LMFDB - Embedded newform 1440.2.bw.a.671.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,2,Mod(191,1440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1, 0]))

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

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

chi := DirichletCharacter("1440.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.bw (of order $6$, 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:	$11.4984578911$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			671.9
Character	$\chi$	$=$	1440.671
Dual form			1440.2.bw.a.191.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.793361 + 1.53967i) q^{3} +(0.866025 + 0.500000i) q^{5} +(2.37166 - 1.36928i) q^{7} +(-1.74116 - 2.44302i) q^{9} +O(q^{10})$	\(q+(-0.793361 + 1.53967i) q^{3} +(0.866025 + 0.500000i) q^{5} +(2.37166 - 1.36928i) q^{7} +(-1.74116 - 2.44302i) q^{9} +(2.13116 + 3.69127i) q^{11} +(-1.63886 + 2.83859i) q^{13} +(-1.45690 + 0.936712i) q^{15} -2.83591i q^{17} +0.727896i q^{19} +(0.226653 + 4.73791i) q^{21} +(-0.0358515 + 0.0620966i) q^{23} +(0.500000 + 0.866025i) q^{25} +(5.14281 - 0.742605i) q^{27} +(-2.08008 + 1.20094i) q^{29} +(9.00852 + 5.20107i) q^{31} +(-7.37411 + 0.352764i) q^{33} +2.73856 q^{35} +2.82072 q^{37} +(-3.07028 - 4.77533i) q^{39} +(-3.93392 - 2.27125i) q^{41} +(5.31712 - 3.06984i) q^{43} +(-0.286374 - 2.98630i) q^{45} +(3.66789 + 6.35297i) q^{47} +(0.249853 - 0.432758i) q^{49} +(4.36636 + 2.24990i) q^{51} +8.55298i q^{53} +4.26231i q^{55} +(-1.12072 - 0.577484i) q^{57} +(-0.127600 + 0.221010i) q^{59} +(-5.20923 - 9.02266i) q^{61} +(-7.47462 - 3.40990i) q^{63} +(-2.83859 + 1.63886i) q^{65} +(5.10230 + 2.94582i) q^{67} +(-0.0671650 - 0.104464i) q^{69} -11.8687 q^{71} +11.0642 q^{73} +(-1.73007 + 0.0827637i) q^{75} +(10.1088 + 5.83630i) q^{77} +(-6.15954 + 3.55621i) q^{79} +(-2.93674 + 8.50738i) q^{81} +(7.46615 + 12.9318i) q^{83} +(1.41795 - 2.45597i) q^{85} +(-0.198788 - 4.15541i) q^{87} +13.2351i q^{89} +8.97624i q^{91} +(-15.1549 + 9.74381i) q^{93} +(-0.363948 + 0.630376i) q^{95} +(-4.75267 - 8.23187i) q^{97} +(5.30719 - 11.6335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{9}+O(q^{10}) $ 48 * q + 4 * q^9	$ 48 q + 4 q^{9} - 8 q^{15} - 4 q^{21} + 24 q^{25} - 24 q^{27} - 12 q^{29} + 20 q^{33} + 24 q^{39} + 36 q^{41} - 8 q^{45} + 24 q^{49} + 80 q^{51} + 20 q^{57} + 24 q^{59} + 40 q^{63} + 72 q^{67} + 36 q^{69} - 24 q^{73} + 48 q^{77} + 72 q^{79} - 64 q^{87} + 16 q^{93} + 12 q^{95} - 12 q^{97} - 40 q^{99}+O(q^{100}) $ 48 * q + 4 * q^9 - 8 * q^15 - 4 * q^21 + 24 * q^25 - 24 * q^27 - 12 * q^29 + 20 * q^33 + 24 * q^39 + 36 * q^41 - 8 * q^45 + 24 * q^49 + 80 * q^51 + 20 * q^57 + 24 * q^59 + 40 * q^63 + 72 * q^67 + 36 * q^69 - 24 * q^73 + 48 * q^77 + 72 * q^79 - 64 * q^87 + 16 * q^93 + 12 * q^95 - 12 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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
$3$	−0.793361	+	1.53967i	−0.458047	+	0.888928i
$3$	−0.793361	+	1.53967i	−0.458047	+	0.888928i
$4$		0			0
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$		0			0
$7$	2.37166	−	1.36928i	0.896404	−	0.517539i	0.0203721	−	0.999792i	$-0.493515\pi$
$7$	2.37166	−	1.36928i	0.896404	−	0.517539i	0.876032	+	0.482253i	$0.160182\pi$
$8$		0			0
$9$	−1.74116	−	2.44302i	−0.580386	−	0.814342i
$10$		0			0
$11$	2.13116	+	3.69127i	0.642568	+	1.11296i	0.984858	+	0.173365i	$0.0554641\pi$
$11$	2.13116	+	3.69127i	0.642568	+	1.11296i	−0.342290	+	0.939594i	$0.611203\pi$
$12$		0			0
$13$	−1.63886	+	2.83859i	−0.454539	+	0.787284i	−0.998662	−	0.0517214i	$-0.983529\pi$
$13$	−1.63886	+	2.83859i	−0.454539	+	0.787284i	0.544123	+	0.839006i	$0.316863\pi$
$14$		0			0
$15$	−1.45690	+	0.936712i	−0.376171	+	0.241858i
$16$		0			0
$17$		−	2.83591i		−	0.687809i	−0.939005	−	0.343904i	$-0.888250\pi$
$17$		−	2.83591i		−	0.687809i	0.939005	−	0.343904i	$-0.111750\pi$
$18$		0			0
$19$			0.727896i			0.166991i	0.996508	+	0.0834953i	$0.0266084\pi$
$19$			0.727896i			0.166991i	−0.996508	+	0.0834953i	$0.973392\pi$
$20$		0			0
$21$	0.226653	+	4.73791i	0.0494598	+	1.03390i
$22$		0			0
$23$	−0.0358515	+	0.0620966i	−0.00747555	+	0.0129480i	−0.869739	−	0.493512i	$-0.835713\pi$
$23$	−0.0358515	+	0.0620966i	−0.00747555	+	0.0129480i	0.862263	+	0.506460i	$0.169046\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$	5.14281	−	0.742605i	0.989735	−	0.142914i
$28$		0			0
$29$	−2.08008	+	1.20094i	−0.386261	+	0.223008i	−0.680539	−	0.732712i	$-0.738254\pi$
$29$	−2.08008	+	1.20094i	−0.386261	+	0.223008i	0.294278	+	0.955720i	$0.404921\pi$
$30$		0			0
$31$	9.00852	+	5.20107i	1.61798	+	0.934140i	0.987442	+	0.157979i	$0.0504980\pi$
$31$	9.00852	+	5.20107i	1.61798	+	0.934140i	0.630535	+	0.776160i	$0.282835\pi$
$32$		0			0
$33$	−7.37411	+	0.352764i	−1.28367	+	0.0614084i
$34$		0			0
$35$	2.73856			0.462901
$36$		0			0
$37$	2.82072			0.463723			0.231862	−	0.972749i	$-0.425518\pi$
$37$	2.82072			0.463723			0.231862	+	0.972749i	$0.425518\pi$
$38$		0			0
$39$	−3.07028	−	4.77533i	−0.491639	−	0.764665i
$40$		0			0
$41$	−3.93392	−	2.27125i	−0.614375	−	0.354709i	0.160301	−	0.987068i	$-0.448754\pi$
$41$	−3.93392	−	2.27125i	−0.614375	−	0.354709i	−0.774676	+	0.632359i	$0.782087\pi$
$42$		0			0
$43$	5.31712	−	3.06984i	0.810853	−	0.468146i	−0.0363988	−	0.999337i	$-0.511589\pi$
$43$	5.31712	−	3.06984i	0.810853	−	0.468146i	0.847252	+	0.531191i	$0.178255\pi$
$44$		0			0
$45$	−0.286374	−	2.98630i	−0.0426901	−	0.445171i
$46$		0			0
$47$	3.66789	+	6.35297i	0.535016	+	0.926676i	0.999163	+	0.0409170i	$0.0130279\pi$
$47$	3.66789	+	6.35297i	0.535016	+	0.926676i	−0.464146	+	0.885759i	$0.653639\pi$
$48$		0			0
$49$	0.249853	−	0.432758i	0.0356933	−	0.0618226i
$50$		0			0
$51$	4.36636	+	2.24990i	0.611412	+	0.315049i
$52$		0			0
$53$			8.55298i			1.17484i	0.809282	+	0.587421i	$0.199857\pi$
$53$			8.55298i			1.17484i	−0.809282	+	0.587421i	$0.800143\pi$
$54$		0			0
$55$			4.26231i			0.574730i
$56$		0			0
$57$	−1.12072	−	0.577484i	−0.148443	−	0.0764896i
$58$		0			0
$59$	−0.127600	+	0.221010i	−0.0166121	+	0.0287731i	−0.874212	−	0.485544i	$-0.838621\pi$
$59$	−0.127600	+	0.221010i	−0.0166121	+	0.0287731i	0.857600	+	0.514318i	$0.171955\pi$
$60$		0			0
$61$	−5.20923	−	9.02266i	−0.666974	−	1.15523i	−0.978746	−	0.205076i	$-0.934256\pi$
$61$	−5.20923	−	9.02266i	−0.666974	−	1.15523i	0.311772	−	0.950157i	$-0.399078\pi$
$62$		0			0
$63$	−7.47462	−	3.40990i	−0.941714	−	0.429607i
$64$		0			0
$65$	−2.83859	+	1.63886i	−0.352084	+	0.203276i
$66$		0			0
$67$	5.10230	+	2.94582i	0.623346	+	0.359889i	0.778170	−	0.628053i	$-0.216148\pi$
$67$	5.10230	+	2.94582i	0.623346	+	0.359889i	−0.154825	+	0.987942i	$0.549481\pi$
$68$		0			0
$69$	−0.0671650	−	0.104464i	−0.00808571	−	0.0125760i
