LMFDB - Embedded newform 27.6.c.a.19.1

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			19.1
Root			$-2.56934i$ of defining polynomial
Character	$\chi$	$=$	27.19
Dual form			27.6.c.a.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.96163 + 8.59380i) q^{2} +(-33.2356 - 57.5657i) q^{4} +(-23.6560 - 40.9735i) q^{5} +(1.01546 - 1.75882i) q^{7} +342.066 q^{8} +O(q^{10})$	\(q+(-4.96163 + 8.59380i) q^{2} +(-33.2356 - 57.5657i) q^{4} +(-23.6560 - 40.9735i) q^{5} +(1.01546 - 1.75882i) q^{7} +342.066 q^{8} +469.490 q^{10} +(91.8836 - 159.147i) q^{11} +(-364.672 - 631.630i) q^{13} +(10.0766 + 17.4532i) q^{14} +(-633.668 + 1097.55i) q^{16} -1212.88 q^{17} -473.092 q^{19} +(-1572.44 + 2723.55i) q^{20} +(911.785 + 1579.26i) q^{22} +(-1806.42 - 3128.81i) q^{23} +(443.283 - 767.788i) q^{25} +7237.47 q^{26} -134.997 q^{28} +(-663.121 + 1148.56i) q^{29} +(2590.41 + 4486.72i) q^{31} +(-814.997 - 1411.62i) q^{32} +(6017.88 - 10423.3i) q^{34} -96.0867 q^{35} -14715.2 q^{37} +(2347.31 - 4065.65i) q^{38} +(-8091.94 - 14015.6i) q^{40} +(3159.83 + 5472.98i) q^{41} +(-3067.89 + 5313.75i) q^{43} -12215.2 q^{44} +35851.1 q^{46} +(1584.17 - 2743.86i) q^{47} +(8401.44 + 14551.7i) q^{49} +(4398.81 + 7618.96i) q^{50} +(-24240.2 + 41985.2i) q^{52} +12265.0 q^{53} -8694.41 q^{55} +(347.353 - 601.633i) q^{56} +(-6580.32 - 11397.5i) q^{58} +(-14773.5 - 25588.5i) q^{59} +(20153.6 - 34907.1i) q^{61} -51410.7 q^{62} -24379.9 q^{64} +(-17253.4 + 29883.8i) q^{65} +(-11748.9 - 20349.7i) q^{67} +(40310.9 + 69820.5i) q^{68} +(476.747 - 825.750i) q^{70} +123.786 q^{71} +35217.6 q^{73} +(73011.4 - 126459. i) q^{74} +(15723.5 + 27233.8i) q^{76} +(-186.607 - 323.214i) q^{77} +(24072.8 - 41695.3i) q^{79} +59960.3 q^{80} -62711.6 q^{82} +(5167.97 - 8951.18i) q^{83} +(28692.0 + 49696.1i) q^{85} +(-30443.5 - 52729.7i) q^{86} +(31430.3 - 54438.8i) q^{88} +42585.7 q^{89} -1481.23 q^{91} +(-120075. + 207976. i) q^{92} +(15720.1 + 27228.1i) q^{94} +(11191.5 + 19384.2i) q^{95} +(-49347.3 + 85472.1i) q^{97} -166739. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.96163	+	8.59380i	−0.877101	+	1.51918i	−0.0225929	+	0.999745i	$0.507192\pi$
$2$	−4.96163	+	8.59380i	−0.877101	+	1.51918i	−0.854508	+	0.519438i	$0.826141\pi$
$3$		0			0
$3$		0			0
$4$	−33.2356	−	57.5657i	−1.03861	−	1.79893i
$5$	−23.6560	−	40.9735i	−0.423172	−	0.732956i	0.573076	−	0.819503i	$-0.305750\pi$
$5$	−23.6560	−	40.9735i	−0.423172	−	0.732956i	−0.996248	+	0.0865467i	$0.972417\pi$
$6$		0			0
$7$	1.01546	−	1.75882i	0.00783278	−	0.0135668i	−0.862082	−	0.506768i	$-0.830840\pi$
$7$	1.01546	−	1.75882i	0.00783278	−	0.0135668i	0.869915	+	0.493201i	$0.164173\pi$
$8$	342.066			1.88967
$9$		0			0
$10$	469.490			1.48466
$11$	91.8836	−	159.147i	0.228958	−	0.396567i	−0.728541	−	0.685002i	$-0.759801\pi$
$11$	91.8836	−	159.147i	0.228958	−	0.396567i	0.957500	+	0.288435i	$0.0931348\pi$
$12$		0			0
$13$	−364.672	−	631.630i	−0.598472	−	1.03658i	−0.993047	−	0.117720i	$-0.962441\pi$
$13$	−364.672	−	631.630i	−0.598472	−	1.03658i	0.394574	−	0.918864i	$-0.370892\pi$
$14$	10.0766	+	17.4532i	0.0137403	+	0.0237989i
$15$		0			0
$16$	−633.668	+	1097.55i	−0.618817	+	1.07182i
$17$	−1212.88			−1.01788			−0.508940	−	0.860802i	$-0.669963\pi$
$17$	−1212.88			−1.01788			−0.508940	+	0.860802i	$0.669963\pi$
$18$		0			0
$19$	−473.092			−0.300650			−0.150325	−	0.988637i	$-0.548032\pi$
$19$	−473.092			−0.300650			−0.150325	+	0.988637i	$0.548032\pi$
$20$	−1572.44	+	2723.55i	−0.879023	+	1.52251i
$21$		0			0
$22$	911.785	+	1579.26i	0.401639	+	0.695659i
$23$	−1806.42	−	3128.81i	−0.712031	−	1.23327i	−0.964094	−	0.265563i	$-0.914442\pi$
$23$	−1806.42	−	3128.81i	−0.712031	−	1.23327i	0.252063	−	0.967711i	$-0.418891\pi$
$24$		0			0
$25$	443.283	−	767.788i	0.141850	−	0.245692i
$26$	7237.47			2.09968
$27$		0			0
$28$	−134.997			−0.0325409
$29$	−663.121	+	1148.56i	−0.146419	+	0.253605i	−0.929901	−	0.367809i	$-0.880108\pi$
$29$	−663.121	+	1148.56i	−0.146419	+	0.253605i	0.783482	+	0.621414i	$0.213441\pi$
$30$		0			0
$31$	2590.41	+	4486.72i	0.484133	+	0.838542i	0.999834	−	0.0182261i	$-0.00580186\pi$
$31$	2590.41	+	4486.72i	0.484133	+	0.838542i	−0.515701	+	0.856769i	$0.672469\pi$
$32$	−814.997	−	1411.62i	−0.140696	−	0.243692i
$33$		0			0
$34$	6017.88	−	10423.3i	0.892784	−	1.54635i
$35$	−96.0867			−0.0132585
$36$		0			0
$37$	−14715.2			−1.76710			−0.883552	−	0.468334i	$-0.844854\pi$
$37$	−14715.2			−1.76710			−0.883552	+	0.468334i	$0.844854\pi$
$38$	2347.31	−	4065.65i	0.263700	−	0.456742i
$39$		0			0
$40$	−8091.94	−	14015.6i	−0.799655	−	1.38504i
$41$	3159.83	+	5472.98i	0.293564	+	0.508469i	0.974650	−	0.223735i	$-0.0718251\pi$
$41$	3159.83	+	5472.98i	0.293564	+	0.508469i	−0.681085	+	0.732204i	$0.738492\pi$
$42$		0			0
$43$	−3067.89	+	5313.75i	−0.253028	+	0.438258i	−0.964358	−	0.264600i	$-0.914760\pi$
$43$	−3067.89	+	5313.75i	−0.253028	+	0.438258i	0.711330	+	0.702858i	$0.248093\pi$
$44$	−12215.2			−0.951195
$45$		0			0
$46$	35851.1			2.49809
$47$	1584.17	−	2743.86i	0.104606	−	0.181183i	−0.808971	−	0.587848i	$-0.799975\pi$
$47$	1584.17	−	2743.86i	0.104606	−	0.181183i	0.913577	+	0.406665i	$0.133308\pi$
$48$		0			0
$49$	8401.44	+	14551.7i	0.499877	+	0.865813i
$50$	4398.81	+	7618.96i	0.248834	+	0.430994i
$51$		0			0
$52$	−24240.2	+	41985.2i	−1.24316	+	2.15322i
$53$	12265.0			0.599763			0.299881	−	0.953977i	$-0.403053\pi$
$53$	12265.0			0.599763			0.299881	+	0.953977i	$0.403053\pi$
$54$		0			0
$55$	−8694.41			−0.387555
$56$	347.353	−	601.633i	0.0148013	−	0.0256367i
$57$		0			0
$58$	−6580.32	−	11397.5i	−0.256849	−	0.444875i
$59$	−14773.5	−	25588.5i	−0.552528	−	0.957006i	−0.998091	−	0.0617560i	$-0.980330\pi$
$59$	−14773.5	−	25588.5i	−0.552528	−	0.957006i	0.445563	−	0.895250i	$-0.353003\pi$
$60$		0			0
$61$	20153.6	−	34907.1i	0.693472	−	1.20113i	−0.277221	−	0.960806i	$-0.589413\pi$
$61$	20153.6	−	34907.1i	0.693472	−	1.20113i	0.970693	−	0.240323i	$-0.0772534\pi$
$62$	−51410.7			−1.69853
$63$		0			0
$64$	−24379.9			−0.744016
$65$	−17253.4	+	29883.8i	−0.506514	+	0.877308i
$66$		0			0
$67$	−11748.9	−	20349.7i	−0.319750	−	0.553823i	0.660686	−	0.750662i	$-0.270266\pi$
$67$	−11748.9	−	20349.7i	−0.319750	−	0.553823i	−0.980436	+	0.196840i	$0.936932\pi$
$68$	40310.9	+	69820.5i	1.05718	+	1.83109i
$69$		0			0
$70$	476.747	−	825.750i	0.0116290	−	0.0201420i
$71$	123.786			0.00291425			0.00145713	−	0.999999i	$-0.499536\pi$
$71$	123.786			0.00291425			0.00145713	+	0.999999i	$0.499536\pi$
$72$		0			0
$73$	35217.6			0.773486			0.386743	−	0.922188i	$-0.373600\pi$
$73$	35217.6			0.773486			0.386743	+	0.922188i	$0.373600\pi$
$74$	73011.4	−	126459.i	1.54993	−	2.68455i
$75$		0			0
$76$	15723.5	+	27233.8i	0.312259	+	0.540848i
$77$	−186.607	−	323.214i	−0.00358676	−	0.00621245i
$78$		0			0
$79$	24072.8	−	41695.3i	0.433969	−	0.751656i	−0.563242	−	0.826292i	$-0.690446\pi$
$79$	24072.8	−	41695.3i	0.433969	−	0.751656i	0.997211	+	0.0746359i	$0.0237794\pi$
$80$	59960.3			1.04746
$81$		0			0
$82$	−62711.6			−1.02994
$83$	5167.97	−	8951.18i	0.0823426	−	0.142622i	−0.821913	−	0.569613i	$-0.807093\pi$
$83$	5167.97	−	8951.18i	0.0823426	−	0.142622i	0.904256	+	0.426991i	$0.140426\pi$
