LMFDB - Embedded newform 325.4.d.e.324.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,4,Mod(324,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.324"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	325.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [28,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$19.1756207519$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			324.27
Character	$\chi$	$=$	325.324
Dual form			325.4.d.e.324.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+5.39779 q^{2} -9.57032i q^{3} +21.1361 q^{4} -51.6586i q^{6} +19.5662 q^{7} +70.9061 q^{8} -64.5911 q^{9} -22.1851i q^{11} -202.280i q^{12} +(-22.2600 + 41.2492i) q^{13} +105.614 q^{14} +213.647 q^{16} -3.19819i q^{17} -348.649 q^{18} +79.9778i q^{19} -187.255i q^{21} -119.751i q^{22} +81.6896i q^{23} -678.595i q^{24} +(-120.155 + 222.654i) q^{26} +359.759i q^{27} +413.555 q^{28} -15.5101 q^{29} +27.4476i q^{31} +585.974 q^{32} -212.319 q^{33} -17.2632i q^{34} -1365.21 q^{36} -418.722 q^{37} +431.703i q^{38} +(394.768 + 213.035i) q^{39} -253.693i q^{41} -1010.76i q^{42} -83.2815i q^{43} -468.908i q^{44} +440.943i q^{46} +388.997 q^{47} -2044.67i q^{48} +39.8376 q^{49} -30.6078 q^{51} +(-470.490 + 871.848i) q^{52} +92.5015i q^{53} +1941.90i q^{54} +1387.37 q^{56} +765.413 q^{57} -83.7202 q^{58} -385.328i q^{59} +734.366 q^{61} +148.156i q^{62} -1263.80 q^{63} +1453.79 q^{64} -1146.05 q^{66} -138.626 q^{67} -67.5975i q^{68} +781.796 q^{69} +497.037i q^{71} -4579.90 q^{72} -716.898 q^{73} -2260.17 q^{74} +1690.42i q^{76} -434.079i q^{77} +(2130.87 + 1149.92i) q^{78} -425.224 q^{79} +1699.05 q^{81} -1369.38i q^{82} +793.338 q^{83} -3957.85i q^{84} -449.536i q^{86} +148.436i q^{87} -1573.06i q^{88} +1007.38i q^{89} +(-435.544 + 807.091i) q^{91} +1726.60i q^{92} +262.682 q^{93} +2099.73 q^{94} -5607.96i q^{96} +740.271 q^{97} +215.035 q^{98} +1432.96i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 112 q^{4} - 316 q^{9} + 184 q^{14} + 560 q^{16} - 568 q^{26} - 36 q^{29} - 4168 q^{36} + 1120 q^{39} - 576 q^{49} + 1072 q^{51} + 4984 q^{56} + 260 q^{61} + 5328 q^{64} - 3960 q^{66} + 4280 q^{69}+ \cdots + 11848 q^{94}+O(q^{100}) $ 28 * q + 112 * q^4 - 316 * q^9 + 184 * q^14 + 560 * q^16 - 568 * q^26 - 36 * q^29 - 4168 * q^36 + 1120 * q^39 - 576 * q^49 + 1072 * q^51 + 4984 * q^56 + 260 * q^61 + 5328 * q^64 - 3960 * q^66 + 4280 * q^69 - 10704 * q^74 - 2512 * q^79 + 8860 * q^81 + 1952 * q^91 + 11848 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$-1$

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 $

$2$	5.39779			1.90841			0.954204	−	0.299158i	$-0.0967058\pi$
$2$	5.39779			1.90841			0.954204	+	0.299158i	$0.0967058\pi$
$3$		−	9.57032i		−	1.84181i	−0.389788	−	0.920905i	$-0.627452\pi$
$3$		−	9.57032i		−	1.84181i	0.389788	−	0.920905i	$-0.372548\pi$
$4$	21.1361			2.64202
$5$		0			0
$5$		0			0
$6$		−	51.6586i		−	3.51492i
$7$	19.5662			1.05648			0.528239	−	0.849096i	$-0.322853\pi$
$7$	19.5662			1.05648			0.528239	+	0.849096i	$0.322853\pi$
$8$	70.9061			3.13364
$9$	−64.5911			−2.39226
$10$		0			0
$11$		−	22.1851i		−	0.608097i	−0.952657	−	0.304049i	$-0.901662\pi$
$11$		−	22.1851i		−	0.608097i	0.952657	−	0.304049i	$-0.0983385\pi$
$12$		−	202.280i		−	4.86609i
$13$	−22.2600	+	41.2492i	−0.474908	+	0.880035i
$13$	−22.2600	+	41.2492i	−0.474908	+	0.880035i
$14$	105.614			2.01619
$15$		0			0
$16$	213.647			3.33824
$17$		−	3.19819i		−	0.0456280i	−0.999740	−	0.0228140i	$-0.992737\pi$
$17$		−	3.19819i		−	0.0456280i	0.999740	−	0.0228140i	$-0.00726255\pi$
$18$	−348.649			−4.56541
$19$			79.9778i			0.965693i	0.875705	+	0.482846i	$0.160397\pi$
$19$			79.9778i			0.965693i	−0.875705	+	0.482846i	$0.839603\pi$
$20$		0			0
$21$		−	187.255i		−	1.94583i
$22$		−	119.751i		−	1.16050i
$23$			81.6896i			0.740585i	0.928915	+	0.370293i	$0.120743\pi$
$23$			81.6896i			0.740585i	−0.928915	+	0.370293i	$0.879257\pi$
$24$		−	678.595i		−	5.77156i
$25$		0			0
$26$	−120.155	+	222.654i	−0.906318	+	1.67947i
$27$			359.759i			2.56428i
$28$	413.555			2.79123
$29$	−15.5101			−0.0993155			−0.0496577	−	0.998766i	$-0.515813\pi$
$29$	−15.5101			−0.0993155			−0.0496577	+	0.998766i	$0.515813\pi$
$30$		0			0
$31$			27.4476i			0.159023i	0.996834	+	0.0795117i	$0.0253361\pi$
$31$			27.4476i			0.159023i	−0.996834	+	0.0795117i	$0.974664\pi$
$32$	585.974			3.23708
$33$	−212.319			−1.12000
$34$		−	17.2632i		−	0.0870768i
$35$		0			0
$36$	−1365.21			−6.32040
$37$	−418.722			−1.86047			−0.930236	−	0.366963i	$-0.880398\pi$
$37$	−418.722			−1.86047			−0.930236	+	0.366963i	$0.880398\pi$
$38$			431.703i			1.84294i
$39$	394.768	+	213.035i	1.62086	+	0.874690i
$40$		0			0
$41$		−	253.693i		−	0.966346i	−0.875525	−	0.483173i	$-0.839484\pi$
$41$		−	253.693i		−	0.966346i	0.875525	−	0.483173i	$-0.160516\pi$
$42$		−	1010.76i		−	3.71344i
$43$		−	83.2815i		−	0.295356i	−0.989035	−	0.147678i	$-0.952820\pi$
$43$		−	83.2815i		−	0.295356i	0.989035	−	0.147678i	$-0.0471799\pi$
$44$		−	468.908i		−	1.60660i
$45$		0			0
$46$			440.943i			1.41334i
$47$	388.997			1.20726			0.603628	−	0.797266i	$-0.293721\pi$
$47$	388.997			1.20726			0.603628	+	0.797266i	$0.293721\pi$
$48$		−	2044.67i		−	6.14840i
$49$	39.8376			0.116145
$50$		0			0
$51$	−30.6078			−0.0840381
$52$	−470.490	+	871.848i	−1.25472	+	2.32507i
$53$			92.5015i			0.239737i	0.992790	+	0.119868i	$0.0382473\pi$
$53$			92.5015i			0.239737i	−0.992790	+	0.119868i	$0.961753\pi$
$54$			1941.90i			4.89369i
$55$		0			0
$56$	1387.37			3.31062
$57$	765.413			1.77862
$58$	−83.7202			−0.189534
$59$		−	385.328i		−	0.850262i	−0.905132	−	0.425131i	$-0.860228\pi$
$59$		−	385.328i		−	0.850262i	0.905132	−	0.425131i	$-0.139772\pi$
$60$		0			0
$61$	734.366			1.54141			0.770704	−	0.637193i	$-0.219905\pi$
$61$	734.366			1.54141			0.770704	+	0.637193i	$0.219905\pi$
$62$			148.156i			0.303482i
$63$	−1263.80			−2.52737
$64$	1453.79			2.83943
$65$		0			0
$66$	−1146.05			−2.13741
$67$	−138.626			−0.252774			−0.126387	−	0.991981i	$-0.540338\pi$
$67$	−138.626			−0.252774			−0.126387	+	0.991981i	$0.540338\pi$
$68$		−	67.5975i		−	0.120550i
