LMFDB - Embedded newform 108.5.f.a.91.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(19,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("108.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			91.5
Character	$\chi$	$=$	108.91
Dual form			108.5.f.a.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.42968 - 2.05847i) q^{2} +(7.52540 + 14.1198i) q^{4} +(-16.6139 + 28.7760i) q^{5} +(-39.9759 + 23.0801i) q^{7} +(3.25547 - 63.9171i) q^{8} +O(q^{10})$	\(q+(-3.42968 - 2.05847i) q^{2} +(7.52540 + 14.1198i) q^{4} +(-16.6139 + 28.7760i) q^{5} +(-39.9759 + 23.0801i) q^{7} +(3.25547 - 63.9171i) q^{8} +(116.215 - 64.4935i) q^{10} +(-63.6109 + 36.7258i) q^{11} +(151.520 - 262.440i) q^{13} +(184.614 + 3.13190i) q^{14} +(-142.737 + 212.514i) q^{16} +182.019 q^{17} -314.215i q^{19} +(-531.337 - 18.0330i) q^{20} +(293.764 + 4.98356i) q^{22} +(-290.919 - 167.962i) q^{23} +(-239.540 - 414.896i) q^{25} +(-1059.89 + 588.185i) q^{26} +(-626.721 - 390.765i) q^{28} +(-357.370 - 618.983i) q^{29} +(-985.186 - 568.798i) q^{31} +(926.995 - 435.035i) q^{32} +(-624.267 - 374.681i) q^{34} -1533.80i q^{35} +1008.45 q^{37} +(-646.803 + 1077.66i) q^{38} +(1785.20 + 1155.59i) q^{40} +(557.553 - 965.709i) q^{41} +(-2182.06 + 1259.82i) q^{43} +(-997.257 - 621.796i) q^{44} +(652.014 + 1174.90i) q^{46} +(980.476 - 566.078i) q^{47} +(-135.117 + 234.029i) q^{49} +(-32.5048 + 1916.05i) q^{50} +(4845.84 + 164.462i) q^{52} +1057.77 q^{53} -2440.63i q^{55} +(1345.07 + 2630.28i) q^{56} +(-48.4939 + 2858.55i) q^{58} +(878.476 + 507.188i) q^{59} +(-430.304 - 745.308i) q^{61} +(2208.02 + 3978.77i) q^{62} +(-4074.80 - 416.161i) q^{64} +(5034.65 + 8720.27i) q^{65} +(-559.041 - 322.762i) q^{67} +(1369.76 + 2570.07i) q^{68} +(-3157.28 + 5260.44i) q^{70} -9567.89i q^{71} +1899.10 q^{73} +(-3458.66 - 2075.86i) q^{74} +(4436.65 - 2364.59i) q^{76} +(1695.27 - 2936.29i) q^{77} +(6768.11 - 3907.57i) q^{79} +(-3743.90 - 7638.08i) q^{80} +(-3900.11 + 2164.37i) q^{82} +(-7052.56 + 4071.80i) q^{83} +(-3024.04 + 5237.78i) q^{85} +(10077.1 + 170.953i) q^{86} +(2140.32 + 4185.39i) q^{88} -7653.39 q^{89} +13988.4i q^{91} +(182.309 - 5371.70i) q^{92} +(-4527.97 - 76.8149i) q^{94} +(9041.87 + 5220.33i) q^{95} +(-6366.75 - 11027.5i) q^{97} +(945.149 - 524.510i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−3.42968	−	2.05847i	−0.857420	−	0.514618i
$2$	−3.42968	−	2.05847i	−0.857420	−	0.514618i
$3$		0			0
$3$		0			0
$4$	7.52540	+	14.1198i	0.470337	+	0.882487i
$5$	−16.6139	+	28.7760i	−0.664554	+	1.15104i	0.314852	+	0.949141i	$0.398045\pi$
$5$	−16.6139	+	28.7760i	−0.664554	+	1.15104i	−0.979406	+	0.201901i	$0.935288\pi$
$6$		0			0
$7$	−39.9759	+	23.0801i	−0.815835	+	0.471023i	−0.848978	−	0.528428i	$-0.822782\pi$
$7$	−39.9759	+	23.0801i	−0.815835	+	0.471023i	0.0331429	+	0.999451i	$0.489448\pi$
$8$	3.25547	−	63.9171i	0.0508667	−	0.998705i
$9$		0			0
$10$	116.215	−	64.4935i	1.16215	−	0.644935i
$11$	−63.6109	+	36.7258i	−0.525710	+	0.303519i	−0.739268	−	0.673412i	$-0.764828\pi$
$11$	−63.6109	+	36.7258i	−0.525710	+	0.303519i	0.213558	+	0.976930i	$0.431495\pi$
$12$		0			0
$13$	151.520	−	262.440i	0.896566	−	1.55290i	0.0647110	−	0.997904i	$-0.479387\pi$
$13$	151.520	−	262.440i	0.896566	−	1.55290i	0.831855	−	0.554993i	$-0.187279\pi$
$14$	184.614	+	3.13190i	0.941910	+	0.0159791i
$15$		0			0
$16$	−142.737	+	212.514i	−0.557566	+	0.830133i
$17$	182.019			0.629823			0.314912	−	0.949121i	$-0.398025\pi$
$17$	182.019			0.629823			0.314912	+	0.949121i	$0.398025\pi$
$18$		0			0
$19$		−	314.215i		−	0.870402i	−0.900333	−	0.435201i	$-0.856677\pi$
$19$		−	314.215i		−	0.870402i	0.900333	−	0.435201i	$-0.143323\pi$
$20$	−531.337	−	18.0330i	−1.32834	−	0.0450824i
$21$		0			0
$22$	293.764	+	4.98356i	0.606950	+	0.0102966i
$23$	−290.919	−	167.962i	−0.549941	−	0.317509i	0.199157	−	0.979968i	$-0.436180\pi$
$23$	−290.919	−	167.962i	−0.549941	−	0.317509i	−0.749098	+	0.662459i	$0.769513\pi$
$24$		0			0
$25$	−239.540	−	414.896i	−0.383265	−	0.663834i
$26$	−1059.89	+	588.185i	−1.56788	+	0.870096i
$27$		0			0
$28$	−626.721	−	390.765i	−0.799389	−	0.498424i
$29$	−357.370	−	618.983i	−0.424935	−	0.736008i	0.571480	−	0.820616i	$-0.306370\pi$
$29$	−357.370	−	618.983i	−0.424935	−	0.736008i	−0.996414	+	0.0846079i	$0.973036\pi$
$30$		0			0
$31$	−985.186	−	568.798i	−1.02517	−	0.591881i	−0.109571	−	0.993979i	$-0.534948\pi$
$31$	−985.186	−	568.798i	−1.02517	−	0.591881i	−0.915597	+	0.402098i	$0.868281\pi$
$32$	926.995	−	435.035i	0.905269	−	0.424839i
$33$		0			0
$34$	−624.267	−	374.681i	−0.540023	−	0.324118i
$35$		−	1533.80i		−	1.25208i
$36$		0			0
$37$	1008.45			0.736632			0.368316	−	0.929701i	$-0.379934\pi$
$37$	1008.45			0.736632			0.368316	+	0.929701i	$0.379934\pi$
$38$	−646.803	+	1077.66i	−0.447924	+	0.746300i
$39$		0			0
$40$	1785.20	+	1155.59i	1.11575	+	0.722244i
$41$	557.553	−	965.709i	0.331679	−	0.574485i	−0.651162	−	0.758939i	$-0.725718\pi$
$41$	557.553	−	965.709i	0.331679	−	0.574485i	0.982841	+	0.184454i	$0.0590516\pi$
$42$		0			0
$43$	−2182.06	+	1259.82i	−1.18013	+	0.681349i	−0.956045	−	0.293220i	$-0.905273\pi$
$43$	−2182.06	+	1259.82i	−1.18013	+	0.681349i	−0.224087	+	0.974569i	$0.571940\pi$
$44$	−997.257	−	621.796i	−0.515112	−	0.321176i
$45$		0			0
$46$	652.014	+	1174.90i	0.308135	+	0.555248i
$47$	980.476	−	566.078i	0.443855	−	0.256260i	−0.261376	−	0.965237i	$-0.584176\pi$
$47$	980.476	−	566.078i	0.443855	−	0.256260i	0.705232	+	0.708977i	$0.250843\pi$
$48$		0			0
$49$	−135.117	+	234.029i	−0.0562752	+	0.0974714i
$50$	−32.5048	+	1916.05i	−0.0130019	+	0.766419i
$51$		0			0
$52$	4845.84	+	164.462i	1.79210	+	0.0608218i
$53$	1057.77			0.376566			0.188283	−	0.982115i	$-0.439708\pi$
$53$	1057.77			0.376566			0.188283	+	0.982115i	$0.439708\pi$
$54$		0			0
$55$		−	2440.63i		−	0.806818i
$56$	1345.07	+	2630.28i	0.428914	+	0.838739i
$57$		0			0
$58$	−48.4939	+	2858.55i	−0.0144156	+	0.849747i
$59$	878.476	+	507.188i	0.252363	+	0.145702i	0.620846	−	0.783933i	$-0.286789\pi$
$59$	878.476	+	507.188i	0.252363	+	0.145702i	−0.368483	+	0.929635i	$0.620123\pi$
$60$		0			0
$61$	−430.304	−	745.308i	−0.115642	−	0.200298i	0.802394	−	0.596794i	$-0.203559\pi$
$61$	−430.304	−	745.308i	−0.115642	−	0.200298i	−0.918036	+	0.396497i	$0.870226\pi$
$62$	2208.02	+	3978.77i	0.574407	+	1.03506i
$63$		0			0
$64$	−4074.80	−	416.161i	−0.994825	−	0.101602i
$65$	5034.65	+	8720.27i	1.19163	+	2.06397i
$66$		0			0
$67$	−559.041	−	322.762i	−0.124536	−	0.0719008i	0.436438	−	0.899734i	$-0.356240\pi$
$67$	−559.041	−	322.762i	−0.124536	−	0.0719008i	−0.560974	+	0.827834i	$0.689573\pi$
$68$	1369.76	+	2570.07i	0.296229	+	0.555811i
$69$		0			0
$70$	−3157.28	+	5260.44i	−0.644343	+	1.07356i
$71$		−	9567.89i		−	1.89801i	−0.315254	−	0.949007i	$-0.602090\pi$
$71$		−	9567.89i		−	1.89801i	0.315254	−	0.949007i	$-0.397910\pi$
$72$		0			0
$73$	1899.10			0.356372			0.178186	−	0.983997i	$-0.442977\pi$
$73$	1899.10			0.356372			0.178186	+	0.983997i	$0.442977\pi$
$74$	−3458.66	−	2075.86i	−0.631603	−	0.379084i
$75$		0			0
$76$	4436.65	−	2364.59i	0.768119	−	0.409383i
$77$	1695.27	−	2936.29i	0.285928	−	0.495242i
$78$		0			0
$79$	6768.11	−	3907.57i	1.08446	−	0.626113i	0.152363	−	0.988325i	$-0.451312\pi$
$79$	6768.11	−	3907.57i	1.08446	−	0.626113i	0.932096	+	0.362212i	$0.117978\pi$
$80$	−3743.90	−	7638.08i	−0.584985	−	1.19345i
