LMFDB - Embedded newform 60.5.b.a.29.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,5,Mod(29,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("60.29");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	60.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.20219778503$
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} + 110x^{6} + 2705x^{4} + 17000x^{2} + 25600 $ x^8 + 110x^6 + 2705x^4 + 17000*x^2 + 25600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{2}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.7
Root			$2.51271i$ of defining polynomial
Character	$\chi$	$=$	60.29
Dual form			60.5.b.a.29.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.97294 - 0.697422i) q^{3} +(-9.58741 - 23.0886i) q^{5} -67.4301i q^{7} +(80.0272 - 12.5158i) q^{9} +O(q^{10})$	\(q+(8.97294 - 0.697422i) q^{3} +(-9.58741 - 23.0886i) q^{5} -67.4301i q^{7} +(80.0272 - 12.5158i) q^{9} +155.791i q^{11} -206.475i q^{13} +(-102.130 - 200.486i) q^{15} +119.476 q^{17} +492.163 q^{19} +(-47.0272 - 605.046i) q^{21} -353.261 q^{23} +(-441.163 + 442.719i) q^{25} +(709.350 - 168.117i) q^{27} +917.942i q^{29} -632.163 q^{31} +(108.652 + 1397.90i) q^{33} +(-1556.86 + 646.480i) q^{35} +1755.93i q^{37} +(-144.000 - 1852.69i) q^{39} +1449.21i q^{41} -627.316i q^{43} +(-1056.23 - 1727.72i) q^{45} +3701.53 q^{47} -2145.82 q^{49} +(1072.05 - 83.3255i) q^{51} -3662.42 q^{53} +(3596.98 - 1493.63i) q^{55} +(4416.15 - 343.245i) q^{57} +1424.52i q^{59} +1737.14 q^{61} +(-843.944 - 5396.24i) q^{63} +(-4767.21 + 1979.56i) q^{65} -6456.19i q^{67} +(-3169.79 + 246.372i) q^{69} -2436.64i q^{71} +2691.70i q^{73} +(-3649.77 + 4280.17i) q^{75} +10505.0 q^{77} +3216.49 q^{79} +(6247.71 - 2003.22i) q^{81} +1517.02 q^{83} +(-1145.47 - 2758.54i) q^{85} +(640.193 + 8236.64i) q^{87} -7466.75i q^{89} -13922.6 q^{91} +(-5672.36 + 440.884i) q^{93} +(-4718.57 - 11363.3i) q^{95} +10716.1i q^{97} +(1949.85 + 12467.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 52 q^{9}+O(q^{10}) $ 8 * q + 52 * q^9	$ 8 q + 52 q^{9} - 100 q^{15} + 408 q^{19} + 212 q^{21} - 1528 q^{31} - 1152 q^{39} - 2900 q^{45} + 480 q^{49} + 7400 q^{51} + 7600 q^{55} - 10808 q^{61} - 8300 q^{69} - 14000 q^{75} + 15144 q^{79} + 34688 q^{81} + 22600 q^{85} - 54912 q^{91} - 24400 q^{99}+O(q^{100}) $ 8 * q + 52 * q^9 - 100 * q^15 + 408 * q^19 + 212 * q^21 - 1528 * q^31 - 1152 * q^39 - 2900 * q^45 + 480 * q^49 + 7400 * q^51 + 7600 * q^55 - 10808 * q^61 - 8300 * q^69 - 14000 * q^75 + 15144 * q^79 + 34688 * q^81 + 22600 * q^85 - 54912 * q^91 - 24400 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$1$	$-1$	$-1$

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
$3$	8.97294	−	0.697422i	0.996993	−	0.0774913i
$3$	8.97294	−	0.697422i	0.996993	−	0.0774913i
$4$		0			0
$5$	−9.58741	−	23.0886i	−0.383496	−	0.923542i
$5$	−9.58741	−	23.0886i	−0.383496	−	0.923542i
$6$		0			0
$7$		−	67.4301i		−	1.37612i	−0.725652	−	0.688062i	$-0.758462\pi$
$7$		−	67.4301i		−	1.37612i	0.725652	−	0.688062i	$-0.241538\pi$
$8$		0			0
$9$	80.0272	−	12.5158i	0.987990	−	0.154517i
$10$		0			0
$11$			155.791i			1.28753i	0.765225	+	0.643763i	$0.222628\pi$
$11$			155.791i			1.28753i	−0.765225	+	0.643763i	$0.777372\pi$
$12$		0			0
$13$		−	206.475i		−	1.22174i	−0.791729	−	0.610872i	$-0.790819\pi$
$13$		−	206.475i		−	1.22174i	0.791729	−	0.610872i	$-0.209181\pi$
$14$		0			0
$15$	−102.130	−	200.486i	−0.453910	−	0.891048i
$16$		0			0
$17$	119.476			0.413413			0.206707	−	0.978403i	$-0.433725\pi$
$17$	119.476			0.413413			0.206707	+	0.978403i	$0.433725\pi$
$18$		0			0
$19$	492.163			1.36333			0.681667	−	0.731663i	$-0.261256\pi$
$19$	492.163			1.36333			0.681667	+	0.731663i	$0.261256\pi$
$20$		0			0
$21$	−47.0272	−	605.046i	−0.106638	−	1.37199i
$22$		0			0
$23$	−353.261			−0.667790			−0.333895	−	0.942610i	$-0.608363\pi$
$23$	−353.261			−0.667790			−0.333895	+	0.942610i	$0.608363\pi$
$24$		0			0
$25$	−441.163	+	442.719i	−0.705861	+	0.708350i
$26$		0			0
$27$	709.350	−	168.117i	0.973046	−	0.230613i
$28$		0			0
$29$			917.942i			1.09149i	0.837952	+	0.545744i	$0.183753\pi$
$29$			917.942i			1.09149i	−0.837952	+	0.545744i	$0.816247\pi$
$30$		0			0
$31$	−632.163			−0.657818			−0.328909	−	0.944362i	$-0.606681\pi$
$31$	−632.163			−0.657818			−0.328909	+	0.944362i	$0.606681\pi$
$32$		0			0
$33$	108.652	+	1397.90i	0.0997720	+	1.28365i
$34$		0			0
$35$	−1556.86	+	646.480i	−1.27091	+	0.527739i
$36$		0			0
$37$			1755.93i			1.28264i	0.767274	+	0.641320i	$0.221613\pi$
$37$			1755.93i			1.28264i	−0.767274	+	0.641320i	$0.778387\pi$
$38$		0			0
$39$	−144.000	−	1852.69i	−0.0946746	−	1.21807i
$40$		0			0
$41$			1449.21i			0.862111i	0.902326	+	0.431055i	$0.141859\pi$
$41$			1449.21i			0.862111i	−0.902326	+	0.431055i	$0.858141\pi$
$42$		0			0
$43$		−	627.316i		−	0.339273i	−0.985507	−	0.169637i	$-0.945741\pi$
$43$		−	627.316i		−	0.339273i	0.985507	−	0.169637i	$-0.0542594\pi$
$44$		0			0
$45$	−1056.23	−	1727.72i	−0.521593	−	0.853194i
$46$		0			0
$47$	3701.53			1.67566			0.837829	−	0.545932i	$-0.183824\pi$
$47$	3701.53			1.67566			0.837829	+	0.545932i	$0.183824\pi$
$48$		0			0
$49$	−2145.82			−0.893718
$50$		0			0
$51$	1072.05	−	83.3255i	0.412170	−	0.0320359i
$52$		0			0
$53$	−3662.42			−1.30382			−0.651909	−	0.758297i	$-0.726031\pi$
$53$	−3662.42			−1.30382			−0.651909	+	0.758297i	$0.726031\pi$
$54$		0			0
$55$	3596.98	−	1493.63i	1.18908	−	0.493761i
$56$		0			0
$57$	4416.15	−	343.245i	1.35923	−	0.105646i
$58$		0			0
$59$			1424.52i			0.409226i	0.978843	+	0.204613i	$0.0655936\pi$
$59$			1424.52i			0.409226i	−0.978843	+	0.204613i	$0.934406\pi$
$60$		0			0
$61$	1737.14			0.466848			0.233424	−	0.972375i	$-0.425007\pi$
$61$	1737.14			0.466848			0.233424	+	0.972375i	$0.425007\pi$
$62$		0			0
$63$	−843.944	−	5396.24i	−0.212634	−	1.35960i
$64$		0			0
$65$	−4767.21	+	1979.56i	−1.12833	+	0.468534i
$66$		0			0
$67$		−	6456.19i		−	1.43822i	−0.694894	−	0.719112i	$-0.744549\pi$
$67$		−	6456.19i		−	1.43822i	0.694894	−	0.719112i	$-0.255451\pi$