$84$		0			0
$85$	28692.0	+	49696.1i	0.430739	+	0.746062i
$86$	−30443.5	−	52729.7i	−0.443863	−	0.768793i
$87$		0			0
$88$	31430.3	−	54438.8i	0.432655	−	0.749380i
$89$	42585.7			0.569887			0.284944	−	0.958544i	$-0.408025\pi$
$89$	42585.7			0.569887			0.284944	+	0.958544i	$0.408025\pi$
$90$		0			0
$91$	−1481.23			−0.0187508
$92$	−120075.	+	207976.i	−1.47905	+	2.56178i
$93$		0			0
$94$	15720.1	+	27228.1i	0.183500	+	0.317832i
$95$	11191.5	+	19384.2i	0.127227	+	0.220363i
$96$		0			0
$97$	−49347.3	+	85472.1i	−0.532518	+	0.922348i	0.466761	+	0.884383i	$0.345421\pi$
$97$	−49347.3	+	85472.1i	−0.532518	+	0.922348i	−0.999279	+	0.0379646i	$0.987913\pi$
$98$	−166739.			−1.75377
$99$		0			0
$100$	−58931.0			−0.589310
$101$	−37818.9	+	65504.3i	−0.368898	+	0.638949i	−0.989393	−	0.145260i	$-0.953598\pi$
$101$	−37818.9	+	65504.3i	−0.368898	+	0.638949i	0.620496	+	0.784210i	$0.286931\pi$
$102$		0			0
$103$	−73869.1	−	127945.i	−0.686072	−	1.18831i	−0.973099	−	0.230389i	$-0.926000\pi$
$103$	−73869.1	−	127945.i	−0.686072	−	1.18831i	0.287026	−	0.957923i	$-0.407333\pi$
$104$	−124742.	−	216059.i	−1.13091	−	1.95880i
$105$		0			0
$106$	−60854.6	+	105403.i	−0.526052	+	0.911149i
$107$	209139.			1.76594			0.882969	−	0.469430i	$-0.155541\pi$
$107$	209139.			1.76594			0.882969	+	0.469430i	$0.155541\pi$
$108$		0			0
$109$	115605.			0.931988			0.465994	−	0.884788i	$-0.345697\pi$
$109$	115605.			0.931988			0.465994	+	0.884788i	$0.345697\pi$
$110$	43138.5	−	74718.0i	0.339925	−	0.588767i
$111$		0			0
$112$	1286.92	+	2229.02i	0.00969411	+	0.0167907i
$113$	23415.8	+	40557.3i	0.172509	+	0.298795i	0.939296	−	0.343107i	$-0.111479\pi$
$113$	23415.8	+	40557.3i	0.172509	+	0.298795i	−0.766787	+	0.641901i	$0.778146\pi$
$114$		0			0
$115$	−85465.5	+	148031.i	−0.602623	+	1.04377i
$116$	88156.8			0.608290
$117$		0			0
$118$	293203.			1.93849
$119$	−1231.63	+	2133.25i	−0.00797283	+	0.0138094i
$120$		0			0
$121$	63640.3	+	110228.i	0.395156	+	0.684431i
$122$	199990.	+	346393.i	1.21649	+	2.10702i
$123$		0			0
$124$	172188.	−	298238.i	1.00565	−	1.74184i
$125$	−189796.			−1.08645
$126$		0			0
$127$	−93444.5			−0.514096			−0.257048	−	0.966399i	$-0.582750\pi$
$127$	−93444.5			−0.514096			−0.257048	+	0.966399i	$0.582750\pi$
$128$	147044.	−	254688.i	0.793273	−	1.37399i
$129$		0			0
$130$	−171210.	−	296544.i	−0.888527	−	1.53897i
$131$	−183869.	−	318470.i	−0.936115	−	1.62140i	−0.772634	−	0.634852i	$-0.781061\pi$
$131$	−183869.	−	318470.i	−0.936115	−	1.62140i	−0.163481	−	0.986546i	$-0.552272\pi$
$132$		0			0
$133$	−480.404	+	832.083i	−0.00235493	+	0.00407885i
$134$	233175.			1.12181
$135$		0			0
$136$	−414887.			−1.92346
$137$	−76809.2	+	133037.i	−0.349632	+	0.605581i	−0.986184	−	0.165653i	$-0.947027\pi$
$137$	−76809.2	+	133037.i	−0.349632	+	0.605581i	0.636552	+	0.771234i	$0.280360\pi$
$138$		0			0
$139$	−122213.	−	211679.i	−0.536513	−	0.929268i	−0.999088	−	0.0426878i	$-0.986408\pi$
$139$	−122213.	−	211679.i	−0.536513	−	0.929268i	0.462575	−	0.886580i	$-0.346925\pi$
$140$	3193.50	+	5531.30i	0.0137704	+	0.0238510i
$141$		0			0
$142$	−614.183	+	1063.80i	−0.00255609	+	0.00442728i
$143$	−134029.			−0.548101
$144$		0			0
$145$	62747.3			0.247842
$146$	−174737.	+	302653.i	−0.678425	+	1.17507i
$147$		0			0
$148$	489068.	+	847091.i	1.83533	+	3.17889i
$149$	−4924.61	−	8529.67i	−0.0181721	−	0.0314751i	0.856796	−	0.515655i	$-0.172451\pi$
$149$	−4924.61	−	8529.67i	−0.0181721	−	0.0314751i	−0.874968	+	0.484180i	$0.839118\pi$
$150$		0			0
$151$	109892.	−	190339.i	0.392216	−	0.679338i	−0.600526	−	0.799606i	$-0.705042\pi$
$151$	109892.	−	190339.i	0.392216	−	0.679338i	0.992741	+	0.120268i	$0.0383753\pi$
$152$	−161829.			−0.568128
$153$		0			0
$154$	3703.51			0.0125838
$155$	122558.	−	212276.i	0.409743	−	0.709696i
$156$		0			0
$157$	−15290.5	−	26483.9i	−0.0495077	−	0.0857498i	0.840210	−	0.542262i	$-0.182432\pi$
$157$	−15290.5	−	26483.9i	−0.0495077	−	0.0857498i	−0.889717	+	0.456512i	$0.849099\pi$
$158$	238881.	+	413753.i	0.761269	+	1.31856i
$159$		0			0
$160$	−38559.2	+	66786.5i	−0.119077	+	0.206248i
$161$	−7337.35			−0.0223087
$162$		0			0
$163$	−272367.			−0.802945			−0.401472	−	0.915871i	$-0.631501\pi$
$163$	−272367.			−0.802945			−0.401472	+	0.915871i	$0.631501\pi$
$164$	210037.	−	363795.i	0.609799	−	1.05620i
$165$		0			0
$166$	51283.1	+	88824.9i	0.144445	+	0.250187i
$167$	−99337.8	−	172058.i	−0.275628	−	0.477402i	0.694665	−	0.719333i	$-0.255552\pi$
$167$	−99337.8	−	172058.i	−0.275628	−	0.477402i	−0.970293	+	0.241931i	$0.922219\pi$
$168$		0			0
$169$	−80324.9	+	139127.i	−0.216338	+	0.374709i
$170$	−569437.			−1.51121
$171$		0			0
$172$	407853.			1.05119
$173$	33895.9	−	58709.5i	0.0861058	−	0.149140i	−0.819756	−	0.572713i	$-0.805891\pi$
$173$	33895.9	−	58709.5i	0.0861058	−	0.149140i	0.905862	+	0.423573i	$0.139224\pi$
$174$		0			0
$175$	−900.268	−	1559.31i	−0.00222217	−	0.00384891i
$176$	116447.	+	201693.i	0.283366	+	0.490805i
$177$		0			0
$178$	−211295.	+	365973.i	−0.499848	+	0.865763i
$179$	−21849.0			−0.0509681			−0.0254840	−	0.999675i	$-0.508113\pi$
$179$	−21849.0			−0.0509681			−0.0254840	+	0.999675i	$0.508113\pi$
$180$		0			0
$181$	188080.			0.426722			0.213361	−	0.976973i	$-0.431559\pi$
$181$	188080.			0.426722			0.213361	+	0.976973i	$0.431559\pi$
$182$	7349.33	−	12729.4i	0.0164463	−	0.0284859i
$183$		0			0
$184$	−617915.	−	1.07026e6i	−1.34550	−	2.33048i
$185$	348104.	+	602933.i	0.747789	+	1.29521i
$186$		0			0
$187$	−111444.	+	193027.i	−0.233052	+	0.403658i
$188$	−210603.			−0.434581
$189$		0			0
$190$	−222112.			−0.446363
$191$	−123200.	+	213389.i	−0.244359	+	0.423241i	−0.961951	−	0.273222i	$-0.911911\pi$
$191$	−123200.	+	213389.i	−0.244359	+	0.423241i	0.717592	+	0.696463i	$0.245244\pi$
$192$		0			0
$193$	113565.	+	196701.i	0.219459	+	0.380114i	0.954643	−	0.297754i	$-0.0962375\pi$
$193$	113565.	+	196701.i	0.219459	+	0.380114i	−0.735184	+	0.677868i	$0.762904\pi$
$194$	−489686.	−	848162.i	−0.934144	−	1.61798i
$195$		0			0
$196$	558453.	−	967269.i	1.03836	−	1.79849i
$197$	503086.			0.923584			0.461792	−	0.886988i	$-0.347207\pi$
$197$	503086.			0.923584			0.461792	+	0.886988i	$0.347207\pi$
$198$		0			0
$199$	4126.65			0.00738694			0.00369347	−	0.999993i	$-0.498824\pi$
$199$	4126.65			0.00738694			0.00369347	+	0.999993i	$0.498824\pi$
$200$	151632.	−	262634.i	0.268050	−	0.464276i
$201$		0			0
$202$	−375287.	−	650016.i	−0.647121	−	1.12085i
$203$	1346.74	+	2332.62i	0.00229374	+	0.00397287i
$204$		0			0
$205$	149498.	−	258938.i	0.248457	−	0.430340i
$206$	1.46605e6			2.40702
$207$		0			0
$208$	924324.			1.48138
$209$	−43469.3	+	75291.1i	−0.0688363	+	0.119228i
$210$		0			0
$211$	494954.	+	857285.i	0.765347	+	1.32562i	0.940063	+	0.341001i	$0.110766\pi$
$211$	494954.	+	857285.i	0.765347	+	1.32562i	−0.174716	+	0.984619i	$0.555901\pi$
$212$	−407636.	−	706046.i	−0.622921	−	1.07893i
$213$		0			0
$214$	−1.03767e6	+	1.79730e6i	−1.54891	+	2.68278i
$215$	290297.			0.428298
$216$		0			0
$217$	10521.8			0.0151684
$218$	−573589.	+	993485.i	−0.817447	+	1.41586i
$219$		0			0
$220$	288964.	+	500500.i	0.402519	+	0.697184i
$221$	442305.	+	766094.i	0.609173	+	1.05512i
