LMFDB - Embedded newform 1035.2.j.b.737.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1035,2,Mod(323,1035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1035, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("1035.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1035 = 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1035.j (of order $4$, 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:	$8.26451660920$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.16
Character	$\chi$	$=$	1035.737
Dual form			1035.2.j.b.323.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.842836 - 0.842836i) q^{2} +0.579255i q^{4} +(0.954547 + 2.02209i) q^{5} +(2.82060 + 2.82060i) q^{7} +(2.17389 + 2.17389i) q^{8} +O(q^{10})$	\(q+(0.842836 - 0.842836i) q^{2} +0.579255i q^{4} +(0.954547 + 2.02209i) q^{5} +(2.82060 + 2.82060i) q^{7} +(2.17389 + 2.17389i) q^{8} +(2.50881 + 0.899762i) q^{10} -4.87027i q^{11} +(-2.18595 + 2.18595i) q^{13} +4.75461 q^{14} +2.50595 q^{16} +(-3.29363 + 3.29363i) q^{17} -2.98645i q^{19} +(-1.17130 + 0.552926i) q^{20} +(-4.10484 - 4.10484i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-3.17768 + 3.86035i) q^{25} +3.68480i q^{26} +(-1.63385 + 1.63385i) q^{28} +2.36928 q^{29} -2.50419 q^{31} +(-2.23567 + 2.23567i) q^{32} +5.55198i q^{34} +(-3.01111 + 8.39591i) q^{35} +(5.89284 + 5.89284i) q^{37} +(-2.51708 - 2.51708i) q^{38} +(-2.32072 + 6.47087i) q^{40} -8.87357i q^{41} +(-1.71270 + 1.71270i) q^{43} +2.82113 q^{44} -1.19195 q^{46} +(8.69581 - 8.69581i) q^{47} +8.91161i q^{49} +(0.575382 + 5.93191i) q^{50} +(-1.26622 - 1.26622i) q^{52} +(-2.30930 - 2.30930i) q^{53} +(9.84812 - 4.64890i) q^{55} +12.2634i q^{56} +(1.99691 - 1.99691i) q^{58} +10.7967 q^{59} -7.72182 q^{61} +(-2.11062 + 2.11062i) q^{62} +8.78051i q^{64} +(-6.50678 - 2.33359i) q^{65} +(-3.80062 - 3.80062i) q^{67} +(-1.90785 - 1.90785i) q^{68} +(4.53850 + 9.61425i) q^{70} -0.183405i q^{71} +(-1.77708 + 1.77708i) q^{73} +9.93339 q^{74} +1.72991 q^{76} +(13.7371 - 13.7371i) q^{77} -8.24935i q^{79} +(2.39205 + 5.06726i) q^{80} +(-7.47896 - 7.47896i) q^{82} +(4.32580 + 4.32580i) q^{83} +(-9.80393 - 3.51609i) q^{85} +2.88704i q^{86} +(10.5874 - 10.5874i) q^{88} +15.2385 q^{89} -12.3314 q^{91} +(0.409595 - 0.409595i) q^{92} -14.6583i q^{94} +(6.03886 - 2.85070i) q^{95} +(12.9432 + 12.9432i) q^{97} +(7.51103 + 7.51103i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{7}+O(q^{10}) $ 44 * q + 12 * q^7	$ 44 q + 12 q^{7} - 20 q^{10} + 4 q^{13} - 44 q^{16} + 16 q^{22} - 8 q^{25} + 40 q^{28} - 32 q^{31} + 56 q^{37} - 16 q^{40} + 72 q^{43} - 4 q^{46} + 76 q^{52} + 56 q^{55} - 12 q^{58} - 96 q^{61} + 12 q^{67} - 48 q^{70} + 68 q^{73} - 112 q^{76} + 52 q^{82} + 32 q^{85} + 56 q^{88} - 176 q^{91} + 76 q^{97}+O(q^{100}) $ 44 * q + 12 * q^7 - 20 * q^10 + 4 * q^13 - 44 * q^16 + 16 * q^22 - 8 * q^25 + 40 * q^28 - 32 * q^31 + 56 * q^37 - 16 * q^40 + 72 * q^43 - 4 * q^46 + 76 * q^52 + 56 * q^55 - 12 * q^58 - 96 * q^61 + 12 * q^67 - 48 * q^70 + 68 * q^73 - 112 * q^76 + 52 * q^82 + 32 * q^85 + 56 * q^88 - 176 * q^91 + 76 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1035\mathbb{Z}\right)^\times$.

$n$	$461$	$622$	$856$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	0.842836	−	0.842836i	0.595975	−	0.595975i	−0.343264	−	0.939239i	$-0.611533\pi$
$2$	0.842836	−	0.842836i	0.595975	−	0.595975i	0.939239	+	0.343264i	$0.111533\pi$
$3$		0			0
$3$		0			0
$4$			0.579255i			0.289628i
$5$	0.954547	+	2.02209i	0.426886	+	0.904305i
$5$	0.954547	+	2.02209i	0.426886	+	0.904305i
$6$		0			0
$7$	2.82060	+	2.82060i	1.06609	+	1.06609i	0.997656	+	0.0684322i	$0.0217997\pi$
$7$	2.82060	+	2.82060i	1.06609	+	1.06609i	0.0684322	+	0.997656i	$0.478200\pi$
$8$	2.17389	+	2.17389i	0.768586	+	0.768586i
$9$		0			0
$10$	2.50881	+	0.899762i	0.793357	+	0.284530i
$11$		−	4.87027i		−	1.46844i	−0.678910	−	0.734221i	$-0.737547\pi$
$11$		−	4.87027i		−	1.46844i	0.678910	−	0.734221i	$-0.262453\pi$
$12$		0			0
$13$	−2.18595	+	2.18595i	−0.606274	+	0.606274i	−0.941970	−	0.335696i	$-0.891028\pi$
$13$	−2.18595	+	2.18595i	−0.606274	+	0.606274i	0.335696	+	0.941970i	$0.391028\pi$
$14$	4.75461			1.27072
$15$		0			0
$16$	2.50595			0.626488
$17$	−3.29363	+	3.29363i	−0.798822	+	0.798822i	−0.982910	−	0.184088i	$-0.941067\pi$
$17$	−3.29363	+	3.29363i	−0.798822	+	0.798822i	0.184088	+	0.982910i	$0.441067\pi$
$18$		0			0
$19$		−	2.98645i		−	0.685138i	−0.939493	−	0.342569i	$-0.888703\pi$
$19$		−	2.98645i		−	0.685138i	0.939493	−	0.342569i	$-0.111297\pi$
$20$	−1.17130	+	0.552926i	−0.261912	+	0.123638i
$21$		0			0
$22$	−4.10484	−	4.10484i	−0.875155	−	0.875155i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$24$		0			0
$25$	−3.17768	+	3.86035i	−0.635536	+	0.772071i
$26$			3.68480i			0.722648i
$27$		0			0
$28$	−1.63385	+	1.63385i	−0.308768	+	0.308768i
$29$	2.36928			0.439964			0.219982	−	0.975504i	$-0.429400\pi$
$29$	2.36928			0.439964			0.219982	+	0.975504i	$0.429400\pi$
$30$		0			0
$31$	−2.50419			−0.449765			−0.224883	−	0.974386i	$-0.572200\pi$
$31$	−2.50419			−0.449765			−0.224883	+	0.974386i	$0.572200\pi$
$32$	−2.23567	+	2.23567i	−0.395214	+	0.395214i
$33$		0			0
$34$			5.55198i			0.952156i
$35$	−3.01111	+	8.39591i	−0.508971	+	1.41917i
$36$		0			0
$37$	5.89284	+	5.89284i	0.968777	+	0.968777i	0.999527	−	0.0307502i	$-0.00978964\pi$
$37$	5.89284	+	5.89284i	0.968777	+	0.968777i	−0.0307502	+	0.999527i	$0.509790\pi$
$38$	−2.51708	−	2.51708i	−0.408325	−	0.408325i
$39$		0			0
$40$	−2.32072	+	6.47087i	−0.366938	+	1.02313i
$41$		−	8.87357i		−	1.38582i	−0.721025	−	0.692909i	$-0.756329\pi$
$41$		−	8.87357i		−	1.38582i	0.721025	−	0.692909i	$-0.243671\pi$
$42$		0			0
$43$	−1.71270	+	1.71270i	−0.261184	+	0.261184i	−0.825535	−	0.564351i	$-0.809126\pi$
$43$	−1.71270	+	1.71270i	−0.261184	+	0.261184i	0.564351	+	0.825535i	$0.309126\pi$
$44$	2.82113			0.425302
$45$		0			0
$46$	−1.19195			−0.175743
$47$	8.69581	−	8.69581i	1.26841	−	1.26841i	0.321506	−	0.946907i	$-0.395811\pi$
$47$	8.69581	−	8.69581i	1.26841	−	1.26841i	0.946907	−	0.321506i	$-0.104189\pi$
$48$		0			0
$49$			8.91161i			1.27309i
$50$	0.575382	+	5.93191i	0.0813712	+	0.838899i
$51$		0			0
$52$	−1.26622	−	1.26622i	−0.175594	−	0.175594i
$53$	−2.30930	−	2.30930i	−0.317207	−	0.317207i	0.530487	−	0.847693i	$-0.322009\pi$
$53$	−2.30930	−	2.30930i	−0.317207	−	0.317207i	−0.847693	+	0.530487i	$0.822009\pi$
$54$		0			0
$55$	9.84812	−	4.64890i	1.32792	−	0.626858i
$56$			12.2634i			1.63876i
$57$		0			0
$58$	1.99691	−	1.99691i	0.262207	−	0.262207i
$59$	10.7967			1.40560			0.702802	−	0.711385i	$-0.251932\pi$
$59$	10.7967			1.40560			0.702802	+	0.711385i	$0.251932\pi$
$60$		0			0
$61$	−7.72182			−0.988678			−0.494339	−	0.869269i	$-0.664590\pi$
$61$	−7.72182			−0.988678			−0.494339	+	0.869269i	$0.664590\pi$
$62$	−2.11062	+	2.11062i	−0.268049	+	0.268049i
$63$		0			0
$64$			8.78051i			1.09756i
$65$	−6.50678	−	2.33359i	−0.807067	−	0.289447i
$66$		0			0
$67$	−3.80062	−	3.80062i	−0.464320	−	0.464320i	0.435748	−	0.900068i	$-0.356484\pi$