$81$		0			0
$82$	−3900.11	+	2164.37i	−0.580028	+	0.321887i
$83$	−7052.56	+	4071.80i	−1.02374	+	0.591058i	−0.915186	−	0.403032i	$-0.867956\pi$
$83$	−7052.56	+	4071.80i	−1.02374	+	0.591058i	−0.108556	+	0.994090i	$0.534623\pi$
$84$		0			0
$85$	−3024.04	+	5237.78i	−0.418552	+	0.724953i
$86$	10077.1	+	170.953i	1.36250	+	0.0231142i
$87$		0			0
$88$	2140.32	+	4185.39i	0.276385	+	0.540468i
$89$	−7653.39			−0.966215			−0.483107	−	0.875561i	$-0.660492\pi$
$89$	−7653.39			−0.966215			−0.483107	+	0.875561i	$0.660492\pi$
$90$		0			0
$91$			13988.4i			1.68921i
$92$	182.309	−	5371.70i	0.0215394	−	0.634652i
$93$		0			0
$94$	−4527.97	−	76.8149i	−0.512446	−	0.00869340i
$95$	9041.87	+	5220.33i	1.00187	+	0.578430i
$96$		0			0
$97$	−6366.75	−	11027.5i	−0.676666	−	1.17202i	−0.975979	−	0.217865i	$-0.930091\pi$
$97$	−6366.75	−	11027.5i	−0.676666	−	1.17202i	0.299313	−	0.954155i	$-0.403243\pi$
$98$	945.149	−	524.510i	0.0984120	−	0.0546137i
$99$		0			0
$100$	4055.61	−	6504.52i	0.405561	−	0.650452i
$101$	−6873.20	−	11904.7i	−0.673777	−	1.16702i	−0.976825	−	0.214040i	$-0.931338\pi$
$101$	−6873.20	−	11904.7i	−0.673777	−	1.16702i	0.303048	−	0.952975i	$-0.401996\pi$
$102$		0			0
$103$	−11251.5	−	6496.03i	−1.06056	−	0.612313i	−0.134971	−	0.990850i	$-0.543094\pi$
$103$	−11251.5	−	6496.03i	−1.06056	−	0.612313i	−0.925587	+	0.378536i	$0.876428\pi$
$104$	−16281.1	−	10539.1i	−1.50528	−	0.974396i
$105$		0			0
$106$	−3627.82	−	2177.40i	−0.322875	−	0.193787i
$107$			14891.8i			1.30071i	0.759631	+	0.650354i	$0.225379\pi$
$107$			14891.8i			1.30071i	−0.759631	+	0.650354i	$0.774621\pi$
$108$		0			0
$109$	7539.02			0.634544			0.317272	−	0.948335i	$-0.397233\pi$
$109$	7539.02			0.634544			0.317272	+	0.948335i	$0.397233\pi$
$110$	−5023.96	+	8370.56i	−0.415203	+	0.691782i
$111$		0			0
$112$	801.189	−	11789.8i	0.0638703	−	0.939878i
$113$	−496.140	+	859.339i	−0.0388550	+	0.0672988i	−0.884799	−	0.465973i	$-0.845704\pi$
$113$	−496.140	+	859.339i	−0.0388550	+	0.0672988i	0.845944	+	0.533272i	$0.179038\pi$
$114$		0			0
$115$	9666.57	−	5581.00i	0.730932	−	0.422004i
$116$	6050.56	−	9704.08i	0.449655	−	0.721171i
$117$		0			0
$118$	−1968.86	−	3547.81i	−0.141400	−	0.254798i
$119$	−7276.38	+	4201.02i	−0.513832	+	0.296661i
$120$		0			0
$121$	−4622.94	+	8007.16i	−0.315753	+	0.546900i
$122$	−58.3908	+	3441.94i	−0.00392306	+	0.231251i
$123$		0			0
$124$	617.383	−	18191.1i	0.0401524	−	1.18308i
$125$	−4848.57			−0.310308
$126$		0			0
$127$			7123.52i			0.441659i	0.975312	+	0.220829i	$0.0708764\pi$
$127$			7123.52i			0.441659i	−0.975312	+	0.220829i	$0.929124\pi$
$128$	13118.6	+	9815.16i	0.800697	+	0.599070i
$129$		0			0
$130$	683.185	−	40271.4i	0.0404252	−	2.38292i
$131$	−6027.16	−	3479.78i	−0.351212	−	0.202773i	0.314007	−	0.949421i	$-0.398329\pi$
$131$	−6027.16	−	3479.78i	−0.351212	−	0.202773i	−0.665219	+	0.746648i	$0.731662\pi$
$132$		0			0
$133$	7252.12	+	12561.0i	0.409979	+	0.710105i
$134$	1252.93	+	2257.74i	0.0697780	+	0.125737i
$135$		0			0
$136$	592.557	−	11634.1i	0.0320371	−	0.629008i
$137$	−4244.42	−	7351.56i	−0.226140	−	0.391686i	0.730521	−	0.682891i	$-0.239277\pi$
$137$	−4244.42	−	7351.56i	−0.226140	−	0.391686i	−0.956661	+	0.291204i	$0.905944\pi$
$138$		0			0
$139$	18483.9	+	10671.7i	0.956673	+	0.552335i	0.895147	−	0.445770i	$-0.147070\pi$
$139$	18483.9	+	10671.7i	0.956673	+	0.552335i	0.0615252	+	0.998106i	$0.480404\pi$
$140$	21656.9	−	11542.4i	1.10494	−	0.588900i
$141$		0			0
$142$	−19695.2	+	32814.8i	−0.976752	+	1.62740i
$143$			22258.7i			1.08850i
$144$		0			0
$145$	23749.2			1.12957
$146$	−6513.32	−	3909.25i	−0.305560	−	0.183395i
$147$		0			0
$148$	7588.98	+	14239.1i	0.346466	+	0.650068i
$149$	−6366.78	+	11027.6i	−0.286779	+	0.496716i	−0.973039	−	0.230640i	$-0.925918\pi$
$149$	−6366.78	+	11027.6i	−0.286779	+	0.496716i	0.686260	+	0.727356i	$0.259251\pi$
$150$		0			0
$151$	3061.84	−	1767.75i	0.134285	−	0.0775296i	−0.431352	−	0.902184i	$-0.641963\pi$
$151$	3061.84	−	1767.75i	0.134285	−	0.0775296i	0.565638	+	0.824654i	$0.308630\pi$
$152$	−20083.7	−	1022.92i	−0.869276	−	0.0442745i
$153$		0			0
$154$	−11858.5	+	6580.88i	−0.500021	+	0.277487i
$155$	32735.5	−	18899.8i	1.36256	−	0.786674i
$156$		0			0
$157$	−14870.6	+	25756.6i	−0.603292	+	1.04493i	0.389027	+	0.921227i	$0.372811\pi$
$157$	−14870.6	+	25756.6i	−0.603292	+	1.04493i	−0.992319	+	0.123706i	$0.960522\pi$
$158$	−31256.1	−	530.244i	−1.25205	−	0.0212404i
$159$		0			0
$160$	−2882.37	+	33902.9i	−0.112593	+	1.32433i
$161$	15506.3			0.598216
$162$		0			0
$163$		−	5903.96i		−	0.222213i	−0.993809	−	0.111106i	$-0.964561\pi$
$163$		−	5903.96i		−	0.222213i	0.993809	−	0.111106i	$-0.0354394\pi$
$164$	17831.4	+	605.177i	0.662976	+	0.0225006i
$165$		0			0
$166$	32569.7	+	552.529i	1.18195	+	0.0200511i
$167$	−17810.7	−	10283.0i	−0.638628	−	0.368712i	0.145458	−	0.989364i	$-0.453535\pi$
$167$	−17810.7	−	10283.0i	−0.638628	−	0.368712i	−0.784086	+	0.620652i	$0.786868\pi$
$168$		0			0
$169$	−31635.9	−	54795.0i	−1.10766	−	1.91852i
$170$	21153.3	−	11739.0i	0.731948	−	0.406195i
$171$		0			0
$172$	−34209.2	−	21329.7i	−1.15634	−	0.720987i
$173$	3054.99	+	5291.39i	0.102074	+	0.176798i	0.912539	−	0.408989i	$-0.134119\pi$
$173$	3054.99	+	5291.39i	0.102074	+	0.176798i	−0.810465	+	0.585787i	$0.800785\pi$
$174$		0			0
$175$	19151.7	+	11057.2i	0.625361	+	0.361053i
$176$	1274.87	−	18760.3i	0.0411569	−	0.605641i
$177$		0			0
$178$	26248.7	+	15754.3i	0.828451	+	0.497231i
$179$			11534.8i			0.360001i	0.983667	+	0.180001i	$0.0576099\pi$
$179$			11534.8i			0.360001i	−0.983667	+	0.180001i	$0.942390\pi$
$180$		0			0
$181$	−25544.2			−0.779713			−0.389857	−	0.920876i	$-0.627475\pi$
$181$	−25544.2			−0.779713			−0.389857	+	0.920876i	$0.627475\pi$
$182$	28794.6	−	47975.6i	0.869298	−	1.44836i
$183$		0			0
$184$	−11682.7	+	18047.9i	−0.345072	+	0.533079i
$185$	−16754.2	+	29019.2i	−0.489532	+	0.847894i
$186$		0			0
$187$	−11578.4	+	6684.78i	−0.331104	+	0.191163i
$188$	15371.4	+	9584.15i	0.434908	+	0.271168i
$189$		0			0
$190$	−20264.8	−	36516.5i	−0.561353	−	1.01154i
$191$	−33833.7	+	19533.9i	−0.927433	+	0.535454i	−0.885999	−	0.463687i	$-0.846526\pi$
$191$	−33833.7	+	19533.9i	−0.927433	+	0.535454i	−0.0414344	+	0.999141i	$0.513193\pi$
$192$		0			0
$193$	−13915.2	+	24101.8i	−0.373572	+	0.647045i	−0.990112	−	0.140278i	$-0.955200\pi$
$193$	−13915.2	+	24101.8i	−0.373572	+	0.647045i	0.616541	+	0.787323i	$0.288534\pi$
$194$	−863.947	+	50926.7i	−0.0229553	+	1.35314i
$195$		0			0
$196$	−4321.25	−	146.658i	−0.112486	−	0.00381763i
$197$	21103.0			0.543765			0.271883	−	0.962330i	$-0.412354\pi$
$197$	21103.0			0.543765			0.271883	+	0.962330i	$0.412354\pi$
$198$		0			0
$199$		−	5447.97i		−	0.137572i	−0.997631	−	0.0687858i	$-0.978087\pi$
$199$		−	5447.97i		−	0.137572i	0.997631	−	0.0687858i	$-0.0219125\pi$
$200$	−27298.8	+	13960.1i	−0.682470	+	0.349001i
$201$		0			0
$202$	−932.670	+	54977.7i	−0.0228573	+	1.34736i
$203$	28572.4	+	16496.3i	0.693353	+	0.400308i
$204$		0			0
$205$	18526.2	+	32088.3i	0.440837	+	0.763553i
$206$	25217.0	+	45440.1i	0.594236	+	1.07079i
$207$		0			0
$208$	34144.7	+	69659.8i	0.789217	+	1.61011i
$209$	11539.8	+	19987.5i	0.264183	+	0.457579i
$210$		0			0
$211$	−59935.1	−	34603.5i	−1.34622	−	0.777241i	−0.358509	−	0.933526i	$-0.616715\pi$
$211$	−59935.1	−	34603.5i	−1.34622	−	0.777241i	−0.987712	+	0.156286i	$0.950048\pi$
