LMFDB - Embedded newform 630.2.m.c.197.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(197,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, 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("630.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.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:	$5.03057532734$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.4
Root			$-3.16053i$ of defining polynomial
Character	$\chi$	$=$	630.197
Dual form			630.2.m.c.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.52773 + 1.63280i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.52773 + 1.63280i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.23483 + 0.0743018i) q^{10} -2.14860i q^{11} +(2.16053 - 2.16053i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(4.46967 - 4.46967i) q^{17} +(1.63280 - 1.52773i) q^{20} +(-1.51929 - 1.51929i) q^{22} +(6.32106 + 6.32106i) q^{23} +(-0.332104 + 4.98896i) q^{25} -3.05545i q^{26} +(-0.707107 + 0.707107i) q^{28} +8.20494 q^{29} -1.85140 q^{31} +(-0.707107 + 0.707107i) q^{32} -6.32106i q^{34} +(0.0743018 - 2.23483i) q^{35} +(-5.13756 - 5.13756i) q^{37} +(0.0743018 - 2.23483i) q^{40} -7.56282i q^{41} +(-7.84035 + 7.84035i) q^{43} -2.14860 q^{44} +8.93933 q^{46} +(-5.01193 + 5.01193i) q^{47} +1.00000i q^{49} +(3.29289 + 3.76256i) q^{50} +(-2.16053 - 2.16053i) q^{52} +(2.35876 + 2.35876i) q^{53} +(3.50825 - 3.28248i) q^{55} +1.00000i q^{56} +(5.80177 - 5.80177i) q^{58} -9.35965 q^{59} -4.46967 q^{61} +(-1.30913 + 1.30913i) q^{62} +1.00000i q^{64} +(6.82843 + 0.227026i) q^{65} +(-3.84035 - 3.84035i) q^{67} +(-4.46967 - 4.46967i) q^{68} +(-1.52773 - 1.63280i) q^{70} -0.420314i q^{71} +(-2.63020 + 2.63020i) q^{73} -7.26561 q^{74} +(-1.51929 + 1.51929i) q^{77} -5.23654i q^{79} +(-1.52773 - 1.63280i) q^{80} +(-5.34772 - 5.34772i) q^{82} +(10.6183 + 10.6183i) q^{83} +(14.1265 + 0.469666i) q^{85} +11.0879i q^{86} +(-1.51929 + 1.51929i) q^{88} -14.5481 q^{89} -3.05545 q^{91} +(6.32106 - 6.32106i) q^{92} +7.08794i q^{94} +(-0.606342 - 0.606342i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 4 q^{13} - 8 q^{14} - 8 q^{16} + 4 q^{20} - 4 q^{22} + 8 q^{23} - 4 q^{25} - 24 q^{29} - 8 q^{31} + 4 q^{35} - 4 q^{37} + 4 q^{40} - 12 q^{43} - 24 q^{44} - 12 q^{47} + 32 q^{50} + 4 q^{52} + 32 q^{53} - 24 q^{55} + 12 q^{58} - 16 q^{59} + 4 q^{62} + 32 q^{65} + 20 q^{67} + 36 q^{73} - 40 q^{74} - 4 q^{77} - 12 q^{82} + 56 q^{83} + 32 q^{85} - 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^20 - 4 * q^22 + 8 * q^23 - 4 * q^25 - 24 * q^29 - 8 * q^31 + 4 * q^35 - 4 * q^37 + 4 * q^40 - 12 * q^43 - 24 * q^44 - 12 * q^47 + 32 * q^50 + 4 * q^52 + 32 * q^53 - 24 * q^55 + 12 * q^58 - 16 * q^59 + 4 * q^62 + 32 * q^65 + 20 * q^67 + 36 * q^73 - 40 * q^74 - 4 * q^77 - 12 * q^82 + 56 * q^83 + 32 * q^85 - 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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
$5$	1.52773	+	1.63280i	0.683220	+	0.730213i
$5$	1.52773	+	1.63280i	0.683220	+	0.730213i
$6$		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
$10$	2.23483	+	0.0743018i	0.706716	+	0.0234963i
$11$		−	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	$-0.610726\pi$
$13$	2.16053	−	2.16053i	0.599224	−	0.599224i	0.940106	+	0.340882i	$0.110726\pi$
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	4.46967	−	4.46967i	1.08405	−	1.08405i	0.0879263	−	0.996127i	$-0.471976\pi$
$17$	4.46967	−	4.46967i	1.08405	−	1.08405i	0.996127	−	0.0879263i	$-0.0280240\pi$
$18$		0			0
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	1.63280	−	1.52773i	0.365106	−	0.341610i
$21$		0			0
$22$	−1.51929	−	1.51929i	−0.323914	−	0.323914i
$23$	6.32106	+	6.32106i	1.31803	+	1.31803i	0.915331	+	0.402701i	$0.131929\pi$
$23$	6.32106	+	6.32106i	1.31803	+	1.31803i	0.402701	+	0.915331i	$0.368071\pi$
$24$		0			0
$25$	−0.332104	+	4.98896i	−0.0664208	+	0.997792i
$26$		−	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
$35$	0.0743018	−	2.23483i	0.0125593	−	0.377756i
$36$		0			0
$37$	−5.13756	−	5.13756i	−0.844610	−	0.844610i	0.144844	−	0.989454i	$-0.453732\pi$
$37$	−5.13756	−	5.13756i	−0.844610	−	0.844610i	−0.989454	+	0.144844i	$0.953732\pi$
$38$		0			0
$39$		0			0
$40$	0.0743018	−	2.23483i	0.0117481	−	0.353358i
$41$		−	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	−0.220185	+	0.975458i	$0.570666\pi$
$43$	−7.84035	+	7.84035i	−1.19564	+	1.19564i	−0.975458	+	0.220185i	$0.929334\pi$
$44$	−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	$-0.922929\pi$
$47$	−5.01193	+	5.01193i	−0.731065	+	0.731065i	0.239766	+	0.970831i	$0.422929\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$	3.29289	+	3.76256i	0.465685	+	0.532106i
