LMFDB - Embedded newform 1008.2.v.e.323.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(323,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1008.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.v (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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.15
Character	$\chi$	$=$	1008.323
Dual form			1008.2.v.e.827.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.890883 + 1.09833i) q^{2} +(-0.412656 + 1.95697i) q^{4} +(1.65702 + 1.65702i) q^{5} +1.00000 q^{7} +(-2.51702 + 1.29019i) q^{8} +O(q^{10})$	\(q+(0.890883 + 1.09833i) q^{2} +(-0.412656 + 1.95697i) q^{4} +(1.65702 + 1.65702i) q^{5} +1.00000 q^{7} +(-2.51702 + 1.29019i) q^{8} +(-0.343745 + 3.29617i) q^{10} +(0.993222 - 0.993222i) q^{11} +(2.62686 + 2.62686i) q^{13} +(0.890883 + 1.09833i) q^{14} +(-3.65943 - 1.61511i) q^{16} +2.77728i q^{17} +(1.56309 - 1.56309i) q^{19} +(-3.92652 + 2.55895i) q^{20} +(1.97573 + 0.206041i) q^{22} +1.05272i q^{23} +0.491445i q^{25} +(-0.544935 + 5.22538i) q^{26} +(-0.412656 + 1.95697i) q^{28} +(-3.47823 + 3.47823i) q^{29} -1.06124i q^{31} +(-1.48620 - 5.45813i) q^{32} +(-3.05037 + 2.47423i) q^{34} +(1.65702 + 1.65702i) q^{35} +(-0.0657126 + 0.0657126i) q^{37} +(3.10933 + 0.324259i) q^{38} +(-6.30864 - 2.03288i) q^{40} -6.31313 q^{41} +(-2.38841 - 2.38841i) q^{43} +(1.53384 + 2.35356i) q^{44} +(-1.15623 + 0.937851i) q^{46} +1.47190 q^{47} +1.00000 q^{49} +(-0.539769 + 0.437820i) q^{50} +(-6.22466 + 4.05668i) q^{52} +(7.63807 + 7.63807i) q^{53} +3.29158 q^{55} +(-2.51702 + 1.29019i) q^{56} +(-6.91894 - 0.721549i) q^{58} +(4.15490 - 4.15490i) q^{59} +(-7.78123 - 7.78123i) q^{61} +(1.16560 - 0.945444i) q^{62} +(4.67080 - 6.49489i) q^{64} +8.70553i q^{65} +(1.98557 - 1.98557i) q^{67} +(-5.43504 - 1.14606i) q^{68} +(-0.343745 + 3.29617i) q^{70} +13.0855i q^{71} -9.50329i q^{73} +(-0.130716 - 0.0136319i) q^{74} +(2.41390 + 3.70394i) q^{76} +(0.993222 - 0.993222i) q^{77} -9.85051i q^{79} +(-3.38748 - 8.74003i) q^{80} +(-5.62425 - 6.93389i) q^{82} +(-1.13002 - 1.13002i) q^{83} +(-4.60202 + 4.60202i) q^{85} +(0.495468 - 4.75105i) q^{86} +(-1.21851 + 3.78141i) q^{88} -7.04453 q^{89} +(2.62686 + 2.62686i) q^{91} +(-2.06014 - 0.434412i) q^{92} +(1.31129 + 1.61663i) q^{94} +5.18016 q^{95} +5.35352 q^{97} +(0.890883 + 1.09833i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{7}+O(q^{10}) $ 40 * q + 40 * q^7	$ 40 q + 40 q^{7} + 48 q^{10} - 24 q^{13} + 12 q^{16} - 32 q^{19} - 8 q^{22} - 56 q^{34} - 8 q^{37} + 32 q^{43} - 52 q^{46} + 40 q^{49} - 8 q^{52} + 48 q^{55} + 56 q^{58} - 24 q^{61} + 48 q^{64} + 48 q^{70} - 24 q^{76} - 64 q^{82} + 64 q^{85} - 120 q^{88} - 24 q^{91} - 128 q^{94} + 64 q^{97}+O(q^{100}) $ 40 * q + 40 * q^7 + 48 * q^10 - 24 * q^13 + 12 * q^16 - 32 * q^19 - 8 * q^22 - 56 * q^34 - 8 * q^37 + 32 * q^43 - 52 * q^46 + 40 * q^49 - 8 * q^52 + 48 * q^55 + 56 * q^58 - 24 * q^61 + 48 * q^64 + 48 * q^70 - 24 * q^76 - 64 * q^82 + 64 * q^85 - 120 * q^88 - 24 * q^91 - 128 * q^94 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.890883	+	1.09833i	0.629949	+	0.776636i
$2$	0.890883	+	1.09833i	0.629949	+	0.776636i
$3$		0			0
$3$		0			0
$4$	−0.412656	+	1.95697i	−0.206328	+	0.978483i
$5$	1.65702	+	1.65702i	0.741043	+	0.741043i	0.972779	−	0.231736i	$-0.0744405\pi$
$5$	1.65702	+	1.65702i	0.741043	+	0.741043i	−0.231736	+	0.972779i	$0.574441\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.51702	+	1.29019i	−0.889902	+	0.456152i
$9$		0			0
$10$	−0.343745	+	3.29617i	−0.108702	+	1.04234i
$11$	0.993222	−	0.993222i	0.299468	−	0.299468i	−0.541338	−	0.840805i	$-0.682082\pi$
$11$	0.993222	−	0.993222i	0.299468	−	0.299468i	0.840805	+	0.541338i	$0.182082\pi$
$12$		0			0
$13$	2.62686	+	2.62686i	0.728560	+	0.728560i	0.970333	−	0.241773i	$-0.0777290\pi$
$13$	2.62686	+	2.62686i	0.728560	+	0.728560i	−0.241773	+	0.970333i	$0.577729\pi$
$14$	0.890883	+	1.09833i	0.238098	+	0.293541i
$15$		0			0
$16$	−3.65943	−	1.61511i	−0.914857	−	0.403777i
$17$			2.77728i			0.673589i	0.941578	+	0.336795i	$0.109343\pi$
$17$			2.77728i			0.673589i	−0.941578	+	0.336795i	$0.890657\pi$
$18$		0			0
$19$	1.56309	−	1.56309i	0.358598	−	0.358598i	−0.504698	−	0.863296i	$-0.668396\pi$
$19$	1.56309	−	1.56309i	0.358598	−	0.358598i	0.863296	+	0.504698i	$0.168396\pi$
$20$	−3.92652	+	2.55895i	−0.877996	+	0.572200i
$21$		0			0
$22$	1.97573	+	0.206041i	0.421227	+	0.0439281i
$23$			1.05272i			0.219507i	0.993959	+	0.109754i	$0.0350062\pi$
$23$			1.05272i			0.219507i	−0.993959	+	0.109754i	$0.964994\pi$
$24$		0			0
$25$			0.491445i			0.0982890i
$26$	−0.544935	+	5.22538i	−0.106870	+	1.02478i
$27$		0			0
$28$	−0.412656	+	1.95697i	−0.0779847	+	0.369832i
$29$	−3.47823	+	3.47823i	−0.645891	+	0.645891i	−0.951997	−	0.306106i	$-0.900974\pi$
$29$	−3.47823	+	3.47823i	−0.645891	+	0.645891i	0.306106	+	0.951997i	$0.400974\pi$
$30$		0			0
$31$		−	1.06124i		−	0.190605i	−0.995448	−	0.0953026i	$-0.969618\pi$
$31$		−	1.06124i		−	0.190605i	0.995448	−	0.0953026i	$-0.0303819\pi$
$32$	−1.48620	−	5.45813i	−0.262725	−	0.964871i
$33$		0			0
$34$	−3.05037	+	2.47423i	−0.523134	+	0.424327i
$35$	1.65702	+	1.65702i	0.280088	+	0.280088i
$36$		0			0
$37$	−0.0657126	+	0.0657126i	−0.0108031	+	0.0108031i	−0.712488	−	0.701685i	$-0.752432\pi$
$37$	−0.0657126	+	0.0657126i	−0.0108031	+	0.0108031i	0.701685	+	0.712488i	$0.252432\pi$
$38$	3.10933	+	0.324259i	0.504399	+	0.0526018i
$39$		0			0
$40$	−6.30864	−	2.03288i	−0.997484	−	0.321427i
$41$	−6.31313			−0.985945			−0.492972	−	0.870045i	$-0.664090\pi$
$41$	−6.31313			−0.985945			−0.492972	+	0.870045i	$0.664090\pi$
$42$		0			0
$43$	−2.38841	−	2.38841i	−0.364229	−	0.364229i	0.501138	−	0.865367i	$-0.332915\pi$
$43$	−2.38841	−	2.38841i	−0.364229	−	0.364229i	−0.865367	+	0.501138i	$0.832915\pi$
$44$	1.53384	+	2.35356i	0.231235	+	0.354813i
$45$		0			0
$46$	−1.15623	+	0.937851i	−0.170478	+	0.138279i
$47$	1.47190			0.214699			0.107349	−	0.994221i	$-0.465764\pi$
$47$	1.47190			0.214699			0.107349	+	0.994221i	$0.465764\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−0.539769	+	0.437820i	−0.0763348	+	0.0619171i
$51$		0			0
$52$	−6.22466	+	4.05668i	−0.863206	+	0.562561i
$53$	7.63807	+	7.63807i	1.04917	+	1.04917i	0.998727	+	0.0504431i	$0.0160634\pi$
$53$	7.63807	+	7.63807i	1.04917	+	1.04917i	0.0504431	+	0.998727i	$0.483937\pi$
$54$		0			0
$55$	3.29158			0.443837
$56$	−2.51702	+	1.29019i	−0.336351	+	0.172409i
$57$		0			0
$58$	−6.91894	−	0.721549i	−0.908501	−	0.0947440i
$59$	4.15490	−	4.15490i	0.540921	−	0.540921i	−0.382878	−	0.923799i	$-0.625067\pi$
$59$	4.15490	−	4.15490i	0.540921	−	0.540921i	0.923799	+	0.382878i	$0.125067\pi$
$60$		0			0
$61$	−7.78123	−	7.78123i	−0.996285	−	0.996285i	0.00370838	−	0.999993i	$-0.498820\pi$
$61$	−7.78123	−	7.78123i	−0.996285	−	0.996285i	−0.999993	+	0.00370838i	$0.998820\pi$
$62$	1.16560	−	0.945444i	0.148031	−	0.120072i
$63$		0			0
$64$	4.67080	−	6.49489i	0.583850	−	0.811862i
$65$			8.70553i			1.07979i
$66$		0			0
$67$	1.98557	−	1.98557i	0.242576	−	0.242576i	−0.575339	−	0.817915i	$-0.695130\pi$
$67$	1.98557	−	1.98557i	0.242576	−	0.242576i	0.817915	+	0.575339i	$0.195130\pi$
$68$	−5.43504	−	1.14606i	−0.659096	−	0.138981i
$69$		0			0
$70$	−0.343745	+	3.29617i	−0.0410853	+	0.393968i
$71$			13.0855i			1.55297i	0.630137	+	0.776484i	$0.282999\pi$
