LMFDB - Embedded newform 912.2.f.h.113.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(113,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("912.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.f (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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.20322144469993472.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - x^{8} - 2x^{7} - 2x^{6} + 22x^{5} - 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 $ x^10 - x^9 - x^8 - 2x^7 - 2x^6 + 22x^5 - 6x^4 - 18x^3 - 27x^2 - 81*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			113.7
Root			$-0.729858 + 1.57077i$ of defining polynomial
Character	$\chi$	$=$	912.113
Dual form			912.2.f.h.113.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.729858 - 1.57077i) q^{3} -1.22502i q^{5} +2.80880 q^{7} +(-1.93462 - 2.29287i) q^{9} +O(q^{10})$	\(q+(0.729858 - 1.57077i) q^{3} -1.22502i q^{5} +2.80880 q^{7} +(-1.93462 - 2.29287i) q^{9} +2.49828i q^{11} -1.86827i q^{13} +(-1.92421 - 0.894087i) q^{15} -4.88146i q^{17} +(4.12897 - 1.39700i) q^{19} +(2.05003 - 4.41197i) q^{21} +0.424059i q^{23} +3.49934 q^{25} +(-5.01356 + 1.36536i) q^{27} -3.86923 q^{29} +0.514909i q^{31} +(3.92421 + 1.82339i) q^{33} -3.44083i q^{35} -5.16750i q^{37} +(-2.93462 - 1.36357i) q^{39} -2.40952 q^{41} -0.420092 q^{43} +(-2.80880 + 2.36993i) q^{45} +10.7405i q^{47} +0.889372 q^{49} +(-7.66763 - 3.56277i) q^{51} -7.71766 q^{53} +3.06043 q^{55} +(0.819206 - 7.50526i) q^{57} -3.63841 q^{59} -1.85900 q^{61} +(-5.43395 - 6.44022i) q^{63} -2.28866 q^{65} -14.1012i q^{67} +(0.666098 + 0.309503i) q^{69} +15.5869 q^{71} +11.9862 q^{73} +(2.55402 - 5.49664i) q^{75} +7.01717i q^{77} -1.61516i q^{79} +(-1.51452 + 8.87165i) q^{81} -5.68241i q^{83} -5.97986 q^{85} +(-2.82399 + 6.07766i) q^{87} -11.4660 q^{89} -5.24760i q^{91} +(0.808803 + 0.375811i) q^{93} +(-1.71134 - 5.05805i) q^{95} -2.48325i q^{97} +(5.72823 - 4.83321i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{3} + 2 q^{7} + 3 q^{9}+O(q^{10}) $ 10 * q - q^3 + 2 * q^7 + 3 * q^9	$ 10 q - q^{3} + 2 q^{7} + 3 q^{9} + 10 q^{15} - 2 q^{19} - 5 q^{21} - 14 q^{25} - 10 q^{27} + 6 q^{29} + 10 q^{33} - 7 q^{39} + 4 q^{41} - 20 q^{43} - 2 q^{45} + 16 q^{49} + q^{51} + 26 q^{53} + 12 q^{55} - 11 q^{57} + 2 q^{59} - 4 q^{61} + 17 q^{63} - 32 q^{65} + 27 q^{69} + 8 q^{71} - 26 q^{73} + 39 q^{75} + 23 q^{81} - 8 q^{85} - 13 q^{87} - 4 q^{89} - 18 q^{93} - 8 q^{95} - 2 q^{99}+O(q^{100}) $ 10 * q - q^3 + 2 * q^7 + 3 * q^9 + 10 * q^15 - 2 * q^19 - 5 * q^21 - 14 * q^25 - 10 * q^27 + 6 * q^29 + 10 * q^33 - 7 * q^39 + 4 * q^41 - 20 * q^43 - 2 * q^45 + 16 * q^49 + q^51 + 26 * q^53 + 12 * q^55 - 11 * q^57 + 2 * q^59 - 4 * q^61 + 17 * q^63 - 32 * q^65 + 27 * q^69 + 8 * q^71 - 26 * q^73 + 39 * q^75 + 23 * q^81 - 8 * q^85 - 13 * q^87 - 4 * q^89 - 18 * q^93 - 8 * q^95 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.729858	−	1.57077i	0.421383	−	0.906883i
$3$	0.729858	−	1.57077i	0.421383	−	0.906883i
$4$		0			0
$5$		−	1.22502i		−	0.547843i	−0.961752	−	0.273922i	$-0.911679\pi$
$5$		−	1.22502i		−	0.547843i	0.961752	−	0.273922i	$-0.0883209\pi$
$6$		0			0
$7$	2.80880			1.06163			0.530814	−	0.847488i	$-0.321886\pi$
$7$	2.80880			1.06163			0.530814	+	0.847488i	$0.321886\pi$
$8$		0			0
$9$	−1.93462	−	2.29287i	−0.644872	−	0.764291i
$10$		0			0
$11$			2.49828i			0.753259i	0.926364	+	0.376630i	$0.122917\pi$
$11$			2.49828i			0.753259i	−0.926364	+	0.376630i	$0.877083\pi$
$12$		0			0
$13$		−	1.86827i		−	0.518165i	−0.965855	−	0.259082i	$-0.916580\pi$
$13$		−	1.86827i		−	0.518165i	0.965855	−	0.259082i	$-0.0834201\pi$
$14$		0			0
$15$	−1.92421	−	0.894087i	−0.496830	−	0.230852i
$16$		0			0
$17$		−	4.88146i		−	1.18393i	−0.805965	−	0.591964i	$-0.798353\pi$
$17$		−	4.88146i		−	1.18393i	0.805965	−	0.591964i	$-0.201647\pi$
$18$		0			0
$19$	4.12897	−	1.39700i	0.947251	−	0.320493i
$19$	4.12897	−	1.39700i	0.947251	−	0.320493i
$20$		0			0
$21$	2.05003	−	4.41197i	0.447352	−	0.962772i
$22$		0			0
$23$			0.424059i			0.0884224i	0.999022	+	0.0442112i	$0.0140775\pi$
$23$			0.424059i			0.0884224i	−0.999022	+	0.0442112i	$0.985923\pi$
$24$		0			0
$25$	3.49934			0.699868
$26$		0			0
$27$	−5.01356	+	1.36536i	−0.964860	+	0.262764i
$28$		0			0
$29$	−3.86923			−0.718498			−0.359249	−	0.933242i	$-0.616967\pi$
$29$	−3.86923			−0.718498			−0.359249	+	0.933242i	$0.616967\pi$
$30$		0			0
$31$			0.514909i			0.0924805i	0.998930	+	0.0462402i	$0.0147240\pi$
$31$			0.514909i			0.0924805i	−0.998930	+	0.0462402i	$0.985276\pi$
$32$		0			0
$33$	3.92421	+	1.82339i	0.683118	+	0.317411i
$34$		0			0
$35$		−	3.44083i		−	0.581606i
$36$		0			0
$37$		−	5.16750i		−	0.849532i	−0.905303	−	0.424766i	$-0.860356\pi$
$37$		−	5.16750i		−	0.849532i	0.905303	−	0.424766i	$-0.139644\pi$
$38$		0			0
$39$	−2.93462	−	1.36357i	−0.469915	−	0.218346i
$40$		0			0
$41$	−2.40952			−0.376303			−0.188152	−	0.982140i	$-0.560250\pi$
$41$	−2.40952			−0.376303			−0.188152	+	0.982140i	$0.560250\pi$
$42$		0			0
$43$	−0.420092			−0.0640635			−0.0320317	−	0.999487i	$-0.510198\pi$
$43$	−0.420092			−0.0640635			−0.0320317	+	0.999487i	$0.510198\pi$
$44$		0			0
$45$	−2.80880	+	2.36993i	−0.418712	+	0.353289i
$46$		0			0
$47$			10.7405i			1.56666i	0.621607	+	0.783329i	$0.286480\pi$
$47$			10.7405i			1.56666i	−0.621607	+	0.783329i	$0.713520\pi$
$48$		0			0
$49$	0.889372			0.127053
$50$		0			0
$51$	−7.66763	−	3.56277i	−1.07368	−	0.498887i
$52$		0			0
$53$	−7.71766			−1.06010			−0.530051	−	0.847966i	$-0.677827\pi$
$53$	−7.71766			−1.06010			−0.530051	+	0.847966i	$0.677827\pi$
$54$		0			0
$55$	3.06043			0.412668
$56$		0			0
$57$	0.819206	−	7.50526i	0.108506	−	0.994096i
$58$		0			0
$59$	−3.63841			−0.473681			−0.236840	−	0.971549i	$-0.576112\pi$
$59$	−3.63841			−0.473681			−0.236840	+	0.971549i	$0.576112\pi$
$60$		0			0
$61$	−1.85900			−0.238021			−0.119010	−	0.992893i	$-0.537972\pi$
