LMFDB - Embedded newform 784.2.bg.b.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(65,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 0, 20]))

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

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

chi := DirichletCharacter("784.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bg (of order $21$, degree $12$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 98)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			81.1
Character	$\chi$	$=$	784.81
Dual form			784.2.bg.b.513.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95066 - 0.601698i) q^{3} +(0.958118 - 0.889004i) q^{5} +(2.43754 + 1.02877i) q^{7} +(0.964304 + 0.657452i) q^{9} +O(q^{10})$	\(q+(-1.95066 - 0.601698i) q^{3} +(0.958118 - 0.889004i) q^{5} +(2.43754 + 1.02877i) q^{7} +(0.964304 + 0.657452i) q^{9} +(2.30365 - 1.57060i) q^{11} +(-0.810304 - 0.390222i) q^{13} +(-2.40387 + 1.15764i) q^{15} +(0.719733 + 1.83385i) q^{17} +(-0.387065 - 0.670417i) q^{19} +(-4.13580 - 3.47345i) q^{21} +(-2.28676 + 5.82658i) q^{23} +(-0.245988 + 3.28248i) q^{25} +(2.33284 + 2.92529i) q^{27} +(6.52548 - 8.18270i) q^{29} +(4.21876 - 7.30711i) q^{31} +(-5.43865 + 1.67760i) q^{33} +(3.25004 - 1.18130i) q^{35} +(3.65860 + 0.551445i) q^{37} +(1.34583 + 1.24875i) q^{39} +(-1.26678 - 5.55015i) q^{41} +(2.00714 - 8.79388i) q^{43} +(1.50839 - 0.227354i) q^{45} +(-0.907661 - 12.1119i) q^{47} +(4.88324 + 5.01537i) q^{49} +(-0.300528 - 4.01027i) q^{51} +(6.87650 - 1.03647i) q^{53} +(0.810897 - 3.55277i) q^{55} +(0.351643 + 1.54065i) q^{57} +(-3.85448 - 3.57644i) q^{59} +(-12.1696 - 1.83427i) q^{61} +(1.67417 + 2.59462i) q^{63} +(-1.12328 + 0.346485i) q^{65} +(-0.734787 + 1.27269i) q^{67} +(7.96653 - 9.98972i) q^{69} +(3.74129 + 4.69143i) q^{71} +(0.00237545 - 0.0316982i) q^{73} +(2.45490 - 6.25498i) q^{75} +(7.23103 - 1.45847i) q^{77} +(6.94343 + 12.0264i) q^{79} +(-4.06960 - 10.3692i) q^{81} +(9.26679 - 4.46265i) q^{83} +(2.31989 + 1.11720i) q^{85} +(-17.6525 + 12.0353i) q^{87} +(2.43024 + 1.65691i) q^{89} +(-1.57370 - 1.78480i) q^{91} +(-12.6260 + 11.7153i) q^{93} +(-0.966857 - 0.298236i) q^{95} +9.86141 q^{97} +3.25401 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 7 q^{3} + 19 q^{9}+O(q^{10}) $ 24 * q + 7 * q^3 + 19 * q^9	$ 24 q + 7 q^{3} + 19 q^{9} + 11 q^{11} - 14 q^{13} - 9 q^{15} - 7 q^{17} + 14 q^{19} - 7 q^{21} + 29 q^{23} - 8 q^{25} + 7 q^{27} + 13 q^{29} + 28 q^{31} - 14 q^{33} + 35 q^{35} + 20 q^{37} - 56 q^{39} + 28 q^{41} - 6 q^{43} + 7 q^{45} - 42 q^{47} + 28 q^{49} - 32 q^{51} - 60 q^{53} + 14 q^{55} + 23 q^{57} - 49 q^{59} - 14 q^{61} + 28 q^{63} - 28 q^{65} - 24 q^{67} + 7 q^{69} - 6 q^{71} - 35 q^{73} + 56 q^{75} + 49 q^{77} - 6 q^{79} - 45 q^{81} + 77 q^{83} - 33 q^{85} - 63 q^{87} + 21 q^{91} - 38 q^{93} - 86 q^{95} + 98 q^{97} + 106 q^{99}+O(q^{100}) $ 24 * q + 7 * q^3 + 19 * q^9 + 11 * q^11 - 14 * q^13 - 9 * q^15 - 7 * q^17 + 14 * q^19 - 7 * q^21 + 29 * q^23 - 8 * q^25 + 7 * q^27 + 13 * q^29 + 28 * q^31 - 14 * q^33 + 35 * q^35 + 20 * q^37 - 56 * q^39 + 28 * q^41 - 6 * q^43 + 7 * q^45 - 42 * q^47 + 28 * q^49 - 32 * q^51 - 60 * q^53 + 14 * q^55 + 23 * q^57 - 49 * q^59 - 14 * q^61 + 28 * q^63 - 28 * q^65 - 24 * q^67 + 7 * q^69 - 6 * q^71 - 35 * q^73 + 56 * q^75 + 49 * q^77 - 6 * q^79 - 45 * q^81 + 77 * q^83 - 33 * q^85 - 63 * q^87 + 21 * q^91 - 38 * q^93 - 86 * q^95 + 98 * q^97 + 106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{21}\right)$

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
$3$	−1.95066	−	0.601698i	−1.12621	−	0.347390i	−0.324966	−	0.945726i	$-0.605353\pi$
$3$	−1.95066	−	0.601698i	−1.12621	−	0.347390i	−0.801246	+	0.598335i	$0.795829\pi$
$4$		0			0
$5$	0.958118	−	0.889004i	0.428484	−	0.397575i	−0.436234	−	0.899833i	$-0.643688\pi$
$5$	0.958118	−	0.889004i	0.428484	−	0.397575i	0.864717	+	0.502259i	$0.167497\pi$
$6$		0			0
$7$	2.43754	+	1.02877i	0.921305	+	0.388840i
$7$	2.43754	+	1.02877i	0.921305	+	0.388840i
$8$		0			0
$9$	0.964304	+	0.657452i	0.321435	+	0.219151i
$10$		0			0
$11$	2.30365	−	1.57060i	0.694575	−	0.473553i	−0.163854	−	0.986485i	$-0.552393\pi$
$11$	2.30365	−	1.57060i	0.694575	−	0.473553i	0.858430	+	0.512931i	$0.171440\pi$
$12$		0			0
$13$	−0.810304	−	0.390222i	−0.224738	−	0.108228i	0.318127	−	0.948048i	$-0.396946\pi$
$13$	−0.810304	−	0.390222i	−0.224738	−	0.108228i	−0.542865	+	0.839820i	$0.682660\pi$
$14$		0			0
$15$	−2.40387	+	1.15764i	−0.620677	+	0.298902i
$16$		0			0
$17$	0.719733	+	1.83385i	0.174561	+	0.444774i	0.991200	−	0.132375i	$-0.0422604\pi$
$17$	0.719733	+	1.83385i	0.174561	+	0.444774i	−0.816639	+	0.577149i	$0.804165\pi$
$18$		0			0
$19$	−0.387065	−	0.670417i	−0.0887989	−	0.153804i	0.818205	−	0.574927i	$-0.194970\pi$
$19$	−0.387065	−	0.670417i	−0.0887989	−	0.153804i	−0.907004	+	0.421123i	$0.861636\pi$
$20$		0			0
$21$	−4.13580	−	3.47345i	−0.902506	−	0.757969i
$22$		0			0
$23$	−2.28676	+	5.82658i	−0.476823	+	1.21493i	0.466936	+	0.884291i	$0.345358\pi$
$23$	−2.28676	+	5.82658i	−0.476823	+	1.21493i	−0.943759	+	0.330635i	$0.892737\pi$
$24$		0			0
$25$	−0.245988	+	3.28248i	−0.0491975	+	0.656495i
$26$		0			0
$27$	2.33284	+	2.92529i	0.448955	+	0.562972i
$28$		0			0
$29$	6.52548	−	8.18270i	1.21175	−	1.51949i	0.421353	−	0.906897i	$-0.361555\pi$
$29$	6.52548	−	8.18270i	1.21175	−	1.51949i	0.790399	−	0.612592i	$-0.209873\pi$
$30$		0			0
$31$	4.21876	−	7.30711i	0.757713	−	1.31240i	−0.186302	−	0.982493i	$-0.559650\pi$
$31$	4.21876	−	7.30711i	0.757713	−	1.31240i	0.944014	−	0.329904i	$-0.107016\pi$
$32$		0			0
$33$	−5.43865	+	1.67760i	−0.946747	+	0.292033i
$34$		0			0
$35$	3.25004	−	1.18130i	0.549357	−	0.199676i
$36$		0			0
$37$	3.65860	+	0.551445i	0.601470	+	0.0906570i	0.442717	−	0.896661i	$-0.354015\pi$
$37$	3.65860	+	0.551445i	0.601470	+	0.0906570i	0.158753	+	0.987318i	$0.449253\pi$
$38$		0			0
$39$	1.34583	+	1.24875i	0.215505	+	0.199959i
$40$		0			0
$41$	−1.26678	−	5.55015i	−0.197838	−	0.866787i	−0.972220	−	0.234068i	$-0.924796\pi$
$41$	−1.26678	−	5.55015i	−0.197838	−	0.866787i	0.774382	−	0.632719i	$-0.218061\pi$
$42$		0			0
$43$	2.00714	−	8.79388i	0.306087	−	1.34105i	−0.554684	−	0.832061i	$-0.687161\pi$
$43$	2.00714	−	8.79388i	0.306087	−	1.34105i	0.860771	−	0.508993i	$-0.169982\pi$
$44$		0			0
$45$	1.50839	−	0.227354i	0.224858	−	0.0338919i
$46$		0			0
$47$	−0.907661	−	12.1119i	−0.132396	−	1.76670i	−0.528915	−	0.848675i	$-0.677401\pi$
$47$	−0.907661	−	12.1119i	−0.132396	−	1.76670i	0.396520	−	0.918026i	$-0.370218\pi$
$48$		0			0
$49$	4.88324	+	5.01537i	0.697606	+	0.716481i
$50$		0			0
$51$	−0.300528	−	4.01027i	−0.0420824	−	0.561551i
$52$		0			0
$53$	6.87650	−	1.03647i	0.944560	−	0.142369i	0.341336	−	0.939941i	$-0.389121\pi$
$53$	6.87650	−	1.03647i	0.944560	−	0.142369i	0.603224	+	0.797572i	$0.293883\pi$
$54$		0			0
$55$	0.810897	−	3.55277i	0.109341	−	0.479055i
$56$		0			0
$57$	0.351643	+	1.54065i	0.0465763	+	0.204064i
$58$		0			0
$59$	−3.85448	−	3.57644i	−0.501811	−	0.465613i	0.388185	−	0.921582i	$-0.373102\pi$
$59$	−3.85448	−	3.57644i	−0.501811	−	0.465613i	−0.889996	+	0.455969i	$0.849293\pi$
$60$		0			0
$61$	−12.1696	−	1.83427i	−1.55815	−	0.234854i	−0.687292	−	0.726381i	$-0.741201\pi$
$61$	−12.1696	−	1.83427i	−1.55815	−	0.234854i	−0.870862	+	0.491527i	$0.836439\pi$
