LMFDB - Embedded newform 945.2.b.b.566.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(566,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("945.566");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 14x^{8} + 63x^{6} + 110x^{4} + 73x^{2} + 12 $ x^10 + 14x^8 + 63x^6 + 110x^4 + 73x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			566.6
Root			$0.489586i$ of defining polynomial
Character	$\chi$	$=$	945.566
Dual form			945.2.b.b.566.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.489586i q^{2} +1.76031 q^{4} +1.00000 q^{5} +(-2.53778 + 0.748102i) q^{7} +1.84099i q^{8} +O(q^{10})$	\(q+0.489586i q^{2} +1.76031 q^{4} +1.00000 q^{5} +(-2.53778 + 0.748102i) q^{7} +1.84099i q^{8} +0.489586i q^{10} +4.16450i q^{11} +4.54514i q^{13} +(-0.366260 - 1.24246i) q^{14} +2.61928 q^{16} -7.50615 q^{17} -5.64281i q^{19} +1.76031 q^{20} -2.03888 q^{22} +7.44928i q^{23} +1.00000 q^{25} -2.22524 q^{26} +(-4.46727 + 1.31689i) q^{28} +3.71784i q^{29} -2.77724i q^{31} +4.96436i q^{32} -3.67491i q^{34} +(-2.53778 + 0.748102i) q^{35} +5.50382 q^{37} +2.76264 q^{38} +1.84099i q^{40} -0.847989 q^{41} +3.87577 q^{43} +7.33079i q^{44} -3.64707 q^{46} +8.17658 q^{47} +(5.88069 - 3.79704i) q^{49} +0.489586i q^{50} +8.00083i q^{52} -12.0648i q^{53} +4.16450i q^{55} +(-1.37725 - 4.67205i) q^{56} -1.82020 q^{58} +2.07878 q^{59} +0.981648i q^{61} +1.35970 q^{62} +2.80809 q^{64} +4.54514i q^{65} +3.76921 q^{67} -13.2131 q^{68} +(-0.366260 - 1.24246i) q^{70} +4.18954i q^{71} +2.92911i q^{73} +2.69459i q^{74} -9.93307i q^{76} +(-3.11547 - 10.5686i) q^{77} -12.4274 q^{79} +2.61928 q^{80} -0.415164i q^{82} -4.40723 q^{83} -7.50615 q^{85} +1.89753i q^{86} -7.66682 q^{88} +1.84785 q^{89} +(-3.40023 - 11.5346i) q^{91} +13.1130i q^{92} +4.00314i q^{94} -5.64281i q^{95} -5.20261i q^{97} +(1.85898 + 2.87911i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 8 q^{4} + 10 q^{5} + 3 q^{7}+O(q^{10}) $ 10 * q - 8 * q^4 + 10 * q^5 + 3 * q^7	$ 10 q - 8 q^{4} + 10 q^{5} + 3 q^{7} + 6 q^{14} + 12 q^{16} - 8 q^{20} + 32 q^{22} + 10 q^{25} - 24 q^{26} - 22 q^{28} + 3 q^{35} + 30 q^{37} - 48 q^{38} + 24 q^{43} - 16 q^{46} + 12 q^{47} - 5 q^{49} - 24 q^{56} - 16 q^{58} + 36 q^{59} - 48 q^{62} - 48 q^{64} + 14 q^{67} - 60 q^{68} + 6 q^{70} - 42 q^{77} - 34 q^{79} + 12 q^{80} - 80 q^{88} + 12 q^{89} - 21 q^{91} + 30 q^{98}+O(q^{100}) $ 10 * q - 8 * q^4 + 10 * q^5 + 3 * q^7 + 6 * q^14 + 12 * q^16 - 8 * q^20 + 32 * q^22 + 10 * q^25 - 24 * q^26 - 22 * q^28 + 3 * q^35 + 30 * q^37 - 48 * q^38 + 24 * q^43 - 16 * q^46 + 12 * q^47 - 5 * q^49 - 24 * q^56 - 16 * q^58 + 36 * q^59 - 48 * q^62 - 48 * q^64 + 14 * q^67 - 60 * q^68 + 6 * q^70 - 42 * q^77 - 34 * q^79 + 12 * q^80 - 80 * q^88 + 12 * q^89 - 21 * q^91 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$			0.489586i			0.346190i	0.984905	+	0.173095i	$0.0553768\pi$
$2$			0.489586i			0.346190i	−0.984905	+	0.173095i	$0.944623\pi$
$3$		0			0
$3$		0			0
$4$	1.76031			0.880153
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−2.53778	+	0.748102i	−0.959192	+	0.282756i
$7$	−2.53778	+	0.748102i	−0.959192	+	0.282756i
$8$			1.84099i			0.650890i
$9$		0			0
$10$			0.489586i			0.154821i
$11$			4.16450i			1.25564i	0.778357	+	0.627822i	$0.216053\pi$
$11$			4.16450i			1.25564i	−0.778357	+	0.627822i	$0.783947\pi$
$12$		0			0
$13$			4.54514i			1.26060i	0.776354	+	0.630298i	$0.217067\pi$
$13$			4.54514i			1.26060i	−0.776354	+	0.630298i	$0.782933\pi$
$14$	−0.366260	−	1.24246i	−0.0978872	−	0.332063i
$15$		0			0
$16$	2.61928			0.654821
$17$	−7.50615			−1.82051			−0.910255	−	0.414048i	$-0.864115\pi$
$17$	−7.50615			−1.82051			−0.910255	+	0.414048i	$0.864115\pi$
$18$		0			0
$19$		−	5.64281i		−	1.29455i	−0.762257	−	0.647275i	$-0.775909\pi$
$19$		−	5.64281i		−	1.29455i	0.762257	−	0.647275i	$-0.224091\pi$
$20$	1.76031			0.393616
$21$		0			0
$22$	−2.03888			−0.434691
$23$			7.44928i			1.55328i	0.629943	+	0.776642i	$0.283078\pi$
$23$			7.44928i			1.55328i	−0.629943	+	0.776642i	$0.716922\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−2.22524			−0.436405
$27$		0			0
$28$	−4.46727	+	1.31689i	−0.844235	+	0.248868i
$29$			3.71784i			0.690386i	0.938532	+	0.345193i	$0.112186\pi$
$29$			3.71784i			0.690386i	−0.938532	+	0.345193i	$0.887814\pi$
$30$		0			0
$31$		−	2.77724i		−	0.498807i	−0.968400	−	0.249403i	$-0.919765\pi$
$31$		−	2.77724i		−	0.498807i	0.968400	−	0.249403i	$-0.0802345\pi$
$32$			4.96436i			0.877582i
$33$		0			0
$34$		−	3.67491i		−	0.630242i
$35$	−2.53778	+	0.748102i	−0.428964	+	0.126452i
$36$		0			0
$37$	5.50382			0.904822			0.452411	−	0.891810i	$-0.350564\pi$
$37$	5.50382			0.904822			0.452411	+	0.891810i	$0.350564\pi$
$38$	2.76264			0.448160
$39$		0			0
$40$			1.84099i			0.291087i
$41$	−0.847989			−0.132434			−0.0662168	−	0.997805i	$-0.521093\pi$
$41$	−0.847989			−0.132434			−0.0662168	+	0.997805i	$0.521093\pi$
$42$		0			0
$43$	3.87577			0.591050			0.295525	−	0.955335i	$-0.404505\pi$
$43$	3.87577			0.591050			0.295525	+	0.955335i	$0.404505\pi$
$44$			7.33079i			1.10516i
$45$		0			0
$46$	−3.64707			−0.537731
$47$	8.17658			1.19268			0.596338	−	0.802733i	$-0.296622\pi$
$47$	8.17658			1.19268			0.596338	+	0.802733i	$0.296622\pi$
$48$		0			0
$49$	5.88069	−	3.79704i	0.840098	−	0.542434i
$50$			0.489586i			0.0692380i
$51$		0			0
$52$			8.00083i			1.10952i
$53$		−	12.0648i		−	1.65723i	−0.559821	−	0.828614i	$-0.689130\pi$
$53$		−	12.0648i		−	1.65723i	0.559821	−	0.828614i	$-0.310870\pi$
$54$		0			0
$55$			4.16450i			0.561541i
$56$	−1.37725	−	4.67205i	−0.184043	−	0.624328i
$57$		0			0
$58$	−1.82020			−0.239005
$59$	2.07878			0.270635			0.135317	−	0.990802i	$-0.456795\pi$
$59$	2.07878			0.270635			0.135317	+	0.990802i	$0.456795\pi$
$60$		0			0
$61$			0.981648i			0.125687i	0.998023	+	0.0628436i	$0.0200169\pi$
$61$			0.981648i			0.125687i	−0.998023	+	0.0628436i	$0.979983\pi$
$62$	1.35970			0.172682
$63$		0			0
$64$	2.80809			0.351011
$65$			4.54514i			0.563755i
$66$		0			0
