LMFDB - Embedded newform 1008.2.v.e.323.2

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			323.2
Character	$\chi$	$=$	1008.323
Dual form			1008.2.v.e.827.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39680 + 0.221233i) q^{2} +(1.90211 - 0.618037i) q^{4} +(-2.51504 - 2.51504i) q^{5} +1.00000 q^{7} +(-2.52014 + 1.28408i) q^{8} +O(q^{10})$	\(q+(-1.39680 + 0.221233i) q^{2} +(1.90211 - 0.618037i) q^{4} +(-2.51504 - 2.51504i) q^{5} +1.00000 q^{7} +(-2.52014 + 1.28408i) q^{8} +(4.06942 + 2.95660i) q^{10} +(-0.984548 + 0.984548i) q^{11} +(-3.26086 - 3.26086i) q^{13} +(-1.39680 + 0.221233i) q^{14} +(3.23606 - 2.35115i) q^{16} +5.50927i q^{17} +(-1.21444 + 1.21444i) q^{19} +(-6.33826 - 3.22950i) q^{20} +(1.15740 - 1.59303i) q^{22} -8.62021i q^{23} +7.65081i q^{25} +(5.27618 + 3.83336i) q^{26} +(1.90211 - 0.618037i) q^{28} +(-2.04663 + 2.04663i) q^{29} +0.164437i q^{31} +(-3.99999 + 4.00001i) q^{32} +(-1.21883 - 7.69536i) q^{34} +(-2.51504 - 2.51504i) q^{35} +(-8.31105 + 8.31105i) q^{37} +(1.42766 - 1.96501i) q^{38} +(9.56777 + 3.10874i) q^{40} +9.56578 q^{41} +(5.01867 + 5.01867i) q^{43} +(-1.26423 + 2.48121i) q^{44} +(1.90707 + 12.0407i) q^{46} +3.37837 q^{47} +1.00000 q^{49} +(-1.69261 - 10.6867i) q^{50} +(-8.21784 - 4.18719i) q^{52} +(3.72717 + 3.72717i) q^{53} +4.95235 q^{55} +(-2.52014 + 1.28408i) q^{56} +(2.40596 - 3.31153i) q^{58} +(-10.0781 + 10.0781i) q^{59} +(-1.07042 - 1.07042i) q^{61} +(-0.0363788 - 0.229686i) q^{62} +(4.70226 - 6.47216i) q^{64} +16.4023i q^{65} +(-3.12073 + 3.12073i) q^{67} +(3.40493 + 10.4793i) q^{68} +(4.06942 + 2.95660i) q^{70} +7.66257i q^{71} -8.40588i q^{73} +(9.77021 - 13.4476i) q^{74} +(-1.55944 + 3.06058i) q^{76} +(-0.984548 + 0.984548i) q^{77} +13.8712i q^{79} +(-14.0520 - 2.22559i) q^{80} +(-13.3615 + 2.11626i) q^{82} +(-7.31214 - 7.31214i) q^{83} +(13.8560 - 13.8560i) q^{85} +(-8.12038 - 5.89979i) q^{86} +(1.21696 - 3.74545i) q^{88} +7.49158 q^{89} +(-3.26086 - 3.26086i) q^{91} +(-5.32760 - 16.3966i) q^{92} +(-4.71891 + 0.747406i) q^{94} +6.10874 q^{95} -7.84085 q^{97} +(-1.39680 + 0.221233i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.39680	+	0.221233i	−0.987688	+	0.156435i
$2$	−1.39680	+	0.221233i	−0.987688	+	0.156435i
$3$		0			0
$3$		0			0
$4$	1.90211	−	0.618037i	0.951056	−	0.309018i
$5$	−2.51504	−	2.51504i	−1.12476	−	1.12476i	−0.991016	−	0.133742i	$-0.957301\pi$
$5$	−2.51504	−	2.51504i	−1.12476	−	1.12476i	−0.133742	−	0.991016i	$-0.542699\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.52014	+	1.28408i	−0.891006	+	0.453992i
$9$		0			0
$10$	4.06942	+	2.95660i	1.28686	+	0.934959i
$11$	−0.984548	+	0.984548i	−0.296852	+	0.296852i	−0.839780	−	0.542927i	$-0.817316\pi$
$11$	−0.984548	+	0.984548i	−0.296852	+	0.296852i	0.542927	+	0.839780i	$0.317316\pi$
$12$		0			0
$13$	−3.26086	−	3.26086i	−0.904399	−	0.904399i	0.0914142	−	0.995813i	$-0.470861\pi$
$13$	−3.26086	−	3.26086i	−0.904399	−	0.904399i	−0.995813	+	0.0914142i	$0.970861\pi$
$14$	−1.39680	+	0.221233i	−0.373311	+	0.0591269i
$15$		0			0
$16$	3.23606	−	2.35115i	0.809015	−	0.587787i
$17$			5.50927i			1.33619i	0.744074	+	0.668097i	$0.232891\pi$
$17$			5.50927i			1.33619i	−0.744074	+	0.668097i	$0.767109\pi$
$18$		0			0
$19$	−1.21444	+	1.21444i	−0.278613	+	0.278613i	−0.832555	−	0.553942i	$-0.813123\pi$
$19$	−1.21444	+	1.21444i	−0.278613	+	0.278613i	0.553942	+	0.832555i	$0.313123\pi$
$20$	−6.33826	−	3.22950i	−1.41728	−	0.722137i
$21$		0			0
$22$	1.15740	−	1.59303i	0.246759	−	0.339636i
$23$		−	8.62021i		−	1.79744i	−0.438526	−	0.898719i	$-0.644499\pi$
$23$		−	8.62021i		−	1.79744i	0.438526	−	0.898719i	$-0.355501\pi$
$24$		0			0
$25$			7.65081i			1.53016i
$26$	5.27618	+	3.83336i	1.03474	+	0.751784i
$27$		0			0
$28$	1.90211	−	0.618037i	0.359465	−	0.116798i
$29$	−2.04663	+	2.04663i	−0.380050	+	0.380050i	−0.871120	−	0.491070i	$-0.836606\pi$
$29$	−2.04663	+	2.04663i	−0.380050	+	0.380050i	0.491070	+	0.871120i	$0.336606\pi$
$30$		0			0
$31$			0.164437i			0.0295337i	0.999891	+	0.0147669i	$0.00470061\pi$
$31$			0.164437i			0.0295337i	−0.999891	+	0.0147669i	$0.995299\pi$
$32$	−3.99999	+	4.00001i	−0.707104	+	0.707109i
$33$		0			0
$34$	−1.21883	−	7.69536i	−0.209028	−	1.31974i
$35$	−2.51504	−	2.51504i	−0.425119	−	0.425119i
$36$		0			0
$37$	−8.31105	+	8.31105i	−1.36633	+	1.36633i	−0.500717	+	0.865611i	$0.666930\pi$
$37$	−8.31105	+	8.31105i	−1.36633	+	1.36633i	−0.865611	+	0.500717i	$0.833070\pi$
$38$	1.42766	−	1.96501i	0.231598	−	0.318767i
$39$		0			0
$40$	9.56777	+	3.10874i	1.51280	+	0.491534i
$41$	9.56578			1.49392			0.746962	−	0.664867i	$-0.231512\pi$
$41$	9.56578			1.49392			0.746962	+	0.664867i	$0.231512\pi$
$42$		0			0
$43$	5.01867	+	5.01867i	0.765340	+	0.765340i	0.977282	−	0.211942i	$-0.0679789\pi$
$43$	5.01867	+	5.01867i	0.765340	+	0.765340i	−0.211942	+	0.977282i	$0.567979\pi$
$44$	−1.26423	+	2.48121i	−0.190590	+	0.374056i
$45$		0			0
$46$	1.90707	+	12.0407i	0.281182	+	1.77531i
$47$	3.37837			0.492786			0.246393	−	0.969170i	$-0.420755\pi$
$47$	3.37837			0.492786			0.246393	+	0.969170i	$0.420755\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−1.69261	−	10.6867i	−0.239371	−	1.51132i
$51$		0			0
$52$	−8.21784	−	4.18719i	−1.13961	−	0.580658i
$53$	3.72717	+	3.72717i	0.511966	+	0.511966i	0.915129	−	0.403162i	$-0.132089\pi$
$53$	3.72717	+	3.72717i	0.511966	+	0.511966i	−0.403162	+	0.915129i	$0.632089\pi$
$54$		0			0
$55$	4.95235			0.667774
$56$	−2.52014	+	1.28408i	−0.336768	+	0.171593i
$57$		0			0
$58$	2.40596	−	3.31153i	0.315918	−	0.434825i
$59$	−10.0781	+	10.0781i	−1.31206	+	1.31206i	−0.392162	+	0.919896i	$0.628273\pi$
$59$	−10.0781	+	10.0781i	−1.31206	+	1.31206i	−0.919896	+	0.392162i	$0.871727\pi$
$60$		0			0
$61$	−1.07042	−	1.07042i	−0.137054	−	0.137054i	0.635252	−	0.772305i	$-0.280896\pi$
$61$	−1.07042	−	1.07042i	−0.137054	−	0.137054i	−0.772305	+	0.635252i	$0.780896\pi$
$62$	−0.0363788	−	0.229686i	−0.00462011	−	0.0291701i
$63$		0			0
$64$	4.70226	−	6.47216i	0.587782	−	0.809019i
$65$			16.4023i			2.03446i
$66$		0			0
$67$	−3.12073	+	3.12073i	−0.381258	+	0.381258i	−0.871555	−	0.490297i	$-0.836888\pi$
$67$	−3.12073	+	3.12073i	−0.381258	+	0.381258i	0.490297	+	0.871555i	$0.336888\pi$
$68$	3.40493	+	10.4793i	0.412909	+	1.27080i
$69$		0			0
$70$	4.06942	+	2.95660i	0.486388	+	0.353381i
$71$			7.66257i			0.909380i	0.890650	+	0.454690i	$0.150250\pi$
$71$			7.66257i			0.909380i	−0.890650	+	0.454690i	$0.849750\pi$
$72$		0			0
$73$		−	8.40588i		−	0.983834i	−0.870642	−	0.491917i	$-0.836296\pi$
$73$		−	8.40588i		−	0.983834i	0.870642	−	0.491917i	$-0.163704\pi$
$74$	9.77021	−	13.4476i	1.13576	−	1.56325i
$75$		0			0
$76$	−1.55944	+	3.06058i	−0.178880	+	0.351073i
$77$	−0.984548	+	0.984548i	−0.112200	+	0.112200i
$78$		0			0
$79$			13.8712i			1.56063i	0.625387	+	0.780315i	$0.284941\pi$
$79$			13.8712i			1.56063i	−0.625387	+	0.780315i	$0.715059\pi$
$80$	−14.0520	−	2.22559i	−1.57107	−	0.248828i
$81$		0			0
$82$	−13.3615	+	2.11626i	−1.47553	+	0.233702i
$83$	−7.31214	−	7.31214i	−0.802611	−	0.802611i	0.180892	−	0.983503i	$-0.442102\pi$
