LMFDB - Embedded newform 81.5.f.a.8.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,5,Mod(8,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	81.f (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:	$8.37296700979$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			8.9
Character	$\chi$	$=$	81.8
Dual form			81.5.f.a.71.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.35935 + 0.768672i) q^{2} +(3.37802 + 1.22950i) q^{4} +(-27.2417 - 32.4654i) q^{5} +(-49.1081 + 17.8739i) q^{7} +(-47.5559 - 27.4564i) q^{8} +(-93.8009 - 162.468i) q^{10} +(-11.4420 + 13.6360i) q^{11} +(21.2681 + 120.617i) q^{13} +(-227.819 + 40.1706i) q^{14} +(-230.269 - 193.218i) q^{16} +(377.223 - 217.790i) q^{17} +(65.4306 - 113.329i) q^{19} +(-52.1069 - 143.162i) q^{20} +(-60.3613 + 50.6491i) q^{22} +(240.426 - 660.564i) q^{23} +(-203.361 + 1153.32i) q^{25} +542.162i q^{26} -187.864 q^{28} +(-809.117 - 142.669i) q^{29} +(-367.484 - 133.753i) q^{31} +(-290.544 - 346.257i) q^{32} +(1811.86 - 659.462i) q^{34} +(1918.07 + 1107.40i) q^{35} +(-905.030 - 1567.56i) q^{37} +(372.348 - 443.747i) q^{38} +(404.120 + 2291.88i) q^{40} +(-1779.62 + 313.795i) q^{41} +(201.781 + 169.314i) q^{43} +(-55.4168 + 31.9949i) q^{44} +(1555.86 - 2694.82i) q^{46} +(-31.4023 - 86.2770i) q^{47} +(252.856 - 212.171i) q^{49} +(-1773.05 + 4871.41i) q^{50} +(-76.4550 + 433.598i) q^{52} +1069.64i q^{53} +754.398 q^{55} +(2826.13 + 498.323i) q^{56} +(-3417.56 - 1243.89i) q^{58} +(-239.279 - 285.161i) q^{59} +(1175.69 - 427.916i) q^{61} +(-1499.18 - 865.552i) q^{62} +(1404.33 + 2432.37i) q^{64} +(3336.51 - 3976.30i) q^{65} +(781.472 + 4431.95i) q^{67} +(1542.04 - 271.903i) q^{68} +(7510.32 + 6301.90i) q^{70} +(4815.68 - 2780.33i) q^{71} +(-1761.03 + 3050.19i) q^{73} +(-2740.41 - 7529.21i) q^{74} +(360.364 - 302.381i) q^{76} +(318.165 - 874.152i) q^{77} +(1741.86 - 9878.58i) q^{79} +12739.4i q^{80} -7999.21 q^{82} +(-4460.90 - 786.577i) q^{83} +(-17346.8 - 6313.72i) q^{85} +(749.486 + 893.203i) q^{86} +(918.530 - 334.318i) q^{88} +(-11590.4 - 6691.71i) q^{89} +(-3200.34 - 5543.15i) q^{91} +(1624.33 - 1935.80i) q^{92} +(-70.5749 - 400.250i) q^{94} +(-5461.71 + 963.047i) q^{95} +(-5334.35 - 4476.05i) q^{97} +(1265.38 - 730.567i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) $ 66 * q + 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 492 * q^11 - 6 * q^13 - 1137 * q^14 - 54 * q^16 + 9 * q^17 - 3 * q^19 + 2487 * q^20 + 1002 * q^22 + 2724 * q^23 + 435 * q^25 - 12 * q^28 - 5016 * q^29 - 1671 * q^31 - 10224 * q^32 - 342 * q^34 + 2682 * q^35 - 3 * q^37 + 6564 * q^38 - 1113 * q^40 - 5754 * q^41 - 1266 * q^43 + 4545 * q^44 - 3 * q^46 + 9159 * q^47 + 5898 * q^49 + 34977 * q^50 + 2871 * q^52 - 12 * q^55 - 39243 * q^56 - 12291 * q^58 - 24762 * q^59 - 8358 * q^61 - 38304 * q^62 + 6141 * q^64 - 23727 * q^65 + 15996 * q^67 + 43533 * q^68 - 7251 * q^70 + 19773 * q^71 + 6108 * q^73 + 74847 * q^74 - 28614 * q^76 + 33909 * q^77 - 5658 * q^79 - 12 * q^82 - 18813 * q^83 + 24219 * q^85 - 96474 * q^86 + 36042 * q^88 - 110232 * q^89 - 6042 * q^91 - 73545 * q^92 + 2631 * q^94 + 65163 * q^95 - 3696 * q^97 + 259938 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	4.35935	+	0.768672i	1.08984	+	0.192168i	0.689562	−	0.724227i	$-0.257803\pi$
$2$	4.35935	+	0.768672i	1.08984	+	0.192168i	0.400276	+	0.916395i	$0.368914\pi$
$3$		0			0
$3$		0			0
$4$	3.37802	+	1.22950i	0.211126	+	0.0768437i
$5$	−27.2417	−	32.4654i	−1.08967	−	1.29862i	−0.951311	−	0.308233i	$-0.900262\pi$
$5$	−27.2417	−	32.4654i	−1.08967	−	1.29862i	−0.138357	−	0.990382i	$-0.544182\pi$
$6$		0			0
$7$	−49.1081	+	17.8739i	−1.00221	+	0.364773i	−0.790435	−	0.612546i	$-0.790145\pi$
$7$	−49.1081	+	17.8739i	−1.00221	+	0.364773i	−0.211771	+	0.977319i	$0.567923\pi$
$8$	−47.5559	−	27.4564i	−0.743061	−	0.429006i
$9$		0			0
$10$	−93.8009	−	162.468i	−0.938009	−	1.62468i
$11$	−11.4420	+	13.6360i	−0.0945619	+	0.112694i	−0.811250	−	0.584699i	$-0.801213\pi$
$11$	−11.4420	+	13.6360i	−0.0945619	+	0.112694i	0.716688	+	0.697394i	$0.245657\pi$
$12$		0			0
$13$	21.2681	+	120.617i	0.125847	+	0.713713i	0.980801	+	0.195010i	$0.0624739\pi$
$13$	21.2681	+	120.617i	0.125847	+	0.713713i	−0.854954	+	0.518703i	$0.826415\pi$
$14$	−227.819	+	40.1706i	−1.16234	+	0.204952i
$15$		0			0
$16$	−230.269	−	193.218i	−0.899487	−	0.754759i
$17$	377.223	−	217.790i	1.30527	−	0.753597i	0.323966	−	0.946069i	$-0.394984\pi$
$17$	377.223	−	217.790i	1.30527	−	0.753597i	0.981303	+	0.192471i	$0.0616502\pi$
$18$		0			0
$19$	65.4306	−	113.329i	0.181248	−	0.313931i	−0.761058	−	0.648684i	$-0.775320\pi$
$19$	65.4306	−	113.329i	0.181248	−	0.313931i	0.942306	+	0.334753i	$0.108653\pi$
$20$	−52.1069	−	143.162i	−0.130267	−	0.357906i
$21$		0			0
$22$	−60.3613	+	50.6491i	−0.124713	+	0.104647i
$23$	240.426	−	660.564i	0.454491	−	1.24870i	−0.475041	−	0.879963i	$-0.657567\pi$
$23$	240.426	−	660.564i	0.454491	−	1.24870i	0.929532	−	0.368740i	$-0.120211\pi$
$24$		0			0
$25$	−203.361	+	1153.32i	−0.325378	+	1.84531i
$26$			542.162i			0.802016i
$27$		0			0
$28$	−187.864			−0.239623
$29$	−809.117	−	142.669i	−0.962090	−	0.169642i	−0.329522	−	0.944148i	$-0.606888\pi$
$29$	−809.117	−	142.669i	−0.962090	−	0.169642i	−0.632567	+	0.774505i	$0.717999\pi$
$30$		0			0
$31$	−367.484	−	133.753i	−0.382397	−	0.139181i	0.143667	−	0.989626i	$-0.454111\pi$
$31$	−367.484	−	133.753i	−0.382397	−	0.139181i	−0.526064	+	0.850445i	$0.676333\pi$
$32$	−290.544	−	346.257i	−0.283735	−	0.338142i
$33$		0			0
$34$	1811.86	−	659.462i	1.56735	−	0.570469i
$35$	1918.07	+	1107.40i	1.56577	+	0.903998i
$36$		0			0
$37$	−905.030	−	1567.56i	−0.661088	−	1.14504i	−0.980330	−	0.197365i	$-0.936762\pi$
$37$	−905.030	−	1567.56i	−0.661088	−	1.14504i	0.319242	−	0.947673i	$-0.396572\pi$
$38$	372.348	−	443.747i	0.257859	−	0.307304i
$39$		0			0
$40$	404.120	+	2291.88i	0.252575	+	1.43242i
$41$	−1779.62	+	313.795i	−1.05867	+	0.186672i	−0.675766	−	0.737117i	$-0.736187\pi$
$41$	−1779.62	+	313.795i	−1.05867	+	0.186672i	−0.382903	+	0.923789i	$0.625076\pi$
$42$		0			0
$43$	201.781	+	169.314i	0.109130	+	0.0915706i	0.695720	−	0.718313i	$-0.255086\pi$
$43$	201.781	+	169.314i	0.109130	+	0.0915706i	−0.586590	+	0.809884i	$0.699530\pi$
$44$	−55.4168	+	31.9949i	−0.0286244	+	0.0165263i
$45$		0			0
$46$	1555.86	−	2694.82i	0.735283	−	1.27355i
$47$	−31.4023	−	86.2770i	−0.0142156	−	0.0390570i	0.932382	−	0.361475i	$-0.117727\pi$
$47$	−31.4023	−	86.2770i	−0.0142156	−	0.0390570i	−0.946597	+	0.322418i	$0.895504\pi$
$48$		0			0
$49$	252.856	−	212.171i	0.105313	−	0.0883679i
$50$	−1773.05	+	4871.41i	−0.709219	+	1.94856i
$51$		0			0
$52$	−76.4550	+	433.598i	−0.0282748	+	0.160354i
$53$			1069.64i			0.380791i	0.981707	+	0.190395i	$0.0609770\pi$
$53$			1069.64i			0.380791i	−0.981707	+	0.190395i	$0.939023\pi$
$54$		0			0
$55$	754.398			0.249388
$56$	2826.13	+	498.323i	0.901190	+	0.158904i
$57$		0			0
$58$	−3417.56	−	1243.89i	−1.01592	−	0.369766i
$59$	−239.279	−	285.161i	−0.0687385	−	0.0819194i	0.730579	−	0.682828i	$-0.239250\pi$
$59$	−239.279	−	285.161i	−0.0687385	−	0.0819194i	−0.799318	+	0.600908i	$0.794806\pi$
$60$		0			0
$61$	1175.69	−	427.916i	0.315961	−	0.115000i	−0.179172	−	0.983818i	$-0.557342\pi$
$61$	1175.69	−	427.916i	0.315961	−	0.115000i	0.495132	+	0.868818i	$0.335120\pi$
$62$	−1499.18	−	865.552i	−0.390005	−	0.225170i
$63$		0			0
$64$	1404.33	+	2432.37i	0.342853	+	0.593839i
$65$	3336.51	−	3976.30i	0.789707	−	0.941137i
$66$		0			0
$67$	781.472	+	4431.95i	0.174086	+	0.987291i	0.939194	+	0.343388i	$0.111575\pi$
$67$	781.472	+	4431.95i	0.174086	+	0.987291i	−0.765108	+	0.643903i	$0.777314\pi$
$68$	1542.04	−	271.903i	0.333486	−	0.0588026i