$62$		0			0
$63$	1.67417	+	2.59462i	0.210925	+	0.326891i
$64$		0			0
$65$	−1.12328	+	0.346485i	−0.139325	+	0.0429761i
$66$		0			0
$67$	−0.734787	+	1.27269i	−0.0897685	+	0.155484i	−0.907413	−	0.420240i	$-0.861946\pi$
$67$	−0.734787	+	1.27269i	−0.0897685	+	0.155484i	0.817645	+	0.575723i	$0.195279\pi$
$68$		0			0
$69$	7.96653	−	9.98972i	0.959058	−	1.20262i
$70$		0			0
$71$	3.74129	+	4.69143i	0.444010	+	0.556771i	0.952595	−	0.304241i	$-0.0984028\pi$
$71$	3.74129	+	4.69143i	0.444010	+	0.556771i	−0.508585	+	0.861012i	$0.669831\pi$
$72$		0			0
$73$	0.00237545	−	0.0316982i	0.000278025	−	0.00370999i	−0.997063	−	0.0765850i	$-0.975598\pi$
$73$	0.00237545	−	0.0316982i	0.000278025	−	0.00370999i	0.997341	+	0.0728750i	$0.0232174\pi$
$74$		0			0
$75$	2.45490	−	6.25498i	0.283467	−	0.722262i
$76$		0			0
$77$	7.23103	−	1.45847i	0.824052	−	0.166208i
$78$		0			0
$79$	6.94343	+	12.0264i	0.781196	+	1.35307i	0.931245	+	0.364393i	$0.118724\pi$
$79$	6.94343	+	12.0264i	0.781196	+	1.35307i	−0.150049	+	0.988679i	$0.547943\pi$
$80$		0			0
$81$	−4.06960	−	10.3692i	−0.452178	−	1.15213i
$82$		0			0
$83$	9.26679	−	4.46265i	1.01716	−	0.489840i	0.150434	−	0.988620i	$-0.451933\pi$
$83$	9.26679	−	4.46265i	1.01716	−	0.489840i	0.866728	+	0.498780i	$0.166219\pi$
$84$		0			0
$85$	2.31989	+	1.11720i	0.251627	+	0.121177i
$86$		0			0
$87$	−17.6525	+	12.0353i	−1.89255	+	1.29032i
$88$		0			0
$89$	2.43024	+	1.65691i	0.257605	+	0.175632i	0.685236	−	0.728321i	$-0.259699\pi$
$89$	2.43024	+	1.65691i	0.257605	+	0.175632i	−0.427631	+	0.903954i	$0.640652\pi$
$90$		0			0
$91$	−1.57370	−	1.78480i	−0.164969	−	0.187098i
$92$		0			0
$93$	−12.6260	+	11.7153i	−1.30926	+	1.21481i
$94$		0			0
$95$	−0.966857	−	0.298236i	−0.0991975	−	0.0305984i
$96$		0			0
$97$	9.86141			1.00127			0.500637	−	0.865657i	$-0.333099\pi$
$97$	9.86141			1.00127			0.500637	+	0.865657i	$0.333099\pi$
$98$		0			0
$99$	3.25401			0.327040
$100$		0			0
$101$	−5.62063	−	1.73374i	−0.559274	−	0.172513i	0.00221489	−	0.999998i	$-0.499295\pi$
$101$	−5.62063	−	1.73374i	−0.559274	−	0.172513i	−0.561489	+	0.827484i	$0.689771\pi$
$102$		0			0
$103$	−13.3780	+	12.4130i	−1.31817	+	1.22308i	−0.361342	+	0.932433i	$0.617681\pi$
$103$	−13.3780	+	12.4130i	−1.31817	+	1.22308i	−0.956829	+	0.290651i	$0.906128\pi$
$104$		0			0
$105$	−7.05050	+	0.348765i	−0.688058	+	0.0340360i
$106$		0			0
$107$	6.87906	+	4.69006i	0.665024	+	0.453405i	0.848201	−	0.529674i	$-0.177686\pi$
$107$	6.87906	+	4.69006i	0.665024	+	0.453405i	−0.183177	+	0.983080i	$0.558638\pi$
$108$		0			0
$109$	−5.04810	+	3.44174i	−0.483521	+	0.329659i	−0.780426	−	0.625248i	$-0.784998\pi$
$109$	−5.04810	+	3.44174i	−0.483521	+	0.329659i	0.296905	+	0.954907i	$0.404045\pi$
$110$		0			0
$111$	−6.80486	−	3.27705i	−0.645889	−	0.311044i
$112$		0			0
$113$	11.4501	−	5.51408i	1.07714	−	0.518721i	0.190736	−	0.981641i	$-0.438913\pi$
$113$	11.4501	−	5.51408i	1.07714	−	0.518721i	0.886400	+	0.462920i	$0.153198\pi$
$114$		0			0
$115$	2.98886	+	7.61550i	0.278713	+	0.710149i
$116$		0			0
$117$	−0.524827	−	0.909028i	−0.0485203	−	0.0840397i
$118$		0			0
$119$	−0.132237	+	5.21053i	−0.0121222	+	0.477649i
$120$		0			0
$121$	−1.17875	+	3.00340i	−0.107159	+	0.273037i
$122$		0			0
$123$	−0.868449	+	11.5886i	−0.0783054	+	1.04491i
$124$		0			0
$125$	6.75704	+	8.47306i	0.604368	+	0.757853i
$126$		0			0
$127$	1.38226	−	1.73330i	0.122656	−	0.153805i	−0.716712	−	0.697369i	$-0.754354\pi$
$127$	1.38226	−	1.73330i	0.122656	−	0.153805i	0.839368	+	0.543564i	$0.182925\pi$
$128$		0			0
$129$	−9.20651	+	15.9461i	−0.810588	+	1.40398i
$130$		0			0
$131$	−3.85124	+	1.18795i	−0.336484	+	0.103792i	−0.458393	−	0.888750i	$-0.651575\pi$
$131$	−3.85124	+	1.18795i	−0.336484	+	0.103792i	0.121909	+	0.992541i	$0.461098\pi$
$132$		0			0
$133$	−0.253781	−	2.03237i	−0.0220056	−	0.176229i
$134$		0			0
$135$	4.83573	+	0.728869i	0.416193	+	0.0627310i
$136$		0			0
$137$	−1.61689	−	1.50025i	−0.138140	−	0.128175i	0.608077	−	0.793878i	$-0.291941\pi$
$137$	−1.61689	−	1.50025i	−0.138140	−	0.128175i	−0.746217	+	0.665703i	$0.768132\pi$
$138$		0			0
$139$	−2.32127	−	10.1701i	−0.196887	−	0.862620i	−0.972776	−	0.231749i	$-0.925555\pi$
$139$	−2.32127	−	10.1701i	−0.196887	−	0.862620i	0.775888	−	0.630871i	$-0.217302\pi$
$140$		0			0
$141$	−5.51716	+	24.1723i	−0.464629	+	2.03567i
$142$		0			0
$143$	−2.47953	+	0.373730i	−0.207349	+	0.0312528i
$144$		0			0
$145$	−1.02226	−	13.6412i	−0.0848945	−	1.13284i
$146$		0			0
$147$	−6.50780	−	12.7215i	−0.536754	−	1.04925i
$148$		0			0
$149$	0.246120	+	3.28424i	0.0201629	+	0.269056i	0.998169	+	0.0604809i	$0.0192634\pi$
$149$	0.246120	+	3.28424i	0.0201629	+	0.269056i	−0.978006	+	0.208575i	$0.933118\pi$
$150$		0			0
$151$	−13.8574	+	2.08866i	−1.12770	+	0.169973i	−0.686285	−	0.727332i	$-0.740760\pi$
$151$	−13.8574	+	2.08866i	−1.12770	+	0.169973i	−0.441411	+	0.897305i	$0.645522\pi$
$152$		0			0
$153$	−0.511626	+	2.24158i	−0.0413625	+	0.181221i
$154$		0			0
$155$	−2.45398	−	10.7516i	−0.197108	−	0.863588i
$156$		0			0
$157$	−2.22740	−	2.06673i	−0.177766	−	0.164943i	0.586271	−	0.810115i	$-0.300595\pi$
$157$	−2.22740	−	2.06673i	−0.177766	−	0.164943i	−0.764037	+	0.645172i	$0.776786\pi$
$158$		0			0
$159$	−14.0373	−	2.11579i	−1.11323	−	0.167793i
$160$		0			0
$161$	−11.5683	+	11.8500i	−0.911712	+	0.933909i
$162$		0			0
$163$	−8.08053	+	2.49251i	−0.632916	+	0.195229i	−0.594580	−	0.804036i	$-0.702682\pi$
$163$	−8.08053	+	2.49251i	−0.632916	+	0.195229i	−0.0383356	+	0.999265i	$0.512206\pi$
$164$		0			0
$165$	−3.71947	+	6.44232i	−0.289561	+	0.501534i
$166$		0			0
$167$	−6.48156	+	8.12762i	−0.501558	+	0.628934i	−0.966580	−	0.256365i	$-0.917475\pi$
$167$	−6.48156	+	8.12762i	−0.501558	+	0.628934i	0.465022	+	0.885299i	$0.346046\pi$
$168$		0			0
$169$	−7.60105	−	9.53141i	−0.584696	−	0.733186i
$170$		0			0
$171$	0.0675178	−	0.900963i	0.00516322	−	0.0688983i
$172$		0			0
$173$	0.215003	−	0.547818i	0.0163464	−	0.0416499i	−0.922468	−	0.386075i	$-0.873831\pi$
$173$	0.215003	−	0.547818i	0.0163464	−	0.0416499i	0.938814	+	0.344425i	$0.111926\pi$
$174$		0			0
$175$	−3.97654	+	7.74812i	−0.300598	+	0.585703i
$176$		0			0
$177$	5.36684	+	9.29564i	0.403396	+	0.698703i
$178$		0			0
$179$	3.75370	+	9.56427i	0.280565	+	0.714867i	0.999798	+	0.0200985i	$0.00639800\pi$
$179$	3.75370	+	9.56427i	0.280565	+	0.714867i	−0.719233	+	0.694769i	$0.755507\pi$
$180$		0			0
$181$	−7.89317	+	3.80115i	−0.586694	+	0.282537i	−0.703589	−	0.710607i	$-0.748420\pi$
$181$	−7.89317	+	3.80115i	−0.586694	+	0.282537i	0.116895	+	0.993144i	$0.462706\pi$
$182$		0			0
$183$	22.6350	+	10.9004i	1.67323	+	0.805784i
$184$		0			0
$185$	3.99561	−	2.72416i	0.293763	−	0.200284i
$186$		0			0
$187$	4.53825	+	3.09413i	0.331870	+	0.226265i
$188$		0			0
$189$	2.67694	+	9.53049i	0.194718	+	0.693241i
$190$		0			0
$191$	−1.39907	+	1.29815i	−0.101233	+	0.0939309i	−0.729166	−	0.684337i	$-0.760092\pi$
$191$	−1.39907	+	1.29815i	−0.101233	+	0.0939309i	0.627933	+	0.778268i	$0.283901\pi$
$192$		0			0
$193$	−5.90845	−	1.82252i	−0.425300	−	0.131188i	0.0747142	−	0.997205i	$-0.476196\pi$
$193$	−5.90845	−	1.82252i	−0.425300	−	0.131188i	−0.500014	+	0.866017i	$0.666672\pi$
$194$		0			0
$195$	2.39960			0.171839
$196$		0			0
$197$	1.17887			0.0839912			0.0419956	−	0.999118i	$-0.486628\pi$