$69$	781.796			1.36402
$70$		0			0
$71$			497.037i			0.830809i	0.909637	+	0.415404i	$0.136360\pi$
$71$			497.037i			0.830809i	−0.909637	+	0.415404i	$0.863640\pi$
$72$	−4579.90			−7.49648
$73$	−716.898			−1.14941			−0.574703	−	0.818362i	$-0.694882\pi$
$73$	−716.898			−1.14941			−0.574703	+	0.818362i	$0.694882\pi$
$74$	−2260.17			−3.55054
$75$		0			0
$76$			1690.42i			2.55138i
$77$		−	434.079i		−	0.642441i
$78$	2130.87	+	1149.92i	3.09326	+	1.66926i
$79$	−425.224			−0.605588			−0.302794	−	0.953056i	$-0.597919\pi$
$79$	−425.224			−0.605588			−0.302794	+	0.953056i	$0.597919\pi$
$80$		0			0
$81$	1699.05			2.33066
$82$		−	1369.38i		−	1.84418i
$83$	793.338			1.04916			0.524579	−	0.851362i	$-0.324223\pi$
$83$	793.338			1.04916			0.524579	+	0.851362i	$0.324223\pi$
$84$		−	3957.85i		−	5.14092i
$85$		0			0
$86$		−	449.536i		−	0.563659i
$87$			148.436i			0.182920i
$88$		−	1573.06i		−	1.90556i
$89$			1007.38i			1.19980i	0.800074	+	0.599901i	$0.204793\pi$
$89$			1007.38i			1.19980i	−0.800074	+	0.599901i	$0.795207\pi$
$90$		0			0
$91$	−435.544	+	807.091i	−0.501730	+	0.929738i
$92$			1726.60i			1.95664i
$93$	262.682			0.292891
$94$	2099.73			2.30394
$95$		0			0
$96$		−	5607.96i		−	5.96209i
$97$	740.271			0.774878			0.387439	−	0.921895i	$-0.373360\pi$
$97$	740.271			0.774878			0.387439	+	0.921895i	$0.373360\pi$
$98$	215.035			0.221651
$99$			1432.96i			1.45473i
$100$		0			0
$101$	1241.26			1.22287			0.611435	−	0.791295i	$-0.290593\pi$
$101$	1241.26			1.22287			0.611435	+	0.791295i	$0.290593\pi$
$102$	−165.214			−0.160379
$103$		−	539.693i		−	0.516286i	−0.966107	−	0.258143i	$-0.916889\pi$
$103$		−	539.693i		−	0.516286i	0.966107	−	0.258143i	$-0.0831106\pi$
$104$	−1578.37	+	2924.82i	−1.48819	+	2.75771i
$105$		0			0
$106$			499.304i			0.457516i
$107$			1978.96i			1.78798i	0.448092	+	0.893988i	$0.352104\pi$
$107$			1978.96i			1.78798i	−0.448092	+	0.893988i	$0.647896\pi$
$108$			7603.91i			6.77488i
$109$		−	695.416i		−	0.611089i	−0.952178	−	0.305545i	$-0.901161\pi$
$109$		−	695.416i		−	0.611089i	0.952178	−	0.305545i	$-0.0988386\pi$
$110$		0			0
$111$			4007.30i			3.42663i
$112$	4180.27			3.52677
$113$		−	929.958i		−	0.774187i	−0.922041	−	0.387093i	$-0.873479\pi$
$113$		−	929.958i		−	0.774187i	0.922041	−	0.387093i	$-0.126521\pi$
$114$	4131.54			3.39434
$115$		0			0
$116$	−327.823			−0.262393
$117$	1437.80	−	2664.33i	1.13610	−	2.10528i
$118$		−	2079.92i		−	1.62265i
$119$		−	62.5766i		−	0.0482050i
$120$		0			0
$121$	838.820			0.630218
$122$	3963.95			2.94164
$123$	−2427.92			−1.77982
$124$			580.136i			0.420143i
$125$		0			0
$126$	−6821.75			−4.82325
$127$		−	1018.39i		−	0.711558i	−0.934570	−	0.355779i	$-0.884216\pi$
$127$		−	1018.39i		−	0.711558i	0.934570	−	0.355779i	$-0.115784\pi$
$128$	3159.45			2.18171
$129$	−797.031			−0.543989
$130$		0			0
$131$	181.321			0.120932			0.0604659	−	0.998170i	$-0.480741\pi$
$131$	181.321			0.120932			0.0604659	+	0.998170i	$0.480741\pi$
$132$	−4487.60			−2.95906
$133$			1564.86i			1.02023i
$134$	−748.274			−0.482395
$135$		0			0
$136$		−	226.772i		−	0.142982i
$137$	−16.8451			−0.0105049			−0.00525245	−	0.999986i	$-0.501672\pi$
$137$	−16.8451			−0.0105049			−0.00525245	+	0.999986i	$0.501672\pi$
$138$	4219.97			2.60310
$139$	303.101			0.184954			0.0924772	−	0.995715i	$-0.470521\pi$
$139$	303.101			0.184954			0.0924772	+	0.995715i	$0.470521\pi$
$140$		0			0
$141$		−	3722.83i		−	2.22354i
$142$			2682.90i			1.58552i
$143$	915.118	+	493.840i	0.535147	+	0.288790i
$144$	−13799.7			−7.98594
$145$		0			0
$146$	−3869.67			−2.19353
$147$		−	381.258i		−	0.213916i
$148$	−8850.16			−4.91540
$149$		−	908.684i		−	0.499612i	−0.968296	−	0.249806i	$-0.919633\pi$
$149$		−	908.684i		−	0.499612i	0.968296	−	0.249806i	$-0.0803669\pi$
$150$		0			0
$151$		−	2598.33i		−	1.40032i	−0.713985	−	0.700161i	$-0.753111\pi$
$151$		−	2598.33i		−	1.40032i	0.713985	−	0.700161i	$-0.246889\pi$
$152$			5670.92i			3.02613i
$153$			206.575i			0.109154i
$154$		−	2343.07i		−	1.22604i
$155$		0			0
$156$	8343.87	+	4502.74i	4.28233	+	2.31095i
$157$		−	2512.22i		−	1.27705i	−0.769600	−	0.638526i	$-0.779544\pi$
$157$		−	2512.22i		−	1.27705i	0.769600	−	0.638526i	$-0.220456\pi$
$158$	−2295.27			−1.15571
$159$	885.269			0.441550
$160$		0			0
$161$			1598.36i			0.782412i
$162$	9171.11			4.44784
$163$	−2128.77			−1.02293			−0.511467	−	0.859303i	$-0.670898\pi$
$163$	−2128.77			−1.02293			−0.511467	+	0.859303i	$0.670898\pi$
$164$		−	5362.09i		−	2.55310i
$165$		0			0
$166$	4282.27			2.00222
$167$	−1924.60			−0.891798			−0.445899	−	0.895083i	$-0.647116\pi$
$167$	−1924.60			−0.891798			−0.445899	+	0.895083i	$0.647116\pi$
$168$		−	13277.5i		−	6.09753i
$169$	−1205.99	−	1836.41i	−0.548925	−	0.835872i
$170$		0			0
$171$		−	5165.85i		−	2.31019i
$172$		−	1760.25i		−	0.780336i
$173$			3623.82i			1.59256i	0.604926	+	0.796282i	$0.293203\pi$
$173$			3623.82i			1.59256i	−0.604926	+	0.796282i	$0.706797\pi$
$174$			801.229i			0.349086i
$175$		0			0
$176$		−	4739.79i		−	2.02997i
$177$	−3687.71			−1.56602
$178$			5437.64i			2.28971i
$179$	−2895.47			−1.20904			−0.604518	−	0.796592i	$-0.706634\pi$
$179$	−2895.47			−1.20904			−0.604518	+	0.796592i	$0.706634\pi$
$180$		0			0
$181$	−1833.42			−0.752913			−0.376457	−	0.926434i	$-0.622858\pi$
$181$	−1833.42			−0.752913			−0.376457	+	0.926434i	$0.622858\pi$
$182$	−2350.97	+	4356.51i	−0.957504	+	1.77432i
$183$		−	7028.12i		−	2.83898i
$184$			5792.29i			2.32073i
$185$		0			0
$186$	1417.90			0.558955
$187$	−70.9524			−0.0277463
$188$	8221.90			3.18959
$189$			7039.13i			2.70911i
$190$		0			0
$191$	−1377.00			−0.521654			−0.260827	−	0.965385i	$-0.583995\pi$
$191$	−1377.00			−0.521654			−0.260827	+	0.965385i	$0.583995\pi$
$192$		−	13913.2i		−	5.22969i
$193$	−3493.38			−1.30290			−0.651449	−	0.758693i	$-0.725838\pi$
$193$	−3493.38			−1.30290			−0.651449	+	0.758693i	$0.725838\pi$
$194$	3995.83			1.47878
$195$		0			0
$196$	842.012			0.306856
$197$	−4698.05			−1.69910			−0.849549	−	0.527510i	$-0.823126\pi$
$197$	−4698.05			−1.69910			−0.849549	+	0.527510i	$0.823126\pi$
$198$			7734.82i			2.77621i
