LMFDB - Embedded newform 3150.2.m.i.2843.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1457,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("3150.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.m (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:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2843.1
Root			$2.16053i$ of defining polynomial
Character	$\chi$	$=$	3150.2843
Dual form			3150.2.m.i.1457.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.14860i q^{11} +(-2.16053 - 2.16053i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-4.46967 - 4.46967i) q^{17} +(1.51929 - 1.51929i) q^{22} +(-6.32106 + 6.32106i) q^{23} +3.05545i q^{26} +(0.707107 + 0.707107i) q^{28} +8.20494 q^{29} -1.85140 q^{31} +(0.707107 + 0.707107i) q^{32} +6.32106i q^{34} +(5.13756 - 5.13756i) q^{37} +7.56282i q^{41} +(7.84035 + 7.84035i) q^{43} -2.14860 q^{44} +8.93933 q^{46} +(5.01193 + 5.01193i) q^{47} -1.00000i q^{49} +(2.16053 - 2.16053i) q^{52} +(-2.35876 + 2.35876i) q^{53} -1.00000i q^{56} +(-5.80177 - 5.80177i) q^{58} -9.35965 q^{59} -4.46967 q^{61} +(1.30913 + 1.30913i) q^{62} -1.00000i q^{64} +(3.84035 - 3.84035i) q^{67} +(4.46967 - 4.46967i) q^{68} +0.420314i q^{71} +(2.63020 + 2.63020i) q^{73} -7.26561 q^{74} +(1.51929 + 1.51929i) q^{77} +5.23654i q^{79} +(5.34772 - 5.34772i) q^{82} +(-10.6183 + 10.6183i) q^{83} -11.0879i q^{86} +(1.51929 + 1.51929i) q^{88} -14.5481 q^{89} -3.05545 q^{91} +(-6.32106 - 6.32106i) q^{92} -7.08794i q^{94} +(0.606342 - 0.606342i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 4 q^{13} - 8 q^{14} - 8 q^{16} + 4 q^{22} - 8 q^{23} - 24 q^{29} - 8 q^{31} + 4 q^{37} + 12 q^{43} - 24 q^{44} + 12 q^{47} - 4 q^{52} - 32 q^{53} - 12 q^{58} - 16 q^{59} - 4 q^{62} - 20 q^{67} - 36 q^{73} - 40 q^{74} + 4 q^{77} + 12 q^{82} - 56 q^{83} + 4 q^{88} - 72 q^{89} - 8 q^{92} + 4 q^{97}+O(q^{100}) $ 8 * q + 4 * q^13 - 8 * q^14 - 8 * q^16 + 4 * q^22 - 8 * q^23 - 24 * q^29 - 8 * q^31 + 4 * q^37 + 12 * q^43 - 24 * q^44 + 12 * q^47 - 4 * q^52 - 32 * q^53 - 12 * q^58 - 16 * q^59 - 4 * q^62 - 20 * q^67 - 36 * q^73 - 40 * q^74 + 4 * q^77 + 12 * q^82 - 56 * q^83 + 4 * q^88 - 72 * q^89 - 8 * q^92 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$			2.14860i			0.647828i	0.946086	+	0.323914i	$0.104999\pi$
$11$			2.14860i			0.647828i	−0.946086	+	0.323914i	$0.895001\pi$
$12$		0			0
$13$	−2.16053	−	2.16053i	−0.599224	−	0.599224i	0.340882	−	0.940106i	$-0.389274\pi$
$13$	−2.16053	−	2.16053i	−0.599224	−	0.599224i	−0.940106	+	0.340882i	$0.889274\pi$
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.46967	−	4.46967i	−1.08405	−	1.08405i	−0.996127	−	0.0879263i	$-0.971976\pi$
$17$	−4.46967	−	4.46967i	−1.08405	−	1.08405i	−0.0879263	−	0.996127i	$-0.528024\pi$
$18$		0			0
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$		0			0
$22$	1.51929	−	1.51929i	0.323914	−	0.323914i
$23$	−6.32106	+	6.32106i	−1.31803	+	1.31803i	−0.402701	+	0.915331i	$0.631929\pi$
$23$	−6.32106	+	6.32106i	−1.31803	+	1.31803i	−0.915331	+	0.402701i	$0.868071\pi$
$24$		0			0
$25$		0			0
$26$			3.05545i			0.599224i
$27$		0			0
$28$	0.707107	+	0.707107i	0.133631	+	0.133631i
$29$	8.20494			1.52362			0.761810	−	0.647801i	$-0.224311\pi$
$29$	8.20494			1.52362			0.761810	+	0.647801i	$0.224311\pi$
$30$		0			0
$31$	−1.85140			−0.332521			−0.166260	−	0.986082i	$-0.553169\pi$
$31$	−1.85140			−0.332521			−0.166260	+	0.986082i	$0.553169\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$			6.32106i			1.08405i
$35$		0			0
$36$		0			0
$37$	5.13756	−	5.13756i	0.844610	−	0.844610i	−0.144844	−	0.989454i	$-0.546268\pi$
$37$	5.13756	−	5.13756i	0.844610	−	0.844610i	0.989454	+	0.144844i	$0.0462682\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			7.56282i			1.18111i	0.806996	+	0.590557i	$0.201092\pi$
$41$			7.56282i			1.18111i	−0.806996	+	0.590557i	$0.798908\pi$
$42$		0			0
$43$	7.84035	+	7.84035i	1.19564	+	1.19564i	0.975458	+	0.220185i	$0.0706660\pi$
$43$	7.84035	+	7.84035i	1.19564	+	1.19564i	0.220185	+	0.975458i	$0.429334\pi$
$44$	−2.14860			−0.323914
$45$		0			0
$46$	8.93933			1.31803
$47$	5.01193	+	5.01193i	0.731065	+	0.731065i	0.970831	−	0.239766i	$-0.0770707\pi$
$47$	5.01193	+	5.01193i	0.731065	+	0.731065i	−0.239766	+	0.970831i	$0.577071\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$		0			0
$52$	2.16053	−	2.16053i	0.299612	−	0.299612i
$53$	−2.35876	+	2.35876i	−0.324001	+	0.324001i	−0.850300	−	0.526299i	$-0.823579\pi$
$53$	−2.35876	+	2.35876i	−0.324001	+	0.324001i	0.526299	+	0.850300i	$0.323579\pi$
$54$		0			0
$55$		0			0
$56$		−	1.00000i		−	0.133631i
$57$		0			0
$58$	−5.80177	−	5.80177i	−0.761810	−	0.761810i
$59$	−9.35965			−1.21852			−0.609261	−	0.792970i	$-0.708534\pi$
$59$	−9.35965			−1.21852			−0.609261	+	0.792970i	$0.708534\pi$
$60$		0			0
$61$	−4.46967			−0.572282			−0.286141	−	0.958188i	$-0.592373\pi$
$61$	−4.46967			−0.572282			−0.286141	+	0.958188i	$0.592373\pi$
$62$	1.30913	+	1.30913i	0.166260	+	0.166260i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		0			0
$67$	3.84035	−	3.84035i	0.469174	−	0.469174i	−0.432473	−	0.901647i	$-0.642359\pi$
$67$	3.84035	−	3.84035i	0.469174	−	0.469174i	0.901647	+	0.432473i	$0.142359\pi$
$68$	4.46967	−	4.46967i	0.542027	−	0.542027i
$69$		0			0
$70$		0			0
$71$			0.420314i			0.0498821i	0.999689	+	0.0249411i	$0.00793981\pi$
$71$			0.420314i			0.0498821i	−0.999689	+	0.0249411i	$0.992060\pi$
$72$		0			0
$73$	2.63020	+	2.63020i	0.307841	+	0.307841i	0.844072	−	0.536230i	$-0.180152\pi$
$73$	2.63020	+	2.63020i	0.307841	+	0.307841i	−0.536230	+	0.844072i	$0.680152\pi$
$74$	−7.26561			−0.844610
$75$		0			0
$76$		0			0
$77$	1.51929	+	1.51929i	0.173139	+	0.173139i
$78$		0			0
$79$			5.23654i			0.589157i	0.955627	+	0.294578i	$0.0951792\pi$
$79$			5.23654i			0.589157i	−0.955627	+	0.294578i	$0.904821\pi$
$80$		0			0
$81$		0			0
$82$	5.34772	−	5.34772i	0.590557	−	0.590557i
$83$	−10.6183	+	10.6183i	−1.16551	+	1.16551i	−0.182255	+	0.983251i	$0.558340\pi$
$83$	−10.6183	+	10.6183i	−1.16551	+	1.16551i	−0.983251	+	0.182255i	$0.941660\pi$
$84$		0			0
