LMFDB - Embedded newform 1764.2.bm.c.1685.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1685,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 5]))

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

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

chi := DirichletCharacter("1764.1685");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.bm (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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1685.5
Character	$\chi$	$=$	1764.1685
Dual form			1764.2.bm.c.1697.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34187 + 1.09516i) q^{3} +0.113102 q^{5} +(0.601240 - 2.93913i) q^{9} +O(q^{10})$	\(q+(-1.34187 + 1.09516i) q^{3} +0.113102 q^{5} +(0.601240 - 2.93913i) q^{9} -5.62303i q^{11} +(-2.71286 + 1.56627i) q^{13} +(-0.151769 + 0.123865i) q^{15} +(0.615632 + 1.06631i) q^{17} +(3.38980 + 1.95710i) q^{19} +4.69173i q^{23} -4.98721 q^{25} +(2.41204 + 4.60240i) q^{27} +(-0.117222 - 0.0676783i) q^{29} +(-5.91314 - 3.41395i) q^{31} +(6.15813 + 7.54538i) q^{33} +(-3.39182 + 5.87480i) q^{37} +(1.92499 - 5.07276i) q^{39} +(1.27192 + 2.20303i) q^{41} +(-2.88806 + 5.00226i) q^{43} +(0.0680015 - 0.332422i) q^{45} +(2.66323 + 4.61285i) q^{47} +(-1.99388 - 0.756629i) q^{51} +(-2.48935 + 1.43723i) q^{53} -0.635976i q^{55} +(-6.69202 + 1.08620i) q^{57} +(-5.72290 + 9.91236i) q^{59} +(-0.0334465 + 0.0193104i) q^{61} +(-0.306830 + 0.177148i) q^{65} +(5.24496 - 9.08454i) q^{67} +(-5.13821 - 6.29570i) q^{69} -12.4663i q^{71} +(-11.3768 + 6.56842i) q^{73} +(6.69219 - 5.46180i) q^{75} +(-5.61180 - 9.71993i) q^{79} +(-8.27702 - 3.53425i) q^{81} +(0.344701 - 0.597040i) q^{83} +(0.0696293 + 0.120601i) q^{85} +(0.231416 - 0.0375618i) q^{87} +(-5.37075 + 9.30241i) q^{89} +(11.6735 - 1.89476i) q^{93} +(0.383393 + 0.221352i) q^{95} +(5.89327 + 3.40248i) q^{97} +(-16.5268 - 3.38079i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{9}+O(q^{10}) $ 48 * q - 8 * q^9	$ 48 q - 8 q^{9} + 24 q^{15} + 48 q^{25} - 16 q^{39} - 48 q^{51} + 48 q^{53} + 16 q^{57} + 72 q^{65} - 24 q^{79} - 72 q^{81} - 24 q^{85} + 144 q^{93} - 96 q^{95} - 40 q^{99}+O(q^{100}) $ 48 * q - 8 * q^9 + 24 * q^15 + 48 * q^25 - 16 * q^39 - 48 * q^51 + 48 * q^53 + 16 * q^57 + 72 * q^65 - 24 * q^79 - 72 * q^81 - 24 * q^85 + 144 * q^93 - 96 * q^95 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−1.34187	+	1.09516i	−0.774730	+	0.632292i
$3$	−1.34187	+	1.09516i	−0.774730	+	0.632292i
$4$		0			0
$5$	0.113102			0.0505808			0.0252904	−	0.999680i	$-0.491949\pi$
$5$	0.113102			0.0505808			0.0252904	+	0.999680i	$0.491949\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.601240	−	2.93913i	0.200413	−	0.979711i
$10$		0			0
$11$		−	5.62303i		−	1.69541i	−0.530471	−	0.847703i	$-0.677985\pi$
$11$		−	5.62303i		−	1.69541i	0.530471	−	0.847703i	$-0.322015\pi$
$12$		0			0
$13$	−2.71286	+	1.56627i	−0.752412	+	0.434405i	−0.826565	−	0.562842i	$-0.809708\pi$
$13$	−2.71286	+	1.56627i	−0.752412	+	0.434405i	0.0741527	+	0.997247i	$0.476375\pi$
$14$		0			0
$15$	−0.151769	+	0.123865i	−0.0391865	+	0.0319818i
$16$		0			0
$17$	0.615632	+	1.06631i	0.149313	+	0.258617i	0.930974	−	0.365086i	$-0.118961\pi$
$17$	0.615632	+	1.06631i	0.149313	+	0.258617i	−0.781661	+	0.623704i	$0.785627\pi$
$18$		0			0
$19$	3.38980	+	1.95710i	0.777673	+	0.448990i	0.835605	−	0.549331i	$-0.185117\pi$
$19$	3.38980	+	1.95710i	0.777673	+	0.448990i	−0.0579318	+	0.998321i	$0.518451\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			4.69173i			0.978293i	0.872202	+	0.489147i	$0.162692\pi$
$23$			4.69173i			0.978293i	−0.872202	+	0.489147i	$0.837308\pi$
$24$		0			0
$25$	−4.98721			−0.997442
$26$		0			0
$27$	2.41204	+	4.60240i	0.464198	+	0.885732i
$28$		0			0
$29$	−0.117222	−	0.0676783i	−0.0217676	−	0.0125675i	0.489077	−	0.872241i	$-0.337334\pi$
$29$	−0.117222	−	0.0676783i	−0.0217676	−	0.0125675i	−0.510844	+	0.859673i	$0.670667\pi$
$30$		0			0
$31$	−5.91314	−	3.41395i	−1.06203	−	0.613164i	−0.136038	−	0.990704i	$-0.543437\pi$
$31$	−5.91314	−	3.41395i	−1.06203	−	0.613164i	−0.925993	+	0.377540i	$0.876770\pi$
$32$		0			0
$33$	6.15813	+	7.54538i	1.07199	+	1.31348i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.39182	+	5.87480i	−0.557611	+	0.965811i	0.440084	+	0.897957i	$0.354949\pi$
$37$	−3.39182	+	5.87480i	−0.557611	+	0.965811i	−0.997695	+	0.0678544i	$0.978385\pi$
$38$		0			0
$39$	1.92499	−	5.07276i	0.308245	−	0.812291i
$40$		0			0
$41$	1.27192	+	2.20303i	0.198640	+	0.344055i	0.948088	−	0.318009i	$-0.103014\pi$
$41$	1.27192	+	2.20303i	0.198640	+	0.344055i	−0.749448	+	0.662064i	$0.769681\pi$
$42$		0			0
$43$	−2.88806	+	5.00226i	−0.440425	+	0.762838i	−0.997721	−	0.0674759i	$-0.978505\pi$
$43$	−2.88806	+	5.00226i	−0.440425	+	0.762838i	0.557296	+	0.830314i	$0.311839\pi$
$44$		0			0
$45$	0.0680015	−	0.332422i	0.0101371	−	0.0495546i
$46$		0			0
$47$	2.66323	+	4.61285i	0.388472	+	0.672853i	0.992244	−	0.124304i	$-0.0396697\pi$
$47$	2.66323	+	4.61285i	0.388472	+	0.672853i	−0.603772	+	0.797157i	$0.706336\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.99388	−	0.756629i	−0.279199	−	0.105949i
$52$		0			0
$53$	−2.48935	+	1.43723i	−0.341939	+	0.197419i	−0.661129	−	0.750272i	$-0.729922\pi$
$53$	−2.48935	+	1.43723i	−0.341939	+	0.197419i	0.319190	+	0.947691i	$0.396589\pi$
$54$		0			0
$55$		−	0.635976i		−	0.0857550i
$56$		0			0
$57$	−6.69202	+	1.08620i	−0.886380	+	0.143871i
$58$		0			0
$59$	−5.72290	+	9.91236i	−0.745058	+	1.29048i	0.205109	+	0.978739i	$0.434245\pi$
$59$	−5.72290	+	9.91236i	−0.745058	+	1.29048i	−0.950167	+	0.311740i	$0.899088\pi$
$60$		0			0
$61$	−0.0334465	+	0.0193104i	−0.00428239	+	0.00247244i	−0.502140	−	0.864787i	$-0.667454\pi$
$61$	−0.0334465	+	0.0193104i	−0.00428239	+	0.00247244i	0.497857	+	0.867259i	$0.334120\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.306830	+	0.177148i	−0.0380576	+	0.0219726i
$66$		0			0
$67$	5.24496	−	9.08454i	0.640774	−	1.10985i	−0.344486	−	0.938791i	$-0.611947\pi$
$67$	5.24496	−	9.08454i	0.640774	−	1.10985i	0.985260	−	0.171062i	$-0.0547198\pi$
$68$		0			0
$69$	−5.13821	−	6.29570i	−0.618567	−	0.757913i
$70$		0			0
$71$		−	12.4663i		−	1.47948i	−0.672894	−	0.739739i	$-0.734949\pi$
$71$		−	12.4663i		−	1.47948i	0.672894	−	0.739739i	$-0.265051\pi$
$72$		0			0
$73$	−11.3768	+	6.56842i	−1.33156	+	0.768775i	−0.985538	−	0.169452i	$-0.945800\pi$
$73$	−11.3768	+	6.56842i	−1.33156	+	0.768775i	−0.346019	+	0.938227i	$0.612467\pi$
$74$		0			0