$222$		0			0
$223$	523910.	−	907438.i	0.705496	−	1.22195i	−0.261017	−	0.965334i	$-0.584058\pi$
$223$	523910.	−	907438.i	0.705496	−	1.22195i	0.966512	−	0.256620i	$-0.0826089\pi$
$224$	−3310.37			−0.00440816
$225$		0			0
$226$	−464722.			−0.605232
$227$	355537.	−	615808.i	0.457952	−	0.793196i	−0.540900	−	0.841087i	$-0.681916\pi$
$227$	355537.	−	615808.i	0.457952	−	0.793196i	0.998853	+	0.0478902i	$0.0152498\pi$
$228$		0			0
$229$	−147071.	−	254734.i	−0.185327	−	0.320995i	0.758360	−	0.651836i	$-0.226001\pi$
$229$	−147071.	−	254734.i	−0.185327	−	0.320995i	−0.943687	+	0.330841i	$0.892668\pi$
$230$	−848096.	−	1.46895e6i	−1.05712	−	1.83099i
$231$		0			0
$232$	−226831.	+	392883.i	−0.276683	+	0.479230i
$233$	−1.56670e6			−1.89059			−0.945294	−	0.326218i	$-0.894226\pi$
$233$	−1.56670e6			−1.89059			−0.945294	+	0.326218i	$0.894226\pi$
$234$		0			0
$235$	−149901.			−0.177066
$236$	−982013.	+	1.70090e6i	−1.14772	+	1.98792i
$237$		0			0
$238$	−12221.8	−	21168.8i	−0.0139860	−	0.0242244i
$239$	260961.	+	451998.i	0.295516	+	0.511849i	0.975105	−	0.221744i	$-0.0711750\pi$
$239$	260961.	+	451998.i	0.295516	+	0.511849i	−0.679589	+	0.733593i	$0.737842\pi$
$240$		0			0
$241$	213855.	−	370407.i	0.237179	−	0.410806i	−0.722725	−	0.691136i	$-0.757111\pi$
$241$	213855.	−	370407.i	0.237179	−	0.410806i	0.959904	+	0.280330i	$0.0904439\pi$
$242$	−1.26304e6			−1.38637
$243$		0			0
$244$	−2.67927e6			−2.88099
$245$	397490.	−	688472.i	0.423068	−	0.732776i
$246$		0			0
$247$	172523.	+	298819.i	0.179931	+	0.311649i
$248$	886092.	+	1.53476e6i	0.914849	+	1.58457i
$249$		0			0
$250$	941696.	−	1.63106e6i	0.952929	−	1.65052i
$251$	231914.			0.232350			0.116175	−	0.993229i	$-0.462937\pi$
$251$	231914.			0.232350			0.116175	+	0.993229i	$0.462937\pi$
$252$		0			0
$253$	−663921.			−0.652101
$254$	463637.	−	803043.i	0.450914	−	0.781006i
$255$		0			0
$256$	1.06908e6	+	1.85170e6i	1.01955	+	1.76592i
$257$	−707127.	−	1.22478e6i	−0.667828	−	1.15671i	−0.978510	−	0.206199i	$-0.933891\pi$
$257$	−707127.	−	1.22478e6i	−0.667828	−	1.15671i	0.310682	−	0.950514i	$-0.399443\pi$
$258$		0			0
$259$	−14942.6	+	25881.4i	−0.0138413	+	0.0239739i
$260$	2.29371e6			2.10428
$261$		0			0
$262$	3.64915e6			3.28427
$263$	−615838.	+	1.06666e6i	−0.549006	+	0.950907i	0.449336	+	0.893363i	$0.351660\pi$
$263$	−615838.	+	1.06666e6i	−0.549006	+	0.950907i	−0.998343	+	0.0575445i	$0.981673\pi$
$264$		0			0
$265$	−290143.	−	502542.i	−0.253803	−	0.439600i
$266$	−4767.17	−	8256.98i	−0.00413101	−	0.00715513i
$267$		0			0
$268$	−780963.	+	1.35267e6i	−0.664192	+	1.15041i
$269$	−119245.			−0.100475			−0.0502377	−	0.998737i	$-0.515998\pi$
$269$	−119245.			−0.100475			−0.0502377	+	0.998737i	$0.515998\pi$
$270$		0			0
$271$	50141.4			0.0414738			0.0207369	−	0.999785i	$-0.493399\pi$
$271$	50141.4			0.0414738			0.0207369	+	0.999785i	$0.493399\pi$
$272$	768566.	−	1.33120e6i	0.629881	−	1.09099i
$273$		0			0
$274$	−762198.	−	1.32017e6i	−0.613326	−	1.06231i
$275$	−81460.8	−	141094.i	−0.0649557	−	0.112506i
$276$		0			0
$277$	−235820.	+	408452.i	−0.184663	+	0.319846i	−0.943463	−	0.331478i	$-0.892453\pi$
$277$	−235820.	+	408452.i	−0.184663	+	0.319846i	0.758800	+	0.651324i	$0.225786\pi$
$278$	2.42550e6			1.88230
$279$		0			0
$280$	−32868.0			−0.0250541
$281$	1.03652e6	−	1.79530e6i	0.783087	−	1.35635i	−0.147048	−	0.989129i	$-0.546977\pi$
$281$	1.03652e6	−	1.79530e6i	0.783087	−	1.35635i	0.930135	−	0.367217i	$-0.119689\pi$
$282$		0			0
$283$	−758046.	−	1.31297e6i	−0.562639	−	0.974519i	−0.997265	−	0.0739079i	$-0.976453\pi$
$283$	−758046.	−	1.31297e6i	−0.562639	−	0.974519i	0.434626	−	0.900611i	$-0.356880\pi$
$284$	−4114.11	−	7125.86i	−0.00302678	−	0.00524253i
$285$		0			0
$286$	665005.	−	1.15182e6i	0.480739	−	0.832665i
$287$	12834.7			0.00919770
$288$		0			0
$289$	51229.6			0.0360808
$290$	−311329.	+	539237.i	−0.217382	+	0.376517i
$291$		0			0
$292$	−1.17048e6	−	2.02733e6i	−0.803352	−	1.39145i
$293$	385100.	+	667013.i	0.262062	+	0.453905i	0.966790	−	0.255573i	$-0.0822641\pi$
$293$	385100.	+	667013.i	0.262062	+	0.453905i	−0.704727	+	0.709478i	$0.748931\pi$
$294$		0			0
$295$	−698967.	+	1.21065e6i	−0.467629	+	0.809957i
$296$	−5.03357e6			−3.33924
$297$		0			0
$298$	97736.4			0.0637552
$299$	−1.31750e6	+	2.28198e6i	−0.852262	+	1.47616i
$300$		0			0
$301$	6230.62	+	10791.8i	0.00396383	+	0.00686556i
$302$	1.09049e6	+	1.88879e6i	0.688026	+	1.19170i
$303$		0			0
$304$	299783.	−	519240.i	0.186047	−	0.322243i
$305$	−1.90702e6			−1.17383
$306$		0			0
$307$	2.13559e6			1.29322			0.646610	−	0.762821i	$-0.276186\pi$
$307$	2.13559e6			1.29322			0.646610	+	0.762821i	$0.276186\pi$
$308$	−12404.0	+	21484.4i	−0.00745050	+	0.0129046i
$309$		0			0
$310$	1.21617e6	+	2.10647e6i	0.718772	+	1.24495i
$311$	−301713.	−	522582.i	−0.176886	−	0.306375i	0.763927	−	0.645303i	$-0.223269\pi$
$311$	−301713.	−	522582.i	−0.176886	−	0.306375i	−0.940812	+	0.338928i	$0.889936\pi$
$312$		0			0
$313$	−1.08619e6	+	1.88133e6i	−0.626677	+	1.08544i	0.361537	+	0.932358i	$0.382252\pi$
$313$	−1.08619e6	+	1.88133e6i	−0.626677	+	1.08544i	−0.988214	+	0.153079i	$0.951081\pi$
$314$	303463.			0.173693
$315$		0			0
$316$	−3.20029e6			−1.80290
$317$	1.60049e6	−	2.77213e6i	0.894550	−	1.54941i	0.0601886	−	0.998187i	$-0.480830\pi$
$317$	1.60049e6	−	2.77213e6i	0.894550	−	1.54941i	0.834361	−	0.551218i	$-0.185837\pi$
$318$		0			0
$319$	121860.	+	211067.i	0.0670477	+	0.116130i
$320$	576732.	+	998930.i	0.314847	+	0.545331i
$321$		0			0
$322$	36405.2	−	63055.7i	0.0195670	−	0.0338910i
$323$	573805.			0.306026
$324$		0			0
$325$	−646611.			−0.339574
$326$	1.35139e6	−	2.34067e6i	0.704263	−	1.21982i
$327$		0			0
$328$	1.08087e6	+	1.87212e6i	0.554739	+	0.960836i
$329$	−3217.31	−	5572.54i	−0.00163871	−	0.00283834i
$330$		0			0
$331$	−1.30413e6	+	2.25883e6i	−0.654263	+	1.13322i	0.327815	+	0.944742i	$0.393688\pi$
$331$	−1.30413e6	+	2.25883e6i	−0.654263	+	1.13322i	−0.982078	+	0.188475i	$0.939645\pi$
$332$	−687041.			−0.342088
$333$		0			0
$334$	1.97151e6			0.967014
$335$	−555865.	+	962787.i	−0.270618	+	0.468725i
$336$		0			0
$337$	414934.	+	718687.i	0.199024	+	0.344719i	0.948212	−	0.317638i	$-0.102890\pi$
$337$	414934.	+	718687.i	0.199024	+	0.344719i	−0.749189	+	0.662357i	$0.769556\pi$
$338$	−797085.	−	1.38059e6i	−0.379501	−	0.657315i
$339$		0			0
$340$	1.90719e6	−	3.30335e6i	0.894741	−	1.54974i
$341$	952065.			0.443385
$342$		0			0
$343$	68258.7			0.0313273
$344$	−1.04942e6	+	1.81765e6i	−0.478139	+	0.828161i
$345$		0			0
$346$	336358.	+	582589.i	0.151047	+	0.261621i
$347$	1.15930e6	+	2.00796e6i	0.516858	+	0.895224i	0.999808	+	0.0195761i	$0.00623167\pi$
$347$	1.15930e6	+	2.00796e6i	0.516858	+	0.895224i	−0.482951	+	0.875648i	$0.660435\pi$
$348$		0			0
$349$	1.56680e6	−	2.71377e6i	0.688572	−	1.19264i	−0.283728	−	0.958905i	$-0.591571\pi$
$349$	1.56680e6	−	2.71377e6i	0.688572	−	1.19264i	0.972300	−	0.233737i	$-0.0750955\pi$
$350$	17867.2			0.00779626
$351$		0			0
$352$	−299539.			−0.128854
$353$	−1.33508e6	+	2.31243e6i	−0.570259	+	0.987717i	0.426280	+	0.904591i	$0.359824\pi$
$353$	−1.33508e6	+	2.31243e6i	−0.570259	+	0.987717i	−0.996539	+	0.0831261i	$0.973510\pi$
$354$		0			0
