LMFDB - Embedded newform 900.3.u.d.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(149,900)]

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, 5, 3]))

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

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

chi := DirichletCharacter("900.149");

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.u (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.1
Character	$\chi$	$=$	900.149
Dual form			900.3.u.d.749.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.83603 - 0.978225i) q^{3} +(4.69840 - 2.71262i) q^{7} +(7.08615 + 5.54856i) q^{9} +O(q^{10})$	\(q+(-2.83603 - 0.978225i) q^{3} +(4.69840 - 2.71262i) q^{7} +(7.08615 + 5.54856i) q^{9} +(-8.81872 + 5.09149i) q^{11} +(4.42184 + 2.55295i) q^{13} -17.4550 q^{17} +17.4980 q^{19} +(-15.9784 + 3.09699i) q^{21} +(9.41558 - 16.3083i) q^{23} +(-14.6688 - 22.6677i) q^{27} +(-29.0817 + 16.7903i) q^{29} +(-25.4881 + 44.1467i) q^{31} +(29.9908 - 5.81293i) q^{33} +0.605498i q^{37} +(-10.0431 - 11.5658i) q^{39} +(-12.4241 - 7.17303i) q^{41} +(44.0400 - 25.4265i) q^{43} +(-1.13494 - 1.96577i) q^{47} +(-9.78337 + 16.9453i) q^{49} +(49.5028 + 17.0749i) q^{51} +18.4881 q^{53} +(-49.6249 - 17.1170i) q^{57} +(70.8221 + 40.8892i) q^{59} +(4.70398 + 8.14754i) q^{61} +(48.3447 + 6.84729i) q^{63} +(31.8445 + 18.3854i) q^{67} +(-42.6560 + 37.0402i) q^{69} +57.2046i q^{71} +78.9324i q^{73} +(-27.6226 + 47.8437i) q^{77} +(19.1524 + 33.1729i) q^{79} +(19.4270 + 78.6358i) q^{81} +(38.6629 + 66.9661i) q^{83} +(98.9012 - 19.1694i) q^{87} +138.264i q^{89} +27.7008 q^{91} +(115.471 - 100.268i) q^{93} +(-101.290 + 58.4800i) q^{97} +(-90.7412 - 12.8521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 28 q^{9}+O(q^{10}) $ 32 * q - 28 * q^9	$ 32 q - 28 q^{9} - 4 q^{19} + 2 q^{21} - 18 q^{29} + 16 q^{31} - 38 q^{39} + 108 q^{41} + 90 q^{49} + 180 q^{51} - 18 q^{59} - 110 q^{61} + 294 q^{69} - 22 q^{79} - 260 q^{81} - 268 q^{91} - 504 q^{99}+O(q^{100}) $ 32 * q - 28 * q^9 - 4 * q^19 + 2 * q^21 - 18 * q^29 + 16 * q^31 - 38 * q^39 + 108 * q^41 + 90 * q^49 + 180 * q^51 - 18 * q^59 - 110 * q^61 + 294 * q^69 - 22 * q^79 - 260 * q^81 - 268 * q^91 - 504 * 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
$3$	−2.83603	−	0.978225i	−0.945344	−	0.326075i
$3$	−2.83603	−	0.978225i	−0.945344	−	0.326075i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	4.69840	−	2.71262i	0.671200	−	0.387517i	−0.125331	−	0.992115i	$-0.539999\pi$
$7$	4.69840	−	2.71262i	0.671200	−	0.387517i	0.796531	+	0.604598i	$0.206666\pi$
$8$		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
$13$	4.42184	+	2.55295i	0.340142	+	0.196381i	0.660335	−	0.750971i	$-0.270414\pi$
$13$	4.42184	+	2.55295i	0.340142	+	0.196381i	−0.320193	+	0.947352i	$0.603748\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−17.4550			−1.02676			−0.513381	−	0.858161i	$-0.671607\pi$
$17$	−17.4550			−1.02676			−0.513381	+	0.858161i	$0.671607\pi$
$18$		0			0
$19$	17.4980			0.920947			0.460474	−	0.887673i	$-0.347680\pi$
$19$	17.4980			0.920947			0.460474	+	0.887673i	$0.347680\pi$
$20$		0			0
$21$	−15.9784	+	3.09699i	−0.760874	+	0.147476i
$22$		0			0
$23$	9.41558	−	16.3083i	0.409373	−	0.709055i	−0.585447	−	0.810711i	$-0.699081\pi$
$23$	9.41558	−	16.3083i	0.409373	−	0.709055i	0.994820	+	0.101656i	$0.0324142\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−14.6688	−	22.6677i	−0.543289	−	0.839546i
$28$		0			0
$29$	−29.0817	+	16.7903i	−1.00282	+	0.578976i	−0.909080	−	0.416621i	$-0.863214\pi$
$29$	−29.0817	+	16.7903i	−1.00282	+	0.578976i	−0.0937354	+	0.995597i	$0.529881\pi$
$30$		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
$33$	29.9908	−	5.81293i	0.908812	−	0.176149i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			0.605498i			0.0163648i	0.999967	+	0.00818241i	$0.00260457\pi$
$37$			0.605498i			0.0163648i	−0.999967	+	0.00818241i	$0.997395\pi$
$38$		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
$43$	44.0400	−	25.4265i	1.02419	−	0.591314i	0.108873	−	0.994056i	$-0.465276\pi$
$43$	44.0400	−	25.4265i	1.02419	−	0.591314i	0.915314	+	0.402741i	$0.131943\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.13494	−	1.96577i	−0.0241477	−	0.0418250i	0.853699	−	0.520767i	$-0.174354\pi$
$47$	−1.13494	−	1.96577i	−0.0241477	−	0.0418250i	−0.877847	+	0.478942i	$0.841021\pi$
$48$		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
$53$	18.4881			0.348832			0.174416	−	0.984672i	$-0.444196\pi$
$53$	18.4881			0.348832			0.174416	+	0.984672i	$0.444196\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−49.6249	−	17.1170i	−0.870612	−	0.300298i
$58$		0			0
$59$	70.8221	+	40.8892i	1.20038	+	0.693037i	0.960639	−	0.277801i	$-0.0896056\pi$
$59$	70.8221	+	40.8892i	1.20038	+	0.693037i	0.239737	+	0.970838i	$0.422939\pi$
$60$		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
$63$	48.3447	+	6.84729i	0.767376	+	0.108687i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	31.8445	+	18.3854i	0.475291	+	0.274409i	0.718452	−	0.695577i	$-0.244851\pi$
$67$	31.8445	+	18.3854i	0.475291	+	0.274409i	−0.243161	+	0.969986i	$0.578184\pi$
