LMFDB - Embedded newform 126.4.d.a.125.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,4,Mod(125,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("126.125");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.d (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:	$7.43424066072$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.849346560000.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 50625 $ x^8 + 50625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			125.7
Root			$-1.48213 + 3.57817i$ of defining polynomial
Character	$\chi$	$=$	126.125
Dual form			126.4.d.a.125.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -4.00000 q^{4} +5.92851 q^{5} +(0.757359 + 18.5048i) q^{7} -8.00000i q^{8} +O(q^{10})$	\(q+2.00000i q^{2} -4.00000 q^{4} +5.92851 q^{5} +(0.757359 + 18.5048i) q^{7} -8.00000i q^{8} +11.8570i q^{10} -0.301515i q^{11} +72.5806i q^{13} +(-37.0095 + 1.51472i) q^{14} +16.0000 q^{16} -44.3765 q^{17} +84.4376i q^{19} -23.7140 q^{20} +0.603030 q^{22} +63.2132i q^{23} -89.8528 q^{25} -145.161 q^{26} +(-3.02944 - 74.0191i) q^{28} -183.037i q^{29} +50.3050i q^{31} +32.0000i q^{32} -88.7531i q^{34} +(4.49001 + 109.706i) q^{35} +285.470 q^{37} -168.875 q^{38} -47.4280i q^{40} +216.129 q^{41} -14.2498 q^{43} +1.20606i q^{44} -126.426 q^{46} +423.626 q^{47} +(-341.853 + 28.0295i) q^{49} -179.706i q^{50} -290.322i q^{52} +202.919i q^{53} -1.78753i q^{55} +(148.038 - 6.05887i) q^{56} +366.073 q^{58} +734.437 q^{59} -633.827i q^{61} -100.610 q^{62} -64.0000 q^{64} +430.294i q^{65} +133.970 q^{67} +177.506 q^{68} +(-219.411 + 8.98002i) q^{70} -1048.82i q^{71} -152.354i q^{73} +570.940i q^{74} -337.750i q^{76} +(5.57947 - 0.228355i) q^{77} +819.675 q^{79} +94.8561 q^{80} +432.257i q^{82} -583.173 q^{83} -263.087 q^{85} -28.4996i q^{86} -2.41212 q^{88} -1312.03 q^{89} +(-1343.09 + 54.9696i) q^{91} -252.853i q^{92} +847.253i q^{94} +500.589i q^{95} -409.633i q^{97} +(-56.0590 - 683.706i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{4} + 40 q^{7}+O(q^{10}) $ 8 * q - 32 * q^4 + 40 * q^7	$ 8 q - 32 q^{4} + 40 q^{7} + 128 q^{16} + 480 q^{22} - 40 q^{25} - 160 q^{28} - 160 q^{37} + 1040 q^{43} - 672 q^{46} - 2056 q^{49} + 960 q^{58} - 512 q^{64} - 3680 q^{67} + 960 q^{70} + 448 q^{79} + 6720 q^{85} - 1920 q^{88} - 1920 q^{91}+O(q^{100}) $ 8 * q - 32 * q^4 + 40 * q^7 + 128 * q^16 + 480 * q^22 - 40 * q^25 - 160 * q^28 - 160 * q^37 + 1040 * q^43 - 672 * q^46 - 2056 * q^49 + 960 * q^58 - 512 * q^64 - 3680 * q^67 + 960 * q^70 + 448 * q^79 + 6720 * q^85 - 1920 * q^88 - 1920 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$-1$	$-1$

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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−4.00000			−0.500000
$5$	5.92851			0.530262			0.265131	−	0.964212i	$-0.414585\pi$
$5$	5.92851			0.530262			0.265131	+	0.964212i	$0.414585\pi$
$6$		0			0
$7$	0.757359	+	18.5048i	0.0408936	+	0.999164i
$7$	0.757359	+	18.5048i	0.0408936	+	0.999164i
$8$		−	8.00000i		−	0.353553i
$9$		0			0
$10$			11.8570i			0.374952i
$11$		−	0.301515i		−	0.00826457i	−0.999991	−	0.00413228i	$-0.998685\pi$
$11$		−	0.301515i		−	0.00826457i	0.999991	−	0.00413228i	$-0.00131535\pi$
$12$		0			0
$13$			72.5806i			1.54848i	0.632893	+	0.774240i	$0.281867\pi$
$13$			72.5806i			1.54848i	−0.632893	+	0.774240i	$0.718133\pi$
$14$	−37.0095	+	1.51472i	−0.706515	+	0.0289161i
$15$		0			0
$16$	16.0000			0.250000
$17$	−44.3765			−0.633111			−0.316556	−	0.948574i	$-0.602526\pi$
$17$	−44.3765			−0.633111			−0.316556	+	0.948574i	$0.602526\pi$
$18$		0			0
$19$			84.4376i			1.01954i	0.860310	+	0.509771i	$0.170270\pi$
$19$			84.4376i			1.01954i	−0.860310	+	0.509771i	$0.829730\pi$
$20$	−23.7140			−0.265131
$21$		0			0
$22$	0.603030			0.00584393
$23$			63.2132i			0.573081i	0.958068	+	0.286541i	$0.0925053\pi$
$23$			63.2132i			0.573081i	−0.958068	+	0.286541i	$0.907495\pi$
$24$		0			0
$25$	−89.8528			−0.718823
$26$	−145.161			−1.09494
$27$		0			0
$28$	−3.02944	−	74.0191i	−0.0204468	−	0.499582i
$29$		−	183.037i		−	1.17204i	−0.810298	−	0.586018i	$-0.800695\pi$
$29$		−	183.037i		−	1.17204i	0.810298	−	0.586018i	$-0.199305\pi$
$30$		0			0
$31$			50.3050i			0.291453i	0.989325	+	0.145727i	$0.0465520\pi$
$31$			50.3050i			0.291453i	−0.989325	+	0.145727i	$0.953448\pi$
$32$			32.0000i			0.176777i
$33$		0			0
$34$		−	88.7531i		−	0.447677i
$35$	4.49001	+	109.706i	0.0216843	+	0.529818i
$36$		0			0
$37$	285.470			1.26841			0.634203	−	0.773167i	$-0.281328\pi$
$37$	285.470			1.26841			0.634203	+	0.773167i	$0.281328\pi$
$38$	−168.875			−0.720926
$39$		0			0
$40$		−	47.4280i		−	0.187476i
$41$	216.129			0.823259			0.411630	−	0.911351i	$-0.364960\pi$
$41$	216.129			0.823259			0.411630	+	0.911351i	$0.364960\pi$
$42$		0			0
$43$	−14.2498			−0.0505365			−0.0252683	−	0.999681i	$-0.508044\pi$
$43$	−14.2498			−0.0505365			−0.0252683	+	0.999681i	$0.508044\pi$
$44$			1.20606i			0.00413228i
$45$		0			0
$46$	−126.426			−0.405229
$47$	423.626			1.31473			0.657365	−	0.753573i	$-0.271671\pi$
$47$	423.626			1.31473			0.657365	+	0.753573i	$0.271671\pi$
$48$		0			0
$49$	−341.853	+	28.0295i	−0.996655	+	0.0817187i
$50$		−	179.706i		−	0.508284i
$51$		0			0
$52$		−	290.322i		−	0.774240i
$53$			202.919i			0.525907i	0.964809	+	0.262953i	$0.0846965\pi$
$53$			202.919i			0.525907i	−0.964809	+	0.262953i	$0.915303\pi$
$54$		0			0
$55$		−	1.78753i		−	0.00438238i
$56$	148.038	−	6.05887i	0.353258	−	0.0144581i
$57$		0			0
$58$	366.073			0.828754
$59$	734.437			1.62060			0.810301	−	0.586014i	$-0.199304\pi$
$59$	734.437			1.62060			0.810301	+	0.586014i	$0.199304\pi$
$60$		0			0
$61$		−	633.827i		−	1.33038i	−0.746674	−	0.665190i	$-0.768351\pi$
$61$		−	633.827i		−	1.33038i	0.746674	−	0.665190i	$-0.231649\pi$
$62$	−100.610			−0.206089
$63$		0			0
$64$	−64.0000			−0.125000
$65$			430.294i			0.821099i
$66$		0			0
$67$	133.970			0.244284			0.122142	−	0.992513i	$-0.461024\pi$
$67$	133.970			0.244284			0.122142	+	0.992513i	$0.461024\pi$
$68$	177.506			0.316556
$69$		0			0