$67$	−3.80062	−	3.80062i	−0.464320	−	0.464320i	−0.900068	+	0.435748i	$0.856484\pi$
$68$	−1.90785	−	1.90785i	−0.231361	−	0.231361i
$69$		0			0
$70$	4.53850	+	9.61425i	0.542454	+	1.14912i
$71$		−	0.183405i		−	0.0217662i	−0.999941	−	0.0108831i	$-0.996536\pi$
$71$		−	0.183405i		−	0.0217662i	0.999941	−	0.0108831i	$-0.00346426\pi$
$72$		0			0
$73$	−1.77708	+	1.77708i	−0.207992	+	0.207992i	−0.803414	−	0.595421i	$-0.796985\pi$
$73$	−1.77708	+	1.77708i	−0.207992	+	0.207992i	0.595421	+	0.803414i	$0.296985\pi$
$74$	9.93339			1.15473
$75$		0			0
$76$	1.72991			0.198435
$77$	13.7371	−	13.7371i	1.56549	−	1.56549i
$78$		0			0
$79$		−	8.24935i		−	0.928124i	−0.885803	−	0.464062i	$-0.846391\pi$
$79$		−	8.24935i		−	0.928124i	0.885803	−	0.464062i	$-0.153609\pi$
$80$	2.39205	+	5.06726i	0.267439	+	0.566537i
$81$		0			0
$82$	−7.47896	−	7.47896i	−0.825913	−	0.825913i
$83$	4.32580	+	4.32580i	0.474818	+	0.474818i	0.903470	−	0.428652i	$-0.141011\pi$
$83$	4.32580	+	4.32580i	0.474818	+	0.474818i	−0.428652	+	0.903470i	$0.641011\pi$
$84$		0			0
$85$	−9.80393	−	3.51609i	−1.06339	−	0.381373i
$86$			2.88704i			0.311318i
$87$		0			0
$88$	10.5874	−	10.5874i	1.12862	−	1.12862i
$89$	15.2385			1.61527			0.807636	−	0.589681i	$-0.200746\pi$
$89$	15.2385			1.61527			0.807636	+	0.589681i	$0.200746\pi$
$90$		0			0
$91$	−12.3314			−1.29268
$92$	0.409595	−	0.409595i	0.0427033	−	0.0427033i
$93$		0			0
$94$		−	14.6583i		−	1.51189i
$95$	6.03886	−	2.85070i	0.619574	−	0.292476i
$96$		0			0
$97$	12.9432	+	12.9432i	1.31419	+	1.31419i	0.918300	+	0.395886i	$0.129562\pi$
$97$	12.9432	+	12.9432i	1.31419	+	1.31419i	0.395886	+	0.918300i	$0.370438\pi$
$98$	7.51103	+	7.51103i	0.758728	+	0.758728i
$99$		0			0
$100$	−2.23613	−	1.84069i	−0.223613	−	0.184069i
$101$			3.24825i			0.323213i	0.986855	+	0.161606i	$0.0516675\pi$
$101$			3.24825i			0.323213i	−0.986855	+	0.161606i	$0.948333\pi$
$102$		0			0
$103$	12.5769	−	12.5769i	1.23924	−	1.23924i	0.278922	−	0.960314i	$-0.410023\pi$
$103$	12.5769	−	12.5769i	1.23924	−	1.23924i	0.960314	−	0.278922i	$-0.0899771\pi$
$104$	−9.50403			−0.931947
$105$		0			0
$106$	−3.89272			−0.378094
$107$	−0.552928	+	0.552928i	−0.0534536	+	0.0534536i	−0.733328	−	0.679875i	$-0.762034\pi$
$107$	−0.552928	+	0.552928i	−0.0534536	+	0.0534536i	0.679875	+	0.733328i	$0.262034\pi$
$108$		0			0
$109$			4.80634i			0.460364i	0.973148	+	0.230182i	$0.0739322\pi$
$109$			4.80634i			0.460364i	−0.973148	+	0.230182i	$0.926068\pi$
$110$	4.38209	−	12.2186i	0.417816	−	1.16500i
$111$		0			0
$112$	7.06830	+	7.06830i	0.667892	+	0.667892i
$113$	−10.7870	−	10.7870i	−1.01476	−	1.01476i	−0.999889	−	0.0148671i	$-0.995267\pi$
$113$	−10.7870	−	10.7870i	−1.01476	−	1.01476i	−0.0148671	−	0.999889i	$-0.504733\pi$
$114$		0			0
$115$	0.754866	−	2.10480i	0.0703916	−	0.196273i
$116$			1.37242i			0.127426i
$117$		0			0
$118$	9.09981	−	9.09981i	0.837705	−	0.837705i
$119$	−18.5800			−1.70323
$120$		0			0
$121$	−12.7196			−1.15632
$122$	−6.50823	+	6.50823i	−0.589227	+	0.589227i
$123$		0			0
$124$		−	1.45056i		−	0.130264i
$125$	−10.8392	−	2.74066i	−0.969490	−	0.245132i
$126$		0			0
$127$	0.754402	+	0.754402i	0.0669424	+	0.0669424i	0.739785	−	0.672843i	$-0.234927\pi$
$127$	0.754402	+	0.754402i	0.0669424	+	0.0669424i	−0.672843	+	0.739785i	$0.734927\pi$
$128$	2.92919	+	2.92919i	0.258906	+	0.258906i
$129$		0			0
$130$	−7.45099	+	3.51731i	−0.653495	+	0.308489i
$131$		−	7.73662i		−	0.675951i	−0.941155	−	0.337976i	$-0.890258\pi$
$131$		−	7.73662i		−	0.675951i	0.941155	−	0.337976i	$-0.109742\pi$
$132$		0			0
$133$	8.42358	−	8.42358i	0.730417	−	0.730417i
$134$	−6.40660			−0.553446
$135$		0			0
$136$	−14.3200			−1.22793
$137$	3.02364	−	3.02364i	0.258327	−	0.258327i	−0.566046	−	0.824373i	$-0.691528\pi$
$137$	3.02364	−	3.02364i	0.258327	−	0.258327i	0.824373	+	0.566046i	$0.191528\pi$
$138$		0			0
$139$			0.619965i			0.0525848i	0.999654	+	0.0262924i	$0.00837009\pi$
$139$			0.619965i			0.0525848i	−0.999654	+	0.0262924i	$0.991630\pi$
$140$	−4.86337	−	1.74420i	−0.411030	−	0.147412i
$141$		0			0
$142$	−0.154580	−	0.154580i	−0.0129721	−	0.0129721i
$143$	10.6462	+	10.6462i	0.890279	+	0.890279i
$144$		0			0
$145$	2.26159	+	4.79089i	0.187814	+	0.397862i
$146$			2.99558i			0.247916i
$147$		0			0
$148$	−3.41346	+	3.41346i	−0.280584	+	0.280584i
$149$	−8.52197			−0.698147			−0.349074	−	0.937095i	$-0.613504\pi$
$149$	−8.52197			−0.698147			−0.349074	+	0.937095i	$0.613504\pi$
$150$		0			0
$151$	−21.4841			−1.74835			−0.874174	−	0.485612i	$-0.838597\pi$
$151$	−21.4841			−1.74835			−0.874174	+	0.485612i	$0.838597\pi$
$152$	6.49220	−	6.49220i	0.526587	−	0.526587i
$153$		0			0
$154$		−	23.1563i		−	1.86598i
$155$	−2.39036	−	5.06368i	−0.191998	−	0.406725i
$156$		0			0
$157$	5.84071	+	5.84071i	0.466140	+	0.466140i	0.900661	−	0.434522i	$-0.143083\pi$
$157$	5.84071	+	5.84071i	0.466140	+	0.466140i	−0.434522	+	0.900661i	$0.643083\pi$
$158$	−6.95285	−	6.95285i	−0.553139	−	0.553139i
$159$		0			0
$160$	−6.65477	−	2.38667i	−0.526106	−	0.188683i
$161$		−	3.98894i		−	0.314372i
$162$		0			0
$163$	−2.16500	+	2.16500i	−0.169576	+	0.169576i	−0.786793	−	0.617217i	$-0.788260\pi$
$163$	−2.16500	+	2.16500i	−0.169576	+	0.169576i	0.617217	+	0.786793i	$0.288260\pi$
$164$	5.14006			0.401371
$165$		0			0
$166$	7.29187			0.565959
$167$	−12.9717	+	12.9717i	−1.00378	+	1.00378i	−0.00378691	+	0.999993i	$0.501205\pi$
$167$	−12.9717	+	12.9717i	−1.00378	+	1.00378i	−0.999993	+	0.00378691i	$0.998795\pi$
$168$		0			0
$169$			3.44323i			0.264864i
$170$	−11.2266	+	5.29962i	−0.861040	+	0.406462i
$171$		0			0
$172$	−0.992088	−	0.992088i	−0.0756460	−	0.0756460i
$173$	−1.25463	−	1.25463i	−0.0953874	−	0.0953874i	0.657803	−	0.753190i	$-0.271486\pi$
$173$	−1.25463	−	1.25463i	−0.0953874	−	0.0953874i	−0.753190	+	0.657803i	$0.771486\pi$
$174$		0			0
$175$	−19.8515	+	1.92555i	−1.50063	+	0.145558i
$176$		−	12.2047i		−	0.919962i
$177$		0			0
$178$	12.8435	−	12.8435i	0.962662	−	0.962662i
$179$	12.3423			0.922508			0.461254	−	0.887268i	$-0.347400\pi$
$179$	12.3423			0.922508			0.461254	+	0.887268i	$0.347400\pi$
$180$		0			0
$181$	5.23631			0.389212			0.194606	−	0.980881i	$-0.437657\pi$
$181$	5.23631			0.389212			0.194606	+	0.980881i	$0.437657\pi$
$182$	−10.3934	+	10.3934i	−0.770407	+	0.770407i
$183$		0			0
$184$		−	3.07434i		−	0.226644i
$185$	−6.29085	+	17.5408i	−0.462513	+	1.28963i
$186$		0			0
$187$	16.0409	+	16.0409i	1.17302	+	1.17302i
$188$	5.03709	+	5.03709i	0.367368	+	0.367368i
$189$		0			0
$190$	2.68709	−	7.49244i	0.194942	−	0.543559i
$191$		−	14.5743i		−	1.05456i	−0.849693	−	0.527279i	$-0.823212\pi$
$191$		−	14.5743i		−	1.05456i	0.849693	−	0.527279i	$-0.176788\pi$
$192$		0			0
$193$	1.28314	−	1.28314i	0.0923625	−	0.0923625i	−0.659416	−	0.751778i	$-0.729196\pi$
$193$	1.28314	−	1.28314i	0.0923625	−	0.0923625i	0.751778	+	0.659416i	$0.229196\pi$
$194$	21.8180			1.56644
$195$		0			0
$196$	−5.16210			−0.368721
$197$	11.8909	−	11.8909i	0.847188	−	0.847188i	−0.142593	−	0.989781i	$-0.545544\pi$
