26} -2.54225i q^{28} +(5.21445 - 14.3266i) q^{29} +(-9.90161 - 8.30843i) q^{31} +(-1.93215 + 10.9578i) q^{32} +(32.8665 - 27.5783i) q^{34} +(-5.45826 - 17.2342i) q^{35} +(-9.23883 - 5.33404i) q^{37} +(-9.16248 - 51.9630i) q^{38} +(4.71171 + 35.4372i) q^{40} +(23.8792 + 65.6075i) q^{41} +(58.3296 - 10.2851i) q^{43} +(5.37950 + 3.10586i) q^{44} +(-6.72346 - 11.6454i) q^{46} +(12.6408 - 10.6069i) q^{47} +(6.23877 - 35.3818i) q^{49} +(-23.0392 - 49.0781i) q^{50} +(2.21654 - 6.08989i) q^{52} +85.3480 q^{53} +(43.1365 + 9.50501i) q^{55} +(8.84144 - 24.2917i) q^{56} +(-21.2529 + 25.3282i) q^{58} +(60.9628 + 10.7494i) q^{59} +(55.8155 - 46.8348i) q^{61} +(14.0157 + 24.2760i) q^{62} +(-24.5711 + 42.5584i) q^{64} +(1.95102 - 46.0428i) q^{65} +(7.87234 + 21.6291i) q^{67} +(-13.0717 + 4.75773i) q^{68} +(-1.65978 + 39.1698i) q^{70} +(-49.0653 - 28.3279i) q^{71} +(101.360 - 58.5204i) q^{73} +(14.8713 + 17.7229i) q^{74} +(-2.97071 + 16.8478i) q^{76} +(-24.4681 - 20.5312i) q^{77} +(-7.55144 - 2.74850i) q^{79} +(19.7090 - 89.4451i) q^{80} -151.413i q^{82} +(77.8706 + 28.3426i) q^{83} +(-78.3997 + 60.3183i) q^{85} +(-126.498 - 22.3050i) q^{86} +(40.6005 + 48.3858i) q^{88} +(-102.638 + 59.2583i) q^{89} +(-16.6621 + 28.8595i) q^{91} +(0.757079 + 4.29361i) q^{92} +(-33.6278 + 12.2395i) q^{94} +(16.0337 + 120.591i) q^{95} +(30.2613 - 5.33588i) q^{97} +(-38.9576 + 67.4766i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.222082	−	0.975028i	$-0.571285\pi$
$2$	−2.03789	−	0.741730i	−1.01894	−	0.370865i	−0.796861	+	0.604163i	$0.793508\pi$
$3$		0			0
$3$		0			0
$4$	0.538636	+	0.451970i	0.134659	+	0.112992i
$5$	4.62185	+	1.90748i	0.924370	+	0.381496i
$5$	4.62185	+	1.90748i	0.924370	+	0.381496i
$6$		0			0
$7$	−2.32404	−	2.76969i	−0.332006	−	0.395670i	0.574055	−	0.818817i	$-0.305370\pi$
$7$	−2.32404	−	2.76969i	−0.332006	−	0.395670i	−0.906061	+	0.423147i	$0.860925\pi$
$8$	3.57490	+	6.19192i	0.446863	+	0.773990i
$9$		0			0
$10$	−8.00397	−	7.31539i	−0.800397	−	0.731539i
$11$	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	$-0.995764\pi$
$13$	−3.15234	−	8.66099i	−0.242488	−	0.666230i	0.757424	−	0.652924i	$-0.226458\pi$
$14$	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	$0.364346\pi$
$17$	−9.89182	+	17.1331i	−0.581872	+	1.00783i	−0.995258	+	0.0972754i	$0.968987\pi$
$18$		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	$0.612155\pi$
$20$	1.62737	+	3.11638i	0.0813687	+	0.155819i
$21$		0			0
$22$	−18.8675	−	3.32686i	−0.857615	−	0.151221i
$23$	4.74988	+	3.98563i	0.206517	+	0.173288i	0.740180	−	0.672409i	$-0.234740\pi$
$23$	4.74988	+	3.98563i	0.206517	+	0.173288i	−0.533663	+	0.845697i	$0.679185\pi$
$24$		0			0
$25$	17.7230	+	17.6322i	0.708921	+	0.705288i
$26$			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
$35$	−5.45826	−	17.2342i	−0.155950	−	0.492405i
$36$		0			0
$37$	−9.23883	−	5.33404i	−0.249698	−	0.144163i	0.369928	−	0.929060i	$-0.379382\pi$
$37$	−9.23883	−	5.33404i	−0.249698	−	0.144163i	−0.619626	+	0.784897i	$0.712716\pi$
$38$	−9.16248	−	51.9630i	−0.241118	−	1.36745i
$39$		0			0
$40$	4.71171	+	35.4372i	0.117793	+	0.885930i
$41$	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	0.552351	−	0.833612i	$-0.313731\pi$
$43$	58.3296	−	10.2851i	1.35650	−	0.239188i	0.804152	+	0.594424i	$0.202620\pi$
$44$	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	−0.498330	−	0.866988i	$-0.666053\pi$
$47$	12.6408	−	10.6069i	0.268952	−	0.225678i	0.767282	+	0.641310i	$0.221609\pi$
$48$		0			0
$49$	6.23877	−	35.3818i	0.127322	−	0.722078i
$50$	−23.0392	−	49.0781i	−0.460784	−	0.981562i
$51$		0			0
$52$	2.21654	−	6.08989i	0.0426257	−	0.117113i
$53$	85.3480			1.61034			0.805169	−	0.593045i	$-0.202074\pi$
$53$	85.3480			1.61034			0.805169	+	0.593045i	$0.202074\pi$
$54$		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
$65$	1.95102	−	46.0428i	0.0300157	−	0.708351i
$66$		0			0
$67$	7.87234	+	21.6291i	0.117498	+	0.322822i	0.984475	−	0.175526i	$-0.0561625\pi$
$67$	7.87234	+	21.6291i	0.117498	+	0.322822i	−0.866977	+	0.498348i	$0.833940\pi$
$68$	−13.0717	+	4.75773i	−0.192232	+	0.0699666i
$69$		0			0
$70$	−1.65978	+	39.1698i	−0.0237111	+	0.559569i
$71$	−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	0.395352	−	0.918530i	$-0.370623\pi$
