LMFDB - Embedded newform 3150.2.m.j.2843.4

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			2843.4
Root			$-2.16053i$ of defining polynomial
Character	$\chi$	$=$	3150.2843
Dual form			3150.2.m.j.1457.3

$q$-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	$-0.895001\pi$
$11$		−	2.14860i		−	0.647828i	0.946086	−	0.323914i	$-0.104999\pi$
$12$		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	$0.0280240\pi$
$17$	4.46967	+	4.46967i	1.08405	+	1.08405i	0.0879263	+	0.996127i	$0.471976\pi$
$18$		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	$-0.368071\pi$
$23$	6.32106	−	6.32106i	1.31803	−	1.31803i	0.915331	−	0.402701i	$-0.131929\pi$
$24$		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	$-0.775689\pi$
$29$	−8.20494			−1.52362			−0.761810	+	0.647801i	$0.775689\pi$
$30$		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	$-0.798908\pi$
$41$		−	7.56282i		−	1.18111i	0.806996	−	0.590557i	$-0.201092\pi$
$42$		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	0.239766	−	0.970831i	$-0.422929\pi$
$47$	−5.01193	−	5.01193i	−0.731065	−	0.731065i	−0.970831	+	0.239766i	$0.922929\pi$
$48$		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	−0.526299	−	0.850300i	$-0.676421\pi$
$53$	2.35876	−	2.35876i	0.324001	−	0.324001i	0.850300	+	0.526299i	$0.176421\pi$
$54$		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	$-0.291466\pi$
$59$	9.35965			1.21852			0.609261	+	0.792970i	$0.291466\pi$
$60$		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	$-0.992060\pi$
$71$		−	0.420314i		−	0.0498821i	0.999689	−	0.0249411i	$-0.00793981\pi$
$72$		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	$-0.441660\pi$
$83$	10.6183	−	10.6183i	1.16551	−	1.16551i	0.983251	−	0.182255i	$-0.0583397\pi$
$84$		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	$-0.219733\pi$
$89$	14.5481			1.54209			0.771047	+	0.636778i	$0.219733\pi$
$90$		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	$-0.913442\pi$
$101$		−	5.39860i		−	0.537181i	0.963255	−	0.268590i	$-0.0865578\pi$
$102$		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	0.581060	−	0.813861i	$-0.302638\pi$
$107$	−2.40811	−	2.40811i	−0.232801	−	0.232801i	−0.813861	+	0.581060i	$0.802638\pi$
$108$		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	−0.479757	−	0.877402i	$-0.659275\pi$
$113$	4.22703	−	4.22703i	0.397645	−	0.397645i	0.877402	+	0.479757i	$0.159275\pi$
$114$		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	$0.0330762\pi$
$131$			2.37438i			0.207450i	−0.994606	+	0.103725i	$0.966924\pi$
$132$		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	0.144995	−	0.989432i	$-0.453683\pi$
$137$	−9.88388	−	9.88388i	−0.844437	−	0.844437i	−0.989432	+	0.144995i	$0.953683\pi$
$138$		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	$-0.627221\pi$
$149$	−9.49962			−0.778239			−0.389120	+	0.921187i	$0.627221\pi$
$150$		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	0.802785	−	0.596269i	$-0.203351\pi$
$167$	2.66878	+	2.66878i	0.206517	+	0.206517i	−0.596269	+	0.802785i	$0.703351\pi$
$168$		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	−0.914369	−	0.404881i	$-0.867313\pi$
$173$	−6.70127	+	6.70127i	−0.509488	+	0.509488i	0.404881	+	0.914369i	$0.367313\pi$
$174$		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	$-0.458146\pi$
$179$	3.50825			0.262219			0.131109	+	0.991368i	$0.458146\pi$
$180$		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	$0.00597739\pi$
$191$			0.519018i			0.0375548i	−0.999824	+	0.0187774i	$0.994023\pi$
