LMFDB - Embedded newform 1064.2.q.n.457.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1064,2,Mod(305,1064)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1064, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1064.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1064 = 2^{3} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1064.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.49608277506$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + \cdots + 256 $ x^16 + 15x^14 - 2x^13 + 159x^12 - 19x^11 + 839x^10 - 62x^9 + 3204x^8 + 8x^7 + 4560x^6 + 1376x^5 + 4688x^4 + 736x^3 + 1280x^2 - 128x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.3
Root			$-0.456148 - 0.790072i$ of defining polynomial
Character	$\chi$	$=$	1064.457
Dual form			1064.2.q.n.305.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.456148 - 0.790072i) q^{3} +(0.832641 - 1.44218i) q^{5} +(-0.462738 - 2.60497i) q^{7} +(1.08386 - 1.87730i) q^{9} +O(q^{10})$	\(q+(-0.456148 - 0.790072i) q^{3} +(0.832641 - 1.44218i) q^{5} +(-0.462738 - 2.60497i) q^{7} +(1.08386 - 1.87730i) q^{9} +(0.121120 + 0.209787i) q^{11} -5.76999 q^{13} -1.51923 q^{15} +(-2.88319 - 4.99382i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-1.84704 + 1.55385i) q^{21} +(-3.30773 + 5.72915i) q^{23} +(1.11342 + 1.92850i) q^{25} -4.71449 q^{27} +8.91381 q^{29} +(2.96642 + 5.13799i) q^{31} +(0.110498 - 0.191388i) q^{33} +(-4.14212 - 1.50166i) q^{35} +(4.90185 - 8.49026i) q^{37} +(2.63197 + 4.55870i) q^{39} -2.00000 q^{41} -7.83237 q^{43} +(-1.80493 - 3.12623i) q^{45} +(-0.789589 + 1.36761i) q^{47} +(-6.57175 + 2.41084i) q^{49} +(-2.63032 + 4.55585i) q^{51} +(-3.24073 - 5.61311i) q^{53} +0.403399 q^{55} +0.912296 q^{57} +(-0.537488 - 0.930957i) q^{59} +(-4.55454 + 7.88869i) q^{61} +(-5.39185 - 1.95472i) q^{63} +(-4.80433 + 8.32134i) q^{65} +(-4.01270 - 6.95021i) q^{67} +6.03525 q^{69} +1.22955 q^{71} +(-0.400685 - 0.694007i) q^{73} +(1.01577 - 1.75936i) q^{75} +(0.490441 - 0.412591i) q^{77} +(3.79101 - 6.56622i) q^{79} +(-1.10107 - 1.90711i) q^{81} -8.91292 q^{83} -9.60264 q^{85} +(-4.06602 - 7.04255i) q^{87} +(6.55732 - 11.3576i) q^{89} +(2.66999 + 15.0307i) q^{91} +(2.70625 - 4.68737i) q^{93} +(0.832641 + 1.44218i) q^{95} +1.11664 q^{97} +0.525109 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) $ 16 * q + q^5 + 5 * q^7 - 6 * q^9	$ 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100}) $ 16 * q + q^5 + 5 * q^7 - 6 * q^9 - 9 * q^11 + 16 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 - 25 * q^23 - 15 * q^25 + 6 * q^27 + 12 * q^29 - 8 * q^33 + 5 * q^35 - 13 * q^37 + 11 * q^39 - 32 * q^41 + 34 * q^43 - 17 * q^45 + 24 * q^47 - 13 * q^49 - 5 * q^51 - 2 * q^53 + 10 * q^55 - 2 * q^59 + 13 * q^61 - 52 * q^63 + 26 * q^65 - 2 * q^67 - 22 * q^69 + 20 * q^71 - 5 * q^73 + 20 * q^75 + 28 * q^77 - 16 * q^79 + 12 * q^81 - 86 * q^83 + 48 * q^85 - 20 * q^87 - 8 * q^89 - 34 * q^91 - 2 * q^93 + q^95 - 24 * q^97 + 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−0.456148	−	0.790072i	−0.263357	−	0.456148i	0.703775	−	0.710423i	$-0.251496\pi$
$3$	−0.456148	−	0.790072i	−0.263357	−	0.456148i	−0.967132	+	0.254275i	$0.918163\pi$
$4$		0			0
$5$	0.832641	−	1.44218i	0.372368	−	0.644961i	−0.617561	−	0.786523i	$-0.711879\pi$
$5$	0.832641	−	1.44218i	0.372368	−	0.644961i	0.989929	+	0.141562i	$0.0452125\pi$
$6$		0			0
$7$	−0.462738	−	2.60497i	−0.174898	−	0.984586i
$7$	−0.462738	−	2.60497i	−0.174898	−	0.984586i
$8$		0			0
$9$	1.08386	−	1.87730i	0.361286	−	0.625766i
$10$		0			0
$11$	0.121120	+	0.209787i	0.0365192	+	0.0632531i	0.883707	−	0.468040i	$-0.155040\pi$
$11$	0.121120	+	0.209787i	0.0365192	+	0.0632531i	−0.847188	+	0.531293i	$0.821706\pi$
$12$		0			0
$13$	−5.76999			−1.60031			−0.800154	−	0.599795i	$-0.795249\pi$
$13$	−5.76999			−1.60031			−0.800154	+	0.599795i	$0.795249\pi$
$14$		0			0
$15$	−1.51923			−0.392264
$16$		0			0
$17$	−2.88319	−	4.99382i	−0.699275	−	1.21118i	−0.968718	−	0.248164i	$-0.920173\pi$
$17$	−2.88319	−	4.99382i	−0.699275	−	1.21118i	0.269443	−	0.963016i	$-0.413160\pi$
$18$		0			0
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$		0			0
$21$	−1.84704	+	1.55385i	−0.403056	+	0.339077i
$22$		0			0
$23$	−3.30773	+	5.72915i	−0.689709	+	1.19461i	0.282224	+	0.959349i	$0.408928\pi$
$23$	−3.30773	+	5.72915i	−0.689709	+	1.19461i	−0.971932	+	0.235262i	$0.924405\pi$
$24$		0			0
$25$	1.11342	+	1.92850i	0.222684	+	0.385699i
$26$		0			0
$27$	−4.71449			−0.907303
$28$		0			0
$29$	8.91381			1.65525			0.827627	−	0.561279i	$-0.189690\pi$
$29$	8.91381			1.65525			0.827627	+	0.561279i	$0.189690\pi$
$30$		0			0
$31$	2.96642	+	5.13799i	0.532785	+	0.922810i	0.999267	+	0.0382794i	$0.0121877\pi$
$31$	2.96642	+	5.13799i	0.532785	+	0.922810i	−0.466483	+	0.884530i	$0.654479\pi$
$32$		0			0
$33$	0.110498	−	0.191388i	0.0192352	−	0.0333163i
$34$		0			0
$35$	−4.14212	−	1.50166i	−0.700147	−	0.253826i
$36$		0			0
$37$	4.90185	−	8.49026i	0.805860	−	1.39579i	−0.109849	−	0.993948i	$-0.535037\pi$
$37$	4.90185	−	8.49026i	0.805860	−	1.39579i	0.915709	−	0.401842i	$-0.131630\pi$
$38$		0			0
$39$	2.63197	+	4.55870i	0.421452	+	0.729977i
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$	−7.83237			−1.19443			−0.597213	−	0.802083i	$-0.703725\pi$
$43$	−7.83237			−1.19443			−0.597213	+	0.802083i	$0.703725\pi$
$44$		0			0
$45$	−1.80493	−	3.12623i	−0.269063	−	0.466031i
$46$		0			0
$47$	−0.789589	+	1.36761i	−0.115173	+	0.199486i	−0.917849	−	0.396930i	$-0.870076\pi$
$47$	−0.789589	+	1.36761i	−0.115173	+	0.199486i	0.802676	+	0.596416i	$0.203409\pi$
$48$		0			0
$49$	−6.57175	+	2.41084i	−0.938821	+	0.344405i
$50$		0			0
$51$	−2.63032	+	4.55585i	−0.368318	+	0.637946i
$52$		0			0
$53$	−3.24073	−	5.61311i	−0.445148	−	0.771019i	0.552914	−	0.833238i	$-0.313516\pi$
$53$	−3.24073	−	5.61311i	−0.445148	−	0.771019i	−0.998063	+	0.0622187i	$0.980182\pi$
$54$		0			0
$55$	0.403399			0.0543944
$56$		0			0
$57$	0.912296			0.120837
$58$		0			0
$59$	−0.537488	−	0.930957i	−0.0699750	−	0.121200i	0.828915	−	0.559375i	$-0.188959\pi$
$59$	−0.537488	−	0.930957i	−0.0699750	−	0.121200i	−0.898890	+	0.438174i	$0.855625\pi$
$60$		0			0
$61$	−4.55454	+	7.88869i	−0.583149	+	1.01004i	0.411955	+	0.911204i	$0.364846\pi$
$61$	−4.55454	+	7.88869i	−0.583149	+	1.01004i	−0.995103	+	0.0988387i	$0.968487\pi$
$62$		0			0
$63$	−5.39185	−	1.95472i	−0.679309	−	0.246272i
$64$		0			0
$65$	−4.80433	+	8.32134i	−0.595904	+	1.03214i
$66$		0			0
$67$	−4.01270	−	6.95021i	−0.490230	−	0.849103i	0.509707	−	0.860348i	$-0.329754\pi$
