LMFDB - Embedded newform 504.4.s.f.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,4,Mod(289,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("504.289");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	504.s (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$29.7369626429$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{505})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 127x^{2} + 126x + 15876 $ x^4 - x^3 + 127x^2 + 126x + 15876
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$5.86805 + 10.1638i$ of defining polynomial
Character	$\chi$	$=$	504.361
Dual form			504.4.s.f.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.86805 + 13.6279i) q^{5} +(11.2361 - 14.7224i) q^{7} +O(q^{10})$	$q+(7.86805 + 13.6279i) q^{5} +(11.2361 - 14.7224i) q^{7} +(29.3403 - 50.8188i) q^{11} -20.7361 q^{13} +(21.4722 - 37.1910i) q^{17} +(-68.5764 - 118.778i) q^{19} +(14.5278 + 25.1629i) q^{23} +(-61.3125 + 106.196i) q^{25} -8.68051 q^{29} +(101.236 - 175.346i) q^{31} +(289.042 + 37.2872i) q^{35} +(7.63195 + 13.2189i) q^{37} -117.250 q^{41} -101.875 q^{43} +(294.250 + 509.656i) q^{47} +(-90.5000 - 330.846i) q^{49} +(202.340 - 350.464i) q^{53} +923.403 q^{55} +(5.43738 - 9.41783i) q^{59} +(447.305 + 774.756i) q^{61} +(-163.153 - 282.589i) q^{65} +(351.868 - 609.453i) q^{67} -1161.94 q^{71} +(558.187 - 966.809i) q^{73} +(-418.506 - 1002.97i) q^{77} +(-69.1665 - 119.800i) q^{79} +894.319 q^{83} +675.778 q^{85} +(-340.903 - 590.461i) q^{89} +(-232.993 + 305.286i) q^{91} +(1079.12 - 1869.10i) q^{95} +246.514 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 9 q^{5}+O(q^{10}) $ 4 * q + 9 * q^5	$ 4 q + 9 q^{5} + 5 q^{11} - 38 q^{13} - 4 q^{17} - 117 q^{19} + 148 q^{23} - 43 q^{25} + 190 q^{29} + 360 q^{31} + 482 q^{35} + 53 q^{37} + 340 q^{41} + 806 q^{43} + 368 q^{47} - 362 q^{49} + 697 q^{53} + 2570 q^{55} - 585 q^{59} + 1160 q^{61} - 338 q^{65} - 233 q^{67} - 1232 q^{71} + 817 q^{73} + 1135 q^{77} + 802 q^{79} + 566 q^{83} + 1984 q^{85} - 1858 q^{89} - 505 q^{91} + 2294 q^{95} + 3458 q^{97}+O(q^{100}) $ 4 * q + 9 * q^5 + 5 * q^11 - 38 * q^13 - 4 * q^17 - 117 * q^19 + 148 * q^23 - 43 * q^25 + 190 * q^29 + 360 * q^31 + 482 * q^35 + 53 * q^37 + 340 * q^41 + 806 * q^43 + 368 * q^47 - 362 * q^49 + 697 * q^53 + 2570 * q^55 - 585 * q^59 + 1160 * q^61 - 338 * q^65 - 233 * q^67 - 1232 * q^71 + 817 * q^73 + 1135 * q^77 + 802 * q^79 + 566 * q^83 + 1984 * q^85 - 1858 * q^89 - 505 * q^91 + 2294 * q^95 + 3458 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	7.86805	+	13.6279i	0.703740	+	1.21891i	0.967144	+	0.254228i	$0.0818213\pi$
$5$	7.86805	+	13.6279i	0.703740	+	1.21891i	−0.263404	+	0.964685i	$0.584845\pi$
$6$		0			0
$7$	11.2361	−	14.7224i	0.606693	−	0.794937i
$7$	11.2361	−	14.7224i	0.606693	−	0.794937i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	29.3403	−	50.8188i	0.804220	−	1.39295i	−0.112596	−	0.993641i	$-0.535917\pi$
$11$	29.3403	−	50.8188i	0.804220	−	1.39295i	0.916816	−	0.399309i	$-0.130750\pi$
$12$		0			0
$13$	−20.7361			−0.442397			−0.221198	−	0.975229i	$-0.570997\pi$
$13$	−20.7361			−0.442397			−0.221198	+	0.975229i	$0.570997\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	21.4722	−	37.1910i	0.306340	−	0.530596i	−0.671219	−	0.741259i	$-0.734229\pi$
$17$	21.4722	−	37.1910i	0.306340	−	0.530596i	0.977559	+	0.210663i	$0.0675623\pi$
$18$		0			0
$19$	−68.5764	−	118.778i	−0.828026	−	1.43418i	−0.899584	−	0.436747i	$-0.856131\pi$
$19$	−68.5764	−	118.778i	−0.828026	−	1.43418i	0.0715584	−	0.997436i	$-0.477203\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	14.5278	+	25.1629i	0.131707	+	0.228123i	0.924335	−	0.381583i	$-0.124621\pi$
$23$	14.5278	+	25.1629i	0.131707	+	0.228123i	−0.792628	+	0.609706i	$0.791288\pi$
$24$		0			0
$25$	−61.3125	+	106.196i	−0.490500	+	0.849570i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−8.68051			−0.0555838			−0.0277919	−	0.999614i	$-0.508848\pi$
$29$	−8.68051			−0.0555838			−0.0277919	+	0.999614i	$0.508848\pi$
$30$		0			0
$31$	101.236	−	175.346i	0.586534	−	1.01591i	−0.408149	−	0.912915i	$-0.633826\pi$
$31$	101.236	−	175.346i	0.586534	−	1.01591i	0.994682	−	0.102991i	$-0.0328411\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	289.042	+	37.2872i	1.39591	+	0.180077i
$36$		0			0
$37$	7.63195	+	13.2189i	0.0339104	+	0.0587345i	0.882483	−	0.470345i	$-0.155871\pi$
$37$	7.63195	+	13.2189i	0.0339104	+	0.0587345i	−0.848572	+	0.529080i	$0.822537\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−117.250			−0.446618			−0.223309	−	0.974748i	$-0.571686\pi$
$41$	−117.250			−0.446618			−0.223309	+	0.974748i	$0.571686\pi$
$42$		0			0
$43$	−101.875			−0.361297			−0.180648	−	0.983548i	$-0.557820\pi$
$43$	−101.875			−0.361297			−0.180648	+	0.983548i	$0.557820\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	294.250	+	509.656i	0.913207	+	1.58172i	0.809505	+	0.587113i	$0.199736\pi$
$47$	294.250	+	509.656i	0.913207	+	1.58172i	0.103703	+	0.994608i	$0.466931\pi$
$48$		0			0
$49$	−90.5000	−	330.846i	−0.263848	−	0.964564i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	202.340	−	350.464i	0.524407	−	0.908300i	−0.475189	−	0.879884i	$-0.657620\pi$
$53$	202.340	−	350.464i	0.524407	−	0.908300i	0.999596	−	0.0284159i	$-0.00904629\pi$
$54$		0			0
$55$	923.403			2.26385
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.43738	−	9.41783i	0.0119981	−	0.0207813i	−0.859964	−	0.510355i	$-0.829514\pi$
$59$	5.43738	−	9.41783i	0.0119981	−	0.0207813i	0.871962	+	0.489573i	$0.162847\pi$
$60$		0			0
$61$	447.305	+	774.756i	0.938879	+	1.62619i	0.767567	+	0.640968i	$0.221467\pi$
$61$	447.305	+	774.756i	0.938879	+	1.62619i	0.171311	+	0.985217i	$0.445200\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−163.153	−	282.589i	−0.311332	−	0.539243i
$66$		0			0
$67$	351.868	−	609.453i	0.641604	−	1.11129i	−0.343470	−	0.939164i	$-0.611602\pi$
$67$	351.868	−	609.453i	0.641604	−	1.11129i	0.985075	−	0.172128i	$-0.0550642\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1161.94			−1.94222			−0.971108	−	0.238640i	$-0.923298\pi$