$197$	1.17887			0.0839912			0.0419956	+	0.999118i	$0.486628\pi$
$198$		0			0
$199$	24.2165	+	7.46981i	1.71666	+	0.529521i	0.987880	−	0.155222i	$-0.0496094\pi$
$199$	24.2165	+	7.46981i	1.71666	+	0.529521i	0.728785	+	0.684743i	$0.240086\pi$
$200$		0			0
$201$	2.19909	−	2.04046i	0.155112	−	0.143923i
$202$		0			0
$203$	24.3243	−	13.2324i	1.70723	−	0.928735i
$204$		0			0
$205$	−6.14783	−	4.19152i	−0.429383	−	0.292748i
$206$		0			0
$207$	−6.03583	+	4.11516i	−0.419519	+	0.286023i
$208$		0			0
$209$	−1.94462	−	0.936478i	−0.134512	−	0.0647776i
$210$		0			0
$211$	2.62115	−	1.26228i	0.180447	−	0.0868988i	−0.341479	−	0.939889i	$-0.610928\pi$
$211$	2.62115	−	1.26228i	0.180447	−	0.0868988i	0.521926	+	0.852991i	$0.325214\pi$
$212$		0			0
$213$	−4.47515	−	11.4025i	−0.306632	−	0.781286i
$214$		0			0
$215$	−5.89471	−	10.2099i	−0.402016	−	0.696312i
$216$		0			0
$217$	17.8008	−	13.4713i	1.20840	−	0.914489i
$218$		0			0
$219$	−0.0237064	+	0.0604029i	−0.00160193	+	0.00408165i
$220$		0			0
$221$	0.132406	−	1.76683i	0.00890657	−	0.118850i
$222$		0			0
$223$	−4.76555	−	5.97581i	−0.319125	−	0.400170i	0.596233	−	0.802811i	$-0.296663\pi$
$223$	−4.76555	−	5.97581i	−0.319125	−	0.400170i	−0.915358	+	0.402642i	$0.868092\pi$
$224$		0			0
$225$	−2.39528	+	3.00358i	−0.159685	+	0.200239i
$226$		0			0
$227$	1.33112	−	2.30558i	0.0883498	−	0.153026i	−0.818464	−	0.574558i	$-0.805174\pi$
$227$	1.33112	−	2.30558i	0.0883498	−	0.153026i	0.906814	+	0.421532i	$0.138507\pi$
$228$		0			0
$229$	−6.98904	+	2.15583i	−0.461848	+	0.142461i	−0.516943	−	0.856020i	$-0.672930\pi$
$229$	−6.98904	+	2.15583i	−0.461848	+	0.142461i	0.0550947	+	0.998481i	$0.482454\pi$
$230$		0			0
$231$	−14.9828	−	1.50592i	−0.985797	−	0.0990821i
$232$		0			0
$233$	22.1214	+	3.33426i	1.44922	+	0.218434i	0.826025	−	0.563634i	$-0.190597\pi$
$233$	22.1214	+	3.33426i	1.44922	+	0.218434i	0.623193	+	0.782068i	$0.285835\pi$
$234$		0			0
$235$	−11.6372	−	10.7977i	−0.759125	−	0.704365i
$236$		0			0
$237$	−6.30800	−	27.6372i	−0.409749	−	1.79523i
$238$		0			0
$239$	−6.35223	+	27.8309i	−0.410892	+	1.80023i	0.169087	+	0.985601i	$0.445918\pi$
$239$	−6.35223	+	27.8309i	−0.410892	+	1.80023i	−0.579978	+	0.814632i	$0.696939\pi$
$240$		0			0
$241$	−23.4344	+	3.53217i	−1.50954	+	0.227527i	−0.851060	−	0.525068i	$-0.824040\pi$
$241$	−23.4344	+	3.53217i	−1.50954	+	0.227527i	−0.658483	+	0.752595i	$0.728802\pi$
$242$		0			0
$243$	0.860456	+	11.4820i	0.0551983	+	0.736570i
$244$		0			0
$245$	9.13741	+	0.464093i	0.583768	+	0.0296498i
$246$		0			0
$247$	0.0520293	+	0.694282i	0.00331054	+	0.0441761i
$248$		0			0
$249$	−20.7615	+	3.12929i	−1.31571	+	0.198311i
$250$		0			0
$251$	4.43306	−	19.4225i	0.279813	−	1.22594i	−0.618218	−	0.786006i	$-0.712145\pi$
$251$	4.43306	−	19.4225i	0.279813	−	1.22594i	0.898031	−	0.439933i	$-0.144998\pi$
$252$		0			0
$253$	3.88333	+	17.0140i	0.244143	+	1.06966i
$254$		0			0
$255$	−3.85309	−	3.57515i	−0.241290	−	0.223884i
$256$		0			0
$257$	18.8787	+	2.84551i	1.17762	+	0.177498i	0.708550	−	0.705661i	$-0.249350\pi$
$257$	18.8787	+	2.84551i	1.17762	+	0.177498i	0.469073	+	0.883159i	$0.344588\pi$
$258$		0			0
$259$	8.35068	+	5.10804i	0.518886	+	0.317398i
$260$		0			0
$261$	11.6723	−	3.60042i	0.722496	−	0.222861i
$262$		0			0
$263$	4.17870	−	7.23772i	0.257670	−	0.446297i	−0.707947	−	0.706265i	$-0.750379\pi$
$263$	4.17870	−	7.23772i	0.257670	−	0.446297i	0.965617	+	0.259968i	$0.0837120\pi$
$264$		0			0
$265$	5.66708	−	7.10629i	0.348126	−	0.436536i
$266$		0			0
$267$	−3.74361	−	4.69433i	−0.229105	−	0.287289i
$268$		0			0
$269$	−0.180738	+	2.41178i	−0.0110198	+	0.147049i	−0.999999	−	0.00100230i	$-0.999681\pi$
$269$	−0.180738	+	2.41178i	−0.0110198	+	0.147049i	0.988980	+	0.148051i	$0.0473000\pi$
$270$		0			0
$271$	3.86903	−	9.85814i	0.235027	−	0.598839i	−0.763891	−	0.645345i	$-0.776713\pi$
$271$	3.86903	−	9.85814i	0.235027	−	0.598839i	0.998918	+	0.0465061i	$0.0148087\pi$
$272$		0			0
$273$	1.99584	+	4.42843i	0.120794	+	0.268021i
$274$		0			0
$275$	4.58879	+	7.94801i	0.276714	+	0.479283i
$276$		0			0
$277$	7.54038	+	19.2126i	0.453057	+	1.15437i	0.956859	+	0.290552i	$0.0938390\pi$
$277$	7.54038	+	19.2126i	0.453057	+	1.15437i	−0.503802	+	0.863819i	$0.668066\pi$
$278$		0			0
$279$	8.87225	−	4.27265i	0.531168	−	0.255797i
$280$		0			0
$281$	−9.57033	−	4.60883i	−0.570918	−	0.274940i	0.126071	−	0.992021i	$-0.459763\pi$
$281$	−9.57033	−	4.60883i	−0.570918	−	0.274940i	−0.696989	+	0.717082i	$0.745477\pi$
$282$		0			0
$283$	−20.3972	+	13.9065i	−1.21249	+	0.826658i	−0.988981	−	0.148045i	$-0.952702\pi$
$283$	−20.3972	+	13.9065i	−1.21249	+	0.826658i	−0.223504	+	0.974703i	$0.571750\pi$
$284$		0			0
$285$	1.70656	+	1.16351i	0.101088	+	0.0689205i
$286$		0			0
$287$	2.62201	−	14.8320i	0.154772	−	0.875503i
$288$		0			0
$289$	9.61689	−	8.92317i	0.565700	−	0.524892i
$290$		0			0
$291$	−19.2362	−	5.93359i	−1.12765	−	0.347833i
$292$		0			0
$293$	−10.9148			−0.637647			−0.318823	−	0.947814i	$-0.603288\pi$
$293$	−10.9148			−0.637647			−0.318823	+	0.947814i	$0.603288\pi$
$294$		0			0
$295$	−6.87252			−0.400133
$296$		0			0
$297$	9.96849	+	3.07487i	0.578430	+	0.178422i
$298$		0			0
$299$	4.12663	−	3.82895i	0.238649	−	0.221434i
$300$		0			0
$301$	13.9394	−	19.3706i	0.803455	−	1.11650i
$302$		0			0
$303$	9.92074	+	6.76384i	0.569931	+	0.388573i
$304$		0			0
$305$	−13.2906	+	9.06136i	−0.761016	+	0.518852i
$306$		0			0
$307$	11.4673	+	5.52234i	0.654471	+	0.315177i	0.731489	−	0.681853i	$-0.238826\pi$
$307$	11.4673	+	5.52234i	0.654471	+	0.315177i	−0.0770182	+	0.997030i	$0.524540\pi$
$308$		0			0
$309$	33.5647	−	16.1639i	1.90943	−	0.919532i
$310$		0			0
$311$	1.43091	+	3.64589i	0.0811394	+	0.206740i	0.965686	−	0.259712i	$-0.0836275\pi$
$311$	1.43091	+	3.64589i	0.0811394	+	0.206740i	−0.884547	+	0.466451i	$0.845532\pi$
$312$		0			0
$313$	−8.01115	−	13.8757i	−0.452817	−	0.784302i	0.545743	−	0.837953i	$-0.316248\pi$
$313$	−8.01115	−	13.8757i	−0.452817	−	0.784302i	−0.998560	+	0.0536505i	$0.982914\pi$
$314$		0			0
$315$	3.91068	+	0.997613i	0.220342	+	0.0562091i
$316$		0			0
$317$	−12.7743	+	32.5483i	−0.717474	+	1.82809i	−0.182545	+	0.983197i	$0.558434\pi$
$317$	−12.7743	+	32.5483i	−0.717474	+	1.82809i	−0.534929	+	0.844897i	$0.679662\pi$
$318$		0			0
$319$	2.18067	−	29.0990i	0.122094	−	1.62923i
$320$		0			0
$321$	−10.5967	−	13.2878i	−0.591449	−	0.741653i
$322$		0			0
$323$	0.950860	−	1.19234i	0.0529073	−	0.0663436i
$324$		0			0
$325$	1.48022	−	2.56381i	0.0821077	−	0.142215i
$326$		0			0
$327$	11.9180	−	3.67622i	0.659067	−	0.203295i
$328$		0			0
$329$	10.2479	−	30.4570i	0.564987	−	1.67915i
$330$		0			0
$331$	−32.3808	−	4.88062i	−1.77981	−	0.268263i	−0.824926	−	0.565241i	$-0.808783\pi$
$331$	−32.3808	−	4.88062i	−1.77981	−	0.268263i	−0.954885	+	0.296977i	$0.904021\pi$
$332$		0			0
$333$	3.16545	+	2.93711i	0.173466	+	0.160953i
$334$		0			0
$335$	0.427412	+	1.87261i	0.0233520	+	0.102312i
$336$		0			0
$337$	−5.67596	+	24.8680i	−0.309189	+	1.35465i	0.546631	+	0.837374i	$0.315910\pi$
$337$	−5.67596	+	24.8680i	−0.309189	+	1.35465i	−0.855820	+	0.517274i	$0.826947\pi$
$338$		0			0
$339$	−25.6531	+	3.86658i	−1.39328	+	0.210004i
$340$		0			0
$341$	−1.75801	−	23.4590i	−0.0952015	−	1.27038i
$342$		0			0
$343$	6.74344	+	17.2489i	0.364112	+	0.931355i
