LMFDB - Embedded newform 27.6.c.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,6,Mod(10,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("27.10");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	27.c (of order $3$, 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:	$4.33036313495$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 40x^{6} + 568x^{4} + 3363x^{2} + 7056 $ x^8 + 40x^6 + 568x^4 + 3363*x^2 + 7056
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			19.2
Root			$3.84183i$ of defining polynomial
Character	$\chi$	$=$	27.19
Dual form			27.6.c.a.10.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.78978 + 3.09998i) q^{2} +(9.59340 + 16.6162i) q^{4} +(-4.05388 - 7.02152i) q^{5} +(-87.7139 + 151.925i) q^{7} -183.226 q^{8} +O(q^{10})$	\(q+(-1.78978 + 3.09998i) q^{2} +(9.59340 + 16.6162i) q^{4} +(-4.05388 - 7.02152i) q^{5} +(-87.7139 + 151.925i) q^{7} -183.226 q^{8} +29.0221 q^{10} +(-206.795 + 358.179i) q^{11} +(-61.8514 - 107.130i) q^{13} +(-313.977 - 543.824i) q^{14} +(20.9448 - 36.2775i) q^{16} +2223.70 q^{17} +891.313 q^{19} +(77.7809 - 134.720i) q^{20} +(-740.234 - 1282.12i) q^{22} +(-293.902 - 509.053i) q^{23} +(1529.63 - 2649.40i) q^{25} +442.801 q^{26} -3365.90 q^{28} +(-2467.97 + 4274.65i) q^{29} +(2832.69 + 4906.37i) q^{31} +(-2856.64 - 4947.85i) q^{32} +(-3979.93 + 6893.45i) q^{34} +1422.33 q^{35} +1204.25 q^{37} +(-1595.25 + 2763.06i) q^{38} +(742.775 + 1286.52i) q^{40} +(1194.48 + 2068.90i) q^{41} +(2885.71 - 4998.19i) q^{43} -7935.46 q^{44} +2104.08 q^{46} +(3532.81 - 6119.00i) q^{47} +(-6983.97 - 12096.6i) q^{49} +(5475.40 + 9483.67i) q^{50} +(1186.73 - 2055.48i) q^{52} +11521.6 q^{53} +3353.28 q^{55} +(16071.5 - 27836.6i) q^{56} +(-8834.24 - 15301.4i) q^{58} +(4876.49 + 8446.33i) q^{59} +(932.881 - 1615.80i) q^{61} -20279.5 q^{62} +21791.5 q^{64} +(-501.476 + 868.582i) q^{65} +(19671.5 + 34072.0i) q^{67} +(21332.9 + 36949.6i) q^{68} +(-2545.65 + 4409.19i) q^{70} -43602.4 q^{71} -52142.6 q^{73} +(-2155.33 + 3733.15i) q^{74} +(8550.72 + 14810.3i) q^{76} +(-36277.6 - 62834.6i) q^{77} +(-25384.2 + 43966.8i) q^{79} -339.631 q^{80} -8551.41 q^{82} +(-27810.6 + 48169.3i) q^{83} +(-9014.62 - 15613.8i) q^{85} +(10329.5 + 17891.3i) q^{86} +(37890.2 - 65627.7i) q^{88} +46554.3 q^{89} +21700.9 q^{91} +(5639.04 - 9767.10i) q^{92} +(12645.9 + 21903.3i) q^{94} +(-3613.27 - 6258.38i) q^{95} +(21616.0 - 37440.1i) q^{97} +49999.0 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} - 49 q^{4} - 78 q^{5} + 28 q^{7} + 750 q^{8}+O(q^{10}) $ 8 * q - 3 * q^2 - 49 * q^4 - 78 * q^5 + 28 * q^7 + 750 * q^8	$ 8 q - 3 q^{2} - 49 q^{4} - 78 q^{5} + 28 q^{7} + 750 q^{8} + 60 q^{10} - 444 q^{11} - 182 q^{13} - 1392 q^{14} - 289 q^{16} + 4356 q^{17} + 952 q^{19} - 6684 q^{20} + 1011 q^{22} - 8844 q^{23} - 1654 q^{25} + 24888 q^{26} - 1604 q^{28} - 12018 q^{29} + 1132 q^{31} - 8703 q^{32} + 10125 q^{34} + 16224 q^{35} - 15176 q^{37} + 11145 q^{38} - 8736 q^{40} - 1248 q^{41} - 6092 q^{43} - 49530 q^{44} + 45960 q^{46} + 60 q^{47} + 9090 q^{49} + 57057 q^{50} - 32510 q^{52} - 20952 q^{53} - 36120 q^{55} + 61170 q^{56} + 8328 q^{58} - 2076 q^{59} + 48142 q^{61} - 241764 q^{62} - 20926 q^{64} + 13146 q^{65} - 7148 q^{67} + 123129 q^{68} - 654 q^{70} + 71856 q^{71} + 122452 q^{73} + 160320 q^{74} - 49571 q^{76} - 39534 q^{77} - 59516 q^{79} - 124512 q^{80} - 233598 q^{82} - 117696 q^{83} + 28836 q^{85} + 15915 q^{86} + 104523 q^{88} + 451728 q^{89} + 111392 q^{91} - 134034 q^{92} + 169464 q^{94} - 294888 q^{95} + 33976 q^{97} - 57654 q^{98}+O(q^{100}) $ 8 * q - 3 * q^2 - 49 * q^4 - 78 * q^5 + 28 * q^7 + 750 * q^8 + 60 * q^10 - 444 * q^11 - 182 * q^13 - 1392 * q^14 - 289 * q^16 + 4356 * q^17 + 952 * q^19 - 6684 * q^20 + 1011 * q^22 - 8844 * q^23 - 1654 * q^25 + 24888 * q^26 - 1604 * q^28 - 12018 * q^29 + 1132 * q^31 - 8703 * q^32 + 10125 * q^34 + 16224 * q^35 - 15176 * q^37 + 11145 * q^38 - 8736 * q^40 - 1248 * q^41 - 6092 * q^43 - 49530 * q^44 + 45960 * q^46 + 60 * q^47 + 9090 * q^49 + 57057 * q^50 - 32510 * q^52 - 20952 * q^53 - 36120 * q^55 + 61170 * q^56 + 8328 * q^58 - 2076 * q^59 + 48142 * q^61 - 241764 * q^62 - 20926 * q^64 + 13146 * q^65 - 7148 * q^67 + 123129 * q^68 - 654 * q^70 + 71856 * q^71 + 122452 * q^73 + 160320 * q^74 - 49571 * q^76 - 39534 * q^77 - 59516 * q^79 - 124512 * q^80 - 233598 * q^82 - 117696 * q^83 + 28836 * q^85 + 15915 * q^86 + 104523 * q^88 + 451728 * q^89 + 111392 * q^91 - 134034 * q^92 + 169464 * q^94 - 294888 * q^95 + 33976 * q^97 - 57654 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.78978	+	3.09998i	−0.316391	+	0.548005i	−0.979732	−	0.200312i	$-0.935804\pi$
$2$	−1.78978	+	3.09998i	−0.316391	+	0.548005i	0.663341	+	0.748317i	$0.269138\pi$
$3$		0			0
$3$		0			0
$4$	9.59340	+	16.6162i	0.299794	+	0.519258i
$5$	−4.05388	−	7.02152i	−0.0725179	−	0.125605i	0.827486	−	0.561486i	$-0.189770\pi$
$5$	−4.05388	−	7.02152i	−0.0725179	−	0.125605i	−0.900004	+	0.435881i	$0.856437\pi$
$6$		0			0
$7$	−87.7139	+	151.925i	−0.676587	+	1.17188i	0.299416	+	0.954123i	$0.403208\pi$
$7$	−87.7139	+	151.925i	−0.676587	+	1.17188i	−0.976002	+	0.217760i	$0.930125\pi$
$8$	−183.226			−1.01219
$9$		0			0
$10$	29.0221			0.0917761
$11$	−206.795	+	358.179i	−0.515298	+	0.892522i	0.484545	+	0.874767i	$0.338985\pi$
$11$	−206.795	+	358.179i	−0.515298	+	0.892522i	−0.999842	+	0.0177554i	$0.994348\pi$
$12$		0			0
$13$	−61.8514	−	107.130i	−0.101506	−	0.175813i	0.810799	−	0.585324i	$-0.199033\pi$
$13$	−61.8514	−	107.130i	−0.101506	−	0.175813i	−0.912305	+	0.409511i	$0.865699\pi$
$14$	−313.977	−	543.824i	−0.428132	−	0.741546i
$15$		0			0
$16$	20.9448	−	36.2775i	0.0204539	−	0.0354273i
$17$	2223.70			1.86618			0.933092	−	0.359638i	$-0.117100\pi$
$17$	2223.70			1.86618			0.933092	+	0.359638i	$0.117100\pi$
$18$		0			0
$19$	891.313			0.566430			0.283215	−	0.959056i	$-0.408599\pi$
$19$	891.313			0.566430			0.283215	+	0.959056i	$0.408599\pi$
$20$	77.7809	−	134.720i	0.0434808	−	0.0753110i
$21$		0			0
$22$	−740.234	−	1282.12i	−0.326071	−	0.564772i
$23$	−293.902	−	509.053i	−0.115846	−	0.200652i	0.802271	−	0.596960i	$-0.203625\pi$
$23$	−293.902	−	509.053i	−0.115846	−	0.200652i	−0.918118	+	0.396308i	$0.870291\pi$
$24$		0			0
$25$	1529.63	−	2649.40i	0.489482	−	0.847808i
$26$	442.801			0.128462
$27$		0			0
$28$	−3365.90			−0.811346
$29$	−2467.97	+	4274.65i	−0.544936	+	0.943856i	0.453675	+	0.891167i	$0.350113\pi$
$29$	−2467.97	+	4274.65i	−0.544936	+	0.943856i	−0.998611	+	0.0526894i	$0.983221\pi$
$30$		0			0
$31$	2832.69	+	4906.37i	0.529414	+	0.916971i	0.999411	+	0.0343037i	$0.0109213\pi$
$31$	2832.69	+	4906.37i	0.529414	+	0.916971i	−0.469998	+	0.882668i	$0.655745\pi$
$32$	−2856.64	−	4947.85i	−0.493152	−	0.854164i
$33$		0			0
$34$	−3979.93	+	6893.45i	−0.590444	+	1.02268i
$35$	1422.33			0.196259
$36$		0			0
$37$	1204.25			0.144614			0.0723071	−	0.997382i	$-0.476964\pi$
$37$	1204.25			0.144614			0.0723071	+	0.997382i	$0.476964\pi$
$38$	−1595.25	+	2763.06i	−0.179213	+	0.310407i
$39$		0			0
$40$	742.775	+	1286.52i	0.0734019	+	0.127136i
$41$	1194.48	+	2068.90i	0.110973	+	0.192212i	0.916163	−	0.400806i	$-0.131270\pi$
$41$	1194.48	+	2068.90i	0.110973	+	0.192212i	−0.805190	+	0.593018i	$0.797936\pi$
$42$		0			0
$43$	2885.71	−	4998.19i	0.238002	−	0.412232i	−0.722139	−	0.691748i	$-0.756841\pi$
$43$	2885.71	−	4998.19i	0.238002	−	0.412232i	0.960141	+	0.279516i	$0.0901741\pi$
$44$	−7935.46			−0.617932
$45$		0			0
$46$	2104.08			0.146611
$47$	3532.81	−	6119.00i	0.233279	−	0.404051i	−0.725492	−	0.688230i	$-0.758388\pi$
$47$	3532.81	−	6119.00i	0.233279	−	0.404051i	0.958771	+	0.284180i	$0.0917212\pi$
$48$		0			0
$49$	−6983.97	−	12096.6i	−0.415539	−	0.719735i
