LMFDB - Embedded newform 288.2.v.c.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(37,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("288.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.v (of order $8$, degree $4$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.1
Character	$\chi$	$=$	288.109
Dual form			288.2.v.c.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41364 + 0.0402136i) q^{2} +(1.99677 - 0.113695i) q^{4} +(-1.51282 + 0.626632i) q^{5} +(-1.32530 + 1.32530i) q^{7} +(-2.81814 + 0.241022i) q^{8} +O(q^{10})$	\(q+(-1.41364 + 0.0402136i) q^{2} +(1.99677 - 0.113695i) q^{4} +(-1.51282 + 0.626632i) q^{5} +(-1.32530 + 1.32530i) q^{7} +(-2.81814 + 0.241022i) q^{8} +(2.11339 - 0.946670i) q^{10} +(-0.938971 - 2.26688i) q^{11} +(-4.73458 - 1.96113i) q^{13} +(1.82020 - 1.92679i) q^{14} +(3.97415 - 0.454046i) q^{16} +5.78108i q^{17} +(-1.04283 - 0.431956i) q^{19} +(-2.94951 + 1.42324i) q^{20} +(1.41853 + 3.16679i) q^{22} +(-4.29232 - 4.29232i) q^{23} +(-1.63956 + 1.63956i) q^{25} +(6.77187 + 2.58194i) q^{26} +(-2.49563 + 2.79699i) q^{28} +(0.389398 - 0.940091i) q^{29} -7.43150 q^{31} +(-5.59976 + 0.801673i) q^{32} +(-0.232478 - 8.17238i) q^{34} +(1.17447 - 2.83541i) q^{35} +(-3.67926 + 1.52400i) q^{37} +(1.49156 + 0.568695i) q^{38} +(4.11232 - 2.13056i) q^{40} +(-0.474313 - 0.474313i) q^{41} +(-0.409042 - 0.987514i) q^{43} +(-2.13264 - 4.41967i) q^{44} +(6.24042 + 5.89520i) q^{46} +2.73234i q^{47} +3.48718i q^{49} +(2.25182 - 2.38369i) q^{50} +(-9.67683 - 3.37761i) q^{52} +(4.55362 + 10.9934i) q^{53} +(2.84100 + 2.84100i) q^{55} +(3.41544 - 4.05429i) q^{56} +(-0.512665 + 1.34461i) q^{58} +(8.68022 - 3.59546i) q^{59} +(1.48345 - 3.58137i) q^{61} +(10.5055 - 0.298848i) q^{62} +(7.88382 - 1.35847i) q^{64} +8.39150 q^{65} +(6.11281 - 14.7576i) q^{67} +(0.657282 + 11.5435i) q^{68} +(-1.54625 + 4.05549i) q^{70} +(10.5767 - 10.5767i) q^{71} +(6.86117 + 6.86117i) q^{73} +(5.13987 - 2.30235i) q^{74} +(-2.13141 - 0.743950i) q^{76} +(4.24870 + 1.75987i) q^{77} +11.4744i q^{79} +(-5.72767 + 3.17722i) q^{80} +(0.689582 + 0.651435i) q^{82} +(-15.2335 - 6.30991i) q^{83} +(-3.62261 - 8.74577i) q^{85} +(0.617950 + 1.37954i) q^{86} +(3.19252 + 6.16206i) q^{88} +(-6.07620 + 6.07620i) q^{89} +(8.87380 - 3.67565i) q^{91} +(-9.05878 - 8.08275i) q^{92} +(-0.109877 - 3.86255i) q^{94} +1.84830 q^{95} +15.4135 q^{97} +(-0.140232 - 4.92962i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} - 8 q^{16} - 24 q^{22} - 40 q^{28} + 48 q^{31} - 40 q^{34} - 72 q^{40} + 16 q^{43} - 32 q^{46} - 8 q^{52} + 32 q^{55} - 32 q^{58} - 32 q^{61} + 72 q^{64} + 16 q^{67} + 120 q^{70} + 72 q^{76} + 120 q^{82} + 128 q^{88} - 48 q^{91} + 80 q^{94}+O(q^{100}) $ 32 * q - 8 * q^10 - 8 * q^16 - 24 * q^22 - 40 * q^28 + 48 * q^31 - 40 * q^34 - 72 * q^40 + 16 * q^43 - 32 * q^46 - 8 * q^52 + 32 * q^55 - 32 * q^58 - 32 * q^61 + 72 * q^64 + 16 * q^67 + 120 * q^70 + 72 * q^76 + 120 * q^82 + 128 * q^88 - 48 * q^91 + 80 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	−1.41364	+	0.0402136i	−0.999596	+	0.0284353i
$2$	−1.41364	+	0.0402136i	−0.999596	+	0.0284353i
$3$		0			0
$3$		0			0
$4$	1.99677	−	0.113695i	0.998383	−	0.0568477i
$5$	−1.51282	+	0.626632i	−0.676556	+	0.280239i	−0.694386	−	0.719602i	$-0.744324\pi$
$5$	−1.51282	+	0.626632i	−0.676556	+	0.280239i	0.0178305	+	0.999841i	$0.494324\pi$
$6$		0			0
$7$	−1.32530	+	1.32530i	−0.500915	+	0.500915i	−0.911722	−	0.410807i	$-0.865247\pi$
$7$	−1.32530	+	1.32530i	−0.500915	+	0.500915i	0.410807	+	0.911722i	$0.365247\pi$
$8$	−2.81814	+	0.241022i	−0.996363	+	0.0852141i
$9$		0			0
$10$	2.11339	−	0.946670i	0.668313	−	0.299363i
$11$	−0.938971	−	2.26688i	−0.283110	−	0.683489i	0.716794	−	0.697285i	$-0.245609\pi$
$11$	−0.938971	−	2.26688i	−0.283110	−	0.683489i	−0.999905	+	0.0137954i	$0.995609\pi$
$12$		0			0
$13$	−4.73458	−	1.96113i	−1.31314	−	0.543919i	−0.387339	−	0.921937i	$-0.626606\pi$
$13$	−4.73458	−	1.96113i	−1.31314	−	0.543919i	−0.925798	+	0.378018i	$0.876606\pi$
$14$	1.82020	−	1.92679i	0.486469	−	0.514956i
$15$		0			0
$16$	3.97415	−	0.454046i	0.993537	−	0.113512i
$17$			5.78108i			1.40212i	0.713103	+	0.701059i	$0.247289\pi$
$17$			5.78108i			1.40212i	−0.713103	+	0.701059i	$0.752711\pi$
$18$		0			0
$19$	−1.04283	−	0.431956i	−0.239243	−	0.0990975i	0.259841	−	0.965651i	$-0.416330\pi$
$19$	−1.04283	−	0.431956i	−0.239243	−	0.0990975i	−0.499083	+	0.866554i	$0.666330\pi$
$20$	−2.94951	+	1.42324i	−0.659531	+	0.318246i
$21$		0			0
$22$	1.41853	+	3.16679i	0.302431	+	0.675162i
$23$	−4.29232	−	4.29232i	−0.895011	−	0.895011i	0.0999784	−	0.994990i	$-0.468123\pi$
$23$	−4.29232	−	4.29232i	−0.895011	−	0.895011i	−0.994990	+	0.0999784i	$0.968123\pi$
$24$		0			0
$25$	−1.63956	+	1.63956i	−0.327913	+	0.327913i
$26$	6.77187	+	2.58194i	1.32807	+	0.506360i
$27$		0			0
$28$	−2.49563	+	2.79699i	−0.471629	+	0.528581i
$29$	0.389398	−	0.940091i	0.0723095	−	0.174570i	−0.883592	−	0.468257i	$-0.844882\pi$
$29$	0.389398	−	0.940091i	0.0723095	−	0.174570i	0.955902	+	0.293686i	$0.0948822\pi$
$30$		0			0
$31$	−7.43150			−1.33474			−0.667369	−	0.744727i	$-0.732580\pi$
$31$	−7.43150			−1.33474			−0.667369	+	0.744727i	$0.732580\pi$
$32$	−5.59976	+	0.801673i	−0.989907	+	0.141717i
$33$		0			0
$34$	−0.232478	−	8.17238i	−0.0398697	−	1.40155i
$35$	1.17447	−	2.83541i	0.198521	−	0.479272i
$36$		0			0
$37$	−3.67926	+	1.52400i	−0.604867	+	0.250544i	−0.664032	−	0.747704i	$-0.731156\pi$
$37$	−3.67926	+	1.52400i	−0.604867	+	0.250544i	0.0591650	+	0.998248i	$0.481156\pi$
$38$	1.49156	+	0.568695i	0.241964	+	0.0922545i
$39$		0			0
$40$	4.11232	−	2.13056i	0.650215	−	0.336871i
$41$	−0.474313	−	0.474313i	−0.0740752	−	0.0740752i	0.669098	−	0.743174i	$-0.266680\pi$
$41$	−0.474313	−	0.474313i	−0.0740752	−	0.0740752i	−0.743174	+	0.669098i	$0.766680\pi$
$42$		0			0
$43$	−0.409042	−	0.987514i	−0.0623783	−	0.150594i	0.889617	−	0.456708i	$-0.150971\pi$
$43$	−0.409042	−	0.987514i	−0.0623783	−	0.150594i	−0.951995	+	0.306113i	$0.900971\pi$
$44$	−2.13264	−	4.41967i	−0.321507	−	0.666290i
$45$		0			0
$46$	6.24042	+	5.89520i	0.920099	+	0.869199i
$47$			2.73234i			0.398553i	0.979943	+	0.199277i	$0.0638592\pi$
$47$			2.73234i			0.398553i	−0.979943	+	0.199277i	$0.936141\pi$
$48$		0			0
$49$			3.48718i			0.498169i
$50$	2.25182	−	2.38369i	0.318456	−	0.337104i
$51$		0			0
$52$	−9.67683	−	3.37761i	−1.34193	−	0.468391i
$53$	4.55362	+	10.9934i	0.625488	+	1.51006i	0.845174	+	0.534491i	$0.179497\pi$
$53$	4.55362	+	10.9934i	0.625488	+	1.51006i	−0.219686	+	0.975571i	$0.570503\pi$
$54$		0			0
$55$	2.84100	+	2.84100i	0.383080	+	0.383080i
$56$	3.41544	−	4.05429i	0.456408	−	0.541778i
$57$		0			0
$58$	−0.512665	+	1.34461i	−0.0673163	+	0.176556i
$59$	8.68022	−	3.59546i	1.13007	−	0.468089i	0.262264	−	0.964996i	$-0.415531\pi$
$59$	8.68022	−	3.59546i	1.13007	−	0.468089i	0.867804	+	0.496907i	$0.165531\pi$
$60$		0			0
$61$	1.48345	−	3.58137i	0.189937	−	0.458548i	−0.800010	−	0.599986i	$-0.795173\pi$
$61$	1.48345	−	3.58137i	0.189937	−	0.458548i	0.989947	+	0.141438i	$0.0451727\pi$
$62$	10.5055	−	0.298848i	1.33420	−	0.0379537i
$63$		0			0
$64$	7.88382	−	1.35847i	0.985477	−	0.169808i
$65$	8.39150			1.04084
$66$		0			0
$67$	6.11281	−	14.7576i	0.746799	−	1.80293i	0.171131	−	0.985248i	$-0.445258\pi$
$67$	6.11281	−	14.7576i	0.746799	−	1.80293i	0.575668	−	0.817683i	$-0.304742\pi$
$68$	0.657282	+	11.5435i	0.0797072	+	1.39985i
$69$		0			0
$70$	−1.54625	+	4.05549i	−0.184813	+	0.484724i
$71$	10.5767	−	10.5767i	1.25522	−	1.25522i	0.301869	−	0.953349i	$-0.402389\pi$
