LMFDB - Embedded newform 4410.2.d.b.4409.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4410,2,Mod(4409,4410)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4410, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("4410.4409");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4410.d (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:	$35.2140272914$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 113 x^{12} - 168 x^{11} + 186 x^{10} - 84 x^{9} + \cdots + 390625 $ x^16 - 6x^15 + 21x^14 - 54x^13 + 113x^12 - 168x^11 + 186x^10 - 84x^9 - 6x^8 - 420x^7 + 4650x^6 - 21000x^5 + 70625x^4 - 168750x^3 + 328125x^2 - 468750*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4409.5
Root			$-0.442358 + 2.19188i$ of defining polynomial
Character	$\chi$	$=$	4410.4409
Dual form			4410.2.d.b.4409.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-1.67704 - 1.47903i) q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.67704 - 1.47903i) q^{5} +1.00000 q^{8} +(-1.67704 - 1.47903i) q^{10} -6.33033i q^{11} +1.05290 q^{13} +1.00000 q^{16} +4.63684i q^{17} -6.17914i q^{19} +(-1.67704 - 1.47903i) q^{20} -6.33033i q^{22} +7.04472 q^{23} +(0.624933 + 4.96079i) q^{25} +1.05290 q^{26} -2.98101i q^{29} +6.31561i q^{31} +1.00000 q^{32} +4.63684i q^{34} -3.47982i q^{37} -6.17914i q^{38} +(-1.67704 - 1.47903i) q^{40} -6.97007 q^{41} +2.58650i q^{43} -6.33033i q^{44} +7.04472 q^{46} -8.15421i q^{47} +(0.624933 + 4.96079i) q^{50} +1.05290 q^{52} -8.87365 q^{53} +(-9.36276 + 10.6162i) q^{55} -2.98101i q^{58} -0.904592 q^{59} +10.1735i q^{61} +6.31561i q^{62} +1.00000 q^{64} +(-1.76575 - 1.55727i) q^{65} -9.83224i q^{67} +4.63684i q^{68} -14.4282i q^{71} -8.36666 q^{73} -3.47982i q^{74} -6.17914i q^{76} -5.46566 q^{79} +(-1.67704 - 1.47903i) q^{80} -6.97007 q^{82} -14.6297i q^{83} +(6.85803 - 7.77617i) q^{85} +2.58650i q^{86} -6.33033i q^{88} -3.83964 q^{89} +7.04472 q^{92} -8.15421i q^{94} +(-9.13913 + 10.3627i) q^{95} -5.87891 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8	$ 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} + 16 q^{16} + 16 q^{23} + 12 q^{25} + 16 q^{32} + 16 q^{46} + 12 q^{50} - 32 q^{53} + 16 q^{64} + 40 q^{65} - 8 q^{79} + 64 q^{85} + 16 q^{92} + 24 q^{95}+O(q^{100}) $ 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 + 16 * q^16 + 16 * q^23 + 12 * q^25 + 16 * q^32 + 16 * q^46 + 12 * q^50 - 32 * q^53 + 16 * q^64 + 40 * q^65 - 8 * q^79 + 64 * q^85 + 16 * q^92 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times$.

$n$	$1081$	$2647$	$3431$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.67704	−	1.47903i	−0.749996	−	0.661443i
$5$	−1.67704	−	1.47903i	−0.749996	−	0.661443i
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.67704	−	1.47903i	−0.530327	−	0.467711i
$11$		−	6.33033i		−	1.90867i	−0.298743	−	0.954334i	$-0.596567\pi$
$11$		−	6.33033i		−	1.90867i	0.298743	−	0.954334i	$-0.403433\pi$
$12$		0			0
$13$	1.05290			0.292021			0.146011	−	0.989283i	$-0.453357\pi$
$13$	1.05290			0.292021			0.146011	+	0.989283i	$0.453357\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$			4.63684i			1.12460i	0.826934	+	0.562299i	$0.190083\pi$
$17$			4.63684i			1.12460i	−0.826934	+	0.562299i	$0.809917\pi$
$18$		0			0
$19$		−	6.17914i		−	1.41759i	−0.705414	−	0.708795i	$-0.749239\pi$
$19$		−	6.17914i		−	1.41759i	0.705414	−	0.708795i	$-0.250761\pi$
$20$	−1.67704	−	1.47903i	−0.374998	−	0.330721i
$21$		0			0
$22$		−	6.33033i		−	1.34963i
$23$	7.04472			1.46893			0.734463	−	0.678649i	$-0.237434\pi$
$23$	7.04472			1.46893			0.734463	+	0.678649i	$0.237434\pi$
$24$		0			0
$25$	0.624933	+	4.96079i	0.124987	+	0.992158i
$26$	1.05290			0.206490
$27$		0			0
$28$		0			0
$29$		−	2.98101i		−	0.553560i	−0.960933	−	0.276780i	$-0.910733\pi$
$29$		−	2.98101i		−	0.553560i	0.960933	−	0.276780i	$-0.0892674\pi$
$30$		0			0
$31$			6.31561i			1.13432i	0.823608	+	0.567159i	$0.191957\pi$
$31$			6.31561i			1.13432i	−0.823608	+	0.567159i	$0.808043\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$			4.63684i			0.795211i
$35$		0			0
$36$		0			0
$37$		−	3.47982i		−	0.572078i	−0.958218	−	0.286039i	$-0.907661\pi$
$37$		−	3.47982i		−	0.572078i	0.958218	−	0.286039i	$-0.0923388\pi$
$38$		−	6.17914i		−	1.00239i
$39$		0			0
$40$	−1.67704	−	1.47903i	−0.265163	−	0.233855i
$41$	−6.97007			−1.08854			−0.544271	−	0.838909i	$-0.683194\pi$
$41$	−6.97007			−1.08854			−0.544271	+	0.838909i	$0.683194\pi$
$42$		0			0
$43$			2.58650i			0.394437i	0.980360	+	0.197218i	$0.0631908\pi$
$43$			2.58650i			0.394437i	−0.980360	+	0.197218i	$0.936809\pi$
$44$		−	6.33033i		−	0.954334i
$45$		0			0
$46$	7.04472			1.03869
$47$		−	8.15421i		−	1.18941i	−0.803942	−	0.594707i	$-0.797268\pi$
$47$		−	8.15421i		−	1.18941i	0.803942	−	0.594707i	$-0.202732\pi$
$48$		0			0
$49$		0			0
$50$	0.624933	+	4.96079i	0.0883789	+	0.701562i
$51$		0			0
$52$	1.05290			0.146011
$53$	−8.87365			−1.21889			−0.609445	−	0.792829i	$-0.708608\pi$
$53$	−8.87365			−1.21889			−0.609445	+	0.792829i	$0.708608\pi$
$54$		0			0
$55$	−9.36276	+	10.6162i	−1.26247	+	1.43149i
$56$		0			0
$57$		0			0
$58$		−	2.98101i		−	0.391426i
$59$	−0.904592			−0.117768			−0.0588839	−	0.998265i	$-0.518754\pi$
$59$	−0.904592			−0.117768			−0.0588839	+	0.998265i	$0.518754\pi$
$60$		0			0
$61$			10.1735i			1.30258i	0.758830	+	0.651289i	$0.225771\pi$
$61$			10.1735i			1.30258i	−0.758830	+	0.651289i	$0.774229\pi$
$62$			6.31561i			0.802084i
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.76575	−	1.55727i	−0.219015	−	0.193155i
$66$		0			0
$67$		−	9.83224i		−	1.20120i	−0.799550	−	0.600600i	$-0.794929\pi$
$67$		−	9.83224i		−	1.20120i	0.799550	−	0.600600i	$-0.205071\pi$
$68$			4.63684i			0.562299i
$69$		0			0
$70$		0			0
$71$		−	14.4282i		−	1.71232i	−0.516713	−	0.856159i	$-0.672844\pi$
$71$		−	14.4282i		−	1.71232i	0.516713	−	0.856159i	$-0.327156\pi$
$72$		0			0