$83$	−7.31214	−	7.31214i	−0.802611	−	0.802611i	−0.983503	+	0.180892i	$0.942102\pi$
$84$		0			0
$85$	13.8560	−	13.8560i	1.50290	−	1.50290i
$86$	−8.12038	−	5.89979i	−0.875643	−	0.636191i
$87$		0			0
$88$	1.21696	−	3.74545i	0.129728	−	0.399266i
$89$	7.49158			0.794106			0.397053	−	0.917796i	$-0.370033\pi$
$89$	7.49158			0.794106			0.397053	+	0.917796i	$0.370033\pi$
$90$		0			0
$91$	−3.26086	−	3.26086i	−0.341831	−	0.341831i
$92$	−5.32760	−	16.3966i	−0.555441	−	1.70946i
$93$		0			0
$94$	−4.71891	+	0.747406i	−0.486719	+	0.0770890i
$95$	6.10874			0.626744
$96$		0			0
$97$	−7.84085			−0.796118			−0.398059	−	0.917360i	$-0.630316\pi$
$97$	−7.84085			−0.796118			−0.398059	+	0.917360i	$0.630316\pi$
$98$	−1.39680	+	0.221233i	−0.141098	+	0.0223479i
$99$		0			0
$100$	4.72848	+	14.5527i	0.472848	+	1.45527i
$101$	0.748257	+	0.748257i	0.0744543	+	0.0744543i	0.743353	−	0.668899i	$-0.233234\pi$
$101$	0.748257	+	0.748257i	0.0744543	+	0.0744543i	−0.668899	+	0.743353i	$0.733234\pi$
$102$		0			0
$103$	−11.8161			−1.16428			−0.582140	−	0.813089i	$-0.697784\pi$
$103$	−11.8161			−1.16428			−0.582140	+	0.813089i	$0.697784\pi$
$104$	12.4050	+	4.03061i	1.21641	+	0.395234i
$105$		0			0
$106$	−6.03069	−	4.38155i	−0.585753	−	0.425574i
$107$	−4.41189	+	4.41189i	−0.426514	+	0.426514i	−0.887439	−	0.460925i	$-0.847518\pi$
$107$	−4.41189	+	4.41189i	−0.426514	+	0.426514i	0.460925	+	0.887439i	$0.347518\pi$
$108$		0			0
$109$	−0.128743	−	0.128743i	−0.0123314	−	0.0123314i	0.700914	−	0.713246i	$-0.252776\pi$
$109$	−0.128743	−	0.128743i	−0.0123314	−	0.0123314i	−0.713246	+	0.700914i	$0.752776\pi$
$110$	−6.91745	+	1.09562i	−0.659553	+	0.104463i
$111$		0			0
$112$	3.23606	−	2.35115i	0.305779	−	0.222163i
$113$			14.3042i			1.34563i	0.739811	+	0.672815i	$0.234915\pi$
$113$			14.3042i			1.34563i	−0.739811	+	0.672815i	$0.765085\pi$
$114$		0			0
$115$	−21.6801	+	21.6801i	−2.02168	+	2.02168i
$116$	−2.62803	+	5.15782i	−0.244007	+	0.478892i
$117$		0			0
$118$	11.8475	−	16.3067i	1.09065	−	1.50116i
$119$			5.50927i			0.505034i
$120$		0			0
$121$			9.06133i			0.823757i
$122$	1.73198	+	1.25836i	0.156806	+	0.113926i
$123$		0			0
$124$	0.101628	+	0.312777i	0.00912646	+	0.0280882i
$125$	6.66689	−	6.66689i	0.596304	−	0.596304i
$126$		0			0
$127$			1.31914i			0.117055i	0.998286	+	0.0585274i	$0.0186405\pi$
$127$			1.31914i			0.117055i	−0.998286	+	0.0585274i	$0.981359\pi$
$128$	−5.13627	+	10.0806i	−0.453986	+	0.891009i
$129$		0			0
$130$	−3.62873	−	22.9108i	−0.318261	−	2.00941i
$131$	−3.84141	−	3.84141i	−0.335626	−	0.335626i	0.519093	−	0.854718i	$-0.326270\pi$
$131$	−3.84141	−	3.84141i	−0.335626	−	0.335626i	−0.854718	+	0.519093i	$0.826270\pi$
$132$		0			0
$133$	−1.21444	+	1.21444i	−0.105306	+	0.105306i
$134$	3.66863	−	5.04945i	0.316922	−	0.436206i
$135$		0			0
$136$	−7.07437	−	13.8842i	−0.606622	−	1.19056i
$137$	−11.8262			−1.01038			−0.505191	−	0.863008i	$-0.668578\pi$
$137$	−11.8262			−1.01038			−0.505191	+	0.863008i	$0.668578\pi$
$138$		0			0
$139$	−10.6322	−	10.6322i	−0.901814	−	0.901814i	0.0937788	−	0.995593i	$-0.470105\pi$
$139$	−10.6322	−	10.6322i	−0.901814	−	0.901814i	−0.995593	+	0.0937788i	$0.970105\pi$
$140$	−6.33826	−	3.22950i	−0.535681	−	0.272942i
$141$		0			0
$142$	−1.69521	−	10.7031i	−0.142259	−	0.898184i
$143$	6.42094			0.536946
$144$		0			0
$145$	10.2947			0.854930
$146$	1.85966	+	11.7413i	0.153906	+	0.971721i
$147$		0			0
$148$	−10.6720	+	20.9451i	−0.877234	+	1.72167i
$149$	9.66703	+	9.66703i	0.791954	+	0.791954i	0.981812	−	0.189858i	$-0.0608027\pi$
$149$	9.66703	+	9.66703i	0.791954	+	0.791954i	−0.189858	+	0.981812i	$0.560803\pi$
$150$		0			0
$151$	−5.05132			−0.411070			−0.205535	−	0.978650i	$-0.565893\pi$
$151$	−5.05132			−0.411070			−0.205535	+	0.978650i	$0.565893\pi$
$152$	1.50113	−	4.62002i	0.121757	−	0.374733i
$153$		0			0
$154$	1.15740	−	1.59303i	0.0932663	−	0.128370i
$155$	0.413565	−	0.413565i	0.0332183	−	0.0332183i
$156$		0			0
$157$	11.1102	+	11.1102i	0.886692	+	0.886692i	0.994204	−	0.107512i	$-0.0342884\pi$
$157$	11.1102	+	11.1102i	0.886692	+	0.886692i	−0.107512	+	0.994204i	$0.534288\pi$
$158$	−3.06876	−	19.3753i	−0.244137	−	1.54142i
$159$		0			0
$160$	20.1203		6.79865e-5i	1.59065		5.37480e-6i
$161$		−	8.62021i		−	0.679367i
$162$		0			0
$163$	0.936756	−	0.936756i	0.0733724	−	0.0733724i	−0.669468	−	0.742841i	$-0.733478\pi$
$163$	0.936756	−	0.936756i	0.0733724	−	0.0733724i	0.742841	+	0.669468i	$0.233478\pi$
$164$	18.1952	−	5.91200i	1.42080	−	0.461650i
$165$		0			0
$166$	11.8313	+	8.59592i	0.918286	+	0.667173i
$167$		−	17.9147i		−	1.38628i	−0.720804	−	0.693139i	$-0.756227\pi$
$167$		−	17.9147i		−	1.38628i	0.720804	−	0.693139i	$-0.243773\pi$
$168$		0			0
$169$			8.26636i			0.635874i
$170$	−16.2887	+	22.4195i	−1.24929	+	1.71950i
$171$		0			0
$172$	12.6478	+	6.44435i	0.964385	+	0.491377i
$173$	−1.95689	+	1.95689i	−0.148780	+	0.148780i	−0.777573	−	0.628793i	$-0.783549\pi$
$173$	−1.95689	+	1.95689i	−0.148780	+	0.148780i	0.628793	+	0.777573i	$0.283549\pi$
$174$		0			0
$175$			7.65081i			0.578347i
$176$	−0.871238	+	5.50088i	−0.0656720	+	0.414644i
$177$		0			0
$178$	−10.4643	+	1.65738i	−0.784329	+	0.124226i
$179$	16.4536	+	16.4536i	1.22980	+	1.22980i	0.964039	+	0.265760i	$0.0856230\pi$
$179$	16.4536	+	16.4536i	1.22980	+	1.22980i	0.265760	+	0.964039i	$0.414377\pi$
$180$		0			0
$181$	2.01639	−	2.01639i	0.149877	−	0.149877i	−0.628186	−	0.778063i	$-0.716202\pi$
$181$	2.01639	−	2.01639i	0.149877	−	0.149877i	0.778063	+	0.628186i	$0.216202\pi$
$182$	5.27618	+	3.83336i	0.391096	+	0.284148i
$183$		0			0
$184$	11.0691	+	21.7242i	0.816023	+	1.60153i
$185$	41.8052			3.07358
$186$		0			0
$187$	−5.42414	−	5.42414i	−0.396653	−	0.396653i
$188$	6.42604	−	2.08796i	0.468667	−	0.152280i
$189$		0			0
$190$	−8.53270	+	1.35145i	−0.619027	+	0.0980447i
$191$	−6.72330			−0.486481			−0.243240	−	0.969966i	$-0.578210\pi$
$191$	−6.72330			−0.486481			−0.243240	+	0.969966i	$0.578210\pi$
$192$		0			0
$193$	1.37543			0.0990058			0.0495029	−	0.998774i	$-0.484236\pi$
$193$	1.37543			0.0990058			0.0495029	+	0.998774i	$0.484236\pi$
$194$	10.9521	−	1.73465i	0.786316	−	0.124541i
$195$		0			0
$196$	1.90211	−	0.618037i	0.135865	−	0.0441455i
$197$	−10.2035	−	10.2035i	−0.726967	−	0.726967i	0.243048	−	0.970014i	$-0.421853\pi$
$197$	−10.2035	−	10.2035i	−0.726967	−	0.726967i	−0.970014	+	0.243048i	$0.921853\pi$
$198$		0			0
$199$	−14.9391			−1.05900			−0.529501	−	0.848309i	$-0.677621\pi$
$199$	−14.9391			−1.05900			−0.529501	+	0.848309i	$0.677621\pi$
$200$	−9.82429	−	19.2811i	−0.694682	−	1.36338i
$201$		0			0
$202$	−1.21071	−	0.879628i	−0.0851849	−	0.0618904i
$203$	−2.04663	+	2.04663i	−0.143646	+	0.143646i
$204$		0			0
$205$	−24.0583	−	24.0583i	−1.68030	−	1.68030i
$206$	16.5048	−	2.61412i	1.14994	−	0.182134i
$207$		0			0
$208$	−18.2191	−	2.88557i	−1.26327	−	0.200078i
$209$		−	2.39136i		−	0.165414i
$210$		0			0
$211$	4.93531	−	4.93531i	0.339761	−	0.339761i	−0.516516	−	0.856277i	$-0.672772\pi$
$211$	4.93531	−	4.93531i	0.339761	−	0.339761i	0.856277	+	0.516516i	$0.172772\pi$
$212$	9.39303	+	4.78597i	0.645116	+	0.328702i
$213$		0			0
