LMFDB - Embedded newform 900.3.p.d.401.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(101,900)]

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, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.p (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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 10 x^{14} - 12 x^{13} + 6 x^{12} - 27 x^{11} - 585 x^{10} + 3618 x^{9} + \cdots + 43046721 $ x^16 - 2x^15 + 10x^14 - 12x^13 + 6x^12 - 27x^11 - 585x^10 + 3618x^9 - 12150x^8 + 32562x^7 - 47385x^6 - 19683x^5 + 39366x^4 - 708588x^3 + 5314410x^2 - 9565938*x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{41}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			401.5
Root			$2.94519 - 0.570848i$ of defining polynomial
Character	$\chi$	$=$	900.401
Dual form			900.3.p.d.101.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978225 - 2.83603i) q^{3} +(-2.71262 - 4.69840i) q^{7} +(-7.08615 - 5.54856i) q^{9} +O(q^{10})$	\(q+(0.978225 - 2.83603i) q^{3} +(-2.71262 - 4.69840i) q^{7} +(-7.08615 - 5.54856i) q^{9} +(-8.81872 + 5.09149i) q^{11} +(-2.55295 + 4.42184i) q^{13} +17.4550i q^{17} -17.4980 q^{19} +(-15.9784 + 3.09699i) q^{21} +(16.3083 + 9.41558i) q^{23} +(-22.6677 + 14.6688i) q^{27} +(29.0817 - 16.7903i) q^{29} +(-25.4881 + 44.1467i) q^{31} +(5.81293 + 29.9908i) q^{33} +0.605498 q^{37} +(10.0431 + 11.5658i) q^{39} +(-12.4241 - 7.17303i) q^{41} +(25.4265 + 44.0400i) q^{43} +(-1.96577 + 1.13494i) q^{47} +(9.78337 - 16.9453i) q^{49} +(49.5028 + 17.0749i) q^{51} +18.4881i q^{53} +(-17.1170 + 49.6249i) q^{57} +(-70.8221 - 40.8892i) q^{59} +(4.70398 + 8.14754i) q^{61} +(-6.84729 + 48.3447i) q^{63} +(18.3854 - 31.8445i) q^{67} +(42.6560 - 37.0402i) q^{69} +57.2046i q^{71} -78.9324 q^{73} +(47.8437 + 27.6226i) q^{77} +(-19.1524 - 33.1729i) q^{79} +(19.4270 + 78.6358i) q^{81} +(-66.9661 + 38.6629i) q^{83} +(-19.1694 - 98.9012i) q^{87} -138.264i q^{89} +27.7008 q^{91} +(100.268 + 115.471i) q^{93} +(58.4800 + 101.290i) q^{97} +(90.7412 + 12.8521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + q^{7} + 14 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 + q^7 + 14 * q^9	$ 16 q - 2 q^{3} + q^{7} + 14 q^{9} + 10 q^{13} + 2 q^{19} + q^{21} - 27 q^{23} + 16 q^{27} + 9 q^{29} + 8 q^{31} - 36 q^{33} + 22 q^{37} + 19 q^{39} + 54 q^{41} - 44 q^{43} + 108 q^{47} - 45 q^{49} + 90 q^{51} + 68 q^{57} + 9 q^{59} - 55 q^{61} + 107 q^{63} + 28 q^{67} - 147 q^{69} - 86 q^{73} - 342 q^{77} + 11 q^{79} - 130 q^{81} + 306 q^{83} - 375 q^{87} - 134 q^{91} + 83 q^{93} - 41 q^{97} + 252 q^{99}+O(q^{100}) $ 16 * q - 2 * q^3 + q^7 + 14 * q^9 + 10 * q^13 + 2 * q^19 + q^21 - 27 * q^23 + 16 * q^27 + 9 * q^29 + 8 * q^31 - 36 * q^33 + 22 * q^37 + 19 * q^39 + 54 * q^41 - 44 * q^43 + 108 * q^47 - 45 * q^49 + 90 * q^51 + 68 * q^57 + 9 * q^59 - 55 * q^61 + 107 * q^63 + 28 * q^67 - 147 * q^69 - 86 * q^73 - 342 * q^77 + 11 * q^79 - 130 * q^81 + 306 * q^83 - 375 * q^87 - 134 * q^91 + 83 * q^93 - 41 * q^97 + 252 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$	0.978225	−	2.83603i	0.326075	−	0.945344i
$3$	0.978225	−	2.83603i	0.326075	−	0.945344i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.71262	−	4.69840i	−0.387517	−	0.671200i	0.604598	−	0.796531i	$-0.293334\pi$
$7$	−2.71262	−	4.69840i	−0.387517	−	0.671200i	−0.992115	+	0.125331i	$0.960001\pi$
$8$		0			0
$9$	−7.08615	−	5.54856i	−0.787350	−	0.616506i
$10$		0			0
$11$	−8.81872	+	5.09149i	−0.801702	+	0.462863i	−0.844066	−	0.536239i	$-0.819844\pi$
$11$	−8.81872	+	5.09149i	−0.801702	+	0.462863i	0.0423639	+	0.999102i	$0.486511\pi$
$12$		0			0
$13$	−2.55295	+	4.42184i	−0.196381	+	0.340142i	−0.947352	−	0.320193i	$-0.896252\pi$
$13$	−2.55295	+	4.42184i	−0.196381	+	0.340142i	0.750971	+	0.660335i	$0.229586\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			17.4550i			1.02676i	0.858161	+	0.513381i	$0.171607\pi$
$17$			17.4550i			1.02676i	−0.858161	+	0.513381i	$0.828393\pi$
$18$		0			0
$19$	−17.4980			−0.920947			−0.460474	−	0.887673i	$-0.652320\pi$
$19$	−17.4980			−0.920947			−0.460474	+	0.887673i	$0.652320\pi$
$20$		0			0
$21$	−15.9784	+	3.09699i	−0.760874	+	0.147476i
$22$		0			0
$23$	16.3083	+	9.41558i	0.709055	+	0.409373i	0.810711	−	0.585447i	$-0.199081\pi$
$23$	16.3083	+	9.41558i	0.709055	+	0.409373i	−0.101656	+	0.994820i	$0.532414\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−22.6677	+	14.6688i	−0.839546	+	0.543289i
$28$		0			0
$29$	29.0817	−	16.7903i	1.00282	−	0.578976i	0.0937354	−	0.995597i	$-0.470119\pi$
$29$	29.0817	−	16.7903i	1.00282	−	0.578976i	0.909080	+	0.416621i	$0.136786\pi$
$30$		0			0
$31$	−25.4881	+	44.1467i	−0.822197	+	1.42409i	0.0818455	+	0.996645i	$0.473919\pi$
$31$	−25.4881	+	44.1467i	−0.822197	+	1.42409i	−0.904043	+	0.427442i	$0.859415\pi$
$32$		0			0
$33$	5.81293	+	29.9908i	0.176149	+	0.908812i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.605498			0.0163648			0.00818241	−	0.999967i	$-0.497395\pi$
$37$	0.605498			0.0163648			0.00818241	+	0.999967i	$0.497395\pi$
$38$		0			0
$39$	10.0431	+	11.5658i	0.257516	+	0.296559i
$40$		0			0
$41$	−12.4241	−	7.17303i	−0.303026	−	0.174952i	0.340776	−	0.940145i	$-0.389310\pi$
$41$	−12.4241	−	7.17303i	−0.303026	−	0.174952i	−0.643801	+	0.765193i	$0.722644\pi$
$42$		0			0
$43$	25.4265	+	44.0400i	0.591314	+	1.02419i	0.994056	+	0.108873i	$0.0347241\pi$
$43$	25.4265	+	44.0400i	0.591314	+	1.02419i	−0.402741	+	0.915314i	$0.631943\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.96577	+	1.13494i	−0.0418250	+	0.0241477i	−0.520767	−	0.853699i	$-0.674354\pi$
$47$	−1.96577	+	1.13494i	−0.0418250	+	0.0241477i	0.478942	+	0.877847i	$0.341021\pi$
$48$		0			0
$49$	9.78337	−	16.9453i	0.199661	−	0.345822i
$50$		0			0
$51$	49.5028	+	17.0749i	0.970643	+	0.334802i
$52$		0			0
$53$			18.4881i			0.348832i	0.984672	+	0.174416i	$0.0558038\pi$
$53$			18.4881i			0.348832i	−0.984672	+	0.174416i	$0.944196\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−17.1170	+	49.6249i	−0.300298	+	0.870612i
$58$		0			0
$59$	−70.8221	−	40.8892i	−1.20038	−	0.693037i	−0.239737	−	0.970838i	$-0.577061\pi$
$59$	−70.8221	−	40.8892i	−1.20038	−	0.693037i	−0.960639	+	0.277801i	$0.910394\pi$
$60$		0			0
$61$	4.70398	+	8.14754i	0.0771145	+	0.133566i	0.902004	−	0.431728i	$-0.142096\pi$
$61$	4.70398	+	8.14754i	0.0771145	+	0.133566i	−0.824889	+	0.565294i	$0.808763\pi$
$62$		0			0