$212$	7960.17	+	14935.5i	0.177113	+	0.332314i
$213$		0			0
$214$	30654.4	−	51074.1i	0.669367	−	1.11525i
$215$		−	83721.5i		−	1.81117i
$216$		0			0
$217$	52511.7			1.11516
$218$	−25856.4	−	15518.9i	−0.544071	−	0.326548i
$219$		0			0
$220$	34461.1	−	18366.7i	0.712007	−	0.379477i
$221$	27579.4	−	47769.0i	0.564678	−	0.978051i
$222$		0			0
$223$	21934.5	−	12663.9i	0.441080	−	0.254658i	−0.262976	−	0.964802i	$-0.584704\pi$
$223$	21934.5	−	12663.9i	0.441080	−	0.254658i	0.704056	+	0.710145i	$0.251371\pi$
$224$	−27016.8	+	38786.1i	−0.538441	+	0.773001i
$225$		0			0
$226$	3470.52	−	1925.97i	0.0679482	−	0.0377079i
$227$	84184.1	−	48603.7i	1.63372	−	0.943230i	0.650792	−	0.759256i	$-0.274437\pi$
$227$	84184.1	−	48603.7i	1.63372	−	0.943230i	0.982931	−	0.183975i	$-0.0588964\pi$
$228$		0			0
$229$	42946.4	−	74385.3i	0.818947	−	1.41846i	−0.0875119	−	0.996163i	$-0.527892\pi$
$229$	42946.4	−	74385.3i	0.818947	−	1.41846i	0.906459	−	0.422294i	$-0.138775\pi$
$230$	−44641.6	−	757.323i	−0.843886	−	0.0143161i
$231$		0			0
$232$	−40727.0	+	20827.0i	−0.756671	+	0.386946i
$233$	12774.0			0.235297			0.117649	−	0.993055i	$-0.462464\pi$
$233$	12774.0			0.235297			0.117649	+	0.993055i	$0.462464\pi$
$234$		0			0
$235$			37619.0i			0.681194i
$236$	−550.511	+	16220.7i	−0.00988421	+	0.291236i
$237$		0			0
$238$	33603.3	+	570.064i	0.593237	+	0.0100640i
$239$	−91748.4	−	52971.0i	−1.60621	−	0.927347i	−0.990207	−	0.139605i	$-0.955417\pi$
$239$	−91748.4	−	52971.0i	−1.60621	−	0.927347i	−0.616005	−	0.787742i	$-0.711250\pi$
$240$		0			0
$241$	5089.73	+	8815.67i	0.0876316	+	0.151782i	0.906510	−	0.422185i	$-0.138737\pi$
$241$	5089.73	+	8815.67i	0.0876316	+	0.151782i	−0.818878	+	0.573968i	$0.805404\pi$
$242$	32337.7	−	17945.8i	0.552177	−	0.306431i
$243$		0			0
$244$	7285.38	−	11684.5i	0.122369	−	0.196260i
$245$	−4489.62	−	7776.25i	−0.0747958	−	0.129550i
$246$		0			0
$247$	−82462.6	−	47609.8i	−1.35165	−	0.780373i
$248$	−39563.2	+	61118.6i	−0.643262	+	0.993734i
$249$		0			0
$250$	16629.0	+	9980.63i	0.266064	+	0.159690i
$251$			21848.1i			0.346790i	0.984852	+	0.173395i	$0.0554738\pi$
$251$			21848.1i			0.346790i	−0.984852	+	0.173395i	$0.944526\pi$
$252$		0			0
$253$	24674.2			0.385479
$254$	14663.5	−	24431.4i	0.227285	−	0.378687i
$255$		0			0
$256$	−24788.4	−	60667.1i	−0.378241	−	0.925707i
$257$	27780.7	−	48117.6i	0.420608	−	0.728514i	−0.575391	−	0.817878i	$-0.695150\pi$
$257$	27780.7	−	48117.6i	0.420608	−	0.728514i	0.995999	+	0.0893643i	$0.0284835\pi$
$258$		0			0
$259$	−40313.7	+	23275.1i	−0.600971	+	0.346971i
$260$	−85240.6	+	136712.i	−1.26096	+	2.02236i
$261$		0			0
$262$	13508.2	+	24341.3i	0.196786	+	0.354601i
$263$	−21792.0	+	12581.6i	−0.315055	+	0.181897i	−0.649186	−	0.760629i	$-0.724890\pi$
$263$	−21792.0	+	12581.6i	−0.315055	+	0.181897i	0.334131	+	0.942527i	$0.391557\pi$
$264$		0			0
$265$	−17573.7	+	30438.5i	−0.250248	+	0.433443i
$266$	984.089	−	58008.6i	0.0139082	−	0.819841i
$267$		0			0
$268$	350.332	−	10322.5i	0.00487765	−	0.143719i
$269$	−54154.0			−0.748386			−0.374193	−	0.927351i	$-0.622080\pi$
$269$	−54154.0			−0.748386			−0.374193	+	0.927351i	$0.622080\pi$
$270$		0			0
$271$		−	94942.5i		−	1.29277i	−0.763011	−	0.646386i	$-0.776280\pi$
$271$		−	94942.5i		−	1.29277i	0.763011	−	0.646386i	$-0.223720\pi$
$272$	−25980.8	+	38681.6i	−0.351168	+	0.522837i
$273$		0			0
$274$	−575.954	+	33950.5i	−0.00767162	+	0.452215i
$275$	30474.7	+	17594.6i	0.402972	+	0.232656i
$276$		0			0
$277$	−54019.7	−	93564.9i	−0.704033	−	1.21942i	−0.967039	−	0.254627i	$-0.918047\pi$
$277$	−54019.7	−	93564.9i	−0.704033	−	1.21942i	0.263006	−	0.964794i	$-0.415286\pi$
$278$	−41426.4	−	74648.9i	−0.536029	−	0.965904i
$279$		0			0
$280$	−98036.0	−	4993.24i	−1.25046	−	0.0636893i
$281$	−34463.0	−	59691.7i	−0.436456	−	0.755964i	0.560957	−	0.827845i	$-0.310433\pi$
$281$	−34463.0	−	59691.7i	−0.436456	−	0.755964i	−0.997413	+	0.0718805i	$0.977100\pi$
$282$		0			0
$283$	39154.2	+	22605.7i	0.488884	+	0.282257i	0.724111	−	0.689683i	$-0.242250\pi$
$283$	39154.2	+	22605.7i	0.488884	+	0.282257i	−0.235228	+	0.971940i	$0.575584\pi$
$284$	135097.	−	72002.2i	1.67497	−	0.892707i
$285$		0			0
$286$	45818.9	−	76340.2i	0.560160	−	0.933299i
$287$			51473.5i			0.624914i
$288$		0			0
$289$	−50390.1			−0.603323
$290$	−81452.0	−	48887.0i	−0.968514	−	0.581296i
$291$		0			0
$292$	14291.5	+	26814.9i	0.167615	+	0.314493i
$293$	−35853.6	+	62100.3i	−0.417636	+	0.723366i	−0.995701	−	0.0926242i	$-0.970474\pi$
$293$	−35853.6	+	62100.3i	−0.417636	+	0.723366i	0.578065	+	0.815990i	$0.303808\pi$
$294$		0			0
$295$	−29189.7	+	16852.7i	−0.335418	+	0.193654i
$296$	3282.98	−	64457.2i	0.0374701	−	0.735679i
$297$		0			0
$298$	44536.0	−	24715.3i	0.501509	−	0.278313i
$299$	−88159.9	+	50899.1i	−0.986117	+	0.569335i
$300$		0			0
$301$	58153.4	−	100725.i	0.641862	−	1.11174i
$302$	−14140.0	−	239.878i	−0.155037	−	0.00263013i
$303$		0			0
$304$	66775.2	+	44850.1i	0.722550	+	0.485306i
$305$	28596.0			0.307401
$306$		0			0
$307$			95866.9i			1.01717i	0.861013	+	0.508583i	$0.169830\pi$
$307$			95866.9i			1.01717i	−0.861013	+	0.508583i	$0.830170\pi$
$308$	54217.4	+	1840.08i	0.571528	+	0.0193970i
$309$		0			0
$310$	−151177.	−	2564.65i	−1.57312	−	0.0266873i
$311$	20844.0	+	12034.3i	0.215506	+	0.124423i	0.603868	−	0.797085i	$-0.293626\pi$
$311$	20844.0	+	12034.3i	0.215506	+	0.124423i	−0.388362	+	0.921507i	$0.626959\pi$
$312$		0			0
$313$	49654.5	+	86004.2i	0.506839	+	0.877871i	0.999969	+	0.00791525i	$0.00251953\pi$
$313$	49654.5	+	86004.2i	0.506839	+	0.877871i	−0.493130	+	0.869956i	$0.664147\pi$
$314$	104020.	−	57726.1i	1.05502	−	0.585481i
$315$		0			0
$316$	106107.	+	66158.2i	1.06260	+	0.662536i
$317$	29720.5	+	51477.4i	0.295759	+	0.512269i	0.975161	−	0.221497i	$-0.0710942\pi$
$317$	29720.5	+	51477.4i	0.295759	+	0.512269i	−0.679402	+	0.733766i	$0.737761\pi$
$318$		0			0
$319$	45465.2	+	26249.4i	0.446785	+	0.257951i
$320$	79673.7	−	110343.i	0.778063	−	1.07757i
$321$		0			0
$322$	−53181.8	−	31919.4i	−0.512922	−	0.307852i
$323$		−	57193.1i		−	0.548200i
$324$		0			0
$325$	−145180.			−1.37449
$326$	−12153.1	+	20248.7i	−0.114354	+	0.190529i
$327$		0			0
$328$	−59910.3	−	38781.0i	−0.556870	−	0.360472i
$329$	−26130.3	+	45259.0i	−0.241408	+	0.418132i
$330$		0			0
$331$	79852.0	−	46102.6i	0.728836	−	0.420794i	−0.0891599	−	0.996017i	$-0.528418\pi$
$331$	79852.0	−	46102.6i	0.728836	−	0.420794i	0.817996	+	0.575223i	$0.195085\pi$
$332$	−110566.	−	68938.8i	−1.00310	−	0.625442i
$333$		0			0
$334$	39917.7	+	71930.3i	0.357827	+	0.644791i
$335$	18575.7	−	10724.7i	0.165522	−	0.0955639i
$336$		0			0
$337$	−22954.2	+	39757.8i	−0.202117	+	0.350076i	−0.949210	−	0.314643i	$-0.898115\pi$
$337$	−22954.2	+	39757.8i	−0.202117	+	0.350076i	0.747094	+	0.664719i	$0.231449\pi$
$338$	−4292.89	+	253051.i	−0.0375765	+	2.21500i
$339$		0			0
$340$	−96713.5	−	3282.34i	−0.836622	−	0.0283940i
$341$	83558.1			0.718588
$342$		0			0
$343$		−	123305.i		−	1.04807i
$344$	73420.1	+	143573.i	0.620438	+	1.21326i
$345$		0			0
$346$	414.552	−	24436.4i	0.00346279	−	0.204120i
$347$	131615.	+	75987.9i	1.09306	+	0.631081i	0.934391	−	0.356250i	$-0.115945\pi$
$347$	131615.	+	75987.9i	1.09306	+	0.631081i	0.158674	+	0.987331i	$0.449278\pi$
$348$		0			0
$349$	93645.6	+	162199.i	0.768841	+	1.33167i	0.938192	+	0.346116i	$0.112500\pi$
