LMFDB - Embedded newform 900.3.p.b.401.2

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			401.2
Root			$-1.93649 - 1.11803i$ of defining polynomial
Character	$\chi$	$=$	900.401
Dual form			900.3.p.b.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} +(1.87298 + 3.24410i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	$q+(1.50000 + 2.59808i) q^{3} +(1.87298 + 3.24410i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-10.1190 + 5.84218i) q^{11} +(-1.12702 + 1.95205i) q^{13} -11.6844i q^{17} -26.7460 q^{19} +(-5.61895 + 9.73231i) q^{21} +(17.2379 + 9.95231i) q^{23} -27.0000 q^{27} +(-38.2379 + 22.0767i) q^{29} +(26.1109 - 45.2254i) q^{31} +(-30.3569 - 17.5265i) q^{33} -14.0000 q^{37} -6.76210 q^{39} +(-22.5000 - 12.9904i) q^{41} +(20.9919 + 36.3591i) q^{43} +(-39.3810 + 22.7367i) q^{47} +(17.4839 - 30.2829i) q^{49} +(30.3569 - 17.5265i) q^{51} +10.8323i q^{53} +(-40.1190 - 69.4881i) q^{57} +(-31.8810 - 18.4065i) q^{59} +(22.6190 + 39.1772i) q^{61} -33.7137 q^{63} +(-49.9758 + 86.5606i) q^{67} +59.7138i q^{69} +102.603i q^{71} +13.7621 q^{73} +(-37.9052 - 21.8846i) q^{77} +(-28.3810 - 49.1574i) q^{79} +(-40.5000 - 70.1481i) q^{81} +(78.0000 - 45.0333i) q^{83} +(-114.714 - 66.2300i) q^{87} -95.2349i q^{89} -8.44353 q^{91} +156.665 q^{93} +(-50.8488 - 88.0727i) q^{97} -105.159i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - 8 q^{7} - 18 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 - 8 * q^7 - 18 * q^9	$ 4 q + 6 q^{3} - 8 q^{7} - 18 q^{9} + 6 q^{11} - 20 q^{13} - 76 q^{19} + 24 q^{21} - 24 q^{23} - 108 q^{27} - 60 q^{29} - 4 q^{31} + 18 q^{33} - 56 q^{37} - 120 q^{39} - 90 q^{41} + 22 q^{43} - 204 q^{47} - 54 q^{49} - 18 q^{51} - 114 q^{57} - 174 q^{59} + 44 q^{61} + 144 q^{63} - 14 q^{67} + 148 q^{73} - 384 q^{77} - 160 q^{79} - 162 q^{81} + 312 q^{83} - 180 q^{87} + 400 q^{91} - 24 q^{93} - 2 q^{97}+O(q^{100}) $ 4 * q + 6 * q^3 - 8 * q^7 - 18 * q^9 + 6 * q^11 - 20 * q^13 - 76 * q^19 + 24 * q^21 - 24 * q^23 - 108 * q^27 - 60 * q^29 - 4 * q^31 + 18 * q^33 - 56 * q^37 - 120 * q^39 - 90 * q^41 + 22 * q^43 - 204 * q^47 - 54 * q^49 - 18 * q^51 - 114 * q^57 - 174 * q^59 + 44 * q^61 + 144 * q^63 - 14 * q^67 + 148 * q^73 - 384 * q^77 - 160 * q^79 - 162 * q^81 + 312 * q^83 - 180 * q^87 + 400 * q^91 - 24 * q^93 - 2 * q^97

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
$3$	1.50000	+	2.59808i	0.500000	+	0.866025i
$3$	1.50000	+	2.59808i	0.500000	+	0.866025i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.87298	+	3.24410i	0.267569	+	0.463443i	0.968234	−	0.250048i	$-0.0804463\pi$
$7$	1.87298	+	3.24410i	0.267569	+	0.463443i	−0.700664	+	0.713491i	$0.747113\pi$
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$10$		0			0
$11$	−10.1190	+	5.84218i	−0.919905	+	0.531107i	−0.883605	−	0.468234i	$-0.844891\pi$
$11$	−10.1190	+	5.84218i	−0.919905	+	0.531107i	−0.0362999	+	0.999341i	$0.511557\pi$
$12$		0			0
$13$	−1.12702	+	1.95205i	−0.0866936	+	0.150158i	−0.906112	−	0.423039i	$-0.860963\pi$
$13$	−1.12702	+	1.95205i	−0.0866936	+	0.150158i	0.819418	+	0.573196i	$0.194297\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	11.6844i		−	0.687315i	−0.939095	−	0.343658i	$-0.888334\pi$
$17$		−	11.6844i		−	0.687315i	0.939095	−	0.343658i	$-0.111666\pi$
$18$		0			0
$19$	−26.7460			−1.40768			−0.703841	−	0.710357i	$-0.748533\pi$
$19$	−26.7460			−1.40768			−0.703841	+	0.710357i	$0.748533\pi$
$20$		0			0
$21$	−5.61895	+	9.73231i	−0.267569	+	0.463443i
$22$		0			0
$23$	17.2379	+	9.95231i	0.749474	+	0.432709i	0.825504	−	0.564397i	$-0.190891\pi$
$23$	17.2379	+	9.95231i	0.749474	+	0.432709i	−0.0760299	+	0.997106i	$0.524224\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−27.0000			−1.00000
$28$		0			0
$29$	−38.2379	+	22.0767i	−1.31855	+	0.761264i	−0.983495	−	0.180935i	$-0.942088\pi$
$29$	−38.2379	+	22.0767i	−1.31855	+	0.761264i	−0.335053	+	0.942199i	$0.608754\pi$
$30$		0			0
$31$	26.1109	−	45.2254i	0.842287	−	1.45888i	−0.0456704	−	0.998957i	$-0.514542\pi$
$31$	26.1109	−	45.2254i	0.842287	−	1.45888i	0.887957	−	0.459927i	$-0.152124\pi$
$32$		0			0
$33$	−30.3569	−	17.5265i	−0.919905	−	0.531107i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−14.0000			−0.378378			−0.189189	−	0.981941i	$-0.560586\pi$
$37$	−14.0000			−0.378378			−0.189189	+	0.981941i	$0.560586\pi$
$38$		0			0
$39$	−6.76210			−0.173387
$40$		0			0
$41$	−22.5000	−	12.9904i	−0.548780	−	0.316839i	0.199849	−	0.979827i	$-0.435955\pi$
$41$	−22.5000	−	12.9904i	−0.548780	−	0.316839i	−0.748630	+	0.662988i	$0.769288\pi$
$42$		0			0
$43$	20.9919	+	36.3591i	0.488184	+	0.845560i	0.999908	−	0.0135900i	$-0.00432598\pi$
$43$	20.9919	+	36.3591i	0.488184	+	0.845560i	−0.511723	+	0.859150i	$0.670993\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−39.3810	+	22.7367i	−0.837895	+	0.483759i	−0.856548	−	0.516067i	$-0.827395\pi$
$47$	−39.3810	+	22.7367i	−0.837895	+	0.483759i	0.0186534	+	0.999826i	$0.494062\pi$
$48$		0			0
$49$	17.4839	−	30.2829i	0.356814	−	0.618019i
$50$		0			0
$51$	30.3569	−	17.5265i	0.595232	−	0.343658i
$52$		0			0
$53$			10.8323i			0.204383i	0.994765	+	0.102192i	$0.0325855\pi$
$53$			10.8323i			0.204383i	−0.994765	+	0.102192i	$0.967415\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−40.1190	−	69.4881i	−0.703841	−	1.21909i
$58$		0			0
$59$	−31.8810	−	18.4065i	−0.540357	−	0.311975i	0.204867	−	0.978790i	$-0.434324\pi$
$59$	−31.8810	−	18.4065i	−0.540357	−	0.311975i	−0.745224	+	0.666815i	$0.767657\pi$
$60$		0			0
$61$	22.6190	+	39.1772i	0.370802	+	0.642249i	0.989689	−	0.143232i	$-0.0457494\pi$
$61$	22.6190	+	39.1772i	0.370802	+	0.642249i	−0.618887	+	0.785480i	$0.712416\pi$
$62$		0			0
$63$	−33.7137			−0.535138
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−49.9758	+	86.5606i	−0.745907	+	1.29195i	0.203862	+	0.979000i	$0.434651\pi$
$67$	−49.9758	+	86.5606i	−0.745907	+	1.29195i	−0.949770	+	0.312950i	$0.898683\pi$
$68$		0			0
$69$			59.7138i			0.865418i
$70$		0			0
$71$			102.603i			1.44511i	0.691312	+	0.722557i	$0.257033\pi$
$71$			102.603i			1.44511i	−0.691312	+	0.722557i	$0.742967\pi$
$72$		0			0
$73$	13.7621			0.188522			0.0942610	−	0.995548i	$-0.469951\pi$
$73$	13.7621			0.188522			0.0942610	+	0.995548i	$0.469951\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−37.9052	−	21.8846i	−0.492276	−	0.284216i