$73$	101.360	−	58.5204i	1.38850	−	0.801650i	0.993146	+	0.116880i	$0.0372894\pi$
$74$	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	0.765455	−	0.643490i	$-0.222514\pi$
$83$	77.8706	+	28.3426i	0.938200	+	0.341477i	0.172745	+	0.984967i	$0.444736\pi$
$84$		0			0
$85$	−78.3997	+	60.3183i	−0.922349	+	0.709628i
$86$	−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
$95$	16.0337	+	120.591i	0.168776	+	1.26937i
$96$		0			0
$97$	30.2613	−	5.33588i	0.311972	−	0.0550090i	−0.0154702	−	0.999880i	$-0.504925\pi$
$97$	30.2613	−	5.33588i	0.311972	−	0.0550090i	0.327442	+	0.944871i	$0.393813\pi$
$98$	−38.9576	+	67.4766i	−0.397527	+	0.688537i
$99$		0			0
$100$	1.57705	+	17.5076i	0.0157705	+	0.175076i
$101$	−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	0.0112492	−	0.999937i	$-0.496419\pi$
$103$	−32.9784	−	5.81498i	−0.320179	−	0.0564561i	−0.331428	+	0.943481i	$0.607530\pi$
$104$	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	$-0.172072\pi$
$107$	183.486			1.71482			0.857411	+	0.514632i	$0.172072\pi$
$108$		0			0
$109$	−75.0243			−0.688297			−0.344148	−	0.938915i	$-0.611832\pi$
$109$	−75.0243			−0.688297			−0.344148	+	0.938915i	$0.611832\pi$
$110$	−80.8570	−	51.3657i	−0.735064	−	0.466961i
$111$		0			0
$112$	−42.5722	+	50.7356i	−0.380109	+	0.452996i
$113$	−31.4551	+	178.391i	−0.278364	+	1.57868i	0.449705	+	0.893177i	$0.351529\pi$
$113$	−31.4551	+	178.391i	−0.278364	+	1.57868i	−0.728069	+	0.685504i	$0.759582\pi$
$114$		0			0
$115$	14.3508	+	27.4813i	0.124789	+	0.238968i
$116$	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
$125$	48.2801	+	115.300i	0.386241	+	0.922398i
$126$		0			0
$127$	−107.545	+	62.0910i	−0.846809	+	0.488905i	−0.859573	−	0.511013i	$-0.829270\pi$
$127$	−107.545	+	62.0910i	−0.846809	+	0.488905i	0.0127639	+	0.999919i	$0.495937\pi$
$128$	115.734	−	97.1127i	0.904175	−	0.758693i
$129$		0			0
$130$	−38.1273	+	92.3829i	−0.293287	+	0.710638i
$131$	−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	−0.406153	−	0.913805i	$-0.633130\pi$
$137$	−178.739	−	65.0558i	−1.30467	−	0.474860i	−0.898514	+	0.438946i	$0.855352\pi$
$138$		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	$0.391001\pi$
$140$	4.84930	−	11.7499i	0.0346379	−	0.0839280i
$141$		0			0
$142$	78.9778	+	94.1221i	0.556182	+	0.662832i
$143$	−40.7119	−	70.5151i	−0.284699	−	0.493112i
$144$		0			0
$145$	51.4281	−	56.2688i	0.354676	−	0.388061i
$146$	−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
$155$	−29.9156	−	57.2875i	−0.193004	−	0.369597i
$156$		0			0
$157$	−87.5981	−	15.4459i	−0.557949	−	0.0983815i	−0.112440	−	0.993659i	$-0.535866\pi$
$157$	−87.5981	−	15.4459i	−0.557949	−	0.0983815i	−0.445510	+	0.895277i	$0.646978\pi$
$158$	13.3503	+	11.2023i	0.0844958	+	0.0709004i
$159$		0			0
$160$	−29.8319	+	46.9598i	−0.186450	+	0.293498i
$161$		−	22.4185i		−	0.139245i
$162$		0			0
$163$			95.4121i			0.585350i	0.956212	+	0.292675i	$0.0945454\pi$
$163$			95.4121i			0.585350i	−0.956212	+	0.292675i	$0.905455\pi$
$164$	−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	$-0.854284\pi$
$167$	16.2091	−	91.9261i	0.0970602	−	0.550456i	0.994097	−	0.108499i	$-0.0346045\pi$
$168$		0			0
$169$	64.3861	−	54.0263i	0.380983	−	0.319682i
$170$	204.509	−	64.7705i	1.20300	−	0.381003i
$171$		0			0
$172$	36.0670	+	20.8233i	0.209692	+	0.121066i
$173$	−9.71927	−	55.1207i	−0.0561808	−	0.318617i	0.943747	−	0.330670i	$-0.107275\pi$
$173$	−9.71927	−	55.1207i	−0.0561808	−	0.318617i	−0.999927	+	0.0120526i	$0.996163\pi$
$174$		0			0
$175$	7.64658	−	90.0653i	0.0436947	−	0.514659i
$176$	−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
$185$	−32.5259	−	42.2760i	−0.175816	−	0.228519i
$186$		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	−0.604200	−	0.796833i	$-0.706507\pi$
$193$	55.0909	−	65.6548i	0.285445	−	0.340180i	0.889645	+	0.456652i	$0.150952\pi$
$194$	−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	0.581776	−	0.813349i	$-0.302358\pi$
$197$	−81.4582	−	141.090i	−0.413493	−	0.716191i	−0.995269	+	0.0971578i	$0.969025\pi$
$198$		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	$0.316580\pi$
$200$	−45.8189	+	172.773i	−0.229095	+	0.863865i
$201$		0			0
$202$	80.2564	+	220.503i	0.397309	+	1.09160i
$203$	−51.7988	+	18.8532i	−0.255166	+	0.0928729i
$204$		0			0
$205$	−14.7791	+	348.777i	−0.0720931	+	1.70135i