$68$		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
$73$			78.9324i			1.08127i	0.841259	+	0.540633i	$0.181815\pi$
$73$			78.9324i			1.08127i	−0.841259	+	0.540633i	$0.818185\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−27.6226	+	47.8437i	−0.358735	+	0.621347i
$78$		0			0
$79$	19.1524	+	33.1729i	0.242435	+	0.419910i	0.961407	−	0.275129i	$-0.0887206\pi$
$79$	19.1524	+	33.1729i	0.242435	+	0.419910i	−0.718972	+	0.695039i	$0.755387\pi$
$80$		0			0
$81$	19.4270	+	78.6358i	0.239840	+	0.970812i
$82$		0			0
$83$	38.6629	+	66.9661i	0.465818	+	0.806821i	0.999238	−	0.0390298i	$-0.0124267\pi$
$83$	38.6629	+	66.9661i	0.465818	+	0.806821i	−0.533420	+	0.845851i	$0.679093\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	98.9012	−	19.1694i	1.13680	−	0.220338i
$88$		0			0
$89$			138.264i			1.55353i	0.629790	+	0.776766i	$0.283141\pi$
$89$			138.264i			1.55353i	−0.629790	+	0.776766i	$0.716859\pi$
$90$		0			0
$91$	27.7008			0.304404
$92$		0			0
$93$	115.471	−	100.268i	1.24162	−	1.07815i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−101.290	+	58.4800i	−1.04423	+	0.602887i	−0.921029	−	0.389495i	$-0.872650\pi$
$97$	−101.290	+	58.4800i	−1.04423	+	0.602887i	−0.123202	+	0.992382i	$0.539316\pi$
$98$		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
$103$	163.182	+	94.2134i	1.58429	+	0.914693i	0.994222	+	0.107343i	$0.0342344\pi$
$103$	163.182	+	94.2134i	1.58429	+	0.914693i	0.590073	+	0.807350i	$0.299099\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−170.277			−1.59137			−0.795685	−	0.605711i	$-0.792889\pi$
$107$	−170.277			−1.59137			−0.795685	+	0.605711i	$0.792889\pi$
$108$		0			0
$109$	79.0188			0.724943			0.362471	−	0.931995i	$-0.381933\pi$
$109$	79.0188			0.724943			0.362471	+	0.931995i	$0.381933\pi$
$110$		0			0
$111$	0.592314	−	1.71721i	0.00533616	−	0.0154704i
$112$		0			0
$113$	−24.5318	+	42.4903i	−0.217095	+	0.376020i	−0.953919	−	0.300065i	$-0.902992\pi$
$113$	−24.5318	+	42.4903i	−0.217095	+	0.376020i	0.736823	+	0.676085i	$0.236325\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	17.1686	+	42.6254i	0.146740	+	0.364320i
$118$		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
$123$	28.2182	+	32.4965i	0.229416	+	0.264199i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			54.4343i			0.428617i	0.976766	+	0.214308i	$0.0687497\pi$
$127$			54.4343i			0.428617i	−0.976766	+	0.214308i	$0.931250\pi$
$128$		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
$133$	82.2126	−	47.4654i	0.618140	−	0.356883i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	16.0288	+	27.7627i	0.116999	+	0.202648i	0.918577	−	0.395242i	$-0.129339\pi$
$137$	16.0288	+	27.7627i	0.116999	+	0.202648i	−0.801578	+	0.597890i	$0.796006\pi$
$138$		0			0
$139$	122.331	−	211.884i	0.880080	−	1.52434i	0.0288281	−	0.999584i	$-0.490822\pi$
$139$	122.331	−	211.884i	0.880080	−	1.52434i	0.851251	−	0.524758i	$-0.175844\pi$
$140$		0			0
$141$	1.29576	+	6.68522i	0.00918976	+	0.0474129i
$142$		0			0
$143$	−51.9933			−0.363590
$144$		0			0
$145$		0			0
$146$		0			0
$147$	44.3223	−	38.4870i	0.301512	−	0.261817i
$148$		0			0
$149$	142.535	+	82.2928i	0.956613	+	0.552301i	0.895129	−	0.445807i	$-0.147083\pi$
$149$	142.535	+	82.2928i	0.956613	+	0.552301i	0.0614839	+	0.998108i	$0.480417\pi$
$150$		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
$153$	−123.688	−	96.8498i	−0.808421	−	0.633005i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	113.488	+	65.5221i	0.722851	+	0.417338i	0.815801	−	0.578332i	$-0.196296\pi$
$157$	113.488	+	65.5221i	0.722851	+	0.417338i	−0.0929500	+	0.995671i	$0.529630\pi$
$158$		0			0
$159$	−52.4329	−	18.0856i	−0.329767	−	0.113746i
$160$		0			0
$161$		−	102.164i		−	0.634556i
$162$		0			0
$163$		−	16.6333i		−	0.102044i	−0.998698	−	0.0510222i	$-0.983752\pi$
$163$		−	16.6333i		−	0.102044i	0.998698	−	0.0510222i	$-0.0162479\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	141.991	−	245.936i	0.850248	−	1.47267i	−0.0307367	−	0.999528i	$-0.509785\pi$
$167$	141.991	−	245.936i	0.850248	−	1.47267i	0.880985	−	0.473145i	$-0.156881\pi$
$168$		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
$173$	−105.377	−	182.518i	−0.609115	−	1.05502i	−0.991387	−	0.130969i	$-0.958191\pi$
$173$	−105.377	−	182.518i	−0.609115	−	1.05502i	0.382271	−	0.924050i	$-0.375142\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−160.855	−	185.243i	−0.908785	−	1.04657i
$178$		0			0
$179$			236.272i			1.31996i	0.751285	+	0.659978i	$0.229434\pi$
$179$			236.272i			1.31996i	−0.751285	+	0.659978i	$0.770566\pi$
$180$		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
$183$	−5.37052	−	27.7082i	−0.0293471	−	0.151411i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	153.930	−	88.8718i	0.823157	−	0.475250i
$188$		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
$193$	112.158	+	64.7547i	0.581131	+	0.335516i	0.761583	−	0.648068i	$-0.224423\pi$
$193$	112.158	+	64.7547i	0.581131	+	0.335516i	−0.180452	+	0.983584i	$0.557756\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−335.209			−1.70157			−0.850784	−	0.525515i	$-0.823873\pi$
$197$	−335.209			−1.70157			−0.850784	+	0.525515i	$0.823873\pi$
$198$		0			0
