LMFDB - Embedded newform 270.4.c.e.109.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [270,4,Mod(109,270)] 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("270.109"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(270, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	270.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-32,0] 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:	$15.9305157015$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 24x^{6} + 164x^{4} - 111x^{2} + 100 $ x^8 - 24x^6 + 164x^4 - 111*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.7
Root			$-0.755706 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	270.109
Dual form			270.4.c.e.109.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000i q^{2} -4.00000 q^{4} +(6.93656 - 8.76836i) q^{5} +22.9416i q^{7} -8.00000i q^{8} +(17.5367 + 13.8731i) q^{10} +22.9416 q^{11} -92.3072i q^{13} -45.8832 q^{14} +16.0000 q^{16} +112.684i q^{17} +74.6836 q^{19} +(-27.7462 + 35.0735i) q^{20} +45.8832i q^{22} +54.6836i q^{23} +(-28.7684 - 121.644i) q^{25} +184.614 q^{26} -91.7663i q^{28} +276.921 q^{29} +270.367 q^{31} +32.0000i q^{32} -225.367 q^{34} +(201.160 + 159.136i) q^{35} +44.8016i q^{37} +149.367i q^{38} +(-70.1469 - 55.4925i) q^{40} -228.875 q^{41} +322.805i q^{43} -91.7663 q^{44} -109.367 q^{46} +363.367i q^{47} -183.316 q^{49} +(243.289 - 57.5367i) q^{50} +369.229i q^{52} +247.735i q^{53} +(159.136 - 201.160i) q^{55} +183.533 q^{56} +553.843i q^{58} +412.408 q^{59} -35.4181 q^{61} +540.735i q^{62} -64.0000 q^{64} +(-809.383 - 640.294i) q^{65} -689.329i q^{67} -450.735i q^{68} +(-318.271 + 402.320i) q^{70} +461.536 q^{71} -623.749i q^{73} -89.6031 q^{74} -298.735 q^{76} +526.316i q^{77} -1070.05 q^{79} +(110.985 - 140.294i) q^{80} -457.750i q^{82} -195.102i q^{83} +(988.051 + 781.636i) q^{85} -645.609 q^{86} -183.533i q^{88} -137.109 q^{89} +2117.67 q^{91} -218.735i q^{92} -726.735 q^{94} +(518.047 - 654.853i) q^{95} +25.6456i q^{97} -366.633i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{4} + 4 q^{10} + 128 q^{16} - 84 q^{19} - 162 q^{25} + 800 q^{31} - 440 q^{34} - 16 q^{40} + 488 q^{46} - 2148 q^{49} - 158 q^{55} + 3124 q^{61} - 512 q^{64} + 316 q^{70} + 336 q^{76} - 6516 q^{79}+ \cdots - 3088 q^{94}+O(q^{100}) $ 8 * q - 32 * q^4 + 4 * q^10 + 128 * q^16 - 84 * q^19 - 162 * q^25 + 800 * q^31 - 440 * q^34 - 16 * q^40 + 488 * q^46 - 2148 * q^49 - 158 * q^55 + 3124 * q^61 - 512 * q^64 + 316 * q^70 + 336 * q^76 - 6516 * q^79 + 5860 * q^85 + 3312 * q^91 - 3088 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$1$	$-1$

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
$5$	6.93656	−	8.76836i	0.620424	−	0.784266i
$5$	6.93656	−	8.76836i	0.620424	−	0.784266i
$6$		0			0
$7$			22.9416i			1.23873i	0.785103	+	0.619365i	$0.212610\pi$
$7$			22.9416i			1.23873i	−0.785103	+	0.619365i	$0.787390\pi$
$8$		−	8.00000i		−	0.353553i
$9$		0			0
$10$	17.5367	+	13.8731i	0.554560	+	0.438706i
$11$	22.9416			0.628832			0.314416	−	0.949285i	$-0.398191\pi$
$11$	22.9416			0.628832			0.314416	+	0.949285i	$0.398191\pi$
$12$		0			0
$13$		−	92.3072i		−	1.96934i	−0.174432	−	0.984669i	$-0.555809\pi$
$13$		−	92.3072i		−	1.96934i	0.174432	−	0.984669i	$-0.444191\pi$
$14$	−45.8832			−0.875914
$15$		0			0
$16$	16.0000			0.250000
$17$			112.684i			1.60763i	0.594876	+	0.803817i	$0.297201\pi$
$17$			112.684i			1.60763i	−0.594876	+	0.803817i	$0.702799\pi$
$18$		0			0
$19$	74.6836			0.901768			0.450884	−	0.892582i	$-0.351109\pi$
$19$	74.6836			0.901768			0.450884	+	0.892582i	$0.351109\pi$
$20$	−27.7462	+	35.0735i	−0.310212	+	0.392133i
$21$		0			0
$22$			45.8832i			0.444651i
$23$			54.6836i			0.495753i	0.968792	+	0.247877i	$0.0797328\pi$
$23$			54.6836i			0.495753i	−0.968792	+	0.247877i	$0.920267\pi$
$24$		0			0
$25$	−28.7684	−	121.644i	−0.230147	−	0.973156i
$26$	184.614			1.39253
$27$		0			0
$28$		−	91.7663i		−	0.619365i
$29$	276.921			1.77321			0.886604	−	0.462530i	$-0.153058\pi$
$29$	276.921			1.77321			0.886604	+	0.462530i	$0.153058\pi$
$30$		0			0
$31$	270.367			1.56643			0.783216	−	0.621750i	$-0.213578\pi$
$31$	270.367			1.56643			0.783216	+	0.621750i	$0.213578\pi$
$32$			32.0000i			0.176777i
$33$		0			0
$34$	−225.367			−1.13677
$35$	201.160	+	159.136i	0.971493	+	0.768538i
$36$		0			0
$37$			44.8016i			0.199063i	0.995034	+	0.0995315i	$0.0317344\pi$
$37$			44.8016i			0.199063i	−0.995034	+	0.0995315i	$0.968266\pi$
$38$			149.367i			0.637647i
$39$		0			0
$40$	−70.1469	−	55.4925i	−0.277280	−	0.219353i
$41$	−228.875			−0.871812			−0.435906	−	0.899992i	$-0.643572\pi$
$41$	−228.875			−0.871812			−0.435906	+	0.899992i	$0.643572\pi$
$42$		0			0
$43$			322.805i			1.14482i	0.819968	+	0.572410i	$0.193991\pi$
$43$			322.805i			1.14482i	−0.819968	+	0.572410i	$0.806009\pi$
$44$	−91.7663			−0.314416
$45$		0			0
$46$	−109.367			−0.350550
$47$			363.367i			1.12771i	0.825872	+	0.563857i	$0.190683\pi$
$47$			363.367i			1.12771i	−0.825872	+	0.563857i	$0.809317\pi$
$48$		0			0
$49$	−183.316			−0.534450
$50$	243.289	−	57.5367i	0.688125	−	0.162738i
$51$		0			0
$52$			369.229i			0.984669i
$53$			247.735i			0.642056i	0.947070	+	0.321028i	$0.104028\pi$
$53$			247.735i			0.642056i	−0.947070	+	0.321028i	$0.895972\pi$
$54$		0			0
$55$	159.136	−	201.160i	0.390143	−	0.493171i
$56$	183.533			0.437957
$57$		0			0
$58$			553.843i			1.25385i
$59$	412.408			0.910016			0.455008	−	0.890487i	$-0.349636\pi$
$59$	412.408			0.910016			0.455008	+	0.890487i	$0.349636\pi$
$60$		0			0
$61$	−35.4181			−0.0743414			−0.0371707	−	0.999309i	$-0.511835\pi$
$61$	−35.4181			−0.0743414			−0.0371707	+	0.999309i	$0.511835\pi$
$62$			540.735i			1.10763i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−809.383	−	640.294i	−1.54449	−	1.22183i
$66$		0			0
$67$		−	689.329i		−	1.25694i	−0.777834	−	0.628470i	$-0.783682\pi$
$67$		−	689.329i		−	1.25694i	0.777834	−	0.628470i	$-0.216318\pi$
$68$		−	450.735i		−	0.803817i
$69$		0			0
$70$	−318.271	+	402.320i	−0.543438	+	0.686950i