$67$	3.76921			0.460482			0.230241	−	0.973134i	$-0.426049\pi$
$67$	3.76921			0.460482			0.230241	+	0.973134i	$0.426049\pi$
$68$	−13.2131			−1.60233
$69$		0			0
$70$	−0.366260	−	1.24246i	−0.0437765	−	0.148503i
$71$			4.18954i			0.497206i	0.968605	+	0.248603i	$0.0799715\pi$
$71$			4.18954i			0.497206i	−0.968605	+	0.248603i	$0.920028\pi$
$72$		0			0
$73$			2.92911i			0.342827i	0.985199	+	0.171413i	$0.0548333\pi$
$73$			2.92911i			0.342827i	−0.985199	+	0.171413i	$0.945167\pi$
$74$			2.69459i			0.313240i
$75$		0			0
$76$		−	9.93307i		−	1.13940i
$77$	−3.11547	−	10.5686i	−0.355041	−	1.20440i
$78$		0			0
$79$	−12.4274			−1.39819			−0.699094	−	0.715030i	$-0.746413\pi$
$79$	−12.4274			−1.39819			−0.699094	+	0.715030i	$0.746413\pi$
$80$	2.61928			0.292845
$81$		0			0
$82$		−	0.415164i		−	0.0458472i
$83$	−4.40723			−0.483757			−0.241878	−	0.970307i	$-0.577763\pi$
$83$	−4.40723			−0.483757			−0.241878	+	0.970307i	$0.577763\pi$
$84$		0			0
$85$	−7.50615			−0.814157
$86$			1.89753i			0.204615i
$87$		0			0
$88$	−7.66682			−0.817286
$89$	1.84785			0.195871			0.0979357	−	0.995193i	$-0.468776\pi$
$89$	1.84785			0.195871			0.0979357	+	0.995193i	$0.468776\pi$
$90$		0			0
$91$	−3.40023	−	11.5346i	−0.356441	−	1.20915i
$92$			13.1130i			1.36713i
$93$		0			0
$94$			4.00314i			0.412893i
$95$		−	5.64281i		−	0.578940i
$96$		0			0
$97$		−	5.20261i		−	0.528245i	−0.964489	−	0.264122i	$-0.914918\pi$
$97$		−	5.20261i		−	0.528245i	0.964489	−	0.264122i	$-0.0850823\pi$
$98$	1.85898	+	2.87911i	0.187785	+	0.290834i
$99$		0			0
$100$	1.76031			0.176031
$101$	16.1222			1.60422			0.802111	−	0.597176i	$-0.203710\pi$
$101$	16.1222			1.60422			0.802111	+	0.597176i	$0.203710\pi$
$102$		0			0
$103$			13.0371i			1.28459i	0.766459	+	0.642294i	$0.222017\pi$
$103$			13.0371i			1.28459i	−0.766459	+	0.642294i	$0.777983\pi$
$104$	−8.36758			−0.820509
$105$		0			0
$106$	5.90676			0.573715
$107$			9.44463i			0.913046i	0.889711	+	0.456523i	$0.150905\pi$
$107$			9.44463i			0.913046i	−0.889711	+	0.456523i	$0.849095\pi$
$108$		0			0
$109$	6.97470			0.668055			0.334027	−	0.942563i	$-0.391592\pi$
$109$	6.97470			0.668055			0.334027	+	0.942563i	$0.391592\pi$
$110$	−2.03888			−0.194400
$111$		0			0
$112$	−6.64718	+	1.95949i	−0.628099	+	0.185154i
$113$		−	2.00773i		−	0.188871i	−0.995531	−	0.0944357i	$-0.969895\pi$
$113$		−	2.00773i		−	0.188871i	0.995531	−	0.0944357i	$-0.0301047\pi$
$114$		0			0
$115$			7.44928i			0.694649i
$116$			6.54453i			0.607645i
$117$		0			0
$118$			1.01774i			0.0936909i
$119$	19.0490	−	5.61537i	1.74622	−	0.514760i
$120$		0			0
$121$	−6.34305			−0.576641
$122$	−0.480602			−0.0435116
$123$		0			0
$124$		−	4.88879i		−	0.439026i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−1.48173			−0.131482			−0.0657411	−	0.997837i	$-0.520941\pi$
$127$	−1.48173			−0.131482			−0.0657411	+	0.997837i	$0.520941\pi$
$128$			11.3035i			0.999099i
$129$		0			0
$130$	−2.22524			−0.195166
$131$	−16.8238			−1.46990			−0.734949	−	0.678122i	$-0.762794\pi$
$131$	−16.8238			−1.46990			−0.734949	+	0.678122i	$0.762794\pi$
$132$		0			0
$133$	4.22140	+	14.3202i	0.366041	+	1.24172i
$134$			1.84535i			0.159414i
$135$		0			0
$136$		−	13.8188i		−	1.18495i
$137$		−	15.2023i		−	1.29882i	−0.760438	−	0.649411i	$-0.775016\pi$
$137$		−	15.2023i		−	1.29882i	0.760438	−	0.649411i	$-0.224984\pi$
$138$		0			0
$139$			9.17426i			0.778150i	0.921206	+	0.389075i	$0.127205\pi$
$139$			9.17426i			0.778150i	−0.921206	+	0.389075i	$0.872795\pi$
$140$	−4.46727	+	1.31689i	−0.377553	+	0.111297i
$141$		0			0
$142$	−2.05114			−0.172128
$143$	−18.9282			−1.58286
$144$		0			0
$145$			3.71784i			0.308750i
$146$	−1.43405			−0.118683
$147$		0			0
$148$	9.68840			0.796381
$149$		−	5.25667i		−	0.430643i	−0.976543	−	0.215321i	$-0.930920\pi$
$149$		−	5.25667i		−	0.430643i	0.976543	−	0.215321i	$-0.0690799\pi$
$150$		0			0
$151$	18.5651			1.51080			0.755402	−	0.655262i	$-0.227442\pi$
$151$	18.5651			1.51080			0.755402	+	0.655262i	$0.227442\pi$
$152$	10.3884			0.842609
$153$		0			0
$154$	5.17424	−	1.52529i	0.416952	−	0.122911i
$155$		−	2.77724i		−	0.223073i
$156$		0			0
$157$		−	25.0371i		−	1.99818i	−0.0427071	−	0.999088i	$-0.513598\pi$
$157$		−	25.0371i		−	1.99818i	0.0427071	−	0.999088i	$-0.486402\pi$
$158$		−	6.08427i		−	0.484039i
$159$		0			0
$160$			4.96436i			0.392467i
$161$	−5.57282	−	18.9047i	−0.439200	−	1.48990i
$162$		0			0
$163$	−16.7137			−1.30912			−0.654560	−	0.756010i	$-0.727146\pi$
$163$	−16.7137			−1.30912			−0.654560	+	0.756010i	$0.727146\pi$
$164$	−1.49272			−0.116562
$165$		0			0
$166$		−	2.15772i		−	0.167472i
$167$	−8.40751			−0.650593			−0.325297	−	0.945612i	$-0.605464\pi$
$167$	−8.40751			−0.650593			−0.325297	+	0.945612i	$0.605464\pi$
$168$		0			0
$169$	−7.65831			−0.589101
$170$		−	3.67491i		−	0.281853i
$171$		0			0
$172$	6.82254			0.520214
$173$	24.6539			1.87440			0.937202	−	0.348788i	$-0.113407\pi$
$173$	24.6539			1.87440			0.937202	+	0.348788i	$0.113407\pi$
$174$		0			0
$175$	−2.53778	+	0.748102i	−0.191838	+	0.0565512i
$176$			10.9080i			0.822222i
$177$		0			0
$178$			0.904681i			0.0678087i
$179$		−	19.9793i		−	1.49332i	−0.665206	−	0.746660i	$-0.731656\pi$
$179$		−	19.9793i		−	1.49332i	0.665206	−	0.746660i	$-0.268344\pi$
$180$		0			0
$181$		−	7.68266i		−	0.571047i	−0.958372	−	0.285524i	$-0.907832\pi$
$181$		−	7.68266i		−	0.571047i	0.958372	−	0.285524i	$-0.0921675\pi$
$182$	5.64718	−	1.66471i	0.418597	−	0.123396i
$183$		0			0
$184$	−13.7141			−1.01102
$185$	5.50382			0.404649
$186$		0			0
$187$		−	31.2594i		−	2.28591i
$188$	14.3933			1.04974
$189$		0			0
$190$	2.76264			0.200423
$191$		−	10.9269i		−	0.790644i	−0.918543	−	0.395322i	$-0.870633\pi$
$191$		−	10.9269i		−	0.790644i	0.918543	−	0.395322i	$-0.129367\pi$
$192$		0			0
$193$	2.76157			0.198782			0.0993912	−	0.995048i	$-0.468310\pi$
$193$	2.76157			0.198782			0.0993912	+	0.995048i	$0.468310\pi$
$194$	2.54713			0.182873
$195$		0			0
$196$	10.3518	−	6.68395i	0.739415	−	0.477425i
