LMFDB - Embedded newform 2268.2.t.c.1781.12

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			1781.12
Character	$\chi$	$=$	2268.1781
Dual form			2268.2.t.c.2105.12

$q$-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	0.993848	−	0.110749i	$-0.0353249\pi$
$5$	0.896692	+	1.55312i	0.401013	+	0.694575i	−0.592835	+	0.805324i	$0.701992\pi$
$6$		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	0.246277	−	0.969199i	$-0.420793\pi$
$11$	−1.55860	−	0.899858i	−0.469936	−	0.271318i	−0.716213	+	0.697882i	$0.754126\pi$
$12$		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	−0.896511	−	0.443022i	$-0.853907\pi$
$17$	−0.266302	+	0.461248i	−0.0645876	+	0.111869i	0.831923	+	0.554891i	$0.187240\pi$
$18$		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	$0.673391\pi$
$23$	−7.27988	+	4.20304i	−1.51796	+	0.876394i	−0.999777	+	0.0211245i	$0.993275\pi$
$24$		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	$-0.779639\pi$
$29$		−	6.87468i		−	1.27660i	0.769789	−	0.638298i	$-0.220361\pi$
$30$		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	$-0.542549\pi$
$41$	−1.70674			−0.266549			−0.133274	+	0.991079i	$0.542549\pi$
$42$		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	0.998626	−	0.0523985i	$-0.0166866\pi$
$47$	3.11202	+	5.39018i	0.453935	+	0.786238i	−0.544692	+	0.838636i	$0.683353\pi$
$48$		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	0.510494	−	0.859882i	$-0.329463\pi$
$53$	0.153326	+	0.0885228i	0.0210610	+	0.0121595i	−0.489433	+	0.872041i	$0.662796\pi$
$54$		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	$0.430690\pi$
$59$	−5.66533	+	9.81264i	−0.737563	+	1.27750i	−0.953590	+	0.301109i	$0.902643\pi$
$60$		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	$-0.924197\pi$
$71$		−	3.97543i		−	0.471796i	0.971778	−	0.235898i	$-0.0758032\pi$
$72$		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	$-0.282270\pi$
$83$	11.5140			1.26383			0.631913	+	0.775039i	$0.282270\pi$
$84$		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	$-0.923591\pi$
$89$	−6.52416	−	11.3002i	−0.691560	−	1.19782i	0.279767	−	0.960068i	$-0.409743\pi$
$90$		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	$-0.603912\pi$
$101$	6.63240	−	11.4876i	0.659948	−	1.14306i	0.980629	−	0.195876i	$-0.0627551\pi$
$102$		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	0.198492	−	0.980102i	$-0.436396\pi$
$107$	11.8598	−	6.84727i	1.14653	−	0.661951i	0.948040	+	0.318152i	$0.103062\pi$
$108$		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	$0.172380\pi$
$113$			10.9589i			1.03093i	−0.856911	+	0.515464i	$0.827620\pi$
$114$		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	0.966698	−	0.255919i	$-0.0823779\pi$
$131$	2.99549	+	5.18834i	0.261717	+	0.453307i	−0.704981	+	0.709226i	$0.749045\pi$
$132$		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	0.286656	−	0.958034i	$-0.407456\pi$
$137$	−4.67834	−	2.70104i	−0.399697	−	0.230765i	−0.686353	+	0.727268i	$0.740790\pi$
$138$		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	−0.999235	−	0.0391067i	$-0.987549\pi$
$149$	−17.8824	+	10.3244i	−1.46499	+	0.845810i	−0.465750	+	0.884916i	$0.654215\pi$
$150$		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	$-0.383398\pi$
$167$	9.25735			0.716355			0.358177	+	0.933654i	$0.383398\pi$
$168$		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	$-0.940941\pi$
$173$	−8.56493	−	14.8349i	−0.651180	−	1.12788i	0.331657	−	0.943400i	$-0.392392\pi$
$174$		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	0.140884	−	0.990026i	$-0.455006\pi$
$179$	−8.64373	−	4.99046i	−0.646063	−	0.373004i	−0.786946	+	0.617022i	$0.788339\pi$
$180$		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	−0.874134	−	0.485685i	$-0.838570\pi$
