LMFDB - Embedded newform 400.6.n.h.143.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,6,Mod(143,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("400.143");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	400.n (of order $4$, degree $2$, 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:	$64.1535279252$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.1
Character	$\chi$	$=$	400.143
Dual form			400.6.n.h.207.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.8504 + 13.8504i) q^{3} +(-156.283 - 156.283i) q^{7} -140.668i q^{9} +O(q^{10})$	$q+(-13.8504 + 13.8504i) q^{3} +(-156.283 - 156.283i) q^{7} -140.668i q^{9} +402.885i q^{11} +(703.867 + 703.867i) q^{13} +(-899.535 + 899.535i) q^{17} +507.251 q^{19} +4329.18 q^{21} +(-858.099 + 858.099i) q^{23} +(-1417.34 - 1417.34i) q^{27} +6737.48i q^{29} +2290.84i q^{31} +(-5580.12 - 5580.12i) q^{33} +(-6090.42 + 6090.42i) q^{37} -19497.7 q^{39} -4406.15 q^{41} +(5368.74 - 5368.74i) q^{43} +(-20272.4 - 20272.4i) q^{47} +32042.0i q^{49} -24917.9i q^{51} +(-10170.4 - 10170.4i) q^{53} +(-7025.64 + 7025.64i) q^{57} +32508.1 q^{59} +42480.7 q^{61} +(-21984.1 + 21984.1i) q^{63} +(-1676.23 - 1676.23i) q^{67} -23770.1i q^{69} +25272.3i q^{71} +(25346.7 + 25346.7i) q^{73} +(62964.2 - 62964.2i) q^{77} +4185.82 q^{79} +73443.8 q^{81} +(-49368.6 + 49368.6i) q^{83} +(-93316.9 - 93316.9i) q^{87} -133783. i q^{89} -220005. i q^{91} +(-31729.2 - 31729.2i) q^{93} +(100890. - 100890. i) q^{97} +56673.1 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 19936 q^{21} + 32568 q^{41} + 454944 q^{61} + 1059176 q^{81}+O(q^{100}) $ 24 * q + 19936 * q^21 + 32568 * q^41 + 454944 * q^61 + 1059176 * q^81

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−13.8504	+	13.8504i	−0.888505	+	0.888505i	−0.994379	−	0.105875i	$-0.966236\pi$
$3$	−13.8504	+	13.8504i	−0.888505	+	0.888505i	0.105875	+	0.994379i	$0.466236\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−156.283	−	156.283i	−1.20550	−	1.20550i	−0.972469	−	0.233033i	$-0.925135\pi$
$7$	−156.283	−	156.283i	−1.20550	−	1.20550i	−0.233033	−	0.972469i	$-0.574865\pi$
$8$		0			0
$9$		−	140.668i		−	0.578882i
$10$		0			0
$11$			402.885i			1.00392i	0.864891	+	0.501960i	$0.167388\pi$
$11$			402.885i			1.00392i	−0.864891	+	0.501960i	$0.832612\pi$
$12$		0			0
$13$	703.867	+	703.867i	1.15513	+	1.15513i	0.985509	+	0.169624i	$0.0542553\pi$
$13$	703.867	+	703.867i	1.15513	+	1.15513i	0.169624	+	0.985509i	$0.445745\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−899.535	+	899.535i	−0.754911	+	0.754911i	−0.975391	−	0.220481i	$-0.929237\pi$
$17$	−899.535	+	899.535i	−0.754911	+	0.754911i	0.220481	+	0.975391i	$0.429237\pi$
$18$		0			0
$19$	507.251			0.322358			0.161179	−	0.986925i	$-0.448470\pi$
$19$	507.251			0.322358			0.161179	+	0.986925i	$0.448470\pi$
$20$		0			0
$21$	4329.18			2.14219
$22$		0			0
$23$	−858.099	+	858.099i	−0.338234	+	0.338234i	−0.855702	−	0.517468i	$-0.826875\pi$
$23$	−858.099	+	858.099i	−0.338234	+	0.338234i	0.517468	+	0.855702i	$0.326875\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1417.34	−	1417.34i	−0.374165	−	0.374165i
$28$		0			0
$29$			6737.48i			1.48766i	0.668371	+	0.743828i	$0.266992\pi$
$29$			6737.48i			1.48766i	−0.668371	+	0.743828i	$0.733008\pi$
$30$		0			0
$31$			2290.84i			0.428146i	0.976818	+	0.214073i	$0.0686730\pi$
$31$			2290.84i			0.428146i	−0.976818	+	0.214073i	$0.931327\pi$
$32$		0			0
$33$	−5580.12	−	5580.12i	−0.891988	−	0.891988i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6090.42	+	6090.42i	−0.731379	+	0.731379i	−0.970893	−	0.239514i	$-0.923012\pi$
$37$	−6090.42	+	6090.42i	−0.731379	+	0.731379i	0.239514	+	0.970893i	$0.423012\pi$
$38$		0			0
$39$	−19497.7			−2.05268
$40$		0			0
$41$	−4406.15			−0.409355			−0.204677	−	0.978829i	$-0.565615\pi$
$41$	−4406.15			−0.409355			−0.204677	+	0.978829i	$0.565615\pi$
$42$		0			0
$43$	5368.74	−	5368.74i	0.442794	−	0.442794i	−0.450156	−	0.892950i	$-0.648632\pi$
$43$	5368.74	−	5368.74i	0.442794	−	0.442794i	0.892950	+	0.450156i	$0.148632\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−20272.4	−	20272.4i	−1.33863	−	1.33863i	−0.897388	−	0.441242i	$-0.854538\pi$
$47$	−20272.4	−	20272.4i	−1.33863	−	1.33863i	−0.441242	−	0.897388i	$-0.645462\pi$
$48$		0			0
$49$			32042.0i			1.90647i
$50$		0			0
$51$		−	24917.9i		−	1.34148i
$52$		0			0
$53$	−10170.4	−	10170.4i	−0.497333	−	0.497333i	0.413274	−	0.910607i	$-0.364385\pi$
$53$	−10170.4	−	10170.4i	−0.497333	−	0.497333i	−0.910607	+	0.413274i	$0.864385\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−7025.64	+	7025.64i	−0.286417	+	0.286417i
$58$		0			0
$59$	32508.1			1.21580			0.607900	−	0.794014i	$-0.292012\pi$
$59$	32508.1			1.21580			0.607900	+	0.794014i	$0.292012\pi$
$60$		0			0
$61$	42480.7			1.46173			0.730864	−	0.682523i	$-0.239117\pi$
$61$	42480.7			1.46173			0.730864	+	0.682523i	$0.239117\pi$
$62$		0			0
$63$	−21984.1	+	21984.1i	−0.697843	+	0.697843i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1676.23	−	1676.23i	−0.0456191	−	0.0456191i	0.683929	−	0.729548i	$-0.260270\pi$
$67$	−1676.23	−	1676.23i	−0.0456191	−	0.0456191i	−0.729548	+	0.683929i	$0.760270\pi$
$68$		0			0
$69$		−	23770.1i		−	0.601046i
$70$		0			0
$71$			25272.3i			0.594976i	0.954726	+	0.297488i	$0.0961488\pi$
$71$			25272.3i			0.594976i	−0.954726	+	0.297488i	$0.903851\pi$
$72$		0			0
$73$	25346.7	+	25346.7i	0.556690	+	0.556690i	0.928364	−	0.371673i	$-0.121216\pi$
$73$	25346.7	+	25346.7i	0.556690	+	0.556690i	−0.371673	+	0.928364i	$0.621216\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	62964.2	−	62964.2i	1.21023	−	1.21023i
$78$		0			0
$79$	4185.82			0.0754593			0.0377296	−	0.999288i	$-0.487987\pi$
$79$	4185.82			0.0754593			0.0377296	+	0.999288i	$0.487987\pi$
$80$		0			0
$81$	73443.8			1.24378
$82$		0			0
$83$	−49368.6	+	49368.6i	−0.786603	+	0.786603i	−0.980936	−	0.194333i	$-0.937746\pi$
