LMFDB - Embedded newform 81.5.f.a.8.3

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			8.3
Character	$\chi$	$=$	81.8
Dual form			81.5.f.a.71.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.49504 - 0.792597i) q^{2} +(4.54211 + 1.65319i) q^{4} +(3.40574 + 4.05880i) q^{5} +(-28.7185 + 10.4527i) q^{7} +(44.1393 + 25.4838i) q^{8} +(-12.0919 - 20.9439i) q^{10} +(-13.9368 + 16.6092i) q^{11} +(0.515455 + 2.92329i) q^{13} +(137.376 - 24.2231i) q^{14} +(-237.454 - 199.247i) q^{16} +(249.786 - 144.214i) q^{17} +(220.850 - 382.524i) q^{19} +(8.75926 + 24.0659i) q^{20} +(75.8110 - 63.6130i) q^{22} +(301.451 - 828.229i) q^{23} +(103.655 - 587.858i) q^{25} -13.5489i q^{26} -147.723 q^{28} +(-1064.69 - 187.734i) q^{29} +(1637.03 + 595.829i) q^{31} +(385.260 + 459.135i) q^{32} +(-1237.10 + 450.268i) q^{34} +(-140.233 - 80.9637i) q^{35} +(293.810 + 508.894i) q^{37} +(-1295.92 + 1544.42i) q^{38} +(46.8931 + 265.944i) q^{40} +(1376.52 - 242.718i) q^{41} +(-1229.63 - 1031.78i) q^{43} +(-90.7608 + 52.4008i) q^{44} +(-2011.49 + 3484.00i) q^{46} +(754.401 + 2072.70i) q^{47} +(-1123.78 + 942.961i) q^{49} +(-931.870 + 2560.29i) q^{50} +(-2.49151 + 14.1301i) q^{52} -1536.91i q^{53} -114.879 q^{55} +(-1533.99 - 270.484i) q^{56} +(4637.04 + 1687.74i) q^{58} +(844.872 + 1006.88i) q^{59} +(2815.23 - 1024.66i) q^{61} +(-6886.25 - 3975.78i) q^{62} +(1111.94 + 1925.94i) q^{64} +(-10.1095 + 12.0481i) q^{65} +(-1421.14 - 8059.70i) q^{67} +(1372.97 - 242.091i) q^{68} +(566.183 + 475.084i) q^{70} +(4745.40 - 2739.76i) q^{71} +(-1147.66 + 1987.81i) q^{73} +(-917.341 - 2520.37i) q^{74} +(1635.51 - 1372.36i) q^{76} +(226.633 - 622.670i) q^{77} +(1006.95 - 5710.70i) q^{79} -1642.36i q^{80} -6379.91 q^{82} +(5853.36 + 1032.10i) q^{83} +(1436.04 + 522.676i) q^{85} +(4709.43 + 5612.48i) q^{86} +(-1038.43 + 377.957i) q^{88} +(-1843.12 - 1064.13i) q^{89} +(-45.3593 - 78.5647i) q^{91} +(2738.45 - 3263.55i) q^{92} +(-1748.25 - 9914.81i) q^{94} +(2304.75 - 406.389i) q^{95} +(-3155.11 - 2647.45i) q^{97} +(5798.82 - 3347.95i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.49504	−	0.792597i	−1.12376	−	0.198149i	−0.419269	−	0.907862i	$-0.637714\pi$
$2$	−4.49504	−	0.792597i	−1.12376	−	0.198149i	−0.704491	+	0.709713i	$0.748825\pi$
$3$		0			0
$3$		0			0
$4$	4.54211	+	1.65319i	0.283882	+	0.103325i
$5$	3.40574	+	4.05880i	0.136230	+	0.162352i	0.829846	−	0.557992i	$-0.188428\pi$
$5$	3.40574	+	4.05880i	0.136230	+	0.162352i	−0.693617	+	0.720344i	$0.743984\pi$
$6$		0			0
$7$	−28.7185	+	10.4527i	−0.586092	+	0.213320i	−0.618010	−	0.786170i	$-0.712061\pi$
$7$	−28.7185	+	10.4527i	−0.586092	+	0.213320i	0.0319175	+	0.999491i	$0.489839\pi$
$8$	44.1393	+	25.4838i	0.689677	+	0.398185i
$9$		0			0
$10$	−12.0919	−	20.9439i	−0.120919	−	0.209439i
$11$	−13.9368	+	16.6092i	−0.115180	+	0.137266i	−0.820554	−	0.571569i	$-0.806335\pi$
$11$	−13.9368	+	16.6092i	−0.115180	+	0.137266i	0.705374	+	0.708836i	$0.250779\pi$
$12$		0			0
$13$	0.515455	+	2.92329i	0.00305003	+	0.0172976i	0.986295	−	0.164993i	$-0.0527601\pi$
$13$	0.515455	+	2.92329i	0.00305003	+	0.0172976i	−0.983245	+	0.182290i	$0.941649\pi$
$14$	137.376	−	24.2231i	0.700897	−	0.123587i
$15$		0			0
$16$	−237.454	−	199.247i	−0.927554	−	0.778310i
$17$	249.786	−	144.214i	0.864310	−	0.499010i	−0.00114291	−	0.999999i	$-0.500364\pi$
$17$	249.786	−	144.214i	0.864310	−	0.499010i	0.865453	+	0.500989i	$0.167030\pi$
$18$		0			0
$19$	220.850	−	382.524i	0.611774	−	1.05962i	−0.379167	−	0.925328i	$-0.623789\pi$
$19$	220.850	−	382.524i	0.611774	−	1.05962i	0.990941	−	0.134296i	$-0.0428772\pi$
$20$	8.75926	+	24.0659i	0.0218982	+	0.0601647i
$21$		0			0
$22$	75.8110	−	63.6130i	0.156634	−	0.131432i
$23$	301.451	−	828.229i	0.569850	−	1.56565i	−0.234889	−	0.972022i	$-0.575473\pi$
$23$	301.451	−	828.229i	0.569850	−	1.56565i	0.804739	−	0.593629i	$-0.202305\pi$
$24$		0			0
$25$	103.655	−	587.858i	0.165848	−	0.940573i
$26$		−	13.5489i		−	0.0200427i
$27$		0			0
$28$	−147.723			−0.188422
$29$	−1064.69	−	187.734i	−1.26598	−	0.223227i	−0.499965	−	0.866046i	$-0.666654\pi$
$29$	−1064.69	−	187.734i	−1.26598	−	0.223227i	−0.766018	+	0.642819i	$0.777765\pi$
$30$		0			0
$31$	1637.03	+	595.829i	1.70346	+	0.620010i	0.996212	−	0.0869542i	$-0.0277134\pi$
$31$	1637.03	+	595.829i	1.70346	+	0.620010i	0.707250	+	0.706964i	$0.249936\pi$
$32$	385.260	+	459.135i	0.376230	+	0.448374i
$33$		0			0
$34$	−1237.10	+	450.268i	−1.07016	+	0.389505i
$35$	−140.233	−	80.9637i	−0.114476	−	0.0660928i
$36$		0			0
$37$	293.810	+	508.894i	0.214617	+	0.371727i	0.953154	−	0.302486i	$-0.0978165\pi$
$37$	293.810	+	508.894i	0.214617	+	0.371727i	−0.738537	+	0.674213i	$0.764483\pi$
$38$	−1295.92	+	1544.42i	−0.897451	+	1.06954i
$39$		0			0
$40$	46.8931	+	265.944i	0.0293082	+	0.166215i
$41$	1376.52	−	242.718i	0.818872	−	0.144389i	0.251507	−	0.967856i	$-0.419074\pi$
$41$	1376.52	−	242.718i	0.818872	−	0.144389i	0.567365	+	0.823466i	$0.307963\pi$
$42$		0			0
$43$	−1229.63	−	1031.78i	−0.665022	−	0.558020i	0.246566	−	0.969126i	$-0.420698\pi$
$43$	−1229.63	−	1031.78i	−0.665022	−	0.558020i	−0.911587	+	0.411107i	$0.865142\pi$
$44$	−90.7608	+	52.4008i	−0.0468806	+	0.0270665i
$45$		0			0
$46$	−2011.49	+	3484.00i	−0.950608	+	1.64650i
$47$	754.401	+	2072.70i	0.341513	+	0.938298i	0.984956	+	0.172805i	$0.0552829\pi$
$47$	754.401	+	2072.70i	0.341513	+	0.938298i	−0.643444	+	0.765494i	$0.722495\pi$
$48$		0			0
$49$	−1123.78	+	942.961i	−0.468046	+	0.392737i
$50$	−931.870	+	2560.29i	−0.372748	+	1.02412i
$51$		0			0
$52$	−2.49151	+	14.1301i	−0.000921416	+	0.00522561i
$53$		−	1536.91i		−	0.547138i	−0.961852	−	0.273569i	$-0.911796\pi$
$53$		−	1536.91i		−	0.547138i	0.961852	−	0.273569i	$-0.0882042\pi$
$54$		0			0
$55$	−114.879			−0.0379764
$56$	−1533.99	−	270.484i	−0.489155	−	0.0862513i
$57$		0			0
$58$	4637.04	+	1687.74i	1.37843	+	0.501707i
$59$	844.872	+	1006.88i	0.242710	+	0.289250i	0.873623	−	0.486603i	$-0.161764\pi$
$59$	844.872	+	1006.88i	0.242710	+	0.289250i	−0.630914	+	0.775853i	$0.717320\pi$
$60$		0			0
$61$	2815.23	−	1024.66i	0.756578	−	0.275372i	0.0652071	−	0.997872i	$-0.479229\pi$
$61$	2815.23	−	1024.66i	0.756578	−	0.275372i	0.691371	+	0.722500i	$0.257007\pi$
$62$	−6886.25	−	3975.78i	−1.79143	−	1.03428i
$63$		0			0
$64$	1111.94	+	1925.94i	0.271470	+	0.470200i
$65$	−10.1095	+	12.0481i	−0.00239279	+	0.00285162i
$66$		0			0
$67$	−1421.14	−	8059.70i	−0.316583	−	1.79543i	−0.563200	−	0.826320i	$-0.690430\pi$
$67$	−1421.14	−	8059.70i	−0.316583	−	1.79543i	0.246617	−	0.969113i	$-0.420681\pi$
$68$	1372.97	−	242.091i	0.296922	−	0.0523554i
$69$		0			0
$70$	566.183	+	475.084i	0.115547	+	0.0969558i
$71$	4745.40	−	2739.76i	0.941360	−	0.543495i	0.0509738	−	0.998700i	$-0.483767\pi$
$71$	4745.40	−	2739.76i	0.941360	−	0.543495i	0.890386	+	0.455205i	$0.150434\pi$
$72$		0			0
$73$	−1147.66	+	1987.81i	−0.215362	+	0.373017i	−0.953384	−	0.301759i	$-0.902426\pi$
$73$	−1147.66	+	1987.81i	−0.215362	+	0.373017i	0.738023	+	0.674776i	$0.235760\pi$
$74$	−917.341	−	2520.37i	−0.167520	−	0.460258i
$75$		0			0
$76$	1635.51	−	1372.36i	0.283157	−	0.237597i
$77$	226.633	−	622.670i	0.0382246	−	0.105021i
$78$		0			0
$79$	1006.95	−	5710.70i	0.161344	−	0.915029i	−0.791410	−	0.611286i	$-0.790652\pi$
$79$	1006.95	−	5710.70i	0.161344	−	0.915029i	0.952754	−	0.303743i	$-0.0982365\pi$
$80$		−	1642.36i		−	0.256619i
$81$		0			0
$82$	−6379.91			−0.948826
$83$	5853.36	+	1032.10i	0.849667	+	0.149819i	0.581493	−	0.813551i	$-0.302469\pi$
