LMFDB - Embedded newform 1232.2.bi.a.527.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(527,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 2, 3]))

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

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

chi := DirichletCharacter("1232.527");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			527.5
Character	$\chi$	$=$	1232.527
Dual form			1232.2.bi.a.879.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31308 + 0.758109i) q^{3} +(-0.222329 + 0.385085i) q^{5} +(-2.33979 + 1.23506i) q^{7} +(-0.350541 + 0.607155i) q^{9} +O(q^{10})$	\(q+(-1.31308 + 0.758109i) q^{3} +(-0.222329 + 0.385085i) q^{5} +(-2.33979 + 1.23506i) q^{7} +(-0.350541 + 0.607155i) q^{9} +(1.27102 - 3.06342i) q^{11} +3.68613i q^{13} -0.674199i q^{15} +(1.86739 - 1.07814i) q^{17} +(-2.83947 + 4.91811i) q^{19} +(2.13603 - 3.39556i) q^{21} +(-7.10168 - 4.10016i) q^{23} +(2.40114 + 4.15890i) q^{25} -5.61165i q^{27} -4.09291i q^{29} +(3.31121 - 1.91173i) q^{31} +(0.653455 + 4.98609i) q^{33} +(0.0445993 - 1.17561i) q^{35} +(0.522119 - 0.904337i) q^{37} +(-2.79449 - 4.84020i) q^{39} -2.32406i q^{41} -11.4945 q^{43} +(-0.155871 - 0.269977i) q^{45} +(1.79602 + 1.03693i) q^{47} +(3.94924 - 5.77957i) q^{49} +(-1.63469 + 2.83137i) q^{51} +(-5.30025 - 9.18031i) q^{53} +(0.897093 + 1.17054i) q^{55} -8.61051i q^{57} +(11.4146 - 6.59023i) q^{59} +(-10.3396 - 5.96955i) q^{61} +(0.0703188 - 1.85356i) q^{63} +(-1.41948 - 0.819534i) q^{65} +(-1.50977 + 0.871668i) q^{67} +12.4335 q^{69} +2.53120i q^{71} +(7.15659 - 4.13186i) q^{73} +(-6.30579 - 3.64065i) q^{75} +(0.809599 + 8.73754i) q^{77} +(2.17540 - 3.76790i) q^{79} +(3.20262 + 5.54710i) q^{81} -14.8881 q^{83} +0.958806i q^{85} +(3.10288 + 5.37434i) q^{87} +(2.62144 - 4.54047i) q^{89} +(-4.55260 - 8.62478i) q^{91} +(-2.89859 + 5.02051i) q^{93} +(-1.26259 - 2.18688i) q^{95} +12.2783 q^{97} +(1.41443 + 1.84556i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{5} + 12 q^{9}+O(q^{10}) $ 32 * q - 2 * q^5 + 12 * q^9	$ 32 q - 2 q^{5} + 12 q^{9} - 9 q^{11} - 18 q^{23} - 6 q^{25} + 5 q^{33} - 6 q^{37} - 10 q^{45} - 36 q^{47} - 32 q^{49} - 42 q^{59} - 18 q^{67} - 24 q^{69} - 78 q^{75} - 19 q^{77} - 24 q^{81} - 8 q^{89} - 18 q^{91} + 2 q^{93} + 12 q^{97}+O(q^{100}) $ 32 * q - 2 * q^5 + 12 * q^9 - 9 * q^11 - 18 * q^23 - 6 * q^25 + 5 * q^33 - 6 * q^37 - 10 * q^45 - 36 * q^47 - 32 * q^49 - 42 * q^59 - 18 * q^67 - 24 * q^69 - 78 * q^75 - 19 * q^77 - 24 * q^81 - 8 * q^89 - 18 * q^91 + 2 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.31308	+	0.758109i	−0.758109	+	0.437694i	−0.828616	−	0.559817i	$-0.810872\pi$
$3$	−1.31308	+	0.758109i	−0.758109	+	0.437694i	0.0705073	+	0.997511i	$0.477538\pi$
$4$		0			0
$5$	−0.222329	+	0.385085i	−0.0994286	+	0.172215i	−0.911448	−	0.411415i	$-0.865035\pi$
$5$	−0.222329	+	0.385085i	−0.0994286	+	0.172215i	0.812020	+	0.583630i	$0.198368\pi$
$6$		0			0
$7$	−2.33979	+	1.23506i	−0.884358	+	0.466810i
$7$	−2.33979	+	1.23506i	−0.884358	+	0.466810i
$8$		0			0
$9$	−0.350541	+	0.607155i	−0.116847	+	0.202385i