$355$	−2928.30	−	5071.96i	−0.00123323	−	0.00213602i
$356$	−1.41536e6	−	2.45148e6i	−0.591891	−	1.02519i
$357$		0			0
$358$	108407.	−	187766.i	0.0447041	−	0.0774299i
$359$	2.05907e6			0.843210			0.421605	−	0.906780i	$-0.361467\pi$
$359$	2.05907e6			0.843210			0.421605	+	0.906780i	$0.361467\pi$
$360$		0			0
$361$	−2.25228e6			−0.909610
$362$	−933182.	+	1.61632e6i	−0.374278	+	0.648269i
$363$		0			0
$364$	49229.6	+	85268.2i	0.0194748	+	0.0337314i
$365$	−833109.	−	1.44299e6i	−0.327318	−	0.566931i
$366$		0			0
$367$	509190.	−	881943.i	0.197340	−	0.341803i	−0.750325	−	0.661069i	$-0.770103\pi$
$367$	509190.	−	881943.i	0.197340	−	0.341803i	0.947665	+	0.319266i	$0.103436\pi$
$368$	4.57868e6			1.76247
$369$		0			0
$370$	−6.90865e6			−2.62355
$371$	12454.6	−	21572.0i	0.00469781	−	0.00813685i
$372$		0			0
$373$	−2.61768e6	−	4.53395e6i	−0.974191	−	1.68735i	−0.682579	−	0.730812i	$-0.739142\pi$
$373$	−2.61768e6	−	4.53395e6i	−0.974191	−	1.68735i	−0.291612	−	0.956537i	$-0.594192\pi$
$374$	−1.10589e6	−	1.91546e6i	−0.408820	−	0.708098i
$375$		0			0
$376$	541891.	−	938583.i	0.197671	−	0.342376i
$377$	967286.			0.350511
$378$		0			0
$379$	2.73883e6			0.979417			0.489708	−	0.871886i	$-0.337103\pi$
$379$	2.73883e6			0.979417			0.489708	+	0.871886i	$0.337103\pi$
$380$	743910.	−	1.28849e6i	0.264278	−	0.457743i
$381$		0			0
$382$	−1.22255e6	−	2.11751e6i	−0.428654	−	0.742451i
$383$	−2.17454e6	−	3.76641e6i	−0.757478	−	1.31199i	−0.944133	−	0.329564i	$-0.893098\pi$
$383$	−2.17454e6	−	3.76641e6i	−0.757478	−	1.31199i	0.186655	−	0.982425i	$-0.440235\pi$
$384$		0			0
$385$	−8828.79	+	15291.9i	−0.00303563	+	0.00525787i
$386$	−2.25388e6			−0.769950
$387$		0			0
$388$	6.56035e6			2.21232
$389$	1.50378e6	−	2.60462e6i	0.503860	−	0.872712i	−0.496130	−	0.868248i	$-0.665246\pi$
$389$	1.50378e6	−	2.60462e6i	0.503860	−	0.872712i	0.999990	−	0.00446327i	$-0.00142071\pi$
$390$		0			0
$391$	2.19098e6	+	3.79488e6i	0.724762	+	1.25533i
$392$	2.87385e6	+	4.97765e6i	0.944602	+	1.63610i
$393$		0			0
$394$	−2.49613e6	+	4.32342e6i	−0.810077	+	1.40309i
$395$	−2.27787e6			−0.734574
$396$		0			0
$397$	2.16602e6			0.689740			0.344870	−	0.938650i	$-0.387923\pi$
$397$	2.16602e6			0.689740			0.344870	+	0.938650i	$0.387923\pi$
$398$	−20474.9	+	35463.6i	−0.00647910	+	0.0112221i
$399$		0			0
$400$	561788.	+	973046.i	0.175559	+	0.304077i
$401$	1.76996e6	+	3.06566e6i	0.549670	+	0.952057i	0.998297	+	0.0583377i	$0.0185800\pi$
$401$	1.76996e6	+	3.06566e6i	0.549670	+	0.952057i	−0.448626	+	0.893719i	$0.648087\pi$
$402$		0			0
$403$	1.88930e6	−	3.27236e6i	0.579480	−	1.00369i
$404$	5.02774e6			1.53257
$405$		0			0
$406$	−26728.1			−0.00804735
$407$	−1.35209e6	+	2.34188e6i	−0.404593	+	0.700775i
$408$		0			0
$409$	783644.	+	1.35731e6i	0.231638	+	0.401210i	0.958290	−	0.285796i	$-0.0922580\pi$
$409$	783644.	+	1.35731e6i	0.231638	+	0.401210i	−0.726652	+	0.687006i	$0.758925\pi$
$410$	1.48351e6	+	2.56951e6i	0.435843	+	0.754902i
$411$		0			0
$412$	−4.91016e6	+	8.50465e6i	−1.42513	+	2.46839i
$413$	−60007.5			−0.0173113
$414$		0			0
$415$	−489015.			−0.139380
$416$	−594413.	+	1.02955e6i	−0.168405	+	0.291686i
$417$		0			0
$418$	−431358.	−	747133.i	−0.120753	−	0.209150i
$419$	−1.18321e6	−	2.04937e6i	−0.329250	−	0.570277i	0.653114	−	0.757260i	$-0.273462\pi$
$419$	−1.18321e6	−	2.04937e6i	−0.329250	−	0.570277i	−0.982363	+	0.186983i	$0.940129\pi$
$420$		0			0
$421$	1.84288e6	−	3.19196e6i	0.506747	−	0.877712i	−0.493222	−	0.869903i	$-0.664181\pi$
$421$	1.84288e6	−	3.19196e6i	0.506747	−	0.877712i	0.999970	−	0.00780885i	$-0.00248566\pi$
$422$	−9.82311e6			−2.68515
$423$		0			0
$424$	4.19546e6			1.13335
$425$	−537650.	+	931238.i	−0.144387	+	0.250085i
$426$		0			0
$427$	−40930.3	−	70893.3i	−0.0108636	−	0.0188164i
$428$	−6.95086e6	−	1.20392e7i	−1.83412	−	3.17680i
$429$		0			0
$430$	−1.44035e6	+	2.49475e6i	−0.375661	+	0.650664i
$431$	6.78152e6			1.75847			0.879233	−	0.476391i	$-0.158055\pi$
$431$	6.78152e6			1.75847			0.879233	+	0.476391i	$0.158055\pi$
$432$		0			0
$433$	−3.20434e6			−0.821332			−0.410666	−	0.911786i	$-0.634704\pi$
$433$	−3.20434e6			−0.821332			−0.410666	+	0.911786i	$0.634704\pi$
$434$	−52205.2	+	90422.1i	−0.0133042	+	0.0230436i
$435$		0			0
$436$	−3.84220e6	−	6.65488e6i	−0.967973	−	1.67658i
$437$	854601.	+	1.48021e6i	0.214072	+	0.370784i
$438$		0			0
$439$	−698435.	+	1.20972e6i	−0.172967	+	0.299588i	−0.939456	−	0.342670i	$-0.888669\pi$
$439$	−698435.	+	1.20972e6i	−0.172967	+	0.299588i	0.766489	+	0.642258i	$0.222002\pi$
$440$	−2.97406e6			−0.732350
$441$		0			0
$442$	−8.77821e6			−2.13723
$443$	−2.48597e6	+	4.30583e6i	−0.601847	+	1.04243i	0.390694	+	0.920521i	$0.372235\pi$
$443$	−2.48597e6	+	4.30583e6i	−0.601847	+	1.04243i	−0.992541	+	0.121910i	$0.961098\pi$
$444$		0			0
$445$	−1.00741e6	−	1.74488e6i	−0.241160	−	0.417702i
$446$	5.19889e6	+	9.00475e6i	1.23758	+	2.14355i
$447$		0			0
$448$	−24756.7	+	42879.9i	−0.00582771	+	0.0100939i
$449$	−4.85114e6			−1.13561			−0.567804	−	0.823164i	$-0.692207\pi$
$449$	−4.85114e6			−1.13561			−0.567804	+	0.823164i	$0.692207\pi$
$450$		0			0
$451$	1.16134e6			0.268856
$452$	1.55647e6	−	2.69589e6i	0.358340	−	0.620663i
$453$		0			0
$454$	3.52809e6	+	6.11083e6i	0.803340	+	1.39143i
$455$	35040.1	+	60691.3i	0.00793482	+	0.0137435i
$456$		0			0
$457$	−2.14244e6	+	3.71081e6i	−0.479864	+	0.831149i	−0.999733	−	0.0230972i	$-0.992647\pi$
$457$	−2.14244e6	+	3.71081e6i	−0.479864	+	0.831149i	0.519869	+	0.854246i	$0.325981\pi$
$458$	2.91885e6			0.650201
$459$		0			0
$460$	1.13620e7			2.50357
$461$	11973.0	−	20737.8i	0.00262392	−	0.00454476i	−0.864710	−	0.502271i	$-0.832498\pi$
$461$	11973.0	−	20737.8i	0.00262392	−	0.00454476i	0.867334	+	0.497726i	$0.165831\pi$
$462$		0			0
$463$	1.76420e6	+	3.05569e6i	0.382469	+	0.662456i	0.991415	−	0.130756i	$-0.0417405\pi$
$463$	1.76420e6	+	3.05569e6i	0.382469	+	0.662456i	−0.608945	+	0.793212i	$0.708407\pi$
$464$	−840397.	−	1.45561e6i	−0.181213	−	0.313870i
$465$		0			0
$466$	7.77341e6	−	1.34639e7i	1.65824	−	2.87215i
$467$	4.66263e6			0.989324			0.494662	−	0.869086i	$-0.335292\pi$
$467$	4.66263e6			0.989324			0.494662	+	0.869086i	$0.335292\pi$
$468$		0			0
$469$	−47722.0			−0.0100181
$470$	743753.	−	1.28822e6i	0.155304	−	0.268995i
$471$		0			0
$472$	−5.05353e6	−	8.75296e6i	−1.04409	−	1.80842i
$473$	563778.	+	976492.i	0.115866	+	0.200686i
$474$		0			0
$475$	−209713.	+	363234.i	−0.0426473	+	0.0738673i
$476$	163736.			0.0331227
$477$		0			0
$478$	−5.17917e6			−1.03679
$479$	3.27492e6	−	5.67232e6i	0.652171	−	1.12959i	−0.330424	−	0.943832i	$-0.607192\pi$
$479$	3.27492e6	−	5.67232e6i	0.652171	−	1.12959i	0.982595	−	0.185760i	$-0.0594748\pi$
$480$		0			0
$481$	5.36622e6	+	9.29457e6i	1.05756	+	1.83175i
$482$	2.12214e6	+	3.67565e6i	0.416060	+	0.720637i
$483$		0			0
$484$	4.23024e6	−	7.32700e6i	0.820828	−	1.42172i
$485$	4.66945e6			0.901387
$486$		0			0
$487$	−9.23457e6			−1.76439			−0.882194	−	0.470886i	$-0.843934\pi$
$487$	−9.23457e6			−1.76439			−0.882194	+	0.470886i	$0.843934\pi$
$488$	6.89388e6	−	1.19406e7i	1.31043	−	2.26973i
$489$		0			0
$490$	3.94439e6	+	6.83189e6i	0.742147	+	1.28544i
