LMFDB - Embedded newform 27.8.c.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,8,Mod(10,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("27.10");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	27.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.43439568807$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 375 x^{10} - 1820 x^{9} + 50808 x^{8} - 192378 x^{7} + 3002887 x^{6} + \cdots + 754412211 $ x^12 - 6x^11 + 375x^10 - 1820x^9 + 50808x^8 - 192378x^7 + 3002887x^6 - 8342916x^5 + 72369348x^4 - 131054670x^3 + 513267363x^2 - 449098992*x + 754412211
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{21} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			19.2
Root			$0.500000 - 9.08282i$ of defining polynomial
Character	$\chi$	$=$	27.19
Dual form			27.8.c.a.10.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.11595 + 12.3252i) q^{2} +(-37.2735 - 64.5595i) q^{4} +(145.304 + 251.673i) q^{5} +(-555.940 + 962.916i) q^{7} -760.739 q^{8} +O(q^{10})$	\(q+(-7.11595 + 12.3252i) q^{2} +(-37.2735 - 64.5595i) q^{4} +(145.304 + 251.673i) q^{5} +(-555.940 + 962.916i) q^{7} -760.739 q^{8} -4135.89 q^{10} +(2245.36 - 3889.07i) q^{11} +(-1218.29 - 2110.14i) q^{13} +(-7912.08 - 13704.1i) q^{14} +(10184.4 - 17639.9i) q^{16} -15905.4 q^{17} -49949.6 q^{19} +(10831.9 - 18761.5i) q^{20} +(31955.7 + 55348.9i) q^{22} +(34692.5 + 60089.2i) q^{23} +(-3163.73 + 5479.74i) q^{25} +34677.2 q^{26} +82887.2 q^{28} +(-47035.8 + 81468.4i) q^{29} +(9963.58 + 17257.4i) q^{31} +(96255.8 + 166720. i) q^{32} +(113182. - 196037. i) q^{34} -323120. q^{35} +331750. q^{37} +(355439. - 615638. i) q^{38} +(-110538. - 191457. i) q^{40} +(121133. + 209809. i) q^{41} +(-415713. + 720036. i) q^{43} -334769. q^{44} -987481. q^{46} +(-80005.3 + 138573. i) q^{47} +(-206366. - 357437. i) q^{49} +(-45025.8 - 77987.1i) q^{50} +(-90819.7 + 157304. i) q^{52} -311589. q^{53} +1.30503e6 q^{55} +(422925. - 732527. i) q^{56} +(-669408. - 1.15945e6i) q^{58} +(-156177. - 270506. i) q^{59} +(28723.9 - 49751.3i) q^{61} -283601. q^{62} -132603. q^{64} +(354044. - 613221. i) q^{65} +(2.05100e6 + 3.55243e6i) q^{67} +(592849. + 1.02684e6i) q^{68} +(2.29930e6 - 3.98251e6i) q^{70} +403110. q^{71} -823496. q^{73} +(-2.36072e6 + 4.08889e6i) q^{74} +(1.86180e6 + 3.22472e6i) q^{76} +(2.49656e6 + 4.32418e6i) q^{77} +(-489414. + 847689. i) q^{79} +5.91931e6 q^{80} -3.44791e6 q^{82} +(-1.85204e6 + 3.20782e6i) q^{83} +(-2.31111e6 - 4.00296e6i) q^{85} +(-5.91638e6 - 1.02475e7i) q^{86} +(-1.70813e6 + 2.95857e6i) q^{88} -2.09023e6 q^{89} +2.70918e6 q^{91} +(2.58622e6 - 4.47947e6i) q^{92} +(-1.13863e6 - 1.97216e6i) q^{94} +(-7.25786e6 - 1.25710e7i) q^{95} +(-1.75125e6 + 3.03325e6i) q^{97} +5.87396e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8}+O(q^{10}) $ 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8	\( 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8} + 252 q^{10} + 8460 q^{11} - 1848 q^{13} + 16272 q^{14} - 12417 q^{16} - 30564 q^{17} + 24432 q^{19} + 40788 q^{20} - 35001 q^{22} + 51588 q^{23} + 4746 q^{25} - 536472 q^{26} + 75516 q^{28} + 414648 q^{29} + 8196 q^{31} + 1048977 q^{32} - 106623 q^{34} - 2210616 q^{35} + 139344 q^{37} + 1952685 q^{38} + 305496 q^{40} + 1731582 q^{41} + 408372 q^{43} - 5169114 q^{44} - 1684008 q^{46} + 1631484 q^{47} - 179010 q^{49} + 1654461 q^{50} + 681594 q^{52} - 2835648 q^{53} - 16056 q^{55} + 1784466 q^{56} - 948384 q^{58} + 2055636 q^{59} - 2723196 q^{61} + 1026828 q^{62} + 7178178 q^{64} + 1387620 q^{65} + 3806556 q^{67} - 2142639 q^{68} + 953442 q^{70} - 2408400 q^{71} - 10670052 q^{73} - 9846504 q^{74} - 6727827 q^{76} - 3478824 q^{77} + 6020916 q^{79} + 38072448 q^{80} + 9403002 q^{82} - 9605052 q^{83} - 1698624 q^{85} - 34278561 q^{86} - 16459029 q^{88} + 24630264 q^{89} + 13570104 q^{91} - 39143394 q^{92} + 12602808 q^{94} - 10422072 q^{95} + 9977226 q^{97} + 95833314 q^{98}+O(q^{100}) \) 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8 + 252 * q^10 + 8460 * q^11 - 1848 * q^13 + 16272 * q^14 - 12417 * q^16 - 30564 * q^17 + 24432 * q^19 + 40788 * q^20 - 35001 * q^22 + 51588 * q^23 + 4746 * q^25 - 536472 * q^26 + 75516 * q^28 + 414648 * q^29 + 8196 * q^31 + 1048977 * q^32 - 106623 * q^34 - 2210616 * q^35 + 139344 * q^37 + 1952685 * q^38 + 305496 * q^40 + 1731582 * q^41 + 408372 * q^43 - 5169114 * q^44 - 1684008 * q^46 + 1631484 * q^47 - 179010 * q^49 + 1654461 * q^50 + 681594 * q^52 - 2835648 * q^53 - 16056 * q^55 + 1784466 * q^56 - 948384 * q^58 + 2055636 * q^59 - 2723196 * q^61 + 1026828 * q^62 + 7178178 * q^64 + 1387620 * q^65 + 3806556 * q^67 - 2142639 * q^68 + 953442 * q^70 - 2408400 * q^71 - 10670052 * q^73 - 9846504 * q^74 - 6727827 * q^76 - 3478824 * q^77 + 6020916 * q^79 + 38072448 * q^80 + 9403002 * q^82 - 9605052 * q^83 - 1698624 * q^85 - 34278561 * q^86 - 16459029 * q^88 + 24630264 * q^89 + 13570104 * q^91 - 39143394 * q^92 + 12602808 * q^94 - 10422072 * q^95 + 9977226 * q^97 + 95833314 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−7.11595	+	12.3252i	−0.628967	+	1.08940i	0.358792	+	0.933417i	$0.383189\pi$
$2$	−7.11595	+	12.3252i	−0.628967	+	1.08940i	−0.987759	+	0.155985i	$0.950145\pi$
$3$		0			0
$3$		0			0
$4$	−37.2735	−	64.5595i	−0.291199	−	0.504371i
$5$	145.304	+	251.673i	0.519854	+	0.900413i	0.999734	+	0.0230788i	$0.00734688\pi$
$5$	145.304	+	251.673i	0.519854	+	0.900413i	−0.479880	+	0.877334i	$0.659320\pi$
$6$		0			0
$7$	−555.940	+	962.916i	−0.612611	+	1.06107i	0.378188	+	0.925729i	$0.376547\pi$
$7$	−555.940	+	962.916i	−0.612611	+	1.06107i	−0.990799	+	0.135344i	$0.956786\pi$
$8$	−760.739			−0.525316
$9$		0			0
$10$	−4135.89			−1.30788
$11$	2245.36	−	3889.07i	0.508640	−	0.880991i	−0.491310	−	0.870985i	$-0.663482\pi$
$11$	2245.36	−	3889.07i	0.508640	−	0.880991i	0.999950	−	0.0100060i	$-0.00318506\pi$
$12$		0			0
$13$	−1218.29	−	2110.14i	−0.153797	−	0.266385i	0.778823	−	0.627244i	$-0.215817\pi$
$13$	−1218.29	−	2110.14i	−0.153797	−	0.266385i	−0.932620	+	0.360859i	$0.882484\pi$
$14$	−7912.08	−	13704.1i	−0.770624	−	1.33476i
$15$		0			0
$16$	10184.4	−	17639.9i	0.621605	−	1.07665i
$17$	−15905.4			−0.785187			−0.392593	−	0.919712i	$-0.628422\pi$
$17$	−15905.4			−0.785187			−0.392593	+	0.919712i	$0.628422\pi$
$18$		0			0
$19$	−49949.6			−1.67069			−0.835343	−	0.549730i	$-0.814731\pi$
$19$	−49949.6			−1.67069			−0.835343	+	0.549730i	$0.814731\pi$
$20$	10831.9	−	18761.5i	0.302762	−	0.524399i
$21$		0			0
$22$	31955.7	+	55348.9i	0.639836	+	1.10823i
$23$	34692.5	+	60089.2i	0.594550	+	1.02979i	0.993610	+	0.112867i	$0.0360033\pi$
$23$	34692.5	+	60089.2i	0.594550	+	1.02979i	−0.399060	+	0.916925i	$0.630663\pi$
$24$		0			0
$25$	−3163.73	+	5479.74i	−0.0404957	+	0.0701406i
$26$	34677.2			0.386934
$27$		0			0
$28$	82887.2			0.713566
$29$	−47035.8	+	81468.4i	−0.358126	+	0.620292i	−0.987648	−	0.156691i	$-0.949917\pi$
$29$	−47035.8	+	81468.4i	−0.358126	+	0.620292i	0.629522	+	0.776983i	$0.283251\pi$
$30$		0			0
$31$	9963.58	+	17257.4i	0.0600689	+	0.104042i	0.894496	−	0.447076i	$-0.147535\pi$
$31$	9963.58	+	17257.4i	0.0600689	+	0.104042i	−0.834427	+	0.551118i	$0.814201\pi$
$32$	96255.8	+	166720.i	0.519280	+	0.899420i
$33$		0			0
$34$	113182.	−	196037.i	0.493857	−	0.855385i
$35$	−323120.			−1.27387
$36$		0			0
$37$	331750.			1.07673			0.538363	−	0.842713i	$-0.319043\pi$
$37$	331750.			1.07673			0.538363	+	0.842713i	$0.319043\pi$
$38$	355439.	−	615638.i	1.05081	−	1.82005i
$39$		0			0
$40$	−110538.	−	191457.i	−0.273087	−	0.473001i
$41$	121133.	+	209809.i	0.274486	+	0.475423i	0.970005	−	0.243084i	$-0.0781591\pi$
$41$	121133.	+	209809.i	0.274486	+	0.475423i	−0.695520	+	0.718507i	$0.744826\pi$
$42$		0			0
$43$	−415713.	+	720036.i	−0.797359	+	1.38107i	0.123971	+	0.992286i	$0.460437\pi$
$43$	−415713.	+	720036.i	−0.797359	+	1.38107i	−0.921330	+	0.388781i	$0.872896\pi$
$44$	−334769.			−0.592462
$45$		0			0
$46$	−987481.			−1.49581