$61$	−1.85900			−0.238021			−0.119010	+	0.992893i	$0.537972\pi$
$62$		0			0
$63$	−5.43395	−	6.44022i	−0.684614	−	0.811392i
$64$		0			0
$65$	−2.28866			−0.283873
$66$		0			0
$67$		−	14.1012i		−	1.72274i	−0.507982	−	0.861368i	$-0.669608\pi$
$67$		−	14.1012i		−	1.72274i	0.507982	−	0.861368i	$-0.330392\pi$
$68$		0			0
$69$	0.666098	+	0.309503i	0.0801888	+	0.0372598i
$70$		0			0
$71$	15.5869			1.84982			0.924912	−	0.380182i	$-0.124139\pi$
$71$	15.5869			1.84982			0.924912	+	0.380182i	$0.124139\pi$
$72$		0			0
$73$	11.9862			1.40288			0.701438	−	0.712731i	$-0.252542\pi$
$73$	11.9862			1.40288			0.701438	+	0.712731i	$0.252542\pi$
$74$		0			0
$75$	2.55402	−	5.49664i	0.294913	−	0.634698i
$76$		0			0
$77$			7.01717i			0.799681i
$78$		0			0
$79$		−	1.61516i		−	0.181719i	−0.995864	−	0.0908597i	$-0.971039\pi$
$79$		−	1.61516i		−	0.181719i	0.995864	−	0.0908597i	$-0.0289615\pi$
$80$		0			0
$81$	−1.51452	+	8.87165i	−0.168280	+	0.985739i
$82$		0			0
$83$		−	5.68241i		−	0.623726i	−0.950127	−	0.311863i	$-0.899047\pi$
$83$		−	5.68241i		−	0.623726i	0.950127	−	0.311863i	$-0.100953\pi$
$84$		0			0
$85$	−5.97986			−0.648607
$86$		0			0
$87$	−2.82399	+	6.07766i	−0.302763	+	0.651594i
$88$		0			0
$89$	−11.4660			−1.21540			−0.607698	−	0.794168i	$-0.707907\pi$
$89$	−11.4660			−1.21540			−0.607698	+	0.794168i	$0.707907\pi$
$90$		0			0
$91$		−	5.24760i		−	0.550098i
$92$		0			0
$93$	0.808803	+	0.375811i	0.0838689	+	0.0389697i
$94$		0			0
$95$	−1.71134	−	5.05805i	−0.175580	−	0.518945i
$96$		0			0
$97$		−	2.48325i		−	0.252136i	−0.992022	−	0.126068i	$-0.959764\pi$
$97$		−	2.48325i		−	0.252136i	0.992022	−	0.126068i	$-0.0402358\pi$
$98$		0			0
$99$	5.72823	−	4.83321i	0.575709	−	0.485756i
$100$		0			0
$101$			15.9455i			1.58663i	0.608809	+	0.793317i	$0.291647\pi$
$101$			15.9455i			1.58663i	−0.608809	+	0.793317i	$0.708353\pi$
$102$		0			0
$103$			17.8913i			1.76289i	0.472290	+	0.881443i	$0.343427\pi$
$103$			17.8913i			1.76289i	−0.472290	+	0.881443i	$0.656573\pi$
$104$		0			0
$105$	−5.40473	−	2.51131i	−0.527448	−	0.245079i
$106$		0			0
$107$	1.33220			0.128788			0.0643941	−	0.997925i	$-0.479489\pi$
$107$	1.33220			0.128788			0.0643941	+	0.997925i	$0.479489\pi$
$108$		0			0
$109$			16.5645i			1.58659i	0.608838	+	0.793294i	$0.291636\pi$
$109$			16.5645i			1.58659i	−0.608838	+	0.793294i	$0.708364\pi$
$110$		0			0
$111$	−8.11694	−	3.77154i	−0.770426	−	0.357979i
$112$		0			0
$113$	16.7157			1.57248			0.786242	−	0.617919i	$-0.212024\pi$
$113$	16.7157			1.57248			0.786242	+	0.617919i	$0.212024\pi$
$114$		0			0
$115$	0.519479			0.0484417
$116$		0			0
$117$	−4.28370	+	3.61438i	−0.396029	+	0.334150i
$118$		0			0
$119$		−	13.7111i		−	1.25689i
$120$		0			0
$121$	4.75860			0.432600
$122$		0			0
$123$	−1.75860	+	3.78479i	−0.158568	+	0.341263i
$124$		0			0
$125$		−	10.4118i		−	0.931261i
$126$		0			0
$127$			7.20314i			0.639176i	0.947557	+	0.319588i	$0.103544\pi$
$127$			7.20314i			0.639176i	−0.947557	+	0.319588i	$0.896456\pi$
$128$		0			0
$129$	−0.306608	+	0.659867i	−0.0269953	+	0.0580980i
$130$		0			0
$131$			0.0482485i			0.00421550i	0.999998	+	0.00210775i	$0.000670917\pi$
$131$			0.0482485i			0.00421550i	−0.999998	+	0.00210775i	$0.999329\pi$
$132$		0			0
$133$	11.5975	−	3.92389i	1.00563	−	0.340244i
$134$		0			0
$135$	1.67259	+	6.14169i	0.143953	+	0.528592i
$136$		0			0
$137$		−	16.8562i		−	1.44012i	−0.693912	−	0.720060i	$-0.744114\pi$
$137$		−	16.8562i		−	1.44012i	0.693912	−	0.720060i	$-0.255886\pi$
$138$		0			0
$139$	−10.5169			−0.892031			−0.446016	−	0.895025i	$-0.647157\pi$
$139$	−10.5169			−0.892031			−0.446016	+	0.895025i	$0.647157\pi$
$140$		0			0
$141$	16.8708	+	7.83901i	1.42077	+	0.660164i
$142$		0			0
$143$	4.66746			0.390312
$144$		0			0
$145$			4.73987i			0.393625i
$146$		0			0
$147$	0.649115	−	1.39700i	0.0535381	−	0.115222i
$148$		0			0
$149$			4.61966i			0.378457i	0.981933	+	0.189229i	$0.0605987\pi$
$149$			4.61966i			0.378457i	−0.981933	+	0.189229i	$0.939401\pi$
$150$		0			0
$151$			17.9811i			1.46328i	0.681690	+	0.731641i	$0.261245\pi$
$151$			17.9811i			1.46328i	−0.681690	+	0.731641i	$0.738755\pi$
$152$		0			0
$153$	−11.1926	+	9.44375i	−0.904865	+	0.763482i
$154$		0			0
$155$	0.630772			0.0506648
$156$		0			0
$157$	−1.77874			−0.141959			−0.0709796	−	0.997478i	$-0.522613\pi$
$157$	−1.77874			−0.141959			−0.0709796	+	0.997478i	$0.522613\pi$
$158$		0			0
$159$	−5.63279	+	12.1226i	−0.446709	+	0.961388i
$160$		0			0
$161$			1.19110i			0.0938717i
$162$		0			0
$163$	15.4565			1.21064			0.605322	−	0.795981i	$-0.293044\pi$
$163$	15.4565			1.21064			0.605322	+	0.795981i	$0.293044\pi$
$164$		0			0
$165$	2.23368	−	4.80722i	0.173892	−	0.374242i
$166$		0			0
$167$	−4.46164			−0.345252			−0.172626	−	0.984987i	$-0.555225\pi$
$167$	−4.46164			−0.345252			−0.172626	+	0.984987i	$0.555225\pi$
$168$		0			0
$169$	9.50957			0.731505
$170$		0			0
$171$	−11.1911	−	6.76455i	−0.855805	−	0.517298i
$172$		0			0
$173$	19.0529			1.44857			0.724283	−	0.689502i	$-0.242171\pi$
$173$	19.0529			1.44857			0.724283	+	0.689502i	$0.242171\pi$
$174$		0			0
$175$	9.82895			0.742999
$176$		0			0
$177$	−2.65552	+	5.71510i	−0.199601	+	0.429573i
$178$		0			0
$179$	15.9759			1.19410			0.597049	−	0.802205i	$-0.296340\pi$
$179$	15.9759			1.19410			0.597049	+	0.802205i	$0.296340\pi$
$180$		0			0
$181$		−	5.25727i		−	0.390770i	−0.980727	−	0.195385i	$-0.937404\pi$
$181$		−	5.25727i		−	0.390770i	0.980727	−	0.195385i	$-0.0625956\pi$
$182$		0			0
$183$	−1.35681	+	2.92006i	−0.100298	+	0.215857i
$184$		0			0
$185$	−6.33027			−0.465411
$186$		0			0
$187$	12.1952			0.891804
$188$		0			0
$189$	−14.0821	+	3.83503i	−1.02432	+	0.278957i
$190$		0			0
$191$			5.33309i			0.385889i	0.981210	+	0.192945i	$0.0618038\pi$
$191$			5.33309i			0.385889i	−0.981210	+	0.192945i	$0.938196\pi$
$192$		0			0
$193$			21.2027i			1.52621i	0.646277	+	0.763103i	$0.276325\pi$
$193$			21.2027i			1.52621i	−0.646277	+	0.763103i	$0.723675\pi$