$63$	−6.84729	+	48.3447i	−0.108687	+	0.767376i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	18.3854	−	31.8445i	0.274409	−	0.475291i	−0.695577	−	0.718452i	$-0.744851\pi$
$67$	18.3854	−	31.8445i	0.274409	−	0.475291i	0.969986	+	0.243161i	$0.0781844\pi$
$68$		0			0
$69$	42.6560	−	37.0402i	0.618203	−	0.536814i
$70$		0			0
$71$			57.2046i			0.805699i	0.915266	+	0.402849i	$0.131980\pi$
$71$			57.2046i			0.805699i	−0.915266	+	0.402849i	$0.868020\pi$
$72$		0			0
$73$	−78.9324			−1.08127			−0.540633	−	0.841259i	$-0.681815\pi$
$73$	−78.9324			−1.08127			−0.540633	+	0.841259i	$0.681815\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	47.8437	+	27.6226i	0.621347	+	0.358735i
$78$		0			0
$79$	−19.1524	−	33.1729i	−0.242435	−	0.419910i	0.718972	−	0.695039i	$-0.244613\pi$
$79$	−19.1524	−	33.1729i	−0.242435	−	0.419910i	−0.961407	+	0.275129i	$0.911279\pi$
$80$		0			0
$81$	19.4270	+	78.6358i	0.239840	+	0.970812i
$82$		0			0
$83$	−66.9661	+	38.6629i	−0.806821	+	0.465818i	−0.845851	−	0.533420i	$-0.820907\pi$
$83$	−66.9661	+	38.6629i	−0.806821	+	0.465818i	0.0390298	+	0.999238i	$0.487573\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−19.1694	−	98.9012i	−0.220338	−	1.13680i
$88$		0			0
$89$		−	138.264i		−	1.55353i	−0.629790	−	0.776766i	$-0.716859\pi$
$89$		−	138.264i		−	1.55353i	0.629790	−	0.776766i	$-0.283141\pi$
$90$		0			0
$91$	27.7008			0.304404
$92$		0			0
$93$	100.268	+	115.471i	1.07815	+	1.24162i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	58.4800	+	101.290i	0.602887	+	1.04423i	0.992382	+	0.123202i	$0.0393163\pi$
$97$	58.4800	+	101.290i	0.602887	+	1.04423i	−0.389495	+	0.921029i	$0.627350\pi$
$98$		0			0
$99$	90.7412	+	12.8521i	0.916578	+	0.129819i
$100$		0			0
$101$	76.0357	−	43.8993i	0.752829	−	0.434646i	−0.0738861	−	0.997267i	$-0.523540\pi$
$101$	76.0357	−	43.8993i	0.752829	−	0.434646i	0.826715	+	0.562621i	$0.190207\pi$
$102$		0			0
$103$	−94.2134	+	163.182i	−0.914693	+	1.58429i	−0.107343	+	0.994222i	$0.534234\pi$
$103$	−94.2134	+	163.182i	−0.914693	+	1.58429i	−0.807350	+	0.590073i	$0.799099\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			170.277i			1.59137i	0.605711	+	0.795685i	$0.292889\pi$
$107$			170.277i			1.59137i	−0.605711	+	0.795685i	$0.707111\pi$
$108$		0			0
$109$	−79.0188			−0.724943			−0.362471	−	0.931995i	$-0.618067\pi$
$109$	−79.0188			−0.724943			−0.362471	+	0.931995i	$0.618067\pi$
$110$		0			0
$111$	0.592314	−	1.71721i	0.00533616	−	0.0154704i
$112$		0			0
$113$	−42.4903	−	24.5318i	−0.376020	−	0.217095i	0.300065	−	0.953919i	$-0.402992\pi$
$113$	−42.4903	−	24.5318i	−0.376020	−	0.217095i	−0.676085	+	0.736823i	$0.736325\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	42.6254	−	17.1686i	0.364320	−	0.146740i
$118$		0			0
$119$	82.0104	−	47.3487i	0.689163	−	0.397888i
$120$		0			0
$121$	−8.65342	+	14.9882i	−0.0715159	+	0.123869i
$122$		0			0
$123$	−32.4965	+	28.2182i	−0.264199	+	0.229416i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	54.4343			0.428617			0.214308	−	0.976766i	$-0.431250\pi$
$127$	54.4343			0.428617			0.214308	+	0.976766i	$0.431250\pi$
$128$		0			0
$129$	149.772	−	29.0293i	1.16102	−	0.225034i
$130$		0			0
$131$	−5.09750	−	2.94304i	−0.0389122	−	0.0224660i	0.480418	−	0.877040i	$-0.340485\pi$
$131$	−5.09750	−	2.94304i	−0.0389122	−	0.0224660i	−0.519330	+	0.854574i	$0.673818\pi$
$132$		0			0
$133$	47.4654	+	82.2126i	0.356883	+	0.618140i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	27.7627	−	16.0288i	0.202648	−	0.116999i	−0.395242	−	0.918577i	$-0.629339\pi$
$137$	27.7627	−	16.0288i	0.202648	−	0.116999i	0.597890	+	0.801578i	$0.296006\pi$
$138$		0			0
$139$	−122.331	+	211.884i	−0.880080	+	1.52434i	−0.0288281	+	0.999584i	$0.509178\pi$
$139$	−122.331	+	211.884i	−0.880080	+	1.52434i	−0.851251	+	0.524758i	$0.824156\pi$
$140$		0			0
$141$	1.29576	+	6.68522i	0.00918976	+	0.0474129i
$142$		0			0
$143$		−	51.9933i		−	0.363590i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−38.4870	−	44.3223i	−0.261817	−	0.301512i
$148$		0			0
$149$	−142.535	−	82.2928i	−0.956613	−	0.552301i	−0.0614839	−	0.998108i	$-0.519583\pi$
$149$	−142.535	−	82.2928i	−0.956613	−	0.552301i	−0.895129	+	0.445807i	$0.852917\pi$
$150$		0			0
$151$	49.5167	+	85.7655i	0.327925	+	0.567984i	0.982100	−	0.188360i	$-0.0603172\pi$
$151$	49.5167	+	85.7655i	0.327925	+	0.567984i	−0.654175	+	0.756344i	$0.726984\pi$
$152$		0			0
$153$	96.8498	−	123.688i	0.633005	−	0.808421i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	65.5221	−	113.488i	0.417338	−	0.722851i	−0.578332	−	0.815801i	$-0.696296\pi$
$157$	65.5221	−	113.488i	0.417338	−	0.722851i	0.995671	+	0.0929500i	$0.0296297\pi$
$158$		0			0
$159$	52.4329	+	18.0856i	0.329767	+	0.113746i
$160$		0			0
$161$		−	102.164i		−	0.634556i
$162$		0			0
$163$	16.6333			0.102044			0.0510222	−	0.998698i	$-0.483752\pi$
$163$	16.6333			0.102044			0.0510222	+	0.998698i	$0.483752\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−245.936	−	141.991i	−1.47267	−	0.850248i	−0.473145	−	0.880985i	$-0.656881\pi$
$167$	−245.936	−	141.991i	−1.47267	−	0.850248i	−0.999528	+	0.0307367i	$0.990215\pi$
$168$		0			0
$169$	71.4649	+	123.781i	0.422869	+	0.732431i
$170$		0			0
$171$	123.993	+	97.0886i	0.725108	+	0.567770i
$172$		0			0
$173$	182.518	−	105.377i	1.05502	−	0.609115i	0.130969	−	0.991387i	$-0.458191\pi$
$173$	182.518	−	105.377i	1.05502	−	0.609115i	0.924050	+	0.382271i	$0.124858\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−185.243	+	160.855i	−1.04657	+	0.908785i
$178$		0			0
$179$		−	236.272i		−	1.31996i	−0.751285	−	0.659978i	$-0.770566\pi$
$179$		−	236.272i		−	1.31996i	0.751285	−	0.659978i	$-0.229434\pi$
$180$		0			0
$181$	−325.181			−1.79658			−0.898290	−	0.439404i	$-0.855190\pi$
$181$	−325.181			−1.79658			−0.898290	+	0.439404i	$0.855190\pi$
$182$		0			0
$183$	27.7082	−	5.37052i	0.151411	−	0.0293471i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−88.8718	−	153.930i	−0.475250	−	0.823157i
$188$		0			0
$189$	130.409	+	66.7111i	0.689994	+	0.352969i
$190$		0			0
$191$	−96.0546	+	55.4571i	−0.502903	+	0.290351i	−0.729912	−	0.683541i	$-0.760439\pi$
$191$	−96.0546	+	55.4571i	−0.502903	+	0.290351i	0.227008	+	0.973893i	$0.427106\pi$
$192$		0			0
$193$	−64.7547	+	112.158i	−0.335516	+	0.581131i	−0.983584	−	0.180452i	$-0.942244\pi$
$193$	−64.7547	+	112.158i	−0.335516	+	0.581131i	0.648068	+	0.761583i	$0.275577\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			335.209i			1.70157i	0.525515	+	0.850784i	$0.323873\pi$