$47$	−80005.3	+	138573.i	−0.112403	+	0.194687i	−0.916738	−	0.399488i	$-0.869188\pi$
$47$	−80005.3	+	138573.i	−0.112403	+	0.194687i	0.804336	+	0.594175i	$0.202521\pi$
$48$		0			0
$49$	−206366.	−	357437.i	−0.250583	−	0.434023i
$50$	−45025.8	−	77987.1i	−0.0509409	−	0.0882323i
$51$		0			0
$52$	−90819.7	+	157304.i	−0.0895712	+	0.155142i
$53$	−311589.			−0.287486			−0.143743	−	0.989615i	$-0.545914\pi$
$53$	−311589.			−0.287486			−0.143743	+	0.989615i	$0.545914\pi$
$54$		0			0
$55$	1.30503e6			1.05767
$56$	422925.	−	732527.i	0.321814	−	0.557398i
$57$		0			0
$58$	−669408.	−	1.15945e6i	−0.450498	−	0.780286i
$59$	−156177.	−	270506.i	−0.0989997	−	0.171473i	0.812271	−	0.583280i	$-0.198231\pi$
$59$	−156177.	−	270506.i	−0.0989997	−	0.171473i	−0.911271	+	0.411807i	$0.864898\pi$
$60$		0			0
$61$	28723.9	−	49751.3i	0.0162028	−	0.0280640i	−0.857810	−	0.513966i	$-0.828176\pi$
$61$	28723.9	−	49751.3i	0.0162028	−	0.0280640i	0.874013	+	0.485902i	$0.161509\pi$
$62$	−283601.			−0.151125
$63$		0			0
$64$	−132603.			−0.0632302
$65$	354044.	−	613221.i	0.159904	−	0.276962i
$66$		0			0
$67$	2.05100e6	+	3.55243e6i	0.833111	+	1.44299i	0.895559	+	0.444943i	$0.146776\pi$
$67$	2.05100e6	+	3.55243e6i	0.833111	+	1.44299i	−0.0624478	+	0.998048i	$0.519891\pi$
$68$	592849.	+	1.02684e6i	0.228646	+	0.396026i
$69$		0			0
$70$	2.29930e6	−	3.98251e6i	0.801223	−	1.38776i
$71$	403110.			0.133666			0.0668328	−	0.997764i	$-0.478711\pi$
$71$	403110.			0.133666			0.0668328	+	0.997764i	$0.478711\pi$
$72$		0			0
$73$	−823496.			−0.247760			−0.123880	−	0.992297i	$-0.539534\pi$
$73$	−823496.			−0.247760			−0.123880	+	0.992297i	$0.539534\pi$
$74$	−2.36072e6	+	4.08889e6i	−0.677226	+	1.17299i
$75$		0			0
$76$	1.86180e6	+	3.22472e6i	0.486502	+	0.842646i
$77$	2.49656e6	+	4.32418e6i	0.623197	+	1.07941i
$78$		0			0
$79$	−489414.	+	847689.i	−0.111682	+	0.193438i	−0.916448	−	0.400153i	$-0.868957\pi$
$79$	−489414.	+	847689.i	−0.111682	+	0.193438i	0.804767	+	0.593591i	$0.202290\pi$
$80$	5.91931e6			1.29258
$81$		0			0
$82$	−3.44791e6			−0.690569
$83$	−1.85204e6	+	3.20782e6i	−0.355530	+	0.615796i	−0.987209	−	0.159434i	$-0.949033\pi$
$83$	−1.85204e6	+	3.20782e6i	−0.355530	+	0.615796i	0.631678	+	0.775231i	$0.282366\pi$
$84$		0			0
$85$	−2.31111e6	−	4.00296e6i	−0.408182	−	0.706993i
$86$	−5.91638e6	−	1.02475e7i	−1.00303	−	1.73729i
$87$		0			0
$88$	−1.70813e6	+	2.95857e6i	−0.267197	+	0.462799i
$89$	−2.09023e6			−0.314289			−0.157145	−	0.987576i	$-0.550229\pi$
$89$	−2.09023e6			−0.314289			−0.157145	+	0.987576i	$0.550229\pi$
$90$		0			0
$91$	2.70918e6			0.376872
$92$	2.58622e6	−	4.47947e6i	0.346265	−	0.599748i
$93$		0			0
$94$	−1.13863e6	−	1.97216e6i	−0.141395	−	0.244903i
$95$	−7.25786e6	−	1.25710e7i	−0.868512	−	1.50431i
$96$		0			0
$97$	−1.75125e6	+	3.03325e6i	−0.194826	+	0.337448i	−0.946843	−	0.321695i	$-0.895747\pi$
$97$	−1.75125e6	+	3.03325e6i	−0.194826	+	0.337448i	0.752018	+	0.659143i	$0.229081\pi$
$98$	5.87396e6			0.630435
$99$		0			0
$100$	471692.			0.0471692
$101$	277361.	−	480403.i	0.0267868	−	0.0463960i	−0.852321	−	0.523019i	$-0.824806\pi$
$101$	277361.	−	480403.i	0.0267868	−	0.0463960i	0.879108	+	0.476623i	$0.158139\pi$
$102$		0			0
$103$	−1.01746e7	−	1.76229e7i	−0.917459	−	1.58909i	−0.803260	−	0.595628i	$-0.796903\pi$
$103$	−1.01746e7	−	1.76229e7i	−0.917459	−	1.58909i	−0.114199	−	0.993458i	$-0.536430\pi$
$104$	926800.	+	1.60527e6i	0.0807922	+	0.139936i
$105$		0			0
$106$	2.21725e6	−	3.84039e6i	0.180819	−	0.313188i
$107$	−6.49941e6			−0.512897			−0.256449	−	0.966558i	$-0.582552\pi$
$107$	−6.49941e6			−0.512897			−0.256449	+	0.966558i	$0.582552\pi$
$108$		0			0
$109$	2.79312e6			0.206584			0.103292	−	0.994651i	$-0.467062\pi$
$109$	2.79312e6			0.206584			0.103292	+	0.994651i	$0.467062\pi$
$110$	−9.28655e6	+	1.60848e7i	−0.665242	+	1.15223i
$111$		0			0
$112$	1.13238e7	+	1.96134e7i	0.761604	+	1.31914i
$113$	1.04172e7	+	1.80431e7i	0.679167	+	1.17635i	0.975232	+	0.221184i	$0.0709922\pi$
$113$	1.04172e7	+	1.80431e7i	0.679167	+	1.17635i	−0.296065	+	0.955168i	$0.595674\pi$
$114$		0			0
$115$	−1.00819e7	+	1.74624e7i	−0.618158	+	1.07068i
$116$	7.01274e6			0.417143
$117$		0			0
$118$	4.44538e6			0.249070
$119$	8.84244e6	−	1.53155e7i	0.481014	−	0.833140i
$120$		0			0
$121$	−339665.	−	588316.i	−0.0174302	−	0.0301899i
$122$	408796.	+	708055.i	0.0203820	+	0.0353027i
$123$		0			0
$124$	742754.	−	1.28649e6i	0.0349840	−	0.0605940i
$125$	2.08649e7			0.955500
$126$		0			0
$127$	8.89911e6			0.385508			0.192754	−	0.981247i	$-0.438258\pi$
$127$	8.89911e6			0.385508			0.192754	+	0.981247i	$0.438258\pi$
$128$	−1.13771e7	+	1.97058e7i	−0.479511	+	0.830537i
$129$		0			0
$130$	5.03871e6	+	8.72731e6i	0.201149	+	0.348400i
$131$	6.35869e6	+	1.10136e7i	0.247126	+	0.428034i	0.962727	−	0.270475i	$-0.0871806\pi$
$131$	6.35869e6	+	1.10136e7i	0.247126	+	0.428034i	−0.715601	+	0.698509i	$0.753847\pi$
$132$		0			0
$133$	2.77690e7	−	4.80973e7i	1.02348	−	1.77272i
$134$	−5.83791e7			−2.09600
$135$		0			0
$136$	1.20998e7			0.412471
$137$	2.45052e7	−	4.24442e7i	0.814209	−	1.41025i	−0.0956855	−	0.995412i	$-0.530504\pi$
$137$	2.45052e7	−	4.24442e7i	0.814209	−	1.41025i	0.909895	−	0.414840i	$-0.136162\pi$
$138$		0			0
$139$	789537.	+	1.36752e6i	0.0249357	+	0.0431898i	0.878224	−	0.478250i	$-0.158729\pi$
$139$	789537.	+	1.36752e6i	0.0249357	+	0.0431898i	−0.853288	+	0.521439i	$0.825395\pi$
$140$	1.20438e7	+	2.08605e7i	0.370950	+	0.642504i
$141$		0			0
$142$	−2.86851e6	+	4.96841e6i	−0.0840713	+	0.145616i
$143$	−1.09420e7			−0.312910
$144$		0			0
$145$	−2.73379e7			−0.744692
$146$	5.85996e6	−	1.01497e7i	0.155833	−	0.269911i
$147$		0			0
$148$	−1.23655e7	−	2.14177e7i	−0.313542	−	0.543070i
$149$	−1.95734e7	−	3.39021e7i	−0.484746	−	0.839605i	0.515100	−	0.857130i	$-0.327755\pi$
$149$	−1.95734e7	−	3.39021e7i	−0.484746	−	0.839605i	−0.999846	+	0.0175249i	$0.994421\pi$
$150$		0			0
$151$	−9.19094e6	+	1.59192e7i	−0.217240	+	0.376271i	−0.953963	−	0.299923i	$-0.903039\pi$
$151$	−9.19094e6	+	1.59192e7i	−0.217240	+	0.376271i	0.736723	+	0.676195i	$0.236372\pi$
$152$	3.79986e7			0.877638
$153$		0			0
$154$	−7.10617e7			−1.56788
$155$	−2.89549e6	+	5.01513e6i	−0.0624540	+	0.108174i
$156$		0			0
$157$	3.32168e7	+	5.75332e7i	0.685029	+	1.18650i	0.973428	+	0.228994i	$0.0735437\pi$
$157$	3.32168e7	+	5.75332e7i	0.685029	+	1.18650i	−0.288399	+	0.957510i	$0.593123\pi$
$158$	−6.96529e6	−	1.20642e7i	−0.140488	−	0.243332i
$159$		0			0
$160$	−2.79726e7	+	4.84500e7i	−0.539900	+	0.935134i
$161$	−7.71478e7			−1.45691
$162$		0			0
$163$	−3.94682e7			−0.713823			−0.356912	−	0.934138i	$-0.616170\pi$
$163$	−3.94682e7			−0.713823			−0.356912	+	0.934138i	$0.616170\pi$
$164$	9.03010e6	−	1.56406e7i	0.159860	−	0.276885i
$165$		0			0
$166$	−2.63580e7	−	4.56534e7i	−0.447234	−	0.774631i
$167$	4.86177e7	+	8.42084e7i	0.807769	+	1.39910i	0.914406	+	0.404799i	$0.132658\pi$
$167$	4.86177e7	+	8.42084e7i	0.807769	+	1.39910i	−0.106637	+	0.994298i	$0.534008\pi$
$168$		0			0
$169$	2.84058e7	−	4.92003e7i	0.452693	−	0.784087i
$170$	6.57829e7			1.02693
$171$		0			0
$172$	6.19802e7			0.928760
$173$	2.77015e7	−	4.79804e7i	0.406763	−	0.704534i	−0.587762	−	0.809034i	$-0.699991\pi$
$173$	2.77015e7	−	4.79804e7i	0.406763	−	0.704534i	0.994525	+	0.104500i	$0.0333242\pi$
$174$		0			0
$175$	−3.51768e6	−	6.09281e6i	−0.0496162	−	0.0859378i
$176$	−4.57351e7	−	7.92156e7i	−0.632347	−	1.09526i
$177$		0			0
$178$	1.48740e7	−	2.57625e7i	0.197678	−	0.342388i
$179$	−9.87173e7			−1.28649			−0.643247	−	0.765659i	$-0.722413\pi$
$179$	−9.87173e7			−1.28649			−0.643247	+	0.765659i	$0.722413\pi$
$180$		0			0
$181$	9.03305e7			1.13230			0.566148	−	0.824304i	$-0.308433\pi$
$181$	9.03305e7			1.13230			0.566148	+	0.824304i	$0.308433\pi$
$182$	−1.92784e7	+	3.33912e7i	−0.237040	+	0.410565i
$183$		0			0
$184$	−2.63920e7	−	4.57122e7i	−0.312327	−	0.540966i
$185$	4.82045e7	+	8.34927e7i	0.559740	+	0.969499i
$186$		0			0
$187$	−3.57133e7	+	6.18572e7i	−0.399378	+	0.691743i
