LMFDB - Embedded newform 1150.3.c.a.1149.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,3,Mod(1149,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1150.1149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1150.c (of order $2$, degree $1$, not 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:	$31.3352304014$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1504920469504.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 24x^{6} + 142x^{4} + 904x^{3} - 2668x^{2} + 28000x + 91250 $ x^8 - 4x^7 + 24x^6 + 142x^4 + 904x^3 - 2668x^2 + 28000x + 91250
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 46)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1149.3
Root			$-2.83753 - 0.175342i$ of defining polynomial
Character	$\chi$	$=$	1150.1149
Dual form			1150.3.c.a.1149.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +2.41421i q^{3} -2.00000 q^{4} +3.41421 q^{6} -3.91016 q^{7} +2.82843i q^{8} +3.17157 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +2.41421i q^{3} -2.00000 q^{4} +3.41421 q^{6} -3.91016 q^{7} +2.82843i q^{8} +3.17157 q^{9} -3.91016i q^{11} -4.82843i q^{12} -10.3137i q^{13} +5.52980i q^{14} +4.00000 q^{16} -17.2603 q^{17} -4.48528i q^{18} +26.7002i q^{19} -9.43995i q^{21} -5.52980 q^{22} +(22.7901 - 3.10051i) q^{23} -6.82843 q^{24} -14.5858 q^{26} +29.3848i q^{27} +7.82031 q^{28} -35.1421 q^{29} +33.2426 q^{31} -5.65685i q^{32} +9.43995 q^{33} +24.4097i q^{34} -6.34315 q^{36} -39.3794 q^{37} +37.7598 q^{38} +24.8995 q^{39} +13.4853 q^{41} -13.3501 q^{42} -29.9395 q^{43} +7.82031i q^{44} +(-4.38478 - 32.2300i) q^{46} -31.0416i q^{47} +9.65685i q^{48} -33.7107 q^{49} -41.6700i q^{51} +20.6274i q^{52} -61.2207 q^{53} +41.5563 q^{54} -11.0596i q^{56} -64.4600 q^{57} +49.6985i q^{58} +26.2010 q^{59} +15.6406i q^{61} -47.0122i q^{62} -12.4013 q^{63} -8.00000 q^{64} -13.3501i q^{66} -68.3702 q^{67} +34.5205 q^{68} +(7.48528 + 55.0201i) q^{69} -111.267 q^{71} +8.97056i q^{72} -47.8528i q^{73} +55.6910i q^{74} -53.4004i q^{76} +15.2893i q^{77} -35.2132i q^{78} -117.860i q^{79} -42.3970 q^{81} -19.0711i q^{82} -74.8487 q^{83} +18.8799i q^{84} +42.3408i q^{86} -84.8406i q^{87} +11.0596 q^{88} +39.1016i q^{89} +40.3282i q^{91} +(-45.5801 + 6.20101i) q^{92} +80.2548i q^{93} -43.8995 q^{94} +13.6569 q^{96} -66.0797 q^{97} +47.6741i q^{98} -12.4013i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{4} + 16 q^{6} + 48 q^{9}+O(q^{10}) $ 8 * q - 16 * q^4 + 16 * q^6 + 48 * q^9	$ 8 q - 16 q^{4} + 16 q^{6} + 48 q^{9} + 32 q^{16} - 32 q^{24} - 128 q^{26} - 168 q^{29} + 232 q^{31} - 96 q^{36} + 120 q^{39} + 40 q^{41} + 112 q^{46} + 296 q^{49} + 208 q^{54} + 368 q^{59} - 64 q^{64} - 8 q^{69} - 200 q^{71} + 136 q^{81} - 272 q^{94} + 64 q^{96}+O(q^{100}) $ 8 * q - 16 * q^4 + 16 * q^6 + 48 * q^9 + 32 * q^16 - 32 * q^24 - 128 * q^26 - 168 * q^29 + 232 * q^31 - 96 * q^36 + 120 * q^39 + 40 * q^41 + 112 * q^46 + 296 * q^49 + 208 * q^54 + 368 * q^59 - 64 * q^64 - 8 * q^69 - 200 * q^71 + 136 * q^81 - 272 * q^94 + 64 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$			2.41421i			0.804738i	0.915478	+	0.402369i	$0.131813\pi$
$3$			2.41421i			0.804738i	−0.915478	+	0.402369i	$0.868187\pi$
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	3.41421			0.569036
$7$	−3.91016			−0.558594			−0.279297	−	0.960205i	$-0.590101\pi$
$7$	−3.91016			−0.558594			−0.279297	+	0.960205i	$0.590101\pi$
$8$			2.82843i			0.353553i
$9$	3.17157			0.352397
$10$		0			0
$11$		−	3.91016i		−	0.355469i	−0.984078	−	0.177734i	$-0.943123\pi$
$11$		−	3.91016i		−	0.355469i	0.984078	−	0.177734i	$-0.0568768\pi$
$12$		−	4.82843i		−	0.402369i
$13$		−	10.3137i		−	0.793362i	−0.917956	−	0.396681i	$-0.870162\pi$
$13$		−	10.3137i		−	0.793362i	0.917956	−	0.396681i	$-0.129838\pi$
$14$			5.52980i			0.394985i
$15$		0			0
$16$	4.00000			0.250000
$17$	−17.2603			−1.01531			−0.507655	−	0.861561i	$-0.669487\pi$
$17$	−17.2603			−1.01531			−0.507655	+	0.861561i	$0.669487\pi$
$18$		−	4.48528i		−	0.249182i
$19$			26.7002i			1.40527i	0.711548	+	0.702637i	$0.247994\pi$
$19$			26.7002i			1.40527i	−0.711548	+	0.702637i	$0.752006\pi$
$20$		0			0
$21$		−	9.43995i		−	0.449522i
$22$	−5.52980			−0.251354
$23$	22.7901	−	3.10051i	0.990872	−	0.134805i
$23$	22.7901	−	3.10051i	0.990872	−	0.134805i
$24$	−6.82843			−0.284518
$25$		0			0
$26$	−14.5858			−0.560992
$27$			29.3848i			1.08833i
$28$	7.82031			0.279297
$29$	−35.1421			−1.21180			−0.605899	−	0.795542i	$-0.707186\pi$
$29$	−35.1421			−1.21180			−0.605899	+	0.795542i	$0.707186\pi$
$30$		0			0
$31$	33.2426			1.07234			0.536172	−	0.844109i	$-0.319870\pi$
$31$	33.2426			1.07234			0.536172	+	0.844109i	$0.319870\pi$
$32$		−	5.65685i		−	0.176777i
$33$	9.43995			0.286059
$34$			24.4097i			0.717932i
$35$		0			0
$36$	−6.34315			−0.176198
$37$	−39.3794			−1.06431			−0.532155	−	0.846647i	$-0.678618\pi$
$37$	−39.3794			−1.06431			−0.532155	+	0.846647i	$0.678618\pi$
$38$	37.7598			0.993679
$39$	24.8995			0.638449
$40$		0			0
$41$	13.4853			0.328909			0.164455	−	0.986385i	$-0.447414\pi$
$41$	13.4853			0.328909			0.164455	+	0.986385i	$0.447414\pi$
$42$	−13.3501			−0.317860
$43$	−29.9395			−0.696267			−0.348134	−	0.937445i	$-0.613184\pi$
$43$	−29.9395			−0.696267			−0.348134	+	0.937445i	$0.613184\pi$
$44$			7.82031i			0.177734i
$45$		0			0
$46$	−4.38478	−	32.2300i	−0.0953212	−	0.700652i
$47$		−	31.0416i		−	0.660460i	−0.943900	−	0.330230i	$-0.892874\pi$
$47$		−	31.0416i		−	0.660460i	0.943900	−	0.330230i	$-0.107126\pi$
$48$			9.65685i			0.201184i
$49$	−33.7107			−0.687973
$50$		0			0
$51$		−	41.6700i		−	0.817058i
$52$			20.6274i			0.396681i
$53$	−61.2207			−1.15511			−0.577554	−	0.816352i	$-0.695993\pi$
$53$	−61.2207			−1.15511			−0.577554	+	0.816352i	$0.695993\pi$
$54$	41.5563			0.769562
$55$		0			0
$56$		−	11.0596i		−	0.197493i
$57$	−64.4600			−1.13088
$58$			49.6985i			0.856870i
$59$	26.2010			0.444085			0.222042	−	0.975037i	$-0.428728\pi$
$59$	26.2010			0.444085			0.222042	+	0.975037i	$0.428728\pi$
$60$		0			0
$61$			15.6406i			0.256404i	0.991748	+	0.128202i	$0.0409205\pi$
$61$			15.6406i			0.256404i	−0.991748	+	0.128202i	$0.959079\pi$
$62$		−	47.0122i		−	0.758261i
$63$	−12.4013			−0.196847
$64$	−8.00000			−0.125000