$83$	5853.36	+	1032.10i	0.849667	+	0.149819i	0.268174	+	0.963371i	$0.413580\pi$
$84$		0			0
$85$	1436.04	+	522.676i	0.198760	+	0.0723427i
$86$	4709.43	+	5612.48i	0.636754	+	0.758854i
$87$		0			0
$88$	−1038.43	+	377.957i	−0.134095	+	0.0488064i
$89$	−1843.12	−	1064.13i	−0.232688	−	0.134343i	0.379123	−	0.925346i	$-0.376226\pi$
$89$	−1843.12	−	1064.13i	−0.232688	−	0.134343i	−0.611812	+	0.791003i	$0.709559\pi$
$90$		0			0
$91$	−45.3593	−	78.5647i	−0.00547752	−	0.00948734i
$92$	2738.45	−	3263.55i	0.323540	−	0.385581i
$93$		0			0
$94$	−1748.25	−	9914.81i	−0.197855	−	1.12209i
$95$	2304.75	−	406.389i	0.255374	−	0.0450293i
$96$		0			0
$97$	−3155.11	−	2647.45i	−0.335329	−	0.281374i	0.459538	−	0.888158i	$-0.348015\pi$
$97$	−3155.11	−	2647.45i	−0.335329	−	0.281374i	−0.794867	+	0.606784i	$0.792459\pi$
$98$	5798.82	−	3347.95i	0.603792	−	0.348599i
$99$		0			0
$100$	1442.66	−	2498.76i	0.144266	−	0.249876i
$101$	1786.17	+	4907.47i	0.175098	+	0.481077i	0.995934	−	0.0900866i	$-0.0287144\pi$
$101$	1786.17	+	4907.47i	0.175098	+	0.481077i	−0.820836	+	0.571164i	$0.806492\pi$
$102$		0			0
$103$	−14168.9	+	11889.2i	−1.33556	+	1.12067i	−0.352815	+	0.935693i	$0.614775\pi$
$103$	−14168.9	+	11889.2i	−1.33556	+	1.12067i	−0.982744	+	0.184973i	$0.940780\pi$
$104$	−51.7448	+	142.168i	−0.00478410	+	0.0131442i
$105$		0			0
$106$	−1218.15	+	6908.48i	−0.108415	+	0.614852i
$107$			17775.6i			1.55259i	0.630369	+	0.776295i	$0.282904\pi$
$107$			17775.6i			1.55259i	−0.630369	+	0.776295i	$0.717096\pi$
$108$		0			0
$109$	6129.70			0.515925			0.257962	−	0.966155i	$-0.416949\pi$
$109$	6129.70			0.515925			0.257962	+	0.966155i	$0.416949\pi$
$110$	516.385	+	91.0526i	0.0426764	+	0.00752501i
$111$		0			0
$112$	8902.00	+	3240.06i	0.709662	+	0.258296i
$113$	−11400.7	−	13586.8i	−0.892839	−	1.06404i	−0.997579	−	0.0695439i	$-0.977846\pi$
$113$	−11400.7	−	13586.8i	−0.892839	−	1.06404i	0.104740	−	0.994500i	$-0.466599\pi$
$114$		0			0
$115$	4388.28	−	1597.20i	0.331817	−	0.120772i
$116$	−4525.59	−	2612.85i	−0.336325	−	0.194177i
$117$		0			0
$118$	−2999.69	−	5195.61i	−0.215433	−	0.373141i
$119$	−5666.06	+	6752.54i	−0.400117	+	0.476841i
$120$		0			0
$121$	2460.75	+	13955.6i	0.168073	+	0.953187i
$122$	−13466.7	+	2374.54i	−0.904777	+	0.159537i
$123$		0			0
$124$	6450.54	+	5412.65i	0.419520	+	0.352019i
$125$	5606.86	−	3237.12i	0.358839	−	0.207176i
$126$		0			0
$127$	12573.1	−	21777.2i	0.779531	−	1.35019i	−0.152681	−	0.988276i	$-0.548791\pi$
$127$	12573.1	−	21777.2i	0.779531	−	1.35019i	0.932212	−	0.361912i	$-0.117876\pi$
$128$	−6751.61	−	18549.9i	−0.412086	−	1.13220i
$129$		0			0
$130$	54.9921	−	46.1439i	0.00325397	−	0.00273041i
$131$	6605.88	−	18149.5i	0.384936	−	1.05760i	−0.584315	−	0.811527i	$-0.698637\pi$
$131$	6605.88	−	18149.5i	0.384936	−	1.05760i	0.969251	−	0.246075i	$-0.0791410\pi$
$132$		0			0
$133$	−2344.09	+	13294.0i	−0.132517	+	0.751541i
$134$			37355.1i			2.08037i
$135$		0			0
$136$	14700.5			0.794793
$137$	−10731.9	−	1892.33i	−0.571790	−	0.100822i	−0.119725	−	0.992807i	$-0.538201\pi$
$137$	−10731.9	−	1892.33i	−0.571790	−	0.100822i	−0.452065	+	0.891985i	$0.649312\pi$
$138$		0			0
$139$	−8824.67	−	3211.92i	−0.456740	−	0.166240i	0.103396	−	0.994640i	$-0.467029\pi$
$139$	−8824.67	−	3211.92i	−0.456740	−	0.166240i	−0.560136	+	0.828400i	$0.689251\pi$
$140$	−503.106	−	599.579i	−0.0256687	−	0.0305907i
$141$		0			0
$142$	−23502.3	+	8554.13i	−1.16556	+	0.424228i
$143$	−55.7374	−	32.1800i	−0.00272568	−	0.00157367i
$144$		0			0
$145$	−2864.09	−	4960.74i	−0.136223	−	0.235945i
$146$	6734.32	−	8025.65i	0.315928	−	0.376508i
$147$		0			0
$148$	493.218	+	2797.18i	0.0225173	+	0.127702i
$149$	−14743.3	+	2599.65i	−0.664084	+	0.117096i	−0.495522	−	0.868595i	$-0.665023\pi$
$149$	−14743.3	+	2599.65i	−0.664084	+	0.117096i	−0.168562	+	0.985691i	$0.553912\pi$
$150$		0			0
$151$	10574.2	+	8872.78i	0.463759	+	0.389140i	0.844512	−	0.535537i	$-0.179891\pi$
$151$	10574.2	+	8872.78i	0.463759	+	0.389140i	−0.380753	+	0.924677i	$0.624335\pi$
$152$	19496.4	−	11256.2i	0.843853	−	0.487199i
$153$		0			0
$154$	−1512.25	+	2619.30i	−0.0637651	+	0.110444i
$155$	3156.93	+	8673.61i	0.131402	+	0.361024i
$156$		0			0
$157$	−17443.2	+	14636.6i	−0.707664	+	0.593800i	−0.923943	−	0.382531i	$-0.875052\pi$
$157$	−17443.2	+	14636.6i	−0.707664	+	0.593800i	0.216279	+	0.976332i	$0.430608\pi$
$158$	−9052.57	+	24871.7i	−0.362625	+	0.996304i
$159$		0			0
$160$	−551.442	+	3127.39i	−0.0215407	+	0.122163i
$161$			26936.5i			1.03918i
$162$		0			0
$163$	8385.18			0.315600			0.157800	−	0.987471i	$-0.449560\pi$
$163$	8385.18			0.315600			0.157800	+	0.987471i	$0.449560\pi$
$164$	6653.58	+	1173.21i	0.247382	+	0.0436201i
$165$		0			0
$166$	−25493.0	−	9278.71i	−0.925136	−	0.336722i
$167$	−14490.7	−	17269.3i	−0.519585	−	0.619217i	0.440898	−	0.897557i	$-0.354660\pi$
$167$	−14490.7	−	17269.3i	−0.519585	−	0.619217i	−0.960483	+	0.278340i	$0.910216\pi$
$168$		0			0
$169$	26830.3	−	9765.42i	0.939403	−	0.341915i
$170$	−6040.79	−	3487.65i	−0.209024	−	0.120680i
$171$		0			0
$172$	−3879.37	−	6719.26i	−0.131131	−	0.227125i
$173$	10444.2	−	12446.9i	0.348965	−	0.415880i	−0.562800	−	0.826593i	$-0.690276\pi$
$173$	10444.2	−	12446.9i	0.348965	−	0.415880i	0.911765	+	0.410713i	$0.134720\pi$
$174$		0			0
$175$	3167.87	+	17965.9i	0.103441	+	0.586642i
$176$	6618.70	−	1167.06i	0.213672	−	0.0376761i
$177$		0			0
$178$	7441.50	+	6244.16i	0.234866	+	0.197076i
$179$	−3194.81	+	1844.53i	−0.0997101	+	0.0575677i	−0.549026	−	0.835805i	$-0.685001\pi$
$179$	−3194.81	+	1844.53i	−0.0997101	+	0.0575677i	0.449316	+	0.893373i	$0.351668\pi$
$180$		0			0
$181$	−4327.00	+	7494.59i	−0.132078	+	0.228765i	−0.924477	−	0.381237i	$-0.875498\pi$
$181$	−4327.00	+	7494.59i	−0.132078	+	0.228765i	0.792400	+	0.610002i	$0.208832\pi$
$182$	141.622	+	389.103i	0.00427551	+	0.0117469i
$183$		0			0
$184$	34412.3	−	28875.3i	1.01643	−	0.852887i
$185$	−1064.86	+	2925.68i	−0.0311135	+	0.0854836i
$186$		0			0
$187$	−1085.93	+	6158.63i	−0.0310542	+	0.176117i
$188$			10661.6i			0.301653i
$189$		0			0
$190$	−10682.0			−0.295902
$191$	41395.1	+	7299.08i	1.13470	+	0.200079i	0.709288	−	0.704919i	$-0.249017\pi$
$191$	41395.1	+	7299.08i	1.13470	+	0.200079i	0.425416	+	0.904998i	$0.360128\pi$
$192$		0			0
$193$	−42862.3	−	15600.6i	−1.15070	−	0.418820i	−0.304932	−	0.952374i	$-0.598634\pi$
$193$	−42862.3	−	15600.6i	−1.15070	−	0.418820i	−0.845766	+	0.533555i	$0.820856\pi$
$194$	12084.0	+	14401.1i	0.321075	+	0.382643i
$195$		0			0
$196$	−6663.22	+	2425.21i	−0.173449	+	0.0631303i
$197$	−64536.0	−	37259.9i	−1.66291	−	0.960083i	−0.971314	−	0.237800i	$-0.923574\pi$
$197$	−64536.0	−	37259.9i	−1.66291	−	0.960083i	−0.691598	−	0.722283i	$-0.743093\pi$
$198$		0			0
$199$	−11151.7	−	19315.3i	−0.281601	−	0.487747i	0.690178	−	0.723639i	$-0.257532\pi$
$199$	−11151.7	−	19315.3i	−0.281601	−	0.487747i	−0.971779	+	0.235892i	$0.924199\pi$
$200$	19556.2	−	23306.1i	0.488904	−	0.582653i
$201$		0			0
$202$	−4139.27	−	23475.0i	−0.101443	−	0.575311i
$203$	32538.7	−	5737.45i	0.789602	−	0.139228i
$204$		0			0
$205$	5673.22	+	4760.40i	0.134996	+	0.113275i
$206$	73113.3	−	42212.0i	1.72291	−	0.994721i
$207$		0			0
$208$	460.061	−	796.849i	0.0106338	−	0.0184183i
$209$	3275.49	+	8999.33i	0.0749865	+	0.206024i
$210$		0			0
$211$	41046.5	−	34442.1i	0.921958	−	0.773615i	−0.0523980	−	0.998626i	$-0.516686\pi$
$211$	41046.5	−	34442.1i	0.921958	−	0.773615i	0.974356	+	0.225012i	$0.0722420\pi$
