LMFDB - Embedded newform 900.3.u.b.749.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 $ x^8 - 3x^6 + 8x^4 - 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			749.2
Root			$1.40126 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	900.749
Dual form			900.3.u.b.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59808 - 1.50000i) q^{3} +(3.24410 + 1.87298i) q^{7} +(4.50000 + 7.79423i) q^{9} +O(q^{10})$	$q+(-2.59808 - 1.50000i) q^{3} +(3.24410 + 1.87298i) q^{7} +(4.50000 + 7.79423i) q^{9} +(-10.1190 - 5.84218i) q^{11} +(-1.95205 + 1.12702i) q^{13} -11.6844 q^{17} +26.7460 q^{19} +(-5.61895 - 9.73231i) q^{21} +(-9.95231 - 17.2379i) q^{23} -27.0000i q^{27} +(38.2379 + 22.0767i) q^{29} +(26.1109 + 45.2254i) q^{31} +(17.5265 + 30.3569i) q^{33} -14.0000i q^{37} +6.76210 q^{39} +(-22.5000 + 12.9904i) q^{41} +(-36.3591 - 20.9919i) q^{43} +(22.7367 - 39.3810i) q^{47} +(-17.4839 - 30.2829i) q^{49} +(30.3569 + 17.5265i) q^{51} -10.8323 q^{53} +(-69.4881 - 40.1190i) q^{57} +(31.8810 - 18.4065i) q^{59} +(22.6190 - 39.1772i) q^{61} +33.7137i q^{63} +(86.5606 - 49.9758i) q^{67} +59.7138i q^{69} -102.603i q^{71} -13.7621i q^{73} +(-21.8846 - 37.9052i) q^{77} +(28.3810 - 49.1574i) q^{79} +(-40.5000 + 70.1481i) q^{81} +(45.0333 - 78.0000i) q^{83} +(-66.2300 - 114.714i) q^{87} -95.2349i q^{89} -8.44353 q^{91} -156.665i q^{93} +(-88.0727 - 50.8488i) q^{97} -105.159i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 36 q^{9}+O(q^{10}) $ 8 * q + 36 * q^9	$ 8 q + 36 q^{9} + 12 q^{11} + 152 q^{19} + 48 q^{21} + 120 q^{29} - 8 q^{31} + 240 q^{39} - 180 q^{41} + 108 q^{49} - 36 q^{51} + 348 q^{59} + 88 q^{61} + 320 q^{79} - 324 q^{81} + 800 q^{91}+O(q^{100}) $ 8 * q + 36 * q^9 + 12 * q^11 + 152 * q^19 + 48 * q^21 + 120 * q^29 - 8 * q^31 + 240 * q^39 - 180 * q^41 + 108 * q^49 - 36 * q^51 + 348 * q^59 + 88 * q^61 + 320 * q^79 - 324 * q^81 + 800 * q^91

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−2.59808	−	1.50000i	−0.866025	−	0.500000i
$3$	−2.59808	−	1.50000i	−0.866025	−	0.500000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.24410	+	1.87298i	0.463443	+	0.267569i	0.713491	−	0.700664i	$-0.247113\pi$
$7$	3.24410	+	1.87298i	0.463443	+	0.267569i	−0.250048	+	0.968234i	$0.580446\pi$
$8$		0			0
$9$	4.50000	+	7.79423i	0.500000	+	0.866025i
$10$		0			0
$11$	−10.1190	−	5.84218i	−0.919905	−	0.531107i	−0.0362999	−	0.999341i	$-0.511557\pi$
$11$	−10.1190	−	5.84218i	−0.919905	−	0.531107i	−0.883605	+	0.468234i	$0.844891\pi$
$12$		0			0
$13$	−1.95205	+	1.12702i	−0.150158	+	0.0866936i	−0.573196	−	0.819418i	$-0.694297\pi$
$13$	−1.95205	+	1.12702i	−0.150158	+	0.0866936i	0.423039	+	0.906112i	$0.360963\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−11.6844			−0.687315			−0.343658	−	0.939095i	$-0.611666\pi$
$17$	−11.6844			−0.687315			−0.343658	+	0.939095i	$0.611666\pi$
$18$		0			0
$19$	26.7460			1.40768			0.703841	−	0.710357i	$-0.251467\pi$
$19$	26.7460			1.40768			0.703841	+	0.710357i	$0.251467\pi$
$20$		0			0
$21$	−5.61895	−	9.73231i	−0.267569	−	0.463443i
$22$		0			0
$23$	−9.95231	−	17.2379i	−0.432709	−	0.749474i	0.564397	−	0.825504i	$-0.309109\pi$
$23$	−9.95231	−	17.2379i	−0.432709	−	0.749474i	−0.997106	+	0.0760299i	$0.975776\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	27.0000i		−	1.00000i
$28$		0			0
$29$	38.2379	+	22.0767i	1.31855	+	0.761264i	0.983495	−	0.180935i	$-0.0579124\pi$
$29$	38.2379	+	22.0767i	1.31855	+	0.761264i	0.335053	+	0.942199i	$0.391246\pi$
$30$		0			0
$31$	26.1109	+	45.2254i	0.842287	+	1.45888i	0.887957	+	0.459927i	$0.152124\pi$
$31$	26.1109	+	45.2254i	0.842287	+	1.45888i	−0.0456704	+	0.998957i	$0.514542\pi$
$32$		0			0
$33$	17.5265	+	30.3569i	0.531107	+	0.919905i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	14.0000i		−	0.378378i	−0.981941	−	0.189189i	$-0.939414\pi$
$37$		−	14.0000i		−	0.378378i	0.981941	−	0.189189i	$-0.0605859\pi$
$38$		0			0
$39$	6.76210			0.173387
$40$		0			0
$41$	−22.5000	+	12.9904i	−0.548780	+	0.316839i	−0.748630	−	0.662988i	$-0.769288\pi$
$41$	−22.5000	+	12.9904i	−0.548780	+	0.316839i	0.199849	+	0.979827i	$0.435955\pi$
$42$		0			0
$43$	−36.3591	−	20.9919i	−0.845560	−	0.488184i	0.0135900	−	0.999908i	$-0.495674\pi$
$43$	−36.3591	−	20.9919i	−0.845560	−	0.488184i	−0.859150	+	0.511723i	$0.829007\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	22.7367	−	39.3810i	0.483759	−	0.837895i	−0.516067	−	0.856548i	$-0.672605\pi$
$47$	22.7367	−	39.3810i	0.483759	−	0.837895i	0.999826	+	0.0186534i	$0.00593789\pi$
$48$		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
$53$	−10.8323			−0.204383			−0.102192	−	0.994765i	$-0.532585\pi$
$53$	−10.8323			−0.204383			−0.102192	+	0.994765i	$0.532585\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−69.4881	−	40.1190i	−1.21909	−	0.703841i
$58$		0			0
$59$	31.8810	−	18.4065i	0.540357	−	0.311975i	−0.204867	−	0.978790i	$-0.565676\pi$
$59$	31.8810	−	18.4065i	0.540357	−	0.311975i	0.745224	+	0.666815i	$0.232343\pi$
$60$		0			0
$61$	22.6190	−	39.1772i	0.370802	−	0.642249i	−0.618887	−	0.785480i	$-0.712416\pi$
$61$	22.6190	−	39.1772i	0.370802	−	0.642249i	0.989689	+	0.143232i	$0.0457494\pi$
$62$		0			0
$63$			33.7137i			0.535138i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	86.5606	−	49.9758i	1.29195	−	0.745907i	0.312950	−	0.949770i	$-0.398683\pi$
$67$	86.5606	−	49.9758i	1.29195	−	0.745907i	0.979000	+	0.203862i	$0.0653494\pi$
$68$		0			0
$69$			59.7138i			0.865418i
$70$		0			0
$71$		−	102.603i		−	1.44511i	−0.691312	−	0.722557i	$-0.742967\pi$
$71$		−	102.603i		−	1.44511i	0.691312	−	0.722557i	$-0.257033\pi$
$72$		0			0
$73$		−	13.7621i		−	0.188522i	−0.995548	−	0.0942610i	$-0.969951\pi$
$73$		−	13.7621i		−	0.188522i	0.995548	−	0.0942610i	$-0.0300488\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−21.8846	−	37.9052i	−0.284216	−	0.492276i