$206$	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
$220$	18.9389	+	24.6161i	0.0860859	+	0.111891i
$221$	179.572	+	31.6634i	0.812544	+	0.143273i
$222$		0			0
$223$	−7.70503	−	9.18250i	−0.0345517	−	0.0411771i	0.748492	−	0.663144i	$-0.230778\pi$
$223$	−7.70503	−	9.18250i	−0.0345517	−	0.0411771i	−0.783044	+	0.621967i	$0.786334\pi$
$224$	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	$-0.915721\pi$
$227$	−33.5298	−	190.157i	−0.147709	−	0.837697i	0.817444	−	0.576008i	$-0.195390\pi$
$228$		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	$-0.0206817\pi$
$230$	−8.86150	−	66.6481i	−0.0385283	−	0.289774i
$231$		0			0
$232$	107.350	−	18.9287i	0.462716	−	0.0815893i
$233$	−79.8540	+	138.311i	−0.342721	+	0.593611i	−0.984937	−	0.172913i	$-0.944682\pi$
$233$	−79.8540	+	138.311i	−0.342721	+	0.593611i	0.642216	+	0.766524i	$0.278015\pi$
$234$		0			0
$235$	78.6561	−	24.9113i	0.334707	−	0.106005i
$236$	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
$245$	96.3248	−	151.629i	0.393163	−	0.618895i
$246$		0			0
$247$	144.144	−	171.785i	0.583581	−	0.695484i
$248$	16.0478	−	91.0118i	0.0647090	−	0.366983i
$249$		0			0
$250$	−12.8681	−	270.778i	−0.0514725	−	1.08311i
$251$	−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	−0.137700	−	0.990474i	$-0.543971\pi$
$257$	101.124	−	36.8062i	0.393480	−	0.143215i	0.531180	+	0.847259i	$0.321749\pi$
$258$		0			0
$259$	6.69782	+	37.9852i	0.0258603	+	0.146661i
$260$	21.8608	−	23.9185i	0.0840802	−	0.0919944i
$261$		0			0
$262$	232.171	−	134.044i	0.886149	−	0.511618i
$263$	−29.1199	+	24.4345i	−0.110722	+	0.0929069i	−0.696468	−	0.717588i	$-0.745246\pi$
$263$	−29.1199	+	24.4345i	−0.110722	+	0.0929069i	0.585746	+	0.810495i	$0.300802\pi$
$264$		0			0
$265$	394.466	+	162.800i	1.48855	+	0.614338i
$266$	−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
$275$	181.240	+	126.213i	0.659054	+	0.458955i
$276$		0			0
$277$	−242.799	−	289.356i	−0.876529	−	1.04461i	−0.998642	−	0.0520907i	$-0.983412\pi$
$277$	−242.799	−	289.356i	−0.876529	−	1.04461i	0.122113	−	0.992516i	$-0.461033\pi$
$278$	−260.054	−	450.426i	−0.935445	−	1.62024i
$279$		0			0
$280$	87.1997	−	95.4076i	0.311428	−	0.340741i
$281$	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	$-0.755653\pi$
$283$	−173.966	−	477.966i	−0.614719	−	1.68893i	0.104834	−	0.994490i	$-0.466569\pi$
$284$	−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
$290$	−146.541	+	76.5237i	−0.505313	+	0.263875i
$291$		0			0
$292$	81.0458	+	14.2906i	0.277554	+	0.0489403i
$293$	161.315	+	135.359i	0.550562	+	0.461976i	0.875131	−	0.483886i	$-0.160775\pi$
$293$	161.315	+	135.359i	0.550562	+	0.461976i	−0.324569	+	0.945862i	$0.605219\pi$
$294$		0			0
$295$	261.257	+	165.968i	0.885616	+	0.562602i
$296$		−	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
$305$	347.308	−	109.996i	1.13871	−	0.360644i
$306$		0			0
$307$	46.5102	+	26.8527i	0.151499	+	0.0874681i	0.573833	−	0.818972i	$-0.305456\pi$
$307$	46.5102	+	26.8527i	0.151499	+	0.0874681i	−0.422334	+	0.906440i	$0.638789\pi$
$308$	−3.89995	−	22.1177i	−0.0126622	−	0.0718107i
$309$		0			0
$310$	18.4727	+	138.935i	0.0595893	+	0.448176i
$311$	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	−0.331532	−	0.943444i	$-0.607565\pi$
$313$	−100.283	+	17.6826i	−0.320393	+	0.0564939i	0.0111389	+	0.999938i	$0.496454\pi$
$314$	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	$0.574299\pi$
$317$	−389.774	+	327.059i	−1.22957	+	1.03173i	−0.998267	+	0.0588511i	$0.981256\pi$
$318$		0			0
$319$	23.3882	−	132.641i	0.0733172	−	0.415802i
$320$	−194.743	+	149.830i	−0.608572	+	0.468217i
$321$		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
$335$	−4.87227	+	114.983i	−0.0145441	+	0.343232i
$336$		0			0
$337$	57.8789	+	159.021i	0.171748	+	0.471873i	0.995465	−	0.0951279i	$-0.0303260\pi$
$337$	57.8789	+	159.021i	0.171748	+	0.471873i	−0.823718	+	0.567000i	$0.808104\pi$
$338$	−171.284	+	62.3424i	−0.506759	+	0.184445i
$339$		0			0
$340$	−69.4910	−	2.94461i	−0.204385	−	0.00866061i
$341$	−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	0.633293	−	0.773912i	$-0.281703\pi$
$347$	−6.55502	−	5.50032i	−0.0188905	−	0.0158511i	−0.652184	+	0.758061i	$0.726147\pi$
$348$		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	−0.203995	−	0.978972i	$-0.565393\pi$