$70$		0			0
$71$	−11.8687			−1.40855			−0.704277	−	0.709925i	$-0.748729\pi$
$71$	−11.8687			−1.40855			−0.704277	+	0.709925i	$0.748729\pi$
$72$		0			0
$73$	11.0642			1.29496			0.647481	−	0.762082i	$-0.275822\pi$
$73$	11.0642			1.29496			0.647481	+	0.762082i	$0.275822\pi$
$74$		0			0
$75$	−1.73007	+	0.0827637i	−0.199772	+	0.00955672i
$76$		0			0
$77$	10.1088	+	5.83630i	1.15200	+	0.665108i
$78$		0			0
$79$	−6.15954	+	3.55621i	−0.693003	+	0.400105i	−0.804736	−	0.593633i	$-0.797693\pi$
$79$	−6.15954	+	3.55621i	−0.693003	+	0.400105i	0.111733	+	0.993738i	$0.464360\pi$
$80$		0			0
$81$	−2.93674	+	8.50738i	−0.326305	+	0.945265i
$82$		0			0
$83$	7.46615	+	12.9318i	0.819516	+	1.41944i	0.906039	+	0.423194i	$0.139091\pi$
$83$	7.46615	+	12.9318i	0.819516	+	1.41944i	−0.0865226	+	0.996250i	$0.527575\pi$
$84$		0			0
$85$	1.41795	−	2.45597i	0.153799	−	0.266387i
$86$		0			0
$87$	−0.198788	−	4.15541i	−0.0213123	−	0.445507i
$88$		0			0
$89$			13.2351i			1.40292i	0.712708	+	0.701460i	$0.247468\pi$
$89$			13.2351i			1.40292i	−0.712708	+	0.701460i	$0.752532\pi$
$90$		0			0
$91$			8.97624i			0.940966i
$92$		0			0
$93$	−15.1549	+	9.74381i	−1.57149	+	1.01039i
$94$		0			0
$95$	−0.363948	+	0.630376i	−0.0373403	+	0.0646752i
$96$		0			0
$97$	−4.75267	−	8.23187i	−0.482561	−	0.835820i	0.517239	−	0.855841i	$-0.326960\pi$
$97$	−4.75267	−	8.23187i	−0.482561	−	0.835820i	−0.999800	+	0.0200212i	$0.993627\pi$
$98$		0			0
$99$	5.30719	−	11.6335i	0.533392	−	1.16922i
$100$		0			0
$101$	−8.75224	+	5.05311i	−0.870880	+	0.502803i	−0.867641	−	0.497192i	$-0.834365\pi$
$101$	−8.75224	+	5.05311i	−0.870880	+	0.502803i	−0.00323951	+	0.999995i	$0.501031\pi$
$102$		0			0
$103$	−10.7206	−	6.18955i	−1.05633	−	0.609874i	−0.131917	−	0.991261i	$-0.542113\pi$
$103$	−10.7206	−	6.18955i	−1.05633	−	0.609874i	−0.924416	+	0.381387i	$0.875447\pi$
$104$		0			0
$105$	−2.17267	+	4.21647i	−0.212030	+	0.411486i
$106$		0			0
$107$	−11.7672			−1.13758			−0.568791	−	0.822482i	$-0.692589\pi$
$107$	−11.7672			−1.13758			−0.568791	+	0.822482i	$0.692589\pi$
$108$		0			0
$109$	−17.4975			−1.67595			−0.837977	−	0.545705i	$-0.816262\pi$
$109$	−17.4975			−1.67595			−0.837977	+	0.545705i	$0.816262\pi$
$110$		0			0
$111$	−2.23785	+	4.34297i	−0.212407	+	0.412217i
$112$		0			0
$113$	0.575714	+	0.332388i	0.0541586	+	0.0312685i	0.526835	−	0.849968i	$-0.323379\pi$
$113$	0.575714	+	0.332388i	0.0541586	+	0.0312685i	−0.472676	+	0.881236i	$0.656712\pi$
$114$		0			0
$115$	−0.0620966	+	0.0358515i	−0.00579053	+	0.00334317i
$116$		0			0
$117$	9.78827	−	0.938656i	0.904926	−	0.0867788i
$118$		0			0
$119$	−3.88315	−	6.72581i	−0.355968	−	0.616554i
$120$		0			0
$121$	−3.58365	+	6.20706i	−0.325786	+	0.564278i
$122$		0			0
$123$	6.61798	−	4.25501i	0.596724	−	0.383661i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			5.30857i			0.471059i	0.971867	+	0.235530i	$0.0756825\pi$
$127$			5.30857i			0.471059i	−0.971867	+	0.235530i	$0.924317\pi$
$128$		0			0
$129$	0.508143	+	10.6221i	0.0447395	+	0.935223i
$130$		0			0
$131$	0.0573156	−	0.0992736i	0.00500769	−	0.00867357i	−0.863511	−	0.504331i	$-0.831739\pi$
$131$	0.0573156	−	0.0992736i	0.00500769	−	0.00867357i	0.868518	+	0.495657i	$0.165073\pi$
$132$		0			0
$133$	0.996693	+	1.72632i	0.0864242	+	0.149691i
$134$		0			0
$135$	4.82511	+	1.92829i	0.415279	+	0.165961i
$136$		0			0
$137$	12.8710	−	7.43106i	1.09964	−	0.634878i	0.163515	−	0.986541i	$-0.447717\pi$
$137$	12.8710	−	7.43106i	1.09964	−	0.634878i	0.936127	+	0.351662i	$0.114383\pi$
$138$		0			0
$139$	13.7489	+	7.93791i	1.16616	+	0.673285i	0.952773	−	0.303682i	$-0.0982161\pi$
$139$	13.7489	+	7.93791i	1.16616	+	0.673285i	0.213390	+	0.976967i	$0.431549\pi$
$140$		0			0
$141$	−12.6914	+	0.607136i	−1.06881	+	0.0511300i
$142$		0			0
$143$	−13.9707			−1.16829
$144$		0			0
$145$	−2.40187			−0.199465
$146$		0			0
$147$	0.468080	+	0.728024i	0.0386066	+	0.0600464i
$148$		0			0
$149$	18.3980	+	10.6221i	1.50723	+	0.870197i	0.999965	+	0.00840423i	$0.00267518\pi$
$149$	18.3980	+	10.6221i	1.50723	+	0.870197i	0.507261	+	0.861793i	$0.330658\pi$
$150$		0			0
$151$	11.2204	−	6.47813i	0.913107	−	0.527182i	0.0316774	−	0.999498i	$-0.489915\pi$
$151$	11.2204	−	6.47813i	0.913107	−	0.527182i	0.881429	+	0.472316i	$0.156582\pi$
$152$		0			0
$153$	−6.92819	+	4.93776i	−0.560111	+	0.399194i
$154$		0			0
$155$	5.20107	+	9.00852i	0.417760	+	0.723582i
$156$		0			0
$157$	4.26408	−	7.38561i	0.340311	−	0.589436i	−0.644180	−	0.764874i	$-0.722801\pi$
$157$	4.26408	−	7.38561i	0.340311	−	0.589436i	0.984490	+	0.175439i	$0.0561344\pi$
$158$		0			0
$159$	−13.1687	−	6.78560i	−1.04435	−	0.538133i
$160$		0			0
$161$			0.196363i			0.0154755i
$162$		0			0
$163$		−	11.6869i		−	0.915387i	−0.889110	−	0.457693i	$-0.848676\pi$
$163$		−	11.6869i		−	0.915387i	0.889110	−	0.457693i	$-0.151324\pi$
$164$		0			0
$165$	−6.56255	−	3.38155i	−0.510893	−	0.263253i
$166$		0			0
$167$	−1.33242	+	2.30781i	−0.103106	+	0.178584i	−0.912963	−	0.408043i	$-0.866211\pi$
$167$	−1.33242	+	2.30781i	−0.103106	+	0.178584i	0.809857	+	0.586627i	$0.199545\pi$
$168$		0			0
$169$	1.12826	+	1.95420i	0.0867892	+	0.150323i
$170$		0			0
$171$	1.77827	−	1.26738i	0.135987	−	0.0969190i
$172$		0			0
$173$	12.1307	−	7.00365i	0.922279	−	0.532478i	0.0379173	−	0.999281i	$-0.487928\pi$
$173$	12.1307	−	7.00365i	0.922279	−	0.532478i	0.884361	+	0.466803i	$0.154594\pi$
$174$		0			0
$175$	2.37166	+	1.36928i	0.179281	+	0.103508i
$176$		0			0
$177$	−0.239049	−	0.371803i	−0.0179681	−	0.0279464i
$178$		0			0
$179$	4.41219			0.329782			0.164891	−	0.986312i	$-0.447273\pi$
$179$	4.41219			0.329782			0.164891	+	0.986312i	$0.447273\pi$
$180$		0			0
$181$	−14.4164			−1.07157			−0.535783	−	0.844356i	$-0.679983\pi$
$181$	−14.4164			−1.07157			−0.535783	+	0.844356i	$0.679983\pi$
$182$		0			0
$183$	18.0247	−	0.862271i	1.33242	−	0.0637409i
$184$		0			0
$185$	2.44281	+	1.41036i	0.179599	+	0.103692i
$186$		0			0
$187$	10.4681	−	6.04376i	0.765503	−	0.441964i
$188$		0			0
$189$	11.1802	−	8.80316i	0.813239	−	0.640336i
$190$		0			0
$191$	−0.405607	−	0.702531i	−0.0293487	−	0.0508334i	0.850978	−	0.525201i	$-0.176010\pi$
$191$	−0.405607	−	0.702531i	−0.0293487	−	0.0508334i	−0.880327	+	0.474368i	$0.842677\pi$
$192$		0			0
$193$	10.8228	−	18.7456i	0.779039	−	1.34934i	−0.153457	−	0.988155i	$-0.549041\pi$
$193$	10.8228	−	18.7456i	0.779039	−	1.34934i	0.932496	−	0.361180i	$-0.117626\pi$
$194$		0			0
$195$	−0.271276	−	5.67070i	−0.0194265	−	0.406087i
$196$		0			0
$197$			4.24503i			0.302446i	0.988500	+	0.151223i	$0.0483212\pi$
$197$			4.24503i			0.302446i	−0.988500	+	0.151223i	$0.951679\pi$
$198$		0			0
$199$		−	13.2906i		−	0.942145i	−0.882094	−	0.471073i	$-0.843867\pi$