$188$	1.19283e7			0.130926
$189$		0			0
$190$	2.06586e8			2.18506
$191$	−5.20912e7	+	9.02247e7i	−0.540938	+	0.936933i	0.457912	+	0.888998i	$0.348597\pi$
$191$	−5.20912e7	+	9.02247e7i	−0.540938	+	0.936933i	−0.998850	+	0.0479353i	$0.984736\pi$
$192$		0			0
$193$	−6.65147e6	−	1.15207e7i	−0.0665989	−	0.115353i	0.830803	−	0.556566i	$-0.187881\pi$
$193$	−6.65147e6	−	1.15207e7i	−0.0665989	−	0.115353i	−0.897402	+	0.441214i	$0.854548\pi$
$194$	−2.49236e7	−	4.31689e7i	−0.245078	−	0.424487i
$195$		0			0
$196$	−1.53840e7	+	2.66458e7i	−0.145939	+	0.252774i
$197$	1.71308e8			1.59641			0.798206	−	0.602384i	$-0.205783\pi$
$197$	1.71308e8			1.59641			0.798206	+	0.602384i	$0.205783\pi$
$198$		0			0
$199$	−1.24021e8			−1.11561			−0.557803	−	0.829974i	$-0.688355\pi$
$199$	−1.24021e8			−1.11561			−0.557803	+	0.829974i	$0.688355\pi$
$200$	2.40677e6	−	4.16865e6i	0.0212730	−	0.0368460i
$201$		0			0
$202$	3.94737e6	+	6.83704e6i	0.0336960	+	0.0583631i
$203$	−5.22981e7	−	9.05830e7i	−0.438783	−	0.759994i
$204$		0			0
$205$	−3.52021e7	+	6.09719e7i	−0.285385	+	0.494301i
$206$	2.89608e8			2.30821
$207$		0			0
$208$	−4.96301e7			−0.382405
$209$	−1.12155e8	+	1.94258e8i	−0.849778	+	1.47186i
$210$		0			0
$211$	9.32487e7	+	1.61511e8i	0.683367	+	1.18363i	0.973947	+	0.226776i	$0.0728185\pi$
$211$	9.32487e7	+	1.61511e8i	0.683367	+	1.18363i	−0.290580	+	0.956851i	$0.593848\pi$
$212$	1.16140e7	+	2.01160e7i	0.0837156	+	0.145000i
$213$		0			0
$214$	4.62495e7	−	8.01064e7i	0.322596	−	0.558752i
$215$	−2.41618e8			−1.65804
$216$		0			0
$217$	−2.21566e7			−0.147195
$218$	−1.98757e7	+	3.44257e7i	−0.129935	+	0.225053i
$219$		0			0
$220$	−4.86431e7	−	8.42523e7i	−0.307994	−	0.533461i
$221$	1.93774e7	+	3.35626e7i	0.120760	+	0.209162i
$222$		0			0
$223$	2.10250e7	−	3.64164e7i	0.126961	−	0.219902i	−0.795537	−	0.605905i	$-0.792811\pi$
$223$	2.10250e7	−	3.64164e7i	0.126961	−	0.219902i	0.922498	+	0.386003i	$0.126144\pi$
$224$	−2.14050e8			−1.27247
$225$		0			0
$226$	−2.96513e8			−1.70869
$227$	1.56517e8	−	2.71095e8i	0.888117	−	1.53826i	0.0460190	−	0.998941i	$-0.485347\pi$
$227$	1.56517e8	−	2.71095e8i	0.888117	−	1.53826i	0.842098	−	0.539324i	$-0.181320\pi$
$228$		0			0
$229$	−8.35576e7	−	1.44726e8i	−0.459792	−	0.796384i	0.539157	−	0.842205i	$-0.318743\pi$
$229$	−8.35576e7	−	1.44726e8i	−0.459792	−	0.796384i	−0.998950	+	0.0458213i	$0.985410\pi$
$230$	−1.43485e8	−	2.48522e8i	−0.777602	−	1.34685i
$231$		0			0
$232$	3.57819e7	−	6.19761e7i	0.188129	−	0.325849i
$233$	2.55430e8			1.32290			0.661449	−	0.749990i	$-0.269942\pi$
$233$	2.55430e8			1.32290			0.661449	+	0.749990i	$0.269942\pi$
$234$		0			0
$235$	−4.65002e7			−0.233732
$236$	−1.16425e7	+	2.01654e7i	−0.0576572	+	0.0998652i
$237$		0			0
$238$	1.25845e8	+	2.17969e8i	0.605084	+	1.04804i
$239$	−8.84471e7	−	1.53195e8i	−0.419074	−	0.725858i	0.576772	−	0.816905i	$-0.304312\pi$
$239$	−8.84471e7	−	1.53195e8i	−0.419074	−	0.725858i	−0.995847	+	0.0910472i	$0.970979\pi$
$240$		0			0
$241$	1.56994e8	−	2.71922e8i	0.722478	−	1.25137i	−0.237526	−	0.971381i	$-0.576336\pi$
$241$	1.56994e8	−	2.71922e8i	0.722478	−	1.25137i	0.960004	−	0.279987i	$-0.0903303\pi$
$242$	9.66814e6			0.0438520
$243$		0			0
$244$	−4.28256e6			−0.0188729
$245$	5.99715e7	−	1.03874e8i	0.260533	−	0.451257i
$246$		0			0
$247$	6.08531e7	+	1.05401e8i	0.256947	+	0.445045i
$248$	−7.57968e6	−	1.31284e7i	−0.0315551	−	0.0546551i
$249$		0			0
$250$	−1.48473e8	+	2.57163e8i	−0.600978	+	1.04092i
$251$	−1.34891e8			−0.538425			−0.269212	−	0.963081i	$-0.586763\pi$
$251$	−1.34891e8			−0.538425			−0.269212	+	0.963081i	$0.586763\pi$
$252$		0			0
$253$	3.11588e8			1.20965
$254$	−6.33256e7	+	1.09683e8i	−0.242472	+	0.419974i
$255$		0			0
$256$	−1.70405e8	−	2.95150e8i	−0.634808	−	1.09952i
$257$	1.17761e8	+	2.03969e8i	0.432750	+	0.749545i	0.997109	−	0.0759845i	$-0.0242099\pi$
$257$	1.17761e8	+	2.03969e8i	0.432750	+	0.749545i	−0.564359	+	0.825529i	$0.690877\pi$
$258$		0			0
$259$	−1.84433e8	+	3.19448e8i	−0.659614	+	1.14249i
$260$	−5.27857e7			−0.186256
$261$		0			0
$262$	−1.80992e8			−0.621736
$263$	−8.33326e7	+	1.44336e8i	−0.282468	+	0.489249i	−0.971992	−	0.235014i	$-0.924487\pi$
$263$	−8.33326e7	+	1.44336e8i	−0.282468	+	0.489249i	0.689524	+	0.724263i	$0.257820\pi$
$264$		0			0
$265$	−4.52750e7	−	7.84186e7i	−0.149451	−	0.258856i
$266$	3.95205e8	+	6.84515e8i	1.28747	+	2.22996i
$267$		0			0
$268$	1.52895e8	−	2.64823e8i	0.485202	−	0.840395i
$269$	1.49508e8			0.468308			0.234154	−	0.972200i	$-0.424768\pi$
$269$	1.49508e8			0.468308			0.234154	+	0.972200i	$0.424768\pi$
$270$		0			0
$271$	3.02665e8			0.923783			0.461892	−	0.886936i	$-0.347171\pi$
$271$	3.02665e8			0.923783			0.461892	+	0.886936i	$0.347171\pi$
$272$	−1.61987e8	+	2.80569e8i	−0.488076	+	0.845373i
$273$		0			0
$274$	3.48755e8	+	6.04062e8i	1.02422	+	1.77400i
$275$	1.42074e7	+	2.46079e7i	0.0411955	+	0.0713527i
$276$		0			0
$277$	−1.63479e7	+	2.83153e7i	−0.0462148	+	0.0800465i	−0.888207	−	0.459443i	$-0.848049\pi$
$277$	−1.63479e7	+	2.83153e7i	−0.0462148	+	0.0800465i	0.841993	+	0.539489i	$0.181383\pi$
$278$	−2.24732e7			−0.0627348
$279$		0			0
$280$	2.45810e8			0.669185
$281$	2.50968e8	−	4.34689e8i	0.674755	−	1.16871i	−0.301786	−	0.953376i	$-0.597583\pi$
$281$	2.50968e8	−	4.34689e8i	0.674755	−	1.16871i	0.976540	−	0.215334i	$-0.0690840\pi$
$282$		0			0
$283$	−1.62635e8	−	2.81691e8i	−0.426541	−	0.738790i	0.570022	−	0.821629i	$-0.306935\pi$
$283$	−1.62635e8	−	2.81691e8i	−0.426541	−	0.738790i	−0.996563	+	0.0828391i	$0.973601\pi$
$284$	−1.50253e7	−	2.60246e7i	−0.0389233	−	0.0674171i
$285$		0			0
$286$	7.78626e7	−	1.34862e8i	0.196810	−	0.340885i
$287$	−2.69371e8			−0.672611
$288$		0			0
$289$	−1.57357e8			−0.383481
$290$	1.94535e8	−	3.36944e8i	0.468386	−	0.811269i
$291$		0			0
$292$	3.06945e7	+	5.31645e7i	0.0721475	+	0.124963i
$293$	−7.17572e7	−	1.24287e8i	−0.166659	−	0.288662i	0.770584	−	0.637338i	$-0.219965\pi$
$293$	−7.17572e7	−	1.24287e8i	−0.166659	−	0.288662i	−0.937243	+	0.348676i	$0.886631\pi$
$294$		0			0
$295$	4.53860e7	−	7.86109e7i	0.102931	−	0.178281i
$296$	−2.52375e8			−0.565622
$297$		0			0
$298$	5.57133e8			1.21956
$299$	8.45311e7	−	1.46412e8i	0.182881	−	0.316758i
$300$		0			0
$301$	−4.62223e8	−	8.00593e8i	−0.976941	−	1.69211i
$302$	−1.30805e8	−	2.26560e8i	−0.273274	−	0.473325i
$303$		0			0
$304$	−5.08706e8	+	8.81105e8i	−1.03851	+	1.79875i
$305$	1.66947e7			0.0336923
$306$		0			0
$307$	−6.60558e8			−1.30295			−0.651474	−	0.758671i	$-0.725849\pi$
$307$	−6.60558e8			−1.30295			−0.651474	+	0.758671i	$0.725849\pi$
$308$	1.86111e8	−	3.22354e8i	0.362949	−	0.628645i
$309$		0			0
$310$	−4.12083e7	−	7.13748e7i	−0.0785630	−	0.136075i
$311$	5.28703e7	+	9.15740e7i	0.0996667	+	0.172628i	0.911547	−	0.411197i	$-0.134889\pi$
$311$	5.28703e7	+	9.15740e7i	0.0996667	+	0.172628i	−0.811880	+	0.583824i	$0.801556\pi$
$312$		0			0
$313$	5.93605e7	−	1.02815e8i	0.109419	−	0.189519i	−0.806116	−	0.591757i	$-0.798434\pi$
$313$	5.93605e7	−	1.02815e8i	0.109419	−	0.189519i	0.915535	+	0.402238i	$0.131768\pi$
$314$	−9.45476e8			−1.72344
$315$		0			0
$316$	7.29686e7			0.130086
$317$	−2.17334e8	+	3.76434e8i	−0.383196	+	0.663715i	−0.991517	−	0.129976i	$-0.958510\pi$
$317$	−2.17334e8	+	3.76434e8i	−0.383196	+	0.663715i	0.608321	+	0.793691i	$0.291843\pi$
$318$		0			0
$319$	2.11224e8	+	3.65851e8i	0.364314	+	0.631011i
$320$	−1.92677e7	−	3.33727e7i	−0.0328705	−	0.0569333i
$321$		0			0
$322$	5.48980e8	−	9.50861e8i	0.916349	−	1.58716i
$323$	7.94468e8			1.31180
$324$		0			0
$325$	1.54173e7			0.0249125
$326$	2.80854e8	−	4.86453e8i	0.448971	−	0.777641i
$327$		0			0
$328$	−9.21507e7	−	1.59610e8i	−0.144192	−	0.249747i
$329$	−8.89563e7	−	1.54077e8i	−0.137718	−	0.238535i
$330$		0			0
$331$	−3.67129e8	+	6.35887e8i	−0.556444	+	0.963789i	0.441346	+	0.897337i	$0.354501\pi$
$331$	−3.67129e8	+	6.35887e8i	−0.556444	+	0.963789i	−0.997790	+	0.0664518i	$0.978832\pi$
$332$	2.76127e8			0.414120
$333$		0			0
