LMFDB - Embedded newform 90.4.c.c.19.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [90,4,Mod(19,90)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("90.19"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(90, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	90.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-16,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31017190052$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{31})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 15x^{2} + 64 $ x^4 - 15*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.3
Root			$2.78388 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	90.19
Dual form			90.4.c.c.19.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000i q^{2} -4.00000 q^{4} +(-11.1355 - 1.00000i) q^{5} -22.2711i q^{7} -8.00000i q^{8} +(2.00000 - 22.2711i) q^{10} -22.2711 q^{11} -66.8132i q^{13} +44.5421 q^{14} +16.0000 q^{16} +62.0000i q^{17} -84.0000 q^{19} +(44.5421 + 4.00000i) q^{20} -44.5421i q^{22} -140.000i q^{23} +(123.000 + 22.2711i) q^{25} +133.626 q^{26} +89.0842i q^{28} -200.440 q^{29} +16.0000 q^{31} +32.0000i q^{32} -124.000 q^{34} +(-22.2711 + 248.000i) q^{35} +244.982i q^{37} -168.000i q^{38} +(-8.00000 + 89.0842i) q^{40} -222.711 q^{41} +356.337i q^{43} +89.0842 q^{44} +280.000 q^{46} +100.000i q^{47} -153.000 q^{49} +(-44.5421 + 246.000i) q^{50} +267.253i q^{52} -738.000i q^{53} +(248.000 + 22.2711i) q^{55} -178.168 q^{56} -400.879i q^{58} +645.861 q^{59} -358.000 q^{61} +32.0000i q^{62} -64.0000 q^{64} +(-66.8132 + 744.000i) q^{65} -846.300i q^{67} -248.000i q^{68} +(-496.000 - 44.5421i) q^{70} +935.384 q^{71} -445.421i q^{73} -489.963 q^{74} +336.000 q^{76} +496.000i q^{77} +936.000 q^{79} +(-178.168 - 16.0000i) q^{80} -445.421i q^{82} -1304.00i q^{83} +(62.0000 - 690.403i) q^{85} -712.674 q^{86} +178.168i q^{88} -712.674 q^{89} -1488.00 q^{91} +560.000i q^{92} -200.000 q^{94} +(935.384 + 84.0000i) q^{95} +757.216i q^{97} -306.000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{4} + 8 q^{10} + 64 q^{16} - 336 q^{19} + 492 q^{25} + 64 q^{31} - 496 q^{34} - 32 q^{40} + 1120 q^{46} - 612 q^{49} + 992 q^{55} - 1432 q^{61} - 256 q^{64} - 1984 q^{70} + 1344 q^{76} + 3744 q^{79}+ \cdots - 800 q^{94}+O(q^{100}) $ 4 * q - 16 * q^4 + 8 * q^10 + 64 * q^16 - 336 * q^19 + 492 * q^25 + 64 * q^31 - 496 * q^34 - 32 * q^40 + 1120 * q^46 - 612 * q^49 + 992 * q^55 - 1432 * q^61 - 256 * q^64 - 1984 * q^70 + 1344 * q^76 + 3744 * q^79 + 248 * q^85 - 5952 * q^91 - 800 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$-1$

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
$5$	−11.1355	−	1.00000i	−0.995992	−	0.0894427i
$5$	−11.1355	−	1.00000i	−0.995992	−	0.0894427i
$6$		0			0
$7$		−	22.2711i		−	1.20252i	−0.799052	−	0.601262i	$-0.794665\pi$
$7$		−	22.2711i		−	1.20252i	0.799052	−	0.601262i	$-0.205335\pi$
$8$		−	8.00000i		−	0.353553i
$9$		0			0
$10$	2.00000	−	22.2711i	0.0632456	−	0.704273i
$11$	−22.2711			−0.610452			−0.305226	−	0.952280i	$-0.598732\pi$
$11$	−22.2711			−0.610452			−0.305226	+	0.952280i	$0.598732\pi$
$12$		0			0
$13$		−	66.8132i		−	1.42543i	−0.701452	−	0.712717i	$-0.747464\pi$
$13$		−	66.8132i		−	1.42543i	0.701452	−	0.712717i	$-0.252536\pi$
$14$	44.5421			0.850313
$15$		0			0
$16$	16.0000			0.250000
$17$			62.0000i			0.884542i	0.896882	+	0.442271i	$0.145827\pi$
$17$			62.0000i			0.884542i	−0.896882	+	0.442271i	$0.854173\pi$
$18$		0			0
$19$	−84.0000			−1.01426			−0.507130	−	0.861870i	$-0.669293\pi$
$19$	−84.0000			−1.01426			−0.507130	+	0.861870i	$0.669293\pi$
$20$	44.5421	+	4.00000i	0.497996	+	0.0447214i
$21$		0			0
$22$		−	44.5421i		−	0.431655i
$23$		−	140.000i		−	1.26922i	−0.772833	−	0.634609i	$-0.781161\pi$
$23$		−	140.000i		−	1.26922i	0.772833	−	0.634609i	$-0.218839\pi$
$24$		0			0
$25$	123.000	+	22.2711i	0.984000	+	0.178168i
$26$	133.626			1.00793
$27$		0			0
$28$			89.0842i			0.601262i
$29$	−200.440			−1.28347			−0.641736	−	0.766926i	$-0.721785\pi$
$29$	−200.440			−1.28347			−0.641736	+	0.766926i	$0.721785\pi$
$30$		0			0
$31$	16.0000			0.0926995			0.0463498	−	0.998925i	$-0.485241\pi$
$31$	16.0000			0.0926995			0.0463498	+	0.998925i	$0.485241\pi$
$32$			32.0000i			0.176777i
$33$		0			0
$34$	−124.000			−0.625465
$35$	−22.2711	+	248.000i	−0.107557	+	1.19770i
$36$		0			0
$37$			244.982i			1.08851i	0.838921	+	0.544253i	$0.183187\pi$
$37$			244.982i			1.08851i	−0.838921	+	0.544253i	$0.816813\pi$
$38$		−	168.000i		−	0.717189i
$39$		0			0
$40$	−8.00000	+	89.0842i	−0.0316228	+	0.352136i
$41$	−222.711			−0.848330			−0.424165	−	0.905585i	$-0.639432\pi$
$41$	−222.711			−0.848330			−0.424165	+	0.905585i	$0.639432\pi$
$42$		0			0
$43$			356.337i			1.26374i	0.775074	+	0.631871i	$0.217713\pi$
$43$			356.337i			1.26374i	−0.775074	+	0.631871i	$0.782287\pi$
$44$	89.0842			0.305226
$45$		0			0
$46$	280.000			0.897473
$47$			100.000i			0.310351i	0.987887	+	0.155176i	$0.0495943\pi$
$47$			100.000i			0.310351i	−0.987887	+	0.155176i	$0.950406\pi$
$48$		0			0
$49$	−153.000			−0.446064
$50$	−44.5421	+	246.000i	−0.125984	+	0.695793i
$51$		0			0
$52$			267.253i			0.712717i
$53$		−	738.000i		−	1.91268i	−0.292255	−	0.956341i	$-0.594405\pi$
$53$		−	738.000i		−	1.91268i	0.292255	−	0.956341i	$-0.405595\pi$
$54$		0			0
$55$	248.000	+	22.2711i	0.608006	+	0.0546005i
$56$	−178.168			−0.425156
$57$		0			0
$58$		−	400.879i		−	0.907552i
$59$	645.861			1.42515			0.712575	−	0.701596i	$-0.247529\pi$
$59$	645.861			1.42515			0.712575	+	0.701596i	$0.247529\pi$
$60$		0			0
$61$	−358.000			−0.751430			−0.375715	−	0.926735i	$-0.622603\pi$
$61$	−358.000			−0.751430			−0.375715	+	0.926735i	$0.622603\pi$
$62$			32.0000i			0.0655485i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−66.8132	+	744.000i	−0.127495	+	1.41972i
$66$		0			0
$67$		−	846.300i		−	1.54316i	−0.636130	−	0.771582i	$-0.719466\pi$
$67$		−	846.300i		−	1.54316i	0.636130	−	0.771582i	$-0.280534\pi$
$68$		−	248.000i		−	0.442271i
$69$		0			0
$70$	−496.000	−	44.5421i	−0.846905	−	0.0760543i
