LMFDB - Embedded newform 1008.2.v.e.323.19

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			323.19
Character	$\chi$	$=$	1008.323
Dual form			1008.2.v.e.827.19

$q$-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	$0.0426994\pi$
$5$	2.51504	+	2.51504i	1.12476	+	1.12476i	0.133742	+	0.991016i	$0.457301\pi$
$6$		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	−0.542927	−	0.839780i	$-0.682684\pi$
$11$	0.984548	−	0.984548i	0.296852	−	0.296852i	0.839780	+	0.542927i	$0.182684\pi$
$12$		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	$-0.767109\pi$
$17$		−	5.50927i		−	1.33619i	0.744074	−	0.668097i	$-0.232891\pi$
$18$		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	$0.355501\pi$
$23$			8.62021i			1.79744i	−0.438526	+	0.898719i	$0.644499\pi$
$24$		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	−0.491070	−	0.871120i	$-0.663394\pi$
$29$	2.04663	−	2.04663i	0.380050	−	0.380050i	0.871120	+	0.491070i	$0.163394\pi$
$30$		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	$-0.768488\pi$
$41$	−9.56578			−1.49392			−0.746962	+	0.664867i	$0.768488\pi$
$42$		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	$-0.579245\pi$
$47$	−3.37837			−0.492786			−0.246393	+	0.969170i	$0.579245\pi$
$48$		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	0.403162	−	0.915129i	$-0.367911\pi$
$53$	−3.72717	−	3.72717i	−0.511966	−	0.511966i	−0.915129	+	0.403162i	$0.867911\pi$
$54$		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	$-0.371727\pi$
$59$	10.0781	−	10.0781i	1.31206	−	1.31206i	0.919896	−	0.392162i	$-0.128273\pi$
$60$		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	$-0.849750\pi$
$71$		−	7.66257i		−	0.909380i	0.890650	−	0.454690i	$-0.150250\pi$
$72$		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	0.983503	−	0.180892i	$-0.0578984\pi$
$83$	7.31214	+	7.31214i	0.802611	+	0.802611i	−0.180892	+	0.983503i	$0.557898\pi$
$84$		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	$-0.629967\pi$
$89$	−7.49158			−0.794106			−0.397053	+	0.917796i	$0.629967\pi$
$90$		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	0.668899	−	0.743353i	$-0.266766\pi$
$101$	−0.748257	−	0.748257i	−0.0744543	−	0.0744543i	−0.743353	+	0.668899i	$0.766766\pi$
$102$		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	−0.460925	−	0.887439i	$-0.652482\pi$
$107$	4.41189	−	4.41189i	0.426514	−	0.426514i	0.887439	+	0.460925i	$0.152482\pi$
$108$		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	$-0.765085\pi$
$113$		−	14.3042i		−	1.34563i	0.739811	−	0.672815i	$-0.234915\pi$
$114$		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	0.854718	−	0.519093i	$-0.173730\pi$
$131$	3.84141	+	3.84141i	0.335626	+	0.335626i	−0.519093	+	0.854718i	$0.673730\pi$
$132$		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	$-0.331422\pi$
$137$	11.8262			1.01038			0.505191	+	0.863008i	$0.331422\pi$
$138$		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	0.189858	−	0.981812i	$-0.439197\pi$
$149$	−9.66703	−	9.66703i	−0.791954	−	0.791954i	−0.981812	+	0.189858i	$0.939197\pi$
$150$		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	$0.243773\pi$
$167$			17.9147i			1.38628i	−0.720804	+	0.693139i	$0.756227\pi$
$168$		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	−0.628793	−	0.777573i	$-0.716451\pi$
$173$	1.95689	−	1.95689i	0.148780	−	0.148780i	0.777573	+	0.628793i	$0.216451\pi$
$174$		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	$-0.914377\pi$
$179$	−16.4536	−	16.4536i	−1.22980	−	1.22980i	−0.265760	−	0.964039i	$-0.585623\pi$
$180$		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	$-0.421790\pi$