$78$		0			0
$79$	28.3810	−	49.1574i	0.359254	−	0.622246i	−0.628583	−	0.777743i	$-0.716365\pi$
$79$	28.3810	−	49.1574i	0.359254	−	0.622246i	0.987836	+	0.155497i	$0.0496979\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.500000	+	0.866025i
$82$		0			0
$83$	45.0333	−	78.0000i	0.542570	−	0.939759i	−0.456185	−	0.889885i	$-0.650785\pi$
$83$	45.0333	−	78.0000i	0.542570	−	0.939759i	0.998756	−	0.0498743i	$-0.0158821\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−66.2300	−	114.714i	−0.761264	−	1.31855i
$88$		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
$93$		−	156.665i		−	1.68457i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−88.0727	−	50.8488i	−0.907966	−	0.524214i	−0.0281897	−	0.999603i	$-0.508974\pi$
$97$	−88.0727	−	50.8488i	−0.907966	−	0.524214i	−0.879776	+	0.475388i	$0.842308\pi$
$98$		0			0
$99$		−	105.159i		−	1.06221i
$100$		0			0
$101$	−87.7621	−	50.6695i	−0.868932	−	0.501678i	−0.00193860	−	0.999998i	$-0.500617\pi$
$101$	−87.7621	−	50.6695i	−0.868932	−	0.501678i	−0.866993	+	0.498320i	$0.833950\pi$
$102$		0			0
$103$	14.1043	−	8.14315i	0.136935	−	0.0790597i	−0.429967	−	0.902844i	$-0.641475\pi$
$103$	14.1043	−	8.14315i	0.136935	−	0.0790597i	0.566903	+	0.823785i	$0.308142\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	84.8705			0.793182			0.396591	−	0.917995i	$-0.370193\pi$
$107$	84.8705			0.793182			0.396591	+	0.917995i	$0.370193\pi$
$108$		0			0
$109$	161.968			1.48594			0.742971	−	0.669323i	$-0.233416\pi$
$109$	161.968			1.48594			0.742971	+	0.669323i	$0.233416\pi$
$110$		0			0
$111$	−21.0000	+	36.3731i	−0.189189	+	0.327685i
$112$		0			0
$113$	3.46410	+	6.00000i	0.0306558	+	0.0530973i	0.880946	−	0.473216i	$-0.156907\pi$
$113$	3.46410	+	6.00000i	0.0306558	+	0.0530973i	−0.850290	+	0.526314i	$0.823574\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−17.5685	−	10.1431i	−0.150158	−	0.0866936i
$118$		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
$123$	77.9423			0.633677
$124$		0			0
$125$		0			0
$126$		0			0
$127$			225.903i			1.77877i	0.457163	+	0.889383i	$0.348865\pi$
$127$			225.903i			1.77877i	−0.457163	+	0.889383i	$0.651135\pi$
$128$		0			0
$129$	62.9758	+	109.077i	0.488184	+	0.845560i
$130$		0			0
$131$	−81.7137	+	47.1774i	−0.623769	+	0.360133i	−0.778335	−	0.627849i	$-0.783935\pi$
$131$	−81.7137	+	47.1774i	−0.623769	+	0.360133i	0.154566	+	0.987982i	$0.450602\pi$
$132$		0			0
$133$	86.7667	+	50.0948i	0.652381	+	0.376652i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	103.689	−	179.595i	0.756855	−	1.31091i	−0.187592	−	0.982247i	$-0.560068\pi$
$137$	103.689	−	179.595i	0.756855	−	1.31091i	0.944447	−	0.328664i	$-0.106598\pi$
$138$		0			0
$139$	16.3569	+	28.3309i	0.117675	+	0.203819i	0.918846	−	0.394616i	$-0.129123\pi$
$139$	16.3569	+	28.3309i	0.117675	+	0.203819i	−0.801171	+	0.598436i	$0.795789\pi$
$140$		0			0
$141$	−118.143	+	68.2100i	−0.837895	+	0.483759i
$142$		0			0
$143$	26.3369			0.184174
$144$		0			0
$145$		0			0
$146$		0			0
$147$			104.903i			0.713627i
$148$		0			0
$149$	−18.3327	+	10.5844i	−0.123038	+	0.0710360i	−0.560256	−	0.828320i	$-0.689297\pi$
$149$	−18.3327	+	10.5844i	−0.123038	+	0.0710360i	0.437218	+	0.899356i	$0.355964\pi$
$150$		0			0
$151$	137.714	−	238.527i	0.912011	−	1.57965i	0.100792	−	0.994908i	$-0.467862\pi$
$151$	137.714	−	238.527i	0.912011	−	1.57965i	0.811219	−	0.584742i	$-0.198804\pi$
$152$		0			0
$153$	−52.5796	−	91.0706i	−0.343658	−	0.595232i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−155.829	+	89.9677i	−0.992539	+	0.573043i	−0.906032	−	0.423208i	$-0.860904\pi$
$157$	−155.829	+	89.9677i	−0.992539	+	0.573043i	−0.0865070	+	0.996251i	$0.527570\pi$
$158$		0			0
$159$	28.1431	+	16.2485i	0.177001	+	0.102192i
$160$		0			0
$161$		−	74.5620i		−	0.463118i
$162$		0			0
$163$		−	264.411i		−	1.62216i	−0.584939	−	0.811078i	$-0.698881\pi$
$163$		−	264.411i		−	1.62216i	0.584939	−	0.811078i	$-0.301119\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−86.3267	−	149.522i	−0.516926	−	0.895342i	−0.999807	−	0.0196561i	$-0.993743\pi$
$167$	−86.3267	−	149.522i	−0.516926	−	0.895342i	0.482881	−	0.875686i	$-0.339590\pi$
$168$		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
$173$	−147.168	+	254.903i	−0.850685	+	1.47343i	0.0299069	+	0.999553i	$0.490479\pi$
$173$	−147.168	+	254.903i	−0.850685	+	1.47343i	−0.880591	+	0.473876i	$0.842854\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−110.439			−0.623950
$178$		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
$183$	−117.532	+	67.8569i	−0.642249	+	0.370802i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	118.233	+	68.2621i	0.632264	+	0.365038i
$188$		0			0
$189$	50.5706	−	87.5908i	0.267569	−	0.463443i
$190$		0			0
$191$	13.8085	+	7.97231i	0.0722956	+	0.0417399i	0.535712	−	0.844401i	$-0.320043\pi$
$191$	13.8085	+	7.97231i	0.0722956	+	0.0417399i	−0.463416	+	0.886141i	$0.653377\pi$
$192$		0			0
$193$	−211.928	+	122.357i	−1.09807	+	0.633973i	−0.935714	−	0.352758i	$-0.885244\pi$
$193$	−211.928	+	122.357i	−1.09807	+	0.633973i	−0.162360	+	0.986732i	$0.551910\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	210.374			1.06789			0.533945	−	0.845519i	$-0.320709\pi$
$197$	210.374			1.06789			0.533945	+	0.845519i	$0.320709\pi$
$198$		0			0
$199$	102.730			0.516230			0.258115	−	0.966114i	$-0.416899\pi$
$199$	102.730			0.516230			0.258115	+	0.966114i	$0.416899\pi$
$200$		0			0
$201$	−299.855			−1.49181
$202$		0			0
$203$	82.6984	+	143.238i	0.407381	+	0.705605i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	89.5708	−	155.141i	0.432709	−	0.749474i
$208$		0			0
$209$	−270.641	−	156.255i	−1.29493	−	0.747630i
$210$		0			0
$211$	113.984	+	197.426i	0.540208	+	0.935668i	0.998892	+	0.0470680i	$0.0149877\pi$