$214$	5.18648	−	7.13859i	0.354541	−	0.487984i
$215$		−	25.2443i		−	1.72164i
$216$		0			0
$217$			0.164437i			0.0111627i
$218$	0.208311	+	0.151347i	0.0141086	+	0.0102505i
$219$		0			0
$220$	9.41992	−	3.06073i	0.635091	−	0.206354i
$221$	17.9649	−	17.9649i	1.20845	−	1.20845i
$222$		0			0
$223$		−	5.25747i		−	0.352066i	−0.984384	−	0.176033i	$-0.943673\pi$
$223$		−	5.25747i		−	0.352066i	0.984384	−	0.176033i	$-0.0563266\pi$
$224$	−3.99999	+	4.00001i	−0.267260	+	0.267262i
$225$		0			0
$226$	−3.16456	−	19.9802i	−0.210504	−	1.32906i
$227$	−6.30931	−	6.30931i	−0.418763	−	0.418763i	0.466014	−	0.884777i	$-0.345690\pi$
$227$	−6.30931	−	6.30931i	−0.418763	−	0.418763i	−0.884777	+	0.466014i	$0.845690\pi$
$228$		0			0
$229$	19.1785	−	19.1785i	1.26735	−	1.26735i	0.319899	−	0.947452i	$-0.396351\pi$
$229$	19.1785	−	19.1785i	1.26735	−	1.26735i	0.947452	−	0.319899i	$-0.103649\pi$
$230$	25.4865	−	35.0792i	1.68053	−	2.31305i
$231$		0			0
$232$	2.52976	−	7.78586i	0.166087	−	0.511167i
$233$	−0.555029			−0.0363611			−0.0181806	−	0.999835i	$-0.505787\pi$
$233$	−0.555029			−0.0363611			−0.0181806	+	0.999835i	$0.505787\pi$
$234$		0			0
$235$	−8.49672	−	8.49672i	−0.554265	−	0.554265i
$236$	−12.9411	+	25.3983i	−0.842391	+	1.65329i
$237$		0			0
$238$	−1.21883	−	7.69536i	−0.0790051	−	0.498816i
$239$	−23.0408			−1.49039			−0.745194	−	0.666848i	$-0.767643\pi$
$239$	−23.0408			−1.49039			−0.745194	+	0.666848i	$0.767643\pi$
$240$		0			0
$241$	−7.47827			−0.481718			−0.240859	−	0.970560i	$-0.577429\pi$
$241$	−7.47827			−0.481718			−0.240859	+	0.970560i	$0.577429\pi$
$242$	−2.00466	−	12.6569i	−0.128865	−	0.813615i
$243$		0			0
$244$	−2.69762	−	1.37450i	−0.172698	−	0.0879936i
$245$	−2.51504	−	2.51504i	−0.160680	−	0.160680i
$246$		0			0
$247$	7.92026			0.503954
$248$	−0.211151	−	0.414405i	−0.0134081	−	0.0263147i
$249$		0			0
$250$	−7.83739	+	10.7873i	−0.495680	+	0.682246i
$251$	18.7049	−	18.7049i	1.18064	−	1.18064i	0.201066	−	0.979578i	$-0.435559\pi$
$251$	18.7049	−	18.7049i	1.18064	−	1.18064i	0.979578	−	0.201066i	$-0.0644407\pi$
$252$		0			0
$253$	8.48701	+	8.48701i	0.533574	+	0.533574i
$254$	−0.291837	−	1.84258i	−0.0183115	−	0.115614i
$255$		0			0
$256$	4.94419	−	15.2169i	0.309012	−	0.951058i
$257$		−	18.3076i		−	1.14200i	−0.820951	−	0.570998i	$-0.806556\pi$
$257$		−	18.3076i		−	1.14200i	0.820951	−	0.570998i	$-0.193444\pi$
$258$		0			0
$259$	−8.31105	+	8.31105i	−0.516423	+	0.516423i
$260$	10.1372	+	31.1991i	0.628685	+	1.93489i
$261$		0			0
$262$	6.21554	+	4.51584i	0.383997	+	0.278990i
$263$		−	20.1306i		−	1.24130i	−0.784086	−	0.620652i	$-0.786868\pi$
$263$		−	20.1306i		−	1.24130i	0.784086	−	0.620652i	$-0.213132\pi$
$264$		0			0
$265$		−	18.7479i		−	1.15168i
$266$	1.42766	−	1.96501i	0.0875357	−	0.120483i
$267$		0			0
$268$	−4.00725	+	7.86470i	−0.244782	+	0.480413i
$269$	−8.69779	+	8.69779i	−0.530313	+	0.530313i	−0.920666	−	0.390352i	$-0.872353\pi$
$269$	−8.69779	+	8.69779i	−0.530313	+	0.530313i	0.390352	+	0.920666i	$0.372353\pi$
$270$		0			0
$271$			11.6299i			0.706466i	0.935535	+	0.353233i	$0.114918\pi$
$271$			11.6299i			0.706466i	−0.935535	+	0.353233i	$0.885082\pi$
$272$	12.9531	+	17.8283i	0.785399	+	1.08100i
$273$		0			0
$274$	16.5189	−	2.61635i	0.997942	−	0.158059i
$275$	−7.53259	−	7.53259i	−0.454232	−	0.454232i
$276$		0			0
$277$	22.9876	−	22.9876i	1.38119	−	1.38119i	0.538679	−	0.842511i	$-0.318923\pi$
$277$	22.9876	−	22.9876i	1.38119	−	1.38119i	0.842511	−	0.538679i	$-0.181077\pi$
$278$	17.2033	+	12.4989i	1.03179	+	0.749636i
$279$		0			0
$280$	9.56777	+	3.10874i	0.571784	+	0.185783i
$281$	11.5187			0.687148			0.343574	−	0.939126i	$-0.388362\pi$
$281$	11.5187			0.687148			0.343574	+	0.939126i	$0.388362\pi$
$282$		0			0
$283$	−15.6255	−	15.6255i	−0.928839	−	0.928839i	0.0687924	−	0.997631i	$-0.478085\pi$
$283$	−15.6255	−	15.6255i	−0.928839	−	0.928839i	−0.997631	+	0.0687924i	$0.978085\pi$
$284$	4.73575	+	14.5751i	0.281015	+	0.864872i
$285$		0			0
$286$	−8.96878	+	1.42052i	−0.530335	+	0.0839972i
$287$	9.56578			0.564650
$288$		0			0
$289$	−13.3521			−0.785417
$290$	−14.3797	+	2.27753i	−0.844404	+	0.133741i
$291$		0			0
$292$	−5.19514	−	15.9889i	−0.304023	−	0.935681i
$293$	−3.77816	−	3.77816i	−0.220722	−	0.220722i	0.588080	−	0.808803i	$-0.299884\pi$
$293$	−3.77816	−	3.77816i	−0.220722	−	0.220722i	−0.808803	+	0.588080i	$0.799884\pi$
$294$		0			0
$295$	50.6936			2.95150
$296$	10.2730	−	31.6171i	0.597104	−	1.83771i
$297$		0			0
$298$	−15.6416	−	11.3643i	−0.906093	−	0.658314i
$299$	−28.1093	+	28.1093i	−1.62560	+	1.62560i
$300$		0			0
$301$	5.01867	+	5.01867i	0.289271	+	0.289271i
$302$	7.05569	−	1.11752i	0.406009	−	0.0643058i
$303$		0			0
$304$	−1.07468	+	6.78536i	−0.0616369	+	0.389167i
$305$			5.38430i			0.308304i
$306$		0			0
$307$	0.708546	−	0.708546i	0.0404389	−	0.0404389i	−0.686598	−	0.727037i	$-0.740897\pi$
$307$	0.708546	−	0.708546i	0.0404389	−	0.0404389i	0.727037	+	0.686598i	$0.240897\pi$
$308$	−1.26423	+	2.48121i	−0.0720364	+	0.141380i
$309$		0			0
$310$	−0.486174	+	0.669162i	−0.0276128	+	0.0380058i
$311$			21.6074i			1.22525i	0.790376	+	0.612623i	$0.209885\pi$
$311$			21.6074i			1.22525i	−0.790376	+	0.612623i	$0.790115\pi$
$312$		0			0
$313$			5.11637i			0.289194i	0.989491	+	0.144597i	$0.0461886\pi$
$313$			5.11637i			0.289194i	−0.989491	+	0.144597i	$0.953811\pi$
$314$	−17.9767	−	13.0608i	−1.01448	−	0.737065i
$315$		0			0
$316$	8.57290	+	26.3845i	0.482263	+	1.48425i
$317$	−7.88622	+	7.88622i	−0.442934	+	0.442934i	−0.892997	−	0.450063i	$-0.851402\pi$
$317$	−7.88622	+	7.88622i	−0.442934	+	0.442934i	0.450063	+	0.892997i	$0.351402\pi$
$318$		0			0
$319$		−	4.03002i		−	0.225638i
$320$	−28.1040	+	4.45136i	−1.57106	+	0.248839i
$321$		0			0
$322$	1.90707	+	12.0407i	0.106277	+	0.671003i
$323$	−6.69070	−	6.69070i	−0.372281	−	0.372281i
$324$		0			0
$325$	24.9482	−	24.9482i	1.38388	−	1.38388i
$326$	−1.10122	+	1.51570i	−0.0609911	+	0.0839471i
$327$		0			0
$328$	−24.1071	+	12.2833i	−1.33109	+	0.678230i
$329$	3.37837			0.186256
$330$		0			0
$331$	0.144453	+	0.144453i	0.00793985	+	0.00793985i	0.711066	−	0.703126i	$-0.248213\pi$
$331$	0.144453	+	0.144453i	0.00793985	+	0.00793985i	−0.703126	+	0.711066i	$0.748213\pi$
$332$	−18.4277	−	9.38934i	−1.01135	−	0.515307i
$333$		0			0
$334$	3.96331	+	25.0232i	0.216862	+	1.36921i
$335$	15.6975			0.857646
$336$		0			0
$337$	−18.3255			−0.998256			−0.499128	−	0.866528i	$-0.666346\pi$
$337$	−18.3255			−0.998256			−0.499128	+	0.866528i	$0.666346\pi$
$338$	−1.82879	−	11.5465i	−0.0994731	−	0.628045i
$339$		0			0
$340$	17.7922	−	34.9192i	0.964916	−	1.89376i
$341$	−0.161896	−	0.161896i	−0.00876716	−	0.00876716i
$342$		0			0
$343$	1.00000			0.0539949
$344$	−19.0922	−	6.20338i	−1.02938	−	0.334464i
$345$		0			0
$346$	2.30046	−	3.16632i	0.123674	−	0.170222i
$347$	−7.70010	+	7.70010i	−0.413363	+	0.413363i	−0.882908	−	0.469545i	$-0.844418\pi$
$347$	−7.70010	+	7.70010i	−0.413363	+	0.413363i	0.469545	+	0.882908i	$0.344418\pi$
$348$		0			0
$349$	9.23902	+	9.23902i	0.494553	+	0.494553i	0.909737	−	0.415184i	$-0.136283\pi$
$349$	9.23902	+	9.23902i	0.494553	+	0.494553i	−0.415184	+	0.909737i	$0.636283\pi$