$71$	10.5767	−	10.5767i	1.25522	−	1.25522i	0.953349	−	0.301869i	$-0.0976105\pi$
$72$		0			0
$73$	6.86117	+	6.86117i	0.803040	+	0.803040i	0.983570	−	0.180530i	$-0.0577812\pi$
$73$	6.86117	+	6.86117i	0.803040	+	0.803040i	−0.180530	+	0.983570i	$0.557781\pi$
$74$	5.13987	−	2.30235i	0.597498	−	0.267642i
$75$		0			0
$76$	−2.13141	−	0.743950i	−0.244489	−	0.0853369i
$77$	4.24870	+	1.75987i	0.484184	+	0.200556i
$78$		0			0
$79$			11.4744i			1.29097i	0.763771	+	0.645487i	$0.223345\pi$
$79$			11.4744i			1.29097i	−0.763771	+	0.645487i	$0.776655\pi$
$80$	−5.72767	+	3.17722i	−0.640373	+	0.355224i
$81$		0			0
$82$	0.689582	+	0.651435i	0.0761516	+	0.0719389i
$83$	−15.2335	−	6.30991i	−1.67209	−	0.692603i	−0.673191	−	0.739469i	$-0.735077\pi$
$83$	−15.2335	−	6.30991i	−1.67209	−	0.692603i	−0.998901	+	0.0468660i	$0.985077\pi$
$84$		0			0
$85$	−3.62261	−	8.74577i	−0.392928	−	0.948611i
$86$	0.617950	+	1.37954i	0.0666353	+	0.148760i
$87$		0			0
$88$	3.19252	+	6.16206i	0.340324	+	0.656878i
$89$	−6.07620	+	6.07620i	−0.644076	+	0.644076i	−0.951555	−	0.307479i	$-0.900515\pi$
$89$	−6.07620	+	6.07620i	−0.644076	+	0.644076i	0.307479	+	0.951555i	$0.400515\pi$
$90$		0			0
$91$	8.87380	−	3.67565i	0.930227	−	0.385313i
$92$	−9.05878	−	8.08275i	−0.944443	−	0.842685i
$93$		0			0
$94$	−0.109877	−	3.86255i	−0.0113330	−	0.398392i
$95$	1.84830			0.189632
$96$		0			0
$97$	15.4135			1.56500			0.782501	−	0.622649i	$-0.213944\pi$
$97$	15.4135			1.56500			0.782501	+	0.622649i	$0.213944\pi$
$98$	−0.140232	−	4.92962i	−0.0141656	−	0.497967i
$99$		0			0
$100$	−3.08741	+	3.46024i	−0.308741	+	0.346024i
$101$	−10.3874	+	4.30260i	−1.03358	+	0.428124i	−0.834005	−	0.551757i	$-0.813957\pi$
$101$	−10.3874	+	4.30260i	−1.03358	+	0.428124i	−0.199579	+	0.979882i	$0.563957\pi$
$102$		0			0
$103$	−8.05089	+	8.05089i	−0.793278	+	0.793278i	−0.982026	−	0.188748i	$-0.939557\pi$
$103$	−8.05089	+	8.05089i	−0.793278	+	0.793278i	0.188748	+	0.982026i	$0.439557\pi$
$104$	13.8154	+	4.38560i	1.35471	+	0.430043i
$105$		0			0
$106$	−6.87927	−	15.3576i	−0.668174	−	1.49167i
$107$	1.76437	+	4.25957i	0.170568	+	0.411788i	0.985929	−	0.167165i	$-0.0534613\pi$
$107$	1.76437	+	4.25957i	0.170568	+	0.411788i	−0.815361	+	0.578953i	$0.803461\pi$
$108$		0			0
$109$	−5.20159	−	2.15457i	−0.498222	−	0.206370i	0.119399	−	0.992846i	$-0.461903\pi$
$109$	−5.20159	−	2.15457i	−0.498222	−	0.206370i	−0.617621	+	0.786476i	$0.711903\pi$
$110$	−4.13040	−	3.90191i	−0.393818	−	0.372032i
$111$		0			0
$112$	−4.66518	+	5.86867i	−0.440818	+	0.554537i
$113$			4.12616i			0.388156i	0.980986	+	0.194078i	$0.0621715\pi$
$113$			4.12616i			0.388156i	−0.980986	+	0.194078i	$0.937829\pi$
$114$		0			0
$115$	9.18324	+	3.80382i	0.856342	+	0.354708i
$116$	0.670653	−	1.92141i	0.0622686	−	0.178399i
$117$		0			0
$118$	−12.1261	+	5.43176i	−1.11630	+	0.500034i
$119$	−7.66165	−	7.66165i	−0.702342	−	0.702342i
$120$		0			0
$121$	3.52111	−	3.52111i	0.320101	−	0.320101i
$122$	−1.95305	+	5.12243i	−0.176821	+	0.463763i
$123$		0			0
$124$	−14.8390	+	0.844928i	−1.33258	+	0.0758767i
$125$	4.58613	−	11.0719i	0.410196	−	0.990301i
$126$		0			0
$127$	7.68466			0.681904			0.340952	−	0.940081i	$-0.389251\pi$
$127$	7.68466			0.681904			0.340952	+	0.940081i	$0.389251\pi$
$128$	−11.0903	+	2.23742i	−0.980250	+	0.197762i
$129$		0			0
$130$	−11.8626	+	0.337453i	−1.04042	+	0.0295966i
$131$	−6.42051	+	15.5005i	−0.560963	+	1.35428i	0.348034	+	0.937482i	$0.386849\pi$
$131$	−6.42051	+	15.5005i	−0.560963	+	1.35428i	−0.908997	+	0.416802i	$0.863151\pi$
$132$		0			0
$133$	1.95453	−	0.809594i	0.169480	−	0.0702007i
$134$	−8.04787	+	21.1078i	−0.695230	+	1.82344i
$135$		0			0
$136$	−1.39337	−	16.2919i	−0.119480	−	1.39702i
$137$	−16.1360	−	16.1360i	−1.37859	−	1.37859i	−0.846997	−	0.531598i	$-0.821592\pi$
$137$	−16.1360	−	16.1360i	−1.37859	−	1.37859i	−0.531598	−	0.846997i	$-0.678408\pi$
$138$		0			0
$139$	−2.88036	−	6.95381i	−0.244309	−	0.589814i	0.753393	−	0.657571i	$-0.228416\pi$
$139$	−2.88036	−	6.95381i	−0.244309	−	0.589814i	−0.997702	+	0.0677564i	$0.978416\pi$
$140$	2.02276	−	5.79519i	0.170955	−	0.489783i
$141$		0			0
$142$	−14.5263	+	15.3769i	−1.21902	+	1.29040i
$143$			12.5742i			1.05150i
$144$		0			0
$145$			1.66620i			0.138371i
$146$	−9.97516	−	9.42333i	−0.825550	−	0.779880i
$147$		0			0
$148$	−7.17336	+	3.46139i	−0.589646	+	0.284524i
$149$	−1.57271	−	3.79687i	−0.128842	−	0.311051i	0.846274	−	0.532748i	$-0.178841\pi$
$149$	−1.57271	−	3.79687i	−0.128842	−	0.311051i	−0.975116	+	0.221696i	$0.928841\pi$
$150$		0			0
$151$	−4.12337	−	4.12337i	−0.335555	−	0.335555i	0.519136	−	0.854692i	$-0.326254\pi$
$151$	−4.12337	−	4.12337i	−0.335555	−	0.335555i	−0.854692	+	0.519136i	$0.826254\pi$
$152$	3.04296	+	0.965966i	0.246817	+	0.0783502i
$153$		0			0
$154$	−6.07691	−	2.31697i	−0.489691	−	0.186707i
$155$	11.2426	−	4.65682i	0.903024	−	0.374045i
$156$		0			0
$157$	0.772760	−	1.86561i	0.0616730	−	0.148892i	−0.890039	−	0.455885i	$-0.849323\pi$
$157$	0.772760	−	1.86561i	0.0616730	−	0.148892i	0.951712	+	0.306993i	$0.0993229\pi$
$158$	−0.461428	−	16.2207i	−0.0367093	−	1.29045i
$159$		0			0
$160$	7.96910	−	4.72178i	0.630013	−	0.373290i
$161$	11.3772			0.896649
$162$		0			0
$163$	−4.46436	+	10.7779i	−0.349676	+	0.844192i	0.646982	+	0.762505i	$0.276031\pi$
$163$	−4.46436	+	10.7779i	−0.349676	+	0.844192i	−0.996658	+	0.0816870i	$0.973969\pi$
$164$	−1.00102	−	0.893165i	−0.0781665	−	0.0697444i
$165$		0			0
$166$	21.7884	+	8.30736i	1.69111	+	0.644777i
$167$	−9.15618	+	9.15618i	−0.708527	+	0.708527i	−0.966225	−	0.257699i	$-0.917036\pi$
$167$	−9.15618	+	9.15618i	−0.708527	+	0.708527i	0.257699	+	0.966225i	$0.417036\pi$
$168$		0			0
$169$	9.37787	+	9.37787i	0.721374	+	0.721374i
$170$	5.47278	+	12.2177i	0.419743	+	0.937055i
$171$		0			0
$172$	−0.929036	−	1.92533i	−0.0708383	−	0.146805i
$173$	7.27037	+	3.01148i	0.552756	+	0.228959i	0.641537	−	0.767092i	$-0.278297\pi$
$173$	7.27037	+	3.01148i	0.552756	+	0.228959i	−0.0887811	+	0.996051i	$0.528297\pi$
$174$		0			0
$175$		−	4.34581i		−	0.328513i
$176$	−4.76088	−	8.58257i	−0.358865	−	0.646935i
$177$		0			0
$178$	8.34522	−	8.83391i	0.625501	−	0.662130i
$179$	−5.62849	−	2.33140i	−0.420693	−	0.174257i	0.162286	−	0.986744i	$-0.448113\pi$
$179$	−5.62849	−	2.33140i	−0.420693	−	0.174257i	−0.582979	+	0.812487i	$0.698113\pi$
$180$		0			0
$181$	−1.09419	−	2.64161i	−0.0813306	−	0.196349i	0.877983	−	0.478691i	$-0.158889\pi$
$181$	−1.09419	−	2.64161i	−0.0813306	−	0.196349i	−0.959314	+	0.282342i	$0.908889\pi$
$182$	−12.3966	+	5.55290i	−0.918894	+	0.411608i
$183$		0			0
$184$	13.1309	+	11.0618i	0.968023	+	0.815488i
$185$	4.61109	−	4.61109i	0.339014	−	0.339014i
$186$		0			0
$187$	13.1050	−	5.42827i	0.958333	−	0.396955i
$188$	0.310655	+	5.45585i	0.0226568	+	0.397909i
$189$		0			0
$190$	−2.61284	+	0.0743270i	−0.189555	+	0.00539225i
$191$	4.24424			0.307102			0.153551	−	0.988141i	$-0.450929\pi$
$191$	4.24424			0.307102			0.153551	+	0.988141i	$0.450929\pi$
$192$		0			0
$193$	−8.04323			−0.578964			−0.289482	−	0.957183i	$-0.593483\pi$
$193$	−8.04323			−0.578964			−0.289482	+	0.957183i	$0.593483\pi$
$194$	−21.7891	+	0.619832i	−1.56437	+	0.0445014i
$195$		0			0
$196$	0.396476	+	6.96308i	0.0283197	+	0.497363i
$197$	−20.4709	+	8.47934i	−1.45849	+	0.604128i	−0.964202	−	0.265169i	$-0.914572\pi$
$197$	−20.4709	+	8.47934i	−1.45849	+	0.604128i	−0.494291	+	0.869296i	$0.664572\pi$
$198$		0			0
$199$	2.58390	−	2.58390i	0.183168	−	0.183168i	−0.609567	−	0.792735i	$-0.708657\pi$
$199$	2.58390	−	2.58390i	0.183168	−	0.183168i	0.792735	+	0.609567i	$0.208657\pi$
$200$	4.22535	−	5.01569i	0.298777	−	0.354663i
$201$		0			0