$70$	−219.411	+	8.98002i	−0.374638	+	0.0153331i
$71$		−	1048.82i		−	1.75312i	−0.481293	−	0.876560i	$-0.659833\pi$
$71$		−	1048.82i		−	1.75312i	0.481293	−	0.876560i	$-0.340167\pi$
$72$		0			0
$73$		−	152.354i		−	0.244269i	−0.992514	−	0.122135i	$-0.961026\pi$
$73$		−	152.354i		−	0.244269i	0.992514	−	0.122135i	$-0.0389739\pi$
$74$			570.940i			0.896898i
$75$		0			0
$76$		−	337.750i		−	0.509771i
$77$	5.57947	−	0.228355i	0.00825765	−	0.000337968i
$78$		0			0
$79$	819.675			1.16735			0.583675	−	0.811987i	$-0.301614\pi$
$79$	819.675			1.16735			0.583675	+	0.811987i	$0.301614\pi$
$80$	94.8561			0.132565
$81$		0			0
$82$			432.257i			0.582132i
$83$	−583.173			−0.771223			−0.385611	−	0.922661i	$-0.626009\pi$
$83$	−583.173			−0.771223			−0.385611	+	0.922661i	$0.626009\pi$
$84$		0			0
$85$	−263.087			−0.335715
$86$		−	28.4996i		−	0.0357347i
$87$		0			0
$88$	−2.41212			−0.00292197
$89$	−1312.03			−1.56264			−0.781320	−	0.624131i	$-0.785453\pi$
$89$	−1312.03			−1.56264			−0.781320	+	0.624131i	$0.785453\pi$
$90$		0			0
$91$	−1343.09	+	54.9696i	−1.54718	+	0.0633228i
$92$		−	252.853i		−	0.286541i
$93$		0			0
$94$			847.253i			0.929654i
$95$			500.589i			0.540624i
$96$		0			0
$97$		−	409.633i		−	0.428783i	−0.976748	−	0.214391i	$-0.931223\pi$
$97$		−	409.633i		−	0.428783i	0.976748	−	0.214391i	$-0.0687768\pi$
$98$	−56.0590	−	683.706i	−0.0577838	−	0.704742i
$99$		0			0
$100$	359.411			0.359411
$101$	−1824.76			−1.79773			−0.898863	−	0.438231i	$-0.855605\pi$
$101$	−1824.76			−1.79773			−0.898863	+	0.438231i	$0.855605\pi$
$102$		0			0
$103$			1238.19i			1.18449i	0.805760	+	0.592243i	$0.201757\pi$
$103$			1238.19i			1.18449i	−0.805760	+	0.592243i	$0.798243\pi$
$104$	580.645			0.547470
$105$		0			0
$106$	−405.838			−0.371872
$107$			1663.02i			1.50253i	0.660003	+	0.751263i	$0.270555\pi$
$107$			1663.02i			1.50253i	−0.660003	+	0.751263i	$0.729445\pi$
$108$		0			0
$109$	1384.85			1.21693			0.608463	−	0.793583i	$-0.291787\pi$
$109$	1384.85			1.21693			0.608463	+	0.793583i	$0.291787\pi$
$110$	3.57507			0.00309881
$111$		0			0
$112$	12.1177	+	296.076i	0.0102234	+	0.249791i
$113$		−	1244.76i		−	1.03626i	−0.855303	−	0.518128i	$-0.826629\pi$
$113$		−	1244.76i		−	1.03626i	0.855303	−	0.518128i	$-0.173371\pi$
$114$		0			0
$115$			374.760i			0.303883i
$116$			732.146i			0.586018i
$117$		0			0
$118$			1468.87i			1.14594i
$119$	−33.6090	−	821.177i	−0.0258902	−	0.632582i
$120$		0			0
$121$	1330.91			0.999932
$122$	1267.65			0.940721
$123$		0			0
$124$		−	201.220i		−	0.145727i
$125$	−1273.76			−0.911426
$126$		0			0
$127$	−1503.09			−1.05022			−0.525108	−	0.851036i	$-0.675975\pi$
$127$	−1503.09			−1.05022			−0.525108	+	0.851036i	$0.675975\pi$
$128$		−	128.000i		−	0.0883883i
$129$		0			0
$130$	−860.589			−0.580605
$131$	1246.47			0.831331			0.415665	−	0.909518i	$-0.363549\pi$
$131$	1246.47			0.831331			0.415665	+	0.909518i	$0.363549\pi$
$132$		0			0
$133$	−1562.50	+	63.9496i	−1.01869	+	0.0416927i
$134$			267.939i			0.172735i
$135$		0			0
$136$			355.012i			0.223839i
$137$		−	1404.56i		−	0.875912i	−0.898996	−	0.437956i	$-0.855703\pi$
$137$		−	1404.56i		−	0.875912i	0.898996	−	0.437956i	$-0.144297\pi$
$138$		0			0
$139$			1205.14i			0.735387i	0.929947	+	0.367694i	$0.119852\pi$
$139$			1205.14i			0.735387i	−0.929947	+	0.367694i	$0.880148\pi$
$140$	−17.9600	−	438.823i	−0.0108421	−	0.264909i
$141$		0			0
$142$	2097.63			1.23964
$143$	21.8841			0.0127975
$144$		0			0
$145$		−	1085.13i		−	0.621486i
$146$	304.707			0.172724
$147$		0			0
$148$	−1141.88			−0.634203
$149$			2236.35i			1.22959i	0.788688	+	0.614794i	$0.210761\pi$
$149$			2236.35i			1.22959i	−0.788688	+	0.614794i	$0.789239\pi$
$150$		0			0
$151$	1606.40			0.865739			0.432870	−	0.901456i	$-0.357501\pi$
$151$	1606.40			0.865739			0.432870	+	0.901456i	$0.357501\pi$
$152$	675.501			0.360463
$153$		0			0
$154$	0.456711	+	11.1589i	0.000238979	+	0.00583904i
$155$			298.234i			0.154547i
$156$		0			0
$157$		−	1389.80i		−	0.706484i	−0.935532	−	0.353242i	$-0.885079\pi$
$157$		−	1389.80i		−	0.706484i	0.935532	−	0.353242i	$-0.114921\pi$
$158$			1639.35i			0.825441i
$159$		0			0
$160$			189.712i			0.0937379i
$161$	−1169.75	+	47.8751i	−0.572602	+	0.0234353i
$162$		0			0
$163$	1740.14			0.836187			0.418094	−	0.908404i	$-0.362698\pi$
$163$	1740.14			0.836187			0.418094	+	0.908404i	$0.362698\pi$
$164$	−864.515			−0.411630
$165$		0			0
$166$		−	1166.35i		−	0.545337i
$167$	4077.15			1.88922			0.944609	−	0.328197i	$-0.106441\pi$
$167$	4077.15			1.88922			0.944609	+	0.328197i	$0.106441\pi$
$168$		0			0
$169$	−3070.94			−1.39779
$170$		−	526.173i		−	0.237386i
$171$		0			0
$172$	56.9991			0.0252683
$173$	−1149.96			−0.505373			−0.252686	−	0.967548i	$-0.581314\pi$
$173$	−1149.96			−0.505373			−0.252686	+	0.967548i	$0.581314\pi$
$174$		0			0
$175$	−68.0509	−	1662.71i	−0.0293952	−	0.718221i
$176$		−	4.82424i		−	0.00206614i
$177$		0			0
$178$		−	2624.06i		−	1.10495i
$179$		−	3661.64i		−	1.52896i	−0.644648	−	0.764479i	$-0.722996\pi$
$179$		−	3661.64i		−	1.52896i	0.644648	−	0.764479i	$-0.277004\pi$
$180$		0			0
$181$		−	4309.63i		−	1.76979i	−0.465790	−	0.884895i	$-0.654230\pi$
$181$		−	4309.63i		−	1.76979i	0.465790	−	0.884895i	$-0.345770\pi$
$182$	−109.939	−	2686.17i	−0.0447760	−	1.09402i
$183$		0			0
$184$	505.706			0.202615
$185$	1692.41			0.672587
$186$		0			0
$187$			13.3802i			0.00523239i
$188$	−1694.51			−0.657365
$189$		0			0
$190$	−1001.18			−0.382279
$191$			4214.99i			1.59678i	0.602138	+	0.798392i	$0.294316\pi$
$191$			4214.99i			1.59678i	−0.602138	+	0.798392i	$0.705684\pi$
$192$		0			0
$193$	1447.26			0.539774			0.269887	−	0.962892i	$-0.413014\pi$
$193$	1447.26			0.539774			0.269887	+	0.962892i	$0.413014\pi$
$194$	819.266			0.303195
$195$		0			0
$196$	1367.41	−	112.118i	0.498328	−	0.0408594i
$197$			524.696i			0.189762i	0.995489	+	0.0948808i	$0.0302470\pi$
$197$			524.696i			0.189762i	−0.995489	+	0.0948808i	$0.969753\pi$
$198$		0			0
$199$			241.805i			0.0861361i	0.999072	+	0.0430681i	$0.0137132\pi$
$199$			241.805i			0.0861361i	−0.999072	+	0.0430681i	$0.986287\pi$