$192$		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	0.548710	−	0.836013i	$-0.315119\pi$
$197$	−4.03248	−	4.03248i	−0.287303	−	0.287303i	−0.836013	+	0.548710i	$0.815119\pi$
$198$		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	0.202534	−	0.979275i	$-0.435082\pi$
$227$	−11.7028	−	11.7028i	−0.776742	−	0.776742i	−0.979275	+	0.202534i	$0.935082\pi$
$228$		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	$-0.344528\pi$
$233$	20.6421	−	20.6421i	1.35231	−	1.35231i	0.883071	−	0.469240i	$-0.155472\pi$
$234$		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	$-0.608916\pi$
$239$	−10.3744			−0.671063			−0.335531	+	0.942029i	$0.608916\pi$
$240$		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	$0.0768893\pi$
$251$			7.57969i			0.478426i	−0.970967	+	0.239213i	$0.923111\pi$
$252$		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	$0.0739866\pi$
$257$	19.2929	+	19.2929i	1.20346	+	1.20346i	0.230349	+	0.973108i	$0.426013\pi$
$258$		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	$-0.470798\pi$
$263$	17.6348	−	17.6348i	1.08741	−	1.08741i	0.995795	−	0.0916118i	$-0.0292019\pi$
$264$		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	$-0.285784\pi$
$269$	20.4463			1.24663			0.623317	+	0.781969i	$0.285784\pi$
$270$		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	$-0.825425\pi$
$281$		−	17.4792i		−	1.04272i	0.853337	−	0.521360i	$-0.174575\pi$
$282$		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	−0.745818	−	0.666150i	$-0.767941\pi$
$293$	−1.36370	+	1.36370i	−0.0796683	+	0.0796683i	0.666150	+	0.745818i	$0.267941\pi$
$294$		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	$-0.968122\pi$
$311$		−	3.52637i		−	0.199962i	0.994989	−	0.0999811i	$-0.0318782\pi$
$312$		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	0.495036	−	0.868872i	$-0.335155\pi$
$317$	−6.65597	−	6.65597i	−0.373836	−	0.373836i	−0.868872	+	0.495036i	$0.835155\pi$
$318$		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	0.353960	−	0.935261i	$-0.384835\pi$
$347$	−10.8284	−	10.8284i	−0.581300	−	0.581300i	−0.935261	+	0.353960i	$0.884835\pi$
$348$		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	−0.851543	−	0.524285i	$-0.824332\pi$
$353$	−6.14860	+	6.14860i	−0.327257	+	0.327257i	0.524285	+	0.851543i	$0.324332\pi$
$354$		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	$-0.772770\pi$
$359$	−28.6421			−1.51167			−0.755837	+	0.654760i	$0.772770\pi$
$360$		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	$0.598503\pi$
$383$	−24.6008	+	24.6008i	−1.25704	+	1.25704i	−0.952499	+	0.304541i	$0.901497\pi$
$384$		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	$-0.424627\pi$
$389$	9.25341			0.469166			0.234583	+	0.972096i	$0.424627\pi$
$390$		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	$0.105578\pi$
$401$			13.0416i			0.651267i	−0.945496	+	0.325633i	$0.894422\pi$
$402$		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	$-0.680316\pi$
$419$	−21.9705			−1.07333			−0.536666	+	0.843795i	$0.680316\pi$
$420$		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	$0.186739\pi$
$431$			22.9853i			1.10716i	−0.832795	+	0.553581i	$0.813261\pi$
$432$		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	−0.921892	−	0.387448i	$-0.873357\pi$
$443$	−11.2487	+	11.2487i	−0.534444	+	0.534444i	0.387448	+	0.921892i	$0.373357\pi$
$444$		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	$-0.663236\pi$
$449$	−20.7929			−0.981277			−0.490639	+	0.871363i	$0.663236\pi$
$450$		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	$-0.755057\pi$
$461$		−	29.8783i		−	1.39157i	0.718250	−	0.695785i	$-0.244943\pi$