$334$	−1.38385e9			−2.03224
$335$	−5.96034e8	+	1.03236e9i	−0.866192	+	1.50029i
$336$		0			0
$337$	2.35772e8	+	4.08370e8i	0.335574	+	0.581231i	0.983595	−	0.180391i	$-0.0577364\pi$
$337$	2.35772e8	+	4.08370e8i	0.335574	+	0.581231i	−0.648021	+	0.761622i	$0.724403\pi$
$338$	4.04268e8	+	7.00213e8i	0.569458	+	0.986329i
$339$		0			0
$340$	−1.72286e8	+	2.98408e8i	−0.237724	+	0.411751i
$341$	8.94871e7			0.122214
$342$		0			0
$343$	−4.56772e8			−0.611181
$344$	3.16249e8	−	5.47759e8i	0.418866	−	0.725496i
$345$		0			0
$346$	3.94244e8	+	6.82851e8i	0.511681	+	0.886257i
$347$	−5.53356e8	−	9.58441e8i	−0.710970	−	1.23144i	−0.964493	−	0.264107i	$-0.914923\pi$
$347$	−5.53356e8	−	9.58441e8i	−0.710970	−	1.23144i	0.253523	−	0.967329i	$-0.418411\pi$
$348$		0			0
$349$	3.98088e7	−	6.89509e7i	0.0501291	−	0.0868262i	−0.839872	−	0.542784i	$-0.817370\pi$
$349$	3.98088e7	−	6.89509e7i	0.0501291	−	0.0868262i	0.890001	+	0.455958i	$0.150703\pi$
$350$	1.00127e8			0.124828
$351$		0			0
$352$	8.64514e8			1.05651
$353$	−5.09107e7	+	8.81799e7i	−0.0616024	+	0.106698i	−0.895182	−	0.445701i	$-0.852954\pi$
$353$	−5.09107e7	+	8.81799e7i	−0.0616024	+	0.106698i	0.833579	+	0.552400i	$0.186288\pi$
$354$		0			0
$355$	5.85734e7	+	1.01452e8i	0.0694866	+	0.120354i
$356$	7.79102e7	+	1.34944e8i	0.0915207	+	0.158518i
$357$		0			0
$358$	7.02468e8	−	1.21671e9i	0.809162	−	1.40151i
$359$	−9.69307e7			−0.110568			−0.0552842	−	0.998471i	$-0.517606\pi$
$359$	−9.69307e7			−0.110568			−0.0552842	+	0.998471i	$0.517606\pi$
$360$		0			0
$361$	1.60109e9			1.79119
$362$	−6.42788e8	+	1.11334e9i	−0.712176	+	1.23353i
$363$		0			0
$364$	−1.00981e8	−	1.74903e8i	−0.109745	−	0.190083i
$365$	−1.19657e8	−	2.07252e8i	−0.128799	−	0.223086i
$366$		0			0
$367$	7.72007e8	−	1.33716e9i	0.815249	−	1.41205i	−0.0939003	−	0.995582i	$-0.529933\pi$
$367$	7.72007e8	−	1.33716e9i	0.815249	−	1.41205i	0.909149	−	0.416471i	$-0.136733\pi$
$368$	1.41329e9			1.47830
$369$		0			0
$370$	−1.37208e9			−1.40823
$371$	1.73225e8	−	3.00034e8i	0.176117	−	0.305043i
$372$		0			0
$373$	6.74772e8	+	1.16874e9i	0.673250	+	1.16610i	0.976977	+	0.213344i	$0.0684355\pi$
$373$	6.74772e8	+	1.16874e9i	0.673250	+	1.16610i	−0.303727	+	0.952759i	$0.598231\pi$
$374$	−5.08268e8	−	8.80345e8i	−0.502391	−	0.870167i
$375$		0			0
$376$	6.08632e7	−	1.05418e8i	0.0590469	−	0.102272i
$377$	2.29213e8			0.220315
$378$		0			0
$379$	1.61145e9			1.52048			0.760238	−	0.649645i	$-0.225082\pi$
$379$	1.61145e9			1.52048			0.760238	+	0.649645i	$0.225082\pi$
$380$	−5.41051e8	+	9.37127e8i	−0.505819	+	0.876105i
$381$		0			0
$382$	−7.41357e8	−	1.28407e9i	−0.680465	−	1.17860i
$383$	6.32119e8	+	1.09486e9i	0.574915	+	0.995781i	0.996051	+	0.0887840i	$0.0282981\pi$
$383$	6.32119e8	+	1.09486e9i	0.574915	+	0.995781i	−0.421136	+	0.906997i	$0.638369\pi$
$384$		0			0
$385$	−7.25519e8	+	1.25664e9i	−0.647942	+	1.12227i
$386$	1.89326e8			0.167554
$387$		0			0
$388$	2.61100e8			0.226932
$389$	−9.18665e8	+	1.59117e9i	−0.791286	+	1.37055i	0.133885	+	0.990997i	$0.457255\pi$
$389$	−9.18665e8	+	1.59117e9i	−0.791286	+	1.37055i	−0.925171	+	0.379551i	$0.876079\pi$
$390$		0			0
$391$	−5.51798e8	−	9.55743e8i	−0.466833	−	0.808579i
$392$	1.56991e8	+	2.71916e8i	0.131635	+	0.227999i
$393$		0			0
$394$	−1.21902e9	+	2.11140e9i	−1.00409	+	1.73914i
$395$	−2.84454e8			−0.232232
$396$		0			0
$397$	−1.85478e9			−1.48773			−0.743867	−	0.668327i	$-0.767011\pi$
$397$	−1.85478e9			−1.48773			−0.743867	+	0.668327i	$0.767011\pi$
$398$	8.82529e8	−	1.52859e9i	0.701679	−	1.21534i
$399$		0			0
$400$	6.44412e7	+	1.11615e8i	0.0503447	+	0.0871996i
$401$	−6.04284e8	−	1.04665e9i	−0.467989	−	0.810580i	0.531342	−	0.847157i	$-0.321688\pi$
$401$	−6.04284e8	−	1.04665e9i	−0.467989	−	0.810580i	−0.999331	+	0.0365770i	$0.988355\pi$
$402$		0			0
$403$	2.42770e7	−	4.20491e7i	0.0184769	−	0.0320029i
$404$	−4.13528e7			−0.0312011
$405$		0			0
$406$	1.48860e9			1.10392
$407$	7.44898e8	−	1.29020e9i	0.547667	−	0.948587i
$408$		0			0
$409$	6.10716e8	+	1.05779e9i	0.441375	+	0.764484i	0.997792	−	0.0664194i	$-0.0211575\pi$
$409$	6.10716e8	+	1.05779e9i	0.441375	+	0.764484i	−0.556417	+	0.830903i	$0.687824\pi$
$410$	−5.00993e8	−	8.67746e8i	−0.358995	−	0.621798i
$411$		0			0
$412$	−7.58485e8	+	1.31373e9i	−0.534326	+	0.925480i
$413$	3.47299e8			0.242593
$414$		0			0
$415$	−1.07643e9			−0.739295
$416$	2.34535e8	−	4.06226e8i	0.159728	−	0.276657i
$417$		0			0
$418$	−1.59617e9	−	2.76466e9i	−1.06896	−	1.85150i
$419$	7.60350e8	+	1.31697e9i	0.504969	+	0.874632i	0.999983	+	0.00574729i	$0.00182943\pi$
$419$	7.60350e8	+	1.31697e9i	0.504969	+	0.874632i	−0.495014	+	0.868885i	$0.664837\pi$
$420$		0			0
$421$	−5.43681e8	+	9.41684e8i	−0.355105	+	0.615060i	−0.987136	−	0.159883i	$-0.948888\pi$
$421$	−5.43681e8	+	9.41684e8i	−0.355105	+	0.615060i	0.632031	+	0.774943i	$0.282222\pi$
$422$	−2.65421e9			−1.71926
$423$		0			0
$424$	2.37038e8			0.151021
$425$	5.03203e7	−	8.71573e7i	0.0317967	−	0.0550735i
$426$		0			0
$427$	3.19375e7	+	5.53174e7i	0.0198520	+	0.0343846i
$428$	2.42255e8	+	4.19599e8i	0.149355	+	0.258691i
$429$		0			0
$430$	1.71934e9	−	2.97799e9i	1.04285	−	1.80627i
$431$	1.33391e9			0.802521			0.401261	−	0.915964i	$-0.368572\pi$
$431$	1.33391e9			0.802521			0.401261	+	0.915964i	$0.368572\pi$
$432$		0			0
$433$	−3.41286e8			−0.202027			−0.101014	−	0.994885i	$-0.532209\pi$
$433$	−3.41286e8			−0.202027			−0.101014	+	0.994885i	$0.532209\pi$
$434$	1.57665e8	−	2.73084e8i	0.0925810	−	0.160355i
$435$		0			0
$436$	−1.04109e8	−	1.80323e8i	−0.0601571	−	0.104195i
$437$	−1.73288e9	−	3.00144e9i	−0.993307	−	1.72046i
$438$		0			0
$439$	6.78117e8	−	1.17453e9i	0.382541	−	0.662581i	−0.608883	−	0.793260i	$-0.708382\pi$
$439$	6.78117e8	−	1.17453e9i	0.382541	−	0.662581i	0.991425	+	0.130679i	$0.0417156\pi$
$440$	−9.92789e8			−0.555613
$441$		0			0
$442$	−5.51554e8			−0.303815
$443$	−5.79697e8	+	1.00407e9i	−0.316802	+	0.548717i	−0.979819	−	0.199887i	$-0.935942\pi$
$443$	−5.79697e8	+	1.00407e9i	−0.316802	+	0.548717i	0.663017	+	0.748605i	$0.269276\pi$
$444$		0			0
$445$	−3.03718e8	−	5.26055e8i	−0.163384	−	0.282990i
$446$	2.99226e8	+	5.18274e8i	0.159708	+	0.276622i
$447$		0			0
$448$	7.37195e7	−	1.27686e8i	0.0387355	−	0.0670918i
$449$	−9.76057e8			−0.508877			−0.254439	−	0.967089i	$-0.581891\pi$
$449$	−9.76057e8			−0.508877			−0.254439	+	0.967089i	$0.581891\pi$
$450$		0			0
$451$	1.08795e9			0.558458
$452$	7.76570e8	−	1.34506e9i	0.395545	−	0.685105i
$453$		0			0
$454$	2.22753e9	+	3.85820e9i	1.11719	+	1.93504i
$455$	3.93654e8	+	6.81828e8i	0.195918	+	0.339340i
$456$		0			0
$457$	9.44190e8	−	1.63539e9i	0.462757	−	0.801518i	−0.536340	−	0.844002i	$-0.680194\pi$
$457$	9.44190e8	−	1.63539e9i	0.462757	−	0.801518i	0.999097	+	0.0424836i	$0.0135270\pi$
$458$	2.37837e9			1.15678
$459$		0			0
$460$	1.50315e9			0.720028
$461$	−7.07086e8	+	1.22471e9i	−0.336139	+	0.582210i	−0.983703	−	0.179801i	$-0.942455\pi$
$461$	−7.07086e8	+	1.22471e9i	−0.336139	+	0.582210i	0.647564	+	0.762011i	$0.275788\pi$
$462$		0			0
$463$	5.13035e8	+	8.88602e8i	0.240222	+	0.416077i	0.960778	−	0.277320i	$-0.0894463\pi$
$463$	5.13035e8	+	8.88602e8i	0.240222	+	0.416077i	−0.720555	+	0.693398i	$0.756113\pi$
$464$	9.58061e8	+	1.65941e9i	0.445226	+	0.771153i
$465$		0			0
$466$	−1.81763e9	+	3.14822e9i	−0.832059	+	1.44117i
$467$	−4.39875e8			−0.199858			−0.0999288	−	0.994995i	$-0.531861\pi$
$467$	−4.39875e8			−0.199858			−0.0999288	+	0.994995i	$0.531861\pi$
$468$		0			0
$469$	−4.56092e9			−2.04149
$470$	3.30893e8	−	5.73124e8i	0.147009	−	0.254628i
$471$		0			0
$472$	1.18810e8	+	2.05784e8i	0.0520061	+	0.0900773i
$473$	1.86685e9	+	3.23347e9i	0.811138	+	1.40493i
$474$		0			0
$475$	1.58027e8	−	2.73711e8i	0.0676556	−	0.117183i
$476$	−1.31835e9			−0.560283
$477$		0			0
$478$	2.51754e9			1.05434
$479$	1.23369e9	−	2.13681e9i	0.512899	−	0.888367i	−0.486989	−	0.873408i	$-0.661905\pi$
$479$	1.23369e9	−	2.13681e9i	0.512899	−	0.888367i	0.999888	−	0.0149590i	$-0.00476178\pi$
