LMFDB - Embedded newform 333.6.c.d.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,6,Mod(73,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("333.73");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	333.c (of order $2$, degree $1$, 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:	$53.4078119977$
Analytic rank:	$0$
Dimension:	$16$
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} + 390 x^{14} + 60701 x^{12} + 4799932 x^{10} + 203487156 x^{8} + 4519465040 x^{6} + \cdots + 178006118400 $ x^16 + 390x^14 + 60701x^12 + 4799932x^10 + 203487156x^8 + 4519465040x^6 + 48993644736x^4 + 211923220224*x^2 + 178006118400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 37)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			73.2
Root			$-9.87320i$ of defining polynomial
Character	$\chi$	$=$	333.73
Dual form			333.6.c.d.73.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.87320i q^{2} -65.4800 q^{4} +100.817i q^{5} -37.8971 q^{7} +330.555i q^{8} +O(q^{10})$	\(q-9.87320i q^{2} -65.4800 q^{4} +100.817i q^{5} -37.8971 q^{7} +330.555i q^{8} +995.382 q^{10} +284.206 q^{11} +736.146i q^{13} +374.166i q^{14} +1168.27 q^{16} +1303.38i q^{17} -2224.12i q^{19} -6601.47i q^{20} -2806.02i q^{22} -2543.87i q^{23} -7038.98 q^{25} +7268.11 q^{26} +2481.50 q^{28} -606.649i q^{29} +5882.99i q^{31} -956.815i q^{32} +12868.6 q^{34} -3820.66i q^{35} +(-3504.92 - 7553.78i) q^{37} -21959.2 q^{38} -33325.4 q^{40} +9705.95 q^{41} -5693.02i q^{43} -18609.8 q^{44} -25116.2 q^{46} -25290.9 q^{47} -15370.8 q^{49} +69497.2i q^{50} -48202.8i q^{52} -9013.32 q^{53} +28652.6i q^{55} -12527.1i q^{56} -5989.57 q^{58} +15172.6i q^{59} +29053.1i q^{61} +58083.9 q^{62} +27937.8 q^{64} -74215.7 q^{65} -149.609 q^{67} -85345.6i q^{68} -37722.1 q^{70} +39655.1 q^{71} -39371.7 q^{73} +(-74579.9 + 34604.7i) q^{74} +145635. i q^{76} -10770.6 q^{77} -83704.0i q^{79} +117781. i q^{80} -95828.7i q^{82} +36443.3 q^{83} -131403. q^{85} -56208.3 q^{86} +93945.5i q^{88} -63406.6i q^{89} -27897.8i q^{91} +166573. i q^{92} +249702. i q^{94} +224228. q^{95} -16855.7i q^{97} +151759. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 268 q^{4} + 190 q^{7}+O(q^{10}) $ 16 * q - 268 * q^4 + 190 * q^7	$ 16 q - 268 q^{4} + 190 q^{7} - 74 q^{10} + 1110 q^{11} + 2900 q^{16} - 12052 q^{25} - 4902 q^{26} - 16824 q^{28} + 20556 q^{34} - 11400 q^{37} - 12108 q^{38} + 16966 q^{40} - 3918 q^{41} - 125394 q^{44} + 17470 q^{46} - 3822 q^{47} - 32618 q^{49} + 24126 q^{53} - 164718 q^{58} + 81426 q^{62} + 158076 q^{64} - 98976 q^{65} + 23560 q^{67} - 222404 q^{70} + 50046 q^{71} - 196274 q^{73} - 141216 q^{74} + 239574 q^{77} + 215814 q^{83} - 346472 q^{85} - 197640 q^{86} + 132504 q^{95}+O(q^{100}) $ 16 * q - 268 * q^4 + 190 * q^7 - 74 * q^10 + 1110 * q^11 + 2900 * q^16 - 12052 * q^25 - 4902 * q^26 - 16824 * q^28 + 20556 * q^34 - 11400 * q^37 - 12108 * q^38 + 16966 * q^40 - 3918 * q^41 - 125394 * q^44 + 17470 * q^46 - 3822 * q^47 - 32618 * q^49 + 24126 * q^53 - 164718 * q^58 + 81426 * q^62 + 158076 * q^64 - 98976 * q^65 + 23560 * q^67 - 222404 * q^70 + 50046 * q^71 - 196274 * q^73 - 141216 * q^74 + 239574 * q^77 + 215814 * q^83 - 346472 * q^85 - 197640 * q^86 + 132504 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	9.87320i		−	1.74535i	−0.488301	−	0.872675i	$-0.662383\pi$
$2$		−	9.87320i		−	1.74535i	0.488301	−	0.872675i	$-0.337617\pi$
$3$		0			0
$3$		0			0
$4$	−65.4800			−2.04625
$5$			100.817i			1.80346i	0.432298	+	0.901731i	$0.357703\pi$
$5$			100.817i			1.80346i	−0.432298	+	0.901731i	$0.642297\pi$
$6$		0			0
$7$	−37.8971			−0.292322			−0.146161	−	0.989261i	$-0.546692\pi$
$7$	−37.8971			−0.292322			−0.146161	+	0.989261i	$0.546692\pi$
$8$			330.555i			1.82607i
$9$		0			0
$10$	995.382			3.14767
$11$	284.206			0.708192			0.354096	−	0.935209i	$-0.384789\pi$
$11$	284.206			0.708192			0.354096	+	0.935209i	$0.384789\pi$
$12$		0			0
$13$			736.146i			1.20811i	0.796944	+	0.604054i	$0.206449\pi$
$13$			736.146i			1.20811i	−0.796944	+	0.604054i	$0.793551\pi$
$14$			374.166i			0.510204i
$15$		0			0
$16$	1168.27			1.14089
$17$			1303.38i			1.09383i	0.837188	+	0.546916i	$0.184198\pi$
$17$			1303.38i			1.09383i	−0.837188	+	0.546916i	$0.815802\pi$
$18$		0			0
$19$		−	2224.12i		−	1.41343i	−0.707499	−	0.706715i	$-0.750176\pi$
$19$		−	2224.12i		−	1.41343i	0.707499	−	0.706715i	$-0.249824\pi$
$20$		−	6601.47i		−	3.69033i
$21$		0			0
$22$		−	2806.02i		−	1.23604i
$23$		−	2543.87i		−	1.00271i	−0.865241	−	0.501356i	$-0.832835\pi$
$23$		−	2543.87i		−	1.00271i	0.865241	−	0.501356i	$-0.167165\pi$
$24$		0			0
$25$	−7038.98			−2.25247
$26$	7268.11			2.10857
$27$		0			0
$28$	2481.50			0.598163
$29$		−	606.649i		−	0.133950i	−0.997755	−	0.0669750i	$-0.978665\pi$
$29$		−	606.649i		−	0.133950i	0.997755	−	0.0669750i	$-0.0213348\pi$
$30$		0			0
$31$			5882.99i			1.09950i	0.835331	+	0.549748i	$0.185276\pi$
$31$			5882.99i			1.09950i	−0.835331	+	0.549748i	$0.814724\pi$
$32$		−	956.815i		−	0.165178i
$33$		0			0
$34$	12868.6			1.90912
$35$		−	3820.66i		−	0.527191i
$36$		0			0
$37$	−3504.92	−	7553.78i	−0.420895	−	0.907110i
$37$	−3504.92	−	7553.78i	−0.420895	−	0.907110i
$38$	−21959.2			−2.46693
$39$		0			0
$40$	−33325.4			−3.29325
$41$	9705.95			0.901734			0.450867	−	0.892591i	$-0.351115\pi$
$41$	9705.95			0.901734			0.450867	+	0.892591i	$0.351115\pi$
$42$		0			0
$43$		−	5693.02i		−	0.469539i	−0.972051	−	0.234770i	$-0.924566\pi$
$43$		−	5693.02i		−	0.469539i	0.972051	−	0.234770i	$-0.0754335\pi$
$44$	−18609.8			−1.44914
$45$		0			0
$46$	−25116.2			−1.75008
$47$	−25290.9			−1.67001			−0.835004	−	0.550243i	$-0.814535\pi$
$47$	−25290.9			−1.67001			−0.835004	+	0.550243i	$0.814535\pi$
$48$		0			0
$49$	−15370.8			−0.914548
$50$			69497.2i			3.93136i
$51$		0			0
$52$		−	48202.8i		−	2.47209i
$53$	−9013.32			−0.440753			−0.220376	−	0.975415i	$-0.570729\pi$
$53$	−9013.32			−0.440753			−0.220376	+	0.975415i	$0.570729\pi$
$54$		0			0
$55$			28652.6i			1.27720i
$56$		−	12527.1i		−	0.533801i