$344$		0			0
$345$	−1.24802	−	16.6536i	−0.0671909	−	0.896600i
$346$		0			0
$347$	2.44095	−	0.367914i	0.131037	−	0.0197507i	−0.0831962	−	0.996533i	$-0.526513\pi$
$347$	2.44095	−	0.367914i	0.131037	−	0.0197507i	0.214233	+	0.976783i	$0.431275\pi$
$348$		0			0
$349$	−4.98979	+	21.8617i	−0.267097	+	1.17023i	0.646275	+	0.763104i	$0.276326\pi$
$349$	−4.98979	+	21.8617i	−0.267097	+	1.17023i	−0.913373	+	0.407125i	$0.866531\pi$
$350$		0			0
$351$	−0.748797	−	3.28070i	−0.0399678	−	0.175111i
$352$		0			0
$353$	17.6865	+	16.4107i	0.941359	+	0.873453i	0.992124	−	0.125257i	$-0.0399757\pi$
$353$	17.6865	+	16.4107i	0.941359	+	0.873453i	−0.0507656	+	0.998711i	$0.516166\pi$
$354$		0			0
$355$	7.75530	+	1.16892i	0.411609	+	0.0620400i
$356$		0			0
$357$	3.39312	−	10.0844i	0.179583	−	0.533723i
$358$		0			0
$359$	−0.376522	+	0.116142i	−0.0198721	+	0.00612972i	−0.304675	−	0.952456i	$-0.598548\pi$
$359$	−0.376522	+	0.116142i	−0.0198721	+	0.00612972i	0.284803	+	0.958586i	$0.408072\pi$
$360$		0			0
$361$	9.20036	−	15.9355i	0.484230	−	0.838710i
$362$		0			0
$363$	4.10648	−	5.14936i	0.215534	−	0.270271i
$364$		0			0
$365$	−0.0259038	−	0.0324824i	−0.00135587	−	0.00170021i
$366$		0			0
$367$	−1.16772	+	15.5822i	−0.0609546	+	0.813383i	0.880027	+	0.474924i	$0.157525\pi$
$367$	−1.16772	+	15.5822i	−0.0609546	+	0.813383i	−0.940981	+	0.338459i	$0.890094\pi$
$368$		0			0
$369$	2.42739	−	6.18488i	0.126365	−	0.321972i
$370$		0			0
$371$	17.8281	+	4.54794i	0.925587	+	0.236117i
$372$		0			0
$373$	−2.63813	−	4.56937i	−0.136597	−	0.236593i	0.789609	−	0.613610i	$-0.210283\pi$
$373$	−2.63813	−	4.56937i	−0.136597	−	0.236593i	−0.926206	+	0.377017i	$0.876950\pi$
$374$		0			0
$375$	−8.08244	−	20.5937i	−0.417375	−	1.06346i
$376$		0			0
$377$	−8.48069	+	4.08408i	−0.436778	+	0.210341i
$378$		0			0
$379$	32.2676	+	15.5393i	1.65748	+	0.798199i	0.998958	+	0.0456335i	$0.0145307\pi$
$379$	32.2676	+	15.5393i	1.65748	+	0.798199i	0.658518	+	0.752565i	$0.271184\pi$
$380$		0			0
$381$	−3.73923	+	2.54937i	−0.191567	+	0.130608i
$382$		0			0
$383$	12.5326	+	8.54457i	0.640385	+	0.436607i	0.839493	−	0.543370i	$-0.182852\pi$
$383$	12.5326	+	8.54457i	0.640385	+	0.436607i	−0.199108	+	0.979978i	$0.563804\pi$
$384$		0			0
$385$	5.63160	−	7.82580i	0.287013	−	0.398840i
$386$		0			0
$387$	7.71705	−	7.16037i	0.392280	−	0.363982i
$388$		0			0
$389$	−23.0643	−	7.11438i	−1.16940	−	0.360714i	−0.351567	−	0.936163i	$-0.614351\pi$
$389$	−23.0643	−	7.11438i	−1.16940	−	0.360714i	−0.817838	+	0.575449i	$0.804827\pi$
$390$		0			0
$391$	−12.3309			−0.623602
$392$		0			0
$393$	8.22722			0.415009
$394$		0			0
$395$	17.3441	+	5.34995i	0.872677	+	0.269185i
$396$		0			0
$397$	−28.0957	+	26.0690i	−1.41008	+	1.30837i	−0.518815	+	0.854886i	$0.673627\pi$
$397$	−28.0957	+	26.0690i	−1.41008	+	1.30837i	−0.891267	+	0.453479i	$0.850183\pi$
$398$		0			0
$399$	−0.727835	+	4.11716i	−0.0364373	+	0.206116i
$400$		0			0
$401$	6.81287	+	4.64494i	0.340219	+	0.231957i	0.721361	−	0.692559i	$-0.243517\pi$
$401$	6.81287	+	4.64494i	0.340219	+	0.231957i	−0.381142	+	0.924516i	$0.624469\pi$
$402$		0			0
$403$	−6.26987	+	4.27473i	−0.312325	+	0.212939i
$404$		0			0
$405$	−13.1174	−	6.31700i	−0.651808	−	0.313894i
$406$		0			0
$407$	9.29421	−	4.47586i	0.460697	−	0.221860i
$408$		0			0
$409$	3.36816	+	8.58193i	0.166545	+	0.424349i	0.989643	−	0.143550i	$-0.0458517\pi$
$409$	3.36816	+	8.58193i	0.166545	+	0.424349i	−0.823098	+	0.567899i	$0.807756\pi$
$410$		0			0
$411$	2.25129	+	3.89935i	0.111048	+	0.192341i
$412$		0			0
$413$	−5.71612	−	12.6831i	−0.281272	−	0.624096i
$414$		0			0
$415$	4.91137	−	12.5140i	0.241090	−	0.614286i
$416$		0			0
$417$	−1.59135	+	21.2352i	−0.0779290	+	1.03989i
$418$		0			0
$419$	5.67594	+	7.11741i	0.277288	+	0.347708i	0.900901	−	0.434025i	$-0.142907\pi$
$419$	5.67594	+	7.11741i	0.277288	+	0.347708i	−0.623613	+	0.781733i	$0.714336\pi$
$420$		0			0
$421$	−5.52252	+	6.92502i	−0.269151	+	0.337505i	−0.897978	−	0.440041i	$-0.854964\pi$
$421$	−5.52252	+	6.92502i	−0.269151	+	0.337505i	0.628827	+	0.777545i	$0.283535\pi$
$422$		0			0
$423$	7.08772	−	12.2763i	0.344617	−	0.596894i
$424$		0			0
$425$	−6.19662	+	1.91140i	−0.300580	+	0.0927167i
$426$		0			0
$427$	−27.7768	−	16.9909i	−1.34422	−	0.822246i
$428$		0			0
$429$	5.06159	+	0.762912i	0.244376	+	0.0368337i
$430$		0			0
$431$	8.29095	+	7.69288i	0.399361	+	0.370553i	0.854133	−	0.520055i	$-0.174089\pi$
$431$	8.29095	+	7.69288i	0.399361	+	0.370553i	−0.454772	+	0.890608i	$0.650279\pi$
$432$		0			0
$433$	4.98736	+	21.8511i	0.239677	+	1.05010i	0.941307	+	0.337553i	$0.109599\pi$
$433$	4.98736	+	21.8511i	0.239677	+	1.05010i	−0.701629	+	0.712542i	$0.747544\pi$
$434$		0			0
$435$	−6.21378	+	27.2243i	−0.297928	+	1.30531i
$436$		0			0
$437$	4.79136	−	0.722182i	0.229202	−	0.0345466i
$438$		0			0
$439$	−0.909800	−	12.1404i	−0.0434224	−	0.579431i	−0.975902	−	0.218209i	$-0.929979\pi$
$439$	−0.909800	−	12.1404i	−0.0434224	−	0.579431i	0.932480	−	0.361222i	$-0.117640\pi$
$440$		0			0
$441$	1.41157	+	8.04684i	0.0672177	+	0.383183i
$442$		0			0
$443$	−1.15486	−	15.4105i	−0.0548689	−	0.732175i	−0.955010	−	0.296575i	$-0.904155\pi$
$443$	−1.15486	−	15.4105i	−0.0548689	−	0.732175i	0.900141	−	0.435599i	$-0.143464\pi$
$444$		0			0
$445$	3.80146	−	0.572978i	0.180206	−	0.0271617i
$446$		0			0
$447$	1.49603	−	6.55452i	0.0707596	−	0.310018i
$448$		0			0
$449$	−7.02794	−	30.7914i	−0.331669	−	1.45314i	−0.815898	−	0.578196i	$-0.803757\pi$
$449$	−7.02794	−	30.7914i	−0.331669	−	1.45314i	0.484229	−	0.874942i	$-0.339100\pi$
$450$		0			0
$451$	−11.6353	−	10.7960i	−0.547884	−	0.508362i
$452$		0			0
$453$	28.2877	+	4.26368i	1.32907	+	0.200325i
$454$		0			0
$455$	−3.09449	−	0.311026i	−0.145072	−	0.0145811i
$456$		0			0
$457$	−0.891393	+	0.274958i	−0.0416976	+	0.0128620i	−0.315534	−	0.948914i	$-0.602184\pi$
$457$	−0.891393	+	0.274958i	−0.0416976	+	0.0128620i	0.273836	+	0.961776i	$0.411707\pi$
$458$		0			0
$459$	−3.68552	+	6.38350i	−0.172025	+	0.297956i
$460$		0			0
$461$	12.5568	−	15.7457i	0.584827	−	0.733350i	−0.398101	−	0.917342i	$-0.630331\pi$
$461$	12.5568	−	15.7457i	0.584827	−	0.733350i	0.982928	+	0.183992i	$0.0589019\pi$
$462$		0			0
$463$	2.87011	+	3.59901i	0.133385	+	0.167260i	0.844038	−	0.536283i	$-0.180172\pi$
$463$	2.87011	+	3.59901i	0.133385	+	0.167260i	−0.710653	+	0.703543i	$0.751600\pi$
$464$		0			0
$465$	−1.68233	+	22.4492i	−0.0780164	+	1.04106i
$466$		0			0
$467$	6.33240	−	16.1347i	0.293028	−	0.746624i	−0.706225	−	0.707987i	$-0.749603\pi$
$467$	6.33240	−	16.1347i	0.293028	−	0.746624i	0.999253	−	0.0386366i	$-0.0123015\pi$
$468$		0			0
$469$	−3.10039	+	2.34630i	−0.143163	+	0.108342i
$470$		0			0
$471$	3.10135	+	5.37170i	0.142903	+	0.247515i
$472$		0			0
$473$	−9.18790	−	23.4104i	−0.422460	−	1.07641i
$474$		0			0
$475$	2.29584	−	1.10562i	0.105340	−	0.0507293i
$476$		0			0
$477$	7.31246	+	3.52150i	0.334815	+	0.161238i
$478$		0			0
$479$	23.4773	−	16.0065i	1.07270	−	0.731357i	0.107856	−	0.994167i	$-0.465602\pi$
$479$	23.4773	−	16.0065i	1.07270	−	0.731357i	0.964848	+	0.262810i	$0.0846491\pi$
$480$		0			0
$481$	−2.74939	−	1.87450i	−0.125361	−	0.0854699i
$482$		0			0
$483$	29.6959	−	16.1546i	1.35121	−	0.735060i
$484$		0			0
$485$	9.44840	−	8.76683i	0.429030	−	0.398081i
$486$		0			0