$480$		0			0
$481$	−4.04168e8	−	7.00040e8i	−0.165598	−	0.286824i
$482$	2.23433e9	+	3.86997e9i	0.908830	+	1.57414i
$483$		0			0
$484$	−2.53209e7	+	4.38572e7i	−0.0101513	+	0.0175825i
$485$	−1.01785e9			−0.405123
$486$		0			0
$487$	9.54719e8			0.374563			0.187281	−	0.982306i	$-0.440032\pi$
$487$	9.54719e8			0.374563			0.187281	+	0.982306i	$0.440032\pi$
$488$	−2.18514e7	+	3.78477e7i	−0.00851157	+	0.0147425i
$489$		0			0
$490$	8.53508e8	+	1.47832e9i	0.327734	+	0.567652i
$491$	9.83801e8	+	1.70399e9i	0.375079	+	0.649655i	0.990339	−	0.138669i	$-0.0442824\pi$
$491$	9.83801e8	+	1.70399e9i	0.375079	+	0.649655i	−0.615260	+	0.788324i	$0.710949\pi$
$492$		0			0
$493$	7.48122e8	−	1.29579e9i	0.281196	−	0.487045i
$494$	−1.73211e9			−0.646445
$495$		0			0
$496$	4.05891e8			0.149356
$497$	−2.24105e8	+	3.88161e8i	−0.0818850	+	0.141829i
$498$		0			0
$499$	−5.22725e8	−	9.05387e8i	−0.188331	−	0.326199i	0.756363	−	0.654152i	$-0.226974\pi$
$499$	−5.22725e8	−	9.05387e8i	−0.188331	−	0.326199i	−0.944694	+	0.327953i	$0.893641\pi$
$500$	−7.77706e8	−	1.34703e9i	−0.278241	−	0.481927i
$501$		0			0
$502$	9.59877e8	−	1.66256e9i	0.338651	−	0.586561i
$503$	−1.15052e9			−0.403093			−0.201546	−	0.979479i	$-0.564597\pi$
$503$	−1.15052e9			−0.403093			−0.201546	+	0.979479i	$0.564597\pi$
$504$		0			0
$505$	1.61206e8			0.0557008
$506$	−2.21725e9	+	3.84039e9i	−0.760830	+	1.31780i
$507$		0			0
$508$	−3.31701e8	−	5.74522e8i	−0.112260	−	0.194439i
$509$	−2.50094e9	−	4.33176e9i	−0.840603	−	1.45597i	−0.889385	−	0.457158i	$-0.848867\pi$
$509$	−2.50094e9	−	4.33176e9i	−0.840603	−	1.45597i	0.0487822	−	0.998809i	$-0.484466\pi$
$510$		0			0
$511$	4.57814e8	−	7.92957e8i	0.151781	−	0.262892i
$512$	1.93782e9			0.638071
$513$		0			0
$514$	−3.35194e9			−1.08874
$515$	2.95681e9	−	5.12134e9i	0.953889	−	1.65218i
$516$		0			0
$517$	3.59281e8	+	6.22293e8i	0.114345	+	0.198051i
$518$	−2.62483e9	−	4.54635e9i	−0.829751	−	1.43717i
$519$		0			0
$520$	−2.69335e8	+	4.66501e8i	−0.0840003	+	0.145493i
$521$	1.31851e9			0.408460			0.204230	−	0.978923i	$-0.434531\pi$
$521$	1.31851e9			0.408460			0.204230	+	0.978923i	$0.434531\pi$
$522$		0			0
$523$	1.46804e9			0.448727			0.224363	−	0.974506i	$-0.427970\pi$
$523$	1.46804e9			0.448727			0.224363	+	0.974506i	$0.427970\pi$
$524$	4.74020e8	−	8.21028e8i	0.143925	−	0.249286i
$525$		0			0
$526$	−1.18598e9	−	2.05418e9i	−0.355326	−	0.615443i
$527$	−1.58475e8	−	2.74486e8i	−0.0471653	−	0.0816927i
$528$		0			0
$529$	−7.04732e8	+	1.22063e9i	−0.206980	+	0.358501i
$530$	1.28870e9			0.375998
$531$		0			0
$532$	−4.14018e9			−1.19214
$533$	2.95151e8	−	5.11216e8i	0.0844303	−	0.146238i
$534$		0			0
$535$	−9.44387e8	−	1.63573e9i	−0.266632	−	0.461820i
$536$	−1.56027e9	−	2.70247e9i	−0.437647	−	0.758026i
$537$		0			0
$538$	−1.06389e9	+	1.84271e9i	−0.294550	+	0.510176i
$539$	−1.85346e9			−0.509827
$540$		0			0
$541$	3.28515e9			0.892000			0.446000	−	0.895033i	$-0.352848\pi$
$541$	3.28515e9			0.892000			0.446000	+	0.895033i	$0.352848\pi$
$542$	−2.15375e9	+	3.73040e9i	−0.581029	+	1.00637i
$543$		0			0
$544$	−1.53099e9	−	2.65175e9i	−0.407732	−	0.706213i
$545$	4.05850e8	+	7.02954e8i	0.107394	+	0.186011i
$546$		0			0
$547$	−1.71890e9	+	2.97722e9i	−0.449050	+	0.777778i	−0.998324	−	0.0578644i	$-0.981571\pi$
$547$	−1.71890e9	+	2.97722e9i	−0.449050	+	0.777778i	0.549274	+	0.835642i	$0.314904\pi$
$548$	−3.65357e9			−0.948387
$549$		0			0
$550$	−4.04396e8			−0.103642
$551$	2.34942e9	−	4.06931e9i	0.598315	−	1.03631i
$552$		0			0
$553$	−5.44169e8	−	9.42528e8i	−0.136835	−	0.237004i
$554$	−2.32661e8	−	4.02981e8i	−0.0581352	−	0.100693i
$555$		0			0
$556$	5.88576e7	−	1.01944e8i	0.0145225	−	0.0251537i
$557$	7.14256e9			1.75130			0.875651	−	0.482945i	$-0.160433\pi$
$557$	7.14256e9			1.75130			0.875651	+	0.482945i	$0.160433\pi$
$558$		0			0
$559$	2.02584e9			0.490527
$560$	−3.29078e9	+	5.69979e9i	−0.791845	+	1.37152i
$561$		0			0
$562$	3.57175e9	+	6.18645e9i	0.848797	+	1.47016i
$563$	2.31348e9	+	4.00706e9i	0.546369	+	0.946338i	0.998519	+	0.0543966i	$0.0173235\pi$
$563$	2.31348e9	+	4.00706e9i	0.546369	+	0.946338i	−0.452151	+	0.891941i	$0.649343\pi$
$564$		0			0
$565$	−3.02731e9	+	5.24346e9i	−0.706135	+	1.22306i
$566$	4.62920e9			1.07312
$567$		0			0
$568$	−3.06662e8			−0.0702167
$569$	−2.82742e9	+	4.89724e9i	−0.643425	+	1.11444i	0.341238	+	0.939977i	$0.389154\pi$
$569$	−2.82742e9	+	4.89724e9i	−0.643425	+	1.11444i	−0.984663	+	0.174468i	$0.944180\pi$
$570$		0			0
$571$	−3.84013e9	−	6.65130e9i	−0.863216	−	1.49513i	−0.868808	−	0.495149i	$-0.835113\pi$
$571$	−3.84013e9	−	6.65130e9i	−0.863216	−	1.49513i	0.00559216	−	0.999984i	$-0.498220\pi$
$572$	4.07845e8	+	7.06409e8i	0.0911191	+	0.157823i
$573$		0			0
$574$	1.91683e9	−	3.32005e9i	0.423050	−	0.732744i
$575$	−4.39031e8			−0.0963070
$576$		0			0
$577$	2.51579e9			0.545204			0.272602	−	0.962127i	$-0.412116\pi$
$577$	2.51579e9			0.545204			0.272602	+	0.962127i	$0.412116\pi$
$578$	1.11975e9	−	1.93946e9i	0.241197	−	0.417766i
$579$		0			0
$580$	1.01898e9	+	1.76492e9i	0.216853	+	0.375601i
$581$	−2.05924e9	−	3.56671e9i	−0.435603	−	0.754487i
$582$		0			0
$583$	−6.99628e8	+	1.21179e9i	−0.146227	+	0.253273i
$584$	6.26465e8			0.130152
$585$		0			0
$586$	2.04248e9			0.419292
$587$	−2.25025e9	+	3.89755e9i	−0.459196	+	0.795351i	−0.998919	−	0.0464920i	$-0.985196\pi$
$587$	−2.25025e9	+	3.89755e9i	−0.459196	+	0.795351i	0.539723	+	0.841843i	$0.318529\pi$
$588$		0			0
$589$	−4.97677e8	−	8.62002e8i	−0.100356	−	0.173822i
$590$	6.45929e8	+	1.11878e9i	0.129480	+	0.224266i
$591$		0			0
$592$	3.37867e9	−	5.85203e9i	0.669299	−	1.15926i
$593$	−8.41758e9			−1.65766			−0.828831	−	0.559499i	$-0.810993\pi$
$593$	−8.41758e9			−1.65766			−0.828831	+	0.559499i	$0.810993\pi$
$594$		0			0
$595$	5.13935e9			1.00023
$596$	−1.45914e9	+	2.52730e9i	−0.282315	+	0.488984i
$597$		0			0
$598$	1.20304e9	+	2.08372e9i	0.230052	+	0.398461i
$599$	1.91250e9	+	3.31254e9i	0.363586	+	0.629749i	0.988548	−	0.150906i	$-0.0482191\pi$
$599$	1.91250e9	+	3.31254e9i	0.363586	+	0.629749i	−0.624963	+	0.780655i	$0.714886\pi$
$600$		0			0
$601$	3.62512e8	−	6.27889e8i	0.0681179	−	0.117984i	−0.829955	−	0.557830i	$-0.811634\pi$
$601$	3.62512e8	−	6.27889e8i	0.0681179	−	0.117984i	0.898073	+	0.439847i	$0.144967\pi$
$602$	1.31566e10			2.45786
$603$		0			0
$604$	1.37031e9			0.253041
$605$	9.87089e7	−	1.70969e8i	0.0181223	−	0.0313887i
$606$		0			0
$607$	5.42460e9	+	9.39569e9i	0.984481	+	1.70517i	0.644218	+	0.764842i	$0.277183\pi$
$607$	5.42460e9	+	9.39569e9i	0.984481	+	1.70517i	0.340263	+	0.940330i	$0.389484\pi$
$608$	−4.80794e9	−	8.32760e9i	−0.867554	−	1.50265i
$609$		0			0
$610$	−1.18799e8	+	2.05766e8i	−0.0211913	+	0.0367044i
$611$	3.89879e8			0.0691489
$612$		0			0
$613$	−7.59484e9			−1.33170			−0.665851	−	0.746085i	$-0.731931\pi$
$613$	−7.59484e9			−1.33170			−0.665851	+	0.746085i	$0.731931\pi$
$614$	4.70050e9	−	8.14150e9i	0.819511	−	1.41943i
$615$		0			0
$616$	−1.89923e9	−	3.28957e9i	−0.327375	−	0.567031i
$617$	5.91168e8	+	1.02393e9i	0.101324	+	0.175498i	0.912230	−	0.409678i	$-0.134359\pi$
$617$	5.91168e8	+	1.02393e9i	0.101324	+	0.175498i	−0.810906	+	0.585176i	$0.801025\pi$
$618$		0			0
$619$	4.81004e9	−	8.33123e9i	0.815138	−	1.41186i	−0.0940908	−	0.995564i	$-0.529994\pi$
$619$	4.81004e9	−	8.33123e9i	0.815138	−	1.41186i	0.909229	−	0.416297i	$-0.136672\pi$
$620$	4.31699e8			0.0727462
$621$		0			0
$622$	−1.50489e9			−0.250748
$623$	1.16204e9	−	2.01272e9i	0.192537	−	0.333484i
$624$		0			0
$625$	3.27891e9	+	5.67923e9i	0.537216	+	0.930485i
$626$	8.44813e8	+	1.46326e9i	0.137642	+	0.238403i
$627$		0			0
$628$	2.47621e9	−	4.28892e9i	0.398959	−	0.691018i
$629$	−5.27662e9			−0.845432
$630$		0			0
$631$	−4.21153e9			−0.667325			−0.333662	−	0.942693i	$-0.608285\pi$
$631$	−4.21153e9			−0.667325			−0.333662	+	0.942693i	$0.608285\pi$
$632$	3.72316e8	−	6.44870e8i	0.0586681	−	0.101616i
$633$		0			0
$634$	−3.09308e9	−	5.35737e9i	−0.482035	−	0.834909i