$71$			13.0855i			1.55297i	−0.630137	+	0.776484i	$0.717001\pi$
$72$		0			0
$73$		−	9.50329i		−	1.11228i	−0.831090	−	0.556138i	$-0.812283\pi$
$73$		−	9.50329i		−	1.11228i	0.831090	−	0.556138i	$-0.187717\pi$
$74$	−0.130716	−	0.0136319i	−0.0151955	−	0.00158468i
$75$		0			0
$76$	2.41390	+	3.70394i	0.276893	+	0.424871i
$77$	0.993222	−	0.993222i	0.113188	−	0.113188i
$78$		0			0
$79$		−	9.85051i		−	1.10827i	−0.832427	−	0.554134i	$-0.813049\pi$
$79$		−	9.85051i		−	1.10827i	0.832427	−	0.554134i	$-0.186951\pi$
$80$	−3.38748	−	8.74003i	−0.378732	−	0.977165i
$81$		0			0
$82$	−5.62425	−	6.93389i	−0.621095	−	0.765721i
$83$	−1.13002	−	1.13002i	−0.124036	−	0.124036i	0.642364	−	0.766400i	$-0.277954\pi$
$83$	−1.13002	−	1.13002i	−0.124036	−	0.124036i	−0.766400	+	0.642364i	$0.777954\pi$
$84$		0			0
$85$	−4.60202	+	4.60202i	−0.499159	+	0.499159i
$86$	0.495468	−	4.75105i	0.0534277	−	0.512319i
$87$		0			0
$88$	−1.21851	+	3.78141i	−0.129894	+	0.403100i
$89$	−7.04453			−0.746718			−0.373359	−	0.927687i	$-0.621794\pi$
$89$	−7.04453			−0.746718			−0.373359	+	0.927687i	$0.621794\pi$
$90$		0			0
$91$	2.62686	+	2.62686i	0.275370	+	0.275370i
$92$	−2.06014	−	0.434412i	−0.214784	−	0.0452906i
$93$		0			0
$94$	1.31129	+	1.61663i	0.135249	+	0.166743i
$95$	5.18016			0.531473
$96$		0			0
$97$	5.35352			0.543568			0.271784	−	0.962358i	$-0.412386\pi$
$97$	5.35352			0.543568			0.271784	+	0.962358i	$0.412386\pi$
$98$	0.890883	+	1.09833i	0.0899927	+	0.110948i
$99$		0			0
$100$	−0.961741	−	0.202798i	−0.0961741	−	0.0202798i
$101$	5.34591	+	5.34591i	0.531938	+	0.531938i	0.921149	−	0.389211i	$-0.127252\pi$
$101$	5.34591	+	5.34591i	0.531938	+	0.531938i	−0.389211	+	0.921149i	$0.627252\pi$
$102$		0			0
$103$	3.41355			0.336347			0.168173	−	0.985757i	$-0.446213\pi$
$103$	3.41355			0.336347			0.168173	+	0.985757i	$0.446213\pi$
$104$	−10.0010	−	3.22271i	−0.980681	−	0.316012i
$105$		0			0
$106$	−1.58450	+	15.1937i	−0.153900	+	1.47575i
$107$	10.7004	−	10.7004i	1.03445	−	1.03445i	0.0350640	−	0.999385i	$-0.488836\pi$
$107$	10.7004	−	10.7004i	1.03445	−	1.03445i	0.999385	−	0.0350640i	$-0.0111635\pi$
$108$		0			0
$109$	−5.36354	−	5.36354i	−0.513734	−	0.513734i	0.401934	−	0.915668i	$-0.368338\pi$
$109$	−5.36354	−	5.36354i	−0.513734	−	0.513734i	−0.915668	+	0.401934i	$0.868338\pi$
$110$	2.93241	+	3.61524i	0.279595	+	0.344700i
$111$		0			0
$112$	−3.65943	−	1.61511i	−0.345784	−	0.152613i
$113$			18.2463i			1.71647i	0.513256	+	0.858236i	$0.328439\pi$
$113$			18.2463i			1.71647i	−0.513256	+	0.858236i	$0.671561\pi$
$114$		0			0
$115$	−1.74438	+	1.74438i	−0.162664	+	0.162664i
$116$	−5.37146	−	8.24209i	−0.498728	−	0.765259i
$117$		0			0
$118$	8.26497	+	0.861922i	0.760852	+	0.0793463i
$119$			2.77728i			0.254593i
$120$		0			0
$121$			9.02702i			0.820638i
$122$	1.61419	−	15.4785i	0.146142	−	1.40136i
$123$		0			0
$124$	2.07682	+	0.437930i	0.186504	+	0.0393272i
$125$	7.47078	−	7.47078i	0.668206	−	0.668206i
$126$		0			0
$127$		−	0.0998053i		−	0.00885629i	−0.999990	−	0.00442814i	$-0.998590\pi$
$127$		−	0.0998053i		−	0.00885629i	0.999990	−	0.00442814i	$-0.00140953\pi$
$128$	11.2947	−	0.656108i	0.998317	−	0.0579923i
$129$		0			0
$130$	−9.56154	+	7.75560i	−0.838603	+	0.680211i
$131$	−12.8436	−	12.8436i	−1.12215	−	1.12215i	−0.991417	−	0.130734i	$-0.958266\pi$
$131$	−12.8436	−	12.8436i	−1.12215	−	1.12215i	−0.130734	−	0.991417i	$-0.541734\pi$
$132$		0			0
$133$	1.56309	−	1.56309i	0.135537	−	0.135537i
$134$	3.94972	+	0.411901i	0.341204	+	0.0355828i
$135$		0			0
$136$	−3.58323	−	6.99048i	−0.307259	−	0.599428i
$137$	3.10918			0.265635			0.132817	−	0.991141i	$-0.457598\pi$
$137$	3.10918			0.265635			0.132817	+	0.991141i	$0.457598\pi$
$138$		0			0
$139$	10.5794	+	10.5794i	0.897330	+	0.897330i	0.995199	−	0.0978696i	$-0.0312028\pi$
$139$	10.5794	+	10.5794i	0.897330	+	0.897330i	−0.0978696	+	0.995199i	$0.531203\pi$
$140$	−3.92652	+	2.55895i	−0.331851	+	0.216271i
$141$		0			0
$142$	−14.3722	+	11.6577i	−1.20609	+	0.978291i
$143$	5.21811			0.436360
$144$		0			0
$145$	−11.5270			−0.957266
$146$	10.4377	−	8.46631i	0.863834	−	0.700677i
$147$		0			0
$148$	−0.101481	−	0.155714i	−0.00834166	−	0.0127996i
$149$	6.32230	+	6.32230i	0.517943	+	0.517943i	0.916948	−	0.399006i	$-0.130645\pi$
$149$	6.32230	+	6.32230i	0.517943	+	0.517943i	−0.399006	+	0.916948i	$0.630645\pi$
$150$		0			0
$151$	22.9393			1.86677			0.933385	−	0.358877i	$-0.116840\pi$
$151$	22.9393			1.86677			0.933385	+	0.358877i	$0.116840\pi$
$152$	−1.91765	+	5.95104i	−0.155542	+	0.482693i
$153$		0			0
$154$	1.97573	+	0.206041i	0.159209	+	0.0166033i
$155$	1.75851	−	1.75851i	0.141247	−	0.141247i
$156$		0			0
$157$	−12.7269	−	12.7269i	−1.01571	−	1.01571i	−0.999875	−	0.0158402i	$-0.994958\pi$
$157$	−12.7269	−	12.7269i	−1.01571	−	1.01571i	−0.0158402	−	0.999875i	$-0.505042\pi$
$158$	10.8191	−	8.77564i	0.860722	−	0.698153i
$159$		0			0
$160$	6.58158	−	11.5069i	0.520320	−	0.909701i
$161$			1.05272i			0.0829660i
$162$		0			0
$163$	5.66445	−	5.66445i	0.443674	−	0.443674i	−0.449571	−	0.893245i	$-0.648423\pi$
$163$	5.66445	−	5.66445i	0.443674	−	0.443674i	0.893245	+	0.449571i	$0.148423\pi$
$164$	2.60515	−	12.3546i	0.203428	−	0.964730i
$165$		0			0
$166$	0.234420	−	2.24785i	0.0181945	−	0.174467i
$167$		−	20.3445i		−	1.57431i	−0.616756	−	0.787154i	$-0.711554\pi$
$167$		−	20.3445i		−	1.57431i	0.616756	−	0.787154i	$-0.288446\pi$
$168$		0			0
$169$			0.800782i			0.0615986i
$170$	−9.15439	−	0.954675i	−0.702109	−	0.0732202i
$171$		0			0
$172$	5.65962	−	3.68844i	0.431542	−	0.281241i
$173$	3.94764	−	3.94764i	0.300133	−	0.300133i	−0.540933	−	0.841066i	$-0.681929\pi$
$173$	3.94764	−	3.94764i	0.300133	−	0.300133i	0.841066	+	0.540933i	$0.181929\pi$
$174$		0			0
$175$			0.491445i			0.0371497i
$176$	−5.23879	+	2.03046i	−0.394888	+	0.153052i
$177$		0			0
$178$	−6.27585	−	7.73721i	−0.470395	−	0.579929i
$179$	−12.5761	−	12.5761i	−0.939982	−	0.939982i	0.0583166	−	0.998298i	$-0.481427\pi$
$179$	−12.5761	−	12.5761i	−0.939982	−	0.939982i	−0.998298	+	0.0583166i	$0.981427\pi$
$180$		0			0
$181$	16.0136	−	16.0136i	1.19028	−	1.19028i	0.213295	−	0.976988i	$-0.431580\pi$
$181$	16.0136	−	16.0136i	1.19028	−	1.19028i	0.976988	−	0.213295i	$-0.0684196\pi$
$182$	−0.544935	+	5.22538i	−0.0403932	+	0.387331i
$183$		0			0
$184$	−1.35821	−	2.64972i	−0.100129	−	0.195340i
$185$	−0.217775			−0.0160111
$186$		0			0
$187$	2.75846	+	2.75846i	0.201718	+	0.201718i
$188$	−0.607389	+	2.88046i	−0.0442984	+	0.210079i
$189$		0			0
$190$	4.61492	+	5.68953i	0.334801	+	0.412762i
$191$	11.8336			0.856251			0.428126	−	0.903719i	$-0.359174\pi$
$191$	11.8336			0.856251			0.428126	+	0.903719i	$0.359174\pi$
$192$		0			0
$193$	21.1021			1.51896			0.759481	−	0.650529i	$-0.225453\pi$
$193$	21.1021			1.51896			0.759481	+	0.650529i	$0.225453\pi$
$194$	4.76936	+	5.87994i	0.342420	+	0.422155i
$195$		0			0
$196$	−0.412656	+	1.95697i	−0.0294755	+	0.139783i
$197$	−5.83308	−	5.83308i	−0.415590	−	0.415590i	0.468091	−	0.883680i	$-0.344942\pi$
$197$	−5.83308	−	5.83308i	−0.415590	−	0.415590i	−0.883680	+	0.468091i	$0.844942\pi$
$198$		0			0
$199$	23.2865			1.65074			0.825369	−	0.564594i	$-0.190967\pi$
$199$	23.2865			1.65074			0.825369	+	0.564594i	$0.190967\pi$
$200$	−0.634059	−	1.23698i	−0.0448348	−	0.0874675i
$201$		0			0
$202$	−1.10899	+	10.6342i	−0.0780286	+	0.748217i