$65$		0			0
$66$		−	13.3501i		−	0.202274i
$67$	−68.3702			−1.02045			−0.510225	−	0.860041i	$-0.670438\pi$
$67$	−68.3702			−1.02045			−0.510225	+	0.860041i	$0.670438\pi$
$68$	34.5205			0.507655
$69$	7.48528	+	55.0201i	0.108482	+	0.797392i
$70$		0			0
$71$	−111.267			−1.56714			−0.783571	−	0.621303i	$-0.786604\pi$
$71$	−111.267			−1.56714			−0.783571	+	0.621303i	$0.786604\pi$
$72$			8.97056i			0.124591i
$73$		−	47.8528i		−	0.655518i	−0.944761	−	0.327759i	$-0.893707\pi$
$73$		−	47.8528i		−	0.655518i	0.944761	−	0.327759i	$-0.106293\pi$
$74$			55.6910i			0.752580i
$75$		0			0
$76$		−	53.4004i		−	0.702637i
$77$			15.2893i			0.198563i
$78$		−	35.2132i		−	0.451451i
$79$		−	117.860i		−	1.49190i	−0.665999	−	0.745952i	$-0.731995\pi$
$79$		−	117.860i		−	1.49190i	0.665999	−	0.745952i	$-0.268005\pi$
$80$		0			0
$81$	−42.3970			−0.523419
$82$		−	19.0711i		−	0.232574i
$83$	−74.8487			−0.901792			−0.450896	−	0.892576i	$-0.648895\pi$
$83$	−74.8487			−0.901792			−0.450896	+	0.892576i	$0.648895\pi$
$84$			18.8799i			0.224761i
$85$		0			0
$86$			42.3408i			0.492335i
$87$		−	84.8406i		−	0.975180i
$88$	11.0596			0.125677
$89$			39.1016i			0.439343i	0.975574	+	0.219672i	$0.0704986\pi$
$89$			39.1016i			0.439343i	−0.975574	+	0.219672i	$0.929501\pi$
$90$		0			0
$91$			40.3282i			0.443167i
$92$	−45.5801	+	6.20101i	−0.495436	+	0.0674023i
$93$			80.2548i			0.862955i
$94$	−43.8995			−0.467016
$95$		0			0
$96$	13.6569			0.142259
$97$	−66.0797			−0.681234			−0.340617	−	0.940202i	$-0.610636\pi$
$97$	−66.0797			−0.681234			−0.340617	+	0.940202i	$0.610636\pi$
$98$			47.6741i			0.486470i
$99$		−	12.4013i		−	0.125266i
$100$		0			0
$101$	101.338			1.00335			0.501674	−	0.865057i	$-0.332718\pi$
$101$	101.338			1.00335			0.501674	+	0.865057i	$0.332718\pi$
$102$	−58.9302			−0.577747
$103$	−101.549			−0.985912			−0.492956	−	0.870054i	$-0.664084\pi$
$103$	−101.549			−0.985912			−0.492956	+	0.870054i	$0.664084\pi$
$104$	29.1716			0.280496
$105$		0			0
$106$			86.5792i			0.816785i
$107$	−75.5196			−0.705791			−0.352895	−	0.935663i	$-0.614803\pi$
$107$	−75.5196			−0.705791			−0.352895	+	0.935663i	$0.614803\pi$
$108$		−	58.7696i		−	0.544163i
$109$			138.638i			1.27191i	0.771727	+	0.635954i	$0.219393\pi$
$109$			138.638i			1.27191i	−0.771727	+	0.635954i	$0.780607\pi$
$110$		0			0
$111$		−	95.0704i		−	0.856490i
$112$	−15.6406			−0.139648
$113$	−180.701			−1.59912			−0.799561	−	0.600585i	$-0.794935\pi$
$113$	−180.701			−1.59912			−0.799561	+	0.600585i	$0.794935\pi$
$114$			91.1602i			0.799651i
$115$		0			0
$116$	70.2843			0.605899
$117$		−	32.7107i		−	0.279578i
$118$		−	37.0538i		−	0.314015i
$119$	67.4903			0.567146
$120$		0			0
$121$	105.711			0.873642
$122$	22.1192			0.181305
$123$			32.5563i			0.264686i
$124$	−66.4853			−0.536172
$125$		0			0
$126$			17.5382i			0.139192i
$127$			36.3898i			0.286534i	0.989684	+	0.143267i	$0.0457608\pi$
$127$			36.3898i			0.286534i	−0.989684	+	0.143267i	$0.954239\pi$
$128$			11.3137i			0.0883883i
$129$		−	72.2803i		−	0.560313i
$130$		0			0
$131$	−65.3848			−0.499120			−0.249560	−	0.968359i	$-0.580286\pi$
$131$	−65.3848			−0.499120			−0.249560	+	0.968359i	$0.580286\pi$
$132$	−18.8799			−0.143030
$133$		−	104.402i		−	0.784978i
$134$			96.6900i			0.721567i
$135$		0			0
$136$		−	48.8194i		−	0.358966i
$137$	−65.8018			−0.480305			−0.240152	−	0.970735i	$-0.577197\pi$
$137$	−65.8018			−0.480305			−0.240152	+	0.970735i	$0.577197\pi$
$138$	77.8101	−	10.5858i	0.563842	−	0.0767086i
$139$	−29.4092			−0.211577			−0.105788	−	0.994389i	$-0.533737\pi$
$139$	−29.4092			−0.211577			−0.105788	+	0.994389i	$0.533737\pi$
$140$		0			0
$141$	74.9411			0.531497
$142$			157.355i			1.10814i
$143$	−40.3282			−0.282015
$144$	12.6863			0.0880992
$145$		0			0
$146$	−67.6741			−0.463521
$147$		−	81.3848i		−	0.553638i
$148$	78.7589			0.532155
$149$		−	3.23928i		−	0.0217401i	−0.999941	−	0.0108701i	$-0.996540\pi$
$149$		−	3.23928i		−	0.0217401i	0.999941	−	0.0108701i	$-0.00346012\pi$
$150$		0			0
$151$	−2.41421			−0.0159882			−0.00799408	−	0.999968i	$-0.502545\pi$
$151$	−2.41421			−0.0159882			−0.00799408	+	0.999968i	$0.502545\pi$
$152$	−75.5196			−0.496840
$153$	−54.7422			−0.357792
$154$	21.6224			0.140405
$155$		0			0
$156$	−49.7990			−0.319224
$157$	73.6221			0.468931			0.234465	−	0.972124i	$-0.424666\pi$
$157$	73.6221			0.468931			0.234465	+	0.972124i	$0.424666\pi$
$158$	−166.680			−1.05494
$159$		−	147.800i		−	0.929559i
$160$		0			0
$161$	−89.1127	+	12.1235i	−0.553495	+	0.0753010i
$162$			59.9584i			0.370113i
$163$		−	125.586i		−	0.770465i	−0.922820	−	0.385232i	$-0.874121\pi$
$163$		−	125.586i		−	0.770465i	0.922820	−	0.385232i	$-0.125879\pi$
$164$	−26.9706			−0.164455
$165$		0			0
$166$			105.852i			0.637663i
$167$		−	92.8284i		−	0.555859i	−0.960601	−	0.277929i	$-0.910352\pi$
$167$		−	92.8284i		−	0.555859i	0.960601	−	0.277929i	$-0.0896481\pi$
$168$	26.7002			0.158930
$169$	62.6274			0.370576
$170$		0			0
$171$			84.6817i			0.495215i
$172$	59.8790			0.348134
$173$			6.71068i			0.0387900i	0.999812	+	0.0193950i	$0.00617401\pi$
$173$			6.71068i			0.0387900i	−0.999812	+	0.0193950i	$0.993826\pi$
$174$	−119.983			−0.689556
$175$		0			0
$176$		−	15.6406i		−	0.0888672i
$177$			63.2548i			0.357372i
$178$	55.2980			0.310663
$179$	−278.262			−1.55454			−0.777268	−	0.629170i	$-0.783395\pi$
$179$	−278.262			−1.55454			−0.777268	+	0.629170i	$0.783395\pi$
$180$		0			0
$181$		−	53.6783i		−	0.296565i	−0.988945	−	0.148283i	$-0.952625\pi$
$181$		−	53.6783i		−	0.296565i	0.988945	−	0.148283i	$-0.0473745\pi$
$182$	57.0327			0.313367
$183$	−37.7598			−0.206338
$184$	8.76955	+	64.4600i	0.0476606	+	0.350326i
$185$		0			0
$186$	113.497			0.610201
$187$			67.4903i			0.360911i
$188$			62.0833i			0.330230i
$189$		−	114.899i		−	0.607932i
$190$		0			0
$191$		−	168.692i		−	0.883207i	−0.897210	−	0.441603i	$-0.854410\pi$
$191$		−	168.692i		−	0.883207i	0.897210	−	0.441603i	$-0.145590\pi$
$192$		−	19.3137i		−	0.100592i
$193$			95.3188i			0.493880i	0.969031	+	0.246940i	$0.0794250\pi$
$193$			95.3188i			0.493880i	−0.969031	+	0.246940i	$0.920575\pi$
$194$			93.4508i			0.481705i
$195$		0			0
$196$	67.4214			0.343987
$197$			249.083i			1.26438i	0.774813	+	0.632191i	$0.217844\pi$