$194$		0			0
$195$	−1.67039	+	3.59495i	−0.119619	+	0.257440i
$196$		0			0
$197$		−	20.6853i		−	1.47377i	−0.676019	−	0.736884i	$-0.736296\pi$
$197$		−	20.6853i		−	1.47377i	0.676019	−	0.736884i	$-0.263704\pi$
$198$		0			0
$199$	−3.09080			−0.219101			−0.109550	−	0.993981i	$-0.534941\pi$
$199$	−3.09080			−0.219101			−0.109550	+	0.993981i	$0.534941\pi$
$200$		0			0
$201$	−22.1497	−	10.2919i	−1.56232	−	0.725932i
$202$		0			0
$203$	−10.8679			−0.762778
$204$		0			0
$205$			2.95169i			0.206155i
$206$		0			0
$207$	0.972313	−	0.820392i	0.0675804	−	0.0570212i
$208$		0			0
$209$	3.49009	+	10.3153i	0.241414	+	0.713526i
$210$		0			0
$211$			6.02995i			0.415119i	0.978222	+	0.207560i	$0.0665521\pi$
$211$			6.02995i			0.415119i	−0.978222	+	0.207560i	$0.933448\pi$
$212$		0			0
$213$	11.3762	−	24.4834i	0.779485	−	1.67757i
$214$		0			0
$215$			0.514619i			0.0350967i
$216$		0			0
$217$			1.44628i			0.0981798i
$218$		0			0
$219$	8.74820	−	18.8275i	0.591149	−	1.27224i
$220$		0			0
$221$	−9.11988			−0.613470
$222$		0			0
$223$			12.5462i			0.840153i	0.907489	+	0.420076i	$0.137997\pi$
$223$			12.5462i			0.840153i	−0.907489	+	0.420076i	$0.862003\pi$
$224$		0			0
$225$	−6.76987	−	8.02353i	−0.451325	−	0.534902i
$226$		0			0
$227$	−23.0562			−1.53029			−0.765146	−	0.643857i	$-0.777333\pi$
$227$	−23.0562			−1.53029			−0.765146	+	0.643857i	$0.777333\pi$
$228$		0			0
$229$	−11.4971			−0.759748			−0.379874	−	0.925038i	$-0.624033\pi$
$229$	−11.4971			−0.759748			−0.379874	+	0.925038i	$0.624033\pi$
$230$		0			0
$231$	11.0223	+	5.12154i	0.725217	+	0.336972i
$232$		0			0
$233$			14.7204i			0.964369i	0.876070	+	0.482184i	$0.160156\pi$
$233$			14.7204i			0.964369i	−0.876070	+	0.482184i	$0.839844\pi$
$234$		0			0
$235$	13.1572			0.858283
$236$		0			0
$237$	−2.53704	−	1.17884i	−0.164798	−	0.0765736i
$238$		0			0
$239$			25.6025i			1.65609i	0.560663	+	0.828044i	$0.310546\pi$
$239$			25.6025i			1.65609i	−0.560663	+	0.828044i	$0.689454\pi$
$240$		0			0
$241$			3.66611i			0.236155i	0.993004	+	0.118077i	$0.0376731\pi$
$241$			3.66611i			0.236155i	−0.993004	+	0.118077i	$0.962327\pi$
$242$		0			0
$243$	12.8299	+	8.85401i	0.823039	+	0.567985i
$244$		0			0
$245$		−	1.08949i		−	0.0696052i
$246$		0			0
$247$	−2.60997	−	7.71403i	−0.166068	−	0.490832i
$248$		0			0
$249$	−8.92575	−	4.14735i	−0.565646	−	0.262828i
$250$		0			0
$251$			27.2774i			1.72173i	0.508832	+	0.860866i	$0.330077\pi$
$251$			27.2774i			1.72173i	−0.508832	+	0.860866i	$0.669923\pi$
$252$		0			0
$253$	−1.05942			−0.0666050
$254$		0			0
$255$	−4.36445	+	9.39296i	−0.273312	+	0.588210i
$256$		0			0
$257$	10.5562			0.658476			0.329238	−	0.944247i	$-0.393208\pi$
$257$	10.5562			0.658476			0.329238	+	0.944247i	$0.393208\pi$
$258$		0			0
$259$		−	14.5145i		−	0.901887i
$260$		0			0
$261$	7.48548	+	8.87165i	0.463339	+	0.549142i
$262$		0			0
$263$		−	13.8784i		−	0.855780i	−0.903831	−	0.427890i	$-0.859257\pi$
$263$		−	13.8784i		−	0.855780i	0.903831	−	0.427890i	$-0.140743\pi$
$264$		0			0
$265$			9.45425i			0.580770i
$266$		0			0
$267$	−8.36857	+	18.0105i	−0.512148	+	1.10222i
$268$		0			0
$269$	9.60804			0.585813			0.292906	−	0.956141i	$-0.405378\pi$
$269$	9.60804			0.585813			0.292906	+	0.956141i	$0.405378\pi$
$270$		0			0
$271$	−18.5859			−1.12901			−0.564507	−	0.825428i	$-0.690934\pi$
$271$	−18.5859			−1.12901			−0.564507	+	0.825428i	$0.690934\pi$
$272$		0			0
$273$	−8.24276	−	3.83000i	−0.498874	−	0.231802i
$274$		0			0
$275$			8.74232i			0.527182i
$276$		0			0
$277$	−11.4363			−0.687142			−0.343571	−	0.939127i	$-0.611637\pi$
$277$	−11.4363			−0.687142			−0.343571	+	0.939127i	$0.611637\pi$
$278$		0			0
$279$	1.18062	−	0.996152i	0.0706820	−	0.0596381i
$280$		0			0
$281$	21.1774			1.26334			0.631668	−	0.775239i	$-0.282371\pi$
$281$	21.1774			1.26334			0.631668	+	0.775239i	$0.282371\pi$
$282$		0			0
$283$	−4.67803			−0.278080			−0.139040	−	0.990287i	$-0.544402\pi$
$283$	−4.67803			−0.278080			−0.139040	+	0.990287i	$0.544402\pi$
$284$		0			0
$285$	−9.19405	−	1.00354i	−0.544609	−	0.0594445i
$286$		0			0
$287$	−6.76786			−0.399494
$288$		0			0
$289$	−6.82863			−0.401684
$290$		0			0
$291$	−3.90061	−	1.81242i	−0.228658	−	0.106246i
$292$		0			0
$293$	13.4049			0.783125			0.391563	−	0.920151i	$-0.371935\pi$
$293$	13.4049			0.783125			0.391563	+	0.920151i	$0.371935\pi$
$294$		0			0
$295$			4.45711i			0.259503i
$296$		0			0
$297$	−3.41105	−	12.5253i	−0.197929	−	0.726790i
$298$		0			0
$299$	0.792257			0.0458174
$300$		0			0
$301$	−1.17996			−0.0680115
$302$		0			0
$303$	25.0466	+	11.6379i	1.43889	+	0.668581i
$304$		0			0
$305$			2.27730i			0.130398i
$306$		0			0
$307$			26.2565i			1.49854i	0.662266	+	0.749269i	$0.269595\pi$
$307$			26.2565i			1.49854i	−0.662266	+	0.749269i	$0.730405\pi$
$308$		0			0
$309$	28.1031	+	13.0581i	1.59873	+	0.742851i
$310$		0			0
$311$			10.4261i			0.591213i	0.955310	+	0.295606i	$0.0955217\pi$
$311$			10.4261i			0.591213i	−0.955310	+	0.295606i	$0.904478\pi$
$312$		0			0
$313$	−11.0678			−0.625587			−0.312793	−	0.949821i	$-0.601265\pi$
$313$	−11.0678			−0.625587			−0.312793	+	0.949821i	$0.601265\pi$
$314$		0			0
$315$	−7.88937	+	6.65668i	−0.444516	+	0.375061i
$316$		0			0
$317$	2.95937			0.166215			0.0831073	−	0.996541i	$-0.473516\pi$
$317$	2.95937			0.166215			0.0831073	+	0.996541i	$0.473516\pi$
$318$		0			0
$319$		−	9.66642i		−	0.541216i
$320$		0			0
$321$	0.972313	−	2.09257i	0.0542692	−	0.116796i
$322$		0			0
$323$	−6.81938	−	20.1554i	−0.379440	−	1.12148i
$324$		0			0
$325$		−	6.53771i		−	0.362647i
$326$		0			0
$327$	26.0189	+	12.0897i	1.43885	+	0.668562i
$328$		0			0
$329$			30.1678i			1.66321i
$330$		0			0
$331$		−	4.55718i		−	0.250485i	−0.992126	−	0.125243i	$-0.960029\pi$
$331$		−	4.55718i		−	0.250485i	0.992126	−	0.125243i	$-0.0399710\pi$
$332$		0			0
$333$	−11.8484	+	9.99714i	−0.649290	+	0.547840i
$334$		0			0
$335$	−17.2742			−0.943789
$336$		0			0