$78$		0			0
$79$	−28.3810	−	49.1574i	−0.359254	−	0.622246i	0.628583	−	0.777743i	$-0.283635\pi$
$79$	−28.3810	−	49.1574i	−0.359254	−	0.622246i	−0.987836	+	0.155497i	$0.950302\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.500000	−	0.866025i
$82$		0			0
$83$	78.0000	−	45.0333i	0.939759	−	0.542570i	0.0498743	−	0.998756i	$-0.484118\pi$
$83$	78.0000	−	45.0333i	0.939759	−	0.542570i	0.889885	+	0.456185i	$0.150785\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−114.714	−	66.2300i	−1.31855	−	0.761264i
$88$		0			0
$89$		−	95.2349i		−	1.07005i	−0.844835	−	0.535027i	$-0.820301\pi$
$89$		−	95.2349i		−	1.07005i	0.844835	−	0.535027i	$-0.179699\pi$
$90$		0			0
$91$	−8.44353			−0.0927861
$92$		0			0
$93$	156.665			1.68457
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−50.8488	−	88.0727i	−0.524214	−	0.907966i	−0.999603	−	0.0281897i	$-0.991026\pi$
$97$	−50.8488	−	88.0727i	−0.524214	−	0.907966i	0.475388	−	0.879776i	$-0.342308\pi$
$98$		0			0
$99$		−	105.159i		−	1.06221i
$100$		0			0
$101$	−87.7621	+	50.6695i	−0.868932	+	0.501678i	−0.866993	−	0.498320i	$-0.833950\pi$
$101$	−87.7621	+	50.6695i	−0.868932	+	0.501678i	−0.00193860	+	0.999998i	$0.500617\pi$
$102$		0			0
$103$	8.14315	−	14.1043i	0.0790597	−	0.136935i	−0.823785	−	0.566903i	$-0.808142\pi$
$103$	8.14315	−	14.1043i	0.0790597	−	0.136935i	0.902844	+	0.429967i	$0.141475\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			84.8705i			0.793182i	0.917995	+	0.396591i	$0.129807\pi$
$107$			84.8705i			0.793182i	−0.917995	+	0.396591i	$0.870193\pi$
$108$		0			0
$109$	−161.968			−1.48594			−0.742971	−	0.669323i	$-0.766584\pi$
$109$	−161.968			−1.48594			−0.742971	+	0.669323i	$0.766584\pi$
$110$		0			0
$111$	−21.0000	−	36.3731i	−0.189189	−	0.327685i
$112$		0			0
$113$	−6.00000	−	3.46410i	−0.0530973	−	0.0306558i	0.473216	−	0.880946i	$-0.343093\pi$
$113$	−6.00000	−	3.46410i	−0.0530973	−	0.0306558i	−0.526314	+	0.850290i	$0.676426\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−10.1431	−	17.5685i	−0.0866936	−	0.150158i
$118$		0			0
$119$	37.9052	−	21.8846i	0.318532	−	0.183904i
$120$		0			0
$121$	7.76210	−	13.4444i	0.0641496	−	0.111110i
$122$		0			0
$123$		−	77.9423i		−	0.633677i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	225.903			1.77877			0.889383	−	0.457163i	$-0.151135\pi$
$127$	225.903			1.77877			0.889383	+	0.457163i	$0.151135\pi$
$128$		0			0
$129$	−62.9758	+	109.077i	−0.488184	+	0.845560i
$130$		0			0
$131$	−81.7137	−	47.1774i	−0.623769	−	0.360133i	0.154566	−	0.987982i	$-0.450602\pi$
$131$	−81.7137	−	47.1774i	−0.623769	−	0.360133i	−0.778335	+	0.627849i	$0.783935\pi$
$132$		0			0
$133$	−50.0948	−	86.7667i	−0.376652	−	0.652381i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−179.595	+	103.689i	−1.31091	+	0.756855i	−0.982247	−	0.187592i	$-0.939932\pi$
$137$	−179.595	+	103.689i	−1.31091	+	0.756855i	−0.328664	+	0.944447i	$0.606598\pi$
$138$		0			0
$139$	−16.3569	+	28.3309i	−0.117675	+	0.203819i	−0.918846	−	0.394616i	$-0.870877\pi$
$139$	−16.3569	+	28.3309i	−0.117675	+	0.203819i	0.801171	+	0.598436i	$0.204211\pi$
$140$		0			0
$141$	−118.143	−	68.2100i	−0.837895	−	0.483759i
$142$		0			0
$143$		−	26.3369i		−	0.184174i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	104.903			0.713627
$148$		0			0
$149$	18.3327	+	10.5844i	0.123038	+	0.0710360i	0.560256	−	0.828320i	$-0.310703\pi$
$149$	18.3327	+	10.5844i	0.123038	+	0.0710360i	−0.437218	+	0.899356i	$0.644036\pi$
$150$		0			0
$151$	137.714	+	238.527i	0.912011	+	1.57965i	0.811219	+	0.584742i	$0.198804\pi$
$151$	137.714	+	238.527i	0.912011	+	1.57965i	0.100792	+	0.994908i	$0.467862\pi$
$152$		0			0
$153$	91.0706	+	52.5796i	0.595232	+	0.343658i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	89.9677	−	155.829i	0.573043	−	0.992539i	−0.423208	−	0.906032i	$-0.639096\pi$
$157$	89.9677	−	155.829i	0.573043	−	0.992539i	0.996251	−	0.0865070i	$-0.0275705\pi$
$158$		0			0
$159$	−28.1431	+	16.2485i	−0.177001	+	0.102192i
$160$		0			0
$161$			74.5620i			0.463118i
$162$		0			0
$163$	264.411			1.62216			0.811078	−	0.584939i	$-0.198881\pi$
$163$	264.411			1.62216			0.811078	+	0.584939i	$0.198881\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−149.522	−	86.3267i	−0.895342	−	0.516926i	−0.0196561	−	0.999807i	$-0.506257\pi$
$167$	−149.522	−	86.3267i	−0.895342	−	0.516926i	−0.875686	+	0.482881i	$0.839590\pi$
$168$		0			0
$169$	81.9597	+	141.958i	0.484968	+	0.839990i
$170$		0			0
$171$	120.357	−	208.464i	0.703841	−	1.21909i
$172$		0			0
$173$	−254.903	+	147.168i	−1.47343	+	0.850685i	−0.999553	−	0.0299069i	$-0.990479\pi$
$173$	−254.903	+	147.168i	−1.47343	+	0.850685i	−0.473876	+	0.880591i	$0.657146\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	110.439i		−	0.623950i
$178$		0			0
$179$			64.1138i			0.358178i	0.983833	+	0.179089i	$0.0573150\pi$
$179$			64.1138i			0.358178i	−0.983833	+	0.179089i	$0.942685\pi$
$180$		0			0
$181$	291.206			1.60887			0.804435	−	0.594040i	$-0.202468\pi$
$181$	291.206			1.60887			0.804435	+	0.594040i	$0.202468\pi$
$182$		0			0
$183$	−67.8569	+	117.532i	−0.370802	+	0.642249i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	68.2621	+	118.233i	0.365038	+	0.632264i
$188$		0			0
$189$	−50.5706	−	87.5908i	−0.267569	−	0.463443i
$190$		0			0
$191$	13.8085	−	7.97231i	0.0722956	−	0.0417399i	−0.463416	−	0.886141i	$-0.653377\pi$
$191$	13.8085	−	7.97231i	0.0722956	−	0.0417399i	0.535712	+	0.844401i	$0.320043\pi$
$192$		0			0
$193$	−122.357	+	211.928i	−0.633973	+	1.09807i	0.352758	+	0.935714i	$0.385244\pi$
$193$	−122.357	+	211.928i	−0.633973	+	1.09807i	−0.986732	+	0.162360i	$0.948090\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			210.374i			1.06789i	0.845519	+	0.533945i	$0.179291\pi$
$197$			210.374i			1.06789i	−0.845519	+	0.533945i	$0.820709\pi$
$198$		0			0
$199$	−102.730			−0.516230			−0.258115	−	0.966114i	$-0.583101\pi$
$199$	−102.730			−0.516230			−0.258115	+	0.966114i	$0.583101\pi$
$200$		0			0
$201$	−299.855			−1.49181
$202$		0			0
$203$	−143.238	−	82.6984i	−0.705605	−	0.407381i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−155.141	+	89.5708i	−0.749474	+	0.432709i
$208$		0			0
$209$	270.641	−	156.255i	1.29493	−	0.747630i
$210$		0			0