$203$	−3.47823	+	3.47823i	−0.244124	+	0.244124i
$204$		0			0
$205$	−10.4610	−	10.4610i	−0.730627	−	0.730627i
$206$	3.04107	+	3.74920i	0.211881	+	0.261219i
$207$		0			0
$208$	−5.37014	−	13.8555i	−0.372352	−	0.960704i
$209$		−	3.10500i		−	0.214777i
$210$		0			0
$211$	−16.2720	+	16.2720i	−1.12021	+	1.12021i	−0.128501	+	0.991709i	$0.541017\pi$
$211$	−16.2720	+	16.2720i	−1.12021	+	1.12021i	−0.991709	+	0.128501i	$0.958983\pi$
$212$	−18.0993	+	11.7955i	−1.24307	+	0.810121i
$213$		0			0
$214$	21.2854	+	2.21977i	1.45504	+	0.151741i
$215$		−	7.91529i		−	0.539818i
$216$		0			0
$217$		−	1.06124i		−	0.0720420i
$218$	1.11265	−	10.6692i	0.0753583	−	0.722611i
$219$		0			0
$220$	−1.35829	+	6.44151i	−0.0915761	+	0.434287i
$221$	−7.29553	+	7.29553i	−0.490750	+	0.490750i
$222$		0			0
$223$		−	22.8221i		−	1.52828i	−0.645051	−	0.764139i	$-0.723164\pi$
$223$		−	22.8221i		−	1.52828i	0.645051	−	0.764139i	$-0.276836\pi$
$224$	−1.48620	−	5.45813i	−0.0993009	−	0.364687i
$225$		0			0
$226$	−20.0405	+	16.2553i	−1.33307	+	1.08129i
$227$	−6.09419	−	6.09419i	−0.404486	−	0.404486i	0.475325	−	0.879810i	$-0.342331\pi$
$227$	−6.09419	−	6.09419i	−0.404486	−	0.404486i	−0.879810	+	0.475325i	$0.842331\pi$
$228$		0			0
$229$	−8.57148	+	8.57148i	−0.566420	+	0.566420i	−0.931124	−	0.364704i	$-0.881170\pi$
$229$	−8.57148	+	8.57148i	−0.566420	+	0.566420i	0.364704	+	0.931124i	$0.381170\pi$
$230$	−3.46995	−	0.361867i	−0.228801	−	0.0238608i
$231$		0			0
$232$	4.26719	−	13.2424i	0.280155	−	0.869404i
$233$	−4.90649			−0.321435			−0.160717	−	0.987000i	$-0.551381\pi$
$233$	−4.90649			−0.321435			−0.160717	+	0.987000i	$0.551381\pi$
$234$		0			0
$235$	2.43897	+	2.43897i	0.159101	+	0.159101i
$236$	6.41644	+	9.84553i	0.417675	+	0.640890i
$237$		0			0
$238$	−3.05037	+	2.47423i	−0.197726	+	0.160381i
$239$	−11.1659			−0.722260			−0.361130	−	0.932515i	$-0.617609\pi$
$239$	−11.1659			−0.722260			−0.361130	+	0.932515i	$0.617609\pi$
$240$		0			0
$241$	−17.8083			−1.14713			−0.573566	−	0.819159i	$-0.694440\pi$
$241$	−17.8083			−1.14713			−0.573566	+	0.819159i	$0.694440\pi$
$242$	−9.91464	+	8.04202i	−0.637338	+	0.516960i
$243$		0			0
$244$	18.4386	−	12.0166i	1.18041	−	0.769286i
$245$	1.65702	+	1.65702i	0.105863	+	0.105863i
$246$		0			0
$247$	8.21206			0.522521
$248$	1.36921	+	2.67118i	0.0869450	+	0.169620i
$249$		0			0
$250$	14.8610	+	1.54979i	0.939890	+	0.0980174i
$251$	10.7431	−	10.7431i	0.678099	−	0.678099i	−0.281471	−	0.959570i	$-0.590822\pi$
$251$	10.7431	−	10.7431i	0.678099	−	0.678099i	0.959570	+	0.281471i	$0.0908222\pi$
$252$		0			0
$253$	1.04559	+	1.04559i	0.0657354	+	0.0657354i
$254$	0.109619	−	0.0889148i	0.00687811	−	0.00557901i
$255$		0			0
$256$	10.7828	+	11.8208i	0.673928	+	0.738797i
$257$			1.20282i			0.0750300i	0.999296	+	0.0375150i	$0.0119442\pi$
$257$			1.20282i			0.0750300i	−0.999296	+	0.0375150i	$0.988056\pi$
$258$		0			0
$259$	−0.0657126	+	0.0657126i	−0.00408318	+	0.00408318i
$260$	−17.0364	−	3.59239i	−1.05655	−	0.222791i
$261$		0			0
$262$	2.66437	−	25.5487i	0.164605	−	1.57840i
$263$			14.9654i			0.922803i	0.887191	+	0.461402i	$0.152653\pi$
$263$			14.9654i			0.922803i	−0.887191	+	0.461402i	$0.847347\pi$
$264$		0			0
$265$			25.3129i			1.55496i
$266$	3.10933	+	0.324259i	0.190645	+	0.0198816i
$267$		0			0
$268$	3.06634	+	4.70505i	0.187306	+	0.287407i
$269$	6.58780	−	6.58780i	0.401665	−	0.401665i	−0.477154	−	0.878819i	$-0.658332\pi$
$269$	6.58780	−	6.58780i	0.401665	−	0.401665i	0.878819	+	0.477154i	$0.158332\pi$
$270$		0			0
$271$			27.1436i			1.64886i	0.565965	+	0.824429i	$0.308504\pi$
$271$			27.1436i			1.64886i	−0.565965	+	0.824429i	$0.691496\pi$
$272$	4.48561	−	10.1633i	0.271980	−	0.616238i
$273$		0			0
$274$	2.76991	+	3.41490i	0.167336	+	0.206302i
$275$	0.488114	+	0.488114i	0.0294344	+	0.0294344i
$276$		0			0
$277$	12.0118	−	12.0118i	0.721720	−	0.721720i	−0.247235	−	0.968955i	$-0.579522\pi$
$277$	12.0118	−	12.0118i	0.721720	−	0.721720i	0.968955	+	0.247235i	$0.0795221\pi$
$278$	−2.19466	+	21.0446i	−0.131627	+	1.26217i
$279$		0			0
$280$	−6.30864	−	2.03288i	−0.377013	−	0.121488i
$281$	−8.46830			−0.505176			−0.252588	−	0.967574i	$-0.581282\pi$
$281$	−8.46830			−0.505176			−0.252588	+	0.967574i	$0.581282\pi$
$282$		0			0
$283$	8.77919	+	8.77919i	0.521868	+	0.521868i	0.918135	−	0.396267i	$-0.129695\pi$
$283$	8.77919	+	8.77919i	0.521868	+	0.521868i	−0.396267	+	0.918135i	$0.629695\pi$
$284$	−25.6080	−	5.39984i	−1.51955	−	0.320421i
$285$		0			0
$286$	4.64872	+	5.73120i	0.274885	+	0.338893i
$287$	−6.31313			−0.372652
$288$		0			0
$289$	9.28671			0.546277
$290$	−10.2692	−	12.6605i	−0.603029	−	0.743447i
$291$		0			0
$292$	18.5976	+	3.92159i	1.08834	+	0.229494i
$293$	−9.25965	−	9.25965i	−0.540955	−	0.540955i	0.382854	−	0.923809i	$-0.374941\pi$
$293$	−9.25965	−	9.25965i	−0.540955	−	0.540955i	−0.923809	+	0.382854i	$0.874941\pi$
$294$		0			0
$295$	13.7695			0.801692
$296$	0.0806181	−	0.250182i	0.00468583	−	0.0145415i
$297$		0			0
$298$	−1.31154	+	12.5764i	−0.0759756	+	0.728531i
$299$	−2.76535	+	2.76535i	−0.159924	+	0.159924i
$300$		0			0
$301$	−2.38841	−	2.38841i	−0.137665	−	0.137665i
$302$	20.4362	+	25.1949i	1.17597	+	1.44980i
$303$		0			0
$304$	−8.24460	+	3.19546i	−0.472860	+	0.183272i
$305$		−	25.7873i		−	1.47658i
$306$		0			0
$307$	−9.60065	+	9.60065i	−0.547938	+	0.547938i	−0.925844	−	0.377906i	$-0.876644\pi$
$307$	−9.60065	+	9.60065i	−0.547938	+	0.547938i	0.377906	+	0.925844i	$0.376644\pi$
$308$	1.53384	+	2.35356i	0.0873987	+	0.134107i
$309$		0			0
$310$	3.49804	+	0.364797i	0.198675	+	0.0207191i
$311$		−	23.1840i		−	1.31464i	−0.753611	−	0.657321i	$-0.771690\pi$
$311$		−	23.1840i		−	1.31464i	0.753611	−	0.657321i	$-0.228310\pi$
$312$		0			0
$313$			27.9361i			1.57904i	0.613723	+	0.789522i	$0.289671\pi$
$313$			27.9361i			1.57904i	−0.613723	+	0.789522i	$0.710329\pi$
$314$	2.64015	−	25.3164i	0.148992	−	1.42869i
$315$		0			0
$316$	19.2771	+	4.06488i	1.08442	+	0.228667i
$317$	−21.5910	+	21.5910i	−1.21267	+	1.21267i	−0.242529	+	0.970144i	$0.577977\pi$
$317$	−21.5910	+	21.5910i	−1.21267	+	1.21267i	−0.970144	+	0.242529i	$0.922023\pi$
$318$		0			0
$319$			6.90931i			0.386847i
$320$	18.5018	−	3.02256i	1.03428	−	0.168966i
$321$		0			0
$322$	−1.15623	+	0.937851i	−0.0644344	+	0.0522644i
$323$	4.34115	+	4.34115i	0.241548	+	0.241548i
$324$		0			0
$325$	−1.29096	+	1.29096i	−0.0716094	+	0.0716094i
$326$	11.2678	+	1.17507i	0.624065	+	0.0650813i
$327$		0			0
$328$	15.8903	−	8.14516i	0.877394	−	0.449741i
$329$	1.47190			0.0811485
$330$		0			0
$331$	−18.4892	−	18.4892i	−1.01626	−	1.01626i	−0.999866	−	0.0163917i	$-0.994782\pi$
$331$	−18.4892	−	18.4892i	−1.01626	−	1.01626i	−0.0163917	−	0.999866i	$-0.505218\pi$
$332$	2.67772	−	1.74510i	0.146959	−	0.0957749i
$333$		0			0
$334$	22.3450	−	18.1246i	1.22267	−	0.991734i
$335$	6.58027			0.359519
$336$		0			0
$337$	−8.58189			−0.467486			−0.233743	−	0.972298i	$-0.575097\pi$
$337$	−8.58189			−0.467486			−0.233743	+	0.972298i	$0.575097\pi$
$338$	−0.879523	+	0.713403i	−0.0478397	+	0.0388040i
$339$		0			0
$340$	−7.10694	−	10.9050i	−0.385428	−	0.591409i
$341$	−1.05405	−	1.05405i	−0.0570801	−	0.0570801i
$342$		0			0
$343$	1.00000			0.0539949
$344$	9.09318	+	2.93017i	0.490271	+	0.157984i
$345$		0			0
$346$	7.85268	+	0.818926i	0.422163	+	0.0440257i
