LMFDB - Embedded newform 2268.2.t.c.1781.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(1781,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("2268.1781");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.t (of order $6$, degree $2$, 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:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1781.5
Character	$\chi$	$=$	2268.1781
Dual form			2268.2.t.c.2105.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.896692 - 1.55312i) q^{5} +(-0.0850948 - 2.64438i) q^{7} +O(q^{10})$	$q+(-0.896692 - 1.55312i) q^{5} +(-0.0850948 - 2.64438i) q^{7} +(1.55860 + 0.899858i) q^{11} -3.65730i q^{13} +(0.266302 - 0.461248i) q^{17} +(-2.21112 + 1.27659i) q^{19} +(7.27988 - 4.20304i) q^{23} +(0.891886 - 1.54479i) q^{25} +6.87468i q^{29} +(-2.55471 - 1.47496i) q^{31} +(-4.03073 + 2.50336i) q^{35} +(-0.449707 - 0.778915i) q^{37} +1.70674 q^{41} -10.3476 q^{43} +(-3.11202 - 5.39018i) q^{47} +(-6.98552 + 0.450046i) q^{49} +(-0.153326 - 0.0885228i) q^{53} -3.22758i q^{55} +(5.66533 - 9.81264i) q^{59} +(-2.00450 + 1.15730i) q^{61} +(-5.68021 + 3.27947i) q^{65} +(0.178749 - 0.309602i) q^{67} +3.97543i q^{71} +(-11.0109 - 6.35714i) q^{73} +(2.24694 - 4.19811i) q^{77} +(4.29742 + 7.44334i) q^{79} -11.5140 q^{83} -0.955162 q^{85} +(6.52416 + 11.3002i) q^{89} +(-9.67130 + 0.311217i) q^{91} +(3.96539 + 2.28942i) q^{95} -17.2395i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{7}+O(q^{10}) $ 32 * q - 8 * q^7	$ 32 q - 8 q^{7} - 16 q^{25} + 24 q^{31} - 4 q^{37} + 8 q^{43} - 4 q^{49} + 12 q^{61} + 4 q^{67} - 36 q^{73} + 28 q^{79} - 24 q^{85} - 36 q^{91}+O(q^{100}) $ 32 * q - 8 * q^7 - 16 * q^25 + 24 * q^31 - 4 * q^37 + 8 * q^43 - 4 * q^49 + 12 * q^61 + 4 * q^67 - 36 * q^73 + 28 * q^79 - 24 * q^85 - 36 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.896692	−	1.55312i	−0.401013	−	0.694575i	0.592835	−	0.805324i	$-0.298008\pi$
$5$	−0.896692	−	1.55312i	−0.401013	−	0.694575i	−0.993848	+	0.110749i	$0.964675\pi$
$6$		0			0
$7$	−0.0850948	−	2.64438i	−0.0321628	−	0.999483i
$7$	−0.0850948	−	2.64438i	−0.0321628	−	0.999483i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.55860	+	0.899858i	0.469936	+	0.271318i	0.716213	−	0.697882i	$-0.245874\pi$
$11$	1.55860	+	0.899858i	0.469936	+	0.271318i	−0.246277	+	0.969199i	$0.579207\pi$
$12$		0			0
$13$		−	3.65730i		−	1.01435i	−0.861842	−	0.507176i	$-0.830689\pi$
$13$		−	3.65730i		−	1.01435i	0.861842	−	0.507176i	$-0.169311\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.266302	−	0.461248i	0.0645876	−	0.111869i	−0.831923	−	0.554891i	$-0.812760\pi$
$17$	0.266302	−	0.461248i	0.0645876	−	0.111869i	0.896511	+	0.443022i	$0.146093\pi$
$18$		0			0
$19$	−2.21112	+	1.27659i	−0.507266	+	0.292870i	−0.731709	−	0.681617i	$-0.761277\pi$
$19$	−2.21112	+	1.27659i	−0.507266	+	0.292870i	0.224443	+	0.974487i	$0.427944\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	7.27988	−	4.20304i	1.51796	−	0.876394i	0.518183	−	0.855270i	$-0.326609\pi$
$23$	7.27988	−	4.20304i	1.51796	−	0.876394i	0.999777	−	0.0211245i	$-0.00672463\pi$
$24$		0			0
$25$	0.891886	−	1.54479i	0.178377	−	0.308958i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			6.87468i			1.27660i	0.769789	+	0.638298i	$0.220361\pi$
$29$			6.87468i			1.27660i	−0.769789	+	0.638298i	$0.779639\pi$
$30$		0			0
$31$	−2.55471	−	1.47496i	−0.458840	−	0.264911i	0.252717	−	0.967540i	$-0.418676\pi$
$31$	−2.55471	−	1.47496i	−0.458840	−	0.264911i	−0.711556	+	0.702629i	$0.752009\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.03073	+	2.50336i	−0.681318	+	0.423145i
$36$		0			0
$37$	−0.449707	−	0.778915i	−0.0739314	−	0.128053i	0.826690	−	0.562658i	$-0.190221\pi$
$37$	−0.449707	−	0.778915i	−0.0739314	−	0.128053i	−0.900621	+	0.434605i	$0.856888\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.70674			0.266549			0.133274	−	0.991079i	$-0.457451\pi$
$41$	1.70674			0.266549			0.133274	+	0.991079i	$0.457451\pi$
$42$		0			0
$43$	−10.3476			−1.57800			−0.788999	−	0.614395i	$-0.789400\pi$
$43$	−10.3476			−1.57800			−0.788999	+	0.614395i	$0.789400\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.11202	−	5.39018i	−0.453935	−	0.786238i	0.544692	−	0.838636i	$-0.316647\pi$
$47$	−3.11202	−	5.39018i	−0.453935	−	0.786238i	−0.998626	+	0.0523985i	$0.983313\pi$
$48$		0			0
$49$	−6.98552	+	0.450046i	−0.997931	+	0.0642923i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.153326	−	0.0885228i	−0.0210610	−	0.0121595i	0.489433	−	0.872041i	$-0.337204\pi$
$53$	−0.153326	−	0.0885228i	−0.0210610	−	0.0121595i	−0.510494	+	0.859882i	$0.670537\pi$
$54$		0			0
$55$		−	3.22758i		−	0.435207i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.66533	−	9.81264i	0.737563	−	1.27750i	−0.216026	−	0.976388i	$-0.569310\pi$
$59$	5.66533	−	9.81264i	0.737563	−	1.27750i	0.953590	−	0.301109i	$-0.0973569\pi$
$60$		0			0
$61$	−2.00450	+	1.15730i	−0.256650	+	0.148177i	−0.622805	−	0.782377i	$-0.714007\pi$
$61$	−2.00450	+	1.15730i	−0.256650	+	0.148177i	0.366156	+	0.930554i	$0.380674\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.68021	+	3.27947i	−0.704544	+	0.406769i
$66$		0			0
$67$	0.178749	−	0.309602i	0.0218376	−	0.0378239i	−0.854900	−	0.518793i	$-0.826382\pi$
$67$	0.178749	−	0.309602i	0.0218376	−	0.0378239i	0.876738	+	0.480969i	$0.159715\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			3.97543i			0.471796i	0.971778	+	0.235898i	$0.0758032\pi$
$71$			3.97543i			0.471796i	−0.971778	+	0.235898i	$0.924197\pi$
$72$		0			0
$73$	−11.0109	−	6.35714i	−1.28873	−	0.744046i	−0.310299	−	0.950639i	$-0.600429\pi$
$73$	−11.0109	−	6.35714i	−1.28873	−	0.744046i	−0.978427	+	0.206592i	$0.933763\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.24694	−	4.19811i	0.256063	−	0.478419i
$78$		0			0
$79$	4.29742	+	7.44334i	0.483497	+	0.837441i	0.999820	−	0.0189523i	$-0.00603306\pi$
