LMFDB - Embedded newform 108.5.f.a.19.11

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			19.11
Character	$\chi$	$=$	108.19
Dual form			108.5.f.a.91.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0678484 + 3.99942i) q^{2} +(-15.9908 - 0.542709i) q^{4} +(-16.6139 - 28.7760i) q^{5} +(39.9759 + 23.0801i) q^{7} +(3.25547 - 63.9171i) q^{8} +O(q^{10})$	\(q+(-0.0678484 + 3.99942i) q^{2} +(-15.9908 - 0.542709i) q^{4} +(-16.6139 - 28.7760i) q^{5} +(39.9759 + 23.0801i) q^{7} +(3.25547 - 63.9171i) q^{8} +(116.215 - 64.4935i) q^{10} +(63.6109 + 36.7258i) q^{11} +(151.520 + 262.440i) q^{13} +(-95.0195 + 158.315i) q^{14} +(255.411 + 17.3567i) q^{16} +182.019 q^{17} -314.215i q^{19} +(250.052 + 469.168i) q^{20} +(-151.198 + 251.915i) q^{22} +(290.919 - 167.962i) q^{23} +(-239.540 + 414.896i) q^{25} +(-1059.89 + 588.185i) q^{26} +(-626.721 - 390.765i) q^{28} +(-357.370 + 618.983i) q^{29} +(985.186 - 568.798i) q^{31} +(-86.7460 + 1020.32i) q^{32} +(-12.3497 + 727.971i) q^{34} -1533.80i q^{35} +1008.45 q^{37} +(1256.68 + 21.3190i) q^{38} +(-1893.37 + 968.231i) q^{40} +(557.553 + 965.709i) q^{41} +(2182.06 + 1259.82i) q^{43} +(-997.257 - 621.796i) q^{44} +(652.014 + 1174.90i) q^{46} +(-980.476 - 566.078i) q^{47} +(-135.117 - 234.029i) q^{49} +(-1643.09 - 986.173i) q^{50} +(-2280.49 - 4278.85i) q^{52} +1057.77 q^{53} -2440.63i q^{55} +(1605.36 - 2480.01i) q^{56} +(-2451.33 - 1471.27i) q^{58} +(-878.476 + 507.188i) q^{59} +(-430.304 + 745.308i) q^{61} +(2208.02 + 3978.77i) q^{62} +(-4074.80 - 416.161i) q^{64} +(5034.65 - 8720.27i) q^{65} +(559.041 - 322.762i) q^{67} +(-2910.63 - 98.7833i) q^{68} +(6134.31 + 104.066i) q^{70} -9567.89i q^{71} +1899.10 q^{73} +(-68.4216 + 4033.22i) q^{74} +(-170.527 + 5024.55i) q^{76} +(1695.27 + 2936.29i) q^{77} +(-6768.11 - 3907.57i) q^{79} +(-3743.90 - 7638.08i) q^{80} +(-3900.11 + 2164.37i) q^{82} +(7052.56 + 4071.80i) q^{83} +(-3024.04 - 5237.78i) q^{85} +(-5186.58 + 8641.52i) q^{86} +(2554.49 - 3946.27i) q^{88} -7653.39 q^{89} +13988.4i q^{91} +(-4743.18 + 2527.96i) q^{92} +(2330.51 - 3882.93i) q^{94} +(-9041.87 + 5220.33i) q^{95} +(-6366.75 + 11027.5i) q^{97} +(945.149 - 524.510i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.0678484	+	3.99942i	−0.0169621	+	0.999856i
$2$	−0.0678484	+	3.99942i	−0.0169621	+	0.999856i
$3$		0			0
$3$		0			0
$4$	−15.9908	−	0.542709i	−0.999425	−	0.0339193i
$5$	−16.6139	−	28.7760i	−0.664554	−	1.15104i	−0.979406	−	0.201901i	$-0.935288\pi$
$5$	−16.6139	−	28.7760i	−0.664554	−	1.15104i	0.314852	−	0.949141i	$-0.398045\pi$
$6$		0			0
$7$	39.9759	+	23.0801i	0.815835	+	0.471023i	0.848978	−	0.528428i	$-0.177218\pi$
$7$	39.9759	+	23.0801i	0.815835	+	0.471023i	−0.0331429	+	0.999451i	$0.510552\pi$
$8$	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	$-0.235172\pi$
$11$	63.6109	+	36.7258i	0.525710	+	0.303519i	−0.213558	+	0.976930i	$0.568505\pi$
$12$		0			0
$13$	151.520	+	262.440i	0.896566	+	1.55290i	0.831855	+	0.554993i	$0.187279\pi$
$13$	151.520	+	262.440i	0.896566	+	1.55290i	0.0647110	+	0.997904i	$0.479387\pi$
$14$	−95.0195	+	158.315i	−0.484793	+	0.807728i
$15$		0			0
$16$	255.411	+	17.3567i	0.997699	+	0.0677996i
$17$	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	$-0.143323\pi$
$20$	250.052	+	469.168i	0.625129	+	1.17292i
$21$		0			0
$22$	−151.198	+	251.915i	−0.312392	+	0.520486i
$23$	290.919	−	167.962i	0.549941	−	0.317509i	−0.199157	−	0.979968i	$-0.563820\pi$
$23$	290.919	−	167.962i	0.549941	−	0.317509i	0.749098	+	0.662459i	$0.230487\pi$
$24$		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	−0.996414	−	0.0846079i	$-0.973036\pi$
$29$	−357.370	+	618.983i	−0.424935	+	0.736008i	0.571480	+	0.820616i	$0.306370\pi$
$30$		0			0
$31$	985.186	−	568.798i	1.02517	−	0.591881i	0.109571	−	0.993979i	$-0.465052\pi$
$31$	985.186	−	568.798i	1.02517	−	0.591881i	0.915597	+	0.402098i	$0.131719\pi$
$32$	−86.7460	+	1020.32i	−0.0847129	+	0.996405i
$33$		0			0
$34$	−12.3497	+	727.971i	−0.0106831	+	0.629733i
$35$		−	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	$0.379934\pi$
$38$	1256.68	+	21.3190i	0.870277	+	0.0147638i
$39$		0			0
$40$	−1893.37	+	968.231i	−1.18336	+	0.605144i
$41$	557.553	+	965.709i	0.331679	+	0.574485i	0.982841	−	0.184454i	$-0.0590516\pi$
$41$	557.553	+	965.709i	0.331679	+	0.574485i	−0.651162	+	0.758939i	$0.725718\pi$
$42$		0			0
$43$	2182.06	+	1259.82i	1.18013	+	0.681349i	0.956045	−	0.293220i	$-0.0947268\pi$
$43$	2182.06	+	1259.82i	1.18013	+	0.681349i	0.224087	+	0.974569i	$0.428060\pi$
$44$	−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	$-0.415824\pi$
$47$	−980.476	−	566.078i	−0.443855	−	0.256260i	−0.705232	+	0.708977i	$0.749157\pi$
$48$		0			0
$49$	−135.117	−	234.029i	−0.0562752	−	0.0974714i
$50$	−1643.09	−	986.173i	−0.657237	−	0.394469i
$51$		0			0
$52$	−2280.49	−	4278.85i	−0.843377	−	1.58241i
$53$	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
$56$	1605.36	−	2480.01i	0.511912	−	0.790820i
$57$		0			0
$58$	−2451.33	−	1471.27i	−0.728695	−	0.437358i
$59$	−878.476	+	507.188i	−0.252363	+	0.145702i	−0.620846	−	0.783933i	$-0.713211\pi$
$59$	−878.476	+	507.188i	−0.252363	+	0.145702i	0.368483	+	0.929635i	$0.379877\pi$
$60$		0			0
$61$	−430.304	+	745.308i	−0.115642	+	0.200298i	−0.918036	−	0.396497i	$-0.870226\pi$
$61$	−430.304	+	745.308i	−0.115642	+	0.200298i	0.802394	+	0.596794i	$0.203559\pi$
