LMFDB - Embedded newform 27.9.d.a.8.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,9,Mod(8,27)]

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([1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("27.8");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	27.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.9992224717$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 427 x^{12} - 1362 x^{11} + 135762 x^{10} - 371244 x^{9} + 18261508 x^{8} + \cdots + 872385888256 $ x^14 - x^13 + 427x^12 - 1362x^11 + 135762x^10 - 371244x^9 + 18261508x^8 - 29352736x^7 + 1757083840x^6 - 1434930432x^5 + 61638378240x^4 + 183604924416x^3 + 1254910111744x^2 + 1078377512960x + 872385888256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{30} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			8.7
Root			$7.38374 + 12.7890i$ of defining polynomial
Character	$\chi$	$=$	27.8
Dual form			27.9.d.a.17.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(22.1512 + 12.7890i) q^{2} +(199.117 + 344.881i) q^{4} +(-570.352 + 329.293i) q^{5} +(-1512.41 + 2619.58i) q^{7} +3638.08i q^{8} +O(q^{10})$	\(q+(22.1512 + 12.7890i) q^{2} +(199.117 + 344.881i) q^{4} +(-570.352 + 329.293i) q^{5} +(-1512.41 + 2619.58i) q^{7} +3638.08i q^{8} -16845.3 q^{10} +(8016.93 + 4628.57i) q^{11} +(21771.9 + 37710.0i) q^{13} +(-67003.6 + 38684.6i) q^{14} +(4446.57 - 7701.69i) q^{16} -107702. i q^{17} -22386.6 q^{19} +(-227134. - 131136. i) q^{20} +(118390. + 205057. i) q^{22} +(115959. - 66949.2i) q^{23} +(21555.4 - 37335.0i) q^{25} +1.11376e6i q^{26} -1.20459e6 q^{28} +(219270. + 126596. i) q^{29} +(393886. + 682230. i) q^{31} +(1.00357e6 - 579409. i) q^{32} +(1.37740e6 - 2.38573e6i) q^{34} -1.99211e6i q^{35} +1.55379e6 q^{37} +(-495890. - 286302. i) q^{38} +(-1.19800e6 - 2.07499e6i) q^{40} +(1.91891e6 - 1.10788e6i) q^{41} +(-277061. + 479883. i) q^{43} +3.68652e6i q^{44} +3.42486e6 q^{46} +(-2.05696e6 - 1.18759e6i) q^{47} +(-1.69239e6 - 2.93131e6i) q^{49} +(954955. - 551344. i) q^{50} +(-8.67033e6 + 1.50175e7i) q^{52} +7.83903e6i q^{53} -6.09663e6 q^{55} +(-9.53025e6 - 5.50229e6i) q^{56} +(3.23806e6 + 5.60849e6i) q^{58} +(-4.48638e6 + 2.59021e6i) q^{59} +(-4.77454e6 + 8.26974e6i) q^{61} +2.01496e7i q^{62} +2.73636e7 q^{64} +(-2.48353e7 - 1.43387e7i) q^{65} +(-4.31500e6 - 7.47380e6i) q^{67} +(3.71444e7 - 2.14453e7i) q^{68} +(2.54771e7 - 4.41277e7i) q^{70} -3.31572e7i q^{71} -5.28831e7 q^{73} +(3.44184e7 + 1.98715e7i) q^{74} +(-4.45756e6 - 7.72072e6i) q^{76} +(-2.42498e7 + 1.40006e7i) q^{77} +(4.50350e6 - 7.80029e6i) q^{79} +5.85691e6i q^{80} +5.66748e7 q^{82} +(3.31421e7 + 1.91346e7i) q^{83} +(3.54655e7 + 6.14281e7i) q^{85} +(-1.22745e7 + 7.08666e6i) q^{86} +(-1.68391e7 + 2.91662e7i) q^{88} +1.41720e7i q^{89} -1.31713e8 q^{91} +(4.61791e7 + 2.66615e7i) q^{92} +(-3.03761e7 - 5.26130e7i) q^{94} +(1.27682e7 - 7.37175e6i) q^{95} +(7.52257e7 - 1.30295e8i) q^{97} -8.65761e7i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{2} + 767 q^{4} - 438 q^{5} + 922 q^{7}+O(q^{10}) $ 14 * q + 3 * q^2 + 767 * q^4 - 438 * q^5 + 922 * q^7	$ 14 q + 3 q^{2} + 767 q^{4} - 438 q^{5} + 922 q^{7} - 516 q^{10} + 28677 q^{11} + 1684 q^{13} - 120966 q^{14} - 65281 q^{16} - 269630 q^{19} - 539454 q^{20} + 61311 q^{22} + 1000452 q^{23} + 65177 q^{25} + 1075708 q^{28} - 3797682 q^{29} - 164132 q^{31} + 8461881 q^{32} + 654993 q^{34} - 1671668 q^{37} - 10967691 q^{38} + 613326 q^{40} + 10239447 q^{41} + 791815 q^{43} + 1189536 q^{46} - 31148628 q^{47} - 4826637 q^{49} + 63849453 q^{50} - 5552720 q^{52} + 8107476 q^{55} - 116638674 q^{56} + 14211822 q^{58} + 83493795 q^{59} - 5255600 q^{61} - 26813830 q^{64} - 69232992 q^{65} - 8288855 q^{67} + 77746743 q^{68} + 27813756 q^{70} - 36721682 q^{73} + 10383450 q^{74} - 42822959 q^{76} - 56158710 q^{77} - 32771822 q^{79} + 236099418 q^{82} + 198915996 q^{83} + 97486146 q^{85} - 146190669 q^{86} + 24955827 q^{88} - 201514504 q^{91} + 295365804 q^{92} - 36698244 q^{94} - 386813838 q^{95} + 127049161 q^{97}+O(q^{100}) $ 14 * q + 3 * q^2 + 767 * q^4 - 438 * q^5 + 922 * q^7 - 516 * q^10 + 28677 * q^11 + 1684 * q^13 - 120966 * q^14 - 65281 * q^16 - 269630 * q^19 - 539454 * q^20 + 61311 * q^22 + 1000452 * q^23 + 65177 * q^25 + 1075708 * q^28 - 3797682 * q^29 - 164132 * q^31 + 8461881 * q^32 + 654993 * q^34 - 1671668 * q^37 - 10967691 * q^38 + 613326 * q^40 + 10239447 * q^41 + 791815 * q^43 + 1189536 * q^46 - 31148628 * q^47 - 4826637 * q^49 + 63849453 * q^50 - 5552720 * q^52 + 8107476 * q^55 - 116638674 * q^56 + 14211822 * q^58 + 83493795 * q^59 - 5255600 * q^61 - 26813830 * q^64 - 69232992 * q^65 - 8288855 * q^67 + 77746743 * q^68 + 27813756 * q^70 - 36721682 * q^73 + 10383450 * q^74 - 42822959 * q^76 - 56158710 * q^77 - 32771822 * q^79 + 236099418 * q^82 + 198915996 * q^83 + 97486146 * q^85 - 146190669 * q^86 + 24955827 * q^88 - 201514504 * q^91 + 295365804 * q^92 - 36698244 * q^94 - 386813838 * q^95 + 127049161 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	22.1512	+	12.7890i	1.38445	+	0.799313i	0.992683	−	0.120751i	$-0.0385303\pi$
$2$	22.1512	+	12.7890i	1.38445	+	0.799313i	0.391768	+	0.920064i	$0.371864\pi$
$3$		0			0
$3$		0			0
$4$	199.117	+	344.881i	0.777802	+	1.34719i
$5$	−570.352	+	329.293i	−0.912564	+	0.526869i	−0.881255	−	0.472641i	$-0.843301\pi$
$5$	−570.352	+	329.293i	−0.912564	+	0.526869i	−0.0313086	+	0.999510i	$0.509967\pi$
$6$		0			0
$7$	−1512.41	+	2619.58i	−0.629910	+	1.09104i	0.357659	+	0.933852i	$0.383575\pi$
$7$	−1512.41	+	2619.58i	−0.629910	+	1.09104i	−0.987569	+	0.157184i	$0.949758\pi$
$8$			3638.08i			0.888204i
$9$		0			0
$10$	−16845.3			−1.68453
$11$	8016.93	+	4628.57i	0.547567	+	0.316138i	0.748140	−	0.663541i	$-0.230947\pi$
$11$	8016.93	+	4628.57i	0.547567	+	0.316138i	−0.200573	+	0.979679i	$0.564280\pi$
$12$		0			0
$13$	21771.9	+	37710.0i	0.762295	+	1.32033i	0.941665	+	0.336552i	$0.109261\pi$
$13$	21771.9	+	37710.0i	0.762295	+	1.32033i	−0.179370	+	0.983782i	$0.557406\pi$
$14$	−67003.6	+	38684.6i	−1.74416	+	1.00699i
$15$		0			0
$16$	4446.57	−	7701.69i	0.0678493	−	0.117519i
$17$		−	107702.i		−	1.28952i	−0.764385	−	0.644760i	$-0.776957\pi$
$17$		−	107702.i		−	1.28952i	0.764385	−	0.644760i	$-0.223043\pi$
$18$		0			0
$19$	−22386.6			−0.171780			−0.0858902	−	0.996305i	$-0.527373\pi$
$19$	−22386.6			−0.171780			−0.0858902	+	0.996305i	$0.527373\pi$
$20$	−227134.	−	131136.i	−1.41959	−	0.819600i
$21$		0			0
$22$	118390.	+	205057.i	0.505386	+	0.875354i
$23$	115959.	−	66949.2i	0.414376	−	0.239240i	−0.278292	−	0.960496i	$-0.589768\pi$
$23$	115959.	−	66949.2i	0.414376	−	0.239240i	0.692668	+	0.721256i	$0.256435\pi$
$24$		0			0
$25$	21555.4	−	37335.0i	0.0551818	−	0.0955776i
$26$			1.11376e6i			2.43725i
$27$		0			0
$28$	−1.20459e6			−1.95978
$29$	219270.	+	126596.i	0.310018	+	0.178989i	0.646935	−	0.762546i	$-0.276051\pi$
$29$	219270.	+	126596.i	0.310018	+	0.178989i	−0.336916	+	0.941535i	$0.609384\pi$
$30$		0			0
$31$	393886.	+	682230.i	0.426504	+	0.738727i	0.996560	−	0.0828793i	$-0.0264116\pi$
$31$	393886.	+	682230.i	0.426504	+	0.738727i	−0.570055	+	0.821606i	$0.693078\pi$
$32$	1.00357e6	−	579409.i	0.957075	−	0.552568i
$33$		0			0
$34$	1.37740e6	−	2.38573e6i	1.03073	−	1.78528i
$35$		−	1.99211e6i		−	1.32752i
$36$		0			0
$37$	1.55379e6			0.829062			0.414531	−	0.910035i	$-0.363946\pi$
$37$	1.55379e6			0.829062			0.414531	+	0.910035i	$0.363946\pi$
$38$	−495890.	−	286302.i	−0.237822	−	0.137306i
$39$		0			0
$40$	−1.19800e6	−	2.07499e6i	−0.467967	−	0.810543i
$41$	1.91891e6	−	1.10788e6i	0.679076	−	0.392065i	−0.120431	−	0.992722i	$-0.538428\pi$
$41$	1.91891e6	−	1.10788e6i	0.679076	−	0.392065i	0.799507	+	0.600657i	$0.205094\pi$
$42$		0			0
$43$	−277061.	+	479883.i	−0.0810403	+	0.140366i	−0.903697	−	0.428172i	$-0.859158\pi$
$43$	−277061.	+	479883.i	−0.0810403	+	0.140366i	0.822657	+	0.568538i	$0.192491\pi$
$44$			3.68652e6i			0.983571i
$45$		0			0
$46$	3.42486e6			0.764911
$47$	−2.05696e6	−	1.18759e6i	−0.421536	−	0.243374i	0.274198	−	0.961673i	$-0.411587\pi$