$337$		−	8.27943i		−	0.451009i	−0.974242	−	0.225505i	$-0.927597\pi$
$337$		−	8.27943i		−	0.451009i	0.974242	−	0.225505i	$-0.0724031\pi$
$338$		0			0
$339$	12.2001	−	26.2565i	0.662619	−	1.42606i
$340$		0			0
$341$	−1.28639			−0.0696618
$342$		0			0
$343$	−17.1635			−0.926744
$344$		0			0
$345$	0.379146	−	0.815980i	0.0204125	−	0.0439309i
$346$		0			0
$347$		−	18.3626i		−	0.985754i	−0.870099	−	0.492877i	$-0.835945\pi$
$347$		−	18.3626i		−	0.985754i	0.870099	−	0.492877i	$-0.164055\pi$
$348$		0			0
$349$	3.25535			0.174255			0.0871275	−	0.996197i	$-0.472231\pi$
$349$	3.25535			0.174255			0.0871275	+	0.996197i	$0.472231\pi$
$350$		0			0
$351$	2.55086	+	9.36668i	0.136155	+	0.499957i
$352$		0			0
$353$		−	2.48890i		−	0.132471i	−0.997804	−	0.0662354i	$-0.978901\pi$
$353$		−	2.48890i		−	0.132471i	0.997804	−	0.0662354i	$-0.0210988\pi$
$354$		0			0
$355$		−	19.0942i		−	1.01341i
$356$		0			0
$357$	−21.5369	−	10.0071i	−1.13985	−	0.529633i
$358$		0			0
$359$		−	26.8512i		−	1.41715i	−0.705634	−	0.708577i	$-0.749338\pi$
$359$		−	26.8512i		−	1.41715i	0.705634	−	0.708577i	$-0.250662\pi$
$360$		0			0
$361$	15.0968	−	11.5363i	0.794569	−	0.607174i
$362$		0			0
$363$	3.47310	−	7.47466i	0.182291	−	0.392318i
$364$		0			0
$365$		−	14.6832i		−	0.768556i
$366$		0			0
$367$	−6.67905			−0.348643			−0.174322	−	0.984689i	$-0.555773\pi$
$367$	−6.67905			−0.348643			−0.174322	+	0.984689i	$0.555773\pi$
$368$		0			0
$369$	4.66149	+	5.52471i	0.242667	+	0.287605i
$370$		0			0
$371$	−21.6774			−1.12543
$372$		0			0
$373$		−	29.6103i		−	1.53317i	−0.642146	−	0.766583i	$-0.721956\pi$
$373$		−	29.6103i		−	1.53317i	0.642146	−	0.766583i	$-0.278044\pi$
$374$		0			0
$375$	−16.3545	−	7.59914i	−0.844545	−	0.392418i
$376$		0			0
$377$			7.22877i			0.372301i
$378$		0			0
$379$		−	3.41300i		−	0.175314i	−0.996151	−	0.0876570i	$-0.972062\pi$
$379$		−	3.41300i		−	0.175314i	0.996151	−	0.0876570i	$-0.0279379\pi$
$380$		0			0
$381$	11.3145	+	5.25727i	0.579657	+	0.269338i
$382$		0			0
$383$	4.40661			0.225167			0.112584	−	0.993642i	$-0.464087\pi$
$383$	4.40661			0.225167			0.112584	+	0.993642i	$0.464087\pi$
$384$		0			0
$385$	8.59614			0.438100
$386$		0			0
$387$	0.812717	+	0.963218i	0.0413127	+	0.0489631i
$388$		0			0
$389$		−	3.20661i		−	0.162581i	−0.996690	−	0.0812907i	$-0.974096\pi$
$389$		−	3.20661i		−	0.162581i	0.996690	−	0.0812907i	$-0.0259042\pi$
$390$		0			0
$391$	2.07003			0.104686
$392$		0			0
$393$	0.0757872	+	0.0352146i	0.00382296	+	0.00177634i
$394$		0			0
$395$	−1.97859			−0.0995538
$396$		0			0
$397$	−15.9925			−0.802640			−0.401320	−	0.915938i	$-0.631448\pi$
$397$	−15.9925			−0.802640			−0.401320	+	0.915938i	$0.631448\pi$
$398$		0			0
$399$	2.30099	−	21.0808i	0.115193	−	1.05536i
$400$		0			0
$401$	−30.7131			−1.53374			−0.766869	−	0.641804i	$-0.778186\pi$
$401$	−30.7131			−1.53374			−0.766869	+	0.641804i	$0.778186\pi$
$402$		0			0
$403$	0.961990			0.0479201
$404$		0			0
$405$	10.8679	+	1.85531i	0.540031	+	0.0921913i
$406$		0			0
$407$	12.9099			0.639918
$408$		0			0
$409$		−	36.9136i		−	1.82526i	−0.408789	−	0.912629i	$-0.634049\pi$
$409$		−	36.9136i		−	1.82526i	0.408789	−	0.912629i	$-0.365951\pi$
$410$		0			0
$411$	−26.4771	−	12.3026i	−1.30602	−	0.606842i
$412$		0			0
$413$	−10.2196			−0.502873
$414$		0			0
$415$	−6.96104			−0.341704
$416$		0			0
$417$	−7.67584	+	16.5196i	−0.375887	+	0.808968i
$418$		0			0
$419$		−	14.7287i		−	0.719546i	−0.933040	−	0.359773i	$-0.882854\pi$
$419$		−	14.7287i		−	0.719546i	0.933040	−	0.359773i	$-0.117146\pi$
$420$		0			0
$421$			23.4457i			1.14267i	0.820716	+	0.571337i	$0.193575\pi$
$421$			23.4457i			1.14267i	−0.820716	+	0.571337i	$0.806425\pi$
$422$		0			0
$423$	24.6265	−	20.7787i	1.19738	−	1.01029i
$424$		0			0
$425$		−	17.0819i		−	0.828592i
$426$		0			0
$427$	−5.22157			−0.252689
$428$		0			0
$429$	3.40658	−	7.33149i	0.164471	−	0.353968i
$430$		0			0
$431$	25.4449			1.22564			0.612818	−	0.790224i	$-0.290036\pi$
$431$	25.4449			1.22564			0.612818	+	0.790224i	$0.290036\pi$
$432$		0			0
$433$			21.2027i			1.01894i	0.860489	+	0.509469i	$0.170158\pi$
$433$			21.2027i			1.01894i	−0.860489	+	0.509469i	$0.829842\pi$
$434$		0			0
$435$	7.44522	+	3.45943i	0.356971	+	0.165867i
$436$		0			0
$437$	0.592409	+	1.75093i	0.0283388	+	0.0837582i
$438$		0			0
$439$		−	27.5578i		−	1.31526i	−0.753341	−	0.657630i	$-0.771559\pi$
$439$		−	27.5578i		−	1.31526i	0.753341	−	0.657630i	$-0.228441\pi$
$440$		0			0
$441$	−1.72059	−	2.03922i	−0.0819330	−	0.0971056i
$442$		0			0
$443$		−	23.8168i		−	1.13157i	−0.824552	−	0.565786i	$-0.808573\pi$
$443$		−	23.8168i		−	1.13157i	0.824552	−	0.565786i	$-0.191427\pi$
$444$		0			0
$445$			14.0461i			0.665847i
$446$		0			0
$447$	7.25641	+	3.37169i	0.343216	+	0.159476i
$448$		0			0
$449$	−35.3561			−1.66856			−0.834278	−	0.551344i	$-0.814115\pi$
$449$	−35.3561			−1.66856			−0.834278	+	0.551344i	$0.814115\pi$
$450$		0			0
$451$		−	6.01964i		−	0.283454i
$452$		0			0
$453$	28.2441	+	13.1236i	1.32702	+	0.616603i
$454$		0			0
$455$	−6.42839			−0.301368
$456$		0			0
$457$	26.1233			1.22199			0.610997	−	0.791633i	$-0.290769\pi$
$457$	26.1233			1.22199			0.610997	+	0.791633i	$0.290769\pi$
$458$		0			0
$459$	6.66495	+	24.4735i	0.311093	+	1.14232i
$460$		0			0
$461$			17.1158i			0.797162i	0.917133	+	0.398581i	$0.130497\pi$
$461$			17.1158i			0.797162i	−0.917133	+	0.398581i	$0.869503\pi$
$462$		0			0
$463$	−0.341102			−0.0158524			−0.00792618	−	0.999969i	$-0.502523\pi$
$463$	−0.341102			−0.0158524			−0.00792618	+	0.999969i	$0.502523\pi$
$464$		0			0
$465$	0.460374	−	0.990795i	0.0213493	−	0.0459470i
$466$		0			0
$467$			30.7092i			1.42105i	0.703671	+	0.710526i	$0.251543\pi$
$467$			30.7092i			1.42105i	−0.703671	+	0.710526i	$0.748457\pi$
$468$		0			0
$469$		−	39.6075i		−	1.82890i
$470$		0			0
$471$	−1.29823	+	2.79399i	−0.0598193	+	0.128740i
$472$		0			0
$473$		−	1.04951i		−	0.0482564i
$474$		0			0
$475$	14.4487	−	4.88856i	0.662950	−	0.224303i