$199$	622.741			0.221834			0.110917	−	0.993830i	$-0.464621\pi$
$199$	622.741			0.221834			0.110917	+	0.993830i	$0.464621\pi$
$200$		0			0
$201$			1326.69i			0.465561i
$202$	6700.05			2.33373
$203$	−303.474			−0.104925
$204$	−646.930			−0.222030
$205$		0			0
$206$		−	2913.15i		−	0.985284i
$207$		−	5276.42i		−	1.77167i
$208$	−4755.78	+	8812.77i	−1.58536	+	2.93777i
$209$	1774.32			0.587235
$210$		0			0
$211$	1343.25			0.438261			0.219131	−	0.975696i	$-0.429678\pi$
$211$	1343.25			0.438261			0.219131	+	0.975696i	$0.429678\pi$
$212$			1955.12i			0.633389i
$213$	4756.80			1.53019
$214$			10682.0i			3.41218i
$215$		0			0
$216$			25509.1i			8.03553i
$217$			537.045i			0.168005i
$218$		−	3753.71i		−	1.16621i
$219$			6860.95i			2.11699i
$220$		0			0
$221$	131.923	+	71.1917i	0.0401543	+	0.0216691i
$222$			21630.6i			6.53941i
$223$	1081.45			0.324751			0.162375	−	0.986729i	$-0.448084\pi$
$223$	1081.45			0.324751			0.162375	+	0.986729i	$0.448084\pi$
$224$	11465.3			3.41990
$225$		0			0
$226$		−	5019.72i		−	1.47746i
$227$	−4333.06			−1.26694			−0.633470	−	0.773767i	$-0.718370\pi$
$227$	−4333.06			−1.26694			−0.633470	+	0.773767i	$0.718370\pi$
$228$	16177.9			4.69915
$229$		−	4091.36i		−	1.18063i	−0.807172	−	0.590316i	$-0.799003\pi$
$229$		−	4091.36i		−	1.18063i	0.807172	−	0.590316i	$-0.200997\pi$
$230$		0			0
$231$	−4154.28			−1.18325
$232$	−1099.76			−0.311219
$233$			4921.94i			1.38389i	0.721949	+	0.691946i	$0.243246\pi$
$233$			4921.94i			1.38389i	−0.721949	+	0.691946i	$0.756754\pi$
$234$	7760.92	−	14381.5i	2.16815	−	4.01772i
$235$		0			0
$236$		−	8144.35i		−	2.24641i
$237$			4069.53i			1.11538i
$238$		−	337.776i		−	0.0919947i
$239$		−	1848.41i		−	0.500265i	−0.968212	−	0.250133i	$-0.919526\pi$
$239$		−	1848.41i		−	0.500265i	0.968212	−	0.250133i	$-0.0804743\pi$
$240$		0			0
$241$		−	2033.42i		−	0.543501i	−0.962368	−	0.271751i	$-0.912397\pi$
$241$		−	2033.42i		−	0.543501i	0.962368	−	0.271751i	$-0.0876026\pi$
$242$	4527.78			1.20271
$243$		−	6546.96i		−	1.72834i
$244$	15521.7			4.07243
$245$		0			0
$246$	−13105.4			−3.39663
$247$	−3299.02	−	1780.30i	−0.849844	−	0.458615i
$248$			1946.20i			0.498322i
$249$		−	7592.50i		−	1.93235i
$250$		0			0
$251$	2624.85			0.660075			0.330038	−	0.943968i	$-0.392939\pi$
$251$	2624.85			0.660075			0.330038	+	0.943968i	$0.392939\pi$
$252$	−26711.9			−6.67736
$253$	1812.29			0.450348
$254$		−	5497.08i		−	1.35794i
$255$		0			0
$256$	5423.74			1.32415
$257$		−	2704.07i		−	0.656323i	−0.944622	−	0.328162i	$-0.893571\pi$
$257$		−	2704.07i		−	0.656323i	0.944622	−	0.328162i	$-0.106429\pi$
$258$	−4302.20			−1.03815
$259$	−8192.81			−1.96555
$260$		0			0
$261$	1001.81			0.237589
$262$	978.732			0.230787
$263$		−	7024.27i		−	1.64690i	−0.567387	−	0.823451i	$-0.692046\pi$
$263$		−	7024.27i		−	1.64690i	0.567387	−	0.823451i	$-0.307954\pi$
$264$	−15054.7			−3.50967
$265$		0			0
$266$			8446.81i			1.94702i
$267$	9640.98			2.20981
$268$	−2930.02			−0.667833
$269$	−3126.72			−0.708697			−0.354348	−	0.935113i	$-0.615297\pi$
$269$	−3126.72			−0.708697			−0.354348	+	0.935113i	$0.615297\pi$
$270$		0			0
$271$			7754.38i			1.73817i	0.494659	+	0.869087i	$0.335293\pi$
$271$			7754.38i			1.73817i	−0.494659	+	0.869087i	$0.664707\pi$
$272$		−	683.286i		−	0.152317i
$273$	7724.12	+	4168.29i	1.71240	+	0.924090i
$274$	−90.9262			−0.0200476
$275$		0			0
$276$	16524.2			3.60376
$277$			3379.40i			0.733028i	0.930413	+	0.366514i	$0.119449\pi$
$277$			3379.40i			0.733028i	−0.930413	+	0.366514i	$0.880551\pi$
$278$	1636.07			0.352968
$279$		−	1772.87i		−	0.380426i
$280$		0			0
$281$		−	3717.14i		−	0.789131i	−0.918868	−	0.394566i	$-0.870895\pi$
$281$		−	3717.14i		−	0.789131i	0.918868	−	0.394566i	$-0.129105\pi$
$282$		−	20095.1i		−	4.24341i
$283$			3975.48i			0.835045i	0.908667	+	0.417522i	$0.137102\pi$
$283$			3975.48i			0.835045i	−0.908667	+	0.417522i	$0.862898\pi$
$284$			10505.4i			2.19501i
$285$		0			0
$286$	4939.62	+	2665.65i	1.02128	+	0.551129i
$287$		−	4963.81i		−	1.02092i
$288$	−37848.7			−7.74395
$289$	4902.77			0.997918
$290$		0			0
$291$		−	7084.64i		−	1.42718i
$292$	−15152.5			−3.03675
$293$	−7351.82			−1.46586			−0.732932	−	0.680302i	$-0.761849\pi$
$293$	−7351.82			−1.46586			−0.732932	+	0.680302i	$0.761849\pi$
$294$		−	2057.95i		−	0.408239i
$295$		0			0
$296$	−29689.9			−5.83004
$297$	7981.29			1.55933
$298$		−	4904.88i		−	0.953464i
$299$	−3369.63	−	1818.41i	−0.651741	−	0.351710i
$300$		0			0
$301$		−	1629.50i		−	0.312037i
$302$		−	14025.2i		−	2.67239i
$303$		−	11879.2i		−	2.25229i
$304$			17087.0i			3.22371i
$305$		0			0
$306$			1115.05i			0.208311i
$307$	5822.03			1.08235			0.541174	−	0.840911i	$-0.317980\pi$
$307$	5822.03			1.08235			0.541174	+	0.840911i	$0.317980\pi$
$308$		−	9174.76i		−	1.69734i
$309$	−5165.03			−0.950901
$310$		0			0
$311$	8275.18			1.50882			0.754409	−	0.656405i	$-0.227924\pi$
$311$	8275.18			1.50882			0.754409	+	0.656405i	$0.227924\pi$
$312$	27991.5	+	15105.5i	5.07918	+	2.74096i
$313$			4922.13i			0.888866i	0.895812	+	0.444433i	$0.146595\pi$
$313$			4922.13i			0.888866i	−0.895812	+	0.444433i	$0.853405\pi$
$314$		−	13560.5i		−	2.43714i
$315$		0			0
$316$	−8987.60			−1.59997
$317$	−2991.37			−0.530006			−0.265003	−	0.964248i	$-0.585373\pi$
$317$	−2991.37			−0.530006			−0.265003	+	0.964248i	$0.585373\pi$
$318$	4778.50			0.842657
$319$			344.093i			0.0603935i
$320$		0			0
$321$	18939.3			3.29311
$322$			8627.60i			1.49316i
$323$	255.785			0.0440626
$324$	35911.3			6.15764
$325$		0			0
$326$	−11490.7			−1.95217
$327$	−6655.35			−1.12551
$328$		−	17988.4i		−	3.02818i
$329$	7611.21			1.27544
$330$		0			0
$331$			5421.39i			0.900262i	0.892963	+	0.450131i	$0.148623\pi$
$331$			5421.39i			0.900262i	−0.892963	+	0.450131i	$0.851377\pi$
$332$	16768.1			2.77190
$333$	27045.7			4.45074
$334$	−10388.6			−1.70191
$335$		0			0
$336$		−	40006.6i		−	6.49565i
$337$			7639.38i			1.23485i	0.786631	+	0.617424i	$0.211824\pi$
$337$			7639.38i			1.23485i	−0.786631	+	0.617424i	$0.788176\pi$
$338$	−6509.67	−	9912.56i	−1.04757	−	1.59518i
$339$	−8900.00			−1.42590
$340$		0			0
$341$	608.928			0.0967017
