LMFDB - Embedded newform 99.6.f.a.82.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,6,Mod(37,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, 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:	$15.8779981615$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 86 x^{14} - 146 x^{13} + 7205 x^{12} - 23732 x^{11} + 774165 x^{10} + \cdots + 393784336 $ x^16 - 5x^15 + 86x^14 - 146x^13 + 7205x^12 - 23732x^11 + 774165x^10 - 1228996x^9 + 44649817x^8 - 92720004x^7 + 943915592x^6 - 1892495035x^5 + 8611100939x^4 - 17760110698x^3 + 18348896492x^2 - 4224271656*x + 393784336
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			82.4
Root			$7.81150 + 5.67539i$ of defining polynomial
Character	$\chi$	$=$	99.82
Dual form			99.6.f.a.64.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.29275 + 10.1340i) q^{2} +(-65.9678 + 47.9284i) q^{4} +(-20.4388 + 62.9043i) q^{5} +(58.3278 - 42.3777i) q^{7} +(-427.066 - 310.282i) q^{8} +O(q^{10})$	\(q+(3.29275 + 10.1340i) q^{2} +(-65.9678 + 47.9284i) q^{4} +(-20.4388 + 62.9043i) q^{5} +(58.3278 - 42.3777i) q^{7} +(-427.066 - 310.282i) q^{8} -704.774 q^{10} +(-369.555 - 156.461i) q^{11} +(177.228 + 545.453i) q^{13} +(621.515 + 451.557i) q^{14} +(931.866 - 2867.99i) q^{16} +(84.6769 - 260.609i) q^{17} +(404.202 + 293.670i) q^{19} +(-1666.60 - 5129.26i) q^{20} +(368.729 - 4260.27i) q^{22} +605.239 q^{23} +(-1011.03 - 734.554i) q^{25} +(-4944.06 + 3592.07i) q^{26} +(-1816.67 + 5591.12i) q^{28} +(-43.2242 + 31.4042i) q^{29} +(-1253.55 - 3858.02i) q^{31} +15240.4 q^{32} +2919.83 q^{34} +(1473.58 + 4535.22i) q^{35} +(-11517.7 + 8368.08i) q^{37} +(-1645.13 + 5063.18i) q^{38} +(28246.8 - 20522.5i) q^{40} +(-6373.96 - 4630.95i) q^{41} +10231.1 q^{43} +(31877.7 - 7390.80i) q^{44} +(1992.90 + 6133.51i) q^{46} +(-12580.0 - 9139.87i) q^{47} +(-3587.38 + 11040.8i) q^{49} +(4114.94 - 12664.5i) q^{50} +(-37834.0 - 27488.0i) q^{52} +(6006.53 + 18486.2i) q^{53} +(17395.3 - 20048.7i) q^{55} -38058.9 q^{56} +(-460.577 - 334.629i) q^{58} +(-35337.2 + 25674.0i) q^{59} +(-8313.59 + 25586.6i) q^{61} +(34969.7 - 25407.0i) q^{62} +(20363.1 + 62671.1i) q^{64} -37933.7 q^{65} -30124.0 q^{67} +(6904.61 + 21250.2i) q^{68} +(-41107.9 + 29866.7i) q^{70} +(-5598.42 + 17230.2i) q^{71} +(-24776.0 + 18000.8i) q^{73} +(-122727. - 89166.5i) q^{74} -40739.5 q^{76} +(-28185.8 + 6534.85i) q^{77} +(-3378.39 - 10397.6i) q^{79} +(161363. + 117237. i) q^{80} +(25942.4 - 79842.4i) q^{82} +(32089.5 - 98761.3i) q^{83} +(14662.7 + 10653.1i) q^{85} +(33688.3 + 103682. i) q^{86} +(109278. + 181485. i) q^{88} +96723.3 q^{89} +(33452.4 + 24304.6i) q^{91} +(-39926.3 + 29008.1i) q^{92} +(51201.1 - 157581. i) q^{94} +(-26734.5 + 19423.8i) q^{95} +(-1931.29 - 5943.90i) q^{97} -123700. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - 73 q^{4} + 10 q^{5} + 196 q^{7} - 527 q^{8}+O(q^{10}) $ 16 * q + q^2 - 73 * q^4 + 10 * q^5 + 196 * q^7 - 527 * q^8	$ 16 q + q^{2} - 73 q^{4} + 10 q^{5} + 196 q^{7} - 527 q^{8} - 672 q^{10} + 692 q^{11} + 1162 q^{13} - 560 q^{14} + 6399 q^{16} + 22 q^{17} - 3236 q^{19} + 5514 q^{20} - 13059 q^{22} + 10848 q^{23} + 15686 q^{25} - 16216 q^{26} + 8838 q^{28} - 13070 q^{29} - 14764 q^{31} + 58812 q^{32} - 26966 q^{34} - 43368 q^{35} + 4638 q^{37} - 68144 q^{38} + 52284 q^{40} + 14806 q^{41} - 24376 q^{43} + 104960 q^{44} + 50452 q^{46} - 40364 q^{47} + 32246 q^{49} - 10839 q^{50} - 80654 q^{52} + 11654 q^{53} + 7052 q^{55} - 70632 q^{56} + 10276 q^{58} - 70804 q^{59} - 31446 q^{61} + 153388 q^{62} + 17695 q^{64} + 41284 q^{65} - 64200 q^{67} + 94114 q^{68} - 103768 q^{70} + 184380 q^{71} - 1750 q^{73} - 306048 q^{74} + 174806 q^{76} - 384646 q^{77} + 24324 q^{79} + 386444 q^{80} - 316255 q^{82} + 46028 q^{83} + 63914 q^{85} - 22931 q^{86} + 211871 q^{88} - 148364 q^{89} - 258448 q^{91} + 58658 q^{92} - 55370 q^{94} + 4716 q^{95} + 484296 q^{97} - 743692 q^{98}+O(q^{100}) $ 16 * q + q^2 - 73 * q^4 + 10 * q^5 + 196 * q^7 - 527 * q^8 - 672 * q^10 + 692 * q^11 + 1162 * q^13 - 560 * q^14 + 6399 * q^16 + 22 * q^17 - 3236 * q^19 + 5514 * q^20 - 13059 * q^22 + 10848 * q^23 + 15686 * q^25 - 16216 * q^26 + 8838 * q^28 - 13070 * q^29 - 14764 * q^31 + 58812 * q^32 - 26966 * q^34 - 43368 * q^35 + 4638 * q^37 - 68144 * q^38 + 52284 * q^40 + 14806 * q^41 - 24376 * q^43 + 104960 * q^44 + 50452 * q^46 - 40364 * q^47 + 32246 * q^49 - 10839 * q^50 - 80654 * q^52 + 11654 * q^53 + 7052 * q^55 - 70632 * q^56 + 10276 * q^58 - 70804 * q^59 - 31446 * q^61 + 153388 * q^62 + 17695 * q^64 + 41284 * q^65 - 64200 * q^67 + 94114 * q^68 - 103768 * q^70 + 184380 * q^71 - 1750 * q^73 - 306048 * q^74 + 174806 * q^76 - 384646 * q^77 + 24324 * q^79 + 386444 * q^80 - 316255 * q^82 + 46028 * q^83 + 63914 * q^85 - 22931 * q^86 + 211871 * q^88 - 148364 * q^89 - 258448 * q^91 + 58658 * q^92 - 55370 * q^94 + 4716 * q^95 + 484296 * q^97 - 743692 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	3.29275	+	10.1340i	0.582081	+	1.79146i	0.610691	+	0.791869i	$0.290892\pi$
$2$	3.29275	+	10.1340i	0.582081	+	1.79146i	−0.0286101	+	0.999591i	$0.509108\pi$
$3$		0			0
$3$		0			0
$4$	−65.9678	+	47.9284i	−2.06149	+	1.49776i
$5$	−20.4388	+	62.9043i	−0.365621	+	1.12527i	0.583970	+	0.811775i	$0.301499\pi$
$5$	−20.4388	+	62.9043i	−0.365621	+	1.12527i	−0.949591	+	0.313491i	$0.898501\pi$
$6$		0			0
$7$	58.3278	−	42.3777i	0.449915	−	0.326883i	−0.339647	−	0.940553i	$-0.610308\pi$
$7$	58.3278	−	42.3777i	0.449915	−	0.326883i	0.789562	+	0.613670i	$0.210308\pi$
$8$	−427.066	−	310.282i	−2.35923	−	1.71408i
$9$		0			0
$10$	−704.774			−2.22869
$11$	−369.555	−	156.461i	−0.920868	−	0.389874i
$11$	−369.555	−	156.461i	−0.920868	−	0.389874i
$12$		0			0
$13$	177.228	+	545.453i	0.290854	+	0.895156i	0.984583	+	0.174920i	$0.0559666\pi$
$13$	177.228	+	545.453i	0.290854	+	0.895156i	−0.693729	+	0.720236i	$0.744033\pi$
$14$	621.515	+	451.557i	0.847484	+	0.615733i
$15$		0			0
$16$	931.866	−	2867.99i	0.910025	−	2.80077i
$17$	84.6769	−	260.609i	0.0710628	−	0.218709i	−0.909217	−	0.416322i	$-0.863319\pi$
$17$	84.6769	−	260.609i	0.0710628	−	0.218709i	0.980280	+	0.197613i	$0.0633189\pi$
$18$		0			0
$19$	404.202	+	293.670i	0.256871	+	0.186628i	0.708766	−	0.705443i	$-0.249252\pi$
$19$	404.202	+	293.670i	0.256871	+	0.186628i	−0.451896	+	0.892071i	$0.649252\pi$
$20$	−1666.60	−	5129.26i	−0.931656	−	2.86734i
$21$		0			0
$22$	368.729	−	4260.27i	0.162424	−	1.87664i
$23$	605.239			0.238565			0.119283	−	0.992860i	$-0.461941\pi$
$23$	605.239			0.238565			0.119283	+	0.992860i	$0.461941\pi$
$24$		0			0
$25$	−1011.03	−	734.554i	−0.323529	−	0.235057i
$26$	−4944.06	+	3592.07i	−1.43434	+	1.04211i
$27$		0			0
$28$	−1816.67	+	5591.12i	−0.437905	+	1.34773i
$29$	−43.2242	+	31.4042i	−0.00954403	+	0.00693415i	−0.592547	−	0.805536i	$-0.701878\pi$
$29$	−43.2242	+	31.4042i	−0.00954403	+	0.00693415i	0.583003	+	0.812470i	$0.301878\pi$
$30$		0			0
$31$	−1253.55	−	3858.02i	−0.234281	−	0.721042i	−0.997216	−	0.0745673i	$-0.976242\pi$
$31$	−1253.55	−	3858.02i	−0.234281	−	0.721042i	0.762935	−	0.646475i	$-0.223758\pi$
$32$	15240.4			2.63100
$33$		0			0
$34$	2919.83			0.433173
$35$	1473.58	+	4535.22i	0.203331	+	0.625790i
$36$		0			0
$37$	−11517.7	+	8368.08i	−1.38312	+	1.00490i	−0.386542	+	0.922272i	$0.626330\pi$
$37$	−11517.7	+	8368.08i	−1.38312	+	1.00490i	−0.996581	+	0.0826252i	$0.973670\pi$
$38$	−1645.13	+	5063.18i	−0.184816	+	0.568806i
$39$		0			0
$40$	28246.8	−	20522.5i	2.79138	−	2.02806i
$41$	−6373.96	−	4630.95i	−0.592174	−	0.430240i	0.250918	−	0.968008i	$-0.419267\pi$
$41$	−6373.96	−	4630.95i	−0.592174	−	0.430240i	−0.843093	+	0.537769i	$0.819267\pi$
$42$		0			0
$43$	10231.1			0.843820			0.421910	−	0.906638i	$-0.361360\pi$
$43$	10231.1			0.843820			0.421910	+	0.906638i	$0.361360\pi$
$44$	31877.7	−	7390.80i	2.48230	−	0.575519i
$45$		0			0
$46$	1992.90	+	6133.51i	0.138864	+	0.427380i
$47$	−12580.0	−	9139.87i	−0.830681	−	0.603525i	0.0890707	−	0.996025i	$-0.471610\pi$
$47$	−12580.0	−	9139.87i	−0.830681	−	0.603525i	−0.919752	+	0.392500i	$0.871610\pi$
$48$		0			0