$83$	−49368.6	+	49368.6i	−0.786603	+	0.786603i	0.194333	+	0.980936i	$0.437746\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−93316.9	−	93316.9i	−1.32179	−	1.32179i
$88$		0			0
$89$		−	133783.i		−	1.79030i	−0.445760	−	0.895152i	$-0.647067\pi$
$89$		−	133783.i		−	1.79030i	0.445760	−	0.895152i	$-0.352933\pi$
$90$		0			0
$91$		−	220005.i		−	2.78503i
$92$		0			0
$93$	−31729.2	−	31729.2i	−0.380409	−	0.380409i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	100890.	−	100890.i	1.08873	−	1.08873i	0.0930659	−	0.995660i	$-0.470333\pi$
$97$	100890.	−	100890.i	1.08873	−	1.08873i	0.995660	−	0.0930659i	$-0.0296667\pi$
$98$		0			0
$99$	56673.1			0.581151
$100$		0			0
$101$	−162431.			−1.58441			−0.792203	−	0.610257i	$-0.791066\pi$
$101$	−162431.			−1.58441			−0.792203	+	0.610257i	$0.791066\pi$
$102$		0			0
$103$	−82560.9	+	82560.9i	−0.766799	+	0.766799i	−0.977542	−	0.210743i	$-0.932412\pi$
$103$	−82560.9	+	82560.9i	−0.766799	+	0.766799i	0.210743	+	0.977542i	$0.432412\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	21383.5	+	21383.5i	0.180559	+	0.180559i	0.791600	−	0.611040i	$-0.209249\pi$
$107$	21383.5	+	21383.5i	0.180559	+	0.180559i	−0.611040	+	0.791600i	$0.709249\pi$
$108$		0			0
$109$			69497.9i			0.560280i	0.959959	+	0.280140i	$0.0903809\pi$
$109$			69497.9i			0.560280i	−0.959959	+	0.280140i	$0.909619\pi$
$110$		0			0
$111$		−	168710.i		−	1.29967i
$112$		0			0
$113$	−108382.	−	108382.i	−0.798472	−	0.798472i	0.184382	−	0.982855i	$-0.440972\pi$
$113$	−108382.	−	108382.i	−0.798472	−	0.798472i	−0.982855	+	0.184382i	$0.940972\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	99011.7	−	99011.7i	0.668686	−	0.668686i
$118$		0			0
$119$	281165.			1.82009
$120$		0			0
$121$	−1265.11			−0.00785532
$122$		0			0
$123$	61027.1	−	61027.1i	0.363714	−	0.363714i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−163525.	−	163525.i	−0.899653	−	0.899653i	0.0957521	−	0.995405i	$-0.469474\pi$
$127$	−163525.	−	163525.i	−0.899653	−	0.899653i	−0.995405	+	0.0957521i	$0.969474\pi$
$128$		0			0
$129$			148719.i			0.786849i
$130$		0			0
$131$		−	371491.i		−	1.89134i	−0.325122	−	0.945672i	$-0.605405\pi$
$131$		−	371491.i		−	1.89134i	0.325122	−	0.945672i	$-0.394595\pi$
$132$		0			0
$133$	−79274.9	−	79274.9i	−0.388604	−	0.388604i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	263445.	−	263445.i	1.19919	−	1.19919i	0.224781	−	0.974409i	$-0.427833\pi$
$137$	263445.	−	263445.i	1.19919	−	1.19919i	0.974409	−	0.224781i	$-0.0721668\pi$
$138$		0			0
$139$	−400169.			−1.75674			−0.878368	−	0.477985i	$-0.841367\pi$
$139$	−400169.			−1.75674			−0.878368	+	0.477985i	$0.841367\pi$
$140$		0			0
$141$	561563.			2.37876
$142$		0			0
$143$	−283577.	+	283577.i	−1.15966	+	1.15966i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−443796.	−	443796.i	−1.69391	−	1.69391i
$148$		0			0
$149$		−	299849.i		−	1.10646i	−0.833028	−	0.553231i	$-0.813395\pi$
$149$		−	299849.i		−	1.10646i	0.833028	−	0.553231i	$-0.186605\pi$
$150$		0			0
$151$			296720.i			1.05902i	0.848304	+	0.529510i	$0.177624\pi$
$151$			296720.i			1.05902i	−0.848304	+	0.529510i	$0.822376\pi$
$152$		0			0
$153$	126536.	+	126536.i	0.437004	+	0.437004i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−329445.	+	329445.i	−1.06668	+	1.06668i	−0.0690665	+	0.997612i	$0.522002\pi$
$157$	−329445.	+	329445.i	−1.06668	+	1.06668i	−0.997612	+	0.0690665i	$0.977998\pi$
$158$		0			0
$159$	281728.			0.883766
$160$		0			0
$161$	268213.			0.815484
$162$		0			0
$163$	−2597.69	+	2597.69i	−0.00765804	+	0.00765804i	−0.710925	−	0.703267i	$-0.751724\pi$
$163$	−2597.69	+	2597.69i	−0.00765804	+	0.00765804i	0.703267	+	0.710925i	$0.251724\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	26835.4	+	26835.4i	0.0744591	+	0.0744591i	0.743356	−	0.668896i	$-0.233233\pi$
$167$	26835.4	+	26835.4i	0.0744591	+	0.0744591i	−0.668896	+	0.743356i	$0.733233\pi$
$168$		0			0
$169$			619563.i			1.66866i
$170$		0			0
$171$		−	71354.2i		−	0.186607i
$172$		0			0
$173$	5477.68	+	5477.68i	0.0139149	+	0.0139149i	0.714030	−	0.700115i	$-0.246868\pi$
$173$	5477.68	+	5477.68i	0.0139149	+	0.0139149i	−0.700115	+	0.714030i	$0.746868\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−450251.	+	450251.i	−1.08024	+	1.08024i
$178$		0			0
$179$	−293898.			−0.685590			−0.342795	−	0.939410i	$-0.611374\pi$
$179$	−293898.			−0.685590			−0.342795	+	0.939410i	$0.611374\pi$
$180$		0			0
$181$	271764.			0.616588			0.308294	−	0.951291i	$-0.400242\pi$
$181$	271764.			0.616588			0.308294	+	0.951291i	$0.400242\pi$
$182$		0			0
$183$	−588375.	+	588375.i	−1.29875	+	1.29875i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−362409.	−	362409.i	−0.757870	−	0.757870i
$188$		0			0
$189$			443012.i			0.902114i
$190$		0			0
$191$		−	546685.i		−	1.08431i	−0.840278	−	0.542156i	$-0.817608\pi$
$191$		−	546685.i		−	1.08431i	0.840278	−	0.542156i	$-0.182392\pi$
$192$		0			0
$193$	−337284.	−	337284.i	−0.651783	−	0.651783i	0.301639	−	0.953422i	$-0.402466\pi$
$193$	−337284.	−	337284.i	−0.651783	−	0.651783i	−0.953422	+	0.301639i	$0.902466\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	268400.	−	268400.i	0.492739	−	0.492739i	−0.416429	−	0.909168i	$-0.636719\pi$
$197$	268400.	−	268400.i	0.492739	−	0.492739i	0.909168	+	0.416429i	$0.136719\pi$
$198$		0			0
$199$	133444.			0.238872			0.119436	−	0.992842i	$-0.461891\pi$
$199$	133444.			0.238872			0.119436	+	0.992842i	$0.461891\pi$
$200$		0			0
$201$	46433.0			0.0810656
$202$		0			0
$203$	1.05296e6	−	1.05296e6i	1.79337	−	1.79337i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	120707.	+	120707.i	0.195798	+	0.195798i
$208$		0			0
$209$			204364.i			0.323622i
$210$		0			0
$211$		−	4751.30i		−	0.00734693i	−0.999993	−	0.00367347i	$-0.998831\pi$
$211$		−	4751.30i		−	0.00734693i	0.999993	−	0.00367347i	$-0.00116930\pi$
$212$		0			0