$69$		0			0
$70$	7510.32	+	6301.90i	1.53272	+	1.28610i
$71$	4815.68	−	2780.33i	0.955303	−	0.551544i	0.0605786	−	0.998163i	$-0.480705\pi$
$71$	4815.68	−	2780.33i	0.955303	−	0.551544i	0.894724	+	0.446619i	$0.147372\pi$
$72$		0			0
$73$	−1761.03	+	3050.19i	−0.330461	+	0.572375i	−0.982602	−	0.185722i	$-0.940538\pi$
$73$	−1761.03	+	3050.19i	−0.330461	+	0.572375i	0.652141	+	0.758097i	$0.273871\pi$
$74$	−2740.41	−	7529.21i	−0.500440	−	1.37495i
$75$		0			0
$76$	360.364	−	302.381i	0.0623899	−	0.0523513i
$77$	318.165	−	874.152i	0.0536626	−	0.147437i
$78$		0			0
$79$	1741.86	−	9878.58i	0.279099	−	1.58285i	−0.446532	−	0.894768i	$-0.647341\pi$
$79$	1741.86	−	9878.58i	0.279099	−	1.58285i	0.725631	−	0.688084i	$-0.241548\pi$
$80$			12739.4i			1.99052i
$81$		0			0
$82$	−7999.21			−1.18965
$83$	−4460.90	−	786.577i	−0.647540	−	0.114179i	−0.159775	−	0.987154i	$-0.551077\pi$
$83$	−4460.90	−	786.577i	−0.647540	−	0.114179i	−0.487765	+	0.872975i	$0.662188\pi$
$84$		0			0
$85$	−17346.8	−	6313.72i	−2.40094	−	0.873871i
$86$	749.486	+	893.203i	0.101337	+	0.120768i
$87$		0			0
$88$	918.530	−	334.318i	0.118612	−	0.0431712i
$89$	−11590.4	−	6691.71i	−1.46325	−	0.844807i	−0.464088	−	0.885789i	$-0.653618\pi$
$89$	−11590.4	−	6691.71i	−1.46325	−	0.844807i	−0.999160	+	0.0409821i	$0.986951\pi$
$90$		0			0
$91$	−3200.34	−	5543.15i	−0.386468	−	0.669382i
$92$	1624.33	−	1935.80i	0.191910	−	0.228710i
$93$		0			0
$94$	−70.5749	−	400.250i	−0.00798720	−	0.0452976i
$95$	−5461.71	+	963.047i	−0.605176	+	0.106709i
$96$		0			0
$97$	−5334.35	−	4476.05i	−0.566942	−	0.475721i	0.313688	−	0.949526i	$-0.398435\pi$
$97$	−5334.35	−	4476.05i	−0.566942	−	0.475721i	−0.880629	+	0.473806i	$0.842880\pi$
$98$	1265.38	−	730.567i	0.131755	−	0.0760690i
$99$		0			0
$100$	−2104.96	+	3645.90i	−0.210496	+	0.364590i
$101$	1327.24	+	3646.56i	0.130109	+	0.357471i	0.987592	−	0.157041i	$-0.0501954\pi$
$101$	1327.24	+	3646.56i	0.130109	+	0.357471i	−0.857483	+	0.514512i	$0.827973\pi$
$102$		0			0
$103$	6389.00	−	5361.01i	0.602224	−	0.505326i	−0.289935	−	0.957046i	$-0.593634\pi$
$103$	6389.00	−	5361.01i	0.602224	−	0.505326i	0.892160	+	0.451720i	$0.149189\pi$
$104$	2300.30	−	6320.02i	0.212676	−	0.584321i
$105$		0			0
$106$	−822.203	+	4662.94i	−0.0731758	+	0.415000i
$107$		−	12245.4i		−	1.06956i	−0.844991	−	0.534781i	$-0.820394\pi$
$107$		−	12245.4i		−	1.06956i	0.844991	−	0.534781i	$-0.179606\pi$
$108$		0			0
$109$	21833.7			1.83770			0.918852	−	0.394603i	$-0.129118\pi$
$109$	21833.7			1.83770			0.918852	+	0.394603i	$0.129118\pi$
$110$	3288.69	+	579.884i	0.271792	+	0.0479243i
$111$		0			0
$112$	14761.6	+	5372.79i	1.17679	+	0.428315i
$113$	−325.882	−	388.371i	−0.0255213	−	0.0304151i	0.753133	−	0.657868i	$-0.228542\pi$
$113$	−325.882	−	388.371i	−0.0255213	−	0.0304151i	−0.778654	+	0.627453i	$0.784097\pi$
$114$		0			0
$115$	−27995.1	+	10189.4i	−2.11683	+	0.770463i
$116$	−2557.81	−	1476.75i	−0.190087	−	0.109747i
$117$		0			0
$118$	−823.905	−	1427.05i	−0.0591716	−	0.102488i
$119$	−14631.9	+	17437.7i	−1.03326	+	1.23139i
$120$		0			0
$121$	2487.36	+	14106.5i	0.169890	+	0.963495i
$122$	5454.17	−	961.718i	0.366445	−	0.0646142i
$123$		0			0
$124$	−1076.92	−	903.643i	−0.0700390	−	0.0587697i
$125$	20043.7	−	11572.2i	1.28280	−	0.740623i
$126$		0			0
$127$	4191.94	−	7260.66i	0.259901	−	0.450162i	−0.706314	−	0.707899i	$-0.749643\pi$
$127$	4191.94	−	7260.66i	0.259901	−	0.450162i	0.966215	+	0.257737i	$0.0829767\pi$
$128$	6725.80	+	18479.0i	0.410510	+	1.12787i
$129$		0			0
$130$	17601.5	−	14769.4i	1.04151	−	0.873930i
$131$	433.685	−	1191.54i	0.0252716	−	0.0694330i	−0.926415	−	0.376503i	$-0.877126\pi$
$131$	433.685	−	1191.54i	0.0252716	−	0.0694330i	0.951687	+	0.307070i	$0.0993486\pi$
$132$		0			0
$133$	−1187.54	+	6734.87i	−0.0671344	+	0.380738i
$134$			19921.1i			1.10944i
$135$		0			0
$136$	−23918.9			−1.29319
$137$	6325.87	+	1115.42i	0.337038	+	0.0594290i	0.339606	−	0.940568i	$-0.389706\pi$
$137$	6325.87	+	1115.42i	0.337038	+	0.0594290i	−0.00256773	+	0.999997i	$0.500817\pi$
$138$		0			0
$139$	25528.9	+	9291.76i	1.32130	+	0.480915i	0.903876	−	0.427795i	$-0.140709\pi$
$139$	25528.9	+	9291.76i	1.32130	+	0.480915i	0.417428	+	0.908710i	$0.362932\pi$
$140$	5117.74	+	6099.08i	0.261109	+	0.311178i
$141$		0			0
$142$	23130.4	−	8418.78i	1.14711	−	0.417516i
$143$	−1888.09	−	1090.09i	−0.0923318	−	0.0533078i
$144$		0			0
$145$	17409.9	+	30154.9i	0.828058	+	1.43424i
$146$	−10021.5	+	11943.2i	−0.470141	+	0.560292i
$147$		0			0
$148$	−1129.90	−	6407.98i	−0.0515842	−	0.292548i
$149$	20092.3	−	3542.81i	0.905016	−	0.159579i	0.298277	−	0.954479i	$-0.403588\pi$
$149$	20092.3	−	3542.81i	0.905016	−	0.159579i	0.606740	+	0.794901i	$0.292477\pi$
$150$		0			0
$151$	−19325.9	−	16216.3i	−0.847589	−	0.711211i	0.111669	−	0.993745i	$-0.464380\pi$
$151$	−19325.9	−	16216.3i	−0.847589	−	0.711211i	−0.959257	+	0.282534i	$0.908825\pi$
$152$	−6223.22	+	3592.98i	−0.269357	+	0.155513i
$153$		0			0
$154$	2058.93	−	3566.17i	0.0868161	−	0.150370i
$155$	5668.53	+	15574.2i	0.235943	+	0.648249i
$156$		0			0
$157$	3606.81	−	3026.47i	0.146327	−	0.122783i	−0.566686	−	0.823934i	$-0.691775\pi$
$157$	3606.81	−	3026.47i	0.146327	−	0.122783i	0.713013	+	0.701151i	$0.247330\pi$
$158$	15186.8	−	41725.3i	0.608346	−	1.67142i
$159$		0			0
$160$	−3326.46	+	18865.3i	−0.129940	+	0.736925i
$161$			36736.4i			1.41724i
$162$		0			0
$163$	21591.9			0.812674			0.406337	−	0.913723i	$-0.366806\pi$
$163$	21591.9			0.812674			0.406337	+	0.913723i	$0.366806\pi$
$164$	−6397.42	−	1128.04i	−0.237858	−	0.0419407i
$165$		0			0
$166$	−18842.0	−	6857.94i	−0.683772	−	0.248873i
$167$	−3328.14	−	3966.32i	−0.119335	−	0.142218i	0.703069	−	0.711121i	$-0.251812\pi$
$167$	−3328.14	−	3966.32i	−0.119335	−	0.142218i	−0.822405	+	0.568903i	$0.807368\pi$
$168$		0			0
$169$	12742.3	−	4637.82i	0.446144	−	0.162383i
$170$	−70767.7	−	40857.7i	−2.44871	−	1.41376i
$171$		0			0
$172$	473.448	+	820.036i	0.0160035	+	0.0277189i
$173$	−1271.62	+	1515.46i	−0.0424878	+	0.0506350i	−0.786870	−	0.617119i	$-0.788300\pi$
$173$	−1271.62	+	1515.46i	−0.0424878	+	0.0506350i	0.744382	+	0.667754i	$0.232744\pi$
$174$		0			0
$175$	−10627.6	−	60272.1i	−0.347024	−	1.96807i
$176$	5269.46	−	929.148i	0.170114	−	0.0299957i
$177$		0			0
$178$	−45382.9	−	38080.8i	−1.43236	−	1.20189i
$179$	40882.5	−	23603.5i	1.27594	−	0.736666i	0.299842	−	0.953989i	$-0.403066\pi$
$179$	40882.5	−	23603.5i	1.27594	−	0.736666i	0.976100	+	0.217323i	$0.0697326\pi$
$180$		0			0
$181$	−27157.1	+	47037.5i	−0.828946	+	1.43578i	0.0699192	+	0.997553i	$0.477726\pi$
$181$	−27157.1	+	47037.5i	−0.828946	+	1.43578i	−0.898866	+	0.438225i	$0.855607\pi$
$182$	−9690.55	−	26624.6i	−0.292554	−	0.803785i
$183$		0			0
$184$	−29570.4	+	24812.5i	−0.873417	+	0.732884i
$185$	−26236.8	+	72085.0i	−0.766598	+	2.10621i
$186$		0			0
$187$	−1346.39	+	7635.77i	−0.0385024	+	0.218358i
$188$		−	330.055i		−	0.00933835i
$189$		0			0
$190$	−24549.8			−0.680050
$191$	−44953.9	−	7926.59i	−1.23226	−	0.217280i	−0.480662	−	0.876906i	$-0.659604\pi$
$191$	−44953.9	−	7926.59i	−1.23226	−	0.217280i	−0.751594	+	0.659626i	$0.770715\pi$
$192$		0			0
$193$	20916.3	+	7612.90i	0.561526	+	0.204379i	0.607160	−	0.794580i	$-0.292309\pi$
$193$	20916.3	+	7612.90i	0.561526	+	0.204379i	−0.0456344	+	0.998958i	$0.514531\pi$
$194$	−19813.7	−	23613.1i	−0.526457	−	0.627406i
$195$		0			0
$196$	1115.02	−	405.833i	0.0290248	−	0.0105642i
$197$	−34055.1	−	19661.7i	−0.877506	−	0.506628i	−0.00767091	−	0.999971i	$-0.502442\pi$
$197$	−34055.1	−	19661.7i	−0.877506	−	0.506628i	−0.869835	+	0.493342i	$0.835775\pi$
$198$		0			0
$199$	−12706.2	−	22007.8i	−0.320856	−	0.555739i	0.659809	−	0.751433i	$-0.270637\pi$