$212$	2540.81	−	6980.82i	0.0565328	−	0.155323i
$213$		0			0
$214$	14088.9	−	79902.1i	0.307645	−	1.74474i
$215$		−	8504.77i		−	0.183986i
$216$		0			0
$217$	−53241.0			−1.13065
$218$	−27553.3	−	4858.38i	−0.579776	−	0.102230i
$219$		0			0
$220$	−521.792	−	189.917i	−0.0107808	−	0.00392390i
$221$	550.332	+	655.860i	0.0112678	+	0.0134285i
$222$		0			0
$223$	45179.2	−	16443.9i	0.908509	−	0.330670i	0.154852	−	0.987938i	$-0.450510\pi$
$223$	45179.2	−	16443.9i	0.908509	−	0.330670i	0.753657	+	0.657268i	$0.228288\pi$
$224$	−15863.3	−	9158.67i	−0.316153	−	0.182531i
$225$		0			0
$226$	40477.6	+	70109.2i	0.792497	+	1.37265i
$227$	5517.87	−	6575.94i	0.107083	−	0.127616i	−0.709841	−	0.704362i	$-0.751233\pi$
$227$	5517.87	−	6575.94i	0.107083	−	0.127616i	0.816924	+	0.576746i	$0.195678\pi$
$228$		0			0
$229$	4767.31	+	27036.7i	0.0909080	+	0.515565i	0.995925	+	0.0901889i	$0.0287471\pi$
$229$	4767.31	+	27036.7i	0.0909080	+	0.515565i	−0.905017	+	0.425376i	$0.860142\pi$
$230$	−20991.4	+	3701.36i	−0.396814	+	0.0699690i
$231$		0			0
$232$	−42210.6	−	35418.9i	−0.784233	−	0.658050i
$233$	−26428.8	+	15258.7i	−0.486817	+	0.281064i	−0.723253	−	0.690583i	$-0.757354\pi$
$233$	−26428.8	+	15258.7i	−0.486817	+	0.281064i	0.236436	+	0.971647i	$0.424021\pi$
$234$		0			0
$235$	−5843.39	+	10121.0i	−0.105811	+	0.183269i
$236$	2172.94	+	5970.10i	0.0390142	+	0.107191i
$237$		0			0
$238$	30821.2	−	25862.1i	0.544121	−	0.456572i
$239$	−11167.1	+	30681.4i	−0.195499	+	0.537129i	−0.998247	−	0.0591894i	$-0.981148\pi$
$239$	−11167.1	+	30681.4i	−0.195499	+	0.537129i	0.802748	+	0.596319i	$0.203371\pi$
$240$		0			0
$241$	−14816.1	+	84026.5i	−0.255095	+	1.44671i	0.540735	+	0.841193i	$0.318146\pi$
$241$	−14816.1	+	84026.5i	−0.255095	+	1.44671i	−0.795830	+	0.605520i	$0.792965\pi$
$242$		−	64681.4i		−	1.10446i
$243$		0			0
$244$	14481.0			0.243232
$245$	−7654.58	−	1349.71i	−0.127523	−	0.0224858i
$246$		0			0
$247$	1232.07	+	448.436i	0.0201948	+	0.00735032i
$248$	57073.2	+	68017.2i	0.927960	+	1.10590i
$249$		0			0
$250$	−27768.8	+	10107.0i	−0.444301	+	0.161712i
$251$	−29664.6	−	17126.9i	−0.470859	−	0.271851i	0.245740	−	0.969336i	$-0.420969\pi$
$251$	−29664.6	−	17126.9i	−0.470859	−	0.271851i	−0.716599	+	0.697485i	$0.754302\pi$
$252$		0			0
$253$	9555.00	+	16549.7i	0.149276	+	0.258553i
$254$	−73777.0	+	87923.9i	−1.14355	+	1.36282i
$255$		0			0
$256$	9467.40	+	53692.3i	0.144461	+	0.819280i
$257$	−9684.06	+	1707.56i	−0.146619	+	0.0258529i	−0.246476	−	0.969149i	$-0.579273\pi$
$257$	−9684.06	+	1707.56i	−0.146619	+	0.0258529i	0.0998567	+	0.995002i	$0.468162\pi$
$258$		0			0
$259$	−13757.1	−	11543.6i	−0.205082	−	0.172084i
$260$	−65.8365	+	38.0107i	−0.000973913	+	0.000562289i
$261$		0			0
$262$	−44079.0	+	76347.0i	−0.642139	+	1.11222i
$263$	4436.12	+	12188.1i	0.0641345	+	0.176208i	0.967621	−	0.252409i	$-0.0812230\pi$
$263$	4436.12	+	12188.1i	0.0641345	+	0.176208i	−0.903486	+	0.428618i	$0.859001\pi$
$264$		0			0
$265$	6238.02	−	5234.32i	0.0888290	−	0.0745364i
$266$	21073.6	−	57899.2i	0.297835	−	0.818294i
$267$		0			0
$268$	6869.26	−	38957.5i	0.0956401	−	0.542402i
$269$			59552.5i			0.822992i	0.911412	+	0.411496i	$0.134994\pi$
$269$			59552.5i			0.822992i	−0.911412	+	0.411496i	$0.865006\pi$
$270$		0			0
$271$	−9217.27			−0.125506			−0.0627529	−	0.998029i	$-0.519988\pi$
$271$	−9217.27			−0.125506			−0.0627529	+	0.998029i	$0.519988\pi$
$272$	−88046.8	−	15525.0i	−1.19008	−	0.209843i
$273$		0			0
$274$	46740.6	+	17012.2i	0.622577	+	0.226600i
$275$	8319.26	+	9914.51i	0.110007	+	0.131101i
$276$		0			0
$277$	−47228.6	+	17189.8i	−0.615525	+	0.224033i	−0.630919	−	0.775849i	$-0.717322\pi$
$277$	−47228.6	+	17189.8i	−0.615525	+	0.224033i	0.0153938	+	0.999882i	$0.495100\pi$
$278$	37121.5	+	21432.1i	0.480326	+	0.277316i
$279$		0			0
$280$	−4126.53	−	7147.36i	−0.0526343	−	0.0911653i
$281$	−54411.4	+	64845.0i	−0.689092	+	0.821228i	−0.991246	−	0.132032i	$-0.957850\pi$
$281$	−54411.4	+	64845.0i	−0.689092	+	0.821228i	0.302154	+	0.953259i	$0.402294\pi$
$282$		0			0
$283$	18732.8	+	106239.i	0.233900	+	1.32651i	0.844918	+	0.534896i	$0.179649\pi$
$283$	18732.8	+	106239.i	0.233900	+	1.32651i	−0.611018	+	0.791617i	$0.709240\pi$
$284$	26083.5	−	4599.22i	0.323392	−	0.0570227i
$285$		0			0
$286$	225.036	+	188.828i	0.00275119	+	0.00230852i
$287$	−36994.7	+	21358.9i	−0.449133	+	0.259307i
$288$		0			0
$289$	−165.227	+	286.182i	−0.00197827	+	0.00342647i
$290$	8942.32	+	24568.8i	0.106330	+	0.292138i
$291$		0			0
$292$	−8499.04	+	7131.54i	−0.0996791	+	0.0836407i
$293$	4123.53	−	11329.3i	0.0480323	−	0.131968i	−0.913357	−	0.407160i	$-0.866519\pi$
$293$	4123.53	−	11329.3i	0.0480323	−	0.131968i	0.961389	+	0.275192i	$0.0887414\pi$
$294$		0			0
$295$	−1209.31	+	6858.34i	−0.0138961	+	0.0788088i
$296$			29949.6i			0.341828i
$297$		0			0
$298$	68332.4			0.769474
$299$	2576.54	+	454.313i	0.0288200	+	0.00508175i
$300$		0			0
$301$	46097.9	+	16778.3i	0.508801	+	0.185188i
$302$	−40498.8	−	48264.6i	−0.444046	−	0.529194i
$303$		0			0
$304$	−128659.	+	46828.0i	−1.39217	+	0.506708i
$305$	13746.8	+	7936.73i	0.147775	+	0.0853182i
$306$		0			0
$307$	−57424.8	−	99462.6i	−0.609288	−	1.05532i	−0.991358	−	0.131184i	$-0.958122\pi$
$307$	−57424.8	−	99462.6i	−0.609288	−	1.05532i	0.382070	−	0.924133i	$-0.375211\pi$
$308$	2058.79	−	2453.57i	0.0217025	−	0.0258641i
$309$		0			0
$310$	−7315.88	−	41490.4i	−0.0761278	−	0.431742i
$311$	178521.	−	31478.1i	1.84574	−	0.325453i	0.862256	−	0.506473i	$-0.169051\pi$
$311$	178521.	−	31478.1i	1.84574	−	0.325453i	0.983479	+	0.181020i	$0.0579400\pi$
$312$		0			0
$313$	−74737.6	−	62712.3i	−0.762870	−	0.640124i	0.176002	−	0.984390i	$-0.443683\pi$
$313$	−74737.6	−	62712.3i	−0.762870	−	0.640124i	−0.938872	+	0.344266i	$0.888128\pi$
$314$	90008.8	−	51966.6i	0.912906	−	0.527066i
$315$		0			0
$316$	14014.6	−	24273.9i	0.140348	−	0.243090i
$317$	−12894.1	−	35426.2i	−0.128313	−	0.352538i	0.858855	−	0.512218i	$-0.171176\pi$
$317$	−12894.1	−	35426.2i	−0.128313	−	0.352538i	−0.987169	+	0.159680i	$0.948954\pi$
$318$		0			0
$319$	17956.5	−	15067.3i	0.176458	−	0.148066i
$320$	−4030.02	+	11072.4i	−0.0393557	+	0.108129i
$321$		0			0
$322$	21349.8	−	121081.i	0.205912	−	1.16779i
$323$		−	127399.i		−	1.22113i
$324$		0			0
$325$	1771.91			0.0167755
$326$	−37691.7	−	6646.07i	−0.354659	−	0.0625359i
$327$		0			0
$328$	66944.2	+	24365.7i	0.622250	+	0.226481i
$329$	−43330.6	−	51639.4i	−0.400316	−	0.477078i
$330$		0			0
$331$	173465.	−	63136.1i	1.58327	−	0.576264i	0.607360	−	0.794427i	$-0.292228\pi$
$331$	173465.	−	63136.1i	1.58327	−	0.576264i	0.975912	+	0.218162i	$0.0700062\pi$
$332$	24880.3	+	14364.7i	0.225725	+	0.130322i
$333$		0			0
$334$	51448.7	+	89111.7i	0.461192	+	0.798807i
$335$	27872.7	−	33217.4i	0.248364	−	0.295989i
$336$		0			0
$337$	−30162.8	−	171062.i	−0.265590	−	1.50623i	−0.767350	−	0.641228i	$-0.778425\pi$
$337$	−30162.8	−	171062.i	−0.265590	−	1.50623i	0.501761	−	0.865007i	$-0.332686\pi$
$338$	−128343.	+	22630.4i	−1.12341	+	0.198088i
$339$		0			0
$340$	5658.57	+	4748.10i	0.0489496	+	0.0410736i
$341$	−32711.2	+	18885.8i	−0.281312	+	0.162415i
$342$		0			0
$343$	59106.0	−	102375.i	0.502393	−	0.870169i
$344$	−27981.1	−	76877.6i	−0.236455	−	0.649655i
$345$		0			0
$346$	−56812.3	+	47671.2i	−0.474559	+	0.398203i
$347$	11813.0	−	32455.8i	0.0981070	−	0.269547i	−0.880924	−	0.473257i	$-0.843078\pi$
$347$	11813.0	−	32455.8i	0.0981070	−	0.269547i	0.979031	+	0.203711i	$0.0653002\pi$