$347$	−19.6238	+	19.6238i	−1.05346	+	1.05346i	−0.0549718	+	0.998488i	$0.517507\pi$
$347$	−19.6238	+	19.6238i	−1.05346	+	1.05346i	−0.998488	+	0.0549718i	$0.982493\pi$
$348$		0			0
$349$	7.67820	+	7.67820i	0.411004	+	0.411004i	0.882088	−	0.471084i	$-0.156137\pi$
$349$	7.67820	+	7.67820i	0.411004	+	0.411004i	−0.471084	+	0.882088i	$0.656137\pi$
$350$	−0.539769	+	0.437820i	−0.0288518	+	0.0234024i
$351$		0			0
$352$	−6.89726	−	3.94501i	−0.367625	−	0.210270i
$353$			25.9405i			1.38067i	0.723489	+	0.690336i	$0.242537\pi$
$353$			25.9405i			1.38067i	−0.723489	+	0.690336i	$0.757463\pi$
$354$		0			0
$355$	−21.6830	+	21.6830i	−1.15082	+	1.15082i
$356$	2.90697	−	13.7859i	0.154069	−	0.730651i
$357$		0			0
$358$	2.60888	−	25.0165i	0.137883	−	1.32216i
$359$		−	3.08367i		−	0.162750i	−0.996684	−	0.0813750i	$-0.974069\pi$
$359$		−	3.08367i		−	0.162750i	0.996684	−	0.0813750i	$-0.0259312\pi$
$360$		0			0
$361$			14.1135i			0.742814i
$362$	31.8545	+	3.32198i	1.67423	+	0.174599i
$363$		0			0
$364$	−6.22466	+	4.05668i	−0.326261	+	0.212628i
$365$	15.7472	−	15.7472i	0.824244	−	0.824244i
$366$		0			0
$367$		−	18.1386i		−	0.946825i	−0.880841	−	0.473412i	$-0.843022\pi$
$367$		−	18.1386i		−	0.946825i	0.880841	−	0.473412i	$-0.156978\pi$
$368$	1.70026	−	3.85236i	0.0886321	−	0.200818i
$369$		0			0
$370$	−0.194012	−	0.239188i	−0.0100862	−	0.0124348i
$371$	7.63807	+	7.63807i	0.396549	+	0.396549i
$372$		0			0
$373$	−1.70711	+	1.70711i	−0.0883908	+	0.0883908i	−0.749920	−	0.661529i	$-0.769908\pi$
$373$	−1.70711	+	1.70711i	−0.0883908	+	0.0883908i	0.661529	+	0.749920i	$0.269908\pi$
$374$	−0.572234	+	5.48716i	−0.0295895	+	0.283734i
$375$		0			0
$376$	−3.70481	+	1.89904i	−0.191061	+	0.0979354i
$377$	−18.2736			−0.941140
$378$		0			0
$379$	−24.2888	−	24.2888i	−1.24763	−	1.24763i	−0.956762	−	0.290870i	$-0.906055\pi$
$379$	−24.2888	−	24.2888i	−1.24763	−	1.24763i	−0.290870	−	0.956762i	$-0.593945\pi$
$380$	−2.13763	+	10.1374i	−0.109658	+	0.520038i
$381$		0			0
$382$	10.5424	+	12.9972i	0.539395	+	0.664996i
$383$	10.2655			0.524544			0.262272	−	0.964994i	$-0.415528\pi$
$383$	10.2655			0.524544			0.262272	+	0.964994i	$0.415528\pi$
$384$		0			0
$385$	3.29158			0.167755
$386$	18.7995	+	23.1771i	0.956869	+	1.17968i
$387$		0			0
$388$	−2.20917	+	10.4767i	−0.112153	+	0.531872i
$389$	−0.924351	−	0.924351i	−0.0468664	−	0.0468664i	0.683285	−	0.730152i	$-0.260551\pi$
$389$	−0.924351	−	0.924351i	−0.0468664	−	0.0468664i	−0.730152	+	0.683285i	$0.760551\pi$
$390$		0			0
$391$	−2.92370			−0.147858
$392$	−2.51702	+	1.29019i	−0.127129	+	0.0651646i
$393$		0			0
$394$	1.21006	−	11.6032i	0.0609617	−	0.584562i
$395$	16.3225	−	16.3225i	0.821275	−	0.821275i
$396$		0			0
$397$	−18.2727	−	18.2727i	−0.917080	−	0.917080i	0.0797361	−	0.996816i	$-0.474592\pi$
$397$	−18.2727	−	18.2727i	−0.917080	−	0.917080i	−0.996816	+	0.0797361i	$0.974592\pi$
$398$	20.7455	+	25.5763i	1.03988	+	1.28202i
$399$		0			0
$400$	0.793737	−	1.79841i	0.0396869	−	0.0899204i
$401$			36.9686i			1.84612i	0.384651	+	0.923062i	$0.374322\pi$
$401$			36.9686i			1.84612i	−0.384651	+	0.923062i	$0.625678\pi$
$402$		0			0
$403$	2.78774	−	2.78774i	0.138867	−	0.138867i
$404$	−12.6678	+	8.25574i	−0.630246	+	0.410739i
$405$		0			0
$406$	−6.91894	−	0.721549i	−0.343381	−	0.0358099i
$407$			0.130534i			0.00647035i
$408$		0			0
$409$			4.66305i			0.230573i	0.993332	+	0.115286i	$0.0367786\pi$
$409$			4.66305i			0.230573i	−0.993332	+	0.115286i	$0.963221\pi$
$410$	2.17010	−	20.8091i	0.107174	−	1.02769i
$411$		0			0
$412$	−1.40862	+	6.68019i	−0.0693978	+	0.329109i
$413$	4.15490	−	4.15490i	0.204449	−	0.204449i
$414$		0			0
$415$		−	3.74494i		−	0.183832i
$416$	10.4337	−	18.2418i	0.511555	−	0.894377i
$417$		0			0
$418$	3.41031	−	2.76619i	0.166804	−	0.135299i
$419$	−20.9392	−	20.9392i	−1.02294	−	1.02294i	−0.999731	−	0.0232142i	$-0.992610\pi$
$419$	−20.9392	−	20.9392i	−1.02294	−	1.02294i	−0.0232142	−	0.999731i	$-0.507390\pi$
$420$		0			0
$421$	−18.0980	+	18.0980i	−0.882042	+	0.882042i	−0.993742	−	0.111700i	$-0.964370\pi$
$421$	−18.0980	+	18.0980i	−0.882042	+	0.882042i	0.111700	+	0.993742i	$0.464370\pi$
$422$	−32.3685	−	3.37558i	−1.57567	−	0.164321i
$423$		0			0
$424$	−29.0798	−	9.37060i	−1.41224	−	0.455077i
$425$	−1.36488			−0.0662064
$426$		0			0
$427$	−7.78123	−	7.78123i	−0.376560	−	0.376560i
$428$	16.5248	+	25.3560i	0.798755	+	1.22563i
$429$		0			0
$430$	8.69359	−	7.05159i	0.419242	−	0.340058i
$431$	30.3329			1.46108			0.730541	−	0.682868i	$-0.239268\pi$
$431$	30.3329			1.46108			0.730541	+	0.682868i	$0.239268\pi$
$432$		0			0
$433$	−25.8726			−1.24336			−0.621679	−	0.783272i	$-0.713549\pi$
$433$	−25.8726			−1.24336			−0.621679	+	0.783272i	$0.713549\pi$
$434$	1.16560	−	0.945444i	0.0559504	−	0.0453828i
$435$		0			0
$436$	12.7096	−	8.28297i	0.608678	−	0.396682i
$437$	1.64550	+	1.64550i	0.0787150	+	0.0787150i
$438$		0			0
$439$	−18.1840			−0.867874			−0.433937	−	0.900943i	$-0.642876\pi$
$439$	−18.1840			−0.867874			−0.433937	+	0.900943i	$0.642876\pi$
$440$	−8.28498	+	4.24678i	−0.394971	+	0.202457i
$441$		0			0
$442$	−14.5124	−	1.51344i	−0.690282	−	0.0719868i
$443$	−0.0172574	+	0.0172574i	−0.000819922	+	0.000819922i	−0.707517	−	0.706697i	$-0.750185\pi$
$443$	−0.0172574	+	0.0172574i	−0.000819922	+	0.000819922i	0.706697	+	0.707517i	$0.250185\pi$
$444$		0			0
$445$	−11.6729	−	11.6729i	−0.553350	−	0.553350i
$446$	25.0662	−	20.3318i	1.18692	−	0.962738i
$447$		0			0
$448$	4.67080	−	6.49489i	0.220675	−	0.306855i
$449$		−	8.83335i		−	0.416872i	−0.978036	−	0.208436i	$-0.933163\pi$
$449$		−	8.83335i		−	0.416872i	0.978036	−	0.208436i	$-0.0668372\pi$
$450$		0			0
$451$	−6.27034	+	6.27034i	−0.295259	+	0.295259i
$452$	−35.7075	−	7.52947i	−1.67954	−	0.354156i
$453$		0			0
$454$	1.26422	−	12.1226i	0.0593329	−	0.568944i
$455$			8.70553i			0.408121i
$456$		0			0
$457$			3.53330i			0.165281i	0.996579	+	0.0826404i	$0.0263353\pi$
$457$			3.53330i			0.165281i	−0.996579	+	0.0826404i	$0.973665\pi$
$458$	−17.0505	−	1.77813i	−0.796718	−	0.0830866i
$459$		0			0
$460$	−2.69387	−	4.13353i	−0.125602	−	0.192727i
$461$	13.9587	−	13.9587i	0.650123	−	0.650123i	−0.302900	−	0.953022i	$-0.597955\pi$
$461$	13.9587	−	13.9587i	0.650123	−	0.650123i	0.953022	+	0.302900i	$0.0979547\pi$
$462$		0			0
$463$			10.6448i			0.494705i	0.968926	+	0.247353i	$0.0795606\pi$
$463$			10.6448i			0.494705i	−0.968926	+	0.247353i	$0.920439\pi$
$464$	18.3461	−	7.11061i	0.851694	−	0.330102i
$465$		0			0
$466$	−4.37111	−	5.38895i	−0.202488	−	0.249638i
$467$	−12.4545	−	12.4545i	−0.576325	−	0.576325i	0.357564	−	0.933889i	$-0.383607\pi$
$467$	−12.4545	−	12.4545i	−0.576325	−	0.576325i	−0.933889	+	0.357564i	$0.883607\pi$
$468$		0			0
$469$	1.98557	−	1.98557i	0.0916852	−	0.0916852i
$470$	−0.505958	+	4.85163i	−0.0233381	+	0.223789i
$471$		0			0
$472$	−5.09734	+	15.8186i	−0.234624	+	0.728110i
$473$	−4.74444			−0.218149
$474$		0			0
$475$	0.768175	+	0.768175i	0.0352463	+	0.0352463i
$476$	−5.43504	−	1.14606i	−0.249115	−	0.0525297i
$477$		0			0
$478$	−9.94748	−	12.2638i	−0.454987	−	0.560933i
$479$	−22.0204			−1.00614			−0.503068	−	0.864247i	$-0.667795\pi$
$479$	−22.0204			−1.00614			−0.503068	+	0.864247i	$0.667795\pi$
$480$		0			0
$481$	−0.345236			−0.0157414
$482$	−15.8651	−	19.5594i	−0.722635	−	0.890905i
$483$		0			0
$484$	−17.6656	−	3.72506i	−0.802980	−	0.169321i