$71$	461.536			0.771468			0.385734	−	0.922610i	$-0.373948\pi$
$71$	461.536			0.771468			0.385734	+	0.922610i	$0.373948\pi$
$72$		0			0
$73$		−	623.749i		−	1.00006i	−0.866008	−	0.500030i	$-0.833322\pi$
$73$		−	623.749i		−	1.00006i	0.866008	−	0.500030i	$-0.166678\pi$
$74$	−89.6031			−0.140759
$75$		0			0
$76$	−298.735			−0.450884
$77$			526.316i			0.778952i
$78$		0			0
$79$	−1070.05			−1.52393			−0.761963	−	0.647621i	$-0.775764\pi$
$79$	−1070.05			−1.52393			−0.761963	+	0.647621i	$0.775764\pi$
$80$	110.985	−	140.294i	0.155106	−	0.196067i
$81$		0			0
$82$		−	457.750i		−	0.616464i
$83$		−	195.102i		−	0.258014i	−0.991644	−	0.129007i	$-0.958821\pi$
$83$		−	195.102i		−	0.258014i	0.991644	−	0.129007i	$-0.0411790\pi$
$84$		0			0
$85$	988.051	+	781.636i	1.26081	+	0.997416i
$86$	−645.609			−0.809510
$87$		0			0
$88$		−	183.533i		−	0.222326i
$89$	−137.109			−0.163298			−0.0816488	−	0.996661i	$-0.526019\pi$
$89$	−137.109			−0.163298			−0.0816488	+	0.996661i	$0.526019\pi$
$90$		0			0
$91$	2117.67			2.43948
$92$		−	218.735i		−	0.247877i
$93$		0			0
$94$	−726.735			−0.797414
$95$	518.047	−	654.853i	0.559479	−	0.707226i
$96$		0			0
$97$			25.6456i			0.0268445i	0.999910	+	0.0134223i	$0.00427257\pi$
$97$			25.6456i			0.0268445i	−0.999910	+	0.0134223i	$0.995727\pi$
$98$		−	366.633i		−	0.377913i
$99$		0			0
$100$	115.073	+	486.578i	0.115073	+	0.486578i
$101$	569.754			0.561313			0.280657	−	0.959808i	$-0.409448\pi$
$101$	569.754			0.561313			0.280657	+	0.959808i	$0.409448\pi$
$102$		0			0
$103$		−	1156.81i		−	1.10664i	−0.832968	−	0.553322i	$-0.813360\pi$
$103$		−	1156.81i		−	1.10664i	0.832968	−	0.553322i	$-0.186640\pi$
$104$	−738.457			−0.696266
$105$		0			0
$106$	−495.469			−0.454002
$107$		−	327.153i		−	0.295580i	−0.989019	−	0.147790i	$-0.952784\pi$
$107$		−	327.153i		−	0.295580i	0.989019	−	0.147790i	$-0.0472159\pi$
$108$		0			0
$109$	372.254			0.327115			0.163557	−	0.986534i	$-0.447703\pi$
$109$	372.254			0.327115			0.163557	+	0.986534i	$0.447703\pi$
$110$	402.320	+	318.271i	0.348725	+	0.275872i
$111$		0			0
$112$			367.065i			0.309682i
$113$		−	628.735i		−	0.523419i	−0.965147	−	0.261710i	$-0.915714\pi$
$113$		−	628.735i		−	0.523419i	0.965147	−	0.261710i	$-0.0842863\pi$
$114$		0			0
$115$	479.486	+	379.316i	0.388802	+	0.307577i
$116$	−1107.69			−0.886604
$117$		0			0
$118$			824.815i			0.643478i
$119$	−2585.14			−1.99142
$120$		0			0
$121$	−804.684			−0.604571
$122$		−	70.8363i		−	0.0525673i
$123$		0			0
$124$	−1081.47			−0.783216
$125$	−1266.18	−	591.542i	−0.906002	−	0.423273i
$126$		0			0
$127$		−	1368.16i		−	0.955938i	−0.878377	−	0.477969i	$-0.841373\pi$
$127$		−	1368.16i		−	0.955938i	0.878377	−	0.477969i	$-0.158627\pi$
$128$		−	128.000i		−	0.0883883i
$129$		0			0
$130$	1280.59	−	1618.77i	0.863961	−	1.09212i
$131$	−1675.28			−1.11733			−0.558663	−	0.829395i	$-0.688685\pi$
$131$	−1675.28			−1.11733			−0.558663	+	0.829395i	$0.688685\pi$
$132$		0			0
$133$			1713.36i			1.11705i
$134$	1378.66			0.888791
$135$		0			0
$136$	901.469			0.568385
$137$		−	1012.25i		−	0.631261i	−0.948882	−	0.315630i	$-0.897784\pi$
$137$		−	1012.25i		−	0.631261i	0.948882	−	0.315630i	$-0.102216\pi$
$138$		0			0
$139$	158.938			0.0969852			0.0484926	−	0.998824i	$-0.484558\pi$
$139$	158.938			0.0969852			0.0484926	+	0.998824i	$0.484558\pi$
$140$	−804.641	−	636.542i	−0.485747	−	0.384269i
$141$		0			0
$142$			923.072i			0.545510i
$143$		−	2117.67i		−	1.23838i
$144$		0			0
$145$	1920.88	−	2428.15i	1.10014	−	1.39067i
$146$	1247.50			0.707149
$147$		0			0
$148$		−	179.206i		−	0.0995315i
$149$	996.223			0.547743			0.273872	−	0.961766i	$-0.411696\pi$
$149$	996.223			0.547743			0.273872	+	0.961766i	$0.411696\pi$
$150$		0			0
$151$	242.113			0.130483			0.0652413	−	0.997870i	$-0.479218\pi$
$151$	242.113			0.130483			0.0652413	+	0.997870i	$0.479218\pi$
$152$		−	597.469i		−	0.318823i
$153$		0			0
$154$	−1052.63			−0.550802
$155$	1875.42	−	2370.68i	0.971853	−	1.22850i
$156$		0			0
$157$			1470.97i			0.747744i	0.927480	+	0.373872i	$0.121970\pi$
$157$			1470.97i			0.747744i	−0.927480	+	0.373872i	$0.878030\pi$
$158$		−	2140.10i		−	1.07758i
$159$		0			0
$160$	280.588	+	221.970i	0.138640	+	0.109677i
$161$	−1254.53			−0.614104
$162$		0			0
$163$		−	1381.90i		−	0.664043i	−0.943272	−	0.332022i	$-0.892269\pi$
$163$		−	1381.90i		−	0.664043i	0.943272	−	0.332022i	$-0.107731\pi$
$164$	915.500			0.435906
$165$		0			0
$166$	390.204			0.182444
$167$			3313.72i			1.53547i	0.640767	+	0.767735i	$0.278616\pi$
$167$			3313.72i			1.53547i	−0.640767	+	0.767735i	$0.721384\pi$
$168$		0			0
$169$	−6323.61			−2.87829
$170$	−1563.27	+	1976.10i	−0.705280	+	0.891530i
$171$		0			0
$172$		−	1291.22i		−	0.572410i
$173$			1739.63i			0.764519i	0.924055	+	0.382260i	$0.124854\pi$
$173$			1739.63i			0.764519i	−0.924055	+	0.382260i	$0.875146\pi$
$174$		0			0
$175$	2790.72	−	659.992i	1.20548	−	0.285090i
$176$	367.065			0.157208
$177$		0			0
$178$		−	274.217i		−	0.115469i
$179$	−942.227			−0.393438			−0.196719	−	0.980460i	$-0.563029\pi$
$179$	−942.227			−0.393438			−0.196719	+	0.980460i	$0.563029\pi$
$180$		0			0
$181$	−1253.09			−0.514594			−0.257297	−	0.966332i	$-0.582832\pi$
$181$	−1253.09			−0.514594			−0.257297	+	0.966332i	$0.582832\pi$
$182$			4235.35i			1.72497i
$183$		0			0
$184$	437.469			0.175275
$185$	392.836	+	310.769i	0.156118	+	0.123504i
$186$		0			0
$187$			2585.14i			1.01093i
$188$		−	1453.47i		−	0.563857i
$189$		0			0
$190$	1309.71	+	1036.09i	0.500085	+	0.395612i
$191$	−2021.02			−0.765634			−0.382817	−	0.923824i	$-0.625046\pi$
$191$	−2021.02			−0.765634			−0.382817	+	0.923824i	$0.625046\pi$
$192$		0			0
$193$			2377.04i			0.886546i	0.896387	+	0.443273i	$0.146183\pi$
$193$			2377.04i			0.886546i	−0.896387	+	0.443273i	$0.853817\pi$
$194$	−51.2913			−0.0189819
$195$		0			0
$196$	733.265			0.267225
$197$		−	2616.90i		−	0.946428i	−0.880948	−	0.473214i	$-0.843094\pi$
$197$		−	2616.90i		−	0.946428i	0.880948	−	0.473214i	$-0.156906\pi$
$198$		0			0
$199$	−3354.32			−1.19488			−0.597440	−	0.801913i	$-0.703815\pi$