$487$	−6.54184	−	2.01789i	−0.296439	−	0.0914394i	0.142968	−	0.989727i	$-0.454335\pi$
$487$	−6.54184	−	2.01789i	−0.296439	−	0.0914394i	−0.439407	+	0.898288i	$0.644812\pi$
$488$		0			0
$489$	17.2621			0.780618
$490$		0			0
$491$	−2.07001			−0.0934182			−0.0467091	−	0.998909i	$-0.514873\pi$
$491$	−2.07001			−0.0934182			−0.0467091	+	0.998909i	$0.514873\pi$
$492$		0			0
$493$	19.7024	+	6.07740i	0.887354	+	0.273712i
$494$		0			0
$495$	3.11773	−	2.89283i	0.140131	−	0.130023i
$496$		0			0
$497$	4.29314	+	15.2845i	0.192574	+	0.685604i
$498$		0			0
$499$	−28.9169	−	19.7152i	−1.29450	−	0.882575i	−0.297115	−	0.954842i	$-0.596024\pi$
$499$	−28.9169	−	19.7152i	−1.29450	−	0.882575i	−0.997385	+	0.0722666i	$0.976977\pi$
$500$		0			0
$501$	17.5337	−	11.9543i	0.783347	−	0.534077i
$502$		0			0
$503$	−26.7920	−	12.9023i	−1.19460	−	0.575287i	−0.272465	−	0.962166i	$-0.587839\pi$
$503$	−26.7920	−	12.9023i	−1.19460	−	0.575287i	−0.922131	+	0.386879i	$0.873553\pi$
$504$		0			0
$505$	−6.92653	+	3.33564i	−0.308226	+	0.148434i
$506$		0			0
$507$	9.09200	+	23.1660i	0.403790	+	1.02884i
$508$		0			0
$509$	12.1114	+	20.9775i	0.536827	+	0.929811i	0.999073	+	0.0430594i	$0.0137105\pi$
$509$	12.1114	+	20.9775i	0.536827	+	0.929811i	−0.462246	+	0.886752i	$0.652956\pi$
$510$		0			0
$511$	0.0384005	−	0.0748219i	0.00169874	−	0.00330993i
$512$		0			0
$513$	1.05820	−	2.69625i	0.0467207	−	0.119042i
$514$		0			0
$515$	−1.78253	+	23.7862i	−0.0785475	+	1.04814i
$516$		0			0
$517$	−21.1139	−	26.4759i	−0.928586	−	1.16441i
$518$		0			0
$519$	−0.749018	+	0.939239i	−0.0328782	+	0.0412280i
$520$		0			0
$521$	3.63482	−	6.29570i	0.159244	−	0.275820i	−0.775352	−	0.631529i	$-0.782428\pi$
$521$	3.63482	−	6.29570i	0.159244	−	0.275820i	0.934596	+	0.355710i	$0.115761\pi$
$522$		0			0
$523$	−27.4232	+	8.45895i	−1.19913	+	0.369884i	−0.829082	−	0.559127i	$-0.811136\pi$
$523$	−27.4232	+	8.45895i	−1.19913	+	0.369884i	−0.370052	+	0.929011i	$0.620660\pi$
$524$		0			0
$525$	12.4189	−	12.7212i	0.542004	−	0.555201i
$526$		0			0
$527$	16.4365	+	2.47741i	0.715987	+	0.107918i
$528$		0			0
$529$	−11.8596	−	11.0041i	−0.515633	−	0.478437i
$530$		0			0
$531$	−1.36556	−	5.98291i	−0.0592603	−	0.259636i
$532$		0			0
$533$	−1.13931	+	4.99163i	−0.0493489	+	0.216211i
$534$		0			0
$535$	10.7604	−	1.62187i	0.465214	−	0.0701198i
$536$		0			0
$537$	−1.56738	−	20.9152i	−0.0676373	−	0.902558i
$538$		0			0
$539$	19.1264	+	3.88401i	0.823832	+	0.167296i
$540$		0			0
$541$	−1.28289	−	17.1190i	−0.0551559	−	0.736005i	−0.954395	−	0.298547i	$-0.903498\pi$
$541$	−1.28289	−	17.1190i	−0.0551559	−	0.736005i	0.899239	−	0.437458i	$-0.144121\pi$
$542$		0			0
$543$	17.6840	−	2.66543i	0.758893	−	0.114385i
$544$		0			0
$545$	−1.77696	+	7.78538i	−0.0761167	+	0.333489i
$546$		0			0
$547$	−2.85144	−	12.4930i	−0.121919	−	0.534161i	−0.998591	−	0.0530721i	$-0.983099\pi$
$547$	−2.85144	−	12.4930i	−0.121919	−	0.534161i	0.876672	−	0.481089i	$-0.159758\pi$
$548$		0			0
$549$	−10.5292	−	9.76970i	−0.449377	−	0.416961i
$550$		0			0
$551$	−8.01161	−	1.20756i	−0.341306	−	0.0514436i
$552$		0			0
$553$	4.55249	+	36.4580i	0.193591	+	1.55035i
$554$		0			0
$555$	−9.43318	+	2.90975i	−0.400416	+	0.123512i
$556$		0			0
$557$	8.24287	−	14.2771i	0.349262	−	0.604939i	−0.636857	−	0.770982i	$-0.719766\pi$
$557$	8.24287	−	14.2771i	0.349262	−	0.604939i	0.986118	+	0.166043i	$0.0530991\pi$
$558$		0			0
$559$	−5.05796	+	6.34248i	−0.213929	+	0.268258i
$560$		0			0
$561$	−6.99084	−	8.76624i	−0.295154	−	0.370111i
$562$		0			0
$563$	−1.76787	+	23.5906i	−0.0745068	+	0.994224i	0.827209	+	0.561895i	$0.189927\pi$
$563$	−1.76787	+	23.5906i	−0.0745068	+	0.994224i	−0.901716	+	0.432330i	$0.857692\pi$
$564$		0			0
$565$	6.06852	−	15.4623i	0.255305	−	0.650506i
$566$		0			0
$567$	0.747712	−	29.4620i	0.0314010	−	1.23729i
$568$		0			0
$569$	5.28419	+	9.15248i	0.221525	+	0.383692i	0.955271	−	0.295731i	$-0.0955633\pi$
$569$	5.28419	+	9.15248i	0.221525	+	0.383692i	−0.733746	+	0.679423i	$0.762230\pi$
$570$		0			0
$571$	−4.15751	−	10.5932i	−0.173986	−	0.443310i	0.817106	−	0.576488i	$-0.195577\pi$
$571$	−4.15751	−	10.5932i	−0.173986	−	0.443310i	−0.991092	+	0.133178i	$0.957482\pi$
$572$		0			0
$573$	3.51021	−	1.69043i	0.146641	−	0.0706186i
$574$		0			0
$575$	−18.5631	−	8.93952i	−0.774135	−	0.372804i
$576$		0			0
$577$	−21.5931	+	14.7219i	−0.898932	+	0.612882i	−0.922143	−	0.386849i	$-0.873563\pi$
$577$	−21.5931	+	14.7219i	−0.898932	+	0.612882i	0.0232108	+	0.999731i	$0.492611\pi$
$578$		0			0
$579$	10.4288	+	7.11020i	0.433404	+	0.295490i
$580$		0			0
$581$	27.1793	−	1.34447i	1.12759	−	0.0557780i
$582$		0			0
$583$	14.2131	−	13.1879i	0.588648	−	0.546186i
$584$		0			0
$585$	−1.31098	−	0.404383i	−0.0542022	−	0.0167192i
$586$		0			0
$587$	14.8726			0.613856			0.306928	−	0.951733i	$-0.400699\pi$
$587$	14.8726			0.613856			0.306928	+	0.951733i	$0.400699\pi$
$588$		0			0
$589$	−6.53175			−0.269136
$590$		0			0
$591$	−2.29958	−	0.709325i	−0.0945919	−	0.0291777i
$592$		0			0
$593$	23.9114	−	22.1865i	0.981924	−	0.911092i	−0.0141252	−	0.999900i	$-0.504496\pi$
$593$	23.9114	−	22.1865i	0.981924	−	0.911092i	0.996049	+	0.0888083i	$0.0283059\pi$
$594$		0			0
$595$	4.50549	+	5.10987i	0.184707	+	0.209484i
$596$		0			0
$597$	−42.7436	−	29.1421i	−1.74938	−	1.19271i
$598$		0			0
$599$	−7.22033	+	4.92274i	−0.295015	+	0.201138i	−0.701777	−	0.712396i	$-0.747610\pi$
$599$	−7.22033	+	4.92274i	−0.295015	+	0.201138i	0.406763	+	0.913534i	$0.366658\pi$
$600$		0			0
$601$	34.6215	+	16.6728i	1.41224	+	0.680099i	0.975604	−	0.219539i	$-0.0704554\pi$
$601$	34.6215	+	16.6728i	1.41224	+	0.680099i	0.436636	+	0.899638i	$0.356170\pi$
$602$		0			0
$603$	−1.54529	+	0.744172i	−0.0629290	+	0.0303050i
$604$		0			0
$605$	1.54066	+	3.92553i	0.0626366	+	0.159595i
$606$		0			0
$607$	−7.79218	−	13.4965i	−0.316275	−	0.547804i	0.663433	−	0.748236i	$-0.269099\pi$
$607$	−7.79218	−	13.4965i	−0.316275	−	0.547804i	−0.979708	+	0.200432i	$0.935766\pi$
$608$		0			0
$609$	−55.4103	+	11.1761i	−2.24534	+	0.452877i
$610$		0			0
$611$	−3.99084	+	10.1685i	−0.161452	+	0.411373i
$612$		0			0
$613$	1.74858	−	23.3332i	0.0706244	−	0.942418i	−0.843538	−	0.537070i	$-0.819531\pi$
$613$	1.74858	−	23.3332i	0.0706244	−	0.942418i	0.914162	−	0.405348i	$-0.132850\pi$
$614$		0			0
$615$	9.47028	+	11.8754i	0.381878	+	0.478860i
$616$		0			0
$617$	3.98193	−	4.99318i	0.160307	−	0.201018i	−0.695191	−	0.718825i	$-0.744680\pi$
$617$	3.98193	−	4.99318i	0.160307	−	0.201018i	0.855497	+	0.517807i	$0.173252\pi$
$618$		0			0
$619$	−3.54447	+	6.13920i	−0.142464	+	0.246755i	−0.928424	−	0.371522i	$-0.878836\pi$
$619$	−3.54447	+	6.13920i	−0.142464	+	0.246755i	0.785960	+	0.618278i	$0.212169\pi$
$620$		0			0
$621$	−22.3791	+	6.90303i	−0.898041	+	0.277009i
$622$		0			0
$623$	4.21923	+	6.53896i	0.169040	+	0.261978i
$624$		0			0
$625$	−2.26795	−	0.341839i	−0.0907182	−	0.0136736i
$626$		0			0
$627$	3.22980	+	2.99682i	0.128986	+	0.119681i
$628$		0			0
$629$	1.62195	+	7.10621i	0.0646712	+	0.283343i
$630$		0			0
$631$	1.78951	−	7.84035i	0.0712392	−	0.312119i	−0.926737	−	0.375711i	$-0.877398\pi$
$631$	1.78951	−	7.84035i	0.0712392	−	0.312119i	0.997976	+	0.0635919i	$0.0202556\pi$
$632$		0			0
$633$	−5.87247	+	0.885132i	−0.233410	+	0.0351808i
$634$		0			0
$635$	−0.216541	−	2.88954i	−0.00859316	−	0.114668i