$353$	−349.306	−	127.137i	−0.989535	−	0.360161i	−0.785540	+	0.618811i	$0.787615\pi$
$354$		0			0
$355$	−172.738	−	224.518i	−0.486585	−	0.632446i
$356$	−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
$365$	580.099	−	77.1297i	1.58931	−	0.211314i
$366$		0			0
$367$	−597.597	+	105.372i	−1.62833	+	0.287118i	−0.911860	−	0.410501i	$-0.865354\pi$
$367$	−597.597	+	105.372i	−1.62833	+	0.287118i	−0.716469	+	0.697619i	$0.754243\pi$
$368$	56.7912	−	98.3652i	0.154324	−	0.267297i
$369$		0			0
$370$	34.9267	+	110.279i	0.0943965	+	0.298052i
$371$	−198.352	−	236.387i	−0.534643	−	0.637162i
$372$		0			0
$373$	−15.9903	−	2.81952i	−0.0428694	−	0.00755902i	0.152172	−	0.988354i	$-0.451373\pi$
$373$	−15.9903	−	2.81952i	−0.0428694	−	0.00755902i	−0.195042	+	0.980795i	$0.562484\pi$
$374$	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	$0.586093\pi$
$380$	−45.8670	+	72.2012i	−0.120703	+	0.190003i
$381$		0			0
$382$	460.237	−	548.489i	1.20481	−	1.43584i
$383$	−113.044	+	641.106i	−0.295155	+	1.67391i	0.371417	+	0.928466i	$0.378872\pi$
$383$	−113.044	+	641.106i	−0.295155	+	1.67391i	−0.666572	+	0.745441i	$0.732239\pi$
$384$		0			0
$385$	−73.9252	−	141.565i	−0.192013	−	0.367700i
$386$	−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
$395$	−29.6589	−	27.1074i	−0.0750859	−	0.0686263i
$396$		0			0
$397$	131.369	−	75.8460i	0.330904	−	0.191048i	−0.325338	−	0.945598i	$-0.605478\pi$
$397$	131.369	−	75.8460i	0.330904	−	0.191048i	0.656243	+	0.754550i	$0.272145\pi$
$398$	300.017	−	251.744i	0.753812	−	0.632523i
$399$		0			0
$400$	261.707	−	375.807i	0.654267	−	0.939519i
$401$	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	$0.996254\pi$
$410$	288.817	−	699.806i	0.704431	−	1.70684i
$411$		0			0
$412$	−15.1352	−	18.0374i	−0.0367358	−	0.0437801i
$413$	−111.908	−	193.830i	−0.270963	−	0.469322i
$414$		0			0
$415$	305.843	+	279.532i	0.736972	+	0.673571i
$416$	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
$425$	−477.408	+	129.237i	−1.12331	+	0.304086i
$426$		0			0
$427$	−259.436	−	45.7455i	−0.607578	−	0.107132i
$428$	98.8322	+	82.9301i	0.230916	+	0.193762i
$429$		0			0
$430$	−542.108	−	344.382i	−1.26072	−	0.800889i
$431$		−	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	$0.298275\pi$
$433$			697.839i			1.61164i	−0.592162	+	0.805819i	$0.701725\pi$
$434$	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	$0.126651\pi$
$440$	95.3546	+	301.077i	0.216715	+	0.684266i
$441$		0			0
$442$	−342.462	−	197.720i	−0.774801	−	0.447331i
$443$	0.222903	+	1.26415i	0.000503168	+	0.00285361i	0.985058	−	0.172221i	$-0.0550944\pi$
$443$	0.222903	+	1.26415i	0.000503168	+	0.00285361i	−0.984555	+	0.175075i	$0.943983\pi$
$444$		0			0
$445$	−587.413	+	78.1022i	−1.32003	+	0.175511i
$446$	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
$455$	−132.059	+	101.602i	−0.290239	+	0.223301i
$456$		0			0
$457$	96.5574	−	265.289i	0.211285	−	0.580502i	−0.788100	−	0.615547i	$-0.788935\pi$
$457$	96.5574	−	265.289i	0.211285	−	0.580502i	0.999386	+	0.0350451i	$0.0111575\pi$
$458$	−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	$-0.494202\pi$
$463$	462.859	−	551.614i	0.999695	−	1.19139i	0.981482	−	0.191556i	$-0.0613534\pi$
$464$	−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	0.995030	−	0.0995750i	$-0.0317483\pi$
$467$	192.068	+	332.672i	0.411281	+	0.712359i	−0.583750	+	0.811934i	$0.698415\pi$
$468$		0			0
$469$	41.6101	−	72.0708i	0.0887209	−	0.153669i
$470$	−178.769	−	7.57517i	−0.380361	−	0.0161174i
$471$		0			0
$472$	151.377	+	415.905i	0.320714	+	0.881154i
$473$	491.692	−	178.961i	1.03952	−	0.378354i
$474$		0			0
$475$	−155.919	+	587.936i	−0.328251	+	1.23776i
$476$	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	$0.0472629\pi$
$487$			144.089i			0.295871i	−0.988997	+	0.147936i	$0.952737\pi$
$488$	489.532	+	178.175i	1.00314	+	0.365113i
$489$		0			0
$490$	−308.767	+	237.556i	−0.630136	+	0.484808i
$491$	−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	$0.547891\pi$
$500$	−26.1065	+	83.9258i	−0.0522131	+	0.167852i
$501$		0			0
$502$	220.815	−	38.9357i	0.439871	−	0.0775611i
$503$	293.589	−	508.511i	0.583676	−	1.01096i	−0.411363	−	0.911472i	$-0.634947\pi$
$503$	293.589	−	508.511i	0.583676	−	1.01096i	0.995039	−	0.0994853i	$-0.0317196\pi$
$504$		0			0
$505$	−163.347	−	515.759i	−0.323459	−	1.02131i