$68$		0			0
$69$	−3169.79	+	246.372i	−0.665782	+	0.0517479i
$70$		0			0
$71$		−	2436.64i		−	0.483365i	−0.970355	−	0.241683i	$-0.922301\pi$
$71$		−	2436.64i		−	0.483365i	0.970355	−	0.241683i	$-0.0776993\pi$
$72$		0			0
$73$			2691.70i			0.505104i	0.967583	+	0.252552i	$0.0812699\pi$
$73$			2691.70i			0.505104i	−0.967583	+	0.252552i	$0.918730\pi$
$74$		0			0
$75$	−3649.77	+	4280.17i	−0.648848	+	0.760918i
$76$		0			0
$77$	10505.0			1.77179
$78$		0			0
$79$	3216.49			0.515381			0.257690	−	0.966228i	$-0.417039\pi$
$79$	3216.49			0.515381			0.257690	+	0.966228i	$0.417039\pi$
$80$		0			0
$81$	6247.71	−	2003.22i	0.952249	−	0.305322i
$82$		0			0
$83$	1517.02			0.220208			0.110104	−	0.993920i	$-0.464882\pi$
$83$	1517.02			0.220208			0.110104	+	0.993920i	$0.464882\pi$
$84$		0			0
$85$	−1145.47	−	2758.54i	−0.158542	−	0.381805i
$86$		0			0
$87$	640.193	+	8236.64i	0.0845809	+	1.08821i
$88$		0			0
$89$		−	7466.75i		−	0.942652i	−0.881959	−	0.471326i	$-0.843776\pi$
$89$		−	7466.75i		−	0.942652i	0.881959	−	0.471326i	$-0.156224\pi$
$90$		0			0
$91$	−13922.6			−1.68127
$92$		0			0
$93$	−5672.36	+	440.884i	−0.655840	+	0.0509752i
$94$		0			0
$95$	−4718.57	−	11363.3i	−0.522833	−	1.25910i
$96$		0			0
$97$			10716.1i			1.13892i	0.822018	+	0.569462i	$0.192848\pi$
$97$			10716.1i			1.13892i	−0.822018	+	0.569462i	$0.807152\pi$
$98$		0			0
$99$	1949.85	+	12467.5i	0.198944	+	1.27206i
$100$		0			0
$101$			3399.39i			0.333241i	0.986021	+	0.166620i	$0.0532855\pi$
$101$			3399.39i			0.333241i	−0.986021	+	0.166620i	$0.946715\pi$
$102$		0			0
$103$			8880.69i			0.837090i	0.908196	+	0.418545i	$0.137460\pi$
$103$			8880.69i			0.837090i	−0.908196	+	0.418545i	$0.862540\pi$
$104$		0			0
$105$	−13518.8	+	6886.61i	−1.22619	+	0.624636i
$106$		0			0
$107$	4732.46			0.413351			0.206676	−	0.978410i	$-0.433736\pi$
$107$	4732.46			0.413351			0.206676	+	0.978410i	$0.433736\pi$
$108$		0			0
$109$	10138.4			0.853333			0.426666	−	0.904409i	$-0.359688\pi$
$109$	10138.4			0.853333			0.426666	+	0.904409i	$0.359688\pi$
$110$		0			0
$111$	1224.63	+	15755.9i	0.0993934	+	1.27878i
$112$		0			0
$113$	−5594.72			−0.438149			−0.219074	−	0.975708i	$-0.570304\pi$
$113$	−5594.72			−0.438149			−0.219074	+	0.975708i	$0.570304\pi$
$114$		0			0
$115$	3386.86	+	8156.29i	0.256095	+	0.616733i
$116$		0			0
$117$	−2584.21	−	16523.6i	−0.188780	−	1.20707i
$118$		0			0
$119$		−	8056.30i		−	0.568908i
$120$		0			0
$121$	−9629.69			−0.657721
$122$		0			0
$123$	1010.71	+	13003.7i	0.0668061	+	0.859518i
$124$		0			0
$125$	14451.4	+	5941.30i	0.924887	+	0.380243i
$126$		0			0
$127$			3557.28i			0.220552i	0.993901	+	0.110276i	$0.0351735\pi$
$127$			3557.28i			0.220552i	−0.993901	+	0.110276i	$0.964827\pi$
$128$		0			0
$129$	−437.504	−	5628.87i	−0.0262907	−	0.338253i
$130$		0			0
$131$		−	31645.8i		−	1.84406i	−0.387124	−	0.922028i	$-0.626531\pi$
$131$		−	31645.8i		−	1.84406i	0.387124	−	0.922028i	$-0.373469\pi$
$132$		0			0
$133$		−	33186.6i		−	1.87612i
$134$		0			0
$135$	−10682.4	−	14766.1i	−0.586140	−	0.810210i
$136$		0			0
$137$	−19253.1			−1.02579			−0.512897	−	0.858450i	$-0.671428\pi$
$137$	−19253.1			−1.02579			−0.512897	+	0.858450i	$0.671428\pi$
$138$		0			0
$139$	10124.2			0.523998			0.261999	−	0.965068i	$-0.415618\pi$
$139$	10124.2			0.523998			0.261999	+	0.965068i	$0.415618\pi$
$140$		0			0
$141$	33213.6	−	2581.53i	1.67062	−	0.129849i
$142$		0			0
$143$	32166.8			1.57303
$144$		0			0
$145$	21194.0	−	8800.68i	1.00804	−	0.418582i
$146$		0			0
$147$	−19254.3	+	1496.54i	−0.891030	+	0.0692553i
$148$		0			0
$149$			25686.3i			1.15699i	0.815686	+	0.578495i	$0.196360\pi$
$149$			25686.3i			1.15699i	−0.815686	+	0.578495i	$0.803640\pi$
$150$		0			0
$151$	−19518.2			−0.856024			−0.428012	−	0.903773i	$-0.640786\pi$
$151$	−19518.2			−0.856024			−0.428012	+	0.903773i	$0.640786\pi$
$152$		0			0
$153$	9561.36	−	1495.35i	0.408448	−	0.0638792i
$154$		0			0
$155$	6060.81	+	14595.7i	0.252271	+	0.607523i
$156$		0			0
$157$		−	30918.8i		−	1.25436i	−0.778874	−	0.627181i	$-0.784209\pi$
$157$		−	30918.8i		−	1.25436i	0.778874	−	0.627181i	$-0.215791\pi$
$158$		0			0
$159$	−32862.7	+	2554.25i	−1.29990	+	0.101035i
$160$		0			0
$161$			23820.4i			0.918962i
$162$		0			0
$163$		−	2799.63i		−	0.105372i	−0.998611	−	0.0526861i	$-0.983222\pi$
$163$		−	2799.63i		−	0.105372i	0.998611	−	0.0526861i	$-0.0167783\pi$
$164$		0			0
$165$	31233.8	−	15910.8i	1.14725	−	0.584420i
$166$		0			0
$167$	−47351.4			−1.69785			−0.848925	−	0.528513i	$-0.822750\pi$
$167$	−47351.4			−1.69785			−0.848925	+	0.528513i	$0.822750\pi$
$168$		0			0
$169$	−14070.8			−0.492659
$170$		0			0
$171$	39386.4	−	6159.84i	1.34696	−	0.210658i
$172$		0			0
$173$	−33731.6			−1.12705			−0.563526	−	0.826098i	$-0.690556\pi$
$173$	−33731.6			−1.12705			−0.563526	+	0.826098i	$0.690556\pi$
$174$		0			0
$175$	29852.6	+	29747.7i	0.974778	+	0.971353i
$176$		0			0
$177$	993.489	+	12782.1i	0.0317115	+	0.407996i
$178$		0			0
$179$		−	33394.2i		−	1.04223i	−0.853486	−	0.521116i	$-0.825516\pi$
$179$		−	33394.2i		−	1.04223i	0.853486	−	0.521116i	$-0.174484\pi$
$180$		0			0
$181$	−29913.7			−0.913088			−0.456544	−	0.889701i	$-0.650913\pi$
$181$	−29913.7			−0.913088			−0.456544	+	0.889701i	$0.650913\pi$
$182$		0			0
$183$	15587.3	−	1211.52i	0.465445	−	0.0361767i
$184$		0			0
$185$	40542.0	−	16834.9i	1.18457	−	0.491888i
$186$		0			0
$187$			18613.3i			0.532280i
$188$		0			0
$189$	−11336.1	−	47831.5i	−0.317352	−	1.33903i
$190$		0			0
$191$			68732.1i			1.88405i	0.335539	+	0.942026i	$0.391082\pi$
$191$			68732.1i			1.88405i	−0.335539	+	0.942026i	$0.608918\pi$
$192$		0			0
$193$			68685.9i			1.84397i	0.387230	+	0.921983i	$0.373432\pi$
$193$			68685.9i			1.84397i	−0.387230	+	0.921983i	$0.626568\pi$
$194$		0			0
$195$	−41395.2	+	21087.2i	−1.08863	+	0.554562i
$196$		0			0
$197$	−41628.9			−1.07266			−0.536330	−	0.844008i	$-0.680190\pi$
$197$	−41628.9			−1.07266			−0.536330	+	0.844008i	$0.680190\pi$
$198$		0			0
$199$	−8360.65			−0.211122			−0.105561	−	0.994413i	$-0.533664\pi$