$636$		0			0
$637$	−1.99981	−	5.96952i	−0.0792352	−	0.236521i
$638$		0			0
$639$	0.523355	+	6.98369i	0.0207036	+	0.276270i
$640$		0			0
$641$	−11.9061	+	1.79455i	−0.470261	+	0.0708805i	−0.379898	−	0.925028i	$-0.624041\pi$
$641$	−11.9061	+	1.79455i	−0.470261	+	0.0708805i	−0.0903633	+	0.995909i	$0.528803\pi$
$642$		0			0
$643$	−7.58886	+	33.2490i	−0.299276	+	1.31121i	0.571934	+	0.820300i	$0.306194\pi$
$643$	−7.58886	+	33.2490i	−0.299276	+	1.31121i	−0.871209	+	0.490912i	$0.836664\pi$
$644$		0			0
$645$	5.35526	+	23.4629i	0.210863	+	0.923851i
$646$		0			0
$647$	−5.96156	−	5.53152i	−0.234373	−	0.217466i	0.554239	−	0.832358i	$-0.313009\pi$
$647$	−5.96156	−	5.53152i	−0.234373	−	0.217466i	−0.788612	+	0.614891i	$0.789200\pi$
$648$		0			0
$649$	−14.4965	−	2.18500i	−0.569038	−	0.0857687i
$650$		0			0
$651$	−42.8289	+	15.5671i	−1.67860	+	0.610122i
$652$		0			0
$653$	−29.1599	+	8.99463i	−1.14111	+	0.351987i	−0.807003	−	0.590547i	$-0.798912\pi$
$653$	−29.1599	+	8.99463i	−1.14111	+	0.351987i	−0.334110	+	0.942534i	$0.608436\pi$
$654$		0			0
$655$	−2.63385	+	4.56196i	−0.102913	+	0.178250i
$656$		0			0
$657$	0.0231307	−	0.0290049i	0.000902413	−	0.00113159i
$658$		0			0
$659$	−28.4700	−	35.7003i	−1.10903	−	1.39068i	−0.911952	−	0.410297i	$-0.865425\pi$
$659$	−28.4700	−	35.7003i	−1.10903	−	1.39068i	−0.197082	−	0.980387i	$-0.563146\pi$
$660$		0			0
$661$	1.59640	−	21.3025i	0.0620927	−	0.828570i	−0.876028	−	0.482261i	$-0.839816\pi$
$661$	1.59640	−	21.3025i	0.0620927	−	0.828570i	0.938120	−	0.346309i	$-0.112565\pi$
$662$		0			0
$663$	−1.32138	+	3.36681i	−0.0513180	+	0.130756i
$664$		0			0
$665$	−2.04994	−	1.72164i	−0.0794933	−	0.0667624i
$666$		0			0
$667$	32.7549	+	56.7332i	1.26827	+	2.19672i
$668$		0			0
$669$	5.70032	+	14.5242i	0.220387	+	0.561537i
$670$		0			0
$671$	−30.9153	+	14.8880i	−1.19347	+	0.574746i
$672$		0			0
$673$	30.9578	+	14.9085i	1.19333	+	0.574679i	0.921768	−	0.387741i	$-0.126744\pi$
$673$	30.9578	+	14.9085i	1.19333	+	0.574679i	0.271565	+	0.962420i	$0.412459\pi$
$674$		0			0
$675$	−10.1760	+	6.93791i	−0.391676	+	0.267040i
$676$		0			0
$677$	2.03381	+	1.38663i	0.0781658	+	0.0532925i	0.601772	−	0.798668i	$-0.294461\pi$
$677$	2.03381	+	1.38663i	0.0781658	+	0.0532925i	−0.523607	+	0.851960i	$0.675414\pi$
$678$		0			0
$679$	24.0376	+	10.1452i	0.922479	+	0.389336i
$680$		0			0
$681$	−3.98383	+	3.69645i	−0.152661	+	0.141648i
$682$		0			0
$683$	20.7884	+	6.41236i	0.795445	+	0.245362i	0.665733	−	0.746190i	$-0.268119\pi$
$683$	20.7884	+	6.41236i	0.795445	+	0.245362i	0.129711	+	0.991552i	$0.458595\pi$
$684$		0			0
$685$	−2.88290			−0.110150
$686$		0			0
$687$	14.9304			0.569629
$688$		0			0
$689$	−5.97650	−	1.84351i	−0.227687	−	0.0702320i
$690$		0			0
$691$	−13.3249	+	12.3637i	−0.506901	+	0.470336i	−0.891676	−	0.452675i	$-0.850470\pi$
$691$	−13.3249	+	12.3637i	−0.506901	+	0.470336i	0.384774	+	0.923011i	$0.374279\pi$
$692$		0			0
$693$	7.93179	+	3.34764i	0.301304	+	0.127166i
$694$		0			0
$695$	−11.2653	−	7.68058i	−0.427319	−	0.291341i
$696$		0			0
$697$	9.26639	−	6.31772i	0.350989	−	0.239301i
$698$		0			0
$699$	−41.1449	−	19.8144i	−1.55624	−	0.749448i
$700$		0			0
$701$	−18.6892	+	9.00026i	−0.705882	+	0.339935i	−0.752148	−	0.658994i	$-0.770982\pi$
$701$	−18.6892	+	9.00026i	−0.705882	+	0.339935i	0.0462657	+	0.998929i	$0.485268\pi$
$702$		0			0
$703$	−1.04642	−	2.66623i	−0.0394664	−	0.100559i
$704$		0			0
$705$	16.2032	+	28.0647i	0.610246	+	1.05698i
$706$		0			0
$707$	−11.9169	−	10.0084i	−0.448182	−	0.376405i
$708$		0			0
$709$	−7.99824	+	20.3792i	−0.300380	+	0.765356i	0.698387	+	0.715720i	$0.253901\pi$
$709$	−7.99824	+	20.3792i	−0.300380	+	0.765356i	−0.998767	+	0.0496362i	$0.984194\pi$
$710$		0			0
$711$	−1.21118	+	16.1620i	−0.0454227	+	0.606124i
$712$		0			0
$713$	32.9282	+	41.2906i	1.23317	+	1.54635i
$714$		0			0
$715$	−2.04344	+	2.56239i	−0.0764203	+	0.0958281i
$716$		0			0
$717$	29.1368	−	50.4665i	1.08813	−	1.88470i
$718$		0			0
$719$	−35.3017	+	10.8891i	−1.31653	+	0.406096i	−0.871929	−	0.489632i	$-0.837131\pi$
$719$	−35.3017	+	10.8891i	−1.31653	+	0.406096i	−0.444602	+	0.895728i	$0.646655\pi$
$720$		0			0
$721$	−45.3795	+	16.4942i	−1.69002	+	0.614276i
$722$		0			0
$723$	47.8378	+	7.21039i	1.77911	+	0.268157i
$724$		0			0
$725$	25.2543	+	23.4326i	0.937922	+	0.870265i
$726$		0			0
$727$	−1.96182	−	8.59528i	−0.0727598	−	0.318781i	0.925430	−	0.378918i	$-0.123704\pi$
$727$	−1.96182	−	8.59528i	−0.0727598	−	0.318781i	−0.998190	+	0.0601362i	$0.980846\pi$
$728$		0			0
$729$	−2.20587	+	9.66453i	−0.0816987	+	0.357946i
$730$		0			0
$731$	17.5713	−	2.64844i	0.649897	−	0.0979561i
$732$		0			0
$733$	2.41969	+	32.2885i	0.0893732	+	1.19260i	0.843962	+	0.536404i	$0.180217\pi$
$733$	2.41969	+	32.2885i	0.0893732	+	1.19260i	−0.754588	+	0.656198i	$0.772163\pi$
$734$		0			0
$735$	−17.5447	−	6.40324i	−0.647146	−	0.236187i
$736$		0			0
$737$	0.306194	+	4.08588i	0.0112788	+	0.150505i
$738$		0			0
$739$	10.7112	−	1.61446i	0.394019	−	0.0593888i	0.0509554	−	0.998701i	$-0.483773\pi$
$739$	10.7112	−	1.61446i	0.394019	−	0.0593888i	0.343064	+	0.939312i	$0.388535\pi$
$740$		0			0
$741$	0.316257	−	1.38561i	0.0116180	−	0.0509017i
$742$		0			0
$743$	−4.99972	−	21.9052i	−0.183422	−	0.803624i	−0.979985	−	0.199069i	$-0.936208\pi$
$743$	−4.99972	−	21.9052i	−0.183422	−	0.803624i	0.796563	−	0.604555i	$-0.206649\pi$
$744$		0			0
$745$	3.15552	+	2.92789i	0.115609	+	0.107270i
$746$		0			0
$747$	11.8700	+	1.78911i	0.434300	+	0.0654602i
$748$		0			0
$749$	11.9430	+	18.5092i	0.436387	+	0.676313i
$750$		0			0
$751$	−3.44913	+	1.06392i	−0.125861	+	0.0388229i	−0.357046	−	0.934087i	$-0.616216\pi$
$751$	−3.44913	+	1.06392i	−0.125861	+	0.0388229i	0.231185	+	0.972910i	$0.425740\pi$
$752$		0			0
$753$	−20.3339	+	35.2193i	−0.741008	+	1.28346i
$754$		0			0
$755$	−11.4202	+	14.3204i	−0.415622	+	0.521174i
$756$		0			0
$757$	−6.57798	−	8.24853i	−0.239081	−	0.299798i	0.647787	−	0.761822i	$-0.275695\pi$
$757$	−6.57798	−	8.24853i	−0.239081	−	0.299798i	−0.886867	+	0.462024i	$0.847123\pi$
$758$		0			0
$759$	2.66223	−	35.5250i	0.0966328	−	1.28948i
$760$		0			0
$761$	2.61759	−	6.66950i	0.0948874	−	0.241769i	−0.875548	−	0.483132i	$-0.839499\pi$
$761$	2.61759	−	6.66950i	0.0948874	−	0.241769i	0.970435	+	0.241363i	$0.0775944\pi$
$762$		0			0
$763$	−15.8458	+	3.19603i	−0.573655	+	0.115704i
$764$		0			0
$765$	1.50257	+	2.60254i	0.0543257	+	0.0940949i
$766$		0			0
$767$	1.72770	+	4.40210i	0.0623836	+	0.158951i
$768$		0			0
$769$	−34.9092	+	16.8114i	−1.25886	+	0.606233i	−0.939872	−	0.341527i	$-0.889056\pi$
$769$	−34.9092	+	16.8114i	−1.25886	+	0.606233i	−0.318984	+	0.947760i	$0.603342\pi$
$770$		0			0
$771$	−35.1138	−	16.9099i	−1.26459	−	0.608995i
$772$		0			0
$773$	−41.2797	+	28.1440i	−1.48473	+	1.01227i	−0.495064	+	0.868857i	$0.664855\pi$
$773$	−41.2797	+	28.1440i	−1.48473	+	1.01227i	−0.989663	+	0.143413i	$0.954192\pi$
$774$		0			0
$775$	22.9477	+	15.6455i	0.824305	+	0.562001i
$776$		0			0
$777$	−13.2158	−	14.9886i	−0.474115	−	0.537714i
$778$		0			0
$779$	−3.23058	+	2.99754i	−0.115748	+	0.107398i
$780$		0			0
$781$	15.9870	+	4.93133i	0.572059	+	0.176457i
$782$		0			0
$783$	39.1597			1.39945
$784$		0			0
$785$	−3.97145			−0.141747
$786$		0			0
$787$	−19.6095	−	6.04872i	−0.699002	−	0.215614i	−0.0751685	−	0.997171i	$-0.523949\pi$
