LMFDB - Embedded newform 560.2.q.l.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(81,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("560.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.q (of order $3$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.11337408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 18x^{4} + 81x^{2} + 12 $ x^6 + 18x^4 + 81x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.2
Root			$-3.17656i$ of defining polynomial
Character	$\chi$	$=$	560.81
Dual form			560.2.q.l.401.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.352860 - 0.611171i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.647140 + 2.56539i) q^{7} +(1.25098 + 2.16676i) q^{9} +O(q^{10})$	\(q+(0.352860 - 0.611171i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.647140 + 2.56539i) q^{7} +(1.25098 + 2.16676i) q^{9} +(-2.25098 + 3.89881i) q^{11} +5.09052 q^{13} -0.705720 q^{15} +(-1.00000 + 1.73205i) q^{17} +(-1.54526 - 2.67647i) q^{19} +(1.33954 + 1.30074i) q^{21} +(2.89812 + 5.01969i) q^{23} +(-0.500000 + 0.866025i) q^{25} +3.88284 q^{27} +9.50196 q^{29} +(2.70572 - 4.68644i) q^{31} +(1.58856 + 2.75147i) q^{33} +(2.54526 - 0.722254i) q^{35} +(-3.54526 - 6.14057i) q^{37} +(1.79624 - 3.11118i) q^{39} -6.59248 q^{41} -4.70572 q^{43} +(1.25098 - 2.16676i) q^{45} +(5.04722 + 8.74204i) q^{47} +(-6.16242 - 3.32033i) q^{49} +(0.705720 + 1.22234i) q^{51} +(-4.95670 + 8.58526i) q^{53} +4.50196 q^{55} -2.18104 q^{57} +(4.00000 - 6.92820i) q^{59} +(4.45670 + 7.71923i) q^{61} +(-6.36814 + 1.80705i) q^{63} +(-2.54526 - 4.40852i) q^{65} +(-0.0585795 + 0.101463i) q^{67} +4.09052 q^{69} +(-4.09052 + 7.08499i) q^{73} +(0.352860 + 0.611171i) q^{75} +(-8.54526 - 8.29771i) q^{77} +(-7.09052 - 12.2811i) q^{79} +(-2.38284 + 4.12720i) q^{81} +10.7057 q^{83} +2.00000 q^{85} +(3.35286 - 5.80732i) q^{87} +(-2.04526 - 3.54249i) q^{89} +(-3.29428 + 13.0592i) q^{91} +(-1.90948 - 3.30732i) q^{93} +(-1.54526 + 2.67647i) q^{95} -2.00000 q^{97} -11.2637 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 6 q^{7} - 9 q^{9}+O(q^{10}) $ 6 * q - 3 * q^5 - 6 * q^7 - 9 * q^9	$ 6 q - 3 q^{5} - 6 q^{7} - 9 q^{9} + 3 q^{11} + 6 q^{13} - 6 q^{17} + 3 q^{19} + 3 q^{23} - 3 q^{25} + 36 q^{27} + 24 q^{29} + 12 q^{31} + 18 q^{33} + 3 q^{35} - 9 q^{37} - 18 q^{39} + 18 q^{41} - 24 q^{43} - 9 q^{45} - 15 q^{47} - 12 q^{49} - 9 q^{53} - 6 q^{55} + 36 q^{57} + 24 q^{59} + 6 q^{61} - 9 q^{63} - 3 q^{65} + 6 q^{67} - 39 q^{77} - 18 q^{79} - 27 q^{81} + 60 q^{83} + 12 q^{85} + 18 q^{87} - 24 q^{91} - 36 q^{93} + 3 q^{95} - 12 q^{97} - 126 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 - 6 * q^7 - 9 * q^9 + 3 * q^11 + 6 * q^13 - 6 * q^17 + 3 * q^19 + 3 * q^23 - 3 * q^25 + 36 * q^27 + 24 * q^29 + 12 * q^31 + 18 * q^33 + 3 * q^35 - 9 * q^37 - 18 * q^39 + 18 * q^41 - 24 * q^43 - 9 * q^45 - 15 * q^47 - 12 * q^49 - 9 * q^53 - 6 * q^55 + 36 * q^57 + 24 * q^59 + 6 * q^61 - 9 * q^63 - 3 * q^65 + 6 * q^67 - 39 * q^77 - 18 * q^79 - 27 * q^81 + 60 * q^83 + 12 * q^85 + 18 * q^87 - 24 * q^91 - 36 * q^93 + 3 * q^95 - 12 * q^97 - 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$3$	0.352860	−	0.611171i	0.203724	−	0.352860i	−0.746002	−	0.665944i	$-0.768029\pi$
$3$	0.352860	−	0.611171i	0.203724	−	0.352860i	0.949725	+	0.313084i	$0.101362\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−0.647140	+	2.56539i	−0.244596	+	0.969625i
$7$	−0.647140	+	2.56539i	−0.244596	+	0.969625i
$8$		0			0
$9$	1.25098	+	2.16676i	0.416993	+	0.722254i
$10$		0			0
$11$	−2.25098	+	3.89881i	−0.678696	+	1.17554i	0.296678	+	0.954978i	$0.404121\pi$
$11$	−2.25098	+	3.89881i	−0.678696	+	1.17554i	−0.975374	+	0.220558i	$0.929212\pi$
$12$		0			0
$13$	5.09052			1.41186			0.705928	−	0.708283i	$-0.250530\pi$
$13$	5.09052			1.41186			0.705928	+	0.708283i	$0.250530\pi$
$14$		0			0
$15$	−0.705720			−0.182216
$16$		0			0
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$		0			0
$19$	−1.54526	−	2.67647i	−0.354507	−	0.614024i	0.632526	−	0.774539i	$-0.282018\pi$
$19$	−1.54526	−	2.67647i	−0.354507	−	0.614024i	−0.987033	+	0.160515i	$0.948685\pi$
$20$		0			0
$21$	1.33954	+	1.30074i	0.292312	+	0.283844i
$22$		0			0
$23$	2.89812	+	5.01969i	0.604300	+	1.04668i	0.992162	+	0.124960i	$0.0398804\pi$
$23$	2.89812	+	5.01969i	0.604300	+	1.04668i	−0.387862	+	0.921717i	$0.626786\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	3.88284			0.747253
$28$		0			0
$29$	9.50196			1.76447			0.882235	−	0.470810i	$-0.156038\pi$
$29$	9.50196			1.76447			0.882235	+	0.470810i	$0.156038\pi$
$30$		0			0
$31$	2.70572	−	4.68644i	0.485962	−	0.841710i	−0.513908	−	0.857845i	$-0.671803\pi$
$31$	2.70572	−	4.68644i	0.485962	−	0.841710i	0.999870	+	0.0161350i	$0.00513615\pi$
$32$		0			0
$33$	1.58856	+	2.75147i	0.276533	+	0.478969i
$34$		0			0
$35$	2.54526	−	0.722254i	0.430228	−	0.122083i
$36$		0			0
$37$	−3.54526	−	6.14057i	−0.582837	−	1.00950i	−0.995141	−	0.0984573i	$-0.968609\pi$
$37$	−3.54526	−	6.14057i	−0.582837	−	1.00950i	0.412304	−	0.911046i	$-0.364724\pi$
$38$		0			0
$39$	1.79624	−	3.11118i	0.287629	−	0.498187i
$40$		0			0
$41$	−6.59248			−1.02957			−0.514786	−	0.857319i	$-0.672129\pi$
$41$	−6.59248			−1.02957			−0.514786	+	0.857319i	$0.672129\pi$
$42$		0			0
$43$	−4.70572			−0.717616			−0.358808	−	0.933411i	$-0.616817\pi$
$43$	−4.70572			−0.717616			−0.358808	+	0.933411i	$0.616817\pi$
$44$		0			0
$45$	1.25098	−	2.16676i	0.186485	−	0.323002i
$46$		0			0
$47$	5.04722	+	8.74204i	0.736213	+	1.27516i	0.954189	+	0.299204i	$0.0967210\pi$
$47$	5.04722	+	8.74204i	0.736213	+	1.27516i	−0.217977	+	0.975954i	$0.569946\pi$
$48$		0			0
$49$	−6.16242	−	3.32033i	−0.880346	−	0.474333i
$50$		0			0
$51$	0.705720	+	1.22234i	0.0988205	+	0.171162i
$52$		0			0
$53$	−4.95670	+	8.58526i	−0.680855	+	1.17928i	0.293865	+	0.955847i	$0.405058\pi$
$53$	−4.95670	+	8.58526i	−0.680855	+	1.17928i	−0.974720	+	0.223429i	$0.928275\pi$
$54$		0			0
$55$	4.50196			0.607044
$56$		0			0
$57$	−2.18104			−0.288886
$58$		0			0
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	−0.478953	−	0.877841i	$-0.658984\pi$
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	0.999709	−	0.0241347i	$-0.00768307\pi$
$60$		0			0
$61$	4.45670	+	7.71923i	0.570622	+	0.988346i	0.996502	+	0.0835666i	$0.0266311\pi$
$61$	4.45670	+	7.71923i	0.570622	+	0.988346i	−0.425880	+	0.904780i	$0.640036\pi$
$62$		0			0
$63$	−6.36814	+	1.80705i	−0.802310	+	0.227667i
$64$		0			0
$65$	−2.54526	−	4.40852i	−0.315701	−	0.546810i
$66$		0			0
$67$	−0.0585795	+	0.101463i	−0.00715662	+	0.0123956i	−0.869582	−	0.493789i	$-0.835611\pi$
$67$	−0.0585795	+	0.101463i	−0.00715662	+	0.0123956i	0.862425	+	0.506185i	$0.168945\pi$