$67$	−4.01270	−	6.95021i	−0.490230	−	0.849103i	−0.999937	+	0.0112451i	$0.996421\pi$
$68$		0			0
$69$	6.03525			0.726559
$70$		0			0
$71$	1.22955			0.145921			0.0729606	−	0.997335i	$-0.476755\pi$
$71$	1.22955			0.145921			0.0729606	+	0.997335i	$0.476755\pi$
$72$		0			0
$73$	−0.400685	−	0.694007i	−0.0468966	−	0.0812274i	0.841624	−	0.540064i	$-0.181600\pi$
$73$	−0.400685	−	0.694007i	−0.0468966	−	0.0812274i	−0.888521	+	0.458836i	$0.848266\pi$
$74$		0			0
$75$	1.01577	−	1.75936i	0.117291	−	0.203153i
$76$		0			0
$77$	0.490441	−	0.412591i	0.0558910	−	0.0470192i
$78$		0			0
$79$	3.79101	−	6.56622i	0.426522	−	0.738758i	−0.570039	−	0.821617i	$-0.693072\pi$
$79$	3.79101	−	6.56622i	0.426522	−	0.738758i	0.996561	+	0.0828597i	$0.0264053\pi$
$80$		0			0
$81$	−1.10107	−	1.90711i	−0.122341	−	0.211901i
$82$		0			0
$83$	−8.91292			−0.978320			−0.489160	−	0.872194i	$-0.662697\pi$
$83$	−8.91292			−0.978320			−0.489160	+	0.872194i	$0.662697\pi$
$84$		0			0
$85$	−9.60264			−1.04155
$86$		0			0
$87$	−4.06602	−	7.04255i	−0.435923	−	0.755041i
$88$		0			0
$89$	6.55732	−	11.3576i	0.695074	−	1.20390i	−0.275082	−	0.961421i	$-0.588705\pi$
$89$	6.55732	−	11.3576i	0.695074	−	1.20390i	0.970156	−	0.242483i	$-0.0779618\pi$
$90$		0			0
$91$	2.66999	+	15.0307i	0.279891	+	1.57564i
$92$		0			0
$93$	2.70625	−	4.68737i	0.280625	−	0.486057i
$94$		0			0
$95$	0.832641	+	1.44218i	0.0854272	+	0.147964i
$96$		0			0
$97$	1.11664			0.113377			0.0566886	−	0.998392i	$-0.481946\pi$
$97$	1.11664			0.113377			0.0566886	+	0.998392i	$0.481946\pi$
$98$		0			0
$99$	0.525109			0.0527755
$100$		0			0
$101$	−6.51382	−	11.2823i	−0.648149	−	1.12263i	−0.983565	−	0.180557i	$-0.942210\pi$
$101$	−6.51382	−	11.2823i	−0.648149	−	1.12263i	0.335416	−	0.942070i	$-0.391123\pi$
$102$		0			0
$103$	6.86294	−	11.8870i	0.676226	−	1.17126i	−0.299883	−	0.953976i	$-0.596948\pi$
$103$	6.86294	−	11.8870i	0.676226	−	1.17126i	0.976109	−	0.217282i	$-0.0697190\pi$
$104$		0			0
$105$	0.703005	+	3.95755i	0.0686063	+	0.386217i
$106$		0			0
$107$	−1.88424	+	3.26359i	−0.182156	+	0.315503i	−0.942614	−	0.333883i	$-0.891641\pi$
$107$	−1.88424	+	3.26359i	−0.182156	+	0.315503i	0.760459	+	0.649386i	$0.224974\pi$
$108$		0			0
$109$	0.337127	+	0.583921i	0.0322909	+	0.0559295i	0.881719	−	0.471774i	$-0.156386\pi$
$109$	0.337127	+	0.583921i	0.0322909	+	0.0559295i	−0.849428	+	0.527704i	$0.823053\pi$
$110$		0			0
$111$	−8.94388			−0.848916
$112$		0			0
$113$	10.1480			0.954646			0.477323	−	0.878728i	$-0.341607\pi$
$113$	10.1480			0.954646			0.477323	+	0.878728i	$0.341607\pi$
$114$		0			0
$115$	5.50830	+	9.54065i	0.513651	+	0.889670i
$116$		0			0
$117$	−6.25385	+	10.8320i	−0.578169	+	1.00142i
$118$		0			0
$119$	−11.6746	+	9.82145i	−1.07021	+	0.900330i
$120$		0			0
$121$	5.47066	−	9.47546i	0.497333	−	0.861406i
$122$		0			0
$123$	0.912296	+	1.58014i	0.0822590	+	0.142477i
$124$		0			0
$125$	12.0347			1.07642
$126$		0			0
$127$	18.5974			1.65025			0.825126	−	0.564949i	$-0.191104\pi$
$127$	18.5974			1.65025			0.825126	+	0.564949i	$0.191104\pi$
$128$		0			0
$129$	3.57272	+	6.18813i	0.314561	+	0.544835i
$130$		0			0
$131$	−3.98570	+	6.90344i	−0.348233	+	0.603157i	−0.985936	−	0.167126i	$-0.946551\pi$
$131$	−3.98570	+	6.90344i	−0.348233	+	0.603157i	0.637703	+	0.770282i	$0.279885\pi$
$132$		0			0
$133$	2.48734	+	0.901743i	0.215680	+	0.0781910i
$134$		0			0
$135$	−3.92548	+	6.79912i	−0.337851	+	0.585175i
$136$		0			0
$137$	0.159382	+	0.276057i	0.0136169	+	0.0235852i	0.872754	−	0.488161i	$-0.162332\pi$
$137$	0.159382	+	0.276057i	0.0136169	+	0.0235852i	−0.859137	+	0.511746i	$0.828999\pi$
$138$		0			0
$139$	−5.80115			−0.492047			−0.246024	−	0.969264i	$-0.579124\pi$
$139$	−5.80115			−0.492047			−0.246024	+	0.969264i	$0.579124\pi$
$140$		0			0
$141$	1.44068			0.121327
$142$		0			0
$143$	−0.698864	−	1.21047i	−0.0584419	−	0.101224i
$144$		0			0
$145$	7.42201	−	12.8553i	0.616364	−	1.06757i
$146$		0			0
$147$	4.90242	+	4.09245i	0.404345	+	0.337540i
$148$		0			0
$149$	−6.83503	+	11.8386i	−0.559948	+	0.969858i	0.437552	+	0.899193i	$0.355845\pi$
$149$	−6.83503	+	11.8386i	−0.559948	+	0.969858i	−0.997500	+	0.0706649i	$0.977488\pi$
$150$		0			0
$151$	−5.51411	−	9.55072i	−0.448732	−	0.777226i	0.549572	−	0.835446i	$-0.314791\pi$
$151$	−5.51411	−	9.55072i	−0.448732	−	0.777226i	−0.998304	+	0.0582201i	$0.981457\pi$
$152$		0			0
$153$	−12.4999			−1.01055
$154$		0			0
$155$	9.87985			0.793568
$156$		0			0
$157$	−8.92830	−	15.4643i	−0.712556	−	1.23418i	−0.963895	−	0.266283i	$-0.914204\pi$
$157$	−8.92830	−	15.4643i	−0.712556	−	1.23418i	0.251339	−	0.967899i	$-0.419129\pi$
$158$		0			0
$159$	−2.95650	+	5.12081i	−0.234466	+	0.406107i
$160$		0			0
$161$	16.4549	+	5.96544i	1.29683	+	0.470142i
$162$		0			0
$163$	−5.59851	+	9.69690i	−0.438509	+	0.759520i	−0.997575	−	0.0696035i	$-0.977827\pi$
$163$	−5.59851	+	9.69690i	−0.438509	+	0.759520i	0.559066	+	0.829123i	$0.311160\pi$
$164$		0			0
$165$	−0.184010	−	0.318714i	−0.0143251	−	0.0248119i
$166$		0			0
$167$	1.44712			0.111981			0.0559906	−	0.998431i	$-0.482168\pi$
$167$	1.44712			0.111981			0.0559906	+	0.998431i	$0.482168\pi$
$168$		0			0
$169$	20.2928			1.56098
$170$		0			0
$171$	1.08386	+	1.87730i	0.0828847	+	0.143560i
$172$		0			0
$173$	−5.94705	+	10.3006i	−0.452146	+	0.783140i	−0.998519	−	0.0544023i	$-0.982675\pi$
$173$	−5.94705	+	10.3006i	−0.452146	+	0.783140i	0.546373	+	0.837542i	$0.316008\pi$
$174$		0			0
$175$	4.50846	−	3.79281i	0.340807	−	0.286709i
$176$		0			0
$177$	−0.490348	+	0.849308i	−0.0368568	+	0.0638379i
$178$		0			0
$179$	−12.5864	−	21.8003i	−0.940751	−	1.62943i	−0.764043	−	0.645165i	$-0.776788\pi$
$179$	−12.5864	−	21.8003i	−0.940751	−	1.62943i	−0.176708	−	0.984263i	$-0.556545\pi$
$180$		0			0
$181$	18.7410			1.39301			0.696503	−	0.717554i	$-0.254738\pi$
$181$	18.7410			1.39301			0.696503	+	0.717554i	$0.254738\pi$
$182$		0			0
$183$	8.31017			0.614305
$184$		0			0
$185$	−8.16297	−	14.1387i	−0.600154	−	1.03950i
$186$		0			0
$187$	0.698425	−	1.20971i	0.0510739	−	0.0884626i
$188$		0			0
$189$	2.18157	+	12.2811i	0.158686	+	0.893319i
$190$		0			0
$191$	−0.178001	+	0.308307i	−0.0128797	+	0.0223083i	−0.872393	−	0.488804i	$-0.837433\pi$
$191$	−0.178001	+	0.308307i	−0.0128797	+	0.0223083i	0.859514	+	0.511113i	$0.170767\pi$
$192$		0			0
$193$	−8.54939	−	14.8080i	−0.615398	−	1.06590i	−0.990314	−	0.138842i	$-0.955662\pi$
$193$	−8.54939	−	14.8080i	−0.615398	−	1.06590i	0.374916	−	0.927059i	$-0.377671\pi$
$194$		0			0
$195$	8.76594			0.627742
$196$		0			0