$50$	5475.40	+	9483.67i	0.309735	+	0.536478i
$51$		0			0
$52$	1186.73	−	2055.48i	0.0608616	−	0.105415i
$53$	11521.6			0.563406			0.281703	−	0.959502i	$-0.409101\pi$
$53$	11521.6			0.563406			0.281703	+	0.959502i	$0.409101\pi$
$54$		0			0
$55$	3353.28			0.149473
$56$	16071.5	−	27836.6i	0.684834	−	1.18617i
$57$		0			0
$58$	−8834.24	−	15301.4i	−0.344825	−	0.597255i
$59$	4876.49	+	8446.33i	0.182380	+	0.315892i	0.942691	−	0.333668i	$-0.108287\pi$
$59$	4876.49	+	8446.33i	0.182380	+	0.315892i	−0.760310	+	0.649560i	$0.774953\pi$
$60$		0			0
$61$	932.881	−	1615.80i	0.0320997	−	0.0555984i	−0.849529	−	0.527542i	$-0.823114\pi$
$61$	932.881	−	1615.80i	0.0320997	−	0.0555984i	0.881629	+	0.471943i	$0.156447\pi$
$62$	−20279.5			−0.670006
$63$		0			0
$64$	21791.5			0.665023
$65$	−501.476	+	868.582i	−0.0147220	+	0.0254992i
$66$		0			0
$67$	19671.5	+	34072.0i	0.535366	+	0.927281i	0.999146	+	0.0413301i	$0.0131595\pi$
$67$	19671.5	+	34072.0i	0.535366	+	0.927281i	−0.463780	+	0.885950i	$0.653507\pi$
$68$	21332.9	+	36949.6i	0.559470	+	0.969031i
$69$		0			0
$70$	−2545.65	+	4409.19i	−0.0620945	+	0.107551i
$71$	−43602.4			−1.02651			−0.513257	−	0.858235i	$-0.671561\pi$
$71$	−43602.4			−1.02651			−0.513257	+	0.858235i	$0.671561\pi$
$72$		0			0
$73$	−52142.6			−1.14521			−0.572605	−	0.819831i	$-0.694067\pi$
$73$	−52142.6			−1.14521			−0.572605	+	0.819831i	$0.694067\pi$
$74$	−2155.33	+	3733.15i	−0.0457546	+	0.0792494i
$75$		0			0
$76$	8550.72	+	14810.3i	0.169812	+	0.294123i
$77$	−36277.6	−	62834.6i	−0.697287	−	1.20774i
$78$		0			0
$79$	−25384.2	+	43966.8i	−0.457611	+	0.792605i	−0.998834	−	0.0482737i	$-0.984628\pi$
$79$	−25384.2	+	43966.8i	−0.457611	+	0.792605i	0.541223	+	0.840879i	$0.317961\pi$
$80$	−339.631			−0.00593311
$81$		0			0
$82$	−8551.41			−0.140444
$83$	−27810.6	+	48169.3i	−0.443113	+	0.767494i	−0.997919	−	0.0644858i	$-0.979459\pi$
$83$	−27810.6	+	48169.3i	−0.443113	+	0.767494i	0.554806	+	0.831980i	$0.312793\pi$
$84$		0			0
$85$	−9014.62	−	15613.8i	−0.135332	−	0.234402i
$86$	10329.5	+	17891.3i	0.150604	+	0.260853i
$87$		0			0
$88$	37890.2	−	65627.7i	0.521579	−	0.903401i
$89$	46554.3			0.622996			0.311498	−	0.950247i	$-0.399169\pi$
$89$	46554.3			0.622996			0.311498	+	0.950247i	$0.399169\pi$
$90$		0			0
$91$	21700.9			0.274710
$92$	5639.04	−	9767.10i	0.0694601	−	0.120308i
$93$		0			0
$94$	12645.9	+	21903.3i	0.147615	+	0.255676i
$95$	−3613.27	−	6258.38i	−0.0410764	−	0.0711463i
$96$		0			0
$97$	21616.0	−	37440.1i	0.233264	−	0.404024i	−0.725503	−	0.688219i	$-0.758393\pi$
$97$	21616.0	−	37440.1i	0.233264	−	0.404024i	0.958767	+	0.284195i	$0.0917262\pi$
$98$	49999.0			0.525891
$99$		0			0
$100$	58697.5			0.586975
$101$	37727.5	−	65345.9i	0.368005	−	0.637404i	−0.621248	−	0.783614i	$-0.713374\pi$
$101$	37727.5	−	65345.9i	0.368005	−	0.637404i	0.989254	+	0.146210i	$0.0467075\pi$
$102$		0			0
$103$	−50758.5	−	87916.3i	−0.471428	−	0.816538i	0.528038	−	0.849221i	$-0.322928\pi$
$103$	−50758.5	−	87916.3i	−0.471428	−	0.816538i	−0.999466	+	0.0326834i	$0.989595\pi$
$104$	11332.8	+	19629.0i	0.102743	+	0.177956i
$105$		0			0
$106$	−20621.0	+	35716.7i	−0.178257	+	0.308750i
$107$	178800.			1.50976			0.754882	−	0.655860i	$-0.227694\pi$
$107$	178800.			1.50976			0.754882	+	0.655860i	$0.227694\pi$
$108$		0			0
$109$	−37985.3			−0.306231			−0.153116	−	0.988208i	$-0.548931\pi$
$109$	−37985.3			−0.306231			−0.153116	+	0.988208i	$0.548931\pi$
$110$	−6001.63	+	10395.1i	−0.0472920	+	0.0819121i
$111$		0			0
$112$	3674.31	+	6364.09i	0.0276777	+	0.0479392i
$113$	−100834.	−	174650.i	−0.742867	−	1.28668i	−0.951185	−	0.308622i	$-0.900132\pi$
$113$	−100834.	−	174650.i	−0.742867	−	1.28668i	0.208318	−	0.978061i	$-0.433201\pi$
$114$		0			0
$115$	−2382.88	+	4127.28i	−0.0168019	+	0.0291017i
$116$	−94705.0			−0.653473
$117$		0			0
$118$	−34911.3			−0.230814
$119$	−195050.	+	337836.i	−1.26264	+	2.18695i
$120$		0			0
$121$	−5002.82	−	8665.14i	−0.0310636	−	0.0538037i
$122$	3339.30	+	5783.83i	0.0203121	+	0.0351816i
$123$		0			0
$124$	−54350.3	+	94137.4i	−0.317430	+	0.549804i
$125$	−50140.5			−0.287021
$126$		0			0
$127$	255248.			1.40428			0.702138	−	0.712041i	$-0.252229\pi$
$127$	255248.			1.40428			0.702138	+	0.712041i	$0.252229\pi$
$128$	52410.6	−	90777.9i	0.282745	−	0.489728i
$129$		0			0
$130$	−1795.06	−	3109.14i	−0.00931581	−	0.0161355i
$131$	16914.0	+	29295.9i	0.0861129	+	0.149152i	0.905865	−	0.423567i	$-0.139222\pi$
$131$	16914.0	+	29295.9i	0.0861129	+	0.149152i	−0.819752	+	0.572719i	$0.805889\pi$
$132$		0			0
$133$	−78180.6	+	135413.i	−0.383239	+	0.663790i
$134$	−140830.			−0.677539
$135$		0			0
$136$	−407440.			−1.88893
$137$	93918.5	−	162672.i	0.427514	−	0.740475i	−0.569138	−	0.822242i	$-0.692723\pi$
$137$	93918.5	−	162672.i	0.427514	−	0.740475i	0.996651	+	0.0817669i	$0.0260563\pi$
$138$		0			0
$139$	169712.	+	293951.i	0.745035	+	1.29044i	0.950178	+	0.311706i	$0.100901\pi$
$139$	169712.	+	293951.i	0.745035	+	1.29044i	−0.205144	+	0.978732i	$0.565766\pi$
$140$	13644.9	+	23633.7i	0.0588371	+	0.101909i
$141$		0			0
$142$	78038.6	−	135167.i	0.324780	−	0.562535i
$143$	51162.2			0.209223
$144$		0			0
$145$	40019.4			0.158070
$146$	93323.6	−	161641.i	0.362334	−	0.627581i
$147$		0			0
$148$	11552.8	+	20010.1i	0.0433544	+	0.0750921i
$149$	193953.	+	335937.i	0.715700	+	1.23963i	0.962689	+	0.270611i	$0.0872257\pi$
$149$	193953.	+	335937.i	0.715700	+	1.23963i	−0.246988	+	0.969018i	$0.579441\pi$
$150$		0			0
$151$	138084.	−	239168.i	0.492833	−	0.853611i	−0.507133	−	0.861868i	$-0.669295\pi$
$151$	138084.	−	239168.i	0.492833	−	0.853611i	0.999966	+	0.00825649i	$0.00262815\pi$
$152$	−163312.			−0.573335
$153$		0			0
$154$	259715.			0.882461
$155$	22966.8	−	39779.6i	0.0767840	−	0.132994i
$156$		0			0
$157$	−256623.	−	444485.i	−0.830897	−	1.43916i	−0.897328	−	0.441364i	$-0.854495\pi$
$157$	−256623.	−	444485.i	−0.830897	−	1.43916i	0.0664312	−	0.997791i	$-0.478839\pi$
$158$	−90864.2	−	157381.i	−0.289568	−	0.501546i
$159$		0			0
$160$	−23160.9	+	40115.9i	−0.0715247	+	0.123884i
$161$	103117.			0.313521
$162$		0			0
$163$	−236294.			−0.696601			−0.348300	−	0.937383i	$-0.613241\pi$
$163$	−236294.			−0.696601			−0.348300	+	0.937383i	$0.613241\pi$
$164$	−22918.2	+	39695.5i	−0.0665383	+	0.115248i
$165$		0			0
$166$	−99549.4	−	172425.i	−0.280394	−	0.485656i
$167$	125015.	+	216533.i	0.346875	+	0.600805i	0.985693	−	0.168553i	$-0.0539096\pi$
$167$	125015.	+	216533.i	0.346875	+	0.600805i	−0.638818	+	0.769358i	$0.720576\pi$
$168$		0			0
$169$	177995.	−	308297.i	0.479393	−	0.830333i
$170$	64536.6			0.171271
$171$		0			0
$172$	110735.			0.285406
$173$	255819.	−	443091.i	0.649856	−	1.12558i	−0.333301	−	0.942820i	$-0.608163\pi$
$173$	255819.	−	443091.i	0.649856	−	1.12558i	0.983157	−	0.182763i	$-0.0585041\pi$
$174$		0			0
$175$	268340.	+	464779.i	0.662354	+	1.14723i
$176$	8662.58	+	15004.0i	0.0210797	+	0.0365112i
$177$		0			0
$178$	−83321.9	+	144318.i	−0.197110	+	0.341405i
$179$	−254552.			−0.593806			−0.296903	−	0.954908i	$-0.595954\pi$
$179$	−254552.			−0.593806			−0.296903	+	0.954908i	$0.595954\pi$
$180$		0			0
$181$	−42413.6			−0.0962296			−0.0481148	−	0.998842i	$-0.515321\pi$
$181$	−42413.6			−0.0962296			−0.0481148	+	0.998842i	$0.515321\pi$
$182$	−38839.8	+	67272.5i	−0.0869158	+	0.150543i
$183$		0			0
$184$	53850.4	+	93271.7i	0.117259	+	0.203098i
$185$	−4881.87	−	8455.64i	−0.0104871	−	0.0181642i
$186$		0			0
$187$	−459851.	+	796485.i	−0.961640	+	1.66561i
$188$	135566.			0.279742
$189$		0			0
$190$	25867.8			0.0519847
$191$	−133628.	+	231451.i	−0.265042	+	0.459067i	−0.967575	−	0.252585i	$-0.918719\pi$
$191$	−133628.	+	231451.i	−0.265042	+	0.459067i	0.702532	+	0.711652i	$0.252053\pi$
$192$		0			0