$68$		0			0
$69$	4.09052			0.492441
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−4.09052	+	7.08499i	−0.478759	+	0.829235i	−0.999703	−	0.0243555i	$-0.992247\pi$
$73$	−4.09052	+	7.08499i	−0.478759	+	0.829235i	0.520944	+	0.853591i	$0.325580\pi$
$74$		0			0
$75$	0.352860	+	0.611171i	0.0407447	+	0.0705720i
$76$		0			0
$77$	−8.54526	−	8.29771i	−0.973823	−	0.945612i
$78$		0			0
$79$	−7.09052	−	12.2811i	−0.797746	−	1.38174i	−0.921081	−	0.389371i	$-0.872692\pi$
$79$	−7.09052	−	12.2811i	−0.797746	−	1.38174i	0.123335	−	0.992365i	$-0.460641\pi$
$80$		0			0
$81$	−2.38284	+	4.12720i	−0.264760	+	0.458578i
$82$		0			0
$83$	10.7057			1.17511			0.587553	−	0.809186i	$-0.300091\pi$
$83$	10.7057			1.17511			0.587553	+	0.809186i	$0.300091\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$		0			0
$87$	3.35286	−	5.80732i	0.359464	−	0.622610i
$88$		0			0
$89$	−2.04526	−	3.54249i	−0.216797	−	0.375504i	0.737030	−	0.675860i	$-0.236228\pi$
$89$	−2.04526	−	3.54249i	−0.216797	−	0.375504i	−0.953827	+	0.300356i	$0.902894\pi$
$90$		0			0
$91$	−3.29428	+	13.0592i	−0.345334	+	1.36897i
$92$		0			0
$93$	−1.90948	−	3.30732i	−0.198004	−	0.342953i
$94$		0			0
$95$	−1.54526	+	2.67647i	−0.158540	+	0.274600i
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	−11.2637			−1.13205
$100$		0			0
$101$	1.66046	−	2.87600i	0.165222	−	0.286173i	−0.771512	−	0.636215i	$-0.780499\pi$
$101$	1.66046	−	2.87600i	0.165222	−	0.286173i	0.936734	+	0.350042i	$0.113833\pi$
$102$		0			0
$103$	−5.44338	−	9.42821i	−0.536352	−	0.928989i	−0.999097	−	0.0424975i	$-0.986469\pi$
$103$	−5.44338	−	9.42821i	−0.536352	−	0.928989i	0.462744	−	0.886492i	$-0.346865\pi$
$104$		0			0
$105$	0.456700	−	1.81044i	0.0445693	−	0.176681i
$106$		0			0
$107$	1.94142	+	3.36264i	0.187684	+	0.325079i	0.944478	−	0.328575i	$-0.106569\pi$
$107$	1.94142	+	3.36264i	0.187684	+	0.325079i	−0.756794	+	0.653654i	$0.773235\pi$
$108$		0			0
$109$	5.13578	−	8.89543i	0.491919	−	0.852028i	−0.508038	−	0.861335i	$-0.669629\pi$
$109$	5.13578	−	8.89543i	0.491919	−	0.852028i	0.999957	+	0.00930661i	$0.00296243\pi$
$110$		0			0
$111$	−5.00392			−0.474951
$112$		0			0
$113$	2.82288			0.265554			0.132777	−	0.991146i	$-0.457611\pi$
$113$	2.82288			0.265554			0.132777	+	0.991146i	$0.457611\pi$
$114$		0			0
$115$	2.89812	−	5.01969i	0.270251	−	0.468089i
$116$		0			0
$117$	6.36814	+	11.0299i	0.588735	+	1.01972i
$118$		0			0
$119$	−3.79624	−	3.68627i	−0.348001	−	0.337919i
$120$		0			0
$121$	−4.63382	−	8.02601i	−0.421256	−	0.729638i
$122$		0			0
$123$	−2.32622	+	4.02913i	−0.209748	+	0.363295i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	1.73236			0.153722			0.0768610	−	0.997042i	$-0.475510\pi$
$127$	1.73236			0.153722			0.0768610	+	0.997042i	$0.475510\pi$
$128$		0			0
$129$	−1.66046	+	2.87600i	−0.146195	+	0.253218i
$130$		0			0
$131$	−6.36814	−	11.0299i	−0.556387	−	0.963690i	−0.997794	−	0.0663835i	$-0.978854\pi$
$131$	−6.36814	−	11.0299i	−0.556387	−	0.963690i	0.441407	−	0.897307i	$-0.354479\pi$
$132$		0			0
$133$	7.86618	−	2.23214i	0.682084	−	0.193551i
$134$		0			0
$135$	−1.94142	−	3.36264i	−0.167091	−	0.289410i
$136$		0			0
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	−0.938725	−	0.344668i	$-0.887992\pi$
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	0.767853	+	0.640626i	$0.221325\pi$
$138$		0			0
$139$	1.41144			0.119717			0.0598584	−	0.998207i	$-0.480935\pi$
$139$	1.41144			0.119717			0.0598584	+	0.998207i	$0.480935\pi$
$140$		0			0
$141$	7.12384			0.599936
$142$		0			0
$143$	−11.4587	+	19.8470i	−0.958221	+	1.65969i
$144$		0			0
$145$	−4.75098	−	8.22894i	−0.394547	−	0.683376i
$146$		0			0
$147$	−4.20376	+	2.59468i	−0.346720	+	0.214006i
$148$		0			0
$149$	−11.5472	−	20.0004i	−0.945985	−	1.63849i	−0.753767	−	0.657142i	$-0.771765\pi$
$149$	−11.5472	−	20.0004i	−0.945985	−	1.63849i	−0.192218	−	0.981352i	$-0.561568\pi$
$150$		0			0
$151$	−0.203760	+	0.352922i	−0.0165817	+	0.0287204i	−0.874197	−	0.485571i	$-0.838612\pi$
$151$	−0.203760	+	0.352922i	−0.0165817	+	0.0287204i	0.857615	+	0.514291i	$0.171945\pi$
$152$		0			0
$153$	−5.00392			−0.404543
$154$		0			0
$155$	−5.41144			−0.434657
$156$		0			0
$157$	7.04722	−	12.2061i	0.562429	−	0.974156i	−0.434854	−	0.900501i	$-0.643200\pi$
$157$	7.04722	−	12.2061i	0.562429	−	0.974156i	0.997284	−	0.0736555i	$-0.0234665\pi$
$158$		0			0
$159$	3.49804	+	6.05878i	0.277413	+	0.480493i
$160$		0			0
$161$	−14.7529	+	4.18636i	−1.16269	+	0.329931i
$162$		0			0
$163$	−8.09052	−	14.0132i	−0.633698	−	1.09760i	−0.986789	−	0.162009i	$-0.948203\pi$
$163$	−8.09052	−	14.0132i	−0.633698	−	1.09760i	0.353091	−	0.935589i	$-0.385131\pi$
$164$		0			0
$165$	1.58856	−	2.75147i	0.123669	−	0.214201i
$166$		0			0
$167$	−7.79624			−0.603291			−0.301646	−	0.953420i	$-0.597536\pi$
$167$	−7.79624			−0.603291			−0.301646	+	0.953420i	$0.597536\pi$
$168$		0			0
$169$	12.9134			0.993338
$170$		0			0
$171$	3.86618	−	6.69642i	0.295654	−	0.512088i
$172$		0			0
$173$	4.45474	+	7.71584i	0.338688	+	0.586624i	0.984186	−	0.177137i	$-0.0566837\pi$
$173$	4.45474	+	7.71584i	0.338688	+	0.586624i	−0.645499	+	0.763762i	$0.723350\pi$
$174$		0			0
$175$	−1.89812	−	1.84313i	−0.143484	−	0.139328i
$176$		0			0
$177$	−2.82288	−	4.88937i	−0.212181	−	0.367507i
$178$		0			0
$179$	0.839541	−	1.45413i	0.0627502	−	0.108687i	−0.832944	−	0.553358i	$-0.813346\pi$
$179$	0.839541	−	1.45413i	0.0627502	−	0.108687i	0.895694	+	0.444671i	$0.146680\pi$
$180$		0			0
$181$	12.5059			0.929555			0.464777	−	0.885428i	$-0.346134\pi$
$181$	12.5059			0.929555			0.464777	+	0.885428i	$0.346134\pi$
$182$		0			0
$183$	6.29036			0.464997
$184$		0			0
$185$	−3.54526	+	6.14057i	−0.260653	+	0.451464i
$186$		0			0
$187$	−4.50196	−	7.79762i	−0.329216	−	0.570219i
$188$		0			0
$189$	−2.51274	+	9.96099i	−0.182775	+	0.724555i
$190$		0			0
$191$	3.29428	+	5.70586i	0.238366	+	0.412862i	0.960245	−	0.279157i	$-0.0900550\pi$
$191$	3.29428	+	5.70586i	0.238366	+	0.412862i	−0.721880	+	0.692019i	$0.756722\pi$
$192$		0			0
$193$	−8.91340	+	15.4385i	−0.641601	+	1.11128i	0.343475	+	0.939162i	$0.388396\pi$
$193$	−8.91340	+	15.4385i	−0.641601	+	1.11128i	−0.985075	+	0.172123i	$0.944937\pi$
$194$		0			0
$195$	−3.59248			−0.257263
$196$		0			0
$197$	5.09052			0.362685			0.181342	−	0.983420i	$-0.441956\pi$
$197$	5.09052			0.362685			0.181342	+	0.983420i	$0.441956\pi$
$198$		0			0
$199$	12.1810	−	21.0982i	0.863491	−	1.49561i	−0.00504654	−	0.999987i	$-0.501606\pi$
$199$	12.1810	−	21.0982i	0.863491	−	1.49561i	0.868538	−	0.495623i	$-0.165060\pi$
$200$		0			0
$201$	0.0413407	+	0.0716041i	0.00291595	+	0.00505057i
$202$		0			0
$203$	−6.14910	+	24.3762i	−0.431582	+	1.71087i