$199$	−3354.32			−1.19488			−0.597440	+	0.801913i	$0.703815\pi$
$200$	−973.156	+	230.147i	−0.344063	+	0.0813692i
$201$		0			0
$202$			1139.51i			0.396908i
$203$			6353.02i			2.19652i
$204$		0			0
$205$	−1587.60	+	2006.86i	−0.540893	+	0.683732i
$206$	2313.63			0.782515
$207$		0			0
$208$		−	1476.91i		−	0.492335i
$209$	1713.36			0.567061
$210$		0			0
$211$	−457.113			−0.149142			−0.0745710	−	0.997216i	$-0.523759\pi$
$211$	−457.113			−0.149142			−0.0745710	+	0.997216i	$0.523759\pi$
$212$		−	990.938i		−	0.321028i
$213$		0			0
$214$	654.305			0.209006
$215$	2830.47	+	2239.15i	0.897843	+	0.710274i
$216$		0			0
$217$			6202.65i			1.94039i
$218$			744.509i			0.231305i
$219$		0			0
$220$	−636.542	+	804.641i	−0.195071	+	0.246586i
$221$	10401.5			3.16598
$222$		0			0
$223$		−	1256.15i		−	0.377211i	−0.982053	−	0.188606i	$-0.939603\pi$
$223$		−	1256.15i		−	0.377211i	0.982053	−	0.188606i	$-0.0603968\pi$
$224$	−734.131			−0.218978
$225$		0			0
$226$	1257.47			0.370113
$227$		−	4313.09i		−	1.26110i	−0.776148	−	0.630550i	$-0.782829\pi$
$227$		−	4313.09i		−	1.26110i	0.776148	−	0.630550i	$-0.217171\pi$
$228$		0			0
$229$	−6814.33			−1.96639			−0.983196	−	0.182552i	$-0.941564\pi$
$229$	−6814.33			−1.96639			−0.983196	+	0.182552i	$0.941564\pi$
$230$	−758.632	+	958.972i	−0.217490	+	0.274925i
$231$		0			0
$232$		−	2215.37i		−	0.626924i
$233$			5086.20i			1.43008i	0.699084	+	0.715039i	$0.253591\pi$
$233$			5086.20i			1.43008i	−0.699084	+	0.715039i	$0.746409\pi$
$234$		0			0
$235$	3186.14	+	2520.52i	0.884428	+	0.699661i
$236$	−1649.63			−0.455008
$237$		0			0
$238$		−	5170.28i		−	1.40815i
$239$	1905.01			0.515584			0.257792	−	0.966200i	$-0.417005\pi$
$239$	1905.01			0.515584			0.257792	+	0.966200i	$0.417005\pi$
$240$		0			0
$241$	5688.05			1.52033			0.760165	−	0.649730i	$-0.225118\pi$
$241$	5688.05			1.52033			0.760165	+	0.649730i	$0.225118\pi$
$242$		−	1609.37i		−	0.427496i
$243$		0			0
$244$	141.673			0.0371707
$245$	−1271.58	+	1607.38i	−0.331586	+	0.419151i
$246$		0			0
$247$		−	6893.83i		−	1.77589i
$248$		−	2162.94i		−	0.553817i
$249$		0			0
$250$	1183.08	−	2532.35i	0.299299	−	0.640640i
$251$	−1595.09			−0.401121			−0.200561	−	0.979681i	$-0.564276\pi$
$251$	−1595.09			−0.401121			−0.200561	+	0.979681i	$0.564276\pi$
$252$		0			0
$253$			1254.53i			0.311745i
$254$	2736.31			0.675950
$255$		0			0
$256$	256.000			0.0625000
$257$			4413.60i			1.07126i	0.844454	+	0.535628i	$0.179925\pi$
$257$			4413.60i			1.07126i	−0.844454	+	0.535628i	$0.820075\pi$
$258$		0			0
$259$	−1027.82			−0.246585
$260$	3237.53	+	2561.18i	0.772243	+	0.610913i
$261$		0			0
$262$		−	3350.55i		−	0.790068i
$263$			2312.43i			0.542169i	0.962556	+	0.271085i	$0.0873823\pi$
$263$			2312.43i			0.542169i	−0.962556	+	0.271085i	$0.912618\pi$
$264$		0			0
$265$	2172.23	+	1718.42i	0.503543	+	0.398347i
$266$	−3426.72			−0.789871
$267$		0			0
$268$			2757.32i			0.628470i
$269$	−1671.26			−0.378806			−0.189403	−	0.981899i	$-0.560655\pi$
$269$	−1671.26			−0.378806			−0.189403	+	0.981899i	$0.560655\pi$
$270$		0			0
$271$	1727.43			0.387210			0.193605	−	0.981080i	$-0.437982\pi$
$271$	1727.43			0.387210			0.193605	+	0.981080i	$0.437982\pi$
$272$			1802.94i			0.401909i
$273$		0			0
$274$	2024.51			0.446369
$275$	−659.992	−	2790.72i	−0.144724	−	0.611951i
$276$		0			0
$277$		−	7181.03i		−	1.55764i	−0.627248	−	0.778820i	$-0.715819\pi$
$277$		−	7181.03i		−	1.55764i	0.627248	−	0.778820i	$-0.284181\pi$
$278$			317.876i			0.0685789i
$279$		0			0
$280$	1273.08	−	1609.28i	0.271719	−	0.343475i
$281$	−4134.35			−0.877704			−0.438852	−	0.898559i	$-0.644615\pi$
$281$	−4134.35			−0.877704			−0.438852	+	0.898559i	$0.644615\pi$
$282$		0			0
$283$			5027.77i			1.05608i	0.849221	+	0.528038i	$0.177072\pi$
$283$			5027.77i			1.05608i	−0.849221	+	0.528038i	$0.822928\pi$
$284$	−1846.14			−0.385734
$285$		0			0
$286$	4235.35			0.875669
$287$		−	5250.76i		−	1.07994i
$288$		0			0
$289$	−7784.60			−1.58449
$290$	4856.30	+	3841.76i	0.983350	+	0.777918i
$291$		0			0
$292$			2495.00i			0.500030i
$293$			135.644i			0.0270457i	0.999909	+	0.0135229i	$0.00430459\pi$
$293$			135.644i			0.0270457i	−0.999909	+	0.0135229i	$0.995695\pi$
$294$		0			0
$295$	2860.69	−	3616.14i	0.564596	−	0.713694i
$296$	358.412			0.0703794
$297$		0			0
$298$			1992.45i			0.387313i
$299$	5047.69			0.976306
$300$		0			0
$301$	−7405.65			−1.41812
$302$			484.226i			0.0922651i
$303$		0			0
$304$	1194.94			0.225442
$305$	−245.680	+	310.559i	−0.0461232	+	0.0583035i
$306$		0			0
$307$		−	2594.33i		−	0.482301i	−0.970488	−	0.241151i	$-0.922475\pi$
$307$		−	2594.33i		−	0.482301i	0.970488	−	0.241151i	$-0.0775248\pi$
$308$		−	2105.27i		−	0.389476i
$309$		0			0
$310$	4741.36	+	3750.84i	0.868680	+	0.687204i
$311$	518.235			0.0944901			0.0472450	−	0.998883i	$-0.484956\pi$
$311$	518.235			0.0944901			0.0472450	+	0.998883i	$0.484956\pi$
$312$		0			0
$313$		−	682.071i		−	0.123172i	−0.998102	−	0.0615862i	$-0.980384\pi$
$313$		−	682.071i		−	0.123172i	0.998102	−	0.0615862i	$-0.0196159\pi$
$314$	−2941.93			−0.528735
$315$		0			0
$316$	4280.20			0.761963
$317$		−	1901.43i		−	0.336892i	−0.985711	−	0.168446i	$-0.946125\pi$
$317$		−	1901.43i		−	0.336892i	0.985711	−	0.168446i	$-0.0538750\pi$
$318$		0			0
$319$	6353.02			1.11505
$320$	−443.940	+	561.175i	−0.0775531	+	0.0980333i
$321$		0			0
$322$		−	2509.06i		−	0.434237i
$323$			8415.62i			1.44971i
$324$		0			0
$325$	−11228.7	+	2655.53i	−1.91647	+	0.453237i
$326$	2763.81			0.469549
$327$		0			0
$328$			1831.00i			0.308232i
$329$	−8336.22			−1.39693
$330$		0			0
$331$	11227.1			1.86435			0.932173	−	0.362014i	$-0.117911\pi$
$331$	11227.1			1.86435			0.932173	+	0.362014i	$0.117911\pi$
$332$			780.407i			0.129007i
$333$		0			0
$334$	−6627.45			−1.08574
$335$	−6044.29	−	4781.57i	−0.985775	−	0.779836i
$336$		0			0
$337$			6467.45i			1.04541i	0.852512	+	0.522707i	$0.175078\pi$
$337$			6467.45i			1.04541i	−0.852512	+	0.522707i	$0.824922\pi$
$338$		−	12647.2i		−	2.03526i
$339$		0			0
$340$	−3952.20	−	3126.55i	−0.630407	−	0.498708i