$191$	−12.3081	+	7.10610i	−0.890585	+	0.514179i	−0.0164509	+	0.999865i	$0.505237\pi$
$192$		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	$1.60571e-5\pi$
$197$			0.00141605i			0.000100890i	−1.00000		5.04448e-5i	$0.999984\pi$
$198$		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	−0.953193	−	0.302362i	$-0.902225\pi$
$227$	−3.23544	+	5.60395i	−0.214744	+	0.371947i	0.738450	+	0.674309i	$0.235558\pi$
$228$		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	−0.146805	−	0.989165i	$-0.546899\pi$
$233$	9.71475	−	5.60881i	0.636434	−	0.367446i	0.783240	+	0.621720i	$0.213566\pi$
$234$		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	$-0.827004\pi$
$239$		−	15.9890i		−	1.03424i	0.855913	−	0.517120i	$-0.172996\pi$
$240$		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	$-0.698604\pi$
$251$	−18.5119			−1.16846			−0.584232	+	0.811587i	$0.698604\pi$
$252$		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	$0.0997993\pi$
$257$	11.9068	+	20.6231i	0.742723	+	1.28643i	−0.208528	+	0.978016i	$0.566867\pi$
$258$		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	0.999970	−	0.00772288i	$-0.00245829\pi$
$263$	24.2167	+	13.9815i	1.49327	+	0.862138i	0.493297	+	0.869861i	$0.335792\pi$
$264$		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	$0.342997\pi$
$269$	−8.62799	+	14.9441i	−0.526058	+	0.911159i	−0.999539	+	0.0303553i	$0.990336\pi$
$270$		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	$0.0125957\pi$
$281$			1.32630i			0.0791204i	−0.999217	+	0.0395602i	$0.987404\pi$
$282$		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	$-0.602860\pi$
$293$	−10.8712			−0.635102			−0.317551	+	0.948241i	$0.602860\pi$
$294$		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	$-0.404771\pi$
$311$	17.1929	−	29.7790i	0.974922	−	1.68861i	0.680194	−	0.733032i	$-0.261896\pi$
$312$		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	−1.00000		0.000909155i	$-0.999711\pi$
$317$	−26.6927	+	15.4110i	−1.49921	+	0.865570i	−0.499212	+	0.866480i	$0.666377\pi$
$318$		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	0.633269	−	0.773932i	$-0.281713\pi$
$347$	5.20946	+	3.00768i	0.279658	+	0.161461i	−0.353610	+	0.935393i	$0.615046\pi$
$348$		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	−0.638197	−	0.769873i	$-0.720319\pi$
$353$	6.53140	−	11.3127i	0.347632	−	0.602116i	0.985828	+	0.167758i	$0.0536527\pi$
$354$		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	0.0686950	−	0.997638i	$-0.478116\pi$
$359$	18.3225	−	10.5785i	0.967022	−	0.558311i	0.898327	+	0.439327i	$0.144783\pi$
$360$		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	0.615707	−	0.787975i	$-0.288870\pi$
$383$	−7.33014	−	12.6962i	−0.374553	−	0.648744i	−0.990260	+	0.139231i	$0.955537\pi$
$384$		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	0.157676	−	0.987491i	$-0.449600\pi$
$389$	−12.2023	−	7.04497i	−0.618679	−	0.357194i	−0.776354	+	0.630297i	$0.782933\pi$
$390$		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	−0.138940	−	0.990301i	$-0.544369\pi$
$401$	13.0005	−	7.50586i	0.649216	−	0.374825i	0.788156	+	0.615476i	$0.211036\pi$
$402$		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	$-0.223092\pi$
$419$	31.2891			1.52857			0.764286	+	0.644877i	$0.223092\pi$
$420$		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	0.635766	−	0.771882i	$-0.280684\pi$
$431$	5.92048	+	3.41819i	0.285179	+	0.164648i	−0.350586	+	0.936530i	$0.614018\pi$
$432$		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	−0.766457	−	0.642296i	$-0.777982\pi$
$443$	−12.4905	+	7.21138i	−0.593441	+	0.342623i	0.173016	+	0.984919i	$0.444649\pi$
$444$		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	$0.359133\pi$
$449$			38.2966i			1.80733i	−0.428242	+	0.903664i	$0.640867\pi$