$211$	113.984	+	197.426i	0.540208	+	0.935668i	−0.458684	+	0.888600i	$0.651679\pi$
$212$		0			0
$213$	−153.905	+	266.571i	−0.722557	+	1.25150i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			195.621i			0.901479i
$218$		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
$223$	241.935	+	139.681i	1.08491	+	0.626374i	0.932217	−	0.361899i	$-0.117872\pi$
$223$	241.935	+	139.681i	1.08491	+	0.626374i	0.152695	+	0.988273i	$0.451205\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	124.282	−	215.262i	0.547496	−	0.948291i	−0.450949	−	0.892550i	$-0.648914\pi$
$227$	124.282	−	215.262i	0.547496	−	0.948291i	0.998445	−	0.0557415i	$-0.0177523\pi$
$228$		0			0
$229$	78.8891	+	136.640i	0.344494	+	0.596681i	0.985262	−	0.171054i	$-0.0547172\pi$
$229$	78.8891	+	136.640i	0.344494	+	0.596681i	−0.640768	+	0.767735i	$0.721384\pi$
$230$		0			0
$231$			131.308i			0.568431i
$232$		0			0
$233$	−332.854			−1.42856			−0.714279	−	0.699861i	$-0.753245\pi$
$233$	−332.854			−1.42856			−0.714279	+	0.699861i	$0.753245\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−147.472	+	85.1431i	−0.622246	+	0.359254i
$238$		0			0
$239$	−207.714	+	119.924i	−0.869095	+	0.501772i	−0.867047	−	0.498226i	$-0.833985\pi$
$239$	−207.714	+	119.924i	−0.869095	+	0.501772i	−0.00204759	+	0.999998i	$0.500652\pi$
$240$		0			0
$241$	94.7540	−	164.119i	0.393170	−	0.680991i	−0.599696	−	0.800228i	$-0.704712\pi$
$241$	94.7540	−	164.119i	0.393170	−	0.680991i	0.992866	+	0.119237i	$0.0380450\pi$
$242$		0			0
$243$	210.444	−	121.500i	0.866025	−	0.500000i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−52.2095	+	30.1431i	−0.211374	+	0.122037i
$248$		0			0
$249$	−234.000	+	135.100i	−0.939759	+	0.542570i
$250$		0			0
$251$		−	447.114i		−	1.78133i	−0.454661	−	0.890664i	$-0.650240\pi$
$251$		−	447.114i		−	1.78133i	0.454661	−	0.890664i	$-0.349760\pi$
$252$		0			0
$253$			232.573i			0.919259i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	223.613	+	387.308i	0.870088	+	1.50704i	0.861905	+	0.507070i	$0.169272\pi$
$257$	223.613	+	387.308i	0.870088	+	1.50704i	0.00818336	+	0.999967i	$0.497395\pi$
$258$		0			0
$259$	26.2218	−	45.4174i	0.101242	−	0.175357i
$260$		0			0
$261$			397.380i			1.52253i
$262$		0			0
$263$	177.273	−	307.046i	0.674043	−	1.16748i	−0.302705	−	0.953084i	$-0.597890\pi$
$263$	177.273	−	307.046i	0.674043	−	1.16748i	0.976748	−	0.214392i	$-0.0687771\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−142.852	+	247.427i	−0.535027	+	0.926694i
$268$		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
$273$	21.9369	+	12.6653i	0.0803551	+	0.0463930i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	381.435	+	220.222i	1.37702	+	0.795024i	0.991800	−	0.127799i	$-0.0407913\pi$
$277$	381.435	+	220.222i	1.37702	+	0.795024i	0.385223	+	0.922824i	$0.374125\pi$
$278$		0			0
$279$	−234.998	+	407.028i	−0.842287	+	1.45888i
$280$		0			0
$281$	−272.190	−	157.149i	−0.968646	−	0.559248i	−0.0698227	−	0.997559i	$-0.522243\pi$
$281$	−272.190	−	157.149i	−0.968646	−	0.559248i	−0.898823	+	0.438311i	$0.855577\pi$
$282$		0			0
$283$	232.067	−	133.984i	0.820024	−	0.473441i	−0.0304006	−	0.999538i	$-0.509678\pi$
$283$	232.067	−	133.984i	0.820024	−	0.473441i	0.850425	+	0.526097i	$0.176345\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−97.3231			−0.339105
$288$		0			0
$289$	−152.476			−0.527598
$290$		0			0
$291$	152.546	+	264.218i	0.524214	+	0.907966i
$292$		0			0
$293$	155.033	+	268.524i	0.529121	+	0.916465i	0.999423	+	0.0339593i	$0.0108117\pi$
$293$	155.033	+	268.524i	0.529121	+	0.916465i	−0.470302	+	0.882506i	$0.655855\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−157.739	+	273.212i	−0.531107	+	0.919905i
$298$		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
$303$	152.008	+	263.286i	0.501678	+	0.868932i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			495.952i			1.61548i	0.589541	+	0.807739i	$0.299309\pi$
$307$			495.952i			1.61548i	−0.589541	+	0.807739i	$0.700691\pi$
$308$		0			0
$309$	−48.8589			−0.158119
$310$		0			0
$311$	−195.762	+	113.023i	−0.629460	+	0.363419i	−0.780543	−	0.625102i	$-0.785057\pi$
$311$	−195.762	+	113.023i	−0.629460	+	0.363419i	0.151083	+	0.988521i	$0.451724\pi$
$312$		0			0
$313$	−283.326	−	163.579i	−0.905196	−	0.522615i	−0.0263139	−	0.999654i	$-0.508377\pi$
$313$	−283.326	−	163.579i	−0.905196	−	0.522615i	−0.878882	+	0.477038i	$0.841710\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.09616	+	7.09475i	−0.0129216	+	0.0223809i	−0.872414	−	0.488768i	$-0.837447\pi$
$317$	−4.09616	+	7.09475i	−0.0129216	+	0.0223809i	0.859492	+	0.511149i	$0.170780\pi$
$318$		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
$323$	−312.509			−0.967521
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−420.805	−	242.952i	−1.28686	−	0.742971i
$328$		0			0
$329$	147.520	−	85.1708i	0.448389	−	0.258878i
$330$		0			0
$331$	−138.903	+	240.587i	−0.419647	+	0.726850i	−0.995904	−	0.0904186i	$-0.971180\pi$
$331$	−138.903	+	240.587i	−0.419647	+	0.726850i	0.576257	+	0.817269i	$0.304513\pi$
$332$		0			0
$333$	109.119	−	63.0000i	0.327685	−	0.189189i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−48.3473	+	27.9133i	−0.143464	+	0.0828288i	−0.570014	−	0.821635i	$-0.693062\pi$
$337$	−48.3473	+	27.9133i	−0.143464	+	0.0828288i	0.426550	+	0.904464i	$0.359729\pi$
$338$		0			0
$339$		−	20.7846i		−	0.0613115i
$340$		0			0
$341$		−	610.178i		−	1.78938i
$342$		0			0
$343$		−	314.540i		−	0.917027i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	254.102	+	440.117i	0.732281	+	1.26835i	0.955906	+	0.293673i	$0.0948777\pi$
$347$	254.102	+	440.117i	0.732281	+	1.26835i	−0.223625	+	0.974675i	$0.571789\pi$
$348$		0			0
$349$	69.2379	−	119.924i	0.198389	−	0.343621i	−0.749617	−	0.661872i	$-0.769762\pi$