$57$		0			0
$58$	−5989.57			−0.233790
$59$			15172.6i			0.567452i	0.958905	+	0.283726i	$0.0915706\pi$
$59$			15172.6i			0.567452i	−0.958905	+	0.283726i	$0.908429\pi$
$60$		0			0
$61$			29053.1i			0.999695i	0.866113	+	0.499847i	$0.166611\pi$
$61$			29053.1i			0.999695i	−0.866113	+	0.499847i	$0.833389\pi$
$62$	58083.9			1.91901
$63$		0			0
$64$	27937.8			0.852595
$65$	−74215.7			−2.17878
$66$		0			0
$67$	−149.609			−0.00407165			−0.00203582	−	0.999998i	$-0.500648\pi$
$67$	−149.609			−0.00407165			−0.00203582	+	0.999998i	$0.500648\pi$
$68$		−	85345.6i		−	2.23825i
$69$		0			0
$70$	−37722.1			−0.920133
$71$	39655.1			0.933584			0.466792	−	0.884367i	$-0.345410\pi$
$71$	39655.1			0.933584			0.466792	+	0.884367i	$0.345410\pi$
$72$		0			0
$73$	−39371.7			−0.864723			−0.432361	−	0.901700i	$-0.642319\pi$
$73$	−39371.7			−0.864723			−0.432361	+	0.901700i	$0.642319\pi$
$74$	−74579.9	+	34604.7i	−1.58322	+	0.734609i
$75$		0			0
$76$			145635.i			2.89223i
$77$	−10770.6			−0.207020
$78$		0			0
$79$		−	83704.0i		−	1.50896i	−0.656322	−	0.754481i	$-0.727889\pi$
$79$		−	83704.0i		−	1.50896i	0.656322	−	0.754481i	$-0.272111\pi$
$80$			117781.i			2.05755i
$81$		0			0
$82$		−	95828.7i		−	1.57384i
$83$	36443.3			0.580660			0.290330	−	0.956927i	$-0.406235\pi$
$83$	36443.3			0.580660			0.290330	+	0.956927i	$0.406235\pi$
$84$		0			0
$85$	−131403.			−1.97268
$86$	−56208.3			−0.819510
$87$		0			0
$88$			93945.5i			1.29321i
$89$		−	63406.6i		−	0.848515i	−0.905542	−	0.424258i	$-0.860535\pi$
$89$		−	63406.6i		−	0.848515i	0.905542	−	0.424258i	$-0.139465\pi$
$90$		0			0
$91$		−	27897.8i		−	0.353156i
$92$			166573.i			2.05180i
$93$		0			0
$94$			249702.i			2.91475i
$95$	224228.			2.54907
$96$		0			0
$97$		−	16855.7i		−	0.181893i	−0.995856	−	0.0909467i	$-0.971011\pi$
$97$		−	16855.7i		−	0.181893i	0.995856	−	0.0909467i	$-0.0289893\pi$
$98$			151759.i			1.59621i
$99$		0			0
$100$	460912.			4.60912
$101$	−119645.			−1.16706			−0.583528	−	0.812093i	$-0.698328\pi$
$101$	−119645.			−1.16706			−0.583528	+	0.812093i	$0.698328\pi$
$102$		0			0
$103$		−	160054.i		−	1.48652i	−0.669000	−	0.743262i	$-0.733277\pi$
$103$		−	160054.i		−	1.48652i	0.669000	−	0.743262i	$-0.266723\pi$
$104$	−243336.			−2.20609
$105$		0			0
$106$			88990.2i			0.769268i
$107$	−95588.2			−0.807133			−0.403566	−	0.914950i	$-0.632230\pi$
$107$	−95588.2			−0.807133			−0.403566	+	0.914950i	$0.632230\pi$
$108$		0			0
$109$		−	82980.7i		−	0.668976i	−0.942400	−	0.334488i	$-0.891437\pi$
$109$		−	82980.7i		−	0.668976i	0.942400	−	0.334488i	$-0.108563\pi$
$110$	282893.			2.22916
$111$		0			0
$112$	−44274.1			−0.333507
$113$		−	51762.8i		−	0.381348i	−0.981653	−	0.190674i	$-0.938933\pi$
$113$		−	51762.8i		−	0.381348i	0.981653	−	0.190674i	$-0.0610674\pi$
$114$		0			0
$115$	256465.			1.80835
$116$			39723.4i			0.274095i
$117$		0			0
$118$	149802.			0.990403
$119$		−	49394.5i		−	0.319751i
$120$		0			0
$121$	−80278.2			−0.498464
$122$	286847.			1.74482
$123$		0			0
$124$		−	385218.i		−	2.24984i
$125$		−	394594.i		−	2.25879i
$126$		0			0
$127$	−239395.			−1.31706			−0.658530	−	0.752555i	$-0.728821\pi$
$127$	−239395.			−1.31706			−0.658530	+	0.752555i	$0.728821\pi$
$128$		−	306454.i		−	1.65326i
$129$		0			0
$130$			732746.i			3.80273i
$131$			294446.i			1.49909i	0.661953	+	0.749545i	$0.269728\pi$
$131$			294446.i			1.49909i	−0.661953	+	0.749545i	$0.730272\pi$
$132$		0			0
$133$			84287.8i			0.413176i
$134$			1477.12i			0.00710645i
$135$		0			0
$136$	−430840.			−1.99742
$137$	157240.			0.715752			0.357876	−	0.933769i	$-0.383501\pi$
$137$	157240.			0.715752			0.357876	+	0.933769i	$0.383501\pi$
$138$		0			0
$139$	208395.			0.914852			0.457426	−	0.889248i	$-0.348771\pi$
$139$	208395.			0.914852			0.457426	+	0.889248i	$0.348771\pi$
$140$			250177.i			1.07876i
$141$		0			0
$142$		−	391523.i		−	1.62943i
$143$			209217.i			0.855572i
$144$		0			0
$145$	61160.3			0.241574
$146$			388724.i			1.50924i
$147$		0			0
$148$	229502.	+	494621.i	0.861256	+	1.85617i
$149$	−324029.			−1.19569			−0.597844	−	0.801612i	$-0.703976\pi$
$149$	−324029.			−1.19569			−0.597844	+	0.801612i	$0.703976\pi$
$150$		0			0
$151$	118246.			0.422032			0.211016	−	0.977483i	$-0.432323\pi$
$151$	118246.			0.422032			0.211016	+	0.977483i	$0.432323\pi$
$152$	735193.			2.58103
$153$		0			0
$154$			106340.i			0.361322i
$155$	−593102.			−1.98290
$156$		0			0
$157$	−572427.			−1.85341			−0.926704	−	0.375792i	$-0.877371\pi$
$157$	−572427.			−1.85341			−0.926704	+	0.375792i	$0.877371\pi$
$158$	−826426.			−2.63367
$159$		0			0
$160$	96462.8			0.297893
$161$			96405.5i			0.293114i
$162$		0			0
$163$			271637.i			0.800792i	0.916342	+	0.400396i	$0.131127\pi$
$163$			271637.i			0.800792i	−0.916342	+	0.400396i	$0.868873\pi$
$164$	−635546.			−1.84517
$165$		0			0
$166$		−	359812.i		−	1.01346i
$167$			13718.7i			0.0380647i	0.999819	+	0.0190323i	$0.00605855\pi$
$167$			13718.7i			0.0380647i	−0.999819	+	0.0190323i	$0.993941\pi$
$168$		0			0
$169$	−170618.			−0.459523
$170$			1.29737e6i			3.44302i
$171$		0			0
$172$			372779.i			0.960794i
$173$	−195002.			−0.495364			−0.247682	−	0.968841i	$-0.579669\pi$
$173$	−195002.			−0.495364			−0.247682	+	0.968841i	$0.579669\pi$
$174$		0			0
$175$	266757.			0.658447
$176$	332029.			0.807968
$177$		0			0
$178$	−626026.			−1.48096
$179$		−	226757.i		−	0.528966i	−0.964390	−	0.264483i	$-0.914799\pi$
$179$		−	226757.i		−	0.528966i	0.964390	−	0.264483i	$-0.0852013\pi$
$180$		0			0
$181$	117568.			0.266742			0.133371	−	0.991066i	$-0.457420\pi$
$181$	117568.			0.266742			0.133371	+	0.991066i	$0.457420\pi$
$182$	−275441.			−0.616381
$183$		0			0
$184$	840889.			1.83102
$185$	761546.	−	353354.i	1.63594	−	0.759067i
$186$		0			0
$187$			370429.i			0.774642i
$188$	1.65604e6			3.41726
$189$		0			0
$190$		−	2.21385e6i		−	4.44901i
$191$			487344.i			0.966611i	0.875452	+	0.483306i	$0.160564\pi$
$191$			487344.i			0.966611i	−0.875452	+	0.483306i	$0.839436\pi$
$192$		0			0
$193$		−	341504.i		−	0.659938i	−0.943992	−	0.329969i	$-0.892962\pi$