$485$	8.87091	+	8.87091i	0.402807	+	0.402807i
$486$		0			0
$487$	−23.2822			−1.05502			−0.527509	−	0.849549i	$-0.676874\pi$
$487$	−23.2822			−1.05502			−0.527509	+	0.849549i	$0.676874\pi$
$488$	29.6248	+	9.54624i	1.34105	+	0.432138i
$489$		0			0
$490$	−0.343745	+	3.29617i	−0.0155288	+	0.148906i
$491$	0.129520	−	0.129520i	0.00584515	−	0.00584515i	−0.704178	−	0.710023i	$-0.748684\pi$
$491$	0.129520	−	0.129520i	0.00584515	−	0.00584515i	0.710023	+	0.704178i	$0.248684\pi$
$492$		0			0
$493$	−9.66002	−	9.66002i	−0.435065	−	0.435065i
$494$	7.31598	+	9.01955i	0.329161	+	0.405809i
$495$		0			0
$496$	−1.71403	+	3.88355i	−0.0769620	+	0.174377i
$497$			13.0855i			0.586967i
$498$		0			0
$499$	−10.7818	+	10.7818i	−0.482661	+	0.482661i	−0.905980	−	0.423319i	$-0.860865\pi$
$499$	−10.7818	+	10.7818i	−0.482661	+	0.482661i	0.423319	+	0.905980i	$0.360865\pi$
$500$	11.5372	+	17.7029i	0.515959	+	0.791698i
$501$		0			0
$502$	21.3703	+	2.22863i	0.953805	+	0.0994686i
$503$			6.04034i			0.269326i	0.990891	+	0.134663i	$0.0429951\pi$
$503$			6.04034i			0.269326i	−0.990891	+	0.134663i	$0.957005\pi$
$504$		0			0
$505$			17.7166i			0.788378i
$506$	−0.216904	+	2.07989i	−0.00964255	+	0.0924625i
$507$		0			0
$508$	0.195316	+	0.0411853i	0.00866572	+	0.00182730i
$509$	−9.74993	+	9.74993i	−0.432158	+	0.432158i	−0.889362	−	0.457204i	$-0.848851\pi$
$509$	−9.74993	+	9.74993i	−0.432158	+	0.432158i	0.457204	+	0.889362i	$0.348851\pi$
$510$		0			0
$511$		−	9.50329i		−	0.420401i
$512$	−3.37684	+	22.3740i	−0.149237	+	0.988802i
$513$		0			0
$514$	−1.32110	+	1.07157i	−0.0582710	+	0.0472651i
$515$	5.65632	+	5.65632i	0.249247	+	0.249247i
$516$		0			0
$517$	1.46192	−	1.46192i	0.0642954	−	0.0642954i
$518$	−0.130716	−	0.0136319i	−0.00574335	−	0.000598951i
$519$		0			0
$520$	−11.2318	−	21.9120i	−0.492548	−	0.960905i
$521$	−1.68047			−0.0736225			−0.0368113	−	0.999322i	$-0.511720\pi$
$521$	−1.68047			−0.0736225			−0.0368113	+	0.999322i	$0.511720\pi$
$522$		0			0
$523$	−16.9606	−	16.9606i	−0.741635	−	0.741635i	0.231258	−	0.972892i	$-0.425716\pi$
$523$	−16.9606	−	16.9606i	−0.741635	−	0.741635i	−0.972892	+	0.231258i	$0.925716\pi$
$524$	30.4345	−	19.8345i	1.32954	−	0.866475i
$525$		0			0
$526$	−16.4369	+	13.3324i	−0.716683	+	0.581319i
$527$	2.94737			0.128390
$528$		0			0
$529$	21.8918			0.951816
$530$	−27.8019	+	22.5508i	−1.20764	+	0.979546i
$531$		0			0
$532$	2.41390	+	3.70394i	0.104656	+	0.160586i
$533$	−16.5837	−	16.5837i	−0.718320	−	0.718320i
$534$		0			0
$535$	35.4617			1.53314
$536$	−2.43596	+	7.55950i	−0.105217	+	0.326521i
$537$		0			0
$538$	13.1045	+	1.36662i	0.564976	+	0.0589192i
$539$	0.993222	−	0.993222i	0.0427811	−	0.0427811i
$540$		0			0
$541$	−5.82266	−	5.82266i	−0.250336	−	0.250336i	0.570773	−	0.821108i	$-0.306644\pi$
$541$	−5.82266	−	5.82266i	−0.250336	−	0.250336i	−0.821108	+	0.570773i	$0.806644\pi$
$542$	−29.8127	+	24.1818i	−1.28056	+	1.03870i
$543$		0			0
$544$	15.1588	−	4.12759i	0.649927	−	0.176969i
$545$		−	17.7750i		−	0.761398i
$546$		0			0
$547$	−15.9661	+	15.9661i	−0.682662	+	0.682662i	−0.960599	−	0.277937i	$-0.910349\pi$
$547$	−15.9661	+	15.9661i	−0.682662	+	0.682662i	0.277937	+	0.960599i	$0.410349\pi$
$548$	−1.28302	+	6.08455i	−0.0548080	+	0.259919i
$549$		0			0
$550$	−0.101258	+	0.970962i	−0.00431765	+	0.0414020i
$551$			10.8736i			0.463231i
$552$		0			0
$553$		−	9.85051i		−	0.418886i
$554$	23.8941	+	2.49182i	1.01516	+	0.105867i
$555$		0			0
$556$	−25.0691	+	16.3378i	−1.06317	+	0.692877i
$557$	14.1695	−	14.1695i	0.600381	−	0.600381i	−0.340033	−	0.940414i	$-0.610438\pi$
$557$	14.1695	−	14.1695i	0.600381	−	0.600381i	0.940414	+	0.340033i	$0.110438\pi$
$558$		0			0
$559$		−	12.5480i		−	0.530725i
$560$	−3.38748	−	8.74003i	−0.143147	−	0.369334i
$561$		0			0
$562$	−7.54426	−	9.30098i	−0.318235	−	0.392338i
$563$	−5.96715	−	5.96715i	−0.251485	−	0.251485i	0.570094	−	0.821579i	$-0.306907\pi$
$563$	−5.96715	−	5.96715i	−0.251485	−	0.251485i	−0.821579	+	0.570094i	$0.806907\pi$
$564$		0			0
$565$	−30.2346	+	30.2346i	−1.27198	+	1.27198i
$566$	−1.82122	+	17.4637i	−0.0765515	+	0.734053i
$567$		0			0
$568$	−16.8829	−	32.9366i	−0.708390	−	1.38199i
$569$	−14.5770			−0.611099			−0.305550	−	0.952176i	$-0.598840\pi$
$569$	−14.5770			−0.611099			−0.305550	+	0.952176i	$0.598840\pi$
$570$		0			0
$571$	−1.94424	−	1.94424i	−0.0813641	−	0.0813641i	0.665253	−	0.746618i	$-0.268323\pi$
$571$	−1.94424	−	1.94424i	−0.0813641	−	0.0813641i	−0.746618	+	0.665253i	$0.768323\pi$
$572$	−2.15329	+	10.2117i	−0.0900334	+	0.426971i
$573$		0			0
$574$	−5.62425	−	6.93389i	−0.234752	−	0.289415i
$575$	−0.517354			−0.0215752
$576$		0			0
$577$	−5.60353			−0.233278			−0.116639	−	0.993174i	$-0.537212\pi$
$577$	−5.60353			−0.233278			−0.116639	+	0.993174i	$0.537212\pi$
$578$	8.27337	+	10.1999i	0.344127	+	0.424259i
$579$		0			0
$580$	4.75669	−	22.5580i	0.197511	−	0.936668i
$581$	−1.13002	−	1.13002i	−0.0468812	−	0.0468812i
$582$		0			0
$583$	15.1726			0.628385
$584$	12.2611	+	23.9200i	0.507367	+	0.989816i
$585$		0			0
$586$	1.92089	−	18.4194i	0.0793512	−	0.760899i
$587$	−15.8040	+	15.8040i	−0.652300	+	0.652300i	−0.953546	−	0.301246i	$-0.902597\pi$
$587$	−15.8040	+	15.8040i	−0.652300	+	0.652300i	0.301246	+	0.953546i	$0.402597\pi$
$588$		0			0
$589$	−1.65883	−	1.65883i	−0.0683507	−	0.0683507i
$590$	12.2670	+	15.1235i	0.505025	+	0.622623i
$591$		0			0
$592$	0.346604	−	0.134338i	0.0142453	−	0.00552124i
$593$		−	8.08911i		−	0.332180i	−0.986111	−	0.166090i	$-0.946886\pi$
$593$		−	8.08911i		−	0.332180i	0.986111	−	0.166090i	$-0.0531142\pi$
$594$		0			0
$595$	−4.60202	+	4.60202i	−0.188664	+	0.188664i
$596$	−14.9815	+	9.76358i	−0.613664	+	0.399932i
$597$		0			0
$598$	−5.50087	−	0.573664i	−0.224947	−	0.0234589i
$599$			25.5885i			1.04552i	0.852480	+	0.522759i	$0.175097\pi$
$599$			25.5885i			1.04552i	−0.852480	+	0.522759i	$0.824903\pi$
$600$		0			0
$601$			26.8368i			1.09470i	0.836905	+	0.547348i	$0.184363\pi$
$601$			26.8368i			1.09470i	−0.836905	+	0.547348i	$0.815637\pi$
$602$	0.495468	−	4.75105i	0.0201938	−	0.193638i
$603$		0			0
$604$	−9.46603	+	44.8913i	−0.385167	+	1.82660i
$605$	−14.9580	+	14.9580i	−0.608128	+	0.608128i
$606$		0			0
$607$			17.9052i			0.726750i	0.931643	+	0.363375i	$0.118376\pi$
$607$			17.9052i			0.726750i	−0.931643	+	0.363375i	$0.881624\pi$
$608$	−10.8546	−	6.20850i	−0.440214	−	0.251788i
$609$		0			0
$610$	28.3230	−	22.9735i	1.14677	−	0.930170i
$611$	3.86648	+	3.86648i	0.156421	+	0.156421i
$612$		0			0
$613$	13.9653	−	13.9653i	0.564053	−	0.564053i	−0.366403	−	0.930456i	$-0.619411\pi$
$613$	13.9653	−	13.9653i	0.564053	−	0.564053i	0.930456	+	0.366403i	$0.119411\pi$
$614$	−19.0977	−	1.99163i	−0.770721	−	0.0803755i
$615$		0			0
$616$	−1.21851	+	3.78141i	−0.0490953	+	0.152357i
$617$	6.19844			0.249540			0.124770	−	0.992186i	$-0.460181\pi$
$617$	6.19844			0.249540			0.124770	+	0.992186i	$0.460181\pi$
$618$		0			0
$619$	26.7837	+	26.7837i	1.07653	+	1.07653i	0.996818	+	0.0797087i	$0.0253990\pi$
$619$	26.7837	+	26.7837i	1.07653	+	1.07653i	0.0797087	+	0.996818i	$0.474601\pi$
$620$	2.71568	+	4.16699i	0.109064	+	0.167351i
$621$		0			0
$622$	25.4636	−	20.6542i	1.02100	−	0.828157i
$623$	−7.04453			−0.282233
$624$		0			0
$625$	27.2157			1.08863
$626$	−30.6831	+	24.8878i	−1.22634	+	0.994717i
$627$		0			0
$628$	30.1579	−	19.6542i	1.20343	−	0.784289i