$341$	6202.65			0.985022
$342$		0			0
$343$			3663.40i			0.576690i
$344$	2582.44			0.404755
$345$		0			0
$346$	−3479.27			−0.540597
$347$		−	2046.90i		−	0.316667i	−0.987386	−	0.158334i	$-0.949388\pi$
$347$		−	2046.90i		−	0.316667i	0.987386	−	0.158334i	$-0.0506122\pi$
$348$		0			0
$349$	−966.073			−0.148174			−0.0740870	−	0.997252i	$-0.523604\pi$
$349$	−966.073			−0.148174			−0.0740870	+	0.997252i	$0.523604\pi$
$350$	1319.98	+	5581.43i	0.201589	+	0.852401i
$351$		0			0
$352$			734.131i			0.111163i
$353$		−	1787.88i		−	0.269572i	−0.990875	−	0.134786i	$-0.956965\pi$
$353$		−	1787.88i		−	0.269572i	0.990875	−	0.134786i	$-0.0430348\pi$
$354$		0			0
$355$	3201.47	−	4046.91i	0.478638	−	0.605036i
$356$	548.435			0.0816488
$357$		0			0
$358$		−	1884.45i		−	0.278203i
$359$	9893.00			1.45441			0.727204	−	0.686421i	$-0.240819\pi$
$359$	9893.00			1.45441			0.727204	+	0.686421i	$0.240819\pi$
$360$		0			0
$361$	−1281.36			−0.186814
$362$		−	2506.18i		−	0.363873i
$363$		0			0
$364$	−8470.69			−1.21974
$365$	−5469.26	−	4326.67i	−0.784313	−	0.620461i
$366$		0			0
$367$			9933.71i			1.41290i	0.707762	+	0.706451i	$0.249705\pi$
$367$			9933.71i			1.41290i	−0.707762	+	0.706451i	$0.750295\pi$
$368$			874.938i			0.123938i
$369$		0			0
$370$	−621.537	+	785.673i	−0.0873302	+	0.110392i
$371$	−5683.42			−0.795333
$372$		0			0
$373$		−	3663.08i		−	0.508491i	−0.967140	−	0.254246i	$-0.918173\pi$
$373$		−	3663.08i		−	0.508491i	0.967140	−	0.254246i	$-0.0818272\pi$
$374$	−5170.28			−0.714837
$375$		0			0
$376$	2906.94			0.398707
$377$		−	25561.8i		−	3.49205i
$378$		0			0
$379$	1754.60			0.237805			0.118902	−	0.992906i	$-0.462062\pi$
$379$	1754.60			0.237805			0.118902	+	0.992906i	$0.462062\pi$
$380$	−2072.19	+	2619.41i	−0.279740	+	0.353613i
$381$		0			0
$382$		−	4042.05i		−	0.541385i
$383$		−	1779.83i		−	0.237454i	−0.992927	−	0.118727i	$-0.962119\pi$
$383$		−	1779.83i		−	0.237454i	0.992927	−	0.118727i	$-0.0378813\pi$
$384$		0			0
$385$	4614.93	+	3650.82i	0.610906	+	0.483281i
$386$	−4754.09			−0.626883
$387$		0			0
$388$		−	102.583i		−	0.0134223i
$389$	−9870.69			−1.28654			−0.643270	−	0.765640i	$-0.722423\pi$
$389$	−9870.69			−1.28654			−0.643270	+	0.765640i	$0.722423\pi$
$390$		0			0
$391$	−6161.95			−0.796990
$392$			1466.53i			0.188957i
$393$		0			0
$394$	5233.80			0.669226
$395$	−7422.47	+	9382.59i	−0.945481	+	1.19516i
$396$		0			0
$397$			8433.48i			1.06616i	0.846066	+	0.533078i	$0.178965\pi$
$397$			8433.48i			1.06616i	−0.846066	+	0.533078i	$0.821035\pi$
$398$		−	6708.63i		−	0.844908i
$399$		0			0
$400$	−460.294	−	1946.31i	−0.0575367	−	0.243289i
$401$	−14407.5			−1.79420			−0.897102	−	0.441824i	$-0.854332\pi$
$401$	−14407.5			−1.79420			−0.897102	+	0.441824i	$0.854332\pi$
$402$		0			0
$403$		−	24956.8i		−	3.08483i
$404$	−2279.02			−0.280657
$405$		0			0
$406$	−12706.0			−1.55318
$407$			1027.82i			0.125177i
$408$		0			0
$409$	2569.33			0.310624			0.155312	−	0.987865i	$-0.450362\pi$
$409$	2569.33			0.310624			0.155312	+	0.987865i	$0.450362\pi$
$410$	−4013.72	−	3175.21i	−0.483472	−	0.382469i
$411$		0			0
$412$			4627.26i			0.553322i
$413$			9461.29i			1.12726i
$414$		0			0
$415$	−1710.72	−	1353.33i	−0.202352	−	0.160078i
$416$	2953.83			0.348133
$417$		0			0
$418$			3426.72i			0.400972i
$419$	12267.6			1.43033			0.715167	−	0.698953i	$-0.246351\pi$
$419$	12267.6			1.43033			0.715167	+	0.698953i	$0.246351\pi$
$420$		0			0
$421$	−1203.72			−0.139349			−0.0696745	−	0.997570i	$-0.522196\pi$
$421$	−1203.72			−0.139349			−0.0696745	+	0.997570i	$0.522196\pi$
$422$		−	914.226i		−	0.105459i
$423$		0			0
$424$	1981.88			0.227001
$425$	13707.3	−	3241.72i	1.56448	−	0.369992i
$426$		0			0
$427$		−	812.548i		−	0.0920889i
$428$			1308.61i			0.147790i
$429$		0			0
$430$	−4478.31	+	5660.94i	−0.502240	+	0.634871i
$431$	−6975.41			−0.779568			−0.389784	−	0.920906i	$-0.627450\pi$
$431$	−6975.41			−0.779568			−0.389784	+	0.920906i	$0.627450\pi$
$432$		0			0
$433$			4595.66i			0.510054i	0.966934	+	0.255027i	$0.0820844\pi$
$433$			4595.66i			0.510054i	−0.966934	+	0.255027i	$0.917916\pi$
$434$	−12405.3			−1.37206
$435$		0			0
$436$	−1489.02			−0.163557
$437$			4083.97i			0.447055i
$438$		0			0
$439$	4709.81			0.512044			0.256022	−	0.966671i	$-0.417588\pi$
$439$	4709.81			0.512044			0.256022	+	0.966671i	$0.417588\pi$
$440$	−1609.28	−	1273.08i	−0.174362	−	0.137936i
$441$		0			0
$442$			20803.0i			2.23868i
$443$		−	10640.9i		−	1.14123i	−0.821216	−	0.570617i	$-0.806704\pi$
$443$		−	10640.9i		−	1.14123i	0.821216	−	0.570617i	$-0.193296\pi$
$444$		0			0
$445$	−951.062	+	1202.22i	−0.101314	+	0.128069i
$446$	2512.30			0.266729
$447$		0			0
$448$		−	1468.26i		−	0.154841i
$449$	−4074.41			−0.428248			−0.214124	−	0.976807i	$-0.568690\pi$
$449$	−4074.41			−0.428248			−0.214124	+	0.976807i	$0.568690\pi$
$450$		0			0
$451$	−5250.76			−0.548223
$452$			2514.94i			0.261710i
$453$		0			0
$454$	8626.18			0.891733
$455$	14689.4	−	18568.5i	1.51351	−	1.91320i
$456$		0			0
$457$		−	14066.1i		−	1.43979i	−0.694084	−	0.719894i	$-0.744191\pi$
$457$		−	14066.1i		−	1.43979i	0.694084	−	0.719894i	$-0.255809\pi$
$458$		−	13628.7i		−	1.39045i
$459$		0			0
$460$	−1917.94	−	1517.26i	−0.194401	−	0.153789i
$461$	13134.3			1.32696			0.663479	−	0.748195i	$-0.269079\pi$
$461$	13134.3			1.32696			0.663479	+	0.748195i	$0.269079\pi$
$462$		0			0
$463$			139.955i			0.0140481i	0.999975	+	0.00702403i	$0.00223584\pi$
$463$			139.955i			0.0140481i	−0.999975	+	0.00702403i	$0.997764\pi$
$464$	4430.74			0.443302
$465$		0			0
$466$	−10172.4			−1.01122
$467$		−	587.270i		−	0.0581919i	−0.999577	−	0.0290960i	$-0.990737\pi$
$467$		−	587.270i		−	0.0581919i	0.999577	−	0.0290960i	$-0.00926284\pi$
$468$		0			0
$469$	15814.3			1.55701
$470$	−5041.04	+	6372.27i	−0.494735	+	0.625385i
$471$		0			0
$472$		−	3299.26i		−	0.321739i
$473$			7405.65i			0.719899i
$474$		0			0
$475$	−2148.53	−	9084.85i	−0.207539	−	0.877561i
$476$	10340.6			0.995712
$477$		0			0
$478$			3810.01i			0.364573i