$350$	−1.69261	−	10.6867i	−0.0904738	−	0.571226i
$351$		0			0
$352$	−2.66143e−5	−	7.87638i	−1.41855e−6	−	0.419813i
$353$			13.9051i			0.740092i	0.929013	+	0.370046i	$0.120658\pi$
$353$			13.9051i			0.740092i	−0.929013	+	0.370046i	$0.879342\pi$
$354$		0			0
$355$	19.2716	−	19.2716i	1.02283	−	1.02283i
$356$	14.2498	−	4.63007i	0.755239	−	0.245393i
$357$		0			0
$358$	−26.6225	−	19.3423i	−1.40704	−	1.02227i
$359$		−	20.3979i		−	1.07656i	−0.842766	−	0.538281i	$-0.819074\pi$
$359$		−	20.3979i		−	1.07656i	0.842766	−	0.538281i	$-0.180926\pi$
$360$		0			0
$361$			16.0503i			0.844750i
$362$	−2.37041	+	3.26259i	−0.124586	+	0.171478i
$363$		0			0
$364$	−8.21784	−	4.18719i	−0.430732	−	0.219468i
$365$	−21.1411	+	21.1411i	−1.10658	+	1.10658i
$366$		0			0
$367$			21.2755i			1.11057i	0.831660	+	0.555285i	$0.187391\pi$
$367$			21.2755i			1.11057i	−0.831660	+	0.555285i	$0.812609\pi$
$368$	−20.2674	−	27.8955i	−1.05651	−	1.45415i
$369$		0			0
$370$	−58.3936	+	9.24867i	−3.03574	+	0.480815i
$371$	3.72717	+	3.72717i	0.193505	+	0.193505i
$372$		0			0
$373$	14.6527	−	14.6527i	0.758688	−	0.758688i	−0.217396	−	0.976084i	$-0.569756\pi$
$373$	14.6527	−	14.6527i	0.758688	−	0.758688i	0.976084	+	0.217396i	$0.0697562\pi$
$374$	8.77645	+	6.37646i	0.453820	+	0.329719i
$375$		0			0
$376$	−8.51398	+	4.33811i	−0.439075	+	0.223721i
$377$	13.3476			0.687434
$378$		0			0
$379$	−8.85565	−	8.85565i	−0.454884	−	0.454884i	0.442088	−	0.896972i	$-0.354238\pi$
$379$	−8.85565	−	8.85565i	−0.454884	−	0.454884i	−0.896972	+	0.442088i	$0.854238\pi$
$380$	11.6195	−	3.77543i	0.596068	−	0.193675i
$381$		0			0
$382$	9.39111	−	1.48741i	0.480491	−	0.0761027i
$383$	−33.3573			−1.70448			−0.852238	−	0.523154i	$-0.824755\pi$
$383$	−33.3573			−1.70448			−0.852238	+	0.523154i	$0.824755\pi$
$384$		0			0
$385$	4.95235			0.252395
$386$	−1.92121	+	0.304291i	−0.0977869	+	0.0154880i
$387$		0			0
$388$	−14.9142	+	4.84593i	−0.757153	+	0.246015i
$389$	2.00738	+	2.00738i	0.101778	+	0.101778i	0.756162	−	0.654384i	$-0.227072\pi$
$389$	2.00738	+	2.00738i	0.101778	+	0.101778i	−0.654384	+	0.756162i	$0.727072\pi$
$390$		0			0
$391$	47.4911			2.40173
$392$	−2.52014	+	1.28408i	−0.127287	+	0.0648560i
$393$		0			0
$394$	16.5096	+	11.9949i	0.831739	+	0.604293i
$395$	34.8865	−	34.8865i	1.75533	−	1.75533i
$396$		0			0
$397$	−2.43985	−	2.43985i	−0.122453	−	0.122453i	0.643225	−	0.765677i	$-0.277596\pi$
$397$	−2.43985	−	2.43985i	−0.122453	−	0.122453i	−0.765677	+	0.643225i	$0.777596\pi$
$398$	20.8669	−	3.30501i	1.04596	−	0.165665i
$399$		0			0
$400$	17.9882	+	24.7585i	0.899410	+	1.23792i
$401$			11.6798i			0.583263i	0.956531	+	0.291632i	$0.0941981\pi$
$401$			11.6798i			0.583263i	−0.956531	+	0.291632i	$0.905802\pi$
$402$		0			0
$403$	0.536205	−	0.536205i	0.0267103	−	0.0267103i
$404$	1.88572	+	0.960818i	0.0938180	+	0.0478025i
$405$		0			0
$406$	2.40596	−	3.31153i	0.119406	−	0.164348i
$407$		−	16.3653i		−	0.811195i
$408$		0			0
$409$			15.2951i			0.756292i	0.925746	+	0.378146i	$0.123438\pi$
$409$			15.2951i			0.756292i	−0.925746	+	0.378146i	$0.876562\pi$
$410$	38.9271	+	28.2822i	1.92247	+	1.39676i
$411$		0			0
$412$	−22.4756	+	7.30281i	−1.10729	+	0.359784i
$413$	−10.0781	+	10.0781i	−0.495911	+	0.495911i
$414$		0			0
$415$			36.7806i			1.80549i
$416$	26.0868		8.81475e-5i	1.27901		4.32179e-6i
$417$		0			0
$418$	0.529046	+	3.34025i	0.0258765	+	0.163377i
$419$	13.1833	+	13.1833i	0.644045	+	0.644045i	0.951547	−	0.307502i	$-0.0994932\pi$
$419$	13.1833	+	13.1833i	0.644045	+	0.644045i	−0.307502	+	0.951547i	$0.599493\pi$
$420$		0			0
$421$	−22.2574	+	22.2574i	−1.08476	+	1.08476i	−0.0887017	+	0.996058i	$0.528272\pi$
$421$	−22.2574	+	22.2574i	−1.08476	+	1.08476i	−0.996058	+	0.0887017i	$0.971728\pi$
$422$	−5.80180	+	7.98550i	−0.282427	+	0.388728i
$423$		0			0
$424$	−14.1790	−	4.60701i	−0.688594	−	0.223736i
$425$	−42.1504			−2.04459
$426$		0			0
$427$	−1.07042	−	1.07042i	−0.0518014	−	0.0518014i
$428$	−5.66520	+	11.1186i	−0.273838	+	0.537439i
$429$		0			0
$430$	5.58486	+	35.2612i	0.269326	+	1.70045i
$431$	−19.0326			−0.916769			−0.458385	−	0.888754i	$-0.651572\pi$
$431$	−19.0326			−0.916769			−0.458385	+	0.888754i	$0.651572\pi$
$432$		0			0
$433$	−31.7120			−1.52398			−0.761992	−	0.647587i	$-0.775778\pi$
$433$	−31.7120			−1.52398			−0.761992	+	0.647587i	$0.775778\pi$
$434$	−0.0363788	−	0.229686i	−0.00174624	−	0.0110253i
$435$		0			0
$436$	−0.324452	−	0.165316i	−0.0155384	−	0.00791720i
$437$	10.4688	+	10.4688i	0.500789	+	0.500789i
$438$		0			0
$439$	32.9521			1.57272			0.786359	−	0.617770i	$-0.211964\pi$
$439$	32.9521			1.57272			0.786359	+	0.617770i	$0.211964\pi$
$440$	−12.4806	+	6.35923i	−0.594991	+	0.303164i
$441$		0			0
$442$	−21.1190	+	29.0679i	−1.00453	+	1.38262i
$443$	−4.94776	+	4.94776i	−0.235075	+	0.235075i	−0.814807	−	0.579732i	$-0.803157\pi$
$443$	−4.94776	+	4.94776i	−0.235075	+	0.235075i	0.579732	+	0.814807i	$0.303157\pi$
$444$		0			0
$445$	−18.8416	−	18.8416i	−0.893177	−	0.893177i
$446$	1.16312	+	7.34365i	0.0550755	+	0.347732i
$447$		0			0
$448$	4.70226	−	6.47216i	0.222161	−	0.305781i
$449$		−	31.5258i		−	1.48779i	−0.668294	−	0.743897i	$-0.732975\pi$
$449$		−	31.5258i		−	1.48779i	0.668294	−	0.743897i	$-0.267025\pi$
$450$		0			0
$451$	−9.41796	+	9.41796i	−0.443475	+	0.443475i
$452$	8.84054	+	27.2083i	0.415824	+	1.27977i
$453$		0			0
$454$	10.2087	+	7.41703i	0.479117	+	0.348098i
$455$			16.4023i			0.768954i
$456$		0			0
$457$			35.2517i			1.64901i	0.565857	+	0.824503i	$0.308545\pi$
$457$			35.2517i			1.64901i	−0.565857	+	0.824503i	$0.691455\pi$
$458$	−22.5456	+	31.0315i	−1.05349	+	1.45001i
$459$		0			0
$460$	−27.8389	+	54.6372i	−1.29800	+	2.54747i
$461$	−15.8769	+	15.8769i	−0.739462	+	0.739462i	−0.972474	−	0.233012i	$-0.925142\pi$
$461$	−15.8769	+	15.8769i	−0.739462	+	0.739462i	0.233012	+	0.972474i	$0.425142\pi$
$462$		0			0
$463$		−	15.9217i		−	0.739946i	−0.929043	−	0.369973i	$-0.879367\pi$
$463$		−	15.9217i		−	0.739946i	0.929043	−	0.369973i	$-0.120633\pi$
$464$	−1.81109	+	11.4350i	−0.0840778	+	0.530855i
$465$		0			0
$466$	0.775265	−	0.122790i	0.0359135	−	0.00568816i
$467$	−6.52420	−	6.52420i	−0.301904	−	0.301904i	0.539854	−	0.841758i	$-0.318479\pi$
$467$	−6.52420	−	6.52420i	−0.301904	−	0.301904i	−0.841758	+	0.539854i	$0.818479\pi$
$468$		0			0
$469$	−3.12073	+	3.12073i	−0.144102	+	0.144102i
$470$	13.7480	+	9.98848i	0.634147	+	0.460734i
$471$		0			0
$472$	12.4572	−	38.3394i	0.573387	−	1.76472i
$473$	−9.88224			−0.454386
$474$		0			0
$475$	−9.29148	−	9.29148i	−0.426323	−	0.426323i
$476$	3.40493	+	10.4793i	0.156065	+	0.480316i
$477$		0			0
$478$	32.1835	−	5.09738i	1.47204	−	0.233149i
$479$	−31.5891			−1.44334			−0.721671	−	0.692237i	$-0.756625\pi$
$479$	−31.5891			−1.44334			−0.721671	+	0.692237i	$0.756625\pi$
$480$		0			0
$481$	54.2023			2.47141
$482$	10.4457	−	1.65444i	0.475787	−	0.0753576i
$483$		0			0
$484$	5.60023	+	17.2357i	0.254556	+	0.783439i
$485$	19.7200	+	19.7200i	0.895440	+	0.895440i
$486$		0			0
$487$	−29.4810			−1.33591			−0.667955	−	0.744202i	$-0.732830\pi$