$629$	−0.182502	−	0.182502i	−0.00727685	−	0.00727685i
$630$		0			0
$631$	−30.5763			−1.21723			−0.608613	−	0.793468i	$-0.708274\pi$
$631$	−30.5763			−1.21723			−0.608613	+	0.793468i	$0.708274\pi$
$632$	12.7091	+	24.7939i	0.505539	+	0.986250i
$633$		0			0
$634$	−42.9491	−	4.47900i	−1.70573	−	0.177884i
$635$	0.165380	−	0.165380i	0.00656289	−	0.00656289i
$636$		0			0
$637$	2.62686	+	2.62686i	0.104080	+	0.104080i
$638$	−7.58870	+	6.15538i	−0.300439	+	0.243694i
$639$		0			0
$640$	19.8027	+	17.6283i	0.782770	+	0.696821i
$641$		−	43.7713i		−	1.72886i	−0.502752	−	0.864431i	$-0.667679\pi$
$641$		−	43.7713i		−	1.72886i	0.502752	−	0.864431i	$-0.332321\pi$
$642$		0			0
$643$	−24.5474	+	24.5474i	−0.968053	+	0.968053i	−0.999505	−	0.0314518i	$-0.989987\pi$
$643$	−24.5474	+	24.5474i	−0.968053	+	0.968053i	0.0314518	+	0.999505i	$0.489987\pi$
$644$	−2.06014	−	0.434412i	−0.0811808	−	0.0171182i
$645$		0			0
$646$	−0.900559	+	8.63547i	−0.0354320	+	0.339758i
$647$		−	0.216780i		−	0.00852248i	−0.999991	−	0.00426124i	$-0.998644\pi$
$647$		−	0.216780i		−	0.00852248i	0.999991	−	0.00426124i	$-0.00135640\pi$
$648$		0			0
$649$		−	8.25347i		−	0.323977i
$650$	−2.56799	−	0.267805i	−0.100725	−	0.0105042i
$651$		0			0
$652$	8.74766	+	13.4226i	0.342585	+	0.525670i
$653$	12.1867	−	12.1867i	0.476904	−	0.476904i	−0.427236	−	0.904140i	$-0.640513\pi$
$653$	12.1867	−	12.1867i	0.476904	−	0.476904i	0.904140	+	0.427236i	$0.140513\pi$
$654$		0			0
$655$		−	42.5643i		−	1.66313i
$656$	23.1024	+	10.1964i	0.901999	+	0.398102i
$657$		0			0
$658$	1.31129	+	1.61663i	0.0511194	+	0.0630229i
$659$	−14.3745	−	14.3745i	−0.559951	−	0.559951i	0.369343	−	0.929293i	$-0.379583\pi$
$659$	−14.3745	−	14.3745i	−0.559951	−	0.559951i	−0.929293	+	0.369343i	$0.879583\pi$
$660$		0			0
$661$	28.7815	−	28.7815i	1.11947	−	1.11947i	0.127651	−	0.991819i	$-0.459256\pi$
$661$	28.7815	−	28.7815i	1.11947	−	1.11947i	0.991819	−	0.127651i	$-0.0407436\pi$
$662$	3.83553	−	36.7789i	0.149072	−	1.42945i
$663$		0			0
$664$	4.30223	+	1.38634i	0.166959	+	0.0538005i
$665$	5.18016			0.200878
$666$		0			0
$667$	−3.66160	−	3.66160i	−0.141778	−	0.141778i
$668$	39.8136	+	8.39531i	1.54043	+	0.324824i
$669$		0			0
$670$	5.86225	+	7.22731i	0.226478	+	0.279215i
$671$	−15.4570			−0.596710
$672$		0			0
$673$	39.5913			1.52613			0.763066	−	0.646320i	$-0.223693\pi$
$673$	39.5913			1.52613			0.763066	+	0.646320i	$0.223693\pi$
$674$	−7.64546	−	9.42575i	−0.294492	−	0.363066i
$675$		0			0
$676$	−1.56710	−	0.330448i	−0.0602732	−	0.0127095i
$677$	−13.7471	−	13.7471i	−0.528342	−	0.528342i	0.391735	−	0.920078i	$-0.371875\pi$
$677$	−13.7471	−	13.7471i	−0.528342	−	0.528342i	−0.920078	+	0.391735i	$0.871875\pi$
$678$		0			0
$679$	5.35352			0.205449
$680$	5.64588	−	17.5209i	0.216510	−	0.671895i
$681$		0			0
$682$	0.218660	−	2.09673i	0.00837293	−	0.0802880i
$683$	−0.00325507	+	0.00325507i	−0.000124552	+	0.000124552i	−0.707169	−	0.707045i	$-0.750028\pi$
$683$	−0.00325507	+	0.00325507i	−0.000124552	+	0.000124552i	0.707045	+	0.707169i	$0.250028\pi$
$684$		0			0
$685$	5.15197	+	5.15197i	0.196847	+	0.196847i
$686$	0.890883	+	1.09833i	0.0340141	+	0.0419344i
$687$		0			0
$688$	4.88267	+	12.5977i	0.186150	+	0.480284i
$689$			40.1283i			1.52877i
$690$		0			0
$691$	−17.5751	+	17.5751i	−0.668590	+	0.668590i	−0.957390	−	0.288800i	$-0.906744\pi$
$691$	−17.5751	+	17.5751i	−0.668590	+	0.668590i	0.288800	+	0.957390i	$0.406744\pi$
$692$	6.09637	+	9.35440i	0.231749	+	0.355601i
$693$		0			0
$694$	−39.0359	−	4.07090i	−1.48178	−	0.154529i
$695$			35.0605i			1.32992i
$696$		0			0
$697$		−	17.5333i		−	0.664122i
$698$	−1.59282	+	15.2736i	−0.0602891	+	0.578113i
$699$		0			0
$700$	−0.961741	−	0.202798i	−0.0363504	−	0.00766504i
$701$	29.3683	−	29.3683i	1.10923	−	1.10923i	0.115975	−	0.993252i	$-0.463001\pi$
$701$	29.3683	−	29.3683i	1.10923	−	1.10923i	0.993252	−	0.115975i	$-0.0369991\pi$
$702$		0			0
$703$			0.205430i			0.00774794i
$704$	−1.81173	−	11.0900i	−0.0682821	−	0.417971i
$705$		0			0
$706$	−28.4912	+	23.1099i	−1.07228	+	0.869752i
$707$	5.34591	+	5.34591i	0.201054	+	0.201054i
$708$		0			0
$709$	−21.5493	+	21.5493i	−0.809300	+	0.809300i	−0.984528	−	0.175228i	$-0.943934\pi$
$709$	−21.5493	+	21.5493i	−0.809300	+	0.809300i	0.175228	+	0.984528i	$0.443934\pi$
$710$	−43.1322	−	4.49809i	−1.61872	−	0.168810i
$711$		0			0
$712$	17.7312	−	9.08880i	0.664506	−	0.340617i
$713$	1.11719			0.0418393
$714$		0			0
$715$	8.64652	+	8.64652i	0.323362	+	0.323362i
$716$	29.8006	−	19.4214i	1.11370	−	0.725811i
$717$		0			0
$718$	3.38689	−	2.74719i	0.126398	−	0.102524i
$719$	−23.1027			−0.861585			−0.430793	−	0.902451i	$-0.641766\pi$
$719$	−23.1027			−0.861585			−0.430793	+	0.902451i	$0.641766\pi$
$720$		0			0
$721$	3.41355			0.127127
$722$	−15.5012	+	12.5734i	−0.576897	+	0.467935i
$723$		0			0
$724$	24.7300	+	37.9462i	0.919083	+	1.41026i
$725$	−1.70936	−	1.70936i	−0.0634840	−	0.0634840i
$726$		0			0
$727$	−10.8397			−0.402024			−0.201012	−	0.979589i	$-0.564423\pi$
$727$	−10.8397			−0.402024			−0.201012	+	0.979589i	$0.564423\pi$
$728$	−10.0010	−	3.22271i	−0.370663	−	0.119441i
$729$		0			0
$730$	31.3244	+	3.26670i	1.15937	+	0.120906i
$731$	6.63328	−	6.63328i	0.245341	−	0.245341i
$732$		0			0
$733$	−5.15354	−	5.15354i	−0.190350	−	0.190350i	0.605497	−	0.795848i	$-0.292974\pi$
$733$	−5.15354	−	5.15354i	−0.190350	−	0.190350i	−0.795848	+	0.605497i	$0.792974\pi$
$734$	19.9221	−	16.1593i	0.735339	−	0.596451i
$735$		0			0
$736$	5.74589	−	1.56455i	0.211796	−	0.0576702i
$737$		−	3.94423i		−	0.145287i
$738$		0			0
$739$	12.6864	−	12.6864i	0.466678	−	0.466678i	−0.434158	−	0.900837i	$-0.642954\pi$
$739$	12.6864	−	12.6864i	0.466678	−	0.466678i	0.900837	+	0.434158i	$0.142954\pi$
$740$	0.0898661	−	0.426177i	0.00330354	−	0.0156666i
$741$		0			0
$742$	−1.58450	+	15.1937i	−0.0581687	+	0.557780i
$743$			24.3109i			0.891879i	0.895063	+	0.445940i	$0.147130\pi$
$743$			24.3109i			0.891879i	−0.895063	+	0.445940i	$0.852870\pi$
$744$		0			0
$745$			20.9524i			0.767635i
$746$	−3.39580	−	0.354135i	−0.124329	−	0.0129658i
$747$		0			0
$748$	−6.53650	+	4.25991i	−0.238998	+	0.155758i
$749$	10.7004	−	10.7004i	0.390985	−	0.390985i
$750$		0			0
$751$			47.8161i			1.74483i	0.488762	+	0.872417i	$0.337449\pi$
$751$			47.8161i			1.74483i	−0.488762	+	0.872417i	$0.662551\pi$
$752$	−5.38632	−	2.37728i	−0.196419	−	0.0866905i
$753$		0			0
$754$	−16.2797	−	20.0705i	−0.592870	−	0.730924i
$755$	38.0109	+	38.0109i	1.38336	+	1.38336i
$756$		0			0
$757$	20.6181	−	20.6181i	0.749377	−	0.749377i	−0.224986	−	0.974362i	$-0.572234\pi$
$757$	20.6181	−	20.6181i	0.749377	−	0.749377i	0.974362	+	0.224986i	$0.0722335\pi$
$758$	5.03865	−	48.3156i	0.183012	−	1.75490i
$759$		0			0
$760$	−13.0386	+	6.68341i	−0.472959	+	0.242433i
$761$	−18.6635			−0.676553			−0.338276	−	0.941047i	$-0.609844\pi$
$761$	−18.6635			−0.676553			−0.338276	+	0.941047i	$0.609844\pi$
$762$		0			0
$763$	−5.36354	−	5.36354i	−0.194173	−	0.194173i
$764$	−4.88322	+	23.1580i	−0.176669	+	0.837827i
$765$		0			0
$766$	9.14538	+	11.2749i	0.330436	+	0.407380i
$767$	21.8287			0.788187
$768$		0			0
$769$	−13.7015			−0.494090			−0.247045	−	0.969004i	$-0.579459\pi$
$769$	−13.7015			−0.494090			−0.247045	+	0.969004i	$0.579459\pi$
$770$	2.93241	+	3.61524i	0.105677	+	0.130284i
$771$		0			0
$772$	−8.70792	+	41.2961i	−0.313405	+	1.48628i