$199$	−8360.65			−0.211122			−0.105561	+	0.994413i	$0.533664\pi$
$200$		0			0
$201$	−4502.68	−	57931.0i	−0.111450	−	1.43390i
$202$		0			0
$203$	61896.9			1.50202
$204$		0			0
$205$	33460.1	−	13894.1i	0.796196	−	0.330616i
$206$		0			0
$207$	−28270.5	+	4421.36i	−0.659770	+	0.103185i
$208$		0			0
$209$			76674.4i			1.75533i
$210$		0			0
$211$	−38745.9			−0.870283			−0.435142	−	0.900362i	$-0.643302\pi$
$211$	−38745.9			−0.870283			−0.435142	+	0.900362i	$0.643302\pi$
$212$		0			0
$213$	−1699.37	−	21863.9i	−0.0374566	−	0.481912i
$214$		0			0
$215$	−14483.8	+	6014.33i	−0.313333	+	0.130110i
$216$		0			0
$217$			42626.8i			0.905239i
$218$		0			0
$219$	1877.25	+	24152.5i	0.0391412	+	0.503585i
$220$		0			0
$221$		−	24668.9i		−	0.505085i
$222$		0			0
$223$			839.566i			0.0168828i	0.999964	+	0.00844141i	$0.00268702\pi$
$223$			839.566i			0.0168828i	−0.999964	+	0.00844141i	$0.997313\pi$
$224$		0			0
$225$	−29764.1	+	40951.1i	−0.587932	+	0.808910i
$226$		0			0
$227$	−41746.0			−0.810147			−0.405073	−	0.914284i	$-0.632754\pi$
$227$	−41746.0			−0.810147			−0.405073	+	0.914284i	$0.632754\pi$
$228$		0			0
$229$	67230.2			1.28202			0.641008	−	0.767534i	$-0.278516\pi$
$229$	67230.2			1.28202			0.641008	+	0.767534i	$0.278516\pi$
$230$		0			0
$231$	94260.4	−	7326.39i	1.76647	−	0.137299i
$232$		0			0
$233$	−61606.5			−1.13479			−0.567394	−	0.823446i	$-0.692048\pi$
$233$	−61606.5			−1.13479			−0.567394	+	0.823446i	$0.692048\pi$
$234$		0			0
$235$	−35488.1	−	85463.0i	−0.642609	−	1.54754i
$236$		0			0
$237$	28861.4	−	2243.25i	0.513831	−	0.0399375i
$238$		0			0
$239$		−	17444.5i		−	0.305395i	−0.988273	−	0.152697i	$-0.951204\pi$
$239$		−	17444.5i		−	0.305395i	0.988273	−	0.152697i	$-0.0487960\pi$
$240$		0			0
$241$	−95187.1			−1.63887			−0.819434	−	0.573173i	$-0.805712\pi$
$241$	−95187.1			−1.63887			−0.819434	+	0.573173i	$0.805712\pi$
$242$		0			0
$243$	54663.2	−	22332.0i	0.925726	−	0.378195i
$244$		0			0
$245$	20572.8	+	49543.8i	0.342737	+	0.825386i
$246$		0			0
$247$		−	101619.i		−	1.66564i
$248$		0			0
$249$	13612.1	−	1058.00i	0.219546	−	0.0170642i
$250$		0			0
$251$		−	72970.0i		−	1.15824i	−0.815244	−	0.579118i	$-0.803397\pi$
$251$		−	72970.0i		−	1.15824i	0.815244	−	0.579118i	$-0.196603\pi$
$252$		0			0
$253$		−	55034.7i		−	0.859797i
$254$		0			0
$255$	−12202.1	−	23953.3i	−0.187652	−	0.368371i
$256$		0			0
$257$	102989.			1.55928			0.779639	−	0.626229i	$-0.215402\pi$
$257$	102989.			1.55928			0.779639	+	0.626229i	$0.215402\pi$
$258$		0			0
$259$	118403.			1.76507
$260$		0			0
$261$	11488.8	+	73460.3i	0.168653	+	1.07838i
$262$		0			0
$263$	31029.3			0.448602			0.224301	−	0.974520i	$-0.427990\pi$
$263$	31029.3			0.448602			0.224301	+	0.974520i	$0.427990\pi$
$264$		0			0
$265$	35113.1	+	84560.1i	0.500009	+	1.20413i
$266$		0			0
$267$	−5207.47	−	66998.6i	−0.0730473	−	0.939817i
$268$		0			0
$269$		−	67187.7i		−	0.928507i	−0.885702	−	0.464254i	$-0.846323\pi$
$269$		−	67187.7i		−	0.928507i	0.885702	−	0.464254i	$-0.153677\pi$
$270$		0			0
$271$	31478.7			0.428626			0.214313	−	0.976765i	$-0.431249\pi$
$271$	31478.7			0.428626			0.214313	+	0.976765i	$0.431249\pi$
$272$		0			0
$273$	−124927.	+	9709.93i	−1.67622	+	0.130284i
$274$		0			0
$275$	−68971.4	−	68729.1i	−0.912019	−	0.908814i
$276$		0			0
$277$			917.662i			0.0119598i	0.999982	+	0.00597989i	$0.00190347\pi$
$277$			917.662i			0.0119598i	−0.999982	+	0.00597989i	$0.998097\pi$
$278$		0			0
$279$	−50590.3	+	7912.06i	−0.649918	+	0.101644i
$280$		0			0
$281$			42100.9i			0.533185i	0.963809	+	0.266593i	$0.0858979\pi$
$281$			42100.9i			0.533185i	−0.963809	+	0.266593i	$0.914102\pi$
$282$		0			0
$283$		−	32677.1i		−	0.408010i	−0.978970	−	0.204005i	$-0.934604\pi$
$283$		−	32677.1i		−	0.408010i	0.978970	−	0.204005i	$-0.0653959\pi$
$284$		0			0
$285$	−50264.5	−	98671.7i	−0.618830	−	1.21479i
$286$		0			0
$287$	97720.2			1.18637
$288$		0			0
$289$	−69246.4			−0.829090
$290$		0			0
$291$	7473.66	+	96155.2i	0.0882567	+	1.13550i
$292$		0			0
$293$	−42688.7			−0.497254			−0.248627	−	0.968599i	$-0.579979\pi$
$293$	−42688.7			−0.497254			−0.248627	+	0.968599i	$0.579979\pi$
$294$		0			0
$295$	32890.0	−	13657.4i	0.377938	−	0.156937i
$296$		0			0
$297$	26191.0	+	110510.i	0.296920	+	1.25282i
$298$		0			0
$299$			72939.5i			0.815869i
$300$		0			0
$301$	−42300.0			−0.466882
$302$		0			0
$303$	2370.81	+	30502.5i	0.0258233	+	0.332239i
$304$		0			0
$305$	−16654.7	−	40108.1i	−0.179035	−	0.431154i
$306$		0			0
$307$			153819.i			1.63205i	0.578018	+	0.816024i	$0.303827\pi$
$307$			153819.i			1.63205i	−0.578018	+	0.816024i	$0.696173\pi$
$308$		0			0
$309$	6193.59	+	79685.9i	0.0648672	+	0.834573i
$310$		0			0
$311$		−	83923.2i		−	0.867684i	−0.900989	−	0.433842i	$-0.857158\pi$
$311$		−	83923.2i		−	0.867684i	0.900989	−	0.433842i	$-0.142842\pi$
$312$		0			0
$313$			53435.9i			0.545437i	0.962094	+	0.272718i	$0.0879227\pi$
$313$			53435.9i			0.545437i	−0.962094	+	0.272718i	$0.912077\pi$
$314$		0			0
$315$	−116500.	+	71221.4i	−1.17410	+	0.717777i
$316$		0			0
$317$	82643.2			0.822410			0.411205	−	0.911543i	$-0.365108\pi$
$317$	82643.2			0.822410			0.411205	+	0.911543i	$0.365108\pi$
$318$		0			0
$319$	−143007.			−1.40532
$320$		0			0
$321$	42464.1	−	3300.52i	0.412108	−	0.0320311i
$322$		0			0
$323$	58801.9			0.563620
$324$		0			0
$325$	91410.3	+	91089.1i	0.865423	+	0.862382i
$326$		0			0
$327$	90971.7	−	7070.77i	0.850767	−	0.0661259i
$328$		0			0
$329$		−	249594.i		−	2.30591i
$330$		0			0
$331$	−13288.6			−0.121289			−0.0606446	−	0.998159i	$-0.519316\pi$
$331$	−13288.6			−0.121289			−0.0606446	+	0.998159i	$0.519316\pi$
$332$		0			0
$333$	21977.0	+	140522.i	0.198189	+	1.26724i
$334$		0			0
$335$	−149064.	+	61898.1i	−1.32826	+	0.551553i
$336$		0			0
$337$		−	64665.3i		−	0.569392i	−0.958618	−	0.284696i	$-0.908107\pi$
$337$		−	64665.3i		−	0.569392i	0.958618	−	0.284696i	$-0.0918927\pi$
$338$		0			0
$339$	−50201.1	+	3901.88i	−0.436831	+	0.0339527i
$340$		0			0
$341$		−	98485.1i		−	0.846957i
$342$		0			0