$197$			335.209i			1.70157i	−0.525515	+	0.850784i	$0.676127\pi$
$198$		0			0
$199$	−341.651			−1.71684			−0.858419	−	0.512950i	$-0.828553\pi$
$199$	−341.651			−1.71684			−0.858419	+	0.512950i	$0.828553\pi$
$200$		0			0
$201$	−72.3269	−	83.2927i	−0.359835	−	0.414392i
$202$		0			0
$203$	−157.775	−	91.0915i	−0.777217	−	0.448726i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−63.3199	−	157.207i	−0.305893	−	0.759456i
$208$		0			0
$209$	154.310	−	89.0909i	0.738325	−	0.426272i
$210$		0			0
$211$	−72.9832	+	126.411i	−0.345892	+	0.599102i	−0.985515	−	0.169586i	$-0.945757\pi$
$211$	−72.9832	+	126.411i	−0.345892	+	0.599102i	0.639623	+	0.768688i	$0.279090\pi$
$212$		0			0
$213$	162.234	+	55.9590i	0.761662	+	0.262718i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	276.558			1.27446
$218$		0			0
$219$	−77.2137	+	223.855i	−0.352574	+	1.02217i
$220$		0			0
$221$	−77.1831	−	44.5617i	−0.349245	−	0.201636i
$222$		0			0
$223$	−170.785	−	295.808i	−0.765851	−	1.32649i	−0.939796	−	0.341737i	$-0.888985\pi$
$223$	−170.785	−	295.808i	−0.765851	−	1.32649i	0.173945	−	0.984755i	$-0.444349\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	71.1813	−	41.0966i	0.313574	−	0.181042i	−0.334951	−	0.942236i	$-0.608720\pi$
$227$	71.1813	−	41.0966i	0.313574	−	0.181042i	0.648525	+	0.761194i	$0.275386\pi$
$228$		0			0
$229$	−153.723	+	266.256i	−0.671280	+	1.16269i	0.306261	+	0.951948i	$0.400922\pi$
$229$	−153.723	+	266.256i	−0.671280	+	1.16269i	−0.977541	+	0.210744i	$0.932411\pi$
$230$		0			0
$231$	125.140	−	108.665i	0.541734	−	0.470412i
$232$		0			0
$233$		−	415.262i		−	1.78224i	−0.453766	−	0.891121i	$-0.649920\pi$
$233$		−	415.262i		−	1.78224i	0.453766	−	0.891121i	$-0.350080\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−112.815	+	21.8662i	−0.476011	+	0.0922623i
$238$		0			0
$239$	−219.813	−	126.909i	−0.919719	−	0.531000i	−0.0361738	−	0.999346i	$-0.511517\pi$
$239$	−219.813	−	126.909i	−0.919719	−	0.531000i	−0.883545	+	0.468345i	$0.844850\pi$
$240$		0			0
$241$	−79.3285	−	137.401i	−0.329164	−	0.570129i	0.653182	−	0.757201i	$-0.273434\pi$
$241$	−79.3285	−	137.401i	−0.329164	−	0.570129i	−0.982346	+	0.187072i	$0.940100\pi$
$242$		0			0
$243$	242.018	+	21.8278i	0.995957	+	0.0898265i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	44.6715	−	77.3734i	0.180856	−	0.313252i
$248$		0			0
$249$	44.1413	+	227.739i	0.177274	+	0.914615i
$250$		0			0
$251$		−	470.630i		−	1.87502i	−0.347961	−	0.937509i	$-0.613126\pi$
$251$		−	470.630i		−	1.87502i	0.347961	−	0.937509i	$-0.386874\pi$
$252$		0			0
$253$	−191.757			−0.757934
$254$		0			0
$255$		0			0
$256$		0			0
$257$	431.909	+	249.363i	1.68058	+	0.970283i	0.961276	+	0.275587i	$0.0888723\pi$
$257$	431.909	+	249.363i	1.68058	+	0.970283i	0.719304	+	0.694696i	$0.244461\pi$
$258$		0			0
$259$	−1.64249	−	2.84487i	−0.00634165	−	0.0109841i
$260$		0			0
$261$	−299.239	−	42.3826i	−1.14651	−	0.162385i
$262$		0			0
$263$	215.375	−	124.347i	0.818915	−	0.472801i	−0.0311270	−	0.999515i	$-0.509910\pi$
$263$	215.375	−	124.347i	0.818915	−	0.472801i	0.850042	+	0.526714i	$0.176576\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−392.122	−	135.254i	−1.46862	−	0.506568i
$268$		0			0
$269$			212.591i			0.790300i	0.918617	+	0.395150i	$0.129307\pi$
$269$			212.591i			0.790300i	−0.918617	+	0.395150i	$0.870693\pi$
$270$		0			0
$271$	150.211			0.554284			0.277142	−	0.960829i	$-0.410613\pi$
$271$	150.211			0.554284			0.277142	+	0.960829i	$0.410613\pi$
$272$		0			0
$273$	27.0976	−	78.5602i	0.0992586	−	0.287766i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−183.153	−	317.231i	−0.661204	−	1.14524i	−0.980300	−	0.197516i	$-0.936713\pi$
$277$	−183.153	−	317.231i	−0.661204	−	1.14524i	0.319096	−	0.947722i	$-0.396621\pi$
$278$		0			0
$279$	425.563	−	171.408i	1.52532	−	0.614365i
$280$		0			0
$281$	−113.933	+	65.7791i	−0.405455	+	0.234089i	−0.688835	−	0.724918i	$-0.741877\pi$
$281$	−113.933	+	65.7791i	−0.405455	+	0.234089i	0.283380	+	0.959008i	$0.408544\pi$
$282$		0			0
$283$	134.661	−	233.240i	0.475834	−	0.824169i	−0.523783	−	0.851852i	$-0.675480\pi$
$283$	134.661	−	233.240i	0.475834	−	0.824169i	0.999617	+	0.0276831i	$0.00881293\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			77.8309i			0.271188i
$288$		0			0
$289$	−15.6756			−0.0542409
$290$		0			0
$291$	344.469	−	66.7664i	1.18374	−	0.229438i
$292$		0			0
$293$	−182.712	−	105.489i	−0.623591	−	0.360030i	0.154675	−	0.987965i	$-0.450567\pi$
$293$	−182.712	−	105.489i	−0.623591	−	0.360030i	−0.778266	+	0.627935i	$0.783900\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	125.214	−	244.773i	0.421597	−	0.824151i
$298$		0			0
$299$	−83.2684	+	48.0750i	−0.278490	+	0.160786i
$300$		0			0
$301$	137.945	−	238.928i	0.458289	−	0.793780i
$302$		0			0
$303$	−50.1196	−	258.583i	−0.165411	−	0.853410i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	44.9444			0.146399			0.0731993	−	0.997317i	$-0.476679\pi$
$307$	44.9444			0.146399			0.0731993	+	0.997317i	$0.476679\pi$
$308$		0			0
$309$	370.628	+	426.821i	1.19944	+	1.38130i
$310$		0			0
$311$	9.48434	+	5.47579i	0.0304963	+	0.0176070i	0.515171	−	0.857088i	$-0.327729\pi$
$311$	9.48434	+	5.47579i	0.0304963	+	0.0176070i	−0.484674	+	0.874695i	$0.661062\pi$
$312$		0			0
$313$	83.8232	+	145.186i	0.267806	+	0.463853i	0.968295	−	0.249810i	$-0.0803681\pi$
$313$	83.8232	+	145.186i	0.267806	+	0.463853i	−0.700489	+	0.713663i	$0.747035\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	204.287	−	117.945i	0.644440	−	0.372068i	−0.141883	−	0.989883i	$-0.545316\pi$
$317$	204.287	−	117.945i	0.644440	−	0.372068i	0.786323	+	0.617816i	$0.211982\pi$
$318$		0			0
$319$	−170.975	+	296.138i	−0.535973	+	0.928332i
$320$		0			0
$321$	482.910	+	166.569i	1.50439	+	0.518906i
$322$		0			0
$323$		−	305.427i		−	0.945594i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−77.2982	+	224.100i	−0.236386	+	0.685320i
$328$		0			0
$329$	10.6648	+	6.15733i	0.0324158	+	0.0187153i
$330$		0			0
$331$	88.5058	+	153.297i	0.267389	+	0.463132i	0.968187	−	0.250228i	$-0.0805057\pi$
$331$	88.5058	+	153.297i	0.267389	+	0.463132i	−0.700798	+	0.713360i	$0.747172\pi$
$332$		0			0
$333$	−4.29065	−	3.35964i	−0.0128848	−	0.0100890i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	161.634	−	279.959i	0.479627	−	0.830738i	−0.520100	−	0.854105i	$-0.674105\pi$
$337$	161.634	−	279.959i	0.479627	−	0.830738i	0.999727	+	0.0233670i	$0.00743863\pi$
$338$		0			0
