LMFDB - Embedded newform 900.2.i.e.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(301,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("900.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.i (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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.142635249.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 3x^{6} + 3x^{5} - 11x^{4} + 6x^{3} + 12x^{2} - 24x + 16 $ x^8 - 3x^7 + 3x^6 + 3x^5 - 11x^4 + 6x^3 + 12x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			301.1
Root			$1.38941 + 0.263711i$ of defining polynomial
Character	$\chi$	$=$	900.301
Dual form			900.2.i.e.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36091 + 1.07141i) q^{3} +(-0.0432397 - 0.0748933i) q^{7} +(0.704170 - 2.91619i) q^{9} +O(q^{10})$	\(q+(-1.36091 + 1.07141i) q^{3} +(-0.0432397 - 0.0748933i) q^{7} +(0.704170 - 2.91619i) q^{9} +(0.456760 + 0.791132i) q^{11} +(-1.31249 + 2.27331i) q^{13} +2.08648 q^{17} +4.93847 q^{19} +(0.139087 + 0.0555960i) q^{21} +(-4.23849 + 7.34128i) q^{23} +(2.16611 + 4.72313i) q^{27} +(-1.19899 - 2.07671i) q^{29} +(-1.81249 + 3.13933i) q^{31} +(-1.46924 - 0.587286i) q^{33} -5.85199 q^{37} +(-0.649447 - 4.49999i) q^{39} +(-3.32497 + 5.75902i) q^{41} +(4.12499 + 7.14469i) q^{43} +(-1.34425 - 2.32831i) q^{47} +(3.49626 - 6.05570i) q^{49} +(-2.83952 + 2.23547i) q^{51} -5.73642 q^{53} +(-6.72083 + 5.29112i) q^{57} +(-6.16922 + 10.6854i) q^{59} +(3.16823 + 5.48753i) q^{61} +(-0.248851 + 0.0733573i) q^{63} +(-3.08274 + 5.33946i) q^{67} +(-2.09729 - 14.5320i) q^{69} -12.3905 q^{71} +5.31349 q^{73} +(0.0395003 - 0.0684166i) q^{77} +(6.72394 + 11.6462i) q^{79} +(-8.00829 - 4.10698i) q^{81} +(3.03950 + 5.26457i) q^{83} +(3.85673 + 1.54162i) q^{87} -8.13440 q^{89} +0.227007 q^{91} +(-0.896857 - 6.21428i) q^{93} +(-5.55098 - 9.61459i) q^{97} +(2.62873 - 0.774907i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{3} - q^{7} + 5 q^{9}+O(q^{10}) $ 8 * q + q^3 - q^7 + 5 * q^9	$ 8 q + q^{3} - q^{7} + 5 q^{9} + 3 q^{11} + 2 q^{13} + 18 q^{17} - 8 q^{19} + 13 q^{21} + 3 q^{23} + 16 q^{27} - 9 q^{29} - 2 q^{31} + 12 q^{33} + 2 q^{37} - 17 q^{39} + 9 q^{41} + 8 q^{43} - 12 q^{47} - 9 q^{49} + 3 q^{51} + 24 q^{53} - 40 q^{57} - 15 q^{59} + q^{61} + 35 q^{63} + 11 q^{67} + 9 q^{69} - 24 q^{71} + 20 q^{73} - 36 q^{77} + 7 q^{79} - 31 q^{81} - 12 q^{83} + 9 q^{87} + 6 q^{89} - 22 q^{91} - 19 q^{93} + 5 q^{97} + 33 q^{99}+O(q^{100}) $ 8 * q + q^3 - q^7 + 5 * q^9 + 3 * q^11 + 2 * q^13 + 18 * q^17 - 8 * q^19 + 13 * q^21 + 3 * q^23 + 16 * q^27 - 9 * q^29 - 2 * q^31 + 12 * q^33 + 2 * q^37 - 17 * q^39 + 9 * q^41 + 8 * q^43 - 12 * q^47 - 9 * q^49 + 3 * q^51 + 24 * q^53 - 40 * q^57 - 15 * q^59 + q^61 + 35 * q^63 + 11 * q^67 + 9 * q^69 - 24 * q^71 + 20 * q^73 - 36 * q^77 + 7 * q^79 - 31 * q^81 - 12 * q^83 + 9 * q^87 + 6 * q^89 - 22 * q^91 - 19 * q^93 + 5 * q^97 + 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.36091	+	1.07141i	−0.785724	+	0.618578i
$3$	−1.36091	+	1.07141i	−0.785724	+	0.618578i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.0432397	−	0.0748933i	−0.0163431	−	0.0283070i	0.857738	−	0.514087i	$-0.171869\pi$
$7$	−0.0432397	−	0.0748933i	−0.0163431	−	0.0283070i	−0.874081	+	0.485780i	$0.838536\pi$
$8$		0			0
$9$	0.704170	−	2.91619i	0.234723	−	0.972062i
$10$		0			0
$11$	0.456760	+	0.791132i	0.137718	+	0.238535i	0.926633	−	0.375968i	$-0.122690\pi$
$11$	0.456760	+	0.791132i	0.137718	+	0.238535i	−0.788914	+	0.614503i	$0.789356\pi$
$12$		0			0
$13$	−1.31249	+	2.27331i	−0.364020	+	0.630501i	−0.988618	−	0.150445i	$-0.951929\pi$
$13$	−1.31249	+	2.27331i	−0.364020	+	0.630501i	0.624598	+	0.780946i	$0.285263\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.08648			0.506046			0.253023	−	0.967460i	$-0.418575\pi$
$17$	2.08648			0.506046			0.253023	+	0.967460i	$0.418575\pi$
$18$		0			0
$19$	4.93847			1.13296			0.566482	−	0.824074i	$-0.308304\pi$
$19$	4.93847			1.13296			0.566482	+	0.824074i	$0.308304\pi$
$20$		0			0
$21$	0.139087	+	0.0555960i	0.0303512	+	0.0121320i
$22$		0			0
$23$	−4.23849	+	7.34128i	−0.883786	+	1.53076i	−0.0366878	+	0.999327i	$0.511681\pi$
$23$	−4.23849	+	7.34128i	−0.883786	+	1.53076i	−0.847098	+	0.531436i	$0.821653\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2.16611	+	4.72313i	0.416868	+	0.908967i
$28$		0			0
$29$	−1.19899	−	2.07671i	−0.222647	−	0.385636i	0.732964	−	0.680267i	$-0.238136\pi$
$29$	−1.19899	−	2.07671i	−0.222647	−	0.385636i	−0.955611	+	0.294632i	$0.904803\pi$
$30$		0			0
$31$	−1.81249	+	3.13933i	−0.325533	+	0.563840i	−0.981620	−	0.190845i	$-0.938877\pi$
$31$	−1.81249	+	3.13933i	−0.325533	+	0.563840i	0.656087	+	0.754685i	$0.272211\pi$
$32$		0			0
$33$	−1.46924	−	0.587286i	−0.255761	−	0.102233i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.85199			−0.962062			−0.481031	−	0.876704i	$-0.659738\pi$
$37$	−5.85199			−0.962062			−0.481031	+	0.876704i	$0.659738\pi$
$38$		0			0
$39$	−0.649447	−	4.49999i	−0.103995	−	0.720575i
$40$		0			0
$41$	−3.32497	+	5.75902i	−0.519273	+	0.899407i	0.480476	+	0.877008i	$0.340464\pi$
$41$	−3.32497	+	5.75902i	−0.519273	+	0.899407i	−0.999749	+	0.0223994i	$0.992869\pi$
$42$		0			0
$43$	4.12499	+	7.14469i	0.629055	+	1.08955i	0.987742	+	0.156097i	$0.0498911\pi$
$43$	4.12499	+	7.14469i	0.629055	+	1.08955i	−0.358687	+	0.933458i	$0.616776\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.34425	−	2.32831i	−0.196079	−	0.339619i	0.751175	−	0.660103i	$-0.229488\pi$
$47$	−1.34425	−	2.32831i	−0.196079	−	0.339619i	−0.947254	+	0.320485i	$0.896154\pi$
$48$		0			0
$49$	3.49626	−	6.05570i	0.499466	−	0.865100i
$50$		0			0
$51$	−2.83952	+	2.23547i	−0.397612	+	0.313028i
$52$		0			0
$53$	−5.73642			−0.787958			−0.393979	−	0.919120i	$-0.628902\pi$
$53$	−5.73642			−0.787958			−0.393979	+	0.919120i	$0.628902\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−6.72083	+	5.29112i	−0.890196	+	0.700826i
$58$		0			0
$59$	−6.16922	+	10.6854i	−0.803164	+	1.39112i	0.114360	+	0.993439i	$0.463518\pi$
$59$	−6.16922	+	10.6854i	−0.803164	+	1.39112i	−0.917524	+	0.397681i	$0.869815\pi$
$60$		0			0
$61$	3.16823	+	5.48753i	0.405650	+	0.702606i	0.994397	−	0.105711i	$-0.0337119\pi$
$61$	3.16823	+	5.48753i	0.405650	+	0.702606i	−0.588747	+	0.808317i	$0.700379\pi$
$62$		0			0
$63$	−0.248851	+	0.0733573i	−0.0313523	+	0.00924215i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−3.08274	+	5.33946i	−0.376617	+	0.652319i	−0.990568	−	0.137025i	$-0.956246\pi$
