LMFDB - Embedded newform 27.9.d.a.17.4

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			17.4
Root			$-0.447645 + 0.775344i$ of defining polynomial
Character	$\chi$	$=$	27.17
Dual form			27.9.d.a.8.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34294 + 0.775344i) q^{2} +(-126.798 + 219.620i) q^{4} +(604.549 + 349.037i) q^{5} +(-1124.45 - 1947.61i) q^{7} -790.223i q^{8} +O(q^{10})$	\(q+(-1.34294 + 0.775344i) q^{2} +(-126.798 + 219.620i) q^{4} +(604.549 + 349.037i) q^{5} +(-1124.45 - 1947.61i) q^{7} -790.223i q^{8} -1082.49 q^{10} +(-18817.0 + 10864.0i) q^{11} +(-9209.84 + 15951.9i) q^{13} +(3020.14 + 1743.68i) q^{14} +(-31847.5 - 55161.5i) q^{16} +56538.1i q^{17} -212375. q^{19} +(-153311. + 88514.1i) q^{20} +(16846.7 - 29179.3i) q^{22} +(-14399.3 - 8313.41i) q^{23} +(48340.5 + 83728.3i) q^{25} -28563.2i q^{26} +570313. q^{28} +(294955. - 170292. i) q^{29} +(-82902.7 + 143592. i) q^{31} +(260733. + 150534. i) q^{32} +(-43836.4 - 75926.9i) q^{34} -1.56990e6i q^{35} +1.11833e6 q^{37} +(285206. - 164664. i) q^{38} +(275817. - 477729. i) q^{40} +(3.60414e6 + 2.08085e6i) q^{41} +(1.28793e6 + 2.23075e6i) q^{43} -5.51012e6i q^{44} +25783.0 q^{46} +(-8.10049e6 + 4.67682e6i) q^{47} +(353608. - 612466. i) q^{49} +(-129836. - 74961.1i) q^{50} +(-2.33557e6 - 4.04533e6i) q^{52} +4.75879e6i q^{53} -1.51677e7 q^{55} +(-1.53905e6 + 888570. i) q^{56} +(-264070. + 457383. i) q^{58} +(8.39702e6 + 4.84802e6i) q^{59} +(-3.04570e6 - 5.27531e6i) q^{61} -257113. i q^{62} +1.58391e7 q^{64} +(-1.11356e7 + 6.42914e6i) q^{65} +(-1.02601e7 + 1.77710e7i) q^{67} +(-1.24169e7 - 7.16890e6i) q^{68} +(1.21721e6 + 2.10828e6i) q^{70} -2.08627e7i q^{71} +9.02632e6 q^{73} +(-1.50184e6 + 867089. i) q^{74} +(2.69287e7 - 4.66418e7i) q^{76} +(4.23177e7 + 2.44321e7i) q^{77} +(1.67238e7 + 2.89665e7i) q^{79} -4.44638e7i q^{80} -6.45351e6 q^{82} +(5.09741e7 - 2.94299e7i) q^{83} +(-1.97339e7 + 3.41800e7i) q^{85} +(-3.45920e6 - 1.99717e6i) q^{86} +(8.58499e6 + 1.48696e7i) q^{88} +8.65172e7i q^{89} +4.14242e7 q^{91} +(3.65158e6 - 2.10824e6i) q^{92} +(7.25229e6 - 1.25613e7i) q^{94} +(-1.28391e8 - 7.41267e7i) q^{95} +(-4.68859e7 - 8.12087e7i) q^{97} +1.09667e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.34294	+	0.775344i	−0.0839334	+	0.0484590i	−0.541379	−	0.840778i	$-0.682098\pi$
$2$	−1.34294	+	0.775344i	−0.0839334	+	0.0484590i	0.457446	+	0.889237i	$0.348764\pi$
$3$		0			0
$3$		0			0
$4$	−126.798	+	219.620i	−0.495303	+	0.857891i
$5$	604.549	+	349.037i	0.967279	+	0.558459i	0.898405	−	0.439167i	$-0.144726\pi$
$5$	604.549	+	349.037i	0.967279	+	0.558459i	0.0688730	+	0.997625i	$0.478060\pi$
$6$		0			0
$7$	−1124.45	−	1947.61i	−0.468327	−	0.811167i	0.531017	−	0.847361i	$-0.321810\pi$
$7$	−1124.45	−	1947.61i	−0.468327	−	0.811167i	−0.999345	+	0.0361942i	$0.988477\pi$
$8$		−	790.223i		−	0.192926i
$9$		0			0
$10$	−1082.49			−0.108249
$11$	−18817.0	+	10864.0i	−1.28523	+	0.742026i	−0.977799	−	0.209545i	$-0.932802\pi$
$11$	−18817.0	+	10864.0i	−1.28523	+	0.742026i	−0.307428	+	0.951571i	$0.599468\pi$
$12$		0			0
$13$	−9209.84	+	15951.9i	−0.322462	+	0.558521i	−0.980995	−	0.194031i	$-0.937844\pi$
$13$	−9209.84	+	15951.9i	−0.322462	+	0.558521i	0.658533	+	0.752552i	$0.271177\pi$
$14$	3020.14	+	1743.68i	0.0786166	+	0.0453893i
$15$		0			0
$16$	−31847.5	−	55161.5i	−0.485954	−	0.841698i
$17$			56538.1i			0.676932i	0.940979	+	0.338466i	$0.109908\pi$
$17$			56538.1i			0.676932i	−0.940979	+	0.338466i	$0.890092\pi$
$18$		0			0
$19$	−212375.			−1.62963			−0.814815	−	0.579721i	$-0.803162\pi$
$19$	−212375.			−1.62963			−0.814815	+	0.579721i	$0.803162\pi$
$20$	−153311.	+	88514.1i	−0.958193	+	0.553213i
$21$		0			0
$22$	16846.7	−	29179.3i	0.0719157	−	0.124562i
$23$	−14399.3	−	8313.41i	−0.0514551	−	0.0297076i	0.474052	−	0.880497i	$-0.342791\pi$
$23$	−14399.3	−	8313.41i	−0.0514551	−	0.0297076i	−0.525507	+	0.850789i	$0.676124\pi$
$24$		0			0
$25$	48340.5	+	83728.3i	0.123752	+	0.214344i
$26$		−	28563.2i		−	0.0625048i
$27$		0			0
$28$	570313.			0.927857
$29$	294955.	−	170292.i	0.417027	−	0.240771i	−0.276778	−	0.960934i	$-0.589267\pi$
$29$	294955.	−	170292.i	0.417027	−	0.240771i	0.693804	+	0.720163i	$0.255933\pi$
$30$		0			0
$31$	−82902.7	+	143592.i	−0.0897681	+	0.155483i	−0.907413	−	0.420240i	$-0.861946\pi$
$31$	−82902.7	+	143592.i	−0.0897681	+	0.155483i	0.817645	+	0.575723i	$0.195279\pi$
$32$	260733.	+	150534.i	0.248654	+	0.143561i
$33$		0			0
$34$	−43836.4	−	75926.9i	−0.0328035	−	0.0568173i
$35$		−	1.56990e6i		−	1.04617i
$36$		0			0
$37$	1.11833e6			0.596709			0.298355	−	0.954455i	$-0.403562\pi$
$37$	1.11833e6			0.596709			0.298355	+	0.954455i	$0.403562\pi$
$38$	285206.	−	164664.i	0.136780	−	0.0789702i
$39$		0			0
$40$	275817.	−	477729.i	0.107741	−	0.186613i
$41$	3.60414e6	+	2.08085e6i	1.27546	+	0.736387i	0.976010	−	0.217725i	$-0.0698637\pi$
$41$	3.60414e6	+	2.08085e6i	1.27546	+	0.736387i	0.299449	+	0.954112i	$0.403197\pi$
$42$		0			0
$43$	1.28793e6	+	2.23075e6i	0.376719	+	0.652496i	0.990583	−	0.136916i	$-0.0437190\pi$
$43$	1.28793e6	+	2.23075e6i	0.376719	+	0.652496i	−0.613864	+	0.789412i	$0.710386\pi$
$44$		−	5.51012e6i		−	1.47011i
$45$		0			0
$46$	25783.0			0.00575841
$47$	−8.10049e6	+	4.67682e6i	−1.66005	+	0.958428i	−0.687356	+	0.726321i	$0.741229\pi$
$47$	−8.10049e6	+	4.67682e6i	−1.66005	+	0.958428i	−0.972690	+	0.232107i	$0.925438\pi$
$48$		0			0
$49$	353608.	−	612466.i	0.0613391	−	0.106242i
$50$	−129836.	−	74961.1i	−0.0207738	−	0.0119938i
$51$		0			0
$52$	−2.33557e6	−	4.04533e6i	−0.319433	−	0.553275i
$53$			4.75879e6i			0.603106i	0.953449	+	0.301553i	$0.0975050\pi$
$53$			4.75879e6i			0.603106i	−0.953449	+	0.301553i	$0.902495\pi$
$54$		0			0
$55$	−1.51677e7			−1.65756
$56$	−1.53905e6	+	888570.i	−0.156495	+	0.0903523i
$57$		0			0
$58$	−264070.	+	457383.i	−0.0233350	+	0.0404174i
$59$	8.39702e6	+	4.84802e6i	0.692974	+	0.400089i	0.804725	−	0.593647i	$-0.202313\pi$
$59$	8.39702e6	+	4.84802e6i	0.692974	+	0.400089i	−0.111751	+	0.993736i	$0.535646\pi$
$60$		0			0
$61$	−3.04570e6	−	5.27531e6i	−0.219972	−	0.381003i	0.734827	−	0.678255i	$-0.237263\pi$
$61$	−3.04570e6	−	5.27531e6i	−0.219972	−	0.381003i	−0.954799	+	0.297252i	$0.903930\pi$
$62$		−	257113.i		−	0.0174003i
$63$		0			0
$64$	1.58391e7			0.944082
$65$	−1.11356e7	+	6.42914e6i	−0.623821	+	0.360164i
$66$		0			0
$67$	−1.02601e7	+	1.77710e7i	−0.509158	+	0.881888i	0.490786	+	0.871280i	$0.336710\pi$
$67$	−1.02601e7	+	1.77710e7i	−0.509158	+	0.881888i	−0.999944	+	0.0106075i	$0.996623\pi$
$68$	−1.24169e7	−	7.16890e6i	−0.580734	−	0.335287i
$69$		0			0
$70$	1.21721e6	+	2.10828e6i	0.0506961	+	0.0878083i
$71$		−	2.08627e7i		−	0.820987i	−0.911863	−	0.410494i	$-0.865356\pi$
$71$		−	2.08627e7i		−	0.820987i	0.911863	−	0.410494i	$-0.134644\pi$
$72$		0			0
$73$	9.02632e6			0.317848			0.158924	−	0.987291i	$-0.449198\pi$
$73$	9.02632e6			0.317848			0.158924	+	0.987291i	$0.449198\pi$
$74$	−1.50184e6	+	867089.i	−0.0500838	+	0.0289159i
$75$		0			0
$76$	2.69287e7	−	4.66418e7i	0.807161	−	1.39804i
$77$	4.23177e7	+	2.44321e7i	1.20381	+	0.695022i
$78$		0			0
$79$	1.67238e7	+	2.89665e7i	0.429366	+	0.743683i	0.996817	−	0.0797237i	$-0.0254038\pi$
$79$	1.67238e7	+	2.89665e7i	0.429366	+	0.743683i	−0.567451	+	0.823407i	$0.692070\pi$
$80$		−	4.44638e7i		−	1.08554i
$81$		0			0
$82$	−6.45351e6			−0.142738
$83$	5.09741e7	−	2.94299e7i	1.07408	−	0.620121i	0.144788	−	0.989463i	$-0.453750\pi$
$83$	5.09741e7	−	2.94299e7i	1.07408	−	0.620121i	0.929294	+	0.369342i	$0.120417\pi$
$84$		0			0