$487$	−29.4810			−1.33591			−0.667955	+	0.744202i	$0.732830\pi$
$488$	4.07213	+	1.32311i	0.184337	+	0.0598942i
$489$		0			0
$490$	4.06942	+	2.95660i	0.183837	+	0.133566i
$491$	−6.06862	+	6.06862i	−0.273873	+	0.273873i	−0.830657	−	0.556784i	$-0.812035\pi$
$491$	−6.06862	+	6.06862i	−0.273873	+	0.273873i	0.556784	+	0.830657i	$0.312035\pi$
$492$		0			0
$493$	−11.2755	−	11.2755i	−0.507821	−	0.507821i
$494$	−11.0630	+	1.75222i	−0.497749	+	0.0788361i
$495$		0			0
$496$	0.386616	+	0.532128i	0.0173596	+	0.0238932i
$497$			7.66257i			0.343713i
$498$		0			0
$499$	15.8968	−	15.8968i	0.711638	−	0.711638i	−0.255240	−	0.966878i	$-0.582154\pi$
$499$	15.8968	−	15.8968i	0.711638	−	0.711638i	0.966878	+	0.255240i	$0.0821544\pi$
$500$	8.56079	−	16.8015i	0.382850	−	0.751388i
$501$		0			0
$502$	−21.9889	+	30.2652i	−0.981414	+	1.35080i
$503$			17.1978i			0.766813i	0.923580	+	0.383406i	$0.125249\pi$
$503$			17.1978i			0.766813i	−0.923580	+	0.383406i	$0.874751\pi$
$504$		0			0
$505$		−	3.76379i		−	0.167486i
$506$	−13.7323	−	9.97707i	−0.610474	−	0.443535i
$507$		0			0
$508$	0.815278	+	2.50916i	0.0361721	+	0.111326i
$509$	0.959431	−	0.959431i	0.0425260	−	0.0425260i	−0.685524	−	0.728050i	$-0.740427\pi$
$509$	0.959431	−	0.959431i	0.0425260	−	0.0425260i	0.728050	+	0.685524i	$0.240427\pi$
$510$		0			0
$511$		−	8.40588i		−	0.371854i
$512$	−3.53957	+	22.3489i	−0.156428	+	0.987689i
$513$		0			0
$514$	4.05024	+	25.5721i	0.178648	+	1.12794i
$515$	29.7180	+	29.7180i	1.30953	+	1.30953i
$516$		0			0
$517$	−3.32617	+	3.32617i	−0.146285	+	0.146285i
$518$	9.77021	−	13.4476i	0.429279	−	0.590852i
$519$		0			0
$520$	−21.0620	−	41.3363i	−0.923629	−	1.81272i
$521$	−9.04026			−0.396061			−0.198030	−	0.980196i	$-0.563454\pi$
$521$	−9.04026			−0.396061			−0.198030	+	0.980196i	$0.563454\pi$
$522$		0			0
$523$	−5.32615	−	5.32615i	−0.232896	−	0.232896i	0.581004	−	0.813901i	$-0.302660\pi$
$523$	−5.32615	−	5.32615i	−0.232896	−	0.232896i	−0.813901	+	0.581004i	$0.802660\pi$
$524$	−9.68093	−	4.93266i	−0.422913	−	0.215484i
$525$		0			0
$526$	4.45354	+	28.1184i	0.194184	+	1.22602i
$527$	−0.905927			−0.0394628
$528$		0			0
$529$	−51.3080			−2.23078
$530$	4.14766	+	26.1872i	0.180163	+	1.13750i
$531$		0			0
$532$	−1.55944	+	3.06058i	−0.0676102	+	0.132693i
$533$	−31.1926	−	31.1926i	−1.35110	−	1.35110i
$534$		0			0
$535$	22.1921			0.959449
$536$	3.85741	−	11.8720i	0.166615	−	0.512791i
$537$		0			0
$538$	10.2249	−	14.0733i	0.440825	−	0.606744i
$539$	−0.984548	+	0.984548i	−0.0424075	+	0.0424075i
$540$		0			0
$541$	12.7082	+	12.7082i	0.546367	+	0.546367i	0.925388	−	0.379021i	$-0.123739\pi$
$541$	12.7082	+	12.7082i	0.546367	+	0.546367i	−0.379021	+	0.925388i	$0.623739\pi$
$542$	−2.57291	−	16.2447i	−0.110516	−	0.697768i
$543$		0			0
$544$	−22.0372	−	22.0370i	−0.944836	−	0.944829i
$545$			0.647588i			0.0277396i
$546$		0			0
$547$	19.7217	−	19.7217i	0.843239	−	0.843239i	−0.146040	−	0.989279i	$-0.546653\pi$
$547$	19.7217	−	19.7217i	0.843239	−	0.843239i	0.989279	+	0.146040i	$0.0466527\pi$
$548$	−22.4948	+	7.30904i	−0.960930	+	0.312227i
$549$		0			0
$550$	12.1880	+	8.85508i	0.519698	+	0.377582i
$551$		−	4.97105i		−	0.211774i
$552$		0			0
$553$			13.8712i			0.589863i
$554$	−27.0235	+	37.1947i	−1.14812	+	1.58025i
$555$		0			0
$556$	−26.7948	−	13.6526i	−1.13635	−	0.578999i
$557$	32.2571	−	32.2571i	1.36678	−	1.36678i	0.501789	−	0.864990i	$-0.332675\pi$
$557$	32.2571	−	32.2571i	1.36678	−	1.36678i	0.864990	−	0.501789i	$-0.167325\pi$
$558$		0			0
$559$		−	32.7303i		−	1.38434i
$560$	−14.0520	−	2.22559i	−0.593807	−	0.0940481i
$561$		0			0
$562$	−16.0893	+	2.54831i	−0.678688	+	0.107494i
$563$	−27.0814	−	27.0814i	−1.14134	−	1.14134i	−0.988205	−	0.153138i	$-0.951062\pi$
$563$	−27.0814	−	27.0814i	−1.14134	−	1.14134i	−0.153138	−	0.988205i	$-0.548938\pi$
$564$		0			0
$565$	35.9757	−	35.9757i	1.51351	−	1.51351i
$566$	25.2826	+	18.3688i	1.06271	+	0.772100i
$567$		0			0
$568$	−9.83939	−	19.3108i	−0.412852	−	0.810263i
$569$	28.4823			1.19404			0.597020	−	0.802226i	$-0.296351\pi$
$569$	28.4823			1.19404			0.597020	+	0.802226i	$0.296351\pi$
$570$		0			0
$571$	15.8844	+	15.8844i	0.664743	+	0.664743i	0.956494	−	0.291751i	$-0.0942380\pi$
$571$	15.8844	+	15.8844i	0.664743	+	0.664743i	−0.291751	+	0.956494i	$0.594238\pi$
$572$	12.2133	−	3.96837i	0.510666	−	0.165926i
$573$		0			0
$574$	−13.3615	+	2.11626i	−0.557698	+	0.0883311i
$575$	65.9516			2.75037
$576$		0			0
$577$	4.65713			0.193879			0.0969395	−	0.995290i	$-0.469095\pi$
$577$	4.65713			0.193879			0.0969395	+	0.995290i	$0.469095\pi$
$578$	18.6502	−	2.95392i	0.775747	−	0.122867i
$579$		0			0
$580$	19.5817	−	6.36251i	0.813086	−	0.264189i
$581$	−7.31214	−	7.31214i	−0.303359	−	0.303359i
$582$		0			0
$583$	−7.33916			−0.303957
$584$	10.7939	+	21.1840i	0.446653	+	0.876601i
$585$		0			0
$586$	6.11319	+	4.44149i	0.252534	+	0.183476i
$587$	−13.2034	+	13.2034i	−0.544963	+	0.544963i	−0.924980	−	0.380017i	$-0.875918\pi$
$587$	−13.2034	+	13.2034i	−0.544963	+	0.544963i	0.380017	+	0.924980i	$0.375918\pi$
$588$		0			0
$589$	−0.199699	−	0.199699i	−0.00822847	−	0.00822847i
$590$	−70.8090	+	11.2151i	−2.91516	+	0.461718i
$591$		0			0
$592$	−7.35455	+	46.4356i	−0.302270	+	1.90849i
$593$			8.00745i			0.328827i	0.986392	+	0.164413i	$0.0525731\pi$
$593$			8.00745i			0.328827i	−0.986392	+	0.164413i	$0.947427\pi$
$594$		0			0
$595$	13.8560	−	13.8560i	0.568041	−	0.568041i
$596$	24.3624	+	12.4132i	0.997921	+	0.508464i
$597$		0			0
$598$	33.0444	−	45.4817i	1.35129	−	1.85989i
$599$		−	29.8782i		−	1.22079i	−0.792096	−	0.610396i	$-0.791010\pi$
$599$		−	29.8782i		−	1.22079i	0.792096	−	0.610396i	$-0.208990\pi$
$600$		0			0
$601$		−	28.4594i		−	1.16088i	−0.814302	−	0.580441i	$-0.802880\pi$
$601$		−	28.4594i		−	1.16088i	0.814302	−	0.580441i	$-0.197120\pi$
$602$	−8.12038	−	5.89979i	−0.330962	−	0.240458i
$603$		0			0
$604$	−9.60817	+	3.12190i	−0.390951	+	0.127028i
$605$	22.7896	−	22.7896i	0.926528	−	0.926528i
$606$		0			0
$607$			27.1606i			1.10242i	0.834368	+	0.551208i	$0.185833\pi$
$607$			27.1606i			1.10242i	−0.834368	+	0.551208i	$0.814167\pi$
$608$	−3.28289e−5	−	9.71555i	−1.33139e−6	−	0.394018i
$609$		0			0
$610$	−1.19118	−	7.52080i	−0.0482296	−	0.304508i
$611$	−11.0164	−	11.0164i	−0.445675	−	0.445675i
$612$		0			0
$613$	−25.1239	+	25.1239i	−1.01474	+	1.01474i	−0.0148539	+	0.999890i	$0.504728\pi$
$613$	−25.1239	+	25.1239i	−1.01474	+	1.01474i	−0.999890	+	0.0148539i	$0.995272\pi$
$614$	−0.832946	+	1.14645i	−0.0336149	+	0.0462671i
$615$		0			0
$616$	1.21696	−	3.74545i	0.0490327	−	0.150908i
$617$	−20.2712			−0.816089			−0.408044	−	0.912962i	$-0.633789\pi$
$617$	−20.2712			−0.816089			−0.408044	+	0.912962i	$0.633789\pi$
$618$		0			0
$619$	−13.2344	−	13.2344i	−0.531937	−	0.531937i	0.389211	−	0.921148i	$-0.372748\pi$
$619$	−13.2344	−	13.2344i	−0.531937	−	0.531937i	−0.921148	+	0.389211i	$0.872748\pi$
$620$	0.531048	−	1.04224i	0.0213274	−	0.0418575i
$621$		0			0
$622$	−4.78027	−	30.1813i	−0.191671	−	1.21016i
$623$	7.49158			0.300144
$624$		0			0
$625$	4.71914			0.188766
$626$	−1.13191	−	7.14655i	−0.0452401	−	0.285634i
$627$		0			0