$193$	−127808.	−	221370.i	−0.246982	−	0.427786i	0.715705	−	0.698403i	$-0.246106\pi$
$193$	−127808.	−	221370.i	−0.246982	−	0.427786i	−0.962687	+	0.270617i	$0.912772\pi$
$194$	77375.8	+	134019.i	0.147605	+	0.255659i
$195$		0			0
$196$	134000.	−	232095.i	0.249152	−	0.431544i
$197$	−650944.			−1.19503			−0.597514	−	0.801859i	$-0.703845\pi$
$197$	−650944.			−1.19503			−0.597514	+	0.801859i	$0.703845\pi$
$198$		0			0
$199$	395656.			0.708248			0.354124	−	0.935199i	$-0.384779\pi$
$199$	395656.			0.708248			0.354124	+	0.935199i	$0.384779\pi$
$200$	−280268.	+	485439.i	−0.495449	+	0.858143i
$201$		0			0
$202$	135047.	+	233909.i	0.232867	+	0.403338i
$203$	−432951.	−	749893.i	−0.737393	−	1.27720i
$204$		0			0
$205$	9684.54	−	16774.1i	0.0160951	−	0.0278776i
$206$	363386.			0.596622
$207$		0			0
$208$	−5181.87			−0.00830478
$209$	−184319.	+	319250.i	−0.291880	+	0.505551i
$210$		0			0
$211$	−309289.	−	535705.i	−0.478254	−	0.828361i	0.521435	−	0.853291i	$-0.325397\pi$
$211$	−309289.	−	535705.i	−0.478254	−	0.828361i	−0.999689	+	0.0249304i	$0.992064\pi$
$212$	110531.	+	191445.i	0.168906	+	0.292553i
$213$		0			0
$214$	−320013.	+	554279.i	−0.477676	+	0.827359i
$215$	−46793.2			−0.0690378
$216$		0			0
$217$	−993866.			−1.43278
$218$	67985.2	−	117754.i	0.0968888	−	0.167816i
$219$		0			0
$220$	32169.4	+	55719.0i	0.0448112	+	0.0776152i
$221$	−137539.	−	238225.i	−0.189429	−	0.328100i
$222$		0			0
$223$	438618.	−	759708.i	0.590642	−	1.02302i	−0.403504	−	0.914978i	$-0.632208\pi$
$223$	438618.	−	759708.i	0.590642	−	1.02302i	0.994146	−	0.108044i	$-0.0344586\pi$
$224$	1.00227e6			1.33464
$225$		0			0
$226$	721881.			0.940145
$227$	265882.	−	460521.i	0.342471	−	0.593177i	−0.642420	−	0.766353i	$-0.722069\pi$
$227$	265882.	−	460521.i	0.342471	−	0.593177i	0.984891	+	0.173176i	$0.0554028\pi$
$228$		0			0
$229$	571507.	+	989880.i	0.720167	+	1.24737i	0.960933	+	0.276782i	$0.0892681\pi$
$229$	571507.	+	989880.i	0.720167	+	1.24737i	−0.240766	+	0.970583i	$0.577399\pi$
$230$	−8529.66	−	14773.8i	−0.0106319	−	0.0184151i
$231$		0			0
$232$	452196.	−	783227.i	0.551578	−	0.955362i
$233$	818670.			0.987913			0.493957	−	0.869487i	$-0.335550\pi$
$233$	818670.			0.987913			0.493957	+	0.869487i	$0.335550\pi$
$234$		0			0
$235$	−57286.2			−0.0676676
$236$	−93564.2	+	162058.i	−0.109353	+	0.189405i
$237$		0			0
$238$	−698191.	−	1.20930e6i	−0.798973	−	1.38386i
$239$	94237.4	+	163224.i	0.106716	+	0.184837i	0.914438	−	0.404726i	$-0.132633\pi$
$239$	94237.4	+	163224.i	0.106716	+	0.184837i	−0.807722	+	0.589563i	$0.799300\pi$
$240$		0			0
$241$	−22511.4	+	38990.8i	−0.0249666	+	0.0432434i	−0.878239	−	0.478222i	$-0.841281\pi$
$241$	−22511.4	+	38990.8i	−0.0249666	+	0.0432434i	0.853272	+	0.521466i	$0.174615\pi$
$242$	35815.7			0.0393129
$243$		0			0
$244$	35798.0			0.0384932
$245$	−56624.3	+	98076.1i	−0.0602681	+	0.104387i
$246$		0			0
$247$	−55129.0	−	95486.2i	−0.0574960	−	0.0995860i
$248$	−519022.	−	898973.i	−0.535867	−	0.928149i
$249$		0			0
$250$	89740.3	−	155435.i	0.0908108	−	0.157289i
$251$	556667.			0.557713			0.278857	−	0.960333i	$-0.410045\pi$
$251$	556667.			0.557713			0.278857	+	0.960333i	$0.410045\pi$
$252$		0			0
$253$	243110.			0.238782
$254$	−456837.	+	791264.i	−0.444300	+	0.769551i
$255$		0			0
$256$	536270.	+	928847.i	0.511427	+	0.885818i
$257$	290077.	+	502428.i	0.273956	+	0.474505i	0.969871	−	0.243618i	$-0.0783345\pi$
$257$	290077.	+	502428.i	0.273956	+	0.474505i	−0.695915	+	0.718124i	$0.745001\pi$
$258$		0			0
$259$	−105629.	+	182955.i	−0.0978441	+	0.169471i
$260$	−19243.4			−0.0176542
$261$		0			0
$262$	−121089.			−0.108981
$263$	30271.7	−	52432.1i	0.0269865	−	0.0467420i	−0.852217	−	0.523189i	$-0.824742\pi$
$263$	30271.7	−	52432.1i	0.0269865	−	0.0467420i	0.879203	+	0.476447i	$0.158076\pi$
$264$		0			0
$265$	−46707.0	−	80898.9i	−0.0408571	−	0.0707665i
$266$	−279852.	−	484717.i	−0.242507	−	0.420034i
$267$		0			0
$268$	−377433.	+	653733.i	−0.320998	+	0.555986i
$269$	−2.17306e6			−1.83101			−0.915507	−	0.402301i	$-0.868211\pi$
$269$	−2.17306e6			−1.83101			−0.915507	+	0.402301i	$0.868211\pi$
$270$		0			0
$271$	−1.72652e6			−1.42806			−0.714032	−	0.700113i	$-0.753133\pi$
$271$	−1.72652e6			−1.42806			−0.714032	+	0.700113i	$0.753133\pi$
$272$	46575.1	−	80670.4i	0.0381708	−	0.0661138i
$273$		0			0
$274$	336186.	+	582292.i	0.270523	+	0.468559i
$275$	632640.	+	1.09577e6i	0.504458	+	0.873747i
$276$		0			0
$277$	−523243.	+	906283.i	−0.409736	+	0.709683i	−0.994860	−	0.101260i	$-0.967712\pi$
$277$	−523243.	+	906283.i	−0.409736	+	0.709683i	0.585124	+	0.810944i	$0.301046\pi$
$278$	−1.21499e6			−0.942889
$279$		0			0
$280$	−260607.			−0.198651
$281$	673149.	−	1.16593e6i	0.508564	−	0.880858i	−0.491387	−	0.870941i	$-0.663510\pi$
$281$	673149.	−	1.16593e6i	0.508564	−	0.880858i	0.999951	−	0.00991669i	$-0.00315663\pi$
$282$		0			0
$283$	−284960.	−	493565.i	−0.211503	−	0.366335i	0.740682	−	0.671856i	$-0.234503\pi$
$283$	−284960.	−	493565.i	−0.211503	−	0.366335i	−0.952185	+	0.305521i	$0.901169\pi$
$284$	−418295.	−	724509.i	−0.307742	−	0.533025i
$285$		0			0
$286$	−91569.0	+	158602.i	−0.0661963	+	0.114655i
$287$	−419090.			−0.300333
$288$		0			0
$289$	3.52500e6			2.48264
$290$	−71625.8	+	124060.i	−0.0500121	+	0.0866234i
$291$		0			0
$292$	−500225.	−	866414.i	−0.343327	−	0.594660i
$293$	1.22915e6	+	2.12896e6i	0.836444	+	1.44876i	0.892849	+	0.450356i	$0.148703\pi$
$293$	1.22915e6	+	2.12896e6i	0.836444	+	1.44876i	−0.0564045	+	0.998408i	$0.517964\pi$
$294$		0			0
$295$	39537.4	−	68480.8i	0.0264517	−	0.0458156i
$296$	−220649.			−0.146377
$297$		0			0
$298$	−1.38853e6			−0.905764
$299$	−36356.5	+	62971.3i	−0.0235182	+	0.0407347i
$300$		0			0
$301$	506234.	+	876822.i	0.322058	+	0.557822i
$302$	494277.	+	856114.i	0.311855	+	0.540150i
$303$		0			0
$304$	18668.4	−	32334.6i	0.0115857	−	0.0200671i
$305$	−15127.1			−0.00931123
$306$		0			0
$307$	1.25805e6			0.761819			0.380910	−	0.924612i	$-0.375611\pi$
$307$	1.25805e6			0.761819			0.380910	+	0.924612i	$0.375611\pi$
$308$	696051.	−	1.20560e6i	0.418085	−	0.724144i
$309$		0			0
$310$	82210.8	+	142393.i	0.0485875	+	0.0841560i
$311$	−1.02249e6	−	1.77101e6i	−0.599457	−	1.03829i	−0.992901	−	0.118942i	$-0.962050\pi$
$311$	−1.02249e6	−	1.77101e6i	−0.599457	−	1.03829i	0.393444	−	0.919349i	$-0.371284\pi$
$312$		0			0
$313$	473219.	−	819640.i	0.273025	−	0.472892i	−0.696610	−	0.717450i	$-0.745309\pi$
$313$	473219.	−	819640.i	0.273025	−	0.472892i	0.969635	+	0.244557i	$0.0786426\pi$
$314$	1.83719e6			1.05155
$315$		0			0
$316$	−974084.			−0.548755
$317$	197117.	−	341417.i	0.110173	−	0.190826i	−0.805667	−	0.592369i	$-0.798193\pi$
$317$	197117.	−	341417.i	0.110173	−	0.190826i	0.915840	+	0.401543i	$0.131526\pi$
$318$		0			0
$319$	−1.02073e6	−	1.76795e6i	−0.561608	−	0.972734i
$320$	−88339.9	−	153009.i	−0.0482261	−	0.0835301i
$321$		0			0
$322$	−184557.	+	319662.i	−0.0991951	+	0.171811i
$323$	1.98202e6			1.05706
$324$		0			0
$325$	−378440.			−0.198741
$326$	422914.	−	732508.i	0.220398	−	0.381741i
$327$		0			0
$328$	−218860.	−	379076.i	−0.112326	−	0.194555i
$329$	619752.	+	1.07344e6i	0.315667	+	0.546750i
$330$		0			0
$331$	1.36828e6	−	2.36992e6i	0.686442	−	1.18895i	−0.286539	−	0.958068i	$-0.592505\pi$
$331$	1.36828e6	−	2.36992e6i	0.686442	−	1.18895i	0.972981	−	0.230884i	$-0.0741617\pi$
$332$	−1.06719e6			−0.531370
$333$		0			0
$334$	−894999.			−0.438992
$335$	159492.	−	276248.i	0.0776472	−	0.134489i
$336$		0			0
$337$	13015.1	+	22542.8i	0.00624269	+	0.0108127i	0.869130	−	0.494584i	$-0.164680\pi$
$337$	13015.1	+	22542.8i	0.00624269	+	0.0108127i	−0.862887	+	0.505397i	$0.831346\pi$
$338$	637144.	+	1.10357e6i	0.303351	+	0.525420i
$339$		0			0
$340$	172962.	−	299578.i	0.0811432	−	0.140544i
