LMFDB - Embedded newform 81.5.f.a.44.5

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			44.5
Character	$\chi$	$=$	81.44
Dual form			81.5.f.a.35.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.868224 - 1.03471i) q^{2} +(2.46156 - 13.9602i) q^{4} +(3.20330 + 8.80100i) q^{5} +(-7.41386 - 42.0461i) q^{7} +(-35.2980 + 20.3793i) q^{8} +(6.32529 - 10.9557i) q^{10} +(6.44259 - 17.7009i) q^{11} +(-37.7989 - 31.7171i) q^{13} +(-37.0686 + 44.1766i) q^{14} +(-161.398 - 58.7439i) q^{16} +(-390.443 - 225.422i) q^{17} +(-57.0245 - 98.7692i) q^{19} +(130.749 - 23.0546i) q^{20} +(-23.9089 + 8.70211i) q^{22} +(-608.929 - 107.371i) q^{23} +(411.581 - 345.358i) q^{25} +66.6484i q^{26} -605.222 q^{28} +(179.539 + 213.967i) q^{29} +(211.710 - 1200.67i) q^{31} +(302.391 + 830.812i) q^{32} +(105.745 + 599.712i) q^{34} +(346.299 - 199.936i) q^{35} +(-1105.90 + 1915.47i) q^{37} +(-52.6874 + 144.758i) q^{38} +(-292.429 - 245.377i) q^{40} +(348.778 - 415.658i) q^{41} +(3152.26 + 1147.33i) q^{43} +(-231.249 - 133.512i) q^{44} +(417.590 + 723.286i) q^{46} +(3962.16 - 698.636i) q^{47} +(543.294 - 197.743i) q^{49} +(-714.690 - 126.019i) q^{50} +(-535.821 + 449.607i) q^{52} -3918.45i q^{53} +176.423 q^{55} +(1118.57 + 1333.05i) q^{56} +(65.5128 - 371.542i) q^{58} +(1539.61 + 4230.04i) q^{59} +(208.280 + 1181.21i) q^{61} +(-1426.15 + 823.390i) q^{62} +(-776.940 + 1345.70i) q^{64} +(158.060 - 434.267i) q^{65} +(-2416.30 - 2027.52i) q^{67} +(-4108.04 + 4895.77i) q^{68} +(-507.540 - 184.729i) q^{70} +(-2478.15 - 1430.76i) q^{71} +(-1176.80 - 2038.28i) q^{73} +(2942.13 - 518.776i) q^{74} +(-1519.21 + 552.947i) q^{76} +(-792.017 - 139.654i) q^{77} +(3852.86 - 3232.93i) q^{79} -1608.63i q^{80} -732.903 q^{82} +(-7265.33 - 8658.48i) q^{83} +(733.235 - 4158.38i) q^{85} +(-1549.72 - 4257.81i) q^{86} +(133.321 + 756.101i) q^{88} +(982.504 - 567.249i) q^{89} +(-1053.34 + 1824.44i) q^{91} +(-2997.83 + 8236.48i) q^{92} +(-4162.93 - 3493.11i) q^{94} +(686.601 - 818.260i) q^{95} +(1751.37 + 637.447i) q^{97} +(-676.307 - 390.466i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−0.868224	−	1.03471i	−0.217056	−	0.258677i	0.646519	−	0.762898i	$-0.276224\pi$
$2$	−0.868224	−	1.03471i	−0.217056	−	0.258677i	−0.863575	+	0.504221i	$0.831780\pi$
$3$		0			0
$3$		0			0
$4$	2.46156	−	13.9602i	0.153848	−	0.872513i
$5$	3.20330	+	8.80100i	0.128132	+	0.352040i	0.987126	−	0.159946i	$-0.0511321\pi$
$5$	3.20330	+	8.80100i	0.128132	+	0.352040i	−0.858994	+	0.511986i	$0.828910\pi$
$6$		0			0
$7$	−7.41386	−	42.0461i	−0.151303	−	0.858083i	−0.962088	−	0.272739i	$-0.912070\pi$
$7$	−7.41386	−	42.0461i	−0.151303	−	0.858083i	0.810785	−	0.585344i	$-0.199041\pi$
$8$	−35.2980	+	20.3793i	−0.551531	+	0.318427i
$9$		0			0
$10$	6.32529	−	10.9557i	0.0632529	−	0.109557i
$11$	6.44259	−	17.7009i	0.0532445	−	0.146288i	−0.910219	−	0.414127i	$-0.864087\pi$
$11$	6.44259	−	17.7009i	0.0532445	−	0.146288i	0.963464	+	0.267838i	$0.0863093\pi$
$12$		0			0
$13$	−37.7989	−	31.7171i	−0.223662	−	0.187675i	0.524070	−	0.851675i	$-0.324413\pi$
$13$	−37.7989	−	31.7171i	−0.223662	−	0.187675i	−0.747732	+	0.664000i	$0.768857\pi$
$14$	−37.0686	+	44.1766i	−0.189125	+	0.225391i
$15$		0			0
$16$	−161.398	−	58.7439i	−0.630459	−	0.229468i
$17$	−390.443	−	225.422i	−1.35101	−	0.780008i	−0.362622	−	0.931936i	$-0.618118\pi$
$17$	−390.443	−	225.422i	−1.35101	−	0.780008i	−0.988391	+	0.151929i	$0.951452\pi$
$18$		0			0
$19$	−57.0245	−	98.7692i	−0.157962	−	0.273599i	0.776171	−	0.630522i	$-0.217159\pi$
$19$	−57.0245	−	98.7692i	−0.157962	−	0.273599i	−0.934134	+	0.356923i	$0.883826\pi$
$20$	130.749	−	23.0546i	0.326872	−	0.0576364i
$21$		0			0
$22$	−23.9089	+	8.70211i	−0.0493985	+	0.0179796i
$23$	−608.929	−	107.371i	−1.15109	−	0.202969i	−0.434641	−	0.900604i	$-0.643125\pi$
$23$	−608.929	−	107.371i	−1.15109	−	0.202969i	−0.716454	+	0.697635i	$0.754236\pi$
$24$		0			0
$25$	411.581	−	345.358i	0.658530	−	0.552572i
$26$			66.6484i			0.0985923i
$27$		0			0
$28$	−605.222			−0.771967
$29$	179.539	+	213.967i	0.213483	+	0.254419i	0.862150	−	0.506653i	$-0.169118\pi$
$29$	179.539	+	213.967i	0.213483	+	0.254419i	−0.648667	+	0.761072i	$0.724673\pi$
$30$		0			0
$31$	211.710	−	1200.67i	0.220302	−	1.24939i	−0.651164	−	0.758937i	$-0.725719\pi$
$31$	211.710	−	1200.67i	0.220302	−	1.24939i	0.871465	−	0.490457i	$-0.163170\pi$
$32$	302.391	+	830.812i	0.295303	+	0.811340i
$33$		0			0
$34$	105.745	+	599.712i	0.0914752	+	0.518782i
$35$	346.299	−	199.936i	0.282693	−	0.163213i
$36$		0			0
$37$	−1105.90	+	1915.47i	−0.807816	+	1.39918i	0.106558	+	0.994306i	$0.466017\pi$
$37$	−1105.90	+	1915.47i	−0.807816	+	1.39918i	−0.914374	+	0.404871i	$0.867316\pi$
$38$	−52.6874	+	144.758i	−0.0364871	+	0.100248i
$39$		0			0
$40$	−292.429	−	245.377i	−0.182768	−	0.153360i
$41$	348.778	−	415.658i	0.207483	−	0.247268i	−0.652260	−	0.757995i	$-0.726179\pi$
$41$	348.778	−	415.658i	0.207483	−	0.247268i	0.859743	+	0.510727i	$0.170624\pi$
$42$		0			0
$43$	3152.26	+	1147.33i	1.70485	+	0.620513i	0.996363	−	0.0852133i	$-0.0271572\pi$
$43$	3152.26	+	1147.33i	1.70485	+	0.620513i	0.708484	+	0.705727i	$0.249379\pi$
$44$	−231.249	−	133.512i	−0.119447	−	0.0689626i
$45$		0			0
$46$	417.590	+	723.286i	0.197349	+	0.341818i
$47$	3962.16	−	698.636i	1.79364	−	0.316268i	0.825077	−	0.565020i	$-0.191132\pi$
$47$	3962.16	−	698.636i	1.79364	−	0.316268i	0.968567	+	0.248752i	$0.0800204\pi$
$48$		0			0
$49$	543.294	−	197.743i	0.226278	−	0.0823585i
$50$	−714.690	−	126.019i	−0.285876	−	0.0504076i
$51$		0			0
$52$	−535.821	+	449.607i	−0.198159	+	0.166275i
$53$		−	3918.45i		−	1.39496i	−0.716603	−	0.697482i	$-0.754304\pi$
$53$		−	3918.45i		−	1.39496i	0.716603	−	0.697482i	$-0.245696\pi$
$54$		0			0
$55$	176.423			0.0583216
$56$	1118.57	+	1333.05i	0.356685	+	0.425081i
$57$		0			0
$58$	65.5128	−	371.542i	0.0194747	−	0.110446i
$59$	1539.61	+	4230.04i	0.442290	+	1.21518i	0.937982	+	0.346683i	$0.112692\pi$
$59$	1539.61	+	4230.04i	0.442290	+	1.21518i	−0.495693	+	0.868498i	$0.665086\pi$
$60$		0			0
$61$	208.280	+	1181.21i	0.0559742	+	0.317446i	0.999920	−	0.0126552i	$-0.00402839\pi$
$61$	208.280	+	1181.21i	0.0559742	+	0.317446i	−0.943946	+	0.330101i	$0.892917\pi$
$62$	−1426.15	+	823.390i	−0.371008	+	0.214201i
$63$		0			0
$64$	−776.940	+	1345.70i	−0.189683	+	0.328540i
$65$	158.060	−	434.267i	0.0374108	−	0.102785i
$66$		0			0
$67$	−2416.30	−	2027.52i	−0.538271	−	0.451663i	0.332675	−	0.943042i	$-0.392049\pi$
$67$	−2416.30	−	2027.52i	−0.538271	−	0.451663i	−0.870946	+	0.491378i	$0.836493\pi$
$68$	−4108.04	+	4895.77i	−0.888417	+	1.05877i
$69$		0			0
$70$	−507.540	−	184.729i	−0.103580	−	0.0376999i
$71$	−2478.15	−	1430.76i	−0.491599	−	0.283825i	0.233639	−	0.972323i	$-0.424937\pi$
$71$	−2478.15	−	1430.76i	−0.491599	−	0.283825i	−0.725237	+	0.688499i	$0.758270\pi$
$72$		0			0
$73$	−1176.80	−	2038.28i	−0.220830	−	0.382488i	0.734231	−	0.678900i	$-0.237543\pi$
$73$	−1176.80	−	2038.28i	−0.220830	−	0.382488i	−0.955060	+	0.296412i	$0.904210\pi$
$74$	2942.13	−	518.776i	0.537277	−	0.0947364i
$75$		0			0
$76$	−1519.21	+	552.947i	−0.263021	+	0.0957317i
$77$	−792.017	−	139.654i	−0.133584	−	0.0235544i
$78$		0			0
$79$	3852.86	−	3232.93i	0.617347	−	0.518015i	−0.279622	−	0.960110i	$-0.590209\pi$
$79$	3852.86	−	3232.93i	0.617347	−	0.518015i	0.896968	+	0.442095i	$0.145765\pi$
$80$		−	1608.63i		−	0.251349i
$81$		0			0
$82$	−732.903			−0.108998
$83$	−7265.33	−	8658.48i	−1.05463	−	1.25686i	−0.965380	−	0.260846i	$-0.915998\pi$