$204$		0			0
$205$	3.29624	+	5.70926i	0.230219	+	0.398752i
$206$		0			0
$207$	−7.25098	+	12.5591i	−0.503978	+	0.872915i
$208$		0			0
$209$	13.9134			0.962410
$210$		0			0
$211$	8.26764			0.569168			0.284584	−	0.958651i	$-0.408145\pi$
$211$	8.26764			0.569168			0.284584	+	0.958651i	$0.408145\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.35286	+	4.07527i	0.160464	+	0.277931i
$216$		0			0
$217$	10.2716	+	9.97400i	0.697279	+	0.677079i
$218$		0			0
$219$	2.88676	+	5.00002i	0.195069	+	0.337870i
$220$		0			0
$221$	−5.09052	+	8.81704i	−0.342425	+	0.593098i
$222$		0			0
$223$	17.8268			1.19377			0.596885	−	0.802327i	$-0.296405\pi$
$223$	17.8268			1.19377			0.596885	+	0.802327i	$0.296405\pi$
$224$		0			0
$225$	−2.50196			−0.166797
$226$		0			0
$227$	2.67908	−	4.64030i	0.177817	−	0.307988i	−0.763316	−	0.646026i	$-0.776430\pi$
$227$	2.67908	−	4.64030i	0.177817	−	0.307988i	0.941133	+	0.338038i	$0.109763\pi$
$228$		0			0
$229$	−12.0905	−	20.9414i	−0.798964	−	1.38385i	−0.920291	−	0.391234i	$-0.872048\pi$
$229$	−12.0905	−	20.9414i	−0.798964	−	1.38385i	0.121327	−	0.992613i	$-0.461285\pi$
$230$		0			0
$231$	−8.08660	+	2.29469i	−0.532059	+	0.150979i
$232$		0			0
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	−0.994283	−	0.106773i	$-0.965948\pi$
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	0.404674	−	0.914461i	$-0.367385\pi$
$234$		0			0
$235$	5.04722	−	8.74204i	0.329244	−	0.570268i
$236$		0			0
$237$	−10.0078			−0.650079
$238$		0			0
$239$	12.7696			0.825997			0.412998	−	0.910732i	$-0.364481\pi$
$239$	12.7696			0.825997			0.412998	+	0.910732i	$0.364481\pi$
$240$		0			0
$241$	11.0472	−	19.1343i	0.711614	−	1.23255i	−0.252637	−	0.967561i	$-0.581298\pi$
$241$	11.0472	−	19.1343i	0.711614	−	1.23255i	0.964251	−	0.264990i	$-0.0853688\pi$
$242$		0			0
$243$	7.50588	+	13.0006i	0.481502	+	0.833987i
$244$		0			0
$245$	0.205720	+	6.99698i	0.0131429	+	0.447020i
$246$		0			0
$247$	−7.86618	−	13.6246i	−0.500513	−	0.866914i
$248$		0			0
$249$	3.77762	−	6.54303i	0.239397	−	0.414647i
$250$		0			0
$251$	13.5059			0.852484			0.426242	−	0.904609i	$-0.359837\pi$
$251$	13.5059			0.852484			0.426242	+	0.904609i	$0.359837\pi$
$252$		0			0
$253$	−26.0944			−1.64054
$254$		0			0
$255$	0.705720	−	1.22234i	0.0441939	−	0.0765460i
$256$		0			0
$257$	8.18104	+	14.1700i	0.510319	+	0.883899i	0.999929	+	0.0119570i	$0.00380612\pi$
$257$	8.18104	+	14.1700i	0.510319	+	0.883899i	−0.489609	+	0.871942i	$0.662861\pi$
$258$		0			0
$259$	18.0472	−	5.12115i	1.12140	−	0.318213i
$260$		0			0
$261$	11.8868	+	20.5885i	0.735772	+	1.27439i
$262$		0			0
$263$	4.55662	−	7.89230i	0.280973	−	0.486660i	−0.690651	−	0.723188i	$-0.742676\pi$
$263$	4.55662	−	7.89230i	0.280973	−	0.486660i	0.971625	+	0.236528i	$0.0760095\pi$
$264$		0			0
$265$	9.91340			0.608975
$266$		0			0
$267$	−2.88676			−0.176667
$268$		0			0
$269$	−4.45670	+	7.71923i	−0.271730	+	0.470650i	−0.969305	−	0.245862i	$-0.920929\pi$
$269$	−4.45670	+	7.71923i	−0.271730	+	0.470650i	0.697575	+	0.716512i	$0.254262\pi$
$270$		0			0
$271$	8.18104	+	14.1700i	0.496963	+	0.860765i	0.999994	−	0.00350346i	$-0.00111519\pi$
$271$	8.18104	+	14.1700i	0.496963	+	0.860765i	−0.503031	+	0.864268i	$0.667782\pi$
$272$		0			0
$273$	6.81896	+	6.62142i	0.412702	+	0.400747i
$274$		0			0
$275$	−2.25098	−	3.89881i	−0.135739	−	0.235107i
$276$		0			0
$277$	−5.58856	+	9.67967i	−0.335784	+	0.581595i	−0.983635	−	0.180172i	$-0.942335\pi$
$277$	−5.58856	+	9.67967i	−0.335784	+	0.581595i	0.647851	+	0.761767i	$0.275668\pi$
$278$		0			0
$279$	13.5392			0.810571
$280$		0			0
$281$	−28.2755			−1.68677			−0.843387	−	0.537307i	$-0.819442\pi$
$281$	−28.2755			−1.68677			−0.843387	+	0.537307i	$0.819442\pi$
$282$		0			0
$283$	−6.41144	+	11.1049i	−0.381121	+	0.660120i	−0.991223	−	0.132203i	$-0.957795\pi$
$283$	−6.41144	+	11.1049i	−0.381121	+	0.660120i	0.610102	+	0.792323i	$0.291128\pi$
$284$		0			0
$285$	1.09052	+	1.88884i	0.0645969	+	0.111885i
$286$		0			0
$287$	4.26626	−	16.9123i	0.251829	−	0.998299i
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	−0.705720	+	1.22234i	−0.0413700	+	0.0716550i
$292$		0			0
$293$	8.90948			0.520497			0.260249	−	0.965542i	$-0.416195\pi$
$293$	8.90948			0.520497			0.260249	+	0.965542i	$0.416195\pi$
$294$		0			0
$295$	−8.00000			−0.465778
$296$		0			0
$297$	−8.74020	+	15.1385i	−0.507158	+	0.878423i
$298$		0			0
$299$	14.7529	+	25.5528i	0.853185	+	1.47776i
$300$		0			0
$301$	3.04526	−	12.0720i	0.175526	−	0.695818i
$302$		0			0
$303$	−1.17182	−	2.02965i	−0.0673192	−	0.116600i
$304$		0			0
$305$	4.45670	−	7.71923i	0.255190	−	0.442002i
$306$		0			0
$307$	9.12108			0.520567			0.260284	−	0.965532i	$-0.416184\pi$
$307$	9.12108			0.520567			0.260284	+	0.965532i	$0.416184\pi$
$308$		0			0
$309$	−7.68300			−0.437071
$310$		0			0
$311$	−6.58856	+	11.4117i	−0.373603	+	0.647099i	−0.990117	−	0.140245i	$-0.955211\pi$
$311$	−6.58856	+	11.4117i	−0.373603	+	0.647099i	0.616514	+	0.787344i	$0.288544\pi$
$312$		0			0
$313$	8.76960	+	15.1894i	0.495687	+	0.858555i	0.999988	−	0.00497286i	$-0.00158292\pi$
$313$	8.76960	+	15.1894i	0.495687	+	0.858555i	−0.504300	+	0.863528i	$0.668250\pi$
$314$		0			0
$315$	4.74902	+	4.61145i	0.267577	+	0.259826i
$316$		0			0
$317$	6.59248	+	11.4185i	0.370271	+	0.641327i	0.989607	−	0.143798i	$-0.0459316\pi$
$317$	6.59248	+	11.4185i	0.370271	+	0.641327i	−0.619336	+	0.785126i	$0.712598\pi$
$318$		0			0
$319$	−21.3887	+	37.0464i	−1.19754	+	2.07420i
$320$		0			0
$321$	2.74020			0.152943
$322$		0			0
$323$	6.18104			0.343922
$324$		0			0
$325$	−2.54526	+	4.40852i	−0.141186	+	0.244541i
$326$		0			0
$327$	−3.62442	−	6.27768i	−0.200431	−	0.347157i
$328$		0			0
$329$	−25.6930	+	7.29075i	−1.41650	+	0.401952i
$330$		0			0
$331$	4.25098	+	7.36291i	0.233655	+	0.404702i	0.958881	−	0.283809i	$-0.0915980\pi$
$331$	4.25098	+	7.36291i	0.233655	+	0.404702i	−0.725226	+	0.688511i	$0.758265\pi$
$332$		0			0
$333$	8.87010	−	15.3635i	0.486078	−	0.841913i
$334$		0			0
$335$	0.117159			0.00640108
$336$		0			0
$337$	28.1889			1.53555			0.767773	−	0.640722i	$-0.221365\pi$
$337$	28.1889			1.53555			0.767773	+	0.640722i	$0.221365\pi$
$338$		0			0
$339$	0.996080	−	1.72526i	0.0540997	−	0.0937034i
$340$		0			0
$341$	12.1810	+	21.0982i	0.659640	+	1.14253i
$342$		0			0
$343$	12.5059	−	13.6603i	0.675254	−	0.737585i
$344$		0			0
$345$	−2.04526	−	3.54249i	−0.110113	−	0.190722i
$346$		0			0
$347$	1.35286	−	2.34322i	0.0726253	−	0.125791i	−0.827426	−	0.561575i	$-0.810196\pi$
$347$	1.35286	−	2.34322i	0.0726253	−	0.125791i	0.900051	+	0.435784i	$0.143529\pi$
$348$		0			0
$349$	−13.6830			−0.732434			−0.366217	−	0.930529i	$-0.619347\pi$