$73$	−8.36666			−0.979244			−0.489622	−	0.871935i	$-0.662865\pi$
$73$	−8.36666			−0.979244			−0.489622	+	0.871935i	$0.662865\pi$
$74$		−	3.47982i		−	0.404520i
$75$		0			0
$76$		−	6.17914i		−	0.708795i
$77$		0			0
$78$		0			0
$79$	−5.46566			−0.614934			−0.307467	−	0.951559i	$-0.599481\pi$
$79$	−5.46566			−0.614934			−0.307467	+	0.951559i	$0.599481\pi$
$80$	−1.67704	−	1.47903i	−0.187499	−	0.165361i
$81$		0			0
$82$	−6.97007			−0.769716
$83$		−	14.6297i		−	1.60581i	−0.596105	−	0.802907i	$-0.703286\pi$
$83$		−	14.6297i		−	1.60581i	0.596105	−	0.802907i	$-0.296714\pi$
$84$		0			0
$85$	6.85803	−	7.77617i	0.743858	−	0.843444i
$86$			2.58650i			0.278909i
$87$		0			0
$88$		−	6.33033i		−	0.674816i
$89$	−3.83964			−0.407001			−0.203500	−	0.979075i	$-0.565232\pi$
$89$	−3.83964			−0.407001			−0.203500	+	0.979075i	$0.565232\pi$
$90$		0			0
$91$		0			0
$92$	7.04472			0.734463
$93$		0			0
$94$		−	8.15421i		−	0.841043i
$95$	−9.13913	+	10.3627i	−0.937655	+	1.06319i
$96$		0			0
$97$	−5.87891			−0.596913			−0.298457	−	0.954423i	$-0.596472\pi$
$97$	−5.87891			−0.596913			−0.298457	+	0.954423i	$0.596472\pi$
$98$		0			0
$99$		0			0
$100$	0.624933	+	4.96079i	0.0624933	+	0.496079i
$101$	−6.70816			−0.667487			−0.333744	−	0.942664i	$-0.608312\pi$
$101$	−6.70816			−0.667487			−0.333744	+	0.942664i	$0.608312\pi$
$102$		0			0
$103$	−4.97432			−0.490135			−0.245067	−	0.969506i	$-0.578810\pi$
$103$	−4.97432			−0.490135			−0.245067	+	0.969506i	$0.578810\pi$
$104$	1.05290			0.103245
$105$		0			0
$106$	−8.87365			−0.861885
$107$	7.33930			0.709517			0.354759	−	0.934958i	$-0.384563\pi$
$107$	7.33930			0.709517			0.354759	+	0.934958i	$0.384563\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	−9.36276	+	10.6162i	−0.892704	+	1.01222i
$111$		0			0
$112$		0			0
$113$	0.184551			0.0173611			0.00868054	−	0.999962i	$-0.497237\pi$
$113$	0.184551			0.0173611			0.00868054	+	0.999962i	$0.497237\pi$
$114$		0			0
$115$	−11.8143	−	10.4194i	−1.10169	−	0.971610i
$116$		−	2.98101i		−	0.276780i
$117$		0			0
$118$	−0.904592			−0.0832745
$119$		0			0
$120$		0			0
$121$	−29.0731			−2.64301
$122$			10.1735i			0.921061i
$123$		0			0
$124$			6.31561i			0.567159i
$125$	6.28913	−	9.24375i	0.562517	−	0.826786i
$126$		0			0
$127$		−	6.70276i		−	0.594774i	−0.954757	−	0.297387i	$-0.903885\pi$
$127$		−	6.70276i		−	0.594774i	0.954757	−	0.297387i	$-0.0961151\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−1.76575	−	1.55727i	−0.154867	−	0.136581i
$131$	4.48232			0.391622			0.195811	−	0.980642i	$-0.437266\pi$
$131$	4.48232			0.391622			0.195811	+	0.980642i	$0.437266\pi$
$132$		0			0
$133$		0			0
$134$		−	9.83224i		−	0.849376i
$135$		0			0
$136$			4.63684i			0.397606i
$137$	17.5627			1.50049			0.750243	−	0.661162i	$-0.229936\pi$
$137$	17.5627			1.50049			0.750243	+	0.661162i	$0.229936\pi$
$138$		0			0
$139$			6.02268i			0.510837i	0.966831	+	0.255418i	$0.0822132\pi$
$139$			6.02268i			0.510837i	−0.966831	+	0.255418i	$0.917787\pi$
$140$		0			0
$141$		0			0
$142$		−	14.4282i		−	1.21079i
$143$		−	6.66519i		−	0.557371i
$144$		0			0
$145$	−4.40901	+	4.99928i	−0.366149	+	0.415168i
$146$	−8.36666			−0.692430
$147$		0			0
$148$		−	3.47982i		−	0.286039i
$149$		−	7.00381i		−	0.573775i	−0.957964	−	0.286887i	$-0.907379\pi$
$149$		−	7.00381i		−	0.573775i	0.957964	−	0.286887i	$-0.0926205\pi$
$150$		0			0
$151$	12.8708			1.04741			0.523706	−	0.851899i	$-0.324549\pi$
$151$	12.8708			1.04741			0.523706	+	0.851899i	$0.324549\pi$
$152$		−	6.17914i		−	0.501194i
$153$		0			0
$154$		0			0
$155$	9.34099	−	10.5915i	0.750286	−	0.850733i
$156$		0			0
$157$	11.0439			0.881396			0.440698	−	0.897655i	$-0.354731\pi$
$157$	11.0439			0.881396			0.440698	+	0.897655i	$0.354731\pi$
$158$	−5.46566			−0.434824
$159$		0			0
$160$	−1.67704	−	1.47903i	−0.132582	−	0.116928i
$161$		0			0
$162$		0			0
$163$			7.24574i			0.567530i	0.958894	+	0.283765i	$0.0915836\pi$
$163$			7.24574i			0.567530i	−0.958894	+	0.283765i	$0.908416\pi$
$164$	−6.97007			−0.544271
$165$		0			0
$166$		−	14.6297i		−	1.13548i
$167$		−	13.8606i		−	1.07257i	−0.844038	−	0.536283i	$-0.819828\pi$
$167$		−	13.8606i		−	1.07257i	0.844038	−	0.536283i	$-0.180172\pi$
$168$		0			0
$169$	−11.8914			−0.914724
$170$	6.85803	−	7.77617i	0.525987	−	0.596405i
$171$		0			0
$172$			2.58650i			0.197218i
$173$			0.958803i			0.0728965i	0.999336	+	0.0364482i	$0.0116044\pi$
$173$			0.958803i			0.0728965i	−0.999336	+	0.0364482i	$0.988396\pi$
$174$		0			0
$175$		0			0
$176$		−	6.33033i		−	0.477167i
$177$		0			0
$178$	−3.83964			−0.287793
$179$			23.3862i			1.74797i	0.485954	+	0.873984i	$0.338472\pi$
$179$			23.3862i			1.74797i	−0.485954	+	0.873984i	$0.661528\pi$
$180$		0			0
$181$		−	19.2865i		−	1.43355i	−0.697303	−	0.716776i	$-0.745617\pi$
$181$		−	19.2865i		−	1.43355i	0.697303	−	0.716776i	$-0.254383\pi$
$182$		0			0
$183$		0			0
$184$	7.04472			0.519344
$185$	−5.14676	+	5.83580i	−0.378397	+	0.429056i
$186$		0			0
$187$	29.3527			2.14648
$188$		−	8.15421i		−	0.594707i
$189$		0			0
$190$	−9.13913	+	10.3627i	−0.663022	+	0.751787i
$191$			2.82843i			0.204658i	0.994751	+	0.102329i	$0.0326294\pi$
$191$			2.82843i			0.204658i	−0.994751	+	0.102329i	$0.967371\pi$
$192$		0			0
$193$			8.21725i			0.591490i	0.955267	+	0.295745i	$0.0955679\pi$
$193$			8.21725i			0.591490i	−0.955267	+	0.295745i	$0.904432\pi$
$194$	−5.87891			−0.422081
$195$		0			0
$196$		0			0
$197$	3.51321			0.250306			0.125153	−	0.992137i	$-0.460058\pi$
$197$	3.51321			0.250306			0.125153	+	0.992137i	$0.460058\pi$
$198$		0			0
$199$		−	3.46410i		−	0.245564i	−0.992434	−	0.122782i	$-0.960818\pi$
$199$		−	3.46410i		−	0.245564i	0.992434	−	0.122782i	$-0.0391815\pi$
$200$	0.624933	+	4.96079i	0.0441895	+	0.350781i
$201$		0			0
$202$	−6.70816			−0.471985
$203$		0			0
$204$		0			0
$205$	11.6891	+	10.3090i	0.816402	+	0.720009i
$206$	−4.97432			−0.346577
$207$		0			0
$208$	1.05290			0.0730053
$209$	−39.1160			−2.70571