$10$		0			0
$11$	1.27102	−	3.06342i	0.383226	−	0.923655i
$11$	1.27102	−	3.06342i	0.383226	−	0.923655i
$12$		0			0
$13$			3.68613i			1.02235i	0.859477	+	0.511175i	$0.170789\pi$
$13$			3.68613i			1.02235i	−0.859477	+	0.511175i	$0.829211\pi$
$14$		0			0
$15$		−	0.674199i		−	0.174077i
$16$		0			0
$17$	1.86739	−	1.07814i	0.452909	−	0.261487i	−0.256149	−	0.966637i	$-0.582454\pi$
$17$	1.86739	−	1.07814i	0.452909	−	0.261487i	0.709058	+	0.705150i	$0.249120\pi$
$18$		0			0
$19$	−2.83947	+	4.91811i	−0.651419	+	1.12829i	0.331360	+	0.943505i	$0.392493\pi$
$19$	−2.83947	+	4.91811i	−0.651419	+	1.12829i	−0.982779	+	0.184787i	$0.940841\pi$
$20$		0			0
$21$	2.13603	−	3.39556i	0.466120	−	0.740971i
$22$		0			0
$23$	−7.10168	−	4.10016i	−1.48080	−	0.854942i	−0.481039	−	0.876699i	$-0.659741\pi$
$23$	−7.10168	−	4.10016i	−1.48080	−	0.854942i	−0.999763	+	0.0217573i	$0.993074\pi$
$24$		0			0
$25$	2.40114	+	4.15890i	0.480228	+	0.831779i
$26$		0			0
$27$		−	5.61165i		−	1.07996i
$28$		0			0
$29$		−	4.09291i		−	0.760035i	−0.924979	−	0.380018i	$-0.875918\pi$
$29$		−	4.09291i		−	0.760035i	0.924979	−	0.380018i	$-0.124082\pi$
$30$		0			0
$31$	3.31121	−	1.91173i	0.594710	−	0.343356i	−0.172248	−	0.985054i	$-0.555103\pi$
$31$	3.31121	−	1.91173i	0.594710	−	0.343356i	0.766958	+	0.641698i	$0.221770\pi$
$32$		0			0
$33$	0.653455	+	4.98609i	0.113752	+	0.867967i
$34$		0			0
$35$	0.0445993	−	1.17561i	0.00753866	−	0.198714i
$36$		0			0
$37$	0.522119	−	0.904337i	0.0858358	−	0.148672i	−0.819911	−	0.572491i	$-0.805977\pi$
$37$	0.522119	−	0.904337i	0.0858358	−	0.148672i	0.905747	+	0.423819i	$0.139311\pi$
$38$		0			0
$39$	−2.79449	−	4.84020i	−0.447477	−	0.775052i
$40$		0			0
$41$		−	2.32406i		−	0.362957i	−0.983395	−	0.181479i	$-0.941912\pi$
$41$		−	2.32406i		−	0.362957i	0.983395	−	0.181479i	$-0.0580884\pi$
$42$		0			0
$43$	−11.4945			−1.75290			−0.876450	−	0.481493i	$-0.840095\pi$
$43$	−11.4945			−1.75290			−0.876450	+	0.481493i	$0.840095\pi$
$44$		0			0
$45$	−0.155871	−	0.269977i	−0.0232359	−	0.0402457i
$46$		0			0
$47$	1.79602	+	1.03693i	0.261976	+	0.151252i	0.625236	−	0.780436i	$-0.285003\pi$
$47$	1.79602	+	1.03693i	0.261976	+	0.151252i	−0.363259	+	0.931688i	$0.618336\pi$
$48$		0			0
$49$	3.94924	−	5.77957i	0.564178	−	0.825653i
$50$		0			0
$51$	−1.63469	+	2.83137i	−0.228903	+	0.396471i
$52$		0			0
$53$	−5.30025	−	9.18031i	−0.728046	−	1.26101i	−0.957708	−	0.287742i	$-0.907095\pi$
$53$	−5.30025	−	9.18031i	−0.728046	−	1.26101i	0.229662	−	0.973270i	$-0.426238\pi$
$54$		0			0
$55$	0.897093	+	1.17054i	0.120964	+	0.157835i
$56$		0			0
$57$		−	8.61051i		−	1.14049i
$58$		0			0
$59$	11.4146	−	6.59023i	1.48606	−	0.857974i	0.486181	−	0.873858i	$-0.338389\pi$
$59$	11.4146	−	6.59023i	1.48606	−	0.857974i	0.999874	+	0.0158836i	$0.00505613\pi$
$60$		0			0
$61$	−10.3396	−	5.96955i	−1.32384	−	0.764322i	−0.339505	−	0.940604i	$-0.610260\pi$
$61$	−10.3396	−	5.96955i	−1.32384	−	0.764322i	−0.984340	+	0.176282i	$0.943593\pi$
$62$		0			0
$63$	0.0703188	−	1.85356i	0.00885933	−	0.233526i
$64$		0			0
$65$	−1.41948	−	0.819534i	−0.176064	−	0.101651i
$66$		0			0