$200$			718.823i			0.254142i
$201$		0			0
$202$		−	3649.52i		−	1.27118i
$203$	3387.05	−	138.624i	1.17106	−	0.0479287i
$204$		0			0
$205$	1281.32			0.436543
$206$	−2476.37			−0.837558
$207$		0			0
$208$			1161.29i			0.387120i
$209$	25.4592			0.00842608
$210$		0			0
$211$	−425.807			−0.138928			−0.0694640	−	0.997584i	$-0.522129\pi$
$211$	−425.807			−0.138928			−0.0694640	+	0.997584i	$0.522129\pi$
$212$		−	811.675i		−	0.262953i
$213$		0			0
$214$	−3326.04			−1.06245
$215$	−84.4799			−0.0267976
$216$		0			0
$217$	−930.883	+	38.0990i	−0.291210	+	0.0119186i
$218$			2769.71i			0.860496i
$219$		0			0
$220$			7.15014i			0.00219119i
$221$		−	3220.87i		−	0.980360i
$222$		0			0
$223$			5867.25i			1.76189i	0.473223	+	0.880943i	$0.343090\pi$
$223$			5867.25i			1.76189i	−0.473223	+	0.880943i	$0.656910\pi$
$224$	−592.153	+	24.2355i	−0.176629	+	0.00722903i
$225$		0			0
$226$	2489.51			0.732743
$227$	3839.58			1.12265			0.561325	−	0.827595i	$-0.310292\pi$
$227$	3839.58			1.12265			0.561325	+	0.827595i	$0.310292\pi$
$228$		0			0
$229$			2402.31i			0.693227i	0.938008	+	0.346614i	$0.112668\pi$
$229$			2402.31i			0.693227i	−0.938008	+	0.346614i	$0.887332\pi$
$230$	−749.520			−0.214878
$231$		0			0
$232$	−1464.29			−0.414377
$233$			2172.44i			0.610822i	0.952221	+	0.305411i	$0.0987938\pi$
$233$			2172.44i			0.610822i	−0.952221	+	0.305411i	$0.901206\pi$
$234$		0			0
$235$	2511.47			0.697150
$236$	−2937.75			−0.810301
$237$		0			0
$238$	1642.35	−	67.2180i	0.447303	−	0.0183071i
$239$		−	1130.57i		−	0.305985i	−0.988227	−	0.152992i	$-0.951109\pi$
$239$		−	1130.57i		−	0.305985i	0.988227	−	0.152992i	$-0.0488910\pi$
$240$		0			0
$241$			4715.64i			1.26042i	0.776425	+	0.630210i	$0.217031\pi$
$241$			4715.64i			1.26042i	−0.776425	+	0.630210i	$0.782969\pi$
$242$			2661.82i			0.707058i
$243$		0			0
$244$			2535.31i			0.665190i
$245$	−2026.68	+	166.173i	−0.528488	+	0.0433323i
$246$		0			0
$247$	−6128.53			−1.57874
$248$	402.440			0.103044
$249$		0			0
$250$		−	2547.51i		−	0.644475i
$251$	−3318.30			−0.834460			−0.417230	−	0.908801i	$-0.636999\pi$
$251$	−3318.30			−0.834460			−0.417230	+	0.908801i	$0.636999\pi$
$252$		0			0
$253$	19.0597			0.00473627
$254$		−	3006.17i		−	0.742614i
$255$		0			0
$256$	256.000			0.0625000
$257$	5086.57			1.23460			0.617298	−	0.786729i	$-0.288227\pi$
$257$	5086.57			1.23460			0.617298	+	0.786729i	$0.288227\pi$
$258$		0			0
$259$	216.203	+	5282.56i	0.0518696	+	1.26734i
$260$		−	1721.18i		−	0.410550i
$261$		0			0
$262$			2492.93i			0.587840i
$263$		−	2529.58i		−	0.593082i	−0.955020	−	0.296541i	$-0.904167\pi$
$263$		−	2529.58i		−	0.593082i	0.955020	−	0.296541i	$-0.0958331\pi$
$264$		0			0
$265$			1203.01i			0.278868i
$266$	−127.899	−	3125.00i	−0.0294812	−	0.720322i
$267$		0			0
$268$	−535.879			−0.122142
$269$	−4282.47			−0.970657			−0.485329	−	0.874332i	$-0.661300\pi$
$269$	−4282.47			−0.970657			−0.485329	+	0.874332i	$0.661300\pi$
$270$		0			0
$271$		−	776.195i		−	0.173987i	−0.996209	−	0.0869936i	$-0.972274\pi$
$271$		−	776.195i		−	0.173987i	0.996209	−	0.0869936i	$-0.0277260\pi$
$272$	−710.025			−0.158278
$273$		0			0
$274$	2809.13			0.619364
$275$			27.0920i			0.00594076i
$276$		0			0
$277$	2901.61			0.629390			0.314695	−	0.949193i	$-0.398098\pi$
$277$	2901.61			0.629390			0.314695	+	0.949193i	$0.398098\pi$
$278$	−2410.28			−0.519997
$279$		0			0
$280$	877.645	−	35.9201i	0.187319	−	0.00766655i
$281$			4406.68i			0.935518i	0.883856	+	0.467759i	$0.154939\pi$
$281$			4406.68i			0.935518i	−0.883856	+	0.467759i	$0.845061\pi$
$282$		0			0
$283$			62.8178i			0.0131948i	0.999978	+	0.00659740i	$0.00210003\pi$
$283$			62.8178i			0.0131948i	−0.999978	+	0.00659740i	$0.997900\pi$
$284$			4195.26i			0.876560i
$285$		0			0
$286$			43.7683i			0.00904921i
$287$	163.687	+	3999.41i	0.0336660	+	0.822571i
$288$		0			0
$289$	−2943.72			−0.599170
$290$	2170.27			0.439457
$291$		0			0
$292$			609.415i			0.122135i
$293$	−3299.73			−0.657927			−0.328963	−	0.944343i	$-0.606699\pi$
$293$	−3299.73			−0.657927			−0.328963	+	0.944343i	$0.606699\pi$
$294$		0			0
$295$	4354.11			0.859343
$296$		−	2283.76i		−	0.448449i
$297$		0			0
$298$	−4472.69			−0.869450
$299$	−4588.05			−0.887404
$300$		0			0
$301$	−10.7922	−	263.689i	−0.00206662	−	0.0504943i
$302$			3212.79i			0.612170i
$303$		0			0
$304$			1351.00i			0.254886i
$305$		−	3757.65i		−	0.705450i
$306$		0			0
$307$		−	5596.99i		−	1.04051i	−0.854011	−	0.520255i	$-0.825837\pi$
$307$		−	5596.99i		−	1.04051i	0.854011	−	0.520255i	$-0.174163\pi$
$308$	−22.3179	+	0.913421i	−0.00412883	+	0.000168984i
$309$		0			0
$310$	−596.468			−0.109281
$311$	−5817.95			−1.06079			−0.530395	−	0.847750i	$-0.677956\pi$
$311$	−5817.95			−1.06079			−0.530395	+	0.847750i	$0.677956\pi$
$312$		0			0
$313$			1129.73i			0.204013i	0.994784	+	0.102006i	$0.0325262\pi$
$313$			1129.73i			0.204013i	−0.994784	+	0.102006i	$0.967474\pi$
$314$	2779.60			0.499560
$315$		0			0
$316$	−3278.70			−0.583675
$317$		−	8132.57i		−	1.44092i	−0.693498	−	0.720459i	$-0.743931\pi$
$317$		−	8132.57i		−	1.44092i	0.693498	−	0.720459i	$-0.256069\pi$
$318$		0			0
$319$	−55.1883			−0.00968637
$320$	−379.424			−0.0662827
$321$		0			0
$322$	−95.7502	−	2339.49i	−0.0165713	−	0.404891i
$323$		−	3747.05i		−	0.645484i
$324$		0			0
$325$		−	6521.57i		−	1.11308i
$326$			3480.29i			0.591274i
$327$		0			0
$328$		−	1729.03i		−	0.291066i
$329$	320.837	+	7839.11i	0.0537639	+	1.31363i
$330$		0			0
$331$	−7743.01			−1.28578			−0.642891	−	0.765957i	$-0.722265\pi$
$331$	−7743.01			−1.28578			−0.642891	+	0.765957i	$0.722265\pi$
$332$	2332.69			0.385611
$333$		0			0
$334$			8154.30i			1.33588i
$335$	794.240			0.129534
$336$		0			0
$337$	10498.7			1.69703			0.848517	−	0.529169i	$-0.177496\pi$
$337$	10498.7			1.69703			0.848517	+	0.529169i	$0.177496\pi$
$338$		−	6141.88i		−	0.988385i
$339$		0			0
$340$	1052.35			0.167857
$341$	15.1677			0.00240874
$342$		0			0
$343$	−777.585	−	6304.68i	−0.122407	−	0.992480i
$344$			113.998i			0.0178674i
$345$		0			0
$346$		−	2299.91i		−	0.357353i