$75$	6.69219	−	5.46180i	0.772748	−	0.630674i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−5.61180	−	9.71993i	−0.631377	−	1.09358i	−0.987270	−	0.159051i	$-0.949157\pi$
$79$	−5.61180	−	9.71993i	−0.631377	−	1.09358i	0.355893	−	0.934527i	$-0.384177\pi$
$80$		0			0
$81$	−8.27702	−	3.53425i	−0.919669	−	0.392694i
$82$		0			0
$83$	0.344701	−	0.597040i	0.0378359	−	0.0655337i	−0.846487	−	0.532409i	$-0.821287\pi$
$83$	0.344701	−	0.597040i	0.0378359	−	0.0655337i	0.884323	+	0.466875i	$0.154620\pi$
$84$		0			0
$85$	0.0696293	+	0.120601i	0.00755235	+	0.0130811i
$86$		0			0
$87$	0.231416	−	0.0375618i	0.0248104	−	0.00402705i
$88$		0			0
$89$	−5.37075	+	9.30241i	−0.569298	+	0.986053i	0.427338	+	0.904092i	$0.359452\pi$
$89$	−5.37075	+	9.30241i	−0.569298	+	0.986053i	−0.996636	+	0.0819609i	$0.973882\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	11.6735	−	1.89476i	1.21049	−	0.196477i
$94$		0			0
$95$	0.383393	+	0.221352i	0.0393353	+	0.0227103i
$96$		0			0
$97$	5.89327	+	3.40248i	0.598371	+	0.345470i	0.768401	−	0.639969i	$-0.221053\pi$
$97$	5.89327	+	3.40248i	0.598371	+	0.345470i	−0.170029	+	0.985439i	$0.554386\pi$
$98$		0			0
$99$	−16.5268	−	3.38079i	−1.66101	−	0.339782i
$100$		0			0
$101$	−16.2951			−1.62143			−0.810713	−	0.585443i	$-0.800921\pi$
$101$	−16.2951			−1.62143			−0.810713	+	0.585443i	$0.800921\pi$
$102$		0			0
$103$		−	17.7455i		−	1.74851i	−0.485465	−	0.874256i	$-0.661350\pi$
$103$		−	17.7455i		−	1.74851i	0.485465	−	0.874256i	$-0.338650\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.2674	+	6.50525i	1.08926	+	0.628887i	0.933380	−	0.358889i	$-0.116844\pi$
$107$	11.2674	+	6.50525i	1.08926	+	0.628887i	0.155883	+	0.987775i	$0.450178\pi$
$108$		0			0
$109$	−0.685898	−	1.18801i	−0.0656971	−	0.113791i	0.831306	−	0.555815i	$-0.187594\pi$
$109$	−0.685898	−	1.18801i	−0.0656971	−	0.113791i	−0.897003	+	0.442024i	$0.854260\pi$
$110$		0			0
$111$	−1.88247	−	11.5978i	−0.178677	−	1.10082i
$112$		0			0
$113$	−7.75422	+	4.47690i	−0.729455	+	0.421151i	−0.818223	−	0.574901i	$-0.805041\pi$
$113$	−7.75422	+	4.47690i	−0.729455	+	0.421151i	0.0887675	+	0.996052i	$0.471707\pi$
$114$		0			0
$115$			0.530645i			0.0494829i
$116$		0			0
$117$	2.97240	+	8.91516i	0.274798	+	0.824207i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−20.6184			−1.87440
$122$		0			0
$123$	−4.11942	−	1.56322i	−0.371436	−	0.140951i
$124$		0			0
$125$	−1.12957			−0.101032
$126$		0			0
$127$	−7.21996			−0.640668			−0.320334	−	0.947305i	$-0.603795\pi$
$127$	−7.21996			−0.640668			−0.320334	+	0.947305i	$0.603795\pi$
$128$		0			0
$129$	−1.60289	−	9.87529i	−0.141126	−	0.869470i
$130$		0			0
$131$	−8.33245			−0.728009			−0.364005	−	0.931397i	$-0.618591\pi$
$131$	−8.33245			−0.728009			−0.364005	+	0.931397i	$0.618591\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.272807	+	0.520541i	0.0234795	+	0.0448010i
$136$		0			0
$137$			8.20926i			0.701364i	0.936495	+	0.350682i	$0.114050\pi$
$137$			8.20926i			0.701364i	−0.936495	+	0.350682i	$0.885950\pi$
$138$		0			0
$139$	−3.19880	+	1.84683i	−0.271318	+	0.156646i	−0.629487	−	0.777011i	$-0.716735\pi$
$139$	−3.19880	+	1.84683i	−0.271318	+	0.156646i	0.358168	+	0.933657i	$0.383401\pi$
$140$		0			0
$141$	−8.62553	−	3.27318i	−0.726401	−	0.275652i
$142$		0			0
$143$	8.80718	+	15.2545i	0.736494	+	1.27564i
$144$		0			0
$145$	−0.0132581	−	0.00765456i	−0.00110102	−	0.000635677i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			23.6028i			1.93362i	0.255498	+	0.966810i	$0.417761\pi$
$149$			23.6028i			1.93362i	−0.255498	+	0.966810i	$0.582239\pi$
$150$		0			0
$151$	4.38389			0.356756			0.178378	−	0.983962i	$-0.442915\pi$
$151$	4.38389			0.356756			0.178378	+	0.983962i	$0.442915\pi$
$152$		0			0
$153$	3.50416	−	1.16832i	0.283294	−	0.0944530i
$154$		0			0
$155$	−0.668788	−	0.386125i	−0.0537184	−	0.0310143i
$156$		0			0
$157$	−12.2155	−	7.05263i	−0.974905	−	0.562861i	−0.0741767	−	0.997245i	$-0.523633\pi$
$157$	−12.2155	−	7.05263i	−0.974905	−	0.562861i	−0.900728	+	0.434384i	$0.856966\pi$
$158$		0			0
$159$	1.76639	−	4.65482i	0.140084	−	0.369151i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−6.80340	+	11.7838i	−0.532884	+	0.922982i	0.466379	+	0.884585i	$0.345558\pi$
$163$	−6.80340	+	11.7838i	−0.532884	+	0.922982i	−0.999263	+	0.0383965i	$0.987775\pi$
$164$		0			0
$165$	0.696497	+	0.853399i	0.0542222	+	0.0664370i
$166$		0			0
$167$	8.49355	+	14.7113i	0.657251	+	1.13839i	0.981324	+	0.192360i	$0.0616141\pi$
$167$	8.49355	+	14.7113i	0.657251	+	1.13839i	−0.324074	+	0.946032i	$0.605053\pi$
$168$		0			0
$169$	−1.59359	+	2.76018i	−0.122584	+	0.212322i
$170$		0			0
$171$	7.79027	−	8.78639i	0.595737	−	0.671912i
$172$		0			0
$173$	−0.885682	−	1.53405i	−0.0673371	−	0.116631i	0.830391	−	0.557181i	$-0.188117\pi$
$173$	−0.885682	−	1.53405i	−0.0673371	−	0.116631i	−0.897728	+	0.440549i	$0.854784\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.17624	−	19.5686i	−0.238741	−	1.47087i
$178$		0			0
$179$	7.13609	−	4.12002i	0.533376	−	0.307945i	−0.209014	−	0.977913i	$-0.567025\pi$
$179$	7.13609	−	4.12002i	0.533376	−	0.307945i	0.742390	+	0.669968i	$0.233692\pi$
$180$		0			0
$181$		−	0.934986i		−	0.0694970i	−0.999396	−	0.0347485i	$-0.988937\pi$
$181$		−	0.934986i		−	0.0694970i	0.999396	−	0.0347485i	$-0.0110630\pi$
$182$		0			0
$183$	0.0237330	−	0.0625414i	0.00175439	−	0.00462319i
$184$		0			0
$185$	−0.383622	+	0.664452i	−0.0282044	+	0.0488515i
$186$		0			0
$187$	5.99587	−	3.46172i	0.438461	−	0.253146i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.77097	−	5.64127i	0.707003	−	0.408188i	−0.102947	−	0.994687i	$-0.532827\pi$
$191$	9.77097	−	5.64127i	0.707003	−	0.408188i	0.809950	+	0.586499i	$0.199494\pi$
$192$		0			0
$193$	−10.4943	+	18.1767i	−0.755396	+	1.30838i	0.189781	+	0.981826i	$0.439222\pi$
$193$	−10.4943	+	18.1767i	−0.755396	+	1.30838i	−0.945177	+	0.326558i	$0.894111\pi$
$194$		0			0
$195$	0.217720	−	0.573739i	0.0155913	−	0.0410863i
$196$		0			0
$197$		−	17.2865i		−	1.23161i	−0.787898	−	0.615805i	$-0.788831\pi$
$197$		−	17.2865i		−	1.23161i	0.787898	−	0.615805i	$-0.211169\pi$
$198$		0			0
$199$	−4.50187	+	2.59915i	−0.319129	+	0.184249i	−0.651004	−	0.759074i	$-0.725652\pi$
$199$	−4.50187	+	2.59915i	−0.319129	+	0.184249i	0.331875	+	0.943323i	$0.392319\pi$
$200$		0			0
$201$	2.91098	+	17.9344i	0.205325	+	1.26499i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.143857	+	0.249167i	0.0100474	+	0.0174026i
$206$		0			0
$207$	13.7896	+	2.82086i	0.958445	+	0.196063i
$208$		0			0
$209$	11.0048	−	19.0609i	0.761220	−	1.31847i
$210$		0			0