$197$	11.8909	−	11.8909i	0.847188	−	0.847188i	0.989781	+	0.142593i	$0.0455440\pi$
$198$		0			0
$199$			2.51310i			0.178149i	0.996025	+	0.0890744i	$0.0283909\pi$
$199$			2.51310i			0.178149i	−0.996025	+	0.0890744i	$0.971609\pi$
$200$	−15.2999	+	1.48406i	−1.08187	+	0.104939i
$201$		0			0
$202$	2.73774	+	2.73774i	0.192627	+	0.192627i
$203$	6.68279	+	6.68279i	0.469040	+	0.469040i
$204$		0			0
$205$	17.9431	−	8.47023i	1.25320	−	0.591587i
$206$		−	21.2005i		−	1.47711i
$207$		0			0
$208$	−5.47789	+	5.47789i	−0.379824	+	0.379824i
$209$	−14.5448			−1.00609
$210$		0			0
$211$	17.2474			1.18736			0.593679	−	0.804702i	$-0.297675\pi$
$211$	17.2474			1.18736			0.593679	+	0.804702i	$0.297675\pi$
$212$	1.33767	−	1.33767i	0.0918718	−	0.0918718i
$213$		0			0
$214$			0.932055i			0.0637140i
$215$	−5.09807	−	1.82837i	−0.347686	−	0.124694i
$216$		0			0
$217$	−7.06332	−	7.06332i	−0.479489	−	0.479489i
$218$	4.05096	+	4.05096i	0.274366	+	0.274366i
$219$		0			0
$220$	2.69290	+	5.70458i	0.181555	+	0.384602i
$221$		−	14.3994i		−	0.968610i
$222$		0			0
$223$	13.3384	−	13.3384i	0.893208	−	0.893208i	−0.101616	−	0.994824i	$-0.532401\pi$
$223$	13.3384	−	13.3384i	0.893208	−	0.893208i	0.994824	+	0.101616i	$0.0324013\pi$
$224$	−12.6119			−0.842667
$225$		0			0
$226$	−18.1834			−1.20954
$227$	−15.5709	+	15.5709i	−1.03348	+	1.03348i	−0.0340579	+	0.999420i	$0.510843\pi$
$227$	−15.5709	+	15.5709i	−1.03348	+	1.03348i	−0.999420	+	0.0340579i	$0.989157\pi$
$228$		0			0
$229$		−	26.9392i		−	1.78019i	−0.455774	−	0.890095i	$-0.650638\pi$
$229$		−	26.9392i		−	1.78019i	0.455774	−	0.890095i	$-0.349362\pi$
$230$	−1.13777	−	2.41023i	−0.0750225	−	0.158926i
$231$		0			0
$232$	5.15055	+	5.15055i	0.338150	+	0.338150i
$233$	−5.62599	−	5.62599i	−0.368571	−	0.368571i	0.498385	−	0.866956i	$-0.333927\pi$
$233$	−5.62599	−	5.62599i	−0.368571	−	0.368571i	−0.866956	+	0.498385i	$0.833927\pi$
$234$		0			0
$235$	25.8842	+	9.28314i	1.68850	+	0.605565i
$236$			6.25402i			0.407102i
$237$		0			0
$238$	−15.6599	+	15.6599i	−1.01508	+	1.01508i
$239$	−13.5837			−0.878658			−0.439329	−	0.898326i	$-0.644784\pi$
$239$	−13.5837			−0.878658			−0.439329	+	0.898326i	$0.644784\pi$
$240$		0			0
$241$	26.4593			1.70439			0.852197	−	0.523222i	$-0.175270\pi$
$241$	26.4593			1.70439			0.852197	+	0.523222i	$0.175270\pi$
$242$	−10.7205	+	10.7205i	−0.689140	+	0.689140i
$243$		0			0
$244$		−	4.47291i		−	0.286348i
$245$	−18.0201	+	8.50655i	−1.15126	+	0.543463i
$246$		0			0
$247$	6.52823	+	6.52823i	0.415381	+	0.415381i
$248$	−5.44382	−	5.44382i	−0.345683	−	0.345683i
$249$		0			0
$250$	−11.4456	+	6.82576i	−0.723884	+	0.431699i
$251$			22.2069i			1.40169i	0.713314	+	0.700845i	$0.247194\pi$
$251$			22.2069i			1.40169i	−0.713314	+	0.700845i	$0.752806\pi$
$252$		0			0
$253$	−3.44380	+	3.44380i	−0.216510	+	0.216510i
$254$	1.27167			0.0797920
$255$		0			0
$256$	−12.6234			−0.788961
$257$	−5.37351	+	5.37351i	−0.335190	+	0.335190i	−0.854553	−	0.519363i	$-0.826169\pi$
$257$	−5.37351	+	5.37351i	−0.335190	+	0.335190i	0.519363	+	0.854553i	$0.326169\pi$
$258$		0			0
$259$			33.2427i			2.06560i
$260$	1.35175	−	3.76909i	0.0838318	−	0.233749i
$261$		0			0
$262$	−6.52070	−	6.52070i	−0.402850	−	0.402850i
$263$	−17.0114	−	17.0114i	−1.04897	−	1.04897i	−0.998738	−	0.0502317i	$-0.984004\pi$
$263$	−17.0114	−	17.0114i	−1.04897	−	1.04897i	−0.0502317	−	0.998738i	$-0.515996\pi$
$264$		0			0
$265$	2.46527	−	6.87394i	0.151441	−	0.422263i
$266$		−	14.1994i		−	0.870621i
$267$		0			0
$268$	2.20153	−	2.20153i	0.134480	−	0.134480i
$269$	−13.2712			−0.809157			−0.404578	−	0.914503i	$-0.632582\pi$
$269$	−13.2712			−0.809157			−0.404578	+	0.914503i	$0.632582\pi$
$270$		0			0
$271$	−14.1006			−0.856551			−0.428276	−	0.903648i	$-0.640879\pi$
$271$	−14.1006			−0.856551			−0.428276	+	0.903648i	$0.640879\pi$
$272$	−8.25368	+	8.25368i	−0.500453	+	0.500453i
$273$		0			0
$274$		−	5.09687i		−	0.307913i
$275$	18.8010	+	15.4762i	1.13374	+	0.933249i
$276$		0			0
$277$	−16.4456	−	16.4456i	−0.988119	−	0.988119i	0.0118117	−	0.999930i	$-0.496240\pi$
$277$	−16.4456	−	16.4456i	−0.988119	−	0.988119i	−0.999930	+	0.0118117i	$0.996240\pi$
$278$	0.522529	+	0.522529i	0.0313392	+	0.0313392i
$279$		0			0
$280$	−24.7976	+	11.7059i	−1.48194	+	0.699564i
$281$		−	24.9592i		−	1.48894i	−0.667655	−	0.744471i	$-0.732702\pi$
$281$		−	24.9592i		−	1.48894i	0.667655	−	0.744471i	$-0.267298\pi$
$282$		0			0
$283$	8.68274	−	8.68274i	0.516135	−	0.516135i	−0.400264	−	0.916400i	$-0.631082\pi$
$283$	8.68274	−	8.68274i	0.516135	−	0.516135i	0.916400	+	0.400264i	$0.131082\pi$
$284$	0.106238			0.00630408
$285$		0			0
$286$	17.9460			1.06117
$287$	25.0288	−	25.0288i	1.47740	−	1.47740i
$288$		0			0
$289$		−	4.69597i		−	0.276234i
$290$	5.94408	+	2.13179i	0.349048	+	0.125183i
$291$		0			0
$292$	−1.02939	−	1.02939i	−0.0602402	−	0.0602402i
$293$	−12.4180	−	12.4180i	−0.725470	−	0.725470i	0.244244	−	0.969714i	$-0.421460\pi$
$293$	−12.4180	−	12.4180i	−0.725470	−	0.725470i	−0.969714	+	0.244244i	$0.921460\pi$
$294$		0			0
$295$	10.3059	+	21.8318i	0.600033	+	1.27110i
$296$			25.6208i			1.48918i
$297$		0			0
$298$	−7.18263	+	7.18263i	−0.416078	+	0.416078i
$299$	3.09140			0.178780
$300$		0			0
$301$	−9.66167			−0.556890
$302$	−18.1075	+	18.1075i	−1.04197	+	1.04197i
$303$		0			0
$304$		−	7.48390i		−	0.429231i
$305$	−7.37084	−	15.6142i	−0.422053	−	0.894067i
$306$		0			0
$307$	21.8263	+	21.8263i	1.24569	+	1.24569i	0.957603	+	0.288091i	$0.0930206\pi$
$307$	21.8263	+	21.8263i	1.24569	+	1.24569i	0.288091	+	0.957603i	$0.406979\pi$
$308$	7.95729	+	7.95729i	0.453409	+	0.453409i
$309$		0			0
$310$	−6.28254	−	2.25317i	−0.356824	−	0.127972i
$311$		−	1.66445i		−	0.0943822i	−0.998886	−	0.0471911i	$-0.984973\pi$
$311$		−	1.66445i		−	0.0943822i	0.998886	−	0.0471911i	$-0.0150270\pi$
$312$		0			0
$313$	19.7384	−	19.7384i	1.11568	−	1.11568i	0.123312	−	0.992368i	$-0.460648\pi$
$313$	19.7384	−	19.7384i	1.11568	−	1.11568i	0.992368	−	0.123312i	$-0.0393515\pi$
$314$	9.84553			0.555615
$315$		0			0
$316$	4.77848			0.268810
$317$	−9.04578	+	9.04578i	−0.508062	+	0.508062i	−0.913931	−	0.405869i	$-0.866969\pi$
$317$	−9.04578	+	9.04578i	−0.508062	+	0.508062i	0.405869	+	0.913931i	$0.366969\pi$
$318$		0			0
$319$		−	11.5390i		−	0.646062i
$320$	−17.7550	+	8.38141i	−0.992533	+	0.468535i
$321$		0			0
$322$	−3.36202	−	3.36202i	−0.187358	−	0.187358i
$323$	9.83625	+	9.83625i	0.547303	+	0.547303i
$324$		0			0
$325$	−1.49229	−	15.3848i	−0.0827774	−	0.853396i
$326$			3.64947i			0.202126i
$327$		0			0
$328$	19.2901	−	19.2901i	1.06512	−	1.06512i
$329$	49.0549			2.70448
$330$		0			0
$331$	−29.8215			−1.63914			−0.819569	−	0.572981i	$-0.805787\pi$
$331$	−29.8215			−1.63914			−0.819569	+	0.572981i	$0.805787\pi$
$332$	−2.50574	+	2.50574i	−0.137520	+	0.137520i
$333$		0			0
$334$			21.8660i			1.19646i
$335$	4.05732	−	11.3131i	0.221675	−	0.618099i
$336$		0			0
$337$	−18.9260	−	18.9260i	−1.03096	−	1.03096i	−0.999505	−	0.0314586i	$-0.989985\pi$
$337$	−18.9260	−	18.9260i	−1.03096	−	1.03096i	−0.0314586	−	0.999505i	$-0.510015\pi$