$635$	1.29307e9	+	2.23967e9i	0.200408	+	0.347116i
$636$		0			0
$637$	−5.02828e8	+	8.70923e8i	−0.0770781	+	0.133503i
$638$	−6.01224e9			−0.916567
$639$		0			0
$640$	−6.61256e9			−0.997102
$641$	−3.96142e9	+	6.86139e9i	−0.594084	+	1.02898i	0.399591	+	0.916694i	$0.369152\pi$
$641$	−3.96142e9	+	6.86139e9i	−0.594084	+	1.02898i	−0.993675	+	0.112291i	$0.964181\pi$
$642$		0			0
$643$	1.46169e9	+	2.53172e9i	0.216829	+	0.375558i	0.953837	−	0.300326i	$-0.0970953\pi$
$643$	1.46169e9	+	2.53172e9i	0.216829	+	0.375558i	−0.737008	+	0.675884i	$0.763762\pi$
$644$	2.87557e9	+	4.98063e9i	0.424251	+	0.734824i
$645$		0			0
$646$	−5.65340e9	+	9.79197e9i	−0.825079	+	1.42908i
$647$	−1.00413e10			−1.45755			−0.728774	−	0.684754i	$-0.759910\pi$
$647$	−1.00413e10			−1.45755			−0.728774	+	0.684754i	$0.759910\pi$
$648$		0			0
$649$	−1.40269e9			−0.201421
$650$	−1.09709e8	+	1.90022e8i	−0.0156692	+	0.0271398i
$651$		0			0
$652$	1.47112e9	+	2.54805e9i	0.207865	+	0.360032i
$653$	7.41652e8	+	1.28458e9i	0.104233	+	0.180536i	0.913424	−	0.407008i	$-0.133428\pi$
$653$	7.41652e8	+	1.28458e9i	0.104233	+	0.180536i	−0.809192	+	0.587545i	$0.800095\pi$
$654$		0			0
$655$	−1.84788e9	+	3.20062e9i	−0.256938	+	0.445030i
$656$	4.93466e9			0.682487
$657$		0			0
$658$	2.53203e9			0.346480
$659$	−1.67543e9	+	2.90193e9i	−0.228048	+	0.394991i	−0.957230	−	0.289329i	$-0.906568\pi$
$659$	−1.67543e9	+	2.90193e9i	−0.228048	+	0.394991i	0.729181	+	0.684320i	$0.239901\pi$
$660$		0			0
$661$	−1.70018e9	−	2.94480e9i	−0.228976	−	0.396598i	0.728529	−	0.685015i	$-0.240204\pi$
$661$	−1.70018e9	−	2.94480e9i	−0.228976	−	0.396598i	−0.957505	+	0.288417i	$0.906871\pi$
$662$	−5.22495e9	−	9.04988e9i	−0.699969	−	1.21238i
$663$		0			0
$664$	1.40892e9	−	2.44032e9i	0.186766	−	0.323488i
$665$	1.61397e10			2.12824
$666$		0			0
$667$	−6.52716e9			−0.851695
$668$	3.62430e9	−	6.27748e9i	0.470443	−	0.814831i
$669$		0			0
$670$	−8.48269e9	−	1.46925e10i	−1.08961	−	1.88726i
$671$	−1.28991e8	−	2.23419e8i	−0.0164828	−	0.0285490i
$672$		0			0
$673$	−4.48300e9	+	7.76478e9i	−0.566912	+	0.981921i	0.429957	+	0.902850i	$0.358529\pi$
$673$	−4.48300e9	+	7.76478e9i	−0.566912	+	0.981921i	−0.996869	+	0.0790714i	$0.974804\pi$
$674$	−6.71098e9			−0.844260
$675$		0			0
$676$	−4.23513e9			−0.527294
$677$	7.44416e9	−	1.28937e10i	0.922052	−	1.59704i	0.125816	−	0.992054i	$-0.459845\pi$
$677$	7.44416e9	−	1.28937e10i	0.922052	−	1.59704i	0.796235	−	0.604987i	$-0.206822\pi$
$678$		0			0
$679$	−1.94717e9	−	3.37261e9i	−0.238705	−	0.413448i
$680$	1.75815e9	+	3.04521e9i	0.214425	+	0.371395i
$681$		0			0
$682$	−6.36786e8	+	1.10295e9i	−0.0768684	+	0.133140i
$683$	−7.71503e9			−0.926542			−0.463271	−	0.886217i	$-0.653324\pi$
$683$	−7.71503e9			−0.926542			−0.463271	+	0.886217i	$0.653324\pi$
$684$		0			0
$685$	1.42428e10			1.69308
$686$	3.25037e9	−	5.62980e9i	0.384413	−	0.665822i
$687$		0			0
$688$	8.46756e9	+	1.46662e10i	0.991285	+	1.71696i
$689$	3.79606e8	+	6.57496e8i	0.0442146	+	0.0765819i
$690$		0			0
$691$	1.26498e9	−	2.19101e9i	0.145851	−	0.252622i	−0.783839	−	0.620964i	$-0.786741\pi$
$691$	1.26498e9	−	2.19101e9i	0.145851	−	0.252622i	0.929690	+	0.368342i	$0.120075\pi$
$692$	−4.13012e9			−0.473796
$693$		0			0
$694$	1.57506e10			1.78871
$695$	−2.29445e8	+	3.97411e8i	−0.0259258	+	0.0449048i
$696$		0			0
$697$	−1.92667e9	−	3.33709e9i	−0.215522	−	0.373296i
$698$	5.66555e8	+	9.81302e8i	0.0630591	+	0.109222i
$699$		0			0
$700$	−2.62232e8	+	4.54200e8i	−0.0288964	+	0.0500500i
$701$	−1.41167e10			−1.54782			−0.773908	−	0.633298i	$-0.781701\pi$
$701$	−1.41167e10			−1.54782			−0.773908	+	0.633298i	$0.781701\pi$
$702$		0			0
$703$	−1.65708e10			−1.79887
$704$	−2.97742e8	+	5.15704e8i	−0.0321614	+	0.0557053i
$705$		0			0
$706$	−7.24555e8	−	1.25497e9i	−0.0774917	−	0.134220i
$707$	3.08392e8	+	5.34150e8i	0.0328197	+	0.0568454i
$708$		0			0
$709$	6.46733e9	−	1.12017e10i	0.681496	−	1.18039i	−0.293028	−	0.956104i	$-0.594663\pi$
$709$	6.46733e9	−	1.12017e10i	0.681496	−	1.18039i	0.974524	−	0.224282i	$-0.0720037\pi$
$710$	−1.66722e9			−0.174819
$711$		0			0
$712$	1.59012e9			0.165101
$713$	−6.91324e8	+	1.19741e9i	−0.0714279	+	0.123717i
$714$		0			0
$715$	−1.58991e9	−	2.75380e9i	−0.162668	−	0.281748i
$716$	3.67954e9	+	6.37314e9i	0.374626	+	0.648871i
$717$		0			0
$718$	6.89754e8	−	1.19469e9i	0.0695438	−	0.120453i
$719$	1.22962e10			1.23373			0.616864	−	0.787070i	$-0.288403\pi$
$719$	1.22962e10			1.23373			0.616864	+	0.787070i	$0.288403\pi$
$720$		0			0
$721$	2.26258e10			2.24818
$722$	−1.13933e10	+	1.97338e10i	−1.12660	+	1.95133i
$723$		0			0
$724$	−3.36693e9	−	5.83170e9i	−0.329723	−	0.571097i
$725$	−2.97617e8	−	5.15487e8i	−0.0290051	−	0.0502383i
$726$		0			0
$727$	−3.37402e9	+	5.84398e9i	−0.325670	+	0.564077i	−0.981648	−	0.190704i	$-0.938923\pi$
$727$	−3.37402e9	+	5.84398e9i	−0.325670	+	0.564077i	0.655978	+	0.754780i	$0.272256\pi$
$728$	−2.06098e9			−0.197977
$729$		0			0
$730$	3.40589e9			0.324041
$731$	6.61208e9	−	1.14525e10i	0.626076	−	1.08440i
$732$		0			0
$733$	−1.87123e9	−	3.24106e9i	−0.175494	−	0.303965i	0.764838	−	0.644223i	$-0.222819\pi$
$733$	−1.87123e9	−	3.24106e9i	−0.175494	−	0.303965i	−0.940332	+	0.340258i	$0.889486\pi$
$734$	1.09871e10	+	1.90303e10i	1.02553	+	1.77627i
$735$		0			0
$736$	−6.67872e9	+	1.15679e10i	−0.617477	+	1.06950i
$737$	1.84209e10			1.69502
$738$		0			0
$739$	1.27399e9			0.116121			0.0580606	−	0.998313i	$-0.481508\pi$
$739$	1.27399e9			0.116121			0.0580606	+	0.998313i	$0.481508\pi$
$740$	3.59350e9	−	6.22412e9i	0.325992	−	0.564634i
$741$		0			0
$742$	2.46532e9	+	4.27005e9i	0.221543	+	0.383724i
$743$	3.62517e9	+	6.27897e9i	0.324240	+	0.561601i	0.981358	−	0.192187i	$-0.0615580\pi$
$743$	3.62517e9	+	6.27897e9i	0.324240	+	0.561601i	−0.657118	+	0.753788i	$0.728225\pi$
$744$		0			0
$745$	5.68817e9	−	9.85220e9i	0.503994	−	0.872944i
$746$	−1.92066e10			−1.69381
$747$		0			0
$748$	5.32463e9			0.465194
$749$	3.61328e9	−	6.25838e9i	0.314206	−	0.544221i
$750$		0			0
$751$	9.82411e9	+	1.70159e10i	0.846357	+	1.46593i	0.884437	+	0.466659i	$0.154542\pi$
$751$	9.82411e9	+	1.70159e10i	0.846357	+	1.46593i	−0.0380804	+	0.999275i	$0.512124\pi$
$752$	1.62961e9	+	2.82257e9i	0.139740	+	0.242037i
$753$		0			0
$754$	−1.63107e9	+	2.82509e9i	−0.138571	+	0.240012i
$755$	−5.34190e9			−0.451733
$756$		0			0
$757$	−1.81025e10			−1.51671			−0.758356	−	0.651841i	$-0.773997\pi$
$757$	−1.81025e10			−1.51671			−0.758356	+	0.651841i	$0.773997\pi$
$758$	−1.14670e10	+	1.98614e10i	−0.956329	+	1.65641i
$759$		0			0
$760$	5.52133e9	+	9.56323e9i	0.456243	+	0.790236i
$761$	−2.43280e9	−	4.21373e9i	−0.200106	−	0.346593i	0.748457	−	0.663184i	$-0.230795\pi$
$761$	−2.43280e9	−	4.21373e9i	−0.200106	−	0.346593i	−0.948562	+	0.316590i	$0.897462\pi$
$762$		0			0
$763$	−1.55281e9	+	2.68954e9i	−0.126556	+	0.219201i
$764$	7.76648e9			0.630083
$765$		0			0
$766$	−1.79925e10			−1.44641
$767$	−3.80537e8	+	6.59109e8i	−0.0304518	+	0.0527440i
$768$		0			0
$769$	3.32352e9	+	5.75651e9i	0.263546	+	0.456475i	0.967182	−	0.254086i	$-0.0817746\pi$
$769$	3.32352e9	+	5.75651e9i	0.263546	+	0.456475i	−0.703636	+	0.710561i	$0.748441\pi$
$770$	−1.03255e10	−	1.78843e10i	−0.815069	−	1.41174i
$771$		0			0
$772$	−4.95846e8	+	8.58831e8i	−0.0387870	+	0.0671811i
$773$	1.79263e10			1.39593			0.697963	−	0.716134i	$-0.254090\pi$
$773$	1.79263e10			1.39593			0.697963	+	0.716134i	$0.254090\pi$
$774$		0			0
$775$	−1.26088e8			−0.00973012
$776$	1.33224e9	−	2.30751e9i	0.102345	−	0.177267i
$777$		0			0
$778$	−1.30743e10	−	2.26454e10i	−0.995385	−	1.72406i
$779$	−6.05056e9	−	1.04799e10i	−0.458579	−	0.794282i
$780$		0			0
$781$	9.05127e8	−	1.56773e9i	0.0679878	−	0.117758i
$782$	1.57063e10			1.17449
$783$		0			0
$784$	−8.40685e9			−0.623056
$785$	−9.65303e9	+	1.67195e10i	−0.712229	+	1.23362i
$786$		0			0
$787$	−4.95269e9	−	8.57831e9i	−0.362184	−	0.627321i	0.626136	−	0.779714i	$-0.284635\pi$
$787$	−4.95269e9	−	8.57831e9i	−0.362184	−	0.627321i	−0.988320	+	0.152393i	$0.951302\pi$