$83$	−7265.33	−	8658.48i	−1.05463	−	1.25686i	−0.0892470	−	0.996010i	$-0.528446\pi$
$84$		0			0
$85$	733.235	−	4158.38i	0.101486	−	0.575555i
$86$	−1549.72	−	4257.81i	−0.209534	−	0.575691i
$87$		0			0
$88$	133.321	+	756.101i	0.0172160	+	0.0976370i
$89$	982.504	−	567.249i	0.124038	−	0.0716133i	−0.436697	−	0.899609i	$-0.643852\pi$
$89$	982.504	−	567.249i	0.124038	−	0.0716133i	0.560735	+	0.827995i	$0.310519\pi$
$90$		0			0
$91$	−1053.34	+	1824.44i	−0.127200	+	0.220317i
$92$	−2997.83	+	8236.48i	−0.354186	+	0.973119i
$93$		0			0
$94$	−4162.93	−	3493.11i	−0.471133	−	0.395327i
$95$	686.601	−	818.260i	0.0760777	−	0.0906659i
$96$		0			0
$97$	1751.37	+	637.447i	0.186138	+	0.0677486i	0.433407	−	0.901198i	$-0.357311\pi$
$97$	1751.37	+	637.447i	0.186138	+	0.0677486i	−0.247270	+	0.968947i	$0.579533\pi$
$98$	−676.307	−	390.466i	−0.0704193	−	0.0406566i
$99$		0			0
$100$	−3808.13	−	6595.88i	−0.380813	−	0.659588i
$101$	845.823	−	149.141i	0.0829157	−	0.0146203i	−0.132036	−	0.991245i	$-0.542152\pi$
$101$	845.823	−	149.141i	0.0829157	−	0.0146203i	0.214952	+	0.976625i	$0.431040\pi$
$102$		0			0
$103$	4752.33	−	1729.71i	0.447952	−	0.163041i	−0.108187	−	0.994131i	$-0.534504\pi$
$103$	4752.33	−	1729.71i	0.447952	−	0.163041i	0.556139	+	0.831089i	$0.312282\pi$
$104$	1980.60	+	349.233i	0.183117	+	0.0322886i
$105$		0			0
$106$	−4054.46	+	3402.09i	−0.360845	+	0.302785i
$107$			10768.0i			0.940518i	0.882529	+	0.470259i	$0.155839\pi$
$107$			10768.0i			0.940518i	−0.882529	+	0.470259i	$0.844161\pi$
$108$		0			0
$109$	2700.53			0.227298			0.113649	−	0.993521i	$-0.463746\pi$
$109$	2700.53			0.227298			0.113649	+	0.993521i	$0.463746\pi$
$110$	−153.175	−	182.546i	−0.0126591	−	0.0150865i
$111$		0			0
$112$	−1273.37	+	7221.65i	−0.101512	+	0.575706i
$113$	−4381.95	−	12039.3i	−0.343171	−	0.942855i	−0.984468	−	0.175562i	$-0.943826\pi$
$113$	−4381.95	−	12039.3i	−0.343171	−	0.942855i	0.641297	−	0.767293i	$-0.278397\pi$
$114$		0			0
$115$	−1005.61	−	5703.13i	−0.0760389	−	0.431238i
$116$	3428.96	−	1979.71i	0.254828	−	0.147125i
$117$		0			0
$118$	3040.14	−	5265.67i	0.218338	−	0.378173i
$119$	−6583.44	+	18087.8i	−0.464899	+	1.27730i
$120$		0			0
$121$	10943.8	+	9182.97i	0.747479	+	0.627210i
$122$	1041.38	−	1241.07i	0.0699664	−	0.0833827i
$123$		0			0
$124$	−16240.4	−	5911.03i	−1.05622	−	0.384433i
$125$	9427.31	+	5442.86i	0.603348	+	0.348343i
$126$		0			0
$127$	5755.85	+	9969.42i	0.356863	+	0.618105i	0.987435	−	0.158026i	$-0.0505129\pi$
$127$	5755.85	+	9969.42i	0.356863	+	0.618105i	−0.630572	+	0.776131i	$0.717180\pi$
$128$	15998.2	−	2820.91i	0.976450	−	0.172174i
$129$		0			0
$130$	−586.572	+	213.495i	−0.0347084	+	0.0126328i
$131$	20719.2	+	3653.35i	1.20734	+	0.212887i	0.740869	−	0.671650i	$-0.234414\pi$
$131$	20719.2	+	3653.35i	1.20734	+	0.212887i	0.466471	+	0.884536i	$0.345525\pi$
$132$		0			0
$133$	−3730.09	+	3129.92i	−0.210871	+	0.176941i
$134$			4260.51i			0.237275i
$135$		0			0
$136$	18375.8			0.993502
$137$	−21898.4	−	26097.6i	−1.16673	−	1.39046i	−0.905049	−	0.425307i	$-0.860166\pi$
$137$	−21898.4	−	26097.6i	−1.16673	−	1.39046i	−0.261686	−	0.965153i	$-0.584278\pi$
$138$		0			0
$139$	−2943.24	+	16692.0i	−0.152334	+	0.863928i	0.808849	+	0.588016i	$0.200091\pi$
$139$	−2943.24	+	16692.0i	−0.152334	+	0.863928i	−0.961183	+	0.275912i	$0.911020\pi$
$140$	−1938.71	−	5326.56i	−0.0989136	−	0.271763i
$141$		0			0
$142$	671.168	+	3806.38i	0.0332855	+	0.188771i
$143$	−804.942	+	464.734i	−0.0393634	+	0.0227265i
$144$		0			0
$145$	−1308.00	+	2265.52i	−0.0622117	+	0.107754i
$146$	−1087.30	+	2987.33i	−0.0510086	+	0.140145i
$147$		0			0
$148$	24018.2	+	20153.6i	1.09652	+	0.920090i
$149$	17955.5	−	21398.5i	0.808768	−	0.963852i	−0.191075	−	0.981575i	$-0.561197\pi$
$149$	17955.5	−	21398.5i	0.808768	−	0.963852i	0.999843	+	0.0177231i	$0.00564172\pi$
$150$		0			0
$151$	−3119.16	−	1135.28i	−0.136799	−	0.0497908i	0.272713	−	0.962095i	$-0.412079\pi$
$151$	−3119.16	−	1135.28i	−0.136799	−	0.0497908i	−0.409512	+	0.912305i	$0.634301\pi$
$152$	4025.70	+	2324.24i	0.174243	+	0.100599i
$153$		0			0
$154$	543.147	+	940.758i	0.0229021	+	0.0396676i
$155$	11245.2	−	1982.84i	0.468064	−	0.0825324i
$156$		0			0
$157$	−20046.5	+	7296.35i	−0.813280	+	0.296010i	−0.714978	−	0.699147i	$-0.753563\pi$
$157$	−20046.5	+	7296.35i	−0.813280	+	0.296010i	−0.0983021	+	0.995157i	$0.531341\pi$
$158$	−6690.29	−	1179.68i	−0.267998	−	0.0472552i
$159$		0			0
$160$	−6343.32	+	5322.68i	−0.247786	+	0.207917i
$161$			26399.1i			1.01845i
$162$		0			0
$163$	−3741.11			−0.140807			−0.0704036	−	0.997519i	$-0.522429\pi$
$163$	−3741.11			−0.140807			−0.0704036	+	0.997519i	$0.522429\pi$
$164$	−4944.13	−	5892.18i	−0.183824	−	0.219073i
$165$		0			0
$166$	−2651.08	+	15035.0i	−0.0962069	+	0.545616i
$167$	4391.73	+	12066.2i	0.157472	+	0.432650i	0.993190	−	0.116509i	$-0.0371703\pi$
$167$	4391.73	+	12066.2i	0.157472	+	0.432650i	−0.835718	+	0.549159i	$0.814948\pi$
$168$		0			0
$169$	−4536.78	−	25729.4i	−0.158845	−	0.900856i
$170$	−4939.33	+	2851.72i	−0.170911	+	0.0986755i
$171$		0			0
$172$	23776.4	−	41182.0i	0.803693	−	1.39204i
$173$	−14623.8	+	40178.7i	−0.488618	+	1.34247i	0.413314	+	0.910588i	$0.364371\pi$
$173$	−14623.8	+	40178.7i	−0.488618	+	1.34247i	−0.901932	+	0.431878i	$0.857851\pi$
$174$		0			0
$175$	−17572.4	−	14745.0i	−0.573791	−	0.481468i
$176$	−2079.64	+	2478.41i	−0.0671370	+	0.0800108i
$177$		0			0
$178$	−1439.97	−	524.107i	−0.0454479	−	0.0165417i
$179$	23006.7	+	13282.9i	0.718040	+	0.414561i	0.814031	−	0.580822i	$-0.197269\pi$
$179$	23006.7	+	13282.9i	0.718040	+	0.414561i	−0.0959908	+	0.995382i	$0.530602\pi$
$180$		0			0
$181$	−8497.75	−	14718.5i	−0.259386	−	0.449270i	0.706692	−	0.707522i	$-0.250187\pi$
$181$	−8497.75	−	14718.5i	−0.259386	−	0.449270i	−0.966078	+	0.258252i	$0.916854\pi$
$182$	2802.30	−	494.122i	0.0846004	−	0.0149173i
$183$		0			0
$184$	23682.1	−	8619.59i	0.699496	−	0.254596i
$185$	−20400.6	−	3597.18i	−0.596074	−	0.105104i
$186$		0			0
$187$	−6505.63	+	5458.87i	−0.186040	+	0.156106i
$188$		−	57032.3i		−	1.61363i
$189$		0			0
$190$	−1442.78			−0.0399663
$191$	−33917.8	−	40421.7i	−0.929739	−	1.10802i	−0.993923	−	0.110082i	$-0.964889\pi$
$191$	−33917.8	−	40421.7i	−0.929739	−	1.10802i	0.0641834	−	0.997938i	$-0.479556\pi$
$192$		0			0
$193$	8157.94	−	46266.0i	0.219011	−	1.24207i	−0.654798	−	0.755804i	$-0.727246\pi$
$193$	8157.94	−	46266.0i	0.219011	−	1.24207i	0.873809	−	0.486269i	$-0.161643\pi$
$194$	−861.010	−	2365.61i	−0.0228773	−	0.0628549i
$195$		0			0
$196$	−1423.18	−	8071.25i	−0.0370465	−	0.210101i
$197$	−20705.7	+	11954.4i	−0.533528	+	0.308032i	−0.742452	−	0.669899i	$-0.766337\pi$
$197$	−20705.7	+	11954.4i	−0.533528	+	0.308032i	0.208924	+	0.977932i	$0.433004\pi$
$198$		0			0
$199$	−9654.27	+	16721.7i	−0.243789	+	0.422254i	−0.961790	−	0.273787i	$-0.911724\pi$
$199$	−9654.27	+	16721.7i	−0.243789	+	0.422254i	0.718002	+	0.696041i	$0.245057\pi$
$200$	−7489.85	+	20578.2i	−0.187246	+	0.514455i
$201$		0			0
$202$	−888.682	−	745.693i	−0.0217793	−	0.0182750i
$203$	7665.38	−	9135.24i	0.186012	−	0.221681i
$204$		0			0
$205$	4775.45	+	1738.12i	0.113633	+	0.0413592i
$206$	−5915.83	−	3415.50i	−0.139406	−	0.0804860i
$207$		0			0
$208$	4237.47	+	7339.51i	0.0979444	+	0.169645i
$209$	−2115.69	+	373.053i	−0.0484349	+	0.00854038i
$210$		0			0
$211$	−27331.4	+	9947.83i	−0.613900	+	0.223441i	−0.630209	−	0.776426i	$-0.717031\pi$
$211$	−27331.4	+	9947.83i	−0.613900	+	0.223441i	0.0163089	+	0.999867i	$0.494808\pi$