$85$	−1.97339e7	+	3.41800e7i	−0.378039	+	0.654782i
$86$	−3.45920e6	−	1.99717e6i	−0.0632386	−	0.0365108i
$87$		0			0
$88$	8.58499e6	+	1.48696e7i	0.143156	+	0.247953i
$89$			8.65172e7i			1.37893i	0.724319	+	0.689465i	$0.242154\pi$
$89$			8.65172e7i			1.37893i	−0.724319	+	0.689465i	$0.757846\pi$
$90$		0			0
$91$	4.14242e7			0.604071
$92$	3.65158e6	−	2.10824e6i	0.0509718	−	0.0294286i
$93$		0			0
$94$	7.25229e6	−	1.25613e7i	0.0928889	−	0.160888i
$95$	−1.28391e8	−	7.41267e7i	−1.57631	−	0.910081i
$96$		0			0
$97$	−4.68859e7	−	8.12087e7i	−0.529609	−	0.917309i	−0.999404	−	0.0345336i	$-0.989005\pi$
$97$	−4.68859e7	−	8.12087e7i	−0.529609	−	0.917309i	0.469795	−	0.882776i	$-0.344328\pi$
$98$			1.09667e6i			0.0118897i
$99$		0			0
$100$	−2.45179e7			−0.245179
$101$	−8.70183e6	+	5.02401e6i	−0.0836229	+	0.0482797i	−0.541228	−	0.840876i	$-0.682041\pi$
$101$	−8.70183e6	+	5.02401e6i	−0.0836229	+	0.0482797i	0.457605	+	0.889155i	$0.348707\pi$
$102$		0			0
$103$	−8.92310e6	+	1.54553e7i	−0.0792806	+	0.137318i	−0.902940	−	0.429767i	$-0.858596\pi$
$103$	−8.92310e6	+	1.54553e7i	−0.0792806	+	0.137318i	0.823659	+	0.567085i	$0.191929\pi$
$104$	1.26056e7	+	7.27783e6i	0.107753	+	0.0622112i
$105$		0			0
$106$	−3.68970e6	−	6.39075e6i	−0.0292259	−	0.0506207i
$107$			2.12170e8i			1.61864i	0.587370	+	0.809319i	$0.300163\pi$
$107$			2.12170e8i			1.61864i	−0.587370	+	0.809319i	$0.699837\pi$
$108$		0			0
$109$	−1.64501e8			−1.16537			−0.582683	−	0.812699i	$-0.697997\pi$
$109$	−1.64501e8			−1.16537			−0.582683	+	0.812699i	$0.697997\pi$
$110$	2.03693e7	−	1.17602e7i	0.139125	−	0.0803239i
$111$		0			0
$112$	−7.16221e7	+	1.24053e8i	−0.455171	+	0.788380i
$113$	−8.35524e7	−	4.82390e7i	−0.512442	−	0.295859i	0.221395	−	0.975184i	$-0.428939\pi$
$113$	−8.35524e7	−	4.82390e7i	−0.512442	−	0.295859i	−0.733837	+	0.679326i	$0.762272\pi$
$114$		0			0
$115$	−5.80337e6	−	1.00517e7i	−0.0331810	−	0.0574711i
$116$			8.63708e7i			0.477018i
$117$		0			0
$118$	−1.50355e7			−0.0775516
$119$	1.10114e8	−	6.35744e7i	0.549105	−	0.317026i
$120$		0			0
$121$	1.28874e8	−	2.23216e8i	0.601206	−	1.04132i
$122$	8.18035e6	+	4.72293e6i	0.0369260	+	0.0213193i
$123$		0			0
$124$	−2.10238e7	−	3.64142e7i	−0.0889249	−	0.154022i
$125$		−	2.05194e8i		−	0.840476i
$126$		0			0
$127$	2.30345e8			0.885448			0.442724	−	0.896658i	$-0.354012\pi$
$127$	2.30345e8			0.885448			0.442724	+	0.896658i	$0.354012\pi$
$128$	−8.80184e7	+	5.08175e7i	−0.327894	+	0.189310i
$129$		0			0
$130$	9.96960e6	−	1.72678e7i	0.0349063	−	0.0604595i
$131$	−9.84848e7	−	5.68602e7i	−0.334414	−	0.193074i	0.323385	−	0.946267i	$-0.395179\pi$
$131$	−9.84848e7	−	5.68602e7i	−0.334414	−	0.193074i	−0.657799	+	0.753194i	$0.728512\pi$
$132$		0			0
$133$	2.38806e8	+	4.13624e8i	0.763200	+	1.32190i
$134$		−	3.18205e7i		−	0.0986932i
$135$		0			0
$136$	4.46777e7			0.130598
$137$	2.61214e8	−	1.50812e8i	0.741505	−	0.428108i	−0.0811112	−	0.996705i	$-0.525847\pi$
$137$	2.61214e8	−	1.50812e8i	0.741505	−	0.428108i	0.822616	+	0.568597i	$0.192514\pi$
$138$		0			0
$139$	−2.17400e6	+	3.76548e6i	−0.00582372	+	0.0100870i	−0.868923	−	0.494948i	$-0.835187\pi$
$139$	−2.17400e6	+	3.76548e6i	−0.00582372	+	0.0100870i	0.863099	+	0.505035i	$0.168520\pi$
$140$	3.44782e8	+	1.99060e8i	0.897496	+	0.518169i
$141$		0			0
$142$	1.61757e7	+	2.80172e7i	0.0397842	+	0.0689083i
$143$		−	4.00223e8i		−	0.957102i
$144$		0			0
$145$	2.37753e8			0.537841
$146$	−1.21218e7	+	6.99850e6i	−0.0266781	+	0.0154026i
$147$		0			0
$148$	−1.41802e8	+	2.45607e8i	−0.295552	+	0.511911i
$149$	1.07668e8	+	6.21619e7i	0.218444	+	0.126119i	0.605230	−	0.796051i	$-0.293081\pi$
$149$	1.07668e8	+	6.21619e7i	0.218444	+	0.126119i	−0.386786	+	0.922170i	$0.626415\pi$
$150$		0			0
$151$	−4.29306e8	−	7.43579e8i	−0.825769	−	1.43027i	−0.901330	−	0.433133i	$-0.857408\pi$
$151$	−4.29306e8	−	7.43579e8i	−0.825769	−	1.43027i	0.0755603	−	0.997141i	$-0.475925\pi$
$152$			1.67824e8i			0.314397i
$153$		0			0
$154$	−7.57733e7			−0.134720
$155$	−1.00238e8	+	5.78722e7i	−0.173662	+	0.100264i
$156$		0			0
$157$	5.15099e7	−	8.92177e7i	0.0847797	−	0.146843i	−0.820518	−	0.571621i	$-0.806315\pi$
$157$	5.15099e7	−	8.92177e7i	0.0847797	−	0.146843i	0.905297	+	0.424779i	$0.139648\pi$
$158$	−4.49180e7	−	2.59334e7i	−0.0720763	−	0.0416133i
$159$		0			0
$160$	1.05084e8	+	1.82011e8i	0.160345	+	0.277726i
$161$			3.73922e7i			0.0556516i
$162$		0			0
$163$	−2.40441e8			−0.340610			−0.170305	−	0.985391i	$-0.554475\pi$
$163$	−2.40441e8			−0.340610			−0.170305	+	0.985391i	$0.554475\pi$
$164$	−9.13994e8	+	5.27695e8i	−1.26348	+	0.729470i
$165$		0			0
$166$	−4.56366e7	+	7.90449e7i	−0.0601009	+	0.104098i
$167$	−5.13723e8	−	2.96598e8i	−0.660485	−	0.381331i	0.131977	−	0.991253i	$-0.457868\pi$
$167$	−5.13723e8	−	2.96598e8i	−0.660485	−	0.381331i	−0.792462	+	0.609921i	$0.791201\pi$
$168$		0			0
$169$	2.38223e8	+	4.12614e8i	0.292036	+	0.505822i
$170$		−	6.12021e7i		−	0.0732775i
$171$		0			0
$172$	−6.53224e8			−0.746360
$173$	−4.78569e8	+	2.76302e8i	−0.534269	+	0.308460i	−0.742753	−	0.669565i	$-0.766480\pi$
$173$	−4.78569e8	+	2.76302e8i	−0.534269	+	0.308460i	0.208484	+	0.978026i	$0.433147\pi$
$174$		0			0
$175$	1.08713e8	−	1.88297e8i	0.115913	−	0.200767i
$176$	1.19855e9	+	6.91983e8i	1.24912	+	0.721182i
$177$		0			0
$178$	−6.70806e7	−	1.16187e8i	−0.0668216	−	0.115738i
$179$			4.28843e8i			0.417721i	0.977945	+	0.208860i	$0.0669754\pi$
$179$			4.28843e8i			0.417721i	−0.977945	+	0.208860i	$0.933025\pi$
$180$		0			0
$181$	−5.89026e8			−0.548808			−0.274404	−	0.961615i	$-0.588481\pi$
$181$	−5.89026e8			−0.548808			−0.274404	+	0.961615i	$0.588481\pi$
$182$	−5.56300e7	+	3.21180e7i	−0.0507018	+	0.0292727i
$183$		0			0
$184$	−6.56945e6	+	1.13786e7i	−0.00573136	+	0.00992701i
$185$	6.76085e8	+	3.90338e8i	0.577184	+	0.333237i
$186$		0			0
$187$	−6.14230e8	−	1.06388e9i	−0.502302	−	0.870012i
$188$		−	2.37204e9i		−	1.89885i
$189$		0			0
$190$	2.29895e8			0.176406
$191$	−8.27443e8	+	4.77725e8i	−0.621734	+	0.358958i	−0.777544	−	0.628829i	$-0.783535\pi$
$191$	−8.27443e8	+	4.77725e8i	−0.621734	+	0.358958i	0.155810	+	0.987787i	$0.450201\pi$
$192$		0			0
$193$	−9.75155e7	+	1.68902e8i	−0.0702820	+	0.121732i	−0.899025	−	0.437898i	$-0.855723\pi$
$193$	−9.75155e7	+	1.68902e8i	−0.0702820	+	0.121732i	0.828743	+	0.559630i	$0.189057\pi$
$194$	1.25929e8	+	7.27054e7i	0.0889038	+	0.0513286i
$195$		0			0
$196$	8.96732e7	+	1.55319e8i	0.0607629	+	0.105244i
$197$			3.42083e8i			0.227126i	0.993531	+	0.113563i	$0.0362264\pi$
$197$			3.42083e8i			0.227126i	−0.993531	+	0.113563i	$0.963774\pi$
$198$		0			0
$199$	1.74610e9			1.11341			0.556707	−	0.830709i	$-0.312064\pi$
$199$	1.74610e9			1.11341			0.556707	+	0.830709i	$0.312064\pi$
$200$	6.61640e7	−	3.81998e7i	0.0413525	−	0.0238749i
$201$		0			0
$202$	7.79067e6	−	1.34938e7i	0.00467917	−	0.00810456i
$203$	−6.63327e8	−	3.82972e8i	−0.390610	−	0.225519i
$204$		0			0
$205$	1.45259e9	+	2.51596e9i	0.822483	+	1.42458i
$206$		−	2.76739e7i		−	0.0153674i
$207$		0			0
$208$	1.17324e9			0.626808
$209$	3.99626e9	−	2.30724e9i	2.09444	−	1.20923i
$210$		0			0
$211$	−3.91226e8	+	6.77624e8i	−0.197378	+	0.341868i	−0.947677	−	0.319230i	$-0.896576\pi$
$211$	−3.91226e8	+	6.77624e8i	−0.197378	+	0.341868i	0.750300	+	0.661098i	$0.229909\pi$
$212$	−1.04513e9	−	6.03404e8i	−0.517399	−	0.298720i
$213$		0			0
$214$	−1.64505e8	−	2.84931e8i	−0.0784375	−	0.135858i
$215$			1.79813e9i			0.841527i
$216$		0			0
$217$	3.72881e8			0.168163
$218$	2.20914e8	−	1.27545e8i	0.0978133	−	0.0564725i
$219$		0			0