$211$	12.6664	+	21.9388i	0.871990	+	1.51033i	0.859935	+	0.510404i	$0.170504\pi$
$211$	12.6664	+	21.9388i	0.871990	+	1.51033i	0.0120556	+	0.999927i	$0.496162\pi$
$212$		0			0
$213$	13.6526	+	16.7282i	0.935462	+	1.14620i
$214$		0			0
$215$	−0.326645	+	0.565766i	−0.0222770	+	0.0385849i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	8.07277	−	21.2735i	0.545507	−	1.43753i
$220$		0			0
$221$	−3.34025	−	1.92849i	−0.224689	−	0.129724i
$222$		0			0
$223$	−23.0004	−	13.2793i	−1.54022	−	0.889247i	−0.998824	−	0.0484802i	$-0.984562\pi$
$223$	−23.0004	−	13.2793i	−1.54022	−	0.889247i	−0.541397	−	0.840767i	$-0.682104\pi$
$224$		0			0
$225$	−2.99851	+	14.6581i	−0.199901	+	0.977205i
$226$		0			0
$227$	2.30461			0.152963			0.0764813	−	0.997071i	$-0.475631\pi$
$227$	2.30461			0.152963			0.0764813	+	0.997071i	$0.475631\pi$
$228$		0			0
$229$			1.52838i			0.100998i	0.998724	+	0.0504990i	$0.0160812\pi$
$229$			1.52838i			0.100998i	−0.998724	+	0.0504990i	$0.983919\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.60738	−	0.928021i	−0.105303	−	0.0607966i	0.446424	−	0.894822i	$-0.352697\pi$
$233$	−1.60738	−	0.928021i	−0.105303	−	0.0607966i	−0.551727	+	0.834025i	$0.686031\pi$
$234$		0			0
$235$	0.301217	+	0.521723i	0.0196492	+	0.0340335i
$236$		0			0
$237$	18.1752	+	6.89706i	1.18061	+	0.448013i
$238$		0			0
$239$	26.5014	−	15.3006i	1.71423	−	0.989712i	0.785578	−	0.618763i	$-0.212366\pi$
$239$	26.5014	−	15.3006i	1.71423	−	0.989712i	0.928653	−	0.370949i	$-0.120968\pi$
$240$		0			0
$241$		−	23.7153i		−	1.52763i	−0.645432	−	0.763817i	$-0.723323\pi$
$241$		−	23.7153i		−	1.52763i	0.645432	−	0.763817i	$-0.276677\pi$
$242$		0			0
$243$	14.9773	−	4.32217i	0.960793	−	0.277267i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−12.2614			−0.780174
$248$		0			0
$249$	0.191311	+	1.17866i	0.0121238	+	0.0746942i
$250$		0			0
$251$	−14.5555			−0.918736			−0.459368	−	0.888246i	$-0.651924\pi$
$251$	−14.5555			−0.918736			−0.459368	+	0.888246i	$0.651924\pi$
$252$		0			0
$253$	26.3817			1.65861
$254$		0			0
$255$	−0.225512	−	0.0855763i	−0.0141221	−	0.00535900i
$256$		0			0
$257$	−18.4711			−1.15219			−0.576097	−	0.817381i	$-0.695425\pi$
$257$	−18.4711			−1.15219			−0.576097	+	0.817381i	$0.695425\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.269394	+	0.303841i	−0.0166751	+	0.0188073i
$262$		0			0
$263$		−	23.5431i		−	1.45173i	−0.687837	−	0.725865i	$-0.741440\pi$
$263$		−	23.5431i		−	1.45173i	0.687837	−	0.725865i	$-0.258560\pi$
$264$		0			0
$265$	−0.281551	+	0.162554i	−0.0172955	+	0.00998559i
$266$		0			0
$267$	−2.98079	−	18.3645i	−0.182421	−	1.12389i
$268$		0			0
$269$	15.1399	+	26.2232i	0.923099	+	1.59885i	0.794590	+	0.607146i	$0.207686\pi$
$269$	15.1399	+	26.2232i	0.923099	+	1.59885i	0.128509	+	0.991708i	$0.458981\pi$
$270$		0			0
$271$	−24.9128	−	14.3834i	−1.51334	−	0.873730i	−0.999878	−	0.0156202i	$-0.995028\pi$
$271$	−24.9128	−	14.3834i	−1.51334	−	0.873730i	−0.513467	−	0.858110i	$-0.671639\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			28.0432i			1.69107i
$276$		0			0
$277$	−5.00206			−0.300544			−0.150272	−	0.988645i	$-0.548015\pi$
$277$	−5.00206			−0.300544			−0.150272	+	0.988645i	$0.548015\pi$
$278$		0			0
$279$	−13.5893	+	15.3269i	−0.813569	+	0.917598i
$280$		0			0
$281$	11.4362	+	6.60270i	0.682227	+	0.393884i	0.800694	−	0.599074i	$-0.204465\pi$
$281$	11.4362	+	6.60270i	0.682227	+	0.393884i	−0.118467	+	0.992958i	$0.537798\pi$
$282$		0			0
$283$	−9.82871	−	5.67461i	−0.584256	−	0.337321i	0.178567	−	0.983928i	$-0.442854\pi$
$283$	−9.82871	−	5.67461i	−0.584256	−	0.337321i	−0.762823	+	0.646607i	$0.776187\pi$
$284$		0			0
$285$	−0.756881	+	0.122852i	−0.0448338	+	0.00727710i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.74199	−	13.4095i	0.455411	−	0.788796i
$290$		0			0
$291$	−11.6343	+	1.88839i	−0.682014	+	0.110700i
$292$		0			0
$293$	4.62606	+	8.01258i	0.270258	+	0.468100i	0.968928	−	0.247344i	$-0.0795578\pi$
$293$	4.62606	+	8.01258i	0.270258	+	0.468100i	−0.698670	+	0.715444i	$0.746224\pi$
$294$		0			0
$295$	−0.647272	+	1.12111i	−0.0376857	+	0.0652735i
$296$		0			0
$297$	25.8794	−	13.5630i	1.50168	−	0.787004i
$298$		0			0
$299$	−7.34852	−	12.7280i	−0.424976	−	0.736080i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	21.8660	−	17.8458i	1.25617	−	1.02522i
$304$		0			0
$305$	−0.00378287	+	0.00218404i	−0.000216607	+	0.000125058i
$306$		0			0
$307$			25.1926i			1.43782i	0.695104	+	0.718909i	$0.255358\pi$
$307$			25.1926i			1.43782i	−0.695104	+	0.718909i	$0.744642\pi$
$308$		0			0
$309$	19.4342	+	23.8121i	1.10557	+	1.35463i
$310$		0			0
$311$	11.5932	−	20.0801i	0.657392	−	1.13864i	−0.323896	−	0.946093i	$-0.604993\pi$
$311$	11.5932	−	20.0801i	0.657392	−	1.13864i	0.981288	−	0.192544i	$-0.0616739\pi$
$312$		0			0
$313$	20.6523	−	11.9236i	1.16734	−	0.673963i	0.214286	−	0.976771i	$-0.431257\pi$
$313$	20.6523	−	11.9236i	1.16734	−	0.673963i	0.953052	+	0.302808i	$0.0979241\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.95907	−	5.17252i	0.503192	−	0.290518i	−0.226839	−	0.973932i	$-0.572839\pi$
$317$	8.95907	−	5.17252i	0.503192	−	0.290518i	0.730031	+	0.683414i	$0.239506\pi$
$318$		0			0
$319$	−0.380557	+	0.659144i	−0.0213071	+	0.0369050i
$320$		0			0
$321$	−22.2438	+	3.61045i	−1.24153	+	0.201515i
$322$		0			0
$323$			4.81942i			0.268159i
$324$		0			0
$325$	13.5296	−	7.81132i	0.750487	−	0.433294i
$326$		0			0
$327$	2.22145	+	0.842988i	0.122847	+	0.0466173i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	3.64478	+	6.31295i	0.200335	+	0.346991i	0.948636	−	0.316368i	$-0.102464\pi$
$331$	3.64478	+	6.31295i	0.200335	+	0.346991i	−0.748301	+	0.663359i	$0.769130\pi$
$332$		0			0
$333$	15.2275	+	13.5012i	0.834463	+	0.739859i
$334$		0			0
$335$	0.593216	−	1.02748i	0.0324109	−	0.0561373i
$336$		0			0
$337$	7.67533	+	13.2941i	0.418102	+	0.724173i	0.995749	−	0.0921135i	$-0.0293623\pi$
$337$	7.67533	+	13.2941i	0.418102	+	0.724173i	−0.577647	+	0.816287i	$0.696029\pi$
$338$		0			0
$339$	5.50223	−	14.4996i	0.298840	−	0.787507i
$340$		0			0
$341$	−19.1967	+	33.2497i	−1.03956	+	1.80057i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−0.581142	−	0.712057i	−0.0312876	−	0.0383359i
$346$		0			0
$347$	15.9006	+	9.18021i	0.853588	+	0.492819i	0.861860	−	0.507146i	$-0.169300\pi$
$347$	15.9006	+	9.18021i	0.853588	+	0.492819i	−0.00827163	+	0.999966i	$0.502633\pi$
$348$		0			0
$349$	14.6555	+	8.46135i	0.784490	+	0.452925i	0.838019	−	0.545641i	$-0.183714\pi$
$349$	14.6555	+	8.46135i	0.784490	+	0.452925i	−0.0535293	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	−13.7521	−	8.70775i	−0.734034	−	0.464785i
