LMFDB - Embedded newform 1456.2.cc.d.225.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not 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:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			225.5
Root			$0.500000 + 3.15681i$ of defining polynomial
Character	$\chi$	$=$	1456.225
Dual form			1456.2.cc.d.673.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14539 - 1.98388i) q^{3} +0.901839i q^{5} +(-0.866025 + 0.500000i) q^{7} +(-1.12385 - 1.94657i) q^{9} +O(q^{10})$	\(q+(1.14539 - 1.98388i) q^{3} +0.901839i q^{5} +(-0.866025 + 0.500000i) q^{7} +(-1.12385 - 1.94657i) q^{9} +(3.75609 + 2.16858i) q^{11} +(-0.426876 + 3.58019i) q^{13} +(1.78914 + 1.03296i) q^{15} +(2.53296 + 4.38722i) q^{17} +(-5.34544 + 3.08619i) q^{19} +2.29079i q^{21} +(-4.22559 + 7.31893i) q^{23} +4.18669 q^{25} +1.72335 q^{27} +(1.09643 - 1.89907i) q^{29} -0.873062i q^{31} +(8.60441 - 4.96776i) q^{33} +(-0.450919 - 0.781015i) q^{35} +(0.124973 + 0.0721531i) q^{37} +(6.61373 + 4.94760i) q^{39} +(-3.46110 - 1.99827i) q^{41} +(-3.85426 - 6.67577i) q^{43} +(1.75549 - 1.01353i) q^{45} +2.92115i q^{47} +(0.500000 - 0.866025i) q^{49} +11.6049 q^{51} +1.69699 q^{53} +(-1.95571 + 3.38739i) q^{55} +14.1396i q^{57} +(7.40394 - 4.27467i) q^{59} +(-4.16720 - 7.21780i) q^{61} +(1.94657 + 1.12385i) q^{63} +(-3.22876 - 0.384973i) q^{65} +(8.99180 + 5.19142i) q^{67} +(9.67992 + 16.7661i) q^{69} +(2.83932 - 1.63928i) q^{71} +0.539023i q^{73} +(4.79540 - 8.30588i) q^{75} -4.33716 q^{77} -6.53349 q^{79} +(5.34547 - 9.25862i) q^{81} +13.2348i q^{83} +(-3.95656 + 2.28432i) q^{85} +(-2.51168 - 4.35037i) q^{87} +(-6.74790 - 3.89590i) q^{89} +(-1.42041 - 3.31398i) q^{91} +(-1.73205 - 1.00000i) q^{93} +(-2.78325 - 4.82072i) q^{95} +(10.1378 - 5.85305i) q^{97} -9.74866i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 6 q^{9}+O(q^{10}) $ 12 * q + 2 * q^3 - 6 * q^9	$ 12 q + 2 q^{3} - 6 q^{9} + 18 q^{11} - 8 q^{13} + 6 q^{15} + 4 q^{17} - 12 q^{19} + 6 q^{23} - 24 q^{25} - 40 q^{27} - 10 q^{29} + 12 q^{33} - 2 q^{35} - 6 q^{37} + 54 q^{39} - 24 q^{41} - 26 q^{43} + 72 q^{45} + 6 q^{49} + 36 q^{51} + 36 q^{53} + 6 q^{55} - 6 q^{59} - 28 q^{61} - 34 q^{65} + 42 q^{67} + 32 q^{69} - 48 q^{71} + 48 q^{75} - 4 q^{77} - 44 q^{79} - 34 q^{81} + 54 q^{85} - 2 q^{87} + 12 q^{89} + 16 q^{91} - 32 q^{95} + 60 q^{97}+O(q^{100}) $ 12 * q + 2 * q^3 - 6 * q^9 + 18 * q^11 - 8 * q^13 + 6 * q^15 + 4 * q^17 - 12 * q^19 + 6 * q^23 - 24 * q^25 - 40 * q^27 - 10 * q^29 + 12 * q^33 - 2 * q^35 - 6 * q^37 + 54 * q^39 - 24 * q^41 - 26 * q^43 + 72 * q^45 + 6 * q^49 + 36 * q^51 + 36 * q^53 + 6 * q^55 - 6 * q^59 - 28 * q^61 - 34 * q^65 + 42 * q^67 + 32 * q^69 - 48 * q^71 + 48 * q^75 - 4 * q^77 - 44 * q^79 - 34 * q^81 + 54 * q^85 - 2 * q^87 + 12 * q^89 + 16 * q^91 - 32 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	1.14539	−	1.98388i	0.661293	−	1.14539i	−0.318983	−	0.947760i	$-0.603341\pi$
$3$	1.14539	−	1.98388i	0.661293	−	1.14539i	0.980276	−	0.197633i	$-0.0633254\pi$
$4$		0			0
$5$			0.901839i			0.403315i	0.979456	+	0.201657i	$0.0646327\pi$
$5$			0.901839i			0.403315i	−0.979456	+	0.201657i	$0.935367\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$		0			0
$9$	−1.12385	−	1.94657i	−0.374617	−	0.648856i
$10$		0			0
$11$	3.75609	+	2.16858i	1.13251	+	0.653852i	0.944564	−	0.328328i	$-0.106485\pi$
$11$	3.75609	+	2.16858i	1.13251	+	0.653852i	0.187941	+	0.982180i	$0.439819\pi$
$12$		0			0
$13$	−0.426876	+	3.58019i	−0.118394	+	0.992967i
$13$	−0.426876	+	3.58019i	−0.118394	+	0.992967i
$14$		0			0
$15$	1.78914	+	1.03296i	0.461954	+	0.266709i
$16$		0			0
$17$	2.53296	+	4.38722i	0.614333	+	1.06406i	0.990501	+	0.137505i	$0.0439082\pi$
$17$	2.53296	+	4.38722i	0.614333	+	1.06406i	−0.376168	+	0.926551i	$0.622758\pi$
$18$		0			0
$19$	−5.34544	+	3.08619i	−1.22633	+	0.708021i	−0.966260	−	0.257570i	$-0.917078\pi$
$19$	−5.34544	+	3.08619i	−1.22633	+	0.708021i	−0.260068	+	0.965590i	$0.583745\pi$
$20$		0			0
$21$			2.29079i			0.499891i
$22$		0			0
$23$	−4.22559	+	7.31893i	−0.881096	+	1.52610i	−0.0309711	+	0.999520i	$0.509860\pi$
$23$	−4.22559	+	7.31893i	−0.881096	+	1.52610i	−0.850124	+	0.526582i	$0.823473\pi$
$24$		0			0
$25$	4.18669			0.837337
$26$		0			0
$27$	1.72335			0.331659
$28$		0			0
$29$	1.09643	−	1.89907i	0.203602	−	0.352649i	−0.746085	−	0.665851i	$-0.768069\pi$
$29$	1.09643	−	1.89907i	0.203602	−	0.352649i	0.949686	+	0.313203i	$0.101402\pi$
$30$		0			0
$31$		−	0.873062i		−	0.156807i	−0.996922	−	0.0784033i	$-0.975018\pi$
$31$		−	0.873062i		−	0.156807i	0.996922	−	0.0784033i	$-0.0249822\pi$
$32$		0			0
$33$	8.60441	−	4.96776i	1.49784	−	0.864776i
$34$		0			0
$35$	−0.450919	−	0.781015i	−0.0762193	−	0.132016i
$36$		0			0
$37$	0.124973	+	0.0721531i	0.0205454	+	0.0118619i	0.510238	−	0.860034i	$-0.329557\pi$
$37$	0.124973	+	0.0721531i	0.0205454	+	0.0118619i	−0.489692	+	0.871895i	$0.662891\pi$
$38$		0			0
$39$	6.61373	+	4.94760i	1.05904	+	0.792250i
$40$		0			0
$41$	−3.46110	−	1.99827i	−0.540533	−	0.312077i	0.204762	−	0.978812i	$-0.434358\pi$
$41$	−3.46110	−	1.99827i	−0.540533	−	0.312077i	−0.745295	+	0.666735i	$0.767691\pi$
$42$		0			0
$43$	−3.85426	−	6.67577i	−0.587768	−	1.01804i	−0.994524	−	0.104508i	$-0.966673\pi$
$43$	−3.85426	−	6.67577i	−0.587768	−	1.01804i	0.406756	−	0.913537i	$-0.366660\pi$
$44$		0			0
$45$	1.75549	−	1.01353i	0.261693	−	0.151089i
$46$		0			0
$47$			2.92115i			0.426093i	0.977042	+	0.213047i	$0.0683387\pi$
$47$			2.92115i			0.426093i	−0.977042	+	0.213047i	$0.931661\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$		0			0
$51$	11.6049			1.62502
$52$		0			0
$53$	1.69699			0.233099			0.116549	−	0.993185i	$-0.462817\pi$
$53$	1.69699			0.233099			0.116549	+	0.993185i	$0.462817\pi$
$54$		0			0
$55$	−1.95571	+	3.38739i	−0.263708	+	0.456756i
$56$		0			0
$57$			14.1396i			1.87284i
$58$		0			0
$59$	7.40394	−	4.27467i	0.963911	−	0.556514i	0.0665363	−	0.997784i	$-0.478805\pi$
$59$	7.40394	−	4.27467i	0.963911	−	0.556514i	0.897374	+	0.441270i	$0.145472\pi$
$60$		0			0
$61$	−4.16720	−	7.21780i	−0.533555	−	0.924145i	−0.999232	−	0.0391900i	$-0.987522\pi$
$61$	−4.16720	−	7.21780i	−0.533555	−	0.924145i	0.465676	−	0.884955i	$-0.345811\pi$
$62$		0			0
$63$	1.94657	+	1.12385i	0.245245	+	0.141592i
$64$		0			0
$65$	−3.22876	−	0.384973i	−0.400478	−	0.0477501i
$66$		0			0
$67$	8.99180	+	5.19142i	1.09852	+	0.634233i	0.935833	−	0.352444i	$-0.114649\pi$
$67$	8.99180	+	5.19142i	1.09852	+	0.634233i	0.162691	+	0.986677i	$0.447983\pi$
$68$		0			0
$69$	9.67992	+	16.7661i	1.16532	+	2.01840i
$70$		0			0
$71$	2.83932	−	1.63928i	0.336965	−	0.194547i	−0.321964	−	0.946752i	$-0.604343\pi$
$71$	2.83932	−	1.63928i	0.336965	−	0.194547i	0.658929	+	0.752205i	$0.271010\pi$