$197$	13.1088			0.933964			0.466982	−	0.884267i	$-0.345341\pi$
$197$	13.1088			0.933964			0.466982	+	0.884267i	$0.345341\pi$
$198$		0			0
$199$	−2.38489	−	4.13074i	−0.169060	−	0.292821i	0.769030	−	0.639213i	$-0.220740\pi$
$199$	−2.38489	−	4.13074i	−0.169060	−	0.292821i	−0.938090	+	0.346393i	$0.887407\pi$
$200$		0			0
$201$	−3.66077	+	6.34065i	−0.258211	+	0.447235i
$202$		0			0
$203$	−4.12476	−	23.2202i	−0.289501	−	1.62974i
$204$		0			0
$205$	−1.66528	+	2.88435i	−0.116308	+	0.201452i
$206$		0			0
$207$	7.17021	+	12.4192i	0.498364	+	0.863192i
$208$		0			0
$209$	−0.242241			−0.0167561
$210$		0			0
$211$	22.0442			1.51759			0.758794	−	0.651331i	$-0.225789\pi$
$211$	22.0442			1.51759			0.758794	+	0.651331i	$0.225789\pi$
$212$		0			0
$213$	−0.560858	−	0.971435i	−0.0384294	−	0.0665616i
$214$		0			0
$215$	−6.52156	+	11.2957i	−0.444766	+	0.770358i
$216$		0			0
$217$	12.0116	−	10.1050i	0.815403	−	0.685970i
$218$		0			0
$219$	−0.365543	+	0.633140i	−0.0247011	+	0.0427836i
$220$		0			0
$221$	16.6360	+	28.8143i	1.11906	+	1.93826i
$222$		0			0
$223$	19.5836			1.31142			0.655708	−	0.755014i	$-0.272370\pi$
$223$	19.5836			1.31142			0.655708	+	0.755014i	$0.272370\pi$
$224$		0			0
$225$	4.82715			0.321810
$226$		0			0
$227$	2.89414	+	5.01280i	0.192091	+	0.332712i	0.945943	−	0.324333i	$-0.105140\pi$
$227$	2.89414	+	5.01280i	0.192091	+	0.332712i	−0.753852	+	0.657044i	$0.771806\pi$
$228$		0			0
$229$	9.55372	−	16.5475i	0.631328	−	1.09349i	−0.355953	−	0.934504i	$-0.615844\pi$
$229$	9.55372	−	16.5475i	0.631328	−	1.09349i	0.987281	−	0.158988i	$-0.0508231\pi$
$230$		0			0
$231$	−0.549691	−	0.199281i	−0.0361670	−	0.0131117i
$232$		0			0
$233$	3.08563	−	5.34446i	0.202146	−	0.350127i	−0.747074	−	0.664741i	$-0.768542\pi$
$233$	3.08563	−	5.34446i	0.202146	−	0.350127i	0.949220	+	0.314614i	$0.101875\pi$
$234$		0			0
$235$	1.31489	+	2.27745i	0.0857739	+	0.148565i
$236$		0			0
$237$	−6.91705			−0.449311
$238$		0			0
$239$	26.1425			1.69101			0.845507	−	0.533964i	$-0.179298\pi$
$239$	26.1425			1.69101			0.845507	+	0.533964i	$0.179298\pi$
$240$		0			0
$241$	9.79581	+	16.9668i	0.631003	+	1.09293i	0.987347	+	0.158575i	$0.0506899\pi$
$241$	9.79581	+	16.9668i	0.631003	+	1.09293i	−0.356344	+	0.934355i	$0.615977\pi$
$242$		0			0
$243$	−8.07623	+	13.9884i	−0.518091	+	0.897359i
$244$		0			0
$245$	−1.99506	+	11.4850i	−0.127459	+	0.733749i
$246$		0			0
$247$	2.88499	−	4.99696i	0.183568	−	0.317949i
$248$		0			0
$249$	4.06561	+	7.04184i	0.257647	+	0.446259i
$250$		0			0
$251$	−6.39080			−0.403384			−0.201692	−	0.979449i	$-0.564644\pi$
$251$	−6.39080			−0.403384			−0.201692	+	0.979449i	$0.564644\pi$
$252$		0			0
$253$	−1.60253			−0.100750
$254$		0			0
$255$	4.38022	+	7.58677i	0.274300	+	0.475102i
$256$		0			0
$257$	−10.9371	+	18.9436i	−0.682238	+	1.18167i	0.292058	+	0.956401i	$0.405660\pi$
$257$	−10.9371	+	18.9436i	−0.682238	+	1.18167i	−0.974296	+	0.225271i	$0.927673\pi$
$258$		0			0
$259$	−24.3852	−	8.84043i	−1.51522	−	0.549317i
$260$		0			0
$261$	9.66131	−	16.7339i	0.598020	−	1.03580i
$262$		0			0
$263$	14.8618	+	25.7414i	0.916420	+	1.58729i	0.804809	+	0.593534i	$0.202268\pi$
$263$	14.8618	+	25.7414i	0.916420	+	1.58729i	0.111611	+	0.993752i	$0.464399\pi$
$264$		0			0
$265$	−10.7935			−0.663037
$266$		0			0
$267$	−11.9644			−0.732211
$268$		0			0
$269$	−6.69279	−	11.5923i	−0.408067	−	0.706792i	0.586606	−	0.809872i	$-0.300464\pi$
$269$	−6.69279	−	11.5923i	−0.408067	−	0.706792i	−0.994673	+	0.103080i	$0.967130\pi$
$270$		0			0
$271$	12.8866	−	22.3202i	0.782805	−	1.35586i	−0.147496	−	0.989063i	$-0.547121\pi$
$271$	12.8866	−	22.3202i	0.782805	−	1.35586i	0.930301	−	0.366796i	$-0.119545\pi$
$272$		0			0
$273$	10.6574	−	8.96569i	0.645014	−	0.542628i
$274$		0			0
$275$	−0.269715	+	0.467161i	−0.0162644	+	0.0281708i
$276$		0			0
$277$	1.48701	+	2.57558i	0.0893458	+	0.154751i	0.907235	−	0.420625i	$-0.138189\pi$
$277$	1.48701	+	2.57558i	0.0893458	+	0.154751i	−0.817889	+	0.575376i	$0.804856\pi$
$278$		0			0
$279$	12.8607			0.769950
$280$		0			0
$281$	−18.8947			−1.12716			−0.563582	−	0.826060i	$-0.690577\pi$
$281$	−18.8947			−1.12716			−0.563582	+	0.826060i	$0.690577\pi$
$282$		0			0
$283$	−11.4150	−	19.7713i	−0.678551	−	1.17528i	−0.975417	−	0.220365i	$-0.929275\pi$
$283$	−11.4150	−	19.7713i	−0.678551	−	1.17528i	0.296867	−	0.954919i	$-0.404058\pi$
$284$		0			0
$285$	0.759615	−	1.31569i	0.0449957	−	0.0779349i
$286$		0			0
$287$	0.925475	+	5.20994i	0.0546291	+	0.307533i
$288$		0			0
$289$	−8.12552	+	14.0738i	−0.477972	+	0.827872i
$290$		0			0
$291$	−0.509351	−	0.882222i	−0.0298587	−	0.0517168i
$292$		0			0
$293$	11.3710			0.664299			0.332150	−	0.943227i	$-0.392226\pi$
$293$	11.3710			0.664299			0.332150	+	0.943227i	$0.392226\pi$
$294$		0			0
$295$	−1.79014			−0.104226
$296$		0			0
$297$	−0.571021	−	0.989037i	−0.0331340	−	0.0573897i
$298$		0			0
$299$	19.0855	−	33.0571i	1.10375	−	1.91174i
$300$		0			0
$301$	3.62433	+	20.4031i	0.208903	+	1.17602i
$302$		0			0
$303$	−5.94253	+	10.2928i	−0.341389	+	0.591304i
$304$		0			0
$305$	7.58459	+	13.1369i	0.434292	+	0.752216i
$306$		0			0
$307$	−3.87636			−0.221236			−0.110618	−	0.993863i	$-0.535283\pi$
$307$	−3.87636			−0.221236			−0.110618	+	0.993863i	$0.535283\pi$
$308$		0			0
$309$	−12.5221			−0.712356
$310$		0			0
$311$	−11.0281	−	19.1012i	−0.625344	−	1.08313i	−0.988474	−	0.151389i	$-0.951625\pi$
$311$	−11.0281	−	19.1012i	−0.625344	−	1.08313i	0.363130	−	0.931738i	$-0.381708\pi$
$312$		0			0
$313$	15.5322	−	26.9025i	0.877930	−	1.52062i	0.0243207	−	0.999704i	$-0.492258\pi$
$313$	15.5322	−	26.9025i	0.877930	−	1.52062i	0.853609	−	0.520914i	$-0.174409\pi$
$314$		0			0
$315$	−7.30853	+	6.14841i	−0.411789	+	0.346424i
$316$		0			0
$317$	−16.6431	+	28.8268i	−0.934772	+	1.61907i	−0.159731	+	0.987161i	$0.551063\pi$
$317$	−16.6431	+	28.8268i	−0.934772	+	1.61907i	−0.775040	+	0.631912i	$0.782271\pi$
$318$		0			0
$319$	1.07965	+	1.87000i	0.0604485	+	0.104700i
$320$		0			0
$321$	3.43796			0.191888
$322$		0			0
$323$	5.76637			0.320850
$324$		0			0
$325$	−6.42441	−	11.1274i	−0.356362	−	0.617237i
$326$		0			0
$327$	0.307560	−	0.532709i	0.0170081	−	0.0294589i
$328$		0			0
$329$	3.92795	+	1.42401i	0.216555	+	0.0785084i
$330$		0			0
$331$	−4.18690	+	7.25192i	−0.230133	+	0.398601i	−0.957847	−	0.287279i	$-0.907249\pi$
$331$	−4.18690	+	7.25192i	−0.230133	+	0.398601i	0.727714	+	0.685880i	$0.240583\pi$
$332$		0			0
$333$	−10.6258	−	18.4045i	−0.582292	−	1.00856i
$334$		0			0
$335$	−13.3646			−0.730184
$336$		0			0
$337$	−1.87908			−0.102360			−0.0511799	−	0.998689i	$-0.516298\pi$