$67$	−3.08274	+	5.33946i	−0.376617	+	0.652319i	0.613951	+	0.789344i	$0.289579\pi$
$68$		0			0
$69$	−2.09729	−	14.5320i	−0.252484	−	1.74945i
$70$		0			0
$71$	−12.3905			−1.47048			−0.735241	−	0.677806i	$-0.762931\pi$
$71$	−12.3905			−1.47048			−0.735241	+	0.677806i	$0.762931\pi$
$72$		0			0
$73$	5.31349			0.621897			0.310948	−	0.950427i	$-0.399353\pi$
$73$	5.31349			0.621897			0.310948	+	0.950427i	$0.399353\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.0395003	−	0.0684166i	0.00450148	−	0.00779679i
$78$		0			0
$79$	6.72394	+	11.6462i	0.756503	+	1.31030i	0.944624	+	0.328155i	$0.106427\pi$
$79$	6.72394	+	11.6462i	0.756503	+	1.31030i	−0.188121	+	0.982146i	$0.560240\pi$
$80$		0			0
$81$	−8.00829	−	4.10698i	−0.889810	−	0.456331i
$82$		0			0
$83$	3.03950	+	5.26457i	0.333629	+	0.577862i	0.983220	−	0.182422i	$-0.0583936\pi$
$83$	3.03950	+	5.26457i	0.333629	+	0.577862i	−0.649592	+	0.760283i	$0.725060\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.85673	+	1.54162i	0.413484	+	0.165279i
$88$		0			0
$89$	−8.13440			−0.862244			−0.431122	−	0.902294i	$-0.641882\pi$
$89$	−8.13440			−0.862244			−0.431122	+	0.902294i	$0.641882\pi$
$90$		0			0
$91$	0.227007			0.0237968
$92$		0			0
$93$	−0.896857	−	6.21428i	−0.0929998	−	0.644390i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.55098	−	9.61459i	−0.563617	−	0.976213i	−0.997177	−	0.0750885i	$-0.976076\pi$
$97$	−5.55098	−	9.61459i	−0.563617	−	0.976213i	0.433560	−	0.901125i	$-0.357257\pi$
$98$		0			0
$99$	2.62873	−	0.774907i	0.264197	−	0.0778811i
$100$		0			0
$101$	6.03950	+	10.4607i	0.600953	+	1.04088i	0.992677	+	0.120798i	$0.0385454\pi$
$101$	6.03950	+	10.4607i	0.600953	+	1.04088i	−0.391724	+	0.920083i	$0.628121\pi$
$102$		0			0
$103$	2.18377	−	3.78240i	0.215173	−	0.372691i	−0.738153	−	0.674633i	$-0.764302\pi$
$103$	2.18377	−	3.78240i	0.215173	−	0.372691i	0.953326	+	0.301943i	$0.0976351\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	18.9614			1.83307			0.916536	−	0.399953i	$-0.130973\pi$
$107$	18.9614			1.83307			0.916536	+	0.399953i	$0.130973\pi$
$108$		0			0
$109$	15.1904			1.45498			0.727490	−	0.686119i	$-0.240687\pi$
$109$	15.1904			1.45498			0.727490	+	0.686119i	$0.240687\pi$
$110$		0			0
$111$	7.96406	−	6.26987i	0.755915	−	0.595110i
$112$		0			0
$113$	−3.30101	+	5.71752i	−0.310533	+	0.537859i	−0.978478	−	0.206352i	$-0.933841\pi$
$113$	−3.30101	+	5.71752i	−0.310533	+	0.537859i	0.667945	+	0.744211i	$0.267174\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	5.70516	+	5.42827i	0.527443	+	0.501844i
$118$		0			0
$119$	−0.0902186	−	0.156263i	−0.00827033	−	0.0143246i
$120$		0			0
$121$	5.08274	−	8.80356i	0.462067	−	0.800324i
$122$		0			0
$123$	−1.64526	−	11.3999i	−0.148348	−	1.02790i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−7.42492			−0.658855			−0.329427	−	0.944181i	$-0.606856\pi$
$127$	−7.42492			−0.658855			−0.329427	+	0.944181i	$0.606856\pi$
$128$		0			0
$129$	−13.2686	−	5.30376i	−1.16824	−	0.466970i
$130$		0			0
$131$	7.98072	−	13.8230i	0.697279	−	1.20772i	−0.272128	−	0.962261i	$-0.587727\pi$
$131$	7.98072	−	13.8230i	0.697279	−	1.20772i	0.969406	−	0.245461i	$-0.0789393\pi$
$132$		0			0
$133$	−0.213538	−	0.369858i	−0.0185161	−	0.0320708i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.19525	−	15.9266i	−0.785603	−	1.36070i	−0.928638	−	0.370987i	$-0.879019\pi$
$137$	−9.19525	−	15.9266i	−0.785603	−	1.36070i	0.143035	−	0.989718i	$-0.454314\pi$
$138$		0			0
$139$	−2.78074	+	4.81638i	−0.235859	+	0.408520i	−0.959522	−	0.281634i	$-0.909124\pi$
$139$	−2.78074	+	4.81638i	−0.235859	+	0.408520i	0.723663	+	0.690154i	$0.242457\pi$
$140$		0			0
$141$	4.32398	+	1.72839i	0.364144	+	0.145556i
$142$		0			0
$143$	−2.39798			−0.200529
$144$		0			0
$145$		0			0
$146$		0			0
$147$	1.73002	+	11.9872i	0.142690	+	0.988688i
$148$		0			0
$149$	−11.7780	+	20.4001i	−0.964891	+	1.67124i	−0.254982	+	0.966946i	$0.582069\pi$
$149$	−11.7780	+	20.4001i	−0.964891	+	1.67124i	−0.709909	+	0.704294i	$0.751264\pi$
$150$		0			0
$151$	−0.0114831	−	0.0198893i	−0.000934479	−	0.00161856i	0.865558	−	0.500809i	$-0.166964\pi$
$151$	−0.0114831	−	0.0198893i	−0.000934479	−	0.00161856i	−0.866492	+	0.499190i	$0.833631\pi$
$152$		0			0
$153$	1.46924	−	6.08456i	0.118781	−	0.491908i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	6.07967	−	10.5303i	0.485211	−	0.840410i	−0.514645	−	0.857404i	$-0.672076\pi$
$157$	6.07967	−	10.5303i	0.485211	−	0.840410i	0.999856	+	0.0169936i	$0.00540950\pi$
$158$		0			0
$159$	7.80677	−	6.14604i	0.619117	−	0.487413i
$160$		0			0
$161$	0.733083			0.0577751
$162$		0			0
$163$	19.0654			1.49332			0.746658	−	0.665208i	$-0.231657\pi$
$163$	19.0654			1.49332			0.746658	+	0.665208i	$0.231657\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.911449	−	1.57868i	0.0705300	−	0.122162i	−0.828604	−	0.559836i	$-0.810864\pi$
$167$	0.911449	−	1.57868i	0.0705300	−	0.122162i	0.899134	+	0.437674i	$0.144198\pi$
$168$		0			0
$169$	3.05472	+	5.29093i	0.234979	+	0.406995i
$170$		0			0
$171$	3.47753	−	14.4015i	0.265933	−	1.10131i
$172$		0			0
$173$	−10.3942	−	18.0034i	−0.790259	−	1.36877i	−0.925806	−	0.377999i	$-0.876612\pi$
$173$	−10.3942	−	18.0034i	−0.790259	−	1.36877i	0.135547	−	0.990771i	$-0.456721\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.05265	−	21.1517i	−0.229451	−	1.58986i
$178$		0			0
$179$	−3.12692			−0.233717			−0.116858	−	0.993149i	$-0.537282\pi$
$179$	−3.12692			−0.233717			−0.116858	+	0.993149i	$0.537282\pi$
$180$		0			0
$181$	22.9249			1.70399			0.851996	−	0.523549i	$-0.175392\pi$
$181$	22.9249			1.70399			0.851996	+	0.523549i	$0.175392\pi$
$182$		0			0
$183$	−10.1911	−	4.07359i	−0.753345	−	0.301128i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.953021	+	1.65068i	0.0696918	+	0.120710i
$188$		0			0
$189$	0.260069	−	0.366454i	0.0189172	−	0.0266556i
$190$		0			0
$191$	−3.97698	−	6.88833i	−0.287764	−	0.498422i	0.685512	−	0.728062i	$-0.259579\pi$
$191$	−3.97698	−	6.88833i	−0.287764	−	0.498422i	−0.973276	+	0.229640i	$0.926245\pi$
$192$		0			0
$193$	2.59422	−	4.49333i	0.186736	−	0.323437i	−0.757424	−	0.652923i	$-0.773542\pi$
$193$	2.59422	−	4.49333i	0.186736	−	0.323437i	0.944160	+	0.329487i	$0.106876\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	21.3384			1.52030			0.760150	−	0.649747i	$-0.225125\pi$
$197$	21.3384			1.52030			0.760150	+	0.649747i	$0.225125\pi$
$198$		0			0
$199$	9.50608			0.673868			0.336934	−	0.941528i	$-0.390610\pi$
$199$	9.50608			0.673868			0.336934	+	0.941528i	$0.390610\pi$