$197$		−	4.72844i		−	0.336887i	−0.985711	−	0.168444i	$-0.946126\pi$
$197$		−	4.72844i		−	0.336887i	0.985711	−	0.168444i	$-0.0538741\pi$
$198$		0			0
$199$			26.6006i			1.88567i	0.333263	+	0.942834i	$0.391850\pi$
$199$			26.6006i			1.88567i	−0.333263	+	0.942834i	$0.608150\pi$
$200$			1.84099i			0.130178i
$201$		0			0
$202$			7.89322i			0.555365i
$203$	−2.78132	−	9.43507i	−0.195211	−	0.662212i
$204$		0			0
$205$	−0.847989			−0.0592261
$206$	−6.38281			−0.444711
$207$		0			0
$208$			11.9050i			0.825464i
$209$	23.4995			1.62549
$210$		0			0
$211$	10.6693			0.734502			0.367251	−	0.930122i	$-0.380299\pi$
$211$	10.6693			0.734502			0.367251	+	0.930122i	$0.380299\pi$
$212$		−	21.2377i		−	1.45861i
$213$		0			0
$214$	−4.62396			−0.316087
$215$	3.87577			0.264326
$216$		0			0
$217$	2.07766	+	7.04803i	0.141041	+	0.478451i
$218$			3.41472i			0.231274i
$219$		0			0
$220$			7.33079i			0.494242i
$221$		−	34.1165i		−	2.29493i
$222$		0			0
$223$			17.6502i			1.18194i	0.806692	+	0.590972i	$0.201255\pi$
$223$			17.6502i			1.18194i	−0.806692	+	0.590972i	$0.798745\pi$
$224$	−3.71384	−	12.5985i	−0.248142	−	0.841770i
$225$		0			0
$226$	0.982958			0.0653854
$227$	5.12904			0.340427			0.170213	−	0.985407i	$-0.445554\pi$
$227$	5.12904			0.340427			0.170213	+	0.985407i	$0.445554\pi$
$228$		0			0
$229$		−	11.6687i		−	0.771092i	−0.922689	−	0.385546i	$-0.874013\pi$
$229$		−	11.6687i		−	0.771092i	0.922689	−	0.385546i	$-0.125987\pi$
$230$	−3.64707			−0.240481
$231$		0			0
$232$	−6.84452			−0.449365
$233$		−	23.1090i		−	1.51392i	−0.653461	−	0.756960i	$-0.726684\pi$
$233$		−	23.1090i		−	1.51392i	0.653461	−	0.756960i	$-0.273316\pi$
$234$		0			0
$235$	8.17658			0.533381
$236$	3.65929			0.238200
$237$		0			0
$238$	2.74921	+	9.32613i	0.178205	+	0.604523i
$239$			19.9293i			1.28912i	0.764554	+	0.644560i	$0.222959\pi$
$239$			19.9293i			1.28912i	−0.764554	+	0.644560i	$0.777041\pi$
$240$		0			0
$241$		−	20.4478i		−	1.31716i	−0.752510	−	0.658581i	$-0.771157\pi$
$241$		−	20.4478i		−	1.31716i	0.752510	−	0.658581i	$-0.228843\pi$
$242$		−	3.10547i		−	0.199627i
$243$		0			0
$244$			1.72800i			0.110624i
$245$	5.88069	−	3.79704i	0.375703	−	0.242584i
$246$		0			0
$247$	25.6474			1.63190
$248$	5.11288			0.324668
$249$		0			0
$250$			0.489586i			0.0309642i
$251$	4.51044			0.284697			0.142348	−	0.989817i	$-0.454535\pi$
$251$	4.51044			0.284697			0.142348	+	0.989817i	$0.454535\pi$
$252$		0			0
$253$	−31.0225			−1.95037
$254$		−	0.725434i		−	0.0455178i
$255$		0			0
$256$	0.0821285			0.00513303
$257$	0.292913			0.0182714			0.00913569	−	0.999958i	$-0.497092\pi$
$257$	0.292913			0.0182714			0.00913569	+	0.999958i	$0.497092\pi$
$258$		0			0
$259$	−13.9675	+	4.11741i	−0.867898	+	0.255844i
$260$			8.00083i			0.496191i
$261$		0			0
$262$		−	8.23668i		−	0.508864i
$263$		−	13.3119i		−	0.820849i	−0.911895	−	0.410424i	$-0.865381\pi$
$263$		−	13.3119i		−	0.820849i	0.911895	−	0.410424i	$-0.134619\pi$
$264$		0			0
$265$		−	12.0648i		−	0.741135i
$266$	−7.01099	+	2.06674i	−0.429871	+	0.126720i
$267$		0			0
$268$	6.63495			0.405294
$269$	−19.0180			−1.15955			−0.579774	−	0.814777i	$-0.696859\pi$
$269$	−19.0180			−1.15955			−0.579774	+	0.814777i	$0.696859\pi$
$270$		0			0
$271$			13.7296i			0.834012i	0.908904	+	0.417006i	$0.136921\pi$
$271$			13.7296i			0.834012i	−0.908904	+	0.417006i	$0.863079\pi$
$272$	−19.6608			−1.19211
$273$		0			0
$274$	7.44285			0.449639
$275$			4.16450i			0.251129i
$276$		0			0
$277$	0.946770			0.0568859			0.0284429	−	0.999595i	$-0.490945\pi$
$277$	0.946770			0.0568859			0.0284429	+	0.999595i	$0.490945\pi$
$278$	−4.49159			−0.269388
$279$		0			0
$280$	−1.37725	−	4.67205i	−0.0823065	−	0.279208i
$281$			14.3606i			0.856682i	0.903617	+	0.428341i	$0.140902\pi$
$281$			14.3606i			0.856682i	−0.903617	+	0.428341i	$0.859098\pi$
$282$		0			0
$283$			8.19962i			0.487417i	0.969849	+	0.243708i	$0.0783640\pi$
$283$			8.19962i			0.487417i	−0.969849	+	0.243708i	$0.921636\pi$
$284$			7.37486i			0.437617i
$285$		0			0
$286$		−	9.26701i		−	0.547970i
$287$	2.15201	−	0.634382i	0.127029	−	0.0374464i
$288$		0			0
$289$	39.3424			2.31426
$290$	−1.82020			−0.106886
$291$		0			0
$292$			5.15613i			0.301740i
$293$	15.7693			0.921255			0.460628	−	0.887594i	$-0.347624\pi$
$293$	15.7693			0.921255			0.460628	+	0.887594i	$0.347624\pi$
$294$		0			0
$295$	2.07878			0.121031
$296$			10.1325i			0.588939i
$297$		0			0
$298$	2.57359			0.149084
$299$	−33.8580			−1.95806
$300$		0			0
$301$	−9.83587	+	2.89947i	−0.566930	+	0.167123i
$302$			9.08921i			0.523025i
$303$		0			0
$304$		−	14.7801i		−	0.847698i
$305$			0.981648i			0.0562090i
$306$		0			0
$307$		−	15.3869i		−	0.878179i	−0.898443	−	0.439090i	$-0.855301\pi$
$307$		−	15.3869i		−	0.878179i	0.898443	−	0.439090i	$-0.144699\pi$
$308$	−5.48417	−	18.6039i	−0.312490	−	1.06006i
$309$		0			0
$310$	1.35970			0.0772257
$311$	34.2945			1.94466			0.972331	−	0.233607i	$-0.0750529\pi$
$311$	34.2945			1.94466			0.972331	+	0.233607i	$0.0750529\pi$
$312$		0			0
$313$			34.7802i			1.96589i	0.183889	+	0.982947i	$0.441131\pi$
$313$			34.7802i			1.96589i	−0.183889	+	0.982947i	$0.558869\pi$
$314$	12.2578			0.691748
$315$		0			0
$316$	−21.8760			−1.23062
$317$			13.7391i			0.771662i	0.922569	+	0.385831i	$0.126085\pi$
$317$			13.7391i			0.771662i	−0.922569	+	0.385831i	$0.873915\pi$
$318$		0			0
$319$	−15.4829			−0.866878
$320$	2.80809			0.156977
$321$		0			0
$322$	9.25547	−	2.72838i	0.515787	−	0.152047i
$323$			42.3558i			2.35674i
$324$		0			0
$325$			4.54514i			0.252119i
$326$		−	8.18281i		−	0.453204i
$327$		0			0
$328$		−	1.56114i		−	0.0861997i
$329$	−20.7504	+	6.11691i	−1.14401	+	0.337236i
$330$		0			0
$331$	4.47628			0.246039			0.123019	−	0.992404i	$-0.460742\pi$
$331$	4.47628			0.246039			0.123019	+	0.992404i	$0.460742\pi$
$332$	−7.75807			−0.425780
$333$		0			0
$334$		−	4.11621i		−	0.225229i
$335$	3.76921			0.205934
$336$		0			0
$337$	8.16854			0.444969			0.222484	−	0.974936i	$-0.428583\pi$