$349$	−13.6830			−0.732434			−0.366217	+	0.930529i	$0.619347\pi$
$350$		0			0
$351$	19.7657			1.05501
$352$		0			0
$353$	10.1810	−	17.6341i	0.541882	−	0.938567i	−0.456914	−	0.889511i	$-0.651045\pi$
$353$	10.1810	−	17.6341i	0.541882	−	0.938567i	0.998796	−	0.0490565i	$-0.0156214\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−3.59248	+	1.01942i	−0.190134	+	0.0539533i
$358$		0			0
$359$	−9.20768	−	15.9482i	−0.485963	−	0.841712i	0.513907	−	0.857846i	$-0.328198\pi$
$359$	−9.20768	−	15.9482i	−0.485963	−	0.841712i	−0.999870	+	0.0161337i	$0.994864\pi$
$360$		0			0
$361$	4.72434	−	8.18280i	0.248650	−	0.430674i
$362$		0			0
$363$	−6.54036			−0.343280
$364$		0			0
$365$	8.18104			0.428215
$366$		0			0
$367$	−12.8115	+	22.1902i	−0.668756	+	1.15832i	0.309496	+	0.950901i	$0.399840\pi$
$367$	−12.8115	+	22.1902i	−0.668756	+	1.15832i	−0.978252	+	0.207419i	$0.933494\pi$
$368$		0			0
$369$	−8.24706	−	14.2843i	−0.429325	−	0.743612i
$370$		0			0
$371$	−18.8168	−	18.2717i	−0.976921	−	0.948620i
$372$		0			0
$373$	−14.0944	−	24.4123i	−0.729782	−	1.26402i	−0.956975	−	0.290170i	$-0.906288\pi$
$373$	−14.0944	−	24.4123i	−0.729782	−	1.26402i	0.227193	−	0.973850i	$-0.427045\pi$
$374$		0			0
$375$	0.352860	−	0.611171i	0.0182216	−	0.0315607i
$376$		0			0
$377$	48.3699			2.49118
$378$		0			0
$379$	−21.7402			−1.11672			−0.558359	−	0.829599i	$-0.688569\pi$
$379$	−21.7402			−1.11672			−0.558359	+	0.829599i	$0.688569\pi$
$380$		0			0
$381$	0.611280	−	1.05877i	0.0313168	−	0.0542423i
$382$		0			0
$383$	−10.1058	−	17.5038i	−0.516382	−	0.894400i	−0.999819	−	0.0190210i	$-0.993945\pi$
$383$	−10.1058	−	17.5038i	−0.516382	−	0.894400i	0.483437	−	0.875379i	$-0.339388\pi$
$384$		0			0
$385$	−2.91340	+	11.5493i	−0.148481	+	0.588605i
$386$		0			0
$387$	−5.88676	−	10.1962i	−0.299241	−	0.518300i
$388$		0			0
$389$	−6.91340	+	11.9744i	−0.350523	+	0.607124i	−0.986341	−	0.164715i	$-0.947330\pi$
$389$	−6.91340	+	11.9744i	−0.350523	+	0.607124i	0.635818	+	0.771839i	$0.280663\pi$
$390$		0			0
$391$	−11.5925			−0.586257
$392$		0			0
$393$	−8.98824			−0.453397
$394$		0			0
$395$	−7.09052	+	12.2811i	−0.356763	+	0.617931i
$396$		0			0
$397$	−18.1850	−	31.4973i	−0.912677	−	1.58080i	−0.810267	−	0.586061i	$-0.800678\pi$
$397$	−18.1850	−	31.4973i	−0.912677	−	1.58080i	−0.102410	−	0.994742i	$-0.532655\pi$
$398$		0			0
$399$	1.41144	−	5.59521i	0.0706603	−	0.280111i
$400$		0			0
$401$	3.40948	+	5.90539i	0.170261	+	0.294901i	0.938511	−	0.345249i	$-0.112205\pi$
$401$	3.40948	+	5.90539i	0.170261	+	0.294901i	−0.768250	+	0.640150i	$0.778872\pi$
$402$		0			0
$403$	13.7735	−	23.8564i	0.686108	−	1.18837i
$404$		0			0
$405$	4.76568			0.236809
$406$		0			0
$407$	31.9212			1.58228
$408$		0			0
$409$	8.93202	−	15.4707i	0.441660	−	0.764978i	−0.556153	−	0.831080i	$-0.687723\pi$
$409$	8.93202	−	15.4707i	0.441660	−	0.764978i	0.997813	+	0.0661025i	$0.0210564\pi$
$410$		0			0
$411$	1.41144	+	2.44468i	0.0696212	+	0.120587i
$412$		0			0
$413$	15.1850	+	14.7451i	0.747203	+	0.725557i
$414$		0			0
$415$	−5.35286	−	9.27143i	−0.262762	−	0.455116i
$416$		0			0
$417$	0.498040	−	0.862631i	0.0243891	−	0.0422432i
$418$		0			0
$419$	−18.4487			−0.901277			−0.450639	−	0.892706i	$-0.648804\pi$
$419$	−18.4487			−0.901277			−0.450639	+	0.892706i	$0.648804\pi$
$420$		0			0
$421$	−10.7324			−0.523063			−0.261532	−	0.965195i	$-0.584228\pi$
$421$	−10.7324			−0.523063			−0.261532	+	0.965195i	$0.584228\pi$
$422$		0			0
$423$	−12.6279	+	21.8722i	−0.613992	+	1.06346i
$424$		0			0
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$		0			0
$427$	−22.6869	+	6.43773i	−1.09790	+	0.311544i
$428$		0			0
$429$	8.08660	+	14.0064i	0.390425	+	0.676236i
$430$		0			0
$431$	3.29428	−	5.70586i	0.158680	−	0.274842i	−0.775713	−	0.631086i	$-0.782610\pi$
$431$	3.29428	−	5.70586i	0.158680	−	0.274842i	0.934393	+	0.356244i	$0.115943\pi$
$432$		0			0
$433$	5.17712			0.248797			0.124398	−	0.992232i	$-0.460300\pi$
$433$	5.17712			0.248797			0.124398	+	0.992232i	$0.460300\pi$
$434$		0			0
$435$	−6.70572			−0.321515
$436$		0			0
$437$	8.95670	−	15.5135i	0.428457	−	0.742109i
$438$		0			0
$439$	15.5059	+	26.8570i	0.740055	+	1.28181i	0.952470	+	0.304634i	$0.0985340\pi$
$439$	15.5059	+	26.8570i	0.740055	+	1.28181i	−0.212414	+	0.977180i	$0.568133\pi$
$440$		0			0
$441$	−0.514702	−	17.5062i	−0.0245096	−	0.833626i
$442$		0			0
$443$	2.43946	+	4.22527i	0.115902	+	0.200749i	0.918140	−	0.396256i	$-0.129691\pi$
$443$	2.43946	+	4.22527i	0.115902	+	0.200749i	−0.802238	+	0.597005i	$0.796357\pi$
$444$		0			0
$445$	−2.04526	+	3.54249i	−0.0969546	+	0.167930i
$446$		0			0
$447$	−16.2982			−0.770878
$448$		0			0
$449$	27.7696			1.31053			0.655264	−	0.755400i	$-0.272557\pi$
$449$	27.7696			1.31053			0.655264	+	0.755400i	$0.272557\pi$
$450$		0			0
$451$	14.8395	−	25.7028i	0.698767	−	1.21030i
$452$		0			0
$453$	0.143797	+	0.249064i	0.00675619	+	0.0117021i
$454$		0			0
$455$	12.9567	−	3.67665i	0.607419	−	0.172364i
$456$		0			0
$457$	12.5020	+	21.6540i	0.584817	+	1.01293i	0.994898	+	0.100884i	$0.0321670\pi$
$457$	12.5020	+	21.6540i	0.584817	+	1.01293i	−0.410081	+	0.912049i	$0.634500\pi$
$458$		0			0
$459$	−3.88284	+	6.72528i	−0.181236	+	0.313909i
$460$		0			0
$461$	−4.00784			−0.186664			−0.0933318	−	0.995635i	$-0.529752\pi$
$461$	−4.00784			−0.186664			−0.0933318	+	0.995635i	$0.529752\pi$
$462$		0			0
$463$	36.8002			1.71025			0.855124	−	0.518423i	$-0.173481\pi$
$463$	36.8002			1.71025			0.855124	+	0.518423i	$0.173481\pi$
$464$		0			0
$465$	−1.90948	+	3.30732i	−0.0885500	+	0.153373i
$466$		0			0
$467$	−11.7377	−	20.3302i	−0.543154	−	0.940771i	−0.998721	−	0.0505688i	$-0.983897\pi$
$467$	−11.7377	−	20.3302i	−0.543154	−	0.940771i	0.455566	−	0.890202i	$-0.349437\pi$
$468$		0			0
$469$	−0.222382	−	0.215939i	−0.0102686	−	0.00997116i
$470$		0			0
$471$	−4.97336	−	8.61411i	−0.229160	−	0.396917i
$472$		0			0
$473$	10.5925	−	18.3467i	0.487043	−	0.843583i
$474$		0			0
$475$	3.09052			0.141803
$476$		0			0
$477$	−24.8029			−1.13565
$478$		0			0
$479$	−18.8868	+	32.7128i	−0.862958	+	1.49469i	0.00610232	+	0.999981i	$0.498058\pi$
$479$	−18.8868	+	32.7128i	−0.862958	+	1.49469i	−0.869060	+	0.494706i	$0.835276\pi$
$480$		0			0
$481$	−18.0472	−	31.2587i	−0.822882	−	1.42527i
$482$		0			0
$483$	−2.64714	+	10.4938i	−0.120449	+	0.477483i
$484$		0			0
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$		0			0
$487$	−3.08660	+	5.34615i	−0.139867	+	0.242257i	−0.927446	−	0.373957i	$-0.878001\pi$
$487$	−3.08660	+	5.34615i	−0.139867	+	0.242257i	0.787579	+	0.616214i	$0.211334\pi$
$488$		0			0
$489$	−11.4193			−0.516398
$490$		0			0
$491$	−39.7814			−1.79531			−0.897654	−	0.440701i	$-0.854730\pi$