$47$	−2.05696e6	−	1.18759e6i	−0.421536	−	0.243374i	−0.695734	+	0.718299i	$0.744921\pi$
$48$		0			0
$49$	−1.69239e6	−	2.93131e6i	−0.293574	−	0.508484i
$50$	954955.	−	551344.i	0.152793	−	0.0882150i
$51$		0			0
$52$	−8.67033e6	+	1.50175e7i	−1.18583	+	2.05392i
$53$			7.83903e6i			0.993480i	0.867899	+	0.496740i	$0.165470\pi$
$53$			7.83903e6i			0.993480i	−0.867899	+	0.496740i	$0.834530\pi$
$54$		0			0
$55$	−6.09663e6			−0.666253
$56$	−9.53025e6	−	5.50229e6i	−0.969063	−	0.559489i
$57$		0			0
$58$	3.23806e6	+	5.60849e6i	0.286136	+	0.495603i
$59$	−4.48638e6	+	2.59021e6i	−0.370244	+	0.213760i	−0.673565	−	0.739128i	$-0.735238\pi$
$59$	−4.48638e6	+	2.59021e6i	−0.370244	+	0.213760i	0.303321	+	0.952888i	$0.401904\pi$
$60$		0			0
$61$	−4.77454e6	+	8.26974e6i	−0.344836	+	0.597273i	−0.985324	−	0.170695i	$-0.945399\pi$
$61$	−4.77454e6	+	8.26974e6i	−0.344836	+	0.597273i	0.640488	+	0.767968i	$0.278732\pi$
$62$			2.01496e7i			1.36364i
$63$		0			0
$64$	2.73636e7			1.63100
$65$	−2.48353e7	−	1.43387e7i	−1.39129	−	0.803259i
$66$		0			0
$67$	−4.31500e6	−	7.47380e6i	−0.214132	−	0.370887i	0.738872	−	0.673846i	$-0.235359\pi$
$67$	−4.31500e6	−	7.47380e6i	−0.214132	−	0.370887i	−0.953004	+	0.302959i	$0.902026\pi$
$68$	3.71444e7	−	2.14453e7i	1.73723	−	1.00299i
$69$		0			0
$70$	2.54771e7	−	4.41277e7i	1.06110	−	1.83789i
$71$		−	3.31572e7i		−	1.30480i	−0.757873	−	0.652402i	$-0.773762\pi$
$71$		−	3.31572e7i		−	1.30480i	0.757873	−	0.652402i	$-0.226238\pi$
$72$		0			0
$73$	−5.28831e7			−1.86219			−0.931097	−	0.364770i	$-0.881147\pi$
$73$	−5.28831e7			−1.86219			−0.931097	+	0.364770i	$0.881147\pi$
$74$	3.44184e7	+	1.98715e7i	1.14779	+	0.662680i
$75$		0			0
$76$	−4.45756e6	−	7.72072e6i	−0.133611	−	0.231421i
$77$	−2.42498e7	+	1.40006e7i	−0.689836	+	0.398277i
$78$		0			0
$79$	4.50350e6	−	7.80029e6i	0.115622	−	0.200264i	−0.802406	−	0.596778i	$-0.796447\pi$
$79$	4.50350e6	−	7.80029e6i	0.115622	−	0.200264i	0.918028	+	0.396515i	$0.129780\pi$
$80$			5.85691e6i			0.142991i
$81$		0			0
$82$	5.66748e7			1.25353
$83$	3.31421e7	+	1.91346e7i	0.698341	+	0.403188i	0.806729	−	0.590921i	$-0.201236\pi$
$83$	3.31421e7	+	1.91346e7i	0.698341	+	0.403188i	−0.108388	+	0.994109i	$0.534569\pi$
$84$		0			0
$85$	3.54655e7	+	6.14281e7i	0.679408	+	1.17677i
$86$	−1.22745e7	+	7.08666e6i	−0.224393	+	0.129553i
$87$		0			0
$88$	−1.68391e7	+	2.91662e7i	−0.280795	+	0.486351i
$89$			1.41720e7i			0.225876i	0.993602	+	0.112938i	$0.0360262\pi$
$89$			1.41720e7i			0.225876i	−0.993602	+	0.112938i	$0.963974\pi$
$90$		0			0
$91$	−1.31713e8			−1.92071
$92$	4.61791e7	+	2.66615e7i	0.644605	+	0.372163i
$93$		0			0
$94$	−3.03761e7	−	5.26130e7i	−0.389064	−	0.673878i
$95$	1.27682e7	−	7.37175e6i	0.156761	−	0.0905058i
$96$		0			0
$97$	7.52257e7	−	1.30295e8i	0.849727	−	1.47177i	−0.0317254	−	0.999497i	$-0.510100\pi$
$97$	7.52257e7	−	1.30295e8i	0.849727	−	1.47177i	0.881452	−	0.472273i	$-0.156566\pi$
$98$		−	8.65761e7i		−	0.938629i
$99$		0			0
$100$	1.71682e7			0.171682
$101$	−8.40858e7	−	4.85470e7i	−0.808048	−	0.466527i	0.0382294	−	0.999269i	$-0.487828\pi$
$101$	−8.40858e7	−	4.85470e7i	−0.808048	−	0.466527i	−0.846278	+	0.532742i	$0.821162\pi$
$102$		0			0
$103$	4.24958e7	+	7.36049e7i	0.377570	+	0.653970i	0.990708	−	0.136006i	$-0.0434265\pi$
$103$	4.24958e7	+	7.36049e7i	0.377570	+	0.653970i	−0.613138	+	0.789976i	$0.710093\pi$
$104$	−1.37192e8	+	7.92080e7i	−1.17273	+	0.677073i
$105$		0			0
$106$	−1.00253e8	+	1.73644e8i	−0.794101	+	1.37542i
$107$		−	4.67026e7i		−	0.356292i	−0.984004	−	0.178146i	$-0.942990\pi$
$107$		−	4.67026e7i		−	0.356292i	0.984004	−	0.178146i	$-0.0570099\pi$
$108$		0			0
$109$	2.22397e8			1.57551			0.787757	−	0.615987i	$-0.211243\pi$
$109$	2.22397e8			1.57551			0.787757	+	0.615987i	$0.211243\pi$
$110$	−1.35048e8	−	7.79698e7i	−0.922394	−	0.532544i
$111$		0			0
$112$	1.34501e7	+	2.32963e7i	0.0854780	+	0.148052i
$113$	2.58364e7	−	1.49166e7i	0.158459	−	0.0914866i	−0.418673	−	0.908137i	$-0.637505\pi$
$113$	2.58364e7	−	1.49166e7i	0.158459	−	0.0914866i	0.577133	+	0.816650i	$0.304171\pi$
$114$		0			0
$115$	−4.40918e7	+	7.63693e7i	−0.252096	+	0.436644i
$116$			1.00829e8i			0.556872i
$117$		0			0
$118$	−1.32505e8			−0.683445
$119$	2.82134e8	+	1.62890e8i	1.40691	+	0.812282i
$120$		0			0
$121$	−6.43320e7	−	1.11426e8i	−0.300114	−	0.519812i
$122$	−2.11524e8	+	1.22123e8i	−0.954816	+	0.551263i
$123$		0			0
$124$	−1.56859e8	+	2.71688e8i	−0.663472	+	1.14917i
$125$		−	2.28868e8i		−	0.937444i
$126$		0			0
$127$	7.78822e7			0.299381			0.149690	−	0.988733i	$-0.452172\pi$
$127$	7.78822e7			0.299381			0.149690	+	0.988733i	$0.452172\pi$
$128$	3.49225e8	+	2.01625e8i	1.30096	+	0.751111i
$129$		0			0
$130$	−3.66755e8	−	6.35238e8i	−1.28411	−	2.22414i
$131$	−1.49752e8	+	8.64595e7i	−0.508497	+	0.293581i	−0.732215	−	0.681073i	$-0.761514\pi$
$131$	−1.49752e8	+	8.64595e7i	−0.508497	+	0.293581i	0.223719	+	0.974654i	$0.428180\pi$
$132$		0			0
$133$	3.38578e7	−	5.86434e7i	0.108206	−	0.187419i
$134$		−	2.20738e8i		−	0.684634i
$135$		0			0
$136$	3.91829e8			1.14536
$137$	2.81349e8	+	1.62437e8i	0.798662	+	0.461108i	0.843003	−	0.537908i	$-0.180785\pi$
$137$	2.81349e8	+	1.62437e8i	0.798662	+	0.461108i	−0.0443408	+	0.999016i	$0.514119\pi$
$138$		0			0
$139$	2.69917e8	+	4.67509e8i	0.723054	+	1.25237i	0.959770	+	0.280787i	$0.0905954\pi$
$139$	2.69917e8	+	4.67509e8i	0.723054	+	1.25237i	−0.236717	+	0.971579i	$0.576071\pi$
$140$	6.87042e8	−	3.96664e8i	1.78843	−	1.03255i
$141$		0			0
$142$	4.24048e8	−	7.34473e8i	1.04295	−	1.80644i
$143$			4.03091e8i			0.963961i
$144$		0			0
$145$	−1.66748e8			−0.377215
$146$	−1.17142e9	−	6.76322e8i	−2.57812	−	1.48848i
$147$		0			0
$148$	3.09388e8	+	5.35875e8i	0.644846	+	1.11691i
$149$	2.88344e8	−	1.66475e8i	0.585013	−	0.337757i	−0.178110	−	0.984011i	$-0.556998\pi$
$149$	2.88344e8	−	1.66475e8i	0.585013	−	0.337757i	0.763123	+	0.646253i	$0.223665\pi$
$150$		0			0
$151$	3.59005e8	−	6.21816e8i	0.690547	−	1.19606i	−0.281112	−	0.959675i	$-0.590703\pi$
$151$	3.59005e8	−	6.21816e8i	0.690547	−	1.19606i	0.971659	−	0.236388i	$-0.0759635\pi$
$152$		−	8.14443e7i		−	0.152576i
$153$		0			0
$154$	−7.16217e8			−1.27339
$155$	−4.49307e8	−	2.59408e8i	−0.778425	−	0.449424i
$156$		0			0
$157$	−2.46878e8	−	4.27605e8i	−0.406334	−	0.703792i	0.588141	−	0.808758i	$-0.299860\pi$
$157$	−2.46878e8	−	4.27605e8i	−0.406334	−	0.703792i	−0.994476	+	0.104966i	$0.966527\pi$
$158$	1.99516e8	−	1.15191e8i	0.320147	−	0.184837i
$159$		0			0
$160$	−3.81591e8	+	6.60935e8i	−0.582262	+	1.00851i
$161$			4.05020e8i			0.602799i
$162$		0			0
$163$	−3.60955e8			−0.511331			−0.255666	−	0.966765i	$-0.582295\pi$
$163$	−3.60955e8			−0.511331			−0.255666	+	0.966765i	$0.582295\pi$
$164$	7.64175e8	+	4.41197e8i	1.05637	+	0.609898i
$165$		0			0
$166$	4.89425e8	+	8.47709e8i	0.644546	+	1.11639i
$167$	−7.75381e8	+	4.47667e8i	−0.996895	+	0.575558i	−0.907328	−	0.420423i	$-0.861882\pi$
$167$	−7.75381e8	+	4.47667e8i	−0.996895	+	0.575558i	−0.0895670	+	0.995981i	$0.528548\pi$
$168$		0			0
$169$	−5.40166e8	+	9.35595e8i	−0.662187	+	1.14694i
$170$			1.81428e9i			2.17224i
$171$		0			0
$172$	−2.20670e8			−0.252133
$173$	2.83205e8	+	1.63508e8i	0.316167	+	0.182539i	0.649683	−	0.760206i	$-0.274902\pi$
$173$	2.83205e8	+	1.63508e8i	0.316167	+	0.182539i	−0.333516	+	0.942744i	$0.608235\pi$
$174$		0			0
$175$	6.52013e7	+	1.12932e8i	0.0695191	+	0.120411i
$176$	7.12957e7	−	4.11626e7i	0.0743041	−	0.0428995i
$177$		0			0
$178$	−1.81246e8	+	3.13927e8i	−0.180546	+	0.312715i
$179$		−	6.26395e8i		−	0.610150i	−0.952328	−	0.305075i	$-0.901319\pi$
$179$		−	6.26395e8i		−	0.610150i	0.952328	−	0.305075i	$-0.0986815\pi$
$180$		0			0
$181$	1.46351e8			0.136359			0.0681793	−	0.997673i	$-0.478281\pi$
$181$	1.46351e8			0.136359			0.0681793	+	0.997673i	$0.478281\pi$
$182$	−2.91759e9	−	1.68447e9i	−2.65913	−	1.53525i
$183$		0			0
$184$	2.43567e8	+	4.21870e8i	0.212494	+	0.368051i
$185$	−8.86211e8	+	5.11654e8i	−0.756572	+	0.436807i
$186$		0			0
$187$	4.98507e8	−	8.63439e8i	0.407666	−	0.706098i
$188$		−	9.45876e8i		−	0.757187i
$189$		0			0
$190$	3.77110e8			0.289370