$210$		0			0
$211$	−9.96592			−0.686082			−0.343041	−	0.939320i	$-0.611457\pi$
$211$	−9.96592			−0.686082			−0.343041	+	0.939320i	$0.611457\pi$
$212$	−8.87365			−0.609445
$213$		0			0
$214$	7.33930			0.501705
$215$	3.82551	−	4.33766i	0.260897	−	0.295826i
$216$		0			0
$217$		0			0
$218$	2.00000			0.135457
$219$		0			0
$220$	−9.36276	+	10.6162i	−0.631237	+	0.715746i
$221$			4.88212i			0.328407i
$222$		0			0
$223$	−11.1087			−0.743894			−0.371947	−	0.928254i	$-0.621310\pi$
$223$	−11.1087			−0.743894			−0.371947	+	0.928254i	$0.621310\pi$
$224$		0			0
$225$		0			0
$226$	0.184551			0.0122761
$227$		−	23.5238i		−	1.56133i	−0.624949	−	0.780665i	$-0.714880\pi$
$227$		−	23.5238i		−	1.56133i	0.624949	−	0.780665i	$-0.285120\pi$
$228$		0			0
$229$			9.48678i			0.626904i	0.949604	+	0.313452i	$0.101485\pi$
$229$			9.48678i			0.626904i	−0.949604	+	0.313452i	$0.898515\pi$
$230$	−11.8143	−	10.4194i	−0.779011	−	0.687032i
$231$		0			0
$232$		−	2.98101i		−	0.195713i
$233$	10.3734			0.679583			0.339791	−	0.940501i	$-0.389644\pi$
$233$	10.3734			0.679583			0.339791	+	0.940501i	$0.389644\pi$
$234$		0			0
$235$	−12.0603	+	13.6750i	−0.786730	+	0.892056i
$236$	−0.904592			−0.0588839
$237$		0			0
$238$		0			0
$239$			12.3746i			0.800444i	0.916418	+	0.400222i	$0.131067\pi$
$239$			12.3746i			0.800444i	−0.916418	+	0.400222i	$0.868933\pi$
$240$		0			0
$241$		−	12.4947i		−	0.804858i	−0.915451	−	0.402429i	$-0.868166\pi$
$241$		−	12.4947i		−	0.804858i	0.915451	−	0.402429i	$-0.131834\pi$
$242$	−29.0731			−1.86889
$243$		0			0
$244$			10.1735i			0.651289i
$245$		0			0
$246$		0			0
$247$		−	6.50600i		−	0.413967i
$248$			6.31561i			0.401042i
$249$		0			0
$250$	6.28913	−	9.24375i	0.397759	−	0.584626i
$251$	13.5304			0.854034			0.427017	−	0.904244i	$-0.359564\pi$
$251$	13.5304			0.854034			0.427017	+	0.904244i	$0.359564\pi$
$252$		0			0
$253$		−	44.5954i		−	2.80369i
$254$		−	6.70276i		−	0.420569i
$255$		0			0
$256$	1.00000			0.0625000
$257$			4.41799i			0.275587i	0.990461	+	0.137793i	$0.0440010\pi$
$257$			4.41799i			0.275587i	−0.990461	+	0.137793i	$0.955999\pi$
$258$		0			0
$259$		0			0
$260$	−1.76575	−	1.55727i	−0.109507	−	0.0965777i
$261$		0			0
$262$	4.48232			0.276919
$263$	−6.12635			−0.377767			−0.188884	−	0.981999i	$-0.560487\pi$
$263$	−6.12635			−0.377767			−0.188884	+	0.981999i	$0.560487\pi$
$264$		0			0
$265$	14.8815	+	13.1244i	0.914162	+	0.806226i
$266$		0			0
$267$		0			0
$268$		−	9.83224i		−	0.600600i
$269$	−4.18740			−0.255310			−0.127655	−	0.991819i	$-0.540745\pi$
$269$	−4.18740			−0.255310			−0.127655	+	0.991819i	$0.540745\pi$
$270$		0			0
$271$		−	0.292938i		−	0.0177947i	−0.999960	−	0.00889737i	$-0.997168\pi$
$271$		−	0.292938i		−	0.0177947i	0.999960	−	0.00889737i	$-0.00283216\pi$
$272$			4.63684i			0.281150i
$273$		0			0
$274$	17.5627			1.06100
$275$	31.4035	−	3.95604i	1.89370	−	0.238558i
$276$		0			0
$277$			14.6220i			0.878550i	0.898353	+	0.439275i	$0.144765\pi$
$277$			14.6220i			0.878550i	−0.898353	+	0.439275i	$0.855235\pi$
$278$			6.02268i			0.361216i
$279$		0			0
$280$		0			0
$281$		−	18.1691i		−	1.08388i	−0.840419	−	0.541938i	$-0.817691\pi$
$281$		−	18.1691i		−	1.08388i	0.840419	−	0.541938i	$-0.182309\pi$
$282$		0			0
$283$	21.2133			1.26100			0.630499	−	0.776190i	$-0.282850\pi$
$283$	21.2133			1.26100			0.630499	+	0.776190i	$0.282850\pi$
$284$		−	14.4282i		−	0.856159i
$285$		0			0
$286$		−	6.66519i		−	0.394121i
$287$		0			0
$288$		0			0
$289$	−4.50027			−0.264722
$290$	−4.40901	+	4.99928i	−0.258906	+	0.293568i
$291$		0			0
$292$	−8.36666			−0.489622
$293$			7.64481i			0.446615i	0.974748	+	0.223307i	$0.0716853\pi$
$293$			7.64481i			0.446615i	−0.974748	+	0.223307i	$0.928315\pi$
$294$		0			0
$295$	1.51704	+	1.33792i	0.0883254	+	0.0778967i
$296$		−	3.47982i		−	0.202260i
$297$		0			0
$298$		−	7.00381i		−	0.405720i
$299$	7.41737			0.428957
$300$		0			0
$301$		0			0
$302$	12.8708			0.740632
$303$		0			0
$304$		−	6.17914i		−	0.354398i
$305$	15.0469	−	17.0613i	0.861581	−	0.976927i
$306$		0			0
$307$	−13.1561			−0.750859			−0.375429	−	0.926851i	$-0.622505\pi$
$307$	−13.1561			−0.750859			−0.375429	+	0.926851i	$0.622505\pi$
$308$		0			0
$309$		0			0
$310$	9.34099	−	10.5915i	0.530533	−	0.601559i
$311$	6.26087			0.355021			0.177511	−	0.984119i	$-0.443196\pi$
$311$	6.26087			0.355021			0.177511	+	0.984119i	$0.443196\pi$
$312$		0			0
$313$	−17.4813			−0.988101			−0.494051	−	0.869433i	$-0.664484\pi$
$313$	−17.4813			−0.988101			−0.494051	+	0.869433i	$0.664484\pi$
$314$	11.0439			0.623241
$315$		0			0
$316$	−5.46566			−0.307467
$317$	−1.53381			−0.0861474			−0.0430737	−	0.999072i	$-0.513715\pi$
$317$	−1.53381			−0.0861474			−0.0430737	+	0.999072i	$0.513715\pi$
$318$		0			0
$319$	−18.8708			−1.05656
$320$	−1.67704	−	1.47903i	−0.0937494	−	0.0826804i
$321$		0			0
$322$		0			0
$323$	28.6516			1.59422
$324$		0			0
$325$	0.657991	+	5.22321i	0.0364988	+	0.289731i
$326$			7.24574i			0.401305i
$327$		0			0
$328$	−6.97007			−0.384858
$329$		0			0
$330$		0			0
$331$	−1.51321			−0.0831737			−0.0415869	−	0.999135i	$-0.513241\pi$
$331$	−1.51321			−0.0831737			−0.0415869	+	0.999135i	$0.513241\pi$
$332$		−	14.6297i		−	0.802907i
$333$		0			0
$334$		−	13.8606i		−	0.758419i
$335$	−14.5422	+	16.4891i	−0.794525	+	0.900894i
$336$		0			0
$337$		−	3.14064i		−	0.171082i	−0.996335	−	0.0855408i	$-0.972738\pi$
$337$		−	3.14064i		−	0.171082i	0.996335	−	0.0855408i	$-0.0272618\pi$
$338$	−11.8914			−0.646807
$339$		0			0
$340$	6.85803	−	7.77617i	0.371929	−	0.421722i
$341$	39.9799			2.16504
$342$		0			0
$343$		0			0
$344$			2.58650i			0.139455i
$345$		0			0
$346$			0.958803i			0.0515456i
$347$	−27.4052			−1.47119			−0.735593	−	0.677424i	$-0.763096\pi$
$347$	−27.4052			−1.47119			−0.735593	+	0.677424i	$0.763096\pi$
$348$		0			0
$349$			19.5594i			1.04699i	0.852028	+	0.523496i	$0.175373\pi$
$349$			19.5594i			1.04699i	−0.852028	+	0.523496i	$0.824627\pi$