$506$	−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
$515$	−141.329	−	89.7816i	−0.274426	−	0.174333i
$516$		0			0
$517$	93.7036	−	111.672i	0.181245	−	0.215999i
$518$	14.5254	−	82.3775i	0.0280413	−	0.159030i
$519$		0			0
$520$	292.068	−	152.518i	0.561669	−	0.293304i
$521$	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	0.962811	−	0.270175i	$-0.0870816\pi$
$523$	632.955	+	365.437i	1.21024	+	0.698731i	0.247427	+	0.968906i	$0.420415\pi$
$524$	−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
$530$	−683.122	−	624.354i	−1.28891	−	1.17803i
$531$		0			0
$532$	53.5671	−	30.9270i	0.100690	−	0.0581334i
$533$	492.951	−	413.635i	0.924861	−	0.776050i
$534$		0			0
$535$	848.045	+	349.996i	1.58513	+	0.654198i
$536$	−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
$545$	−346.751	−	143.108i	−0.636241	−	0.262583i
$546$		0			0
$547$	−429.435	−	511.781i	−0.785074	−	0.935615i	0.214077	−	0.976817i	$-0.431326\pi$
$547$	−429.435	−	511.781i	−0.785074	−	0.935615i	−0.999151	+	0.0412022i	$0.986881\pi$
$548$	−66.8723	−	115.826i	−0.122030	−	0.211362i
$549$		0			0
$550$	−275.730	−	391.638i	−0.501327	−	0.712069i
$551$	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	$-0.552976\pi$
$557$	429.574	−	744.043i	0.771227	−	1.33581i	0.936891	−	0.349623i	$-0.113690\pi$
$558$		0			0
$559$	−272.954	−	472.770i	−0.488289	−	0.845742i
$560$	−293.540	+	153.287i	−0.524178	+	0.273726i
$561$		0			0
$562$	−121.988	−	21.5098i	−0.217061	−	0.0382736i
$563$	51.6792	+	43.3640i	0.0917926	+	0.0770232i	0.687529	−	0.726157i	$-0.258695\pi$
$563$	51.6792	+	43.3640i	0.0917926	+	0.0770232i	−0.595737	+	0.803180i	$0.703140\pi$
$564$		0			0
$565$	−485.658	+	764.496i	−0.859572	+	1.35309i
$566$			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
$575$	13.9070	+	154.388i	0.0241861	+	0.268501i
$576$		0			0
$577$	675.220	+	389.839i	1.17023	+	0.675630i	0.953733	−	0.300654i	$-0.0972050\pi$
$577$	675.220	+	389.839i	1.17023	+	0.675630i	0.216492	+	0.976284i	$0.430538\pi$
$578$	38.5595	+	218.682i	0.0667120	+	0.378342i
$579$		0			0
$580$	53.1328	−	7.06452i	0.0916083	−	0.0121802i
$581$	−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	−0.571614	−	0.820522i	$-0.693683\pi$
$587$	80.5262	−	67.5695i	0.137183	−	0.115110i	0.708797	+	0.705412i	$0.249238\pi$
$588$		0			0
$589$	54.6098	−	309.708i	0.0927161	−	0.525819i
$590$	−409.308	−	532.005i	−0.693743	−	0.901703i
$591$		0			0
$592$	−66.8374	+	183.634i	−0.112901	+	0.310193i
$593$	−56.8607			−0.0958864			−0.0479432	−	0.998850i	$-0.515267\pi$
$593$	−56.8607			−0.0958864			−0.0479432	+	0.998850i	$0.515267\pi$
$594$		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
$605$	−214.587	−	9.09292i	−0.354690	−	0.0150296i
$606$		0			0
$607$	237.324	+	652.041i	0.390978	+	1.07420i	0.966556	+	0.256456i	$0.0825549\pi$
$607$	237.324	+	652.041i	0.390978	+	1.07420i	−0.575578	+	0.817747i	$0.695223\pi$
$608$	−254.394	+	92.5917i	−0.418411	+	0.152289i
$609$		0			0
$610$	−789.361	−	33.4484i	−1.29403	−	0.0548334i
$611$	−131.714	−	76.0450i	−0.215571	−	0.124460i
$612$		0			0
$613$	−820.457	+	473.691i	−1.33843	+	0.772742i	−0.986574	−	0.163312i	$-0.947782\pi$
$613$	−820.457	+	473.691i	−1.33843	+	0.772742i	−0.351855	+	0.936055i	$0.614449\pi$
$614$	−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	$-0.984849\pi$
$617$	−752.232	−	631.198i	−1.21918	−	1.02301i	−0.220310	−	0.975430i	$-0.570707\pi$
$618$		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
$625$	3.21146	+	624.992i	0.00513834	+	0.999987i
$626$	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
$635$	−615.493	+	81.8357i	−0.969281	+	0.128875i
$636$		0			0
$637$	−326.108	+	57.5017i	−0.511944	+	0.0902695i
$638$	−146.046	+	252.959i	−0.228912	+	0.396488i
$639$		0			0
$640$	720.148	−	228.079i	1.12523	−	0.356374i
$641$	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	0.0871943	−	0.996191i	$-0.472210\pi$
$643$	−110.331	−	19.4543i	−0.171587	−	0.0302555i	−0.258782	+	0.965936i	$0.583321\pi$
$644$	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	$-0.502642\pi$
$647$	−10.7396			−0.0165990			−0.00829952	+	0.999966i	$0.502642\pi$
$648$		0			0
$649$	546.869			0.842633
$650$	−352.437	+	354.253i	−0.542211	+	0.545004i
$651$		0			0
$652$	−43.1234	+	51.3924i	−0.0661401	+	0.0788227i