$193$		−	341504.i		−	0.659938i	0.943992	−	0.329969i	$-0.107038\pi$
$194$	−166419.			−0.317468
$195$		0			0
$196$	1.00648e6			1.87139
$197$	651239.			1.19557			0.597785	−	0.801657i	$-0.296048\pi$
$197$	651239.			1.19557			0.597785	+	0.801657i	$0.296048\pi$
$198$		0			0
$199$		−	779867.i		−	1.39601i	−0.716094	−	0.698004i	$-0.754072\pi$
$199$		−	779867.i		−	1.39601i	0.716094	−	0.698004i	$-0.245928\pi$
$200$		−	2.32677e6i		−	4.11318i
$201$		0			0
$202$			1.18128e6i			2.03692i
$203$			22990.3i			0.0391565i
$204$		0			0
$205$			978520.i			1.62624i
$206$	−1.58024e6			−2.59451
$207$		0			0
$208$			860017.i			1.37832i
$209$		−	632107.i		−	1.00098i
$210$		0			0
$211$	−1.15677e6			−1.78871			−0.894356	−	0.447356i	$-0.852366\pi$
$211$	−1.15677e6			−1.78871			−0.894356	+	0.447356i	$0.852366\pi$
$212$	590192.			0.901890
$213$		0			0
$214$			943761.i			1.40873i
$215$	573951.			0.846796
$216$		0			0
$217$		−	222948.i		−	0.321407i
$218$	−819284.			−1.16760
$219$		0			0
$220$		−	1.87617e6i		−	2.61346i
$221$	−959481.			−1.32147
$222$		0			0
$223$	−759581.			−1.02285			−0.511425	−	0.859328i	$-0.670882\pi$
$223$	−759581.			−1.02285			−0.511425	+	0.859328i	$0.670882\pi$
$224$			36260.5i			0.0482852i
$225$		0			0
$226$	−511065.			−0.665587
$227$		−	49088.1i		−	0.0632283i	−0.999500	−	0.0316142i	$-0.989935\pi$
$227$		−	49088.1i		−	0.0632283i	0.999500	−	0.0316142i	$-0.0100648\pi$
$228$		0			0
$229$	−1.16335e6			−1.46596			−0.732978	−	0.680252i	$-0.761870\pi$
$229$	−1.16335e6			−1.46596			−0.732978	+	0.680252i	$0.761870\pi$
$230$		−	2.53213e6i		−	3.15621i
$231$		0			0
$232$	200531.			0.244603
$233$	386330.			0.466196			0.233098	−	0.972453i	$-0.425114\pi$
$233$	386330.			0.466196			0.233098	+	0.972453i	$0.425114\pi$
$234$		0			0
$235$		−	2.54974e6i		−	3.01180i
$236$		−	993500.i		−	1.16115i
$237$		0			0
$238$	−487682.			−0.558077
$239$		−	690828.i		−	0.782303i	−0.920326	−	0.391152i	$-0.872077\pi$
$239$		−	690828.i		−	0.782303i	0.920326	−	0.391152i	$-0.127923\pi$
$240$		0			0
$241$			1.38199e6i			1.53272i	0.642410	+	0.766362i	$0.277935\pi$
$241$			1.38199e6i			1.53272i	−0.642410	+	0.766362i	$0.722065\pi$
$242$			792602.i			0.869995i
$243$		0			0
$244$		−	1.90240e6i		−	2.04563i
$245$		−	1.54963e6i		−	1.64935i
$246$		0			0
$247$	1.63728e6			1.70757
$248$	−1.94465e6			−2.00776
$249$		0			0
$250$	−3.89590e6			−3.94238
$251$		−	60032.8i		−	0.0601457i	−0.999548	−	0.0300728i	$-0.990426\pi$
$251$		−	60032.8i		−	0.0601457i	0.999548	−	0.0300728i	$-0.00957393\pi$
$252$		0			0
$253$		−	722983.i		−	0.710112i
$254$			2.36359e6i			2.29873i
$255$		0			0
$256$	−2.13167e6			−2.03292
$257$			371424.i			0.350782i	0.984499	+	0.175391i	$0.0561189\pi$
$257$			371424.i			0.350782i	−0.984499	+	0.175391i	$0.943881\pi$
$258$		0			0
$259$	132826.	+	286266.i	0.123037	+	0.265168i
$260$	4.85964e6			4.45832
$261$		0			0
$262$	2.90712e6			2.61644
$263$	−732517.			−0.653022			−0.326511	−	0.945193i	$-0.605873\pi$
$263$	−732517.			−0.653022			−0.326511	+	0.945193i	$0.605873\pi$
$264$		0			0
$265$		−	908691.i		−	0.794880i
$266$	832190.			0.721138
$267$		0			0
$268$	9796.38			0.00833160
$269$	−116693.			−0.0983252			−0.0491626	−	0.998791i	$-0.515655\pi$
$269$	−116693.			−0.0983252			−0.0491626	+	0.998791i	$0.515655\pi$
$270$		0			0
$271$	1.13684e6			0.940317			0.470158	−	0.882582i	$-0.344197\pi$
$271$	1.13684e6			0.940317			0.470158	+	0.882582i	$0.344197\pi$
$272$			1.52271e6i			1.24794i
$273$		0			0
$274$		−	1.55246e6i		−	1.24924i
$275$	−2.00052e6			−1.59518
$276$		0			0
$277$			715969.i			0.560654i	0.959905	+	0.280327i	$0.0904429\pi$
$277$			715969.i			0.560654i	−0.959905	+	0.280327i	$0.909557\pi$
$278$		−	2.05753e6i		−	1.59674i
$279$		0			0
$280$	1.26294e6			0.962690
$281$			139202.i			0.105167i	0.998617	+	0.0525836i	$0.0167456\pi$
$281$			139202.i			0.105167i	−0.998617	+	0.0525836i	$0.983254\pi$
$282$		0			0
$283$			572225.i			0.424718i	0.977192	+	0.212359i	$0.0681146\pi$
$283$			572225.i			0.424718i	−0.977192	+	0.212359i	$0.931885\pi$
$284$	−2.59662e6			−1.91035
$285$		0			0
$286$	2.06564e6			1.49327
$287$	−367828.			−0.263596
$288$		0			0
$289$	−278955.			−0.196467
$290$		−	603848.i		−	0.421631i
$291$		0			0
$292$	2.57806e6			1.76944
$293$	1.62064e6			1.10285			0.551425	−	0.834224i	$-0.314084\pi$
$293$	1.62064e6			1.10285			0.551425	+	0.834224i	$0.314084\pi$
$294$		0			0
$295$	−1.52965e6			−1.02338
$296$	2.49694e6	−	1.15857e6i	1.65645	−	0.768584i
$297$		0			0
$298$			3.19920e6i			2.08690i
$299$	1.87266e6			1.21138
$300$		0			0
$301$			215749.i			0.137257i
$302$		−	1.16747e6i		−	0.736594i
$303$		0			0
$304$		−	2.59837e6i		−	1.61257i
$305$	−2.92903e6			−1.80291
$306$		0			0
$307$	1.74662e6			1.05768			0.528839	−	0.848722i	$-0.322628\pi$
$307$	1.74662e6			1.05768			0.528839	+	0.848722i	$0.322628\pi$
$308$	705257.			0.423614
$309$		0			0
$310$			5.85582e6i			3.46085i
$311$		−	1.86359e6i		−	1.09257i	−0.837600	−	0.546284i	$-0.816042\pi$
$311$		−	1.86359e6i		−	1.09257i	0.837600	−	0.546284i	$-0.183958\pi$
$312$		0			0
$313$		−	2.96662e6i		−	1.71159i	−0.517311	−	0.855797i	$-0.673067\pi$
$313$		−	2.96662e6i		−	1.71159i	0.517311	−	0.855797i	$-0.326933\pi$
$314$			5.65169e6i			3.23485i
$315$		0			0
$316$			5.48094e6i			3.08771i
$317$	−950355.			−0.531175			−0.265587	−	0.964087i	$-0.585566\pi$
$317$	−950355.			−0.531175			−0.265587	+	0.964087i	$0.585566\pi$
$318$		0			0
$319$		−	172413.i		−	0.0948623i
$320$			2.81660e6i			1.53762i
$321$		0			0
$322$	951830.			0.511587
$323$	2.89888e6			1.54605
$324$		0			0
$325$		−	5.18172e6i		−	2.72123i
$326$	2.68192e6			1.39766
$327$		0			0
$328$			3.20835e6i			1.64663i
$329$	958451.			0.488180
$330$		0			0
$331$			1.92675e6i			0.966618i	0.875450	+	0.483309i	$0.160565\pi$
$331$			1.92675e6i			0.966618i	−0.875450	+	0.483309i	$0.839435\pi$
$332$	−2.38631e6			−1.18818
$333$		0			0
$334$	135448.			0.0664363
$335$		−	15083.0i		−	0.00734306i
$336$		0			0
$337$	−2.20780e6			−1.05897			−0.529485	−	0.848319i	$-0.677615\pi$