$85$		0			0
$86$		−	11.0879i		−	1.19564i
$87$		0			0
$88$	1.51929	+	1.51929i	0.161957	+	0.161957i
$89$	−14.5481			−1.54209			−0.771047	−	0.636778i	$-0.780267\pi$
$89$	−14.5481			−1.54209			−0.771047	+	0.636778i	$0.780267\pi$
$90$		0			0
$91$	−3.05545			−0.320298
$92$	−6.32106	−	6.32106i	−0.659016	−	0.659016i
$93$		0			0
$94$		−	7.08794i		−	0.731065i
$95$		0			0
$96$		0			0
$97$	0.606342	−	0.606342i	0.0615647	−	0.0615647i	−0.675654	−	0.737219i	$-0.736139\pi$
$97$	0.606342	−	0.606342i	0.0615647	−	0.0615647i	0.737219	+	0.675654i	$0.236139\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$		0			0
$100$		0			0
$101$			5.39860i			0.537181i	0.963255	+	0.268590i	$0.0865578\pi$
$101$			5.39860i			0.537181i	−0.963255	+	0.268590i	$0.913442\pi$
$102$		0			0
$103$	7.80546	+	7.80546i	0.769095	+	0.769095i	0.977947	−	0.208853i	$-0.0669729\pi$
$103$	7.80546	+	7.80546i	0.769095	+	0.769095i	−0.208853	+	0.977947i	$0.566973\pi$
$104$	−3.05545			−0.299612
$105$		0			0
$106$	3.33579			0.324001
$107$	2.40811	+	2.40811i	0.232801	+	0.232801i	0.813861	−	0.581060i	$-0.197362\pi$
$107$	2.40811	+	2.40811i	0.232801	+	0.232801i	−0.581060	+	0.813861i	$0.697362\pi$
$108$		0			0
$109$		−	9.90075i		−	0.948320i	−0.880439	−	0.474160i	$-0.842752\pi$
$109$		−	9.90075i		−	0.948320i	0.880439	−	0.474160i	$-0.157248\pi$
$110$		0			0
$111$		0			0
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$	−4.22703	+	4.22703i	−0.397645	+	0.397645i	−0.877402	−	0.479757i	$-0.840725\pi$
$113$	−4.22703	+	4.22703i	−0.397645	+	0.397645i	0.479757	+	0.877402i	$0.340725\pi$
$114$		0			0
$115$		0			0
$116$			8.20494i			0.761810i
$117$		0			0
$118$	6.61827	+	6.61827i	0.609261	+	0.609261i
$119$	−6.32106			−0.579451
$120$		0			0
$121$	6.38350			0.580318
$122$	3.16053	+	3.16053i	0.286141	+	0.286141i
$123$		0			0
$124$		−	1.85140i		−	0.166260i
$125$		0			0
$126$		0			0
$127$	−2.32106	+	2.32106i	−0.205961	+	0.205961i	−0.802548	−	0.596587i	$-0.796523\pi$
$127$	−2.32106	+	2.32106i	−0.205961	+	0.205961i	0.596587	+	0.802548i	$0.296523\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$		−	2.37438i		−	0.207450i	−0.994606	−	0.103725i	$-0.966924\pi$
$131$		−	2.37438i		−	0.207450i	0.994606	−	0.103725i	$-0.0330762\pi$
$132$		0			0
$133$		0			0
$134$	−5.43108			−0.469174
$135$		0			0
$136$	−6.32106			−0.542027
$137$	9.88388	+	9.88388i	0.844437	+	0.844437i	0.989432	−	0.144995i	$-0.0463168\pi$
$137$	9.88388	+	9.88388i	0.844437	+	0.844437i	−0.144995	+	0.989432i	$0.546317\pi$
$138$		0			0
$139$			15.6109i			1.32410i	0.749459	+	0.662050i	$0.230313\pi$
$139$			15.6109i			1.32410i	−0.749459	+	0.662050i	$0.769687\pi$
$140$		0			0
$141$		0			0
$142$	0.297207	−	0.297207i	0.0249411	−	0.0249411i
$143$	4.64213	−	4.64213i	0.388194	−	0.388194i
$144$		0			0
$145$		0			0
$146$		−	3.71966i		−	0.307841i
$147$		0			0
$148$	5.13756	+	5.13756i	0.422305	+	0.422305i
$149$	9.49962			0.778239			0.389120	−	0.921187i	$-0.372779\pi$
$149$	9.49962			0.778239			0.389120	+	0.921187i	$0.372779\pi$
$150$		0			0
$151$	−13.5815			−1.10524			−0.552622	−	0.833432i	$-0.686373\pi$
$151$	−13.5815			−1.10524			−0.552622	+	0.833432i	$0.686373\pi$
$152$		0			0
$153$		0			0
$154$		−	2.14860i		−	0.173139i
$155$		0			0
$156$		0			0
$157$	−14.0613	+	14.0613i	−1.12221	+	1.12221i	−0.130804	+	0.991408i	$0.541756\pi$
$157$	−14.0613	+	14.0613i	−1.12221	+	1.12221i	−0.991408	+	0.130804i	$0.958244\pi$
$158$	3.70279	−	3.70279i	0.294578	−	0.294578i
$159$		0			0
$160$		0			0
$161$			8.93933i			0.704518i
$162$		0			0
$163$	−8.80177	−	8.80177i	−0.689408	−	0.689408i	0.272693	−	0.962101i	$-0.412086\pi$
$163$	−8.80177	−	8.80177i	−0.689408	−	0.689408i	−0.962101	+	0.272693i	$0.912086\pi$
$164$	−7.56282			−0.590557
$165$		0			0
$166$	15.0165			1.16551
$167$	−2.66878	−	2.66878i	−0.206517	−	0.206517i	0.596269	−	0.802785i	$-0.296649\pi$
$167$	−2.66878	−	2.66878i	−0.206517	−	0.206517i	−0.802785	+	0.596269i	$0.796649\pi$
$168$		0			0
$169$		−	3.66421i		−	0.281862i
$170$		0			0
$171$		0			0
$172$	−7.84035	+	7.84035i	−0.597821	+	0.597821i
$173$	6.70127	−	6.70127i	0.509488	−	0.509488i	−0.404881	−	0.914369i	$-0.632687\pi$
$173$	6.70127	−	6.70127i	0.509488	−	0.509488i	0.914369	+	0.404881i	$0.132687\pi$
$174$		0			0
$175$		0			0
$176$		−	2.14860i		−	0.161957i
$177$		0			0
$178$	10.2871	+	10.2871i	0.771047	+	0.771047i
$179$	−3.50825			−0.262219			−0.131109	−	0.991368i	$-0.541854\pi$
$179$	−3.50825			−0.262219			−0.131109	+	0.991368i	$0.541854\pi$
$180$		0			0
$181$	13.7981			1.02560			0.512802	−	0.858507i	$-0.328608\pi$
$181$	13.7981			1.02560			0.512802	+	0.858507i	$0.328608\pi$
$182$	2.16053	+	2.16053i	0.160149	+	0.160149i
$183$		0			0
$184$			8.93933i			0.659016i
$185$		0			0
$186$		0			0
$187$	9.60354	−	9.60354i	0.702280	−	0.702280i
$188$	−5.01193	+	5.01193i	−0.365532	+	0.365532i
$189$		0			0
$190$		0			0
$191$		−	0.519018i		−	0.0375548i	−0.999824	−	0.0187774i	$-0.994023\pi$
$191$		−	0.519018i		−	0.0375548i	0.999824	−	0.0187774i	$-0.00597739\pi$
$192$		0			0
$193$	17.1759	+	17.1759i	1.23635	+	1.23635i	0.961483	+	0.274863i	$0.0886325\pi$
$193$	17.1759	+	17.1759i	1.23635	+	1.23635i	0.274863	+	0.961483i	$0.411368\pi$
$194$	−0.857497			−0.0615647
$195$		0			0
$196$	1.00000			0.0714286
$197$	4.03248	+	4.03248i	0.287303	+	0.287303i	0.836013	−	0.548710i	$-0.184881\pi$
$197$	4.03248	+	4.03248i	0.287303	+	0.287303i	−0.548710	+	0.836013i	$0.684881\pi$
$198$		0			0
$199$			21.1651i			1.50035i	0.661237	+	0.750177i	$0.270032\pi$
$199$			21.1651i			1.50035i	−0.661237	+	0.750177i	$0.729968\pi$
$200$		0			0
$201$		0			0
$202$	3.81739	−	3.81739i	0.268590	−	0.268590i
$203$	5.80177	−	5.80177i	0.407204	−	0.407204i
$204$		0			0
$205$		0			0
$206$		−	11.0386i		−	0.769095i
$207$		0			0
$208$	2.16053	+	2.16053i	0.149806	+	0.149806i
$209$		0			0
$210$		0			0
$211$	21.8787			1.50619			0.753095	−	0.657912i	$-0.228560\pi$
$211$	21.8787			1.50619			0.753095	+	0.657912i	$0.228560\pi$
$212$	−2.35876	−	2.35876i	−0.162000	−	0.162000i
$213$		0			0
$214$		−	3.40559i		−	0.232801i
$215$		0			0
$216$		0			0
$217$	−1.30913	+	1.30913i	−0.0888699	+	0.0888699i