$199$	−12706.2	−	22007.8i	−0.320856	−	0.555739i	−0.980665	+	0.195694i	$0.937304\pi$
$200$	41337.0	−	49263.5i	1.03343	−	1.23159i
$201$		0			0
$202$	2982.90	+	16916.9i	0.0731031	+	0.414589i
$203$	42284.3	−	7455.86i	1.02609	−	0.180928i
$204$		0			0
$205$	58667.4	+	49227.8i	1.39601	+	1.17139i
$206$	31972.8	−	18459.5i	0.753435	−	0.434996i
$207$		0			0
$208$	18408.1	−	31883.8i	0.425484	−	0.736960i
$209$	796.703	+	2188.92i	0.0182391	+	0.0501116i
$210$		0			0
$211$	−27165.9	+	22794.9i	−0.610183	+	0.512004i	−0.894700	−	0.446667i	$-0.852611\pi$
$211$	−27165.9	+	22794.9i	−0.610183	+	0.512004i	0.284518	+	0.958671i	$0.408167\pi$
$212$	−1315.12	+	3613.27i	−0.0292614	+	0.0803950i
$213$		0			0
$214$	9412.70	−	53382.1i	0.205535	−	1.16565i
$215$		−	11163.3i		−	0.241499i
$216$		0			0
$217$	20437.1			0.434011
$218$	95181.0	+	16783.0i	2.00280	+	0.353148i
$219$		0			0
$220$	2548.37	+	927.532i	0.0526523	+	0.0191639i
$221$	34292.1	+	40867.7i	0.702116	+	0.836750i
$222$		0			0
$223$	−62151.6	+	22621.3i	−1.24981	+	0.454892i	−0.880336	−	0.474350i	$-0.842683\pi$
$223$	−62151.6	+	22621.3i	−1.24981	+	0.454892i	−0.369470	+	0.929243i	$0.620461\pi$
$224$	20457.0	+	11810.9i	0.407706	+	0.235389i
$225$		0			0
$226$	−1122.10	−	1943.54i	−0.0219693	−	0.0380520i
$227$	928.758	−	1106.85i	0.0180240	−	0.0214802i	−0.756957	−	0.653465i	$-0.773315\pi$
$227$	928.758	−	1106.85i	0.0180240	−	0.0214802i	0.774981	+	0.631984i	$0.217759\pi$
$228$		0			0
$229$	−9704.08	−	55034.6i	−0.185048	−	1.04946i	−0.925894	−	0.377783i	$-0.876687\pi$
$229$	−9704.08	−	55034.6i	−0.185048	−	1.04946i	0.740847	−	0.671674i	$-0.234425\pi$
$230$	−129873.	+	22900.1i	−2.45506	+	0.432893i
$231$		0			0
$232$	34561.1	+	29000.2i	0.642114	+	0.538797i
$233$	−58380.7	+	33706.1i	−1.07537	+	0.620864i	−0.929643	−	0.368461i	$-0.879885\pi$
$233$	−58380.7	+	33706.1i	−1.07537	+	0.620864i	−0.145725	+	0.989325i	$0.546551\pi$
$234$		0			0
$235$	−1945.57	+	3369.82i	−0.0352298	+	0.0610198i
$236$	−457.683	−	1257.47i	−0.00821753	−	0.0225775i
$237$		0			0
$238$	−77189.6	+	64769.8i	−1.36272	+	1.14345i
$239$	19327.5	−	53101.8i	0.338360	−	0.929637i	−0.647500	−	0.762066i	$-0.724185\pi$
$239$	19327.5	−	53101.8i	0.338360	−	0.929637i	0.985860	−	0.167571i	$-0.0535924\pi$
$240$		0			0
$241$	6917.70	−	39232.2i	0.119104	−	0.675474i	−0.865532	−	0.500854i	$-0.833019\pi$
$241$	6917.70	−	39232.2i	0.119104	−	0.675474i	0.984636	−	0.174620i	$-0.0558697\pi$
$242$			63407.3i			1.08270i
$243$		0			0
$244$	4497.63			0.0755447
$245$	−13776.5	−	2429.16i	−0.229512	−	0.0404691i
$246$		0			0
$247$	15061.1	+	5481.78i	0.246866	+	0.0898519i
$248$	13803.6	+	16450.5i	0.224435	+	0.267471i
$249$		0			0
$250$	96272.8	−	35040.4i	1.54036	−	0.560647i
$251$	55624.5	+	32114.8i	0.882915	+	0.509751i	0.871618	−	0.490185i	$-0.163071\pi$
$251$	55624.5	+	32114.8i	0.882915	+	0.509751i	0.0112966	+	0.999936i	$0.496404\pi$
$252$		0			0
$253$	6256.53	+	10836.6i	0.0977445	+	0.169298i
$254$	23855.2	−	28429.6i	0.369757	−	0.440659i
$255$		0			0
$256$	7312.37	+	41470.5i	0.111578	+	0.632790i
$257$	3054.16	−	538.531i	0.0462409	−	0.00815351i	−0.150480	−	0.988613i	$-0.548082\pi$
$257$	3054.16	−	538.531i	0.0462409	−	0.00815351i	0.196721	+	0.980460i	$0.436971\pi$
$258$		0			0
$259$	72462.6	+	60803.4i	1.08023	+	0.906417i
$260$	16159.7	−	9329.80i	0.239049	−	0.138015i
$261$		0			0
$262$	2806.49	−	4860.98i	0.0408847	−	0.0708144i
$263$	−44238.4	−	121544.i	−0.639570	−	1.75720i	−0.653073	−	0.757295i	$-0.726520\pi$
$263$	−44238.4	−	121544.i	−0.639570	−	1.75720i	0.0135029	−	0.999909i	$-0.495702\pi$
$264$		0			0
$265$	34726.3	−	29138.8i	0.494501	−	0.414935i
$266$	−10353.8	+	28446.9i	−0.146331	+	0.402042i
$267$		0			0
$268$	−2809.25	+	15932.0i	−0.0391130	+	0.221821i
$269$			10362.6i			0.143207i	0.997433	+	0.0716037i	$0.0228117\pi$
$269$			10362.6i			0.143207i	−0.997433	+	0.0716037i	$0.977188\pi$
$270$		0			0
$271$	−42827.0			−0.583149			−0.291574	−	0.956548i	$-0.594179\pi$
$271$	−42827.0			−0.583149			−0.291574	+	0.956548i	$0.594179\pi$
$272$	−128944.	−	22736.2i	−1.74286	−	0.307313i
$273$		0			0
$274$	26719.3	+	9725.04i	0.355897	+	0.129536i
$275$	−13399.8	−	15969.3i	−0.177188	−	0.211164i
$276$		0			0
$277$	−21952.1	+	7989.92i	−0.286099	+	0.104132i	−0.481084	−	0.876675i	$-0.659757\pi$
$277$	−21952.1	+	7989.92i	−0.286099	+	0.104132i	0.194984	+	0.980806i	$0.437534\pi$
$278$	104147.	+	60129.4i	1.34759	+	0.778032i
$279$		0			0
$280$	−60810.4	−	105327.i	−0.775642	−	1.34345i
$281$	−66242.6	+	78944.8i	−0.838927	+	0.999795i	0.160990	+	0.986956i	$0.448531\pi$
$281$	−66242.6	+	78944.8i	−0.838927	+	0.999795i	−0.999918	+	0.0128388i	$0.995913\pi$
$282$		0			0
$283$	−3530.34	−	20021.5i	−0.0440802	−	0.249991i	0.954803	−	0.297239i	$-0.0960659\pi$
$283$	−3530.34	−	20021.5i	−0.0440802	−	0.249991i	−0.998883	+	0.0472483i	$0.984955\pi$
$284$	19685.9	−	3471.16i	0.244072	−	0.0430365i
$285$		0			0
$286$	−7392.94	−	6203.42i	−0.0903827	−	0.0758401i
$287$	81785.1	−	47218.6i	0.992911	−	0.573257i
$288$		0			0
$289$	53104.2	−	91979.1i	0.635818	−	1.10127i
$290$	52716.8	+	144838.i	0.626835	+	1.72221i
$291$		0			0
$292$	−9698.99	+	8138.42i	−0.113752	+	0.0954497i
$293$	−27201.9	+	74736.6i	−0.316858	+	0.870559i	0.674370	+	0.738394i	$0.264415\pi$
$293$	−27201.9	+	74736.6i	−0.316858	+	0.870559i	−0.991228	+	0.132166i	$0.957807\pi$
$294$		0			0
$295$	−2739.51	+	15536.6i	−0.0314796	+	0.178530i
$296$			99395.5i			1.13444i
$297$		0			0
$298$	90312.6			1.01699
$299$	84789.0	+	14950.6i	0.948412	+	0.167231i
$300$		0			0
$301$	−12935.4	−	4708.09i	−0.142773	−	0.0519651i
$302$	−71783.2	−	85547.9i	−0.787062	−	0.937985i
$303$		0			0
$304$	−36963.9	+	13453.7i	−0.399973	+	0.145578i
$305$	−45920.2	−	26512.1i	−0.493633	−	0.284999i
$306$		0			0
$307$	10753.3	+	18625.2i	0.114094	+	0.197617i	0.917417	−	0.397926i	$-0.130270\pi$
$307$	10753.3	+	18625.2i	0.114094	+	0.197617i	−0.803323	+	0.595544i	$0.796937\pi$
$308$	2149.54	−	2561.72i	0.0226592	−	0.0270041i
$309$		0			0
$310$	12739.7	+	72250.6i	0.132567	+	0.751827i
$311$	−90486.2	+	15955.2i	−0.935539	+	0.164961i	−0.620579	−	0.784144i	$-0.713102\pi$
$311$	−90486.2	+	15955.2i	−0.935539	+	0.164961i	−0.314960	+	0.949105i	$0.601991\pi$
$312$		0			0
$313$	−45646.6	−	38302.0i	−0.465929	−	0.390961i	0.379378	−	0.925242i	$-0.376138\pi$
$313$	−45646.6	−	38302.0i	−0.465929	−	0.390961i	−0.845307	+	0.534281i	$0.820582\pi$
$314$	18049.7	−	10421.0i	0.183068	−	0.105694i
$315$		0			0
$316$	18029.7	−	31228.4i	0.180557	−	0.312735i
$317$	−16439.9	−	45168.1i	−0.163599	−	0.449483i	0.830622	−	0.556836i	$-0.187985\pi$
$317$	−16439.9	−	45168.1i	−0.163599	−	0.449483i	−0.994221	+	0.107353i	$0.965763\pi$
$318$		0			0
$319$	11203.4	−	9400.73i	0.110095	−	0.0923805i
$320$	40711.5	−	111854.i	0.397573	−	1.09232i
$321$		0			0
$322$	−28238.2	+	160147.i	−0.272349	+	1.54457i
$323$		−	57000.4i		−	0.546352i
$324$		0			0
$325$	−143436.			−1.35797
$326$	94126.9	+	16597.1i	0.885683	+	0.156170i
$327$		0			0
$328$	93247.2	+	33939.2i	0.866739	+	0.315467i
$329$	3084.21	+	3675.62i	0.0284939	+	0.0339577i
$330$		0			0
$331$	−66799.4	+	24313.0i	−0.609701	+	0.221913i	−0.628372	−	0.777913i	$-0.716279\pi$
$331$	−66799.4	+	24313.0i	−0.609701	+	0.221913i	0.0186716	+	0.999826i	$0.494056\pi$
$332$	−14101.9	−	8141.76i	−0.127939	−	0.0738655i
$333$		0			0
$334$	−11459.7	−	19848.9i	−0.102726	−	0.177927i
$335$	122596.	−	146105.i	1.09241	−	1.30189i
$336$		0			0
$337$	27724.6	+	157234.i	0.244121	+	1.38448i	0.822526	+	0.568728i	$0.192564\pi$
$337$	27724.6	+	157234.i	0.244121	+	1.38448i	−0.578405	+	0.815750i	$0.696325\pi$
$338$	59113.2	−	10423.3i	0.517429	−	0.0912368i
$339$		0			0
$340$	−50835.2	−	42655.8i	−0.439751	−	0.368995i