$339$	−111.138	+	96.5061i	−0.327840	+	0.284679i
$340$		0			0
$341$		−	519.090i		−	1.52226i
$342$		0			0
$343$	−371.991			−1.08452
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−334.543	−	193.149i	−0.964102	−	0.556625i	−0.0666690	−	0.997775i	$-0.521237\pi$
$347$	−334.543	−	193.149i	−0.964102	−	0.556625i	−0.897433	+	0.441151i	$0.854570\pi$
$348$		0			0
$349$	−30.3447	−	52.5585i	−0.0869474	−	0.150597i	0.819272	−	0.573405i	$-0.194378\pi$
$349$	−30.3447	−	52.5585i	−0.0869474	−	0.150597i	−0.906219	+	0.422808i	$0.861045\pi$
$350$		0			0
$351$	−6.99351	−	137.682i	−0.0199245	−	0.392256i
$352$		0			0
$353$	−102.180	+	58.9936i	−0.289462	+	0.167121i	−0.637699	−	0.770286i	$-0.720114\pi$
$353$	−102.180	+	58.9936i	−0.289462	+	0.167121i	0.348237	+	0.937406i	$0.386780\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−54.0578	−	278.902i	−0.151422	−	0.781237i
$358$		0			0
$359$		−	503.014i		−	1.40115i	−0.713577	−	0.700577i	$-0.752926\pi$
$359$		−	503.014i		−	1.40115i	0.713577	−	0.700577i	$-0.247074\pi$
$360$		0			0
$361$	−54.8201			−0.151856
$362$		0			0
$363$	34.0419	+	39.2032i	0.0937794	+	0.107998i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	93.4535	+	161.866i	0.254642	+	0.441052i	0.964798	−	0.262992i	$-0.0847091\pi$
$367$	93.4535	+	161.866i	0.254642	+	0.441052i	−0.710156	+	0.704044i	$0.751376\pi$
$368$		0			0
$369$	48.2388	+	119.765i	0.130728	+	0.324566i
$370$		0			0
$371$	86.8646	−	50.1513i	0.234136	−	0.135179i
$372$		0			0
$373$	−25.7792	+	44.6509i	−0.0691132	+	0.119708i	−0.898511	−	0.438951i	$-0.855350\pi$
$373$	−25.7792	+	44.6509i	−0.0691132	+	0.119708i	0.829398	+	0.558658i	$0.188684\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			171.459i			0.454799i
$378$		0			0
$379$	−52.8882			−0.139547			−0.0697733	−	0.997563i	$-0.522228\pi$
$379$	−52.8882			−0.139547			−0.0697733	+	0.997563i	$0.522228\pi$
$380$		0			0
$381$	53.2490	−	154.377i	0.139761	−	0.405190i
$382$		0			0
$383$	−365.915	−	211.261i	−0.955391	−	0.551595i	−0.0606395	−	0.998160i	$-0.519314\pi$
$383$	−365.915	−	211.261i	−0.955391	−	0.551595i	−0.894751	+	0.446565i	$0.852647\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	64.1824	−	453.155i	0.165846	−	1.17094i
$388$		0			0
$389$	535.036	−	308.903i	1.37541	−	0.794095i	0.383810	−	0.923412i	$-0.374612\pi$
$389$	535.036	−	308.903i	1.37541	−	0.794095i	0.991603	+	0.129317i	$0.0412786\pi$
$390$		0			0
$391$	−164.349	+	284.660i	−0.420329	+	0.728031i
$392$		0			0
$393$	−13.3331	+	11.5777i	−0.0339264	+	0.0294598i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	451.909			1.13831			0.569155	−	0.822230i	$-0.307270\pi$
$397$	451.909			1.13831			0.569155	+	0.822230i	$0.307270\pi$
$398$		0			0
$399$	279.589	−	54.1911i	0.700725	−	0.135817i
$400$		0			0
$401$	644.660	+	372.195i	1.60763	+	0.928167i	0.989898	+	0.141779i	$0.0452823\pi$
$401$	644.660	+	372.195i	1.60763	+	0.928167i	0.617734	+	0.786387i	$0.288051\pi$
$402$		0			0
$403$	−130.140	−	225.409i	−0.322928	−	0.559327i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.33972	+	3.08289i	−0.0131197	+	0.00757466i
$408$		0			0
$409$	−245.998	+	426.081i	−0.601462	+	1.04176i	0.391138	+	0.920332i	$0.372081\pi$
$409$	−245.998	+	426.081i	−0.601462	+	1.04176i	−0.992600	+	0.121430i	$0.961252\pi$
$410$		0			0
$411$	−18.3000	−	94.4158i	−0.0445256	−	0.229722i
$412$		0			0
$413$			443.668i			1.07426i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	481.241	+	554.205i	1.15406	+	1.32903i
$418$		0			0
$419$	−459.193	−	265.115i	−1.09593	−	0.632733i	−0.160778	−	0.986991i	$-0.551400\pi$
$419$	−459.193	−	265.115i	−1.09593	−	0.632733i	−0.935148	+	0.354257i	$0.884734\pi$
$420$		0			0
$421$	−303.646	−	525.931i	−0.721250	−	1.24924i	−0.960499	−	0.278284i	$-0.910234\pi$
$421$	−303.646	−	525.931i	−0.721250	−	1.24924i	0.239249	−	0.970958i	$-0.423099\pi$
$422$		0			0
$423$	20.2270	+	2.86485i	0.0478181	+	0.00677270i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	25.5203	−	44.2024i	0.0597664	−	0.103518i
$428$		0			0
$429$	−147.455	−	50.8612i	−0.343717	−	0.118558i
$430$		0			0
$431$		−	162.849i		−	0.377841i	−0.981992	−	0.188921i	$-0.939501\pi$
$431$		−	162.849i		−	0.377841i	0.981992	−	0.188921i	$-0.0604989\pi$
$432$		0			0
$433$	283.902			0.655662			0.327831	−	0.944736i	$-0.393682\pi$
$433$	283.902			0.655662			0.327831	+	0.944736i	$0.393682\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−285.362	−	164.754i	−0.653002	−	0.377011i
$438$		0			0
$439$	235.420	+	407.760i	0.536265	+	0.928838i	0.999101	+	0.0423939i	$0.0134984\pi$
$439$	235.420	+	407.760i	0.536265	+	0.928838i	−0.462836	+	0.886444i	$0.653168\pi$
$440$		0			0
$441$	−163.348	+	65.7933i	−0.370404	+	0.149191i
$442$		0			0
$443$	691.428	−	399.196i	1.56079	−	0.901120i	0.563607	−	0.826043i	$-0.309413\pi$
$443$	691.428	−	399.196i	1.56079	−	0.901120i	0.997178	−	0.0750770i	$-0.0239202\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−372.817	+	323.734i	−0.834042	+	0.724237i
$448$		0			0
$449$			605.367i			1.34826i	0.738615	+	0.674128i	$0.235480\pi$
$449$			605.367i			1.34826i	−0.738615	+	0.674128i	$0.764520\pi$
$450$		0			0
$451$	146.086			0.323915
$452$		0			0
$453$	291.672	−	56.5330i	0.643868	−	0.124797i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	201.161	+	348.420i	0.440176	+	0.762408i	0.997702	−	0.0677516i	$-0.0215826\pi$
$457$	201.161	+	348.420i	0.440176	+	0.762408i	−0.557526	+	0.830160i	$0.688249\pi$
$458$		0			0
$459$	−256.043	−	395.664i	−0.557829	−	0.862014i
$460$		0			0
$461$	−416.769	+	240.622i	−0.904054	+	0.521956i	−0.878513	−	0.477718i	$-0.841464\pi$
$461$	−416.769	+	240.622i	−0.904054	+	0.521956i	−0.0255410	+	0.999674i	$0.508131\pi$
$462$		0			0
$463$	−265.841	+	460.450i	−0.574171	+	0.994493i	0.421960	+	0.906614i	$0.361342\pi$
$463$	−265.841	+	460.450i	−0.574171	+	0.994493i	−0.996131	+	0.0878790i	$0.971991\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			534.278i			1.14406i	0.820231	+	0.572032i	$0.193845\pi$
$467$			534.278i			1.14406i	−0.820231	+	0.572032i	$0.806155\pi$
$468$		0			0
$469$	−199.491			−0.425353
$470$		0			0
$471$	−257.759	−	296.839i	−0.547259	−	0.630232i
$472$		0			0
$473$	−448.459	−	258.918i	−0.948116	−	0.547395i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	102.582	−	131.010i	0.215057	−	0.274653i
$478$		0			0
$479$	−53.6506	+	30.9752i	−0.112005	+	0.0646664i	−0.554956	−	0.831880i	$-0.687265\pi$
$479$	−53.6506	+	30.9752i	−0.112005	+	0.0646664i	0.442951	+	0.896546i	$0.353932\pi$