$349$	93645.6	+	162199.i	0.768841	+	1.33167i	−0.169350	+	0.985556i	$0.554167\pi$
$350$	−42923.2	−	77346.0i	−0.350393	−	0.631396i
$351$		0			0
$352$	−42990.0	+	61717.6i	−0.346962	+	0.498108i
$353$	22707.8	+	39331.1i	0.182232	+	0.315636i	0.942640	−	0.333810i	$-0.108334\pi$
$353$	22707.8	+	39331.1i	0.182232	+	0.315636i	−0.760408	+	0.649446i	$0.775001\pi$
$354$		0			0
$355$	275326.	+	158960.i	2.18469	+	1.26133i
$356$	−57594.8	−	108064.i	−0.454447	−	0.852671i
$357$		0			0
$358$	23744.0	−	39560.6i	0.185263	−	0.308672i
$359$		−	71504.2i		−	0.554808i	−0.960753	−	0.277404i	$-0.910526\pi$
$359$		−	71504.2i		−	0.554808i	0.960753	−	0.277404i	$-0.0894740\pi$
$360$		0			0
$361$	31589.8			0.242400
$362$	87608.4	+	52582.0i	0.668542	+	0.401254i
$363$		0			0
$364$	−197513.	+	105268.i	−1.49071	+	0.794499i
$365$	−31551.4	+	54648.7i	−0.236828	+	0.410199i
$366$		0			0
$367$	57406.0	−	33143.4i	0.426211	−	0.246073i	−0.271520	−	0.962433i	$-0.587526\pi$
$367$	57406.0	−	33143.4i	0.426211	−	0.246073i	0.697731	+	0.716360i	$0.254193\pi$
$368$	77219.2	−	37850.0i	0.570203	−	0.279492i
$369$		0			0
$370$	117197.	−	65038.4i	0.856076	−	0.475080i
$371$	−42285.5	+	24413.5i	−0.307216	+	0.177371i
$372$		0			0
$373$	−71784.3	+	124334.i	−0.515955	+	0.893660i	0.483873	+	0.875138i	$0.339229\pi$
$373$	−71784.3	+	124334.i	−0.515955	+	0.893660i	−0.999828	+	0.0185223i	$0.994104\pi$
$374$	53470.6	+	907.103i	0.382271	+	0.00648505i
$375$		0			0
$376$	−32990.2	−	64512.1i	−0.233351	−	0.456316i
$377$	−216594.			−1.52393
$378$		0			0
$379$			183178.i			1.27525i	0.770348	+	0.637624i	$0.220083\pi$
$379$			183178.i			1.27525i	−0.770348	+	0.637624i	$0.779917\pi$
$380$	−5666.23	+	166954.i	−0.0392398	+	1.15619i
$381$		0			0
$382$	156249.	+	2650.69i	1.07075	+	0.0181648i
$383$	15175.9	+	8761.79i	0.103456	+	0.0597303i	0.550835	−	0.834614i	$-0.314309\pi$
$383$	15175.9	+	8761.79i	0.103456	+	0.0597303i	−0.447379	+	0.894344i	$0.647643\pi$
$384$		0			0
$385$	56329.9	+	97566.3i	0.380030	+	0.658231i
$386$	97337.4	−	54017.4i	0.653288	−	0.362543i
$387$		0			0
$388$	107794.	−	172884.i	0.716031	−	1.14839i
$389$	38430.8	+	66564.0i	0.253968	+	0.439886i	0.964615	−	0.263663i	$-0.0849307\pi$
$389$	38430.8	+	66564.0i	0.253968	+	0.439886i	−0.710646	+	0.703549i	$0.751597\pi$
$390$		0			0
$391$	−52952.8	−	30572.3i	−0.346366	−	0.199974i
$392$	14518.6	+	9398.15i	0.0944827	+	0.0611604i
$393$		0			0
$394$	−72376.5	−	43439.9i	−0.466235	−	0.279831i
$395$			259679.i			1.66434i
$396$		0			0
$397$	−73295.7			−0.465047			−0.232524	−	0.972591i	$-0.574698\pi$
$397$	−73295.7			−0.465047			−0.232524	+	0.972591i	$0.574698\pi$
$398$	−11214.5	+	18684.8i	−0.0707968	+	0.117957i
$399$		0			0
$400$	122362.	+	8315.25i	0.764765	+	0.0519703i
$401$	142274.	−	246426.i	0.884784	−	1.53249i	0.0388226	−	0.999246i	$-0.487639\pi$
$401$	142274.	−	246426.i	0.884784	−	1.53249i	0.845961	−	0.533244i	$-0.179027\pi$
$402$		0			0
$403$	−298550.	+	172368.i	−1.83826	+	1.06132i
$404$	116369.	−	186636.i	0.712973	−	1.14349i
$405$		0			0
$406$	−64037.0	−	115392.i	−0.388489	−	0.700044i
$407$	−64148.4	+	37036.1i	−0.387255	+	0.223582i
$408$		0			0
$409$	56577.0	−	97994.2i	0.338215	−	0.585806i	−0.645882	−	0.763437i	$-0.723510\pi$
$409$	56577.0	−	97994.2i	0.338215	−	0.585806i	0.984097	+	0.177632i	$0.0568435\pi$
$410$	2513.94	−	148188.i	0.0149550	−	0.881548i
$411$		0			0
$412$	7050.91	−	207753.i	0.0415385	−	1.22392i
$413$	−46823.9			−0.274516
$414$		0			0
$415$		−	270593.i		−	1.57116i
$416$	26287.4	−	309197.i	0.151901	−	1.78669i
$417$		0			0
$418$	1565.91	−	92305.1i	0.00896220	−	0.528291i
$419$	237314.	+	137013.i	1.35175	+	0.780431i	0.988494	−	0.151260i	$-0.0483331\pi$
$419$	237314.	+	137013.i	1.35175	+	0.780431i	0.363252	+	0.931691i	$0.381666\pi$
$420$		0			0
$421$	−6241.89	−	10811.3i	−0.0352170	−	0.0609976i	0.847880	−	0.530189i	$-0.177879\pi$
$421$	−6241.89	−	10811.3i	−0.0352170	−	0.0609976i	−0.883097	+	0.469191i	$0.844546\pi$
$422$	134328.	+	242054.i	0.754294	+	1.35921i
$423$		0			0
$424$	3443.55	−	67609.9i	0.0191547	−	0.376078i
$425$	−43600.9	−	75518.9i	−0.241389	−	0.418098i
$426$		0			0
$427$	34403.6	+	19862.9i	0.188690	+	0.108940i
$428$	−210269.	+	112067.i	−1.14786	+	0.611772i
$429$		0			0
$430$	−172338.	+	287138.i	−0.932062	+	1.55294i
$431$		−	119855.i		−	0.645211i	−0.946533	−	0.322606i	$-0.895441\pi$
$431$		−	119855.i		−	0.645211i	0.946533	−	0.322606i	$-0.104559\pi$
$432$		0			0
$433$	−282465.			−1.50657			−0.753284	−	0.657696i	$-0.771531\pi$
$433$	−282465.			−1.50657			−0.753284	+	0.657696i	$0.771531\pi$
$434$	−180098.	−	108094.i	−0.956158	−	0.573880i
$435$		0			0
$436$	56734.1	+	106449.i	0.298450	+	0.559977i
$437$	−52776.3	+	91411.2i	−0.276360	+	0.478670i
$438$		0			0
$439$	148459.	−	85712.8i	0.770331	−	0.444751i	−0.0626618	−	0.998035i	$-0.519959\pi$
$439$	148459.	−	85712.8i	0.770331	−	0.444751i	0.832993	+	0.553284i	$0.186626\pi$
$440$	−155998.	−	7945.39i	−0.805774	−	0.0410402i
$441$		0			0
$442$	−192920.	+	107061.i	−0.987488	+	0.548007i
$443$	−71888.2	+	41504.7i	−0.366311	+	0.211490i	−0.671846	−	0.740691i	$-0.734498\pi$
$443$	−71888.2	+	41504.7i	−0.366311	+	0.211490i	0.305535	+	0.952181i	$0.401165\pi$
$444$		0			0
$445$	127152.	−	220234.i	0.642102	−	1.11215i
$446$	−101296.	−	1718.45i	−0.509242	−	0.00863905i
$447$		0			0
$448$	172499.	−	77410.5i	0.859470	−	0.385695i
$449$	−252767.			−1.25380			−0.626898	−	0.779101i	$-0.715676\pi$
$449$	−252767.			−1.25380			−0.626898	+	0.779101i	$0.715676\pi$
$450$		0			0
$451$			81906.2i			0.402683i
$452$	−15867.3	−	538.519i	−0.0776653	−	0.00263587i
$453$		0			0
$454$	−388774.	−	6595.37i	−1.88619	−	0.0319983i
$455$	−402530.	−	232401.i	−1.94435	−	1.12257i
$456$		0			0
$457$	9489.80	+	16436.8i	0.0454386	+	0.0787019i	0.887850	−	0.460133i	$-0.152198\pi$
$457$	9489.80	+	16436.8i	0.0454386	+	0.0787019i	−0.842412	+	0.538835i	$0.818865\pi$
$458$	−300412.	+	166714.i	−1.43214	+	0.794769i
$459$		0			0
$460$	151547.	+	94490.7i	0.716197	+	0.446554i
$461$	−97075.9	−	168140.i	−0.456783	−	0.791171i	0.542006	−	0.840375i	$-0.317665\pi$
$461$	−97075.9	−	168140.i	−0.456783	−	0.791171i	−0.998789	+	0.0492038i	$0.984332\pi$
$462$		0			0
$463$	86227.9	+	49783.7i	0.402240	+	0.232234i	0.687450	−	0.726232i	$-0.258730\pi$
$463$	86227.9	+	49783.7i	0.402240	+	0.232234i	−0.285210	+	0.958465i	$0.592063\pi$
$464$	182552.	+	12405.5i	0.847914	+	0.0576208i
$465$		0			0
$466$	−43810.9	−	26295.0i	−0.201748	−	0.121088i
$467$		−	126990.i		−	0.582287i	−0.956679	−	0.291144i	$-0.905964\pi$
$467$		−	126990.i		−	0.582287i	0.956679	−	0.291144i	$-0.0940358\pi$
$468$		0			0
$469$	29797.6			0.135468
$470$	77437.5	−	129021.i	0.350555	−	0.584069i
$471$		0			0
$472$	35277.9	−	54498.5i	0.158350	−	0.244625i
$473$	92535.3	−	160276.i	0.413605	−	0.716384i
$474$		0			0
$475$	−130367.	+	75267.2i	−0.577802	+	0.333594i
$476$	−114075.	−	71126.6i	−0.503474	−	0.313919i
$477$		0			0
$478$	205628.	+	370535.i	0.899969	+	1.62171i
$479$	48437.8	−	27965.6i	0.211112	−	0.121886i	−0.390716	−	0.920511i	$-0.627773\pi$
$479$	48437.8	−	27965.6i	0.211112	−	0.121886i	0.601828	+	0.798626i	$0.294439\pi$
$480$		0			0
$481$	152800.	−	264657.i	0.660439	−	1.14391i
$482$	690.660	−	40712.0i	0.00297283	−	0.175238i
$483$		0			0
$484$	−147849.	−	5017.82i	−0.631142	−	0.0214202i
$485$	423105.			1.79872
$486$		0			0
$487$		−	274913.i		−	1.15914i	−0.814921	−	0.579572i	$-0.803220\pi$