$191$	1.93012e9	+	1.11436e9i	1.45028	+	0.837320i	0.998497	−	0.0548082i	$-0.0174547\pi$
$191$	1.93012e9	+	1.11436e9i	1.45028	+	0.837320i	0.451783	+	0.892128i	$0.350788\pi$
$192$		0			0
$193$	−8.57309e8	−	1.48490e9i	−0.617886	−	1.07021i	−0.989871	−	0.141971i	$-0.954656\pi$
$193$	−8.57309e8	−	1.48490e9i	−0.617886	−	1.07021i	0.371985	−	0.928239i	$-0.378677\pi$
$194$	3.33268e9	−	1.92412e9i	2.35281	−	1.35840i
$195$		0			0
$196$	6.73970e8	−	1.16735e9i	0.456684	−	0.791001i
$197$		−	1.93330e9i		−	1.28361i	−0.766866	−	0.641807i	$-0.778185\pi$
$197$		−	1.93330e9i		−	1.28361i	0.766866	−	0.641807i	$-0.221815\pi$
$198$		0			0
$199$	2.64799e9			1.68851			0.844254	−	0.535943i	$-0.180044\pi$
$199$	2.64799e9			1.68851			0.844254	+	0.535943i	$0.180044\pi$
$200$	1.35828e8	+	7.84203e7i	0.0848924	+	0.0490127i
$201$		0			0
$202$	−1.24174e9	−	2.15075e9i	−0.745802	−	1.29177i
$203$	−6.63254e8	+	3.82930e8i	−0.390567	+	0.225494i
$204$		0			0
$205$	−7.29635e8	+	1.26377e9i	−0.413133	+	0.715568i
$206$			2.17392e9i			1.20719i
$207$		0			0
$208$	3.87242e8			0.206885
$209$	−1.79472e8	−	1.03618e8i	−0.0940613	−	0.0543063i
$210$		0			0
$211$	9.38787e8	+	1.62603e9i	0.473628	+	0.820347i	0.999544	−	0.0301889i	$-0.00961089\pi$
$211$	9.38787e8	+	1.62603e9i	0.473628	+	0.820347i	−0.525916	+	0.850536i	$0.676278\pi$
$212$	−2.70354e9	+	1.56089e9i	−1.33841	+	0.772731i
$213$		0			0
$214$	5.97280e8	−	1.03452e9i	0.284789	−	0.493268i
$215$		−	3.64937e8i		−	0.170791i
$216$		0			0
$217$	−2.38287e9			−1.07464
$218$	4.92635e9	+	2.84423e9i	2.18122	+	1.25933i
$219$		0			0
$220$	−1.21395e9	−	2.10261e9i	−0.518213	−	0.897571i
$221$	4.06145e9	−	2.34488e9i	1.70260	−	0.982994i
$222$		0			0
$223$	−1.91832e9	+	3.32263e9i	−0.775713	+	1.34358i	0.158679	+	0.987330i	$0.449276\pi$
$223$	−1.91832e9	+	3.32263e9i	−0.775713	+	1.34358i	−0.934393	+	0.356245i	$0.884057\pi$
$224$			3.50523e9i			1.39227i
$225$		0			0
$226$	7.63076e8			0.292506
$227$	−3.45300e9	−	1.99359e9i	−1.30045	−	0.750813i	−0.319966	−	0.947429i	$-0.603671\pi$
$227$	−3.45300e9	−	1.99359e9i	−1.30045	−	0.750813i	−0.980481	+	0.196616i	$0.937005\pi$
$228$		0			0
$229$	−9.26279e8	−	1.60436e9i	−0.336821	−	0.583392i	0.647012	−	0.762480i	$-0.276019\pi$
$229$	−9.26279e8	−	1.60436e9i	−0.336821	−	0.583392i	−0.983833	+	0.179088i	$0.942685\pi$
$230$	−1.95337e9	+	1.12778e9i	−0.698030	+	0.403008i
$231$		0			0
$232$	−4.60565e8	+	7.97722e8i	−0.158979	+	0.275359i
$233$		−	5.85169e9i		−	1.98544i	−0.120431	−	0.992722i	$-0.538428\pi$
$233$		−	5.85169e9i		−	1.98544i	0.120431	−	0.992722i	$-0.461572\pi$
$234$		0			0
$235$	1.56426e9			0.512904
$236$	−1.78663e9	−	1.03151e9i	−0.575953	−	0.332526i
$237$		0			0
$238$	4.16640e9	+	7.21642e9i	1.29853	+	2.24913i
$239$	−3.97738e9	+	2.29634e9i	−1.21901	+	0.703793i	−0.964705	−	0.263332i	$-0.915179\pi$
$239$	−3.97738e9	+	2.29634e9i	−1.21901	+	0.703793i	−0.254300	+	0.967125i	$0.581845\pi$
$240$		0			0
$241$	1.07396e9	−	1.86015e9i	0.318361	−	0.551417i	−0.661785	−	0.749693i	$-0.730201\pi$
$241$	1.07396e9	−	1.86015e9i	0.318361	−	0.551417i	0.980146	+	0.198276i	$0.0635343\pi$
$242$		−	3.29097e9i		−	0.959539i
$243$		0			0
$244$	−3.80278e9			−1.07286
$245$	1.93052e9	+	1.11459e9i	0.535809	+	0.309350i
$246$		0			0
$247$	−4.87399e8	−	8.44200e8i	−0.130947	−	0.226807i
$248$	−2.48201e9	+	1.43299e9i	−0.656140	+	0.378823i
$249$		0			0
$250$	2.92700e9	−	5.06970e9i	0.749311	−	1.29784i
$251$			6.17017e9i			1.55454i	0.629166	+	0.777271i	$0.283397\pi$
$251$			6.17017e9i			1.55454i	−0.629166	+	0.777271i	$0.716603\pi$
$252$		0			0
$253$	1.23952e9			0.302531
$254$	1.72519e9	+	9.96037e8i	0.414478	+	0.239299i
$255$		0			0
$256$	1.65462e9	+	2.86589e9i	0.385246	+	0.667266i
$257$	−4.17836e9	+	2.41238e9i	−0.957797	+	0.552984i	−0.895494	−	0.445073i	$-0.853178\pi$
$257$	−4.17836e9	+	2.41238e9i	−0.957797	+	0.552984i	−0.0623027	+	0.998057i	$0.519844\pi$
$258$		0			0
$259$	−2.34998e9	+	4.07029e9i	−0.522234	+	0.904536i
$260$		−	1.14203e10i		−	2.49911i
$261$		0			0
$262$	−4.42292e9			−0.938651
$263$	2.74533e9	+	1.58501e9i	0.573814	+	0.331292i	0.758671	−	0.651474i	$-0.225849\pi$
$263$	2.74533e9	+	1.58501e9i	0.573814	+	0.331292i	−0.184857	+	0.982765i	$0.559182\pi$
$264$		0			0
$265$	−2.58134e9	−	4.47101e9i	−0.523434	−	0.906614i
$266$	1.49998e9	−	8.66016e8i	0.299612	−	0.172981i
$267$		0			0
$268$	1.71838e9	−	2.97633e9i	0.333105	−	0.576954i
$269$		−	4.01247e9i		−	0.766306i	−0.923685	−	0.383153i	$-0.874838\pi$
$269$		−	4.01247e9i		−	0.766306i	0.923685	−	0.383153i	$-0.125162\pi$
$270$		0			0
$271$	−5.85354e9			−1.08528			−0.542640	−	0.839966i	$-0.682575\pi$
$271$	−5.85354e9			−1.08528			−0.542640	+	0.839966i	$0.682575\pi$
$272$	−8.29488e8	−	4.78905e8i	−0.151542	−	0.0874931i
$273$		0			0
$274$	4.15482e9	+	7.19635e9i	0.737139	+	1.27676i
$275$	3.45616e8	−	1.99541e8i	0.0604314	−	0.0348901i
$276$		0			0
$277$	2.71626e9	−	4.70470e9i	0.461373	−	0.799121i	−0.537657	−	0.843164i	$-0.680690\pi$
$277$	2.71626e9	−	4.70470e9i	0.461373	−	0.799121i	0.999030	+	0.0440427i	$0.0140238\pi$
$278$			1.38079e10i			2.31178i
$279$		0			0
$280$	7.24746e9			1.17911
$281$	−9.77406e7	−	5.64306e7i	−0.0156765	−	0.00905084i	0.492141	−	0.870515i	$-0.336214\pi$
$281$	−9.77406e7	−	5.64306e7i	−0.0156765	−	0.00905084i	−0.507818	+	0.861465i	$0.669548\pi$
$282$		0			0
$283$	3.05787e9	+	5.29639e9i	0.476732	+	0.825723i	0.999644	−	0.0266628i	$-0.00848805\pi$
$283$	3.05787e9	+	5.29639e9i	0.476732	+	0.825723i	−0.522913	+	0.852386i	$0.675155\pi$
$284$	1.14353e10	−	6.60218e9i	1.75782	−	1.01488i
$285$		0			0
$286$	−5.15514e9	+	8.92896e9i	−0.770506	+	1.33456i
$287$			6.70230e9i			0.987862i
$288$		0			0
$289$	−4.62396e9			−0.662861
$290$	−3.69367e9	−	2.13254e9i	−0.522236	−	0.301513i
$291$		0			0
$292$	−1.05299e10	−	1.82384e10i	−1.44842	−	2.50874i
$293$	−5.72464e9	+	3.30512e9i	−0.776744	+	0.448453i	−0.835275	−	0.549832i	$-0.814692\pi$
$293$	−5.72464e9	+	3.30512e9i	−0.776744	+	0.448453i	0.0585311	+	0.998286i	$0.481358\pi$
$294$		0			0
$295$	1.70588e9	−	2.95467e9i	0.225247	−	0.390140i
$296$			5.65284e9i			0.736376i
$297$		0			0
$298$	8.51622e9			1.07990
$299$	5.04932e9	+	2.91522e9i	0.631754	+	0.364743i
$300$		0			0
$301$	−8.38061e8	−	1.45156e9i	−0.102096	−	0.176836i
$302$	1.59048e10	−	9.18265e9i	1.91206	−	1.10393i
$303$		0			0
$304$	−9.95437e7	+	1.72415e8i	−0.0116552	+	0.0201874i
$305$		−	6.28889e9i		−	0.726733i
$306$		0			0
$307$	1.46067e10			1.64437			0.822184	−	0.569222i	$-0.192755\pi$
$307$	1.46067e10			1.64437			0.822184	+	0.569222i	$0.192755\pi$
$308$	−9.65712e9	−	5.57554e9i	−1.07311	−	0.619561i
$309$		0			0
$310$	−6.63513e9	−	1.14924e10i	−0.718460	−	1.24441i
$311$	6.95108e9	−	4.01321e9i	0.743038	−	0.428993i	−0.0801351	−	0.996784i	$-0.525535\pi$
$311$	6.95108e9	−	4.01321e9i	0.743038	−	0.428993i	0.823173	+	0.567791i	$0.192202\pi$
$312$		0			0
$313$	1.74799e9	−	3.02760e9i	0.182121	−	0.315443i	−0.760481	−	0.649360i	$-0.775037\pi$
$313$	1.74799e9	−	3.02760e9i	0.182121	−	0.315443i	0.942603	+	0.333916i	$0.108370\pi$
$314$		−	1.26293e10i		−	1.29915i
$315$		0			0
$316$	3.58690e9			0.359725
$317$	−3.16758e9	−	1.82880e9i	−0.313683	−	0.181105i	0.334890	−	0.942257i	$-0.391301\pi$
$317$	−3.16758e9	−	1.82880e9i	−0.313683	−	0.181105i	−0.648573	+	0.761152i	$0.724634\pi$
$318$		0			0
$319$	1.17191e9	+	2.02981e9i	0.113170	+	0.196017i
$320$	−1.56069e10	+	9.01065e9i	−1.48839	+	0.859323i
$321$		0			0
$322$	−5.17980e9	+	8.97168e9i	−0.481825	+	0.834546i
$323$			2.41108e9i			0.221514i
$324$		0			0
$325$	1.87721e9			0.168259
$326$	−7.99559e9	−	4.61625e9i	−0.707913	−	0.408714i
$327$		0			0
$328$	4.03056e9	+	6.98114e9i	0.348233	+	0.603158i
$329$	6.22195e9	−	3.59225e9i	0.531059	−	0.306607i
$330$		0			0
$331$	1.28320e9	−	2.22257e9i	0.106901	−	0.185159i	−0.807612	−	0.589714i	$-0.799240\pi$
$331$	1.28320e9	−	2.22257e9i	0.106901	−	0.185159i	0.914513	+	0.404555i	$0.132574\pi$
$332$			1.52401e10i			1.25440i
$333$		0			0
$334$	−2.29008e10			−1.84020
$335$	4.92214e9	+	2.84180e9i	0.390818	+	0.225639i
$336$		0			0
$337$	8.78453e9	+	1.52153e10i	0.681081	+	1.17967i	0.974651	+	0.223730i	$0.0718233\pi$