$199$		−	13.2906i		−	0.942145i	0.882094	−	0.471073i	$-0.156133\pi$
$200$		0			0
$201$	−8.58355	+	5.51876i	−0.605437	+	0.389263i
$202$		0			0
$203$	−3.28883	+	5.69643i	−0.230831	+	0.399811i
$204$		0			0
$205$	−2.27125	−	3.93392i	−0.158631	−	0.274757i
$206$		0			0
$207$	0.214126	−	0.0205339i	0.0148828	−	0.00142720i
$208$		0			0
$209$	−2.68686	+	1.55126i	−0.185854	+	0.107303i
$210$		0			0
$211$	17.7019	+	10.2202i	1.21865	+	0.703589i	0.964630	−	0.263609i	$-0.0849128\pi$
$211$	17.7019	+	10.2202i	1.21865	+	0.703589i	0.254023	+	0.967198i	$0.418246\pi$
$212$		0			0
$213$	9.41615	−	18.2738i	0.645184	−	1.25210i
$214$		0			0
$215$	6.13968			0.418723
$216$		0			0
$217$	28.4869			1.93382
$218$		0			0
$219$	−8.77787	+	17.0351i	−0.593154	+	1.15113i
$220$		0			0
$221$	8.04999	+	4.64766i	0.541501	+	0.312636i
$222$		0			0
$223$	−6.58694	+	3.80297i	−0.441094	+	0.254666i	−0.704062	−	0.710139i	$-0.748632\pi$
$223$	−6.58694	+	3.80297i	−0.441094	+	0.254666i	0.262968	+	0.964805i	$0.415299\pi$
$224$		0			0
$225$	1.24514	−	2.72940i	0.0830095	−	0.181960i
$226$		0			0
$227$	−10.0598	−	17.4241i	−0.667695	−	1.15648i	−0.978547	−	0.206023i	$-0.933948\pi$
$227$	−10.0598	−	17.4241i	−0.667695	−	1.15648i	0.310852	−	0.950458i	$-0.399386\pi$
$228$		0			0
$229$	11.2582	−	19.4999i	0.743966	−	1.28859i	−0.206710	−	0.978402i	$-0.566276\pi$
$229$	11.2582	−	19.4999i	0.743966	−	1.28859i	0.950676	−	0.310185i	$-0.100391\pi$
$230$		0			0
$231$	−17.0059	+	10.9339i	−1.11890	+	0.719395i
$232$		0			0
$233$		−	27.8539i		−	1.82477i	−0.409330	−	0.912386i	$-0.634238\pi$
$233$		−	27.8539i		−	1.82477i	0.409330	−	0.912386i	$-0.365762\pi$
$234$		0			0
$235$			7.33578i			0.478533i
$236$		0			0
$237$	−0.588650	−	12.3050i	−0.0382370	−	0.799296i
$238$		0			0
$239$	−2.55154	+	4.41940i	−0.165046	+	0.285867i	−0.936671	−	0.350209i	$-0.886110\pi$
$239$	−2.55154	+	4.41940i	−0.165046	+	0.285867i	0.771626	+	0.636077i	$0.219444\pi$
$240$		0			0
$241$	−7.96107	−	13.7890i	−0.512817	−	0.888226i	−0.999890	−	0.0148641i	$-0.995268\pi$
$241$	−7.96107	−	13.7890i	−0.512817	−	0.888226i	0.487072	−	0.873362i	$-0.338065\pi$
$242$		0			0
$243$	−10.7687	−	11.2710i	−0.690809	−	0.723037i
$244$		0			0
$245$	0.432758	−	0.249853i	0.0276479	−	0.0159625i
$246$		0			0
$247$	−2.06620	−	1.19292i	−0.131469	−	0.0759037i
$248$		0			0
$249$	−25.8340	+	1.23585i	−1.63716	+	0.0783189i
$250$		0			0
$251$	−20.5073			−1.29441			−0.647206	−	0.762315i	$-0.724063\pi$
$251$	−20.5073			−1.29441			−0.647206	+	0.762315i	$0.724063\pi$
$252$		0			0
$253$	−0.305620			−0.0192142
$254$		0			0
$255$	2.65643	+	4.13165i	0.166352	+	0.258734i
$256$		0			0
$257$	11.2924	+	6.51968i	0.704401	+	0.406686i	0.808985	−	0.587830i	$-0.200018\pi$
$257$	11.2924	+	6.51968i	0.704401	+	0.406686i	−0.104583	+	0.994516i	$0.533351\pi$
$258$		0			0
$259$	6.68979	−	3.86235i	0.415683	−	0.239995i
$260$		0			0
$261$	6.55567	+	2.99067i	0.405786	+	0.185118i
$262$		0			0
$263$	2.46501	+	4.26952i	0.151999	+	0.263270i	0.931962	−	0.362555i	$-0.118096\pi$
$263$	2.46501	+	4.26952i	0.151999	+	0.263270i	−0.779963	+	0.625825i	$0.784762\pi$
$264$		0			0
$265$	−4.27649	+	7.40710i	−0.262703	+	0.455014i
$266$		0			0
$267$	−20.3777	−	10.5002i	−1.24710	−	0.642604i
$268$		0			0
$269$		−	17.6006i		−	1.07313i	−0.843859	−	0.536564i	$-0.819722\pi$
$269$		−	17.6006i		−	1.07313i	0.843859	−	0.536564i	$-0.180278\pi$
$270$		0			0
$271$		−	9.91265i		−	0.602150i	−0.953600	−	0.301075i	$-0.902654\pi$
$271$		−	9.91265i		−	0.602150i	0.953600	−	0.301075i	$-0.0973455\pi$
$272$		0			0
$273$	−13.8204	−	7.12140i	−0.836451	−	0.431007i
$274$		0			0
$275$	−2.13116	+	3.69127i	−0.128514	+	0.222592i
$276$		0			0
$277$	−5.72542	−	9.91671i	−0.344007	−	0.595838i	0.641166	−	0.767402i	$-0.278451\pi$
$277$	−5.72542	−	9.91671i	−0.344007	−	0.595838i	−0.985173	+	0.171565i	$0.945118\pi$
$278$		0			0
$279$	−2.97891	−	31.0639i	−0.178342	−	1.85975i
$280$		0			0
$281$	−14.8952	+	8.59973i	−0.888571	+	0.513017i	−0.873475	−	0.486869i	$-0.838139\pi$
$281$	−14.8952	+	8.59973i	−0.888571	+	0.513017i	−0.0150962	+	0.999886i	$0.504805\pi$
$282$		0			0
$283$	18.4145	+	10.6316i	1.09463	+	0.631985i	0.934805	−	0.355161i	$-0.115574\pi$
$283$	18.4145	+	10.6316i	1.09463	+	0.631985i	0.159824	+	0.987145i	$0.448907\pi$
$284$		0			0
$285$	−0.681828	−	1.06047i	−0.0403880	−	0.0628171i
$286$		0			0
$287$	−12.4399			−0.734304
$288$		0			0
$289$	8.95763			0.526919
$290$		0			0
$291$	16.4449	−	0.786697i	0.964019	−	0.0461170i
$292$		0			0
$293$	6.41060	+	3.70116i	0.374511	+	0.216224i	0.675427	−	0.737426i	$-0.263959\pi$
$293$	6.41060	+	3.70116i	0.374511	+	0.216224i	−0.300916	+	0.953651i	$0.597292\pi$
$294$		0			0
$295$	−0.221010	+	0.127600i	−0.0128677	+	0.00742918i
$296$		0			0
$297$	13.7013	+	17.4009i	0.795030	+	1.00970i
$298$		0			0
$299$	−0.117511	−	0.203535i	−0.00679585	−	0.0117708i
$300$		0			0
$301$	8.40694	−	14.5613i	0.484568	−	0.839297i
$302$		0			0
$303$	−0.836427	−	17.4845i	−0.0480515	−	1.00446i
$304$		0			0
$305$		−	10.4185i		−	0.596560i
$306$		0			0
$307$		−	28.3797i		−	1.61972i	−0.586625	−	0.809859i	$-0.699544\pi$
$307$		−	28.3797i		−	1.61972i	0.586625	−	0.809859i	$-0.300456\pi$
$308$		0			0
$309$	18.0352	−	11.5956i	1.02598	−	0.659653i
$310$		0			0
$311$	−16.4715	+	28.5295i	−0.934014	+	1.61776i	−0.157630	+	0.987498i	$0.550385\pi$
$311$	−16.4715	+	28.5295i	−0.934014	+	1.61776i	−0.776384	+	0.630261i	$0.782948\pi$
$312$		0			0
$313$	15.6844	+	27.1663i	0.886537	+	1.53553i	0.843941	+	0.536435i	$0.180229\pi$
$313$	15.6844	+	27.1663i	0.886537	+	1.53553i	0.0425960	+	0.999092i	$0.486437\pi$
$314$		0			0
$315$	−4.76826	−	6.69037i	−0.268661	−	0.376960i
$316$		0			0
$317$	−15.1181	+	8.72843i	−0.849117	+	0.490238i	−0.860353	−	0.509699i	$-0.829757\pi$
$317$	−15.1181	+	8.72843i	−0.849117	+	0.490238i	0.0112361	+	0.999937i	$0.496423\pi$
$318$		0			0
$319$	−8.86596	−	5.11876i	−0.496398	−	0.286596i
$320$		0			0
$321$	9.33567	−	18.1177i	0.521066	−	1.01123i
$322$		0			0
$323$	2.06424			0.114858
$324$		0			0
$325$	−3.27773			−0.181815
$326$		0			0
$327$	13.8818	−	26.9403i	0.767666	−	1.48980i
$328$		0			0
$329$	17.3980	+	10.0447i	0.959182	+	0.553784i
$330$		0			0
$331$	−17.8042	+	10.2793i	−0.978609	+	0.565000i	−0.901850	−	0.432050i	$-0.857790\pi$
$331$	−17.8042	+	10.2793i	−0.978609	+	0.565000i	−0.0767588	+	0.997050i	$0.524457\pi$
$332$		0			0
$333$	−4.91132	−	6.89109i	−0.269139	−	0.377629i
$334$		0			0
$335$	2.94582	+	5.10230i	0.160947	+	0.278769i
$336$		0			0
$337$	11.0494	−	19.1381i	0.601897	−	1.04252i	−0.390636	−	0.920545i	$-0.627745\pi$
$337$	11.0494	−	19.1381i	0.601897	−	1.04252i	0.992534	−	0.121972i	$-0.0389217\pi$
$338$		0			0
$339$	−0.968516	+	0.622704i	−0.0526026	+	0.0338206i
$340$		0			0