$71$	935.384			1.56352			0.781758	−	0.623581i	$-0.214323\pi$
$71$	935.384			1.56352			0.781758	+	0.623581i	$0.214323\pi$
$72$		0			0
$73$		−	445.421i		−	0.714145i	−0.934077	−	0.357073i	$-0.883775\pi$
$73$		−	445.421i		−	0.714145i	0.934077	−	0.357073i	$-0.116225\pi$
$74$	−489.963			−0.769690
$75$		0			0
$76$	336.000			0.507130
$77$			496.000i			0.734084i
$78$		0			0
$79$	936.000			1.33302			0.666508	−	0.745498i	$-0.267788\pi$
$79$	936.000			1.33302			0.666508	+	0.745498i	$0.267788\pi$
$80$	−178.168	−	16.0000i	−0.248998	−	0.0223607i
$81$		0			0
$82$		−	445.421i		−	0.599860i
$83$		−	1304.00i		−	1.72449i	−0.506492	−	0.862245i	$-0.669058\pi$
$83$		−	1304.00i		−	1.72449i	0.506492	−	0.862245i	$-0.330942\pi$
$84$		0			0
$85$	62.0000	−	690.403i	0.0791158	−	0.880996i
$86$	−712.674			−0.893600
$87$		0			0
$88$			178.168i			0.215828i
$89$	−712.674			−0.848801			−0.424400	−	0.905475i	$-0.639515\pi$
$89$	−712.674			−0.848801			−0.424400	+	0.905475i	$0.639515\pi$
$90$		0			0
$91$	−1488.00			−1.71412
$92$			560.000i			0.634609i
$93$		0			0
$94$	−200.000			−0.219451
$95$	935.384	+	84.0000i	1.01019	+	0.0907181i
$96$		0			0
$97$			757.216i			0.792615i	0.918118	+	0.396307i	$0.129709\pi$
$97$			757.216i			0.792615i	−0.918118	+	0.396307i	$0.870291\pi$
$98$		−	306.000i		−	0.315415i
$99$		0			0
$100$	−492.000	−	89.0842i	−0.492000	−	0.0890842i
$101$	−645.861			−0.636292			−0.318146	−	0.948042i	$-0.603060\pi$
$101$	−645.861			−0.636292			−0.318146	+	0.948042i	$0.603060\pi$
$102$		0			0
$103$		−	690.403i		−	0.660460i	−0.943900	−	0.330230i	$-0.892874\pi$
$103$		−	690.403i		−	0.660460i	0.943900	−	0.330230i	$-0.107126\pi$
$104$	−534.505			−0.503967
$105$		0			0
$106$	1476.00			1.35247
$107$			696.000i			0.628830i	0.949286	+	0.314415i	$0.101808\pi$
$107$			696.000i			0.628830i	−0.949286	+	0.314415i	$0.898192\pi$
$108$		0			0
$109$	1142.00			1.00352			0.501760	−	0.865007i	$-0.332686\pi$
$109$	1142.00			1.00352			0.501760	+	0.865007i	$0.332686\pi$
$110$	−44.5421	+	496.000i	−0.0386084	+	0.429925i
$111$		0			0
$112$		−	356.337i		−	0.300631i
$113$			78.0000i			0.0649347i	0.999473	+	0.0324674i	$0.0103365\pi$
$113$			78.0000i			0.0649347i	−0.999473	+	0.0324674i	$0.989664\pi$
$114$		0			0
$115$	−140.000	+	1558.97i	−0.113522	+	1.26413i
$116$	801.758			0.641736
$117$		0			0
$118$			1291.72i			1.00773i
$119$	1380.81			1.06368
$120$		0			0
$121$	−835.000			−0.627348
$122$		−	716.000i		−	0.531341i
$123$		0			0
$124$	−64.0000			−0.0463498
$125$	−1347.40	−	371.000i	−0.964120	−	0.265466i
$126$		0			0
$127$			1313.99i			0.918094i	0.888412	+	0.459047i	$0.151809\pi$
$127$			1313.99i			0.918094i	−0.888412	+	0.459047i	$0.848191\pi$
$128$		−	128.000i		−	0.0883883i
$129$		0			0
$130$	−1488.00	−	133.626i	−1.00389	−	0.0901524i
$131$	467.692			0.311927			0.155964	−	0.987763i	$-0.450152\pi$
$131$	467.692			0.311927			0.155964	+	0.987763i	$0.450152\pi$
$132$		0			0
$133$			1870.77i			1.21967i
$134$	1692.60			1.09118
$135$		0			0
$136$	496.000			0.312733
$137$		−	1062.00i		−	0.662283i	−0.943581	−	0.331142i	$-0.892566\pi$
$137$		−	1062.00i		−	0.662283i	0.943581	−	0.331142i	$-0.107434\pi$
$138$		0			0
$139$	860.000			0.524779			0.262389	−	0.964962i	$-0.415490\pi$
$139$	860.000			0.524779			0.262389	+	0.964962i	$0.415490\pi$
$140$	89.0842	−	992.000i	0.0537785	−	0.598852i
$141$		0			0
$142$			1870.77i			1.10557i
$143$			1488.00i			0.870160i
$144$		0			0
$145$	2232.00	+	200.440i	1.27833	+	0.114797i
$146$	890.842			0.504977
$147$		0			0
$148$		−	979.927i		−	0.544253i
$149$	−1358.53			−0.746950			−0.373475	−	0.927640i	$-0.621834\pi$
$149$	−1358.53			−0.746950			−0.373475	+	0.927640i	$0.621834\pi$
$150$		0			0
$151$	−1376.00			−0.741571			−0.370786	−	0.928718i	$-0.620912\pi$
$151$	−1376.00			−0.741571			−0.370786	+	0.928718i	$0.620912\pi$
$152$			672.000i			0.358595i
$153$		0			0
$154$	−992.000			−0.519076
$155$	−178.168	−	16.0000i	−0.0923280	−	0.00829130i
$156$		0			0
$157$		−	1848.50i		−	0.939657i	−0.882758	−	0.469829i	$-0.844316\pi$
$157$		−	1848.50i		−	0.939657i	0.882758	−	0.469829i	$-0.155684\pi$
$158$			1872.00i			0.942584i
$159$		0			0
$160$	32.0000	−	356.337i	0.0158114	−	0.176068i
$161$	−3117.95			−1.52627
$162$		0			0
$163$		−	222.711i		−	0.107019i	−0.998567	−	0.0535093i	$-0.982959\pi$
$163$		−	222.711i		−	0.107019i	0.998567	−	0.0535093i	$-0.0170407\pi$
$164$	890.842			0.424165
$165$		0			0
$166$	2608.00			1.21940
$167$		−	2172.00i		−	1.00643i	−0.864160	−	0.503217i	$-0.832150\pi$
$167$		−	2172.00i		−	1.00643i	0.864160	−	0.503217i	$-0.167850\pi$
$168$		0			0
$169$	−2267.00			−1.03186
$170$	1380.81	+	124.000i	0.622959	+	0.0559433i
$171$		0			0
$172$		−	1425.35i		−	0.631871i
$173$			3434.00i			1.50915i	0.656216	+	0.754573i	$0.272156\pi$
$173$			3434.00i			1.50915i	−0.656216	+	0.754573i	$0.727844\pi$
$174$		0			0
$175$	496.000	−	2739.34i	0.214252	−	1.18328i
$176$	−356.337			−0.152613
$177$		0			0
$178$		−	1425.35i		−	0.600193i
$179$	−3362.93			−1.40423			−0.702115	−	0.712064i	$-0.747761\pi$
$179$	−3362.93			−1.40423			−0.702115	+	0.712064i	$0.747761\pi$
$180$		0			0
$181$	−1678.00			−0.689087			−0.344544	−	0.938770i	$-0.611966\pi$
$181$	−1678.00			−0.689087			−0.344544	+	0.938770i	$0.611966\pi$
$182$		−	2976.00i		−	1.21206i
$183$		0			0
$184$	−1120.00			−0.448736
$185$	244.982	−	2728.00i	0.0973590	−	1.08414i
$186$		0			0
$187$		−	1380.81i		−	0.539971i
$188$		−	400.000i		−	0.155176i
$189$		0			0
$190$	−168.000	+	1870.77i	−0.0641474	+	0.714315i
$191$	1737.14			0.658090			0.329045	−	0.944314i	$-0.393273\pi$
$191$	1737.14			0.658090			0.329045	+	0.944314i	$0.393273\pi$
$192$		0			0
$193$		−	2449.82i		−	0.913687i	−0.889547	−	0.456844i	$-0.848980\pi$
$193$		−	2449.82i		−	0.913687i	0.889547	−	0.456844i	$-0.151020\pi$
$194$	−1514.43			−0.560463
$195$		0			0
$196$	612.000			0.223032
$197$			526.000i			0.190233i	0.995466	+	0.0951166i	$0.0303224\pi$
$197$			526.000i			0.190233i	−0.995466	+	0.0951166i	$0.969678\pi$
$198$		0			0
$199$	744.000			0.265029			0.132514	−	0.991181i	$-0.457695\pi$