$480$		0			0
$481$	−1.54581	+	2.67742i	−0.00321374	+	0.00556635i
$482$		0			0
$483$	−289.739	−	99.9390i	−0.599874	−	0.206913i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−693.387			−1.42379			−0.711896	−	0.702284i	$-0.752163\pi$
$487$	−693.387			−1.42379			−0.711896	+	0.702284i	$0.752163\pi$
$488$		0			0
$489$	16.2711	−	47.1724i	0.0332742	−	0.0964671i
$490$		0			0
$491$	−87.8499	−	50.7202i	−0.178920	−	0.103300i	0.407865	−	0.913042i	$-0.366273\pi$
$491$	−87.8499	−	50.7202i	−0.178920	−	0.103300i	−0.586785	+	0.809743i	$0.699607\pi$
$492$		0			0
$493$	293.074	+	507.619i	0.594471	+	1.02965i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	268.770	−	155.174i	0.540785	−	0.312222i
$498$		0			0
$499$	342.467	−	593.170i	0.686307	−	1.18872i	−0.286718	−	0.958015i	$-0.592564\pi$
$499$	342.467	−	593.170i	0.686307	−	1.18872i	0.973024	−	0.230703i	$-0.0741025\pi$
$500$		0			0
$501$	−643.273	+	558.584i	−1.28398	+	1.11494i
$502$		0			0
$503$			487.981i			0.970141i	0.874475	+	0.485071i	$0.161206\pi$
$503$			487.981i			0.970141i	−0.874475	+	0.485071i	$0.838794\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	420.955	−	81.5911i	0.830286	−	0.160929i
$508$		0			0
$509$	−305.197	−	176.206i	−0.599601	−	0.346180i	0.169283	−	0.985567i	$-0.445855\pi$
$509$	−305.197	−	176.206i	−0.599601	−	0.346180i	−0.768885	+	0.639387i	$0.779188\pi$
$510$		0			0
$511$	214.114	+	370.856i	0.419009	+	0.725745i
$512$		0			0
$513$	396.640	−	256.675i	0.773177	−	0.500341i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	11.5571	−	20.0174i	0.0223541	−	0.0387185i
$518$		0			0
$519$	−120.308	−	620.710i	−0.231808	−	1.19597i
$520$		0			0
$521$			297.921i			0.571825i	0.958256	+	0.285912i	$0.0922966\pi$
$521$			297.921i			0.571825i	−0.958256	+	0.285912i	$0.907703\pi$
$522$		0			0
$523$	66.5684			0.127282			0.0636409	−	0.997973i	$-0.479729\pi$
$523$	66.5684			0.127282			0.0636409	+	0.997973i	$0.479729\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−770.579	−	444.894i	−1.46220	−	0.844201i
$528$		0			0
$529$	−87.1938	−	151.024i	−0.164828	−	0.285490i
$530$		0			0
$531$	274.980	+	682.708i	0.517854	+	1.28570i
$532$		0			0
$533$	63.4360	−	36.6248i	0.119017	−	0.0687145i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−670.075	−	231.127i	−1.24781	−	0.430405i
$538$		0			0
$539$			199.248i			0.369662i
$540$		0			0
$541$	−72.7607			−0.134493			−0.0672465	−	0.997736i	$-0.521421\pi$
$541$	−72.7607			−0.134493			−0.0672465	+	0.997736i	$0.521421\pi$
$542$		0			0
$543$	−318.100	+	922.223i	−0.585820	+	1.69839i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	79.9536	+	138.484i	0.146167	+	0.253169i	0.929808	−	0.368045i	$-0.119973\pi$
$547$	79.9536	+	138.484i	0.146167	+	0.253169i	−0.783640	+	0.621215i	$0.786640\pi$
$548$		0			0
$549$	11.8739	−	83.8350i	0.0216283	−	0.152705i
$550$		0			0
$551$	−508.871	+	293.797i	−0.923540	+	0.533206i
$552$		0			0
$553$	−103.906	+	179.971i	−0.187895	+	0.325445i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			610.336i			1.09576i	0.836558	+	0.547878i	$0.184564\pi$
$557$			610.336i			1.09576i	−0.836558	+	0.547878i	$0.815436\pi$
$558$		0			0
$559$	−259.651			−0.464491
$560$		0			0
$561$	−523.488	+	101.465i	−0.933134	+	0.180864i
$562$		0			0
$563$	787.017	+	454.385i	1.39790	+	0.807078i	0.994172	−	0.107802i	$-0.0343812\pi$
$563$	787.017	+	454.385i	1.39790	+	0.807078i	0.403727	+	0.914879i	$0.367715\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	316.764	−	304.585i	0.558667	−	0.537187i
$568$		0			0
$569$	329.712	−	190.360i	0.579459	−	0.334551i	−0.181459	−	0.983398i	$-0.558082\pi$
$569$	329.712	−	190.360i	0.579459	−	0.334551i	0.760919	+	0.648847i	$0.224749\pi$
$570$		0			0
$571$	−155.321	+	269.024i	−0.272016	+	0.471145i	−0.969378	−	0.245574i	$-0.921024\pi$
$571$	−155.321	+	269.024i	−0.272016	+	0.471145i	0.697362	+	0.716719i	$0.254357\pi$
$572$		0			0
$573$	63.3151	+	326.663i	0.110498	+	0.570093i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−761.001			−1.31889			−0.659446	−	0.751752i	$-0.729209\pi$
$577$	−761.001			−1.31889			−0.659446	+	0.751752i	$0.729209\pi$
$578$		0			0
$579$	254.740	+	293.362i	0.439965	+	0.506671i
$580$		0			0
$581$	363.308	+	209.756i	0.625314	+	0.361025i
$582$		0			0
$583$	−94.1321	−	163.042i	−0.161462	−	0.279660i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	360.828	−	208.324i	0.614699	−	0.354897i	−0.160103	−	0.987100i	$-0.551183\pi$
$587$	360.828	−	208.324i	0.614699	−	0.354897i	0.774802	+	0.632204i	$0.217849\pi$
$588$		0			0
$589$	445.991	−	772.479i	0.757200	−	1.31151i
$590$		0			0
$591$	950.663	+	327.910i	1.60857	+	0.554839i
$592$		0			0
$593$			775.358i			1.30752i	0.756703	+	0.653759i	$0.226809\pi$
$593$			775.358i			1.30752i	−0.756703	+	0.653759i	$0.773191\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−334.211	+	968.932i	−0.559818	+	1.62300i
$598$		0			0
$599$	215.994	+	124.704i	0.360591	+	0.208187i	0.669340	−	0.742956i	$-0.266577\pi$
$599$	215.994	+	124.704i	0.360591	+	0.208187i	−0.308749	+	0.951144i	$0.599910\pi$
$600$		0			0
$601$	109.343	+	189.388i	0.181936	+	0.315122i	0.942540	−	0.334094i	$-0.108430\pi$
$601$	109.343	+	189.388i	0.181936	+	0.315122i	−0.760604	+	0.649216i	$0.775097\pi$
$602$		0			0
$603$	−306.973	+	123.642i	−0.509076	+	0.205045i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−450.926	+	781.026i	−0.742876	+	1.28670i	0.208305	+	0.978064i	$0.433205\pi$
$607$	−450.926	+	781.026i	−0.742876	+	1.28670i	−0.951181	+	0.308635i	$0.900128\pi$
$608$		0			0
$609$	−412.678	+	358.347i	−0.677632	+	0.588419i
$610$		0			0
$611$		−	11.5898i		−	0.0189686i
$612$		0			0
$613$	334.064			0.544965			0.272483	−	0.962161i	$-0.412155\pi$
$613$	334.064			0.544965			0.272483	+	0.962161i	$0.412155\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	154.959	+	89.4659i	0.251150	+	0.145001i	0.620291	−	0.784372i	$-0.287015\pi$
$617$	154.959	+	89.4659i	0.251150	+	0.145001i	−0.369141	+	0.929373i	$0.620348\pi$
$618$		0			0
$619$	−201.857	−	349.626i	−0.326102	−	0.564825i	0.655633	−	0.755080i	$-0.272402\pi$
$619$	−201.857	−	349.626i	−0.326102	−	0.564825i	−0.981735	+	0.190255i	$0.939069\pi$
$620$		0			0
$621$	−507.787	+	25.7929i	−0.817692	+	0.0415344i
$622$		0			0
$623$	−649.621	+	375.059i	−1.04273	+	0.602020i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−101.715	−	524.779i	−0.162224	−	0.836968i
$628$		0			0
$629$			10.5689i			0.0168028i