$341$	−2.34315e6			−1.09122
$342$		0			0
$343$	−498052.			−0.228580
$344$	−528736.	+	915798.i	−0.240904	+	0.417257i
$345$		0			0
$346$	915717.	+	1.58607e6i	0.411217	+	0.712249i
$347$	−935583.	−	1.62048e6i	−0.417118	−	0.722469i	0.578531	−	0.815661i	$-0.303626\pi$
$347$	−935583.	−	1.62048e6i	−0.417118	−	0.722469i	−0.995648	+	0.0931918i	$0.970293\pi$
$348$		0			0
$349$	−644297.	+	1.11595e6i	−0.283154	+	0.490437i	−0.972160	−	0.234319i	$-0.924714\pi$
$349$	−644297.	+	1.11595e6i	−0.283154	+	0.490437i	0.689006	+	0.724756i	$0.258047\pi$
$350$	−1.92108e6			−0.838252
$351$		0			0
$352$	2.36296e6			1.01648
$353$	−697250.	+	1.20767e6i	−0.297818	+	0.515837i	−0.975637	−	0.219393i	$-0.929592\pi$
$353$	−697250.	+	1.20767e6i	−0.297818	+	0.515837i	0.677818	+	0.735230i	$0.262926\pi$
$354$		0			0
$355$	176759.	+	306155.i	0.0744407	+	0.128935i
$356$	446614.	+	773559.i	0.186770	+	0.323495i
$357$		0			0
$358$	455592.	−	789108.i	0.187875	−	0.325408i
$359$	3.14929e6			1.28967			0.644833	−	0.764324i	$-0.276927\pi$
$359$	3.14929e6			1.28967			0.644833	+	0.764324i	$0.276927\pi$
$360$		0			0
$361$	−1.68166e6			−0.679157
$362$	75910.9	−	131482.i	0.0304462	−	0.0527343i
$363$		0			0
$364$	208186.	+	360588.i	0.0823563	+	0.142645i
$365$	211380.	+	366120.i	0.0830483	+	0.143844i
$366$		0			0
$367$	−1.79452e6	+	3.10820e6i	−0.695478	+	1.20460i	0.274541	+	0.961575i	$0.411474\pi$
$367$	−1.79452e6	+	3.10820e6i	−0.695478	+	1.20460i	−0.970019	+	0.243028i	$0.921859\pi$
$368$	−24622.9			−0.00947807
$369$		0			0
$370$	34949.8			0.0132721
$371$	−1.01060e6	+	1.75041e6i	−0.381193	+	0.660246i
$372$		0			0
$373$	1.68552e6	+	2.91941e6i	0.627280	+	1.08648i	0.988095	+	0.153844i	$0.0491654\pi$
$373$	1.68552e6	+	2.91941e6i	0.627280	+	1.08648i	−0.360815	+	0.932638i	$0.617501\pi$
$374$	−1.64606e6	−	2.85106e6i	−0.608509	−	1.05397i
$375$		0			0
$376$	−647301.	+	1.12116e6i	−0.236122	+	0.408976i
$377$	610590.			0.221257
$378$		0			0
$379$	−1.82703e6			−0.653352			−0.326676	−	0.945136i	$-0.605929\pi$
$379$	−1.82703e6			−0.653352			−0.326676	+	0.945136i	$0.605929\pi$
$380$	69327.1	−	120078.i	0.0246289	−	0.0426584i
$381$		0			0
$382$	−478330.	−	828492.i	−0.167714	−	0.290489i
$383$	−2.84772e6	−	4.93239e6i	−0.991973	−	1.71815i	−0.605494	−	0.795850i	$-0.707024\pi$
$383$	−2.84772e6	−	4.93239e6i	−0.991973	−	1.71815i	−0.386480	−	0.922298i	$-0.626309\pi$
$384$		0			0
$385$	−294130.	+	509448.i	−0.101132	+	0.175165i
$386$	914993.			0.312572
$387$		0			0
$388$	829485.			0.279724
$389$	−1.43125e6	+	2.47899e6i	−0.479557	+	0.830617i	−0.999725	−	0.0234470i	$-0.992536\pi$
$389$	−1.43125e6	+	2.47899e6i	−0.479557	+	0.830617i	0.520168	+	0.854064i	$0.325869\pi$
$390$		0			0
$391$	−653551.	−	1.13198e6i	−0.216191	−	0.374454i
$392$	1.27964e6	+	2.21641e6i	0.420604	+	0.728508i
$393$		0			0
$394$	1.16504e6	−	2.01792e6i	0.378096	−	0.654881i
$395$	411618.			0.132740
$396$		0			0
$397$	−373432.			−0.118915			−0.0594574	−	0.998231i	$-0.518937\pi$
$397$	−373432.			−0.118915			−0.0594574	+	0.998231i	$0.518937\pi$
$398$	−708136.	+	1.22653e6i	−0.224083	+	0.388123i
$399$		0			0
$400$	−64075.8	−	110983.i	−0.0200237	−	0.0346820i
$401$	1.18967e6	+	2.06056e6i	0.369457	+	0.639918i	0.989481	−	0.144665i	$-0.0462104\pi$
$401$	1.18967e6	+	2.06056e6i	0.369457	+	0.639918i	−0.620024	+	0.784583i	$0.712877\pi$
$402$		0			0
$403$	350412.	−	606931.i	0.107477	−	0.186156i
$404$	1.44774e6			0.441303
$405$		0			0
$406$	3.09954e6			0.933217
$407$	−249032.	+	431336.i	−0.0745194	+	0.129071i
$408$		0			0
$409$	−2.02677e6	−	3.51046e6i	−0.599094	−	1.03766i	−0.992955	−	0.118492i	$-0.962194\pi$
$409$	−2.02677e6	−	3.51046e6i	−0.599094	−	1.03766i	0.393861	−	0.919170i	$-0.371139\pi$
$410$	34666.3	+	60043.9i	0.0101847	+	0.0176404i
$411$		0			0
$412$	973893.	−	1.68683e6i	0.282662	−	0.489586i
$413$	−1.71094e6			−0.493584
$414$		0			0
$415$	450962.			0.128535
$416$	−353375.	+	612063.i	−0.100116	+	0.173405i
$417$		0			0
$418$	−659780.	−	1.14277e6i	−0.184697	−	0.319904i
$419$	−2.01845e6	−	3.49605e6i	−0.561671	−	0.972843i	−0.997351	−	0.0727412i	$-0.976825\pi$
$419$	−2.01845e6	−	3.49605e6i	−0.561671	−	0.972843i	0.435680	−	0.900102i	$-0.356508\pi$
$420$		0			0
$421$	295419.	−	511680.i	0.0812330	−	0.140700i	−0.822547	−	0.568697i	$-0.807448\pi$
$421$	295419.	−	511680.i	0.0812330	−	0.140700i	0.903780	+	0.427998i	$0.140781\pi$
$422$	2.21424e6			0.605261
$423$		0			0
$424$	−2.11105e6			−0.570274
$425$	3.40145e6	−	5.89148e6i	0.913464	−	1.58217i
$426$		0			0
$427$	163653.	+	283456.i	0.0434365	+	0.0752343i
$428$	1.71530e6	+	2.97099e6i	0.452618	+	0.783957i
$429$		0			0
$430$	83749.4	−	145058.i	0.0218429	−	0.0378330i
$431$	5.06059e6			1.31222			0.656112	−	0.754663i	$-0.272200\pi$
$431$	5.06059e6			1.31222			0.656112	+	0.754663i	$0.272200\pi$
$432$		0			0
$433$	3.37592e6			0.865312			0.432656	−	0.901559i	$-0.357576\pi$
$433$	3.37592e6			0.865312			0.432656	+	0.901559i	$0.357576\pi$
$434$	1.77880e6	−	3.08097e6i	0.453317	−	0.785169i
$435$		0			0
$436$	−364408.	−	631173.i	−0.0918062	−	0.159013i
$437$	−261959.	−	453726.i	−0.0656190	−	0.113655i
$438$		0			0
$439$	−1.69856e6	+	2.94199e6i	−0.420648	+	0.728584i	−0.996003	−	0.0893200i	$-0.971531\pi$
$439$	−1.69856e6	+	2.94199e6i	−0.420648	+	0.728584i	0.575355	+	0.817904i	$0.304864\pi$
$440$	−614409.			−0.151295
$441$		0			0
$442$	984658.			0.239734
$443$	−2.12190e6	+	3.67523e6i	−0.513706	+	0.889765i	0.486167	+	0.873866i	$0.338395\pi$
$443$	−2.12190e6	+	3.67523e6i	−0.513706	+	0.889765i	−0.999874	+	0.0158995i	$0.994939\pi$
$444$		0			0
$445$	−188726.	−	326882.i	−0.0451784	−	0.0782512i
$446$	1.57006e6	+	2.71942e6i	0.373747	+	0.647349i
$447$		0			0
$448$	−1.91142e6	+	3.31067e6i	−0.449946	+	0.779329i
$449$	−519362.			−0.121578			−0.0607889	−	0.998151i	$-0.519362\pi$
$449$	−519362.			−0.121578			−0.0607889	+	0.998151i	$0.519362\pi$
$450$		0			0
$451$	−988049.			−0.228737
$452$	1.93468e6	−	3.35097e6i	0.445413	−	0.771479i
$453$		0			0
$454$	951738.	+	1.64846e6i	0.216709	+	0.375352i
$455$	−87972.8	−	152373.i	−0.0199214	−	0.0345049i
$456$		0			0
$457$	4.02545e6	−	6.97228e6i	0.901621	−	1.56165i	0.0762309	−	0.997090i	$-0.475711\pi$
$457$	4.02545e6	−	6.97228e6i	0.901621	−	1.56165i	0.825390	−	0.564563i	$-0.190955\pi$
$458$	−4.09148e6			−0.911417
$459$		0			0
$460$	−91439.8			−0.0201484
$461$	−1.76486e6	+	3.05683e6i	−0.386775	+	0.669914i	−0.992014	−	0.126130i	$-0.959744\pi$
$461$	−1.76486e6	+	3.05683e6i	−0.386775	+	0.669914i	0.605239	+	0.796044i	$0.293078\pi$
$462$		0			0
$463$	3.80617e6	+	6.59248e6i	0.825156	+	1.42921i	0.901800	+	0.432153i	$0.142246\pi$
$463$	3.80617e6	+	6.59248e6i	0.825156	+	1.42921i	−0.0766442	+	0.997059i	$0.524421\pi$
$464$	103383.	+	179064.i	0.0222922	+	0.0386112i
$465$		0			0
$466$	−1.46524e6	+	2.53786e6i	−0.312567	+	0.541382i
$467$	−7.10090e6			−1.50668			−0.753340	−	0.657631i	$-0.771559\pi$
$467$	−7.10090e6			−1.50668			−0.753340	+	0.657631i	$0.771559\pi$
$468$		0			0
$469$	−6.90186e6			−1.44889
$470$	102530.	−	177586.i	0.0214094	−	0.0370822i
$471$		0			0
$472$	−893499.	−	1.54759e6i	−0.184603	−	0.319742i
$473$	1.19350e6	+	2.06720e6i	0.245284	+	0.424845i
$474$		0			0
$475$	1.36338e6	−	2.36145e6i	0.277258	−	0.480224i
$476$	−7.48476e6			−1.51412
$477$		0			0
$478$	−674656.			−0.135056
$479$	−564151.	+	977138.i	−0.112346	+	0.194589i	−0.916716	−	0.399540i	$-0.869170\pi$
$479$	−564151.	+	977138.i	−0.112346	+	0.194589i	0.804370	+	0.594129i	$0.202503\pi$
$480$		0			0
$481$	−74484.4	−	129011.i	−0.0146792	−	0.0254251i
$482$	−80580.6	−	139570.i	−0.0157984	−	0.0273636i
$483$		0			0
$484$	95988.1	−	166256.i	0.0186253	−	0.0322600i
$485$	−350515.			−0.0676632
$486$		0			0
$487$	2.19304e6			0.419009			0.209505	−	0.977808i	$-0.432815\pi$