$220$	1.92323e9	−	3.33114e9i	0.820997	−	1.42201i
$221$	−9.01890e8	−	5.20707e8i	−0.378081	−	0.218285i
$222$		0			0
$223$	−7.87235e8	−	1.36353e9i	−0.318335	−	0.551373i	0.661806	−	0.749675i	$-0.269790\pi$
$223$	−7.87235e8	−	1.36353e9i	−0.318335	−	0.551373i	−0.980141	+	0.198303i	$0.936457\pi$
$224$		−	6.77075e8i		−	0.268933i
$225$		0			0
$226$	1.49607e8			0.0573481
$227$	7.54169e8	−	4.35419e8i	0.284031	−	0.163985i	−0.351216	−	0.936294i	$-0.614232\pi$
$227$	7.54169e8	−	4.35419e8i	0.284031	−	0.163985i	0.635247	+	0.772309i	$0.280898\pi$
$228$		0			0
$229$	−1.86296e9	+	3.22674e9i	−0.677425	+	1.17334i	0.298328	+	0.954463i	$0.403571\pi$
$229$	−1.86296e9	+	3.22674e9i	−0.677425	+	1.17334i	−0.975754	+	0.218872i	$0.929762\pi$
$230$	1.55871e7	+	8.99921e6i	0.00556998	+	0.00321583i
$231$		0			0
$232$	−1.34569e8	−	2.33080e8i	−0.0464508	−	0.0804552i
$233$			3.81360e9i			1.29393i	0.762519	+	0.646966i	$0.223963\pi$
$233$			3.81360e9i			1.29393i	−0.762519	+	0.646966i	$0.776037\pi$
$234$		0			0
$235$	−6.52953e9			−2.14097
$236$	−2.12944e9	+	1.22944e9i	−0.686465	+	0.396331i
$237$		0			0
$238$	−9.85841e7	+	1.70753e8i	−0.0307255	+	0.0532181i
$239$	−1.45580e9	−	8.40504e8i	−0.446179	−	0.257601i	0.260036	−	0.965599i	$-0.416265\pi$
$239$	−1.45580e9	−	8.40504e8i	−0.446179	−	0.257601i	−0.706215	+	0.707997i	$0.749599\pi$
$240$		0			0
$241$	2.41777e8	+	4.18769e8i	0.0716714	+	0.124139i	0.899634	−	0.436645i	$-0.143833\pi$
$241$	2.41777e8	+	4.18769e8i	0.0716714	+	0.124139i	−0.827963	+	0.560783i	$0.810500\pi$
$242$			3.99686e8i			0.116535i
$243$		0			0
$244$	1.54475e9			0.435812
$245$	4.27546e8	−	2.46844e8i	0.118664	−	0.0685107i
$246$		0			0
$247$	1.95594e9	−	3.38779e9i	0.525494	−	0.910183i
$248$	1.13470e8	+	6.55117e7i	0.0299966	+	0.0173186i
$249$		0			0
$250$	1.59096e8	+	2.75563e8i	0.0407286	+	0.0705440i
$251$			2.22445e9i			0.560438i	0.959936	+	0.280219i	$0.0904070\pi$
$251$			2.22445e9i			0.560438i	−0.959936	+	0.280219i	$0.909593\pi$
$252$		0			0
$253$	3.61268e8			0.0881753
$254$	−3.09338e8	+	1.78596e8i	−0.0743187	+	0.0429079i
$255$		0			0
$256$	−1.94860e9	+	3.37507e9i	−0.453693	+	0.785820i
$257$	−1.51490e9	−	8.74631e8i	−0.347258	−	0.200490i	0.316219	−	0.948686i	$-0.397587\pi$
$257$	−1.51490e9	−	8.74631e8i	−0.347258	−	0.200490i	−0.663477	+	0.748197i	$0.730920\pi$
$258$		0			0
$259$	−1.25751e9	−	2.17807e9i	−0.279455	−	0.484031i
$260$		−	3.26080e9i		−	0.713561i
$261$		0			0
$262$	1.76345e8			0.0374246
$263$	−3.84885e9	+	2.22214e9i	−0.804467	+	0.464459i	−0.845031	−	0.534718i	$-0.820418\pi$
$263$	−3.84885e9	+	2.22214e9i	−0.804467	+	0.464459i	0.0405638	+	0.999177i	$0.487085\pi$
$264$		0			0
$265$	−1.66099e9	+	2.87692e9i	−0.336810	+	0.583371i
$266$	−6.41402e8	−	3.70313e8i	−0.128116	−	0.0739678i
$267$		0			0
$268$	−2.60192e9	−	4.50665e9i	−0.504376	−	0.873604i
$269$			5.21729e9i			0.996405i	0.867061	+	0.498203i	$0.166006\pi$
$269$			5.21729e9i			0.996405i	−0.867061	+	0.498203i	$0.833994\pi$
$270$		0			0
$271$	3.10877e9			0.576383			0.288191	−	0.957573i	$-0.406946\pi$
$271$	3.10877e9			0.576383			0.288191	+	0.957573i	$0.406946\pi$
$272$	3.11872e9	−	1.80060e9i	0.569772	−	0.328958i
$273$		0			0
$274$	−2.33862e8	+	4.05061e8i	−0.0414914	+	0.0718652i
$275$	−1.81925e9	−	1.05034e9i	−0.318098	−	0.183654i
$276$		0			0
$277$	2.64734e9	+	4.58533e9i	0.449667	+	0.778846i	0.998364	−	0.0571750i	$-0.0182093\pi$
$277$	2.64734e9	+	4.58533e9i	0.449667	+	0.778846i	−0.548697	+	0.836021i	$0.684876\pi$
$278$		−	6.74240e6i		−	0.00112885i
$279$		0			0
$280$	−1.24057e9			−0.201832
$281$	8.33058e9	−	4.80966e9i	1.33613	−	0.771417i	0.349902	−	0.936786i	$-0.386215\pi$
$281$	8.33058e9	−	4.80966e9i	1.33613	−	0.771417i	0.986232	+	0.165369i	$0.0528815\pi$
$282$		0			0
$283$	3.79931e9	−	6.58060e9i	0.592323	−	1.02593i	−0.401595	−	0.915817i	$-0.631544\pi$
$283$	3.79931e9	−	6.58060e9i	0.592323	−	1.02593i	0.993919	−	0.110117i	$-0.0351225\pi$
$284$	4.58186e9	+	2.64534e9i	0.704317	+	0.406638i
$285$		0			0
$286$	3.10311e8	+	5.37474e8i	0.0463802	+	0.0803328i
$287$		−	9.35929e9i		−	1.37948i
$288$		0			0
$289$	3.77920e9			0.541763
$290$	−3.19287e8	+	1.84340e8i	−0.0451429	+	0.0260633i
$291$		0			0
$292$	−1.14452e9	+	1.98236e9i	−0.157431	+	0.272679i
$293$	5.56560e9	+	3.21330e9i	0.755164	+	0.435994i	0.827557	−	0.561382i	$-0.189730\pi$
$293$	5.56560e9	+	3.21330e9i	0.755164	+	0.435994i	−0.0723925	+	0.997376i	$0.523063\pi$
$294$		0			0
$295$	3.38427e9	+	5.86173e9i	0.446866	+	0.773995i
$296$		−	8.83730e8i		−	0.115120i
$297$		0			0
$298$	−1.92787e8			−0.0244463
$299$	2.65230e8	−	1.53130e8i	0.0331847	−	0.0191592i
$300$		0			0
$301$	2.89643e9	−	5.01676e9i	0.352855	−	0.611163i
$302$	1.15306e9	+	6.65719e8i	0.138619	+	0.0800319i
$303$		0			0
$304$	6.76362e9	+	1.17149e10i	0.791926	+	1.37166i
$305$		−	4.25224e9i		−	0.491381i
$306$		0			0
$307$	5.43787e9			0.612174			0.306087	−	0.952003i	$-0.400980\pi$
$307$	5.43787e9			0.612174			0.306087	+	0.952003i	$0.400980\pi$
$308$	−1.07316e10	+	6.19588e9i	−1.19251	+	0.688494i
$309$		0			0
$310$	8.97417e7	−	1.55437e8i	0.00971734	−	0.0168309i
$311$	−1.27840e10	−	7.38087e9i	−1.36655	−	0.788980i	−0.376067	−	0.926593i	$-0.622724\pi$
$311$	−1.27840e10	−	7.38087e9i	−1.36655	−	0.788980i	−0.990486	+	0.137613i	$0.956057\pi$
$312$		0			0
$313$	−8.94368e9	−	1.54909e10i	−0.931834	−	1.61398i	−0.780184	−	0.625550i	$-0.784874\pi$
$313$	−8.94368e9	−	1.54909e10i	−0.931834	−	1.61398i	−0.151651	−	0.988434i	$-0.548459\pi$
$314$			1.59751e8i			0.0164333i
$315$		0			0
$316$	−8.48217e9			−0.850665
$317$	−3.92566e9	+	2.26648e9i	−0.388754	+	0.224447i	−0.681620	−	0.731706i	$-0.738724\pi$
$317$	−3.92566e9	+	2.26648e9i	−0.388754	+	0.224447i	0.292866	+	0.956154i	$0.405391\pi$
$318$		0			0
$319$	−3.70012e9	+	6.40879e9i	−0.357316	+	0.618890i
$320$	9.57549e9	+	5.52841e9i	0.913190	+	0.527230i
$321$		0			0
$322$	−2.89918e7	−	5.02153e7i	−0.00269682	−	0.00467103i
$323$		−	1.20073e10i		−	1.10315i
$324$		0			0
$325$	−1.78084e9			−0.159621
$326$	3.22896e8	−	1.86424e8i	0.0285886	−	0.0165056i
$327$		0			0
$328$	1.64434e9	−	2.84808e9i	0.142068	−	0.246069i
$329$	1.82173e10	+	1.05177e10i	1.55489	+	0.897716i
$330$		0			0
$331$	−4.98842e9	−	8.64019e9i	−0.415576	−	0.719800i	0.579912	−	0.814679i	$-0.303087\pi$
$331$	−4.98842e9	−	8.64019e9i	−0.415576	−	0.719800i	−0.995489	+	0.0948794i	$0.969753\pi$
$332$			1.49266e10i			1.22859i
$333$		0			0
$334$	9.19862e8			0.0739157
$335$	−1.24055e10	+	7.16231e9i	−0.984996	+	0.568687i
$336$		0			0
$337$	−6.66219e9	+	1.15392e10i	−0.516532	+	0.894660i	0.483284	+	0.875464i	$0.339444\pi$
$337$	−6.66219e9	+	1.15392e10i	−0.516532	+	0.894660i	−0.999816	+	0.0191959i	$0.993889\pi$
$338$	−6.39836e8	−	3.69409e8i	−0.0490232	−	0.0283036i
$339$		0			0
$340$	−5.00441e9	−	8.66790e9i	−0.374488	−	0.648632i
$341$		−	3.60262e9i		−	0.266441i
$342$		0			0
$343$	−1.45550e10			−1.05156
$344$	1.76279e9	−	1.01775e9i	0.125883	−	0.0726787i
$345$		0			0
$346$	4.28458e8	−	7.42111e8i	0.0298954	−	0.0517803i
$347$	−7.37200e8	−	4.25623e8i	−0.0508473	−	0.0293567i	0.474361	−	0.880330i	$-0.342679\pi$
$347$	−7.37200e8	−	4.25623e8i	−0.0508473	−	0.0293567i	−0.525208	+	0.850974i	$0.676013\pi$
$348$		0			0
$349$	1.04327e10	+	1.80700e10i	0.703228	+	1.21803i	0.967327	+	0.253531i	$0.0815919\pi$
$349$	1.04327e10	+	1.80700e10i	0.703228	+	1.21803i	−0.264099	+	0.964495i	$0.585075\pi$
$350$			3.37161e8i			0.0224681i
$351$		0			0
$352$	−6.54161e9			−0.426103
$353$	−1.54516e10	+	8.92099e9i	−0.995119	+	0.574532i	−0.906800	−	0.421560i	$-0.861483\pi$