$337$	−1.87908			−0.102360			−0.0511799	+	0.998689i	$0.516298\pi$
$338$		0			0
$339$	−4.62900	−	8.01767i	−0.251413	−	0.435460i
$340$		0			0
$341$	−0.718588	+	1.24463i	−0.0389137	+	0.0674005i
$342$		0			0
$343$	9.32115	+	16.0036i	0.503295	+	0.864115i
$344$		0			0
$345$	5.02520	−	8.70390i	0.270548	−	0.468602i
$346$		0			0
$347$	3.06863	+	5.31502i	0.164733	+	0.285325i	0.936560	−	0.350506i	$-0.113991\pi$
$347$	3.06863	+	5.31502i	0.164733	+	0.285325i	−0.771828	+	0.635832i	$0.780657\pi$
$348$		0			0
$349$	−18.9103			−1.01225			−0.506123	−	0.862461i	$-0.668922\pi$
$349$	−18.9103			−1.01225			−0.506123	+	0.862461i	$0.668922\pi$
$350$		0			0
$351$	27.2025			1.45196
$352$		0			0
$353$	4.97227	+	8.61222i	0.264647	+	0.458382i	0.967471	−	0.252982i	$-0.0814112\pi$
$353$	4.97227	+	8.61222i	0.264647	+	0.458382i	−0.702824	+	0.711364i	$0.748078\pi$
$354$		0			0
$355$	1.02378	−	1.77323i	0.0543364	−	0.0941134i
$356$		0			0
$357$	13.0850	+	4.74374i	0.692531	+	0.251066i
$358$		0			0
$359$	−9.19502	+	15.9262i	−0.485295	+	0.840555i	−0.999857	−	0.0168977i	$-0.994621\pi$
$359$	−9.19502	+	15.9262i	−0.485295	+	0.840555i	0.514562	+	0.857453i	$0.327954\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$		0			0
$363$	−9.98172			−0.523905
$364$		0			0
$365$	−1.33451			−0.0698513
$366$		0			0
$367$	7.10761	+	12.3107i	0.371014	+	0.642616i	0.989722	−	0.143006i	$-0.0456767\pi$
$367$	7.10761	+	12.3107i	0.371014	+	0.642616i	−0.618707	+	0.785621i	$0.712343\pi$
$368$		0			0
$369$	−2.16772	+	3.75459i	−0.112847	+	0.195456i
$370$		0			0
$371$	−13.1224	+	11.0394i	−0.681280	+	0.573137i
$372$		0			0
$373$	−12.8008	+	22.1716i	−0.662800	+	1.14800i	0.317076	+	0.948400i	$0.397299\pi$
$373$	−12.8008	+	22.1716i	−0.662800	+	1.14800i	−0.979877	+	0.199604i	$0.936034\pi$
$374$		0			0
$375$	−5.48961	−	9.50829i	−0.283482	−	0.491006i
$376$		0			0
$377$	−51.4326			−2.64891
$378$		0			0
$379$	−8.51685			−0.437481			−0.218741	−	0.975783i	$-0.570195\pi$
$379$	−8.51685			−0.437481			−0.218741	+	0.975783i	$0.570195\pi$
$380$		0			0
$381$	−8.48316	−	14.6933i	−0.434606	−	0.752759i
$382$		0			0
$383$	5.00847	−	8.67492i	0.255921	−	0.443268i	−0.709224	−	0.704983i	$-0.750955\pi$
$383$	5.00847	−	8.67492i	0.255921	−	0.443268i	0.965145	+	0.261715i	$0.0842881\pi$
$384$		0			0
$385$	−0.186668	−	1.05084i	−0.00951348	−	0.0535559i
$386$		0			0
$387$	−8.48918	+	14.7037i	−0.431529	+	0.747431i
$388$		0			0
$389$	10.1401	+	17.5631i	0.514123	+	0.890487i	0.999866	+	0.0163851i	$0.00521577\pi$
$389$	10.1401	+	17.5631i	0.514123	+	0.890487i	−0.485743	+	0.874102i	$0.661451\pi$
$390$		0			0
$391$	38.1472			1.92918
$392$		0			0
$393$	7.27229			0.366838
$394$		0			0
$395$	−6.31310	−	10.9346i	−0.317647	−	0.550180i
$396$		0			0
$397$	13.4137	−	23.2333i	0.673216	−	1.16604i	−0.303770	−	0.952745i	$-0.598246\pi$
$397$	13.4137	−	23.2333i	0.673216	−	1.16604i	0.976987	−	0.213300i	$-0.0684211\pi$
$398$		0			0
$399$	−0.422154	−	2.37650i	−0.0211341	−	0.118974i
$400$		0			0
$401$	6.92911	−	12.0016i	0.346023	−	0.599330i	−0.639516	−	0.768778i	$-0.720865\pi$
$401$	6.92911	−	12.0016i	0.346023	−	0.599330i	0.985539	+	0.169448i	$0.0541985\pi$
$402$		0			0
$403$	−17.1162	−	29.6461i	−0.852619	−	1.47678i
$404$		0			0
$405$	−3.66719			−0.182224
$406$		0			0
$407$	2.37486			0.117717
$408$		0			0
$409$	3.09715	+	5.36442i	0.153144	+	0.265253i	0.932382	−	0.361475i	$-0.117727\pi$
$409$	3.09715	+	5.36442i	0.153144	+	0.265253i	−0.779238	+	0.626729i	$0.784393\pi$
$410$		0			0
$411$	0.145403	−	0.251846i	0.00717222	−	0.0124226i
$412$		0			0
$413$	−2.17640	+	1.83093i	−0.107094	+	0.0900942i
$414$		0			0
$415$	−7.42126	+	12.8540i	−0.364295	+	0.630978i
$416$		0			0
$417$	2.64618	+	4.58333i	0.129584	+	0.224446i
$418$		0			0
$419$	14.4938			0.708068			0.354034	−	0.935233i	$-0.384810\pi$
$419$	14.4938			0.708068			0.354034	+	0.935233i	$0.384810\pi$
$420$		0			0
$421$	29.8753			1.45603			0.728016	−	0.685560i	$-0.240443\pi$
$421$	29.8753			1.45603			0.728016	+	0.685560i	$0.240443\pi$
$422$		0			0
$423$	1.71161	+	2.96459i	0.0832211	+	0.144143i
$424$		0			0
$425$	6.42038	−	11.1204i	0.311434	−	0.539420i
$426$		0			0
$427$	22.6574	+	8.21404i	1.09647	+	0.397505i
$428$		0			0
$429$	−0.637570	+	1.10430i	−0.0307822	+	0.0533163i
$430$		0			0
$431$	−10.9304	−	18.9321i	−0.526501	−	0.911926i	−0.999523	−	0.0308754i	$-0.990170\pi$
$431$	−10.9304	−	18.9321i	−0.526501	−	0.911926i	0.473023	−	0.881050i	$-0.343163\pi$
$432$		0			0
$433$	−11.1847			−0.537500			−0.268750	−	0.963210i	$-0.586611\pi$
$433$	−11.1847			−0.537500			−0.268750	+	0.963210i	$0.586611\pi$
$434$		0			0
$435$	−13.5421			−0.649296
$436$		0			0
$437$	−3.30773	−	5.72915i	−0.158230	−	0.274062i
$438$		0			0
$439$	7.70936	−	13.3530i	0.367948	−	0.637304i	−0.621297	−	0.783575i	$-0.713394\pi$
$439$	7.70936	−	13.3530i	0.367948	−	0.637304i	0.989245	+	0.146271i	$0.0467272\pi$
$440$		0			0
$441$	−2.59699	+	14.9501i	−0.123666	+	0.711911i
$442$		0			0
$443$	0.469742	−	0.813616i	0.0223181	−	0.0386561i	−0.854651	−	0.519203i	$-0.826229\pi$
$443$	0.469742	−	0.813616i	0.0223181	−	0.0386561i	0.876969	+	0.480547i	$0.159562\pi$
$444$		0			0
$445$	−10.9198	−	18.9136i	−0.517647	−	0.896591i
$446$		0			0
$447$	12.4711			0.589865
$448$		0			0
$449$	−28.2058			−1.33112			−0.665558	−	0.746346i	$-0.731806\pi$
$449$	−28.2058			−1.33112			−0.665558	+	0.746346i	$0.731806\pi$
$450$		0			0
$451$	−0.242241	−	0.419573i	−0.0114067	−	0.0197569i
$452$		0			0
$453$	−5.03050	+	8.71308i	−0.236353	+	0.409376i
$454$		0			0
$455$	23.9000	+	8.66454i	1.12045	+	0.406200i
$456$		0			0
$457$	−0.388913	+	0.673617i	−0.0181926	+	0.0315105i	−0.874978	−	0.484162i	$-0.839125\pi$
$457$	−0.388913	+	0.673617i	−0.0181926	+	0.0315105i	0.856786	+	0.515672i	$0.172458\pi$
$458$		0			0
$459$	13.5927	+	23.5433i	0.634455	+	1.09891i
$460$		0			0
$461$	−19.3614			−0.901751			−0.450875	−	0.892587i	$-0.648888\pi$
$461$	−19.3614			−0.901751			−0.450875	+	0.892587i	$0.648888\pi$
$462$		0			0
$463$	34.5688			1.60655			0.803275	−	0.595608i	$-0.203089\pi$
$463$	34.5688			1.60655			0.803275	+	0.595608i	$0.203089\pi$
$464$		0			0
$465$	−4.50667	−	7.80579i	−0.208992	−	0.361985i
$466$		0			0
$467$	14.9272	−	25.8547i	0.690750	−	1.19641i	−0.280843	−	0.959754i	$-0.590614\pi$
$467$	14.9272	−	25.8547i	0.690750	−	1.19641i	0.971593	−	0.236660i	$-0.0760527\pi$
$468$		0			0
$469$	−16.2483	+	13.6691i	−0.750275	+	0.631180i
$470$		0			0
$471$	−8.14525	+	14.1080i	−0.375313	+	0.650062i
$472$		0			0
$473$	−0.948660	−	1.64313i	−0.0436194	−	0.0755511i
$474$		0			0