$341$	6028.61	−	3480.62i	0.0518452	−	0.0299328i
$342$		0			0
$343$	54112.9	−	93726.2i	0.459952	−	0.796660i
$344$	−4947.10	−	13592.1i	−0.0418056	−	0.114860i
$345$		0			0
$346$	−6708.32	+	5628.95i	−0.0560353	+	0.0470192i
$347$	−28075.2	+	77135.9i	−0.233165	+	0.640616i	−0.999999	−	0.00122960i	$-0.999609\pi$
$347$	−28075.2	+	77135.9i	−0.233165	+	0.640616i	0.766834	+	0.641845i	$0.221831\pi$
$348$		0			0
$349$	9101.46	−	51616.9i	0.0747240	−	0.423781i	−0.924381	−	0.381472i	$-0.875417\pi$
$349$	9101.46	−	51616.9i	0.0747240	−	0.423781i	0.999105	−	0.0423093i	$-0.0134715\pi$
$350$		−	270917.i		−	2.21156i
$351$		0			0
$352$	8045.98			0.0649372
$353$	−118759.	−	20940.4i	−0.953051	−	0.168049i	−0.324560	−	0.945865i	$-0.605216\pi$
$353$	−118759.	−	20940.4i	−0.953051	−	0.168049i	−0.628491	+	0.777817i	$0.716327\pi$
$354$		0			0
$355$	−221452.	−	80601.9i	−1.75721	−	0.639571i
$356$	−30925.1	−	36855.1i	−0.244012	−	0.290803i
$357$		0			0
$358$	196364.	−	71470.8i	1.53213	−	0.557651i
$359$	9051.70	+	5226.00i	0.0702330	+	0.0405491i	0.534705	−	0.845039i	$-0.320423\pi$
$359$	9051.70	+	5226.00i	0.0702330	+	0.0405491i	−0.464472	+	0.885588i	$0.653756\pi$
$360$		0			0
$361$	56598.2	+	98030.9i	0.434298	+	0.752227i
$362$	−154544.	+	184178.i	−1.17933	+	1.40547i
$363$		0			0
$364$	−3995.52	−	22659.7i	−0.0301558	−	0.171022i
$365$	146999.	−	25919.9i	1.10339	−	0.194557i
$366$		0			0
$367$	−109964.	−	92270.6i	−0.816427	−	0.685064i	0.135705	−	0.990749i	$-0.456670\pi$
$367$	−109964.	−	92270.6i	−0.816427	−	0.685064i	−0.952133	+	0.305685i	$0.901114\pi$
$368$	−182996.	+	105653.i	−1.35128	+	0.780162i
$369$		0			0
$370$	−169785.	+	294077.i	−1.24021	+	2.14811i
$371$	−19118.6	−	52528.0i	−0.138902	−	0.381631i
$372$		0			0
$373$	107946.	−	90577.5i	0.775870	−	0.651033i	−0.166335	−	0.986069i	$-0.553193\pi$
$373$	107946.	−	90577.5i	0.775870	−	0.651033i	0.942205	+	0.335037i	$0.108749\pi$
$374$	−11738.8	+	32252.1i	−0.0839229	+	0.230576i
$375$		0			0
$376$	−875.494	+	4965.17i	−0.00619266	+	0.0351203i
$377$		−	100628.i		−	0.708005i
$378$		0			0
$379$	10893.2			0.0758359			0.0379180	−	0.999281i	$-0.487927\pi$
$379$	10893.2			0.0758359			0.0379180	+	0.999281i	$0.487927\pi$
$380$	−19633.9	−	3461.98i	−0.135968	−	0.0239749i
$381$		0			0
$382$	−189877.	−	69109.6i	−1.30121	−	0.473600i
$383$	24052.4	+	28664.5i	0.163969	+	0.195410i	0.841772	−	0.539833i	$-0.181513\pi$
$383$	24052.4	+	28664.5i	0.163969	+	0.195410i	−0.677804	+	0.735243i	$0.737068\pi$
$384$		0			0
$385$	−37047.0	+	13484.0i	−0.249938	+	0.0909699i
$386$	85329.6	+	49265.1i	0.572697	+	0.330647i
$387$		0			0
$388$	−12516.3	−	21678.8i	−0.0831402	−	0.144003i
$389$	−9786.81	+	11663.5i	−0.0646758	+	0.0770777i	−0.797412	−	0.603435i	$-0.793798\pi$
$389$	−9786.81	+	11663.5i	−0.0646758	+	0.0770777i	0.732736	+	0.680512i	$0.238243\pi$
$390$		0			0
$391$	−53170.0	−	301542.i	−0.347787	−	1.97240i
$392$	−17850.3	+	3147.48i	−0.116164	+	0.0204829i
$393$		0			0
$394$	−133345.	−	111890.i	−0.858982	−	0.720772i
$395$	−368163.	+	212559.i	−2.35964	+	1.36234i
$396$		0			0
$397$	−112818.	+	195407.i	−0.715810	+	1.23982i	0.246836	+	0.969057i	$0.420609\pi$
$397$	−112818.	+	195407.i	−0.715810	+	1.23982i	−0.962646	+	0.270762i	$0.912724\pi$
$398$	−38474.1	−	105707.i	−0.242886	−	0.667324i
$399$		0			0
$400$	269670.	−	226280.i	1.68544	−	1.41425i
$401$	64345.7	−	176788.i	0.400157	−	1.09942i	−0.562049	−	0.827104i	$-0.689987\pi$
$401$	64345.7	−	176788.i	0.400157	−	1.09942i	0.962207	−	0.272320i	$-0.0877908\pi$
$402$		0			0
$403$	8317.29	−	47169.7i	0.0512120	−	0.290438i
$404$			13950.0i			0.0854697i
$405$		0			0
$406$	190063.			1.15304
$407$	31730.6	+	5594.96i	0.191553	+	0.0337760i
$408$		0			0
$409$	12257.3	+	4461.29i	0.0732738	+	0.0266695i	0.378397	−	0.925643i	$-0.376475\pi$
$409$	12257.3	+	4461.29i	0.0732738	+	0.0266695i	−0.305123	+	0.952313i	$0.598698\pi$
$410$	217912.	+	259697.i	1.29632	+	1.54490i
$411$		0			0
$412$	28173.5	−	10254.3i	0.165977	−	0.0604106i
$413$	16847.5	+	9726.89i	0.0987721	+	0.0570261i
$414$		0			0
$415$	95986.0	+	166253.i	0.557329	+	0.965322i
$416$	35585.4	−	42409.0i	0.205629	−	0.245059i
$417$		0			0
$418$	1790.55	+	10154.7i	0.0102479	+	0.0581185i
$419$	281965.	−	49718.0i	1.60608	−	0.283195i	0.702522	−	0.711662i	$-0.252057\pi$
$419$	281965.	−	49718.0i	1.60608	−	0.283195i	0.903557	+	0.428467i	$0.140946\pi$
$420$		0			0
$421$	222464.	+	186669.i	1.25515	+	1.05319i	0.996181	+	0.0873075i	$0.0278263\pi$
$421$	222464.	+	186669.i	1.25515	+	1.05319i	0.258966	+	0.965886i	$0.416618\pi$
$422$	−135948.	+	78489.5i	−0.763391	+	0.440744i
$423$		0			0
$424$	29368.5	−	50867.8i	0.163362	−	0.282951i
$425$	174468.	+	479348.i	0.965915	+	2.65383i
$426$		0			0
$427$	−50087.3	+	42028.3i	−0.274709	+	0.230508i
$428$	15055.7	−	41365.3i	0.0821891	−	0.225813i
$429$		0			0
$430$	8580.90	−	48664.7i	0.0464083	−	0.263195i
$431$		−	227489.i		−	1.22463i	−0.790612	−	0.612317i	$-0.790237\pi$
$431$		−	227489.i		−	1.22463i	0.790612	−	0.612317i	$-0.209763\pi$
$432$		0			0
$433$	70235.0			0.374608			0.187304	−	0.982302i	$-0.440025\pi$
$433$	70235.0			0.374608			0.187304	+	0.982302i	$0.440025\pi$
$434$	89092.7	+	15709.4i	0.473001	+	0.0834029i
$435$		0			0
$436$	73754.9	+	26844.6i	0.387988	+	0.141216i
$437$	−59130.0	−	70468.3i	−0.309631	−	0.369004i
$438$		0			0
$439$	51104.1	−	18600.4i	0.265172	−	0.0965146i	−0.206013	−	0.978549i	$-0.566049\pi$
$439$	51104.1	−	18600.4i	0.265172	−	0.0965146i	0.471184	+	0.882035i	$0.343827\pi$
$440$	−35876.1	−	20713.1i	−0.185310	−	0.106989i
$441$		0			0
$442$	118077.	+	204516.i	0.604397	+	1.04685i
$443$	55328.2	−	65937.6i	0.281929	−	0.335989i	−0.606432	−	0.795135i	$-0.707400\pi$
$443$	55328.2	−	65937.6i	0.281929	−	0.335989i	0.888361	+	0.459146i	$0.151844\pi$
$444$		0			0
$445$	98492.7	+	558580.i	0.497375	+	2.82075i
$446$	−288329.	+	50840.2i	−1.44950	+	0.255586i
$447$		0			0
$448$	−112440.	−	94348.1i	−0.560226	−	0.470086i
$449$	218166.	−	125958.i	1.08217	−	0.624788i	0.150685	−	0.988582i	$-0.451852\pi$
$449$	218166.	−	125958.i	1.08217	−	0.624788i	0.931480	+	0.363793i	$0.118519\pi$
$450$		0			0
$451$	16083.5	−	27857.4i	0.0790728	−	0.136958i
$452$	−623.334	−	1712.60i	−0.00305101	−	0.00838259i
$453$		0			0
$454$	4899.59	−	4111.24i	0.0237710	−	0.0199463i
$455$	−92777.8	+	254905.i	−0.448148	+	1.23128i
$456$		0			0
$457$	23424.5	−	132847.i	0.112160	−	0.636090i	−0.875957	−	0.482388i	$-0.839769\pi$
$457$	23424.5	−	132847.i	0.112160	−	0.636090i	0.988117	−	0.153702i	$-0.0491195\pi$
$458$		−	247374.i		−	1.17930i
$459$		0			0
$460$	−107096.			−0.506124
$461$	114630.	+	20212.4i	0.539382	+	0.0951077i	0.436701	−	0.899607i	$-0.356147\pi$
$461$	114630.	+	20212.4i	0.539382	+	0.0951077i	0.102681	+	0.994714i	$0.467258\pi$
$462$		0			0
$463$	174719.	+	63592.5i	0.815038	+	0.296650i	0.715703	−	0.698405i	$-0.246106\pi$
$463$	174719.	+	63592.5i	0.815038	+	0.296650i	0.0993347	+	0.995054i	$0.468329\pi$
$464$	158748.	+	189189.i	0.737348	+	0.878737i
$465$		0			0
$466$	−280411.	+	102061.i	−1.29129	+	0.469990i
$467$	85090.9	+	49127.3i	0.390166	+	0.225262i	0.682232	−	0.731136i	$-0.261009\pi$
$467$	85090.9	+	49127.3i	0.390166	+	0.225262i	−0.292066	+	0.956398i	$0.594343\pi$
$468$		0			0
$469$	−117593.	−	203677.i	−0.534607	−	0.925967i
$470$	−11071.7	+	13194.7i	−0.0501208	+	0.0597317i
$471$		0			0
$472$	3549.61	+	20130.8i	0.0159330	+	0.0903603i
$473$	−4617.54	+	814.197i	−0.0206390	+	0.00363921i
$474$		0			0
$475$	117398.	+	98509.0i	0.520326	+	0.436605i
$476$	−70866.6	+	40914.9i	−0.312772	+	0.180579i
$477$		0			0
$478$	125073.	−	216633.i	0.547404	−	0.948132i
$479$	−19047.2	−	52331.7i	−0.0830156	−	0.228083i	0.891239	−	0.453534i	$-0.149837\pi$