$212$	−54702.4	−	9645.51i	−1.21712	−	0.214612i
$213$		0			0
$214$	11141.7	−	9349.02i	0.243291	−	0.204145i
$215$			31418.3i			0.679682i
$216$		0			0
$217$	−52053.0			−1.10542
$218$	−2344.67	−	2794.26i	−0.0493365	−	0.0587969i
$219$		0			0
$220$	434.276	−	2462.90i	0.00897263	−	0.0508863i
$221$	7608.58	+	20904.4i	0.155783	+	0.428010i
$222$		0			0
$223$	14655.3	+	83114.6i	0.294704	+	1.67135i	0.668403	+	0.743800i	$0.266978\pi$
$223$	14655.3	+	83114.6i	0.294704	+	1.67135i	−0.373699	+	0.927550i	$0.621911\pi$
$224$	32690.5	−	18873.9i	0.651517	−	0.376153i
$225$		0			0
$226$	−8652.67	+	14986.9i	−0.169408	+	0.293423i
$227$	−1755.16	+	4822.25i	−0.0340615	+	0.0935832i	−0.955558	−	0.294804i	$-0.904746\pi$
$227$	−1755.16	+	4822.25i	−0.0340615	+	0.0935832i	0.921496	+	0.388387i	$0.126968\pi$
$228$		0			0
$229$	−46872.0	−	39330.2i	−0.893804	−	0.749990i	0.0751658	−	0.997171i	$-0.476051\pi$
$229$	−46872.0	−	39330.2i	−0.893804	−	0.749990i	−0.968969	+	0.247181i	$0.920496\pi$
$230$	−5027.98	+	5992.11i	−0.0950468	+	0.113272i
$231$		0			0
$232$	−10697.9	−	3893.71i	−0.198757	−	0.0723415i
$233$	−65323.4	−	37714.5i	−1.20325	−	0.694699i	−0.241976	−	0.970282i	$-0.577796\pi$
$233$	−65323.4	−	37714.5i	−1.20325	−	0.694699i	−0.961277	+	0.275584i	$0.911129\pi$
$234$		0			0
$235$	18840.7	+	32633.0i	0.341162	+	0.590910i
$236$	62842.1	−	11080.8i	1.12831	−	0.198951i
$237$		0			0
$238$	24431.5	−	8892.36i	0.431318	−	0.156987i
$239$	57194.9	+	10085.0i	1.00129	+	0.176555i	0.650182	−	0.759778i	$-0.274693\pi$
$239$	57194.9	+	10085.0i	1.00129	+	0.176555i	0.351112	+	0.936334i	$0.385804\pi$
$240$		0			0
$241$	54221.6	−	45497.3i	0.933552	−	0.783343i	−0.0428999	−	0.999079i	$-0.513660\pi$
$241$	54221.6	−	45497.3i	0.933552	−	0.783343i	0.976452	+	0.215736i	$0.0692152\pi$
$242$		−	19296.6i		−	0.329495i
$243$		0			0
$244$	17002.7			0.285587
$245$	3480.67	+	4148.10i	0.0579869	+	0.0691061i
$246$		0			0
$247$	−977.207	+	5542.02i	−0.0160174	+	0.0908394i
$248$	16995.8	+	46695.7i	0.276337	+	0.759230i
$249$		0			0
$250$	−2553.24	−	14480.1i	−0.0408519	−	0.231682i
$251$	8013.71	−	4626.72i	0.127200	−	0.0734388i	−0.435050	−	0.900406i	$-0.643269\pi$
$251$	8013.71	−	4626.72i	0.127200	−	0.0734388i	0.562250	+	0.826967i	$0.309936\pi$
$252$		0			0
$253$	−5823.63	+	10086.8i	−0.0909815	+	0.157585i
$254$	5318.09	−	14611.3i	0.0824305	−	0.226476i
$255$		0			0
$256$	2236.65	+	1876.78i	0.0341286	+	0.0286373i
$257$	−51197.8	+	61015.2i	−0.775149	+	0.923787i	−0.998704	−	0.0509044i	$-0.983790\pi$
$257$	−51197.8	+	61015.2i	−0.775149	+	0.923787i	0.223554	+	0.974692i	$0.428234\pi$
$258$		0			0
$259$	88737.2	+	32297.7i	1.32284	+	0.481473i
$260$	−5673.39	−	3275.53i	−0.0839259	−	0.0484546i
$261$		0			0
$262$	−14208.7	−	24610.2i	−0.206992	−	0.358520i
$263$	112009.	−	19750.3i	1.61936	−	0.285537i	0.710831	−	0.703363i	$-0.248319\pi$
$263$	112009.	−	19750.3i	1.61936	−	0.285537i	0.908527	+	0.417826i	$0.137208\pi$
$264$		0			0
$265$	34486.3	−	12552.0i	0.491083	−	0.178739i
$266$	6477.11	+	1142.09i	0.0915414	+	0.0161412i
$267$		0			0
$268$	−34252.4	+	28741.2i	−0.476894	+	0.400161i
$269$		−	225.820i		−	0.00312074i	−0.999999	−	0.00156037i	$-0.999503\pi$
$269$		−	225.820i		−	0.00312074i	0.999999	−	0.00156037i	$-0.000496682\pi$
$270$		0			0
$271$	−23425.8			−0.318974			−0.159487	−	0.987200i	$-0.550984\pi$
$271$	−23425.8			−0.318974			−0.159487	+	0.987200i	$0.550984\pi$
$272$	49774.3	+	59318.7i	0.672771	+	0.801778i
$273$		0			0
$274$	−7990.62	+	45317.0i	−0.106434	+	0.603616i
$275$	−3461.48	−	9510.34i	−0.0457717	−	0.125757i
$276$		0			0
$277$	−5680.28	−	32214.5i	−0.0740304	−	0.419847i	−0.999189	−	0.0402664i	$-0.987179\pi$
$277$	−5680.28	−	32214.5i	−0.0740304	−	0.419847i	0.925159	−	0.379581i	$-0.123932\pi$
$278$	19826.7	−	11447.0i	0.256544	−	0.148115i
$279$		0			0
$280$	−8149.10	+	14114.7i	−0.103943	+	0.180034i
$281$	18690.8	−	51352.6i	0.236710	−	0.650355i	−0.763281	−	0.646067i	$-0.776413\pi$
$281$	18690.8	−	51352.6i	0.236710	−	0.650355i	0.999991	−	0.00428802i	$-0.00136492\pi$
$282$		0			0
$283$	39160.2	+	32859.3i	0.488959	+	0.410285i	0.853653	−	0.520842i	$-0.174382\pi$
$283$	39160.2	+	32859.3i	0.488959	+	0.410285i	−0.364694	+	0.931127i	$0.618827\pi$
$284$	−26073.8	+	31073.6i	−0.323272	+	0.385260i
$285$		0			0
$286$	1179.73	+	429.388i	0.0144229	+	0.00524950i
$287$	−20062.6	−	11583.1i	−0.243570	−	0.140625i
$288$		0			0
$289$	59869.9	+	103698.i	0.716824	+	1.24158i
$290$	3479.80	−	613.582i	0.0413769	−	0.00729586i
$291$		0			0
$292$	−31351.6	+	11411.0i	−0.367700	+	0.133832i
$293$	16271.7	+	2869.13i	0.189538	+	0.0334207i	0.267611	−	0.963527i	$-0.413766\pi$
$293$	16271.7	+	2869.13i	0.189538	+	0.0334207i	−0.0780733	+	0.996948i	$0.524877\pi$
$294$		0			0
$295$	−32296.8	+	27100.2i	−0.371121	+	0.311407i
$296$		−	90149.9i		−	1.02892i
$297$		0			0
$298$	−37730.6			−0.424875
$299$	19611.4	+	23371.9i	0.219364	+	0.261428i
$300$		0			0
$301$	24870.3	−	141046.i	0.274503	−	1.55679i
$302$	1533.44	+	4213.09i	0.0168133	+	0.0461942i
$303$		0			0
$304$	3401.52	+	19291.0i	0.0368066	+	0.208740i
$305$	−9728.68	+	5616.86i	−0.104581	+	0.0603801i
$306$		0			0
$307$	−51266.0	+	88795.3i	−0.543942	+	0.942135i	0.454731	+	0.890629i	$0.349735\pi$
$307$	−51266.0	+	88795.3i	−0.543942	+	0.942135i	−0.998673	+	0.0515059i	$0.983598\pi$
$308$	−3899.19	+	10712.9i	−0.0411030	+	0.112930i
$309$		0			0
$310$	−11815.1	−	9914.01i	−0.122945	−	0.103163i
$311$	19903.6	−	23720.2i	0.205784	−	0.245243i	−0.653275	−	0.757121i	$-0.726605\pi$
$311$	19903.6	−	23720.2i	0.205784	−	0.245243i	0.859058	+	0.511877i	$0.171050\pi$
$312$		0			0
$313$	60314.9	+	21952.8i	0.615652	+	0.224079i	0.630975	−	0.775803i	$-0.282655\pi$
$313$	60314.9	+	21952.8i	0.615652	+	0.224079i	−0.0153222	+	0.999883i	$0.504877\pi$
$314$	24954.5	+	14407.5i	0.253098	+	0.146126i
$315$		0			0
$316$	−35648.4	−	61744.8i	−0.356998	−	0.618338i
$317$	−99398.3	+	17526.6i	−0.989146	+	0.174413i	−0.644735	−	0.764406i	$-0.723032\pi$
$317$	−99398.3	+	17526.6i	−0.989146	+	0.174413i	−0.344411	+	0.938819i	$0.611921\pi$
$318$		0			0
$319$	4944.09	−	1799.50i	0.0485853	−	0.0176836i
$320$	−14332.3	−	2527.17i	−0.139964	−	0.0246794i
$321$		0			0
$322$	27315.4	−	22920.4i	0.263449	−	0.221060i
$323$			51418.3i			0.492848i
$324$		0			0
$325$	−26511.1			−0.250992
$326$	3248.12	+	3870.96i	0.0305630	+	0.0364236i
$327$		0			0
$328$	−3840.36	+	21779.8i	−0.0356964	+	0.202444i
$329$	−58749.8	−	161414.i	−0.542769	−	1.49124i
$330$		0			0
$331$	−194.082	−	1100.69i	−0.00177145	−	0.0100464i	0.983909	−	0.178669i	$-0.0571792\pi$
$331$	−194.082	−	1100.69i	−0.00177145	−	0.0100464i	−0.985681	+	0.168623i	$0.946068\pi$
$332$	−138758.	+	80112.1i	−1.25887	+	0.726812i
$333$		0			0
$334$	8671.99	−	15020.3i	0.0777366	−	0.134644i
$335$	10104.0	−	27760.6i	0.0900337	−	0.247366i
$336$		0			0
$337$	−93620.4	−	78556.9i	−0.824349	−	0.691711i	0.129637	−	0.991561i	$-0.458619\pi$
$337$	−93620.4	−	78556.9i	−0.824349	−	0.691711i	−0.953986	+	0.299851i	$0.903063\pi$
$338$	−22683.5	+	27033.1i	−0.198553	+	0.236626i
$339$		0			0
$340$	−56247.0	−	20472.2i	−0.486565	−	0.177095i
$341$	−19888.9	−	11482.9i	−0.171042	−	0.0987510i
$342$		0			0
$343$	−63597.2	−	110154.i	−0.540567	−	0.936290i
$344$	−134650.	+	23742.5i	−1.13786	+	0.200636i
$345$		0			0
$346$	54270.0	−	19752.7i	0.453323	−	0.164996i
$347$	18668.4	+	3291.75i	0.155042	+	0.0273381i	0.250630	−	0.968083i	$-0.419362\pi$
$347$	18668.4	+	3291.75i	0.155042	+	0.0273381i	−0.0955884	+	0.995421i	$0.530473\pi$