$199$	744.000			0.265029			0.132514	+	0.991181i	$0.457695\pi$
$200$	178.168	−	984.000i	0.0629921	−	0.347897i
$201$		0			0
$202$		−	1291.72i		−	0.449927i
$203$			4464.00i			1.54341i
$204$		0			0
$205$	2480.00	+	222.711i	0.844930	+	0.0758770i
$206$	1380.81			0.467016
$207$		0			0
$208$		−	1069.01i		−	0.356358i
$209$	1870.77			0.619157
$210$		0			0
$211$	1476.00			0.481574			0.240787	−	0.970578i	$-0.422595\pi$
$211$	1476.00			0.481574			0.240787	+	0.970578i	$0.422595\pi$
$212$			2952.00i			0.956341i
$213$		0			0
$214$	−1392.00			−0.444650
$215$	356.337	−	3968.00i	0.113032	−	1.25868i
$216$		0			0
$217$		−	356.337i		−	0.111473i
$218$			2284.00i			0.709596i
$219$		0			0
$220$	−992.000	−	89.0842i	−0.304003	−	0.0273003i
$221$	4142.42			1.26086
$222$		0			0
$223$			824.029i			0.247449i	0.992317	+	0.123724i	$0.0394839\pi$
$223$			824.029i			0.247449i	−0.992317	+	0.123724i	$0.960516\pi$
$224$	712.674			0.212578
$225$		0			0
$226$	−156.000			−0.0459158
$227$		−	2200.00i		−	0.643256i	−0.946866	−	0.321628i	$-0.895770\pi$
$227$		−	2200.00i		−	0.643256i	0.946866	−	0.321628i	$-0.104230\pi$
$228$		0			0
$229$	−5246.00			−1.51382			−0.756911	−	0.653517i	$-0.773293\pi$
$229$	−5246.00			−1.51382			−0.756911	+	0.653517i	$0.773293\pi$
$230$	−3117.95	−	280.000i	−0.893876	−	0.0802724i
$231$		0			0
$232$			1603.52i			0.453776i
$233$			842.000i			0.236744i	0.992969	+	0.118372i	$0.0377675\pi$
$233$			842.000i			0.236744i	−0.992969	+	0.118372i	$0.962233\pi$
$234$		0			0
$235$	100.000	−	1113.55i	0.0277586	−	0.309107i
$236$	−2583.44			−0.712575
$237$		0			0
$238$			2761.61i			0.752137i
$239$	5835.02			1.57923			0.789615	−	0.613603i	$-0.210280\pi$
$239$	5835.02			1.57923			0.789615	+	0.613603i	$0.210280\pi$
$240$		0			0
$241$	2530.00			0.676231			0.338115	−	0.941105i	$-0.390211\pi$
$241$	2530.00			0.676231			0.338115	+	0.941105i	$0.390211\pi$
$242$		−	1670.00i		−	0.443602i
$243$		0			0
$244$	1432.00			0.375715
$245$	1703.74	+	153.000i	0.444276	+	0.0398972i
$246$		0			0
$247$			5612.31i			1.44576i
$248$		−	128.000i		−	0.0327742i
$249$		0			0
$250$	742.000	−	2694.80i	0.187713	−	0.681736i
$251$	−6748.13			−1.69696			−0.848482	−	0.529223i	$-0.822483\pi$
$251$	−6748.13			−1.69696			−0.848482	+	0.529223i	$0.822483\pi$
$252$		0			0
$253$			3117.95i			0.774797i
$254$	−2627.98			−0.649191
$255$		0			0
$256$	256.000			0.0625000
$257$			258.000i			0.0626210i	0.999510	+	0.0313105i	$0.00996807\pi$
$257$			258.000i			0.0626210i	−0.999510	+	0.0313105i	$0.990032\pi$
$258$		0			0
$259$	5456.00			1.30895
$260$	267.253	−	2976.00i	0.0637473	−	0.709860i
$261$		0			0
$262$			935.384i			0.220566i
$263$			772.000i			0.181002i	0.995896	+	0.0905011i	$0.0288469\pi$
$263$			772.000i			0.181002i	−0.995896	+	0.0905011i	$0.971153\pi$
$264$		0			0
$265$	−738.000	+	8218.02i	−0.171075	+	1.90501i
$266$	−3741.54			−0.862438
$267$		0			0
$268$			3385.20i			0.771582i
$269$	2605.71			0.590607			0.295303	−	0.955404i	$-0.404579\pi$
$269$	2605.71			0.590607			0.295303	+	0.955404i	$0.404579\pi$
$270$		0			0
$271$	−6392.00			−1.43279			−0.716395	−	0.697694i	$-0.754209\pi$
$271$	−6392.00			−1.43279			−0.716395	+	0.697694i	$0.754209\pi$
$272$			992.000i			0.221135i
$273$		0			0
$274$	2124.00			0.468305
$275$	−2739.34	−	496.000i	−0.600685	−	0.108763i
$276$		0			0
$277$		−	1759.41i		−	0.381635i	−0.981626	−	0.190818i	$-0.938886\pi$
$277$		−	1759.41i		−	0.381635i	0.981626	−	0.190818i	$-0.0611139\pi$
$278$			1720.00i			0.371075i
$279$		0			0
$280$	1984.00	+	178.168i	0.423452	+	0.0380272i
$281$	6414.06			1.36168			0.680838	−	0.732434i	$-0.261616\pi$
$281$	6414.06			1.36168			0.680838	+	0.732434i	$0.261616\pi$
$282$		0			0
$283$			1380.81i			0.290037i	0.989429	+	0.145018i	$0.0463241\pi$
$283$			1380.81i			0.290037i	−0.989429	+	0.145018i	$0.953676\pi$
$284$	−3741.54			−0.781758
$285$		0			0
$286$	−2976.00			−0.615296
$287$			4960.00i			1.02014i
$288$		0			0
$289$	1069.00			0.217586
$290$	−400.879	+	4464.00i	−0.0811739	+	0.903914i
$291$		0			0
$292$			1781.68i			0.357073i
$293$		−	1374.00i		−	0.273959i	−0.990574	−	0.136979i	$-0.956261\pi$
$293$		−	1374.00i		−	0.273959i	0.990574	−	0.136979i	$-0.0437394\pi$
$294$		0			0
$295$	−7192.00	−	645.861i	−1.41944	−	0.127469i
$296$	1959.85			0.384845
$297$		0			0
$298$		−	2717.07i		−	0.528173i
$299$	−9353.84			−1.80919
$300$		0			0
$301$	7936.00			1.51968
$302$		−	2752.00i		−	0.524370i
$303$		0			0
$304$	−1344.00			−0.253565
$305$	3986.52	+	358.000i	0.748418	+	0.0672099i
$306$		0			0
$307$		−	267.253i		−	0.0496838i	−0.999691	−	0.0248419i	$-0.992092\pi$
$307$		−	267.253i		−	0.0496838i	0.999691	−	0.0248419i	$-0.00790823\pi$
$308$		−	1984.00i		−	0.367042i
$309$		0			0
$310$	32.0000	−	356.337i	0.00586283	−	0.0652857i
$311$	3607.91			0.657832			0.328916	−	0.944359i	$-0.393317\pi$
$311$	3607.91			0.657832			0.328916	+	0.944359i	$0.393317\pi$
$312$		0			0
$313$		−	7794.87i		−	1.40764i	−0.710377	−	0.703821i	$-0.751476\pi$
$313$		−	7794.87i		−	1.40764i	0.710377	−	0.703821i	$-0.248524\pi$
$314$	3697.00			0.664438
$315$		0			0
$316$	−3744.00			−0.666508
$317$		−	9334.00i		−	1.65378i	−0.562360	−	0.826892i	$-0.690107\pi$
$317$		−	9334.00i		−	1.65378i	0.562360	−	0.826892i	$-0.309893\pi$
$318$		0			0
$319$	4464.00			0.783498
$320$	712.674	+	64.0000i	0.124499	+	0.0111803i
$321$		0			0
$322$		−	6235.90i		−	1.07923i
$323$		−	5208.00i		−	0.897154i
$324$		0			0
$325$	1488.00	−	8218.02i	0.253967	−	1.40263i
$326$	445.421			0.0756736
$327$		0			0
$328$			1781.68i			0.299930i
$329$	2227.11			0.373205
$330$		0			0
$331$	1636.00			0.271670			0.135835	−	0.990731i	$-0.456628\pi$
$331$	1636.00			0.271670			0.135835	+	0.990731i	$0.456628\pi$
$332$			5216.00i			0.862245i
$333$		0			0
$334$	4344.00			0.711656
$335$	−846.300	+	9424.00i	−0.138025	+	1.53698i
$336$		0			0
$337$			178.168i			0.0287996i	0.999896	+	0.0143998i	$0.00458375\pi$
$337$			178.168i			0.0287996i	−0.999896	+	0.0143998i	$0.995416\pi$
$338$		−	4534.00i		−	0.729636i
$339$		0			0
$340$	−248.000	+	2761.61i	−0.0395579	+	0.440498i
$341$	−356.337			−0.0565886
$342$		0			0