$337$	−2.20780e6			−1.05897			−0.529485	+	0.848319i	$0.677615\pi$
$338$			1.68454e6i			0.802030i
$339$		0			0
$340$	8.60425e6			4.03660
$341$			1.67198e6i			0.778654i
$342$		0			0
$343$	1.21945e6			0.559664
$344$	1.88185e6			0.857413
$345$		0			0
$346$			1.92530e6i			0.864584i
$347$			1.78913e6i			0.797662i	0.917024	+	0.398831i	$0.130584\pi$
$347$			1.78913e6i			0.797662i	−0.917024	+	0.398831i	$0.869416\pi$
$348$		0			0
$349$	−593448.			−0.260807			−0.130403	−	0.991461i	$-0.541627\pi$
$349$	−593448.			−0.260807			−0.130403	+	0.991461i	$0.541627\pi$
$350$		−	2.63374e6i		−	1.14922i
$351$		0			0
$352$		−	271932.i		−	0.116978i
$353$			1.18246e6i			0.505066i	0.967588	+	0.252533i	$0.0812636\pi$
$353$			1.18246e6i			0.505066i	−0.967588	+	0.252533i	$0.918736\pi$
$354$		0			0
$355$			3.99789e6i			1.68368i
$356$			4.15187e6i			1.73627i
$357$		0			0
$358$	−2.23881e6			−0.923231
$359$	−1.64233e6			−0.672549			−0.336275	−	0.941764i	$-0.609167\pi$
$359$	−1.64233e6			−0.672549			−0.336275	+	0.941764i	$0.609167\pi$
$360$		0			0
$361$	−2.47061e6			−0.997783
$362$		−	1.16077e6i		−	0.465559i
$363$		0			0
$364$			1.82675e6i			0.722646i
$365$		−	3.96932e6i		−	1.55949i
$366$		0			0
$367$	3.30858e6			1.28226			0.641131	−	0.767432i	$-0.278466\pi$
$367$	3.30858e6			1.28226			0.641131	+	0.767432i	$0.278466\pi$
$368$		−	2.97193e6i		−	1.14398i
$369$		0			0
$370$	−3.48873e6	−	7.51889e6i	−1.32484	−	2.85528i
$371$	341579.			0.128842
$372$		0			0
$373$	−3.59546e6			−1.33808			−0.669041	−	0.743225i	$-0.733295\pi$
$373$	−3.59546e6			−1.33808			−0.669041	+	0.743225i	$0.733295\pi$
$374$	3.65732e6			1.35202
$375$		0			0
$376$		−	8.36001e6i		−	3.04956i
$377$	446582.			0.161826
$378$		0			0
$379$	−1.61202e6			−0.576463			−0.288232	−	0.957561i	$-0.593067\pi$
$379$	−1.61202e6			−0.576463			−0.288232	+	0.957561i	$0.593067\pi$
$380$	−1.46825e7			−5.21603
$381$		0			0
$382$	4.81164e6			1.68708
$383$			2.35743e6i			0.821185i	0.911819	+	0.410592i	$0.134678\pi$
$383$			2.35743e6i			0.821185i	−0.911819	+	0.410592i	$0.865322\pi$
$384$		0			0
$385$		−	1.08585e6i		−	0.373352i
$386$	−3.37174e6			−1.15182
$387$		0			0
$388$			1.10371e6i			0.372199i
$389$		−	1.24614e6i		−	0.417534i	−0.977965	−	0.208767i	$-0.933055\pi$
$389$		−	1.24614e6i		−	0.417534i	0.977965	−	0.208767i	$-0.0669450\pi$
$390$		0			0
$391$	3.31565e6			1.09680
$392$		−	5.08089e6i		−	1.67003i
$393$		0			0
$394$		−	6.42981e6i		−	2.08669i
$395$	8.43875e6			2.72136
$396$		0			0
$397$	2.29513e6			0.730856			0.365428	−	0.930840i	$-0.380923\pi$
$397$	2.29513e6			0.730856			0.365428	+	0.930840i	$0.380923\pi$
$398$	−7.69978e6			−2.43652
$399$		0			0
$400$	−8.22343e6			−2.56982
$401$			1.93165e6i			0.599884i	0.953958	+	0.299942i	$0.0969672\pi$
$401$			1.93165e6i			0.599884i	−0.953958	+	0.299942i	$0.903033\pi$
$402$		0			0
$403$	−4.33074e6			−1.32831
$404$	7.83436e6			2.38809
$405$		0			0
$406$	226987.			0.0683418
$407$	−996117.	−	2.14682e6i	−0.298074	−	0.642407i
$408$		0			0
$409$			706587.i			0.208861i	0.994532	+	0.104431i	$0.0333020\pi$
$409$			706587.i			0.208861i	−0.994532	+	0.104431i	$0.966698\pi$
$410$	9.66112e6			2.83836
$411$		0			0
$412$			1.04803e7i			3.04180i
$413$		−	574997.i		−	0.165879i
$414$		0			0
$415$			3.67409e6i			1.04720i
$416$	704356.			0.199553
$417$		0			0
$418$	−6.24092e6			−1.74706
$419$	−2.20124e6			−0.612538			−0.306269	−	0.951945i	$-0.599081\pi$
$419$	−2.20124e6			−0.612538			−0.306269	+	0.951945i	$0.599081\pi$
$420$		0			0
$421$		−	1.32734e6i		−	0.364988i	−0.983207	−	0.182494i	$-0.941583\pi$
$421$		−	1.32734e6i		−	0.364988i	0.983207	−	0.182494i	$-0.0584170\pi$
$422$			1.14210e7i			3.12193i
$423$		0			0
$424$		−	2.97939e6i		−	0.804847i
$425$		−	9.17450e6i		−	2.46383i
$426$		0			0
$427$		−	1.10103e6i		−	0.292233i
$428$	6.25912e6			1.65160
$429$		0			0
$430$		−	5.66673e6i		−	1.47796i
$431$		−	5.50972e6i		−	1.42868i	−0.699797	−	0.714342i	$-0.746726\pi$
$431$		−	5.50972e6i		−	1.42868i	0.699797	−	0.714342i	$-0.253274\pi$
$432$		0			0
$433$	4.94787e6			1.26823			0.634116	−	0.773238i	$-0.281364\pi$
$433$	4.94787e6			1.26823			0.634116	+	0.773238i	$0.281364\pi$
$434$	−2.20121e6			−0.560967
$435$		0			0
$436$			5.43357e6i			1.36889i
$437$	−5.65788e6			−1.41726
$438$		0			0
$439$			1.57962e6i			0.391194i	0.980684	+	0.195597i	$0.0626645\pi$
$439$			1.57962e6i			0.391194i	−0.980684	+	0.195597i	$0.937336\pi$
$440$	−9.47126e6			−2.33225
$441$		0			0
$442$			9.47315e6i			2.30642i
$443$	−262118.			−0.0634583			−0.0317291	−	0.999497i	$-0.510101\pi$
$443$	−262118.			−0.0634583			−0.0317291	+	0.999497i	$0.510101\pi$
$444$		0			0
$445$	6.39244e6			1.53026
$446$			7.49949e6i			1.78523i
$447$		0			0
$448$	−1.05876e6			−0.249232
$449$		−	448765.i		−	0.105052i	−0.998620	−	0.0525259i	$-0.983273\pi$
$449$		−	448765.i		−	0.105052i	0.998620	−	0.0525259i	$-0.0167272\pi$
$450$		0			0
$451$	2.75848e6			0.638600
$452$			3.38943e6i			0.780334i
$453$		0			0
$454$	−484656.			−0.110356
$455$	2.81256e6			0.636903
$456$		0			0
$457$		−	239106.i		−	0.0535551i	−0.999641	−	0.0267775i	$-0.991475\pi$
$457$		−	239106.i		−	0.0535551i	0.999641	−	0.0267775i	$-0.00852457\pi$
$458$			1.14860e7i			2.55861i
$459$		0			0
$460$	−1.67933e7			−3.70034
$461$			7.68350e6i			1.68386i	0.539585	+	0.841931i	$0.318581\pi$
$461$			7.68350e6i			1.68386i	−0.539585	+	0.841931i	$0.681419\pi$
$462$		0			0
$463$		−	5.61085e6i		−	1.21640i	−0.793784	−	0.608200i	$-0.791892\pi$
$463$		−	5.61085e6i		−	1.21640i	0.793784	−	0.608200i	$-0.208108\pi$
$464$		−	708730.i		−	0.152822i
$465$		0			0
$466$		−	3.81431e6i		−	0.813676i
$467$		−	4.46838e6i		−	0.948109i	−0.880496	−	0.474054i	$-0.842790\pi$
$467$		−	4.46838e6i		−	0.948109i	0.880496	−	0.474054i	$-0.157210\pi$
$468$		0			0
$469$	5669.74			0.00119023
$470$	−2.51740e7			−5.25664
$471$		0			0
$472$	−5.01536e6			−1.03621
$473$		−	1.61799e6i		−	0.332524i
$474$		0			0
$475$			1.56555e7i			3.18371i
$476$			3.23435e6i			0.654290i
$477$		0			0
$478$	−6.82068e6			−1.36539
$479$		−	1.44578e6i		−	0.287915i	−0.989584	−	0.143957i	$-0.954017\pi$