$348$		0			0
$349$	95678.3	−	80283.6i	0.785530	−	0.659138i	−0.159105	−	0.987262i	$-0.550861\pi$
$349$	95678.3	−	80283.6i	0.785530	−	0.659138i	0.944635	+	0.328124i	$0.106416\pi$
$350$			30984.2i			0.252932i
$351$		0			0
$352$	16654.3			0.134413
$353$	25396.8	+	30266.7i	0.203812	+	0.242893i	0.858262	−	0.513212i	$-0.171544\pi$
$353$	25396.8	+	30266.7i	0.203812	+	0.242893i	−0.654450	+	0.756105i	$0.727100\pi$
$354$		0			0
$355$	4653.86	−	26393.3i	0.0369281	−	0.209429i
$356$	−5500.42	−	15112.3i	−0.0434006	−	0.119242i
$357$		0			0
$358$	−6231.01	−	35337.8i	−0.0486175	−	0.275723i
$359$	89204.5	−	51502.2i	0.692146	−	0.399611i	−0.112269	−	0.993678i	$-0.535812\pi$
$359$	89204.5	−	51502.2i	0.692146	−	0.399611i	0.804415	+	0.594067i	$0.202479\pi$
$360$		0			0
$361$	58656.9	−	101597.i	0.450096	−	0.779589i
$362$	−7851.45	+	21571.7i	−0.0599146	+	0.164614i
$363$		0			0
$364$	22876.7	+	19195.9i	0.172660	+	0.144879i
$365$	14169.2	−	16886.2i	0.106356	−	0.126750i
$366$		0			0
$367$	−189399.	−	68935.5i	−1.40619	−	0.511812i	−0.476183	−	0.879346i	$-0.657980\pi$
$367$	−189399.	−	68935.5i	−1.40619	−	0.511812i	−0.930010	+	0.367534i	$0.880202\pi$
$368$	91972.3	+	53100.2i	0.679143	+	0.392104i
$369$		0			0
$370$	13990.3	+	24231.9i	0.102193	+	0.177004i
$371$	−164756.	+	29050.8i	−1.19699	+	0.211062i
$372$		0			0
$373$	−100938.	+	36738.3i	−0.725497	+	0.264059i	−0.678257	−	0.734824i	$-0.737265\pi$
$373$	−100938.	+	36738.3i	−0.725497	+	0.264059i	−0.0472394	+	0.998884i	$0.515042\pi$
$374$	11296.7	+	1991.91i	0.0807622	+	0.0142405i
$375$		0			0
$376$	−125619.	+	105407.i	−0.888543	+	0.745576i
$377$		−	13782.2i		−	0.0969694i
$378$		0			0
$379$	221758.			1.54384			0.771918	−	0.635722i	$-0.219297\pi$
$379$	221758.			1.54384			0.771918	+	0.635722i	$0.219297\pi$
$380$	−9732.96	−	11599.3i	−0.0674028	−	0.0803275i
$381$		0			0
$382$	−12376.4	+	70190.1i	−0.0848141	+	0.481005i
$383$	42635.0	+	117139.i	0.290649	+	0.798552i	0.995972	+	0.0896658i	$0.0285799\pi$
$383$	42635.0	+	117139.i	0.290649	+	0.798552i	−0.705323	+	0.708886i	$0.749198\pi$
$384$		0			0
$385$	−1307.97	−	7417.89i	−0.00882425	−	0.0500448i
$386$	−54954.8	+	31728.1i	−0.368834	+	0.212946i
$387$		0			0
$388$	13210.0	−	22880.4i	0.0877484	−	0.151985i
$389$	74280.1	−	204083.i	0.490877	−	1.34867i	−0.409001	−	0.912534i	$-0.634123\pi$
$389$	74280.1	−	204083.i	0.490877	−	1.34867i	0.899878	−	0.436141i	$-0.143655\pi$
$390$		0			0
$391$	213548.	+	179188.i	1.39683	+	1.17208i
$392$	−15147.3	+	18051.9i	−0.0985743	+	0.117476i
$393$		0			0
$394$	30346.5	+	11045.2i	0.195486	+	0.0711512i
$395$	40794.9	+	23553.0i	0.261464	+	0.150956i
$396$		0			0
$397$	−59824.4	−	103619.i	−0.379575	−	0.657443i	0.611426	−	0.791302i	$-0.290596\pi$
$397$	−59824.4	−	103619.i	−0.379575	−	0.657443i	−0.991000	+	0.133859i	$0.957263\pi$
$398$	25684.2	−	4528.81i	0.162143	−	0.0285903i
$399$		0			0
$400$	−86715.9	+	31562.0i	−0.541974	+	0.197262i
$401$	−78697.1	−	13876.4i	−0.489407	−	0.0862956i	−0.0765013	−	0.997069i	$-0.524375\pi$
$401$	−78697.1	−	13876.4i	−0.489407	−	0.0862956i	−0.412906	+	0.910774i	$0.635486\pi$
$402$		0			0
$403$	−46084.1	+	38669.1i	−0.283753	+	0.238097i
$404$		−	12175.0i		−	0.0745943i
$405$		0			0
$406$	−16107.6			−0.0977188
$407$	26780.7	+	31916.0i	0.161671	+	0.192672i
$408$		0			0
$409$	−44493.9	+	252337.i	−0.265983	+	1.50846i	0.500239	+	0.865887i	$0.333245\pi$
$409$	−44493.9	+	252337.i	−0.265983	+	1.50846i	−0.766222	+	0.642576i	$0.777866\pi$
$410$	−2347.71	−	6450.27i	−0.0139661	−	0.0383716i
$411$		0			0
$412$	−12448.9	−	70601.2i	−0.0733393	−	0.415928i
$413$	166442.	−	96095.6i	0.975807	−	0.563382i
$414$		0			0
$415$	52930.2	−	91677.9i	0.307332	−	0.532314i
$416$	14920.9	−	40994.7i	0.0862198	−	0.236887i
$417$		0			0
$418$	2222.89	+	1865.23i	0.0127223	+	0.0106753i
$419$	194699.	−	232033.i	1.10901	−	1.32167i	0.167048	−	0.985949i	$-0.446577\pi$
$419$	194699.	−	232033.i	1.10901	−	1.32167i	0.941962	−	0.335718i	$-0.108979\pi$
$420$		0			0
$421$	−61184.4	−	22269.3i	−0.345205	−	0.125644i	0.163599	−	0.986527i	$-0.447690\pi$
$421$	−61184.4	−	22269.3i	−0.345205	−	0.125644i	−0.508803	+	0.860883i	$0.669912\pi$
$422$	34022.9	+	19643.1i	0.191050	+	0.110303i
$423$		0			0
$424$	79855.4	+	138314.i	0.444194	+	0.769366i
$425$	−238550.	+	42062.9i	−1.32069	+	0.232874i
$426$		0			0
$427$	48121.3	−	17514.7i	0.263926	−	0.0960611i
$428$	150323.	+	26506.1i	0.820614	+	0.144696i
$429$		0			0
$430$	32508.8	−	27278.1i	0.175818	−	0.147529i
$431$			247253.i			1.33103i	0.746385	+	0.665514i	$0.231788\pi$
$431$			247253.i			1.33103i	−0.746385	+	0.665514i	$0.768212\pi$
$432$		0			0
$433$	229960.			1.22652			0.613262	−	0.789880i	$-0.289857\pi$
$433$	229960.			1.22652			0.613262	+	0.789880i	$0.289857\pi$
$434$	45193.6	+	53859.7i	0.239937	+	0.285946i
$435$		0			0
$436$	6647.52	−	37700.0i	0.0349693	−	0.198321i
$437$	24118.9	+	66266.2i	0.126298	+	0.347000i
$438$		0			0
$439$	13862.8	+	78620.1i	0.0719322	+	0.407948i	0.999419	+	0.0340912i	$0.0108537\pi$
$439$	13862.8	+	78620.1i	0.0719322	+	0.407948i	−0.927487	+	0.373857i	$0.878035\pi$
$440$	−6227.38	+	3595.38i	−0.0321662	+	0.0185712i
$441$		0			0
$442$	15024.0	−	26022.4i	0.0769028	−	0.133199i
$443$	37093.8	−	101914.i	0.189014	−	0.519312i	−0.808599	−	0.588360i	$-0.799774\pi$
$443$	37093.8	−	101914.i	0.189014	−	0.519312i	0.997613	+	0.0690480i	$0.0219962\pi$
$444$		0			0
$445$	8139.62	+	6829.95i	0.0411040	+	0.0344903i
$446$	73275.3	−	87326.1i	0.368373	−	0.439010i
$447$		0			0
$448$	62341.5	+	22690.5i	0.310614	+	0.113054i
$449$	−26892.6	−	15526.5i	−0.133395	−	0.0770158i	0.431817	−	0.901961i	$-0.357873\pi$
$449$	−26892.6	−	15526.5i	−0.133395	−	0.0770158i	−0.565213	+	0.824945i	$0.691206\pi$
$450$		0			0
$451$	−5110.47	−	8851.59i	−0.0251251	−	0.0435179i
$452$	−178858.	+	31537.4i	−0.875449	+	0.154365i
$453$		0			0
$454$	6513.49	−	2370.72i	0.0316011	−	0.0115019i
$455$	−19431.1	−	3426.22i	−0.0938586	−	0.0165498i
$456$		0			0
$457$	−126339.	+	106011.i	−0.604930	+	0.507597i	−0.893026	−	0.450005i	$-0.851422\pi$
$457$	−126339.	+	106011.i	−0.604930	+	0.507597i	0.288096	+	0.957602i	$0.406978\pi$
$458$			82646.3i			0.393996i
$459$		0			0
$460$	−82092.2			−0.387959
$461$	188614.	+	224781.i	0.887507	+	1.05769i	0.997962	+	0.0638087i	$0.0203248\pi$
$461$	188614.	+	224781.i	0.887507	+	1.05769i	−0.110455	+	0.993881i	$0.535231\pi$
$462$		0			0
$463$	−12545.1	+	71146.6i	−0.0585209	+	0.331889i	−0.999986	−	0.00522092i	$-0.998338\pi$
$463$	−12545.1	+	71146.6i	−0.0585209	+	0.331889i	0.941465	+	0.337109i	$0.109449\pi$
$464$	−16408.0	−	45080.5i	−0.0762112	−	0.209389i
$465$		0			0
$466$	17691.8	+	100335.i	0.0814706	+	0.462043i
$467$	−35163.8	+	20301.9i	−0.161236	+	0.0930898i	−0.578447	−	0.815720i	$-0.696341\pi$
$467$	−35163.8	+	20301.9i	−0.161236	+	0.0930898i	0.417211	+	0.908810i	$0.363008\pi$
$468$		0			0
$469$	−67335.0	+	116628.i	−0.306123	+	0.530220i
$470$	17407.7	−	47827.4i	0.0788038	−	0.216512i
$471$		0			0
$472$	−140551.	−	117936.i	−0.630883	−	0.529374i
$473$	40617.4	−	48406.0i	0.181548	−	0.216360i
$474$		0			0
$475$	−57580.9	−	20957.7i	−0.255206	−	0.0928875i
$476$	236304.	+	136430.i	1.04294	+	0.602140i
$477$		0			0
$478$	−39222.9	−	67936.1i	−0.171666	−	0.297334i
$479$	−54719.7	+	9648.55i	−0.238491	+	0.0420524i	−0.291616	−	0.956535i	$-0.594193\pi$
$479$	−54719.7	+	9648.55i	−0.238491	+	0.0420524i	0.0531249	+	0.998588i	$0.483082\pi$
$480$		0			0
$481$	102555.	−	37327.0i	0.443268	−	0.161337i
$482$	−94153.0	−	16601.7i	−0.405266	−	0.0714593i