$343$		−	4231.50i		−	0.666121i
$344$	2850.70			0.446800
$345$		0			0
$346$	−6868.00			−1.06713
$347$			3840.00i			0.594069i	0.954867	+	0.297035i	$0.0959977\pi$
$347$			3840.00i			0.594069i	−0.954867	+	0.297035i	$0.904002\pi$
$348$		0			0
$349$	−6682.00			−1.02487			−0.512434	−	0.858726i	$-0.671256\pi$
$349$	−6682.00			−1.02487			−0.512434	+	0.858726i	$0.671256\pi$
$350$	5478.68	+	992.000i	0.836708	+	0.151499i
$351$		0			0
$352$		−	712.674i		−	0.107914i
$353$		−	2110.00i		−	0.318142i	−0.987267	−	0.159071i	$-0.949150\pi$
$353$		−	2110.00i		−	0.318142i	0.987267	−	0.159071i	$-0.0508498\pi$
$354$		0			0
$355$	−10416.0	−	935.384i	−1.55725	−	0.139845i
$356$	2850.70			0.424400
$357$		0			0
$358$		−	6725.86i		−	0.992941i
$359$	−1870.77			−0.275029			−0.137514	−	0.990500i	$-0.543911\pi$
$359$	−1870.77			−0.275029			−0.137514	+	0.990500i	$0.543911\pi$
$360$		0			0
$361$	197.000			0.0287214
$362$		−	3356.00i		−	0.487258i
$363$		0			0
$364$	5952.00			0.857059
$365$	−445.421	+	4960.00i	−0.0638751	+	0.711283i
$366$		0			0
$367$		−	9643.37i		−	1.37161i	−0.727787	−	0.685803i	$-0.759451\pi$
$367$		−	9643.37i		−	1.37161i	0.727787	−	0.685803i	$-0.240549\pi$
$368$		−	2240.00i		−	0.317305i
$369$		0			0
$370$	5456.00	+	489.963i	0.766605	+	0.0688432i
$371$	−16436.0			−2.30005
$372$		0			0
$373$			11558.7i			1.60452i	0.596975	+	0.802260i	$0.296369\pi$
$373$			11558.7i			1.60452i	−0.596975	+	0.802260i	$0.703631\pi$
$374$	2761.61			0.381817
$375$		0			0
$376$	800.000			0.109726
$377$			13392.0i			1.82950i
$378$		0			0
$379$	6220.00			0.843008			0.421504	−	0.906827i	$-0.361502\pi$
$379$	6220.00			0.843008			0.421504	+	0.906827i	$0.361502\pi$
$380$	−3741.54	−	336.000i	−0.505097	−	0.0453590i
$381$		0			0
$382$			3474.28i			0.465340i
$383$		−	13900.0i		−	1.85446i	−0.374497	−	0.927228i	$-0.622185\pi$
$383$		−	13900.0i		−	1.85446i	0.374497	−	0.927228i	$-0.377815\pi$
$384$		0			0
$385$	496.000	−	5523.22i	0.0656584	−	0.731141i
$386$	4899.63			0.646074
$387$		0			0
$388$		−	3028.86i		−	0.396307i
$389$	3630.18			0.473156			0.236578	−	0.971613i	$-0.423974\pi$
$389$	3630.18			0.473156			0.236578	+	0.971613i	$0.423974\pi$
$390$		0			0
$391$	8680.00			1.12268
$392$			1224.00i			0.157707i
$393$		0			0
$394$	−1052.00			−0.134515
$395$	−10422.9	−	936.000i	−1.32767	−	0.119229i
$396$		0			0
$397$			512.234i			0.0647564i	0.999476	+	0.0323782i	$0.0103081\pi$
$397$			512.234i			0.0647564i	−0.999476	+	0.0323782i	$0.989692\pi$
$398$			1488.00i			0.187404i
$399$		0			0
$400$	1968.00	+	356.337i	0.246000	+	0.0445421i
$401$	−2984.32			−0.371646			−0.185823	−	0.982583i	$-0.559495\pi$
$401$	−2984.32			−0.371646			−0.185823	+	0.982583i	$0.559495\pi$
$402$		0			0
$403$		−	1069.01i		−	0.132137i
$404$	2583.44			0.318146
$405$		0			0
$406$	−8928.00			−1.09135
$407$		−	5456.00i		−	0.664481i
$408$		0			0
$409$	−14822.0			−1.79193			−0.895967	−	0.444121i	$-0.853516\pi$
$409$	−14822.0			−1.79193			−0.895967	+	0.444121i	$0.853516\pi$
$410$	−445.421	+	4960.00i	−0.0536531	+	0.597456i
$411$		0			0
$412$			2761.61i			0.330230i
$413$		−	14384.0i		−	1.71378i
$414$		0			0
$415$	−1304.00	+	14520.7i	−0.154243	+	1.71758i
$416$	2138.02			0.251983
$417$		0			0
$418$			3741.54i			0.437810i
$419$	−8663.44			−1.01011			−0.505056	−	0.863087i	$-0.668528\pi$
$419$	−8663.44			−1.01011			−0.505056	+	0.863087i	$0.668528\pi$
$420$		0			0
$421$	4894.00			0.566553			0.283277	−	0.959038i	$-0.408579\pi$
$421$	4894.00			0.566553			0.283277	+	0.959038i	$0.408579\pi$
$422$			2952.00i			0.340524i
$423$		0			0
$424$	−5904.00			−0.676235
$425$	−1380.81	+	7626.00i	−0.157597	+	0.870389i
$426$		0			0
$427$			7973.04i			0.903612i
$428$		−	2784.00i		−	0.314415i
$429$		0			0
$430$	7936.00	+	712.674i	0.890018	+	0.0799260i
$431$	9799.27			1.09516			0.547580	−	0.836753i	$-0.315549\pi$
$431$	9799.27			1.09516			0.547580	+	0.836753i	$0.315549\pi$
$432$		0			0
$433$			3697.00i			0.410315i	0.978729	+	0.205157i	$0.0657706\pi$
$433$			3697.00i			0.410315i	−0.978729	+	0.205157i	$0.934229\pi$
$434$	712.674			0.0788236
$435$		0			0
$436$	−4568.00			−0.501760
$437$			11760.0i			1.28732i
$438$		0			0
$439$	9288.00			1.00978			0.504888	−	0.863185i	$-0.331534\pi$
$439$	9288.00			1.00978			0.504888	+	0.863185i	$0.331534\pi$
$440$	178.168	−	1984.00i	0.0193042	−	0.214962i
$441$		0			0
$442$			8284.83i			0.891560i
$443$			7368.00i			0.790213i	0.918635	+	0.395106i	$0.129292\pi$
$443$			7368.00i			0.790213i	−0.918635	+	0.395106i	$0.870708\pi$
$444$		0			0
$445$	7936.00	+	712.674i	0.845399	+	0.0759191i
$446$	−1648.06			−0.174973
$447$		0			0
$448$			1425.35i			0.150316i
$449$	−400.879			−0.0421351			−0.0210675	−	0.999778i	$-0.506707\pi$
$449$	−400.879			−0.0421351			−0.0210675	+	0.999778i	$0.506707\pi$
$450$		0			0
$451$	4960.00			0.517865
$452$		−	312.000i		−	0.0324674i
$453$		0			0
$454$	4400.00			0.454851
$455$	16569.7	+	1488.00i	1.70725	+	0.153315i
$456$		0			0
$457$			14743.4i			1.50912i	0.656230	+	0.754561i	$0.272150\pi$
$457$			14743.4i			1.50912i	−0.656230	+	0.754561i	$0.727850\pi$
$458$		−	10492.0i		−	1.07043i
$459$		0			0
$460$	560.000	−	6235.90i	0.0567612	−	0.632066i
$461$	4743.74			0.479258			0.239629	−	0.970865i	$-0.422974\pi$
$461$	4743.74			0.479258			0.239629	+	0.970865i	$0.422974\pi$
$462$		0			0
$463$			7282.64i			0.731000i	0.930811	+	0.365500i	$0.119102\pi$
$463$			7282.64i			0.731000i	−0.930811	+	0.365500i	$0.880898\pi$
$464$	−3207.03			−0.320868
$465$		0			0
$466$	−1684.00			−0.167403
$467$			5664.00i			0.561239i	0.959819	+	0.280620i	$0.0905399\pi$
$467$			5664.00i			0.561239i	−0.959819	+	0.280620i	$0.909460\pi$
$468$		0			0
$469$	−18848.0			−1.85569
$470$	2227.11	+	200.000i	0.218572	+	0.0196283i
$471$		0			0
$472$		−	5166.89i		−	0.503867i
$473$		−	7936.00i		−	0.771454i
$474$		0			0
$475$	−10332.0	−	1870.77i	−0.998031	−	0.180709i
$476$	−5523.22			−0.531841
$477$		0			0
$478$			11670.0i			1.11668i
$479$	10111.1			0.964480			0.482240	−	0.876039i	$-0.339823\pi$
$479$	10111.1			0.964480			0.482240	+	0.876039i	$0.339823\pi$
$480$		0			0