$462$		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	0.133048	−	0.991110i	$-0.457524\pi$
$467$	−18.5429	−	18.5429i	−0.858062	−	0.858062i	−0.991110	+	0.133048i	$0.957524\pi$
$468$		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	$-0.464166\pi$
$479$	4.91725			0.224675			0.112337	+	0.993670i	$0.464166\pi$
$480$		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	$-0.850743\pi$
$491$		−	20.0273i		−	0.903818i	0.892064	−	0.451909i	$-0.149257\pi$
$492$		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	−0.630605	−	0.776104i	$-0.717193\pi$
$503$	3.26320	−	3.26320i	0.145499	−	0.145499i	0.776104	+	0.630605i	$0.217193\pi$
$504$		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	$-0.725464\pi$
$509$	−29.3544			−1.30111			−0.650556	+	0.759458i	$0.725464\pi$
$510$		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	$0.0871655\pi$
$521$			12.3453i			0.540858i	−0.962740	+	0.270429i	$0.912835\pi$
$522$		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	0.979471	−	0.201585i	$-0.0646093\pi$
$557$	18.3588	+	18.3588i	0.777886	+	0.777886i	−0.201585	+	0.979471i	$0.564609\pi$
$558$		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	$0.526739\pi$
$563$	−25.6348	+	25.6348i	−1.08038	+	1.08038i	−0.996474	+	0.0839029i	$0.973261\pi$
$564$		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	$-0.108479\pi$
$569$	44.9637			1.88498			0.942488	+	0.334239i	$0.108479\pi$
$570$		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	0.840884	−	0.541215i	$-0.182036\pi$
$587$	7.26040	+	7.26040i	0.299669	+	0.299669i	−0.541215	+	0.840884i	$0.682036\pi$
$588$		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	−0.524033	−	0.851698i	$-0.675573\pi$
$593$	7.97917	−	7.97917i	0.327665	−	0.327665i	0.851698	+	0.524033i	$0.175573\pi$
$594$		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	$-0.459732\pi$
$599$	6.17587			0.252339			0.126170	+	0.992009i	$0.459732\pi$
$600$		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	0.688965	−	0.724794i	$-0.258065\pi$
$617$	−0.889981	−	0.889981i	−0.0358293	−	0.0358293i	−0.724794	+	0.688965i	$0.758065\pi$
$618$		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	$0.133958\pi$
$641$			20.6863i			0.817058i	−0.912745	+	0.408529i	$0.866042\pi$
$642$		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	$0.0971759\pi$
$647$	31.9053	+	31.9053i	1.25433	+	1.25433i	0.300567	+	0.953761i	$0.402824\pi$
$648$		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	−0.948903	−	0.315569i	$-0.897805\pi$
$653$	−16.1841	+	16.1841i	−0.633333	+	0.633333i	0.315569	+	0.948903i	$0.397805\pi$
$654$		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	$-0.455617\pi$
$659$	7.13565			0.277965			0.138983	+	0.990295i	$0.455617\pi$
$660$		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	0.733182	−	0.680033i	$-0.238035\pi$
$677$	1.38289	+	1.38289i	0.0531488	+	0.0531488i	−0.680033	+	0.733182i	$0.738035\pi$
$678$		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	−0.0682116	−	0.997671i	$-0.521729\pi$
$683$	24.2907	−	24.2907i	0.929459	−	0.929459i	0.997671	+	0.0682116i	$0.0217293\pi$
$684$		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	$-0.990140\pi$
$701$		−	1.63999i		−	0.0619414i	0.999520	−	0.0309707i	$-0.00985986\pi$
$702$		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	$-0.602490\pi$
$719$	−16.9706			−0.632895			−0.316448	+	0.948610i	$0.602490\pi$
$720$		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	−0.833443	−	0.552605i	$-0.813634\pi$
$743$	−7.65508	+	7.65508i	−0.280838	+	0.280838i	0.552605	+	0.833443i	$0.313634\pi$