$479$	−19047.2	−	52331.7i	−0.0830156	−	0.228083i	−0.974255	+	0.225450i	$0.927615\pi$
$480$		0			0
$481$	169827.	−	142501.i	0.734033	−	0.615927i
$482$	60313.4	−	165710.i	0.259609	−	0.713270i
$483$		0			0
$484$	−8941.61	+	50710.4i	−0.0381702	+	0.216474i
$485$			295117.i			1.25462i
$486$		0			0
$487$	−97946.7			−0.412983			−0.206491	−	0.978448i	$-0.566205\pi$
$487$	−97946.7			−0.412983			−0.206491	+	0.978448i	$0.566205\pi$
$488$	−67660.0	−	11930.3i	−0.284114	−	0.0500969i
$489$		0			0
$490$	−58189.2	−	21179.1i	−0.242354	−	0.0882096i
$491$	−301734.	−	359593.i	−1.25159	−	1.49158i	−0.800775	−	0.598965i	$-0.795579\pi$
$491$	−301734.	−	359593.i	−1.25159	−	1.49158i	−0.450812	−	0.892619i	$-0.648866\pi$
$492$		0			0
$493$	−336289.	+	122399.i	−1.38363	+	0.503599i
$494$	61442.8	+	35474.0i	0.251777	+	0.145364i
$495$		0			0
$496$	58776.5	+	101804.i	0.238913	+	0.413810i
$497$	−186794.	+	222612.i	−0.756221	+	0.901230i
$498$		0			0
$499$	−44740.9	−	253738.i	−0.179681	−	1.01902i	−0.932600	−	0.360911i	$-0.882466\pi$
$499$	−44740.9	−	253738.i	−0.179681	−	1.01902i	0.752919	−	0.658113i	$-0.228645\pi$
$500$	81936.1	−	14447.5i	0.327744	−	0.0577902i
$501$		0			0
$502$	217801.	+	182757.i	0.864277	+	0.725214i
$503$	16024.7	−	9251.85i	0.0633364	−	0.0365673i	−0.467997	−	0.883730i	$-0.655024\pi$
$503$	16024.7	−	9251.85i	0.0633364	−	0.0365673i	0.531334	+	0.847163i	$0.321691\pi$
$504$		0			0
$505$	82230.8	−	142428.i	0.322442	−	0.558486i
$506$	18944.6	+	52049.9i	0.0739920	+	0.203291i
$507$		0			0
$508$	23087.5	−	19372.7i	0.0894641	−	0.0750693i
$509$	71499.4	−	196443.i	0.275973	−	0.758230i	−0.721836	−	0.692065i	$-0.756701\pi$
$509$	71499.4	−	196443.i	0.275973	−	0.758230i	0.997809	−	0.0661652i	$-0.0210764\pi$
$510$		0			0
$511$	31962.0	−	181265.i	0.122403	−	0.694181i
$512$		−	128233.i		−	0.489170i
$513$		0			0
$514$	13728.1			0.0519619
$515$	−348094.	−	61378.4i	−1.31245	−	0.231420i
$516$		0			0
$517$	1535.78	+	558.978i	0.00574577	+	0.00209129i
$518$	269152.	+	320763.i	1.00309	+	1.19543i
$519$		0			0
$520$	−267846.	+	97487.9i	−0.990554	+	0.360532i
$521$	162542.	+	93843.8i	0.598812	+	0.345724i	0.768574	−	0.639761i	$-0.220967\pi$
$521$	162542.	+	93843.8i	0.598812	+	0.345724i	−0.169762	+	0.985485i	$0.554300\pi$
$522$		0			0
$523$	−153569.	−	265990.i	−0.561436	−	0.972436i	−0.997371	−	0.0724581i	$-0.976916\pi$
$523$	−153569.	−	265990.i	−0.561436	−	0.972436i	0.435935	−	0.899978i	$-0.356418\pi$
$524$	2930.00	−	3491.83i	0.0106710	−	0.0127172i
$525$		0			0
$526$	−99423.4	−	563858.i	−0.359350	−	2.03797i
$527$	−167753.	+	29579.4i	−0.604018	+	0.106505i
$528$		0			0
$529$	−164170.	−	137755.i	−0.586655	−	0.492262i
$530$	173782.	−	100333.i	0.618663	−	0.357185i
$531$		0			0
$532$	−12292.1	+	21290.5i	−0.0434312	+	0.0752250i
$533$	−75698.4	−	207980.i	−0.266460	−	0.732094i
$534$		0			0
$535$	−397552.	+	333586.i	−1.38895	+	1.16547i
$536$	84521.8	−	232222.i	0.294198	−	0.808301i
$537$		0			0
$538$	−7965.46	+	45174.4i	−0.0275199	+	0.156073i
$539$			5875.61i			0.0202244i
$540$		0			0
$541$	−221911.			−0.758201			−0.379101	−	0.925355i	$-0.623767\pi$
$541$	−221911.			−0.758201			−0.379101	+	0.925355i	$0.623767\pi$
$542$	−186698.	−	32919.9i	−0.635538	−	0.112062i
$543$		0			0
$544$	−185011.	−	67338.6i	−0.625173	−	0.227544i
$545$	−594788.	−	708841.i	−2.00249	−	2.38647i
$546$		0			0
$547$	329388.	−	119887.i	1.10086	−	0.400681i	0.273229	−	0.961949i	$-0.411908\pi$
$547$	329388.	−	119887.i	1.10086	−	0.400681i	0.827634	+	0.561268i	$0.189686\pi$
$548$	19997.5	+	11545.6i	0.0665910	+	0.0384463i
$549$		0			0
$550$	−46139.4	−	79915.9i	−0.152527	−	0.264185i
$551$	−69109.6	+	82361.6i	−0.227633	+	0.271282i
$552$		0			0
$553$	91029.1	+	516252.i	0.297667	+	1.68815i
$554$	−101839.	+	17956.9i	−0.331813	+	0.0585075i
$555$		0			0
$556$	74813.0	+	62775.6i	0.242007	+	0.203068i
$557$	−388091.	+	224064.i	−1.25090	+	0.722208i	−0.971289	−	0.237905i	$-0.923539\pi$
$557$	−388091.	+	224064.i	−1.25090	+	0.722208i	−0.279613	+	0.960113i	$0.590206\pi$
$558$		0			0
$559$	−16130.7	+	27939.3i	−0.0516215	+	0.0894111i
$560$	−227702.	−	625605.i	−0.726090	−	1.99491i
$561$		0			0
$562$	−349457.	+	293229.i	−1.10642	+	0.928400i
$563$	−190646.	+	523794.i	−0.601464	+	1.65251i	0.146844	+	0.989160i	$0.453088\pi$
$563$	−190646.	+	523794.i	−0.601464	+	1.65251i	−0.748309	+	0.663350i	$0.769134\pi$
$564$		0			0
$565$	−3731.04	+	21159.8i	−0.0116878	+	0.0662848i
$566$		−	89994.6i		−	0.280921i
$567$		0			0
$568$	−305352.			−0.946464
$569$	310611.	+	54769.1i	0.959383	+	0.169165i	0.631347	−	0.775500i	$-0.282502\pi$
$569$	310611.	+	54769.1i	0.959383	+	0.169165i	0.328036	+	0.944665i	$0.393613\pi$
$570$		0			0
$571$	304743.	+	110917.i	0.934676	+	0.340194i	0.764061	−	0.645143i	$-0.223202\pi$
$571$	304743.	+	110917.i	0.934676	+	0.340194i	0.170615	+	0.985338i	$0.445425\pi$
$572$	−5037.76	−	6003.76i	−0.0153973	−	0.0183498i
$573$		0			0
$574$	392826.	−	142977.i	1.19227	−	0.433952i
$575$	712948.	+	411621.i	2.15636	+	1.24498i
$576$		0			0
$577$	−238820.	−	413649.i	−0.717330	−	1.24245i	−0.962054	−	0.272860i	$-0.912030\pi$
$577$	−238820.	−	413649.i	−0.717330	−	1.24245i	0.244723	−	0.969593i	$-0.421303\pi$
$578$	302201.	−	360150.i	0.904567	−	1.07802i
$579$		0			0
$580$	21735.7	+	123269.i	0.0646127	+	0.366437i
$581$	233126.	−	41106.3i	0.690618	−	0.121775i
$582$		0			0
$583$	−14585.7	−	12238.8i	−0.0429130	−	0.0360083i
$584$	167494.	−	96702.9i	0.491105	−	0.283540i
$585$		0			0
$586$	−176031.	+	304894.i	−0.512617	+	0.887879i
$587$	103294.	+	283799.i	0.299779	+	0.823635i	0.994536	+	0.104391i	$0.0332893\pi$
$587$	103294.	+	283799.i	0.299779	+	0.823635i	−0.694758	+	0.719244i	$0.744488\pi$
$588$		0			0
$589$	−39202.8	+	32895.1i	−0.113002	+	0.0948201i
$590$	−23885.0	+	65623.5i	−0.0686154	+	0.188519i
$591$		0			0
$592$	−94480.9	+	535828.i	−0.269588	+	1.52891i
$593$			6608.51i			0.0187929i	0.999956	+	0.00939645i	$0.00299103\pi$
$593$			6608.51i			0.0187929i	−0.999956	+	0.00939645i	$0.997009\pi$
$594$		0			0
$595$	964719.			2.72500
$596$	72228.0	+	12735.8i	0.203336	+	0.0358535i
$597$		0			0
$598$	358133.	+	130350.i	1.00148	+	0.364509i
$599$	203927.	+	243031.i	0.568356	+	0.677341i	0.971293	−	0.237887i	$-0.0764549\pi$
$599$	203927.	+	243031.i	0.568356	+	0.677341i	−0.402936	+	0.915228i	$0.632010\pi$
$600$		0			0
$601$	616277.	−	224306.i	1.70619	−	0.621002i	0.709682	−	0.704522i	$-0.248839\pi$
$601$	616277.	−	224306.i	1.70619	−	0.621002i	0.996506	+	0.0835209i	$0.0266165\pi$
$602$	−52770.8	−	30467.3i	−0.145613	−	0.0840699i
$603$		0			0
$604$	−45345.2	−	78540.3i	−0.124296	−	0.215287i
$605$	390214.	−	465039.i	1.06608	−	1.27051i
$606$		0			0
$607$	−30799.0	−	174670.i	−0.0835910	−	0.474068i	−0.997652	−	0.0684907i	$-0.978182\pi$
$607$	−30799.0	−	174670.i	−0.0835910	−	0.474068i	0.914061	−	0.405577i	$-0.132929\pi$
$608$	−58251.5	+	10271.3i	−0.157580	+	0.0277855i
$609$		0			0
$610$	−179803.	−	150873.i	−0.483213	−	0.405464i
$611$	9738.65	−	5622.61i	0.0260865	−	0.0150611i
$612$		0			0
$613$	142754.	−	247258.i	0.379899	−	0.658004i	−0.611148	−	0.791516i	$-0.709292\pi$
$613$	142754.	−	247258.i	0.379899	−	0.658004i	0.991047	+	0.133512i	$0.0426254\pi$
$614$	32560.7	+	89459.7i	0.0863687	+	0.237296i
$615$		0			0
$616$	−39131.7	+	32835.4i	−0.103126	+	0.0865329i
$617$	−145072.	+	398581.i	−0.381076	+	1.04700i	0.589828	+	0.807529i	$0.299196\pi$
$617$	−145072.	+	398581.i	−0.381076	+	1.04700i	−0.970904	+	0.239469i	$0.923026\pi$
$618$		0			0
$619$	−76502.9	+	433869.i	−0.199662	+	1.13234i	0.705958	+	0.708253i	$0.250517\pi$
$619$	−76502.9	+	433869.i	−0.199662	+	1.13234i	−0.905621	+	0.424089i	$0.860595\pi$
$620$			59579.4i			0.154993i