$49$	−3587.38	+	11040.8i	−0.213445	+	0.656917i
$50$	4114.94	−	12664.5i	0.232776	−	0.716411i
$51$		0			0
$52$	−37834.0	−	27488.0i	−1.94032	−	1.40973i
$53$	6006.53	+	18486.2i	0.293720	+	0.903978i	0.983648	+	0.180100i	$0.0576422\pi$
$53$	6006.53	+	18486.2i	0.293720	+	0.903978i	−0.689928	+	0.723878i	$0.742358\pi$
$54$		0			0
$55$	17395.3	−	20048.7i	0.775401	−	0.893676i
$56$	−38058.9			−1.62176
$57$		0			0
$58$	−460.577	−	334.629i	−0.0179776	−	0.0130615i
$59$	−35337.2	+	25674.0i	−1.32161	+	0.960205i	−0.321697	+	0.946843i	$0.604253\pi$
$59$	−35337.2	+	25674.0i	−1.32161	+	0.960205i	−0.999911	+	0.0133620i	$0.995747\pi$
$60$		0			0
$61$	−8313.59	+	25586.6i	−0.286065	+	0.880416i	0.700013	+	0.714130i	$0.253178\pi$
$61$	−8313.59	+	25586.6i	−0.286065	+	0.880416i	−0.986078	+	0.166286i	$0.946822\pi$
$62$	34969.7	−	25407.0i	1.15535	−	0.839410i
$63$		0			0
$64$	20363.1	+	62671.1i	0.621431	+	1.91257i
$65$	−37933.7			−1.11363
$66$		0			0
$67$	−30124.0			−0.819834			−0.409917	−	0.912123i	$-0.634442\pi$
$67$	−30124.0			−0.819834			−0.409917	+	0.912123i	$0.634442\pi$
$68$	6904.61	+	21250.2i	0.181079	+	0.557302i
$69$		0			0
$70$	−41107.9	+	29866.7i	−1.00272	+	0.728520i
$71$	−5598.42	+	17230.2i	−0.131801	+	0.405643i	−0.995079	−	0.0990870i	$-0.968408\pi$
$71$	−5598.42	+	17230.2i	−0.131801	+	0.405643i	0.863278	+	0.504730i	$0.168408\pi$
$72$		0			0
$73$	−24776.0	+	18000.8i	−0.544158	+	0.395354i	−0.825627	−	0.564217i	$-0.809178\pi$
$73$	−24776.0	+	18000.8i	−0.544158	+	0.395354i	0.281469	+	0.959570i	$0.409178\pi$
$74$	−122727.	−	89166.5i	−2.60532	−	1.89288i
$75$		0			0
$76$	−40739.5			−0.809061
$77$	−28185.8	+	6534.85i	−0.541756	+	0.125606i
$78$		0			0
$79$	−3378.39	−	10397.6i	−0.0609035	−	0.187442i	0.915976	−	0.401234i	$-0.131418\pi$
$79$	−3378.39	−	10397.6i	−0.0609035	−	0.187442i	−0.976879	+	0.213792i	$0.931418\pi$
$80$	161363.	+	117237.i	2.81889	+	2.04804i
$81$		0			0
$82$	25942.4	−	79842.4i	0.426064	−	1.31129i
$83$	32089.5	−	98761.3i	0.511291	−	1.57359i	−0.278641	−	0.960395i	$-0.589884\pi$
$83$	32089.5	−	98761.3i	0.511291	−	1.57359i	0.789931	−	0.613195i	$-0.210116\pi$
$84$		0			0
$85$	14662.7	+	10653.1i	0.220124	+	0.159929i
$86$	33688.3	+	103682.i	0.491171	+	1.51167i
$87$		0			0
$88$	109278.	+	181485.i	1.50426	+	2.49825i
$89$	96723.3			1.29436			0.647181	−	0.762336i	$-0.275948\pi$
$89$	96723.3			1.29436			0.647181	+	0.762336i	$0.275948\pi$
$90$		0			0
$91$	33452.4	+	24304.6i	0.423471	+	0.307669i
$92$	−39926.3	+	29008.1i	−0.491801	+	0.357314i
$93$		0			0
$94$	51201.1	−	157581.i	0.597668	−	1.83943i
$95$	−26734.5	+	19423.8i	−0.303923	+	0.220813i
$96$		0			0
$97$	−1931.29	−	5943.90i	−0.0208410	−	0.0641419i	0.940095	−	0.340912i	$-0.110736\pi$
$97$	−1931.29	−	5943.90i	−0.0208410	−	0.0641419i	−0.960936	+	0.276770i	$0.910736\pi$
$98$	−123700.			−1.30108
$99$		0			0
$100$	101901.			1.01901
$101$	40837.2	+	125684.i	0.398339	+	1.22596i	0.926330	+	0.376712i	$0.122945\pi$
$101$	40837.2	+	125684.i	0.398339	+	1.22596i	−0.527991	+	0.849250i	$0.677055\pi$
$102$		0			0
$103$	−30027.4	+	21816.2i	−0.278885	+	0.202622i	−0.718431	−	0.695598i	$-0.755139\pi$
$103$	−30027.4	+	21816.2i	−0.278885	+	0.202622i	0.439546	+	0.898220i	$0.355139\pi$
$104$	93555.8	−	287935.i	0.848179	−	2.61043i
$105$		0			0
$106$	−167562.	+	121741.i	−1.44847	+	1.05238i
$107$	−13527.9	−	9828.59i	−0.114228	−	0.0829912i	0.529205	−	0.848494i	$-0.322490\pi$
$107$	−13527.9	−	9828.59i	−0.114228	−	0.0829912i	−0.643432	+	0.765503i	$0.722490\pi$
$108$		0			0
$109$	148877.			1.20022			0.600110	−	0.799917i	$-0.295123\pi$
$109$	148877.			1.20022			0.600110	+	0.799917i	$0.295123\pi$
$110$	260453.	+	110270.i	2.05233	+	0.868909i
$111$		0			0
$112$	−67184.9	−	206774.i	−0.506089	−	1.55758i
$113$	9416.66	+	6841.60i	0.0693746	+	0.0504036i	0.621932	−	0.783071i	$-0.286348\pi$
$113$	9416.66	+	6841.60i	0.0693746	+	0.0504036i	−0.552557	+	0.833475i	$0.686348\pi$
$114$		0			0
$115$	−12370.4	+	38072.1i	−0.0872246	+	0.268450i
$116$	1346.25	−	4143.33i	0.00928926	−	0.0285894i
$117$		0			0
$118$	−376538.	−	273571.i	−2.48945	−	1.80869i
$119$	−6104.96	−	18789.1i	−0.0395199	−	0.121630i
$120$		0			0
$121$	112091.	+	115642.i	0.695997	+	0.718045i
$122$	−286670.			−1.74374
$123$		0			0
$124$	267603.	+	194425.i	1.56292	+	1.13553i
$125$	−100347.	+	72906.1i	−0.574418	+	0.417339i
$126$		0			0
$127$	−70688.8	+	217558.i	−0.388903	+	1.19692i	0.544706	+	0.838627i	$0.316641\pi$
$127$	−70688.8	+	217558.i	−0.388903	+	1.19692i	−0.933609	+	0.358293i	$0.883359\pi$
$128$	−173508.	+	126061.i	−0.936040	+	0.680073i
$129$		0			0
$130$	−124906.	−	384421.i	−0.648223	−	1.99503i
$131$	293521.			1.49438			0.747189	−	0.664612i	$-0.231403\pi$
$131$	293521.			1.49438			0.747189	+	0.664612i	$0.231403\pi$
$132$		0			0
$133$	36021.3			0.176575
$134$	−99190.7	−	305277.i	−0.477209	−	1.46870i
$135$		0			0
$136$	−117025.	+	85023.5i	−0.542538	+	0.394177i
$137$	39808.9	−	122519.i	0.181209	−	0.557703i	−0.818654	−	0.574287i	$-0.805279\pi$
$137$	39808.9	−	122519.i	0.181209	−	0.557703i	0.999862	+	0.0165846i	$0.00527928\pi$
$138$		0			0
$139$	260773.	−	189463.i	1.14479	−	0.831738i	0.157010	−	0.987597i	$-0.449814\pi$
$139$	260773.	−	189463.i	1.14479	−	0.831738i	0.987779	+	0.155859i	$0.0498145\pi$
$140$	−314575.	−	228552.i	−1.35645	−	0.985520i
$141$		0			0
$142$	−193045.			−0.803411
$143$	19846.4	−	229304.i	0.0811600	−	0.937717i
$144$		0			0
$145$	−1092.01	−	3360.85i	−0.00431326	−	0.0132749i
$146$	−264002.	−	191809.i	−1.02500	−	0.744709i
$147$		0			0
$148$	358727.	−	1.10405e6i	1.34620	−	4.14318i
$149$	−126819.	+	390308.i	−0.467970	+	1.44026i	0.387238	+	0.921980i	$0.373429\pi$
$149$	−126819.	+	390308.i	−0.467970	+	1.44026i	−0.855208	+	0.518285i	$0.826571\pi$
$150$		0			0
$151$	28744.5	+	20884.1i	0.102592	+	0.0745373i	0.637898	−	0.770121i	$-0.279804\pi$
$151$	28744.5	+	20884.1i	0.102592	+	0.0745373i	−0.535307	+	0.844658i	$0.679804\pi$
$152$	−81500.6	−	250833.i	−0.286123	−	0.880595i
$153$		0			0
$154$	−159033.	−	264118.i	−0.540363	−	0.897421i
$155$	268307.			0.897023
$156$		0			0
$157$	−338268.	−	245766.i	−1.09525	−	0.795742i	−0.114968	−	0.993369i	$-0.536677\pi$
$157$	−338268.	−	245766.i	−1.09525	−	0.795742i	−0.980277	+	0.197627i	$0.936677\pi$
$158$	94245.5	−	68473.4i	0.300343	−	0.218212i
$159$		0			0
$160$	−311496.	+	958687.i	−0.961951	+	2.96058i
$161$	35302.3	−	25648.6i	0.107334	−	0.0779829i
$162$		0			0
$163$	154528.	+	475589.i	0.455553	+	1.40205i	0.870484	+	0.492196i	$0.163806\pi$
$163$	154528.	+	475589.i	0.455553	+	1.40205i	−0.414931	+	0.909853i	$0.636194\pi$
$164$	642430.			1.86516
$165$		0			0
$166$	1.10651e6			3.11664
$167$	99846.4	+	307296.i	0.277039	+	0.852639i	0.988673	+	0.150088i	$0.0479557\pi$
$167$	99846.4	+	307296.i	0.277039	+	0.852639i	−0.711633	+	0.702551i	$0.752044\pi$
$168$		0			0
$169$	34273.6	−	24901.3i	0.0923089	−	0.0670663i
$170$	−59678.1	+	183670.i	−0.158377	+	0.487435i
$171$		0			0
$172$	−674921.	+	490359.i	−1.73953	+	1.26384i
$173$	416200.	+	302387.i	1.05727	+	0.768153i	0.973582	−	0.228339i	$-0.0733294\pi$
$173$	416200.	+	302387.i	1.05727	+	0.768153i	0.0836902	+	0.996492i	$0.473329\pi$
$174$		0			0
$175$	−90099.7			−0.222397
$176$	−793104.	+	914079.i	−1.92996	+	2.22434i
$177$		0			0
$178$	318485.	+	980196.i	0.753423	+	2.31880i
$179$	43160.1	+	31357.7i	0.100682	+	0.0731494i	0.636987	−	0.770875i	$-0.280180\pi$
$179$	43160.1	+	31357.7i	0.100682	+	0.0731494i	−0.536305	+	0.844024i	$0.680180\pi$
$180$		0			0
$181$	−48440.3	+	149084.i	−0.109903	+	0.338247i	−0.990850	−	0.134968i	$-0.956907\pi$
$181$	−48440.3	+	149084.i	−0.109903	+	0.338247i	0.880947	+	0.473216i	$0.156907\pi$
$182$	−136153.	+	419036.i	−0.304683	+	0.937719i
$183$		0			0
$184$	−258477.	−	187795.i	−0.562831	−	0.408920i
$185$	−290980.	−	895545.i	−0.625078	−	1.92379i
$186$		0			0
$187$	−72067.9	+	83060.6i	−0.150708	+	0.173697i
$188$	1.26793e6			2.61638
$189$		0			0
$190$	−284871.	−	206971.i	−0.572485	−	0.415935i
$191$	−577.919	+	419.883i	−0.00114626	+	0.000832808i	−0.588358	−	0.808600i	$-0.700225\pi$
$191$	−577.919	+	419.883i	−0.00114626	+	0.000832808i	0.587212	+	0.809433i	$0.300225\pi$