$337$	8.16854			0.444969			0.222484	+	0.974936i	$0.428583\pi$
$338$		−	3.74940i		−	0.203941i
$339$		0			0
$340$	−13.2131			−0.716582
$341$	11.5658			0.626324
$342$		0			0
$343$	−12.0833	+	14.0354i	−0.652439	+	0.757841i
$344$			7.13528i			0.384708i
$345$		0			0
$346$			12.0702i			0.648900i
$347$		−	15.4339i		−	0.828533i	−0.910156	−	0.414267i	$-0.864038\pi$
$347$		−	15.4339i		−	0.828533i	0.910156	−	0.414267i	$-0.135962\pi$
$348$		0			0
$349$			14.9776i			0.801732i	0.916137	+	0.400866i	$0.131291\pi$
$349$			14.9776i			0.801732i	−0.916137	+	0.400866i	$0.868709\pi$
$350$	−0.366260	−	1.24246i	−0.0195774	−	0.0664125i
$351$		0			0
$352$	−20.6740			−1.10193
$353$	−11.0258			−0.586846			−0.293423	−	0.955983i	$-0.594794\pi$
$353$	−11.0258			−0.586846			−0.293423	+	0.955983i	$0.594794\pi$
$354$		0			0
$355$			4.18954i			0.222357i
$356$	3.25278			0.172397
$357$		0			0
$358$	9.78157			0.516972
$359$		−	6.41739i		−	0.338697i	−0.985556	−	0.169348i	$-0.945834\pi$
$359$		−	6.41739i		−	0.338697i	0.985556	−	0.169348i	$-0.0541663\pi$
$360$		0			0
$361$	−12.8413			−0.675858
$362$	3.76132			0.197691
$363$		0			0
$364$	−5.98544	−	20.3044i	−0.313722	−	1.06424i
$365$			2.92911i			0.153317i
$366$		0			0
$367$		−	8.44387i		−	0.440767i	−0.975413	−	0.220383i	$-0.929269\pi$
$367$		−	8.44387i		−	0.440767i	0.975413	−	0.220383i	$-0.0707308\pi$
$368$			19.5118i			1.01712i
$369$		0			0
$370$			2.69459i			0.140085i
$371$	9.02569	+	30.6178i	0.468591	+	1.58960i
$372$		0			0
$373$	−4.96774			−0.257220			−0.128610	−	0.991695i	$-0.541052\pi$
$373$	−4.96774			−0.257220			−0.128610	+	0.991695i	$0.541052\pi$
$374$	15.3042			0.791359
$375$		0			0
$376$			15.0530i			0.776301i
$377$	−16.8981			−0.870297
$378$		0			0
$379$	26.5208			1.36228			0.681142	−	0.732151i	$-0.261484\pi$
$379$	26.5208			1.36228			0.681142	+	0.732151i	$0.261484\pi$
$380$		−	9.93307i		−	0.509556i
$381$		0			0
$382$	5.34967			0.273713
$383$	−13.5683			−0.693305			−0.346653	−	0.937994i	$-0.612682\pi$
$383$	−13.5683			−0.693305			−0.346653	+	0.937994i	$0.612682\pi$
$384$		0			0
$385$	−3.11547	−	10.5686i	−0.158779	−	0.538625i
$386$			1.35203i			0.0688164i
$387$		0			0
$388$		−	9.15818i		−	0.464936i
$389$		−	30.5253i		−	1.54769i	−0.633373	−	0.773847i	$-0.718330\pi$
$389$		−	30.5253i		−	1.54769i	0.633373	−	0.773847i	$-0.281670\pi$
$390$		0			0
$391$		−	55.9155i		−	2.82777i
$392$	6.99033	+	10.8263i	0.353065	+	0.546811i
$393$		0			0
$394$	2.31498			0.116627
$395$	−12.4274			−0.625289
$396$		0			0
$397$		−	25.1088i		−	1.26017i	−0.776525	−	0.630086i	$-0.783019\pi$
$397$		−	25.1088i		−	1.26017i	0.776525	−	0.630086i	$-0.216981\pi$
$398$	−13.0233			−0.652799
$399$		0			0
$400$	2.61928			0.130964
$401$			23.2004i			1.15857i	0.815124	+	0.579287i	$0.196669\pi$
$401$			23.2004i			1.15857i	−0.815124	+	0.579287i	$0.803331\pi$
$402$		0			0
$403$	12.6229			0.628794
$404$	28.3800			1.41196
$405$		0			0
$406$	4.61928	−	1.36170i	0.229251	−	0.0675799i
$407$			22.9206i			1.13613i
$408$		0			0
$409$			15.2890i			0.755993i	0.925807	+	0.377996i	$0.123387\pi$
$409$			15.2890i			0.755993i	−0.925807	+	0.377996i	$0.876613\pi$
$410$		−	0.415164i		−	0.0205035i
$411$		0			0
$412$			22.9493i			1.13063i
$413$	−5.27550	+	1.55514i	−0.259590	+	0.0765235i
$414$		0			0
$415$	−4.40723			−0.216343
$416$	−22.5637			−1.10628
$417$		0			0
$418$			11.5050i			0.562729i
$419$	1.98146			0.0968008			0.0484004	−	0.998828i	$-0.484588\pi$
$419$	1.98146			0.0968008			0.0484004	+	0.998828i	$0.484588\pi$
$420$		0			0
$421$	−2.48271			−0.121000			−0.0605000	−	0.998168i	$-0.519270\pi$
$421$	−2.48271			−0.121000			−0.0605000	+	0.998168i	$0.519270\pi$
$422$			5.22353i			0.254277i
$423$		0			0
$424$	22.2112			1.07867
$425$	−7.50615			−0.364102
$426$		0			0
$427$	−0.734373	−	2.49121i	−0.0355388	−	0.120558i
$428$			16.6254i			0.803620i
$429$		0			0
$430$			1.89753i			0.0915068i
$431$		−	13.3430i		−	0.642710i	−0.946959	−	0.321355i	$-0.895862\pi$
$431$		−	13.3430i		−	0.642710i	0.946959	−	0.321355i	$-0.104138\pi$
$432$		0			0
$433$			9.47081i			0.455138i	0.973762	+	0.227569i	$0.0730777\pi$
$433$			9.47081i			0.455138i	−0.973762	+	0.227569i	$0.926922\pi$
$434$	−3.45062	+	1.01719i	−0.165635	+	0.0488268i
$435$		0			0
$436$	12.2776			0.587990
$437$	42.0349			2.01080
$438$		0			0
$439$		−	29.9302i		−	1.42849i	−0.699895	−	0.714245i	$-0.746770\pi$
$439$		−	29.9302i		−	1.42849i	0.699895	−	0.714245i	$-0.253230\pi$
$440$	−7.66682			−0.365501
$441$		0			0
$442$	16.7030			0.794480
$443$			7.48012i			0.355391i	0.984086	+	0.177696i	$0.0568642\pi$
$443$			7.48012i			0.355391i	−0.984086	+	0.177696i	$0.943136\pi$
$444$		0			0
$445$	1.84785			0.0875964
$446$	−8.64129			−0.409177
$447$		0			0
$448$	−7.12632	+	2.10073i	−0.336687	+	0.0992504i
$449$			6.48371i			0.305985i	0.988227	+	0.152993i	$0.0488911\pi$
$449$			6.48371i			0.305985i	−0.988227	+	0.152993i	$0.951109\pi$
$450$		0			0
$451$		−	3.53145i		−	0.166289i
$452$		−	3.53422i		−	0.166236i
$453$		0			0
$454$			2.51111i			0.117852i
$455$	−3.40023	−	11.5346i	−0.159405	−	0.540750i
$456$		0			0
$457$	−24.5251			−1.14724			−0.573618	−	0.819123i	$-0.694460\pi$
$457$	−24.5251			−1.14724			−0.573618	+	0.819123i	$0.694460\pi$
$458$	5.71286			0.266944
$459$		0			0
$460$			13.1130i			0.611397i
$461$	−35.9551			−1.67460			−0.837299	−	0.546746i	$-0.815866\pi$
$461$	−35.9551			−1.67460			−0.837299	+	0.546746i	$0.815866\pi$
$462$		0			0
$463$	−26.2752			−1.22111			−0.610556	−	0.791973i	$-0.709054\pi$
$463$	−26.2752			−1.22111			−0.610556	+	0.791973i	$0.709054\pi$
$464$			9.73808i			0.452079i
$465$		0			0
$466$	11.3139			0.524104
$467$	−6.43937			−0.297978			−0.148989	−	0.988839i	$-0.547602\pi$
$467$	−6.43937			−0.297978			−0.148989	+	0.988839i	$0.547602\pi$
$468$		0			0
$469$	−9.56543	+	2.81975i	−0.441690	+	0.130204i
$470$			4.00314i			0.184651i
$471$		0			0
$472$			3.82703i			0.176153i
$473$			16.1406i			0.742148i
$474$		0			0
$475$		−	5.64281i		−	0.258910i
$476$	33.5320	−	9.88476i	1.53694	−	0.453067i