$476$		0			0
$477$	14.9307	+	17.6956i	0.683630	+	0.810226i
$478$		0			0
$479$		−	30.2160i		−	1.38060i	−0.723522	−	0.690302i	$-0.757478\pi$
$479$		−	30.2160i		−	1.38060i	0.723522	−	0.690302i	$-0.242522\pi$
$480$		0			0
$481$	−9.65429			−0.440198
$482$		0			0
$483$	1.87094	+	0.869332i	0.0851306	+	0.0395560i
$484$		0			0
$485$	−3.04202			−0.138131
$486$		0			0
$487$		−	35.1534i		−	1.59295i	−0.604670	−	0.796476i	$-0.706695\pi$
$487$		−	35.1534i		−	1.59295i	0.604670	−	0.796476i	$-0.293305\pi$
$488$		0			0
$489$	11.2810	−	24.2785i	0.510145	−	1.09791i
$490$		0			0
$491$		−	26.8286i		−	1.21076i	−0.795937	−	0.605379i	$-0.793022\pi$
$491$		−	26.8286i		−	1.21076i	0.795937	−	0.605379i	$-0.206978\pi$
$492$		0			0
$493$			18.8875i			0.850650i
$494$		0			0
$495$	−5.92075	−	7.01717i	−0.266118	−	0.315398i
$496$		0			0
$497$	43.7805			1.96382
$498$		0			0
$499$	−40.1309			−1.79651			−0.898253	−	0.439479i	$-0.855163\pi$
$499$	−40.1309			−1.79651			−0.898253	+	0.439479i	$0.855163\pi$
$500$		0			0
$501$	−3.25636	+	7.00820i	−0.145484	+	0.313103i
$502$		0			0
$503$			29.4746i			1.31421i	0.753801	+	0.657103i	$0.228218\pi$
$503$			29.4746i			1.31421i	−0.753801	+	0.657103i	$0.771782\pi$
$504$		0			0
$505$	19.5334			0.869226
$506$		0			0
$507$	6.94063	−	14.9373i	0.308244	−	0.663389i
$508$		0			0
$509$	5.81464			0.257729			0.128865	−	0.991662i	$-0.458867\pi$
$509$	5.81464			0.257729			0.128865	+	0.991662i	$0.458867\pi$
$510$		0			0
$511$	33.6668			1.48933
$512$		0			0
$513$	−18.7934	+	12.6415i	−0.829751	+	0.558134i
$514$		0			0
$515$	21.9172			0.965785
$516$		0			0
$517$	−26.8327			−1.18010
$518$		0			0
$519$	13.9059	−	29.9277i	0.610402	−	1.31368i
$520$		0			0
$521$	−38.2332			−1.67503			−0.837513	−	0.546417i	$-0.815991\pi$
$521$	−38.2332			−1.67503			−0.837513	+	0.546417i	$0.815991\pi$
$522$		0			0
$523$		−	2.17499i		−	0.0951055i	−0.998869	−	0.0475528i	$-0.984858\pi$
$523$		−	2.17499i		−	0.0951055i	0.998869	−	0.0475528i	$-0.0151422\pi$
$524$		0			0
$525$	7.17373	−	15.4390i	0.313087	−	0.673813i
$526$		0			0
$527$	2.51351			0.109490
$528$		0			0
$529$	22.8202			0.992181
$530$		0			0
$531$	7.03893	+	8.34241i	0.305463	+	0.362030i
$532$		0			0
$533$			4.50163i			0.194987i
$534$		0			0
$535$		−	1.63196i		−	0.0705558i
$536$		0			0
$537$	11.6602	−	25.0945i	0.503173	−	1.08291i
$538$		0			0
$539$			2.22190i			0.0957040i
$540$		0			0
$541$	−26.8781			−1.15558			−0.577791	−	0.816185i	$-0.696085\pi$
$541$	−26.8781			−1.15558			−0.577791	+	0.816185i	$0.696085\pi$
$542$		0			0
$543$	−8.25794	−	3.83706i	−0.354382	−	0.164664i
$544$		0			0
$545$	20.2917			0.869202
$546$		0			0
$547$			29.0152i			1.24060i	0.784364	+	0.620300i	$0.212989\pi$
$547$			29.0152i			1.24060i	−0.784364	+	0.620300i	$0.787011\pi$
$548$		0			0
$549$	3.59645	+	4.26245i	0.153493	+	0.181917i
$550$		0			0
$551$	−15.9759	+	5.40530i	−0.680598	+	0.230274i
$552$		0			0
$553$		−	4.53666i		−	0.192918i
$554$		0			0
$555$	−4.62020	+	9.94338i	−0.196116	+	0.422073i
$556$		0			0
$557$			19.5680i			0.829122i	0.910021	+	0.414561i	$0.136065\pi$
$557$			19.5680i			0.829122i	−0.910021	+	0.414561i	$0.863935\pi$
$558$		0			0
$559$			0.784846i			0.0331954i
$560$		0			0
$561$	8.90079	−	19.1559i	0.375792	−	0.808762i
$562$		0			0
$563$	18.3253			0.772321			0.386161	−	0.922432i	$-0.373801\pi$
$563$	18.3253			0.772321			0.386161	+	0.922432i	$0.373801\pi$
$564$		0			0
$565$		−	20.4770i		−	0.861475i
$566$		0			0
$567$	−4.25400	+	24.9187i	−0.178651	+	1.04649i
$568$		0			0
$569$	17.7539			0.744282			0.372141	−	0.928176i	$-0.378624\pi$
$569$	17.7539			0.744282			0.372141	+	0.928176i	$0.378624\pi$
$570$		0			0
$571$	−8.25794			−0.345584			−0.172792	−	0.984958i	$-0.555279\pi$
$571$	−8.25794			−0.345584			−0.172792	+	0.984958i	$0.555279\pi$
$572$		0			0
$573$	8.37705	+	3.89240i	0.349956	+	0.162607i
$574$		0			0
$575$			1.48393i			0.0618840i
$576$		0			0
$577$	−9.96477			−0.414839			−0.207419	−	0.978252i	$-0.566506\pi$
$577$	−9.96477			−0.414839			−0.207419	+	0.978252i	$0.566506\pi$
$578$		0			0
$579$	33.3045	+	15.4750i	1.38409	+	0.643118i
$580$		0			0
$581$		−	15.9608i		−	0.662165i
$582$		0			0
$583$		−	19.2809i		−	0.798532i
$584$		0			0
$585$	4.42767	+	5.24760i	0.183062	+	0.216962i
$586$		0			0
$587$			33.1772i			1.36937i	0.728840	+	0.684685i	$0.240060\pi$
$587$			33.1772i			1.36937i	−0.728840	+	0.684685i	$0.759940\pi$
$588$		0			0
$589$	0.719327	+	2.12605i	0.0296393	+	0.0876022i
$590$		0			0
$591$	−32.4918	−	15.0973i	−1.33654	−	0.621022i
$592$		0			0
$593$		−	23.1507i		−	0.950684i	−0.879801	−	0.475342i	$-0.842324\pi$
$593$		−	23.1507i		−	0.950684i	0.879801	−	0.475342i	$-0.157676\pi$
$594$		0			0
$595$	−16.7962			−0.688579
$596$		0			0
$597$	−2.25584	+	4.85493i	−0.0923255	+	0.198699i
$598$		0			0
$599$	−42.9672			−1.75559			−0.877796	−	0.479035i	$-0.840987\pi$
$599$	−42.9672			−1.75559			−0.877796	+	0.479035i	$0.840987\pi$
$600$		0			0
$601$		−	34.0425i		−	1.38862i	−0.719675	−	0.694311i	$-0.755709\pi$
$601$		−	34.0425i		−	1.38862i	0.719675	−	0.694311i	$-0.244291\pi$
$602$		0			0
$603$	−32.3322	+	27.2804i	−1.31667	+	1.11094i
$604$		0			0
$605$		−	5.82936i		−	0.236997i
$606$		0			0
$607$			20.7358i			0.841641i	0.907144	+	0.420821i	$0.138258\pi$
$607$			20.7358i			0.841641i	−0.907144	+	0.420821i	$0.861742\pi$
$608$		0			0
$609$	−7.93203	+	17.0709i	−0.321422	+	0.691750i
$610$		0			0
$611$	20.0661			0.811787
$612$		0			0
$613$	−37.2732			−1.50545			−0.752724	−	0.658336i	$-0.771261\pi$
$613$	−37.2732			−1.50545			−0.752724	+	0.658336i	$0.771261\pi$
$614$		0			0
$615$	4.63642	+	2.15432i	0.186959	+	0.0868704i
$616$		0			0
$617$		−	31.6733i		−	1.27512i	−0.770402	−	0.637559i	$-0.779944\pi$
$617$		−	31.6733i		−	1.27512i	0.770402	−	0.637559i	$-0.220056\pi$
$618$		0			0
$619$	28.2177			1.13416			0.567082	−	0.823662i	$-0.308072\pi$
$619$	28.2177			1.13416			0.567082	+	0.823662i	$0.308072\pi$
$620$		0			0