$479$		−	1.44578e6i		−	0.287915i	0.989584	−	0.143957i	$-0.0459828\pi$
$480$		0			0
$481$	5.56068e6	−	2.58013e6i	1.09589	−	0.508486i
$482$	1.36447e7			2.67514
$483$		0			0
$484$	5.25662e6			1.01998
$485$	1.69933e6			0.328038
$486$		0			0
$487$		−	2.94284e6i		−	0.562270i	−0.959668	−	0.281135i	$-0.909289\pi$
$487$		−	2.94284e6i		−	0.562270i	0.959668	−	0.281135i	$-0.0907108\pi$
$488$	−9.60363e6			−1.82552
$489$		0			0
$490$	−1.52998e7			−2.87870
$491$	2.50545e6			0.469010			0.234505	−	0.972115i	$-0.424653\pi$
$491$	2.50545e6			0.469010			0.234505	+	0.972115i	$0.424653\pi$
$492$		0			0
$493$	790698.			0.146519
$494$		−	1.61652e7i		−	2.98032i
$495$		0			0
$496$			6.87292e6i			1.25440i
$497$	−1.50282e6			−0.272907
$498$		0			0
$499$		−	2.64448e6i		−	0.475433i	−0.971335	−	0.237716i	$-0.923601\pi$
$499$		−	2.64448e6i		−	0.475433i	0.971335	−	0.237716i	$-0.0763989\pi$
$500$			2.58380e7i			4.62204i
$501$		0			0
$502$	−592716.			−0.104975
$503$			1.50302e6i			0.264878i	0.991191	+	0.132439i	$0.0422808\pi$
$503$			1.50302e6i			0.264878i	−0.991191	+	0.132439i	$0.957719\pi$
$504$		0			0
$505$		−	1.20622e7i		−	2.10474i
$506$	−7.13815e6			−1.23939
$507$		0			0
$508$	1.56756e7			2.69503
$509$	2.14855e6			0.367580			0.183790	−	0.982966i	$-0.441163\pi$
$509$	2.14855e6			0.367580			0.183790	+	0.982966i	$0.441163\pi$
$510$		0			0
$511$	1.49207e6			0.252777
$512$			1.12398e7i			1.89490i
$513$		0			0
$514$	3.66714e6			0.612237
$515$	1.61360e7			2.68089
$516$		0			0
$517$	−7.18780e6			−1.18269
$518$	2.82636e6	−	1.31142e6i	0.462811	−	0.214742i
$519$		0			0
$520$		−	2.45323e7i		−	3.97860i
$521$	4.84841e6			0.782537			0.391269	−	0.920277i	$-0.372036\pi$
$521$	4.84841e6			0.782537			0.391269	+	0.920277i	$0.372036\pi$
$522$		0			0
$523$			9.46409e6i			1.51295i	0.654023	+	0.756475i	$0.273080\pi$
$523$			9.46409e6i			1.51295i	−0.654023	+	0.756475i	$0.726920\pi$
$524$		−	1.92803e7i		−	3.06751i
$525$		0			0
$526$			7.23228e6i			1.13975i
$527$	−7.66780e6			−1.20266
$528$		0			0
$529$	−34949.8			−0.00543007
$530$	−8.97169e6			−1.38735
$531$		0			0
$532$		−	5.51916e6i		−	0.845462i
$533$			7.14499e6i			1.08939i
$534$		0			0
$535$		−	9.63687e6i		−	1.45563i
$536$		−	49453.9i		−	0.00743512i
$537$		0			0
$538$			1.15213e6i			0.171612i
$539$	−4.36847e6			−0.647675
$540$		0			0
$541$			7.78843e6i			1.14408i	0.820226	+	0.572040i	$0.193848\pi$
$541$			7.78843e6i			1.14408i	−0.820226	+	0.572040i	$0.806152\pi$
$542$		−	1.12242e7i		−	1.64118i
$543$		0			0
$544$	1.24710e6			0.180677
$545$	8.36582e6			1.20647
$546$		0			0
$547$		−	2.41496e6i		−	0.345098i	−0.985001	−	0.172549i	$-0.944800\pi$
$547$		−	2.41496e6i		−	0.345098i	0.985001	−	0.172549i	$-0.0552002\pi$
$548$	−1.02961e7			−1.46461
$549$		0			0
$550$			1.97515e7i			2.78415i
$551$	−1.34926e6			−0.189329
$552$		0			0
$553$			3.17214e6i			0.441103i
$554$	7.06890e6			0.978538
$555$		0			0
$556$	−1.36457e7			−1.87202
$557$		−	464341.i		−	0.0634161i	−0.999497	−	0.0317080i	$-0.989905\pi$
$557$		−	464341.i		−	0.0634161i	0.999497	−	0.0317080i	$-0.0100947\pi$
$558$		0			0
$559$	4.19090e6			0.567254
$560$		−	4.46356e6i		−	0.601467i
$561$		0			0
$562$	1.37437e6			0.183554
$563$		−	5.16246e6i		−	0.686413i	−0.939260	−	0.343207i	$-0.888487\pi$
$563$		−	5.16246e6i		−	0.686413i	0.939260	−	0.343207i	$-0.111513\pi$
$564$		0			0
$565$	5.21855e6			0.687747
$566$	5.64969e6			0.741282
$567$		0			0
$568$			1.31082e7i			1.70479i
$569$			6.84241e6i			0.885989i	0.896524	+	0.442994i	$0.146084\pi$
$569$			6.84241e6i			0.885989i	−0.896524	+	0.442994i	$0.853916\pi$
$570$		0			0
$571$	1.37986e7			1.77111			0.885554	−	0.464537i	$-0.153779\pi$
$571$	1.37986e7			1.77111			0.885554	+	0.464537i	$0.153779\pi$
$572$		−	1.36995e7i		−	1.75071i
$573$		0			0
$574$			3.63163e6i			0.460068i
$575$			1.79063e7i			2.25858i
$576$		0			0
$577$			6.17747e6i			0.772451i	0.922404	+	0.386226i	$0.126221\pi$
$577$			6.17747e6i			0.772451i	−0.922404	+	0.386226i	$0.873779\pi$
$578$			2.75418e6i			0.342904i
$579$		0			0
$580$	−4.00478e6			−0.494320
$581$	−1.38110e6			−0.169740
$582$		0			0
$583$	−2.56163e6			−0.312137
$584$		−	1.30145e7i		−	1.57905i
$585$		0			0
$586$		−	1.60009e7i		−	1.92486i
$587$			383466.i			0.0459338i	0.999736	+	0.0229669i	$0.00731123\pi$
$587$			383466.i			0.0459338i	−0.999736	+	0.0229669i	$0.992689\pi$
$588$		0			0
$589$	1.30845e7			1.55406
$590$			1.51025e7i			1.78615i
$591$		0			0
$592$	−4.09469e6	−	8.82485e6i	−0.480194	−	1.03491i
$593$	−408757.			−0.0477340			−0.0238670	−	0.999715i	$-0.507598\pi$
$593$	−408757.			−0.0477340			−0.0238670	+	0.999715i	$0.507598\pi$
$594$		0			0
$595$	4.97979e6			0.576658
$596$	2.12174e7			2.44668
$597$		0			0
$598$		−	1.84892e7i		−	2.11429i
$599$	2.89241e6			0.329377			0.164688	−	0.986346i	$-0.447338\pi$
$599$	2.89241e6			0.329377			0.164688	+	0.986346i	$0.447338\pi$
$600$		0			0
$601$	−2.65283e6			−0.299587			−0.149793	−	0.988717i	$-0.547861\pi$
$601$	−2.65283e6			−0.299587			−0.149793	+	0.988717i	$0.547861\pi$
$602$	2.13013e6			0.239561
$603$		0			0
$604$	−7.74277e6			−0.863583
$605$		−	8.09337e6i		−	0.898961i
$606$		0			0
$607$		−	1.35595e7i		−	1.49373i	−0.664975	−	0.746866i	$-0.731558\pi$
$607$		−	1.35595e7i		−	1.49373i	0.664975	−	0.746866i	$-0.268442\pi$
$608$	−2.12807e6			−0.233468
$609$		0			0
$610$			2.89189e7i			3.14671i
$611$		−	1.86178e7i		−	2.01755i
$612$		0			0
$613$	−1.43925e7			−1.54698			−0.773489	−	0.633809i	$-0.781490\pi$
$613$	−1.43925e7			−1.54698			−0.773489	+	0.633809i	$0.781490\pi$
$614$		−	1.72448e7i		−	1.84602i
$615$		0			0
$616$		−	3.56026e6i		−	0.378034i
$617$	−3.48129e6			−0.368152			−0.184076	−	0.982912i	$-0.558929\pi$
$617$	−3.48129e6			−0.368152			−0.184076	+	0.982912i	$0.558929\pi$
$618$		0			0
$619$	7.64539e6			0.801997			0.400999	−	0.916079i	$-0.368663\pi$
$619$	7.64539e6			0.801997			0.400999	+	0.916079i	$0.368663\pi$
$620$	3.88363e7			4.05751
$621$		0			0
$622$	−1.83996e7			−1.90692
$623$			2.40293e6i			0.248039i
$624$		0			0
$625$	1.77848e7			1.82116