$192$		0			0
$193$	−116055.	+	357181.i	−0.224270	+	0.690232i	0.774095	+	0.633070i	$0.218205\pi$
$193$	−116055.	+	357181.i	−0.224270	+	0.690232i	−0.998365	+	0.0571626i	$0.981795\pi$
$194$	53876.4	−	39143.5i	0.102777	−	0.0746716i
$195$		0			0
$196$	−292517.	−	900275.i	−0.543890	−	1.67392i
$197$	132856.			0.243902			0.121951	−	0.992536i	$-0.461085\pi$
$197$	132856.			0.243902			0.121951	+	0.992536i	$0.461085\pi$
$198$		0			0
$199$	861557.			1.54224			0.771119	−	0.636691i	$-0.219697\pi$
$199$	861557.			1.54224			0.771119	+	0.636691i	$0.219697\pi$
$200$	203857.	+	627407.i	0.360371	+	1.10911i
$201$		0			0
$202$	−1.13922e6	+	827691.i	−1.96440	+	1.42722i
$203$	−1190.34	+	3663.48i	−0.00202736	+	0.00623956i
$204$		0			0
$205$	421583.	−	306298.i	0.700646	−	0.509049i
$206$	−319959.	−	232464.i	−0.525323	−	0.381669i
$207$		0			0
$208$	1.72950e6			2.77181
$209$	−103427.	−	171769.i	−0.163783	−	0.272007i
$210$		0			0
$211$	−162286.	−	499466.i	−0.250943	−	0.772325i	−0.994602	−	0.103765i	$-0.966911\pi$
$211$	−162286.	−	499466.i	−0.250943	−	0.772325i	0.743658	−	0.668560i	$-0.233089\pi$
$212$	−1.28225e6	−	931610.i	−1.95945	−	1.42362i
$213$		0			0
$214$	55059.3	−	169455.i	0.0821857	−	0.252942i
$215$	−209111.	+	643578.i	−0.308518	+	0.949522i
$216$		0			0
$217$	−236611.	−	171908.i	−0.341103	−	0.247826i
$218$	490214.	+	1.50872e6i	0.698625	+	2.15015i
$219$		0			0
$220$	−186629.	+	2.15630e6i	−0.259970	+	3.00367i
$221$	157157.			0.216447
$222$		0			0
$223$	−295544.	−	214726.i	−0.397979	−	0.289149i	0.370738	−	0.928737i	$-0.379105\pi$
$223$	−295544.	−	214726.i	−0.397979	−	0.289149i	−0.768717	+	0.639589i	$0.779105\pi$
$224$	888940.	−	645853.i	1.18373	−	0.860030i
$225$		0			0
$226$	−38326.3	+	117956.i	−0.0499144	+	0.153621i
$227$	−708821.	+	514989.i	−0.913002	+	0.663335i	−0.941772	−	0.336251i	$-0.890841\pi$
$227$	−708821.	+	514989.i	−0.913002	+	0.663335i	0.0287700	+	0.999586i	$0.490841\pi$
$228$		0			0
$229$	−188656.	−	580623.i	−0.237728	−	0.731653i	−0.996748	−	0.0805849i	$-0.974321\pi$
$229$	−188656.	−	580623.i	−0.237728	−	0.731653i	0.759019	−	0.651068i	$-0.225679\pi$
$230$	−426557.			−0.531688
$231$		0			0
$232$	28203.8			0.0344023
$233$	−379536.	−	1.16809e6i	−0.457998	−	1.40957i	−0.867579	−	0.497299i	$-0.834325\pi$
$233$	−379536.	−	1.16809e6i	−0.457998	−	1.40957i	0.409581	−	0.912274i	$-0.365675\pi$
$234$		0			0
$235$	832057.	−	604525.i	0.982842	−	0.714076i
$236$	1.10061e6	−	3.38732e6i	1.28633	−	3.95891i
$237$		0			0
$238$	170308.	−	123736.i	0.194891	−	0.141597i
$239$	25865.3	+	18792.3i	0.0292903	+	0.0212806i	0.602334	−	0.798244i	$-0.294238\pi$
$239$	25865.3	+	18792.3i	0.0292903	+	0.0212806i	−0.573044	+	0.819525i	$0.694238\pi$
$240$		0			0
$241$	−1.30607e6			−1.44852			−0.724258	−	0.689529i	$-0.757818\pi$
$241$	−1.30607e6			−1.44852			−0.724258	+	0.689529i	$0.757818\pi$
$242$	−802831.	+	1.51671e6i	−0.881223	+	1.66481i
$243$		0			0
$244$	−677896.	−	2.08635e6i	−0.728934	−	2.24343i
$245$	−621193.	−	451323.i	−0.661167	−	0.480366i
$246$		0			0
$247$	−88547.0	+	272520.i	−0.0923489	+	0.284221i
$248$	−661727.	+	2.03659e6i	−0.683203	+	2.10268i
$249$		0			0
$250$	−1.06925e6	−	776854.i	−1.08200	−	0.786121i
$251$	10510.7	+	32348.6i	0.0105305	+	0.0324094i	0.956184	−	0.292767i	$-0.0945762\pi$
$251$	10510.7	+	32348.6i	0.0105305	+	0.0324094i	−0.945653	+	0.325177i	$0.894576\pi$
$252$		0			0
$253$	−223669.	−	94696.3i	−0.219687	−	0.0930104i
$254$	−2.43750e6			−2.37061
$255$		0			0
$256$	−142865.	−	103797.i	−0.136246	−	0.0989888i
$257$	1.08194e6	−	786077.i	1.02181	−	0.742391i	0.0551594	−	0.998478i	$-0.482433\pi$
$257$	1.08194e6	−	786077.i	1.02181	−	0.742391i	0.966654	+	0.256087i	$0.0824333\pi$
$258$		0			0
$259$	−317182.	+	976184.i	−0.293805	+	0.904237i
$260$	2.50240e6	−	1.81810e6i	2.29574	−	1.66796i
$261$		0			0
$262$	966489.	+	2.97455e6i	0.869848	+	2.67712i
$263$	−1.73779e6			−1.54921			−0.774603	−	0.632448i	$-0.782050\pi$
$263$	−1.73779e6			−1.54921			−0.774603	+	0.632448i	$0.782050\pi$
$264$		0			0
$265$	−1.28563e6			−1.12461
$266$	118609.	+	365041.i	0.102781	+	0.316328i
$267$		0			0
$268$	1.98721e6	−	1.44380e6i	1.69008	−	1.22792i
$269$	−464311.	+	1.42900e6i	−0.391227	+	1.20407i	0.540635	+	0.841257i	$0.318184\pi$
$269$	−464311.	+	1.42900e6i	−0.391227	+	1.20407i	−0.931862	+	0.362814i	$0.881816\pi$
$270$		0			0
$271$	−1.42329e6	+	1.03408e6i	−1.17725	+	0.855324i	−0.991859	−	0.127340i	$-0.959356\pi$
$271$	−1.42329e6	+	1.03408e6i	−1.17725	+	0.855324i	−0.185394	+	0.982664i	$0.559356\pi$
$272$	−668515.	−	485704.i	−0.547884	−	0.398061i
$273$		0			0
$274$	1.37269e6			1.10458
$275$	258701.	+	429645.i	0.206285	+	0.342592i
$276$		0			0
$277$	−159536.	−	491002.i	−0.124928	−	0.384489i	0.868960	−	0.494882i	$-0.164789\pi$
$277$	−159536.	−	491002.i	−0.124928	−	0.384489i	−0.993888	+	0.110394i	$0.964789\pi$
$278$	2.77868e6	+	2.01883e6i	2.15639	+	1.56671i
$279$		0			0
$280$	777880.	−	2.39407e6i	0.592949	−	1.82491i
$281$	93789.4	−	288654.i	0.0708578	−	0.218078i	−0.909356	−	0.416018i	$-0.863425\pi$
$281$	93789.4	−	288654.i	0.0708578	−	0.218078i	0.980214	+	0.197940i	$0.0634252\pi$
$282$		0			0
$283$	980700.	+	712520.i	0.727897	+	0.528848i	0.888897	−	0.458106i	$-0.151472\pi$
$283$	980700.	+	712520.i	0.727897	+	0.528848i	−0.161000	+	0.986954i	$0.551472\pi$
$284$	−456499.	−	1.40496e6i	−0.335849	−	1.03364i
$285$		0			0
$286$	2.38912e6	−	553916.i	1.72712	−	0.400432i
$287$	−568028.			−0.407066
$288$		0			0
$289$	1.08794e6	+	790436.i	0.766233	+	0.556701i
$290$	30463.3	−	22132.9i	0.0212707	−	0.0154541i
$291$		0			0
$292$	771669.	−	2.37495e6i	0.529631	−	1.63004i
$293$	−467825.	+	339895.i	−0.318357	+	0.231300i	−0.735474	−	0.677553i	$-0.763041\pi$
$293$	−467825.	+	339895.i	−0.318357	+	0.231300i	0.417117	+	0.908853i	$0.363041\pi$
$294$		0			0
$295$	−892753.	−	2.74761e6i	−0.597278	−	1.83823i
$296$	7.51528e6			4.98558
$297$		0			0
$298$	−4.37298e6			−2.85257
$299$	107266.	+	330129.i	0.0693876	+	0.213553i
$300$		0			0
$301$	596756.	−	433569.i	0.379648	−	0.275830i
$302$	−116992.	+	360064.i	−0.0738139	+	0.227176i
$303$		0			0
$304$	1.21890e6	−	885586.i	0.756459	−	0.549600i
$305$	−1.43959e6	−	1.04592e6i	−0.886112	−	0.643798i
$306$		0			0
$307$	669166.			0.405217			0.202609	−	0.979260i	$-0.435058\pi$
$307$	669166.			0.405217			0.202609	+	0.979260i	$0.435058\pi$
$308$	1.54615e6	−	1.78199e6i	0.928699	−	1.07036i
$309$		0			0
$310$	883468.	+	2.71904e6i	0.522140	+	1.60698i
$311$	697316.	+	506629.i	0.408816	+	0.297023i	0.773122	−	0.634257i	$-0.218694\pi$
$311$	697316.	+	506629.i	0.408816	+	0.297023i	−0.364306	+	0.931279i	$0.618694\pi$
$312$		0			0
$313$	298241.	−	917891.i	0.172070	−	0.529578i	−0.827417	−	0.561588i	$-0.810191\pi$
$313$	298241.	−	917891.i	0.172070	−	0.529578i	0.999488	+	0.0320095i	$0.0101907\pi$
$314$	1.37677e6	−	4.23726e6i	0.788019	−	2.42527i
$315$		0			0
$316$	721206.	+	523987.i	0.406295	+	0.295191i
$317$	376906.	+	1.16000e6i	0.210662	+	0.648350i	0.999433	+	0.0336633i	$0.0107174\pi$
$317$	376906.	+	1.16000e6i	0.210662	+	0.648350i	−0.788772	+	0.614686i	$0.789283\pi$
$318$		0			0
$319$	20887.3	−	4842.69i	0.0114922	−	0.00266446i
$320$	−4.35848e6			−2.37936
$321$		0			0
$322$	376165.	+	273300.i	0.202180	+	0.146893i
$323$	110760.	−	80471.5i	0.0590711	−	0.0429176i
$324$		0			0
$325$	221482.	−	681651.i	0.116313	−	0.357976i
$326$	−4.31081e6	+	3.13199e6i	−2.24655	+	1.63221i
$327$		0			0
$328$	1.28520e6	+	3.95545e6i	0.659610	+	2.03007i
$329$	−1.12109e6			−0.571018
$330$		0			0
$331$	460854.			0.231203			0.115601	−	0.993296i	$-0.463120\pi$
$331$	460854.			0.231203			0.115601	+	0.993296i	$0.463120\pi$
$332$	2.61660e6	+	8.05307e6i	1.30284	+	4.00974i
$333$		0			0
$334$	−2.78537e6	+	2.02369e6i	−1.36621	+	0.992609i
$335$	615700.	−	1.89493e6i	0.299749	−	0.922531i
$336$		0			0
$337$	−1.14004e6	+	828286.i	−0.546820	+	0.397288i	−0.826612	−	0.562773i	$-0.809735\pi$
$337$	−1.14004e6	+	828286.i	−0.546820	+	0.397288i	0.279792	+	0.960061i	$0.409735\pi$
$338$	365204.	+	265337.i	0.173878	+	0.126330i
$339$		0			0
$340$	−1.47785e6			−0.693320
$341$	−140375.	+	1.62188e6i	−0.0653739	+	0.755325i