$72$		0			0
$73$			0.539023i			0.0630879i	0.999502	+	0.0315439i	$0.0100424\pi$
$73$			0.539023i			0.0630879i	−0.999502	+	0.0315439i	$0.989958\pi$
$74$		0			0
$75$	4.79540	−	8.30588i	0.553725	−	0.959081i
$76$		0			0
$77$	−4.33716			−0.494266
$78$		0			0
$79$	−6.53349			−0.735075			−0.367537	−	0.930009i	$-0.619799\pi$
$79$	−6.53349			−0.735075			−0.367537	+	0.930009i	$0.619799\pi$
$80$		0			0
$81$	5.34547	−	9.25862i	0.593941	−	1.02874i
$82$		0			0
$83$			13.2348i			1.45271i	0.687319	+	0.726356i	$0.258788\pi$
$83$			13.2348i			1.45271i	−0.687319	+	0.726356i	$0.741212\pi$
$84$		0			0
$85$	−3.95656	+	2.28432i	−0.429149	+	0.247769i
$86$		0			0
$87$	−2.51168	−	4.35037i	−0.269281	−	0.466408i
$88$		0			0
$89$	−6.74790	−	3.89590i	−0.715276	−	0.412965i	0.0977357	−	0.995212i	$-0.468840\pi$
$89$	−6.74790	−	3.89590i	−0.715276	−	0.412965i	−0.813011	+	0.582248i	$0.802173\pi$
$90$		0			0
$91$	−1.42041	−	3.31398i	−0.148900	−	0.347399i
$92$		0			0
$93$	−1.73205	−	1.00000i	−0.179605	−	0.103695i
$94$		0			0
$95$	−2.78325	−	4.82072i	−0.285555	−	0.494596i
$96$		0			0
$97$	10.1378	−	5.85305i	1.02934	−	0.594287i	0.112541	−	0.993647i	$-0.464101\pi$
$97$	10.1378	−	5.85305i	1.02934	−	0.594287i	0.916794	+	0.399360i	$0.130768\pi$
$98$		0			0
$99$		−	9.74866i		−	0.979777i
$100$		0			0
$101$	−5.37145	+	9.30362i	−0.534479	+	0.925745i	0.464709	+	0.885463i	$0.346159\pi$
$101$	−5.37145	+	9.30362i	−0.534479	+	0.925745i	−0.999188	+	0.0402814i	$0.987175\pi$
$102$		0			0
$103$	−4.81099			−0.474041			−0.237021	−	0.971505i	$-0.576171\pi$
$103$	−4.81099			−0.474041			−0.237021	+	0.971505i	$0.576171\pi$
$104$		0			0
$105$	−2.06592			−0.201613
$106$		0			0
$107$	6.82652	−	11.8239i	0.659944	−	1.14306i	−0.320686	−	0.947186i	$-0.603913\pi$
$107$	6.82652	−	11.8239i	0.659944	−	1.14306i	0.980630	−	0.195871i	$-0.0627534\pi$
$108$		0			0
$109$			5.11747i			0.490165i	0.969502	+	0.245082i	$0.0788150\pi$
$109$			5.11747i			0.490165i	−0.969502	+	0.245082i	$0.921185\pi$
$110$		0			0
$111$	0.286286	−	0.165287i	0.0271731	−	0.0156884i
$112$		0			0
$113$	−8.96603	−	15.5296i	−0.843453	−	1.46090i	−0.886958	−	0.461850i	$-0.847186\pi$
$113$	−8.96603	−	15.5296i	−0.843453	−	1.46090i	0.0435052	−	0.999053i	$-0.486147\pi$
$114$		0			0
$115$	−6.60049	−	3.81080i	−0.615499	−	0.355359i
$116$		0			0
$117$	7.44884	−	3.19266i	0.688645	−	0.295162i
$118$		0			0
$119$	−4.38722	−	2.53296i	−0.402175	−	0.232196i
$120$		0			0
$121$	3.90550	+	6.76452i	0.355045	+	0.614956i
$122$		0			0
$123$	−7.92864	+	4.57761i	−0.714902	+	0.412749i
$124$		0			0
$125$			8.28491i			0.741025i
$126$		0			0
$127$	9.75681	−	16.8993i	0.865777	−	1.49957i	−0.000496195	−	1.00000i	$-0.500158\pi$
$127$	9.75681	−	16.8993i	0.865777	−	1.49957i	0.866273	−	0.499570i	$-0.166509\pi$
$128$		0			0
$129$	−17.6586			−1.55475
$130$		0			0
$131$	20.6496			1.80417			0.902083	−	0.431562i	$-0.142037\pi$
$131$	20.6496			1.80417			0.902083	+	0.431562i	$0.142037\pi$
$132$		0			0
$133$	3.08619	−	5.34544i	0.267607	−	0.463508i
$134$		0			0
$135$			1.55418i			0.133763i
$136$		0			0
$137$	2.76224	−	1.59478i	0.235994	−	0.136251i	−0.377340	−	0.926075i	$-0.623161\pi$
$137$	2.76224	−	1.59478i	0.235994	−	0.136251i	0.613334	+	0.789823i	$0.289828\pi$
$138$		0			0
$139$	−0.297855	−	0.515900i	−0.0252637	−	0.0437581i	0.853117	−	0.521719i	$-0.174709\pi$
$139$	−0.297855	−	0.515900i	−0.0252637	−	0.0437581i	−0.878381	+	0.477961i	$0.841376\pi$
$140$		0			0
$141$	5.79521	+	3.34587i	0.488045	+	0.281773i
$142$		0			0
$143$	−9.36733	+	12.5218i	−0.783335	+	1.04713i
$144$		0			0
$145$	1.71266	+	0.988802i	0.142228	+	0.0821155i
$146$		0			0
$147$	−1.14539	−	1.98388i	−0.0944705	−	0.163628i
$148$		0			0
$149$	9.70783	−	5.60482i	0.795297	−	0.459165i	−0.0465273	−	0.998917i	$-0.514815\pi$
$149$	9.70783	−	5.60482i	0.795297	−	0.459165i	0.841824	+	0.539752i	$0.181482\pi$
$150$		0			0
$151$			13.0731i			1.06387i	0.846785	+	0.531935i	$0.178535\pi$
$151$			13.0731i			1.06387i	−0.846785	+	0.531935i	$0.821465\pi$
$152$		0			0
$153$	5.69334	−	9.86116i	0.460280	−	0.797228i
$154$		0			0
$155$	0.787362			0.0632424
$156$		0			0
$157$	17.9245			1.43053			0.715266	−	0.698853i	$-0.246306\pi$
$157$	17.9245			1.43053			0.715266	+	0.698853i	$0.246306\pi$
$158$		0			0
$159$	1.94372	−	3.36661i	0.154147	−	0.266990i
$160$		0			0
$161$		−	8.45117i		−	0.666046i
$162$		0			0
$163$	−17.5958	+	10.1589i	−1.37821	+	0.795710i	−0.991944	−	0.126677i	$-0.959569\pi$
$163$	−17.5958	+	10.1589i	−1.37821	+	0.795710i	−0.386266	+	0.922387i	$0.626235\pi$
$164$		0			0
$165$	4.48012	+	7.75979i	0.348777	+	0.604099i
$166$		0			0
$167$	2.79770	+	1.61525i	0.216493	+	0.124992i	0.604325	−	0.796738i	$-0.293443\pi$
$167$	2.79770	+	1.61525i	0.216493	+	0.124992i	−0.387833	+	0.921730i	$0.626776\pi$
$168$		0			0
$169$	−12.6356	−	3.05660i	−0.971966	−	0.235123i
$170$		0			0
$171$	12.0150	+	6.93684i	0.918807	+	0.530474i
$172$		0			0
$173$	−4.58522	−	7.94183i	−0.348608	−	0.603806i	0.637395	−	0.770538i	$-0.280012\pi$
$173$	−4.58522	−	7.94183i	−0.348608	−	0.603806i	−0.986002	+	0.166731i	$0.946679\pi$
$174$		0			0
$175$	−3.62578	+	2.09334i	−0.274083	+	0.158242i
$176$		0			0
$177$		−	19.5847i		−	1.47208i
$178$		0			0
$179$	8.47747	−	14.6834i	0.633636	−	1.09749i	−0.353166	−	0.935561i	$-0.614895\pi$
$179$	8.47747	−	14.6834i	0.633636	−	1.09749i	0.986802	−	0.161929i	$-0.0517717\pi$
$180$		0			0
$181$	−2.65743			−0.197525			−0.0987626	−	0.995111i	$-0.531488\pi$
$181$	−2.65743			−0.197525			−0.0987626	+	0.995111i	$0.531488\pi$
$182$		0			0
$183$	−19.0923			−1.41135
$184$		0			0
$185$	−0.0650705	+	0.112705i	−0.00478408	+	0.00828627i
$186$		0			0
$187$			21.9717i			1.60673i
$188$		0			0
$189$	−1.49246	+	0.861675i	−0.108561	+	0.0626776i
$190$		0			0
$191$	−12.2430	−	21.2056i	−0.885875	−	1.53438i	−0.844708	−	0.535228i	$-0.820226\pi$
$191$	−12.2430	−	21.2056i	−0.885875	−	1.53438i	−0.0411671	−	0.999152i	$-0.513108\pi$
$192$		0			0
$193$	10.6009	+	6.12046i	0.763072	+	0.440560i	0.830398	−	0.557171i	$-0.188113\pi$
$193$	10.6009	+	6.12046i	0.763072	+	0.440560i	−0.0673254	+	0.997731i	$0.521447\pi$
$194$		0			0
$195$	−4.46194	+	5.96452i	−0.319526	+	0.427128i
$196$		0			0
$197$	4.72634	+	2.72876i	0.336738	+	0.194416i	0.658829	−	0.752293i	$-0.271052\pi$
$197$	4.72634	+	2.72876i	0.336738	+	0.194416i	−0.322091	+	0.946709i	$0.604386\pi$
$198$		0			0
$199$	6.40832	+	11.0995i	0.454274	+	0.786825i	0.998646	−	0.0520184i	$-0.0165654\pi$
$199$	6.40832	+	11.0995i	0.454274	+	0.786825i	−0.544372	+	0.838844i	$0.683232\pi$
$200$		0			0
$201$	20.5983	−	11.8924i	1.45289	−	0.838828i
$202$		0			0
$203$			2.19286i			0.153908i
$204$		0			0
$205$	1.80212	−	3.12136i	0.125865	−	0.218005i
$206$		0			0