$349$	69.2379	−	119.924i	0.198389	−	0.343621i	0.948006	+	0.318251i	$0.103096\pi$
$350$		0			0
$351$	30.4294	+	52.7054i	0.0866936	+	0.150158i
$352$		0			0
$353$	288.027	−	498.877i	0.815940	−	1.41325i	−0.0927114	−	0.995693i	$-0.529553\pi$
$353$	288.027	−	498.877i	0.815940	−	1.41325i	0.908651	−	0.417556i	$-0.137113\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	65.6538	+	113.716i	0.183904	+	0.318532i
$358$		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
$363$		−	46.5726i		−	0.128299i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	52.3736	+	30.2379i	0.142707	+	0.0823921i	0.569654	−	0.821885i	$-0.307077\pi$
$367$	52.3736	+	30.2379i	0.142707	+	0.0823921i	−0.426946	+	0.904277i	$0.640411\pi$
$368$		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
$373$	−187.501	+	108.254i	−0.502685	+	0.290225i	−0.729822	−	0.683638i	$-0.760397\pi$
$373$	−187.501	+	108.254i	−0.502685	+	0.290225i	0.227137	+	0.973863i	$0.427064\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−99.5231			−0.263987
$378$		0			0
$379$	−285.254			−0.752649			−0.376325	−	0.926488i	$-0.622812\pi$
$379$	−285.254			−0.752649			−0.376325	+	0.926488i	$0.622812\pi$
$380$		0			0
$381$	338.855	−	586.914i	0.889383	−	1.54046i
$382$		0			0
$383$	81.7905	+	141.665i	0.213552	+	0.369883i	0.952824	−	0.303524i	$-0.0981633\pi$
$383$	81.7905	+	141.665i	0.213552	+	0.369883i	−0.739272	+	0.673407i	$0.764830\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	377.855i		−	0.976369i
$388$		0			0
$389$	−250.760	−	144.776i	−0.644627	−	0.372176i	0.141767	−	0.989900i	$-0.454721\pi$
$389$	−250.760	−	144.776i	−0.644627	−	0.372176i	−0.786395	+	0.617724i	$0.788055\pi$
$390$		0			0
$391$	116.286	+	201.414i	0.297407	+	0.515125i
$392$		0			0
$393$	283.065			0.720266
$394$		0			0
$395$		0			0
$396$		0			0
$397$			66.5081i			0.167527i	0.996486	+	0.0837633i	$0.0266940\pi$
$397$			66.5081i			0.167527i	−0.996486	+	0.0837633i	$0.973306\pi$
$398$		0			0
$399$	−150.284	−	260.300i	−0.376652	−	0.652381i
$400$		0			0
$401$	−392.165	+	226.417i	−0.977968	+	0.564630i	−0.901656	−	0.432454i	$-0.857648\pi$
$401$	−392.165	+	226.417i	−0.977968	+	0.564630i	−0.0763122	+	0.997084i	$0.524315\pi$
$402$		0			0
$403$	−101.940	−	58.8548i	−0.252952	−	0.146042i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−81.7905	+	141.665i	−0.200959	+	0.348072i
$408$		0			0
$409$	150.435	+	260.562i	0.367813	+	0.637071i	0.989223	−	0.146415i	$-0.0467734\pi$
$409$	150.435	+	260.562i	0.367813	+	0.637071i	−0.621410	+	0.783485i	$0.713440\pi$
$410$		0			0
$411$	−538.784	+	311.067i	−1.31091	+	0.756855i
$412$		0			0
$413$	137.901			0.333900
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	98.1411i		−	0.235350i
$418$		0			0
$419$	−103.524	+	59.7697i	−0.247074	+	0.142649i	−0.618424	−	0.785845i	$-0.712229\pi$
$419$	−103.524	+	59.7697i	−0.247074	+	0.142649i	0.371349	+	0.928493i	$0.378895\pi$
$420$		0			0
$421$	81.1431	−	140.544i	0.192739	−	0.333834i	−0.753418	−	0.657542i	$-0.771596\pi$
$421$	81.1431	−	140.544i	0.192739	−	0.333834i	0.946157	+	0.323708i	$0.104930\pi$
$422$		0			0
$423$	409.260			0.967517
$424$		0			0
$425$		0			0
$426$		0			0
$427$	146.756	−	84.7298i	0.343692	−	0.198431i
$428$		0			0
$429$	−68.4254	−	39.5054i	−0.159500	−	0.0920872i
$430$		0			0
$431$			499.815i			1.15966i	0.814736	+	0.579832i	$0.196882\pi$
$431$			499.815i			1.15966i	−0.814736	+	0.579832i	$0.803118\pi$
$432$		0			0
$433$			739.883i			1.70874i	0.519668	+	0.854368i	$0.326056\pi$
$433$			739.883i			1.70874i	−0.519668	+	0.854368i	$0.673944\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−266.184	−	461.044i	−0.609117	−	1.05502i
$438$		0			0
$439$	124.333	−	215.350i	0.283218	−	0.490548i	−0.688958	−	0.724802i	$-0.741931\pi$
$439$	124.333	−	215.350i	0.283218	−	0.490548i	0.972175	+	0.234254i	$0.0752647\pi$
$440$		0			0
$441$	157.355	−	272.547i	0.356814	−	0.618019i
$442$		0			0
$443$	45.5432	−	78.8831i	0.102806	−	0.178066i	−0.810034	−	0.586384i	$-0.800551\pi$
$443$	45.5432	−	78.8831i	0.102806	−	0.178066i	0.912840	+	0.408318i	$0.133884\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	63.5062			0.142072
$448$		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
$453$	−715.581	+	413.141i	−1.57965	+	0.912011i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	349.005	+	201.498i	0.763686	+	0.440915i	0.830618	−	0.556843i	$-0.187988\pi$
$457$	349.005	+	201.498i	0.763686	+	0.440915i	−0.0669313	+	0.997758i	$0.521321\pi$
$458$		0			0
$459$			315.478i			0.687315i
$460$		0			0
$461$	−57.9496	−	33.4572i	−0.125704	−	0.0725752i	0.435829	−	0.900029i	$-0.356455\pi$
$461$	−57.9496	−	33.4572i	−0.125704	−	0.0725752i	−0.561533	+	0.827454i	$0.689788\pi$
$462$		0			0
$463$	153.824	−	88.8105i	0.332234	−	0.191815i	−0.324599	−	0.945852i	$-0.605229\pi$
$463$	153.824	−	88.8105i	0.332234	−	0.191815i	0.656832	+	0.754037i	$0.271896\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	620.647			1.32901			0.664504	−	0.747285i	$-0.268643\pi$
$467$	620.647			1.32901			0.664504	+	0.747285i	$0.268643\pi$
$468$		0			0
$469$	374.415			0.798327
$470$		0			0
$471$	539.806			1.14609
$472$		0			0
$473$	245.277	+	424.833i	0.518557	+	0.898166i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−48.7454	−	84.4294i	−0.102192	−	0.177001i
$478$		0			0
$479$	−146.044	−	84.3187i	−0.304894	−	0.176031i	0.339745	−	0.940517i	$-0.389659\pi$
$479$	−146.044	−	84.3187i	−0.304894	−	0.176031i	−0.644639	+	0.764487i	$0.722992\pi$
$480$		0			0
$481$	15.7782	+	27.3287i	0.0328030	+	0.0568164i
$482$		0			0
$483$	−111.843	+	193.718i	−0.231559	+	0.401072i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	401.935i		−	0.825330i	−0.910883	−	0.412665i	$-0.864598\pi$
$487$		−	401.935i		−	0.825330i	0.910883	−	0.412665i	$-0.135402\pi$
$488$		0			0