$491$	−39.7814			−1.79531			−0.897654	+	0.440701i	$0.854730\pi$
$492$		0			0
$493$	−9.50196	+	16.4579i	−0.427947	+	0.741226i
$494$		0			0
$495$	5.63186	+	9.75467i	0.253133	+	0.438440i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.88284	+	3.26118i	0.0842875	+	0.145990i	0.905087	−	0.425226i	$-0.139805\pi$
$499$	1.88284	+	3.26118i	0.0842875	+	0.145990i	−0.820800	+	0.571216i	$0.806472\pi$
$500$		0			0
$501$	−2.75098	+	4.76484i	−0.122905	+	0.212877i
$502$		0			0
$503$	−18.7057			−0.834047			−0.417023	−	0.908896i	$-0.636927\pi$
$503$	−18.7057			−0.834047			−0.417023	+	0.908896i	$0.636927\pi$
$504$		0			0
$505$	−3.32092			−0.147779
$506$		0			0
$507$	4.55662	−	7.89230i	0.202367	−	0.350509i
$508$		0			0
$509$	−6.16242	−	10.6736i	−0.273144	−	0.473100i	0.696521	−	0.717537i	$-0.254730\pi$
$509$	−6.16242	−	10.6736i	−0.273144	−	0.473100i	−0.969665	+	0.244437i	$0.921397\pi$
$510$		0			0
$511$	−15.5286	−	15.0787i	−0.686945	−	0.667045i
$512$		0			0
$513$	−6.00000	−	10.3923i	−0.264906	−	0.458831i
$514$		0			0
$515$	−5.44338	+	9.42821i	−0.239864	+	0.415457i
$516$		0			0
$517$	−45.4448			−1.99866
$518$		0			0
$519$	6.28759			0.275995
$520$		0			0
$521$	14.7796	−	25.5990i	0.647505	−	1.12151i	−0.336212	−	0.941786i	$-0.609146\pi$
$521$	14.7796	−	25.5990i	0.647505	−	1.12151i	0.983717	−	0.179725i	$-0.0575209\pi$
$522$		0			0
$523$	−21.5020	−	37.2425i	−0.940215	−	1.62850i	−0.765060	−	0.643959i	$-0.777291\pi$
$523$	−21.5020	−	37.2425i	−0.940215	−	1.62850i	−0.175155	−	0.984541i	$-0.556043\pi$
$524$		0			0
$525$	−1.79624	+	0.509709i	−0.0783943	+	0.0222455i
$526$		0			0
$527$	5.41144	+	9.37289i	0.235726	+	0.408289i
$528$		0			0
$529$	−5.29820	+	9.17675i	−0.230357	+	0.398989i
$530$		0			0
$531$	20.0157			0.868606
$532$		0			0
$533$	−33.5592			−1.45361
$534$		0			0
$535$	1.94142	−	3.36264i	0.0839349	−	0.145380i
$536$		0			0
$537$	−0.592480	−	1.02621i	−0.0255674	−	0.0442841i
$538$		0			0
$539$	26.8168	−	16.5521i	1.15508	−	0.712950i
$540$		0			0
$541$	2.48334	+	4.30127i	0.106767	+	0.184926i	0.914459	−	0.404679i	$-0.132617\pi$
$541$	2.48334	+	4.30127i	0.106767	+	0.184926i	−0.807692	+	0.589605i	$0.799283\pi$
$542$		0			0
$543$	4.41282	−	7.64323i	0.189372	−	0.328003i
$544$		0			0
$545$	−10.2716			−0.439985
$546$		0			0
$547$	22.1250			0.945997			0.472998	−	0.881063i	$-0.343172\pi$
$547$	22.1250			0.945997			0.472998	+	0.881063i	$0.343172\pi$
$548$		0			0
$549$	−11.1505	+	19.3132i	−0.475891	+	0.824267i
$550$		0			0
$551$	−14.6830	−	25.4317i	−0.625517	−	1.08343i
$552$		0			0
$553$	36.0944	−	10.2423i	1.53489	−	0.435547i
$554$		0			0
$555$	2.50196	+	4.33352i	0.106202	+	0.183948i
$556$		0			0
$557$	−2.77958	+	4.81437i	−0.117775	+	0.203991i	−0.918885	−	0.394524i	$-0.870909\pi$
$557$	−2.77958	+	4.81437i	−0.117775	+	0.203991i	0.801111	+	0.598516i	$0.204243\pi$
$558$		0			0
$559$	−23.9546			−1.01317
$560$		0			0
$561$	−6.35424			−0.268276
$562$		0			0
$563$	4.74158	−	8.21266i	0.199834	−	0.346122i	−0.748641	−	0.662976i	$-0.769293\pi$
$563$	4.74158	−	8.21266i	0.199834	−	0.346122i	0.948474	+	0.316854i	$0.102626\pi$
$564$		0			0
$565$	−1.41144	−	2.44468i	−0.0593797	−	0.102849i
$566$		0			0
$567$	−9.04584	−	8.78379i	−0.379889	−	0.368884i
$568$		0			0
$569$	17.1417	+	29.6902i	0.718616	+	1.24468i	0.961548	+	0.274636i	$0.0885573\pi$
$569$	17.1417	+	29.6902i	0.718616	+	1.24468i	−0.242933	+	0.970043i	$0.578109\pi$
$570$		0			0
$571$	−15.7735	+	27.3205i	−0.660101	+	1.14333i	0.320487	+	0.947253i	$0.396153\pi$
$571$	−15.7735	+	27.3205i	−0.660101	+	1.14333i	−0.980589	+	0.196076i	$0.937180\pi$
$572$		0			0
$573$	4.64968			0.194243
$574$		0			0
$575$	−5.79624			−0.241720
$576$		0			0
$577$	5.32092	−	9.21610i	0.221513	−	0.383671i	−0.733755	−	0.679414i	$-0.762234\pi$
$577$	5.32092	−	9.21610i	0.221513	−	0.383671i	0.955268	+	0.295743i	$0.0955672\pi$
$578$		0			0
$579$	6.29036	+	10.8952i	0.261418	+	0.452790i
$580$		0			0
$581$	−6.92810	+	27.4643i	−0.287426	+	1.13941i
$582$		0			0
$583$	−22.3149	−	38.6505i	−0.924187	−	1.60074i
$584$		0			0
$585$	6.36814	−	11.0299i	0.263290	−	0.456032i
$586$		0			0
$587$	−6.64184			−0.274138			−0.137069	−	0.990562i	$-0.543768\pi$
$587$	−6.64184			−0.274138			−0.137069	+	0.990562i	$0.543768\pi$
$588$		0			0
$589$	−16.7242			−0.689107
$590$		0			0
$591$	1.79624	−	3.11118i	0.0738874	−	0.127977i
$592$		0			0
$593$	−6.76960	−	11.7253i	−0.277994	−	0.481500i	0.692892	−	0.721041i	$-0.256336\pi$
$593$	−6.76960	−	11.7253i	−0.277994	−	0.481500i	−0.970886	+	0.239541i	$0.923003\pi$
$594$		0			0
$595$	−1.29428	+	5.13077i	−0.0530603	+	0.210341i
$596$		0			0
$597$	−8.59640	−	14.8894i	−0.351827	−	0.609383i
$598$		0			0
$599$	13.0905	−	22.6734i	0.534864	−	0.926412i	−0.464306	−	0.885675i	$-0.653696\pi$
$599$	13.0905	−	22.6734i	0.534864	−	0.926412i	0.999170	−	0.0407369i	$-0.0129706\pi$
$600$		0			0
$601$	−36.0078			−1.46879			−0.734395	−	0.678722i	$-0.762534\pi$
$601$	−36.0078			−1.46879			−0.734395	+	0.678722i	$0.762534\pi$
$602$		0			0
$603$	−0.293127			−0.0119371
$604$		0			0
$605$	−4.63382	+	8.02601i	−0.188392	+	0.326304i
$606$		0			0
$607$	11.8715	+	20.5620i	0.481849	+	0.834586i	0.999783	−	0.0208341i	$-0.00663219\pi$
$607$	11.8715	+	20.5620i	0.481849	+	0.834586i	−0.517934	+	0.855420i	$0.673299\pi$
$608$		0			0
$609$	12.7283	+	12.3595i	0.515775	+	0.500834i
$610$		0			0
$611$	25.6930	+	44.5015i	1.03943	+	1.80034i
$612$		0			0
$613$	4.77958	−	8.27847i	0.193045	−	0.334364i	−0.753213	−	0.657777i	$-0.771497\pi$
$613$	4.77958	−	8.27847i	0.193045	−	0.334364i	0.946258	+	0.323413i	$0.104830\pi$
$614$		0			0
$615$	4.65244			0.187605
$616$		0			0
$617$	−19.8268			−0.798197			−0.399098	−	0.916908i	$-0.630677\pi$
$617$	−19.8268			−0.798197			−0.399098	+	0.916908i	$0.630677\pi$
$618$		0			0
$619$	13.5758	−	23.5140i	0.545658	−	0.945108i	−0.452907	−	0.891558i	$-0.649613\pi$
$619$	13.5758	−	23.5140i	0.545658	−	0.945108i	0.998565	−	0.0535500i	$-0.0170536\pi$
$620$		0			0
$621$	11.2529	+	19.4907i	0.451565	+	0.782133i
$622$		0			0
$623$	10.4114	−	2.95439i	0.417126	−	0.118365i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	4.90948	−	8.50347i	0.196066	−	0.339596i
$628$		0			0
$629$	14.1810			0.565435
$630$		0			0
$631$	49.7735			1.98145			0.990726	−	0.135873i	$-0.0433838\pi$
$631$	49.7735			1.98145			0.990726	+	0.135873i	$0.0433838\pi$
$632$		0			0
$633$	2.91732	−	5.05294i	0.115953	−	0.200836i
$634$		0			0
$635$	−0.866179	−	1.50027i	−0.0343733	−	0.0595362i
$636$		0			0
$637$	−31.3699	−	16.9022i	−1.24292	−	0.669690i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−10.1152	+	17.5200i	−0.399526	+	0.692000i	−0.993667	−	0.112361i	$-0.964159\pi$