$191$	6.72330			0.486481			0.243240	+	0.969966i	$0.421790\pi$
$192$		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	0.970014	−	0.243048i	$-0.0781472\pi$
$197$	10.2035	+	10.2035i	0.726967	+	0.726967i	−0.243048	+	0.970014i	$0.578147\pi$
$198$		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	0.884777	−	0.466014i	$-0.154310\pi$
$227$	6.30931	+	6.30931i	0.418763	+	0.418763i	−0.466014	+	0.884777i	$0.654310\pi$
$228$		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	$-0.494213\pi$
$233$	0.555029			0.0363611			0.0181806	+	0.999835i	$0.494213\pi$
$234$		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	$-0.232357\pi$
$239$	23.0408			1.49039			0.745194	+	0.666848i	$0.232357\pi$
$240$		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	$0.564441\pi$
$251$	−18.7049	+	18.7049i	−1.18064	+	1.18064i	−0.979578	+	0.201066i	$0.935559\pi$
$252$		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	$0.193444\pi$
$257$			18.3076i			1.14200i	−0.820951	+	0.570998i	$0.806556\pi$
$258$		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	$0.213132\pi$
$263$			20.1306i			1.24130i	−0.784086	+	0.620652i	$0.786868\pi$
$264$		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	−0.390352	−	0.920666i	$-0.627647\pi$
$269$	8.69779	−	8.69779i	0.530313	−	0.530313i	0.920666	+	0.390352i	$0.127647\pi$
$270$		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	$-0.611638\pi$
$281$	−11.5187			−0.687148			−0.343574	+	0.939126i	$0.611638\pi$
$282$		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	0.808803	−	0.588080i	$-0.200116\pi$
$293$	3.77816	+	3.77816i	0.220722	+	0.220722i	−0.588080	+	0.808803i	$0.700116\pi$
$294$		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	$-0.790115\pi$
$311$		−	21.6074i		−	1.22525i	0.790376	−	0.612623i	$-0.209885\pi$
$312$		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	−0.450063	−	0.892997i	$-0.648598\pi$
$317$	7.88622	−	7.88622i	0.442934	−	0.442934i	0.892997	+	0.450063i	$0.148598\pi$
$318$		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	−0.469545	−	0.882908i	$-0.655582\pi$
$347$	7.70010	−	7.70010i	0.413363	−	0.413363i	0.882908	+	0.469545i	$0.155582\pi$
$348$		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	$-0.879342\pi$
$353$		−	13.9051i		−	0.740092i	0.929013	−	0.370046i	$-0.120658\pi$
$354$		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	$0.180926\pi$
$359$			20.3979i			1.07656i	−0.842766	+	0.538281i	$0.819074\pi$
$360$		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	$-0.175245\pi$
$383$	33.3573			1.70448			0.852238	+	0.523154i	$0.175245\pi$
$384$		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	0.654384	−	0.756162i	$-0.272928\pi$
$389$	−2.00738	−	2.00738i	−0.101778	−	0.101778i	−0.756162	+	0.654384i	$0.772928\pi$
$390$		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	$-0.905802\pi$
$401$		−	11.6798i		−	0.583263i	0.956531	−	0.291632i	$-0.0941981\pi$
$402$		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	0.307502	−	0.951547i	$-0.400507\pi$
$419$	−13.1833	−	13.1833i	−0.644045	−	0.644045i	−0.951547	+	0.307502i	$0.900507\pi$
$420$		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	$-0.348428\pi$
$431$	19.0326			0.916769			0.458385	+	0.888754i	$0.348428\pi$
$432$		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	−0.579732	−	0.814807i	$-0.696843\pi$
$443$	4.94776	−	4.94776i	0.235075	−	0.235075i	0.814807	+	0.579732i	$0.196843\pi$
$444$		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	$0.267025\pi$
$449$			31.5258i			1.48779i	−0.668294	+	0.743897i	$0.732975\pi$