$197$			249.083i			1.26438i	−0.774813	+	0.632191i	$0.782156\pi$
$198$	−17.5382			−0.0885765
$199$			76.1905i			0.382867i	0.981506	+	0.191433i	$0.0613136\pi$
$199$			76.1905i			0.382867i	−0.981506	+	0.191433i	$0.938686\pi$
$200$		0			0
$201$		−	165.060i		−	0.821195i
$202$		−	143.314i		−	0.709474i
$203$	137.411			0.676903
$204$			83.3399i			0.408529i
$205$		0			0
$206$			143.612i			0.697145i
$207$	72.2803	−	9.83348i	0.349180	−	0.0475047i
$208$		−	41.2548i		−	0.198341i
$209$	104.402			0.499531
$210$		0			0
$211$	−71.1716			−0.337306			−0.168653	−	0.985675i	$-0.553942\pi$
$211$	−71.1716			−0.337306			−0.168653	+	0.985675i	$0.553942\pi$
$212$	122.441			0.577554
$213$		−	268.622i		−	1.26114i
$214$			106.801i			0.499069i
$215$		0			0
$216$	−83.1127			−0.384781
$217$	−129.984			−0.599004
$218$	196.064			0.899374
$219$	115.527			0.527520
$220$		0			0
$221$			178.017i			0.805508i
$222$	−134.450			−0.605630
$223$			84.0833i			0.377055i	0.982068	+	0.188527i	$0.0603715\pi$
$223$			84.0833i			0.377055i	−0.982068	+	0.188527i	$0.939629\pi$
$224$			22.1192i			0.0987464i
$225$		0			0
$226$			255.550i			1.13075i
$227$	263.092			1.15900			0.579498	−	0.814974i	$-0.303249\pi$
$227$	263.092			1.15900			0.579498	+	0.814974i	$0.303249\pi$
$228$	128.920			0.565439
$229$			141.321i			0.617124i	0.951204	+	0.308562i	$0.0998477\pi$
$229$			141.321i			0.617124i	−0.951204	+	0.308562i	$0.900152\pi$
$230$		0			0
$231$	−36.9117			−0.159791
$232$		−	99.3970i		−	0.428435i
$233$			353.784i			1.51839i	0.650866	+	0.759193i	$0.274406\pi$
$233$			353.784i			1.51839i	−0.650866	+	0.759193i	$0.725594\pi$
$234$	−46.2599			−0.197692
$235$		0			0
$236$	−52.4020			−0.222042
$237$	284.540			1.20059
$238$		−	95.4457i		−	0.401033i
$239$	272.286			1.13927			0.569637	−	0.821897i	$-0.307084\pi$
$239$	272.286			1.13927			0.569637	+	0.821897i	$0.307084\pi$
$240$		0			0
$241$			443.678i			1.84099i	0.390758	+	0.920493i	$0.372213\pi$
$241$			443.678i			1.84099i	−0.390758	+	0.920493i	$0.627787\pi$
$242$		−	149.497i		−	0.617758i
$243$			162.108i			0.667110i
$244$		−	31.2812i		−	0.128202i
$245$		0			0
$246$	46.0416			0.187161
$247$	275.378			1.11489
$248$			94.0244i			0.379131i
$249$		−	180.701i		−	0.725706i
$250$		0			0
$251$		−	194.607i		−	0.775326i	−0.921801	−	0.387663i	$-0.873282\pi$
$251$		−	194.607i		−	0.775326i	0.921801	−	0.387663i	$-0.126718\pi$
$252$	24.8027			0.0984234
$253$	−12.1235	−	89.1127i	−0.0479188	−	0.352224i
$254$	51.4630			0.202610
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	22.1371i		−	0.0861365i	−0.999072	−	0.0430683i	$-0.986287\pi$
$257$		−	22.1371i		−	0.0861365i	0.999072	−	0.0430683i	$-0.0137133\pi$
$258$	−102.220			−0.396201
$259$	153.980			0.594517
$260$		0			0
$261$	−111.456			−0.427034
$262$			92.4680i			0.352931i
$263$	425.076			1.61626			0.808129	−	0.589006i	$-0.200481\pi$
$263$	425.076			1.61626			0.808129	+	0.589006i	$0.200481\pi$
$264$			26.7002i			0.101137i
$265$		0			0
$266$	−147.647			−0.555063
$267$	−94.3995			−0.353556
$268$	136.740			0.510225
$269$	−411.215			−1.52868			−0.764341	−	0.644813i	$-0.776935\pi$
$269$	−411.215			−1.52868			−0.764341	+	0.644813i	$0.776935\pi$
$270$		0			0
$271$	−98.8183			−0.364643			−0.182322	−	0.983239i	$-0.558361\pi$
$271$	−98.8183			−0.364643			−0.182322	+	0.983239i	$0.558361\pi$
$272$	−69.0411			−0.253827
$273$	−97.3609			−0.356633
$274$			93.0578i			0.339627i
$275$		0			0
$276$	−14.9706	−	110.040i	−0.0542412	−	0.398696i
$277$		−	207.319i		−	0.748443i	−0.927339	−	0.374222i	$-0.877910\pi$
$277$		−	207.319i		−	0.748443i	0.927339	−	0.374222i	$-0.122090\pi$
$278$			41.5908i			0.149607i
$279$	105.431			0.377891
$280$		0			0
$281$		−	31.0034i		−	0.110332i	−0.998477	−	0.0551661i	$-0.982431\pi$
$281$		−	31.0034i		−	0.110332i	0.998477	−	0.0551661i	$-0.0175688\pi$
$282$		−	105.983i		−	0.375825i
$283$	−225.888			−0.798191			−0.399095	−	0.916909i	$-0.630676\pi$
$283$	−225.888			−0.798191			−0.399095	+	0.916909i	$0.630676\pi$
$284$	222.534			0.783571
$285$		0			0
$286$			57.0327i			0.199415i
$287$	−52.7296			−0.183727
$288$		−	17.9411i		−	0.0622956i
$289$	8.91674			0.0308538
$290$		0			0
$291$		−	159.530i		−	0.548215i
$292$			95.7056i			0.327759i
$293$	162.099			0.553238			0.276619	−	0.960980i	$-0.410786\pi$
$293$	162.099			0.553238			0.276619	+	0.960980i	$0.410786\pi$
$294$	−115.095			−0.391481
$295$		0			0
$296$		−	111.382i		−	0.376290i
$297$	114.899			0.386866
$298$	−4.58103			−0.0153726
$299$	−31.9777	−	235.050i	−0.106949	−	0.786121i
$300$		0			0
$301$	117.068			0.388931
$302$			3.41421i			0.0113053i
$303$			244.652i			0.807432i
$304$			106.801i			0.351319i
$305$		0			0
$306$			77.4171i			0.252997i
$307$			342.299i			1.11498i	0.830184	+	0.557490i	$0.188235\pi$
$307$			342.299i			1.11498i	−0.830184	+	0.557490i	$0.811765\pi$
$308$		−	30.5786i		−	0.0992813i
$309$		−	245.161i		−	0.793401i
$310$		0			0
$311$	464.654			1.49406			0.747032	−	0.664788i	$-0.231478\pi$
$311$	464.654			1.49406			0.747032	+	0.664788i	$0.231478\pi$
$312$			70.4264i			0.225726i
$313$	95.1855			0.304107			0.152054	−	0.988372i	$-0.451411\pi$
$313$	95.1855			0.304107			0.152054	+	0.988372i	$0.451411\pi$
$314$		−	104.117i		−	0.331584i
$315$		0			0
$316$			235.721i			0.745952i
$317$		−	210.142i		−	0.662909i	−0.943471	−	0.331454i	$-0.892461\pi$
$317$		−	210.142i		−	0.662909i	0.943471	−	0.331454i	$-0.107539\pi$
$318$	−209.021			−0.657298
$319$			137.411i			0.430756i
$320$		0			0
$321$		−	182.320i		−	0.567977i
$322$	17.1452	+	126.024i	0.0532458	+	0.391380i
$323$		−	460.853i		−	1.42679i
$324$	84.7939			0.261710
$325$		0			0
$326$	−177.605			−0.544801
$327$	−334.701			−1.02355
$328$			38.1421i			0.116287i
$329$			121.378i			0.368929i
$330$		0			0
$331$	66.2822			0.200248			0.100124	−	0.994975i	$-0.468076\pi$
$331$	66.2822			0.200248			0.100124	+	0.994975i	$0.468076\pi$
$332$	149.697			0.450896
$333$	−124.895			−0.375059
$334$	−131.279			−0.393052
$335$		0			0
$336$		−	37.7598i		−	0.112380i
$337$	453.348			1.34525			0.672623	−	0.739985i	$-0.265168\pi$
$337$	453.348			1.34525			0.672623	+	0.739985i	$0.265168\pi$
$338$		−	88.5685i		−	0.262037i
$339$		−	436.250i		−	1.28687i
$340$		0			0
$341$		−	129.984i		−	0.381185i
$342$	119.758			0.350170