$641$	−10.1152	+	17.5200i	−0.399526	+	0.692000i	0.594141	+	0.804361i	$0.297492\pi$
$642$		0			0
$643$	25.1850			0.993198			0.496599	−	0.867980i	$-0.334582\pi$
$643$	25.1850			0.993198			0.496599	+	0.867980i	$0.334582\pi$
$644$		0			0
$645$	3.32092			0.130761
$646$		0			0
$647$	9.78488	−	16.9479i	0.384683	−	0.666291i	−0.607042	−	0.794670i	$-0.707644\pi$
$647$	9.78488	−	16.9479i	0.384683	−	0.666291i	0.991725	+	0.128379i	$0.0409773\pi$
$648$		0			0
$649$	18.0078	+	31.1905i	0.706870	+	1.22433i
$650$		0			0
$651$	9.72024	−	2.75826i	0.380966	−	0.108105i
$652$		0			0
$653$	−9.13382	−	15.8202i	−0.357434	−	0.619094i	0.630097	−	0.776516i	$-0.283015\pi$
$653$	−9.13382	−	15.8202i	−0.357434	−	0.619094i	−0.987531	+	0.157422i	$0.949682\pi$
$654$		0			0
$655$	−6.36814	+	11.0299i	−0.248824	+	0.430975i
$656$		0			0
$657$	−20.4686			−0.798558
$658$		0			0
$659$	−46.0078			−1.79221			−0.896105	−	0.443841i	$-0.853615\pi$
$659$	−46.0078			−1.79221			−0.896105	+	0.443841i	$0.853615\pi$
$660$		0			0
$661$	24.2302	−	41.9680i	0.942446	−	1.63236i	0.181661	−	0.983361i	$-0.441853\pi$
$661$	24.2302	−	41.9680i	0.942446	−	1.63236i	0.760785	−	0.649004i	$-0.224814\pi$
$662$		0			0
$663$	3.59248	+	6.22236i	0.139520	+	0.241656i
$664$		0			0
$665$	−5.86618	−	5.69624i	−0.227481	−	0.220891i
$666$		0			0
$667$	27.5378	+	47.6969i	1.06627	+	1.84683i
$668$		0			0
$669$	6.29036	−	10.8952i	0.243199	−	0.421234i
$670$		0			0
$671$	−40.1278			−1.54912
$672$		0			0
$673$	−15.0118			−0.578661			−0.289330	−	0.957229i	$-0.593433\pi$
$673$	−15.0118			−0.578661			−0.289330	+	0.957229i	$0.593433\pi$
$674$		0			0
$675$	−1.94142	+	3.36264i	−0.0747253	+	0.129428i
$676$		0			0
$677$	−3.95670	−	6.85320i	−0.152068	−	0.263390i	0.779919	−	0.625880i	$-0.215260\pi$
$677$	−3.95670	−	6.85320i	−0.152068	−	0.263390i	−0.931988	+	0.362490i	$0.881927\pi$
$678$		0			0
$679$	1.29428	−	5.13077i	0.0496699	−	0.196901i
$680$		0			0
$681$	−1.89068	−	3.27475i	−0.0724510	−	0.125489i
$682$		0			0
$683$	14.8548	−	25.7293i	0.568404	−	0.984504i	−0.428320	−	0.903627i	$-0.640894\pi$
$683$	14.8548	−	25.7293i	0.568404	−	0.984504i	0.996724	−	0.0808774i	$-0.0257722\pi$
$684$		0			0
$685$	4.00000			0.152832
$686$		0			0
$687$	−17.0650			−0.651072
$688$		0			0
$689$	−25.2322	+	43.7034i	−0.961270	+	1.66497i
$690$		0			0
$691$	−10.8868	−	18.8564i	−0.414152	−	0.717332i	0.581187	−	0.813770i	$-0.302588\pi$
$691$	−10.8868	−	18.8564i	−0.414152	−	0.717332i	−0.995339	+	0.0964378i	$0.969255\pi$
$692$		0			0
$693$	7.28921	−	28.8958i	0.276894	−	1.09766i
$694$		0			0
$695$	−0.705720	−	1.22234i	−0.0267695	−	0.0463661i
$696$		0			0
$697$	6.59248	−	11.4185i	0.249708	−	0.432507i
$698$		0			0
$699$	−12.7030			−0.480470
$700$		0			0
$701$	24.0905			0.909886			0.454943	−	0.890520i	$-0.349660\pi$
$701$	24.0905			0.909886			0.454943	+	0.890520i	$0.349660\pi$
$702$		0			0
$703$	−10.9567	+	18.9776i	−0.413240	+	0.715752i
$704$		0			0
$705$	−3.56192	−	6.16943i	−0.134150	−	0.232354i
$706$		0			0
$707$	6.30350	+	6.12090i	0.237068	+	0.230200i
$708$		0			0
$709$	12.0186	+	20.8169i	0.451369	+	0.781794i	0.998471	−	0.0552719i	$-0.0176026\pi$
$709$	12.0186	+	20.8169i	0.451369	+	0.781794i	−0.547103	+	0.837066i	$0.684269\pi$
$710$		0			0
$711$	17.7402	−	30.7269i	0.665309	−	1.15235i
$712$		0			0
$713$	31.3660			1.17467
$714$		0			0
$715$	22.9173			0.857059
$716$		0			0
$717$	4.50588	−	7.80441i	0.168275	−	0.291461i
$718$		0			0
$719$	−0.117159	−	0.202925i	−0.00436929	−	0.00756783i	0.863832	−	0.503779i	$-0.168057\pi$
$719$	−0.117159	−	0.202925i	−0.00436929	−	0.00756783i	−0.868202	+	0.496211i	$0.834724\pi$
$720$		0			0
$721$	27.7096	−	7.86300i	1.03196	−	0.292833i
$722$		0			0
$723$	−7.79624	−	13.5035i	−0.289945	−	0.502200i
$724$		0			0
$725$	−4.75098	+	8.22894i	−0.176447	+	0.305615i
$726$		0			0
$727$	−9.44200			−0.350184			−0.175092	−	0.984552i	$-0.556022\pi$
$727$	−9.44200			−0.350184			−0.175092	+	0.984552i	$0.556022\pi$
$728$		0			0
$729$	−3.70295			−0.137146
$730$		0			0
$731$	4.70572	−	8.15055i	0.174047	−	0.301459i
$732$		0			0
$733$	14.3721	+	24.8931i	0.530844	+	0.919449i	0.999352	+	0.0359897i	$0.0114584\pi$
$733$	14.3721	+	24.8931i	0.530844	+	0.919449i	−0.468508	+	0.883459i	$0.655208\pi$
$734$		0			0
$735$	4.34894	+	2.34322i	0.160413	+	0.0864310i
$736$		0			0
$737$	−0.263722	−	0.456781i	−0.00971434	−	0.0168257i
$738$		0			0
$739$	−13.0739	+	22.6446i	−0.480930	+	0.832995i	−0.999761	−	0.0218823i	$-0.993034\pi$
$739$	−13.0739	+	22.6446i	−0.480930	+	0.832995i	0.518831	+	0.854877i	$0.326367\pi$
$740$		0			0
$741$	−11.1026			−0.407865
$742$		0			0
$743$	−32.7547			−1.20165			−0.600827	−	0.799379i	$-0.705162\pi$
$743$	−32.7547			−1.20165			−0.600827	+	0.799379i	$0.705162\pi$
$744$		0			0
$745$	−11.5472	+	20.0004i	−0.423057	+	0.732757i
$746$		0			0
$747$	13.3926	+	23.1967i	0.490011	+	0.848724i
$748$		0			0
$749$	−9.88284	+	2.80440i	−0.361111	+	0.102470i
$750$		0			0
$751$	13.0905	+	22.6734i	0.477680	+	0.827366i	0.999673	−	0.0255841i	$-0.00814455\pi$
$751$	13.0905	+	22.6734i	0.477680	+	0.827366i	−0.521993	+	0.852950i	$0.674811\pi$
$752$		0			0
$753$	4.76568	−	8.25440i	0.173671	−	0.300807i
$754$		0			0
$755$	0.407520			0.0148312
$756$		0			0
$757$	16.8229			0.611438			0.305719	−	0.952122i	$-0.401103\pi$
$757$	16.8229			0.611438			0.305719	+	0.952122i	$0.401103\pi$
$758$		0			0
$759$	−9.20768	+	15.9482i	−0.334218	+	0.578882i
$760$		0			0
$761$	2.95278	+	5.11436i	0.107038	+	0.185396i	0.914569	−	0.404430i	$-0.132530\pi$
$761$	2.95278	+	5.11436i	0.107038	+	0.185396i	−0.807531	+	0.589825i	$0.799197\pi$
$762$		0			0
$763$	19.4967	+	18.9319i	0.705826	+	0.685379i
$764$		0			0
$765$	2.50196	+	4.33352i	0.0904585	+	0.156679i
$766$		0			0
$767$	20.3621	−	35.2682i	0.735232	−	1.27346i
$768$		0			0
$769$	0.275481			0.00993410			0.00496705	−	0.999988i	$-0.498419\pi$
$769$	0.275481			0.00993410			0.00496705	+	0.999988i	$0.498419\pi$
$770$		0			0
$771$	11.5470			0.415857
$772$		0			0
$773$	−3.68906	+	6.38964i	−0.132686	+	0.229819i	−0.924711	−	0.380669i	$-0.875694\pi$
$773$	−3.68906	+	6.38964i	−0.132686	+	0.229819i	0.792025	+	0.610489i	$0.209027\pi$
$774$		0			0
$775$	2.70572	+	4.68644i	0.0971923	+	0.168342i
$776$		0			0
$777$	3.23824	−	12.8370i	0.116171	−	0.460524i
$778$		0			0
$779$	10.1871	+	17.6446i	0.364991	+	0.632182i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	36.8946			1.31851
$784$		0			0
$785$	−14.0944			−0.503052
$786$		0			0
$787$	−9.33014	+	16.1603i	−0.332584	+	0.576052i	−0.983018	−	0.183511i	$-0.941254\pi$
$787$	−9.33014	+	16.1603i	−0.332584	+	0.576052i	0.650434	+	0.759563i	$0.274587\pi$
$788$		0			0
$789$	−3.21570	−	5.56975i	−0.114482	−	0.198288i
$790$		0			0