$491$	−2.62130e6	−	4.54023e6i	−0.490697	−	0.849912i	0.509246	−	0.860621i	$-0.329925\pi$
$491$	−2.62130e6	−	4.54023e6i	−0.490697	−	0.849912i	−0.999943	+	0.0107089i	$0.996591\pi$
$492$		0			0
$493$	804288.	−	1.39307e6i	0.149037	−	0.258140i
$494$	−3.42399e6			−0.631269
$495$		0			0
$496$	−6.56584e6			−1.19836
$497$	125.700	−	217.718i	2.28267e−5	−	3.95370e-5i
$498$		0			0
$499$	−3.23974e6	−	5.61140e6i	−0.582451	−	1.00883i	−0.995188	−	0.0979844i	$-0.968760\pi$
$499$	−3.23974e6	−	5.61140e6i	−0.582451	−	1.00883i	0.412737	−	0.910850i	$-0.364573\pi$
$500$	6.30796e6	+	1.09257e7i	1.12840	+	1.95445i
$501$		0			0
$502$	−1.15067e6	+	1.99302e6i	−0.203794	+	0.352982i
$503$	−4.42908e6			−0.780538			−0.390269	−	0.920701i	$-0.627618\pi$
$503$	−4.42908e6			−0.780538			−0.390269	+	0.920701i	$0.627618\pi$
$504$		0			0
$505$	3.57859e6			0.624429
$506$	3.29413e6	−	5.70560e6i	0.571959	−	0.990661i
$507$		0			0
$508$	3.10568e6	+	5.37920e6i	0.533946	+	0.924822i
$509$	2.14026e6	+	3.70704e6i	0.366162	+	0.634210i	0.988962	−	0.148170i	$-0.0473384\pi$
$509$	2.14026e6	+	3.70704e6i	0.366162	+	0.634210i	−0.622800	+	0.782381i	$0.714005\pi$
$510$		0			0
$511$	35761.9	−	61941.4i	0.00605855	−	0.0104937i
$512$	−1.18067e7			−1.99046
$513$		0			0
$514$	1.40340e7			2.34301
$515$	−3.49490e6	+	6.05335e6i	−0.580653	+	1.00572i
$516$		0			0
$517$	−291118.	−	504232.i	−0.0479009	−	0.0829667i
$518$	−148280.	−	256828.i	−0.0242805	−	0.0420550i
$519$		0			0
$520$	−5.90181e6	+	1.02222e7i	−0.957142	+	1.65782i
$521$	−8.64335e6			−1.39504			−0.697522	−	0.716564i	$-0.745714\pi$
$521$	−8.64335e6			−1.39504			−0.697522	+	0.716564i	$0.745714\pi$
$522$		0			0
$523$	−9.11201e6			−1.45667			−0.728333	−	0.685224i	$-0.759704\pi$
$523$	−9.11201e6			−1.45667			−0.728333	+	0.685224i	$0.759704\pi$
$524$	−1.22220e7	+	2.11690e7i	−1.94452	+	3.36801i
$525$		0			0
$526$	−6.11113e6	−	1.05848e7i	−0.963068	−	1.66808i
$527$	−3.14187e6	−	5.44187e6i	−0.492789	−	0.853536i
$528$		0			0
$529$	−3.30813e6	+	5.72984e6i	−0.513976	+	0.890233i
$530$	5.75832e6			0.890443
$531$		0			0
$532$	63865.9			0.00978341
$533$	2.30460e6	−	3.99168e6i	0.351380	−	0.608609i
$534$		0			0
$535$	−4.94740e6	−	8.56915e6i	−0.747296	−	1.29436i
$536$	−4.01890e6	−	6.96094e6i	−0.604221	−	1.04654i
$537$		0			0
$538$	591650.	−	1.02477e6i	0.0881271	−	0.152641i
$539$	3.08782e6			0.457804
$540$		0			0
$541$	5.76360e6			0.846643			0.423322	−	0.905979i	$-0.360864\pi$
$541$	5.76360e6			0.846643			0.423322	+	0.905979i	$0.360864\pi$
$542$	−248783.	+	430905.i	−0.0363767	+	0.0630062i
$543$		0			0
$544$	988496.	+	1.71213e6i	0.143211	+	0.248050i
$545$	−2.73476e6	−	4.73674e6i	−0.394391	−	0.683106i
$546$		0			0
$547$	2.80744e6	−	4.86263e6i	0.401183	−	0.694869i	−0.592686	−	0.805434i	$-0.701933\pi$
$547$	2.80744e6	−	4.86263e6i	0.401183	−	0.694869i	0.993869	+	0.110564i	$0.0352659\pi$
$548$	1.02112e7			1.45253
$549$		0			0
$550$	1.61671e6			0.227891
$551$	313717.	−	543374.i	0.0440209	−	0.0762464i
$552$		0			0
$553$	−48889.7	−	84679.4i	−0.00679837	−	0.0117751i
$554$	−2.34010e6	−	4.05317e6i	−0.323937	−	0.561075i
$555$		0			0
$556$	−8.12364e6	+	1.40705e7i	−1.11446	+	1.93030i
$557$	−2.18422e6			−0.298303			−0.149152	−	0.988814i	$-0.547654\pi$
$557$	−2.18422e6			−0.298303			−0.149152	+	0.988814i	$0.547654\pi$
$558$		0			0
$559$	4.47510e6			0.605722
$560$	60887.1	−	105460.i	0.00820456	−	0.0142107i
$561$		0			0
$562$	1.02856e7	+	1.78152e7i	1.37369	+	2.37931i
$563$	339673.	+	588330.i	0.0451637	+	0.0782258i	0.887724	−	0.460377i	$-0.152286\pi$
$563$	339673.	+	588330.i	0.0451637	+	0.0782258i	−0.842560	+	0.538603i	$0.818952\pi$
$564$		0			0
$565$	1.10785e6	−	1.91885e6i	0.146002	−	0.252883i
$566$	1.50446e7			1.97396
$567$		0			0
$568$	42343.2			0.00550697
$569$	−3.28195e6	+	5.68451e6i	−0.424964	+	0.736059i	−0.996417	−	0.0845759i	$-0.973046\pi$
$569$	−3.28195e6	+	5.68451e6i	−0.424964	+	0.736059i	0.571453	+	0.820635i	$0.306380\pi$
$570$		0			0
$571$	952119.	+	1.64912e6i	0.122208	+	0.211671i	0.920638	−	0.390417i	$-0.127669\pi$
$571$	952119.	+	1.64912e6i	0.122208	+	0.211671i	−0.798430	+	0.602088i	$0.794336\pi$
$572$	4.45455e6	+	7.71550e6i	0.569264	+	0.985994i
$573$		0			0
$574$	−63680.8	+	110298.i	−0.00806731	+	0.0139730i
$575$	−3.20302e6			−0.404008
$576$		0			0
$577$	1.13367e7			1.41758			0.708792	−	0.705417i	$-0.249240\pi$
$577$	1.13367e7			1.41758			0.708792	+	0.705417i	$0.249240\pi$
$578$	−254182.	+	440257.i	−0.0316465	+	0.0548133i
$579$		0			0
$580$	−2.08544e6	−	3.61209e6i	−0.257412	−	0.445850i
$581$	−10495.7	−	18179.1i	−0.00128994	−	0.00223425i
$582$		0			0
$583$	1.12696e6	−	1.95195e6i	0.137321	−	0.237846i
$584$	1.20467e7			1.46163
$585$		0			0
$586$	−7.64290e6			−0.919420
$587$	6.88666e6	−	1.19280e7i	0.824923	−	1.42881i	−0.0770557	−	0.997027i	$-0.524552\pi$
$587$	6.88666e6	−	1.19280e7i	0.824923	−	1.42881i	0.901978	−	0.431781i	$-0.142115\pi$
$588$		0			0
$589$	−1.22550e6	−	2.12263e6i	−0.145554	−	0.252108i
$590$	−6.93603e6	−	1.20136e7i	−0.820315	−	1.42083i
$591$		0			0
$592$	9.32456e6	−	1.61506e7i	1.09351	−	1.89402i
$593$	−9.94674e6			−1.16157			−0.580783	−	0.814058i	$-0.697254\pi$
$593$	−9.94674e6			−1.16157			−0.580783	+	0.814058i	$0.697254\pi$
$594$		0			0
$595$	116542.			0.0134955
$596$	−327344.	+	566977.i	−0.0377476	+	0.0653807i
$597$		0			0
$598$	−1.30739e7	−	2.26447e7i	−1.49504	−	2.58948i
$599$	2.77125e6	+	4.79995e6i	0.315579	+	0.546600i	0.979561	−	0.201150i	$-0.0644678\pi$
$599$	2.77125e6	+	4.79995e6i	0.315579	+	0.546600i	−0.663981	+	0.747749i	$0.731134\pi$
$600$		0			0
$601$	−6.63325e6	+	1.14891e7i	−0.749101	+	1.29748i	0.199153	+	0.979968i	$0.436181\pi$
$601$	−6.63325e6	+	1.14891e7i	−0.749101	+	1.29748i	−0.948254	+	0.317513i	$0.897152\pi$
$602$	−123656.			−0.0139067
$603$		0			0
$604$	−1.46093e7			−1.62944
$605$	3.01096e6	−	5.21513e6i	0.334438	−	0.579264i
$606$		0			0
$607$	−3.04326e6	−	5.27108e6i	−0.335249	−	0.580668i	0.648284	−	0.761399i	$-0.275487\pi$
$607$	−3.04326e6	−	5.27108e6i	−0.335249	−	0.580668i	−0.983533	+	0.180731i	$0.942154\pi$
$608$	385568.	+	667824.i	0.0423002	+	0.0732660i
$609$		0			0
$610$	9.46194e6	−	1.63886e7i	1.02957	−	1.78327i
$611$	−2.31081e6			−0.250416
$612$		0			0
$613$	−4.59806e6			−0.494223			−0.247112	−	0.968987i	$-0.579481\pi$
$613$	−4.59806e6			−0.494223			−0.247112	+	0.968987i	$0.579481\pi$
$614$	−1.05960e7	+	1.83528e7i	−1.13428	+	1.96464i
$615$		0			0
$616$	−63832.1	−	110560.i	−0.00677778	−	0.0117395i
$617$	8.01311e6	+	1.38791e7i	0.847399	+	1.46774i	0.883521	+	0.468391i	$0.155166\pi$
$617$	8.01311e6	+	1.38791e7i	0.847399	+	1.46774i	−0.0361221	+	0.999347i	$0.511501\pi$
$618$		0			0
$619$	−1.19878e6	+	2.07634e6i	−0.125751	+	0.217807i	−0.922026	−	0.387127i	$-0.873467\pi$
$619$	−1.19878e6	+	2.07634e6i	−0.125751	+	0.217807i	0.796275	+	0.604934i	$0.206801\pi$
$620$	−1.62931e7			−1.70226
$621$		0			0
$622$	5.98795e6			0.620587
$623$	43243.9	−	74900.6i	0.00446380	−	0.00773153i
$624$		0			0
$625$	3.10456e6	+	5.37725e6i	0.317906	+	0.550630i
$626$	−1.07785e7	−	1.86689e7i	−1.09932	−	1.90407i
$627$		0			0
$628$	−1.01638e6	+	1.76042e6i	−0.102839	+	0.178122i
$629$	1.78478e7			1.79870
$630$		0			0
$631$	6.25228e6			0.625122			0.312561	−	0.949898i	$-0.398813\pi$