$343$	323.412			0.942891
$344$		−	84.6817i		−	0.246168i
$345$		0			0
$346$	9.49033			0.0274287
$347$		−	291.750i		−	0.840779i	−0.907344	−	0.420389i	$-0.861893\pi$
$347$		−	291.750i		−	0.840779i	0.907344	−	0.420389i	$-0.138107\pi$
$348$			169.681i			0.487590i
$349$	−150.951			−0.432525			−0.216263	−	0.976335i	$-0.569387\pi$
$349$	−150.951			−0.432525			−0.216263	+	0.976335i	$0.569387\pi$
$350$		0			0
$351$	303.066			0.863436
$352$	−22.1192			−0.0628386
$353$		−	377.059i		−	1.06816i	−0.845435	−	0.534078i	$-0.820659\pi$
$353$		−	377.059i		−	1.06816i	0.845435	−	0.534078i	$-0.179341\pi$
$354$	89.4558			0.252700
$355$		0			0
$356$		−	78.2031i		−	0.219672i
$357$			162.936i			0.456404i
$358$			393.522i			1.09922i
$359$		−	352.240i		−	0.981169i	−0.871394	−	0.490584i	$-0.836783\pi$
$359$		−	352.240i		−	0.981169i	0.871394	−	0.490584i	$-0.163217\pi$
$360$		0			0
$361$	−351.902			−0.974797
$362$	−75.9126			−0.209703
$363$			255.208i			0.703053i
$364$		−	80.6564i		−	0.221584i
$365$		0			0
$366$			53.4004i			0.145903i
$367$	320.843			0.874232			0.437116	−	0.899405i	$-0.356000\pi$
$367$	320.843			0.874232			0.437116	+	0.899405i	$0.356000\pi$
$368$	91.1602	−	12.4020i	0.247718	−	0.0337011i
$369$	42.7696			0.115907
$370$		0			0
$371$	239.383			0.645236
$372$		−	160.510i		−	0.431478i
$373$	156.128			0.418575			0.209287	−	0.977854i	$-0.432886\pi$
$373$	156.128			0.418575			0.209287	+	0.977854i	$0.432886\pi$
$374$	95.4457			0.255203
$375$		0			0
$376$	87.7990			0.233508
$377$			362.446i			0.961395i
$378$	−162.492			−0.429873
$379$		−	451.220i		−	1.19055i	−0.803520	−	0.595277i	$-0.797042\pi$
$379$		−	451.220i		−	1.19055i	0.803520	−	0.595277i	$-0.202958\pi$
$380$		0			0
$381$	−87.8528			−0.230585
$382$	−238.567			−0.624521
$383$	−423.178			−1.10490			−0.552452	−	0.833545i	$-0.686308\pi$
$383$	−423.178			−1.10490			−0.552452	+	0.833545i	$0.686308\pi$
$384$	−27.3137			−0.0711294
$385$		0			0
$386$	134.801			0.349226
$387$	−94.9553			−0.245363
$388$	132.159			0.340617
$389$		−	11.0596i		−	0.0284308i	−0.999899	−	0.0142154i	$-0.995475\pi$
$389$		−	11.0596i		−	0.0284308i	0.999899	−	0.0142154i	$-0.00452506\pi$
$390$		0			0
$391$	−393.362	+	53.5155i	−1.00604	+	0.136868i
$392$		−	95.3482i		−	0.243235i
$393$		−	157.853i		−	0.401661i
$394$	352.257			0.894053
$395$		0			0
$396$			24.8027i			0.0626331i
$397$		−	332.578i		−	0.837727i	−0.908049	−	0.418864i	$-0.862429\pi$
$397$		−	332.578i		−	0.837727i	0.908049	−	0.418864i	$-0.137571\pi$
$398$	107.750			0.270728
$399$	252.049			0.631701
$400$		0			0
$401$			51.7808i			0.129129i	0.997914	+	0.0645646i	$0.0205658\pi$
$401$			51.7808i			0.129129i	−0.997914	+	0.0645646i	$0.979434\pi$
$402$	−233.430			−0.580673
$403$		−	342.855i		−	0.850757i
$404$	−202.676			−0.501674
$405$		0			0
$406$		−	194.329i		−	0.478642i
$407$			153.980i			0.378329i
$408$	117.860			0.288874
$409$	−256.088			−0.626133			−0.313066	−	0.949731i	$-0.601356\pi$
$409$	−256.088			−0.626133			−0.313066	+	0.949731i	$0.601356\pi$
$410$		0			0
$411$		−	158.860i		−	0.386520i
$412$	203.098			0.492956
$413$	−102.450			−0.248063
$414$	−13.9066	−	102.220i	−0.0335909	−	0.246908i
$415$		0			0
$416$	−58.3431			−0.140248
$417$		−	71.0000i		−	0.170264i
$418$		−	147.647i		−	0.353222i
$419$		−	241.644i		−	0.576715i	−0.957523	−	0.288358i	$-0.906891\pi$
$419$		−	241.644i		−	0.576715i	0.957523	−	0.288358i	$-0.0931092\pi$
$420$		0			0
$421$			312.860i			0.743136i	0.928406	+	0.371568i	$0.121180\pi$
$421$			312.860i			0.743136i	−0.928406	+	0.371568i	$0.878820\pi$
$422$			100.652i			0.238511i
$423$		−	98.4508i		−	0.232744i
$424$		−	173.158i		−	0.408392i
$425$		0			0
$426$	−379.889			−0.891759
$427$		−	61.1573i		−	0.143225i
$428$	151.039			0.352895
$429$		−	97.3609i		−	0.226949i
$430$		0			0
$431$		−	672.412i		−	1.56012i	−0.625704	−	0.780060i	$-0.715188\pi$
$431$		−	672.412i		−	1.56012i	0.625704	−	0.780060i	$-0.284812\pi$
$432$			117.539i			0.272081i
$433$	−395.414			−0.913197			−0.456598	−	0.889673i	$-0.650932\pi$
$433$	−395.414			−0.913197			−0.456598	+	0.889673i	$0.650932\pi$
$434$			183.825i			0.423560i
$435$		0			0
$436$		−	277.276i		−	0.635954i
$437$	82.7842	+	608.500i	0.189437	+	1.39245i
$438$		−	163.380i		−	0.373013i
$439$	−836.997			−1.90660			−0.953300	−	0.302026i	$-0.902337\pi$
$439$	−836.997			−1.90660			−0.953300	+	0.302026i	$0.902337\pi$
$440$		0			0
$441$	−106.916			−0.242440
$442$	251.755			0.569580
$443$			227.905i			0.514457i	0.966351	+	0.257229i	$0.0828093\pi$
$443$			227.905i			0.514457i	−0.966351	+	0.257229i	$0.917191\pi$
$444$			190.141i			0.428245i
$445$		0			0
$446$	118.912			0.266618
$447$	7.82031			0.0174951
$448$	31.2812			0.0698242
$449$	439.019			0.977771			0.488886	−	0.872348i	$-0.337404\pi$
$449$	439.019			0.977771			0.488886	+	0.872348i	$0.337404\pi$
$450$		0			0
$451$		−	52.7296i		−	0.116917i
$452$	361.402			0.799561
$453$		−	5.82843i		−	0.0128663i
$454$		−	372.068i		−	0.819534i
$455$		0			0
$456$		−	182.320i		−	0.399826i
$457$	40.1654			0.0878893			0.0439447	−	0.999034i	$-0.486007\pi$
$457$	40.1654			0.0878893			0.0439447	+	0.999034i	$0.486007\pi$
$458$	199.859			0.436373
$459$		−	507.189i		−	1.10499i
$460$		0			0
$461$	65.6762			0.142465			0.0712323	−	0.997460i	$-0.477307\pi$
$461$	65.6762			0.142465			0.0712323	+	0.997460i	$0.477307\pi$
$462$			52.2010i			0.112989i
$463$			673.436i			1.45450i	0.686370	+	0.727252i	$0.259203\pi$
$463$			673.436i			1.45450i	−0.686370	+	0.727252i	$0.740797\pi$
$464$	−140.569			−0.302949
$465$		0			0
$466$	500.326			1.07366
$467$	310.685			0.665278			0.332639	−	0.943054i	$-0.392061\pi$
$467$	310.685			0.665278			0.332639	+	0.943054i	$0.392061\pi$
$468$			65.4214i			0.139789i
$469$	267.338			0.570017
$470$		0			0
$471$			177.739i			0.377366i
$472$			74.1076i			0.157008i
$473$			117.068i			0.247501i
$474$		−	402.401i		−	0.848947i
$475$		0			0
$476$	−134.981			−0.283573
$477$	−194.166			−0.407057
$478$		−	385.071i		−	0.805588i
$479$		−	230.469i		−	0.481146i	−0.970631	−	0.240573i	$-0.922665\pi$
$479$		−	230.469i		−	0.481146i	0.970631	−	0.240573i	$-0.0773354\pi$
$480$		0			0
$481$			406.148i			0.844383i
$482$	627.455			1.30177
$483$	−29.2686	−	215.137i	−0.0605976	−	0.445418i
$484$	−211.421			−0.436821