$630$		0			0
$631$	−625.992			−0.992063			−0.496032	−	0.868304i	$-0.665210\pi$
$631$	−625.992			−0.992063			−0.496032	+	0.868304i	$0.665210\pi$
$632$		0			0
$633$	287.110	+	330.641i	0.453571	+	0.522339i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	49.9529	+	86.5210i	0.0784190	+	0.135826i
$638$		0			0
$639$	317.403	−	405.361i	0.496718	−	0.634367i
$640$		0			0
$641$	−84.0852	+	48.5466i	−0.131178	+	0.0757357i	−0.564153	−	0.825670i	$-0.690797\pi$
$641$	−84.0852	+	48.5466i	−0.131178	+	0.0757357i	0.432975	+	0.901406i	$0.357464\pi$
$642$		0			0
$643$	548.925	−	950.767i	0.853694	−	1.47864i	−0.0241567	−	0.999708i	$-0.507690\pi$
$643$	548.925	−	950.767i	0.853694	−	1.47864i	0.877851	−	0.478934i	$-0.158977\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	104.927i		−	0.162175i	−0.996707	−	0.0810875i	$-0.974161\pi$
$647$		−	104.927i		−	0.162175i	0.996707	−	0.0810875i	$-0.0258393\pi$
$648$		0			0
$649$	832.748			1.28312
$650$		0			0
$651$	270.536	−	784.328i	0.415571	−	1.20481i
$652$		0			0
$653$	7.49573	+	4.32766i	0.0114789	+	0.00662735i	0.505728	−	0.862693i	$-0.331224\pi$
$653$	7.49573	+	4.32766i	0.0114789	+	0.00662735i	−0.494250	+	0.869320i	$0.664557\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	559.327	+	437.961i	0.851334	+	0.666607i
$658$		0			0
$659$	−421.081	+	243.111i	−0.638969	+	0.368909i	−0.784217	−	0.620486i	$-0.786935\pi$
$659$	−421.081	+	243.111i	−0.638969	+	0.368909i	0.145248	+	0.989395i	$0.453602\pi$
$660$		0			0
$661$	149.965	−	259.746i	0.226875	−	0.392960i	−0.730005	−	0.683442i	$-0.760482\pi$
$661$	149.965	−	259.746i	0.226875	−	0.392960i	0.956880	+	0.290482i	$0.0938157\pi$
$662$		0			0
$663$	−201.881	+	175.302i	−0.304496	+	0.264408i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	632.361			0.948068
$668$		0			0
$669$	−1005.99	+	194.984i	−1.50372	+	0.291456i
$670$		0			0
$671$	−82.9662	−	47.9006i	−0.123646	−	0.0713869i
$672$		0			0
$673$	251.254	+	435.185i	0.373335	+	0.646635i	0.990076	−	0.140531i	$-0.0448810\pi$
$673$	251.254	+	435.185i	0.373335	+	0.646635i	−0.616742	+	0.787166i	$0.711548\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	969.711	−	559.863i	1.43236	−	0.826976i	0.435064	−	0.900399i	$-0.356726\pi$
$677$	969.711	−	559.863i	1.43236	−	0.826976i	0.997301	+	0.0734232i	$0.0233924\pi$
$678$		0			0
$679$	317.268	−	549.525i	0.467258	−	0.809315i
$680$		0			0
$681$	−46.9198	−	242.074i	−0.0688983	−	0.355469i
$682$		0			0
$683$			819.088i			1.19925i	0.800281	+	0.599625i	$0.204684\pi$
$683$			819.088i			1.19925i	−0.800281	+	0.599625i	$0.795316\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	604.736	+	696.423i	0.880256	+	1.01372i
$688$		0			0
$689$	−81.7515	−	47.1993i	−0.118652	−	0.0685040i
$690$		0			0
$691$	381.408	+	660.618i	0.551965	+	0.956032i	0.998133	+	0.0610826i	$0.0194553\pi$
$691$	381.408	+	660.618i	0.551965	+	0.956032i	−0.446167	+	0.894950i	$0.647211\pi$
$692$		0			0
$693$	−185.762	−	461.201i	−0.268055	−	0.665514i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	125.205	−	216.861i	0.179634	−	0.311135i
$698$		0			0
$699$	−1177.70	−	406.220i	−1.68483	−	0.581145i
$700$		0			0
$701$			362.687i			0.517386i	0.965960	+	0.258693i	$0.0832918\pi$
$701$			362.687i			0.517386i	−0.965960	+	0.258693i	$0.916708\pi$
$702$		0			0
$703$	−10.5950			−0.0150711
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−412.512	−	238.164i	−0.583469	−	0.336866i
$708$		0			0
$709$	−306.313	−	530.550i	−0.432036	−	0.748308i	0.565013	−	0.825082i	$-0.308871\pi$
$709$	−306.313	−	530.550i	−0.432036	−	0.748308i	−0.997048	+	0.0767744i	$0.975538\pi$
$710$		0			0
$711$	−48.3450	+	341.336i	−0.0679958	+	0.480078i
$712$		0			0
$713$	−831.333	+	479.971i	−1.16597	+	0.673171i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−574.945	+	499.251i	−0.801875	+	0.696305i
$718$		0			0
$719$			1031.79i			1.43503i	0.696544	+	0.717515i	$0.254720\pi$
$719$			1031.79i			1.43503i	−0.696544	+	0.717515i	$0.745280\pi$
$720$		0			0
$721$	1022.26			1.41784
$722$		0			0
$723$	−467.275	+	90.5690i	−0.646300	+	0.125268i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−10.7096	−	18.5495i	−0.0147312	−	0.0255152i	0.858566	−	0.512703i	$-0.171356\pi$
$727$	−10.7096	−	18.5495i	−0.0147312	−	0.0255152i	−0.873297	+	0.487188i	$0.838023\pi$
$728$		0			0
$729$	298.652	−	665.017i	0.409674	−	0.912232i
$730$		0			0
$731$	−768.717	+	443.819i	−1.05160	+	0.607139i
$732$		0			0
$733$	−335.373	+	580.882i	−0.457534	+	0.792472i	−0.998830	−	0.0483598i	$-0.984601\pi$
$733$	−335.373	+	580.882i	−0.457534	+	0.792472i	0.541296	+	0.840832i	$0.317934\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			374.437i			0.508055i
$738$		0			0
$739$	925.156			1.25190			0.625951	−	0.779862i	$-0.284711\pi$
$739$	925.156			1.25190			0.625951	+	0.779862i	$0.284711\pi$
$740$		0			0
$741$	−175.734	−	202.378i	−0.237159	−	0.273115i
$742$		0			0
$743$	440.281	+	254.196i	0.592572	+	0.342122i	0.766114	−	0.642705i	$-0.222188\pi$
$743$	440.281	+	254.196i	0.592572	+	0.342122i	−0.173542	+	0.984827i	$0.555521\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	689.055	+	97.5942i	0.922430	+	0.130648i
$748$		0			0
$749$	800.027	−	461.896i	1.06813	−	0.616683i
$750$		0			0
$751$	208.849	−	361.737i	0.278094	−	0.481674i	−0.692817	−	0.721114i	$-0.743631\pi$
$751$	208.849	−	361.737i	0.278094	−	0.481674i	0.970911	+	0.239440i	$0.0769639\pi$
$752$		0			0
$753$	−1334.72	−	460.382i	−1.77254	−	0.611397i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−183.878			−0.242904			−0.121452	−	0.992597i	$-0.538755\pi$
$757$	−183.878			−0.242904			−0.121452	+	0.992597i	$0.538755\pi$
$758$		0			0
$759$	−187.582	+	543.830i	−0.247143	+	0.716508i
$760$		0			0
$761$	991.942	+	572.698i	1.30347	+	0.752560i	0.980998	−	0.194019i	$-0.0621522\pi$
$761$	991.942	+	572.698i	1.30347	+	0.752560i	0.322474	+	0.946578i	$0.395486\pi$
$762$		0			0
$763$	214.348	+	371.262i	0.280928	+	0.486581i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	361.611	−	208.776i	0.471461	−	0.272198i
$768$		0			0
$769$	652.189	−	1129.63i	0.848101	−	1.46895i	−0.0348004	−	0.999394i	$-0.511080\pi$
$769$	652.189	−	1129.63i	0.848101	−	1.46895i	0.882901	−	0.469559i	$-0.155587\pi$
$770$		0			0
$771$	1129.70	−	980.974i	1.46525	−	1.27234i
$772$		0			0
$773$		−	312.549i		−	0.404332i	−0.979351	−	0.202166i	$-0.935202\pi$
$773$		−	312.549i		−	0.404332i	0.979351	−	0.202166i	$-0.0647981\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−9.67487	+	1.87522i	−0.0124516	+	0.00241341i