$211$	113.984	−	197.426i	0.540208	−	0.935668i	−0.458684	−	0.888600i	$-0.651679\pi$
$211$	113.984	−	197.426i	0.540208	−	0.935668i	0.998892	−	0.0470680i	$-0.0149877\pi$
$212$		0			0
$213$	−266.571	+	153.905i	−1.25150	+	0.722557i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	195.621			0.901479
$218$		0			0
$219$	20.6431	+	35.7550i	0.0942610	+	0.163265i
$220$		0			0
$221$	22.8085	+	13.1685i	0.103206	+	0.0595858i
$222$		0			0
$223$	−139.681	−	241.935i	−0.626374	−	1.08491i	−0.988273	−	0.152695i	$-0.951205\pi$
$223$	−139.681	−	241.935i	−0.626374	−	1.08491i	0.361899	−	0.932217i	$-0.382128\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−215.262	+	124.282i	−0.948291	+	0.547496i	−0.892550	−	0.450949i	$-0.851086\pi$
$227$	−215.262	+	124.282i	−0.948291	+	0.547496i	−0.0557415	+	0.998445i	$0.517752\pi$
$228$		0			0
$229$	−78.8891	+	136.640i	−0.344494	+	0.596681i	−0.985262	−	0.171054i	$-0.945283\pi$
$229$	−78.8891	+	136.640i	−0.344494	+	0.596681i	0.640768	+	0.767735i	$0.278616\pi$
$230$		0			0
$231$		−	131.308i		−	0.568431i
$232$		0			0
$233$			332.854i			1.42856i	0.699861	+	0.714279i	$0.253245\pi$
$233$			332.854i			1.42856i	−0.699861	+	0.714279i	$0.746755\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	85.1431	−	147.472i	0.359254	−	0.622246i
$238$		0			0
$239$	207.714	+	119.924i	0.869095	+	0.501772i	0.867047	−	0.498226i	$-0.166015\pi$
$239$	207.714	+	119.924i	0.869095	+	0.501772i	0.00204759	+	0.999998i	$0.499348\pi$
$240$		0			0
$241$	94.7540	+	164.119i	0.393170	+	0.680991i	0.992866	−	0.119237i	$-0.0380450\pi$
$241$	94.7540	+	164.119i	0.393170	+	0.680991i	−0.599696	+	0.800228i	$0.704712\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.500000	−	0.866025i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	30.1431	−	52.2095i	0.122037	−	0.211374i
$248$		0			0
$249$	234.000	+	135.100i	0.939759	+	0.542570i
$250$		0			0
$251$			447.114i			1.78133i	0.454661	+	0.890664i	$0.349760\pi$
$251$			447.114i			1.78133i	−0.454661	+	0.890664i	$0.650240\pi$
$252$		0			0
$253$	−232.573			−0.919259
$254$		0			0
$255$		0			0
$256$		0			0
$257$	387.308	+	223.613i	1.50704	+	0.870088i	0.999967	+	0.00818336i	$0.00260487\pi$
$257$	387.308	+	223.613i	1.50704	+	0.870088i	0.507070	+	0.861905i	$0.330728\pi$
$258$		0			0
$259$	−26.2218	−	45.4174i	−0.101242	−	0.175357i
$260$		0			0
$261$		−	397.380i		−	1.52253i
$262$		0			0
$263$	307.046	−	177.273i	1.16748	−	0.674043i	0.214392	−	0.976748i	$-0.431223\pi$
$263$	307.046	−	177.273i	1.16748	−	0.674043i	0.953084	+	0.302705i	$0.0978896\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	247.427	−	142.852i	0.926694	−	0.535027i
$268$		0			0
$269$		−	227.367i		−	0.845229i	−0.906310	−	0.422614i	$-0.861112\pi$
$269$		−	227.367i		−	0.845229i	0.906310	−	0.422614i	$-0.138888\pi$
$270$		0			0
$271$	228.573			0.843441			0.421721	−	0.906726i	$-0.361426\pi$
$271$	228.573			0.843441			0.421721	+	0.906726i	$0.361426\pi$
$272$		0			0
$273$	−12.6653	−	21.9369i	−0.0463930	−	0.0803551i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	220.222	+	381.435i	0.795024	+	1.37702i	0.922824	+	0.385223i	$0.125875\pi$
$277$	220.222	+	381.435i	0.795024	+	1.37702i	−0.127799	+	0.991800i	$0.540791\pi$
$278$		0			0
$279$	234.998	+	407.028i	0.842287	+	1.45888i
$280$		0			0
$281$	−272.190	+	157.149i	−0.968646	+	0.559248i	−0.898823	−	0.438311i	$-0.855577\pi$
$281$	−272.190	+	157.149i	−0.968646	+	0.559248i	−0.0698227	+	0.997559i	$0.522243\pi$
$282$		0			0
$283$	133.984	−	232.067i	0.473441	−	0.820024i	−0.526097	−	0.850425i	$-0.676345\pi$
$283$	133.984	−	232.067i	0.473441	−	0.820024i	0.999538	+	0.0304006i	$0.00967830\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	97.3231i		−	0.339105i
$288$		0			0
$289$	152.476			0.527598
$290$		0			0
$291$	152.546	−	264.218i	0.524214	−	0.907966i
$292$		0			0
$293$	−268.524	−	155.033i	−0.916465	−	0.529121i	−0.0339593	−	0.999423i	$-0.510812\pi$
$293$	−268.524	−	155.033i	−0.916465	−	0.529121i	−0.882506	+	0.470302i	$0.844145\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	273.212	−	157.739i	0.919905	−	0.531107i
$298$		0			0
$299$	−38.8548	+	22.4328i	−0.129949	+	0.0750262i
$300$		0			0
$301$	−78.6351	+	136.200i	−0.261246	+	0.452492i
$302$		0			0
$303$	−263.286	−	152.008i	−0.868932	−	0.501678i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	495.952			1.61548			0.807739	−	0.589541i	$-0.200691\pi$
$307$	495.952			1.61548			0.807739	+	0.589541i	$0.200691\pi$
$308$		0			0
$309$	48.8589			0.158119
$310$		0			0
$311$	−195.762	−	113.023i	−0.629460	−	0.363419i	0.151083	−	0.988521i	$-0.451724\pi$
$311$	−195.762	−	113.023i	−0.629460	−	0.363419i	−0.780543	+	0.625102i	$0.785057\pi$
$312$		0			0
$313$	163.579	+	283.326i	0.522615	+	0.905196i	0.999654	+	0.0263139i	$0.00837695\pi$
$313$	163.579	+	283.326i	0.522615	+	0.905196i	−0.477038	+	0.878882i	$0.658290\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.09475	−	4.09616i	0.0223809	−	0.0129216i	−0.488768	−	0.872414i	$-0.662553\pi$
$317$	7.09475	−	4.09616i	0.0223809	−	0.0129216i	0.511149	+	0.859492i	$0.329220\pi$
$318$		0			0
$319$	257.952	−	446.785i	0.808626	−	1.40058i
$320$		0			0
$321$	−220.500	+	127.306i	−0.686916	+	0.396591i
$322$		0			0
$323$			312.509i			0.967521i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−242.952	−	420.805i	−0.742971	−	1.28686i
$328$		0			0
$329$	−147.520	−	85.1708i	−0.448389	−	0.258878i
$330$		0			0
$331$	−138.903	−	240.587i	−0.419647	−	0.726850i	0.576257	−	0.817269i	$-0.304513\pi$
$331$	−138.903	−	240.587i	−0.419647	−	0.726850i	−0.995904	+	0.0904186i	$0.971180\pi$
$332$		0			0
$333$	63.0000	−	109.119i	0.189189	−	0.327685i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	27.9133	−	48.3473i	0.0828288	−	0.143464i	−0.821635	−	0.570014i	$-0.806938\pi$
$337$	27.9133	−	48.3473i	0.0828288	−	0.143464i	0.904464	+	0.426550i	$0.140271\pi$
$338$		0			0
$339$		−	20.7846i		−	0.0613115i
$340$		0			0
$341$			610.178i			1.78938i
$342$		0			0
$343$	314.540			0.917027
$344$		0			0
$345$		0			0
$346$		0			0
$347$	440.117	+	254.102i	1.26835	+	0.732281i	0.974675	−	0.223625i	$-0.0717890\pi$
$347$	440.117	+	254.102i	1.26835	+	0.732281i	0.293673	+	0.955906i	$0.405122\pi$
$348$		0			0
$349$	−69.2379	−	119.924i	−0.198389	−	0.343621i	0.749617	−	0.661872i	$-0.230238\pi$