$621$	−0.578993	−	2.12605i	−0.0232342	−	0.0853153i
$622$		0			0
$623$	−32.2058			−1.29030
$624$		0			0
$625$	4.74206			0.189682
$626$		0			0
$627$	18.7502	+	2.04660i	0.748812	+	0.0817335i
$628$		0			0
$629$	−25.2250			−1.00578
$630$		0			0
$631$	−12.0994			−0.481669			−0.240834	−	0.970566i	$-0.577421\pi$
$631$	−12.0994			−0.481669			−0.240834	+	0.970566i	$0.577421\pi$
$632$		0			0
$633$	9.47165	+	4.40101i	0.376464	+	0.174924i
$634$		0			0
$635$	8.82396			0.350168
$636$		0			0
$637$		−	1.66159i		−	0.0658345i
$638$		0			0
$639$	−30.1546	−	35.7387i	−1.19290	−	1.41380i
$640$		0			0
$641$	−24.2308			−0.957060			−0.478530	−	0.878071i	$-0.658830\pi$
$641$	−24.2308			−0.957060			−0.478530	+	0.878071i	$0.658830\pi$
$642$		0			0
$643$	−21.0981			−0.832026			−0.416013	−	0.909359i	$-0.636573\pi$
$643$	−21.0981			−0.832026			−0.416013	+	0.909359i	$0.636573\pi$
$644$		0			0
$645$	0.808347	+	0.375599i	0.0318286	+	0.0147892i
$646$		0			0
$647$			0.254891i			0.0100208i	0.999987	+	0.00501039i	$0.00159486\pi$
$647$			0.254891i			0.0100208i	−0.999987	+	0.00501039i	$0.998405\pi$
$648$		0			0
$649$		−	9.08977i		−	0.356804i
$650$		0			0
$651$	2.27177	+	1.05558i	0.0890376	+	0.0413714i
$652$		0			0
$653$			24.0777i			0.942232i	0.882071	+	0.471116i	$0.156149\pi$
$653$			24.0777i			0.942232i	−0.882071	+	0.471116i	$0.843851\pi$
$654$		0			0
$655$	0.0591052			0.00230943
$656$		0			0
$657$	−23.1886	−	27.4828i	−0.904675	−	1.07220i
$658$		0			0
$659$	−8.53072			−0.332310			−0.166155	−	0.986100i	$-0.553135\pi$
$659$	−8.53072			−0.332310			−0.166155	+	0.986100i	$0.553135\pi$
$660$		0			0
$661$		−	38.4286i		−	1.49470i	−0.664430	−	0.747350i	$-0.731326\pi$
$661$		−	38.4286i		−	1.49470i	0.664430	−	0.747350i	$-0.268674\pi$
$662$		0			0
$663$	−6.65621	+	14.3252i	−0.258506	+	0.556345i
$664$		0			0
$665$	−4.80682	−	14.2071i	−0.186401	−	0.550926i
$666$		0			0
$667$		−	1.64078i		−	0.0635314i
$668$		0			0
$669$	19.7071	+	9.15691i	0.761920	+	0.354026i
$670$		0			0
$671$		−	4.64430i		−	0.179291i
$672$		0			0
$673$			46.8954i			1.80768i	0.427867	+	0.903842i	$0.359265\pi$
$673$			46.8954i			1.80768i	−0.427867	+	0.903842i	$0.640735\pi$
$674$		0			0
$675$	−17.5441	+	4.77786i	−0.675274	+	0.183900i
$676$		0			0
$677$	−21.6890			−0.833575			−0.416787	−	0.909004i	$-0.636844\pi$
$677$	−21.6890			−0.833575			−0.416787	+	0.909004i	$0.636844\pi$
$678$		0			0
$679$		−	6.97497i		−	0.267675i
$680$		0			0
$681$	−16.8277	+	36.2159i	−0.644840	+	1.38779i
$682$		0			0
$683$	38.8523			1.48664			0.743321	−	0.668935i	$-0.233250\pi$
$683$	38.8523			1.48664			0.743321	+	0.668935i	$0.233250\pi$
$684$		0			0
$685$	−20.6491			−0.788960
$686$		0			0
$687$	−8.39122	+	18.0592i	−0.320145	+	0.689002i
$688$		0			0
$689$			14.4187i			0.549307i
$690$		0			0
$691$	7.39377			0.281272			0.140636	−	0.990061i	$-0.455085\pi$
$691$	7.39377			0.281272			0.140636	+	0.990061i	$0.455085\pi$
$692$		0			0
$693$	16.0895	−	13.5755i	0.611189	−	0.515692i
$694$		0			0
$695$			12.8834i			0.488693i
$696$		0			0
$697$			11.7620i			0.445516i
$698$		0			0
$699$	23.1224	+	10.7438i	0.874569	+	0.406369i
$700$		0			0
$701$		−	31.8613i		−	1.20338i	−0.798728	−	0.601692i	$-0.794493\pi$
$701$		−	31.8613i		−	1.20338i	0.798728	−	0.601692i	$-0.205507\pi$
$702$		0			0
$703$	−7.21898	−	21.3365i	−0.272269	−	0.804720i
$704$		0			0
$705$	9.60291	−	20.6669i	0.361666	−	0.778362i
$706$		0			0
$707$			44.7877i			1.68441i
$708$		0			0
$709$	14.7371			0.553465			0.276732	−	0.960947i	$-0.410748\pi$
$709$	14.7371			0.553465			0.276732	+	0.960947i	$0.410748\pi$
$710$		0			0
$711$	−3.70335	+	3.12471i	−0.138886	+	0.117186i
$712$		0			0
$713$	−0.218352			−0.00817735
$714$		0			0
$715$		−	5.71771i		−	0.213830i
$716$		0			0
$717$	40.2156	+	18.6862i	1.50188	+	0.697848i
$718$		0			0
$719$			21.7645i			0.811678i	0.913945	+	0.405839i	$0.133021\pi$
$719$			21.7645i			0.811678i	−0.913945	+	0.405839i	$0.866979\pi$
$720$		0			0
$721$			50.2532i			1.87153i
$722$		0			0
$723$	5.75860	+	2.67574i	0.214165	+	0.0995118i
$724$		0			0
$725$	−13.5397			−0.502854
$726$		0			0
$727$	1.44554			0.0536123			0.0268061	−	0.999641i	$-0.491466\pi$
$727$	1.44554			0.0536123			0.0268061	+	0.999641i	$0.491466\pi$
$728$		0			0
$729$	23.2716	−	13.6906i	0.861911	−	0.507060i
$730$		0			0
$731$			2.05066i			0.0758465i
$732$		0			0
$733$	−15.6302			−0.577316			−0.288658	−	0.957432i	$-0.593209\pi$
$733$	−15.6302			−0.577316			−0.288658	+	0.957432i	$0.593209\pi$
$734$		0			0
$735$	−1.71134	−	0.795176i	−0.0631238	−	0.0293305i
$736$		0			0
$737$	35.2287			1.29767
$738$		0			0
$739$	−41.1663			−1.51433			−0.757163	−	0.653226i	$-0.773415\pi$
$739$	−41.1663			−1.51433			−0.757163	+	0.653226i	$0.773415\pi$
$740$		0			0
$741$	−14.0218	−	1.53050i	−0.515105	−	0.0562242i
$742$		0			0
$743$	42.2089			1.54849			0.774247	−	0.632884i	$-0.218129\pi$
$743$	42.2089			1.54849			0.774247	+	0.632884i	$0.218129\pi$
$744$		0			0
$745$	5.65915			0.207335
$746$		0			0
$747$	−13.0290	+	10.9933i	−0.476708	+	0.402223i
$748$		0			0
$749$	3.74188			0.136725
$750$		0			0
$751$		−	0.203487i		−	0.00742536i	−0.999993	−	0.00371268i	$-0.998818\pi$
$751$		−	0.203487i		−	0.00742536i	0.999993	−	0.00371268i	$-0.00118178\pi$
$752$		0			0
$753$	42.8464	+	19.9086i	1.56141	+	0.725509i
$754$		0			0
$755$	22.0271			0.801649
$756$		0			0
$757$	−43.0897			−1.56612			−0.783060	−	0.621946i	$-0.786342\pi$
$757$	−43.0897			−1.56612			−0.783060	+	0.621946i	$0.786342\pi$
$758$		0			0
$759$	−0.773224	+	1.66410i	−0.0280663	+	0.0604029i
$760$		0			0
$761$		−	17.4848i		−	0.633823i	−0.948455	−	0.316912i	$-0.897354\pi$
$761$		−	17.4848i		−	0.633823i	0.948455	−	0.316912i	$-0.102646\pi$
$762$		0			0
$763$			46.5263i			1.68437i
$764$		0			0
$765$	11.5687	+	13.7111i	0.418268	+	0.495724i
$766$		0			0
$767$			6.79753i			0.245445i
$768$		0			0
$769$	−31.9862			−1.15345			−0.576725	−	0.816938i	$-0.695670\pi$