$202$	14.5110	−	6.50004i	1.02099	−	0.457342i
$203$	0.729831	+	1.76197i	0.0512241	+	0.123666i
$204$		0			0
$205$	1.01477	+	0.420332i	0.0708748	+	0.0293573i
$206$	11.0573	−	11.7048i	0.770400	−	0.815514i
$207$		0			0
$208$	−19.7064	−	5.64409i	−1.36639	−	0.391348i
$209$			2.76957i			0.191575i
$210$		0			0
$211$	−1.04546	−	0.433043i	−0.0719723	−	0.0298119i	0.346407	−	0.938084i	$-0.387402\pi$
$211$	−1.04546	−	0.433043i	−0.0719723	−	0.0298119i	−0.418379	+	0.908272i	$0.637402\pi$
$212$	10.3424	+	21.4335i	0.710320	+	1.47206i
$213$		0			0
$214$	−2.66548	−	5.95055i	−0.182209	−	0.406771i
$215$	1.23762	+	1.23762i	0.0844048	+	0.0844048i
$216$		0			0
$217$	9.84894	−	9.84894i	0.668590	−	0.668590i
$218$	7.43982	+	2.83661i	0.503889	+	0.192120i
$219$		0			0
$220$	5.99582	+	5.34980i	0.404238	+	0.360683i
$221$	11.3374	−	27.3710i	0.762639	−	1.84117i
$222$		0			0
$223$	−7.40345			−0.495772			−0.247886	−	0.968789i	$-0.579736\pi$
$223$	−7.40345			−0.495772			−0.247886	+	0.968789i	$0.579736\pi$
$224$	6.35889	−	8.48379i	0.424871	−	0.566847i
$225$		0			0
$226$	−0.165928	−	5.83290i	−0.0110373	−	0.387999i
$227$	−5.13477	+	12.3964i	−0.340806	+	0.822780i	0.656828	+	0.754040i	$0.271898\pi$
$227$	−5.13477	+	12.3964i	−0.340806	+	0.822780i	−0.997635	+	0.0687393i	$0.978102\pi$
$228$		0			0
$229$	−10.6519	+	4.41217i	−0.703899	+	0.291564i	−0.705777	−	0.708434i	$-0.749402\pi$
$229$	−10.6519	+	4.41217i	−0.703899	+	0.291564i	0.00187845	+	0.999998i	$0.499402\pi$
$230$	−13.1348	−	5.00795i	−0.866082	−	0.330215i
$231$		0			0
$232$	−0.870797	+	2.74316i	−0.0571706	+	0.180097i
$233$	−10.6029	−	10.6029i	−0.694620	−	0.694620i	0.268625	−	0.963245i	$-0.413431\pi$
$233$	−10.6029	−	10.6029i	−0.694620	−	0.694620i	−0.963245	+	0.268625i	$0.913431\pi$
$234$		0			0
$235$	−1.71217	−	4.13355i	−0.111690	−	0.269643i
$236$	16.9236	−	8.16620i	1.10163	−	0.531574i
$237$		0			0
$238$	11.1389	+	10.5227i	0.722029	+	0.682087i
$239$			27.7222i			1.79320i	0.442844	+	0.896598i	$0.353969\pi$
$239$			27.7222i			1.79320i	−0.442844	+	0.896598i	$0.646031\pi$
$240$		0			0
$241$			19.1370i			1.23273i	0.787462	+	0.616363i	$0.211394\pi$
$241$			19.1370i			1.23273i	−0.787462	+	0.616363i	$0.788606\pi$
$242$	−4.83599	+	5.11918i	−0.310869	+	0.329074i
$243$		0			0
$244$	2.55492	−	7.31982i	0.163562	−	0.468604i
$245$	−2.18518	−	5.27549i	−0.139606	−	0.337039i
$246$		0			0
$247$	4.09026	+	4.09026i	0.260257	+	0.260257i
$248$	20.9430	−	1.79115i	1.32988	−	0.113738i
$249$		0			0
$250$	−6.03790	+	15.8361i	−0.381871	+	1.00156i
$251$	22.9873	−	9.52164i	1.45094	−	0.601001i	0.488520	−	0.872553i	$-0.337537\pi$
$251$	22.9873	−	9.52164i	1.45094	−	0.601001i	0.962424	+	0.271552i	$0.0875368\pi$
$252$		0			0
$253$	−5.69980	+	13.7605i	−0.358343	+	0.865118i
$254$	−10.8634	+	0.309028i	−0.681628	+	0.0193902i
$255$		0			0
$256$	15.5877	−	3.60889i	0.974230	−	0.225556i
$257$	11.2303			0.700525			0.350263	−	0.936651i	$-0.386092\pi$
$257$	11.2303			0.700525			0.350263	+	0.936651i	$0.386092\pi$
$258$		0			0
$259$	2.85636	−	6.89587i	0.177486	−	0.428488i
$260$	16.7559	−	0.954075i	1.03915	−	0.0591692i
$261$		0			0
$262$	8.45297	−	22.1703i	0.522227	−	1.36969i
$263$	8.63436	−	8.63436i	0.532417	−	0.532417i	−0.388874	−	0.921291i	$-0.627136\pi$
$263$	8.63436	−	8.63436i	0.532417	−	0.532417i	0.921291	+	0.388874i	$0.127136\pi$
$264$		0			0
$265$	−13.7777	−	13.7777i	−0.846355	−	0.846355i
$266$	−2.73045	+	1.22308i	−0.167415	+	0.0749915i
$267$		0			0
$268$	10.5280	−	30.1625i	0.643099	−	1.84247i
$269$	−11.4515	−	4.74335i	−0.698208	−	0.289207i	0.00520737	−	0.999986i	$-0.498342\pi$
$269$	−11.4515	−	4.74335i	−0.698208	−	0.289207i	−0.703415	+	0.710779i	$0.748342\pi$
$270$		0			0
$271$			4.02905i			0.244747i	0.992484	+	0.122374i	$0.0390506\pi$
$271$			4.02905i			0.244747i	−0.992484	+	0.122374i	$0.960949\pi$
$272$	2.62488	+	22.9749i	0.159157	+	1.39306i
$273$		0			0
$274$	23.4595	+	22.1617i	1.41724	+	1.33884i
$275$	5.25619	+	2.17719i	0.316960	+	0.131289i
$276$		0			0
$277$	−4.46812	−	10.7870i	−0.268464	−	0.648128i	0.730948	−	0.682433i	$-0.239078\pi$
$277$	−4.46812	−	10.7870i	−0.268464	−	0.648128i	−0.999411	+	0.0343049i	$0.989078\pi$
$278$	4.35144	+	9.71436i	0.260982	+	0.582629i
$279$		0			0
$280$	−2.62641	+	8.27366i	−0.156958	+	0.494446i
$281$	4.45827	−	4.45827i	0.265958	−	0.265958i	−0.561511	−	0.827469i	$-0.689780\pi$
$281$	4.45827	−	4.45827i	0.265958	−	0.265958i	0.827469	+	0.561511i	$0.189780\pi$
$282$		0			0
$283$	−16.9317	+	7.01336i	−1.00649	+	0.416901i	−0.824172	−	0.566339i	$-0.808359\pi$
$283$	−16.9317	+	7.01336i	−1.00649	+	0.416901i	−0.182315	+	0.983240i	$0.558359\pi$
$284$	19.9166	−	22.3216i	1.18183	−	1.32454i
$285$		0			0
$286$	−0.505653	−	17.7754i	−0.0298999	−	1.05108i
$287$	1.25721			0.0742108
$288$		0			0
$289$	−16.4209			−0.965937
$290$	−0.0670041	−	2.35541i	−0.00393461	−	0.138315i
$291$		0			0
$292$	14.4802	+	12.9201i	0.847392	+	0.756090i
$293$	16.9534	−	7.02234i	0.990429	−	0.410249i	0.172150	−	0.985071i	$-0.444928\pi$
$293$	16.9534	−	7.02234i	0.990429	−	0.410249i	0.818279	+	0.574821i	$0.194928\pi$
$294$		0			0
$295$	−10.8786	+	10.8786i	−0.633377	+	0.633377i
$296$	10.0014	−	5.18163i	0.581317	−	0.301176i
$297$		0			0
$298$	2.37594	+	5.30416i	0.137634	+	0.307262i
$299$	11.9046	+	28.7402i	0.688459	+	1.66209i
$300$		0			0
$301$	1.85085	+	0.766647i	0.106681	+	0.0441888i
$302$	5.99479	+	5.66316i	0.344961	+	0.325878i
$303$		0			0
$304$	−4.34050	−	1.24316i	−0.248945	−	0.0713002i
$305$			6.34757i			0.363461i
$306$		0			0
$307$	−26.8443	−	11.1193i	−1.53209	−	0.634611i	−0.552118	−	0.833766i	$-0.686180\pi$
$307$	−26.8443	−	11.1193i	−1.53209	−	0.634611i	−0.979968	+	0.199155i	$0.936180\pi$
$308$	8.68374	+	3.03099i	0.494802	+	0.172707i
$309$		0			0
$310$	−15.7057	+	7.03518i	−0.892023	+	0.399572i
$311$	−11.6197	−	11.6197i	−0.658895	−	0.658895i	0.296224	−	0.955119i	$-0.404273\pi$
$311$	−11.6197	−	11.6197i	−0.658895	−	0.658895i	−0.955119	+	0.296224i	$0.904273\pi$
$312$		0			0
$313$	−12.9034	+	12.9034i	−0.729344	+	0.729344i	−0.970489	−	0.241145i	$-0.922477\pi$
$313$	−12.9034	+	12.9034i	−0.729344	+	0.729344i	0.241145	+	0.970489i	$0.422477\pi$
$314$	−1.01738	+	2.66838i	−0.0574143	+	0.150585i
$315$		0			0
$316$	1.30459	+	22.9117i	0.0733889	+	1.28889i
$317$	6.08877	−	14.6996i	0.341979	−	0.825612i	−0.655536	−	0.755164i	$-0.727557\pi$
$317$	6.08877	−	14.6996i	0.341979	−	0.825612i	0.997515	−	0.0704476i	$-0.0224428\pi$
$318$		0			0
$319$	−2.49670			−0.139789
$320$	−11.0756	+	6.99538i	−0.619143	+	0.391053i
$321$		0			0
$322$	−16.0833	+	0.457519i	−0.896286	+	0.0254965i
$323$	2.49717	−	6.02871i	0.138946	−	0.335446i
$324$		0			0
$325$	10.9780	−	4.54726i	0.608953	−	0.252236i
$326$	5.87759	−	15.4156i	0.325530	−	0.853794i
$327$		0			0
$328$	1.45100	+	1.22236i	0.0801181	+	0.0674936i
$329$	−3.62116	−	3.62116i	−0.199641	−	0.199641i
$330$		0			0
$331$	3.88508	+	9.37942i	0.213543	+	0.515539i	0.993963	−	0.109717i	$-0.0349944\pi$
$331$	3.88508	+	9.37942i	0.213543	+	0.515539i	−0.780419	+	0.625256i	$0.784994\pi$
$332$	−31.1351	−	10.8674i	−1.70876	−	0.596429i
$333$		0			0
$334$	12.5754	−	13.3118i	0.688093	−	0.728387i
$335$			26.1562i			1.42907i
$336$		0			0
$337$		−	26.4416i		−	1.44037i	−0.693784	−	0.720183i	$-0.744058\pi$
$337$		−	26.4416i		−	1.44037i	0.693784	−	0.720183i	$-0.255942\pi$
$338$	−13.6341	−	12.8798i	−0.741595	−	0.700570i
$339$		0			0
$340$	−8.22787	−	17.0514i	−0.446219	−	0.924740i
$341$	6.97797	+	16.8463i	0.377878	+	0.912279i
$342$		0			0
$343$	−13.8986	−	13.8986i	−0.750455	−	0.750455i
$344$	1.39075	+	2.68436i	0.0749842	+	0.144731i
$345$		0			0