$200$		0			0
$201$	−1.52540	−	10.5694i	−0.107593	−	0.745509i
$202$		0			0
$203$	−0.103688	+	0.179593i	−0.00727746	+	0.0126049i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	18.4239	+	17.5297i	1.28055	+	1.21840i
$208$		0			0
$209$	2.25570	+	3.90698i	0.156030	+	0.270252i
$210$		0			0
$211$	0.295285	−	0.511448i	0.0203282	−	0.0352096i	−0.855682	−	0.517501i	$-0.826862\pi$
$211$	0.295285	−	0.511448i	0.0203282	−	0.0352096i	0.876011	+	0.482292i	$0.160196\pi$
$212$		0			0
$213$	16.8624	−	13.2753i	1.15539	−	0.909607i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.313486			0.0212808
$218$		0			0
$219$	−7.23119	+	5.69291i	−0.488639	+	0.384691i
$220$		0			0
$221$	−2.73849	+	4.74320i	−0.184211	+	0.319062i
$222$		0			0
$223$	−2.88276	−	4.99308i	−0.193044	−	0.334361i	0.753214	−	0.657776i	$-0.228503\pi$
$223$	−2.88276	−	4.99308i	−0.193044	−	0.334361i	−0.946257	+	0.323414i	$0.895169\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.62805	−	11.4801i	−0.439919	−	0.761962i	0.557764	−	0.830000i	$-0.311660\pi$
$227$	−6.62805	−	11.4801i	−0.439919	−	0.761962i	−0.997683	+	0.0680374i	$0.978326\pi$
$228$		0			0
$229$	−3.92500	+	6.79831i	−0.259372	+	0.449245i	−0.966074	−	0.258266i	$-0.916849\pi$
$229$	−3.92500	+	6.79831i	−0.259372	+	0.449245i	0.706702	+	0.707511i	$0.250182\pi$
$230$		0			0
$231$	0.0195455	+	0.135430i	0.00128600	+	0.00891064i
$232$		0			0
$233$	15.9094			1.04226			0.521129	−	0.853478i	$-0.325511\pi$
$233$	15.9094			1.04226			0.521129	+	0.853478i	$0.325511\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−21.6285	−	8.64540i	−1.40492	−	0.561579i
$238$		0			0
$239$	−7.23849	+	12.5374i	−0.468219	+	0.810979i	−0.999340	−	0.0363167i	$-0.988438\pi$
$239$	−7.23849	+	12.5374i	−0.468219	+	0.810979i	0.531121	+	0.847296i	$0.321771\pi$
$240$		0			0
$241$	−3.32803	−	5.76432i	−0.214378	−	0.371313i	0.738702	−	0.674032i	$-0.235439\pi$
$241$	−3.32803	−	5.76432i	−0.214378	−	0.371313i	−0.953080	+	0.302719i	$0.902106\pi$
$242$		0			0
$243$	15.2988	−	2.99090i	0.981421	−	0.191866i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−6.48171	+	11.2267i	−0.412421	+	0.714335i
$248$		0			0
$249$	−9.77700	−	3.90808i	−0.619592	−	0.247664i
$250$		0			0
$251$	−14.6885			−0.927130			−0.463565	−	0.886063i	$-0.653430\pi$
$251$	−14.6885			−0.927130			−0.463565	+	0.886063i	$0.653430\pi$
$252$		0			0
$253$	−7.74390			−0.486855
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.54324	+	14.7973i	−0.532913	+	0.923032i	0.466349	+	0.884601i	$0.345569\pi$
$257$	−8.54324	+	14.7973i	−0.532913	+	0.923032i	−0.999261	+	0.0384308i	$0.987764\pi$
$258$		0			0
$259$	0.253038	+	0.438275i	0.0157230	+	0.0272331i
$260$		0			0
$261$	−6.90037	+	2.03412i	−0.427122	+	0.125909i
$262$		0			0
$263$	1.67129	+	2.89476i	0.103056	+	0.178499i	0.912942	−	0.408088i	$-0.133805\pi$
$263$	1.67129	+	2.89476i	0.103056	+	0.178499i	−0.809886	+	0.586587i	$0.800471\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	11.0702	−	8.71526i	0.677486	−	0.533365i
$268$		0			0
$269$	1.82704			0.111397			0.0556983	−	0.998448i	$-0.482261\pi$
$269$	1.82704			0.111397			0.0556983	+	0.998448i	$0.482261\pi$
$270$		0			0
$271$	−24.0634			−1.46175			−0.730874	−	0.682513i	$-0.760887\pi$
$271$	−24.0634			−1.46175			−0.730874	+	0.682513i	$0.760887\pi$
$272$		0			0
$273$	−0.308937	+	0.243217i	−0.0186977	+	0.0147202i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−6.96550	−	12.0646i	−0.418516	−	0.724891i	0.577274	−	0.816550i	$-0.304116\pi$
$277$	−6.96550	−	12.0646i	−0.418516	−	0.724891i	−0.995790	+	0.0916590i	$0.970783\pi$
$278$		0			0
$279$	7.87857	+	7.49619i	0.471678	+	0.448785i
$280$		0			0
$281$	9.62391	+	16.6691i	0.574114	+	0.994395i	0.996137	+	0.0878099i	$0.0279868\pi$
$281$	9.62391	+	16.6691i	0.574114	+	0.994395i	−0.422023	+	0.906585i	$0.638680\pi$
$282$		0			0
$283$	11.1375	−	19.2907i	0.662053	−	1.14671i	−0.318022	−	0.948083i	$-0.603019\pi$
$283$	11.1375	−	19.2907i	0.662053	−	1.14671i	0.980075	−	0.198627i	$-0.0636482\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.575082			0.0339460
$288$		0			0
$289$	−12.6466			−0.743918
$290$		0			0
$291$	17.8556	+	7.13725i	1.04671	+	0.418393i
$292$		0			0
$293$	−1.04531	+	1.81053i	−0.0610678	+	0.105772i	−0.894943	−	0.446181i	$-0.852784\pi$
$293$	−1.04531	+	1.81053i	−0.0610678	+	0.105772i	0.833875	+	0.551953i	$0.186117\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.74723	+	3.87102i	−0.159410	+	0.224619i
$298$		0			0
$299$	−11.1260	−	19.2708i	−0.643432	−	1.11446i
$300$		0			0
$301$	0.356726	−	0.617868i	0.0205613	−	0.0356133i
$302$		0			0
$303$	−19.4269	−	7.76537i	−1.11605	−	0.446109i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−1.74056			−0.0993391			−0.0496696	−	0.998766i	$-0.515817\pi$
$307$	−1.74056			−0.0993391			−0.0496696	+	0.998766i	$0.515817\pi$
$308$		0			0
$309$	1.08057	+	7.48722i	0.0614715	+	0.425933i
$310$		0			0
$311$	11.8682	−	20.5563i	0.672984	−	1.16564i	−0.304069	−	0.952650i	$-0.598345\pi$
$311$	11.8682	−	20.5563i	0.672984	−	1.16564i	0.977054	−	0.212993i	$-0.0683212\pi$
$312$		0			0
$313$	5.44054	+	9.42330i	0.307518	+	0.532636i	0.977819	−	0.209453i	$-0.0671683\pi$
$313$	5.44054	+	9.42330i	0.307518	+	0.532636i	−0.670301	+	0.742089i	$0.733835\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.00374	−	6.93468i	−0.224872	−	0.389490i	0.731409	−	0.681939i	$-0.238863\pi$
$317$	−4.00374	−	6.93468i	−0.224872	−	0.389490i	−0.956281	+	0.292449i	$0.905530\pi$
$318$		0			0
$319$	1.09530	−	1.89712i	0.0613251	−	0.106218i
$320$		0			0
$321$	−25.8049	+	20.3154i	−1.44029	+	1.13390i
$322$		0			0
$323$	10.3040			0.573331
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−20.6729	+	16.2751i	−1.14321	+	0.900018i
$328$		0			0
$329$	−0.116250	+	0.201351i	−0.00640906	+	0.0111008i
$330$		0			0
$331$	2.10976	+	3.65422i	0.115963	+	0.200854i	0.918164	−	0.396200i	$-0.129671\pi$
$331$	2.10976	+	3.65422i	0.115963	+	0.200854i	−0.802201	+	0.597054i	$0.796338\pi$
$332$		0			0
$333$	−4.12080	+	17.0655i	−0.225818	+	0.935184i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	3.19832	−	5.53964i	0.174223	−	0.301764i	−0.765669	−	0.643235i	$-0.777592\pi$
$337$	3.19832	−	5.53964i	0.174223	−	0.301764i	0.939892	+	0.341471i	$0.110925\pi$
$338$		0			0
$339$	−1.63340	−	11.3178i	−0.0887144	−	0.614697i
$340$		0			0
$341$	−3.31150			−0.179328
$342$		0			0
$343$	−1.21006			−0.0653373
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.75777	+	11.7048i	−0.362776	+	0.628347i	−0.988417	−	0.151765i	$-0.951504\pi$