$343$		−	17207.1i		−	0.146258i
$344$		0			0
$345$	36078.4	+	70823.8i	0.303116	+	0.595033i
$346$		0			0
$347$	115966.			0.963104			0.481552	−	0.876418i	$-0.340073\pi$
$347$	115966.			0.963104			0.481552	+	0.876418i	$0.340073\pi$
$348$		0			0
$349$	−98097.2			−0.805389			−0.402694	−	0.915334i	$-0.631926\pi$
$349$	−98097.2			−0.805389			−0.402694	+	0.915334i	$0.631926\pi$
$350$		0			0
$351$	−34711.8	−	146463.i	−0.281750	−	1.18881i
$352$		0			0
$353$	−188093.			−1.50947			−0.754735	−	0.656030i	$-0.772234\pi$
$353$	−188093.			−1.50947			−0.754735	+	0.656030i	$0.772234\pi$
$354$		0			0
$355$	−56258.6	+	23361.1i	−0.446408	+	0.185369i
$356$		0			0
$357$	−5618.64	−	72288.7i	−0.0440854	−	0.567197i
$358$		0			0
$359$			84492.4i			0.655585i	0.944750	+	0.327792i	$0.106305\pi$
$359$			84492.4i			0.655585i	−0.944750	+	0.327792i	$0.893695\pi$
$360$		0			0
$361$	111904.			0.858677
$362$		0			0
$363$	−86406.6	+	6715.96i	−0.655743	+	0.0509677i
$364$		0			0
$365$	62147.5	−	25806.4i	0.466485	−	0.193706i
$366$		0			0
$367$			88794.7i			0.659257i	0.944111	+	0.329629i	$0.106924\pi$
$367$			88794.7i			0.659257i	−0.944111	+	0.329629i	$0.893076\pi$
$368$		0			0
$369$	18138.1	+	115976.i	0.133210	+	0.851757i
$370$		0			0
$371$			246957.i			1.79421i
$372$		0			0
$373$		−	148706.i		−	1.06883i	−0.845222	−	0.534416i	$-0.820532\pi$
$373$		−	148706.i		−	1.06883i	0.845222	−	0.534416i	$-0.179468\pi$
$374$		0			0
$375$	133815.	+	43232.2i	0.951571	+	0.307429i
$376$		0			0
$377$	189532.			1.33352
$378$		0			0
$379$	204699.			1.42508			0.712538	−	0.701634i	$-0.247546\pi$
$379$	204699.			1.42508			0.712538	+	0.701634i	$0.247546\pi$
$380$		0			0
$381$	2480.93	+	31919.3i	0.0170909	+	0.219889i
$382$		0			0
$383$	17100.8			0.116579			0.0582893	−	0.998300i	$-0.481435\pi$
$383$	17100.8			0.116579			0.0582893	+	0.998300i	$0.481435\pi$
$384$		0			0
$385$	−100715.	−	242545.i	−0.679477	−	1.63633i
$386$		0			0
$387$	−7851.39	−	50202.3i	−0.0524233	−	0.335198i
$388$		0			0
$389$			212163.i			1.40207i	0.713126	+	0.701036i	$0.247279\pi$
$389$			212163.i			1.40207i	−0.713126	+	0.701036i	$0.752721\pi$
$390$		0			0
$391$	−42206.4			−0.276073
$392$		0			0
$393$	−22070.5	−	283956.i	−0.142898	−	1.83851i
$394$		0			0
$395$	−30837.8	−	74264.1i	−0.197647	−	0.475976i
$396$		0			0
$397$		−	99063.8i		−	0.628542i	−0.949333	−	0.314271i	$-0.898240\pi$
$397$		−	99063.8i		−	0.628542i	0.949333	−	0.314271i	$-0.101760\pi$
$398$		0			0
$399$	−23145.1	−	297781.i	−0.145383	−	1.87047i
$400$		0			0
$401$		−	11025.4i		−	0.0685658i	−0.999412	−	0.0342829i	$-0.989085\pi$
$401$		−	11025.4i		−	0.0685658i	0.999412	−	0.0342829i	$-0.0109147\pi$
$402$		0			0
$403$			130526.i			0.803686i
$404$		0			0
$405$	−106151.	−	125045.i	−0.647162	−	0.762353i
$406$		0			0
$407$	−273558.			−1.65143
$408$		0			0
$409$	103902.			0.621122			0.310561	−	0.950553i	$-0.399483\pi$
$409$	103902.			0.621122			0.310561	+	0.950553i	$0.399483\pi$
$410$		0			0
$411$	−172757.	+	13427.5i	−1.02271	+	0.0794901i
$412$		0			0
$413$	96055.3			0.563146
$414$		0			0
$415$	−14544.2	−	35025.7i	−0.0844491	−	0.203372i
$416$		0			0
$417$	90843.5	−	7060.81i	0.522422	−	0.0406053i
$418$		0			0
$419$		−	116135.i		−	0.661509i	−0.943717	−	0.330755i	$-0.892697\pi$
$419$		−	116135.i		−	0.661509i	0.943717	−	0.330755i	$-0.107303\pi$
$420$		0			0
$421$	288576.			1.62816			0.814078	−	0.580756i	$-0.197243\pi$
$421$	288576.			1.62816			0.814078	+	0.580756i	$0.197243\pi$
$422$		0			0
$423$	296223.	−	46327.8i	1.65553	−	0.258917i
$424$		0			0
$425$	−52708.6	+	52894.5i	−0.291812	+	0.292841i
$426$		0			0
$427$		−	117136.i		−	0.642441i
$428$		0			0
$429$	288631.	−	22433.8i	1.56830	−	0.121896i
$430$		0			0
$431$			42439.1i			0.228461i	0.993454	+	0.114230i	$0.0364402\pi$
$431$			42439.1i			0.228461i	−0.993454	+	0.114230i	$0.963560\pi$
$432$		0			0
$433$			95739.7i			0.510642i	0.966856	+	0.255321i	$0.0821811\pi$
$433$			95739.7i			0.510642i	−0.966856	+	0.255321i	$0.917819\pi$
$434$		0			0
$435$	184034.	−	93749.1i	0.972569	−	0.495437i
$436$		0			0
$437$	−173862.			−0.910420
$438$		0			0
$439$	45614.7			0.236688			0.118344	−	0.992973i	$-0.462241\pi$
$439$	45614.7			0.236688			0.118344	+	0.992973i	$0.462241\pi$
$440$		0			0
$441$	−171724.	+	26856.7i	−0.882984	+	0.138094i
$442$		0			0
$443$	−30310.8			−0.154451			−0.0772253	−	0.997014i	$-0.524606\pi$
$443$	−30310.8			−0.154451			−0.0772253	+	0.997014i	$0.524606\pi$
$444$		0			0
$445$	−172396.	+	71586.7i	−0.870579	+	0.361503i
$446$		0			0
$447$	17914.2	+	230482.i	0.0896567	+	1.15351i
$448$		0			0
$449$			133743.i			0.663406i	0.943384	+	0.331703i	$0.107623\pi$
$449$			133743.i			0.663406i	−0.943384	+	0.331703i	$0.892377\pi$
$450$		0			0
$451$	−225773.			−1.10999
$452$		0			0
$453$	−175136.	+	13612.4i	−0.853450	+	0.0663344i
$454$		0			0
$455$	133482.	+	321453.i	0.644762	+	1.55273i
$456$		0			0
$457$		−	95910.3i		−	0.459233i	−0.973281	−	0.229616i	$-0.926253\pi$
$457$		−	95910.3i		−	0.459233i	0.973281	−	0.229616i	$-0.0737472\pi$
$458$		0			0
$459$	84750.6	−	20086.0i	0.402270	−	0.0953383i
$460$		0			0
$461$		−	19465.2i		−	0.0915920i	−0.998951	−	0.0457960i	$-0.985418\pi$
$461$		−	19465.2i		−	0.0915920i	0.998951	−	0.0457960i	$-0.0145824\pi$
$462$		0			0
$463$			152228.i			0.710120i	0.934843	+	0.355060i	$0.115540\pi$
$463$			152228.i			0.710120i	−0.934843	+	0.355060i	$0.884460\pi$
$464$		0			0
$465$	64562.6	+	126740.i	0.298590	+	0.586147i
$466$		0			0
$467$	−225192.			−1.03257			−0.516284	−	0.856418i	$-0.672685\pi$
$467$	−225192.			−1.03257			−0.516284	+	0.856418i	$0.672685\pi$
$468$		0			0
$469$	−435341.			−1.97917
$470$		0			0
$471$	−21563.4	−	277432.i	−0.0972021	−	1.25059i
$472$		0			0
$473$	97729.9			0.436823
$474$		0			0
$475$	−217124.	+	217890.i	−0.962324	+	0.965717i
$476$		0			0
$477$	−293093.	+	45838.3i	−1.28816	+	0.201461i
$478$		0			0
$479$			419939.i			1.83027i	0.403148	+	0.915135i	$0.367916\pi$
$479$			419939.i			1.83027i	−0.403148	+	0.915135i	$0.632084\pi$
$480$		0			0
$481$	362556.			1.56706