$79$	4.29742	+	7.44334i	0.483497	+	0.837441i	−0.516323	+	0.856394i	$0.672700\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−11.5140			−1.26383			−0.631913	−	0.775039i	$-0.717730\pi$
$83$	−11.5140			−1.26383			−0.631913	+	0.775039i	$0.717730\pi$
$84$		0			0
$85$	−0.955162			−0.103602
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.52416	+	11.3002i	0.691560	+	1.19782i	0.971327	+	0.237749i	$0.0764095\pi$
$89$	6.52416	+	11.3002i	0.691560	+	1.19782i	−0.279767	+	0.960068i	$0.590257\pi$
$90$		0			0
$91$	−9.67130	+	0.311217i	−1.01383	+	0.0326244i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.96539	+	2.28942i	0.406841	+	0.234890i
$96$		0			0
$97$		−	17.2395i		−	1.75040i	−0.483758	−	0.875202i	$-0.660729\pi$
$97$		−	17.2395i		−	1.75040i	0.483758	−	0.875202i	$-0.339271\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.63240	+	11.4876i	−0.659948	+	1.14306i	0.320681	+	0.947187i	$0.396088\pi$
$101$	−6.63240	+	11.4876i	−0.659948	+	1.14306i	−0.980629	+	0.195876i	$0.937245\pi$
$102$		0			0
$103$	−0.967083	+	0.558346i	−0.0952895	+	0.0550154i	−0.546888	−	0.837206i	$-0.684187\pi$
$103$	−0.967083	+	0.558346i	−0.0952895	+	0.0550154i	0.451598	+	0.892222i	$0.350854\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−11.8598	+	6.84727i	−1.14653	+	0.661951i	−0.948040	−	0.318152i	$-0.896938\pi$
$107$	−11.8598	+	6.84727i	−1.14653	+	0.661951i	−0.198492	+	0.980102i	$0.563604\pi$
$108$		0			0
$109$	5.99996	−	10.3922i	0.574692	−	0.995396i	−0.421383	−	0.906883i	$-0.638455\pi$
$109$	5.99996	−	10.3922i	0.574692	−	0.995396i	0.996075	−	0.0885134i	$-0.0282116\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	10.9589i		−	1.03093i	−0.856911	−	0.515464i	$-0.827620\pi$
$113$		−	10.9589i		−	1.03093i	0.856911	−	0.515464i	$-0.172380\pi$
$114$		0			0
$115$	−13.0556	−	7.53767i	−1.21744	−	0.702891i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.24238	−	0.664953i	−0.113888	−	0.0609562i
$120$		0			0
$121$	−3.88051	−	6.72124i	−0.352774	−	0.611022i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.1659			−1.08815
$126$		0			0
$127$	−8.90303			−0.790016			−0.395008	−	0.918678i	$-0.629258\pi$
$127$	−8.90303			−0.790016			−0.395008	+	0.918678i	$0.629258\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.99549	−	5.18834i	−0.261717	−	0.453307i	0.704981	−	0.709226i	$-0.250955\pi$
$131$	−2.99549	−	5.18834i	−0.261717	−	0.453307i	−0.966698	+	0.255919i	$0.917622\pi$
$132$		0			0
$133$	3.56395	+	5.73842i	0.309034	+	0.497584i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.67834	+	2.70104i	0.399697	+	0.230765i	0.686353	−	0.727268i	$-0.259210\pi$
$137$	4.67834	+	2.70104i	0.399697	+	0.230765i	−0.286656	+	0.958034i	$0.592544\pi$
$138$		0			0
$139$			3.11410i			0.264135i	0.991241	+	0.132067i	$0.0421615\pi$
$139$			3.11410i			0.264135i	−0.991241	+	0.132067i	$0.957838\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.29105	−	5.70027i	0.275212	−	0.476680i
$144$		0			0
$145$	10.6772	−	6.16448i	0.886692	−	0.511932i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	17.8824	−	10.3244i	1.46499	−	0.845810i	0.465750	−	0.884916i	$-0.345785\pi$
$149$	17.8824	−	10.3244i	1.46499	−	0.845810i	0.999235	+	0.0391067i	$0.0124512\pi$
$150$		0			0
$151$	−1.88497	+	3.26486i	−0.153396	+	0.265690i	−0.932474	−	0.361237i	$-0.882354\pi$
$151$	−1.88497	+	3.26486i	−0.153396	+	0.265690i	0.779078	+	0.626928i	$0.215688\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			5.29035i			0.424931i
$156$		0			0
$157$	−5.20107	−	3.00284i	−0.415090	−	0.239653i	0.277884	−	0.960615i	$-0.410367\pi$
$157$	−5.20107	−	3.00284i	−0.415090	−	0.239653i	−0.692975	+	0.720962i	$0.743700\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−11.7339	−	18.8931i	−0.924763	−	1.48899i
$162$		0			0
$163$	−3.68141	−	6.37638i	−0.288350	−	0.499437i	0.685066	−	0.728481i	$-0.259773\pi$
$163$	−3.68141	−	6.37638i	−0.288350	−	0.499437i	−0.973416	+	0.229044i	$0.926440\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.25735			−0.716355			−0.358177	−	0.933654i	$-0.616602\pi$
$167$	−9.25735			−0.716355			−0.358177	+	0.933654i	$0.616602\pi$
$168$		0			0
$169$	−0.375844			−0.0289111
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.56493	+	14.8349i	0.651180	+	1.12788i	0.982837	+	0.184477i	$0.0590590\pi$
$173$	8.56493	+	14.8349i	0.651180	+	1.12788i	−0.331657	+	0.943400i	$0.607608\pi$
$174$		0			0
$175$	−4.16091	−	2.22703i	−0.314536	−	0.168348i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.64373	+	4.99046i	0.646063	+	0.373004i	0.786946	−	0.617022i	$-0.211661\pi$
$179$	8.64373	+	4.99046i	0.646063	+	0.373004i	−0.140884	+	0.990026i	$0.544994\pi$
$180$		0			0
$181$			10.6789i			0.793756i	0.917871	+	0.396878i	$0.129906\pi$
$181$			10.6789i			0.793756i	−0.917871	+	0.396878i	$0.870094\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.806498	+	1.39690i	−0.0592949	+	0.102702i
$186$		0			0
$187$	0.830115	−	0.479267i	0.0607040	−	0.0350475i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.3081	−	7.10610i	0.890585	−	0.514179i	0.0164509	−	0.999865i	$-0.494763\pi$
$191$	12.3081	−	7.10610i	0.890585	−	0.514179i	0.874134	+	0.485685i	$0.161430\pi$
$192$		0			0
$193$	5.00848	−	8.67493i	0.360518	−	0.624435i	−0.627528	−	0.778594i	$-0.715933\pi$
$193$	5.00848	−	8.67493i	0.360518	−	0.624435i	0.988046	+	0.154158i	$0.0492666\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	0.00141605i		−	0.000100890i	−1.00000		5.04448e-5i	$-0.999984\pi$
$197$		−	0.00141605i		−	0.000100890i	1.00000		5.04448e-5i	$-1.60571e-5\pi$
$198$		0			0
$199$	−0.717527	−	0.414264i	−0.0508641	−	0.0293664i	0.474352	−	0.880335i	$-0.342682\pi$
$199$	−0.717527	−	0.414264i	−0.0508641	−	0.0293664i	−0.525216	+	0.850969i	$0.676016\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	18.1793	−	0.585000i	1.27594	−	0.0410589i
$204$		0			0
$205$	−1.53043	−	2.65077i	−0.106890	−	0.185138i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.59501			−0.317843