$347$	−6.75777	+	11.7048i	−0.362776	+	0.628347i	0.625641	+	0.780112i	$0.284838\pi$
$348$		0			0
$349$	−0.408788	−	0.708042i	−0.0218819	−	0.0379006i	0.854877	−	0.518831i	$-0.173632\pi$
$349$	−0.408788	−	0.708042i	−0.0218819	−	0.0379006i	−0.876759	+	0.480930i	$0.840299\pi$
$350$		0			0
$351$	−13.5801	−	1.27485i	−0.724853	−	0.0680463i
$352$		0			0
$353$	−9.47023	−	16.4029i	−0.504049	−	0.873039i	−0.999989	−	0.00468224i	$-0.998510\pi$
$353$	−9.47023	−	16.4029i	−0.504049	−	0.873039i	0.495940	−	0.868357i	$-0.334824\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.290201	+	0.116000i	0.0153591	+	0.00613936i
$358$		0			0
$359$	36.4863			1.92568			0.962838	−	0.270081i	$-0.0870505\pi$
$359$	36.4863			1.92568			0.962838	+	0.270081i	$0.0870505\pi$
$360$		0			0
$361$	5.38851			0.283606
$362$		0			0
$363$	2.51504	+	17.4266i	0.132005	+	0.914658i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	9.71246	+	16.8225i	0.506986	+	0.878126i	0.999967	+	0.00808588i	$0.00257384\pi$
$367$	9.71246	+	16.8225i	0.506986	+	0.878126i	−0.492981	+	0.870040i	$0.664093\pi$
$368$		0			0
$369$	14.4530	+	13.7516i	0.752394	+	0.715878i
$370$		0			0
$371$	0.248041	+	0.429619i	0.0128776	+	0.0223047i
$372$		0			0
$373$	−14.5884	+	25.2679i	−0.755359	+	1.30832i	0.189836	+	0.981816i	$0.439204\pi$
$373$	−14.5884	+	25.2679i	−0.755359	+	1.30832i	−0.945195	+	0.326505i	$0.894129\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.29466			0.324192
$378$		0			0
$379$	−21.8060			−1.12010			−0.560048	−	0.828460i	$-0.689217\pi$
$379$	−21.8060			−1.12010			−0.560048	+	0.828460i	$0.689217\pi$
$380$		0			0
$381$	10.1047	−	7.95512i	0.517678	−	0.407553i
$382$		0			0
$383$	−4.83546	+	8.37526i	−0.247080	+	0.427956i	−0.962714	−	0.270520i	$-0.912805\pi$
$383$	−4.83546	+	8.37526i	−0.247080	+	0.427956i	0.715634	+	0.698475i	$0.246138\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	23.7399	−	6.99816i	1.20677	−	0.355736i
$388$		0			0
$389$	−7.86447	−	13.6217i	−0.398744	−	0.690646i	0.594827	−	0.803854i	$-0.297221\pi$
$389$	−7.86447	−	13.6217i	−0.398744	−	0.690646i	−0.993571	+	0.113208i	$0.963887\pi$
$390$		0			0
$391$	−8.84352	+	15.3174i	−0.447236	+	0.774636i
$392$		0			0
$393$	3.94902	+	27.3625i	0.199202	+	1.38026i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	22.8999			1.14931			0.574657	−	0.818394i	$-0.305136\pi$
$397$	22.8999			1.14931			0.574657	+	0.818394i	$0.305136\pi$
$398$		0			0
$399$	0.686876	+	0.274559i	0.0343868	+	0.0137451i
$400$		0			0
$401$	−3.04999	+	5.28274i	−0.152309	+	0.263807i	−0.932076	−	0.362263i	$-0.882004\pi$
$401$	−3.04999	+	5.28274i	−0.152309	+	0.263807i	0.779767	+	0.626070i	$0.215338\pi$
$402$		0			0
$403$	−4.75777	−	8.24070i	−0.237001	−	0.410499i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.67296	−	4.62970i	−0.132494	−	0.229486i
$408$		0			0
$409$	14.4344	−	25.0011i	0.713736	−	1.23623i	−0.249709	−	0.968321i	$-0.580335\pi$
$409$	14.4344	−	25.0011i	0.713736	−	1.23623i	0.963445	−	0.267906i	$-0.0863316\pi$
$410$		0			0
$411$	29.5779	+	11.8229i	1.45897	+	0.583181i
$412$		0			0
$413$	1.06702			0.0525046
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.37596	−	9.53398i	−0.0673812	−	0.466881i
$418$		0			0
$419$	8.97117	−	15.5385i	0.438270	−	0.759106i	−0.559286	−	0.828975i	$-0.688925\pi$
$419$	8.97117	−	15.5385i	0.438270	−	0.759106i	0.997556	+	0.0698684i	$0.0222579\pi$
$420$		0			0
$421$	0.361544	+	0.626213i	0.0176206	+	0.0305198i	0.874701	−	0.484662i	$-0.161058\pi$
$421$	0.361544	+	0.626213i	0.0176206	+	0.0305198i	−0.857081	+	0.515182i	$0.827724\pi$
$422$		0			0
$423$	−7.73636	+	2.28056i	−0.376155	+	0.110885i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.273986	−	0.474558i	0.0132591	−	0.0229655i
$428$		0			0
$429$	3.26344	−	2.56921i	0.157560	−	0.124043i
$430$		0			0
$431$	−8.19656			−0.394815			−0.197407	−	0.980322i	$-0.563252\pi$
$431$	−8.19656			−0.394815			−0.197407	+	0.980322i	$0.563252\pi$
$432$		0			0
$433$	−35.7464			−1.71786			−0.858931	−	0.512091i	$-0.828871\pi$
$433$	−35.7464			−1.71786			−0.858931	+	0.512091i	$0.828871\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−20.9317	+	36.2547i	−1.00130	+	1.73430i
$438$		0			0
$439$	−9.13440	−	15.8212i	−0.435961	−	0.755107i	0.561413	−	0.827536i	$-0.310258\pi$
$439$	−9.13440	−	15.8212i	−0.435961	−	0.755107i	−0.997374	+	0.0724295i	$0.976925\pi$
$440$		0			0
$441$	−15.1976	−	14.4600i	−0.723695	−	0.688571i
$442$		0			0
$443$	14.9161	+	25.8355i	0.708687	+	1.22748i	0.965345	+	0.260979i	$0.0840453\pi$
$443$	14.9161	+	25.8355i	0.708687	+	1.22748i	−0.256658	+	0.966502i	$0.582621\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−5.82798	−	40.3818i	−0.275654	−	1.90999i
$448$		0			0
$449$	38.9423			1.83780			0.918901	−	0.394488i	$-0.129078\pi$
$449$	38.9423			1.83780			0.918901	+	0.394488i	$0.129078\pi$
$450$		0			0
$451$	−6.07486			−0.286054
$452$		0			0
$453$	0.0369370	+	0.0147645i	0.00173545	+	0.000693697i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	10.2452	+	17.7453i	0.479252	+	0.830089i	0.999717	−	0.0237941i	$-0.00757461\pi$
$457$	10.2452	+	17.7453i	0.479252	+	0.830089i	−0.520465	+	0.853883i	$0.674241\pi$
$458$		0			0
$459$	4.51955	+	9.85471i	0.210954	+	0.459979i
$460$		0			0
$461$	14.0858	+	24.3972i	0.656039	+	1.13629i	0.981632	+	0.190783i	$0.0611026\pi$
$461$	14.0858	+	24.3972i	0.656039	+	1.13629i	−0.325593	+	0.945510i	$0.605564\pi$
$462$		0			0
$463$	−17.1598	+	29.7216i	−0.797481	+	1.38128i	0.123770	+	0.992311i	$0.460501\pi$
$463$	−17.1598	+	29.7216i	−0.797481	+	1.38128i	−0.921252	+	0.388967i	$0.872832\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.33096			−0.200413			−0.100206	−	0.994967i	$-0.531950\pi$
$467$	−4.33096			−0.200413			−0.100206	+	0.994967i	$0.531950\pi$
$468$		0			0
$469$	0.533186			0.0246203
$470$		0			0
$471$	3.00834	+	20.8446i	0.138617	+	0.960471i
$472$		0			0
$473$	−3.76826	+	6.52682i	−0.173265	+	0.300103i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−4.03941	+	16.7285i	−0.184952	+	0.765944i
$478$		0			0
$479$	−14.4925	−	25.1018i	−0.662180	−	1.14693i	−0.980042	−	0.198793i	$-0.936298\pi$
$479$	−14.4925	−	25.1018i	−0.662180	−	1.14693i	0.317861	−	0.948137i	$-0.397035\pi$
$480$		0			0
$481$	7.68070	−	13.3034i	0.350210	−	0.606581i
$482$		0			0
$483$	−0.997663	+	0.785431i	−0.0453952	+	0.0357384i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−11.2189			−0.508376			−0.254188	−	0.967155i	$-0.581808\pi$
$487$	−11.2189			−0.508376			−0.254188	+	0.967155i	$0.581808\pi$