$349$	−69.2379	−	119.924i	−0.198389	−	0.343621i	−0.948006	+	0.318251i	$0.896904\pi$
$350$		0			0
$351$	30.4294	−	52.7054i	0.0866936	−	0.150158i
$352$		0			0
$353$	498.877	−	288.027i	1.41325	−	0.815940i	0.417556	−	0.908651i	$-0.362887\pi$
$353$	498.877	−	288.027i	1.41325	−	0.815940i	0.995693	+	0.0927114i	$0.0295534\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	113.716	+	65.6538i	0.318532	+	0.183904i
$358$		0			0
$359$			267.888i			0.746207i	0.927790	+	0.373103i	$0.121706\pi$
$359$			267.888i			0.746207i	−0.927790	+	0.373103i	$0.878294\pi$
$360$		0			0
$361$	354.347			0.981570
$362$		0			0
$363$	46.5726			0.128299
$364$		0			0
$365$		0			0
$366$		0			0
$367$	30.2379	+	52.3736i	0.0823921	+	0.142707i	0.904277	−	0.426946i	$-0.140411\pi$
$367$	30.2379	+	52.3736i	0.0823921	+	0.142707i	−0.821885	+	0.569654i	$0.807077\pi$
$368$		0			0
$369$	202.500	−	116.913i	0.548780	−	0.316839i
$370$		0			0
$371$	−35.1411	+	20.2887i	−0.0947199	+	0.0546866i
$372$		0			0
$373$	−108.254	+	187.501i	−0.290225	+	0.502685i	−0.973863	−	0.227137i	$-0.927064\pi$
$373$	−108.254	+	187.501i	−0.290225	+	0.502685i	0.683638	+	0.729822i	$0.260397\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	99.5231i		−	0.263987i
$378$		0			0
$379$	285.254			0.752649			0.376325	−	0.926488i	$-0.377188\pi$
$379$	285.254			0.752649			0.376325	+	0.926488i	$0.377188\pi$
$380$		0			0
$381$	338.855	+	586.914i	0.889383	+	1.54046i
$382$		0			0
$383$	−141.665	−	81.7905i	−0.369883	−	0.213552i	0.303524	−	0.952824i	$-0.401837\pi$
$383$	−141.665	−	81.7905i	−0.369883	−	0.213552i	−0.673407	+	0.739272i	$0.735170\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−377.855			−0.976369
$388$		0			0
$389$	250.760	−	144.776i	0.644627	−	0.372176i	−0.141767	−	0.989900i	$-0.545279\pi$
$389$	250.760	−	144.776i	0.644627	−	0.372176i	0.786395	+	0.617724i	$0.211945\pi$
$390$		0			0
$391$	116.286	−	201.414i	0.297407	−	0.515125i
$392$		0			0
$393$		−	283.065i		−	0.720266i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	66.5081			0.167527			0.0837633	−	0.996486i	$-0.473306\pi$
$397$	66.5081			0.167527			0.0837633	+	0.996486i	$0.473306\pi$
$398$		0			0
$399$	150.284	−	260.300i	0.376652	−	0.652381i
$400$		0			0
$401$	−392.165	−	226.417i	−0.977968	−	0.564630i	−0.0763122	−	0.997084i	$-0.524315\pi$
$401$	−392.165	−	226.417i	−0.977968	−	0.564630i	−0.901656	+	0.432454i	$0.857648\pi$
$402$		0			0
$403$	58.8548	+	101.940i	0.146042	+	0.252952i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	141.665	−	81.7905i	0.348072	−	0.200959i
$408$		0			0
$409$	−150.435	+	260.562i	−0.367813	+	0.637071i	−0.989223	−	0.146415i	$-0.953227\pi$
$409$	−150.435	+	260.562i	−0.367813	+	0.637071i	0.621410	+	0.783485i	$0.286560\pi$
$410$		0			0
$411$	−538.784	−	311.067i	−1.31091	−	0.756855i
$412$		0			0
$413$		−	137.901i		−	0.333900i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−98.1411			−0.235350
$418$		0			0
$419$	103.524	+	59.7697i	0.247074	+	0.142649i	0.618424	−	0.785845i	$-0.287771\pi$
$419$	103.524	+	59.7697i	0.247074	+	0.142649i	−0.371349	+	0.928493i	$0.621105\pi$
$420$		0			0
$421$	81.1431	+	140.544i	0.192739	+	0.333834i	0.946157	−	0.323708i	$-0.104930\pi$
$421$	81.1431	+	140.544i	0.192739	+	0.333834i	−0.753418	+	0.657542i	$0.771596\pi$
$422$		0			0
$423$		−	409.260i		−	0.967517i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−84.7298	+	146.756i	−0.198431	+	0.343692i
$428$		0			0
$429$	68.4254	−	39.5054i	0.159500	−	0.0920872i
$430$		0			0
$431$		−	499.815i		−	1.15966i	−0.814736	−	0.579832i	$-0.803118\pi$
$431$		−	499.815i		−	1.15966i	0.814736	−	0.579832i	$-0.196882\pi$
$432$		0			0
$433$	−739.883			−1.70874			−0.854368	−	0.519668i	$-0.826056\pi$
$433$	−739.883			−1.70874			−0.854368	+	0.519668i	$0.826056\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−461.044	−	266.184i	−1.05502	−	0.609117i
$438$		0			0
$439$	−124.333	−	215.350i	−0.283218	−	0.490548i	0.688958	−	0.724802i	$-0.258069\pi$
$439$	−124.333	−	215.350i	−0.283218	−	0.490548i	−0.972175	+	0.234254i	$0.924735\pi$
$440$		0			0
$441$	157.355	+	272.547i	0.356814	+	0.618019i
$442$		0			0
$443$	78.8831	−	45.5432i	0.178066	−	0.102806i	−0.408318	−	0.912840i	$-0.633884\pi$
$443$	78.8831	−	45.5432i	0.178066	−	0.102806i	0.586384	+	0.810034i	$0.300551\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			63.5062i			0.142072i
$448$		0			0
$449$		−	93.6705i		−	0.208620i	−0.994545	−	0.104310i	$-0.966737\pi$
$449$		−	93.6705i		−	0.208620i	0.994545	−	0.104310i	$-0.0332634\pi$
$450$		0			0
$451$	303.569			0.673101
$452$		0			0
$453$	−413.141	+	715.581i	−0.912011	+	1.57965i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	201.498	+	349.005i	0.440915	+	0.763686i	0.997758	−	0.0669313i	$-0.0213208\pi$
$457$	201.498	+	349.005i	0.440915	+	0.763686i	−0.556843	+	0.830618i	$0.687988\pi$
$458$		0			0
$459$			315.478i			0.687315i
$460$		0			0
$461$	−57.9496	+	33.4572i	−0.125704	+	0.0725752i	−0.561533	−	0.827454i	$-0.689788\pi$
$461$	−57.9496	+	33.4572i	−0.125704	+	0.0725752i	0.435829	+	0.900029i	$0.356455\pi$
$462$		0			0
$463$	88.8105	−	153.824i	0.191815	−	0.332234i	−0.754037	−	0.656832i	$-0.771896\pi$
$463$	88.8105	−	153.824i	0.191815	−	0.332234i	0.945852	+	0.324599i	$0.105229\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			620.647i			1.32901i	0.747285	+	0.664504i	$0.231357\pi$
$467$			620.647i			1.32901i	−0.747285	+	0.664504i	$0.768643\pi$
$468$		0			0
$469$	−374.415			−0.798327
$470$		0			0
$471$	539.806			1.14609
$472$		0			0
$473$	−424.833	−	245.277i	−0.898166	−	0.518557i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−84.4294	−	48.7454i	−0.177001	−	0.102192i
$478$		0			0
$479$	146.044	−	84.3187i	0.304894	−	0.176031i	−0.339745	−	0.940517i	$-0.610341\pi$
$479$	146.044	−	84.3187i	0.304894	−	0.176031i	0.644639	+	0.764487i	$0.277008\pi$
$480$		0			0
$481$	15.7782	−	27.3287i	0.0328030	−	0.0568164i
$482$		0			0
$483$	−193.718	+	111.843i	−0.401072	+	0.231559i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−401.935			−0.825330			−0.412665	−	0.910883i	$-0.635402\pi$
$487$	−401.935			−0.825330			−0.412665	+	0.910883i	$0.635402\pi$
$488$		0			0
$489$	396.617	+	686.961i	0.811078	+	1.40483i
$490$		0			0
$491$	−307.833	−	177.727i	−0.626950	−	0.361970i	0.152620	−	0.988285i	$-0.451229\pi$