$626$	−2.92900e7			−2.98733
$627$		0			0
$628$	3.74825e7			3.79254
$629$	9.84548e6	−	4.56826e6i	0.992225	−	0.460388i
$630$		0			0
$631$			1.47961e7i			1.47936i	0.672958	+	0.739681i	$0.265023\pi$
$631$			1.47961e7i			1.47936i	−0.672958	+	0.739681i	$0.734977\pi$
$632$	2.76687e7			2.75548
$633$		0			0
$634$			9.38304e6i			0.927087i
$635$		−	2.41350e7i		−	2.37527i
$636$		0			0
$637$		−	1.13152e7i		−	1.10487i
$638$	−1.70227e6			−0.165568
$639$		0			0
$640$	3.08956e7			2.98158
$641$	−1.65084e6			−0.158693			−0.0793467	−	0.996847i	$-0.525283\pi$
$641$	−1.65084e6			−0.158693			−0.0793467	+	0.996847i	$0.525283\pi$
$642$		0			0
$643$		−	8.15538e6i		−	0.777888i	−0.921261	−	0.388944i	$-0.872840\pi$
$643$		−	8.15538e6i		−	0.777888i	0.921261	−	0.388944i	$-0.127160\pi$
$644$		−	6.31263e6i		−	0.599785i
$645$		0			0
$646$		−	2.86213e7i		−	2.69841i
$647$			9.93861e6i			0.933394i	0.884417	+	0.466697i	$0.154556\pi$
$647$			9.93861e6i			0.933394i	−0.884417	+	0.466697i	$0.845444\pi$
$648$		0			0
$649$			4.31213e6i			0.401865i
$650$	−5.11601e7			−4.74950
$651$		0			0
$652$		−	1.77868e7i		−	1.63862i
$653$			1.49370e7i			1.37082i	0.728157	+	0.685410i	$0.240377\pi$
$653$			1.49370e7i			1.37082i	−0.728157	+	0.685410i	$0.759623\pi$
$654$		0			0
$655$	−2.96850e7			−2.70355
$656$	1.13392e7			1.02878
$657$		0			0
$658$		−	9.46297e6i		−	0.852045i
$659$	−2.84687e6			−0.255361			−0.127681	−	0.991815i	$-0.540753\pi$
$659$	−2.84687e6			−0.255361			−0.127681	+	0.991815i	$0.540753\pi$
$660$		0			0
$661$			9.70917e6i			0.864328i	0.901795	+	0.432164i	$0.142250\pi$
$661$			9.70917e6i			0.864328i	−0.901795	+	0.432164i	$0.857750\pi$
$662$	1.90232e7			1.68709
$663$		0			0
$664$			1.20465e7i			1.06033i
$665$	−8.49760e6			−0.745148
$666$		0			0
$667$	−1.54324e6			−0.134313
$668$		−	898302.i		−	0.0778899i
$669$		0			0
$670$	−148918.			−0.0128162
$671$			8.25704e6i			0.707976i
$672$		0			0
$673$	2.68585e6			0.228583			0.114291	−	0.993447i	$-0.463540\pi$
$673$	2.68585e6			0.228583			0.114291	+	0.993447i	$0.463540\pi$
$674$			2.17980e7i			1.84828i
$675$		0			0
$676$	1.11721e7			0.940300
$677$	−9.96835e6			−0.835894			−0.417947	−	0.908471i	$-0.637250\pi$
$677$	−9.96835e6			−0.835894			−0.417947	+	0.908471i	$0.637250\pi$
$678$		0			0
$679$			638782.i			0.0531714i
$680$		−	4.34358e7i		−	3.60226i
$681$		0			0
$682$	1.65078e7			1.35902
$683$			9.53625e6i			0.782214i	0.920345	+	0.391107i	$0.127908\pi$
$683$			9.53625e6i			0.782214i	−0.920345	+	0.391107i	$0.872092\pi$
$684$		0			0
$685$			1.58524e7i			1.29083i
$686$		−	1.20398e7i		−	0.976810i
$687$		0			0
$688$		−	6.65099e6i		−	0.535692i
$689$		−	6.63512e6i		−	0.532476i
$690$		0			0
$691$	2.11608e7			1.68592			0.842959	−	0.537977i	$-0.180811\pi$
$691$	2.11608e7			1.68592			0.842959	+	0.537977i	$0.180811\pi$
$692$	1.27687e7			1.01364
$693$		0			0
$694$	1.76645e7			1.39220
$695$			2.10097e7i			1.64990i
$696$		0			0
$697$			1.26506e7i			0.986345i
$698$			5.85923e6i			0.455200i
$699$		0			0
$700$	−1.74673e7			−1.34735
$701$		−	1.53923e7i		−	1.18306i	−0.806282	−	0.591531i	$-0.798524\pi$
$701$		−	1.53923e7i		−	1.18306i	0.806282	−	0.591531i	$-0.201476\pi$
$702$		0			0
$703$	−1.68005e7	+	7.79535e6i	−1.28214	+	0.594905i
$704$	7.94009e6			0.603801
$705$		0			0
$706$	1.16746e7			0.881517
$707$	4.53421e6			0.341156
$708$		0			0
$709$			3.65791e6i			0.273286i	0.990620	+	0.136643i	$0.0436313\pi$
$709$			3.65791e6i			0.273286i	−0.990620	+	0.136643i	$0.956369\pi$
$710$	3.94720e7			2.93862
$711$		0			0
$712$	2.09594e7			1.54945
$713$	1.49656e7			1.10248
$714$		0			0
$715$	−2.10925e7			−1.54299
$716$			1.48480e7i			1.08240i
$717$		0			0
$718$			1.62150e7i			1.17383i
$719$	−9.26542e6			−0.668410			−0.334205	−	0.942500i	$-0.608468\pi$
$719$	−9.26542e6			−0.668410			−0.334205	+	0.942500i	$0.608468\pi$
$720$		0			0
$721$			6.06557e6i			0.434544i
$722$			2.43928e7i			1.74148i
$723$		0			0
$724$	−7.69834e6			−0.545822
$725$			4.27019e6i			0.301719i
$726$		0			0
$727$		−	5.28381e6i		−	0.370776i	−0.982665	−	0.185388i	$-0.940646\pi$
$727$		−	5.28381e6i		−	0.370776i	0.982665	−	0.185388i	$-0.0593541\pi$
$728$	9.22175e6			0.644889
$729$		0			0
$730$	−3.91898e7			−2.72186
$731$	7.42020e6			0.513597
$732$		0			0
$733$	−1.60458e7			−1.10306			−0.551532	−	0.834154i	$-0.685957\pi$
$733$	−1.60458e7			−1.10306			−0.551532	+	0.834154i	$0.685957\pi$
$734$		−	3.26663e7i		−	2.23800i
$735$		0			0
$736$	−2.43402e6			−0.165626
$737$	−42519.6			−0.00288351
$738$		0			0
$739$	9.45250e6			0.636701			0.318350	−	0.947973i	$-0.396871\pi$
$739$	9.45250e6			0.636701			0.318350	+	0.947973i	$0.396871\pi$
$740$	−4.98660e7	+	2.31376e7i	−3.34754	+	1.55324i
$741$		0			0
$742$		−	3.37247e6i		−	0.224874i
$743$	−2.54624e7			−1.69211			−0.846053	−	0.533099i	$-0.821027\pi$
$743$	−2.54624e7			−1.69211			−0.846053	+	0.533099i	$0.821027\pi$
$744$		0			0
$745$		−	3.26675e7i		−	2.15638i
$746$			3.54987e7i			2.33542i
$747$		0			0
$748$		−	2.42557e7i		−	1.58511i
$749$	3.62252e6			0.235942
$750$		0			0
$751$	−2.61898e7			−1.69446			−0.847231	−	0.531225i	$-0.821732\pi$
$751$	−2.61898e7			−1.69446			−0.847231	+	0.531225i	$0.821732\pi$
$752$	−2.95466e7			−1.90529
$753$		0			0
$754$		−	4.40920e6i		−	0.282443i
$755$			1.19212e7i			0.761119i
$756$		0			0
$757$			1.11682e7i			0.708345i	0.935180	+	0.354173i	$0.115237\pi$
$757$			1.11682e7i			0.708345i	−0.935180	+	0.354173i	$0.884763\pi$
$758$			1.59158e7i			1.00613i
$759$		0			0
$760$			7.41196e7i			4.65478i
$761$	5.61182e6			0.351271			0.175636	−	0.984455i	$-0.443802\pi$
$761$	5.61182e6			0.351271			0.175636	+	0.984455i	$0.443802\pi$
$762$		0			0
$763$			3.14473e6i			0.195556i
$764$		−	3.19113e7i		−	1.97793i
$765$		0			0
$766$	2.32753e7			1.43326
$767$	−1.11692e7			−0.685543
$768$		0			0
$769$			1.21930e7i			0.743522i	0.928329	+	0.371761i	$0.121246\pi$
$769$			1.21930e7i			0.743522i	−0.928329	+	0.371761i	$0.878754\pi$
$770$	−1.07208e7			−0.651631
$771$		0			0
$772$			2.23617e7i			1.35040i
$773$	1.18645e7			0.714166			0.357083	−	0.934073i	$-0.383771\pi$