$342$		−	27884.2i		−	4.40878i
$343$	−5931.75			−0.933773
$344$		−	5905.17i		−	0.925539i
$345$		0			0
$346$			19560.6i			3.03926i
$347$			10145.0i			1.56948i	0.619823	+	0.784741i	$0.287204\pi$
$347$			10145.0i			1.56948i	−0.619823	+	0.784741i	$0.712796\pi$
$348$			3137.37i			0.483278i
$349$		−	1126.84i		−	0.172831i	−0.996259	−	0.0864157i	$-0.972459\pi$
$349$		−	1126.84i		−	0.172831i	0.996259	−	0.0864157i	$-0.0275413\pi$
$350$		0			0
$351$	−14839.8	−	8008.22i	−2.25666	−	1.21780i
$352$		−	12999.9i		−	1.96846i
$353$	9532.90			1.43735			0.718676	−	0.695345i	$-0.244749\pi$
$353$	9532.90			1.43735			0.718676	+	0.695345i	$0.244749\pi$
$354$	−19905.5			−2.98860
$355$		0			0
$356$			21292.2i			3.16990i
$357$	−598.879			−0.0887844
$358$	−15629.1			−2.30733
$359$		−	6852.10i		−	1.00735i	−0.863892	−	0.503677i	$-0.831980\pi$
$359$		−	6852.10i		−	1.00735i	0.863892	−	0.503677i	$-0.168020\pi$
$360$		0			0
$361$	462.551			0.0674371
$362$	−9896.44			−1.43686
$363$		−	8027.78i		−	1.16074i
$364$	−9205.71	+	17058.8i	−1.32558	+	2.45638i
$365$		0			0
$366$		−	37936.3i		−	5.41793i
$367$		−	2453.68i		−	0.348995i	−0.984658	−	0.174497i	$-0.944170\pi$
$367$		−	2453.68i		−	0.348995i	0.984658	−	0.174497i	$-0.0558300\pi$
$368$			17452.8i			2.47225i
$369$			16386.3i			2.31175i
$370$		0			0
$371$			1809.91i			0.253277i
$372$	5552.08			0.773823
$373$			1900.82i			0.263862i	0.991259	+	0.131931i	$0.0421178\pi$
$373$			1900.82i			0.263862i	−0.991259	+	0.131931i	$0.957882\pi$
$374$	−382.986			−0.0529512
$375$		0			0
$376$	27582.3			3.78311
$377$	345.254	−	639.778i	0.0471657	−	0.0874012i
$378$			37995.7i			5.17008i
$379$		−	12116.2i		−	1.64213i	−0.570831	−	0.821067i	$-0.693379\pi$
$379$		−	12116.2i		−	1.64213i	0.570831	−	0.821067i	$-0.306621\pi$
$380$		0			0
$381$	−9746.36			−1.31055
$382$	−7432.74			−0.995529
$383$	−6754.44			−0.901138			−0.450569	−	0.892742i	$-0.648779\pi$
$383$	−6754.44			−0.901138			−0.450569	+	0.892742i	$0.648779\pi$
$384$		−	30236.9i		−	4.01829i
$385$		0			0
$386$	−18856.5			−2.48646
$387$			5379.24i			0.706569i
$388$	15646.5			2.04724
$389$	−2535.39			−0.330461			−0.165231	−	0.986255i	$-0.552837\pi$
$389$	−2535.39			−0.330461			−0.165231	+	0.986255i	$0.552837\pi$
$390$		0			0
$391$	261.259			0.0337914
$392$	2824.73			0.363955
$393$		−	1735.30i		−	0.222733i
$394$	−25359.1			−3.24257
$395$		0			0
$396$			30287.3i			3.84342i
$397$	−3881.63			−0.490713			−0.245357	−	0.969433i	$-0.578905\pi$
$397$	−3881.63			−0.490713			−0.245357	+	0.969433i	$0.578905\pi$
$398$	3361.42			0.423349
$399$	14976.3			1.87907
$400$		0			0
$401$			10458.0i			1.30237i	0.758920	+	0.651184i	$0.225727\pi$
$401$			10458.0i			1.30237i	−0.758920	+	0.651184i	$0.774273\pi$
$402$			7161.22i			0.888480i
$403$	−1132.19	−	610.982i	−0.139946	−	0.0755215i
$404$	26235.4			3.23084
$405$		0			0
$406$	−1638.09			−0.200239
$407$			9289.40i			1.13135i
$408$	−2170.28			−0.263345
$409$		−	12296.3i		−	1.48658i	−0.668970	−	0.743289i	$-0.733265\pi$
$409$		−	12296.3i		−	1.48658i	0.668970	−	0.743289i	$-0.266735\pi$
$410$		0			0
$411$			161.213i			0.0193480i
$412$		−	11407.0i		−	1.36404i
$413$		−	7539.42i		−	0.898282i
$414$		−	28481.0i		−	3.38108i
$415$		0			0
$416$	−13043.8	+	24171.0i	−1.53732	+	2.84875i
$417$		−	2900.77i		−	0.340651i
$418$	9577.39			1.12068
$419$	9401.01			1.09611			0.548054	−	0.836443i	$-0.315369\pi$
$419$	9401.01			1.09611			0.548054	+	0.836443i	$0.315369\pi$
$420$		0			0
$421$		−	16241.2i		−	1.88016i	−0.340951	−	0.940081i	$-0.610749\pi$
$421$		−	16241.2i		−	1.88016i	0.340951	−	0.940081i	$-0.389251\pi$
$422$	7250.58			0.836381
$423$	−25125.8			−2.88808
$424$			6558.92i			0.751249i
$425$		0			0
$426$	25676.2			2.92023
$427$	14368.8			1.62846
$428$			41827.6i			4.72386i
$429$	4726.21	−	8757.98i	0.531896	−	0.985639i
$430$		0			0
$431$		−	2664.58i		−	0.297792i	−0.988853	−	0.148896i	$-0.952428\pi$
$431$		−	2664.58i		−	0.297792i	0.988853	−	0.148896i	$-0.0475720\pi$
$432$			76861.5i			8.56019i
$433$			10804.1i			1.19910i	0.800336	+	0.599551i	$0.204654\pi$
$433$			10804.1i			1.19910i	−0.800336	+	0.599551i	$0.795346\pi$
$434$			2898.86i			0.320621i
$435$		0			0
$436$		−	14698.4i		−	1.61451i
$437$	−6533.36			−0.715178
$438$			37033.9i			4.04007i
$439$	8612.49			0.936337			0.468168	−	0.883639i	$-0.344914\pi$
$439$	8612.49			0.936337			0.468168	+	0.883639i	$0.344914\pi$
$440$		0			0
$441$	−2573.15			−0.277848
$442$	712.092	+	384.278i	0.0766307	+	0.0413535i
$443$		−	2565.27i		−	0.275123i	−0.990493	−	0.137561i	$-0.956074\pi$
$443$		−	2565.27i		−	0.275123i	0.990493	−	0.137561i	$-0.0439265\pi$
$444$			84698.9i			9.05323i
$445$		0			0
$446$	5837.45			0.619757
$447$	−8696.40			−0.920191
$448$	28445.2			2.99979
$449$			7527.86i			0.791229i	0.918417	+	0.395614i	$0.129468\pi$
$449$			7527.86i			0.791229i	−0.918417	+	0.395614i	$0.870532\pi$
$450$		0			0
$451$	−5628.21			−0.587632
$452$		−	19655.7i		−	2.04541i
$453$	−24866.8			−2.57913
$454$	−23389.0			−2.41784
$455$		0			0
$456$	54272.5			5.57356
$457$	6433.57			0.658534			0.329267	−	0.944237i	$-0.393198\pi$
$457$	6433.57			0.658534			0.329267	+	0.944237i	$0.393198\pi$
$458$		−	22084.3i		−	2.25313i
$459$	1150.58			0.117003
$460$		0			0
$461$		−	4993.42i		−	0.504483i	−0.967664	−	0.252242i	$-0.918832\pi$
$461$		−	4993.42i		−	0.504483i	0.967664	−	0.252242i	$-0.0811678\pi$
$462$	−22423.9			−2.25813
$463$	15182.4			1.52395			0.761974	−	0.647608i	$-0.224230\pi$
$463$	15182.4			1.52395			0.761974	+	0.647608i	$0.224230\pi$
$464$	−3313.69			−0.331539
$465$		0			0
$466$			26567.6i			2.64103i
$467$		−	10748.1i		−	1.06502i	−0.846425	−	0.532509i	$-0.821249\pi$
$467$		−	10748.1i		−	1.06502i	0.846425	−	0.532509i	$-0.178751\pi$
$468$	30389.4	−	56313.6i	3.00161	−	5.56218i
$469$	−2712.39			−0.267050
$470$		0			0
$471$	−24042.8			−2.35209
$472$		−	27322.1i		−	2.66441i
$473$	−1847.61			−0.179605
$474$			21966.5i			2.12860i
$475$		0			0
$476$		−	1322.63i		−	0.127358i
$477$		−	5974.77i		−	0.573514i
$478$		−	9977.31i		−	0.954710i
$479$		−	567.128i		−	0.0540976i	−0.999634	−	0.0270488i	$-0.991389\pi$