$337$	8.78453e9	+	1.52153e10i	0.681081	+	1.17967i	−0.293570	+	0.955938i	$0.594843\pi$
$338$	−2.39307e10	+	1.38164e10i	−1.83353	+	1.05859i
$339$		0			0
$340$	−1.41236e10	+	2.44628e10i	−1.05689	+	1.83059i
$341$			7.29251e9i			0.539336i
$342$		0			0
$343$	−7.19914e9			−0.520120
$344$	−1.74586e9	−	1.00797e9i	−0.124674	−	0.0719804i
$345$		0			0
$346$	4.18222e9	+	7.24381e9i	0.291811	+	0.505432i
$347$	3.87244e9	−	2.23576e9i	0.267096	−	0.154208i	−0.360471	−	0.932770i	$-0.617384\pi$
$347$	3.87244e9	−	2.23576e9i	0.267096	−	0.154208i	0.627567	+	0.778562i	$0.284051\pi$
$348$		0			0
$349$	3.34797e9	−	5.79885e9i	0.225673	−	0.390877i	−0.730848	−	0.682540i	$-0.760875\pi$
$349$	3.34797e9	−	5.79885e9i	0.225673	−	0.390877i	0.956521	+	0.291663i	$0.0942086\pi$
$350$			3.33544e9i			0.222270i
$351$		0			0
$352$	1.07274e10			0.698750
$353$	5.93593e9	+	3.42711e9i	0.382287	+	0.220714i	0.678813	−	0.734311i	$-0.262495\pi$
$353$	5.93593e9	+	3.42711e9i	0.382287	+	0.220714i	−0.296526	+	0.955025i	$0.595828\pi$
$354$		0			0
$355$	1.09185e10	+	1.89113e10i	0.687460	+	1.19072i
$356$	−4.88766e9	+	2.82189e9i	−0.304299	+	0.175687i
$357$		0			0
$358$	8.01098e9	−	1.38754e10i	0.487701	−	0.844722i
$359$		−	1.73526e9i		−	0.104469i	−0.998635	−	0.0522343i	$-0.983366\pi$
$359$		−	1.73526e9i		−	0.104469i	0.998635	−	0.0522343i	$-0.0166343\pi$
$360$		0			0
$361$	−1.64824e10			−0.970491
$362$	3.24186e9	+	1.87169e9i	0.188782	+	0.108993i
$363$		0			0
$364$	−2.62263e10	−	4.54252e10i	−1.49393	−	2.58757i
$365$	3.01620e10	−	1.74140e10i	1.69937	−	0.981133i
$366$		0			0
$367$	5.88774e9	−	1.01979e10i	0.324552	−	0.562140i	−0.656870	−	0.754004i	$-0.728120\pi$
$367$	5.88774e9	−	1.01979e10i	0.324552	−	0.562140i	0.981422	+	0.191864i	$0.0614532\pi$
$368$		−	1.19078e9i		−	0.0649292i
$369$		0			0
$370$	−2.61742e10			−1.39658
$371$	−2.05350e10	−	1.18559e10i	−1.08392	−	0.625803i
$372$		0			0
$373$	−3.90182e9	−	6.75815e9i	−0.201573	−	0.349134i	0.747463	−	0.664304i	$-0.231272\pi$
$373$	−3.90182e9	−	6.75815e9i	−0.201573	−	0.349134i	−0.949035	+	0.315170i	$0.897939\pi$
$374$	2.20850e10	−	1.27508e10i	1.12879	−	0.651705i
$375$		0			0
$376$	4.32054e9	−	7.48339e9i	0.216166	−	0.374410i
$377$			1.10249e10i			0.545770i
$378$		0			0
$379$	2.60617e10			1.26312			0.631561	−	0.775326i	$-0.282415\pi$
$379$	2.60617e10			1.26312			0.631561	+	0.775326i	$0.282415\pi$
$380$	5.08476e9	+	2.93569e9i	0.243858	+	0.140791i
$381$		0			0
$382$	2.85031e10	+	4.93688e10i	1.33856	+	2.31846i
$383$	−3.06119e10	+	1.76738e10i	−1.42264	+	0.821361i	−0.996524	−	0.0833079i	$-0.973452\pi$
$383$	−3.06119e10	+	1.76738e10i	−1.42264	+	0.821361i	−0.426115	+	0.904669i	$0.640118\pi$
$384$		0			0
$385$	9.22063e9	−	1.59706e10i	0.419679	−	0.726906i
$386$		−	4.38565e10i		−	1.97554i
$387$		0			0
$388$	5.99150e10			2.64368
$389$	−1.63388e10	−	9.43321e9i	−0.713545	−	0.411966i	0.0988271	−	0.995105i	$-0.468491\pi$
$389$	−1.63388e10	−	9.43321e9i	−0.713545	−	0.411966i	−0.812372	+	0.583139i	$0.801824\pi$
$390$		0			0
$391$	−7.21056e9	−	1.24891e10i	−0.308505	−	0.534346i
$392$	1.06644e10	−	6.15707e9i	0.451638	−	0.260753i
$393$		0			0
$394$	2.47250e10	−	4.28250e10i	1.02601	−	1.77710i
$395$			5.93188e9i			0.243671i
$396$		0			0
$397$	−3.41481e10			−1.37469			−0.687345	−	0.726331i	$-0.741224\pi$
$397$	−3.41481e10			−1.37469			−0.687345	+	0.726331i	$0.741224\pi$
$398$	5.86561e10	+	3.38651e10i	2.33766	+	1.34965i
$399$		0			0
$400$	−1.91695e8	−	3.32026e8i	−0.00748809	−	0.0129698i
$401$	−3.01595e9	+	1.74126e9i	−0.116640	+	0.0673420i	−0.557185	−	0.830388i	$-0.688119\pi$
$401$	−3.01595e9	+	1.74126e9i	−0.116640	+	0.0673420i	0.440545	+	0.897730i	$0.354785\pi$
$402$		0			0
$403$	−1.71513e10	+	2.97069e10i	−0.650244	+	1.12626i
$404$		−	3.86662e10i		−	1.45146i
$405$		0			0
$406$	−1.95892e10			−0.720961
$407$	1.24567e10	+	7.19185e9i	0.453967	+	0.262098i
$408$		0			0
$409$	−1.46758e10	−	2.54192e10i	−0.524455	−	0.908382i	−0.999595	−	0.0284717i	$-0.990936\pi$
$409$	−1.46758e10	−	2.54192e10i	−0.524455	−	0.908382i	0.475140	−	0.879910i	$-0.342397\pi$
$410$	−3.23246e10	+	1.86626e10i	−1.14393	+	0.660446i
$411$		0			0
$412$	−1.69233e10	+	2.93120e10i	−0.587349	+	1.01732i
$413$		−	1.56699e10i		−	0.538599i
$414$		0			0
$415$	−2.52036e10			−0.849708
$416$	4.36991e10	+	2.52297e10i	1.45915	+	0.842439i
$417$		0			0
$418$	−2.65034e9	−	4.59053e9i	−0.0868154	−	0.150369i
$419$	−2.87848e10	+	1.66189e10i	−0.933914	+	0.539195i	−0.888047	−	0.459752i	$-0.847938\pi$
$419$	−2.87848e10	+	1.66189e10i	−0.933914	+	0.539195i	−0.0458666	+	0.998948i	$0.514605\pi$
$420$		0			0
$421$	−1.38303e10	+	2.39548e10i	−0.440254	+	0.762542i	−0.997708	−	0.0676654i	$-0.978445\pi$
$421$	−1.38303e10	+	2.39548e10i	−0.440254	+	0.762542i	0.557454	+	0.830208i	$0.311778\pi$
$422$			4.80246e10i			1.51431i
$423$		0			0
$424$	−2.85191e10			−0.882413
$425$	−4.02105e9	−	2.32156e9i	−0.123249	−	0.0711580i
$426$		0			0
$427$	−1.44422e10	−	2.50146e10i	−0.434431	−	0.752456i
$428$	1.61069e10	−	9.29929e9i	0.479994	−	0.277125i
$429$		0			0
$430$	4.66718e9	−	8.08379e9i	0.136515	−	0.236451i
$431$			3.24621e10i			0.940734i	0.882471	+	0.470367i	$0.155879\pi$
$431$			3.24621e10i			0.940734i	−0.882471	+	0.470367i	$0.844121\pi$
$432$		0			0
$433$	2.13330e10			0.606876			0.303438	−	0.952851i	$-0.401865\pi$
$433$	2.13330e10			0.606876			0.303438	+	0.952851i	$0.401865\pi$
$434$	−5.27835e10	−	3.04746e10i	−1.48778	−	0.858972i
$435$		0			0
$436$	4.42830e10	+	7.67004e10i	1.22544	+	2.12252i
$437$	−2.59594e9	+	1.49877e9i	−0.0711817	+	0.0410968i
$438$		0			0
$439$	−9.84950e9	+	1.70598e10i	−0.265189	+	0.459322i	−0.967613	−	0.252437i	$-0.918768\pi$
$439$	−9.84950e9	+	1.70598e10i	−0.265189	+	0.459322i	0.702424	+	0.711759i	$0.252101\pi$
$440$		−	2.21800e10i		−	0.591768i
$441$		0			0
$442$	1.19955e11			3.14288
$443$	−2.42267e10	−	1.39873e10i	−0.629042	−	0.363177i	0.151339	−	0.988482i	$-0.451641\pi$
$443$	−2.42267e10	−	1.39873e10i	−0.629042	−	0.363177i	−0.780381	+	0.625305i	$0.784975\pi$
$444$		0			0
$445$	−4.66674e9	−	8.08303e9i	−0.119007	−	0.206127i
$446$	−8.49862e10	+	4.90668e10i	−2.14787	+	1.24008i
$447$		0			0
$448$	−4.13851e10	+	7.16812e10i	−1.02738	+	1.77948i
$449$		−	3.38588e10i		−	0.833080i	−0.909117	−	0.416540i	$-0.863243\pi$
$449$		−	3.38588e10i		−	0.833080i	0.909117	−	0.416540i	$-0.136757\pi$
$450$		0			0
$451$	2.05116e10			0.495786
$452$	1.02889e10	+	5.94033e9i	0.246500	+	0.142317i
$453$		0			0
$454$	−5.09920e10	−	8.83208e10i	−1.20027	−	2.07893i
$455$	7.51226e10	−	4.33720e10i	1.75277	−	1.01196i
$456$		0			0
$457$	−2.42880e10	+	4.20680e10i	−0.556834	+	0.964466i	0.440924	+	0.897545i	$0.354651\pi$
$457$	−2.42880e10	+	4.20680e10i	−0.556834	+	0.964466i	−0.997758	+	0.0669210i	$0.978682\pi$
$458$		−	4.73847e10i		−	1.07690i
$459$		0			0
$460$	−3.51178e10			−0.784325
$461$	−3.83976e10	−	2.21689e10i	−0.850159	−	0.490840i	0.0105452	−	0.999944i	$-0.496643\pi$
$461$	−3.83976e10	−	2.21689e10i	−0.850159	−	0.490840i	−0.860705	+	0.509105i	$0.829977\pi$
$462$		0			0
$463$	7.25514e9	+	1.25663e10i	0.157878	+	0.273453i	0.934103	−	0.357003i	$-0.116201\pi$
$463$	7.25514e9	+	1.25663e10i	0.157878	+	0.273453i	−0.776225	+	0.630456i	$0.782868\pi$
$464$	1.95000e9	−	1.12583e9i	0.0420690	−	0.0242886i
$465$		0			0
$466$	7.48373e10	−	1.29622e11i	1.58699	−	2.74875i
$467$		−	5.53421e10i		−	1.16356i	−0.813347	−	0.581779i	$-0.802357\pi$
$467$		−	5.53421e10i		−	1.16356i	0.813347	−	0.581779i	$-0.197643\pi$
$468$		0			0
$469$	2.61043e10			0.539535
$470$	3.46502e10	+	2.00053e10i	0.710091	+	0.409971i
$471$		0			0
$472$	−9.42340e9	−	1.63218e10i	−0.189863	−	0.328852i
$473$	−4.44235e9	+	2.56479e9i	−0.0887500	+	0.0512398i
$474$		0			0
$475$	−4.82552e8	+	8.35804e8i	−0.00947915	+	0.0164184i
$476$			1.29737e11i			2.52718i
$477$		0			0
$478$	−1.17472e11			−2.25020
$479$	−3.37571e10	−	1.94897e10i	−0.641243	−	0.370222i	0.143850	−	0.989599i	$-0.454052\pi$
$479$	−3.37571e10	−	1.94897e10i	−0.641243	−	0.370222i	−0.785093	+	0.619378i	$0.787385\pi$
$480$		0			0
$481$	3.38291e10	+	5.85937e10i	0.631989	+	1.09464i