$631$	6.25228e6			0.625122			0.312561	+	0.949898i	$0.398813\pi$
$632$	8.23449e6	−	1.42625e7i	0.820057	−	1.42038i
$633$		0			0
$634$	1.58821e7	+	2.75086e7i	1.56922	+	2.71797i
$635$	2.21053e6	+	3.82875e6i	0.217551	+	0.376810i
$636$		0			0
$637$	6.12754e6	−	1.06132e7i	0.598325	−	1.03633i
$638$	−2.41849e6			−0.235230
$639$		0			0
$640$	−1.39139e7			−1.34276
$641$	−9.48142e6	+	1.64223e7i	−0.911440	+	1.57866i	−0.0994090	+	0.995047i	$0.531695\pi$
$641$	−9.48142e6	+	1.64223e7i	−0.911440	+	1.57866i	−0.812031	+	0.583614i	$0.801638\pi$
$642$		0			0
$643$	1.64962e6	+	2.85722e6i	0.157346	+	0.272532i	0.933911	−	0.357506i	$-0.116373\pi$
$643$	1.64962e6	+	2.85722e6i	0.157346	+	0.272532i	−0.776565	+	0.630038i	$0.783039\pi$
$644$	243861.	+	422380.i	0.0231701	+	0.0401318i
$645$		0			0
$646$	−2.84701e6	+	4.93116e6i	−0.268415	+	0.464909i
$647$	1.56481e7			1.46961			0.734805	−	0.678278i	$-0.237274\pi$
$647$	1.56481e7			1.46961			0.734805	+	0.678278i	$0.237274\pi$
$648$		0			0
$649$	−5.42978e6			−0.506023
$650$	3.20825e6	−	5.55685e6i	0.297841	−	0.515876i
$651$		0			0
$652$	9.05228e6	+	1.56790e7i	0.833948	+	1.44444i
$653$	7.78514e6	+	1.34843e7i	0.714469	+	1.23750i	0.963164	+	0.268915i	$0.0866650\pi$
$653$	7.78514e6	+	1.34843e7i	0.714469	+	1.23750i	−0.248695	+	0.968582i	$0.580002\pi$
$654$		0			0
$655$	−8.69921e6	+	1.50675e7i	−0.792276	+	1.37226i
$656$	−8.00912e6			−0.726650
$657$		0			0
$658$	63852.4			0.00574927
$659$	6.40513e6	−	1.10940e7i	0.574532	−	0.995119i	−0.421560	−	0.906800i	$-0.638517\pi$
$659$	6.40513e6	−	1.10940e7i	0.574532	−	0.995119i	0.996092	−	0.0883184i	$-0.0281493\pi$
$660$		0			0
$661$	−230248.	−	398801.i	−0.0204971	−	0.0355020i	0.855595	−	0.517646i	$-0.173192\pi$
$661$	−230248.	−	398801.i	−0.0204971	−	0.0355020i	−0.876092	+	0.482144i	$0.839858\pi$
$662$	−1.29413e7	−	2.24149e7i	−1.14771	−	1.98789i
$663$		0			0
$664$	1.76779e6	−	3.06190e6i	0.155600	−	0.269507i
$665$	45457.8			0.00398616
$666$		0			0
$667$	4.79150e6			0.417020
$668$	−6.60310e6	+	1.14369e7i	−0.572541	+	0.991670i
$669$		0			0
$670$	−5.51600e6	−	9.55399e6i	−0.474719	−	0.822238i
$671$	−3.70358e6	−	6.41479e6i	−0.317552	−	0.550017i
$672$		0			0
$673$	4.03608e6	−	6.99069e6i	0.343496	−	0.594952i	−0.641583	−	0.767053i	$-0.721722\pi$
$673$	4.03608e6	−	6.99069e6i	0.343496	−	0.594952i	0.985079	+	0.172101i	$0.0550555\pi$
$674$	−8.23500e6			−0.698255
$675$		0			0
$676$	1.06786e7			0.898766
$677$	1.82149e6	−	3.15491e6i	0.152741	−	0.264554i	−0.779493	−	0.626410i	$-0.784523\pi$
$677$	1.82149e6	−	3.15491e6i	0.152741	−	0.264554i	0.932234	+	0.361856i	$0.117857\pi$
$678$		0			0
$679$	100220.	+	173586.i	0.00834219	+	0.0144491i
$680$	9.81458e6	+	1.69993e7i	0.813953	+	1.40981i
$681$		0			0
$682$	−4.72380e6	+	8.18185e6i	−0.388893	+	0.673582i
$683$	−9.57475e6			−0.785373			−0.392686	−	0.919672i	$-0.628454\pi$
$683$	−9.57475e6			−0.785373			−0.392686	+	0.919672i	$0.628454\pi$
$684$		0			0
$685$	7.26801e6			0.591819
$686$	−338674.	+	586601.i	−0.0274772	+	0.0475919i
$687$		0			0
$688$	−3.88805e6	−	6.73431e6i	−0.313156	−	0.542403i
$689$	−4.47272e6	−	7.74698e6i	−0.358941	−	0.621705i
$690$		0			0
$691$	−3.01871e6	+	5.22857e6i	−0.240506	+	0.416569i	−0.960859	−	0.277039i	$-0.910647\pi$
$691$	−3.01871e6	+	5.22857e6i	−0.240506	+	0.416569i	0.720352	+	0.693608i	$0.243980\pi$
$692$	−4.50620e6			−0.357722
$693$		0			0
$694$	−2.30080e7			−1.81334
$695$	−5.78215e6	+	1.00150e7i	−0.454075	+	0.786481i
$696$		0			0
$697$	−3.83250e6	−	6.63809e6i	−0.298814	−	0.517560i
$698$	1.55478e7	+	2.69295e7i	1.20789	+	2.09213i
$699$		0			0
$700$	−59841.8	+	103649.i	−0.00461594	+	0.00799504i
$701$	−1.37603e7			−1.05763			−0.528813	−	0.848739i	$-0.677363\pi$
$701$	−1.37603e7			−1.05763			−0.528813	+	0.848739i	$0.677363\pi$
$702$		0			0
$703$	6.96164e6			0.531279
$704$	−2.24011e6	+	3.87999e6i	−0.170349	+	0.295052i
$705$		0			0
$706$	−1.32484e7	−	2.29469e7i	−1.00035	−	1.73266i
$707$	76806.9	+	133033.i	0.00577899	+	0.0100095i
$708$		0			0
$709$	809892.	−	1.40277e6i	0.0605078	−	0.104803i	−0.834185	−	0.551485i	$-0.814061\pi$
$709$	809892.	−	1.40277e6i	0.0605078	−	0.104803i	0.894693	+	0.446683i	$0.147395\pi$
$710$	58116.6			0.00432667
$711$		0			0
$712$	1.45671e7			1.07690
$713$	9.35873e6	−	1.62098e7i	0.689435	−	1.19414i
$714$		0			0
$715$	3.17061e6	+	5.49165e6i	0.231941	+	0.401734i
$716$	726163.	+	1.25775e6i	0.0529360	+	0.0916879i
$717$		0			0
$718$	−1.02164e7	+	1.76953e7i	−0.739580	+	1.28099i
$719$	−1.42931e7			−1.03111			−0.515555	−	0.856856i	$-0.672414\pi$
$719$	−1.42931e7			−1.03111			−0.515555	+	0.856856i	$0.672414\pi$
$720$		0			0
$721$	−300043.			−0.0214954
$722$	1.11750e7	−	1.93557e7i	0.797819	−	1.38186i
$723$		0			0
$724$	−6.25093e6	−	1.08269e7i	−0.443199	−	0.767643i
$725$	587900.	+	1.01827e6i	0.0415392	+	0.0719481i
$726$		0			0
$727$	1.37208e7	−	2.37652e7i	0.962818	−	1.66765i	0.247450	−	0.968901i	$-0.420407\pi$
$727$	1.37208e7	−	2.37652e7i	0.962818	−	1.66765i	0.715367	−	0.698749i	$-0.246259\pi$
$728$	−506680.			−0.0354328
$729$		0			0
$730$	1.65343e7			1.14836
$731$	3.72100e6	−	6.44496e6i	0.257553	−	0.446094i
$732$		0			0
$733$	2.55310e6	+	4.42209e6i	0.175512	+	0.303996i	0.940338	−	0.340241i	$-0.110509\pi$
$733$	2.55310e6	+	4.42209e6i	0.175512	+	0.303996i	−0.764826	+	0.644237i	$0.777175\pi$
$734$	5.05283e6	+	8.75175e6i	0.346174	+	0.599591i
$735$		0			0
$736$	−2.94445e6	+	5.09994e6i	−0.200359	+	0.347033i
$737$	−4.31812e6			−0.292837
$738$		0			0
$739$	−1.34356e7			−0.904997			−0.452498	−	0.891765i	$-0.649467\pi$
$739$	−1.34356e7			−0.904997			−0.452498	+	0.891765i	$0.649467\pi$
$740$	2.31388e7	−	4.00776e7i	1.55332	−	2.69044i
$741$		0			0
$742$	123590.	+	214065.i	0.00824091	+	0.0142737i
$743$	−343246.	−	594519.i	−0.0228104	−	0.0395088i	0.854395	−	0.519624i	$-0.173928\pi$
$743$	−343246.	−	594519.i	−0.0228104	−	0.0395088i	−0.877205	+	0.480116i	$0.840595\pi$
$744$		0			0
$745$	−232994.	+	403557.i	−0.0153799	+	0.0266387i
$746$	5.19518e7			3.41786
$747$		0			0
$748$	1.48156e7			0.968203
$749$	212371.	−	367838.i	0.0138322	−	0.0239581i
$750$		0			0
$751$	−5.46542e6	−	9.46639e6i	−0.353610	−	0.612470i	0.633269	−	0.773931i	$-0.281712\pi$
$751$	−5.46542e6	−	9.46639e6i	−0.353610	−	0.612470i	−0.986879	+	0.161462i	$0.948379\pi$
$752$	2.00768e6	+	3.47740e6i	0.129464	+	0.224238i
$753$		0			0
$754$	−4.79932e6	+	8.31266e6i	−0.307434	+	0.532491i
$755$	−1.03985e7			−0.663900
$756$		0			0
$757$	−2.31128e7			−1.46593			−0.732966	−	0.680265i	$-0.761865\pi$
$757$	−2.31128e7			−1.46593			−0.732966	+	0.680265i	$0.761865\pi$
$758$	−1.35891e7	+	2.35370e7i	−0.859047	+	1.48791i
$759$		0			0
$760$	3.82823e6	+	6.63068e6i	0.240416	+	0.416413i
$761$	−5.94528e6	−	1.02975e7i	−0.372144	−	0.644572i	0.617751	−	0.786374i	$-0.288044\pi$
$761$	−5.94528e6	−	1.02975e7i	−0.372144	−	0.644572i	−0.989895	+	0.141801i	$0.954711\pi$
$762$		0			0
$763$	117392.	−	203328.i	0.00730005	−	0.0126441i
$764$	1.63785e7			1.01517
$765$		0			0
$766$	4.31570e7			2.65754
$767$	−1.07750e7	+	1.86628e7i	−0.661345	+	1.14548i
$768$		0			0
$769$	−1.32545e6	−	2.29575e6i	−0.0808253	−	0.139994i	0.822779	−	0.568361i	$-0.192422\pi$