$62$	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	$-0.643760\pi$
$67$	559.041	−	322.762i	0.124536	−	0.0719008i	0.560974	+	0.827834i	$0.310427\pi$
$68$	−2910.63	−	98.7833i	−0.629461	−	0.0213632i
$69$		0			0
$70$	6134.31	+	104.066i	1.25190	+	0.0212379i
$71$		−	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	$0.442977\pi$
$74$	−68.4216	+	4033.22i	−0.0124948	+	0.736526i
$75$		0			0
$76$	−170.527	+	5024.55i	−0.0295234	+	0.869902i
$77$	1695.27	+	2936.29i	0.285928	+	0.495242i
$78$		0			0
$79$	−6768.11	−	3907.57i	−1.08446	−	0.626113i	−0.152363	−	0.988325i	$-0.548688\pi$
$79$	−6768.11	−	3907.57i	−1.08446	−	0.626113i	−0.932096	+	0.362212i	$0.882022\pi$
$80$	−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	$-0.132044\pi$
$83$	7052.56	+	4071.80i	1.02374	+	0.591058i	0.108556	+	0.994090i	$0.465377\pi$
$84$		0			0
$85$	−3024.04	−	5237.78i	−0.418552	−	0.724953i
$86$	−5186.58	+	8641.52i	−0.701269	+	1.16840i
$87$		0			0
$88$	2554.49	−	3946.27i	0.329867	−	0.509590i
$89$	−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
$92$	−4743.18	+	2527.96i	−0.560395	+	0.298673i
$93$		0			0
$94$	2330.51	−	3882.93i	0.263752	−	0.439445i
$95$	−9041.87	+	5220.33i	−1.00187	+	0.578430i
$96$		0			0
$97$	−6366.75	+	11027.5i	−0.676666	+	1.17202i	0.299313	+	0.954155i	$0.403243\pi$
$97$	−6366.75	+	11027.5i	−0.676666	+	1.17202i	−0.975979	+	0.217865i	$0.930091\pi$
$98$	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	0.303048	+	0.952975i	$0.401996\pi$
$101$	−6873.20	+	11904.7i	−0.673777	+	1.16702i	−0.976825	+	0.214040i	$0.931338\pi$
$102$		0			0
$103$	11251.5	−	6496.03i	1.06056	−	0.612313i	0.134971	−	0.990850i	$-0.456906\pi$
$103$	11251.5	−	6496.03i	1.06056	−	0.612313i	0.925587	+	0.378536i	$0.123572\pi$
$104$	17267.7	−	8830.34i	1.59649	−	0.816414i
$105$		0			0
$106$	−71.7682	+	4230.49i	−0.00638734	+	0.376512i
$107$			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	$0.397233\pi$
$110$	9761.10	+	165.592i	0.806702	+	0.0136853i
$111$		0			0
$112$	9809.70	+	6588.76i	0.782023	+	0.525252i
$113$	−496.140	−	859.339i	−0.0388550	−	0.0672988i	0.845944	−	0.533272i	$-0.179038\pi$
$113$	−496.140	−	859.339i	−0.0388550	−	0.0672988i	−0.884799	+	0.465973i	$0.845704\pi$
$114$		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
$122$	−2951.61	−	1771.54i	−0.198307	−	0.119023i
$123$		0			0
$124$	−16062.6	+	8560.86i	−1.04465	+	0.556767i
$125$	−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	$0.929124\pi$
$128$	1940.87	−	16268.6i	0.118461	−	0.992959i
$129$		0			0
$130$	34534.5	+	20727.4i	2.04346	+	1.22647i
$131$	6027.16	−	3479.78i	0.351212	−	0.202773i	−0.314007	−	0.949421i	$-0.601671\pi$
$131$	6027.16	−	3479.78i	0.351212	−	0.202773i	0.665219	+	0.746648i	$0.268338\pi$
$132$		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	−0.956661	−	0.291204i	$-0.905944\pi$
$137$	−4244.42	+	7351.56i	−0.226140	+	0.391686i	0.730521	+	0.682891i	$0.239277\pi$
$138$		0			0
$139$	−18483.9	+	10671.7i	−0.956673	+	0.552335i	−0.895147	−	0.445770i	$-0.852930\pi$
$139$	−18483.9	+	10671.7i	−0.956673	+	0.552335i	−0.0615252	+	0.998106i	$0.519596\pi$
$140$	−832.406	+	24526.7i	−0.0424697	+	1.25136i
$141$		0			0
$142$	38266.1	+	649.166i	1.89774	+	0.0321943i
$143$			22258.7i			1.08850i
$144$		0			0
$145$	23749.2			1.12957
$146$	−128.851	+	7595.32i	−0.00604481	+	0.356320i
$147$		0			0
$148$	−16125.9	−	547.294i	−0.736208	−	0.0249860i
$149$	−6366.78	−	11027.6i	−0.286779	−	0.496716i	0.686260	−	0.727356i	$-0.259251\pi$
$149$	−6366.78	−	11027.6i	−0.286779	−	0.496716i	−0.973039	+	0.230640i	$0.925918\pi$
$150$		0			0
$151$	−3061.84	−	1767.75i	−0.134285	−	0.0775296i	0.431352	−	0.902184i	$-0.358037\pi$
$151$	−3061.84	−	1767.75i	−0.134285	−	0.0775296i	−0.565638	+	0.824654i	$0.691370\pi$
$152$	−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	−0.992319	−	0.123706i	$-0.960522\pi$
$157$	−14870.6	−	25756.6i	−0.603292	−	1.04493i	0.389027	−	0.921227i	$-0.372811\pi$
$158$	16087.2	−	26803.4i	0.644417	−	1.07368i
$159$		0			0
$160$	30801.9	−	14455.2i	1.20320	−	0.564657i
$161$	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	$-0.0354394\pi$
$164$	−8391.61	−	15745.0i	−0.312002	−	0.585405i
$165$		0			0
$166$	−16763.4	+	27929.9i	−0.608338	+	1.01357i
$167$	17810.7	−	10283.0i	0.638628	−	0.368712i	−0.145458	−	0.989364i	$-0.546465\pi$
$167$	17810.7	−	10283.0i	0.638628	−	0.368712i	0.784086	+	0.620652i	$0.213132\pi$
$168$		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	−0.810465	−	0.585787i	$-0.800785\pi$
$173$	3054.99	−	5291.39i	0.102074	−	0.176798i	0.912539	+	0.408989i	$0.134119\pi$
$174$		0			0
$175$	−19151.7	+	11057.2i	−0.625361	+	0.361053i
$176$	15609.5	+	10484.2i	0.503922	+	0.338463i
$177$		0			0
$178$	519.270	−	30609.1i	0.0163890	−	0.966076i
$179$			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	$0.627475\pi$
$182$	−55945.4	−	949.087i	−1.68897	−	0.0286526i
$183$		0			0
$184$	−9788.59	−	19141.5i	−0.289124	−	0.565380i
$185$	−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	$-0.153474\pi$
$191$	33833.7	+	19533.9i	0.927433	+	0.535454i	0.0414344	+	0.999141i	$0.486807\pi$
$192$		0			0
$193$	−13915.2	−	24101.8i	−0.373572	−	0.647045i	0.616541	−	0.787323i	$-0.288534\pi$
$193$	−13915.2	−	24101.8i	−0.373572	−	0.647045i	−0.990112	+	0.140278i	$0.955200\pi$
$194$	−43671.8	−	26211.5i	−1.16037	−	0.696449i
$195$		0			0