$489$	−396.617	+	686.961i	−0.811078	+	1.40483i
$490$		0			0
$491$	−307.833	+	177.727i	−0.626950	+	0.361970i	−0.779570	−	0.626315i	$-0.784562\pi$
$491$	−307.833	+	177.727i	−0.626950	+	0.361970i	0.152620	+	0.988285i	$0.451229\pi$
$492$		0			0
$493$	−446.785	−	257.952i	−0.906258	−	0.523228i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	192.174	−	332.855i	0.386668	−	0.669728i
$498$		0			0
$499$	−8.30845	−	14.3907i	−0.0166502	−	0.0288390i	0.857580	−	0.514350i	$-0.171967\pi$
$499$	−8.30845	−	14.3907i	−0.0166502	−	0.0288390i	−0.874230	+	0.485511i	$0.838634\pi$
$500$		0			0
$501$			517.960i			1.03385i
$502$		0			0
$503$	−362.522			−0.720721			−0.360360	−	0.932813i	$-0.617346\pi$
$503$	−362.522			−0.720721			−0.360360	+	0.932813i	$0.617346\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	425.875	−	245.879i	0.839990	−	0.484968i
$508$		0			0
$509$	578.286	−	333.874i	1.13612	−	0.655941i	0.190655	−	0.981657i	$-0.438939\pi$
$509$	578.286	−	333.874i	1.13612	−	0.655941i	0.945467	+	0.325717i	$0.105606\pi$
$510$		0			0
$511$	25.7762	−	44.6457i	0.0504426	−	0.0873692i
$512$		0			0
$513$		−	722.141i		−	1.40768i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−460.142	+	265.663i	−0.890024	+	0.513855i
$518$		0			0
$519$	764.710	−	441.505i	1.47343	−	0.850685i
$520$		0			0
$521$		−	676.352i		−	1.29818i	−0.760712	−	0.649090i	$-0.775150\pi$
$521$		−	676.352i		−	1.29818i	0.760712	−	0.649090i	$-0.224850\pi$
$522$		0			0
$523$			189.427i			0.362194i	0.983465	+	0.181097i	$0.0579648\pi$
$523$			189.427i			0.362194i	−0.983465	+	0.181097i	$0.942035\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−305.089	−	528.429i	−0.578916	−	1.00271i
$528$		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
$533$	29.2808	−	50.7157i	0.0549357	−	0.0951515i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	96.1707	−	166.573i	0.179089	−	0.310191i
$538$		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
$543$	−756.574	−	436.808i	−1.39332	−	0.804435i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−683.783	−	394.782i	−1.25006	−	0.721722i	−0.278939	−	0.960309i	$-0.589983\pi$
$547$	−683.783	−	394.782i	−1.25006	−	0.721722i	−0.971121	+	0.238586i	$0.923316\pi$
$548$		0			0
$549$	407.141			0.741605
$550$		0			0
$551$	1022.71	+	590.462i	1.85610	+	1.07162i
$552$		0			0
$553$	184.142	−	106.314i	0.332987	−	0.192250i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1004.69			−1.80376			−0.901880	−	0.431987i	$-0.857813\pi$
$557$	−1004.69			−1.80376			−0.901880	+	0.431987i	$0.857813\pi$
$558$		0			0
$559$	94.6330			0.169290
$560$		0			0
$561$	−204.786	−	354.700i	−0.365038	−	0.632264i
$562$		0			0
$563$	−157.603	−	272.976i	−0.279934	−	0.484859i	0.691434	−	0.722439i	$-0.256979\pi$
$563$	−157.603	−	272.976i	−0.279934	−	0.484859i	−0.971368	+	0.237580i	$0.923646\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−262.772	+	151.712i	−0.463443	+	0.267569i
$568$		0			0
$569$	823.923	+	475.692i	1.44802	+	0.836015i	0.998363	−	0.0571870i	$-0.0182131\pi$
$569$	823.923	+	475.692i	1.44802	+	0.836015i	0.449656	+	0.893202i	$0.351546\pi$
$570$		0			0
$571$	−229.183	−	396.957i	−0.401372	−	0.695197i	0.592520	−	0.805556i	$-0.298133\pi$
$571$	−229.183	−	396.957i	−0.401372	−	0.695197i	−0.993892	+	0.110359i	$0.964800\pi$
$572$		0			0
$573$	−23.9169	−	41.4254i	−0.0417399	−	0.0722956i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	991.190i		−	1.71783i	−0.512116	−	0.858916i	$-0.671138\pi$
$577$		−	991.190i		−	1.71783i	0.512116	−	0.858916i	$-0.328862\pi$
$578$		0			0
$579$	734.141			1.26795
$580$		0			0
$581$	292.185	−	168.693i	0.502901	−	0.290350i
$582$		0			0
$583$	109.612	+	63.2843i	0.188013	+	0.108549i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	83.6483	−	144.883i	0.142501	−	0.246820i	−0.785937	−	0.618307i	$-0.787819\pi$
$587$	83.6483	−	144.883i	0.142501	−	0.246820i	0.928438	+	0.371488i	$0.121152\pi$
$588$		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
$593$	−868.330			−1.46430			−0.732150	−	0.681143i	$-0.761483\pi$
$593$	−868.330			−1.46430			−0.732150	+	0.681143i	$0.761483\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−266.900	−	154.095i	−0.447069	−	0.258115i
$598$		0			0
$599$	170.335	−	98.3428i	0.284365	−	0.164178i	−0.351033	−	0.936363i	$-0.614169\pi$
$599$	170.335	−	98.3428i	0.284365	−	0.164178i	0.635398	+	0.772185i	$0.280836\pi$
$600$		0			0
$601$	−332.181	+	575.355i	−0.552715	+	0.957330i	0.445363	+	0.895350i	$0.353075\pi$
$601$	−332.181	+	575.355i	−0.552715	+	0.957330i	−0.998077	+	0.0619795i	$0.980259\pi$
$602$		0			0
$603$	779.046	+	449.782i	1.29195	+	0.745907i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	64.4979	−	37.2379i	0.106257	−	0.0613474i	−0.445930	−	0.895068i	$-0.647127\pi$
$607$	64.4979	−	37.2379i	0.106257	−	0.0613474i	0.552187	+	0.833720i	$0.313794\pi$
$608$		0			0
$609$		−	496.191i		−	0.814763i
$610$		0			0
$611$			102.498i			0.167755i
$612$		0			0
$613$		−	304.569i		−	0.496849i	−0.968651	−	0.248425i	$-0.920087\pi$
$613$		−	304.569i		−	0.496849i	0.968651	−	0.248425i	$-0.0799128\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	470.744	+	815.353i	0.762956	+	1.32148i	0.941320	+	0.337515i	$0.109586\pi$
$617$	470.744	+	815.353i	0.762956	+	1.32148i	−0.178364	+	0.983965i	$0.557080\pi$
$618$		0			0
$619$	−117.736	+	203.924i	−0.190203	+	0.329442i	−0.945318	−	0.326151i	$-0.894248\pi$
$619$	−117.736	+	203.924i	−0.190203	+	0.329442i	0.755114	+	0.655593i	$0.227581\pi$
$620$		0			0
$621$	−465.423	+	268.712i	−0.749474	+	0.432709i
$622$		0			0
$623$	178.373	−	308.952i	0.286313	−	0.495909i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	468.764	+	811.923i	0.747630	+	1.29493i
$628$		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