$353$	−1.54516e10	+	8.92099e9i	−0.995119	+	0.574532i	−0.0883185	+	0.996092i	$0.528149\pi$
$354$		0			0
$355$	7.28183e9	−	1.26125e10i	0.458487	−	0.794123i
$356$	−1.90009e10	−	1.09702e10i	−1.18297	−	0.682989i
$357$		0			0
$358$	−3.32501e8	−	5.75908e8i	−0.0202423	−	0.0350607i
$359$		−	5.27791e9i		−	0.317749i	−0.987299	−	0.158875i	$-0.949213\pi$
$359$		−	5.27791e9i		−	0.317749i	0.987299	−	0.158875i	$-0.0507865\pi$
$360$		0			0
$361$	2.81196e10			1.65569
$362$	7.91024e8	−	4.56698e8i	0.0460633	−	0.0265947i
$363$		0			0
$364$	−5.25249e9	+	9.09758e9i	−0.299199	+	0.518227i
$365$	5.45685e9	+	3.15051e9i	0.307447	+	0.177505i
$366$		0			0
$367$	−9.26843e9	−	1.60534e10i	−0.510907	−	0.884917i	−0.999920	−	0.0126403i	$-0.995976\pi$
$367$	−9.26843e9	−	1.60534e10i	−0.510907	−	0.884917i	0.489013	−	0.872276i	$-0.337357\pi$
$368$			1.05905e9i			0.0577462i
$369$		0			0
$370$	−1.21058e9			−0.0645934
$371$	9.26828e9	−	5.35104e9i	0.489219	−	0.282451i
$372$		0			0
$373$	4.63639e9	−	8.03046e9i	0.239522	−	0.414864i	−0.721056	−	0.692877i	$-0.756343\pi$
$373$	4.63639e9	−	8.03046e9i	0.239522	−	0.414864i	0.960577	+	0.278014i	$0.0896761\pi$
$374$	1.64974e9	+	9.52479e8i	0.0843198	+	0.0486821i
$375$		0			0
$376$	3.69573e9	+	6.40120e9i	0.184905	+	0.320265i
$377$			6.27347e9i			0.310558i
$378$		0			0
$379$	−1.41434e10			−0.685485			−0.342743	−	0.939429i	$-0.611356\pi$
$379$	−1.41434e10			−0.685485			−0.342743	+	0.939429i	$0.611356\pi$
$380$	3.25594e10	−	1.87982e10i	1.56150	−	0.901532i
$381$		0			0
$382$	7.40802e8	−	1.28311e9i	0.0347895	−	0.0602572i
$383$	−4.91342e9	−	2.83677e9i	−0.228344	−	0.131834i	0.381464	−	0.924384i	$-0.375420\pi$
$383$	−4.91342e9	−	2.83677e9i	−0.228344	−	0.131834i	−0.609808	+	0.792549i	$0.708753\pi$
$384$		0			0
$385$	1.70554e10	+	2.95409e10i	0.776282	+	1.34456i
$386$		−	3.02432e8i		−	0.0136232i
$387$		0			0
$388$	2.37801e10			1.04927
$389$	3.71981e10	−	2.14764e10i	1.62451	−	0.937912i	0.638819	−	0.769357i	$-0.279423\pi$
$389$	3.71981e10	−	2.14764e10i	1.62451	−	0.937912i	0.985692	−	0.168555i	$-0.0539100\pi$
$390$		0			0
$391$	4.70024e8	−	8.14106e8i	0.0201101	−	0.0348316i
$392$	−4.83985e8	−	2.79429e8i	−0.0204969	−	0.0118339i
$393$		0			0
$394$	−2.65232e8	−	4.59395e8i	−0.0110063	−	0.0190635i
$395$			2.33489e10i			0.959132i
$396$		0			0
$397$	−1.29576e10			−0.521629			−0.260815	−	0.965389i	$-0.583991\pi$
$397$	−1.29576e10			−0.521629			−0.260815	+	0.965389i	$0.583991\pi$
$398$	−2.34490e9	+	1.35383e9i	−0.0934527	+	0.0539550i
$399$		0			0
$400$	3.07905e9	−	5.33308e9i	0.120275	−	0.208323i
$401$	−2.41518e10	−	1.39441e10i	−0.934055	−	0.539277i	−0.0459636	−	0.998943i	$-0.514636\pi$
$401$	−2.41518e10	−	1.39441e10i	−0.934055	−	0.539277i	−0.888092	+	0.459666i	$0.847969\pi$
$402$		0			0
$403$	−1.52704e9	−	2.64491e9i	−0.0578936	−	0.100275i
$404$		−	2.54813e9i		−	0.0956524i
$405$		0			0
$406$	1.18774e9			0.0437137
$407$	−2.10436e10	+	1.21495e10i	−0.766907	+	0.442774i
$408$		0			0
$409$	−4.27541e9	+	7.40523e9i	−0.152786	+	0.264634i	−0.932251	−	0.361813i	$-0.882158\pi$
$409$	−4.27541e9	+	7.40523e9i	−0.152786	+	0.264634i	0.779464	+	0.626446i	$0.215491\pi$
$410$	−3.90146e9	−	2.25251e9i	−0.138068	−	0.0797134i
$411$		0			0
$412$	−2.26286e9	−	3.91939e9i	−0.0785359	−	0.136028i
$413$		−	2.18055e10i		−	0.749490i
$414$		0			0
$415$	4.10885e10			1.38525
$416$	−4.80262e9	+	2.77279e9i	−0.160363	+	0.0925857i
$417$		0			0
$418$	−3.57781e9	+	6.19696e9i	−0.117196	+	0.202989i
$419$	3.62561e10	+	2.09324e10i	1.17632	+	0.679147i	0.955160	−	0.296091i	$-0.0956832\pi$
$419$	3.62561e10	+	2.09324e10i	1.17632	+	0.679147i	0.221157	+	0.975238i	$0.429017\pi$
$420$		0			0
$421$	−2.25988e10	−	3.91422e10i	−0.719377	−	1.24600i	−0.961247	−	0.275689i	$-0.911094\pi$
$421$	−2.25988e10	−	3.91422e10i	−0.719377	−	1.24600i	0.241870	−	0.970309i	$-0.422239\pi$
$422$		−	1.21334e9i		−	0.0382589i
$423$		0			0
$424$	3.76051e9			0.116355
$425$	−4.73384e9	+	2.73308e9i	−0.145097	+	0.0837716i
$426$		0			0
$427$	−6.84950e9	+	1.18637e10i	−0.206038	+	0.356868i
$428$	−4.65969e10	−	2.69027e10i	−1.38861	−	0.801717i
$429$		0			0
$430$	−1.39417e9	−	2.41478e9i	−0.0407796	−	0.0706323i
$431$			3.78891e10i			1.09801i	0.835820	+	0.549003i	$0.184993\pi$
$431$			3.78891e10i			1.09801i	−0.835820	+	0.549003i	$0.815007\pi$
$432$		0			0
$433$	−5.16116e10			−1.46824			−0.734118	−	0.679022i	$-0.762404\pi$
$433$	−5.16116e10			−1.46824			−0.734118	+	0.679022i	$0.762404\pi$
$434$	−5.00755e8	+	2.89111e8i	−0.0141145	+	0.00814903i
$435$		0			0
$436$	2.08584e10	−	3.61277e10i	0.577210	−	0.999758i
$437$	3.05804e9	+	1.76556e9i	0.0838528	+	0.0484124i
$438$		0			0
$439$	2.71931e10	+	4.70998e10i	0.732151	+	1.26812i	0.955962	+	0.293490i	$0.0948167\pi$
$439$	2.71931e10	+	4.70998e10i	0.732151	+	1.26812i	−0.223811	+	0.974633i	$0.571850\pi$
$440$			1.19859e10i			0.319786i
$441$		0			0
$442$	1.61491e9			0.0423115
$443$	−1.66107e10	+	9.59019e9i	−0.431293	+	0.249007i	−0.699897	−	0.714243i	$-0.746771\pi$
$443$	−1.66107e10	+	9.59019e9i	−0.431293	+	0.249007i	0.268604	+	0.963251i	$0.413438\pi$
$444$		0			0
$445$	−3.01977e10	+	5.23039e10i	−0.770075	+	1.33381i
$446$	2.11441e9	+	1.22075e9i	0.0534379	+	0.0308524i
$447$		0			0
$448$	−1.78103e10	−	3.08483e10i	−0.442139	−	0.765808i
$449$			4.22624e10i			1.03984i	0.854213	+	0.519922i	$0.174039\pi$
$449$			4.22624e10i			1.03984i	−0.854213	+	0.519922i	$0.825961\pi$
$450$		0			0
$451$	−9.04256e10			−2.18567
$452$	2.11885e10	−	1.22332e10i	0.507629	−	0.293080i
$453$		0			0
$454$	−6.75200e8	+	1.16948e9i	−0.0158931	+	0.0275277i
$455$	2.50429e10	+	1.44586e10i	0.584305	+	0.337349i
$456$		0			0
$457$	−1.00776e9	−	1.74548e9i	−0.0231042	−	0.0400176i	0.854242	−	0.519875i	$-0.174022\pi$
$457$	−1.00776e9	−	1.74548e9i	−0.0231042	−	0.0400176i	−0.877346	+	0.479858i	$0.840688\pi$
$458$		−	5.77774e9i		−	0.131309i
$459$		0			0
$460$	2.94342e9			0.0657386
$461$	−2.17450e10	+	1.25545e10i	−0.481454	+	0.277968i	−0.721022	−	0.692912i	$-0.756327\pi$
$461$	−2.17450e10	+	1.25545e10i	−0.481454	+	0.277968i	0.239568	+	0.970880i	$0.422994\pi$
$462$		0			0
$463$	3.43212e10	−	5.94461e10i	0.746859	−	1.29360i	−0.202462	−	0.979290i	$-0.564894\pi$
$463$	3.43212e10	−	5.94461e10i	0.746859	−	1.29360i	0.949321	−	0.314308i	$-0.101772\pi$
$464$	−1.87872e10	−	1.08468e10i	−0.405312	−	0.234007i
$465$		0			0
$466$	−2.95685e9	−	5.12142e9i	−0.0627027	−	0.108604i
$467$		−	3.96558e10i		−	0.833757i	−0.908962	−	0.416878i	$-0.863124\pi$
$467$		−	3.96558e10i		−	0.833757i	0.908962	−	0.416878i	$-0.136876\pi$
$468$		0			0
$469$	4.61481e10			0.953811
$470$	8.76873e9	−	5.06263e9i	0.179699	−	0.103749i
$471$		0			0
$472$	3.83102e9	−	6.63552e9i	0.0771874	−	0.133692i
$473$	−4.84699e10	−	2.79841e10i	−0.968338	−	0.559070i
$474$		0			0
$475$	−1.02663e10	−	1.77818e10i	−0.201670	−	0.349302i
$476$			3.22444e10i			0.628096i
$477$		0			0
$478$	2.60672e9			0.0499324
$479$	2.67898e10	−	1.54671e10i	0.508894	−	0.293810i	−0.223485	−	0.974707i	$-0.571743\pi$
$479$	2.67898e10	−	1.54671e10i	0.508894	−	0.293810i	0.732379	+	0.680897i	$0.238410\pi$
$480$		0			0
$481$	−1.02996e10	+	1.78395e10i	−0.192416	+	0.333274i
$482$	−6.49380e8	−	3.74920e8i	−0.0120313	−	0.00694625i
$483$		0			0
$484$	3.26818e10	+	5.66065e10i	0.595559	+	1.03154i
$485$		−	6.54595e10i		−	1.18306i
$486$		0			0
$487$	1.04034e11			1.84952			0.924761	−	0.380549i	$-0.124265\pi$
$487$	1.04034e11			1.84952			0.924761	+	0.380549i	$0.124265\pi$
$488$	−4.16867e9	+	2.40678e9i	−0.0735052	+	0.0424383i
$489$		0			0
$490$	−3.82778e8	+	6.62991e8i	−0.00663992	+	0.0115007i