$213$	−350033.	−	350033.i	−0.528639	−	0.528639i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	358021.	−	358021.i	0.516130	−	0.516130i
$218$		0			0
$219$	−702124.			−0.989244
$220$		0			0
$221$	−1.26630e6			−1.74404
$222$		0			0
$223$	469241.	−	469241.i	0.631879	−	0.631879i	−0.316660	−	0.948539i	$-0.602561\pi$
$223$	469241.	−	469241.i	0.631879	−	0.631879i	0.948539	+	0.316660i	$0.102561\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	600480.	+	600480.i	0.773452	+	0.773452i	0.978708	−	0.205256i	$-0.0658027\pi$
$227$	600480.	+	600480.i	0.773452	+	0.773452i	−0.205256	+	0.978708i	$0.565803\pi$
$228$		0			0
$229$		−	339396.i		−	0.427680i	−0.976869	−	0.213840i	$-0.931403\pi$
$229$		−	339396.i		−	0.427680i	0.976869	−	0.213840i	$-0.0685971\pi$
$230$		0			0
$231$			1.74416e6i			2.15059i
$232$		0			0
$233$	587632.	+	587632.i	0.709113	+	0.709113i	0.966349	−	0.257235i	$-0.0828116\pi$
$233$	587632.	+	587632.i	0.709113	+	0.709113i	−0.257235	+	0.966349i	$0.582812\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−57975.3	+	57975.3i	−0.0670459	+	0.0670459i
$238$		0			0
$239$	−2464.07			−0.00279035			−0.00139517	−	0.999999i	$-0.500444\pi$
$239$	−2464.07			−0.00279035			−0.00139517	+	0.999999i	$0.500444\pi$
$240$		0			0
$241$	−974878.			−1.08120			−0.540602	−	0.841278i	$-0.681804\pi$
$241$	−974878.			−1.08120			−0.540602	+	0.841278i	$0.681804\pi$
$242$		0			0
$243$	−672815.	+	672815.i	−0.730937	+	0.730937i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	357037.	+	357037.i	0.372367	+	0.372367i
$248$		0			0
$249$		−	1.36755e6i		−	1.39780i
$250$		0			0
$251$		−	789453.i		−	0.790937i	−0.918480	−	0.395468i	$-0.870582\pi$
$251$		−	789453.i		−	0.790937i	0.918480	−	0.395468i	$-0.129418\pi$
$252$		0			0
$253$	−345715.	−	345715.i	−0.339560	−	0.339560i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−16055.5	+	16055.5i	−0.0151633	+	0.0151633i	−0.714648	−	0.699485i	$-0.753413\pi$
$257$	−16055.5	+	16055.5i	−0.0151633	+	0.0151633i	0.699485	+	0.714648i	$0.253413\pi$
$258$		0			0
$259$	1.90366e6			1.76336
$260$		0			0
$261$	947750.			0.861177
$262$		0			0
$263$	−303160.	+	303160.i	−0.270260	+	0.270260i	−0.829205	−	0.558945i	$-0.811206\pi$
$263$	−303160.	+	303160.i	−0.270260	+	0.270260i	0.558945	+	0.829205i	$0.311206\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.85296e6	+	1.85296e6i	1.59069	+	1.59069i
$268$		0			0
$269$		−	1.81772e6i		−	1.53160i	−0.643077	−	0.765802i	$-0.722342\pi$
$269$		−	1.81772e6i		−	1.53160i	0.643077	−	0.765802i	$-0.277658\pi$
$270$		0			0
$271$		−	11145.2i		−	0.00921856i	−0.999989	−	0.00460928i	$-0.998533\pi$
$271$		−	11145.2i		−	0.00921856i	0.999989	−	0.00460928i	$-0.00146718\pi$
$272$		0			0
$273$	3.04717e6	+	3.04717e6i	2.47451	+	2.47451i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−966548.	+	966548.i	−0.756875	+	0.756875i	−0.975752	−	0.218877i	$-0.929761\pi$
$277$	−966548.	+	966548.i	−0.756875	+	0.756875i	0.218877	+	0.975752i	$0.429761\pi$
$278$		0			0
$279$	322249.			0.247846
$280$		0			0
$281$	−894758.			−0.675989			−0.337995	−	0.941148i	$-0.609749\pi$
$281$	−894758.			−0.675989			−0.337995	+	0.941148i	$0.609749\pi$
$282$		0			0
$283$	396992.	−	396992.i	0.294656	−	0.294656i	−0.544260	−	0.838917i	$-0.683190\pi$
$283$	396992.	−	396992.i	0.294656	−	0.294656i	0.838917	+	0.544260i	$0.183190\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	688609.	+	688609.i	0.493478	+	0.493478i
$288$		0			0
$289$		−	198468.i		−	0.139780i
$290$		0			0
$291$			2.79474e6i			1.93468i
$292$		0			0
$293$	−840875.	−	840875.i	−0.572219	−	0.572219i	0.360529	−	0.932748i	$-0.382596\pi$
$293$	−840875.	−	840875.i	−0.572219	−	0.572219i	−0.932748	+	0.360529i	$0.882596\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	571023.	−	571023.i	0.375632	−	0.375632i
$298$		0			0
$299$	−1.20797e6			−0.781411
$300$		0			0
$301$	−1.67809e6			−1.06758
$302$		0			0
$303$	2.24974e6	−	2.24974e6i	1.40775	−	1.40775i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	1.58244e6	+	1.58244e6i	0.958254	+	0.958254i	0.999163	−	0.0409086i	$-0.0130252\pi$
$307$	1.58244e6	+	1.58244e6i	0.958254	+	0.958254i	−0.0409086	+	0.999163i	$0.513025\pi$
$308$		0			0
$309$		−	2.28701e6i		−	1.36261i
$310$		0			0
$311$			2.98849e6i			1.75207i	0.482252	+	0.876033i	$0.339819\pi$
$311$			2.98849e6i			1.75207i	−0.482252	+	0.876033i	$0.660181\pi$
$312$		0			0
$313$	−835797.	−	835797.i	−0.482214	−	0.482214i	0.423624	−	0.905838i	$-0.360758\pi$
$313$	−835797.	−	835797.i	−0.482214	−	0.482214i	−0.905838	+	0.423624i	$0.860758\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−576912.	+	576912.i	−0.322449	+	0.322449i	−0.849706	−	0.527257i	$-0.823221\pi$
$317$	−576912.	+	576912.i	−0.322449	+	0.322449i	0.527257	+	0.849706i	$0.323221\pi$
$318$		0			0
$319$	−2.71443e6			−1.49349
$320$		0			0
$321$	−592342.			−0.320856
$322$		0			0
$323$	−456290.	+	456290.i	−0.243352	+	0.243352i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−962575.	−	962575.i	−0.497812	−	0.497812i
$328$		0			0
$329$			6.33648e6i			3.22744i
$330$		0			0
$331$		−	274475.i		−	0.137700i	−0.997627	−	0.0688499i	$-0.978067\pi$
$331$		−	274475.i		−	0.137700i	0.997627	−	0.0688499i	$-0.0219329\pi$
$332$		0			0
$333$	856729.	+	856729.i	0.423382	+	0.423382i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	898029.	−	898029.i	0.430740	−	0.430740i	−0.458140	−	0.888880i	$-0.651484\pi$
$337$	898029.	−	898029.i	0.430740	−	0.430740i	0.888880	+	0.458140i	$0.151484\pi$
$338$		0			0
$339$	3.00226e6			1.41889
$340$		0			0
$341$	−922946.			−0.429824
$342$		0			0
$343$	2.38098e6	−	2.38098e6i	1.09275	−	1.09275i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−210191.	−	210191.i	−0.0937109	−	0.0937109i	0.658697	−	0.752408i	$-0.271108\pi$
$347$	−210191.	−	210191.i	−0.0937109	−	0.0937109i	−0.752408	+	0.658697i	$0.771108\pi$
$348$		0			0
$349$			356245.i			0.156562i	0.996931	+	0.0782808i	$0.0249431\pi$
$349$			356245.i			0.156562i	−0.996931	+	0.0782808i	$0.975057\pi$