$51$		0			0
$52$	−2.16053	−	2.16053i	−0.299612	−	0.299612i
$53$	2.35876	+	2.35876i	0.324001	+	0.324001i	0.850300	−	0.526299i	$-0.176421\pi$
$53$	2.35876	+	2.35876i	0.324001	+	0.324001i	−0.526299	+	0.850300i	$0.676421\pi$
$54$		0			0
$55$	3.50825	−	3.28248i	0.473052	−	0.442609i
$56$			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
$65$	6.82843	+	0.227026i	0.846962	+	0.0281591i
$66$		0			0
$67$	−3.84035	−	3.84035i	−0.469174	−	0.469174i	0.432473	−	0.901647i	$-0.357641\pi$
$67$	−3.84035	−	3.84035i	−0.469174	−	0.469174i	−0.901647	+	0.432473i	$0.857641\pi$
$68$	−4.46967	−	4.46967i	−0.542027	−	0.542027i
$69$		0			0
$70$	−1.52773	−	1.63280i	−0.182598	−	0.195158i
$71$		−	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	$-0.819848\pi$
$73$	−2.63020	+	2.63020i	−0.307841	+	0.307841i	0.536230	+	0.844072i	$0.319848\pi$
$74$	−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	$-0.904821\pi$
$79$		−	5.23654i		−	0.589157i	0.955627	−	0.294578i	$-0.0951792\pi$
$80$	−1.52773	−	1.63280i	−0.170805	−	0.182553i
$81$		0			0
$82$	−5.34772	−	5.34772i	−0.590557	−	0.590557i
$83$	10.6183	+	10.6183i	1.16551	+	1.16551i	0.983251	+	0.182255i	$0.0583397\pi$
$83$	10.6183	+	10.6183i	1.16551	+	1.16551i	0.182255	+	0.983251i	$0.441660\pi$
$84$		0			0
$85$	14.1265	+	0.469666i	1.53224	+	0.0509425i
$86$			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	$-0.263861\pi$
$97$	−0.606342	−	0.606342i	−0.0615647	−	0.0615647i	−0.737219	+	0.675654i	$0.763861\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		0			0
$100$	4.98896	+	0.332104i	0.498896	+	0.0332104i
$101$		−	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	$-0.933027\pi$
$103$	−7.80546	+	7.80546i	−0.769095	+	0.769095i	0.208853	+	0.977947i	$0.433027\pi$
$104$	−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	$-0.802638\pi$
$107$	−2.40811	+	2.40811i	−0.232801	+	0.232801i	0.581060	+	0.813861i	$0.302638\pi$
$108$		0			0
$109$			9.90075i			0.948320i	0.880439	+	0.474160i	$0.157248\pi$
$109$			9.90075i			0.948320i	−0.880439	+	0.474160i	$0.842752\pi$
$110$	0.159645	−	4.80177i	0.0152216	−	0.457831i
$111$		0			0
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	4.22703	+	4.22703i	0.397645	+	0.397645i	0.877402	−	0.479757i	$-0.159275\pi$
$113$	4.22703	+	4.22703i	0.397645	+	0.397645i	−0.479757	+	0.877402i	$0.659275\pi$
$114$		0			0
$115$	−0.664208	+	19.9779i	−0.0619378	+	1.86295i
$116$		−	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
$125$	−8.65336	+	7.07950i	−0.773980	+	0.633210i
$126$		0			0
$127$	2.32106	+	2.32106i	0.205961	+	0.205961i	0.802548	−	0.596587i	$-0.203477\pi$
$127$	2.32106	+	2.32106i	0.205961	+	0.205961i	−0.596587	+	0.802548i	$0.703477\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	4.98896	−	4.66790i	0.437561	−	0.409402i
$131$			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	−0.989432	−	0.144995i	$-0.953683\pi$
$137$	−9.88388	+	9.88388i	−0.844437	+	0.844437i	0.144995	+	0.989432i	$0.453683\pi$
$138$		0			0
$139$		−	15.6109i		−	1.32410i	−0.749459	−	0.662050i	$-0.769687\pi$
$139$		−	15.6109i		−	1.32410i	0.749459	−	0.662050i	$-0.230313\pi$
$140$	−2.23483	−	0.0743018i	−0.188878	−	0.00627965i
$141$		0			0
$142$	−0.297207	−	0.297207i	−0.0249411	−	0.0249411i
$143$	−4.64213	−	4.64213i	−0.388194	−	0.388194i
$144$		0			0
$145$	12.5349	+	13.3971i	1.04097	+	1.11257i
$146$			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
$155$	−2.82843	−	3.02297i	−0.227185	−	0.242811i
$156$		0			0
$157$	14.0613	+	14.0613i	1.12221	+	1.12221i	0.991408	+	0.130804i	$0.0417559\pi$
$157$	14.0613	+	14.0613i	1.12221	+	1.12221i	0.130804	+	0.991408i	$0.458244\pi$
$158$	−3.70279	−	3.70279i	−0.294578	−	0.294578i
$159$		0			0
$160$	−2.23483	−	0.0743018i	−0.176679	−	0.00587407i
$161$		−	8.93933i		−	0.704518i
$162$		0			0
$163$	8.80177	−	8.80177i	0.689408	−	0.689408i	−0.272693	−	0.962101i	$-0.587914\pi$
$163$	8.80177	−	8.80177i	0.689408	−	0.689408i	0.962101	+	0.272693i	$0.0879144\pi$
$164$	−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	$-0.703351\pi$
$167$	2.66878	−	2.66878i	0.206517	−	0.206517i	0.802785	+	0.596269i	$0.203351\pi$
$168$		0			0
$169$			3.66421i			0.281862i
$170$	10.3211	−	9.65685i	0.791589	−	0.740647i
$171$		0			0
$172$	7.84035	+	7.84035i	0.597821	+	0.597821i
$173$	−6.70127	−	6.70127i	−0.509488	−	0.509488i	0.404881	−	0.914369i	$-0.367313\pi$
$173$	−6.70127	−	6.70127i	−0.509488	−	0.509488i	−0.914369	+	0.404881i	$0.867313\pi$
$174$		0			0
$175$	3.76256	−	3.29289i	0.284423	−	0.248919i
$176$			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
$185$	0.539848	−	16.2374i	0.0396904	−	1.19380i