$210$		0			0
$211$	−9.00349			−0.619826			−0.309913	−	0.950765i	$-0.600300\pi$
$211$	−9.00349			−0.619826			−0.309913	+	0.950765i	$0.600300\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	9.27863	+	16.0711i	0.632797	+	1.09604i
$216$		0			0
$217$	−3.68297	+	6.88114i	−0.250017	+	0.467123i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.68692	−	0.973945i	−0.113475	−	0.0655146i
$222$		0			0
$223$		−	12.5040i		−	0.837327i	−0.908142	−	0.418663i	$-0.862499\pi$
$223$		−	12.5040i		−	0.837327i	0.908142	−	0.418663i	$-0.137501\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.23544	−	5.60395i	0.214744	−	0.371947i	−0.738450	−	0.674309i	$-0.764442\pi$
$227$	3.23544	−	5.60395i	0.214744	−	0.371947i	0.953193	+	0.302362i	$0.0977750\pi$
$228$		0			0
$229$	20.1322	−	11.6233i	1.33037	−	0.768090i	0.345015	−	0.938597i	$-0.387874\pi$
$229$	20.1322	−	11.6233i	1.33037	−	0.768090i	0.985356	+	0.170507i	$0.0545406\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.71475	+	5.60881i	−0.636434	+	0.367446i	−0.783240	−	0.621720i	$-0.786434\pi$
$233$	−9.71475	+	5.60881i	−0.636434	+	0.367446i	0.146805	+	0.989165i	$0.453101\pi$
$234$		0			0
$235$	−5.58105	+	9.66666i	−0.364067	+	0.630583i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			15.9890i			1.03424i	0.855913	+	0.517120i	$0.172996\pi$
$239$			15.9890i			1.03424i	−0.855913	+	0.517120i	$0.827004\pi$
$240$		0			0
$241$	4.52675	+	2.61352i	0.291594	+	0.168352i	0.638660	−	0.769489i	$-0.279489\pi$
$241$	4.52675	+	2.61352i	0.291594	+	0.168352i	−0.347067	+	0.937840i	$0.612822\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.96283	+	10.4458i	0.444839	+	0.667356i
$246$		0			0
$247$	4.66888	+	8.08674i	0.297074	+	0.514547i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	18.5119			1.16846			0.584232	−	0.811587i	$-0.301396\pi$
$251$	18.5119			1.16846			0.584232	+	0.811587i	$0.301396\pi$
$252$		0			0
$253$	15.1286			0.951125
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.9068	−	20.6231i	−0.742723	−	1.28643i	−0.951251	−	0.308417i	$-0.900201\pi$
$257$	−11.9068	−	20.6231i	−0.742723	−	1.28643i	0.208528	−	0.978016i	$-0.433133\pi$
$258$		0			0
$259$	−2.02148	+	1.25548i	−0.125609	+	0.0780117i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−24.2167	−	13.9815i	−1.49327	−	0.862138i	−0.493297	−	0.869861i	$-0.664208\pi$
$263$	−24.2167	−	13.9815i	−1.49327	−	0.862138i	−0.999970	+	0.00772288i	$0.997542\pi$
$264$		0			0
$265$			0.317511i			0.0195045i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.62799	−	14.9441i	0.526058	−	0.911159i	−0.473481	−	0.880804i	$-0.657003\pi$
$269$	8.62799	−	14.9441i	0.526058	−	0.911159i	0.999539	−	0.0303553i	$-0.00966387\pi$
$270$		0			0
$271$	6.39382	−	3.69147i	0.388397	−	0.224241i	−0.293068	−	0.956091i	$-0.594676\pi$
$271$	6.39382	−	3.69147i	0.388397	−	0.224241i	0.681465	+	0.731850i	$0.261343\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.78019	−	1.60514i	0.167652	−	0.0967937i
$276$		0			0
$277$	−2.13496	+	3.69786i	−0.128277	+	0.222183i	−0.923009	−	0.384778i	$-0.874278\pi$
$277$	−2.13496	+	3.69786i	−0.128277	+	0.222183i	0.794732	+	0.606961i	$0.207611\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	1.32630i		−	0.0791204i	−0.999217	−	0.0395602i	$-0.987404\pi$
$281$		−	1.32630i		−	0.0791204i	0.999217	−	0.0395602i	$-0.0125957\pi$
$282$		0			0
$283$	−28.0769	−	16.2102i	−1.66900	−	0.963598i	−0.968178	−	0.250262i	$-0.919483\pi$
$283$	−28.0769	−	16.2102i	−1.66900	−	0.963598i	−0.700822	−	0.713336i	$-0.747183\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.145235	−	4.51329i	−0.00857295	−	0.266411i
$288$		0			0
$289$	8.35817	+	14.4768i	0.491657	+	0.851575i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	10.8712			0.635102			0.317551	−	0.948241i	$-0.397140\pi$
$293$	10.8712			0.635102			0.317551	+	0.948241i	$0.397140\pi$
$294$		0			0
$295$	−20.3202			−1.18309
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−15.3718	−	26.6247i	−0.888973	−	1.53975i
$300$		0			0
$301$	0.880528	+	27.3631i	0.0507528	+	1.57718i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.59484	+	2.07548i	0.205840	+	0.118842i
$306$		0			0
$307$		−	6.75922i		−	0.385769i	−0.981221	−	0.192885i	$-0.938216\pi$
$307$		−	6.75922i		−	0.385769i	0.981221	−	0.192885i	$-0.0617843\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−17.1929	+	29.7790i	−0.974922	+	1.68861i	−0.294728	+	0.955581i	$0.595229\pi$
$311$	−17.1929	+	29.7790i	−0.974922	+	1.68861i	−0.680194	+	0.733032i	$0.738104\pi$
$312$		0			0
$313$	26.4851	−	15.2912i	1.49703	−	0.864309i	0.497033	−	0.867732i	$-0.334423\pi$
$313$	26.4851	−	15.2912i	1.49703	−	0.864309i	0.999994	+	0.00342295i	$0.00108956\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	26.6927	−	15.4110i	1.49921	−	0.865570i	0.499212	−	0.866480i	$-0.333623\pi$
$317$	26.6927	−	15.4110i	1.49921	−	0.865570i	1.00000		0.000909155i	$0.000289393\pi$
$318$		0			0
$319$	−6.18624	+	10.7149i	−0.346363	+	0.599918i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			1.35983i			0.0756631i
$324$		0			0
$325$	−5.64977	−	3.26189i	−0.313393	−	0.180937i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−13.9889	+	8.68805i	−0.771231	+	0.478987i
$330$		0			0
$331$	11.6593	+	20.1944i	0.640850	+	1.10999i	0.985243	+	0.171160i	$0.0547515\pi$
$331$	11.6593	+	20.1944i	0.640850	+	1.10999i	−0.344393	+	0.938826i	$0.611915\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.641131			−0.0350287
$336$		0			0
$337$	16.4037			0.893566			0.446783	−	0.894642i	$-0.352570\pi$
$337$	16.4037			0.893566			0.446783	+	0.894642i	$0.352570\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.65452	−	4.59776i	−0.143750	−	0.248982i
$342$		0			0
$343$	1.78453	+	18.4341i	0.0963553	+	0.995347i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5.20946	−	3.00768i	−0.279658	−	0.161461i	0.353610	−	0.935393i	$-0.384954\pi$