$487$	2.19304e6			0.419009			0.209505	+	0.977808i	$0.432815\pi$
$488$	−170928.	+	296056.i	−0.0324910	+	0.0562761i
$489$		0			0
$490$	−202690.	−	351069.i	−0.0381365	−	0.0660544i
$491$	2.08709e6	+	3.61494e6i	0.390694	+	0.676701i	0.992541	−	0.121910i	$-0.0389018\pi$
$491$	2.08709e6	+	3.61494e6i	0.390694	+	0.676701i	−0.601847	+	0.798611i	$0.705568\pi$
$492$		0			0
$493$	−5.48804e6	+	9.50556e6i	−1.01695	+	1.76141i
$494$	394674.			0.0727649
$495$		0			0
$496$	237321.			0.0433144
$497$	3.82454e6	−	6.62430e6i	0.694526	−	1.20295i
$498$		0			0
$499$	−2.01487e6	−	3.48985e6i	−0.362239	−	0.627416i	0.626090	−	0.779751i	$-0.284654\pi$
$499$	−2.01487e6	−	3.48985e6i	−0.362239	−	0.627416i	−0.988329	+	0.152335i	$0.951321\pi$
$500$	−481018.	−	833147.i	−0.0860470	−	0.149038i
$501$		0			0
$502$	−996309.	+	1.72566e6i	−0.176455	+	0.305630i
$503$	3.13647e6			0.552740			0.276370	−	0.961051i	$-0.410868\pi$
$503$	3.13647e6			0.552740			0.276370	+	0.961051i	$0.410868\pi$
$504$		0			0
$505$	−611770.			−0.106748
$506$	−435112.	+	753637.i	−0.0755484	+	0.130854i
$507$		0			0
$508$	2.44869e6	+	4.24126e6i	0.420993	+	0.729181i
$509$	−2.68135e6	−	4.64424e6i	−0.458733	−	0.794548i	0.540161	−	0.841561i	$-0.318363\pi$
$509$	−2.68135e6	−	4.64424e6i	−0.458733	−	0.794548i	−0.998894	+	0.0470129i	$0.985030\pi$
$510$		0			0
$511$	4.57363e6	−	7.92176e6i	0.774834	−	1.34205i
$512$	−484936.			−0.0817542
$513$		0			0
$514$	−2.07669e6			−0.346708
$515$	−411537.	+	712803.i	−0.0683740	+	0.118427i
$516$		0			0
$517$	1.46113e6	+	2.53076e6i	0.240416	+	0.416413i
$518$	−378106.	−	654898.i	−0.0619140	−	0.107238i
$519$		0			0
$520$	91883.4	−	159147.i	0.0149015	−	0.0258101i
$521$	7.05392e6			1.13851			0.569254	−	0.822162i	$-0.307232\pi$
$521$	7.05392e6			1.13851			0.569254	+	0.822162i	$0.307232\pi$
$522$		0			0
$523$	5.48751e6			0.877246			0.438623	−	0.898671i	$-0.355466\pi$
$523$	5.48751e6			0.877246			0.438623	+	0.898671i	$0.355466\pi$
$524$	−324526.	+	562095.i	−0.0516322	+	0.0894296i
$525$		0			0
$526$	108359.	+	187683.i	0.0170766	+	0.0295775i
$527$	6.29906e6	+	1.09103e7i	0.987983	+	1.71124i
$528$		0			0
$529$	3.04541e6	−	5.27481e6i	0.473159	−	0.819536i
$530$	334380.			0.0517072
$531$		0			0
$532$	−3.00007e6			−0.459571
$533$	147760.	−	255929.i	0.0225289	−	0.0390212i
$534$		0			0
$535$	−724835.	−	1.25545e6i	−0.109485	−	0.189634i
$536$	−3.60433e6	−	6.24288e6i	−0.541892	−	0.938584i
$537$		0			0
$538$	3.88930e6	−	6.73647e6i	0.579316	−	1.00341i
$539$	5.77700e6			0.856506
$540$		0			0
$541$	9.61784e6			1.41281			0.706406	−	0.707807i	$-0.250315\pi$
$541$	9.61784e6			1.41281			0.706406	+	0.707807i	$0.250315\pi$
$542$	3.09008e6	−	5.35218e6i	0.451827	−	0.782587i
$543$		0			0
$544$	−6.35232e6	−	1.10025e7i	−0.920312	−	1.59403i
$545$	153988.	+	266715.i	0.0222073	+	0.0384641i
$546$		0			0
$547$	−3.52168e6	+	6.09973e6i	−0.503247	+	0.871650i	0.496745	+	0.867896i	$0.334528\pi$
$547$	−3.52168e6	+	6.09973e6i	−0.503247	+	0.871650i	−0.999993	+	0.00375395i	$0.998805\pi$
$548$	3.60399e6			0.512663
$549$		0			0
$550$	−4.52914e6			−0.638424
$551$	−2.19974e6	+	3.81006e6i	−0.308668	+	0.534629i
$552$		0			0
$553$	−4.45310e6	−	7.71300e6i	−0.619227	−	1.07253i
$554$	−1.87298e6	−	3.24409e6i	−0.259273	−	0.449075i
$555$		0			0
$556$	−3.25624e6	+	5.63997e6i	−0.446713	+	0.773730i
$557$	−1.13517e7			−1.55032			−0.775162	−	0.631762i	$-0.782332\pi$
$557$	−1.13517e7			−1.55032			−0.775162	+	0.631762i	$0.782332\pi$
$558$		0			0
$559$	−713941.			−0.0966346
$560$	29790.4	−	51598.5i	0.00401426	−	0.00695291i
$561$		0			0
$562$	2.40957e6	+	4.17350e6i	0.321810	+	0.557391i
$563$	1.47052e6	+	2.54702e6i	0.195524	+	0.338658i	0.947072	−	0.321020i	$-0.104026\pi$
$563$	1.47052e6	+	2.54702e6i	0.195524	+	0.338658i	−0.751548	+	0.659678i	$0.770692\pi$
$564$		0			0
$565$	−817537.	+	1.41602e6i	−0.107742	+	0.186615i
$566$	2.04006e6			0.267671
$567$		0			0
$568$	7.98909e6			1.03903
$569$	2.60302e6	−	4.50857e6i	0.337052	−	0.583792i	−0.646825	−	0.762639i	$-0.723903\pi$
$569$	2.60302e6	−	4.50857e6i	0.337052	−	0.583792i	0.983877	+	0.178847i	$0.0572368\pi$
$570$		0			0
$571$	3.43649e6	+	5.95217e6i	0.441087	+	0.763986i	0.997770	−	0.0667391i	$-0.0212595\pi$
$571$	3.43649e6	+	5.95217e6i	0.441087	+	0.763986i	−0.556683	+	0.830725i	$0.687926\pi$
$572$	490820.	+	850125.i	0.0627237	+	0.108641i
$573$		0			0
$574$	750078.	−	1.29917e6i	0.0950225	−	0.164584i
$575$	−1.79825e6			−0.226819
$576$		0			0
$577$	−6.61342e6			−0.826964			−0.413482	−	0.910512i	$-0.635688\pi$
$577$	−6.61342e6			−0.826964			−0.413482	+	0.910512i	$0.635688\pi$
$578$	−6.30896e6	+	1.09274e7i	−0.785485	+	1.36050i
$579$		0			0
$580$	383922.	+	664973.i	0.0473885	+	0.0820793i
$581$	−4.87875e6	−	8.45024e6i	−0.599609	−	1.03855i
$582$		0			0
$583$	−2.38260e6	+	4.12679e6i	−0.290322	+	0.502853i
$584$	9.55387e6			1.15917
$585$		0			0
$586$	−8.79964e6			−1.05857
$587$	−3.31969e6	+	5.74987e6i	−0.397651	+	0.688751i	−0.993436	−	0.114393i	$-0.963508\pi$
$587$	−3.31969e6	+	5.74987e6i	−0.397651	+	0.688751i	0.595785	+	0.803144i	$0.296841\pi$
$588$		0			0
$589$	2.52482e6	+	4.37311e6i	0.299876	+	0.519400i
$590$	141526.	+	245131.i	0.0167381	+	0.0289913i
$591$		0			0
$592$	25222.8	−	43687.1i	0.00295793	−	0.00512329i
$593$	2.49082e6			0.290875			0.145437	−	0.989367i	$-0.453541\pi$
$593$	2.49082e6			0.290875			0.145437	+	0.989367i	$0.453541\pi$
$594$		0			0
$595$	3.16283e6			0.366255
$596$	−3.72134e6	+	6.44555e6i	−0.429125	+	0.743266i
$597$		0			0
$598$	−130140.	−	225409.i	−0.0148819	−	0.0257762i
$599$	−6.54109e6	−	1.13295e7i	−0.744875	−	1.29016i	−0.950253	−	0.311478i	$-0.899176\pi$
$599$	−6.54109e6	−	1.13295e7i	−0.744875	−	1.29016i	0.205378	−	0.978683i	$-0.434158\pi$
$600$		0			0
$601$	−1.50119e6	+	2.60013e6i	−0.169531	+	0.293636i	−0.938255	−	0.345944i	$-0.887559\pi$
$601$	−1.50119e6	+	2.60013e6i	−0.169531	+	0.293636i	0.768724	+	0.639580i	$0.220892\pi$
$602$	−3.62418e6			−0.407585
$603$		0			0
$604$	5.29876e6			0.590992
$605$	−40561.6	+	70254.8i	−0.00450533	+	0.00780347i
$606$		0			0
$607$	757606.	+	1.31221e6i	0.0834587	+	0.144555i	0.904733	−	0.425978i	$-0.140070\pi$
$607$	757606.	+	1.31221e6i	0.0834587	+	0.144555i	−0.821275	+	0.570533i	$0.806737\pi$
$608$	−2.54616e6	−	4.41008e6i	−0.279336	−	0.483824i
$609$		0			0
$610$	27074.2	−	46893.9i	0.00294599	−	0.00510260i
$611$	−874036.			−0.0947166
$612$		0			0
$613$	−6.71159e6			−0.721397			−0.360698	−	0.932683i	$-0.617462\pi$
$613$	−6.71159e6			−0.721397			−0.360698	+	0.932683i	$0.617462\pi$
$614$	−2.25163e6	+	3.89994e6i	−0.241033	+	0.417481i
$615$		0			0
$616$	6.64700e6	+	1.15129e7i	0.705787	+	1.22246i
$617$	3.98994e6	+	6.91077e6i	0.421942	+	0.730826i	0.996129	−	0.0878986i	$-0.0280151\pi$
$617$	3.98994e6	+	6.91077e6i	0.421942	+	0.730826i	−0.574187	+	0.818724i	$0.694682\pi$
$618$		0			0
$619$	335377.	−	580890.i	0.0351809	−	0.0609351i	−0.847899	−	0.530158i	$-0.822133\pi$
$619$	335377.	−	580890.i	0.0351809	−	0.0609351i	0.883080	+	0.469223i	$0.155466\pi$
$620$	881317.			0.0920774
$621$		0			0
$622$	7.32012e6			0.758652
$623$	−4.08346e6	+	7.07277e6i	−0.421511	+	0.730078i
$624$		0			0
$625$	−4.57684e6	−	7.92731e6i	−0.468668	−	0.811757i
$626$	1.69391e6	+	2.93395e6i	0.172765	+	0.299238i
$627$		0			0
$628$	4.92378e6	−	8.52824e6i	0.498195	−	0.862899i
$629$	2.67789e6			0.269877
$630$		0			0
$631$	−4.37169e6			−0.437095			−0.218548	−	0.975826i	$-0.570132\pi$
$631$	−4.37169e6			−0.437095			−0.218548	+	0.975826i	$0.570132\pi$
$632$	4.65105e6	−	8.05585e6i	0.463189	−	0.802267i
$633$		0			0
$634$	705591.	+	1.22212e6i	0.0697156	+	0.120751i
$635$	−1.03474e6	−	1.79223e6i	−0.101835	−	0.176384i
$636$		0			0
$637$	−863936.	+	1.49638e6i	−0.0843593	+	0.146115i
$638$	7.30751e6			0.710751