$71$	−1161.94			−1.94222			−0.971108	+	0.238640i	$0.923298\pi$
$72$		0			0
$73$	558.187	−	966.809i	0.894943	−	1.55009i	0.0610689	−	0.998134i	$-0.480549\pi$
$73$	558.187	−	966.809i	0.894943	−	1.55009i	0.833875	−	0.551954i	$-0.186118\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−418.506	−	1002.97i	−0.619393	−	1.48440i
$78$		0			0
$79$	−69.1665	−	119.800i	−0.0985042	−	0.170614i	0.812561	−	0.582875i	$-0.198072\pi$
$79$	−69.1665	−	119.800i	−0.0985042	−	0.170614i	−0.911066	+	0.412261i	$0.864739\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	894.319			1.18270			0.591351	−	0.806414i	$-0.298595\pi$
$83$	894.319			1.18270			0.591351	+	0.806414i	$0.298595\pi$
$84$		0			0
$85$	675.778			0.862334
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−340.903	−	590.461i	−0.406018	−	0.703244i	0.588421	−	0.808555i	$-0.299750\pi$
$89$	−340.903	−	590.461i	−0.406018	−	0.703244i	−0.994439	+	0.105310i	$0.966416\pi$
$90$		0			0
$91$	−232.993	+	305.286i	−0.268399	+	0.351678i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1079.12	−	1869.10i	1.16543	−	2.01858i
$96$		0			0
$97$	246.514			0.258039			0.129019	−	0.991642i	$-0.458817\pi$
$97$	246.514			0.258039			0.129019	+	0.991642i	$0.458817\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−544.972	+	943.919i	−0.536898	+	0.929935i	0.462171	+	0.886791i	$0.347071\pi$
$101$	−544.972	+	943.919i	−0.536898	+	0.929935i	−0.999069	+	0.0431441i	$0.986263\pi$
$102$		0			0
$103$	15.1182	+	26.1855i	0.0144625	+	0.0250498i	0.873166	−	0.487423i	$-0.162063\pi$
$103$	15.1182	+	26.1855i	0.0144625	+	0.0250498i	−0.858704	+	0.512473i	$0.828730\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	943.812	+	1634.73i	0.852727	+	1.47697i	0.878738	+	0.477305i	$0.158386\pi$
$107$	943.812	+	1634.73i	0.852727	+	1.47697i	−0.0260107	+	0.999662i	$0.508280\pi$
$108$		0			0
$109$	482.298	−	835.365i	0.423815	−	0.734069i	−0.572494	−	0.819909i	$-0.694024\pi$
$109$	482.298	−	835.365i	0.423815	−	0.734069i	0.996309	+	0.0858401i	$0.0273574\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−119.806			−0.0997378			−0.0498689	−	0.998756i	$-0.515880\pi$
$113$	−119.806			−0.0997378			−0.0498689	+	0.998756i	$0.515880\pi$
$114$		0			0
$115$	−228.611	+	395.966i	−0.185375	+	0.321078i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−306.277	−	734.004i	−0.235936	−	0.565429i
$120$		0			0
$121$	−1056.20	−	1829.39i	−0.793540	−	1.37445i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	37.3745			0.0267430
$126$		0			0
$127$	683.722			0.477721			0.238860	−	0.971054i	$-0.423226\pi$
$127$	683.722			0.477721			0.238860	+	0.971054i	$0.423226\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	130.119	+	225.372i	0.0867825	+	0.150312i	0.906149	−	0.422958i	$-0.139008\pi$
$131$	130.119	+	225.372i	0.0867825	+	0.150312i	−0.819367	+	0.573269i	$0.805675\pi$
$132$		0			0
$133$	−2519.23	−	324.988i	−1.64244	−	0.211880i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−365.847	+	633.666i	−0.228149	+	0.395166i	−0.957260	−	0.289230i	$-0.906601\pi$
$137$	−365.847	+	633.666i	−0.228149	+	0.395166i	0.729110	+	0.684396i	$0.239934\pi$
$138$		0			0
$139$	2287.74			1.39599			0.697997	−	0.716101i	$-0.254075\pi$
$139$	2287.74			1.39599			0.697997	+	0.716101i	$0.254075\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−608.403	+	1053.78i	−0.355784	+	0.616237i
$144$		0			0
$145$	−68.2987	−	118.297i	−0.0391166	−	0.0677519i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1719.60	+	2978.43i	0.945469	+	1.63760i	0.754810	+	0.655944i	$0.227729\pi$
$149$	1719.60	+	2978.43i	0.945469	+	1.63760i	0.190659	+	0.981656i	$0.438937\pi$
$150$		0			0
$151$	−1425.88	+	2469.70i	−0.768455	+	1.33100i	0.169946	+	0.985453i	$0.445641\pi$
$151$	−1425.88	+	2469.70i	−0.768455	+	1.33100i	−0.938401	+	0.345549i	$0.887693\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3186.12			1.65107
$156$		0			0
$157$	−1220.12	+	2113.32i	−0.620232	+	1.07427i	0.369210	+	0.929346i	$0.379628\pi$
$157$	−1220.12	+	2113.32i	−0.620232	+	1.07427i	−0.989442	+	0.144928i	$0.953705\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	533.695	+	68.8482i	0.261249	+	0.0337019i
$162$		0			0
$163$	−120.695	−	209.050i	−0.0579974	−	0.100454i	0.835569	−	0.549386i	$-0.185138\pi$
$163$	−120.695	−	209.050i	−0.0579974	−	0.100454i	−0.893566	+	0.448931i	$0.851805\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−326.445			−0.151264			−0.0756319	−	0.997136i	$-0.524097\pi$
$167$	−326.445			−0.151264			−0.0756319	+	0.997136i	$0.524097\pi$
$168$		0			0
$169$	−1767.01			−0.804285
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−797.847	−	1381.91i	−0.350631	−	0.607311i	0.635729	−	0.771912i	$-0.280700\pi$
$173$	−797.847	−	1381.91i	−0.350631	−	0.607311i	−0.986360	+	0.164601i	$0.947366\pi$
$174$		0			0
$175$	874.555	+	2095.90i	0.377772	+	0.905344i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1441.43	−	2496.63i	0.601886	−	1.04250i	−0.390650	−	0.920539i	$-0.627750\pi$
$179$	1441.43	−	2496.63i	0.601886	−	1.04250i	0.992535	−	0.121957i	$-0.0389171\pi$
$180$		0			0
$181$	1128.60			0.463470			0.231735	−	0.972779i	$-0.425560\pi$
$181$	1128.60			0.463470			0.231735	+	0.972779i	$0.425560\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−120.097	+	208.014i	−0.0477282	+	0.0826677i
$186$		0			0
$187$	−1260.00	−	2182.38i	−0.492729	−	0.853432i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1102.62	+	1909.80i	0.417713	+	0.723500i	0.995709	−	0.0925397i	$-0.0294985\pi$
$191$	1102.62	+	1909.80i	0.417713	+	0.723500i	−0.577996	+	0.816039i	$0.696165\pi$
$192$		0			0
$193$	−1897.68	+	3286.88i	−0.707761	+	1.22588i	0.257924	+	0.966165i	$0.416962\pi$
$193$	−1897.68	+	3286.88i	−0.707761	+	1.22588i	−0.965686	+	0.259714i	$0.916372\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3701.25			−1.33859			−0.669297	−	0.742995i	$-0.733405\pi$
$197$	−3701.25			−1.33859			−0.669297	+	0.742995i	$0.733405\pi$