$769$	−1.32545e6	−	2.29575e6i	−0.0808253	−	0.139994i	−0.903605	+	0.428367i	$0.859089\pi$
$770$	−87610.4	−	151746.i	−0.00532511	−	0.00922337i
$771$		0			0
$772$	7.54883e6	−	1.30750e7i	0.455865	−	0.789581i
$773$	2.12893e7			1.28148			0.640742	−	0.767757i	$-0.278627\pi$
$773$	2.12893e7			1.28148			0.640742	+	0.767757i	$0.278627\pi$
$774$		0			0
$775$	4.59314e6			0.274698
$776$	−1.68801e7	+	2.92371e7i	−1.00628	+	1.74293i
$777$		0			0
$778$	1.49224e7	+	2.58464e7i	0.883873	+	1.53091i
$779$	−1.49489e6	−	2.58922e6i	−0.0882601	−	0.152871i
$780$		0			0
$781$	11373.9	−	19700.3i	0.000667242	−	0.00115570i
$782$	−4.34833e7			−2.54276
$783$		0			0
$784$	−2.12949e7			−1.23733
$785$	−723426.	+	1.25301e6i	−0.0419006	+	0.0725739i
$786$		0			0
$787$	1.14439e7	+	1.98214e7i	0.658623	+	1.14077i	0.980972	+	0.194148i	$0.0621942\pi$
$787$	1.14439e7	+	1.98214e7i	0.658623	+	1.14077i	−0.322349	+	0.946621i	$0.604472\pi$
$788$	−1.67203e7	−	2.89605e7i	−0.959246	−	1.66146i
$789$		0			0
$790$	1.13019e7	−	1.95755e7i	0.644296	−	1.11595i
$791$	95110.7			0.00540491
$792$		0			0
$793$	−2.93979e7			−1.66010
$794$	−1.07470e7	+	1.86143e7i	−0.604972	+	1.04784i
$795$		0			0
$796$	−137152.	−	237553.i	−0.00767217	−	0.0132886i
$797$	−1.28424e7	−	2.22437e7i	−0.716146	−	1.24040i	−0.962516	−	0.271225i	$-0.912571\pi$
$797$	−1.28424e7	−	2.22437e7i	−0.716146	−	1.24040i	0.246370	−	0.969176i	$-0.420762\pi$
$798$		0			0
$799$	−1.92141e6	+	3.32799e6i	−0.106477	+	0.184423i
$800$	−1.44510e6			−0.0798310
$801$		0			0
$802$	−3.51275e7			−1.92847
$803$	3.23592e6	−	5.60478e6i	0.177096	−	0.306739i
$804$		0			0
$805$	173573.	+	300637.i	0.00944043	+	0.0163513i
$806$	1.87480e7	+	3.24725e7i	1.01652	+	1.76067i
$807$		0			0
$808$	−1.29366e7	+	2.24068e7i	−0.697094	+	1.20740i
$809$	5.88061e6			0.315901			0.157951	−	0.987447i	$-0.449511\pi$
$809$	5.88061e6			0.315901			0.157951	+	0.987447i	$0.449511\pi$
$810$		0			0
$811$	−2.04938e7			−1.09414			−0.547068	−	0.837088i	$-0.684256\pi$
$811$	−2.04938e7			−1.09414			−0.547068	+	0.837088i	$0.684256\pi$
$812$	89519.3	−	155052.i	0.00476460	−	0.00825254i
$813$		0			0
$814$	−1.34171e7	−	2.32391e7i	−0.709737	−	1.22930i
$815$	6.44313e6	+	1.11598e7i	0.339784	+	0.588523i
$816$		0			0
$817$	1.45139e6	−	2.51389e6i	0.0760730	−	0.131762i
$818$	−1.55526e7			−0.812681
$819$		0			0
$820$	−1.98746e7			−1.03220
$821$	−1.81711e6	+	3.14732e6i	−0.0940855	+	0.162961i	−0.909227	−	0.416302i	$-0.863326\pi$
$821$	−1.81711e6	+	3.14732e6i	−0.0940855	+	0.162961i	0.815141	+	0.579263i	$0.196659\pi$
$822$		0			0
$823$	7.90337e6	+	1.36890e7i	0.406736	+	0.704488i	0.994522	−	0.104529i	$-0.0333335\pi$
$823$	7.90337e6	+	1.36890e7i	0.406736	+	0.704488i	−0.587786	+	0.809017i	$0.700000\pi$
$824$	−2.52681e7	−	4.37657e7i	−1.29645	−	2.24551i
$825$		0			0
$826$	297735.	−	515692.i	0.0151838	−	0.0262991i
$827$	1.98096e6			0.100719			0.0503597	−	0.998731i	$-0.483963\pi$
$827$	1.98096e6			0.100719			0.0503597	+	0.998731i	$0.483963\pi$
$828$		0			0
$829$	2.56811e7			1.29786			0.648929	−	0.760849i	$-0.275217\pi$
$829$	2.56811e7			1.29786			0.648929	+	0.760849i	$0.275217\pi$
$830$	2.42631e6	−	4.20249e6i	0.122251	−	0.211744i
$831$		0			0
$832$	8.89067e6	+	1.53991e7i	0.445273	+	0.771235i
$833$	−1.01900e7	−	1.76495e7i	−0.508815	−	0.881294i
$834$		0			0
$835$	−4.69988e6	+	8.14043e6i	−0.233276	+	0.404046i
$836$	5.77891e6			0.285977
$837$		0			0
$838$	2.34825e7			1.15514
$839$	2.27342e6	−	3.93767e6i	0.111500	−	0.193123i	−0.804875	−	0.593444i	$-0.797768\pi$
$839$	2.27342e6	−	3.93767e6i	0.111500	−	0.193123i	0.916375	+	0.400321i	$0.131101\pi$
$840$		0			0
$841$	9.37612e6	+	1.62399e7i	0.457123	+	0.791760i
$842$	1.82874e7	+	3.16747e7i	0.888937	+	1.53968i
$843$		0			0
$844$	3.29001e7	−	5.69847e7i	1.58980	−	2.75361i
$845$	7.60068e6			0.366193
$846$		0			0
$847$	258496.			0.0123807
$848$	−7.77197e6	+	1.34614e7i	−0.371143	+	0.642839i
$849$		0			0
$850$	−5.33525e6	−	9.24092e6i	−0.253284	−	0.438700i
$851$	2.65818e7	+	4.60411e7i	1.25823	+	2.17932i
$852$		0			0
$853$	−708511.	+	1.22718e6i	−0.0333407	+	0.0577477i	−0.882214	−	0.470848i	$-0.843948\pi$
$853$	−708511.	+	1.22718e6i	−0.0333407	+	0.0577477i	0.848874	+	0.528596i	$0.177281\pi$
$854$	812324.			0.0381140
$855$		0			0
$856$	7.15394e7			3.33704
$857$	−4.07200e6	+	7.05290e6i	−0.189389	+	0.328032i	−0.945047	−	0.326935i	$-0.893984\pi$
$857$	−4.07200e6	+	7.05290e6i	−0.189389	+	0.328032i	0.755658	+	0.654967i	$0.227317\pi$
$858$		0			0
$859$	−5.33500e6	−	9.24050e6i	−0.246690	−	0.427280i	0.715915	−	0.698187i	$-0.246010\pi$
$859$	−5.33500e6	−	9.24050e6i	−0.246690	−	0.427280i	−0.962605	+	0.270907i	$0.912676\pi$
$860$	−9.64819e6	−	1.67111e7i	−0.444836	−	0.770478i
$861$		0			0
$862$	−3.36474e7	+	5.82791e7i	−1.54235	+	2.67143i
$863$	1.21144e7			0.553701			0.276851	−	0.960913i	$-0.410709\pi$
$863$	1.21144e7			0.553701			0.276851	+	0.960913i	$0.410709\pi$
$864$		0			0
$865$	−3.20737e6			−0.145750
$866$	1.58987e7	−	2.75374e7i	0.720391	−	1.24775i
$867$		0			0
$868$	−349698.	−	605694.i	−0.0157541	−	0.0272869i
$869$	−4.42379e6	−	7.66222e6i	−0.198721	−	0.344196i
$870$		0			0
$871$	−8.56899e6	+	1.48419e7i	−0.382723	+	0.662895i
$872$	3.95445e7			1.76115
$873$		0			0
$874$	−1.69609e7			−0.751051
$875$	−192729.	+	333816.i	−0.00850995	+	0.0147397i
$876$		0			0
$877$	−1.65673e7	−	2.86954e7i	−0.727366	−	1.25983i	−0.957993	−	0.286792i	$-0.907411\pi$
$877$	−1.65673e7	−	2.86954e7i	−0.727366	−	1.25983i	0.230627	−	0.973042i	$-0.425922\pi$
$878$	−6.93075e6	−	1.20044e7i	−0.303420	−	0.525538i
$879$		0			0
$880$	5.50937e6	−	9.54251e6i	0.239826	−	0.415390i
$881$	−49573.7			−0.00215185			−0.00107592	−	0.999999i	$-0.500342\pi$
$881$	−49573.7			−0.00215185			−0.00107592	+	0.999999i	$0.500342\pi$
$882$		0			0
$883$	4.21109e7			1.81758			0.908788	−	0.417259i	$-0.137009\pi$
$883$	4.21109e7			1.81758			0.908788	+	0.417259i	$0.137009\pi$
$884$	2.94005e7	−	5.09232e7i	1.26539	−	2.19172i
$885$		0			0
$886$	−2.46689e7	−	4.27278e7i	−1.05576	−	1.82863i
$887$	550680.	+	953806.i	0.0235012	+	0.0407053i	0.877537	−	0.479509i	$-0.159185\pi$
$887$	550680.	+	953806.i	0.0235012	+	0.0407053i	−0.854036	+	0.520215i	$0.825852\pi$
$888$		0			0
$889$	−94888.8	+	164352.i	−0.00402680	+	0.00697463i
$890$	1.99936e7			0.846088
$891$		0			0
$892$	−6.96498e7			−2.93094
$893$	−749458.	+	1.29810e6i	−0.0314498	+	0.0544727i
$894$		0			0
$895$	516860.	+	895228.i	0.0215683	+	0.0373574i
$896$	−298633.	−	517248.i	−0.0124271	−	0.0215243i
$897$		0			0
$898$	2.40696e7	−	4.16898e7i	0.996042	−	1.72520i
$899$	−6.87102e6			−0.283545
$900$		0			0
$901$	−1.48761e7			−0.610487
$902$	−5.76216e6	+	9.98036e6i	−0.235814	+	0.408441i
$903$		0			0
$904$	8.00974e6	+	1.38733e7i	0.325985	+	0.564622i
$905$	−4.44922e6	−	7.70627e6i	−0.180577	−	0.312769i
$906$		0			0
$907$	3.72157e6	−	6.44595e6i	0.150213	−	0.260177i	−0.781093	−	0.624415i	$-0.785337\pi$
$907$	3.72157e6	−	6.44595e6i	0.150213	−	0.260177i	0.931306	+	0.364238i	$0.118671\pi$
$908$	−4.72659e7			−1.90254
$909$		0			0
$910$	−695425.			−0.0278386
$911$	−1.61672e7	+	2.80024e7i	−0.645414	+	1.11789i	0.338792	+	0.940861i	$0.389982\pi$
$911$	−1.61672e7	+	2.80024e7i	−0.645414	+	1.11789i	−0.984206	+	0.177028i	$0.943352\pi$