$67$	−1.50977	+	0.871668i	−0.184448	+	0.106491i	−0.589381	−	0.807855i	$-0.700628\pi$
$67$	−1.50977	+	0.871668i	−0.184448	+	0.106491i	0.404933	+	0.914346i	$0.367295\pi$
$68$		0			0
$69$	12.4335			1.49681
$70$		0			0
$71$			2.53120i			0.300398i	0.988656	+	0.150199i	$0.0479915\pi$
$71$			2.53120i			0.300398i	−0.988656	+	0.150199i	$0.952009\pi$
$72$		0			0
$73$	7.15659	−	4.13186i	0.837615	−	0.483597i	−0.0188377	−	0.999823i	$-0.505997\pi$
$73$	7.15659	−	4.13186i	0.837615	−	0.483597i	0.856453	+	0.516225i	$0.172663\pi$
$74$		0			0
$75$	−6.30579	−	3.64065i	−0.728130	−	0.420386i
$76$		0			0
$77$	0.809599	+	8.73754i	0.0922624	+	0.995735i
$78$		0			0
$79$	2.17540	−	3.76790i	0.244751	−	0.423921i	−0.717310	−	0.696754i	$-0.754627\pi$
$79$	2.17540	−	3.76790i	0.244751	−	0.423921i	0.962062	+	0.272832i	$0.0879604\pi$
$80$		0			0
$81$	3.20262	+	5.54710i	0.355846	+	0.616344i
$82$		0			0
$83$	−14.8881			−1.63418			−0.817092	−	0.576507i	$-0.804415\pi$
$83$	−14.8881			−1.63418			−0.817092	+	0.576507i	$0.804415\pi$
$84$		0			0
$85$			0.958806i			0.103997i
$86$		0			0
$87$	3.10288	+	5.37434i	0.332663	+	0.576190i
$88$		0			0
$89$	2.62144	−	4.54047i	0.277872	−	0.481289i	−0.692983	−	0.720954i	$-0.743704\pi$
$89$	2.62144	−	4.54047i	0.277872	−	0.481289i	0.970856	+	0.239664i	$0.0770374\pi$
$90$		0			0
$91$	−4.55260	−	8.62478i	−0.477242	−	0.904123i
$92$		0			0
$93$	−2.89859	+	5.02051i	−0.300570	+	0.520603i
$94$		0			0
$95$	−1.26259	−	2.18688i	−0.129539	−	0.224369i
$96$		0			0
$97$	12.2783			1.24667			0.623335	−	0.781955i	$-0.285777\pi$
$97$	12.2783			1.24667			0.623335	+	0.781955i	$0.285777\pi$
$98$		0			0
$99$	1.41443	+	1.84556i	0.142155	+	0.185486i
$100$		0			0
$101$	−14.3051	+	8.25906i	−1.42341	+	0.821807i	−0.996589	−	0.0825286i	$-0.973700\pi$
$101$	−14.3051	+	8.25906i	−1.42341	+	0.821807i	−0.426822	+	0.904335i	$0.640367\pi$
$102$		0			0
$103$	1.01188	+	0.584209i	0.0997035	+	0.0575638i	0.549023	−	0.835807i	$-0.315000\pi$
$103$	1.01188	+	0.584209i	0.0997035	+	0.0575638i	−0.449319	+	0.893371i	$0.648333\pi$
$104$		0			0
$105$	0.832677	+	1.57748i	0.0812610	+	0.153947i
$106$		0			0
$107$	8.58515	−	14.8699i	0.829958	−	1.43753i	−0.0681122	−	0.997678i	$-0.521698\pi$
$107$	8.58515	−	14.8699i	0.829958	−	1.43753i	0.898070	−	0.439852i	$-0.144969\pi$
$108$		0			0
$109$	2.14649	−	1.23928i	0.205597	−	0.118701i	−0.393667	−	0.919253i	$-0.628794\pi$
$109$	2.14649	−	1.23928i	0.205597	−	0.118701i	0.599263	+	0.800552i	$0.295460\pi$
$110$		0			0
$111$			1.58329i			0.150279i
$112$		0			0
$113$	−16.0680			−1.51155			−0.755775	−	0.654831i	$-0.772740\pi$
$113$	−16.0680			−1.51155			−0.755775	+	0.654831i	$0.772740\pi$
$114$		0			0
$115$	3.15782	−	1.82317i	0.294468	−	0.170011i
$116$		0			0
$117$	−2.23805	−	1.29214i	−0.206908	−	0.119459i
$118$		0			0
$119$	−3.03774	+	4.82896i	−0.278469	+	0.442670i
$120$		0			0
$121$	−7.76904	−	7.78730i	−0.706276	−	0.707936i
$122$		0			0
$123$	1.76189	+	3.05169i	0.158864	+	0.275161i
$124$		0			0
$125$	−4.35866			−0.389851
$126$		0			0
$127$	−15.5441			−1.37932			−0.689659	−	0.724134i	$-0.742240\pi$