$479$	−15456.7			−1.47439			−0.737196	−	0.675679i	$-0.763851\pi$
$479$	−15456.7			−1.47439			−0.737196	+	0.675679i	$0.763851\pi$
$480$		0			0
$481$	4135.50			0.392022
$482$			11376.1i			1.07504i
$483$		0			0
$484$	3218.73			0.302285
$485$	224.870	+	177.892i	0.0210533	+	0.0166550i
$486$		0			0
$487$		−	18448.4i		−	1.71658i	−0.513164	−	0.858291i	$-0.671527\pi$
$487$		−	18448.4i		−	1.71658i	0.513164	−	0.858291i	$-0.328473\pi$
$488$			283.345i			0.0262837i
$489$		0			0
$490$	−3214.77	−	2543.17i	−0.296385	−	0.234467i
$491$	−518.918			−0.0476954			−0.0238477	−	0.999716i	$-0.507592\pi$
$491$	−518.918			−0.0476954			−0.0238477	+	0.999716i	$0.507592\pi$
$492$		0			0
$493$			31204.5i			2.85067i
$494$	13787.7			1.25574
$495$		0			0
$496$	4325.88			0.391608
$497$			10588.4i			0.955640i
$498$		0			0
$499$	5853.01			0.525084			0.262542	−	0.964921i	$-0.415439\pi$
$499$	5853.01			0.525084			0.262542	+	0.964921i	$0.415439\pi$
$500$	5064.71	+	2366.17i	0.453001	+	0.211637i
$501$		0			0
$502$		−	3190.19i		−	0.283636i
$503$			15178.2i			1.34546i	0.739890	+	0.672728i	$0.234877\pi$
$503$			15178.2i			1.34546i	−0.739890	+	0.672728i	$0.765123\pi$
$504$		0			0
$505$	3952.13	−	4995.81i	0.348253	−	0.440219i
$506$	−2509.06			−0.220437
$507$		0			0
$508$			5472.62i			0.477969i
$509$	5421.02			0.472068			0.236034	−	0.971745i	$-0.424152\pi$
$509$	5421.02			0.472068			0.236034	+	0.971745i	$0.424152\pi$
$510$		0			0
$511$	14309.8			1.23880
$512$			512.000i			0.0441942i
$513$		0			0
$514$	−8827.20			−0.757492
$515$	−10143.4	−	8024.30i	−0.867903	−	0.686589i
$516$		0			0
$517$			8336.22i			0.709142i
$518$		−	2055.64i		−	0.174362i
$519$		0			0
$520$	−5122.35	+	6475.06i	−0.431981	+	0.546058i
$521$	−8494.96			−0.714340			−0.357170	−	0.934039i	$-0.616258\pi$
$521$	−8494.96			−0.714340			−0.357170	+	0.934039i	$0.616258\pi$
$522$		0			0
$523$		−	4363.31i		−	0.364808i	−0.983224	−	0.182404i	$-0.941612\pi$
$523$		−	4363.31i		−	0.364808i	0.983224	−	0.182404i	$-0.0583878\pi$
$524$	6701.11			0.558663
$525$		0			0
$526$	−4624.86			−0.383372
$527$			30466.0i			2.51825i
$528$		0			0
$529$	9176.70			0.754229
$530$	−3436.85	+	4344.45i	−0.281674	+	0.356058i
$531$		0			0
$532$		−	6853.44i		−	0.558523i
$533$			21126.8i			1.71689i
$534$		0			0
$535$	−2868.59	−	2269.31i	−0.231813	−	0.183385i
$536$	−5514.63			−0.444395
$537$		0			0
$538$		−	3342.53i		−	0.267856i
$539$	−4205.57			−0.336079
$540$		0			0
$541$	−16112.3			−1.28044			−0.640222	−	0.768190i	$-0.721158\pi$
$541$	−16112.3			−1.28044			−0.640222	+	0.768190i	$0.721158\pi$
$542$			3454.86i			0.273799i
$543$		0			0
$544$	−3605.88			−0.284192
$545$	2582.16	−	3264.06i	0.202950	−	0.256545i
$546$		0			0
$547$		−	9522.61i		−	0.744346i	−0.928163	−	0.372173i	$-0.878613\pi$
$547$		−	9522.61i		−	0.744346i	0.928163	−	0.372173i	$-0.121387\pi$
$548$			4049.02i			0.315630i
$549$		0			0
$550$	5581.43	−	1319.98i	0.432715	−	0.102335i
$551$	20681.5			1.59902
$552$		0			0
$553$		−	24548.7i		−	1.88773i
$554$	14362.1			1.10142
$555$		0			0
$556$	−635.752			−0.0484926
$557$		−	21740.5i		−	1.65381i	−0.562339	−	0.826907i	$-0.690098\pi$
$557$		−	21740.5i		−	1.65381i	0.562339	−	0.826907i	$-0.309902\pi$
$558$		0			0
$559$	29797.2			2.25454
$560$	3218.56	+	2546.17i	0.242873	+	0.192134i
$561$		0			0
$562$		−	8268.71i		−	0.620630i
$563$		−	6514.93i		−	0.487693i	−0.969814	−	0.243847i	$-0.921591\pi$
$563$		−	6514.93i		−	0.487693i	0.969814	−	0.243847i	$-0.0784094\pi$
$564$		0			0
$565$	−5512.97	−	4361.25i	−0.410500	−	0.324742i
$566$	−10055.5			−0.746759
$567$		0			0
$568$		−	3692.29i		−	0.272755i
$569$	25108.1			1.84989			0.924944	−	0.380105i	$-0.124112\pi$
$569$	25108.1			1.84989			0.924944	+	0.380105i	$0.124112\pi$
$570$		0			0
$571$	1863.83			0.136600			0.0683000	−	0.997665i	$-0.478242\pi$
$571$	1863.83			0.136600			0.0683000	+	0.997665i	$0.478242\pi$
$572$			8470.69i			0.619191i
$573$		0			0
$574$	10501.5			0.763632
$575$	6651.96	−	1573.16i	0.482445	−	0.114096i
$576$		0			0
$577$		−	20829.5i		−	1.50285i	−0.659819	−	0.751424i	$-0.729367\pi$
$577$		−	20829.5i		−	1.50285i	0.659819	−	0.751424i	$-0.270633\pi$
$578$		−	15569.2i		−	1.12040i
$579$		0			0
$580$	−7683.53	+	9712.59i	−0.550071	+	0.695333i
$581$	4475.94			0.319610
$582$		0			0
$583$			5683.42i			0.403745i
$584$	−4989.99			−0.353574
$585$		0			0
$586$	−271.288			−0.0191242
$587$			15537.3i			1.09249i	0.837624	+	0.546247i	$0.183944\pi$
$587$			15537.3i			1.09249i	−0.837624	+	0.546247i	$0.816056\pi$
$588$		0			0
$589$	20192.0			1.41256
$590$	7232.28	+	5721.38i	0.504658	+	0.399230i
$591$		0			0
$592$			716.825i			0.0497657i
$593$			4495.44i			0.311308i	0.987812	+	0.155654i	$0.0497485\pi$
$593$			4495.44i			0.311308i	−0.987812	+	0.155654i	$0.950252\pi$
$594$		0			0
$595$	−17932.0	+	22667.5i	−1.23553	+	1.56181i
$596$	−3984.89			−0.273872
$597$		0			0
$598$			10095.4i			0.690352i
$599$	−27270.9			−1.86020			−0.930100	−	0.367307i	$-0.880280\pi$
$599$	−27270.9			−1.86020			−0.930100	+	0.367307i	$0.880280\pi$
$600$		0			0
$601$	−22616.8			−1.53504			−0.767520	−	0.641025i	$-0.778509\pi$
$601$	−22616.8			−1.53504			−0.767520	+	0.641025i	$0.778509\pi$
$602$		−	14811.3i		−	1.00276i
$603$		0			0
$604$	−968.451			−0.0652413
$605$	−5581.73	+	7055.76i	−0.375090	+	0.474144i
$606$		0			0
$607$			19720.3i			1.31865i	0.751857	+	0.659326i	$0.229158\pi$
$607$			19720.3i			1.31865i	−0.751857	+	0.659326i	$0.770842\pi$
$608$			2389.88i			0.159412i
$609$		0			0
$610$	−621.118	−	491.360i	−0.0412268	−	0.0326141i
$611$	33541.4			2.22085
$612$		0			0
$613$		−	5447.29i		−	0.358913i	−0.983766	−	0.179457i	$-0.942566\pi$
$613$		−	5447.29i		−	0.358913i	0.983766	−	0.179457i	$-0.0574340\pi$
$614$	5188.67			0.341039
$615$		0			0
$616$	4210.53			0.275401
$617$			12015.4i			0.783993i	0.919967	+	0.391996i	$0.128215\pi$
$617$			12015.4i			0.783993i	−0.919967	+	0.391996i	$0.871785\pi$
$618$		0			0
$619$	−2316.36			−0.150408			−0.0752039	−	0.997168i	$-0.523961\pi$
$619$	−2316.36			−0.150408			−0.0752039	+	0.997168i	$0.523961\pi$