$773$	21.1383	+	21.1383i	0.760294	+	0.760294i	0.976375	−	0.216082i	$-0.0693278\pi$
$773$	21.1383	+	21.1383i	0.760294	+	0.760294i	−0.216082	+	0.976375i	$0.569328\pi$
$774$		0			0
$775$	0.521543			0.0187344
$776$	−13.4749	+	6.90708i	−0.483722	+	0.247950i
$777$		0			0
$778$	0.191754	−	1.83873i	0.00687471	−	0.0659217i
$779$	−9.86801	+	9.86801i	−0.353558	+	0.353558i
$780$		0			0
$781$	12.9969	+	12.9969i	0.465064	+	0.465064i
$782$	−2.60467	−	3.21119i	−0.0931430	−	0.114832i
$783$		0			0
$784$	−3.65943	−	1.61511i	−0.130694	−	0.0576825i
$785$		−	42.1774i		−	1.50538i
$786$		0			0
$787$	25.7503	−	25.7503i	0.917899	−	0.917899i	−0.0789778	−	0.996876i	$-0.525166\pi$
$787$	25.7503	−	25.7503i	0.917899	−	0.917899i	0.996876	+	0.0789778i	$0.0251656\pi$
$788$	13.8222	−	9.00808i	0.492395	−	0.320899i
$789$		0			0
$790$	32.4689	+	3.38606i	1.15519	+	0.120471i
$791$			18.2463i			0.648765i
$792$		0			0
$793$		−	40.8804i		−	1.45171i
$794$	3.79062	−	36.3483i	0.134524	−	1.28995i
$795$		0			0
$796$	−9.60933	+	45.5709i	−0.340594	+	1.61522i
$797$	13.2613	−	13.2613i	0.469739	−	0.469739i	−0.432091	−	0.901830i	$-0.642224\pi$
$797$	13.2613	−	13.2613i	0.469739	−	0.469739i	0.901830	+	0.432091i	$0.142224\pi$
$798$		0			0
$799$			4.08788i			0.144619i
$800$	2.68237	−	0.730385i	0.0948362	−	0.0258230i
$801$		0			0
$802$	−40.6037	+	32.9347i	−1.43377	+	1.16296i
$803$	−9.43887	−	9.43887i	−0.333091	−	0.333091i
$804$		0			0
$805$	−1.74438	+	1.74438i	−0.0614814	+	0.0614814i
$806$	5.54541	+	0.578309i	0.195329	+	0.0203701i
$807$		0			0
$808$	−20.3530	−	6.55852i	−0.716018	−	0.230728i
$809$	39.0568			1.37316			0.686582	−	0.727053i	$-0.259110\pi$
$809$	39.0568			1.37316			0.686582	+	0.727053i	$0.259110\pi$
$810$		0			0
$811$	11.8627	+	11.8627i	0.416554	+	0.416554i	0.884014	−	0.467460i	$-0.154831\pi$
$811$	11.8627	+	11.8627i	0.416554	+	0.416554i	−0.467460	+	0.884014i	$0.654831\pi$
$812$	−5.37146	−	8.24209i	−0.188501	−	0.289241i
$813$		0			0
$814$	−0.143370	+	0.116291i	−0.00502511	+	0.00407599i
$815$	18.7722			0.657563
$816$		0			0
$817$	−7.46661			−0.261224
$818$	−5.12156	+	4.15423i	−0.179071	+	0.145249i
$819$		0			0
$820$	24.7886	−	16.1550i	0.865655	−	0.564157i
$821$	7.89485	+	7.89485i	0.275532	+	0.275532i	0.831323	−	0.555790i	$-0.187584\pi$
$821$	7.89485	+	7.89485i	0.275532	+	0.275532i	−0.555790	+	0.831323i	$0.687584\pi$
$822$		0			0
$823$	−23.6159			−0.823199			−0.411600	−	0.911365i	$-0.635030\pi$
$823$	−23.6159			−0.823199			−0.411600	+	0.911365i	$0.635030\pi$
$824$	−8.59197	+	4.40414i	−0.299315	+	0.153425i
$825$		0			0
$826$	8.26497	+	0.861922i	0.287575	+	0.0299901i
$827$	−2.44372	+	2.44372i	−0.0849766	+	0.0849766i	−0.748317	−	0.663341i	$-0.769138\pi$
$827$	−2.44372	+	2.44372i	−0.0849766	+	0.0849766i	0.663341	+	0.748317i	$0.269138\pi$
$828$		0			0
$829$	29.3029	+	29.3029i	1.01773	+	1.01773i	0.999840	+	0.0178910i	$0.00569520\pi$
$829$	29.3029	+	29.3029i	1.01773	+	1.01773i	0.0178910	+	0.999840i	$0.494305\pi$
$830$	4.11318	−	3.33630i	0.142770	−	0.115805i
$831$		0			0
$832$	29.3307	−	4.79163i	1.01686	−	0.166120i
$833$			2.77728i			0.0962271i
$834$		0			0
$835$	33.7114	−	33.7114i	1.16663	−	1.16663i
$836$	6.07638	+	1.28130i	0.210156	+	0.0443146i
$837$		0			0
$838$	4.34377	−	41.6524i	0.150053	−	1.43886i
$839$			25.2593i			0.872047i	0.899935	+	0.436024i	$0.143614\pi$
$839$			25.2593i			0.872047i	−0.899935	+	0.436024i	$0.856386\pi$
$840$		0			0
$841$			4.80385i			0.165650i
$842$	−36.0007	−	3.75438i	−1.24067	−	0.129384i
$843$		0			0
$844$	−25.1290	−	38.5585i	−0.864976	−	1.32724i
$845$	−1.32691	+	1.32691i	−0.0456472	+	0.0456472i
$846$		0			0
$847$			9.02702i			0.310172i
$848$	−15.6147	−	40.2873i	−0.536210	−	1.38347i
$849$		0			0
$850$	−1.21595	−	1.49909i	−0.0417067	−	0.0514183i
$851$	−0.0691771	−	0.0691771i	−0.00237136	−	0.00237136i
$852$		0			0
$853$	25.7213	−	25.7213i	0.880680	−	0.880680i	−0.112924	−	0.993604i	$-0.536022\pi$
$853$	25.7213	−	25.7213i	0.880680	−	0.880680i	0.993604	+	0.112924i	$0.0360215\pi$
$854$	1.61419	−	15.4785i	0.0552366	−	0.529664i
$855$		0			0
$856$	−13.1276	+	40.7388i	−0.448692	+	1.39242i
$857$	−46.7116			−1.59564			−0.797819	−	0.602897i	$-0.794013\pi$
$857$	−46.7116			−1.59564			−0.797819	+	0.602897i	$0.794013\pi$
$858$		0			0
$859$	−2.01594	−	2.01594i	−0.0687829	−	0.0687829i	0.671878	−	0.740661i	$-0.265488\pi$
$859$	−2.01594	−	2.01594i	−0.0687829	−	0.0687829i	−0.740661	+	0.671878i	$0.765488\pi$
$860$	15.4899	+	3.26629i	0.528203	+	0.111380i
$861$		0			0
$862$	27.0230	+	33.3155i	0.920408	+	1.13473i
$863$	−7.21180			−0.245493			−0.122746	−	0.992438i	$-0.539170\pi$
$863$	−7.21180			−0.245493			−0.122746	+	0.992438i	$0.539170\pi$
$864$		0			0
$865$	13.0826			0.444823
$866$	−23.0494	−	28.4166i	−0.783252	−	0.965637i
$867$		0			0
$868$	2.07682	+	0.437930i	0.0704918	+	0.0148643i
$869$	−9.78374	−	9.78374i	−0.331891	−	0.331891i
$870$		0			0
$871$	10.4316			0.353462
$872$	20.4202	+	6.58014i	0.691514	+	0.222832i
$873$		0			0
$874$	−0.341355	+	3.27325i	−0.0115465	+	0.110719i
$875$	7.47078	−	7.47078i	0.252558	−	0.252558i
$876$		0			0
$877$	−8.12742	−	8.12742i	−0.274443	−	0.274443i	0.556443	−	0.830886i	$-0.312166\pi$
$877$	−8.12742	−	8.12742i	−0.274443	−	0.274443i	−0.830886	+	0.556443i	$0.812166\pi$
$878$	−16.1998	−	19.9720i	−0.546716	−	0.674023i
$879$		0			0
$880$	−12.0453	−	5.31626i	−0.406047	−	0.179211i
$881$		−	41.1175i		−	1.38529i	−0.721281	−	0.692643i	$-0.756446\pi$
$881$		−	41.1175i		−	1.38529i	0.721281	−	0.692643i	$-0.243554\pi$
$882$		0			0
$883$	9.38694	−	9.38694i	0.315896	−	0.315896i	−0.531293	−	0.847188i	$-0.678294\pi$
$883$	9.38694	−	9.38694i	0.315896	−	0.315896i	0.847188	+	0.531293i	$0.178294\pi$
$884$	−11.2665	−	17.2876i	−0.378935	−	0.581446i
$885$		0			0
$886$	−0.0343286	−	0.00357999i	−0.00115329	−	0.000120272i
$887$			17.8506i			0.599366i	0.954039	+	0.299683i	$0.0968809\pi$
$887$			17.8506i			0.599366i	−0.954039	+	0.299683i	$0.903119\pi$
$888$		0			0
$889$		−	0.0998053i		−	0.00334736i
$890$	2.42152	−	23.2199i	0.0811695	−	0.778334i
$891$		0			0
$892$	44.6620	+	9.41767i	1.49539	+	0.315327i
$893$	2.30072	−	2.30072i	0.0769906	−	0.0769906i
$894$		0			0
$895$		−	41.6777i		−	1.39313i
$896$	11.2947	−	0.656108i	0.377328	−	0.0219190i
$897$		0			0
$898$	9.70193	−	7.86948i	0.323758	−	0.262608i
$899$	3.69125	+	3.69125i	0.123110	+	0.123110i
$900$		0			0
$901$	−21.2131	+	21.2131i	−0.706710	+	0.706710i
$902$	−12.4730	−	1.30076i	−0.415306	−	0.0433107i
$903$		0			0
$904$	−23.5413	−	45.9264i	−0.782972	−	1.52749i
$905$	53.0698			1.76410
$906$		0			0
$907$	−16.6866	−	16.6866i	−0.554070	−	0.554070i	0.373543	−	0.927613i	$-0.378143\pi$
$907$	−16.6866	−	16.6866i	−0.554070	−	0.554070i	−0.927613	+	0.373543i	$0.878143\pi$
$908$	14.4409	−	9.41132i	0.479239	−	0.312326i
$909$		0			0
$910$	−9.56154	+	7.75560i	−0.316962	+	0.257096i
$911$	−49.1236			−1.62754			−0.813769	−	0.581189i	$-0.802588\pi$
$911$	−49.1236			−1.62754			−0.813769	+	0.581189i	$0.802588\pi$
$912$		0			0
$913$	−2.24472			−0.0742895
$914$	−3.88073	+	3.14776i	−0.128363	+	0.104119i
$915$		0			0
$916$	−13.2370	−	20.3112i	−0.437364	−	0.671100i
$917$	−12.8436	−	12.8436i	−0.424134	−	0.424134i
$918$		0			0
$919$	46.5272			1.53479			0.767395	−	0.641174i	$-0.221552\pi$
$919$	46.5272			1.53479			0.767395	+	0.641174i	$0.221552\pi$