$207$	18.9957			1.32029
$208$		0			0
$209$	−26.7706			−1.85176
$210$		0			0
$211$	−9.65552	+	16.7239i	−0.664713	+	1.15132i	0.314649	+	0.949208i	$0.398113\pi$
$211$	−9.65552	+	16.7239i	−0.664713	+	1.15132i	−0.979363	+	0.202110i	$0.935220\pi$
$212$		0			0
$213$		−	7.51048i		−	0.514610i
$214$		0			0
$215$	6.02046	−	3.47592i	0.410592	−	0.237056i
$216$		0			0
$217$	0.436531	+	0.756094i	0.0296337	+	0.0513270i
$218$		0			0
$219$	1.06936	+	0.617393i	0.0722604	+	0.0417196i
$220$		0			0
$221$	−16.7883	+	7.19569i	−1.12931	+	0.484034i
$222$		0			0
$223$	9.21079	+	5.31785i	0.616800	+	0.356110i	0.775622	−	0.631197i	$-0.217436\pi$
$223$	9.21079	+	5.31785i	0.616800	+	0.356110i	−0.158822	+	0.987307i	$0.550770\pi$
$224$		0			0
$225$	−4.70522	−	8.14967i	−0.313681	−	0.543312i
$226$		0			0
$227$	−19.6776	+	11.3609i	−1.30605	+	0.754047i	−0.981434	−	0.191800i	$-0.938567\pi$
$227$	−19.6776	+	11.3609i	−1.30605	+	0.754047i	−0.324613	+	0.945847i	$0.605234\pi$
$228$		0			0
$229$			20.3094i			1.34208i	0.741420	+	0.671042i	$0.234153\pi$
$229$			20.3094i			1.34208i	−0.741420	+	0.671042i	$0.765847\pi$
$230$		0			0
$231$	−4.96776	+	8.60441i	−0.326855	+	0.566129i
$232$		0			0
$233$	10.6446			0.697352			0.348676	−	0.937243i	$-0.386631\pi$
$233$	10.6446			0.697352			0.348676	+	0.937243i	$0.386631\pi$
$234$		0			0
$235$	−2.63441			−0.171850
$236$		0			0
$237$	−7.48341	+	12.9617i	−0.486100	+	0.841950i
$238$		0			0
$239$			0.311564i			0.0201534i	0.999949	+	0.0100767i	$0.00320757\pi$
$239$			0.311564i			0.0201534i	−0.999949	+	0.0100767i	$0.996792\pi$
$240$		0			0
$241$	−21.9100	+	12.6498i	−1.41135	+	0.814843i	−0.995516	−	0.0945983i	$-0.969843\pi$
$241$	−21.9100	+	12.6498i	−1.41135	+	0.814843i	−0.415833	+	0.909441i	$0.636510\pi$
$242$		0			0
$243$	−9.66031	−	16.7321i	−0.619709	−	1.07337i
$244$		0			0
$245$	0.781015	+	0.450919i	0.0498972	+	0.0288082i
$246$		0			0
$247$	−8.76732	−	20.4551i	−0.557851	−	1.30153i
$248$		0			0
$249$	26.2563	+	15.1591i	1.66393	+	0.960669i
$250$		0			0
$251$	−4.02015	−	6.96311i	−0.253750	−	0.439507i	0.710805	−	0.703389i	$-0.248331\pi$
$251$	−4.02015	−	6.96311i	−0.253750	−	0.439507i	−0.964555	+	0.263881i	$0.914997\pi$
$252$		0			0
$253$	−31.7434	+	18.3271i	−1.99569	+	1.15221i
$254$		0			0
$255$			10.4658i			0.655393i
$256$		0			0
$257$	−8.46634	+	14.6641i	−0.528116	+	0.914723i	0.471347	+	0.881948i	$0.343768\pi$
$257$	−8.46634	+	14.6641i	−0.528116	+	0.914723i	−0.999463	+	0.0327753i	$0.989565\pi$
$258$		0			0
$259$	−0.144306			−0.00896676
$260$		0			0
$261$	−4.92890			−0.305091
$262$		0			0
$263$	5.16045	−	8.93817i	0.318207	−	0.551151i	−0.661907	−	0.749586i	$-0.730253\pi$
$263$	5.16045	−	8.93817i	0.318207	−	0.551151i	0.980114	+	0.198435i	$0.0635859\pi$
$264$		0			0
$265$			1.53041i			0.0940122i
$266$		0			0
$267$	−15.4580	+	8.92468i	−0.946014	+	0.546181i
$268$		0			0
$269$	3.06999	+	5.31738i	0.187181	+	0.324207i	0.944309	−	0.329059i	$-0.106732\pi$
$269$	3.06999	+	5.31738i	0.187181	+	0.324207i	−0.757128	+	0.653266i	$0.773398\pi$
$270$		0			0
$271$	−9.24673	−	5.33860i	−0.561699	−	0.324297i	0.192128	−	0.981370i	$-0.438461\pi$
$271$	−9.24673	−	5.33860i	−0.561699	−	0.324297i	−0.753827	+	0.657073i	$0.771794\pi$
$272$		0			0
$273$	−8.20146	−	0.977882i	−0.496375	−	0.0591841i
$274$		0			0
$275$	15.7256	+	9.07917i	0.948289	+	0.547495i
$276$		0			0
$277$	10.9545	+	18.9737i	0.658191	+	1.14002i	0.981084	+	0.193585i	$0.0620114\pi$
$277$	10.9545	+	18.9737i	0.658191	+	1.14002i	−0.322892	+	0.946436i	$0.604655\pi$
$278$		0			0
$279$	−1.69948	+	0.981193i	−0.101745	+	0.0587425i
$280$		0			0
$281$		−	25.7719i		−	1.53743i	−0.639594	−	0.768713i	$-0.720898\pi$
$281$		−	25.7719i		−	1.53743i	0.639594	−	0.768713i	$-0.279102\pi$
$282$		0			0
$283$	5.66344	−	9.80937i	0.336657	−	0.583107i	−0.647145	−	0.762367i	$-0.724037\pi$
$283$	5.66344	−	9.80937i	0.336657	−	0.583107i	0.983802	+	0.179260i	$0.0573704\pi$
$284$		0			0
$285$	−12.7516			−0.755342
$286$		0			0
$287$	3.99654			0.235908
$288$		0			0
$289$	−4.33177	+	7.50285i	−0.254810	+	0.441344i
$290$		0			0
$291$		−	26.8162i		−	1.57199i
$292$		0			0
$293$	20.5646	−	11.8730i	1.20140	−	0.693626i	0.240530	−	0.970642i	$-0.422679\pi$
$293$	20.5646	−	11.8730i	1.20140	−	0.693626i	0.960865	+	0.277016i	$0.0893454\pi$
$294$		0			0
$295$	3.85506	+	6.67716i	0.224450	+	0.388759i
$296$		0			0
$297$	6.47306	+	3.73723i	0.375605	+	0.216856i
$298$		0			0
$299$	−24.3994	−	18.2527i	−1.41105	−	1.05558i
$300$		0			0
$301$	6.67577	+	3.85426i	0.384785	+	0.222156i
$302$		0			0
$303$	12.3048	+	21.3126i	0.706894	+	1.22438i
$304$		0			0
$305$	6.50930	−	3.75814i	0.372721	−	0.215191i
$306$		0			0
$307$			6.68810i			0.381710i	0.981618	+	0.190855i	$0.0611261\pi$
$307$			6.68810i			0.381710i	−0.981618	+	0.190855i	$0.938874\pi$
$308$		0			0
$309$	−5.51048	+	9.54443i	−0.313480	+	0.542964i
$310$		0			0
$311$	−9.18724			−0.520961			−0.260480	−	0.965479i	$-0.583881\pi$
$311$	−9.18724			−0.520961			−0.260480	+	0.965479i	$0.583881\pi$
$312$		0			0
$313$	−17.1631			−0.970118			−0.485059	−	0.874481i	$-0.661202\pi$
$313$	−17.1631			−0.970118			−0.485059	+	0.874481i	$0.661202\pi$
$314$		0			0
$315$	−1.01353	+	1.75549i	−0.0571061	+	0.0989107i
$316$		0			0
$317$		−	3.76247i		−	0.211322i	−0.994402	−	0.105661i	$-0.966304\pi$
$317$		−	3.76247i		−	0.211322i	0.994402	−	0.105661i	$-0.0336958\pi$
$318$		0			0
$319$	8.23658	−	4.75539i	0.461160	−	0.266251i
$320$		0			0
$321$	−15.6381	−	27.0860i	−0.872833	−	1.51179i
$322$		0			0
$323$	−27.0796	−	15.6344i	−1.50675	−	0.869921i
$324$		0			0
$325$	−1.78720	+	14.9891i	−0.0991358	+	0.831448i
$326$		0			0
$327$	10.1524	+	5.86152i	0.561432	+	0.324143i
$328$		0			0
$329$	−1.46057	−	2.52979i	−0.0805241	−	0.139472i
$330$		0			0
$331$	27.9083	−	16.1129i	1.53398	−	0.885643i	0.534806	−	0.844975i	$-0.320385\pi$
$331$	27.9083	−	16.1129i	1.53398	−	0.885643i	0.999173	−	0.0406683i	$-0.0129487\pi$
$332$		0			0
$333$		−	0.324358i		−	0.0177747i
$334$		0			0
$335$	−4.68182	+	8.10916i	−0.255795	+	0.443051i
$336$		0			0
$337$	−3.01703			−0.164348			−0.0821740	−	0.996618i	$-0.526186\pi$
$337$	−3.01703			−0.164348			−0.0821740	+	0.996618i	$0.526186\pi$
$338$		0			0
$339$	−41.0785			−2.23108
$340$		0			0
$341$	1.89331	−	3.27931i	0.102528	−	0.177584i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$	−15.1203	+	8.72972i	−0.814051	+	0.469993i
$346$		0			0
$347$	0.234270	+	0.405768i	0.0125763	+	0.0217828i	0.872245	−	0.489069i	$-0.162663\pi$
$347$	0.234270	+	0.405768i	0.0125763	+	0.0217828i	−0.859669	+	0.510852i	$0.829330\pi$
$348$		0			0
$349$	−27.9044	−	16.1106i	−1.49369	−	0.862380i	−0.493712	−	0.869625i	$-0.664360\pi$
$349$	−27.9044	−	16.1106i	−1.49369	−	0.862380i	−0.999974	+	0.00724565i	$0.997694\pi$