$347$			3366.62i			0.520835i	0.965496	+	0.260418i	$0.0838603\pi$
$347$			3366.62i			0.520835i	−0.965496	+	0.260418i	$0.916140\pi$
$348$		0			0
$349$			1047.69i			0.160692i	0.996767	+	0.0803461i	$0.0256026\pi$
$349$			1047.69i			0.160692i	−0.996767	+	0.0803461i	$0.974397\pi$
$350$	3325.41	−	136.102i	0.507859	−	0.0207856i
$351$		0			0
$352$	9.64849			0.00146098
$353$	5443.68			0.820786			0.410393	−	0.911909i	$-0.365391\pi$
$353$	5443.68			0.820786			0.410393	+	0.911909i	$0.365391\pi$
$354$		0			0
$355$		−	6217.91i		−	0.929612i
$356$	5248.12			0.781320
$357$		0			0
$358$	7323.27			1.08114
$359$			1116.78i			0.164183i	0.996625	+	0.0820913i	$0.0261599\pi$
$359$			1116.78i			0.164183i	−0.996625	+	0.0820913i	$0.973840\pi$
$360$		0			0
$361$	−270.706			−0.0394672
$362$	8619.26			1.25143
$363$		0			0
$364$	5372.35	−	219.878i	0.773592	−	0.0316614i
$365$		−	903.229i		−	0.129527i
$366$		0			0
$367$		−	7652.87i		−	1.08849i	−0.838926	−	0.544246i	$-0.816816\pi$
$367$		−	7652.87i		−	1.08849i	0.838926	−	0.544246i	$-0.183184\pi$
$368$			1011.41i			0.143270i
$369$		0			0
$370$			3384.82i			0.475591i
$371$	−3754.97	+	153.682i	−0.525467	+	0.0215062i
$372$		0			0
$373$	−11492.1			−1.59527			−0.797635	−	0.603140i	$-0.793916\pi$
$373$	−11492.1			−1.59527			−0.797635	+	0.603140i	$0.793916\pi$
$374$	−26.7604			−0.00369986
$375$		0			0
$376$		−	3389.01i		−	0.464827i
$377$	13284.9			1.81487
$378$		0			0
$379$	8186.54			1.10954			0.554768	−	0.832005i	$-0.312807\pi$
$379$	8186.54			1.10954			0.554768	+	0.832005i	$0.312807\pi$
$380$		−	2002.35i		−	0.270312i
$381$		0			0
$382$	−8429.98			−1.12910
$383$	−2070.01			−0.276168			−0.138084	−	0.990421i	$-0.544094\pi$
$383$	−2070.01			−0.276168			−0.138084	+	0.990421i	$0.544094\pi$
$384$		0			0
$385$	33.0779	−	1.35381i	0.00437872	−	0.000179211i
$386$			2894.53i			0.381678i
$387$		0			0
$388$			1638.53i			0.214391i
$389$		−	641.370i		−	0.0835958i	−0.999126	−	0.0417979i	$-0.986691\pi$
$389$		−	641.370i		−	0.0835958i	0.999126	−	0.0417979i	$-0.0133086\pi$
$390$		0			0
$391$		−	2805.18i		−	0.362824i
$392$	224.236	+	2734.82i	0.0288919	+	0.352371i
$393$		0			0
$394$	−1049.39			−0.134182
$395$	4859.45			0.619001
$396$		0			0
$397$		−	10496.2i		−	1.32693i	−0.748207	−	0.663465i	$-0.769085\pi$
$397$		−	10496.2i		−	1.32693i	0.748207	−	0.663465i	$-0.230915\pi$
$398$	−483.610			−0.0609074
$399$		0			0
$400$	−1437.65			−0.179706
$401$		−	8862.36i		−	1.10365i	−0.833959	−	0.551827i	$-0.813931\pi$
$401$		−	8862.36i		−	1.10365i	0.833959	−	0.551827i	$-0.186069\pi$
$402$		0			0
$403$	−3651.17			−0.451309
$404$	7299.03			0.898863
$405$		0			0
$406$	277.249	+	6774.10i	0.0338907	+	0.828061i
$407$		−	86.0736i		−	0.0104828i
$408$		0			0
$409$			8896.63i			1.07557i	0.843080	+	0.537787i	$0.180740\pi$
$409$			8896.63i			1.07557i	−0.843080	+	0.537787i	$0.819260\pi$
$410$			2562.64i			0.308682i
$411$		0			0
$412$		−	4952.74i		−	0.592243i
$413$	556.232	+	13590.6i	0.0662722	+	1.61925i
$414$		0			0
$415$	−3457.34			−0.408950
$416$	−2322.58			−0.273735
$417$		0			0
$418$			50.9184i			0.00595814i
$419$	−14741.9			−1.71883			−0.859415	−	0.511279i	$-0.829172\pi$
$419$	−14741.9			−1.71883			−0.859415	+	0.511279i	$0.829172\pi$
$420$		0			0
$421$	841.087			0.0973683			0.0486841	−	0.998814i	$-0.484497\pi$
$421$	841.087			0.0973683			0.0486841	+	0.998814i	$0.484497\pi$
$422$		−	851.615i		−	0.0982369i
$423$		0			0
$424$	1623.35			0.185936
$425$	3987.36			0.455095
$426$		0			0
$427$	11728.8	−	480.034i	1.32927	−	0.0544040i
$428$		−	6652.08i		−	0.751263i
$429$		0			0
$430$		−	168.960i		−	0.0189488i
$431$		−	7707.57i		−	0.861393i	−0.902497	−	0.430697i	$-0.858268\pi$
$431$		−	7707.57i		−	0.861393i	0.902497	−	0.430697i	$-0.141732\pi$
$432$		0			0
$433$			9675.58i			1.07385i	0.843629	+	0.536927i	$0.180415\pi$
$433$			9675.58i			1.07385i	−0.843629	+	0.536927i	$0.819585\pi$
$434$	−76.1980	−	1861.77i	−0.00842770	−	0.205916i
$435$		0			0
$436$	−5539.41			−0.608463
$437$	−5337.57			−0.584281
$438$		0			0
$439$			6444.15i			0.700598i	0.936638	+	0.350299i	$0.113920\pi$
$439$			6444.15i			0.700598i	−0.936638	+	0.350299i	$0.886080\pi$
$440$	−14.3003			−0.00154941
$441$		0			0
$442$	6441.75			0.693219
$443$			272.880i			0.0292662i	0.999893	+	0.0146331i	$0.00465802\pi$
$443$			272.880i			0.0292662i	−0.999893	+	0.0146331i	$0.995342\pi$
$444$		0			0
$445$	−7778.38			−0.828608
$446$	−11734.5			−1.24584
$447$		0			0
$448$	−48.4710	−	1184.31i	−0.00511169	−	0.124895i
$449$			599.676i			0.0630299i	0.999503	+	0.0315150i	$0.0100332\pi$
$449$			599.676i			0.0630299i	−0.999503	+	0.0315150i	$0.989967\pi$
$450$		0			0
$451$		−	65.1661i		−	0.00680388i
$452$			4979.03i			0.518128i
$453$		0			0
$454$			7679.16i			0.793834i
$455$	−7962.50	+	325.887i	−0.820412	+	0.0335777i
$456$		0			0
$457$	945.127			0.0967422			0.0483711	−	0.998829i	$-0.484597\pi$
$457$	945.127			0.0967422			0.0483711	+	0.998829i	$0.484597\pi$
$458$	−4804.62			−0.490186
$459$		0			0
$460$		−	1499.04i		−	0.151941i
$461$	−1164.43			−0.117641			−0.0588207	−	0.998269i	$-0.518734\pi$
$461$	−1164.43			−0.117641			−0.0588207	+	0.998269i	$0.518734\pi$
$462$		0			0
$463$	17312.8			1.73778			0.868892	−	0.495002i	$-0.164833\pi$
$463$	17312.8			1.73778			0.868892	+	0.495002i	$0.164833\pi$
$464$		−	2928.59i		−	0.293009i
$465$		0			0
$466$	−4344.89			−0.431916
$467$	−1193.81			−0.118294			−0.0591468	−	0.998249i	$-0.518838\pi$
$467$	−1193.81			−0.118294			−0.0591468	+	0.998249i	$0.518838\pi$
$468$		0			0
$469$	101.463	+	2479.08i	0.00998963	+	0.244079i
$470$			5022.94i			0.492960i
$471$		0			0
$472$		−	5875.49i		−	0.572969i
$473$			4.29653i			0.000417663i
$474$		0			0
$475$		−	7586.95i		−	0.732870i
$476$	134.436	+	3284.71i	0.0129451	+	0.316291i
$477$		0			0
$478$	2261.13			0.216364
$479$	−13684.7			−1.30537			−0.652684	−	0.757630i	$-0.726357\pi$
$479$	−13684.7			−1.30537			−0.652684	+	0.757630i	$0.726357\pi$
$480$		0			0
$481$			20719.6i			1.96410i
$482$	−9431.29			−0.891252
$483$		0			0
$484$	−5323.64			−0.499966
$485$		−	2428.51i		−	0.227367i