$788$	−6.38523e9	−	1.10595e10i	−0.464873	−	0.805185i
$789$		0			0
$790$	2.02416e9	−	3.50595e9i	0.146066	−	0.252994i
$791$	−2.31653e10			−1.66426
$792$		0			0
$793$	−1.39976e8			−0.00996777
$794$	1.31985e10	−	2.28605e10i	0.935736	−	1.62074i
$795$		0			0
$796$	4.62270e9	+	8.00676e9i	0.324863	+	0.562679i
$797$	−1.18602e10	−	2.05424e10i	−0.829824	−	1.43730i	−0.898176	−	0.439637i	$-0.855107\pi$
$797$	−1.18602e10	−	2.05424e10i	−0.829824	−	1.43730i	0.0683515	−	0.997661i	$-0.478226\pi$
$798$		0			0
$799$	1.27252e9	−	2.20406e9i	0.0882571	−	0.152866i
$800$	−1.21811e9			−0.0841145
$801$		0			0
$802$	1.72002e10			1.17740
$803$	−1.84904e9	+	3.20263e9i	−0.126021	+	0.218275i
$804$		0			0
$805$	−1.12099e10	−	1.94160e10i	−0.757381	−	1.31182i
$806$	3.45508e8	+	5.98438e8i	0.0232427	+	0.0402575i
$807$		0			0
$808$	−2.10999e8	+	3.65461e8i	−0.0140715	+	0.0243726i
$809$	2.49700e10			1.65805			0.829027	−	0.559208i	$-0.188895\pi$
$809$	2.49700e10			1.65805			0.829027	+	0.559208i	$0.188895\pi$
$810$		0			0
$811$	−1.12321e9			−0.0739412			−0.0369706	−	0.999316i	$-0.511771\pi$
$811$	−1.12321e9			−0.0739412			−0.0369706	+	0.999316i	$0.511771\pi$
$812$	−3.89866e9	+	6.75268e9i	−0.255546	+	0.442619i
$813$		0			0
$814$	1.06013e10	+	1.83620e10i	0.688929	+	1.19326i
$815$	−5.73487e9	−	9.93308e9i	−0.371084	−	0.642736i
$816$		0			0
$817$	2.07647e10	−	3.59655e10i	1.33214	−	2.30733i
$818$	−1.73833e10			−1.11044
$819$		0			0
$820$	5.24842e9			0.332415
$821$	−7.45639e9	+	1.29148e10i	−0.470249	+	0.814494i	−0.999421	−	0.0340198i	$-0.989169\pi$
$821$	−7.45639e9	+	1.29148e10i	−0.470249	+	0.814494i	0.529173	+	0.848514i	$0.322502\pi$
$822$		0			0
$823$	1.40501e9	+	2.43356e9i	0.0878580	+	0.152175i	0.906605	−	0.421979i	$-0.138664\pi$
$823$	1.40501e9	+	2.43356e9i	0.0878580	+	0.152175i	−0.818747	+	0.574154i	$0.805331\pi$
$824$	7.74021e9	+	1.34064e10i	0.481956	+	0.834772i
$825$		0			0
$826$	−2.47136e9	+	4.28053e9i	−0.152583	+	0.264282i
$827$	−1.92634e10			−1.18430			−0.592151	−	0.805827i	$-0.701721\pi$
$827$	−1.92634e10			−1.18430			−0.592151	+	0.805827i	$0.701721\pi$
$828$		0			0
$829$	−3.12798e10			−1.90688			−0.953440	−	0.301582i	$-0.902485\pi$
$829$	−3.12798e10			−1.90688			−0.953440	+	0.301582i	$0.902485\pi$
$830$	7.65982e9	−	1.32672e10i	0.464992	−	0.805390i
$831$		0			0
$832$	1.61549e8	+	2.79812e8i	0.00972464	+	0.0168436i
$833$	3.28233e9	+	5.68517e9i	0.196755	+	0.340789i
$834$		0			0
$835$	−1.41287e10	+	2.44716e10i	−0.839843	+	1.45465i
$836$	1.67216e10			0.989818
$837$		0			0
$838$	−2.16425e10			−1.27044
$839$	7.65355e9	−	1.32563e10i	0.447400	−	0.774920i	−0.550816	−	0.834627i	$-0.685683\pi$
$839$	7.65355e9	−	1.32563e10i	0.447400	−	0.774920i	0.998216	+	0.0597070i	$0.0190166\pi$
$840$		0			0
$841$	4.20021e9	+	7.27498e9i	0.243492	+	0.421741i
$842$	−7.73762e9	−	1.34019e10i	−0.446699	−	0.773705i
$843$		0			0
$844$	6.95140e9	−	1.20402e10i	0.397992	−	0.689342i
$845$	1.65099e10			0.941336
$846$		0			0
$847$	7.55332e8			0.0427116
$848$	−3.17334e9	+	5.49639e9i	−0.178703	+	0.309522i
$849$		0			0
$850$	7.16154e8	+	1.24041e9i	0.0399982	+	0.0692788i
$851$	1.15093e10	+	1.99346e10i	0.640168	+	1.10880i
$852$		0			0
$853$	−1.59603e10	+	2.76441e10i	−0.880480	+	1.52504i	−0.0296720	+	0.999560i	$0.509446\pi$
$853$	−1.59603e10	+	2.76441e10i	−0.880480	+	1.52504i	−0.850808	+	0.525477i	$0.823887\pi$
$854$	−9.09063e8			−0.0499449
$855$		0			0
$856$	4.94435e9			0.269433
$857$	−1.48319e10	+	2.56895e10i	−0.804938	+	1.39419i	0.111395	+	0.993776i	$0.464468\pi$
$857$	−1.48319e10	+	2.56895e10i	−0.804938	+	1.39419i	−0.916333	+	0.400417i	$0.868865\pi$
$858$		0			0
$859$	8.51597e9	+	1.47501e10i	0.458414	+	0.793997i	0.998877	−	0.0473709i	$-0.0150843\pi$
$859$	8.51597e9	+	1.47501e10i	0.458414	+	0.793997i	−0.540463	+	0.841368i	$0.681751\pi$
$860$	9.00595e9	+	1.55988e10i	0.482820	+	0.836268i
$861$		0			0
$862$	−9.49204e9	+	1.64407e10i	−0.504759	+	0.874269i
$863$	3.16249e9			0.167491			0.0837454	−	0.996487i	$-0.473312\pi$
$863$	3.16249e9			0.167491			0.0837454	+	0.996487i	$0.473312\pi$
$864$		0			0
$865$	1.61005e10			0.845829
$866$	2.42857e9	−	4.20641e9i	0.127069	−	0.220089i
$867$		0			0
$868$	8.25853e8	+	1.43042e9i	0.0428631	+	0.0742411i
$869$	2.19782e9	+	3.80673e9i	0.113611	+	0.196781i
$870$		0			0
$871$	4.99741e9	−	8.65578e9i	0.256261	−	0.443856i
$872$	−2.12484e9			−0.108522
$873$		0			0
$874$	4.93243e10			2.49903
$875$	−1.15996e10	+	2.00911e10i	−0.585349	+	1.01385i
$876$		0			0
$877$	−3.19898e9	−	5.54079e9i	−0.160145	−	0.277379i	0.774776	−	0.632236i	$-0.217863\pi$
$877$	−3.19898e9	−	5.54079e9i	−0.160145	−	0.277379i	−0.934920	+	0.354857i	$0.884529\pi$
$878$	9.65089e9	+	1.67158e10i	0.481212	+	0.833484i
$879$		0			0
$880$	1.32910e10	−	2.30206e10i	0.657456	−	1.13875i
$881$	1.45065e10			0.714739			0.357369	−	0.933963i	$-0.383674\pi$
$881$	1.45065e10			0.714739			0.357369	+	0.933963i	$0.383674\pi$
$882$		0			0
$883$	2.39105e10			1.16876			0.584382	−	0.811479i	$-0.301337\pi$
$883$	2.39105e10			1.16876			0.584382	+	0.811479i	$0.301337\pi$
$884$	1.44452e9	−	2.50199e9i	0.0703302	−	0.121815i
$885$		0			0
$886$	−8.25019e9	−	1.42898e10i	−0.398516	−	0.690250i
$887$	−1.54012e10	−	2.66757e10i	−0.741007	−	1.28346i	−0.952037	−	0.305982i	$-0.901015\pi$
$887$	−1.54012e10	−	2.66757e10i	−0.741007	−	1.28346i	0.211030	−	0.977480i	$-0.432318\pi$
$888$		0			0
$889$	−4.94737e9	+	8.56909e9i	−0.236166	+	0.409052i
$890$	8.64497e9			0.411054
$891$		0			0
$892$	−3.13470e9			−0.147883
$893$	3.99624e9	−	6.92168e9i	0.187789	−	0.325261i
$894$		0			0
$895$	−1.43440e10	−	2.48445e10i	−0.668789	−	1.15838i
$896$	−1.26500e10	−	2.19105e10i	−0.587507	−	1.01759i
$897$		0			0
$898$	6.94557e9	−	1.20301e10i	0.320067	−	0.554372i
$899$	−1.87458e9			−0.0860488
$900$		0			0
$901$	4.95594e9			0.225730
$902$	−7.74178e9	+	1.34092e10i	−0.351252	+	0.608385i
$903$		0			0
$904$	−7.92477e9	−	1.37261e10i	−0.356777	−	0.617957i
$905$	1.31253e10	+	2.27338e10i	0.588628	+	1.01953i
$906$		0			0
$907$	−6.06562e9	+	1.05060e10i	−0.269929	+	0.467531i	−0.968843	−	0.247675i	$-0.920334\pi$
$907$	−6.06562e9	+	1.05060e10i	−0.269929	+	0.467531i	0.698914	+	0.715206i	$0.253667\pi$
$908$	−2.33357e10			−1.03448
$909$		0			0
$910$	−1.12049e10			−0.492904
$911$	9.73568e9	−	1.68627e10i	0.426630	−	0.738945i	−0.569941	−	0.821686i	$-0.693034\pi$
$911$	9.73568e9	−	1.68627e10i	0.426630	−	0.738945i	0.996571	+	0.0827403i	$0.0263672\pi$
$912$		0			0
$913$	8.31697e9	+	1.44054e10i	0.361674	+	0.626438i
$914$	1.34376e10	+	2.32746e10i	0.582117	+	1.00826i
$915$		0			0
$916$	−6.22896e9	+	1.07889e10i	−0.267782	+	0.463812i
$917$	−1.41402e10			−0.605567
$918$		0			0
$919$	2.10755e10			0.895721			0.447861	−	0.894103i	$-0.352186\pi$
$919$	2.10755e10			0.895721			0.447861	+	0.894103i	$0.352186\pi$
$920$	7.66969e9	−	1.32843e10i	0.324729	−	0.562446i
$921$		0			0
$922$	−1.00632e10	−	1.74299e10i	−0.422841	−	0.732382i
$923$	−4.91105e8	−	8.50619e8i	−0.0205574	−	0.0356065i
$924$		0			0
$925$	−1.04957e9	+	1.81791e9i	−0.0436028	+	0.0755223i
$926$	−1.46029e10			−0.604368
$927$		0			0
$928$	−1.81099e10			−0.743870
$929$	3.48141e9	−	6.02997e9i	0.142462	−	0.246752i	−0.785961	−	0.618276i	$-0.787831\pi$
$929$	3.48141e9	−	6.02997e9i	0.142462	−	0.246752i	0.928423	+	0.371524i	$0.121165\pi$
$930$		0			0
$931$	1.03079e10	+	1.78538e10i	0.418646	+	0.725116i
$932$	−9.52076e9	−	1.64904e10i	−0.385226	−	0.667232i
$933$		0			0
$934$	3.13013e9	−	5.42155e9i	0.125704	−	0.217725i
$935$	−2.07571e10			−0.830472
$936$		0			0
$937$	1.58623e10			0.629908			0.314954	−	0.949107i	$-0.398011\pi$
$937$	1.58623e10			0.629908			0.314954	+	0.949107i	$0.398011\pi$
$938$	3.24553e10	−	5.62142e10i	1.28403	−	2.22401i
$939$		0			0
$940$	1.73322e9	+	3.00203e9i	0.0680624	+	0.117888i
$941$	−1.62492e10	−	2.81444e10i	−0.635722	−	1.10110i	−0.986362	−	0.164592i	$-0.947369\pi$
$941$	−1.62492e10	−	2.81444e10i	−0.635722	−	1.10110i	0.350640	−	0.936510i	$-0.385964\pi$