$450$		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	−0.233012	−	0.972474i	$-0.574858\pi$
$461$	15.8769	−	15.8769i	0.739462	−	0.739462i	0.972474	+	0.233012i	$0.0748582\pi$
$462$		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	0.841758	−	0.539854i	$-0.181521\pi$
$467$	6.52420	+	6.52420i	0.301904	+	0.301904i	−0.539854	+	0.841758i	$0.681521\pi$
$468$		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	$-0.243375\pi$
$479$	31.5891			1.44334			0.721671	+	0.692237i	$0.243375\pi$
$480$		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	−0.556784	−	0.830657i	$-0.687965\pi$
$491$	6.06862	−	6.06862i	0.273873	−	0.273873i	0.830657	+	0.556784i	$0.187965\pi$
$492$		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	$-0.874751\pi$
$503$		−	17.1978i		−	0.766813i	0.923580	−	0.383406i	$-0.125249\pi$
$504$		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	−0.728050	−	0.685524i	$-0.759573\pi$
$509$	−0.959431	+	0.959431i	−0.0425260	+	0.0425260i	0.685524	+	0.728050i	$0.259573\pi$
$510$		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	$-0.436546\pi$
$521$	9.04026			0.396061			0.198030	+	0.980196i	$0.436546\pi$
$522$		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	$0.667325\pi$
$557$	−32.2571	+	32.2571i	−1.36678	+	1.36678i	−0.864990	+	0.501789i	$0.832675\pi$
$558$		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	$0.0489380\pi$
$563$	27.0814	+	27.0814i	1.14134	+	1.14134i	0.153138	+	0.988205i	$0.451062\pi$
$564$		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	$-0.703649\pi$
$569$	−28.4823			−1.19404			−0.597020	+	0.802226i	$0.703649\pi$
$570$		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	−0.380017	−	0.924980i	$-0.624082\pi$
$587$	13.2034	−	13.2034i	0.544963	−	0.544963i	0.924980	+	0.380017i	$0.124082\pi$
$588$		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	$-0.947427\pi$
$593$		−	8.00745i		−	0.328827i	0.986392	−	0.164413i	$-0.0525731\pi$
$594$		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	$0.208990\pi$
$599$			29.8782i			1.22079i	−0.792096	+	0.610396i	$0.791010\pi$
$600$		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	$-0.366211\pi$
$617$	20.2712			0.816089			0.408044	+	0.912962i	$0.366211\pi$
$618$		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	$-0.845768\pi$
$641$		−	23.5861i		−	0.931595i	0.884891	−	0.465797i	$-0.154232\pi$
$642$		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	$0.248973\pi$
$647$			35.8559i			1.40964i	−0.709385	+	0.704821i	$0.751027\pi$
$648$		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	$-0.484117\pi$
$653$	26.7966	−	26.7966i	1.04863	−	1.04863i	0.998755	−	0.0498765i	$-0.0158828\pi$
$654$		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	0.979157	−	0.203107i	$-0.0651038\pi$
$659$	19.9220	+	19.9220i	0.776050	+	0.776050i	−0.203107	+	0.979157i	$0.565104\pi$
$660$		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	0.886974	−	0.461820i	$-0.152803\pi$
$677$	11.0622	+	11.0622i	0.425154	+	0.425154i	−0.461820	+	0.886974i	$0.652803\pi$
$678$		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	−0.0170687	−	0.999854i	$-0.505433\pi$
$683$	25.6844	−	25.6844i	0.982786	−	0.982786i	0.999854	+	0.0170687i	$0.00543339\pi$
$684$		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	−0.620000	−	0.784601i	$-0.712868\pi$
$701$	4.35804	−	4.35804i	0.164601	−	0.164601i	0.784601	+	0.620000i	$0.212868\pi$
$702$		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	$-0.621085\pi$
$719$	−19.9117			−0.742581			−0.371290	+	0.928517i	$0.621085\pi$
$720$		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	$-0.824009\pi$