$920$	2.14006	−	6.64124i	0.0705556	−	0.218955i
$921$		0			0
$922$	27.7669	+	2.89570i	0.914453	+	0.0953648i
$923$	−34.3739	+	34.3739i	−1.13143	+	1.13143i
$924$		0			0
$925$	−0.0322941	−	0.0322941i	−0.00106182	−	0.00106182i
$926$	−11.6915	+	9.48326i	−0.384206	+	0.311639i
$927$		0			0
$928$	24.1540	+	13.8153i	0.792893	+	0.453509i
$929$			4.44879i			0.145960i	0.997333	+	0.0729800i	$0.0232509\pi$
$929$			4.44879i			0.145960i	−0.997333	+	0.0729800i	$0.976749\pi$
$930$		0			0
$931$	1.56309	−	1.56309i	0.0512283	−	0.0512283i
$932$	2.02470	−	9.60184i	0.0663211	−	0.314519i
$933$		0			0
$934$	2.58365	−	24.7746i	0.0845395	−	0.810650i
$935$			9.14165i			0.298964i
$936$		0			0
$937$		−	45.1282i		−	1.47428i	−0.675742	−	0.737138i	$-0.736177\pi$
$937$		−	45.1282i		−	1.47428i	0.675742	−	0.737138i	$-0.263823\pi$
$938$	3.94972	+	0.411901i	0.128963	+	0.0134491i
$939$		0			0
$940$	−5.77944	+	3.76653i	−0.188505	+	0.122851i
$941$	−7.54964	+	7.54964i	−0.246111	+	0.246111i	−0.819373	−	0.573261i	$-0.805678\pi$
$941$	−7.54964	+	7.54964i	−0.246111	+	0.246111i	0.573261	+	0.819373i	$0.305678\pi$
$942$		0			0
$943$		−	6.64596i		−	0.216422i
$944$	−21.9152	+	8.49394i	−0.713278	+	0.276454i
$945$		0			0
$946$	−4.22674	−	5.21096i	−0.137423	−	0.169423i
$947$	−16.1642	−	16.1642i	−0.525265	−	0.525265i	0.393892	−	0.919157i	$-0.371128\pi$
$947$	−16.1642	−	16.1642i	−0.525265	−	0.525265i	−0.919157	+	0.393892i	$0.871128\pi$
$948$		0			0
$949$	24.9638	−	24.9638i	0.810359	−	0.810359i
$950$	−0.159356	+	1.52806i	−0.00517018	+	0.0495769i
$951$		0			0
$952$	−3.58323	−	6.99048i	−0.116133	−	0.226563i
$953$	−19.4691			−0.630667			−0.315334	−	0.948981i	$-0.602116\pi$
$953$	−19.4691			−0.630667			−0.315334	+	0.948981i	$0.602116\pi$
$954$		0			0
$955$	19.6086	+	19.6086i	0.634519	+	0.634519i
$956$	4.60767	−	21.8512i	0.149023	−	0.706719i
$957$		0			0
$958$	−19.6175	−	24.1856i	−0.633814	−	0.781402i
$959$	3.10918			0.100401
$960$		0			0
$961$	29.8738			0.963670
$962$	−0.307565	−	0.379183i	−0.00991628	−	0.0122253i
$963$		0			0
$964$	7.34870	−	34.8502i	0.236686	−	1.12245i
$965$	34.9667	+	34.9667i	1.12562	+	1.12562i
$966$		0			0
$967$	−47.4224			−1.52500			−0.762501	−	0.646987i	$-0.776029\pi$
$967$	−47.4224			−1.52500			−0.762501	+	0.646987i	$0.776029\pi$
$968$	−11.6466	−	22.7212i	−0.374336	−	0.730287i
$969$		0			0
$970$	−1.84024	+	17.6461i	−0.0590867	+	0.566583i
$971$	26.3134	−	26.3134i	0.844437	−	0.844437i	−0.144995	−	0.989432i	$-0.546317\pi$
$971$	26.3134	−	26.3134i	0.844437	−	0.844437i	0.989432	+	0.144995i	$0.0463167\pi$
$972$		0			0
$973$	10.5794	+	10.5794i	0.339159	+	0.339159i
$974$	−20.7417	−	25.5716i	−0.664608	−	0.819366i
$975$		0			0
$976$	15.9073	+	41.0424i	0.509181	+	1.31374i
$977$		−	15.9988i		−	0.511848i	−0.966697	−	0.255924i	$-0.917620\pi$
$977$		−	15.9988i		−	0.511848i	0.966697	−	0.255924i	$-0.0823797\pi$
$978$		0			0
$979$	−6.99678	+	6.99678i	−0.223618	+	0.223618i
$980$	−3.92652	+	2.55895i	−0.125428	+	0.0817428i
$981$		0			0
$982$	0.257643	+	0.0268685i	0.00822171	+	0.000857410i
$983$		−	26.1634i		−	0.834483i	−0.908796	−	0.417242i	$-0.862997\pi$
$983$		−	26.1634i		−	0.834483i	0.908796	−	0.417242i	$-0.137003\pi$
$984$		0			0
$985$		−	19.3311i		−	0.615939i
$986$	2.00394	−	19.2158i	0.0638186	−	0.611957i
$987$		0			0
$988$	−3.38876	+	16.0707i	−0.107811	+	0.511277i
$989$	2.51433	−	2.51433i	0.0799509	−	0.0799509i
$990$		0			0
$991$			18.2140i			0.578587i	0.957240	+	0.289294i	$0.0934204\pi$
$991$			18.2140i			0.578587i	−0.957240	+	0.289294i	$0.906580\pi$
$992$	−5.79241	+	1.57722i	−0.183909	+	0.0500768i
$993$		0			0
$994$	−14.3722	+	11.6577i	−0.455860	+	0.369759i
$995$	38.5863	+	38.5863i	1.22327	+	1.22327i
$996$		0			0
$997$	−10.0322	+	10.0322i	−0.317722	+	0.317722i	−0.847892	−	0.530170i	$-0.822128\pi$
$997$	−10.0322	+	10.0322i	−0.317722	+	0.317722i	0.530170	+	0.847892i	$0.322128\pi$
$998$	−21.4474	−	2.23666i	−0.678904	−	0.0708002i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.v.e.323.15	yes	40
3.2	odd	2	inner	1008.2.v.e.323.6	✓	40
4.3	odd	2		4032.2.v.e.1583.16		40
12.11	even	2		4032.2.v.e.1583.5		40
16.5	even	4		4032.2.v.e.3599.5		40
16.11	odd	4	inner	1008.2.v.e.827.6	yes	40
48.5	odd	4		4032.2.v.e.3599.16		40
48.11	even	4	inner	1008.2.v.e.827.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.v.e.323.6	✓	40	3.2	odd	2	inner
1008.2.v.e.323.15	yes	40	1.1	even	1	trivial
1008.2.v.e.827.6	yes	40	16.11	odd	4	inner
1008.2.v.e.827.15	yes	40	48.11	even	4	inner
4032.2.v.e.1583.5		40	12.11	even	2
4032.2.v.e.1583.16		40	4.3	odd	2
4032.2.v.e.3599.5		40	16.5	even	4
4032.2.v.e.3599.16		40	48.5	odd	4

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.890883 + 1.09833i) q^{2} +(-0.412656 + 1.95697i) q^{4} +(1.65702 + 1.65702i) q^{5} +1.00000 q^{7} +(-2.51702 + 1.29019i) q^{8} +O(q^{10})\)	\(q+(0.890883 + 1.09833i) q^{2} +(-0.412656 + 1.95697i) q^{4} +(1.65702 + 1.65702i) q^{5} +1.00000 q^{7} +(-2.51702 + 1.29019i) q^{8} +(-0.343745 + 3.29617i) q^{10} +(0.993222 - 0.993222i) q^{11} +(2.62686 + 2.62686i) q^{13} +(0.890883 + 1.09833i) q^{14} +(-3.65943 - 1.61511i) q^{16} +2.77728i q^{17} +(1.56309 - 1.56309i) q^{19} +(-3.92652 + 2.55895i) q^{20} +(1.97573 + 0.206041i) q^{22} +1.05272i q^{23} +0.491445i q^{25} +(-0.544935 + 5.22538i) q^{26} +(-0.412656 + 1.95697i) q^{28} +(-3.47823 + 3.47823i) q^{29} -1.06124i q^{31} +(-1.48620 - 5.45813i) q^{32} +(-3.05037 + 2.47423i) q^{34} +(1.65702 + 1.65702i) q^{35} +(-0.0657126 + 0.0657126i) q^{37} +(3.10933 + 0.324259i) q^{38} +(-6.30864 - 2.03288i) q^{40} -6.31313 q^{41} +(-2.38841 - 2.38841i) q^{43} +(1.53384 + 2.35356i) q^{44} +(-1.15623 + 0.937851i) q^{46} +1.47190 q^{47} +1.00000 q^{49} +(-0.539769 + 0.437820i) q^{50} +(-6.22466 + 4.05668i) q^{52} +(7.63807 + 7.63807i) q^{53} +3.29158 q^{55} +(-2.51702 + 1.29019i) q^{56} +(-6.91894 - 0.721549i) q^{58} +(4.15490 - 4.15490i) q^{59} +(-7.78123 - 7.78123i) q^{61} +(1.16560 - 0.945444i) q^{62} +(4.67080 - 6.49489i) q^{64} +8.70553i q^{65} +(1.98557 - 1.98557i) q^{67} +(-5.43504 - 1.14606i) q^{68} +(-0.343745 + 3.29617i) q^{70} +13.0855i q^{71} -9.50329i q^{73} +(-0.130716 - 0.0136319i) q^{74} +(2.41390 + 3.70394i) q^{76} +(0.993222 - 0.993222i) q^{77} -9.85051i q^{79} +(-3.38748 - 8.74003i) q^{80} +(-5.62425 - 6.93389i) q^{82} +(-1.13002 - 1.13002i) q^{83} +(-4.60202 + 4.60202i) q^{85} +(0.495468 - 4.75105i) q^{86} +(-1.21851 + 3.78141i) q^{88} -7.04453 q^{89} +(2.62686 + 2.62686i) q^{91} +(-2.06014 - 0.434412i) q^{92} +(1.31129 + 1.61663i) q^{94} +5.18016 q^{95} +5.35352 q^{97} +(0.890883 + 1.09833i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{7}+O(q^{10}) \) 40 * q + 40 * q^7	\( 40 q + 40 q^{7} + 48 q^{10} - 24 q^{13} + 12 q^{16} - 32 q^{19} - 8 q^{22} - 56 q^{34} - 8 q^{37} + 32 q^{43} - 52 q^{46} + 40 q^{49} - 8 q^{52} + 48 q^{55} + 56 q^{58} - 24 q^{61} + 48 q^{64} + 48 q^{70} - 24 q^{76} - 64 q^{82} + 64 q^{85} - 120 q^{88} - 24 q^{91} - 128 q^{94} + 64 q^{97}+O(q^{100}) \) 40 * q + 40 * q^7 + 48 * q^10 - 24 * q^13 + 12 * q^16 - 32 * q^19 - 8 * q^22 - 56 * q^34 - 8 * q^37 + 32 * q^43 - 52 * q^46 + 40 * q^49 - 8 * q^52 + 48 * q^55 + 56 * q^58 - 24 * q^61 + 48 * q^64 + 48 * q^70 - 24 * q^76 - 64 * q^82 + 64 * q^85 - 120 * q^88 - 24 * q^91 - 128 * q^94 + 64 * q^97

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