$352$		0			0
$353$	22.2116			1.18220			0.591101	−	0.806597i	$-0.298693\pi$
$353$	22.2116			1.18220			0.591101	+	0.806597i	$0.298693\pi$
$354$		0			0
$355$		−	1.40996i		−	0.0748332i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.26853	+	2.46444i	0.225285	+	0.130068i	0.608395	−	0.793635i	$-0.291814\pi$
$359$	4.26853	+	2.46444i	0.225285	+	0.130068i	−0.383110	+	0.923703i	$0.625147\pi$
$360$		0			0
$361$	−1.83951	−	3.18612i	−0.0968162	−	0.167691i
$362$		0			0
$363$	27.6673	−	22.5805i	1.45216	−	1.18517i
$364$		0			0
$365$	−1.28674	+	0.742902i	−0.0673512	+	0.0388853i
$366$		0			0
$367$			7.91358i			0.413086i	0.978438	+	0.206543i	$0.0662213\pi$
$367$			7.91358i			0.413086i	−0.978438	+	0.206543i	$0.933779\pi$
$368$		0			0
$369$	7.23972	−	2.41379i	0.376885	−	0.125657i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−32.3303			−1.67400			−0.837000	−	0.547203i	$-0.815692\pi$
$373$	−32.3303			−1.67400			−0.837000	+	0.547203i	$0.815692\pi$
$374$		0			0
$375$	1.51574	−	1.23707i	0.0782727	−	0.0638819i
$376$		0			0
$377$	0.424010			0.0218376
$378$		0			0
$379$	9.46110			0.485984			0.242992	−	0.970028i	$-0.421871\pi$
$379$	9.46110			0.485984			0.242992	+	0.970028i	$0.421871\pi$
$380$		0			0
$381$	9.68827	−	7.90703i	0.496345	−	0.405089i
$382$		0			0
$383$	15.4210			0.787974			0.393987	−	0.919116i	$-0.371095\pi$
$383$	15.4210			0.787974			0.393987	+	0.919116i	$0.371095\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	12.9659	+	11.4959i	0.659094	+	0.584372i
$388$		0			0
$389$			35.5051i			1.80018i	0.435706	+	0.900089i	$0.356499\pi$
$389$			35.5051i			1.80018i	−0.435706	+	0.900089i	$0.643501\pi$
$390$		0			0
$391$	−5.00282	+	2.88838i	−0.253003	+	0.146072i
$392$		0			0
$393$	11.1811	−	9.12538i	0.564011	−	0.460314i
$394$		0			0
$395$	−0.634707	−	1.09934i	−0.0319356	−	0.0553140i
$396$		0			0
$397$	−14.5897	−	8.42339i	−0.732238	−	0.422758i	0.0870024	−	0.996208i	$-0.472271\pi$
$397$	−14.5897	−	8.42339i	−0.732238	−	0.422758i	−0.819240	+	0.573450i	$0.805605\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			6.33915i			0.316562i	0.987394	+	0.158281i	$0.0505952\pi$
$401$			6.33915i			0.316562i	−0.987394	+	0.158281i	$0.949405\pi$
$402$		0			0
$403$	21.3887			1.06545
$404$		0			0
$405$	−0.936148	−	0.399731i	−0.0465176	−	0.0198628i
$406$		0			0
$407$	33.0342	+	19.0723i	1.63744	+	0.945378i
$408$		0			0
$409$	15.0411	+	8.68400i	0.743736	+	0.429396i	0.823426	−	0.567423i	$-0.192060\pi$
$409$	15.0411	+	8.68400i	0.743736	+	0.429396i	−0.0796900	+	0.996820i	$0.525393\pi$
$410$		0			0
$411$	−8.99047	−	11.0158i	−0.443467	−	0.543368i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	0.0389864	−	0.0675265i	0.00191377	−	0.00331474i
$416$		0			0
$417$	2.26980	−	5.98141i	0.111153	−	0.292911i
$418$		0			0
$419$	18.0242	+	31.2189i	0.880542	+	1.52514i	0.850740	+	0.525587i	$0.176154\pi$
$419$	18.0242	+	31.2189i	0.880542	+	1.52514i	0.0298018	+	0.999556i	$0.490512\pi$
$420$		0			0
$421$	4.22463	−	7.31727i	0.205896	−	0.356622i	−0.744522	−	0.667598i	$-0.767323\pi$
$421$	4.22463	−	7.31727i	0.205896	−	0.356622i	0.950418	+	0.310976i	$0.100656\pi$
$422$		0			0
$423$	15.1590	−	5.05416i	0.737057	−	0.245742i
$424$		0			0
$425$	−3.07028	−	5.31789i	−0.148931	−	0.257955i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−28.5242	−	10.8243i	−1.37716	−	0.522601i
$430$		0			0
$431$	−26.6040	+	15.3598i	−1.28147	+	0.739856i	−0.977117	−	0.212704i	$-0.931773\pi$
$431$	−26.6040	+	15.3598i	−1.28147	+	0.739856i	−0.304351	+	0.952560i	$0.598440\pi$
$432$		0			0
$433$		−	9.85040i		−	0.473380i	−0.971585	−	0.236690i	$-0.923937\pi$
$433$		−	9.85040i		−	0.473380i	0.971585	−	0.236690i	$-0.0760626\pi$
$434$		0			0
$435$	0.0261736	−	0.00424832i	0.00125493	−	0.000203691i
$436$		0			0
$437$	−9.18219	+	15.9040i	−0.439244	+	0.760793i
$438$		0			0
$439$	−8.24235	+	4.75872i	−0.393386	+	0.227121i	−0.683626	−	0.729832i	$-0.739598\pi$
$439$	−8.24235	+	4.75872i	−0.393386	+	0.227121i	0.290240	+	0.956954i	$0.406265\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.5756	−	9.56995i	0.787532	−	0.454682i	−0.0515609	−	0.998670i	$-0.516420\pi$
$443$	16.5756	−	9.56995i	0.787532	−	0.454682i	0.839093	+	0.543988i	$0.183086\pi$
$444$		0			0
$445$	−0.607443	+	1.05212i	−0.0287955	+	0.0498753i
$446$		0			0
$447$	−25.8489	−	31.6720i	−1.22261	−	1.49803i
$448$		0			0
$449$		−	34.8874i		−	1.64644i	−0.567724	−	0.823219i	$-0.692176\pi$
$449$		−	34.8874i		−	1.64644i	0.567724	−	0.823219i	$-0.307824\pi$
$450$		0			0
$451$	12.3877	−	7.15203i	0.583313	−	0.336776i
$452$		0			0
$453$	−5.88261	+	4.80107i	−0.276389	+	0.225574i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−16.2270	−	28.1060i	−0.759067	−	1.31474i	−0.943327	−	0.331865i	$-0.892322\pi$
$457$	−16.2270	−	28.1060i	−0.759067	−	1.31474i	0.184260	−	0.982877i	$-0.441011\pi$
$458$		0			0
$459$	−3.42263	+	5.40536i	−0.159755	+	0.252300i
$460$		0			0
$461$	14.1696	−	24.5425i	0.659946	−	1.14306i	−0.320683	−	0.947186i	$-0.603913\pi$
$461$	14.1696	−	24.5425i	0.659946	−	1.14306i	0.980629	−	0.195873i	$-0.0627541\pi$
$462$		0			0
$463$	2.11604	+	3.66508i	0.0983405	+	0.170331i	0.910998	−	0.412411i	$-0.135313\pi$
$463$	2.11604	+	3.66508i	0.0983405	+	0.170331i	−0.812657	+	0.582742i	$0.801980\pi$
$464$		0			0
$465$	1.32030	−	0.214301i	0.0612274	−	0.00993798i
$466$		0			0
$467$	5.61042	−	9.71752i	0.259619	−	0.449673i	−0.706521	−	0.707692i	$-0.749736\pi$
$467$	5.61042	−	9.71752i	0.259619	−	0.449673i	0.966140	+	0.258019i	$0.0830697\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	24.1154	−	3.91424i	1.11118	−	0.180359i
$472$		0			0
$473$	28.1279	+	16.2396i	1.29332	+	0.746699i
$474$		0			0
$475$	−16.9056	−	9.76047i	−0.775684	−	0.447841i
$476$		0			0
$477$	2.72751	+	8.18066i	0.124884	+	0.374567i
$478$		0			0
$479$	−35.6085			−1.62700			−0.813498	−	0.581568i	$-0.802440\pi$
$479$	−35.6085			−1.62700			−0.813498	+	0.581568i	$0.802440\pi$
$480$		0			0
$481$		−	21.2500i		−	0.968917i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.666542	+	0.384828i	0.0302661	+	0.0174741i
$486$		0			0
$487$	12.3856	+	21.4525i	0.561244	+	0.972104i	0.997388	+	0.0722269i	$0.0230106\pi$
$487$	12.3856	+	21.4525i	0.561244	+	0.972104i	−0.436144	+	0.899877i	$0.643656\pi$
$488$		0			0
$489$	−3.77592	−	23.2632i	−0.170753	−	1.05200i
$490$		0			0
$491$	−14.4482	+	8.34166i	−0.652037	+	0.376454i	−0.789236	−	0.614090i	$-0.789523\pi$
$491$	−14.4482	+	8.34166i	−0.652037	+	0.376454i	0.137199	+	0.990543i	$0.456190\pi$