$186$		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	−0.274863	+	0.961483i	$0.588632\pi$
$193$	−17.1759	+	17.1759i	−1.23635	+	1.23635i	−0.961483	+	0.274863i	$0.911368\pi$
$194$	−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	$-0.815119\pi$
$197$	−4.03248	+	4.03248i	−0.287303	+	0.287303i	0.548710	+	0.836013i	$0.315119\pi$
$198$		0			0
$199$		−	21.1651i		−	1.50035i	−0.661237	−	0.750177i	$-0.729968\pi$
$199$		−	21.1651i		−	1.50035i	0.661237	−	0.750177i	$-0.270032\pi$
$200$	3.76256	−	3.29289i	0.266053	−	0.232843i
$201$		0			0
$202$	−3.81739	−	3.81739i	−0.268590	−	0.268590i
$203$	−5.80177	−	5.80177i	−0.407204	−	0.407204i
$204$		0			0
$205$	12.3486	−	11.5539i	0.862464	−	0.806960i
$206$			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
$215$	−24.7797	−	0.823854i	−1.68996	−	0.0561863i
$216$		0			0
$217$	1.30913	+	1.30913i	0.0888699	+	0.0888699i
$218$	7.00089	+	7.00089i	0.474160	+	0.474160i
$219$		0			0
$220$	−3.28248	−	3.50825i	−0.221305	−	0.236526i
$221$		−	19.3137i		−	1.29918i
$222$		0			0
$223$	−4.42031	+	4.42031i	−0.296006	+	0.296006i	−0.839447	−	0.543441i	$-0.817121\pi$
$223$	−4.42031	+	4.42031i	−0.296006	+	0.296006i	0.543441	+	0.839447i	$0.317121\pi$
$224$	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	$-0.935082\pi$
$227$	−11.7028	+	11.7028i	−0.776742	+	0.776742i	0.202534	+	0.979275i	$0.435082\pi$
$228$		0			0
$229$		−	13.6314i		−	0.900785i	−0.892831	−	0.450393i	$-0.851284\pi$
$229$		−	13.6314i		−	0.900785i	0.892831	−	0.450393i	$-0.148716\pi$
$230$	13.6569	+	14.5962i	0.900506	+	0.962444i
$231$		0			0
$232$	−5.80177	−	5.80177i	−0.380905	−	0.380905i
$233$	20.6421	+	20.6421i	1.35231	+	1.35231i	0.883071	+	0.469240i	$0.155472\pi$
$233$	20.6421	+	20.6421i	1.35231	+	1.35231i	0.469240	+	0.883071i	$0.344528\pi$
$234$		0			0
$235$	−15.8404	−	0.526646i	−1.03331	−	0.0343546i
$236$			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
$245$	−1.63280	+	1.52773i	−0.104316	+	0.0976029i
$246$		0			0
$247$		0			0
$248$	1.30913	+	1.30913i	0.0831302	+	0.0831302i
$249$		0			0
$250$	−1.11289	+	11.1248i	−0.0703851	+	0.703595i
$251$			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	0.230349	−	0.973108i	$-0.426013\pi$
$257$	19.2929	−	19.2929i	1.20346	−	1.20346i	0.973108	−	0.230349i	$-0.0739866\pi$
$258$		0			0
$259$			7.26561i			0.451463i
$260$	0.227026	−	6.82843i	0.0140795	−	0.423481i
$261$		0			0
$262$	1.67894	+	1.67894i	0.103725	+	0.103725i
$263$	17.6348	+	17.6348i	1.08741	+	1.08741i	0.995795	+	0.0916118i	$0.0292019\pi$
$263$	17.6348	+	17.6348i	1.08741	+	1.08741i	0.0916118	+	0.995795i	$0.470798\pi$
$264$		0			0
$265$	−0.247855	+	7.45494i	−0.0152256	+	0.457953i
$266$		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
$275$	10.7193	+	0.713560i	0.646398	+	0.0430293i
$276$		0			0
$277$	−2.22208	−	2.22208i	−0.133512	−	0.133512i	0.637193	−	0.770705i	$-0.280096\pi$
$277$	−2.22208	−	2.22208i	−0.133512	−	0.133512i	−0.770705	+	0.637193i	$0.780096\pi$
$278$	−11.0386	−	11.0386i	−0.662050	−	0.662050i
$279$		0			0
$280$	−1.63280	+	1.52773i	−0.0975788	+	0.0912991i
$281$		−	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	0.0662885	−	0.997800i	$-0.478884\pi$
$283$	17.9007	−	17.9007i	1.06409	−	1.06409i	0.997800	−	0.0662885i	$-0.0211158\pi$
$284$	−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
$290$	18.3367	+	0.609642i	1.07677	+	0.0357994i
$291$		0			0
$292$	2.63020	+	2.63020i	0.153921	+	0.153921i
$293$	−1.36370	−	1.36370i	−0.0796683	−	0.0796683i	0.666150	−	0.745818i	$-0.267941\pi$
$293$	−1.36370	−	1.36370i	−0.0796683	−	0.0796683i	−0.745818	+	0.666150i	$0.767941\pi$
$294$		0			0
$295$	−14.2990	−	15.2825i	−0.832519	−	0.889780i
$296$			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
$305$	−6.82843	−	7.29809i	−0.390995	−	0.417888i
$306$		0			0
$307$	−7.70279	−	7.70279i	−0.439622	−	0.439622i	0.452263	−	0.891885i	$-0.350617\pi$
$307$	−7.70279	−	7.70279i	−0.439622	−	0.439622i	−0.891885	+	0.452263i	$0.850617\pi$
$308$	1.51929	+	1.51929i	0.0865697	+	0.0865697i
$309$		0			0
$310$	−4.13756	−	0.137562i	−0.234998	−	0.00781300i
$311$		−	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	$-0.914072\pi$
$313$	−12.3330	+	12.3330i	−0.697102	+	0.697102i	0.266683	+	0.963784i	$0.414072\pi$
$314$	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	$-0.835155\pi$
$317$	−6.65597	+	6.65597i	−0.373836	+	0.373836i	0.495036	+	0.868872i	$0.335155\pi$
$318$		0			0
$319$		−	17.6292i		−	0.987044i
$320$	−1.63280	+	1.52773i	−0.0912766	+	0.0854025i
$321$		0			0
$322$	−6.32106	−	6.32106i	−0.352259	−	0.352259i
$323$		0			0
$324$		0			0
$325$	10.0613	+	11.4963i	0.558099	+	0.637701i
$326$		−	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