$491$	7.15518e10	+	4.13104e10i	1.23110	+	0.710778i	0.967260	−	0.253788i	$-0.0816764\pi$
$491$	7.15518e10	+	4.13104e10i	1.23110	+	0.710778i	0.263843	+	0.964566i	$0.415010\pi$
$492$		0			0
$493$	9.62801e9	+	1.66762e10i	0.162985	+	0.282299i
$494$			6.06611e9i			0.101860i
$495$		0			0
$496$	1.05610e10			0.174493
$497$	−4.06324e10	+	2.34591e10i	−0.665957	+	0.384491i
$498$		0			0
$499$	−3.38096e10	+	5.85599e10i	−0.545303	+	0.944492i	0.453285	+	0.891366i	$0.350252\pi$
$499$	−3.38096e10	+	5.85599e10i	−0.545303	+	0.944492i	−0.998588	+	0.0531262i	$0.983081\pi$
$500$	4.50648e10	+	2.60182e10i	0.721037	+	0.416291i
$501$		0			0
$502$	−1.72471e9	−	2.98729e9i	−0.0271582	−	0.0470395i
$503$		−	1.23313e11i		−	1.92635i	−0.268867	−	0.963177i	$-0.586649\pi$
$503$		−	1.23313e11i		−	1.92635i	0.268867	−	0.963177i	$-0.413351\pi$
$504$		0			0
$505$	−7.01425e9			−0.107849
$506$	−4.85159e8	+	2.80107e8i	−0.00740086	+	0.00427289i
$507$		0			0
$508$	−2.92072e10	+	5.05883e10i	−0.438566	+	0.759618i
$509$	7.57066e10	+	4.37092e10i	1.12788	+	0.651181i	0.943401	−	0.331655i	$-0.107607\pi$
$509$	7.57066e10	+	4.37092e10i	1.12788	+	0.651181i	0.184479	+	0.982837i	$0.440940\pi$
$510$		0			0
$511$	−1.01497e10	−	1.75798e10i	−0.148857	−	0.257827i
$512$		−	3.20619e10i		−	0.466562i
$513$		0			0
$514$	2.71256e9			0.0388621
$515$	−1.07889e10	+	6.22898e9i	−0.153373	+	0.0885499i
$516$		0			0
$517$	1.01618e11	−	1.76008e11i	1.42236	−	2.46359i
$518$	3.37751e9	+	1.95000e9i	0.0469113	+	0.0270842i
$519$		0			0
$520$	5.08046e9	+	8.79961e9i	0.0694848	+	0.120351i
$521$		−	4.04435e9i		−	0.0548906i	−0.999623	−	0.0274453i	$-0.991263\pi$
$521$		−	4.04435e9i		−	0.0548906i	0.999623	−	0.0274453i	$-0.00873721\pi$
$522$		0			0
$523$	2.72416e10			0.364105			0.182052	−	0.983289i	$-0.441726\pi$
$523$	2.72416e10			0.364105			0.182052	+	0.983289i	$0.441726\pi$
$524$	2.49753e10	−	1.44195e10i	0.331272	−	0.191260i
$525$		0			0
$526$	3.44584e9	−	5.96837e9i	0.0450145	−	0.0779673i
$527$	−8.11840e9	−	4.68716e9i	−0.105251	−	0.0607669i
$528$		0			0
$529$	−3.90173e10	−	6.75799e10i	−0.498235	−	0.862968i
$530$		−	5.15136e9i		−	0.0652858i
$531$		0			0
$532$	−1.21120e11			−1.51206
$533$	−6.63872e10	+	3.83287e10i	−0.822575	+	0.474914i
$534$		0			0
$535$	−7.40552e10	+	1.28267e11i	−0.903942	+	1.56567i
$536$	1.40431e10	+	8.10778e9i	0.170139	+	0.0982297i
$537$		0			0
$538$	−4.04520e9	−	7.00648e9i	−0.0482848	−	0.0836317i
$539$			1.53664e10i			0.182061i
$540$		0			0
$541$	2.24803e10			0.262429			0.131215	−	0.991354i	$-0.458112\pi$
$541$	2.24803e10			0.262429			0.131215	+	0.991354i	$0.458112\pi$
$542$	−4.17487e9	+	2.41036e9i	−0.0483778	+	0.0279309i
$543$		0			0
$544$	−8.51091e9	+	1.47413e10i	−0.0971808	+	0.168322i
$545$	−9.94490e10	−	5.74169e10i	−1.12723	−	0.650809i
$546$		0			0
$547$	5.95117e10	+	1.03077e11i	0.664742	+	1.15137i	0.979355	+	0.202147i	$0.0647917\pi$
$547$	5.95117e10	+	1.03077e11i	0.664742	+	1.15137i	−0.314614	+	0.949220i	$0.601875\pi$
$548$			7.64904e10i			0.848174i
$549$		0			0
$550$	3.25751e9			0.0355988
$551$	−6.26411e10	+	3.61659e10i	−0.679600	+	0.392367i
$552$		0			0
$553$	3.76104e10	−	6.51430e10i	0.402167	−	0.696574i
$554$	−7.11042e9	−	4.10520e9i	−0.0754842	−	0.0435808i
$555$		0			0
$556$	−5.51317e8	−	9.54909e8i	−0.00576902	−	0.00999224i
$557$			4.55371e10i			0.473091i	0.971620	+	0.236545i	$0.0760152\pi$
$557$			4.55371e10i			0.473091i	−0.971620	+	0.236545i	$0.923985\pi$
$558$		0			0
$559$	−4.74464e10			−0.485910
$560$	−8.65982e10	+	4.99975e10i	−0.880555	+	0.508389i
$561$		0			0
$562$	−7.45829e9	+	1.29181e10i	−0.0747642	+	0.129495i
$563$	−4.23095e9	−	2.44274e9i	−0.0421119	−	0.0243133i	0.478796	−	0.877926i	$-0.341073\pi$
$563$	−4.23095e9	−	2.44274e9i	−0.0421119	−	0.0243133i	−0.520908	+	0.853613i	$0.674407\pi$
$564$		0			0
$565$	−3.36743e10	−	5.83257e10i	−0.330450	−	0.572356i
$566$			1.17831e10i			0.114814i
$567$		0			0
$568$	−1.64862e10			−0.158389
$569$	1.35833e11	−	7.84230e10i	1.29585	−	0.748160i	0.316167	−	0.948704i	$-0.397604\pi$
$569$	1.35833e11	−	7.84230e10i	1.29585	−	0.748160i	0.979685	+	0.200544i	$0.0642708\pi$
$570$		0			0
$571$	2.43502e10	−	4.21758e10i	0.229065	−	0.396751i	−0.728467	−	0.685081i	$-0.759767\pi$
$571$	2.43502e10	−	4.21758e10i	0.229065	−	0.396751i	0.957531	+	0.288330i	$0.0931000\pi$
$572$	8.78970e10	+	5.07474e10i	0.821089	+	0.474056i
$573$		0			0
$574$	7.25667e9	+	1.25689e10i	0.0668482	+	0.115785i
$575$		−	1.60750e9i		−	0.0147055i
$576$		0			0
$577$	−1.24459e11			−1.12285			−0.561427	−	0.827526i	$-0.689747\pi$
$577$	−1.24459e11			−1.12285			−0.561427	+	0.827526i	$0.689747\pi$
$578$	−5.07523e9	+	2.93018e9i	−0.0454720	+	0.0262533i
$579$		0			0
$580$	−3.01466e10	+	5.22154e10i	−0.266395	+	0.461409i
$581$	−1.14636e11	−	6.61851e10i	−1.00604	−	0.580839i
$582$		0			0
$583$	−5.16996e10	−	8.95463e10i	−0.447520	−	0.775128i
$584$		−	7.13281e9i		−	0.0613210i
$585$		0			0
$586$	−9.96565e9			−0.0845114
$587$	3.54754e10	−	2.04817e10i	0.298796	−	0.172510i	−0.343106	−	0.939297i	$-0.611479\pi$
$587$	3.54754e10	−	2.04817e10i	0.298796	−	0.172510i	0.641902	+	0.766787i	$0.278146\pi$
$588$		0			0
$589$	1.76065e10	−	3.04953e10i	0.146289	−	0.253380i
$590$	−9.08972e9	−	5.24795e9i	−0.0750140	−	0.0433094i
$591$		0			0
$592$	−3.56160e10	−	6.16887e10i	−0.289973	−	0.502249i
$593$			1.81583e11i			1.46844i	0.678909	+	0.734222i	$0.262453\pi$
$593$			1.81583e11i			1.46844i	−0.678909	+	0.734222i	$0.737547\pi$
$594$		0			0
$595$	8.87592e10			0.708183
$596$	−2.73040e10	+	1.57640e10i	−0.216392	+	0.124934i
$597$		0			0
$598$	−2.37457e8	+	4.11288e8i	−0.00185687	+	0.00321619i
$599$	3.59585e10	+	2.07606e10i	0.279315	+	0.161262i	0.633113	−	0.774059i	$-0.281777\pi$
$599$	3.59585e10	+	2.07606e10i	0.279315	+	0.161262i	−0.353798	+	0.935322i	$0.615110\pi$
$600$		0			0
$601$	2.34314e10	+	4.05843e10i	0.179597	+	0.311072i	0.941743	−	0.336334i	$-0.109187\pi$
$601$	2.34314e10	+	4.05843e10i	0.179597	+	0.311072i	−0.762145	+	0.647406i	$0.775854\pi$
$602$			8.98291e9i			0.0683961i
$603$		0			0
$604$	2.17740e11			1.63603
$605$	1.55821e11	−	8.99633e10i	1.16307	−	0.671497i
$606$		0			0
$607$	−9.46390e10	+	1.63920e11i	−0.697133	+	1.20747i	0.272324	+	0.962206i	$0.412208\pi$
$607$	−9.46390e10	+	1.63920e11i	−0.697133	+	1.20747i	−0.969456	+	0.245264i	$0.921125\pi$
$608$	−5.53731e10	−	3.19697e10i	−0.405214	−	0.233951i
$609$		0			0
$610$	3.29695e9	+	5.71048e9i	0.0238118	+	0.0412433i
$611$		−	1.72291e11i		−	1.23623i
$612$		0			0
$613$	−2.04650e10			−0.144934			−0.0724668	−	0.997371i	$-0.523087\pi$
$613$	−2.04650e10			−0.144934			−0.0724668	+	0.997371i	$0.523087\pi$
$614$	−7.30270e9	+	4.21622e9i	−0.0513819	+	0.0296654i
$615$		0			0
$616$	1.93069e10	−	3.34404e10i	0.134088	−	0.232247i
$617$	−1.33253e11	−	7.69336e10i	−0.919467	−	0.530855i	−0.0360022	−	0.999352i	$-0.511462\pi$
$617$	−1.33253e11	−	7.69336e10i	−0.919467	−	0.530855i	−0.883465	+	0.468497i	$0.844796\pi$
$618$		0			0
$619$	1.26212e11	+	2.18605e11i	0.859681	+	1.48901i	0.872233	+	0.489090i	$0.162671\pi$
$619$	1.26212e11	+	2.18605e11i	0.859681	+	1.48901i	−0.0125525	+	0.999921i	$0.503996\pi$
$620$		−	2.93522e10i		−	0.198643i
$621$		0			0
$622$	2.28908e10			0.152933
$623$	1.68502e11	−	9.72846e10i	1.11854	−	0.645791i
$624$		0			0
$625$	9.05034e10	−	1.56756e11i	0.593123	−	1.02732i
$626$	2.40216e10	+	1.38689e10i	0.156424	+	0.0903115i
$627$		0			0
$628$	1.30627e10	+	2.26252e10i	0.0839833	+	0.145463i
$629$			6.32281e10i			0.403932i
$630$		0			0
$631$	1.64752e11			1.03924			0.519618	−	0.854399i	$-0.326074\pi$