$341$			44.3372i			2.40099i
$342$		0			0
$343$			17.8014i			0.961187i
$344$		0			0
$345$	−0.00593440	−	0.124051i	−0.000319497	−	0.00667870i
$346$		0			0
$347$	15.7942	−	27.3563i	0.847876	−	1.46857i	−0.0352231	−	0.999379i	$-0.511214\pi$
$347$	15.7942	−	27.3563i	0.847876	−	1.46857i	0.883100	−	0.469186i	$-0.155452\pi$
$348$		0			0
$349$	−4.73817	−	8.20675i	−0.253628	−	0.439297i	0.710894	−	0.703299i	$-0.248291\pi$
$349$	−4.73817	−	8.20675i	−0.253628	−	0.439297i	−0.964522	+	0.264002i	$0.914957\pi$
$350$		0			0
$351$	−6.32041	+	15.8154i	−0.337359	+	0.844163i
$352$		0			0
$353$	16.5269	−	9.54183i	0.879640	−	0.507861i	0.00910055	−	0.999959i	$-0.497103\pi$
$353$	16.5269	−	9.54183i	0.879640	−	0.507861i	0.870540	+	0.492098i	$0.163770\pi$
$354$		0			0
$355$	−10.2786	−	5.93434i	−0.545531	−	0.314962i
$356$		0			0
$357$	13.4363	−	0.642767i	0.711122	−	0.0340189i
$358$		0			0
$359$	−12.4556			−0.657380			−0.328690	−	0.944438i	$-0.606607\pi$
$359$	−12.4556			−0.657380			−0.328690	+	0.944438i	$0.606607\pi$
$360$		0			0
$361$	18.4702			0.972114
$362$		0			0
$363$	−6.71369	−	10.4421i	−0.352377	−	0.548066i
$364$		0			0
$365$	9.58184	+	5.53208i	0.501537	+	0.289562i
$366$		0			0
$367$	22.3268	−	12.8904i	1.16545	−	0.672872i	0.212845	−	0.977086i	$-0.431727\pi$
$367$	22.3268	−	12.8904i	1.16545	−	0.672872i	0.952604	+	0.304213i	$0.0983936\pi$
$368$		0			0
$369$	1.30085	+	13.5653i	0.0677197	+	0.706179i
$370$		0			0
$371$	11.7114	+	20.2848i	0.608026	+	1.05313i
$372$		0			0
$373$	−9.85981	+	17.0777i	−0.510521	+	0.884249i	0.489404	+	0.872057i	$0.337214\pi$
$373$	−9.85981	+	17.0777i	−0.510521	+	0.884249i	−0.999926	+	0.0121921i	$0.996119\pi$
$374$		0			0
$375$	−1.53967	−	0.793361i	−0.0795081	−	0.0409690i
$376$		0			0
$377$		−	7.87267i		−	0.405463i
$378$		0			0
$379$			7.31162i			0.375573i	0.982210	+	0.187786i	$0.0601312\pi$
$379$			7.31162i			0.375573i	−0.982210	+	0.187786i	$0.939869\pi$
$380$		0			0
$381$	−8.17344	−	4.21161i	−0.418738	−	0.215767i
$382$		0			0
$383$	10.7945	−	18.6966i	0.551573	−	0.955352i	−0.446588	−	0.894740i	$-0.647361\pi$
$383$	10.7945	−	18.6966i	0.551573	−	0.955352i	0.998161	−	0.0606129i	$-0.0193055\pi$
$384$		0			0
$385$	5.83630	+	10.1088i	0.297445	+	0.515190i
$386$		0			0
$387$	−16.7576	−	7.64478i	−0.851839	−	0.388606i
$388$		0			0
$389$	−10.7396	+	6.20054i	−0.544522	+	0.314380i	−0.746909	−	0.664926i	$-0.768463\pi$
$389$	−10.7396	+	6.20054i	−0.544522	+	0.314380i	0.202388	+	0.979305i	$0.435130\pi$
$390$		0			0
$391$	0.176100	+	0.101671i	0.00890577	+	0.00514175i
$392$		0			0
$393$	0.107376	+	0.167007i	0.00541642	+	0.00842438i
$394$		0			0
$395$	−7.11243			−0.357865
$396$		0			0
$397$	1.97192			0.0989677			0.0494838	−	0.998775i	$-0.484242\pi$
$397$	1.97192			0.0989677			0.0494838	+	0.998775i	$0.484242\pi$
$398$		0			0
$399$	−3.44870	+	0.164980i	−0.172651	+	0.00825932i
$400$		0			0
$401$	−21.6829	−	12.5186i	−1.08279	−	0.625150i	−0.151143	−	0.988512i	$-0.548295\pi$
$401$	−21.6829	−	12.5186i	−1.08279	−	0.625150i	−0.931648	+	0.363362i	$0.881629\pi$
$402$		0			0
$403$	−29.5274	+	17.0477i	−1.47087	+	0.849205i
$404$		0			0
$405$	−6.79698	+	5.89924i	−0.337745	+	0.293136i
$406$		0			0
$407$	6.01139	+	10.4120i	0.297974	+	0.516105i
$408$		0			0
$409$	14.2643	−	24.7064i	0.705322	−	1.22165i	−0.261253	−	0.965270i	$-0.584136\pi$
$409$	14.2643	−	24.7064i	0.705322	−	1.22165i	0.966575	−	0.256384i	$-0.0825310\pi$
$410$		0			0
$411$	1.23004	+	25.7125i	0.0606736	+	1.26831i
$412$		0			0
$413$			0.698882i			0.0343897i
$414$		0			0
$415$			14.9323i			0.732998i
$416$		0			0
$417$	−23.1296	+	14.8711i	−1.13266	+	0.728239i
$418$		0			0
$419$	−1.58528	+	2.74578i	−0.0774458	+	0.134140i	−0.902147	−	0.431428i	$-0.858010\pi$
$419$	−1.58528	+	2.74578i	−0.0774458	+	0.134140i	0.824701	+	0.565568i	$0.191343\pi$
$420$		0			0
$421$	−5.28311	−	9.15062i	−0.257483	−	0.445974i	0.708084	−	0.706128i	$-0.249560\pi$
$421$	−5.28311	−	9.15062i	−0.257483	−	0.445974i	−0.965567	+	0.260155i	$0.916226\pi$
$422$		0			0
$423$	9.13409	−	20.0223i	0.444115	−	0.973516i
$424$		0			0
$425$	2.45597	−	1.41795i	0.119132	−	0.0687809i
$426$		0			0
$427$	−24.7091	−	14.2658i	−1.19576	−	0.690370i
$428$		0			0
$429$	11.0838	−	21.5102i	0.535131	−	1.03852i
$430$		0			0
$431$	18.4311			0.887796			0.443898	−	0.896077i	$-0.353595\pi$
$431$	18.4311			0.887796			0.443898	+	0.896077i	$0.353595\pi$
$432$		0			0
$433$	−19.9114			−0.956880			−0.478440	−	0.878120i	$-0.658798\pi$
$433$	−19.9114			−0.956880			−0.478440	+	0.878120i	$0.658798\pi$
$434$		0			0
$435$	1.90555	−	3.69809i	0.0913642	−	0.177310i
$436$		0			0
$437$	−0.0451998	−	0.0260961i	−0.00216220	−	0.00124835i
$438$		0			0
$439$	19.5238	−	11.2721i	0.931819	−	0.537986i	0.0444328	−	0.999012i	$-0.485852\pi$
$439$	19.5238	−	11.2721i	0.931819	−	0.537986i	0.887387	+	0.461026i	$0.152519\pi$
$440$		0			0
$441$	−1.49227	+	0.143103i	−0.0710606	+	0.00681442i
$442$		0			0
$443$	8.68130	+	15.0365i	0.412461	+	0.714404i	0.995158	−	0.0982858i	$-0.0313359\pi$
$443$	8.68130	+	15.0365i	0.412461	+	0.714404i	−0.582697	+	0.812689i	$0.698003\pi$
$444$		0			0
$445$	−6.61756	+	11.4620i	−0.313703	+	0.543349i
$446$		0			0
$447$	−30.9508	+	19.8997i	−1.46392	+	0.941224i
$448$		0			0
$449$		−	39.0523i		−	1.84299i	−0.388390	−	0.921495i	$-0.626969\pi$
$449$		−	39.0523i		−	1.84299i	0.388390	−	0.921495i	$-0.373031\pi$
$450$		0			0
$451$		−	19.3615i		−	0.911699i
$452$		0			0
$453$	1.07231	+	22.4153i	0.0503814	+	1.05316i
$454$		0			0
$455$	−4.48812	+	7.77366i	−0.210406	+	0.364435i
$456$		0			0
$457$	−8.87760	−	15.3764i	−0.415276	−	0.719280i	0.580181	−	0.814488i	$-0.302982\pi$
$457$	−8.87760	−	15.3764i	−0.415276	−	0.719280i	−0.995457	+	0.0952077i	$0.969648\pi$
$458$		0			0
$459$	−2.10596	−	14.5845i	−0.0982978	−	0.680748i
$460$		0			0
$461$	−20.0721	+	11.5886i	−0.934852	+	0.539737i	−0.888343	−	0.459181i	$-0.848143\pi$
$461$	−20.0721	+	11.5886i	−0.934852	+	0.539737i	−0.0465093	+	0.998918i	$0.514810\pi$
$462$		0			0
$463$	−3.08534	−	1.78132i	−0.143388	−	0.0827850i	0.426590	−	0.904445i	$-0.359715\pi$
$463$	−3.08534	−	1.78132i	−0.143388	−	0.0827850i	−0.569978	+	0.821660i	$0.693048\pi$
$464$		0			0
$465$	−17.9965	+	0.860919i	−0.834566	+	0.0399242i
$466$		0			0
$467$	−29.7483			−1.37659			−0.688294	−	0.725432i	$-0.741640\pi$
$467$	−29.7483			−1.37659			−0.688294	+	0.725432i	$0.741640\pi$
$468$		0			0
$469$	16.1346			0.745026
$470$		0			0
$471$	7.98843	+	12.4247i	0.368087	+	0.572501i
$472$		0			0
$473$	22.6632	+	13.0846i	1.04206	+	0.601631i
$474$		0			0
$475$	−0.630376	+	0.363948i	−0.0289236	+	0.0166991i
$476$		0			0
$477$	20.8951	−	14.8921i	0.956722	−	0.681861i
$478$		0			0
$479$	−8.36836	−	14.4944i	−0.382360	−	0.662267i	0.609039	−	0.793140i	$-0.291555\pi$