$346$	−10.3988	−	3.96479i	−0.559043	−	0.213149i
$347$	−21.7583	+	9.01258i	−1.16805	+	0.483820i	−0.880546	−	0.473960i	$-0.842824\pi$
$347$	−21.7583	+	9.01258i	−1.16805	+	0.483820i	−0.287500	+	0.957781i	$0.592824\pi$
$348$		0			0
$349$	2.65403	−	6.40740i	0.142067	−	0.342980i	−0.836791	−	0.547523i	$-0.815571\pi$
$349$	2.65403	−	6.40740i	0.142067	−	0.342980i	0.978858	+	0.204543i	$0.0655708\pi$
$350$	0.174761	+	6.14343i	0.00934137	+	0.328380i
$351$		0			0
$352$	7.07531	+	11.9412i	0.377115	+	0.636469i
$353$	9.15953			0.487512			0.243756	−	0.969837i	$-0.421620\pi$
$353$	9.15953			0.487512			0.243756	+	0.969837i	$0.421620\pi$
$354$		0			0
$355$	−9.37295	+	22.6283i	−0.497465	+	1.20099i
$356$	−11.4419	+	12.8236i	−0.606420	+	0.679648i
$357$		0			0
$358$	8.05042	+	3.06942i	0.425478	+	0.162224i
$359$	14.5008	−	14.5008i	0.765322	−	0.765322i	−0.211957	−	0.977279i	$-0.567984\pi$
$359$	14.5008	−	14.5008i	0.765322	−	0.765322i	0.977279	+	0.211957i	$0.0679836\pi$
$360$		0			0
$361$	−12.5341	−	12.5341i	−0.659690	−	0.659690i
$362$	1.65302	+	3.69029i	0.0868810	+	0.193957i
$363$		0			0
$364$	17.3010	−	8.34832i	0.906819	−	0.437571i
$365$	−14.6792	−	6.08032i	−0.768344	−	0.318258i
$366$		0			0
$367$		−	5.62846i		−	0.293803i	−0.989151	−	0.146901i	$-0.953070\pi$
$367$		−	5.62846i		−	0.293803i	0.989151	−	0.146901i	$-0.0469300\pi$
$368$	−19.0072	−	15.1094i	−0.990821	−	0.787632i
$369$		0			0
$370$	−6.33300	+	6.70386i	−0.329237	+	0.348517i
$371$	−20.6044	−	8.53463i	−1.06973	−	0.443096i
$372$		0			0
$373$	11.8400	+	28.5842i	0.613050	+	1.48003i	0.859633	+	0.510911i	$0.170692\pi$
$373$	11.8400	+	28.5842i	0.613050	+	1.48003i	−0.246584	+	0.969122i	$0.579308\pi$
$374$	−18.3075	+	8.20063i	−0.946658	+	0.424045i
$375$		0			0
$376$	−0.658554	−	7.70012i	−0.0339623	−	0.397103i
$377$	−3.68728	+	3.68728i	−0.189904	+	0.189904i
$378$		0			0
$379$	−24.8544	+	10.2950i	−1.27668	+	0.528820i	−0.914990	−	0.403477i	$-0.867802\pi$
$379$	−24.8544	+	10.2950i	−1.27668	+	0.528820i	−0.361694	+	0.932297i	$0.617802\pi$
$380$	3.69063	−	0.210143i	0.189325	−	0.0107801i
$381$		0			0
$382$	−5.99983	+	0.170676i	−0.306978	+	0.00873256i
$383$	−3.10697			−0.158759			−0.0793795	−	0.996844i	$-0.525294\pi$
$383$	−3.10697			−0.158759			−0.0793795	+	0.996844i	$0.525294\pi$
$384$		0			0
$385$	−7.53033			−0.383781
$386$	11.3702	−	0.323447i	0.578730	−	0.0164630i
$387$		0			0
$388$	30.7771	−	1.75244i	1.56247	−	0.0889667i
$389$	−8.30581	+	3.44038i	−0.421121	+	0.174434i	−0.583173	−	0.812348i	$-0.698189\pi$
$389$	−8.30581	+	3.44038i	−0.421121	+	0.174434i	0.162051	+	0.986782i	$0.448189\pi$
$390$		0			0
$391$	24.8143	−	24.8143i	1.25491	−	1.25491i
$392$	−0.840486	−	9.82736i	−0.0424510	−	0.496357i
$393$		0			0
$394$	28.5976	−	12.8100i	1.44072	−	0.645356i
$395$	−7.19025	−	17.3588i	−0.361781	−	0.873416i
$396$		0			0
$397$	15.9030	+	6.58725i	0.798150	+	0.330605i	0.744215	−	0.667940i	$-0.232824\pi$
$397$	15.9030	+	6.58725i	0.798150	+	0.330605i	0.0539347	+	0.998544i	$0.482824\pi$
$398$	−3.54880	+	3.75662i	−0.177885	+	0.188302i
$399$		0			0
$400$	−5.77143	+	7.26030i	−0.288571	+	0.363015i
$401$		−	17.8067i		−	0.889227i	−0.895723	−	0.444613i	$-0.853341\pi$
$401$		−	17.8067i		−	0.889227i	0.895723	−	0.444613i	$-0.146659\pi$
$402$		0			0
$403$	35.1851	+	14.5741i	1.75269	+	0.725990i
$404$	−20.2520	+	9.77228i	−1.00757	+	0.486189i
$405$		0			0
$406$	−1.10257	−	2.46144i	−0.0547198	−	0.122159i
$407$	6.90945	+	6.90945i	0.342489	+	0.342489i
$408$		0			0
$409$	−15.4187	+	15.4187i	−0.762408	+	0.762408i	−0.976757	−	0.214349i	$-0.931237\pi$
$409$	−15.4187	+	15.4187i	−0.762408	+	0.762408i	0.214349	+	0.976757i	$0.431237\pi$
$410$	−1.45143	−	0.553392i	−0.0716809	−	0.0273301i
$411$		0			0
$412$	−15.1604	+	16.9911i	−0.746899	+	0.837091i
$413$	−6.73880	+	16.2689i	−0.331595	+	0.800541i
$414$		0			0
$415$	26.9996			1.32536
$416$	28.0847	+	7.18626i	1.37697	+	0.352335i
$417$		0			0
$418$	−0.111375	−	3.91518i	−0.00544751	−	0.191498i
$419$	−5.74289	+	13.8646i	−0.280559	+	0.677328i	−0.999849	−	0.0173813i	$-0.994467\pi$
$419$	−5.74289	+	13.8646i	−0.280559	+	0.677328i	0.719290	+	0.694710i	$0.244467\pi$
$420$		0			0
$421$	3.87628	−	1.60561i	0.188918	−	0.0782525i	−0.286219	−	0.958164i	$-0.592398\pi$
$421$	3.87628	−	1.60561i	0.188918	−	0.0782525i	0.475137	+	0.879912i	$0.342398\pi$
$422$	1.49532	+	0.570126i	0.0727909	+	0.0277533i
$423$		0			0
$424$	−15.4824	−	29.8835i	−0.751891	−	1.45127i
$425$	−9.47846	−	9.47846i	−0.459773	−	0.459773i
$426$		0			0
$427$	2.78036	+	6.71239i	0.134551	+	0.324835i
$428$	4.00733	+	8.30476i	0.193702	+	0.401426i
$429$		0			0
$430$	−1.79932	−	1.69978i	−0.0867707	−	0.0819706i
$431$		−	16.2867i		−	0.784503i	−0.919858	−	0.392252i	$-0.871696\pi$
$431$		−	16.2867i		−	0.784503i	0.919858	−	0.392252i	$-0.128304\pi$
$432$		0			0
$433$		−	28.2864i		−	1.35936i	−0.733510	−	0.679678i	$-0.762119\pi$
$433$		−	28.2864i		−	1.35936i	0.733510	−	0.679678i	$-0.237881\pi$
$434$	−13.5268	+	14.3189i	−0.649308	+	0.687331i
$435$		0			0
$436$	−10.6313	−	3.71077i	−0.509148	−	0.177714i
$437$	2.62209	+	6.33028i	0.125431	+	0.302818i
$438$		0			0
$439$	13.8438	+	13.8438i	0.660730	+	0.660730i	0.955552	−	0.294822i	$-0.0952604\pi$
$439$	13.8438	+	13.8438i	0.660730	+	0.660730i	−0.294822	+	0.955552i	$0.595260\pi$
$440$	−8.69107	−	7.32158i	−0.414330	−	0.349043i
$441$		0			0
$442$	−14.9264	+	39.1487i	−0.709977	+	1.86212i
$443$	5.95791	−	2.46785i	0.283069	−	0.117251i	−0.236632	−	0.971599i	$-0.576043\pi$
$443$	5.95791	−	2.46785i	0.283069	−	0.117251i	0.519701	+	0.854348i	$0.326043\pi$
$444$		0			0
$445$	5.38468	−	12.9998i	0.255258	−	0.616248i
$446$	10.4658	−	0.297720i	0.495571	−	0.0140974i
$447$		0			0
$448$	−8.64802	+	12.2488i	−0.408581	+	0.578700i
$449$	−27.7832			−1.31117			−0.655585	−	0.755121i	$-0.727578\pi$
$449$	−27.7832			−1.31117			−0.655585	+	0.755121i	$0.727578\pi$
$450$		0			0
$451$	−0.629843	+	1.52058i	−0.0296581	+	0.0716011i
$452$	0.469125	+	8.23897i	0.0220658	+	0.387528i
$453$		0			0
$454$	6.76022	−	17.7306i	0.317273	−	0.832138i
$455$	−11.1212	+	11.1212i	−0.521371	+	0.521371i
$456$		0			0
$457$	6.61796	+	6.61796i	0.309575	+	0.309575i	0.844745	−	0.535170i	$-0.179752\pi$
$457$	6.61796	+	6.61796i	0.309575	+	0.309575i	−0.535170	+	0.844745i	$0.679752\pi$
$458$	14.8806	−	6.66558i	0.695323	−	0.311462i
$459$		0			0
$460$	18.7693	+	6.55125i	0.875121	+	0.305454i
$461$	25.1777	+	10.4289i	1.17264	+	0.485724i	0.882065	−	0.471128i	$-0.156153\pi$
$461$	25.1777	+	10.4289i	1.17264	+	0.485724i	0.290576	+	0.956852i	$0.406153\pi$
$462$		0			0
$463$		−	33.3492i		−	1.54987i	−0.632040	−	0.774935i	$-0.717782\pi$
$463$		−	33.3492i		−	1.54987i	0.632040	−	0.774935i	$-0.282218\pi$
$464$	1.12068	−	3.91286i	0.0520263	−	0.181650i
$465$		0			0
$466$	15.4151	+	14.5623i	0.714091	+	0.674588i
$467$	7.09498	+	2.93884i	0.328317	+	0.135993i	0.540752	−	0.841182i	$-0.318140\pi$
$467$	7.09498	+	2.93884i	0.328317	+	0.135993i	−0.212436	+	0.977175i	$0.568140\pi$
$468$		0			0
$469$	11.4569	+	27.6595i	0.529033	+	1.27720i
$470$	2.58663	+	5.77451i	0.119312	+	0.266358i
$471$		0			0
$472$	−23.5955	+	12.2246i	−1.08607	+	0.562685i
$473$	−1.85449	+	1.85449i	−0.0852698	+	0.0852698i
$474$		0			0
$475$	2.41801	−	1.00157i	0.110946	−	0.0459553i
$476$	−16.1696	−	14.4274i	−0.741133	−	0.661280i
$477$		0			0
$478$	−1.11481	−	39.1892i	−0.0509902	−	1.79247i
$479$	1.66547			0.0760971			0.0380485	−	0.999276i	$-0.487886\pi$
$479$	1.66547			0.0760971			0.0380485	+	0.999276i	$0.487886\pi$
$480$		0			0
$481$	20.4085			0.930549
$482$	−0.769570	−	27.0529i	−0.0350530	−	1.23223i
$483$		0			0
$484$	6.63050	−	7.43116i	0.301386	−	0.337780i