$199$	341.651			1.71684			0.858419	−	0.512950i	$-0.171447\pi$
$199$	341.651			1.71684			0.858419	+	0.512950i	$0.171447\pi$
$200$		0			0
$201$	−72.3269	−	83.2927i	−0.359835	−	0.414392i
$202$		0			0
$203$	−91.0915	+	157.775i	−0.448726	+	0.777217i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	157.207	−	63.3199i	0.759456	−	0.305893i
$208$		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
$213$	55.9590	−	162.234i	0.262718	−	0.761662i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			276.558i			1.27446i
$218$		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
$223$	−295.808	+	170.785i	−1.32649	+	0.765851i	−0.984755	−	0.173945i	$-0.944349\pi$
$223$	−295.808	+	170.785i	−1.32649	+	0.765851i	−0.341737	+	0.939796i	$0.611015\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	41.0966	+	71.1813i	0.181042	+	0.313574i	0.942236	−	0.334951i	$-0.108720\pi$
$227$	41.0966	+	71.1813i	0.181042	+	0.313574i	−0.761194	+	0.648525i	$0.775386\pi$
$228$		0			0
$229$	153.723	−	266.256i	0.671280	−	1.16269i	−0.306261	−	0.951948i	$-0.599078\pi$
$229$	153.723	−	266.256i	0.671280	−	1.16269i	0.977541	−	0.210744i	$-0.0675887\pi$
$230$		0			0
$231$	125.140	−	108.665i	0.541734	−	0.470412i
$232$		0			0
$233$	−415.262			−1.78224			−0.891121	−	0.453766i	$-0.850080\pi$
$233$	−415.262			−1.78224			−0.891121	+	0.453766i	$0.850080\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−21.8662	−	112.815i	−0.0922623	−	0.476011i
$238$		0			0
$239$	219.813	+	126.909i	0.919719	+	0.531000i	0.883545	−	0.468345i	$-0.155150\pi$
$239$	219.813	+	126.909i	0.919719	+	0.531000i	0.0361738	+	0.999346i	$0.488483\pi$
$240$		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
$243$	21.8278	−	242.018i	0.0898265	−	0.995957i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	77.3734	+	44.6715i	0.313252	+	0.180856i
$248$		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
$253$			191.757i			0.757934i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−249.363	+	431.909i	−0.970283	+	1.68058i	−0.275587	+	0.961276i	$0.588872\pi$
$257$	−249.363	+	431.909i	−0.970283	+	1.68058i	−0.694696	+	0.719304i	$0.744461\pi$
$258$		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
$263$	−124.347	−	215.375i	−0.472801	−	0.818915i	0.526714	−	0.850042i	$-0.323424\pi$
$263$	−124.347	−	215.375i	−0.472801	−	0.818915i	−0.999515	+	0.0311270i	$0.990090\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	135.254	−	392.122i	0.506568	−	1.46862i
$268$		0			0
$269$		−	212.591i		−	0.790300i	−0.918617	−	0.395150i	$-0.870693\pi$
$269$		−	212.591i		−	0.790300i	0.918617	−	0.395150i	$-0.129307\pi$
$270$		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
$273$	−78.5602	−	27.0976i	−0.287766	−	0.0992586i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	317.231	−	183.153i	1.14524	−	0.661204i	0.197516	−	0.980300i	$-0.436713\pi$
$277$	317.231	−	183.153i	1.14524	−	0.661204i	0.947722	+	0.319096i	$0.103379\pi$
$278$		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
$283$	−233.240	−	134.661i	−0.824169	−	0.475834i	0.0276831	−	0.999617i	$-0.491187\pi$
$283$	−233.240	−	134.661i	−0.824169	−	0.475834i	−0.851852	+	0.523783i	$0.824520\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−77.8309			−0.271188
$288$		0			0
$289$	15.6756			0.0542409
$290$		0			0
$291$	344.469	−	66.7664i	1.18374	−	0.229438i
$292$		0			0
$293$	−105.489	+	182.712i	−0.360030	+	0.623591i	−0.987965	−	0.154675i	$-0.950567\pi$
$293$	−105.489	+	182.712i	−0.360030	+	0.623591i	0.627935	+	0.778266i	$0.283900\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	244.773	+	125.214i	0.824151	+	0.421597i
$298$		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
$303$	−258.583	+	50.1196i	−0.853410	+	0.165411i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			44.9444i			0.146399i	0.997317	+	0.0731993i	$0.0233209\pi$
$307$			44.9444i			0.146399i	−0.997317	+	0.0731993i	$0.976679\pi$
$308$		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
$313$	145.186	−	83.8232i	0.463853	−	0.267806i	−0.249810	−	0.968295i	$-0.580368\pi$
$313$	145.186	−	83.8232i	0.463853	−	0.267806i	0.713663	+	0.700489i	$0.247035\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	117.945	+	204.287i	0.372068	+	0.644440i	0.989883	−	0.141883i	$-0.0453156\pi$
$317$	117.945	+	204.287i	0.372068	+	0.644440i	−0.617816	+	0.786323i	$0.711982\pi$
$318$		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
$323$	−305.427			−0.945594
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−224.100	−	77.2982i	−0.685320	−	0.236386i
$328$		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
$333$	−3.35964	+	4.29065i	−0.0100890	+	0.0128848i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	279.959	+	161.634i	0.830738	+	0.479627i	0.854105	−	0.520100i	$-0.174105\pi$
$337$	279.959	+	161.634i	0.830738	+	0.479627i	−0.0233670	+	0.999727i	$0.507439\pi$
$338$		0			0
$339$	111.138	−	96.5061i	0.327840	−	0.284679i
$340$		0			0
$341$		−	519.090i		−	1.52226i
$342$		0			0
$343$			371.991i			1.08452i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	193.149	−	334.543i	0.556625	−	0.964102i	−0.441151	−	0.897433i	$-0.645430\pi$