$787$	−19.6095	−	6.04872i	−0.699002	−	0.215614i	−0.623833	+	0.781557i	$0.714426\pi$
$788$		0			0
$789$	−12.5061	+	11.6040i	−0.445230	+	0.413113i
$790$		0			0
$791$	33.5829	−	1.66124i	1.19407	−	0.0590668i
$792$		0			0
$793$	9.14528	+	6.23515i	0.324759	+	0.221417i
$794$		0			0
$795$	−15.3304	+	10.4521i	−0.543712	+	0.370696i
$796$		0			0
$797$	−39.4794	−	19.0123i	−1.39843	−	0.673449i	−0.425588	−	0.904917i	$-0.639933\pi$
$797$	−39.4794	−	19.0123i	−1.39843	−	0.673449i	−0.972842	+	0.231468i	$0.925647\pi$
$798$		0			0
$799$	21.5581	−	10.3818i	0.762671	−	0.367283i
$800$		0			0
$801$	1.25415	+	3.19553i	0.0443134	+	0.112909i
$802$		0			0
$803$	−0.0443129	−	0.0767522i	−0.00156377	−	0.00270853i
$804$		0			0
$805$	−0.549147	+	21.6380i	−0.0193549	+	0.762638i
$806$		0			0
$807$	1.80372	−	4.59580i	0.0634940	−	0.161780i
$808$		0			0
$809$	1.37442	−	18.3404i	0.0483221	−	0.644814i	−0.919486	−	0.393123i	$-0.871395\pi$
$809$	1.37442	−	18.3404i	0.0483221	−	0.644814i	0.967808	−	0.251690i	$-0.0809864\pi$
$810$		0			0
$811$	29.3696	+	36.8283i	1.03131	+	1.29322i	0.955151	+	0.296120i	$0.0956930\pi$
$811$	29.3696	+	36.8283i	1.03131	+	1.29322i	0.0761551	+	0.997096i	$0.475736\pi$
$812$		0			0
$813$	−13.4788	+	16.9019i	−0.472721	+	0.592774i
$814$		0			0
$815$	−5.52625	+	9.57175i	−0.193576	+	0.335284i
$816$		0			0
$817$	−6.67246	+	2.05818i	−0.233440	+	0.0720066i
$818$		0			0
$819$	−0.344105	−	2.75573i	−0.0120240	−	0.0962928i
$820$		0			0
$821$	−28.3588	−	4.27441i	−0.989730	−	0.149178i	−0.365830	−	0.930682i	$-0.619215\pi$
$821$	−28.3588	−	4.27441i	−0.989730	−	0.149178i	−0.623900	+	0.781504i	$0.714453\pi$
$822$		0			0
$823$	9.80982	+	9.10218i	0.341949	+	0.317282i	0.832388	−	0.554193i	$-0.186973\pi$
$823$	9.80982	+	9.10218i	0.341949	+	0.317282i	−0.490439	+	0.871475i	$0.663164\pi$
$824$		0			0
$825$	−4.16885	−	18.2649i	−0.145141	−	0.635902i
$826$		0			0
$827$	−5.62773	+	24.6567i	−0.195695	+	0.857398i	0.777767	+	0.628552i	$0.216352\pi$
$827$	−5.62773	+	24.6567i	−0.195695	+	0.857398i	−0.973463	+	0.228846i	$0.926505\pi$
$828$		0			0
$829$	8.45919	−	1.27502i	0.293800	−	0.0442832i	−0.000488539	−	1.00000i	$-0.500156\pi$
$829$	8.45919	−	1.27502i	0.293800	−	0.0442832i	0.294288	+	0.955717i	$0.404917\pi$
$830$		0			0
$831$	−3.14853	−	42.0142i	−0.109221	−	1.45745i
$832$		0			0
$833$	−5.68280	+	12.5649i	−0.196897	+	0.435347i
$834$		0			0
$835$	1.01538	+	13.5494i	0.0351388	+	0.468895i
$836$		0			0
$837$	31.2171	−	4.70522i	1.07902	−	0.162636i
$838$		0			0
$839$	−2.46700	+	10.8086i	−0.0851702	+	0.373155i	−0.999493	−	0.0318306i	$-0.989866\pi$
$839$	−2.46700	+	10.8086i	−0.0851702	+	0.373155i	0.914323	+	0.404986i	$0.132723\pi$
$840$		0			0
$841$	−17.9215	−	78.5192i	−0.617983	−	2.70756i
$842$		0			0
$843$	15.8953	+	14.7487i	0.547463	+	0.507972i
$844$		0			0
$845$	−15.7562	−	2.37486i	−0.542029	−	0.0816977i
$846$		0			0
$847$	−5.96308	+	6.10826i	−0.204894	+	0.209882i
$848$		0			0
$849$	48.1554	−	14.8540i	1.65269	−	0.509787i
$850$		0			0
$851$	−11.5794	+	20.0561i	−0.396936	+	0.687514i
$852$		0			0
$853$	28.5086	−	35.7487i	0.976118	−	1.22401i	0.00153161	−	0.999999i	$-0.499512\pi$
$853$	28.5086	−	35.7487i	0.976118	−	1.22401i	0.974586	−	0.224014i	$-0.0719161\pi$
$854$		0			0
$855$	−0.736269	−	0.923252i	−0.0251799	−	0.0315746i
$856$		0			0
$857$	−0.155888	+	2.08018i	−0.00532502	+	0.0710575i	−0.999233	−	0.0391539i	$-0.987534\pi$
$857$	−0.155888	+	2.08018i	−0.00532502	+	0.0710575i	0.993908	+	0.110211i	$0.0351528\pi$
$858$		0			0
$859$	−7.18902	+	18.3173i	−0.245286	+	0.624979i	−0.999499	−	0.0316512i	$-0.989923\pi$
$859$	−7.18902	+	18.3173i	−0.245286	+	0.624979i	0.754213	+	0.656630i	$0.228019\pi$
$860$		0			0
$861$	−14.0390	+	27.3544i	−0.478448	+	0.932236i
$862$		0			0
$863$	−7.30885	−	12.6593i	−0.248796	−	0.430928i	0.714396	−	0.699742i	$-0.246702\pi$
$863$	−7.30885	−	12.6593i	−0.248796	−	0.430928i	−0.963192	+	0.268814i	$0.913368\pi$
$864$		0			0
$865$	−0.281015	−	0.716013i	−0.00955478	−	0.0243452i
$866$		0			0
$867$	−24.1283	+	11.6196i	−0.819440	+	0.394622i
$868$		0			0
$869$	34.8838	+	16.7991i	1.18335	+	0.569872i
$870$		0			0
$871$	1.09203	−	0.744534i	0.0370021	−	0.0252276i
$872$		0			0
$873$	9.50940	+	6.48340i	0.321844	+	0.219430i
$874$		0			0
$875$	7.75371	+	27.6049i	0.262123	+	0.933217i
$876$		0			0
$877$	−15.1681	+	14.0739i	−0.512189	+	0.475242i	−0.893410	−	0.449242i	$-0.851694\pi$
$877$	−15.1681	+	14.0739i	−0.512189	+	0.475242i	0.381221	+	0.924484i	$0.375504\pi$
$878$		0			0
$879$	21.2909	+	6.56739i	0.718126	+	0.221512i
$880$		0			0
$881$	9.01313			0.303660			0.151830	−	0.988407i	$-0.451483\pi$
$881$	9.01313			0.303660			0.151830	+	0.988407i	$0.451483\pi$
$882$		0			0
$883$	7.70553			0.259312			0.129656	−	0.991559i	$-0.458613\pi$
$883$	7.70553			0.259312			0.129656	+	0.991559i	$0.458613\pi$
$884$		0			0
$885$	13.4059	+	4.13518i	0.450635	+	0.139003i
$886$		0			0
$887$	−7.17257	+	6.65517i	−0.240831	+	0.223459i	−0.791349	−	0.611365i	$-0.790621\pi$
$887$	−7.17257	+	6.65517i	−0.240831	+	0.223459i	0.550518	+	0.834824i	$0.314430\pi$
$888$		0			0
$889$	5.15249	−	2.80296i	0.172809	−	0.0940081i
$890$		0			0
$891$	−25.6607	−	17.4952i	−0.859666	−	0.586111i
$892$		0			0
$893$	−7.76869	+	5.29660i	−0.259969	+	0.177244i
$894$		0			0
$895$	12.0992	+	5.82665i	0.404430	+	0.194763i
$896$		0			0
$897$	−10.3535	+	4.98599i	−0.345694	+	0.166477i
$898$		0			0
$899$	−32.2624	−	82.2033i	−1.07601	−	2.74163i
$900$		0			0
$901$	6.84997	+	11.8645i	0.228205	+	0.395263i
$902$		0			0
$903$	−38.8463	+	29.3980i	−1.29272	+	0.978304i
$904$		0			0
$905$	−4.18335	+	10.6590i	−0.139059	+	0.354317i
$906$		0			0
$907$	0.860141	−	11.4778i	0.0285605	−	0.381114i	−0.964547	−	0.263910i	$-0.914988\pi$
$907$	0.860141	−	11.4778i	0.0285605	−	0.381114i	0.993108	−	0.117204i	$-0.0373931\pi$
$908$		0			0
$909$	−4.28015	−	5.36714i	−0.141964	−	0.178017i
$910$		0			0
$911$	−18.6532	+	23.3904i	−0.618009	+	0.774958i	−0.988063	−	0.154052i	$-0.950768\pi$
$911$	−18.6532	+	23.3904i	−0.618009	+	0.774958i	0.370054	+	0.929010i	$0.379339\pi$
$912$		0			0
$913$	14.3384	−	24.8348i	0.474531	−	0.821911i
$914$		0			0
$915$	31.3775	−	9.67869i	1.03731	−	0.319968i
$916$		0			0
$917$	−10.6097	−	1.06638i	−0.350363	−	0.0352148i
$918$		0			0
$919$	−26.9527	−	4.06247i	−0.889089	−	0.134009i	−0.311413	−	0.950275i	$-0.600802\pi$
$919$	−26.9527	−	4.06247i	−0.889089	−	0.134009i	−0.577676	+	0.816266i	$0.696040\pi$
$920$		0			0
$921$	−19.0459	−	17.6720i	−0.627584	−	0.582313i
$922$		0			0
$923$	−1.20088	−	5.26142i	−0.0395276	−	0.173182i
$924$		0			0
$925$	−2.71007	+	11.8736i	−0.0891067	+	0.390402i
$926$		0			0
$927$	−21.0614	+	3.17449i	−0.691746	+	0.104264i
$928$		0			0
$929$	−2.75547	−	36.7691i	−0.0904039	−	1.20636i	−0.839300	−	0.543669i	$-0.817035\pi$
$929$	−2.75547	−	36.7691i	−0.0904039	−	1.20636i	0.748896	−	0.662687i	$-0.230584\pi$
$930$		0			0
$931$	1.47225	−	5.21508i	0.0482511	−	0.170917i
$932$		0			0
$933$	−0.597483	−	7.97286i	−0.0195607	−	0.261020i
$934$		0			0
$935$	7.09888	−	1.06998i	0.232158	−	0.0349922i
$936$		0			0
$937$	9.07808	−	39.7737i	0.296568	−	1.29935i	−0.578633	−	0.815588i	$-0.696414\pi$
$937$	9.07808	−	39.7737i	0.296568	−	1.29935i	0.875201	−	0.483760i	$-0.160729\pi$
$938$		0			0