$633$		−	683.903i		−	1.08042i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	68.2588	+	39.4092i	0.107157	+	0.0618669i
$638$		0			0
$639$	799.712	−	461.714i	1.25150	−	0.722557i
$640$		0			0
$641$	913.355	+	527.326i	1.42489	+	0.822661i	0.996711	−	0.0810330i	$-0.0258219\pi$
$641$	913.355	+	527.326i	1.42489	+	0.822661i	0.428179	+	0.903694i	$0.359155\pi$
$642$		0			0
$643$	854.928	−	493.593i	1.32959	−	0.767640i	0.344356	−	0.938839i	$-0.388097\pi$
$643$	854.928	−	493.593i	1.32959	−	0.767640i	0.985236	+	0.171199i	$0.0547641\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−75.6097			−0.116862			−0.0584310	−	0.998291i	$-0.518610\pi$
$647$	−75.6097			−0.116862			−0.0584310	+	0.998291i	$0.518610\pi$
$648$		0			0
$649$	−430.137			−0.662769
$650$		0			0
$651$	293.431	−	508.238i	0.450740	−	0.780704i
$652$		0			0
$653$	623.510	+	1079.95i	0.954840	+	1.65383i	0.734734	+	0.678355i	$0.237307\pi$
$653$	623.510	+	1079.95i	0.954840	+	1.65383i	0.220105	+	0.975476i	$0.429360\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	107.265	−	61.9294i	0.163265	−	0.0942610i
$658$		0			0
$659$	−544.851	−	314.570i	−0.826784	−	0.477344i	0.0259662	−	0.999663i	$-0.491734\pi$
$659$	−544.851	−	314.570i	−0.826784	−	0.477344i	−0.852750	+	0.522319i	$0.825067\pi$
$660$		0			0
$661$	−323.282	−	559.941i	−0.489080	−	0.847112i	0.510841	−	0.859675i	$-0.329334\pi$
$661$	−323.282	−	559.941i	−0.489080	−	0.847112i	−0.999921	+	0.0125632i	$0.996001\pi$
$662$		0			0
$663$	−79.0108			−0.119172
$664$		0			0
$665$		0			0
$666$		0			0
$667$		−	878.855i		−	1.31762i
$668$		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
$673$	−79.5905	−	45.9516i	−0.118262	−	0.0682788i	0.439702	−	0.898144i	$-0.355084\pi$
$673$	−79.5905	−	45.9516i	−0.118262	−	0.0682788i	−0.557964	+	0.829865i	$0.688417\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	365.763	−	633.520i	0.540270	−	0.935776i	−0.458618	−	0.888634i	$-0.651655\pi$
$677$	365.763	−	633.520i	0.540270	−	0.935776i	0.998888	−	0.0471421i	$-0.0150113\pi$
$678$		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
$683$	−682.177			−0.998794			−0.499397	−	0.866373i	$-0.666445\pi$
$683$	−682.177			−0.998794			−0.499397	+	0.866373i	$0.666445\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	473.335i		−	0.688988i
$688$		0			0
$689$	21.1452	−	12.2082i	0.0306897	−	0.0177187i
$690$		0			0
$691$	210.331	−	364.303i	0.304386	−	0.527212i	−0.672739	−	0.739880i	$-0.734882\pi$
$691$	210.331	−	364.303i	0.304386	−	0.527212i	0.977124	+	0.212669i	$0.0682155\pi$
$692$		0			0
$693$	196.961	−	341.147i	0.284216	−	0.492276i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	262.898	−	151.784i	0.377185	−	0.217768i
$698$		0			0
$699$	864.780	+	499.281i	1.23717	+	0.714279i
$700$		0			0
$701$		−	70.8185i		−	0.101025i	−0.998723	−	0.0505125i	$-0.983915\pi$
$701$		−	70.8185i		−	0.101025i	0.998723	−	0.0505125i	$-0.0160855\pi$
$702$		0			0
$703$		−	374.444i		−	0.532637i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−189.806	−	328.754i	−0.268467	−	0.464998i
$708$		0			0
$709$	399.696	−	692.293i	0.563745	−	0.976436i	−0.433420	−	0.901192i	$-0.642693\pi$
$709$	399.696	−	692.293i	0.563745	−	0.976436i	0.997165	−	0.0752436i	$-0.0239734\pi$
$710$		0			0
$711$	510.859			0.718508
$712$		0			0
$713$	519.727	−	900.194i	0.728930	−	1.26254i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	719.541			1.00354
$718$		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
$723$	−492.356	+	284.262i	−0.680991	+	0.393170i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−784.783	−	453.095i	−1.07948	−	0.623239i	−0.148725	−	0.988879i	$-0.547517\pi$
$727$	−784.783	−	453.095i	−1.07948	−	0.623239i	−0.930757	+	0.365640i	$0.880850\pi$
$728$		0			0
$729$	−729.000			−1.00000
$730$		0			0
$731$	424.833	+	245.277i	0.581166	+	0.335537i
$732$		0			0
$733$	87.9190	−	50.7601i	0.119944	−	0.0692497i	−0.438828	−	0.898571i	$-0.644606\pi$
$733$	87.9190	−	50.7601i	0.119944	−	0.0692497i	0.558772	+	0.829322i	$0.311273\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1167.87			−1.58463
$738$		0			0
$739$	−557.665			−0.754622			−0.377311	−	0.926087i	$-0.623151\pi$
$739$	−557.665			−0.754622			−0.377311	+	0.926087i	$0.623151\pi$
$740$		0			0
$741$	180.859			0.244074
$742$		0			0
$743$	−178.289	−	308.806i	−0.239959	−	0.415621i	0.720743	−	0.693202i	$-0.243801\pi$
$743$	−178.289	−	308.806i	−0.239959	−	0.415621i	−0.960702	+	0.277581i	$0.910467\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	810.600			1.08514
$748$		0			0
$749$	275.329	+	158.961i	0.367595	+	0.212231i
$750$		0			0
$751$	−244.810	−	424.024i	−0.325979	−	0.564613i	0.655731	−	0.754995i	$-0.272361\pi$
$751$	−244.810	−	424.024i	−0.325979	−	0.564613i	−0.981710	+	0.190382i	$0.939027\pi$
$752$		0			0
$753$	−670.670	+	1161.63i	−0.890664	+	1.54268i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	198.379i		−	0.262059i	−0.991378	−	0.131030i	$-0.958172\pi$
$757$		−	198.379i		−	0.262059i	0.991378	−	0.131030i	$-0.0418283\pi$
$758$		0			0
$759$	348.859	−	604.241i	0.459630	−	0.796102i
$760$		0			0
$761$	−30.6653	+	17.7046i	−0.0402961	+	0.0232649i	−0.520013	−	0.854159i	$-0.674073\pi$
$761$	−30.6653	+	17.7046i	−0.0402961	+	0.0232649i	0.479717	+	0.877423i	$0.340739\pi$
$762$		0			0
$763$	525.440	+	303.363i	0.688650	+	0.397592i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−41.4889	+	71.8609i	−0.0540925	+	0.0936909i
$768$		0			0
$769$	−114.552	−	198.411i	−0.148963	−	0.258011i	0.781882	−	0.623427i	$-0.214260\pi$
$769$	−114.552	−	198.411i	−0.148963	−	0.258011i	−0.930844	+	0.365416i	$0.880927\pi$
$770$		0			0
$771$		−	1341.68i		−	1.74018i
$772$		0			0
$773$	905.388			1.17126			0.585632	−	0.810577i	$-0.300846\pi$
$773$	905.388			1.17126			0.585632	+	0.810577i	$0.300846\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−136.252	+	78.6653i	−0.175357	+	0.101242i