$335$	0.403539	−	12.1376i	0.0220477	−	0.663146i
$336$		0			0
$337$	−11.6183	−	11.6183i	−0.632887	−	0.632887i	0.315904	−	0.948791i	$-0.397692\pi$
$337$	−11.6183	−	11.6183i	−0.632887	−	0.632887i	−0.948791	+	0.315904i	$0.897692\pi$
$338$	2.59099	+	2.59099i	0.140931	+	0.140931i
$339$		0			0
$340$	0.469666	−	14.1265i	0.0254712	−	0.766118i
$341$			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	$-0.884835\pi$
$347$	−10.8284	+	10.8284i	−0.581300	+	0.581300i	0.353960	+	0.935261i	$0.384835\pi$
$348$		0			0
$349$		−	15.3318i		−	0.820694i	−0.911929	−	0.410347i	$-0.865408\pi$
$349$		−	15.3318i		−	0.820694i	0.911929	−	0.410347i	$-0.134592\pi$
$350$	0.332104	−	4.98896i	0.0177517	−	0.266671i
$351$		0			0
$352$	1.51929	+	1.51929i	0.0809785	+	0.0809785i
$353$	−6.14860	−	6.14860i	−0.327257	−	0.327257i	0.524285	−	0.851543i	$-0.324332\pi$
$353$	−6.14860	−	6.14860i	−0.327257	−	0.327257i	−0.851543	+	0.524285i	$0.824332\pi$
$354$		0			0
$355$	0.686292	−	0.642125i	0.0364246	−	0.0340805i
$356$			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
$365$	−8.31282	−	0.276378i	−0.435113	−	0.0144663i
$366$		0			0
$367$	−10.0732	−	10.0732i	−0.525817	−	0.525817i	0.393505	−	0.919322i	$-0.371262\pi$
$367$	−10.0732	−	10.0732i	−0.525817	−	0.525817i	−0.919322	+	0.393505i	$0.871262\pi$
$368$	−6.32106	−	6.32106i	−0.329508	−	0.329508i
$369$		0			0
$370$	−11.0999	−	11.8633i	−0.577054	−	0.616745i
$371$		−	3.33579i		−	0.173186i
$372$		0			0
$373$	19.1614	−	19.1614i	0.992141	−	0.992141i	−0.00782876	−	0.999969i	$-0.502492\pi$
$373$	19.1614	−	19.1614i	0.992141	−	0.992141i	0.999969	+	0.00782876i	$0.00249200\pi$
$374$	−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	$-0.807337\pi$
$379$		−	22.1538i		−	1.13796i	0.822350	−	0.568982i	$-0.192663\pi$
$380$		0			0
$381$		0			0
$382$	0.367001	+	0.367001i	0.0187774	+	0.0187774i
$383$	−24.6008	−	24.6008i	−1.25704	−	1.25704i	−0.952499	−	0.304541i	$-0.901497\pi$
$383$	−24.6008	−	24.6008i	−1.25704	−	1.25704i	−0.304541	−	0.952499i	$-0.598503\pi$
$384$		0			0
$385$	−4.80177	−	0.159645i	−0.244721	−	0.00813627i
$386$			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
$395$	8.55025	−	8.00000i	0.430210	−	0.402524i
$396$		0			0
$397$	14.8282	+	14.8282i	0.744204	+	0.744204i	0.973384	−	0.229180i	$-0.0736045\pi$
$397$	14.8282	+	14.8282i	0.744204	+	0.744204i	−0.229180	+	0.973384i	$0.573605\pi$
$398$	−14.9660	−	14.9660i	−0.750177	−	0.750177i
$399$		0			0
$400$	0.332104	−	4.98896i	0.0166052	−	0.249448i
$401$			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	$0.231794\pi$
$409$			26.9190i			1.33106i	−0.746371	+	0.665530i	$0.768206\pi$
$410$	0.561931	−	16.9016i	0.0277518	−	0.834712i
$411$		0			0
$412$	7.80546	+	7.80546i	0.384547	+	0.384547i
$413$	6.61827	+	6.61827i	0.325664	+	0.325664i
$414$		0			0
$415$	−1.11575	+	33.5594i	−0.0547702	+	1.64736i
$416$			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
$425$	20.8146	+	23.7834i	1.00966	+	1.15366i
$426$		0			0
$427$	3.16053	+	3.16053i	0.152949	+	0.152949i
$428$	2.40811	+	2.40811i	0.116401	+	0.116401i
$429$		0			0
$430$	−18.1044	+	16.9393i	−0.873074	+	0.816887i
$431$			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	$-0.624249\pi$
$433$	11.3256	−	11.3256i	0.544275	−	0.544275i	0.924779	+	0.380504i	$0.124249\pi$
$434$	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	$0.00316269\pi$
$439$			0.416353i			0.0198715i	−0.999951	+	0.00993573i	$0.996837\pi$
$440$	−4.80177	−	0.159645i	−0.228915	−	0.00761078i
$441$		0			0
$442$	−13.6569	−	13.6569i	−0.649590	−	0.649590i
$443$	−11.2487	−	11.2487i	−0.534444	−	0.534444i	0.387448	−	0.921892i	$-0.373357\pi$
$443$	−11.2487	−	11.2487i	−0.534444	−	0.534444i	−0.921892	+	0.387448i	$0.873357\pi$
$444$		0			0
$445$	−22.2255	−	23.7542i	−1.05359	−	1.12606i
$446$			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
$455$	−4.66790	−	4.98896i	−0.218834	−	0.233886i
$456$		0			0
$457$	12.7028	+	12.7028i	0.594212	+	0.594212i	0.938766	−	0.344555i	$-0.111970\pi$
$457$	12.7028	+	12.7028i	0.594212	+	0.594212i	−0.344555	+	0.938766i	$0.611970\pi$
$458$	−9.63883	−	9.63883i	−0.450393	−	0.450393i
$459$		0			0
$460$	19.9779	+	0.664208i	0.931475	+	0.0309689i
$461$		−	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	$-0.917481\pi$
$463$	−15.2825	+	15.2825i	−0.710237	+	0.710237i	0.256348	+	0.966585i	$0.417481\pi$
$464$	−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	$-0.957524\pi$
$467$	−18.5429	+	18.5429i	−0.858062	+	0.858062i	0.133048	+	0.991110i	$0.457524\pi$
$468$		0			0
$469$			5.43108i			0.250784i
$470$	−11.5732	+	10.8284i	−0.533833	+	0.499478i
$471$		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