$198$		0			0
$199$	1800.19	−	3118.03i	0.641268	−	1.11071i	−0.343882	−	0.939013i	$-0.611742\pi$
$199$	1800.19	−	3118.03i	0.641268	−	1.11071i	0.985150	−	0.171696i	$-0.0549246\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−97.5351	+	127.798i	−0.0337223	+	0.0441856i
$204$		0			0
$205$	−922.528	−	1597.87i	−0.314303	−	0.544389i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−8048.19			−2.66366
$210$		0			0
$211$	−4137.64			−1.34998			−0.674992	−	0.737825i	$-0.735853\pi$
$211$	−4137.64			−1.34998			−0.674992	+	0.737825i	$0.735853\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−801.556	−	1388.34i	−0.254259	−	0.440389i
$216$		0			0
$217$	−1444.02	−	3460.65i	−0.451735	−	1.08260i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−445.250	+	771.195i	−0.135524	+	0.234734i
$222$		0			0
$223$	4261.62			1.27973			0.639864	−	0.768488i	$-0.278991\pi$
$223$	4261.62			1.27973			0.639864	+	0.768488i	$0.278991\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−767.063	+	1328.59i	−0.224281	+	0.388466i	−0.956103	−	0.293029i	$-0.905337\pi$
$227$	−767.063	+	1328.59i	−0.224281	+	0.388466i	0.731823	+	0.681495i	$0.238670\pi$
$228$		0			0
$229$	287.452	+	497.881i	0.0829491	+	0.143672i	0.904515	−	0.426441i	$-0.140233\pi$
$229$	287.452	+	497.881i	0.0829491	+	0.143672i	−0.821566	+	0.570113i	$0.806899\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2076.07	−	3595.86i	−0.583724	−	1.01104i	−0.995033	−	0.0995443i	$-0.968261\pi$
$233$	−2076.07	−	3595.86i	−0.583724	−	1.01104i	0.411309	−	0.911496i	$-0.365072\pi$
$234$		0			0
$235$	−4630.35	+	8019.99i	−1.28532	+	2.22624i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4548.36			−1.23100			−0.615500	−	0.788137i	$-0.711046\pi$
$239$	−4548.36			−1.23100			−0.615500	+	0.788137i	$0.711046\pi$
$240$		0			0
$241$	−3504.39	+	6069.79i	−0.936672	+	1.62236i	−0.165046	+	0.986286i	$0.552777\pi$
$241$	−3504.39	+	6069.79i	−0.936672	+	1.62236i	−0.771625	+	0.636077i	$0.780556\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3796.66	−	3836.43i	0.990039	−	1.00041i
$246$		0			0
$247$	1422.01	+	2462.99i	0.366316	+	0.634478i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−682.819			−0.171710			−0.0858548	−	0.996308i	$-0.527362\pi$
$251$	−682.819			−0.171710			−0.0858548	+	0.996308i	$0.527362\pi$
$252$		0			0
$253$	1705.00			0.423685
$254$		0			0
$255$		0			0
$256$		0			0
$257$	851.276	+	1474.45i	0.206619	+	0.357875i	0.950647	−	0.310273i	$-0.100421\pi$
$257$	851.276	+	1474.45i	0.206619	+	0.357875i	−0.744028	+	0.668148i	$0.767087\pi$
$258$		0			0
$259$	280.368	+	36.1683i	0.0672634	+	0.00867718i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1462.12	+	2532.47i	−0.342808	+	0.593760i	−0.984953	−	0.172823i	$-0.944711\pi$
$263$	−1462.12	+	2532.47i	−0.342808	+	0.593760i	0.642145	+	0.766583i	$0.278045\pi$
$264$		0			0
$265$	6368.09			1.47618
$266$		0			0
$267$		0			0
$268$		0			0
$269$	686.910	−	1189.76i	0.155694	−	0.269670i	−0.777618	−	0.628738i	$-0.783572\pi$
$269$	686.910	−	1189.76i	0.155694	−	0.269670i	0.933311	+	0.359068i	$0.116905\pi$
$270$		0			0
$271$	390.756	+	676.809i	0.0875894	+	0.151709i	0.906492	−	0.422224i	$-0.138750\pi$
$271$	390.756	+	676.809i	0.0875894	+	0.151709i	−0.818902	+	0.573933i	$0.805417\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3597.85	+	6231.65i	0.788939	+	1.36648i
$276$		0			0
$277$	1075.81	−	1863.36i	0.233355	−	0.404182i	−0.725439	−	0.688287i	$-0.758363\pi$
$277$	1075.81	−	1863.36i	0.233355	−	0.404182i	0.958793	+	0.284105i	$0.0916964\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2388.25			0.507014			0.253507	−	0.967334i	$-0.418416\pi$
$281$	2388.25			0.507014			0.253507	+	0.967334i	$0.418416\pi$
$282$		0			0
$283$	1647.33	−	2853.25i	0.346019	−	0.599322i	−0.639519	−	0.768775i	$-0.720867\pi$
$283$	1647.33	−	2853.25i	0.346019	−	0.599322i	0.985538	+	0.169453i	$0.0542000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1317.43	+	1726.20i	−0.270960	+	0.355033i
$288$		0			0
$289$	1534.39	+	2657.64i	0.312312	+	0.540940i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4355.37			0.868408			0.434204	−	0.900815i	$-0.357030\pi$
$293$	4355.37			0.868408			0.434204	+	0.900815i	$0.357030\pi$
$294$		0			0
$295$	171.126			0.0337741
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−301.250	−	521.780i	−0.0582667	−	0.100921i
$300$		0			0
$301$	−1144.68	+	1499.84i	−0.219196	+	0.287208i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7038.84	+	12191.6i	−1.32145	+	2.28882i
$306$		0			0
$307$	−8189.87			−1.52254			−0.761271	−	0.648434i	$-0.775424\pi$
$307$	−8189.87			−1.52254			−0.761271	+	0.648434i	$0.775424\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	582.651	−	1009.18i	0.106235	−	0.184004i	−0.808007	−	0.589173i	$-0.799454\pi$
$311$	582.651	−	1009.18i	0.106235	−	0.184004i	0.914242	+	0.405168i	$0.132787\pi$
$312$		0			0
$313$	2892.26	+	5009.54i	0.522301	+	0.904652i	0.999663	+	0.0259457i	$0.00825969\pi$
$313$	2892.26	+	5009.54i	0.522301	+	0.904652i	−0.477362	+	0.878707i	$0.658407\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2283.69	−	3955.46i	−0.404620	−	0.700822i	0.589657	−	0.807654i	$-0.299263\pi$
$317$	−2283.69	−	3955.46i	−0.404620	−	0.700822i	−0.994277	+	0.106831i	$0.965930\pi$
$318$		0			0
$319$	−254.688	+	441.133i	−0.0447016	+	0.0774255i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−5889.94			−1.01463
$324$		0			0
$325$	1271.38	−	2202.10i	0.216996	−	0.375847i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	10809.6	+	1394.47i	1.81140	+	0.233677i
$330$		0			0
$331$	−1770.31	−	3066.27i	−0.293973	−	0.509177i	0.680772	−	0.732495i	$-0.261644\pi$
$331$	−1770.31	−	3066.27i	−0.293973	−	0.509177i	−0.974746	+	0.223319i	$0.928311\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	11074.1			1.80609
$336$		0			0
$337$	−9183.50			−1.48444			−0.742221	−	0.670155i	$-0.766227\pi$
$337$	−9183.50			−1.48444			−0.742221	+	0.670155i	$0.766227\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−5940.59	−	10289.4i	−0.943404	−	1.63402i