$196$	2033.61	+	3815.64i	0.0529366	+	0.0993242i
$197$	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	$-0.0219125\pi$
$200$	25739.2	+	16661.4i	0.643479	+	0.416535i
$201$		0			0
$202$	−47145.7	−	28296.5i	−1.15542	−	0.693475i
$203$	−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	$-0.383285\pi$
$211$	59935.1	−	34603.5i	1.34622	−	0.777241i	0.987712	+	0.156286i	$0.0499520\pi$
$212$	−16914.6	−	574.063i	−0.376349	−	0.0127729i
$213$		0			0
$214$	−59558.7	−	1010.38i	−1.30052	−	0.0220627i
$215$		−	83721.5i		−	1.81117i
$216$		0			0
$217$	52511.7			1.11516
$218$	−511.510	+	30151.8i	−0.0107632	+	0.634453i
$219$		0			0
$220$	−1324.55	+	39027.5i	−0.0273667	+	0.806354i
$221$	27579.4	+	47769.0i	0.564678	+	0.978051i
$222$		0			0
$223$	−21934.5	−	12663.9i	−0.441080	−	0.254658i	0.262976	−	0.964802i	$-0.415296\pi$
$223$	−21934.5	−	12663.9i	−0.441080	−	0.254658i	−0.704056	+	0.710145i	$0.748629\pi$
$224$	−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	−0.982931	−	0.183975i	$-0.941104\pi$
$227$	−84184.1	−	48603.7i	−1.63372	−	0.943230i	−0.650792	−	0.759256i	$-0.725563\pi$
$228$		0			0
$229$	42946.4	+	74385.3i	0.818947	+	1.41846i	0.906459	+	0.422294i	$0.138775\pi$
$229$	42946.4	+	74385.3i	0.818947	+	1.41846i	−0.0875119	+	0.996163i	$0.527892\pi$
$230$	22976.6	−	38282.1i	0.434341	−	0.723669i
$231$		0			0
$232$	38400.2	+	24857.2i	0.713440	+	0.461823i
$233$	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
$236$	14322.8	−	7633.59i	0.257160	−	0.137058i
$237$		0			0
$238$	−17295.3	+	28816.3i	−0.305334	+	0.508726i
$239$	91748.4	−	52971.0i	1.60621	−	0.927347i	0.616005	−	0.787742i	$-0.288750\pi$
$239$	91748.4	−	52971.0i	1.60621	−	0.927347i	0.990207	−	0.139605i	$-0.0445832\pi$
$240$		0			0
$241$	5089.73	−	8815.67i	0.0876316	−	0.151782i	−0.818878	−	0.573968i	$-0.805404\pi$
$241$	5089.73	−	8815.67i	0.0876316	−	0.151782i	0.906510	+	0.422185i	$0.138737\pi$
$242$	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
$248$	−33148.7	−	64822.0i	−0.538968	−	1.05395i
$249$		0			0
$250$	328.967	−	19391.5i	0.00526347	−	0.310264i
$251$			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
$254$	−28490.0	−	483.319i	−0.441595	−	0.00749146i
$255$		0			0
$256$	64933.5	+	8866.17i	0.990806	+	0.135287i
$257$	27780.7	+	48117.6i	0.420608	+	0.728514i	0.995999	−	0.0893643i	$-0.0284835\pi$
$257$	27780.7	+	48117.6i	0.420608	+	0.728514i	−0.575391	+	0.817878i	$0.695150\pi$
$258$		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	$-0.275110\pi$
$263$	21792.0	+	12581.6i	0.315055	+	0.181897i	−0.334131	+	0.942527i	$0.608443\pi$
$264$		0			0
$265$	−17573.7	−	30438.5i	−0.250248	−	0.433443i
$266$	49744.9	+	29856.6i	0.703049	+	0.421965i
$267$		0			0
$268$	−9114.67	+	4857.83i	−0.126903	+	0.0676352i
$269$	−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	$-0.223720\pi$
$272$	46489.6	+	3159.25i	0.628374	+	0.0427017i
$273$		0			0
$274$	−29114.0	−	17474.0i	−0.387794	−	0.232751i
$275$	−30474.7	+	17594.6i	−0.402972	+	0.232656i
$276$		0			0
$277$	−54019.7	+	93564.9i	−0.704033	+	1.21942i	0.263006	+	0.964794i	$0.415286\pi$
$277$	−54019.7	+	93564.9i	−0.704033	+	1.21942i	−0.967039	+	0.254627i	$0.918047\pi$
$278$	−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	−0.997413	−	0.0718805i	$-0.977100\pi$
$281$	−34463.0	+	59691.7i	−0.436456	+	0.755964i	0.560957	+	0.827845i	$0.310433\pi$
$282$		0			0
$283$	−39154.2	+	22605.7i	−0.488884	+	0.282257i	−0.724111	−	0.689683i	$-0.757750\pi$
$283$	−39154.2	+	22605.7i	−0.488884	+	0.282257i	0.235228	+	0.971940i	$0.424416\pi$
$284$	−5192.58	+	152998.i	−0.0643793	+	1.89692i
$285$		0			0
$286$	−89022.0	−	1510.22i	−1.08834	−	0.0184632i
$287$			51473.5i			0.624914i
$288$		0			0
$289$	−50390.1			−0.603323
$290$	−1611.34	+	94983.0i	−0.0191598	+	1.12941i
$291$		0			0
$292$	−30368.2	−	1030.66i	−0.356167	−	0.0120879i
$293$	−35853.6	−	62100.3i	−0.417636	−	0.723366i	0.578065	−	0.815990i	$-0.303808\pi$
$293$	−35853.6	−	62100.3i	−0.417636	−	0.723366i	−0.995701	+	0.0926242i	$0.970474\pi$
$294$		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
$302$	7277.73	−	12125.6i	0.0797962	−	0.132951i
$303$		0			0
$304$	5453.74	−	80254.0i	0.0590129	−	0.868400i
$305$	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	$0.830170\pi$
$308$	−25515.2	−	47873.7i	−0.268966	−	0.504656i
$309$		0			0
$310$	77809.5	−	129641.i	0.809673	−	1.34902i
$311$	−20844.0	+	12034.3i	−0.215506	+	0.124423i	−0.603868	−	0.797085i	$-0.706374\pi$
$311$	−20844.0	+	12034.3i	−0.215506	+	0.124423i	0.388362	+	0.921507i	$0.373041\pi$
$312$		0			0
$313$	49654.5	−	86004.2i	0.506839	−	0.877871i	−0.493130	−	0.869956i	$-0.664147\pi$
$313$	49654.5	−	86004.2i	0.506839	−	0.877871i	0.999969	−	0.00791525i	$-0.00251953\pi$
$314$	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	−0.679402	−	0.733766i	$-0.737761\pi$
$317$	29720.5	−	51477.4i	0.295759	−	0.512269i	0.975161	+	0.221497i	$0.0710942\pi$
$318$		0			0
$319$	−45465.2	+	26249.4i	−0.446785	+	0.257951i
$320$	55722.7	+	124171.i	0.544167	+	1.21261i
$321$		0			0
$322$	−1052.08	+	62016.5i	−0.0101470	+	0.598129i
$323$		−	57193.1i		−	0.548200i
$324$		0			0
$325$	−145180.			−1.37449
$326$	23612.5	+	400.574i	0.222181	+	0.00376919i
$327$		0			0
$328$	63540.5	−	32493.3i	0.590613	−	0.302028i
$329$	−26130.3	−	45259.0i	−0.241408	−	0.418132i
$330$		0			0
$331$	−79852.0	−	46102.6i	−0.728836	−	0.420794i	0.0891599	−	0.996017i	$-0.471582\pi$