$485$		0			0
$486$	229.255			0.471718
$487$			372.360i			0.764599i	0.924039	+	0.382299i	$0.124868\pi$
$487$			372.360i			0.764599i	−0.924039	+	0.382299i	$0.875132\pi$
$488$	−44.2384			−0.0906524
$489$	303.191			0.620022
$490$		0			0
$491$	258.026			0.525512			0.262756	−	0.964862i	$-0.415369\pi$
$491$	258.026			0.525512			0.262756	+	0.964862i	$0.415369\pi$
$492$		−	65.1127i		−	0.132343i
$493$	606.563			1.23035
$494$		−	389.444i		−	0.788347i
$495$		0			0
$496$	132.971			0.268086
$497$	435.071			0.875395
$498$	−255.550			−0.513152
$499$	372.747			0.746988			0.373494	−	0.927632i	$-0.378160\pi$
$499$	372.747			0.746988			0.373494	+	0.927632i	$0.378160\pi$
$500$		0			0
$501$	224.108			0.447321
$502$	−275.215			−0.548238
$503$	611.191			1.21509			0.607546	−	0.794284i	$-0.292154\pi$
$503$	611.191			1.21509			0.607546	+	0.794284i	$0.292154\pi$
$504$		−	35.0763i		−	0.0695958i
$505$		0			0
$506$	−126.024	+	17.1452i	−0.249060	+	0.0338837i
$507$			151.196i			0.298217i
$508$		−	72.7797i		−	0.143267i
$509$	−357.985			−0.703310			−0.351655	−	0.936130i	$-0.614381\pi$
$509$	−357.985			−0.703310			−0.351655	+	0.936130i	$0.614381\pi$
$510$		0			0
$511$			187.112i			0.366168i
$512$		−	22.6274i		−	0.0441942i
$513$	−784.580			−1.52940
$514$	−31.3066			−0.0609077
$515$		0			0
$516$			144.561i			0.280156i
$517$	−121.378			−0.234773
$518$		−	217.760i		−	0.420387i
$519$	−16.2010			−0.0312158
$520$		0			0
$521$		−	123.227i		−	0.236521i	−0.992983	−	0.118261i	$-0.962268\pi$
$521$		−	123.227i		−	0.236521i	0.992983	−	0.118261i	$-0.0377318\pi$
$522$			157.622i			0.301959i
$523$	−246.110			−0.470573			−0.235286	−	0.971926i	$-0.575603\pi$
$523$	−246.110			−0.470573			−0.235286	+	0.971926i	$0.575603\pi$
$524$	130.770			0.249560
$525$		0			0
$526$		−	601.148i		−	1.14287i
$527$	−573.777			−1.08876
$528$	37.7598			0.0715148
$529$	509.774	−	141.321i	0.963655	−	0.267148i
$530$		0			0
$531$	83.0984			0.156494
$532$			208.804i			0.392489i
$533$		−	139.083i		−	0.260944i
$534$			133.501i			0.250002i
$535$		0			0
$536$		−	193.380i		−	0.360784i
$537$		−	671.784i		−	1.25099i
$538$			581.546i			1.08094i
$539$			131.814i			0.244553i
$540$		0			0
$541$	−425.922			−0.787286			−0.393643	−	0.919263i	$-0.628785\pi$
$541$	−425.922			−0.787286			−0.393643	+	0.919263i	$0.628785\pi$
$542$			139.750i			0.257842i
$543$	129.591			0.238657
$544$			97.6388i			0.179483i
$545$		0			0
$546$			137.689i			0.252178i
$547$		−	715.070i		−	1.30726i	−0.756815	−	0.653629i	$-0.773246\pi$
$547$		−	715.070i		−	1.30726i	0.756815	−	0.653629i	$-0.226754\pi$
$548$	131.604			0.240152
$549$			49.6054i			0.0903559i
$550$		0			0
$551$		−	938.303i		−	1.70291i
$552$	−155.620	+	21.1716i	−0.281921	+	0.0383543i
$553$			460.853i			0.833369i
$554$	−293.193			−0.529229
$555$		0			0
$556$	58.8183			0.105788
$557$	325.539			0.584451			0.292226	−	0.956349i	$-0.405604\pi$
$557$	325.539			0.584451			0.292226	+	0.956349i	$0.405604\pi$
$558$		−	149.103i		−	0.267209i
$559$			308.787i			0.552392i
$560$		0			0
$561$	−162.936			−0.290439
$562$	−43.8454			−0.0780167
$563$	636.780			1.13105			0.565524	−	0.824732i	$-0.308674\pi$
$563$	636.780			1.13105			0.565524	+	0.824732i	$0.308674\pi$
$564$	−149.882			−0.265749
$565$		0			0
$566$			319.454i			0.564406i
$567$	165.779			0.292379
$568$		−	314.711i		−	0.554068i
$569$			359.226i			0.631329i	0.948871	+	0.315665i	$0.102227\pi$
$569$			359.226i			0.631329i	−0.948871	+	0.315665i	$0.897773\pi$
$570$		0			0
$571$			766.371i			1.34216i	0.741387	+	0.671078i	$0.234168\pi$
$571$			766.371i			1.34216i	−0.741387	+	0.671078i	$0.765832\pi$
$572$	80.6564			0.141008
$573$	407.260			0.710750
$574$			74.5709i			0.129914i
$575$		0			0
$576$	−25.3726			−0.0440496
$577$		−	966.661i		−	1.67532i	−0.546190	−	0.837661i	$-0.683922\pi$
$577$		−	966.661i		−	1.67532i	0.546190	−	0.837661i	$-0.316078\pi$
$578$		−	12.6102i		−	0.0218169i
$579$	−230.120			−0.397444
$580$		0			0
$581$	292.670			0.503735
$582$	−225.610			−0.387646
$583$			239.383i			0.410605i
$584$	135.348			0.231761
$585$		0			0
$586$		−	229.242i		−	0.391199i
$587$		−	855.933i		−	1.45815i	−0.684435	−	0.729074i	$-0.739951\pi$
$587$		−	855.933i		−	1.45815i	0.684435	−	0.729074i	$-0.260049\pi$
$588$			162.770i			0.276819i
$589$			887.586i			1.50694i
$590$		0			0
$591$	−601.340			−1.01750
$592$	−157.518			−0.266077
$593$		−	159.563i		−	0.269078i	−0.990908	−	0.134539i	$-0.957045\pi$
$593$		−	159.563i		−	0.269078i	0.990908	−	0.134539i	$-0.0429554\pi$
$594$		−	162.492i		−	0.273555i
$595$		0			0
$596$			6.47856i			0.0108701i
$597$	−183.940			−0.308107
$598$	−332.411	+	45.2233i	−0.555871	+	0.0756243i
$599$	46.1320			0.0770151			0.0385075	−	0.999258i	$-0.487740\pi$
$599$	46.1320			0.0770151			0.0385075	+	0.999258i	$0.487740\pi$
$600$		0			0
$601$	−283.010			−0.470899			−0.235449	−	0.971887i	$-0.575656\pi$
$601$	−283.010			−0.470899			−0.235449	+	0.971887i	$0.575656\pi$
$602$		−	165.559i		−	0.275015i
$603$	−216.841			−0.359604
$604$	4.82843			0.00799408
$605$		0			0
$606$	345.990			0.570940
$607$			690.250i			1.13715i	0.822632	+	0.568575i	$0.192505\pi$
$607$			690.250i			1.13715i	−0.822632	+	0.568575i	$0.807495\pi$
$608$	151.039			0.248420
$609$			331.740i			0.544729i
$610$		0			0
$611$	−320.154			−0.523984
$612$	109.484			0.178896
$613$	−247.058			−0.403032			−0.201516	−	0.979485i	$-0.564587\pi$
$613$	−247.058			−0.403032			−0.201516	+	0.979485i	$0.564587\pi$
$614$	484.083			0.788409
$615$		0			0
$616$	−43.2447			−0.0702025
$617$	548.303			0.888660			0.444330	−	0.895863i	$-0.353442\pi$
$617$	548.303			0.888660			0.444330	+	0.895863i	$0.353442\pi$
$618$	−346.710			−0.561019
$619$			1090.68i			1.76201i	0.473108	+	0.881005i	$0.343132\pi$
$619$			1090.68i			1.76201i	−0.473108	+	0.881005i	$0.656868\pi$
$620$		0			0
$621$	91.1076	+	669.681i	0.146711	+	1.07839i
$622$		−	657.120i		−	1.05646i
$623$		−	152.893i		−	0.245414i
$624$	99.5980			0.159612
$625$		0			0
$626$		−	134.613i		−	0.215036i
$627$			252.049i			0.401992i
$628$	−147.244			−0.234465
$629$	679.700			1.08060
$630$		0			0
$631$			132.159i			0.209444i	0.994502	+	0.104722i	$0.0333953\pi$
$631$			132.159i			0.209444i	−0.994502	+	0.104722i	$0.966605\pi$
$632$	333.360			0.527468