$347$	193.149	−	334.543i	0.556625	−	0.964102i	0.997775	−	0.0666690i	$-0.0212372\pi$
$348$		0			0
$349$	30.3447	+	52.5585i	0.0869474	+	0.150597i	0.906219	−	0.422808i	$-0.138955\pi$
$349$	30.3447	+	52.5585i	0.0869474	+	0.150597i	−0.819272	+	0.573405i	$0.805622\pi$
$350$		0			0
$351$	−6.99351	−	137.682i	−0.0199245	−	0.392256i
$352$		0			0
$353$	58.9936	+	102.180i	0.167121	+	0.289462i	0.937406	−	0.348237i	$-0.113220\pi$
$353$	58.9936	+	102.180i	0.167121	+	0.289462i	−0.770286	+	0.637699i	$0.779886\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	278.902	−	54.0578i	0.781237	−	0.151422i
$358$		0			0
$359$			503.014i			1.40115i	0.713577	+	0.700577i	$0.247074\pi$
$359$			503.014i			1.40115i	−0.713577	+	0.700577i	$0.752926\pi$
$360$		0			0
$361$	−54.8201			−0.151856
$362$		0			0
$363$	39.2032	−	34.0419i	0.107998	−	0.0937794i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−161.866	+	93.4535i	−0.441052	+	0.254642i	−0.704044	−	0.710156i	$-0.748624\pi$
$367$	−161.866	+	93.4535i	−0.441052	+	0.254642i	0.262992	+	0.964798i	$0.415291\pi$
$368$		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
$373$	44.6509	+	25.7792i	0.119708	+	0.0691132i	0.558658	−	0.829398i	$-0.311316\pi$
$373$	44.6509	+	25.7792i	0.119708	+	0.0691132i	−0.438951	+	0.898511i	$0.644650\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−171.459			−0.454799
$378$		0			0
$379$	52.8882			0.139547			0.0697733	−	0.997563i	$-0.477772\pi$
$379$	52.8882			0.139547			0.0697733	+	0.997563i	$0.477772\pi$
$380$		0			0
$381$	53.2490	−	154.377i	0.139761	−	0.405190i
$382$		0			0
$383$	−211.261	+	365.915i	−0.551595	+	0.955391i	0.446565	+	0.894751i	$0.352647\pi$
$383$	−211.261	+	365.915i	−0.551595	+	0.955391i	−0.998160	+	0.0606395i	$0.980686\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	453.155	+	64.1824i	1.17094	+	0.165846i
$388$		0			0
$389$	−535.036	+	308.903i	−1.37541	+	0.794095i	−0.991603	−	0.129317i	$-0.958721\pi$
$389$	−535.036	+	308.903i	−1.37541	+	0.794095i	−0.383810	+	0.923412i	$0.625388\pi$
$390$		0			0
$391$	−164.349	+	284.660i	−0.420329	+	0.728031i
$392$		0			0
$393$	11.5777	+	13.3331i	0.0294598	+	0.0339264i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			451.909i			1.13831i	0.822230	+	0.569155i	$0.192730\pi$
$397$			451.909i			1.13831i	−0.822230	+	0.569155i	$0.807270\pi$
$398$		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
$403$	−225.409	+	130.140i	−0.559327	+	0.322928i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.08289	−	5.33972i	−0.00757466	−	0.0131197i
$408$		0			0
$409$	245.998	−	426.081i	0.601462	−	1.04176i	−0.391138	−	0.920332i	$-0.627919\pi$
$409$	245.998	−	426.081i	0.601462	−	1.04176i	0.992600	−	0.121430i	$-0.0387481\pi$
$410$		0			0
$411$	−18.3000	−	94.4158i	−0.0445256	−	0.229722i
$412$		0			0
$413$	443.668			1.07426
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−554.205	+	481.241i	−1.32903	+	1.15406i
$418$		0			0
$419$	459.193	+	265.115i	1.09593	+	0.632733i	0.935148	−	0.354257i	$-0.115266\pi$
$419$	459.193	+	265.115i	1.09593	+	0.632733i	0.160778	+	0.986991i	$0.448600\pi$
$420$		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
$423$	2.86485	−	20.2270i	0.00677270	−	0.0478181i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	44.2024	+	25.5203i	0.103518	+	0.0597664i
$428$		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
$433$		−	283.902i		−	0.655662i	−0.944736	−	0.327831i	$-0.893682\pi$
$433$		−	283.902i		−	0.655662i	0.944736	−	0.327831i	$-0.106318\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	164.754	−	285.362i	0.377011	−	0.653002i
$438$		0			0
$439$	−235.420	−	407.760i	−0.536265	−	0.928838i	−0.999101	−	0.0423939i	$-0.986502\pi$
$439$	−235.420	−	407.760i	−0.536265	−	0.928838i	0.462836	−	0.886444i	$-0.346832\pi$
$440$		0			0
$441$	−163.348	+	65.7933i	−0.370404	+	0.149191i
$442$		0			0
$443$	−399.196	−	691.428i	−0.901120	−	1.56079i	−0.826043	−	0.563607i	$-0.809413\pi$
$443$	−399.196	−	691.428i	−0.901120	−	1.56079i	−0.0750770	−	0.997178i	$-0.523920\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−323.734	−	372.817i	−0.724237	−	0.834042i
$448$		0			0
$449$		−	605.367i		−	1.34826i	−0.738615	−	0.674128i	$-0.764520\pi$
$449$		−	605.367i		−	1.34826i	0.738615	−	0.674128i	$-0.235480\pi$
$450$		0			0
$451$	146.086			0.323915
$452$		0			0
$453$	−56.5330	−	291.672i	−0.124797	−	0.643868i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−348.420	+	201.161i	−0.762408	+	0.440176i	−0.830160	−	0.557526i	$-0.811751\pi$
$457$	−348.420	+	201.161i	−0.762408	+	0.440176i	0.0677516	+	0.997702i	$0.478417\pi$
$458$		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
$463$	460.450	+	265.841i	0.994493	+	0.574171i	0.906614	−	0.421960i	$-0.138658\pi$
$463$	460.450	+	265.841i	0.994493	+	0.574171i	0.0878790	+	0.996131i	$0.471991\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−534.278			−1.14406			−0.572032	−	0.820231i	$-0.693845\pi$
$467$	−534.278			−1.14406			−0.572032	+	0.820231i	$0.693845\pi$
$468$		0			0
$469$	199.491			0.425353
$470$		0			0
$471$	−257.759	−	296.839i	−0.547259	−	0.630232i
$472$		0			0
$473$	−258.918	+	448.459i	−0.547395	+	0.948116i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	131.010	+	102.582i	0.274653	+	0.215057i