$331$	−79852.0	−	46102.6i	−0.728836	−	0.420794i	−0.817996	+	0.575223i	$0.804915\pi$
$332$	−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	0.747094	−	0.664719i	$-0.231449\pi$
$337$	−22954.2	−	39757.8i	−0.202117	−	0.350076i	−0.949210	+	0.314643i	$0.898115\pi$
$338$	−217002.	−	130243.i	−1.89946	−	1.14004i
$339$		0			0
$340$	45514.1	+	85397.5i	0.393721	+	0.738733i
$341$	83558.1			0.718588
$342$		0			0
$343$		−	123305.i		−	1.04807i
$344$	87627.4	−	135370.i	0.740497	−	1.14395i
$345$		0			0
$346$	20955.3	+	12577.2i	0.175041	+	0.105059i
$347$	−131615.	+	75987.9i	−1.09306	+	0.631081i	−0.934391	−	0.356250i	$-0.884055\pi$
$347$	−131615.	+	75987.9i	−1.09306	+	0.631081i	−0.158674	+	0.987331i	$0.550722\pi$
$348$		0			0
$349$	93645.6	−	162199.i	0.768841	−	1.33167i	−0.169350	−	0.985556i	$-0.554167\pi$
$349$	93645.6	−	162199.i	0.768841	−	1.33167i	0.938192	−	0.346116i	$-0.112500\pi$
$350$	−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	−0.760408	−	0.649446i	$-0.775001\pi$
$353$	22707.8	−	39331.1i	0.182232	−	0.315636i	0.942640	+	0.333810i	$0.108334\pi$
$354$		0			0
$355$	−275326.	+	158960.i	−2.18469	+	1.26133i
$356$	122384.	+	4153.56i	0.965659	+	0.0327733i
$357$		0			0
$358$	−46132.5	−	782.617i	−0.359949	−	0.00610637i
$359$		−	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
$362$	1733.13	−	102162.i	0.0132256	−	0.779601i
$363$		0			0
$364$	7591.61	−	223685.i	0.0572969	−	1.68824i
$365$	−31551.4	−	54648.7i	−0.236828	−	0.410199i
$366$		0			0
$367$	−57406.0	−	33143.4i	−0.426211	−	0.246073i	0.271520	−	0.962433i	$-0.412474\pi$
$367$	−57406.0	−	33143.4i	−0.426211	−	0.246073i	−0.697731	+	0.716360i	$0.745807\pi$
$368$	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	−0.999828	−	0.0185223i	$-0.994104\pi$
$373$	−71784.3	−	124334.i	−0.515955	−	0.893660i	0.483873	−	0.875138i	$-0.339229\pi$
$374$	−27520.9	+	45853.3i	−0.196752	+	0.327814i
$375$		0			0
$376$	−39374.0	+	60826.4i	−0.278506	+	0.430245i
$377$	−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	$0.779917\pi$
$380$	147420.	−	78570.1i	1.02091	−	0.544114i
$381$		0			0
$382$	−80419.9	+	133990.i	−0.551108	+	0.918218i
$383$	−15175.9	+	8761.79i	−0.103456	+	0.0597303i	−0.550835	−	0.834614i	$-0.685691\pi$
$383$	−15175.9	+	8761.79i	−0.103456	+	0.0597303i	0.447379	+	0.894344i	$0.352357\pi$
$384$		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	−0.710646	−	0.703549i	$-0.751597\pi$
$389$	38430.8	−	66564.0i	0.253968	−	0.439886i	0.964615	+	0.263663i	$0.0849307\pi$
$390$		0			0
$391$	52952.8	−	30572.3i	0.346366	−	0.199974i
$392$	−15398.3	+	7874.40i	−0.100208	+	0.0512443i
$393$		0			0
$394$	−1431.80	+	84399.8i	−0.00922340	+	0.543687i
$395$			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	$0.574698\pi$
$398$	21788.8	+	369.636i	0.137552	+	0.00233350i
$399$		0			0
$400$	−68382.4	+	101811.i	−0.427390	+	0.636321i
$401$	142274.	+	246426.i	0.884784	+	1.53249i	0.845961	+	0.533244i	$0.179027\pi$
$401$	142274.	+	246426.i	0.884784	+	1.53249i	0.0388226	+	0.999246i	$0.487639\pi$
$402$		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	0.984097	−	0.177632i	$-0.0568435\pi$
$409$	56577.0	+	97994.2i	0.338215	+	0.585806i	−0.645882	+	0.763437i	$0.723510\pi$
$410$	127078.	+	76271.3i	0.755965	+	0.453725i
$411$		0			0
$412$	−183445.	+	97770.4i	−1.08072	+	0.575988i
$413$	−46823.9			−0.274516
$414$		0			0
$415$		−	270593.i		−	1.57116i
$416$	−280916.	+	131833.i	−1.62327	+	0.761793i
$417$		0			0
$418$	79155.6	+	47508.7i	0.453032	+	0.271907i
$419$	−237314.	+	137013.i	−1.35175	+	0.780431i	−0.988494	−	0.151260i	$-0.951667\pi$
$419$	−237314.	+	137013.i	−1.35175	+	0.780431i	−0.363252	+	0.931691i	$0.618334\pi$
$420$		0			0
$421$	−6241.89	+	10811.3i	−0.0352170	+	0.0609976i	−0.883097	−	0.469191i	$-0.844546\pi$
$421$	−6241.89	+	10811.3i	−0.0352170	+	0.0609976i	0.847880	+	0.530189i	$0.177879\pi$
$422$	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
$428$	8081.91	−	238132.i	0.0441191	−	1.29996i
$429$		0			0
$430$	334838.	+	5680.37i	1.81091	+	0.0307213i
$431$		−	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	$0.771531\pi$
$434$	−3562.83	+	210016.i	−0.0189154	+	1.11500i
$435$		0			0
$436$	−120555.	−	4091.49i	−0.634179	−	0.0215233i
$437$	−52776.3	−	91411.2i	−0.276360	−	0.478670i
$438$		0			0
$439$	−148459.	−	85712.8i	−0.770331	−	0.444751i	0.0626618	−	0.998035i	$-0.480041\pi$
$439$	−148459.	−	85712.8i	−0.770331	−	0.444751i	−0.832993	+	0.553284i	$0.813374\pi$
$440$	−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	$-0.265502\pi$
$443$	71888.2	+	41504.7i	0.366311	+	0.211490i	−0.305535	+	0.952181i	$0.598835\pi$
$444$		0			0
$445$	127152.	+	220234.i	0.642102	+	1.11215i
$446$	52136.4	−	86866.0i	0.262103	−	0.436697i
$447$		0			0
$448$	−153289.	−	110683.i	−0.763757	−	0.551476i
$449$	−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
$452$	7467.29	+	14010.8i	0.0365499	+	0.0685780i
$453$		0			0
$454$	200099.	−	333390.i	0.970806	−	1.61749i
$455$	402530.	−	232401.i	1.94435	−	1.12257i
$456$		0			0
$457$	9489.80	−	16436.8i	0.0454386	−	0.0787019i	−0.842412	−	0.538835i	$-0.818865\pi$
$457$	9489.80	−	16436.8i	0.0454386	−	0.0787019i	0.887850	+	0.460133i	$0.152198\pi$
$458$	−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	−0.998789	−	0.0492038i	$-0.984332\pi$
$461$	−97075.9	+	168140.i	−0.456783	+	0.791171i	0.542006	+	0.840375i	$0.317665\pi$