$488$		0			0
$489$	−25.9463	+	20.4268i	−1.17333	+	0.923732i
$490$		0			0
$491$	12.7817	−	22.1386i	0.576831	−	0.999101i	−0.419009	−	0.907982i	$-0.637622\pi$
$491$	12.7817	−	22.1386i	0.576831	−	0.999101i	0.995840	−	0.0911190i	$-0.0290444\pi$
$492$		0			0
$493$	−2.50167	−	4.33301i	−0.112669	−	0.195149i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.535761	+	0.927965i	0.0240322	+	0.0416249i
$498$		0			0
$499$	−9.46856	+	16.4000i	−0.423871	+	0.734166i	−0.996314	−	0.0857782i	$-0.972662\pi$
$499$	−9.46856	+	16.4000i	−0.423871	+	0.734166i	0.572443	+	0.819944i	$0.305996\pi$
$500$		0			0
$501$	0.451003	+	3.12497i	0.0201493	+	0.139614i
$502$		0			0
$503$	−21.1790			−0.944324			−0.472162	−	0.881512i	$-0.656526\pi$
$503$	−21.1790			−0.944324			−0.472162	+	0.881512i	$0.656526\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−9.82596	−	3.92765i	−0.436386	−	0.174433i
$508$		0			0
$509$	16.3280	−	28.2809i	0.723725	−	1.25353i	−0.235772	−	0.971808i	$-0.575762\pi$
$509$	16.3280	−	28.2809i	0.723725	−	1.25353i	0.959497	−	0.281720i	$-0.0909049\pi$
$510$		0			0
$511$	−0.229753	−	0.397944i	−0.0101637	−	0.0176040i
$512$		0			0
$513$	10.6973	+	23.3251i	0.472296	+	1.02983i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	1.22800	−	2.12696i	0.0540074	−	0.0935435i
$518$		0			0
$519$	33.4346	+	13.3645i	1.46762	+	0.586638i
$520$		0			0
$521$	2.06550			0.0904912			0.0452456	−	0.998976i	$-0.485593\pi$
$521$	2.06550			0.0904912			0.0452456	+	0.998976i	$0.485593\pi$
$522$		0			0
$523$	−8.34790			−0.365028			−0.182514	−	0.983203i	$-0.558424\pi$
$523$	−8.34790			−0.365028			−0.182514	+	0.983203i	$0.558424\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.78173	+	6.55015i	−0.164735	+	0.285329i
$528$		0			0
$529$	−24.4296	−	42.3133i	−1.06216	−	1.83971i
$530$		0			0
$531$	26.8164	+	25.5149i	1.16373	+	1.10725i
$532$		0			0
$533$	−8.72800	−	15.1173i	−0.378052	−	0.654805i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	4.25547	−	3.35021i	0.183637	−	0.144572i
$538$		0			0
$539$	6.38781			0.275143
$540$		0			0
$541$	−12.2175			−0.525273			−0.262637	−	0.964895i	$-0.584592\pi$
$541$	−12.2175			−0.525273			−0.262637	+	0.964895i	$0.584592\pi$
$542$		0			0
$543$	−31.1988	+	24.5619i	−1.33887	+	1.05405i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	4.75097	+	8.22891i	0.203137	+	0.351843i	0.949537	−	0.313654i	$-0.101553\pi$
$547$	4.75097	+	8.22891i	0.203137	+	0.351843i	−0.746401	+	0.665497i	$0.768220\pi$
$548$		0			0
$549$	18.2336	−	5.37498i	0.778192	−	0.229399i
$550$		0			0
$551$	−5.92118	−	10.2558i	−0.252251	−	0.436911i
$552$		0			0
$553$	0.581482	−	1.00716i	0.0247271	−	0.0428286i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	19.1999			0.813526			0.406763	−	0.913534i	$-0.366658\pi$
$557$	19.1999			0.813526			0.406763	+	0.913534i	$0.366658\pi$
$558$		0			0
$559$	−21.6561			−0.915954
$560$		0			0
$561$	−3.06553	−	1.22536i	−0.129427	−	0.0517347i
$562$		0			0
$563$	8.11044	−	14.0477i	0.341814	−	0.592040i	−0.642955	−	0.765904i	$-0.722292\pi$
$563$	8.11044	−	14.0477i	0.341814	−	0.592040i	0.984770	+	0.173864i	$0.0556253\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.0386902	+	0.777352i	0.00162484	+	0.0326457i
$568$		0			0
$569$	14.0286	+	24.2983i	0.588111	+	1.01864i	0.994480	+	0.104929i	$0.0334616\pi$
$569$	14.0286	+	24.2983i	0.588111	+	1.01864i	−0.406369	+	0.913709i	$0.633205\pi$
$570$		0			0
$571$	−20.7722	+	35.9785i	−0.869289	+	1.50565i	−0.00656379	+	0.999978i	$0.502089\pi$
$571$	−20.7722	+	35.9785i	−0.869289	+	1.50565i	−0.862725	+	0.505674i	$0.831244\pi$
$572$		0			0
$573$	12.7925	+	5.11345i	0.534416	+	0.213618i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	18.4113			0.766473			0.383236	−	0.923650i	$-0.374809\pi$
$577$	18.4113			0.766473			0.383236	+	0.923650i	$0.374809\pi$
$578$		0			0
$579$	1.28367	+	8.89450i	0.0533476	+	0.369643i
$580$		0			0
$581$	0.262854	−	0.455276i	0.0109050	−	0.0188880i
$582$		0			0
$583$	−2.62017	−	4.53826i	−0.108516	−	0.187956i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−17.9422	−	31.0767i	−0.740552	−	1.28267i	−0.952244	−	0.305338i	$-0.901231\pi$
$587$	−17.9422	−	31.0767i	−0.740552	−	1.28267i	0.211692	−	0.977336i	$-0.432103\pi$
$588$		0			0
$589$	−8.95095	+	15.5035i	−0.368817	+	0.638811i
$590$		0			0
$591$	−29.0398	+	22.8622i	−1.19454	+	0.940424i
$592$		0			0
$593$	47.6039			1.95486			0.977429	−	0.211265i	$-0.0677582\pi$
$593$	47.6039			1.95486			0.977429	+	0.211265i	$0.0677582\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−12.9369	+	10.1849i	−0.529474	+	0.416840i
$598$		0			0
$599$	12.4279	−	21.5258i	0.507791	−	0.879521i	−0.492168	−	0.870500i	$-0.663795\pi$
$599$	12.4279	−	21.5258i	0.507791	−	0.879521i	0.999959	−	0.00902025i	$-0.00287127\pi$
$600$		0			0
$601$	−11.5482	−	20.0021i	−0.471062	−	0.815904i	0.528390	−	0.849002i	$-0.322796\pi$
$601$	−11.5482	−	20.0021i	−0.471062	−	0.815904i	−0.999452	+	0.0330979i	$0.989463\pi$
$602$		0			0
$603$	13.4001	+	12.7497i	0.545694	+	0.519209i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	2.31349	−	4.00708i	0.0939015	−	0.162642i	−0.815248	−	0.579112i	$-0.803399\pi$
$607$	2.31349	−	4.00708i	0.0939015	−	0.162642i	0.909150	+	0.416470i	$0.136733\pi$
$608$		0			0
$609$	−0.0513068	−	0.355502i	−0.00207905	−	0.0144057i
$610$		0			0
$611$	7.05728			0.285507
$612$		0			0
$613$	12.1791			0.491909			0.245954	−	0.969281i	$-0.420899\pi$
$613$	12.1791			0.491909			0.245954	+	0.969281i	$0.420899\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−23.2684	+	40.3021i	−0.936752	+	1.62250i	−0.165273	+	0.986248i	$0.552850\pi$
$617$	−23.2684	+	40.3021i	−0.936752	+	1.62250i	−0.771479	+	0.636254i	$0.780483\pi$
$618$		0			0
$619$	−7.90198	−	13.6866i	−0.317608	−	0.550112i	0.662381	−	0.749167i	$-0.269546\pi$
$619$	−7.90198	−	13.6866i	−0.317608	−	0.550112i	−0.979988	+	0.199055i	$0.936213\pi$
$620$		0			0
$621$	−43.8549	−	4.11692i	−1.75984	−	0.165206i
$622$		0			0
$623$	0.351729	+	0.609212i	0.0140917	+	0.0244076i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−7.25578	−	2.90029i	−0.289768	−	0.115827i
$628$		0			0
$629$	−12.2101			−0.486847
$630$		0			0
$631$	−24.6749			−0.982292			−0.491146	−	0.871077i	$-0.663422\pi$
$631$	−24.6749			−0.982292			−0.491146	+	0.871077i	$0.663422\pi$
$632$		0			0
$633$	0.146113	+	1.01241i	0.00580746	+	0.0402396i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	9.17764	+	15.8961i	0.363631	+	0.629828i
$638$		0			0
$639$	−8.72502	+	36.1330i	−0.345156	+	1.42940i