$478$		0			0
$479$	53.6506	−	30.9752i	0.112005	−	0.0646664i	−0.442951	−	0.896546i	$-0.646068\pi$
$479$	53.6506	−	30.9752i	0.112005	−	0.0646664i	0.554956	+	0.831880i	$0.312735\pi$
$480$		0			0
$481$	−1.54581	+	2.67742i	−0.00321374	+	0.00556635i
$482$		0			0
$483$	−99.9390	+	289.739i	−0.206913	+	0.599874i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	693.387i		−	1.42379i	−0.702284	−	0.711896i	$-0.747837\pi$
$487$		−	693.387i		−	1.42379i	0.702284	−	0.711896i	$-0.252163\pi$
$488$		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
$493$	507.619	−	293.074i	1.02965	−	0.594471i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	155.174	+	268.770i	0.312222	+	0.540785i
$498$		0			0
$499$	−342.467	+	593.170i	−0.686307	+	1.18872i	0.286718	+	0.958015i	$0.407436\pi$
$499$	−342.467	+	593.170i	−0.686307	+	1.18872i	−0.973024	+	0.230703i	$0.925897\pi$
$500$		0			0
$501$	−643.273	+	558.584i	−1.28398	+	1.11494i
$502$		0			0
$503$	487.981			0.970141			0.485071	−	0.874475i	$-0.338794\pi$
$503$	487.981			0.970141			0.485071	+	0.874475i	$0.338794\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	81.5911	+	420.955i	0.160929	+	0.830286i
$508$		0			0
$509$	305.197	+	176.206i	0.599601	+	0.346180i	0.768885	−	0.639387i	$-0.220812\pi$
$509$	305.197	+	176.206i	0.599601	+	0.346180i	−0.169283	+	0.985567i	$0.554145\pi$
$510$		0			0
$511$	214.114	+	370.856i	0.419009	+	0.725745i
$512$		0			0
$513$	−256.675	−	396.640i	−0.500341	−	0.773177i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	20.0174	+	11.5571i	0.0387185	+	0.0223541i
$518$		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
$523$		−	66.5684i		−	0.127282i	−0.997973	−	0.0636409i	$-0.979729\pi$
$523$		−	66.5684i		−	0.127282i	0.997973	−	0.0636409i	$-0.0202712\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	444.894	−	770.579i	0.844201	−	1.46220i
$528$		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
$533$	−36.6248	−	63.4360i	−0.0687145	−	0.119017i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	231.127	−	670.075i	0.430405	−	1.24781i
$538$		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
$543$	922.223	+	318.100i	1.69839	+	0.585820i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−138.484	+	79.9536i	−0.253169	+	0.146167i	−0.621215	−	0.783640i	$-0.713360\pi$
$547$	−138.484	+	79.9536i	−0.253169	+	0.146167i	0.368045	+	0.929808i	$0.380027\pi$
$548$		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
$553$	179.971	+	103.906i	0.325445	+	0.187895i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−610.336			−1.09576			−0.547878	−	0.836558i	$-0.684564\pi$
$557$	−610.336			−1.09576			−0.547878	+	0.836558i	$0.684564\pi$
$558$		0			0
$559$	259.651			0.464491
$560$		0			0
$561$	−523.488	+	101.465i	−0.933134	+	0.180864i
$562$		0			0
$563$	454.385	−	787.017i	0.807078	−	1.39790i	−0.107802	−	0.994172i	$-0.534381\pi$
$563$	454.385	−	787.017i	0.807078	−	1.39790i	0.914879	−	0.403727i	$-0.132285\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	304.585	+	316.764i	0.537187	+	0.558667i
$568$		0			0
$569$	−329.712	+	190.360i	−0.579459	+	0.334551i	−0.760919	−	0.648847i	$-0.775251\pi$
$569$	−329.712	+	190.360i	−0.579459	+	0.334551i	0.181459	+	0.983398i	$0.441918\pi$
$570$		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
$573$	326.663	−	63.3151i	0.570093	−	0.110498i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	761.001i		−	1.31889i	−0.751752	−	0.659446i	$-0.770791\pi$
$577$		−	761.001i		−	1.31889i	0.751752	−	0.659446i	$-0.229209\pi$
$578$		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
$583$	−163.042	+	94.1321i	−0.279660	+	0.161462i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	208.324	+	360.828i	0.354897	+	0.614699i	0.987100	−	0.160103i	$-0.0511828\pi$
$587$	208.324	+	360.828i	0.354897	+	0.614699i	−0.632204	+	0.774802i	$0.717849\pi$
$588$		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
$593$	775.358			1.30752			0.653759	−	0.756703i	$-0.273191\pi$
$593$	775.358			1.30752			0.653759	+	0.756703i	$0.273191\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−968.932	−	334.211i	−1.62300	−	0.559818i
$598$		0			0
$599$	−215.994	−	124.704i	−0.360591	−	0.208187i	0.308749	−	0.951144i	$-0.400090\pi$
$599$	−215.994	−	124.704i	−0.360591	−	0.208187i	−0.669340	+	0.742956i	$0.733423\pi$
$600$		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
$603$	123.642	+	306.973i	0.205045	+	0.509076i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−781.026	−	450.926i	−1.28670	−	0.742876i	−0.308635	−	0.951181i	$-0.599872\pi$
$607$	−781.026	−	450.926i	−1.28670	−	0.742876i	−0.978064	+	0.208305i	$0.933205\pi$
$608$		0			0
$609$	412.678	−	358.347i	0.677632	−	0.588419i
$610$		0			0
$611$		−	11.5898i		−	0.0189686i
$612$		0			0
$613$		−	334.064i		−	0.544965i	−0.962161	−	0.272483i	$-0.912155\pi$
$613$		−	334.064i		−	0.544965i	0.962161	−	0.272483i	$-0.0878447\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−89.4659	+	154.959i	−0.145001	+	0.251150i	−0.929373	−	0.369141i	$-0.879652\pi$
$617$	−89.4659	+	154.959i	−0.145001	+	0.251150i	0.784372	+	0.620291i	$0.212985\pi$