$342$		0			0
$343$	−5887.72	−	2385.03i	−0.926842	−	0.375451i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2977.50	+	5157.18i	−0.460636	+	0.797844i	−0.998993	−	0.0448726i	$-0.985712\pi$
$347$	−2977.50	+	5157.18i	−0.460636	+	0.797844i	0.538357	+	0.842717i	$0.319045\pi$
$348$		0			0
$349$	2816.11			0.431929			0.215964	−	0.976401i	$-0.430711\pi$
$349$	2816.11			0.431929			0.215964	+	0.976401i	$0.430711\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−190.653	+	330.221i	−0.0287463	+	0.0497900i	−0.880041	−	0.474898i	$-0.842485\pi$
$353$	−190.653	+	330.221i	−0.0287463	+	0.0497900i	0.851294	+	0.524688i	$0.175818\pi$
$354$		0			0
$355$	−9142.23	−	15834.8i	−1.36682	−	2.36739i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1497.38	−	2593.53i	−0.220135	−	0.381285i	0.734714	−	0.678377i	$-0.237316\pi$
$359$	−1497.38	−	2593.53i	−0.220135	−	0.381285i	−0.954849	+	0.297092i	$0.903983\pi$
$360$		0			0
$361$	−5975.93	+	10350.6i	−0.871254	+	1.50906i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	17567.4			2.51923
$366$		0			0
$367$	2325.01	−	4027.04i	0.330694	−	0.572779i	−0.651954	−	0.758259i	$-0.726050\pi$
$367$	2325.01	−	4027.04i	0.330694	−	0.572779i	0.982648	+	0.185479i	$0.0593838\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2886.16	−	6916.79i	−0.403887	−	0.967929i
$372$		0			0
$373$	−2414.17	−	4181.47i	−0.335123	−	0.580451i	0.648385	−	0.761312i	$-0.275445\pi$
$373$	−2414.17	−	4181.47i	−0.335123	−	0.580451i	−0.983509	+	0.180862i	$0.942111\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	180.000			0.0245901
$378$		0			0
$379$	13230.5			1.79315			0.896577	−	0.442887i	$-0.146046\pi$
$379$	13230.5			1.79315			0.896577	+	0.442887i	$0.146046\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2204.87	−	3818.95i	−0.294161	−	0.509502i	0.680628	−	0.732629i	$-0.261707\pi$
$383$	−2204.87	−	3818.95i	−0.294161	−	0.509502i	−0.974789	+	0.223127i	$0.928374\pi$
$384$		0			0
$385$	10375.4	−	13594.7i	1.37346	−	1.79961i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	287.691	−	498.296i	0.0374975	−	0.0649476i	−0.846668	−	0.532122i	$-0.821395\pi$
$389$	287.691	−	498.296i	0.0374975	−	0.0649476i	0.884165	+	0.467175i	$0.154728\pi$
$390$		0			0
$391$	1247.78			0.161388
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1088.41	−	1885.18i	0.138643	−	0.240136i
$396$		0			0
$397$	−3620.81	−	6271.43i	−0.457741	−	0.792831i	0.541100	−	0.840958i	$-0.318008\pi$
$397$	−3620.81	−	6271.43i	−0.457741	−	0.792831i	−0.998841	+	0.0481274i	$0.984675\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1123.50	+	1945.96i	0.139912	+	0.242335i	0.927463	−	0.373914i	$-0.121985\pi$
$401$	1123.50	+	1945.96i	0.139912	+	0.242335i	−0.787551	+	0.616250i	$0.788651\pi$
$402$		0			0
$403$	−2099.24	+	3635.99i	−0.259481	+	0.449434i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	895.693			0.109086
$408$		0			0
$409$	825.318	−	1429.49i	0.0997784	−	0.172821i	−0.811814	−	0.583915i	$-0.801520\pi$
$409$	825.318	−	1429.49i	0.0997784	−	0.172821i	0.911593	+	0.411094i	$0.134853\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−77.5583	−	185.871i	−0.00924066	−	0.0221456i
$414$		0			0
$415$	7036.55	+	12187.7i	0.832314	+	1.44161i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3178.64			0.370613			0.185307	−	0.982681i	$-0.440672\pi$
$419$	3178.64			0.370613			0.185307	+	0.982681i	$0.440672\pi$
$420$		0			0
$421$	8781.12			1.01655			0.508273	−	0.861196i	$-0.330284\pi$
$421$	8781.12			1.01655			0.508273	+	0.861196i	$0.330284\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2633.03	+	4560.54i	0.300519	+	0.520514i
$426$		0			0
$427$	16432.3	+	2119.81i	1.86232	+	0.240246i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	4543.35	−	7869.31i	0.507762	−	0.879469i	−0.492198	−	0.870483i	$-0.663806\pi$
$431$	4543.35	−	7869.31i	0.507762	−	0.879469i	0.999960	−	0.00898583i	$-0.00286032\pi$
$432$		0			0
$433$	3150.88			0.349703			0.174852	−	0.984595i	$-0.444055\pi$
$433$	3150.88			0.349703			0.174852	+	0.984595i	$0.444055\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1992.53	−	3451.16i	0.218113	−	0.377783i
$438$		0			0
$439$	−5165.69	−	8947.23i	−0.561605	−	0.972729i	−0.997357	−	0.0726619i	$-0.976851\pi$
$439$	−5165.69	−	8947.23i	−0.561605	−	0.972729i	0.435751	−	0.900067i	$-0.356483\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4136.03	−	7163.82i	−0.443587	−	0.768315i	0.554366	−	0.832273i	$-0.312961\pi$
$443$	−4136.03	−	7163.82i	−0.443587	−	0.768315i	−0.997953	+	0.0639584i	$0.979627\pi$
$444$		0			0
$445$	5364.48	−	9291.56i	0.571463	−	0.989802i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−10111.1			−1.06275			−0.531374	−	0.847137i	$-0.678324\pi$
$449$	−10111.1			−1.06275			−0.531374	+	0.847137i	$0.678324\pi$
$450$		0			0
$451$	−3440.14	+	5958.50i	−0.359179	+	0.622117i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−5993.59	−	773.192i	−0.617547	−	0.0796655i
$456$		0			0
$457$	8920.37	+	15450.5i	0.913080	+	1.58150i	0.809688	+	0.586860i	$0.199636\pi$
$457$	8920.37	+	15450.5i	0.913080	+	1.58150i	0.103392	+	0.994641i	$0.467031\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	15787.7			1.59503			0.797515	−	0.603299i	$-0.206148\pi$
$461$	15787.7			1.59503			0.797515	+	0.603299i	$0.206148\pi$
$462$		0			0
$463$	−5960.87			−0.598326			−0.299163	−	0.954202i	$-0.596707\pi$
$463$	−5960.87			−0.598326			−0.299163	+	0.954202i	$0.596707\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5529.15	−	9576.78i	−0.547877	−	0.948951i	−0.998420	−	0.0561964i	$-0.982103\pi$
$467$	−5529.15	−	9576.78i	−0.547877	−	0.948951i	0.450542	−	0.892755i	$-0.351231\pi$
$468$		0			0
$469$	−5019.01	−	12028.2i	−0.494150	−	1.18425i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2989.03	+	5177.15i	−0.290562	+	0.503268i
$474$		0			0
$475$	16818.3			1.62459
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5931.90	+	10274.3i	−0.565836	+	0.980056i	0.431136	+	0.902287i	$0.358113\pi$