$481$	16368.0			1.55159
$482$			5060.00i			0.478167i
$483$		0			0
$484$	3340.00			0.313674
$485$	757.216	−	8432.00i	0.0708936	−	0.789438i
$486$		0			0
$487$		−	11558.7i		−	1.07551i	−0.843101	−	0.537755i	$-0.819272\pi$
$487$		−	11558.7i		−	1.07551i	0.843101	−	0.537755i	$-0.180728\pi$
$488$			2864.00i			0.265670i
$489$		0			0
$490$	−306.000	+	3407.47i	−0.0282116	+	0.314151i
$491$	467.692			0.0429871			0.0214935	−	0.999769i	$-0.493158\pi$
$491$	467.692			0.0429871			0.0214935	+	0.999769i	$0.493158\pi$
$492$		0			0
$493$		−	12427.3i		−	1.13528i
$494$	−11224.6			−1.02231
$495$		0			0
$496$	256.000			0.0231749
$497$		−	20832.0i		−	1.88017i
$498$		0			0
$499$	−9204.00			−0.825707			−0.412853	−	0.910798i	$-0.635468\pi$
$499$	−9204.00			−0.825707			−0.412853	+	0.910798i	$0.635468\pi$
$500$	5389.60	+	1484.00i	0.482060	+	0.132733i
$501$		0			0
$502$		−	13496.3i		−	1.19994i
$503$			1260.00i			0.111691i	0.998439	+	0.0558455i	$0.0177854\pi$
$503$			1260.00i			0.111691i	−0.998439	+	0.0558455i	$0.982215\pi$
$504$		0			0
$505$	7192.00	+	645.861i	0.633742	+	0.0569117i
$506$	−6235.90			−0.547864
$507$		0			0
$508$		−	5255.97i		−	0.459047i
$509$	−2071.21			−0.180363			−0.0901814	−	0.995925i	$-0.528745\pi$
$509$	−2071.21			−0.180363			−0.0901814	+	0.995925i	$0.528745\pi$
$510$		0			0
$511$	−9920.00			−0.858777
$512$			512.000i			0.0441942i
$513$		0			0
$514$	−516.000			−0.0442797
$515$	−690.403	+	7688.00i	−0.0590734	+	0.657813i
$516$		0			0
$517$		−	2227.11i		−	0.189455i
$518$			10912.0i			0.925571i
$519$		0			0
$520$	5952.00	+	534.505i	0.501947	+	0.0450762i
$521$	5300.51			0.445719			0.222860	−	0.974851i	$-0.428461\pi$
$521$	5300.51			0.445719			0.222860	+	0.974851i	$0.428461\pi$
$522$		0			0
$523$		−	9309.30i		−	0.778331i	−0.921168	−	0.389166i	$-0.872763\pi$
$523$		−	9309.30i		−	0.778331i	0.921168	−	0.389166i	$-0.127237\pi$
$524$	−1870.77			−0.155964
$525$		0			0
$526$	−1544.00			−0.127988
$527$			992.000i			0.0819966i
$528$		0			0
$529$	−7433.00			−0.610915
$530$	−16436.0	−	1476.00i	−1.34705	−	0.120969i
$531$		0			0
$532$		−	7483.08i		−	0.609835i
$533$			14880.0i			1.20924i
$534$		0			0
$535$	696.000	−	7750.33i	0.0562443	−	0.626310i
$536$	−6770.40			−0.545591
$537$		0			0
$538$			5211.43i			0.417622i
$539$	3407.47			0.272301
$540$		0			0
$541$	9658.00			0.767523			0.383761	−	0.923432i	$-0.374629\pi$
$541$	9658.00			0.767523			0.383761	+	0.923432i	$0.374629\pi$
$542$		−	12784.0i		−	1.01314i
$543$		0			0
$544$	−1984.00			−0.156366
$545$	−12716.8	−	1142.00i	−0.999499	−	0.0897576i
$546$		0			0
$547$		−	890.842i		−	0.0696338i	−0.999394	−	0.0348169i	$-0.988915\pi$
$547$		−	890.842i		−	0.0696338i	0.999394	−	0.0348169i	$-0.0110848\pi$
$548$			4248.00i			0.331142i
$549$		0			0
$550$	992.000	−	5478.68i	0.0769073	−	0.424749i
$551$	16836.9			1.30177
$552$		0			0
$553$		−	20845.7i		−	1.60298i
$554$	3518.83			0.269857
$555$		0			0
$556$	−3440.00			−0.262389
$557$			9066.00i			0.689657i	0.938666	+	0.344828i	$0.112063\pi$
$557$			9066.00i			0.689657i	−0.938666	+	0.344828i	$0.887937\pi$
$558$		0			0
$559$	23808.0			1.80138
$560$	−356.337	+	3968.00i	−0.0268893	+	0.299426i
$561$		0			0
$562$			12828.1i			0.962850i
$563$			1568.00i			0.117377i	0.998276	+	0.0586886i	$0.0186919\pi$
$563$			1568.00i			0.117377i	−0.998276	+	0.0586886i	$0.981308\pi$
$564$		0			0
$565$	78.0000	−	868.571i	0.00580794	−	0.0646745i
$566$	−2761.61			−0.205087
$567$		0			0
$568$		−	7483.08i		−	0.552787i
$569$	2093.48			0.154241			0.0771206	−	0.997022i	$-0.475427\pi$
$569$	2093.48			0.154241			0.0771206	+	0.997022i	$0.475427\pi$
$570$		0			0
$571$	−13916.0			−1.01991			−0.509953	−	0.860202i	$-0.670337\pi$
$571$	−13916.0			−1.01991			−0.509953	+	0.860202i	$0.670337\pi$
$572$		−	5952.00i		−	0.435080i
$573$		0			0
$574$	−9920.00			−0.721346
$575$	3117.95	−	17220.0i	0.226135	−	1.24891i
$576$		0			0
$577$		−	8106.66i		−	0.584896i	−0.956281	−	0.292448i	$-0.905530\pi$
$577$		−	8106.66i		−	0.584896i	0.956281	−	0.292448i	$-0.0944698\pi$
$578$			2138.00i			0.153857i
$579$		0			0
$580$	−8928.00	−	801.758i	−0.639164	−	0.0573986i
$581$	−29041.5			−2.07374
$582$		0			0
$583$			16436.0i			1.16760i
$584$	−3563.37			−0.252488
$585$		0			0
$586$	2748.00			0.193718
$587$		−	20808.0i		−	1.46310i	−0.681789	−	0.731549i	$-0.738798\pi$
$587$		−	20808.0i		−	1.46310i	0.681789	−	0.731549i	$-0.261202\pi$
$588$		0			0
$589$	−1344.00			−0.0940213
$590$	1291.72	−	14384.0i	0.0901345	−	1.00369i
$591$		0			0
$592$			3919.71i			0.272127i
$593$			21486.0i			1.48790i	0.668236	+	0.743950i	$0.267050\pi$
$593$			21486.0i			1.48790i	−0.668236	+	0.743950i	$0.732950\pi$
$594$		0			0
$595$	−15376.0	−	1380.81i	−1.05942	−	0.0951387i
$596$	5434.14			0.373475
$597$		0			0
$598$		−	18707.7i		−	1.27929i
$599$	25923.5			1.76829			0.884145	−	0.467212i	$-0.154742\pi$
$599$	25923.5			1.76829			0.884145	+	0.467212i	$0.154742\pi$
$600$		0			0
$601$	−250.000			−0.0169679			−0.00848395	−	0.999964i	$-0.502701\pi$
$601$	−250.000			−0.0169679			−0.00848395	+	0.999964i	$0.502701\pi$
$602$			15872.0i			1.07458i
$603$		0			0
$604$	5504.00			0.370786
$605$	9298.17	+	835.000i	0.624833	+	0.0561117i
$606$		0			0
$607$		−	13340.4i		−	0.892041i	−0.895023	−	0.446020i	$-0.852841\pi$
$607$		−	13340.4i		−	0.892041i	0.895023	−	0.446020i	$-0.147159\pi$
$608$		−	2688.00i		−	0.179297i
$609$		0			0
$610$	−716.000	+	7973.04i	−0.0475246	+	0.529211i
$611$	6681.32			0.442385
$612$		0			0
$613$			14721.2i			0.969955i	0.874527	+	0.484977i	$0.161172\pi$
$613$			14721.2i			0.969955i	−0.874527	+	0.484977i	$0.838828\pi$
$614$	534.505			0.0351317
$615$		0			0
$616$	3968.00			0.259538
$617$		−	14410.0i		−	0.940235i	−0.882604	−	0.470117i	$-0.844212\pi$
$617$		−	14410.0i		−	0.940235i	0.882604	−	0.470117i	$-0.155788\pi$
$618$		0			0
$619$	21580.0			1.40125			0.700625	−	0.713530i	$-0.252905\pi$
$619$	21580.0			1.40125			0.700625	+	0.713530i	$0.252905\pi$
$620$	712.674	+	64.0000i	0.0461640	+	0.00414565i
$621$		0			0
$622$			7215.82i			0.465158i
$623$			15872.0i			1.02070i
$624$		0			0