$477$		0			0
$478$	−9.75712			−0.446280
$479$	−17.8845			−0.817165			−0.408583	−	0.912721i	$-0.633977\pi$
$479$	−17.8845			−0.817165			−0.408583	+	0.912721i	$0.633977\pi$
$480$		0			0
$481$			25.0156i			1.14061i
$482$	10.0110			0.455988
$483$		0			0
$484$	−11.1657			−0.507532
$485$		−	5.20261i		−	0.236238i
$486$		0			0
$487$	−37.6132			−1.70442			−0.852208	−	0.523204i	$-0.824737\pi$
$487$	−37.6132			−1.70442			−0.852208	+	0.523204i	$0.824737\pi$
$488$	−1.80721			−0.0818085
$489$		0			0
$490$	1.85898	+	2.87911i	0.0839801	+	0.130065i
$491$			23.7551i			1.07205i	0.844201	+	0.536027i	$0.180075\pi$
$491$			23.7551i			1.07205i	−0.844201	+	0.536027i	$0.819925\pi$
$492$		0			0
$493$		−	27.9067i		−	1.25685i
$494$			12.5566i			0.564948i
$495$		0			0
$496$		−	7.27438i		−	0.326629i
$497$	−3.13420	−	10.6321i	−0.140588	−	0.476916i
$498$		0			0
$499$	−26.2797			−1.17644			−0.588221	−	0.808700i	$-0.700172\pi$
$499$	−26.2797			−1.17644			−0.588221	+	0.808700i	$0.700172\pi$
$500$	1.76031			0.0787232
$501$		0			0
$502$			2.20825i			0.0985591i
$503$	7.30788			0.325842			0.162921	−	0.986639i	$-0.447908\pi$
$503$	7.30788			0.325842			0.162921	+	0.986639i	$0.447908\pi$
$504$		0			0
$505$	16.1222			0.717429
$506$		−	15.1882i		−	0.675198i
$507$		0			0
$508$	−2.60829			−0.115724
$509$	−10.6023			−0.469941			−0.234970	−	0.972003i	$-0.575499\pi$
$509$	−10.6023			−0.469941			−0.234970	+	0.972003i	$0.575499\pi$
$510$		0			0
$511$	−2.19127	−	7.43345i	−0.0969362	−	0.328836i
$512$			22.6472i			1.00088i
$513$		0			0
$514$			0.143406i			0.00632537i
$515$			13.0371i			0.574485i
$516$		0			0
$517$			34.0513i			1.49758i
$518$	−2.01583	−	6.83830i	−0.0885705	−	0.300457i
$519$		0			0
$520$	−8.36758			−0.366943
$521$	−27.7994			−1.21791			−0.608956	−	0.793204i	$-0.708412\pi$
$521$	−27.7994			−1.21791			−0.608956	+	0.793204i	$0.708412\pi$
$522$		0			0
$523$		−	13.3236i		−	0.582599i	−0.956632	−	0.291300i	$-0.905912\pi$
$523$		−	13.3236i		−	0.582599i	0.956632	−	0.291300i	$-0.0940877\pi$
$524$	−29.6149			−1.29373
$525$		0			0
$526$	6.51734			0.284170
$527$			20.8464i			0.908083i
$528$		0			0
$529$	−32.4918			−1.41269
$530$	5.90676			0.256573
$531$		0			0
$532$	7.43094	+	25.2080i	0.322172	+	1.09290i
$533$		−	3.85423i		−	0.166945i
$534$		0			0
$535$			9.44463i			0.408327i
$536$			6.93909i			0.299723i
$537$		0			0
$538$		−	9.31096i		−	0.401424i
$539$	15.8128	+	24.4901i	0.681104	+	1.05486i
$540$		0			0
$541$	2.63633			0.113345			0.0566723	−	0.998393i	$-0.481951\pi$
$541$	2.63633			0.113345			0.0566723	+	0.998393i	$0.481951\pi$
$542$	−6.72181			−0.288727
$543$		0			0
$544$		−	37.2632i		−	1.59765i
$545$	6.97470			0.298763
$546$		0			0
$547$	20.2052			0.863911			0.431955	−	0.901895i	$-0.357824\pi$
$547$	20.2052			0.863911			0.431955	+	0.901895i	$0.357824\pi$
$548$		−	26.7607i		−	1.14316i
$549$		0			0
$550$	−2.03888			−0.0869382
$551$	20.9791			0.893738
$552$		0			0
$553$	31.5380	−	9.29694i	1.34113	−	0.395346i
$554$			0.463526i			0.0196933i
$555$		0			0
$556$			16.1495i			0.684891i
$557$		−	3.01472i		−	0.127738i	−0.997958	−	0.0638690i	$-0.979656\pi$
$557$		−	3.01472i		−	0.127738i	0.997958	−	0.0638690i	$-0.0203440\pi$
$558$		0			0
$559$			17.6159i			0.745075i
$560$	−6.64718	+	1.95949i	−0.280894	+	0.0828036i
$561$		0			0
$562$	−7.03076			−0.296575
$563$	24.1011			1.01574			0.507870	−	0.861434i	$-0.330433\pi$
$563$	24.1011			1.01574			0.507870	+	0.861434i	$0.330433\pi$
$564$		0			0
$565$		−	2.00773i		−	0.0844659i
$566$	−4.01442			−0.168739
$567$		0			0
$568$	−7.71291			−0.323627
$569$			13.4560i			0.564104i	0.959399	+	0.282052i	$0.0910151\pi$
$569$			13.4560i			0.564104i	−0.959399	+	0.282052i	$0.908985\pi$
$570$		0			0
$571$	−0.807016			−0.0337726			−0.0168863	−	0.999857i	$-0.505375\pi$
$571$	−0.807016			−0.0337726			−0.0168863	+	0.999857i	$0.505375\pi$
$572$	−33.3195			−1.39316
$573$		0			0
$574$	0.310585	+	1.05360i	0.0129636	+	0.0439762i
$575$			7.44928i			0.310657i
$576$		0			0
$577$		−	3.40081i		−	0.141577i	−0.997491	−	0.0707887i	$-0.977448\pi$
$577$		−	3.40081i		−	0.141577i	0.997491	−	0.0707887i	$-0.0225516\pi$
$578$			19.2615i			0.801172i
$579$		0			0
$580$			6.54453i			0.271747i
$581$	11.1846	−	3.29706i	0.464015	−	0.136785i
$582$		0			0
$583$	50.2438			2.08089
$584$	−5.39248			−0.223142
$585$		0			0
$586$			7.72046i			0.318929i
$587$	9.38982			0.387559			0.193780	−	0.981045i	$-0.437925\pi$
$587$	9.38982			0.387559			0.193780	+	0.981045i	$0.437925\pi$
$588$		0			0
$589$	−15.6714			−0.645730
$590$			1.01774i			0.0418999i
$591$		0			0
$592$	14.4161			0.592496
$593$	26.1766			1.07494			0.537472	−	0.843282i	$-0.319380\pi$
$593$	26.1766			1.07494			0.537472	+	0.843282i	$0.319380\pi$
$594$		0			0
$595$	19.0490	−	5.61537i	0.780933	−	0.230208i
$596$		−	9.25333i		−	0.379031i
$597$		0			0
$598$		−	16.5764i		−	0.677861i
$599$			1.78168i			0.0727975i	0.999337	+	0.0363987i	$0.0115886\pi$
$599$			1.78168i			0.0727975i	−0.999337	+	0.0363987i	$0.988411\pi$
$600$		0			0
$601$			5.37450i			0.219230i	0.993974	+	0.109615i	$0.0349619\pi$
$601$			5.37450i			0.219230i	−0.993974	+	0.109615i	$0.965038\pi$
$602$	−1.41954	−	4.81551i	−0.0578562	−	0.196266i
$603$		0			0
$604$	32.6802			1.32974
$605$	−6.34305			−0.257881
$606$		0			0
$607$		−	22.6297i		−	0.918512i	−0.888304	−	0.459256i	$-0.848116\pi$
$607$		−	22.6297i		−	0.918512i	0.888304	−	0.459256i	$-0.151884\pi$
$608$	28.0129			1.13607
$609$		0			0
$610$	−0.480602			−0.0194590
$611$			37.1637i			1.50348i
$612$		0			0
$613$	−26.6965			−1.07826			−0.539130	−	0.842223i	$-0.681247\pi$
$613$	−26.6965			−1.07826			−0.539130	+	0.842223i	$0.681247\pi$
$614$	7.53324			0.304017
$615$		0			0
$616$	19.4567	−	5.73556i	0.783934	−	0.231092i
$617$		−	10.3195i		−	0.415448i	−0.978187	−	0.207724i	$-0.933394\pi$
$617$		−	10.3195i		−	0.415448i	0.978187	−	0.207724i	$-0.0666057\pi$
$618$		0			0
$619$			25.3607i			1.01933i	0.860372	+	0.509666i	$0.170231\pi$
$619$			25.3607i			1.01933i	−0.860372	+	0.509666i	$0.829769\pi$