$486$		0			0
$487$	−7931.28			−0.737989			−0.368994	−	0.929432i	$-0.620298\pi$
$487$	−7931.28			−0.737989			−0.368994	+	0.929432i	$0.620298\pi$
$488$	−5070.61			−0.470360
$489$		0			0
$490$	−332.346	−	4053.35i	−0.0306406	−	0.373698i
$491$		−	486.246i		−	0.0446924i	−0.999750	−	0.0223462i	$-0.992886\pi$
$491$		−	486.246i		−	0.0446924i	0.999750	−	0.0223462i	$-0.00711361\pi$
$492$		0			0
$493$			8122.53i			0.742029i
$494$		−	12257.1i		−	1.11634i
$495$		0			0
$496$			804.881i			0.0728633i
$497$	19408.1	−	794.330i	1.75165	−	0.0716913i
$498$		0			0
$499$	−18932.9			−1.69850			−0.849249	−	0.527992i	$-0.822945\pi$
$499$	−18932.9			−1.69850			−0.849249	+	0.527992i	$0.822945\pi$
$500$	5095.02			0.455713
$501$		0			0
$502$		−	6636.61i		−	0.590052i
$503$	1543.07			0.136784			0.0683918	−	0.997659i	$-0.478213\pi$
$503$	1543.07			0.136784			0.0683918	+	0.997659i	$0.478213\pi$
$504$		0			0
$505$	−10818.1			−0.953265
$506$			38.1195i			0.00334905i
$507$		0			0
$508$	6012.35			0.525108
$509$	−14780.6			−1.28711			−0.643556	−	0.765399i	$-0.722541\pi$
$509$	−14780.6			−1.28711			−0.643556	+	0.765399i	$0.722541\pi$
$510$		0			0
$511$	2819.27	−	115.386i	0.244065	−	0.00998903i
$512$			512.000i			0.0441942i
$513$		0			0
$514$			10173.1i			0.872992i
$515$			7340.59i			0.628087i
$516$		0			0
$517$		−	127.730i		−	0.0108657i
$518$	−10565.1	+	432.407i	−0.896148	+	0.0366774i
$519$		0			0
$520$	3442.35			0.290302
$521$	21874.5			1.83942			0.919712	−	0.392593i	$-0.128422\pi$
$521$	21874.5			1.83942			0.919712	+	0.392593i	$0.128422\pi$
$522$		0			0
$523$			9776.27i			0.817374i	0.912675	+	0.408687i	$0.134013\pi$
$523$			9776.27i			0.817374i	−0.912675	+	0.408687i	$0.865987\pi$
$524$	−4985.87			−0.415665
$525$		0			0
$526$	5059.16			0.419372
$527$		−	2232.36i		−	0.184522i
$528$		0			0
$529$	8171.09			0.671578
$530$	−2406.01			−0.197190
$531$		0			0
$532$	6249.99	−	255.798i	0.509345	−	0.0208464i
$533$			15686.7i			1.27480i
$534$		0			0
$535$			9859.23i			0.796732i
$536$		−	1071.76i		−	0.0863673i
$537$		0			0
$538$		−	8564.94i		−	0.686358i
$539$	8.45132	+	103.074i	0.000675370	+	0.00823693i
$540$		0			0
$541$	21336.7			1.69563			0.847814	−	0.530294i	$-0.177918\pi$
$541$	21336.7			1.69563			0.847814	+	0.530294i	$0.177918\pi$
$542$	1552.39			0.123027
$543$		0			0
$544$		−	1420.05i		−	0.111919i
$545$	8210.11			0.645289
$546$		0			0
$547$	−8314.27			−0.649895			−0.324948	−	0.945732i	$-0.605347\pi$
$547$	−8314.27			−0.649895			−0.324948	+	0.945732i	$0.605347\pi$
$548$			5618.26i			0.437956i
$549$		0			0
$550$	−54.1840			−0.00420075
$551$	15455.2			1.19494
$552$		0			0
$553$	620.789	+	15167.9i	0.0477371	+	1.16637i
$554$			5803.23i			0.445046i
$555$		0			0
$556$		−	4820.57i		−	0.367694i
$557$		−	12293.7i		−	0.935188i	−0.883943	−	0.467594i	$-0.845121\pi$
$557$		−	12293.7i		−	0.935188i	0.883943	−	0.467594i	$-0.154879\pi$
$558$		0			0
$559$		−	1034.26i		−	0.0782548i
$560$	71.8402	+	1755.29i	0.00542107	+	0.132455i
$561$		0			0
$562$	−8813.37			−0.661511
$563$	−4792.23			−0.358736			−0.179368	−	0.983782i	$-0.557405\pi$
$563$	−4792.23			−0.358736			−0.179368	+	0.983782i	$0.557405\pi$
$564$		0			0
$565$		−	7379.55i		−	0.549486i
$566$	−125.636			−0.00933014
$567$		0			0
$568$	−8390.52			−0.619821
$569$		−	16233.6i		−	1.19604i	−0.801481	−	0.598020i	$-0.795954\pi$
$569$		−	16233.6i		−	1.19604i	0.801481	−	0.598020i	$-0.204046\pi$
$570$		0			0
$571$	1595.78			0.116955			0.0584775	−	0.998289i	$-0.481375\pi$
$571$	1595.78			0.116955			0.0584775	+	0.998289i	$0.481375\pi$
$572$	−87.5366			−0.00639876
$573$		0			0
$574$	−7998.82	+	327.374i	−0.581645	+	0.0238055i
$575$		−	5679.88i		−	0.411944i
$576$		0			0
$577$		−	12899.1i		−	0.930671i	−0.885134	−	0.465336i	$-0.845934\pi$
$577$		−	12899.1i		−	0.930671i	0.885134	−	0.465336i	$-0.154066\pi$
$578$		−	5887.45i		−	0.423677i
$579$		0			0
$580$			4340.53i			0.310743i
$581$	−441.671	−	10791.5i	−0.0315380	−	0.770578i
$582$		0			0
$583$	61.1831			0.00434639
$584$	−1218.83			−0.0863622
$585$		0			0
$586$		−	6599.47i		−	0.465225i
$587$	13092.3			0.920575			0.460287	−	0.887770i	$-0.347746\pi$
$587$	13092.3			0.920575			0.460287	+	0.887770i	$0.347746\pi$
$588$		0			0
$589$	−4247.64			−0.297149
$590$			8708.23i			0.607647i
$591$		0			0
$592$	4567.52			0.317101
$593$	19604.9			1.35764			0.678818	−	0.734306i	$-0.262492\pi$
$593$	19604.9			1.35764			0.678818	+	0.734306i	$0.262492\pi$
$594$		0			0
$595$	−199.251	−	4868.36i	−0.0137286	−	0.335434i
$596$		−	8945.38i		−	0.614794i
$597$		0			0
$598$		−	9176.10i		−	0.627489i
$599$			11746.8i			0.801272i	0.916237	+	0.400636i	$0.131211\pi$
$599$			11746.8i			0.801272i	−0.916237	+	0.400636i	$0.868789\pi$
$600$		0			0
$601$			8546.19i			0.580044i	0.957020	+	0.290022i	$0.0936626\pi$
$601$			8546.19i			0.580044i	−0.957020	+	0.290022i	$0.906337\pi$
$602$	527.378	−	21.5844i	0.0357048	−	0.00146132i
$603$		0			0
$604$	−6425.58			−0.432870
$605$	7890.30			0.530225
$606$		0			0
$607$		−	29665.1i		−	1.98364i	−0.127637	−	0.991821i	$-0.540739\pi$
$607$		−	29665.1i		−	1.98364i	0.127637	−	0.991821i	$-0.459261\pi$
$608$	−2702.00			−0.180231
$609$		0			0
$610$	7515.29			0.498828
$611$			30747.0i			2.03583i
$612$		0			0
$613$	5889.13			0.388025			0.194013	−	0.980999i	$-0.437850\pi$
$613$	5889.13			0.388025			0.194013	+	0.980999i	$0.437850\pi$
$614$	11194.0			0.735752
$615$		0			0
$616$	−1.82684	−	44.6357i	−0.000119490	−	0.00291952i
$617$			20676.7i			1.34913i	0.738214	+	0.674566i	$0.235669\pi$
$617$			20676.7i			1.34913i	−0.738214	+	0.674566i	$0.764331\pi$
$618$		0			0
$619$		−	10320.2i		−	0.670120i	−0.942197	−	0.335060i	$-0.891243\pi$
$619$		−	10320.2i		−	0.670120i	0.942197	−	0.335060i	$-0.108757\pi$
$620$		−	1192.94i		−	0.0772733i
$621$		0			0
$622$		−	11635.9i		−	0.750092i
$623$	−993.678	−	24278.8i	−0.0639019	−	1.56133i
$624$		0			0
$625$	3680.13			0.235528
$626$	−2259.45			−0.144259
$627$		0			0
$628$			5559.19i			0.353242i
$629$	−12668.2			−0.803042
$630$		0			0
$631$	−12520.8			−0.789928			−0.394964	−	0.918696i	$-0.629243\pi$