$625$	14633.0	+	5478.68i	0.936512	+	0.350636i
$626$	15589.7			0.995354
$627$		0			0
$628$			7393.99i			0.469829i
$629$	−15188.9			−0.962829
$630$		0			0
$631$	−15160.0			−0.956434			−0.478217	−	0.878242i	$-0.658717\pi$
$631$	−15160.0			−0.956434			−0.478217	+	0.878242i	$0.658717\pi$
$632$		−	7488.00i		−	0.471292i
$633$		0			0
$634$	18668.0			1.16940
$635$	1313.99	−	14632.0i	0.0821168	−	0.914415i
$636$		0			0
$637$			10222.4i			0.635835i
$638$			8928.00i			0.554017i
$639$		0			0
$640$	−128.000	+	1425.35i	−0.00790569	+	0.0880341i
$641$	−6102.27			−0.376014			−0.188007	−	0.982168i	$-0.560203\pi$
$641$	−6102.27			−0.376014			−0.188007	+	0.982168i	$0.560203\pi$
$642$		0			0
$643$			14298.0i			0.876919i	0.898751	+	0.438459i	$0.144476\pi$
$643$			14298.0i			0.876919i	−0.898751	+	0.438459i	$0.855524\pi$
$644$	12471.8			0.763133
$645$		0			0
$646$	10416.0			0.634384
$647$			11916.0i			0.724059i	0.932167	+	0.362030i	$0.117916\pi$
$647$			11916.0i			0.724059i	−0.932167	+	0.362030i	$0.882084\pi$
$648$		0			0
$649$	−14384.0			−0.869987
$650$	16436.0	+	2976.00i	0.991807	+	0.179582i
$651$		0			0
$652$			890.842i			0.0535093i
$653$			24646.0i			1.47699i	0.674261	+	0.738493i	$0.264462\pi$
$653$			24646.0i			1.47699i	−0.674261	+	0.738493i	$0.735538\pi$
$654$		0			0
$655$	−5208.00	−	467.692i	−0.310677	−	0.0278996i
$656$	−3563.37			−0.212083
$657$		0			0
$658$			4454.21i			0.263896i
$659$	−17928.2			−1.05976			−0.529881	−	0.848072i	$-0.677764\pi$
$659$	−17928.2			−1.05976			−0.529881	+	0.848072i	$0.677764\pi$
$660$		0			0
$661$	−14638.0			−0.861350			−0.430675	−	0.902507i	$-0.641724\pi$
$661$	−14638.0			−0.861350			−0.430675	+	0.902507i	$0.641724\pi$
$662$			3272.00i			0.192100i
$663$		0			0
$664$	−10432.0			−0.609699
$665$	1870.77	−	20832.0i	0.109091	−	1.21478i
$666$		0			0
$667$			28061.5i			1.62901i
$668$			8688.00i			0.503217i
$669$		0			0
$670$	−18848.0	−	1692.60i	−1.08681	−	0.0975983i
$671$	7973.04			0.458712
$672$		0			0
$673$			31134.9i			1.78330i	0.452721	+	0.891652i	$0.350453\pi$
$673$			31134.9i			1.78330i	−0.452721	+	0.891652i	$0.649547\pi$
$674$	−356.337			−0.0203644
$675$		0			0
$676$	9068.00			0.515931
$677$		−	6382.00i		−	0.362305i	−0.983455	−	0.181152i	$-0.942017\pi$
$677$		−	6382.00i		−	0.362305i	0.983455	−	0.181152i	$-0.0579827\pi$
$678$		0			0
$679$	16864.0			0.953138
$680$	−5523.22	−	496.000i	−0.311479	−	0.0279717i
$681$		0			0
$682$		−	712.674i		−	0.0400142i
$683$		−	4544.00i		−	0.254570i	−0.991866	−	0.127285i	$-0.959374\pi$
$683$		−	4544.00i		−	0.254570i	0.991866	−	0.127285i	$-0.0406263\pi$
$684$		0			0
$685$	−1062.00	+	11825.9i	−0.0592364	+	0.659629i
$686$	8463.00			0.471019
$687$		0			0
$688$			5701.39i			0.315935i
$689$	−49308.1			−2.72640
$690$		0			0
$691$	13564.0			0.746742			0.373371	−	0.927682i	$-0.378202\pi$
$691$	13564.0			0.746742			0.373371	+	0.927682i	$0.378202\pi$
$692$		−	13736.0i		−	0.754573i
$693$		0			0
$694$	−7680.00			−0.420070
$695$	−9576.55	−	860.000i	−0.522675	−	0.0469376i
$696$		0			0
$697$		−	13808.1i		−	0.750384i
$698$		−	13364.0i		−	0.724692i
$699$		0			0
$700$	−1984.00	+	10957.4i	−0.107126	+	0.591642i
$701$	−1492.16			−0.0803968			−0.0401984	−	0.999192i	$-0.512799\pi$
$701$	−1492.16			−0.0803968			−0.0401984	+	0.999192i	$0.512799\pi$
$702$		0			0
$703$		−	20578.5i		−	1.10403i
$704$	1425.35			0.0763066
$705$		0			0
$706$	4220.00			0.224960
$707$			14384.0i			0.765157i
$708$		0			0
$709$	17826.0			0.944245			0.472122	−	0.881533i	$-0.343488\pi$
$709$	17826.0			0.944245			0.472122	+	0.881533i	$0.343488\pi$
$710$	1870.77	−	20832.0i	0.0988855	−	1.10114i
$711$		0			0
$712$			5701.39i			0.300096i
$713$		−	2240.00i		−	0.117656i
$714$		0			0
$715$	1488.00	−	16569.7i	0.0778294	−	0.866672i
$716$	13451.7			0.702115
$717$		0			0
$718$		−	3741.54i		−	0.194475i
$719$	18796.8			0.974967			0.487484	−	0.873132i	$-0.337915\pi$
$719$	18796.8			0.974967			0.487484	+	0.873132i	$0.337915\pi$
$720$		0			0
$721$	−15376.0			−0.794219
$722$			394.000i			0.0203091i
$723$		0			0
$724$	6712.00			0.344544
$725$	−24654.1	−	4464.00i	−1.26294	−	0.228674i
$726$		0			0
$727$			33072.5i			1.68720i	0.536975	+	0.843598i	$0.319567\pi$
$727$			33072.5i			1.68720i	−0.536975	+	0.843598i	$0.680433\pi$
$728$			11904.0i			0.606032i
$729$		0			0
$730$	−9920.00	−	890.842i	−0.502953	−	0.0451665i
$731$	−22092.9			−1.11783
$732$		0			0
$733$		−	34765.1i		−	1.75181i	−0.482481	−	0.875907i	$-0.660264\pi$
$733$		−	34765.1i		−	1.75181i	0.482481	−	0.875907i	$-0.339736\pi$
$734$	19286.7			0.969872
$735$		0			0
$736$	4480.00			0.224368
$737$			18848.0i			0.942028i
$738$		0			0
$739$	22940.0			1.14190			0.570948	−	0.820986i	$-0.306576\pi$
$739$	22940.0			1.14190			0.570948	+	0.820986i	$0.306576\pi$
$740$	−979.927	+	10912.0i	−0.0486795	+	0.542072i
$741$		0			0
$742$		−	32872.1i		−	1.62638i
$743$			26460.0i			1.30649i	0.757146	+	0.653246i	$0.226593\pi$
$743$			26460.0i			1.30649i	−0.757146	+	0.653246i	$0.773407\pi$
$744$		0			0
$745$	15128.0	+	1358.53i	0.743956	+	0.0668092i
$746$	−23117.4			−1.13457
$747$		0			0
$748$			5523.22i			0.269985i
$749$	15500.7			0.756184
$750$		0			0
$751$	−30160.0			−1.46545			−0.732726	−	0.680524i	$-0.761752\pi$
$751$	−30160.0			−1.46545			−0.732726	+	0.680524i	$0.761752\pi$
$752$			1600.00i			0.0775878i
$753$		0			0
$754$	−26784.0			−1.29365
$755$	15322.5	+	1376.00i	0.738599	+	0.0663282i
$756$		0			0
$757$		−	18596.3i		−	0.892860i	−0.894818	−	0.446430i	$-0.852695\pi$
$757$		−	18596.3i		−	0.892860i	0.894818	−	0.446430i	$-0.147305\pi$
$758$			12440.0i			0.596097i
$759$		0			0
$760$	672.000	−	7483.08i	0.0320737	−	0.357157i
$761$	−5478.68			−0.260975			−0.130488	−	0.991450i	$-0.541654\pi$
$761$	−5478.68			−0.260975			−0.130488	+	0.991450i	$0.541654\pi$
$762$		0			0
$763$		−	25433.5i		−	1.20676i
$764$	−6948.57			−0.329045
$765$		0			0
$766$	27800.0			1.31130
$767$		−	43152.0i		−	2.03146i
$768$		0			0
$769$	−29406.0			−1.37894			−0.689472	−	0.724313i	$-0.742157\pi$
$769$	−29406.0			−1.37894			−0.689472	+	0.724313i	$0.742157\pi$