$462$		0			0
$463$	−86227.9	+	49783.7i	−0.402240	+	0.232234i	−0.687450	−	0.726232i	$-0.741270\pi$
$463$	−86227.9	+	49783.7i	−0.402240	+	0.232234i	0.285210	+	0.958465i	$0.407937\pi$
$464$	−102020.	+	151892.i	−0.473858	+	0.705504i
$465$		0			0
$466$	−866.698	+	51088.8i	−0.00399113	+	0.235263i
$467$		−	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
$470$	−150454.	−	2552.38i	−0.681096	−	0.0115545i
$471$		0			0
$472$	29558.2	+	57800.8i	0.132676	+	0.259448i
$473$	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	$-0.372227\pi$
$479$	−48437.8	−	27965.6i	−0.211112	−	0.121886i	−0.601828	+	0.798626i	$0.705561\pi$
$480$		0			0
$481$	152800.	+	264657.i	0.660439	+	1.14391i
$482$	34912.3	+	20954.1i	0.150274	+	0.0901935i
$483$		0			0
$484$	69578.9	+	130550.i	0.297021	+	0.557295i
$485$	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	$-0.196780\pi$
$488$	46237.1	+	29930.1i	0.194156	+	0.125681i
$489$		0			0
$490$	−30795.9	−	18483.5i	−0.128263	−	0.0769825i
$491$	28037.6	−	16187.5i	0.116299	−	0.0671455i	−0.440722	−	0.897644i	$-0.645277\pi$
$491$	28037.6	−	16187.5i	0.116299	−	0.0671455i	0.557021	+	0.830498i	$0.311944\pi$
$492$		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	$-0.468538\pi$
$499$	251446.	−	145172.i	1.00982	−	0.583019i	0.911139	+	0.412100i	$0.135204\pi$
$500$	77532.4	+	2631.36i	0.310130	+	0.0105254i
$501$		0			0
$502$	−87380.0	−	1482.36i	−0.346740	−	0.00588229i
$503$			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
$506$	−1674.10	+	98682.4i	−0.00653854	+	0.385424i
$507$		0			0
$508$	3865.99	−	113911.i	0.0149808	−	0.441405i
$509$	−146376.	−	253530.i	−0.564980	−	0.978575i	−0.997052	−	0.0767350i	$-0.975550\pi$
$509$	−146376.	−	253530.i	−0.564980	−	0.978575i	0.432071	−	0.901839i	$-0.357783\pi$
$510$		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
$518$	−95822.3	+	159652.i	−0.357114	+	0.594999i
$519$		0			0
$520$	−540985.	−	350189.i	−2.00068	−	1.29508i
$521$	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	$-0.0463198\pi$
$524$	−98267.5	+	52373.4i	−0.357888	+	0.190743i
$525$		0			0
$526$	−51797.9	+	86302.0i	−0.187215	+	0.311924i
$527$	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
$536$	−18810.1	−	36783.1i	−0.0654729	−	0.128032i
$537$		0			0
$538$	3674.26	−	216585.i	0.0126942	−	0.748278i
$539$		−	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	$0.407722\pi$
$542$	379715.	+	6441.69i	1.29259	+	0.0219281i
$543$		0			0
$544$	−15789.4	+	185717.i	−0.0533541	+	0.627559i
$545$	−125252.	−	216943.i	−0.421689	−	0.730387i
$546$		0			0
$547$	−246877.	−	142535.i	−0.825100	−	0.476372i	0.0270722	−	0.999633i	$-0.491382\pi$
$547$	−246877.	−	142535.i	−0.825100	−	0.476372i	−0.852172	+	0.523262i	$0.824715\pi$
$548$	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
$554$	−370541.	−	222396.i	−1.20730	−	0.724616i
$555$		0			0
$556$	301363.	−	160617.i	0.974857	−	0.519568i
$557$	−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
$560$	26621.7	−	391749.i	0.0848905	−	1.24920i
$561$		0			0
$562$	−236394.	−	141882.i	−0.748452	−	0.449216i
$563$	2488.80	−	1436.91i	0.00785187	−	0.00453328i	−0.496069	−	0.868283i	$-0.665224\pi$
$563$	2488.80	−	1436.91i	0.00785187	−	0.00453328i	0.503921	+	0.863750i	$0.331890\pi$
$564$		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	−0.940395	−	0.340085i	$-0.889544\pi$
$569$	−56876.7	+	98513.3i	−0.175675	+	0.304278i	0.764720	+	0.644363i	$0.222877\pi$
$570$		0			0
$571$	−27258.4	+	15737.7i	−0.0836043	+	0.0482689i	−0.541219	−	0.840881i	$-0.682037\pi$
$571$	−27258.4	+	15737.7i	−0.0836043	+	0.0482689i	0.457615	+	0.889150i	$0.348704\pi$
$572$	12080.0	−	355934.i	0.0369211	−	1.08787i
$573$		0			0
$574$	−205864.	−	3492.39i	−0.624824	−	0.0105998i
$575$			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	$0.941526\pi$
$578$	3418.89	−	201531.i	0.0102336	−	0.603236i
$579$		0			0
$580$	−379768.	−	12888.9i	−1.12892	−	0.0383142i
$581$	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	−0.987609	−	0.156937i	$-0.949838\pi$
$587$	−557280.	−	321746.i	−1.61732	−	0.933763i	−0.629716	−	0.776825i	$-0.716829\pi$
$588$		0			0
$589$	−178725.	−	309561.i	−0.515175	−	0.892309i
$590$	−69381.6	+	115599.i	−0.199315	+	0.332085i
$591$		0			0
$592$	257569.	+	17503.3i	0.734937	+	0.0499433i
$593$	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
$596$	95825.2	+	179795.i	0.269766	+	0.506158i
$597$		0			0
$598$	−209549.	+	349135.i	−0.585980	+	0.976318i
$599$	−24104.3	+	13916.6i	−0.0671800	+	0.0387864i	−0.533214	−	0.845981i	$-0.679016\pi$
$599$	−24104.3	+	13916.6i	−0.0671800	+	0.0387864i	0.466034	+	0.884767i	$0.345683\pi$
$600$		0			0
$601$	135764.	−	235150.i	0.375868	−	0.651022i	−0.614589	−	0.788848i	$-0.710678\pi$
$601$	135764.	−	235150.i	0.375868	−	0.651022i	0.990457	+	0.137826i	$0.0440113\pi$
$602$	−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	$-0.623141\pi$
$607$	86991.8	−	50224.8i	0.236103	−	0.136314i	0.613384	+	0.789785i	$0.289808\pi$
$608$	320600.	+	27256.9i	0.867274	+	0.0737343i
$609$		0			0
$610$	−1940.19	+	114368.i	−0.00521417	+	0.307357i
$611$		−	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	$0.291185\pi$
$614$	−383412.	−	6504.41i	−1.01702	−	0.0172533i
$615$		0			0
$616$	193198.	−	98797.8i	0.509146	−	0.260367i
$617$	−237317.	−	411046.i	−0.623389	−	1.07974i	−0.988850	−	0.148915i	$-0.952422\pi$