$621$		0			0
$622$	−406726.			−1.05129
$623$	688789.	+	121452.i	1.77464	+	0.312917i
$624$		0			0
$625$	−233918.	−	85139.3i	−0.598831	−	0.217957i
$626$	−169548.	−	202059.i	−0.432657	−	0.515621i
$627$		0			0
$628$	15904.9	−	5788.92i	0.0403286	−	0.0146784i
$629$	−682796.	−	394212.i	−1.72580	−	0.996389i
$630$		0			0
$631$	281259.	+	487155.i	0.706395	+	1.22351i	0.966186	+	0.257847i	$0.0830129\pi$
$631$	281259.	+	487155.i	0.706395	+	1.22351i	−0.259791	+	0.965665i	$0.583654\pi$
$632$	−354066.	+	421959.i	−0.886441	+	1.05642i
$633$		0			0
$634$	−36947.7	−	209541.i	−0.0919197	−	0.521303i
$635$	−349916.	+	61699.6i	−0.867793	+	0.153015i
$636$		0			0
$637$	30969.4	+	25986.4i	0.0763226	+	0.0640423i
$638$	56065.4	−	32369.4i	0.137738	−	0.0795231i
$639$		0			0
$640$	416705.	−	721754.i	1.01735	−	1.76209i
$641$	71507.0	+	196464.i	0.174033	+	0.478153i	0.995788	−	0.0916893i	$-0.0292267\pi$
$641$	71507.0	+	196464.i	0.174033	+	0.478153i	−0.821754	+	0.569842i	$0.807004\pi$
$642$		0			0
$643$	−595606.	+	499773.i	−1.44058	+	1.20879i	−0.501469	+	0.865176i	$0.667207\pi$
$643$	−595606.	+	499773.i	−1.44058	+	1.20879i	−0.939111	+	0.343614i	$0.888349\pi$
$644$	−45167.4	+	124096.i	−0.108906	+	0.299218i
$645$		0			0
$646$	43814.6	−	248485.i	0.104991	−	0.595436i
$647$			293080.i			0.700127i	0.936726	+	0.350064i	$0.113840\pi$
$647$			293080.i			0.700127i	−0.936726	+	0.350064i	$0.886160\pi$
$648$		0			0
$649$	6626.29			0.0157319
$650$	−625286.	−	110255.i	−1.47997	−	0.260958i
$651$		0			0
$652$	72938.1	+	26547.3i	0.171577	+	0.0624489i
$653$	378601.	+	451199.i	0.887883	+	1.05814i	0.997936	+	0.0642116i	$0.0204533\pi$
$653$	378601.	+	451199.i	0.887883	+	1.05814i	−0.110054	+	0.993926i	$0.535102\pi$
$654$		0			0
$655$	−50498.1	+	18379.8i	−0.117704	+	0.0428409i
$656$	470422.	+	271598.i	1.09315	+	0.631131i
$657$		0			0
$658$	10619.8	+	18394.1i	0.0245282	+	0.0424840i
$659$	23676.2	−	28216.2i	0.0545183	−	0.0649723i	−0.738096	−	0.674696i	$-0.764275\pi$
$659$	23676.2	−	28216.2i	0.0545183	−	0.0649723i	0.792614	+	0.609723i	$0.208719\pi$
$660$		0			0
$661$	−90962.5	−	515874.i	−0.208190	−	1.18070i	−0.892341	−	0.451363i	$-0.850938\pi$
$661$	−90962.5	−	515874.i	−0.208190	−	1.18070i	0.684151	−	0.729341i	$-0.260173\pi$
$662$	−309891.	+	54642.1i	−0.707120	+	0.124684i
$663$		0			0
$664$	190546.	+	159887.i	0.432178	+	0.362641i
$665$	251001.	−	144915.i	0.567586	−	0.327696i
$666$		0			0
$667$	−288775.	+	500173.i	−0.649094	+	1.12426i
$668$	−6365.94	−	17490.3i	−0.0142662	−	0.0391962i
$669$		0			0
$670$	646747.	−	542685.i	1.44074	−	1.20892i
$671$	−7617.15	+	20927.9i	−0.0169179	+	0.0464817i
$672$		0			0
$673$	102301.	−	580177.i	0.225865	−	1.28095i	−0.635159	−	0.772381i	$-0.719065\pi$
$673$	102301.	−	580177.i	0.225865	−	1.28095i	0.861024	−	0.508564i	$-0.169823\pi$
$674$			706749.i			1.55577i
$675$		0			0
$676$	48746.0			0.106671
$677$	6860.36	+	1209.67i	0.0149682	+	0.00263930i	0.181127	−	0.983460i	$-0.442025\pi$
$677$	6860.36	+	1209.67i	0.0149682	+	0.00263930i	−0.166159	+	0.986099i	$0.553137\pi$
$678$		0			0
$679$	341964.	+	124465.i	0.741722	+	0.269965i
$680$	651591.	+	776536.i	1.40915	+	1.67936i
$681$		0			0
$682$	28956.3	−	10539.2i	0.0622550	−	0.0226590i
$683$	−641155.	−	370171.i	−1.37443	−	0.793525i	−0.382944	−	0.923771i	$-0.625090\pi$
$683$	−641155.	−	370171.i	−1.37443	−	0.793525i	−0.991482	+	0.130246i	$0.958423\pi$
$684$		0			0
$685$	−136115.	−	235758.i	−0.290084	−	0.502441i
$686$	307942.	−	366991.i	0.654365	−	0.779842i
$687$		0			0
$688$	−13749.2	−	77975.4i	−0.0290469	−	0.164733i
$689$	−129017.	+	22749.3i	−0.271775	+	0.0479213i
$690$		0			0
$691$	252655.	+	212003.i	0.529142	+	0.444003i	0.867805	−	0.496905i	$-0.165530\pi$
$691$	252655.	+	212003.i	0.529142	+	0.444003i	−0.338663	+	0.940908i	$0.609975\pi$
$692$	−6158.81	+	3555.79i	−0.0128613	+	0.00742547i
$693$		0			0
$694$	−181682.	+	314682.i	−0.377218	+	0.653361i
$695$	−393790.	−	1.08193e6i	−0.815258	−	2.23990i
$696$		0			0
$697$	−602972.	+	505954.i	−1.24117	+	1.04147i
$698$	79352.9	−	218020.i	0.162874	−	0.447493i
$699$		0			0
$700$	38204.3	−	216667.i	0.0779679	−	0.442178i
$701$		−	74351.8i		−	0.151306i	−0.997134	−	0.0756529i	$-0.975896\pi$
$701$		−	74351.8i		−	0.151306i	0.997134	−	0.0756529i	$-0.0241041\pi$
$702$		0			0
$703$	−236866.			−0.479284
$704$	−49236.1	−	8681.66i	−0.0993433	−	0.0175169i
$705$		0			0
$706$	−501615.	−	182573.i	−1.00638	−	0.366292i
$707$	−130356.	−	155353.i	−0.260792	−	0.310799i
$708$		0			0
$709$	716949.	−	260948.i	1.42625	−	0.519112i	0.490395	−	0.871500i	$-0.336852\pi$
$709$	716949.	−	260948.i	1.42625	−	0.519112i	0.935854	+	0.352388i	$0.114630\pi$
$710$	−903431.	−	521596.i	−1.79217	−	1.03471i
$711$		0			0
$712$	367461.	+	636461.i	0.724855	+	1.25549i
$713$	−176705.	+	210589.i	−0.347592	+	0.414245i
$714$		0			0
$715$	16044.6	+	90993.6i	0.0313847	+	0.177991i
$716$	167122.	−	29468.2i	0.325993	−	0.0574814i
$717$		0			0
$718$	35442.5	+	29739.8i	0.0687504	+	0.0576884i
$719$	493734.	−	285058.i	0.955071	−	0.551410i	0.0604184	−	0.998173i	$-0.480757\pi$
$719$	493734.	−	285058.i	0.955071	−	0.551410i	0.894653	+	0.446763i	$0.147423\pi$
$720$		0			0
$721$	−217929.	+	377465.i	−0.419223	+	0.726116i
$722$	171378.	+	470857.i	0.328761	+	0.903264i
$723$		0			0
$724$	−149570.	+	125504.i	−0.285343	+	0.239431i
$725$	329086.	−	904157.i	0.626085	−	1.72016i
$726$		0			0
$727$	−94602.0	+	536514.i	−0.178991	+	1.01511i	0.754445	+	0.656364i	$0.227906\pi$
$727$	−94602.0	+	536514.i	−0.178991	+	1.01511i	−0.933436	+	0.358745i	$0.883205\pi$
$728$			351479.i			0.663189i
$729$		0			0
$730$	660744.			1.23990
$731$	112991.	+	19923.4i	0.211451	+	0.0372845i
$732$		0			0
$733$	−166933.	−	60758.7i	−0.310695	−	0.113084i	0.181966	−	0.983305i	$-0.441754\pi$
$733$	−166933.	−	60758.7i	−0.310695	−	0.113084i	−0.492662	+	0.870221i	$0.663976\pi$
$734$	−408445.	−	486766.i	−0.758126	−	0.903500i
$735$		0			0
$736$	−298580.	+	108674.i	−0.551194	+	0.200618i
$737$	−69375.8	−	40054.1i	−0.127724	−	0.0737415i
$738$		0			0
$739$	−146564.	−	253856.i	−0.268372	−	0.464835i	0.700069	−	0.714075i	$-0.253152\pi$
$739$	−146564.	−	253856.i	−0.268372	−	0.464835i	−0.968442	+	0.249240i	$0.919819\pi$
$740$	−177257.	+	211247.i	−0.323698	+	0.385768i
$741$		0			0
$742$	−42968.1	−	243684.i	−0.0780438	−	0.442608i
$743$	850263.	−	149924.i	1.54019	−	0.271578i	0.661861	−	0.749626i	$-0.269767\pi$
$743$	850263.	−	149924.i	1.54019	−	0.271578i	0.878334	+	0.478048i	$0.158656\pi$
$744$		0			0
$745$	−662366.	−	555791.i	−1.19340	−	1.00138i
$746$	540199.	−	311884.i	0.970681	−	0.560423i
$747$		0			0
$748$	−13936.3	+	24138.4i	−0.0249083	+	0.0431425i
$749$	218873.	+	601349.i	0.390147	+	1.07192i
$750$		0			0
$751$	754773.	−	633330.i	1.33825	−	1.12292i	0.356175	−	0.934419i	$-0.384081\pi$
$751$	754773.	−	633330.i	1.33825	−	1.12292i	0.982072	−	0.188504i	$-0.0603638\pi$
$752$	−9439.34	+	25934.4i	−0.0166919	+	0.0458606i
$753$		0			0
$754$	77349.9	−	438673.i	0.136056	−	0.771611i
$755$			1.06918e6i			1.87568i
$756$		0			0
$757$	−935246.			−1.63205			−0.816026	−	0.578015i	$-0.803827\pi$
$757$	−935246.			−1.63205			−0.816026	+	0.578015i	$0.803827\pi$
$758$	47487.1	+	8373.26i	0.0826489	+	0.0145732i
$759$		0			0
$760$	286178.	+	104160.i	0.495461	+	0.180333i
$761$	−273977.	−	326513.i	−0.473092	−	0.563809i	0.475742	−	0.879585i	$-0.342180\pi$
$761$	−273977.	−	326513.i	−0.473092	−	0.563809i	−0.948834	+	0.315776i	$0.897735\pi$
$762$		0			0
$763$	−1.07221e6	+	390254.i	−1.84176	+	0.670345i
$764$	−142110.	−	82047.1i	−0.243465	−	0.140565i
$765$		0			0
$766$	82819.3	+	143447.i	0.141148	+	0.244475i
$767$	29306.4	−	34926.1i	0.0498164	−	0.0593689i
$768$		0			0