$479$		−	567.128i		−	0.0540976i	0.999634	−	0.0270488i	$-0.00861095\pi$
$480$		0			0
$481$	9320.73	−	17271.9i	0.883553	−	1.63728i
$482$		−	10975.9i		−	1.03722i
$483$	15296.8			1.44105
$484$	17729.4			1.66505
$485$		0			0
$486$		−	35339.1i		−	3.29838i
$487$	−79.6868			−0.00741468			−0.00370734	−	0.999993i	$-0.501180\pi$
$487$	−79.6868			−0.00741468			−0.00370734	+	0.999993i	$0.501180\pi$
$488$	52071.1			4.83022
$489$			20373.0i			1.88405i
$490$		0			0
$491$	4638.66			0.426354			0.213177	−	0.977014i	$-0.431619\pi$
$491$	4638.66			0.426354			0.213177	+	0.977014i	$0.431619\pi$
$492$	−51316.9			−4.70233
$493$			49.6043i			0.00453157i
$494$	−17807.4	−	9609.70i	−1.62185	−	0.875225i
$495$		0			0
$496$			5864.10i			0.530858i
$497$			9725.14i			0.877731i
$498$		−	40982.7i		−	3.68771i
$499$			1508.55i			0.135334i	0.997708	+	0.0676672i	$0.0215556\pi$
$499$			1508.55i			0.135334i	−0.997708	+	0.0676672i	$0.978444\pi$
$500$		0			0
$501$			18419.1i			1.64252i
$502$	14168.4			1.25969
$503$			6657.75i			0.590168i	0.955471	+	0.295084i	$0.0953477\pi$
$503$			6657.75i			0.590168i	−0.955471	+	0.295084i	$0.904652\pi$
$504$	−89611.5			−7.91987
$505$		0			0
$506$	9782.39			0.859447
$507$	−17575.0	+	11541.7i	−1.53952	+	1.01101i
$508$		−	21524.9i		−	1.87995i
$509$			11743.6i			1.02264i	0.859390	+	0.511321i	$0.170844\pi$
$509$			11743.6i			1.02264i	−0.859390	+	0.511321i	$0.829156\pi$
$510$		0			0
$511$	−14027.0			−1.21432
$512$	4000.61			0.345319
$513$	−28772.7			−2.47631
$514$		−	14596.0i		−	1.25253i
$515$		0			0
$516$	−16846.2			−1.43723
$517$		−	8629.95i		−	0.734129i
$518$	−44223.1			−3.75106
$519$	34681.1			2.93320
$520$		0			0
$521$	22239.4			1.87011			0.935054	−	0.354505i	$-0.115350\pi$
$521$	22239.4			1.87011			0.935054	+	0.354505i	$0.115350\pi$
$522$	5407.58			0.453416
$523$			19668.3i			1.64443i	0.569179	+	0.822214i	$0.307261\pi$
$523$			19668.3i			1.64443i	−0.569179	+	0.822214i	$0.692739\pi$
$524$	3832.42			0.319504
$525$		0			0
$526$		−	37915.6i		−	3.14296i
$527$	87.7827			0.00725592
$528$	−45361.3			−3.73882
$529$	5493.81			0.451533
$530$		0			0
$531$			24888.8i			2.03405i
$532$			33075.2i			2.69547i
$533$	10464.6	+	5647.20i	0.850418	+	0.458925i
$534$	52040.0			4.21721
$535$		0			0
$536$	−9829.43			−0.792102
$537$			27710.6i			2.22681i
$538$	−16877.4			−1.35248
$539$		−	883.802i		−	0.0706271i
$540$		0			0
$541$			13725.3i			1.09075i	0.838192	+	0.545375i	$0.183613\pi$
$541$			13725.3i			1.09075i	−0.838192	+	0.545375i	$0.816387\pi$
$542$			41856.5i			3.31714i
$543$			17546.5i			1.38672i
$544$		−	1874.06i		−	0.147702i
$545$		0			0
$546$	41693.2	+	22499.6i	3.26796	+	1.76354i
$547$		−	16200.3i		−	1.26632i	−0.774022	−	0.633158i	$-0.781758\pi$
$547$		−	16200.3i		−	1.26632i	0.774022	−	0.633158i	$-0.218242\pi$
$548$	−356.040			−0.0277541
$549$	−47433.5			−3.68745
$550$		0			0
$551$		−	1240.46i		−	0.0959083i
$552$	55434.1			4.27434
$553$	−8320.04			−0.639790
$554$			18241.3i			1.39892i
$555$		0			0
$556$	6406.38			0.488653
$557$	2529.48			0.192419			0.0962097	−	0.995361i	$-0.469328\pi$
$557$	2529.48			0.192419			0.0962097	+	0.995361i	$0.469328\pi$
$558$		−	9569.57i		−	0.726007i
$559$	3435.29	+	1853.84i	0.259924	+	0.140267i
$560$		0			0
$561$			679.037i			0.0511033i
$562$		−	20064.3i		−	1.50598i
$563$			3787.41i			0.283517i	0.989901	+	0.141759i	$0.0452757\pi$
$563$			3787.41i			0.283517i	−0.989901	+	0.141759i	$0.954724\pi$
$564$		−	78686.2i		−	5.87462i
$565$		0			0
$566$			21458.8i			1.59361i
$567$	33244.0			2.46229
$568$			35243.0i			2.60345i
$569$	−12743.9			−0.938933			−0.469466	−	0.882950i	$-0.655554\pi$
$569$	−12743.9			−0.938933			−0.469466	+	0.882950i	$0.655554\pi$
$570$		0			0
$571$	8991.11			0.658960			0.329480	−	0.944163i	$-0.393127\pi$
$571$	8991.11			0.658960			0.329480	+	0.944163i	$0.393127\pi$
$572$	19342.1	+	10437.9i	1.41387	+	0.762989i
$573$			13178.3i			0.960788i
$574$		−	26793.6i		−	1.94834i
$575$		0			0
$576$	−93901.7			−6.79266
$577$	17423.3			1.25709			0.628544	−	0.777774i	$-0.283651\pi$
$577$	17423.3			1.25709			0.628544	+	0.777774i	$0.283651\pi$
$578$	26464.1			1.90443
$579$			33432.8i			2.39969i
$580$		0			0
$581$	15522.6			1.10841
$582$		−	38241.4i		−	2.72364i
$583$	2052.16			0.145783
$584$	−50832.5			−3.60182
$585$		0			0
$586$	−39683.6			−2.79746
$587$	−14511.5			−1.02036			−0.510181	−	0.860067i	$-0.670422\pi$
$587$	−14511.5			−1.02036			−0.510181	+	0.860067i	$0.670422\pi$
$588$		−	8058.33i		−	0.565170i
$589$	−2195.20			−0.153568
$590$		0			0
$591$			44961.9i			3.12941i
$592$	−89458.8			−6.21070
$593$	267.436			0.0185199			0.00925994	−	0.999957i	$-0.497052\pi$
$593$	267.436			0.0185199			0.00925994	+	0.999957i	$0.497052\pi$
$594$	43081.4			2.97584
$595$		0			0
$596$		−	19206.1i		−	1.31998i
$597$		−	5959.83i		−	0.408576i
$598$	−18188.5	−	9815.39i	−1.24379	−	0.671206i
$599$	−5428.80			−0.370308			−0.185154	−	0.982709i	$-0.559278\pi$
$599$	−5428.80			−0.370308			−0.185154	+	0.982709i	$0.559278\pi$
$600$		0			0
$601$	−25777.8			−1.74958			−0.874790	−	0.484502i	$-0.839001\pi$
$601$	−25777.8			−1.74958			−0.874790	+	0.484502i	$0.839001\pi$
$602$		−	8795.73i		−	0.595493i
$603$	8954.00			0.604701
$604$		−	54918.6i		−	3.69968i
$605$		0			0
$606$		−	64121.6i		−	4.29829i
$607$		−	20383.4i		−	1.36299i	−0.731821	−	0.681497i	$-0.761329\pi$
$607$		−	20383.4i		−	1.36299i	0.731821	−	0.681497i	$-0.238671\pi$
$608$			46864.9i			3.12603i
$609$			2904.34i			0.193251i
$610$		0			0
$611$	−8659.07	+	16045.8i	−0.573336	+	1.06243i
$612$			4366.20i			0.288387i
$613$	7433.13			0.489757			0.244879	−	0.969554i	$-0.421252\pi$
$613$	7433.13			0.489757			0.244879	+	0.969554i	$0.421252\pi$
$614$	31426.1			2.06556
$615$		0			0
$616$		−	30778.9i		−	2.01318i
$617$	5540.71			0.361524			0.180762	−	0.983527i	$-0.442144\pi$
$617$	5540.71			0.361524			0.180762	+	0.983527i	$0.442144\pi$
$618$	−27879.8			−1.81471
$619$		−	15878.2i		−	1.03101i	−0.856886	−	0.515506i	$-0.827604\pi$
$619$		−	15878.2i		−	1.03101i	0.856886	−	0.515506i	$-0.172396\pi$
$620$		0			0
$621$	−29388.6			−1.89907
$622$	44667.7			2.87944
$623$			19710.7i			1.26756i