$479$	−8.36836	−	14.4944i	−0.382360	−	0.662267i	−0.991399	+	0.130873i	$0.958222\pi$
$480$		0			0
$481$	−4.62277	+	8.00688i	−0.210780	+	0.365082i
$482$		0			0
$483$	−0.302333	−	0.155786i	−0.0137566	−	0.00708853i
$484$		0			0
$485$		−	9.50535i		−	0.431616i
$486$		0			0
$487$			8.75583i			0.396765i	0.980125	+	0.198382i	$0.0635688\pi$
$487$			8.75583i			0.396765i	−0.980125	+	0.198382i	$0.936431\pi$
$488$		0			0
$489$	17.9939	+	9.27191i	0.813713	+	0.419290i
$490$		0			0
$491$	17.2099	−	29.8083i	0.776670	−	1.34523i	−0.157181	−	0.987570i	$-0.550241\pi$
$491$	17.2099	−	29.8083i	0.776670	−	1.34523i	0.933851	−	0.357662i	$-0.116426\pi$
$492$		0			0
$493$	3.40574	+	5.89892i	0.153387	+	0.265674i
$494$		0			0
$495$	10.4129	−	7.42135i	0.468026	−	0.333565i
$496$		0			0
$497$	−28.1485	+	16.2516i	−1.26263	+	0.728982i
$498$		0			0
$499$	−10.4214	−	6.01678i	−0.466524	−	0.269348i	0.248259	−	0.968694i	$-0.420141\pi$
$499$	−10.4214	−	6.01678i	−0.466524	−	0.269348i	−0.714784	+	0.699346i	$0.753475\pi$
$500$		0			0
$501$	−2.49618	−	3.88241i	−0.111521	−	0.173453i
$502$		0			0
$503$	1.04758			0.0467092			0.0233546	−	0.999727i	$-0.492565\pi$
$503$	1.04758			0.0467092			0.0233546	+	0.999727i	$0.492565\pi$
$504$		0			0
$505$	−10.1062			−0.449721
$506$		0			0
$507$	−3.90394	+	0.186758i	−0.173380	+	0.00829420i
$508$		0			0
$509$	10.1932	+	5.88503i	0.451805	+	0.260850i	0.708592	−	0.705618i	$-0.249331\pi$
$509$	10.1932	+	5.88503i	0.451805	+	0.260850i	−0.256787	+	0.966468i	$0.582664\pi$
$510$		0			0
$511$	26.2404	−	15.1499i	1.16081	−	0.670193i
$512$		0			0
$513$	0.540539	+	3.74343i	0.0238654	+	0.165277i
$514$		0			0
$515$	−6.18955	−	10.7206i	−0.272744	−	0.472406i
$516$		0			0
$517$	−15.6337	+	27.0783i	−0.687568	+	1.19090i
$518$		0			0
$519$	1.15930	+	24.2336i	0.0508874	+	1.06374i
$520$		0			0
$521$		−	34.5556i		−	1.51391i	−0.653469	−	0.756953i	$-0.726687\pi$
$521$		−	34.5556i		−	1.51391i	0.653469	−	0.756953i	$-0.273313\pi$
$522$		0			0
$523$			0.568961i			0.0248789i	0.999923	+	0.0124395i	$0.00395971\pi$
$523$			0.568961i			0.0248789i	−0.999923	+	0.0124395i	$0.996040\pi$
$524$		0			0
$525$	−3.98982	+	2.56524i	−0.174130	+	0.111956i
$526$		0			0
$527$	14.7498	−	25.5473i	0.642510	−	1.11286i
$528$		0			0
$529$	11.4974	+	19.9141i	0.499888	+	0.865832i
$530$		0			0
$531$	0.762106	−	0.0730829i	0.0330726	−	0.00317153i
$532$		0			0
$533$	12.8943	−	7.44453i	0.558514	−	0.322458i
$534$		0			0
$535$	−10.1907	−	5.88362i	−0.440584	−	0.254371i
$536$		0			0
$537$	−3.50045	+	6.79330i	−0.151056	+	0.293153i
$538$		0			0
$539$	2.12990			0.0917414
$540$		0			0
$541$	−33.2571			−1.42983			−0.714917	−	0.699209i	$-0.753536\pi$
$541$	−33.2571			−1.42983			−0.714917	+	0.699209i	$0.753536\pi$
$542$		0			0
$543$	11.4374	−	22.1965i	0.490827	−	0.952545i
$544$		0			0
$545$	−15.1533	−	8.74874i	−0.649094	−	0.374755i
$546$		0			0
$547$	−23.2529	+	13.4251i	−0.994221	+	0.574014i	−0.906533	−	0.422134i	$-0.861281\pi$
$547$	−23.2529	+	13.4251i	−0.994221	+	0.574014i	−0.0876877	+	0.996148i	$0.527948\pi$
$548$		0			0
$549$	−12.9725	+	28.4362i	−0.553652	+	1.21363i
$550$		0			0
$551$	−0.874156	−	1.51408i	−0.0372403	−	0.0645021i
$552$		0			0
$553$	−9.73890	+	16.8683i	−0.414140	+	0.717312i
$554$		0			0
$555$	−4.10952	+	2.64220i	−0.174439	+	0.112155i
$556$		0			0
$557$		−	7.11788i		−	0.301594i	−0.988565	−	0.150797i	$-0.951816\pi$
$557$		−	7.11788i		−	0.301594i	0.988565	−	0.150797i	$-0.0481840\pi$
$558$		0			0
$559$			20.1242i			0.851163i
$560$		0			0
$561$	1.00041	+	20.9123i	0.0422372	+	0.882917i
$562$		0			0
$563$	−8.15052	+	14.1171i	−0.343503	+	0.594965i	−0.985081	−	0.172093i	$-0.944947\pi$
$563$	−8.15052	+	14.1171i	−0.343503	+	0.594965i	0.641577	+	0.767058i	$0.278280\pi$
$564$		0			0
$565$	0.332388	+	0.575714i	0.0139837	+	0.0242205i
$566$		0			0
$567$	4.68403	+	24.1979i	0.196711	+	1.01621i
$568$		0			0
$569$	3.58511	−	2.06987i	0.150296	−	0.0867733i	−0.422966	−	0.906145i	$-0.639011\pi$
$569$	3.58511	−	2.06987i	0.150296	−	0.0867733i	0.573262	+	0.819372i	$0.305678\pi$
$570$		0			0
$571$	26.5373	+	15.3213i	1.11055	+	0.641177i	0.938972	−	0.343994i	$-0.111780\pi$
$571$	26.5373	+	15.3213i	1.11055	+	0.641177i	0.171579	+	0.985170i	$0.445113\pi$
$572$		0			0
$573$	1.40346	−	0.0671390i	0.0586303	−	0.00280477i
$574$		0			0
$575$	−0.0717029			−0.00299022
$576$		0			0
$577$	19.5268			0.812910			0.406455	−	0.913671i	$-0.366765\pi$
$577$	19.5268			0.812910			0.406455	+	0.913671i	$0.366765\pi$
$578$		0			0
$579$	20.2756	+	31.5355i	0.842625	+	1.31057i
$580$		0			0
$581$	35.4144	+	20.4465i	1.46924	+	0.848263i
$582$		0			0
$583$	−31.5713	+	18.2277i	−1.30755	+	0.754915i
$584$		0			0
$585$	8.94622	+	4.08124i	0.369881	+	0.168738i
$586$		0			0
$587$	−18.7207	−	32.4253i	−0.772687	−	1.33833i	−0.936085	−	0.351773i	$-0.885579\pi$
$587$	−18.7207	−	32.4253i	−0.772687	−	1.33833i	0.163398	−	0.986560i	$-0.447754\pi$
$588$		0			0
$589$	−3.78584	+	6.55726i	−0.155993	+	0.270187i
$590$		0			0
$591$	−6.53594	−	3.36784i	−0.268853	−	0.138535i
$592$		0			0
$593$		−	35.8725i		−	1.47311i	−0.676379	−	0.736554i	$-0.736452\pi$
$593$		−	35.8725i		−	1.47311i	0.676379	−	0.736554i	$-0.263548\pi$
$594$		0			0
$595$		−	7.76630i		−	0.318387i
$596$		0			0
$597$	20.4631	+	10.5442i	0.837499	+	0.431547i
$598$		0			0
$599$	10.5157	−	18.2137i	0.429660	−	0.744194i	−0.567183	−	0.823592i	$-0.691967\pi$
$599$	10.5157	−	18.2137i	0.429660	−	0.744194i	0.996843	+	0.0793985i	$0.0252999\pi$
$600$		0			0
$601$	−7.61935	−	13.1971i	−0.310800	−	0.538321i	0.667736	−	0.744398i	$-0.267264\pi$
$601$	−7.61935	−	13.1971i	−0.310800	−	0.538321i	−0.978536	+	0.206077i	$0.933930\pi$
$602$		0			0
$603$	−1.68721	−	17.5942i	−0.0687086	−	0.716491i
$604$		0			0
$605$	−6.20706	+	3.58365i	−0.252353	+	0.145696i
$606$		0			0
$607$	14.0022	+	8.08418i	0.568333	+	0.328127i	0.756483	−	0.654013i	$-0.226916\pi$
$607$	14.0022	+	8.08418i	0.568333	+	0.328127i	−0.188151	+	0.982140i	$0.560249\pi$
$608$		0			0
$609$	−6.16138	−	9.58303i	−0.249672	−	0.388324i
$610$		0			0
$611$	−24.0447			−0.972743
$612$		0			0
$613$	3.96866			0.160293			0.0801463	−	0.996783i	$-0.474461\pi$
$613$	3.96866			0.160293			0.0801463	+	0.996783i	$0.474461\pi$
$614$		0			0
$615$	7.85885	−	0.375954i	0.316899	−	0.0151599i
$616$		0			0
$617$	23.4545	+	13.5415i	0.944244	+	0.545160i	0.891288	−	0.453437i	$-0.149802\pi$
$617$	23.4545	+	13.5415i	0.944244	+	0.545160i	0.0529559	+	0.998597i	$0.483136\pi$
$618$		0			0
$619$	12.5767	−	7.26114i	0.505499	−	0.291850i	−0.225483	−	0.974247i	$-0.572396\pi$
$619$	12.5767	−	7.26114i	0.505499	−	0.291850i	0.730981	+	0.682397i	$0.239063\pi$
$620$		0			0
$621$	−0.138264	+	0.345975i	−0.00554835	+	0.0138835i
$622$		0			0