$620$	−7501.67	+	9482.71i	−0.485926	+	0.614250i
$621$		0			0
$622$			1036.47i			0.0668146i
$623$		−	3145.49i		−	0.202282i
$624$		0			0
$625$	−13969.8	+	6999.03i	−0.894065	+	0.447938i
$626$	1364.14			0.0870960
$627$		0			0
$628$		−	5883.86i		−	0.373872i
$629$	−5048.40			−0.320021
$630$		0			0
$631$	7324.32			0.462087			0.231043	−	0.972943i	$-0.425786\pi$
$631$	7324.32			0.462087			0.231043	+	0.972943i	$0.425786\pi$
$632$			8560.41i			0.538789i
$633$		0			0
$634$	3802.86			0.238219
$635$	−11996.5	−	9490.29i	−0.749710	−	0.593088i
$636$		0			0
$637$			16921.4i			1.05251i
$638$			12706.0i			0.788459i
$639$		0			0
$640$	−1122.35	−	887.879i	−0.0693200	−	0.0548383i
$641$	90.2295			0.00555983			0.00277991	−	0.999996i	$-0.499115\pi$
$641$	90.2295			0.00555983			0.00277991	+	0.999996i	$0.499115\pi$
$642$		0			0
$643$			11101.0i			0.680842i	0.940273	+	0.340421i	$0.110570\pi$
$643$			11101.0i			0.680842i	−0.940273	+	0.340421i	$0.889430\pi$
$644$	5018.12			0.307052
$645$		0			0
$646$	−16831.2			−1.02510
$647$		−	5204.38i		−	0.316237i	−0.987420	−	0.158118i	$-0.949457\pi$
$647$		−	5204.38i		−	0.316237i	0.987420	−	0.158118i	$-0.0505428\pi$
$648$		0			0
$649$	9461.29			0.572247
$650$	−5311.05	−	22457.3i	−0.320487	−	1.35515i
$651$		0			0
$652$			5527.61i			0.332022i
$653$		−	18852.8i		−	1.12981i	−0.825155	−	0.564907i	$-0.808912\pi$
$653$		−	18852.8i		−	1.12981i	0.825155	−	0.564907i	$-0.191088\pi$
$654$		0			0
$655$	−11620.7	+	14689.4i	−0.693216	+	0.876280i
$656$	−3662.00			−0.217953
$657$		0			0
$658$		−	16672.4i		−	0.987780i
$659$	13402.4			0.792238			0.396119	−	0.918199i	$-0.370357\pi$
$659$	13402.4			0.792238			0.396119	+	0.918199i	$0.370357\pi$
$660$		0			0
$661$	−15928.1			−0.937267			−0.468633	−	0.883393i	$-0.655253\pi$
$661$	−15928.1			−0.937267			−0.468633	+	0.883393i	$0.655253\pi$
$662$			22454.2i			1.31829i
$663$		0			0
$664$	−1560.81			−0.0912219
$665$	15023.4	+	11884.8i	0.876062	+	0.693043i
$666$		0			0
$667$			15143.1i			0.879073i
$668$		−	13254.9i		−	0.767735i
$669$		0			0
$670$	9563.14	−	12088.6i	0.551427	−	0.697048i
$671$	−812.548			−0.0467482
$672$		0			0
$673$			355.395i			0.0203558i	0.999948	+	0.0101779i	$0.00323979\pi$
$673$			355.395i			0.0203558i	−0.999948	+	0.0101779i	$0.996760\pi$
$674$	−12934.9			−0.739219
$675$		0			0
$676$	25294.4			1.43915
$677$			18243.7i			1.03569i	0.855474	+	0.517846i	$0.173266\pi$
$677$			18243.7i			1.03569i	−0.855474	+	0.517846i	$0.826734\pi$
$678$		0			0
$679$	−588.351			−0.0332531
$680$	6253.09	−	7904.41i	0.352640	−	0.445765i
$681$		0			0
$682$			12405.3i			0.696516i
$683$			5682.31i			0.318342i	0.987251	+	0.159171i	$0.0508821\pi$
$683$			5682.31i			0.318342i	−0.987251	+	0.159171i	$0.949118\pi$
$684$		0			0
$685$	−8875.81	−	7021.56i	−0.495076	−	0.391650i
$686$	−7326.79			−0.407782
$687$		0			0
$688$			5164.87i			0.286205i
$689$	22867.7			1.26442
$690$		0			0
$691$	−24469.4			−1.34712			−0.673559	−	0.739133i	$-0.735235\pi$
$691$	−24469.4			−1.34712			−0.673559	+	0.739133i	$0.735235\pi$
$692$		−	6958.53i		−	0.382260i
$693$		0			0
$694$	4093.81			0.223918
$695$	1102.48	−	1393.63i	0.0601720	−	0.0760622i
$696$		0			0
$697$		−	25790.5i		−	1.40155i
$698$		−	1932.15i		−	0.104775i
$699$		0			0
$700$	−11162.9	+	2639.97i	−0.602738	+	0.142545i
$701$	−25286.9			−1.36244			−0.681222	−	0.732077i	$-0.738551\pi$
$701$	−25286.9			−1.36244			−0.681222	+	0.732077i	$0.738551\pi$
$702$		0			0
$703$			3345.94i			0.179509i
$704$	−1468.26			−0.0786040
$705$		0			0
$706$	3575.75			0.190616
$707$			13071.1i			0.695315i
$708$		0			0
$709$	−32374.8			−1.71490			−0.857448	−	0.514570i	$-0.827952\pi$
$709$	−32374.8			−1.71490			−0.857448	+	0.514570i	$0.827952\pi$
$710$	8093.83	+	6402.94i	0.427825	+	0.338448i
$711$		0			0
$712$			1096.87i			0.0577345i
$713$			14784.7i			0.776564i
$714$		0			0
$715$	−18568.5	−	14689.4i	−0.971221	−	0.768323i
$716$	3768.91			0.196719
$717$		0			0
$718$			19786.0i			1.02842i
$719$	−22565.9			−1.17047			−0.585233	−	0.810865i	$-0.698997\pi$
$719$	−22565.9			−1.17047			−0.585233	+	0.810865i	$0.698997\pi$
$720$		0			0
$721$	26539.1			1.37083
$722$		−	2562.71i		−	0.132097i
$723$		0			0
$724$	5012.36			0.257297
$725$	−7966.58	−	33686.0i	−0.408098	−	1.72561i
$726$		0			0
$727$			24371.4i			1.24331i	0.783292	+	0.621654i	$0.213539\pi$
$727$			24371.4i			1.24331i	−0.783292	+	0.621654i	$0.786461\pi$
$728$		−	16941.4i		−	0.862485i
$729$		0			0
$730$	8653.34	−	10938.5i	0.438732	−	0.554593i
$731$	−36374.8			−1.84045
$732$		0			0
$733$		−	13467.4i		−	0.678621i	−0.940674	−	0.339311i	$-0.889806\pi$
$733$		−	13467.4i		−	0.678621i	0.940674	−	0.339311i	$-0.110194\pi$
$734$	−19867.4			−0.999073
$735$		0			0
$736$	−1749.88			−0.0876376
$737$		−	15814.3i		−	0.790404i
$738$		0			0
$739$	16009.5			0.796911			0.398456	−	0.917188i	$-0.369546\pi$
$739$	16009.5			0.796911			0.398456	+	0.917188i	$0.369546\pi$
$740$	−1571.35	−	1243.07i	−0.0780592	−	0.0617518i
$741$		0			0
$742$		−	11366.8i		−	0.562385i
$743$		−	10714.7i		−	0.529052i	−0.964379	−	0.264526i	$-0.914785\pi$
$743$		−	10714.7i		−	0.529052i	0.964379	−	0.264526i	$-0.0852155\pi$
$744$		0			0
$745$	6910.36	−	8735.24i	0.339833	−	0.429577i
$746$	7326.16			0.359558
$747$		0			0
$748$		−	10340.6i		−	0.505466i
$749$	7505.40			0.366143
$750$		0			0
$751$	4772.75			0.231904			0.115952	−	0.993255i	$-0.463008\pi$
$751$	4772.75			0.231904			0.115952	+	0.993255i	$0.463008\pi$
$752$			5813.88i			0.281929i
$753$		0			0
$754$	51123.7			2.46925
$755$	1679.43	−	2122.93i	0.0809546	−	0.102333i
$756$		0			0
$757$			24326.3i			1.16797i	0.811764	+	0.583985i	$0.198507\pi$
$757$			24326.3i			1.16797i	−0.811764	+	0.583985i	$0.801493\pi$
$758$			3509.21i			0.168153i
$759$		0			0
$760$	−5238.82	−	4144.38i	−0.250042	−	0.197806i
$761$	−13038.2			−0.621070			−0.310535	−	0.950562i	$-0.600508\pi$
$761$	−13038.2			−0.621070			−0.310535	+	0.950562i	$0.600508\pi$
$762$		0			0
$763$			8540.11i			0.405207i
$764$	8084.09			0.382817
$765$		0			0
$766$	3559.65			0.167905
$767$		−	38068.2i		−	1.79213i