$342$		0			0
$343$	633087.	+	1.94844e6i	0.290555	+	0.894236i
$344$	−4.36934e6	−	3.17451e6i	−1.99077	−	1.44638i
$345$		0			0
$346$	−1.69396e6	+	5.21346e6i	−0.760698	+	2.34119i
$347$	1.04907e6	−	3.22871e6i	0.467716	−	1.43948i	−0.387819	−	0.921736i	$-0.626771\pi$
$347$	1.04907e6	−	3.22871e6i	0.467716	−	1.43948i	0.855535	−	0.517746i	$-0.173229\pi$
$348$		0			0
$349$	−2.47733e6	−	1.79989e6i	−1.08873	−	0.791009i	−0.109547	−	0.993982i	$-0.534940\pi$
$349$	−2.47733e6	−	1.79989e6i	−1.08873	−	0.791009i	−0.979184	+	0.202972i	$0.934940\pi$
$350$	−296676.	−	913073.i	−0.129453	−	0.398415i
$351$		0			0
$352$	−5.63217e6	−	2.38453e6i	−2.42281	−	1.02576i
$353$	−821144.			−0.350738			−0.175369	−	0.984503i	$-0.556112\pi$
$353$	−821144.			−0.350738			−0.175369	+	0.984503i	$0.556112\pi$
$354$		0			0
$355$	−969426.	−	704329.i	−0.408267	−	0.296623i
$356$	−6.38062e6	+	4.63579e6i	−2.66832	+	1.93865i
$357$		0			0
$358$	−175664.	+	540639.i	−0.0724395	+	0.222946i
$359$	3.09087e6	−	2.24565e6i	1.26574	−	0.919614i	0.266716	−	0.963775i	$-0.414061\pi$
$359$	3.09087e6	−	2.24565e6i	1.26574	−	0.919614i	0.999024	+	0.0441609i	$0.0140614\pi$
$360$		0			0
$361$	−688019.	−	2.11751e6i	−0.277864	−	0.855178i
$362$	−1.67032e6			−0.669929
$363$		0			0
$364$	−3.37166e6			−1.33380
$365$	−625937.	−	1.92644e6i	−0.245923	−	0.756872i
$366$		0			0
$367$	2.42146e6	−	1.75929e6i	0.938453	−	0.681826i	−0.00959494	−	0.999954i	$-0.503054\pi$
$367$	2.42146e6	−	1.75929e6i	0.938453	−	0.681826i	0.948048	+	0.318128i	$0.103054\pi$
$368$	564002.	−	1.73582e6i	0.217100	−	0.668166i
$369$		0			0
$370$	8.11736e6	−	5.89761e6i	3.08255	−	2.23961i
$371$	1.13375e6	+	823717.i	0.427644	+	0.310702i
$372$		0			0
$373$	567346.			0.211143			0.105571	−	0.994412i	$-0.466333\pi$
$373$	567346.			0.211143			0.105571	+	0.994412i	$0.466333\pi$
$374$	−1.07904e6	−	456840.i	−0.398895	−	0.168883i
$375$		0			0
$376$	2.53654e6	+	7.80666e6i	0.925277	+	2.84771i
$377$	−24790.1	−	18011.0i	−0.00898306	−	0.00652657i
$378$		0			0
$379$	−365107.	+	1.12368e6i	−0.130564	+	0.401834i	−0.994874	−	0.101126i	$-0.967756\pi$
$379$	−365107.	+	1.12368e6i	−0.130564	+	0.401834i	0.864310	+	0.502960i	$0.167756\pi$
$380$	832668.	−	2.56269e6i	0.295810	−	0.910409i
$381$		0			0
$382$	−6158.04	−	4474.08i	−0.00215916	−	0.00156872i
$383$	904458.	+	2.78364e6i	0.315059	+	0.969651i	0.975730	+	0.218976i	$0.0702716\pi$
$383$	904458.	+	2.78364e6i	0.315059	+	0.969651i	−0.660672	+	0.750675i	$0.729728\pi$
$384$		0			0
$385$	165015.	−	1.90657e6i	0.0567377	−	0.655544i
$386$	−4.00182e6			−1.36707
$387$		0			0
$388$	412285.	+	299542.i	0.139033	+	0.101013i
$389$	2.79823e6	−	2.03304e6i	0.937584	−	0.681194i	−0.0102541	−	0.999947i	$-0.503264\pi$
$389$	2.79823e6	−	2.03304e6i	0.937584	−	0.681194i	0.947838	+	0.318753i	$0.103264\pi$
$390$		0			0
$391$	51249.8	−	157731.i	0.0169531	−	0.0521764i
$392$	4.95781e6	−	3.60206e6i	1.62958	−	1.18396i
$393$		0			0
$394$	437461.	+	1.34637e6i	0.141971	+	0.436941i
$395$	723105.			0.233189
$396$		0			0
$397$	185830.			0.0591752			0.0295876	−	0.999562i	$-0.490581\pi$
$397$	185830.			0.0591752			0.0295876	+	0.999562i	$0.490581\pi$
$398$	2.83689e6	+	8.73104e6i	0.897707	+	2.76286i
$399$		0			0
$400$	−3.04883e6	+	2.21511e6i	−0.952761	+	0.692221i
$401$	−983478.	+	3.02683e6i	−0.305424	+	0.939999i	0.674094	+	0.738645i	$0.264534\pi$
$401$	−983478.	+	3.02683e6i	−0.305424	+	0.939999i	−0.979519	+	0.201354i	$0.935466\pi$
$402$		0			0
$403$	1.88221e6	−	1.36750e6i	0.577304	−	0.419436i
$404$	−8.71778e6	−	6.33384e6i	−2.65737	−	1.93069i
$405$		0			0
$406$	−41045.3			−0.0123580
$407$	5.56569e6	−	1.29040e6i	1.66546	−	0.386134i
$408$		0			0
$409$	799902.	+	2.46184e6i	0.236444	+	0.727700i	0.996927	+	0.0783415i	$0.0249625\pi$
$409$	799902.	+	2.46184e6i	0.236444	+	0.727700i	−0.760483	+	0.649358i	$0.775038\pi$
$410$	4.49220e6	+	3.26377e6i	1.31977	+	0.958871i
$411$		0			0
$412$	935228.	−	2.87834e6i	0.271440	−	0.835407i
$413$	−973141.	+	2.99502e6i	−0.280738	+	0.864022i
$414$		0			0
$415$	5.55664e6	+	4.03714e6i	1.58377	+	1.15068i
$416$	2.70103e6	+	8.31292e6i	0.765237	+	2.35516i
$417$		0			0
$418$	1.40015e6	−	1.61372e6i	0.391954	−	0.451740i
$419$	1.02374e6			0.284876			0.142438	−	0.989804i	$-0.454506\pi$
$419$	1.02374e6			0.284876			0.142438	+	0.989804i	$0.454506\pi$
$420$		0			0
$421$	−312763.	−	227235.i	−0.0860022	−	0.0624843i	0.543953	−	0.839116i	$-0.316927\pi$
$421$	−312763.	−	227235.i	−0.0860022	−	0.0624843i	−0.629955	+	0.776631i	$0.716927\pi$
$422$	4.52724e6	−	3.28923e6i	1.23752	−	0.899110i
$423$		0			0
$424$	3.17074e6	−	9.75855e6i	0.856538	−	2.63615i
$425$	−277042.	+	201283.i	−0.0744000	+	0.0540548i
$426$		0			0
$427$	599387.	+	1.84472e6i	0.159088	+	0.489622i
$428$	1.36347e6			0.359780
$429$		0			0
$430$	−7.21059e6			−1.88061
$431$	−394527.	−	1.21423e6i	−0.102302	−	0.314853i	0.886786	−	0.462181i	$-0.152933\pi$
$431$	−394527.	−	1.21423e6i	−0.102302	−	0.314853i	−0.989088	+	0.147328i	$0.952933\pi$
$432$		0			0
$433$	−334227.	+	242830.i	−0.0856686	+	0.0622419i	−0.629795	−	0.776761i	$-0.716861\pi$
$433$	−334227.	+	242830.i	−0.0856686	+	0.0622419i	0.544127	+	0.839003i	$0.316861\pi$
$434$	963020.	−	2.96387e6i	0.245420	−	0.755327i
$435$		0			0
$436$	−9.82108e6	+	7.13543e6i	−2.47425	+	1.79765i
$437$	244639.	+	177741.i	0.0612805	+	0.0445229i
$438$		0			0
$439$	−5.84167e6			−1.44669			−0.723345	−	0.690487i	$-0.757396\pi$
$439$	−5.84167e6			−1.44669			−0.723345	+	0.690487i	$0.757396\pi$
$440$	−1.36497e7	+	3.16467e6i	−3.36118	+	0.779287i
$441$		0			0
$442$	517477.	+	1.59263e6i	0.125990	+	0.387757i
$443$	−24112.0	−	17518.4i	−0.00583747	−	0.00424117i	0.584863	−	0.811132i	$-0.301148\pi$
$443$	−24112.0	−	17518.4i	−0.00583747	−	0.00424117i	−0.590700	+	0.806891i	$0.701148\pi$
$444$		0			0
$445$	−1.97691e6	+	6.08431e6i	−0.473246	+	1.45650i
$446$	1.20288e6	−	3.70209e6i	0.286343	−	0.881272i
$447$		0			0
$448$	3.84359e6	+	2.79253e6i	0.904777	+	0.657359i
$449$	−1.18744e6	−	3.65457e6i	−0.277969	−	0.855502i	−0.988418	−	0.151753i	$-0.951508\pi$
$449$	−1.18744e6	−	3.65457e6i	−0.277969	−	0.855502i	0.710449	−	0.703749i	$-0.248492\pi$
$450$		0			0
$451$	1.63097e6	+	2.70867e6i	0.377575	+	0.627067i
$452$	−949103.			−0.218508
$453$		0			0
$454$	−7.55288e6	−	5.48748e6i	−1.71978	−	1.24949i
$455$	−2.21259e6	+	1.60754e6i	−0.501040	+	0.364027i
$456$		0			0
$457$	1.78295e6	−	5.48734e6i	0.399345	−	1.22906i	−0.526181	−	0.850372i	$-0.676377\pi$
$457$	1.78295e6	−	5.48734e6i	0.399345	−	1.22906i	0.925526	−	0.378684i	$-0.123623\pi$
$458$	5.26285e6	−	3.82368e6i	1.17235	−	0.851762i
$459$		0			0
$460$	−1.00869e6	−	3.10443e6i	−0.222261	−	0.684049i
$461$	2.92986e6			0.642088			0.321044	−	0.947064i	$-0.395966\pi$
$461$	2.92986e6			0.642088			0.321044	+	0.947064i	$0.395966\pi$
$462$		0			0
$463$	8.36147e6			1.81272			0.906358	−	0.422510i	$-0.138851\pi$
$463$	8.36147e6			1.81272			0.906358	+	0.422510i	$0.138851\pi$
$464$	49787.8	+	153231.i	0.0107356	+	0.0330409i
$465$		0			0
$466$	1.05878e7	−	7.69246e6i	2.25860	−	1.64097i
$467$	−1.91960e6	+	5.90792e6i	−0.407304	+	1.25355i	0.511653	+	0.859192i	$0.329033\pi$
$467$	−1.91960e6	+	5.90792e6i	−0.407304	+	1.25355i	−0.918956	+	0.394359i	$0.870967\pi$
$468$		0			0
$469$	−1.75707e6	+	1.27658e6i	−0.368856	+	0.267989i
$470$	8.86602e6	+	6.44154e6i	1.85133	+	1.34507i
$471$		0			0
$472$	2.30575e7			4.76385
$473$	−3.78094e6	−	1.60076e6i	−0.777047	−	0.328983i
$474$		0			0
$475$	−192943.	−	593817.i	−0.0392369	−	0.120759i
$476$	1.30327e6	+	946877.i	0.263642	+	0.191547i
$477$		0			0
$478$	−105273.	+	323998.i	−0.0210741	+	0.0648594i
$479$	−360534.	+	1.10961e6i	−0.0717972	+	0.220969i	−0.980516	−	0.196440i	$-0.937062\pi$
$479$	−360534.	+	1.10961e6i	−0.0717972	+	0.220969i	0.908719	+	0.417409i	$0.137062\pi$
$480$		0			0
$481$	−6.60565e6	−	4.79929e6i	−1.30183	−	0.945832i
$482$	−4.30055e6	−	1.32357e7i	−0.843153	−	2.59496i
$483$		0			0
$484$	−1.29369e7	−	2.25630e6i	−2.51025	−	0.437808i
$485$	413370.			0.0797967
$486$		0			0
$487$	−56883.3	−	41328.1i	−0.0108683	−	0.00789630i	0.582338	−	0.812947i	$-0.302138\pi$