$623$	18.1226	+	31.3892i	0.726066	+	1.25758i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−0.256776	−	5.36758i	−0.0102546	−	0.214360i
$628$		0			0
$629$		−	7.99930i		−	0.318953i
$630$		0			0
$631$			38.2960i			1.52454i	0.647260	+	0.762270i	$0.275915\pi$
$631$			38.2960i			1.52454i	−0.647260	+	0.762270i	$0.724085\pi$
$632$		0			0
$633$	−29.7798	+	19.1468i	−1.18364	+	0.761017i
$634$		0			0
$635$	−2.65429	+	4.59736i	−0.105332	+	0.182441i
$636$		0			0
$637$	0.818949	+	1.41846i	0.0324480	+	0.0562015i
$638$		0			0
$639$	20.6653	+	28.9955i	0.817505	+	1.14704i
$640$		0			0
$641$	−40.8259	+	23.5708i	−1.61253	+	0.930992i	−0.623743	+	0.781629i	$0.714389\pi$
$641$	−40.8259	+	23.5708i	−1.61253	+	0.930992i	−0.988782	+	0.149363i	$0.952278\pi$
$642$		0			0
$643$	−7.57122	−	4.37125i	−0.298580	−	0.172385i	0.343225	−	0.939253i	$-0.388481\pi$
$643$	−7.57122	−	4.37125i	−0.298580	−	0.172385i	−0.641805	+	0.766868i	$0.721814\pi$
$644$		0			0
$645$	−4.87098	+	9.45308i	−0.191795	+	0.372214i
$646$		0			0
$647$	22.4033			0.880764			0.440382	−	0.897811i	$-0.354843\pi$
$647$	22.4033			0.880764			0.440382	+	0.897811i	$0.354843\pi$
$648$		0			0
$649$	−1.08774			−0.0426977
$650$		0			0
$651$	−22.6004	+	43.8603i	−0.885778	+	1.71902i
$652$		0			0
$653$	−5.61373	−	3.24109i	−0.219682	−	0.126834i	0.386121	−	0.922448i	$-0.373815\pi$
$653$	−5.61373	−	3.24109i	−0.219682	−	0.126834i	−0.605803	+	0.795615i	$0.707148\pi$
$654$		0			0
$655$	0.0992736	−	0.0573156i	0.00387894	−	0.00223951i
$656$		0			0
$657$	−19.2644	−	27.0300i	−0.751578	−	1.05454i
$658$		0			0
$659$	12.8690	+	22.2897i	0.501305	+	0.868285i	0.999999	+	0.00150700i	$0.000479695\pi$
$659$	12.8690	+	22.2897i	0.501305	+	0.868285i	−0.498694	+	0.866778i	$0.666187\pi$
$660$		0			0
$661$	7.70838	−	13.3513i	0.299821	−	0.519305i	−0.676274	−	0.736650i	$-0.736406\pi$
$661$	7.70838	−	13.3513i	0.299821	−	0.519305i	0.976095	+	0.217345i	$0.0697397\pi$
$662$		0			0
$663$	−13.5424	+	8.70704i	−0.525943	+	0.338153i
$664$		0			0
$665$			1.99339i			0.0773002i
$666$		0			0
$667$		−	0.172221i		−	0.00666843i
$668$		0			0
$669$	−0.629495	−	13.1588i	−0.0243377	−	0.508750i
$670$		0			0
$671$	22.2034	−	38.4574i	0.857152	−	1.48463i
$672$		0			0
$673$	3.51337	+	6.08534i	0.135430	+	0.234572i	0.925762	−	0.378107i	$-0.123425\pi$
$673$	3.51337	+	6.08534i	0.135430	+	0.234572i	−0.790331	+	0.612680i	$0.790092\pi$
$674$		0			0
$675$	3.21452	+	4.08251i	0.123727	+	0.157136i
$676$		0			0
$677$	13.0115	−	7.51222i	0.500074	−	0.288718i	−0.228670	−	0.973504i	$-0.573438\pi$
$677$	13.0115	−	7.51222i	0.500074	−	0.288718i	0.728744	+	0.684786i	$0.240104\pi$
$678$		0			0
$679$	−22.5435	−	13.0155i	−0.865139	−	0.499488i
$680$		0			0
$681$	34.8085	−	1.66518i	1.33386	−	0.0638097i
$682$		0			0
$683$	30.7865			1.17801			0.589007	−	0.808128i	$-0.299519\pi$
$683$	30.7865			1.17801			0.589007	+	0.808128i	$0.299519\pi$
$684$		0			0
$685$	14.8621			0.567853
$686$		0			0
$687$	21.0915	+	32.8044i	0.804689	+	1.25157i
$688$		0			0
$689$	−24.2784	−	14.0172i	−0.924934	−	0.534011i
$690$		0			0
$691$	15.3173	−	8.84344i	0.582697	−	0.336420i	−0.179508	−	0.983757i	$-0.557450\pi$
$691$	15.3173	−	8.84344i	0.582697	−	0.336420i	0.762204	+	0.647336i	$0.224117\pi$
$692$		0			0
$693$	−3.34273	−	34.8579i	−0.126980	−	1.32414i
$694$		0			0
$695$	7.93791	+	13.7489i	0.301102	+	0.521524i
$696$		0			0
$697$	−6.44105	+	11.1562i	−0.243972	+	0.422572i
$698$		0			0
$699$	42.8858	+	22.0982i	1.62209	+	0.835832i
$700$		0			0
$701$			14.0858i			0.532013i	0.963971	+	0.266007i	$0.0857043\pi$
$701$			14.0858i			0.532013i	−0.963971	+	0.266007i	$0.914296\pi$
$702$		0			0
$703$			2.05319i			0.0774375i
$704$		0			0
$705$	−11.2947	−	5.81992i	−0.425382	−	0.219191i
$706$		0			0
$707$	−13.8382	+	23.9685i	−0.520440	+	0.901429i
$708$		0			0
$709$	22.6228	+	39.1838i	0.849616	+	1.47158i	0.881551	+	0.472088i	$0.156500\pi$
$709$	22.6228	+	39.1838i	0.849616	+	1.47158i	−0.0319355	+	0.999490i	$0.510167\pi$
$710$		0			0
$711$	19.4127	+	8.85599i	0.728031	+	0.332125i
$712$		0			0
$713$	−0.645937	+	0.372932i	−0.0241905	+	0.0139664i
$714$		0			0
$715$	−12.0990	−	6.98534i	−0.452476	−	0.261237i
$716$		0			0
$717$	−4.78012	−	7.43471i	−0.178517	−	0.277654i
$718$		0			0
$719$	−15.9218			−0.593783			−0.296891	−	0.954911i	$-0.595950\pi$
$719$	−15.9218			−0.593783			−0.296891	+	0.954911i	$0.595950\pi$
$720$		0			0
$721$	−33.9009			−1.26253
$722$		0			0
$723$	27.5464	−	1.31777i	1.02446	−	0.0490085i
$724$		0			0
$725$	−2.08008	−	1.20094i	−0.0772523	−	0.0446016i
$726$		0			0
$727$	39.2050	−	22.6350i	1.45403	−	0.839487i	0.455327	−	0.890324i	$-0.349522\pi$
$727$	39.2050	−	22.6350i	1.45403	−	0.839487i	0.998707	+	0.0508376i	$0.0161891\pi$
$728$		0			0
$729$	25.8971	−	7.63816i	0.959151	−	0.282895i
$730$		0			0
$731$	−8.70579	−	15.0789i	−0.321995	−	0.557712i
$732$		0			0
$733$	−19.0004	+	32.9096i	−0.701795	+	1.21555i	0.266040	+	0.963962i	$0.414285\pi$
$733$	−19.0004	+	32.9096i	−0.701795	+	1.21555i	−0.967836	+	0.251583i	$0.919049\pi$
$734$		0			0
$735$	0.0413575	+	0.864527i	0.00152549	+	0.0318886i
$736$		0			0
$737$			25.1120i			0.925012i
$738$		0			0
$739$			4.23897i			0.155933i	0.996956	+	0.0779664i	$0.0248427\pi$
$739$			4.23897i			0.155933i	−0.996956	+	0.0779664i	$0.975157\pi$
$740$		0			0
$741$	3.47594	−	2.23485i	0.127692	−	0.0820991i
$742$		0			0
$743$	11.0702	−	19.1742i	0.406127	−	0.703433i	−0.588325	−	0.808625i	$-0.700212\pi$
$743$	11.0702	−	19.1742i	0.406127	−	0.703433i	0.994452	+	0.105192i	$0.0335457\pi$
$744$		0			0
$745$	10.6221	+	18.3980i	0.389164	+	0.674052i
$746$		0			0
$747$	18.5928	−	40.7562i	0.680277	−	1.49119i
$748$		0			0
$749$	−27.9079	+	16.1127i	−1.01973	+	0.588743i
$750$		0			0
$751$	14.1963	+	8.19623i	0.518030	+	0.299085i	0.736128	−	0.676842i	$-0.236652\pi$
$751$	14.1963	+	8.19623i	0.518030	+	0.299085i	−0.218098	+	0.975927i	$0.569985\pi$
$752$		0			0
$753$	16.2697	−	31.5745i	0.592901	−	1.15064i
$754$		0			0
$755$	12.9563			0.471526
$756$		0			0
$757$	−38.7992			−1.41018			−0.705090	−	0.709118i	$-0.749094\pi$
$757$	−38.7992			−1.41018			−0.705090	+	0.709118i	$0.749094\pi$
$758$		0			0
$759$	0.242467	−	0.470554i	0.00880100	−	0.0170800i
$760$		0			0
$761$	−17.2372	−	9.95189i	−0.624847	−	0.360756i	0.153906	−	0.988085i	$-0.450815\pi$
$761$	−17.2372	−	9.95189i	−0.624847	−	0.360756i	−0.778754	+	0.627330i	$0.784148\pi$
$762$		0			0
$763$	−41.4981	+	23.9589i	−1.50233	+	0.867372i
$764$		0			0
$765$	−8.46887	+	0.812131i	−0.306193	+	0.0293627i
$766$		0			0
$767$	−0.418239	−	0.724411i	−0.0151017	−	0.0261570i
$768$		0			0
$769$	12.3910	−	21.4618i	0.446830	−	0.773932i	−0.551348	−	0.834276i	$-0.685886\pi$
$769$	12.3910	−	21.4618i	0.446830	−	0.773932i	0.998178	+	0.0603432i	$0.0192195\pi$