$743$		−	28.6291i		−	1.05030i	0.851010	−	0.525150i	$-0.175991\pi$
$744$		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	$-0.536413\pi$
$761$	−6.29768			−0.228291			−0.114145	+	0.993464i	$0.536413\pi$
$762$		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	0.798180	−	0.602418i	$-0.205796\pi$
$773$	5.44275	+	5.44275i	0.195762	+	0.195762i	−0.602418	+	0.798180i	$0.705796\pi$
$774$		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	−0.883650	−	0.468149i	$-0.844921\pi$
$797$	−11.7301	+	11.7301i	−0.415501	+	0.415501i	0.468149	+	0.883650i	$0.344921\pi$
$798$		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	$-0.422506\pi$
$809$	13.7126			0.482111			0.241055	+	0.970511i	$0.422506\pi$
$810$		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	0.719050	−	0.694958i	$-0.244577\pi$
$821$	0.690329	+	0.690329i	0.0240926	+	0.0240926i	−0.694958	+	0.719050i	$0.744577\pi$
$822$		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	−0.520262	−	0.854007i	$-0.674166\pi$
$827$	9.59770	−	9.59770i	0.333745	−	0.333745i	0.854007	+	0.520262i	$0.174166\pi$
$828$		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	$-0.832978\pi$
$839$		−	29.0214i		−	1.00193i	0.865467	−	0.500965i	$-0.167022\pi$
$840$		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	$-0.597551\pi$
$857$	−17.6637			−0.603379			−0.301690	+	0.953406i	$0.597551\pi$
$858$		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	$-0.731624\pi$
$863$	−39.0789			−1.33026			−0.665131	+	0.746727i	$0.731624\pi$
$864$		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	$-0.881720\pi$
$881$		−	21.5545i		−	0.726190i	0.931752	−	0.363095i	$-0.118280\pi$
$882$		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	$0.155857\pi$
$887$			28.0138i			0.940613i	−0.882503	+	0.470306i	$0.844143\pi$
$888$		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	$-0.783989\pi$
$911$	−46.9910			−1.55688			−0.778441	+	0.627718i	$0.783989\pi$
$912$		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	$-0.778413\pi$
$929$		−	39.0905i		−	1.28252i	0.767325	−	0.641259i	$-0.221587\pi$
$930$		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	−0.0598579	−	0.998207i	$-0.519065\pi$
$941$	28.7845	−	28.7845i	0.938349	−	0.938349i	0.998207	+	0.0598579i	$0.0190648\pi$
$942$		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	0.835737	−	0.549130i	$-0.185041\pi$
$947$	8.81984	+	8.81984i	0.286606	+	0.286606i	−0.549130	+	0.835737i	$0.685041\pi$
$948$		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	$-0.506822\pi$
$953$	−1.32312			−0.0428599			−0.0214300	+	0.999770i	$0.506822\pi$
$954$		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	−0.924017	−	0.382351i	$-0.875114\pi$
$971$	−16.8788	+	16.8788i	−0.541666	+	0.541666i	0.382351	+	0.924017i	$0.375114\pi$
$972$		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	$-0.992524\pi$
$977$		−	1.46807i		−	0.0469676i	0.999724	−	0.0234838i	$-0.00747581\pi$
$978$		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	$0.185180\pi$
$983$			34.4565i			1.09899i	−0.835496	+	0.549496i	$0.814820\pi$
$984$		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.323.19	yes	40
3.2	odd	2	inner	1008.2.v.e.323.2	✓	40
4.3	odd	2		4032.2.v.e.1583.18		40
12.11	even	2		4032.2.v.e.1583.3		40
16.5	even	4		4032.2.v.e.3599.3		40
16.11	odd	4	inner	1008.2.v.e.827.2	yes	40
48.5	odd	4		4032.2.v.e.3599.18		40
48.11	even	4	inner	1008.2.v.e.827.19	yes	40

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

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

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