$631$	1.64752e11			1.03924			0.519618	+	0.854399i	$0.326074\pi$
$632$	2.28900e10	−	1.32156e10i	0.143476	−	0.0828357i
$633$		0			0
$634$	3.51460e9	−	6.08747e9i	0.0217530	−	0.0376773i
$635$	1.39255e11	+	8.03987e10i	0.856475	+	0.494486i
$636$		0			0
$637$	6.51334e9	+	1.12814e10i	0.0395591	+	0.0685183i
$638$		−	1.14755e10i		−	0.0692607i
$639$		0			0
$640$	−7.09486e10			−0.422887
$641$	−2.07985e10	+	1.20080e10i	−0.123197	+	0.0711276i	−0.560332	−	0.828268i	$-0.689326\pi$
$641$	−2.07985e10	+	1.20080e10i	−0.123197	+	0.0711276i	0.437135	+	0.899396i	$0.355993\pi$
$642$		0			0
$643$	6.48791e10	−	1.12374e11i	0.379543	−	0.657388i	−0.611453	−	0.791281i	$-0.709415\pi$
$643$	6.48791e10	−	1.12374e11i	0.379543	−	0.657388i	0.990996	+	0.133893i	$0.0427478\pi$
$644$	−8.21207e9	−	4.74124e9i	−0.0477430	−	0.0275644i
$645$		0			0
$646$	9.30977e9	+	1.61250e10i	0.0534575	+	0.0925911i
$647$			8.11281e10i			0.462971i	0.972838	+	0.231486i	$0.0743587\pi$
$647$			8.11281e10i			0.462971i	−0.972838	+	0.231486i	$0.925641\pi$
$648$		0			0
$649$	−2.10676e11			−1.18751
$650$	2.39155e9	−	1.38076e9i	0.0133975	−	0.00773508i
$651$		0			0
$652$	3.04873e10	−	5.28056e10i	0.168705	−	0.292206i
$653$	−2.09473e11	−	1.20939e11i	−1.15206	−	0.665142i	−0.202672	−	0.979247i	$-0.564962\pi$
$653$	−2.09473e11	−	1.20939e11i	−1.15206	−	0.665142i	−0.949388	+	0.314105i	$0.898296\pi$
$654$		0			0
$655$	−3.96926e10	−	6.87496e10i	−0.215647	−	0.373512i
$656$		−	2.65080e11i		−	1.43140i
$657$		0			0
$658$	−3.26195e10			−0.174010
$659$	−8.16111e10	+	4.71182e10i	−0.432721	+	0.249831i	−0.700505	−	0.713647i	$-0.747042\pi$
$659$	−8.16111e10	+	4.71182e10i	−0.432721	+	0.249831i	0.267784	+	0.963479i	$0.413709\pi$
$660$		0			0
$661$	−1.16496e11	+	2.01777e11i	−0.610245	+	1.05698i	0.380954	+	0.924594i	$0.375596\pi$
$661$	−1.16496e11	+	2.01777e11i	−0.610245	+	1.05698i	−0.991199	+	0.132381i	$0.957738\pi$
$662$	1.33982e10	+	7.73548e9i	0.0697615	+	0.0402768i
$663$		0			0
$664$	−2.32562e10	−	4.02809e10i	−0.119637	−	0.207218i
$665$			3.33408e11i			1.70486i
$666$		0			0
$667$	−5.66284e9			−0.0286109
$668$	1.30278e11	−	7.52159e10i	0.654281	−	0.377749i
$669$		0			0
$670$	1.11065e10	−	1.92370e10i	0.0551160	−	0.0954638i
$671$	1.14622e11	+	6.61770e10i	0.565428	+	0.326450i
$672$		0			0
$673$	−8.39841e10	−	1.45465e11i	−0.409390	−	0.709084i	0.585432	−	0.810722i	$-0.300925\pi$
$673$	−8.39841e10	−	1.45465e11i	−0.409390	−	0.709084i	−0.994821	+	0.101638i	$0.967592\pi$
$674$		−	2.06619e10i		−	0.100122i
$675$		0			0
$676$	−1.20824e11			−0.578586
$677$	−1.68287e11	+	9.71606e10i	−0.801118	+	0.462526i	−0.843862	−	0.536560i	$-0.819723\pi$
$677$	−1.68287e11	+	9.71606e10i	−0.801118	+	0.462526i	0.0427441	+	0.999086i	$0.486390\pi$
$678$		0			0
$679$	−1.05442e11	+	1.82631e11i	−0.496060	+	0.859202i
$680$	2.70099e10	+	1.55942e10i	0.126324	+	0.0729333i
$681$		0			0
$682$	2.79327e9	+	4.83809e9i	0.0129115	+	0.0223633i
$683$			3.79500e11i			1.74393i	0.489570	+	0.871964i	$0.337154\pi$
$683$			3.79500e11i			1.74393i	−0.489570	+	0.871964i	$0.662846\pi$
$684$		0			0
$685$	2.10556e11			0.956323
$686$	1.95464e10	−	1.12851e10i	0.0882612	−	0.0509576i
$687$		0			0
$688$	8.20345e10	−	1.42088e11i	0.366136	−	0.634167i
$689$	−7.59119e10	−	4.38277e10i	−0.336847	−	0.194479i
$690$		0			0
$691$	−3.67841e10	−	6.37120e10i	−0.161342	−	0.279453i	0.774008	−	0.633176i	$-0.218249\pi$
$691$	−3.67841e10	−	6.37120e10i	−0.161342	−	0.279453i	−0.935350	+	0.353723i	$0.884916\pi$
$692$		−	1.40138e11i		−	0.611126i
$693$		0			0
$694$	1.32002e9			0.00569038
$695$	−2.62858e9	+	1.51761e9i	−0.0112663	+	0.00650461i
$696$		0			0
$697$	−1.17647e11	+	2.03771e11i	−0.498484	+	0.863400i
$698$	−2.80209e10	−	1.61779e10i	−0.118049	−	0.0681554i
$699$		0			0
$700$	2.75692e10	+	4.77513e10i	0.114824	+	0.198881i
$701$		−	2.33479e11i		−	0.966885i	−0.875376	−	0.483443i	$-0.839386\pi$
$701$		−	2.33479e11i		−	0.966885i	0.875376	−	0.483443i	$-0.160614\pi$
$702$		0			0
$703$	−2.37505e11			−0.972415
$704$	−2.98044e11	+	1.72076e11i	−1.21336	+	0.700533i
$705$		0			0
$706$	1.38337e10	−	2.39606e10i	0.0556825	−	0.0964449i
$707$	1.95696e10	+	1.12985e10i	0.0783258	+	0.0452214i
$708$		0			0
$709$	−5.62900e10	−	9.74972e10i	−0.222765	−	0.385840i	0.732882	−	0.680356i	$-0.238175\pi$
$709$	−5.62900e10	−	9.74972e10i	−0.222765	−	0.385840i	−0.955646	+	0.294516i	$0.904842\pi$
$710$			2.25837e10i			0.0888713i
$711$		0			0
$712$	6.83679e10			0.266031
$713$	2.38747e9	−	1.37841e9i	0.00923806	−	0.00533360i
$714$		0			0
$715$	1.39693e11	−	2.41955e11i	0.534502	−	0.925784i
$716$	−9.41825e10	−	5.43763e10i	−0.358359	−	0.206899i
$717$		0			0
$718$	4.09220e9	+	7.08789e9i	0.0153978	+	0.0266698i
$719$			8.88990e10i			0.332645i	0.986071	+	0.166323i	$0.0531893\pi$
$719$			8.88990e10i			0.332645i	−0.986071	+	0.166323i	$0.946811\pi$
$720$		0			0
$721$	4.01345e10			0.148517
$722$	−3.77628e10	+	2.18024e10i	−0.138968	+	0.0802333i
$723$		0			0
$724$	7.46872e10	−	1.29362e11i	0.271826	−	0.470817i
$725$	2.85166e10	+	1.64641e10i	0.103216	+	0.0595916i
$726$		0			0
$727$	4.33960e10	+	7.51640e10i	0.155350	+	0.269074i	0.933186	−	0.359393i	$-0.117016\pi$
$727$	4.33960e10	+	7.51640e10i	0.155350	+	0.269074i	−0.777836	+	0.628467i	$0.783683\pi$
$728$		−	3.27343e10i		−	0.116541i
$729$		0			0
$730$	−9.77093e9			−0.0344068
$731$	−1.26123e11	+	7.28169e10i	−0.441696	+	0.255013i
$732$		0			0
$733$	−2.34369e11	+	4.05939e11i	−0.811866	+	1.40619i	0.0996907	+	0.995018i	$0.468215\pi$
$733$	−2.34369e11	+	4.05939e11i	−0.811866	+	1.40619i	−0.911557	+	0.411175i	$0.865119\pi$
$734$	2.48938e10	+	1.43724e10i	0.0857643	+	0.0495161i
$735$		0			0
$736$	−2.50290e9	−	4.33516e9i	−0.00852969	−	0.0147738i
$737$		−	4.45864e11i		−	1.51123i
$738$		0			0
$739$	−3.42168e11			−1.14726			−0.573630	−	0.819114i	$-0.694465\pi$
$739$	−3.42168e11			−1.14726			−0.573630	+	0.819114i	$0.694465\pi$
$740$	−1.71452e11	+	9.89878e10i	−0.571762	+	0.330107i
$741$		0			0
$742$	−8.29780e9	+	1.43722e10i	−0.0273746	+	0.0474141i
$743$	4.81576e11	+	2.78038e11i	1.58019	+	0.912323i	0.994831	+	0.101549i	$0.0323799\pi$
$743$	4.81576e11	+	2.78038e11i	1.58019	+	0.912323i	0.585359	+	0.810774i	$0.300953\pi$
$744$		0			0
$745$	4.33936e10	+	7.51599e10i	0.140864	+	0.243984i
$746$			1.43792e10i			0.0464279i
$747$		0			0
$748$	3.11532e11			0.995167
$749$	4.13225e11	−	2.38576e11i	1.31298	−	0.758052i
$750$		0			0
$751$	1.78639e11	−	3.09411e11i	0.561585	−	0.972695i	−0.435773	−	0.900057i	$-0.643525\pi$
$751$	1.78639e11	−	3.09411e11i	0.561585	−	0.972695i	0.997358	−	0.0726379i	$-0.0231418\pi$
$752$	5.15961e11	+	2.97890e11i	1.61341	+	0.931505i
$753$		0			0
$754$	−4.86409e9	−	8.42486e9i	−0.0150493	−	0.0260662i
$755$		−	5.99373e11i		−	1.84463i
$756$		0			0
$757$	3.78993e11			1.15411			0.577056	−	0.816704i	$-0.304201\pi$
$757$	3.78993e11			1.15411			0.577056	+	0.816704i	$0.304201\pi$
$758$	1.89937e10	−	1.09660e10i	0.0575351	−	0.0332179i
$759$		0			0
$760$	−5.85766e10	+	1.01458e11i	−0.175578	+	0.304110i
$761$	2.04721e11	+	1.18196e11i	0.610413	+	0.352422i	0.773127	−	0.634251i	$-0.218692\pi$
$761$	2.04721e11	+	1.18196e11i	0.610413	+	0.352422i	−0.162714	+	0.986673i	$0.552025\pi$
$762$		0			0
$763$	1.84974e11	+	3.20384e11i	0.545773	+	0.945307i
$764$		−	2.42297e11i		−	0.711173i
$765$		0			0
$766$	8.79788e9			0.0255542
$767$	−1.54670e11	+	8.92990e10i	−0.446916	+	0.258027i
$768$		0			0
$769$	2.41662e11	−	4.18571e11i	0.691040	−	1.19692i	−0.280458	−	0.959866i	$-0.590486\pi$