$348$		0			0
$349$	−9436.44	+	53516.7i	−0.0774743	+	0.439378i	0.921254	+	0.388962i	$0.127166\pi$
$349$	−9436.44	+	53516.7i	−0.0774743	+	0.439378i	−0.998728	+	0.0504169i	$0.983945\pi$
$350$		−	83268.4i		−	0.679742i
$351$		0			0
$352$	−12995.2			−0.104881
$353$	192496.	+	33942.3i	1.54480	+	0.272391i	0.880126	−	0.474740i	$-0.157458\pi$
$353$	192496.	+	33942.3i	1.54480	+	0.272391i	0.664678	+	0.747130i	$0.268569\pi$
$354$		0			0
$355$	27281.7	+	9929.73i	0.216479	+	0.0787917i
$356$	−6612.47	−	7880.43i	−0.0521751	−	0.0621799i
$357$		0			0
$358$	15822.8	−	5759.02i	0.123457	−	0.0449348i
$359$	98785.0	+	57033.5i	0.766482	+	0.442529i	0.831618	−	0.555348i	$-0.187415\pi$
$359$	98785.0	+	57033.5i	0.766482	+	0.442529i	−0.0651363	+	0.997876i	$0.520748\pi$
$360$		0			0
$361$	−32389.4	−	56100.1i	−0.248535	−	0.430476i
$362$	25390.2	−	30258.9i	0.193754	−	0.230907i
$363$		0			0
$364$	−76.1446	−	431.837i	−0.000574693	−	0.00325925i
$365$	−11976.8	+	2111.83i	−0.0898987	+	0.0158516i
$366$		0			0
$367$	4564.10	+	3829.73i	0.0338862	+	0.0284339i	0.659573	−	0.751640i	$-0.270737\pi$
$367$	4564.10	+	3829.73i	0.0338862	+	0.0284339i	−0.625687	+	0.780074i	$0.715181\pi$
$368$	−236603.	+	136603.i	−1.74713	+	1.00871i
$369$		0			0
$370$	7105.47	−	12307.0i	0.0519026	−	0.0898980i
$371$	16064.9	+	44137.8i	0.116716	+	0.320674i
$372$		0			0
$373$	−103345.	+	86717.1i	−0.742803	+	0.623286i	−0.933589	−	0.358346i	$-0.883341\pi$
$373$	−103345.	+	86717.1i	−0.742803	+	0.623286i	0.190786	+	0.981632i	$0.438896\pi$
$374$	9762.63	−	26822.6i	0.0697949	−	0.191760i
$375$		0			0
$376$	−19521.6	+	110713.i	−0.138083	+	0.783108i
$377$		−	3209.17i		−	0.0225793i
$378$		0			0
$379$	−58032.4			−0.404010			−0.202005	−	0.979385i	$-0.564746\pi$
$379$	−58032.4			−0.404010			−0.202005	+	0.979385i	$0.564746\pi$
$380$	11140.3	+	1964.33i	0.0771487	+	0.0136034i
$381$		0			0
$382$	−180288.	−	65619.3i	−1.23549	−	0.449682i
$383$	86216.3	+	102749.i	0.587749	+	0.700452i	0.975172	−	0.221450i	$-0.0710790\pi$
$383$	86216.3	+	102749.i	0.587749	+	0.700452i	−0.387423	+	0.921902i	$0.626635\pi$
$384$		0			0
$385$	3299.15	−	1200.79i	0.0222577	−	0.00810114i
$386$	180303.	+	104098.i	1.21012	+	0.698663i
$387$		0			0
$388$	−9954.11	−	17241.0i	−0.0661210	−	0.114525i
$389$	167201.	−	199262.i	1.10494	−	1.31682i	0.160908	−	0.986969i	$-0.448558\pi$
$389$	167201.	−	199262.i	1.10494	−	1.31682i	0.944034	−	0.329849i	$-0.106998\pi$
$390$		0			0
$391$	−44144.0	−	250353.i	−0.288748	−	1.63757i
$392$	−73633.0	+	12983.5i	−0.479182	+	0.0844927i
$393$		0			0
$394$	260560.	+	218636.i	1.67848	+	1.40841i
$395$	26608.0	−	15362.1i	0.170537	−	0.0984594i
$396$		0			0
$397$	−39496.9	+	68410.6i	−0.250600	+	0.434053i	−0.963691	−	0.267019i	$-0.913961\pi$
$397$	−39496.9	+	68410.6i	−0.250600	+	0.434053i	0.713091	+	0.701072i	$0.247295\pi$
$398$	34818.0	+	95661.8i	0.219805	+	0.603910i
$399$		0			0
$400$	−141743.	+	118936.i	−0.885892	+	0.743351i
$401$	−78196.3	+	214842.i	−0.486292	+	1.33608i	0.417722	+	0.908575i	$0.362829\pi$
$401$	−78196.3	+	214842.i	−0.486292	+	1.33608i	−0.904014	+	0.427502i	$0.859394\pi$
$402$		0			0
$403$	−897.967	+	5092.63i	−0.00552905	+	0.0313568i
$404$			25243.2i			0.154661i
$405$		0			0
$406$	−150810.			−0.914911
$407$	−12547.1	−	2212.40i	−0.0757452	−	0.0133559i
$408$		0			0
$409$	64715.1	+	23554.4i	0.386864	+	0.140807i	0.528128	−	0.849165i	$-0.322894\pi$
$409$	64715.1	+	23554.4i	0.386864	+	0.140807i	−0.141263	+	0.989972i	$0.545116\pi$
$410$	−21728.3	−	25894.8i	−0.129258	−	0.154044i
$411$		0			0
$412$	−84012.0	+	30577.9i	−0.494933	+	0.180141i
$413$	−34788.1	−	20084.9i	−0.203953	−	0.117752i
$414$		0			0
$415$	15745.9	+	27272.7i	0.0914263	+	0.158355i
$416$	−1143.60	+	1362.89i	−0.00660826	+	0.00787542i
$417$		0			0
$418$	−7590.61	−	43048.5i	−0.0434434	−	0.246380i
$419$	−125988.	+	22215.0i	−0.717629	+	0.126537i	−0.520526	−	0.853846i	$-0.674264\pi$
$419$	−125988.	+	22215.0i	−0.717629	+	0.126537i	−0.197103	+	0.980383i	$0.563153\pi$
$420$		0			0
$421$	132517.	+	111195.i	0.747665	+	0.627365i	0.934884	−	0.354953i	$-0.115503\pi$
$421$	132517.	+	111195.i	0.747665	+	0.627365i	−0.187219	+	0.982318i	$0.559947\pi$
$422$	−211804.	+	122285.i	−1.18935	+	0.686672i
$423$		0			0
$424$	39166.4	−	67838.2i	0.217862	−	0.377349i
$425$	−58885.7	−	161787.i	−0.326011	−	0.895708i
$426$		0			0
$427$	−70138.8	+	58853.4i	−0.384682	+	0.322787i
$428$	−29386.5	+	80738.8i	−0.160421	+	0.440753i
$429$		0			0
$430$	−6740.86	+	38229.3i	−0.0364568	+	0.206757i
$431$		−	95875.3i		−	0.516122i	−0.966129	−	0.258061i	$-0.916916\pi$
$431$		−	95875.3i		−	0.516122i	0.966129	−	0.258061i	$-0.0830836\pi$
$432$		0			0
$433$	309887.			1.65283			0.826413	−	0.563064i	$-0.190378\pi$
$433$	309887.			1.65283			0.826413	+	0.563064i	$0.190378\pi$
$434$	239321.	+	42198.7i	1.27058	+	0.224037i
$435$		0			0
$436$	27841.8	+	10133.6i	0.146462	+	0.0533077i
$437$	−250242.	−	298227.i	−1.31038	−	1.56165i
$438$		0			0
$439$	185854.	−	67645.2i	0.964366	−	0.351001i	0.188623	−	0.982050i	$-0.439598\pi$
$439$	185854.	−	67645.2i	0.964366	−	0.351001i	0.775743	+	0.631049i	$0.217375\pi$
$440$	−5070.67	−	2927.55i	−0.0261915	−	0.0151217i
$441$		0			0
$442$	−1953.93	−	3384.31i	−0.0100015	−	0.0173231i
$443$	3449.16	−	4110.54i	0.0175754	−	0.0209456i	−0.757185	−	0.653200i	$-0.773426\pi$
$443$	3449.16	−	4110.54i	0.0175754	−	0.0209456i	0.774761	+	0.632255i	$0.217870\pi$
$444$		0			0
$445$	−1958.11	−	11105.0i	−0.00988822	−	0.0560789i
$446$	−216116.	+	38107.1i	−1.08647	+	0.191574i
$447$		0			0
$448$	−52064.6	−	43687.4i	−0.259410	−	0.217671i
$449$	−94142.3	+	54353.1i	−0.466974	+	0.269607i	−0.714972	−	0.699153i	$-0.753561\pi$
$449$	−94142.3	+	54353.1i	−0.466974	+	0.269607i	0.247998	+	0.968760i	$0.420227\pi$
$450$		0			0
$451$	−15153.0	+	26245.7i	−0.0744980	+	0.129034i
$452$	−29321.5	−	80560.1i	−0.143519	−	0.394315i
$453$		0			0
$454$	−30015.1	+	25185.7i	−0.145623	+	0.122192i
$455$	164.396	−	451.675i	0.000794089	−	0.00218174i
$456$		0			0
$457$	−20255.9	+	114877.i	−0.0969881	+	0.550047i	0.897132	+	0.441763i	$0.145647\pi$
$457$	−20255.9	+	114877.i	−0.0969881	+	0.550047i	−0.994120	+	0.108284i	$0.965464\pi$
$458$		−	125310.i		−	0.597385i
$459$		0			0
$460$	22572.5			0.106676
$461$	−407829.	−	71911.3i	−1.91901	−	0.338373i	−0.920392	−	0.390997i	$-0.872130\pi$
$461$	−407829.	−	71911.3i	−1.91901	−	0.338373i	−0.998614	+	0.0526243i	$0.983241\pi$
$462$		0			0
$463$	55310.7	+	20131.4i	0.258016	+	0.0939102i	0.467790	−	0.883840i	$-0.345050\pi$
$463$	55310.7	+	20131.4i	0.258016	+	0.0939102i	−0.209774	+	0.977750i	$0.567273\pi$
$464$	215410.	+	256715.i	1.00053	+	1.19238i
$465$		0			0
$466$	130893.	−	47641.0i	0.602758	−	0.219386i
$467$	250588.	+	144677.i	1.14902	+	0.663384i	0.948647	−	0.316337i	$-0.102453\pi$
$467$	250588.	+	144677.i	1.14902	+	0.663384i	0.200368	+	0.979721i	$0.435786\pi$
$468$		0			0
$469$	125059.	+	216608.i	0.568549	+	0.984756i
$470$	34288.2	−	40863.1i	0.155220	−	0.184984i
$471$		0			0
$472$	11632.9	+	65973.6i	0.0522161	+	0.296132i
$473$	34274.1	−	6043.45i	0.153195	−	0.0270124i
$474$		0			0
$475$	−201978.	−	169479.i	−0.895192	−	0.751156i
$476$	−36899.1	+	21303.7i	−0.162855	+	0.0940246i
$477$		0			0
$478$	74514.6	−	129063.i	0.326126	−	0.564867i
$479$	99918.0	+	274522.i	0.435484	+	1.19648i	0.942400	+	0.334488i	$0.108563\pi$
$479$	99918.0	+	274522.i	0.435484	+	1.19648i	−0.506916	+	0.861996i	$0.669215\pi$
$480$		0			0