$350$		0			0
$351$		0			0
$352$		−	6.33033i		−	0.337408i
$353$			14.8103i			0.788272i	0.919052	+	0.394136i	$0.128956\pi$
$353$			14.8103i			0.788272i	−0.919052	+	0.394136i	$0.871044\pi$
$354$		0			0
$355$	−21.3398	+	24.1968i	−1.13260	+	1.28423i
$356$	−3.83964			−0.203500
$357$		0			0
$358$			23.3862i			1.23600i
$359$			16.5690i			0.874479i	0.899345	+	0.437239i	$0.144044\pi$
$359$			16.5690i			0.874479i	−0.899345	+	0.437239i	$0.855956\pi$
$360$		0			0
$361$	−19.1817			−1.00956
$362$		−	19.2865i		−	1.01367i
$363$		0			0
$364$		0			0
$365$	14.0312	+	12.3746i	0.734429	+	0.647714i
$366$		0			0
$367$	−14.0131			−0.731478			−0.365739	−	0.930717i	$-0.619184\pi$
$367$	−14.0131			−0.731478			−0.365739	+	0.930717i	$0.619184\pi$
$368$	7.04472			0.367231
$369$		0			0
$370$	−5.14676	+	5.83580i	−0.267567	+	0.303389i
$371$		0			0
$372$		0			0
$373$		−	14.6220i		−	0.757098i	−0.925581	−	0.378549i	$-0.876423\pi$
$373$		−	14.6220i		−	0.757098i	0.925581	−	0.378549i	$-0.123577\pi$
$374$	29.3527			1.51779
$375$		0			0
$376$		−	8.15421i		−	0.420522i
$377$		−	3.13870i		−	0.161651i
$378$		0			0
$379$	−4.68145			−0.240470			−0.120235	−	0.992745i	$-0.538365\pi$
$379$	−4.68145			−0.240470			−0.120235	+	0.992745i	$0.538365\pi$
$380$	−9.13913	+	10.3627i	−0.468828	+	0.531593i
$381$		0			0
$382$			2.82843i			0.144715i
$383$		−	11.6724i		−	0.596433i	−0.954498	−	0.298216i	$-0.903608\pi$
$383$		−	11.6724i		−	0.596433i	0.954498	−	0.298216i	$-0.0963917\pi$
$384$		0			0
$385$		0			0
$386$			8.21725i			0.418247i
$387$		0			0
$388$	−5.87891			−0.298457
$389$			13.1004i			0.664214i	0.943242	+	0.332107i	$0.107760\pi$
$389$			13.1004i			0.664214i	−0.943242	+	0.332107i	$0.892240\pi$
$390$		0			0
$391$			32.6652i			1.65195i
$392$		0			0
$393$		0			0
$394$	3.51321			0.176993
$395$	9.16613	+	8.08388i	0.461198	+	0.406744i
$396$		0			0
$397$	30.6804			1.53981			0.769903	−	0.638161i	$-0.220304\pi$
$397$	30.6804			1.53981			0.769903	+	0.638161i	$0.220304\pi$
$398$		−	3.46410i		−	0.173640i
$399$		0			0
$400$	0.624933	+	4.96079i	0.0312467	+	0.248040i
$401$		−	7.94533i		−	0.396771i	−0.980124	−	0.198385i	$-0.936430\pi$
$401$		−	7.94533i		−	0.396771i	0.980124	−	0.198385i	$-0.0635697\pi$
$402$		0			0
$403$			6.64969i			0.331245i
$404$	−6.70816			−0.333744
$405$		0			0
$406$		0			0
$407$	−22.0284			−1.09191
$408$		0			0
$409$			39.8323i			1.96958i	0.173754	+	0.984789i	$0.444410\pi$
$409$			39.8323i			1.96958i	−0.173754	+	0.984789i	$0.555590\pi$
$410$	11.6891	+	10.3090i	0.577283	+	0.509123i
$411$		0			0
$412$	−4.97432			−0.245067
$413$		0			0
$414$		0			0
$415$	−21.6377	+	24.5345i	−1.06215	+	1.20435i
$416$	1.05290			0.0516226
$417$		0			0
$418$	−39.1160			−1.91323
$419$	11.0357			0.539131			0.269566	−	0.962982i	$-0.413120\pi$
$419$	11.0357			0.539131			0.269566	+	0.962982i	$0.413120\pi$
$420$		0			0
$421$	−7.78421			−0.379379			−0.189690	−	0.981844i	$-0.560748\pi$
$421$	−7.78421			−0.379379			−0.189690	+	0.981844i	$0.560748\pi$
$422$	−9.96592			−0.485134
$423$		0			0
$424$	−8.87365			−0.430942
$425$	−23.0024	+	2.89772i	−1.11578	+	0.140560i
$426$		0			0
$427$		0			0
$428$	7.33930			0.354759
$429$		0			0
$430$	3.82551	−	4.33766i	0.184482	−	0.209181i
$431$		−	10.2338i		−	0.492945i	−0.969150	−	0.246472i	$-0.920729\pi$
$431$		−	10.2338i		−	0.492945i	0.969150	−	0.246472i	$-0.0792714\pi$
$432$		0			0
$433$	40.3902			1.94103			0.970513	−	0.241047i	$-0.0774909\pi$
$433$	40.3902			1.94103			0.970513	+	0.241047i	$0.0774909\pi$
$434$		0			0
$435$		0			0
$436$	2.00000			0.0957826
$437$		−	43.5303i		−	2.08234i
$438$		0			0
$439$			12.9709i			0.619065i	0.950889	+	0.309533i	$0.100173\pi$
$439$			12.9709i			0.619065i	−0.950889	+	0.309533i	$0.899827\pi$
$440$	−9.36276	+	10.6162i	−0.446352	+	0.506109i
$441$		0			0
$442$			4.88212i			0.232219i
$443$	−8.65502			−0.411212			−0.205606	−	0.978635i	$-0.565917\pi$
$443$	−8.65502			−0.411212			−0.205606	+	0.978635i	$0.565917\pi$
$444$		0			0
$445$	6.43923	+	5.67894i	0.305249	+	0.269208i
$446$	−11.1087			−0.526012
$447$		0			0
$448$		0			0
$449$		−	25.4407i		−	1.20062i	−0.799768	−	0.600310i	$-0.795044\pi$
$449$		−	25.4407i		−	1.20062i	0.799768	−	0.600310i	$-0.204956\pi$
$450$		0			0
$451$			44.1229i			2.07767i
$452$	0.184551			0.00868054
$453$		0			0
$454$		−	23.5238i		−	1.10403i
$455$		0			0
$456$		0			0
$457$		−	30.5395i		−	1.42858i	−0.699851	−	0.714289i	$-0.746750\pi$
$457$		−	30.5395i		−	1.42858i	0.699851	−	0.714289i	$-0.253250\pi$
$458$			9.48678i			0.443288i
$459$		0			0
$460$	−11.8143	−	10.4194i	−0.550844	−	0.485805i
$461$	15.6680			0.729734			0.364867	−	0.931060i	$-0.381114\pi$
$461$	15.6680			0.729734			0.364867	+	0.931060i	$0.381114\pi$
$462$		0			0
$463$			32.0462i			1.48931i	0.667448	+	0.744656i	$0.267387\pi$
$463$			32.0462i			1.48931i	−0.667448	+	0.744656i	$0.732613\pi$
$464$		−	2.98101i		−	0.138390i
$465$		0			0
$466$	10.3734			0.480538
$467$		−	0.699158i		−	0.0323532i	−0.999869	−	0.0161766i	$-0.994851\pi$
$467$		−	0.699158i		−	0.0323532i	0.999869	−	0.0161766i	$-0.00514940\pi$
$468$		0			0
$469$		0			0
$470$	−12.0603	+	13.6750i	−0.556302	+	0.630779i
$471$		0			0
$472$	−0.904592			−0.0416372
$473$	16.3734			0.752849
$474$		0			0
$475$	30.6534	−	3.86155i	1.40647	−	0.177180i
$476$		0			0
$477$		0			0
$478$			12.3746i			0.565999i
$479$	−8.54561			−0.390459			−0.195229	−	0.980758i	$-0.562545\pi$
$479$	−8.54561			−0.390459			−0.195229	+	0.980758i	$0.562545\pi$
$480$		0			0
$481$		−	3.66389i		−	0.167059i
$482$		−	12.4947i		−	0.569120i
$483$		0			0
$484$	−29.0731			−1.32151
$485$	9.85918	+	8.69510i	0.447682	+	0.394824i
$486$		0			0
$487$			23.8178i			1.07929i	0.841894	+	0.539643i	$0.181441\pi$
$487$			23.8178i			1.07929i	−0.841894	+	0.539643i	$0.818559\pi$
$488$			10.1735i			0.460531i
$489$		0			0
$490$		0			0
$491$		−	12.9104i		−	0.582638i	−0.956626	−	0.291319i	$-0.905906\pi$