$127$	−15.5441			−1.37932			−0.689659	+	0.724134i	$0.742240\pi$
$128$		0			0
$129$	15.0933	−	8.71411i	1.32889	−	0.767235i
$130$		0			0
$131$	0.826984	−	1.43238i	0.0722539	−	0.125147i	−0.827635	−	0.561267i	$-0.810314\pi$
$131$	0.826984	−	1.43238i	0.0722539	−	0.125147i	0.899889	+	0.436119i	$0.143647\pi$
$132$		0			0
$133$	0.569599	−	15.0143i	0.0493905	−	1.30190i
$134$		0			0
$135$	2.16096	+	1.24763i	0.185986	+	0.107379i
$136$		0			0
$137$	7.88353	+	13.6547i	0.673536	+	1.16660i	0.976895	+	0.213722i	$0.0685586\pi$
$137$	7.88353	+	13.6547i	0.673536	+	1.16660i	−0.303359	+	0.952876i	$0.598108\pi$
$138$		0			0
$139$	−0.0641939			−0.00544485			−0.00272243	−	0.999996i	$-0.500867\pi$
$139$	−0.0641939			−0.00544485			−0.00272243	+	0.999996i	$0.500867\pi$
$140$		0			0
$141$	−3.14443			−0.264809
$142$		0			0
$143$	11.2922	+	4.68513i	0.944298	+	0.391790i
$144$		0			0
$145$	1.57612	+	0.909974i	0.130890	+	0.0755692i
$146$		0			0
$147$	−0.804138	+	10.5830i	−0.0663242	+	0.872873i
$148$		0			0
$149$	−7.11909	−	4.11021i	−0.583219	−	0.336722i	0.179193	−	0.983814i	$-0.442651\pi$
$149$	−7.11909	−	4.11021i	−0.583219	−	0.336722i	−0.762412	+	0.647092i	$0.775985\pi$
$150$		0			0
$151$	10.5612	+	18.2926i	0.859461	+	1.48863i	0.872443	+	0.488715i	$0.162534\pi$
$151$	10.5612	+	18.2926i	0.859461	+	1.48863i	−0.0129820	+	0.999916i	$0.504132\pi$
$152$		0			0
$153$			1.51173i			0.122216i
$154$		0			0
$155$			1.70013i			0.136558i
$156$		0			0
$157$	−8.85762	−	15.3418i	−0.706915	−	1.22441i	−0.965996	−	0.258557i	$-0.916753\pi$
$157$	−8.85762	−	15.3418i	−0.706915	−	1.22441i	0.259081	−	0.965855i	$-0.416580\pi$
$158$		0			0
$159$	13.9193	+	8.03634i	1.10388	+	0.637323i
$160$		0			0
$161$	21.6804	+	0.822494i	1.70865	+	0.0648216i
$162$		0			0
$163$	−13.8719	−	8.00895i	−1.08653	−	0.627309i	−0.153881	−	0.988089i	$-0.549177\pi$
$163$	−13.8719	−	8.00895i	−1.08653	−	0.627309i	−0.932651	+	0.360780i	$0.882511\pi$
$164$		0			0
$165$	−2.06535	−	0.856917i	−0.160787	−	0.0667109i
$166$		0			0
$167$	9.07459			0.702213			0.351106	−	0.936336i	$-0.385806\pi$
$167$	9.07459			0.702213			0.351106	+	0.936336i	$0.385806\pi$
$168$		0			0
$169$	−0.587572			−0.0451978
$170$		0			0
$171$	−1.99070	−	3.44800i	−0.152233	−	0.263675i
$172$		0			0
$173$	5.87165	+	3.39000i	0.446413	+	0.257737i	0.706314	−	0.707899i	$-0.250357\pi$
$173$	5.87165	+	3.39000i	0.446413	+	0.257737i	−0.259901	+	0.965635i	$0.583690\pi$
$174$		0			0
$175$	−10.7547	−	6.76539i	−0.812976	−	0.511415i
$176$		0			0
$177$	−9.99222	+	17.3070i	−0.751061	+	1.30088i
$178$		0			0
$179$	−2.43639	+	1.40665i	−0.182105	+	0.105138i	−0.588281	−	0.808656i	$-0.700195\pi$
$179$	−2.43639	+	1.40665i	−0.182105	+	0.105138i	0.406176	+	0.913795i	$0.366862\pi$
$180$		0			0
$181$	−11.2247			−0.834323			−0.417161	−	0.908832i	$-0.636975\pi$
$181$	−11.2247			−0.834323			−0.417161	+	0.908832i	$0.636975\pi$
$182$		0			0
$183$	18.1023			1.33816
$184$		0			0
$185$	0.232164	+	0.402121i	0.0170691	+	0.0295645i
$186$		0			0
$187$	−0.929305	−	7.09093i	−0.0679575	−	0.518540i
$188$		0			0
$189$	6.93073	+	13.1301i	0.504137	+	0.955073i
$190$		0			0