$475$	−2.22684			−0.102174
$476$		0			0
$477$	−14.0500			−0.643303
$478$		0			0
$479$	13.9432	+	24.1504i	0.637082	+	1.10346i	0.986070	+	0.166332i	$0.0531923\pi$
$479$	13.9432	+	24.1504i	0.637082	+	1.10346i	−0.348987	+	0.937127i	$0.613474\pi$
$480$		0			0
$481$	−28.2836	+	48.9887i	−1.28962	+	2.23369i
$482$		0			0
$483$	−2.79274	−	15.7217i	−0.127074	−	0.715360i
$484$		0			0
$485$	0.929757	−	1.61039i	0.0422181	−	0.0731238i
$486$		0			0
$487$	−5.81119	−	10.0653i	−0.263330	−	0.456101i	0.703795	−	0.710404i	$-0.251488\pi$
$487$	−5.81119	−	10.0653i	−0.263330	−	0.456101i	−0.967125	+	0.254302i	$0.918154\pi$
$488$		0			0
$489$	10.2150			0.461938
$490$		0			0
$491$	−25.4037			−1.14645			−0.573225	−	0.819398i	$-0.694308\pi$
$491$	−25.4037			−1.14645			−0.573225	+	0.819398i	$0.694308\pi$
$492$		0			0
$493$	−25.7002	−	44.5140i	−1.15748	−	2.00481i
$494$		0			0
$495$	0.437228	−	0.757300i	0.0196519	−	0.0340381i
$496$		0			0
$497$	−0.568961	−	3.20295i	−0.0255214	−	0.143672i
$498$		0			0
$499$	−1.33920	+	2.31956i	−0.0599509	+	0.103838i	−0.894443	−	0.447182i	$-0.852428\pi$
$499$	−1.33920	+	2.31956i	−0.0599509	+	0.103838i	0.834492	+	0.551020i	$0.185761\pi$
$500$		0			0
$501$	−0.660099	−	1.14333i	−0.0294911	−	0.0510800i
$502$		0			0
$503$	−37.0893			−1.65373			−0.826866	−	0.562399i	$-0.809879\pi$
$503$	−37.0893			−1.65373			−0.826866	+	0.562399i	$0.809879\pi$
$504$		0			0
$505$	−21.6947			−0.965401
$506$		0			0
$507$	−9.25651	−	16.0327i	−0.411096	−	0.712039i
$508$		0			0
$509$	−7.41214	+	12.8382i	−0.328537	+	0.569043i	−0.982222	−	0.187724i	$-0.939889\pi$
$509$	−7.41214	+	12.8382i	−0.328537	+	0.569043i	0.653685	+	0.756767i	$0.273222\pi$
$510$		0			0
$511$	−1.62246	+	1.36492i	−0.0717732	+	0.0603803i
$512$		0			0
$513$	2.35724	−	4.08287i	0.104075	−	0.180263i
$514$		0			0
$515$	−11.4287	−	19.7951i	−0.503610	−	0.872279i
$516$		0			0
$517$	−0.382542			−0.0168242
$518$		0			0
$519$	10.8509			0.476303
$520$		0			0
$521$	5.24608	+	9.08648i	0.229835	+	0.398086i	0.957759	−	0.287572i	$-0.0928480\pi$
$521$	5.24608	+	9.08648i	0.229835	+	0.398086i	−0.727924	+	0.685658i	$0.759515\pi$
$522$		0			0
$523$	7.73787	−	13.4024i	0.338353	−	0.586045i	−0.645770	−	0.763532i	$-0.723463\pi$
$523$	7.73787	−	13.4024i	0.338353	−	0.586045i	0.984123	+	0.177487i	$0.0567968\pi$
$524$		0			0
$525$	−5.05311	−	1.83192i	−0.220536	−	0.0799516i
$526$		0			0
$527$	17.1055	−	29.6275i	0.745126	−	1.29060i
$528$		0			0
$529$	−10.3821	−	17.9823i	−0.451396	−	0.781840i
$530$		0			0
$531$	−2.33024			−0.101124
$532$		0			0
$533$	11.5400			0.499852
$534$		0			0
$535$	3.13778	+	5.43480i	0.135658	+	0.234967i
$536$		0			0
$537$	−11.4825	+	19.8883i	−0.495507	+	0.858243i
$538$		0			0
$539$	−1.30173	−	1.08666i	−0.0560697	−	0.0468059i
$540$		0			0
$541$	9.39634	−	16.2749i	0.403980	−	0.699715i	−0.590222	−	0.807241i	$-0.700960\pi$
$541$	9.39634	−	16.2749i	0.403980	−	0.699715i	0.994202	+	0.107527i	$0.0342931\pi$
$542$		0			0
$543$	−8.54865	−	14.8067i	−0.366858	−	0.635416i
$544$		0			0
$545$	1.12282			0.0480965
$546$		0			0
$547$	−0.809060			−0.0345929			−0.0172965	−	0.999850i	$-0.505506\pi$
$547$	−0.809060			−0.0345929			−0.0172965	+	0.999850i	$0.505506\pi$
$548$		0			0
$549$	9.87294	+	17.1004i	0.421367	+	0.729829i
$550$		0			0
$551$	−4.45691	+	7.71959i	−0.189871	+	0.328866i
$552$		0			0
$553$	−18.8591	−	6.83703i	−0.801969	−	0.290740i
$554$		0			0
$555$	−7.44705	+	12.8987i	−0.316109	+	0.547518i
$556$		0			0
$557$	8.72680	+	15.1153i	0.369767	+	0.640455i	0.989529	−	0.144335i	$-0.0461043\pi$
$557$	8.72680	+	15.1153i	0.369767	+	0.640455i	−0.619762	+	0.784790i	$0.712771\pi$
$558$		0			0
$559$	45.1927			1.91145
$560$		0			0
$561$	−1.27434			−0.0538027
$562$		0			0
$563$	1.84187	+	3.19022i	0.0776257	+	0.134452i	0.902225	−	0.431265i	$-0.141933\pi$
$563$	1.84187	+	3.19022i	0.0776257	+	0.134452i	−0.824599	+	0.565717i	$0.808599\pi$
$564$		0			0
$565$	8.44967	−	14.6353i	0.355480	−	0.615710i
$566$		0			0
$567$	−4.45846	+	3.75075i	−0.187238	+	0.157517i
$568$		0			0
$569$	4.56612	−	7.90875i	0.191422	−	0.331552i	−0.754300	−	0.656530i	$-0.772024\pi$
$569$	4.56612	−	7.90875i	0.191422	−	0.331552i	0.945722	+	0.324978i	$0.105357\pi$
$570$		0			0
$571$	−10.5623	−	18.2945i	−0.442020	−	0.765601i	0.555820	−	0.831303i	$-0.312405\pi$
$571$	−10.5623	−	18.2945i	−0.442020	−	0.765601i	−0.997839	+	0.0657023i	$0.979071\pi$
$572$		0			0
$573$	0.324779			0.0135678
$574$		0			0
$575$	−14.7315			−0.614347
$576$		0			0
$577$	−2.62137	−	4.54035i	−0.109129	−	0.189017i	0.806289	−	0.591522i	$-0.201473\pi$
$577$	−2.62137	−	4.54035i	−0.109129	−	0.189017i	−0.915418	+	0.402505i	$0.868140\pi$
$578$		0			0
$579$	−7.79957	+	13.5093i	−0.324139	+	0.561425i
$580$		0			0
$581$	4.12434	+	23.2179i	0.171106	+	0.963240i
$582$		0			0
$583$	0.785037	−	1.35972i	0.0325129	−	0.0563140i
$584$		0			0
$585$	10.4144	+	18.0383i	0.430583	+	0.745792i
$586$		0			0
$587$	−3.26045			−0.134573			−0.0672865	−	0.997734i	$-0.521434\pi$
$587$	−3.26045			−0.134573			−0.0672865	+	0.997734i	$0.521434\pi$
$588$		0			0
$589$	−5.93284			−0.244458
$590$		0			0
$591$	−5.97956	−	10.3569i	−0.245966	−	0.426026i
$592$		0			0
$593$	−9.96152	+	17.2539i	−0.409070	+	0.708531i	−0.994786	−	0.101986i	$-0.967480\pi$
$593$	−9.96152	+	17.2539i	−0.409070	+	0.708531i	0.585715	+	0.810517i	$0.300814\pi$
$594$		0			0
$595$	4.44350	+	25.0146i	0.182166	+	1.02550i
$596$		0			0
$597$	−2.17572	+	3.76846i	−0.0890464	+	0.154233i
$598$		0			0
$599$	−22.2325	−	38.5077i	−0.908394	−	1.57338i	−0.816296	−	0.577634i	$-0.803976\pi$
$599$	−22.2325	−	38.5077i	−0.908394	−	1.57338i	−0.0920976	−	0.995750i	$-0.529357\pi$
$600$		0			0
$601$	22.3392			0.911233			0.455617	−	0.890176i	$-0.349419\pi$
$601$	22.3392			0.911233			0.455617	+	0.890176i	$0.349419\pi$
$602$		0			0
$603$	−17.3968			−0.708453
$604$		0			0
$605$	−9.11019	−	15.7793i	−0.370382	−	0.641520i
$606$		0			0
$607$	−17.2044	+	29.7989i	−0.698306	+	1.20950i	0.270747	+	0.962651i	$0.412729\pi$
$607$	−17.2044	+	29.7989i	−0.698306	+	1.20950i	−0.969053	+	0.246851i	$0.920604\pi$
$608$		0			0
$609$	−16.4641	+	13.8507i	−0.667161	+	0.561259i
$610$		0			0
$611$	4.55592	−	7.89109i	0.184313	−	0.319239i
$612$		0			0
$613$	12.1470	+	21.0392i	0.490613	+	0.849766i	0.999942	−	0.0108056i	$-0.00343961\pi$
$613$	12.1470	+	21.0392i	0.490613	+	0.849766i	−0.509329	+	0.860572i	$0.670106\pi$
$614$		0			0
$615$	3.03846			0.122523
$616$		0			0
$617$	−17.0255			−0.685422			−0.342711	−	0.939441i	$-0.611345\pi$
$617$	−17.0255			−0.685422			−0.342711	+	0.939441i	$0.611345\pi$