$481$	−1336.20	+	1121.20i	−0.00577538	+	0.00484612i
$482$	133198.	−	365960.i	0.573330	−	1.57521i
$483$		0			0
$484$	−11894.3	+	67456.0i	−0.0507749	+	0.287959i
$485$		−	21822.5i		−	0.0927728i
$486$		0			0
$487$	−92077.0			−0.388234			−0.194117	−	0.980978i	$-0.562184\pi$
$487$	−92077.0			−0.388234			−0.194117	+	0.980978i	$0.562184\pi$
$488$	150374.	+	26515.1i	0.631443	+	0.111341i
$489$		0			0
$490$	33337.9	+	12134.0i	0.138850	+	0.0505373i
$491$	−80976.3	−	96503.8i	−0.335888	−	0.400296i	0.571491	−	0.820608i	$-0.306365\pi$
$491$	−80976.3	−	96503.8i	−0.335888	−	0.400296i	−0.907380	+	0.420312i	$0.861921\pi$
$492$		0			0
$493$	−293019.	+	106650.i	−1.20559	+	0.438801i
$494$	−5182.77	−	2992.27i	−0.0212377	−	0.0122616i
$495$		0			0
$496$	−270001.	−	467655.i	−1.09749	−	1.90091i
$497$	−107643.	+	128284.i	−0.435786	+	0.519349i
$498$		0			0
$499$	40143.7	+	227666.i	0.161219	+	0.914319i	0.952878	+	0.303355i	$0.0981069\pi$
$499$	40143.7	+	227666.i	0.161219	+	0.914319i	−0.791658	+	0.610964i	$0.790782\pi$
$500$	30818.6	−	5434.15i	0.123274	−	0.0217366i
$501$		0			0
$502$	119769.	+	100498.i	0.475266	+	0.398796i
$503$	−102094.	+	58943.8i	−0.403518	+	0.232971i	−0.688001	−	0.725710i	$-0.741511\pi$
$503$	−102094.	+	58943.8i	−0.403518	+	0.232971i	0.284483	+	0.958681i	$0.408178\pi$
$504$		0			0
$505$	−13835.2	+	23963.3i	−0.0542504	+	0.0939644i
$506$	−29832.8	−	81965.1i	−0.116518	−	0.320131i
$507$		0			0
$508$	93110.1	−	78128.7i	0.360802	−	0.302749i
$509$	−26711.8	+	73390.0i	−0.103102	+	0.283271i	−0.980508	−	0.196477i	$-0.937050\pi$
$509$	−26711.8	+	73390.0i	−0.103102	+	0.283271i	0.877406	+	0.479748i	$0.159272\pi$
$510$		0			0
$511$	12181.2	−	69083.1i	0.0466497	−	0.264564i
$512$			66993.2i			0.255559i
$513$		0			0
$514$	44883.7			0.169888
$515$	−96511.4	−	17017.6i	−0.363885	−	0.0641627i
$516$		0			0
$517$	−44939.9	−	16356.8i	−0.168132	−	0.0611952i
$518$	52689.4	+	62792.7i	0.196365	+	0.234018i
$519$		0			0
$520$	−753.260	+	274.164i	−0.00278572	+	0.00101392i
$521$	433604.	+	250342.i	1.59742	+	0.922269i	0.991983	+	0.126373i	$0.0403336\pi$
$521$	433604.	+	250342.i	1.59742	+	0.922269i	0.605434	+	0.795896i	$0.293000\pi$
$522$		0			0
$523$	7028.79	+	12174.2i	0.0256967	+	0.0445079i	0.878588	−	0.477581i	$-0.158486\pi$
$523$	7028.79	+	12174.2i	0.0256967	+	0.0445079i	−0.852891	+	0.522089i	$0.825153\pi$
$524$	60009.3	−	71516.3i	0.218553	−	0.260461i
$525$		0			0
$526$	−10280.3	−	58302.3i	−0.0371563	−	0.210724i
$527$	494833.	−	87252.4i	1.78171	−	0.314164i
$528$		0			0
$529$	−380721.	−	319462.i	−1.36049	−	1.14159i
$530$	−32188.9	+	18584.2i	−0.114592	+	0.0661597i
$531$		0			0
$532$	−32624.7	+	56507.7i	−0.115272	+	0.199657i
$533$	1419.07	+	3898.86i	0.00499516	+	0.0137241i
$534$		0			0
$535$	−72147.7	+	60539.1i	−0.252066	+	0.211509i
$536$	142664.	−	391966.i	0.496575	−	1.36433i
$537$		0			0
$538$	47201.2	−	267691.i	0.163075	−	0.924846i
$539$		−	31807.0i		−	0.109482i
$540$		0			0
$541$	−88604.0			−0.302732			−0.151366	−	0.988478i	$-0.548367\pi$
$541$	−88604.0			−0.302732			−0.151366	+	0.988478i	$0.548367\pi$
$542$	41432.0	+	7305.58i	0.141038	+	0.0248689i
$543$		0			0
$544$	162446.	+	59125.5i	0.548923	+	0.199792i
$545$	20876.2	+	24879.2i	0.0702842	+	0.0837614i
$546$		0			0
$547$	−268634.	+	97774.9i	−0.897815	+	0.326778i	−0.749377	−	0.662144i	$-0.769647\pi$
$547$	−268634.	+	97774.9i	−0.897815	+	0.326778i	−0.148438	+	0.988922i	$0.547425\pi$
$548$	−45617.2	−	26337.1i	−0.151903	−	0.0877015i
$549$		0			0
$550$	−29537.2	−	51159.9i	−0.0976437	−	0.169124i
$551$	−306950.	+	365809.i	−1.01103	+	1.20490i
$552$		0			0
$553$	30774.0	+	174528.i	0.100632	+	0.570710i
$554$	225919.	−	39835.7i	0.736095	−	0.129793i
$555$		0			0
$556$	−34772.7	−	29177.8i	−0.112484	−	0.0943849i
$557$	439295.	−	253627.i	1.41594	−	0.817496i	0.420005	−	0.907522i	$-0.362028\pi$
$557$	439295.	−	253627.i	1.41594	−	0.817496i	0.995939	+	0.0900257i	$0.0286949\pi$
$558$		0			0
$559$	2382.37	−	4126.38i	0.00762405	−	0.0132052i
$560$	17167.1	+	47166.2i	0.0547421	+	0.150403i
$561$		0			0
$562$	295977.	−	248354.i	0.937100	−	0.786320i
$563$	−174351.	+	479027.i	−0.550058	+	1.51127i	0.283572	+	0.958951i	$0.408480\pi$
$563$	−174351.	+	479027.i	−0.550058	+	1.51127i	−0.833631	+	0.552322i	$0.813742\pi$
$564$		0			0
$565$	16318.4	−	92546.0i	0.0511187	−	0.289908i
$566$		−	492397.i		−	1.53703i
$567$		0			0
$568$	279278.			0.865646
$569$	−202415.	−	35691.1i	−0.625197	−	0.110239i	−0.147931	−	0.988998i	$-0.547261\pi$
$569$	−202415.	−	35691.1i	−0.625197	−	0.110239i	−0.477267	+	0.878759i	$0.658372\pi$
$570$		0			0
$571$	−149528.	−	54423.6i	−0.458616	−	0.166922i	0.102373	−	0.994746i	$-0.467357\pi$
$571$	−149528.	−	54423.6i	−0.458616	−	0.166922i	−0.560988	+	0.827824i	$0.689579\pi$
$572$	−199.966	−	238.310i	−0.000611172	−	0.000728367i
$573$		0			0
$574$	183222.	−	66687.2i	0.556100	−	0.202404i
$575$	−455635.	−	263061.i	−1.37810	−	0.795647i
$576$		0			0
$577$	247561.	+	428789.i	0.743586	+	1.28793i	0.950852	+	0.309645i	$0.100210\pi$
$577$	247561.	+	428789.i	0.743586	+	1.28793i	−0.207266	+	0.978285i	$0.566457\pi$
$578$	969.530	−	1155.44i	0.00290206	−	0.00345854i
$579$		0			0
$580$	−4807.93	−	27267.1i	−0.0142923	−	0.0810557i
$581$	−178888.	+	31542.8i	−0.529943	+	0.0934432i
$582$		0			0
$583$	25526.9	+	21419.6i	0.0751037	+	0.0630195i
$584$	−101314.	+	58493.7i	−0.297060	+	0.171508i
$585$		0			0
$586$	−27515.0	+	47657.4i	−0.0801261	+	0.138783i
$587$	−162016.	−	445137.i	−0.470200	−	1.29187i	−0.917591	−	0.397526i	$-0.869869\pi$
$587$	−162016.	−	445137.i	−0.470200	−	1.29187i	0.447390	−	0.894339i	$-0.352353\pi$
$588$		0			0
$589$	589457.	−	494613.i	1.69911	−	1.42572i
$590$	10871.8	−	29870.0i	0.0312318	−	0.0858087i
$591$		0			0
$592$	31629.5	−	179380.i	0.0902503	−	0.511835i
$593$		−	15066.4i		−	0.0428449i	−0.999771	−	0.0214224i	$-0.993181\pi$
$593$		−	15066.4i		−	0.0428449i	0.999771	−	0.0214224i	$-0.00681949\pi$
$594$		0			0
$595$	−46704.3			−0.131924
$596$	−71263.6	−	12565.7i	−0.200620	−	0.0353748i
$597$		0			0
$598$	−11221.6	−	4084.31i	−0.0313798	−	0.0114213i
$599$	−134668.	−	160491.i	−0.375328	−	0.447298i	0.545006	−	0.838432i	$-0.316527\pi$
$599$	−134668.	−	160491.i	−0.375328	−	0.447298i	−0.920334	+	0.391134i	$0.872083\pi$
$600$		0			0
$601$	75619.0	−	27523.0i	0.209354	−	0.0761987i	−0.235214	−	0.971944i	$-0.575579\pi$
$601$	75619.0	−	27523.0i	0.209354	−	0.0761987i	0.444569	+	0.895745i	$0.353357\pi$
$602$	−193914.	−	111956.i	−0.535076	−	0.308926i
$603$		0			0
$604$	33360.6	+	57782.3i	0.0914451	+	0.158387i
$605$	−48262.4	+	57516.9i	−0.131855	+	0.157139i
$606$		0			0
$607$	71808.1	+	407244.i	0.194893	+	1.10529i	0.912571	+	0.408917i	$0.134094\pi$
$607$	71808.1	+	407244.i	0.194893	+	1.10529i	−0.717679	+	0.696374i	$0.754795\pi$
$608$	260715.	−	45971.1i	0.705276	−	0.124359i
$609$		0			0
$610$	−55501.9	−	46571.6i	−0.149159	−	0.125159i
$611$	−5670.24	+	3273.72i	−0.0151887	+	0.00876917i
$612$		0			0
$613$	−103985.	+	180108.i	−0.276727	+	0.479305i	−0.970569	−	0.240822i	$-0.922583\pi$
$613$	−103985.	+	180108.i	−0.276727	+	0.479305i	0.693843	+	0.720127i	$0.255916\pi$
$614$	179293.	+	492603.i	0.475583	+	1.30665i
$615$		0			0
$616$	25871.5	−	21708.7i	0.0681804	−	0.0572102i
$617$	−32768.0	+	90029.3i	−0.0860755	+	0.236490i	−0.975261	−	0.221056i	$-0.929050\pi$
$617$	−32768.0	+	90029.3i	−0.0860755	+	0.236490i	0.889186	+	0.457547i	$0.151272\pi$
$618$		0			0
$619$	28352.2	−	160793.i	0.0739954	−	0.419649i	−0.925198	−	0.379486i	$-0.876101\pi$