$218$	−7.00089	+	7.00089i	−0.474160	+	0.474160i
$219$		0			0
$220$		0			0
$221$			19.3137i			1.29918i
$222$		0			0
$223$	4.42031	+	4.42031i	0.296006	+	0.296006i	0.839447	−	0.543441i	$-0.182879\pi$
$223$	4.42031	+	4.42031i	0.296006	+	0.296006i	−0.543441	+	0.839447i	$0.682879\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	5.97792			0.397645
$227$	11.7028	+	11.7028i	0.776742	+	0.776742i	0.979275	−	0.202534i	$-0.0649176\pi$
$227$	11.7028	+	11.7028i	0.776742	+	0.776742i	−0.202534	+	0.979275i	$0.564918\pi$
$228$		0			0
$229$			13.6314i			0.900785i	0.892831	+	0.450393i	$0.148716\pi$
$229$			13.6314i			0.900785i	−0.892831	+	0.450393i	$0.851284\pi$
$230$		0			0
$231$		0			0
$232$	5.80177	−	5.80177i	0.380905	−	0.380905i
$233$	−20.6421	+	20.6421i	−1.35231	+	1.35231i	−0.469240	+	0.883071i	$0.655472\pi$
$233$	−20.6421	+	20.6421i	−1.35231	+	1.35231i	−0.883071	+	0.469240i	$0.844528\pi$
$234$		0			0
$235$		0			0
$236$		−	9.35965i		−	0.609261i
$237$		0			0
$238$	4.46967	+	4.46967i	0.289725	+	0.289725i
$239$	10.3744			0.671063			0.335531	−	0.942029i	$-0.391084\pi$
$239$	10.3744			0.671063			0.335531	+	0.942029i	$0.391084\pi$
$240$		0			0
$241$	−13.7028			−0.882674			−0.441337	−	0.897341i	$-0.645496\pi$
$241$	−13.7028			−0.882674			−0.441337	+	0.897341i	$0.645496\pi$
$242$	−4.51382	−	4.51382i	−0.290159	−	0.290159i
$243$		0			0
$244$		−	4.46967i		−	0.286141i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−1.30913	+	1.30913i	−0.0831302	+	0.0831302i
$249$		0			0
$250$		0			0
$251$		−	7.57969i		−	0.478426i	−0.970967	−	0.239213i	$-0.923111\pi$
$251$		−	7.57969i		−	0.478426i	0.970967	−	0.239213i	$-0.0768893\pi$
$252$		0			0
$253$	−13.5815	−	13.5815i	−0.853859	−	0.853859i
$254$	3.28248			0.205961
$255$		0			0
$256$	1.00000			0.0625000
$257$	−19.2929	−	19.2929i	−1.20346	−	1.20346i	−0.973108	−	0.230349i	$-0.926013\pi$
$257$	−19.2929	−	19.2929i	−1.20346	−	1.20346i	−0.230349	−	0.973108i	$-0.573987\pi$
$258$		0			0
$259$		−	7.26561i		−	0.451463i
$260$		0			0
$261$		0			0
$262$	−1.67894	+	1.67894i	−0.103725	+	0.103725i
$263$	−17.6348	+	17.6348i	−1.08741	+	1.08741i	−0.0916118	+	0.995795i	$0.529202\pi$
$263$	−17.6348	+	17.6348i	−1.08741	+	1.08741i	−0.995795	+	0.0916118i	$0.970798\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	3.84035	+	3.84035i	0.234587	+	0.234587i
$269$	−20.4463			−1.24663			−0.623317	−	0.781969i	$-0.714216\pi$
$269$	−20.4463			−1.24663			−0.623317	+	0.781969i	$0.714216\pi$
$270$		0			0
$271$	−20.5707			−1.24958			−0.624790	−	0.780793i	$-0.714816\pi$
$271$	−20.5707			−1.24958			−0.624790	+	0.780793i	$0.714816\pi$
$272$	4.46967	+	4.46967i	0.271013	+	0.271013i
$273$		0			0
$274$		−	13.9779i		−	0.844437i
$275$		0			0
$276$		0			0
$277$	2.22208	−	2.22208i	0.133512	−	0.133512i	−0.637193	−	0.770705i	$-0.719904\pi$
$277$	2.22208	−	2.22208i	0.133512	−	0.133512i	0.770705	+	0.637193i	$0.219904\pi$
$278$	11.0386	−	11.0386i	0.662050	−	0.662050i
$279$		0			0
$280$		0			0
$281$			17.4792i			1.04272i	0.853337	+	0.521360i	$0.174575\pi$
$281$			17.4792i			1.04272i	−0.853337	+	0.521360i	$0.825425\pi$
$282$		0			0
$283$	−17.9007	−	17.9007i	−1.06409	−	1.06409i	−0.997800	−	0.0662885i	$-0.978884\pi$
$283$	−17.9007	−	17.9007i	−1.06409	−	1.06409i	−0.0662885	−	0.997800i	$-0.521116\pi$
$284$	−0.420314			−0.0249411
$285$		0			0
$286$	−6.56496			−0.388194
$287$	5.34772	+	5.34772i	0.315666	+	0.315666i
$288$		0			0
$289$			22.9558i			1.35034i
$290$		0			0
$291$		0			0
$292$	−2.63020	+	2.63020i	−0.153921	+	0.153921i
$293$	1.36370	−	1.36370i	0.0796683	−	0.0796683i	−0.666150	−	0.745818i	$-0.732059\pi$
$293$	1.36370	−	1.36370i	0.0796683	−	0.0796683i	0.745818	+	0.666150i	$0.232059\pi$
$294$		0			0
$295$		0			0
$296$		−	7.26561i		−	0.422305i
$297$		0			0
$298$	−6.71725	−	6.71725i	−0.389120	−	0.389120i
$299$	27.3137			1.57959
$300$		0			0
$301$	11.0879			0.639098
$302$	9.60354	+	9.60354i	0.552622	+	0.552622i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	7.70279	−	7.70279i	0.439622	−	0.439622i	−0.452263	−	0.891885i	$-0.649383\pi$
$307$	7.70279	−	7.70279i	0.439622	−	0.439622i	0.891885	+	0.452263i	$0.149383\pi$
$308$	−1.51929	+	1.51929i	−0.0865697	+	0.0865697i
$309$		0			0
$310$		0			0
$311$			3.52637i			0.199962i	0.994989	+	0.0999811i	$0.0318782\pi$
$311$			3.52637i			0.199962i	−0.994989	+	0.0999811i	$0.968122\pi$
$312$		0			0
$313$	12.3330	+	12.3330i	0.697102	+	0.697102i	0.963784	−	0.266683i	$-0.0859275\pi$
$313$	12.3330	+	12.3330i	0.697102	+	0.697102i	−0.266683	+	0.963784i	$0.585928\pi$
$314$	19.8857			1.12221
$315$		0			0
$316$	−5.23654			−0.294578
$317$	6.65597	+	6.65597i	0.373836	+	0.373836i	0.868872	−	0.495036i	$-0.164845\pi$
$317$	6.65597	+	6.65597i	0.373836	+	0.373836i	−0.495036	+	0.868872i	$0.664845\pi$
$318$		0			0
$319$			17.6292i			0.987044i
$320$		0			0
$321$		0			0
$322$	6.32106	−	6.32106i	0.352259	−	0.352259i
$323$		0			0
$324$		0			0
$325$		0			0
$326$			12.4476i			0.689408i
$327$		0			0
$328$	5.34772	+	5.34772i	0.295278	+	0.295278i
$329$	7.08794			0.390771
$330$		0			0
$331$	−30.7193			−1.68849			−0.844243	−	0.535961i	$-0.819949\pi$
$331$	−30.7193			−1.68849			−0.844243	+	0.535961i	$0.819949\pi$
$332$	−10.6183	−	10.6183i	−0.582753	−	0.582753i
$333$		0			0
$334$			3.77423i			0.206517i
$335$		0			0
$336$		0			0
$337$	11.6183	−	11.6183i	0.632887	−	0.632887i	−0.315904	−	0.948791i	$-0.602308\pi$
$337$	11.6183	−	11.6183i	0.632887	−	0.632887i	0.948791	+	0.315904i	$0.102308\pi$
$338$	−2.59099	+	2.59099i	−0.140931	+	0.140931i
$339$		0			0
$340$		0			0
$341$		−	3.97792i		−	0.215416i
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	11.0879			0.597821
$345$		0			0
$346$	−9.47702			−0.509488
$347$	10.8284	+	10.8284i	0.581300	+	0.581300i	0.935261	−	0.353960i	$-0.115165\pi$
$347$	10.8284	+	10.8284i	0.581300	+	0.581300i	−0.353960	+	0.935261i	$0.615165\pi$
$348$		0			0
$349$			15.3318i			0.820694i	0.911929	+	0.410347i	$0.134592\pi$
$349$			15.3318i			0.820694i	−0.911929	+	0.410347i	$0.865408\pi$
$350$		0			0
$351$		0			0
$352$	−1.51929	+	1.51929i	−0.0809785	+	0.0809785i