$769$	88202.4	+	500221.i	0.149152	+	0.845880i	0.963940	+	0.266121i	$0.0857422\pi$
$769$	88202.4	+	500221.i	0.149152	+	0.845880i	−0.814788	+	0.579759i	$0.803147\pi$
$770$	−171866.	+	30304.6i	−0.289873	+	0.0511125i
$771$		0			0
$772$	61295.6	+	51433.1i	0.102848	+	0.0862995i
$773$	−762508.	+	440234.i	−1.27610	+	0.736758i	−0.976129	−	0.217190i	$-0.930311\pi$
$773$	−762508.	+	440234.i	−1.27610	+	0.736758i	−0.299972	+	0.953948i	$0.596977\pi$
$774$		0			0
$775$	228992.	−	396626.i	0.381256	−	0.660355i
$776$	130784.	+	359325.i	0.217185	+	0.596711i
$777$		0			0
$778$	−51629.6	+	43322.3i	−0.0852981	+	0.0715736i
$779$	−80879.5	+	222215.i	−0.133280	+	0.366183i
$780$		0			0
$781$	−17188.2	+	97479.3i	−0.0281792	+	0.159812i
$782$		−	1.35540e6i		−	2.21643i
$783$		0			0
$784$	−99220.2			−0.161424
$785$	−196511.	−	34650.2i	−0.318895	−	0.0562298i
$786$		0			0
$787$	412868.	+	150272.i	0.666595	+	0.242621i	0.653081	−	0.757288i	$-0.273476\pi$
$787$	412868.	+	150272.i	0.666595	+	0.242621i	0.0135137	+	0.999909i	$0.495698\pi$
$788$	−90864.9	−	108289.i	−0.146334	−	0.174394i
$789$		0			0
$790$	−1.76834e6	+	643623.i	−2.83342	+	1.03128i
$791$	22945.1	+	13247.4i	0.0366722	+	0.0211727i
$792$		0			0
$793$	76618.9	+	132708.i	0.121840	+	0.211033i
$794$	−642018.	+	765127.i	−1.01837	+	1.21365i
$795$		0			0
$796$	−15863.3	−	89965.2i	−0.0250361	−	0.141987i
$797$	1.14147e6	−	201273.i	1.79701	−	0.316861i	0.827415	−	0.561590i	$-0.189810\pi$
$797$	1.14147e6	−	201273.i	1.79701	−	0.316861i	0.969591	+	0.244730i	$0.0786992\pi$
$798$		0			0
$799$	−30635.9	−	25706.6i	−0.0479885	−	0.0402671i
$800$	458430.	−	264675.i	0.716298	−	0.413555i
$801$		0			0
$802$	416398.	−	721222.i	0.647381	−	1.12130i
$803$	−21442.8	−	58913.6i	−0.0332545	−	0.0913660i
$804$		0			0
$805$	1.19266e6	−	1.00076e6i	1.84046	−	1.54433i
$806$	72516.0	−	199236.i	0.111626	−	0.306689i
$807$		0			0
$808$	37003.4	−	209857.i	0.0566786	−	0.321440i
$809$		−	847337.i		−	1.29467i	−0.762206	−	0.647335i	$-0.775884\pi$
$809$		−	847337.i		−	1.29467i	0.762206	−	0.647335i	$-0.224116\pi$
$810$		0			0
$811$	−333614.			−0.507227			−0.253613	−	0.967306i	$-0.581619\pi$
$811$	−333614.			−0.507227			−0.253613	+	0.967306i	$0.581619\pi$
$812$	152004.	+	26802.4i	0.230539	+	0.0406502i
$813$		0			0
$814$	134024.	+	48780.8i	0.202271	+	0.0736208i
$815$	−588201.	−	700990.i	−0.885545	−	1.05535i
$816$		0			0
$817$	32390.8	−	11789.3i	0.0485264	−	0.0176622i
$818$	50004.7	+	28870.2i	0.0747315	+	0.0431463i
$819$		0			0
$820$	137654.	+	238424.i	0.204721	+	0.354587i
$821$	162567.	−	193740.i	0.241183	−	0.287430i	−0.631851	−	0.775090i	$-0.717705\pi$
$821$	162567.	−	193740.i	0.241183	−	0.287430i	0.873034	+	0.487659i	$0.162149\pi$
$822$		0			0
$823$	−37672.7	−	213652.i	−0.0556195	−	0.315434i	0.944287	−	0.329124i	$-0.106753\pi$
$823$	−37672.7	−	213652.i	−0.0556195	−	0.315434i	−0.999906	+	0.0136899i	$0.995642\pi$
$824$	−451029.	+	79528.5i	−0.664278	+	0.117130i
$825$		0			0
$826$	65967.3	+	55353.1i	0.0966871	+	0.0811301i
$827$	993568.	−	573637.i	1.45274	−	0.838737i	0.454099	−	0.890951i	$-0.349961\pi$
$827$	993568.	−	573637.i	1.45274	−	0.838737i	0.998636	+	0.0522142i	$0.0166279\pi$
$828$		0			0
$829$	−380977.	+	659872.i	−0.554357	+	0.960175i	0.443596	+	0.896227i	$0.353703\pi$
$829$	−380977.	+	659872.i	−0.554357	+	0.960175i	−0.997953	+	0.0639483i	$0.979631\pi$
$830$	290643.	+	798535.i	0.421895	+	1.15915i
$831$		0			0
$832$	−263519.	+	221118.i	−0.380684	+	0.319432i
$833$	49174.3	−	135105.i	0.0708677	−	0.194707i
$834$		0			0
$835$	−38104.0	+	216099.i	−0.0546510	+	0.309941i
$836$			8373.78i			0.0119814i
$837$		0			0
$838$	1.26740e6			1.80479
$839$	−1.02198e6	−	180202.i	−1.45183	−	0.255997i	−0.608570	−	0.793500i	$-0.708257\pi$
$839$	−1.02198e6	−	180202.i	−1.45183	−	0.255997i	−0.843262	+	0.537503i	$0.819368\pi$
$840$		0			0
$841$	−30310.2	−	11032.0i	−0.0428545	−	0.0155978i
$842$	826310.	+	984758.i	1.16552	+	1.38901i
$843$		0			0
$844$	−119794.	+	43601.3i	−0.168170	+	0.0612089i
$845$	−497691.	−	287342.i	−0.697022	−	0.402426i
$846$		0			0
$847$	−374288.	−	648286.i	−0.521722	−	0.903649i
$848$	206674.	−	246305.i	0.287405	−	0.342516i
$849$		0			0
$850$	392108.	+	2.22376e6i	0.542710	+	3.07786i
$851$	−1.25307e6	+	220949.i	−1.73027	+	0.305094i
$852$		0			0
$853$	−253262.	−	212512.i	−0.348075	−	0.292069i	0.451942	−	0.892047i	$-0.350732\pi$
$853$	−253262.	−	212512.i	−0.348075	−	0.292069i	−0.800016	+	0.599978i	$0.795176\pi$
$854$	−250654.	+	144715.i	−0.343684	+	0.198426i
$855$		0			0
$856$	−336215.	+	582341.i	−0.458849	+	0.794749i
$857$	−23438.6	−	64397.1i	−0.0319132	−	0.0876808i	0.922713	−	0.385488i	$-0.125967\pi$
$857$	−23438.6	−	64397.1i	−0.0319132	−	0.0876808i	−0.954626	+	0.297807i	$0.903745\pi$
$858$		0			0
$859$	526478.	−	441768.i	0.713500	−	0.598698i	−0.212078	−	0.977253i	$-0.568023\pi$
$859$	526478.	−	441768.i	0.713500	−	0.598698i	0.925579	+	0.378555i	$0.123579\pi$
$860$	13725.3	−	37709.8i	0.0185577	−	0.0509868i
$861$		0			0
$862$	174865.	−	991707.i	0.235336	−	1.33465i
$863$			334665.i			0.449354i	0.974433	+	0.224677i	$0.0721327\pi$
$863$			334665.i			0.449354i	−0.974433	+	0.224677i	$0.927867\pi$
$864$		0			0
$865$	83840.8			0.112053
$866$	306179.	+	53987.6i	0.408263	+	0.0719877i
$867$		0			0
$868$	69037.1	+	25127.4i	0.0916311	+	0.0333510i
$869$	114774.	+	136783.i	0.151986	+	0.181130i
$870$		0			0
$871$	−517950.	+	188518.i	−0.682734	+	0.248495i
$872$	−1.03832e6	−	599476.i	−1.36553	−	0.788386i
$873$		0			0
$874$	−203601.	−	352648.i	−0.266537	−	0.461656i
$875$	−777467.	+	926549.i	−1.01547	+	1.21019i
$876$		0			0
$877$	−188474.	−	1.06889e6i	−0.245049	−	1.38974i	−0.820379	−	0.571820i	$-0.806238\pi$
$877$	−188474.	−	1.06889e6i	−0.245049	−	1.38974i	0.575331	−	0.817921i	$-0.304873\pi$
$878$	237079.	−	41803.4i	0.307541	−	0.0542278i
$879$		0			0
$880$	−173714.	−	145764.i	−0.224321	−	0.188228i
$881$	−349088.	+	201546.i	−0.449763	+	0.259671i	−0.707730	−	0.706483i	$-0.750281\pi$
$881$	−349088.	+	201546.i	−0.449763	+	0.259671i	0.257967	+	0.966154i	$0.416947\pi$
$882$		0			0
$883$	462964.	−	801877.i	0.593780	−	1.02846i	−0.399937	−	0.916543i	$-0.630968\pi$
$883$	462964.	−	801877.i	0.593780	−	1.02846i	0.993718	−	0.111915i	$-0.0356986\pi$
$884$	65592.6	+	180214.i	0.0839363	+	0.230613i
$885$		0			0
$886$	291880.	−	244916.i	0.371823	−	0.311997i
$887$	−117658.	+	323263.i	−0.149546	+	0.410873i	−0.991734	−	0.128310i	$-0.959045\pi$
$887$	−117658.	+	323263.i	−0.149546	+	0.410873i	0.842188	+	0.539183i	$0.181267\pi$
$888$		0			0
$889$	−76082.2	+	431483.i	−0.0962674	+	0.545960i
$890$			2.51076e6i			3.16975i
$891$		0			0
$892$	−237763.			−0.298823
$893$	−11832.4	−	2086.36i	−0.0148378	−	0.00261630i
$894$		0			0
$895$	−1.88000e6	−	684265.i	−2.34700	−	0.854237i
$896$	−660582.	−	787251.i	−0.822831	−	0.980612i
$897$		0			0
$898$	1.04788e6	−	381398.i	1.29945	−	0.472961i
$899$	278255.	+	160651.i	0.344290	+	0.198776i
$900$		0			0
$901$	232957.	+	403493.i	0.286963	+	0.497034i
$902$	91526.8	−	109077.i	0.112496	−	0.134067i
$903$		0			0
$904$	4834.33	+	27416.9i	0.00591561	+	0.0335491i
$905$	2.26690e6	−	399715.i	2.76780	−	0.488037i
$906$		0			0
$907$	673004.	+	564718.i	0.818094	+	0.686462i	0.952525	−	0.304461i	$-0.0984762\pi$
$907$	673004.	+	564718.i	0.818094	+	0.686462i	−0.134431	+	0.990923i	$0.542921\pi$
$908$	4498.24	−	2597.06i	0.00545596	−	0.00315000i
$909$		0			0
$910$	−600390.	+	1.03991e6i	−0.725021	+	1.25577i
$911$	31529.1	+	86625.5i	0.0379905	+	0.104378i	0.957237	−	0.289303i	$-0.0934236\pi$
$911$	31529.1	+	86625.5i	0.0379905	+	0.104378i	−0.919247	+	0.393681i	$0.871201\pi$
$912$		0			0
$913$	61767.4	−	51829.0i	0.0740999	−	0.0621772i
$914$	204231.	−	561120.i	0.244472	−	0.671682i