$350$		0			0
$351$	−0.735656	+	6.16992i	−0.0392664	+	0.329326i
$352$		0			0
$353$	−11.3583	−	6.55771i	−0.604540	−	0.349031i	0.166285	−	0.986078i	$-0.446823\pi$
$353$	−11.3583	−	6.55771i	−0.604540	−	0.349031i	−0.770826	+	0.637046i	$0.780156\pi$
$354$		0			0
$355$	1.47837	+	2.56060i	0.0784635	+	0.135903i
$356$		0			0
$357$	−10.0502	+	5.80247i	−0.531912	+	0.307099i
$358$		0			0
$359$		−	4.37981i		−	0.231157i	−0.993298	−	0.115579i	$-0.963128\pi$
$359$		−	4.37981i		−	0.231157i	0.993298	−	0.115579i	$-0.0368722\pi$
$360$		0			0
$361$	9.54914	−	16.5396i	0.502586	−	0.870505i
$362$		0			0
$363$	17.8933			0.939156
$364$		0			0
$365$	−0.486112			−0.0254443
$366$		0			0
$367$	12.9094	−	22.3597i	0.673865	−	1.16717i	−0.302934	−	0.953011i	$-0.597966\pi$
$367$	12.9094	−	22.3597i	0.673865	−	1.16717i	0.976799	−	0.214157i	$-0.0687004\pi$
$368$		0			0
$369$			8.98303i			0.467638i
$370$		0			0
$371$	−1.46963	+	0.848493i	−0.0762995	+	0.0440515i
$372$		0			0
$373$	−15.3143	−	26.5251i	−0.792942	−	1.37342i	−0.924138	−	0.382059i	$-0.875215\pi$
$373$	−15.3143	−	26.5251i	−0.792942	−	1.37342i	0.131196	−	0.991356i	$-0.458118\pi$
$374$		0			0
$375$	16.4363	+	9.48948i	0.848765	+	0.490035i
$376$		0			0
$377$	6.33100	+	4.73609i	0.326063	+	0.243921i
$378$		0			0
$379$	33.0409	+	19.0762i	1.69720	+	0.979877i	0.948400	+	0.317076i	$0.102701\pi$
$379$	33.0409	+	19.0762i	1.69720	+	0.979877i	0.748796	+	0.662801i	$0.230632\pi$
$380$		0			0
$381$	−22.3508	−	38.7127i	−1.14507	−	1.98331i
$382$		0			0
$383$	27.6783	−	15.9801i	1.41430	−	0.816544i	0.418507	−	0.908214i	$-0.362554\pi$
$383$	27.6783	−	15.9801i	1.41430	−	0.816544i	0.995790	+	0.0916693i	$0.0292203\pi$
$384$		0			0
$385$		−	3.91142i		−	0.199345i
$386$		0			0
$387$	−8.66323	+	15.0051i	−0.440377	+	0.762754i
$388$		0			0
$389$	5.24585			0.265975			0.132988	−	0.991118i	$-0.457543\pi$
$389$	5.24585			0.265975			0.132988	+	0.991118i	$0.457543\pi$
$390$		0			0
$391$	−42.8130			−2.16514
$392$		0			0
$393$	23.6520	−	40.9664i	1.19308	−	2.06648i
$394$		0			0
$395$		−	5.89215i		−	0.296466i
$396$		0			0
$397$	21.2432	−	12.2648i	1.06617	−	0.615552i	0.139035	−	0.990287i	$-0.455600\pi$
$397$	21.2432	−	12.2648i	1.06617	−	0.615552i	0.927132	+	0.374736i	$0.122266\pi$
$398$		0			0
$399$	−7.06980	−	12.2453i	−0.353933	−	0.613030i
$400$		0			0
$401$	3.69916	+	2.13571i	0.184727	+	0.106652i	0.589512	−	0.807760i	$-0.299320\pi$
$401$	3.69916	+	2.13571i	0.184727	+	0.106652i	−0.404784	+	0.914412i	$0.632653\pi$
$402$		0			0
$403$	3.12573	+	0.372689i	0.155704	+	0.0185650i
$404$		0			0
$405$	8.34979	+	4.82075i	0.414904	+	0.239545i
$406$		0			0
$407$	0.312940	+	0.542028i	0.0155119	+	0.0268673i
$408$		0			0
$409$	−1.39990	+	0.808235i	−0.0692208	+	0.0399646i	−0.534211	−	0.845351i	$-0.679391\pi$
$409$	−1.39990	+	0.808235i	−0.0692208	+	0.0399646i	0.464990	+	0.885316i	$0.346058\pi$
$410$		0			0
$411$		−	7.30661i		−	0.360408i
$412$		0			0
$413$	−4.27467	+	7.40394i	−0.210343	+	0.364324i
$414$		0			0
$415$	−11.9357			−0.585900
$416$		0			0
$417$	−1.36464			−0.0668269
$418$		0			0
$419$	−13.0156	+	22.5437i	−0.635854	+	1.10133i	0.350480	+	0.936570i	$0.386018\pi$
$419$	−13.0156	+	22.5437i	−0.635854	+	1.10133i	−0.986334	+	0.164761i	$0.947315\pi$
$420$		0			0
$421$			37.5391i			1.82954i	0.403971	+	0.914772i	$0.367630\pi$
$421$			37.5391i			1.82954i	−0.403971	+	0.914772i	$0.632370\pi$
$422$		0			0
$423$	5.68622	−	3.28294i	0.276473	−	0.159622i
$424$		0			0
$425$	10.6047	+	18.3679i	0.514404	+	0.890974i
$426$		0			0
$427$	7.21780	+	4.16720i	0.349294	+	0.201665i
$428$		0			0
$429$	14.1125	+	32.9261i	0.681359	+	1.58969i
$430$		0			0
$431$	−18.6662	−	10.7769i	−0.899118	−	0.519106i	−0.0222041	−	0.999753i	$-0.507068\pi$
$431$	−18.6662	−	10.7769i	−0.899118	−	0.519106i	−0.876914	+	0.480647i	$0.840402\pi$
$432$		0			0
$433$	1.59958	+	2.77056i	0.0768710	+	0.133145i	0.901898	−	0.431948i	$-0.142174\pi$
$433$	1.59958	+	2.77056i	0.0768710	+	0.133145i	−0.825027	+	0.565093i	$0.808840\pi$
$434$		0			0
$435$	3.92333	−	2.26513i	0.188109	−	0.108605i
$436$		0			0
$437$		−	52.1638i		−	2.49534i
$438$		0			0
$439$	−13.3114	+	23.0560i	−0.635317	+	1.10040i	0.351131	+	0.936326i	$0.385797\pi$
$439$	−13.3114	+	23.0560i	−0.635317	+	1.10040i	−0.986448	+	0.164075i	$0.947536\pi$
$440$		0			0
$441$	−2.24770			−0.107034
$442$		0			0
$443$	−9.09867			−0.432291			−0.216145	−	0.976361i	$-0.569348\pi$
$443$	−9.09867			−0.432291			−0.216145	+	0.976361i	$0.569348\pi$
$444$		0			0
$445$	3.51347	−	6.08551i	0.166555	−	0.288481i
$446$		0			0
$447$		−	25.6789i		−	1.21457i
$448$		0			0
$449$	6.08550	−	3.51346i	0.287192	−	0.165811i	−0.349483	−	0.936943i	$-0.613643\pi$
$449$	6.08550	−	3.51346i	0.287192	−	0.165811i	0.636675	+	0.771132i	$0.280309\pi$
$450$		0			0
$451$	−8.66681	−	15.0114i	−0.408104	−	0.706858i
$452$		0			0
$453$	25.9354	+	14.9738i	1.21855	+	0.703531i
$454$		0			0
$455$	2.98867	−	1.28098i	0.140111	−	0.0600533i
$456$		0			0
$457$	−16.5853	−	9.57556i	−0.775830	−	0.447926i	0.0591204	−	0.998251i	$-0.481170\pi$
$457$	−16.5853	−	9.57556i	−0.775830	−	0.447926i	−0.834950	+	0.550325i	$0.814504\pi$
$458$		0			0
$459$	4.36518	+	7.56071i	0.203749	+	0.352904i
$460$		0			0
$461$	−2.82026	+	1.62828i	−0.131353	+	0.0758365i	−0.564236	−	0.825613i	$-0.690829\pi$
$461$	−2.82026	+	1.62828i	−0.131353	+	0.0758365i	0.432884	+	0.901450i	$0.357496\pi$
$462$		0			0
$463$		−	21.2761i		−	0.988786i	−0.869238	−	0.494393i	$-0.835390\pi$
$463$		−	21.2761i		−	0.988786i	0.869238	−	0.494393i	$-0.164610\pi$
$464$		0			0
$465$	0.901839	−	1.56203i	0.0418218	−	0.0724374i
$466$		0			0
$467$	3.33171			0.154173			0.0770866	−	0.997024i	$-0.475438\pi$
$467$	3.33171			0.154173			0.0770866	+	0.997024i	$0.475438\pi$
$468$		0			0
$469$	−10.3828			−0.479435
$470$		0			0
$471$	20.5306	−	35.5601i	0.946001	−	1.63852i
$472$		0			0
$473$		−	33.4331i		−	1.53725i
$474$		0			0
$475$	−22.3797	+	12.9209i	−1.02685	+	0.592852i
$476$		0			0
$477$	−1.90716	−	3.30330i	−0.0873229	−	0.151248i
$478$		0			0
$479$	0.160402	+	0.0926079i	0.00732894	+	0.00423136i	0.503660	−	0.863902i	$-0.331986\pi$
$479$	0.160402	+	0.0926079i	0.00732894	+	0.00423136i	−0.496331	+	0.868133i	$0.665320\pi$
$480$		0			0
$481$	−0.311670	+	0.416627i	−0.0142109	+	0.0189965i
$482$		0			0
$483$	−16.7661	−	9.67992i	−0.762884	−	0.440451i
$484$		0			0
$485$	5.27851	+	9.14264i	0.239685	+	0.415146i
$486$		0			0
$487$	27.0466	−	15.6154i	1.22560	−	0.707601i	0.259494	−	0.965745i	$-0.416444\pi$
$487$	27.0466	−	15.6154i	1.22560	−	0.707601i	0.966106	+	0.258144i	$0.0831110\pi$
$488$		0			0
$489$			46.5440i			2.10479i
$490$		0			0
$491$	−13.4236	+	23.2504i	−0.605799	+	1.04927i	0.386126	+	0.922446i	$0.373813\pi$