$912$		0			0
$913$	−949703.	−	1.64493e6i	−0.0377060	−	0.0653087i
$914$	−2.12600e7	−	3.68234e7i	−0.841778	−	1.45800i
$915$		0			0
$916$	−9.77597e6	+	1.69325e7i	−0.384965	+	0.666779i
$917$	−746841.			−0.0293295
$918$		0			0
$919$	3.18905e7			1.24558			0.622792	−	0.782388i	$-0.285998\pi$
$919$	3.18905e7			1.24558			0.622792	+	0.782388i	$0.285998\pi$
$920$	−2.92348e7	+	5.06362e7i	−1.13876	+	1.97239i
$921$		0			0
$922$	118811.	+	205787.i	0.00460288	+	0.00797243i
$923$	−45141.5	−	78187.3i	−0.00174410	−	0.00302087i
$924$		0			0
$925$	−6.52299e6	+	1.12982e7i	−0.250664	+	0.434163i
$926$	−3.50133e7			−1.34186
$927$		0			0
$928$	2.16177e6			0.0824022
$929$	−7.20450e6	+	1.24786e7i	−0.273883	+	0.474379i	−0.969853	−	0.243692i	$-0.921641\pi$
$929$	−7.20450e6	+	1.24786e7i	−0.273883	+	0.474379i	0.695970	+	0.718071i	$0.254975\pi$
$930$		0			0
$931$	−3.97465e6	−	6.88429e6i	−0.150288	−	0.260307i
$932$	5.20703e7	+	9.01884e7i	1.96359	+	3.40103i
$933$		0			0
$934$	−2.31342e7	+	4.00697e7i	−0.867737	+	1.50296i
$935$	1.05453e7			0.394485
$936$		0			0
$937$	2.33199e7			0.867718			0.433859	−	0.900981i	$-0.357152\pi$
$937$	2.33199e7			0.867718			0.433859	+	0.900981i	$0.357152\pi$
$938$	236779.	−	410113.i	0.00878690	−	0.0152194i
$939$		0			0
$940$	4.98204e6	+	8.62915e6i	0.183902	+	0.318528i
$941$	−2.35788e7	−	4.08396e7i	−0.868054	−	1.50351i	−0.863982	−	0.503522i	$-0.832037\pi$
$941$	−2.35788e7	−	4.08396e7i	−0.868054	−	1.50351i	−0.00407185	−	0.999992i	$-0.501296\pi$
$942$		0			0
$943$	1.14159e7	−	1.97730e7i	0.418054	−	0.724091i
$944$	3.74461e7			1.36765
$945$		0			0
$946$	−1.11890e7			−0.406504
$947$	1.21868e7	−	2.11081e7i	0.441585	−	0.764847i	−0.556223	−	0.831033i	$-0.687750\pi$
$947$	1.21868e7	−	2.11081e7i	0.441585	−	0.764847i	0.997807	+	0.0661864i	$0.0210832\pi$
$948$		0			0
$949$	−1.28429e7	−	2.22445e7i	−0.462910	−	0.801784i
$950$	−2.08104e6	−	3.60447e6i	−0.0748120	−	0.129578i
$951$		0			0
$952$	−421299.	+	729711.i	−0.0150660	+	0.0260951i
$953$	4.33987e7			1.54790			0.773952	−	0.633244i	$-0.218277\pi$
$953$	4.33987e7			1.54790			0.773952	+	0.633244i	$0.218277\pi$
$954$		0			0
$955$	1.16577e7			0.413623
$956$	1.73464e7	−	3.00448e7i	0.613853	−	1.06322i
$957$		0			0
$958$	3.24978e7	+	5.62879e7i	1.14404	+	1.98153i
$959$	155993.	+	270187.i	0.00547719	+	0.00948677i
$960$		0			0
$961$	894119.	−	1.54866e6i	0.0312311	−	0.0540938i
$962$	−1.06501e8			−3.71035
$963$		0			0
$964$	−2.84303e7			−0.985348
$965$	5.37302e6	−	9.30634e6i	0.185738	−	0.321707i
$966$		0			0
$967$	−137300.	−	237810.i	−0.00472176	−	0.00817832i	0.863655	−	0.504084i	$-0.168170\pi$
$967$	−137300.	−	237810.i	−0.00472176	−	0.00817832i	−0.868377	+	0.495905i	$0.834836\pi$
$968$	2.17692e7	+	3.77054e7i	0.746714	+	1.29335i
$969$		0			0
$970$	−2.31681e7	+	4.01283e7i	−0.790607	+	1.36937i
$971$	−3.36920e7			−1.14678			−0.573388	−	0.819284i	$-0.694371\pi$
$971$	−3.36920e7			−1.14678			−0.573388	+	0.819284i	$0.694371\pi$
$972$		0			0
$973$	−496407.			−0.0168096
$974$	4.58185e7	−	7.93600e7i	1.54755	−	2.68043i
$975$		0			0
$976$	2.55415e7	+	4.42391e7i	0.858264	+	1.48656i
$977$	6.93084e6	+	1.20046e7i	0.232300	+	0.402356i	0.958485	−	0.285144i	$-0.0920415\pi$
$977$	6.93084e6	+	1.20046e7i	0.232300	+	0.402356i	−0.726184	+	0.687500i	$0.758708\pi$
$978$		0			0
$979$	3.91293e6	−	6.77739e6i	0.130480	−	0.225999i
$980$	−5.28432e7			−1.75762
$981$		0			0
$982$	5.20238e7			1.72156
$983$	−4.34952e6	+	7.53359e6i	−0.143568	+	0.248667i	−0.928838	−	0.370487i	$-0.879191\pi$
$983$	−4.34952e6	+	7.53359e6i	−0.143568	+	0.248667i	0.785270	+	0.619154i	$0.212524\pi$
$984$		0			0
$985$	−1.19010e7	−	2.06132e7i	−0.390835	−	0.676947i
$986$	7.98116e6	+	1.38238e7i	0.261441	+	0.452829i
$987$		0			0
$988$	1.14678e7	−	1.98628e7i	0.373756	−	0.647365i
$989$	2.21676e7			0.720656
$990$		0			0
$991$	−4.44501e7			−1.43777			−0.718884	−	0.695130i	$-0.755347\pi$
$991$	−4.44501e7			−1.43777			−0.718884	+	0.695130i	$0.755347\pi$
$992$	4.22235e6	−	7.31333e6i	0.136231	−	0.235959i
$993$		0			0
$994$	1247.35	+	2160.48i	4.00426e−5	+	6.93559e-5i
$995$	−97620.2	−	169083.i	−0.00312595	−	0.00541430i
$996$		0			0
$997$	8.21072e6	−	1.42214e7i	0.261603	−	0.453110i	−0.705065	−	0.709143i	$-0.749082\pi$
$997$	8.21072e6	−	1.42214e7i	0.261603	−	0.453110i	0.966668	+	0.256033i	$0.0824154\pi$
$998$	6.42977e7			2.04347
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.6.c.a.19.1		8
3.2	odd	2		9.6.c.a.7.4	yes	8
4.3	odd	2		432.6.i.c.289.2		8
9.2	odd	6		81.6.a.c.1.1		4
9.4	even	3	inner	27.6.c.a.10.1		8
9.5	odd	6		9.6.c.a.4.4	✓	8
9.7	even	3		81.6.a.d.1.4		4
12.11	even	2		144.6.i.c.97.3		8
36.23	even	6		144.6.i.c.49.3		8
36.31	odd	6		432.6.i.c.145.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.6.c.a.4.4	✓	8	9.5	odd	6
9.6.c.a.7.4	yes	8	3.2	odd	2
27.6.c.a.10.1		8	9.4	even	3	inner
27.6.c.a.19.1		8	1.1	even	1	trivial
81.6.a.c.1.1		4	9.2	odd	6
81.6.a.d.1.4		4	9.7	even	3
144.6.i.c.49.3		8	36.23	even	6
144.6.i.c.97.3		8	12.11	even	2
432.6.i.c.145.2		8	36.31	odd	6
432.6.i.c.289.2		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)

\(f(q)\)	\(=\)	\(q+(-4.96163 + 8.59380i) q^{2} +(-33.2356 - 57.5657i) q^{4} +(-23.6560 - 40.9735i) q^{5} +(1.01546 - 1.75882i) q^{7} +342.066 q^{8} +O(q^{10})\)	\(q+(-4.96163 + 8.59380i) q^{2} +(-33.2356 - 57.5657i) q^{4} +(-23.6560 - 40.9735i) q^{5} +(1.01546 - 1.75882i) q^{7} +342.066 q^{8} +469.490 q^{10} +(91.8836 - 159.147i) q^{11} +(-364.672 - 631.630i) q^{13} +(10.0766 + 17.4532i) q^{14} +(-633.668 + 1097.55i) q^{16} -1212.88 q^{17} -473.092 q^{19} +(-1572.44 + 2723.55i) q^{20} +(911.785 + 1579.26i) q^{22} +(-1806.42 - 3128.81i) q^{23} +(443.283 - 767.788i) q^{25} +7237.47 q^{26} -134.997 q^{28} +(-663.121 + 1148.56i) q^{29} +(2590.41 + 4486.72i) q^{31} +(-814.997 - 1411.62i) q^{32} +(6017.88 - 10423.3i) q^{34} -96.0867 q^{35} -14715.2 q^{37} +(2347.31 - 4065.65i) q^{38} +(-8091.94 - 14015.6i) q^{40} +(3159.83 + 5472.98i) q^{41} +(-3067.89 + 5313.75i) q^{43} -12215.2 q^{44} +35851.1 q^{46} +(1584.17 - 2743.86i) q^{47} +(8401.44 + 14551.7i) q^{49} +(4398.81 + 7618.96i) q^{50} +(-24240.2 + 41985.2i) q^{52} +12265.0 q^{53} -8694.41 q^{55} +(347.353 - 601.633i) q^{56} +(-6580.32 - 11397.5i) q^{58} +(-14773.5 - 25588.5i) q^{59} +(20153.6 - 34907.1i) q^{61} -51410.7 q^{62} -24379.9 q^{64} +(-17253.4 + 29883.8i) q^{65} +(-11748.9 - 20349.7i) q^{67} +(40310.9 + 69820.5i) q^{68} +(476.747 - 825.750i) q^{70} +123.786 q^{71} +35217.6 q^{73} +(73011.4 - 126459. i) q^{74} +(15723.5 + 27233.8i) q^{76} +(-186.607 - 323.214i) q^{77} +(24072.8 - 41695.3i) q^{79} +59960.3 q^{80} -62711.6 q^{82} +(5167.97 - 8951.18i) q^{83} +(28692.0 + 49696.1i) q^{85} +(-30443.5 - 52729.7i) q^{86} +(31430.3 - 54438.8i) q^{88} +42585.7 q^{89} -1481.23 q^{91} +(-120075. + 207976. i) q^{92} +(15720.1 + 27228.1i) q^{94} +(11191.5 + 19384.2i) q^{95} +(-49347.3 + 85472.1i) q^{97} -166739. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} - 49 q^{4} - 78 q^{5} + 28 q^{7} + 750 q^{8}+O(q^{10}) \) 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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