$487$		−	274913.i		−	1.15914i	0.814921	−	0.579572i	$-0.196780\pi$
$488$	−49038.8	+	25077.5i	−0.205921	+	0.105304i
$489$		0			0
$490$	−609.226	+	35911.8i	−0.00253739	+	0.149570i
$491$	−28037.6	−	16187.5i	−0.116299	−	0.0671455i	0.440722	−	0.897644i	$-0.354723\pi$
$491$	−28037.6	−	16187.5i	−0.116299	−	0.0671455i	−0.557021	+	0.830498i	$0.688056\pi$
$492$		0			0
$493$	−65048.1	−	112667.i	−0.267634	−	0.463555i
$494$	184817.	+	333033.i	0.757334	+	1.36469i
$495$		0			0
$496$	261500.	−	128178.i	1.06294	−	0.521013i
$497$	220828.	+	382485.i	0.894008	+	1.54847i
$498$		0			0
$499$	−251446.	−	145172.i	−1.00982	−	0.583019i	−0.0986806	−	0.995119i	$-0.531462\pi$
$499$	−251446.	−	145172.i	−1.00982	−	0.583019i	−0.911139	+	0.412100i	$0.864796\pi$
$500$	−36487.4	−	68460.7i	−0.145950	−	0.273843i
$501$		0			0
$502$	44973.7	−	74932.1i	0.178464	−	0.297345i
$503$			9486.90i			0.0374963i	0.999824	+	0.0187481i	$0.00596807\pi$
$503$			9486.90i			0.0374963i	−0.999824	+	0.0187481i	$0.994032\pi$
$504$		0			0
$505$	456761.			1.79104
$506$	−84624.4	−	50791.0i	−0.330518	−	0.198375i
$507$		0			0
$508$	−100583.	+	53607.3i	−0.389758	+	0.207729i
$509$	−146376.	+	253530.i	−0.564980	+	0.978575i	0.432071	+	0.901839i	$0.357783\pi$
$509$	−146376.	+	253530.i	−0.564980	+	0.978575i	−0.997052	+	0.0767350i	$0.975550\pi$
$510$		0			0
$511$	−75918.5	+	43831.5i	−0.290741	+	0.167859i
$512$	−39865.2	+	259095.i	−0.152074	+	0.988369i
$513$		0			0
$514$	−194328.	+	107842.i	−0.735544	+	0.408190i
$515$	373860.	−	215848.i	1.40960	−	0.813831i
$516$		0			0
$517$	−41579.3	+	72017.4i	−0.155559	+	0.269437i
$518$	186174.	+	3158.36i	0.693841	+	0.0117707i
$519$		0			0
$520$	573765.	−	293412.i	2.12191	−	1.08510i
$521$	344253.			1.26824			0.634120	−	0.773234i	$-0.281362\pi$
$521$	344253.			1.26824			0.634120	+	0.773234i	$0.281362\pi$
$522$		0			0
$523$		−	79326.1i		−	0.290010i	−0.989431	−	0.145005i	$-0.953680\pi$
$523$		−	79326.1i		−	0.290010i	0.989431	−	0.145005i	$-0.0463198\pi$
$524$	3777.01	−	111289.i	0.0137558	−	0.405312i
$525$		0			0
$526$	100639.	+	1707.29i	0.363742	+	0.00617071i
$527$	−179323.	−	103532.i	−0.645675	−	0.372780i
$528$		0			0
$529$	−83497.9	−	144623.i	−0.298376	−	0.516803i
$530$	122929.	−	68219.5i	0.437625	−	0.242860i
$531$		0			0
$532$	−122784.	+	196925.i	−0.433830	+	0.695790i
$533$	−168960.	−	292648.i	−0.594744	−	1.03013i
$534$		0			0
$535$	−428527.	−	247410.i	−1.49717	−	0.864391i
$536$	−22450.0	+	34681.6i	−0.0781424	+	0.120717i
$537$		0			0
$538$	185731.	+	111474.i	0.641681	+	0.385133i
$539$		−	19849.0i		−	0.0683223i
$540$		0			0
$541$	167330.			0.571715			0.285857	−	0.958272i	$-0.407722\pi$
$541$	167330.			0.571715			0.285857	+	0.958272i	$0.407722\pi$
$542$	−195436.	+	325622.i	−0.665283	+	1.10845i
$543$		0			0
$544$	168731.	−	79184.7i	0.570159	−	0.267574i
$545$	−125252.	+	216943.i	−0.421689	+	0.730387i
$546$		0			0
$547$	246877.	−	142535.i	0.825100	−	0.476372i	−0.0270722	−	0.999633i	$-0.508618\pi$
$547$	246877.	−	142535.i	0.825100	−	0.476372i	0.852172	+	0.523262i	$0.175285\pi$
$548$	71861.5	−	115254.i	0.239296	−	0.383790i
$549$		0			0
$550$	−68300.6	−	123075.i	−0.225787	−	0.406860i
$551$	−194494.	+	112291.i	−0.640623	+	0.369864i
$552$		0			0
$553$	−180374.	+	312417.i	−0.589827	+	1.02161i
$554$	−7330.30	+	432096.i	−0.0238837	+	1.40786i
$555$		0			0
$556$	−11583.2	+	341297.i	−0.0374696	+	1.10403i
$557$	−51271.9			−0.165260			−0.0826302	−	0.996580i	$-0.526332\pi$
$557$	−51271.9			−0.165260			−0.0826302	+	0.996580i	$0.526332\pi$
$558$		0			0
$559$			763547.i			2.44350i
$560$	325954.	+	218930.i	1.03939	+	0.698117i
$561$		0			0
$562$	−4676.52	+	275665.i	−0.0148064	+	0.872787i
$563$	−2488.80	−	1436.91i	−0.00785187	−	0.00453328i	0.496069	−	0.868283i	$-0.334776\pi$
$563$	−2488.80	−	1436.91i	−0.00785187	−	0.00453328i	−0.503921	+	0.863750i	$0.668110\pi$
$564$		0			0
$565$	−16485.6	−	28553.9i	−0.0516425	−	0.0894474i
$566$	−87753.2	−	158128.i	−0.273924	−	0.493601i
$567$		0			0
$568$	−611552.	−	31148.0i	−1.89556	−	0.0965458i
$569$	−56876.7	−	98513.3i	−0.175675	−	0.304278i	0.764720	−	0.644363i	$-0.222877\pi$
$569$	−56876.7	−	98513.3i	−0.175675	−	0.304278i	−0.940395	+	0.340085i	$0.889544\pi$
$570$		0			0
$571$	27258.4	+	15737.7i	0.0836043	+	0.0482689i	0.541219	−	0.840881i	$-0.317963\pi$
$571$	27258.4	+	15737.7i	0.0836043	+	0.0482689i	−0.457615	+	0.889150i	$0.651296\pi$
$572$	−314288.	+	167505.i	−0.960585	+	0.511961i
$573$		0			0
$574$	105957.	−	176538.i	0.321592	−	0.535813i
$575$			160935.i			0.486760i
$576$		0			0
$577$	−654654.			−1.96635			−0.983174	−	0.182671i	$-0.941526\pi$
$577$	−654654.			−1.96635			−0.983174	+	0.182671i	$0.941526\pi$
$578$	172822.	+	103727.i	0.517301	+	0.310480i
$579$		0			0
$580$	178722.	+	335333.i	0.531278	+	0.996829i
$581$	187955.	−	325548.i	0.556803	−	0.964412i
$582$		0			0
$583$	−67285.9	+	38847.5i	−0.197964	+	0.114295i
$584$	6182.48	−	121385.i	0.0181275	−	0.355910i
$585$		0			0
$586$	250798.	−	139180.i	0.730346	−	0.405306i
$587$	557280.	−	321746.i	1.61732	−	0.933763i	0.629716	−	0.776825i	$-0.283171\pi$
$587$	557280.	−	321746.i	1.61732	−	0.933763i	0.987609	−	0.156937i	$-0.0501620\pi$
$588$		0			0
$589$	−178725.	+	309561.i	−0.515175	+	0.892309i
$590$	134802.	+	2286.86i	0.387251	+	0.00656954i
$591$		0			0
$592$	−143943.	+	214310.i	−0.410721	+	0.611503i
$593$	183090.			0.520661			0.260330	−	0.965520i	$-0.416169\pi$
$593$	183090.			0.520661			0.260330	+	0.965520i	$0.416169\pi$
$594$		0			0
$595$		−	279180.i		−	0.788589i
$596$	−203620.	−	6910.62i	−0.573228	−	0.0194547i
$597$		0			0
$598$	407134.	+	6906.84i	1.13851	+	0.0193142i
$599$	24104.3	+	13916.6i	0.0671800	+	0.0387864i	0.533214	−	0.845981i	$-0.320984\pi$
$599$	24104.3	+	13916.6i	0.0671800	+	0.0387864i	−0.466034	+	0.884767i	$0.654317\pi$
$600$		0			0
$601$	135764.	+	235150.i	0.375868	+	0.651022i	0.990457	−	0.137826i	$-0.0440113\pi$
$601$	135764.	+	235150.i	0.375868	+	0.651022i	−0.614589	+	0.788848i	$0.710678\pi$
$602$	−406786.	+	225746.i	−1.12247	+	0.622912i
$603$		0			0
$604$	48001.8	+	29929.5i	0.131578	+	0.0820399i
$605$	−153610.	−	266060.i	−0.419670	−	0.726889i
$606$		0			0
$607$	−86991.8	−	50224.8i	−0.236103	−	0.136314i	0.377281	−	0.926099i	$-0.376859\pi$
$607$	−86991.8	−	50224.8i	−0.236103	−	0.136314i	−0.613384	+	0.789785i	$0.710192\pi$
$608$	−136695.	−	291276.i	−0.369781	−	0.787948i
$609$		0			0
$610$	−98075.2	−	58864.1i	−0.263572	−	0.158194i
$611$		−	343088.i		−	0.919015i
$612$		0			0
$613$	458408.			1.21992			0.609960	−	0.792432i	$-0.291185\pi$
$613$	458408.			1.21992			0.609960	+	0.792432i	$0.291185\pi$
$614$	197339.	−	328793.i	0.523451	−	0.872138i
$615$		0			0
$616$	−182161.	−	117916.i	−0.480057	−	0.310750i
$617$	−237317.	+	411046.i	−0.623389	+	1.07974i	0.365461	+	0.930827i	$0.380911\pi$
$617$	−237317.	+	411046.i	−0.623389	+	1.07974i	−0.988850	+	0.148915i	$0.952422\pi$
$618$		0			0
$619$	5714.30	−	3299.15i	0.0149136	−	0.00861036i	−0.492525	−	0.870298i	$-0.663926\pi$
$619$	5714.30	−	3299.15i	0.0149136	−	0.00861036i	0.507438	+	0.861688i	$0.330593\pi$
$620$	513209.	+	319989.i	1.33509	+	0.832438i
$621$		0			0
$622$	−46715.9	−	84180.4i	−0.120749	−	0.217586i
$623$	305951.	−	176641.i	0.788272	−	0.455109i
$624$		0			0
$625$	230266.	−	398833.i	0.589481	−	1.02101i
$626$	6737.96	−	397179.i	0.0171941	−	1.01353i
$627$		0			0