$633$		−	171.823i		−	0.271443i
$634$	−297.186			−0.468747
$635$		0			0
$636$			295.600i			0.464780i
$637$			347.682i			0.545812i
$638$	194.329			0.304591
$639$	−352.891			−0.552256
$640$		0			0
$641$			349.786i			0.545688i	0.962058	+	0.272844i	$0.0879644\pi$
$641$			349.786i			0.545688i	−0.962058	+	0.272844i	$0.912036\pi$
$642$	−257.840			−0.401620
$643$	147.129			0.228817			0.114408	−	0.993434i	$-0.463503\pi$
$643$	147.129			0.228817			0.114408	+	0.993434i	$0.463503\pi$
$644$	178.225	−	24.2469i	0.276748	−	0.0376505i
$645$		0			0
$646$	−651.744			−1.00889
$647$			966.252i			1.49343i	0.665142	+	0.746717i	$0.268371\pi$
$647$			966.252i			1.49343i	−0.665142	+	0.746717i	$0.731629\pi$
$648$		−	119.917i		−	0.185057i
$649$		−	102.450i		−	0.157858i
$650$		0			0
$651$		−	313.809i		−	0.482041i
$652$			251.172i			0.385232i
$653$			817.378i			1.25173i	0.779933	+	0.625863i	$0.215253\pi$
$653$			817.378i			1.25173i	−0.779933	+	0.625863i	$0.784747\pi$
$654$			473.339i			0.723760i
$655$		0			0
$656$	53.9411			0.0822273
$657$		−	151.769i		−	0.231003i
$658$	171.654			0.260872
$659$			1053.82i			1.59913i	0.600581	+	0.799564i	$0.294936\pi$
$659$			1053.82i			1.59913i	−0.600581	+	0.799564i	$0.705064\pi$
$660$		0			0
$661$			1162.41i			1.75856i	0.476305	+	0.879280i	$0.341976\pi$
$661$			1162.41i			1.75856i	−0.476305	+	0.879280i	$0.658024\pi$
$662$		−	93.7372i		−	0.141597i
$663$	−429.772			−0.648223
$664$		−	211.704i		−	0.318832i
$665$		0			0
$666$			176.628i			0.265207i
$667$	−800.891	+	108.958i	−1.20074	+	0.163356i
$668$			185.657i			0.277929i
$669$	−202.995			−0.303430
$670$		0			0
$671$	61.1573			0.0911435
$672$	−53.4004			−0.0794649
$673$			647.461i			0.962052i	0.876706	+	0.481026i	$0.159736\pi$
$673$			647.461i			0.962052i	−0.876706	+	0.481026i	$0.840264\pi$
$674$		−	641.131i		−	0.951233i
$675$		0			0
$676$	−125.255			−0.185288
$677$	−544.278			−0.803956			−0.401978	−	0.915649i	$-0.631677\pi$
$677$	−544.278			−0.803956			−0.401978	+	0.915649i	$0.631677\pi$
$678$	−616.951			−0.909958
$679$	258.382			0.380533
$680$		0			0
$681$			635.160i			0.932688i
$682$	−183.825			−0.269538
$683$		−	77.8314i		−	0.113955i	−0.998375	−	0.0569776i	$-0.981854\pi$
$683$		−	77.8314i		−	0.113955i	0.998375	−	0.0569776i	$-0.0181464\pi$
$684$		−	169.363i		−	0.247607i
$685$		0			0
$686$		−	457.373i		−	0.666725i
$687$	−341.180			−0.496623
$688$	−119.758			−0.174067
$689$			631.413i			0.916419i
$690$		0			0
$691$	−223.769			−0.323833			−0.161917	−	0.986804i	$-0.551768\pi$
$691$	−223.769			−0.323833			−0.161917	+	0.986804i	$0.551768\pi$
$692$		−	13.4214i		−	0.0193950i
$693$			48.4912i			0.0699729i
$694$	−412.597			−0.594520
$695$		0			0
$696$	239.966			0.344778
$697$	−232.760			−0.333945
$698$			213.477i			0.305841i
$699$	−854.110			−1.22190
$700$		0			0
$701$			376.995i			0.537795i	0.963169	+	0.268898i	$0.0866594\pi$
$701$			376.995i			0.537795i	−0.963169	+	0.268898i	$0.913341\pi$
$702$		−	428.600i		−	0.610541i
$703$		−	1051.44i		−	1.49565i
$704$			31.2812i			0.0444336i
$705$		0			0
$706$	−533.242			−0.755300
$707$	−396.248			−0.560464
$708$		−	126.510i		−	0.178686i
$709$			1182.12i			1.66731i	0.552287	+	0.833654i	$0.313755\pi$
$709$			1182.12i			1.66731i	−0.552287	+	0.833654i	$0.686245\pi$
$710$		0			0
$711$		−	373.803i		−	0.525743i
$712$	−110.596			−0.155331
$713$	757.602	−	103.069i	1.06256	−	0.144557i
$714$	230.426			0.322726
$715$		0			0
$716$	556.524			0.777268
$717$			657.357i			0.916817i
$718$	−498.142			−0.693791
$719$	−93.9941			−0.130729			−0.0653645	−	0.997861i	$-0.520821\pi$
$719$	−93.9941			−0.130729			−0.0653645	+	0.997861i	$0.520821\pi$
$720$		0			0
$721$	397.072			0.550724
$722$			497.664i			0.689285i
$723$	−1071.13			−1.48151
$724$			107.357i			0.148283i
$725$		0			0
$726$	360.919			0.497133
$727$	−1303.61			−1.79314			−0.896571	−	0.442900i	$-0.853950\pi$
$727$	−1303.61			−1.79314			−0.896571	+	0.442900i	$0.853950\pi$
$728$	−114.065			−0.156683
$729$	−772.935			−1.06027
$730$		0			0
$731$	516.764			0.706927
$732$	75.5196			0.103169
$733$	−635.946			−0.867594			−0.433797	−	0.901011i	$-0.642826\pi$
$733$	−635.946			−0.867594			−0.433797	+	0.901011i	$0.642826\pi$
$734$		−	453.741i		−	0.618176i
$735$		0			0
$736$	−17.5391	−	128.920i	−0.0238303	−	0.175163i
$737$			267.338i			0.362738i
$738$		−	60.4853i		−	0.0819584i
$739$	−200.380			−0.271150			−0.135575	−	0.990767i	$-0.543288\pi$
$739$	−200.380			−0.271150			−0.135575	+	0.990767i	$0.543288\pi$
$740$		0			0
$741$			664.822i			0.897196i
$742$		−	338.538i		−	0.456251i
$743$	1210.79			1.62959			0.814796	−	0.579748i	$-0.196849\pi$
$743$	1210.79			1.62959			0.814796	+	0.579748i	$0.196849\pi$
$744$	−226.995			−0.305101
$745$		0			0
$746$		−	220.799i		−	0.295977i
$747$	−237.388			−0.317789
$748$		−	134.981i		−	0.180455i
$749$	295.294			0.394250
$750$		0			0
$751$		−	983.883i		−	1.31010i	−0.755587	−	0.655048i	$-0.772648\pi$
$751$		−	983.883i		−	1.31010i	0.755587	−	0.655048i	$-0.227352\pi$
$752$		−	124.167i		−	0.165115i
$753$	469.822			0.623934
$754$	512.576			0.679809
$755$		0			0
$756$			229.798i			0.303966i
$757$	1494.15			1.97378			0.986888	−	0.161407i	$-0.0516032\pi$
$757$	1494.15			1.97378			0.986888	+	0.161407i	$0.0516032\pi$
$758$	−638.122			−0.841849
$759$	215.137	−	29.2686i	0.283448	−	0.0385621i
$760$		0			0
$761$	−779.132			−1.02383			−0.511913	−	0.859037i	$-0.671063\pi$
$761$	−779.132			−1.02383			−0.511913	+	0.859037i	$0.671063\pi$
$762$			124.243i			0.163048i
$763$		−	542.096i		−	0.710479i
$764$			337.385i			0.441603i
$765$		0			0
$766$			598.464i			0.781285i
$767$		−	270.230i		−	0.352320i
$768$			38.6274i			0.0502961i
$769$			155.017i			0.201582i	0.994908	+	0.100791i	$0.0321374\pi$
$769$			155.017i			0.201582i	−0.994908	+	0.100791i	$0.967863\pi$
$770$		0			0
$771$	53.4437			0.0693173
$772$		−	190.638i		−	0.246940i
$773$	97.8690			0.126609			0.0633047	−	0.997994i	$-0.479836\pi$
$773$	97.8690			0.126609			0.0633047	+	0.997994i	$0.479836\pi$
$774$			134.287i			0.173498i
$775$		0			0
$776$		−	186.902i		−	0.240852i
$777$			371.740i			0.478430i
$778$	−15.6406			−0.0201036
$779$			360.060i			0.462208i
$780$		0			0
$781$			435.071i			0.557070i
$782$	75.6824	+	556.299i	0.0967806	+	0.711379i