$939$	7.27802	+	31.8871i	0.237509	+	1.04060i
$940$		0			0
$941$	−33.6083	−	31.1839i	−1.09560	−	1.01657i	−0.999776	−	0.0211684i	$-0.993261\pi$
$941$	−33.6083	−	31.1839i	−1.09560	−	1.01657i	−0.0958226	−	0.995398i	$-0.530548\pi$
$942$		0			0
$943$	35.2352	+	5.31085i	1.14742	+	0.172945i
$944$		0			0
$945$	11.0375	+	6.75153i	0.359049	+	0.219627i
$946$		0			0
$947$	−24.1913	+	7.46202i	−0.786111	+	0.242483i	−0.661721	−	0.749750i	$-0.730174\pi$
$947$	−24.1913	+	7.46202i	−0.786111	+	0.242483i	−0.124390	+	0.992233i	$0.539697\pi$
$948$		0			0
$949$	−0.0142941	+	0.0247582i	−0.000464008	+	0.000803685i
$950$		0			0
$951$	44.5024	−	55.8043i	1.44309	−	1.80958i
$952$		0			0
$953$	−22.7416	−	28.5171i	−0.736673	−	0.923759i	0.262479	−	0.964938i	$-0.415460\pi$
$953$	−22.7416	−	28.5171i	−0.736673	−	0.923759i	−0.999152	+	0.0411790i	$0.986889\pi$
$954$		0			0
$955$	−0.186417	+	2.48756i	−0.00603232	+	0.0804957i
$956$		0			0
$957$	−21.7625	+	55.4500i	−0.703482	+	1.79244i
$958$		0			0
$959$	−2.39781	−	5.32034i	−0.0774294	−	0.171803i
$960$		0			0
$961$	−20.0960	−	34.8072i	−0.648257	−	1.12281i
$962$		0			0
$963$	3.55002	+	9.04529i	0.114398	+	0.291481i
$964$		0			0
$965$	−7.28122	+	3.50645i	−0.234391	+	0.112877i
$966$		0			0
$967$	−17.3723	−	8.36604i	−0.558654	−	0.269034i	0.133178	−	0.991092i	$-0.457482\pi$
$967$	−17.3723	−	8.36604i	−0.558654	−	0.269034i	−0.691832	+	0.722059i	$0.743196\pi$
$968$		0			0
$969$	−2.57223	+	1.75372i	−0.0826319	+	0.0563375i
$970$		0			0
$971$	−0.413401	−	0.281852i	−0.0132667	−	0.00904506i	0.556669	−	0.830735i	$-0.312079\pi$
$971$	−0.413401	−	0.281852i	−0.0132667	−	0.00904506i	−0.569935	+	0.821690i	$0.693032\pi$
$972$		0			0
$973$	4.80459	−	27.1782i	0.154028	−	0.871294i
$974$		0			0
$975$	−4.43004	+	4.11048i	−0.141875	+	0.131641i
$976$		0			0
$977$	55.2462	+	17.0412i	1.76748	+	0.545196i	0.995861	−	0.0908860i	$-0.0289699\pi$
$977$	55.2462	+	17.0412i	1.76748	+	0.545196i	0.771621	+	0.636082i	$0.219446\pi$
$978$		0			0
$979$	8.20076			0.262097
$980$		0			0
$981$	−7.13069			−0.227665
$982$		0			0
$983$	9.11468	+	2.81150i	0.290713	+	0.0896731i	0.436682	−	0.899616i	$-0.356154\pi$
$983$	9.11468	+	2.81150i	0.290713	+	0.0896731i	−0.145969	+	0.989289i	$0.546630\pi$
$984$		0			0
$985$	1.12950	−	1.04802i	0.0359889	−	0.0333928i
$986$		0			0
$987$	−38.3162	+	53.2451i	−1.21962	+	1.69481i
$988$		0			0
$989$	46.6484	+	31.8043i	1.48333	+	1.01132i
$990$		0			0
$991$	29.9345	−	20.4090i	0.950900	−	0.648312i	0.0147413	−	0.999891i	$-0.495308\pi$
$991$	29.9345	−	20.4090i	0.950900	−	0.648312i	0.936158	+	0.351579i	$0.114355\pi$
$992$		0			0
$993$	60.2272	+	29.0039i	1.91125	+	0.920411i
$994$		0			0
$995$	29.8430	−	14.3716i	0.946086	−	0.455611i
$996$		0			0
$997$	7.51602	+	19.1505i	0.238035	+	0.606502i	0.999111	−	0.0421600i	$-0.0134239\pi$
$997$	7.51602	+	19.1505i	0.238035	+	0.606502i	−0.761076	+	0.648662i	$0.775329\pi$
$998$		0			0
$999$	6.92179	+	11.9889i	0.218996	+	0.379311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bg.b.81.1		24
4.3	odd	2		98.2.g.b.81.2	yes	24
12.11	even	2		882.2.z.b.865.1		24
28.3	even	6		686.2.e.d.197.3		24
28.11	odd	6		686.2.e.c.197.2		24
28.19	even	6		686.2.g.d.373.2		24
28.23	odd	6		686.2.g.f.373.1		24
28.27	even	2		686.2.g.e.459.1		24
49.23	even	21	inner	784.2.bg.b.513.1		24
196.11	odd	42		4802.2.a.o.1.9		12
196.23	odd	42		98.2.g.b.23.2	✓	24
196.27	even	14		686.2.g.d.263.2		24
196.71	odd	14		686.2.g.f.263.1		24
196.75	even	42		686.2.g.e.275.1		24
196.87	even	42		4802.2.a.l.1.4		12
196.143	even	42		686.2.e.d.491.3		24
196.151	odd	42		686.2.e.c.491.2		24
588.23	even	42		882.2.z.b.415.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.b.23.2	✓	24	196.23	odd	42
98.2.g.b.81.2	yes	24	4.3	odd	2
686.2.e.c.197.2		24	28.11	odd	6
686.2.e.c.491.2		24	196.151	odd	42
686.2.e.d.197.3		24	28.3	even	6
686.2.e.d.491.3		24	196.143	even	42
686.2.g.d.263.2		24	196.27	even	14
686.2.g.d.373.2		24	28.19	even	6
686.2.g.e.275.1		24	196.75	even	42
686.2.g.e.459.1		24	28.27	even	2
686.2.g.f.263.1		24	196.71	odd	14
686.2.g.f.373.1		24	28.23	odd	6
784.2.bg.b.81.1		24	1.1	even	1	trivial
784.2.bg.b.513.1		24	49.23	even	21	inner
882.2.z.b.415.1		24	588.23	even	42
882.2.z.b.865.1		24	12.11	even	2
4802.2.a.l.1.4		12	196.87	even	42
4802.2.a.o.1.9		12	196.11	odd	42

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bg (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.95066 - 0.601698i) q^{3} +(0.958118 - 0.889004i) q^{5} +(2.43754 + 1.02877i) q^{7} +(0.964304 + 0.657452i) q^{9} +O(q^{10})\)	\(q+(-1.95066 - 0.601698i) q^{3} +(0.958118 - 0.889004i) q^{5} +(2.43754 + 1.02877i) q^{7} +(0.964304 + 0.657452i) q^{9} +(2.30365 - 1.57060i) q^{11} +(-0.810304 - 0.390222i) q^{13} +(-2.40387 + 1.15764i) q^{15} +(0.719733 + 1.83385i) q^{17} +(-0.387065 - 0.670417i) q^{19} +(-4.13580 - 3.47345i) q^{21} +(-2.28676 + 5.82658i) q^{23} +(-0.245988 + 3.28248i) q^{25} +(2.33284 + 2.92529i) q^{27} +(6.52548 - 8.18270i) q^{29} +(4.21876 - 7.30711i) q^{31} +(-5.43865 + 1.67760i) q^{33} +(3.25004 - 1.18130i) q^{35} +(3.65860 + 0.551445i) q^{37} +(1.34583 + 1.24875i) q^{39} +(-1.26678 - 5.55015i) q^{41} +(2.00714 - 8.79388i) q^{43} +(1.50839 - 0.227354i) q^{45} +(-0.907661 - 12.1119i) q^{47} +(4.88324 + 5.01537i) q^{49} +(-0.300528 - 4.01027i) q^{51} +(6.87650 - 1.03647i) q^{53} +(0.810897 - 3.55277i) q^{55} +(0.351643 + 1.54065i) q^{57} +(-3.85448 - 3.57644i) q^{59} +(-12.1696 - 1.83427i) q^{61} +(1.67417 + 2.59462i) q^{63} +(-1.12328 + 0.346485i) q^{65} +(-0.734787 + 1.27269i) q^{67} +(7.96653 - 9.98972i) q^{69} +(3.74129 + 4.69143i) q^{71} +(0.00237545 - 0.0316982i) q^{73} +(2.45490 - 6.25498i) q^{75} +(7.23103 - 1.45847i) q^{77} +(6.94343 + 12.0264i) q^{79} +(-4.06960 - 10.3692i) q^{81} +(9.26679 - 4.46265i) q^{83} +(2.31989 + 1.11720i) q^{85} +(-17.6525 + 12.0353i) q^{87} +(2.43024 + 1.65691i) q^{89} +(-1.57370 - 1.78480i) q^{91} +(-12.6260 + 11.7153i) q^{93} +(-0.966857 - 0.298236i) q^{95} +9.86141 q^{97} +3.25401 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 7 q^{3} + 19 q^{9}+O(q^{10}) \) 24 * q + 7 * q^3 + 19 * q^9	\( 24 q + 7 q^{3} + 19 q^{9} + 11 q^{11} - 14 q^{13} - 9 q^{15} - 7 q^{17} + 14 q^{19} - 7 q^{21} + 29 q^{23} - 8 q^{25} + 7 q^{27} + 13 q^{29} + 28 q^{31} - 14 q^{33} + 35 q^{35} + 20 q^{37} - 56 q^{39} + 28 q^{41} - 6 q^{43} + 7 q^{45} - 42 q^{47} + 28 q^{49} - 32 q^{51} - 60 q^{53} + 14 q^{55} + 23 q^{57} - 49 q^{59} - 14 q^{61} + 28 q^{63} - 28 q^{65} - 24 q^{67} + 7 q^{69} - 6 q^{71} - 35 q^{73} + 56 q^{75} + 49 q^{77} - 6 q^{79} - 45 q^{81} + 77 q^{83} - 33 q^{85} - 63 q^{87} + 21 q^{91} - 38 q^{93} - 86 q^{95} + 98 q^{97} + 106 q^{99}+O(q^{100}) \) 24 * q + 7 * q^3 + 19 * q^9 + 11 * q^11 - 14 * q^13 - 9 * q^15 - 7 * q^17 + 14 * q^19 - 7 * q^21 + 29 * q^23 - 8 * q^25 + 7 * q^27 + 13 * q^29 + 28 * q^31 - 14 * q^33 + 35 * q^35 + 20 * q^37 - 56 * q^39 + 28 * q^41 - 6 * q^43 + 7 * q^45 - 42 * q^47 + 28 * q^49 - 32 * q^51 - 60 * q^53 + 14 * q^55 + 23 * q^57 - 49 * q^59 - 14 * q^61 + 28 * q^63 - 28 * q^65 - 24 * q^67 + 7 * q^69 - 6 * q^71 - 35 * q^73 + 56 * q^75 + 49 * q^77 - 6 * q^79 - 45 * q^81 + 77 * q^83 - 33 * q^85 - 63 * q^87 + 21 * q^91 - 38 * q^93 - 86 * q^95 + 98 * q^97 + 106 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more