$770$	11046.4	+	992.000i	0.516995	+	0.0464275i
$771$		0			0
$772$			9799.27i			0.456844i
$773$		−	31122.0i		−	1.44810i	−0.689748	−	0.724050i	$-0.742279\pi$
$773$		−	31122.0i		−	1.44810i	0.689748	−	0.724050i	$-0.257721\pi$
$774$		0			0
$775$	1968.00	+	356.337i	0.0912163	+	0.0165161i
$776$	6057.73			0.280232
$777$		0			0
$778$			7260.36i			0.334572i
$779$	18707.7			0.860427
$780$		0			0
$781$	−20832.0			−0.954453
$782$			17360.0i			0.793852i
$783$		0			0
$784$	−2448.00			−0.111516
$785$	−1848.50	+	20584.0i	−0.0840455	+	0.935891i
$786$		0			0
$787$		−	34431.1i		−	1.55951i	−0.626085	−	0.779755i	$-0.715344\pi$
$787$		−	34431.1i		−	1.55951i	0.626085	−	0.779755i	$-0.284656\pi$
$788$		−	2104.00i		−	0.0951166i
$789$		0			0
$790$	1872.00	−	20845.7i	0.0843073	−	0.938806i
$791$	1737.14			0.0780856
$792$		0			0
$793$			23919.1i			1.07111i
$794$	−1024.47			−0.0457897
$795$		0			0
$796$	−2976.00			−0.132514
$797$		−	13066.0i		−	0.580704i	−0.956920	−	0.290352i	$-0.906228\pi$
$797$		−	13066.0i		−	0.580704i	0.956920	−	0.290352i	$-0.0937725\pi$
$798$		0			0
$799$	−6200.00			−0.274518
$800$	−712.674	+	3936.00i	−0.0314960	+	0.173948i
$801$		0			0
$802$		−	5968.64i		−	0.262793i
$803$			9920.00i			0.435952i
$804$		0			0
$805$	34720.0	+	3117.95i	1.52015	+	0.136513i
$806$	2138.02			0.0934350
$807$		0			0
$808$			5166.89i			0.224963i
$809$	39954.3			1.73636			0.868181	−	0.496247i	$-0.165289\pi$
$809$	39954.3			1.73636			0.868181	+	0.496247i	$0.165289\pi$
$810$		0			0
$811$	14428.0			0.624705			0.312352	−	0.949966i	$-0.398883\pi$
$811$	14428.0			0.624705			0.312352	+	0.949966i	$0.398883\pi$
$812$		−	17856.0i		−	0.771703i
$813$		0			0
$814$	10912.0			0.469859
$815$	−222.711	+	2480.00i	−0.00957204	+	0.106590i
$816$		0			0
$817$		−	29932.3i		−	1.28176i
$818$		−	29644.0i		−	1.26709i
$819$		0			0
$820$	−9920.00	−	890.842i	−0.422465	−	0.0379385i
$821$	16591.9			0.705314			0.352657	−	0.935753i	$-0.385278\pi$
$821$	16591.9			0.705314			0.352657	+	0.935753i	$0.385278\pi$
$822$		0			0
$823$		−	25322.2i		−	1.07251i	−0.844056	−	0.536255i	$-0.819838\pi$
$823$		−	25322.2i		−	1.07251i	0.844056	−	0.536255i	$-0.180162\pi$
$824$	−5523.22			−0.233508
$825$		0			0
$826$	28768.0			1.21182
$827$			16592.0i			0.697655i	0.937187	+	0.348827i	$0.113420\pi$
$827$			16592.0i			0.697655i	−0.937187	+	0.348827i	$0.886580\pi$
$828$		0			0
$829$	−18234.0			−0.763924			−0.381962	−	0.924178i	$-0.624751\pi$
$829$	−18234.0			−0.763924			−0.381962	+	0.924178i	$0.624751\pi$
$830$	−29041.5	−	2608.00i	−1.21451	−	0.109066i
$831$		0			0
$832$			4276.04i			0.178179i
$833$		−	9486.00i		−	0.394562i
$834$		0			0
$835$	−2172.00	+	24186.4i	−0.0900182	+	1.00240i
$836$	−7483.08			−0.309578
$837$		0			0
$838$		−	17326.9i		−	0.714257i
$839$	−31357.6			−1.29033			−0.645165	−	0.764044i	$-0.723211\pi$
$839$	−31357.6			−1.29033			−0.645165	+	0.764044i	$0.723211\pi$
$840$		0			0
$841$	15787.0			0.647300
$842$			9788.00i			0.400614i
$843$		0			0
$844$	−5904.00			−0.240787
$845$	25244.2	+	2267.00i	1.02773	+	0.0922925i
$846$		0			0
$847$			18596.3i			0.754401i
$848$		−	11808.0i		−	0.478170i
$849$		0			0
$850$	−15252.0	−	2761.61i	−0.615458	−	0.111438i
$851$	34297.4			1.38155
$852$		0			0
$853$			2249.38i			0.0902898i	0.998980	+	0.0451449i	$0.0143750\pi$
$853$			2249.38i			0.0902898i	−0.998980	+	0.0451449i	$0.985625\pi$
$854$	−15946.1			−0.638950
$855$		0			0
$856$	5568.00			0.222325
$857$			25206.0i			1.00469i	0.864667	+	0.502346i	$0.167530\pi$
$857$			25206.0i			1.00469i	−0.864667	+	0.502346i	$0.832470\pi$
$858$		0			0
$859$	−17540.0			−0.696690			−0.348345	−	0.937366i	$-0.613256\pi$
$859$	−17540.0			−0.696690			−0.348345	+	0.937366i	$0.613256\pi$
$860$	−1425.35	+	15872.0i	−0.0565162	+	0.629338i
$861$		0			0
$862$			19598.5i			0.774395i
$863$		−	33108.0i		−	1.30592i	−0.757392	−	0.652960i	$-0.773527\pi$
$863$		−	33108.0i		−	1.30592i	0.757392	−	0.652960i	$-0.226473\pi$
$864$		0			0
$865$	3434.00	−	38239.4i	0.134982	−	1.50310i
$866$	−7393.99			−0.290136
$867$		0			0
$868$			1425.35i			0.0557367i
$869$	−20845.7			−0.813743
$870$		0			0
$871$	−56544.0			−2.19968
$872$		−	9136.00i		−	0.354798i
$873$		0			0
$874$	−23520.0			−0.910270
$875$	−8262.56	+	30008.0i	−0.319229	+	1.15938i
$876$		0			0
$877$			29152.8i			1.12249i	0.827651	+	0.561243i	$0.189677\pi$
$877$			29152.8i			1.12249i	−0.827651	+	0.561243i	$0.810323\pi$
$878$			18576.0i			0.714020i
$879$		0			0
$880$	3968.00	+	356.337i	0.152001	+	0.0136501i
$881$	8819.34			0.337266			0.168633	−	0.985679i	$-0.446065\pi$
$881$	8819.34			0.337266			0.168633	+	0.985679i	$0.446065\pi$
$882$		0			0
$883$			19643.1i			0.748632i	0.927301	+	0.374316i	$0.122122\pi$
$883$			19643.1i			0.748632i	−0.927301	+	0.374316i	$0.877878\pi$
$884$	−16569.7			−0.630428
$885$		0			0
$886$	−14736.0			−0.558765
$887$			8004.00i			0.302985i	0.988458	+	0.151493i	$0.0484080\pi$
$887$			8004.00i			0.302985i	−0.988458	+	0.151493i	$0.951592\pi$
$888$		0			0
$889$	29264.0			1.10403
$890$	−1425.35	+	15872.0i	−0.0536829	+	0.597787i
$891$		0			0
$892$		−	3296.12i		−	0.123724i
$893$		−	8400.00i		−	0.314776i
$894$		0			0
$895$	37448.0	+	3362.93i	1.39860	+	0.125598i
$896$	−2850.70			−0.106289
$897$		0			0
$898$		−	801.758i		−	0.0297940i
$899$	−3207.03			−0.118977
$900$		0			0
$901$	45756.0			1.69185
$902$			9920.00i			0.366186i
$903$		0			0
$904$	624.000			0.0229579
$905$	18685.4	+	1678.00i	0.686325	+	0.0616338i
$906$		0			0
$907$		−	1336.26i		−	0.0489194i	−0.999701	−	0.0244597i	$-0.992213\pi$
$907$		−	1336.26i		−	0.0489194i	0.999701	−	0.0244597i	$-0.00778654\pi$
$908$			8800.00i			0.321628i
$909$		0			0
$910$	−2976.00	+	33139.3i	−0.108410	+	1.20721i
$911$	−32070.3			−1.16634			−0.583171	−	0.812350i	$-0.698188\pi$
$911$	−32070.3			−1.16634			−0.583171	+	0.812350i	$0.698188\pi$
$912$		0			0
$913$			29041.5i			1.05272i
$914$	−29486.9			−1.06711
$915$		0			0
$916$	20984.0			0.756911
$917$		−	10416.0i		−	0.375100i
$918$		0			0
$919$	−2832.00			−0.101653			−0.0508265	−	0.998707i	$-0.516186\pi$
$919$	−2832.00			−0.101653			−0.0508265	+	0.998707i	$0.516186\pi$