$350$		0			0
$351$		−	1.99523e6i		−	0.864421i
$352$		0			0
$353$	−2.59182e6	−	2.59182e6i	−1.10705	−	1.10705i	−0.993536	−	0.113518i	$-0.963788\pi$
$353$	−2.59182e6	−	2.59182e6i	−1.10705	−	1.10705i	−0.113518	−	0.993536i	$-0.536212\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−3.89425e6	+	3.89425e6i	−1.61716	+	1.61716i
$358$		0			0
$359$	−4.25369e6			−1.74193			−0.870963	−	0.491349i	$-0.836504\pi$
$359$	−4.25369e6			−1.74193			−0.870963	+	0.491349i	$0.836504\pi$
$360$		0			0
$361$	−2.21880e6			−0.896085
$362$		0			0
$363$	17522.3	−	17522.3i	0.00697949	−	0.00697949i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.93280e6	+	2.93280e6i	1.13663	+	1.13663i	0.989051	+	0.147574i	$0.0471465\pi$
$367$	2.93280e6	+	2.93280e6i	1.13663	+	1.13663i	0.147574	+	0.989051i	$0.452853\pi$
$368$		0			0
$369$			619806.i			0.236968i
$370$		0			0
$371$			3.17892e6i			1.19907i
$372$		0			0
$373$	198835.	+	198835.i	0.0739983	+	0.0739983i	0.743137	−	0.669139i	$-0.233337\pi$
$373$	198835.	+	198835.i	0.0739983	+	0.0739983i	−0.669139	+	0.743137i	$0.733337\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.74229e6	+	4.74229e6i	−1.71844	+	1.71844i
$378$		0			0
$379$	−1.45216e6			−0.519299			−0.259649	−	0.965703i	$-0.583607\pi$
$379$	−1.45216e6			−0.519299			−0.259649	+	0.965703i	$0.583607\pi$
$380$		0			0
$381$	4.52978e6			1.59869
$382$		0			0
$383$	−472661.	+	472661.i	−0.164647	+	0.164647i	−0.784622	−	0.619975i	$-0.787143\pi$
$383$	−472661.	+	472661.i	−0.164647	+	0.164647i	0.619975	+	0.784622i	$0.287143\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−755212.	−	755212.i	−0.256325	−	0.256325i
$388$		0			0
$389$			1.21306e6i			0.406450i	0.979132	+	0.203225i	$0.0651423\pi$
$389$			1.21306e6i			0.406450i	−0.979132	+	0.203225i	$0.934858\pi$
$390$		0			0
$391$		−	1.54378e6i		−	0.510673i
$392$		0			0
$393$	5.14531e6	+	5.14531e6i	1.68047	+	1.68047i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	378209.	−	378209.i	0.120436	−	0.120436i	−0.644320	−	0.764756i	$-0.722860\pi$
$397$	378209.	−	378209.i	0.120436	−	0.120436i	0.764756	+	0.644320i	$0.222860\pi$
$398$		0			0
$399$	2.19598e6			0.690552
$400$		0			0
$401$	3.20600e6			0.995640			0.497820	−	0.867280i	$-0.334134\pi$
$401$	3.20600e6			0.995640			0.497820	+	0.867280i	$0.334134\pi$
$402$		0			0
$403$	−1.61245e6	+	1.61245e6i	−0.494565	+	0.494565i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.45374e6	−	2.45374e6i	−0.734246	−	0.734246i
$408$		0			0
$409$			1.14226e6i			0.337643i	0.985647	+	0.168822i	$0.0539962\pi$
$409$			1.14226e6i			0.337643i	−0.985647	+	0.168822i	$0.946004\pi$
$410$		0			0
$411$			7.29764e6i			2.13097i
$412$		0			0
$413$	−5.08048e6	−	5.08048e6i	−1.46565	−	1.46565i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.54251e6	−	5.54251e6i	1.56087	−	1.56087i
$418$		0			0
$419$	−1.11746e6			−0.310955			−0.155477	−	0.987839i	$-0.549692\pi$
$419$	−1.11746e6			−0.310955			−0.155477	+	0.987839i	$0.549692\pi$
$420$		0			0
$421$	743945.			0.204567			0.102284	−	0.994755i	$-0.467385\pi$
$421$	743945.			0.204567			0.102284	+	0.994755i	$0.467385\pi$
$422$		0			0
$423$	−2.85169e6	+	2.85169e6i	−0.774909	+	0.774909i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−6.63902e6	−	6.63902e6i	−1.76212	−	1.76212i
$428$		0			0
$429$		−	7.85532e6i		−	2.06073i
$430$		0			0
$431$		−	4.66414e6i		−	1.20942i	−0.796444	−	0.604712i	$-0.793288\pi$
$431$		−	4.66414e6i		−	1.20942i	0.796444	−	0.604712i	$-0.206712\pi$
$432$		0			0
$433$	4.76265e6	+	4.76265e6i	1.22076	+	1.22076i	0.967363	+	0.253393i	$0.0815467\pi$
$433$	4.76265e6	+	4.76265e6i	1.22076	+	1.22076i	0.253393	+	0.967363i	$0.418453\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−435271.	+	435271.i	−0.109033	+	0.109033i
$438$		0			0
$439$	954436.			0.236366			0.118183	−	0.992992i	$-0.462293\pi$
$439$	954436.			0.236366			0.118183	+	0.992992i	$0.462293\pi$
$440$		0			0
$441$	4.50730e6			1.10362
$442$		0			0
$443$	404237.	−	404237.i	0.0978648	−	0.0978648i	−0.656479	−	0.754344i	$-0.727955\pi$
$443$	404237.	−	404237.i	0.0978648	−	0.0978648i	0.754344	+	0.656479i	$0.227955\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	4.15303e6	+	4.15303e6i	0.983098	+	0.983098i
$448$		0			0
$449$			3.25344e6i			0.761601i	0.924657	+	0.380801i	$0.124352\pi$
$449$			3.25344e6i			0.761601i	−0.924657	+	0.380801i	$0.875648\pi$
$450$		0			0
$451$		−	1.77517e6i		−	0.410959i
$452$		0			0
$453$	−4.10970e6	−	4.10970e6i	−0.940945	−	0.940945i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	5.05035e6	−	5.05035e6i	1.13118	−	1.13118i	0.141195	−	0.989982i	$-0.454905\pi$
$457$	5.05035e6	−	5.05035e6i	1.13118	−	1.13118i	0.989982	−	0.141195i	$-0.0450946\pi$
$458$		0			0
$459$	2.54989e6			0.564923
$460$		0			0
$461$	−2.04504e6			−0.448177			−0.224089	−	0.974569i	$-0.571940\pi$
$461$	−2.04504e6			−0.448177			−0.224089	+	0.974569i	$0.571940\pi$
$462$		0			0
$463$	3.52958e6	−	3.52958e6i	0.765193	−	0.765193i	−0.212063	−	0.977256i	$-0.568018\pi$
$463$	3.52958e6	−	3.52958e6i	0.765193	−	0.765193i	0.977256	+	0.212063i	$0.0680181\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.34544e6	+	2.34544e6i	0.497659	+	0.497659i	0.910709	−	0.413049i	$-0.135536\pi$
$467$	2.34544e6	+	2.34544e6i	0.497659	+	0.497659i	−0.413049	+	0.910709i	$0.635536\pi$
$468$		0			0
$469$			523934.i			0.109988i
$470$		0			0
$471$		−	9.12590e6i		−	1.89550i
$472$		0			0
$473$	2.16299e6	+	2.16299e6i	0.444530	+	0.444530i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.43065e6	+	1.43065e6i	−0.287897	+	0.287897i
$478$		0			0
$479$	5.69111e6			1.13333			0.566667	−	0.823947i	$-0.308233\pi$
$479$	5.69111e6			1.13333			0.566667	+	0.823947i	$0.308233\pi$
$480$		0			0
$481$	−8.57368e6			−1.68968
$482$		0			0
$483$	−3.71487e6	+	3.71487e6i	−0.724562	+	0.724562i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−1.13038e6	−	1.13038e6i	−0.215974	−	0.215974i	0.590825	−	0.806799i	$-0.298802\pi$