$338$	2.90208	+	2.90208i	0.157852	+	0.157852i
$339$		0			0
$340$	2.03671	−	5.67898i	0.110456	−	0.307986i
$341$			12.1961i			0.660454i
$342$		0			0
$343$	−5.39190	+	5.39190i	−0.291135	+	0.291135i
$344$	−7.44642			−0.401484
$345$		0			0
$346$	−2.11489			−0.113697
$347$	−12.2339	+	12.2339i	−0.656752	+	0.656752i	−0.954610	−	0.297858i	$-0.903728\pi$
$347$	−12.2339	+	12.2339i	−0.656752	+	0.656752i	0.297858	+	0.954610i	$0.403728\pi$
$348$		0			0
$349$		−	2.29837i		−	0.123029i	−0.998106	−	0.0615146i	$-0.980407\pi$
$349$		−	2.29837i		−	0.123029i	0.998106	−	0.0615146i	$-0.0195931\pi$
$350$	−15.1086	+	18.3545i	−0.807591	+	0.981089i
$351$		0			0
$352$	10.8883	+	10.8883i	0.580350	+	0.580350i
$353$	−19.6363	−	19.6363i	−1.04514	−	1.04514i	−0.998932	−	0.0462034i	$-0.985288\pi$
$353$	−19.6363	−	19.6363i	−1.04514	−	1.04514i	−0.0462034	−	0.998932i	$-0.514712\pi$
$354$		0			0
$355$	0.370861	−	0.175069i	0.0196833	−	0.00929168i
$356$			8.82695i			0.467828i
$357$		0			0
$358$	10.4025	−	10.4025i	0.549792	−	0.549792i
$359$	−13.7873			−0.727664			−0.363832	−	0.931465i	$-0.618532\pi$
$359$	−13.7873			−0.727664			−0.363832	+	0.931465i	$0.618532\pi$
$360$		0			0
$361$	10.0811			0.530586
$362$	4.41335	−	4.41335i	0.231961	−	0.231961i
$363$		0			0
$364$		−	7.14303i		−	0.374397i
$365$	−5.28973	−	1.89711i	−0.276877	−	0.0992994i
$366$		0			0
$367$	9.47643	+	9.47643i	0.494666	+	0.494666i	0.909773	−	0.415107i	$-0.136256\pi$
$367$	9.47643	+	9.47643i	0.494666	+	0.494666i	−0.415107	+	0.909773i	$0.636256\pi$
$368$	−1.77198	−	1.77198i	−0.0923707	−	0.0923707i
$369$		0			0
$370$	9.48189	+	20.0862i	0.492940	+	1.04423i
$371$		−	13.0272i		−	0.676340i
$372$		0			0
$373$	−11.1582	+	11.1582i	−0.577748	+	0.577748i	−0.934282	−	0.356534i	$-0.883958\pi$
$373$	−11.1582	+	11.1582i	−0.577748	+	0.577748i	0.356534	+	0.934282i	$0.383958\pi$
$374$	27.0396			1.39819
$375$		0			0
$376$	37.8074			1.94977
$377$	−5.17913	+	5.17913i	−0.266739	+	0.266739i
$378$		0			0
$379$		−	26.1129i		−	1.34133i	−0.741760	−	0.670665i	$-0.766009\pi$
$379$		−	26.1129i		−	1.34133i	0.741760	−	0.670665i	$-0.233991\pi$
$380$	1.65128	+	3.49804i	0.0847091	+	0.179446i
$381$		0			0
$382$	−12.2837	−	12.2837i	−0.628490	−	0.628490i
$383$	7.79491	+	7.79491i	0.398301	+	0.398301i	0.877634	−	0.479332i	$-0.159121\pi$
$383$	7.79491	+	7.79491i	0.398301	+	0.398301i	−0.479332	+	0.877634i	$0.659121\pi$
$384$		0			0
$385$	40.8904	+	14.6649i	2.08397	+	0.747395i
$386$		−	2.16295i		−	0.110091i
$387$		0			0
$388$	−7.49743	+	7.49743i	−0.380624	+	0.380624i
$389$	14.5503			0.737731			0.368866	−	0.929483i	$-0.379746\pi$
$389$	14.5503			0.737731			0.368866	+	0.929483i	$0.379746\pi$
$390$		0			0
$391$	4.65789			0.235560
$392$	−19.3729	+	19.3729i	−0.978477	+	0.978477i
$393$		0			0
$394$		−	20.0441i		−	1.00981i
$395$	16.6809	−	7.87439i	0.839308	−	0.396203i
$396$		0			0
$397$	−24.8210	−	24.8210i	−1.24573	−	1.24573i	−0.957586	−	0.288146i	$-0.906961\pi$
$397$	−24.8210	−	24.8210i	−1.24573	−	1.24573i	−0.288146	−	0.957586i	$-0.593039\pi$
$398$	2.11813	+	2.11813i	0.106172	+	0.106172i
$399$		0			0
$400$	−7.96312	+	9.67387i	−0.398156	+	0.483693i
$401$			9.48142i			0.473479i	0.971573	+	0.236740i	$0.0760789\pi$
$401$			9.48142i			0.473479i	−0.971573	+	0.236740i	$0.923921\pi$
$402$		0			0
$403$	5.47403	−	5.47403i	0.272681	−	0.272681i
$404$	−1.88156			−0.0936113
$405$		0			0
$406$	11.2650			0.559072
$407$	28.6997	−	28.6997i	1.42259	−	1.42259i
$408$		0			0
$409$			8.93629i			0.441871i	0.975288	+	0.220935i	$0.0709110\pi$
$409$			8.93629i			0.441871i	−0.975288	+	0.220935i	$0.929089\pi$
$410$	7.98410	−	22.2621i	0.394307	−	1.09945i
$411$		0			0
$412$	7.28522	+	7.28522i	0.358917	+	0.358917i
$413$	30.4531	+	30.4531i	1.49850	+	1.49850i
$414$		0			0
$415$	−4.61797	+	12.8763i	−0.226687	+	0.632074i
$416$		−	9.77414i		−	0.479216i
$417$		0			0
$418$	−12.2589	+	12.2589i	−0.599602	+	0.599602i
$419$	−0.874825			−0.0427380			−0.0213690	−	0.999772i	$-0.506802\pi$
$419$	−0.874825			−0.0427380			−0.0213690	+	0.999772i	$0.506802\pi$
$420$		0			0
$421$	9.76956			0.476139			0.238070	−	0.971248i	$-0.423485\pi$
$421$	9.76956			0.476139			0.238070	+	0.971248i	$0.423485\pi$
$422$	14.5367	−	14.5367i	0.707636	−	0.707636i
$423$		0			0
$424$		−	10.0403i		−	0.487601i
$425$	−2.24847	−	23.1807i	−0.109067	−	1.12443i
$426$		0			0
$427$	−21.7802	−	21.7802i	−1.05402	−	1.05402i
$428$	−0.320286	−	0.320286i	−0.0154816	−	0.0154816i
$429$		0			0
$430$	−5.83786	+	2.75582i	−0.281526	+	0.132897i
$431$		−	25.2758i		−	1.21749i	−0.793364	−	0.608747i	$-0.791672\pi$
$431$		−	25.2758i		−	1.21749i	0.793364	−	0.608747i	$-0.208328\pi$
$432$		0			0
$433$	−17.2941	+	17.2941i	−0.831101	+	0.831101i	−0.987667	−	0.156567i	$-0.949957\pi$
$433$	−17.2941	+	17.2941i	−0.831101	+	0.831101i	0.156567	+	0.987667i	$0.449957\pi$
$434$	−11.9064			−0.571527
$435$		0			0
$436$	−2.78410			−0.133334
$437$	−2.11174	+	2.11174i	−0.101018	+	0.101018i
$438$		0			0
$439$		−	16.4294i		−	0.784135i	−0.919937	−	0.392067i	$-0.871760\pi$
$439$		−	16.4294i		−	0.784135i	0.919937	−	0.392067i	$-0.128240\pi$
$440$	31.5149	+	11.3025i	1.50242	+	0.538827i
$441$		0			0
$442$	−12.1364	−	12.1364i	−0.577267	−	0.577267i
$443$	10.3743	+	10.3743i	0.492897	+	0.492897i	0.909218	−	0.416321i	$-0.136681\pi$
$443$	10.3743	+	10.3743i	0.492897	+	0.492897i	−0.416321	+	0.909218i	$0.636681\pi$
$444$		0			0
$445$	14.5458	+	30.8135i	0.689538	+	1.46070i
$446$		−	22.4842i		−	1.06466i
$447$		0			0
$448$	−24.7663	+	24.7663i	−1.17010	+	1.17010i
$449$	−33.5633			−1.58395			−0.791975	−	0.610553i	$-0.790947\pi$
$449$	−33.5633			−1.58395			−0.791975	+	0.610553i	$0.790947\pi$
$450$		0			0
$451$	−43.2167			−2.03499
$452$	6.24843	−	6.24843i	0.293901	−	0.293901i
$453$		0			0
$454$			26.2475i			1.23185i
$455$	−11.7709	−	24.9352i	−0.551828	−	1.16898i
$456$		0			0
$457$	10.9912	+	10.9912i	0.514147	+	0.514147i	0.915794	−	0.401647i	$-0.131562\pi$
$457$	10.9912	+	10.9912i	0.514147	+	0.514147i	−0.401647	+	0.915794i	$0.631562\pi$
$458$	−22.7053	−	22.7053i	−1.06095	−	1.06095i
$459$		0			0
$460$	1.21922	+	0.437260i	0.0568462	+	0.0203874i
$461$			34.4292i			1.60353i	0.597642	+	0.801763i	$0.296104\pi$
$461$			34.4292i			1.60353i	−0.597642	+	0.801763i	$0.703896\pi$
$462$		0			0
$463$	−6.44845	+	6.44845i	−0.299685	+	0.299685i	−0.840890	−	0.541206i	$-0.817968\pi$
$463$	−6.44845	+	6.44845i	−0.299685	+	0.299685i	0.541206	+	0.840890i	$0.317968\pi$
$464$	5.93730			0.275632
$465$		0			0
$466$	−9.48358			−0.439318
$467$	12.5602	−	12.5602i	0.581215	−	0.581215i	−0.354022	−	0.935237i	$-0.615186\pi$
$467$	12.5602	−	12.5602i	0.581215	−	0.581215i	0.935237	+	0.354022i	$0.115186\pi$
$468$		0			0
$469$		−	21.4401i		−	0.990012i
$470$	29.6403	−	13.9920i	1.36721	−	0.645403i
$471$		0			0
$472$	23.4707	+	23.4707i	1.08033	+	1.08033i
$473$	8.34130	+	8.34130i	0.383533	+	0.383533i
$474$		0			0
$475$	11.5287	+	9.48998i	0.528975	+	0.435430i
$476$		−	10.7626i		−	0.493302i
$477$		0			0
$478$	−11.4488	+	11.4488i	−0.523658	+	0.523658i