$483$		0			0
$484$	155135.	−	130174.i	0.662246	−	0.555691i
$485$			17455.7i			0.0742087i
$486$		0			0
$487$	−138957.			−0.585898			−0.292949	−	0.956128i	$-0.594637\pi$
$487$	−138957.			−0.585898			−0.292949	+	0.956128i	$0.594637\pi$
$488$	−31424.2	−	37449.9i	−0.131955	−	0.157258i
$489$		0			0
$490$	1270.07	−	7202.95i	0.00528977	−	0.0299998i
$491$	4504.33	+	12375.5i	0.0186839	+	0.0513335i	0.948684	−	0.316226i	$-0.102416\pi$
$491$	4504.33	+	12375.5i	0.0186839	+	0.0513335i	−0.930000	+	0.367559i	$0.880193\pi$
$492$		0			0
$493$	−21867.0	−	124014.i	−0.0899695	−	0.510242i
$494$	6582.81	−	3800.59i	0.0269748	−	0.0155739i
$495$		0			0
$496$	−104701.	+	181348.i	−0.425588	+	0.737140i
$497$	−41785.2	+	114804.i	−0.169165	+	0.464776i
$498$		0			0
$499$	134809.	+	113118.i	0.541398	+	0.454287i	0.872016	−	0.489478i	$-0.162813\pi$
$499$	134809.	+	113118.i	0.541398	+	0.454287i	−0.330618	+	0.943765i	$0.607257\pi$
$500$	99189.4	−	118209.i	0.396758	−	0.472837i
$501$		0			0
$502$	−11745.0	−	4274.83i	−0.0466064	−	0.0169633i
$503$	−293462.	−	169430.i	−1.15989	−	0.669661i	−0.208610	−	0.977999i	$-0.566894\pi$
$503$	−293462.	−	169430.i	−1.15989	−	0.669661i	−0.951277	+	0.308338i	$0.900227\pi$
$504$		0			0
$505$	4022.02	+	6966.34i	0.0157711	+	0.0273163i
$506$	15493.1	−	2731.86i	0.0605116	−	0.0106698i
$507$		0			0
$508$	153344.	−	55812.5i	0.594207	−	0.216274i
$509$	−267722.	−	47206.7i	−1.03335	−	0.182208i	−0.368847	−	0.929490i	$-0.620247\pi$
$509$	−267722.	−	47206.7i	−1.03335	−	0.182208i	−0.664507	+	0.747282i	$0.731358\pi$
$510$		0			0
$511$	−76977.0	+	64591.4i	−0.294794	+	0.247362i
$512$		−	263863.i		−	1.00656i
$513$		0			0
$514$	107584.			0.407214
$515$	30446.3	+	36284.4i	0.114794	+	0.136806i
$516$		0			0
$517$	13160.1	−	74634.7i	0.0492355	−	0.279228i
$518$	−43625.0	−	119859.i	−0.162583	−	0.446694i
$519$		0			0
$520$	3270.86	+	18549.9i	0.0120964	+	0.0686019i
$521$	212819.	−	122871.i	0.784035	−	0.452663i	−0.0538237	−	0.998550i	$-0.517141\pi$
$521$	212819.	−	122871.i	0.784035	−	0.452663i	0.837858	+	0.545888i	$0.183808\pi$
$522$		0			0
$523$	145495.	−	252005.i	0.531920	−	0.921312i	−0.467386	−	0.884053i	$-0.654804\pi$
$523$	145495.	−	252005.i	0.531920	−	0.921312i	0.999306	−	0.0372584i	$-0.0118625\pi$
$524$	102003.	−	280251.i	0.371493	−	1.02067i
$525$		0			0
$526$	−117685.	−	98749.4i	−0.425353	−	0.356914i
$527$	−353318.	+	421068.i	−1.27217	+	1.51611i
$528$		0			0
$529$	96301.8	+	35051.0i	0.344130	+	0.125253i
$530$	−42929.5	−	24785.3i	−0.152828	−	0.0882354i
$531$		0			0
$532$	34512.4	+	59777.3i	0.121942	+	0.211209i
$533$	−26366.9	+	4649.19i	−0.0928121	+	0.0163653i
$534$		0			0
$535$	−94769.0	+	34493.1i	−0.331100	+	0.120510i
$536$	126610.	+	22324.8i	0.440695	+	0.0777065i
$537$		0			0
$538$	−233.658	+	196.062i	−0.000807266	+	0.000677376i
$539$		−	10890.7i		−	0.0374869i
$540$		0			0
$541$	−462829.			−1.58134			−0.790671	−	0.612241i	$-0.790268\pi$
$541$	−462829.			−1.58134			−0.790671	+	0.612241i	$0.790268\pi$
$542$	20338.8	+	24238.9i	0.0692353	+	0.0825114i
$543$		0			0
$544$	69217.2	−	392550.i	0.233892	−	1.32647i
$545$	8650.61	+	23767.4i	0.0291242	+	0.0800181i
$546$		0			0
$547$	−65549.2	−	371748.i	−0.219075	−	1.24244i	−0.873693	−	0.486477i	$-0.838282\pi$
$547$	−65549.2	−	371748.i	−0.219075	−	1.24244i	0.654618	−	0.755960i	$-0.272829\pi$
$548$	−418232.	+	241466.i	−1.39269	+	0.804072i
$549$		0			0
$550$	−6835.10	+	11838.7i	−0.0225954	+	0.0391363i
$551$	10895.2	−	29934.3i	0.0358865	−	0.0985974i
$552$		0			0
$553$	−164497.	−	138029.i	−0.537907	−	0.451358i
$554$	−28400.8	+	33846.8i	−0.0925362	+	0.110280i
$555$		0			0
$556$	225778.	+	82176.5i	0.730352	+	0.265826i
$557$	−153585.	−	88672.5i	−0.495039	−	0.285811i	0.231624	−	0.972805i	$-0.425596\pi$
$557$	−153585.	−	88672.5i	−0.495039	−	0.285811i	−0.726662	+	0.686995i	$0.758930\pi$
$558$		0			0
$559$	−82762.2	−	143348.i	−0.264855	−	0.458742i
$560$	−67636.8	+	11926.2i	−0.215678	+	0.0380299i
$561$		0			0
$562$	−69362.9	+	25246.0i	−0.219611	+	0.0799319i
$563$	134655.	+	23743.4i	0.424822	+	0.0749076i	0.381972	−	0.924174i	$-0.375245\pi$
$563$	134655.	+	23743.4i	0.424822	+	0.0749076i	0.0428501	+	0.999082i	$0.486356\pi$
$564$		0			0
$565$	91921.3	−	77131.1i	0.287951	−	0.241620i
$566$		−	69048.7i		−	0.215537i
$567$		0			0
$568$	116632.			0.361510
$569$	301401.	+	359196.i	0.930938	+	1.10945i	0.993773	+	0.111425i	$0.0355414\pi$
$569$	301401.	+	359196.i	0.930938	+	1.10945i	−0.0628350	+	0.998024i	$0.520014\pi$
$570$		0			0
$571$	−16388.9	+	92946.2i	−0.0502664	+	0.285075i	−0.999571	−	0.0292821i	$-0.990678\pi$
$571$	−16388.9	+	92946.2i	−0.0502664	+	0.285075i	0.949305	+	0.314357i	$0.101789\pi$
$572$	4506.36	+	12381.1i	0.0137732	+	0.0378415i
$573$		0			0
$574$	5433.64	+	30815.7i	0.0164918	+	0.0935294i
$575$	−287705.	+	166107.i	−0.870186	+	0.502402i
$576$		0			0
$577$	−151696.	+	262746.i	−0.455641	+	0.789194i	−0.998725	−	0.0504846i	$-0.983923\pi$
$577$	−151696.	+	262746.i	−0.455641	+	0.789194i	0.543083	+	0.839679i	$0.317257\pi$
$578$	55316.5	−	151981.i	0.165577	−	0.454918i
$579$		0			0
$580$	28407.5	+	23836.7i	0.0844455	+	0.0708582i
$581$	−310191.	+	369671.i	−0.918919	+	1.09512i
$582$		0			0
$583$	−69360.0	−	25245.0i	−0.204067	−	0.0742741i
$584$	83077.5	+	47964.8i	0.243589	+	0.140636i
$585$		0			0
$586$	−11158.7	−	19327.5i	−0.0324952	−	0.0562833i
$587$	498455.	−	87891.1i	1.44661	−	0.255076i	0.605456	−	0.795879i	$-0.292991\pi$
$587$	498455.	−	87891.1i	1.44661	−	0.255076i	0.841149	+	0.540803i	$0.181880\pi$
$588$		0			0
$589$	−130662.	+	47557.0i	−0.376632	+	0.137083i
$590$	56081.7	+	9888.71i	0.161108	+	0.0284077i
$591$		0			0
$592$	291012.	−	244188.i	0.830362	−	0.696756i
$593$		−	382244.i		−	1.08701i	−0.839407	−	0.543503i	$-0.817098\pi$
$593$		−	382244.i		−	1.08701i	0.839407	−	0.543503i	$-0.182902\pi$
$594$		0			0
$595$	−180280.			−0.509229
$596$	−254529.	−	303336.i	−0.716547	−	0.853947i
$597$		0			0
$598$	7156.08	−	40584.1i	0.0200112	−	0.113489i
$599$	99670.1	+	273841.i	0.277787	+	0.763213i	0.997613	+	0.0690580i	$0.0219994\pi$
$599$	99670.1	+	273841.i	0.277787	+	0.763213i	−0.719826	+	0.694155i	$0.755778\pi$
$600$		0			0
$601$	95074.7	+	539196.i	0.263218	+	1.49279i	0.774061	+	0.633111i	$0.218222\pi$
$601$	95074.7	+	539196.i	0.263218	+	1.49279i	−0.510843	+	0.859674i	$0.670667\pi$
$602$	−167535.	+	96726.4i	−0.462288	+	0.266902i
$603$		0			0
$604$	−23526.7	+	40749.5i	−0.0644893	+	0.111699i
$605$	−45762.9	+	125733.i	−0.125027	+	0.343508i
$606$		0			0
$607$	−172994.	−	145159.i	−0.469519	−	0.393973i	0.377100	−	0.926173i	$-0.376921\pi$
$607$	−172994.	−	145159.i	−0.469519	−	0.393973i	−0.846619	+	0.532199i	$0.821366\pi$
$608$	64815.0	−	77243.5i	0.175335	−	0.208956i
$609$		0			0
$610$	14258.5	+	5189.67i	0.0383190	+	0.0139470i
$611$	−171924.	−	99260.4i	−0.460526	−	0.265885i
$612$		0			0
$613$	295834.	+	512400.i	0.787277	+	1.36360i	0.927629	+	0.373502i	$0.121843\pi$
$613$	295834.	+	512400.i	0.787277	+	1.36360i	−0.140352	+	0.990102i	$0.544823\pi$
$614$	136388.	−	24048.8i	0.361775	−	0.0637906i
$615$		0			0
$616$	30802.7	−	11211.3i	0.0811759	−	0.0295456i
$617$	−111685.	−	19693.0i	−0.293375	−	0.0517300i	0.0250234	−	0.999687i	$-0.492034\pi$
$617$	−111685.	−	19693.0i	−0.293375	−	0.0517300i	−0.318399	+	0.947957i	$0.603145\pi$
$618$		0			0
$619$	−171675.	+	144052.i	−0.448049	+	0.375958i	−0.838711	−	0.544576i	$-0.816690\pi$
$619$	−171675.	+	144052.i	−0.448049	+	0.375958i	0.390662	+	0.920534i	$0.372246\pi$