$619$	28352.2	−	160793.i	0.0739954	−	0.419649i	0.999193	−	0.0401635i	$-0.0127879\pi$
$620$			44615.5i			0.116065i
$621$		0			0
$622$	−827410.			−2.13865
$623$	64054.8	+	11294.6i	0.165035	+	0.0291001i
$624$		0			0
$625$	−318346.	−	115868.i	−0.814965	−	0.296623i
$626$	286243.	+	341131.i	0.730443	+	0.870509i
$627$		0			0
$628$	−103426.	+	37644.0i	−0.262247	+	0.0954502i
$629$	146779.	+	84743.0i	0.370991	+	0.214192i
$630$		0			0
$631$	66259.5	+	114765.i	0.166414	+	0.288237i	0.937156	−	0.348909i	$-0.113448\pi$
$631$	66259.5	+	114765.i	0.166414	+	0.288237i	−0.770743	+	0.637147i	$0.780115\pi$
$632$	189977.	−	226405.i	0.475627	−	0.566830i
$633$		0			0
$634$	29880.7	+	169462.i	0.0743383	+	0.421594i
$635$	131210.	−	23135.8i	0.325401	−	0.0573770i
$636$		0			0
$637$	−3335.80	−	2799.07i	−0.00822094	−	0.00689819i
$638$	−92657.6	+	53495.9i	−0.227635	+	0.131425i
$639$		0			0
$640$	52296.1	−	90579.5i	0.127676	−	0.221141i
$641$	53876.6	+	148025.i	0.131125	+	0.360262i	0.987829	−	0.155547i	$-0.0497139\pi$
$641$	53876.6	+	148025.i	0.131125	+	0.360262i	−0.856704	+	0.515808i	$0.827492\pi$
$642$		0			0
$643$	−13670.2	+	11470.6i	−0.0330637	+	0.0277437i	−0.659170	−	0.751994i	$-0.729092\pi$
$643$	−13670.2	+	11470.6i	−0.0330637	+	0.0277437i	0.626106	+	0.779738i	$0.284648\pi$
$644$	−44531.2	+	122349.i	−0.107373	+	0.295004i
$645$		0			0
$646$	−100976.	+	572663.i	−0.241965	+	1.37225i
$647$		−	484495.i		−	1.15739i	−0.815543	−	0.578696i	$-0.803562\pi$
$647$		−	484495.i		−	1.15739i	0.815543	−	0.578696i	$-0.196438\pi$
$648$		0			0
$649$	−28498.3			−0.0676597
$650$	−7964.81	−	1404.41i	−0.0188516	−	0.00332405i
$651$		0			0
$652$	38086.4	+	13862.3i	0.0895932	+	0.0326092i
$653$	279134.	+	332658.i	0.654615	+	0.780139i	0.986602	−	0.163144i	$-0.0521637\pi$
$653$	279134.	+	332658.i	0.654615	+	0.780139i	−0.331988	+	0.943284i	$0.607719\pi$
$654$		0			0
$655$	96163.2	−	35000.5i	0.224143	−	0.0815816i
$656$	−375222.	−	216634.i	−0.871927	−	0.503408i
$657$		0			0
$658$	153844.	+	266465.i	0.355327	+	0.615444i
$659$	−368729.	+	439434.i	−0.849056	+	1.01187i	0.150673	+	0.988584i	$0.451856\pi$
$659$	−368729.	+	439434.i	−0.849056	+	1.01187i	−0.999729	+	0.0232815i	$0.992589\pi$
$660$		0			0
$661$	−56618.1	−	321097.i	−0.129584	−	0.734909i	−0.978479	−	0.206347i	$-0.933842\pi$
$661$	−56618.1	−	321097.i	−0.129584	−	0.734909i	0.848895	−	0.528562i	$-0.177269\pi$
$662$	−829774.	+	146311.i	−1.89341	+	0.333859i
$663$		0			0
$664$	232061.	+	194722.i	0.526340	+	0.441652i
$665$	−61941.1	+	35761.7i	−0.140067	+	0.0808677i
$666$		0			0
$667$	−476439.	+	825216.i	−1.07092	+	1.85488i
$668$	−37268.8	−	102395.i	−0.0835204	−	0.229470i
$669$		0			0
$670$	−151617.	+	127222.i	−0.337752	+	0.283408i
$671$	−22216.5	+	61039.3i	−0.0493435	+	0.135570i
$672$		0			0
$673$	50573.5	−	286817.i	0.111659	−	0.633248i	−0.876692	−	0.481053i	$-0.840255\pi$
$673$	50573.5	−	286817.i	0.111659	−	0.633248i	0.988350	−	0.152196i	$-0.0486344\pi$
$674$			792836.i			1.74527i
$675$		0			0
$676$	138010.			0.302008
$677$	548456.	+	96707.7i	1.19664	+	0.211001i	0.736247	−	0.676713i	$-0.236596\pi$
$677$	548456.	+	96707.7i	1.19664	+	0.211001i	0.460396	+	0.887713i	$0.347707\pi$
$678$		0			0
$679$	118283.	+	43051.5i	0.256557	+	0.0933790i
$680$	50066.0	+	59666.4i	0.108274	+	0.129036i
$681$		0			0
$682$	162007.	−	58965.8i	0.348309	−	0.126774i
$683$	−680796.	−	393058.i	−1.45941	−	0.842588i	−0.460423	−	0.887700i	$-0.652302\pi$
$683$	−680796.	−	393058.i	−1.45941	−	0.842588i	−0.998982	+	0.0451117i	$0.985636\pi$
$684$		0			0
$685$	−28869.5	−	50003.5i	−0.0615260	−	0.106566i
$686$	−346826.	+	413331.i	−0.736992	+	0.878313i
$687$		0			0
$688$	86400.1	+	489999.i	0.182531	+	1.03519i
$689$	4492.84	−	792.208i	0.00946416	−	0.00166879i
$690$		0			0
$691$	429073.	+	360035.i	0.898618	+	0.754030i	0.969920	−	0.243424i	$-0.0782708\pi$
$691$	429073.	+	360035.i	0.898618	+	0.754030i	−0.0713015	+	0.997455i	$0.522715\pi$
$692$	68015.7	−	39268.9i	0.142035	−	0.0820042i
$693$		0			0
$694$	−78824.2	+	136527.i	−0.163659	+	0.283466i
$695$	−17018.0	−	46756.5i	−0.0352321	−	0.0967994i
$696$		0			0
$697$	308833.	−	259141.i	0.635708	−	0.533422i
$698$	84834.4	−	233081.i	0.174125	−	0.478405i
$699$		0			0
$700$	−15312.3	+	86840.3i	−0.0312496	+	0.177225i
$701$			530883.i			1.08035i	0.841554	+	0.540173i	$0.181641\pi$
$701$			530883.i			1.08035i	−0.841554	+	0.540173i	$0.818359\pi$
$702$		0			0
$703$	259552.			0.525188
$704$	−47485.3	−	8372.94i	−0.0958107	−	0.0168940i
$705$		0			0
$706$	−838377.	−	305144.i	−1.68202	−	0.612204i
$707$	−102592.	−	122265.i	−0.205247	−	0.244604i
$708$		0			0
$709$	−180117.	+	65557.3i	−0.358313	+	0.130415i	−0.514903	−	0.857248i	$-0.672172\pi$
$709$	−180117.	+	65557.3i	−0.358313	+	0.130415i	0.156590	+	0.987664i	$0.449950\pi$
$710$	−114762.	−	66258.0i	−0.227658	−	0.131438i
$711$		0			0
$712$	−54236.2	−	93939.8i	−0.106987	−	0.185306i
$713$	986966.	−	1.17622e6i	1.94144	−	2.31371i
$714$		0			0
$715$	−59.2148	−	335.824i	−0.000115829	−	0.000656900i
$716$	−17560.5	+	3096.40i	−0.0342541	+	0.00603991i
$717$		0			0
$718$	−398838.	−	334665.i	−0.773655	−	0.649174i
$719$	540128.	−	311843.i	1.04481	−	0.603223i	0.123621	−	0.992330i	$-0.460549\pi$
$719$	540128.	−	311843.i	1.04481	−	0.603223i	0.921193	+	0.389106i	$0.127216\pi$
$720$		0			0
$721$	282637.	−	489542.i	0.543700	−	0.941716i
$722$	101127.	+	277844.i	0.193996	+	0.532999i
$723$		0			0
$724$	−32043.7	+	26887.9i	−0.0611316	+	0.0512955i
$725$	−220722.	+	606428.i	−0.419923	+	1.15373i
$726$		0			0
$727$	−2423.03	+	13741.7i	−0.00458448	+	0.0259999i	−0.987014	−	0.160633i	$-0.948646\pi$
$727$	−2423.03	+	13741.7i	−0.00458448	+	0.0259999i	0.982430	+	0.186633i	$0.0597575\pi$
$728$		−	4623.72i		−	0.00872426i
$729$		0			0
$730$	55509.9			0.104166
$731$	−455940.	−	80394.4i	−0.853243	−	0.150450i
$732$		0			0
$733$	231734.	+	84344.2i	0.431302	+	0.156981i	0.548543	−	0.836122i	$-0.315183\pi$
$733$	231734.	+	84344.2i	0.431302	+	0.156981i	−0.117241	+	0.993104i	$0.537405\pi$
$734$	−17480.4	−	20832.3i	−0.0324458	−	0.0386674i
$735$		0			0
$736$	496406.	−	180677.i	0.916392	−	0.333539i
$737$	153672.	+	88722.4i	0.282917	+	0.163342i
$738$		0			0
$739$	−309247.	−	535631.i	−0.566261	−	0.980793i	−0.996931	−	0.0782832i	$-0.975056\pi$
$739$	−309247.	−	535631.i	−0.566261	−	0.980793i	0.430670	−	0.902509i	$-0.358277\pi$
$740$	−9673.42	+	11528.3i	−0.0176651	+	0.0210525i
$741$		0			0
$742$	−37228.7	−	211134.i	−0.0676192	−	0.383488i
$743$	140934.	−	24850.4i	0.255292	−	0.0450149i	−0.0445374	−	0.999008i	$-0.514181\pi$
$743$	140934.	−	24850.4i	0.255292	−	0.0450149i	0.299829	+	0.953993i	$0.403070\pi$
$744$		0			0
$745$	−60763.4	−	50986.5i	−0.109479	−	0.0918635i
$746$	533274.	−	307886.i	0.958237	−	0.553238i
$747$		0			0
$748$	−15113.8	+	26177.9i	−0.0270129	+	0.0467878i
$749$	−185803.	−	510490.i	−0.331199	−	0.909962i
$750$		0			0
$751$	75155.7	−	63063.1i	0.133255	−	0.111814i	−0.573724	−	0.819048i	$-0.694502\pi$
$751$	75155.7	−	63063.1i	0.133255	−	0.111814i	0.706979	+	0.707235i	$0.250058\pi$
$752$	233845.	−	642483.i	0.413516	−	1.13613i
$753$		0			0
$754$	−2543.58	+	14425.4i	−0.00447407	+	0.0253737i
$755$			73136.8i			0.128305i
$756$		0			0
$757$	589321.			1.02840			0.514198	−	0.857672i	$-0.328090\pi$
$757$	589321.			1.02840			0.514198	+	0.857672i	$0.328090\pi$
$758$	260858.	+	45996.3i	0.454010	+	0.0800543i
$759$		0			0
$760$	112086.	+	40796.1i	0.194055	+	0.0706304i