$624$	84341.1	+	45514.4i	5.41081	+	2.91992i
$625$		0			0
$626$			26568.6i			1.69632i
$627$		−	16980.8i		−	1.08158i
$628$		−	53098.7i		−	3.37400i
$629$			1339.15i			0.0848896i
$630$		0			0
$631$		−	7809.85i		−	0.492718i	−0.969179	−	0.246359i	$-0.920766\pi$
$631$		−	7809.85i		−	0.492718i	0.969179	−	0.246359i	$-0.0792343\pi$
$632$	−30151.0			−1.89769
$633$		−	12855.3i		−	0.807194i
$634$	−16146.8			−1.01147
$635$		0			0
$636$	18711.2			1.16658
$637$	−886.783	+	1643.27i	−0.0551580	+	0.102211i
$638$			1857.34i			0.115255i
$639$		−	32104.1i		−	1.98751i
$640$		0			0
$641$	−3286.62			−0.202517			−0.101259	−	0.994860i	$-0.532287\pi$
$641$	−3286.62			−0.202517			−0.101259	+	0.994860i	$0.532287\pi$
$642$	102230.			6.28459
$643$	−9976.67			−0.611884			−0.305942	−	0.952050i	$-0.598971\pi$
$643$	−9976.67			−0.611884			−0.305942	+	0.952050i	$0.598971\pi$
$644$			33783.1i			2.06715i
$645$		0			0
$646$	1380.67			0.0840895
$647$		−	2603.91i		−	0.158223i	−0.996866	−	0.0791115i	$-0.974792\pi$
$647$		−	2603.91i		−	0.158223i	0.996866	−	0.0791115i	$-0.0252083\pi$
$648$	120473.			7.30343
$649$	−8548.55			−0.517042
$650$		0			0
$651$	5139.70			0.309433
$652$	−44994.0			−2.70261
$653$			17296.8i			1.03657i	0.855209	+	0.518283i	$0.173429\pi$
$653$			17296.8i			1.03657i	−0.855209	+	0.518283i	$0.826571\pi$
$654$	−35924.2			−2.14793
$655$		0			0
$656$		−	54200.8i		−	3.22589i
$657$	46305.2			2.74968
$658$	41083.7			2.43406
$659$	−4108.13			−0.242838			−0.121419	−	0.992601i	$-0.538744\pi$
$659$	−4108.13			−0.242838			−0.121419	+	0.992601i	$0.538744\pi$
$660$		0			0
$661$		−	5035.44i		−	0.296303i	−0.988965	−	0.148151i	$-0.952668\pi$
$661$		−	5035.44i		−	0.296303i	0.988965	−	0.148151i	$-0.0473323\pi$
$662$			29263.5i			1.71807i
$663$	681.328	−	1262.54i	0.0399104	−	0.0739565i
$664$	56252.5			3.28768
$665$		0			0
$666$	145987.			8.49381
$667$		−	1267.01i		−	0.0735516i
$668$	−40678.7			−2.35615
$669$		−	10349.8i		−	0.598129i
$670$		0			0
$671$		−	16292.0i		−	0.937326i
$672$		−	109727.i		−	6.29881i
$673$		−	29342.4i		−	1.68063i	−0.542097	−	0.840316i	$-0.682369\pi$
$673$		−	29342.4i		−	1.68063i	0.542097	−	0.840316i	$-0.317631\pi$
$674$			41235.8i			2.35659i
$675$		0			0
$676$	−25489.9	−	38814.6i	−1.45027	−	2.20839i
$677$		−	15091.7i		−	0.856751i	−0.903601	−	0.428375i	$-0.859086\pi$
$677$		−	15091.7i		−	0.856751i	0.903601	−	0.428375i	$-0.140914\pi$
$678$	−48040.3			−2.72121
$679$	14484.3			0.818641
$680$		0			0
$681$			41468.8i			2.33346i
$682$	3286.86			0.184546
$683$	15949.3			0.893533			0.446767	−	0.894651i	$-0.352575\pi$
$683$	15949.3			0.893533			0.446767	+	0.894651i	$0.352575\pi$
$684$		−	109186.i		−	6.10356i
$685$		0			0
$686$	−32018.3			−1.78202
$687$	−39155.6			−2.17450
$688$		−	17792.9i		−	0.985969i
$689$	−3815.61	−	2059.08i	−0.210977	−	0.113853i
$690$		0			0
$691$		−	9086.21i		−	0.500225i	−0.968217	−	0.250113i	$-0.919532\pi$
$691$		−	9086.21i		−	0.500225i	0.968217	−	0.250113i	$-0.0804677\pi$
$692$			76593.5i			4.20758i
$693$			28037.7i			1.53689i
$694$			54760.4i			2.99521i
$695$		0			0
$696$			10525.1i			0.573206i
$697$	−811.359			−0.0440924
$698$		−	6082.42i		−	0.329832i
$699$	47104.5			2.54887
$700$		0			0
$701$	−16228.1			−0.874359			−0.437179	−	0.899374i	$-0.644022\pi$
$701$	−16228.1			−0.874359			−0.437179	+	0.899374i	$0.644022\pi$
$702$	−80101.9	−	43226.7i	−4.30662	−	2.32405i
$703$		−	33488.4i		−	1.79664i
$704$		−	32252.5i		−	1.72665i
$705$		0			0
$706$	51456.6			2.74305
$707$	24286.7			1.29193
$708$	−77944.0			−4.13745
$709$			19425.5i			1.02897i	0.857499	+	0.514485i	$0.172017\pi$
$709$			19425.5i			1.02897i	−0.857499	+	0.514485i	$0.827983\pi$
$710$		0			0
$711$	27465.7			1.44873
$712$			71429.6i			3.75975i
$713$	−2242.18			−0.117770
$714$	−3232.62			−0.169437
$715$		0			0
$716$	−61199.0			−3.19429
$717$	−17689.8			−0.921394
$718$		−	36986.2i		−	1.92244i
$719$	−548.566			−0.0284535			−0.0142268	−	0.999899i	$-0.504529\pi$
$719$	−548.566			−0.0284535			−0.0142268	+	0.999899i	$0.504529\pi$
$720$		0			0
$721$		−	10559.8i		−	0.545445i
$722$	2496.75			0.128697
$723$	−19460.4			−1.00103
$724$	−38751.5			−1.98921
$725$		0			0
$726$		−	43332.3i		−	2.21517i
$727$		−	10550.1i		−	0.538213i	−0.963110	−	0.269107i	$-0.913272\pi$
$727$		−	10550.1i		−	0.538213i	0.963110	−	0.269107i	$-0.0867284\pi$
$728$	−30882.7	+	57227.7i	−1.57224	+	2.91346i
$729$	−16782.2			−0.852623
$730$		0			0
$731$	−266.350			−0.0134765
$732$		−	148547.i		−	7.50064i
$733$	4007.86			0.201956			0.100978	−	0.994889i	$-0.467803\pi$
$733$	4007.86			0.201956			0.100978	+	0.994889i	$0.467803\pi$
$734$		−	13244.4i		−	0.666024i
$735$		0			0
$736$			47868.0i			2.39734i
$737$			3075.43i			0.153711i
$738$			88449.8i			4.41176i
$739$			1960.69i			0.0975984i	0.998809	+	0.0487992i	$0.0155394\pi$
$739$			1960.69i			0.0975984i	−0.998809	+	0.0487992i	$0.984461\pi$
$740$		0			0
$741$	−17038.1	+	31572.7i	−0.844682	+	1.56525i
$742$			9769.49i			0.483355i
$743$	18597.5			0.918272			0.459136	−	0.888366i	$-0.348159\pi$
$743$	18597.5			0.918272			0.459136	+	0.888366i	$0.348159\pi$
$744$	18625.8			0.917814
$745$		0			0
$746$			10260.2i			0.503556i
$747$	−51242.6			−2.50986
$748$	−1499.66			−0.0733061
$749$			38720.8i			1.88896i
$750$		0			0
$751$	17920.4			0.870739			0.435369	−	0.900252i	$-0.356618\pi$
$751$	17920.4			0.870739			0.435369	+	0.900252i	$0.356618\pi$
$752$	83108.2			4.03011
$753$		−	25120.6i		−	1.21573i
$754$	1863.61	−	3453.39i	0.0900114	−	0.166797i
$755$		0			0
$756$			148780.i			7.15751i
$757$		−	9391.11i		−	0.450893i	−0.974256	−	0.225446i	$-0.927616\pi$
$757$		−	9391.11i		−	0.450893i	0.974256	−	0.225446i	$-0.0723840\pi$
$758$		−	65400.9i		−	3.13386i
$759$		−	17344.2i		−	0.829455i
$760$		0			0
$761$			20548.2i			0.978805i	0.872058	+	0.489403i	$0.162785\pi$
$761$			20548.2i			0.978805i	−0.872058	+	0.489403i	$0.837215\pi$
$762$	−52608.8			−2.50107
$763$		−	13606.7i		−	0.645602i
$764$	−29104.4			−1.37822
$765$		0			0
$766$	−36459.1			−1.71974
$767$	15894.5	+	8577.39i	0.748260	+	0.403796i
$768$		−	51906.9i		−	2.43884i
$769$		−	10142.8i		−	0.475627i	−0.971311	−	0.237813i	$-0.923569\pi$