$491$		−	12.9104i		−	0.582638i	0.956626	−	0.291319i	$-0.0940941\pi$
$492$		0			0
$493$	13.8225			0.622533
$494$		−	6.50600i		−	0.292719i
$495$		0			0
$496$			6.31561i			0.283579i
$497$		0			0
$498$		0			0
$499$	−16.3365			−0.731321			−0.365660	−	0.930748i	$-0.619157\pi$
$499$	−16.3365			−0.731321			−0.365660	+	0.930748i	$0.619157\pi$
$500$	6.28913	−	9.24375i	0.281258	−	0.413393i
$501$		0			0
$502$	13.5304			0.603893
$503$		−	28.3413i		−	1.26368i	−0.775100	−	0.631838i	$-0.782301\pi$
$503$		−	28.3413i		−	1.26368i	0.775100	−	0.631838i	$-0.217699\pi$
$504$		0			0
$505$	11.2499	+	9.92158i	0.500613	+	0.441505i
$506$		−	44.5954i		−	1.98251i
$507$		0			0
$508$		−	6.70276i		−	0.297387i
$509$	−2.37821			−0.105412			−0.0527062	−	0.998610i	$-0.516785\pi$
$509$	−2.37821			−0.105412			−0.0527062	+	0.998610i	$0.516785\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$			4.41799i			0.194869i
$515$	8.34214	+	7.35718i	0.367599	+	0.324196i
$516$		0			0
$517$	−51.6189			−2.27020
$518$		0			0
$519$		0			0
$520$	−1.76575	−	1.55727i	−0.0774334	−	0.0682907i
$521$	8.28370			0.362915			0.181458	−	0.983399i	$-0.441918\pi$
$521$	8.28370			0.362915			0.181458	+	0.983399i	$0.441918\pi$
$522$		0			0
$523$	41.8616			1.83048			0.915239	−	0.402910i	$-0.132001\pi$
$523$	41.8616			1.83048			0.915239	+	0.402910i	$0.132001\pi$
$524$	4.48232			0.195811
$525$		0			0
$526$	−6.12635			−0.267122
$527$	−29.2845			−1.27565
$528$		0			0
$529$	26.6281			1.15774
$530$	14.8815	+	13.1244i	0.646410	+	0.570088i
$531$		0			0
$532$		0			0
$533$	−7.33877			−0.317877
$534$		0			0
$535$	−12.3083	−	10.8551i	−0.532135	−	0.469305i
$536$		−	9.83224i		−	0.424688i
$537$		0			0
$538$	−4.18740			−0.180531
$539$		0			0
$540$		0			0
$541$	45.9304			1.97470			0.987352	−	0.158543i	$-0.0506796\pi$
$541$	45.9304			1.97470			0.987352	+	0.158543i	$0.0506796\pi$
$542$		−	0.292938i		−	0.0125828i
$543$		0			0
$544$			4.63684i			0.198803i
$545$	−3.35408	−	2.95806i	−0.143673	−	0.126709i
$546$		0			0
$547$		−	4.88688i		−	0.208948i	−0.994528	−	0.104474i	$-0.966684\pi$
$547$		−	4.88688i		−	0.208948i	0.994528	−	0.104474i	$-0.0333159\pi$
$548$	17.5627			0.750243
$549$		0			0
$550$	31.4035	−	3.95604i	1.33905	−	0.168686i
$551$	−18.4201			−0.784722
$552$		0			0
$553$		0			0
$554$			14.6220i			0.621229i
$555$		0			0
$556$			6.02268i			0.255418i
$557$	29.3677			1.24435			0.622175	−	0.782878i	$-0.286249\pi$
$557$	29.3677			1.24435			0.622175	+	0.782878i	$0.286249\pi$
$558$		0			0
$559$			2.72332i			0.115184i
$560$		0			0
$561$		0			0
$562$		−	18.1691i		−	0.766415i
$563$		−	2.73921i		−	0.115444i	−0.998333	−	0.0577220i	$-0.981616\pi$
$563$		−	2.73921i		−	0.115444i	0.998333	−	0.0577220i	$-0.0183837\pi$
$564$		0			0
$565$	−0.309499	−	0.272956i	−0.0130207	−	0.0114834i
$566$	21.2133			0.891660
$567$		0			0
$568$		−	14.4282i		−	0.605396i
$569$			0.922450i			0.0386711i	0.999813	+	0.0193356i	$0.00615508\pi$
$569$			0.922450i			0.0386711i	−0.999813	+	0.0193356i	$0.993845\pi$
$570$		0			0
$571$	−24.5523			−1.02748			−0.513740	−	0.857946i	$-0.671740\pi$
$571$	−24.5523			−1.02748			−0.513740	+	0.857946i	$0.671740\pi$
$572$		−	6.66519i		−	0.278686i
$573$		0			0
$574$		0			0
$575$	4.40248	+	34.9474i	0.183596	+	1.45741i
$576$		0			0
$577$	27.1333			1.12958			0.564788	−	0.825236i	$-0.308958\pi$
$577$	27.1333			1.12958			0.564788	+	0.825236i	$0.308958\pi$
$578$	−4.50027			−0.187186
$579$		0			0
$580$	−4.40901	+	4.99928i	−0.183074	+	0.207584i
$581$		0			0
$582$		0			0
$583$			56.1731i			2.32645i
$584$	−8.36666			−0.346215
$585$		0			0
$586$			7.64481i			0.315804i
$587$			8.71353i			0.359646i	0.983699	+	0.179823i	$0.0575525\pi$
$587$			8.71353i			0.359646i	−0.983699	+	0.179823i	$0.942448\pi$
$588$		0			0
$589$	39.0250			1.60800
$590$	1.51704	+	1.33792i	0.0624555	+	0.0550813i
$591$		0			0
$592$		−	3.47982i		−	0.143020i
$593$		−	18.2686i		−	0.750203i	−0.926984	−	0.375102i	$-0.877608\pi$
$593$		−	18.2686i		−	0.750203i	0.926984	−	0.375102i	$-0.122392\pi$
$594$		0			0
$595$		0			0
$596$		−	7.00381i		−	0.286887i
$597$		0			0
$598$	7.41737			0.303319
$599$		−	11.4844i		−	0.469239i	−0.972087	−	0.234619i	$-0.924616\pi$
$599$		−	11.4844i		−	0.469239i	0.972087	−	0.234619i	$-0.0753844\pi$
$600$		0			0
$601$		−	34.4022i		−	1.40329i	−0.712525	−	0.701647i	$-0.752448\pi$
$601$		−	34.4022i		−	1.40329i	0.712525	−	0.701647i	$-0.247552\pi$
$602$		0			0
$603$		0			0
$604$	12.8708			0.523706
$605$	48.7568	+	43.0001i	1.98225	+	1.74820i
$606$		0			0
$607$	45.5128			1.84731			0.923653	−	0.383229i	$-0.125188\pi$
$607$	45.5128			1.84731			0.923653	+	0.383229i	$0.125188\pi$
$608$		−	6.17914i		−	0.250597i
$609$		0			0
$610$	15.0469	−	17.0613i	0.609229	−	0.690792i
$611$		−	8.58555i		−	0.347334i
$612$		0			0
$613$		−	11.7041i		−	0.472724i	−0.971665	−	0.236362i	$-0.924045\pi$
$613$		−	11.7041i		−	0.472724i	0.971665	−	0.236362i	$-0.0759552\pi$
$614$	−13.1561			−0.530937
$615$		0			0
$616$		0			0
$617$	−24.0582			−0.968547			−0.484273	−	0.874917i	$-0.660916\pi$
$617$	−24.0582			−0.968547			−0.484273	+	0.874917i	$0.660916\pi$
$618$		0			0
$619$			3.84278i			0.154454i	0.997014	+	0.0772271i	$0.0246067\pi$
$619$			3.84278i			0.154454i	−0.997014	+	0.0772271i	$0.975393\pi$
$620$	9.34099	−	10.5915i	0.375143	−	0.425367i
$621$		0			0
$622$	6.26087			0.251038
$623$		0			0
$624$		0			0
$625$	−24.2189	+	6.20033i	−0.968757	+	0.248013i
$626$	−17.4813			−0.698693
$627$		0			0
$628$	11.0439			0.440698
$629$	16.1353			0.643358
$630$		0			0
$631$	−25.4387			−1.01270			−0.506349	−	0.862328i	$-0.669005\pi$
$631$	−25.4387			−1.01270			−0.506349	+	0.862328i	$0.669005\pi$
$632$	−5.46566			−0.217412
$633$		0			0
$634$	−1.53381			−0.0609154
$635$	−9.91359	+	11.2408i	−0.393409	+	0.446078i
$636$		0			0
$637$		0			0
$638$	−18.8708			−0.747102
$639$		0			0
$640$	−1.67704	−	1.47903i	−0.0662909	−	0.0584638i
$641$			39.5346i			1.56152i	0.624829	+	0.780762i	$0.285169\pi$