$620$		−	4.88879i		−	0.196338i
$621$		0			0
$622$			16.7901i			0.673222i
$623$	−4.68944	+	1.38238i	−0.187878	+	0.0553838i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−17.0279			−0.680573
$627$		0			0
$628$		−	44.0729i		−	1.75870i
$629$	−41.3125			−1.64724
$630$		0			0
$631$	20.8710			0.830862			0.415431	−	0.909625i	$-0.363631\pi$
$631$	20.8710			0.830862			0.415431	+	0.909625i	$0.363631\pi$
$632$		−	22.8787i		−	0.910067i
$633$		0			0
$634$	−6.72646			−0.267142
$635$	−1.48173			−0.0588006
$636$		0			0
$637$	17.2581	+	26.7286i	0.683790	+	1.05902i
$638$		−	7.58024i		−	0.300104i
$639$		0			0
$640$			11.3035i			0.446811i
$641$		−	11.0487i		−	0.436397i	−0.975904	−	0.218199i	$-0.929982\pi$
$641$		−	11.0487i		−	0.436397i	0.975904	−	0.218199i	$-0.0700181\pi$
$642$		0			0
$643$			9.50545i			0.374858i	0.982278	+	0.187429i	$0.0600155\pi$
$643$			9.50545i			0.374858i	−0.982278	+	0.187429i	$0.939985\pi$
$644$	−9.80987	−	33.2780i	−0.386563	−	1.31134i
$645$		0			0
$646$	−20.7368			−0.815880
$647$	3.21015			0.126204			0.0631021	−	0.998007i	$-0.479901\pi$
$647$	3.21015			0.126204			0.0631021	+	0.998007i	$0.479901\pi$
$648$		0			0
$649$			8.65709i			0.339820i
$650$	−2.22524			−0.0872811
$651$		0			0
$652$	−29.4213			−1.15223
$653$			20.4673i			0.800946i	0.916309	+	0.400473i	$0.131154\pi$
$653$			20.4673i			0.800946i	−0.916309	+	0.400473i	$0.868846\pi$
$654$		0			0
$655$	−16.8238			−0.657358
$656$	−2.22112			−0.0867203
$657$		0			0
$658$	−2.99476	−	10.1591i	−0.116748	−	0.396043i
$659$			26.4520i			1.03042i	0.857063	+	0.515212i	$0.172287\pi$
$659$			26.4520i			1.03042i	−0.857063	+	0.515212i	$0.827713\pi$
$660$		0			0
$661$			34.4558i			1.34018i	0.742282	+	0.670088i	$0.233744\pi$
$661$			34.4558i			1.34018i	−0.742282	+	0.670088i	$0.766256\pi$
$662$			2.19153i			0.0851761i
$663$		0			0
$664$		−	8.11369i		−	0.314872i
$665$	4.22140	+	14.3202i	0.163699	+	0.555315i
$666$		0			0
$667$	−27.6952			−1.07236
$668$	−14.7998			−0.572621
$669$		0			0
$670$			1.84535i			0.0712922i
$671$	−4.08807			−0.157818
$672$		0			0
$673$	42.2165			1.62733			0.813664	−	0.581336i	$-0.197470\pi$
$673$	42.2165			1.62733			0.813664	+	0.581336i	$0.197470\pi$
$674$			3.99921i			0.154044i
$675$		0			0
$676$	−13.4810			−0.518498
$677$	−31.8997			−1.22601			−0.613003	−	0.790081i	$-0.710039\pi$
$677$	−31.8997			−1.22601			−0.613003	+	0.790081i	$0.710039\pi$
$678$		0			0
$679$	3.89208	+	13.2031i	0.149364	+	0.506688i
$680$		−	13.8188i		−	0.529926i
$681$		0			0
$682$			5.66246i			0.216827i
$683$		−	11.1140i		−	0.425264i	−0.977132	−	0.212632i	$-0.931796\pi$
$683$		−	11.1140i		−	0.425264i	0.977132	−	0.212632i	$-0.0682036\pi$
$684$		0			0
$685$		−	15.2023i		−	0.580850i
$686$	−6.87155	−	5.91584i	−0.262357	−	0.225868i
$687$		0			0
$688$	10.1518			0.387032
$689$	54.8362			2.08909
$690$		0			0
$691$			37.9833i			1.44495i	0.691396	+	0.722476i	$0.256996\pi$
$691$			37.9833i			1.44495i	−0.691396	+	0.722476i	$0.743004\pi$
$692$	43.3984			1.64976
$693$		0			0
$694$	7.55621			0.286830
$695$			9.17426i			0.347999i
$696$		0			0
$697$	6.36513			0.241097
$698$	−7.33283			−0.277552
$699$		0			0
$700$	−4.46727	+	1.31689i	−0.168847	+	0.0497737i
$701$		−	16.2114i		−	0.612296i	−0.951984	−	0.306148i	$-0.900960\pi$
$701$		−	16.2114i		−	0.612296i	0.951984	−	0.306148i	$-0.0990403\pi$
$702$		0			0
$703$		−	31.0570i		−	1.17134i
$704$			11.6943i			0.440745i
$705$		0			0
$706$		−	5.39810i		−	0.203160i
$707$	−40.9147	+	12.0611i	−1.53876	+	0.453603i
$708$		0			0
$709$	19.1822			0.720404			0.360202	−	0.932874i	$-0.382708\pi$
$709$	19.1822			0.720404			0.360202	+	0.932874i	$0.382708\pi$
$710$	−2.05114			−0.0769779
$711$		0			0
$712$			3.40188i			0.127491i
$713$	20.6884			0.774788
$714$		0			0
$715$	−18.9282			−0.707876
$716$		−	35.1696i		−	1.31435i
$717$		0			0
$718$	3.14186			0.117253
$719$	−4.06672			−0.151663			−0.0758315	−	0.997121i	$-0.524161\pi$
$719$	−4.06672			−0.151663			−0.0758315	+	0.997121i	$0.524161\pi$
$720$		0			0
$721$	−9.75310	−	33.0854i	−0.363225	−	1.23217i
$722$		−	6.28693i		−	0.233975i
$723$		0			0
$724$		−	13.5238i		−	0.502609i
$725$			3.71784i			0.138077i
$726$		0			0
$727$			28.2078i			1.04617i	0.852281	+	0.523084i	$0.175219\pi$
$727$			28.2078i			1.04617i	−0.852281	+	0.523084i	$0.824781\pi$
$728$	21.2351	−	6.25980i	0.787025	−	0.232004i
$729$		0			0
$730$	−1.43405			−0.0530767
$731$	−29.0922			−1.07601
$732$		0			0
$733$		−	25.6461i		−	0.947260i	−0.880724	−	0.473630i	$-0.842943\pi$
$733$		−	25.6461i		−	0.947260i	0.880724	−	0.473630i	$-0.157057\pi$
$734$	4.13401			0.152589
$735$		0			0
$736$	−36.9809			−1.36313
$737$			15.6968i			0.578201i
$738$		0			0
$739$	41.2679			1.51806			0.759031	−	0.651054i	$-0.225673\pi$
$739$	41.2679			1.51806			0.759031	+	0.651054i	$0.225673\pi$
$740$	9.68840			0.356153
$741$		0			0
$742$	−14.9901	+	4.41886i	−0.550303	+	0.162221i
$743$		−	2.90281i		−	0.106494i	−0.998581	−	0.0532469i	$-0.983043\pi$
$743$		−	2.90281i		−	0.106494i	0.998581	−	0.0532469i	$-0.0169570\pi$
$744$		0			0
$745$		−	5.25667i		−	0.192589i
$746$		−	2.43214i		−	0.0890470i
$747$		0			0
$748$		−	55.0260i		−	2.01195i
$749$	−7.06554	−	23.9684i	−0.258169	−	0.875787i
$750$		0			0
$751$	16.6938			0.609165			0.304582	−	0.952486i	$-0.401483\pi$
$751$	16.6938			0.609165			0.304582	+	0.952486i	$0.401483\pi$
$752$	21.4168			0.780990
$753$		0			0
$754$		−	8.27309i		−	0.301288i
$755$	18.5651			0.675652
$756$		0			0
$757$	10.9677			0.398628			0.199314	−	0.979936i	$-0.436129\pi$
$757$	10.9677			0.398628			0.199314	+	0.979936i	$0.436129\pi$
$758$			12.9842i			0.471609i
$759$		0			0
$760$	10.3884			0.376826
$761$	21.8304			0.791350			0.395675	−	0.918391i	$-0.370511\pi$
$761$	21.8304			0.791350			0.395675	+	0.918391i	$0.370511\pi$
$762$		0			0
$763$	−17.7003	+	5.21778i	−0.640793	+	0.188896i
$764$		−	19.2347i		−	0.695887i
$765$		0			0
$766$		−	6.64283i		−	0.240015i
$767$			9.44836i			0.341161i
$768$		0			0