$487$	−1.13038e6	−	1.13038e6i	−0.215974	−	0.215974i	−0.806799	+	0.590825i	$0.798802\pi$
$488$		0			0
$489$		−	71958.1i		−	0.0136084i
$490$		0			0
$491$		−	9.41870e6i		−	1.76314i	−0.472052	−	0.881571i	$-0.656487\pi$
$491$		−	9.41870e6i		−	1.76314i	0.472052	−	0.881571i	$-0.343513\pi$
$492$		0			0
$493$	−6.06059e6	−	6.06059e6i	−1.12305	−	1.12305i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.94965e6	−	3.94965e6i	0.717245	−	0.717245i
$498$		0			0
$499$	4.82057e6			0.866656			0.433328	−	0.901236i	$-0.357339\pi$
$499$	4.82057e6			0.866656			0.433328	+	0.901236i	$0.357339\pi$
$500$		0			0
$501$	−743364.			−0.132315
$502$		0			0
$503$	−1.53202e6	+	1.53202e6i	−0.269989	+	0.269989i	−0.829096	−	0.559107i	$-0.811144\pi$
$503$	−1.53202e6	+	1.53202e6i	−0.269989	+	0.269989i	0.559107	+	0.829096i	$0.311144\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−8.58121e6	−	8.58121e6i	−1.48262	−	1.48262i
$508$		0			0
$509$		−	7.33644e6i		−	1.25514i	−0.778562	−	0.627568i	$-0.784050\pi$
$509$		−	7.33644e6i		−	1.25514i	0.778562	−	0.627568i	$-0.215950\pi$
$510$		0			0
$511$		−	7.92253e6i		−	1.34218i
$512$		0			0
$513$	−718946.	−	718946.i	−0.120615	−	0.120615i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	8.16744e6	−	8.16744e6i	1.34388	−	1.34388i
$518$		0			0
$519$	−151736.			−0.0247270
$520$		0			0
$521$	−3.92126e6			−0.632895			−0.316447	−	0.948610i	$-0.602490\pi$
$521$	−3.92126e6			−0.632895			−0.316447	+	0.948610i	$0.602490\pi$
$522$		0			0
$523$	−6.95979e6	+	6.95979e6i	−1.11261	+	1.11261i	−0.119810	+	0.992797i	$0.538229\pi$
$523$	−6.95979e6	+	6.95979e6i	−1.11261	+	1.11261i	−0.992797	+	0.119810i	$0.961771\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.06069e6	−	2.06069e6i	−0.323212	−	0.323212i
$528$		0			0
$529$			4.96368e6i			0.771195i
$530$		0			0
$531$		−	4.57286e6i		−	0.703804i
$532$		0			0
$533$	−3.10134e6	−	3.10134e6i	−0.472859	−	0.472859i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	4.07062e6	−	4.07062e6i	0.609150	−	0.609150i
$538$		0			0
$539$	−1.29092e7			−1.91394
$540$		0			0
$541$	5.43048e6			0.797710			0.398855	−	0.917014i	$-0.369408\pi$
$541$	5.43048e6			0.797710			0.398855	+	0.917014i	$0.369408\pi$
$542$		0			0
$543$	−3.76404e6	+	3.76404e6i	−0.547841	+	0.547841i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	3.23624e6	+	3.23624e6i	0.462459	+	0.462459i	0.899461	−	0.437002i	$-0.143960\pi$
$547$	3.23624e6	+	3.23624e6i	0.462459	+	0.462459i	−0.437002	+	0.899461i	$0.643960\pi$
$548$		0			0
$549$		−	5.97569e6i		−	0.846168i
$550$		0			0
$551$			3.41759e6i			0.479558i
$552$		0			0
$553$	−654174.	−	654174.i	−0.0909663	−	0.0909663i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	454679.	−	454679.i	0.0620965	−	0.0620965i	−0.675377	−	0.737473i	$-0.736019\pi$
$557$	454679.	−	454679.i	0.0620965	−	0.0620965i	0.737473	+	0.675377i	$0.236019\pi$
$558$		0			0
$559$	7.55776e6			1.02297
$560$		0			0
$561$	1.00390e7			1.34674
$562$		0			0
$563$	2.50898e6	−	2.50898e6i	0.333600	−	0.333600i	−0.520352	−	0.853952i	$-0.674199\pi$
$563$	2.50898e6	−	2.50898e6i	0.333600	−	0.333600i	0.853952	+	0.520352i	$0.174199\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.14781e7	−	1.14781e7i	−1.49938	−	1.49938i
$568$		0			0
$569$		−	4.72863e6i		−	0.612286i	−0.951985	−	0.306143i	$-0.900961\pi$
$569$		−	4.72863e6i		−	0.612286i	0.951985	−	0.306143i	$-0.0990386\pi$
$570$		0			0
$571$			7.24213e6i			0.929557i	0.885427	+	0.464779i	$0.153866\pi$
$571$			7.24213e6i			0.929557i	−0.885427	+	0.464779i	$0.846134\pi$
$572$		0			0
$573$	7.57182e6	+	7.57182e6i	0.963416	+	0.963416i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−6.55049e6	+	6.55049e6i	−0.819095	+	0.819095i	−0.985977	−	0.166882i	$-0.946630\pi$
$577$	−6.55049e6	+	6.55049e6i	−0.819095	+	0.819095i	0.166882	+	0.985977i	$0.446630\pi$
$578$		0			0
$579$	9.34306e6			1.15822
$580$		0			0
$581$	1.54310e7			1.89650
$582$		0			0
$583$	4.09749e6	−	4.09749e6i	0.499282	−	0.499282i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.89090e6	+	3.89090e6i	0.466073	+	0.466073i	0.900640	−	0.434566i	$-0.143098\pi$
$587$	3.89090e6	+	3.89090e6i	0.466073	+	0.466073i	−0.434566	+	0.900640i	$0.643098\pi$
$588$		0			0
$589$			1.16203e6i			0.138016i
$590$		0			0
$591$			7.43490e6i			0.875602i
$592$		0			0
$593$	4.04310e6	+	4.04310e6i	0.472148	+	0.472148i	0.902609	−	0.430461i	$-0.141649\pi$
$593$	4.04310e6	+	4.04310e6i	0.472148	+	0.472148i	−0.430461	+	0.902609i	$0.641649\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.84825e6	+	1.84825e6i	−0.212239	+	0.212239i
$598$		0			0
$599$	−1.01800e7			−1.15927			−0.579633	−	0.814878i	$-0.696804\pi$
$599$	−1.01800e7			−1.15927			−0.579633	+	0.814878i	$0.696804\pi$
$600$		0			0
$601$	7.92925e6			0.895459			0.447729	−	0.894169i	$-0.352233\pi$
$601$	7.92925e6			0.895459			0.447729	+	0.894169i	$0.352233\pi$
$602$		0			0
$603$	−235793.	+	235793.i	−0.0264081	+	0.0264081i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−6.11863e6	−	6.11863e6i	−0.674035	−	0.674035i	0.284609	−	0.958644i	$-0.408136\pi$
$607$	−6.11863e6	−	6.11863e6i	−0.674035	−	0.674035i	−0.958644	+	0.284609i	$0.908136\pi$
$608$		0			0
$609$			2.91678e7i			3.18684i
$610$		0			0
$611$		−	2.85381e7i		−	3.09259i
$612$		0			0
$613$	−6.85884e6	−	6.85884e6i	−0.737224	−	0.737224i	0.234816	−	0.972040i	$-0.424551\pi$
$613$	−6.85884e6	−	6.85884e6i	−0.737224	−	0.737224i	−0.972040	+	0.234816i	$0.924551\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.07004e6	−	6.07004e6i	0.641917	−	0.641917i	−0.309109	−	0.951026i	$-0.600031\pi$
$617$	6.07004e6	−	6.07004e6i	0.641917	−	0.641917i	0.951026	+	0.309109i	$0.100031\pi$
$618$		0			0
$619$	8.19333e6			0.859476			0.429738	−	0.902954i	$-0.358606\pi$
$619$	8.19333e6			0.859476			0.429738	+	0.902954i	$0.358606\pi$
$620$		0			0
$621$	2.43243e6			0.253111
$622$		0			0