$640$		0			0
$641$	−0.757771	−	1.31250i	−0.0299301	−	0.0518405i	0.850672	−	0.525696i	$-0.176195\pi$
$641$	−0.757771	−	1.31250i	−0.0299301	−	0.0518405i	−0.880602	+	0.473856i	$0.842862\pi$
$642$		0			0
$643$	12.1999	−	21.1309i	0.481118	−	0.833321i	−0.518647	−	0.854988i	$-0.673564\pi$
$643$	12.1999	−	21.1309i	0.481118	−	0.833321i	0.999765	+	0.0216672i	$0.00689744\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−26.9195			−1.05832			−0.529158	−	0.848523i	$-0.677492\pi$
$647$	−26.9195			−1.05832			−0.529158	+	0.848523i	$0.677492\pi$
$648$		0			0
$649$	−11.2714			−0.442442
$650$		0			0
$651$	−0.426628	+	0.335872i	−0.0167209	+	0.0131639i
$652$		0			0
$653$	4.09116	−	7.08609i	0.160099	−	0.277300i	−0.774805	−	0.632201i	$-0.782152\pi$
$653$	4.09116	−	7.08609i	0.160099	−	0.277300i	0.934904	+	0.354900i	$0.115485\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	3.74160	−	15.4951i	0.145974	−	0.604522i
$658$		0			0
$659$	−7.55504	−	13.0857i	−0.294303	−	0.509747i	0.680520	−	0.732730i	$-0.261754\pi$
$659$	−7.55504	−	13.0857i	−0.294303	−	0.509747i	−0.974822	+	0.222983i	$0.928421\pi$
$660$		0			0
$661$	17.0300	−	29.4969i	0.662392	−	1.14730i	−0.317594	−	0.948227i	$-0.602875\pi$
$661$	17.0300	−	29.4969i	0.662392	−	1.14730i	0.979985	−	0.199069i	$-0.0637918\pi$
$662$		0			0
$663$	−1.35506	−	9.38913i	−0.0526261	−	0.364644i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	20.3276			0.787089
$668$		0			0
$669$	9.27281	+	3.70654i	0.358508	+	0.143303i
$670$		0			0
$671$	−2.89424	+	5.01297i	−0.111731	+	0.193524i
$672$		0			0
$673$	−14.7067	−	25.4728i	−0.566903	−	0.981905i	−0.996870	−	0.0790600i	$-0.974808\pi$
$673$	−14.7067	−	25.4728i	−0.566903	−	0.981905i	0.429967	−	0.902845i	$-0.358525\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	16.9519	+	29.3615i	0.651514	+	1.12846i	0.982756	+	0.184909i	$0.0591992\pi$
$677$	16.9519	+	29.3615i	0.651514	+	1.12846i	−0.331242	+	0.943546i	$0.607468\pi$
$678$		0			0
$679$	−0.480045	+	0.831463i	−0.0184224	+	0.0319086i
$680$		0			0
$681$	21.3201	+	8.52210i	0.816988	+	0.326568i
$682$		0			0
$683$	29.1078			1.11378			0.556890	−	0.830586i	$-0.311995\pi$
$683$	29.1078			1.11378			0.556890	+	0.830586i	$0.311995\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−1.94217	−	13.4572i	−0.0740984	−	0.513424i
$688$		0			0
$689$	7.52901	−	13.0406i	0.286832	−	0.496808i
$690$		0			0
$691$	5.21079	+	9.02536i	0.198228	+	0.343341i	0.947954	−	0.318408i	$-0.103148\pi$
$691$	5.21079	+	9.02536i	0.198228	+	0.343341i	−0.749726	+	0.661748i	$0.769815\pi$
$692$		0			0
$693$	−0.171701	−	0.163367i	−0.00652236	−	0.00620581i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−6.93748	+	12.0161i	−0.262776	+	0.455141i
$698$		0			0
$699$	−21.6513	+	17.0454i	−0.818927	+	0.644717i
$700$		0			0
$701$	−9.75406			−0.368406			−0.184203	−	0.982888i	$-0.558970\pi$
$701$	−9.75406			−0.368406			−0.184203	+	0.982888i	$0.558970\pi$
$702$		0			0
$703$	−28.8999			−1.08998
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.522292	−	0.904636i	0.0196428	−	0.0340223i
$708$		0			0
$709$	16.1539	+	27.9795i	0.606674	+	1.05079i	0.991785	+	0.127920i	$0.0408300\pi$
$709$	16.1539	+	27.9795i	0.606674	+	1.05079i	−0.385110	+	0.922870i	$0.625837\pi$
$710$		0			0
$711$	38.6973	−	11.4074i	1.45126	−	0.427809i
$712$		0			0
$713$	−15.3645	−	26.6120i	−0.575404	−	0.996629i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−3.58175	−	24.8177i	−0.133763	−	0.926835i
$718$		0			0
$719$	18.4905			0.689579			0.344789	−	0.938680i	$-0.387950\pi$
$719$	18.4905			0.689579			0.344789	+	0.938680i	$0.387950\pi$
$720$		0			0
$721$	−0.377701			−0.0140663
$722$		0			0
$723$	10.7051	+	4.27906i	0.398127	+	0.159140i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−25.7357	−	44.5755i	−0.954484	−	1.65321i	−0.735545	−	0.677476i	$-0.763074\pi$
$727$	−25.7357	−	44.5755i	−0.954484	−	1.65321i	−0.218939	−	0.975739i	$-0.570260\pi$
$728$		0			0
$729$	−17.6159	+	20.4616i	−0.652442	+	0.757839i
$730$		0			0
$731$	8.60670	+	14.9072i	0.318330	+	0.551364i
$732$		0			0
$733$	−3.32029	+	5.75091i	−0.122638	+	0.212415i	−0.920807	−	0.390018i	$-0.872469\pi$
$733$	−3.32029	+	5.75091i	−0.122638	+	0.212415i	0.798169	+	0.602433i	$0.205802\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.63229			−0.207468
$738$		0			0
$739$	−38.6058			−1.42014			−0.710068	−	0.704133i	$-0.751336\pi$
$739$	−38.6058			−1.42014			−0.710068	+	0.704133i	$0.751336\pi$
$740$		0			0
$741$	−3.20728	−	22.2231i	−0.117822	−	0.816385i
$742$		0			0
$743$	12.7952	−	22.1619i	0.469410	−	0.813043i	−0.529978	−	0.848011i	$-0.677800\pi$
$743$	12.7952	−	22.1619i	0.469410	−	0.813043i	0.999388	+	0.0349688i	$0.0111332\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	17.4928	−	5.15660i	0.640028	−	0.188670i
$748$		0			0
$749$	−0.819886	−	1.42008i	−0.0299580	−	0.0518888i
$750$		0			0
$751$	−7.55572	+	13.0869i	−0.275712	+	0.477547i	−0.970315	−	0.241847i	$-0.922247\pi$
$751$	−7.55572	+	13.0869i	−0.275712	+	0.477547i	0.694603	+	0.719394i	$0.255580\pi$
$752$		0			0
$753$	19.9898	−	15.7374i	0.728468	−	0.573502i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	13.2710			0.482341			0.241170	−	0.970483i	$-0.422469\pi$
$757$	13.2710			0.482341			0.241170	+	0.970483i	$0.422469\pi$
$758$		0			0
$759$	10.5388	−	8.29687i	0.382533	−	0.301157i
$760$		0			0
$761$	9.25871	−	16.0366i	0.335628	−	0.581325i	−0.647977	−	0.761660i	$-0.724385\pi$
$761$	9.25871	−	16.0366i	0.335628	−	0.581325i	0.983605	+	0.180335i	$0.0577182\pi$
$762$		0			0
$763$	−0.656829	−	1.13766i	−0.0237788	−	0.0411861i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−16.1941	−	28.0490i	−0.584736	−	1.01279i
$768$		0			0
$769$	1.00941	−	1.74835i	0.0364003	−	0.0630472i	−0.847251	−	0.531192i	$-0.821744\pi$
$769$	1.00941	−	1.74835i	0.0364003	−	0.0630472i	0.883652	+	0.468145i	$0.155078\pi$
$770$		0			0
$771$	−4.22736	−	29.2912i	−0.152245	−	1.05490i
$772$		0			0
$773$	5.76154			0.207228			0.103614	−	0.994618i	$-0.466959\pi$
$773$	5.76154			0.207228			0.103614	+	0.994618i	$0.466959\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.813934	−	0.325347i	−0.0291997	−	0.0116718i
$778$		0			0
$779$	−16.4203	+	28.4407i	−0.588317	+	1.01900i
$780$		0			0
$781$	−5.65949	−	9.80252i	−0.202512	−	0.350762i
$782$		0			0
$783$	7.21143	−	10.1614i	0.257716	−	0.363138i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−3.66521	+	6.34834i	−0.130651	+	0.226294i	−0.923928	−	0.382567i	$-0.875040\pi$