$479$	30.8882			1.41132			0.705658	−	0.708553i	$-0.250652\pi$
$479$	30.8882			1.41132			0.705658	+	0.708553i	$0.250652\pi$
$480$		0			0
$481$	−25.7629			−1.17469
$482$	22.3008	−	22.3008i	1.01578	−	1.01578i
$483$		0			0
$484$		−	7.36787i		−	0.334903i
$485$	−13.8174	+	38.5273i	−0.627417	+	1.74943i
$486$		0			0
$487$	2.58490	+	2.58490i	0.117133	+	0.117133i	0.763244	−	0.646111i	$-0.223606\pi$
$487$	2.58490	+	2.58490i	0.117133	+	0.117133i	−0.646111	+	0.763244i	$0.723606\pi$
$488$	−16.7864	−	16.7864i	−0.759884	−	0.759884i
$489$		0			0
$490$	−8.01833	+	22.3576i	−0.362231	+	1.01001i
$491$			19.4601i			0.878223i	0.898433	+	0.439111i	$0.144707\pi$
$491$			19.4601i			0.878223i	−0.898433	+	0.439111i	$0.855293\pi$
$492$		0			0
$493$	−7.80352	+	7.80352i	−0.351453	+	0.351453i
$494$	11.0045			0.495114
$495$		0			0
$496$	−6.27537			−0.281773
$497$	0.517313	−	0.517313i	0.0232047	−	0.0232047i
$498$		0			0
$499$			28.7513i			1.28709i	0.765410	+	0.643543i	$0.222536\pi$
$499$			28.7513i			1.28709i	−0.765410	+	0.643543i	$0.777464\pi$
$500$	1.58754	−	6.27868i	0.0709971	−	0.280791i
$501$		0			0
$502$	18.7168	+	18.7168i	0.835372	+	0.835372i
$503$	18.3317	+	18.3317i	0.817370	+	0.817370i	0.985726	−	0.168356i	$-0.0538459\pi$
$503$	18.3317	+	18.3317i	0.817370	+	0.817370i	−0.168356	+	0.985726i	$0.553846\pi$
$504$		0			0
$505$	−6.56824	+	3.10060i	−0.292283	+	0.137975i
$506$			5.80512i			0.258069i
$507$		0			0
$508$	−0.436991	+	0.436991i	−0.0193884	+	0.0193884i
$509$	−36.8390			−1.63286			−0.816431	−	0.577443i	$-0.804051\pi$
$509$	−36.8390			−1.63286			−0.816431	+	0.577443i	$0.804051\pi$
$510$		0			0
$511$	−10.0249			−0.443476
$512$	−16.4978	+	16.4978i	−0.729107	+	0.729107i
$513$		0			0
$514$			9.05797i			0.399530i
$515$	37.4368	+	13.4263i	1.64966	+	0.591635i
$516$		0			0
$517$	−42.3510	−	42.3510i	−1.86259	−	1.86259i
$518$	28.0182	+	28.0182i	1.23105	+	1.23105i
$519$		0			0
$520$	−9.07204	−	19.2180i	−0.397835	−	0.842765i
$521$		−	9.38799i		−	0.411295i	−0.978626	−	0.205648i	$-0.934070\pi$
$521$		−	9.38799i		−	0.411295i	0.978626	−	0.205648i	$-0.0659301\pi$
$522$		0			0
$523$	8.29394	−	8.29394i	0.362669	−	0.362669i	−0.502126	−	0.864795i	$-0.667449\pi$
$523$	8.29394	−	8.29394i	0.362669	−	0.362669i	0.864795	+	0.502126i	$0.167449\pi$
$524$	4.48147			0.195774
$525$		0			0
$526$	−28.6757			−1.25032
$527$	8.24786	−	8.24786i	0.359282	−	0.359282i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	−3.71578	−	7.87143i	−0.161403	−	0.341913i
$531$		0			0
$532$	4.87940	+	4.87940i	0.211549	+	0.211549i
$533$	19.3972	+	19.3972i	0.840186	+	0.840186i
$534$		0			0
$535$	−1.64586	−	0.590274i	−0.0711569	−	0.0255198i
$536$		−	16.5243i		−	0.713739i
$537$		0			0
$538$	−11.1854	+	11.1854i	−0.482237	+	0.482237i
$539$	43.4020			1.86946
$540$		0			0
$541$	33.7903			1.45276			0.726380	−	0.687293i	$-0.241201\pi$
$541$	33.7903			1.45276			0.726380	+	0.687293i	$0.241201\pi$
$542$	−11.8845	+	11.8845i	−0.510483	+	0.510483i
$543$		0			0
$544$		−	14.7269i		−	0.631412i
$545$	−9.71885	+	4.58788i	−0.416310	+	0.196523i
$546$		0			0
$547$	30.7563	+	30.7563i	1.31505	+	1.31505i	0.917645	+	0.397402i	$0.130088\pi$
$547$	30.7563	+	30.7563i	1.31505	+	1.31505i	0.397402	+	0.917645i	$0.369912\pi$
$548$	1.75146	+	1.75146i	0.0748186	+	0.0748186i
$549$		0			0
$550$	28.8900	−	2.80227i	1.23187	−	0.119489i
$551$		−	7.07572i		−	0.301436i
$552$		0			0
$553$	23.2681	−	23.2681i	0.989462	−	0.989462i
$554$	−27.7218			−1.17779
$555$		0			0
$556$	−0.359118			−0.0152300
$557$	19.1823	−	19.1823i	0.812778	−	0.812778i	−0.172271	−	0.985050i	$-0.555111\pi$
$557$	19.1823	−	19.1823i	0.812778	−	0.812778i	0.985050	+	0.172271i	$0.0551106\pi$
$558$		0			0
$559$		−	7.48774i		−	0.316698i
$560$	−7.54571	+	21.0398i	−0.318864	+	0.889092i
$561$		0			0
$562$	−21.0365	−	21.0365i	−0.887372	−	0.887372i
$563$	−11.1773	−	11.1773i	−0.471065	−	0.471065i	0.431194	−	0.902259i	$-0.358092\pi$
$563$	−11.1773	−	11.1773i	−0.471065	−	0.471065i	−0.902259	+	0.431194i	$0.858092\pi$
$564$		0			0
$565$	11.5156	−	32.1090i	0.484464	−	1.35084i
$566$		−	14.6363i		−	0.615208i
$567$		0			0
$568$	0.398702	−	0.398702i	0.0167292	−	0.0167292i
$569$	−6.69065			−0.280486			−0.140243	−	0.990117i	$-0.544788\pi$
$569$	−6.69065			−0.280486			−0.140243	+	0.990117i	$0.544788\pi$
$570$		0			0
$571$	0.881378			0.0368845			0.0184423	−	0.999830i	$-0.494129\pi$
$571$	0.881378			0.0368845			0.0184423	+	0.999830i	$0.494129\pi$
$572$	−6.16686	+	6.16686i	−0.257849	+	0.257849i
$573$		0			0
$574$		−	42.1904i		−	1.76099i
$575$	4.97664	−	0.482723i	0.207540	−	0.0201309i
$576$		0			0
$577$	5.80114	+	5.80114i	0.241505	+	0.241505i	0.817472	−	0.575968i	$-0.195375\pi$
$577$	5.80114	+	5.80114i	0.241505	+	0.241505i	−0.575968	+	0.817472i	$0.695375\pi$
$578$	−3.95794	−	3.95794i	−0.164628	−	0.164628i
$579$		0			0
$580$	−2.77515	+	1.31003i	−0.115232	+	0.0543962i
$581$			24.4027i			1.01240i
$582$		0			0
$583$	−11.2469	+	11.2469i	−0.465800	+	0.465800i
$584$	−7.72637			−0.319719
$585$		0			0
$586$	−20.9327			−0.864724
$587$	−3.39815	+	3.39815i	−0.140257	+	0.140257i	−0.773749	−	0.633492i	$-0.781621\pi$
$587$	−3.39815	+	3.39815i	−0.140257	+	0.140257i	0.633492	+	0.773749i	$0.281621\pi$
$588$		0			0
$589$			7.47862i			0.308151i
$590$	27.0868	+	9.71442i	1.11515	+	0.399936i
$591$		0			0
$592$	14.7672	+	14.7672i	0.606927	+	0.606927i
$593$	26.3747	+	26.3747i	1.08308	+	1.08308i	0.996220	+	0.0868607i	$0.0276835\pi$
$593$	26.3747	+	26.3747i	1.08308	+	1.08308i	0.0868607	+	0.996220i	$0.472317\pi$
$594$		0			0
$595$	−17.7355	−	37.5705i	−0.727085	−	1.54024i
$596$		−	4.93640i		−	0.202203i
$597$		0			0
$598$	2.60555	−	2.60555i	0.106549	−	0.106549i
$599$	−28.5185			−1.16524			−0.582618	−	0.812746i	$-0.697972\pi$
$599$	−28.5185			−1.16524			−0.582618	+	0.812746i	$0.697972\pi$
$600$		0			0
$601$	22.8675			0.932787			0.466393	−	0.884577i	$-0.345553\pi$
$601$	22.8675			0.932787			0.466393	+	0.884577i	$0.345553\pi$
$602$	−8.14321	+	8.14321i	−0.331892	+	0.331892i
$603$		0			0
$604$		−	12.4448i		−	0.506370i
$605$	−12.1414	−	25.7201i	−0.493619	−	1.04567i
$606$		0			0
$607$	6.93642	+	6.93642i	0.281541	+	0.281541i	0.833723	−	0.552183i	$-0.186205\pi$
$607$	6.93642	+	6.93642i	0.281541	+	0.281541i	−0.552183	+	0.833723i	$0.686205\pi$
$608$	6.67671	+	6.67671i	0.270776	+	0.270776i
$609$		0			0
$610$	−19.3726	−	6.94781i	−0.784375	−	0.281308i
$611$			38.0172i			1.53801i
$612$		0			0
$613$	−13.7945	+	13.7945i	−0.557153	+	0.557153i	−0.928496	−	0.371343i	$-0.878898\pi$
$613$	−13.7945	+	13.7945i	−0.557153	+	0.557153i	0.371343	+	0.928496i	$0.378898\pi$
$614$	36.7920			1.48481
$615$		0			0
$616$	59.7259			2.40643
$617$	−14.8750	+	14.8750i	−0.598844	+	0.598844i	−0.940005	−	0.341161i	$-0.889180\pi$
$617$	−14.8750	+	14.8750i	−0.598844	+	0.598844i	0.341161	+	0.940005i	$0.389180\pi$
$618$		0			0
$619$			41.8857i			1.68353i	0.539844	+	0.841765i	$0.318483\pi$
$619$			41.8857i			1.68353i	−0.539844	+	0.841765i	$0.681517\pi$
$620$	2.93317	−	1.38463i	0.117799	−	0.0556081i
$621$		0			0