$491$	−307.833	−	177.727i	−0.626950	−	0.361970i	−0.779570	+	0.626315i	$0.784562\pi$
$492$		0			0
$493$	257.952	+	446.785i	0.523228	+	0.906258i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−332.855	+	192.174i	−0.669728	+	0.386668i
$498$		0			0
$499$	8.30845	−	14.3907i	0.0166502	−	0.0288390i	−0.857580	−	0.514350i	$-0.828033\pi$
$499$	8.30845	−	14.3907i	0.0166502	−	0.0288390i	0.874230	+	0.485511i	$0.161366\pi$
$500$		0			0
$501$		−	517.960i		−	1.03385i
$502$		0			0
$503$			362.522i			0.720721i	0.932813	+	0.360360i	$0.117346\pi$
$503$			362.522i			0.720721i	−0.932813	+	0.360360i	$0.882654\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−245.879	+	425.875i	−0.484968	+	0.839990i
$508$		0			0
$509$	−578.286	−	333.874i	−1.13612	−	0.655941i	−0.190655	−	0.981657i	$-0.561061\pi$
$509$	−578.286	−	333.874i	−1.13612	−	0.655941i	−0.945467	+	0.325717i	$0.894394\pi$
$510$		0			0
$511$	25.7762	+	44.6457i	0.0504426	+	0.0873692i
$512$		0			0
$513$	722.141			1.40768
$514$		0			0
$515$		0			0
$516$		0			0
$517$	265.663	−	460.142i	0.513855	−	0.890024i
$518$		0			0
$519$	−764.710	−	441.505i	−1.47343	−	0.850685i
$520$		0			0
$521$			676.352i			1.29818i	0.760712	+	0.649090i	$0.224850\pi$
$521$			676.352i			1.29818i	−0.760712	+	0.649090i	$0.775150\pi$
$522$		0			0
$523$	−189.427			−0.362194			−0.181097	−	0.983465i	$-0.557965\pi$
$523$	−189.427			−0.362194			−0.181097	+	0.983465i	$0.557965\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−528.429	−	305.089i	−1.00271	−	0.578916i
$528$		0			0
$529$	−66.4032	−	115.014i	−0.125526	−	0.217417i
$530$		0			0
$531$	286.929	−	165.659i	0.540357	−	0.311975i
$532$		0			0
$533$	50.7157	−	29.2808i	0.0951515	−	0.0549357i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−166.573	+	96.1707i	−0.310191	+	0.179089i
$538$		0			0
$539$			408.575i			0.758025i
$540$		0			0
$541$	−590.629			−1.09174			−0.545868	−	0.837871i	$-0.683800\pi$
$541$	−590.629			−1.09174			−0.545868	+	0.837871i	$0.683800\pi$
$542$		0			0
$543$	436.808	+	756.574i	0.804435	+	1.39332i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−394.782	−	683.783i	−0.721722	−	1.25006i	−0.960309	−	0.278939i	$-0.910017\pi$
$547$	−394.782	−	683.783i	−0.721722	−	1.25006i	0.238586	−	0.971121i	$-0.423316\pi$
$548$		0			0
$549$	−407.141			−0.741605
$550$		0			0
$551$	1022.71	−	590.462i	1.85610	−	1.07162i
$552$		0			0
$553$	106.314	−	184.142i	0.192250	−	0.332987i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	1004.69i		−	1.80376i	−0.431987	−	0.901880i	$-0.642187\pi$
$557$		−	1004.69i		−	1.80376i	0.431987	−	0.901880i	$-0.357813\pi$
$558$		0			0
$559$	−94.6330			−0.169290
$560$		0			0
$561$	−204.786	+	354.700i	−0.365038	+	0.632264i
$562$		0			0
$563$	272.976	+	157.603i	0.484859	+	0.279934i	0.722439	−	0.691434i	$-0.243021\pi$
$563$	272.976	+	157.603i	0.484859	+	0.279934i	−0.237580	+	0.971368i	$0.576354\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	151.712	−	262.772i	0.267569	−	0.463443i
$568$		0			0
$569$	−823.923	+	475.692i	−1.44802	+	0.836015i	−0.998363	−	0.0571870i	$-0.981787\pi$
$569$	−823.923	+	475.692i	−1.44802	+	0.836015i	−0.449656	+	0.893202i	$0.648454\pi$
$570$		0			0
$571$	−229.183	+	396.957i	−0.401372	+	0.695197i	−0.993892	−	0.110359i	$-0.964800\pi$
$571$	−229.183	+	396.957i	−0.401372	+	0.695197i	0.592520	+	0.805556i	$0.298133\pi$
$572$		0			0
$573$	41.4254	+	23.9169i	0.0722956	+	0.0417399i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−991.190			−1.71783			−0.858916	−	0.512116i	$-0.828862\pi$
$577$	−991.190			−1.71783			−0.858916	+	0.512116i	$0.828862\pi$
$578$		0			0
$579$	−734.141			−1.26795
$580$		0			0
$581$	292.185	+	168.693i	0.502901	+	0.290350i
$582$		0			0
$583$	−63.2843	−	109.612i	−0.108549	−	0.188013i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−144.883	+	83.6483i	−0.246820	+	0.142501i	−0.618307	−	0.785937i	$-0.712181\pi$
$587$	−144.883	+	83.6483i	−0.246820	+	0.142501i	0.371488	+	0.928438i	$0.378848\pi$
$588$		0			0
$589$	−698.361	+	1209.60i	−1.18567	+	2.05364i
$590$		0			0
$591$	−546.569	+	315.561i	−0.924820	+	0.533945i
$592$		0			0
$593$			868.330i			1.46430i	0.681143	+	0.732150i	$0.261483\pi$
$593$			868.330i			1.46430i	−0.681143	+	0.732150i	$0.738517\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−154.095	−	266.900i	−0.258115	−	0.447069i
$598$		0			0
$599$	−170.335	−	98.3428i	−0.284365	−	0.164178i	0.351033	−	0.936363i	$-0.385831\pi$
$599$	−170.335	−	98.3428i	−0.284365	−	0.164178i	−0.635398	+	0.772185i	$0.719164\pi$
$600$		0			0
$601$	−332.181	−	575.355i	−0.552715	−	0.957330i	−0.998077	−	0.0619795i	$-0.980259\pi$
$601$	−332.181	−	575.355i	−0.552715	−	0.957330i	0.445363	−	0.895350i	$-0.353075\pi$
$602$		0			0
$603$	−449.782	−	779.046i	−0.745907	−	1.29195i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−37.2379	+	64.4979i	−0.0613474	+	0.106257i	−0.895068	−	0.445930i	$-0.852873\pi$
$607$	−37.2379	+	64.4979i	−0.0613474	+	0.106257i	0.833720	+	0.552187i	$0.186206\pi$
$608$		0			0
$609$		−	496.191i		−	0.814763i
$610$		0			0
$611$		−	102.498i		−	0.167755i
$612$		0			0
$613$	304.569			0.496849			0.248425	−	0.968651i	$-0.420087\pi$
$613$	304.569			0.496849			0.248425	+	0.968651i	$0.420087\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	815.353	+	470.744i	1.32148	+	0.762956i	0.983965	−	0.178364i	$-0.0570804\pi$
$617$	815.353	+	470.744i	1.32148	+	0.762956i	0.337515	+	0.941320i	$0.390414\pi$
$618$		0			0
$619$	117.736	+	203.924i	0.190203	+	0.329442i	0.945318	−	0.326151i	$-0.105752\pi$
$619$	117.736	+	203.924i	0.190203	+	0.329442i	−0.755114	+	0.655593i	$0.772419\pi$
$620$		0			0
$621$	−465.423	−	268.712i	−0.749474	−	0.432709i
$622$		0			0
$623$	308.952	−	178.373i	0.495909	−	0.286313i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	811.923	+	468.764i	1.29493	+	0.747630i
$628$		0			0
$629$			163.581i			0.260065i
$630$		0			0
$631$	−832.125			−1.31874			−0.659370	−	0.751819i	$-0.729177\pi$
$631$	−832.125			−1.31874			−0.659370	+	0.751819i	$0.729177\pi$
$632$		0			0
$633$	683.903			1.08042
$634$		0			0
$635$		0			0
$636$		0			0
$637$	39.4092	+	68.2588i	0.0618669	+	0.107157i
$638$		0			0
$639$	−799.712	−	461.714i	−1.25150	−	0.722557i
$640$		0			0
$641$	913.355	−	527.326i	1.42489	−	0.822661i	0.428179	−	0.903694i	$-0.359155\pi$