$791$	−1.82680	+	7.24178i	−0.0649535	+	0.257488i
$792$		0			0
$793$	22.6869	+	39.2949i	0.805636	+	1.39540i
$794$		0			0
$795$	3.49804	−	6.05878i	0.124063	−	0.214883i
$796$		0			0
$797$	9.81896			0.347805			0.173903	−	0.984763i	$-0.444362\pi$
$797$	9.81896			0.347805			0.173903	+	0.984763i	$0.444362\pi$
$798$		0			0
$799$	−20.1889			−0.714231
$800$		0			0
$801$	5.11716	−	8.86318i	0.180806	−	0.313165i
$802$		0			0
$803$	−18.4154	−	31.8963i	−0.649864	−	1.12560i
$804$		0			0
$805$	11.0020	+	10.6832i	0.387768	+	0.376535i
$806$		0			0
$807$	3.14518	+	5.44761i	0.110716	+	0.191765i
$808$		0			0
$809$	16.0020	−	27.7162i	0.562599	−	0.974450i	−0.434670	−	0.900590i	$-0.643135\pi$
$809$	16.0020	−	27.7162i	0.562599	−	0.974450i	0.997269	−	0.0738600i	$-0.0235318\pi$
$810$		0			0
$811$	−43.5137			−1.52797			−0.763987	−	0.645232i	$-0.776761\pi$
$811$	−43.5137			−1.52797			−0.763987	+	0.645232i	$0.776761\pi$
$812$		0			0
$813$	11.5470			0.404972
$814$		0			0
$815$	−8.09052	+	14.0132i	−0.283399	+	0.490861i
$816$		0			0
$817$	7.27156	+	12.5947i	0.254400	+	0.440633i
$818$		0			0
$819$	−32.4171	+	9.19882i	−1.13275	+	0.321433i
$820$		0			0
$821$	17.3621	+	30.0720i	0.605941	+	1.04952i	0.991902	+	0.127005i	$0.0405365\pi$
$821$	17.3621	+	30.0720i	0.605941	+	1.04952i	−0.385961	+	0.922515i	$0.626130\pi$
$822$		0			0
$823$	−11.6511	+	20.1802i	−0.406130	+	0.703439i	−0.994452	−	0.105188i	$-0.966455\pi$
$823$	−11.6511	+	20.1802i	−0.406130	+	0.703439i	0.588322	+	0.808627i	$0.299789\pi$
$824$		0			0
$825$	−3.17712			−0.110613
$826$		0			0
$827$	−11.2943			−0.392741			−0.196370	−	0.980530i	$-0.562915\pi$
$827$	−11.2943			−0.392741			−0.196370	+	0.980530i	$0.562915\pi$
$828$		0			0
$829$	−10.0039	+	17.3273i	−0.347450	+	0.601802i	−0.985796	−	0.167948i	$-0.946286\pi$
$829$	−10.0039	+	17.3273i	−0.347450	+	0.601802i	0.638345	+	0.769750i	$0.279619\pi$
$830$		0			0
$831$	3.94396	+	6.83113i	0.136814	+	0.236969i
$832$		0			0
$833$	11.9134	−	7.35329i	0.412775	−	0.254777i
$834$		0			0
$835$	3.89812	+	6.75174i	0.134900	+	0.233654i
$836$		0			0
$837$	10.5059	−	18.1967i	0.363136	−	0.628971i
$838$		0			0
$839$	−13.5846			−0.468994			−0.234497	−	0.972117i	$-0.575344\pi$
$839$	−13.5846			−0.468994			−0.234497	+	0.972117i	$0.575344\pi$
$840$		0			0
$841$	61.2872			2.11335
$842$		0			0
$843$	−9.97728	+	17.2812i	−0.343636	+	0.595195i
$844$		0			0
$845$	−6.45670	−	11.1833i	−0.222117	−	0.384718i
$846$		0			0
$847$	23.5886	−	6.69359i	0.810513	−	0.229994i
$848$		0			0
$849$	4.52468	+	7.83697i	0.155287	+	0.268964i
$850$		0			0
$851$	20.5492	−	35.5922i	0.704417	−	1.22009i
$852$		0			0
$853$	−29.6336			−1.01464			−0.507318	−	0.861759i	$-0.669363\pi$
$853$	−29.6336			−1.01464			−0.507318	+	0.861759i	$0.669363\pi$
$854$		0			0
$855$	−7.73236			−0.264441
$856$		0			0
$857$	9.41536	−	16.3079i	0.321623	−	0.557067i	−0.659200	−	0.751967i	$-0.729105\pi$
$857$	9.41536	−	16.3079i	0.321623	−	0.557067i	0.980823	+	0.194901i	$0.0624385\pi$
$858$		0			0
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	0.926161	−	0.377128i	$-0.123088\pi$
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	−0.789683	+	0.613515i	$0.789755\pi$
$860$		0			0
$861$	−8.83090	−	8.57507i	−0.300956	−	0.292238i
$862$		0			0
$863$	9.92868	+	17.1970i	0.337976	+	0.585392i	0.984052	−	0.177881i	$-0.0569244\pi$
$863$	9.92868	+	17.1970i	0.337976	+	0.585392i	−0.646076	+	0.763273i	$0.723591\pi$
$864$		0			0
$865$	4.45474	−	7.71584i	0.151466	−	0.262346i
$866$		0			0
$867$	9.17436			0.311577
$868$		0			0
$869$	63.8425			2.16571
$870$		0			0
$871$	−0.298200	+	0.516497i	−0.0101041	+	0.0175008i
$872$		0			0
$873$	−2.50196	−	4.33352i	−0.0846785	−	0.146667i
$874$		0			0
$875$	−0.647140	+	2.56539i	−0.0218773	+	0.0867259i
$876$		0			0
$877$	6.77566	+	11.7358i	0.228798	+	0.396289i	0.957452	−	0.288592i	$-0.0931872\pi$
$877$	6.77566	+	11.7358i	0.228798	+	0.396289i	−0.728654	+	0.684882i	$0.759854\pi$
$878$		0			0
$879$	3.14380	−	5.44522i	0.106038	−	0.183663i
$880$		0			0
$881$	−47.5964			−1.60356			−0.801782	−	0.597617i	$-0.796114\pi$
$881$	−47.5964			−1.60356			−0.801782	+	0.597617i	$0.796114\pi$
$882$		0			0
$883$	−36.6497			−1.23336			−0.616680	−	0.787214i	$-0.711523\pi$
$883$	−36.6497			−1.23336			−0.616680	+	0.787214i	$0.711523\pi$
$884$		0			0
$885$	−2.82288	+	4.88937i	−0.0948900	+	0.164354i
$886$		0			0
$887$	23.0625	+	39.9454i	0.774363	+	1.34124i	0.935152	+	0.354247i	$0.115263\pi$
$887$	23.0625	+	39.9454i	0.774363	+	1.34124i	−0.160789	+	0.986989i	$0.551404\pi$
$888$		0			0
$889$	−1.12108	+	4.44417i	−0.0375998	+	0.149053i
$890$		0			0
$891$	−10.7275	−	18.5805i	−0.359383	−	0.622470i
$892$		0			0
$893$	15.5985	−	27.0175i	0.521985	−	0.904105i
$894$		0			0
$895$	−1.67908			−0.0561255
$896$		0			0
$897$	20.8229			0.695256
$898$		0			0
$899$	25.7096	−	44.5304i	0.857464	−	1.48517i
$900$		0			0
$901$	−9.91340	−	17.1705i	−0.330263	−	0.572033i
$902$		0			0
$903$	−6.30350	−	6.12090i	−0.209767	−	0.203691i
$904$		0			0
$905$	−6.25294	−	10.8304i	−0.207855	−	0.360015i
$906$		0			0
$907$	−2.53390	+	4.38884i	−0.0841368	+	0.145729i	−0.905023	−	0.425363i	$-0.860147\pi$
$907$	−2.53390	+	4.38884i	−0.0841368	+	0.145729i	0.820886	+	0.571092i	$0.193480\pi$
$908$		0			0
$909$	8.30881			0.275586
$910$		0			0
$911$	2.41536			0.0800244			0.0400122	−	0.999199i	$-0.487260\pi$
$911$	2.41536			0.0800244			0.0400122	+	0.999199i	$0.487260\pi$
$912$		0			0
$913$	−24.0984	+	41.7396i	−0.797539	+	1.38138i
$914$		0			0
$915$	−3.14518	−	5.44761i	−0.103976	−	0.180093i
$916$		0			0
$917$	32.4171	−	9.19882i	1.07051	−	0.303772i
$918$		0			0
$919$	18.2755	+	31.6541i	0.602852	+	1.04417i	0.992387	+	0.123159i	$0.0393026\pi$
$919$	18.2755	+	31.6541i	0.602852	+	1.04417i	−0.389534	+	0.921012i	$0.627364\pi$
$920$		0			0
$921$	3.21846	−	5.57454i	0.106052	−	0.183687i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	7.09052			0.233135
$926$		0			0
$927$	13.6191	−	23.5890i	0.447311	−	0.774765i
$928$		0			0
$929$	8.11520	+	14.0559i	0.266251	+	0.461160i	0.967891	−	0.251372i	$-0.0808816\pi$
$929$	8.11520	+	14.0559i	0.266251	+	0.461160i	−0.701640	+	0.712532i	$0.747548\pi$
$930$		0			0
$931$	0.635781	+	21.6243i	0.0208369	+	0.708708i
$932$		0			0
$933$	4.64968	+	8.05348i	0.152224	+	0.263659i
$934$		0			0
$935$	−4.50196	+	7.79762i	−0.147230	+	0.255010i
$936$		0			0
$937$	−44.1889			−1.44359			−0.721794	−	0.692108i	$-0.756682\pi$
$937$	−44.1889			−1.44359			−0.721794	+	0.692108i	$0.756682\pi$
$938$		0			0
$939$	12.3778			0.403933
$940$		0			0
$941$	−11.7363	+	20.3278i	−0.382592	+	0.662668i	−0.991432	−	0.130625i	$-0.958302\pi$
$941$	−11.7363	+	20.3278i	−0.382592	+	0.662668i	0.608840	+	0.793293i	$0.291635\pi$