$769$		−	1.80762i		−	0.0651844i	−0.999469	−	0.0325922i	$-0.989624\pi$
$769$		−	1.80762i		−	0.0651844i	0.999469	−	0.0325922i	$-0.0103763\pi$
$770$	5.17424	−	1.52529i	0.186467	−	0.0549677i
$771$		0			0
$772$	4.86121			0.174959
$773$	−21.8828			−0.787071			−0.393535	−	0.919309i	$-0.628748\pi$
$773$	−21.8828			−0.787071			−0.393535	+	0.919309i	$0.628748\pi$
$774$		0			0
$775$		−	2.77724i		−	0.0997614i
$776$	9.57797			0.343829
$777$		0			0
$778$	14.9448			0.535796
$779$			4.78504i			0.171442i
$780$		0			0
$781$	−17.4473			−0.624314
$782$	27.3755			0.978944
$783$		0			0
$784$	15.4032	−	9.94553i	0.550114	−	0.355197i
$785$		−	25.0371i		−	0.893611i
$786$		0			0
$787$			1.95980i			0.0698593i	0.999390	+	0.0349296i	$0.0111207\pi$
$787$			1.95980i			0.0698593i	−0.999390	+	0.0349296i	$0.988879\pi$
$788$		−	8.32349i		−	0.296512i
$789$		0			0
$790$		−	6.08427i		−	0.216469i
$791$	1.50199	+	5.09519i	0.0534045	+	0.181164i
$792$		0			0
$793$	−4.46173			−0.158441
$794$	12.2929			0.436259
$795$		0			0
$796$			46.8252i			1.65968i
$797$	43.8108			1.55186			0.775930	−	0.630819i	$-0.217281\pi$
$797$	43.8108			1.55186			0.775930	+	0.630819i	$0.217281\pi$
$798$		0			0
$799$	−61.3747			−2.17128
$800$			4.96436i			0.175516i
$801$		0			0
$802$	−11.3586			−0.401087
$803$	−12.1983			−0.430468
$804$		0			0
$805$	−5.57282	−	18.9047i	−0.196416	−	0.666302i
$806$			6.18002i			0.217682i
$807$		0			0
$808$			29.6809i			1.04417i
$809$		−	22.0456i		−	0.775081i	−0.921853	−	0.387540i	$-0.873325\pi$
$809$		−	22.0456i		−	0.775081i	0.921853	−	0.387540i	$-0.126675\pi$
$810$		0			0
$811$		−	15.1324i		−	0.531370i	−0.964060	−	0.265685i	$-0.914402\pi$
$811$		−	15.1324i		−	0.531370i	0.964060	−	0.265685i	$-0.0855981\pi$
$812$	−4.89598	−	16.6086i	−0.171815	−	0.582848i
$813$		0			0
$814$	−11.2216			−0.393318
$815$	−16.7137			−0.585456
$816$		0			0
$817$		−	21.8703i		−	0.765143i
$818$	−7.48529			−0.261717
$819$		0			0
$820$	−1.49272			−0.0521280
$821$			14.1352i			0.493321i	0.969102	+	0.246661i	$0.0793333\pi$
$821$			14.1352i			0.493321i	−0.969102	+	0.246661i	$0.920667\pi$
$822$		0			0
$823$	42.6205			1.48566			0.742829	−	0.669481i	$-0.233483\pi$
$823$	42.6205			1.48566			0.742829	+	0.669481i	$0.233483\pi$
$824$	−24.0013			−0.836125
$825$		0			0
$826$	−0.761376	−	2.58281i	−0.0264917	−	0.0898676i
$827$		−	27.1009i		−	0.942391i	−0.882029	−	0.471195i	$-0.843823\pi$
$827$		−	27.1009i		−	0.942391i	0.882029	−	0.471195i	$-0.156177\pi$
$828$		0			0
$829$			4.41734i			0.153420i	0.997053	+	0.0767102i	$0.0244416\pi$
$829$			4.41734i			0.153420i	−0.997053	+	0.0767102i	$0.975558\pi$
$830$		−	2.15772i		−	0.0748956i
$831$		0			0
$832$			12.7632i			0.442483i
$833$	−44.1414	+	28.5012i	−1.52941	+	0.987507i
$834$		0			0
$835$	−8.40751			−0.290954
$836$	41.3662			1.43068
$837$		0			0
$838$			0.970097i			0.0335114i
$839$	−16.0313			−0.553461			−0.276730	−	0.960948i	$-0.589251\pi$
$839$	−16.0313			−0.553461			−0.276730	+	0.960948i	$0.589251\pi$
$840$		0			0
$841$	15.1777			0.523368
$842$		−	1.21550i		−	0.0418890i
$843$		0			0
$844$	18.7812			0.646474
$845$	−7.65831			−0.263454
$846$		0			0
$847$	16.0973	−	4.74524i	0.553109	−	0.163048i
$848$		−	31.6011i		−	1.08519i
$849$		0			0
$850$		−	3.67491i		−	0.126048i
$851$			40.9995i			1.40544i
$852$		0			0
$853$		−	11.4259i		−	0.391216i	−0.980682	−	0.195608i	$-0.937332\pi$
$853$		−	11.4259i		−	0.391216i	0.980682	−	0.195608i	$-0.0626680\pi$
$854$	1.21966	−	0.359539i	0.0417360	−	0.0123032i
$855$		0			0
$856$	−17.3875			−0.594293
$857$	−43.8569			−1.49812			−0.749062	−	0.662500i	$-0.769495\pi$
$857$	−43.8569			−1.49812			−0.749062	+	0.662500i	$0.769495\pi$
$858$		0			0
$859$			36.7156i			1.25272i	0.779533	+	0.626361i	$0.215456\pi$
$859$			36.7156i			1.25272i	−0.779533	+	0.626361i	$0.784544\pi$
$860$	6.82254			0.232647
$861$		0			0
$862$	6.53255			0.222500
$863$			26.9694i			0.918049i	0.888424	+	0.459024i	$0.151801\pi$
$863$			26.9694i			0.918049i	−0.888424	+	0.459024i	$0.848199\pi$
$864$		0			0
$865$	24.6539			0.838259
$866$	−4.63678			−0.157564
$867$		0			0
$868$	3.65731	+	12.4067i	0.124137	+	0.421110i
$869$		−	51.7538i		−	1.75563i
$870$		0			0
$871$			17.1316i			0.580481i
$872$			12.8404i			0.434830i
$873$		0			0
$874$			20.5797i			0.696119i
$875$	−2.53778	+	0.748102i	−0.0857927	+	0.0252904i
$876$		0			0
$877$	45.2340			1.52745			0.763723	−	0.645545i	$-0.223370\pi$
$877$	45.2340			1.52745			0.763723	+	0.645545i	$0.223370\pi$
$878$	14.6534			0.494529
$879$		0			0
$880$			10.9080i			0.367709i
$881$	−27.0860			−0.912549			−0.456275	−	0.889839i	$-0.650817\pi$
$881$	−27.0860			−0.912549			−0.456275	+	0.889839i	$0.650817\pi$
$882$		0			0
$883$	−35.6310			−1.19908			−0.599539	−	0.800345i	$-0.704649\pi$
$883$	−35.6310			−1.19908			−0.599539	+	0.800345i	$0.704649\pi$
$884$		−	60.0555i		−	2.01989i
$885$		0			0
$886$	−3.66216			−0.123033
$887$	−19.3078			−0.648291			−0.324146	−	0.946007i	$-0.605077\pi$
$887$	−19.3078			−0.648291			−0.324146	+	0.946007i	$0.605077\pi$
$888$		0			0
$889$	3.76031	−	1.10848i	0.126117	−	0.0371773i
$890$			0.904681i			0.0303250i
$891$		0			0
$892$			31.0697i			1.04029i
$893$		−	46.1389i		−	1.54398i
$894$		0			0
$895$		−	19.9793i		−	0.667833i
$896$	−8.45618	−	28.6859i	−0.282501	−	0.958327i
$897$		0			0
$898$	−3.17434			−0.105929
$899$	10.3253			0.344369
$900$		0			0
$901$			90.5602i			3.01700i
$902$	1.72895			0.0575677
$903$		0			0
$904$	3.69622			0.122935
$905$		−	7.68266i		−	0.255380i
$906$		0			0
$907$	9.52022			0.316114			0.158057	−	0.987430i	$-0.449477\pi$
$907$	9.52022			0.316114			0.158057	+	0.987430i	$0.449477\pi$
$908$	9.02868			0.299627
$909$		0			0
$910$	5.64718	−	1.66471i	0.187202	−	0.0551844i
$911$		−	48.9710i		−	1.62248i	−0.584712	−	0.811241i	$-0.698792\pi$
$911$		−	48.9710i		−	1.62248i	0.584712	−	0.811241i	$-0.301208\pi$
$912$		0			0
$913$		−	18.3539i		−	0.607426i
$914$		−	12.0072i		−	0.397161i
$915$		0			0
$916$		−	20.5405i		−	0.678679i
$917$	42.6950	−	12.5859i	1.40991	−	0.415622i
$918$		0			0