$641$	913.355	−	527.326i	1.42489	−	0.822661i	0.996711	+	0.0810330i	$0.0258219\pi$
$642$		0			0
$643$	493.593	−	854.928i	0.767640	−	1.32959i	−0.171199	−	0.985236i	$-0.554764\pi$
$643$	493.593	−	854.928i	0.767640	−	1.32959i	0.938839	−	0.344356i	$-0.111903\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	75.6097i		−	0.116862i	−0.998291	−	0.0584310i	$-0.981390\pi$
$647$		−	75.6097i		−	0.116862i	0.998291	−	0.0584310i	$-0.0186098\pi$
$648$		0			0
$649$	430.137			0.662769
$650$		0			0
$651$	293.431	+	508.238i	0.450740	+	0.780704i
$652$		0			0
$653$	−1079.95	−	623.510i	−1.65383	−	0.954840i	−0.975476	−	0.220105i	$-0.929360\pi$
$653$	−1079.95	−	623.510i	−1.65383	−	0.954840i	−0.678355	−	0.734734i	$-0.737307\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−61.9294	+	107.265i	−0.0942610	+	0.163265i
$658$		0			0
$659$	544.851	−	314.570i	0.826784	−	0.477344i	−0.0259662	−	0.999663i	$-0.508266\pi$
$659$	544.851	−	314.570i	0.826784	−	0.477344i	0.852750	+	0.522319i	$0.174933\pi$
$660$		0			0
$661$	−323.282	+	559.941i	−0.489080	+	0.847112i	−0.999921	−	0.0125632i	$-0.996001\pi$
$661$	−323.282	+	559.941i	−0.489080	+	0.847112i	0.510841	+	0.859675i	$0.329334\pi$
$662$		0			0
$663$			79.0108i			0.119172i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−878.855			−1.31762
$668$		0			0
$669$	419.044	−	725.806i	0.626374	−	1.08491i
$670$		0			0
$671$	−457.760	−	264.288i	−0.682206	−	0.393872i
$672$		0			0
$673$	45.9516	+	79.5905i	0.0682788	+	0.118262i	0.898144	−	0.439702i	$-0.144916\pi$
$673$	45.9516	+	79.5905i	0.0682788	+	0.118262i	−0.829865	+	0.557964i	$0.811583\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−633.520	+	365.763i	−0.935776	+	0.540270i	−0.888634	−	0.458618i	$-0.848345\pi$
$677$	−633.520	+	365.763i	−0.935776	+	0.540270i	−0.0471421	+	0.998888i	$0.515011\pi$
$678$		0			0
$679$	190.478	−	329.917i	0.280527	−	0.485887i
$680$		0			0
$681$	−645.786	−	372.845i	−0.948291	−	0.547496i
$682$		0			0
$683$			682.177i			0.998794i	0.866373	+	0.499397i	$0.166445\pi$
$683$			682.177i			0.998794i	−0.866373	+	0.499397i	$0.833555\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−473.335			−0.688988
$688$		0			0
$689$	−21.1452	−	12.2082i	−0.0306897	−	0.0177187i
$690$		0			0
$691$	210.331	+	364.303i	0.304386	+	0.527212i	0.977124	−	0.212669i	$-0.0682155\pi$
$691$	210.331	+	364.303i	0.304386	+	0.527212i	−0.672739	+	0.739880i	$0.734882\pi$
$692$		0			0
$693$	341.147	−	196.961i	0.492276	−	0.284216i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−151.784	+	262.898i	−0.217768	+	0.377185i
$698$		0			0
$699$	−864.780	+	499.281i	−1.23717	+	0.714279i
$700$		0			0
$701$			70.8185i			0.101025i	0.998723	+	0.0505125i	$0.0160855\pi$
$701$			70.8185i			0.101025i	−0.998723	+	0.0505125i	$0.983915\pi$
$702$		0			0
$703$	374.444			0.532637
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−328.754	−	189.806i	−0.464998	−	0.268467i
$708$		0			0
$709$	−399.696	−	692.293i	−0.563745	−	0.976436i	−0.997165	−	0.0752436i	$-0.976027\pi$
$709$	−399.696	−	692.293i	−0.563745	−	0.976436i	0.433420	−	0.901192i	$-0.357307\pi$
$710$		0			0
$711$	510.859			0.718508
$712$		0			0
$713$	900.194	−	519.727i	1.26254	−	0.728930i
$714$		0			0
$715$		0			0
$716$		0			0
$717$			719.541i			1.00354i
$718$		0			0
$719$		−	368.675i		−	0.512761i	−0.966576	−	0.256381i	$-0.917470\pi$
$719$		−	368.675i		−	0.512761i	0.966576	−	0.256381i	$-0.0825300\pi$
$720$		0			0
$721$	61.0079			0.0846157
$722$		0			0
$723$	−284.262	+	492.356i	−0.393170	+	0.680991i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−453.095	−	784.783i	−0.623239	−	1.07948i	−0.988879	−	0.148725i	$-0.952483\pi$
$727$	−453.095	−	784.783i	−0.623239	−	1.07948i	0.365640	−	0.930757i	$-0.380850\pi$
$728$		0			0
$729$	729.000			1.00000
$730$		0			0
$731$	424.833	−	245.277i	0.581166	−	0.335537i
$732$		0			0
$733$	50.7601	−	87.9190i	0.0692497	−	0.119944i	−0.829322	−	0.558772i	$-0.811273\pi$
$733$	50.7601	−	87.9190i	0.0692497	−	0.119944i	0.898571	+	0.438828i	$0.144606\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	1167.87i		−	1.58463i
$738$		0			0
$739$	557.665			0.754622			0.377311	−	0.926087i	$-0.376849\pi$
$739$	557.665			0.754622			0.377311	+	0.926087i	$0.376849\pi$
$740$		0			0
$741$	180.859			0.244074
$742$		0			0
$743$	308.806	+	178.289i	0.415621	+	0.239959i	0.693202	−	0.720743i	$-0.256199\pi$
$743$	308.806	+	178.289i	0.415621	+	0.239959i	−0.277581	+	0.960702i	$0.589533\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			810.600i			1.08514i
$748$		0			0
$749$	−275.329	+	158.961i	−0.367595	+	0.212231i
$750$		0			0
$751$	−244.810	+	424.024i	−0.325979	+	0.564613i	−0.981710	−	0.190382i	$-0.939027\pi$
$751$	−244.810	+	424.024i	−0.325979	+	0.564613i	0.655731	+	0.754995i	$0.272361\pi$
$752$		0			0
$753$	−1161.63	+	670.670i	−1.54268	+	0.890664i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−198.379			−0.262059			−0.131030	−	0.991378i	$-0.541828\pi$
$757$	−198.379			−0.262059			−0.131030	+	0.991378i	$0.541828\pi$
$758$		0			0
$759$	−348.859	−	604.241i	−0.459630	−	0.796102i
$760$		0			0
$761$	−30.6653	−	17.7046i	−0.0402961	−	0.0232649i	0.479717	−	0.877423i	$-0.340739\pi$
$761$	−30.6653	−	17.7046i	−0.0402961	−	0.0232649i	−0.520013	+	0.854159i	$0.674073\pi$
$762$		0			0
$763$	−303.363	−	525.440i	−0.397592	−	0.688650i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	71.8609	−	41.4889i	0.0936909	−	0.0540925i
$768$		0			0
$769$	114.552	−	198.411i	0.148963	−	0.258011i	−0.781882	−	0.623427i	$-0.785740\pi$
$769$	114.552	−	198.411i	0.148963	−	0.258011i	0.930844	+	0.365416i	$0.119073\pi$
$770$		0			0
$771$			1341.68i			1.74018i
$772$		0			0
$773$		−	905.388i		−	1.17126i	−0.810577	−	0.585632i	$-0.800846\pi$
$773$		−	905.388i		−	1.17126i	0.810577	−	0.585632i	$-0.199154\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	78.6653	−	136.252i	0.101242	−	0.175357i
$778$		0			0
$779$	601.784	+	347.440i	0.772509	+	0.446008i
$780$		0			0
$781$	−599.425	−	1038.24i	−0.767510	−	1.32937i
$782$		0			0
$783$	1032.42	−	596.070i	1.31855	−	0.761264i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−74.1452	+	128.423i	−0.0942125	+	0.163181i	−0.909280	−	0.416186i	$-0.863367\pi$
$787$	−74.1452	+	128.423i	−0.0942125	+	0.163181i	0.815067	+	0.579366i	$0.196700\pi$