$778$		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
$783$	596.070	−	1032.42i	0.761264	−	1.31855i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	128.423	−	74.1452i	0.163181	−	0.0942125i	−0.416186	−	0.909280i	$-0.636633\pi$
$787$	128.423	−	74.1452i	0.163181	−	0.0942125i	0.579366	+	0.815067i	$0.303300\pi$
$788$		0			0
$789$	−921.139	+	531.820i	−1.16748	+	0.674043i
$790$		0			0
$791$			25.9528i			0.0328101i
$792$		0			0
$793$			101.968i			0.128585i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−122.864	−	212.806i	−0.154158	−	0.267009i	0.778594	−	0.627528i	$-0.215933\pi$
$797$	−122.864	−	212.806i	−0.154158	−	0.267009i	−0.932752	+	0.360518i	$0.882600\pi$
$798$		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
$803$	−80.4006	+	139.258i	−0.100125	+	0.173422i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−341.050	+	590.716i	−0.422614	+	0.731990i
$808$		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
$813$	−593.849	−	342.859i	−0.730442	−	0.421721i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−972.459	−	561.450i	−1.19028	−	0.687209i
$818$		0			0
$819$	−37.9959	−	65.8108i	−0.0463930	−	0.0803551i
$820$		0			0
$821$	942.187	+	543.972i	1.14761	+	0.662573i	0.948304	−	0.317365i	$-0.102798\pi$
$821$	942.187	+	543.972i	1.14761	+	0.662573i	0.199306	+	0.979937i	$0.436131\pi$
$822$		0			0
$823$	−812.709	+	469.218i	−0.987496	+	0.570131i	−0.904525	−	0.426421i	$-0.859774\pi$
$823$	−812.709	+	469.218i	−0.987496	+	0.570131i	−0.0829708	+	0.996552i	$0.526441\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−615.395			−0.744129			−0.372065	−	0.928207i	$-0.621350\pi$
$827$	−615.395			−0.744129			−0.372065	+	0.928207i	$0.621350\pi$
$828$		0			0
$829$	559.230			0.674583			0.337292	−	0.941400i	$-0.390489\pi$
$829$	559.230			0.674583			0.337292	+	0.941400i	$0.390489\pi$
$830$		0			0
$831$	−660.665	−	1144.31i	−0.795024	−	1.37702i
$832$		0			0
$833$	204.288	+	353.837i	0.245243	+	0.424774i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1221.09	−	704.994i	1.45888	−	0.842287i
$838$		0			0
$839$	914.135	+	527.776i	1.08955	+	0.629054i	0.933457	−	0.358688i	$-0.116776\pi$
$839$	914.135	+	527.776i	1.08955	+	0.629054i	0.156096	+	0.987742i	$0.450109\pi$
$840$		0			0
$841$	554.258	+	960.003i	0.659046	+	1.14150i
$842$		0			0
$843$	471.446	+	816.569i	0.559248	+	0.968646i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			58.1531i			0.0686578i
$848$		0			0
$849$	−803.903			−0.946882
$850$		0			0
$851$	−241.331	+	139.332i	−0.283585	+	0.163728i
$852$		0			0
$853$	79.5941	+	45.9536i	0.0933107	+	0.0538730i	0.545929	−	0.837831i	$-0.316177\pi$
$853$	79.5941	+	45.9536i	0.0933107	+	0.0538730i	−0.452619	+	0.891704i	$0.649510\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−589.498	+	1021.04i	−0.687862	+	1.19141i	0.284666	+	0.958627i	$0.408117\pi$
$857$	−589.498	+	1021.04i	−0.687862	+	1.19141i	−0.972528	+	0.232785i	$0.925216\pi$
$858$		0			0
$859$	−669.784	−	1160.10i	−0.779726	−	1.35052i	−0.932100	−	0.362201i	$-0.882025\pi$
$859$	−669.784	−	1160.10i	−0.779726	−	1.35052i	0.152374	−	0.988323i	$-0.451308\pi$
$860$		0			0
$861$	252.853	+	145.985i	0.293673	+	0.169552i
$862$		0			0
$863$	−1332.42			−1.54393			−0.771967	−	0.635663i	$-0.780727\pi$
$863$	−1332.42			−1.54393			−0.771967	+	0.635663i	$0.780727\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	396.144	+	228.714i	0.456913	+	0.263799i
$868$		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
$873$		−	915.278i		−	1.04843i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	556.537	−	321.317i	0.634591	−	0.366381i	−0.147937	−	0.988997i	$-0.547263\pi$
$877$	556.537	−	321.317i	0.634591	−	0.366381i	0.782528	+	0.622615i	$0.213930\pi$
$878$		0			0
$879$		−	930.195i		−	1.05824i
$880$		0			0
$881$			983.693i			1.11656i	0.829651	+	0.558282i	$0.188539\pi$
$881$			983.693i			1.11656i	−0.829651	+	0.558282i	$0.811461\pi$
$882$		0			0
$883$			197.540i			0.223715i	0.993724	+	0.111857i	$0.0356800\pi$
$883$			197.540i			0.223715i	−0.993724	+	0.111857i	$0.964320\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	655.920	+	1136.09i	0.739481	+	1.28082i	0.952729	+	0.303821i	$0.0982625\pi$
$887$	655.920	+	1136.09i	0.739481	+	1.28082i	−0.213248	+	0.976998i	$0.568404\pi$
$888$		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
$893$	608.114	−	1053.28i	0.680979	−	1.17949i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−67.2985	−	116.564i	−0.0750262	−	0.129949i
$898$		0			0
$899$			2305.76i			2.56481i
$900$		0			0
$901$	126.569			0.140476
$902$		0			0
$903$			471.810i			0.522492i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1499.08	+	865.496i	1.65279	+	0.954240i	0.975917	+	0.218143i	$0.0699999\pi$
$907$	1499.08	+	865.496i	1.65279	+	0.954240i	0.676876	+	0.736097i	$0.263333\pi$
$908$		0			0
$909$		−	912.050i		−	1.00336i
$910$		0			0
$911$	210.720	+	121.659i	0.231306	+	0.133545i	0.611174	−	0.791496i	$-0.290697\pi$
$911$	210.720	+	121.659i	0.231306	+	0.133545i	−0.379868	+	0.925041i	$0.624031\pi$
$912$		0			0
$913$	−911.380	+	526.185i	−0.998225	+	0.576326i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−353.450			−0.385442
$918$		0			0
$919$	−449.145			−0.488733			−0.244366	−	0.969683i	$-0.578580\pi$
$919$	−449.145			−0.488733			−0.244366	+	0.969683i	$0.578580\pi$
$920$		0			0
$921$	743.927	−	1288.52i	0.807739	−	1.39904i
$922$		0			0
$923$	115.635	+	200.286i	0.125282	+	0.216995i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	126.939	+	73.2883i	0.136935	+	0.0790597i
$928$		0			0
$929$	45.2420	+	26.1205i	0.0486997	+	0.0281168i	0.524152	−	0.851625i	$-0.324382\pi$
$929$	45.2420	+	26.1205i	0.0486997	+	0.0281168i	−0.475452	+	0.879741i	$0.657716\pi$