$485$	0.0637136	−	1.91636i	0.00289309	−	0.0870176i
$486$		0			0
$487$	9.63477	+	9.63477i	0.436593	+	0.436593i	0.890864	−	0.454271i	$-0.150100\pi$
$487$	9.63477	+	9.63477i	0.436593	+	0.436593i	−0.454271	+	0.890864i	$0.650100\pi$
$488$	3.16053	+	3.16053i	0.143071	+	0.143071i
$489$		0			0
$490$	−0.0743018	+	2.23483i	−0.00335661	+	0.100959i
$491$		−	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	$0.284191\pi$
$499$			34.7959i			1.55768i	−0.627223	+	0.778840i	$0.715809\pi$
$500$	7.07950	+	8.65336i	0.316605	+	0.386990i
$501$		0			0
$502$	5.35965	+	5.35965i	0.239213	+	0.239213i
$503$	3.26320	+	3.26320i	0.145499	+	0.145499i	0.776104	−	0.630605i	$-0.217193\pi$
$503$	3.26320	+	3.26320i	0.145499	+	0.145499i	−0.630605	+	0.776104i	$0.717193\pi$
$504$		0			0
$505$	8.81486	−	8.24758i	0.392256	−	0.367013i
$506$		−	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
$515$	−24.6694	−	0.820187i	−1.08706	−	0.0361417i
$516$		0			0
$517$	10.7686	+	10.7686i	0.473605	+	0.473605i
$518$	5.13756	+	5.13756i	0.225732	+	0.225732i
$519$		0			0
$520$	−4.66790	−	4.98896i	−0.204701	−	0.218780i
$521$			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	$-0.824760\pi$
$523$	−7.52637	+	7.52637i	−0.329105	+	0.329105i	0.523141	+	0.852246i	$0.324760\pi$
$524$	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
$530$	5.09618	+	5.44670i	0.221364	+	0.236589i
$531$		0			0
$532$		0			0
$533$	−16.3397	−	16.3397i	−0.707751	−	0.707751i
$534$		0			0
$535$	−7.61092	−	0.253041i	−0.329049	−	0.0109399i
$536$			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
$545$	−16.1660	+	15.1256i	−0.692475	+	0.647911i
$546$		0			0
$547$	10.8789	+	10.8789i	0.465150	+	0.465150i	0.900339	−	0.435189i	$-0.143319\pi$
$547$	10.8789	+	10.8789i	0.465150	+	0.465150i	−0.435189	+	0.900339i	$0.643319\pi$
$548$	9.88388	+	9.88388i	0.422218	+	0.422218i
$549$		0			0
$550$	8.08425	−	7.07512i	0.344714	−	0.301684i
$551$		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	$-0.564609\pi$
$557$	18.3588	−	18.3588i	0.777886	−	0.777886i	0.979471	+	0.201585i	$0.0646093\pi$
$558$		0			0
$559$			33.8787i			1.43291i
$560$	−0.0743018	+	2.23483i	−0.00313982	+	0.0944389i
$561$		0			0
$562$	−12.3596	−	12.3596i	−0.521360	−	0.521360i
$563$	−25.6348	−	25.6348i	−1.08038	−	1.08038i	−0.996474	−	0.0839029i	$-0.973261\pi$
$563$	−25.6348	−	25.6348i	−1.08038	−	1.08038i	−0.0839029	−	0.996474i	$-0.526739\pi$
$564$		0			0
$565$	−0.444170	+	13.3596i	−0.0186864	+	0.562045i
$566$		−	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
$575$	−33.6348	+	29.4363i	−1.40267	+	1.22758i
$576$		0			0
$577$	17.1498	+	17.1498i	0.713954	+	0.713954i	0.967360	−	0.253406i	$-0.0815509\pi$
$577$	17.1498	+	17.1498i	0.713954	+	0.713954i	−0.253406	+	0.967360i	$0.581551\pi$
$578$	−16.2322	−	16.2322i	−0.675172	−	0.675172i
$579$		0			0
$580$	13.3971	−	12.5349i	0.556283	−	0.520484i
$581$		−	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	$-0.682036\pi$
$587$	7.26040	−	7.26040i	0.299669	−	0.299669i	0.840884	+	0.541215i	$0.182036\pi$
$588$		0			0
$589$		0			0
$590$	−20.9172	−	0.695439i	−0.861150	−	0.0286308i
$591$		0			0
$592$	5.13756	+	5.13756i	0.211153	+	0.211153i
$593$	7.97917	+	7.97917i	0.327665	+	0.327665i	0.851698	−	0.524033i	$-0.175573\pi$
$593$	7.97917	+	7.97917i	0.327665	+	0.327665i	−0.524033	+	0.851698i	$0.675573\pi$
$594$		0			0
$595$	−9.65685	−	10.3211i	−0.395892	−	0.423122i
$596$		−	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
$605$	9.75225	+	10.4230i	0.396485	+	0.423756i
$606$		0			0
$607$	−3.57969	−	3.57969i	−0.145295	−	0.145295i	0.630718	−	0.776012i	$-0.282761\pi$
$607$	−3.57969	−	3.57969i	−0.145295	−	0.145295i	−0.776012	+	0.630718i	$0.782761\pi$
$608$		0			0
$609$		0			0
$610$	−9.98896	−	0.332104i	−0.404441	−	0.0134465i
$611$			21.6569i			0.876143i
$612$		0			0
$613$	6.77056	−	6.77056i	0.273460	−	0.273460i	−0.557031	−	0.830492i	$-0.688060\pi$
$613$	6.77056	−	6.77056i	0.273460	−	0.273460i	0.830492	+	0.557031i	$0.188060\pi$
$614$	−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	$-0.758065\pi$
$617$	−0.889981	+	0.889981i	−0.0358293	+	0.0358293i	0.688965	+	0.724794i	$0.258065\pi$
$618$		0			0
$619$		−	40.4436i		−	1.62557i	−0.582566	−	0.812783i	$-0.697951\pi$
$619$		−	40.4436i		−	1.62557i	0.582566	−	0.812783i	$-0.302049\pi$
$620$	−3.02297	+	2.82843i	−0.121405	+	0.113592i
$621$		0			0
$622$	−2.49352	−	2.49352i	−0.0999811	−	0.0999811i
$623$	10.2871	+	10.2871i	0.412142	+	0.412142i
$624$		0			0
$625$	−24.7794	−	3.31371i	−0.991177	−	0.132548i
$626$			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
$635$	−0.243894	+	7.33579i	−0.00967864	+	0.291112i
$636$		0			0