$769$	2.41662e11	−	4.18571e11i	0.691040	−	1.19692i	0.971498	−	0.237049i	$-0.0761803\pi$
$770$	−4.58087e10	−	2.64476e10i	−0.130312	−	0.0752357i
$771$		0			0
$772$	−2.47295e10	−	4.28327e10i	−0.0696218	−	0.120589i
$773$			1.76968e11i			0.495651i	0.968805	+	0.247825i	$0.0797159\pi$
$773$			1.76968e11i			0.495651i	−0.968805	+	0.247825i	$0.920284\pi$
$774$		0			0
$775$	−1.60303e10			−0.0444359
$776$	−6.41730e10	+	3.70503e10i	−0.176972	+	0.102175i
$777$		0			0
$778$	−3.33031e10	+	5.76827e10i	−0.0909005	+	0.157444i
$779$	−7.65430e11	−	4.41921e11i	−2.07853	−	1.20004i
$780$		0			0
$781$	2.26652e11	+	3.92573e11i	0.609194	+	1.05515i
$782$			1.45772e9i			0.00389805i
$783$		0			0
$784$	−4.50461e10			−0.119232
$785$	6.22805e10	−	3.59576e10i	0.164011	−	0.0946918i
$786$		0			0
$787$	2.06125e10	−	3.57019e10i	0.0537318	−	0.0930662i	−0.837908	−	0.545811i	$-0.816222\pi$
$787$	2.06125e10	−	3.57019e10i	0.0537318	−	0.0930662i	0.891640	+	0.452745i	$0.149555\pi$
$788$	−7.51283e10	−	4.33754e10i	−0.194849	−	0.112496i
$789$		0			0
$790$	−1.81034e10	−	3.13561e10i	−0.0464786	−	0.0805032i
$791$			2.16970e11i			0.554235i
$792$		0			0
$793$	1.12202e11			0.283731
$794$	1.74012e10	−	1.00466e10i	0.0437821	−	0.0252776i
$795$		0			0
$796$	−2.21402e11	+	3.83479e11i	−0.551478	+	0.955188i
$797$	5.95648e10	+	3.43897e10i	0.147624	+	0.0852306i	0.571993	−	0.820259i	$-0.306171\pi$
$797$	5.95648e10	+	3.43897e10i	0.147624	+	0.0852306i	−0.424369	+	0.905489i	$0.639504\pi$
$798$		0			0
$799$	−2.64418e11	−	4.57986e11i	−0.648791	−	1.12374i
$800$			2.91076e10i			0.0710635i
$801$		0			0
$802$	4.32458e10			0.104531
$803$	−1.69848e11	+	9.80619e10i	−0.408506	+	0.235851i
$804$		0			0
$805$	−1.30512e10	+	2.26054e10i	−0.0310791	+	0.0538306i
$806$	4.10144e9	+	2.36797e9i	0.00971843	+	0.00561094i
$807$		0			0
$808$	3.97009e9	+	6.87639e9i	0.00931439	+	0.0161330i
$809$			6.08714e11i			1.42108i	0.703656	+	0.710541i	$0.251550\pi$
$809$			6.08714e11i			1.42108i	−0.703656	+	0.710541i	$0.748450\pi$
$810$		0			0
$811$	1.12522e11			0.260109			0.130055	−	0.991507i	$-0.458485\pi$
$811$	1.12522e11			0.260109			0.130055	+	0.991507i	$0.458485\pi$
$812$	1.68217e11	−	9.71199e10i	0.386941	−	0.223401i
$813$		0			0
$814$	1.88401e10	−	3.26321e10i	0.0429127	−	0.0743270i
$815$	−1.45358e11	−	8.39226e10i	−0.329465	−	0.190217i
$816$		0			0
$817$	−2.73523e11	−	4.73757e11i	−0.613912	−	1.06333i
$818$		−	1.32596e10i		−	0.0296155i
$819$		0			0
$820$	−7.36739e11			−1.62951
$821$	4.99965e11	−	2.88655e11i	1.10044	−	0.635341i	0.164105	−	0.986443i	$-0.447526\pi$
$821$	4.99965e11	−	2.88655e11i	1.10044	−	0.635341i	0.936337	+	0.351102i	$0.114193\pi$
$822$		0			0
$823$	1.35295e9	−	2.34337e9i	0.00294905	−	0.00510790i	−0.864547	−	0.502552i	$-0.832395\pi$
$823$	1.35295e9	−	2.34337e9i	0.00294905	−	0.00510790i	0.867496	+	0.497444i	$0.165728\pi$
$824$	1.22131e10	+	7.05125e9i	0.0264922	+	0.0152953i
$825$		0			0
$826$	1.69068e10	+	2.92834e10i	0.0363195	+	0.0629073i
$827$		−	5.07821e11i		−	1.08565i	−0.839847	−	0.542824i	$-0.817355\pi$
$827$		−	5.07821e11i		−	1.08565i	0.839847	−	0.542824i	$-0.182645\pi$
$828$		0			0
$829$	2.66902e11			0.565112			0.282556	−	0.959251i	$-0.408818\pi$
$829$	2.66902e11			0.565112			0.282556	+	0.959251i	$0.408818\pi$
$830$	−5.51791e10	+	3.18577e10i	−0.116269	+	0.0671277i
$831$		0			0
$832$	−1.45875e11	+	2.52663e11i	−0.304431	+	0.527289i
$833$	3.46277e10	+	1.99923e10i	0.0719189	+	0.0415224i
$834$		0			0
$835$	−2.07047e11	−	3.58616e11i	−0.425915	−	0.737707i
$836$			1.17021e12i			2.39574i
$837$		0			0
$838$	−6.49194e10			−0.131643
$839$	−4.56007e11	+	2.63276e11i	−0.920287	+	0.531328i	−0.883727	−	0.468003i	$-0.844973\pi$
$839$	−4.56007e11	+	2.63276e11i	−0.920287	+	0.531328i	−0.0365604	+	0.999331i	$0.511640\pi$
$840$		0			0
$841$	−1.92124e11	+	3.32769e11i	−0.384059	+	0.665210i
$842$	6.06974e10	+	3.50436e10i	0.120760	+	0.0697206i
$843$		0			0
$844$	−9.92132e10	−	1.71842e11i	−0.195524	−	0.338657i
$845$			3.32594e11i			0.652361i
$846$		0			0
$847$	−5.79651e11			−1.12624
$848$	2.62502e11	−	1.51556e11i	0.507633	−	0.293082i
$849$		0			0
$850$	4.23816e9	−	7.34070e9i	0.00811897	−	0.0140625i
$851$	−1.61031e10	−	9.29713e9i	−0.0307037	−	0.0177268i
$852$		0			0
$853$	4.85818e11	+	8.41461e11i	0.917651	+	1.58942i	0.802973	+	0.596015i	$0.203250\pi$
$853$	4.85818e11	+	8.41461e11i	0.917651	+	1.58942i	0.114678	+	0.993403i	$0.463416\pi$
$854$		−	2.12429e10i		−	0.0399376i
$855$		0			0
$856$	1.67662e11			0.312277
$857$	−6.11574e11	+	3.53093e11i	−1.13377	+	0.654584i	−0.944881	−	0.327414i	$-0.893823\pi$
$857$	−6.11574e11	+	3.53093e11i	−1.13377	+	0.654584i	−0.188892	+	0.981998i	$0.560490\pi$
$858$		0			0
$859$	2.25749e11	−	3.91008e11i	0.414622	−	0.718147i	−0.580767	−	0.814070i	$-0.697247\pi$
$859$	2.25749e11	−	3.91008e11i	0.414622	−	0.718147i	0.995389	+	0.0959236i	$0.0305804\pi$
$860$	−3.94906e11	−	2.27999e11i	−0.721938	−	0.416811i
$861$		0			0
$862$	−2.93771e10	−	5.08826e10i	−0.0532083	−	0.0921595i
$863$		−	9.00374e11i		−	1.62323i	−0.584193	−	0.811615i	$-0.698589\pi$
$863$		−	9.00374e11i		−	1.62323i	0.584193	−	0.811615i	$-0.301411\pi$
$864$		0			0
$865$	−3.85758e11			−0.689049
$866$	6.93111e10	−	4.00168e10i	0.123234	−	0.0711493i
$867$		0			0
$868$	−4.72805e10	+	8.18922e10i	−0.0832919	+	0.144266i
$869$	−6.29385e11	−	3.63376e11i	−1.10367	−	0.637201i
$870$		0			0
$871$	−1.88988e11	−	3.27337e11i	−0.328369	−	0.568751i
$872$			1.29993e11i			0.224829i
$873$		0			0
$874$	−5.47567e9			−0.00938407
$875$	−3.99639e11	+	2.30732e11i	−0.681766	+	0.393618i
$876$		0			0
$877$	5.67437e11	−	9.82830e11i	0.959222	−	1.66142i	0.234827	−	0.972037i	$-0.424548\pi$
$877$	5.67437e11	−	9.82830e11i	0.959222	−	1.66142i	0.724395	−	0.689385i	$-0.242119\pi$
$878$	−7.30371e10	−	4.21680e10i	−0.122904	−	0.0709586i
$879$		0			0
$880$	4.83055e11	+	8.36675e11i	0.805500	+	1.39517i
$881$			3.16640e11i			0.525609i	0.964849	+	0.262804i	$0.0846474\pi$
$881$			3.16640e11i			0.525609i	−0.964849	+	0.262804i	$0.915353\pi$
$882$		0			0
$883$	7.48388e11			1.23107			0.615537	−	0.788108i	$-0.288939\pi$
$883$	7.48388e11			1.23107			0.615537	+	0.788108i	$0.288939\pi$
$884$	2.28715e11	−	1.32049e11i	0.374530	−	0.216235i
$885$		0			0
$886$	1.48714e10	−	2.57580e10i	0.0241333	−	0.0418001i
$887$	6.38831e11	+	3.68829e11i	1.03203	+	0.595841i	0.917565	−	0.397586i	$-0.130152\pi$
$887$	6.38831e11	+	3.68829e11i	1.03203	+	0.595841i	0.114463	+	0.993428i	$0.463485\pi$
$888$		0			0
$889$	−2.59012e11	−	4.48622e11i	−0.414680	−	0.718246i
$890$		−	9.36543e10i		−	0.149268i
$891$		0			0
$892$	3.99278e11			0.630690
$893$	1.72034e12	−	9.93240e11i	2.70526	−	1.56188i
$894$		0			0
$895$	−1.49682e11	+	2.59257e11i	−0.233280	+	0.404052i
$896$	1.97945e11	+	1.14284e11i	0.307124	+	0.177318i
$897$		0			0
$898$	−3.27679e10	−	5.67556e10i	−0.0503898	−	0.0872778i
$899$			5.64708e10i			0.0864541i
$900$		0			0
$901$	−2.69053e11			−0.408262
$902$	1.21436e11	−	7.01109e10i	0.183451	−	0.105916i
$903$		0			0
$904$	−3.81196e10	+	6.60250e10i	−0.0570787	+	0.0988633i
$905$	−3.56095e11	−	2.05592e11i	−0.530850	−	0.306486i
$906$		0			0
$907$	4.89448e11	+	8.47748e11i	0.723231	+	1.25267i	0.959698	+	0.281034i	$0.0906773\pi$
$907$	4.89448e11	+	8.47748e11i	0.723231	+	1.25267i	−0.236467	+	0.971640i	$0.575989\pi$
$908$			2.20841e11i			0.324890i
$909$		0			0
$910$	−4.48414e10			−0.0653903
$911$	4.63087e11	−	2.67363e11i	0.672340	−	0.388175i	−0.124623	−	0.992204i	$-0.539772\pi$
$911$	4.63087e11	−	2.67363e11i	0.672340	−	0.388175i	0.796963	+	0.604029i	$0.206439\pi$
$912$		0			0