$487$	−56883.3	−	41328.1i	−0.0108683	−	0.00789630i	−0.593206	+	0.805051i	$0.702138\pi$
$488$	1.14895e7	−	8.34762e6i	2.18400	−	1.58677i
$489$		0			0
$490$	2.52829e6	−	7.78128e6i	0.475704	−	1.46407i
$491$	−5.58747e6	+	4.05954e6i	−1.04595	+	0.759929i	−0.971439	−	0.237291i	$-0.923740\pi$
$491$	−5.58747e6	+	4.05954e6i	−1.04595	+	0.759929i	−0.0745136	+	0.997220i	$0.523740\pi$
$492$		0			0
$493$	4524.12	+	13923.8i	0.000838333	+	0.00258013i
$494$	−3.05329e6			−0.562924
$495$		0			0
$496$	−1.22329e7			−2.23267
$497$	403630.	+	1.24225e6i	0.0732981	+	0.225588i
$498$		0			0
$499$	6.39386e6	−	4.64541e6i	1.14951	−	0.835166i	0.161092	−	0.986939i	$-0.448498\pi$
$499$	6.39386e6	−	4.64541e6i	1.14951	−	0.835166i	0.988415	+	0.151773i	$0.0484983\pi$
$500$	3.12537e6	−	9.61891e6i	0.559084	−	1.72068i
$501$		0			0
$502$	−293213.	+	213032.i	−0.0519306	+	0.0377298i
$503$	−1.03146e6	−	749402.i	−0.181775	−	0.132067i	0.493177	−	0.869929i	$-0.335836\pi$
$503$	−1.03146e6	−	749402.i	−0.181775	−	0.132067i	−0.674952	+	0.737862i	$0.735836\pi$
$504$		0			0
$505$	−8.74074e6			−1.52517
$506$	223169.	−	2.57848e6i	0.0387488	−	0.447700i
$507$		0			0
$508$	−5.76401e6	−	1.77398e7i	−0.990981	−	3.04993i
$509$	−1.81014e6	−	1.31514e6i	−0.309683	−	0.224998i	0.422078	−	0.906560i	$-0.361301\pi$
$509$	−1.81014e6	−	1.31514e6i	−0.309683	−	0.224998i	−0.731760	+	0.681562i	$0.761301\pi$
$510$		0			0
$511$	−682299.	+	2.09990e6i	−0.115591	+	0.355751i
$512$	−1.53931e6	+	4.73750e6i	−0.259508	+	0.798682i
$513$		0			0
$514$	1.15287e7	+	8.37608e6i	1.92474	+	1.39841i
$515$	−758608.	−	2.33475e6i	−0.126037	−	0.387903i
$516$		0			0
$517$	3.21895e6	+	5.34596e6i	0.529649	+	0.879628i
$518$	−1.09371e7			−1.79092
$519$		0			0
$520$	1.62002e7	+	1.17701e7i	2.62731	+	1.90885i
$521$	2.79705e6	−	2.03218e6i	0.451447	−	0.327995i	−0.338720	−	0.940887i	$-0.609994\pi$
$521$	2.79705e6	−	2.03218e6i	0.451447	−	0.327995i	0.790167	+	0.612892i	$0.209994\pi$
$522$		0			0
$523$	−3.06458e6	+	9.43180e6i	−0.489910	+	1.50779i	0.334832	+	0.942278i	$0.391321\pi$
$523$	−3.06458e6	+	9.43180e6i	−0.489910	+	1.50779i	−0.824742	+	0.565510i	$0.808679\pi$
$524$	−1.93629e7	+	1.40680e7i	−3.08065	+	2.23822i
$525$		0			0
$526$	−5.72211e6	−	1.76109e7i	−0.901762	−	2.77534i
$527$	−1.11158e6			−0.174347
$528$		0			0
$529$	−6.07003e6			−0.943087
$530$	−4.23324e6	−	1.30286e7i	−0.654612	−	2.01469i
$531$		0			0
$532$	−2.37625e6	+	1.72644e6i	−0.364009	+	0.264468i
$533$	1.39632e6	−	4.29743e6i	0.212896	−	0.655225i
$534$		0			0
$535$	894755.	−	650078.i	0.135151	−	0.0981931i
$536$	1.28649e7	+	9.34693e6i	1.93418	+	1.40526i
$537$		0			0
$538$	−1.60104e7			−2.38477
$539$	3.05319e6	−	3.51890e6i	0.452670	−	0.521718i
$540$		0			0
$541$	3.15125e6	+	9.69856e6i	0.462903	+	1.42467i	0.861600	+	0.507587i	$0.169462\pi$
$541$	3.15125e6	+	9.69856e6i	0.462903	+	1.42467i	−0.398697	+	0.917083i	$0.630538\pi$
$542$	−1.51659e7	−	1.10187e7i	−2.21754	−	1.61113i
$543$		0			0
$544$	1.29051e6	−	3.97178e6i	0.186967	−	0.575424i
$545$	−3.04287e6	+	9.36500e6i	−0.438826	+	1.35057i
$546$		0			0
$547$	−901879.	−	655253.i	−0.128878	−	0.0936356i	0.521479	−	0.853264i	$-0.325381\pi$
$547$	−901879.	−	655253.i	−0.128878	−	0.0936356i	−0.650357	+	0.759629i	$0.725381\pi$
$548$	3.24604e6	+	9.99030e6i	0.461746	+	1.42111i
$549$		0			0
$550$	−3.50219e6	+	4.03640e6i	−0.493666	+	0.568967i
$551$	−26693.8			−0.00374568
$552$		0			0
$553$	−637681.	−	463302.i	−0.0886728	−	0.0644246i
$554$	4.45051e6	−	3.23349e6i	0.616078	−	0.447607i
$555$		0			0
$556$	−8.12197e6	+	2.49969e7i	−1.11423	+	3.42925i
$557$	1.48966e6	−	1.08230e6i	0.203446	−	0.147812i	−0.481397	−	0.876502i	$-0.659871\pi$
$557$	1.48966e6	−	1.08230e6i	0.203446	−	0.147812i	0.684843	+	0.728690i	$0.259871\pi$
$558$		0			0
$559$	1.81323e6	+	5.58056e6i	0.245428	+	0.755350i
$560$	1.43801e7			1.93773
$561$		0			0
$562$	3.23405e6			0.431923
$563$	4.30888e6	+	1.32614e7i	0.572919	+	1.76326i	0.643157	+	0.765734i	$0.277624\pi$
$563$	4.30888e6	+	1.32614e7i	0.572919	+	1.76326i	−0.0702375	+	0.997530i	$0.522376\pi$
$564$		0			0
$565$	−622832.	+	452514.i	−0.0820823	+	0.0596363i
$566$	−3.99150e6	+	1.22846e7i	−0.523715	+	1.61183i
$567$		0			0
$568$	7.73710e6	−	5.62133e6i	1.00625	−	0.731086i
$569$	−879336.	−	638875.i	−0.113861	−	0.0827247i	0.529398	−	0.848374i	$-0.322418\pi$
$569$	−879336.	−	638875.i	−0.113861	−	0.0827247i	−0.643259	+	0.765649i	$0.722418\pi$
$570$		0			0
$571$	6.57297e6			0.843667			0.421834	−	0.906673i	$-0.361387\pi$
$571$	6.57297e6			0.843667			0.421834	+	0.906673i	$0.361387\pi$
$572$	9.68096e6	+	1.60779e7i	1.23717	+	2.05466i
$573$		0			0
$574$	−1.87037e6	−	5.75641e6i	−0.236945	−	0.729243i
$575$	−611913.	−	444581.i	−0.0771828	−	0.0560766i
$576$		0			0
$577$	873764.	−	2.68917e6i	0.109258	−	0.336262i	−0.881448	−	0.472281i	$-0.843431\pi$
$577$	873764.	−	2.68917e6i	0.109258	−	0.336262i	0.990706	+	0.136019i	$0.0434307\pi$
$578$	−4.42798e6	+	1.36279e7i	−0.551298	+	1.69672i
$579$		0			0
$580$	233118.	+	169370.i	0.0287743	+	0.0209058i
$581$	−2.31356e6	−	7.12041e6i	−0.284342	−	0.875115i
$582$		0			0
$583$	672624.	−	7.77146e6i	0.0819599	−	0.946959i
$584$	1.61663e7			1.96146
$585$		0			0
$586$	−4.98493e6	−	3.62177e6i	−0.599674	−	0.435689i
$587$	−1.83768e6	+	1.33515e6i	−0.220127	+	0.159932i	−0.692384	−	0.721529i	$-0.743440\pi$
$587$	−1.83768e6	+	1.33515e6i	−0.220127	+	0.159932i	0.472257	+	0.881461i	$0.343440\pi$
$588$		0			0
$589$	626299.	−	1.92755e6i	0.0743864	−	0.228938i
$590$	2.49048e7	−	1.80944e7i	2.94546	−	2.14000i
$591$		0			0
$592$	1.32666e7	+	4.08305e7i	1.55581	+	4.78829i
$593$	−8.18469e6			−0.955796			−0.477898	−	0.878415i	$-0.658601\pi$
$593$	−8.18469e6			−0.955796			−0.477898	+	0.878415i	$0.658601\pi$
$594$		0			0
$595$	1.30670e6			0.151315
$596$	−1.03409e7	−	3.18260e7i	−1.19246	−	3.67000i
$597$		0			0
$598$	−2.99234e6	+	2.17406e6i	−0.342183	+	0.248610i
$599$	−1.80868e6	+	5.56656e6i	−0.205966	+	0.633899i	0.793706	+	0.608301i	$0.208149\pi$
$599$	−1.80868e6	+	5.56656e6i	−0.205966	+	0.633899i	−0.999672	+	0.0255973i	$0.991851\pi$
$600$		0			0
$601$	7.39574e6	−	5.37332e6i	0.835209	−	0.606815i	−0.0858191	−	0.996311i	$-0.527351\pi$
$601$	7.39574e6	−	5.37332e6i	0.835209	−	0.606815i	0.921028	+	0.389496i	$0.127351\pi$
$602$	6.35876e6	+	4.61991e6i	0.715124	+	0.519568i
$603$		0			0
$604$	−2.89715e6			−0.323131
$605$	−9.56538e6	+	4.68742e6i	−1.06246	+	0.520649i
$606$		0			0
$607$	1.75802e6	+	5.41063e6i	0.193666	+	0.596041i	0.999990	+	0.00456725i	$0.00145381\pi$
$607$	1.75802e6	+	5.41063e6i	0.193666	+	0.596041i	−0.806324	+	0.591474i	$0.798546\pi$
$608$	6.16020e6	+	4.47565e6i	0.675828	+	0.491018i
$609$		0			0
$610$	5.85920e6	−	1.80328e7i	0.637550	−	1.96218i
$611$	2.75584e6	−	8.48161e6i	0.298642	−	0.919127i
$612$		0			0
$613$	−8.29617e6	−	6.02752e6i	−0.891716	−	0.647870i	0.0446088	−	0.999005i	$-0.485796\pi$
$613$	−8.29617e6	−	6.02752e6i	−0.891716	−	0.647870i	−0.936325	+	0.351135i	$0.885796\pi$
$614$	2.20339e6	+	6.78135e6i	0.235869	+	0.725931i
$615$		0			0
$616$	1.40649e7	+	5.95473e6i	1.49342	+	0.632281i
$617$	7.21223e6			0.762705			0.381353	−	0.924430i	$-0.375458\pi$
$617$	7.21223e6			0.762705			0.381353	+	0.924430i	$0.375458\pi$
$618$		0			0
$619$	−6.28879e6	−	4.56907e6i	−0.659691	−	0.479293i	0.206868	−	0.978369i	$-0.433673\pi$
$619$	−6.28879e6	−	4.56907e6i	−0.659691	−	0.479293i	−0.866558	+	0.499076i	$0.833673\pi$
$620$	−1.76997e7	+	1.28596e7i	−1.84921	+	1.34353i
$621$		0			0
$622$	−2.83811e6	+	8.73482e6i	−0.294140	+	0.905269i
$623$	5.64166e6	−	4.09890e6i	0.582354	−	0.423105i
$624$		0			0
$625$	−3.74194e6	−	1.15165e7i	−0.383175	−	1.17929i
$626$	1.02840e7			1.04888
$627$		0			0
$628$	3.40939e7			3.44967
$629$	1.20551e6	+	3.71019e6i	0.121491	+	0.373912i
$630$		0			0
$631$	7.24522e6	−	5.26396e6i	0.724399	−	0.526307i	−0.163388	−	0.986562i	$-0.552242\pi$
$631$	7.24522e6	−	5.26396e6i	0.724399	−	0.526307i	0.887787	+	0.460255i	$0.152242\pi$
$632$	−1.78339e6	+	5.48872e6i	−0.177605	+	0.546611i
$633$		0			0
$634$	−1.05144e7	+	7.63916e6i	−1.03887	+	0.754783i
$635$	−1.22405e7	−	8.89326e6i	−1.20466	−	0.875239i
$636$		0			0