$491$	−13.4236	+	23.2504i	−0.605799	+	1.04927i	−0.991925	+	0.126829i	$0.959520\pi$
$492$		0			0
$493$	11.1088			0.500317
$494$		0			0
$495$	8.79172			0.395158
$496$		0			0
$497$	−1.63928	+	2.83932i	−0.0735317	+	0.127361i
$498$		0			0
$499$			15.2869i			0.684337i	0.939639	+	0.342168i	$0.111161\pi$
$499$			15.2869i			0.684337i	−0.939639	+	0.342168i	$0.888839\pi$
$500$		0			0
$501$	6.40893	−	3.70020i	0.286330	−	0.165313i
$502$		0			0
$503$	−13.0551	−	22.6121i	−0.582097	−	1.00822i	−0.995230	−	0.0975513i	$-0.968899\pi$
$503$	−13.0551	−	22.6121i	−0.582097	−	1.00822i	0.413133	−	0.910671i	$-0.364434\pi$
$504$		0			0
$505$	−8.39036	−	4.84418i	−0.373366	−	0.215563i
$506$		0			0
$507$	−20.5366	+	21.5664i	−0.912062	+	0.957798i
$508$		0			0
$509$	14.7459	+	8.51357i	0.653602	+	0.377357i	0.789835	−	0.613320i	$-0.210166\pi$
$509$	14.7459	+	8.51357i	0.653602	+	0.377357i	−0.136233	+	0.990677i	$0.543500\pi$
$510$		0			0
$511$	−0.269511	−	0.466808i	−0.0119225	−	0.0206504i
$512$		0			0
$513$	−9.21206	+	5.31858i	−0.406722	+	0.234821i
$514$		0			0
$515$		−	4.33874i		−	0.191188i
$516$		0			0
$517$	−6.33475	+	10.9721i	−0.278602	+	0.482553i
$518$		0			0
$519$	−21.0075			−0.922128
$520$		0			0
$521$	−18.7760			−0.822593			−0.411297	−	0.911502i	$-0.634924\pi$
$521$	−18.7760			−0.822593			−0.411297	+	0.911502i	$0.634924\pi$
$522$		0			0
$523$	−1.51624	+	2.62620i	−0.0663004	+	0.114836i	−0.897270	−	0.441482i	$-0.854453\pi$
$523$	−1.51624	+	2.62620i	−0.0663004	+	0.114836i	0.830970	+	0.556318i	$0.187786\pi$
$524$		0			0
$525$			9.59081i			0.418577i
$526$		0			0
$527$	3.83031	−	2.21143i	0.166851	−	0.0963315i
$528$		0			0
$529$	−24.2111	−	41.9349i	−1.05266	−	1.82326i
$530$		0			0
$531$	−16.6419	−	9.60818i	−0.722195	−	0.416960i
$532$		0			0
$533$	8.63164	−	11.5384i	0.373878	−	0.499783i
$534$		0			0
$535$	10.6632	+	6.15642i	0.461011	+	0.266165i
$536$		0			0
$537$	−19.4201	−	33.6366i	−0.838038	−	1.45153i
$538$		0			0
$539$	3.75609	−	2.16858i	0.161786	−	0.0934074i
$540$		0			0
$541$			6.11845i			0.263053i	0.991313	+	0.131526i	$0.0419878\pi$
$541$			6.11845i			0.263053i	−0.991313	+	0.131526i	$0.958012\pi$
$542$		0			0
$543$	−3.04380	+	5.27202i	−0.130622	+	0.226244i
$544$		0			0
$545$	−4.61513			−0.197691
$546$		0			0
$547$	37.4754			1.60233			0.801166	−	0.598442i	$-0.204214\pi$
$547$	37.4754			1.60233			0.801166	+	0.598442i	$0.204214\pi$
$548$		0			0
$549$	−9.36663	+	16.2235i	−0.399758	+	0.692402i
$550$		0			0
$551$			13.5352i			0.576617i
$552$		0			0
$553$	5.65817	−	3.26674i	0.240610	−	0.138916i
$554$		0			0
$555$	0.149063	+	0.258184i	0.00632736	+	0.0109593i
$556$		0			0
$557$	−7.69941	−	4.44526i	−0.326234	−	0.188352i	0.327934	−	0.944701i	$-0.393648\pi$
$557$	−7.69941	−	4.44526i	−0.326234	−	0.188352i	−0.654168	+	0.756349i	$0.726981\pi$
$558$		0			0
$559$	25.5458	−	10.9493i	1.08047	−	0.463104i
$560$		0			0
$561$	43.5893	+	25.1663i	1.84034	+	1.06252i
$562$		0			0
$563$	−8.89598	−	15.4083i	−0.374921	−	0.649382i	0.615394	−	0.788219i	$-0.288997\pi$
$563$	−8.89598	−	15.4083i	−0.374921	−	0.649382i	−0.990315	+	0.138838i	$0.955663\pi$
$564$		0			0
$565$	14.0052	−	8.08591i	0.589204	−	0.340177i
$566$		0			0
$567$			10.6909i			0.448977i
$568$		0			0
$569$	5.58684	−	9.67669i	0.234212	−	0.405668i	−0.724831	−	0.688927i	$-0.758082\pi$
$569$	5.58684	−	9.67669i	0.234212	−	0.405668i	0.959044	+	0.283259i	$0.0914155\pi$
$570$		0			0
$571$	16.7239			0.699873			0.349936	−	0.936773i	$-0.386203\pi$
$571$	16.7239			0.699873			0.349936	+	0.936773i	$0.386203\pi$
$572$		0			0
$573$	−56.0924			−2.34329
$574$		0			0
$575$	−17.6912	+	30.6421i	−0.737774	+	1.27786i
$576$		0			0
$577$			0.798887i			0.0332581i	0.999862	+	0.0166291i	$0.00529344\pi$
$577$			0.798887i			0.0332581i	−0.999862	+	0.0166291i	$0.994707\pi$
$578$		0			0
$579$	24.2845	−	14.0207i	1.00923	−	0.582679i
$580$		0			0
$581$	−6.61742	−	11.4617i	−0.274537	−	0.475512i
$582$		0			0
$583$	6.37404	+	3.68005i	0.263986	+	0.152412i
$584$		0			0
$585$	2.87927	+	6.71765i	0.119043	+	0.277741i
$586$		0			0
$587$	−6.94921	−	4.01213i	−0.286825	−	0.165598i	0.349684	−	0.936868i	$-0.386289\pi$
$587$	−6.94921	−	4.01213i	−0.286825	−	0.165598i	−0.636509	+	0.771269i	$0.719622\pi$
$588$		0			0
$589$	2.69444	+	4.66690i	0.111022	+	0.192296i
$590$		0			0
$591$	10.8270	−	6.25100i	0.445365	−	0.257132i
$592$		0			0
$593$		−	4.93120i		−	0.202500i	−0.994861	−	0.101250i	$-0.967716\pi$
$593$		−	4.93120i		−	0.202500i	0.994861	−	0.101250i	$-0.0322842\pi$
$594$		0			0
$595$	2.28432	−	3.95656i	0.0936481	−	0.162203i
$596$		0			0
$597$	29.3602			1.20163
$598$		0			0
$599$	17.8249			0.728306			0.364153	−	0.931339i	$-0.381358\pi$
$599$	17.8249			0.728306			0.364153	+	0.931339i	$0.381358\pi$
$600$		0			0
$601$	0.0809165	−	0.140152i	0.00330065	−	0.00571690i	−0.864370	−	0.502856i	$-0.832283\pi$
$601$	0.0809165	−	0.140152i	0.00330065	−	0.00571690i	0.867671	+	0.497139i	$0.165616\pi$
$602$		0			0
$603$		−	23.3375i		−	0.950378i
$604$		0			0
$605$	−6.10050	+	3.52213i	−0.248021	+	0.143195i
$606$		0			0
$607$	3.09423	+	5.35937i	0.125591	+	0.217530i	0.921964	−	0.387276i	$-0.126584\pi$
$607$	3.09423	+	5.35937i	0.125591	+	0.217530i	−0.796373	+	0.604806i	$0.793251\pi$
$608$		0			0
$609$	4.35037	+	2.51168i	0.176286	+	0.101779i
$610$		0			0
$611$	−10.4583	−	1.24697i	−0.423097	−	0.0504469i
$612$		0			0
$613$	32.2269	+	18.6062i	1.30163	+	0.751497i	0.980684	−	0.195600i	$-0.0626654\pi$
$613$	32.2269	+	18.6062i	1.30163	+	0.751497i	0.320947	+	0.947097i	$0.395999\pi$
$614$		0			0
$615$	−4.12826	−	7.15036i	−0.166468	−	0.288330i
$616$		0			0
$617$	−5.78536	+	3.34018i	−0.232910	+	0.134471i	−0.611914	−	0.790924i	$-0.709600\pi$
$617$	−5.78536	+	3.34018i	−0.232910	+	0.134471i	0.379004	+	0.925395i	$0.376267\pi$
$618$		0			0
$619$			23.7344i			0.953965i	0.878913	+	0.476982i	$0.158269\pi$
$619$			23.7344i			0.953965i	−0.878913	+	0.476982i	$0.841731\pi$
$620$		0			0
$621$	−7.28216	+	12.6131i	−0.292223	+	0.506145i
$622$		0			0
$623$	7.79180			0.312172
$624$		0			0
$625$	13.4618			0.538471
$626$		0			0
$627$	−30.6629	+	53.1097i	−1.22456	+	2.12100i
$628$		0			0
$629$			0.731044i			0.0291486i
$630$		0			0
$631$	−19.9348	+	11.5093i	−0.793590	+	0.458180i	−0.841225	−	0.540685i	$-0.818165\pi$
$631$	−19.9348	+	11.5093i	−0.793590	+	0.458180i	0.0476346	+	0.998865i	$0.484832\pi$
$632$		0			0
$633$	22.1187	+	38.3108i	0.879141	+	1.52272i
$634$		0			0
$635$	15.2404	+	8.79907i	0.604798	+	0.349181i
$636$		0			0
$637$	2.88710	+	2.15978i	0.114391	+	0.0855737i
$638$		0			0
$639$	−6.38194	−	3.68461i	−0.252466	−	0.145761i
$640$		0			0
$641$	6.32539	+	10.9559i	0.249838	+	0.432732i	0.963481	−	0.267778i	$-0.0862893\pi$
$641$	6.32539	+	10.9559i	0.249838	+	0.432732i	−0.713643	+	0.700510i	$0.752956\pi$