$353$	6.14860	−	6.14860i	0.327257	−	0.327257i	−0.524285	−	0.851543i	$-0.675668\pi$
$353$	6.14860	−	6.14860i	0.327257	−	0.327257i	0.851543	+	0.524285i	$0.175668\pi$
$354$		0			0
$355$		0			0
$356$		−	14.5481i		−	0.771047i
$357$		0			0
$358$	2.48071	+	2.48071i	0.131109	+	0.131109i
$359$	28.6421			1.51167			0.755837	−	0.654760i	$-0.227230\pi$
$359$	28.6421			1.51167			0.755837	+	0.654760i	$0.227230\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$	−9.75672	−	9.75672i	−0.512802	−	0.512802i
$363$		0			0
$364$		−	3.05545i		−	0.160149i
$365$		0			0
$366$		0			0
$367$	10.0732	−	10.0732i	0.525817	−	0.525817i	−0.393505	−	0.919322i	$-0.628738\pi$
$367$	10.0732	−	10.0732i	0.525817	−	0.525817i	0.919322	+	0.393505i	$0.128738\pi$
$368$	6.32106	−	6.32106i	0.329508	−	0.329508i
$369$		0			0
$370$		0			0
$371$			3.33579i			0.173186i
$372$		0			0
$373$	−19.1614	−	19.1614i	−0.992141	−	0.992141i	0.00782876	−	0.999969i	$-0.497508\pi$
$373$	−19.1614	−	19.1614i	−0.992141	−	0.992141i	−0.999969	+	0.00782876i	$0.997508\pi$
$374$	−13.5815			−0.702280
$375$		0			0
$376$	7.08794			0.365532
$377$	−17.7270	−	17.7270i	−0.912989	−	0.912989i
$378$		0			0
$379$			22.1538i			1.13796i	0.822350	+	0.568982i	$0.192663\pi$
$379$			22.1538i			1.13796i	−0.822350	+	0.568982i	$0.807337\pi$
$380$		0			0
$381$		0			0
$382$	−0.367001	+	0.367001i	−0.0187774	+	0.0187774i
$383$	24.6008	−	24.6008i	1.25704	−	1.25704i	0.304541	−	0.952499i	$-0.401497\pi$
$383$	24.6008	−	24.6008i	1.25704	−	1.25704i	0.952499	−	0.304541i	$-0.0985030\pi$
$384$		0			0
$385$		0			0
$386$		−	24.2904i		−	1.23635i
$387$		0			0
$388$	0.606342	+	0.606342i	0.0307824	+	0.0307824i
$389$	−9.25341			−0.469166			−0.234583	−	0.972096i	$-0.575373\pi$
$389$	−9.25341			−0.469166			−0.234583	+	0.972096i	$0.575373\pi$
$390$		0			0
$391$	56.5061			2.85764
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$		0			0
$394$		−	5.70279i		−	0.287303i
$395$		0			0
$396$		0			0
$397$	−14.8282	+	14.8282i	−0.744204	+	0.744204i	−0.973384	−	0.229180i	$-0.926395\pi$
$397$	−14.8282	+	14.8282i	−0.744204	+	0.744204i	0.229180	+	0.973384i	$0.426395\pi$
$398$	14.9660	−	14.9660i	0.750177	−	0.750177i
$399$		0			0
$400$		0			0
$401$		−	13.0416i		−	0.651267i	−0.945496	−	0.325633i	$-0.894422\pi$
$401$		−	13.0416i		−	0.651267i	0.945496	−	0.325633i	$-0.105578\pi$
$402$		0			0
$403$	4.00000	+	4.00000i	0.199254	+	0.199254i
$404$	−5.39860			−0.268590
$405$		0			0
$406$	−8.20494			−0.407204
$407$	11.0386	+	11.0386i	0.547162	+	0.547162i
$408$		0			0
$409$		−	26.9190i		−	1.33106i	−0.746371	−	0.665530i	$-0.768206\pi$
$409$		−	26.9190i		−	1.33106i	0.746371	−	0.665530i	$-0.231794\pi$
$410$		0			0
$411$		0			0
$412$	−7.80546	+	7.80546i	−0.384547	+	0.384547i
$413$	−6.61827	+	6.61827i	−0.325664	+	0.325664i
$414$		0			0
$415$		0			0
$416$		−	3.05545i		−	0.149806i
$417$		0			0
$418$		0			0
$419$	21.9705			1.07333			0.536666	−	0.843795i	$-0.319684\pi$
$419$	21.9705			1.07333			0.536666	+	0.843795i	$0.319684\pi$
$420$		0			0
$421$	−10.5502			−0.514188			−0.257094	−	0.966386i	$-0.582765\pi$
$421$	−10.5502			−0.514188			−0.257094	+	0.966386i	$0.582765\pi$
$422$	−15.4706	−	15.4706i	−0.753095	−	0.753095i
$423$		0			0
$424$			3.33579i			0.162000i
$425$		0			0
$426$		0			0
$427$	−3.16053	+	3.16053i	−0.152949	+	0.152949i
$428$	−2.40811	+	2.40811i	−0.116401	+	0.116401i
$429$		0			0
$430$		0			0
$431$		−	22.9853i		−	1.10716i	−0.832795	−	0.553581i	$-0.813261\pi$
$431$		−	22.9853i		−	1.10716i	0.832795	−	0.553581i	$-0.186739\pi$
$432$		0			0
$433$	−11.3256	−	11.3256i	−0.544275	−	0.544275i	0.380504	−	0.924779i	$-0.375751\pi$
$433$	−11.3256	−	11.3256i	−0.544275	−	0.544275i	−0.924779	+	0.380504i	$0.875751\pi$
$434$	1.85140			0.0888699
$435$		0			0
$436$	9.90075			0.474160
$437$		0			0
$438$		0			0
$439$		−	0.416353i		−	0.0198715i	−0.999951	−	0.00993573i	$-0.996837\pi$
$439$		−	0.416353i		−	0.0198715i	0.999951	−	0.00993573i	$-0.00316269\pi$
$440$		0			0
$441$		0			0
$442$	13.6569	−	13.6569i	0.649590	−	0.649590i
$443$	11.2487	−	11.2487i	0.534444	−	0.534444i	−0.387448	−	0.921892i	$-0.626643\pi$
$443$	11.2487	−	11.2487i	0.534444	−	0.534444i	0.921892	+	0.387448i	$0.126643\pi$
$444$		0			0
$445$		0			0
$446$		−	6.25127i		−	0.296006i
$447$		0			0
$448$	−0.707107	−	0.707107i	−0.0334077	−	0.0334077i
$449$	20.7929			0.981277			0.490639	−	0.871363i	$-0.336764\pi$
$449$	20.7929			0.981277			0.490639	+	0.871363i	$0.336764\pi$
$450$		0			0
$451$	−16.2495			−0.765159
$452$	−4.22703	−	4.22703i	−0.198823	−	0.198823i
$453$		0			0
$454$		−	16.5502i		−	0.776742i
$455$		0			0
$456$		0			0
$457$	−12.7028	+	12.7028i	−0.594212	+	0.594212i	−0.938766	−	0.344555i	$-0.888030\pi$
$457$	−12.7028	+	12.7028i	−0.594212	+	0.594212i	0.344555	+	0.938766i	$0.388030\pi$
$458$	9.63883	−	9.63883i	0.450393	−	0.450393i
$459$		0			0
$460$		0			0
$461$			29.8783i			1.39157i	0.718250	+	0.695785i	$0.244943\pi$
$461$			29.8783i			1.39157i	−0.718250	+	0.695785i	$0.755057\pi$
$462$		0			0
$463$	15.2825	+	15.2825i	0.710237	+	0.710237i	0.966585	−	0.256348i	$-0.0825192\pi$
$463$	15.2825	+	15.2825i	0.710237	+	0.710237i	−0.256348	+	0.966585i	$0.582519\pi$
$464$	−8.20494			−0.380905
$465$		0			0
$466$	29.1924			1.35231
$467$	18.5429	+	18.5429i	0.858062	+	0.858062i	0.991110	−	0.133048i	$-0.0424764\pi$
$467$	18.5429	+	18.5429i	0.858062	+	0.858062i	−0.133048	+	0.991110i	$0.542476\pi$
$468$		0			0
$469$		−	5.43108i		−	0.250784i
$470$		0			0
$471$		0			0
$472$	−6.61827	+	6.61827i	−0.304631	+	0.304631i
$473$	−16.8458	+	16.8458i	−0.774571	+	0.774571i
$474$		0			0
$475$		0			0
$476$		−	6.32106i		−	0.289725i
$477$		0			0
$478$	−7.33579	−	7.33579i	−0.335531	−	0.335531i
$479$	−4.91725			−0.224675			−0.112337	−	0.993670i	$-0.535834\pi$
$479$	−4.91725			−0.224675			−0.112337	+	0.993670i	$0.535834\pi$
$480$		0			0
$481$	−22.1997			−1.01222
$482$	9.68934	+	9.68934i	0.441337	+	0.441337i
$483$		0			0
$484$			6.38350i			0.290159i
$485$		0			0
$486$		0			0
$487$	−9.63477	+	9.63477i	−0.436593	+	0.436593i	−0.890864	−	0.454271i	$-0.849900\pi$