$485$	−23.3179	+	9.65859i	−1.05881	+	0.438574i
$486$		0			0
$487$	15.4292	−	15.4292i	0.699165	−	0.699165i	−0.265066	−	0.964230i	$-0.585394\pi$
$487$	15.4292	−	15.4292i	0.699165	−	0.699165i	0.964230	+	0.265066i	$0.0853936\pi$
$488$	−3.31739	+	10.4504i	−0.150171	+	0.473065i
$489$		0			0
$490$	3.30121	+	7.36978i	0.149133	+	0.332933i
$491$	−7.65362	−	18.4775i	−0.345403	−	0.833877i	−0.997150	−	0.0754405i	$-0.975964\pi$
$491$	−7.65362	−	18.4775i	−0.345403	−	0.833877i	0.651747	−	0.758436i	$-0.274036\pi$
$492$		0			0
$493$	5.43474	+	2.25114i	0.244769	+	0.101386i
$494$	−5.94665	−	5.61768i	−0.267553	−	0.252751i
$495$		0			0
$496$	−29.5339	+	3.37425i	−1.32611	+	0.151508i
$497$			28.0344i			1.25751i
$498$		0			0
$499$	−27.2740	−	11.2973i	−1.22095	−	0.505735i	−0.323240	−	0.946317i	$-0.604772\pi$
$499$	−27.2740	−	11.2973i	−1.22095	−	0.505735i	−0.897712	+	0.440582i	$0.854772\pi$
$500$	7.89861	−	22.6294i	0.353236	−	1.01202i
$501$		0			0
$502$	−32.1129	+	14.3846i	−1.43327	+	0.642016i
$503$	−22.9821	−	22.9821i	−1.02472	−	1.02472i	−0.999687	−	0.0250340i	$-0.992031\pi$
$503$	−22.9821	−	22.9821i	−1.02472	−	1.02472i	−0.0250340	−	0.999687i	$-0.507969\pi$
$504$		0			0
$505$	13.0181	−	13.0181i	0.579300	−	0.579300i
$506$	7.50412	−	19.6817i	0.333599	−	0.874957i
$507$		0			0
$508$	15.3445	−	0.873711i	0.680801	−	0.0387646i
$509$	−6.17413	+	14.9057i	−0.273663	+	0.660682i	−0.999634	−	0.0270437i	$-0.991391\pi$
$509$	−6.17413	+	14.9057i	−0.273663	+	0.660682i	0.725971	+	0.687725i	$0.241391\pi$
$510$		0			0
$511$	−18.1862			−0.804509
$512$	−21.8903	+	5.72852i	−0.967423	+	0.253167i
$513$		0			0
$514$	−15.8756	+	0.451610i	−0.700242	+	0.0199197i
$515$	7.13463	−	17.2245i	0.314390	−	0.759004i
$516$		0			0
$517$	6.19388	−	2.56559i	0.272407	−	0.112835i
$518$	−3.76056	+	9.86315i	−0.165230	+	0.433362i
$519$		0			0
$520$	−23.6484	+	2.02253i	−1.03705	+	0.0886940i
$521$	10.2507	+	10.2507i	0.449093	+	0.449093i	0.895053	−	0.445960i	$-0.147138\pi$
$521$	10.2507	+	10.2507i	0.449093	+	0.449093i	−0.445960	+	0.895053i	$0.647138\pi$
$522$		0			0
$523$	7.70945	+	18.6123i	0.337111	+	0.813857i	0.997990	+	0.0633655i	$0.0201834\pi$
$523$	7.70945	+	18.6123i	0.337111	+	0.813857i	−0.660880	+	0.750492i	$0.729817\pi$
$524$	−11.0579	+	31.6808i	−0.483068	+	1.38398i
$525$		0			0
$526$	−11.8587	+	12.5531i	−0.517063	+	0.547342i
$527$		−	42.9622i		−	1.87146i
$528$		0			0
$529$			13.8481i			0.602090i
$530$	20.0307	+	18.9226i	0.870079	+	0.821946i
$531$		0			0
$532$	3.81070	−	1.83879i	0.165215	−	0.0797217i
$533$	1.31549	+	3.17586i	0.0569800	+	0.137562i
$534$		0			0
$535$	−5.33837	−	5.33837i	−0.230798	−	0.230798i
$536$	−13.6698	+	43.0624i	−0.590447	+	1.86001i
$537$		0			0
$538$	16.3790	+	6.24489i	0.706149	+	0.269236i
$539$	7.90501	−	3.27436i	0.340493	−	0.141037i
$540$		0			0
$541$	−10.8201	+	26.1221i	−0.465194	+	1.12308i	0.501043	+	0.865422i	$0.332950\pi$
$541$	−10.8201	+	26.1221i	−0.465194	+	1.12308i	−0.966237	+	0.257655i	$0.917050\pi$
$542$	−0.162023	−	5.69563i	−0.00695947	−	0.244648i
$543$		0			0
$544$	−4.63454	−	32.3727i	−0.198704	−	1.38797i
$545$	9.21921			0.394908
$546$		0			0
$547$	3.17792	−	7.67217i	0.135878	−	0.328038i	−0.841265	−	0.540624i	$-0.818188\pi$
$547$	3.17792	−	7.67217i	0.135878	−	0.328038i	0.977143	+	0.212585i	$0.0681883\pi$
$548$	−34.0545	−	30.3853i	−1.45474	−	1.29800i
$549$		0			0
$550$	−7.51793	−	2.86639i	−0.320565	−	0.122223i
$551$	−0.812156	+	0.812156i	−0.0345990	+	0.0345990i
$552$		0			0
$553$	−15.2070	−	15.2070i	−0.646668	−	0.646668i
$554$	6.75011	+	15.0693i	0.286785	+	0.640233i
$555$		0			0
$556$	−6.54202	−	13.5576i	−0.277444	−	0.574972i
$557$	21.1381	+	8.75569i	0.895650	+	0.370991i	0.782546	−	0.622593i	$-0.213921\pi$
$557$	21.1381	+	8.75569i	0.895650	+	0.370991i	0.113104	+	0.993583i	$0.463921\pi$
$558$		0			0
$559$			5.47765i			0.231680i
$560$	3.38010	−	11.8016i	0.142835	−	0.498709i
$561$		0			0
$562$	−6.12311	+	6.48168i	−0.258288	+	0.273413i
$563$	4.49306	+	1.86108i	0.189360	+	0.0784354i	0.475348	−	0.879798i	$-0.342322\pi$
$563$	4.49306	+	1.86108i	0.189360	+	0.0784354i	−0.285989	+	0.958233i	$0.592322\pi$
$564$		0			0
$565$	−2.58558	−	6.24215i	−0.108776	−	0.262609i
$566$	23.6534	−	10.5953i	0.994226	−	0.445352i
$567$		0			0
$568$	−27.2573	+	32.3557i	−1.14369	+	1.35762i
$569$	−1.97117	+	1.97117i	−0.0826359	+	0.0826359i	−0.747217	−	0.664581i	$-0.768610\pi$
$569$	−1.97117	+	1.97117i	−0.0826359	+	0.0826359i	0.664581	+	0.747217i	$0.268610\pi$
$570$		0			0
$571$	−4.41522	+	1.82884i	−0.184771	+	0.0765347i	−0.473151	−	0.880981i	$-0.656883\pi$
$571$	−4.41522	+	1.82884i	−0.184771	+	0.0765347i	0.288380	+	0.957516i	$0.406883\pi$
$572$	1.42962	+	25.1077i	0.0597756	+	1.04980i
$573$		0			0
$574$	−1.77724	+	0.0505570i	−0.0741808	+	0.00211021i
$575$	14.0751			0.586971
$576$		0			0
$577$	−5.08446			−0.211669			−0.105834	−	0.994384i	$-0.533751\pi$
$577$	−5.08446			−0.211669			−0.105834	+	0.994384i	$0.533751\pi$
$578$	23.2133	−	0.660345i	0.965546	−	0.0274667i
$579$		0			0
$580$	0.189439	+	3.32702i	0.00786605	+	0.138147i
$581$	28.5514	−	11.8264i	1.18451	−	0.490640i
$582$		0			0
$583$	20.6450	−	20.6450i	0.855029	−	0.855029i
$584$	−20.9894	−	17.6821i	−0.868549	−	0.731689i
$585$		0			0
$586$	−23.6837	+	10.6088i	−0.978363	+	0.438247i
$587$	−1.78191	−	4.30191i	−0.0735473	−	0.177559i	0.882830	−	0.469692i	$-0.155635\pi$
$587$	−1.78191	−	4.30191i	−0.0735473	−	0.177559i	−0.956378	+	0.292133i	$0.905635\pi$
$588$		0			0
$589$	7.74983	+	3.21008i	0.319326	+	0.132269i
$590$	14.9410	−	15.8159i	0.615111	−	0.651131i
$591$		0			0
$592$	−13.9300	+	7.72716i	−0.572518	+	0.317584i
$593$			29.2644i			1.20174i	0.799345	+	0.600872i	$0.205180\pi$
$593$			29.2644i			1.20174i	−0.799345	+	0.600872i	$0.794820\pi$
$594$		0			0
$595$	16.3918	+	6.78969i	0.671997	+	0.278350i
$596$	−3.57203	−	7.40264i	−0.146316	−	0.303224i
$597$		0			0
$598$	−17.9845	−	40.1496i	−0.735442	−	1.64184i
$599$	26.1363	+	26.1363i	1.06790	+	1.06790i	0.997520	+	0.0703791i	$0.0224209\pi$
$599$	26.1363	+	26.1363i	1.06790	+	1.06790i	0.0703791	+	0.997520i	$0.477579\pi$
$600$		0			0
$601$	6.06830	−	6.06830i	0.247531	−	0.247531i	−0.572426	−	0.819957i	$-0.693997\pi$
$601$	6.06830	−	6.06830i	0.247531	−	0.247531i	0.819957	+	0.572426i	$0.193997\pi$
$602$	−2.64727	−	1.00933i	−0.107895	−	0.0411374i
$603$		0			0
$604$	−8.70222	−	7.76461i	−0.354088	−	0.315937i
$605$	−3.12038	+	7.53326i	−0.126861	+	0.306271i
$606$		0			0
$607$	22.7677			0.924111			0.462055	−	0.886851i	$-0.347112\pi$
$607$	22.7677			0.924111			0.462055	+	0.886851i	$0.347112\pi$
$608$	6.18591	+	1.58284i	0.250872	+	0.0641926i
$609$		0			0
$610$	−0.255259	−	8.97319i	−0.0103351	−	0.363314i
$611$	5.35847	−	12.9365i	0.216781	−	0.523355i
$612$		0			0
$613$	24.3883	−	10.1020i	0.985034	−	0.408015i	0.168746	−	0.985660i	$-0.446028\pi$
$613$	24.3883	−	10.1020i	0.985034	−	0.408015i	0.816288	+	0.577645i	$0.196028\pi$
$614$	38.3954	+	14.6392i	1.54951	+	0.590789i
$615$		0			0
$616$	−12.3976	−	3.93553i	−0.499513	−	0.158567i
$617$	28.1146	+	28.1146i	1.13185	+	1.13185i	0.989870	+	0.141980i	$0.0453467\pi$
$617$	28.1146	+	28.1146i	1.13185	+	1.13185i	0.141980	+	0.989870i	$0.454653\pi$
$618$		0			0
$619$	9.80079	+	23.6612i	0.393927	+	0.951024i	0.989076	+	0.147408i	$0.0470931\pi$
$619$	9.80079	+	23.6612i	0.393927	+	0.951024i	−0.595149	+	0.803616i	$0.702907\pi$
$620$	21.9193	−	10.5768i	0.880301	−	0.424775i
$621$		0			0
$622$	16.8934	+	15.9589i	0.677364	+	0.639892i
$623$		−	16.1055i		−	0.645254i
$624$		0			0
$625$			8.03019i			0.321208i
$626$	17.7219	−	18.7597i	0.708310	−	0.749788i
$627$		0			0