$769$	−31.9862			−1.15345			−0.576725	+	0.816938i	$0.695670\pi$
$770$		0			0
$771$	7.70450	−	16.5813i	0.277471	−	0.597160i
$772$		0			0
$773$	−47.1338			−1.69529			−0.847643	−	0.530567i	$-0.821979\pi$
$773$	−47.1338			−1.69529			−0.847643	+	0.530567i	$0.821979\pi$
$774$		0			0
$775$			1.80184i			0.0647241i
$776$		0			0
$777$	−22.7989	−	10.5935i	−0.817906	−	0.380040i
$778$		0			0
$779$	−9.94882	+	3.36609i	−0.356454	+	0.120603i
$780$		0			0
$781$			38.9404i			1.39340i
$782$		0			0
$783$	19.3986	−	5.28289i	0.693250	−	0.188795i
$784$		0			0
$785$			2.17899i			0.0777714i
$786$		0			0
$787$			28.4779i			1.01513i	0.861614	+	0.507564i	$0.169454\pi$
$787$			28.4779i			1.01513i	−0.861614	+	0.507564i	$0.830546\pi$
$788$		0			0
$789$	−21.7998	−	10.1293i	−0.776092	−	0.360612i
$790$		0			0
$791$	46.9512			1.66939
$792$		0			0
$793$			3.47312i			0.123334i
$794$		0			0
$795$	14.8504	+	6.90025i	0.526690	+	0.244727i
$796$		0			0
$797$	42.8013			1.51610			0.758050	−	0.652197i	$-0.226152\pi$
$797$	42.8013			1.51610			0.758050	+	0.652197i	$0.226152\pi$
$798$		0			0
$799$	52.4291			1.85481
$800$		0			0
$801$	22.1824	+	26.2901i	0.783775	+	0.928916i
$802$		0			0
$803$			29.9448i			1.05673i
$804$		0			0
$805$	1.45911			0.0514270
$806$		0			0
$807$	7.01250	−	15.0920i	0.246852	−	0.531263i
$808$		0			0
$809$			0.248801i			0.00874739i	0.999990	+	0.00437369i	$0.00139219\pi$
$809$			0.248801i			0.00874739i	−0.999990	+	0.00437369i	$0.998608\pi$
$810$		0			0
$811$			9.07141i			0.318540i	0.987235	+	0.159270i	$0.0509141\pi$
$811$			9.07141i			0.318540i	−0.987235	+	0.159270i	$0.949086\pi$
$812$		0			0
$813$	−13.5651	+	29.1941i	−0.475748	+	1.02388i
$814$		0			0
$815$		−	18.9344i		−	0.663243i
$816$		0			0
$817$	−1.73455	+	0.586867i	−0.0606842	+	0.0205319i
$818$		0			0
$819$	−12.0321	+	10.1521i	−0.420435	+	0.354743i
$820$		0			0
$821$			6.31807i			0.220502i	0.993904	+	0.110251i	$0.0351655\pi$
$821$			6.31807i			0.220502i	−0.993904	+	0.110251i	$0.964835\pi$
$822$		0			0
$823$	−9.46537			−0.329942			−0.164971	−	0.986298i	$-0.552753\pi$
$823$	−9.46537			−0.329942			−0.164971	+	0.986298i	$0.552753\pi$
$824$		0			0
$825$	13.7321	+	6.38065i	0.478092	+	0.222146i
$826$		0			0
$827$	−0.938117			−0.0326215			−0.0163108	−	0.999867i	$-0.505192\pi$
$827$	−0.938117			−0.0326215			−0.0163108	+	0.999867i	$0.505192\pi$
$828$		0			0
$829$		−	47.9726i		−	1.66616i	−0.553153	−	0.833079i	$-0.686576\pi$
$829$		−	47.9726i		−	1.66616i	0.553153	−	0.833079i	$-0.313424\pi$
$830$		0			0
$831$	−8.34689	+	17.9638i	−0.289550	+	0.623157i
$832$		0			0
$833$		−	4.34143i		−	0.150422i
$834$		0			0
$835$			5.46558i			0.189144i
$836$		0			0
$837$	−0.703037	−	2.58153i	−0.0243005	−	0.0892307i
$838$		0			0
$839$	−14.7186			−0.508144			−0.254072	−	0.967185i	$-0.581770\pi$
$839$	−14.7186			−0.508144			−0.254072	+	0.967185i	$0.581770\pi$
$840$		0			0
$841$	−14.0290			−0.483760
$842$		0			0
$843$	15.4565	−	33.2647i	0.532349	−	1.14570i
$844$		0			0
$845$		−	11.6494i		−	0.400750i
$846$		0			0
$847$	13.3660			0.459260
$848$		0			0
$849$	−3.41430	+	7.34810i	−0.117178	+	0.252186i
$850$		0			0
$851$	2.19133			0.0751177
$852$		0			0
$853$	41.4691			1.41987			0.709937	−	0.704265i	$-0.248723\pi$
$853$	41.4691			1.41987			0.709937	+	0.704265i	$0.248723\pi$
$854$		0			0
$855$	−8.28668	+	13.7093i	−0.283398	+	0.468847i
$856$		0			0
$857$	−39.4595			−1.34791			−0.673956	−	0.738772i	$-0.735406\pi$
$857$	−39.4595			−1.34791			−0.673956	+	0.738772i	$0.735406\pi$
$858$		0			0
$859$	−38.5338			−1.31475			−0.657377	−	0.753561i	$-0.728334\pi$
$859$	−38.5338			−1.31475			−0.657377	+	0.753561i	$0.728334\pi$
$860$		0			0
$861$	−4.93957	+	10.6307i	−0.168340	+	0.362294i
$862$		0			0
$863$	25.8874			0.881217			0.440609	−	0.897699i	$-0.354763\pi$
$863$	25.8874			0.881217			0.440609	+	0.897699i	$0.354763\pi$
$864$		0			0
$865$		−	23.3401i		−	0.793588i
$866$		0			0
$867$	−4.98393	+	10.7262i	−0.169263	+	0.364280i
$868$		0			0
$869$	4.03511			0.136882
$870$		0			0
$871$	−26.3448			−0.892661
$872$		0			0
$873$	−5.69378	+	4.80414i	−0.192705	+	0.162596i
$874$		0			0
$875$		−	29.2447i		−	0.988653i
$876$		0			0
$877$			14.1823i			0.478901i	0.970909	+	0.239451i	$0.0769673\pi$
$877$			14.1823i			0.478901i	−0.970909	+	0.239451i	$0.923033\pi$
$878$		0			0
$879$	9.78370	−	21.0560i	0.329996	−	0.710203i
$880$		0			0
$881$			26.2348i			0.883871i	0.897047	+	0.441936i	$0.145708\pi$
$881$			26.2348i			0.883871i	−0.897047	+	0.441936i	$0.854292\pi$
$882$		0			0
$883$	−22.2365			−0.748317			−0.374158	−	0.927365i	$-0.622068\pi$
$883$	−22.2365			−0.748317			−0.374158	+	0.927365i	$0.622068\pi$
$884$		0			0
$885$	7.00108	+	3.25305i	0.235339	+	0.109350i
$886$		0			0
$887$	−48.4735			−1.62758			−0.813790	−	0.581159i	$-0.802600\pi$
$887$	−48.4735			−1.62758			−0.813790	+	0.581159i	$0.802600\pi$
$888$		0			0
$889$			20.2322i			0.678566i
$890$		0			0
$891$	−22.1639	−	3.78370i	−0.742517	−	0.126759i
$892$		0			0
$893$	15.0044	+	44.3471i	0.502103	+	1.48402i
$894$		0			0
$895$		−	19.5708i		−	0.654179i
$896$		0			0
$897$	0.578235	−	1.24445i	0.0193067	−	0.0415510i
$898$		0			0
$899$		−	1.99230i		−	0.0664471i
$900$		0			0
$901$			37.6734i			1.25508i
$902$		0			0
$903$	−0.861200	+	1.85344i	−0.0286589	+	0.0616785i
$904$		0			0
$905$	−6.44023			−0.214081
$906$		0			0
$907$			41.9850i			1.39409i	0.717028	+	0.697045i	$0.245502\pi$
$907$			41.9850i			1.39409i	−0.717028	+	0.697045i	$0.754498\pi$
$908$		0			0
$909$	36.5609	−	30.8483i	1.21265	−	1.02318i
$910$		0			0
$911$	24.8668			0.823873			0.411937	−	0.911213i	$-0.364853\pi$
$911$	24.8668			0.823873			0.411937	+	0.911213i	$0.364853\pi$
$912$		0			0
$913$	14.1963			0.469827
$914$		0			0
$915$	3.57711	+	1.66211i	0.118256	+	0.0549476i
$916$		0			0
$917$			0.135521i			0.00447529i
$918$		0			0
$919$	−36.4355			−1.20190			−0.600948	−	0.799288i	$-0.705210\pi$
$919$	−36.4355			−1.20190			−0.600948	+	0.799288i	$0.705210\pi$
$920$		0			0