$487$	−9.63477	+	9.63477i	−0.436593	+	0.436593i	0.454271	+	0.890864i	$0.349900\pi$
$488$	−3.16053	+	3.16053i	−0.143071	+	0.143071i
$489$		0			0
$490$		0			0
$491$			20.0273i			0.903818i	0.892064	+	0.451909i	$0.149257\pi$
$491$			20.0273i			0.903818i	−0.892064	+	0.451909i	$0.850743\pi$
$492$		0			0
$493$	−36.6734	−	36.6734i	−1.65168	−	1.65168i
$494$		0			0
$495$		0			0
$496$	1.85140			0.0831302
$497$	0.297207	+	0.297207i	0.0133316	+	0.0133316i
$498$		0			0
$499$		−	34.7959i		−	1.55768i	−0.627223	−	0.778840i	$-0.715809\pi$
$499$		−	34.7959i		−	1.55768i	0.627223	−	0.778840i	$-0.284191\pi$
$500$		0			0
$501$		0			0
$502$	−5.35965	+	5.35965i	−0.239213	+	0.239213i
$503$	−3.26320	+	3.26320i	−0.145499	+	0.145499i	−0.776104	−	0.630605i	$-0.782807\pi$
$503$	−3.26320	+	3.26320i	−0.145499	+	0.145499i	0.630605	+	0.776104i	$0.282807\pi$
$504$		0			0
$505$		0			0
$506$			19.2071i			0.853859i
$507$		0			0
$508$	−2.32106	−	2.32106i	−0.102981	−	0.102981i
$509$	29.3544			1.30111			0.650556	−	0.759458i	$-0.274536\pi$
$509$	29.3544			1.30111			0.650556	+	0.759458i	$0.274536\pi$
$510$		0			0
$511$	3.71966			0.164548
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			27.2843i			1.20346i
$515$		0			0
$516$		0			0
$517$	−10.7686	+	10.7686i	−0.473605	+	0.473605i
$518$	−5.13756	+	5.13756i	−0.225732	+	0.225732i
$519$		0			0
$520$		0			0
$521$		−	12.3453i		−	0.540858i	−0.962740	−	0.270429i	$-0.912835\pi$
$521$		−	12.3453i		−	0.540858i	0.962740	−	0.270429i	$-0.0871655\pi$
$522$		0			0
$523$	7.52637	+	7.52637i	0.329105	+	0.329105i	0.852246	−	0.523141i	$-0.175240\pi$
$523$	7.52637	+	7.52637i	0.329105	+	0.329105i	−0.523141	+	0.852246i	$0.675240\pi$
$524$	2.37438			0.103725
$525$		0			0
$526$	24.9393			1.08741
$527$	8.27512	+	8.27512i	0.360470	+	0.360470i
$528$		0			0
$529$		−	56.9117i		−	2.47442i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	16.3397	−	16.3397i	0.707751	−	0.707751i
$534$		0			0
$535$		0			0
$536$		−	5.43108i		−	0.234587i
$537$		0			0
$538$	14.4577	+	14.4577i	0.623317	+	0.623317i
$539$	2.14860			0.0925469
$540$		0			0
$541$	−40.9172			−1.75917			−0.879585	−	0.475742i	$-0.842180\pi$
$541$	−40.9172			−1.75917			−0.879585	+	0.475742i	$0.842180\pi$
$542$	14.5457	+	14.5457i	0.624790	+	0.624790i
$543$		0			0
$544$		−	6.32106i		−	0.271013i
$545$		0			0
$546$		0			0
$547$	−10.8789	+	10.8789i	−0.465150	+	0.465150i	−0.900339	−	0.435189i	$-0.856681\pi$
$547$	−10.8789	+	10.8789i	−0.465150	+	0.465150i	0.435189	+	0.900339i	$0.356681\pi$
$548$	−9.88388	+	9.88388i	−0.422218	+	0.422218i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	3.70279	+	3.70279i	0.157459	+	0.157459i
$554$	−3.14250			−0.133512
$555$		0			0
$556$	−15.6109			−0.662050
$557$	−18.3588	−	18.3588i	−0.777886	−	0.777886i	0.201585	−	0.979471i	$-0.435391\pi$
$557$	−18.3588	−	18.3588i	−0.777886	−	0.777886i	−0.979471	+	0.201585i	$0.935391\pi$
$558$		0			0
$559$		−	33.8787i		−	1.43291i
$560$		0			0
$561$		0			0
$562$	12.3596	−	12.3596i	0.521360	−	0.521360i
$563$	25.6348	−	25.6348i	1.08038	−	1.08038i	0.0839029	−	0.996474i	$-0.473261\pi$
$563$	25.6348	−	25.6348i	1.08038	−	1.08038i	0.996474	−	0.0839029i	$-0.0267385\pi$
$564$		0			0
$565$		0			0
$566$			25.3155i			1.06409i
$567$		0			0
$568$	0.297207	+	0.297207i	0.0124705	+	0.0124705i
$569$	−44.9637			−1.88498			−0.942488	−	0.334239i	$-0.891521\pi$
$569$	−44.9637			−1.88498			−0.942488	+	0.334239i	$0.891521\pi$
$570$		0			0
$571$	−13.0380			−0.545625			−0.272812	−	0.962067i	$-0.587954\pi$
$571$	−13.0380			−0.545625			−0.272812	+	0.962067i	$0.587954\pi$
$572$	4.64213	+	4.64213i	0.194097	+	0.194097i
$573$		0			0
$574$		−	7.56282i		−	0.315666i
$575$		0			0
$576$		0			0
$577$	−17.1498	+	17.1498i	−0.713954	+	0.713954i	−0.967360	−	0.253406i	$-0.918449\pi$
$577$	−17.1498	+	17.1498i	−0.713954	+	0.713954i	0.253406	+	0.967360i	$0.418449\pi$
$578$	16.2322	−	16.2322i	0.675172	−	0.675172i
$579$		0			0
$580$		0			0
$581$			15.0165i			0.622989i
$582$		0			0
$583$	−5.06804	−	5.06804i	−0.209897	−	0.209897i
$584$	3.71966			0.153921
$585$		0			0
$586$	−1.92857			−0.0796683
$587$	−7.26040	−	7.26040i	−0.299669	−	0.299669i	0.541215	−	0.840884i	$-0.317964\pi$
$587$	−7.26040	−	7.26040i	−0.299669	−	0.299669i	−0.840884	+	0.541215i	$0.817964\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−5.13756	+	5.13756i	−0.211153	+	0.211153i
$593$	−7.97917	+	7.97917i	−0.327665	+	0.327665i	−0.851698	−	0.524033i	$-0.824427\pi$
$593$	−7.97917	+	7.97917i	−0.327665	+	0.327665i	0.524033	+	0.851698i	$0.324427\pi$
$594$		0			0
$595$		0			0
$596$			9.49962i			0.389120i
$597$		0			0
$598$	−19.3137	−	19.3137i	−0.789796	−	0.789796i
$599$	−6.17587			−0.252339			−0.126170	−	0.992009i	$-0.540268\pi$
$599$	−6.17587			−0.252339			−0.126170	+	0.992009i	$0.540268\pi$
$600$		0			0
$601$	−15.8106			−0.644930			−0.322465	−	0.946581i	$-0.604511\pi$
$601$	−15.8106			−0.644930			−0.322465	+	0.946581i	$0.604511\pi$
$602$	−7.84035	−	7.84035i	−0.319549	−	0.319549i
$603$		0			0
$604$		−	13.5815i		−	0.552622i
$605$		0			0
$606$		0			0
$607$	3.57969	−	3.57969i	0.145295	−	0.145295i	−0.630718	−	0.776012i	$-0.717239\pi$
$607$	3.57969	−	3.57969i	0.145295	−	0.145295i	0.776012	+	0.630718i	$0.217239\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	21.6569i		−	0.876143i
$612$		0			0
$613$	−6.77056	−	6.77056i	−0.273460	−	0.273460i	0.557031	−	0.830492i	$-0.311940\pi$
$613$	−6.77056	−	6.77056i	−0.273460	−	0.273460i	−0.830492	+	0.557031i	$0.811940\pi$
$614$	−10.8934			−0.439622
$615$		0			0
$616$	2.14860			0.0865697
$617$	0.889981	+	0.889981i	0.0358293	+	0.0358293i	0.724794	−	0.688965i	$-0.241935\pi$
$617$	0.889981	+	0.889981i	0.0358293	+	0.0358293i	−0.688965	+	0.724794i	$0.741935\pi$
$618$		0			0
$619$			40.4436i			1.62557i	0.582566	+	0.812783i	$0.302049\pi$
$619$			40.4436i			1.62557i	−0.582566	+	0.812783i	$0.697951\pi$
$620$		0			0
$621$		0			0
$622$	2.49352	−	2.49352i	0.0999811	−	0.0999811i
$623$	−10.2871	+	10.2871i	−0.412142	+	0.412142i
$624$		0			0
$625$		0			0
$626$		−	17.4415i		−	0.697102i
$627$		0			0
$628$	−14.0613	−	14.0613i	−0.561106	−	0.561106i