$942$		0			0
$943$	−8.40483e9	+	1.45576e10i	−0.326391	+	0.565326i
$944$	−6.36225e9			−0.246155
$945$		0			0
$946$	−5.31376e10			−2.04072
$947$	2.70871e9	−	4.69162e9i	0.103642	−	0.179514i	−0.809540	−	0.587064i	$-0.800284\pi$
$947$	2.70871e9	−	4.69162e9i	0.103642	−	0.179514i	0.913183	+	0.407550i	$0.133617\pi$
$948$		0			0
$949$	1.00326e9	+	1.73769e9i	0.0381049	+	0.0659996i
$950$	2.24902e9	+	3.89542e9i	0.0851063	+	0.147408i
$951$		0			0
$952$	−6.72678e9	+	1.16511e10i	−0.252684	+	0.437662i
$953$	−2.62658e9			−0.0983028			−0.0491514	−	0.998791i	$-0.515652\pi$
$953$	−2.62658e9			−0.0983028			−0.0491514	+	0.998791i	$0.515652\pi$
$954$		0			0
$955$	−3.02762e10			−1.12484
$956$	−6.59346e9	+	1.14202e10i	−0.244068	+	0.422738i
$957$		0			0
$958$	1.75578e10	+	3.04109e10i	0.645193	+	1.11751i
$959$	2.72468e10	+	4.71928e10i	0.997586	+	1.72787i
$960$		0			0
$961$	1.35578e10	−	2.34827e10i	0.492783	−	0.853526i
$962$	1.15042e10			0.416622
$963$		0			0
$964$	−2.34069e10			−0.841539
$965$	1.93296e9	−	3.34799e9i	0.0692433	−	0.119933i
$966$		0			0
$967$	−1.95753e10	−	3.39054e10i	−0.696171	−	1.20580i	−0.969784	−	0.243963i	$-0.921552\pi$
$967$	−1.95753e10	−	3.39054e10i	−0.696171	−	1.20580i	0.273614	−	0.961840i	$-0.411781\pi$
$968$	2.58396e8	+	4.47555e8i	0.00915635	+	0.0158593i
$969$		0			0
$970$	7.24296e9	−	1.25452e10i	0.254809	−	0.441343i
$971$	2.49003e10			0.872846			0.436423	−	0.899742i	$-0.356245\pi$
$971$	2.49003e10			0.872846			0.436423	+	0.899742i	$0.356245\pi$
$972$		0			0
$973$	−1.75574e9			−0.0611034
$974$	−6.79373e9	+	1.17671e10i	−0.235587	+	0.408050i
$975$		0			0
$976$	−5.85070e8	−	1.01337e9i	−0.0201434	−	0.0348895i
$977$	2.22902e9	+	3.86078e9i	0.0764686	+	0.132448i	0.901724	−	0.432312i	$-0.142302\pi$
$977$	2.22902e9	+	3.86078e9i	0.0764686	+	0.132448i	−0.825255	+	0.564760i	$0.808969\pi$
$978$		0			0
$979$	−4.69332e9	+	8.12906e9i	−0.159860	+	0.276886i
$980$	−8.94137e9			−0.303468
$981$		0			0
$982$	−2.80027e10			−0.943648
$983$	−1.32778e10	+	2.29979e10i	−0.445851	+	0.772237i	−0.998111	−	0.0614353i	$-0.980432\pi$
$983$	−1.32778e10	+	2.29979e10i	−0.445851	+	0.772237i	0.552260	+	0.833672i	$0.313766\pi$
$984$		0			0
$985$	2.48916e10	+	4.31135e10i	0.829901	+	1.43743i
$986$	1.06472e10	+	1.84415e10i	0.353725	+	0.612670i
$987$		0			0
$988$	4.53641e9	−	7.85730e9i	0.149645	−	0.259193i
$989$	−5.76886e10			−1.89628
$990$		0			0
$991$	6.89473e9			0.225040			0.112520	−	0.993649i	$-0.464108\pi$
$991$	6.89473e9			0.225040			0.112520	+	0.993649i	$0.464108\pi$
$992$	−1.91810e9	+	3.32225e9i	−0.0623852	+	0.108054i
$993$		0			0
$994$	−3.18944e9	−	5.52427e9i	−0.103006	−	0.178411i
$995$	−1.80207e10	−	3.12128e10i	−0.579951	−	1.00451i
$996$		0			0
$997$	2.56614e8	−	4.44468e8i	0.00820062	−	0.0142039i	−0.861896	−	0.507085i	$-0.830723\pi$
$997$	2.56614e8	−	4.44468e8i	0.00820062	−	0.0142039i	0.870097	+	0.492881i	$0.164056\pi$
$998$	1.48787e10			0.473816
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.8.c.a.19.2		12
3.2	odd	2		9.8.c.a.7.5	yes	12
4.3	odd	2		432.8.i.c.289.5		12
9.2	odd	6		81.8.a.e.1.2		6
9.4	even	3	inner	27.8.c.a.10.2		12
9.5	odd	6		9.8.c.a.4.5	✓	12
9.7	even	3		81.8.a.c.1.5		6
12.11	even	2		144.8.i.c.97.1		12
36.23	even	6		144.8.i.c.49.1		12
36.31	odd	6		432.8.i.c.145.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.8.c.a.4.5	✓	12	9.5	odd	6
9.8.c.a.7.5	yes	12	3.2	odd	2
27.8.c.a.10.2		12	9.4	even	3	inner
27.8.c.a.19.2		12	1.1	even	1	trivial
81.8.a.c.1.5		6	9.7	even	3
81.8.a.e.1.2		6	9.2	odd	6
144.8.i.c.49.1		12	36.23	even	6
144.8.i.c.97.1		12	12.11	even	2
432.8.i.c.145.5		12	36.31	odd	6
432.8.i.c.289.5		12	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-7.11595 + 12.3252i) q^{2} +(-37.2735 - 64.5595i) q^{4} +(145.304 + 251.673i) q^{5} +(-555.940 + 962.916i) q^{7} -760.739 q^{8} +O(q^{10})\)	\(q+(-7.11595 + 12.3252i) q^{2} +(-37.2735 - 64.5595i) q^{4} +(145.304 + 251.673i) q^{5} +(-555.940 + 962.916i) q^{7} -760.739 q^{8} -4135.89 q^{10} +(2245.36 - 3889.07i) q^{11} +(-1218.29 - 2110.14i) q^{13} +(-7912.08 - 13704.1i) q^{14} +(10184.4 - 17639.9i) q^{16} -15905.4 q^{17} -49949.6 q^{19} +(10831.9 - 18761.5i) q^{20} +(31955.7 + 55348.9i) q^{22} +(34692.5 + 60089.2i) q^{23} +(-3163.73 + 5479.74i) q^{25} +34677.2 q^{26} +82887.2 q^{28} +(-47035.8 + 81468.4i) q^{29} +(9963.58 + 17257.4i) q^{31} +(96255.8 + 166720. i) q^{32} +(113182. - 196037. i) q^{34} -323120. q^{35} +331750. q^{37} +(355439. - 615638. i) q^{38} +(-110538. - 191457. i) q^{40} +(121133. + 209809. i) q^{41} +(-415713. + 720036. i) q^{43} -334769. q^{44} -987481. q^{46} +(-80005.3 + 138573. i) q^{47} +(-206366. - 357437. i) q^{49} +(-45025.8 - 77987.1i) q^{50} +(-90819.7 + 157304. i) q^{52} -311589. q^{53} +1.30503e6 q^{55} +(422925. - 732527. i) q^{56} +(-669408. - 1.15945e6i) q^{58} +(-156177. - 270506. i) q^{59} +(28723.9 - 49751.3i) q^{61} -283601. q^{62} -132603. q^{64} +(354044. - 613221. i) q^{65} +(2.05100e6 + 3.55243e6i) q^{67} +(592849. + 1.02684e6i) q^{68} +(2.29930e6 - 3.98251e6i) q^{70} +403110. q^{71} -823496. q^{73} +(-2.36072e6 + 4.08889e6i) q^{74} +(1.86180e6 + 3.22472e6i) q^{76} +(2.49656e6 + 4.32418e6i) q^{77} +(-489414. + 847689. i) q^{79} +5.91931e6 q^{80} -3.44791e6 q^{82} +(-1.85204e6 + 3.20782e6i) q^{83} +(-2.31111e6 - 4.00296e6i) q^{85} +(-5.91638e6 - 1.02475e7i) q^{86} +(-1.70813e6 + 2.95857e6i) q^{88} -2.09023e6 q^{89} +2.70918e6 q^{91} +(2.58622e6 - 4.47947e6i) q^{92} +(-1.13863e6 - 1.97216e6i) q^{94} +(-7.25786e6 - 1.25710e7i) q^{95} +(-1.75125e6 + 3.03325e6i) q^{97} +5.87396e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8}+O(q^{10}) \) 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8	\( 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8} + 252 q^{10} + 8460 q^{11} - 1848 q^{13} + 16272 q^{14} - 12417 q^{16} - 30564 q^{17} + 24432 q^{19} + 40788 q^{20} - 35001 q^{22} + 51588 q^{23} + 4746 q^{25} - 536472 q^{26} + 75516 q^{28} + 414648 q^{29} + 8196 q^{31} + 1048977 q^{32} - 106623 q^{34} - 2210616 q^{35} + 139344 q^{37} + 1952685 q^{38} + 305496 q^{40} + 1731582 q^{41} + 408372 q^{43} - 5169114 q^{44} - 1684008 q^{46} + 1631484 q^{47} - 179010 q^{49} + 1654461 q^{50} + 681594 q^{52} - 2835648 q^{53} - 16056 q^{55} + 1784466 q^{56} - 948384 q^{58} + 2055636 q^{59} - 2723196 q^{61} + 1026828 q^{62} + 7178178 q^{64} + 1387620 q^{65} + 3806556 q^{67} - 2142639 q^{68} + 953442 q^{70} - 2408400 q^{71} - 10670052 q^{73} - 9846504 q^{74} - 6727827 q^{76} - 3478824 q^{77} + 6020916 q^{79} + 38072448 q^{80} + 9403002 q^{82} - 9605052 q^{83} - 1698624 q^{85} - 34278561 q^{86} - 16459029 q^{88} + 24630264 q^{89} + 13570104 q^{91} - 39143394 q^{92} + 12602808 q^{94} - 10422072 q^{95} + 9977226 q^{97} + 95833314 q^{98}+O(q^{100}) \) 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8 + 252 * q^10 + 8460 * q^11 - 1848 * q^13 + 16272 * q^14 - 12417 * q^16 - 30564 * q^17 + 24432 * q^19 + 40788 * q^20 - 35001 * q^22 + 51588 * q^23 + 4746 * q^25 - 536472 * q^26 + 75516 * q^28 + 414648 * q^29 + 8196 * q^31 + 1048977 * q^32 - 106623 * q^34 - 2210616 * q^35 + 139344 * q^37 + 1952685 * q^38 + 305496 * q^40 + 1731582 * q^41 + 408372 * q^43 - 5169114 * q^44 - 1684008 * q^46 + 1631484 * q^47 - 179010 * q^49 + 1654461 * q^50 + 681594 * q^52 - 2835648 * q^53 - 16056 * q^55 + 1784466 * q^56 - 948384 * q^58 + 2055636 * q^59 - 2723196 * q^61 + 1026828 * q^62 + 7178178 * q^64 + 1387620 * q^65 + 3806556 * q^67 - 2142639 * q^68 + 953442 * q^70 - 2408400 * q^71 - 10670052 * q^73 - 9846504 * q^74 - 6727827 * q^76 - 3478824 * q^77 + 6020916 * q^79 + 38072448 * q^80 + 9403002 * q^82 - 9605052 * q^83 - 1698624 * q^85 - 34278561 * q^86 - 16459029 * q^88 + 24630264 * q^89 + 13570104 * q^91 - 39143394 * q^92 + 12602808 * q^94 - 10422072 * q^95 + 9977226 * q^97 + 95833314 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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