$347$	−5.20946	−	3.00768i	−0.279658	−	0.161461i	−0.633269	+	0.773932i	$0.718287\pi$
$348$		0			0
$349$			23.6293i			1.26485i	0.774622	+	0.632424i	$0.217940\pi$
$349$			23.6293i			1.26485i	−0.774622	+	0.632424i	$0.782060\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.53140	+	11.3127i	−0.347632	+	0.602116i	−0.985828	−	0.167758i	$-0.946347\pi$
$353$	−6.53140	+	11.3127i	−0.347632	+	0.602116i	0.638197	+	0.769873i	$0.279681\pi$
$354$		0			0
$355$	6.17430	−	3.56473i	0.327698	−	0.189196i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−18.3225	+	10.5785i	−0.967022	+	0.558311i	−0.898327	−	0.439327i	$-0.855217\pi$
$359$	−18.3225	+	10.5785i	−0.967022	+	0.558311i	−0.0686950	+	0.997638i	$0.521884\pi$
$360$		0			0
$361$	−6.24063	+	10.8091i	−0.328454	+	0.568899i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			22.8016i			1.19349i
$366$		0			0
$367$	2.23574	+	1.29080i	0.116705	+	0.0673794i	0.557216	−	0.830368i	$-0.311870\pi$
$367$	2.23574	+	1.29080i	0.116705	+	0.0673794i	−0.440511	+	0.897747i	$0.645203\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.221041	+	0.412986i	−0.0114759	+	0.0214411i
$372$		0			0
$373$	17.5666	+	30.4262i	0.909563	+	1.57541i	0.814672	+	0.579923i	$0.196917\pi$
$373$	17.5666	+	30.4262i	0.909563	+	1.57541i	0.0948919	+	0.995488i	$0.469749\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	25.1428			1.29492
$378$		0			0
$379$	−16.4049			−0.842662			−0.421331	−	0.906907i	$-0.638437\pi$
$379$	−16.4049			−0.842662			−0.421331	+	0.906907i	$0.638437\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.33014	+	12.6962i	0.374553	+	0.648744i	0.990260	−	0.139231i	$-0.0444630\pi$
$383$	7.33014	+	12.6962i	0.374553	+	0.648744i	−0.615707	+	0.787975i	$0.711130\pi$
$384$		0			0
$385$	−8.53497	+	0.274651i	−0.434982	+	0.0139975i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	12.2023	+	7.04497i	0.618679	+	0.357194i	0.776354	−	0.630297i	$-0.217067\pi$
$389$	12.2023	+	7.04497i	0.618679	+	0.357194i	−0.157676	+	0.987491i	$0.550400\pi$
$390$		0			0
$391$		−	4.47710i		−	0.226417i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	7.70692	−	13.3488i	0.387777	−	0.671650i
$396$		0			0
$397$	15.7769	−	9.10877i	0.791817	−	0.457156i	−0.0487845	−	0.998809i	$-0.515535\pi$
$397$	15.7769	−	9.10877i	0.791817	−	0.457156i	0.840602	+	0.541653i	$0.182201\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.0005	+	7.50586i	−0.649216	+	0.374825i	−0.788156	−	0.615476i	$-0.788964\pi$
$401$	−13.0005	+	7.50586i	−0.649216	+	0.374825i	0.138940	+	0.990301i	$0.455631\pi$
$402$		0			0
$403$	−5.39438	+	9.34335i	−0.268713	+	0.465425i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	1.61869i		−	0.0802355i
$408$		0			0
$409$	19.2233	+	11.0986i	0.950531	+	0.548789i	0.893246	−	0.449569i	$-0.148422\pi$
$409$	19.2233	+	11.0986i	0.950531	+	0.548789i	0.0572850	+	0.998358i	$0.481756\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−26.4305	−	14.1463i	−1.30056	−	0.696094i
$414$		0			0
$415$	10.3245	+	17.8826i	0.506811	+	0.877822i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−31.2891			−1.52857			−0.764286	−	0.644877i	$-0.776908\pi$
$419$	−31.2891			−1.52857			−0.764286	+	0.644877i	$0.776908\pi$
$420$		0			0
$421$	9.04759			0.440953			0.220476	−	0.975392i	$-0.429239\pi$
$421$	9.04759			0.440953			0.220476	+	0.975392i	$0.429239\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.475021	−	0.822761i	−0.0230419	−	0.0399098i
$426$		0			0
$427$	3.23091	+	5.20218i	0.156355	+	0.251751i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−5.92048	−	3.41819i	−0.285179	−	0.164648i	0.350586	−	0.936530i	$-0.385982\pi$
$431$	−5.92048	−	3.41819i	−0.285179	−	0.164648i	−0.635766	+	0.771882i	$0.719316\pi$
$432$		0			0
$433$		−	39.3578i		−	1.89141i	−0.325021	−	0.945707i	$-0.605371\pi$
$433$		−	39.3578i		−	1.89141i	0.325021	−	0.945707i	$-0.394629\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.7311	+	18.5869i	−0.513340	+	0.889130i
$438$		0			0
$439$	25.0314	−	14.4519i	1.19469	−	0.689752i	0.235320	−	0.971918i	$-0.424386\pi$
$439$	25.0314	−	14.4519i	1.19469	−	0.689752i	0.959365	+	0.282166i	$0.0910530\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	12.4905	−	7.21138i	0.593441	−	0.342623i	−0.173016	−	0.984919i	$-0.555351\pi$
$443$	12.4905	−	7.21138i	0.593441	−	0.342623i	0.766457	+	0.642296i	$0.222018\pi$
$444$		0			0
$445$	11.7003	−	20.2656i	0.554649	−	0.960680i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	38.2966i		−	1.80733i	−0.428242	−	0.903664i	$-0.640867\pi$
$449$		−	38.2966i		−	1.80733i	0.428242	−	0.903664i	$-0.359133\pi$
$450$		0			0
$451$	2.66013	+	1.53583i	0.125261	+	0.0723193i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	9.15554	+	14.7416i	0.429218	+	0.691096i
$456$		0			0
$457$	14.2484	+	24.6790i	0.666514	+	1.15444i	0.978873	+	0.204471i	$0.0655475\pi$
$457$	14.2484	+	24.6790i	0.666514	+	1.15444i	−0.312359	+	0.949964i	$0.601119\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	18.0671			0.841470			0.420735	−	0.907184i	$-0.361772\pi$
$461$	18.0671			0.841470			0.420735	+	0.907184i	$0.361772\pi$
$462$		0			0
$463$	−16.5206			−0.767779			−0.383890	−	0.923379i	$-0.625416\pi$
$463$	−16.5206			−0.767779			−0.383890	+	0.923379i	$0.625416\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.2104	+	33.2734i	0.888952	+	1.53971i	0.841116	+	0.540855i	$0.181899\pi$
$467$	19.2104	+	33.2734i	0.888952	+	1.53971i	0.0478359	+	0.998855i	$0.484768\pi$
$468$		0			0
$469$	−0.833917	−	0.446335i	−0.0385067	−	0.0206098i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−16.1278	−	9.31139i	−0.741557	−	0.428138i
$474$		0			0
$475$			4.55430i			0.208965i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	7.80737	−	13.5228i	0.356728	−	0.617871i	−0.630684	−	0.776040i	$-0.717226\pi$
$479$	7.80737	−	13.5228i	0.356728	−	0.617871i	0.987412	+	0.158169i	$0.0505590\pi$
$480$		0			0