$479$	−5931.90	+	10274.3i	−0.565836	+	0.980056i	−0.996971	+	0.0777692i	$0.975220\pi$
$480$		0			0
$481$	−158.257	−	274.109i	−0.0150019	−	0.0259840i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1939.59	+	3359.46i	0.181592	+	0.314527i
$486$		0			0
$487$	2962.48	−	5131.17i	0.275653	−	0.477445i	−0.694647	−	0.719351i	$-0.744439\pi$
$487$	2962.48	−	5131.17i	0.275653	−	0.477445i	0.970300	+	0.241906i	$0.0777727\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9203.12			0.845888			0.422944	−	0.906156i	$-0.360997\pi$
$491$	9203.12			0.845888			0.422944	+	0.906156i	$0.360997\pi$
$492$		0			0
$493$	−186.390	+	322.837i	−0.0170275	+	0.0294925i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−13055.7	+	17106.6i	−1.17833	+	1.54394i
$498$		0			0
$499$	4903.80	+	8493.63i	0.439928	+	0.761978i	0.997683	−	0.0680273i	$-0.0216705\pi$
$499$	4903.80	+	8493.63i	0.439928	+	0.761978i	−0.557755	+	0.830006i	$0.688337\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−10462.6			−0.927446			−0.463723	−	0.885980i	$-0.653487\pi$
$503$	−10462.6			−0.927446			−0.463723	+	0.885980i	$0.653487\pi$
$504$		0			0
$505$	−17151.5			−1.51135
$506$		0			0
$507$		0			0
$508$		0			0
$509$	2670.91	+	4626.16i	0.232586	+	0.402850i	0.958568	−	0.284863i	$-0.0919481\pi$
$509$	2670.91	+	4626.16i	0.232586	+	0.402850i	−0.725983	+	0.687713i	$0.758615\pi$
$510$		0			0
$511$	−7961.93	−	19081.0i	−0.689266	−	1.65185i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−237.902	+	412.058i	−0.0203557	+	0.0352572i
$516$		0			0
$517$	34533.5			2.93768
$518$		0			0
$519$		0			0
$520$		0			0
$521$	5776.63	−	10005.4i	0.485755	−	0.841353i	−0.514111	−	0.857724i	$-0.671878\pi$
$521$	5776.63	−	10005.4i	0.485755	−	0.841353i	0.999866	+	0.0163709i	$0.00521125\pi$
$522$		0			0
$523$	−2625.76	−	4547.94i	−0.219534	−	0.380244i	0.735132	−	0.677925i	$-0.237120\pi$
$523$	−2625.76	−	4547.94i	−0.219534	−	0.380244i	−0.954666	+	0.297680i	$0.903787\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4347.52	−	7530.13i	−0.359357	−	0.622425i
$528$		0			0
$529$	5661.39	−	9805.81i	0.465307	−	0.805935i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2431.30			0.197583
$534$		0			0
$535$	−14851.9	+	25724.3i	−1.20020	+	2.07880i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−19468.5	−	5107.99i	−1.55578	−	0.408194i
$540$		0			0
$541$	10308.8	+	17855.4i	0.819241	+	1.41897i	0.906242	+	0.422759i	$0.138938\pi$
$541$	10308.8	+	17855.4i	0.819241	+	1.41897i	−0.0870006	+	0.996208i	$0.527728\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	15179.0			1.19302
$546$		0			0
$547$	10669.4			0.833985			0.416993	−	0.908910i	$-0.363084\pi$
$547$	10669.4			0.833985			0.416993	+	0.908910i	$0.363084\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	595.278	+	1031.05i	0.0460249	+	0.0797174i
$552$		0			0
$553$	−2540.91	−	327.785i	−0.195389	−	0.0252058i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2688.94	+	4657.38i	−0.204549	+	0.354290i	−0.949989	−	0.312283i	$-0.898906\pi$
$557$	−2688.94	+	4657.38i	−0.204549	+	0.354290i	0.745440	+	0.666573i	$0.232240\pi$
$558$		0			0
$559$	2112.49			0.159837
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1759.44	+	3047.43i	−0.131708	+	0.228124i	−0.924335	−	0.381582i	$-0.875379\pi$
$563$	−1759.44	+	3047.43i	−0.131708	+	0.228124i	0.792627	+	0.609706i	$0.208713\pi$
$564$		0			0
$565$	−942.638	−	1632.70i	−0.0701895	−	0.121572i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1275.15	+	2208.63i	0.0939492	+	0.162725i	0.909170	−	0.416426i	$-0.136718\pi$
$569$	1275.15	+	2208.63i	0.0939492	+	0.162725i	−0.815220	+	0.579151i	$0.803384\pi$
$570$		0			0
$571$	−6827.67	+	11825.9i	−0.500401	+	0.866721i	0.499599	+	0.866257i	$0.333481\pi$
$571$	−6827.67	+	11825.9i	−0.500401	+	0.866721i	−1.00000		0.000463542i	$0.999852\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3562.94			−0.258408
$576$		0			0
$577$	8347.94	−	14459.1i	0.602304	−	1.04322i	−0.390168	−	0.920744i	$-0.627583\pi$
$577$	8347.94	−	14459.1i	0.602304	−	1.04322i	0.992471	−	0.122477i	$-0.0390837\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	10048.7	−	13166.5i	0.717536	−	0.940173i
$582$		0			0
$583$	−11873.4	−	20565.4i	−0.843477	−	1.46095i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	16341.4			1.14903			0.574517	−	0.818493i	$-0.305190\pi$
$587$	16341.4			1.14903			0.574517	+	0.818493i	$0.305190\pi$
$588$		0			0
$589$	−27769.6			−1.94266
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9962.59	+	17255.7i	0.689906	+	1.19495i	0.971868	+	0.235527i	$0.0756817\pi$
$593$	9962.59	+	17255.7i	0.689906	+	1.19495i	−0.281961	+	0.959426i	$0.590985\pi$
$594$		0			0
$595$	7593.11	−	9949.09i	0.523171	−	0.685501i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7390.84	−	12801.3i	0.504143	−	0.873201i	−0.495846	−	0.868411i	$-0.665142\pi$
$599$	7390.84	−	12801.3i	0.504143	−	0.873201i	0.999989	−	0.00479026i	$-0.00152479\pi$
$600$		0			0
$601$	−20487.7			−1.39054			−0.695268	−	0.718751i	$-0.744714\pi$
$601$	−20487.7			−1.39054			−0.695268	+	0.718751i	$0.744714\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	16620.5	−	28787.5i	1.11689	−	1.93451i
$606$		0			0
$607$	−3762.02	−	6516.01i	−0.251558	−	0.435711i	0.712397	−	0.701777i	$-0.247610\pi$
$607$	−3762.02	−	6516.01i	−0.251558	−	0.435711i	−0.963955	+	0.266066i	$0.914276\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6101.59	−	10568.3i	−0.404000	−	0.699749i
$612$		0			0
$613$	−1707.32	+	2957.16i	−0.112493	+	0.194843i	−0.916775	−	0.399405i	$-0.869217\pi$
$613$	−1707.32	+	2957.16i	−0.112493	+	0.194843i	0.804282	+	0.594248i	$0.202550\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−22219.4			−1.44979			−0.724895	−	0.688859i	$-0.758112\pi$
$617$	−22219.4			−1.44979			−0.724895	+	0.688859i	$0.758112\pi$
$618$		0			0
$619$	−10931.7	+	18934.3i	−0.709828	+	1.22946i	0.255092	+	0.966917i	$0.417894\pi$