$629$	−45.9264			−1.83120
$630$		0			0
$631$	8.38908			0.333964			0.166982	−	0.985960i	$-0.446598\pi$
$631$	8.38908			0.333964			0.166982	+	0.985960i	$0.446598\pi$
$632$	3.70279	+	3.70279i	0.147289	+	0.147289i
$633$		0			0
$634$		−	9.41296i		−	0.373836i
$635$		0			0
$636$		0			0
$637$	−2.16053	+	2.16053i	−0.0856034	+	0.0856034i
$638$	12.4657	−	12.4657i	0.493522	−	0.493522i
$639$		0			0
$640$		0			0
$641$		−	20.6863i		−	0.817058i	−0.912745	−	0.408529i	$-0.866042\pi$
$641$		−	20.6863i		−	0.817058i	0.912745	−	0.408529i	$-0.133958\pi$
$642$		0			0
$643$	−1.55583	−	1.55583i	−0.0613559	−	0.0613559i	0.675763	−	0.737119i	$-0.263814\pi$
$643$	−1.55583	−	1.55583i	−0.0613559	−	0.0613559i	−0.737119	+	0.675763i	$0.763814\pi$
$644$	−8.93933			−0.352259
$645$		0			0
$646$		0			0
$647$	−31.9053	−	31.9053i	−1.25433	−	1.25433i	−0.953761	−	0.300567i	$-0.902824\pi$
$647$	−31.9053	−	31.9053i	−1.25433	−	1.25433i	−0.300567	−	0.953761i	$-0.597176\pi$
$648$		0			0
$649$		−	20.1102i		−	0.789393i
$650$		0			0
$651$		0			0
$652$	8.80177	−	8.80177i	0.344704	−	0.344704i
$653$	16.1841	−	16.1841i	0.633333	−	0.633333i	−0.315569	−	0.948903i	$-0.602195\pi$
$653$	16.1841	−	16.1841i	0.633333	−	0.633333i	0.948903	+	0.315569i	$0.102195\pi$
$654$		0			0
$655$		0			0
$656$		−	7.56282i		−	0.295278i
$657$		0			0
$658$	−5.01193	−	5.01193i	−0.195385	−	0.195385i
$659$	−7.13565			−0.277965			−0.138983	−	0.990295i	$-0.544383\pi$
$659$	−7.13565			−0.277965			−0.138983	+	0.990295i	$0.544383\pi$
$660$		0			0
$661$	−29.3103			−1.14004			−0.570019	−	0.821631i	$-0.693064\pi$
$661$	−29.3103			−1.14004			−0.570019	+	0.821631i	$0.693064\pi$
$662$	21.7218	+	21.7218i	0.844243	+	0.844243i
$663$		0			0
$664$			15.0165i			0.582753i
$665$		0			0
$666$		0			0
$667$	−51.8640	+	51.8640i	−2.00818	+	2.00818i
$668$	2.66878	−	2.66878i	0.103258	−	0.103258i
$669$		0			0
$670$		0			0
$671$		−	9.60354i		−	0.370741i
$672$		0			0
$673$	13.3431	+	13.3431i	0.514340	+	0.514340i	0.915853	−	0.401513i	$-0.131516\pi$
$673$	13.3431	+	13.3431i	0.514340	+	0.514340i	−0.401513	+	0.915853i	$0.631516\pi$
$674$	−16.4307			−0.632887
$675$		0			0
$676$	3.66421			0.140931
$677$	−1.38289	−	1.38289i	−0.0531488	−	0.0531488i	0.680033	−	0.733182i	$-0.261965\pi$
$677$	−1.38289	−	1.38289i	−0.0531488	−	0.0531488i	−0.733182	+	0.680033i	$0.761965\pi$
$678$		0			0
$679$		−	0.857497i		−	0.0329077i
$680$		0			0
$681$		0			0
$682$	−2.81281	+	2.81281i	−0.107708	+	0.107708i
$683$	−24.2907	+	24.2907i	−0.929459	+	0.929459i	−0.997671	−	0.0682116i	$-0.978271\pi$
$683$	−24.2907	+	24.2907i	−0.929459	+	0.929459i	0.0682116	+	0.997671i	$0.478271\pi$
$684$		0			0
$685$		0			0
$686$			1.00000i			0.0381802i
$687$		0			0
$688$	−7.84035	−	7.84035i	−0.298911	−	0.298911i
$689$	10.1924			0.388298
$690$		0			0
$691$	27.0642			1.02957			0.514786	−	0.857319i	$-0.327872\pi$
$691$	27.0642			1.02957			0.514786	+	0.857319i	$0.327872\pi$
$692$	6.70127	+	6.70127i	0.254744	+	0.254744i
$693$		0			0
$694$		−	15.3137i		−	0.581300i
$695$		0			0
$696$		0			0
$697$	33.8033	−	33.8033i	1.28039	−	1.28039i
$698$	10.8412	−	10.8412i	0.410347	−	0.410347i
$699$		0			0
$700$		0			0
$701$			1.63999i			0.0619414i	0.999520	+	0.0309707i	$0.00985986\pi$
$701$			1.63999i			0.0619414i	−0.999520	+	0.0309707i	$0.990140\pi$
$702$		0			0
$703$		0			0
$704$	2.14860			0.0809785
$705$		0			0
$706$	−8.69544			−0.327257
$707$	3.81739	+	3.81739i	0.143568	+	0.143568i
$708$		0			0
$709$			8.35963i			0.313952i	0.987602	+	0.156976i	$0.0501746\pi$
$709$			8.35963i			0.313952i	−0.987602	+	0.156976i	$0.949825\pi$
$710$		0			0
$711$		0			0
$712$	−10.2871	+	10.2871i	−0.385524	+	0.385524i
$713$	11.7028	−	11.7028i	0.438273	−	0.438273i
$714$		0			0
$715$		0			0
$716$		−	3.50825i		−	0.131109i
$717$		0			0
$718$	−20.2530	−	20.2530i	−0.755837	−	0.755837i
$719$	16.9706			0.632895			0.316448	−	0.948610i	$-0.397510\pi$
$719$	16.9706			0.632895			0.316448	+	0.948610i	$0.397510\pi$
$720$		0			0
$721$	11.0386			0.411098
$722$	−13.4350	−	13.4350i	−0.500000	−	0.500000i
$723$		0			0
$724$			13.7981i			0.512802i
$725$		0			0
$726$		0			0
$727$	−0.221811	+	0.221811i	−0.00822652	+	0.00822652i	−0.711208	−	0.702982i	$-0.751852\pi$
$727$	−0.221811	+	0.221811i	−0.00822652	+	0.00822652i	0.702982	+	0.711208i	$0.251852\pi$
$728$	−2.16053	+	2.16053i	−0.0800746	+	0.0800746i
$729$		0			0
$730$		0			0
$731$		−	70.0875i		−	2.59228i
$732$		0			0
$733$	−4.28705	−	4.28705i	−0.158346	−	0.158346i	0.623487	−	0.781833i	$-0.285715\pi$
$733$	−4.28705	−	4.28705i	−0.158346	−	0.158346i	−0.781833	+	0.623487i	$0.785715\pi$
$734$	−14.2457			−0.525817
$735$		0			0
$736$	−8.93933			−0.329508
$737$	8.25140	+	8.25140i	0.303944	+	0.303944i
$738$		0			0
$739$		−	11.6182i		−	0.427384i	−0.976901	−	0.213692i	$-0.931451\pi$
$739$		−	11.6182i		−	0.427384i	0.976901	−	0.213692i	$-0.0685489\pi$
$740$		0			0
$741$		0			0
$742$	2.35876	−	2.35876i	0.0865928	−	0.0865928i
$743$	7.65508	−	7.65508i	0.280838	−	0.280838i	−0.552605	−	0.833443i	$-0.686366\pi$
$743$	7.65508	−	7.65508i	0.280838	−	0.280838i	0.833443	+	0.552605i	$0.186366\pi$
$744$		0			0
$745$		0			0
$746$			27.0983i			0.992141i
$747$		0			0
$748$	9.60354	+	9.60354i	0.351140	+	0.351140i
$749$	3.40559			0.124437
$750$		0			0
$751$	−23.7505			−0.866668			−0.433334	−	0.901233i	$-0.642663\pi$
$751$	−23.7505			−0.866668			−0.433334	+	0.901233i	$0.642663\pi$
$752$	−5.01193	−	5.01193i	−0.182766	−	0.182766i
$753$		0			0
$754$			25.0698i			0.912989i
$755$		0			0
$756$		0			0
$757$	31.4825	−	31.4825i	1.14425	−	1.14425i	0.156586	−	0.987664i	$-0.449951\pi$
$757$	31.4825	−	31.4825i	1.14425	−	1.14425i	0.987664	−	0.156586i	$-0.0500488\pi$
$758$	15.6651	−	15.6651i	0.568982	−	0.568982i
$759$		0			0
$760$		0			0
$761$		−	19.2552i		−	0.698000i	−0.937123	−	0.349000i	$-0.886521\pi$
$761$		−	19.2552i		−	0.698000i	0.937123	−	0.349000i	$-0.113479\pi$
$762$		0			0
$763$	−7.00089	−	7.00089i	−0.253449	−	0.253449i
$764$	0.519018			0.0187774
$765$		0			0
$766$	−34.7907			−1.25704
$767$	20.2218	+	20.2218i	0.730167	+	0.730167i
$768$		0			0