$482$	4.75790e10	−	2.74697e10i	0.881510	−	0.508940i
$483$		0			0
$484$	2.56193e10	−	4.43739e10i	0.466858	−	0.808622i
$485$			9.90852e10i			1.79078i
$486$		0			0
$487$	−2.22852e10			−0.396188			−0.198094	−	0.980183i	$-0.563475\pi$
$487$	−2.22852e10			−0.396188			−0.198094	+	0.980183i	$0.563475\pi$
$488$	−3.00860e10	−	1.73702e10i	−0.530500	−	0.306284i
$489$		0			0
$490$	2.85089e10	+	4.93789e10i	0.494534	+	0.856559i
$491$	5.32333e10	−	3.07343e10i	0.915920	−	0.528807i	0.0335890	−	0.999436i	$-0.489306\pi$
$491$	5.32333e10	−	3.07343e10i	0.915920	−	0.528807i	0.882331	+	0.470629i	$0.155973\pi$
$492$		0			0
$493$	1.36346e10	−	2.36158e10i	0.230810	−	0.399774i
$494$		−	2.49334e10i		−	0.418672i
$495$		0			0
$496$	7.00577e9			0.115752
$497$	8.68580e10	+	5.01475e10i	1.42359	+	0.821909i
$498$		0			0
$499$	−2.77415e10	−	4.80496e10i	−0.447432	−	0.774975i	0.550786	−	0.834647i	$-0.314328\pi$
$499$	−2.77415e10	−	4.80496e10i	−0.447432	−	0.774975i	−0.998218	+	0.0596714i	$0.980995\pi$
$500$	7.89324e10	−	4.55716e10i	1.26292	−	0.729146i
$501$		0			0
$502$	−7.89104e10	+	1.36677e11i	−1.24257	+	2.15219i
$503$			9.38955e10i			1.46681i	0.679794	+	0.733403i	$0.262069\pi$
$503$			9.38955e10i			1.46681i	−0.679794	+	0.733403i	$0.737931\pi$
$504$		0			0
$505$	6.39447e10			0.983194
$506$	2.74568e10	+	1.58522e10i	0.418840	+	0.241817i
$507$		0			0
$508$	1.55077e10	+	2.68601e10i	0.232859	+	0.403323i
$509$	−2.97149e10	+	1.71559e10i	−0.442693	+	0.255589i	−0.704739	−	0.709466i	$-0.748936\pi$
$509$	−2.97149e10	+	1.71559e10i	−0.442693	+	0.255589i	0.262046	+	0.965055i	$0.415603\pi$
$510$		0			0
$511$	7.99811e10	−	1.38531e11i	1.17302	−	2.03172i
$512$		−	1.85882e10i		−	0.270494i
$513$		0			0
$514$	−1.23408e11			−1.76803
$515$	−4.84752e10	−	2.79871e10i	−0.689113	−	0.397860i
$516$		0			0
$517$	−1.09937e10	−	1.90416e10i	−0.153879	−	0.266527i
$518$	−1.04110e11	+	6.01079e10i	−1.44602	+	0.834857i
$519$		0			0
$520$	5.21653e10	−	9.03530e10i	0.713458	−	1.23575i
$521$		−	1.04659e11i		−	1.42045i	−0.703975	−	0.710225i	$-0.748593\pi$
$521$		−	1.04659e11i		−	1.42045i	0.703975	−	0.710225i	$-0.251407\pi$
$522$		0			0
$523$	−6.66398e8			−0.00890690			−0.00445345	−	0.999990i	$-0.501418\pi$
$523$	−6.66398e8			−0.00890690			−0.00445345	+	0.999990i	$0.501418\pi$
$524$	−5.96365e10	−	3.44312e10i	−0.791020	−	0.456695i
$525$		0			0
$526$	4.05415e10	+	7.02200e10i	0.529611	+	0.917314i
$527$	7.34775e10	−	4.24223e10i	0.952603	−	0.549986i
$528$		0			0
$529$	−3.01911e10	+	5.22925e10i	−0.385528	+	0.667755i
$530$		−	1.32051e11i		−	1.67355i
$531$		0			0
$532$	2.69667e10			0.336652
$533$	8.35565e10	+	4.82414e10i	1.03531	+	0.597738i
$534$		0			0
$535$	1.53788e10	+	2.66369e10i	0.187719	+	0.325139i
$536$	2.71903e10	−	1.56983e10i	0.329424	−	0.190193i
$537$		0			0
$538$	5.13155e10	−	8.88810e10i	0.612518	−	1.06091i
$539$		−	3.13335e10i		−	0.371239i
$540$		0			0
$541$	5.96762e10			0.696646			0.348323	−	0.937375i	$-0.386751\pi$
$541$	5.96762e10			0.696646			0.348323	+	0.937375i	$0.386751\pi$
$542$	−1.29663e11	−	7.48610e10i	−1.50252	−	0.867478i
$543$		0			0
$544$	−6.24035e10	−	1.08086e11i	−0.712547	−	1.23417i
$545$	−1.26844e11	+	7.32336e10i	−1.43776	+	0.830089i
$546$		0			0
$547$	−2.65388e10	+	4.59665e10i	−0.296436	+	0.513443i	−0.975318	−	0.220805i	$-0.929132\pi$
$547$	−2.65388e10	+	4.59665e10i	−0.296436	+	0.513443i	0.678882	+	0.734248i	$0.262465\pi$
$548$			1.29376e11i			1.43460i
$549$		0			0
$550$	1.02077e10			0.111552
$551$	−4.90871e9	−	2.83404e9i	−0.0532550	−	0.0307468i
$552$		0			0
$553$	1.36223e10	+	2.35945e10i	0.145663	+	0.252296i
$554$	1.20337e11	−	6.94765e10i	1.27750	−	0.737562i
$555$		0			0
$556$	−1.07490e11	+	1.86178e11i	−1.12479	+	1.94819i
$557$			1.10596e11i			1.14900i	0.818504	+	0.574500i	$0.194804\pi$
$557$			1.10596e11i			1.14900i	−0.818504	+	0.574500i	$0.805196\pi$
$558$		0			0
$559$	−2.41286e10			−0.247107
$560$	−1.53426e10	−	8.85807e9i	−0.156008	−	0.0900714i
$561$		0			0
$562$	−1.44338e9	−	2.50001e9i	−0.0144689	−	0.0250609i
$563$	3.72727e10	−	2.15194e10i	0.370986	−	0.214189i	−0.302903	−	0.953021i	$-0.597956\pi$
$563$	3.72727e10	−	2.15194e10i	0.370986	−	0.214189i	0.673889	+	0.738832i	$0.264623\pi$
$564$		0			0
$565$	−9.82390e9	+	1.70155e10i	−0.0964029	+	0.166975i
$566$			1.56429e11i			1.52423i
$567$		0			0
$568$	1.20629e11			1.15893
$569$	7.58502e9	+	4.37922e9i	0.0723616	+	0.0417780i	0.535744	−	0.844380i	$-0.320031\pi$
$569$	7.58502e9	+	4.37922e9i	0.0723616	+	0.0417780i	−0.463383	+	0.886158i	$0.653364\pi$
$570$		0			0
$571$	1.64763e9	+	2.85377e9i	0.0154994	+	0.0268457i	0.873671	−	0.486517i	$-0.161733\pi$
$571$	1.64763e9	+	2.85377e9i	0.0154994	+	0.0268457i	−0.858172	+	0.513363i	$0.828400\pi$
$572$	−1.39019e11	+	8.02625e10i	−1.29864	+	0.749771i
$573$		0			0
$574$	−8.57158e10	+	1.48464e11i	−0.789611	+	1.36765i
$575$		−	5.77246e9i		−	0.0528068i
$576$		0			0
$577$	7.03112e10			0.634338			0.317169	−	0.948369i	$-0.397268\pi$
$577$	7.03112e10			0.634338			0.317169	+	0.948369i	$0.397268\pi$
$578$	−1.02426e11	−	5.91358e10i	−0.917699	−	0.529834i
$579$		0			0
$580$	−3.32025e10	−	5.75083e10i	−0.293399	−	0.508182i
$581$	−1.00249e11	+	5.78789e10i	−0.879785	+	0.507944i
$582$		0			0
$583$	−3.62836e10	+	6.28450e10i	−0.314077	+	0.543997i
$584$		−	1.92393e11i		−	1.65401i
$585$		0			0
$586$	−1.69077e11			−1.43382
$587$	9.15067e9	+	5.28314e9i	0.0770726	+	0.0444979i	0.538041	−	0.842919i	$-0.319165\pi$
$587$	9.15067e9	+	5.28314e9i	0.0770726	+	0.0444979i	−0.460968	+	0.887417i	$0.652498\pi$
$588$		0			0
$589$	−8.81776e9	−	1.52728e10i	−0.0732651	−	0.126899i
$590$	7.55745e10	−	4.36329e10i	0.623688	−	0.360086i
$591$		0			0
$592$	6.90906e9	−	1.19669e10i	0.0562513	−	0.0974301i
$593$			6.75771e10i			0.546488i	0.961945	+	0.273244i	$0.0880967\pi$
$593$			6.75771e10i			0.546488i	−0.961945	+	0.273244i	$0.911903\pi$
$594$		0			0
$595$	−2.14554e11			−1.71186
$596$	1.14829e11	+	6.62963e10i	0.910049	+	0.525417i
$597$		0			0
$598$	7.45656e10	+	1.29151e11i	0.583088	+	1.00994i
$599$	1.08819e11	−	6.28266e10i	0.845273	−	0.488019i	−0.0137800	−	0.999905i	$-0.504386\pi$
$599$	1.08819e11	−	6.28266e10i	0.845273	−	0.488019i	0.859053	+	0.511886i	$0.171053\pi$
$600$		0			0
$601$	4.01255e10	−	6.94994e10i	0.307555	−	0.532701i	−0.670272	−	0.742116i	$-0.733823\pi$
$601$	4.01255e10	−	6.94994e10i	0.307555	−	0.532701i	0.977827	+	0.209415i	$0.0671558\pi$
$602$		−	4.28719e10i		−	0.326427i
$603$		0			0
$604$	2.85937e11			2.14844
$605$	7.33839e10	+	4.23682e10i	0.547746	+	0.316241i
$606$		0			0
$607$	−1.03080e11	−	1.78540e11i	−0.759313	−	1.31517i	−0.943201	−	0.332222i	$-0.892202\pi$
$607$	−1.03080e11	−	1.78540e11i	−0.759313	−	1.31517i	0.183888	−	0.982947i	$-0.441132\pi$
$608$	−2.24664e10	+	1.29710e10i	−0.164407	+	0.0949203i
$609$		0			0
$610$	8.04287e10	−	1.39307e11i	0.580887	−	1.00613i
$611$		−	1.03424e11i		−	0.742090i
$612$		0			0
$613$	7.28984e10			0.516269			0.258134	−	0.966109i	$-0.416892\pi$
$613$	7.28984e10			0.516269			0.258134	+	0.966109i	$0.416892\pi$
$614$	3.23556e11	+	1.86805e11i	2.27655	+	1.31436i
$615$		0			0
$616$	−5.09355e10	−	8.82229e10i	−0.353751	−	0.612715i
$617$	−2.23320e11	+	1.28934e11i	−1.54094	+	0.889663i	−0.542162	+	0.840274i	$0.682394\pi$
$617$	−2.23320e11	+	1.28934e11i	−1.54094	+	0.889663i	−0.998780	+	0.0493888i	$0.984273\pi$
$618$		0			0
$619$	1.06461e10	−	1.84395e10i	0.0725148	−	0.125599i	−0.827488	−	0.561483i	$-0.810231\pi$
$619$	1.06461e10	−	1.84395e10i	0.0725148	−	0.125599i	0.900003	+	0.435884i	$0.143564\pi$
$620$		−	2.06610e11i		−	1.39825i
$621$		0			0
$622$	2.05300e11			1.37160
$623$	−3.71247e10	−	2.14339e10i	−0.246439	−	0.142282i
$624$		0			0
$625$	8.37847e10	+	1.45119e11i	0.549092	+	0.951055i
$626$	7.74400e10	−	4.47100e10i	0.504276	−	0.291144i
$627$		0			0
$628$	9.83154e10	−	1.70287e11i	0.632096	−	1.09482i
$629$		−	1.67347e11i		−	1.06909i
$630$		0			0
$631$	−9.46727e10			−0.597183			−0.298591	−	0.954381i	$-0.596517\pi$
$631$	−9.46727e10			−0.597183			−0.298591	+	0.954381i	$0.596517\pi$
$632$	2.83781e10	+	1.63841e10i	0.177875	+	0.102696i
$633$		0			0
$634$	−4.67772e10	−	8.10205e10i	−0.289519	−	0.501462i