$921$	41.2429	+	19.1635i	1.35900	+	0.631459i
$922$		0			0
$923$		−	29.1205i		−	0.958513i
$924$		0			0
$925$		−	18.0828i		−	0.594560i
$926$		0			0
$927$	41.0225	−	34.6129i	1.34736	−	1.13684i
$928$		0			0
$929$			20.7869i			0.681997i	0.940064	+	0.340999i	$0.110765\pi$
$929$			20.7869i			0.681997i	−0.940064	+	0.340999i	$0.889235\pi$
$930$		0			0
$931$	3.67219	−	1.24245i	0.120351	−	0.0407196i
$932$		0			0
$933$	16.3770	+	7.60960i	0.536160	+	0.249127i
$934$		0			0
$935$		−	14.9394i		−	0.488569i
$936$		0			0
$937$	29.1210			0.951341			0.475671	−	0.879623i	$-0.342205\pi$
$937$	29.1210			0.951341			0.475671	+	0.879623i	$0.342205\pi$
$938$		0			0
$939$	−8.07789	+	17.3849i	−0.263612	+	0.567334i
$940$		0			0
$941$	20.7848			0.677565			0.338783	−	0.940865i	$-0.389985\pi$
$941$	20.7848			0.677565			0.338783	+	0.940865i	$0.389985\pi$
$942$		0			0
$943$		−	1.02178i		−	0.0332737i
$944$		0			0
$945$	4.69797	+	17.2508i	0.152825	+	0.561168i
$946$		0			0
$947$		−	16.5344i		−	0.537294i	−0.963239	−	0.268647i	$-0.913423\pi$
$947$		−	16.5344i		−	0.537294i	0.963239	−	0.268647i	$-0.0865766\pi$
$948$		0			0
$949$		−	22.3934i		−	0.726921i
$950$		0			0
$951$	2.15992	−	4.64847i	0.0700401	−	0.150737i
$952$		0			0
$953$	1.99710			0.0646923			0.0323462	−	0.999477i	$-0.489702\pi$
$953$	1.99710			0.0646923			0.0323462	+	0.999477i	$0.489702\pi$
$954$		0			0
$955$	6.53312			0.211407
$956$		0			0
$957$	−15.1837	−	7.05511i	−0.490819	−	0.228059i
$958$		0			0
$959$		−	47.3456i		−	1.52887i
$960$		0			0
$961$	30.7349			0.991447
$962$		0			0
$963$	−2.57729	−	3.05455i	−0.0830519	−	0.0984316i
$964$		0			0
$965$	25.9737			0.836122
$966$		0			0
$967$	36.0754			1.16011			0.580053	−	0.814579i	$-0.303032\pi$
$967$	36.0754			1.16011			0.580053	+	0.814579i	$0.303032\pi$
$968$		0			0
$969$	−36.6366	−	3.99892i	−1.17694	−	0.128464i
$970$		0			0
$971$	−14.9370			−0.479351			−0.239675	−	0.970853i	$-0.577041\pi$
$971$	−14.9370			−0.479351			−0.239675	+	0.970853i	$0.577041\pi$
$972$		0			0
$973$	−29.5399			−0.947005
$974$		0			0
$975$	−10.2692	−	4.77160i	−0.328878	−	0.152813i
$976$		0			0
$977$	20.0411			0.641171			0.320586	−	0.947220i	$-0.396120\pi$
$977$	20.0411			0.641171			0.320586	+	0.947220i	$0.396120\pi$
$978$		0			0
$979$		−	28.6453i		−	0.915509i
$980$		0			0
$981$	37.9802	−	32.0459i	1.21261	−	1.02315i
$982$		0			0
$983$	16.3031			0.519990			0.259995	−	0.965610i	$-0.416279\pi$
$983$	16.3031			0.519990			0.259995	+	0.965610i	$0.416279\pi$
$984$		0			0
$985$	−25.3398			−0.807395
$986$		0			0
$987$	47.3866	+	22.0182i	1.50833	+	0.700848i
$988$		0			0
$989$		−	0.178144i		−	0.00566465i
$990$		0			0
$991$			17.5862i			0.558645i	0.960197	+	0.279322i	$0.0901098\pi$
$991$			17.5862i			0.558645i	−0.960197	+	0.279322i	$0.909890\pi$
$992$		0			0
$993$	−7.15827	−	3.32610i	−0.227161	−	0.105550i
$994$		0			0
$995$			3.78628i			0.120033i
$996$		0			0
$997$	44.8255			1.41964			0.709819	−	0.704384i	$-0.248777\pi$
$997$	44.8255			1.41964			0.709819	+	0.704384i	$0.248777\pi$
$998$		0			0
$999$	7.05550	+	25.9076i	0.223226	+	0.819680i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.f.h.113.7		10
3.2	odd	2		912.2.f.i.113.3		10
4.3	odd	2		456.2.f.b.113.4	yes	10
12.11	even	2		456.2.f.a.113.8	yes	10
19.18	odd	2		912.2.f.i.113.4		10
57.56	even	2	inner	912.2.f.h.113.8		10
76.75	even	2		456.2.f.a.113.7	✓	10
228.227	odd	2		456.2.f.b.113.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.f.a.113.7	✓	10	76.75	even	2
456.2.f.a.113.8	yes	10	12.11	even	2
456.2.f.b.113.3	yes	10	228.227	odd	2
456.2.f.b.113.4	yes	10	4.3	odd	2
912.2.f.h.113.7		10	1.1	even	1	trivial
912.2.f.h.113.8		10	57.56	even	2	inner
912.2.f.i.113.3		10	3.2	odd	2
912.2.f.i.113.4		10	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.729858 - 1.57077i) q^{3} -1.22502i q^{5} +2.80880 q^{7} +(-1.93462 - 2.29287i) q^{9} +O(q^{10})\)	\(q+(0.729858 - 1.57077i) q^{3} -1.22502i q^{5} +2.80880 q^{7} +(-1.93462 - 2.29287i) q^{9} +2.49828i q^{11} -1.86827i q^{13} +(-1.92421 - 0.894087i) q^{15} -4.88146i q^{17} +(4.12897 - 1.39700i) q^{19} +(2.05003 - 4.41197i) q^{21} +0.424059i q^{23} +3.49934 q^{25} +(-5.01356 + 1.36536i) q^{27} -3.86923 q^{29} +0.514909i q^{31} +(3.92421 + 1.82339i) q^{33} -3.44083i q^{35} -5.16750i q^{37} +(-2.93462 - 1.36357i) q^{39} -2.40952 q^{41} -0.420092 q^{43} +(-2.80880 + 2.36993i) q^{45} +10.7405i q^{47} +0.889372 q^{49} +(-7.66763 - 3.56277i) q^{51} -7.71766 q^{53} +3.06043 q^{55} +(0.819206 - 7.50526i) q^{57} -3.63841 q^{59} -1.85900 q^{61} +(-5.43395 - 6.44022i) q^{63} -2.28866 q^{65} -14.1012i q^{67} +(0.666098 + 0.309503i) q^{69} +15.5869 q^{71} +11.9862 q^{73} +(2.55402 - 5.49664i) q^{75} +7.01717i q^{77} -1.61516i q^{79} +(-1.51452 + 8.87165i) q^{81} -5.68241i q^{83} -5.97986 q^{85} +(-2.82399 + 6.07766i) q^{87} -11.4660 q^{89} -5.24760i q^{91} +(0.808803 + 0.375811i) q^{93} +(-1.71134 - 5.05805i) q^{95} -2.48325i q^{97} +(5.72823 - 4.83321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{3} + 2 q^{7} + 3 q^{9}+O(q^{10}) \) 10 * q - q^3 + 2 * q^7 + 3 * q^9	\( 10 q - q^{3} + 2 q^{7} + 3 q^{9} + 10 q^{15} - 2 q^{19} - 5 q^{21} - 14 q^{25} - 10 q^{27} + 6 q^{29} + 10 q^{33} - 7 q^{39} + 4 q^{41} - 20 q^{43} - 2 q^{45} + 16 q^{49} + q^{51} + 26 q^{53} + 12 q^{55} - 11 q^{57} + 2 q^{59} - 4 q^{61} + 17 q^{63} - 32 q^{65} + 27 q^{69} + 8 q^{71} - 26 q^{73} + 39 q^{75} + 23 q^{81} - 8 q^{85} - 13 q^{87} - 4 q^{89} - 18 q^{93} - 8 q^{95} - 2 q^{99}+O(q^{100}) \) 10 * q - q^3 + 2 * q^7 + 3 * q^9 + 10 * q^15 - 2 * q^19 - 5 * q^21 - 14 * q^25 - 10 * q^27 + 6 * q^29 + 10 * q^33 - 7 * q^39 + 4 * q^41 - 20 * q^43 - 2 * q^45 + 16 * q^49 + q^51 + 26 * q^53 + 12 * q^55 - 11 * q^57 + 2 * q^59 - 4 * q^61 + 17 * q^63 - 32 * q^65 + 27 * q^69 + 8 * q^71 - 26 * q^73 + 39 * q^75 + 23 * q^81 - 8 * q^85 - 13 * q^87 - 4 * q^89 - 18 * q^93 - 8 * q^95 - 2 * q^99

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