$618$		0			0
$619$	−14.3397	−	24.8372i	−0.576363	−	0.998290i	−0.995892	−	0.0905479i	$-0.971138\pi$
$619$	−14.3397	−	24.8372i	−0.576363	−	0.998290i	0.419529	−	0.907742i	$-0.362195\pi$
$620$		0			0
$621$	15.5942	−	27.0100i	0.625775	−	1.08387i
$622$		0			0
$623$	−32.6205	−	11.8260i	−1.30691	−	0.473800i
$624$		0			0
$625$	4.45351	−	7.71371i	0.178141	−	0.308548i
$626$		0			0
$627$	0.110498	+	0.191388i	0.00441285	+	0.00764328i
$628$		0			0
$629$	−56.5318			−2.25407
$630$		0			0
$631$	−29.4675			−1.17308			−0.586542	−	0.809919i	$-0.699511\pi$
$631$	−29.4675			−1.17308			−0.586542	+	0.809919i	$0.699511\pi$
$632$		0			0
$633$	−10.0554	−	17.4165i	−0.399668	−	0.692244i
$634$		0			0
$635$	15.4849	−	26.8207i	0.614501	−	1.06435i
$636$		0			0
$637$	37.9189	−	13.9105i	1.50240	−	0.551154i
$638$		0			0
$639$	1.33266	−	2.30824i	0.0527193	−	0.0913124i
$640$		0			0
$641$	8.06837	+	13.9748i	0.318681	+	0.551972i	0.980213	−	0.197945i	$-0.0634266\pi$
$641$	8.06837	+	13.9748i	0.318681	+	0.551972i	−0.661532	+	0.749917i	$0.730093\pi$
$642$		0			0
$643$	22.8353			0.900535			0.450267	−	0.892894i	$-0.351329\pi$
$643$	22.8353			0.900535			0.450267	+	0.892894i	$0.351329\pi$
$644$		0			0
$645$	11.8992			0.468530
$646$		0			0
$647$	−10.3699	−	17.9613i	−0.407685	−	0.706131i	0.586945	−	0.809627i	$-0.300330\pi$
$647$	−10.3699	−	17.9613i	−0.407685	−	0.706131i	−0.994630	+	0.103496i	$0.966997\pi$
$648$		0			0
$649$	0.130202	−	0.225516i	0.00511086	−	0.00885227i
$650$		0			0
$651$	−13.4627	−	4.88069i	−0.527646	−	0.191289i
$652$		0			0
$653$	9.68834	−	16.7807i	0.379134	−	0.656679i	−0.611802	−	0.791011i	$-0.709555\pi$
$653$	9.68834	−	16.7807i	0.379134	−	0.656679i	0.990936	+	0.134331i	$0.0428886\pi$
$654$		0			0
$655$	6.63732	+	11.4962i	0.259342	+	0.449193i
$656$		0			0
$657$	−1.73714			−0.0677724
$658$		0			0
$659$	7.33347			0.285672			0.142836	−	0.989746i	$-0.454378\pi$
$659$	7.33347			0.285672			0.142836	+	0.989746i	$0.454378\pi$
$660$		0			0
$661$	18.8535	+	32.6552i	0.733315	+	1.27014i	0.955459	+	0.295124i	$0.0953611\pi$
$661$	18.8535	+	32.6552i	0.733315	+	1.27014i	−0.222144	+	0.975014i	$0.571306\pi$
$662$		0			0
$663$	15.1769	−	26.2872i	0.589422	−	1.02091i
$664$		0			0
$665$	3.37153	−	2.83636i	0.130742	−	0.109989i
$666$		0			0
$667$	−29.4845	+	51.0686i	−1.14164	+	1.97738i
$668$		0			0
$669$	−8.93303	−	15.4725i	−0.345371	−	0.598200i
$670$		0			0
$671$	−2.20659			−0.0851844
$672$		0			0
$673$	48.4005			1.86570			0.932851	−	0.360263i	$-0.117313\pi$
$673$	48.4005			1.86570			0.932851	+	0.360263i	$0.117313\pi$
$674$		0			0
$675$	−5.24919	−	9.09187i	−0.202042	−	0.349946i
$676$		0			0
$677$	−7.93290	+	13.7402i	−0.304886	+	0.528078i	−0.977236	−	0.212155i	$-0.931952\pi$
$677$	−7.93290	+	13.7402i	−0.304886	+	0.528078i	0.672350	+	0.740233i	$0.265285\pi$
$678$		0			0
$679$	−0.516709	−	2.90880i	−0.0198295	−	0.111630i
$680$		0			0
$681$	2.64032	−	4.57316i	0.101177	−	0.175244i
$682$		0			0
$683$	−8.63354	−	14.9537i	−0.330353	−	0.572189i	0.652228	−	0.758023i	$-0.273835\pi$
$683$	−8.63354	−	14.9537i	−0.330353	−	0.572189i	−0.982581	+	0.185834i	$0.940501\pi$
$684$		0			0
$685$	0.530831			0.0202820
$686$		0			0
$687$	−17.4316			−0.665059
$688$		0			0
$689$	18.6990	+	32.3876i	0.712374	+	1.23387i
$690$		0			0
$691$	24.6306	−	42.6614i	0.936992	−	1.62292i	0.165949	−	0.986134i	$-0.446931\pi$
$691$	24.6306	−	42.6614i	0.936992	−	1.62292i	0.771043	−	0.636783i	$-0.219735\pi$
$692$		0			0
$693$	−0.242988	−	1.36789i	−0.00923034	−	0.0519620i
$694$		0			0
$695$	−4.83028	+	8.36629i	−0.183223	+	0.317351i
$696$		0			0
$697$	5.76637	+	9.98765i	0.218417	+	0.378309i
$698$		0			0
$699$	−5.63001			−0.212947
$700$		0			0
$701$	10.1609			0.383770			0.191885	−	0.981417i	$-0.438540\pi$
$701$	10.1609			0.383770			0.191885	+	0.981417i	$0.438540\pi$
$702$		0			0
$703$	4.90185	+	8.49026i	0.184877	+	0.320216i
$704$		0			0
$705$	1.19957	−	2.07771i	0.0451784	−	0.0782512i
$706$		0			0
$707$	−26.3758	+	22.1890i	−0.991963	+	0.834504i
$708$		0			0
$709$	−3.86510	+	6.69454i	−0.145157	+	0.251419i	−0.929431	−	0.368995i	$-0.879702\pi$
$709$	−3.86510	+	6.69454i	−0.145157	+	0.251419i	0.784275	+	0.620414i	$0.213035\pi$
$710$		0			0
$711$	−8.21783	−	14.2337i	−0.308193	−	0.533806i
$712$		0			0
$713$	−39.2484			−1.46986
$714$		0			0
$715$	−2.32761			−0.0870477
$716$		0			0
$717$	−11.9248	−	20.6544i	−0.445341	−	0.771353i
$718$		0			0
$719$	−12.6604	+	21.9284i	−0.472152	+	0.817791i	−0.999492	−	0.0318632i	$-0.989856\pi$
$719$	−12.6604	+	21.9284i	−0.472152	+	0.817791i	0.527340	+	0.849654i	$0.323189\pi$
$720$		0			0
$721$	−34.1409	−	12.3772i	−1.27148	−	0.460952i
$722$		0			0
$723$	8.93667	−	15.4788i	0.332358	−	0.575662i
$724$		0			0
$725$	9.92480	+	17.1903i	0.368598	+	0.638430i
$726$		0			0
$727$	24.5601			0.910884			0.455442	−	0.890266i	$-0.349481\pi$
$727$	24.5601			0.910884			0.455442	+	0.890266i	$0.349481\pi$
$728$		0			0
$729$	8.12941			0.301089
$730$		0			0
$731$	22.5822	+	39.1135i	0.835232	+	1.44666i
$732$		0			0
$733$	13.6516	−	23.6453i	0.504235	−	0.873361i	−0.495753	−	0.868464i	$-0.665108\pi$
$733$	13.6516	−	23.6453i	0.504235	−	0.873361i	0.999988	−	0.00489700i	$-0.00155877\pi$
$734$		0			0
$735$	9.98400	−	3.66261i	0.368265	−	0.135098i
$736$		0			0
$737$	0.972041	−	1.68362i	0.0358056	−	0.0620171i
$738$		0			0
$739$	−24.0188	−	41.6017i	−0.883544	−	1.53034i	−0.847373	−	0.530998i	$-0.821817\pi$
$739$	−24.0188	−	41.6017i	−0.883544	−	1.53034i	−0.0361706	−	0.999346i	$-0.511516\pi$
$740$		0			0
$741$	−5.26394			−0.193376
$742$		0			0
$743$	10.8539			0.398190			0.199095	−	0.979980i	$-0.436200\pi$
$743$	10.8539			0.398190			0.199095	+	0.979980i	$0.436200\pi$
$744$		0			0
$745$	11.3823	+	19.7146i	0.417014	+	0.722289i
$746$		0			0
$747$	−9.66033	+	16.7322i	−0.353453	+	0.612199i
$748$		0			0
$749$	9.37347	+	3.39819i	0.342499	+	0.124167i
$750$		0			0
$751$	−8.95718	+	15.5143i	−0.326852	+	0.566125i	−0.981885	−	0.189475i	$-0.939321\pi$
$751$	−8.95718	+	15.5143i	−0.326852	+	0.566125i	0.655033	+	0.755600i	$0.272655\pi$
$752$		0			0
$753$	2.91515	+	5.04919i	0.106234	+	0.184003i
$754$		0			0
$755$	−18.3651			−0.668374
$756$		0			0
$757$	19.7888			0.719235			0.359617	−	0.933100i	$-0.382907\pi$
$757$	19.7888			0.719235			0.359617	+	0.933100i	$0.382907\pi$
$758$		0			0
$759$	0.730992	+	1.26612i	0.0265333	+	0.0459571i
$760$		0			0
$761$	−25.7301	+	44.5659i	−0.932717	+	1.61551i	−0.154062	+	0.988061i	$0.549235\pi$
$761$	−25.7301	+	44.5659i	−0.932717	+	1.61551i	−0.778655	+	0.627452i	$0.784098\pi$
$762$		0			0