$642$		0			0
$643$	13.1971	−	7.61938i	0.520445	−	0.300479i	−0.216672	−	0.976244i	$-0.569520\pi$
$643$	13.1971	−	7.61938i	0.520445	−	0.300479i	0.737117	+	0.675766i	$0.236187\pi$
$644$		0			0
$645$		−	15.9252i		−	0.627053i
$646$		0			0
$647$	14.6821	−	25.4301i	0.577213	−	0.999762i	−0.418585	−	0.908178i	$-0.637474\pi$
$647$	14.6821	−	25.4301i	0.577213	−	0.999762i	0.995797	−	0.0915840i	$-0.0291930\pi$
$648$		0			0
$649$	37.0799			1.45551
$650$		0			0
$651$	2.00000			0.0783862
$652$		0			0
$653$	14.5106	−	25.1330i	0.567842	−	0.983532i	−0.428937	−	0.903335i	$-0.641112\pi$
$653$	14.5106	−	25.1330i	0.567842	−	0.983532i	0.996779	−	0.0801974i	$-0.0255551\pi$
$654$		0			0
$655$			18.6226i			0.727647i
$656$		0			0
$657$	1.04925	−	0.605782i	0.0409350	−	0.0236338i
$658$		0			0
$659$	3.98651	+	6.90484i	0.155293	+	0.268975i	0.933166	−	0.359447i	$-0.117035\pi$
$659$	3.98651	+	6.90484i	0.155293	+	0.268975i	−0.777873	+	0.628422i	$0.783701\pi$
$660$		0			0
$661$	3.40668	+	1.96685i	0.132505	+	0.0765015i	0.564787	−	0.825237i	$-0.308958\pi$
$661$	3.40668	+	1.96685i	0.132505	+	0.0765015i	−0.432282	+	0.901738i	$0.642292\pi$
$662$		0			0
$663$	−4.95387	+	41.5479i	−0.192392	+	1.61359i
$664$		0			0
$665$	4.82072	+	2.78325i	0.186940	+	0.107930i
$666$		0			0
$667$	9.26611	+	16.0494i	0.358785	+	0.621434i
$668$		0			0
$669$	21.1000	−	12.1821i	0.815772	−	0.470986i
$670$		0			0
$671$		−	36.1477i		−	1.39547i
$672$		0			0
$673$	18.1599	−	31.4539i	0.700014	−	1.21246i	−0.268447	−	0.963295i	$-0.586510\pi$
$673$	18.1599	−	31.4539i	0.700014	−	1.21246i	0.968461	−	0.249166i	$-0.0801563\pi$
$674$		0			0
$675$	7.21513			0.277710
$676$		0			0
$677$	−21.1068			−0.811201			−0.405600	−	0.914051i	$-0.632938\pi$
$677$	−21.1068			−0.811201			−0.405600	+	0.914051i	$0.632938\pi$
$678$		0			0
$679$	−5.85305	+	10.1378i	−0.224619	+	0.389052i
$680$		0			0
$681$			52.0506i			1.99458i
$682$		0			0
$683$	22.8854	−	13.2129i	0.875685	−	0.505577i	0.00645161	−	0.999979i	$-0.497946\pi$
$683$	22.8854	−	13.2129i	0.875685	−	0.505577i	0.869233	+	0.494402i	$0.164613\pi$
$684$		0			0
$685$	1.43824	+	2.49110i	0.0549522	+	0.0951799i
$686$		0			0
$687$	40.2914	+	23.2623i	1.53721	+	0.887511i
$688$		0			0
$689$	−0.724402	+	6.07553i	−0.0275975	+	0.231459i
$690$		0			0
$691$	−0.675291	−	0.389880i	−0.0256893	−	0.0148317i	0.487100	−	0.873346i	$-0.338055\pi$
$691$	−0.675291	−	0.389880i	−0.0256893	−	0.0148317i	−0.512790	+	0.858514i	$0.671388\pi$
$692$		0			0
$693$	4.87433	+	8.44259i	0.185161	+	0.320707i
$694$		0			0
$695$	0.465259	−	0.268617i	0.0176483	−	0.0101892i
$696$		0			0
$697$		−	20.2461i		−	0.766877i
$698$		0			0
$699$	12.1923	−	21.1176i	0.461154	−	0.798742i
$700$		0			0
$701$	21.5491			0.813899			0.406950	−	0.913451i	$-0.366592\pi$
$701$	21.5491			0.813899			0.406950	+	0.913451i	$0.366592\pi$
$702$		0			0
$703$	−0.890713			−0.0335939
$704$		0			0
$705$	−3.01743	+	5.22634i	−0.113643	+	0.196835i
$706$		0			0
$707$		−	10.7429i		−	0.404028i
$708$		0			0
$709$	−3.92952	+	2.26871i	−0.147576	+	0.0852031i	−0.571970	−	0.820275i	$-0.693821\pi$
$709$	−3.92952	+	2.26871i	−0.147576	+	0.0852031i	0.424394	+	0.905478i	$0.360487\pi$
$710$		0			0
$711$	7.34267	+	12.7179i	0.275372	+	0.476958i
$712$		0			0
$713$	6.38988	+	3.68920i	0.239303	+	0.138162i
$714$		0			0
$715$	−11.2927	−	8.44782i	−0.422322	−	0.315931i
$716$		0			0
$717$	0.618106	+	0.356863i	0.0230836	+	0.0133273i
$718$		0			0
$719$	7.30036	+	12.6446i	0.272258	+	0.471564i	0.969440	−	0.245330i	$-0.0788964\pi$
$719$	7.30036	+	12.6446i	0.272258	+	0.471564i	−0.697182	+	0.716894i	$0.745563\pi$
$720$		0			0
$721$	4.16644	−	2.40550i	0.155166	−	0.0895854i
$722$		0			0
$723$			57.9558i			2.15540i
$724$		0			0
$725$	4.59040	−	7.95081i	0.170483	−	0.295286i
$726$		0			0
$727$	−30.6315			−1.13606			−0.568030	−	0.823008i	$-0.692294\pi$
$727$	−30.6315			−1.13606			−0.568030	+	0.823008i	$0.692294\pi$
$728$		0			0
$729$	−12.1866			−0.451355
$730$		0			0
$731$	19.5254	−	33.8189i	0.722171	−	1.25084i
$732$		0			0
$733$			17.7195i			0.654484i	0.944941	+	0.327242i	$0.106119\pi$
$733$			17.7195i			0.654484i	−0.944941	+	0.327242i	$0.893881\pi$
$734$		0			0
$735$	1.78914	−	1.03296i	0.0659934	−	0.0381013i
$736$		0			0
$737$	22.5160	+	38.9989i	0.829389	+	1.43654i
$738$		0			0
$739$	9.05014	+	5.22510i	0.332915	+	0.192208i	0.657134	−	0.753773i	$-0.271768\pi$
$739$	9.05014	+	5.22510i	0.332915	+	0.192208i	−0.324220	+	0.945982i	$0.605102\pi$
$740$		0			0
$741$	−50.6225	−	6.03586i	−1.85966	−	0.221733i
$742$		0			0
$743$	−42.0103	−	24.2547i	−1.54121	−	0.889818i	−0.998763	−	0.0497278i	$-0.984165\pi$
$743$	−42.0103	−	24.2547i	−1.54121	−	0.889818i	−0.542447	−	0.840090i	$-0.682502\pi$
$744$		0			0
$745$	5.05464	+	8.75490i	0.185188	+	0.320755i
$746$		0			0
$747$	25.7625	−	14.8740i	0.942601	−	0.544211i
$748$		0			0
$749$			13.6530i			0.498871i
$750$		0			0
$751$	−15.7278	+	27.2413i	−0.573914	+	0.994049i	0.422244	+	0.906482i	$0.361242\pi$
$751$	−15.7278	+	27.2413i	−0.573914	+	0.994049i	−0.996159	+	0.0875667i	$0.972091\pi$
$752$		0			0
$753$	−18.4186			−0.671212
$754$		0			0
$755$	−11.7898			−0.429075
$756$		0			0
$757$	−24.3442	+	42.1654i	−0.884805	+	1.53253i	−0.0388676	+	0.999244i	$0.512375\pi$
$757$	−24.3442	+	42.1654i	−0.884805	+	1.53253i	−0.845937	+	0.533283i	$0.820958\pi$
$758$		0			0
$759$			83.9668i			3.04780i
$760$		0			0
$761$	−40.3350	+	23.2874i	−1.46214	+	0.844169i	−0.999110	−	0.0421718i	$-0.986572\pi$
$761$	−40.3350	+	23.2874i	−1.46214	+	0.844169i	−0.463033	+	0.886341i	$0.653239\pi$
$762$		0			0
$763$	−2.55874	−	4.43186i	−0.0926325	−	0.160444i
$764$		0			0
$765$	8.89318	+	5.13448i	0.321534	+	0.185637i
$766$		0			0
$767$	12.1436	+	28.3323i	0.438479	+	1.02302i
$768$		0			0
$769$	−24.1069	−	13.9181i	−0.869315	−	0.501899i	−0.00219468	−	0.999998i	$-0.500699\pi$
$769$	−24.1069	−	13.9181i	−0.869315	−	0.501899i	−0.867121	+	0.498098i	$0.834032\pi$
$770$		0			0
$771$	19.3946	+	33.5924i	0.698479	+	1.20980i
$772$		0			0
$773$	24.6578	−	14.2362i	0.886880	−	0.512040i	0.0139594	−	0.999903i	$-0.495556\pi$
$773$	24.6578	−	14.2362i	0.886880	−	0.512040i	0.872921	+	0.487862i	$0.162223\pi$
$774$		0			0
$775$		−	3.65524i		−	0.131300i
$776$		0			0
$777$	−0.165287	+	0.286286i	−0.00592965	+	0.0102705i
$778$		0			0
$779$	24.6681			0.883828
$780$		0			0
$781$	14.2196			0.508819
$782$		0			0
$783$	1.88953	−	3.27276i	0.0675263	−	0.116959i
$784$		0			0
$785$			16.1650i			0.576954i
$786$		0			0
$787$	−13.1046	+	7.56594i	−0.467128	+	0.269697i	−0.715037	−	0.699087i	$-0.753590\pi$
$787$	−13.1046	+	7.56594i	−0.467128	+	0.269697i	0.247908	+	0.968783i	$0.420257\pi$
$788$		0			0
$789$	−11.8215	−	20.4754i	−0.420856	−	0.728945i