$761$	−511608.	−	609711.i	−0.883422	−	1.05282i	−0.998232	−	0.0594341i	$-0.981070\pi$
$761$	−511608.	−	609711.i	−0.883422	−	1.05282i	0.114810	−	0.993387i	$-0.463374\pi$
$762$		0			0
$763$	−176036.	+	64071.9i	−0.302380	+	0.110057i
$764$	175955.	+	101587.i	0.301449	+	0.174042i
$765$		0			0
$766$	−306108.	−	530194.i	−0.521695	−	0.903603i
$767$	−2507.91	+	2988.81i	−0.00426305	+	0.00508051i
$768$		0			0
$769$	−165095.	−	936298.i	−0.279177	−	1.58329i	−0.725372	−	0.688357i	$-0.758332\pi$
$769$	−165095.	−	936298.i	−0.279177	−	1.58329i	0.446194	−	0.894936i	$-0.352779\pi$
$770$	−15781.6	+	2782.71i	−0.0266176	+	0.00469340i
$771$		0			0
$772$	−168895.	−	141719.i	−0.283388	−	0.237791i
$773$	360204.	−	207964.i	0.602822	−	0.348039i	−0.167329	−	0.985901i	$-0.553514\pi$
$773$	360204.	−	207964.i	0.602822	−	0.348039i	0.770151	+	0.637862i	$0.220181\pi$
$774$		0			0
$775$	519950.	−	900579.i	0.865681	−	1.49940i
$776$	−71797.1	−	197261.i	−0.119230	−	0.327580i
$777$		0			0
$778$	−909510.	+	763169.i	−1.50262	+	1.26084i
$779$	211160.	−	580158.i	0.347966	−	0.956030i
$780$		0			0
$781$	−20630.4	+	117001.i	−0.0338225	+	0.191817i
$782$			1.16034e6i			1.89745i
$783$		0			0
$784$	454728.			0.739809
$785$	−118814.	−	20950.1i	−0.192809	−	0.0339975i
$786$		0			0
$787$	107226.	+	39027.2i	0.173122	+	0.0630113i	0.427127	−	0.904192i	$-0.359526\pi$
$787$	107226.	+	39027.2i	0.173122	+	0.0630113i	−0.254005	+	0.967203i	$0.581748\pi$
$788$	−231532.	−	275929.i	−0.372871	−	0.444370i
$789$		0			0
$790$	−131780.	+	47964.0i	−0.211152	+	0.0768531i
$791$	469428.	+	271025.i	0.750268	+	0.433167i
$792$		0			0
$793$	4446.50	+	7701.56i	0.00707085	+	0.0122471i
$794$	231762.	−	276203.i	0.367622	−	0.438115i
$795$		0			0
$796$	−18720.3	−	106168.i	−0.0295452	−	0.167559i
$797$	569418.	−	100404.i	0.896426	−	0.158064i	0.293592	−	0.955931i	$-0.405149\pi$
$797$	569418.	−	100404.i	0.896426	−	0.158064i	0.602834	+	0.797867i	$0.294038\pi$
$798$		0			0
$799$	487351.	+	408936.i	0.763393	+	0.640563i
$800$	309840.	−	178886.i	0.484126	−	0.279510i
$801$		0			0
$802$	521779.	−	903748.i	0.811219	−	1.40507i
$803$	−17021.3	−	46765.5i	−0.0263974	−	0.0725262i
$804$		0			0
$805$	−109330.	+	91738.7i	−0.168712	+	0.141567i
$806$	8072.80	−	22179.8i	0.0124267	−	0.0341420i
$807$		0			0
$808$	−46220.7	+	262131.i	−0.0707969	+	0.401509i
$809$			602261.i			0.920212i	0.887864	+	0.460106i	$0.152189\pi$
$809$			602261.i			0.920212i	−0.887864	+	0.460106i	$0.847811\pi$
$810$		0			0
$811$	−990076.			−1.50531			−0.752657	−	0.658413i	$-0.771228\pi$
$811$	−990076.			−1.50531			−0.752657	+	0.658413i	$0.771228\pi$
$812$	157280.	+	27732.6i	0.238539	+	0.0420609i
$813$		0			0
$814$	54646.3	+	19889.6i	0.0824730	+	0.0300177i
$815$	28557.7	+	34033.8i	0.0429940	+	0.0512383i
$816$		0			0
$817$	−666244.	+	242493.i	−0.998134	+	0.363291i
$818$	−272228.	−	157171.i	−0.406842	−	0.234890i
$819$		0			0
$820$	17898.6	+	31001.2i	0.0266189	+	0.0461053i
$821$	114448.	−	136394.i	0.169794	−	0.202352i	−0.674437	−	0.738333i	$-0.735614\pi$
$821$	114448.	−	136394.i	0.169794	−	0.202352i	0.844230	+	0.535981i	$0.180058\pi$
$822$		0			0
$823$	127178.	+	721264.i	0.187764	+	1.06487i	0.922352	+	0.386351i	$0.126265\pi$
$823$	127178.	+	721264.i	0.187764	+	1.06487i	−0.734587	+	0.678514i	$0.762624\pi$
$824$	−928388.	+	163700.i	−1.36734	+	0.241098i
$825$		0			0
$826$	140455.	+	117855.i	0.205862	+	0.172739i
$827$	−772587.	+	446053.i	−1.12963	+	0.652192i	−0.943842	−	0.330397i	$-0.892817\pi$
$827$	−772587.	+	446053.i	−1.12963	+	0.652192i	−0.185788	+	0.982590i	$0.559484\pi$
$828$		0			0
$829$	312772.	−	541738.i	0.455113	−	0.788279i	−0.543582	−	0.839356i	$-0.682932\pi$
$829$	312772.	−	541738.i	0.455113	−	0.788279i	0.998695	+	0.0510773i	$0.0162655\pi$
$830$	−49162.2	−	135072.i	−0.0713633	−	0.196069i
$831$		0			0
$832$	−5056.92	+	4243.26i	−0.00730533	+	0.00612990i
$833$	−144715.	+	397603.i	−0.208557	+	0.573006i
$834$		0			0
$835$	20741.3	−	117630.i	0.0297484	−	0.168711i
$836$			46291.0i			0.0662344i
$837$		0			0
$838$	583927.			0.831516
$839$	386607.	+	68169.3i	0.549220	+	0.0968423i	0.441370	−	0.897325i	$-0.354492\pi$
$839$	386607.	+	68169.3i	0.549220	+	0.0968423i	0.107849	+	0.994167i	$0.465604\pi$
$840$		0			0
$841$	433698.	+	157853.i	0.613190	+	0.223183i
$842$	−507536.	−	604858.i	−0.715884	−	0.853158i
$843$		0			0
$844$	243377.	−	88582.1i	0.341661	−	0.124354i
$845$	131013.	+	75640.3i	0.183485	+	0.105935i
$846$		0			0
$847$	−216543.	−	375063.i	−0.301840	−	0.522802i
$848$	−306226.	+	364946.i	−0.425843	+	0.507500i
$849$		0			0
$850$	136462.	+	773913.i	0.188874	+	1.07116i
$851$	510050.	−	89935.6i	0.704294	−	0.124186i
$852$		0			0
$853$	−237020.	−	198883.i	−0.325752	−	0.273338i	0.465214	−	0.885198i	$-0.345977\pi$
$853$	−237020.	−	198883.i	−0.325752	−	0.273338i	−0.790966	+	0.611860i	$0.790422\pi$
$854$	361924.	−	208957.i	0.496251	−	0.286511i
$855$		0			0
$856$	−452991.	+	784603.i	−0.618219	+	1.07079i
$857$	255551.	+	702119.i	0.347949	+	0.955981i	0.983015	+	0.183524i	$0.0587504\pi$
$857$	255551.	+	702119.i	0.347949	+	0.955981i	−0.635067	+	0.772457i	$0.719027\pi$
$858$		0			0
$859$	−1.12397e6	+	943124.i	−1.52324	+	1.27815i	−0.692644	+	0.721279i	$0.743554\pi$
$859$	−1.12397e6	+	943124.i	−1.52324	+	1.27815i	−0.830598	+	0.556872i	$0.812001\pi$
$860$	14060.0	−	38629.6i	0.0190103	−	0.0522304i
$861$		0			0
$862$	−75990.5	+	430964.i	−0.102269	+	0.579998i
$863$			888778.i			1.19336i	0.802479	+	0.596680i	$0.203514\pi$
$863$			888778.i			1.19336i	−0.802479	+	0.596680i	$0.796486\pi$
$864$		0			0
$865$	86089.5			0.115058
$866$	−1.39295e6	−	245615.i	−1.85738	−	0.327506i
$867$		0			0
$868$	−241827.	−	88017.7i	−0.320970	−	0.116824i
$869$	80816.7	+	96313.6i	0.107019	+	0.127540i
$870$		0			0
$871$	22828.3	−	8308.82i	0.0300910	−	0.0109522i
$872$	270561.	+	156208.i	0.355821	+	0.205434i
$873$		0			0
$874$	888475.	+	1.53888e6i	1.16311	+	2.01457i
$875$	−127184.	+	151572.i	−0.166118	+	0.197972i
$876$		0			0
$877$	−220776.	−	1.25208e6i	−0.287047	−	1.62793i	−0.697880	−	0.716215i	$-0.745873\pi$
$877$	−220776.	−	1.25208e6i	−0.287047	−	1.62793i	0.410833	−	0.911711i	$-0.365238\pi$
$878$	−889035.	+	156761.i	−1.15327	+	0.203352i
$879$		0			0
$880$	27278.4	+	22889.3i	0.0352252	+	0.0295575i
$881$	492960.	−	284611.i	0.635126	−	0.366690i	−0.147608	−	0.989046i	$-0.547157\pi$
$881$	492960.	−	284611.i	0.635126	−	0.366690i	0.782735	+	0.622355i	$0.213824\pi$
$882$		0			0
$883$	−154742.	+	268020.i	−0.198466	+	0.343753i	−0.948031	−	0.318177i	$-0.896929\pi$
$883$	−154742.	+	268020.i	−0.198466	+	0.343753i	0.749565	+	0.661930i	$0.230263\pi$
$884$	1415.41	+	3888.80i	0.00181124	+	0.00497635i
$885$		0			0
$886$	−18762.1	+	15743.3i	−0.0239009	+	0.0200552i
$887$	−259048.	+	711728.i	−0.329255	+	0.904622i	0.659045	+	0.752103i	$0.270961\pi$
$887$	−259048.	+	711728.i	−0.329255	+	0.904622i	−0.988301	+	0.152518i	$0.951262\pi$
$888$		0			0
$889$	−133450.	+	756831.i	−0.168855	+	0.957624i
$890$			51469.5i			0.0649786i
$891$		0			0
$892$	232394.			0.292076
$893$	959468.	+	169180.i	1.20317	+	0.212152i
$894$		0			0
$895$	−18367.3	−	6685.13i	−0.0229297	−	0.00834572i
$896$	387793.	+	462153.i	0.483041	+	0.575665i
$897$		0			0
$898$	466254.	−	169703.i	0.578189	−	0.210444i
$899$	−1.63107e6	−	941700.i	−2.01815	−	1.16518i
$900$		0			0
$901$	−221644.	−	383899.i	−0.273027	−	0.472897i
$902$	88915.6	−	105965.i	0.109286	−	0.130242i
$903$		0			0