$763$	1.36510	−	1.14841i	0.0494198	−	0.0415752i
$764$		0			0
$765$	−10.4079	+	18.0270i	−0.376298	+	0.651768i
$766$		0			0
$767$	3.10130	+	5.37161i	0.111981	+	0.193958i
$768$		0			0
$769$	−26.2468			−0.946485			−0.473243	−	0.880932i	$-0.656917\pi$
$769$	−26.2468			−0.946485			−0.473243	+	0.880932i	$0.656917\pi$
$770$		0			0
$771$	19.9558			0.718689
$772$		0			0
$773$	−3.02611	−	5.24138i	−0.108842	−	0.188519i	0.806460	−	0.591289i	$-0.201381\pi$
$773$	−3.02611	−	5.24138i	−0.108842	−	0.188519i	−0.915301	+	0.402770i	$0.868048\pi$
$774$		0			0
$775$	−6.60573	+	11.4415i	−0.237285	+	0.410989i
$776$		0			0
$777$	4.13867	+	23.2986i	0.148474	+	0.835831i
$778$		0			0
$779$	1.00000	−	1.73205i	0.0358287	−	0.0620572i
$780$		0			0
$781$	0.148924	+	0.257944i	0.00532892	+	0.00922996i
$782$		0			0
$783$	−42.0241			−1.50182
$784$		0			0
$785$	−29.7363			−1.06133
$786$		0			0
$787$	6.22879	+	10.7886i	0.222032	+	0.384571i	0.955425	−	0.295234i	$-0.0953976\pi$
$787$	6.22879	+	10.7886i	0.222032	+	0.384571i	−0.733393	+	0.679805i	$0.762064\pi$
$788$		0			0
$789$	13.5584	−	23.4838i	0.482691	−	0.836046i
$790$		0			0
$791$	−4.69587	−	26.4353i	−0.166966	−	0.939932i
$792$		0			0
$793$	26.2796	−	45.5176i	0.933217	−	1.61638i
$794$		0			0
$795$	4.92341	+	8.52760i	0.174615	+	0.302443i
$796$		0			0
$797$	7.13423			0.252707			0.126354	−	0.991985i	$-0.459673\pi$
$797$	7.13423			0.252707			0.126354	+	0.991985i	$0.459673\pi$
$798$		0			0
$799$	9.10613			0.322152
$800$		0			0
$801$	−14.2144	−	24.6201i	−0.502241	−	0.869907i
$802$		0			0
$803$	0.0970623	−	0.168117i	0.00342525	−	0.00593271i
$804$		0			0
$805$	22.3042	−	18.7638i	0.786121	−	0.661336i
$806$		0			0
$807$	−6.10581	+	10.5756i	−0.214935	+	0.372278i
$808$		0			0
$809$	−4.87901	−	8.45069i	−0.171537	−	0.297110i	0.767421	−	0.641144i	$-0.221540\pi$
$809$	−4.87901	−	8.45069i	−0.171537	−	0.297110i	−0.938957	+	0.344034i	$0.888207\pi$
$810$		0			0
$811$	−1.23879			−0.0434998			−0.0217499	−	0.999763i	$-0.506924\pi$
$811$	−1.23879			−0.0434998			−0.0217499	+	0.999763i	$0.506924\pi$
$812$		0			0
$813$	−23.5128			−0.824630
$814$		0			0
$815$	9.32310	+	16.1481i	0.326574	+	0.565642i
$816$		0			0
$817$	3.91619	−	6.78303i	0.137010	−	0.237308i
$818$		0			0
$819$	31.1109	+	11.2787i	1.08710	+	0.394111i
$820$		0			0
$821$	−21.4406	+	37.1361i	−0.748281	+	1.29606i	0.200365	+	0.979721i	$0.435787\pi$
$821$	−21.4406	+	37.1361i	−0.748281	+	1.29606i	−0.948646	+	0.316339i	$0.897546\pi$
$822$		0			0
$823$	6.37704	+	11.0454i	0.222290	+	0.385017i	0.955503	−	0.294982i	$-0.0953136\pi$
$823$	6.37704	+	11.0454i	0.222290	+	0.385017i	−0.733213	+	0.679999i	$0.761980\pi$
$824$		0			0
$825$	0.492120			0.0171334
$826$		0			0
$827$	52.6536			1.83095			0.915473	−	0.402380i	$-0.131817\pi$
$827$	52.6536			1.83095			0.915473	+	0.402380i	$0.131817\pi$
$828$		0			0
$829$	0.0607719	+	0.105260i	0.00211070	+	0.00365583i	0.867079	−	0.498171i	$-0.165995\pi$
$829$	0.0607719	+	0.105260i	0.00211070	+	0.00365583i	−0.864968	+	0.501827i	$0.832661\pi$
$830$		0			0
$831$	1.35659	−	2.34969i	0.0470597	−	0.0815098i
$832$		0			0
$833$	30.9869	+	25.8673i	1.07363	+	0.896248i
$834$		0			0
$835$	1.20493	−	2.08700i	0.0416983	−	0.0722235i
$836$		0			0
$837$	−13.9851	−	24.2230i	−0.483397	−	0.837268i
$838$		0			0
$839$	45.8707			1.58363			0.791816	−	0.610759i	$-0.209136\pi$
$839$	45.8707			1.58363			0.791816	+	0.610759i	$0.209136\pi$
$840$		0			0
$841$	50.4561			1.73987
$842$		0			0
$843$	8.61878	+	14.9282i	0.296847	+	0.514153i
$844$		0			0
$845$	16.8966	−	29.2658i	0.581261	−	1.00677i
$846$		0			0
$847$	−27.2148	−	9.86626i	−0.935111	−	0.339009i
$848$		0			0
$849$	−10.4138	+	18.0373i	−0.357402	+	0.619039i
$850$		0			0
$851$	32.4280	+	56.1669i	1.11162	+	1.92538i
$852$		0			0
$853$	−18.8106			−0.644064			−0.322032	−	0.946729i	$-0.604366\pi$
$853$	−18.8106			−0.644064			−0.322032	+	0.946729i	$0.604366\pi$
$854$		0			0
$855$	3.60986			0.123455
$856$		0			0
$857$	10.9968	+	19.0470i	0.375644	+	0.650635i	0.990423	−	0.138065i	$-0.0440882\pi$
$857$	10.9968	+	19.0470i	0.375644	+	0.650635i	−0.614779	+	0.788699i	$0.710755\pi$
$858$		0			0
$859$	−16.9879	+	29.4238i	−0.579619	+	1.00393i	0.415904	+	0.909408i	$0.363465\pi$
$859$	−16.9879	+	29.4238i	−0.579619	+	1.00393i	−0.995523	+	0.0945204i	$0.969868\pi$
$860$		0			0
$861$	3.69407	−	3.10770i	0.125894	−	0.105910i
$862$		0			0
$863$	16.5221	−	28.6171i	0.562419	−	0.974139i	−0.434865	−	0.900496i	$-0.643204\pi$
$863$	16.5221	−	28.6171i	0.562419	−	0.974139i	0.997285	−	0.0736435i	$-0.0234627\pi$
$864$		0			0
$865$	9.90352	+	17.1534i	0.336730	+	0.583233i
$866$		0			0
$867$	14.8258			0.503509
$868$		0			0
$869$	1.83668			0.0623049
$870$		0			0
$871$	23.1533	+	40.1026i	0.784518	+	1.35883i
$872$		0			0
$873$	1.21027	−	2.09626i	0.0409616	−	0.0709475i
$874$		0			0
$875$	−5.56892	−	31.3501i	−0.188264	−	1.05983i
$876$		0			0
$877$	13.3633	−	23.1459i	0.451247	−	0.781583i	−0.547217	−	0.836991i	$-0.684313\pi$
$877$	13.3633	−	23.1459i	0.451247	−	0.781583i	0.998464	+	0.0554081i	$0.0176460\pi$
$878$		0			0
$879$	−5.18685	−	8.98388i	−0.174948	−	0.303019i
$880$		0			0
$881$	33.6752			1.13454			0.567272	−	0.823530i	$-0.307999\pi$
$881$	33.6752			1.13454			0.567272	+	0.823530i	$0.307999\pi$
$882$		0			0
$883$	−15.6753			−0.527516			−0.263758	−	0.964589i	$-0.584962\pi$
$883$	−15.6753			−0.527516			−0.263758	+	0.964589i	$0.584962\pi$
$884$		0			0
$885$	0.816568	+	1.41434i	0.0274486	+	0.0475424i
$886$		0			0
$887$	−2.59856	+	4.50083i	−0.0872510	+	0.151123i	−0.906348	−	0.422532i	$-0.861142\pi$
$887$	−2.59856	+	4.50083i	−0.0872510	+	0.151123i	0.819097	+	0.573655i	$0.194475\pi$
$888$		0			0
$889$	−8.60571	−	48.4457i	−0.288626	−	1.62482i
$890$		0			0
$891$	0.266724	−	0.461980i	0.00893560	−	0.0154769i
$892$		0			0
$893$	−0.789589	−	1.36761i	−0.0264226	−	0.0457653i
$894$		0			0
$895$	−41.9198			−1.40122
$896$		0			0
$897$	−34.8233			−1.16272
$898$		0			0
$899$	26.4421	+	45.7991i	0.881894	+	1.52748i
$900$		0			0
$901$	−18.6872	+	32.3673i	−0.622562	+	1.07831i
$902$		0			0
$903$	14.4667	−	12.1703i	0.481421	−	0.405003i
$904$		0			0
$905$	15.6045	−	27.0278i	0.518711	−	0.898434i
$906$		0			0
$907$	18.7915	+	32.5478i	0.623962	+	1.08073i	0.988741	+	0.149639i	$0.0478113\pi$
$907$	18.7915	+	32.5478i	0.623962	+	1.08073i	−0.364779	+	0.931094i	$0.618855\pi$
$908$		0			0
$909$	−28.2402			−0.936669
$910$		0			0
$911$	19.9982			0.662571			0.331286	−	0.943530i	$-0.392518\pi$
$911$	19.9982			0.662571			0.331286	+	0.943530i	$0.392518\pi$
$912$		0			0