$450$		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	$-0.638228\pi$
$461$	−18.0671			−0.841470			−0.420735	+	0.907184i	$0.638228\pi$
$462$		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	$-0.818101\pi$
$467$	−19.2104	−	33.2734i	−0.888952	−	1.53971i	−0.0478359	−	0.998855i	$-0.515232\pi$
$468$		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	−0.987412	−	0.158169i	$-0.949441\pi$
$479$	−7.80737	+	13.5228i	−0.356728	+	0.617871i	0.630684	+	0.776040i	$0.282774\pi$
$480$		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	$-0.894548\pi$
$491$		−	14.4145i		−	0.650519i	0.945625	−	0.325260i	$-0.105452\pi$
$492$		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	$-0.689455\pi$
$503$	−25.1488			−1.12133			−0.560665	+	0.828042i	$0.689455\pi$
$504$		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	$0.0800304\pi$
$509$	15.7867	+	27.3433i	0.699732	+	1.21197i	−0.268828	+	0.963188i	$0.586636\pi$
$510$		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	$0.594959\pi$
$521$	−22.2487	+	38.5359i	−0.974733	+	1.68829i	−0.680815	+	0.732456i	$0.738374\pi$
$522$		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	0.346877	−	0.937911i	$-0.387242\pi$
$557$	−6.89002	−	3.97795i	−0.291939	−	0.168551i	−0.638816	+	0.769359i	$0.720576\pi$
$558$		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	$-0.542531\pi$
$563$	18.7851	−	32.5367i	0.791697	−	1.37126i	0.924915	−	0.380173i	$-0.124136\pi$
$564$		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	−0.158996	−	0.987279i	$-0.550826\pi$
$569$	14.7062	−	8.49062i	0.616515	−	0.355945i	0.775511	+	0.631334i	$0.217492\pi$
$570$		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	$-0.577079\pi$
$587$	−11.6194			−0.479585			−0.239793	+	0.970824i	$0.577079\pi$
$588$		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	$-0.858023\pi$
$593$	−20.0822	−	34.7834i	−0.824677	−	1.42838i	0.0774886	−	0.996993i	$-0.475310\pi$
$594$		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	0.509381	−	0.860541i	$-0.329874\pi$
$599$	0.460629	+	0.265944i	0.0188208	+	0.0108662i	−0.490560	+	0.871407i	$0.663208\pi$
$600$		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	$-0.969112\pi$
$617$		−	4.81320i		−	0.193772i	0.995295	−	0.0968860i	$-0.0308882\pi$
$618$		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	0.00301109	−	0.999995i	$-0.499042\pi$
$641$	−21.8116	−	12.5929i	−0.861505	−	0.497390i	−0.864516	+	0.502605i	$0.832375\pi$
$642$		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	$0.337773\pi$
$647$	−13.0241	+	22.5584i	−0.512030	+	0.886862i	−0.999903	+	0.0139470i	$0.995560\pi$
$648$		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	−0.809543	−	0.587061i	$-0.800285\pi$
$653$	−18.0386	+	10.4146i	−0.705905	+	0.407554i	0.103638	+	0.994615i	$0.466952\pi$
$654$		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	$0.215059\pi$
$659$			32.1086i			1.25077i	−0.780314	+	0.625387i	$0.784941\pi$
$660$		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	$0.0572108\pi$
$677$	16.8283	+	29.1474i	0.646763	+	1.12023i	−0.337129	+	0.941458i	$0.609456\pi$
$678$		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	0.623273	−	0.782004i	$-0.285802\pi$
$683$	6.73414	+	3.88796i	0.257675	+	0.148769i	−0.365599	+	0.930773i	$0.619136\pi$
$684$		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	$0.305343\pi$
$701$			43.3561i			1.63754i	−0.574124	+	0.818769i	$0.694657\pi$
$702$		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	$-0.954667\pi$
$719$	−16.5674	−	28.6955i	−0.617859	−	1.07016i	0.372017	−	0.928226i	$-0.378666\pi$
$720$		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	$0.356392\pi$
$743$			49.0613i			1.79989i	−0.436008	+	0.899943i	$0.643608\pi$
$744$		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	0.930408	−	0.366526i	$-0.119453\pi$