$619$	−10931.7	+	18934.3i	−0.709828	+	1.22946i	−0.964921	+	0.262542i	$0.915439\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−12523.4	−	1615.56i	−0.805363	−	0.103894i
$624$		0			0
$625$	7958.12	+	13783.9i	0.509320	+	0.882168i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	655.499			0.0415524
$630$		0			0
$631$	−16080.8			−1.01452			−0.507262	−	0.861792i	$-0.669342\pi$
$631$	−16080.8			−1.01452			−0.507262	+	0.861792i	$0.669342\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5379.56	+	9317.67i	0.336191	+	0.582300i
$636$		0			0
$637$	1876.62	+	6860.45i	0.116726	+	0.426720i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9231.90	+	15990.1i	−0.568858	+	0.985292i	0.427821	+	0.903864i	$0.359281\pi$
$641$	−9231.90	+	15990.1i	−0.568858	+	0.985292i	−0.996679	+	0.0814280i	$0.974052\pi$
$642$		0			0
$643$	−3110.87			−0.190794			−0.0953971	−	0.995439i	$-0.530412\pi$
$643$	−3110.87			−0.190794			−0.0953971	+	0.995439i	$0.530412\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12364.5	+	21416.0i	−0.751313	+	1.30131i	0.195873	+	0.980629i	$0.437246\pi$
$647$	−12364.5	+	21416.0i	−0.751313	+	1.30131i	−0.947186	+	0.320683i	$0.896087\pi$
$648$		0			0
$649$	−319.068	−	552.643i	−0.0192982	−	0.0334255i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3526.32	+	6107.76i	0.211325	+	0.366026i	0.952130	−	0.305695i	$-0.0988887\pi$
$653$	3526.32	+	6107.76i	0.211325	+	0.366026i	−0.740804	+	0.671721i	$0.765555\pi$
$654$		0			0
$655$	−2047.56	+	3546.47i	−0.122145	+	0.211561i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−7895.55			−0.466718			−0.233359	−	0.972391i	$-0.574972\pi$
$659$	−7895.55			−0.466718			−0.233359	+	0.972391i	$0.574972\pi$
$660$		0			0
$661$	6550.56	−	11345.9i	0.385457	−	0.667631i	−0.606375	−	0.795179i	$-0.707377\pi$
$661$	6550.56	−	11345.9i	0.385457	−	0.667631i	0.991833	+	0.127547i	$0.0407104\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−15392.5	−	36888.7i	−0.897589	−	2.15110i
$666$		0			0
$667$	−126.109	−	218.427i	−0.00732076	−	0.0126799i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	52496.2			3.02026
$672$		0			0
$673$	−9128.25			−0.522836			−0.261418	−	0.965226i	$-0.584190\pi$
$673$	−9128.25			−0.522836			−0.261418	+	0.965226i	$0.584190\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8014.93	+	13882.3i	0.455006	+	0.788093i	0.998689	−	0.0511978i	$-0.0163039\pi$
$677$	8014.93	+	13882.3i	0.455006	+	0.788093i	−0.543683	+	0.839291i	$0.682971\pi$
$678$		0			0
$679$	2769.86	−	3629.29i	0.156550	−	0.205124i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−11088.2	+	19205.3i	−0.621197	+	1.07594i	0.368066	+	0.929800i	$0.380020\pi$
$683$	−11088.2	+	19205.3i	−0.621197	+	1.07594i	−0.989263	+	0.146145i	$0.953313\pi$
$684$		0			0
$685$	−11514.0			−0.642231
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4195.75	+	7267.25i	−0.231996	+	0.401829i
$690$		0			0
$691$	592.072	+	1025.50i	0.0325955	+	0.0564570i	0.881863	−	0.471506i	$-0.156289\pi$
$691$	592.072	+	1025.50i	0.0325955	+	0.0564570i	−0.849267	+	0.527963i	$0.822956\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	18000.0	+	31176.9i	0.982417	+	1.70160i
$696$		0			0
$697$	−2517.61	+	4360.63i	−0.136817	+	0.236974i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−31064.6			−1.67374			−0.836870	−	0.547401i	$-0.815617\pi$
$701$	−31064.6			−1.67374			−0.836870	+	0.547401i	$0.815617\pi$
$702$		0			0
$703$	1046.74	−	1813.01i	0.0561574	−	0.0972674i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7773.42	+	18629.3i	0.413507	+	0.990985i
$708$		0			0
$709$	−287.946	−	498.736i	−0.0152525	−	0.0264181i	0.858298	−	0.513151i	$-0.171522\pi$
$709$	−287.946	−	498.736i	−0.0152525	−	0.0264181i	−0.873551	+	0.486733i	$0.838189\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	5882.95			0.309002
$714$		0			0
$715$	−19147.8			−1.00152
$716$		0			0
$717$		0			0
$718$		0			0
$719$	2417.77	+	4187.70i	0.125407	+	0.217211i	0.921892	−	0.387447i	$-0.126643\pi$
$719$	2417.77	+	4187.70i	0.125407	+	0.217211i	−0.796485	+	0.604658i	$0.793310\pi$
$720$		0			0
$721$	555.384	+	71.6462i	0.0286874	+	0.00370076i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	532.224	−	921.838i	0.0272638	−	0.0472224i
$726$		0			0
$727$	−17999.8			−0.918259			−0.459129	−	0.888369i	$-0.651839\pi$
$727$	−17999.8			−0.918259			−0.459129	+	0.888369i	$0.651839\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2187.48	+	3788.82i	−0.110680	+	0.191703i
$732$		0			0
$733$	−2556.70	−	4428.33i	−0.128832	−	0.223144i	0.794392	−	0.607405i	$-0.207789\pi$
$733$	−2556.70	−	4428.33i	−0.128832	−	0.223144i	−0.923224	+	0.384261i	$0.874456\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−20647.8	−	35763.0i	−1.03198	−	1.78745i
$738$		0			0
$739$	−6528.06	+	11306.9i	−0.324951	+	0.562831i	−0.981502	−	0.191450i	$-0.938681\pi$
$739$	−6528.06	+	11306.9i	−0.324951	+	0.562831i	0.656552	+	0.754281i	$0.272014\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	28402.9			1.40242			0.701212	−	0.712953i	$-0.252643\pi$
$743$	28402.9			1.40242			0.701212	+	0.712953i	$0.252643\pi$
$744$		0			0
$745$	−27059.8	+	46868.9i	−1.33073	+	2.30489i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	34672.0	+	4472.79i	1.69144	+	0.218201i
$750$		0			0
$751$	16635.1	+	28812.9i	0.808288	+	1.40000i	0.914049	+	0.405605i	$0.132939\pi$
$751$	16635.1	+	28812.9i	0.808288	+	1.40000i	−0.105760	+	0.994392i	$0.533728\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−44875.7			−2.16317
$756$		0			0
$757$	18331.2			0.880129			0.440064	−	0.897966i	$-0.354956\pi$
$757$	18331.2			0.880129			0.440064	+	0.897966i	$0.354956\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2498.50	+	4327.53i	0.119015	+	0.206141i	0.919378	−	0.393376i	$-0.128693\pi$
$761$	2498.50	+	4327.53i	0.119015	+	0.206141i	−0.800362	+	0.599517i	$0.795360\pi$
$762$		0			0
$763$	−6879.46	−	16486.9i	−0.326413	−	0.782260i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−112.750	+	195.289i	−0.00530792	+	0.00919358i
$768$		0			0