$191$	−6.40235	−	3.69640i	−0.463258	−	0.267462i	0.250155	−	0.968206i	$-0.419518\pi$
$191$	−6.40235	−	3.69640i	−0.463258	−	0.267462i	−0.713413	+	0.700744i	$0.752852\pi$
$192$		0			0
$193$	−17.8092	+	10.2822i	−1.28194	+	0.740126i	−0.977202	−	0.212311i	$-0.931901\pi$
$193$	−17.8092	+	10.2822i	−1.28194	+	0.740126i	−0.304734	+	0.952438i	$0.598568\pi$
$194$		0			0
$195$	2.48519			0.177968
$196$		0			0
$197$		−	1.46118i		−	0.104105i	−0.998644	−	0.0520524i	$-0.983424\pi$
$197$		−	1.46118i		−	0.104105i	0.998644	−	0.0520524i	$-0.0165763\pi$
$198$		0			0
$199$	−2.35358	+	1.35884i	−0.166841	+	0.0963258i	−0.581096	−	0.813835i	$-0.697376\pi$
$199$	−2.35358	+	1.35884i	−0.166841	+	0.0963258i	0.414254	+	0.910161i	$0.364042\pi$
$200$		0			0
$201$	1.32164	−	2.28915i	0.0932212	−	0.161464i
$202$		0			0
$203$	5.05500	+	9.57656i	0.354792	+	0.672143i
$204$		0			0
$205$	0.894962	+	0.516706i	0.0625068	+	0.0360883i
$206$		0			0
$207$	4.97886	−	2.87455i	0.346055	−	0.199795i
$208$		0			0
$209$	11.4572	+	14.9495i	0.792511	+	1.03408i
$210$		0			0
$211$	16.1309			1.11050			0.555248	−	0.831685i	$-0.312623\pi$
$211$	16.1309			1.11050			0.555248	+	0.831685i	$0.312623\pi$
$212$		0			0
$213$	−1.91893	−	3.32368i	−0.131483	−	0.227735i
$214$		0			0
$215$	2.55557	−	4.42638i	0.174288	−	0.301876i
$216$		0			0
$217$	−5.38643	+	8.56258i	−0.365655	+	0.581266i
$218$		0			0
$219$	−6.26480	+	10.8509i	−0.423336	+	0.733239i
$220$		0			0
$221$	3.97416	+	6.88345i	0.267331	+	0.463031i
$222$		0			0
$223$			3.69783i			0.247625i	0.992306	+	0.123812i	$0.0395121\pi$
$223$			3.69783i			0.247625i	−0.992306	+	0.123812i	$0.960488\pi$
$224$		0			0
$225$	−3.36679			−0.224453
$226$		0			0
$227$	10.4176	+	18.0438i	0.691439	+	1.19761i	0.971366	+	0.237586i	$0.0763563\pi$
$227$	10.4176	+	18.0438i	0.691439	+	1.19761i	−0.279927	+	0.960021i	$0.590310\pi$
$228$		0			0
$229$	−7.73473	+	13.3969i	−0.511125	+	0.885295i	0.488792	+	0.872401i	$0.337438\pi$
$229$	−7.73473	+	13.3969i	−0.511125	+	0.885295i	−0.999917	+	0.0128943i	$0.995896\pi$
$230$		0			0
$231$	−7.68708	−	10.8594i	−0.505773	−	0.714493i
$232$		0			0
$233$	5.43672	+	3.13889i	0.356172	+	0.205636i	0.667400	−	0.744699i	$-0.267407\pi$
$233$	5.43672	+	3.13889i	0.356172	+	0.205636i	−0.311229	+	0.950335i	$0.600740\pi$
$234$		0			0
$235$	−0.798615	+	0.461080i	−0.0520959	+	0.0300776i
$236$		0			0
$237$			6.59675i			0.428505i
$238$		0			0
$239$	3.14626			0.203515			0.101757	−	0.994809i	$-0.467553\pi$
$239$	3.14626			0.203515			0.101757	+	0.994809i	$0.467553\pi$
$240$		0			0
$241$	17.9004	−	10.3348i	1.15306	−	0.665722i	0.203432	−	0.979089i	$-0.434790\pi$
$241$	17.9004	−	10.3348i	1.15306	−	0.665722i	0.949632	+	0.313367i	$0.101457\pi$
$242$		0			0
$243$	6.16888	+	3.56161i	0.395734	+	0.228477i
$244$		0			0
$245$	1.34760	+	2.80576i	0.0860948	+	0.179254i
$246$		0			0
$247$	−18.1288	−	10.4667i	−1.15351	−	0.665978i
$248$		0			0
$249$	19.5494	−	11.2868i	1.23889	−	0.715274i
$250$		0			0
$251$			30.1273i			1.90162i	0.309779	+	0.950809i	$0.399745\pi$
$251$			30.1273i			1.90162i	−0.309779	+	0.950809i	$0.600255\pi$
$252$		0			0