$628$	−475584.	−	16140.8i	−1.20589	−	0.0409265i
$629$	183557.			0.463948
$630$		0			0
$631$		−	102946.i		−	0.258553i	−0.991609	−	0.129277i	$-0.958734\pi$
$631$		−	102946.i		−	0.258553i	0.991609	−	0.129277i	$-0.0412655\pi$
$632$	−227727.	−	445319.i	−0.570139	−	1.11490i
$633$		0			0
$634$	4032.97	−	237730.i	0.0100334	−	0.591432i
$635$	−204987.	−	118349.i	−0.508368	−	0.293506i
$636$		0			0
$637$	40945.7	+	70919.9i	0.100909	+	0.174779i
$638$	−101898.	−	183616.i	−0.250336	−	0.451096i
$639$		0			0
$640$	−500392.	+	214434.i	−1.22166	+	0.523521i
$641$	202403.	+	350572.i	0.492607	+	0.853221i	0.999964	−	0.00851530i	$-0.00271054\pi$
$641$	202403.	+	350572.i	0.492607	+	0.853221i	−0.507356	+	0.861736i	$0.669377\pi$
$642$		0			0
$643$	426111.	+	246015.i	1.03063	+	0.595032i	0.917164	−	0.398510i	$-0.130473\pi$
$643$	426111.	+	246015.i	1.03063	+	0.595032i	0.113462	+	0.993542i	$0.463806\pi$
$644$	116691.	+	218946.i	0.281363	+	0.527917i
$645$		0			0
$646$	−117730.	+	196154.i	−0.282113	+	0.470037i
$647$			306912.i			0.733171i	0.930384	+	0.366586i	$0.119473\pi$
$647$			306912.i			0.733171i	−0.930384	+	0.366586i	$0.880527\pi$
$648$		0			0
$649$	−74507.5			−0.176893
$650$	497922.	+	298849.i	1.17851	+	0.707335i
$651$		0			0
$652$	83362.7	−	44429.7i	0.196100	−	0.104515i
$653$	97661.8	−	169155.i	0.229033	−	0.396697i	−0.728489	−	0.685058i	$-0.759777\pi$
$653$	97661.8	−	169155.i	0.229033	−	0.396697i	0.957522	+	0.288361i	$0.0931103\pi$
$654$		0			0
$655$	200269.	−	115625.i	0.466799	−	0.269507i
$656$	125644.	+	256330.i	0.291966	+	0.595651i
$657$		0			0
$658$	182783.	−	101435.i	0.422166	−	0.234281i
$659$	−678872.	+	391947.i	−1.56321	+	0.902519i	−0.566279	+	0.824213i	$0.691618\pi$
$659$	−678872.	+	391947.i	−1.56321	+	0.902519i	−0.996929	+	0.0783055i	$0.975049\pi$
$660$		0			0
$661$	−371075.	+	642721.i	−0.849295	+	1.47102i	0.0325431	+	0.999470i	$0.489639\pi$
$661$	−371075.	+	642721.i	−0.849295	+	1.47102i	−0.881838	+	0.471552i	$0.843694\pi$
$662$	−368768.	−	6255.97i	−0.841467	−	0.0142751i
$663$		0			0
$664$	237298.	+	464035.i	0.538218	+	1.05248i
$665$	−481943.			−1.08981
$666$		0			0
$667$			240099.i			0.539682i
$668$	11161.4	−	328867.i	0.0250129	−	0.737000i
$669$		0			0
$670$	−85784.9	−	1455.30i	−0.191100	−	0.00324193i
$671$	54744.0	+	31606.5i	0.121588	+	0.0701990i
$672$		0			0
$673$	−211601.	−	366503.i	−0.467183	−	0.809185i	0.532114	−	0.846673i	$-0.321398\pi$
$673$	−211601.	−	366503.i	−0.467183	−	0.809185i	−0.999297	+	0.0374878i	$0.988064\pi$
$674$	160566.	−	89106.0i	0.353454	−	0.196149i
$675$		0			0
$676$	535621.	−	859046.i	1.17210	−	1.87985i
$677$	154122.	+	266947.i	0.336269	+	0.582435i	0.983728	−	0.179665i	$-0.0575015\pi$
$677$	154122.	+	266947.i	0.336269	+	0.582435i	−0.647459	+	0.762100i	$0.724168\pi$
$678$		0			0
$679$	509034.	+	293891.i	1.10410	+	0.637450i
$680$	324940.	+	210339.i	0.702724	+	0.454886i
$681$		0			0
$682$	−286577.	−	172002.i	−0.616131	−	0.369798i
$683$			760287.i			1.62981i	0.579597	+	0.814903i	$0.303210\pi$
$683$			760287.i			1.62981i	−0.579597	+	0.814903i	$0.696790\pi$
$684$		0			0
$685$	282065.			0.601130
$686$	−253819.	+	422896.i	−0.539357	+	0.898639i
$687$		0			0
$688$	43732.4	−	643541.i	0.0923904	−	1.35956i
$689$	160273.	−	277602.i	0.337616	−	0.584768i
$690$		0			0
$691$	313235.	−	180846.i	0.656016	−	0.378751i	−0.134742	−	0.990881i	$-0.543020\pi$
$691$	313235.	−	180846.i	0.656016	−	0.378751i	0.790757	+	0.612130i	$0.209687\pi$
$692$	−51723.4	+	82955.6i	−0.108013	+	0.173234i
$693$		0			0
$694$	−294978.	−	531539.i	−0.612450	−	1.10361i
$695$	−614177.	+	354595.i	−1.27152	+	0.734113i
$696$		0			0
$697$	101485.	−	175777.i	0.208899	−	0.361824i
$698$	12707.4	−	749057.i	0.0260823	−	1.53746i
$699$		0			0
$700$	−12001.7	+	353628.i	−0.0244933	+	0.721690i
$701$	−878492.			−1.78773			−0.893864	−	0.448337i	$-0.852016\pi$
$701$	−878492.			−1.78773			−0.893864	+	0.448337i	$0.852016\pi$
$702$		0			0
$703$		−	316870.i		−	0.641167i
$704$	274486.	−	123178.i	0.553827	−	0.248535i
$705$		0			0
$706$	3081.37	−	181636.i	0.00618208	−	0.364412i
$707$	549525.	+	317268.i	1.09938	+	0.634728i
$708$		0			0
$709$	−431190.	−	746844.i	−0.857781	−	1.48572i	−0.874041	−	0.485853i	$-0.838509\pi$
$709$	−431190.	−	746844.i	−0.857781	−	1.48572i	0.0162593	−	0.999868i	$-0.494824\pi$
$710$	−617066.	−	1.11193e6i	−1.22409	−	2.20577i
$711$		0			0
$712$	−24915.4	+	489183.i	−0.0491482	+	0.964964i
$713$	191073.	+	330948.i	0.375855	+	0.651000i
$714$		0			0
$715$	−640517.	−	369803.i	−1.25291	−	0.723366i
$716$	−162869.	+	86803.9i	−0.317696	+	0.169322i
$717$		0			0
$718$	−147189.	+	245236.i	−0.285514	+	0.475703i
$719$		−	424008.i		−	0.820193i	−0.912042	−	0.410097i	$-0.865495\pi$
$719$		−	424008.i		−	0.820193i	0.912042	−	0.410097i	$-0.134505\pi$
$720$		0			0
$721$	599717.			1.15365
$722$	−108343.	−	65026.6i	−0.207838	−	0.124743i
$723$		0			0
$724$	−192230.	−	360679.i	−0.366728	−	0.688087i
$725$	−171209.	+	296543.i	−0.325725	+	0.564172i
$726$		0			0
$727$	−78836.8	+	45516.5i	−0.149163	+	0.0861191i	−0.572724	−	0.819748i	$-0.694113\pi$
$727$	−78836.8	+	45516.5i	−0.149163	+	0.0861191i	0.423561	+	0.905868i	$0.360780\pi$
$728$	894096.	+	45538.7i	1.68702	+	0.0859247i
$729$		0			0
$730$	220704.	−	122480.i	0.414157	−	0.229836i
$731$	−397177.	+	229310.i	−0.743275	+	0.429130i
$732$		0			0
$733$	6638.99	−	11499.1i	0.0123565	−	0.0214020i	−0.859781	−	0.510663i	$-0.829400\pi$
$733$	6638.99	−	11499.1i	0.0123565	−	0.0214020i	0.872138	+	0.489261i	$0.162733\pi$
$734$	−265109.	−	4497.44i	−0.492076	−	0.00834783i
$735$		0			0
$736$	−342750.	−	29140.1i	−0.632735	−	0.0537942i
$737$	47414.8			0.0872929
$738$		0			0
$739$			622195.i			1.13930i	0.821888	+	0.569650i	$0.192921\pi$
$739$			622195.i			1.13930i	−0.821888	+	0.569650i	$0.807079\pi$
$740$	−535827.	−	18185.3i	−0.978501	−	0.0332092i
$741$		0			0
$742$	195280.	+	3312.84i	0.354691	+	0.00601717i
$743$	606588.	+	350214.i	1.09879	+	0.634389i	0.935904	−	0.352255i	$-0.114585\pi$
$743$	606588.	+	350214.i	1.09879	+	0.634389i	0.162890	+	0.986644i	$0.447918\pi$
$744$		0			0
$745$	−211554.	−	366422.i	−0.381161	−	0.660189i
$746$	502135.	−	278660.i	0.902283	−	0.500722i
$747$		0			0
$748$	−181520.	−	113179.i	−0.324430	−	0.202284i
$749$	−343705.	−	595314.i	−0.612663	−	1.06116i
$750$		0			0
$751$	73727.4	+	42566.6i	0.130722	+	0.0754725i	0.563935	−	0.825819i	$-0.309287\pi$
$751$	73727.4	+	42566.6i	0.130722	+	0.0754725i	−0.433213	+	0.901292i	$0.642620\pi$
$752$	−19650.5	+	289165.i	−0.0347486	+	0.511340i
$753$		0			0
$754$	742849.	+	445853.i	1.30665	+	0.784240i
$755$			117477.i			0.206091i
$756$		0			0
$757$	319528.			0.557592			0.278796	−	0.960350i	$-0.410065\pi$
$757$	319528.			0.557592			0.278796	+	0.960350i	$0.410065\pi$
$758$	377066.	−	628241.i	0.656265	−	1.09342i
$759$		0			0
$760$	363104.	−	560936.i	0.628643	−	0.971150i
$761$	376888.	−	652790.i	0.650794	−	1.12721i	−0.332137	−	0.943231i	$-0.607770\pi$
$761$	376888.	−	652790.i	0.650794	−	1.12721i	0.982931	−	0.183977i	$-0.0588971\pi$
$762$		0			0
$763$	−301379.	+	174001.i	−0.517684	+	0.298885i
$764$	−530426.	−	330724.i	−0.908737	−	0.566604i
$765$		0			0
$766$	−34012.4	−	61289.2i	−0.0579669	−	0.104454i
$767$	266213.	−	153698.i	0.452520	−	0.261263i
$768$		0			0
$769$	−425156.	+	736392.i	−0.718945	+	1.24525i	0.242473	+	0.970158i	$0.422041\pi$