$622$	−1.40286	−	1.40286i	−0.0562494	−	0.0562494i
$623$	42.9816	+	42.9816i	1.72202	+	1.72202i
$624$		0			0
$625$	−4.80468	−	24.5340i	−0.192187	−	0.981358i
$626$		−	33.2724i		−	1.32983i
$627$		0			0
$628$	−3.38326	+	3.38326i	−0.135007	+	0.135007i
$629$	−38.8176			−1.54776
$630$		0			0
$631$	−30.4784			−1.21333			−0.606663	−	0.794959i	$-0.707492\pi$
$631$	−30.4784			−1.21333			−0.606663	+	0.794959i	$0.707492\pi$
$632$	17.9332	−	17.9332i	0.713343	−	0.713343i
$633$		0			0
$634$			15.2482i			0.605584i
$635$	−0.805356	+	2.24558i	−0.0319596	+	0.0891131i
$636$		0			0
$637$	−19.4804	−	19.4804i	−0.771840	−	0.771840i
$638$	−9.72551	−	9.72551i	−0.385037	−	0.385037i
$639$		0			0
$640$	−3.12703	+	8.71913i	−0.123607	+	0.344654i
$641$			11.5448i			0.455991i	0.973662	+	0.227995i	$0.0732171\pi$
$641$			11.5448i			0.455991i	−0.973662	+	0.227995i	$0.926783\pi$
$642$		0			0
$643$	−1.73999	+	1.73999i	−0.0686186	+	0.0686186i	−0.740583	−	0.671965i	$-0.765451\pi$
$643$	−1.73999	+	1.73999i	−0.0686186	+	0.0686186i	0.671965	+	0.740583i	$0.265451\pi$
$644$	2.31061			0.0910509
$645$		0			0
$646$	16.5807			0.652358
$647$	25.8085	−	25.8085i	1.01464	−	1.01464i	0.0147459	−	0.999891i	$-0.495306\pi$
$647$	25.8085	−	25.8085i	1.01464	−	1.01464i	0.999891	−	0.0147459i	$-0.00469393\pi$
$648$		0			0
$649$		−	52.5827i		−	2.06405i
$650$	−14.2246	−	11.7091i	−0.557936	−	0.459269i
$651$		0			0
$652$	−1.25408	−	1.25408i	−0.0491137	−	0.0491137i
$653$	9.74559	+	9.74559i	0.381374	+	0.381374i	0.871597	−	0.490223i	$-0.163085\pi$
$653$	9.74559	+	9.74559i	0.381374	+	0.381374i	−0.490223	+	0.871597i	$0.663085\pi$
$654$		0			0
$655$	15.6441	−	7.38496i	0.611266	−	0.288554i
$656$		−	22.2367i		−	0.868199i
$657$		0			0
$658$	41.3452	−	41.3452i	1.61180	−	1.61180i
$659$	9.46665			0.368769			0.184384	−	0.982854i	$-0.440971\pi$
$659$	9.46665			0.368769			0.184384	+	0.982854i	$0.440971\pi$
$660$		0			0
$661$	−32.6994			−1.27186			−0.635930	−	0.771747i	$-0.719383\pi$
$661$	−32.6994			−1.27186			−0.635930	+	0.771747i	$0.719383\pi$
$662$	−25.1346	+	25.1346i	−0.976885	+	0.976885i
$663$		0			0
$664$			18.8076i			0.729877i
$665$	25.0739	+	8.99252i	0.972325	+	0.348715i
$666$		0			0
$667$	−1.67533	−	1.67533i	−0.0648691	−	0.0648691i
$668$	−7.51392	−	7.51392i	−0.290722	−	0.290722i
$669$		0			0
$670$	−6.11540	−	12.9547i	−0.236259	−	0.500484i
$671$			37.6074i			1.45182i
$672$		0			0
$673$	−15.8302	+	15.8302i	−0.610210	+	0.610210i	−0.943001	−	0.332791i	$-0.892010\pi$
$673$	−15.8302	+	15.8302i	−0.610210	+	0.610210i	0.332791	+	0.943001i	$0.392010\pi$
$674$	−31.9030			−1.22886
$675$		0			0
$676$	−1.99451			−0.0767118
$677$	4.27892	−	4.27892i	0.164452	−	0.164452i	−0.620083	−	0.784536i	$-0.712901\pi$
$677$	4.27892	−	4.27892i	0.164452	−	0.164452i	0.784536	+	0.620083i	$0.212901\pi$
$678$		0			0
$679$			73.0154i			2.80208i
$680$	−13.6691	−	28.9562i	−0.524185	−	1.11042i
$681$		0			0
$682$	10.2793	+	10.2793i	0.393614	+	0.393614i
$683$	20.4133	+	20.4133i	0.781094	+	0.781094i	0.980015	−	0.198921i	$-0.0637438\pi$
$683$	20.4133	+	20.4133i	0.781094	+	0.781094i	−0.198921	+	0.980015i	$0.563744\pi$
$684$		0			0
$685$	9.00028	+	3.22786i	0.343883	+	0.123330i
$686$			9.08897i			0.347018i
$687$		0			0
$688$	−4.29194	+	4.29194i	−0.163629	+	0.163629i
$689$	10.0960			0.384628
$690$		0			0
$691$	2.62362			0.0998071			0.0499036	−	0.998754i	$-0.484109\pi$
$691$	2.62362			0.0998071			0.0499036	+	0.998754i	$0.484109\pi$
$692$	0.726748	−	0.726748i	0.0276268	−	0.0276268i
$693$		0			0
$694$			20.6224i			0.782815i
$695$	−1.25362	+	0.591786i	−0.0475527	+	0.0224477i
$696$		0			0
$697$	29.2262	+	29.2262i	1.10702	+	1.10702i
$698$	−1.93715	−	1.93715i	−0.0733223	−	0.0733223i
$699$		0			0
$700$	−1.11539	−	11.4991i	−0.0421576	−	0.434625i
$701$		−	49.5768i		−	1.87249i	−0.351348	−	0.936245i	$-0.614276\pi$
$701$		−	49.5768i		−	1.87249i	0.351348	−	0.936245i	$-0.385724\pi$
$702$		0			0
$703$	17.5987	−	17.5987i	0.663746	−	0.663746i
$704$	42.7635			1.61171
$705$		0			0
$706$	−33.1004			−1.24575
$707$	−9.16202	+	9.16202i	−0.344573	+	0.344573i
$708$		0			0
$709$			8.14090i			0.305738i	0.988246	+	0.152869i	$0.0488513\pi$
$709$			8.14090i			0.305738i	−0.988246	+	0.152869i	$0.951149\pi$
$710$	0.165021	−	0.460129i	0.00619313	−	0.0172683i
$711$		0			0
$712$	33.1267	+	33.1267i	1.24148	+	1.24148i
$713$	1.77073	+	1.77073i	0.0663142	+	0.0663142i
$714$		0			0
$715$	−11.3652	+	31.6898i	−0.425036	+	1.18513i
$716$			7.14935i			0.267184i
$717$		0			0
$718$	−11.6204	+	11.6204i	−0.433670	+	0.433670i
$719$	−22.6663			−0.845311			−0.422655	−	0.906291i	$-0.638902\pi$
$719$	−22.6663			−0.845311			−0.422655	+	0.906291i	$0.638902\pi$
$720$		0			0
$721$	70.9487			2.64227
$722$	8.49674	−	8.49674i	0.316216	−	0.316216i
$723$		0			0
$724$			3.03316i			0.112727i
$725$	−7.52881	+	9.14625i	−0.279613	+	0.339683i
$726$		0			0
$727$	3.32177	+	3.32177i	0.123198	+	0.123198i	0.766017	−	0.642820i	$-0.222236\pi$
$727$	3.32177	+	3.32177i	0.123198	+	0.123198i	−0.642820	+	0.766017i	$0.722236\pi$
$728$	−26.8071	−	26.8071i	−0.993538	−	0.993538i
$729$		0			0
$730$	−6.05733	+	2.85942i	−0.224192	+	0.105832i
$731$		−	11.2820i		−	0.417279i
$732$		0			0
$733$	−35.7043	+	35.7043i	−1.31877	+	1.31877i	−0.404020	+	0.914750i	$0.632387\pi$
$733$	−35.7043	+	35.7043i	−1.31877	+	1.31877i	−0.914750	+	0.404020i	$0.867613\pi$
$734$	15.9742			0.589617
$735$		0			0
$736$	3.16172			0.116542
$737$	−18.5101	+	18.5101i	−0.681827	+	0.681827i
$738$		0			0
$739$			45.1118i			1.65946i	0.558161	+	0.829732i	$0.311507\pi$
$739$			45.1118i			1.65946i	−0.558161	+	0.829732i	$0.688493\pi$
$740$	−10.1606	−	3.64401i	−0.373512	−	0.133956i
$741$		0			0
$742$	−10.9798	−	10.9798i	−0.403082	−	0.403082i
$743$	12.5775	+	12.5775i	0.461424	+	0.461424i	0.899122	−	0.437698i	$-0.144206\pi$
$743$	12.5775	+	12.5775i	0.461424	+	0.461424i	−0.437698	+	0.899122i	$0.644206\pi$
$744$		0			0
$745$	−8.13462	−	17.2322i	−0.298029	−	0.631338i
$746$			18.8090i			0.688647i
$747$		0			0
$748$	−9.29176	+	9.29176i	−0.339740	+	0.339740i
$749$	−3.11918			−0.113972
$750$		0			0
$751$	24.1792			0.882311			0.441156	−	0.897431i	$-0.354569\pi$
$751$	24.1792			0.882311			0.441156	+	0.897431i	$0.354569\pi$
$752$	21.7913	−	21.7913i	0.794646	−	0.794646i
$753$		0			0
$754$			8.73031i			0.317939i
$755$	−20.5075	−	43.4427i	−0.746346	−	1.58104i
$756$		0			0
$757$	−26.1128	−	26.1128i	−0.949084	−	0.949084i	0.0496810	−	0.998765i	$-0.484180\pi$
$757$	−26.1128	−	26.1128i	−0.949084	−	0.949084i	−0.998765	+	0.0496810i	$0.984180\pi$
$758$	−22.0089	−	22.0089i	−0.799399	−	0.799399i
$759$		0			0
$760$	19.3249	+	6.93070i	0.700988	+	0.251403i
$761$			21.1857i			0.767980i	0.923337	+	0.383990i	$0.125450\pi$
$761$			21.1857i			0.767980i	−0.923337	+	0.383990i	$0.874550\pi$
$762$		0			0
$763$	−13.5568	+	13.5568i	−0.490789	+	0.490789i
$764$	8.44222			0.305429
$765$		0			0
$766$	13.1397			0.474755
$767$	−23.6010	+	23.6010i	−0.852181	+	0.852181i
$768$		0			0
$769$			27.7670i			1.00130i	0.865649	+	0.500652i	$0.166906\pi$