$920$	12471.8	+	1120.00i	0.446938	+	0.0401362i
$921$		0			0
$922$			9487.47i			0.338886i
$923$		−	62496.0i		−	2.22869i
$924$		0			0
$925$	−5456.00	+	30132.7i	−0.193937	+	1.07109i
$926$	−14565.3			−0.516895
$927$		0			0
$928$		−	6414.06i		−	0.226888i
$929$	31936.7			1.12789			0.563945	−	0.825813i	$-0.309283\pi$
$929$	31936.7			1.12789			0.563945	+	0.825813i	$0.309283\pi$
$930$		0			0
$931$	12852.0			0.452425
$932$		−	3368.00i		−	0.118372i
$933$		0			0
$934$	−11328.0			−0.396856
$935$	−1380.81	+	15376.0i	−0.0482964	+	0.537806i
$936$		0			0
$937$			25745.3i			0.897613i	0.893629	+	0.448807i	$0.148151\pi$
$937$			25745.3i			0.897613i	−0.893629	+	0.448807i	$0.851849\pi$
$938$		−	37696.0i		−	1.31217i
$939$		0			0
$940$	−400.000	+	4454.21i	−0.0138793	+	0.154554i
$941$	7059.93			0.244577			0.122289	−	0.992495i	$-0.460977\pi$
$941$	7059.93			0.244577			0.122289	+	0.992495i	$0.460977\pi$
$942$		0			0
$943$			31179.5i			1.07672i
$944$	10333.8			0.356288
$945$		0			0
$946$	15872.0			0.545500
$947$			1752.00i			0.0601186i	0.999548	+	0.0300593i	$0.00956962\pi$
$947$			1752.00i			0.0601186i	−0.999548	+	0.0300593i	$0.990430\pi$
$948$		0			0
$949$	−29760.0			−1.01797
$950$	3741.54	−	20664.0i	0.127781	−	0.705714i
$951$		0			0
$952$		−	11046.4i		−	0.376069i
$953$		−	3850.00i		−	0.130864i	−0.997857	−	0.0654322i	$-0.979157\pi$
$953$		−	3850.00i		−	0.130864i	0.997857	−	0.0654322i	$-0.0208426\pi$
$954$		0			0
$955$	−19344.0	−	1737.14i	−0.655453	−	0.0588614i
$956$	−23340.1			−0.789615
$957$		0			0
$958$			20222.1i			0.681991i
$959$	−23651.9			−0.796411
$960$		0			0
$961$	−29535.0			−0.991407
$962$			32736.0i			1.09714i
$963$		0			0
$964$	−10120.0			−0.338115
$965$	−2449.82	+	27280.0i	−0.0817227	+	0.910025i
$966$		0			0
$967$			24475.9i			0.813952i	0.913439	+	0.406976i	$0.133417\pi$
$967$			24475.9i			0.813952i	−0.913439	+	0.406976i	$0.866583\pi$
$968$			6680.00i			0.221801i
$969$		0			0
$970$	16864.0	+	1514.43i	0.558217	+	0.0501294i
$971$	−2204.83			−0.0728697			−0.0364349	−	0.999336i	$-0.511600\pi$
$971$	−2204.83			−0.0728697			−0.0364349	+	0.999336i	$0.511600\pi$
$972$		0			0
$973$		−	19153.1i		−	0.631059i
$974$	23117.4			0.760501
$975$		0			0
$976$	−5728.00			−0.187857
$977$			29982.0i			0.981790i	0.871219	+	0.490895i	$0.163330\pi$
$977$			29982.0i			0.981790i	−0.871219	+	0.490895i	$0.836670\pi$
$978$		0			0
$979$	15872.0			0.518153
$980$	−6814.94	−	612.000i	−0.222138	−	0.0199486i
$981$		0			0
$982$			935.384i			0.0303965i
$983$		−	35284.0i		−	1.14485i	−0.819958	−	0.572424i	$-0.806003\pi$
$983$		−	35284.0i		−	1.14485i	0.819958	−	0.572424i	$-0.193997\pi$
$984$		0			0
$985$	526.000	−	5857.29i	0.0170150	−	0.189471i
$986$	24854.5			0.802767
$987$		0			0
$988$		−	22449.2i		−	0.722880i
$989$	49887.2			1.60396
$990$		0			0
$991$	−11528.0			−0.369525			−0.184762	−	0.982783i	$-0.559152\pi$
$991$	−11528.0			−0.369525			−0.184762	+	0.982783i	$0.559152\pi$
$992$			512.000i			0.0163871i
$993$		0			0
$994$	41664.0			1.32948
$995$	−8284.83	−	744.000i	−0.263967	−	0.0237049i
$996$		0			0
$997$		−	9955.16i		−	0.316232i	−0.987421	−	0.158116i	$-0.949458\pi$
$997$		−	9955.16i		−	0.316232i	0.987421	−	0.158116i	$-0.0505420\pi$
$998$		−	18408.0i		−	0.583863i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.4.c.c.19.3	yes	4
3.2	odd	2	inner	90.4.c.c.19.2	yes	4
4.3	odd	2		720.4.f.l.289.1		4
5.2	odd	4		450.4.a.u.1.2		2
5.3	odd	4		450.4.a.v.1.1		2
5.4	even	2	inner	90.4.c.c.19.1	✓	4
12.11	even	2		720.4.f.l.289.4		4
15.2	even	4		450.4.a.v.1.2		2
15.8	even	4		450.4.a.u.1.1		2
15.14	odd	2	inner	90.4.c.c.19.4	yes	4
20.19	odd	2		720.4.f.l.289.2		4
60.59	even	2		720.4.f.l.289.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.4.c.c.19.1	✓	4	5.4	even	2	inner
90.4.c.c.19.2	yes	4	3.2	odd	2	inner
90.4.c.c.19.3	yes	4	1.1	even	1	trivial
90.4.c.c.19.4	yes	4	15.14	odd	2	inner
450.4.a.u.1.1		2	15.8	even	4
450.4.a.u.1.2		2	5.2	odd	4
450.4.a.v.1.1		2	5.3	odd	4
450.4.a.v.1.2		2	15.2	even	4
720.4.f.l.289.1		4	4.3	odd	2
720.4.f.l.289.2		4	20.19	odd	2
720.4.f.l.289.3		4	60.59	even	2
720.4.f.l.289.4		4	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	90.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -4.00000 q^{4} +(-11.1355 - 1.00000i) q^{5} -22.2711i q^{7} -8.00000i q^{8} +(2.00000 - 22.2711i) q^{10} -22.2711 q^{11} -66.8132i q^{13} +44.5421 q^{14} +16.0000 q^{16} +62.0000i q^{17} -84.0000 q^{19} +(44.5421 + 4.00000i) q^{20} -44.5421i q^{22} -140.000i q^{23} +(123.000 + 22.2711i) q^{25} +133.626 q^{26} +89.0842i q^{28} -200.440 q^{29} +16.0000 q^{31} +32.0000i q^{32} -124.000 q^{34} +(-22.2711 + 248.000i) q^{35} +244.982i q^{37} -168.000i q^{38} +(-8.00000 + 89.0842i) q^{40} -222.711 q^{41} +356.337i q^{43} +89.0842 q^{44} +280.000 q^{46} +100.000i q^{47} -153.000 q^{49} +(-44.5421 + 246.000i) q^{50} +267.253i q^{52} -738.000i q^{53} +(248.000 + 22.2711i) q^{55} -178.168 q^{56} -400.879i q^{58} +645.861 q^{59} -358.000 q^{61} +32.0000i q^{62} -64.0000 q^{64} +(-66.8132 + 744.000i) q^{65} -846.300i q^{67} -248.000i q^{68} +(-496.000 - 44.5421i) q^{70} +935.384 q^{71} -445.421i q^{73} -489.963 q^{74} +336.000 q^{76} +496.000i q^{77} +936.000 q^{79} +(-178.168 - 16.0000i) q^{80} -445.421i q^{82} -1304.00i q^{83} +(62.0000 - 690.403i) q^{85} -712.674 q^{86} +178.168i q^{88} -712.674 q^{89} -1488.00 q^{91} +560.000i q^{92} -200.000 q^{94} +(935.384 + 84.0000i) q^{95} +757.216i q^{97} -306.000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{4} + 8 q^{10} + 64 q^{16} - 336 q^{19} + 492 q^{25} + 64 q^{31} - 496 q^{34} - 32 q^{40} + 1120 q^{46} - 612 q^{49} + 992 q^{55} - 1432 q^{61} - 256 q^{64} - 1984 q^{70} + 1344 q^{76} + 3744 q^{79}+ \cdots - 800 q^{94}+O(q^{100}) \) 4 * q - 16 * q^4 + 8 * q^10 + 64 * q^16 - 336 * q^19 + 492 * q^25 + 64 * q^31 - 496 * q^34 - 32 * q^40 + 1120 * q^46 - 612 * q^49 + 992 * q^55 - 1432 * q^61 - 256 * q^64 - 1984 * q^70 + 1344 * q^76 + 3744 * q^79 + 248 * q^85 - 5952 * q^91 - 800 * q^94

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