$635$	−4.44203e10	+	2.56461e10i	−0.273204	+	0.157734i
$636$		0			0
$637$	7.36933e10	−	1.27640e11i	0.447579	−	0.775230i
$638$			5.99504e10i			0.361834i
$639$		0			0
$640$	−2.65575e11			−1.58295
$641$	−9.25489e10	−	5.34331e10i	−0.548200	−	0.316504i	0.200196	−	0.979756i	$-0.435842\pi$
$641$	−9.25489e10	−	5.34331e10i	−0.548200	−	0.316504i	−0.748396	+	0.663252i	$0.769176\pi$
$642$		0			0
$643$	−2.30544e10	−	3.99314e10i	−0.134868	−	0.233599i	0.790679	−	0.612231i	$-0.209728\pi$
$643$	−2.30544e10	−	3.99314e10i	−0.134868	−	0.233599i	−0.925547	+	0.378632i	$0.876395\pi$
$644$	−1.39684e11	+	8.06465e10i	−0.812087	+	0.468859i
$645$		0			0
$646$	−3.08353e10	+	5.34084e10i	−0.177059	+	0.306676i
$647$		−	1.54353e11i		−	0.880842i	−0.897791	−	0.440421i	$-0.854829\pi$
$647$		−	1.54353e11i		−	0.880842i	0.897791	−	0.440421i	$-0.145171\pi$
$648$		0			0
$649$	−4.79559e10			−0.270311
$650$	4.15824e10	+	2.40076e10i	0.232946	+	0.134492i
$651$		0			0
$652$	−7.18724e10	−	1.24487e11i	−0.397715	−	0.688862i
$653$	2.92739e11	−	1.69013e11i	1.61001	−	0.929539i	0.620643	−	0.784093i	$-0.286872\pi$
$653$	2.92739e11	−	1.69013e11i	1.61001	−	0.929539i	0.989366	−	0.145446i	$-0.0464617\pi$
$654$		0			0
$655$	5.69410e10	−	9.86247e10i	0.309357	−	0.535822i
$656$		−	1.97051e10i		−	0.106405i
$657$		0			0
$658$	1.83765e11			0.980300
$659$	1.65476e11	+	9.55374e10i	0.877389	+	0.506561i	0.869797	−	0.493410i	$-0.164250\pi$
$659$	1.65476e11	+	9.55374e10i	0.877389	+	0.506561i	0.00759244	+	0.999971i	$0.497583\pi$
$660$		0			0
$661$	1.43958e11	+	2.49342e11i	0.754099	+	1.30614i	0.945821	+	0.324689i	$0.105260\pi$
$661$	1.43958e11	+	2.49342e11i	0.754099	+	1.30614i	−0.191721	+	0.981449i	$0.561407\pi$
$662$	5.68490e10	−	3.28218e10i	0.296000	−	0.170895i
$663$		0			0
$664$	−6.96133e10	+	1.20574e11i	−0.358113	+	0.620270i
$665$			4.45966e10i			0.228042i
$666$		0			0
$667$	3.39019e10			0.171285
$668$	−3.08784e11	−	1.78276e11i	−1.55077	−	0.895340i
$669$		0			0
$670$	7.26876e10	+	1.25899e11i	0.360712	+	0.624772i
$671$	−7.65542e10	+	4.41986e10i	−0.377641	+	0.218031i
$672$		0			0
$673$	−1.61459e11	+	2.79655e11i	−0.787050	+	1.36321i	0.140717	+	0.990050i	$0.455059\pi$
$673$	−1.61459e11	+	2.79655e11i	−0.787050	+	1.36321i	−0.927767	+	0.373160i	$0.878274\pi$
$674$			4.49382e11i			2.17759i
$675$		0			0
$676$	−4.30226e11			−2.06020
$677$	1.05215e11	+	6.07462e10i	0.500870	+	0.289177i	0.729073	−	0.684436i	$-0.239952\pi$
$677$	1.05215e11	+	6.07462e10i	0.500870	+	0.289177i	−0.228203	+	0.973614i	$0.573285\pi$
$678$		0			0
$679$	2.27545e11	+	3.94119e11i	1.07050	+	1.85417i
$680$	−2.23481e11	+	1.29027e11i	−1.04521	+	0.603453i
$681$		0			0
$682$	−9.32640e10	+	1.61538e11i	−0.431099	+	0.746685i
$683$			2.88173e11i			1.32425i	0.749393	+	0.662126i	$0.230346\pi$
$683$			2.88173e11i			1.32425i	−0.749393	+	0.662126i	$0.769654\pi$
$684$		0			0
$685$	−2.13957e11			−0.971774
$686$	−1.59470e11	−	9.20698e10i	−0.720081	−	0.415739i
$687$		0			0
$688$	2.46394e9	+	4.26767e9i	0.0109971	+	0.0190475i
$689$	−2.95610e11	+	1.70671e11i	−1.31172	+	0.757325i
$690$		0			0
$691$	1.41426e11	−	2.44956e11i	0.620320	−	1.07443i	−0.369106	−	0.929387i	$-0.620336\pi$
$691$	1.41426e11	−	2.44956e11i	0.620320	−	1.07443i	0.989426	−	0.145039i	$-0.0463306\pi$
$692$			1.30229e11i			0.567917i
$693$		0			0
$694$	1.14372e11			0.493042
$695$	−3.07895e11	−	1.77763e11i	−1.31966	−	0.761909i
$696$		0			0
$697$	−1.19321e11	−	2.06670e11i	−0.505575	−	0.875682i
$698$	1.48323e11	−	8.56343e10i	0.624866	−	0.360767i
$699$		0			0
$700$	−2.59654e10	+	4.49734e10i	−0.108144	+	0.187311i
$701$		−	4.37155e11i		−	1.81035i	−0.425035	−	0.905177i	$-0.639738\pi$
$701$		−	4.37155e11i		−	1.81035i	0.425035	−	0.905177i	$-0.360262\pi$
$702$		0			0
$703$	−3.47842e10			−0.142417
$704$	2.19372e11	+	1.26655e11i	0.893081	+	0.515621i
$705$		0			0
$706$	8.76587e10	+	1.51829e11i	0.352839	+	0.611134i
$707$	2.54345e11	−	1.46846e11i	1.01800	−	0.587740i
$708$		0			0
$709$	1.01719e11	−	1.76183e11i	0.402549	−	0.697235i	−0.591484	−	0.806317i	$-0.701458\pi$
$709$	1.01719e11	−	1.76183e11i	0.402549	−	0.697235i	0.994033	+	0.109082i	$0.0347911\pi$
$710$			5.58545e11i			2.19798i
$711$		0			0
$712$	−5.15589e10			−0.200624
$713$	9.13495e10	+	5.27407e10i	0.353466	+	0.204074i
$714$		0			0
$715$	−1.32735e11	−	2.29904e11i	−0.507881	−	0.879676i
$716$	2.16032e11	−	1.24726e11i	0.821990	−	0.474576i
$717$		0			0
$718$	2.21922e10	−	3.84380e10i	0.0835031	−	0.144632i
$719$		−	3.44324e11i		−	1.28840i	−0.764856	−	0.644201i	$-0.777190\pi$
$719$		−	3.44324e11i		−	1.28840i	0.764856	−	0.644201i	$-0.222810\pi$
$720$		0			0
$721$	−2.57085e11			−0.951340
$722$	−3.65105e11	−	2.10794e11i	−1.34360	−	0.775726i
$723$		0			0
$724$	2.91411e10	+	5.04739e10i	0.106060	+	0.183701i
$725$	9.45289e9	−	5.45763e9i	0.0342147	−	0.0197539i
$726$		0			0
$727$	−5.98468e10	+	1.03658e11i	−0.214241	+	0.371077i	−0.953038	−	0.302852i	$-0.902061\pi$
$727$	−5.98468e10	+	1.03658e11i	−0.214241	+	0.371077i	0.738796	+	0.673929i	$0.235395\pi$
$728$		−	4.79181e11i		−	1.70598i
$729$		0			0
$730$	8.90832e11			3.13693
$731$	5.16844e10	+	2.98400e10i	0.181005	+	0.104503i
$732$		0			0
$733$	−8.94181e10	−	1.54877e11i	−0.309749	−	0.536500i	0.668559	−	0.743659i	$-0.266912\pi$
$733$	−8.94181e10	−	1.54877e11i	−0.309749	−	0.536500i	−0.978307	+	0.207159i	$0.933578\pi$
$734$	2.60841e11	−	1.50597e11i	0.898652	−	0.518837i
$735$		0			0
$736$	7.75820e10	−	1.34376e11i	0.264393	−	0.457942i
$737$		−	7.98891e10i		−	0.270781i
$738$		0			0
$739$	3.08096e11			1.03302			0.516509	−	0.856282i	$-0.327231\pi$
$739$	3.08096e11			1.03302			0.516509	+	0.856282i	$0.327231\pi$
$740$	−3.52920e11	−	2.03758e11i	−1.17693	−	0.679499i
$741$		0			0
$742$	−3.03250e11	−	5.25244e11i	−1.00043	−	1.73279i
$743$	−3.63187e11	+	2.09686e11i	−1.19172	+	0.688041i	−0.958697	−	0.284430i	$-0.908196\pi$
$743$	−3.63187e11	+	2.09686e11i	−1.19172	+	0.688041i	−0.233025	+	0.972471i	$0.574862\pi$
$744$		0			0
$745$	−1.09638e11	+	1.89899e11i	−0.355908	+	0.616450i
$746$		−	1.99602e11i		−	0.644479i
$747$		0			0
$748$	3.97045e11			1.26833
$749$	1.22341e11	+	7.06336e10i	0.388727	+	0.224432i
$750$		0			0
$751$	3.24484e9	+	5.62023e9i	0.0102008	+	0.0176683i	0.871081	−	0.491140i	$-0.163420\pi$
$751$	3.24484e9	+	5.62023e9i	0.0102008	+	0.0176683i	−0.860880	+	0.508808i	$0.830086\pi$
$752$	−1.82929e10	+	1.05614e10i	−0.0572019	+	0.0330255i
$753$		0			0
$754$	−1.40998e11	+	2.44215e11i	−0.436241	+	0.755591i
$755$			4.72872e11i			1.45531i
$756$		0			0
$757$	2.62150e11			0.798299			0.399150	−	0.916886i	$-0.369305\pi$
$757$	2.62150e11			0.798299			0.399150	+	0.916886i	$0.369305\pi$
$758$	5.77297e11	+	3.33303e11i	1.74873	+	1.00963i
$759$		0			0
$760$	2.68191e10	+	4.64520e10i	0.0803876	+	0.139235i
$761$	9.29283e10	−	5.36522e10i	0.277083	−	0.159974i	−0.355019	−	0.934859i	$-0.615526\pi$
$761$	9.29283e10	−	5.36522e10i	0.277083	−	0.159974i	0.632102	+	0.774885i	$0.282192\pi$
$762$		0			0
$763$	−3.36356e11	+	5.82585e11i	−0.992432	+	1.71894i
$764$			8.87552e11i			2.60508i
$765$		0			0
$766$	−9.04120e11			−2.62610
$767$	−1.95354e11	−	1.12788e11i	−0.564470	−	0.325897i
$768$		0			0
$769$	1.20233e11	+	2.08249e11i	0.343808	+	0.595494i	0.985137	−	0.171773i	$-0.0549496\pi$
$769$	1.20233e11	+	2.08249e11i	0.343808	+	0.595494i	−0.641328	+	0.767267i	$0.721616\pi$
$770$	4.08496e11	−	2.35845e11i	1.16205	−	0.670910i
$771$		0			0
$772$	3.41410e11	−	5.91340e11i	0.961186	−	1.66482i
$773$			1.08257e11i			0.303206i	0.988441	+	0.151603i	$0.0484436\pi$
$773$			1.08257e11i			0.303206i	−0.988441	+	0.151603i	$0.951556\pi$
$774$		0			0
$775$	3.39614e10			0.0941410
$776$	4.74023e11	+	2.73677e11i	1.30723	+	0.754731i
$777$		0			0
$778$	−2.41283e11	−	4.17914e11i	−0.658579	−	1.14069i
$779$	−4.29578e10	+	2.48017e10i	−0.116652	+	0.0673490i
$780$		0			0
$781$	1.53471e11	−	2.65819e11i	0.412498	−	0.714467i
$782$		−	3.68864e11i		−	0.986368i
$783$		0			0
$784$	−3.01014e10			−0.0796751
$785$	2.81615e11	+	1.62590e11i	0.741612	+	0.428170i
$786$		0			0
$787$	−3.25844e11	−	5.64378e11i	−0.849397	−	1.47120i	−0.881747	−	0.471723i	$-0.843632\pi$