$641$			39.5346i			1.56152i	−0.624829	+	0.780762i	$0.714831\pi$
$642$		0			0
$643$	12.2816			0.484341			0.242170	−	0.970234i	$-0.422141\pi$
$643$	12.2816			0.484341			0.242170	+	0.970234i	$0.422141\pi$
$644$		0			0
$645$		0			0
$646$	28.6516			1.12728
$647$		−	13.3894i		−	0.526392i	−0.964742	−	0.263196i	$-0.915223\pi$
$647$		−	13.3894i		−	0.526392i	0.964742	−	0.263196i	$-0.0847766\pi$
$648$		0			0
$649$			5.72637i			0.224780i
$650$	0.657991	+	5.22321i	0.0258085	+	0.204871i
$651$		0			0
$652$			7.24574i			0.283765i
$653$	49.5777			1.94012			0.970062	−	0.242857i	$-0.0780847\pi$
$653$	49.5777			1.94012			0.970062	+	0.242857i	$0.0780847\pi$
$654$		0			0
$655$	−7.51704	−	6.62949i	−0.293715	−	0.259036i
$656$	−6.97007			−0.272136
$657$		0			0
$658$		0			0
$659$			40.7622i			1.58787i	0.608002	+	0.793936i	$0.291971\pi$
$659$			40.7622i			1.58787i	−0.608002	+	0.793936i	$0.708029\pi$
$660$		0			0
$661$		−	35.7556i		−	1.39073i	−0.718657	−	0.695365i	$-0.755243\pi$
$661$		−	35.7556i		−	1.39073i	0.718657	−	0.695365i	$-0.244757\pi$
$662$	−1.51321			−0.0588127
$663$		0			0
$664$		−	14.6297i		−	0.567741i
$665$		0			0
$666$		0			0
$667$		−	21.0004i		−	0.813139i
$668$		−	13.8606i		−	0.536283i
$669$		0			0
$670$	−14.5422	+	16.4891i	−0.561814	+	0.637028i
$671$	64.4014			2.48619
$672$		0			0
$673$			35.1987i			1.35681i	0.734687	+	0.678406i	$0.237329\pi$
$673$			35.1987i			1.35681i	−0.734687	+	0.678406i	$0.762671\pi$
$674$		−	3.14064i		−	0.120973i
$675$		0			0
$676$	−11.8914			−0.457362
$677$		−	38.4422i		−	1.47745i	−0.674005	−	0.738727i	$-0.735427\pi$
$677$		−	38.4422i		−	1.47745i	0.674005	−	0.738727i	$-0.264573\pi$
$678$		0			0
$679$		0			0
$680$	6.85803	−	7.77617i	0.262993	−	0.298202i
$681$		0			0
$682$	39.9799			1.53091
$683$	38.4023			1.46942			0.734712	−	0.678379i	$-0.237317\pi$
$683$	38.4023			1.46942			0.734712	+	0.678379i	$0.237317\pi$
$684$		0			0
$685$	−29.4534	−	25.9758i	−1.12536	−	0.992486i
$686$		0			0
$687$		0			0
$688$			2.58650i			0.0986092i
$689$	−9.34304			−0.355942
$690$		0			0
$691$		−	20.3469i		−	0.774033i	−0.922073	−	0.387016i	$-0.873506\pi$
$691$		−	20.3469i		−	0.774033i	0.922073	−	0.387016i	$-0.126494\pi$
$692$			0.958803i			0.0364482i
$693$		0			0
$694$	−27.4052			−1.04029
$695$	8.90772	−	10.1003i	0.337889	−	0.383125i
$696$		0			0
$697$		−	32.3191i		−	1.22417i
$698$			19.5594i			0.740335i
$699$		0			0
$700$		0			0
$701$		−	6.98574i		−	0.263848i	−0.991260	−	0.131924i	$-0.957885\pi$
$701$		−	6.98574i		−	0.263848i	0.991260	−	0.131924i	$-0.0421154\pi$
$702$		0			0
$703$	−21.5023			−0.810973
$704$		−	6.33033i		−	0.238583i
$705$		0			0
$706$			14.8103i			0.557393i
$707$		0			0
$708$		0			0
$709$	12.0270			0.451682			0.225841	−	0.974164i	$-0.427487\pi$
$709$	12.0270			0.451682			0.225841	+	0.974164i	$0.427487\pi$
$710$	−21.3398	+	24.1968i	−0.800869	+	0.908088i
$711$		0			0
$712$	−3.83964			−0.143896
$713$			44.4917i			1.66623i
$714$		0			0
$715$	−9.85803	+	11.1778i	−0.368669	+	0.418026i
$716$			23.3862i			0.873984i
$717$		0			0
$718$			16.5690i			0.618350i
$719$	1.67139			0.0623323			0.0311661	−	0.999514i	$-0.490078\pi$
$719$	1.67139			0.0623323			0.0311661	+	0.999514i	$0.490078\pi$
$720$		0			0
$721$		0			0
$722$	−19.1817			−0.713869
$723$		0			0
$724$		−	19.2865i		−	0.716776i
$725$	14.7882	−	1.86294i	0.549220	−	0.0691877i
$726$		0			0
$727$	42.5043			1.57640			0.788198	−	0.615422i	$-0.211014\pi$
$727$	42.5043			1.57640			0.788198	+	0.615422i	$0.211014\pi$
$728$		0			0
$729$		0			0
$730$	14.0312	+	12.3746i	0.519319	+	0.458003i
$731$	−11.9932			−0.443583
$732$		0			0
$733$	−31.8759			−1.17736			−0.588681	−	0.808365i	$-0.700353\pi$
$733$	−31.8759			−1.17736			−0.588681	+	0.808365i	$0.700353\pi$
$734$	−14.0131			−0.517233
$735$		0			0
$736$	7.04472			0.259672
$737$	−62.2414			−2.29269
$738$		0			0
$739$	16.4186			0.603969			0.301985	−	0.953313i	$-0.402351\pi$
$739$	16.4186			0.603969			0.301985	+	0.953313i	$0.402351\pi$
$740$	−5.14676	+	5.83580i	−0.189199	+	0.214528i
$741$		0			0
$742$		0			0
$743$	−4.52385			−0.165964			−0.0829821	−	0.996551i	$-0.526444\pi$
$743$	−4.52385			−0.165964			−0.0829821	+	0.996551i	$0.526444\pi$
$744$		0			0
$745$	−10.3589	+	11.7457i	−0.379519	+	0.430328i
$746$		−	14.6220i		−	0.535349i
$747$		0			0
$748$	29.3527			1.07324
$749$		0			0
$750$		0			0
$751$	−17.3975			−0.634844			−0.317422	−	0.948284i	$-0.602817\pi$
$751$	−17.3975			−0.634844			−0.317422	+	0.948284i	$0.602817\pi$
$752$		−	8.15421i		−	0.297354i
$753$		0			0
$754$		−	3.13870i		−	0.114305i
$755$	−21.5849	−	19.0363i	−0.785554	−	0.692803i
$756$		0			0
$757$		−	5.25454i		−	0.190980i	−0.995430	−	0.0954898i	$-0.969558\pi$
$757$		−	5.25454i		−	0.190980i	0.995430	−	0.0954898i	$-0.0304417\pi$
$758$	−4.68145			−0.170038
$759$		0			0
$760$	−9.13913	+	10.3627i	−0.331511	+	0.375893i
$761$	14.6280			0.530266			0.265133	−	0.964212i	$-0.414584\pi$
$761$	14.6280			0.530266			0.265133	+	0.964212i	$0.414584\pi$
$762$		0			0
$763$		0			0
$764$			2.82843i			0.102329i
$765$		0			0
$766$		−	11.6724i		−	0.421742i
$767$	−0.952443			−0.0343907
$768$		0			0
$769$		−	12.4548i		−	0.449131i	−0.974459	−	0.224566i	$-0.927904\pi$
$769$		−	12.4548i		−	0.449131i	0.974459	−	0.224566i	$-0.0720963\pi$
$770$		0			0
$771$		0			0
$772$			8.21725i			0.295745i
$773$		−	8.30576i		−	0.298737i	−0.988782	−	0.149369i	$-0.952276\pi$
$773$		−	8.30576i		−	0.298737i	0.988782	−	0.149369i	$-0.0477241\pi$
$774$		0			0
$775$	−31.3304	+	3.94684i	−1.12542	+	0.141775i
$776$	−5.87891			−0.211041
$777$		0			0
$778$			13.1004i			0.469670i
$779$			43.0690i			1.54311i
$780$		0			0
$781$	−91.3356			−3.26824
$782$			32.6652i			1.16811i
$783$		0			0
$784$		0			0
$785$	−18.5210	−	16.3342i	−0.661043	−	0.582993i
$786$		0			0
$787$	50.6071			1.80395			0.901975	−	0.431788i	$-0.142117\pi$
$787$	50.6071			1.80395			0.901975	+	0.431788i	$0.142117\pi$
$788$	3.51321			0.125153
$789$		0			0