$769$	−9834.47			−0.461171			−0.230585	−	0.973052i	$-0.574064\pi$
$769$	−9834.47			−0.461171			−0.230585	+	0.973052i	$0.574064\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−6991.49	+	12109.6i	−0.325312	+	0.563458i	−0.981576	−	0.191074i	$-0.938803\pi$
$773$	−6991.49	+	12109.6i	−0.325312	+	0.563458i	0.656263	+	0.754532i	$0.272136\pi$
$774$		0			0
$775$	12414.1	+	21501.8i	0.575389	+	0.996603i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	8040.57	+	13926.7i	0.369812	+	0.640532i
$780$		0			0
$781$	−34091.7	+	59048.6i	−1.56197	+	2.70541i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−38400.0			−1.74593
$786$		0			0
$787$	15639.3	−	27088.1i	0.708362	−	1.22692i	−0.257102	−	0.966384i	$-0.582768\pi$
$787$	15639.3	−	27088.1i	0.708362	−	1.22692i	0.965464	−	0.260535i	$-0.0838990\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1346.15	+	1763.83i	−0.0605102	+	0.0792853i
$792$		0			0
$793$	−9275.37	−	16065.4i	−0.415357	−	0.719419i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−30546.9			−1.35762			−0.678811	−	0.734313i	$-0.737505\pi$
$797$	−30546.9			−1.35762			−0.678811	+	0.734313i	$0.737505\pi$
$798$		0			0
$799$	25272.8			1.11901
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−32754.7	−	56732.8i	−1.43946	−	2.49322i
$804$		0			0
$805$	3260.88	+	7814.82i	0.142771	+	0.342157i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−14786.3	+	25610.7i	−0.642596	+	1.11301i	0.342256	+	0.939607i	$0.388809\pi$
$809$	−14786.3	+	25610.7i	−0.642596	+	1.11301i	−0.984851	+	0.173401i	$0.944524\pi$
$810$		0			0
$811$	45069.0			1.95140			0.975701	−	0.219107i	$-0.0703144\pi$
$811$	45069.0			1.95140			0.975701	+	0.219107i	$0.0703144\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1899.27	−	3289.64i	0.0816302	−	0.141388i
$816$		0			0
$817$	6986.20	+	12100.5i	0.299163	+	0.518166i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	4700.47	+	8141.45i	0.199814	+	0.346088i	0.948468	−	0.316873i	$-0.102633\pi$
$821$	4700.47	+	8141.45i	0.199814	+	0.346088i	−0.748654	+	0.662961i	$0.769299\pi$
$822$		0			0
$823$	14004.4	−	24256.4i	0.593152	−	1.02737i	−0.400653	−	0.916230i	$-0.631217\pi$
$823$	14004.4	−	24256.4i	0.593152	−	1.02737i	0.993805	−	0.111139i	$-0.0354499\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	28650.8			1.20470			0.602349	−	0.798232i	$-0.294231\pi$
$827$	28650.8			1.20470			0.602349	+	0.798232i	$0.294231\pi$
$828$		0			0
$829$	2124.82	−	3680.29i	0.0890205	−	0.154188i	−0.818077	−	0.575109i	$-0.804960\pi$
$829$	2124.82	−	3680.29i	0.0890205	−	0.154188i	0.907097	+	0.420921i	$0.138293\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−14247.7	−	3738.20i	−0.592621	−	0.155487i
$834$		0			0
$835$	−2568.48	−	4448.74i	−0.106450	−	0.184377i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−9265.50			−0.381264			−0.190632	−	0.981662i	$-0.561054\pi$
$839$	−9265.50			−0.381264			−0.190632	+	0.981662i	$0.561054\pi$
$840$		0			0
$841$	−24313.6			−0.996910
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−13903.0	−	24080.6i	−0.566007	−	0.980354i
$846$		0			0
$847$	−38800.7	−	5005.41i	−1.57404	−	0.203055i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−221.751	+	384.084i	−0.00893245	+	0.0154715i
$852$		0			0
$853$	36321.1			1.45793			0.728964	−	0.684552i	$-0.240002\pi$
$853$	36321.1			1.45793			0.728964	+	0.684552i	$0.240002\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11838.1	+	20504.2i	−0.471858	+	0.817282i	−0.999482	−	0.0321962i	$-0.989750\pi$
$857$	−11838.1	+	20504.2i	−0.471858	+	0.817282i	0.527623	+	0.849478i	$0.323083\pi$
$858$		0			0
$859$	−13706.2	−	23739.8i	−0.544410	−	0.942946i	−0.998644	−	0.0520636i	$-0.983420\pi$
$859$	−13706.2	−	23739.8i	−0.544410	−	0.942946i	0.454233	−	0.890883i	$-0.349913\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−11362.7	−	19680.9i	−0.448195	−	0.776297i	0.550074	−	0.835116i	$-0.314600\pi$
$863$	−11362.7	−	19680.9i	−0.448195	−	0.776297i	−0.998269	+	0.0588195i	$0.981266\pi$
$864$		0			0
$865$	12555.0	−	21745.9i	0.493506	−	0.854778i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−8117.45			−0.316876
$870$		0			0
$871$	−7296.37	+	12637.7i	−0.283844	+	0.491632i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	419.943	−	550.243i	0.0162248	−	0.0212590i
$876$		0			0
$877$	−5990.93	−	10376.6i	−0.230672	−	0.399536i	0.727334	−	0.686284i	$-0.240759\pi$
$877$	−5990.93	−	10376.6i	−0.230672	−	0.399536i	−0.958006	+	0.286748i	$0.907426\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	22891.8			0.875419			0.437709	−	0.899117i	$-0.355790\pi$
$881$	22891.8			0.875419			0.437709	+	0.899117i	$0.355790\pi$
$882$		0			0
$883$	36489.6			1.39068			0.695341	−	0.718680i	$-0.255253\pi$
$883$	36489.6			1.39068			0.695341	+	0.718680i	$0.255253\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12052.9	+	20876.2i	0.456253	+	0.790254i	0.998759	−	0.0497981i	$-0.0158578\pi$
$887$	12052.9	+	20876.2i	0.456253	+	0.790254i	−0.542506	+	0.840052i	$0.682524\pi$
$888$		0			0
$889$	7682.37	−	10066.1i	0.289830	−	0.379758i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	40357.2	−	69900.7i	1.51232	−	2.61941i
$894$		0			0
$895$	45365.0			1.69428
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−878.781	+	1522.09i	−0.0326018	+	0.0564679i
$900$		0			0
$901$	−8689.38	−	15050.5i	−0.321293	−	0.556496i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	8879.87	+	15380.4i	0.326162	+	0.564929i
$906$		0			0
$907$	−11181.6	+	19367.2i	−0.409350	+	0.709014i	−0.994817	−	0.101682i	$-0.967578\pi$
$907$	−11181.6	+	19367.2i	−0.409350	+	0.709014i	0.585467	+	0.810696i	$0.300911\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	21426.3			0.779238			0.389619	−	0.920976i	$-0.372607\pi$
$911$	21426.3			0.779238			0.389619	+	0.920976i	$0.372607\pi$
$912$		0			0
$913$	26239.5	−	45448.2i	0.951152	−	1.64744i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4780.05	+	616.641i	0.172139	+	0.0222064i
$918$		0			0
$919$	15263.0	+	26436.4i	0.547858	+	0.948917i	0.998421	+	0.0561730i	$0.0178898\pi$