$253$	−21.5868	+	16.5440i	−1.35715	+	1.04011i
$254$		0			0
$255$	−0.726880	−	1.25899i	−0.0455190	−	0.0788412i
$256$		0			0
$257$	−10.8381	+	18.7721i	−0.676062	+	1.17097i	0.300096	+	0.953909i	$0.402981\pi$
$257$	−10.8381	+	18.7721i	−0.676062	+	1.17097i	−0.976157	+	0.217064i	$0.930352\pi$
$258$		0			0
$259$	−0.104737	+	2.76081i	−0.00650806	+	0.171548i
$260$		0			0
$261$	2.48503	+	1.43474i	0.153820	+	0.0888079i
$262$		0			0
$263$	−3.84367	−	6.65744i	−0.237011	−	0.410515i	0.722844	−	0.691011i	$-0.242834\pi$
$263$	−3.84367	−	6.65744i	−0.237011	−	0.410515i	−0.959855	+	0.280496i	$0.909501\pi$
$264$		0			0
$265$	4.71360			0.289554
$266$		0			0
$267$			7.94936i			0.486493i
$268$		0			0
$269$	−7.02034	−	12.1596i	−0.428038	−	0.741383i	0.568661	−	0.822572i	$-0.307462\pi$
$269$	−7.02034	−	12.1596i	−0.428038	−	0.741383i	−0.996699	+	0.0811891i	$0.974128\pi$
$270$		0			0
$271$	−10.9634	+	18.9892i	−0.665982	+	1.15351i	0.313036	+	0.949741i	$0.398654\pi$
$271$	−10.9634	+	18.9892i	−0.665982	+	1.15351i	−0.979018	+	0.203773i	$0.934680\pi$
$272$		0			0
$273$	12.5165	+	7.87369i	0.757531	+	0.476537i
$274$		0			0
$275$	15.7923	−	2.06967i	0.952312	−	0.124806i
$276$		0			0
$277$	−26.9931	+	15.5844i	−1.62186	+	0.936379i	−0.635432	+	0.772157i	$0.719178\pi$
$277$	−26.9931	+	15.5844i	−1.62186	+	0.936379i	−0.986423	+	0.164222i	$0.947489\pi$
$278$		0			0
$279$			2.68055i			0.160481i
$280$		0			0
$281$		−	12.6275i		−	0.753293i	−0.926357	−	0.376646i	$-0.877077\pi$
$281$		−	12.6275i		−	0.753293i	0.926357	−	0.376646i	$-0.122923\pi$
$282$		0			0
$283$	11.5556	+	20.0149i	0.686910	+	1.18976i	0.972832	+	0.231510i	$0.0743667\pi$
$283$	11.5556	+	20.0149i	0.686910	+	1.18976i	−0.285922	+	0.958253i	$0.592300\pi$
$284$		0			0
$285$	3.31578	+	1.91437i	0.196410	+	0.113397i
$286$		0			0
$287$	2.87036	+	5.43782i	0.169432	+	0.320984i
$288$		0			0
$289$	−6.17523	+	10.6958i	−0.363249	+	0.629166i
$290$		0			0
$291$	−16.1224	+	9.30827i	−0.945112	+	0.545661i
$292$		0			0
$293$			10.4853i			0.612555i	0.951942	+	0.306278i	$0.0990836\pi$
$293$			10.4853i			0.612555i	−0.951942	+	0.306278i	$0.900916\pi$
$294$		0			0
$295$			5.86079i			0.341229i
$296$		0			0
$297$	−17.1908	−	7.13249i	−0.997512	−	0.413869i
$298$		0			0
$299$	15.1137	−	26.1777i	0.874049	−	1.51390i
$300$		0			0
$301$	26.8948	−	14.1965i	1.55019	−	0.818271i
$302$		0			0
$303$	12.5225	−	21.6897i	0.719401	−	1.24604i
$304$		0			0
$305$	4.59757	−	2.65441i	0.263256	−	0.151991i
$306$		0			0
$307$	8.97370			0.512156			0.256078	−	0.966656i	$-0.417570\pi$
$307$	8.97370			0.512156			0.256078	+	0.966656i	$0.417570\pi$
$308$		0			0
$309$	−1.77158			−0.100782
$310$		0			0
$311$	16.8641	−	9.73650i	0.956276	−	0.552106i	0.0612509	−	0.998122i	$-0.480491\pi$
$311$	16.8641	−	9.73650i	0.956276	−	0.552106i	0.895025	+	0.446016i	$0.147158\pi$
$312$		0			0
$313$	5.15640	−	8.93115i	0.291457	−	0.504818i	−0.682698	−	0.730701i	$-0.739193\pi$
$313$	5.15640	−	8.93115i	0.291457	−	0.504818i	0.974154	+	0.225883i	$0.0725267\pi$
$314$		0			0
$315$	0.698143	+	0.439178i	0.0393359	+	0.0247449i
$316$		0			0