$628$	1.33091	−	3.81304i	0.0531091	−	0.152157i
$629$	−8.81038	−	21.2701i	−0.351293	−	0.848096i
$630$		0			0
$631$	29.2246	+	29.2246i	1.16341	+	1.16341i	0.983723	+	0.179689i	$0.0575091\pi$
$631$	29.2246	+	29.2246i	1.16341	+	1.16341i	0.179689	+	0.983723i	$0.442491\pi$
$632$	−2.76559	−	32.3365i	−0.110009	−	1.28628i
$633$		0			0
$634$	−8.01622	+	21.0248i	−0.318365	+	0.835002i
$635$	−11.6255	+	4.81546i	−0.461346	+	0.191096i
$636$		0			0
$637$	6.83881	−	16.5104i	0.270964	−	0.654164i
$638$	3.52945	−	0.100402i	0.139732	−	0.00397494i
$639$		0			0
$640$	15.3756	−	10.3343i	0.607773	−	0.408501i
$641$	23.2229			0.917249			0.458624	−	0.888630i	$-0.348342\pi$
$641$	23.2229			0.917249			0.458624	+	0.888630i	$0.348342\pi$
$642$		0			0
$643$	−2.52528	+	6.09658i	−0.0995875	+	0.240425i	−0.965819	−	0.259217i	$-0.916535\pi$
$643$	−2.52528	+	6.09658i	−0.0995875	+	0.240425i	0.866232	+	0.499643i	$0.166535\pi$
$644$	22.7176	−	1.29353i	0.895199	−	0.0509724i
$645$		0			0
$646$	−3.28767	+	8.62286i	−0.129352	+	0.339262i
$647$	2.80148	−	2.80148i	0.110138	−	0.110138i	−0.649890	−	0.760028i	$-0.725185\pi$
$647$	2.80148	−	2.80148i	0.110138	−	0.110138i	0.760028	+	0.649890i	$0.225185\pi$
$648$		0			0
$649$	−16.3009	−	16.3009i	−0.639868	−	0.639868i
$650$	−15.3362	+	6.86966i	−0.601534	+	0.269450i
$651$		0			0
$652$	−7.68888	+	22.0286i	−0.301120	+	0.862705i
$653$	−13.9194	−	5.76560i	−0.544708	−	0.225625i	0.0933235	−	0.995636i	$-0.470251\pi$
$653$	−13.9194	−	5.76560i	−0.544708	−	0.225625i	−0.638031	+	0.770011i	$0.720251\pi$
$654$		0			0
$655$		−	27.4728i		−	1.07345i
$656$	−2.10035	−	1.66963i	−0.0820049	−	0.0651881i
$657$		0			0
$658$	5.26465	+	4.97341i	0.205237	+	0.193884i
$659$	3.09009	+	1.27996i	0.120373	+	0.0498600i	0.442057	−	0.896987i	$-0.354249\pi$
$659$	3.09009	+	1.27996i	0.120373	+	0.0498600i	−0.321684	+	0.946847i	$0.604249\pi$
$660$		0			0
$661$	4.40456	+	10.6336i	0.171318	+	0.413598i	0.986096	−	0.166175i	$-0.0531415\pi$
$661$	4.40456	+	10.6336i	0.171318	+	0.413598i	−0.814779	+	0.579772i	$0.803142\pi$
$662$	−5.86929	−	13.1029i	−0.228117	−	0.509259i
$663$		0			0
$664$	44.4509	+	14.1106i	1.72503	+	0.547598i
$665$	−2.44955	+	2.44955i	−0.0949894	+	0.0949894i
$666$		0			0
$667$	−5.70660	+	2.36375i	−0.220960	+	0.0915248i
$668$	−17.2417	+	19.3238i	−0.667103	+	0.747659i
$669$		0			0
$670$	−1.05184	−	36.9755i	−0.0406360	−	1.42849i
$671$	−9.51145			−0.367186
$672$		0			0
$673$	−32.6492			−1.25853			−0.629267	−	0.777190i	$-0.716645\pi$
$673$	−32.6492			−1.25853			−0.629267	+	0.777190i	$0.716645\pi$
$674$	1.06331	+	37.3790i	0.0409573	+	1.43978i
$675$		0			0
$676$	19.7916	+	17.6592i	0.761216	+	0.679199i
$677$	−5.71034	+	2.36530i	−0.219466	+	0.0909059i	−0.489708	−	0.871887i	$-0.662896\pi$
$677$	−5.71034	+	2.36530i	−0.219466	+	0.0909059i	0.270241	+	0.962793i	$0.412896\pi$
$678$		0			0
$679$	−20.4274	+	20.4274i	−0.783933	+	0.783933i
$680$	12.3170	+	23.7737i	0.472334	+	0.911678i
$681$		0			0
$682$	−10.5418	−	23.5340i	−0.403666	−	0.901165i
$683$	−5.03873	−	12.1646i	−0.192802	−	0.465465i	0.797685	−	0.603075i	$-0.206058\pi$
$683$	−5.03873	−	12.1646i	−0.192802	−	0.465465i	−0.990486	+	0.137610i	$0.956058\pi$
$684$		0			0
$685$	34.5224	+	14.2996i	1.31903	+	0.546361i
$686$	20.2066	+	19.0888i	0.771491	+	0.728812i
$687$		0			0
$688$	−2.07397	−	3.73880i	−0.0790693	−	0.142540i
$689$		−	60.9795i		−	2.32313i
$690$		0			0
$691$	−33.3930	−	13.8318i	−1.27033	−	0.526187i	−0.357265	−	0.934003i	$-0.616291\pi$
$691$	−33.3930	−	13.8318i	−1.27033	−	0.526187i	−0.913064	+	0.407816i	$0.866291\pi$
$692$	14.8596	+	5.18662i	0.564878	+	0.197166i
$693$		0			0
$694$	30.3960	−	13.6155i	1.15382	−	0.516839i
$695$	8.71497	+	8.71497i	0.330577	+	0.330577i
$696$		0			0
$697$	2.74204	−	2.74204i	0.103862	−	0.103862i
$698$	−3.49419	+	9.16450i	−0.132257	+	0.346881i
$699$		0			0
$700$	−0.494099	−	8.67757i	−0.0186752	−	0.327981i
$701$	−10.9582	+	26.4553i	−0.413884	+	0.999204i	0.570201	+	0.821505i	$0.306865\pi$
$701$	−10.9582	+	26.4553i	−0.413884	+	0.999204i	−0.984085	+	0.177699i	$0.943135\pi$
$702$		0			0
$703$	4.49516			0.169538
$704$	−10.4822	−	16.5961i	−0.395061	−	0.625488i
$705$		0			0
$706$	−12.9483	+	0.368338i	−0.487315	+	0.0138626i
$707$	8.06415	−	19.4686i	0.303284	−	0.732191i
$708$		0			0
$709$	7.29870	−	3.02322i	0.274109	−	0.113539i	−0.241395	−	0.970427i	$-0.577605\pi$
$709$	7.29870	−	3.02322i	0.274109	−	0.113539i	0.515503	+	0.856887i	$0.327605\pi$
$710$	12.3400	−	32.3652i	0.463113	−	1.21465i
$711$		0			0
$712$	15.6591	−	18.5881i	0.586849	−	0.696617i
$713$	31.8984	+	31.8984i	1.19461	+	1.19461i
$714$		0			0
$715$	−7.87938	−	19.0225i	−0.294672	−	0.711401i
$716$	−11.5038	−	4.01532i	−0.429919	−	0.150059i
$717$		0			0
$718$	−19.9158	+	21.0820i	−0.743251	+	0.786775i
$719$		−	18.4601i		−	0.688447i	−0.938888	−	0.344223i	$-0.888142\pi$
$719$		−	18.4601i		−	0.688447i	0.938888	−	0.344223i	$-0.111858\pi$
$720$		0			0
$721$		−	21.3396i		−	0.794729i
$722$	18.2228	+	17.2147i	0.678182	+	0.640665i
$723$		0			0
$724$	−2.48518	−	5.15027i	−0.0923611	−	0.191408i
$725$	0.902895	+	2.17978i	0.0335327	+	0.0809551i
$726$		0			0
$727$	−30.9545	−	30.9545i	−1.14804	−	1.14804i	−0.986938	−	0.161099i	$-0.948496\pi$
$727$	−30.9545	−	30.9545i	−1.14804	−	1.14804i	−0.161099	−	0.986938i	$-0.551504\pi$
$728$	−24.1217	+	12.4973i	−0.894009	+	0.463180i
$729$		0			0
$730$	20.9956	+	8.00509i	0.777083	+	0.296282i
$731$	5.70890	−	2.36470i	0.211151	−	0.0874618i
$732$		0			0
$733$	2.44239	−	5.89645i	0.0902118	−	0.217791i	−0.872334	−	0.488911i	$-0.837394\pi$
$733$	2.44239	−	5.89645i	0.0902118	−	0.217791i	0.962545	+	0.271121i	$0.0873942\pi$
$734$	0.226341	+	7.95662i	0.00835439	+	0.293684i
$735$		0			0
$736$	27.4770	+	20.5949i	1.01282	+	0.759140i
$737$	−39.1935			−1.44371
$738$		0			0
$739$	−17.8479	+	43.0886i	−0.656545	+	1.58504i	0.146559	+	0.989202i	$0.453180\pi$
$739$	−17.8479	+	43.0886i	−0.656545	+	1.58504i	−0.803104	+	0.595839i	$0.796820\pi$
$740$	8.68301	−	9.73153i	0.319194	−	0.357738i
$741$		0			0
$742$	29.4705	+	11.2363i	1.08190	+	0.412499i
$743$	−18.7851	+	18.7851i	−0.689157	+	0.689157i	−0.962046	−	0.272889i	$-0.912021\pi$
$743$	−18.7851	+	18.7851i	−0.689157	+	0.689157i	0.272889	+	0.962046i	$0.412021\pi$
$744$		0			0
$745$	4.75848	+	4.75848i	0.174337	+	0.174337i
$746$	−17.8869	−	39.9317i	−0.654887	−	1.46200i
$747$		0			0
$748$	25.5505	−	12.3290i	0.934217	−	0.450792i
$749$	−7.98350	−	3.30688i	−0.291711	−	0.120831i
$750$		0			0
$751$			31.0990i			1.13482i	0.823436	+	0.567409i	$0.192054\pi$
$751$			31.0990i			1.13482i	−0.823436	+	0.567409i	$0.807946\pi$
$752$	1.24061	+	10.8587i	0.0452404	+	0.395977i
$753$		0			0
$754$	5.06421	−	5.36077i	0.184428	−	0.195228i
$755$	8.82178	+	3.65410i	0.321058	+	0.132986i
$756$		0			0
$757$	0.986433	+	2.38146i	0.0358525	+	0.0865556i	0.940792	−	0.338986i	$-0.110084\pi$
$757$	0.986433	+	2.38146i	0.0358525	+	0.0865556i	−0.904939	+	0.425541i	$0.860084\pi$
$758$	34.7212	−	15.5530i	1.26113	−	0.564909i
$759$		0			0
$760$	−5.20877	+	0.445481i	−0.188942	+	0.0161593i
$761$	−28.0768	+	28.0768i	−1.01778	+	1.01778i	−0.0179435	+	0.999839i	$0.505712\pi$
$761$	−28.0768	+	28.0768i	−1.01778	+	1.01778i	−0.999839	+	0.0179435i	$0.994288\pi$
$762$		0			0
$763$	9.74908	−	4.03820i	0.352941	−	0.146193i
$764$	8.47475	−	0.482550i	0.306606	−	0.0174581i
$765$		0			0
$766$	4.39215	−	0.124943i	0.158695	−	0.00451437i
$767$	−48.1484			−1.73854
$768$		0			0
$769$	1.73480			0.0625585			0.0312793	−	0.999511i	$-0.490042\pi$
$769$	1.73480			0.0625585			0.0312793	+	0.999511i	$0.490042\pi$
$770$	10.6452	−	0.302822i	0.383626	−	0.0109129i