$620$		−	161867.i		−	0.421090i
$621$		0			0
$622$	−41824.3			−0.108105
$623$	−31134.8	−	37105.0i	−0.0802176	−	0.0955996i
$624$		0			0
$625$	40607.1	−	230294.i	0.103954	−	0.589554i
$626$	−29652.0	−	81468.3i	−0.0756669	−	0.207893i
$627$		0			0
$628$	52512.7	+	297814.i	0.133151	+	0.755138i
$629$	863581.	−	498589.i	2.18274	−	1.26021i
$630$		0			0
$631$	36775.4	−	63696.9i	0.0923633	−	0.159978i	−0.816142	−	0.577852i	$-0.803891\pi$
$631$	36775.4	−	63696.9i	0.0923633	−	0.159978i	0.908505	+	0.417874i	$0.137225\pi$
$632$	−70113.4	+	192635.i	−0.175536	+	0.482282i
$633$		0			0
$634$	104435.	+	87631.3i	0.259817	+	0.218012i
$635$	−69303.1	+	82592.3i	−0.171872	+	0.204829i
$636$		0			0
$637$	−26807.7	−	9757.21i	−0.0660665	−	0.0240462i
$638$	−6154.54	−	3553.32i	−0.0151201	−	0.00872958i
$639$		0			0
$640$	76073.7	+	131764.i	0.185727	+	0.321688i
$641$	337744.	−	59553.3i	0.821999	−	0.144941i	0.253197	−	0.967415i	$-0.418518\pi$
$641$	337744.	−	59553.3i	0.821999	−	0.144941i	0.568802	+	0.822474i	$0.307407\pi$
$642$		0			0
$643$	201474.	−	73330.5i	0.487300	−	0.177363i	−0.0866731	−	0.996237i	$-0.527624\pi$
$643$	201474.	−	73330.5i	0.487300	−	0.177363i	0.573973	+	0.818874i	$0.305401\pi$
$644$	368537.	+	64983.1i	0.888607	+	0.156685i
$645$		0			0
$646$	53203.0	−	44642.6i	0.127489	−	0.106976i
$647$			20926.3i			0.0499902i	0.999688	+	0.0249951i	$0.00795701\pi$
$647$			20926.3i			0.0499902i	−0.999688	+	0.0249951i	$0.992043\pi$
$648$		0			0
$649$	84794.5			0.201316
$650$	23017.5	+	27431.2i	0.0544794	+	0.0649260i
$651$		0			0
$652$	−9208.96	+	52226.6i	−0.0216628	+	0.122856i
$653$	−64062.7	−	176011.i	−0.150238	−	0.412774i	0.841629	−	0.540056i	$-0.181597\pi$
$653$	−64062.7	−	176011.i	−0.150238	−	0.412774i	−0.991867	+	0.127282i	$0.959375\pi$
$654$		0			0
$655$	34216.6	+	194052.i	0.0797544	+	0.452310i
$656$	−80709.3	+	46597.5i	−0.187550	+	0.108282i
$657$		0			0
$658$	−116008.	+	200932.i	−0.267940	+	0.464085i
$659$	34435.2	−	94610.0i	0.0792925	−	0.217854i	−0.893712	−	0.448642i	$-0.851908\pi$
$659$	34435.2	−	94610.0i	0.0792925	−	0.217854i	0.973004	+	0.230787i	$0.0741302\pi$
$660$		0			0
$661$	377130.	+	316450.i	0.863154	+	0.724272i	0.962645	−	0.270766i	$-0.0872770\pi$
$661$	377130.	+	316450.i	0.863154	+	0.724272i	−0.0994911	+	0.995038i	$0.531721\pi$
$662$	−970.390	+	1156.47i	−0.00221427	+	0.00263886i
$663$		0			0
$664$	432906.	+	157565.i	0.981877	+	0.357374i
$665$	−39495.0	−	22802.4i	−0.0893097	−	0.0515630i
$666$		0			0
$667$	−86353.0	−	149568.i	−0.194100	−	0.336191i
$668$	179257.	−	31607.8i	0.401720	−	0.0708340i
$669$		0			0
$670$	−37496.7	+	13647.7i	−0.0835302	+	0.0304025i
$671$	22250.4	+	3923.34i	0.0494188	+	0.00871387i
$672$		0			0
$673$	133890.	−	112347.i	0.295609	−	0.248045i	−0.482905	−	0.875673i	$-0.660418\pi$
$673$	133890.	−	112347.i	0.295609	−	0.248045i	0.778514	+	0.627628i	$0.215974\pi$
$674$			165075.i			0.363380i
$675$		0			0
$676$	−370355.			−0.810447
$677$	66906.1	+	79735.6i	0.145978	+	0.173970i	0.834079	−	0.551645i	$-0.186000\pi$
$677$	66906.1	+	79735.6i	0.145978	+	0.173970i	−0.688101	+	0.725615i	$0.741555\pi$
$678$		0			0
$679$	13817.7	−	78364.3i	0.0299707	−	0.169972i
$680$	58863.2	+	161725.i	0.127299	+	0.349752i
$681$		0			0
$682$	5386.60	+	30548.9i	0.0115810	+	0.0656791i
$683$	316965.	−	183000.i	0.679469	−	0.392292i	−0.120186	−	0.992751i	$-0.538349\pi$
$683$	316965.	−	183000.i	0.679469	−	0.392292i	0.799655	+	0.600460i	$0.205016\pi$
$684$		0			0
$685$	159537.	−	276327.i	0.340001	−	0.588900i
$686$	−58760.3	+	161443.i	−0.124864	+	0.343060i
$687$		0			0
$688$	−441369.	−	370352.i	−0.932448	−	0.782417i
$689$	−124282.	+	148113.i	−0.261800	+	0.312001i
$690$		0			0
$691$	126437.	+	46019.3i	0.264800	+	0.0963793i	0.471008	−	0.882129i	$-0.343890\pi$
$691$	126437.	+	46019.3i	0.264800	+	0.0963793i	−0.206208	+	0.978508i	$0.566112\pi$
$692$	524905.	+	303054.i	1.09615	+	0.632860i
$693$		0			0
$694$	−12802.4	−	22174.4i	−0.0265810	−	0.0460397i
$695$	−156334.	+	27565.9i	−0.323656	+	0.0570693i
$696$		0			0
$697$	−229877.	+	83668.2i	−0.473183	+	0.172224i
$698$	−166140.	−	29295.0i	−0.341008	−	0.0601289i
$699$		0			0
$700$	−249098.	+	209018.i	−0.508363	+	0.426567i
$701$			730976.i			1.48753i	0.668439	+	0.743767i	$0.266963\pi$
$701$			730976.i			1.48753i	−0.668439	+	0.743767i	$0.733037\pi$
$702$		0			0
$703$	252253.			0.510418
$704$	18814.5	+	22422.3i	0.0379619	+	0.0452413i
$705$		0			0
$706$	9267.14	−	52556.5i	0.0185924	−	0.105443i
$707$	−12541.6	−	34457.8i	−0.0250908	−	0.0689365i
$708$		0			0
$709$	−84369.5	−	478483.i	−0.167839	−	0.951863i	−0.946089	−	0.323908i	$-0.895003\pi$
$709$	−84369.5	−	478483.i	−0.167839	−	0.951863i	0.778250	−	0.627955i	$-0.216108\pi$
$710$	−31350.0	+	18099.9i	−0.0621901	+	0.0359055i
$711$		0			0
$712$	−23120.3	+	40045.5i	−0.0456072	+	0.0789940i
$713$	−257833.	+	708390.i	−0.507177	+	1.39346i
$714$		0			0
$715$	−6668.59	−	5595.61i	−0.0130443	−	0.0109455i
$716$	242065.	−	288482.i	0.472178	−	0.562720i
$717$		0			0
$718$	−130739.	−	47585.2i	−0.253605	−	0.0923045i
$719$	−555622.	−	320788.i	−1.07479	−	0.620527i	−0.145300	−	0.989388i	$-0.546415\pi$
$719$	−555622.	−	320788.i	−1.07479	−	0.620527i	−0.929485	+	0.368860i	$0.879748\pi$
$720$		0			0
$721$	−107960.	−	186993.i	−0.207680	−	0.359712i
$722$	−156050.	+	27515.9i	−0.299358	+	0.0527849i
$723$		0			0
$724$	−226391.	+	82399.7i	−0.431900	+	0.157199i
$725$	147790.	+	26059.4i	0.281170	+	0.0495779i
$726$		0			0
$727$	−204709.	+	171771.i	−0.387318	+	0.324999i	−0.815567	−	0.578662i	$-0.803575\pi$
$727$	−204709.	+	171771.i	−0.387318	+	0.324999i	0.428249	+	0.903661i	$0.359131\pi$
$728$		−	85865.6i		−	0.162015i
$729$		0			0
$730$	−29774.4			−0.0558724
$731$	−972144.	−	1.15856e6i	−1.81927	−	2.16812i
$732$		0			0
$733$	−68087.6	+	386144.i	−0.126724	+	0.718690i	0.853544	+	0.521020i	$0.174448\pi$
$733$	−68087.6	+	386144.i	−0.126724	+	0.718690i	−0.980269	+	0.197670i	$0.936663\pi$
$734$	93112.3	+	255824.i	0.172828	+	0.474842i
$735$		0			0
$736$	−94929.8	−	538373.i	−0.175245	−	0.993866i
$737$	−51456.0	+	29708.1i	−0.0947330	+	0.0546941i
$738$		0			0
$739$	169462.	−	293516.i	0.310301	−	0.537456i	−0.668127	−	0.744047i	$-0.732904\pi$
$739$	169462.	−	293516.i	0.310301	−	0.537456i	0.978427	+	0.206591i	$0.0662370\pi$
$740$	−100435.	+	275942.i	−0.183409	+	0.503912i
$741$		0			0
$742$	173104.	+	145251.i	0.314412	+	0.263823i
$743$	445339.	−	530734.i	0.806701	−	0.961389i	−0.193103	−	0.981178i	$-0.561855\pi$
$743$	445339.	−	530734.i	0.806701	−	0.961389i	0.999804	+	0.0197896i	$0.00629962\pi$
$744$		0			0
$745$	245845.	+	89480.2i	0.442944	+	0.161218i
$746$	125650.	+	72544.0i	0.225780	+	0.130354i
$747$		0			0
$748$	60193.0	+	104257.i	0.107583	+	0.186339i
$749$	452752.	−	79832.4i	0.807043	−	0.142303i
$750$		0			0
$751$	688146.	−	250465.i	1.22012	−	0.444086i	0.349914	−	0.936782i	$-0.386211\pi$
$751$	688146.	−	250465.i	1.22012	−	0.444086i	0.870201	+	0.492696i	$0.163989\pi$
$752$	−680524.	−	119995.i	−1.20339	−	0.212191i
$753$		0			0
$754$	−14260.5	+	11966.0i	−0.0250838	+	0.0210478i
$755$		−	31088.3i		−	0.0545385i
$756$		0			0
$757$	347674.			0.606709			0.303355	−	0.952878i	$-0.401893\pi$
$757$	347674.			0.606709			0.303355	+	0.952878i	$0.401893\pi$
$758$	−192536.	−	229455.i	−0.335099	−	0.399355i
$759$		0			0
$760$	−7560.09	+	42875.4i	−0.0130888	+	0.0742303i
$761$	−227751.	−	625741.i	−0.393270	−	1.08050i	−0.965499	−	0.260407i	$-0.916143\pi$
$761$	−227751.	−	625741.i	−0.393270	−	1.08050i	0.572229	−	0.820094i	$-0.306079\pi$