$769$		−	52.3541i		−	1.88794i	−0.330037	−	0.943968i	$-0.607061\pi$
$769$		−	52.3541i		−	1.88794i	0.330037	−	0.943968i	$-0.392939\pi$
$770$		0			0
$771$		0			0
$772$	−17.1759	+	17.1759i	−0.618173	+	0.618173i
$773$	−24.6410	+	24.6410i	−0.886274	+	0.886274i	−0.994163	−	0.107889i	$-0.965591\pi$
$773$	−24.6410	+	24.6410i	−0.886274	+	0.886274i	0.107889	+	0.994163i	$0.465591\pi$
$774$		0			0
$775$		0			0
$776$		−	0.857497i		−	0.0307824i
$777$		0			0
$778$	6.54315	+	6.54315i	0.234583	+	0.234583i
$779$		0			0
$780$		0			0
$781$	−0.903089			−0.0323151
$782$	−39.9558	−	39.9558i	−1.42882	−	1.42882i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$		0			0
$786$		0			0
$787$	−33.9264	+	33.9264i	−1.20934	+	1.20934i	−0.238105	+	0.971239i	$0.576526\pi$
$787$	−33.9264	+	33.9264i	−1.20934	+	1.20934i	−0.971239	+	0.238105i	$0.923474\pi$
$788$	−4.03248	+	4.03248i	−0.143651	+	0.143651i
$789$		0			0
$790$		0			0
$791$			5.97792i			0.212550i
$792$		0			0
$793$	9.65685	+	9.65685i	0.342925	+	0.342925i
$794$	20.9702			0.744204
$795$		0			0
$796$	−21.1651			−0.750177
$797$	−13.8269	−	13.8269i	−0.489774	−	0.489774i	0.418461	−	0.908235i	$-0.362570\pi$
$797$	−13.8269	−	13.8269i	−0.489774	−	0.489774i	−0.908235	+	0.418461i	$0.862570\pi$
$798$		0			0
$799$		−	44.8033i		−	1.58503i
$800$		0			0
$801$		0			0
$802$	−9.22181	+	9.22181i	−0.325633	+	0.325633i
$803$	−5.65125	+	5.65125i	−0.199428	+	0.199428i
$804$		0			0
$805$		0			0
$806$		−	5.65685i		−	0.199254i
$807$		0			0
$808$	3.81739	+	3.81739i	0.134295	+	0.134295i
$809$	32.8743			1.15580			0.577900	−	0.816108i	$-0.303872\pi$
$809$	32.8743			1.15580			0.577900	+	0.816108i	$0.303872\pi$
$810$		0			0
$811$	−34.1794			−1.20020			−0.600101	−	0.799924i	$-0.704873\pi$
$811$	−34.1794			−1.20020			−0.600101	+	0.799924i	$0.704873\pi$
$812$	5.80177	+	5.80177i	0.203602	+	0.203602i
$813$		0			0
$814$		−	15.6109i		−	0.547162i
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−19.0346	+	19.0346i	−0.665530	+	0.665530i
$819$		0			0
$820$		0			0
$821$			54.3392i			1.89645i	0.317600	+	0.948225i	$0.397123\pi$
$821$			54.3392i			1.89645i	−0.317600	+	0.948225i	$0.602877\pi$
$822$		0			0
$823$	−2.09365	−	2.09365i	−0.0729800	−	0.0729800i	0.669675	−	0.742655i	$-0.266434\pi$
$823$	−2.09365	−	2.09365i	−0.0729800	−	0.0729800i	−0.742655	+	0.669675i	$0.766434\pi$
$824$	11.0386			0.384547
$825$		0			0
$826$	9.35965			0.325664
$827$	−34.5273	−	34.5273i	−1.20063	−	1.20063i	−0.973975	−	0.226655i	$-0.927221\pi$
$827$	−34.5273	−	34.5273i	−1.20063	−	1.20063i	−0.226655	−	0.973975i	$-0.572779\pi$
$828$		0			0
$829$			20.4697i			0.710941i	0.934688	+	0.355470i	$0.115679\pi$
$829$			20.4697i			0.710941i	−0.934688	+	0.355470i	$0.884321\pi$
$830$		0			0
$831$		0			0
$832$	−2.16053	+	2.16053i	−0.0749029	+	0.0749029i
$833$	−4.46967	+	4.46967i	−0.154865	+	0.154865i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−15.5355	−	15.5355i	−0.536666	−	0.536666i
$839$	37.0472			1.27901			0.639505	−	0.768787i	$-0.279139\pi$
$839$	37.0472			1.27901			0.639505	+	0.768787i	$0.279139\pi$
$840$		0			0
$841$	38.3211			1.32142
$842$	7.46015	+	7.46015i	0.257094	+	0.257094i
$843$		0			0
$844$			21.8787i			0.753095i
$845$		0			0
$846$		0			0
$847$	4.51382	−	4.51382i	0.155097	−	0.155097i
$848$	2.35876	−	2.35876i	0.0810002	−	0.0810002i
$849$		0			0
$850$		0			0
$851$			64.9497i			2.22645i
$852$		0			0
$853$	−0.806618	−	0.806618i	−0.0276181	−	0.0276181i	0.693163	−	0.720781i	$-0.256217\pi$
$853$	−0.806618	−	0.806618i	−0.0276181	−	0.0276181i	−0.720781	+	0.693163i	$0.756217\pi$
$854$	4.46967			0.152949
$855$		0			0
$856$	3.40559			0.116401
$857$	−17.6075	−	17.6075i	−0.601461	−	0.601461i	0.339239	−	0.940700i	$-0.389830\pi$
$857$	−17.6075	−	17.6075i	−0.601461	−	0.601461i	−0.940700	+	0.339239i	$0.889830\pi$
$858$		0			0
$859$			37.4748i			1.27862i	0.768947	+	0.639312i	$0.220781\pi$
$859$			37.4748i			1.27862i	−0.768947	+	0.639312i	$0.779219\pi$
$860$		0			0
$861$		0			0
$862$	−16.2530	+	16.2530i	−0.553581	+	0.553581i
$863$	37.1924	−	37.1924i	1.26604	−	1.26604i	0.317928	−	0.948115i	$-0.397013\pi$
$863$	37.1924	−	37.1924i	1.26604	−	1.26604i	0.948115	−	0.317928i	$-0.102987\pi$
$864$		0			0
$865$		0			0
$866$			16.0169i			0.544275i
$867$		0			0
$868$	−1.30913	−	1.30913i	−0.0444349	−	0.0444349i
$869$	−11.2512			−0.381672
$870$		0			0
$871$	−16.5944			−0.562280
$872$	−7.00089	−	7.00089i	−0.237080	−	0.237080i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	26.3997	−	26.3997i	0.891456	−	0.891456i	−0.103205	−	0.994660i	$-0.532910\pi$
$877$	26.3997	−	26.3997i	0.891456	−	0.891456i	0.994660	+	0.103205i	$0.0329096\pi$
$878$	−0.294406	+	0.294406i	−0.00993573	+	0.00993573i
$879$		0			0
$880$		0			0
$881$		−	56.1098i		−	1.89039i	−0.326511	−	0.945193i	$-0.605873\pi$
$881$		−	56.1098i		−	1.89039i	0.326511	−	0.945193i	$-0.394127\pi$
$882$		0			0
$883$	−5.55052	−	5.55052i	−0.186790	−	0.186790i	0.607517	−	0.794307i	$-0.292166\pi$
$883$	−5.55052	−	5.55052i	−0.186790	−	0.186790i	−0.794307	+	0.607517i	$0.792166\pi$
$884$	−19.3137			−0.649590
$885$		0			0
$886$	−15.9081			−0.534444
$887$	−17.9292	−	17.9292i	−0.602003	−	0.602003i	0.338841	−	0.940844i	$-0.389965\pi$
$887$	−17.9292	−	17.9292i	−0.602003	−	0.602003i	−0.940844	+	0.338841i	$0.889965\pi$
$888$		0			0
$889$			3.28248i			0.110091i
$890$		0			0
$891$		0			0
$892$	−4.42031	+	4.42031i	−0.148003	+	0.148003i
$893$		0			0
$894$		0			0
$895$		0			0
$896$			1.00000i			0.0334077i
$897$		0			0
$898$	−14.7028	−	14.7028i	−0.490639	−	0.490639i
$899$	−15.1906			−0.506635
$900$		0			0
$901$	21.0857			0.702468
$902$	11.4901	+	11.4901i	0.382579	+	0.382579i
$903$		0			0
$904$			5.97792i			0.198823i
$905$		0			0
$906$		0			0
$907$	11.4734	−	11.4734i	0.380966	−	0.380966i	−0.490484	−	0.871450i	$-0.663180\pi$
$907$	11.4734	−	11.4734i	0.380966	−	0.380966i	0.871450	+	0.490484i	$0.163180\pi$
$908$	−11.7028	+	11.7028i	−0.388371	+	0.388371i
$909$		0			0
$910$		0			0
$911$			22.2383i			0.736789i	0.929670	+	0.368394i	$0.120092\pi$
$911$			22.2383i			0.736789i	−0.929670	+	0.368394i	$0.879908\pi$
$912$		0			0