$904$	−156974.	−	890243.i	−0.192084	−	1.08936i
$905$	−45155.7	+	7962.16i	−0.0551334	+	0.00972151i
$906$		0			0
$907$	365489.	+	306682.i	0.444283	+	0.372798i	0.837309	−	0.546729i	$-0.184127\pi$
$907$	365489.	+	306682.i	0.444283	+	0.372798i	−0.393026	+	0.919527i	$0.628572\pi$
$908$	35934.1	−	20746.6i	0.0435848	−	0.0251637i
$909$		0			0
$910$	−1096.96	+	1900.00i	−0.00132468	+	0.00229441i
$911$	44060.5	+	121055.i	0.0530900	+	0.145864i	0.963403	−	0.268057i	$-0.0863814\pi$
$911$	44060.5	+	121055.i	0.0530900	+	0.145864i	−0.910313	+	0.413920i	$0.864159\pi$
$912$		0			0
$913$	−98719.6	+	82835.6i	−0.118430	+	0.0993746i
$914$	182102.	−	500321.i	0.217983	−	0.598903i
$915$		0			0
$916$	−23043.3	+	130685.i	−0.0274634	+	0.155753i
$917$			590277.i			0.701967i
$918$		0			0
$919$	−1.05227e6			−1.24593			−0.622967	−	0.782248i	$-0.714073\pi$
$919$	−1.05227e6			−1.24593			−0.622967	+	0.782248i	$0.714073\pi$
$920$	234399.	+	41330.8i	0.276936	+	0.0488313i
$921$		0			0
$922$	1.77621e6	+	646489.i	2.08946	+	0.760500i
$923$	10455.1	+	12459.9i	0.0122723	+	0.0146256i
$924$		0			0
$925$	329613.	−	119969.i	0.385230	−	0.140212i
$926$	−232668.	−	134331.i	−0.271340	−	0.156658i
$927$		0			0
$928$	−323988.	−	561163.i	−0.376212	−	0.651618i
$929$	142424.	−	169734.i	0.165026	−	0.196670i	−0.677194	−	0.735805i	$-0.736804\pi$
$929$	142424.	−	169734.i	0.165026	−	0.196670i	0.842220	+	0.539135i	$0.181249\pi$
$930$		0			0
$931$	112519.	+	638126.i	0.129815	+	0.736219i
$932$	−145268.	+	25614.7i	−0.167239	+	0.0294888i
$933$		0			0
$934$	−1.01173e6	−	848943.i	−1.15977	−	0.973161i
$935$	−28695.1	+	16567.1i	−0.0328234	+	0.0189506i
$936$		0			0
$937$	−424606.	+	735439.i	−0.483623	+	0.837659i	−0.999823	−	0.0188087i	$-0.994013\pi$
$937$	−424606.	+	735439.i	−0.483623	+	0.837659i	0.516200	+	0.856468i	$0.327346\pi$
$938$	−390461.	−	1.07278e6i	−0.443785	−	1.21929i
$939$		0			0
$940$	−43273.4	+	36310.7i	−0.0489739	+	0.0410940i
$941$	−14623.8	+	40178.5i	−0.0165151	+	0.0453748i	−0.947676	−	0.319233i	$-0.896575\pi$
$941$	−14623.8	+	40178.5i	−0.0165151	+	0.0453748i	0.931161	+	0.364608i	$0.118797\pi$
$942$		0			0
$943$	213928.	−	1.21324e6i	0.240571	−	1.36435i
$944$		−	407426.i		−	0.457199i
$945$		0			0
$946$	−158854.			−0.177507
$947$	−242807.	−	42813.5i	−0.270746	−	0.0477398i	0.0366269	−	0.999329i	$-0.488339\pi$
$947$	−242807.	−	42813.5i	−0.270746	−	0.0477398i	−0.307373	+	0.951589i	$0.599450\pi$
$948$		0			0
$949$	−6402.51	−	2330.32i	−0.00710915	−	0.00258752i
$950$	773570.	+	921904.i	0.857141	+	1.02150i
$951$		0			0
$952$	−422177.	+	153660.i	−0.465822	+	0.169545i
$953$	−105421.	−	60864.6i	−0.116075	−	0.0670160i	0.440838	−	0.897587i	$-0.354681\pi$
$953$	−105421.	−	60864.6i	−0.116075	−	0.0670160i	−0.556914	+	0.830570i	$0.688015\pi$
$954$		0			0
$955$	111356.	+	192873.i	0.122097	+	0.211478i
$956$	−101444.	+	120897.i	−0.110997	+	0.132282i
$957$		0			0
$958$	−231550.	−	1.31318e6i	−0.252298	−	1.43085i
$959$	327985.	−	57832.6i	0.356629	−	0.0628833i
$960$		0			0
$961$	1.61739e6	+	1.35715e6i	1.75133	+	1.46954i
$962$	6894.93	−	3980.79i	0.00745040	−	0.00430149i
$963$		0			0
$964$	−206209.	+	357164.i	−0.221898	+	0.384338i
$965$	−82658.1	−	227101.i	−0.0887627	−	0.243874i
$966$		0			0
$967$	490606.	−	411668.i	0.524663	−	0.440244i	−0.341591	−	0.939849i	$-0.610966\pi$
$967$	490606.	−	411668.i	0.524663	−	0.440244i	0.866254	+	0.499604i	$0.166521\pi$
$968$	−247027.	+	678700.i	−0.263629	+	0.724315i
$969$		0			0
$970$	−17296.4	+	98093.0i	−0.0183829	+	0.104254i
$971$		−	1.59726e6i		−	1.69410i	−0.531516	−	0.847048i	$-0.678377\pi$
$971$		−	1.59726e6i		−	1.69410i	0.531516	−	0.847048i	$-0.321623\pi$
$972$		0			0
$973$	287005.			0.303154
$974$	413890.	+	72980.0i	0.436282	+	0.0769282i
$975$		0			0
$976$	−872647.	−	317618.i	−0.916092	−	0.333430i
$977$	−673083.	−	802149.i	−0.705146	−	0.840361i	0.287952	−	0.957645i	$-0.407026\pi$
$977$	−673083.	−	802149.i	−0.705146	−	0.840361i	−0.993098	+	0.117284i	$0.962581\pi$
$978$		0			0
$979$	43361.6	−	15782.3i	0.0452419	−	0.0164667i
$980$	−32536.6	−	18785.0i	−0.0338782	−	0.0195596i
$981$		0			0
$982$	287503.	+	497970.i	0.298140	+	0.516393i
$983$	−460198.	+	548442.i	−0.476253	+	0.567576i	−0.949666	−	0.313265i	$-0.898577\pi$
$983$	−460198.	+	548442.i	−0.476253	+	0.567576i	0.473413	+	0.880840i	$0.343022\pi$
$984$		0			0
$985$	−68562.3	−	388836.i	−0.0706664	−	0.400769i
$986$	1.40166e6	−	247151.i	1.44175	−	0.254219i
$987$		0			0
$988$	4854.84	+	4073.69i	0.00497348	+	0.00417325i
$989$	−1.22522e6	+	707381.i	−1.25263	+	0.723204i
$990$		0			0
$991$	−257375.	+	445787.i	−0.262071	+	0.453921i	−0.966792	−	0.255564i	$-0.917739\pi$
$991$	−257375.	+	445787.i	−0.262071	+	0.453921i	0.704721	+	0.709485i	$0.251072\pi$
$992$	357115.	+	981165.i	0.362898	+	0.997054i
$993$		0			0
$994$	585537.	−	491324.i	0.592628	−	0.497274i
$995$	40417.2	−	111045.i	0.0408244	−	0.112164i
$996$		0			0
$997$	200557.	−	1.13742e6i	0.201766	−	1.14427i	−0.700682	−	0.713473i	$-0.747121\pi$
$997$	200557.	−	1.13742e6i	0.201766	−	1.14427i	0.902448	−	0.430798i	$-0.141768\pi$
$998$		−	1.05519e6i		−	1.05942i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.8.3		66
3.2	odd	2		27.5.f.a.2.9	✓	66
27.13	even	9		27.5.f.a.14.9	yes	66
27.14	odd	18	inner	81.5.f.a.71.3		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.2.9	✓	66	3.2	odd	2
27.5.f.a.14.9	yes	66	27.13	even	9
81.5.f.a.8.3		66	1.1	even	1	trivial
81.5.f.a.71.3		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)

\(f(q)\)	\(=\)	\(q+(-4.49504 - 0.792597i) q^{2} +(4.54211 + 1.65319i) q^{4} +(3.40574 + 4.05880i) q^{5} +(-28.7185 + 10.4527i) q^{7} +(44.1393 + 25.4838i) q^{8} +(-12.0919 - 20.9439i) q^{10} +(-13.9368 + 16.6092i) q^{11} +(0.515455 + 2.92329i) q^{13} +(137.376 - 24.2231i) q^{14} +(-237.454 - 199.247i) q^{16} +(249.786 - 144.214i) q^{17} +(220.850 - 382.524i) q^{19} +(8.75926 + 24.0659i) q^{20} +(75.8110 - 63.6130i) q^{22} +(301.451 - 828.229i) q^{23} +(103.655 - 587.858i) q^{25} -13.5489i q^{26} -147.723 q^{28} +(-1064.69 - 187.734i) q^{29} +(1637.03 + 595.829i) q^{31} +(385.260 + 459.135i) q^{32} +(-1237.10 + 450.268i) q^{34} +(-140.233 - 80.9637i) q^{35} +(293.810 + 508.894i) q^{37} +(-1295.92 + 1544.42i) q^{38} +(46.8931 + 265.944i) q^{40} +(1376.52 - 242.718i) q^{41} +(-1229.63 - 1031.78i) q^{43} +(-90.7608 + 52.4008i) q^{44} +(-2011.49 + 3484.00i) q^{46} +(754.401 + 2072.70i) q^{47} +(-1123.78 + 942.961i) q^{49} +(-931.870 + 2560.29i) q^{50} +(-2.49151 + 14.1301i) q^{52} -1536.91i q^{53} -114.879 q^{55} +(-1533.99 - 270.484i) q^{56} +(4637.04 + 1687.74i) q^{58} +(844.872 + 1006.88i) q^{59} +(2815.23 - 1024.66i) q^{61} +(-6886.25 - 3975.78i) q^{62} +(1111.94 + 1925.94i) q^{64} +(-10.1095 + 12.0481i) q^{65} +(-1421.14 - 8059.70i) q^{67} +(1372.97 - 242.091i) q^{68} +(566.183 + 475.084i) q^{70} +(4745.40 - 2739.76i) q^{71} +(-1147.66 + 1987.81i) q^{73} +(-917.341 - 2520.37i) q^{74} +(1635.51 - 1372.36i) q^{76} +(226.633 - 622.670i) q^{77} +(1006.95 - 5710.70i) q^{79} -1642.36i q^{80} -6379.91 q^{82} +(5853.36 + 1032.10i) q^{83} +(1436.04 + 522.676i) q^{85} +(4709.43 + 5612.48i) q^{86} +(-1038.43 + 377.957i) q^{88} +(-1843.12 - 1064.13i) q^{89} +(-45.3593 - 78.5647i) q^{91} +(2738.45 - 3263.55i) q^{92} +(-1748.25 - 9914.81i) q^{94} +(2304.75 - 406.389i) q^{95} +(-3155.11 - 2647.45i) q^{97} +(5798.82 - 3347.95i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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