$482$		0			0
$483$	16612.9	+	213739.i	0.0712116	+	0.916199i
$484$		0			0
$485$	247420.	−	102740.i	1.05184	−	0.436773i
$486$		0			0
$487$			45776.8i			0.193013i	0.995332	+	0.0965067i	$0.0307669\pi$
$487$			45776.8i			0.193013i	−0.995332	+	0.0965067i	$0.969233\pi$
$488$		0			0
$489$	−1952.53	−	25120.9i	−0.00816543	−	0.105055i
$490$		0			0
$491$		−	142734.i		−	0.592057i	−0.955179	−	0.296028i	$-0.904338\pi$
$491$		−	142734.i		−	0.592057i	0.955179	−	0.296028i	$-0.0956623\pi$
$492$		0			0
$493$			109672.i			0.451236i
$494$		0			0
$495$	269162.	−	164550.i	1.09851	−	0.671564i
$496$		0			0
$497$	−164303.			−0.665171
$498$		0			0
$499$	79974.9			0.321183			0.160592	−	0.987021i	$-0.448660\pi$
$499$	79974.9			0.321183			0.160592	+	0.987021i	$0.448660\pi$
$500$		0			0
$501$	−424881.	+	33023.9i	−1.69275	+	0.131569i
$502$		0			0
$503$	−140135.			−0.553872			−0.276936	−	0.960888i	$-0.589319\pi$
$503$	−140135.			−0.553872			−0.276936	+	0.960888i	$0.589319\pi$
$504$		0			0
$505$	78487.0	−	32591.3i	0.307762	−	0.127797i
$506$		0			0
$507$	−126257.	+	9813.31i	−0.491178	+	0.0381768i
$508$		0			0
$509$		−	369825.i		−	1.42745i	−0.700427	−	0.713724i	$-0.747007\pi$
$509$		−	369825.i		−	1.42745i	0.700427	−	0.713724i	$-0.252993\pi$
$510$		0			0
$511$	181502.			0.695086
$512$		0			0
$513$	349116.	−	82740.8i	1.32659	−	0.314402i
$514$		0			0
$515$	205042.	−	85142.8i	0.773088	−	0.321021i
$516$		0			0
$517$			576663.i			2.15745i
$518$		0			0
$519$	−302671.	+	23525.1i	−1.12366	+	0.0873368i
$520$		0			0
$521$			60637.1i			0.223390i	0.993743	+	0.111695i	$0.0356279\pi$
$521$			60637.1i			0.223390i	−0.993743	+	0.111695i	$0.964372\pi$
$522$		0			0
$523$		−	296749.i		−	1.08489i	−0.840091	−	0.542445i	$-0.817499\pi$
$523$		−	296749.i		−	1.08489i	0.840091	−	0.542445i	$-0.182501\pi$
$524$		0			0
$525$	288612.	+	246104.i	1.04712	+	0.892895i
$526$		0			0
$527$	−75528.6			−0.271951
$528$		0			0
$529$	−155048.			−0.554056
$530$		0			0
$531$	17829.0	+	114000.i	0.0632322	+	0.404312i
$532$		0			0
$533$	299225.			1.05328
$534$		0			0
$535$	−45372.0	−	109266.i	−0.158519	−	0.381747i
$536$		0			0
$537$	−23289.8	−	299644.i	−0.0807639	−	1.03910i
$538$		0			0
$539$		−	334298.i		−	1.15068i
$540$		0			0
$541$	239602.			0.818645			0.409323	−	0.912390i	$-0.365765\pi$
$541$	239602.			0.818645			0.409323	+	0.912390i	$0.365765\pi$
$542$		0			0
$543$	−268414.	+	20862.4i	−0.910342	+	0.0707564i
$544$		0			0
$545$	−97201.4	−	234082.i	−0.327250	−	0.788089i
$546$		0			0
$547$		−	388724.i		−	1.29917i	−0.760288	−	0.649586i	$-0.774942\pi$
$547$		−	388724.i		−	1.29917i	0.760288	−	0.649586i	$-0.225058\pi$
$548$		0			0
$549$	139019.	−	21741.8i	0.461242	−	0.0721358i
$550$		0			0
$551$			451777.i			1.48806i
$552$		0			0
$553$		−	216888.i		−	0.709228i
$554$		0			0
$555$	352040.	−	179333.i	1.14289	−	0.582203i
$556$		0			0
$557$	−568369.			−1.83198			−0.915988	−	0.401206i	$-0.868591\pi$
$557$	−568369.			−1.83198			−0.915988	+	0.401206i	$0.868591\pi$
$558$		0			0
$559$	−129525.			−0.414505
$560$		0			0
$561$	12981.3	+	167016.i	0.0412471	+	0.530679i
$562$		0			0
$563$	195184.			0.615782			0.307891	−	0.951422i	$-0.400377\pi$
$563$	195184.			0.615782			0.307891	+	0.951422i	$0.400377\pi$
$564$		0			0
$565$	53638.8	+	129174.i	0.168028	+	0.404649i
$566$		0			0
$567$	−135077.	−	421283.i	−0.420161	−	1.31041i
$568$		0			0
$569$		−	159125.i		−	0.491490i	−0.969334	−	0.245745i	$-0.920967\pi$
$569$		−	159125.i		−	0.491490i	0.969334	−	0.245745i	$-0.0790327\pi$
$570$		0			0
$571$	482080.			1.47859			0.739294	−	0.673383i	$-0.235160\pi$
$571$	482080.			1.47859			0.739294	+	0.673383i	$0.235160\pi$
$572$		0			0
$573$	47935.3	+	616729.i	0.145998	+	1.87839i
$574$		0			0
$575$	155846.	−	156395.i	0.471367	−	0.473029i
$576$		0			0
$577$		−	319133.i		−	0.958560i	−0.877662	−	0.479280i	$-0.840898\pi$
$577$		−	319133.i		−	0.958560i	0.877662	−	0.479280i	$-0.159102\pi$
$578$		0			0
$579$	47903.0	+	616314.i	0.142891	+	1.83842i
$580$		0			0
$581$		−	102293.i		−	0.303034i
$582$		0			0
$583$		−	570571.i		−	1.67870i
$584$		0			0
$585$	−356730.	+	218084.i	−1.04239	+	0.637254i
$586$		0			0
$587$	357229.			1.03674			0.518371	−	0.855156i	$-0.326539\pi$
$587$	357229.			1.03674			0.518371	+	0.855156i	$0.326539\pi$
$588$		0			0
$589$	−311128.			−0.896825
$590$		0			0
$591$	−373533.	+	29032.9i	−1.06944	+	0.0831219i
$592$		0			0
$593$	306233.			0.870848			0.435424	−	0.900226i	$-0.356598\pi$
$593$	306233.			0.870848			0.435424	+	0.900226i	$0.356598\pi$
$594$		0			0
$595$	−186008.	+	77239.1i	−0.525411	+	0.218174i
$596$		0			0
$597$	−75019.6	+	5830.90i	−0.210487	+	0.0163601i
$598$		0			0
$599$			27985.3i			0.0779967i	0.999239	+	0.0389984i	$0.0124167\pi$
$599$			27985.3i			0.0779967i	−0.999239	+	0.0389984i	$0.987583\pi$
$600$		0			0
$601$	−200646.			−0.555497			−0.277748	−	0.960654i	$-0.589588\pi$
$601$	−200646.			−0.555497			−0.277748	+	0.960654i	$0.589588\pi$
$602$		0			0
$603$	−80804.6	−	516671.i	−0.222229	−	1.42095i
$604$		0			0
$605$	92323.8	+	222336.i	0.252234	+	0.607433i
$606$		0			0
$607$			104545.i			0.283742i	0.989885	+	0.141871i	$0.0453119\pi$
$607$			104545.i			0.283742i	−0.989885	+	0.141871i	$0.954688\pi$
$608$		0			0
$609$	555397.	−	43168.2i	1.49751	−	0.116394i
$610$		0			0
$611$		−	764273.i		−	2.04723i
$612$		0			0
$613$			263612.i			0.701526i	0.936464	+	0.350763i	$0.114078\pi$
$613$			263612.i			0.701526i	−0.936464	+	0.350763i	$0.885922\pi$
$614$		0			0
$615$	290545.	−	148007.i	0.768182	−	0.391320i
$616$		0			0
$617$	343423.			0.902110			0.451055	−	0.892496i	$-0.351048\pi$
$617$	343423.			0.902110			0.451055	+	0.892496i	$0.351048\pi$
$618$		0			0
$619$	269937.			0.704501			0.352250	−	0.935906i	$-0.385417\pi$
$619$	269937.			0.704501			0.352250	+	0.935906i	$0.385417\pi$
$620$		0			0
$621$	−250586.	+	59389.0i	−0.649790	+	0.154001i
$622$		0			0
$623$	−503483.			−1.29721
$624$		0			0
$625$	−1375.00	−	390623.i	−0.00352000	−	0.999994i
$626$		0			0
$627$	53474.4	+	687994.i	0.136022	+	1.75005i
$628$		0			0