$637$	−6.65802e6			−0.650125
$638$	117852.	+	195726.i	0.0114627	+	0.0190370i
$639$		0			0
$640$	−4.38347e6	−	1.34909e7i	−0.423027	−	1.30194i
$641$	−7.74345e6	−	5.62595e6i	−0.744371	−	0.540817i	0.149706	−	0.988731i	$-0.452167\pi$
$641$	−7.74345e6	−	5.62595e6i	−0.744371	−	0.540817i	−0.894077	+	0.447913i	$0.852167\pi$
$642$		0			0
$643$	−5.25167e6	+	1.61630e7i	−0.500922	+	1.54168i	0.306599	+	0.951839i	$0.400809\pi$
$643$	−5.25167e6	+	1.61630e7i	−0.500922	+	1.54168i	−0.807520	+	0.589840i	$0.799191\pi$
$644$	−1.09952e6	+	3.38397e6i	−0.104469	+	0.321522i
$645$		0			0
$646$	1.18020e6	+	857468.i	0.111269	+	0.0808419i
$647$	3.05671e6	+	9.40759e6i	0.287074	+	0.883523i	0.985769	+	0.168104i	$0.0537643\pi$
$647$	3.05671e6	+	9.40759e6i	0.287074	+	0.883523i	−0.698695	+	0.715419i	$0.746236\pi$
$648$		0			0
$649$	1.70760e7	−	3.95906e6i	1.59139	−	0.368961i
$650$	7.63716e6			0.709003
$651$		0			0
$652$	−3.29881e7	−	2.39673e7i	−3.03906	−	2.20800i
$653$	7.94229e6	−	5.77041e6i	0.728891	−	0.529570i	−0.160321	−	0.987065i	$-0.551253\pi$
$653$	7.94229e6	−	5.77041e6i	0.728891	−	0.529570i	0.889212	+	0.457494i	$0.151253\pi$
$654$		0			0
$655$	−5.99922e6	+	1.84637e7i	−0.546376	+	1.68157i
$656$	−1.92212e7	+	1.39650e7i	−1.74390	+	1.26701i
$657$		0			0
$658$	−3.69146e6	−	1.13611e7i	−0.332379	−	1.02296i
$659$	−3.66539e6			−0.328781			−0.164390	−	0.986395i	$-0.552566\pi$
$659$	−3.66539e6			−0.328781			−0.164390	+	0.986395i	$0.552566\pi$
$660$		0			0
$661$	−1.37346e7			−1.22268			−0.611340	−	0.791368i	$-0.709369\pi$
$661$	−1.37346e7			−1.22268			−0.611340	+	0.791368i	$0.709369\pi$
$662$	1.51747e6	+	4.67031e6i	0.134579	+	0.414191i
$663$		0			0
$664$	−4.43482e7	+	3.22209e7i	−3.90351	+	2.83607i
$665$	−736234.	+	2.26589e6i	−0.0645597	+	0.198694i
$666$		0			0
$667$	−26161.0	+	19007.1i	−0.00227688	+	0.00165425i
$668$	−2.13148e7	−	1.54861e7i	−1.84817	−	1.34277i
$669$		0			0
$670$	2.12306e7			1.82716
$671$	7.07564e6	−	8.15491e6i	0.606679	−	0.699218i
$672$		0			0
$673$	2.84987e6	+	8.77099e6i	0.242542	+	0.746468i	0.996031	+	0.0890072i	$0.0283694\pi$
$673$	2.84987e6	+	8.77099e6i	0.242542	+	0.746468i	−0.753489	+	0.657461i	$0.771631\pi$
$674$	−1.21477e7	−	8.82584e6i	−1.03002	−	0.748352i
$675$		0			0
$676$	−1.06748e6	+	3.28536e6i	−0.0898447	+	0.276514i
$677$	1.99869e6	−	6.15134e6i	0.167600	−	0.515820i	−0.831618	−	0.555347i	$-0.812585\pi$
$677$	1.99869e6	−	6.15134e6i	0.167600	−	0.515820i	0.999218	+	0.0395276i	$0.0125853\pi$
$678$		0			0
$679$	−364537.	−	264851.i	−0.0303436	−	0.0220459i
$680$	−2.95649e6	−	9.09914e6i	−0.245191	−	0.754620i
$681$		0			0
$682$	−1.68984e7	+	3.91789e6i	−1.39119	+	0.322545i
$683$	2.01977e7			1.65672			0.828360	−	0.560196i	$-0.189274\pi$
$683$	2.01977e7			1.65672			0.828360	+	0.560196i	$0.189274\pi$
$684$		0			0
$685$	6.89334e6	+	5.00830e6i	0.561310	+	0.407816i
$686$	−1.76610e7	+	1.28314e7i	−1.43286	+	1.04103i
$687$		0			0
$688$	9.53398e6	−	2.93426e7i	0.767897	−	2.36334i
$689$	−9.01882e6	+	6.55255e6i	−0.723772	+	0.525851i
$690$		0			0
$691$	−5.53560e6	−	1.70368e7i	−0.441032	−	1.35736i	−0.886778	−	0.462196i	$-0.847062\pi$
$691$	−5.53560e6	−	1.70368e7i	−0.441032	−	1.35736i	0.445746	−	0.895160i	$-0.352938\pi$
$692$	−4.19487e7			−3.33007
$693$		0			0
$694$	3.61742e7			2.85102
$695$	6.58812e6	+	2.02761e7i	0.517368	+	1.59229i
$696$		0			0
$697$	−1.74659e6	+	1.26897e6i	−0.136179	+	0.0989397i
$698$	1.00829e7	−	3.10319e7i	0.783332	−	2.41085i
$699$		0			0
$700$	5.94368e6	−	4.31834e6i	0.458470	−	0.333098i
$701$	−873359.	−	634532.i	−0.0671271	−	0.0487707i	0.553716	−	0.832706i	$-0.313209\pi$
$701$	−873359.	−	634532.i	−0.0671271	−	0.0487707i	−0.620843	+	0.783935i	$0.713209\pi$
$702$		0			0
$703$	−7.11293e6			−0.542825
$704$	2.28030e6	−	2.63464e7i	0.173405	−	2.00350i
$705$		0			0
$706$	−2.70382e6	−	8.32150e6i	−0.204158	−	0.628333i
$707$	7.70815e6	+	5.60030e6i	0.579964	+	0.421369i
$708$		0			0
$709$	5.85590e6	−	1.80226e7i	0.437500	−	1.34649i	−0.453003	−	0.891509i	$-0.649647\pi$
$709$	5.85590e6	−	1.80226e7i	0.437500	−	1.34649i	0.890503	−	0.454978i	$-0.150353\pi$
$710$	3.94562e6	−	1.21434e7i	0.293744	−	0.904052i
$711$		0			0
$712$	−4.13072e7	−	3.00115e7i	−3.05370	−	2.21864i
$713$	−758696.	−	2.33503e6i	−0.0558913	−	0.172016i
$714$		0			0
$715$	1.40186e7	+	5.93514e6i	1.02551	+	0.434176i
$716$	−4.35010e6			−0.317115
$717$		0			0
$718$	3.29349e7	+	2.39286e7i	2.38421	+	1.73223i
$719$	2.05645e6	−	1.49410e6i	0.148353	−	0.107785i	−0.511133	−	0.859502i	$-0.670774\pi$
$719$	2.05645e6	−	1.49410e6i	0.148353	−	0.107785i	0.659486	+	0.751717i	$0.270774\pi$
$720$		0			0
$721$	−826916.	+	2.54499e6i	−0.0592411	+	0.182325i
$722$	1.91934e7	−	1.39448e7i	1.37028	−	0.995565i
$723$		0			0
$724$	−3.94986e6	−	1.21564e7i	−0.280050	−	0.861904i
$725$	66769.0			0.00471769
$726$		0			0
$727$	7.53115e6			0.528476			0.264238	−	0.964457i	$-0.414880\pi$
$727$	7.53115e6			0.528476			0.264238	+	0.964457i	$0.414880\pi$
$728$	−6.74511e6	−	2.07593e7i	−0.471694	−	1.45173i
$729$		0			0
$730$	1.74615e7	−	1.26865e7i	1.21276	−	0.881121i
$731$	866335.	−	2.66630e6i	0.0599642	−	0.184551i
$732$		0			0
$733$	2.51367e6	−	1.82629e6i	0.172802	−	0.125548i	−0.498023	−	0.867164i	$-0.665940\pi$
$733$	2.51367e6	−	1.82629e6i	0.172802	−	0.125548i	0.670825	+	0.741616i	$0.265940\pi$
$734$	2.58020e7	+	1.87462e7i	1.76772	+	1.28432i
$735$		0			0
$736$	9.22409e6			0.627666
$737$	1.11325e7	+	4.71323e6i	0.754959	+	0.319632i
$738$		0			0
$739$	−521584.	−	1.60527e6i	−0.0351329	−	0.108128i	0.931952	−	0.362581i	$-0.118104\pi$
$739$	−521584.	−	1.60527e6i	−0.0351329	−	0.108128i	−0.967085	+	0.254453i	$0.918104\pi$
$740$	6.21174e7	+	4.51309e7i	4.16998	+	3.02967i
$741$		0			0
$742$	−4.61443e6	+	1.42017e7i	−0.307686	+	0.946960i
$743$	1.67512e6	−	5.15548e6i	0.111320	−	0.342608i	−0.879842	−	0.475267i	$-0.842352\pi$
$743$	1.67512e6	−	5.15548e6i	0.111320	−	0.342608i	0.991162	+	0.132659i	$0.0423516\pi$
$744$		0			0
$745$	−2.19600e7	−	1.59549e7i	−1.44958	−	1.05318i
$746$	1.86813e6	+	5.74950e6i	0.122902	+	0.378253i
$747$		0			0
$748$	773194.	−	8.93342e6i	0.0505283	−	0.583800i
$749$	−1.20557e6			−0.0785211
$750$		0			0
$751$	6.46888e6	+	4.69992e6i	0.418533	+	0.304082i	0.777047	−	0.629442i	$-0.216717\pi$
$751$	6.46888e6	+	4.69992e6i	0.418533	+	0.304082i	−0.358515	+	0.933524i	$0.616717\pi$
$752$	−3.79359e7	+	2.75620e7i	−2.44628	+	1.77732i
$753$		0			0
$754$	100897.	−	310529.i	0.00646323	−	0.0198918i
$755$	−1.90120e6	+	1.38131e6i	−0.121384	+	0.0881907i
$756$		0			0
$757$	4.46596e6	+	1.37448e7i	0.283253	+	0.871764i	0.986917	+	0.161231i	$0.0515463\pi$
$757$	4.46596e6	+	1.37448e7i	0.283253	+	0.871764i	−0.703663	+	0.710533i	$0.748454\pi$
$758$	−1.25897e7			−0.795868
$759$		0			0
$760$	1.74443e7			1.09552
$761$	−1.98555e6	−	6.11089e6i	−0.124285	−	0.382510i	0.869485	−	0.493959i	$-0.164451\pi$
$761$	−1.98555e6	−	6.11089e6i	−0.124285	−	0.382510i	−0.993770	+	0.111449i	$0.964451\pi$
$762$		0			0
$763$	8.68367e6	−	6.30906e6i	0.539998	−	0.392331i
$764$	17999.7	−	55397.5i	0.00111566	−	0.00343366i
$765$		0			0
$766$	−2.52313e7	+	1.83316e7i	−1.55370	+	1.12883i
$767$	−2.02667e7	−	1.47246e7i	−1.24393	−	0.903766i
$768$		0			0
$769$	793762.			0.0484032			0.0242016	−	0.999707i	$-0.492296\pi$
$769$	793762.			0.0484032			0.0242016	+	0.999707i	$0.492296\pi$
$770$	1.98646e7	−	4.60559e6i	1.20741	−	0.279936i
$771$		0			0
$772$	−9.46322e6	−	2.91248e7i	−0.571473	−	1.75881i
$773$	830545.	+	603426.i	0.0499936	+	0.0363225i	0.612501	−	0.790469i	$-0.290163\pi$
$773$	830545.	+	603426.i	0.0499936	+	0.0363225i	−0.562508	+	0.826792i	$0.690163\pi$
$774$		0			0
$775$	−1.56656e6	+	4.82137e6i	−0.0936898	+	0.288347i
$776$	−1.01950e6	+	3.13768e6i	−0.0607758	+	0.187049i
$777$		0			0
$778$	2.98167e7	+	2.16631e7i	1.76608	+	1.28313i
$779$	−1.21640e6	−	3.74368e6i	−0.0718177	−	0.221032i
$780$		0			0
$781$	4.76477e6	−	5.49156e6i	0.279521	−	0.322157i
$782$	1.76720e6			0.103340
$783$		0			0
$784$	2.83220e7	+	2.05771e7i	1.64563	+	1.19562i
$785$	2.23735e7	−	1.62553e7i	1.29587	−	0.941503i
$786$		0			0
$787$	6.61607e6	−	2.03622e7i	0.380770	−	1.17189i	−0.558732	−	0.829348i	$-0.688712\pi$