$768$		0			0
$769$	21815.7			1.02301			0.511505	−	0.859280i	$-0.329088\pi$
$769$	21815.7			1.02301			0.511505	+	0.859280i	$0.329088\pi$
$770$	−7301.65	+	9229.87i	−0.341731	+	0.431976i
$771$		0			0
$772$		−	9508.18i		−	0.443273i
$773$		−	23946.0i		−	1.11420i	−0.830446	−	0.557100i	$-0.811914\pi$
$773$		−	23946.0i		−	1.11420i	0.830446	−	0.557100i	$-0.188086\pi$
$774$		0			0
$775$	−7778.02	−	32888.7i	−0.360509	−	1.52438i
$776$	205.165			0.00949097
$777$		0			0
$778$		−	19741.4i		−	0.909721i
$779$	−17093.2			−0.786172
$780$		0			0
$781$	10588.4			0.485123
$782$		−	12323.9i		−	0.563557i
$783$		0			0
$784$	−2933.06			−0.133613
$785$	12898.0	+	10203.4i	0.586430	+	0.463919i
$786$		0			0
$787$		−	13567.9i		−	0.614540i	−0.951622	−	0.307270i	$-0.900584\pi$
$787$		−	13567.9i		−	0.614540i	0.951622	−	0.307270i	$-0.0994156\pi$
$788$			10467.6i			0.473214i
$789$		0			0
$790$	−18765.2	−	14844.9i	−0.845108	−	0.668556i
$791$	14424.2			0.648375
$792$		0			0
$793$			3269.35i			0.146403i
$794$	−16867.0			−0.753887
$795$		0			0
$796$	13417.3			0.597440
$797$		−	39913.7i		−	1.77392i	−0.461843	−	0.886962i	$-0.652812\pi$
$797$		−	39913.7i		−	1.77392i	0.461843	−	0.886962i	$-0.347188\pi$
$798$		0			0
$799$	−40945.5			−1.81295
$800$	3892.62	−	920.588i	0.172031	−	0.0406846i
$801$		0			0
$802$		−	28815.0i		−	1.26869i
$803$		−	14309.8i		−	0.628869i
$804$		0			0
$805$	−8702.11	+	11000.2i	−0.381005	+	0.481621i
$806$	49913.7			2.18131
$807$		0			0
$808$		−	4558.03i		−	0.198454i
$809$	13891.2			0.603696			0.301848	−	0.953356i	$-0.402396\pi$
$809$	13891.2			0.603696			0.301848	+	0.953356i	$0.402396\pi$
$810$		0			0
$811$	−24237.7			−1.04945			−0.524723	−	0.851273i	$-0.675831\pi$
$811$	−24237.7			−1.04945			−0.524723	+	0.851273i	$0.675831\pi$
$812$		−	25412.1i		−	1.09826i
$813$		0			0
$814$	−2055.64			−0.0885136
$815$	−12117.0	−	9585.65i	−0.520787	−	0.411989i
$816$		0			0
$817$			24108.2i			1.03236i
$818$			5138.65i			0.219644i
$819$		0			0
$820$	6350.42	−	8027.44i	0.270447	−	0.341866i
$821$	−19978.0			−0.849254			−0.424627	−	0.905368i	$-0.639595\pi$
$821$	−19978.0			−0.849254			−0.424627	+	0.905368i	$0.639595\pi$
$822$		0			0
$823$			42871.5i			1.81580i	0.419182	+	0.907902i	$0.362317\pi$
$823$			42871.5i			1.81580i	−0.419182	+	0.907902i	$0.637683\pi$
$824$	−9254.51			−0.391257
$825$		0			0
$826$	−18922.6			−0.797095
$827$			360.143i			0.0151432i	0.999971	+	0.00757159i	$0.00241013\pi$
$827$			360.143i			0.0151432i	−0.999971	+	0.00757159i	$0.997590\pi$
$828$		0			0
$829$	15020.5			0.629294			0.314647	−	0.949209i	$-0.398114\pi$
$829$	15020.5			0.629294			0.314647	+	0.949209i	$0.398114\pi$
$830$	2706.67	−	3421.45i	0.113193	−	0.143084i
$831$		0			0
$832$			5907.66i			0.246167i
$833$		−	20656.8i		−	0.859201i
$834$		0			0
$835$	29055.9	+	22985.8i	1.20422	+	0.952644i
$836$	−6853.44			−0.283530
$837$		0			0
$838$			24535.1i			1.01140i
$839$	−29440.2			−1.21143			−0.605714	−	0.795682i	$-0.707113\pi$
$839$	−29440.2			−1.21143			−0.605714	+	0.795682i	$0.707113\pi$
$840$		0			0
$841$	52296.5			2.14427
$842$		−	2407.45i		−	0.0985346i
$843$		0			0
$844$	1828.45			0.0745710
$845$	−43864.1	+	55447.7i	−1.78576	+	2.25735i
$846$		0			0
$847$		−	18460.7i		−	0.748899i
$848$			3963.75i			0.160514i
$849$		0			0
$850$	6483.45	+	27414.7i	0.261624	+	1.10625i
$851$	−2449.91			−0.0986861
$852$		0			0
$853$		−	14688.6i		−	0.589601i	−0.955559	−	0.294801i	$-0.904747\pi$
$853$		−	14688.6i		−	0.589601i	0.955559	−	0.294801i	$-0.0952532\pi$
$854$	1625.10			0.0651167
$855$		0			0
$856$	−2617.22			−0.104503
$857$		−	7812.22i		−	0.311389i	−0.987805	−	0.155694i	$-0.950238\pi$
$857$		−	7812.22i		−	0.311389i	0.987805	−	0.155694i	$-0.0497615\pi$
$858$		0			0
$859$	−4035.68			−0.160298			−0.0801488	−	0.996783i	$-0.525540\pi$
$859$	−4035.68			−0.160298			−0.0801488	+	0.996783i	$0.525540\pi$
$860$	−11321.9	−	8956.61i	−0.448922	−	0.355137i
$861$		0			0
$862$		−	13950.8i		−	0.551238i
$863$			32201.0i			1.27015i	0.772452	+	0.635073i	$0.219030\pi$
$863$			32201.0i			1.27015i	−0.772452	+	0.635073i	$0.780970\pi$
$864$		0			0
$865$	15253.7	+	12067.1i	0.599587	+	0.474326i
$866$	−9191.32			−0.360663
$867$		0			0
$868$		−	24810.6i		−	0.970193i
$869$	−24548.7			−0.958293
$870$		0			0
$871$	−63630.0			−2.47534
$872$		−	2978.04i		−	0.115653i
$873$		0			0
$874$	−8167.94			−0.316115
$875$	13570.9	−	29048.1i	0.524321	−	1.12229i
$876$		0			0
$877$			18350.3i			0.706551i	0.935519	+	0.353275i	$0.114932\pi$
$877$			18350.3i			0.706551i	−0.935519	+	0.353275i	$0.885068\pi$
$878$			9419.63i			0.362070i
$879$		0			0
$880$	2546.17	−	3218.56i	0.0975356	−	0.123293i
$881$	−32914.7			−1.25871			−0.629356	−	0.777117i	$-0.716681\pi$
$881$	−32914.7			−1.25871			−0.629356	+	0.777117i	$0.716681\pi$
$882$		0			0
$883$		−	27122.2i		−	1.03367i	−0.856084	−	0.516837i	$-0.827109\pi$
$883$		−	27122.2i		−	1.03367i	0.856084	−	0.516837i	$-0.172891\pi$
$884$	−41606.0			−1.58299
$885$		0			0
$886$	21281.9			0.806974
$887$			35660.0i			1.34988i	0.737872	+	0.674941i	$0.235831\pi$
$887$			35660.0i			1.34988i	−0.737872	+	0.674941i	$0.764169\pi$
$888$		0			0
$889$	31387.7			1.18415
$890$	−2404.44	−	1902.12i	−0.0905584	−	0.0716397i
$891$		0			0
$892$			5024.61i			0.188606i
$893$			27137.6i			1.01694i
$894$		0			0
$895$	−6535.81	+	8261.79i	−0.244099	+	0.308560i
$896$	2936.52			0.109489
$897$		0			0
$898$		−	8148.82i		−	0.302817i
$899$	74870.5			2.77761
$900$		0			0
$901$	−27915.6			−1.03219
$902$		−	10501.5i		−	0.387652i
$903$		0			0
$904$	−5029.88			−0.185057
$905$	−8692.13	+	10987.6i	−0.319267	+	0.403579i
$906$		0			0
$907$		−	13630.5i		−	0.499002i	−0.968375	−	0.249501i	$-0.919733\pi$
$907$		−	13630.5i		−	0.499002i	0.968375	−	0.249501i	$-0.0802666\pi$
$908$			17252.4i			0.630550i
$909$		0			0
$910$	37137.0	+	29378.7i	1.35284	+	1.07021i
$911$	36521.1			1.32821			0.664104	−	0.747640i	$-0.268813\pi$
$911$	36521.1			1.32821			0.664104	+	0.747640i	$0.268813\pi$
$912$		0			0
$913$		−	4475.94i		−	0.162248i
$914$	28132.1			1.01808