$628$	27.9994	+	14.2664i	1.11730	+	0.569290i
$629$	−45.7878	−	45.7878i	−1.82568	−	1.82568i
$630$		0			0
$631$	−47.8911			−1.90651			−0.953257	−	0.302161i	$-0.902292\pi$
$631$	−47.8911			−1.90651			−0.953257	+	0.302161i	$0.902292\pi$
$632$	−17.8118	−	34.9574i	−0.708514	−	1.39053i
$633$		0			0
$634$	9.27080	−	12.7602i	0.368191	−	0.506771i
$635$	3.31769	−	3.31769i	0.131658	−	0.131658i
$636$		0			0
$637$	−3.26086	−	3.26086i	−0.129200	−	0.129200i
$638$	0.891572	+	5.62914i	0.0352977	+	0.222860i
$639$		0			0
$640$	38.2710	−	12.4352i	1.51279	−	0.491545i
$641$			23.5861i			0.931595i	0.884891	+	0.465797i	$0.154232\pi$
$641$			23.5861i			0.931595i	−0.884891	+	0.465797i	$0.845768\pi$
$642$		0			0
$643$	−29.9073	+	29.9073i	−1.17943	+	1.17943i	−0.199537	+	0.979890i	$0.563944\pi$
$643$	−29.9073	+	29.9073i	−1.17943	+	1.17943i	−0.979890	+	0.199537i	$0.936056\pi$
$644$	−5.32760	−	16.3966i	−0.209937	−	0.646117i
$645$		0			0
$646$	10.8258	+	7.86539i	0.425935	+	0.309460i
$647$		−	35.8559i		−	1.40964i	−0.709385	−	0.704821i	$-0.751027\pi$
$647$		−	35.8559i		−	1.40964i	0.709385	−	0.704821i	$-0.248973\pi$
$648$		0			0
$649$		−	19.8448i		−	0.778975i
$650$	−29.3283	+	40.3670i	−1.15035	+	1.58333i
$651$		0			0
$652$	1.20287	−	2.36077i	0.0471079	−	0.0924547i
$653$	−26.7966	+	26.7966i	−1.04863	+	1.04863i	−0.0498765	+	0.998755i	$0.515883\pi$
$653$	−26.7966	+	26.7966i	−1.04863	+	1.04863i	−0.998755	+	0.0498765i	$0.984117\pi$
$654$		0			0
$655$			19.3226i			0.754995i
$656$	30.9554	−	22.4906i	1.20861	−	0.878109i
$657$		0			0
$658$	−4.71891	+	0.747406i	−0.183962	+	0.0291369i
$659$	−19.9220	−	19.9220i	−0.776050	−	0.776050i	0.203107	−	0.979157i	$-0.434896\pi$
$659$	−19.9220	−	19.9220i	−0.776050	−	0.776050i	−0.979157	+	0.203107i	$0.934896\pi$
$660$		0			0
$661$	3.02969	−	3.02969i	0.117841	−	0.117841i	−0.645727	−	0.763568i	$-0.723446\pi$
$661$	3.02969	−	3.02969i	0.117841	−	0.117841i	0.763568	+	0.645727i	$0.223446\pi$
$662$	−0.233730	−	0.169814i	−0.00908417	−	0.00660003i
$663$		0			0
$664$	27.8170	+	9.03824i	1.07951	+	0.350752i
$665$	6.10874			0.236887
$666$		0			0
$667$	17.6424	+	17.6424i	0.683117	+	0.683117i
$668$	−11.0719	−	34.0757i	−0.428385	−	1.31843i
$669$		0			0
$670$	−21.9263	+	3.47280i	−0.847087	+	0.134166i
$671$	2.10776			0.0813693
$672$		0			0
$673$	41.8102			1.61166			0.805832	−	0.592144i	$-0.201718\pi$
$673$	41.8102			1.61166			0.805832	+	0.592144i	$0.201718\pi$
$674$	25.5972	−	4.05421i	0.985965	−	0.156162i
$675$		0			0
$676$	5.10892	+	15.7236i	0.196497	+	0.604752i
$677$	−11.0622	−	11.0622i	−0.425154	−	0.425154i	0.461820	−	0.886974i	$-0.347197\pi$
$677$	−11.0622	−	11.0622i	−0.425154	−	0.425154i	−0.886974	+	0.461820i	$0.847197\pi$
$678$		0			0
$679$	−7.84085			−0.300904
$680$	−17.1269	+	52.7115i	−0.656786	+	2.02139i
$681$		0			0
$682$	0.261953	+	0.190320i	0.0100307	+	0.00728773i
$683$	−25.6844	+	25.6844i	−0.982786	+	0.982786i	−0.999854	−	0.0170687i	$-0.994567\pi$
$683$	−25.6844	+	25.6844i	−0.982786	+	0.982786i	0.0170687	+	0.999854i	$0.494567\pi$
$684$		0			0
$685$	29.7434	+	29.7434i	1.13644	+	1.13644i
$686$	−1.39680	+	0.221233i	−0.0533302	+	0.00844670i
$687$		0			0
$688$	28.0404	+	4.44108i	1.06903	+	0.169315i
$689$		−	24.3075i		−	0.926044i
$690$		0			0
$691$	15.7276	−	15.7276i	0.598306	−	0.598306i	−0.341556	−	0.939862i	$-0.610954\pi$
$691$	15.7276	−	15.7276i	0.598306	−	0.598306i	0.939862	+	0.341556i	$0.110954\pi$
$692$	−2.51280	+	4.93166i	−0.0955222	+	0.187474i
$693$		0			0
$694$	9.05200	−	12.4590i	0.343609	−	0.472938i
$695$			53.4809i			2.02865i
$696$		0			0
$697$			52.7005i			1.99617i
$698$	−14.9490	−	10.8611i	−0.565830	−	0.411099i
$699$		0			0
$700$	4.72848	+	14.5527i	0.178720	+	0.550040i
$701$	−4.35804	+	4.35804i	−0.164601	+	0.164601i	−0.784601	−	0.620000i	$-0.787132\pi$
$701$	−4.35804	+	4.35804i	−0.164601	+	0.164601i	0.620000	+	0.784601i	$0.287132\pi$
$702$		0			0
$703$		−	20.1866i		−	0.761352i
$704$	1.74255	+	11.0017i	0.0656748	+	0.414644i
$705$		0			0
$706$	−3.07626	−	19.4226i	−0.115776	−	0.730981i
$707$	0.748257	+	0.748257i	0.0281411	+	0.0281411i
$708$		0			0
$709$	−2.68056	+	2.68056i	−0.100670	+	0.100670i	−0.755648	−	0.654978i	$-0.772678\pi$
$709$	−2.68056	+	2.68056i	−0.100670	+	0.100670i	0.654978	+	0.755648i	$0.272678\pi$
$710$	−22.6552	+	31.1822i	−0.850233	+	1.17025i
$711$		0			0
$712$	−18.8799	+	9.61982i	−0.707553	+	0.360518i
$713$	1.41748			0.0530850
$714$		0			0
$715$	−16.1489	−	16.1489i	−0.603934	−	0.603934i
$716$	41.4655	+	21.1277i	1.54964	+	0.789578i
$717$		0			0
$718$	4.51269	+	28.4919i	0.168412	+	1.06331i
$719$	19.9117			0.742581			0.371290	−	0.928517i	$-0.378915\pi$
$719$	19.9117			0.742581			0.371290	+	0.928517i	$0.378915\pi$
$720$		0			0
$721$	−11.8161			−0.440056
$722$	−3.55084	−	22.4190i	−0.132149	−	0.834350i
$723$		0			0
$724$	2.58920	−	5.08160i	0.0962268	−	0.188856i
$725$	−15.6584	−	15.6584i	−0.581539	−	0.581539i
$726$		0			0
$727$	24.0642			0.892491			0.446246	−	0.894911i	$-0.352761\pi$
$727$	24.0642			0.892491			0.446246	+	0.894911i	$0.352761\pi$
$728$	12.4050	+	4.03061i	0.459761	+	0.149385i
$729$		0			0
$730$	24.8528	−	34.2070i	0.919844	−	1.26606i
$731$	−27.6492	+	27.6492i	−1.02264	+	1.02264i
$732$		0			0
$733$	−3.18890	−	3.18890i	−0.117785	−	0.117785i	0.645758	−	0.763542i	$-0.276542\pi$
$733$	−3.18890	−	3.18890i	−0.117785	−	0.117785i	−0.763542	+	0.645758i	$0.776542\pi$
$734$	−4.70683	−	29.7176i	−0.173732	−	1.09690i
$735$		0			0
$736$	34.4809	+	34.4807i	1.27098	+	1.27098i
$737$		−	6.14502i		−	0.226355i
$738$		0			0
$739$	20.8311	−	20.8311i	0.766285	−	0.766285i	−0.211165	−	0.977450i	$-0.567726\pi$
$739$	20.8311	−	20.8311i	0.766285	−	0.766285i	0.977450	+	0.211165i	$0.0677258\pi$
$740$	79.5181	−	25.8371i	2.92314	−	0.949792i
$741$		0			0
$742$	−6.03069	−	4.38155i	−0.221394	−	0.160852i
$743$			28.6291i			1.05030i	0.851010	+	0.525150i	$0.175991\pi$
$743$			28.6291i			1.05030i	−0.851010	+	0.525150i	$0.824009\pi$
$744$		0			0
$745$		−	48.6258i		−	1.78151i
$746$	−17.2253	+	23.7086i	−0.630662	+	0.868032i
$747$		0			0
$748$	−13.6696	−	6.96501i	−0.499812	−	0.254666i
$749$	−4.41189	+	4.41189i	−0.161207	+	0.161207i
$750$		0			0
$751$		−	28.1706i		−	1.02796i	−0.857802	−	0.513980i	$-0.828170\pi$
$751$		−	28.1706i		−	1.02796i	0.857802	−	0.513980i	$-0.171830\pi$
$752$	10.9326	−	7.94305i	0.398671	−	0.289653i
$753$		0			0
$754$	−18.6439	+	2.95292i	−0.678971	+	0.107539i
$755$	12.7042	+	12.7042i	0.462355	+	0.462355i
$756$		0			0
$757$	−4.64056	+	4.64056i	−0.168664	+	0.168664i	−0.786392	−	0.617728i	$-0.788053\pi$
$757$	−4.64056	+	4.64056i	−0.168664	+	0.168664i	0.617728	+	0.786392i	$0.288053\pi$
$758$	14.3287	+	10.4104i	0.520444	+	0.378124i
$759$		0			0
$760$	−15.3949	+	7.84414i	−0.558432	+	0.284537i
$761$	6.29768			0.228291			0.114145	−	0.993464i	$-0.463587\pi$
$761$	6.29768			0.228291			0.114145	+	0.993464i	$0.463587\pi$
$762$		0			0
$763$	−0.128743	−	0.128743i	−0.00466082	−	0.00466082i
$764$	−12.7885	+	4.15524i	−0.462670	+	0.150331i
$765$		0			0
$766$	46.5935	−	7.37972i	1.68349	−	0.266640i
$767$	65.7265			2.37325
$768$		0			0