$930$		0			0
$931$	−467.623	−	809.947i	−0.502280	−	0.869975i
$932$		0			0
$933$	678.140			0.726838
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	196.798i		−	0.210030i	−0.994471	−	0.105015i	$-0.966511\pi$
$937$		−	196.798i		−	0.210030i	0.994471	−	0.105015i	$-0.0334891\pi$
$938$		0			0
$939$	490.736	+	849.979i	0.522615	+	0.905196i
$940$		0			0
$941$	−822.375	+	474.798i	−0.873937	+	0.504568i	−0.868655	−	0.495418i	$-0.835015\pi$
$941$	−822.375	+	474.798i	−0.873937	+	0.504568i	−0.00528258	+	0.999986i	$0.501682\pi$
$942$		0			0
$943$	447.854	+	258.569i	0.474924	+	0.274198i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−814.378	+	1410.54i	−0.859956	+	1.48949i	0.0120142	+	0.999928i	$0.496176\pi$
$947$	−814.378	+	1410.54i	−0.859956	+	1.48949i	−0.871970	+	0.489559i	$0.837158\pi$
$948$		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
$953$	789.836			0.828789			0.414395	−	0.910097i	$-0.363993\pi$
$953$	789.836			0.828789			0.414395	+	0.910097i	$0.363993\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			1547.71i			1.61725i
$958$		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
$963$	381.917	+	661.500i	0.396591	+	0.686916i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−456.689	+	263.669i	−0.472274	+	0.272667i	−0.717191	−	0.696877i	$-0.754573\pi$
$967$	−456.689	+	263.669i	−0.472274	+	0.272667i	0.244917	+	0.969544i	$0.421239\pi$
$968$		0			0
$969$	811.923	+	468.764i	0.837898	+	0.483761i
$970$		0			0
$971$		−	179.700i		−	0.185067i	−0.995710	−	0.0925337i	$-0.970503\pi$
$971$		−	179.700i		−	0.185067i	0.995710	−	0.0925337i	$-0.0294966\pi$
$972$		0			0
$973$			122.544i			0.125945i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	463.376	+	802.591i	0.474284	+	0.821485i	0.999566	−	0.0294434i	$-0.00937349\pi$
$977$	463.376	+	802.591i	0.474284	+	0.821485i	−0.525282	+	0.850928i	$0.676040\pi$
$978$		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
$983$	−282.492	+	489.290i	−0.287377	+	0.497752i	−0.973183	−	0.230033i	$-0.926117\pi$
$983$	−282.492	+	489.290i	−0.287377	+	0.497752i	0.685806	+	0.727785i	$0.259450\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−511.025			−0.517755
$988$		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
$993$	721.762	−	416.710i	0.726850	−	0.419647i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	590.961	+	341.192i	0.592739	+	0.342218i	0.766180	−	0.642626i	$-0.222155\pi$
$997$	590.961	+	341.192i	0.592739	+	0.342218i	−0.173441	+	0.984844i	$0.555488\pi$
$998$		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.u.b.749.2		8
3.2	odd	2		2700.3.u.a.2249.3		8
5.2	odd	4		180.3.o.a.101.1	yes	4
5.3	odd	4		900.3.p.b.101.2		4
5.4	even	2	inner	900.3.u.b.749.3		8
9.4	even	3		2700.3.u.a.449.2		8
9.5	odd	6	inner	900.3.u.b.149.3		8
15.2	even	4		540.3.o.a.521.2		4
15.8	even	4		2700.3.p.a.1601.2		4
15.14	odd	2		2700.3.u.a.2249.2		8
20.7	even	4		720.3.bs.a.641.1		4
45.2	even	12		1620.3.g.a.161.4		4
45.4	even	6		2700.3.u.a.449.3		8
45.7	odd	12		1620.3.g.a.161.2		4
45.13	odd	12		2700.3.p.a.2501.2		4
45.14	odd	6	inner	900.3.u.b.149.2		8
45.22	odd	12		540.3.o.a.341.2		4
45.23	even	12		900.3.p.b.401.2		4
45.32	even	12		180.3.o.a.41.1	✓	4
60.47	odd	4		2160.3.bs.a.1601.2		4
180.67	even	12		2160.3.bs.a.881.2		4
180.167	odd	12		720.3.bs.a.401.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.o.a.41.1	✓	4	45.32	even	12
180.3.o.a.101.1	yes	4	5.2	odd	4
540.3.o.a.341.2		4	45.22	odd	12
540.3.o.a.521.2		4	15.2	even	4
720.3.bs.a.401.1		4	180.167	odd	12
720.3.bs.a.641.1		4	20.7	even	4
900.3.p.b.101.2		4	5.3	odd	4
900.3.p.b.401.2		4	45.23	even	12
900.3.u.b.149.2		8	45.14	odd	6	inner
900.3.u.b.149.3		8	9.5	odd	6	inner
900.3.u.b.749.2		8	1.1	even	1	trivial
900.3.u.b.749.3		8	5.4	even	2	inner
1620.3.g.a.161.2		4	45.7	odd	12
1620.3.g.a.161.4		4	45.2	even	12
2160.3.bs.a.881.2		4	180.67	even	12
2160.3.bs.a.1601.2		4	60.47	odd	4
2700.3.p.a.1601.2		4	15.8	even	4
2700.3.p.a.2501.2		4	45.13	odd	12
2700.3.u.a.449.2		8	9.4	even	3
2700.3.u.a.449.3		8	45.4	even	6
2700.3.u.a.2249.2		8	15.14	odd	2
2700.3.u.a.2249.3		8	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-2.59808 - 1.50000i) q^{3} +(3.24410 + 1.87298i) q^{7} +(4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-2.59808 - 1.50000i) q^{3} +(3.24410 + 1.87298i) q^{7} +(4.50000 + 7.79423i) q^{9} +(-10.1190 - 5.84218i) q^{11} +(-1.95205 + 1.12702i) q^{13} -11.6844 q^{17} +26.7460 q^{19} +(-5.61895 - 9.73231i) q^{21} +(-9.95231 - 17.2379i) q^{23} -27.0000i q^{27} +(38.2379 + 22.0767i) q^{29} +(26.1109 + 45.2254i) q^{31} +(17.5265 + 30.3569i) q^{33} -14.0000i q^{37} +6.76210 q^{39} +(-22.5000 + 12.9904i) q^{41} +(-36.3591 - 20.9919i) q^{43} +(22.7367 - 39.3810i) q^{47} +(-17.4839 - 30.2829i) q^{49} +(30.3569 + 17.5265i) q^{51} -10.8323 q^{53} +(-69.4881 - 40.1190i) q^{57} +(31.8810 - 18.4065i) q^{59} +(22.6190 - 39.1772i) q^{61} +33.7137i q^{63} +(86.5606 - 49.9758i) q^{67} +59.7138i q^{69} -102.603i q^{71} -13.7621i q^{73} +(-21.8846 - 37.9052i) q^{77} +(28.3810 - 49.1574i) q^{79} +(-40.5000 + 70.1481i) q^{81} +(45.0333 - 78.0000i) q^{83} +(-66.2300 - 114.714i) q^{87} -95.2349i q^{89} -8.44353 q^{91} -156.665i q^{93} +(-88.0727 - 50.8488i) q^{97} -105.159i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 36 q^{9}+O(q^{10}) \) 8 * q + 36 * q^9	\( 8 q + 36 q^{9} + 12 q^{11} + 152 q^{19} + 48 q^{21} + 120 q^{29} - 8 q^{31} + 240 q^{39} - 180 q^{41} + 108 q^{49} - 36 q^{51} + 348 q^{59} + 88 q^{61} + 320 q^{79} - 324 q^{81} + 800 q^{91}+O(q^{100}) \) 8 * q + 36 * q^9 + 12 * q^11 + 152 * q^19 + 48 * q^21 + 120 * q^29 - 8 * q^31 + 240 * q^39 - 180 * q^41 + 108 * q^49 - 36 * q^51 + 348 * q^59 + 88 * q^61 + 320 * q^79 - 324 * q^81 + 800 * q^91

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