$913$	−6.39453e11	+	1.10757e12i	−0.920292	+	1.59399i
$914$	2.70670e9	+	1.56271e9i	0.00387843	+	0.00223921i
$915$		0			0
$916$	−4.72438e11	−	8.18286e11i	−0.671062	−	1.16231i
$917$			2.55747e11i			0.361687i
$918$		0			0
$919$	9.48007e11			1.32908			0.664538	−	0.747255i	$-0.268629\pi$
$919$	9.48007e11			1.32908			0.664538	+	0.747255i	$0.268629\pi$
$920$	−7.94311e9	+	4.58596e9i	−0.0110876	+	0.00640146i
$921$		0			0
$922$	1.94680e10	−	3.37196e10i	0.0269401	−	0.0466616i
$923$	3.32799e11	+	1.92142e11i	0.458539	+	0.264737i
$924$		0			0
$925$	5.40606e10	+	9.36358e10i	0.0738438	+	0.127901i
$926$			1.06443e11i			0.144768i
$927$		0			0
$928$	1.02539e11			0.138261
$929$	−7.42540e10	+	4.28705e10i	−0.0996912	+	0.0575567i	−0.549017	−	0.835811i	$-0.684998\pi$
$929$	−7.42540e10	+	4.28705e10i	−0.0996912	+	0.0575567i	0.449326	+	0.893368i	$0.351664\pi$
$930$		0			0
$931$	−7.50974e10	+	1.30073e11i	−0.0999600	+	0.173136i
$932$	−8.37543e11	−	4.83556e11i	−1.11005	−	0.640889i
$933$		0			0
$934$	3.07469e10	+	5.32552e10i	0.0404030	+	0.0699801i
$935$		−	8.57555e11i		−	1.12206i
$936$		0			0
$937$	−1.19514e11			−0.155046			−0.0775232	−	0.996991i	$-0.524701\pi$
$937$	−1.19514e11			−0.155046			−0.0775232	+	0.996991i	$0.524701\pi$
$938$	−6.19739e10	+	3.57806e10i	−0.0800566	+	0.0462207i
$939$		0			0
$940$	8.27929e11	−	1.43402e12i	1.06043	−	1.83672i
$941$	4.72022e11	+	2.72522e11i	0.602010	+	0.347571i	0.769832	−	0.638247i	$-0.220340\pi$
$941$	4.72022e11	+	2.72522e11i	0.602010	+	0.347571i	−0.167822	+	0.985817i	$0.553673\pi$
$942$		0			0
$943$	−3.45980e10	−	5.99255e10i	−0.0437526	−	0.0757817i
$944$		−	6.17590e11i		−	0.777700i
$945$		0			0
$946$	8.67892e10			0.108368
$947$	−8.11905e11	+	4.68754e11i	−1.00950	+	0.582834i	−0.911045	−	0.412308i	$-0.864723\pi$
$947$	−8.11905e11	+	4.68754e11i	−1.00950	+	0.582834i	−0.0984531	+	0.995142i	$0.531389\pi$
$948$		0			0
$949$	−8.31310e10	+	1.43987e11i	−0.102494	+	0.177525i
$950$	2.75740e10	+	1.59199e10i	0.0338537	+	0.0195454i
$951$		0			0
$952$	−5.02380e10	−	8.70148e10i	−0.0611624	−	0.105936i
$953$			6.35142e11i			0.770015i	0.922913	+	0.385008i	$0.125801\pi$
$953$			6.35142e11i			0.770015i	−0.922913	+	0.385008i	$0.874199\pi$
$954$		0			0
$955$	−6.66973e11			−0.801853
$956$	3.69183e11	−	2.13148e11i	0.441988	−	0.255182i
$957$		0			0
$958$	−2.39846e10	+	4.15426e10i	−0.0284755	+	0.0493210i
$959$	−5.87446e11	−	3.39162e11i	−0.694534	−	0.400989i
$960$		0			0
$961$	4.12700e11	+	7.14817e11i	0.483883	+	0.838111i
$962$		−	3.19430e10i		−	0.0372972i
$963$		0			0
$964$	−1.22627e11			−0.141996
$965$	−1.17906e11	+	6.80729e10i	−0.135965	+	0.0784992i
$966$		0			0
$967$	−4.94231e10	+	8.56034e10i	−0.0565229	+	0.0979005i	−0.892902	−	0.450250i	$-0.851335\pi$
$967$	−4.94231e10	+	8.56034e10i	−0.0565229	+	0.0979005i	0.836379	+	0.548151i	$0.184668\pi$
$968$	−1.76390e11	−	1.01839e11i	−0.200897	−	0.115988i
$969$		0			0
$970$	5.07537e10	+	8.79079e10i	0.0573298	+	0.0992981i
$971$			2.77838e11i			0.312546i	0.987714	+	0.156273i	$0.0499480\pi$
$971$			2.77838e11i			0.312546i	−0.987714	+	0.156273i	$0.950052\pi$
$972$		0			0
$973$	9.77826e9			0.0109096
$974$	−1.39711e11	+	8.06621e10i	−0.155237	+	0.0896259i
$975$		0			0
$976$	−1.93996e11	+	3.36011e11i	−0.213793	+	0.370300i
$977$	1.06001e12	+	6.11996e11i	1.16341	+	0.671693i	0.952118	−	0.305731i	$-0.0989009\pi$
$977$	1.06001e12	+	6.11996e11i	1.16341	+	0.671693i	0.211288	+	0.977424i	$0.432234\pi$
$978$		0			0
$979$	−9.39923e11	−	1.62799e12i	−1.02320	−	1.77224i
$980$			1.25197e11i			0.135734i
$981$		0			0
$982$	−1.28119e11			−0.137774
$983$	−1.46935e12	+	8.48329e11i	−1.57366	+	0.908553i	−0.577946	+	0.816075i	$0.696146\pi$
$983$	−1.46935e12	+	8.48329e11i	−1.57366	+	0.908553i	−0.995715	+	0.0924783i	$0.970521\pi$
$984$		0			0
$985$	−1.19400e11	+	2.06806e11i	−0.126840	+	0.219694i
$986$	−2.58596e10	−	1.49300e10i	−0.0273598	−	0.0157962i
$987$		0			0
$988$	4.96018e11	+	8.59128e11i	0.520558	+	0.901633i
$989$		−	4.28283e10i		−	0.0447657i
$990$		0			0
$991$	−1.54307e11			−0.159990			−0.0799949	−	0.996795i	$-0.525490\pi$
$991$	−1.54307e11			−0.159990			−0.0799949	+	0.996795i	$0.525490\pi$
$992$	−4.32309e10	+	2.49594e10i	−0.0446424	+	0.0257743i
$993$		0			0
$994$	3.63777e10	−	6.30081e10i	0.0372641	−	0.0645433i
$995$	1.05560e12	+	6.09453e11i	1.07698	+	0.621796i
$996$		0			0
$997$	−8.00414e9	−	1.38636e10i	−0.00810091	−	0.0140312i	0.861947	−	0.506999i	$-0.169245\pi$
$997$	−8.00414e9	−	1.38636e10i	−0.00810091	−	0.0140312i	−0.870047	+	0.492968i	$0.835912\pi$
$998$		−	1.04856e11i		−	0.105699i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.9.d.a.17.4		14
3.2	odd	2		9.9.d.a.5.4	yes	14
4.3	odd	2		432.9.q.a.17.6		14
9.2	odd	6	inner	27.9.d.a.8.4		14
9.4	even	3		81.9.b.a.80.7		14
9.5	odd	6		81.9.b.a.80.8		14
9.7	even	3		9.9.d.a.2.4	✓	14
12.11	even	2		144.9.q.a.113.5		14
36.7	odd	6		144.9.q.a.65.5		14
36.11	even	6		432.9.q.a.305.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.9.d.a.2.4	✓	14	9.7	even	3
9.9.d.a.5.4	yes	14	3.2	odd	2
27.9.d.a.8.4		14	9.2	odd	6	inner
27.9.d.a.17.4		14	1.1	even	1	trivial
81.9.b.a.80.7		14	9.4	even	3
81.9.b.a.80.8		14	9.5	odd	6
144.9.q.a.65.5		14	36.7	odd	6
144.9.q.a.113.5		14	12.11	even	2
432.9.q.a.17.6		14	4.3	odd	2
432.9.q.a.305.6		14	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.34294 + 0.775344i) q^{2} +(-126.798 + 219.620i) q^{4} +(604.549 + 349.037i) q^{5} +(-1124.45 - 1947.61i) q^{7} -790.223i q^{8} +O(q^{10})\)	\(q+(-1.34294 + 0.775344i) q^{2} +(-126.798 + 219.620i) q^{4} +(604.549 + 349.037i) q^{5} +(-1124.45 - 1947.61i) q^{7} -790.223i q^{8} -1082.49 q^{10} +(-18817.0 + 10864.0i) q^{11} +(-9209.84 + 15951.9i) q^{13} +(3020.14 + 1743.68i) q^{14} +(-31847.5 - 55161.5i) q^{16} +56538.1i q^{17} -212375. q^{19} +(-153311. + 88514.1i) q^{20} +(16846.7 - 29179.3i) q^{22} +(-14399.3 - 8313.41i) q^{23} +(48340.5 + 83728.3i) q^{25} -28563.2i q^{26} +570313. q^{28} +(294955. - 170292. i) q^{29} +(-82902.7 + 143592. i) q^{31} +(260733. + 150534. i) q^{32} +(-43836.4 - 75926.9i) q^{34} -1.56990e6i q^{35} +1.11833e6 q^{37} +(285206. - 164664. i) q^{38} +(275817. - 477729. i) q^{40} +(3.60414e6 + 2.08085e6i) q^{41} +(1.28793e6 + 2.23075e6i) q^{43} -5.51012e6i q^{44} +25783.0 q^{46} +(-8.10049e6 + 4.67682e6i) q^{47} +(353608. - 612466. i) q^{49} +(-129836. - 74961.1i) q^{50} +(-2.33557e6 - 4.04533e6i) q^{52} +4.75879e6i q^{53} -1.51677e7 q^{55} +(-1.53905e6 + 888570. i) q^{56} +(-264070. + 457383. i) q^{58} +(8.39702e6 + 4.84802e6i) q^{59} +(-3.04570e6 - 5.27531e6i) q^{61} -257113. i q^{62} +1.58391e7 q^{64} +(-1.11356e7 + 6.42914e6i) q^{65} +(-1.02601e7 + 1.77710e7i) q^{67} +(-1.24169e7 - 7.16890e6i) q^{68} +(1.21721e6 + 2.10828e6i) q^{70} -2.08627e7i q^{71} +9.02632e6 q^{73} +(-1.50184e6 + 867089. i) q^{74} +(2.69287e7 - 4.66418e7i) q^{76} +(4.23177e7 + 2.44321e7i) q^{77} +(1.67238e7 + 2.89665e7i) q^{79} -4.44638e7i q^{80} -6.45351e6 q^{82} +(5.09741e7 - 2.94299e7i) q^{83} +(-1.97339e7 + 3.41800e7i) q^{85} +(-3.45920e6 - 1.99717e6i) q^{86} +(8.58499e6 + 1.48696e7i) q^{88} +8.65172e7i q^{89} +4.14242e7 q^{91} +(3.65158e6 - 2.10824e6i) q^{92} +(7.25229e6 - 1.25613e7i) q^{94} +(-1.28391e8 - 7.41267e7i) q^{95} +(-4.68859e7 - 8.12087e7i) q^{97} +1.09667e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{2} + 767 q^{4} - 438 q^{5} + 922 q^{7}+O(q^{10}) \) 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

Representations

Groups

Database

Properties

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