$631$	−12520.8			−0.789928			−0.394964	+	0.918696i	$0.629243\pi$
$632$		−	6557.40i		−	0.412721i
$633$		0			0
$634$	16265.1			1.01888
$635$	−8911.06			−0.556889
$636$		0			0
$637$	−2034.40	−	24811.9i	−0.126540	−	1.54330i
$638$		−	110.377i		−	0.00684930i
$639$		0			0
$640$		−	758.849i		−	0.0468690i
$641$			19266.2i			1.18716i	0.804776	+	0.593579i	$0.202286\pi$
$641$			19266.2i			1.18716i	−0.804776	+	0.593579i	$0.797714\pi$
$642$		0			0
$643$		−	7084.07i		−	0.434477i	−0.976119	−	0.217238i	$-0.930295\pi$
$643$		−	7084.07i		−	0.434477i	0.976119	−	0.217238i	$-0.0697049\pi$
$644$	4678.98	−	191.500i	0.286301	−	0.0117177i
$645$		0			0
$646$	7494.10			0.456426
$647$	3614.81			0.219649			0.109825	−	0.993951i	$-0.464971\pi$
$647$	3614.81			0.219649			0.109825	+	0.993951i	$0.464971\pi$
$648$		0			0
$649$		−	221.444i		−	0.0133936i
$650$	13043.1			0.787068
$651$		0			0
$652$	−6960.57			−0.418094
$653$		−	10984.8i		−	0.658296i	−0.944278	−	0.329148i	$-0.893238\pi$
$653$		−	10984.8i		−	0.658296i	0.944278	−	0.329148i	$-0.106762\pi$
$654$		0			0
$655$	7389.69			0.440823
$656$	3458.06			0.205815
$657$		0			0
$658$	−15678.2	+	641.675i	−0.928876	+	0.0380169i
$659$		−	8581.81i		−	0.507283i	−0.967298	−	0.253642i	$-0.918372\pi$
$659$		−	8581.81i		−	0.507283i	0.967298	−	0.253642i	$-0.0816284\pi$
$660$		0			0
$661$		−	13607.9i		−	0.800736i	−0.916354	−	0.400368i	$-0.868882\pi$
$661$		−	13607.9i		−	0.800736i	0.916354	−	0.400368i	$-0.131118\pi$
$662$		−	15486.0i		−	0.909186i
$663$		0			0
$664$			4665.38i			0.272668i
$665$	−9263.28	+	379.126i	−0.540172	+	0.0221081i
$666$		0			0
$667$	11570.3			0.671672
$668$	−16308.6			−0.944609
$669$		0			0
$670$			1588.48i			0.0915946i
$671$	−191.108			−0.0109950
$672$		0			0
$673$	−21092.1			−1.20809			−0.604043	−	0.796951i	$-0.706445\pi$
$673$	−21092.1			−1.20809			−0.604043	+	0.796951i	$0.706445\pi$
$674$			20997.4i			1.19998i
$675$		0			0
$676$	12283.8			0.698894
$677$	−16074.4			−0.912542			−0.456271	−	0.889841i	$-0.650815\pi$
$677$	−16074.4			−0.912542			−0.456271	+	0.889841i	$0.650815\pi$
$678$		0			0
$679$	7580.16	−	310.239i	0.428424	−	0.0175344i
$680$			2104.69i			0.118693i
$681$		0			0
$682$			30.3355i			0.00170323i
$683$		−	15210.3i		−	0.852129i	−0.904693	−	0.426065i	$-0.859900\pi$
$683$		−	15210.3i		−	0.852129i	0.904693	−	0.426065i	$-0.140100\pi$
$684$		0			0
$685$		−	8326.97i		−	0.464463i
$686$	12609.4	−	1555.17i	0.701789	−	0.0865549i
$687$		0			0
$688$	−227.997			−0.0126341
$689$	−14728.0			−0.814355
$690$		0			0
$691$			14907.7i			0.820715i	0.911925	+	0.410358i	$0.134596\pi$
$691$			14907.7i			0.820715i	−0.911925	+	0.410358i	$0.865404\pi$
$692$	4599.82			0.252686
$693$		0			0
$694$	−6733.25			−0.368286
$695$			7144.69i			0.389948i
$696$		0			0
$697$	−9591.04			−0.521215
$698$	−2095.38			−0.113627
$699$		0			0
$700$	272.203	+	6650.82i	0.0146976	+	0.359111i
$701$			2306.38i			0.124266i	0.998068	+	0.0621331i	$0.0197903\pi$
$701$			2306.38i			0.124266i	−0.998068	+	0.0621331i	$0.980210\pi$
$702$		0			0
$703$			24104.4i			1.29319i
$704$			19.2970i			0.00103307i
$705$		0			0
$706$			10887.4i			0.580384i
$707$	−1382.00	−	33766.7i	−0.0735154	−	1.79622i
$708$		0			0
$709$	26416.6			1.39929			0.699645	−	0.714491i	$-0.253341\pi$
$709$	26416.6			1.39929			0.699645	+	0.714491i	$0.253341\pi$
$710$	12435.8			0.657335
$711$		0			0
$712$			10496.2i			0.552476i
$713$	−3179.94			−0.167026
$714$		0			0
$715$	129.740			0.00678603
$716$			14646.5i			0.764479i
$717$		0			0
$718$	−2233.57			−0.116095
$719$	−17606.4			−0.913225			−0.456613	−	0.889666i	$-0.650937\pi$
$719$	−17606.4			−0.913225			−0.456613	+	0.889666i	$0.650937\pi$
$720$		0			0
$721$	−22912.3	+	937.751i	−1.18349	+	0.0484378i
$722$		−	541.411i		−	0.0279075i
$723$		0			0
$724$			17238.5i			0.884895i
$725$			16446.4i			0.842486i
$726$		0			0
$727$			5209.41i			0.265758i	0.991132	+	0.132879i	$0.0424222\pi$
$727$			5209.41i			0.265758i	−0.991132	+	0.132879i	$0.957578\pi$
$728$	439.757	+	10744.7i	0.0223880	+	0.547012i
$729$		0			0
$730$	1806.46			0.0915891
$731$	632.356			0.0319953
$732$		0			0
$733$			2004.06i			0.100984i	0.998724	+	0.0504922i	$0.0160790\pi$
$733$			2004.06i			0.100984i	−0.998724	+	0.0504922i	$0.983921\pi$
$734$	15305.7			0.769680
$735$		0			0
$736$	−2022.82			−0.101307
$737$		−	40.3939i		−	0.00201890i
$738$		0			0
$739$	3694.38			0.183897			0.0919485	−	0.995764i	$-0.470690\pi$
$739$	3694.38			0.183897			0.0919485	+	0.995764i	$0.470690\pi$
$740$	−6769.65			−0.336293
$741$		0			0
$742$	−307.365	−	7509.93i	−0.0152072	−	0.371561i
$743$		−	15503.5i		−	0.765502i	−0.923851	−	0.382751i	$-0.874977\pi$
$743$		−	15503.5i		−	0.765502i	0.923851	−	0.382751i	$-0.125023\pi$
$744$		0			0
$745$			13258.2i			0.652003i
$746$		−	22984.1i		−	1.12803i
$747$		0			0
$748$		−	53.5208i		−	0.00261620i
$749$	−30773.8	+	1259.50i	−1.50127	+	0.0614436i
$750$		0			0
$751$	13993.6			0.679937			0.339968	−	0.940437i	$-0.389584\pi$
$751$	13993.6			0.679937			0.339968	+	0.940437i	$0.389584\pi$
$752$	6778.02			0.328682
$753$		0			0
$754$			26569.8i			1.28331i
$755$	9523.53			0.459069
$756$		0			0
$757$	−21959.1			−1.05431			−0.527157	−	0.849768i	$-0.676742\pi$
$757$	−21959.1			−1.05431			−0.527157	+	0.849768i	$0.676742\pi$
$758$			16373.1i			0.784561i
$759$		0			0
$760$	4004.71			0.191140
$761$	20362.1			0.969939			0.484970	−	0.874531i	$-0.338831\pi$
$761$	20362.1			0.969939			0.484970	+	0.874531i	$0.338831\pi$
$762$		0			0
$763$	1048.83	+	25626.4i	0.0497644	+	1.21591i
$764$		−	16860.0i		−	0.798392i
$765$		0			0
$766$		−	4140.01i		−	0.195280i
$767$			53305.8i			2.50947i
$768$		0			0
$769$			11078.4i			0.519501i	0.965676	+	0.259750i	$0.0836403\pi$
$769$			11078.4i			0.519501i	−0.965676	+	0.259750i	$0.916360\pi$
$770$	2.70761	+	66.1558i	0.000126722	+	0.00309622i
$771$		0			0
$772$	−5789.06			−0.269887
$773$	−32027.3			−1.49022			−0.745112	−	0.666939i	$-0.767604\pi$
$773$	−32027.3			−1.49022			−0.745112	+	0.666939i	$0.767604\pi$
$774$		0			0
$775$		−	4520.05i		−	0.209503i
$776$	−3277.06			−0.151598