$617$	−237317.	−	411046.i	−0.623389	−	1.07974i	0.365461	−	0.930827i	$-0.380911\pi$
$618$		0			0
$619$	−5714.30	−	3299.15i	−0.0149136	−	0.00861036i	0.492525	−	0.870298i	$-0.336074\pi$
$619$	−5714.30	−	3299.15i	−0.0149136	−	0.00861036i	−0.507438	+	0.861688i	$0.669407\pi$
$620$	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
$626$	340598.	+	204425.i	0.869148	+	0.521657i
$627$		0			0
$628$	223814.	+	419938.i	0.567502	+	1.06479i
$629$	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	$-0.0412655\pi$
$632$	−271794.	+	419877.i	−0.680465	+	1.05121i
$633$		0			0
$634$	203864.	+	122358.i	0.507179	+	0.304405i
$635$	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	−0.507356	−	0.861736i	$-0.669377\pi$
$641$	202403.	−	350572.i	0.492607	−	0.853221i	0.999964	+	0.00851530i	$0.00271054\pi$
$642$		0			0
$643$	−426111.	+	246015.i	−1.03063	+	0.595032i	−0.917164	−	0.398510i	$-0.869527\pi$
$643$	−426111.	+	246015.i	−1.03063	+	0.595032i	−0.113462	+	0.993542i	$0.536194\pi$
$644$	−247959.	−	8415.43i	−0.597871	−	0.0202911i
$645$		0			0
$646$	228740.	+	3880.46i	0.548121	+	0.00929861i
$647$			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
$650$	9850.24	−	580637.i	0.0233142	−	1.37429i
$651$		0			0
$652$	−3204.13	+	94409.1i	−0.00753729	+	0.222085i
$653$	97661.8	+	169155.i	0.229033	+	0.396697i	0.957522	−	0.288361i	$-0.0931103\pi$
$653$	97661.8	+	169155.i	0.229033	+	0.396697i	−0.728489	+	0.685058i	$0.759777\pi$
$654$		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	0.996929	+	0.0783055i	$0.0249510\pi$
$659$	678872.	+	391947.i	1.56321	+	0.902519i	0.566279	+	0.824213i	$0.308382\pi$
$660$		0			0
$661$	−371075.	−	642721.i	−0.849295	−	1.47102i	−0.881838	−	0.471552i	$-0.843694\pi$
$661$	−371075.	−	642721.i	−0.849295	−	1.47102i	0.0325431	−	0.999470i	$-0.489639\pi$
$662$	189802.	−	316234.i	0.433096	−	0.721594i
$663$		0			0
$664$	283217.	−	437524.i	0.642367	−	0.992352i
$665$	−481943.			−1.08981
$666$		0			0
$667$			240099.i			0.539682i
$668$	−290388.	+	154768.i	−0.650767	+	0.346838i
$669$		0			0
$670$	44152.8	−	73564.3i	0.0983577	−	0.163877i
$671$	−54744.0	+	31606.5i	−0.121588	+	0.0701990i
$672$		0			0
$673$	−211601.	+	366503.i	−0.467183	+	0.809185i	−0.999297	−	0.0374878i	$-0.988064\pi$
$673$	−211601.	+	366503.i	−0.467183	+	0.809185i	0.532114	+	0.846673i	$0.321398\pi$
$674$	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	−0.647459	−	0.762100i	$-0.724168\pi$
$677$	154122.	−	266947.i	0.336269	−	0.582435i	0.983728	+	0.179665i	$0.0575015\pi$
$678$		0			0
$679$	−509034.	+	293891.i	−1.10410	+	0.637450i
$680$	−344629.	+	176236.i	−0.745305	+	0.381134i
$681$		0			0
$682$	−5669.28	+	334184.i	−0.0121887	+	0.718484i
$683$			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
$686$	493148.	+	8366.02i	1.04792	+	0.0177775i
$687$		0			0
$688$	535457.	+	359644.i	1.13122	+	0.759794i
$689$	160273.	+	277602.i	0.337616	+	0.584768i
$690$		0			0
$691$	−313235.	−	180846.i	−0.656016	−	0.378751i	0.134742	−	0.990881i	$-0.456980\pi$
$691$	−313235.	−	180846.i	−0.656016	−	0.378751i	−0.790757	+	0.612130i	$0.790313\pi$
$692$	−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
$698$	642349.	+	385534.i	1.31844	+	0.791319i
$699$		0			0
$700$	312252.	−	166420.i	0.637248	−	0.339633i
$701$	−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
$704$	−243918.	−	176123.i	−0.492151	−	0.355361i
$705$		0			0
$706$	155761.	+	93486.7i	0.312499	+	0.187560i
$707$	−549525.	+	317268.i	−1.09938	+	0.634728i
$708$		0			0
$709$	−431190.	+	746844.i	−0.857781	+	1.48572i	0.0162593	+	0.999868i	$0.494824\pi$
$709$	−431190.	+	746844.i	−0.857781	+	1.48572i	−0.874041	+	0.485853i	$0.838509\pi$
$710$	−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
$716$	6260.03	−	184450.i	0.0122110	−	0.359794i
$717$		0			0
$718$	285976.	+	4851.44i	0.554728	+	0.00941070i
$719$		−	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
$722$	−2143.31	+	126341.i	−0.00411160	+	0.242365i
$723$		0			0
$724$	408472.	+	13863.1i	0.779265	+	0.0264473i
$725$	−171209.	−	296543.i	−0.325725	−	0.564172i
$726$		0			0
$727$	78836.8	+	45516.5i	0.149163	+	0.0861191i	0.572724	−	0.819748i	$-0.305887\pi$
$727$	78836.8	+	45516.5i	0.149163	+	0.0861191i	−0.423561	+	0.905868i	$0.639220\pi$
$728$	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	0.872138	−	0.489261i	$-0.162733\pi$
$733$	6638.99	+	11499.1i	0.0123565	+	0.0214020i	−0.859781	+	0.510663i	$0.829400\pi$
$734$	136449.	−	227342.i	0.253267	−	0.421976i
$735$		0			0
$736$	146139.	+	311400.i	0.269780	+	0.574862i
$737$	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	$0.807079\pi$
$740$	252165.	+	473132.i	0.460490	+	0.864011i
$741$		0			0
$742$	−100509.	+	167461.i	−0.182557	+	0.304163i
$743$	−606588.	+	350214.i	−1.09879	+	0.634389i	−0.935904	−	0.352255i	$-0.885415\pi$
$743$	−606588.	+	350214.i	−1.09879	+	0.634389i	−0.162890	+	0.986644i	$0.552082\pi$
$744$		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	$-0.690713\pi$
$751$	−73727.4	+	42566.6i	−0.130722	+	0.0754725i	0.433213	+	0.901292i	$0.357380\pi$
$752$	−240599.	−	161600.i	−0.425459	−	0.285763i
$753$		0			0
$754$	14695.6	−	866252.i	0.0258490	−	1.52371i
$755$			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	$0.410065\pi$
$758$	−732606.	−	12428.3i	−1.27506	−	0.0216309i
$759$		0			0
$760$	304233.	+	594925.i	0.526719	+	1.03000i