$787$	6.61607e6	−	2.03622e7i	0.380770	−	1.17189i	0.939502	−	0.342542i	$-0.111288\pi$
$788$	−8.76421e6	+	6.36757e6i	−0.502802	+	0.365307i
$789$		0			0
$790$	2.38100e6	+	7.32797e6i	0.135735	+	0.417749i
$791$	839184.			0.0476888
$792$		0			0
$793$	−1.54297e7			−0.871313
$794$	611891.	+	1.88321e6i	0.0344447	+	0.106010i
$795$		0			0
$796$	−5.68350e7	+	4.12930e7i	−3.17931	+	2.30991i
$797$	−80574.7	+	247983.i	−0.00449317	+	0.0138286i	−0.953278	−	0.302095i	$-0.902314\pi$
$797$	−80574.7	+	247983.i	−0.00449317	+	0.0138286i	0.948785	+	0.315923i	$0.102314\pi$
$798$		0			0
$799$	−3.44716e6	+	2.50451e6i	−0.191027	+	0.138789i
$800$	−1.54085e7	−	1.11949e7i	−0.851206	−	0.618437i
$801$		0			0
$802$	−3.39123e7			−1.86175
$803$	1.19725e7	−	2.77582e6i	0.655236	−	0.151916i
$804$		0			0
$805$	891870.	+	2.74489e6i	0.0485078	+	0.149292i
$806$	2.00559e7	+	1.45715e7i	1.08744	+	0.790071i
$807$		0			0
$808$	2.15573e7	−	6.63465e7i	1.16162	−	3.57511i
$809$	596982.	−	1.83732e6i	0.0320693	−	0.0986992i	−0.933741	−	0.357950i	$-0.883476\pi$
$809$	596982.	−	1.83732e6i	0.0320693	−	0.0986992i	0.965810	+	0.259251i	$0.0834757\pi$
$810$		0			0
$811$	4.07864e6	+	2.96330e6i	0.217752	+	0.158206i	0.691314	−	0.722554i	$-0.257032\pi$
$811$	4.07864e6	+	2.96330e6i	0.217752	+	0.158206i	−0.473562	+	0.880760i	$0.657032\pi$
$812$	−97060.9	−	298723.i	−0.00516600	−	0.0158993i
$813$		0			0
$814$	3.14034e7	+	5.21539e7i	1.66117	+	2.75884i
$815$	−3.30750e7			−1.74424
$816$		0			0
$817$	4.13542e6	+	3.00456e6i	0.216753	+	0.157480i
$818$	−2.23145e7	+	1.62125e7i	−1.16602	+	0.847160i
$819$		0			0
$820$	−1.31305e7	+	4.04116e7i	−0.681942	+	2.09880i
$821$	−3.86238e6	+	2.80618e6i	−0.199985	+	0.145297i	−0.683271	−	0.730165i	$-0.739443\pi$
$821$	−3.86238e6	+	2.80618e6i	−0.199985	+	0.145297i	0.483286	+	0.875462i	$0.339443\pi$
$822$		0			0
$823$	−9.09780e6	−	2.80001e7i	−0.468206	−	1.44099i	−0.854906	−	0.518784i	$-0.826385\pi$
$823$	−9.09780e6	−	2.80001e7i	−0.468206	−	1.44099i	0.386700	−	0.922206i	$-0.373615\pi$
$824$	1.95929e7			1.00526
$825$		0			0
$826$	−3.35559e7			−1.71127
$827$	−5.71840e6	−	1.75994e7i	−0.290744	−	0.894818i	−0.984618	−	0.174722i	$-0.944097\pi$
$827$	−5.71840e6	−	1.75994e7i	−0.290744	−	0.894818i	0.693874	−	0.720097i	$-0.255903\pi$
$828$		0			0
$829$	2.57582e7	−	1.87144e7i	1.30175	−	0.945779i	0.301782	−	0.953377i	$-0.402419\pi$
$829$	2.57582e7	−	1.87144e7i	1.30175	−	0.945779i	0.999971	+	0.00759794i	$0.00241852\pi$
$830$	−2.26158e7	+	6.96044e7i	−1.13951	+	3.50705i
$831$		0			0
$832$	−3.05752e7	+	2.22142e7i	−1.53130	+	1.11256i
$833$	2.57356e6	+	1.86980e6i	0.128506	+	0.0933648i
$834$		0			0
$835$	−2.13710e7			−1.06074
$836$	1.50555e7	+	6.37414e6i	0.745039	+	0.315432i
$837$		0			0
$838$	3.37092e6	+	1.03746e7i	0.165821	+	0.510343i
$839$	2.65961e7	+	1.93232e7i	1.30441	+	0.947708i	0.999988	−	0.00483004i	$-0.00153745\pi$
$839$	2.65961e7	+	1.93232e7i	1.30441	+	0.947708i	0.304420	+	0.952538i	$0.401537\pi$
$840$		0			0
$841$	−6.33741e6	+	1.95045e7i	−0.308974	+	0.950924i
$842$	1.27296e6	−	3.91777e6i	0.0618779	−	0.190440i
$843$		0			0
$844$	3.46443e7	+	2.51705e7i	1.67408	+	1.21629i
$845$	865883.	+	2.66491e6i	0.0417174	+	0.128393i
$846$		0			0
$847$	1.14387e7	+	1.99499e6i	0.547856	+	0.0955504i
$848$	5.86155e7			2.79913
$849$		0			0
$850$	−2.95203e6	−	2.14478e6i	−0.140144	−	0.101820i
$851$	−6.97095e6	+	5.06469e6i	−0.329965	+	0.239734i
$852$		0			0
$853$	4.75432e6	−	1.46323e7i	0.223726	−	0.688557i	−0.774693	−	0.632338i	$-0.782095\pi$
$853$	4.75432e6	−	1.46323e7i	0.223726	−	0.688557i	0.998418	−	0.0562190i	$-0.0179045\pi$
$854$	−1.67208e7	+	1.21484e7i	−0.784537	+	0.569999i
$855$		0			0
$856$	2.72768e6	+	8.39492e6i	0.127235	+	0.391591i
$857$	2.72088e7			1.26549			0.632744	−	0.774361i	$-0.281929\pi$
$857$	2.72088e7			1.26549			0.632744	+	0.774361i	$0.281929\pi$
$858$		0			0
$859$	2.50657e7			1.15904			0.579519	−	0.814959i	$-0.303241\pi$
$859$	2.50657e7			1.15904			0.579519	+	0.814959i	$0.303241\pi$
$860$	−1.70511e7	−	5.24778e7i	−0.786150	−	2.41952i
$861$		0			0
$862$	1.10060e7	−	7.99629e6i	0.504498	−	0.366539i
$863$	2.96864e6	−	9.13654e6i	0.135685	−	0.417594i	−0.860011	−	0.510275i	$-0.829544\pi$
$863$	2.96864e6	−	9.13654e6i	0.135685	−	0.417594i	0.995696	+	0.0926807i	$0.0295436\pi$
$864$		0			0
$865$	−2.75281e7	+	2.00003e7i	−1.25094	+	0.908860i
$866$	−3.56137e6	−	2.58749e6i	−0.161370	−	0.117242i
$867$		0			0
$868$	2.38480e7			1.07437
$869$	−378319.	+	4.37108e6i	−0.0169945	+	0.196354i
$870$		0			0
$871$	−5.33883e6	−	1.64312e7i	−0.238452	−	0.733879i
$872$	−6.35803e7	−	4.61938e7i	−2.83160	−	2.05728i
$873$		0			0
$874$	−995694.	+	3.06443e6i	−0.0440908	+	0.135697i
$875$	−2.76341e6	+	8.50491e6i	−0.122018	+	0.375534i
$876$		0			0
$877$	−2.47925e7	−	1.80128e7i	−1.08848	−	0.790828i	−0.109339	−	0.994005i	$-0.534873\pi$
$877$	−2.47925e7	−	1.80128e7i	−1.08848	−	0.790828i	−0.979142	+	0.203177i	$0.934873\pi$
$878$	−1.92351e7	−	5.91996e7i	−0.842090	−	2.59169i
$879$		0			0
$880$	−4.12894e7	−	6.85724e7i	−1.79735	−	2.98499i
$881$	−2.59015e7			−1.12431			−0.562154	−	0.827033i	$-0.690027\pi$
$881$	−2.59015e7			−1.12431			−0.562154	+	0.827033i	$0.690027\pi$
$882$		0			0
$883$	−1.61409e7	−	1.17271e7i	−0.696669	−	0.506160i	0.182177	−	0.983266i	$-0.441686\pi$
$883$	−1.61409e7	−	1.17271e7i	−0.696669	−	0.506160i	−0.878846	+	0.477106i	$0.841686\pi$
$884$	−1.03673e7	+	7.53228e6i	−0.446205	+	0.324187i
$885$		0			0
$886$	98137.3	−	302036.i	0.00420001	−	0.0129263i
$887$	−1.55985e7	+	1.13330e7i	−0.665693	+	0.483654i	−0.868581	−	0.495548i	$-0.834967\pi$
$887$	−1.55985e7	+	1.13330e7i	−0.665693	+	0.483654i	0.202888	+	0.979202i	$0.434967\pi$
$888$		0			0
$889$	5.09646e6	+	1.56853e7i	0.216279	+	0.665638i
$890$	−6.81680e7			−2.88473
$891$		0			0
$892$	2.97879e7			1.25351
$893$	−2.40074e6	−	7.38871e6i	−0.100743	−	0.310056i
$894$		0			0
$895$	−2.85467e6	+	2.07404e6i	−0.119124	+	0.0865486i
$896$	−4.77818e6	+	1.47057e7i	−0.198835	+	0.611951i
$897$		0			0
$898$	3.31256e7	−	2.40672e7i	1.37080	−	0.995942i
$899$	175342.	+	127393.i	0.00723580	+	0.00525711i
$900$		0			0
$901$	5.32628e6			0.218581
$902$	−2.20794e7	+	2.54472e7i	−0.903587	+	1.04141i
$903$		0			0
$904$	−1.89871e6	−	5.84364e6i	−0.0772748	−	0.237827i
$905$	−8.38796e6	−	6.09421e6i	−0.340436	−	0.247341i
$906$		0			0
$907$	−2.94725e6	+	9.07069e6i	−0.118959	+	0.366119i	−0.992752	−	0.120179i	$-0.961653\pi$
$907$	−2.94725e6	+	9.07069e6i	−0.118959	+	0.366119i	0.873793	+	0.486298i	$0.161653\pi$
$908$	2.20768e7	−	6.79453e7i	0.888630	−	2.73492i
$909$		0			0
$910$	−2.35763e7	−	1.71292e7i	−0.943785	−	0.685700i
$911$	−8.44256e6	−	2.59835e7i	−0.337038	−	1.03730i	−0.965710	−	0.259625i	$-0.916401\pi$
$911$	−8.44256e6	−	2.59835e7i	−0.337038	−	1.03730i	0.628672	−	0.777671i	$-0.283599\pi$
$912$		0			0
$913$	−2.73111e7	+	3.14770e7i	−1.08433	+	1.24973i
$914$	6.14797e7			2.43426
$915$		0			0
$916$	4.02735e7	+	2.92604e7i	1.58592	+	1.15224i
$917$	1.71204e7	−	1.24387e7i	0.672343	−	0.488486i
$918$		0			0
$919$	2.29376e6	−	7.05948e6i	0.0895901	−	0.275730i	−0.896216	−	0.443618i	$-0.853695\pi$
$919$	2.29376e6	−	7.05948e6i	0.0895901	−	0.275730i	0.985806	+	0.167888i	$0.0536947\pi$
$920$	1.70961e7	−	1.24210e7i	0.665927	−	0.483825i
$921$		0			0
$922$	9.64729e6	+	2.96913e7i	0.373747	+	1.15028i
$923$	−1.03904e7			−0.401448
$924$		0			0
$925$	1.77915e7			0.683688
$926$	2.75322e7	+	8.47353e7i	1.05515	+	3.24741i
$927$		0			0
$928$	−658754.	+	478613.i	−0.0251104	+	0.0182438i
$929$	−820020.	+	2.52376e6i	−0.0311735	+	0.0959421i	−0.965433	−	0.260653i	$-0.916062\pi$
$929$	−820020.	+	2.52376e6i	−0.0311735	+	0.0959421i	0.934259	+	0.356595i	$0.116062\pi$
$930$		0			0
$931$	−4.69238e6	+	3.40921e6i	−0.177427	+	0.128908i
$932$	8.10220e7	+	5.88659e7i	3.05537	+	2.21985i
$933$		0			0
$934$	−6.61918e7			−2.48277
$935$	−3.75189e6	−	6.23104e6i	−0.140353	−	0.233094i
$936$		0			0
$937$	1.13865e7	+	3.50440e7i	0.423683	+	1.30396i	0.904250	+	0.427004i	$0.140431\pi$
$937$	1.13865e7	+	3.50440e7i	0.423683	+	1.30396i	−0.480567	+	0.876958i	$0.659569\pi$
$938$	−1.87225e7	−	1.36027e7i	−0.694796	−	0.504799i