$777$		0			0
$778$	1282.74			0.0591112
$779$			18249.4i			0.839348i
$780$		0			0
$781$	−316.234			−0.0144888
$782$	5610.37			0.256555
$783$		0			0
$784$	−5469.65	+	448.472i	−0.249164	+	0.0204297i
$785$		−	8239.43i		−	0.374621i
$786$		0			0
$787$		−	17955.9i		−	0.813287i	−0.913587	−	0.406644i	$-0.866699\pi$
$787$		−	17955.9i		−	0.813287i	0.913587	−	0.406644i	$-0.133301\pi$
$788$		−	2098.78i		−	0.0948808i
$789$		0			0
$790$			9718.90i			0.437700i
$791$	23033.9	−	942.728i	1.03539	−	0.0423762i
$792$		0			0
$793$	46003.5			2.06007
$794$	20992.5			0.938281
$795$		0			0
$796$		−	967.219i		−	0.0430681i
$797$	−34542.4			−1.53520			−0.767601	−	0.640928i	$-0.778550\pi$
$797$	−34542.4			−1.53520			−0.767601	+	0.640928i	$0.778550\pi$
$798$		0			0
$799$	−18799.1			−0.832370
$800$		−	2875.29i		−	0.127071i
$801$		0			0
$802$	17724.7			0.780401
$803$	−45.9369			−0.00201878
$804$		0			0
$805$	−6934.84	+	283.828i	−0.303629	+	0.0124269i
$806$		−	7302.34i		−	0.319124i
$807$		0			0
$808$			14598.1i			0.635592i
$809$		−	33624.2i		−	1.46127i	−0.682770	−	0.730633i	$-0.739225\pi$
$809$		−	33624.2i		−	1.46127i	0.682770	−	0.730633i	$-0.260775\pi$
$810$		0			0
$811$			27864.3i			1.20647i	0.797563	+	0.603235i	$0.206122\pi$
$811$			27864.3i			1.20647i	−0.797563	+	0.603235i	$0.793878\pi$
$812$	−13548.2	+	554.498i	−0.585528	+	0.0239644i
$813$		0			0
$814$	172.147			0.00741248
$815$	10316.4			0.443398
$816$		0			0
$817$		−	1203.22i		−	0.0515242i
$818$	−17793.3			−0.760546
$819$		0			0
$820$	−5125.28			−0.218271
$821$		−	25524.8i		−	1.08505i	−0.840041	−	0.542523i	$-0.817469\pi$
$821$		−	25524.8i		−	1.08505i	0.840041	−	0.542523i	$-0.182531\pi$
$822$		0			0
$823$	−34757.5			−1.47214			−0.736069	−	0.676907i	$-0.763320\pi$
$823$	−34757.5			−1.47214			−0.736069	+	0.676907i	$0.763320\pi$
$824$	9905.48			0.418779
$825$		0			0
$826$	−27181.2	+	1112.46i	−1.14498	+	0.0468615i
$827$		−	11443.1i		−	0.481155i	−0.970630	−	0.240577i	$-0.922663\pi$
$827$		−	11443.1i		−	0.481155i	0.970630	−	0.240577i	$-0.0773368\pi$
$828$		0			0
$829$		−	20680.2i		−	0.866410i	−0.901295	−	0.433205i	$-0.857383\pi$
$829$		−	20680.2i		−	0.866410i	0.901295	−	0.433205i	$-0.142617\pi$
$830$		−	6914.68i		−	0.289171i
$831$		0			0
$832$		−	4645.16i		−	0.193560i
$833$	15170.2	−	1243.85i	0.630994	−	0.0517370i
$834$		0			0
$835$	24171.4			1.00178
$836$	−101.837			−0.00421304
$837$		0			0
$838$		−	29483.8i		−	1.21540i
$839$	−18946.5			−0.779626			−0.389813	−	0.920894i	$-0.627460\pi$
$839$	−18946.5			−0.779626			−0.389813	+	0.920894i	$0.627460\pi$
$840$		0			0
$841$	−9113.39			−0.373668
$842$			1682.17i			0.0688498i
$843$		0			0
$844$	1703.23			0.0694640
$845$	−18206.1			−0.741193
$846$		0			0
$847$	1007.98	+	24628.2i	0.0408908	+	0.999095i
$848$			3246.70i			0.131477i
$849$		0			0
$850$			7974.71i			0.321800i
$851$			18045.5i			0.726899i
$852$		0			0
$853$		−	31070.4i		−	1.24716i	−0.781758	−	0.623582i	$-0.785677\pi$
$853$		−	31070.4i		−	1.24716i	0.781758	−	0.623582i	$-0.214323\pi$
$854$	960.069	+	23457.6i	0.0384694	+	0.939934i
$855$		0			0
$856$	13304.2			0.531223
$857$	4547.25			0.181250			0.0906249	−	0.995885i	$-0.471114\pi$
$857$	4547.25			0.181250			0.0906249	+	0.995885i	$0.471114\pi$
$858$		0			0
$859$		−	9345.98i		−	0.371223i	−0.982623	−	0.185612i	$-0.940573\pi$
$859$		−	9345.98i		−	0.371223i	0.982623	−	0.185612i	$-0.0594266\pi$
$860$	337.920			0.0133988
$861$		0			0
$862$	15415.1			0.609097
$863$			46599.6i			1.83809i	0.394155	+	0.919044i	$0.371037\pi$
$863$			46599.6i			1.83809i	−0.394155	+	0.919044i	$0.628963\pi$
$864$		0			0
$865$	−6817.52			−0.267980
$866$	−19351.2			−0.759329
$867$		0			0
$868$	3723.53	−	152.396i	0.145605	−	0.00595928i
$869$		−	247.145i		−	0.00964765i
$870$		0			0
$871$			9723.60i			0.378268i
$872$		−	11078.8i		−	0.430248i
$873$		0			0
$874$		−	10675.1i		−	0.413149i
$875$	−964.691	−	23570.6i	−0.0372714	−	0.910663i
$876$		0			0
$877$	28853.5			1.11096			0.555482	−	0.831529i	$-0.312534\pi$
$877$	28853.5			1.11096			0.555482	+	0.831529i	$0.312534\pi$
$878$	−12888.3			−0.495398
$879$		0			0
$880$		−	28.6006i		−	0.00109560i
$881$	−5508.01			−0.210635			−0.105317	−	0.994439i	$-0.533586\pi$
$881$	−5508.01			−0.210635			−0.105317	+	0.994439i	$0.533586\pi$
$882$		0			0
$883$	23461.7			0.894168			0.447084	−	0.894492i	$-0.352463\pi$
$883$	23461.7			0.894168			0.447084	+	0.894492i	$0.352463\pi$
$884$			12883.5i			0.490180i
$885$		0			0
$886$	−545.760			−0.0206943
$887$	31840.3			1.20529			0.602646	−	0.798009i	$-0.294113\pi$
$887$	31840.3			1.20529			0.602646	+	0.798009i	$0.294113\pi$
$888$		0			0
$889$	−1138.38	−	27814.3i	−0.0429470	−	1.04934i
$890$		−	15556.8i		−	0.585914i
$891$		0			0
$892$		−	23469.0i		−	0.880943i
$893$			35770.0i			1.34042i
$894$		0			0
$895$		−	21708.0i		−	0.810748i
$896$	2368.61	−	96.9420i	0.0883144	−	0.00361451i
$897$		0			0
$898$	−1199.35			−0.0445689
$899$	9207.66			0.341594
$900$		0			0
$901$		−	9004.84i		−	0.332957i
$902$	130.332			0.00481107
$903$		0			0
$904$	−9958.05			−0.366372
$905$		−	25549.7i		−	0.938452i
$906$		0			0
$907$	−25415.8			−0.930451			−0.465225	−	0.885192i	$-0.654027\pi$
$907$	−25415.8			−0.930451			−0.465225	+	0.885192i	$0.654027\pi$
$908$	−15358.3			−0.561325
$909$		0			0
$910$	−651.775	−	15925.0i	−0.0237430	−	0.580119i
$911$		−	45216.6i		−	1.64445i	−0.569165	−	0.822224i	$-0.692733\pi$
$911$		−	45216.6i		−	1.64445i	0.569165	−	0.822224i	$-0.307267\pi$
$912$		0			0
$913$			175.835i			0.00637382i
$914$			1890.25i			0.0684071i
$915$		0			0
$916$		−	9609.24i		−	0.346614i
$917$	944.024	+	23065.6i	0.0339961	+	0.830635i
$918$		0			0
$919$	−25172.0			−0.903534			−0.451767	−	0.892136i	$-0.649206\pi$
$919$	−25172.0			−0.903534			−0.451767	+	0.892136i	$0.649206\pi$
$920$	2998.08			0.107439
$921$		0			0
$922$		−	2328.85i		−	0.0831850i
$923$	76123.6			2.71467
$924$		0			0
$925$	−25650.3			−0.911758
$926$			34625.6i			1.22880i
$927$		0			0
$928$	5857.17			0.207189
$929$	−6261.47			−0.221133			−0.110566	−	0.993869i	$-0.535266\pi$