$769$	−425156.	+	736392.i	−0.718945	+	1.24525i	−0.961418	+	0.275091i	$0.911292\pi$
$770$	7643.78	−	450575.i	0.0128922	−	0.759950i
$771$		0			0
$772$	−445029.	−	15103.8i	−0.746713	−	0.0253426i
$773$	−13034.7			−0.0218143			−0.0109071	−	0.999941i	$-0.503472\pi$
$773$	−13034.7			−0.0218143			−0.0109071	+	0.999941i	$0.503472\pi$
$774$		0			0
$775$			545000.i			0.907388i
$776$	−725575.	+	371045.i	−1.20492	+	0.616173i
$777$		0			0
$778$	5214.93	−	307402.i	0.00861567	−	0.507864i
$779$	−303441.	−	175192.i	−0.500033	−	0.288694i
$780$		0			0
$781$	351388.	+	608622.i	0.576083	+	0.997805i
$782$	118679.	+	213855.i	0.194071	+	0.349708i
$783$		0			0
$784$	−30448.3	−	62118.7i	−0.0495372	−	0.101063i
$785$	−494114.	−	855831.i	−0.801841	−	1.38883i
$786$		0			0
$787$	473891.	+	273601.i	0.765120	+	0.441742i	0.831131	−	0.556077i	$-0.187694\pi$
$787$	473891.	+	273601.i	0.765120	+	0.441742i	−0.0660112	+	0.997819i	$0.521027\pi$
$788$	158808.	+	297970.i	0.255753	+	0.479866i
$789$		0			0
$790$	534542.	−	890616.i	0.856500	−	1.42704i
$791$		−	45803.8i		−	0.0732064i
$792$		0			0
$793$	−260798.			−0.414723
$794$	251381.	+	150877.i	0.398741	+	0.239322i
$795$		0			0
$796$	76924.2	−	40998.2i	0.121405	−	0.0647050i
$797$	−104227.	+	180527.i	−0.164083	+	0.284201i	−0.936329	−	0.351123i	$-0.885800\pi$
$797$	−104227.	+	180527.i	−0.164083	+	0.284201i	0.772246	+	0.635324i	$0.219133\pi$
$798$		0			0
$799$	178465.	−	103037.i	0.279550	−	0.161398i
$800$	−402547.	−	280398.i	−0.628980	−	0.438122i
$801$		0			0
$802$	−995215.	+	552295.i	−1.54728	+	0.858662i
$803$	−120804.	+	69746.0i	−0.187348	+	0.108165i
$804$		0			0
$805$	−257620.	+	446211.i	−0.397547	+	0.688571i
$806$	1.37875e6	+	23389.8i	2.12234	+	0.0360044i
$807$		0			0
$808$	−783292.	+	400560.i	−1.19978	+	0.613542i
$809$	−844500.			−1.29034			−0.645168	−	0.764041i	$-0.723213\pi$
$809$	−844500.			−1.29034			−0.645168	+	0.764041i	$0.723213\pi$
$810$		0			0
$811$		−	769174.i		−	1.16945i	−0.811230	−	0.584727i	$-0.801202\pi$
$811$		−	769174.i		−	1.16945i	0.811230	−	0.584727i	$-0.198798\pi$
$812$	−17905.4	+	527577.i	−0.0271563	+	0.800155i
$813$		0			0
$814$	296246.	+	5025.67i	0.447099	+	0.00758482i
$815$	169893.	+	98087.6i	0.255776	+	0.147672i
$816$		0			0
$817$	395853.	+	685638.i	0.593048	+	1.02719i
$818$	−395759.	+	219627.i	−0.591458	+	0.328230i
$819$		0			0
$820$	−313663.	+	503063.i	−0.466483	+	0.748161i
$821$	322867.	+	559222.i	0.479002	+	0.829656i	0.999710	−	0.0240788i	$-0.00766527\pi$
$821$	322867.	+	559222.i	0.479002	+	0.829656i	−0.520708	+	0.853735i	$0.674332\pi$
$822$		0			0
$823$	202697.	+	117027.i	0.299260	+	0.172778i	0.642110	−	0.766612i	$-0.278059\pi$
$823$	202697.	+	117027.i	0.299260	+	0.172778i	−0.342851	+	0.939390i	$0.611392\pi$
$824$	−451837.	+	698013.i	−0.665468	+	1.02804i
$825$		0			0
$826$	160591.	+	96385.5i	0.235375	+	0.141271i
$827$		−	1.14409e6i		−	1.67282i	−0.548108	−	0.836408i	$-0.684652\pi$
$827$		−	1.14409e6i		−	1.67282i	0.548108	−	0.836408i	$-0.315348\pi$
$828$		0			0
$829$	−563769.			−0.820336			−0.410168	−	0.912010i	$-0.634530\pi$
$829$	−563769.			−0.820336			−0.410168	+	0.912010i	$0.634530\pi$
$830$	−557008.	+	928047.i	−0.808547	+	1.34714i
$831$		0			0
$832$	−726630.	+	1.00633e6i	−1.04970	+	1.45377i
$833$	−24593.8	+	42597.7i	−0.0354434	+	0.0613898i
$834$		0			0
$835$	591809.	−	341681.i	0.848806	−	0.490059i
$836$	−195378.	+	313353.i	−0.279552	+	0.448355i
$837$		0			0
$838$	−531873.	−	958415.i	−0.757390	−	1.36479i
$839$	231599.	−	133714.i	0.329013	−	0.189956i	−0.326390	−	0.945235i	$-0.605832\pi$
$839$	231599.	−	133714.i	0.329013	−	0.189956i	0.655403	+	0.755279i	$0.272499\pi$
$840$		0			0
$841$	98213.9	−	170111.i	0.138861	−	0.240515i
$842$	−847.004	+	49927.9i	−0.00119471	+	0.0704238i
$843$		0			0
$844$	37559.3	−	1.10668e6i	0.0527269	−	1.55359i
$845$	2.10238e6			2.94440
$846$		0			0
$847$		−	426792.i		−	0.594907i
$848$	−150983.	+	224792.i	−0.209960	+	0.312600i
$849$		0			0
$850$	−5916.50	+	348757.i	−0.00818892	+	0.482708i
$851$	−293377.	−	169381.i	−0.405105	−	0.233887i
$852$		0			0
$853$	−183417.	−	317688.i	−0.252082	−	0.436619i	0.712017	−	0.702162i	$-0.247782\pi$
$853$	−183417.	−	317688.i	−0.252082	−	0.436619i	−0.964099	+	0.265544i	$0.914449\pi$
$854$	−77106.0	−	138942.i	−0.105724	−	0.190510i
$855$		0			0
$856$	951842.	+	48479.9i	1.29902	+	0.0661628i
$857$	576064.	+	997772.i	0.784348	+	1.35853i	0.929388	+	0.369105i	$0.120336\pi$
$857$	576064.	+	997772.i	0.784348	+	1.35853i	−0.145039	+	0.989426i	$0.546331\pi$
$858$		0			0
$859$	−1.26237e6	−	728827.i	−1.71080	−	0.987730i	−0.933486	−	0.358615i	$-0.883249\pi$
$859$	−1.26237e6	−	728827.i	−1.71080	−	0.987730i	−0.777313	−	0.629115i	$-0.783418\pi$
$860$	1.18213e6	−	630038.i	1.59834	−	0.851863i
$861$		0			0
$862$	−246718.	+	411064.i	−0.332037	+	0.553217i
$863$		−	237901.i		−	0.319430i	−0.987163	−	0.159715i	$-0.948943\pi$
$863$		−	237901.i		−	0.319430i	0.987163	−	0.159715i	$-0.0510575\pi$
$864$		0			0
$865$	−203020.			−0.271336
$866$	968764.	+	581445.i	1.29176	+	0.775306i
$867$		0			0
$868$	395171.	+	741453.i	0.524500	+	0.984112i
$869$	−287017.	+	497128.i	−0.380074	+	0.658307i
$870$		0			0
$871$	−169411.	+	97809.7i	−0.223309	+	0.128928i
$872$	24543.1	−	481873.i	0.0322772	−	0.633723i
$873$		0			0
$874$	369173.	−	204873.i	0.483289	−	0.268201i
$875$	193826.	−	111905.i	0.253160	−	0.146162i
$876$		0			0
$877$	331033.	−	573367.i	0.430400	−	0.745475i	−0.566507	−	0.824057i	$-0.691706\pi$
$877$	331033.	−	573367.i	0.430400	−	0.745475i	0.996908	+	0.0785815i	$0.0250391\pi$
$878$	−685604.	−	11630.9i	−0.889373	−	0.0150878i
$879$		0			0
$880$	518667.	+	348367.i	0.669766	+	0.449854i
$881$	−245234.			−0.315957			−0.157979	−	0.987443i	$-0.550498\pi$
$881$	−245234.			−0.315957			−0.157979	+	0.987443i	$0.550498\pi$
$882$		0			0
$883$			924835.i			1.18616i	0.805144	+	0.593079i	$0.202088\pi$
$883$			924835.i			1.18616i	−0.805144	+	0.593079i	$0.797912\pi$
$884$	882034.	+	29935.2i	1.12871	+	0.0383070i
$885$		0			0
$886$	331990.	+	5632.05i	0.422919	+	0.00717462i
$887$	1.09941e6	+	634747.i	1.39738	+	0.806776i	0.994117	−	0.108309i	$-0.0345436\pi$
$887$	1.09941e6	+	634747.i	1.39738	+	0.806776i	0.403260	+	0.915085i	$0.367877\pi$
$888$		0			0
$889$	−164412.	−	284769.i	−0.208031	−	0.360321i
$890$	−889437.	+	493593.i	−1.12288	+	0.623145i
$891$		0			0
$892$	343877.	+	214409.i	0.432188	+	0.269472i
$893$	−177870.	−	308081.i	−0.223049	−	0.386333i
$894$		0			0
$895$	−331926.	−	191637.i	−0.414376	−	0.239240i
$896$	−750964.	−	89591.1i	−0.935412	−	0.111596i
$897$		0			0
$898$	866908.	+	520313.i	1.07503	+	0.645226i
$899$			813085.i			1.00604i
$900$		0			0
$901$	192535.			0.237170
$902$	168601.	−	280912.i	0.207228	−	0.345269i
$903$		0			0
$904$	53311.3	+	34509.4i	0.0652353	+	0.0422280i
$905$	424388.	−	735061.i	0.518162	−	0.897483i
$906$		0			0
$907$	−41146.3	+	23755.8i	−0.0500169	+	0.0288772i	−0.524800	−	0.851226i	$-0.675860\pi$
$907$	−41146.3	+	23755.8i	−0.0500169	+	0.0288772i	0.474783	+	0.880103i	$0.342527\pi$
$908$	1.31979e6	+	822900.i	1.60079	+	0.998102i
$909$		0			0
$910$	902158.	+	1.62565e6i	1.08943	+	1.96311i
$911$	421729.	−	243485.i	0.508155	−	0.293383i	−0.223920	−	0.974608i	$-0.571885\pi$
$911$	421729.	−	243485.i	0.508155	−	0.293383i	0.732075	+	0.681224i	$0.238552\pi$
$912$		0			0
$913$	299080.	−	518021.i	0.358794	−	0.621450i