$787$	−3.25844e11	−	5.64378e11i	−0.849397	−	1.47120i	0.0323497	−	0.999477i	$-0.489701\pi$
$788$	6.66760e11	−	3.84954e11i	1.72928	−	0.998399i
$789$		0			0
$790$	−7.58629e10	+	1.31398e11i	−0.194770	+	0.337351i
$791$			9.02406e10i			0.230513i
$792$		0			0
$793$	−4.15803e11			−1.05147
$794$	−7.56422e11	−	4.36721e11i	−1.90319	−	1.09881i
$795$		0			0
$796$	5.27260e11	+	9.13241e11i	1.31333	+	2.27475i
$797$	−3.93581e10	+	2.27234e10i	−0.0975440	+	0.0563170i	−0.547978	−	0.836492i	$-0.684602\pi$
$797$	−3.93581e10	+	2.27234e10i	−0.0975440	+	0.0563170i	0.450434	+	0.892809i	$0.351269\pi$
$798$		0			0
$799$	−1.27905e11	+	2.21539e11i	−0.313835	+	0.543579i
$800$		−	4.99575e10i		−	0.121967i
$801$		0			0
$802$	−8.90759e10			−0.215309
$803$	−4.23960e11	−	2.44773e11i	−1.01968	−	0.588710i
$804$		0			0
$805$	−1.33370e11	−	2.31004e11i	−0.317596	−	0.550093i
$806$	−7.59843e11	+	4.38696e11i	−1.80046	+	1.03950i
$807$		0			0
$808$	1.76618e11	−	3.05911e11i	0.414371	−	0.717712i
$809$			1.21628e11i			0.283948i	0.989870	+	0.141974i	$0.0453449\pi$
$809$			1.21628e11i			0.283948i	−0.989870	+	0.141974i	$0.954655\pi$
$810$		0			0
$811$	8.42541e11			1.94764			0.973818	−	0.227330i	$-0.0729997\pi$
$811$	8.42541e11			1.94764			0.973818	+	0.227330i	$0.0729997\pi$
$812$	−2.64131e11	−	1.52496e11i	−0.607568	−	0.350780i
$813$		0			0
$814$	1.83953e11	+	3.18617e11i	0.418996	+	0.725723i
$815$	2.05871e11	−	1.18860e11i	0.466622	−	0.269405i
$816$		0			0
$817$	6.20245e9	−	1.07430e10i	0.0139211	−	0.0241121i
$818$		−	7.50754e11i		−	1.67681i
$819$		0			0
$820$	−5.81132e11			−1.28534
$821$	6.43734e11	+	3.71660e11i	1.41688	+	0.818037i	0.996024	−	0.0890890i	$-0.0283955\pi$
$821$	6.43734e11	+	3.71660e11i	1.41688	+	0.818037i	0.420859	+	0.907126i	$0.361729\pi$
$822$		0			0
$823$	1.94548e11	+	3.36968e11i	0.424061	+	0.734495i	0.996332	−	0.0855694i	$-0.0272709\pi$
$823$	1.94548e11	+	3.36968e11i	0.424061	+	0.734495i	−0.572271	+	0.820064i	$0.693938\pi$
$824$	−2.67781e11	+	1.54603e11i	−0.580859	+	0.335359i
$825$		0			0
$826$	2.00402e11	−	3.47107e11i	0.430509	−	0.745664i
$827$			4.56038e11i			0.974942i	0.873139	+	0.487471i	$0.162080\pi$
$827$			4.56038e11i			0.974942i	−0.873139	+	0.487471i	$0.837920\pi$
$828$		0			0
$829$	1.17595e11			0.248983			0.124491	−	0.992221i	$-0.460270\pi$
$829$	1.17595e11			0.248983			0.124491	+	0.992221i	$0.460270\pi$
$830$	−5.58290e11	−	3.22329e11i	−1.17638	−	0.679183i
$831$		0			0
$832$	5.95758e11	+	1.03188e12i	1.24330	+	2.15346i
$833$	−3.15708e11	+	1.82274e11i	−0.655701	+	0.378569i
$834$		0			0
$835$	2.94827e11	−	5.10655e11i	0.606487	−	1.05047i
$836$		−	8.25286e10i		−	0.168958i
$837$		0			0
$838$	−8.50157e11			−1.72394
$839$	2.58758e11	+	1.49394e11i	0.522212	+	0.301499i	0.737839	−	0.674977i	$-0.235846\pi$
$839$	2.58758e11	+	1.49394e11i	0.522212	+	0.301499i	−0.215627	+	0.976476i	$0.569180\pi$
$840$		0			0
$841$	−2.18070e11	−	3.77709e11i	−0.435926	−	0.755046i
$842$	−6.12716e11	+	3.53752e11i	−1.21902	+	0.703802i
$843$		0			0
$844$	−3.73858e11	+	6.47540e11i	−0.736778	+	1.27614i
$845$		−	7.11492e11i		−	1.39554i
$846$		0			0
$847$	3.89187e11			0.756179
$848$	6.03738e10	+	3.48569e10i	0.116752	+	0.0674070i
$849$		0			0
$850$	−5.93808e10	−	1.02851e11i	−0.113755	−	0.197029i
$851$	1.80177e11	−	1.04025e11i	0.343543	−	0.198345i
$852$		0			0
$853$	9.91795e10	−	1.71784e11i	0.187338	−	0.324479i	−0.757024	−	0.653387i	$-0.773347\pi$
$853$	9.91795e10	−	1.71784e11i	0.187338	−	0.324479i	0.944362	+	0.328908i	$0.106681\pi$
$854$		−	7.38804e11i		−	1.38898i
$855$		0			0
$856$	1.69908e11			0.316460
$857$	−6.49453e11	−	3.74962e11i	−1.20399	−	0.695127i	−0.242554	−	0.970138i	$-0.577985\pi$
$857$	−6.49453e11	−	3.74962e11i	−1.20399	−	0.695127i	−0.961441	+	0.275011i	$0.911318\pi$
$858$		0			0
$859$	1.95861e11	+	3.39241e11i	0.359728	+	0.623068i	0.987915	−	0.154994i	$-0.0495360\pi$
$859$	1.95861e11	+	3.39241e11i	0.359728	+	0.623068i	−0.628187	+	0.778063i	$0.716203\pi$
$860$	1.25860e11	−	7.26653e10i	0.230088	−	0.132841i
$861$		0			0
$862$	−4.15158e11	+	7.19074e11i	−0.751941	+	1.30240i
$863$			7.72271e11i			1.39228i	0.717906	+	0.696140i	$0.245101\pi$
$863$			7.72271e11i			1.39228i	−0.717906	+	0.696140i	$0.754899\pi$
$864$		0			0
$865$	−2.15369e11			−0.384696
$866$	4.72552e11	+	2.72828e11i	0.840191	+	0.485084i
$867$		0			0
$868$	−4.74471e11	−	8.21809e11i	−0.835855	−	1.44774i
$869$	7.22084e10	−	4.16896e10i	0.126622	−	0.0731052i
$870$		0			0
$871$	1.87891e11	−	3.25438e11i	0.326463	−	0.565451i
$872$			8.09097e11i			1.39938i
$873$		0			0
$874$	−7.66709e10			−0.131397
$875$	5.99538e11	+	3.46143e11i	1.02279	+	0.590505i
$876$		0			0
$877$	1.02235e11	+	1.77075e11i	0.172822	+	0.299337i	0.939405	−	0.342808i	$-0.111378\pi$
$877$	1.02235e11	+	1.77075e11i	0.172822	+	0.299337i	−0.766583	+	0.642145i	$0.778045\pi$
$878$	−4.36357e11	+	2.51931e11i	−0.734283	+	0.423939i
$879$		0			0
$880$	−2.71091e10	+	4.69544e10i	−0.0452048	+	0.0782970i
$881$		−	4.46549e11i		−	0.741251i	−0.928782	−	0.370625i	$-0.879143\pi$
$881$		−	4.46549e11i		−	0.741251i	0.928782	−	0.370625i	$-0.120857\pi$
$882$		0			0
$883$	−3.48668e11			−0.573547			−0.286774	−	0.957998i	$-0.592583\pi$
$883$	−3.48668e11			−0.573547			−0.286774	+	0.957998i	$0.592583\pi$
$884$	1.61741e12	+	9.33812e11i	2.64857	+	1.52915i
$885$		0			0
$886$	−3.57767e11	−	6.19671e11i	−0.580585	−	1.00560i
$887$	4.44551e11	−	2.56662e11i	0.718171	−	0.414636i	−0.0959084	−	0.995390i	$-0.530576\pi$
$887$	4.44551e11	−	2.56662e11i	0.718171	−	0.414636i	0.814079	+	0.580754i	$0.197242\pi$
$888$		0			0
$889$	−1.17790e11	+	2.04019e11i	−0.188583	+	0.326635i
$890$		−	2.38732e11i		−	0.380496i
$891$		0			0
$892$	−1.52788e12			−2.41341
$893$	4.60483e10	+	2.65860e10i	0.0724116	+	0.0418069i
$894$		0			0
$895$	2.06268e11	+	3.57266e11i	0.321469	+	0.556801i
$896$	−1.05634e12	+	6.09881e11i	−1.63898	+	0.946265i
$897$		0			0
$898$	4.33021e11	−	7.50014e11i	0.665892	−	1.15336i
$899$			1.99457e11i			0.305358i
$900$		0			0
$901$	8.44280e11			1.28111
$902$	4.54358e11	+	2.62323e11i	0.686391	+	0.396288i
$903$		0			0
$904$	5.42680e10	+	9.39949e10i	0.0812587	+	0.140744i
$905$	−8.34718e10	+	4.81925e10i	−0.124436	+	0.0718431i
$906$		0			0
$907$	−6.59250e11	+	1.14185e12i	−0.974139	+	1.68726i	−0.291393	+	0.956603i	$0.594119\pi$
$907$	−6.59250e11	+	1.14185e12i	−0.974139	+	1.68726i	−0.682746	+	0.730656i	$0.739214\pi$
$908$		−	1.58783e12i		−	2.33594i
$909$		0			0
$910$	2.21874e12			3.23550
$911$	−5.13588e11	−	2.96520e11i	−0.745661	−	0.430508i	0.0784630	−	0.996917i	$-0.474999\pi$
$911$	−5.13588e11	−	2.96520e11i	−0.745661	−	0.430508i	−0.824124	+	0.566409i	$0.808332\pi$
$912$		0			0
$913$	1.77132e11	+	3.06801e11i	0.254926	+	0.441544i
$914$	−1.07602e12	+	6.21238e11i	−1.54182	+	0.890170i
$915$		0			0
$916$	3.68876e11	−	6.38913e11i	0.523961	−	0.907527i
$917$		−	5.23050e11i		−	0.739718i
$918$		0			0
$919$	1.29362e11			0.181361			0.0906807	−	0.995880i	$-0.471096\pi$
$919$	1.29362e11			0.181361			0.0906807	+	0.995880i	$0.471096\pi$
$920$	−2.77838e11	−	1.60410e11i	−0.387829	−	0.223913i
$921$		0			0
$922$	−5.67036e11	−	9.82134e11i	−0.784669	−	1.35909i
$923$	1.25036e12	−	7.21896e11i	1.72278	−	0.994645i
$924$		0			0
$925$	3.34926e10	−	5.80109e10i	0.0457491	−	0.0792397i
$926$			3.71144e11i			0.504776i
$927$		0			0
$928$	2.93403e11			0.395614
$929$	−6.57533e11	−	3.79627e11i	−0.882785	−	0.509676i	−0.0112093	−	0.999937i	$-0.503568\pi$
$929$	−6.57533e11	−	3.79627e11i	−0.882785	−	0.509676i	−0.871576	+	0.490261i	$0.836901\pi$
$930$		0			0
$931$	3.78869e10	+	6.56221e10i	0.0504302	+	0.0873477i
$932$	2.01814e12	−	1.16517e12i	2.67478	−	1.54428i
$933$		0			0
$934$	7.07771e11	−	1.22589e12i	0.930048	−	1.61089i
$935$			6.56619e11i			0.859146i
$936$		0			0
$937$	8.60250e11			1.11601			0.558003	−	0.829839i	$-0.311568\pi$
$937$	8.60250e11			1.11601			0.558003	+	0.829839i	$0.311568\pi$
$938$	5.78241e11	+	3.33848e11i	0.746960	+	0.431258i
$939$		0			0
$940$	3.11471e11	+	5.39483e11i	0.398938	+	0.690981i
$941$	7.69338e11	−	4.44178e11i	0.981203	−	0.566498i	0.0785697	−	0.996909i	$-0.474965\pi$