$762$		0			0
$763$	−20021.4	−	113547.i	−0.0343910	−	0.195041i
$764$	−647786.	+	373999.i	−1.10980	+	0.640743i
$765$		0			0
$766$	84187.8	−	145818.i	0.143480	−	0.248515i
$767$	75969.0	−	208723.i	0.129135	−	0.354797i
$768$		0			0
$769$	−69815.7	−	58582.4i	−0.118059	−	0.0990636i	0.581847	−	0.813299i	$-0.302330\pi$
$769$	−69815.7	−	58582.4i	−0.118059	−	0.0990636i	−0.699906	+	0.714235i	$0.746775\pi$
$770$	−6539.74	+	7793.76i	−0.0110301	+	0.0131452i
$771$		0			0
$772$	−625802.	−	227773.i	−1.05003	−	0.382180i
$773$	75723.2	+	43718.8i	0.126727	+	0.0731660i	0.562024	−	0.827121i	$-0.310023\pi$
$773$	75723.2	+	43718.8i	0.126727	+	0.0731660i	−0.435296	+	0.900287i	$0.643356\pi$
$774$		0			0
$775$	−327524.	−	567288.i	−0.545305	−	0.944497i
$776$	−74810.7	+	13191.1i	−0.124234	+	0.0219058i
$777$		0			0
$778$	−275658.	+	100331.i	−0.455419	+	0.165759i
$779$	−60943.1	−	10745.9i	−0.100427	−	0.0177080i
$780$		0			0
$781$	−41291.4	+	34647.6i	−0.0676951	+	0.0568029i
$782$		−	376536.i		−	0.615734i
$783$		0			0
$784$	−99302.4			−0.161558
$785$	−128430.	−	153057.i	−0.208415	−	0.248379i
$786$		0			0
$787$	−152733.	+	866190.i	−0.246594	+	1.39850i	0.570168	+	0.821528i	$0.306878\pi$
$787$	−152733.	+	866190.i	−0.246594	+	1.39850i	−0.816762	+	0.576975i	$0.804233\pi$
$788$	115918.	+	318482.i	0.186680	+	0.512900i
$789$		0			0
$790$	−11048.7	−	62660.1i	−0.0177034	−	0.100401i
$791$	−473719.	+	273502.i	−0.757125	+	0.437126i
$792$		0			0
$793$	29591.9	−	51254.7i	0.0470572	−	0.0815055i
$794$	−55274.4	+	151865.i	−0.0876765	+	0.240889i
$795$		0			0
$796$	209674.	+	175937.i	0.330916	+	0.277672i
$797$	123272.	−	146910.i	0.194065	−	0.231278i	−0.660233	−	0.751061i	$-0.729543\pi$
$797$	123272.	−	146910.i	0.194065	−	0.231278i	0.854299	+	0.519783i	$0.173987\pi$
$798$		0			0
$799$	−1.70449e6	−	620382.i	−2.66993	−	0.971775i
$800$	411386.	+	237514.i	0.642790	+	0.371115i
$801$		0			0
$802$	53968.7	+	93476.4i	0.0839060	+	0.145329i
$803$	−43660.9	+	7698.60i	−0.0677114	+	0.0119393i
$804$		0			0
$805$	−232339.	+	84564.3i	−0.358533	+	0.130495i
$806$	80022.6	+	14110.1i	0.123181	+	0.0217201i
$807$		0			0
$808$	−26816.5	+	22501.7i	−0.0410751	+	0.0344661i
$809$			342800.i			0.523774i	0.965099	+	0.261887i	$0.0843447\pi$
$809$			342800.i			0.523774i	−0.965099	+	0.261887i	$0.915655\pi$
$810$		0			0
$811$	1.12925e6			1.71691			0.858453	−	0.512892i	$-0.171426\pi$
$811$	1.12925e6			1.71691			0.858453	+	0.512892i	$0.171426\pi$
$812$	−108661.	−	129497.i	−0.164802	−	0.196403i
$813$		0			0
$814$	9772.12	−	55420.5i	0.0147482	−	0.0836414i
$815$	−11983.9	−	32925.5i	−0.0180419	−	0.0495697i
$816$		0			0
$817$	−66435.1	−	376772.i	−0.0995299	−	0.564462i
$818$	299726.	−	173047.i	0.447938	−	0.258617i
$819$		0			0
$820$	36019.6	−	62387.7i	0.0535687	−	0.0927836i
$821$	−391161.	+	1.07471e6i	−0.580323	+	1.59442i	0.207308	+	0.978276i	$0.433530\pi$
$821$	−391161.	+	1.07471e6i	−0.580323	+	1.59442i	−0.787631	+	0.616148i	$0.788692\pi$
$822$		0			0
$823$	474071.	+	397792.i	0.699912	+	0.587296i	0.921749	−	0.387788i	$-0.126761\pi$
$823$	474071.	+	397792.i	0.699912	+	0.587296i	−0.221837	+	0.975084i	$0.571205\pi$
$824$	−132497.	+	157904.i	−0.195143	+	0.232562i
$825$		0			0
$826$	−243940.	−	88787.0i	−0.357539	−	0.130134i
$827$	−106515.	−	61496.6i	−0.155740	−	0.0899167i	0.420104	−	0.907476i	$-0.361993\pi$
$827$	−106515.	−	61496.6i	−0.155740	−	0.0899167i	−0.575845	+	0.817559i	$0.695327\pi$
$828$		0			0
$829$	235237.	+	407442.i	0.342291	+	0.592866i	0.984858	−	0.173364i	$-0.0554637\pi$
$829$	235237.	+	407442.i	0.342291	+	0.592866i	−0.642567	+	0.766230i	$0.722130\pi$
$830$	−140815.	+	24829.5i	−0.204406	+	0.0360423i
$831$		0			0
$832$	72049.1	−	26223.7i	0.104084	−	0.0378833i
$833$	−256701.	−	45263.3i	−0.369945	−	0.0652313i
$834$		0			0
$835$	−92126.5	+	77303.3i	−0.132133	+	0.110873i
$836$			30453.7i			0.0435740i
$837$		0			0
$838$	−409129.			−0.582602
$839$	−42223.1	−	50319.5i	−0.0599827	−	0.0714846i	0.735219	−	0.677830i	$-0.237079\pi$
$839$	−42223.1	−	50319.5i	−0.0599827	−	0.0714846i	−0.795202	+	0.606345i	$0.792635\pi$
$840$		0			0
$841$	109271.	−	619705.i	0.154494	−	0.876179i
$842$	30079.5	+	82642.8i	0.0424274	+	0.116568i
$843$		0			0
$844$	71595.7	+	406040.i	0.100508	+	0.570011i
$845$	211911.	−	122347.i	0.296784	−	0.171348i
$846$		0			0
$847$	304972.	−	528227.i	0.425102	−	0.736298i
$848$	−230185.	+	632428.i	−0.320100	+	0.879467i
$849$		0			0
$850$	250638.	+	210310.i	0.346904	+	0.291087i
$851$	879080.	−	1.04765e6i	1.21386	−	1.44662i
$852$		0			0
$853$	913792.	+	332593.i	1.25588	+	0.457104i	0.882386	−	0.470527i	$-0.155936\pi$
$853$	913792.	+	332593.i	1.25588	+	0.457104i	0.373498	+	0.927631i	$0.378158\pi$
$854$	−59902.7	−	34584.8i	−0.0821355	−	0.0474209i
$855$		0			0
$856$	−219444.	−	380089.i	−0.299486	−	0.518725i
$857$	1.09569e6	−	193200.i	1.49185	−	0.263054i	0.632550	−	0.774519i	$-0.282008\pi$
$857$	1.09569e6	−	193200.i	1.49185	−	0.263054i	0.859304	+	0.511465i	$0.170897\pi$
$858$		0			0
$859$	507014.	−	184538.i	0.687122	−	0.250092i	0.0252197	−	0.999682i	$-0.491971\pi$
$859$	507014.	−	184538.i	0.687122	−	0.250092i	0.661903	+	0.749590i	$0.269749\pi$
$860$	438606.	+	77338.0i	0.593031	+	0.104567i
$861$		0			0
$862$	255835.	−	214671.i	0.344307	−	0.288908i
$863$			924852.i			1.24180i	0.783891	+	0.620899i	$0.213232\pi$
$863$			924852.i			1.24180i	−0.783891	+	0.620899i	$0.786768\pi$
$864$		0			0
$865$	−400457.			−0.535209
$866$	−199656.	−	237941.i	−0.266224	−	0.317274i
$867$		0			0
$868$	−128132.	+	726670.i	−0.170066	+	0.964491i
$869$	−32403.3	−	89027.4i	−0.0429092	−	0.117892i
$870$		0			0
$871$	27026.7	+	153276.i	0.0356251	+	0.202040i
$872$	−95323.4	+	55035.0i	−0.125362	+	0.0723779i
$873$		0			0
$874$	47625.6	−	82490.0i	0.0623473	−	0.107989i
$875$	158958.	−	436734.i	0.207619	−	0.570428i
$876$		0			0
$877$	−732255.	−	614435.i	−0.952057	−	0.798871i	0.0275855	−	0.999619i	$-0.491218\pi$
$877$	−732255.	−	614435.i	−0.952057	−	0.798871i	−0.979643	+	0.200748i	$0.935663\pi$
$878$	69312.9	−	82603.9i	0.0899135	−	0.107155i
$879$		0			0
$880$	−28474.2	−	10363.8i	−0.0367694	−	0.0133830i
$881$	1.16480e6	+	672499.i	1.50072	+	0.866443i	1.00000		0.000835760i	$0.000266031\pi$
$881$	1.16480e6	+	672499.i	1.50072	+	0.866443i	0.500724	+	0.865607i	$0.333067\pi$
$882$		0			0
$883$	−195760.	−	339066.i	−0.251074	−	0.434873i	0.712748	−	0.701421i	$-0.247450\pi$
$883$	−195760.	−	339066.i	−0.251074	−	0.434873i	−0.963822	+	0.266547i	$0.914117\pi$
$884$	310559.	−	54759.9i	0.397411	−	0.0700742i
$885$		0			0
$886$	−137657.	+	50103.2i	−0.175361	+	0.0638261i
$887$	163507.	+	28830.7i	0.207821	+	0.0366444i	0.276589	−	0.960988i	$-0.410796\pi$
$887$	163507.	+	28830.7i	0.207821	+	0.0366444i	−0.0687684	+	0.997633i	$0.521907\pi$
$888$		0			0
$889$	376502.	−	315923.i	0.476391	−	0.399740i
$890$		−	14352.1i		−	0.0181190i
$891$		0			0
$892$	1.19637e6			1.50361
$893$	−294944.	−	351500.i	−0.369859	−	0.440781i
$894$		0			0
$895$	−43205.6	+	245031.i	−0.0539379	+	0.305897i
$896$	−237216.	−	651746.i	−0.295480	−	0.811825i
$897$		0			0
$898$	7283.44	+	41306.5i	0.00903200	+	0.0512230i
$899$	294913.	−	170268.i	0.364901	−	0.210675i
$900$		0			0
$901$	−883306.	+	1.52993e6i	−1.08808	+	1.88461i
$902$	−4721.79	+	12973.0i	−0.00580355	+	0.0159451i
$903$		0			0
$904$	400027.	+	335663.i	0.489500	+	0.410739i
$905$	102317.	−	121937.i	0.124925	−	0.148880i
$906$		0			0
$907$	1.28533e6	+	467822.i	1.56243	+	0.568678i	0.971292	−	0.237892i	$-0.0764565\pi$