$919$	7.37896			0.243409			0.121705	−	0.992566i	$-0.461164\pi$
$919$	7.37896			0.243409			0.121705	+	0.992566i	$0.461164\pi$
$920$	−13.7141			−0.452140
$921$		0			0
$922$		−	17.6031i		−	0.579729i
$923$	−19.0420			−0.626776
$924$		0			0
$925$	5.50382			0.180964
$926$		−	12.8640i		−	0.422737i
$927$		0			0
$928$	−18.4567			−0.605870
$929$	55.2640			1.81315			0.906577	−	0.422040i	$-0.138686\pi$
$929$	55.2640			1.81315			0.906577	+	0.422040i	$0.138686\pi$
$930$		0			0
$931$	−21.4260	−	33.1836i	−0.702208	−	1.08755i
$932$		−	40.6789i		−	1.33248i
$933$		0			0
$934$		−	3.15263i		−	0.103157i
$935$		−	31.2594i		−	1.02229i
$936$		0			0
$937$			15.2336i			0.497661i	0.968547	+	0.248831i	$0.0800462\pi$
$937$			15.2336i			0.497661i	−0.968547	+	0.248831i	$0.919954\pi$
$938$	−1.38051	−	4.68310i	−0.0450753	−	0.152909i
$939$		0			0
$940$	14.3933			0.469457
$941$	49.3378			1.60837			0.804183	−	0.594382i	$-0.202603\pi$
$941$	49.3378			1.60837			0.804183	+	0.594382i	$0.202603\pi$
$942$		0			0
$943$		−	6.31691i		−	0.205707i
$944$	5.44492			0.177217
$945$		0			0
$946$	−7.90224			−0.256924
$947$		−	11.2264i		−	0.364808i	−0.983224	−	0.182404i	$-0.941612\pi$
$947$		−	11.2264i		−	0.364808i	0.983224	−	0.182404i	$-0.0583879\pi$
$948$		0			0
$949$	−13.3132			−0.432166
$950$	2.76264			0.0896320
$951$		0			0
$952$	10.3379	+	35.0691i	0.335052	+	1.13660i
$953$		−	56.5926i		−	1.83321i	−0.399789	−	0.916607i	$-0.630917\pi$
$953$		−	56.5926i		−	1.83321i	0.399789	−	0.916607i	$-0.369083\pi$
$954$		0			0
$955$		−	10.9269i		−	0.353587i
$956$			35.0817i			1.13462i
$957$		0			0
$958$		−	8.75602i		−	0.282894i
$959$	11.3729	+	38.5802i	0.367249	+	1.24582i
$960$		0			0
$961$	23.2869			0.751192
$962$	−12.2473			−0.394869
$963$		0			0
$964$		−	35.9945i		−	1.15930i
$965$	2.76157			0.0888982
$966$		0			0
$967$	−27.9391			−0.898462			−0.449231	−	0.893416i	$-0.648302\pi$
$967$	−27.9391			−0.898462			−0.449231	+	0.893416i	$0.648302\pi$
$968$		−	11.6775i		−	0.375329i
$969$		0			0
$970$	2.54713			0.0817833
$971$	34.2336			1.09861			0.549304	−	0.835623i	$-0.314893\pi$
$971$	34.2336			1.09861			0.549304	+	0.835623i	$0.314893\pi$
$972$		0			0
$973$	−6.86328	−	23.2823i	−0.220027	−	0.746396i
$974$		−	18.4149i		−	0.590051i
$975$		0			0
$976$			2.57122i			0.0823026i
$977$		−	14.4101i		−	0.461019i	−0.973070	−	0.230509i	$-0.925961\pi$
$977$		−	14.4101i		−	0.461019i	0.973070	−	0.230509i	$-0.0740392\pi$
$978$		0			0
$979$			7.69536i			0.245945i
$980$	10.3518	−	6.68395i	0.330676	−	0.213511i
$981$		0			0
$982$	−11.6302			−0.371134
$983$	−13.3410			−0.425511			−0.212755	−	0.977105i	$-0.568244\pi$
$983$	−13.3410			−0.425511			−0.212755	+	0.977105i	$0.568244\pi$
$984$		0			0
$985$		−	4.72844i		−	0.150661i
$986$	13.6627			0.435110
$987$		0			0
$988$	45.1472			1.43632
$989$			28.8717i			0.918068i
$990$		0			0
$991$	−6.39839			−0.203251			−0.101626	−	0.994823i	$-0.532404\pi$
$991$	−6.39839			−0.203251			−0.101626	+	0.994823i	$0.532404\pi$
$992$	13.7872			0.437744
$993$		0			0
$994$	5.20535	−	1.53446i	0.165104	−	0.0486702i
$995$			26.6006i			0.843296i
$996$		0			0
$997$		−	34.0634i		−	1.07880i	−0.842051	−	0.539399i	$-0.818652\pi$
$997$		−	34.0634i		−	1.07880i	0.842051	−	0.539399i	$-0.181348\pi$
$998$		−	12.8662i		−	0.407272i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.b.b.566.6	yes	10
3.2	odd	2		945.2.b.a.566.5	✓	10
7.6	odd	2		945.2.b.a.566.6	yes	10
21.20	even	2	inner	945.2.b.b.566.5	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.b.a.566.5	✓	10	3.2	odd	2
945.2.b.a.566.6	yes	10	7.6	odd	2
945.2.b.b.566.5	yes	10	21.20	even	2	inner
945.2.b.b.566.6	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.489586i q^{2} +1.76031 q^{4} +1.00000 q^{5} +(-2.53778 + 0.748102i) q^{7} +1.84099i q^{8} +O(q^{10})\)	\(q+0.489586i q^{2} +1.76031 q^{4} +1.00000 q^{5} +(-2.53778 + 0.748102i) q^{7} +1.84099i q^{8} +0.489586i q^{10} +4.16450i q^{11} +4.54514i q^{13} +(-0.366260 - 1.24246i) q^{14} +2.61928 q^{16} -7.50615 q^{17} -5.64281i q^{19} +1.76031 q^{20} -2.03888 q^{22} +7.44928i q^{23} +1.00000 q^{25} -2.22524 q^{26} +(-4.46727 + 1.31689i) q^{28} +3.71784i q^{29} -2.77724i q^{31} +4.96436i q^{32} -3.67491i q^{34} +(-2.53778 + 0.748102i) q^{35} +5.50382 q^{37} +2.76264 q^{38} +1.84099i q^{40} -0.847989 q^{41} +3.87577 q^{43} +7.33079i q^{44} -3.64707 q^{46} +8.17658 q^{47} +(5.88069 - 3.79704i) q^{49} +0.489586i q^{50} +8.00083i q^{52} -12.0648i q^{53} +4.16450i q^{55} +(-1.37725 - 4.67205i) q^{56} -1.82020 q^{58} +2.07878 q^{59} +0.981648i q^{61} +1.35970 q^{62} +2.80809 q^{64} +4.54514i q^{65} +3.76921 q^{67} -13.2131 q^{68} +(-0.366260 - 1.24246i) q^{70} +4.18954i q^{71} +2.92911i q^{73} +2.69459i q^{74} -9.93307i q^{76} +(-3.11547 - 10.5686i) q^{77} -12.4274 q^{79} +2.61928 q^{80} -0.415164i q^{82} -4.40723 q^{83} -7.50615 q^{85} +1.89753i q^{86} -7.66682 q^{88} +1.84785 q^{89} +(-3.40023 - 11.5346i) q^{91} +13.1130i q^{92} +4.00314i q^{94} -5.64281i q^{95} -5.20261i q^{97} +(1.85898 + 2.87911i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 8 q^{4} + 10 q^{5} + 3 q^{7}+O(q^{10}) \) 10 * q - 8 * q^4 + 10 * q^5 + 3 * q^7	\( 10 q - 8 q^{4} + 10 q^{5} + 3 q^{7} + 6 q^{14} + 12 q^{16} - 8 q^{20} + 32 q^{22} + 10 q^{25} - 24 q^{26} - 22 q^{28} + 3 q^{35} + 30 q^{37} - 48 q^{38} + 24 q^{43} - 16 q^{46} + 12 q^{47} - 5 q^{49} - 24 q^{56} - 16 q^{58} + 36 q^{59} - 48 q^{62} - 48 q^{64} + 14 q^{67} - 60 q^{68} + 6 q^{70} - 42 q^{77} - 34 q^{79} + 12 q^{80} - 80 q^{88} + 12 q^{89} - 21 q^{91} + 30 q^{98}+O(q^{100}) \) 10 * q - 8 * q^4 + 10 * q^5 + 3 * q^7 + 6 * q^14 + 12 * q^16 - 8 * q^20 + 32 * q^22 + 10 * q^25 - 24 * q^26 - 22 * q^28 + 3 * q^35 + 30 * q^37 - 48 * q^38 + 24 * q^43 - 16 * q^46 + 12 * q^47 - 5 * q^49 - 24 * q^56 - 16 * q^58 + 36 * q^59 - 48 * q^62 - 48 * q^64 + 14 * q^67 - 60 * q^68 + 6 * q^70 - 42 * q^77 - 34 * q^79 + 12 * q^80 - 80 * q^88 + 12 * q^89 - 21 * q^91 + 30 * q^98

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