$941$	7.69338e11	−	4.44178e11i	0.981203	−	0.566498i	0.902633	+	0.430411i	$0.141631\pi$
$942$		0			0
$943$	1.48344e11	−	2.56938e11i	0.187595	−	0.324924i
$944$			4.60703e10i			0.0580140i
$945$		0			0
$946$	−1.31205e11			−0.163827
$947$	−1.09842e12	−	6.34171e11i	−1.36574	−	0.788509i	−0.375357	−	0.926880i	$-0.622480\pi$
$947$	−1.09842e12	−	6.34171e11i	−1.36574	−	0.788509i	−0.990380	+	0.138371i	$0.955813\pi$
$948$		0			0
$949$	−1.15136e12	−	1.99422e12i	−1.41954	−	2.45872i
$950$	−2.13782e10	+	1.23427e10i	−0.0262468	+	0.0151536i
$951$		0			0
$952$	−5.92608e11	+	1.02643e12i	−0.721472	+	1.24963i
$953$		−	6.14560e11i		−	0.745062i	−0.928020	−	0.372531i	$-0.878490\pi$
$953$		−	6.14560e11i		−	0.745062i	0.928020	−	0.372531i	$-0.121510\pi$
$954$		0			0
$955$	−1.46780e12			−1.76463
$956$	−1.58393e12	−	9.14484e11i	−1.89629	−	1.09482i
$957$		0			0
$958$	−4.98507e11	−	8.63439e11i	−0.591846	−	1.02511i
$959$	−8.51033e11	+	4.91344e11i	−1.00617	+	0.580913i
$960$		0			0
$961$	1.16154e11	−	2.01184e11i	0.136188	−	0.235885i
$962$			1.73056e12i			2.02063i
$963$		0			0
$964$	8.55376e11			0.990487
$965$	9.77937e11	+	5.64612e11i	1.12772	+	0.651090i
$966$		0			0
$967$	4.23691e11	+	7.33855e11i	0.484555	+	0.839275i	0.999843	−	0.0177429i	$-0.00564804\pi$
$967$	4.23691e11	+	7.33855e11i	0.484555	+	0.839275i	−0.515287	+	0.857018i	$0.672315\pi$
$968$	4.05379e11	−	2.34045e11i	0.461699	−	0.266562i
$969$		0			0
$970$	−1.26720e12	+	2.19486e12i	−1.43139	+	2.47924i
$971$			9.02982e11i			1.01579i	0.861420	+	0.507893i	$0.169576\pi$
$971$			9.02982e11i			1.01579i	−0.861420	+	0.507893i	$0.830424\pi$
$972$		0			0
$973$	−1.63290e12			−1.82184
$974$	−4.93645e11	−	2.85006e11i	−0.548503	−	0.316678i
$975$		0			0
$976$	4.24607e10	+	7.35441e10i	0.0467937	+	0.0810491i
$977$	−7.67027e11	+	4.42844e11i	−0.841846	+	0.486040i	−0.857891	−	0.513831i	$-0.828226\pi$
$977$	−7.67027e11	+	4.42844e11i	−0.841846	+	0.486040i	0.0160453	+	0.999871i	$0.494892\pi$
$978$		0			0
$979$	−6.55961e10	+	1.13616e11i	−0.0714081	+	0.123682i
$980$			8.87735e11i			0.962451i
$981$		0			0
$982$	1.57224e12			1.69073
$983$	7.45908e11	+	4.30650e11i	0.798861	+	0.461223i	0.843073	−	0.537800i	$-0.180744\pi$
$983$	7.45908e11	+	4.30650e11i	0.798861	+	0.461223i	−0.0442118	+	0.999022i	$0.514078\pi$
$984$		0			0
$985$	6.36623e11	+	1.10266e12i	0.676297	+	1.17138i
$986$	6.04045e11	−	3.48746e11i	0.639090	−	0.368979i
$987$		0			0
$988$	1.94099e11	−	3.36190e11i	0.203702	−	0.352823i
$989$			7.41960e10i			0.0775524i
$990$		0			0
$991$	−1.05517e12			−1.09403			−0.547013	−	0.837124i	$-0.684235\pi$
$991$	−1.05517e12			−1.09403			−0.547013	+	0.837124i	$0.684235\pi$
$992$	7.90581e11	+	4.56442e11i	0.816393	+	0.471345i
$993$		0			0
$994$	1.28267e12	+	2.22166e12i	1.31392	+	2.27578i
$995$	−1.51028e12	+	8.71963e11i	−1.54087	+	0.889623i
$996$		0			0
$997$	4.03544e11	−	6.98959e11i	0.408423	−	0.707410i	−0.586290	−	0.810101i	$-0.699412\pi$
$997$	4.03544e11	−	6.98959e11i	0.408423	−	0.707410i	0.994713	+	0.102691i	$0.0327454\pi$
$998$		−	1.41914e12i		−	1.43055i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.9.d.a.8.7		14
3.2	odd	2		9.9.d.a.2.1	✓	14
4.3	odd	2		432.9.q.a.305.2		14
9.2	odd	6		81.9.b.a.80.13		14
9.4	even	3		9.9.d.a.5.1	yes	14
9.5	odd	6	inner	27.9.d.a.17.7		14
9.7	even	3		81.9.b.a.80.2		14
12.11	even	2		144.9.q.a.65.7		14
36.23	even	6		432.9.q.a.17.2		14
36.31	odd	6		144.9.q.a.113.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.9.d.a.2.1	✓	14	3.2	odd	2
9.9.d.a.5.1	yes	14	9.4	even	3
27.9.d.a.8.7		14	1.1	even	1	trivial
27.9.d.a.17.7		14	9.5	odd	6	inner
81.9.b.a.80.2		14	9.7	even	3
81.9.b.a.80.13		14	9.2	odd	6
144.9.q.a.65.7		14	12.11	even	2
144.9.q.a.113.7		14	36.31	odd	6
432.9.q.a.17.2		14	36.23	even	6
432.9.q.a.305.2		14	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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	27.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(22.1512 + 12.7890i) q^{2} +(199.117 + 344.881i) q^{4} +(-570.352 + 329.293i) q^{5} +(-1512.41 + 2619.58i) q^{7} +3638.08i q^{8} +O(q^{10})\)	\(q+(22.1512 + 12.7890i) q^{2} +(199.117 + 344.881i) q^{4} +(-570.352 + 329.293i) q^{5} +(-1512.41 + 2619.58i) q^{7} +3638.08i q^{8} -16845.3 q^{10} +(8016.93 + 4628.57i) q^{11} +(21771.9 + 37710.0i) q^{13} +(-67003.6 + 38684.6i) q^{14} +(4446.57 - 7701.69i) q^{16} -107702. i q^{17} -22386.6 q^{19} +(-227134. - 131136. i) q^{20} +(118390. + 205057. i) q^{22} +(115959. - 66949.2i) q^{23} +(21555.4 - 37335.0i) q^{25} +1.11376e6i q^{26} -1.20459e6 q^{28} +(219270. + 126596. i) q^{29} +(393886. + 682230. i) q^{31} +(1.00357e6 - 579409. i) q^{32} +(1.37740e6 - 2.38573e6i) q^{34} -1.99211e6i q^{35} +1.55379e6 q^{37} +(-495890. - 286302. i) q^{38} +(-1.19800e6 - 2.07499e6i) q^{40} +(1.91891e6 - 1.10788e6i) q^{41} +(-277061. + 479883. i) q^{43} +3.68652e6i q^{44} +3.42486e6 q^{46} +(-2.05696e6 - 1.18759e6i) q^{47} +(-1.69239e6 - 2.93131e6i) q^{49} +(954955. - 551344. i) q^{50} +(-8.67033e6 + 1.50175e7i) q^{52} +7.83903e6i q^{53} -6.09663e6 q^{55} +(-9.53025e6 - 5.50229e6i) q^{56} +(3.23806e6 + 5.60849e6i) q^{58} +(-4.48638e6 + 2.59021e6i) q^{59} +(-4.77454e6 + 8.26974e6i) q^{61} +2.01496e7i q^{62} +2.73636e7 q^{64} +(-2.48353e7 - 1.43387e7i) q^{65} +(-4.31500e6 - 7.47380e6i) q^{67} +(3.71444e7 - 2.14453e7i) q^{68} +(2.54771e7 - 4.41277e7i) q^{70} -3.31572e7i q^{71} -5.28831e7 q^{73} +(3.44184e7 + 1.98715e7i) q^{74} +(-4.45756e6 - 7.72072e6i) q^{76} +(-2.42498e7 + 1.40006e7i) q^{77} +(4.50350e6 - 7.80029e6i) q^{79} +5.85691e6i q^{80} +5.66748e7 q^{82} +(3.31421e7 + 1.91346e7i) q^{83} +(3.54655e7 + 6.14281e7i) q^{85} +(-1.22745e7 + 7.08666e6i) q^{86} +(-1.68391e7 + 2.91662e7i) q^{88} +1.41720e7i q^{89} -1.31713e8 q^{91} +(4.61791e7 + 2.66615e7i) q^{92} +(-3.03761e7 - 5.26130e7i) q^{94} +(1.27682e7 - 7.37175e6i) q^{95} +(7.52257e7 - 1.30295e8i) q^{97} -8.65761e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{2} + 767 q^{4} - 438 q^{5} + 922 q^{7}+O(q^{10}) \) 14 * q + 3 * q^2 + 767 * q^4 - 438 * q^5 + 922 * q^7	\( 14 q + 3 q^{2} + 767 q^{4} - 438 q^{5} + 922 q^{7} - 516 q^{10} + 28677 q^{11} + 1684 q^{13} - 120966 q^{14} - 65281 q^{16} - 269630 q^{19} - 539454 q^{20} + 61311 q^{22} + 1000452 q^{23} + 65177 q^{25} + 1075708 q^{28} - 3797682 q^{29} - 164132 q^{31} + 8461881 q^{32} + 654993 q^{34} - 1671668 q^{37} - 10967691 q^{38} + 613326 q^{40} + 10239447 q^{41} + 791815 q^{43} + 1189536 q^{46} - 31148628 q^{47} - 4826637 q^{49} + 63849453 q^{50} - 5552720 q^{52} + 8107476 q^{55} - 116638674 q^{56} + 14211822 q^{58} + 83493795 q^{59} - 5255600 q^{61} - 26813830 q^{64} - 69232992 q^{65} - 8288855 q^{67} + 77746743 q^{68} + 27813756 q^{70} - 36721682 q^{73} + 10383450 q^{74} - 42822959 q^{76} - 56158710 q^{77} - 32771822 q^{79} + 236099418 q^{82} + 198915996 q^{83} + 97486146 q^{85} - 146190669 q^{86} + 24955827 q^{88} - 201514504 q^{91} + 295365804 q^{92} - 36698244 q^{94} - 386813838 q^{95} + 127049161 q^{97}+O(q^{100}) \) 14 * q + 3 * q^2 + 767 * q^4 - 438 * q^5 + 922 * q^7 - 516 * q^10 + 28677 * q^11 + 1684 * q^13 - 120966 * q^14 - 65281 * q^16 - 269630 * q^19 - 539454 * q^20 + 61311 * q^22 + 1000452 * q^23 + 65177 * q^25 + 1075708 * q^28 - 3797682 * q^29 - 164132 * q^31 + 8461881 * q^32 + 654993 * q^34 - 1671668 * q^37 - 10967691 * q^38 + 613326 * q^40 + 10239447 * q^41 + 791815 * q^43 + 1189536 * q^46 - 31148628 * q^47 - 4826637 * q^49 + 63849453 * q^50 - 5552720 * q^52 + 8107476 * q^55 - 116638674 * q^56 + 14211822 * q^58 + 83493795 * q^59 - 5255600 * q^61 - 26813830 * q^64 - 69232992 * q^65 - 8288855 * q^67 + 77746743 * q^68 + 27813756 * q^70 - 36721682 * q^73 + 10383450 * q^74 - 42822959 * q^76 - 56158710 * q^77 - 32771822 * q^79 + 236099418 * q^82 + 198915996 * q^83 + 97486146 * q^85 - 146190669 * q^86 + 24955827 * q^88 - 201514504 * q^91 + 295365804 * q^92 - 36698244 * q^94 - 386813838 * q^95 + 127049161 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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