$778$		0			0
$779$	217.396	+	125.514i	0.279071	+	0.161122i
$780$		0			0
$781$	−291.257	−	504.472i	−0.372928	−	0.645930i
$782$		0			0
$783$	−412.921	+	807.191i	−0.527358	+	1.03090i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−105.303	+	182.390i	−0.133803	+	0.231754i	−0.925140	−	0.379627i	$-0.876052\pi$
$787$	−105.303	+	182.390i	−0.133803	+	0.231754i	0.791337	+	0.611381i	$0.209386\pi$
$788$		0			0
$789$	−141.966	−	732.449i	−0.179932	−	0.928325i
$790$		0			0
$791$			266.182i			0.336513i
$792$		0			0
$793$	−48.0362			−0.0605752
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−962.245	−	555.552i	−1.20733	−	0.697054i	−0.245158	−	0.969483i	$-0.578840\pi$
$797$	−962.245	−	555.552i	−1.20733	−	0.697054i	−0.962176	+	0.272429i	$0.912173\pi$
$798$		0			0
$799$	−19.8103	−	34.3125i	−0.0247939	−	0.0429443i
$800$		0			0
$801$	−767.167	+	979.761i	−0.957762	+	1.22317i
$802$		0			0
$803$	696.083	−	401.884i	0.866853	−	0.500478i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	602.914	+	207.962i	0.747105	+	0.257697i
$808$		0			0
$809$			1552.47i			1.91900i	0.281702	+	0.959502i	$0.409101\pi$
$809$			1552.47i			1.91900i	−0.281702	+	0.959502i	$0.590899\pi$
$810$		0			0
$811$	893.971			1.10231			0.551154	−	0.834404i	$-0.314188\pi$
$811$	893.971			1.10231			0.551154	+	0.834404i	$0.314188\pi$
$812$		0			0
$813$	146.940	−	426.003i	0.180738	−	0.523989i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−444.913	−	770.612i	−0.544569	−	0.943222i
$818$		0			0
$819$	−196.292	−	153.699i	−0.239672	−	0.187667i
$820$		0			0
$821$	1232.21	−	711.419i	1.50087	−	0.866528i	0.500870	−	0.865522i	$-0.333013\pi$
$821$	1232.21	−	711.419i	1.50087	−	0.866528i	0.999999	−	0.00100512i	$-0.000319940\pi$
$822$		0			0
$823$	192.219	−	332.933i	0.233559	−	0.404536i	−0.725294	−	0.688439i	$-0.758296\pi$
$823$	192.219	−	332.933i	0.233559	−	0.404536i	0.958853	+	0.283903i	$0.0916295\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			228.210i			0.275949i	0.990436	+	0.137974i	$0.0440592\pi$
$827$			228.210i			0.275949i	−0.990436	+	0.137974i	$0.955941\pi$
$828$		0			0
$829$	108.877			0.131335			0.0656674	−	0.997842i	$-0.479082\pi$
$829$	108.877			0.131335			0.0656674	+	0.997842i	$0.479082\pi$
$830$		0			0
$831$	−1078.84	+	209.105i	−1.29825	+	0.251631i
$832$		0			0
$833$	295.779	+	170.768i	0.355077	+	0.205004i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−69.8217	−	1374.59i	−0.0834190	−	1.64228i
$838$		0			0
$839$	809.618	−	467.433i	0.964980	−	0.557131i	0.0672778	−	0.997734i	$-0.478569\pi$
$839$	809.618	−	467.433i	0.964980	−	0.557131i	0.897702	+	0.440603i	$0.145235\pi$
$840$		0			0
$841$	143.328	−	248.252i	0.170426	−	0.295187i
$842$		0			0
$843$	75.0997	+	387.464i	0.0890862	+	0.459625i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	93.8939			0.110855
$848$		0			0
$849$	−529.747	−	610.064i	−0.623965	−	0.718568i
$850$		0			0
$851$	9.87462	+	5.70111i	0.0116035	+	0.00669931i
$852$		0			0
$853$	−590.914	−	1023.49i	−0.692748	−	1.19988i	−0.970934	−	0.239348i	$-0.923066\pi$
$853$	−590.914	−	1023.49i	−0.692748	−	1.19988i	0.278185	−	0.960527i	$-0.410267\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	851.303	−	491.500i	0.993352	−	0.573512i	0.0870776	−	0.996202i	$-0.472247\pi$
$857$	851.303	−	491.500i	0.993352	−	0.573512i	0.906275	+	0.422689i	$0.138914\pi$
$858$		0			0
$859$	−764.988	+	1325.00i	−0.890557	+	1.54249i	−0.0513472	+	0.998681i	$0.516352\pi$
$859$	−764.988	+	1325.00i	−0.890557	+	1.54249i	−0.839209	+	0.543808i	$0.816982\pi$
$860$		0			0
$861$	220.731	+	76.1362i	0.256366	+	0.0884276i
$862$		0			0
$863$			932.711i			1.08078i	0.841415	+	0.540389i	$0.181723\pi$
$863$			932.711i			1.08078i	−0.841415	+	0.540389i	$0.818277\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−15.3343	+	44.4566i	−0.0176866	+	0.0512763i
$868$		0			0
$869$	337.799	+	195.028i	0.388721	+	0.224428i
$870$		0			0
$871$	93.8742	+	162.595i	0.107777	+	0.186676i
$872$		0			0
$873$	147.617	−	1042.24i	0.169092	−	1.19386i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−628.419	+	1088.45i	−0.716555	+	1.24111i	0.245802	+	0.969320i	$0.420949\pi$
$877$	−628.419	+	1088.45i	−0.716555	+	1.24111i	−0.962357	+	0.271790i	$0.912385\pi$
$878$		0			0
$879$	−477.903	+	414.985i	−0.543690	+	0.472111i
$880$		0			0
$881$		−	652.425i		−	0.740551i	−0.928922	−	0.370275i	$-0.879263\pi$
$881$		−	652.425i		−	0.740551i	0.928922	−	0.370275i	$-0.120737\pi$
$882$		0			0
$883$	618.566			0.700527			0.350264	−	0.936651i	$-0.386092\pi$
$883$	618.566			0.700527			0.350264	+	0.936651i	$0.386092\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1291.63	−	745.723i	−1.45618	−	0.840725i	−0.457357	−	0.889283i	$-0.651204\pi$
$887$	−1291.63	−	745.723i	−1.45618	−	0.840725i	−0.998820	+	0.0485585i	$0.984537\pi$
$888$		0			0
$889$	−147.660	−	255.754i	−0.166096	−	0.287687i
$890$		0			0
$891$	−571.695	−	594.555i	−0.641633	−	0.667289i
$892$		0			0
$893$	34.3971	−	19.8592i	0.0385186	−	0.0222387i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	54.8870	+	283.180i	0.0611895	+	0.315697i
$898$		0			0
$899$			1711.81i			1.90413i
$900$		0			0
$901$	−322.709			−0.358168
$902$		0			0
$903$	−542.666	−	624.942i	−0.600959	−	0.692073i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	230.332	+	398.947i	0.253949	+	0.439853i	0.964610	−	0.263682i	$-0.0849370\pi$
$907$	230.332	+	398.947i	0.253949	+	0.439853i	−0.710660	+	0.703535i	$0.751604\pi$
$908$		0			0
$909$	−782.378	−	110.812i	−0.860702	−	0.121905i
$910$		0			0
$911$	−1190.05	+	687.076i	−1.30631	+	0.754200i	−0.981479	−	0.191571i	$-0.938642\pi$
$911$	−1190.05	+	687.076i	−1.30631	+	0.754200i	−0.324834	+	0.945771i	$0.605308\pi$
$912$		0			0
$913$	393.704	−	681.915i	0.431220	−	0.746895i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			31.9334i			0.0348238i
$918$		0			0
$919$	1651.74			1.79733			0.898663	−	0.438639i	$-0.144539\pi$
$919$	1651.74			1.79733			0.898663	+	0.438639i	$0.144539\pi$
$920$		0			0
$921$	43.9657	−	127.464i	0.0477369	−	0.138397i
$922$		0			0
$923$	−252.950	−	146.041i	−0.274052	−	0.158224i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1573.04	−	633.587i	1.69691	−	0.683481i
$928$		0			0
$929$	−632.169	+	364.983i	−0.680483	+	0.392877i	−0.800037	−	0.599951i	$-0.795187\pi$
$929$	−632.169	+	364.983i	−0.680483	+	0.392877i	0.119554	+	0.992828i	$0.461854\pi$
$930$		0			0