$769$		−	10142.8i		−	0.475627i	0.971311	−	0.237813i	$-0.0764307\pi$
$770$		0			0
$771$	−25878.8			−1.20882
$772$	−73836.6			−3.44228
$773$	213.912			0.00995327			0.00497664	−	0.999988i	$-0.498416\pi$
$773$	213.912			0.00995327			0.00497664	+	0.999988i	$0.498416\pi$
$774$			29036.0i			1.34842i
$775$		0			0
$776$	52489.8			2.42819
$777$			78407.8i			3.62016i
$778$	−13685.5			−0.630654
$779$	20289.8			0.933193
$780$		0			0
$781$	11026.8			0.505212
$782$	1410.22			0.0644878
$783$		−	5579.89i		−	0.254673i
$784$	8511.19			0.387718
$785$		0			0
$786$		−	9366.78i		−	0.425066i
$787$	−13315.9			−0.603127			−0.301563	−	0.953446i	$-0.597508\pi$
$787$	−13315.9			−0.603127			−0.301563	+	0.953446i	$0.597508\pi$
$788$	−99298.7			−4.48905
$789$	−67224.6			−3.03328
$790$		0			0
$791$		−	18195.8i		−	0.817911i
$792$			101606.i			4.55859i
$793$	−16347.0	+	30292.0i	−0.732027	+	1.35649i
$794$	−20952.2			−0.936481
$795$		0			0
$796$	13162.3			0.586089
$797$		−	1432.22i		−	0.0636537i	−0.999493	−	0.0318268i	$-0.989867\pi$
$797$		−	1432.22i		−	0.0636537i	0.999493	−	0.0318268i	$-0.0101325\pi$
$798$	80838.7			3.58604
$799$		−	1244.09i		−	0.0550847i
$800$		0			0
$801$		−	65068.0i		−	2.87024i
$802$			56450.3i			2.48545i
$803$			15904.5i			0.698950i
$804$			28041.2i			1.23002i
$805$		0			0
$806$	−6111.32	−	3297.95i	−0.267075	−	0.144126i
$807$			29923.7i			1.30528i
$808$	88012.8			3.83203
$809$	1717.53			0.0746416			0.0373208	−	0.999303i	$-0.488118\pi$
$809$	1717.53			0.0746416			0.0373208	+	0.999303i	$0.488118\pi$
$810$		0			0
$811$		−	26684.7i		−	1.15539i	−0.816251	−	0.577697i	$-0.803951\pi$
$811$		−	26684.7i		−	1.15539i	0.816251	−	0.577697i	$-0.196049\pi$
$812$	−6414.27			−0.277213
$813$	74211.9			3.20138
$814$			50142.2i			2.15907i
$815$		0			0
$816$	−6539.27			−0.280539
$817$	6660.67			0.285223
$818$		−	66372.6i		−	2.83700i
$819$	28132.2	−	52130.9i	1.20027	−	2.22418i
$820$		0			0
$821$		−	28453.9i		−	1.20956i	−0.796394	−	0.604779i	$-0.793262\pi$
$821$		−	28453.9i		−	1.20956i	0.796394	−	0.604779i	$-0.206738\pi$
$822$			870.193i			0.0369239i
$823$			24406.1i			1.03371i	0.856073	+	0.516855i	$0.172898\pi$
$823$			24406.1i			1.03371i	−0.856073	+	0.516855i	$0.827102\pi$
$824$		−	38267.5i		−	1.61785i
$825$		0			0
$826$		−	40696.2i		−	1.71429i
$827$	−23423.5			−0.984902			−0.492451	−	0.870340i	$-0.663899\pi$
$827$	−23423.5			−0.984902			−0.492451	+	0.870340i	$0.663899\pi$
$828$		−	111523.i		−	4.68079i
$829$	18813.3			0.788193			0.394097	−	0.919069i	$-0.371058\pi$
$829$	18813.3			0.788193			0.394097	+	0.919069i	$0.371058\pi$
$830$		0			0
$831$	32342.0			1.35010
$832$	−32361.3	+	59967.6i	−1.34847	+	2.49880i
$833$		−	127.408i		−	0.00529944i
$834$		−	15657.7i		−	0.650100i
$835$		0			0
$836$	37502.2			1.55149
$837$	−9874.50			−0.407781
$838$	50744.7			2.09182
$839$			2274.01i			0.0935726i	0.998905	+	0.0467863i	$0.0148980\pi$
$839$			2274.01i			0.0935726i	−0.998905	+	0.0467863i	$0.985102\pi$
$840$		0			0
$841$	−24148.4			−0.990136
$842$		−	87666.7i		−	3.58811i
$843$	−35574.2			−1.45343
$844$	28391.1			1.15789
$845$		0			0
$846$	−135624.			−5.51162
$847$	16412.6			0.665811
$848$			19762.7i			0.800299i
$849$	38046.6			1.53799
$850$		0			0
$851$		−	34205.2i		−	1.37784i
$852$	100540.			4.04279
$853$	−8197.12			−0.329032			−0.164516	−	0.986374i	$-0.552606\pi$
$853$	−8197.12			−0.329032			−0.164516	+	0.986374i	$0.552606\pi$
$854$	77559.7			3.10777
$855$		0			0
$856$			140320.i			5.60287i
$857$			43282.5i			1.72521i	0.505879	+	0.862604i	$0.331168\pi$
$857$			43282.5i			1.72521i	−0.505879	+	0.862604i	$0.668832\pi$
$858$	25511.1	−	47273.7i	1.01507	−	1.88100i
$859$	−14884.8			−0.591226			−0.295613	−	0.955308i	$-0.595524\pi$
$859$	−14884.8			−0.591226			−0.295613	+	0.955308i	$0.595524\pi$
$860$		0			0
$861$	−47505.3			−1.88034
$862$		−	14382.9i		−	0.568309i
$863$	29421.4			1.16050			0.580252	−	0.814437i	$-0.302954\pi$
$863$	29421.4			1.16050			0.580252	+	0.814437i	$0.302954\pi$
$864$			210809.i			8.30079i
$865$		0			0
$866$			58318.2i			2.28838i
$867$		−	46921.1i		−	1.83798i
$868$			11351.1i			0.443871i
$869$			9433.65i			0.368256i
$870$		0			0
$871$	3085.81	−	5718.20i	0.120044	−	0.222450i
$872$		−	49309.2i		−	1.91493i
$873$	−47814.9			−1.85371
$874$	−35265.7			−1.36485
$875$		0			0
$876$			145014.i			5.59311i
$877$	44242.4			1.70349			0.851744	−	0.523958i	$-0.175545\pi$
$877$	44242.4			1.70349			0.851744	+	0.523958i	$0.175545\pi$
$878$	46488.4			1.78691
$879$			70359.3i			2.69984i
$880$		0			0
$881$	6344.23			0.242614			0.121307	−	0.992615i	$-0.461292\pi$
$881$	6344.23			0.242614			0.121307	+	0.992615i	$0.461292\pi$
$882$	−13889.3			−0.530247
$883$			31600.7i			1.20436i	0.798362	+	0.602178i	$0.205700\pi$
$883$			31600.7i			1.20436i	−0.798362	+	0.602178i	$0.794300\pi$
$884$	2788.34	+	1504.72i	0.106088	+	0.0572502i
$885$		0			0
$886$		−	13846.8i		−	0.525047i
$887$		−	22725.3i		−	0.860250i	−0.902769	−	0.430125i	$-0.858469\pi$
$887$		−	22725.3i		−	0.860250i	0.902769	−	0.430125i	$-0.141531\pi$
$888$			284142.i			10.7378i
$889$		−	19926.1i		−	0.751745i
$890$		0			0
$891$		−	37693.6i		−	1.41727i
$892$	22857.7			0.857997
$893$			31111.1i			1.16584i
$894$	−46941.3			−1.75610
$895$		0			0
$896$	61818.5			2.30492
$897$	−17402.8	+	32248.4i	−0.647783	+	1.20038i
$898$			40633.8i			1.50999i
$899$		−	425.714i		−	0.0157935i
$900$		0			0
$901$	295.838			0.0109387
$902$	−30379.9			−1.12144
$903$	−15594.9			−0.574713
$904$		−	65939.7i		−	2.42602i
$905$		0			0
$906$	−134226.			−4.92203
$907$		−	21217.0i		−	0.776736i	−0.921504	−	0.388368i	$-0.873039\pi$
$907$		−	21217.0i		−	0.776736i	0.921504	−	0.388368i	$-0.126961\pi$
$908$	−91584.2			−3.34728
$909$	−80174.2			−2.92542
$910$		0			0
$911$	7009.14			0.254910			0.127455	−	0.991844i	$-0.459319\pi$
$911$	7009.14			0.254910			0.127455	+	0.991844i	$0.459319\pi$
$912$	163529.			5.93747
$913$		−	17600.3i		−	0.637990i
$914$	34727.1			1.25675
$915$		0			0
$916$		−	86475.6i		−	3.11925i
$917$	3547.77			0.127762
$918$	6210.58			0.223290
$919$	−26748.5			−0.960121			−0.480061	−	0.877235i	$-0.659385\pi$