$629$			209793.i			0.530260i
$630$		0			0
$631$	543880.			1.36598			0.682990	−	0.730428i	$-0.260679\pi$
$631$	543880.			1.36598			0.682990	+	0.730428i	$0.260679\pi$
$632$		0			0
$633$	−347664.	+	27022.2i	−0.867666	+	0.0674394i
$634$		0			0
$635$	82132.6	−	34105.1i	0.203689	−	0.0845809i
$636$		0			0
$637$			443057.i			1.09189i
$638$		0			0
$639$	−30496.7	−	194998.i	−0.0746880	−	0.477560i
$640$		0			0
$641$		−	647339.i		−	1.57549i	−0.616001	−	0.787745i	$-0.711248\pi$
$641$		−	647339.i		−	1.57549i	0.616001	−	0.787745i	$-0.288752\pi$
$642$		0			0
$643$			647221.i			1.56542i	0.622387	+	0.782710i	$0.286163\pi$
$643$			647221.i			1.56542i	−0.622387	+	0.782710i	$0.713837\pi$
$644$		0			0
$645$	−125768.	+	64067.6i	−0.302308	+	0.153999i
$646$		0			0
$647$	334797.			0.799784			0.399892	−	0.916562i	$-0.369048\pi$
$647$	334797.			0.799784			0.399892	+	0.916562i	$0.369048\pi$
$648$		0			0
$649$	−221926.			−0.526889
$650$		0			0
$651$	29728.9	+	382488.i	0.0701482	+	0.902517i
$652$		0			0
$653$	−45027.6			−0.105597			−0.0527986	−	0.998605i	$-0.516814\pi$
$653$	−45027.6			−0.105597			−0.0527986	+	0.998605i	$0.516814\pi$
$654$		0			0
$655$	−730657.	+	303402.i	−1.70306	+	0.707189i
$656$		0			0
$657$	33688.9	+	215409.i	0.0780470	+	0.499038i
$658$		0			0
$659$		−	428579.i		−	0.986870i	−0.869783	−	0.493435i	$-0.835741\pi$
$659$		−	428579.i		−	0.986870i	0.869783	−	0.493435i	$-0.164259\pi$
$660$		0			0
$661$	−570406.			−1.30551			−0.652757	−	0.757568i	$-0.726388\pi$
$661$	−570406.			−1.30551			−0.652757	+	0.757568i	$0.726388\pi$
$662$		0			0
$663$	−17204.6	−	221352.i	−0.0391397	−	0.503566i
$664$		0			0
$665$	−766231.	+	318174.i	−1.73267	+	0.719483i
$666$		0			0
$667$		−	324273.i		−	0.728885i
$668$		0			0
$669$	585.532	+	7533.37i	0.00130827	+	0.0168321i
$670$		0			0
$671$			270630.i			0.601079i
$672$		0			0
$673$			196875.i			0.434670i	0.976097	+	0.217335i	$0.0697364\pi$
$673$			196875.i			0.434670i	−0.976097	+	0.217335i	$0.930264\pi$
$674$		0			0
$675$	−238511.	+	388210.i	−0.523481	+	0.852038i
$676$		0			0
$677$	74588.7			0.162741			0.0813703	−	0.996684i	$-0.474070\pi$
$677$	74588.7			0.162741			0.0813703	+	0.996684i	$0.474070\pi$
$678$		0			0
$679$	722590.			1.56730
$680$		0			0
$681$	−374585.	+	29114.6i	−0.807711	+	0.0627793i
$682$		0			0
$683$	−331599.			−0.710839			−0.355420	−	0.934707i	$-0.615662\pi$
$683$	−331599.			−0.710839			−0.355420	+	0.934707i	$0.615662\pi$
$684$		0			0
$685$	184587.	+	444527.i	0.393388	+	0.947364i
$686$		0			0
$687$	603253.	−	46887.8i	1.27816	−	0.0993452i
$688$		0			0
$689$			756198.i			1.59293i
$690$		0			0
$691$	−321604.			−0.673544			−0.336772	−	0.941586i	$-0.609335\pi$
$691$	−321604.			−0.673544			−0.336772	+	0.941586i	$0.609335\pi$
$692$		0			0
$693$	840683.	−	131479.i	1.75052	−	0.273772i
$694$		0			0
$695$	−97064.5	−	233752.i	−0.200951	−	0.483934i
$696$		0			0
$697$			173146.i			0.356408i
$698$		0			0
$699$	−552791.	+	42965.7i	−1.13138	+	0.0879362i
$700$		0			0
$701$			918547.i			1.86924i	0.355647	+	0.934620i	$0.384261\pi$
$701$			918547.i			1.86924i	−0.355647	+	0.934620i	$0.615739\pi$
$702$		0			0
$703$			864206.i			1.74867i
$704$		0			0
$705$	−378036.	−	742104.i	−0.760598	−	1.49309i
$706$		0			0
$707$	229221.			0.458581
$708$		0			0
$709$	456638.			0.908405			0.454202	−	0.890899i	$-0.349924\pi$
$709$	456638.			0.908405			0.454202	+	0.890899i	$0.349924\pi$
$710$		0			0
$711$	257407.	−	40257.1i	0.509191	−	0.0796348i
$712$		0			0
$713$	223319.			0.439285
$714$		0			0
$715$	−308396.	−	742686.i	−0.603250	−	1.45276i
$716$		0			0
$717$	−12166.1	−	156528.i	−0.0236654	−	0.304476i
$718$		0			0
$719$		−	167509.i		−	0.324027i	−0.986789	−	0.162014i	$-0.948201\pi$
$719$		−	167509.i		−	0.324027i	0.986789	−	0.162014i	$-0.0517989\pi$
$720$		0			0
$721$	598826.			1.15194
$722$		0			0
$723$	−854108.	+	66385.6i	−1.63394	+	0.126998i
$724$		0			0
$725$	−406390.	−	404962.i	−0.773156	−	0.770439i
$726$		0			0
$727$		−	38860.6i		−	0.0735259i	−0.999324	−	0.0367629i	$-0.988295\pi$
$727$		−	38860.6i		−	0.0735259i	0.999324	−	0.0367629i	$-0.0117046\pi$
$728$		0			0
$729$	474915.	−	238507.i	0.893636	−	0.448793i
$730$		0			0
$731$		−	74949.4i		−	0.140260i
$732$		0			0
$733$		−	740222.i		−	1.37770i	−0.724905	−	0.688849i	$-0.758116\pi$
$733$		−	740222.i		−	1.37770i	0.724905	−	0.688849i	$-0.241884\pi$
$734$		0			0
$735$	219151.	+	430206.i	0.405667	+	0.796345i
$736$		0			0
$737$	1.00581e6			1.85175
$738$		0			0
$739$	−705765.			−1.29232			−0.646162	−	0.763201i	$-0.723627\pi$
$739$	−705765.			−1.29232			−0.646162	+	0.763201i	$0.723627\pi$
$740$		0			0
$741$	−70871.5	−	911824.i	−0.129073	−	1.66064i
$742$		0			0
$743$	−504628.			−0.914100			−0.457050	−	0.889441i	$-0.651094\pi$
$743$	−504628.			−0.914100			−0.457050	+	0.889441i	$0.651094\pi$
$744$		0			0
$745$	593061.	−	246265.i	1.06853	−	0.443702i
$746$		0			0
$747$	121403.	−	18986.7i	0.217564	−	0.0340259i
$748$		0			0
$749$		−	319110.i		−	0.568823i
$750$		0			0
$751$	−413475.			−0.733111			−0.366555	−	0.930396i	$-0.619463\pi$
$751$	−413475.			−0.733111			−0.366555	+	0.930396i	$0.619463\pi$
$752$		0			0
$753$	−50890.9	−	654756.i	−0.0897532	−	1.15475i
$754$		0			0
$755$	187129.	+	450647.i	0.328282	+	0.790575i
$756$		0			0
$757$		−	803866.i		−	1.40279i	−0.712774	−	0.701394i	$-0.752561\pi$
$757$		−	803866.i		−	1.40279i	0.712774	−	0.701394i	$-0.247439\pi$
$758$		0			0
$759$	−38382.4	−	493823.i	−0.0666268	−	0.857211i
$760$		0			0
$761$			582961.i			1.00663i	0.864103	+	0.503315i	$0.167887\pi$
$761$			582961.i			1.00663i	−0.864103	+	0.503315i	$0.832113\pi$
$762$		0			0
$763$		−	683636.i		−	1.17429i
$764$		0			0
$765$	−126194.	−	206422.i	−0.215634	−	0.352722i
$766$		0			0
$767$	294127.			0.499970
$768$		0			0
$769$	−655679.			−1.10876			−0.554381	−	0.832263i	$-0.687045\pi$
$769$	−655679.			−1.10876			−0.554381	+	0.832263i	$0.687045\pi$
$770$		0			0
$771$	924112.	−	71826.6i	1.55459	−	0.120831i
$772$		0			0
$773$	−102465.			−0.171481			−0.0857404	−	0.996318i	$-0.527326\pi$