$919$	15263.0	+	26436.4i	0.547858	+	0.948917i	−0.450563	+	0.892744i	$0.648777\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	24094.2			0.859231
$924$		0			0
$925$	−1871.73			−0.0665322
$926$		0			0
$927$		0			0
$928$		0			0
$929$	2319.45	+	4017.40i	0.0819146	+	0.141880i	0.904072	−	0.427380i	$-0.140563\pi$
$929$	2319.45	+	4017.40i	0.0819146	+	0.141880i	−0.822158	+	0.569260i	$0.807230\pi$
$930$		0			0
$931$	−33090.9	+	33437.6i	−1.16489	+	1.17709i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	19827.5	−	34342.2i	0.693506	−	1.20119i
$936$		0			0
$937$	−7713.38			−0.268928			−0.134464	−	0.990919i	$-0.542931\pi$
$937$	−7713.38			−0.268928			−0.134464	+	0.990919i	$0.542931\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3745.31	+	6487.07i	−0.129749	+	0.224732i	−0.923579	−	0.383408i	$-0.874750\pi$
$941$	−3745.31	+	6487.07i	−0.129749	+	0.224732i	0.793830	+	0.608139i	$0.208084\pi$
$942$		0			0
$943$	−1703.38	−	2950.34i	−0.0588226	−	0.101884i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	12569.6	+	21771.1i	0.431316	+	0.747061i	0.996987	−	0.0775698i	$-0.0247161\pi$
$947$	12569.6	+	21771.1i	0.431316	+	0.747061i	−0.565671	+	0.824631i	$0.691383\pi$
$948$		0			0
$949$	−11574.6	+	20047.8i	−0.395920	+	0.685754i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	2505.29			0.0851568			0.0425784	−	0.999093i	$-0.486443\pi$
$953$	2505.29			0.0851568			0.0425784	+	0.999093i	$0.486443\pi$
$954$		0			0
$955$	−17351.0	+	30052.8i	−0.587922	+	1.01831i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	5218.41	+	12506.1i	0.175716	+	0.421108i
$960$		0			0
$961$	−5602.00	−	9702.94i	−0.188043	−	0.325700i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−59724.2			−1.99232
$966$		0			0
$967$	−9331.61			−0.310325			−0.155162	−	0.987889i	$-0.549590\pi$
$967$	−9331.61			−0.310325			−0.155162	+	0.987889i	$0.549590\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−20993.0	−	36360.9i	−0.693817	−	1.20173i	−0.970578	−	0.240787i	$-0.922594\pi$
$971$	−20993.0	−	36360.9i	−0.693817	−	1.20173i	0.276761	−	0.960939i	$-0.410739\pi$
$972$		0			0
$973$	25705.2	−	33681.0i	0.846939	−	1.10973i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3975.47	+	6885.72i	−0.130181	+	0.225480i	−0.923746	−	0.383005i	$-0.874889\pi$
$977$	−3975.47	+	6885.72i	−0.130181	+	0.225480i	0.793565	+	0.608485i	$0.208222\pi$
$978$		0			0
$979$	−40008.7			−1.30611
$980$		0			0
$981$		0			0
$982$		0			0
$983$	5269.74	−	9127.47i	0.170986	−	0.296156i	−0.767779	−	0.640715i	$-0.778638\pi$
$983$	5269.74	−	9127.47i	0.170986	−	0.296156i	0.938765	+	0.344559i	$0.111972\pi$
$984$		0			0
$985$	−29121.6	−	50440.1i	−0.942022	−	1.63163i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1480.02	−	2563.46i	−0.0475852	−	0.0824200i
$990$		0			0
$991$	2215.93	−	3838.10i	0.0710306	−	0.123029i	−0.828323	−	0.560251i	$-0.810705\pi$
$991$	2215.93	−	3838.10i	0.0710306	−	0.123029i	0.899353	+	0.437223i	$0.144038\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	56656.0			1.80514
$996$		0			0
$997$	19707.8	−	34134.9i	0.626031	−	1.08432i	−0.362310	−	0.932058i	$-0.618012\pi$
$997$	19707.8	−	34134.9i	0.626031	−	1.08432i	0.988341	−	0.152259i	$-0.0486548\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.4.s.f.361.2		4
3.2	odd	2		168.4.q.d.25.1	✓	4
7.2	even	3	inner	504.4.s.f.289.2		4
12.11	even	2		336.4.q.g.193.1		4
21.2	odd	6		168.4.q.d.121.1	yes	4
21.11	odd	6		1176.4.a.r.1.2		2
21.17	even	6		1176.4.a.u.1.1		2
84.11	even	6		2352.4.a.cc.1.2		2
84.23	even	6		336.4.q.g.289.1		4
84.59	odd	6		2352.4.a.bo.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.q.d.25.1	✓	4	3.2	odd	2
168.4.q.d.121.1	yes	4	21.2	odd	6
336.4.q.g.193.1		4	12.11	even	2
336.4.q.g.289.1		4	84.23	even	6
504.4.s.f.289.2		4	7.2	even	3	inner
504.4.s.f.361.2		4	1.1	even	1	trivial
1176.4.a.r.1.2		2	21.11	odd	6
1176.4.a.u.1.1		2	21.17	even	6
2352.4.a.bo.1.1		2	84.59	odd	6
2352.4.a.cc.1.2		2	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	504.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(7.86805 + 13.6279i) q^{5} +(11.2361 - 14.7224i) q^{7} +O(q^{10})\)	\(q+(7.86805 + 13.6279i) q^{5} +(11.2361 - 14.7224i) q^{7} +(29.3403 - 50.8188i) q^{11} -20.7361 q^{13} +(21.4722 - 37.1910i) q^{17} +(-68.5764 - 118.778i) q^{19} +(14.5278 + 25.1629i) q^{23} +(-61.3125 + 106.196i) q^{25} -8.68051 q^{29} +(101.236 - 175.346i) q^{31} +(289.042 + 37.2872i) q^{35} +(7.63195 + 13.2189i) q^{37} -117.250 q^{41} -101.875 q^{43} +(294.250 + 509.656i) q^{47} +(-90.5000 - 330.846i) q^{49} +(202.340 - 350.464i) q^{53} +923.403 q^{55} +(5.43738 - 9.41783i) q^{59} +(447.305 + 774.756i) q^{61} +(-163.153 - 282.589i) q^{65} +(351.868 - 609.453i) q^{67} -1161.94 q^{71} +(558.187 - 966.809i) q^{73} +(-418.506 - 1002.97i) q^{77} +(-69.1665 - 119.800i) q^{79} +894.319 q^{83} +675.778 q^{85} +(-340.903 - 590.461i) q^{89} +(-232.993 + 305.286i) q^{91} +(1079.12 - 1869.10i) q^{95} +246.514 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 9 q^{5}+O(q^{10}) \) 4 * q + 9 * q^5	\( 4 q + 9 q^{5} + 5 q^{11} - 38 q^{13} - 4 q^{17} - 117 q^{19} + 148 q^{23} - 43 q^{25} + 190 q^{29} + 360 q^{31} + 482 q^{35} + 53 q^{37} + 340 q^{41} + 806 q^{43} + 368 q^{47} - 362 q^{49} + 697 q^{53} + 2570 q^{55} - 585 q^{59} + 1160 q^{61} - 338 q^{65} - 233 q^{67} - 1232 q^{71} + 817 q^{73} + 1135 q^{77} + 802 q^{79} + 566 q^{83} + 1984 q^{85} - 1858 q^{89} - 505 q^{91} + 2294 q^{95} + 3458 q^{97}+O(q^{100}) \) 4 * q + 9 * q^5 + 5 * q^11 - 38 * q^13 - 4 * q^17 - 117 * q^19 + 148 * q^23 - 43 * q^25 + 190 * q^29 + 360 * q^31 + 482 * q^35 + 53 * q^37 + 340 * q^41 + 806 * q^43 + 368 * q^47 - 362 * q^49 + 697 * q^53 + 2570 * q^55 - 585 * q^59 + 1160 * q^61 - 338 * q^65 - 233 * q^67 - 1232 * q^71 + 817 * q^73 + 1135 * q^77 + 802 * q^79 + 566 * q^83 + 1984 * q^85 - 1858 * q^89 - 505 * q^91 + 2294 * q^95 + 3458 * q^97

Introduction

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