$783$		−	1032.64i		−	1.31883i
$784$	−134.843			−0.171993
$785$		0			0
$786$	−223.238			−0.284017
$787$	−728.726			−0.925954			−0.462977	−	0.886370i	$-0.653219\pi$
$787$	−728.726			−0.925954			−0.462977	+	0.886370i	$0.653219\pi$
$788$		−	498.167i		−	0.632191i
$789$			1026.22i			1.30066i
$790$		0			0
$791$	706.569			0.893260
$792$	35.0763			0.0442883
$793$	161.313			0.203421
$794$	−470.336			−0.592363
$795$		0			0
$796$		−	152.381i		−	0.191433i
$797$	279.729			0.350978			0.175489	−	0.984481i	$-0.443849\pi$
$797$	279.729			0.350978			0.175489	+	0.984481i	$0.443849\pi$
$798$		−	356.451i		−	0.446680i
$799$			535.787i			0.670572i
$800$		0			0
$801$			124.013i			0.154823i
$802$	73.2291			0.0913081
$803$	−187.112			−0.233016
$804$			330.120i			0.410598i
$805$		0			0
$806$	−484.870			−0.601576
$807$		−	992.762i		−	1.23019i
$808$			286.627i			0.354737i
$809$	−1156.82			−1.42994			−0.714968	−	0.699157i	$-0.753559\pi$
$809$	−1156.82			−1.42994			−0.714968	+	0.699157i	$0.753559\pi$
$810$		0			0
$811$	1178.54			1.45319			0.726594	−	0.687067i	$-0.241102\pi$
$811$	1178.54			1.45319			0.726594	+	0.687067i	$0.241102\pi$
$812$	−274.822			−0.338451
$813$		−	238.569i		−	0.293442i
$814$	217.760			0.267519
$815$		0			0
$816$		−	166.680i		−	0.204265i
$817$		−	799.391i		−	0.978447i
$818$			362.164i			0.442743i
$819$			127.904i			0.156171i
$820$		0			0
$821$	−732.347			−0.892019			−0.446009	−	0.895028i	$-0.647155\pi$
$821$	−732.347			−0.892019			−0.446009	+	0.895028i	$0.647155\pi$
$822$	−224.661			−0.273311
$823$			882.012i			1.07170i	0.844312	+	0.535852i	$0.180009\pi$
$823$			882.012i			1.07170i	−0.844312	+	0.535852i	$0.819991\pi$
$824$		−	287.224i		−	0.348573i
$825$		0			0
$826$			144.886i			0.175407i
$827$	−1039.74			−1.25724			−0.628619	−	0.777713i	$-0.716380\pi$
$827$	−1039.74			−1.25724			−0.628619	+	0.777713i	$0.716380\pi$
$828$	−144.561	+	19.6670i	−0.174590	+	0.0237524i
$829$	−413.505			−0.498799			−0.249400	−	0.968401i	$-0.580233\pi$
$829$	−413.505			−0.498799			−0.249400	+	0.968401i	$0.580233\pi$
$830$		0			0
$831$	500.512			0.602301
$832$			82.5097i			0.0991703i
$833$	581.855			0.698506
$834$	−100.409			−0.120395
$835$		0			0
$836$	−208.804			−0.249766
$837$			976.828i			1.16706i
$838$	−341.736			−0.407799
$839$		−	254.486i		−	0.303320i	−0.988433	−	0.151660i	$-0.951538\pi$
$839$		−	254.486i		−	0.303320i	0.988433	−	0.151660i	$-0.0484619\pi$
$840$		0			0
$841$	393.970			0.468454
$842$	442.451			0.525476
$843$	74.8487			0.0887885
$844$	142.343			0.168653
$845$		0			0
$846$	−139.230			−0.164575
$847$	−413.345			−0.488011
$848$	−244.883			−0.288777
$849$		−	545.342i		−	0.642334i
$850$		0			0
$851$	−897.460	+	122.096i	−1.05459	+	0.143474i
$852$			537.245i			0.630569i
$853$		−	744.132i		−	0.872370i	−0.899857	−	0.436185i	$-0.856329\pi$
$853$		−	744.132i		−	0.872370i	0.899857	−	0.436185i	$-0.143671\pi$
$854$	−86.4895			−0.101276
$855$		0			0
$856$		−	213.602i		−	0.249535i
$857$		−	578.921i		−	0.675520i	−0.941232	−	0.337760i	$-0.890331\pi$
$857$		−	578.921i		−	0.675520i	0.941232	−	0.337760i	$-0.109669\pi$
$858$	−137.689			−0.160477
$859$	1395.20			1.62421			0.812106	−	0.583510i	$-0.198321\pi$
$859$	1395.20			1.62421			0.812106	+	0.583510i	$0.198321\pi$
$860$		0			0
$861$		−	127.300i		−	0.147852i
$862$	−950.934			−1.10317
$863$		−	565.704i		−	0.655508i	−0.944763	−	0.327754i	$-0.893708\pi$
$863$		−	565.704i		−	0.655508i	0.944763	−	0.327754i	$-0.106292\pi$
$864$	166.225			0.192391
$865$		0			0
$866$			559.200i			0.645728i
$867$			21.5269i			0.0248292i
$868$	259.968			0.299502
$869$	−460.853			−0.530325
$870$		0			0
$871$			705.150i			0.809587i
$872$	−392.127			−0.449687
$873$	−209.576			−0.240065
$874$	860.548	−	117.074i	0.984609	−	0.133952i
$875$		0			0
$876$	−231.054			−0.263760
$877$		−	468.112i		−	0.533765i	−0.963729	−	0.266882i	$-0.914006\pi$
$877$		−	468.112i		−	0.533765i	0.963729	−	0.266882i	$-0.0859935\pi$
$878$			1183.69i			1.34817i
$879$			391.341i			0.445212i
$880$		0			0
$881$		−	1317.52i		−	1.49548i	−0.663990	−	0.747741i	$-0.731138\pi$
$881$		−	1317.52i		−	1.49548i	0.663990	−	0.747741i	$-0.268862\pi$
$882$			151.202i			0.171431i
$883$			257.377i			0.291480i	0.989323	+	0.145740i	$0.0465563\pi$
$883$			257.377i			0.291480i	−0.989323	+	0.145740i	$0.953444\pi$
$884$		−	356.035i		−	0.402754i
$885$		0			0
$886$	322.306			0.363776
$887$			331.722i			0.373982i	0.982362	+	0.186991i	$0.0598735\pi$
$887$			331.722i			0.373982i	−0.982362	+	0.186991i	$0.940126\pi$
$888$	268.900			0.302815
$889$		−	142.290i		−	0.160056i
$890$		0			0
$891$			165.779i			0.186059i
$892$		−	168.167i		−	0.188527i
$893$	828.818			0.928128
$894$		−	11.0596i		−	0.0123709i
$895$		0			0
$896$		−	44.2384i		−	0.0493732i
$897$	567.461	−	77.2010i	0.632621	−	0.0860658i
$898$		−	620.867i		−	0.691389i
$899$	−1168.22			−1.29946
$900$		0			0
$901$	1056.69			1.17279
$902$	−74.5709			−0.0826728
$903$			282.627i			0.312987i
$904$		−	511.099i		−	0.565375i
$905$		0			0
$906$	−8.24264			−0.00909784
$907$	−436.596			−0.481362			−0.240681	−	0.970604i	$-0.577371\pi$
$907$	−436.596			−0.481362			−0.240681	+	0.970604i	$0.577371\pi$
$908$	−526.184			−0.579498
$909$	321.401			0.353577
$910$		0			0
$911$		−	1530.29i		−	1.67979i	−0.542749	−	0.839895i	$-0.682617\pi$
$911$		−	1530.29i		−	1.67979i	0.542749	−	0.839895i	$-0.317383\pi$
$912$	−257.840			−0.282719
$913$			292.670i			0.320559i
$914$		−	56.8025i		−	0.0621472i
$915$		0			0
$916$		−	282.643i		−	0.308562i
$917$	255.665			0.278806
$918$	−717.274			−0.781344
$919$			676.783i			0.736434i	0.929740	+	0.368217i	$0.120032\pi$
$919$			676.783i			0.736434i	−0.929740	+	0.368217i	$0.879968\pi$
$920$		0			0
$921$	−826.382			−0.897266
$922$		−	92.8802i		−	0.100738i
$923$			1147.58i			1.24331i
$924$	73.8234			0.0798954
$925$		0			0
$926$	952.382			1.02849
$927$	−322.070			−0.347432
$928$			198.794i			0.214218i
$929$	686.535			0.739004			0.369502	−	0.929230i	$-0.379528\pi$
$929$	686.535			0.739004			0.369502	+	0.929230i	$0.379528\pi$
$930$		0			0
$931$		−	900.082i		−	0.966791i
$932$		−	707.568i		−	0.759193i
$933$			1121.77i			1.20233i
$934$		−	439.375i		−	0.470422i
$935$		0			0
$936$	92.5198			0.0988459