$639$		0			0
$640$	−849865.			−0.0820163
$641$	6.89117e6	−	1.19359e7i	0.662442	−	1.14738i	−0.317530	−	0.948248i	$-0.602853\pi$
$641$	6.89117e6	−	1.19359e7i	0.662442	−	1.14738i	0.979972	−	0.199135i	$-0.0638133\pi$
$642$		0			0
$643$	746906.	+	1.29368e6i	0.0712424	+	0.123395i	0.899446	−	0.437032i	$-0.143970\pi$
$643$	746906.	+	1.29368e6i	0.0712424	+	0.123395i	−0.828204	+	0.560427i	$0.810637\pi$
$644$	989244.	+	1.71342e6i	0.0939915	+	0.162798i
$645$		0			0
$646$	−3.54737e6	+	6.14422e6i	−0.334445	+	0.579276i
$647$	−1.27773e7			−1.19999			−0.599997	−	0.800002i	$-0.704832\pi$
$647$	−1.27773e7			−1.19999			−0.599997	+	0.800002i	$0.704832\pi$
$648$		0			0
$649$	−4.03374e6			−0.375920
$650$	677323.	−	1.17316e6i	0.0628799	−	0.108911i
$651$		0			0
$652$	−2.26686e6	−	3.92632e6i	−0.208836	−	0.361715i
$653$	2.42085e6	+	4.19304e6i	0.222170	+	0.384810i	0.955467	−	0.295099i	$-0.0953526\pi$
$653$	2.42085e6	+	4.19304e6i	0.222170	+	0.384810i	−0.733297	+	0.679909i	$0.762019\pi$
$654$		0			0
$655$	137135.	−	237524.i	0.0124895	−	0.0216324i
$656$	100073.			0.00907938
$657$		0			0
$658$	−4.43688e6			−0.399496
$659$	6.63829e6	−	1.14979e7i	0.595447	−	1.03134i	−0.398037	−	0.917369i	$-0.630308\pi$
$659$	6.63829e6	−	1.14979e7i	0.595447	−	1.03134i	0.993484	−	0.113975i	$-0.0363582\pi$
$660$		0			0
$661$	−8.76351e6	−	1.51788e7i	−0.780143	−	1.35125i	−0.931858	−	0.362823i	$-0.881813\pi$
$661$	−8.76351e6	−	1.51788e7i	−0.780143	−	1.35125i	0.151715	−	0.988424i	$-0.451520\pi$
$662$	4.89782e6	+	8.48327e6i	0.434368	+	0.752347i
$663$		0			0
$664$	5.09561e6	−	8.82586e6i	0.448514	−	0.776850i
$665$	1.26774e6			0.111167
$666$		0			0
$667$	2.90137e6			0.252516
$668$	−2.39865e6	+	4.15458e6i	−0.207982	+	0.360235i
$669$		0			0
$670$	570909.	+	988843.i	0.0491338	+	0.0851022i
$671$	385830.	+	668277.i	0.0330819	+	0.0572995i
$672$		0			0
$673$	9.25108e6	−	1.60233e7i	0.787326	−	1.36369i	−0.140273	−	0.990113i	$-0.544798\pi$
$673$	9.25108e6	−	1.60233e7i	0.787326	−	1.36369i	0.927599	−	0.373576i	$-0.121869\pi$
$674$	−93176.3			−0.00790052
$675$		0			0
$676$	6.83032e6			0.574876
$677$	1.97541e6	−	3.42152e6i	0.165648	−	0.286911i	−0.771237	−	0.636548i	$-0.780362\pi$
$677$	1.97541e6	−	3.42152e6i	0.165648	−	0.286911i	0.936885	+	0.349637i	$0.113695\pi$
$678$		0			0
$679$	3.79206e6	+	6.56803e6i	0.315646	+	0.546715i
$680$	1.65171e6	+	2.86085e6i	0.136981	+	0.237259i
$681$		0			0
$682$	4.19371e6	−	7.26372e6i	0.345253	−	0.597995i
$683$	−746853.			−0.0612609			−0.0306304	−	0.999531i	$-0.509751\pi$
$683$	−746853.			−0.0612609			−0.0306304	+	0.999531i	$0.509751\pi$
$684$		0			0
$685$	−1.52294e6			−0.124010
$686$	891401.	−	1.54395e6i	0.0723208	−	0.125263i
$687$		0			0
$688$	−120881.	−	209373.i	−0.00973618	−	0.0168636i
$689$	−712625.	−	1.23430e6i	−0.0571891	−	0.0990544i
$690$		0			0
$691$	−4.00126e6	+	6.93039e6i	−0.318788	+	0.552157i	−0.980235	−	0.197835i	$-0.936609\pi$
$691$	−4.00126e6	+	6.93039e6i	−0.318788	+	0.552157i	0.661448	+	0.749991i	$0.269942\pi$
$692$	9.81668e6			0.779291
$693$		0			0
$694$	6.69794e6			0.527889
$695$	1.37599e6	−	2.38328e6i	0.108057	−	0.187160i
$696$		0			0
$697$	2.65617e6	+	4.60062e6i	0.207097	+	0.358702i
$698$	−2.30629e6	−	3.99462e6i	−0.179175	−	0.310339i
$699$		0			0
$700$	−5.14859e6	+	8.91761e6i	−0.397139	+	0.687865i
$701$	−1.57926e7			−1.21383			−0.606914	−	0.794767i	$-0.707593\pi$
$701$	−1.57926e7			−1.21383			−0.606914	+	0.794767i	$0.707593\pi$
$702$		0			0
$703$	1.07336e6			0.0819139
$704$	−4.50637e6	+	7.80526e6i	−0.342685	+	0.593548i
$705$		0			0
$706$	−2.49584e6	−	4.32293e6i	−0.188454	−	0.326412i
$707$	6.61845e6	+	1.14635e7i	0.497975	+	0.862518i
$708$		0			0
$709$	−9.54046e6	+	1.65246e7i	−0.712777	+	1.23457i	0.251033	+	0.967978i	$0.419230\pi$
$709$	−9.54046e6	+	1.65246e7i	−0.712777	+	1.23457i	−0.963811	+	0.266588i	$0.914104\pi$
$710$	−1.26544e6			−0.0942094
$711$		0			0
$712$	−8.52996e6			−0.630590
$713$	1.66507e6	−	2.88398e6i	0.122661	−	0.212456i
$714$		0			0
$715$	−207405.	−	359237.i	−0.0151724	−	0.0262794i
$716$	−2.44202e6	−	4.22970e6i	−0.178019	−	0.308338i
$717$		0			0
$718$	−5.63653e6	+	9.76276e6i	−0.408038	+	0.706743i
$719$	−1.74493e6			−0.125880			−0.0629399	−	0.998017i	$-0.520048\pi$
$719$	−1.74493e6			−0.125880			−0.0629399	+	0.998017i	$0.520048\pi$
$720$		0			0
$721$	1.78089e7			1.27585
$722$	3.00980e6	−	5.21312e6i	0.214879	−	0.372181i
$723$		0			0
$724$	−406890.	−	704755.i	−0.0288490	−	0.0499680i
$725$	7.55018e6	+	1.30773e7i	0.533473	+	0.924002i
$726$		0			0
$727$	−1.04470e6	+	1.80947e6i	−0.0733087	+	0.126974i	−0.900350	−	0.435167i	$-0.856689\pi$
$727$	−1.04470e6	+	1.80947e6i	−0.0733087	+	0.126974i	0.827041	+	0.562142i	$0.190022\pi$
$728$	−3.97617e6			−0.278059
$729$		0			0
$730$	−1.51329e6			−0.105103
$731$	6.41696e6	−	1.11145e7i	0.444156	−	0.769301i
$732$		0			0
$733$	1.00097e7	+	1.73373e7i	0.688114	+	1.19185i	0.972447	+	0.233123i	$0.0748946\pi$
$733$	1.00097e7	+	1.73373e7i	0.688114	+	1.19185i	−0.284333	+	0.958726i	$0.591772\pi$
$734$	−6.42359e6	−	1.11260e7i	−0.440086	−	0.762251i
$735$		0			0
$736$	−1.67914e6	+	2.90836e6i	−0.114260	+	0.197904i
$737$	−1.62719e7			−1.10349
$738$		0			0
$739$	−1.93522e6			−0.130353			−0.0651763	−	0.997874i	$-0.520761\pi$
$739$	−1.93522e6			−0.130353			−0.0651763	+	0.997874i	$0.520761\pi$
$740$	93667.4	−	162237.i	0.00628795	−	0.0108910i
$741$		0			0
$742$	−3.61750e6	−	6.26570e6i	−0.241212	−	0.417792i
$743$	−4.52092e6	−	7.83046e6i	−0.300438	−	0.520373i	0.675797	−	0.737087i	$-0.263799\pi$
$743$	−4.52092e6	−	7.83046e6i	−0.300438	−	0.520373i	−0.976235	+	0.216714i	$0.930466\pi$
$744$		0			0
$745$	1.57252e6	−	2.72369e6i	0.103802	−	0.179791i
$746$	−1.20668e7			−0.793863
$747$		0			0
$748$	−1.76461e7			−1.15317
$749$	−1.56833e7	+	2.71643e7i	−1.02149	+	1.76927i
$750$		0			0
$751$	−9.16416e6	−	1.58728e7i	−0.592915	−	1.02696i	−0.993837	−	0.110847i	$-0.964644\pi$
$751$	−9.16416e6	−	1.58728e7i	−0.592915	−	1.02696i	0.400922	−	0.916112i	$-0.368690\pi$
$752$	−147988.	−	256323.i	−0.00954294	−	0.0165289i
$753$		0			0
$754$	−1.09282e6	+	1.89282e6i	−0.0700036	+	0.121250i
$755$	−2.23909e6			−0.142957
$756$		0			0
$757$	−2.00372e7			−1.27086			−0.635429	−	0.772159i	$-0.719177\pi$
$757$	−2.00372e7			−1.27086			−0.635429	+	0.772159i	$0.719177\pi$
$758$	3.26997e6	−	5.66376e6i	0.206715	−	0.358040i
$759$		0			0
$760$	662045.	+	1.14670e6i	0.0415771	+	0.0720136i
$761$	7.82878e6	+	1.35598e7i	0.490041	+	0.848776i	0.999934	−	0.0114616i	$-0.00364841\pi$
$761$	7.82878e6	+	1.35598e7i	0.490041	+	0.848776i	−0.509893	+	0.860238i	$0.670315\pi$
$762$		0			0
$763$	3.33184e6	−	5.77092e6i	0.207192	−	0.358867i
$764$	−5.12780e6			−0.317832
$765$		0			0
$766$	2.03871e7			1.25541
$767$	603236.	−	1.04483e6i	0.0370253	−	0.0641297i
$768$		0			0
$769$	8.33840e6	+	1.44425e7i	0.508472	+	0.880699i	0.999952	+	0.00981049i	$0.00312282\pi$
$769$	8.33840e6	+	1.44425e7i	0.508472	+	0.880699i	−0.491480	+	0.870889i	$0.663544\pi$
$770$	−1.05285e6	−	1.82360e6i	−0.0639943	−	0.110841i
$771$		0			0
$772$	2.45223e6	−	4.24739e6i	0.148087	−	0.256495i
$773$	1.89296e7			1.13944			0.569721	−	0.821838i	$-0.307051\pi$
$773$	1.89296e7			1.13944			0.569721	+	0.821838i	$0.307051\pi$
$774$		0			0
$775$	1.73319e7			1.03655
$776$	−3.96062e6	+	6.85999e6i	−0.236107	+	0.408949i
$777$		0			0
$778$	−5.12322e6	−	8.87368e6i	−0.303455	−	0.525599i
$779$	1.06466e6	+	1.84404e6i	0.0628587	+	0.108874i
$780$		0			0
$781$	9.01676e6	−	1.56175e7i	0.528960	−	0.916186i
$782$	4.67884e6			0.273603
$783$		0			0
$784$	−585112.			−0.0339977
$785$	−2.08064e6	+	3.60377e6i	−0.120510	+	0.208729i
$786$		0			0
$787$	1.87371e6	+	3.24536e6i	0.107837	+	0.186778i	0.914894	−	0.403695i	$-0.132274\pi$