$317$	−5.69923	+	9.87136i	−0.320101	+	0.554431i	−0.980509	−	0.196476i	$-0.937050\pi$
$317$	−5.69923	+	9.87136i	−0.320101	+	0.554431i	0.660408	+	0.750907i	$0.270383\pi$
$318$		0			0
$319$	−12.5383	−	5.20216i	−0.702010	−	0.291265i
$320$		0			0
$321$			26.0339i			1.45307i
$322$		0			0
$323$			12.2454i			0.681351i
$324$		0			0
$325$	−15.3302	+	8.85092i	−0.850369	+	0.490961i
$326$		0			0
$327$	−1.87902	+	3.25455i	−0.103910	+	0.179977i
$328$		0			0
$329$	−5.48299	−	0.208009i	−0.302287	−	0.0114679i
$330$		0			0
$331$	10.0115	+	5.78015i	0.550283	+	0.317706i	0.749236	−	0.662303i	$-0.230421\pi$
$331$	10.0115	+	5.78015i	0.550283	+	0.317706i	−0.198953	+	0.980009i	$0.563754\pi$
$332$		0			0
$333$	0.366048	+	0.634015i	0.0200593	+	0.0347438i
$334$		0			0
$335$		−	0.775188i		−	0.0423531i
$336$		0			0
$337$		−	30.3252i		−	1.65192i	−0.563731	−	0.825959i	$-0.690634\pi$
$337$		−	30.3252i		−	1.65192i	0.563731	−	0.825959i	$-0.309366\pi$
$338$		0			0
$339$	21.0986	−	12.1813i	1.14592	−	0.661597i
$340$		0			0
$341$	−1.64782	−	12.5734i	−0.0892343	−	0.680890i
$342$		0			0
$343$	−2.10227	+	18.4006i	−0.113512	+	0.993537i
$344$		0			0
$345$	−2.76432	+	4.78794i	−0.148826	+	0.257774i
$346$		0			0
$347$	−8.19003	−	14.1856i	−0.439664	−	0.761521i	0.557999	−	0.829841i	$-0.311569\pi$
$347$	−8.19003	−	14.1856i	−0.439664	−	0.761521i	−0.997663	+	0.0683209i	$0.978236\pi$
$348$		0			0
$349$		−	12.5196i		−	0.670160i	−0.942190	−	0.335080i	$-0.891237\pi$
$349$		−	12.5196i		−	0.670160i	0.942190	−	0.335080i	$-0.108763\pi$
$350$		0			0
$351$	20.6853			1.10410
$352$		0			0
$353$	−11.4965	−	19.9126i	−0.611899	−	1.05984i	−0.990920	−	0.134452i	$-0.957073\pi$
$353$	−11.4965	−	19.9126i	−0.611899	−	1.05984i	0.379021	−	0.925388i	$-0.376261\pi$
$354$		0			0
$355$	−0.974728	−	0.562759i	−0.0517332	−	0.0298682i
$356$		0			0
$357$	0.327920	−	8.64377i	0.0173554	−	0.457477i
$358$		0			0
$359$	−3.25828	+	5.64352i	−0.171966	+	0.297853i	−0.939107	−	0.343625i	$-0.888345\pi$
$359$	−3.25828	+	5.64352i	−0.171966	+	0.297853i	0.767141	+	0.641478i	$0.221678\pi$
$360$		0			0
$361$	−6.62518	−	11.4752i	−0.348694	−	0.603955i
$362$		0			0
$363$	16.1050	+	4.33559i	0.845294	+	0.227560i
$364$		0			0
$365$			3.67453i			0.192334i
$366$		0			0
$367$	−15.8110	+	9.12851i	−0.825330	+	0.476505i	−0.852251	−	0.523133i	$-0.824763\pi$
$367$	−15.8110	+	9.12851i	−0.825330	+	0.476505i	0.0269210	+	0.999638i	$0.491430\pi$
$368$		0			0
$369$	1.41107	+	0.814680i	0.0734572	+	0.0424105i
$370$		0			0
$371$	23.7397	+	14.9339i	1.23251	+	0.775327i
$372$		0			0
$373$	−21.1887	−	12.2333i	−1.09711	−	0.633416i	−0.161649	−	0.986848i	$-0.551681\pi$
$373$	−21.1887	−	12.2333i	−1.09711	−	0.633416i	−0.935460	+	0.353432i	$0.885015\pi$
$374$		0			0
$375$	5.72329	−	3.30434i	0.295549	−	0.170635i
$376$		0			0
$377$	15.0870			0.777021
$378$		0			0
$379$		−	17.9742i		−	0.923274i	−0.887069	−	0.461637i	$-0.847262\pi$
$379$		−	17.9742i		−	0.923274i	0.887069	−	0.461637i	$-0.152738\pi$
$380$		0			0
$381$	20.4107	−	11.7841i	1.04567	−	0.603720i
$382$		0			0
$383$	−10.9906	−	6.34544i	−0.561595	−	0.324237i	0.192191	−	0.981358i	$-0.438441\pi$