$937$	774.354			0.826418			0.413209	−	0.910636i	$-0.364408\pi$
$937$	774.354			0.826418			0.413209	+	0.910636i	$0.364408\pi$
$938$		−	378.073i		−	0.403063i
$939$			229.798i			0.244726i
$940$		0			0
$941$		−	774.814i		−	0.823395i	−0.911321	−	0.411697i	$-0.864936\pi$
$941$		−	774.814i		−	0.823395i	0.911321	−	0.411697i	$-0.135064\pi$
$942$	251.362			0.266838
$943$	307.330	−	41.8112i	0.325907	−	0.0443385i
$944$	104.804			0.111021
$945$		0			0
$946$	165.559			0.175010
$947$		−	1090.69i		−	1.15173i	−0.817545	−	0.575865i	$-0.804665\pi$
$947$		−	1090.69i		−	1.15173i	0.817545	−	0.575865i	$-0.195335\pi$
$948$	−569.081			−0.600296
$949$	−493.540			−0.520063
$950$		0			0
$951$	507.328			0.533468
$952$			190.891i			0.200516i
$953$	−60.7603			−0.0637569			−0.0318785	−	0.999492i	$-0.510149\pi$
$953$	−60.7603			−0.0637569			−0.0318785	+	0.999492i	$0.510149\pi$
$954$			274.592i			0.287833i
$955$		0			0
$956$	−544.573			−0.569637
$957$	−331.740			−0.346646
$958$	−325.932			−0.340222
$959$	257.295			0.268295
$960$		0			0
$961$	144.073			0.149920
$962$	574.380			0.597069
$963$	−239.516			−0.248719
$964$		−	887.356i		−	0.920493i
$965$		0			0
$966$	−304.250	+	41.3921i	−0.314958	+	0.0428489i
$967$			1715.83i			1.77438i	0.461400	+	0.887192i	$0.347347\pi$
$967$			1715.83i			1.77438i	−0.461400	+	0.887192i	$0.652653\pi$
$968$			298.995i			0.308879i
$969$	1112.60			1.14819
$970$		0			0
$971$		−	1071.57i		−	1.10358i	−0.833984	−	0.551789i	$-0.813946\pi$
$971$		−	1071.57i		−	1.10358i	0.833984	−	0.551789i	$-0.186054\pi$
$972$		−	324.215i		−	0.333555i
$973$	114.994			0.118185
$974$	526.596			0.540653
$975$		0			0
$976$			62.5625i			0.0641009i
$977$	−456.079			−0.466816			−0.233408	−	0.972379i	$-0.574988\pi$
$977$	−456.079			−0.466816			−0.233408	+	0.972379i	$0.574988\pi$
$978$		−	428.777i		−	0.438422i
$979$	152.893			0.156173
$980$		0			0
$981$			439.700i			0.448216i
$982$		−	364.905i		−	0.371593i
$983$	−216.055			−0.219791			−0.109896	−	0.993943i	$-0.535052\pi$
$983$	−216.055			−0.219791			−0.109896	+	0.993943i	$0.535052\pi$
$984$	−92.0833			−0.0935805
$985$		0			0
$986$		−	857.809i		−	0.869989i
$987$	−293.032			−0.296891
$988$	−550.757			−0.557446
$989$	−682.323	+	92.8276i	−0.689912	+	0.0938600i
$990$		0			0
$991$	−520.142			−0.524866			−0.262433	−	0.964950i	$-0.584525\pi$
$991$	−520.142			−0.524866			−0.262433	+	0.964950i	$0.584525\pi$
$992$		−	188.049i		−	0.189565i
$993$			160.019i			0.161147i
$994$		−	615.284i		−	0.618998i
$995$		0			0
$996$			361.402i			0.362853i
$997$			466.877i			0.468282i	0.972203	+	0.234141i	$0.0752277\pi$
$997$			466.877i			0.468282i	−0.972203	+	0.234141i	$0.924772\pi$
$998$		−	527.144i		−	0.528201i
$999$		−	1157.16i		−	1.15831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.3.c.a.1149.3		8
5.2	odd	4		1150.3.d.a.551.3		4
5.3	odd	4		46.3.b.a.45.2	yes	4
5.4	even	2	inner	1150.3.c.a.1149.6		8
15.8	even	4		414.3.b.a.91.3		4
20.3	even	4		368.3.f.c.321.4		4
23.22	odd	2	inner	1150.3.c.a.1149.4		8
40.3	even	4		1472.3.f.c.321.1		4
40.13	odd	4		1472.3.f.f.321.3		4
115.22	even	4		1150.3.d.a.551.4		4
115.68	even	4		46.3.b.a.45.1	✓	4
115.114	odd	2	inner	1150.3.c.a.1149.5		8
345.68	odd	4		414.3.b.a.91.4		4
460.183	odd	4		368.3.f.c.321.3		4
920.413	even	4		1472.3.f.f.321.4		4
920.643	odd	4		1472.3.f.c.321.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.3.b.a.45.1	✓	4	115.68	even	4
46.3.b.a.45.2	yes	4	5.3	odd	4
368.3.f.c.321.3		4	460.183	odd	4
368.3.f.c.321.4		4	20.3	even	4
414.3.b.a.91.3		4	15.8	even	4
414.3.b.a.91.4		4	345.68	odd	4
1150.3.c.a.1149.3		8	1.1	even	1	trivial
1150.3.c.a.1149.4		8	23.22	odd	2	inner
1150.3.c.a.1149.5		8	115.114	odd	2	inner
1150.3.c.a.1149.6		8	5.4	even	2	inner
1150.3.d.a.551.3		4	5.2	odd	4
1150.3.d.a.551.4		4	115.22	even	4
1472.3.f.c.321.1		4	40.3	even	4
1472.3.f.c.321.2		4	920.643	odd	4
1472.3.f.f.321.3		4	40.13	odd	4
1472.3.f.f.321.4		4	920.413	even	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1150.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +2.41421i q^{3} -2.00000 q^{4} +3.41421 q^{6} -3.91016 q^{7} +2.82843i q^{8} +3.17157 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +2.41421i q^{3} -2.00000 q^{4} +3.41421 q^{6} -3.91016 q^{7} +2.82843i q^{8} +3.17157 q^{9} -3.91016i q^{11} -4.82843i q^{12} -10.3137i q^{13} +5.52980i q^{14} +4.00000 q^{16} -17.2603 q^{17} -4.48528i q^{18} +26.7002i q^{19} -9.43995i q^{21} -5.52980 q^{22} +(22.7901 - 3.10051i) q^{23} -6.82843 q^{24} -14.5858 q^{26} +29.3848i q^{27} +7.82031 q^{28} -35.1421 q^{29} +33.2426 q^{31} -5.65685i q^{32} +9.43995 q^{33} +24.4097i q^{34} -6.34315 q^{36} -39.3794 q^{37} +37.7598 q^{38} +24.8995 q^{39} +13.4853 q^{41} -13.3501 q^{42} -29.9395 q^{43} +7.82031i q^{44} +(-4.38478 - 32.2300i) q^{46} -31.0416i q^{47} +9.65685i q^{48} -33.7107 q^{49} -41.6700i q^{51} +20.6274i q^{52} -61.2207 q^{53} +41.5563 q^{54} -11.0596i q^{56} -64.4600 q^{57} +49.6985i q^{58} +26.2010 q^{59} +15.6406i q^{61} -47.0122i q^{62} -12.4013 q^{63} -8.00000 q^{64} -13.3501i q^{66} -68.3702 q^{67} +34.5205 q^{68} +(7.48528 + 55.0201i) q^{69} -111.267 q^{71} +8.97056i q^{72} -47.8528i q^{73} +55.6910i q^{74} -53.4004i q^{76} +15.2893i q^{77} -35.2132i q^{78} -117.860i q^{79} -42.3970 q^{81} -19.0711i q^{82} -74.8487 q^{83} +18.8799i q^{84} +42.3408i q^{86} -84.8406i q^{87} +11.0596 q^{88} +39.1016i q^{89} +40.3282i q^{91} +(-45.5801 + 6.20101i) q^{92} +80.2548i q^{93} -43.8995 q^{94} +13.6569 q^{96} -66.0797 q^{97} +47.6741i q^{98} -12.4013i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{4} + 16 q^{6} + 48 q^{9}+O(q^{10}) \) 8 * q - 16 * q^4 + 16 * q^6 + 48 * q^9	\( 8 q - 16 q^{4} + 16 q^{6} + 48 q^{9} + 32 q^{16} - 32 q^{24} - 128 q^{26} - 168 q^{29} + 232 q^{31} - 96 q^{36} + 120 q^{39} + 40 q^{41} + 112 q^{46} + 296 q^{49} + 208 q^{54} + 368 q^{59} - 64 q^{64} - 8 q^{69} - 200 q^{71} + 136 q^{81} - 272 q^{94} + 64 q^{96}+O(q^{100}) \) 8 * q - 16 * q^4 + 16 * q^6 + 48 * q^9 + 32 * q^16 - 32 * q^24 - 128 * q^26 - 168 * q^29 + 232 * q^31 - 96 * q^36 + 120 * q^39 + 40 * q^41 + 112 * q^46 + 296 * q^49 + 208 * q^54 + 368 * q^59 - 64 * q^64 - 8 * q^69 - 200 * q^71 + 136 * q^81 - 272 * q^94 + 64 * q^96

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