$653$	−135.331	+	767.498i	−0.207244	+	1.17534i	0.686624	+	0.727013i	$0.259092\pi$
$653$	−135.331	+	767.498i	−0.207244	+	1.17534i	−0.893869	+	0.448329i	$0.852019\pi$
$654$		0			0
$655$	−547.887	+	286.107i	−0.836469	+	0.436805i
$656$	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
$665$	296.735	−	324.666i	0.446219	−	0.488220i
$666$		0			0
$667$	81.8684	−	47.2667i	0.122741	−	0.0708647i
$668$	50.2786	−	42.1888i	0.0752674	−	0.0631568i
$669$		0			0
$670$	95.2152	−	230.708i	0.142112	−	0.344340i
$671$	413.750	−	493.089i	0.616618	−	0.734856i
$672$		0			0
$673$	256.931	−	705.911i	0.381769	−	1.04890i	−0.588842	−	0.808248i	$-0.700416\pi$
$673$	256.931	−	705.911i	0.381769	−	1.04890i	0.970611	−	0.240654i	$-0.0773619\pi$
$674$		−	366.997i		−	0.544506i
$675$		0			0
$676$	59.0990			0.0874245
$677$	−89.4060	−	32.5411i	−0.132062	−	0.0480667i	0.275144	−	0.961403i	$-0.411275\pi$
$677$	−89.4060	−	32.5411i	−0.132062	−	0.0480667i	−0.407206	+	0.913336i	$0.633497\pi$
$678$		0			0
$679$	−85.1072	−	71.4135i	−0.125342	−	0.105174i
$680$	−653.757	−	269.812i	−0.961408	−	0.396782i
$681$		0			0
$682$	159.178	+	189.701i	0.233399	+	0.278154i
$683$	207.041	+	358.606i	0.303135	+	0.525045i	0.976844	−	0.213951i	$-0.0686334\pi$
$683$	207.041	+	358.606i	0.303135	+	0.525045i	−0.673709	+	0.738996i	$0.735300\pi$
$684$		0			0
$685$	−702.014	−	641.620i	−1.02484	−	0.936672i
$686$	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
$695$	555.066	+	1062.94i	0.798656	+	1.52940i
$696$		0			0
$697$	−1360.27	−	239.853i	−1.95161	−	0.344121i
$698$	702.103	+	589.134i	1.00588	+	0.844032i
$699$		0			0
$700$	44.8255	−	45.0564i	0.0640364	−	0.0643663i
$701$		−	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	$0.286644\pi$
$710$	185.488	+	585.667i	0.261250	+	0.824883i
$711$		0			0
$712$	−733.845	−	423.685i	−1.03068	−	0.595064i
$713$	−13.9172	−	78.9282i	−0.0195192	−	0.110699i
$714$		0			0
$715$	−53.6581	−	403.567i	−0.0750464	−	0.564430i
$716$	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
$725$	345.025	−	161.968i	0.475896	−	0.223404i
$726$		0			0
$727$	−290.996	+	799.505i	−0.400270	+	1.09973i	0.561882	+	0.827217i	$0.310078\pi$
$727$	−290.996	+	799.505i	−0.400270	+	1.09973i	−0.962152	+	0.272515i	$0.912145\pi$
$728$	−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	−0.977601	−	0.210467i	$-0.932501\pi$
$733$	−440.220	+	524.633i	−0.600573	+	0.715735i	0.377028	+	0.926202i	$0.376946\pi$
$734$	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	$-0.0360359\pi$
$740$	1.58784	−	37.4721i	0.00214573	−	0.0506380i
$741$		0			0
$742$	228.884	+	628.854i	0.308469	+	0.847512i
$743$	−403.184	+	146.747i	−0.542643	+	0.197506i	−0.598775	−	0.800918i	$-0.704346\pi$
$743$	−403.184	+	146.747i	−0.542643	+	0.197506i	0.0561318	+	0.998423i	$0.482123\pi$
$744$		0			0
$745$	53.3630	−	1259.33i	0.0716282	−	1.69038i
$746$	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	$-0.917634\pi$
$757$		−	387.406i		−	0.511765i	0.966708	−	0.255883i	$-0.0823660\pi$
$758$	412.723	+	150.219i	0.544490	+	0.198178i
$759$		0			0
$760$	−689.368	+	530.379i	−0.907063	+	0.697867i
$761$	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	$0.507840\pi$
$770$	45.6484	+	343.325i	0.0592836	+	0.445877i
$771$		0			0
$772$	59.3480	−	10.4646i	0.0768756	−	0.0135552i
$773$	189.771	−	328.693i	0.245499	−	0.425217i	−0.716773	−	0.697307i	$-0.754382\pi$
$773$	189.771	−	328.693i	0.245499	−	0.425217i	0.962272	+	0.272090i	$0.0877148\pi$
$774$		0			0
$775$	−28.9905	−	321.838i	−0.0374071	−	0.415274i
$776$	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
$785$	−375.403	−	238.480i	−0.478220	−	0.303797i
$786$		0			0
$787$	646.804	−	770.831i	0.821860	−	0.979455i	−0.178130	−	0.984007i	$-0.557005\pi$
$787$	646.804	−	770.831i	0.821860	−	0.979455i	0.999990	+	0.00455231i	$0.00144905\pi$
$788$	19.8919	−	112.813i	0.0252436	−	0.143163i
$789$		0			0
$790$	40.3352	+	77.2407i	0.0510572	+	0.0977730i
$791$	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	−0.349176	−	0.937057i	$-0.613538\pi$
$797$	−11.4218	+	4.15721i	−0.0143310	+	0.00521607i	0.334845	+	0.942273i	$0.391316\pi$
$798$		0			0
$799$	56.6886	+	321.497i	0.0709494	+	0.402374i
$800$	−227.454	+	160.137i	−0.284317	+	0.200171i
$801$		0			0
$802$	−480.341	+	277.325i	−0.598929	+	0.345792i
$803$	792.066	−	664.622i	0.986383	−	0.827674i