$618$		0			0
$619$	201.857	+	349.626i	0.326102	+	0.564825i	0.981735	−	0.190255i	$-0.0609315\pi$
$619$	201.857	+	349.626i	0.326102	+	0.564825i	−0.655633	+	0.755080i	$0.727598\pi$
$620$		0			0
$621$	−507.787	+	25.7929i	−0.817692	+	0.0415344i
$622$		0			0
$623$	375.059	+	649.621i	0.602020	+	1.04273i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	524.779	−	101.715i	0.836968	−	0.162224i
$628$		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
$633$	330.641	−	287.110i	0.522339	−	0.453571i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−86.5210	+	49.9529i	−0.135826	+	0.0784190i
$638$		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
$643$	−950.767	−	548.925i	−1.47864	−	0.853694i	−0.478934	−	0.877851i	$-0.658977\pi$
$643$	−950.767	−	548.925i	−1.47864	−	0.853694i	−0.999708	+	0.0241567i	$0.992310\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	104.927			0.162175			0.0810875	−	0.996707i	$-0.474161\pi$
$647$	104.927			0.162175			0.0810875	+	0.996707i	$0.474161\pi$
$648$		0			0
$649$	−832.748			−1.28312
$650$		0			0
$651$	270.536	−	784.328i	0.415571	−	1.20481i
$652$		0			0
$653$	4.32766	−	7.49573i	0.00662735	−	0.0114789i	−0.862693	−	0.505728i	$-0.831224\pi$
$653$	4.32766	−	7.49573i	0.00662735	−	0.0114789i	0.869320	+	0.494250i	$0.164557\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−437.961	+	559.327i	−0.666607	+	0.851334i
$658$		0			0
$659$	421.081	−	243.111i	0.638969	−	0.368909i	−0.145248	−	0.989395i	$-0.546398\pi$
$659$	421.081	−	243.111i	0.638969	−	0.368909i	0.784217	+	0.620486i	$0.213065\pi$
$660$		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
$663$	175.302	+	201.881i	0.264408	+	0.304496i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			632.361i			0.948068i
$668$		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
$673$	435.185	−	251.254i	0.646635	−	0.373335i	−0.140531	−	0.990076i	$-0.544881\pi$
$673$	435.185	−	251.254i	0.646635	−	0.373335i	0.787166	+	0.616742i	$0.211548\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	559.863	+	969.711i	0.826976	+	1.43236i	0.900399	+	0.435064i	$0.143274\pi$
$677$	559.863	+	969.711i	0.826976	+	1.43236i	−0.0734232	+	0.997301i	$0.523392\pi$
$678$		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
$683$	819.088			1.19925			0.599625	−	0.800281i	$-0.295316\pi$
$683$	819.088			1.19925			0.599625	+	0.800281i	$0.295316\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−696.423	+	604.736i	−1.01372	+	0.880256i
$688$		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
$693$	−461.201	+	185.762i	−0.665514	+	0.268055i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	216.861	+	125.205i	0.311135	+	0.179634i
$698$		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
$703$			10.5950i			0.0150711i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	238.164	−	412.512i	0.336866	−	0.583469i
$708$		0			0
$709$	306.313	+	530.550i	0.432036	+	0.748308i	0.997048	−	0.0767744i	$-0.0244621\pi$
$709$	306.313	+	530.550i	0.432036	+	0.748308i	−0.565013	+	0.825082i	$0.691129\pi$
$710$		0			0
$711$	−48.3450	+	341.336i	−0.0679958	+	0.480078i
$712$		0			0
$713$	479.971	+	831.333i	0.673171	+	1.16597i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−499.251	−	574.945i	−0.696305	−	0.801875i
$718$		0			0
$719$		−	1031.79i		−	1.43503i	−0.696544	−	0.717515i	$-0.745280\pi$
$719$		−	1031.79i		−	1.43503i	0.696544	−	0.717515i	$-0.254720\pi$
$720$		0			0
$721$	1022.26			1.41784
$722$		0			0
$723$	90.5690	+	467.275i	0.125268	+	0.646300i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	18.5495	−	10.7096i	0.0255152	−	0.0147312i	−0.487188	−	0.873297i	$-0.661977\pi$
$727$	18.5495	−	10.7096i	0.0255152	−	0.0147312i	0.512703	+	0.858566i	$0.328644\pi$
$728$		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
$733$	580.882	+	335.373i	0.792472	+	0.457534i	0.840832	−	0.541296i	$-0.182066\pi$
$733$	580.882	+	335.373i	0.792472	+	0.457534i	−0.0483598	+	0.998830i	$0.515399\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−374.437			−0.508055
$738$		0			0
$739$	−925.156			−1.25190			−0.625951	−	0.779862i	$-0.715289\pi$
$739$	−925.156			−1.25190			−0.625951	+	0.779862i	$0.715289\pi$
$740$		0			0
$741$	−175.734	−	202.378i	−0.237159	−	0.273115i
$742$		0			0
$743$	254.196	−	440.281i	0.342122	−	0.592572i	−0.642705	−	0.766114i	$-0.722188\pi$
$743$	254.196	−	440.281i	0.342122	−	0.592572i	0.984827	+	0.173542i	$0.0555212\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−97.5942	+	689.055i	−0.130648	+	0.922430i
$748$		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
$753$	−460.382	+	1334.72i	−0.611397	+	1.77254i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	183.878i		−	0.242904i	−0.992597	−	0.121452i	$-0.961245\pi$
$757$		−	183.878i		−	0.242904i	0.992597	−	0.121452i	$-0.0387550\pi$
$758$		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
$763$	371.262	−	214.348i	0.486581	−	0.280928i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	208.776	+	361.611i	0.272198	+	0.471461i
$768$		0			0
$769$	−652.189	+	1129.63i	−0.848101	+	1.46895i	0.0348004	+	0.999394i	$0.488920\pi$