$481$	−2.84873	+	1.64471i	−0.129891	+	0.0749925i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−26.7749	+	15.4585i	−1.21579	+	0.701934i
$486$		0			0
$487$	19.1146	−	33.1074i	0.866164	−	1.50024i	0.000276553	−	1.00000i	$-0.499912\pi$
$487$	19.1146	−	33.1074i	0.866164	−	1.50024i	0.865887	−	0.500239i	$-0.166755\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			14.4145i			0.650519i	0.945625	+	0.325260i	$0.105452\pi$
$491$			14.4145i			0.650519i	−0.945625	+	0.325260i	$0.894548\pi$
$492$		0			0
$493$	3.17093	+	1.83074i	0.142812	+	0.0824523i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10.5125	−	0.338288i	0.471552	−	0.0151743i
$498$		0			0
$499$	8.09424	+	14.0196i	0.362348	+	0.627605i	0.988347	−	0.152219i	$-0.0486419\pi$
$499$	8.09424	+	14.0196i	0.362348	+	0.627605i	−0.625999	+	0.779824i	$0.715309\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	25.1488			1.12133			0.560665	−	0.828042i	$-0.310545\pi$
$503$	25.1488			1.12133			0.560665	+	0.828042i	$0.310545\pi$
$504$		0			0
$505$	23.7889			1.05859
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−15.7867	−	27.3433i	−0.699732	−	1.21197i	−0.968559	−	0.248782i	$-0.919970\pi$
$509$	−15.7867	−	27.3433i	−0.699732	−	1.21197i	0.268828	−	0.963188i	$-0.413364\pi$
$510$		0			0
$511$	−15.8737	+	29.6579i	−0.702212	+	1.31199i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.73435	+	1.00133i	0.0764247	+	0.0441238i
$516$		0			0
$517$		−	11.2015i		−	0.492642i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	22.2487	−	38.5359i	0.974733	−	1.68829i	0.293918	−	0.955831i	$-0.405041\pi$
$521$	22.2487	−	38.5359i	0.974733	−	1.68829i	0.680815	−	0.732456i	$-0.261626\pi$
$522$		0			0
$523$	6.17951	−	3.56774i	0.270211	−	0.156006i	−0.358772	−	0.933425i	$-0.616805\pi$
$523$	6.17951	−	3.56774i	0.270211	−	0.156006i	0.628984	+	0.777419i	$0.283471\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.36065	+	0.785570i	−0.0592707	+	0.0342200i
$528$		0			0
$529$	23.8311	−	41.2767i	1.03613	−	1.79464i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	6.24208i		−	0.270374i
$534$		0			0
$535$	21.2692	+	12.2798i	0.919549	+	0.530902i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−11.2926	−	5.58453i	−0.486407	−	0.240543i
$540$		0			0
$541$	14.4389	+	25.0089i	0.620778	+	1.07522i	0.989341	+	0.145616i	$0.0465163\pi$
$541$	14.4389	+	25.0089i	0.620778	+	1.07522i	−0.368564	+	0.929602i	$0.620150\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−21.5205			−0.921836
$546$		0			0
$547$	34.8208			1.48883			0.744415	−	0.667717i	$-0.232728\pi$
$547$	34.8208			1.48883			0.744415	+	0.667717i	$0.232728\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−8.77616	−	15.2008i	−0.373877	−	0.647574i
$552$		0			0
$553$	19.3174	−	11.9974i	0.821458	−	0.510181i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	6.89002	+	3.97795i	0.291939	+	0.168551i	0.638816	−	0.769359i	$-0.279424\pi$
$557$	6.89002	+	3.97795i	0.291939	+	0.168551i	−0.346877	+	0.937911i	$0.612758\pi$
$558$		0			0
$559$			37.8444i			1.60065i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−18.7851	+	32.5367i	−0.791697	+	1.37126i	0.133218	+	0.991087i	$0.457469\pi$
$563$	−18.7851	+	32.5367i	−0.791697	+	1.37126i	−0.924915	+	0.380173i	$0.875864\pi$
$564$		0			0
$565$	−17.0205	+	9.82677i	−0.716056	+	0.413415i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.7062	+	8.49062i	−0.616515	+	0.355945i	−0.775511	−	0.631334i	$-0.782508\pi$
$569$	−14.7062	+	8.49062i	−0.616515	+	0.355945i	0.158996	+	0.987279i	$0.449174\pi$
$570$		0			0
$571$	−11.2152	+	19.4253i	−0.469341	+	0.812922i	−0.999386	−	0.0350474i	$-0.988842\pi$
$571$	−11.2152	+	19.4253i	−0.469341	+	0.812922i	0.530045	+	0.847970i	$0.322175\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	14.9945i		−	0.625315i
$576$		0			0
$577$	−1.26124	−	0.728179i	−0.0525063	−	0.0303145i	0.473517	−	0.880785i	$-0.342984\pi$
$577$	−1.26124	−	0.728179i	−0.0525063	−	0.0303145i	−0.526023	+	0.850470i	$0.676318\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.979782	+	30.4474i	0.0406482	+	1.26317i
$582$		0			0
$583$	−0.159316	−	0.275943i	−0.00659820	−	0.0114284i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.6194			0.479585			0.239793	−	0.970824i	$-0.422921\pi$
$587$	11.6194			0.479585			0.239793	+	0.970824i	$0.422921\pi$
$588$		0			0
$589$	7.53170			0.310338
$590$		0			0
$591$		0			0
$592$		0			0
$593$	20.0822	+	34.7834i	0.824677	+	1.42838i	0.902166	+	0.431390i	$0.141977\pi$
$593$	20.0822	+	34.7834i	0.824677	+	1.42838i	−0.0774886	+	0.996993i	$0.524690\pi$
$594$		0			0
$595$	0.0812793	+	2.52581i	0.00333213	+	0.103548i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−0.460629	−	0.265944i	−0.0188208	−	0.0108662i	0.490560	−	0.871407i	$-0.336792\pi$
$599$	−0.460629	−	0.265944i	−0.0188208	−	0.0108662i	−0.509381	+	0.860541i	$0.670126\pi$
$600$		0			0
$601$		−	21.1382i		−	0.862246i	−0.902293	−	0.431123i	$-0.858118\pi$
$601$		−	21.1382i		−	0.862246i	0.902293	−	0.431123i	$-0.141882\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.95925	+	12.0538i	−0.282934	+	0.490055i
$606$		0			0
$607$	19.5504	−	11.2874i	0.793525	−	0.458142i	−0.0476773	−	0.998863i	$-0.515182\pi$
$607$	19.5504	−	11.2874i	0.793525	−	0.458142i	0.841202	+	0.540721i	$0.181849\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−19.7135	+	11.3816i	−0.797522	+	0.460450i
$612$		0			0
$613$	−18.6984	+	32.3865i	−0.755219	+	1.30808i	0.190046	+	0.981775i	$0.439136\pi$
$613$	−18.6984	+	32.3865i	−0.755219	+	1.30808i	−0.945265	+	0.326303i	$0.894197\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			4.81320i			0.193772i	0.995295	+	0.0968860i	$0.0308882\pi$
$617$			4.81320i			0.193772i	−0.995295	+	0.0968860i	$0.969112\pi$
$618$		0			0
$619$	−23.3720	−	13.4938i	−0.939401	−	0.542364i	−0.0496287	−	0.998768i	$-0.515804\pi$
$619$	−23.3720	−	13.4938i	−0.939401	−	0.542364i	−0.889773	+	0.456404i	$0.849137\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	29.3268	−	18.2140i	1.17495	−	0.729727i