$492$		0			0
$493$		−	0.166660i		−	0.00750598i
$494$		0			0
$495$	−1.86922	−	0.382374i	−0.0840152	−	0.0171864i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	17.1729			0.768764			0.384382	−	0.923174i	$-0.374415\pi$
$499$	17.1729			0.768764			0.384382	+	0.923174i	$0.374415\pi$
$500$		0			0
$501$	−27.5085	−	10.4388i	−1.22899	−	0.466372i
$502$		0			0
$503$	−38.7122			−1.72609			−0.863045	−	0.505127i	$-0.831446\pi$
$503$	−38.7122			−1.72609			−0.863045	+	0.505127i	$0.831446\pi$
$504$		0			0
$505$	−1.84301			−0.0820131
$506$		0			0
$507$	−0.884452	−	5.44906i	−0.0392799	−	0.242001i
$508$		0			0
$509$	−28.9867			−1.28481			−0.642406	−	0.766365i	$-0.722064\pi$
$509$	−28.9867			−1.28481			−0.642406	+	0.766365i	$0.722064\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−0.831020	+	20.3218i	−0.0366904	+	0.897230i
$514$		0			0
$515$		−	2.00705i		−	0.0884411i
$516$		0			0
$517$	25.9382	−	14.9754i	1.14076	−	0.658618i
$518$		0			0
$519$	2.86850	+	1.08853i	0.125913	+	0.0477811i
$520$		0			0
$521$	3.43678	+	5.95267i	0.150568	+	0.260791i	0.931436	−	0.363904i	$-0.118556\pi$
$521$	3.43678	+	5.95267i	0.150568	+	0.260791i	−0.780868	+	0.624696i	$0.785223\pi$
$522$		0			0
$523$	−16.8198	−	9.71091i	−0.735478	−	0.424628i	0.0849449	−	0.996386i	$-0.472929\pi$
$523$	−16.8198	−	9.71091i	−0.735478	−	0.424628i	−0.820423	+	0.571757i	$0.806262\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	8.40695i		−	0.366213i
$528$		0			0
$529$	0.987669			0.0429421
$530$		0			0
$531$	25.6929	+	22.7801i	1.11498	+	0.988571i
$532$		0			0
$533$	−6.90107	−	3.98434i	−0.298919	−	0.172581i
$534$		0			0
$535$	1.27437	+	0.735758i	0.0550958	+	0.0318096i
$536$		0			0
$537$	−5.06362	+	13.3437i	−0.218511	+	0.575824i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−9.62684	+	16.6742i	−0.413890	+	0.716879i	−0.995311	−	0.0967242i	$-0.969164\pi$
$541$	−9.62684	+	16.6742i	−0.413890	+	0.716879i	0.581421	+	0.813603i	$0.302497\pi$
$542$		0			0
$543$	1.02396	+	1.25463i	0.0439424	+	0.0538414i
$544$		0			0
$545$	−0.0775765	−	0.134366i	−0.00332301	−	0.00575563i
$546$		0			0
$547$	−9.03080	+	15.6418i	−0.386129	+	0.668795i	−0.991925	−	0.126825i	$-0.959521\pi$
$547$	−9.03080	+	15.6418i	−0.386129	+	0.668795i	0.605796	+	0.795620i	$0.292855\pi$
$548$		0			0
$549$	0.0366464	+	0.109914i	0.00156403	+	0.00469102i
$550$		0			0
$551$	−0.264907	−	0.458832i	−0.0112854	−	0.0195469i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.212912	−	1.31174i	−0.00903760	−	0.0556801i
$556$		0			0
$557$	3.79413	−	2.19054i	0.160763	−	0.0928163i	−0.417460	−	0.908695i	$-0.637080\pi$
$557$	3.79413	−	2.19054i	0.160763	−	0.0928163i	0.578223	+	0.815879i	$0.303746\pi$
$558$		0			0
$559$		−	18.0939i		−	0.765291i
$560$		0			0
$561$	−4.25455	+	11.2116i	−0.179627	+	0.473355i
$562$		0			0
$563$	21.9486	−	38.0161i	0.925024	−	1.60219i	0.133501	−	0.991049i	$-0.457378\pi$
$563$	21.9486	−	38.0161i	0.925024	−	1.60219i	0.791523	−	0.611140i	$-0.209289\pi$
$564$		0			0
$565$	−0.877018	+	0.506347i	−0.0368964	+	0.0213022i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.96737	−	2.29056i	0.166321	−	0.0960254i	−0.414529	−	0.910036i	$-0.636054\pi$
$569$	3.96737	−	2.29056i	0.166321	−	0.0960254i	0.580850	+	0.814011i	$0.302720\pi$
$570$		0			0
$571$	−1.58435	+	2.74417i	−0.0663029	+	0.114840i	−0.897271	−	0.441480i	$-0.854454\pi$
$571$	−1.58435	+	2.74417i	−0.0663029	+	0.114840i	0.830968	+	0.556320i	$0.187787\pi$
$572$		0			0
$573$	−6.93328	+	18.2707i	−0.289642	+	0.763268i
$574$		0			0
$575$		−	23.3986i		−	0.975790i
$576$		0			0
$577$	−10.4992	+	6.06171i	−0.437087	+	0.252352i	−0.702361	−	0.711821i	$-0.747871\pi$
$577$	−10.4992	+	6.06171i	−0.437087	+	0.252352i	0.265274	+	0.964173i	$0.414538\pi$
$578$		0			0
$579$	−5.82439	−	35.8837i	−0.242053	−	1.49128i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	8.08158	+	13.9977i	0.334705	+	0.579726i
$584$		0			0
$585$	0.336185	+	1.00832i	0.0138995	+	0.0416891i
$586$		0			0
$587$	3.40737	−	5.90173i	0.140637	−	0.243591i	−0.787100	−	0.616826i	$-0.788418\pi$
$587$	3.40737	−	5.90173i	0.140637	−	0.243591i	0.927737	+	0.373235i	$0.121752\pi$
$588$		0			0
$589$	−13.3629	−	23.1452i	−0.550609	−	0.953682i
$590$		0			0
$591$	18.9315	+	23.1962i	0.778738	+	0.954166i
$592$		0			0
$593$	15.0992	−	26.1526i	0.620050	−	1.07396i	−0.369426	−	0.929260i	$-0.620446\pi$
$593$	15.0992	−	26.1526i	0.620050	−	1.07396i	0.989476	−	0.144697i	$-0.0462209\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.19443	−	8.41801i	0.130739	−	0.344526i
$598$		0			0
$599$	−15.2524	−	8.80600i	−0.623198	−	0.359803i	0.154915	−	0.987928i	$-0.450490\pi$
$599$	−15.2524	−	8.80600i	−0.623198	−	0.359803i	−0.778113	+	0.628124i	$0.783823\pi$
$600$		0			0
$601$	27.0004	+	15.5887i	1.10137	+	0.635875i	0.936580	−	0.350454i	$-0.113973\pi$
$601$	27.0004	+	15.5887i	1.10137	+	0.635875i	0.164788	+	0.986329i	$0.447306\pi$
$602$		0			0
$603$	−23.5472	−	20.8776i	−0.958916	−	0.850203i
$604$		0			0
$605$	−2.33199			−0.0948089
$606$		0			0
$607$		−	0.883861i		−	0.0358748i	−0.999839	−	0.0179374i	$-0.994290\pi$
$607$		−	0.883861i		−	0.0358748i	0.999839	−	0.0179374i	$-0.00570996\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−14.4499	−	8.34268i	−0.584582	−	0.337509i
$612$		0			0
$613$	0.112197	+	0.194331i	0.00453159	+	0.00784895i	0.868282	−	0.496070i	$-0.165224\pi$
$613$	0.112197	+	0.194331i	0.00453159	+	0.00784895i	−0.863751	+	0.503919i	$0.831891\pi$
$614$		0			0
$615$	−0.465915	−	0.176804i	−0.0187875	−	0.00712942i
$616$		0			0
$617$	−41.3032	+	23.8464i	−1.66280	+	0.960020i	−0.691436	+	0.722438i	$0.743022\pi$
$617$	−41.3032	+	23.8464i	−1.66280	+	0.960020i	−0.971367	+	0.237583i	$0.923645\pi$
$618$		0			0
$619$		−	11.7458i		−	0.472106i	−0.971740	−	0.236053i	$-0.924146\pi$
$619$		−	11.7458i		−	0.472106i	0.971740	−	0.236053i	$-0.0758538\pi$
$620$		0			0
$621$	−21.5932	+	11.3166i	−0.866505	+	0.454121i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	24.8083			0.992331
$626$		0			0
$627$	6.10773	+	37.6294i	0.243919	+	1.50277i
$628$		0			0
$629$	−8.35244			−0.333034
$630$		0			0
$631$	−17.4415			−0.694335			−0.347168	−	0.937803i	$-0.612857\pi$
$631$	−17.4415			−0.694335			−0.347168	+	0.937803i	$0.612857\pi$
$632$		0			0
$633$	−41.0232	−	15.5673i	−1.63053	−	0.618747i
$634$		0			0
$635$	−0.816593			−0.0324055
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−36.6401	−	7.49524i	−1.44946	−	0.296507i
$640$		0			0
$641$		−	32.2668i		−	1.27446i	−0.770672	−	0.637231i	$-0.780080\pi$