$769$	−652.189	+	1129.63i	−0.848101	+	1.46895i	−0.882901	+	0.469559i	$0.844413\pi$
$770$		0			0
$771$	1129.70	−	980.974i	1.46525	−	1.27234i
$772$		0			0
$773$	−312.549			−0.404332			−0.202166	−	0.979351i	$-0.564798\pi$
$773$	−312.549			−0.404332			−0.202166	+	0.979351i	$0.564798\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.87522	−	9.67487i	−0.00241341	−	0.0124516i
$778$		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
$783$	807.191	+	412.921i	1.03090	+	0.527358i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−182.390	−	105.303i	−0.231754	−	0.133803i	0.379627	−	0.925140i	$-0.376052\pi$
$787$	−182.390	−	105.303i	−0.231754	−	0.133803i	−0.611381	+	0.791337i	$0.709386\pi$
$788$		0			0
$789$	141.966	+	732.449i	0.179932	+	0.928325i
$790$		0			0
$791$			266.182i			0.336513i
$792$		0			0
$793$			48.0362i			0.0605752i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	555.552	−	962.245i	0.697054	−	1.20733i	−0.272429	−	0.962176i	$-0.587827\pi$
$797$	555.552	−	962.245i	0.697054	−	1.20733i	0.969483	−	0.245158i	$-0.0788398\pi$
$798$		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
$803$	−401.884	−	696.083i	−0.500478	−	0.866853i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−207.962	+	602.914i	−0.257697	+	0.747105i
$808$		0			0
$809$		−	1552.47i		−	1.91900i	−0.281702	−	0.959502i	$-0.590899\pi$
$809$		−	1552.47i		−	1.91900i	0.281702	−	0.959502i	$-0.409101\pi$
$810$		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
$813$	−426.003	−	146.940i	−0.523989	−	0.180738i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	770.612	−	444.913i	0.943222	−	0.544569i
$818$		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
$823$	−332.933	−	192.219i	−0.404536	−	0.233559i	0.283903	−	0.958853i	$-0.408371\pi$
$823$	−332.933	−	192.219i	−0.404536	−	0.233559i	−0.688439	+	0.725294i	$0.741704\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−228.210			−0.275949			−0.137974	−	0.990436i	$-0.544059\pi$
$827$	−228.210			−0.275949			−0.137974	+	0.990436i	$0.544059\pi$
$828$		0			0
$829$	−108.877			−0.131335			−0.0656674	−	0.997842i	$-0.520918\pi$
$829$	−108.877			−0.131335			−0.0656674	+	0.997842i	$0.520918\pi$
$830$		0			0
$831$	−1078.84	+	209.105i	−1.29825	+	0.251631i
$832$		0			0
$833$	170.768	−	295.779i	0.205004	−	0.355077i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1374.59	−	69.8217i	1.64228	−	0.0834190i
$838$		0			0
$839$	−809.618	+	467.433i	−0.964980	+	0.557131i	−0.897702	−	0.440603i	$-0.854765\pi$
$839$	−809.618	+	467.433i	−0.964980	+	0.557131i	−0.0672778	+	0.997734i	$0.521431\pi$
$840$		0			0
$841$	143.328	−	248.252i	0.170426	−	0.295187i
$842$		0			0
$843$	387.464	−	75.0997i	0.459625	−	0.0890862i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			93.8939i			0.110855i
$848$		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
$853$	−1023.49	+	590.914i	−1.19988	+	0.692748i	−0.960527	−	0.278185i	$-0.910267\pi$
$853$	−1023.49	+	590.914i	−1.19988	+	0.692748i	−0.239348	+	0.970934i	$0.576934\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	491.500	+	851.303i	0.573512	+	0.993352i	0.996202	+	0.0870776i	$0.0277528\pi$
$857$	491.500	+	851.303i	0.573512	+	0.993352i	−0.422689	+	0.906275i	$0.638914\pi$
$858$		0			0
$859$	764.988	−	1325.00i	0.890557	−	1.54249i	0.0513472	−	0.998681i	$-0.483648\pi$
$859$	764.988	−	1325.00i	0.890557	−	1.54249i	0.839209	−	0.543808i	$-0.183018\pi$
$860$		0			0
$861$	220.731	+	76.1362i	0.256366	+	0.0884276i
$862$		0			0
$863$	932.711			1.08078			0.540389	−	0.841415i	$-0.318277\pi$
$863$	932.711			1.08078			0.540389	+	0.841415i	$0.318277\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−44.4566	−	15.3343i	−0.0512763	−	0.0176866i
$868$		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
$873$	−1042.24	−	147.617i	−1.19386	−	0.169092i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1088.45	−	628.419i	−1.24111	−	0.716555i	−0.271790	−	0.962357i	$-0.587615\pi$
$877$	−1088.45	−	628.419i	−1.24111	−	0.716555i	−0.969320	+	0.245802i	$0.920949\pi$
$878$		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
$883$		−	618.566i		−	0.700527i	−0.936651	−	0.350264i	$-0.886092\pi$
$883$		−	618.566i		−	0.700527i	0.936651	−	0.350264i	$-0.113908\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	745.723	−	1291.63i	0.840725	−	1.45618i	−0.0485585	−	0.998820i	$-0.515463\pi$
$887$	745.723	−	1291.63i	0.840725	−	1.45618i	0.889283	−	0.457357i	$-0.151204\pi$
$888$		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
$893$	−19.8592	−	34.3971i	−0.0222387	−	0.0385186i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−283.180	+	54.8870i	−0.315697	+	0.0611895i
$898$		0			0
$899$		−	1711.81i		−	1.90413i
$900$		0			0
$901$	−322.709			−0.358168
$902$		0			0
$903$	−624.942	+	542.666i	−0.692073	+	0.600959i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−398.947	+	230.332i	−0.439853	+	0.253949i	−0.703535	−	0.710660i	$-0.748396\pi$
$907$	−398.947	+	230.332i	−0.439853	+	0.253949i	0.263682	+	0.964610i	$0.415063\pi$
$908$		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
$913$	−681.915	−	393.704i	−0.746895	−	0.431220i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−31.9334			−0.0348238