$915$		0			0
$916$	34884.4	−	197839.i	0.0415758	−	0.235788i
$917$			66265.9i			0.0788046i
$918$		0			0
$919$	1.07969e6			1.27840			0.639200	−	0.769040i	$-0.279266\pi$
$919$	1.07969e6			1.27840			0.639200	+	0.769040i	$0.279266\pi$
$920$	1.61109e6	+	284079.i	1.90347	+	0.335633i
$921$		0			0
$922$	484176.	+	176226.i	0.569563	+	0.207304i
$923$	437777.	+	521723.i	0.513866	+	0.612402i
$924$		0			0
$925$	1.99194e6	−	725007.i	2.32805	−	0.847342i
$926$	712780.	+	411523.i	0.831253	+	0.479924i
$927$		0			0
$928$	185684.	+	321615.i	0.215615	+	0.373456i
$929$	455255.	−	542551.i	0.527501	−	0.628651i	−0.434837	−	0.900509i	$-0.643194\pi$
$929$	455255.	−	542551.i	0.527501	−	0.628651i	0.962337	+	0.271859i	$0.0876383\pi$
$930$		0			0
$931$	−7500.67	−	42538.4i	−0.00865368	−	0.0490775i
$932$	−238653.	+	42080.9i	−0.274748	+	0.0484455i
$933$		0			0
$934$	333179.	+	279570.i	0.381930	+	0.320477i
$935$	284576.	−	164300.i	0.325518	−	0.187938i
$936$		0			0
$937$	−231874.	+	401617.i	−0.264102	+	0.457439i	−0.967328	−	0.253528i	$-0.918409\pi$
$937$	−231874.	+	401617.i	−0.264102	+	0.457439i	0.703226	+	0.710967i	$0.251742\pi$
$938$	−356068.	−	978288.i	−0.404694	−	1.11189i
$939$		0			0
$940$	−10715.4	+	8991.25i	−0.0121269	+	0.0101757i
$941$	−523629.	+	1.43866e6i	−0.591350	+	1.62472i	0.176651	+	0.984274i	$0.443474\pi$
$941$	−523629.	+	1.43866e6i	−0.591350	+	1.62472i	−0.768001	+	0.640448i	$0.778749\pi$
$942$		0			0
$943$	−220585.	+	1.25100e6i	−0.248058	+	1.40680i
$944$			111897.i			0.125566i
$945$		0			0
$946$	−20755.3			−0.0231925
$947$	−520059.	−	91700.5i	−0.579900	−	0.102252i	−0.123999	−	0.992282i	$-0.539572\pi$
$947$	−520059.	−	91700.5i	−0.579900	−	0.102252i	−0.455901	+	0.890030i	$0.650683\pi$
$948$		0			0
$949$	−405360.	−	147539.i	−0.450099	−	0.163823i
$950$	436060.	+	519677.i	0.483169	+	0.575819i
$951$		0			0
$952$	1.17461e6	−	427523.i	1.29605	−	0.471722i
$953$	−754093.	−	435376.i	−0.830308	−	0.479379i	0.0236499	−	0.999720i	$-0.492471\pi$
$953$	−754093.	−	435376.i	−0.830308	−	0.479379i	−0.853958	+	0.520342i	$0.825805\pi$
$954$		0			0
$955$	967281.	+	1.67538e6i	1.06059	+	1.83699i
$956$	130577.	−	155616.i	0.142874	−	0.170270i
$957$		0			0
$958$	−42807.5	−	242773.i	−0.0466433	−	0.264527i
$959$	−330589.	+	58291.7i	−0.359460	+	0.0633825i
$960$		0			0
$961$	−590304.	−	495324.i	−0.639188	−	0.536342i
$962$	849871.	−	490673.i	0.918339	−	0.530203i
$963$		0			0
$964$	71604.2	−	124022.i	0.0770521	−	0.133458i
$965$	−322639.	−	886443.i	−0.346467	−	0.951910i
$966$		0			0
$967$	333747.	−	280047.i	0.356915	−	0.299487i	−0.446645	−	0.894711i	$-0.647381\pi$
$967$	333747.	−	280047.i	0.356915	−	0.299487i	0.803560	+	0.595224i	$0.202937\pi$
$968$	269026.	−	739142.i	0.287107	−	0.788819i
$969$		0			0
$970$	−226848.	+	1.28652e6i	−0.241097	+	1.36733i
$971$			921697.i			0.977574i	0.872403	+	0.488787i	$0.162560\pi$
$971$			921697.i			0.977574i	−0.872403	+	0.488787i	$0.837440\pi$
$972$		0			0
$973$	−1.41976e6			−1.49964
$974$	−426984.	−	75288.8i	−0.450084	−	0.0793620i
$975$		0			0
$976$	−353406.	−	128629.i	−0.371000	−	0.135033i
$977$	578976.	+	689997.i	0.606557	+	0.722866i	0.978697	−	0.205311i	$-0.0658204\pi$
$977$	578976.	+	689997.i	0.606557	+	0.722866i	−0.372140	+	0.928176i	$0.621376\pi$
$978$		0			0
$979$	223866.	−	81480.4i	0.233573	−	0.0850135i
$980$	−43550.5	−	25143.9i	−0.0453462	−	0.0261807i
$981$		0			0
$982$	−1.03896e6	−	1.79953e6i	−1.07739	−	1.86610i
$983$	387453.	−	461748.i	0.400970	−	0.477857i	−0.527346	−	0.849651i	$-0.676813\pi$
$983$	387453.	−	461748.i	0.400970	−	0.477857i	0.928315	+	0.371794i	$0.121257\pi$
$984$		0			0
$985$	289394.	+	1.64123e6i	0.298275	+	1.69160i
$986$	−1.56009e6	+	275086.i	−1.60471	+	0.282953i
$987$		0			0
$988$	44136.7	+	37035.1i	0.0452154	+	0.0379402i
$989$	160356.	−	92581.6i	0.163943	−	0.0946525i
$990$		0			0
$991$	503873.	−	872734.i	0.513067	−	0.888658i	−0.486818	−	0.873503i	$-0.661843\pi$
$991$	503873.	−	872734.i	0.513067	−	0.888658i	0.999885	−	0.0151546i	$-0.00482405\pi$
$992$	60457.4	+	166105.i	0.0614364	+	0.168795i
$993$		0			0
$994$	−985414.	+	826861.i	−0.997347	+	0.836873i
$995$	−368353.	+	1.01204e6i	−0.372065	+	1.02224i
$996$		0			0
$997$	152374.	−	864154.i	0.153292	−	0.869363i	−0.807039	−	0.590499i	$-0.798931\pi$
$997$	152374.	−	864154.i	0.153292	−	0.869363i	0.960331	−	0.278864i	$-0.0899578\pi$
$998$		−	1.14053e6i		−	1.14510i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.8.9		66
3.2	odd	2		27.5.f.a.2.3	✓	66
27.13	even	9		27.5.f.a.14.3	yes	66
27.14	odd	18	inner	81.5.f.a.71.9		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.2.3	✓	66	3.2	odd	2
27.5.f.a.14.3	yes	66	27.13	even	9
81.5.f.a.8.9		66	1.1	even	1	trivial
81.5.f.a.71.9		66	27.14	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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.35935 + 0.768672i) q^{2} +(3.37802 + 1.22950i) q^{4} +(-27.2417 - 32.4654i) q^{5} +(-49.1081 + 17.8739i) q^{7} +(-47.5559 - 27.4564i) q^{8} +(-93.8009 - 162.468i) q^{10} +(-11.4420 + 13.6360i) q^{11} +(21.2681 + 120.617i) q^{13} +(-227.819 + 40.1706i) q^{14} +(-230.269 - 193.218i) q^{16} +(377.223 - 217.790i) q^{17} +(65.4306 - 113.329i) q^{19} +(-52.1069 - 143.162i) q^{20} +(-60.3613 + 50.6491i) q^{22} +(240.426 - 660.564i) q^{23} +(-203.361 + 1153.32i) q^{25} +542.162i q^{26} -187.864 q^{28} +(-809.117 - 142.669i) q^{29} +(-367.484 - 133.753i) q^{31} +(-290.544 - 346.257i) q^{32} +(1811.86 - 659.462i) q^{34} +(1918.07 + 1107.40i) q^{35} +(-905.030 - 1567.56i) q^{37} +(372.348 - 443.747i) q^{38} +(404.120 + 2291.88i) q^{40} +(-1779.62 + 313.795i) q^{41} +(201.781 + 169.314i) q^{43} +(-55.4168 + 31.9949i) q^{44} +(1555.86 - 2694.82i) q^{46} +(-31.4023 - 86.2770i) q^{47} +(252.856 - 212.171i) q^{49} +(-1773.05 + 4871.41i) q^{50} +(-76.4550 + 433.598i) q^{52} +1069.64i q^{53} +754.398 q^{55} +(2826.13 + 498.323i) q^{56} +(-3417.56 - 1243.89i) q^{58} +(-239.279 - 285.161i) q^{59} +(1175.69 - 427.916i) q^{61} +(-1499.18 - 865.552i) q^{62} +(1404.33 + 2432.37i) q^{64} +(3336.51 - 3976.30i) q^{65} +(781.472 + 4431.95i) q^{67} +(1542.04 - 271.903i) q^{68} +(7510.32 + 6301.90i) q^{70} +(4815.68 - 2780.33i) q^{71} +(-1761.03 + 3050.19i) q^{73} +(-2740.41 - 7529.21i) q^{74} +(360.364 - 302.381i) q^{76} +(318.165 - 874.152i) q^{77} +(1741.86 - 9878.58i) q^{79} +12739.4i q^{80} -7999.21 q^{82} +(-4460.90 - 786.577i) q^{83} +(-17346.8 - 6313.72i) q^{85} +(749.486 + 893.203i) q^{86} +(918.530 - 334.318i) q^{88} +(-11590.4 - 6691.71i) q^{89} +(-3200.34 - 5543.15i) q^{91} +(1624.33 - 1935.80i) q^{92} +(-70.5749 - 400.250i) q^{94} +(-5461.71 + 963.047i) q^{95} +(-5334.35 - 4476.05i) q^{97} +(1265.38 - 730.567i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) \) 66 * q + 6 * q^2 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 + 492 * q^11 - 6 * q^13 - 1137 * q^14 - 54 * q^16 + 9 * q^17 - 3 * q^19 + 2487 * q^20 + 1002 * q^22 + 2724 * q^23 + 435 * q^25 - 12 * q^28 - 5016 * q^29 - 1671 * q^31 - 10224 * q^32 - 342 * q^34 + 2682 * q^35 - 3 * q^37 + 6564 * q^38 - 1113 * q^40 - 5754 * q^41 - 1266 * q^43 + 4545 * q^44 - 3 * q^46 + 9159 * q^47 + 5898 * q^49 + 34977 * q^50 + 2871 * q^52 - 12 * q^55 - 39243 * q^56 - 12291 * q^58 - 24762 * q^59 - 8358 * q^61 - 38304 * q^62 + 6141 * q^64 - 23727 * q^65 + 15996 * q^67 + 43533 * q^68 - 7251 * q^70 + 19773 * q^71 + 6108 * q^73 + 74847 * q^74 - 28614 * q^76 + 33909 * q^77 - 5658 * q^79 - 12 * q^82 - 18813 * q^83 + 24219 * q^85 - 96474 * q^86 + 36042 * q^88 - 110232 * q^89 - 6042 * q^91 - 73545 * q^92 + 2631 * q^94 + 65163 * q^95 - 3696 * q^97 + 259938 * q^98

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