$773$	−102465.			−0.171481			−0.0857404	+	0.996318i	$0.527326\pi$
$774$		0			0
$775$	278887.	−	279871.i	0.464328	−	0.465966i
$776$		0			0
$777$	1.06242e6	−	82576.7i	1.75976	−	0.136778i
$778$		0			0
$779$			713247.i			1.17534i
$780$		0			0
$781$	379606.			0.622345
$782$		0			0
$783$	154321.	+	651142.i	0.251711	+	1.06207i
$784$		0			0
$785$	−713869.	+	296431.i	−1.15846	+	0.481043i
$786$		0			0
$787$			1.01738e6i			1.64261i	0.570488	+	0.821306i	$0.306754\pi$
$787$			1.01738e6i			1.64261i	−0.570488	+	0.821306i	$0.693246\pi$
$788$		0			0
$789$	278424.	−	21640.5i	0.447253	−	0.0347627i
$790$		0			0
$791$			377252.i			0.602947i
$792$		0			0
$793$		−	358676.i		−	0.570369i
$794$		0			0
$795$	374042.	+	734264.i	0.591815	+	1.16176i
$796$		0			0
$797$	−952098.			−1.49887			−0.749437	−	0.662076i	$-0.769676\pi$
$797$	−952098.			−1.49887			−0.749437	+	0.662076i	$0.769676\pi$
$798$		0			0
$799$	442246.			0.692739
$800$		0			0
$801$	−93452.6	−	597543.i	−0.145655	−	0.931331i
$802$		0			0
$803$	−419341.			−0.650334
$804$		0			0
$805$	549979.	−	228376.i	0.848701	−	0.352419i
$806$		0			0
$807$	−46858.2	−	602871.i	−0.0719512	−	0.925715i
$808$		0			0
$809$			273009.i			0.417138i	0.978008	+	0.208569i	$0.0668806\pi$
$809$			273009.i			0.417138i	−0.978008	+	0.208569i	$0.933119\pi$
$810$		0			0
$811$	−164169.			−0.249603			−0.124801	−	0.992182i	$-0.539829\pi$
$811$	−164169.			−0.249603			−0.124801	+	0.992182i	$0.539829\pi$
$812$		0			0
$813$	282456.	−	21953.9i	0.427337	−	0.0332148i
$814$		0			0
$815$	−64639.5	+	26841.2i	−0.0973157	+	0.0404099i
$816$		0			0
$817$		−	308742.i		−	0.462542i
$818$		0			0
$819$	−1.11419e6	+	174253.i	−1.66108	+	0.259784i
$820$		0			0
$821$		−	306236.i		−	0.454329i	−0.973856	−	0.227165i	$-0.927054\pi$
$821$		−	306236.i		−	0.454329i	0.973856	−	0.227165i	$-0.0729455\pi$
$822$		0			0
$823$		−	514884.i		−	0.760169i	−0.924952	−	0.380084i	$-0.875895\pi$
$823$		−	514884.i		−	0.760169i	0.924952	−	0.380084i	$-0.124105\pi$
$824$		0			0
$825$	−666809.	−	568599.i	−0.979701	−	0.835408i
$826$		0			0
$827$	732893.			1.07159			0.535796	−	0.844347i	$-0.320012\pi$
$827$	732893.			1.07159			0.535796	+	0.844347i	$0.320012\pi$
$828$		0			0
$829$	−739391.			−1.07588			−0.537942	−	0.842982i	$-0.680798\pi$
$829$	−739391.			−1.07588			−0.537942	+	0.842982i	$0.680798\pi$
$830$		0			0
$831$	639.997	+	8234.12i	0.000926779	+	0.0119238i
$832$		0			0
$833$	−256374.			−0.369475
$834$		0			0
$835$	453977.	+	1.09327e6i	0.651119	+	1.56804i
$836$		0			0
$837$	−448425.	+	106277.i	−0.640087	+	0.151701i
$838$		0			0
$839$		−	360957.i		−	0.512780i	−0.966573	−	0.256390i	$-0.917467\pi$
$839$		−	360957.i		−	0.512780i	0.966573	−	0.256390i	$-0.0825331\pi$
$840$		0			0
$841$	−135336.			−0.191348
$842$		0			0
$843$	29362.1	+	377768.i	0.0413172	+	0.531582i
$844$		0			0
$845$	134903.	+	324875.i	0.188933	+	0.454992i
$846$		0			0
$847$			649331.i			0.905106i
$848$		0			0
$849$	−22789.7	−	293210.i	−0.0316173	−	0.406783i
$850$		0			0
$851$		−	620303.i		−	0.856534i
$852$		0			0
$853$			1.10949e6i			1.52484i	0.647083	+	0.762419i	$0.275989\pi$
$853$			1.10949e6i			1.52484i	−0.647083	+	0.762419i	$0.724011\pi$
$854$		0			0
$855$	−519836.	−	850320.i	−0.711105	−	1.16319i
$856$		0			0
$857$	3132.46			0.00426505			0.00213253	−	0.999998i	$-0.499321\pi$
$857$	3132.46			0.00426505			0.00213253	+	0.999998i	$0.499321\pi$
$858$		0			0
$859$	696854.			0.944399			0.472200	−	0.881492i	$-0.343460\pi$
$859$	696854.			0.944399			0.472200	+	0.881492i	$0.343460\pi$
$860$		0			0
$861$	876837.	−	68152.2i	1.18280	−	0.0919334i
$862$		0			0
$863$	248786.			0.334045			0.167022	−	0.985953i	$-0.446585\pi$
$863$	248786.			0.334045			0.167022	+	0.985953i	$0.446585\pi$
$864$		0			0
$865$	323398.	+	778813.i	0.432221	+	1.04088i
$866$		0			0
$867$	−621343.	+	48293.9i	−0.826596	+	0.0642472i
$868$		0			0
$869$			501099.i			0.663565i
$870$		0			0
$871$	−1.33304e6			−1.75714
$872$		0			0
$873$	134121.	+	857582.i	0.175983	+	1.12525i
$874$		0			0
$875$	400622.	−	974456.i	0.523262	−	1.27276i
$876$		0			0
$877$		−	579821.i		−	0.753867i	−0.926240	−	0.376933i	$-0.876979\pi$
$877$		−	579821.i		−	0.753867i	0.926240	−	0.376933i	$-0.123021\pi$
$878$		0			0
$879$	−383043.	+	29772.1i	−0.495759	+	0.0385328i
$880$		0			0
$881$			597254.i			0.769498i	0.923021	+	0.384749i	$0.125712\pi$
$881$			597254.i			0.769498i	−0.923021	+	0.384749i	$0.874288\pi$
$882$		0			0
$883$			52207.6i			0.0669595i	0.999439	+	0.0334797i	$0.0106589\pi$
$883$			52207.6i			0.0669595i	−0.999439	+	0.0334797i	$0.989341\pi$
$884$		0			0
$885$	285595.	−	145485.i	0.364640	−	0.185752i
$886$		0			0
$887$	−69800.2			−0.0887176			−0.0443588	−	0.999016i	$-0.514124\pi$
$887$	−69800.2			−0.0887176			−0.0443588	+	0.999016i	$0.514124\pi$
$888$		0			0
$889$	239868.			0.303507
$890$		0			0
$891$	312082.	+	973334.i	0.393109	+	1.22604i
$892$		0			0
$893$	1.82176e6			2.28448
$894$		0			0
$895$	−771023.	+	320163.i	−0.962546	+	0.399692i
$896$		0			0
$897$	50869.6	+	654481.i	0.0632227	+	0.813416i
$898$		0			0
$899$		−	580289.i		−	0.718001i
$900$		0			0
$901$	−437573.			−0.539015
$902$		0			0
$903$	−379555.	+	29500.9i	−0.465478	+	0.0361793i
$904$		0			0
$905$	286795.	+	690664.i	0.350166	+	0.843275i
$906$		0			0
$907$			262086.i			0.318588i	0.987231	+	0.159294i	$0.0509218\pi$
$907$			262086.i			0.318588i	−0.987231	+	0.159294i	$0.949078\pi$
$908$		0			0
$909$	42546.2	+	272044.i	0.0514912	+	0.329239i
$910$		0			0
$911$		−	640805.i		−	0.772128i	−0.922472	−	0.386064i	$-0.873834\pi$
$911$		−	640805.i		−	0.772128i	0.922472	−	0.386064i	$-0.126166\pi$
$912$		0			0
$913$			236337.i			0.283524i
$914$		0			0
$915$	−177414.	−	348272.i	−0.211907	−	0.415984i
$916$		0			0
$917$	−2.13388e6			−2.53765
$918$		0			0
$919$	868444.			1.02828			0.514139	−	0.857707i	$-0.328112\pi$
$919$	868444.			1.02828			0.514139	+	0.857707i	$0.328112\pi$
$920$		0			0
$921$	107277.	+	1.38021e6i	0.126470	+	1.62714i
$922$		0			0
$923$	−503106.			−0.590549
$924$		0			0