$790$		0			0
$791$	15.5296	+	8.96603i	0.552170	+	0.318795i
$792$		0			0
$793$	27.6200	−	11.8383i	0.980815	−	0.420389i
$794$		0			0
$795$	3.03614	+	1.75292i	0.107681	+	0.0621696i
$796$		0			0
$797$	6.97234	+	12.0764i	0.246973	+	0.427770i	0.962684	−	0.270626i	$-0.0872308\pi$
$797$	6.97234	+	12.0764i	0.246973	+	0.427770i	−0.715712	+	0.698396i	$0.753897\pi$
$798$		0			0
$799$	−12.8157	+	7.39916i	−0.453387	+	0.261763i
$800$		0			0
$801$			17.5137i			0.618815i
$802$		0			0
$803$	−1.16892	+	2.02462i	−0.0412501	+	0.0714473i
$804$		0			0
$805$	7.62159			0.268626
$806$		0			0
$807$	14.0654			0.495125
$808$		0			0
$809$	10.8714	−	18.8299i	0.382220	−	0.662024i	−0.609159	−	0.793048i	$-0.708493\pi$
$809$	10.8714	−	18.8299i	0.382220	−	0.662024i	0.991379	+	0.131024i	$0.0418264\pi$
$810$		0			0
$811$		−	21.1256i		−	0.741819i	−0.928669	−	0.370910i	$-0.879046\pi$
$811$		−	21.1256i		−	0.741819i	0.928669	−	0.370910i	$-0.120954\pi$
$812$		0			0
$813$	−21.1823	+	12.2296i	−0.742895	+	0.428911i
$814$		0			0
$815$	−9.16173	−	15.8686i	−0.320921	−	0.555852i
$816$		0			0
$817$	41.2054	+	23.7899i	1.44159	+	0.832304i
$818$		0			0
$819$	−4.85455	+	6.48935i	−0.169632	+	0.226756i
$820$		0			0
$821$	−14.0933	−	8.13678i	−0.491860	−	0.283976i	0.233486	−	0.972360i	$-0.424987\pi$
$821$	−14.0933	−	8.13678i	−0.491860	−	0.283976i	−0.725346	+	0.688385i	$0.758320\pi$
$822$		0			0
$823$	−9.32713	−	16.1551i	−0.325123	−	0.563130i	0.656414	−	0.754401i	$-0.272072\pi$
$823$	−9.32713	−	16.1551i	−0.325123	−	0.563130i	−0.981537	+	0.191271i	$0.938739\pi$
$824$		0			0
$825$	36.0240	−	20.7985i	1.25419	−	0.724109i
$826$		0			0
$827$		−	47.3361i		−	1.64604i	−0.568015	−	0.823018i	$-0.692288\pi$
$827$		−	47.3361i		−	1.64604i	0.568015	−	0.823018i	$-0.307712\pi$
$828$		0			0
$829$	0.460988	−	0.798454i	0.0160108	−	0.0277315i	−0.857909	−	0.513802i	$-0.828237\pi$
$829$	0.460988	−	0.798454i	0.0160108	−	0.0277315i	0.873920	+	0.486070i	$0.161570\pi$
$830$		0			0
$831$	50.1888			1.74103
$832$		0			0
$833$	5.06592			0.175524
$834$		0			0
$835$	−1.45670	+	2.52307i	−0.0504111	+	0.0873146i
$836$		0			0
$837$		−	1.50459i		−	0.0520063i
$838$		0			0
$839$	14.3894	−	8.30775i	0.496779	−	0.286815i	−0.230604	−	0.973048i	$-0.574070\pi$
$839$	14.3894	−	8.30775i	0.496779	−	0.286815i	0.727382	+	0.686232i	$0.240737\pi$
$840$		0			0
$841$	12.0957	+	20.9503i	0.417093	+	0.722426i
$842$		0			0
$843$	−51.1284	−	29.5190i	−1.76096	−	1.01669i
$844$		0			0
$845$	2.75656	−	11.3952i	0.0948284	−	0.392008i
$846$		0			0
$847$	−6.76452	−	3.90550i	−0.232432	−	0.134194i
$848$		0			0
$849$	−12.9737	−	22.4712i	−0.445258	−	0.771209i
$850$		0			0
$851$	−1.05617	+	0.609779i	−0.0362050	+	0.0209029i
$852$		0			0
$853$		−	26.3277i		−	0.901445i	−0.892664	−	0.450722i	$-0.851166\pi$
$853$		−	26.3277i		−	0.901445i	0.892664	−	0.450722i	$-0.148834\pi$
$854$		0			0
$855$	−6.25591	+	10.8356i	−0.213948	+	0.370568i
$856$		0			0
$857$	14.1058			0.481845			0.240923	−	0.970544i	$-0.422550\pi$
$857$	14.1058			0.481845			0.240923	+	0.970544i	$0.422550\pi$
$858$		0			0
$859$	−23.4719			−0.800850			−0.400425	−	0.916329i	$-0.631138\pi$
$859$	−23.4719			−0.800850			−0.400425	+	0.916329i	$0.631138\pi$
$860$		0			0
$861$	4.57761	−	7.92864i	0.156004	−	0.270207i
$862$		0			0
$863$		−	11.9484i		−	0.406727i	−0.979103	−	0.203364i	$-0.934813\pi$
$863$		−	11.9484i		−	0.406727i	0.979103	−	0.203364i	$-0.0651874\pi$
$864$		0			0
$865$	7.16225	−	4.13513i	0.243524	−	0.140599i
$866$		0			0
$867$	9.92317	+	17.1874i	0.337009	+	0.583716i
$868$		0			0
$869$	−24.5404	−	14.1684i	−0.832476	−	0.480630i
$870$		0			0
$871$	−22.4247	+	29.9763i	−0.759831	+	1.01571i
$872$		0			0
$873$	−22.7867	−	13.1559i	−0.771214	−	0.445261i
$874$		0			0
$875$	−4.14246	−	7.17494i	−0.140041	−	0.242557i
$876$		0			0
$877$	−28.3486	+	16.3671i	−0.957264	+	0.552677i	−0.895330	−	0.445403i	$-0.853060\pi$
$877$	−28.3486	+	16.3671i	−0.957264	+	0.552677i	−0.0619342	+	0.998080i	$0.519727\pi$
$878$		0			0
$879$		−	54.3969i		−	1.83476i
$880$		0			0
$881$	−5.29540	+	9.17190i	−0.178407	+	0.309009i	−0.941335	−	0.337474i	$-0.890428\pi$
$881$	−5.29540	+	9.17190i	−0.178407	+	0.309009i	0.762928	+	0.646483i	$0.223761\pi$
$882$		0			0
$883$	38.6713			1.30139			0.650696	−	0.759338i	$-0.274477\pi$
$883$	38.6713			1.30139			0.650696	+	0.759338i	$0.274477\pi$
$884$		0			0
$885$	17.6622			0.593710
$886$		0			0
$887$	2.36082	−	4.08906i	0.0792685	−	0.137297i	−0.823666	−	0.567075i	$-0.808075\pi$
$887$	2.36082	−	4.08906i	0.0792685	−	0.137297i	0.902935	+	0.429778i	$0.141408\pi$
$888$		0			0
$889$			19.5136i			0.654466i
$890$		0			0
$891$	40.1562	−	23.1842i	1.34528	−	0.776699i
$892$		0			0
$893$	−9.01522	−	15.6148i	−0.301683	−	0.522530i
$894$		0			0
$895$	13.2421	+	7.64531i	0.442634	+	0.255555i
$896$		0			0
$897$	−64.1580	+	27.4989i	−2.14217	+	0.918162i
$898$		0			0
$899$	−1.65801	−	0.957251i	−0.0552976	−	0.0319261i
$900$		0			0
$901$	4.29840	+	7.44504i	0.143200	+	0.248030i
$902$		0			0
$903$	15.2928	−	8.82928i	0.508911	−	0.293820i
$904$		0			0
$905$		−	2.39657i		−	0.0796648i
$906$		0			0
$907$	20.9654	−	36.3132i	0.696146	−	1.20576i	−0.273646	−	0.961830i	$-0.588230\pi$
$907$	20.9654	−	36.3132i	0.696146	−	1.20576i	0.969793	−	0.243930i	$-0.0784368\pi$
$908$		0			0
$909$	24.1468			0.800900
$910$		0			0
$911$	54.1425			1.79382			0.896910	−	0.442213i	$-0.145806\pi$
$911$	54.1425			1.79382			0.896910	+	0.442213i	$0.145806\pi$
$912$		0			0
$913$	−28.7008	+	49.7113i	−0.949859	+	1.64520i
$914$		0			0
$915$		−	17.2182i		−	0.569216i
$916$		0			0
$917$	−17.8831	+	10.3248i	−0.590552	+	0.340956i
$918$		0			0
$919$	−12.9117	−	22.3636i	−0.425916	−	0.737708i	0.570589	−	0.821236i	$-0.306715\pi$
$919$	−12.9117	−	22.3636i	−0.425916	−	0.737708i	−0.996506	+	0.0835271i	$0.973381\pi$
$920$		0			0
$921$	13.2684	+	7.66051i	0.437208	+	0.252422i
$922$		0			0
$923$	4.65690	+	10.8651i	0.153284	+	0.357628i
$924$		0			0
$925$	0.523222	+	0.302083i	0.0172034	+	0.00993241i
$926$		0			0
$927$	5.40684	+	9.36493i	0.177584	+	0.307585i
$928$		0			0
$929$	13.8843	−	8.01610i	0.455529	−	0.263000i	−0.254633	−	0.967038i	$-0.581955\pi$
$929$	13.8843	−	8.01610i	0.455529	−	0.263000i	0.710162	+	0.704038i	$0.248621\pi$
$930$		0			0
$931$			6.17238i			0.202292i
$932$		0			0
$933$	−10.5230	+	18.2264i	−0.344508	+	0.596705i
$934$		0			0
$935$	−19.8150			−0.648018
$936$		0			0
$937$	47.0232			1.53618			0.768091	−	0.640340i	$-0.221207\pi$
$937$	47.0232			1.53618			0.768091	+	0.640340i	$0.221207\pi$
$938$		0			0
$939$	−19.6586	+	34.0496i	−0.641533	+	1.11117i
$940$		0			0
$941$		−	52.8569i		−	1.72308i	−0.507686	−	0.861542i	$-0.669499\pi$
$941$		−	52.8569i		−	1.72308i	0.507686	−	0.861542i	$-0.330501\pi$