$907$	1.28533e6	+	467822.i	1.56243	+	0.568678i	0.591138	+	0.806570i	$0.298679\pi$
$908$	62999.2	+	36372.6i	0.0764123	+	0.0441167i
$909$		0			0
$910$	13325.4	+	23080.2i	0.0160915	+	0.0278713i
$911$	−950257.	+	167556.i	−1.14500	+	0.201894i	−0.713791	−	0.700359i	$-0.753023\pi$
$911$	−950257.	+	167556.i	−1.14500	+	0.201894i	−0.431207	+	0.902253i	$0.641912\pi$
$912$		0			0
$913$	−200070.	+	72819.6i	−0.240016	+	0.0873588i
$914$	219381.	+	38682.8i	0.262607	+	0.0463048i
$915$		0			0
$916$	−664436.	+	557528.i	−0.791886	+	0.664471i
$917$		−	898246.i		−	1.06821i
$918$		0			0
$919$	−1.00521e6			−1.19021			−0.595107	−	0.803647i	$-0.702890\pi$
$919$	−1.00521e6			−1.19021			−0.595107	+	0.803647i	$0.702890\pi$
$920$	151722.	+	180815.i	0.179256	+	0.213629i
$921$		0			0
$922$	68824.1	−	390321.i	0.0809616	−	0.459156i
$923$	48291.9	+	132681.i	0.0566853	+	0.155742i
$924$		0			0
$925$	206356.	+	1.17030e6i	0.241176	+	1.36778i
$926$	84508.0	−	48790.7i	0.0985543	−	0.0569004i
$927$		0			0
$928$	−123475.	+	213865.i	−0.143378	+	0.248338i
$929$	−100931.	+	277305.i	−0.116948	+	0.321312i	−0.984331	−	0.176328i	$-0.943578\pi$
$929$	−100931.	+	277305.i	−0.116948	+	0.321312i	0.867383	+	0.497641i	$0.165800\pi$
$930$		0			0
$931$	−50511.9	−	42384.5i	−0.0582766	−	0.0488999i
$932$	−687300.	+	819092.i	−0.791251	+	0.942976i
$933$		0			0
$934$	51536.6	+	18757.8i	0.0590775	+	0.0215024i
$935$	−68883.0	−	39769.6i	−0.0787932	−	0.0454913i
$936$		0			0
$937$	848848.	+	1.47025e6i	0.966831	+	1.67460i	0.704612	+	0.709592i	$0.251121\pi$
$937$	848848.	+	1.47025e6i	0.966831	+	1.67460i	0.262219	+	0.965008i	$0.415546\pi$
$938$	179138.	−	31586.8i	0.203602	−	0.0359004i
$939$		0			0
$940$	501941.	−	182692.i	0.568064	−	0.206758i
$941$	921233.	+	162438.i	1.04038	+	0.183446i	0.667635	−	0.744489i	$-0.267307\pi$
$941$	921233.	+	162438.i	1.04038	+	0.183446i	0.372741	+	0.927935i	$0.378418\pi$
$942$		0			0
$943$	−257011.	+	215658.i	−0.289020	+	0.242517i
$944$		−	773162.i		−	0.867613i
$945$		0			0
$946$	−85351.1			−0.0953734
$947$	−3750.59	−	4469.77i	−0.00418215	−	0.00498409i	0.763949	−	0.645276i	$-0.223258\pi$
$947$	−3750.59	−	4469.77i	−0.00418215	−	0.00498409i	−0.768131	+	0.640292i	$0.778813\pi$
$948$		0			0
$949$	−20166.4	+	114369.i	−0.0223922	+	0.126992i
$950$	28308.0	+	77775.5i	0.0313662	+	0.0861779i
$951$		0			0
$952$	−136236.	−	772631.i	−0.150320	−	0.852507i
$953$	532595.	−	307494.i	0.586423	−	0.338571i	−0.177259	−	0.984164i	$-0.556723\pi$
$953$	532595.	−	307494.i	0.586423	−	0.338571i	0.763682	+	0.645593i	$0.223390\pi$
$954$		0			0
$955$	247102.	−	427993.i	0.270938	−	0.469278i
$956$	281578.	−	773628.i	0.308093	−	0.846479i
$957$		0			0
$958$	57492.4	+	48241.8i	0.0626440	+	0.0525645i
$959$	−934948.	+	1.11423e6i	−1.01660	+	1.21154i
$960$		0			0
$961$	−528956.	−	192524.i	−0.572760	−	0.208468i
$962$	−127663.	−	73706.4i	−0.137948	−	0.0796444i
$963$		0			0
$964$	−501682.	−	868939.i	−0.539852	−	0.935051i
$965$	433319.	−	76405.9i	0.465322	−	0.0820488i
$966$		0			0
$967$	−1.36323e6	+	496176.i	−1.45786	+	0.530619i	−0.944776	−	0.327718i	$-0.893720\pi$
$967$	−1.36323e6	+	496176.i	−1.45786	+	0.530619i	−0.513087	+	0.858337i	$0.671498\pi$
$968$	−573439.	−	101113.i	−0.611979	−	0.107908i
$969$		0			0
$970$	18061.6	−	15155.5i	0.0191961	−	0.0161074i
$971$			1.14407e6i			1.21343i	0.794921	+	0.606713i	$0.207512\pi$
$971$			1.14407e6i			1.21343i	−0.794921	+	0.606713i	$0.792488\pi$
$972$		0			0
$973$	723652.			0.764371
$974$	120646.	+	143780.i	0.127173	+	0.151559i
$975$		0			0
$976$	35773.3	−	202880.i	0.0375542	−	0.212981i
$977$	87019.9	+	239085.i	0.0911653	+	0.250474i	0.976892	−	0.213732i	$-0.0685619\pi$
$977$	87019.9	+	239085.i	0.0911653	+	0.250474i	−0.885727	+	0.464206i	$0.846340\pi$
$978$		0			0
$979$	−3710.93	−	21045.7i	−0.00387184	−	0.0219583i
$980$	66476.2	−	38380.0i	0.0692172	−	0.0399625i
$981$		0			0
$982$	8894.31	−	15405.4i	0.00922336	−	0.0159753i
$983$	−80074.8	+	220004.i	−0.0828684	+	0.227679i	−0.974206	−	0.225662i	$-0.927546\pi$
$983$	−80074.8	+	220004.i	−0.0828684	+	0.227679i	0.891337	+	0.453341i	$0.149768\pi$
$984$		0			0
$985$	−171537.	−	143937.i	−0.176802	−	0.148354i
$986$	−109333.	+	130298.i	−0.112460	+	0.134024i
$987$		0			0
$988$	74962.3	+	27284.0i	0.0767943	+	0.0279508i
$989$	−1.79631e6	−	1.03710e6i	−1.83650	−	1.06030i
$990$		0			0
$991$	−638655.	−	1.10618e6i	−0.650308	−	1.12637i	−0.983048	−	0.183348i	$-0.941306\pi$
$991$	−638655.	−	1.10618e6i	−0.650308	−	1.12637i	0.332740	−	0.943019i	$-0.392027\pi$
$992$	1.06155e6	−	187180.i	1.07874	−	0.190211i
$993$		0			0
$994$	155068.	−	56440.0i	0.156945	−	0.0571234i
$995$	−178093.	−	31402.6i	−0.179888	−	0.0317190i
$996$		0			0
$997$	1.09814e6	−	921445.i	1.10475	−	0.926999i	0.107018	−	0.994257i	$-0.465870\pi$
$997$	1.09814e6	−	921445.i	1.10475	−	0.926999i	0.997736	+	0.0672585i	$0.0214252\pi$
$998$		−	237699.i		−	0.238653i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.f.a.44.5		66
3.2	odd	2		27.5.f.a.5.7	✓	66
27.11	odd	18	inner	81.5.f.a.35.5		66
27.16	even	9		27.5.f.a.11.7	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.f.a.5.7	✓	66	3.2	odd	2
27.5.f.a.11.7	yes	66	27.16	even	9
81.5.f.a.35.5		66	27.11	odd	18	inner
81.5.f.a.44.5		66	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.868224 - 1.03471i) q^{2} +(2.46156 - 13.9602i) q^{4} +(3.20330 + 8.80100i) q^{5} +(-7.41386 - 42.0461i) q^{7} +(-35.2980 + 20.3793i) q^{8} +(6.32529 - 10.9557i) q^{10} +(6.44259 - 17.7009i) q^{11} +(-37.7989 - 31.7171i) q^{13} +(-37.0686 + 44.1766i) q^{14} +(-161.398 - 58.7439i) q^{16} +(-390.443 - 225.422i) q^{17} +(-57.0245 - 98.7692i) q^{19} +(130.749 - 23.0546i) q^{20} +(-23.9089 + 8.70211i) q^{22} +(-608.929 - 107.371i) q^{23} +(411.581 - 345.358i) q^{25} +66.6484i q^{26} -605.222 q^{28} +(179.539 + 213.967i) q^{29} +(211.710 - 1200.67i) q^{31} +(302.391 + 830.812i) q^{32} +(105.745 + 599.712i) q^{34} +(346.299 - 199.936i) q^{35} +(-1105.90 + 1915.47i) q^{37} +(-52.6874 + 144.758i) q^{38} +(-292.429 - 245.377i) q^{40} +(348.778 - 415.658i) q^{41} +(3152.26 + 1147.33i) q^{43} +(-231.249 - 133.512i) q^{44} +(417.590 + 723.286i) q^{46} +(3962.16 - 698.636i) q^{47} +(543.294 - 197.743i) q^{49} +(-714.690 - 126.019i) q^{50} +(-535.821 + 449.607i) q^{52} -3918.45i q^{53} +176.423 q^{55} +(1118.57 + 1333.05i) q^{56} +(65.5128 - 371.542i) q^{58} +(1539.61 + 4230.04i) q^{59} +(208.280 + 1181.21i) q^{61} +(-1426.15 + 823.390i) q^{62} +(-776.940 + 1345.70i) q^{64} +(158.060 - 434.267i) q^{65} +(-2416.30 - 2027.52i) q^{67} +(-4108.04 + 4895.77i) q^{68} +(-507.540 - 184.729i) q^{70} +(-2478.15 - 1430.76i) q^{71} +(-1176.80 - 2038.28i) q^{73} +(2942.13 - 518.776i) q^{74} +(-1519.21 + 552.947i) q^{76} +(-792.017 - 139.654i) q^{77} +(3852.86 - 3232.93i) q^{79} -1608.63i q^{80} -732.903 q^{82} +(-7265.33 - 8658.48i) q^{83} +(733.235 - 4158.38i) q^{85} +(-1549.72 - 4257.81i) q^{86} +(133.321 + 756.101i) q^{88} +(982.504 - 567.249i) q^{89} +(-1053.34 + 1824.44i) q^{91} +(-2997.83 + 8236.48i) q^{92} +(-4162.93 - 3493.11i) q^{94} +(686.601 - 818.260i) q^{95} +(1751.37 + 637.447i) q^{97} +(-676.307 - 390.466i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} + 492 q^{11} - 6 q^{13} - 1137 q^{14} - 54 q^{16} + 9 q^{17} - 3 q^{19} + 2487 q^{20} + 1002 q^{22} + 2724 q^{23} + 435 q^{25} - 12 q^{28}+ \cdots + 259938 q^{98}+O(q^{100}) \) 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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