$637$	2.16053	+	2.16053i	0.0856034	+	0.0856034i
$638$	−12.4657	−	12.4657i	−0.493522	−	0.493522i
$639$		0			0
$640$	−0.0743018	+	2.23483i	−0.00293704	+	0.0883395i
$641$			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	$-0.736186\pi$
$643$	1.55583	−	1.55583i	0.0613559	−	0.0613559i	0.737119	+	0.675763i	$0.236186\pi$
$644$	−8.93933			−0.352259
$645$		0			0
$646$		0			0
$647$	31.9053	−	31.9053i	1.25433	−	1.25433i	0.300567	−	0.953761i	$-0.402824\pi$
$647$	31.9053	−	31.9053i	1.25433	−	1.25433i	0.953761	−	0.300567i	$-0.0971759\pi$
$648$		0			0
$649$			20.1102i			0.789393i
$650$	15.2435	+	1.01473i	0.597900	+	0.0398009i
$651$		0			0
$652$	−8.80177	−	8.80177i	−0.344704	−	0.344704i
$653$	−16.1841	−	16.1841i	−0.633333	−	0.633333i	0.315569	−	0.948903i	$-0.397805\pi$
$653$	−16.1841	−	16.1841i	−0.633333	−	0.633333i	−0.948903	+	0.315569i	$0.897805\pi$
$654$		0			0
$655$	−3.87689	+	3.62740i	−0.151483	+	0.141734i
$656$			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
$670$	−8.29721	−	8.86790i	−0.320549	−	0.342597i
$671$			9.60354i			0.370741i
$672$		0			0
$673$	−13.3431	+	13.3431i	−0.514340	+	0.514340i	−0.915853	−	0.401513i	$-0.868484\pi$
$673$	−13.3431	+	13.3431i	−0.514340	+	0.514340i	0.401513	+	0.915853i	$0.368484\pi$
$674$	−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	$-0.738035\pi$
$677$	1.38289	−	1.38289i	0.0531488	−	0.0531488i	0.733182	+	0.680033i	$0.238035\pi$
$678$		0			0
$679$			0.857497i			0.0329077i
$680$	−9.65685	−	10.3211i	−0.370323	−	0.395795i
$681$		0			0
$682$	2.81281	+	2.81281i	0.107708	+	0.107708i
$683$	24.2907	+	24.2907i	0.929459	+	0.929459i	0.997671	−	0.0682116i	$-0.0217293\pi$
$683$	24.2907	+	24.2907i	0.929459	+	0.929459i	−0.0682116	+	0.997671i	$0.521729\pi$
$684$		0			0
$685$	−31.2383	−	1.03858i	−1.19355	−	0.0396823i
$686$		−	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
$695$	25.4896	−	23.8492i	0.966875	−	0.904652i
$696$		0			0
$697$	−33.8033	−	33.8033i	−1.28039	−	1.28039i
$698$	−10.8412	−	10.8412i	−0.410347	−	0.410347i
$699$		0			0
$700$	−3.29289	−	3.76256i	−0.124460	−	0.142211i
$701$		−	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	$-0.949825\pi$
$709$		−	8.35963i		−	0.313952i	0.987602	−	0.156976i	$-0.0501746\pi$
$710$	0.0312301	−	0.939333i	0.00117205	−	0.0352525i
$711$		0			0
$712$	10.2871	+	10.2871i	0.385524	+	0.385524i
$713$	−11.7028	−	11.7028i	−0.438273	−	0.438273i
$714$		0			0
$715$	0.487788	−	14.6716i	0.0182422	−	0.548686i
$716$			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
$725$	−2.72490	+	40.9341i	−0.101200	+	1.52025i
$726$		0			0
$727$	0.221811	+	0.221811i	0.00822652	+	0.00822652i	0.711208	−	0.702982i	$-0.248148\pi$
$727$	0.221811	+	0.221811i	0.00822652	+	0.00822652i	−0.702982	+	0.711208i	$0.748148\pi$
$728$	2.16053	+	2.16053i	0.0800746	+	0.0800746i
$729$		0			0
$730$	−6.07348	+	5.68262i	−0.224790	+	0.210323i
$731$			70.0875i			2.59228i
$732$		0			0
$733$	4.28705	−	4.28705i	0.158346	−	0.158346i	−0.623487	−	0.781833i	$-0.714285\pi$
$733$	4.28705	−	4.28705i	0.158346	−	0.158346i	0.781833	+	0.623487i	$0.214285\pi$
$734$	−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	$0.0685489\pi$
$739$			11.6182i			0.427384i	−0.976901	+	0.213692i	$0.931451\pi$
$740$	−16.2374	−	0.539848i	−0.596900	−	0.0198452i
$741$		0			0
$742$	−2.35876	−	2.35876i	−0.0865928	−	0.0865928i
$743$	−7.65508	−	7.65508i	−0.280838	−	0.280838i	0.552605	−	0.833443i	$-0.313634\pi$
$743$	−7.65508	−	7.65508i	−0.280838	−	0.280838i	−0.833443	+	0.552605i	$0.813634\pi$
$744$		0			0
$745$	14.5128	+	15.5110i	0.531709	+	0.568280i
$746$		−	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
$755$	−20.7488	−	22.1759i	−0.755124	−	0.807063i
$756$		0			0
$757$	−31.4825	−	31.4825i	−1.14425	−	1.14425i	−0.987664	−	0.156586i	$-0.949951\pi$
$757$	−31.4825	−	31.4825i	−1.14425	−	1.14425i	−0.156586	−	0.987664i	$-0.550049\pi$
$758$	−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	$0.392939\pi$
$769$			52.3541i			1.88794i	−0.330037	+	0.943968i	$0.607061\pi$
$770$	−3.50825	+	3.28248i	−0.126429	+	0.118292i
$771$		0			0
$772$	17.1759	+	17.1759i	0.618173	+	0.618173i
$773$	24.6410	+	24.6410i	0.886274	+	0.886274i	0.994163	−	0.107889i	$-0.0344091\pi$
$773$	24.6410	+	24.6410i	0.886274	+	0.886274i	−0.107889	+	0.994163i	$0.534409\pi$
$774$		0			0
$775$	0.614857	−	9.23654i	0.0220863	−	0.331786i
$776$			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
$785$	−1.47754	+	44.4411i	−0.0527357	+	1.58617i
$786$		0			0
$787$	33.9264	+	33.9264i	1.20934	+	1.20934i	0.971239	+	0.238105i	$0.0765264\pi$
$787$	33.9264	+	33.9264i	1.20934	+	1.20934i	0.238105	+	0.971239i	$0.423474\pi$
$788$	4.03248	+	4.03248i	0.143651	+	0.143651i