$761$	4.07677	+	7.06117i	0.147783	+	0.255967i	−0.782625	+	0.622493i	$0.786120\pi$
$762$		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	−0.768862	−	0.639415i	$-0.779177\pi$
$773$	4.70753	−	8.15369i	0.169318	−	0.293268i	0.938180	+	0.346147i	$0.112510\pi$
$774$		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	$-0.591145\pi$
$797$	−15.9474			−0.564885			−0.282443	+	0.959284i	$0.591145\pi$
$798$		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	−0.253300	−	0.967388i	$-0.581516\pi$
$809$	−34.6359	−	19.9970i	−1.21773	−	0.703058i	−0.964432	+	0.264329i	$0.914849\pi$
$810$		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	−0.766708	−	0.641996i	$-0.778107\pi$
$821$	−17.0221	+	9.82774i	−0.594077	+	0.342990i	0.172631	+	0.984987i	$0.444773\pi$
$822$		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	$-0.819529\pi$
$827$		−	30.8900i		−	1.07415i	0.843534	−	0.537075i	$-0.180471\pi$
$828$		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	$-0.578158\pi$
$839$	−14.0820			−0.486164			−0.243082	+	0.970006i	$0.578158\pi$
$840$		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	−0.610612	−	0.791930i	$-0.709077\pi$
$857$	11.1397	−	19.2945i	0.380525	−	0.659089i	0.991137	+	0.132841i	$0.0424100\pi$
$858$		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	−0.163507	−	0.986542i	$-0.552281\pi$
$863$	17.8937	−	10.3310i	0.609110	−	0.351670i	0.772617	+	0.634872i	$0.218947\pi$
$864$		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	$-0.562745\pi$
$881$	−11.6261			−0.391693			−0.195847	+	0.980635i	$0.562745\pi$
$882$		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	$0.100278\pi$
$887$	22.1501	+	38.3652i	0.743729	+	1.28818i	−0.207057	+	0.978329i	$0.566389\pi$
$888$		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	$-0.791452\pi$
$911$		−	36.7805i		−	1.21859i	0.792943	−	0.609296i	$-0.208548\pi$
$912$		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	0.795098	−	0.606481i	$-0.207419\pi$
$929$	−3.89160	−	6.74045i	−0.127679	−	0.221147i	−0.922777	+	0.385334i	$0.874086\pi$
$930$		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	−0.975335	−	0.220732i	$-0.929156\pi$
$941$	−9.09560	+	15.7540i	−0.296508	+	0.513567i	0.678826	+	0.734299i	$0.262489\pi$
$942$		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	−0.235416	−	0.971895i	$-0.575645\pi$
$947$	15.0347	−	8.68027i	0.488561	−	0.282071i	0.723977	+	0.689824i	$0.242312\pi$
$948$		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	$0.0332047\pi$
$953$			6.42892i			0.208253i	−0.994564	+	0.104127i	$0.966795\pi$
$954$		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	0.996846	−	0.0793552i	$-0.0252861\pi$
$971$	13.3898	+	23.1918i	0.429700	+	0.744262i	−0.567147	+	0.823617i	$0.691953\pi$
$972$		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	0.903831	−	0.427890i	$-0.140743\pi$
$977$	30.7939	+	17.7788i	0.985183	+	0.568796i	0.0813520	+	0.996685i	$0.474076\pi$
$978$		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	−0.712444	−	0.701729i	$-0.752412\pi$
$983$	7.88504	−	13.6573i	0.251494	−	0.435600i	0.963937	+	0.266130i	$0.0857449\pi$
$984$		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.1781.12	yes	32
3.2	odd	2	inner	2268.2.t.c.1781.5	✓	32
7.5	odd	6	inner	2268.2.t.c.2105.5	yes	32
9.2	odd	6		2268.2.bm.j.1025.12		32
9.4	even	3		2268.2.w.j.269.12		32
9.5	odd	6		2268.2.w.j.269.5		32
9.7	even	3		2268.2.bm.j.1025.5		32
21.5	even	6	inner	2268.2.t.c.2105.12	yes	32
63.5	even	6		2268.2.bm.j.593.5		32
63.40	odd	6		2268.2.bm.j.593.12		32
63.47	even	6		2268.2.w.j.1349.12		32
63.61	odd	6		2268.2.w.j.1349.5		32

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

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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