$771$		0			0
$772$	−16.0604	+	0.914478i	−0.578028	+	0.0329128i
$773$	31.1210	−	12.8907i	1.11934	−	0.463647i	0.255197	−	0.966889i	$-0.417860\pi$
$773$	31.1210	−	12.8907i	1.11934	−	0.463647i	0.864146	+	0.503242i	$0.167860\pi$
$774$		0			0
$775$	12.1844	−	12.1844i	0.437678	−	0.437678i
$776$	−43.4373	+	3.71498i	−1.55931	+	0.133360i
$777$		0			0
$778$	11.6031	−	5.19747i	0.415991	−	0.186338i
$779$	0.289747	+	0.699512i	0.0103813	+	0.0250626i
$780$		0			0
$781$	−33.9072	−	14.0448i	−1.21329	−	0.502563i
$782$	−34.0806	+	36.0764i	−1.21872	+	1.29009i
$783$		0			0
$784$	1.58334	+	13.8586i	0.0565479	+	0.494949i
$785$			3.30658i			0.118017i
$786$		0			0
$787$	45.0368	+	18.6548i	1.60539	+	0.664974i	0.992165	−	0.124936i	$-0.0398726\pi$
$787$	45.0368	+	18.6548i	1.60539	+	0.664974i	0.613223	+	0.789910i	$0.289873\pi$
$788$	−39.9116	+	19.2587i	−1.42179	+	0.686063i
$789$		0			0
$790$	10.8625	+	24.2500i	0.386470	+	0.862775i
$791$	−5.46838	−	5.46838i	−0.194433	−	0.194433i
$792$		0			0
$793$	−14.0471	+	14.0471i	−0.498826	+	0.498826i
$794$	−22.7461	−	8.67249i	−0.807228	−	0.307775i
$795$		0			0
$796$	4.86566	−	5.45322i	0.172459	−	0.193284i
$797$	−12.8982	+	31.1390i	−0.456877	+	1.10300i	0.512778	+	0.858521i	$0.328616\pi$
$797$	−12.8982	+	31.1390i	−0.456877	+	1.10300i	−0.969655	+	0.244478i	$0.921384\pi$
$798$		0			0
$799$	−15.7959			−0.558819
$800$	7.86677	−	10.4956i	0.278132	−	0.371074i
$801$		0			0
$802$	0.716074	+	25.1724i	0.0252855	+	0.888867i
$803$	9.11099	−	21.9959i	0.321520	−	0.776218i
$804$		0			0
$805$	−17.2117	+	7.12932i	−0.606633	+	0.251276i
$806$	−50.3252	−	19.1877i	−1.77263	−	0.675857i
$807$		0			0
$808$	28.2361	−	14.6289i	0.993342	−	0.514643i
$809$	−1.33912	−	1.33912i	−0.0470811	−	0.0470811i	0.683174	−	0.730255i	$-0.260599\pi$
$809$	−1.33912	−	1.33912i	−0.0470811	−	0.0470811i	−0.730255	+	0.683174i	$0.760599\pi$
$810$		0			0
$811$	−19.8815	−	47.9981i	−0.698132	−	1.68544i	−0.727716	−	0.685878i	$-0.759418\pi$
$811$	−19.8815	−	47.9981i	−0.698132	−	1.68544i	0.0295838	−	0.999562i	$-0.490582\pi$
$812$	1.65763	+	3.43526i	0.0581713	+	0.120554i
$813$		0			0
$814$	−10.0453	−	9.48963i	−0.352089	−	0.332611i
$815$		−	19.1026i		−	0.669136i
$816$		0			0
$817$			1.20650i			0.0422101i
$818$	21.1765	−	22.4166i	0.740420	−	0.783779i
$819$		0			0
$820$	2.07405	+	0.723930i	0.0724290	+	0.0252807i
$821$	0.106271	+	0.256562i	0.00370889	+	0.00895406i	0.925723	−	0.378202i	$-0.123457\pi$
$821$	0.106271	+	0.256562i	0.00370889	+	0.00895406i	−0.922014	+	0.387156i	$0.873457\pi$
$822$		0			0
$823$	1.33537	+	1.33537i	0.0465479	+	0.0465479i	0.729998	−	0.683450i	$-0.239521\pi$
$823$	1.33537	+	1.33537i	0.0465479	+	0.0465479i	−0.683450	+	0.729998i	$0.739521\pi$
$824$	20.7481	−	24.6290i	0.722794	−	0.857991i
$825$		0			0
$826$	8.87202	−	23.2694i	0.308697	−	0.809646i
$827$	−23.3468	+	9.67056i	−0.811848	+	0.336278i	−0.749691	−	0.661788i	$-0.769798\pi$
$827$	−23.3468	+	9.67056i	−0.811848	+	0.336278i	−0.0621568	+	0.998066i	$0.519798\pi$
$828$		0			0
$829$	−10.2848	+	24.8297i	−0.357205	+	0.862370i	0.638486	+	0.769634i	$0.279561\pi$
$829$	−10.2848	+	24.8297i	−0.357205	+	0.862370i	−0.995691	+	0.0927359i	$0.970439\pi$
$830$	−38.1677	+	1.08575i	−1.32482	+	0.0376870i
$831$		0			0
$832$	−39.9907	−	9.02941i	−1.38643	−	0.313039i
$833$	−20.1597			−0.698492
$834$		0			0
$835$	8.11414	−	19.5893i	0.280801	−	0.677914i
$836$	0.314887	+	5.53018i	0.0108906	+	0.191265i
$837$		0			0
$838$	7.56084	−	19.8305i	0.261185	−	0.685032i
$839$	7.12216	−	7.12216i	0.245884	−	0.245884i	−0.573395	−	0.819279i	$-0.694374\pi$
$839$	7.12216	−	7.12216i	0.245884	−	0.245884i	0.819279	+	0.573395i	$0.194374\pi$
$840$		0			0
$841$	19.7740	+	19.7740i	0.681861	+	0.681861i
$842$	−5.41510	+	2.42563i	−0.186617	+	0.0835928i
$843$		0			0
$844$	−2.13677	−	0.745821i	−0.0735506	−	0.0256722i
$845$	−20.0635	−	8.31059i	−0.690207	−	0.285893i
$846$		0			0
$847$			9.33302i			0.320687i
$848$	23.0883	+	41.6219i	0.792855	+	1.42930i
$849$		0			0
$850$	13.7803	+	13.0180i	0.472661	+	0.446513i
$851$	22.3341	+	9.25108i	0.765603	+	0.317123i
$852$		0			0
$853$	−10.6705	−	25.7608i	−0.365349	−	0.882032i	−0.994499	−	0.104747i	$-0.966597\pi$
$853$	−10.6705	−	25.7608i	−0.365349	−	0.882032i	0.629149	−	0.777284i	$-0.283403\pi$
$854$	−4.20037	−	9.37711i	−0.143734	−	0.320878i
$855$		0			0
$856$	−5.99889	−	11.5788i	−0.205038	−	0.395755i
$857$	20.0048	−	20.0048i	0.683349	−	0.683349i	−0.277404	−	0.960753i	$-0.589474\pi$
$857$	20.0048	−	20.0048i	0.683349	−	0.683349i	0.960753	+	0.277404i	$0.0894741\pi$
$858$		0			0
$859$	−1.53664	+	0.636496i	−0.0524294	+	0.0217170i	−0.408744	−	0.912649i	$-0.634033\pi$
$859$	−1.53664	+	0.636496i	−0.0524294	+	0.0217170i	0.356315	+	0.934366i	$0.384033\pi$
$860$	2.61194	+	2.33052i	0.0890665	+	0.0794701i
$861$		0			0
$862$	0.654948	+	23.0236i	0.0223076	+	0.784186i
$863$	3.22858			0.109902			0.0549510	−	0.998489i	$-0.482500\pi$
$863$	3.22858			0.109902			0.0549510	+	0.998489i	$0.482500\pi$
$864$		0			0
$865$	−12.8859			−0.438133
$866$	1.13750	+	39.9868i	0.0386538	+	1.35881i
$867$		0			0
$868$	18.5463	−	20.7858i	0.629501	−	0.705516i
$869$	26.0111	−	10.7742i	0.882366	−	0.365488i
$870$		0			0
$871$	−57.8832	+	57.8832i	−1.96130	+	1.96130i
$872$	15.1781	+	4.81818i	0.513995	+	0.163164i
$873$		0			0
$874$	−3.96125	−	8.84330i	−0.133991	−	0.299129i
$875$	8.59556	+	20.7515i	0.290583	+	0.701530i
$876$		0			0
$877$	−23.7751	−	9.84797i	−0.802828	−	0.332542i	−0.0567395	−	0.998389i	$-0.518070\pi$
$877$	−23.7751	−	9.84797i	−0.802828	−	0.332542i	−0.746089	+	0.665847i	$0.768070\pi$
$878$	−20.1269	−	19.0135i	−0.679251	−	0.641675i
$879$		0			0
$880$	12.5805	+	10.0006i	0.424088	+	0.337120i
$881$		−	2.67200i		−	0.0900220i	−0.998986	−	0.0450110i	$-0.985668\pi$
$881$		−	2.67200i		−	0.0900220i	0.998986	−	0.0450110i	$-0.0143323\pi$
$882$		0			0
$883$	−39.5907	−	16.3990i	−1.33233	−	0.551870i	−0.401013	−	0.916072i	$-0.631342\pi$
$883$	−39.5907	−	16.3990i	−1.33233	−	0.551870i	−0.931320	+	0.364202i	$0.881342\pi$
$884$	19.5263	−	55.9425i	0.656740	−	1.88155i
$885$		0			0
$886$	−8.32311	+	3.72824i	−0.279620	+	0.125253i
$887$	33.5579	+	33.5579i	1.12676	+	1.12676i	0.990700	+	0.136063i	$0.0434450\pi$
$887$	33.5579	+	33.5579i	1.12676	+	1.12676i	0.136063	+	0.990700i	$0.456555\pi$
$888$		0			0
$889$	−10.1845	+	10.1845i	−0.341576	+	0.341576i
$890$	−7.08924	+	18.5935i	−0.237632	+	0.623257i
$891$		0			0
$892$	−14.7830	+	0.841738i	−0.494970	+	0.0281835i
$893$	1.18025	−	2.84938i	0.0394956	−	0.0953508i
$894$		0			0
$895$	9.97584			0.333456
$896$	11.7326	−	17.6631i	0.391960	−	0.590084i
$897$		0			0
$898$	39.2755	−	1.11726i	1.31064	−	0.0372836i
$899$	−2.89382	+	6.98629i	−0.0965142	+	0.233006i
$900$		0			0
$901$	−63.5538	+	26.3249i	−2.11729	+	0.877008i
$902$	0.829224	−	2.17488i	0.0276102	−	0.0724155i
$903$		0			0
$904$	−0.994493	−	11.6281i	−0.0330763	−	0.386744i
$905$	3.31064	+	3.31064i	0.110049	+	0.110049i
$906$		0			0
$907$	−6.58909	−	15.9075i	−0.218787	−	0.528199i	0.775934	−	0.630814i	$-0.217279\pi$
$907$	−6.58909	−	15.9075i	−0.218787	−	0.528199i	−0.994721	+	0.102615i	$0.967279\pi$
$908$	−8.84351	+	25.3366i	−0.293482	+	0.840823i
$909$		0			0
$910$	15.2742	−	16.1686i	0.506335	−	0.535986i
$911$			16.6033i			0.550091i	0.961431	+	0.275045i	$0.0886929\pi$
$911$			16.6033i			0.550091i	−0.961431	+	0.275045i	$0.911307\pi$
$912$		0			0
$913$			40.4573i			1.33894i
$914$	−9.62155	−	9.08929i	−0.318253	−	0.300647i
$915$		0			0
$916$	−20.7677	+	10.0211i	−0.686186	+	0.331108i
$917$	−12.0337	−	29.0518i	−0.397386	−	0.959376i
$918$		0			0
$919$	−29.2819	−	29.2819i	−0.965922	−	0.965922i	0.0335164	−	0.999438i	$-0.489329\pi$