$914$	1287.73	−	75907.4i	0.00154147	−	0.0908640i
$915$		0			0
$916$	1.37349e6	+	46614.8i	1.63695	+	0.0555562i
$917$	321255.			0.382042
$918$		0			0
$919$			1.08957e6i			1.29010i	0.764141	+	0.645049i	$0.223163\pi$
$919$			1.08957e6i			1.29010i	−0.764141	+	0.645049i	$0.776837\pi$
$920$	−325252.	−	636029.i	−0.384277	−	0.751452i
$921$		0			0
$922$	−13172.9	+	776495.i	−0.0154960	+	0.913434i
$923$	−2.51099e6	−	1.44972e6i	−2.94742	−	1.70169i
$924$		0			0
$925$	−241564.	−	418402.i	−0.282325	−	0.489001i
$926$	−193256.	−	348240.i	−0.225377	−	0.406122i
$927$		0			0
$928$	−600560.	−	418326.i	−0.697365	−	0.485757i
$929$	671427.	+	1.16295e6i	0.777978	+	1.34750i	0.933106	+	0.359603i	$0.117088\pi$
$929$	671427.	+	1.16295e6i	0.777978	+	1.34750i	−0.155128	+	0.987894i	$0.549579\pi$
$930$		0			0
$931$	73535.5	+	42455.7i	0.0848394	+	0.0489820i
$932$	96129.8	+	180367.i	0.110669	+	0.207647i
$933$		0			0
$934$	−261406.	+	435537.i	−0.299655	+	0.499265i
$935$		−	444240.i		−	0.508153i
$936$		0			0
$937$	1.37506e6			1.56618			0.783089	−	0.621909i	$-0.213643\pi$
$937$	1.37506e6			1.56618			0.783089	+	0.621909i	$0.213643\pi$
$938$	−102196.	−	61337.4i	−0.116153	−	0.0697140i
$939$		0			0
$940$	−531172.	+	283098.i	−0.601145	+	0.320391i
$941$	−786864.	+	1.36289e6i	−0.888628	+	1.53915i	−0.0471309	+	0.998889i	$0.515008\pi$
$941$	−786864.	+	1.36289e6i	−0.888628	+	1.53915i	−0.841498	+	0.540261i	$0.818326\pi$
$942$		0			0
$943$	−324405.	+	187295.i	−0.364808	+	0.210622i
$944$	−233175.	+	114294.i	−0.261661	+	0.128257i
$945$		0			0
$946$	−647290.	+	359214.i	−0.723297	+	0.401394i
$947$	938964.	−	542111.i	1.04701	−	0.604489i	0.125196	−	0.992132i	$-0.460044\pi$
$947$	938964.	−	542111.i	1.04701	−	0.604489i	0.921810	+	0.387643i	$0.126711\pi$
$948$		0			0
$949$	287752.	−	498400.i	0.319511	−	0.553409i
$950$	602051.	+	10213.5i	0.667093	+	0.0113169i
$951$		0			0
$952$	244829.	+	478762.i	0.270140	+	0.528257i
$953$	−461469.			−0.508108			−0.254054	−	0.967190i	$-0.581764\pi$
$953$	−461469.			−0.508108			−0.254054	+	0.967190i	$0.581764\pi$
$954$		0			0
$955$		−	1.29813e6i		−	1.42335i
$956$	57495.6	−	1.69410e6i	0.0629099	−	1.85363i
$957$		0			0
$958$	−223692.	−	3794.83i	−0.243736	−	0.00413487i
$959$	339350.	+	195924.i	0.368986	+	0.213034i
$960$		0			0
$961$	185301.	+	320951.i	0.200646	+	0.347530i
$962$	−1.06884e6	+	593155.i	−1.15495	+	0.640941i
$963$		0			0
$964$	−86173.2	+	138207.i	−0.0927295	+	0.148723i
$965$	−462369.	−	800847.i	−0.496517	−	0.859993i
$966$		0			0
$967$	−998780.	−	576646.i	−1.06811	−	0.616675i	−0.140447	−	0.990088i	$-0.544854\pi$
$967$	−998780.	−	576646.i	−1.06811	−	0.616675i	−0.927665	+	0.373413i	$0.878187\pi$
$968$	496745.	+	321552.i	0.530131	+	0.343163i
$969$		0			0
$970$	−1.45111e6	−	870949.i	−1.54226	−	0.925656i
$971$		−	438562.i		−	0.465149i	−0.972579	−	0.232575i	$-0.925285\pi$
$971$		−	438562.i		−	0.465149i	0.972579	−	0.232575i	$-0.0747150\pi$
$972$		0			0
$973$	−985213.			−1.04065
$974$	−565900.	+	942864.i	−0.596516	+	0.993873i
$975$		0			0
$976$	219809.	+	14937.3i	0.230752	+	0.0156810i
$977$	388615.	−	673100.i	0.407127	−	0.705165i	−0.587439	−	0.809268i	$-0.699864\pi$
$977$	388615.	−	673100.i	0.407127	−	0.705165i	0.994566	+	0.104103i	$0.0331972\pi$
$978$		0			0
$979$	486839.	−	281076.i	0.507948	−	0.293264i
$980$	76012.8	−	121912.i	0.0791470	−	0.126939i
$981$		0			0
$982$	62838.4	+	113233.i	0.0651632	+	0.117422i
$983$	−695782.	+	401710.i	−0.720056	+	0.415724i	−0.814773	−	0.579780i	$-0.803139\pi$
$983$	−695782.	+	401710.i	−0.720056	+	0.415724i	0.0947175	+	0.995504i	$0.469805\pi$
$984$		0			0
$985$	−350602.	+	607260.i	−0.361362	+	0.625897i
$986$	−8826.81	+	520310.i	−0.00907925	+	0.535190i
$987$		0			0
$988$	51676.5	−	1.52264e6i	0.0529394	−	1.55985i
$989$	846405.			0.865338
$990$		0			0
$991$		−	206876.i		−	0.210651i	−0.994438	−	0.105325i	$-0.966412\pi$
$991$		−	206876.i		−	0.210651i	0.994438	−	0.105325i	$-0.0335884\pi$
$992$	−1.16071e6	−	98681.8i	−1.17951	−	0.100280i
$993$		0			0
$994$	29965.6	−	1.76637e6i	0.0303285	−	1.78776i
$995$	156771.	+	90511.8i	0.158351	+	0.0914238i
$996$		0			0
$997$	14831.3	+	25688.6i	0.0149207	+	0.0258435i	0.873389	−	0.487023i	$-0.161917\pi$
$997$	14831.3	+	25688.6i	0.0149207	+	0.0258435i	−0.858469	+	0.512866i	$0.828584\pi$
$998$	563546.	+	1.01549e6i	0.565807	+	1.01956i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.f.a.91.5		44
3.2	odd	2		36.5.f.a.31.18	yes	44
4.3	odd	2	inner	108.5.f.a.91.11		44
9.2	odd	6		36.5.f.a.7.12	✓	44
9.4	even	3		324.5.d.e.163.19		22
9.5	odd	6		324.5.d.f.163.4		22
9.7	even	3	inner	108.5.f.a.19.11		44
12.11	even	2		36.5.f.a.31.12	yes	44
36.7	odd	6	inner	108.5.f.a.19.5		44
36.11	even	6		36.5.f.a.7.18	yes	44
36.23	even	6		324.5.d.f.163.3		22
36.31	odd	6		324.5.d.e.163.20		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.12	✓	44	9.2	odd	6
36.5.f.a.7.18	yes	44	36.11	even	6
36.5.f.a.31.12	yes	44	12.11	even	2
36.5.f.a.31.18	yes	44	3.2	odd	2
108.5.f.a.19.5		44	36.7	odd	6	inner
108.5.f.a.19.11		44	9.7	even	3	inner
108.5.f.a.91.5		44	1.1	even	1	trivial
108.5.f.a.91.11		44	4.3	odd	2	inner
324.5.d.e.163.19		22	9.4	even	3
324.5.d.e.163.20		22	36.31	odd	6
324.5.d.f.163.3		22	36.23	even	6
324.5.d.f.163.4		22	9.5	odd	6

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.42968 - 2.05847i) q^{2} +(7.52540 + 14.1198i) q^{4} +(-16.6139 + 28.7760i) q^{5} +(-39.9759 + 23.0801i) q^{7} +(3.25547 - 63.9171i) q^{8} +O(q^{10})\)	\(q+(-3.42968 - 2.05847i) q^{2} +(7.52540 + 14.1198i) q^{4} +(-16.6139 + 28.7760i) q^{5} +(-39.9759 + 23.0801i) q^{7} +(3.25547 - 63.9171i) q^{8} +(116.215 - 64.4935i) q^{10} +(-63.6109 + 36.7258i) q^{11} +(151.520 - 262.440i) q^{13} +(184.614 + 3.13190i) q^{14} +(-142.737 + 212.514i) q^{16} +182.019 q^{17} -314.215i q^{19} +(-531.337 - 18.0330i) q^{20} +(293.764 + 4.98356i) q^{22} +(-290.919 - 167.962i) q^{23} +(-239.540 - 414.896i) q^{25} +(-1059.89 + 588.185i) q^{26} +(-626.721 - 390.765i) q^{28} +(-357.370 - 618.983i) q^{29} +(-985.186 - 568.798i) q^{31} +(926.995 - 435.035i) q^{32} +(-624.267 - 374.681i) q^{34} -1533.80i q^{35} +1008.45 q^{37} +(-646.803 + 1077.66i) q^{38} +(1785.20 + 1155.59i) q^{40} +(557.553 - 965.709i) q^{41} +(-2182.06 + 1259.82i) q^{43} +(-997.257 - 621.796i) q^{44} +(652.014 + 1174.90i) q^{46} +(980.476 - 566.078i) q^{47} +(-135.117 + 234.029i) q^{49} +(-32.5048 + 1916.05i) q^{50} +(4845.84 + 164.462i) q^{52} +1057.77 q^{53} -2440.63i q^{55} +(1345.07 + 2630.28i) q^{56} +(-48.4939 + 2858.55i) q^{58} +(878.476 + 507.188i) q^{59} +(-430.304 - 745.308i) q^{61} +(2208.02 + 3978.77i) q^{62} +(-4074.80 - 416.161i) q^{64} +(5034.65 + 8720.27i) q^{65} +(-559.041 - 322.762i) q^{67} +(1369.76 + 2570.07i) q^{68} +(-3157.28 + 5260.44i) q^{70} -9567.89i q^{71} +1899.10 q^{73} +(-3458.66 - 2075.86i) q^{74} +(4436.65 - 2364.59i) q^{76} +(1695.27 - 2936.29i) q^{77} +(6768.11 - 3907.57i) q^{79} +(-3743.90 - 7638.08i) q^{80} +(-3900.11 + 2164.37i) q^{82} +(-7052.56 + 4071.80i) q^{83} +(-3024.04 + 5237.78i) q^{85} +(10077.1 + 170.953i) q^{86} +(2140.32 + 4185.39i) q^{88} -7653.39 q^{89} +13988.4i q^{91} +(182.309 - 5371.70i) q^{92} +(-4527.97 - 76.8149i) q^{94} +(9041.87 + 5220.33i) q^{95} +(-6366.75 - 11027.5i) q^{97} +(945.149 - 524.510i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

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