$769$	4.73382			0.170706			0.0853529	−	0.996351i	$-0.472798\pi$
$769$	4.73382			0.170706			0.0853529	+	0.996351i	$0.472798\pi$
$770$	−6.91745	+	1.09562i	−0.249288	+	0.0394834i
$771$		0			0
$772$	2.61623	−	0.850068i	0.0941601	−	0.0305946i
$773$	−5.44275	−	5.44275i	−0.195762	−	0.195762i	0.602418	−	0.798180i	$-0.294204\pi$
$773$	−5.44275	−	5.44275i	−0.195762	−	0.195762i	−0.798180	+	0.602418i	$0.794204\pi$
$774$		0			0
$775$	−1.25808			−0.0451914
$776$	19.7601	−	10.0683i	0.709346	−	0.361431i
$777$		0			0
$778$	−3.24801	−	2.35982i	−0.116447	−	0.0846035i
$779$	−11.6171	+	11.6171i	−0.416226	+	0.416226i
$780$		0			0
$781$	−7.54417	−	7.54417i	−0.269952	−	0.269952i
$782$	−66.3356	+	10.5066i	−2.37216	+	0.375714i
$783$		0			0
$784$	3.23606	−	2.35115i	0.115574	−	0.0839696i
$785$		−	55.8852i		−	1.99463i
$786$		0			0
$787$	−27.1082	+	27.1082i	−0.966302	+	0.966302i	−0.999450	−	0.0331485i	$-0.989447\pi$
$787$	−27.1082	+	27.1082i	−0.966302	+	0.966302i	0.0331485	+	0.999450i	$0.489447\pi$
$788$	−25.7142	−	13.1020i	−0.916032	−	0.466740i
$789$		0			0
$790$	−41.0115	+	56.4476i	−1.45912	+	2.00832i
$791$			14.3042i			0.508600i
$792$		0			0
$793$			6.98099i			0.247902i
$794$	3.94777	+	2.86822i	0.140101	+	0.101789i
$795$		0			0
$796$	−28.4158	+	9.23289i	−1.00717	+	0.327251i
$797$	11.7301	−	11.7301i	0.415501	−	0.415501i	−0.468149	−	0.883650i	$-0.655079\pi$
$797$	11.7301	−	11.7301i	0.415501	−	0.415501i	0.883650	+	0.468149i	$0.155079\pi$
$798$		0			0
$799$			18.6124i			0.658458i
$800$	−30.6033	−	30.6031i	−1.08199	−	1.08198i
$801$		0			0
$802$	−2.58396	−	16.3144i	−0.0912429	−	0.576082i
$803$	8.27599	+	8.27599i	0.292053	+	0.292053i
$804$		0			0
$805$	−21.6801	+	21.6801i	−0.764124	+	0.764124i
$806$	−0.630346	+	0.867598i	−0.0222030	+	0.0305598i
$807$		0			0
$808$	−2.84654	−	0.924890i	−0.100141	−	0.0325375i
$809$	−13.7126			−0.482111			−0.241055	−	0.970511i	$-0.577494\pi$
$809$	−13.7126			−0.482111			−0.241055	+	0.970511i	$0.577494\pi$
$810$		0			0
$811$	22.2730	+	22.2730i	0.782111	+	0.782111i	0.980187	−	0.198076i	$-0.0634692\pi$
$811$	22.2730	+	22.2730i	0.782111	+	0.782111i	−0.198076	+	0.980187i	$0.563469\pi$
$812$	−2.62803	+	5.15782i	−0.0922259	+	0.181004i
$813$		0			0
$814$	3.62053	+	22.8590i	0.126899	+	0.801208i
$815$	−4.71195			−0.165052
$816$		0			0
$817$	−12.1898			−0.426467
$818$	−3.38377	−	21.3642i	−0.118311	−	0.746981i
$819$		0			0
$820$	−60.6304	−	30.8926i	−2.11731	−	1.07882i
$821$	−0.690329	−	0.690329i	−0.0240926	−	0.0240926i	0.694958	−	0.719050i	$-0.255423\pi$
$821$	−0.690329	−	0.690329i	−0.0240926	−	0.0240926i	−0.719050	+	0.694958i	$0.755423\pi$
$822$		0			0
$823$	−1.43063			−0.0498688			−0.0249344	−	0.999689i	$-0.507938\pi$
$823$	−1.43063			−0.0498688			−0.0249344	+	0.999689i	$0.507938\pi$
$824$	29.7784	−	15.1729i	1.03738	−	0.528574i
$825$		0			0
$826$	11.8475	−	16.3067i	0.412228	−	0.567384i
$827$	−9.59770	+	9.59770i	−0.333745	+	0.333745i	−0.854007	−	0.520262i	$-0.825834\pi$
$827$	−9.59770	+	9.59770i	−0.333745	+	0.333745i	0.520262	+	0.854007i	$0.325834\pi$
$828$		0			0
$829$	17.0260	+	17.0260i	0.591337	+	0.591337i	0.937992	−	0.346656i	$-0.112683\pi$
$829$	17.0260	+	17.0260i	0.591337	+	0.591337i	−0.346656	+	0.937992i	$0.612683\pi$
$830$	−8.13706	−	51.3752i	−0.282442	−	1.78326i
$831$		0			0
$832$	−36.4381	+	5.77139i	−1.26327	+	0.200087i
$833$			5.50927i			0.190885i
$834$		0			0
$835$	−45.0560	+	45.0560i	−1.55923	+	1.55923i
$836$	−1.47795	−	4.54863i	−0.0511158	−	0.157318i
$837$		0			0
$838$	−21.3310	−	15.4979i	−0.736867	−	0.535364i
$839$			29.0214i			1.00193i	0.865467	+	0.500965i	$0.167022\pi$
$839$			29.0214i			1.00193i	−0.865467	+	0.500965i	$0.832978\pi$
$840$		0			0
$841$			20.6226i			0.711123i
$842$	26.1651	−	36.0133i	0.901710	−	1.24110i
$843$		0			0
$844$	6.33731	−	12.4377i	0.218139	−	0.428124i
$845$	20.7902	−	20.7902i	0.715205	−	0.715205i
$846$		0			0
$847$			9.06133i			0.311351i
$848$	20.8245	+	3.29822i	0.715116	+	0.113261i
$849$		0			0
$850$	58.8758	−	9.32505i	2.01942	−	0.319846i
$851$	71.6430	+	71.6430i	2.45589	+	2.45589i
$852$		0			0
$853$	17.4096	−	17.4096i	0.596092	−	0.596092i	−0.343178	−	0.939270i	$-0.611503\pi$
$853$	17.4096	−	17.4096i	0.596092	−	0.596092i	0.939270	+	0.343178i	$0.111503\pi$
$854$	1.73198	+	1.25836i	0.0592672	+	0.0430600i
$855$		0			0
$856$	5.45336	−	16.7838i	0.186392	−	0.573660i
$857$	17.6637			0.603379			0.301690	−	0.953406i	$-0.402449\pi$
$857$	17.6637			0.603379			0.301690	+	0.953406i	$0.402449\pi$
$858$		0			0
$859$	5.79823	+	5.79823i	0.197833	+	0.197833i	0.799070	−	0.601237i	$-0.205325\pi$
$859$	5.79823	+	5.79823i	0.197833	+	0.197833i	−0.601237	+	0.799070i	$0.705325\pi$
$860$	−15.6019	−	48.0174i	−0.532020	−	1.63738i
$861$		0			0
$862$	26.5848	−	4.21064i	0.905482	−	0.143415i
$863$	39.0789			1.33026			0.665131	−	0.746727i	$-0.268376\pi$
$863$	39.0789			1.33026			0.665131	+	0.746727i	$0.268376\pi$
$864$		0			0
$865$	9.84331			0.334683
$866$	44.2954	−	7.01574i	1.50522	−	0.238405i
$867$		0			0
$868$	0.101628	+	0.312777i	0.00344948	+	0.0106164i
$869$	−13.6568	−	13.6568i	−0.463277	−	0.463277i
$870$		0			0
$871$	20.3525			0.689618
$872$	0.489769	+	0.159134i	0.0165857	+	0.00538897i
$873$		0			0
$874$	−16.9388	−	12.3068i	−0.572964	−	0.416282i
$875$	6.66689	−	6.66689i	0.225382	−	0.225382i
$876$		0			0
$877$	6.28950	+	6.28950i	0.212381	+	0.212381i	0.805278	−	0.592897i	$-0.202016\pi$
$877$	6.28950	+	6.28950i	0.212381	+	0.212381i	−0.592897	+	0.805278i	$0.702016\pi$
$878$	−46.0276	+	7.29008i	−1.55336	+	0.246028i
$879$		0			0
$880$	16.0261	−	11.6437i	0.540240	−	0.392509i
$881$			21.5545i			0.726190i	0.931752	+	0.363095i	$0.118280\pi$
$881$			21.5545i			0.726190i	−0.931752	+	0.363095i	$0.881720\pi$
$882$		0			0
$883$	5.85864	−	5.85864i	0.197159	−	0.197159i	−0.601622	−	0.798781i	$-0.705479\pi$
$883$	5.85864	−	5.85864i	0.197159	−	0.197159i	0.798781	+	0.601622i	$0.205479\pi$
$884$	23.0683	−	45.2743i	0.775872	−	1.52274i
$885$		0			0
$886$	5.81643	−	8.00565i	0.195407	−	0.268955i
$887$		−	28.0138i		−	0.940613i	−0.882503	−	0.470306i	$-0.844143\pi$
$887$		−	28.0138i		−	0.940613i	0.882503	−	0.470306i	$-0.155857\pi$
$888$		0			0
$889$			1.31914i			0.0442426i
$890$	30.4863	+	22.1496i	1.02190	+	0.742456i
$891$		0			0
$892$	−3.24931	−	10.0003i	−0.108795	−	0.334835i
$893$	−4.10284	+	4.10284i	−0.137296	+	0.137296i
$894$		0			0
$895$		−	82.7628i		−	2.76645i
$896$	−5.13627	+	10.0806i	−0.171591	+	0.336770i
$897$		0			0
$898$	6.97454	+	44.0353i	0.232743	+	1.46948i
$899$	−0.336542	−	0.336542i	−0.0112243	−	0.0112243i
$900$		0			0
$901$	−20.5340	+	20.5340i	−0.684087	+	0.684087i
$902$	11.0715	−	15.2386i	0.368640	−	0.507390i
$903$		0			0
$904$	−18.3678	−	36.0487i	−0.610905	−	1.19896i
$905$	−10.1426			−0.337151
$906$		0			0
$907$	3.74119	+	3.74119i	0.124224	+	0.124224i	0.766486	−	0.642262i	$-0.222004\pi$
$907$	3.74119	+	3.74119i	0.124224	+	0.124224i	−0.642262	+	0.766486i	$0.722004\pi$
$908$	−15.9004	−	8.10163i	−0.527673	−	0.268862i
$909$		0			0
$910$	−3.62873	−	22.9108i	−0.120291	−	0.759486i
$911$	46.9910			1.55688			0.778441	−	0.627718i	$-0.216011\pi$