$942$		0			0
$943$	−19.1058	−	33.0922i	−0.622170	−	1.07763i
$944$		0			0
$945$	9.88284	−	2.80440i	0.321489	−	0.0912270i
$946$		0			0
$947$	28.0359	+	48.5595i	0.911043	+	1.57797i	0.812594	+	0.582831i	$0.198055\pi$
$947$	28.0359	+	48.5595i	0.911043	+	1.57797i	0.0984495	+	0.995142i	$0.468612\pi$
$948$		0			0
$949$	−20.8229	+	36.0663i	−0.675939	+	1.17076i
$950$		0			0
$951$	9.30489			0.301732
$952$		0			0
$953$	−22.7163			−0.735854			−0.367927	−	0.929855i	$-0.619932\pi$
$953$	−22.7163			−0.735854			−0.367927	+	0.929855i	$0.619932\pi$
$954$		0			0
$955$	3.29428	−	5.70586i	0.106600	−	0.184637i
$956$		0			0
$957$	15.0944	+	26.1443i	0.487934	+	0.845126i
$958$		0			0
$959$	−7.59248	−	7.37253i	−0.245174	−	0.238072i
$960$		0			0
$961$	0.858162	+	1.48638i	0.0276827	+	0.0479478i
$962$		0			0
$963$	−4.85736	+	8.41319i	−0.156526	+	0.271111i
$964$		0			0
$965$	17.8268			0.573865
$966$		0			0
$967$	−10.9400			−0.351808			−0.175904	−	0.984407i	$-0.556285\pi$
$967$	−10.9400			−0.351808			−0.175904	+	0.984407i	$0.556285\pi$
$968$		0			0
$969$	2.18104	−	3.77767i	0.0700651	−	0.121356i
$970$		0			0
$971$	12.8701	+	22.2917i	0.413021	+	0.715374i	0.995218	−	0.0976739i	$-0.0311402\pi$
$971$	12.8701	+	22.2917i	0.413021	+	0.715374i	−0.582197	+	0.813048i	$0.697807\pi$
$972$		0			0
$973$	−0.913399	+	3.62089i	−0.0292822	+	0.116080i
$974$		0			0
$975$	1.79624	+	3.11118i	0.0575257	+	0.0996375i
$976$		0			0
$977$	−8.41144	+	14.5690i	−0.269106	+	0.466105i	−0.968631	−	0.248503i	$-0.920061\pi$
$977$	−8.41144	+	14.5690i	−0.269106	+	0.466105i	0.699525	+	0.714608i	$0.253395\pi$
$978$		0			0
$979$	18.4154			0.588557
$980$		0			0
$981$	25.6990			0.820507
$982$		0			0
$983$	−21.9926	+	38.0922i	−0.701454	+	1.21495i	0.266502	+	0.963834i	$0.414132\pi$
$983$	−21.9926	+	38.0922i	−0.701454	+	1.21495i	−0.967956	+	0.251119i	$0.919201\pi$
$984$		0			0
$985$	−2.54526	−	4.40852i	−0.0810987	−	0.140467i
$986$		0			0
$987$	−4.61013	+	18.2754i	−0.146742	+	0.581713i
$988$		0			0
$989$	−13.6377	−	23.6213i	−0.433655	−	0.751112i
$990$		0			0
$991$	−22.1172	+	38.3080i	−0.702575	+	1.21690i	0.264985	+	0.964253i	$0.414633\pi$
$991$	−22.1172	+	38.3080i	−0.702575	+	1.21690i	−0.967560	+	0.252643i	$0.918700\pi$
$992$		0			0
$993$	6.00000			0.190404
$994$		0			0
$995$	−24.3621			−0.772330
$996$		0			0
$997$	−17.0984	+	29.6152i	−0.541510	+	0.937924i	0.457307	+	0.889309i	$0.348814\pi$
$997$	−17.0984	+	29.6152i	−0.541510	+	0.937924i	−0.998818	+	0.0486148i	$0.984519\pi$
$998$		0			0
$999$	−13.7657	−	23.8429i	−0.435527	−	0.754355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.q.l.81.2		6
4.3	odd	2		280.2.q.e.81.2	✓	6
7.2	even	3	inner	560.2.q.l.401.2		6
7.3	odd	6		3920.2.a.cb.1.2		3
7.4	even	3		3920.2.a.cc.1.2		3
12.11	even	2		2520.2.bi.q.361.2		6
20.3	even	4		1400.2.bh.i.249.3		12
20.7	even	4		1400.2.bh.i.249.4		12
20.19	odd	2		1400.2.q.j.1201.2		6
28.3	even	6		1960.2.a.v.1.2		3
28.11	odd	6		1960.2.a.w.1.2		3
28.19	even	6		1960.2.q.w.961.2		6
28.23	odd	6		280.2.q.e.121.2	yes	6
28.27	even	2		1960.2.q.w.361.2		6
84.23	even	6		2520.2.bi.q.1801.2		6
140.23	even	12		1400.2.bh.i.849.4		12
140.39	odd	6		9800.2.a.ce.1.2		3
140.59	even	6		9800.2.a.cf.1.2		3
140.79	odd	6		1400.2.q.j.401.2		6
140.107	even	12		1400.2.bh.i.849.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.e.81.2	✓	6	4.3	odd	2
280.2.q.e.121.2	yes	6	28.23	odd	6
560.2.q.l.81.2		6	1.1	even	1	trivial
560.2.q.l.401.2		6	7.2	even	3	inner
1400.2.q.j.401.2		6	140.79	odd	6
1400.2.q.j.1201.2		6	20.19	odd	2
1400.2.bh.i.249.3		12	20.3	even	4
1400.2.bh.i.249.4		12	20.7	even	4
1400.2.bh.i.849.3		12	140.107	even	12
1400.2.bh.i.849.4		12	140.23	even	12
1960.2.a.v.1.2		3	28.3	even	6
1960.2.a.w.1.2		3	28.11	odd	6
1960.2.q.w.361.2		6	28.27	even	2
1960.2.q.w.961.2		6	28.19	even	6
2520.2.bi.q.361.2		6	12.11	even	2
2520.2.bi.q.1801.2		6	84.23	even	6
3920.2.a.cb.1.2		3	7.3	odd	6
3920.2.a.cc.1.2		3	7.4	even	3
9800.2.a.ce.1.2		3	140.39	odd	6
9800.2.a.cf.1.2		3	140.59	even	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.352860 - 0.611171i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.647140 + 2.56539i) q^{7} +(1.25098 + 2.16676i) q^{9} +O(q^{10})\)	\(q+(0.352860 - 0.611171i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-0.647140 + 2.56539i) q^{7} +(1.25098 + 2.16676i) q^{9} +(-2.25098 + 3.89881i) q^{11} +5.09052 q^{13} -0.705720 q^{15} +(-1.00000 + 1.73205i) q^{17} +(-1.54526 - 2.67647i) q^{19} +(1.33954 + 1.30074i) q^{21} +(2.89812 + 5.01969i) q^{23} +(-0.500000 + 0.866025i) q^{25} +3.88284 q^{27} +9.50196 q^{29} +(2.70572 - 4.68644i) q^{31} +(1.58856 + 2.75147i) q^{33} +(2.54526 - 0.722254i) q^{35} +(-3.54526 - 6.14057i) q^{37} +(1.79624 - 3.11118i) q^{39} -6.59248 q^{41} -4.70572 q^{43} +(1.25098 - 2.16676i) q^{45} +(5.04722 + 8.74204i) q^{47} +(-6.16242 - 3.32033i) q^{49} +(0.705720 + 1.22234i) q^{51} +(-4.95670 + 8.58526i) q^{53} +4.50196 q^{55} -2.18104 q^{57} +(4.00000 - 6.92820i) q^{59} +(4.45670 + 7.71923i) q^{61} +(-6.36814 + 1.80705i) q^{63} +(-2.54526 - 4.40852i) q^{65} +(-0.0585795 + 0.101463i) q^{67} +4.09052 q^{69} +(-4.09052 + 7.08499i) q^{73} +(0.352860 + 0.611171i) q^{75} +(-8.54526 - 8.29771i) q^{77} +(-7.09052 - 12.2811i) q^{79} +(-2.38284 + 4.12720i) q^{81} +10.7057 q^{83} +2.00000 q^{85} +(3.35286 - 5.80732i) q^{87} +(-2.04526 - 3.54249i) q^{89} +(-3.29428 + 13.0592i) q^{91} +(-1.90948 - 3.30732i) q^{93} +(-1.54526 + 2.67647i) q^{95} -2.00000 q^{97} -11.2637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 6 q^{7} - 9 q^{9}+O(q^{10}) \) 6 * q - 3 * q^5 - 6 * q^7 - 9 * q^9	\( 6 q - 3 q^{5} - 6 q^{7} - 9 q^{9} + 3 q^{11} + 6 q^{13} - 6 q^{17} + 3 q^{19} + 3 q^{23} - 3 q^{25} + 36 q^{27} + 24 q^{29} + 12 q^{31} + 18 q^{33} + 3 q^{35} - 9 q^{37} - 18 q^{39} + 18 q^{41} - 24 q^{43} - 9 q^{45} - 15 q^{47} - 12 q^{49} - 9 q^{53} - 6 q^{55} + 36 q^{57} + 24 q^{59} + 6 q^{61} - 9 q^{63} - 3 q^{65} + 6 q^{67} - 39 q^{77} - 18 q^{79} - 27 q^{81} + 60 q^{83} + 12 q^{85} + 18 q^{87} - 24 q^{91} - 36 q^{93} + 3 q^{95} - 12 q^{97} - 126 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 - 6 * q^7 - 9 * q^9 + 3 * q^11 + 6 * q^13 - 6 * q^17 + 3 * q^19 + 3 * q^23 - 3 * q^25 + 36 * q^27 + 24 * q^29 + 12 * q^31 + 18 * q^33 + 3 * q^35 - 9 * q^37 - 18 * q^39 + 18 * q^41 - 24 * q^43 - 9 * q^45 - 15 * q^47 - 12 * q^49 - 9 * q^53 - 6 * q^55 + 36 * q^57 + 24 * q^59 + 6 * q^61 - 9 * q^63 - 3 * q^65 + 6 * q^67 - 39 * q^77 - 18 * q^79 - 27 * q^81 + 60 * q^83 + 12 * q^85 + 18 * q^87 - 24 * q^91 - 36 * q^93 + 3 * q^95 - 12 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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