$624$		0			0
$625$	6.44965	+	11.1711i	0.257986	+	0.446845i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−0.479031			−0.0191002
$630$		0			0
$631$	−41.9772			−1.67109			−0.835543	−	0.549426i	$-0.814847\pi$
$631$	−41.9772			−1.67109			−0.835543	+	0.549426i	$0.814847\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	7.98328	+	13.8274i	0.316807	+	0.548725i
$636$		0			0
$637$	1.64595	+	25.5481i	0.0652151	+	1.01225i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	21.8116	+	12.5929i	0.861505	+	0.497390i	0.864516	−	0.502605i	$-0.167625\pi$
$641$	21.8116	+	12.5929i	0.861505	+	0.497390i	−0.00301109	+	0.999995i	$0.500958\pi$
$642$		0			0
$643$			17.3713i			0.685057i	0.939507	+	0.342529i	$0.111283\pi$
$643$			17.3713i			0.685057i	−0.939507	+	0.342529i	$0.888717\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.0241	−	22.5584i	0.512030	−	0.886862i	−0.487873	−	0.872915i	$-0.662227\pi$
$647$	13.0241	−	22.5584i	0.512030	−	0.886862i	0.999903	−	0.0139470i	$-0.00443960\pi$
$648$		0			0
$649$	17.6600	−	10.1960i	0.693215	−	0.400228i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	18.0386	−	10.4146i	0.705905	−	0.407554i	−0.103638	−	0.994615i	$-0.533048\pi$
$653$	18.0386	−	10.4146i	0.705905	−	0.407554i	0.809543	+	0.587061i	$0.199715\pi$
$654$		0			0
$655$	−5.37206	+	9.30469i	−0.209904	+	0.363564i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	32.1086i		−	1.25077i	−0.780314	−	0.625387i	$-0.784941\pi$
$659$		−	32.1086i		−	1.25077i	0.780314	−	0.625387i	$-0.215059\pi$
$660$		0			0
$661$	−28.6909	−	16.5647i	−1.11595	−	0.644293i	−0.175585	−	0.984464i	$-0.556182\pi$
$661$	−28.6909	−	16.5647i	−1.11595	−	0.644293i	−0.940363	+	0.340171i	$0.889515\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.71667	−	10.6808i	0.221683	−	0.414185i
$666$		0			0
$667$	28.8946	+	50.0469i	1.11880	+	1.93782i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.16562			−0.160812
$672$		0			0
$673$	24.5087			0.944741			0.472371	−	0.881400i	$-0.343398\pi$
$673$	24.5087			0.944741			0.472371	+	0.881400i	$0.343398\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.8283	−	29.1474i	−0.646763	−	1.12023i	−0.983891	−	0.178767i	$-0.942789\pi$
$677$	−16.8283	−	29.1474i	−0.646763	−	1.12023i	0.337129	−	0.941458i	$-0.390544\pi$
$678$		0			0
$679$	−45.5878	+	1.46699i	−1.74950	+	0.0562979i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−6.73414	−	3.88796i	−0.257675	−	0.148769i	0.365599	−	0.930773i	$-0.380864\pi$
$683$	−6.73414	−	3.88796i	−0.257675	−	0.148769i	−0.623273	+	0.782004i	$0.714198\pi$
$684$		0			0
$685$		−	9.68800i		−	0.370160i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.323755	+	0.560759i	−0.0123341	+	0.0213632i
$690$		0			0
$691$	1.47140	−	0.849514i	0.0559747	−	0.0323170i	−0.471751	−	0.881732i	$-0.656378\pi$
$691$	1.47140	−	0.849514i	0.0559747	−	0.0323170i	0.527726	+	0.849415i	$0.323045\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.83656	−	2.79239i	0.183461	−	0.105921i
$696$		0			0
$697$	0.454509	−	0.787232i	0.0172157	−	0.0298185i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	43.3561i		−	1.63754i	−0.574124	−	0.818769i	$-0.694657\pi$
$701$		−	43.3561i		−	1.63754i	0.574124	−	0.818769i	$-0.305343\pi$
$702$		0			0
$703$	1.98871	+	1.14818i	0.0750058	+	0.0433046i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	30.9421	+	16.5611i	1.16370	+	0.622843i
$708$		0			0
$709$	1.30241	+	2.25584i	0.0489130	+	0.0847198i	0.889445	−	0.457042i	$-0.151091\pi$
$709$	1.30241	+	2.25584i	0.0489130	+	0.0847198i	−0.840532	+	0.541761i	$0.817758\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−24.7973			−0.928667
$714$		0			0
$715$	−11.8042			−0.441454
$716$		0			0
$717$		0			0
$718$		0			0
$719$	16.5674	+	28.6955i	0.617859	+	1.07016i	0.989876	+	0.141937i	$0.0453329\pi$
$719$	16.5674	+	28.6955i	0.617859	+	1.07016i	−0.372017	+	0.928226i	$0.621334\pi$
$720$		0			0
$721$	1.55877	+	2.50983i	0.0580518	+	0.0934708i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10.6200	+	6.13143i	0.394415	+	0.227716i
$726$		0			0
$727$			37.4906i			1.39045i	0.718792	+	0.695225i	$0.244695\pi$
$727$			37.4906i			1.39045i	−0.718792	+	0.695225i	$0.755305\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.75559	+	4.77282i	−0.101919	+	0.176529i
$732$		0			0
$733$	10.0735	−	5.81597i	0.372075	−	0.214818i	−0.302290	−	0.953216i	$-0.597751\pi$
$733$	10.0735	−	5.81597i	0.372075	−	0.214818i	0.674365	+	0.738399i	$0.264418\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.557196	−	0.321697i	0.0205246	−	0.0118499i
$738$		0			0
$739$	8.83519	−	15.3030i	0.325008	−	0.562930i	−0.656506	−	0.754321i	$-0.727966\pi$
$739$	8.83519	−	15.3030i	0.325008	−	0.562930i	0.981514	+	0.191391i	$0.0612998\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	49.0613i		−	1.79989i	−0.436008	−	0.899943i	$-0.643608\pi$
$743$		−	49.0613i		−	1.79989i	0.436008	−	0.899943i	$-0.356392\pi$
$744$		0			0
$745$	−32.0701	−	18.5157i	−1.17496	−	0.678361i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	19.1160	+	30.7792i	0.698484	+	1.12465i
$750$		0			0
$751$	20.6611	+	35.7861i	0.753936	+	1.30585i	0.945902	+	0.324453i	$0.105180\pi$
$751$	20.6611	+	35.7861i	0.753936	+	1.30585i	−0.191966	+	0.981402i	$0.561486\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	6.76094			0.246056
$756$		0			0
$757$	2.72054			0.0988797			0.0494398	−	0.998777i	$-0.484256\pi$
$757$	2.72054			0.0988797			0.0494398	+	0.998777i	$0.484256\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−4.07677	−	7.06117i	−0.147783	−	0.255967i	0.782625	−	0.622493i	$-0.213880\pi$
$761$	−4.07677	−	7.06117i	−0.147783	−	0.255967i	−0.930408	+	0.366526i	$0.880547\pi$
$762$		0			0
$763$	−27.9916	−	14.9819i	−1.01337	−	0.542380i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−35.8878	−	20.7198i	−1.29583	−	0.748149i
$768$		0			0