$769$			27.7670i			1.00130i	−0.865649	+	0.500652i	$0.833094\pi$
$770$	46.8240	−	22.1037i	1.68742	−	0.796563i
$771$		0			0
$772$	0.743266	+	0.743266i	0.0267507	+	0.0267507i
$773$	−5.89368	−	5.89368i	−0.211981	−	0.211981i	0.593127	−	0.805109i	$-0.297893\pi$
$773$	−5.89368	−	5.89368i	−0.211981	−	0.211981i	−0.805109	+	0.593127i	$0.797893\pi$
$774$		0			0
$775$	7.95751	−	9.66705i	0.285842	−	0.347251i
$776$			56.2743i			2.02013i
$777$		0			0
$778$	12.2635	−	12.2635i	0.439669	−	0.439669i
$779$	−26.5004			−0.949477
$780$		0			0
$781$	−0.893233			−0.0319624
$782$	3.92584	−	3.92584i	0.140388	−	0.140388i
$783$		0			0
$784$			22.3321i			0.797574i
$785$	−6.23520	+	17.3857i	−0.222544	+	0.620521i
$786$		0			0
$787$	−4.83570	−	4.83570i	−0.172374	−	0.172374i	0.615648	−	0.788022i	$-0.288895\pi$
$787$	−4.83570	−	4.83570i	−0.172374	−	0.172374i	−0.788022	+	0.615648i	$0.788895\pi$
$788$	6.88784	+	6.88784i	0.245369	+	0.245369i
$789$		0			0
$790$	7.42245	−	20.6961i	0.264079	−	0.736334i
$791$		−	60.8518i		−	2.16364i
$792$		0			0
$793$	16.8795	−	16.8795i	0.599410	−	0.599410i
$794$	−41.8401			−1.48485
$795$		0			0
$796$	−1.45572			−0.0515968
$797$	−10.8866	+	10.8866i	−0.385622	+	0.385622i	−0.873123	−	0.487501i	$-0.837909\pi$
$797$	−10.8866	+	10.8866i	−0.385622	+	0.385622i	0.487501	+	0.873123i	$0.337909\pi$
$798$		0			0
$799$			57.2815i			2.02647i
$800$	−1.52623	−	15.7347i	−0.0539605	−	0.556307i
$801$		0			0
$802$	7.99128	+	7.99128i	0.282182	+	0.282182i
$803$	8.65489	+	8.65489i	0.305424	+	0.305424i
$804$		0			0
$805$	8.06598	−	3.80763i	0.284288	−	0.134201i
$806$		−	9.22742i		−	0.325022i
$807$		0			0
$808$	−7.06133	+	7.06133i	−0.248417	+	0.248417i
$809$	−53.0493			−1.86512			−0.932558	−	0.361021i	$-0.882428\pi$
$809$	−53.0493			−1.86512			−0.932558	+	0.361021i	$0.882428\pi$
$810$		0			0
$811$	−19.2272			−0.675159			−0.337579	−	0.941297i	$-0.609608\pi$
$811$	−19.2272			−0.675159			−0.337579	+	0.941297i	$0.609608\pi$
$812$	−3.87104	+	3.87104i	−0.135847	+	0.135847i
$813$		0			0
$814$		−	48.3784i		−	1.69566i
$815$	−6.44440	−	2.31122i	−0.225738	−	0.0809586i
$816$		0			0
$817$	5.11488	+	5.11488i	0.178947	+	0.178947i
$818$	7.53182	+	7.53182i	0.263344	+	0.263344i
$819$		0			0
$820$	4.90643	+	10.3937i	0.171340	+	0.362962i
$821$		−	28.8227i		−	1.00592i	−0.864310	−	0.502960i	$-0.832244\pi$
$821$		−	28.8227i		−	1.00592i	0.864310	−	0.502960i	$-0.167756\pi$
$822$		0			0
$823$	30.8882	−	30.8882i	1.07669	−	1.07669i	0.0798901	−	0.996804i	$-0.474543\pi$
$823$	30.8882	−	30.8882i	1.07669	−	1.07669i	0.996804	−	0.0798901i	$-0.0254569\pi$
$824$	54.6814			1.90492
$825$		0			0
$826$	51.3339			1.78613
$827$	−10.9994	+	10.9994i	−0.382488	+	0.382488i	−0.871998	−	0.489510i	$-0.837176\pi$
$827$	−10.9994	+	10.9994i	−0.382488	+	0.382488i	0.489510	+	0.871998i	$0.337176\pi$
$828$		0			0
$829$			13.2689i			0.460847i	0.973090	+	0.230423i	$0.0740111\pi$
$829$			13.2689i			0.460847i	−0.973090	+	0.230423i	$0.925989\pi$
$830$	6.96043	+	14.7448i	0.241600	+	0.511800i
$831$		0			0
$832$	−19.1938	−	19.1938i	−0.665425	−	0.665425i
$833$	−29.3515	−	29.3515i	−1.01697	−	1.01697i
$834$		0			0
$835$	−38.6120	−	13.8478i	−1.33622	−	0.479224i
$836$		−	8.42516i		−	0.291390i
$837$		0			0
$838$	−0.737334	+	0.737334i	−0.0254708	+	0.0254708i
$839$	−7.71744			−0.266436			−0.133218	−	0.991087i	$-0.542531\pi$
$839$	−7.71744			−0.266436			−0.133218	+	0.991087i	$0.542531\pi$
$840$		0			0
$841$	−23.3865			−0.806432
$842$	8.23413	−	8.23413i	0.283767	−	0.283767i
$843$		0			0
$844$			9.99063i			0.343892i
$845$	−6.96251	+	3.28672i	−0.239518	+	0.113067i
$846$		0			0
$847$	−35.8769	−	35.8769i	−1.23274	−	1.23274i
$848$	−5.78700	−	5.78700i	−0.198726	−	0.198726i
$849$		0			0
$850$	−21.4326	−	17.6424i	−0.735132	−	0.605130i
$851$		−	8.33373i		−	0.285677i
$852$		0			0
$853$	0.0999657	−	0.0999657i	0.00342276	−	0.00342276i	−0.705393	−	0.708816i	$-0.749230\pi$
$853$	0.0999657	−	0.0999657i	0.00342276	−	0.00342276i	0.708816	+	0.705393i	$0.249230\pi$
$854$	−36.7143			−1.25634
$855$		0			0
$856$	−2.40401			−0.0821673
$857$	−12.6383	+	12.6383i	−0.431715	+	0.431715i	−0.889211	−	0.457497i	$-0.848746\pi$
$857$	−12.6383	+	12.6383i	−0.431715	+	0.431715i	0.457497	+	0.889211i	$0.348746\pi$
$858$		0			0
$859$		−	22.6958i		−	0.774370i	−0.922002	−	0.387185i	$-0.873447\pi$
$859$		−	22.6958i		−	0.774370i	0.922002	−	0.387185i	$-0.126553\pi$
$860$	1.05910	−	2.95308i	0.0361149	−	0.100699i
$861$		0			0
$862$	−21.3034	−	21.3034i	−0.725596	−	0.725596i
$863$	1.43400	+	1.43400i	0.0488139	+	0.0488139i	0.731092	−	0.682278i	$-0.239011\pi$
$863$	1.43400	+	1.43400i	0.0488139	+	0.0488139i	−0.682278	+	0.731092i	$0.739011\pi$
$864$		0			0
$865$	1.33936	−	3.73456i	0.0455398	−	0.126979i
$866$			29.1522i			0.990630i
$867$		0			0
$868$	4.09146	−	4.09146i	0.138873	−	0.138873i
$869$	−40.1766			−1.36290
$870$		0			0
$871$	16.6160			0.563010
$872$	−10.4485	+	10.4485i	−0.353830	+	0.353830i
$873$		0			0
$874$			3.55970i			0.120408i
$875$	−22.8428	−	38.3035i	−0.772228	−	1.29489i
$876$		0			0
$877$	−14.9794	−	14.9794i	−0.505819	−	0.505819i	0.407422	−	0.913240i	$-0.366428\pi$
$877$	−14.9794	−	14.9794i	−0.505819	−	0.505819i	−0.913240	+	0.407422i	$0.866428\pi$
$878$	−13.8473	−	13.8473i	−0.467325	−	0.467325i
$879$		0			0
$880$	24.6789	−	11.6499i	0.831927	−	0.392719i
$881$		−	12.6725i		−	0.426946i	−0.976949	−	0.213473i	$-0.931522\pi$
$881$		−	12.6725i		−	0.426946i	0.976949	−	0.213473i	$-0.0684776\pi$
$882$		0			0
$883$	−14.4554	+	14.4554i	−0.486463	+	0.486463i	−0.907188	−	0.420725i	$-0.861776\pi$
$883$	−14.4554	+	14.4554i	−0.486463	+	0.486463i	0.420725	+	0.907188i	$0.361776\pi$
$884$	8.34094			0.280536
$885$		0			0
$886$	17.4876			0.587508
$887$	−0.892028	+	0.892028i	−0.0299514	+	0.0299514i	−0.721924	−	0.691972i	$-0.756742\pi$
$887$	−0.892028	+	0.892028i	−0.0299514	+	0.0299514i	0.691972	+	0.721924i	$0.256742\pi$
$888$		0			0
$889$			4.25574i			0.142733i
$890$	38.2305	+	13.7110i	1.28149	+	0.459593i
$891$		0			0
$892$	7.72636	+	7.72636i	0.258698	+	0.258698i
$893$	−25.9696	−	25.9696i	−0.869038	−	0.869038i
$894$		0			0
$895$	11.7813	+	24.9573i	0.393806	+	0.834229i
$896$			16.5242i			0.552034i
$897$		0			0
$898$	−28.2884	+	28.2884i	−0.943995	+	0.943995i
$899$	−5.93311			−0.197880
$900$		0			0
$901$	15.2119			0.506783
$902$	−36.4246	+	36.4246i	−1.21281	+	1.21281i
$903$		0			0
$904$		−	46.8995i		−	1.55986i
$905$	4.99830	+	10.5883i	0.166149	+	0.351967i
$906$		0			0
$907$	−38.8087	−	38.8087i	−1.28862	−	1.28862i	−0.935625	−	0.352996i	$-0.885163\pi$
$907$	−38.8087	−	38.8087i	−1.28862	−	1.28862i	−0.352996	−	0.935625i	$-0.614837\pi$
$908$	−9.01953	−	9.01953i	−0.299324	−	0.299324i
$909$		0			0
$910$	−30.9372	−	11.0953i	−1.02556	−	0.367807i
$911$			34.7663i			1.15186i	0.817500	+	0.575929i	$0.195360\pi$
$911$			34.7663i			1.15186i	−0.817500	+	0.575929i	$0.804640\pi$
$912$		0			0
$913$	21.0678	−	21.0678i	0.697243	−	0.697243i
$914$	18.5276			0.612838
$915$		0			0
$916$	15.6047			0.515592
$917$	21.8219	−	21.8219i	0.720624	−	0.720624i