$925$	−777385.	−	774653.i	−0.908558	−	0.905366i
$926$		0			0
$927$	111149.	+	710697.i	0.129344	+	0.827037i
$928$		0			0
$929$		−	1.52215e6i		−	1.76370i	−0.471527	−	0.881852i	$-0.656297\pi$
$929$		−	1.52215e6i		−	1.76370i	0.471527	−	0.881852i	$-0.343703\pi$
$930$		0			0
$931$	−1.05609e6			−1.21843
$932$		0			0
$933$	−58529.9	−	753038.i	−0.0672379	−	0.865075i
$934$		0			0
$935$	429754.	−	178453.i	0.491583	−	0.204127i
$936$		0			0
$937$			714034.i			0.813279i	0.913589	+	0.406640i	$0.133300\pi$
$937$			714034.i			0.813279i	−0.913589	+	0.406640i	$0.866700\pi$
$938$		0			0
$939$	37267.3	+	479477.i	0.0422666	+	0.543796i
$940$		0			0
$941$			153242.i			0.173061i	0.996249	+	0.0865306i	$0.0275780\pi$
$941$			153242.i			0.173061i	−0.996249	+	0.0865306i	$0.972422\pi$
$942$		0			0
$943$		−	511949.i		−	0.575709i
$944$		0			0
$945$	−995678.	+	720315.i	−1.11495	+	0.806601i
$946$		0			0
$947$	−329584.			−0.367507			−0.183754	−	0.982972i	$-0.558825\pi$
$947$	−329584.			−0.367507			−0.183754	+	0.982972i	$0.558825\pi$
$948$		0			0
$949$	555768.			0.617108
$950$		0			0
$951$	741552.	−	57637.1i	0.819937	−	0.0637296i
$952$		0			0
$953$	−1.25777e6			−1.38489			−0.692445	−	0.721470i	$-0.743467\pi$
$953$	−1.25777e6			−1.38489			−0.692445	+	0.721470i	$0.743467\pi$
$954$		0			0
$955$	1.58693e6	−	658963.i	1.74000	−	0.722527i
$956$		0			0
$957$	−1.28319e6	+	99736.0i	−1.40109	+	0.108900i
$958$		0			0
$959$			1.29824e6i			1.41162i
$960$		0			0
$961$	−523891.			−0.567275
$962$		0			0
$963$	378725.	−	59230.7i	0.408387	−	0.0638696i
$964$		0			0
$965$	1.58586e6	−	658520.i	1.70298	−	0.707154i
$966$		0			0
$967$		−	947106.i		−	1.01285i	−0.862284	−	0.506426i	$-0.830966\pi$
$967$		−	947106.i		−	1.01285i	0.862284	−	0.506426i	$-0.169034\pi$
$968$		0			0
$969$	527626.	−	41009.7i	0.561925	−	0.0436756i
$970$		0			0
$971$		−	910287.i		−	0.965472i	−0.875766	−	0.482736i	$-0.839643\pi$
$971$		−	910287.i		−	0.965472i	0.875766	−	0.482736i	$-0.160357\pi$
$972$		0			0
$973$		−	682673.i		−	0.721086i
$974$		0			0
$975$	883746.	+	753585.i	0.929648	+	0.792726i
$976$		0			0
$977$	989219.			1.03634			0.518171	−	0.855277i	$-0.326613\pi$
$977$	989219.			1.03634			0.518171	+	0.855277i	$0.326613\pi$
$978$		0			0
$979$	1.16325e6			1.21369
$980$		0			0
$981$	811352.	−	126891.i	0.843085	−	0.131854i
$982$		0			0
$983$	1.06218e6			1.09923			0.549616	−	0.835417i	$-0.314774\pi$
$983$	1.06218e6			1.09923			0.549616	+	0.835417i	$0.314774\pi$
$984$		0			0
$985$	399113.	+	961151.i	0.411361	+	0.990648i
$986$		0			0
$987$	−174073.	−	2.23960e6i	−0.178688	−	2.29898i
$988$		0			0
$989$			221606.i			0.226563i
$990$		0			0
$991$	−332884.			−0.338957			−0.169479	−	0.985534i	$-0.554208\pi$
$991$	−332884.			−0.338957			−0.169479	+	0.985534i	$0.554208\pi$
$992$		0			0
$993$	−119238.	+	9267.74i	−0.120925	+	0.00939886i
$994$		0			0
$995$	80157.0	+	193035.i	0.0809646	+	0.194980i
$996$		0			0
$997$		−	1.10583e6i		−	1.11249i	−0.831018	−	0.556245i	$-0.812242\pi$
$997$		−	1.10583e6i		−	1.11249i	0.831018	−	0.556245i	$-0.187758\pi$
$998$		0			0
$999$	295202.	+	1.24557e6i	0.295793	+	1.24807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.b.a.29.7	yes	8
3.2	odd	2	inner	60.5.b.a.29.1	✓	8
4.3	odd	2		240.5.c.e.209.2		8
5.2	odd	4		300.5.g.h.101.3		8
5.3	odd	4		300.5.g.h.101.6		8
5.4	even	2	inner	60.5.b.a.29.2	yes	8
12.11	even	2		240.5.c.e.209.8		8
15.2	even	4		300.5.g.h.101.4		8
15.8	even	4		300.5.g.h.101.5		8
15.14	odd	2	inner	60.5.b.a.29.8	yes	8
20.19	odd	2		240.5.c.e.209.7		8
60.59	even	2		240.5.c.e.209.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.b.a.29.1	✓	8	3.2	odd	2	inner
60.5.b.a.29.2	yes	8	5.4	even	2	inner
60.5.b.a.29.7	yes	8	1.1	even	1	trivial
60.5.b.a.29.8	yes	8	15.14	odd	2	inner
240.5.c.e.209.1		8	60.59	even	2
240.5.c.e.209.2		8	4.3	odd	2
240.5.c.e.209.7		8	20.19	odd	2
240.5.c.e.209.8		8	12.11	even	2
300.5.g.h.101.3		8	5.2	odd	4
300.5.g.h.101.4		8	15.2	even	4
300.5.g.h.101.5		8	15.8	even	4
300.5.g.h.101.6		8	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	60.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(8.97294 - 0.697422i) q^{3} +(-9.58741 - 23.0886i) q^{5} -67.4301i q^{7} +(80.0272 - 12.5158i) q^{9} +O(q^{10})\)	\(q+(8.97294 - 0.697422i) q^{3} +(-9.58741 - 23.0886i) q^{5} -67.4301i q^{7} +(80.0272 - 12.5158i) q^{9} +155.791i q^{11} -206.475i q^{13} +(-102.130 - 200.486i) q^{15} +119.476 q^{17} +492.163 q^{19} +(-47.0272 - 605.046i) q^{21} -353.261 q^{23} +(-441.163 + 442.719i) q^{25} +(709.350 - 168.117i) q^{27} +917.942i q^{29} -632.163 q^{31} +(108.652 + 1397.90i) q^{33} +(-1556.86 + 646.480i) q^{35} +1755.93i q^{37} +(-144.000 - 1852.69i) q^{39} +1449.21i q^{41} -627.316i q^{43} +(-1056.23 - 1727.72i) q^{45} +3701.53 q^{47} -2145.82 q^{49} +(1072.05 - 83.3255i) q^{51} -3662.42 q^{53} +(3596.98 - 1493.63i) q^{55} +(4416.15 - 343.245i) q^{57} +1424.52i q^{59} +1737.14 q^{61} +(-843.944 - 5396.24i) q^{63} +(-4767.21 + 1979.56i) q^{65} -6456.19i q^{67} +(-3169.79 + 246.372i) q^{69} -2436.64i q^{71} +2691.70i q^{73} +(-3649.77 + 4280.17i) q^{75} +10505.0 q^{77} +3216.49 q^{79} +(6247.71 - 2003.22i) q^{81} +1517.02 q^{83} +(-1145.47 - 2758.54i) q^{85} +(640.193 + 8236.64i) q^{87} -7466.75i q^{89} -13922.6 q^{91} +(-5672.36 + 440.884i) q^{93} +(-4718.57 - 11363.3i) q^{95} +10716.1i q^{97} +(1949.85 + 12467.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 52 q^{9}+O(q^{10}) \) 8 * q + 52 * q^9	\( 8 q + 52 q^{9} - 100 q^{15} + 408 q^{19} + 212 q^{21} - 1528 q^{31} - 1152 q^{39} - 2900 q^{45} + 480 q^{49} + 7400 q^{51} + 7600 q^{55} - 10808 q^{61} - 8300 q^{69} - 14000 q^{75} + 15144 q^{79} + 34688 q^{81} + 22600 q^{85} - 54912 q^{91} - 24400 q^{99}+O(q^{100}) \) 8 * q + 52 * q^9 - 100 * q^15 + 408 * q^19 + 212 * q^21 - 1528 * q^31 - 1152 * q^39 - 2900 * q^45 + 480 * q^49 + 7400 * q^51 + 7600 * q^55 - 10808 * q^61 - 8300 * q^69 - 14000 * q^75 + 15144 * q^79 + 34688 * q^81 + 22600 * q^85 - 54912 * q^91 - 24400 * q^99

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