$761$	376888.	+	652790.i	0.650794	+	1.12721i	0.982931	+	0.183977i	$0.0588971\pi$
$761$	376888.	+	652790.i	0.650794	+	1.12721i	−0.332137	+	0.943231i	$0.607770\pi$
$762$		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	−0.961418	−	0.275091i	$-0.911292\pi$
$769$	−425156.	−	736392.i	−0.718945	−	1.24525i	0.242473	−	0.970158i	$-0.422041\pi$
$770$	386387.	+	231907.i	0.651690	+	0.391140i
$771$		0			0
$772$	209434.	+	392958.i	0.351409	+	0.659344i
$773$	−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
$776$	684122.	+	442844.i	1.13608	+	0.735407i
$777$		0			0
$778$	263610.	+	158217.i	0.435515	+	0.261393i
$779$	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	$-0.812306\pi$
$787$	−473891.	+	273601.i	−0.765120	+	0.441742i	0.0660112	+	0.997819i	$0.478973\pi$
$788$	−337454.	−	11452.8i	−0.543452	−	0.0184441i
$789$		0			0
$790$	−1.03857e6	−	17618.8i	−1.66410	−	0.0282307i
$791$		−	45803.8i		−	0.0732064i
$792$		0			0
$793$	−260798.			−0.414723
$794$	4972.99	−	293140.i	0.00788818	−	0.464981i
$795$		0			0
$796$	−2956.66	+	87117.4i	−0.00466633	+	0.137492i
$797$	−104227.	−	180527.i	−0.164083	−	0.284201i	0.772246	−	0.635324i	$-0.219133\pi$
$797$	−104227.	−	180527.i	−0.164083	−	0.284201i	−0.936329	+	0.351123i	$0.885800\pi$
$798$		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
$806$	−709629.	+	1.18233e6i	−1.09235	+	1.81999i
$807$		0			0
$808$	738541.	+	478071.i	1.13123	+	0.732267i
$809$	−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	$-0.198798\pi$
$812$	465848.	−	248282.i	0.706532	−	0.376559i
$813$		0			0
$814$	−152475.	+	254044.i	−0.230118	+	0.383407i
$815$	−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	−0.520708	−	0.853735i	$-0.674332\pi$
$821$	322867.	−	559222.i	0.479002	−	0.829656i	0.999710	+	0.0240788i	$0.00766527\pi$
$822$		0			0
$823$	−202697.	+	117027.i	−0.299260	+	0.172778i	−0.642110	−	0.766612i	$-0.721941\pi$
$823$	−202697.	+	117027.i	−0.299260	+	0.172778i	0.342851	+	0.939390i	$0.388608\pi$
$824$	−378579.	−	740309.i	−0.557574	−	1.09033i
$825$		0			0
$826$	3176.92	−	187268.i	0.00465636	−	0.274476i
$827$		−	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	$0.634530\pi$
$830$	1.08222e6	+	18359.3i	1.57093	+	0.0266502i
$831$		0			0
$832$	−508196.	−	1.13245e6i	−0.734149	−	1.63595i
$833$	−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	$-0.394168\pi$
$839$	−231599.	−	133714.i	−0.329013	−	0.189956i	−0.655403	+	0.755279i	$0.727501\pi$
$840$		0			0
$841$	98213.9	+	170111.i	0.138861	+	0.240515i
$842$	−42815.4	−	25697.5i	−0.0603914	−	0.0362465i
$843$		0			0
$844$	−977189.	+	520811.i	−1.37181	+	0.731131i
$845$	2.10238e6			2.94440
$846$		0			0
$847$		−	426792.i		−	0.594907i
$848$	270167.	+	18359.4i	0.375699	+	0.0255310i
$849$		0			0
$850$	−299074.	−	179502.i	−0.413943	−	0.248446i
$851$	293377.	−	169381.i	0.405105	−	0.233887i
$852$		0			0
$853$	−183417.	+	317688.i	−0.252082	+	0.436619i	−0.964099	−	0.265544i	$-0.914449\pi$
$853$	−183417.	+	317688.i	−0.252082	+	0.436619i	0.712017	+	0.702162i	$0.247782\pi$
$854$	−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	−0.145039	−	0.989426i	$-0.546331\pi$
$857$	576064.	−	997772.i	0.784348	−	1.35853i	0.929388	−	0.369105i	$-0.120336\pi$
$858$		0			0
$859$	1.26237e6	−	728827.i	1.71080	−	0.987730i	0.777313	−	0.629115i	$-0.216582\pi$
$859$	1.26237e6	−	728827.i	1.71080	−	0.987730i	0.933486	−	0.358615i	$-0.116751\pi$
$860$	−45436.4	+	1.33877e6i	−0.0614338	+	1.81013i
$861$		0			0
$862$	479351.	+	8131.97i	0.645118	+	0.0109441i
$863$		−	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
$866$	19164.8	−	1.12970e6i	0.0255545	−	1.50635i
$867$		0			0
$868$	−839703.	−	28498.5i	−1.11452	−	0.0378254i
$869$	−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	0.996908	−	0.0785815i	$-0.0250391\pi$
$877$	331033.	+	573367.i	0.430400	+	0.745475i	−0.566507	+	0.824057i	$0.691706\pi$
$878$	352875.	−	587935.i	0.457753	−	0.762676i
$879$		0			0
$880$	42361.2	−	623362.i	0.0547019	−	0.804962i
$881$	−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	$0.797912\pi$
$884$	−415092.	−	778832.i	−0.531178	−	0.996642i
$885$		0			0
$886$	−170872.	+	284695.i	−0.217673	+	0.362671i
$887$	−1.09941e6	+	634747.i	−1.39738	+	0.806776i	−0.994117	−	0.108309i	$-0.965456\pi$
$887$	−1.09941e6	+	634747.i	−1.39738	+	0.806776i	−0.403260	+	0.915085i	$0.632123\pi$
$888$		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
$896$	453070.	−	605558.i	0.564351	−	0.754293i
$897$		0			0
$898$	17149.8	−	1.01092e6i	0.0212670	−	1.25362i
$899$			813085.i			1.00604i
$900$		0			0
$901$	192535.			0.237170
$902$	−327578.	−	5557.20i	−0.402625	−	0.00683035i
$903$		0			0
$904$	−56541.7	+	28914.3i	−0.0691881	+	0.0353814i
$905$	424388.	+	735061.i	0.518162	+	0.897483i
$906$		0			0
$907$	41146.3	+	23755.8i	0.0500169	+	0.0288772i	0.524800	−	0.851226i	$-0.324140\pi$
$907$	41146.3	+	23755.8i	0.0500169	+	0.0288772i	−0.474783	+	0.880103i	$0.657473\pi$
$908$	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	$-0.428115\pi$
$911$	−421729.	−	243485.i	−0.508155	−	0.293383i	−0.732075	+	0.681224i	$0.761448\pi$
$912$		0			0
$913$	299080.	+	518021.i	0.358794	+	0.621450i
$914$	65093.9	+	39068.9i	0.0779198	+	0.0467670i
$915$		0			0
$916$	−646377.	−	1.21279e6i	−0.770363	−	1.44542i
$917$	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	$0.776837\pi$