$789$		0			0
$790$	0.389084	−	11.7028i	0.0138430	−	0.416367i
$791$		−	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	$-0.637430\pi$
$797$	13.8269	−	13.8269i	0.489774	−	0.489774i	0.908235	+	0.418461i	$0.137430\pi$
$798$		0			0
$799$			44.8033i			1.58503i
$800$	−3.29289	−	3.76256i	−0.116421	−	0.133027i
$801$		0			0
$802$	9.22181	+	9.22181i	0.325633	+	0.325633i
$803$	5.65125	+	5.65125i	0.199428	+	0.199428i
$804$		0			0
$805$	14.5962	−	13.6569i	0.514448	−	0.481341i
$806$			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
$815$	27.8183	+	0.924878i	0.974432	+	0.0323971i
$816$		0			0
$817$		0			0
$818$	19.0346	+	19.0346i	0.665530	+	0.665530i
$819$		0			0
$820$	−11.5539	−	12.3486i	−0.403480	−	0.431232i
$821$		−	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	$-0.733566\pi$
$823$	2.09365	−	2.09365i	0.0729800	−	0.0729800i	0.742655	+	0.669675i	$0.233566\pi$
$824$	11.0386			0.384547
$825$		0			0
$826$	9.35965			0.325664
$827$	34.5273	−	34.5273i	1.20063	−	1.20063i	0.226655	−	0.973975i	$-0.427221\pi$
$827$	34.5273	−	34.5273i	1.20063	−	1.20063i	0.973975	−	0.226655i	$-0.0727791\pi$
$828$		0			0
$829$		−	20.4697i		−	0.710941i	−0.934688	−	0.355470i	$-0.884321\pi$
$829$		−	20.4697i		−	0.710941i	0.934688	−	0.355470i	$-0.115679\pi$
$830$	22.9411	+	24.5190i	0.796297	+	0.851068i
$831$		0			0
$832$	2.16053	+	2.16053i	0.0749029	+	0.0749029i
$833$	4.46967	+	4.46967i	0.154865	+	0.154865i
$834$		0			0
$835$	8.43477	+	0.280432i	0.291897	+	0.00970475i
$836$		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
$845$	−5.98294	+	5.59791i	−0.205819	+	0.192574i
$846$		0			0
$847$	−4.51382	−	4.51382i	−0.155097	−	0.155097i
$848$	−2.35876	−	2.35876i	−0.0810002	−	0.0810002i
$849$		0			0
$850$	31.5355	+	2.09925i	1.08166	+	0.0720037i
$851$		−	64.9497i		−	2.22645i
$852$		0			0
$853$	0.806618	−	0.806618i	0.0276181	−	0.0276181i	−0.693163	−	0.720781i	$-0.743783\pi$
$853$	0.806618	−	0.806618i	0.0276181	−	0.0276181i	0.720781	+	0.693163i	$0.243783\pi$
$854$	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	$-0.610170\pi$
$857$	17.6075	−	17.6075i	0.601461	−	0.601461i	0.940700	+	0.339239i	$0.110170\pi$
$858$		0			0
$859$		−	37.4748i		−	1.27862i	−0.768947	−	0.639312i	$-0.779219\pi$
$859$		−	37.4748i		−	1.27862i	0.768947	−	0.639312i	$-0.220781\pi$
$860$	−0.823854	+	24.7797i	−0.0280932	+	0.844980i
$861$		0			0
$862$	16.2530	+	16.2530i	0.553581	+	0.553581i
$863$	−37.1924	−	37.1924i	−1.26604	−	1.26604i	−0.948115	−	0.317928i	$-0.897013\pi$
$863$	−37.1924	−	37.1924i	−1.26604	−	1.26604i	−0.317928	−	0.948115i	$-0.602987\pi$
$864$		0			0
$865$	0.704160	−	21.1796i	0.0239421	−	0.720127i
$866$		−	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
$875$	11.1248	+	1.11289i	0.376087	+	0.0376224i
$876$		0			0
$877$	−26.3997	−	26.3997i	−0.891456	−	0.891456i	0.103205	−	0.994660i	$-0.467090\pi$
$877$	−26.3997	−	26.3997i	−0.891456	−	0.891456i	−0.994660	+	0.103205i	$0.967090\pi$
$878$	0.294406	+	0.294406i	0.00993573	+	0.00993573i
$879$		0			0
$880$	−3.50825	+	3.28248i	−0.118263	+	0.110652i
$881$			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	$-0.707834\pi$
$883$	5.55052	−	5.55052i	0.186790	−	0.186790i	0.794307	+	0.607517i	$0.207834\pi$
$884$	−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	$-0.610035\pi$
$887$	17.9292	−	17.9292i	0.602003	−	0.602003i	0.940844	+	0.338841i	$0.110035\pi$
$888$		0			0
$889$		−	3.28248i		−	0.110091i
$890$	−32.5126	−	1.08095i	−1.08982	−	0.0362335i
$891$		0			0
$892$	4.42031	+	4.42031i	0.148003	+	0.148003i
$893$		0			0
$894$		0			0
$895$	−5.35965	−	5.72829i	−0.179153	−	0.191476i
$896$		−	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
$905$	21.0797	+	22.5296i	0.700713	+	0.748909i
$906$		0			0
$907$	−11.4734	−	11.4734i	−0.380966	−	0.380966i	0.490484	−	0.871450i	$-0.336820\pi$
$907$	−11.4734	−	11.4734i	−0.380966	−	0.380966i	−0.871450	+	0.490484i	$0.836820\pi$
$908$	11.7028	+	11.7028i	0.388371	+	0.388371i
$909$		0			0
$910$	−6.82843	−	0.227026i	−0.226360	−	0.00752583i
$911$		−	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	$-0.982881\pi$
$919$		−	3.25917i		−	0.107510i	0.998554	−	0.0537551i	$-0.0171190\pi$
$920$	14.5962	−	13.6569i	0.481222	−	0.450253i
$921$		0			0
$922$	−21.1271	−	21.1271i	−0.695785	−	0.695785i
$923$	−0.908103	−	0.908103i	−0.0298906	−	0.0298906i
$924$		0			0
$925$	27.3373	−	23.9249i	0.898845	−	0.786645i
$926$			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
$935$	1.00913	−	30.3523i	0.0330020	−	0.992626i
$936$		0			0
$937$	−40.8061	−	40.8061i	−1.33308	−	1.33308i	−0.902604	−	0.430473i	$-0.858347\pi$
$937$	−40.8061	−	40.8061i	−1.33308	−	1.33308i	−0.430473	−	0.902604i	$-0.641653\pi$