$804$		0			0
$805$	42.7628	−	103.615i	0.0531215	−	0.128714i
$806$	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
$815$	−181.997	+	440.981i	−0.223309	+	0.541080i
$816$		0			0
$817$	926.304	+	1103.93i	1.13379	+	1.35120i
$818$	672.715	+	1165.18i	0.822390	+	1.42442i
$819$		0			0
$820$	−165.597	+	181.185i	−0.201948	+	0.220957i
$821$	−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	$-0.906037\pi$
$823$	−338.120	−	928.977i	−0.410838	−	1.12877i	0.545908	−	0.837845i	$-0.316185\pi$
$824$	−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	−0.850873	−	0.525372i	$-0.823926\pi$
$827$	24.4367	−	42.3257i	0.0295486	−	0.0511798i	0.880422	+	0.474192i	$0.157260\pi$
$828$		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	$-0.395562\pi$
$830$	−415.937	−	796.507i	−0.501129	−	0.959647i
$831$		0			0
$832$	446.054	+	78.6513i	0.536122	+	0.0945328i
$833$	544.489	+	456.880i	0.653648	+	0.548476i
$834$		0			0
$835$	250.263	−	393.951i	0.299717	−	0.471797i
$836$			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
$845$	400.637	−	126.886i	0.474127	−	0.150161i
$846$		0			0
$847$	134.503	+	77.6553i	0.158799	+	0.0916827i
$848$	−271.485	−	1539.67i	−0.320147	−	1.81564i
$849$		0			0
$850$	1068.76	+	90.7382i	1.25737	+	0.106751i
$851$	−22.6239	−	62.1586i	−0.0265850	−	0.0730418i
$852$		0			0
$853$	−490.805	+	86.5422i	−0.575387	+	0.101456i	−0.453767	−	0.891120i	$-0.649920\pi$
$853$	−490.805	+	86.5422i	−0.575387	+	0.101456i	−0.121620	+	0.992577i	$0.538809\pi$
$854$	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	−0.921656	−	0.388007i	$-0.873163\pi$
$857$	−599.546	+	503.079i	−0.699587	+	0.587024i	0.222069	+	0.975031i	$0.428719\pi$
$858$		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	$0.940096\pi$
$860$	126.976	+	165.039i	0.147647	+	0.191906i
$861$		0			0
$862$	−143.992	+	395.615i	−0.167044	+	0.458950i
$863$	72.8410			0.0844044			0.0422022	−	0.999109i	$-0.486563\pi$
$863$	72.8410			0.0844044			0.0422022	+	0.999109i	$0.486563\pi$
$864$		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
$875$	207.139	−	401.683i	0.236731	−	0.459066i
$876$		0			0
$877$	544.678	+	1496.49i	0.621070	+	1.70638i	0.704353	+	0.709849i	$0.251237\pi$
$877$	544.678	+	1496.49i	0.621070	+	1.70638i	−0.0832836	+	0.996526i	$0.526541\pi$
$878$	−817.948	+	297.709i	−0.931603	+	0.339076i
$879$		0			0
$880$	34.2556	−	808.410i	0.0389268	−	0.918648i
$881$	−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	0.0726604	−	0.997357i	$-0.476851\pi$
$883$	858.918	−	495.896i	0.972727	−	0.561604i	0.900066	+	0.435753i	$0.143518\pi$
$884$	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	0.0113051	−	0.999936i	$-0.496401\pi$
$887$	−861.700	−	723.052i	−0.971477	−	0.815166i	−0.982782	+	0.184770i	$0.940846\pi$
$888$		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
$895$	153.651	+	199.710i	0.171677	+	0.223139i
$896$	−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
$905$	−158.734	−	1193.85i	−0.175396	−	1.31917i
$906$		0			0
$907$	784.120	−	138.261i	0.864520	−	0.152438i	0.276233	−	0.961091i	$-0.410914\pi$
$907$	784.120	−	138.261i	0.864520	−	0.152438i	0.588287	+	0.808652i	$0.299803\pi$
$908$	67.8849	−	117.580i	0.0747631	−	0.129493i
$909$		0			0
$910$	344.481	−	109.101i	0.378551	−	0.119891i
$911$	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	$0.257092\pi$
$920$	−118.859	+	187.102i	−0.129195	+	0.203371i
$921$		0			0
$922$	−395.918	+	471.837i	−0.429413	+	0.511754i
$923$	−90.6767	+	514.253i	−0.0982412	+	0.557154i
$924$		0			0
$925$	−69.6892	−	257.436i	−0.0753397	−	0.278309i
$926$	−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
$935$	−589.549	+	645.041i	−0.630533	+	0.689883i
$936$		0			0
$937$	417.683	−	241.149i	0.445766	−	0.257363i	−0.260274	−	0.965535i	$-0.583813\pi$
$937$	417.683	−	241.149i	0.445766	−	0.257363i	0.706040	+	0.708172i	$0.250480\pi$
$938$	−138.254	+	116.009i	−0.147392	+	0.123677i
$939$		0			0
$940$	53.6262	+	22.1320i	0.0570491	+	0.0235447i
$941$	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	0.255150	−	0.966901i	$-0.417875\pi$
$947$	−161.848	−	58.9078i	−0.170906	−	0.0622046i	−0.426056	+	0.904697i	$0.640097\pi$
$948$		0			0
$949$	−826.367	−	693.404i	−0.870776	−	0.730668i
$950$	753.835	−	1082.50i	0.793510	−	1.13947i
$951$		0			0
$952$	328.734	+	391.770i	0.345309	+	0.411524i