$931$	−171.189	+	296.509i	−0.183877	+	0.318484i
$932$		0			0
$933$	24.8073	−	21.5413i	0.0265888	−	0.0230883i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−1098.36			−1.17221			−0.586104	−	0.810236i	$-0.699339\pi$
$937$	−1098.36			−1.17221			−0.586104	+	0.810236i	$0.699339\pi$
$938$		0			0
$939$	493.750	−	95.7006i	0.525826	−	0.101918i
$940$		0			0
$941$	827.540	+	477.781i	0.879426	+	0.507737i	0.870469	−	0.492223i	$-0.163816\pi$
$941$	827.540	+	477.781i	0.879426	+	0.507737i	0.00895707	+	0.999960i	$0.497149\pi$
$942$		0			0
$943$	−135.077	−	233.959i	−0.143241	−	0.248101i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	688.125	−	397.289i	0.726636	−	0.419524i	−0.0905541	−	0.995892i	$-0.528864\pi$
$947$	688.125	−	397.289i	0.726636	−	0.419524i	0.817190	+	0.576368i	$0.195530\pi$
$948$		0			0
$949$	201.511	−	349.026i	0.212340	−	0.367783i
$950$		0			0
$951$	−134.658	−	694.743i	−0.141596	−	0.730539i
$952$		0			0
$953$		−	493.659i		−	0.518005i	−0.965877	−	0.259003i	$-0.916606\pi$
$953$		−	493.659i		−	0.518005i	0.965877	−	0.259003i	$-0.0833939\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	672.604	+	774.581i	0.702826	+	0.809385i
$958$		0			0
$959$	−150.620	−	86.9602i	−0.157059	−	0.0906780i
$960$		0			0
$961$	−818.788	−	1418.18i	−0.852016	−	1.47574i
$962$		0			0
$963$	944.789	−	1206.61i	0.981089	−	1.25296i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−628.097	+	1087.90i	−0.649532	+	1.12502i	0.333703	+	0.942678i	$0.391702\pi$
$967$	−628.097	+	1087.90i	−0.649532	+	1.12502i	−0.983235	+	0.182344i	$0.941632\pi$
$968$		0			0
$969$	−866.200	−	298.776i	−0.893911	−	0.308335i
$970$		0			0
$971$		−	832.692i		−	0.857562i	−0.903409	−	0.428781i	$-0.858943\pi$
$971$		−	832.692i		−	0.857562i	0.903409	−	0.428781i	$-0.141057\pi$
$972$		0			0
$973$	1327.35			1.36418
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−872.160	−	503.542i	−0.892691	−	0.515396i	−0.0178695	−	0.999840i	$-0.505688\pi$
$977$	−872.160	−	503.542i	−0.892691	−	0.515396i	−0.874822	+	0.484445i	$0.839022\pi$
$978$		0			0
$979$	703.971	+	1219.31i	0.719072	+	1.24547i
$980$		0			0
$981$	559.939	+	438.440i	0.570784	+	0.446932i
$982$		0			0
$983$	473.595	−	273.430i	0.481785	−	0.278159i	−0.239375	−	0.970927i	$-0.576942\pi$
$983$	473.595	−	273.430i	0.481785	−	0.278159i	0.721160	+	0.692768i	$0.243609\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	27.8950	−	24.2225i	0.0282624	−	0.0245415i
$988$		0			0
$989$			957.622i			0.968273i
$990$		0			0
$991$	−610.924			−0.616472			−0.308236	−	0.951310i	$-0.599739\pi$
$991$	−610.924			−0.616472			−0.308236	+	0.951310i	$0.599739\pi$
$992$		0			0
$993$	521.333	−	101.047i	0.525008	−	0.101759i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−267.733	−	463.727i	−0.268539	−	0.465123i	0.699946	−	0.714196i	$-0.253207\pi$
$997$	−267.733	−	463.727i	−0.268539	−	0.465123i	−0.968485	+	0.249073i	$0.919874\pi$
$998$		0			0
$999$	−13.7253	+	8.88193i	−0.0137390	+	0.00889083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.p.d.401.5	yes	16
3.2	odd	2		2700.3.p.e.2501.3		16
5.2	odd	4		900.3.u.d.149.1		32
5.3	odd	4		900.3.u.d.149.16		32
5.4	even	2		900.3.p.e.401.4	yes	16
9.2	odd	6	inner	900.3.p.d.101.5	✓	16
9.7	even	3		2700.3.p.e.1601.3		16
15.2	even	4		2700.3.u.d.449.12		32
15.8	even	4		2700.3.u.d.449.5		32
15.14	odd	2		2700.3.p.d.2501.6		16
45.2	even	12		900.3.u.d.749.16		32
45.7	odd	12		2700.3.u.d.2249.5		32
45.29	odd	6		900.3.p.e.101.4	yes	16
45.34	even	6		2700.3.p.d.1601.6		16
45.38	even	12		900.3.u.d.749.1		32
45.43	odd	12		2700.3.u.d.2249.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.p.d.101.5	✓	16	9.2	odd	6	inner
900.3.p.d.401.5	yes	16	1.1	even	1	trivial
900.3.p.e.101.4	yes	16	45.29	odd	6
900.3.p.e.401.4	yes	16	5.4	even	2
900.3.u.d.149.1		32	5.2	odd	4
900.3.u.d.149.16		32	5.3	odd	4
900.3.u.d.749.1		32	45.38	even	12
900.3.u.d.749.16		32	45.2	even	12
2700.3.p.d.1601.6		16	45.34	even	6
2700.3.p.d.2501.6		16	15.14	odd	2
2700.3.p.e.1601.3		16	9.7	even	3
2700.3.p.e.2501.3		16	3.2	odd	2
2700.3.u.d.449.5		32	15.8	even	4
2700.3.u.d.449.12		32	15.2	even	4
2700.3.u.d.2249.5		32	45.7	odd	12
2700.3.u.d.2249.12		32	45.43	odd	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.978225 - 2.83603i) q^{3} +(-2.71262 - 4.69840i) q^{7} +(-7.08615 - 5.54856i) q^{9} +O(q^{10})\)	\(q+(0.978225 - 2.83603i) q^{3} +(-2.71262 - 4.69840i) q^{7} +(-7.08615 - 5.54856i) q^{9} +(-8.81872 + 5.09149i) q^{11} +(-2.55295 + 4.42184i) q^{13} +17.4550i q^{17} -17.4980 q^{19} +(-15.9784 + 3.09699i) q^{21} +(16.3083 + 9.41558i) q^{23} +(-22.6677 + 14.6688i) q^{27} +(29.0817 - 16.7903i) q^{29} +(-25.4881 + 44.1467i) q^{31} +(5.81293 + 29.9908i) q^{33} +0.605498 q^{37} +(10.0431 + 11.5658i) q^{39} +(-12.4241 - 7.17303i) q^{41} +(25.4265 + 44.0400i) q^{43} +(-1.96577 + 1.13494i) q^{47} +(9.78337 - 16.9453i) q^{49} +(49.5028 + 17.0749i) q^{51} +18.4881i q^{53} +(-17.1170 + 49.6249i) q^{57} +(-70.8221 - 40.8892i) q^{59} +(4.70398 + 8.14754i) q^{61} +(-6.84729 + 48.3447i) q^{63} +(18.3854 - 31.8445i) q^{67} +(42.6560 - 37.0402i) q^{69} +57.2046i q^{71} -78.9324 q^{73} +(47.8437 + 27.6226i) q^{77} +(-19.1524 - 33.1729i) q^{79} +(19.4270 + 78.6358i) q^{81} +(-66.9661 + 38.6629i) q^{83} +(-19.1694 - 98.9012i) q^{87} -138.264i q^{89} +27.7008 q^{91} +(100.268 + 115.471i) q^{93} +(58.4800 + 101.290i) q^{97} +(90.7412 + 12.8521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + q^{7} + 14 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 + q^7 + 14 * q^9	\( 16 q - 2 q^{3} + q^{7} + 14 q^{9} + 10 q^{13} + 2 q^{19} + q^{21} - 27 q^{23} + 16 q^{27} + 9 q^{29} + 8 q^{31} - 36 q^{33} + 22 q^{37} + 19 q^{39} + 54 q^{41} - 44 q^{43} + 108 q^{47} - 45 q^{49} + 90 q^{51} + 68 q^{57} + 9 q^{59} - 55 q^{61} + 107 q^{63} + 28 q^{67} - 147 q^{69} - 86 q^{73} - 342 q^{77} + 11 q^{79} - 130 q^{81} + 306 q^{83} - 375 q^{87} - 134 q^{91} + 83 q^{93} - 41 q^{97} + 252 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 + q^7 + 14 * q^9 + 10 * q^13 + 2 * q^19 + q^21 - 27 * q^23 + 16 * q^27 + 9 * q^29 + 8 * q^31 - 36 * q^33 + 22 * q^37 + 19 * q^39 + 54 * q^41 - 44 * q^43 + 108 * q^47 - 45 * q^49 + 90 * q^51 + 68 * q^57 + 9 * q^59 - 55 * q^61 + 107 * q^63 + 28 * q^67 - 147 * q^69 - 86 * q^73 - 342 * q^77 + 11 * q^79 - 130 * q^81 + 306 * q^83 - 375 * q^87 - 134 * q^91 + 83 * q^93 - 41 * q^97 + 252 * q^99

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