$938$	3.84035	+	3.84035i	0.125392	+	0.125392i
$939$		0			0
$940$	−0.526646	+	15.8404i	−0.0171773	+	0.516655i
$941$		−	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	−0.252265	−	0.967658i	$-0.581175\pi$
$947$	22.0151	−	22.0151i	0.715394	−	0.715394i	0.967658	+	0.252265i	$0.0811754\pi$
$948$		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	$-0.202355\pi$
$953$	6.51039	+	6.51039i	0.210892	+	0.210892i	−0.593754	+	0.804646i	$0.702355\pi$
$954$		0			0
$955$	−0.847456	+	0.792918i	−0.0274230	+	0.0256582i
$956$		−	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
$965$	−54.2849	−	1.80482i	−1.74749	−	0.0580991i
$966$		0			0
$967$	28.1299	+	28.1299i	0.904598	+	0.904598i	0.995830	−	0.0912320i	$-0.0290805\pi$
$967$	28.1299	+	28.1299i	0.904598	+	0.904598i	−0.0912320	+	0.995830i	$0.529080\pi$
$968$	−4.51382	−	4.51382i	−0.145080	−	0.145080i
$969$		0			0
$970$	−1.31002	−	1.40013i	−0.0420622	−	0.0449553i
$971$			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	−0.0209224	−	0.999781i	$-0.506660\pi$
$977$	30.5962	−	30.5962i	0.978859	−	0.978859i	0.999781	+	0.0209224i	$0.00666028\pi$
$978$		0			0
$979$			31.2581i			0.999012i
$980$	1.52773	+	1.63280i	0.0488014	+	0.0521580i
$981$		0			0
$982$	−14.1614	−	14.1614i	−0.451909	−	0.451909i
$983$	−4.87234	−	4.87234i	−0.155403	−	0.155403i	0.625123	−	0.780526i	$-0.285049\pi$
$983$	−4.87234	−	4.87234i	−0.155403	−	0.155403i	−0.780526	+	0.625123i	$0.785049\pi$
$984$		0			0
$985$	−12.7448	−	0.423728i	−0.406083	−	0.0135011i
$986$		−	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
$995$	34.5585	−	32.3345i	1.09558	−	1.02507i
$996$		0			0
$997$	−16.5094	−	16.5094i	−0.522858	−	0.522858i	0.395575	−	0.918434i	$-0.370545\pi$
$997$	−16.5094	−	16.5094i	−0.522858	−	0.522858i	−0.918434	+	0.395575i	$0.870545\pi$
$998$	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	630.2.m.c.197.4	✓	8
3.2	odd	2		630.2.m.d.197.1	yes	8
5.2	odd	4		3150.2.m.j.2843.4		8
5.3	odd	4		630.2.m.d.323.1	yes	8
5.4	even	2		3150.2.m.i.1457.2		8
15.2	even	4		3150.2.m.i.2843.1		8
15.8	even	4	inner	630.2.m.c.323.4	yes	8
15.14	odd	2		3150.2.m.j.1457.3		8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.52773 + 1.63280i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.52773 + 1.63280i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.23483 + 0.0743018i) q^{10} -2.14860i q^{11} +(2.16053 - 2.16053i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(4.46967 - 4.46967i) q^{17} +(1.63280 - 1.52773i) q^{20} +(-1.51929 - 1.51929i) q^{22} +(6.32106 + 6.32106i) q^{23} +(-0.332104 + 4.98896i) q^{25} -3.05545i q^{26} +(-0.707107 + 0.707107i) q^{28} +8.20494 q^{29} -1.85140 q^{31} +(-0.707107 + 0.707107i) q^{32} -6.32106i q^{34} +(0.0743018 - 2.23483i) q^{35} +(-5.13756 - 5.13756i) q^{37} +(0.0743018 - 2.23483i) q^{40} -7.56282i q^{41} +(-7.84035 + 7.84035i) q^{43} -2.14860 q^{44} +8.93933 q^{46} +(-5.01193 + 5.01193i) q^{47} +1.00000i q^{49} +(3.29289 + 3.76256i) q^{50} +(-2.16053 - 2.16053i) q^{52} +(2.35876 + 2.35876i) q^{53} +(3.50825 - 3.28248i) q^{55} +1.00000i q^{56} +(5.80177 - 5.80177i) q^{58} -9.35965 q^{59} -4.46967 q^{61} +(-1.30913 + 1.30913i) q^{62} +1.00000i q^{64} +(6.82843 + 0.227026i) q^{65} +(-3.84035 - 3.84035i) q^{67} +(-4.46967 - 4.46967i) q^{68} +(-1.52773 - 1.63280i) q^{70} -0.420314i q^{71} +(-2.63020 + 2.63020i) q^{73} -7.26561 q^{74} +(-1.51929 + 1.51929i) q^{77} -5.23654i q^{79} +(-1.52773 - 1.63280i) q^{80} +(-5.34772 - 5.34772i) q^{82} +(10.6183 + 10.6183i) q^{83} +(14.1265 + 0.469666i) q^{85} +11.0879i q^{86} +(-1.51929 + 1.51929i) q^{88} -14.5481 q^{89} -3.05545 q^{91} +(6.32106 - 6.32106i) q^{92} +7.08794i q^{94} +(-0.606342 - 0.606342i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 4 q^{13} - 8 q^{14} - 8 q^{16} + 4 q^{20} - 4 q^{22} + 8 q^{23} - 4 q^{25} - 24 q^{29} - 8 q^{31} + 4 q^{35} - 4 q^{37} + 4 q^{40} - 12 q^{43} - 24 q^{44} - 12 q^{47} + 32 q^{50} + 4 q^{52} + 32 q^{53} - 24 q^{55} + 12 q^{58} - 16 q^{59} + 4 q^{62} + 32 q^{65} + 20 q^{67} + 36 q^{73} - 40 q^{74} - 4 q^{77} - 12 q^{82} + 56 q^{83} + 32 q^{85} - 4 q^{88} - 72 q^{89} + 8 q^{92} - 4 q^{97}+O(q^{100}) \) 8 * q - 4 * q^13 - 8 * q^14 - 8 * q^16 + 4 * q^20 - 4 * q^22 + 8 * q^23 - 4 * q^25 - 24 * q^29 - 8 * q^31 + 4 * q^35 - 4 * q^37 + 4 * q^40 - 12 * q^43 - 24 * q^44 - 12 * q^47 + 32 * q^50 + 4 * q^52 + 32 * q^53 - 24 * q^55 + 12 * q^58 - 16 * q^59 + 4 * q^62 + 32 * q^65 + 20 * q^67 + 36 * q^73 - 40 * q^74 - 4 * q^77 - 12 * q^82 + 56 * q^83 + 32 * q^85 - 4 * q^88 - 72 * q^89 + 8 * q^92 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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