$787$	1.87371e6	+	3.24536e6i	0.107837	+	0.186778i	−0.807057	+	0.590473i	$0.798941\pi$
$788$	−6.24476e6	−	1.08162e7i	−0.358262	−	0.620527i
$789$		0			0
$790$	−736705.	+	1.27601e6i	−0.0419977	+	0.0727422i
$791$	3.53782e7			2.01045
$792$		0			0
$793$	−230800.			−0.0130333
$794$	668361.	−	1.15763e6i	0.0376235	−	0.0651659i
$795$		0			0
$796$	3.79568e6	+	6.57432e6i	0.212328	+	0.367763i
$797$	−7.58701e6	−	1.31411e7i	−0.423082	−	0.732800i	0.573157	−	0.819446i	$-0.305719\pi$
$797$	−7.58701e6	−	1.31411e7i	−0.423082	−	0.732800i	−0.996239	+	0.0866454i	$0.972385\pi$
$798$		0			0
$799$	7.85591e6	−	1.36068e7i	0.435341	−	0.754033i
$800$	−1.74784e7			−0.965557
$801$		0			0
$802$	−8.51694e6			−0.467571
$803$	1.07828e7	−	1.86764e7i	0.590125	−	1.02213i
$804$		0			0
$805$	−418024.	−	724039.i	−0.0227359	−	0.0393797i
$806$	1.25432e6	+	2.17254e6i	0.0680096	+	0.117796i
$807$		0			0
$808$	−6.91265e6	+	1.19731e7i	−0.372491	+	0.645174i
$809$	3.67446e7			1.97389			0.986943	−	0.161067i	$-0.0514936\pi$
$809$	3.67446e7			1.97389			0.986943	+	0.161067i	$0.0514936\pi$
$810$		0			0
$811$	−3.10069e7			−1.65541			−0.827706	−	0.561162i	$-0.810355\pi$
$811$	−3.10069e7			−1.65541			−0.827706	+	0.561162i	$0.810355\pi$
$812$	8.30694e6	−	1.43880e7i	0.442131	−	0.765794i
$813$		0			0
$814$	−891424.	−	1.54399e6i	−0.0471545	−	0.0816740i
$815$	957907.	+	1.65914e6i	0.0505160	+	0.0874963i
$816$		0			0
$817$	2.57207e6	−	4.45496e6i	0.134812	−	0.233501i
$818$	1.45098e7			0.758192
$819$		0			0
$820$	371631.			0.0193009
$821$	−2.14433e6	+	3.71409e6i	−0.111028	+	0.192307i	−0.916185	−	0.400755i	$-0.868748\pi$
$821$	−2.14433e6	+	3.71409e6i	−0.111028	+	0.192307i	0.805157	+	0.593062i	$0.202081\pi$
$822$		0			0
$823$	−6.66686e6	−	1.15473e7i	−0.343101	−	0.594268i	0.641906	−	0.766783i	$-0.278144\pi$
$823$	−6.66686e6	−	1.15473e7i	−0.343101	−	0.594268i	−0.985007	+	0.172515i	$0.944811\pi$
$824$	9.30027e6	+	1.61085e7i	0.477175	+	0.826491i
$825$		0			0
$826$	3.06221e6	−	5.30390e6i	0.156165	−	0.270486i
$827$	−6.58421e6			−0.334765			−0.167382	−	0.985892i	$-0.553531\pi$
$827$	−6.58421e6			−0.334765			−0.167382	+	0.985892i	$0.553531\pi$
$828$		0			0
$829$	3.49408e7			1.76582			0.882909	−	0.469544i	$-0.155582\pi$
$829$	3.49408e7			1.76582			0.882909	+	0.469544i	$0.155582\pi$
$830$	−807122.	+	1.39798e6i	−0.0406672	+	0.0704376i
$831$		0			0
$832$	−1.34783e6	−	2.33452e6i	−0.0675038	−	0.116920i
$833$	−1.55303e7	−	2.68992e7i	−0.775472	−	1.34316i
$834$		0			0
$835$	1.01359e6	−	1.75560e6i	0.0503093	−	0.0871382i
$836$	−7.07299e6			−0.350015
$837$		0			0
$838$	1.44503e7			0.710831
$839$	−1.85769e7	+	3.21761e7i	−0.911105	+	1.57808i	−0.0985980	+	0.995127i	$0.531436\pi$
$839$	−1.85769e7	+	3.21761e7i	−0.911105	+	1.57808i	−0.812507	+	0.582952i	$0.801898\pi$
$840$		0			0
$841$	−1.92620e6	−	3.33628e6i	−0.0939100	−	0.162657i
$842$	1.05747e6	+	1.83159e6i	0.0514028	+	0.0890322i
$843$		0			0
$844$	5.93427e6	−	1.02785e7i	0.286755	−	0.496674i
$845$	−2.88628e6			−0.139058
$846$		0			0
$847$	1.75527e6			0.0840688
$848$	241317.	−	417974.i	0.0115239	−	0.0199600i
$849$		0			0
$850$	1.21757e7	+	2.10889e7i	0.578023	+	1.00117i
$851$	−353931.	−	613026.i	−0.0167531	−	0.0290171i
$852$		0			0
$853$	−6.28069e6	+	1.08785e7i	−0.295552	+	0.511912i	−0.975113	−	0.221707i	$-0.928837\pi$
$853$	−6.28069e6	+	1.08785e7i	−0.295552	+	0.511912i	0.679561	+	0.733619i	$0.262170\pi$
$854$	−1.17161e6			−0.0549717
$855$		0			0
$856$	−3.27609e7			−1.52817
$857$	−1.88788e7	+	3.26990e7i	−0.878055	+	1.52084i	−0.0245827	+	0.999698i	$0.507826\pi$
$857$	−1.88788e7	+	3.26990e7i	−0.878055	+	1.52084i	−0.853472	+	0.521138i	$0.825508\pi$
$858$		0			0
$859$	−4.11422e6	−	7.12604e6i	−0.190241	−	0.329507i	0.755089	−	0.655622i	$-0.227594\pi$
$859$	−4.11422e6	−	7.12604e6i	−0.190241	−	0.329507i	−0.945330	+	0.326115i	$0.894260\pi$
$860$	−448906.	−	777528.i	−0.0206971	−	0.0358484i
$861$		0			0
$862$	−9.05733e6	+	1.56878e7i	−0.415176	+	0.719105i
$863$	−2.85773e7			−1.30615			−0.653077	−	0.757291i	$-0.726522\pi$
$863$	−2.85773e7			−1.30615			−0.653077	+	0.757291i	$0.726522\pi$
$864$		0			0
$865$	−4.14823e6			−0.188505
$866$	−6.04215e6	+	1.04653e7i	−0.273777	+	0.474195i
$867$		0			0
$868$	−9.53455e6	−	1.65143e7i	−0.429537	−	0.743980i
$869$	−1.04987e7	−	1.81842e7i	−0.471612	−	0.816855i
$870$		0			0
$871$	2.43342e6	−	4.21481e6i	0.108686	−	0.188249i
$872$	6.95989e6			0.309964
$873$		0			0
$874$	1.87539e6			0.0830450
$875$	4.39802e6	−	7.61759e6i	0.194195	−	0.336355i
$876$		0			0
$877$	1.58797e7	+	2.75045e7i	0.697180	+	1.20755i	0.969440	+	0.245327i	$0.0788953\pi$
$877$	1.58797e7	+	2.75045e7i	0.697180	+	1.20755i	−0.272261	+	0.962223i	$0.587771\pi$
$878$	−6.08008e6	−	1.05310e7i	−0.266178	−	0.461035i
$879$		0			0
$880$	70234.0	−	121649.i	0.00305732	−	0.00529543i
$881$	1.74609e7			0.757924			0.378962	−	0.925412i	$-0.376281\pi$
$881$	1.74609e7			0.757924			0.378962	+	0.925412i	$0.376281\pi$
$882$		0			0
$883$	−1.63763e7			−0.706829			−0.353415	−	0.935467i	$-0.614979\pi$
$883$	−1.63763e7			−0.706829			−0.353415	+	0.935467i	$0.614979\pi$
$884$	2.63894e6	−	4.57077e6i	0.113579	−	0.196725i
$885$		0			0
$886$	−7.59544e6	−	1.31557e7i	−0.325064	−	0.563027i
$887$	−2.53921e6	−	4.39804e6i	−0.108365	−	0.187694i	0.806743	−	0.590903i	$-0.201228\pi$
$887$	−2.53921e6	−	4.39804e6i	−0.108365	−	0.187694i	−0.915108	+	0.403209i	$0.867895\pi$
$888$		0			0
$889$	−2.23888e7	+	3.87785e7i	−0.950115	+	1.64565i
$890$	1.35111e6			0.0571761
$891$		0			0
$892$	1.68313e7			0.708282
$893$	3.14884e6	−	5.45395e6i	0.132136	−	0.228866i
$894$		0			0
$895$	1.03192e6	+	1.78734e6i	0.0430616	+	0.0745848i
$896$	9.19429e6	+	1.59250e7i	0.382603	+	0.662687i
$897$		0			0
$898$	929542.	−	1.61001e6i	0.0384661	−	0.0666252i
$899$	−2.79640e7			−1.15399
$900$		0			0
$901$	2.56205e7			1.05142
$902$	1.76839e6	−	3.06294e6i	0.0723704	−	0.125349i
$903$		0			0
$904$	1.84754e7	+	3.20003e7i	0.751922	+	1.30237i
$905$	171939.	+	297808.i	0.00697837	+	0.0120869i
$906$		0			0
$907$	923315.	−	1.59923e6i	0.0372676	−	0.0645494i	−0.846790	−	0.531927i	$-0.821468\pi$
$907$	923315.	−	1.59923e6i	0.0372676	−	0.0645494i	0.884058	+	0.467378i	$0.154801\pi$
$908$	1.02028e7			0.410682
$909$		0			0
$910$	629807.			0.0252118
$911$	2.19578e7	−	3.80320e7i	0.876582	−	1.51829i	0.0215150	−	0.999769i	$-0.493151\pi$
$911$	2.19578e7	−	3.80320e7i	0.876582	−	1.51829i	0.855067	−	0.518517i	$-0.173516\pi$
$912$		0			0
$913$	−1.15022e7	−	1.99223e7i	−0.456670	−	0.790976i
$914$	1.44093e7	+	2.49577e7i	0.570529	+	0.988186i
$915$		0			0
$916$	−1.09654e7	+	1.89926e7i	−0.431803	+	0.747904i
$917$	−5.93438e6			−0.233051
$918$		0			0
$919$	−2.53760e7			−0.991140			−0.495570	−	0.868568i	$-0.665041\pi$
$919$	−2.53760e7			−0.991140			−0.495570	+	0.868568i	$0.665041\pi$
$920$	436606.	−	756224.i	0.0170067	−	0.0294565i
$921$		0			0
$922$	−6.31742e6	−	1.09421e7i	−0.244744	−	0.423909i
$923$	2.69687e6	+	4.67112e6i	0.104197	+	0.180475i
$924$		0			0
$925$	1.84205e6	−	3.19053e6i	0.0707861	−	0.122605i
$926$	−2.72488e7			−1.04429
$927$		0			0
$928$	2.82004e7			1.07494
$929$	−2.02111e7	+	3.50067e7i	−0.768336	+	1.33080i	0.170129	+	0.985422i	$0.445582\pi$
$929$	−2.02111e7	+	3.50067e7i	−0.768336	+	1.33080i	−0.938465	+	0.345375i	$0.887752\pi$
$930$		0			0
$931$	−6.22490e6	−	1.07818e7i	−0.235374	−	0.407680i
$932$	7.85382e6	+	1.36032e7i	0.296170	+	0.512982i
$933$		0			0
$934$	1.27090e7	−	2.20127e7i	0.476700	−	0.825668i
$935$	7.45671e6			0.278945
$936$		0			0
$937$	1.79012e7			0.666089			0.333044	−	0.942911i	$-0.391924\pi$
$937$	1.79012e7			0.666089			0.333044	+	0.942911i	$0.391924\pi$
$938$	1.23528e7	−	2.13957e7i	0.458414	−	0.793996i
$939$		0			0
$940$	−549569.	−	951882.i	−0.0202863	−	0.0351369i
$941$	−412928.	−	715212.i	−0.0152020	−	0.0263306i	0.858324	−	0.513108i	$-0.171506\pi$