$641$		−	32.2668i		−	1.27446i	0.770672	−	0.637231i	$-0.219920\pi$
$642$		0			0
$643$	−23.4858	+	13.5595i	−0.926191	+	0.534736i	−0.885605	−	0.464440i	$-0.846256\pi$
$643$	−23.4858	+	13.5595i	−0.926191	+	0.534736i	−0.0405858	+	0.999176i	$0.512922\pi$
$644$		0			0
$645$	−0.181290	−	1.11692i	−0.00713827	−	0.0439785i
$646$		0			0
$647$	20.2588	+	35.0893i	0.796456	+	1.37950i	0.921910	+	0.387403i	$0.126628\pi$
$647$	20.2588	+	35.0893i	0.796456	+	1.37950i	−0.125454	+	0.992099i	$0.540039\pi$
$648$		0			0
$649$	55.7375	+	32.1800i	2.18789	+	1.26318i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			20.7326i			0.811330i	0.914022	+	0.405665i	$0.132960\pi$
$653$			20.7326i			0.811330i	−0.914022	+	0.405665i	$0.867040\pi$
$654$		0			0
$655$	−0.942417			−0.0368233
$656$		0			0
$657$	12.4653	+	37.3872i	0.486316	+	1.45862i
$658$		0			0
$659$	15.2785	+	8.82104i	0.595165	+	0.343619i	0.767137	−	0.641483i	$-0.221681\pi$
$659$	15.2785	+	8.82104i	0.595165	+	0.343619i	−0.171972	+	0.985102i	$0.555014\pi$
$660$		0			0
$661$	−4.01032	−	2.31536i	−0.155983	−	0.0900571i	0.419977	−	0.907535i	$-0.362038\pi$
$661$	−4.01032	−	2.31536i	−0.155983	−	0.0900571i	−0.575960	+	0.817478i	$0.695372\pi$
$662$		0			0
$663$	6.59419	−	1.07032i	0.256097	−	0.0415679i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.317528	−	0.549975i	0.0122947	−	0.0212951i
$668$		0			0
$669$	45.4066	−	7.37007i	1.75552	−	0.284943i
$670$		0			0
$671$	0.108583	+	0.188071i	0.00419179	+	0.00726039i
$672$		0			0
$673$	7.90990	−	13.7004i	0.304904	−	0.528110i	−0.672336	−	0.740246i	$-0.734709\pi$
$673$	7.90990	−	13.7004i	0.304904	−	0.528110i	0.977240	+	0.212137i	$0.0680422\pi$
$674$		0			0
$675$	−12.0294	−	22.9531i	−0.463010	−	0.883466i
$676$		0			0
$677$	−6.13362	−	10.6237i	−0.235734	−	0.408303i	0.723752	−	0.690060i	$-0.242416\pi$
$677$	−6.13362	−	10.6237i	−0.235734	−	0.408303i	−0.959486	+	0.281757i	$0.909083\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−3.09249	+	2.52392i	−0.118505	+	0.0967170i
$682$		0			0
$683$	6.56676	−	3.79132i	0.251270	−	0.145071i	−0.369076	−	0.929399i	$-0.620326\pi$
$683$	6.56676	−	3.79132i	0.251270	−	0.145071i	0.620346	+	0.784329i	$0.286992\pi$
$684$		0			0
$685$			0.928484i			0.0354756i
$686$		0			0
$687$	−1.67382	−	2.05089i	−0.0638602	−	0.0782461i
$688$		0			0
$689$	4.50218	−	7.79800i	0.171519	−	0.297080i
$690$		0			0
$691$	−25.0490	+	14.4620i	−0.952909	+	0.550162i	−0.893983	−	0.448100i	$-0.852101\pi$
$691$	−25.0490	+	14.4620i	−0.952909	+	0.550162i	−0.0589254	+	0.998262i	$0.518767\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.361791	+	0.208880i	−0.0137235	+	0.00792327i
$696$		0			0
$697$	−1.56607	+	2.71251i	−0.0593190	+	0.102744i
$698$		0			0
$699$	3.17323	−	0.515056i	0.120023	−	0.0194812i
$700$		0			0
$701$			14.8034i			0.559118i	0.960128	+	0.279559i	$0.0901883\pi$
$701$			14.8034i			0.559118i	−0.960128	+	0.279559i	$0.909812\pi$
$702$		0			0
$703$	−22.9952	+	13.2763i	−0.867279	+	0.500724i
$704$		0			0
$705$	−0.975566	−	0.370204i	−0.0367419	−	0.0139427i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	4.42947	+	7.67206i	0.166352	+	0.288130i	0.937135	−	0.348968i	$-0.113468\pi$
$709$	4.42947	+	7.67206i	0.166352	+	0.288130i	−0.770782	+	0.637098i	$0.780134\pi$
$710$		0			0
$711$	−31.9422	+	10.6498i	−1.19793	+	0.399400i
$712$		0			0
$713$	16.0173	−	27.7429i	0.599854	−	1.03898i
$714$		0			0
$715$	0.996111	+	1.72531i	0.0372524	+	0.0645231i
$716$		0			0
$717$	−18.8048	+	49.5547i	−0.702279	+	1.85065i
$718$		0			0
$719$	3.59102	−	6.21983i	0.133923	−	0.231961i	−0.791263	−	0.611476i	$-0.790576\pi$
$719$	3.59102	−	6.21983i	0.133923	−	0.231961i	0.925185	+	0.379516i	$0.123909\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	25.9721	+	31.8229i	0.965912	+	1.18350i
$724$		0			0
$725$	0.584612	+	0.337526i	0.0217119	+	0.0125354i
$726$		0			0
$727$	−9.90439	−	5.71830i	−0.367333	−	0.212080i	0.304959	−	0.952365i	$-0.401357\pi$
$727$	−9.90439	−	5.71830i	−0.367333	−	0.212080i	−0.672293	+	0.740285i	$0.734690\pi$
$728$		0			0
$729$	−15.3641	+	22.2023i	−0.569041	+	0.822309i
$730$		0			0
$731$	−7.11192			−0.263044
$732$		0			0
$733$			13.3718i			0.493898i	0.969028	+	0.246949i	$0.0794280\pi$
$733$			13.3718i			0.493898i	−0.969028	+	0.246949i	$0.920572\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−51.0826	−	29.4926i	−1.88165	−	1.08637i
$738$		0			0
$739$	−8.75603	−	15.1659i	−0.322096	−	0.557886i	0.658824	−	0.752297i	$-0.271054\pi$
$739$	−8.75603	−	15.1659i	−0.322096	−	0.557886i	−0.980920	+	0.194410i	$0.937721\pi$
$740$		0			0
$741$	16.4532	−	13.4282i	0.604424	−	0.493298i
$742$		0			0
$743$	7.36210	−	4.25051i	0.270089	−	0.155936i	−0.358839	−	0.933399i	$-0.616827\pi$
$743$	7.36210	−	4.25051i	0.270089	−	0.155936i	0.628928	+	0.777463i	$0.283494\pi$
$744$		0			0
$745$			2.66953i			0.0978040i
$746$		0			0
$747$	−1.54753	−	1.37209i	−0.0566213	−	0.0502021i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	22.7215			0.829119			0.414560	−	0.910022i	$-0.363936\pi$
$751$	22.7215			0.829119			0.414560	+	0.910022i	$0.363936\pi$
$752$		0			0
$753$	19.5316	−	15.9407i	0.711773	−	0.580910i
$754$		0			0
$755$	0.495827			0.0180450
$756$		0			0
$757$	2.31506			0.0841425			0.0420712	−	0.999115i	$-0.486604\pi$
$757$	2.31506			0.0841425			0.0420712	+	0.999115i	$0.486604\pi$
$758$		0			0
$759$	−35.4009	+	28.8923i	−1.28497	+	1.04872i
$760$		0			0
$761$	27.1312			0.983504			0.491752	−	0.870735i	$-0.336357\pi$
$761$	27.1312			0.983504			0.491752	+	0.870735i	$0.336357\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.396328	−	0.132139i	0.0143293	−	0.00477751i
$766$		0			0
$767$		−	35.8545i		−	1.29463i
$768$		0			0
$769$	−19.1716	+	11.0687i	−0.691345	+	0.399148i	−0.804116	−	0.594473i	$-0.797361\pi$
$769$	−19.1716	+	11.0687i	−0.691345	+	0.399148i	0.112771	+	0.993621i	$0.464027\pi$
$770$		0			0
$771$	24.7858	−	20.2288i	0.892640	−	0.728523i
$772$		0			0
$773$	−24.2570	−	42.0143i	−0.872462	−	1.51115i	−0.859442	−	0.511234i	$-0.829189\pi$
$773$	−24.2570	−	42.0143i	−0.872462	−	1.51115i	−0.0130206	−	0.999915i	$-0.504145\pi$
$774$		0			0
$775$	29.4901	+	17.0261i	1.05931	+	0.611595i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			9.95709i			0.356750i
$780$		0			0
$781$	−70.0984			−2.50832
$782$		0			0
$783$	0.0287374	−	0.702746i	0.00102699	−	0.0251141i
$784$		0			0
$785$	−1.38160	−	0.797668i	−0.0493115	−	0.0284700i
$786$		0			0
$787$	3.74991	+	2.16501i	0.133670	+	0.0771744i	0.565344	−	0.824855i	$-0.308744\pi$