$623$	−2.09081e7	+	2.09081e7i	−2.15822	+	2.15822i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−2.83052e6	−	2.83052e6i	−0.287540	−	0.287540i
$628$		0			0
$629$		−	1.09571e7i		−	1.10425i
$630$		0			0
$631$			9.10825e6i			0.910671i	0.890320	+	0.455336i	$0.150481\pi$
$631$			9.10825e6i			0.910671i	−0.890320	+	0.455336i	$0.849519\pi$
$632$		0			0
$633$	65807.5	+	65807.5i	0.00652779	+	0.00652779i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−2.25533e7	+	2.25533e7i	−2.20223	+	2.20223i
$638$		0			0
$639$	3.55502e6			0.344421
$640$		0			0
$641$	−9.28244e6			−0.892313			−0.446156	−	0.894955i	$-0.647207\pi$
$641$	−9.28244e6			−0.892313			−0.446156	+	0.894955i	$0.647207\pi$
$642$		0			0
$643$	9.79219e6	−	9.79219e6i	0.934012	−	0.934012i	−0.0639417	−	0.997954i	$-0.520367\pi$
$643$	9.79219e6	−	9.79219e6i	0.934012	−	0.934012i	0.997954	+	0.0639417i	$0.0203672\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−958264.	−	958264.i	−0.0899962	−	0.0899962i	0.660675	−	0.750672i	$-0.270270\pi$
$647$	−958264.	−	958264.i	−0.0899962	−	0.0899962i	−0.750672	+	0.660675i	$0.770270\pi$
$648$		0			0
$649$			1.30970e7i			1.22057i
$650$		0			0
$651$			9.91749e6i			0.917169i
$652$		0			0
$653$	−8.27395e6	−	8.27395e6i	−0.759329	−	0.759329i	0.216871	−	0.976200i	$-0.430415\pi$
$653$	−8.27395e6	−	8.27395e6i	−0.759329	−	0.759329i	−0.976200	+	0.216871i	$0.930415\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	3.56547e6	−	3.56547e6i	0.322258	−	0.322258i
$658$		0			0
$659$	−9.04814e6			−0.811607			−0.405804	−	0.913960i	$-0.633008\pi$
$659$	−9.04814e6			−0.811607			−0.405804	+	0.913960i	$0.633008\pi$
$660$		0			0
$661$	−6.33192e6			−0.563679			−0.281839	−	0.959462i	$-0.590945\pi$
$661$	−6.33192e6			−0.563679			−0.281839	+	0.959462i	$0.590945\pi$
$662$		0			0
$663$	1.75389e7	−	1.75389e7i	1.54959	−	1.54959i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.78142e6	−	5.78142e6i	−0.503176	−	0.503176i
$668$		0			0
$669$			1.29984e7i			1.12286i
$670$		0			0
$671$			1.71148e7i			1.46746i
$672$		0			0
$673$	7.04129e6	+	7.04129e6i	0.599259	+	0.599259i	0.940115	−	0.340857i	$-0.110717\pi$
$673$	7.04129e6	+	7.04129e6i	0.599259	+	0.599259i	−0.340857	+	0.940115i	$0.610717\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4.36946e6	+	4.36946e6i	−0.366400	+	0.366400i	−0.866163	−	0.499762i	$-0.833421\pi$
$677$	−4.36946e6	+	4.36946e6i	−0.366400	+	0.366400i	0.499762	+	0.866163i	$0.333421\pi$
$678$		0			0
$679$	−3.15349e7			−2.62492
$680$		0			0
$681$	−1.66338e7			−1.37443
$682$		0			0
$683$	3.85257e6	−	3.85257e6i	0.316008	−	0.316008i	−0.531223	−	0.847232i	$-0.678268\pi$
$683$	3.85257e6	−	3.85257e6i	0.316008	−	0.316008i	0.847232	+	0.531223i	$0.178268\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	4.70078e6	+	4.70078e6i	0.379996	+	0.379996i
$688$		0			0
$689$		−	1.43172e7i		−	1.14897i
$690$		0			0
$691$		−	1.19137e7i		−	0.949188i	−0.880205	−	0.474594i	$-0.842595\pi$
$691$		−	1.19137e7i		−	0.949188i	0.880205	−	0.474594i	$-0.157405\pi$
$692$		0			0
$693$	−8.85707e6	−	8.85707e6i	−0.700579	−	0.700579i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	3.96349e6	−	3.96349e6i	0.309026	−	0.309026i
$698$		0			0
$699$	−1.62779e7			−1.26010
$700$		0			0
$701$	−1.21367e7			−0.932838			−0.466419	−	0.884564i	$-0.654456\pi$
$701$	−1.21367e7			−0.932838			−0.466419	+	0.884564i	$0.654456\pi$
$702$		0			0
$703$	−3.08937e6	+	3.08937e6i	−0.235766	+	0.235766i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.53853e7	+	2.53853e7i	1.91000	+	1.91000i
$708$		0			0
$709$		−	2.58003e6i		−	0.192757i	−0.995345	−	0.0963783i	$-0.969274\pi$
$709$		−	2.58003e6i		−	0.192757i	0.995345	−	0.0963783i	$-0.0307258\pi$
$710$		0			0
$711$		−	588812.i		−	0.0436820i
$712$		0			0
$713$	−1.96577e6	−	1.96577e6i	−0.144814	−	0.144814i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	34128.4	−	34128.4i	0.00247924	−	0.00247924i
$718$		0			0
$719$	1.94000e7			1.39952			0.699760	−	0.714378i	$-0.253290\pi$
$719$	1.94000e7			1.39952			0.699760	+	0.714378i	$0.253290\pi$
$720$		0			0
$721$	2.58058e7			1.84875
$722$		0			0
$723$	1.35025e7	−	1.35025e7i	0.960655	−	0.960655i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−1.94019e6	−	1.94019e6i	−0.136147	−	0.136147i	0.635749	−	0.771896i	$-0.280691\pi$
$727$	−1.94019e6	−	1.94019e6i	−0.136147	−	0.136147i	−0.771896	+	0.635749i	$0.780691\pi$
$728$		0			0
$729$		−	790696.i		−	0.0551050i
$730$		0			0
$731$			9.65874e6i			0.668540i
$732$		0			0
$733$	−1.15105e6	−	1.15105e6i	−0.0791286	−	0.0791286i	0.666435	−	0.745563i	$-0.267819\pi$
$733$	−1.15105e6	−	1.15105e6i	−0.0791286	−	0.0791286i	−0.745563	+	0.666435i	$0.767819\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	675328.	−	675328.i	0.0457979	−	0.0457979i
$738$		0			0
$739$	2.25458e7			1.51864			0.759319	−	0.650718i	$-0.225532\pi$
$739$	2.25458e7			1.51864			0.759319	+	0.650718i	$0.225532\pi$
$740$		0			0
$741$	−9.89023e6			−0.661699
$742$		0			0
$743$	−2.04763e7	+	2.04763e7i	−1.36075	+	1.36075i	−0.487798	+	0.872957i	$0.662200\pi$
$743$	−2.04763e7	+	2.04763e7i	−1.36075	+	1.36075i	−0.872957	+	0.487798i	$0.837800\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	6.94460e6	+	6.94460e6i	0.455350	+	0.455350i
$748$		0			0
$749$		−	6.68379e6i		−	0.435329i
$750$		0			0
$751$			1.51324e7i			0.979057i	0.871987	+	0.489529i	$0.162831\pi$
$751$			1.51324e7i			0.979057i	−0.871987	+	0.489529i	$0.837169\pi$
$752$		0			0
$753$	1.09343e7	+	1.09343e7i	0.702751	+	0.702751i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.47400e7	−	1.47400e7i	0.934884	−	0.934884i	−0.0631214	−	0.998006i	$-0.520106\pi$
$757$	1.47400e7	−	1.47400e7i	0.934884	−	0.934884i	0.998006	+	0.0631214i	$0.0201055\pi$
$758$		0			0
$759$	9.57659e6			0.603402
$760$		0			0
$761$	−7.88762e6			−0.493724			−0.246862	−	0.969051i	$-0.579399\pi$
$761$	−7.88762e6			−0.493724			−0.246862	+	0.969051i	$0.579399\pi$
$762$		0			0