$744$		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	$0.113479\pi$
$761$			19.2552i			0.698000i	−0.937123	+	0.349000i	$0.886521\pi$
$762$		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	−0.107889	−	0.994163i	$-0.534409\pi$
$773$	24.6410	−	24.6410i	0.886274	−	0.886274i	0.994163	+	0.107889i	$0.0344091\pi$
$774$		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	0.908235	−	0.418461i	$-0.137430\pi$
$797$	13.8269	+	13.8269i	0.489774	+	0.489774i	−0.418461	+	0.908235i	$0.637430\pi$
$798$		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	$-0.696128\pi$
$809$	−32.8743			−1.15580			−0.577900	+	0.816108i	$0.696128\pi$
$810$		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	$-0.602877\pi$
$821$		−	54.3392i		−	1.89645i	0.317600	−	0.948225i	$-0.397123\pi$
$822$		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	$0.0727791\pi$
$827$	34.5273	+	34.5273i	1.20063	+	1.20063i	0.226655	+	0.973975i	$0.427221\pi$
$828$		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	$-0.720861\pi$
$839$	−37.0472			−1.27901			−0.639505	+	0.768787i	$0.720861\pi$
$840$		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	0.940700	−	0.339239i	$-0.110170\pi$
$857$	17.6075	+	17.6075i	0.601461	+	0.601461i	−0.339239	+	0.940700i	$0.610170\pi$
$858$		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	$0.602987\pi$
$863$	−37.1924	+	37.1924i	−1.26604	+	1.26604i	−0.948115	+	0.317928i	$0.897013\pi$
$864$		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	$0.394127\pi$
$881$			56.1098i			1.89039i	−0.326511	+	0.945193i	$0.605873\pi$
$882$		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	0.940844	−	0.338841i	$-0.110035\pi$
$887$	17.9292	+	17.9292i	0.602003	+	0.602003i	−0.338841	+	0.940844i	$0.610035\pi$
$888$		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	$-0.879908\pi$
$911$		−	22.2383i		−	0.736789i	0.929670	−	0.368394i	$-0.120092\pi$
$912$		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	$-0.464431\pi$
$929$	6.79758			0.223022			0.111511	+	0.993763i	$0.464431\pi$
$930$		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	$-0.848327\pi$
$941$		−	28.1400i		−	0.917337i	0.888607	−	0.458668i	$-0.151673\pi$
$942$		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	0.967658	−	0.252265i	$-0.0811754\pi$
$947$	22.0151	+	22.0151i	0.715394	+	0.715394i	−0.252265	+	0.967658i	$0.581175\pi$
$948$		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	−0.593754	−	0.804646i	$-0.702355\pi$
$953$	6.51039	−	6.51039i	0.210892	−	0.210892i	0.804646	+	0.593754i	$0.202355\pi$
$954$		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	$0.200065\pi$
$971$			36.6421i			1.17590i	−0.808897	+	0.587951i	$0.799935\pi$
$972$		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	0.999781	−	0.0209224i	$-0.00666028\pi$
$977$	30.5962	+	30.5962i	0.978859	+	0.978859i	−0.0209224	+	0.999781i	$0.506660\pi$
$978$		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	−0.780526	−	0.625123i	$-0.785049\pi$
$983$	−4.87234	+	4.87234i	−0.155403	+	0.155403i	0.625123	+	0.780526i	$0.285049\pi$
$984$		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.j.2843.4		8
3.2	odd	2		3150.2.m.i.2843.1		8
5.2	odd	4		3150.2.m.i.1457.2		8
5.3	odd	4		630.2.m.c.197.4	✓	8
5.4	even	2		630.2.m.d.323.1	yes	8
15.2	even	4	inner	3150.2.m.j.1457.3		8
15.8	even	4		630.2.m.d.197.1	yes	8
15.14	odd	2		630.2.m.c.323.4	yes	8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
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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