$770$		0			0
$771$	−18.9971	+	12.2141i	−0.684164	+	0.439881i
$772$		0			0
$773$		−	22.1378i		−	0.796240i	−0.917333	−	0.398120i	$-0.869663\pi$
$773$		−	22.1378i		−	0.796240i	0.917333	−	0.398120i	$-0.130337\pi$
$774$		0			0
$775$			10.4021i			0.373656i
$776$		0			0
$777$	0.639325	+	13.3643i	0.0229357	+	0.479442i
$778$		0			0
$779$	1.65323	−	2.86348i	0.0592332	−	0.102595i
$780$		0			0
$781$	−25.2940	−	43.8105i	−0.905091	−	1.56766i
$782$		0			0
$783$	−9.80565	+	7.72087i	−0.350425	+	0.275921i
$784$		0			0
$785$	7.38561	−	4.26408i	0.263604	−	0.152192i
$786$		0			0
$787$	−21.8042	−	12.5886i	−0.777235	−	0.448737i	0.0582148	−	0.998304i	$-0.481459\pi$
$787$	−21.8042	−	12.5886i	−0.777235	−	0.448737i	−0.835449	+	0.549568i	$0.814793\pi$
$788$		0			0
$789$	−8.52929	+	0.408027i	−0.303651	+	0.0145261i
$790$		0			0
$791$	1.82053			0.0647306
$792$		0			0
$793$	34.1489			1.21266
$794$		0			0
$795$	−8.01167	−	12.4609i	−0.284145	−	0.441942i
$796$		0			0
$797$	−35.2552	−	20.3546i	−1.24880	−	0.720996i	−0.277932	−	0.960601i	$-0.589649\pi$
$797$	−35.2552	−	20.3546i	−1.24880	−	0.720996i	−0.970871	+	0.239604i	$0.922982\pi$
$798$		0			0
$799$	18.0164	−	10.4018i	0.637376	−	0.367989i
$800$		0			0
$801$	32.3337	−	23.0444i	1.14246	−	0.814235i
$802$		0			0
$803$	23.5794	+	40.8408i	0.832101	+	1.44124i
$804$		0			0
$805$	−0.0981814	+	0.170055i	−0.00346044	+	0.00599365i
$806$		0			0
$807$	27.0991	+	13.9636i	0.953934	+	0.491543i
$808$		0			0
$809$			20.1066i			0.706909i	0.935452	+	0.353455i	$0.114993\pi$
$809$			20.1066i			0.706909i	−0.935452	+	0.353455i	$0.885007\pi$
$810$		0			0
$811$		−	16.7556i		−	0.588370i	−0.955749	−	0.294185i	$-0.904952\pi$
$811$		−	16.7556i		−	0.588370i	0.955749	−	0.294185i	$-0.0950481\pi$
$812$		0			0
$813$	15.2622	+	7.86430i	0.535268	+	0.275813i
$814$		0			0
$815$	5.84344	−	10.1211i	0.204687	−	0.354528i
$816$		0			0
$817$	2.23452	+	3.87031i	0.0781761	+	0.135405i
$818$		0			0
$819$	21.9292	−	15.6291i	0.766268	−	0.546123i
$820$		0			0
$821$	−9.10725	+	5.25807i	−0.317845	+	0.183508i	−0.650432	−	0.759565i	$-0.725412\pi$
$821$	−9.10725	+	5.25807i	−0.317845	+	0.183508i	0.332587	+	0.943073i	$0.392079\pi$
$822$		0			0
$823$	−26.6937	−	15.4116i	−0.930483	−	0.537215i	−0.0435187	−	0.999053i	$-0.513857\pi$
$823$	−26.6937	−	15.4116i	−0.930483	−	0.537215i	−0.886964	+	0.461838i	$0.847190\pi$
$824$		0			0
$825$	−3.99256	−	6.20978i	−0.139003	−	0.216197i
$826$		0			0
$827$	3.43690			0.119513			0.0597563	−	0.998213i	$-0.480968\pi$
$827$	3.43690			0.119513			0.0597563	+	0.998213i	$0.480968\pi$
$828$		0			0
$829$	−47.5380			−1.65106			−0.825532	−	0.564355i	$-0.809125\pi$
$829$	−47.5380			−1.65106			−0.825532	+	0.564355i	$0.809125\pi$
$830$		0			0
$831$	19.8108	−	0.947713i	0.687228	−	0.0328758i
$832$		0			0
$833$	−1.22726	−	0.708560i	−0.0425221	−	0.0245502i
$834$		0			0
$835$	−2.30781	+	1.33242i	−0.0798652	+	0.0461102i
$836$		0			0
$837$	50.1915	+	20.0584i	1.73487	+	0.693319i
$838$		0			0
$839$	20.5672	+	35.6234i	0.710058	+	1.22986i	0.964835	+	0.262857i	$0.0846648\pi$
$839$	20.5672	+	35.6234i	0.710058	+	1.22986i	−0.254776	+	0.967000i	$0.582002\pi$
$840$		0			0
$841$	−11.6155	+	20.1186i	−0.400535	+	0.693746i
$842$		0			0
$843$	−1.42349	−	29.7563i	−0.0490276	−	1.02486i
$844$		0			0
$845$			2.25652i			0.0776266i
$846$		0			0
$847$			19.6281i			0.674428i
$848$		0			0
$849$	−30.9785	+	19.9175i	−1.06318	+	0.683568i
$850$		0			0
$851$	−0.101127	+	0.175157i	−0.00346659	+	0.00600430i
$852$		0			0
$853$	−15.9918	−	27.6986i	−0.547548	−	0.948381i	−0.998442	−	0.0558032i	$-0.982228\pi$
$853$	−15.9918	−	27.6986i	−0.547548	−	0.948381i	0.450894	−	0.892578i	$-0.351105\pi$
$854$		0			0
$855$	2.17371	−	0.208451i	0.0743395	−	0.00712886i
$856$		0			0
$857$	−25.1055	+	14.4947i	−0.857589	+	0.495129i	−0.863204	−	0.504855i	$-0.831546\pi$
$857$	−25.1055	+	14.4947i	−0.857589	+	0.495129i	0.00561546	+	0.999984i	$0.498213\pi$
$858$		0			0
$859$	19.5773	+	11.3030i	0.667969	+	0.385652i	0.795307	−	0.606207i	$-0.207310\pi$
$859$	19.5773	+	11.3030i	0.667969	+	0.385652i	−0.127338	+	0.991859i	$0.540643\pi$
$860$		0			0
$861$	9.86932	−	19.1533i	0.336346	−	0.652743i
$862$		0			0
$863$	33.1803			1.12947			0.564735	−	0.825272i	$-0.308978\pi$
$863$	33.1803			1.12947			0.564735	+	0.825272i	$0.308978\pi$
$864$		0			0
$865$	14.0073			0.476263
$866$		0			0
$867$	−7.10663	+	13.7918i	−0.241354	+	0.468393i
$868$		0			0
$869$	−26.2539	−	15.1577i	−0.890602	−	0.514189i
$870$		0			0
$871$	−16.7240	+	9.65558i	−0.566670	+	0.327167i
$872$		0			0
$873$	−11.8355	+	25.9439i	−0.400571	+	0.878067i
$874$		0			0
$875$	1.36928	+	2.37166i	0.0462901	+	0.0801768i
$876$		0			0
$877$	−7.48370	+	12.9621i	−0.252707	+	0.437701i	−0.964270	−	0.264921i	$-0.914654\pi$
$877$	−7.48370	+	12.9621i	−0.252707	+	0.437701i	0.711564	+	0.702622i	$0.247987\pi$
$878$		0			0
$879$	−10.7845	+	6.93384i	−0.363751	+	0.233873i
$880$		0			0
$881$			8.10012i			0.272900i	0.990647	+	0.136450i	$0.0435693\pi$
$881$			8.10012i			0.272900i	−0.990647	+	0.136450i	$0.956431\pi$
$882$		0			0
$883$		−	4.85664i		−	0.163439i	−0.996655	−	0.0817194i	$-0.973959\pi$
$883$		−	4.85664i		−	0.163439i	0.996655	−	0.0817194i	$-0.0260411\pi$
$884$		0			0
$885$	−0.0211213	−	0.441516i	−0.000709986	−	0.0148414i
$886$		0			0
$887$	−5.19427	+	8.99675i	−0.174407	+	0.302081i	−0.939956	−	0.341296i	$-0.889134\pi$
$887$	−5.19427	+	8.99675i	−0.174407	+	0.302081i	0.765549	+	0.643377i	$0.222467\pi$
$888$		0			0
$889$	7.26892	+	12.5901i	0.243792	+	0.422260i
$890$		0			0
$891$	−37.6617	+	7.29025i	−1.26171	+	0.244233i
$892$		0			0
$893$	−4.62430	+	2.66984i	−0.154746	+	0.0893428i
$894$		0			0
$895$	3.82106	+	2.20609i	0.127724	+	0.0737415i
$896$		0			0
$897$	0.406606	−	0.0194513i	0.0135762	−	0.000649461i
$898$		0			0
$899$	−24.9846			−0.833283
$900$		0			0
$901$	24.2555			0.808066
$902$		0			0
$903$	15.7498	+	24.4962i	0.524119	+	0.815183i
$904$		0			0
$905$	−12.4850	−	7.20822i	−0.415016	−	0.239609i
$906$		0			0
$907$	6.46502	−	3.73258i	0.214667	−	0.123938i	−0.388811	−	0.921317i	$-0.627114\pi$
$907$	6.46502	−	3.73258i	0.214667	−	0.123938i	0.603479	+	0.797379i	$0.293781\pi$
$908$		0			0
$909$	27.5839	+	12.5837i	0.914900	+	0.417374i
$910$		0			0
$911$	−12.4178	−	21.5082i	−0.411419	−	0.712598i	0.583626	−	0.812022i	$-0.301633\pi$
$911$	−12.4178	−	21.5082i	−0.411419	−	0.712598i	−0.995045	+	0.0994240i	$0.968300\pi$
$912$		0			0
$913$	−31.8231	+	55.1191i	−1.05319	+	1.82418i
$914$		0			0
$915$	16.0410	+	8.26560i	0.530299	+	0.273252i
$916$		0			0
$917$		−	0.313924i		−	0.0103667i
$918$		0			0
$919$		−	33.8320i		−	1.11601i	−0.829836	−	0.558007i	$-0.811566\pi$
$919$		−	33.8320i		−	1.11601i	0.829836	−	0.558007i	$-0.188434\pi$
$920$		0			0