$787$	−3.66521	+	6.34834i	−0.130651	+	0.226294i	0.793277	+	0.608861i	$0.208373\pi$
$788$		0			0
$789$	−5.37595	−	2.14888i	−0.191389	−	0.0765023i
$790$		0			0
$791$	0.570938			0.0203002
$792$		0			0
$793$	−16.6331			−0.590659
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3.56179	−	6.16920i	0.126165	−	0.218524i	−0.796023	−	0.605267i	$-0.793066\pi$
$797$	3.56179	−	6.16920i	0.126165	−	0.218524i	0.922188	+	0.386742i	$0.126400\pi$
$798$		0			0
$799$	−2.80475	−	4.85797i	−0.0992249	−	0.171863i
$800$		0			0
$801$	−5.72800	+	23.7214i	−0.202389	+	0.838155i
$802$		0			0
$803$	2.42699	+	4.20367i	0.0856466	+	0.148344i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.48644	+	1.95751i	−0.0875270	+	0.0689075i
$808$		0			0
$809$	29.0809			1.02243			0.511215	−	0.859453i	$-0.329196\pi$
$809$	29.0809			1.02243			0.511215	+	0.859453i	$0.329196\pi$
$810$		0			0
$811$	34.3214			1.20519			0.602593	−	0.798048i	$-0.294134\pi$
$811$	34.3214			1.20519			0.602593	+	0.798048i	$0.294134\pi$
$812$		0			0
$813$	32.7482	−	25.7817i	1.14853	−	0.904205i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	20.3711	+	35.2838i	0.712696	+	1.23443i
$818$		0			0
$819$	0.159852	−	0.661995i	0.00558567	−	0.0231320i
$820$		0			0
$821$	−21.4384	−	37.1324i	−0.748206	−	1.29593i	−0.948682	−	0.316232i	$-0.897582\pi$
$821$	−21.4384	−	37.1324i	−0.748206	−	1.29593i	0.200476	−	0.979699i	$-0.435751\pi$
$822$		0			0
$823$	23.1154	−	40.0371i	0.805753	−	1.39561i	−0.110028	−	0.993929i	$-0.535094\pi$
$823$	23.1154	−	40.0371i	0.805753	−	1.39561i	0.915781	−	0.401677i	$-0.131573\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	23.6350			0.821869			0.410934	−	0.911665i	$-0.365203\pi$
$827$	23.6350			0.821869			0.410934	+	0.911665i	$0.365203\pi$
$828$		0			0
$829$	−18.8979			−0.656352			−0.328176	−	0.944617i	$-0.606434\pi$
$829$	−18.8979			−0.656352			−0.328176	+	0.944617i	$0.606434\pi$
$830$		0			0
$831$	22.4055	+	8.95598i	0.777240	+	0.310679i
$832$		0			0
$833$	7.29488	−	12.6351i	0.252752	−	0.437780i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−18.7535	−	1.76050i	−0.648217	−	0.0608519i
$838$		0			0
$839$	−5.21547	−	9.03346i	−0.180058	−	0.311870i	0.761842	−	0.647763i	$-0.224295\pi$
$839$	−5.21547	−	9.03346i	−0.180058	−	0.311870i	−0.941900	+	0.335893i	$0.890962\pi$
$840$		0			0
$841$	11.6248	−	20.1348i	0.400857	−	0.694304i
$842$		0			0
$843$	−30.9567	−	12.3741i	−1.06621	−	0.426185i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.879104			−0.0302064
$848$		0			0
$849$	5.51104	+	38.1857i	0.189138	+	1.31053i
$850$		0			0
$851$	24.8036	−	42.9611i	0.850257	−	1.47269i
$852$		0			0
$853$	19.9405	+	34.5379i	0.682748	+	1.18255i	0.974139	+	0.225951i	$0.0725488\pi$
$853$	19.9405	+	34.5379i	0.682748	+	1.18255i	−0.291390	+	0.956604i	$0.594118\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9.06346	+	15.6984i	0.309602	+	0.536246i	0.978275	−	0.207310i	$-0.0664709\pi$
$857$	9.06346	+	15.6984i	0.309602	+	0.536246i	−0.668673	+	0.743556i	$0.733138\pi$
$858$		0			0
$859$	−2.01040	+	3.48212i	−0.0685941	+	0.118808i	−0.898283	−	0.439418i	$-0.855185\pi$
$859$	−2.01040	+	3.48212i	−0.0685941	+	0.118808i	0.829689	+	0.558227i	$0.188518\pi$
$860$		0			0
$861$	−0.782637	+	0.616148i	−0.0266722	+	0.0209983i
$862$		0			0
$863$	−43.9540			−1.49621			−0.748105	−	0.663580i	$-0.769036\pi$
$863$	−43.9540			−1.49621			−0.748105	+	0.663580i	$0.769036\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	17.2109	−	13.5497i	0.584514	−	0.460171i
$868$		0			0
$869$	−6.14246	+	10.6391i	−0.208369	+	0.360905i
$870$		0			0
$871$	−8.09215	−	14.0160i	−0.274192	−	0.474915i
$872$		0			0
$873$	−31.9468	+	9.41740i	−1.08123	+	0.318731i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	24.7864	−	42.9313i	0.836978	−	1.44969i	−0.0554326	−	0.998462i	$-0.517654\pi$
$877$	24.7864	−	42.9313i	0.836978	−	1.44969i	0.892410	−	0.451225i	$-0.149013\pi$
$878$		0			0
$879$	−0.517241	−	3.58393i	−0.0174461	−	0.120883i
$880$		0			0
$881$	51.0775			1.72085			0.860423	−	0.509580i	$-0.170199\pi$
$881$	51.0775			1.72085			0.860423	+	0.509580i	$0.170199\pi$
$882$		0			0
$883$	51.1113			1.72003			0.860017	−	0.510266i	$-0.170453\pi$
$883$	51.1113			1.72003			0.860017	+	0.510266i	$0.170453\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.9786	−	29.4079i	0.570087	−	0.987420i	−0.426469	−	0.904502i	$-0.640243\pi$
$887$	16.9786	−	29.4079i	0.570087	−	0.987420i	0.996556	−	0.0829179i	$-0.0264239\pi$
$888$		0			0
$889$	0.321051	+	0.556076i	0.0107677	+	0.0186502i
$890$		0			0
$891$	−0.408702	−	8.21152i	−0.0136920	−	0.275096i
$892$		0			0
$893$	−6.63854	−	11.4983i	−0.222150	−	0.384776i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	35.7883	+	14.3054i	1.19494	+	0.477643i
$898$		0			0
$899$	8.69264			0.289916
$900$		0			0
$901$	−11.9689			−0.398742
$902$		0			0
$903$	0.176515	+	1.22306i	0.00587405	+	0.0407010i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−2.90198	−	5.02638i	−0.0963588	−	0.166898i	0.813816	−	0.581122i	$-0.197386\pi$
$907$	−2.90198	−	5.02638i	−0.0963588	−	0.166898i	−0.910175	+	0.414224i	$0.864053\pi$
$908$		0			0
$909$	34.7583	−	10.2462i	1.15286	−	0.339844i
$910$		0			0
$911$	2.09995	+	3.63722i	0.0695744	+	0.120506i	0.898714	−	0.438535i	$-0.144503\pi$
$911$	2.09995	+	3.63722i	0.0695744	+	0.120506i	−0.829140	+	0.559042i	$0.811169\pi$
$912$		0			0
$913$	−2.77665	+	4.80929i	−0.0918936	+	0.159164i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.38033			−0.0455827
$918$		0			0
$919$	25.2655			0.833431			0.416715	−	0.909037i	$-0.363181\pi$
$919$	25.2655			0.833431			0.416715	+	0.909037i	$0.363181\pi$
$920$		0			0
$921$	2.36875	−	1.86485i	0.0780531	−	0.0614490i
$922$		0			0
$923$	16.2624	−	28.1674i	0.535285	−	0.927141i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−9.49243	−	9.03172i	−0.311772	−	0.296641i
$928$		0			0
$929$	18.1932	+	31.5115i	0.596899	+	1.03386i	0.993276	+	0.115771i	$0.0369340\pi$
$929$	18.1932	+	31.5115i	0.596899	+	1.03386i	−0.396377	+	0.918088i	$0.629733\pi$
$930$		0			0
$931$	17.2662	−	29.9059i	0.565876	−	0.980127i
$932$		0			0
$933$	5.87262	+	40.6911i	0.192261	+	1.33217i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	17.5425			0.573088			0.286544	−	0.958067i	$-0.407494\pi$
$937$	17.5425			0.573088			0.286544	+	0.958067i	$0.407494\pi$
$938$		0			0
$939$	−17.5003	−	6.99525i	−0.571101	−	0.228281i
$940$		0			0
$941$	−12.1692	+	21.0777i	−0.396705	+	0.687114i	−0.993317	−	0.115416i	$-0.963180\pi$
$941$	−12.1692	+	21.0777i	−0.396705	+	0.687114i	0.596612	+	0.802530i	$0.296513\pi$