$788$		0			0
$789$	921.139	+	531.820i	1.16748	+	0.674043i
$790$		0			0
$791$		−	25.9528i		−	0.0328101i
$792$		0			0
$793$	−101.968			−0.128585
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−212.806	−	122.864i	−0.267009	−	0.154158i	0.360518	−	0.932752i	$-0.382600\pi$
$797$	−212.806	−	122.864i	−0.267009	−	0.154158i	−0.627528	+	0.778594i	$0.715933\pi$
$798$		0			0
$799$	265.663	+	460.142i	0.332495	+	0.575898i
$800$		0			0
$801$	742.282	+	428.557i	0.926694	+	0.535027i
$802$		0			0
$803$	−139.258	+	80.4006i	−0.173422	+	0.100125i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	590.716	−	341.050i	0.731990	−	0.422614i
$808$		0			0
$809$		−	1551.44i		−	1.91773i	−0.283865	−	0.958864i	$-0.591617\pi$
$809$		−	1551.44i		−	1.91773i	0.283865	−	0.958864i	$-0.408383\pi$
$810$		0			0
$811$	−439.512			−0.541939			−0.270969	−	0.962588i	$-0.587344\pi$
$811$	−439.512			−0.541939			−0.270969	+	0.962588i	$0.587344\pi$
$812$		0			0
$813$	342.859	+	593.849i	0.421721	+	0.730442i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−561.450	−	972.459i	−0.687209	−	1.19028i
$818$		0			0
$819$	37.9959	−	65.8108i	0.0463930	−	0.0803551i
$820$		0			0
$821$	942.187	−	543.972i	1.14761	−	0.662573i	0.199306	−	0.979937i	$-0.436131\pi$
$821$	942.187	−	543.972i	1.14761	−	0.662573i	0.948304	+	0.317365i	$0.102798\pi$
$822$		0			0
$823$	−469.218	+	812.709i	−0.570131	+	0.987496i	0.426421	+	0.904525i	$0.359774\pi$
$823$	−469.218	+	812.709i	−0.570131	+	0.987496i	−0.996552	+	0.0829708i	$0.973559\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	615.395i		−	0.744129i	−0.928207	−	0.372065i	$-0.878650\pi$
$827$		−	615.395i		−	0.744129i	0.928207	−	0.372065i	$-0.121350\pi$
$828$		0			0
$829$	−559.230			−0.674583			−0.337292	−	0.941400i	$-0.609511\pi$
$829$	−559.230			−0.674583			−0.337292	+	0.941400i	$0.609511\pi$
$830$		0			0
$831$	−660.665	+	1144.31i	−0.795024	+	1.37702i
$832$		0			0
$833$	−353.837	−	204.288i	−0.424774	−	0.245243i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−704.994	+	1221.09i	−0.842287	+	1.45888i
$838$		0			0
$839$	−914.135	+	527.776i	−1.08955	+	0.629054i	−0.933457	−	0.358688i	$-0.883224\pi$
$839$	−914.135	+	527.776i	−1.08955	+	0.629054i	−0.156096	+	0.987742i	$0.549891\pi$
$840$		0			0
$841$	554.258	−	960.003i	0.659046	−	1.14150i
$842$		0			0
$843$	−816.569	−	471.446i	−0.968646	−	0.559248i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	58.1531			0.0686578
$848$		0			0
$849$	803.903			0.946882
$850$		0			0
$851$	−241.331	−	139.332i	−0.283585	−	0.163728i
$852$		0			0
$853$	−45.9536	−	79.5941i	−0.0538730	−	0.0933107i	0.837831	−	0.545929i	$-0.183823\pi$
$853$	−45.9536	−	79.5941i	−0.0538730	−	0.0933107i	−0.891704	+	0.452619i	$0.850490\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1021.04	−	589.498i	1.19141	−	0.687862i	0.232785	−	0.972528i	$-0.425216\pi$
$857$	1021.04	−	589.498i	1.19141	−	0.687862i	0.958627	+	0.284666i	$0.0918827\pi$
$858$		0			0
$859$	669.784	−	1160.10i	0.779726	−	1.35052i	−0.152374	−	0.988323i	$-0.548692\pi$
$859$	669.784	−	1160.10i	0.779726	−	1.35052i	0.932100	−	0.362201i	$-0.117975\pi$
$860$		0			0
$861$	252.853	−	145.985i	0.293673	−	0.169552i
$862$		0			0
$863$			1332.42i			1.54393i	0.635663	+	0.771967i	$0.280727\pi$
$863$			1332.42i			1.54393i	−0.635663	+	0.771967i	$0.719273\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	228.714	+	396.144i	0.263799	+	0.456913i
$868$		0			0
$869$	574.373	+	331.614i	0.660958	+	0.381605i
$870$		0			0
$871$	−112.647	−	195.111i	−0.129331	−	0.224007i
$872$		0			0
$873$	915.278			1.04843
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−321.317	+	556.537i	−0.366381	+	0.634591i	−0.988997	−	0.147937i	$-0.952737\pi$
$877$	−321.317	+	556.537i	−0.366381	+	0.634591i	0.622615	+	0.782528i	$0.286070\pi$
$878$		0			0
$879$		−	930.195i		−	1.05824i
$880$		0			0
$881$		−	983.693i		−	1.11656i	−0.829651	−	0.558282i	$-0.811461\pi$
$881$		−	983.693i		−	1.11656i	0.829651	−	0.558282i	$-0.188539\pi$
$882$		0			0
$883$	−197.540			−0.223715			−0.111857	−	0.993724i	$-0.535680\pi$
$883$	−197.540			−0.223715			−0.111857	+	0.993724i	$0.535680\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1136.09	+	655.920i	1.28082	+	0.739481i	0.976998	−	0.213248i	$-0.0684042\pi$
$887$	1136.09	+	655.920i	1.28082	+	0.739481i	0.303821	+	0.952729i	$0.401738\pi$
$888$		0			0
$889$	423.113	+	732.853i	0.475943	+	0.824357i
$890$		0			0
$891$	819.635	+	473.216i	0.919905	+	0.531107i
$892$		0			0
$893$	1053.28	−	608.114i	1.17949	−	0.680979i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−116.564	−	67.2985i	−0.129949	−	0.0750262i
$898$		0			0
$899$			2305.76i			2.56481i
$900$		0			0
$901$	126.569			0.140476
$902$		0			0
$903$	−471.810			−0.522492
$904$		0			0
$905$		0			0
$906$		0			0
$907$	865.496	+	1499.08i	0.954240	+	1.65279i	0.736097	+	0.676876i	$0.236667\pi$
$907$	865.496	+	1499.08i	0.954240	+	1.65279i	0.218143	+	0.975917i	$0.430000\pi$
$908$		0			0
$909$		−	912.050i		−	1.00336i
$910$		0			0
$911$	210.720	−	121.659i	0.231306	−	0.133545i	−0.379868	−	0.925041i	$-0.624031\pi$
$911$	210.720	−	121.659i	0.231306	−	0.133545i	0.611174	+	0.791496i	$0.290697\pi$
$912$		0			0
$913$	−526.185	+	911.380i	−0.576326	+	0.998225i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	353.450i		−	0.385442i
$918$		0			0
$919$	449.145			0.488733			0.244366	−	0.969683i	$-0.421420\pi$
$919$	449.145			0.488733			0.244366	+	0.969683i	$0.421420\pi$
$920$		0			0
$921$	743.927	+	1288.52i	0.807739	+	1.39904i
$922$		0			0
$923$	−200.286	−	115.635i	−0.216995	−	0.125282i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	73.2883	+	126.939i	0.0790597	+	0.136935i
$928$		0			0
$929$	−45.2420	+	26.1205i	−0.0486997	+	0.0281168i	−0.524152	−	0.851625i	$-0.675618\pi$
$929$	−45.2420	+	26.1205i	−0.0486997	+	0.0281168i	0.475452	+	0.879741i	$0.342284\pi$
$930$		0			0
$931$	−467.623	+	809.947i	−0.502280	+	0.869975i
$932$		0			0
$933$		−	678.140i		−	0.726838i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−196.798			−0.210030			−0.105015	−	0.994471i	$-0.533489\pi$
$937$	−196.798			−0.210030			−0.105015	+	0.994471i	$0.533489\pi$
$938$		0			0
$939$	−490.736	+	849.979i	−0.522615	+	0.905196i
$940$		0			0