$918$		0			0
$919$	−1651.74			−1.79733			−0.898663	−	0.438639i	$-0.855461\pi$
$919$	−1651.74			−1.79733			−0.898663	+	0.438639i	$0.855461\pi$
$920$		0			0
$921$	43.9657	−	127.464i	0.0477369	−	0.138397i
$922$		0			0
$923$	−146.041	+	252.950i	−0.158224	+	0.274052i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	633.587	+	1573.04i	0.683481	+	1.69691i
$928$		0			0
$929$	632.169	−	364.983i	0.680483	−	0.392877i	−0.119554	−	0.992828i	$-0.538146\pi$
$929$	632.169	−	364.983i	0.680483	−	0.392877i	0.800037	+	0.599951i	$0.204813\pi$
$930$		0			0
$931$	−171.189	+	296.509i	−0.183877	+	0.318484i
$932$		0			0
$933$	−21.5413	−	24.8073i	−0.0230883	−	0.0265888i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	1098.36i		−	1.17221i	−0.810236	−	0.586104i	$-0.800661\pi$
$937$		−	1098.36i		−	1.17221i	0.810236	−	0.586104i	$-0.199339\pi$
$938$		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
$943$	−233.959	+	135.077i	−0.248101	+	0.143241i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	397.289	+	688.125i	0.419524	+	0.726636i	0.995892	−	0.0905541i	$-0.0288638\pi$
$947$	397.289	+	688.125i	0.419524	+	0.726636i	−0.576368	+	0.817190i	$0.695530\pi$
$948$		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
$953$	−493.659			−0.518005			−0.259003	−	0.965877i	$-0.583394\pi$
$953$	−493.659			−0.518005			−0.259003	+	0.965877i	$0.583394\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−774.581	+	672.604i	−0.809385	+	0.702826i
$958$		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
$963$	−1206.61	−	944.789i	−1.25296	−	0.981089i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1087.90	−	628.097i	−1.12502	−	0.649532i	−0.182344	−	0.983235i	$-0.558368\pi$
$967$	−1087.90	−	628.097i	−1.12502	−	0.649532i	−0.942678	+	0.333703i	$0.891702\pi$
$968$		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
$973$		−	1327.35i		−	1.36418i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	503.542	−	872.160i	0.515396	−	0.892691i	−0.484445	−	0.874822i	$-0.660978\pi$
$977$	503.542	−	872.160i	0.515396	−	0.892691i	0.999840	−	0.0178695i	$-0.00568835\pi$
$978$		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
$983$	−273.430	−	473.595i	−0.278159	−	0.481785i	0.692768	−	0.721160i	$-0.256391\pi$
$983$	−273.430	−	473.595i	−0.278159	−	0.481785i	−0.970927	+	0.239375i	$0.923058\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	24.2225	+	27.8950i	0.0245415	+	0.0282624i
$988$		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
$993$	−101.047	−	521.333i	−0.101759	−	0.525008i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	463.727	−	267.733i	0.465123	−	0.268539i	−0.249073	−	0.968485i	$-0.580126\pi$
$997$	463.727	−	267.733i	0.465123	−	0.268539i	0.714196	+	0.699946i	$0.246793\pi$
$998$		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.u.d.149.1		32
3.2	odd	2		2700.3.u.d.449.12		32
5.2	odd	4		900.3.p.e.401.4	yes	16
5.3	odd	4		900.3.p.d.401.5	yes	16
5.4	even	2	inner	900.3.u.d.149.16		32
9.2	odd	6	inner	900.3.u.d.749.16		32
9.7	even	3		2700.3.u.d.2249.5		32
15.2	even	4		2700.3.p.d.2501.6		16
15.8	even	4		2700.3.p.e.2501.3		16
15.14	odd	2		2700.3.u.d.449.5		32
45.2	even	12		900.3.p.e.101.4	yes	16
45.7	odd	12		2700.3.p.d.1601.6		16
45.29	odd	6	inner	900.3.u.d.749.1		32
45.34	even	6		2700.3.u.d.2249.12		32
45.38	even	12		900.3.p.d.101.5	✓	16
45.43	odd	12		2700.3.p.e.1601.3		16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.83603 - 0.978225i) q^{3} +(4.69840 - 2.71262i) q^{7} +(7.08615 + 5.54856i) q^{9} +O(q^{10})\)	\(q+(-2.83603 - 0.978225i) q^{3} +(4.69840 - 2.71262i) q^{7} +(7.08615 + 5.54856i) q^{9} +(-8.81872 + 5.09149i) q^{11} +(4.42184 + 2.55295i) q^{13} -17.4550 q^{17} +17.4980 q^{19} +(-15.9784 + 3.09699i) q^{21} +(9.41558 - 16.3083i) q^{23} +(-14.6688 - 22.6677i) q^{27} +(-29.0817 + 16.7903i) q^{29} +(-25.4881 + 44.1467i) q^{31} +(29.9908 - 5.81293i) q^{33} +0.605498i q^{37} +(-10.0431 - 11.5658i) q^{39} +(-12.4241 - 7.17303i) q^{41} +(44.0400 - 25.4265i) q^{43} +(-1.13494 - 1.96577i) q^{47} +(-9.78337 + 16.9453i) q^{49} +(49.5028 + 17.0749i) q^{51} +18.4881 q^{53} +(-49.6249 - 17.1170i) q^{57} +(70.8221 + 40.8892i) q^{59} +(4.70398 + 8.14754i) q^{61} +(48.3447 + 6.84729i) q^{63} +(31.8445 + 18.3854i) q^{67} +(-42.6560 + 37.0402i) q^{69} +57.2046i q^{71} +78.9324i q^{73} +(-27.6226 + 47.8437i) q^{77} +(19.1524 + 33.1729i) q^{79} +(19.4270 + 78.6358i) q^{81} +(38.6629 + 66.9661i) q^{83} +(98.9012 - 19.1694i) q^{87} +138.264i q^{89} +27.7008 q^{91} +(115.471 - 100.268i) q^{93} +(-101.290 + 58.4800i) q^{97} +(-90.7412 - 12.8521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 28 q^{9}+O(q^{10}) \) 32 * q - 28 * q^9	\( 32 q - 28 q^{9} - 4 q^{19} + 2 q^{21} - 18 q^{29} + 16 q^{31} - 38 q^{39} + 108 q^{41} + 90 q^{49} + 180 q^{51} - 18 q^{59} - 110 q^{61} + 294 q^{69} - 22 q^{79} - 260 q^{81} - 268 q^{91} - 504 q^{99}+O(q^{100}) \) 32 * q - 28 * q^9 - 4 * q^19 + 2 * q^21 - 18 * q^29 + 16 * q^31 - 38 * q^39 + 108 * q^41 + 90 * q^49 + 180 * q^51 - 18 * q^59 - 110 * q^61 + 294 * q^69 - 22 * q^79 - 260 * q^81 - 268 * q^91 - 504 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more