$763$	1.08614e7	−	1.08614e7i	0.675419	−	0.675419i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.28814e7	+	2.28814e7i	1.40441	+	1.40441i
$768$		0			0
$769$		−	1.80060e7i		−	1.09800i	−0.835824	−	0.548998i	$-0.815009\pi$
$769$		−	1.80060e7i		−	1.09800i	0.835824	−	0.548998i	$-0.184991\pi$
$770$		0			0
$771$		−	444752.i		−	0.0269452i
$772$		0			0
$773$	1.99945e7	+	1.99945e7i	1.20354	+	1.20354i	0.973082	+	0.230461i	$0.0740233\pi$
$773$	1.99945e7	+	1.99945e7i	1.20354	+	1.20354i	0.230461	+	0.973082i	$0.425977\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−2.63665e7	+	2.63665e7i	−1.56675	+	1.56675i
$778$		0			0
$779$	−2.23503e6			−0.131959
$780$		0			0
$781$	−1.01818e7			−0.597308
$782$		0			0
$783$	9.54927e6	−	9.54927e6i	0.556629	−	0.556629i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−971153.	−	971153.i	−0.0558921	−	0.0558921i	0.678608	−	0.734500i	$-0.262583\pi$
$787$	−971153.	−	971153.i	−0.0558921	−	0.0558921i	−0.734500	+	0.678608i	$0.762583\pi$
$788$		0			0
$789$		−	8.39778e6i		−	0.480255i
$790$		0			0
$791$			3.38765e7i			1.92512i
$792$		0			0
$793$	2.99007e7	+	2.99007e7i	1.68849	+	1.68849i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.34755e6	−	1.34755e6i	0.0751448	−	0.0751448i	−0.668535	−	0.743680i	$-0.733079\pi$
$797$	1.34755e6	−	1.34755e6i	0.0751448	−	0.0751448i	0.743680	+	0.668535i	$0.233079\pi$
$798$		0			0
$799$	3.64715e7			2.02109
$800$		0			0
$801$	−1.88191e7			−1.03638
$802$		0			0
$803$	−1.02118e7	+	1.02118e7i	−0.558873	+	0.558873i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.51762e7	+	2.51762e7i	1.36084	+	1.36084i
$808$		0			0
$809$		−	3.09303e7i		−	1.66155i	−0.556609	−	0.830775i	$-0.687898\pi$
$809$		−	3.09303e7i		−	1.66155i	0.556609	−	0.830775i	$-0.312102\pi$
$810$		0			0
$811$			2.90946e7i			1.55332i	0.629922	+	0.776658i	$0.283087\pi$
$811$			2.90946e7i			1.55332i	−0.629922	+	0.776658i	$0.716913\pi$
$812$		0			0
$813$	154365.	+	154365.i	0.00819073	+	0.00819073i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	2.72330e6	−	2.72330e6i	0.142738	−	0.142738i
$818$		0			0
$819$	−3.09478e7			−1.61220
$820$		0			0
$821$	4.03596e6			0.208973			0.104486	−	0.994526i	$-0.466680\pi$
$821$	4.03596e6			0.208973			0.104486	+	0.994526i	$0.466680\pi$
$822$		0			0
$823$	1.66143e7	−	1.66143e7i	0.855033	−	0.855033i	−0.135715	−	0.990748i	$-0.543333\pi$
$823$	1.66143e7	−	1.66143e7i	0.855033	−	0.855033i	0.990748	+	0.135715i	$0.0433332\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−7.24914e6	−	7.24914e6i	−0.368572	−	0.368572i	0.498384	−	0.866956i	$-0.333927\pi$
$827$	−7.24914e6	−	7.24914e6i	−0.368572	−	0.368572i	−0.866956	+	0.498384i	$0.833927\pi$
$828$		0			0
$829$		−	2.34252e7i		−	1.18385i	−0.805993	−	0.591926i	$-0.798368\pi$
$829$		−	2.34252e7i		−	1.18385i	0.805993	−	0.591926i	$-0.201632\pi$
$830$		0			0
$831$		−	2.67742e7i		−	1.34497i
$832$		0			0
$833$	−2.88229e7	−	2.88229e7i	−1.43921	−	1.43921i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	3.24690e6	−	3.24690e6i	0.160197	−	0.160197i
$838$		0			0
$839$	−1.19055e7			−0.583905			−0.291953	−	0.956433i	$-0.594305\pi$
$839$	−1.19055e7			−0.583905			−0.291953	+	0.956433i	$0.594305\pi$
$840$		0			0
$841$	−2.48825e7			−1.21312
$842$		0			0
$843$	1.23928e7	−	1.23928e7i	0.600620	−	0.600620i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	197715.	+	197715.i	0.00946960	+	0.00946960i
$848$		0			0
$849$			1.09970e7i			0.523607i
$850$		0			0
$851$		−	1.04524e7i		−	0.494755i
$852$		0			0
$853$	2.29562e7	+	2.29562e7i	1.08026	+	1.08026i	0.996485	+	0.0837713i	$0.0266965\pi$
$853$	2.29562e7	+	2.29562e7i	1.08026	+	1.08026i	0.0837713	+	0.996485i	$0.473303\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.79377e6	−	4.79377e6i	0.222959	−	0.222959i	−0.586784	−	0.809743i	$-0.699606\pi$
$857$	4.79377e6	−	4.79377e6i	0.222959	−	0.222959i	0.809743	+	0.586784i	$0.199606\pi$
$858$		0			0
$859$	−3.01469e7			−1.39399			−0.696994	−	0.717077i	$-0.745480\pi$
$859$	−3.01469e7			−1.39399			−0.696994	+	0.717077i	$0.745480\pi$
$860$		0			0
$861$	−1.90750e7			−0.876915
$862$		0			0
$863$	−1.14791e7	+	1.14791e7i	−0.524664	+	0.524664i	−0.918976	−	0.394312i	$-0.870983\pi$
$863$	−1.14791e7	+	1.14791e7i	−0.524664	+	0.524664i	0.394312	+	0.918976i	$0.370983\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	2.74886e6	+	2.74886e6i	0.124195	+	0.124195i
$868$		0			0
$869$			1.68640e6i			0.0757551i
$870$		0			0
$871$		−	2.35968e6i		−	0.105392i
$872$		0			0
$873$	−1.41920e7	−	1.41920e7i	−0.630244	−	0.630244i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	4.50478e6	−	4.50478e6i	0.197776	−	0.197776i	−0.601270	−	0.799046i	$-0.705338\pi$
$877$	4.50478e6	−	4.50478e6i	0.197776	−	0.197776i	0.799046	+	0.601270i	$0.205338\pi$
$878$		0			0
$879$	2.32929e7			1.01684
$880$		0			0
$881$	1.22798e7			0.533032			0.266516	−	0.963831i	$-0.414128\pi$
$881$	1.22798e7			0.533032			0.266516	+	0.963831i	$0.414128\pi$
$882$		0			0
$883$	5.02936e6	−	5.02936e6i	0.217076	−	0.217076i	−0.590189	−	0.807265i	$-0.700947\pi$
$883$	5.02936e6	−	5.02936e6i	0.217076	−	0.217076i	0.807265	+	0.590189i	$0.200947\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2864.53	+	2864.53i	0.000122249	+	0.000122249i	0.707168	−	0.707046i	$-0.249972\pi$
$887$	2864.53	+	2864.53i	0.000122249	+	0.000122249i	−0.707046	+	0.707168i	$0.749972\pi$
$888$		0			0
$889$			5.11125e7i			2.16907i
$890$		0			0
$891$			2.95894e7i			1.24865i
$892$		0			0
$893$	−1.02832e7	−	1.02832e7i	−0.431519	−	0.431519i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.67309e7	−	1.67309e7i	0.694288	−	0.694288i
$898$		0			0
$899$	−1.54345e7			−0.636933
$900$		0			0
$901$	1.82972e7			0.750884
$902$		0			0
$903$	2.32423e7	−	2.32423e7i	0.948548	−	0.948548i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	3.04921e7	+	3.04921e7i	1.23075	+	1.23075i	0.963677	+	0.267070i	$0.0860554\pi$
$907$	3.04921e7	+	3.04921e7i	1.23075	+	1.23075i	0.267070	+	0.963677i	$0.413945\pi$