$790$	9.16613	+	8.08388i	0.326116	+	0.287611i
$791$		0			0
$792$		0			0
$793$			10.7116i			0.380380i
$794$	30.6804			1.08881
$795$		0			0
$796$		−	3.46410i		−	0.122782i
$797$			36.6354i			1.29769i	0.760920	+	0.648846i	$0.224748\pi$
$797$			36.6354i			1.29769i	−0.760920	+	0.648846i	$0.775252\pi$
$798$		0			0
$799$	37.8098			1.33761
$800$	0.624933	+	4.96079i	0.0220947	+	0.175390i
$801$		0			0
$802$		−	7.94533i		−	0.280559i
$803$			52.9638i			1.86905i
$804$		0			0
$805$		0			0
$806$			6.64969i			0.234225i
$807$		0			0
$808$	−6.70816			−0.235992
$809$			43.5386i			1.53074i	0.643593	+	0.765368i	$0.277443\pi$
$809$			43.5386i			1.53074i	−0.643593	+	0.765368i	$0.722557\pi$
$810$		0			0
$811$			13.8915i			0.487795i	0.969801	+	0.243897i	$0.0784260\pi$
$811$			13.8915i			0.487795i	−0.969801	+	0.243897i	$0.921574\pi$
$812$		0			0
$813$		0			0
$814$	−22.0284			−0.772095
$815$	10.7167	−	12.1514i	0.375389	−	0.425645i
$816$		0			0
$817$	15.9823			0.559150
$818$			39.8323i			1.39270i
$819$		0			0
$820$	11.6891	+	10.3090i	0.408201	+	0.360004i
$821$			9.54514i			0.333128i	0.986031	+	0.166564i	$0.0532672\pi$
$821$			9.54514i			0.333128i	−0.986031	+	0.166564i	$0.946733\pi$
$822$		0			0
$823$		−	10.7960i		−	0.376323i	−0.982138	−	0.188162i	$-0.939747\pi$
$823$		−	10.7960i		−	0.376323i	0.982138	−	0.188162i	$-0.0602529\pi$
$824$	−4.97432			−0.173289
$825$		0			0
$826$		0			0
$827$	10.5599			0.367204			0.183602	−	0.983001i	$-0.441224\pi$
$827$	10.5599			0.367204			0.183602	+	0.983001i	$0.441224\pi$
$828$		0			0
$829$		−	35.4826i		−	1.23236i	−0.787605	−	0.616181i	$-0.788679\pi$
$829$		−	35.4826i		−	1.23236i	0.787605	−	0.616181i	$-0.211321\pi$
$830$	−21.6377	+	24.5345i	−0.751056	+	0.851606i
$831$		0			0
$832$	1.05290			0.0365027
$833$		0			0
$834$		0			0
$835$	−20.5003	+	23.2448i	−0.709441	+	0.804420i
$836$	−39.1160			−1.35285
$837$		0			0
$838$	11.0357			0.381223
$839$	−32.5932			−1.12524			−0.562621	−	0.826715i	$-0.690207\pi$
$839$	−32.5932			−1.12524			−0.562621	+	0.826715i	$0.690207\pi$
$840$		0			0
$841$	20.1136			0.693571
$842$	−7.78421			−0.268262
$843$		0			0
$844$	−9.96592			−0.343041
$845$	19.9424	+	17.5878i	0.686039	+	0.605037i
$846$		0			0
$847$		0			0
$848$	−8.87365			−0.304722
$849$		0			0
$850$	−23.0024	+	2.89772i	−0.788975	+	0.0993908i
$851$		−	24.5143i		−	0.840340i
$852$		0			0
$853$	−20.2310			−0.692695			−0.346347	−	0.938106i	$-0.612578\pi$
$853$	−20.2310			−0.692695			−0.346347	+	0.938106i	$0.612578\pi$
$854$		0			0
$855$		0			0
$856$	7.33930			0.250852
$857$			44.9710i			1.53618i	0.640341	+	0.768091i	$0.278793\pi$
$857$			44.9710i			1.53618i	−0.640341	+	0.768091i	$0.721207\pi$
$858$		0			0
$859$			43.7042i			1.49117i	0.666411	+	0.745585i	$0.267830\pi$
$859$			43.7042i			1.49117i	−0.666411	+	0.745585i	$0.732170\pi$
$860$	3.82551	−	4.33766i	0.130449	−	0.147913i
$861$		0			0
$862$		−	10.2338i		−	0.348565i
$863$	−35.6382			−1.21314			−0.606569	−	0.795031i	$-0.707454\pi$
$863$	−35.6382			−1.21314			−0.606569	+	0.795031i	$0.707454\pi$
$864$		0			0
$865$	1.41810	−	1.60795i	0.0482168	−	0.0546720i
$866$	40.3902			1.37251
$867$		0			0
$868$		0			0
$869$			34.5994i			1.17371i
$870$		0			0
$871$		−	10.3523i		−	0.350776i
$872$	2.00000			0.0677285
$873$		0			0
$874$		−	43.5303i		−	1.47243i
$875$		0			0
$876$		0			0
$877$		−	36.4906i		−	1.23220i	−0.787668	−	0.616100i	$-0.788712\pi$
$877$		−	36.4906i		−	1.23220i	0.787668	−	0.616100i	$-0.211288\pi$
$878$			12.9709i			0.437745i
$879$		0			0
$880$	−9.36276	+	10.6162i	−0.315619	+	0.357873i
$881$	0.487935			0.0164390			0.00821948	−	0.999966i	$-0.497384\pi$
$881$	0.487935			0.0164390			0.00821948	+	0.999966i	$0.497384\pi$
$882$		0			0
$883$			6.26720i			0.210908i	0.994424	+	0.105454i	$0.0336296\pi$
$883$			6.26720i			0.210908i	−0.994424	+	0.105454i	$0.966370\pi$
$884$			4.88212i			0.164203i
$885$		0			0
$886$	−8.65502			−0.290771
$887$		−	56.9197i		−	1.91118i	−0.294706	−	0.955588i	$-0.595222\pi$
$887$		−	56.9197i		−	1.91118i	0.294706	−	0.955588i	$-0.404778\pi$
$888$		0			0
$889$		0			0
$890$	6.43923	+	5.67894i	0.215843	+	0.190359i
$891$		0			0
$892$	−11.1087			−0.371947
$893$	−50.3860			−1.68610
$894$		0			0
$895$	34.5890	−	39.2197i	1.15618	−	1.31097i
$896$		0			0
$897$		0			0
$898$		−	25.4407i		−	0.848966i
$899$	18.8269			0.627913
$900$		0			0
$901$		−	41.1457i		−	1.37076i
$902$			44.1229i			1.46913i
$903$		0			0
$904$	0.184551			0.00613807
$905$	−28.5253	+	32.3442i	−0.948213	+	1.07516i
$906$		0			0
$907$		−	16.6606i		−	0.553207i	−0.960984	−	0.276603i	$-0.910791\pi$
$907$		−	16.6606i		−	0.553207i	0.960984	−	0.276603i	$-0.0892088\pi$
$908$		−	23.5238i		−	0.780665i
$909$		0			0
$910$		0			0
$911$			8.02653i			0.265931i	0.991121	+	0.132965i	$0.0424499\pi$
$911$			8.02653i			0.265931i	−0.991121	+	0.132965i	$0.957550\pi$
$912$		0			0
$913$	−92.6106			−3.06496
$914$		−	30.5395i		−	1.01016i
$915$		0			0
$916$			9.48678i			0.313452i
$917$		0			0
$918$		0			0
$919$	13.7147			0.452405			0.226202	−	0.974080i	$-0.427369\pi$
$919$	13.7147			0.452405			0.226202	+	0.974080i	$0.427369\pi$
$920$	−11.8143	−	10.4194i	−0.389505	−	0.343516i
$921$		0			0
$922$	15.6680			0.516000
$923$		−	15.1915i		−	0.500033i
$924$		0			0
$925$	17.2626	−	2.17465i	0.567592	−	0.0715022i
$926$			32.0462i			1.05310i
$927$		0			0
$928$		−	2.98101i		−	0.0978566i
$929$	45.8959			1.50580			0.752898	−	0.658137i	$-0.228655\pi$
$929$	45.8959			1.50580			0.752898	+	0.658137i	$0.228655\pi$
$930$		0			0
$931$		0			0
$932$	10.3734			0.339791
$933$		0			0
$934$		−	0.699158i		−	0.0228772i
$935$	−49.2257	−	43.4136i	−1.60985	−	1.41978i
$936$		0			0
$937$	6.17552			0.201746			0.100873	−	0.994899i	$-0.467836\pi$
$937$	6.17552			0.201746			0.100873	+	0.994899i	$0.467836\pi$
$938$		0			0
$939$		0			0
$940$	−12.0603	+	13.6750i	−0.393365	+	0.446028i
$941$	−33.4096			−1.08912			−0.544560	−	0.838722i	$-0.683304\pi$