$919$	−26748.5			−0.960121			−0.480061	+	0.877235i	$0.659385\pi$
$920$		0			0
$921$		−	55718.7i		−	1.99348i
$922$		−	26953.4i		−	0.962759i
$923$	−20502.4	−	11064.0i	−0.731141	−	0.394558i
$924$	−87805.5			−3.12618
$925$		0			0
$926$	81951.6			2.90831
$927$			34859.3i			1.23509i
$928$	−9088.51			−0.321492
$929$		−	18623.8i		−	0.657726i	−0.944378	−	0.328863i	$-0.893335\pi$
$929$		−	18623.8i		−	0.657726i	0.944378	−	0.328863i	$-0.106665\pi$
$930$		0			0
$931$			3186.12i			0.112160i
$932$			104031.i			3.65627i
$933$		−	79196.1i		−	2.77895i
$934$		−	58016.0i		−	2.03249i
$935$		0			0
$936$	101949.	−	188917.i	3.56014	−	6.59717i
$937$			40923.2i			1.42679i	0.700761	+	0.713396i	$0.252844\pi$
$937$			40923.2i			1.42679i	−0.700761	+	0.713396i	$0.747156\pi$
$938$	−14640.9			−0.509640
$939$	47106.4			1.63712
$940$		0			0
$941$			55098.3i			1.90877i	0.298576	+	0.954386i	$0.403488\pi$
$941$			55098.3i			1.90877i	−0.298576	+	0.954386i	$0.596512\pi$
$942$	−129778.			−4.48874
$943$	20724.1			0.715661
$944$		−	82324.3i		−	2.83838i
$945$		0			0
$946$	−9973.01			−0.342760
$947$	−40418.2			−1.38692			−0.693460	−	0.720495i	$-0.743915\pi$
$947$	−40418.2			−1.38692			−0.693460	+	0.720495i	$0.743915\pi$
$948$			86014.2i			2.94685i
$949$	15958.1	−	29571.5i	0.545862	−	1.01152i
$950$		0			0
$951$			28628.4i			0.976170i
$952$		−	4437.07i		−	0.151057i
$953$		−	11373.4i		−	0.386591i	−0.981141	−	0.193296i	$-0.938082\pi$
$953$		−	11373.4i		−	0.386591i	0.981141	−	0.193296i	$-0.0619177\pi$
$954$		−	32250.6i		−	1.09450i
$955$		0			0
$956$		−	39068.2i		−	1.32171i
$957$	3293.08			0.111233
$958$		−	3061.24i		−	0.103240i
$959$	−329.595			−0.0110982
$960$		0			0
$961$	29037.6			0.974712
$962$	50311.4	−	93230.2i	1.68618	−	3.12460i
$963$		−	127823.i		−	4.27731i
$964$		−	42978.6i		−	1.43594i
$965$		0			0
$966$	82568.9			2.75012
$967$	12910.4			0.429339			0.214670	−	0.976687i	$-0.431133\pi$
$967$	12910.4			0.429339			0.214670	+	0.976687i	$0.431133\pi$
$968$	59477.5			1.97488
$969$		−	2447.94i		−	0.0811550i
$970$		0			0
$971$	27002.5			0.892432			0.446216	−	0.894925i	$-0.352771\pi$
$971$	27002.5			0.892432			0.446216	+	0.894925i	$0.352771\pi$
$972$		−	138377.i		−	4.56631i
$973$	5930.54			0.195400
$974$	−430.132			−0.0141502
$975$		0			0
$976$	156895.			5.14559
$977$	8403.06			0.275166			0.137583	−	0.990490i	$-0.456067\pi$
$977$	8403.06			0.275166			0.137583	+	0.990490i	$0.456067\pi$
$978$			109969.i			3.59553i
$979$	22348.9			0.729596
$980$		0			0
$981$			44917.7i			1.46189i
$982$	25038.5			0.813656
$983$	41927.2			1.36040			0.680199	−	0.733028i	$-0.261894\pi$
$983$	41927.2			1.36040			0.680199	+	0.733028i	$0.261894\pi$
$984$	−172155.			−5.57733
$985$		0			0
$986$			267.753i			0.00864808i
$987$		−	72841.8i		−	2.34912i
$988$	−69728.5	−	37628.7i	−2.24530	−	1.21167i
$989$	6803.23			0.218736
$990$		0			0
$991$	−21469.8			−0.688206			−0.344103	−	0.938932i	$-0.611817\pi$
$991$	−21469.8			−0.688206			−0.344103	+	0.938932i	$0.611817\pi$
$992$			16083.6i			0.514772i
$993$	51884.5			1.65811
$994$			52494.3i			1.67507i
$995$		0			0
$996$		−	160476.i		−	5.10530i
$997$		−	24074.4i		−	0.764738i	−0.924010	−	0.382369i	$-0.875108\pi$
$997$		−	24074.4i		−	0.764738i	0.924010	−	0.382369i	$-0.124892\pi$
$998$			8142.82i			0.258273i
$999$		−	150639.i		−	4.77077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.4.d.e.324.27		28
5.2	odd	4		325.4.c.d.51.14	yes	14
5.3	odd	4		325.4.c.f.51.1	yes	14
5.4	even	2	inner	325.4.d.e.324.2		28
13.12	even	2	inner	325.4.d.e.324.1		28
65.12	odd	4		325.4.c.d.51.1	✓	14
65.38	odd	4		325.4.c.f.51.14	yes	14
65.64	even	2	inner	325.4.d.e.324.28		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.4.c.d.51.1	✓	14	65.12	odd	4
325.4.c.d.51.14	yes	14	5.2	odd	4
325.4.c.f.51.1	yes	14	5.3	odd	4
325.4.c.f.51.14	yes	14	65.38	odd	4
325.4.d.e.324.1		28	13.12	even	2	inner
325.4.d.e.324.2		28	5.4	even	2	inner
325.4.d.e.324.27		28	1.1	even	1	trivial
325.4.d.e.324.28		28	65.64	even	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	325.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+5.39779 q^{2} -9.57032i q^{3} +21.1361 q^{4} -51.6586i q^{6} +19.5662 q^{7} +70.9061 q^{8} -64.5911 q^{9} -22.1851i q^{11} -202.280i q^{12} +(-22.2600 + 41.2492i) q^{13} +105.614 q^{14} +213.647 q^{16} -3.19819i q^{17} -348.649 q^{18} +79.9778i q^{19} -187.255i q^{21} -119.751i q^{22} +81.6896i q^{23} -678.595i q^{24} +(-120.155 + 222.654i) q^{26} +359.759i q^{27} +413.555 q^{28} -15.5101 q^{29} +27.4476i q^{31} +585.974 q^{32} -212.319 q^{33} -17.2632i q^{34} -1365.21 q^{36} -418.722 q^{37} +431.703i q^{38} +(394.768 + 213.035i) q^{39} -253.693i q^{41} -1010.76i q^{42} -83.2815i q^{43} -468.908i q^{44} +440.943i q^{46} +388.997 q^{47} -2044.67i q^{48} +39.8376 q^{49} -30.6078 q^{51} +(-470.490 + 871.848i) q^{52} +92.5015i q^{53} +1941.90i q^{54} +1387.37 q^{56} +765.413 q^{57} -83.7202 q^{58} -385.328i q^{59} +734.366 q^{61} +148.156i q^{62} -1263.80 q^{63} +1453.79 q^{64} -1146.05 q^{66} -138.626 q^{67} -67.5975i q^{68} +781.796 q^{69} +497.037i q^{71} -4579.90 q^{72} -716.898 q^{73} -2260.17 q^{74} +1690.42i q^{76} -434.079i q^{77} +(2130.87 + 1149.92i) q^{78} -425.224 q^{79} +1699.05 q^{81} -1369.38i q^{82} +793.338 q^{83} -3957.85i q^{84} -449.536i q^{86} +148.436i q^{87} -1573.06i q^{88} +1007.38i q^{89} +(-435.544 + 807.091i) q^{91} +1726.60i q^{92} +262.682 q^{93} +2099.73 q^{94} -5607.96i q^{96} +740.271 q^{97} +215.035 q^{98} +1432.96i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 112 q^{4} - 316 q^{9} + 184 q^{14} + 560 q^{16} - 568 q^{26} - 36 q^{29} - 4168 q^{36} + 1120 q^{39} - 576 q^{49} + 1072 q^{51} + 4984 q^{56} + 260 q^{61} + 5328 q^{64} - 3960 q^{66} + 4280 q^{69}+ \cdots + 11848 q^{94}+O(q^{100}) \) 28 * q + 112 * q^4 - 316 * q^9 + 184 * q^14 + 560 * q^16 - 568 * q^26 - 36 * q^29 - 4168 * q^36 + 1120 * q^39 - 576 * q^49 + 1072 * q^51 + 4984 * q^56 + 260 * q^61 + 5328 * q^64 - 3960 * q^66 + 4280 * q^69 - 10704 * q^74 - 2512 * q^79 + 8860 * q^81 + 1952 * q^91 + 11848 * q^94

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