$908$		0			0
$909$			2.28490e7i			0.917185i
$910$		0			0
$911$		−	4.45936e6i		−	0.178023i	−0.996031	−	0.0890117i	$-0.971629\pi$
$911$		−	4.45936e6i		−	0.178023i	0.996031	−	0.0890117i	$-0.0283708\pi$
$912$		0			0
$913$	−1.98899e7	−	1.98899e7i	−0.789686	−	0.789686i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.80580e7	+	5.80580e7i	−2.28002	+	2.28002i
$918$		0			0
$919$	3.73590e6			0.145917			0.0729586	−	0.997335i	$-0.476756\pi$
$919$	3.73590e6			0.145917			0.0729586	+	0.997335i	$0.476756\pi$
$920$		0			0
$921$	−4.38349e7			−1.70283
$922$		0			0
$923$	−1.77884e7	+	1.77884e7i	−0.687276	+	0.687276i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1.16137e7	+	1.16137e7i	0.443886	+	0.443886i
$928$		0			0
$929$		−	2.00118e6i		−	0.0760758i	−0.999276	−	0.0380379i	$-0.987889\pi$
$929$		−	2.00118e6i		−	0.0760758i	0.999276	−	0.0380379i	$-0.0121108\pi$
$930$		0			0
$931$			1.62534e7i			0.614566i
$932$		0			0
$933$	−4.13918e7	−	4.13918e7i	−1.55672	−	1.55672i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−2.97193e7	+	2.97193e7i	−1.10583	+	1.10583i	−0.112143	+	0.993692i	$0.535771\pi$
$937$	−2.97193e7	+	2.97193e7i	−1.10583	+	1.10583i	−0.993692	+	0.112143i	$0.964229\pi$
$938$		0			0
$939$	2.31523e7			0.856899
$940$		0			0
$941$	3.29493e7			1.21303			0.606515	−	0.795072i	$-0.292567\pi$
$941$	3.29493e7			1.21303			0.606515	+	0.795072i	$0.292567\pi$
$942$		0			0
$943$	3.78091e6	−	3.78091e6i	0.138458	−	0.138458i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.56232e6	−	7.56232e6i	−0.274019	−	0.274019i	0.556697	−	0.830716i	$-0.312068\pi$
$947$	−7.56232e6	−	7.56232e6i	−0.274019	−	0.274019i	−0.830716	+	0.556697i	$0.812068\pi$
$948$		0			0
$949$			3.56813e7i			1.28610i
$950$		0			0
$951$		−	1.59809e7i		−	0.572995i
$952$		0			0
$953$	2.53366e7	+	2.53366e7i	0.903682	+	0.903682i	0.995752	−	0.0920706i	$-0.0293486\pi$
$953$	2.53366e7	+	2.53366e7i	0.903682	+	0.903682i	−0.0920706	+	0.995752i	$0.529349\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	3.75960e7	−	3.75960e7i	1.32697	−	1.32697i
$958$		0			0
$959$	−8.23441e7			−2.89125
$960$		0			0
$961$	2.33812e7			0.816691
$962$		0			0
$963$	3.00799e6	−	3.00799e6i	0.104523	−	0.104523i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−3.73387e7	−	3.73387e7i	−1.28408	−	1.28408i	−0.938324	−	0.345758i	$-0.887622\pi$
$967$	−3.73387e7	−	3.73387e7i	−1.28408	−	1.28408i	−0.345758	−	0.938324i	$-0.612378\pi$
$968$		0			0
$969$		−	1.26396e7i		−	0.432439i
$970$		0			0
$971$		−	1.64926e7i		−	0.561359i	−0.959802	−	0.280680i	$-0.909440\pi$
$971$		−	1.64926e7i		−	0.561359i	0.959802	−	0.280680i	$-0.0905598\pi$
$972$		0			0
$973$	6.25398e7	+	6.25398e7i	2.11775	+	2.11775i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.46145e7	+	2.46145e7i	−0.825000	+	0.825000i	−0.986820	−	0.161820i	$-0.948264\pi$
$977$	−2.46145e7	+	2.46145e7i	−0.825000	+	0.825000i	0.161820	+	0.986820i	$0.448264\pi$
$978$		0			0
$979$	5.38993e7			1.79732
$980$		0			0
$981$	9.77615e6			0.324336
$982$		0			0
$983$	607027.	−	607027.i	0.0200366	−	0.0200366i	−0.697017	−	0.717054i	$-0.745490\pi$
$983$	607027.	−	607027.i	0.0200366	−	0.0200366i	0.717054	+	0.697017i	$0.245490\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−8.77629e7	−	8.77629e7i	−2.86760	−	2.86760i
$988$		0			0
$989$			9.21383e6i			0.299536i
$990$		0			0
$991$		−	1.31220e7i		−	0.424439i	−0.977222	−	0.212220i	$-0.931931\pi$
$991$		−	1.31220e7i		−	0.424439i	0.977222	−	0.212220i	$-0.0680692\pi$
$992$		0			0
$993$	3.80160e6	+	3.80160e6i	0.122347	+	0.122347i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	2.79612e7	−	2.79612e7i	0.890878	−	0.890878i	−0.103728	−	0.994606i	$-0.533077\pi$
$997$	2.79612e7	−	2.79612e7i	0.890878	−	0.890878i	0.994606	+	0.103728i	$0.0330770\pi$
$998$		0			0
$999$	1.72643e7			0.547314

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.6.n.h.143.1	✓	24
4.3	odd	2	inner	400.6.n.h.143.12	yes	24
5.2	odd	4	inner	400.6.n.h.207.12	yes	24
5.3	odd	4	inner	400.6.n.h.207.2	yes	24
5.4	even	2	inner	400.6.n.h.143.11	yes	24
20.3	even	4	inner	400.6.n.h.207.11	yes	24
20.7	even	4	inner	400.6.n.h.207.1	yes	24
20.19	odd	2	inner	400.6.n.h.143.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.6.n.h.143.1	✓	24	1.1	even	1	trivial
400.6.n.h.143.2	yes	24	20.19	odd	2	inner
400.6.n.h.143.11	yes	24	5.4	even	2	inner
400.6.n.h.143.12	yes	24	4.3	odd	2	inner
400.6.n.h.207.1	yes	24	20.7	even	4	inner
400.6.n.h.207.2	yes	24	5.3	odd	4	inner
400.6.n.h.207.11	yes	24	20.3	even	4	inner
400.6.n.h.207.12	yes	24	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	400.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.8504 + 13.8504i) q^{3} +(-156.283 - 156.283i) q^{7} -140.668i q^{9} +O(q^{10})\)	\(q+(-13.8504 + 13.8504i) q^{3} +(-156.283 - 156.283i) q^{7} -140.668i q^{9} +402.885i q^{11} +(703.867 + 703.867i) q^{13} +(-899.535 + 899.535i) q^{17} +507.251 q^{19} +4329.18 q^{21} +(-858.099 + 858.099i) q^{23} +(-1417.34 - 1417.34i) q^{27} +6737.48i q^{29} +2290.84i q^{31} +(-5580.12 - 5580.12i) q^{33} +(-6090.42 + 6090.42i) q^{37} -19497.7 q^{39} -4406.15 q^{41} +(5368.74 - 5368.74i) q^{43} +(-20272.4 - 20272.4i) q^{47} +32042.0i q^{49} -24917.9i q^{51} +(-10170.4 - 10170.4i) q^{53} +(-7025.64 + 7025.64i) q^{57} +32508.1 q^{59} +42480.7 q^{61} +(-21984.1 + 21984.1i) q^{63} +(-1676.23 - 1676.23i) q^{67} -23770.1i q^{69} +25272.3i q^{71} +(25346.7 + 25346.7i) q^{73} +(62964.2 - 62964.2i) q^{77} +4185.82 q^{79} +73443.8 q^{81} +(-49368.6 + 49368.6i) q^{83} +(-93316.9 - 93316.9i) q^{87} -133783. i q^{89} -220005. i q^{91} +(-31729.2 - 31729.2i) q^{93} +(100890. - 100890. i) q^{97} +56673.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 19936 q^{21} + 32568 q^{41} + 454944 q^{61} + 1059176 q^{81}+O(q^{100}) \) 24 * q + 19936 * q^21 + 32568 * q^41 + 454944 * q^61 + 1059176 * q^81

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