$921$	43.6954	+	22.5154i	1.43981	+	0.741907i
$922$		0			0
$923$	19.4512	−	33.6904i	0.640242	−	1.10893i
$924$		0			0
$925$	1.41036	+	2.44281i	0.0463723	+	0.0803193i
$926$		0			0
$927$	3.54505	+	36.9677i	0.116435	+	1.21418i
$928$		0			0
$929$	29.6415	−	17.1135i	0.972507	−	0.561477i	0.0725074	−	0.997368i	$-0.476900\pi$
$929$	29.6415	−	17.1135i	0.972507	−	0.561477i	0.900000	+	0.435891i	$0.143567\pi$
$930$		0			0
$931$	0.315003	+	0.181867i	0.0103238	+	0.00596045i
$932$		0			0
$933$	−30.8581	−	47.9948i	−1.01025	−	1.57128i
$934$		0			0
$935$	12.0875			0.395304
$936$		0			0
$937$	−33.6231			−1.09842			−0.549210	−	0.835684i	$-0.685071\pi$
$937$	−33.6231			−1.09842			−0.549210	+	0.835684i	$0.685071\pi$
$938$		0			0
$939$	−54.2705	+	2.59620i	−1.77105	+	0.0847239i
$940$		0			0
$941$	−37.1942	−	21.4741i	−1.21250	−	0.700035i	−0.249194	−	0.968454i	$-0.580166\pi$
$941$	−37.1942	−	21.4741i	−1.21250	−	0.700035i	−0.963302	+	0.268418i	$0.913499\pi$
$942$		0			0
$943$	0.282073	−	0.162855i	0.00918557	−	0.00530329i
$944$		0			0
$945$	14.0839	−	2.03367i	0.458149	−	0.0661552i
$946$		0			0
$947$	10.5617	+	18.2933i	0.343208	+	0.594453i	0.985026	−	0.172403i	$-0.0551531\pi$
$947$	10.5617	+	18.2933i	0.343208	+	0.594453i	−0.641819	+	0.766856i	$0.721820\pi$
$948$		0			0
$949$	−18.1326	+	31.4067i	−0.588610	+	1.01950i
$950$		0			0
$951$	−1.44479	−	30.2016i	−0.0468507	−	0.979355i
$952$		0			0
$953$			23.8906i			0.773893i	0.922102	+	0.386947i	$0.126470\pi$
$953$			23.8906i			0.773893i	−0.922102	+	0.386947i	$0.873530\pi$
$954$		0			0
$955$		−	0.811213i		−	0.0262502i
$956$		0			0
$957$	14.9151	−	9.58961i	0.482137	−	0.309988i
$958$		0			0
$959$	20.3504	−	35.2479i	0.657149	−	1.13822i
$960$		0			0
$961$	38.6023	+	66.8611i	1.24523	+	2.15681i
$962$		0			0
$963$	20.4886	+	28.7477i	0.660237	+	0.926381i
$964$		0			0
$965$	18.7456	−	10.8228i	0.603441	−	0.348397i
$966$		0			0
$967$	−10.0405	−	5.79691i	−0.322882	−	0.186416i	0.329794	−	0.944053i	$-0.393021\pi$
$967$	−10.0405	−	5.79691i	−0.322882	−	0.186416i	−0.652677	+	0.757637i	$0.726354\pi$
$968$		0			0
$969$	−1.63769	+	3.17825i	−0.0526102	+	0.102100i
$970$		0			0
$971$	−32.2992			−1.03653			−0.518266	−	0.855220i	$-0.673422\pi$
$971$	−32.2992			−1.03653			−0.518266	+	0.855220i	$0.673422\pi$
$972$		0			0
$973$	43.4769			1.39380
$974$		0			0
$975$	2.60042	−	5.04661i	0.0832800	−	0.161621i
$976$		0			0
$977$	−1.59483	−	0.920773i	−0.0510230	−	0.0294581i	0.474272	−	0.880379i	$-0.342712\pi$
$977$	−1.59483	−	0.920773i	−0.0510230	−	0.0294581i	−0.525294	+	0.850920i	$0.676045\pi$
$978$		0			0
$979$	−48.8544	+	28.2061i	−1.56139	+	0.901471i
$980$		0			0
$981$	30.4659	+	42.7468i	0.972700	+	1.36480i
$982$		0			0
$983$	18.3261	+	31.7418i	0.584512	+	1.01241i	0.994936	+	0.100510i	$0.0320475\pi$
$983$	18.3261	+	31.7418i	0.584512	+	1.01241i	−0.410424	+	0.911895i	$0.634619\pi$
$984$		0			0
$985$	−2.12252	+	3.67631i	−0.0676290	+	0.117137i
$986$		0			0
$987$	−29.2684	+	18.8180i	−0.931624	+	0.598984i
$988$		0			0
$989$			0.440233i			0.0139986i
$990$		0			0
$991$		−	2.56293i		−	0.0814142i	−0.999171	−	0.0407071i	$-0.987039\pi$
$991$		−	2.56293i		−	0.0814142i	0.999171	−	0.0407071i	$-0.0129611\pi$
$992$		0			0
$993$	−1.70150	−	35.5678i	−0.0539955	−	1.12871i
$994$		0			0
$995$	6.64530	−	11.5100i	0.210670	−	0.364891i
$996$		0			0
$997$	13.5676	+	23.4998i	0.429691	+	0.744246i	0.996846	−	0.0793648i	$-0.0252892\pi$
$997$	13.5676	+	23.4998i	0.429691	+	0.744246i	−0.567155	+	0.823611i	$0.691956\pi$
$998$		0			0
$999$	14.5064	−	2.09468i	0.458963	−	0.0662728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1440.2.bw.a.671.9	yes	48
3.2	odd	2		4320.2.bw.a.1151.5		48
4.3	odd	2		1440.2.bw.b.671.16	yes	48
9.2	odd	6		1440.2.bw.b.191.16	yes	48
9.7	even	3		4320.2.bw.b.4031.5		48
12.11	even	2		4320.2.bw.b.1151.5		48
36.7	odd	6		4320.2.bw.a.4031.5		48
36.11	even	6	inner	1440.2.bw.a.191.9	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1440.2.bw.a.191.9	✓	48	36.11	even	6	inner
1440.2.bw.a.671.9	yes	48	1.1	even	1	trivial
1440.2.bw.b.191.16	yes	48	9.2	odd	6
1440.2.bw.b.671.16	yes	48	4.3	odd	2
4320.2.bw.a.1151.5		48	3.2	odd	2
4320.2.bw.a.4031.5		48	36.7	odd	6
4320.2.bw.b.1151.5		48	12.11	even	2
4320.2.bw.b.4031.5		48	9.7	even	3

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:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.bw (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.793361 + 1.53967i) q^{3} +(0.866025 + 0.500000i) q^{5} +(2.37166 - 1.36928i) q^{7} +(-1.74116 - 2.44302i) q^{9} +O(q^{10})\)	\(q+(-0.793361 + 1.53967i) q^{3} +(0.866025 + 0.500000i) q^{5} +(2.37166 - 1.36928i) q^{7} +(-1.74116 - 2.44302i) q^{9} +(2.13116 + 3.69127i) q^{11} +(-1.63886 + 2.83859i) q^{13} +(-1.45690 + 0.936712i) q^{15} -2.83591i q^{17} +0.727896i q^{19} +(0.226653 + 4.73791i) q^{21} +(-0.0358515 + 0.0620966i) q^{23} +(0.500000 + 0.866025i) q^{25} +(5.14281 - 0.742605i) q^{27} +(-2.08008 + 1.20094i) q^{29} +(9.00852 + 5.20107i) q^{31} +(-7.37411 + 0.352764i) q^{33} +2.73856 q^{35} +2.82072 q^{37} +(-3.07028 - 4.77533i) q^{39} +(-3.93392 - 2.27125i) q^{41} +(5.31712 - 3.06984i) q^{43} +(-0.286374 - 2.98630i) q^{45} +(3.66789 + 6.35297i) q^{47} +(0.249853 - 0.432758i) q^{49} +(4.36636 + 2.24990i) q^{51} +8.55298i q^{53} +4.26231i q^{55} +(-1.12072 - 0.577484i) q^{57} +(-0.127600 + 0.221010i) q^{59} +(-5.20923 - 9.02266i) q^{61} +(-7.47462 - 3.40990i) q^{63} +(-2.83859 + 1.63886i) q^{65} +(5.10230 + 2.94582i) q^{67} +(-0.0671650 - 0.104464i) q^{69} -11.8687 q^{71} +11.0642 q^{73} +(-1.73007 + 0.0827637i) q^{75} +(10.1088 + 5.83630i) q^{77} +(-6.15954 + 3.55621i) q^{79} +(-2.93674 + 8.50738i) q^{81} +(7.46615 + 12.9318i) q^{83} +(1.41795 - 2.45597i) q^{85} +(-0.198788 - 4.15541i) q^{87} +13.2351i q^{89} +8.97624i q^{91} +(-15.1549 + 9.74381i) q^{93} +(-0.363948 + 0.630376i) q^{95} +(-4.75267 - 8.23187i) q^{97} +(5.30719 - 11.6335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{9}+O(q^{10}) \) 48 * q + 4 * q^9	\( 48 q + 4 q^{9} - 8 q^{15} - 4 q^{21} + 24 q^{25} - 24 q^{27} - 12 q^{29} + 20 q^{33} + 24 q^{39} + 36 q^{41} - 8 q^{45} + 24 q^{49} + 80 q^{51} + 20 q^{57} + 24 q^{59} + 40 q^{63} + 72 q^{67} + 36 q^{69} - 24 q^{73} + 48 q^{77} + 72 q^{79} - 64 q^{87} + 16 q^{93} + 12 q^{95} - 12 q^{97} - 40 q^{99}+O(q^{100}) \) 48 * q + 4 * q^9 - 8 * q^15 - 4 * q^21 + 24 * q^25 - 24 * q^27 - 12 * q^29 + 20 * q^33 + 24 * q^39 + 36 * q^41 - 8 * q^45 + 24 * q^49 + 80 * q^51 + 20 * q^57 + 24 * q^59 + 40 * q^63 + 72 * q^67 + 36 * q^69 - 24 * q^73 + 48 * q^77 + 72 * q^79 - 64 * q^87 + 16 * q^93 + 12 * q^95 - 12 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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