$773$	1.18645e7			0.714166			0.357083	+	0.934073i	$0.383771\pi$
$774$		0			0
$775$		−	4.14102e7i		−	2.47658i
$776$	5.57172e6			0.332151
$777$		0			0
$778$	−1.23034e7			−0.728743
$779$		−	2.15872e7i		−	1.27454i
$780$		0			0
$781$	1.12702e7			0.661157
$782$		−	3.27360e7i		−	1.91430i
$783$		0			0
$784$	−1.79573e7			−1.04340
$785$		−	5.77101e7i		−	3.34255i
$786$		0			0
$787$	−2.50476e7			−1.44155			−0.720773	−	0.693171i	$-0.756213\pi$
$787$	−2.50476e7			−1.44155			−0.720773	+	0.693171i	$0.756213\pi$
$788$	−4.26431e7			−2.44643
$789$		0			0
$790$		−	8.33174e7i		−	4.74972i
$791$			1.96166e6i			0.111476i
$792$		0			0
$793$	−2.13873e7			−1.20774
$794$		−	2.26603e7i		−	1.27560i
$795$		0			0
$796$			5.10657e7i			2.85658i
$797$			5.81614e6i			0.324331i	0.986764	+	0.162166i	$0.0518479\pi$
$797$			5.81614e6i			0.324331i	−0.986764	+	0.162166i	$0.948152\pi$
$798$		0			0
$799$		−	3.29637e7i		−	1.82671i
$800$			6.73500e6i			0.372060i
$801$		0			0
$802$	1.90715e7			1.04701
$803$	−1.11896e7			−0.612389
$804$		0			0
$805$	−9.71927e6			−0.528620
$806$			4.27582e7i			2.31837i
$807$		0			0
$808$		−	3.95492e7i		−	2.13113i
$809$			2.04340e7i			1.09770i	0.835922	+	0.548848i	$0.184933\pi$
$809$			2.04340e7i			1.09770i	−0.835922	+	0.548848i	$0.815067\pi$
$810$		0			0
$811$	−1.77391e7			−0.947066			−0.473533	−	0.880776i	$-0.657022\pi$
$811$	−1.77391e7			−0.947066			−0.473533	+	0.880776i	$0.657022\pi$
$812$		−	1.50540e6i		−	0.0801240i
$813$		0			0
$814$	−2.11960e7	+	9.83486e6i	−1.12123	+	0.520244i
$815$	−2.73855e7			−1.44420
$816$		0			0
$817$	−1.26620e7			−0.663660
$818$	6.97627e6			0.364536
$819$		0			0
$820$		−	6.40735e7i		−	3.32770i
$821$	1.04128e7			0.539153			0.269576	−	0.962979i	$-0.413116\pi$
$821$	1.04128e7			0.539153			0.269576	+	0.962979i	$0.413116\pi$
$822$		0			0
$823$	7.39694e6			0.380673			0.190337	−	0.981719i	$-0.439042\pi$
$823$	7.39694e6			0.380673			0.190337	+	0.981719i	$0.439042\pi$
$824$	5.29064e7			2.71450
$825$		0			0
$826$	−5.67706e6			−0.289516
$827$			2.32075e6i			0.117995i	0.998258	+	0.0589977i	$0.0187905\pi$
$827$			2.32075e6i			0.117995i	−0.998258	+	0.0589977i	$0.981210\pi$
$828$		0			0
$829$		−	2.91531e7i		−	1.47333i	−0.676260	−	0.736663i	$-0.736401\pi$
$829$		−	2.91531e7i		−	1.47333i	0.676260	−	0.736663i	$-0.263599\pi$
$830$	3.62750e7			1.82773
$831$		0			0
$832$			2.05663e7i			1.03003i
$833$		−	2.00341e7i		−	1.00036i
$834$		0			0
$835$	−1.38307e6			−0.0686482
$836$			4.13904e7i			2.04825i
$837$		0			0
$838$			2.17333e7i			1.06909i
$839$	3.42013e7			1.67740			0.838702	−	0.544591i	$-0.183315\pi$
$839$	3.42013e7			1.67740			0.838702	+	0.544591i	$0.183315\pi$
$840$		0			0
$841$	2.01431e7			0.982057
$842$	−1.31051e7			−0.637032
$843$		0			0
$844$	7.57452e7			3.66015
$845$		−	1.72011e7i		−	0.828733i
$846$		0			0
$847$	3.04231e6			0.145712
$848$	−1.05300e7			−0.502850
$849$		0			0
$850$	−9.05816e7			−4.30024
$851$	−1.92158e7	+	8.91606e6i	−0.909569	+	0.422036i
$852$		0			0
$853$		−	1.32406e6i		−	0.0623067i	−0.999515	−	0.0311533i	$-0.990082\pi$
$853$		−	1.32406e6i		−	0.0623067i	0.999515	−	0.0311533i	$-0.00991802\pi$
$854$	−1.08707e7			−0.510048
$855$		0			0
$856$		−	3.15971e7i		−	1.47388i
$857$		−	2.78886e6i		−	0.129710i	−0.997895	−	0.0648551i	$-0.979341\pi$
$857$		−	2.78886e6i		−	0.129710i	0.997895	−	0.0648551i	$-0.0206585\pi$
$858$		0			0
$859$			624964.i			0.0288983i	0.999896	+	0.0144491i	$0.00459947\pi$
$859$			624964.i			0.0288983i	−0.999896	+	0.0144491i	$0.995401\pi$
$860$	−3.75823e7			−1.73276
$861$		0			0
$862$	−5.43985e7			−2.49355
$863$	−4.16503e7			−1.90367			−0.951833	−	0.306617i	$-0.900803\pi$
$863$	−4.16503e7			−1.90367			−0.951833	+	0.306617i	$0.900803\pi$
$864$		0			0
$865$		−	1.96595e7i		−	0.893370i
$866$		−	4.88513e7i		−	2.21351i
$867$		0			0
$868$			1.45987e7i			0.657678i
$869$		−	2.37891e7i		−	1.06863i
$870$		0			0
$871$		−	110134.i		−	0.00491899i
$872$	2.74296e7			1.22160
$873$		0			0
$874$			5.58614e7i			2.47362i
$875$			1.49540e7i			0.660293i
$876$		0			0
$877$	3.26671e6			0.143421			0.0717103	−	0.997426i	$-0.477154\pi$
$877$	3.26671e6			0.143421			0.0717103	+	0.997426i	$0.477154\pi$
$878$	1.55959e7			0.682771
$879$		0			0
$880$			3.34740e7i			1.45714i
$881$	−2.15378e7			−0.934890			−0.467445	−	0.884022i	$-0.654825\pi$
$881$	−2.15378e7			−0.934890			−0.467445	+	0.884022i	$0.654825\pi$
$882$		0			0
$883$			2.95246e7i			1.27433i	0.770727	+	0.637165i	$0.219893\pi$
$883$			2.95246e7i			1.27433i	−0.770727	+	0.637165i	$0.780107\pi$
$884$	6.28268e7			2.70405
$885$		0			0
$886$			2.58795e6i			0.110757i
$887$	−1.97635e7			−0.843439			−0.421720	−	0.906726i	$-0.638573\pi$
$887$	−1.97635e7			−0.843439			−0.421720	+	0.906726i	$0.638573\pi$
$888$		0			0
$889$	9.07238e6			0.385005
$890$		−	6.31138e7i		−	2.67085i
$891$		0			0
$892$	4.97374e7			2.09301
$893$			5.62499e7i			2.36044i
$894$		0			0
$895$	2.28608e7			0.953969
$896$			1.16137e7i			0.483283i
$897$		0			0
$898$	−4.43074e6			−0.183352
$899$	3.56891e6			0.147277
$900$		0			0
$901$		−	1.17478e7i		−	0.482109i
$902$		−	2.72351e7i		−	1.11458i
$903$		0			0
$904$	1.71104e7			0.696370
$905$			1.18528e7i			0.481060i
$906$		0			0
$907$			1.61434e7i			0.651593i	0.945440	+	0.325796i	$0.105632\pi$
$907$			1.61434e7i			0.651593i	−0.945440	+	0.325796i	$0.894368\pi$
$908$			3.21429e6i			0.129381i
$909$		0			0
$910$		−	2.77690e7i		−	1.11162i
$911$			4.35170e7i			1.73725i	0.495467	+	0.868627i	$0.334997\pi$
$911$			4.35170e7i			1.73725i	−0.495467	+	0.868627i	$0.665003\pi$
$912$		0			0
$913$	1.03574e7			0.411219
$914$	−2.36074e6			−0.0934724
$915$		0			0
$916$	7.61761e7			2.99971
$917$		−	1.11587e7i		−	0.438217i
$918$		0			0
$919$			2.20543e7i			0.861398i	0.902496	+	0.430699i	$0.141733\pi$
$919$			2.20543e7i			0.861398i	−0.902496	+	0.430699i	$0.858267\pi$
$920$			8.47755e7i			3.30218i
$921$		0			0
$922$	7.58607e7			2.93893
$923$			2.91920e7i			1.12787i
$924$		0			0
$925$	2.46710e7	+	5.31709e7i	0.948054	+	2.04324i
$926$	−5.53970e7			−2.12304
$927$		0			0