$939$		0			0
$940$	−2.59151e7	+	7.97583e7i	−0.956605	+	2.94413i
$941$	−1.51399e7	+	4.65957e7i	−0.557376	+	1.71543i	0.132209	+	0.991222i	$0.457793\pi$
$941$	−1.51399e7	+	4.65957e7i	−0.557376	+	1.71543i	−0.689585	+	0.724205i	$0.742207\pi$
$942$		0			0
$943$	−3.85777e6	−	2.80283e6i	−0.141272	−	0.102640i
$944$	4.07032e7	+	1.25272e8i	1.48661	+	4.57533i
$945$		0			0
$946$	3.77249e6	−	4.35871e7i	0.137057	−	1.58354i
$947$	−5.76755e6			−0.208986			−0.104493	−	0.994526i	$-0.533322\pi$
$947$	−5.76755e6			−0.208986			−0.104493	+	0.994526i	$0.533322\pi$
$948$		0			0
$949$	−1.42096e7	−	1.03239e7i	−0.512173	−	0.372116i
$950$	5.38245e6	−	3.91058e6i	0.193495	−	0.140583i
$951$		0			0
$952$	−3.22271e6	+	9.91847e6i	−0.115247	+	0.354693i
$953$	−3.35536e7	+	2.43781e7i	−1.19676	+	0.869497i	−0.993962	−	0.109723i	$-0.965004\pi$
$953$	−3.35536e7	+	2.43781e7i	−1.19676	+	0.869497i	−0.202798	+	0.979221i	$0.565004\pi$
$954$		0			0
$955$	−14600.4	−	44935.5i	−0.000518033	−	0.00159434i
$956$	−2.60696e6			−0.0922550
$957$		0			0
$958$	−1.24320e7			−0.437649
$959$	−2.87011e6	−	8.83329e6i	−0.100775	−	0.310153i
$960$		0			0
$961$	9.84850e6	−	7.15535e6i	0.344002	−	0.249932i
$962$	2.68854e7	−	8.27447e7i	0.936652	−	2.88272i
$963$		0			0
$964$	8.61585e7	−	6.25978e7i	2.98611	−	2.16953i
$965$	−2.00962e7	−	1.46007e7i	−0.694697	−	0.504727i
$966$		0			0
$967$	−1.26025e7			−0.433402			−0.216701	−	0.976238i	$-0.569530\pi$
$967$	−1.26025e7			−0.433402			−0.216701	+	0.976238i	$0.569530\pi$
$968$	−1.19887e7	−	8.41665e7i	−0.411228	−	2.88703i
$969$		0			0
$970$	1.36112e6	+	4.18911e6i	0.0464481	+	0.142953i
$971$	−3.60715e7	−	2.62075e7i	−1.22777	−	0.892026i	−0.231047	−	0.972943i	$-0.574215\pi$
$971$	−3.60715e7	−	2.62075e7i	−1.22777	−	0.892026i	−0.996721	+	0.0809171i	$0.974215\pi$
$972$		0			0
$973$	7.18134e6	−	2.21019e7i	0.243178	−	0.748424i
$974$	231518.	−	712540.i	0.00781966	−	0.0240664i
$975$		0			0
$976$	6.56349e7	+	4.76866e7i	2.20552	+	1.60240i
$977$	1.41308e7	+	4.34902e7i	0.473622	+	1.45766i	0.847808	+	0.530304i	$0.177922\pi$
$977$	1.41308e7	+	4.34902e7i	0.473622	+	1.45766i	−0.374186	+	0.927354i	$0.622078\pi$
$978$		0			0
$979$	−3.57446e7	−	1.51334e7i	−1.19194	−	0.504638i
$980$	6.26099e7			2.08247
$981$		0			0
$982$	−5.95376e7	−	4.32566e7i	−1.97021	−	1.43144i
$983$	1.50559e7	−	1.09388e7i	0.496962	−	0.361064i	−0.310893	−	0.950445i	$-0.600628\pi$
$983$	1.50559e7	−	1.09388e7i	0.496962	−	0.361064i	0.807855	+	0.589381i	$0.200628\pi$
$984$		0			0
$985$	−2.71542e6	+	8.35721e6i	−0.0891758	+	0.274455i
$986$	−126207.	+	91695.1i	−0.00413421	+	0.00300368i
$987$		0			0
$988$	−7.22019e6	−	2.22214e7i	−0.235318	−	0.724236i
$989$	6.19224e6			0.201306
$990$		0			0
$991$	947693.			0.0306538			0.0153269	−	0.999883i	$-0.495121\pi$
$991$	947693.			0.0306538			0.0153269	+	0.999883i	$0.495121\pi$
$992$	−1.91046e7	−	5.87979e7i	−0.616394	−	1.89707i
$993$		0			0
$994$	−1.12599e7	+	8.18080e6i	−0.361467	+	0.262621i
$995$	−1.76092e7	+	5.41956e7i	−0.563875	+	1.73543i
$996$		0			0
$997$	1.99646e7	−	1.45051e7i	0.636097	−	0.462151i	−0.222410	−	0.974953i	$-0.571392\pi$
$997$	1.99646e7	−	1.45051e7i	0.636097	−	0.462151i	0.858507	+	0.512802i	$0.171392\pi$
$998$	6.81301e7	+	4.94994e7i	2.16527	+	1.57316i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.6.f.a.82.4		16
3.2	odd	2		11.6.c.a.5.1	✓	16
11.3	even	5		1089.6.a.bg.1.8		8
11.8	odd	10		1089.6.a.bb.1.1		8
11.9	even	5	inner	99.6.f.a.64.4		16
33.8	even	10		121.6.a.i.1.8		8
33.14	odd	10		121.6.a.g.1.1		8
33.20	odd	10		11.6.c.a.9.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.6.c.a.5.1	✓	16	3.2	odd	2
11.6.c.a.9.1	yes	16	33.20	odd	10
99.6.f.a.64.4		16	11.9	even	5	inner
99.6.f.a.82.4		16	1.1	even	1	trivial
121.6.a.g.1.1		8	33.14	odd	10
121.6.a.i.1.8		8	33.8	even	10
1089.6.a.bb.1.1		8	11.8	odd	10
1089.6.a.bg.1.8		8	11.3	even	5

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.29275 + 10.1340i) q^{2} +(-65.9678 + 47.9284i) q^{4} +(-20.4388 + 62.9043i) q^{5} +(58.3278 - 42.3777i) q^{7} +(-427.066 - 310.282i) q^{8} +O(q^{10})\)	\(q+(3.29275 + 10.1340i) q^{2} +(-65.9678 + 47.9284i) q^{4} +(-20.4388 + 62.9043i) q^{5} +(58.3278 - 42.3777i) q^{7} +(-427.066 - 310.282i) q^{8} -704.774 q^{10} +(-369.555 - 156.461i) q^{11} +(177.228 + 545.453i) q^{13} +(621.515 + 451.557i) q^{14} +(931.866 - 2867.99i) q^{16} +(84.6769 - 260.609i) q^{17} +(404.202 + 293.670i) q^{19} +(-1666.60 - 5129.26i) q^{20} +(368.729 - 4260.27i) q^{22} +605.239 q^{23} +(-1011.03 - 734.554i) q^{25} +(-4944.06 + 3592.07i) q^{26} +(-1816.67 + 5591.12i) q^{28} +(-43.2242 + 31.4042i) q^{29} +(-1253.55 - 3858.02i) q^{31} +15240.4 q^{32} +2919.83 q^{34} +(1473.58 + 4535.22i) q^{35} +(-11517.7 + 8368.08i) q^{37} +(-1645.13 + 5063.18i) q^{38} +(28246.8 - 20522.5i) q^{40} +(-6373.96 - 4630.95i) q^{41} +10231.1 q^{43} +(31877.7 - 7390.80i) q^{44} +(1992.90 + 6133.51i) q^{46} +(-12580.0 - 9139.87i) q^{47} +(-3587.38 + 11040.8i) q^{49} +(4114.94 - 12664.5i) q^{50} +(-37834.0 - 27488.0i) q^{52} +(6006.53 + 18486.2i) q^{53} +(17395.3 - 20048.7i) q^{55} -38058.9 q^{56} +(-460.577 - 334.629i) q^{58} +(-35337.2 + 25674.0i) q^{59} +(-8313.59 + 25586.6i) q^{61} +(34969.7 - 25407.0i) q^{62} +(20363.1 + 62671.1i) q^{64} -37933.7 q^{65} -30124.0 q^{67} +(6904.61 + 21250.2i) q^{68} +(-41107.9 + 29866.7i) q^{70} +(-5598.42 + 17230.2i) q^{71} +(-24776.0 + 18000.8i) q^{73} +(-122727. - 89166.5i) q^{74} -40739.5 q^{76} +(-28185.8 + 6534.85i) q^{77} +(-3378.39 - 10397.6i) q^{79} +(161363. + 117237. i) q^{80} +(25942.4 - 79842.4i) q^{82} +(32089.5 - 98761.3i) q^{83} +(14662.7 + 10653.1i) q^{85} +(33688.3 + 103682. i) q^{86} +(109278. + 181485. i) q^{88} +96723.3 q^{89} +(33452.4 + 24304.6i) q^{91} +(-39926.3 + 29008.1i) q^{92} +(51201.1 - 157581. i) q^{94} +(-26734.5 + 19423.8i) q^{95} +(-1931.29 - 5943.90i) q^{97} -123700. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - 73 q^{4} + 10 q^{5} + 196 q^{7} - 527 q^{8}+O(q^{10}) \) 16 * q + q^2 - 73 * q^4 + 10 * q^5 + 196 * q^7 - 527 * q^8	\( 16 q + q^{2} - 73 q^{4} + 10 q^{5} + 196 q^{7} - 527 q^{8} - 672 q^{10} + 692 q^{11} + 1162 q^{13} - 560 q^{14} + 6399 q^{16} + 22 q^{17} - 3236 q^{19} + 5514 q^{20} - 13059 q^{22} + 10848 q^{23} + 15686 q^{25} - 16216 q^{26} + 8838 q^{28} - 13070 q^{29} - 14764 q^{31} + 58812 q^{32} - 26966 q^{34} - 43368 q^{35} + 4638 q^{37} - 68144 q^{38} + 52284 q^{40} + 14806 q^{41} - 24376 q^{43} + 104960 q^{44} + 50452 q^{46} - 40364 q^{47} + 32246 q^{49} - 10839 q^{50} - 80654 q^{52} + 11654 q^{53} + 7052 q^{55} - 70632 q^{56} + 10276 q^{58} - 70804 q^{59} - 31446 q^{61} + 153388 q^{62} + 17695 q^{64} + 41284 q^{65} - 64200 q^{67} + 94114 q^{68} - 103768 q^{70} + 184380 q^{71} - 1750 q^{73} - 306048 q^{74} + 174806 q^{76} - 384646 q^{77} + 24324 q^{79} + 386444 q^{80} - 316255 q^{82} + 46028 q^{83} + 63914 q^{85} - 22931 q^{86} + 211871 q^{88} - 148364 q^{89} - 258448 q^{91} + 58658 q^{92} - 55370 q^{94} + 4716 q^{95} + 484296 q^{97} - 743692 q^{98}+O(q^{100}) \) 16 * q + q^2 - 73 * q^4 + 10 * q^5 + 196 * q^7 - 527 * q^8 - 672 * q^10 + 692 * q^11 + 1162 * q^13 - 560 * q^14 + 6399 * q^16 + 22 * q^17 - 3236 * q^19 + 5514 * q^20 - 13059 * q^22 + 10848 * q^23 + 15686 * q^25 - 16216 * q^26 + 8838 * q^28 - 13070 * q^29 - 14764 * q^31 + 58812 * q^32 - 26966 * q^34 - 43368 * q^35 + 4638 * q^37 - 68144 * q^38 + 52284 * q^40 + 14806 * q^41 - 24376 * q^43 + 104960 * q^44 + 50452 * q^46 - 40364 * q^47 + 32246 * q^49 - 10839 * q^50 - 80654 * q^52 + 11654 * q^53 + 7052 * q^55 - 70632 * q^56 + 10276 * q^58 - 70804 * q^59 - 31446 * q^61 + 153388 * q^62 + 17695 * q^64 + 41284 * q^65 - 64200 * q^67 + 94114 * q^68 - 103768 * q^70 + 184380 * q^71 - 1750 * q^73 - 306048 * q^74 + 174806 * q^76 - 384646 * q^77 + 24324 * q^79 + 386444 * q^80 - 316255 * q^82 + 46028 * q^83 + 63914 * q^85 - 22931 * q^86 + 211871 * q^88 - 148364 * q^89 - 258448 * q^91 + 58658 * q^92 - 55370 * q^94 + 4716 * q^95 + 484296 * q^97 - 743692 * q^98

Introduction

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