$913$	−22.8145	−	22.8145i	−0.755048	−	0.755048i
$914$	17.9645			0.594212
$915$		0			0
$916$	−13.6314			−0.450393
$917$	−1.67894	−	1.67894i	−0.0554434	−	0.0554434i
$918$		0			0
$919$			3.25917i			0.107510i	0.998554	+	0.0537551i	$0.0171190\pi$
$919$			3.25917i			0.107510i	−0.998554	+	0.0537551i	$0.982881\pi$
$920$		0			0
$921$		0			0
$922$	21.1271	−	21.1271i	0.695785	−	0.695785i
$923$	0.908103	−	0.908103i	0.0298906	−	0.0298906i
$924$		0			0
$925$		0			0
$926$		−	21.6127i		−	0.710237i
$927$		0			0
$928$	5.80177	+	5.80177i	0.190452	+	0.190452i
$929$	−6.79758			−0.223022			−0.111511	−	0.993763i	$-0.535569\pi$
$929$	−6.79758			−0.223022			−0.111511	+	0.993763i	$0.535569\pi$
$930$		0			0
$931$		0			0
$932$	−20.6421	−	20.6421i	−0.676155	−	0.676155i
$933$		0			0
$934$		−	26.2236i		−	0.858062i
$935$		0			0
$936$		0			0
$937$	40.8061	−	40.8061i	1.33308	−	1.33308i	0.430473	−	0.902604i	$-0.358347\pi$
$937$	40.8061	−	40.8061i	1.33308	−	1.33308i	0.902604	−	0.430473i	$-0.141653\pi$
$938$	−3.84035	+	3.84035i	−0.125392	+	0.125392i
$939$		0			0
$940$		0			0
$941$			28.1400i			0.917337i	0.888607	+	0.458668i	$0.151673\pi$
$941$			28.1400i			0.917337i	−0.888607	+	0.458668i	$0.848327\pi$
$942$		0			0
$943$	−47.8050	−	47.8050i	−1.55675	−	1.55675i
$944$	9.35965			0.304631
$945$		0			0
$946$	23.8236			0.774571
$947$	−22.0151	−	22.0151i	−0.715394	−	0.715394i	0.252265	−	0.967658i	$-0.418825\pi$
$947$	−22.0151	−	22.0151i	−0.715394	−	0.715394i	−0.967658	+	0.252265i	$0.918825\pi$
$948$		0			0
$949$		−	11.3652i		−	0.368932i
$950$		0			0
$951$		0			0
$952$	−4.46967	+	4.46967i	−0.144863	+	0.144863i
$953$	−6.51039	+	6.51039i	−0.210892	+	0.210892i	−0.804646	−	0.593754i	$-0.797645\pi$
$953$	−6.51039	+	6.51039i	−0.210892	+	0.210892i	0.593754	+	0.804646i	$0.297645\pi$
$954$		0			0
$955$		0			0
$956$			10.3744i			0.335531i
$957$		0			0
$958$	3.47702	+	3.47702i	0.112337	+	0.112337i
$959$	13.9779			0.451370
$960$		0			0
$961$	−27.5723			−0.889430
$962$	15.6976	+	15.6976i	0.506110	+	0.506110i
$963$		0			0
$964$		−	13.7028i		−	0.441337i
$965$		0			0
$966$		0			0
$967$	−28.1299	+	28.1299i	−0.904598	+	0.904598i	−0.995830	−	0.0912320i	$-0.970920\pi$
$967$	−28.1299	+	28.1299i	−0.904598	+	0.904598i	0.0912320	+	0.995830i	$0.470920\pi$
$968$	4.51382	−	4.51382i	0.145080	−	0.145080i
$969$		0			0
$970$		0			0
$971$		−	36.6421i		−	1.17590i	−0.808897	−	0.587951i	$-0.799935\pi$
$971$		−	36.6421i		−	1.17590i	0.808897	−	0.587951i	$-0.200065\pi$
$972$		0			0
$973$	11.0386	+	11.0386i	0.353881	+	0.353881i
$974$	13.6256			0.436593
$975$		0			0
$976$	4.46967			0.143071
$977$	−30.5962	−	30.5962i	−0.978859	−	0.978859i	0.0209224	−	0.999781i	$-0.493340\pi$
$977$	−30.5962	−	30.5962i	−0.978859	−	0.978859i	−0.999781	+	0.0209224i	$0.993340\pi$
$978$		0			0
$979$		−	31.2581i		−	0.999012i
$980$		0			0
$981$		0			0
$982$	14.1614	−	14.1614i	0.451909	−	0.451909i
$983$	4.87234	−	4.87234i	0.155403	−	0.155403i	−0.625123	−	0.780526i	$-0.714951\pi$
$983$	4.87234	−	4.87234i	0.155403	−	0.155403i	0.780526	+	0.625123i	$0.214951\pi$
$984$		0			0
$985$		0			0
$986$			51.8640i			1.65168i
$987$		0			0
$988$		0			0
$989$	−99.1188			−3.15179
$990$		0			0
$991$	54.1317			1.71955			0.859775	−	0.510673i	$-0.170604\pi$
$991$	54.1317			1.71955			0.859775	+	0.510673i	$0.170604\pi$
$992$	−1.30913	−	1.30913i	−0.0415651	−	0.0415651i
$993$		0			0
$994$		−	0.420314i		−	0.0133316i
$995$		0			0
$996$		0			0
$997$	16.5094	−	16.5094i	0.522858	−	0.522858i	−0.395575	−	0.918434i	$-0.629455\pi$
$997$	16.5094	−	16.5094i	0.522858	−	0.522858i	0.918434	+	0.395575i	$0.129455\pi$
$998$	−24.6044	+	24.6044i	−0.778840	+	0.778840i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.m.i.2843.1		8
3.2	odd	2		3150.2.m.j.2843.4		8
5.2	odd	4		3150.2.m.j.1457.3		8
5.3	odd	4		630.2.m.d.197.1	yes	8
5.4	even	2		630.2.m.c.323.4	yes	8
15.2	even	4	inner	3150.2.m.i.1457.2		8
15.8	even	4		630.2.m.c.197.4	✓	8
15.14	odd	2		630.2.m.d.323.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.m.c.197.4	✓	8	15.8	even	4
630.2.m.c.323.4	yes	8	5.4	even	2
630.2.m.d.197.1	yes	8	5.3	odd	4
630.2.m.d.323.1	yes	8	15.14	odd	2
3150.2.m.i.1457.2		8	15.2	even	4	inner
3150.2.m.i.2843.1		8	1.1	even	1	trivial
3150.2.m.j.1457.3		8	5.2	odd	4
3150.2.m.j.2843.4		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.14860i q^{11} +(-2.16053 - 2.16053i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-4.46967 - 4.46967i) q^{17} +(1.51929 - 1.51929i) q^{22} +(-6.32106 + 6.32106i) q^{23} +3.05545i q^{26} +(0.707107 + 0.707107i) q^{28} +8.20494 q^{29} -1.85140 q^{31} +(0.707107 + 0.707107i) q^{32} +6.32106i q^{34} +(5.13756 - 5.13756i) q^{37} +7.56282i q^{41} +(7.84035 + 7.84035i) q^{43} -2.14860 q^{44} +8.93933 q^{46} +(5.01193 + 5.01193i) q^{47} -1.00000i q^{49} +(2.16053 - 2.16053i) q^{52} +(-2.35876 + 2.35876i) q^{53} -1.00000i q^{56} +(-5.80177 - 5.80177i) q^{58} -9.35965 q^{59} -4.46967 q^{61} +(1.30913 + 1.30913i) q^{62} -1.00000i q^{64} +(3.84035 - 3.84035i) q^{67} +(4.46967 - 4.46967i) q^{68} +0.420314i q^{71} +(2.63020 + 2.63020i) q^{73} -7.26561 q^{74} +(1.51929 + 1.51929i) q^{77} +5.23654i q^{79} +(5.34772 - 5.34772i) q^{82} +(-10.6183 + 10.6183i) q^{83} -11.0879i q^{86} +(1.51929 + 1.51929i) q^{88} -14.5481 q^{89} -3.05545 q^{91} +(-6.32106 - 6.32106i) q^{92} -7.08794i q^{94} +(0.606342 - 0.606342i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 4 q^{13} - 8 q^{14} - 8 q^{16} + 4 q^{22} - 8 q^{23} - 24 q^{29} - 8 q^{31} + 4 q^{37} + 12 q^{43} - 24 q^{44} + 12 q^{47} - 4 q^{52} - 32 q^{53} - 12 q^{58} - 16 q^{59} - 4 q^{62} - 20 q^{67} - 36 q^{73} - 40 q^{74} + 4 q^{77} + 12 q^{82} - 56 q^{83} + 4 q^{88} - 72 q^{89} - 8 q^{92} + 4 q^{97}+O(q^{100}) \) 8 * q + 4 * q^13 - 8 * q^14 - 8 * q^16 + 4 * q^22 - 8 * q^23 - 24 * q^29 - 8 * q^31 + 4 * q^37 + 12 * q^43 - 24 * q^44 + 12 * q^47 - 4 * q^52 - 32 * q^53 - 12 * q^58 - 16 * q^59 - 4 * q^62 - 20 * q^67 - 36 * q^73 - 40 * q^74 + 4 * q^77 + 12 * q^82 - 56 * q^83 + 4 * q^88 - 72 * q^89 - 8 * q^92 + 4 * q^97

Introduction

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