$941$	−822.375	−	474.798i	−0.873937	−	0.504568i	−0.00528258	−	0.999986i	$-0.501682\pi$
$941$	−822.375	−	474.798i	−0.873937	−	0.504568i	−0.868655	+	0.495418i	$0.835015\pi$
$942$		0			0
$943$	−258.569	−	447.854i	−0.274198	−	0.474924i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1410.54	−	814.378i	1.48949	−	0.859956i	0.489559	−	0.871970i	$-0.337158\pi$
$947$	1410.54	−	814.378i	1.48949	−	0.859956i	0.999928	+	0.0120142i	$0.00382434\pi$
$948$		0			0
$949$	−15.5101	+	26.8643i	−0.0163436	+	0.0283080i
$950$		0			0
$951$	21.2843	+	12.2885i	0.0223809	+	0.0129216i
$952$		0			0
$953$		−	789.836i		−	0.828789i	−0.910097	−	0.414395i	$-0.863993\pi$
$953$		−	789.836i		−	0.828789i	0.910097	−	0.414395i	$-0.136007\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1547.71			1.61725
$958$		0			0
$959$	−672.756	−	388.416i	−0.701518	−	0.405022i
$960$		0			0
$961$	−883.056	−	1529.50i	−0.918893	−	1.59157i
$962$		0			0
$963$	−661.500	−	381.917i	−0.686916	−	0.396591i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	263.669	−	456.689i	0.272667	−	0.472274i	−0.696877	−	0.717191i	$-0.745427\pi$
$967$	263.669	−	456.689i	0.272667	−	0.472274i	0.969544	+	0.244917i	$0.0787608\pi$
$968$		0			0
$969$	−811.923	+	468.764i	−0.837898	+	0.483761i
$970$		0			0
$971$			179.700i			0.185067i	0.995710	+	0.0925337i	$0.0294966\pi$
$971$			179.700i			0.185067i	−0.995710	+	0.0925337i	$0.970503\pi$
$972$		0			0
$973$	−122.544			−0.125945
$974$		0			0
$975$		0			0
$976$		0			0
$977$	802.591	+	463.376i	0.821485	+	0.474284i	0.850928	−	0.525282i	$-0.176040\pi$
$977$	802.591	+	463.376i	0.821485	+	0.474284i	−0.0294434	+	0.999566i	$0.509373\pi$
$978$		0			0
$979$	556.379	+	963.677i	0.568314	+	0.984348i
$980$		0			0
$981$	728.855	−	1262.41i	0.742971	−	1.28686i
$982$		0			0
$983$	−489.290	+	282.492i	−0.497752	+	0.287377i	−0.727785	−	0.685806i	$-0.759450\pi$
$983$	−489.290	+	282.492i	−0.497752	+	0.287377i	0.230033	+	0.973183i	$0.426117\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	511.025i		−	0.517755i
$988$		0			0
$989$			835.673i			0.844967i
$990$		0			0
$991$	−1815.42			−1.83191			−0.915953	−	0.401285i	$-0.868564\pi$
$991$	−1815.42			−1.83191			−0.915953	+	0.401285i	$0.868564\pi$
$992$		0			0
$993$	416.710	−	721.762i	0.419647	−	0.726850i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	341.192	+	590.961i	0.342218	+	0.592739i	0.984844	−	0.173441i	$-0.0554885\pi$
$997$	341.192	+	590.961i	0.342218	+	0.592739i	−0.642626	+	0.766180i	$0.722155\pi$
$998$		0			0
$999$	378.000			0.378378

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.p.b.401.2		4
3.2	odd	2		2700.3.p.a.2501.2		4
5.2	odd	4		900.3.u.b.149.3		8
5.3	odd	4		900.3.u.b.149.2		8
5.4	even	2		180.3.o.a.41.1	✓	4
9.2	odd	6	inner	900.3.p.b.101.2		4
9.7	even	3		2700.3.p.a.1601.2		4
15.2	even	4		2700.3.u.a.449.2		8
15.8	even	4		2700.3.u.a.449.3		8
15.14	odd	2		540.3.o.a.341.2		4
20.19	odd	2		720.3.bs.a.401.1		4
45.2	even	12		900.3.u.b.749.2		8
45.4	even	6		1620.3.g.a.161.4		4
45.7	odd	12		2700.3.u.a.2249.3		8
45.14	odd	6		1620.3.g.a.161.2		4
45.29	odd	6		180.3.o.a.101.1	yes	4
45.34	even	6		540.3.o.a.521.2		4
45.38	even	12		900.3.u.b.749.3		8
45.43	odd	12		2700.3.u.a.2249.2		8
60.59	even	2		2160.3.bs.a.881.2		4
180.79	odd	6		2160.3.bs.a.1601.2		4
180.119	even	6		720.3.bs.a.641.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.o.a.41.1	✓	4	5.4	even	2
180.3.o.a.101.1	yes	4	45.29	odd	6
540.3.o.a.341.2		4	15.14	odd	2
540.3.o.a.521.2		4	45.34	even	6
720.3.bs.a.401.1		4	20.19	odd	2
720.3.bs.a.641.1		4	180.119	even	6
900.3.p.b.101.2		4	9.2	odd	6	inner
900.3.p.b.401.2		4	1.1	even	1	trivial
900.3.u.b.149.2		8	5.3	odd	4
900.3.u.b.149.3		8	5.2	odd	4
900.3.u.b.749.2		8	45.2	even	12
900.3.u.b.749.3		8	45.38	even	12
1620.3.g.a.161.2		4	45.14	odd	6
1620.3.g.a.161.4		4	45.4	even	6
2160.3.bs.a.881.2		4	60.59	even	2
2160.3.bs.a.1601.2		4	180.79	odd	6
2700.3.p.a.1601.2		4	9.7	even	3
2700.3.p.a.2501.2		4	3.2	odd	2
2700.3.u.a.449.2		8	15.2	even	4
2700.3.u.a.449.3		8	15.8	even	4
2700.3.u.a.2249.2		8	45.43	odd	12
2700.3.u.a.2249.3		8	45.7	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)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +(1.87298 + 3.24410i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} +(1.87298 + 3.24410i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-10.1190 + 5.84218i) q^{11} +(-1.12702 + 1.95205i) q^{13} -11.6844i q^{17} -26.7460 q^{19} +(-5.61895 + 9.73231i) q^{21} +(17.2379 + 9.95231i) q^{23} -27.0000 q^{27} +(-38.2379 + 22.0767i) q^{29} +(26.1109 - 45.2254i) q^{31} +(-30.3569 - 17.5265i) q^{33} -14.0000 q^{37} -6.76210 q^{39} +(-22.5000 - 12.9904i) q^{41} +(20.9919 + 36.3591i) q^{43} +(-39.3810 + 22.7367i) q^{47} +(17.4839 - 30.2829i) q^{49} +(30.3569 - 17.5265i) q^{51} +10.8323i q^{53} +(-40.1190 - 69.4881i) q^{57} +(-31.8810 - 18.4065i) q^{59} +(22.6190 + 39.1772i) q^{61} -33.7137 q^{63} +(-49.9758 + 86.5606i) q^{67} +59.7138i q^{69} +102.603i q^{71} +13.7621 q^{73} +(-37.9052 - 21.8846i) q^{77} +(-28.3810 - 49.1574i) q^{79} +(-40.5000 - 70.1481i) q^{81} +(78.0000 - 45.0333i) q^{83} +(-114.714 - 66.2300i) q^{87} -95.2349i q^{89} -8.44353 q^{91} +156.665 q^{93} +(-50.8488 - 88.0727i) q^{97} -105.159i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - 8 q^{7} - 18 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 - 8 * q^7 - 18 * q^9	\( 4 q + 6 q^{3} - 8 q^{7} - 18 q^{9} + 6 q^{11} - 20 q^{13} - 76 q^{19} + 24 q^{21} - 24 q^{23} - 108 q^{27} - 60 q^{29} - 4 q^{31} + 18 q^{33} - 56 q^{37} - 120 q^{39} - 90 q^{41} + 22 q^{43} - 204 q^{47} - 54 q^{49} - 18 q^{51} - 114 q^{57} - 174 q^{59} + 44 q^{61} + 144 q^{63} - 14 q^{67} + 148 q^{73} - 384 q^{77} - 160 q^{79} - 162 q^{81} + 312 q^{83} - 180 q^{87} + 400 q^{91} - 24 q^{93} - 2 q^{97}+O(q^{100}) \) 4 * q + 6 * q^3 - 8 * q^7 - 18 * q^9 + 6 * q^11 - 20 * q^13 - 76 * q^19 + 24 * q^21 - 24 * q^23 - 108 * q^27 - 60 * q^29 - 4 * q^31 + 18 * q^33 - 56 * q^37 - 120 * q^39 - 90 * q^41 + 22 * q^43 - 204 * q^47 - 54 * q^49 - 18 * q^51 - 114 * q^57 - 174 * q^59 + 44 * q^61 + 144 * q^63 - 14 * q^67 + 148 * q^73 - 384 * q^77 - 160 * q^79 - 162 * q^81 + 312 * q^83 - 180 * q^87 + 400 * q^91 - 24 * q^93 - 2 * q^97

Introduction

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