$787$	3.74991	+	2.16501i	0.133670	+	0.0771744i	−0.431674	+	0.902030i	$0.642077\pi$
$788$		0			0
$789$	25.7835	+	31.5918i	0.917918	+	1.12470i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	0.0604905	−	0.104773i	0.00214808	−	0.00372059i
$794$		0			0
$795$	0.199783	−	0.526470i	0.00708557	−	0.0186720i
$796$		0			0
$797$	0.401963	+	0.696221i	0.0142383	+	0.0246614i	0.873057	−	0.487619i	$-0.162134\pi$
$797$	0.401963	+	0.696221i	0.0142383	+	0.0246614i	−0.858818	+	0.512280i	$0.828801\pi$
$798$		0			0
$799$	−3.27914	+	5.67963i	−0.116008	+	0.200931i
$800$		0			0
$801$	24.1119	+	21.3783i	0.851953	+	0.755366i
$802$		0			0
$803$	36.9344	+	63.9723i	1.30339	+	2.25753i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−49.0345	−	18.6074i	−1.72610	−	0.655012i
$808$		0			0
$809$	−2.89142	+	1.66936i	−0.101657	+	0.0586916i	−0.549966	−	0.835187i	$-0.685360\pi$
$809$	−2.89142	+	1.66936i	−0.101657	+	0.0586916i	0.448310	+	0.893878i	$0.352026\pi$
$810$		0			0
$811$		−	23.9391i		−	0.840616i	−0.907382	−	0.420308i	$-0.861922\pi$
$811$		−	23.9391i		−	0.840616i	0.907382	−	0.420308i	$-0.138078\pi$
$812$		0			0
$813$	49.1819	−	7.98286i	1.72489	−	0.279971i
$814$		0			0
$815$	−0.769479	+	1.33278i	−0.0269537	+	0.0466851i
$816$		0			0
$817$	−19.5799	+	11.3044i	−0.685013	+	0.395492i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	17.5393	−	10.1263i	0.612127	−	0.353411i	−0.161671	−	0.986845i	$-0.551688\pi$
$821$	17.5393	−	10.1263i	0.612127	−	0.353411i	0.773797	+	0.633433i	$0.218355\pi$
$822$		0			0
$823$	13.6864	−	23.7055i	0.477076	−	0.826320i	−0.522579	−	0.852591i	$-0.675030\pi$
$823$	13.6864	−	23.7055i	0.477076	−	0.826320i	0.999655	+	0.0262708i	$0.00836321\pi$
$824$		0			0
$825$	−30.7119	−	37.6304i	−1.06925	−	1.31012i
$826$		0			0
$827$		−	0.732736i		−	0.0254797i	−0.999919	−	0.0127399i	$-0.995945\pi$
$827$		−	0.732736i		−	0.0254797i	0.999919	−	0.0127399i	$-0.00405533\pi$
$828$		0			0
$829$	24.2088	−	13.9770i	0.840806	−	0.485440i	−0.0167319	−	0.999860i	$-0.505326\pi$
$829$	24.2088	−	13.9770i	0.840806	−	0.485440i	0.857538	+	0.514420i	$0.171993\pi$
$830$		0			0
$831$	6.71212	−	5.47806i	0.232841	−	0.190032i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.960639	+	1.66387i	0.0332443	+	0.0575808i
$836$		0			0
$837$	1.44962	−	35.4492i	0.0501064	−	1.22530i
$838$		0			0
$839$	−5.23496	+	9.06722i	−0.180731	+	0.313035i	−0.942130	−	0.335249i	$-0.891180\pi$
$839$	−5.23496	+	9.06722i	−0.180731	+	0.313035i	0.761399	+	0.648284i	$0.224513\pi$
$840$		0			0
$841$	−14.4908	−	25.0989i	−0.499684	−	0.865478i
$842$		0			0
$843$	−22.5769	+	3.66453i	−0.777591	+	0.126213i
$844$		0			0
$845$	−0.180239	+	0.312183i	−0.00620040	+	0.0107394i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	19.4035	−	3.14944i	0.665926	−	0.108088i
$850$		0			0
$851$	−27.5630	−	15.9135i	−0.944846	−	0.545507i
$852$		0			0
$853$	−5.60649	−	3.23691i	−0.191963	−	0.110830i	0.400938	−	0.916105i	$-0.368684\pi$
$853$	−5.60649	−	3.23691i	−0.191963	−	0.110830i	−0.592901	+	0.805275i	$0.702017\pi$
$854$		0			0
$855$	0.881095	−	0.993759i	0.0301328	−	0.0339858i
$856$		0			0
$857$	−30.7035			−1.04881			−0.524407	−	0.851468i	$-0.675713\pi$
$857$	−30.7035			−1.04881			−0.524407	+	0.851468i	$0.675713\pi$
$858$		0			0
$859$			23.4380i			0.799695i	0.916582	+	0.399848i	$0.130937\pi$
$859$			23.4380i			0.799695i	−0.916582	+	0.399848i	$0.869063\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−31.6023	−	18.2456i	−1.07575	−	0.621086i	−0.146006	−	0.989284i	$-0.546642\pi$
$863$	−31.6023	−	18.2456i	−1.07575	−	0.621086i	−0.929748	+	0.368197i	$0.879975\pi$
$864$		0			0
$865$	−0.100172	−	0.173504i	−0.00340597	−	0.00589931i
$866$		0			0
$867$	4.29684	+	26.4726i	0.145928	+	0.899057i
$868$		0			0
$869$	−54.6554	+	31.5553i	−1.85406	+	1.07044i
$870$		0			0
$871$			32.8601i			1.11342i
$872$		0			0
$873$	13.5436	−	15.2754i	0.458382	−	0.516994i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	43.6167			1.47283			0.736415	−	0.676530i	$-0.236517\pi$
$877$	43.6167			1.47283			0.736415	+	0.676530i	$0.236517\pi$
$878$		0			0
$879$	−14.9827	−	5.68556i	−0.505352	−	0.191769i
$880$		0			0
$881$	−18.3722			−0.618974			−0.309487	−	0.950904i	$-0.600157\pi$
$881$	−18.3722			−0.618974			−0.309487	+	0.950904i	$0.600157\pi$
$882$		0			0
$883$	−38.9500			−1.31077			−0.655385	−	0.755295i	$-0.727494\pi$
$883$	−38.9500			−1.31077			−0.655385	+	0.755295i	$0.727494\pi$
$884$		0			0
$885$	−0.359239	−	2.21325i	−0.0120757	−	0.0743977i
$886$		0			0
$887$	39.4534			1.32471			0.662357	−	0.749188i	$-0.269556\pi$
$887$	39.4534			1.32471			0.662357	+	0.749188i	$0.269556\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−19.8732	+	46.5419i	−0.665777	+	1.55921i
$892$		0			0
$893$			20.8488i			0.697680i
$894$		0			0
$895$	0.807106	−	0.465983i	0.0269786	−	0.0155761i
$896$		0			0
$897$	23.8000	+	9.03154i	0.794659	+	0.301554i
$898$		0			0
$899$	0.462101	+	0.800383i	0.0154119	+	0.0266943i
$900$		0			0
$901$	−3.06505	−	1.76961i	−0.102112	−	0.0589542i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	0.105749i		−	0.00351521i
$906$		0			0
$907$	20.6125			0.684427			0.342213	−	0.939622i	$-0.388823\pi$
$907$	20.6125			0.684427			0.342213	+	0.939622i	$0.388823\pi$
$908$		0			0
$909$	−9.79729	+	47.8936i	−0.324955	+	1.58853i
$910$		0			0
$911$	4.40092	+	2.54087i	0.145809	+	0.0841829i	0.571130	−	0.820860i	$-0.306505\pi$
$911$	4.40092	+	2.54087i	0.145809	+	0.0841829i	−0.425321	+	0.905043i	$0.639839\pi$
$912$		0			0
$913$	−3.35717	−	1.93826i	−0.111106	−	0.0641472i
$914$		0			0
$915$	0.00268425	−	0.00707356i	8.87386e−5	−	0.000233845i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	11.7798	−	20.4032i	0.388579	−	0.673038i	−0.603680	−	0.797227i	$-0.706300\pi$
$919$	11.7798	−	20.4032i	0.388579	−	0.673038i	0.992259	+	0.124189i	$0.0396328\pi$
$920$		0			0
$921$	−27.5900	−	33.8053i	−0.909122	−	1.11392i
$922$		0			0
$923$	19.5256	+	33.8193i	0.642693	+	1.11318i
$924$		0			0
$925$	16.9157	−	29.2988i	0.556185	−	0.963340i
$926$		0			0
$927$	−52.1563	−	10.6693i	−1.71304	−	0.350425i
$928$		0			0
$929$	−14.5210	−	25.1511i	−0.476418	−	0.825180i	0.523217	−	0.852199i	$-0.324732\pi$
$929$	−14.5210	−	25.1511i	−0.476418	−	0.825180i	−0.999635	+	0.0270195i	$0.991398\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	6.43430	+	39.6414i	0.210650	+	1.29780i
$934$		0			0
$935$	0.678145	−	0.391527i	0.0221777	−	0.0128043i
$936$		0			0
$937$			48.5954i			1.58754i	0.608217	+	0.793771i	$0.291885\pi$
$937$			48.5954i			1.58754i	−0.608217	+	0.793771i	$0.708115\pi$
$938$		0			0