$953$	−825.741	−	1430.23i	−0.866465	−	1.50076i	−0.865585	−	0.500761i	$-0.833053\pi$
$953$	−825.741	−	1430.23i	−0.866465	−	1.50076i	−0.000879492	−	1.00000i	$-0.500280\pi$
$954$		0			0
$955$	−1113.69	+	1218.52i	−1.16617	+	1.27593i
$956$	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
$965$	379.857	−	198.362i	0.393635	−	0.205556i
$966$		0			0
$967$	−1336.23	−	235.614i	−1.38183	−	0.243654i	−0.567175	−	0.823597i	$-0.691964\pi$
$967$	−1336.23	−	235.614i	−1.38183	−	0.243654i	−0.814657	+	0.579943i	$0.803075\pi$
$968$	−235.273	−	197.418i	−0.243051	−	0.203944i
$969$		0			0
$970$	−281.244	−	178.665i	−0.289942	−	0.184191i
$971$		−	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	−0.966610	−	0.256252i	$-0.917512\pi$
$977$	28.6746	−	162.622i	0.0293497	−	0.166450i	0.995960	+	0.0898018i	$0.0286234\pi$
$978$		0			0
$979$	−802.052	+	673.002i	−0.819257	+	0.687438i
$980$	120.416	−	38.1371i	0.122873	−	0.0389154i
$981$		0			0
$982$	259.021	+	149.546i	0.263769	+	0.152287i
$983$	−72.9652	−	413.806i	−0.0742271	−	0.420963i	−0.999165	−	0.0408456i	$-0.986995\pi$
$983$	−72.9652	−	413.806i	−0.0742271	−	0.420963i	0.924938	−	0.380117i	$-0.124116\pi$
$984$		0			0
$985$	−107.362	−	807.476i	−0.108997	−	0.819772i
$986$	−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
$995$	−715.659	+	550.606i	−0.719255	+	0.553373i
$996$		0			0
$997$	667.318	−	1833.44i	0.669326	−	1.83896i	0.140804	−	0.990037i	$-0.455031\pi$
$997$	667.318	−	1833.44i	0.669326	−	1.83896i	0.528522	−	0.848920i	$-0.322747\pi$
$998$	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.179.9		204
3.2	odd	2		135.3.n.a.104.26	yes	204
5.4	even	2	inner	405.3.n.a.179.26		204
15.14	odd	2		135.3.n.a.104.9	yes	204
27.7	even	9		135.3.n.a.74.9	✓	204
27.20	odd	18	inner	405.3.n.a.224.26		204
135.34	even	18		135.3.n.a.74.26	yes	204
135.74	odd	18	inner	405.3.n.a.224.9		204

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

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

\(f(q)\)	\(=\)	\(q+(-2.03789 - 0.741730i) q^{2} +(0.538636 + 0.451970i) q^{4} +(4.62185 + 1.90748i) q^{5} +(-2.32404 - 2.76969i) q^{7} +(3.57490 + 6.19192i) q^{8} +(-8.00397 - 7.31539i) q^{10} +(8.70004 - 1.53405i) q^{11} +(-3.15234 - 8.66099i) q^{13} +(2.68178 + 7.36812i) q^{14} +(-3.18091 - 18.0399i) q^{16} +(-9.89182 + 17.1331i) q^{17} +(12.1652 + 21.0707i) q^{19} +(1.62737 + 3.11638i) q^{20} +(-18.8675 - 3.32686i) q^{22} +(4.74988 + 3.98563i) q^{23} +(17.7230 + 17.6322i) q^{25} +19.9883i q^{26} -2.54225i q^{28} +(5.21445 - 14.3266i) q^{29} +(-9.90161 - 8.30843i) q^{31} +(-1.93215 + 10.9578i) q^{32} +(32.8665 - 27.5783i) q^{34} +(-5.45826 - 17.2342i) q^{35} +(-9.23883 - 5.33404i) q^{37} +(-9.16248 - 51.9630i) q^{38} +(4.71171 + 35.4372i) q^{40} +(23.8792 + 65.6075i) q^{41} +(58.3296 - 10.2851i) q^{43} +(5.37950 + 3.10586i) q^{44} +(-6.72346 - 11.6454i) q^{46} +(12.6408 - 10.6069i) q^{47} +(6.23877 - 35.3818i) q^{49} +(-23.0392 - 49.0781i) q^{50} +(2.21654 - 6.08989i) q^{52} +85.3480 q^{53} +(43.1365 + 9.50501i) q^{55} +(8.84144 - 24.2917i) q^{56} +(-21.2529 + 25.3282i) q^{58} +(60.9628 + 10.7494i) q^{59} +(55.8155 - 46.8348i) q^{61} +(14.0157 + 24.2760i) q^{62} +(-24.5711 + 42.5584i) q^{64} +(1.95102 - 46.0428i) q^{65} +(7.87234 + 21.6291i) q^{67} +(-13.0717 + 4.75773i) q^{68} +(-1.65978 + 39.1698i) q^{70} +(-49.0653 - 28.3279i) q^{71} +(101.360 - 58.5204i) q^{73} +(14.8713 + 17.7229i) q^{74} +(-2.97071 + 16.8478i) q^{76} +(-24.4681 - 20.5312i) q^{77} +(-7.55144 - 2.74850i) q^{79} +(19.7090 - 89.4451i) q^{80} -151.413i q^{82} +(77.8706 + 28.3426i) q^{83} +(-78.3997 + 60.3183i) q^{85} +(-126.498 - 22.3050i) q^{86} +(40.6005 + 48.3858i) q^{88} +(-102.638 + 59.2583i) q^{89} +(-16.6621 + 28.8595i) q^{91} +(0.757079 + 4.29361i) q^{92} +(-33.6278 + 12.2395i) q^{94} +(16.0337 + 120.591i) q^{95} +(30.2613 - 5.33588i) q^{97} +(-38.9576 + 67.4766i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 12 q^{4} - 3 q^{5} - 3 q^{10} - 6 q^{11} + 48 q^{14} + 12 q^{16} - 6 q^{19} - 63 q^{20} - 15 q^{25} - 96 q^{29} - 102 q^{31} + 12 q^{34} + 252 q^{35} + 117 q^{40} - 96 q^{41} + 666 q^{44} - 6 q^{46}+ \cdots + 543 q^{95}+O(q^{100}) \) 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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