$941$	−33.4096			−1.08912			−0.544560	+	0.838722i	$0.683304\pi$
$942$		0			0
$943$	−49.1022			−1.59899
$944$	−0.904592			−0.0294420
$945$		0			0
$946$	16.3734			0.532345
$947$	−6.55365			−0.212965			−0.106483	−	0.994315i	$-0.533959\pi$
$947$	−6.55365			−0.212965			−0.106483	+	0.994315i	$0.533959\pi$
$948$		0			0
$949$	−8.80924			−0.285960
$950$	30.6534	−	3.86155i	0.994528	−	0.125285i
$951$		0			0
$952$		0			0
$953$	−46.5253			−1.50710			−0.753551	−	0.657389i	$-0.771661\pi$
$953$	−46.5253			−1.50710			−0.753551	+	0.657389i	$0.771661\pi$
$954$		0			0
$955$	4.18333	−	4.74339i	0.135369	−	0.153492i
$956$			12.3746i			0.400222i
$957$		0			0
$958$	−8.54561			−0.276096
$959$		0			0
$960$		0			0
$961$	−8.88697			−0.286677
$962$		−	3.66389i		−	0.118129i
$963$		0			0
$964$		−	12.4947i		−	0.402429i
$965$	12.1536	−	13.7807i	0.391237	−	0.443615i
$966$		0			0
$967$		−	5.93169i		−	0.190750i	−0.995441	−	0.0953752i	$-0.969595\pi$
$967$		−	5.93169i		−	0.190750i	0.995441	−	0.0953752i	$-0.0304051\pi$
$968$	−29.0731			−0.934445
$969$		0			0
$970$	9.85918	+	8.69510i	0.316559	+	0.279183i
$971$	−0.340138			−0.0109155			−0.00545777	−	0.999985i	$-0.501737\pi$
$971$	−0.340138			−0.0109155			−0.00545777	+	0.999985i	$0.501737\pi$
$972$		0			0
$973$		0			0
$974$			23.8178i			0.763171i
$975$		0			0
$976$			10.1735i			0.325644i
$977$	−20.6886			−0.661886			−0.330943	−	0.943651i	$-0.607367\pi$
$977$	−20.6886			−0.661886			−0.330943	+	0.943651i	$0.607367\pi$
$978$		0			0
$979$			24.3062i			0.776829i
$980$		0			0
$981$		0			0
$982$		−	12.9104i		−	0.411987i
$983$			21.2258i			0.676997i	0.940967	+	0.338499i	$0.109919\pi$
$983$			21.2258i			0.676997i	−0.940967	+	0.338499i	$0.890081\pi$
$984$		0			0
$985$	−5.89180	−	5.19615i	−0.187728	−	0.165563i
$986$	13.8225			0.440197
$987$		0			0
$988$		−	6.50600i		−	0.206983i
$989$			18.2211i			0.579398i
$990$		0			0
$991$	58.2067			1.84900			0.924499	−	0.381184i	$-0.124484\pi$
$991$	58.2067			1.84900			0.924499	+	0.381184i	$0.124484\pi$
$992$			6.31561i			0.200521i
$993$		0			0
$994$		0			0
$995$	−5.12351	+	5.80944i	−0.162426	+	0.184172i
$996$		0			0
$997$	38.2832			1.21244			0.606220	−	0.795297i	$-0.292685\pi$
$997$	38.2832			1.21244			0.606220	+	0.795297i	$0.292685\pi$
$998$	−16.3365			−0.517122
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4410.2.d.b.4409.5		16
3.2	odd	2		4410.2.d.a.4409.12		16
5.4	even	2		4410.2.d.a.4409.6		16
7.4	even	3		630.2.bo.a.89.8	yes	16
7.5	odd	6		630.2.bo.a.269.6	yes	16
7.6	odd	2	inner	4410.2.d.b.4409.12		16
15.14	odd	2	inner	4410.2.d.b.4409.11		16
21.5	even	6		630.2.bo.b.269.3	yes	16
21.11	odd	6		630.2.bo.b.89.1	yes	16
21.20	even	2		4410.2.d.a.4409.5		16
35.4	even	6		630.2.bo.b.89.3	yes	16
35.12	even	12		3150.2.bf.f.1151.13		32
35.18	odd	12		3150.2.bf.f.1601.16		32
35.19	odd	6		630.2.bo.b.269.1	yes	16
35.32	odd	12		3150.2.bf.f.1601.3		32
35.33	even	12		3150.2.bf.f.1151.4		32
35.34	odd	2		4410.2.d.a.4409.11		16
105.32	even	12		3150.2.bf.f.1601.15		32
105.47	odd	12		3150.2.bf.f.1151.3		32
105.53	even	12		3150.2.bf.f.1601.4		32
105.68	odd	12		3150.2.bf.f.1151.14		32
105.74	odd	6		630.2.bo.a.89.6	✓	16
105.89	even	6		630.2.bo.a.269.8	yes	16
105.104	even	2	inner	4410.2.d.b.4409.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bo.a.89.6	✓	16	105.74	odd	6
630.2.bo.a.89.8	yes	16	7.4	even	3
630.2.bo.a.269.6	yes	16	7.5	odd	6
630.2.bo.a.269.8	yes	16	105.89	even	6
630.2.bo.b.89.1	yes	16	21.11	odd	6
630.2.bo.b.89.3	yes	16	35.4	even	6
630.2.bo.b.269.1	yes	16	35.19	odd	6
630.2.bo.b.269.3	yes	16	21.5	even	6
3150.2.bf.f.1151.3		32	105.47	odd	12
3150.2.bf.f.1151.4		32	35.33	even	12
3150.2.bf.f.1151.13		32	35.12	even	12
3150.2.bf.f.1151.14		32	105.68	odd	12
3150.2.bf.f.1601.3		32	35.32	odd	12
3150.2.bf.f.1601.4		32	105.53	even	12
3150.2.bf.f.1601.15		32	105.32	even	12
3150.2.bf.f.1601.16		32	35.18	odd	12
4410.2.d.a.4409.5		16	21.20	even	2
4410.2.d.a.4409.6		16	5.4	even	2
4410.2.d.a.4409.11		16	35.34	odd	2
4410.2.d.a.4409.12		16	3.2	odd	2
4410.2.d.b.4409.5		16	1.1	even	1	trivial
4410.2.d.b.4409.6		16	105.104	even	2	inner
4410.2.d.b.4409.11		16	15.14	odd	2	inner
4410.2.d.b.4409.12		16	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4410.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.67704 - 1.47903i) q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.67704 - 1.47903i) q^{5} +1.00000 q^{8} +(-1.67704 - 1.47903i) q^{10} -6.33033i q^{11} +1.05290 q^{13} +1.00000 q^{16} +4.63684i q^{17} -6.17914i q^{19} +(-1.67704 - 1.47903i) q^{20} -6.33033i q^{22} +7.04472 q^{23} +(0.624933 + 4.96079i) q^{25} +1.05290 q^{26} -2.98101i q^{29} +6.31561i q^{31} +1.00000 q^{32} +4.63684i q^{34} -3.47982i q^{37} -6.17914i q^{38} +(-1.67704 - 1.47903i) q^{40} -6.97007 q^{41} +2.58650i q^{43} -6.33033i q^{44} +7.04472 q^{46} -8.15421i q^{47} +(0.624933 + 4.96079i) q^{50} +1.05290 q^{52} -8.87365 q^{53} +(-9.36276 + 10.6162i) q^{55} -2.98101i q^{58} -0.904592 q^{59} +10.1735i q^{61} +6.31561i q^{62} +1.00000 q^{64} +(-1.76575 - 1.55727i) q^{65} -9.83224i q^{67} +4.63684i q^{68} -14.4282i q^{71} -8.36666 q^{73} -3.47982i q^{74} -6.17914i q^{76} -5.46566 q^{79} +(-1.67704 - 1.47903i) q^{80} -6.97007 q^{82} -14.6297i q^{83} +(6.85803 - 7.77617i) q^{85} +2.58650i q^{86} -6.33033i q^{88} -3.83964 q^{89} +7.04472 q^{92} -8.15421i q^{94} +(-9.13913 + 10.3627i) q^{95} -5.87891 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8	\( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} + 16 q^{16} + 16 q^{23} + 12 q^{25} + 16 q^{32} + 16 q^{46} + 12 q^{50} - 32 q^{53} + 16 q^{64} + 40 q^{65} - 8 q^{79} + 64 q^{85} + 16 q^{92} + 24 q^{95}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 + 16 * q^16 + 16 * q^23 + 12 * q^25 + 16 * q^32 + 16 * q^46 + 12 * q^50 - 32 * q^53 + 16 * q^64 + 40 * q^65 - 8 * q^79 + 64 * q^85 + 16 * q^92 + 24 * q^95

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