$939$	−14.6545	+	38.6176i	−0.478230	+	1.26024i
$940$		0			0
$941$	5.31090	−	9.19874i	0.173130	−	0.299870i	−0.766382	−	0.642385i	$-0.777945\pi$
$941$	5.31090	−	9.19874i	0.173130	−	0.299870i	0.939513	+	0.342514i	$0.111279\pi$
$942$		0			0
$943$	−10.3360	+	5.96750i	−0.336587	+	0.194328i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.6602	−	8.46408i	0.476393	−	0.275046i	−0.242519	−	0.970147i	$-0.577974\pi$
$947$	14.6602	−	8.46408i	0.476393	−	0.275046i	0.718912	+	0.695101i	$0.244640\pi$
$948$		0			0
$949$	20.5758	−	35.6384i	0.667920	−	1.15687i
$950$		0			0
$951$	−6.35717	+	16.7525i	−0.206145	+	0.543237i
$952$		0			0
$953$			20.2937i			0.657378i	0.944438	+	0.328689i	$0.106607\pi$
$953$			20.2937i			0.657378i	−0.944438	+	0.328689i	$0.893393\pi$
$954$		0			0
$955$	1.10512	−	0.638040i	0.0357608	−	0.0206465i
$956$		0			0
$957$	−0.211211	−	1.30126i	−0.00682748	−	0.0420637i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	7.81014	+	13.5276i	0.251940	+	0.436373i
$962$		0			0
$963$	25.8942	−	29.2053i	0.834430	−	0.941127i
$964$		0			0
$965$	−1.18693	+	2.05582i	−0.0382085	+	0.0661791i
$966$		0			0
$967$	−9.30930	−	16.1242i	−0.299367	−	0.518519i	0.676624	−	0.736328i	$-0.263442\pi$
$967$	−9.30930	−	16.1242i	−0.299367	−	0.518519i	−0.975991	+	0.217810i	$0.930109\pi$
$968$		0			0
$969$	−5.27804	−	6.46704i	−0.169555	−	0.207751i
$970$		0			0
$971$	0.819339	−	1.41914i	0.0262938	−	0.0455423i	−0.852579	−	0.522598i	$-0.824963\pi$
$971$	0.819339	−	1.41914i	0.0262938	−	0.0455423i	0.878873	+	0.477056i	$0.158296\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−9.60033	+	25.2989i	−0.307457	+	0.810213i
$976$		0			0
$977$	−11.2850	−	6.51542i	−0.361040	−	0.208447i	0.308497	−	0.951225i	$-0.400174\pi$
$977$	−11.2850	−	6.51542i	−0.361040	−	0.208447i	−0.669537	+	0.742779i	$0.733507\pi$
$978$		0			0
$979$	52.3077	+	30.1999i	1.67176	+	0.965192i
$980$		0			0
$981$	−3.90411	+	1.30167i	−0.124649	+	0.0415590i
$982$		0			0
$983$	−37.2729			−1.18882			−0.594410	−	0.804162i	$-0.702614\pi$
$983$	−37.2729			−1.18882			−0.594410	+	0.804162i	$0.702614\pi$
$984$		0			0
$985$		−	1.95514i		−	0.0622959i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−23.4693	−	13.5500i	−0.746279	−	0.430864i
$990$		0			0
$991$	−12.2935	−	21.2929i	−0.390515	−	0.676392i	0.602003	−	0.798494i	$-0.294370\pi$
$991$	−12.2935	−	21.2929i	−0.390515	−	0.676392i	−0.992517	+	0.122103i	$0.961036\pi$
$992$		0			0
$993$	−11.8045	−	4.47954i	−0.374605	−	0.142154i
$994$		0			0
$995$	−0.509171	+	0.293970i	−0.0161418	+	0.00931947i
$996$		0			0
$997$			54.5520i			1.72768i	0.503766	+	0.863840i	$0.331947\pi$
$997$			54.5520i			1.72768i	−0.503766	+	0.863840i	$0.668053\pi$
$998$		0			0
$999$	−35.2194	−	1.44023i	−1.11429	−	0.0455667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.bm.c.1685.5		48
3.2	odd	2		5292.2.bm.c.4625.12		48
7.2	even	3		1764.2.x.c.1469.10	yes	48
7.3	odd	6		1764.2.w.c.1109.3		48
7.4	even	3		1764.2.w.c.1109.22		48
7.5	odd	6		1764.2.x.c.1469.15	yes	48
7.6	odd	2	inner	1764.2.bm.c.1685.20		48
9.4	even	3		5292.2.w.c.1097.12		48
9.5	odd	6		1764.2.w.c.509.3		48
21.2	odd	6		5292.2.x.c.4409.13		48
21.5	even	6		5292.2.x.c.4409.12		48
21.11	odd	6		5292.2.w.c.521.13		48
21.17	even	6		5292.2.w.c.521.12		48
21.20	even	2		5292.2.bm.c.4625.13		48
63.4	even	3		5292.2.bm.c.2285.13		48
63.5	even	6		1764.2.x.c.293.10	✓	48
63.13	odd	6		5292.2.w.c.1097.13		48
63.23	odd	6		1764.2.x.c.293.15	yes	48
63.31	odd	6		5292.2.bm.c.2285.12		48
63.32	odd	6	inner	1764.2.bm.c.1697.20		48
63.40	odd	6		5292.2.x.c.881.13		48
63.41	even	6		1764.2.w.c.509.22		48
63.58	even	3		5292.2.x.c.881.12		48
63.59	even	6	inner	1764.2.bm.c.1697.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.w.c.509.3		48	9.5	odd	6
1764.2.w.c.509.22		48	63.41	even	6
1764.2.w.c.1109.3		48	7.3	odd	6
1764.2.w.c.1109.22		48	7.4	even	3
1764.2.x.c.293.10	✓	48	63.5	even	6
1764.2.x.c.293.15	yes	48	63.23	odd	6
1764.2.x.c.1469.10	yes	48	7.2	even	3
1764.2.x.c.1469.15	yes	48	7.5	odd	6
1764.2.bm.c.1685.5		48	1.1	even	1	trivial
1764.2.bm.c.1685.20		48	7.6	odd	2	inner
1764.2.bm.c.1697.5		48	63.59	even	6	inner
1764.2.bm.c.1697.20		48	63.32	odd	6	inner
5292.2.w.c.521.12		48	21.17	even	6
5292.2.w.c.521.13		48	21.11	odd	6
5292.2.w.c.1097.12		48	9.4	even	3
5292.2.w.c.1097.13		48	63.13	odd	6
5292.2.x.c.881.12		48	63.58	even	3
5292.2.x.c.881.13		48	63.40	odd	6
5292.2.x.c.4409.12		48	21.5	even	6
5292.2.x.c.4409.13		48	21.2	odd	6
5292.2.bm.c.2285.12		48	63.31	odd	6
5292.2.bm.c.2285.13		48	63.4	even	3
5292.2.bm.c.4625.12		48	3.2	odd	2
5292.2.bm.c.4625.13		48	21.20	even	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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.34187 + 1.09516i) q^{3} +0.113102 q^{5} +(0.601240 - 2.93913i) q^{9} +O(q^{10})\)	\(q+(-1.34187 + 1.09516i) q^{3} +0.113102 q^{5} +(0.601240 - 2.93913i) q^{9} -5.62303i q^{11} +(-2.71286 + 1.56627i) q^{13} +(-0.151769 + 0.123865i) q^{15} +(0.615632 + 1.06631i) q^{17} +(3.38980 + 1.95710i) q^{19} +4.69173i q^{23} -4.98721 q^{25} +(2.41204 + 4.60240i) q^{27} +(-0.117222 - 0.0676783i) q^{29} +(-5.91314 - 3.41395i) q^{31} +(6.15813 + 7.54538i) q^{33} +(-3.39182 + 5.87480i) q^{37} +(1.92499 - 5.07276i) q^{39} +(1.27192 + 2.20303i) q^{41} +(-2.88806 + 5.00226i) q^{43} +(0.0680015 - 0.332422i) q^{45} +(2.66323 + 4.61285i) q^{47} +(-1.99388 - 0.756629i) q^{51} +(-2.48935 + 1.43723i) q^{53} -0.635976i q^{55} +(-6.69202 + 1.08620i) q^{57} +(-5.72290 + 9.91236i) q^{59} +(-0.0334465 + 0.0193104i) q^{61} +(-0.306830 + 0.177148i) q^{65} +(5.24496 - 9.08454i) q^{67} +(-5.13821 - 6.29570i) q^{69} -12.4663i q^{71} +(-11.3768 + 6.56842i) q^{73} +(6.69219 - 5.46180i) q^{75} +(-5.61180 - 9.71993i) q^{79} +(-8.27702 - 3.53425i) q^{81} +(0.344701 - 0.597040i) q^{83} +(0.0696293 + 0.120601i) q^{85} +(0.231416 - 0.0375618i) q^{87} +(-5.37075 + 9.30241i) q^{89} +(11.6735 - 1.89476i) q^{93} +(0.383393 + 0.221352i) q^{95} +(5.89327 + 3.40248i) q^{97} +(-16.5268 - 3.38079i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{9}+O(q^{10}) \) 48 * q - 8 * q^9	\( 48 q - 8 q^{9} + 24 q^{15} + 48 q^{25} - 16 q^{39} - 48 q^{51} + 48 q^{53} + 16 q^{57} + 72 q^{65} - 24 q^{79} - 72 q^{81} - 24 q^{85} + 144 q^{93} - 96 q^{95} - 40 q^{99}+O(q^{100}) \) 48 * q - 8 * q^9 + 24 * q^15 + 48 * q^25 - 16 * q^39 - 48 * q^51 + 48 * q^53 + 16 * q^57 + 72 * q^65 - 24 * q^79 - 72 * q^81 - 24 * q^85 + 144 * q^93 - 96 * q^95 - 40 * q^99

Introduction

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