$929$	−6261.47			−0.221133			−0.110566	+	0.993869i	$0.535266\pi$
$930$		0			0
$931$	−2366.74	−	28865.2i	−0.0833157	−	1.01613i
$932$		−	8689.77i		−	0.305411i
$933$		0			0
$934$		−	2387.63i		−	0.0836462i
$935$			79.3246i			0.00277454i
$936$		0			0
$937$		−	11786.7i		−	0.410946i	−0.978663	−	0.205473i	$-0.934127\pi$
$937$		−	11786.7i		−	0.410946i	0.978663	−	0.205473i	$-0.0658732\pi$
$938$	−4958.16	+	202.926i	−0.172590	+	0.00706373i
$939$		0			0
$940$	−10045.9			−0.348575
$941$	27129.7			0.939854			0.469927	−	0.882705i	$-0.344280\pi$
$941$	27129.7			0.939854			0.469927	+	0.882705i	$0.344280\pi$
$942$		0			0
$943$			13662.2i			0.471794i
$944$	11751.0			0.405150
$945$		0			0
$946$	−8.59305			−0.000295332
$947$		−	25850.3i		−	0.887035i	−0.896266	−	0.443517i	$-0.853730\pi$
$947$		−	25850.3i		−	0.887035i	0.896266	−	0.443517i	$-0.146270\pi$
$948$		0			0
$949$	11057.9			0.378246
$950$	15173.9			0.518217
$951$		0			0
$952$	−6569.42	+	268.872i	−0.223651	+	0.00915356i
$953$			832.068i			0.0282826i	0.999900	+	0.0141413i	$0.00450147\pi$
$953$			832.068i			0.0282826i	−0.999900	+	0.0141413i	$0.995499\pi$
$954$		0			0
$955$			24988.6i			0.846714i
$956$			4522.27i			0.152992i
$957$		0			0
$958$		−	27369.5i		−	0.923034i
$959$	25991.1	−	1063.76i	0.875180	−	0.0358192i
$960$		0			0
$961$	27260.4			0.915055
$962$	−41439.2			−1.38883
$963$		0			0
$964$		−	18862.6i		−	0.630210i
$965$	8580.12			0.286222
$966$		0			0
$967$	51021.0			1.69672			0.848358	−	0.529423i	$-0.177592\pi$
$967$	51021.0			1.69672			0.848358	+	0.529423i	$0.177592\pi$
$968$		−	10647.3i		−	0.353529i
$969$		0			0
$970$	4857.02			0.160773
$971$	15178.0			0.501633			0.250816	−	0.968035i	$-0.419301\pi$
$971$	15178.0			0.501633			0.250816	+	0.968035i	$0.419301\pi$
$972$		0			0
$973$	−22300.9	+	912.726i	−0.734772	+	0.0300726i
$974$		−	15862.6i		−	0.521837i
$975$		0			0
$976$		−	10141.2i		−	0.332595i
$977$			39453.3i			1.29194i	0.763363	+	0.645969i	$0.223547\pi$
$977$			39453.3i			1.29194i	−0.763363	+	0.645969i	$0.776453\pi$
$978$		0			0
$979$			395.597i			0.0129145i
$980$	8106.71	−	664.693i	0.264244	−	0.0216662i
$981$		0			0
$982$	972.492			0.0316023
$983$	43663.2			1.41672			0.708361	−	0.705850i	$-0.249435\pi$
$983$	43663.2			1.41672			0.708361	+	0.705850i	$0.249435\pi$
$984$		0			0
$985$			3110.66i			0.100623i
$986$	−16245.1			−0.524694
$987$		0			0
$988$	24514.1			0.789370
$989$		−	900.774i		−	0.0289615i
$990$		0			0
$991$	−8556.56			−0.274277			−0.137138	−	0.990552i	$-0.543790\pi$
$991$	−8556.56			−0.274277			−0.137138	+	0.990552i	$0.543790\pi$
$992$	−1609.76			−0.0515222
$993$		0			0
$994$	1588.66	+	38816.2i	0.0506934	+	1.23861i
$995$			1433.54i			0.0456747i
$996$		0			0
$997$			795.996i			0.0252853i	0.999920	+	0.0126426i	$0.00402439\pi$
$997$			795.996i			0.0252853i	−0.999920	+	0.0126426i	$0.995976\pi$
$998$		−	37865.7i		−	1.20102i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.d.a.125.7	yes	8
3.2	odd	2	inner	126.4.d.a.125.2	✓	8
4.3	odd	2		1008.4.k.c.881.5		8
7.2	even	3		882.4.k.c.521.6		16
7.3	odd	6		882.4.k.c.215.3		16
7.4	even	3		882.4.k.c.215.2		16
7.5	odd	6		882.4.k.c.521.7		16
7.6	odd	2	inner	126.4.d.a.125.6	yes	8
12.11	even	2		1008.4.k.c.881.3		8
21.2	odd	6		882.4.k.c.521.3		16
21.5	even	6		882.4.k.c.521.2		16
21.11	odd	6		882.4.k.c.215.7		16
21.17	even	6		882.4.k.c.215.6		16
21.20	even	2	inner	126.4.d.a.125.3	yes	8
28.27	even	2		1008.4.k.c.881.4		8
84.83	odd	2		1008.4.k.c.881.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.d.a.125.2	✓	8	3.2	odd	2	inner
126.4.d.a.125.3	yes	8	21.20	even	2	inner
126.4.d.a.125.6	yes	8	7.6	odd	2	inner
126.4.d.a.125.7	yes	8	1.1	even	1	trivial
882.4.k.c.215.2		16	7.4	even	3
882.4.k.c.215.3		16	7.3	odd	6
882.4.k.c.215.6		16	21.17	even	6
882.4.k.c.215.7		16	21.11	odd	6
882.4.k.c.521.2		16	21.5	even	6
882.4.k.c.521.3		16	21.2	odd	6
882.4.k.c.521.6		16	7.2	even	3
882.4.k.c.521.7		16	7.5	odd	6
1008.4.k.c.881.3		8	12.11	even	2
1008.4.k.c.881.4		8	28.27	even	2
1008.4.k.c.881.5		8	4.3	odd	2
1008.4.k.c.881.6		8	84.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -4.00000 q^{4} +5.92851 q^{5} +(0.757359 + 18.5048i) q^{7} -8.00000i q^{8} +O(q^{10})\)	\(q+2.00000i q^{2} -4.00000 q^{4} +5.92851 q^{5} +(0.757359 + 18.5048i) q^{7} -8.00000i q^{8} +11.8570i q^{10} -0.301515i q^{11} +72.5806i q^{13} +(-37.0095 + 1.51472i) q^{14} +16.0000 q^{16} -44.3765 q^{17} +84.4376i q^{19} -23.7140 q^{20} +0.603030 q^{22} +63.2132i q^{23} -89.8528 q^{25} -145.161 q^{26} +(-3.02944 - 74.0191i) q^{28} -183.037i q^{29} +50.3050i q^{31} +32.0000i q^{32} -88.7531i q^{34} +(4.49001 + 109.706i) q^{35} +285.470 q^{37} -168.875 q^{38} -47.4280i q^{40} +216.129 q^{41} -14.2498 q^{43} +1.20606i q^{44} -126.426 q^{46} +423.626 q^{47} +(-341.853 + 28.0295i) q^{49} -179.706i q^{50} -290.322i q^{52} +202.919i q^{53} -1.78753i q^{55} +(148.038 - 6.05887i) q^{56} +366.073 q^{58} +734.437 q^{59} -633.827i q^{61} -100.610 q^{62} -64.0000 q^{64} +430.294i q^{65} +133.970 q^{67} +177.506 q^{68} +(-219.411 + 8.98002i) q^{70} -1048.82i q^{71} -152.354i q^{73} +570.940i q^{74} -337.750i q^{76} +(5.57947 - 0.228355i) q^{77} +819.675 q^{79} +94.8561 q^{80} +432.257i q^{82} -583.173 q^{83} -263.087 q^{85} -28.4996i q^{86} -2.41212 q^{88} -1312.03 q^{89} +(-1343.09 + 54.9696i) q^{91} -252.853i q^{92} +847.253i q^{94} +500.589i q^{95} -409.633i q^{97} +(-56.0590 - 683.706i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} + 40 q^{7}+O(q^{10}) \) 8 * q - 32 * q^4 + 40 * q^7	\( 8 q - 32 q^{4} + 40 q^{7} + 128 q^{16} + 480 q^{22} - 40 q^{25} - 160 q^{28} - 160 q^{37} + 1040 q^{43} - 672 q^{46} - 2056 q^{49} + 960 q^{58} - 512 q^{64} - 3680 q^{67} + 960 q^{70} + 448 q^{79} + 6720 q^{85} - 1920 q^{88} - 1920 q^{91}+O(q^{100}) \) 8 * q - 32 * q^4 + 40 * q^7 + 128 * q^16 + 480 * q^22 - 40 * q^25 - 160 * q^28 - 160 * q^37 + 1040 * q^43 - 672 * q^46 - 2056 * q^49 + 960 * q^58 - 512 * q^64 - 3680 * q^67 + 960 * q^70 + 448 * q^79 + 6720 * q^85 - 1920 * q^88 - 1920 * q^91

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