$918$		0			0
$919$		−	57.0692i		−	1.88254i	−0.337657	−	0.941269i	$-0.609634\pi$
$919$		−	57.0692i		−	1.88254i	0.337657	−	0.941269i	$-0.390366\pi$
$920$	6.21659	−	2.93460i	0.204955	−	0.0967510i
$921$		0			0
$922$	29.0181	+	29.0181i	0.955661	+	0.955661i
$923$	0.400915	+	0.400915i	0.0131963	+	0.0131963i
$924$		0			0
$925$	−41.4740	+	4.02288i	−1.36366	+	0.132272i
$926$			10.8700i			0.357209i
$927$		0			0
$928$	−5.29692	+	5.29692i	−0.173880	+	0.173880i
$929$	−37.2688			−1.22275			−0.611375	−	0.791341i	$-0.709383\pi$
$929$	−37.2688			−1.22275			−0.611375	+	0.791341i	$0.709383\pi$
$930$		0			0
$931$	26.6140			0.872240
$932$	3.25888	−	3.25888i	0.106748	−	0.106748i
$933$		0			0
$934$		−	21.1723i		−	0.692780i
$935$	−17.1243	+	47.7478i	−0.560024	+	1.56152i
$936$		0			0
$937$	22.7594	+	22.7594i	0.743518	+	0.743518i	0.973253	−	0.229735i	$-0.0737859\pi$
$937$	22.7594	+	22.7594i	0.743518	+	0.743518i	−0.229735	+	0.973253i	$0.573786\pi$
$938$	−18.0705	−	18.0705i	−0.590022	−	0.590022i
$939$		0			0
$940$	−5.37730	+	14.9936i	−0.175388	+	0.489037i
$941$			25.8601i			0.843015i	0.906825	+	0.421507i	$0.138499\pi$
$941$			25.8601i			0.843015i	−0.906825	+	0.421507i	$0.861501\pi$
$942$		0			0
$943$	−6.27456	+	6.27456i	−0.204328	+	0.204328i
$944$	27.0559			0.880595
$945$		0			0
$946$	14.0607			0.457153
$947$	−32.3712	+	32.3712i	−1.05192	+	1.05192i	−0.0533459	+	0.998576i	$0.516989\pi$
$947$	−32.3712	+	32.3712i	−1.05192	+	1.05192i	−0.998576	+	0.0533459i	$0.983011\pi$
$948$		0			0
$949$		−	7.76924i		−	0.252200i
$950$	17.7153	−	1.71835i	0.574761	−	0.0557505i
$951$		0			0
$952$	−40.3909	−	40.3909i	−1.30908	−	1.30908i
$953$	−33.0775	−	33.0775i	−1.07149	−	1.07149i	−0.997240	−	0.0742457i	$-0.976345\pi$
$953$	−33.0775	−	33.0775i	−1.07149	−	1.07149i	−0.0742457	−	0.997240i	$-0.523655\pi$
$954$		0			0
$955$	29.4705	−	13.9118i	0.953642	−	0.450176i
$956$		−	7.86844i		−	0.254484i
$957$		0			0
$958$	26.0336	−	26.0336i	0.841109	−	0.841109i
$959$	17.0570			0.550799
$960$		0			0
$961$	−24.7291			−0.797711
$962$	−21.7139	+	21.7139i	−0.700085	+	0.700085i
$963$		0			0
$964$			15.3267i			0.493639i
$965$	3.81944	+	1.36981i	0.122952	+	0.0440956i
$966$		0			0
$967$	−9.25675	−	9.25675i	−0.297677	−	0.297677i	0.542426	−	0.840103i	$-0.317506\pi$
$967$	−9.25675	−	9.25675i	−0.297677	−	0.297677i	−0.840103	+	0.542426i	$0.817506\pi$
$968$	−27.6509	−	27.6509i	−0.888734	−	0.888734i
$969$		0			0
$970$	20.8263	+	44.1180i	0.668693	+	1.41654i
$971$			8.05440i			0.258478i	0.991613	+	0.129239i	$0.0412534\pi$
$971$			8.05440i			0.258478i	−0.991613	+	0.129239i	$0.958747\pi$
$972$		0			0
$973$	−1.74868	+	1.74868i	−0.0560600	+	0.0560600i
$974$	4.35729			0.139617
$975$		0			0
$976$	−19.3505			−0.619395
$977$	32.4523	−	32.4523i	1.03824	−	1.03824i	0.0390031	−	0.999239i	$-0.487582\pi$
$977$	32.4523	−	32.4523i	1.03824	−	1.03824i	0.999239	−	0.0390031i	$-0.0124182\pi$
$978$		0			0
$979$		−	74.2154i		−	2.37194i
$980$	−4.92746	−	10.4382i	−0.157402	−	0.333436i
$981$		0			0
$982$	16.4017	+	16.4017i	0.523399	+	0.523399i
$983$	−3.45263	−	3.45263i	−0.110122	−	0.110122i	0.649899	−	0.760021i	$-0.274811\pi$
$983$	−3.45263	−	3.45263i	−0.110122	−	0.110122i	−0.760021	+	0.649899i	$0.774811\pi$
$984$		0			0
$985$	35.3947	+	12.6940i	1.12777	+	0.404464i
$986$			13.1542i			0.418914i
$987$		0			0
$988$	−3.78151	+	3.78151i	−0.120306	+	0.120306i
$989$	2.42212			0.0770189
$990$		0			0
$991$	50.5335			1.60525			0.802624	−	0.596485i	$-0.203436\pi$
$991$	50.5335			1.60525			0.802624	+	0.596485i	$0.203436\pi$
$992$	5.59853	−	5.59853i	0.177754	−	0.177754i
$993$		0			0
$994$		−	0.872020i		−	0.0276588i
$995$	−5.08170	+	2.39887i	−0.161101	+	0.0760492i
$996$		0			0
$997$	11.6444	+	11.6444i	0.368782	+	0.368782i	0.867033	−	0.498251i	$-0.166024\pi$
$997$	11.6444	+	11.6444i	0.368782	+	0.368782i	−0.498251	+	0.867033i	$0.666024\pi$
$998$	24.2326	+	24.2326i	0.767071	+	0.767071i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1035.2.j.b.737.16	yes	44
3.2	odd	2	inner	1035.2.j.b.737.7	yes	44
5.3	odd	4	inner	1035.2.j.b.323.7	✓	44
15.8	even	4	inner	1035.2.j.b.323.16	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1035.2.j.b.323.7	✓	44	5.3	odd	4	inner
1035.2.j.b.323.16	yes	44	15.8	even	4	inner
1035.2.j.b.737.7	yes	44	3.2	odd	2	inner
1035.2.j.b.737.16	yes	44	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1035.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.842836 - 0.842836i) q^{2} +0.579255i q^{4} +(0.954547 + 2.02209i) q^{5} +(2.82060 + 2.82060i) q^{7} +(2.17389 + 2.17389i) q^{8} +O(q^{10})\)	\(q+(0.842836 - 0.842836i) q^{2} +0.579255i q^{4} +(0.954547 + 2.02209i) q^{5} +(2.82060 + 2.82060i) q^{7} +(2.17389 + 2.17389i) q^{8} +(2.50881 + 0.899762i) q^{10} -4.87027i q^{11} +(-2.18595 + 2.18595i) q^{13} +4.75461 q^{14} +2.50595 q^{16} +(-3.29363 + 3.29363i) q^{17} -2.98645i q^{19} +(-1.17130 + 0.552926i) q^{20} +(-4.10484 - 4.10484i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-3.17768 + 3.86035i) q^{25} +3.68480i q^{26} +(-1.63385 + 1.63385i) q^{28} +2.36928 q^{29} -2.50419 q^{31} +(-2.23567 + 2.23567i) q^{32} +5.55198i q^{34} +(-3.01111 + 8.39591i) q^{35} +(5.89284 + 5.89284i) q^{37} +(-2.51708 - 2.51708i) q^{38} +(-2.32072 + 6.47087i) q^{40} -8.87357i q^{41} +(-1.71270 + 1.71270i) q^{43} +2.82113 q^{44} -1.19195 q^{46} +(8.69581 - 8.69581i) q^{47} +8.91161i q^{49} +(0.575382 + 5.93191i) q^{50} +(-1.26622 - 1.26622i) q^{52} +(-2.30930 - 2.30930i) q^{53} +(9.84812 - 4.64890i) q^{55} +12.2634i q^{56} +(1.99691 - 1.99691i) q^{58} +10.7967 q^{59} -7.72182 q^{61} +(-2.11062 + 2.11062i) q^{62} +8.78051i q^{64} +(-6.50678 - 2.33359i) q^{65} +(-3.80062 - 3.80062i) q^{67} +(-1.90785 - 1.90785i) q^{68} +(4.53850 + 9.61425i) q^{70} -0.183405i q^{71} +(-1.77708 + 1.77708i) q^{73} +9.93339 q^{74} +1.72991 q^{76} +(13.7371 - 13.7371i) q^{77} -8.24935i q^{79} +(2.39205 + 5.06726i) q^{80} +(-7.47896 - 7.47896i) q^{82} +(4.32580 + 4.32580i) q^{83} +(-9.80393 - 3.51609i) q^{85} +2.88704i q^{86} +(10.5874 - 10.5874i) q^{88} +15.2385 q^{89} -12.3314 q^{91} +(0.409595 - 0.409595i) q^{92} -14.6583i q^{94} +(6.03886 - 2.85070i) q^{95} +(12.9432 + 12.9432i) q^{97} +(7.51103 + 7.51103i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{7}+O(q^{10}) \) 44 * q + 12 * q^7	\( 44 q + 12 q^{7} - 20 q^{10} + 4 q^{13} - 44 q^{16} + 16 q^{22} - 8 q^{25} + 40 q^{28} - 32 q^{31} + 56 q^{37} - 16 q^{40} + 72 q^{43} - 4 q^{46} + 76 q^{52} + 56 q^{55} - 12 q^{58} - 96 q^{61} + 12 q^{67} - 48 q^{70} + 68 q^{73} - 112 q^{76} + 52 q^{82} + 32 q^{85} + 56 q^{88} - 176 q^{91} + 76 q^{97}+O(q^{100}) \) 44 * q + 12 * q^7 - 20 * q^10 + 4 * q^13 - 44 * q^16 + 16 * q^22 - 8 * q^25 + 40 * q^28 - 32 * q^31 + 56 * q^37 - 16 * q^40 + 72 * q^43 - 4 * q^46 + 76 * q^52 + 56 * q^55 - 12 * q^58 - 96 * q^61 + 12 * q^67 - 48 * q^70 + 68 * q^73 - 112 * q^76 + 52 * q^82 + 32 * q^85 + 56 * q^88 - 176 * q^91 + 76 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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