$915$		0			0
$916$	27257.3			0.983196
$917$		−	38433.5i		−	1.38406i
$918$		0			0
$919$	−13527.6			−0.485565			−0.242782	−	0.970081i	$-0.578060\pi$
$919$	−13527.6			−0.485565			−0.242782	+	0.970081i	$0.578060\pi$
$920$	3034.53	−	3835.89i	0.108745	−	0.137462i
$921$		0			0
$922$			26268.7i			0.938301i
$923$		−	42603.1i		−	1.51928i
$924$		0			0
$925$	5449.86	−	1288.87i	0.193719	−	0.0458137i
$926$	−279.910			−0.00993348
$927$		0			0
$928$			8861.49i			0.313462i
$929$	38200.4			1.34910			0.674550	−	0.738229i	$-0.264338\pi$
$929$	38200.4			1.34910			0.674550	+	0.738229i	$0.264338\pi$
$930$		0			0
$931$	−13690.7			−0.481950
$932$		−	20344.8i		−	0.715039i
$933$		0			0
$934$	1174.54			0.0411479
$935$	22667.5	+	17932.0i	0.792840	+	0.627207i
$936$		0			0
$937$		−	45991.8i		−	1.60351i	−0.597654	−	0.801754i	$-0.703900\pi$
$937$		−	45991.8i		−	1.60351i	0.597654	−	0.801754i	$-0.296100\pi$
$938$			31628.6i			1.10097i
$939$		0			0
$940$	−12744.5	−	10082.1i	−0.442214	−	0.349831i
$941$	−3180.14			−0.110170			−0.0550848	−	0.998482i	$-0.517543\pi$
$941$	−3180.14			−0.110170			−0.0550848	+	0.998482i	$0.517543\pi$
$942$		0			0
$943$		−	12515.7i		−	0.432203i
$944$	6598.52			0.227504
$945$		0			0
$946$	−14811.3			−0.509045
$947$			56742.3i			1.94707i	0.228536	+	0.973535i	$0.426606\pi$
$947$			56742.3i			1.94707i	−0.228536	+	0.973535i	$0.573394\pi$
$948$		0			0
$949$	−57576.5			−1.96946
$950$	18169.7	−	4297.05i	0.620529	−	0.146752i
$951$		0			0
$952$			20681.1i			0.704075i
$953$		−	17765.0i		−	0.603846i	−0.953332	−	0.301923i	$-0.902371\pi$
$953$		−	17765.0i		−	0.603846i	0.953332	−	0.301923i	$-0.0976285\pi$
$954$		0			0
$955$	−14018.9	+	17721.1i	−0.475018	+	0.600461i
$956$	−7620.02			−0.257792
$957$		0			0
$958$		−	30913.4i		−	1.04255i
$959$	23222.7			0.781961
$960$		0			0
$961$	43307.5			1.45371
$962$			8271.01i			0.277202i
$963$		0			0
$964$	−22752.2			−0.760165
$965$	20842.8	+	16488.5i	0.695288	+	0.550035i
$966$		0			0
$967$		−	35530.1i		−	1.18156i	−0.806832	−	0.590781i	$-0.798820\pi$
$967$		−	35530.1i		−	1.18156i	0.806832	−	0.590781i	$-0.201180\pi$
$968$			6437.47i			0.213748i
$969$		0			0
$970$	−355.785	+	449.740i	−0.0117769	+	0.0148869i
$971$	26227.6			0.866822			0.433411	−	0.901196i	$-0.357310\pi$
$971$	26227.6			0.866822			0.433411	+	0.901196i	$0.357310\pi$
$972$		0			0
$973$			3646.29i			0.120138i
$974$	36896.7			1.21381
$975$		0			0
$976$	−566.690			−0.0185854
$977$		−	13869.8i		−	0.454182i	−0.973874	−	0.227091i	$-0.927079\pi$
$977$		−	13869.8i		−	0.454182i	0.973874	−	0.227091i	$-0.0729214\pi$
$978$		0			0
$979$	−3145.49			−0.102687
$980$	5086.34	−	6429.54i	0.165793	−	0.209576i
$981$		0			0
$982$		−	1037.84i		−	0.0337257i
$983$		−	19637.7i		−	0.637177i	−0.947893	−	0.318588i	$-0.896791\pi$
$983$		−	19637.7i		−	0.637177i	0.947893	−	0.318588i	$-0.103209\pi$
$984$		0			0
$985$	−22945.9	−	18152.3i	−0.742251	−	0.587187i
$986$	−62409.0			−2.01573
$987$		0			0
$988$			27575.3i			0.887943i
$989$	−17652.1			−0.567548
$990$		0			0
$991$	−5935.20			−0.190250			−0.0951251	−	0.995465i	$-0.530325\pi$
$991$	−5935.20			−0.190250			−0.0951251	+	0.995465i	$0.530325\pi$
$992$			8651.75i			0.276909i
$993$		0			0
$994$	−21176.7			−0.675739
$995$	−23267.4	+	29411.9i	−0.741333	+	0.937104i
$996$		0			0
$997$		−	42278.0i		−	1.34299i	−0.741011	−	0.671493i	$-0.765653\pi$
$997$		−	42278.0i		−	1.34299i	0.741011	−	0.671493i	$-0.234347\pi$
$998$			11706.0i			0.371290i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.4.c.e.109.7	yes	8
3.2	odd	2	inner	270.4.c.e.109.2	✓	8
5.2	odd	4		1350.4.a.bu.1.2		4
5.3	odd	4		1350.4.a.bv.1.3		4
5.4	even	2	inner	270.4.c.e.109.3	yes	8
15.2	even	4		1350.4.a.bv.1.2		4
15.8	even	4		1350.4.a.bu.1.3		4
15.14	odd	2	inner	270.4.c.e.109.6	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.4.c.e.109.2	✓	8	3.2	odd	2	inner
270.4.c.e.109.3	yes	8	5.4	even	2	inner
270.4.c.e.109.6	yes	8	15.14	odd	2	inner
270.4.c.e.109.7	yes	8	1.1	even	1	trivial
1350.4.a.bu.1.2		4	5.2	odd	4
1350.4.a.bu.1.3		4	15.8	even	4
1350.4.a.bv.1.2		4	15.2	even	4
1350.4.a.bv.1.3		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	270.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -4.00000 q^{4} +(6.93656 - 8.76836i) q^{5} +22.9416i q^{7} -8.00000i q^{8} +(17.5367 + 13.8731i) q^{10} +22.9416 q^{11} -92.3072i q^{13} -45.8832 q^{14} +16.0000 q^{16} +112.684i q^{17} +74.6836 q^{19} +(-27.7462 + 35.0735i) q^{20} +45.8832i q^{22} +54.6836i q^{23} +(-28.7684 - 121.644i) q^{25} +184.614 q^{26} -91.7663i q^{28} +276.921 q^{29} +270.367 q^{31} +32.0000i q^{32} -225.367 q^{34} +(201.160 + 159.136i) q^{35} +44.8016i q^{37} +149.367i q^{38} +(-70.1469 - 55.4925i) q^{40} -228.875 q^{41} +322.805i q^{43} -91.7663 q^{44} -109.367 q^{46} +363.367i q^{47} -183.316 q^{49} +(243.289 - 57.5367i) q^{50} +369.229i q^{52} +247.735i q^{53} +(159.136 - 201.160i) q^{55} +183.533 q^{56} +553.843i q^{58} +412.408 q^{59} -35.4181 q^{61} +540.735i q^{62} -64.0000 q^{64} +(-809.383 - 640.294i) q^{65} -689.329i q^{67} -450.735i q^{68} +(-318.271 + 402.320i) q^{70} +461.536 q^{71} -623.749i q^{73} -89.6031 q^{74} -298.735 q^{76} +526.316i q^{77} -1070.05 q^{79} +(110.985 - 140.294i) q^{80} -457.750i q^{82} -195.102i q^{83} +(988.051 + 781.636i) q^{85} -645.609 q^{86} -183.533i q^{88} -137.109 q^{89} +2117.67 q^{91} -218.735i q^{92} -726.735 q^{94} +(518.047 - 654.853i) q^{95} +25.6456i q^{97} -366.633i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} + 4 q^{10} + 128 q^{16} - 84 q^{19} - 162 q^{25} + 800 q^{31} - 440 q^{34} - 16 q^{40} + 488 q^{46} - 2148 q^{49} - 158 q^{55} + 3124 q^{61} - 512 q^{64} + 316 q^{70} + 336 q^{76} - 6516 q^{79}+ \cdots - 3088 q^{94}+O(q^{100}) \) 8 * q - 32 * q^4 + 4 * q^10 + 128 * q^16 - 84 * q^19 - 162 * q^25 + 800 * q^31 - 440 * q^34 - 16 * q^40 + 488 * q^46 - 2148 * q^49 - 158 * q^55 + 3124 * q^61 - 512 * q^64 + 316 * q^70 + 336 * q^76 - 6516 * q^79 + 5860 * q^85 + 3312 * q^91 - 3088 * q^94

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