$769$		−	45.8153i		−	1.65214i	−0.563566	−	0.826071i	$-0.690571\pi$
$769$		−	45.8153i		−	1.65214i	0.563566	−	0.826071i	$-0.309429\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.70753	+	8.15369i	−0.169318	+	0.293268i	−0.938180	−	0.346147i	$-0.887490\pi$
$773$	−4.70753	+	8.15369i	−0.169318	+	0.293268i	0.768862	+	0.639415i	$0.220823\pi$
$774$		0			0
$775$	−4.55702	+	2.63100i	−0.163693	+	0.0945082i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.77382	+	2.17882i	−0.135211	+	0.0780642i
$780$		0			0
$781$	−3.57732	+	6.19610i	−0.128007	+	0.221714i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			10.7705i			0.384415i
$786$		0			0
$787$	0.794892	+	0.458931i	0.0283348	+	0.0163591i	0.514101	−	0.857730i	$-0.328126\pi$
$787$	0.794892	+	0.458931i	0.0283348	+	0.0163591i	−0.485766	+	0.874089i	$0.661459\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−28.9795	+	0.932546i	−1.03039	+	0.0331575i
$792$		0			0
$793$	4.23259	+	7.33105i	0.150304	+	0.260333i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	15.9474			0.564885			0.282443	−	0.959284i	$-0.408855\pi$
$797$	15.9474			0.564885			0.282443	+	0.959284i	$0.408855\pi$
$798$		0			0
$799$	−3.31494			−0.117274
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−11.4410	−	19.8165i	−0.403746	−	0.699308i
$804$		0			0
$805$	−18.8215	+	35.1655i	−0.663371	+	1.23942i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	34.6359	+	19.9970i	1.21773	+	0.703058i	0.964432	−	0.264329i	$-0.0851506\pi$
$809$	34.6359	+	19.9970i	1.21773	+	0.703058i	0.253300	+	0.967388i	$0.418484\pi$
$810$		0			0
$811$		−	11.6533i		−	0.409204i	−0.978845	−	0.204602i	$-0.934410\pi$
$811$		−	11.6533i		−	0.409204i	0.978845	−	0.204602i	$-0.0655900\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.60218	+	11.4353i	−0.231264	+	0.400561i
$816$		0			0
$817$	22.8798	−	13.2097i	0.800465	−	0.462148i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	17.0221	−	9.82774i	0.594077	−	0.342990i	−0.172631	−	0.984987i	$-0.555227\pi$
$821$	17.0221	−	9.82774i	0.594077	−	0.342990i	0.766708	+	0.641996i	$0.221893\pi$
$822$		0			0
$823$	17.1805	−	29.7575i	0.598875	−	1.03728i	−0.394112	−	0.919062i	$-0.628948\pi$
$823$	17.1805	−	29.7575i	0.598875	−	1.03728i	0.992987	−	0.118220i	$-0.0377188\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			30.8900i			1.07415i	0.843534	+	0.537075i	$0.180471\pi$
$827$			30.8900i			1.07415i	−0.843534	+	0.537075i	$0.819529\pi$
$828$		0			0
$829$	−13.8467	−	7.99438i	−0.480915	−	0.277656i	0.239883	−	0.970802i	$-0.422891\pi$
$829$	−13.8467	−	7.99438i	−0.480915	−	0.277656i	−0.720798	+	0.693146i	$0.756224\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.65267	+	3.34190i	−0.0572617	+	0.115790i
$834$		0			0
$835$	8.30099	+	14.3777i	0.287268	+	0.497562i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	14.0820			0.486164			0.243082	−	0.970006i	$-0.421842\pi$
$839$	14.0820			0.486164			0.243082	+	0.970006i	$0.421842\pi$
$840$		0			0
$841$	−18.2613			−0.629699
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.337017	+	0.583730i	0.0115937	+	0.0200809i
$846$		0			0
$847$	−17.4433	+	10.8335i	−0.599360	+	0.372243i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−6.54763	−	3.78027i	−0.224450	−	0.129586i
$852$		0			0
$853$		−	18.8085i		−	0.643991i	−0.946741	−	0.321995i	$-0.895646\pi$
$853$		−	18.8085i		−	0.643991i	0.946741	−	0.321995i	$-0.104354\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.1397	+	19.2945i	−0.380525	+	0.659089i	−0.991137	−	0.132841i	$-0.957590\pi$
$857$	−11.1397	+	19.2945i	−0.380525	+	0.659089i	0.610612	+	0.791930i	$0.290923\pi$
$858$		0			0
$859$	32.3590	−	18.6825i	1.10407	−	0.637438i	0.166786	−	0.985993i	$-0.446661\pi$
$859$	32.3590	−	18.6825i	1.10407	−	0.637438i	0.937288	+	0.348556i	$0.113328\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−17.8937	+	10.3310i	−0.609110	+	0.351670i	−0.772617	−	0.634872i	$-0.781053\pi$
$863$	−17.8937	+	10.3310i	−0.609110	+	0.351670i	0.163507	+	0.986542i	$0.447719\pi$
$864$		0			0
$865$	15.3602	−	26.6047i	0.522263	−	0.904586i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			15.4683i			0.524725i
$870$		0			0
$871$	−1.13231	−	0.653738i	−0.0383668	−	0.0221511i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.03526	+	32.1713i	0.0349980	+	1.08759i
$876$		0			0
$877$	1.59617	+	2.76464i	0.0538988	+	0.0933554i	0.891716	−	0.452596i	$-0.149502\pi$
$877$	1.59617	+	2.76464i	0.0538988	+	0.0933554i	−0.837817	+	0.545951i	$0.816169\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	11.6261			0.391693			0.195847	−	0.980635i	$-0.437255\pi$
$881$	11.6261			0.391693			0.195847	+	0.980635i	$0.437255\pi$
$882$		0			0
$883$	−16.3938			−0.551694			−0.275847	−	0.961202i	$-0.588958\pi$
$883$	−16.3938			−0.551694			−0.275847	+	0.961202i	$0.588958\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−22.1501	−	38.3652i	−0.743729	−	1.28818i	−0.950786	−	0.309848i	$-0.899722\pi$
$887$	−22.1501	−	38.3652i	−0.743729	−	1.28818i	0.207057	−	0.978329i	$-0.433611\pi$
$888$		0			0
$889$	0.757601	+	23.5430i	0.0254091	+	0.789607i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	13.7621	+	7.94556i	0.460531	+	0.265888i
$894$		0			0
$895$		−	17.8996i		−	0.598318i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	10.1399	−	17.5628i	0.338185	−	0.585753i
$900$		0			0
$901$	−0.0816619	+	0.0471475i	−0.00272055	+	0.00157071i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	16.5856	−	9.57569i	0.551323	−	0.318307i
$906$		0			0
$907$	20.6346	−	35.7401i	0.685160	−	1.18673i	−0.288227	−	0.957562i	$-0.593066\pi$
$907$	20.6346	−	35.7401i	0.685160	−	1.18673i	0.973387	−	0.229169i	$-0.0736009\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			36.7805i			1.21859i	0.792943	+	0.609296i	$0.208548\pi$
$911$			36.7805i			1.21859i	−0.792943	+	0.609296i	$0.791452\pi$
$912$		0			0