$911$	46.9910			1.55688			0.778441	+	0.627718i	$0.216011\pi$
$912$		0			0
$913$	14.3983			0.476514
$914$	−7.79883	−	49.2397i	−0.257963	−	1.62870i
$915$		0			0
$916$	24.6266	−	48.3327i	0.813687	−	1.59696i
$917$	−3.84141	−	3.84141i	−0.126855	−	0.126855i
$918$		0			0
$919$	−28.7166			−0.947272			−0.473636	−	0.880721i	$-0.657059\pi$
$919$	−28.7166			−0.947272			−0.473636	+	0.880721i	$0.657059\pi$
$920$	26.7979	−	82.4762i	0.883502	−	2.71916i
$921$		0			0
$922$	18.6644	−	25.6894i	0.614680	−	0.846035i
$923$	24.9866	−	24.9866i	0.822442	−	0.822442i
$924$		0			0
$925$	−63.5863	−	63.5863i	−2.09070	−	2.09070i
$926$	3.52241	+	22.2395i	0.115754	+	0.730836i
$927$		0			0
$928$	−5.53246e−5	−	16.3731i	−1.81612e−6	−	0.537472i
$929$			39.0905i			1.28252i	0.767325	+	0.641259i	$0.221587\pi$
$929$			39.0905i			1.28252i	−0.767325	+	0.641259i	$0.778413\pi$
$930$		0			0
$931$	−1.21444	+	1.21444i	−0.0398018	+	0.0398018i
$932$	−1.05573	+	0.343028i	−0.0345815	+	0.0112363i
$933$		0			0
$934$	10.5564	+	7.66965i	0.345416	+	0.250959i
$935$			27.2838i			0.892277i
$936$		0			0
$937$			22.0325i			0.719770i	0.932997	+	0.359885i	$0.117184\pi$
$937$			22.0325i			0.719770i	−0.932997	+	0.359885i	$0.882816\pi$
$938$	3.66863	−	5.04945i	0.119785	−	0.164870i
$939$		0			0
$940$	−21.4130	−	10.9104i	−0.698415	−	0.355859i
$941$	−28.7845	+	28.7845i	−0.938349	+	0.938349i	−0.998207	−	0.0598579i	$-0.980935\pi$
$941$	−28.7845	+	28.7845i	−0.938349	+	0.938349i	0.0598579	+	0.998207i	$0.480935\pi$
$942$		0			0
$943$		−	82.4590i		−	2.68523i
$944$	−8.91824	+	56.3085i	−0.290264	+	1.83269i
$945$		0			0
$946$	13.8035	−	2.18627i	0.448792	−	0.0710819i
$947$	−8.81984	−	8.81984i	−0.286606	−	0.286606i	0.549130	−	0.835737i	$-0.314959\pi$
$947$	−8.81984	−	8.81984i	−0.286606	−	0.286606i	−0.835737	+	0.549130i	$0.814959\pi$
$948$		0			0
$949$	−27.4104	+	27.4104i	−0.889778	+	0.889778i
$950$	15.0339	+	10.9228i	0.487766	+	0.354382i
$951$		0			0
$952$	−7.07437	−	13.8842i	−0.229282	−	0.449988i
$953$	1.32312			0.0428599			0.0214300	−	0.999770i	$-0.493178\pi$
$953$	1.32312			0.0428599			0.0214300	+	0.999770i	$0.493178\pi$
$954$		0			0
$955$	16.9093	+	16.9093i	0.547173	+	0.547173i
$956$	−43.8262	+	14.2401i	−1.41744	+	0.460557i
$957$		0			0
$958$	44.1237	−	6.98853i	1.42557	−	0.225789i
$959$	−11.8262			−0.381889
$960$		0			0
$961$	30.9730			0.999128
$962$	−75.7098	+	11.9913i	−2.44098	+	0.386615i
$963$		0			0
$964$	−14.2245	+	4.62184i	−0.458141	+	0.148860i
$965$	−3.45926	−	3.45926i	−0.111358	−	0.111358i
$966$		0			0
$967$	16.3028			0.524263			0.262132	−	0.965032i	$-0.415575\pi$
$967$	16.3028			0.524263			0.262132	+	0.965032i	$0.415575\pi$
$968$	−11.6355	−	22.8359i	−0.373979	−	0.733972i
$969$		0			0
$970$	−31.9077	−	23.1823i	−1.02449	−	0.744338i
$971$	16.8788	−	16.8788i	0.541666	−	0.541666i	−0.382351	−	0.924017i	$-0.624886\pi$
$971$	16.8788	−	16.8788i	0.541666	−	0.541666i	0.924017	+	0.382351i	$0.124886\pi$
$972$		0			0
$973$	−10.6322	−	10.6322i	−0.340854	−	0.340854i
$974$	41.1791	−	6.52215i	1.31946	−	0.208983i
$975$		0			0
$976$	−5.98068	−	0.947229i	−0.191437	−	0.0303201i
$977$			1.46807i			0.0469676i	0.999724	+	0.0234838i	$0.00747581\pi$
$977$			1.46807i			0.0469676i	−0.999724	+	0.0234838i	$0.992524\pi$
$978$		0			0
$979$	−7.37582	+	7.37582i	−0.235732	+	0.235732i
$980$	−6.33826	−	3.22950i	−0.202468	−	0.103162i
$981$		0			0
$982$	7.13408	−	9.81923i	0.227658	−	0.313344i
$983$		−	34.4565i		−	1.09899i	−0.835496	−	0.549496i	$-0.814820\pi$
$983$		−	34.4565i		−	1.09899i	0.835496	−	0.549496i	$-0.185180\pi$
$984$		0			0
$985$			51.3241i			1.63532i
$986$	18.2441	+	13.2551i	0.581010	+	0.422128i
$987$		0			0
$988$	15.0652	−	4.89501i	0.479288	−	0.155731i
$989$	43.2620	−	43.2620i	1.37565	−	1.37565i
$990$		0			0
$991$		−	14.4789i		−	0.459937i	−0.973198	−	0.229969i	$-0.926138\pi$
$991$		−	14.4789i		−	0.459937i	0.973198	−	0.229969i	$-0.0738624\pi$
$992$	−0.657749	−	0.657745i	−0.0208836	−	0.0208834i
$993$		0			0
$994$	−1.69521	−	10.7031i	−0.0537689	−	0.339482i
$995$	37.5723	+	37.5723i	1.19112	+	1.19112i
$996$		0			0
$997$	−32.5498	+	32.5498i	−1.03086	+	1.03086i	−0.0313557	+	0.999508i	$0.509982\pi$
$997$	−32.5498	+	32.5498i	−1.03086	+	1.03086i	−0.999508	+	0.0313557i	$0.990018\pi$
$998$	−18.6878	+	25.7216i	−0.591551	+	0.814202i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.v.e.323.2	✓	40
3.2	odd	2	inner	1008.2.v.e.323.19	yes	40
4.3	odd	2		4032.2.v.e.1583.3		40
12.11	even	2		4032.2.v.e.1583.18		40
16.5	even	4		4032.2.v.e.3599.18		40
16.11	odd	4	inner	1008.2.v.e.827.19	yes	40
48.5	odd	4		4032.2.v.e.3599.3		40
48.11	even	4	inner	1008.2.v.e.827.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.v.e.323.2	✓	40	1.1	even	1	trivial
1008.2.v.e.323.19	yes	40	3.2	odd	2	inner
1008.2.v.e.827.2	yes	40	48.11	even	4	inner
1008.2.v.e.827.19	yes	40	16.11	odd	4	inner
4032.2.v.e.1583.3		40	4.3	odd	2
4032.2.v.e.1583.18		40	12.11	even	2
4032.2.v.e.3599.3		40	48.5	odd	4
4032.2.v.e.3599.18		40	16.5	even	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)

\(f(q)\)	\(=\)	\(q+(-1.39680 + 0.221233i) q^{2} +(1.90211 - 0.618037i) q^{4} +(-2.51504 - 2.51504i) q^{5} +1.00000 q^{7} +(-2.52014 + 1.28408i) q^{8} +O(q^{10})\)	\(q+(-1.39680 + 0.221233i) q^{2} +(1.90211 - 0.618037i) q^{4} +(-2.51504 - 2.51504i) q^{5} +1.00000 q^{7} +(-2.52014 + 1.28408i) q^{8} +(4.06942 + 2.95660i) q^{10} +(-0.984548 + 0.984548i) q^{11} +(-3.26086 - 3.26086i) q^{13} +(-1.39680 + 0.221233i) q^{14} +(3.23606 - 2.35115i) q^{16} +5.50927i q^{17} +(-1.21444 + 1.21444i) q^{19} +(-6.33826 - 3.22950i) q^{20} +(1.15740 - 1.59303i) q^{22} -8.62021i q^{23} +7.65081i q^{25} +(5.27618 + 3.83336i) q^{26} +(1.90211 - 0.618037i) q^{28} +(-2.04663 + 2.04663i) q^{29} +0.164437i q^{31} +(-3.99999 + 4.00001i) q^{32} +(-1.21883 - 7.69536i) q^{34} +(-2.51504 - 2.51504i) q^{35} +(-8.31105 + 8.31105i) q^{37} +(1.42766 - 1.96501i) q^{38} +(9.56777 + 3.10874i) q^{40} +9.56578 q^{41} +(5.01867 + 5.01867i) q^{43} +(-1.26423 + 2.48121i) q^{44} +(1.90707 + 12.0407i) q^{46} +3.37837 q^{47} +1.00000 q^{49} +(-1.69261 - 10.6867i) q^{50} +(-8.21784 - 4.18719i) q^{52} +(3.72717 + 3.72717i) q^{53} +4.95235 q^{55} +(-2.52014 + 1.28408i) q^{56} +(2.40596 - 3.31153i) q^{58} +(-10.0781 + 10.0781i) q^{59} +(-1.07042 - 1.07042i) q^{61} +(-0.0363788 - 0.229686i) q^{62} +(4.70226 - 6.47216i) q^{64} +16.4023i q^{65} +(-3.12073 + 3.12073i) q^{67} +(3.40493 + 10.4793i) q^{68} +(4.06942 + 2.95660i) q^{70} +7.66257i q^{71} -8.40588i q^{73} +(9.77021 - 13.4476i) q^{74} +(-1.55944 + 3.06058i) q^{76} +(-0.984548 + 0.984548i) q^{77} +13.8712i q^{79} +(-14.0520 - 2.22559i) q^{80} +(-13.3615 + 2.11626i) q^{82} +(-7.31214 - 7.31214i) q^{83} +(13.8560 - 13.8560i) q^{85} +(-8.12038 - 5.89979i) q^{86} +(1.21696 - 3.74545i) q^{88} +7.49158 q^{89} +(-3.26086 - 3.26086i) q^{91} +(-5.32760 - 16.3966i) q^{92} +(-4.71891 + 0.747406i) q^{94} +6.10874 q^{95} -7.84085 q^{97} +(-1.39680 + 0.221233i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{7}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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