$913$	−1.07954	−	1.86981i	−0.0357274	−	0.0618817i
$914$		0			0
$915$	6.91939	−	11.9847i	0.228748	−	0.396203i
$916$		0			0
$917$	19.8276	+	7.18816i	0.654765	+	0.237374i
$918$		0			0
$919$	20.8126	−	36.0484i	0.686543	−	1.18913i	−0.286406	−	0.958108i	$-0.592461\pi$
$919$	20.8126	−	36.0484i	0.686543	−	1.18913i	0.972949	−	0.231019i	$-0.0742061\pi$
$920$		0			0
$921$	1.76819	+	3.06260i	0.0582640	+	0.100916i
$922$		0			0
$923$	−7.09451			−0.233519
$924$		0			0
$925$	21.8312			0.717807
$926$		0			0
$927$	−14.8769	−	25.7676i	−0.488622	−	0.846318i
$928$		0			0
$929$	16.1611	−	27.9919i	0.530229	−	0.918384i	−0.469149	−	0.883119i	$-0.655439\pi$
$929$	16.1611	−	27.9919i	0.530229	−	0.918384i	0.999378	−	0.0352650i	$-0.0112275\pi$
$930$		0			0
$931$	1.19803	−	6.89672i	0.0392638	−	0.226031i
$932$		0			0
$933$	−10.0609	+	17.4259i	−0.329378	+	0.570499i
$934$		0			0
$935$	−1.16308	−	2.01451i	−0.0380366	−	0.0658814i
$936$		0			0
$937$	−23.8754			−0.779975			−0.389988	−	0.920820i	$-0.627521\pi$
$937$	−23.8754			−0.779975			−0.389988	+	0.920820i	$0.627521\pi$
$938$		0			0
$939$	−28.3399			−0.924836
$940$		0			0
$941$	15.3481	+	26.5837i	0.500334	+	0.866603i	1.00000		0.000385246i	$0.000122628\pi$
$941$	15.3481	+	26.5837i	0.500334	+	0.866603i	−0.499666	+	0.866218i	$0.666544\pi$
$942$		0			0
$943$	6.61545	−	11.4583i	0.215429	−	0.373134i
$944$		0			0
$945$	19.5280	+	7.07954i	0.635245	+	0.230297i
$946$		0			0
$947$	−13.8689	+	24.0216i	−0.450678	+	0.780598i	−0.998428	−	0.0560442i	$-0.982151\pi$
$947$	−13.8689	+	24.0216i	−0.450678	+	0.780598i	0.547750	+	0.836642i	$0.315485\pi$
$948$		0			0
$949$	2.31195	+	4.00441i	0.0750490	+	0.129989i
$950$		0			0
$951$	30.3669			0.984715
$952$		0			0
$953$	−29.9634			−0.970611			−0.485305	−	0.874345i	$-0.661292\pi$
$953$	−29.9634			−0.970611			−0.485305	+	0.874345i	$0.661292\pi$
$954$		0			0
$955$	0.296422	+	0.513418i	0.00959198	+	0.0166138i
$956$		0			0
$957$	0.984956	−	1.70599i	0.0318391	−	0.0551469i
$958$		0			0
$959$	0.645369	−	0.542927i	0.0208401	−	0.0175320i
$960$		0			0
$961$	−2.09928	+	3.63606i	−0.0677187	+	0.117292i
$962$		0			0
$963$	4.08449	+	7.07454i	0.131621	+	0.227974i
$964$		0			0
$965$	−28.4743			−0.916619
$966$		0			0
$967$	−19.2270			−0.618299			−0.309150	−	0.951013i	$-0.600044\pi$
$967$	−19.2270			−0.618299			−0.309150	+	0.951013i	$0.600044\pi$
$968$		0			0
$969$	−2.63032	−	4.55585i	−0.0844980	−	0.146355i
$970$		0			0
$971$	−8.14680	+	14.1107i	−0.261443	+	0.452833i	−0.966626	−	0.256193i	$-0.917532\pi$
$971$	−8.14680	+	14.1107i	−0.261443	+	0.452833i	0.705182	+	0.709026i	$0.250865\pi$
$972$		0			0
$973$	2.68441	+	15.1118i	0.0860583	+	0.484463i
$974$		0			0
$975$	−5.86096	+	10.1515i	−0.187701	+	0.325108i
$976$		0			0
$977$	10.6532	+	18.4520i	0.340828	+	0.590331i	0.984587	−	0.174898i	$-0.0559594\pi$
$977$	10.6532	+	18.4520i	0.340828	+	0.590331i	−0.643759	+	0.765228i	$0.722626\pi$
$978$		0			0
$979$	3.17690			0.101534
$980$		0			0
$981$	1.46159			0.0466650
$982$		0			0
$983$	3.63704	+	6.29954i	0.116004	+	0.200924i	0.918181	−	0.396162i	$-0.129658\pi$
$983$	3.63704	+	6.29954i	0.116004	+	0.200924i	−0.802177	+	0.597087i	$0.796325\pi$
$984$		0			0
$985$	10.9149	−	18.9052i	0.347779	−	0.602371i
$986$		0			0
$987$	−0.666656	−	3.75293i	−0.0212199	−	0.119457i
$988$		0			0
$989$	25.9073	−	44.8728i	0.823806	−	1.42687i
$990$		0			0
$991$	19.6379	+	34.0138i	0.623818	+	1.08048i	0.988768	+	0.149458i	$0.0477528\pi$
$991$	19.6379	+	34.0138i	0.623818	+	1.08048i	−0.364950	+	0.931027i	$0.618914\pi$
$992$		0			0
$993$	7.63938			0.242428
$994$		0			0
$995$	−7.94301			−0.251811
$996$		0			0
$997$	−4.48646	−	7.77078i	−0.142088	−	0.246103i	0.786195	−	0.617979i	$-0.212048\pi$
$997$	−4.48646	−	7.77078i	−0.142088	−	0.246103i	−0.928283	+	0.371876i	$0.878715\pi$
$998$		0			0
$999$	−23.1097	+	40.0272i	−0.731159	+	1.26641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1064.2.q.n.457.3	yes	16
7.2	even	3		7448.2.a.bq.1.6		8
7.4	even	3	inner	1064.2.q.n.305.3	✓	16
7.5	odd	6		7448.2.a.br.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1064.2.q.n.305.3	✓	16	7.4	even	3	inner
1064.2.q.n.457.3	yes	16	1.1	even	1	trivial
7448.2.a.bq.1.6		8	7.2	even	3
7448.2.a.br.1.3		8	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1064.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.456148 - 0.790072i) q^{3} +(0.832641 - 1.44218i) q^{5} +(-0.462738 - 2.60497i) q^{7} +(1.08386 - 1.87730i) q^{9} +O(q^{10})\)	\(q+(-0.456148 - 0.790072i) q^{3} +(0.832641 - 1.44218i) q^{5} +(-0.462738 - 2.60497i) q^{7} +(1.08386 - 1.87730i) q^{9} +(0.121120 + 0.209787i) q^{11} -5.76999 q^{13} -1.51923 q^{15} +(-2.88319 - 4.99382i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-1.84704 + 1.55385i) q^{21} +(-3.30773 + 5.72915i) q^{23} +(1.11342 + 1.92850i) q^{25} -4.71449 q^{27} +8.91381 q^{29} +(2.96642 + 5.13799i) q^{31} +(0.110498 - 0.191388i) q^{33} +(-4.14212 - 1.50166i) q^{35} +(4.90185 - 8.49026i) q^{37} +(2.63197 + 4.55870i) q^{39} -2.00000 q^{41} -7.83237 q^{43} +(-1.80493 - 3.12623i) q^{45} +(-0.789589 + 1.36761i) q^{47} +(-6.57175 + 2.41084i) q^{49} +(-2.63032 + 4.55585i) q^{51} +(-3.24073 - 5.61311i) q^{53} +0.403399 q^{55} +0.912296 q^{57} +(-0.537488 - 0.930957i) q^{59} +(-4.55454 + 7.88869i) q^{61} +(-5.39185 - 1.95472i) q^{63} +(-4.80433 + 8.32134i) q^{65} +(-4.01270 - 6.95021i) q^{67} +6.03525 q^{69} +1.22955 q^{71} +(-0.400685 - 0.694007i) q^{73} +(1.01577 - 1.75936i) q^{75} +(0.490441 - 0.412591i) q^{77} +(3.79101 - 6.56622i) q^{79} +(-1.10107 - 1.90711i) q^{81} -8.91292 q^{83} -9.60264 q^{85} +(-4.06602 - 7.04255i) q^{87} +(6.55732 - 11.3576i) q^{89} +(2.66999 + 15.0307i) q^{91} +(2.70625 - 4.68737i) q^{93} +(0.832641 + 1.44218i) q^{95} +1.11664 q^{97} +0.525109 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) \) 16 * q + q^5 + 5 * q^7 - 6 * q^9	\( 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100}) \) 16 * q + q^5 + 5 * q^7 - 6 * q^9 - 9 * q^11 + 16 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 - 25 * q^23 - 15 * q^25 + 6 * q^27 + 12 * q^29 - 8 * q^33 + 5 * q^35 - 13 * q^37 + 11 * q^39 - 32 * q^41 + 34 * q^43 - 17 * q^45 + 24 * q^47 - 13 * q^49 - 5 * q^51 - 2 * q^53 + 10 * q^55 - 2 * q^59 + 13 * q^61 - 52 * q^63 + 26 * q^65 - 2 * q^67 - 22 * q^69 + 20 * q^71 - 5 * q^73 + 20 * q^75 + 28 * q^77 - 16 * q^79 + 12 * q^81 - 86 * q^83 + 48 * q^85 - 20 * q^87 - 8 * q^89 - 34 * q^91 - 2 * q^93 + q^95 - 24 * q^97 + 74 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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