$942$		0			0
$943$	−28.1857	−	48.8191i	−0.917853	−	1.58977i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.52603	+	2.64316i	0.0495893	+	0.0858913i	0.889755	−	0.456439i	$-0.150875\pi$
$947$	1.52603	+	2.64316i	0.0495893	+	0.0858913i	−0.840165	+	0.542330i	$0.817542\pi$
$948$		0			0
$949$	−6.97392	+	12.0792i	−0.226383	+	0.392107i
$950$		0			0
$951$	12.8786	+	5.14786i	0.417618	+	0.166931i
$952$		0			0
$953$	11.6054			0.375934			0.187967	−	0.982175i	$-0.439810\pi$
$953$	11.6054			0.375934			0.187967	+	0.982175i	$0.439810\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	0.541977	+	3.75533i	0.0175196	+	0.121393i
$958$		0			0
$959$	−0.795199	+	1.37732i	−0.0256783	+	0.0444761i
$960$		0			0
$961$	8.92974	+	15.4668i	0.288056	+	0.498928i
$962$		0			0
$963$	13.3521	−	55.2951i	0.430265	−	1.78186i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−8.41919	+	14.5825i	−0.270743	+	0.468941i	−0.969052	−	0.246856i	$-0.920603\pi$
$967$	−8.41919	+	14.5825i	−0.270743	+	0.468941i	0.698309	+	0.715796i	$0.253936\pi$
$968$		0			0
$969$	−14.0229	+	11.0398i	−0.450480	+	0.354650i
$970$		0			0
$971$	−18.3864			−0.590046			−0.295023	−	0.955490i	$-0.595327\pi$
$971$	−18.3864			−0.590046			−0.295023	+	0.955490i	$0.595327\pi$
$972$		0			0
$973$	0.480952			0.0154186
$974$		0			0
$975$		0			0
$976$		0			0
$977$	14.7343	−	25.5206i	0.471393	−	0.816477i	−0.528071	−	0.849200i	$-0.677085\pi$
$977$	14.7343	−	25.5206i	0.471393	−	0.816477i	0.999464	+	0.0327228i	$0.0104178\pi$
$978$		0			0
$979$	−3.71547	−	6.43538i	−0.118747	−	0.205676i
$980$		0			0
$981$	10.6966	−	44.2981i	0.341518	−	1.41433i
$982$		0			0
$983$	10.7771	+	18.6664i	0.343735	+	0.595366i	0.985123	−	0.171851i	$-0.0549746\pi$
$983$	10.7771	+	18.6664i	0.343735	+	0.595366i	−0.641388	+	0.767216i	$0.721641\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.0575227	−	0.398572i	−0.00183097	−	0.0126867i
$988$		0			0
$989$	−69.9349			−2.22380
$990$		0			0
$991$	9.01027			0.286221			0.143110	−	0.989707i	$-0.454290\pi$
$991$	9.01027			0.286221			0.143110	+	0.989707i	$0.454290\pi$
$992$		0			0
$993$	−6.78637	−	2.71266i	−0.215359	−	0.0860836i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−15.2499	−	26.4136i	−0.482969	−	0.836526i	0.516840	−	0.856082i	$-0.327108\pi$
$997$	−15.2499	−	26.4136i	−0.482969	−	0.836526i	−0.999809	+	0.0195556i	$0.993775\pi$
$998$		0			0
$999$	−12.6761	−	27.6397i	−0.401053	−	0.874482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.i.e.301.1	yes	8
3.2	odd	2		2700.2.i.d.901.2		8
5.2	odd	4		900.2.s.d.49.6		16
5.3	odd	4		900.2.s.d.49.3		16
5.4	even	2		900.2.i.d.301.4	✓	8
9.2	odd	6		2700.2.i.d.1801.2		8
9.4	even	3		8100.2.a.z.1.3		4
9.5	odd	6		8100.2.a.ba.1.3		4
9.7	even	3	inner	900.2.i.e.601.1	yes	8
15.2	even	4		2700.2.s.d.1549.5		16
15.8	even	4		2700.2.s.d.1549.4		16
15.14	odd	2		2700.2.i.e.901.3		8
45.2	even	12		2700.2.s.d.2449.4		16
45.4	even	6		8100.2.a.x.1.2		4
45.7	odd	12		900.2.s.d.349.3		16
45.13	odd	12		8100.2.d.q.649.4		8
45.14	odd	6		8100.2.a.y.1.2		4
45.22	odd	12		8100.2.d.q.649.5		8
45.23	even	12		8100.2.d.s.649.4		8
45.29	odd	6		2700.2.i.e.1801.3		8
45.32	even	12		8100.2.d.s.649.5		8
45.34	even	6		900.2.i.d.601.4	yes	8
45.38	even	12		2700.2.s.d.2449.5		16
45.43	odd	12		900.2.s.d.349.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.i.d.301.4	✓	8	5.4	even	2
900.2.i.d.601.4	yes	8	45.34	even	6
900.2.i.e.301.1	yes	8	1.1	even	1	trivial
900.2.i.e.601.1	yes	8	9.7	even	3	inner
900.2.s.d.49.3		16	5.3	odd	4
900.2.s.d.49.6		16	5.2	odd	4
900.2.s.d.349.3		16	45.7	odd	12
900.2.s.d.349.6		16	45.43	odd	12
2700.2.i.d.901.2		8	3.2	odd	2
2700.2.i.d.1801.2		8	9.2	odd	6
2700.2.i.e.901.3		8	15.14	odd	2
2700.2.i.e.1801.3		8	45.29	odd	6
2700.2.s.d.1549.4		16	15.8	even	4
2700.2.s.d.1549.5		16	15.2	even	4
2700.2.s.d.2449.4		16	45.2	even	12
2700.2.s.d.2449.5		16	45.38	even	12
8100.2.a.x.1.2		4	45.4	even	6
8100.2.a.y.1.2		4	45.14	odd	6
8100.2.a.z.1.3		4	9.4	even	3
8100.2.a.ba.1.3		4	9.5	odd	6
8100.2.d.q.649.4		8	45.13	odd	12
8100.2.d.q.649.5		8	45.22	odd	12
8100.2.d.s.649.4		8	45.23	even	12
8100.2.d.s.649.5		8	45.32	even	12

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36091 + 1.07141i) q^{3} +(-0.0432397 - 0.0748933i) q^{7} +(0.704170 - 2.91619i) q^{9} +O(q^{10})\)	\(q+(-1.36091 + 1.07141i) q^{3} +(-0.0432397 - 0.0748933i) q^{7} +(0.704170 - 2.91619i) q^{9} +(0.456760 + 0.791132i) q^{11} +(-1.31249 + 2.27331i) q^{13} +2.08648 q^{17} +4.93847 q^{19} +(0.139087 + 0.0555960i) q^{21} +(-4.23849 + 7.34128i) q^{23} +(2.16611 + 4.72313i) q^{27} +(-1.19899 - 2.07671i) q^{29} +(-1.81249 + 3.13933i) q^{31} +(-1.46924 - 0.587286i) q^{33} -5.85199 q^{37} +(-0.649447 - 4.49999i) q^{39} +(-3.32497 + 5.75902i) q^{41} +(4.12499 + 7.14469i) q^{43} +(-1.34425 - 2.32831i) q^{47} +(3.49626 - 6.05570i) q^{49} +(-2.83952 + 2.23547i) q^{51} -5.73642 q^{53} +(-6.72083 + 5.29112i) q^{57} +(-6.16922 + 10.6854i) q^{59} +(3.16823 + 5.48753i) q^{61} +(-0.248851 + 0.0733573i) q^{63} +(-3.08274 + 5.33946i) q^{67} +(-2.09729 - 14.5320i) q^{69} -12.3905 q^{71} +5.31349 q^{73} +(0.0395003 - 0.0684166i) q^{77} +(6.72394 + 11.6462i) q^{79} +(-8.00829 - 4.10698i) q^{81} +(3.03950 + 5.26457i) q^{83} +(3.85673 + 1.54162i) q^{87} -8.13440 q^{89} +0.227007 q^{91} +(-0.896857 - 6.21428i) q^{93} +(-5.55098 - 9.61459i) q^{97} +(2.62873 - 0.774907i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} - q^{7} + 5 q^{9}+O(q^{10}) \) 8 * q + q^3 - q^7 + 5 * q^9	\( 8 q + q^{3} - q^{7} + 5 q^{9} + 3 q^{11} + 2 q^{13} + 18 q^{17} - 8 q^{19} + 13 q^{21} + 3 q^{23} + 16 q^{27} - 9 q^{29} - 2 q^{31} + 12 q^{33} + 2 q^{37} - 17 q^{39} + 9 q^{41} + 8 q^{43} - 12 q^{47} - 9 q^{49} + 3 q^{51} + 24 q^{53} - 40 q^{57} - 15 q^{59} + q^{61} + 35 q^{63} + 11 q^{67} + 9 q^{69} - 24 q^{71} + 20 q^{73} - 36 q^{77} + 7 q^{79} - 31 q^{81} - 12 q^{83} + 9 q^{87} + 6 q^{89} - 22 q^{91} - 19 q^{93} + 5 q^{97} + 33 q^{99}+O(q^{100}) \) 8 * q + q^3 - q^7 + 5 * q^9 + 3 * q^11 + 2 * q^13 + 18 * q^17 - 8 * q^19 + 13 * q^21 + 3 * q^23 + 16 * q^27 - 9 * q^29 - 2 * q^31 + 12 * q^33 + 2 * q^37 - 17 * q^39 + 9 * q^41 + 8 * q^43 - 12 * q^47 - 9 * q^49 + 3 * q^51 + 24 * q^53 - 40 * q^57 - 15 * q^59 + q^61 + 35 * q^63 + 11 * q^67 + 9 * q^69 - 24 * q^71 + 20 * q^73 - 36 * q^77 + 7 * q^79 - 31 * q^81 - 12 * q^83 + 9 * q^87 + 6 * q^89 - 22 * q^91 - 19 * q^93 + 5 * q^97 + 33 * q^99

Introduction

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