$942$		0			0
$943$	29.2504	−	16.8877i	0.952523	−	0.549939i
$944$		0			0
$945$	−0.777092	−	1.34596i	−0.0252788	−	0.0437842i
$946$		0			0
$947$	33.4029	+	19.2852i	1.08545	+	0.626684i	0.932361	−	0.361528i	$-0.117745\pi$
$947$	33.4029	+	19.2852i	1.08545	+	0.626684i	0.153088	+	0.988213i	$0.451078\pi$
$948$		0			0
$949$	−1.92981	−	0.230096i	−0.0626441	−	0.00746923i
$950$		0			0
$951$	−7.46430	−	4.30951i	−0.242046	−	0.139746i
$952$		0			0
$953$	13.6505	+	23.6433i	0.442182	+	0.765882i	0.997851	−	0.0655217i	$-0.0208711\pi$
$953$	13.6505	+	23.6433i	0.442182	+	0.765882i	−0.555669	+	0.831404i	$0.687538\pi$
$954$		0			0
$955$	19.1240	−	11.0412i	0.618838	−	0.357286i
$956$		0			0
$957$		−	21.7872i		−	0.704279i
$958$		0			0
$959$	−1.59478	+	2.76224i	−0.0514982	+	0.0891975i
$960$		0			0
$961$	30.2378			0.975412
$962$		0			0
$963$	−30.6880			−0.988906
$964$		0			0
$965$	−5.51966	+	9.56034i	−0.177684	+	0.307758i
$966$		0			0
$967$			25.2494i			0.811966i	0.913881	+	0.405983i	$0.133071\pi$
$967$			25.2494i			0.811966i	−0.913881	+	0.405983i	$0.866929\pi$
$968$		0			0
$969$	−62.0335	+	35.8151i	−1.99280	+	1.15055i
$970$		0			0
$971$	−3.28682	−	5.69294i	−0.105479	−	0.182695i	0.808455	−	0.588558i	$-0.200304\pi$
$971$	−3.28682	−	5.69294i	−0.105479	−	0.182695i	−0.913934	+	0.405863i	$0.866971\pi$
$972$		0			0
$973$	0.515900	+	0.297855i	0.0165390	+	0.00954879i
$974$		0			0
$975$	27.6896	+	20.7140i	0.886777	+	0.663380i
$976$		0			0
$977$	12.0773	+	6.97285i	0.386388	+	0.223081i	0.680594	−	0.732661i	$-0.261722\pi$
$977$	12.0773	+	6.97285i	0.386388	+	0.223081i	−0.294206	+	0.955742i	$0.595055\pi$
$978$		0			0
$979$	−16.8972	−	29.2667i	−0.540036	−	0.935369i
$980$		0			0
$981$	9.96151	−	5.75128i	0.318047	−	0.183624i
$982$		0			0
$983$		−	47.1390i		−	1.50350i	−0.659449	−	0.751750i	$-0.729210\pi$
$983$		−	47.1390i		−	1.50350i	0.659449	−	0.751750i	$-0.270790\pi$
$984$		0			0
$985$	−2.46090	+	4.26240i	−0.0784107	+	0.135811i
$986$		0			0
$987$	−6.69173			−0.213000
$988$		0			0
$989$	65.1459			2.07152
$990$		0			0
$991$	4.70805	−	8.15458i	0.149556	−	0.259039i	−0.781507	−	0.623896i	$-0.785549\pi$
$991$	4.70805	−	8.15458i	0.149556	−	0.259039i	0.931063	+	0.364857i	$0.118882\pi$
$992$		0			0
$993$		−	73.8223i		−	2.34268i
$994$		0			0
$995$	−10.0100	+	5.77927i	−0.317338	+	0.183215i
$996$		0			0
$997$	−20.2607	−	35.0926i	−0.641664	−	1.11139i	−0.985061	−	0.172204i	$-0.944911\pi$
$997$	−20.2607	−	35.0926i	−0.641664	−	1.11139i	0.343398	−	0.939190i	$-0.388422\pi$
$998$		0			0
$999$	0.215372	+	0.124345i	0.00681407	+	0.00393410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.d.225.5		12
4.3	odd	2		182.2.m.b.43.4	✓	12
12.11	even	2		1638.2.bj.g.1135.2		12
13.10	even	6	inner	1456.2.cc.d.673.5		12
28.3	even	6		1274.2.v.d.667.1		12
28.11	odd	6		1274.2.v.e.667.3		12
28.19	even	6		1274.2.o.e.459.3		12
28.23	odd	6		1274.2.o.d.459.1		12
28.27	even	2		1274.2.m.c.589.6		12
52.7	even	12		2366.2.a.bh.1.5		6
52.19	even	12		2366.2.a.bf.1.5		6
52.23	odd	6		182.2.m.b.127.4	yes	12
52.35	odd	6		2366.2.d.r.337.5		12
52.43	odd	6		2366.2.d.r.337.11		12
156.23	even	6		1638.2.bj.g.127.2		12
364.23	odd	6		1274.2.v.e.361.3		12
364.75	even	6		1274.2.v.d.361.1		12
364.179	odd	6		1274.2.o.d.569.4		12
364.283	even	6		1274.2.o.e.569.6		12
364.335	even	6		1274.2.m.c.491.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.4	✓	12	4.3	odd	2
182.2.m.b.127.4	yes	12	52.23	odd	6
1274.2.m.c.491.6		12	364.335	even	6
1274.2.m.c.589.6		12	28.27	even	2
1274.2.o.d.459.1		12	28.23	odd	6
1274.2.o.d.569.4		12	364.179	odd	6
1274.2.o.e.459.3		12	28.19	even	6
1274.2.o.e.569.6		12	364.283	even	6
1274.2.v.d.361.1		12	364.75	even	6
1274.2.v.d.667.1		12	28.3	even	6
1274.2.v.e.361.3		12	364.23	odd	6
1274.2.v.e.667.3		12	28.11	odd	6
1456.2.cc.d.225.5		12	1.1	even	1	trivial
1456.2.cc.d.673.5		12	13.10	even	6	inner
1638.2.bj.g.127.2		12	156.23	even	6
1638.2.bj.g.1135.2		12	12.11	even	2
2366.2.a.bf.1.5		6	52.19	even	12
2366.2.a.bh.1.5		6	52.7	even	12
2366.2.d.r.337.5		12	52.35	odd	6
2366.2.d.r.337.11		12	52.43	odd	6

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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.14539 - 1.98388i) q^{3} +0.901839i q^{5} +(-0.866025 + 0.500000i) q^{7} +(-1.12385 - 1.94657i) q^{9} +O(q^{10})\)	\(q+(1.14539 - 1.98388i) q^{3} +0.901839i q^{5} +(-0.866025 + 0.500000i) q^{7} +(-1.12385 - 1.94657i) q^{9} +(3.75609 + 2.16858i) q^{11} +(-0.426876 + 3.58019i) q^{13} +(1.78914 + 1.03296i) q^{15} +(2.53296 + 4.38722i) q^{17} +(-5.34544 + 3.08619i) q^{19} +2.29079i q^{21} +(-4.22559 + 7.31893i) q^{23} +4.18669 q^{25} +1.72335 q^{27} +(1.09643 - 1.89907i) q^{29} -0.873062i q^{31} +(8.60441 - 4.96776i) q^{33} +(-0.450919 - 0.781015i) q^{35} +(0.124973 + 0.0721531i) q^{37} +(6.61373 + 4.94760i) q^{39} +(-3.46110 - 1.99827i) q^{41} +(-3.85426 - 6.67577i) q^{43} +(1.75549 - 1.01353i) q^{45} +2.92115i q^{47} +(0.500000 - 0.866025i) q^{49} +11.6049 q^{51} +1.69699 q^{53} +(-1.95571 + 3.38739i) q^{55} +14.1396i q^{57} +(7.40394 - 4.27467i) q^{59} +(-4.16720 - 7.21780i) q^{61} +(1.94657 + 1.12385i) q^{63} +(-3.22876 - 0.384973i) q^{65} +(8.99180 + 5.19142i) q^{67} +(9.67992 + 16.7661i) q^{69} +(2.83932 - 1.63928i) q^{71} +0.539023i q^{73} +(4.79540 - 8.30588i) q^{75} -4.33716 q^{77} -6.53349 q^{79} +(5.34547 - 9.25862i) q^{81} +13.2348i q^{83} +(-3.95656 + 2.28432i) q^{85} +(-2.51168 - 4.35037i) q^{87} +(-6.74790 - 3.89590i) q^{89} +(-1.42041 - 3.31398i) q^{91} +(-1.73205 - 1.00000i) q^{93} +(-2.78325 - 4.82072i) q^{95} +(10.1378 - 5.85305i) q^{97} -9.74866i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 6 q^{9}+O(q^{10}) \) 12 * q + 2 * q^3 - 6 * q^9	\( 12 q + 2 q^{3} - 6 q^{9} + 18 q^{11} - 8 q^{13} + 6 q^{15} + 4 q^{17} - 12 q^{19} + 6 q^{23} - 24 q^{25} - 40 q^{27} - 10 q^{29} + 12 q^{33} - 2 q^{35} - 6 q^{37} + 54 q^{39} - 24 q^{41} - 26 q^{43} + 72 q^{45} + 6 q^{49} + 36 q^{51} + 36 q^{53} + 6 q^{55} - 6 q^{59} - 28 q^{61} - 34 q^{65} + 42 q^{67} + 32 q^{69} - 48 q^{71} + 48 q^{75} - 4 q^{77} - 44 q^{79} - 34 q^{81} + 54 q^{85} - 2 q^{87} + 12 q^{89} + 16 q^{91} - 32 q^{95} + 60 q^{97}+O(q^{100}) \) 12 * q + 2 * q^3 - 6 * q^9 + 18 * q^11 - 8 * q^13 + 6 * q^15 + 4 * q^17 - 12 * q^19 + 6 * q^23 - 24 * q^25 - 40 * q^27 - 10 * q^29 + 12 * q^33 - 2 * q^35 - 6 * q^37 + 54 * q^39 - 24 * q^41 - 26 * q^43 + 72 * q^45 + 6 * q^49 + 36 * q^51 + 36 * q^53 + 6 * q^55 - 6 * q^59 - 28 * q^61 - 34 * q^65 + 42 * q^67 + 32 * q^69 - 48 * q^71 + 48 * q^75 - 4 * q^77 - 44 * q^79 - 34 * q^81 + 54 * q^85 - 2 * q^87 + 12 * q^89 + 16 * q^91 - 32 * q^95 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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