$920$	−388191.	+	599691.i	−0.458637	+	0.708520i
$921$		0			0
$922$	−665878.	−	399656.i	−0.783309	−	0.470137i
$923$	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	−0.155128	−	0.987894i	$-0.549579\pi$
$929$	671427.	−	1.16295e6i	0.777978	−	1.34750i	0.933106	−	0.359603i	$-0.117088\pi$
$930$		0			0
$931$	−73535.5	+	42455.7i	−0.0848394	+	0.0489820i
$932$	−204267.	−	6932.59i	−0.235162	−	0.00798111i
$933$		0			0
$934$	507889.	+	8616.09i	0.582204	+	0.00987681i
$935$		−	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	$0.213643\pi$
$938$	−2021.72	+	119173.i	−0.00229781	+	0.135448i
$939$		0			0
$940$	20416.1	−	601557.i	0.0231056	−	0.680802i
$941$	−786864.	−	1.36289e6i	−0.888628	−	1.53915i	−0.841498	−	0.540261i	$-0.818326\pi$
$941$	−786864.	−	1.36289e6i	−0.888628	−	1.53915i	−0.0471309	−	0.998889i	$-0.515008\pi$
$942$		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	$-0.539956\pi$
$947$	−938964.	−	542111.i	−1.04701	−	0.604489i	−0.921810	+	0.387643i	$0.873289\pi$
$948$		0			0
$949$	287752.	+	498400.i	0.319511	+	0.553409i
$950$	−309871.	+	516285.i	−0.343347	+	0.572061i
$951$		0			0
$952$	292205.	−	451409.i	0.322414	−	0.498077i
$953$	−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
$956$	−1.49588e6	+	797255.i	−1.63674	+	0.872332i
$957$		0			0
$958$	115133.	−	191826.i	0.125449	−	0.209014i
$959$	−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	$-0.455146\pi$
$967$	998780.	−	576646.i	1.06811	−	0.616675i	0.927665	+	0.373413i	$0.121813\pi$
$968$	−526845.	+	269418.i	−0.562253	+	0.287525i
$969$		0			0
$970$	−28707.0	+	1.69218e6i	−0.0305101	+	1.79847i
$971$		−	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
$974$	1.09949e6	+	18652.4i	1.15898	+	0.0196615i
$975$		0			0
$976$	−122840.	+	182891.i	−0.128956	+	0.191996i
$977$	388615.	+	673100.i	0.407127	+	0.705165i	0.994566	−	0.104103i	$-0.0331972\pi$
$977$	388615.	+	673100.i	0.407127	+	0.705165i	−0.587439	+	0.809268i	$0.699864\pi$
$978$		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	$-0.196861\pi$
$983$	695782.	+	401710.i	0.720056	+	0.415724i	−0.0947175	+	0.995504i	$0.530195\pi$
$984$		0			0
$985$	−350602.	−	607260.i	−0.361362	−	0.625897i
$986$	−446188.	−	267799.i	−0.458949	−	0.275458i
$987$		0			0
$988$	−1.34448e6	+	716565.i	−1.37734	+	0.734077i
$989$	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	$-0.0335884\pi$
$992$	494894.	+	1.05455e6i	0.502909	+	1.07162i
$993$		0			0
$994$	1.51474e6	+	909136.i	1.53308	+	0.920145i
$995$	−156771.	+	90511.8i	−0.158351	+	0.0914238i
$996$		0			0
$997$	14831.3	−	25688.6i	0.0149207	−	0.0258435i	−0.858469	−	0.512866i	$-0.828584\pi$
$997$	14831.3	−	25688.6i	0.0149207	−	0.0258435i	0.873389	+	0.487023i	$0.161917\pi$
$998$	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.19.11		44
3.2	odd	2		36.5.f.a.7.12	✓	44
4.3	odd	2	inner	108.5.f.a.19.5		44
9.2	odd	6		324.5.d.f.163.4		22
9.4	even	3	inner	108.5.f.a.91.5		44
9.5	odd	6		36.5.f.a.31.18	yes	44
9.7	even	3		324.5.d.e.163.19		22
12.11	even	2		36.5.f.a.7.18	yes	44
36.7	odd	6		324.5.d.e.163.20		22
36.11	even	6		324.5.d.f.163.3		22
36.23	even	6		36.5.f.a.31.12	yes	44
36.31	odd	6	inner	108.5.f.a.91.11		44

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

\(f(q)\)	\(=\)	\(q+(-0.0678484 + 3.99942i) q^{2} +(-15.9908 - 0.542709i) q^{4} +(-16.6139 - 28.7760i) q^{5} +(39.9759 + 23.0801i) q^{7} +(3.25547 - 63.9171i) q^{8} +O(q^{10})\)	\(q+(-0.0678484 + 3.99942i) q^{2} +(-15.9908 - 0.542709i) q^{4} +(-16.6139 - 28.7760i) q^{5} +(39.9759 + 23.0801i) q^{7} +(3.25547 - 63.9171i) q^{8} +(116.215 - 64.4935i) q^{10} +(63.6109 + 36.7258i) q^{11} +(151.520 + 262.440i) q^{13} +(-95.0195 + 158.315i) q^{14} +(255.411 + 17.3567i) q^{16} +182.019 q^{17} -314.215i q^{19} +(250.052 + 469.168i) q^{20} +(-151.198 + 251.915i) q^{22} +(290.919 - 167.962i) q^{23} +(-239.540 + 414.896i) q^{25} +(-1059.89 + 588.185i) q^{26} +(-626.721 - 390.765i) q^{28} +(-357.370 + 618.983i) q^{29} +(985.186 - 568.798i) q^{31} +(-86.7460 + 1020.32i) q^{32} +(-12.3497 + 727.971i) q^{34} -1533.80i q^{35} +1008.45 q^{37} +(1256.68 + 21.3190i) q^{38} +(-1893.37 + 968.231i) q^{40} +(557.553 + 965.709i) q^{41} +(2182.06 + 1259.82i) q^{43} +(-997.257 - 621.796i) q^{44} +(652.014 + 1174.90i) q^{46} +(-980.476 - 566.078i) q^{47} +(-135.117 - 234.029i) q^{49} +(-1643.09 - 986.173i) q^{50} +(-2280.49 - 4278.85i) q^{52} +1057.77 q^{53} -2440.63i q^{55} +(1605.36 - 2480.01i) q^{56} +(-2451.33 - 1471.27i) q^{58} +(-878.476 + 507.188i) q^{59} +(-430.304 + 745.308i) q^{61} +(2208.02 + 3978.77i) q^{62} +(-4074.80 - 416.161i) q^{64} +(5034.65 - 8720.27i) q^{65} +(559.041 - 322.762i) q^{67} +(-2910.63 - 98.7833i) q^{68} +(6134.31 + 104.066i) q^{70} -9567.89i q^{71} +1899.10 q^{73} +(-68.4216 + 4033.22i) q^{74} +(-170.527 + 5024.55i) q^{76} +(1695.27 + 2936.29i) q^{77} +(-6768.11 - 3907.57i) q^{79} +(-3743.90 - 7638.08i) q^{80} +(-3900.11 + 2164.37i) q^{82} +(7052.56 + 4071.80i) q^{83} +(-3024.04 - 5237.78i) q^{85} +(-5186.58 + 8641.52i) q^{86} +(2554.49 - 3946.27i) q^{88} -7653.39 q^{89} +13988.4i q^{91} +(-4743.18 + 2527.96i) q^{92} +(2330.51 - 3882.93i) q^{94} +(-9041.87 + 5220.33i) q^{95} +(-6366.75 + 11027.5i) q^{97} +(945.149 - 524.510i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 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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