$928$	−580451.			−0.0221256
$929$	4.05513e7			1.54158			0.770788	−	0.637091i	$-0.219863\pi$
$929$	4.05513e7			1.54158			0.770788	+	0.637091i	$0.219863\pi$
$930$		0			0
$931$			3.41865e7i			1.29265i
$932$	−2.52969e7			−0.953954
$933$		0			0
$934$	−4.41172e7			−1.65478
$935$	−3.73454e7			−1.39704
$936$		0			0
$937$	−1.56270e6			−0.0581469			−0.0290734	−	0.999577i	$-0.509256\pi$
$937$	−1.56270e6			−0.0581469			−0.0290734	+	0.999577i	$0.509256\pi$
$938$		−	55978.5i		−	0.00207737i
$939$		0			0
$940$			1.66957e8i			6.16289i
$941$	−1.60631e7			−0.591364			−0.295682	−	0.955286i	$-0.595547\pi$
$941$	−1.60631e7			−0.591364			−0.295682	+	0.955286i	$0.595547\pi$
$942$		0			0
$943$		−	2.46907e7i		−	0.904179i
$944$			1.77257e7i			0.647400i
$945$		0			0
$946$	−1.59747e7			−0.580371
$947$			2.24583e7i			0.813769i	0.913480	+	0.406885i	$0.133385\pi$
$947$			2.24583e7i			0.813769i	−0.913480	+	0.406885i	$0.866615\pi$
$948$		0			0
$949$		−	2.89833e7i		−	1.04468i
$950$	1.54570e8			5.55670
$951$		0			0
$952$	1.63276e7			0.583888
$953$	1.58089e7			0.563856			0.281928	−	0.959435i	$-0.409026\pi$
$953$	1.58089e7			0.563856			0.281928	+	0.959435i	$0.409026\pi$
$954$		0			0
$955$	−4.91323e7			−1.74325
$956$			4.52354e7i			1.60079i
$957$		0			0
$958$	−1.42745e7			−0.502512
$959$	−5.95896e6			−0.209230
$960$		0			0
$961$	−5.98038e6			−0.208891
$962$	−2.54741e7	−	5.49017e7i	−0.887486	−	1.91271i
$963$		0			0
$964$		−	9.04930e7i		−	3.13633i
$965$	3.44293e7			1.19017
$966$		0			0
$967$		−	3.63358e6i		−	0.124959i	−0.998046	−	0.0624796i	$-0.980099\pi$
$967$		−	3.63358e6i		−	0.124959i	0.998046	−	0.0624796i	$-0.0199008\pi$
$968$		−	2.65363e7i		−	0.910233i
$969$		0			0
$970$		−	1.67778e7i		−	0.572541i
$971$	5.02464e6			0.171024			0.0855120	−	0.996337i	$-0.472747\pi$
$971$	5.02464e6			0.171024			0.0855120	+	0.996337i	$0.472747\pi$
$972$		0			0
$973$	−7.89758e6			−0.267431
$974$	−2.90553e7			−0.981358
$975$		0			0
$976$			3.39418e7i			1.14054i
$977$			5.10227e7i			1.71012i	0.518528	+	0.855060i	$0.326480\pi$
$977$			5.10227e7i			1.71012i	−0.518528	+	0.855060i	$0.673520\pi$
$978$		0			0
$979$		−	1.80205e7i		−	0.600911i
$980$			1.01470e8i			3.37499i
$981$		0			0
$982$		−	2.47368e7i		−	0.818586i
$983$	−1.38574e6			−0.0457404			−0.0228702	−	0.999738i	$-0.507280\pi$
$983$	−1.38574e6			−0.0457404			−0.0228702	+	0.999738i	$0.507280\pi$
$984$		0			0
$985$			6.56557e7i			2.15616i
$986$		−	7.80671e6i		−	0.255727i
$987$		0			0
$988$	−1.07209e8			−3.49412
$989$	−1.44823e7			−0.470812
$990$		0			0
$991$		−	2.87127e7i		−	0.928732i	−0.885643	−	0.464366i	$-0.846282\pi$
$991$		−	2.87127e7i		−	0.928732i	0.885643	−	0.464366i	$-0.153718\pi$
$992$	5.62893e6			0.181613
$993$		0			0
$994$			1.48376e7i			0.476318i
$995$	7.86235e7			2.51764
$996$		0			0
$997$		−	3.96980e7i		−	1.26483i	−0.774631	−	0.632413i	$-0.782064\pi$
$997$		−	3.96980e7i		−	1.26483i	0.774631	−	0.632413i	$-0.217936\pi$
$998$	−2.61095e7			−0.829797
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.6.c.d.73.2		16
3.2	odd	2		37.6.b.a.36.15	yes	16
12.11	even	2		592.6.g.c.369.9		16
37.36	even	2	inner	333.6.c.d.73.15		16
111.110	odd	2		37.6.b.a.36.2	✓	16
444.443	even	2		592.6.g.c.369.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.6.b.a.36.2	✓	16	111.110	odd	2
37.6.b.a.36.15	yes	16	3.2	odd	2
333.6.c.d.73.2		16	1.1	even	1	trivial
333.6.c.d.73.15		16	37.36	even	2	inner
592.6.g.c.369.9		16	12.11	even	2
592.6.g.c.369.10		16	444.443	even	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:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	333.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-9.87320i q^{2} -65.4800 q^{4} +100.817i q^{5} -37.8971 q^{7} +330.555i q^{8} +O(q^{10})\)	\(q-9.87320i q^{2} -65.4800 q^{4} +100.817i q^{5} -37.8971 q^{7} +330.555i q^{8} +995.382 q^{10} +284.206 q^{11} +736.146i q^{13} +374.166i q^{14} +1168.27 q^{16} +1303.38i q^{17} -2224.12i q^{19} -6601.47i q^{20} -2806.02i q^{22} -2543.87i q^{23} -7038.98 q^{25} +7268.11 q^{26} +2481.50 q^{28} -606.649i q^{29} +5882.99i q^{31} -956.815i q^{32} +12868.6 q^{34} -3820.66i q^{35} +(-3504.92 - 7553.78i) q^{37} -21959.2 q^{38} -33325.4 q^{40} +9705.95 q^{41} -5693.02i q^{43} -18609.8 q^{44} -25116.2 q^{46} -25290.9 q^{47} -15370.8 q^{49} +69497.2i q^{50} -48202.8i q^{52} -9013.32 q^{53} +28652.6i q^{55} -12527.1i q^{56} -5989.57 q^{58} +15172.6i q^{59} +29053.1i q^{61} +58083.9 q^{62} +27937.8 q^{64} -74215.7 q^{65} -149.609 q^{67} -85345.6i q^{68} -37722.1 q^{70} +39655.1 q^{71} -39371.7 q^{73} +(-74579.9 + 34604.7i) q^{74} +145635. i q^{76} -10770.6 q^{77} -83704.0i q^{79} +117781. i q^{80} -95828.7i q^{82} +36443.3 q^{83} -131403. q^{85} -56208.3 q^{86} +93945.5i q^{88} -63406.6i q^{89} -27897.8i q^{91} +166573. i q^{92} +249702. i q^{94} +224228. q^{95} -16855.7i q^{97} +151759. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 268 q^{4} + 190 q^{7}+O(q^{10}) \) 16 * q - 268 * q^4 + 190 * q^7	\( 16 q - 268 q^{4} + 190 q^{7} - 74 q^{10} + 1110 q^{11} + 2900 q^{16} - 12052 q^{25} - 4902 q^{26} - 16824 q^{28} + 20556 q^{34} - 11400 q^{37} - 12108 q^{38} + 16966 q^{40} - 3918 q^{41} - 125394 q^{44} + 17470 q^{46} - 3822 q^{47} - 32618 q^{49} + 24126 q^{53} - 164718 q^{58} + 81426 q^{62} + 158076 q^{64} - 98976 q^{65} + 23560 q^{67} - 222404 q^{70} + 50046 q^{71} - 196274 q^{73} - 141216 q^{74} + 239574 q^{77} + 215814 q^{83} - 346472 q^{85} - 197640 q^{86} + 132504 q^{95}+O(q^{100}) \) 16 * q - 268 * q^4 + 190 * q^7 - 74 * q^10 + 1110 * q^11 + 2900 * q^16 - 12052 * q^25 - 4902 * q^26 - 16824 * q^28 + 20556 * q^34 - 11400 * q^37 - 12108 * q^38 + 16966 * q^40 - 3918 * q^41 - 125394 * q^44 + 17470 * q^46 - 3822 * q^47 - 32618 * q^49 + 24126 * q^53 - 164718 * q^58 + 81426 * q^62 + 158076 * q^64 - 98976 * q^65 + 23560 * q^67 - 222404 * q^70 + 50046 * q^71 - 196274 * q^73 - 141216 * q^74 + 239574 * q^77 + 215814 * q^83 - 346472 * q^85 - 197640 * q^86 + 132504 * q^95

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