$913$	−17.9457	−	10.3610i	−0.593917	−	0.342898i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−13.4651	+	8.36272i	−0.444655	+	0.276161i
$918$		0			0
$919$	−26.8033	−	46.4247i	−0.884160	−	1.53141i	−0.846673	−	0.532113i	$-0.821398\pi$
$919$	−26.8033	−	46.4247i	−0.884160	−	1.53141i	−0.0374866	−	0.999297i	$-0.511935\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	14.5393			0.478568
$924$		0			0
$925$	−1.60435			−0.0527507
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.89160	+	6.74045i	0.127679	+	0.221147i	0.922777	−	0.385334i	$-0.125914\pi$
$929$	3.89160	+	6.74045i	0.127679	+	0.221147i	−0.795098	+	0.606481i	$0.792581\pi$
$930$		0			0
$931$	14.8713	−	9.91276i	0.487387	−	0.324878i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.48872	−	0.859511i	−0.0486862	−	0.0281090i
$936$		0			0
$937$		−	28.8315i		−	0.941883i	−0.882164	−	0.470941i	$-0.843914\pi$
$937$		−	28.8315i		−	0.941883i	0.882164	−	0.470941i	$-0.156086\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.09560	−	15.7540i	0.296508	−	0.513567i	−0.678826	−	0.734299i	$-0.737511\pi$
$941$	9.09560	−	15.7540i	0.296508	−	0.513567i	0.975335	+	0.220732i	$0.0708445\pi$
$942$		0			0
$943$	12.4249	−	7.17352i	0.404610	−	0.233602i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.0347	+	8.68027i	−0.488561	+	0.282071i	−0.723977	−	0.689824i	$-0.757688\pi$
$947$	−15.0347	+	8.68027i	−0.488561	+	0.282071i	0.235416	+	0.971895i	$0.424355\pi$
$948$		0			0
$949$	−23.2500	+	40.2701i	−0.754725	+	1.30722i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	6.42892i		−	0.208253i	−0.994564	−	0.104127i	$-0.966795\pi$
$953$		−	6.42892i		−	0.208253i	0.994564	−	0.104127i	$-0.0332047\pi$
$954$		0			0
$955$	−22.0732	−	12.7440i	−0.714272	−	0.412385i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.74448	−	12.6012i	0.217791	−	0.406912i
$960$		0			0
$961$	−11.1490	−	19.3106i	−0.359644	−	0.622922i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−17.9642			−0.578290
$966$		0			0
$967$	8.58829			0.276181			0.138090	−	0.990420i	$-0.455904\pi$
$967$	8.58829			0.276181			0.138090	+	0.990420i	$0.455904\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−13.3898	−	23.1918i	−0.429700	−	0.744262i	0.567147	−	0.823617i	$-0.308047\pi$
$971$	−13.3898	−	23.1918i	−0.429700	−	0.744262i	−0.996846	+	0.0793552i	$0.974714\pi$
$972$		0			0
$973$	8.23488	−	0.264994i	0.263998	−	0.00849531i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−30.7939	−	17.7788i	−0.985183	−	0.568796i	−0.0813520	−	0.996685i	$-0.525924\pi$
$977$	−30.7939	−	17.7788i	−0.985183	−	0.568796i	−0.903831	+	0.427890i	$0.859257\pi$
$978$		0			0
$979$			23.4833i			0.750529i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−7.88504	+	13.6573i	−0.251494	+	0.435600i	−0.963937	−	0.266130i	$-0.914255\pi$
$983$	−7.88504	+	13.6573i	−0.251494	+	0.435600i	0.712444	+	0.701729i	$0.247588\pi$
$984$		0			0
$985$	−0.00219930	+	0.00126976i	−7.00754e−5	+	4.04580e-5i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−75.3294	+	43.4915i	−2.39534	+	1.38295i
$990$		0			0
$991$	−6.90469	+	11.9593i	−0.219335	+	0.379899i	−0.954605	−	0.297875i	$-0.903722\pi$
$991$	−6.90469	+	11.9593i	−0.219335	+	0.379899i	0.735270	+	0.677774i	$0.237055\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			1.48587i			0.0471053i
$996$		0			0
$997$	−2.13900	−	1.23495i	−0.0677427	−	0.0391112i	0.465746	−	0.884918i	$-0.345786\pi$
$997$	−2.13900	−	1.23495i	−0.0677427	−	0.0391112i	−0.533489	+	0.845807i	$0.679119\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.t.c.1781.5	✓	32
3.2	odd	2	inner	2268.2.t.c.1781.12	yes	32
7.5	odd	6	inner	2268.2.t.c.2105.12	yes	32
9.2	odd	6		2268.2.bm.j.1025.5		32
9.4	even	3		2268.2.w.j.269.5		32
9.5	odd	6		2268.2.w.j.269.12		32
9.7	even	3		2268.2.bm.j.1025.12		32
21.5	even	6	inner	2268.2.t.c.2105.5	yes	32
63.5	even	6		2268.2.bm.j.593.12		32
63.40	odd	6		2268.2.bm.j.593.5		32
63.47	even	6		2268.2.w.j.1349.5		32
63.61	odd	6		2268.2.w.j.1349.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2268.2.t.c.1781.5	✓	32	1.1	even	1	trivial
2268.2.t.c.1781.12	yes	32	3.2	odd	2	inner
2268.2.t.c.2105.5	yes	32	21.5	even	6	inner
2268.2.t.c.2105.12	yes	32	7.5	odd	6	inner
2268.2.w.j.269.5		32	9.4	even	3
2268.2.w.j.269.12		32	9.5	odd	6
2268.2.w.j.1349.5		32	63.47	even	6
2268.2.w.j.1349.12		32	63.61	odd	6
2268.2.bm.j.593.5		32	63.40	odd	6
2268.2.bm.j.593.12		32	63.5	even	6
2268.2.bm.j.1025.5		32	9.2	odd	6
2268.2.bm.j.1025.12		32	9.7	even	3

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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.896692 - 1.55312i) q^{5} +(-0.0850948 - 2.64438i) q^{7} +O(q^{10})\)	\(q+(-0.896692 - 1.55312i) q^{5} +(-0.0850948 - 2.64438i) q^{7} +(1.55860 + 0.899858i) q^{11} -3.65730i q^{13} +(0.266302 - 0.461248i) q^{17} +(-2.21112 + 1.27659i) q^{19} +(7.27988 - 4.20304i) q^{23} +(0.891886 - 1.54479i) q^{25} +6.87468i q^{29} +(-2.55471 - 1.47496i) q^{31} +(-4.03073 + 2.50336i) q^{35} +(-0.449707 - 0.778915i) q^{37} +1.70674 q^{41} -10.3476 q^{43} +(-3.11202 - 5.39018i) q^{47} +(-6.98552 + 0.450046i) q^{49} +(-0.153326 - 0.0885228i) q^{53} -3.22758i q^{55} +(5.66533 - 9.81264i) q^{59} +(-2.00450 + 1.15730i) q^{61} +(-5.68021 + 3.27947i) q^{65} +(0.178749 - 0.309602i) q^{67} +3.97543i q^{71} +(-11.0109 - 6.35714i) q^{73} +(2.24694 - 4.19811i) q^{77} +(4.29742 + 7.44334i) q^{79} -11.5140 q^{83} -0.955162 q^{85} +(6.52416 + 11.3002i) q^{89} +(-9.67130 + 0.311217i) q^{91} +(3.96539 + 2.28942i) q^{95} -17.2395i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{7}+O(q^{10}) \) 32 * q - 8 * q^7	\( 32 q - 8 q^{7} - 16 q^{25} + 24 q^{31} - 4 q^{37} + 8 q^{43} - 4 q^{49} + 12 q^{61} + 4 q^{67} - 36 q^{73} + 28 q^{79} - 24 q^{85} - 36 q^{91}+O(q^{100}) \) 32 * q - 8 * q^7 - 16 * q^25 + 24 * q^31 - 4 * q^37 + 8 * q^43 - 4 * q^49 + 12 * q^61 + 4 * q^67 - 36 * q^73 + 28 * q^79 - 24 * q^85 - 36 * q^91

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