$919$	−29.2819	−	29.2819i	−0.965922	−	0.965922i	−0.999438	+	0.0335164i	$0.989329\pi$
$920$	−26.7965	−	8.50634i	−0.883453	−	0.280446i
$921$		0			0
$922$	−36.0116	−	13.7303i	−1.18598	−	0.452183i
$923$	−70.8183	+	29.3339i	−2.33101	+	0.965537i
$924$		0			0
$925$	3.53369	−	8.53108i	0.116187	−	0.280500i
$926$	1.34109	+	47.1439i	0.0440711	+	1.54924i
$927$		0			0
$928$	−1.42689	+	5.57645i	−0.0468400	+	0.183056i
$929$	−48.4425			−1.58935			−0.794674	−	0.607036i	$-0.792358\pi$
$929$	−48.4425			−1.58935			−0.794674	+	0.607036i	$0.792358\pi$
$930$		0			0
$931$	1.50631	−	3.63655i	0.0493673	−	0.119183i
$932$	−22.3770	−	19.9660i	−0.732984	−	0.654009i
$933$		0			0
$934$	−10.1479	−	3.86915i	−0.332051	−	0.126602i
$935$	−16.4240	+	16.4240i	−0.537124	+	0.537124i
$936$		0			0
$937$	6.17378	+	6.17378i	0.201689	+	0.201689i	0.800723	−	0.599035i	$-0.204449\pi$
$937$	6.17378	+	6.17378i	0.201689	+	0.201689i	−0.599035	+	0.800723i	$0.704449\pi$
$938$	−17.3083	−	38.6399i	−0.565136	−	1.26164i
$939$		0			0
$940$	−3.88878	−	8.05907i	−0.126838	−	0.262858i
$941$	−28.8812	−	11.9630i	−0.941500	−	0.389982i	−0.141470	−	0.989942i	$-0.545183\pi$
$941$	−28.8812	−	11.9630i	−0.941500	−	0.389982i	−0.800030	+	0.599960i	$0.795183\pi$
$942$		0			0
$943$			4.07181i			0.132596i
$944$	32.8639	−	18.2301i	1.06963	−	0.593340i
$945$		0			0
$946$	2.54702	−	2.69617i	0.0828106	−	0.0876599i
$947$	31.3266	+	12.9759i	1.01798	+	0.421660i	0.828359	−	0.560198i	$-0.189275\pi$
$947$	31.3266	+	12.9759i	1.01798	+	0.421660i	0.189618	+	0.981858i	$0.439275\pi$
$948$		0			0
$949$	−19.0292	−	45.9405i	−0.617713	−	1.49129i
$950$	−3.37793	+	1.51310i	−0.109594	+	0.0490916i
$951$		0			0
$952$	23.4382	+	19.7450i	0.759637	+	0.639938i
$953$	28.8836	−	28.8836i	0.935631	−	0.935631i	−0.0624188	−	0.998050i	$-0.519881\pi$
$953$	28.8836	−	28.8836i	0.935631	−	0.935631i	0.998050	+	0.0624188i	$0.0198814\pi$
$954$		0			0
$955$	−6.42079	+	2.65958i	−0.207772	+	0.0860619i
$956$	3.15188	+	55.3546i	0.101939	+	1.79030i
$957$		0			0
$958$	−2.35437	+	0.0669745i	−0.0760663	+	0.00216385i
$959$	42.7701			1.38112
$960$		0			0
$961$	24.2273			0.781525
$962$	−28.8504	+	0.820702i	−0.930173	+	0.0264605i
$963$		0			0
$964$	2.17579	+	38.2122i	0.0700776	+	1.23073i
$965$	12.1680	−	5.04015i	0.391702	−	0.162248i
$966$		0			0
$967$	17.5627	−	17.5627i	0.564777	−	0.564777i	−0.365884	−	0.930661i	$-0.619233\pi$
$967$	17.5627	−	17.5627i	0.564777	−	0.564777i	0.930661	+	0.365884i	$0.119233\pi$
$968$	−9.07431	+	10.7716i	−0.291659	+	0.346214i
$969$		0			0
$970$	32.5747	−	14.5915i	1.04591	−	0.468504i
$971$	−0.119416	−	0.288295i	−0.00383224	−	0.00925184i	0.921952	−	0.387305i	$-0.126594\pi$
$971$	−0.119416	−	0.288295i	−0.00383224	−	0.00925184i	−0.925784	+	0.378053i	$0.876594\pi$
$972$		0			0
$973$	13.0332	+	5.39852i	0.417825	+	0.173069i
$974$	−21.1909	+	22.4319i	−0.679001	+	0.718763i
$975$		0			0
$976$	4.26935	−	14.9065i	0.136659	−	0.477144i
$977$		−	46.5011i		−	1.48770i	−0.668345	−	0.743851i	$-0.732997\pi$
$977$		−	46.5011i		−	1.48770i	0.668345	−	0.743851i	$-0.267003\pi$
$978$		0			0
$979$	19.4794	+	8.06862i	0.622563	+	0.257874i
$980$	−4.96309	−	10.2855i	−0.158540	−	0.328558i
$981$		0			0
$982$	11.5625	+	25.8127i	0.368975	+	0.823718i
$983$	−12.1301	−	12.1301i	−0.386891	−	0.386891i	0.486686	−	0.873577i	$-0.338205\pi$
$983$	−12.1301	−	12.1301i	−0.386891	−	0.386891i	−0.873577	+	0.486686i	$0.838205\pi$
$984$		0			0
$985$	25.6555	−	25.6555i	0.817452	−	0.817452i
$986$	−7.77331	−	2.96376i	−0.247553	−	0.0943854i
$987$		0			0
$988$	8.63234	+	7.70225i	0.274631	+	0.245041i
$989$	−2.48299	+	5.99447i	−0.0789545	+	0.190613i
$990$		0			0
$991$	−0.0269571			−0.000856319			−0.000428160	−	1.00000i	$-0.500136\pi$
$991$	−0.0269571			−0.000856319			−0.000428160		1.00000i	$0.500136\pi$
$992$	41.6146	−	5.95764i	1.32127	−	0.189155i
$993$		0			0
$994$	−1.12737	−	39.6306i	−0.0357579	−	1.25701i
$995$	−2.28983	+	5.52814i	−0.0725925	+	0.175254i
$996$		0			0
$997$	8.81063	−	3.64948i	0.279036	−	0.115580i	−0.238777	−	0.971074i	$-0.576746\pi$
$997$	8.81063	−	3.64948i	0.279036	−	0.115580i	0.517813	+	0.855494i	$0.326746\pi$
$998$	39.0100	+	14.8735i	1.23484	+	0.470812i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.c.109.1	yes	32
3.2	odd	2	inner	288.2.v.c.109.8	yes	32
4.3	odd	2		1152.2.v.d.145.3		32
12.11	even	2		1152.2.v.d.145.6		32
32.5	even	8	inner	288.2.v.c.37.1	✓	32
32.27	odd	8		1152.2.v.d.1009.3		32
96.5	odd	8	inner	288.2.v.c.37.8	yes	32
96.59	even	8		1152.2.v.d.1009.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.v.c.37.1	✓	32	32.5	even	8	inner
288.2.v.c.37.8	yes	32	96.5	odd	8	inner
288.2.v.c.109.1	yes	32	1.1	even	1	trivial
288.2.v.c.109.8	yes	32	3.2	odd	2	inner
1152.2.v.d.145.3		32	4.3	odd	2
1152.2.v.d.145.6		32	12.11	even	2
1152.2.v.d.1009.3		32	32.27	odd	8
1152.2.v.d.1009.6		32	96.59	even	8

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41364 + 0.0402136i) q^{2} +(1.99677 - 0.113695i) q^{4} +(-1.51282 + 0.626632i) q^{5} +(-1.32530 + 1.32530i) q^{7} +(-2.81814 + 0.241022i) q^{8} +O(q^{10})\)	\(q+(-1.41364 + 0.0402136i) q^{2} +(1.99677 - 0.113695i) q^{4} +(-1.51282 + 0.626632i) q^{5} +(-1.32530 + 1.32530i) q^{7} +(-2.81814 + 0.241022i) q^{8} +(2.11339 - 0.946670i) q^{10} +(-0.938971 - 2.26688i) q^{11} +(-4.73458 - 1.96113i) q^{13} +(1.82020 - 1.92679i) q^{14} +(3.97415 - 0.454046i) q^{16} +5.78108i q^{17} +(-1.04283 - 0.431956i) q^{19} +(-2.94951 + 1.42324i) q^{20} +(1.41853 + 3.16679i) q^{22} +(-4.29232 - 4.29232i) q^{23} +(-1.63956 + 1.63956i) q^{25} +(6.77187 + 2.58194i) q^{26} +(-2.49563 + 2.79699i) q^{28} +(0.389398 - 0.940091i) q^{29} -7.43150 q^{31} +(-5.59976 + 0.801673i) q^{32} +(-0.232478 - 8.17238i) q^{34} +(1.17447 - 2.83541i) q^{35} +(-3.67926 + 1.52400i) q^{37} +(1.49156 + 0.568695i) q^{38} +(4.11232 - 2.13056i) q^{40} +(-0.474313 - 0.474313i) q^{41} +(-0.409042 - 0.987514i) q^{43} +(-2.13264 - 4.41967i) q^{44} +(6.24042 + 5.89520i) q^{46} +2.73234i q^{47} +3.48718i q^{49} +(2.25182 - 2.38369i) q^{50} +(-9.67683 - 3.37761i) q^{52} +(4.55362 + 10.9934i) q^{53} +(2.84100 + 2.84100i) q^{55} +(3.41544 - 4.05429i) q^{56} +(-0.512665 + 1.34461i) q^{58} +(8.68022 - 3.59546i) q^{59} +(1.48345 - 3.58137i) q^{61} +(10.5055 - 0.298848i) q^{62} +(7.88382 - 1.35847i) q^{64} +8.39150 q^{65} +(6.11281 - 14.7576i) q^{67} +(0.657282 + 11.5435i) q^{68} +(-1.54625 + 4.05549i) q^{70} +(10.5767 - 10.5767i) q^{71} +(6.86117 + 6.86117i) q^{73} +(5.13987 - 2.30235i) q^{74} +(-2.13141 - 0.743950i) q^{76} +(4.24870 + 1.75987i) q^{77} +11.4744i q^{79} +(-5.72767 + 3.17722i) q^{80} +(0.689582 + 0.651435i) q^{82} +(-15.2335 - 6.30991i) q^{83} +(-3.62261 - 8.74577i) q^{85} +(0.617950 + 1.37954i) q^{86} +(3.19252 + 6.16206i) q^{88} +(-6.07620 + 6.07620i) q^{89} +(8.87380 - 3.67565i) q^{91} +(-9.05878 - 8.08275i) q^{92} +(-0.109877 - 3.86255i) q^{94} +1.84830 q^{95} +15.4135 q^{97} +(-0.140232 - 4.92962i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} - 8 q^{16} - 24 q^{22} - 40 q^{28} + 48 q^{31} - 40 q^{34} - 72 q^{40} + 16 q^{43} - 32 q^{46} - 8 q^{52} + 32 q^{55} - 32 q^{58} - 32 q^{61} + 72 q^{64} + 16 q^{67} + 120 q^{70} + 72 q^{76} + 120 q^{82} + 128 q^{88} - 48 q^{91} + 80 q^{94}+O(q^{100}) \) 32 * q - 8 * q^10 - 8 * q^16 - 24 * q^22 - 40 * q^28 + 48 * q^31 - 40 * q^34 - 72 * q^40 + 16 * q^43 - 32 * q^46 - 8 * q^52 + 32 * q^55 - 32 * q^58 - 32 * q^61 + 72 * q^64 + 16 * q^67 + 120 * q^70 + 72 * q^76 + 120 * q^82 + 128 * q^88 - 48 * q^91 + 80 * q^94

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