$941$	−412928.	−	715212.i	−0.0152020	−	0.0263306i	−0.873526	+	0.486777i	$0.838172\pi$
$942$		0			0
$943$	702120.	−	1.21611e6i	0.0257118	−	0.0445341i
$944$	408549.			0.0149216
$945$		0			0
$946$	−8.54440e6			−0.310423
$947$	2.71734e7	−	4.70657e7i	0.984620	−	1.70541i	0.341006	−	0.940061i	$-0.389232\pi$
$947$	2.71734e7	−	4.70657e7i	0.984620	−	1.70541i	0.643614	−	0.765351i	$-0.277434\pi$
$948$		0			0
$949$	3.22509e6	+	5.58602e6i	0.116246	+	0.201343i
$950$	4.88030e6	+	8.45293e6i	0.175444	+	0.303877i
$951$		0			0
$952$	3.57382e7	−	6.19003e7i	1.27803	−	2.21361i
$953$	−4.00436e6			−0.142824			−0.0714119	−	0.997447i	$-0.522750\pi$
$953$	−4.00436e6			−0.142824			−0.0714119	+	0.997447i	$0.522750\pi$
$954$		0			0
$955$	2.16685e6			0.0768813
$956$	−1.80811e6	+	3.13174e6i	−0.0639854	+	0.110826i
$957$		0			0
$958$	−2.01941e6	−	3.49772e6i	−0.0710903	−	0.123132i
$959$	1.64759e7	+	2.85371e7i	0.578500	+	1.00199i
$960$		0			0
$961$	−1.73371e6	+	3.00287e6i	−0.0605574	+	0.104889i
$962$	533242.			0.0185775
$963$		0			0
$964$	−863842.			−0.0299393
$965$	−1.03624e6	+	1.79482e6i	−0.0358213	+	0.0620443i
$966$		0			0
$967$	−1.61712e7	−	2.80093e7i	−0.556130	−	0.963245i	−0.997815	−	0.0660745i	$-0.978952\pi$
$967$	−1.61712e7	−	2.80093e7i	−0.556130	−	0.963245i	0.441685	−	0.897170i	$-0.354381\pi$
$968$	916646.	+	1.58768e6i	0.0314422	+	0.0544595i
$969$		0			0
$970$	627344.	−	1.08659e6i	0.0214080	−	0.0370798i
$971$	2.08060e7			0.708176			0.354088	−	0.935212i	$-0.384791\pi$
$971$	2.08060e7			0.708176			0.354088	+	0.935212i	$0.384791\pi$
$972$		0			0
$973$	−5.95446e7			−2.01632
$974$	−3.92505e6	+	6.79838e6i	−0.132571	+	0.229619i
$975$		0			0
$976$	−39078.1	−	67685.2i	−0.00131313	−	0.00227441i
$977$	−1.24444e7	−	2.15543e7i	−0.417097	−	0.722433i	0.578549	−	0.815647i	$-0.303619\pi$
$977$	−1.24444e7	−	2.15543e7i	−0.417097	−	0.722433i	−0.995646	+	0.0932148i	$0.970286\pi$
$978$		0			0
$979$	−9.62720e6	+	1.66748e7i	−0.321028	+	0.556037i
$980$	−2.17288e6			−0.0722719
$981$		0			0
$982$	−1.49417e7			−0.494448
$983$	−2.11280e6	+	3.65948e6i	−0.0697388	+	0.120791i	−0.898786	−	0.438387i	$-0.855550\pi$
$983$	−2.11280e6	+	3.65948e6i	−0.0697388	+	0.120791i	0.829047	+	0.559178i	$0.188883\pi$
$984$		0			0
$985$	2.63885e6	+	4.57062e6i	0.0866610	+	0.150101i
$986$	−1.96447e7	−	3.40257e7i	−0.643508	−	1.11459i
$987$		0			0
$988$	1.05775e6	−	1.83207e6i	0.0344739	−	0.0597105i
$989$	−3.39246e6			−0.110287
$990$		0			0
$991$	3.01661e7			0.975741			0.487871	−	0.872916i	$-0.337774\pi$
$991$	3.01661e7			0.975741			0.487871	+	0.872916i	$0.337774\pi$
$992$	1.61840e7	−	2.80315e7i	0.522163	−	0.904412i
$993$		0			0
$994$	1.36901e7	+	2.37120e7i	0.439483	+	0.761207i
$995$	−1.60394e6	−	2.77811e6i	−0.0513607	−	0.0889593i
$996$		0			0
$997$	3.97488e6	−	6.88470e6i	0.126645	−	0.219355i	−0.795730	−	0.605652i	$-0.792913\pi$
$997$	3.97488e6	−	6.88470e6i	0.126645	−	0.219355i	0.922375	+	0.386297i	$0.126246\pi$
$998$	1.44246e7			0.458436
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.6.c.a.19.2		8
3.2	odd	2		9.6.c.a.7.3	yes	8
4.3	odd	2		432.6.i.c.289.3		8
9.2	odd	6		81.6.a.c.1.2		4
9.4	even	3	inner	27.6.c.a.10.2		8
9.5	odd	6		9.6.c.a.4.3	✓	8
9.7	even	3		81.6.a.d.1.3		4
12.11	even	2		144.6.i.c.97.2		8
36.23	even	6		144.6.i.c.49.2		8
36.31	odd	6		432.6.i.c.145.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.6.c.a.4.3	✓	8	9.5	odd	6
9.6.c.a.7.3	yes	8	3.2	odd	2
27.6.c.a.10.2		8	9.4	even	3	inner
27.6.c.a.19.2		8	1.1	even	1	trivial
81.6.a.c.1.2		4	9.2	odd	6
81.6.a.d.1.3		4	9.7	even	3
144.6.i.c.49.2		8	36.23	even	6
144.6.i.c.97.2		8	12.11	even	2
432.6.i.c.145.3		8	36.31	odd	6
432.6.i.c.289.3		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.78978 + 3.09998i) q^{2} +(9.59340 + 16.6162i) q^{4} +(-4.05388 - 7.02152i) q^{5} +(-87.7139 + 151.925i) q^{7} -183.226 q^{8} +O(q^{10})\)	\(q+(-1.78978 + 3.09998i) q^{2} +(9.59340 + 16.6162i) q^{4} +(-4.05388 - 7.02152i) q^{5} +(-87.7139 + 151.925i) q^{7} -183.226 q^{8} +29.0221 q^{10} +(-206.795 + 358.179i) q^{11} +(-61.8514 - 107.130i) q^{13} +(-313.977 - 543.824i) q^{14} +(20.9448 - 36.2775i) q^{16} +2223.70 q^{17} +891.313 q^{19} +(77.7809 - 134.720i) q^{20} +(-740.234 - 1282.12i) q^{22} +(-293.902 - 509.053i) q^{23} +(1529.63 - 2649.40i) q^{25} +442.801 q^{26} -3365.90 q^{28} +(-2467.97 + 4274.65i) q^{29} +(2832.69 + 4906.37i) q^{31} +(-2856.64 - 4947.85i) q^{32} +(-3979.93 + 6893.45i) q^{34} +1422.33 q^{35} +1204.25 q^{37} +(-1595.25 + 2763.06i) q^{38} +(742.775 + 1286.52i) q^{40} +(1194.48 + 2068.90i) q^{41} +(2885.71 - 4998.19i) q^{43} -7935.46 q^{44} +2104.08 q^{46} +(3532.81 - 6119.00i) q^{47} +(-6983.97 - 12096.6i) q^{49} +(5475.40 + 9483.67i) q^{50} +(1186.73 - 2055.48i) q^{52} +11521.6 q^{53} +3353.28 q^{55} +(16071.5 - 27836.6i) q^{56} +(-8834.24 - 15301.4i) q^{58} +(4876.49 + 8446.33i) q^{59} +(932.881 - 1615.80i) q^{61} -20279.5 q^{62} +21791.5 q^{64} +(-501.476 + 868.582i) q^{65} +(19671.5 + 34072.0i) q^{67} +(21332.9 + 36949.6i) q^{68} +(-2545.65 + 4409.19i) q^{70} -43602.4 q^{71} -52142.6 q^{73} +(-2155.33 + 3733.15i) q^{74} +(8550.72 + 14810.3i) q^{76} +(-36277.6 - 62834.6i) q^{77} +(-25384.2 + 43966.8i) q^{79} -339.631 q^{80} -8551.41 q^{82} +(-27810.6 + 48169.3i) q^{83} +(-9014.62 - 15613.8i) q^{85} +(10329.5 + 17891.3i) q^{86} +(37890.2 - 65627.7i) q^{88} +46554.3 q^{89} +21700.9 q^{91} +(5639.04 - 9767.10i) q^{92} +(12645.9 + 21903.3i) q^{94} +(-3613.27 - 6258.38i) q^{95} +(21616.0 - 37440.1i) q^{97} +49999.0 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} - 49 q^{4} - 78 q^{5} + 28 q^{7} + 750 q^{8}+O(q^{10}) \) 8 * q - 3 * q^2 - 49 * q^4 - 78 * q^5 + 28 * q^7 + 750 * q^8	\( 8 q - 3 q^{2} - 49 q^{4} - 78 q^{5} + 28 q^{7} + 750 q^{8} + 60 q^{10} - 444 q^{11} - 182 q^{13} - 1392 q^{14} - 289 q^{16} + 4356 q^{17} + 952 q^{19} - 6684 q^{20} + 1011 q^{22} - 8844 q^{23} - 1654 q^{25} + 24888 q^{26} - 1604 q^{28} - 12018 q^{29} + 1132 q^{31} - 8703 q^{32} + 10125 q^{34} + 16224 q^{35} - 15176 q^{37} + 11145 q^{38} - 8736 q^{40} - 1248 q^{41} - 6092 q^{43} - 49530 q^{44} + 45960 q^{46} + 60 q^{47} + 9090 q^{49} + 57057 q^{50} - 32510 q^{52} - 20952 q^{53} - 36120 q^{55} + 61170 q^{56} + 8328 q^{58} - 2076 q^{59} + 48142 q^{61} - 241764 q^{62} - 20926 q^{64} + 13146 q^{65} - 7148 q^{67} + 123129 q^{68} - 654 q^{70} + 71856 q^{71} + 122452 q^{73} + 160320 q^{74} - 49571 q^{76} - 39534 q^{77} - 59516 q^{79} - 124512 q^{80} - 233598 q^{82} - 117696 q^{83} + 28836 q^{85} + 15915 q^{86} + 104523 q^{88} + 451728 q^{89} + 111392 q^{91} - 134034 q^{92} + 169464 q^{94} - 294888 q^{95} + 33976 q^{97} - 57654 q^{98}+O(q^{100}) \) 8 * q - 3 * q^2 - 49 * q^4 - 78 * q^5 + 28 * q^7 + 750 * q^8 + 60 * q^10 - 444 * q^11 - 182 * q^13 - 1392 * q^14 - 289 * q^16 + 4356 * q^17 + 952 * q^19 - 6684 * q^20 + 1011 * q^22 - 8844 * q^23 - 1654 * q^25 + 24888 * q^26 - 1604 * q^28 - 12018 * q^29 + 1132 * q^31 - 8703 * q^32 + 10125 * q^34 + 16224 * q^35 - 15176 * q^37 + 11145 * q^38 - 8736 * q^40 - 1248 * q^41 - 6092 * q^43 - 49530 * q^44 + 45960 * q^46 + 60 * q^47 + 9090 * q^49 + 57057 * q^50 - 32510 * q^52 - 20952 * q^53 - 36120 * q^55 + 61170 * q^56 + 8328 * q^58 - 2076 * q^59 + 48142 * q^61 - 241764 * q^62 - 20926 * q^64 + 13146 * q^65 - 7148 * q^67 + 123129 * q^68 - 654 * q^70 + 71856 * q^71 + 122452 * q^73 + 160320 * q^74 - 49571 * q^76 - 39534 * q^77 - 59516 * q^79 - 124512 * q^80 - 233598 * q^82 - 117696 * q^83 + 28836 * q^85 + 15915 * q^86 + 104523 * q^88 + 451728 * q^89 + 111392 * q^91 - 134034 * q^92 + 169464 * q^94 - 294888 * q^95 + 33976 * q^97 - 57654 * q^98

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