$383$	−10.9906	−	6.34544i	−0.561595	−	0.324237i	−0.753785	+	0.657121i	$0.771774\pi$
$384$		0			0
$385$	−3.54469	−	1.63084i	−0.180654	−	0.0831155i
$386$		0			0
$387$	4.02931	−	6.97897i	0.204821	−	0.354761i
$388$		0			0
$389$	−10.0005	−	17.3213i	−0.507043	−	0.878225i	−0.999967	−	0.00815194i	$-0.997405\pi$
$389$	−10.0005	−	17.3213i	−0.507043	−	0.878225i	0.492924	−	0.870073i	$-0.335928\pi$
$390$		0			0
$391$	−17.6821			−0.894225
$392$		0			0
$393$			2.50778i			0.126501i
$394$		0			0
$395$	0.967307	+	1.67543i	0.0486705	+	0.0842998i
$396$		0			0
$397$	−3.65096	+	6.32365i	−0.183237	+	0.317375i	−0.942981	−	0.332847i	$-0.891991\pi$
$397$	−3.65096	+	6.32365i	−0.183237	+	0.317375i	0.759744	+	0.650222i	$0.225324\pi$
$398$		0			0
$399$	10.6345	+	20.1468i	0.532392	+	1.00860i
$400$		0			0
$401$	−0.687115	+	1.19012i	−0.0343129	+	0.0594317i	−0.882672	−	0.469990i	$-0.844258\pi$
$401$	−0.687115	+	1.19012i	−0.0343129	+	0.0594317i	0.848359	+	0.529421i	$0.177591\pi$
$402$		0			0
$403$	7.04687	+	12.2055i	0.351030	+	0.608001i
$404$		0			0
$405$	−2.84814			−0.141525
$406$		0			0
$407$	−2.10674	−	2.74889i	−0.104427	−	0.136258i
$408$		0			0
$409$	17.3944	−	10.0426i	0.860095	−	0.496576i	−0.00394883	−	0.999992i	$-0.501257\pi$
$409$	17.3944	−	10.0426i	0.860095	−	0.496576i	0.864044	+	0.503416i	$0.167924\pi$
$410$		0			0
$411$	−20.7035	−	11.9532i	−1.02123	−	0.589606i
$412$		0			0
$413$	−18.5685	+	29.5175i	−0.913694	+	1.45246i
$414$		0			0
$415$	3.31006	−	5.73320i	0.162485	−	0.281432i
$416$		0			0
$417$	0.0842919	−	0.0486660i	0.00412779	−	0.00238318i
$418$		0			0
$419$		−	0.428111i		−	0.0209146i	−0.999945	−	0.0104573i	$-0.996671\pi$
$419$		−	0.428111i		−	0.0209146i	0.999945	−	0.0104573i	$-0.00332872\pi$
$420$		0			0
$421$	7.15342			0.348636			0.174318	−	0.984689i	$-0.444228\pi$
$421$	7.15342			0.348636			0.174318	+	0.984689i	$0.444228\pi$
$422$		0			0
$423$	−1.25916	+	0.726975i	−0.0612224	+	0.0353468i
$424$		0			0
$425$	8.96773	+	5.17752i	0.434999	+	0.251147i
$426$		0			0
$427$	31.5652	+	1.19749i	1.52755	+	0.0579508i
$428$		0			0
$429$	−18.3794	+	2.40872i	−0.887365	+	0.116294i
$430$		0			0
$431$	−2.54908	−	4.41514i	−0.122785	−	0.212670i	0.798080	−	0.602551i	$-0.205849\pi$
$431$	−2.54908	−	4.41514i	−0.122785	−	0.212670i	−0.920865	+	0.389882i	$0.872516\pi$
$432$		0			0
$433$	−0.544832			−0.0261830			−0.0130915	−	0.999914i	$-0.504167\pi$
$433$	−0.544832			−0.0261830			−0.0130915	+	0.999914i	$0.504167\pi$
$434$		0			0
$435$	−2.75944			−0.132305
$436$		0			0
$437$	40.3300	−	23.2845i	1.92925	−	1.11385i
$438$		0			0
$439$	1.06575	−	1.84593i	0.0508653	−	0.0881012i	−0.839472	−	0.543403i	$-0.817135\pi$
$439$	1.06575	−	1.84593i	0.0508653	−	0.0881012i	0.890337	+	0.455302i	$0.150469\pi$
$440$		0			0
$441$	2.12473	+	4.42378i	0.101177	+	0.210656i
$442$		0			0
$443$	−4.89496	−	2.82611i	−0.232567	−	0.134272i	0.379189	−	0.925319i	$-0.376203\pi$
$443$	−4.89496	−	2.82611i	−0.232567	−	0.134272i	−0.611756	+	0.791047i	$0.709536\pi$
$444$		0			0
$445$	1.16565	+	2.01896i	0.0552569	+	0.0957078i
$446$		0			0
$447$	12.4639			0.589525
$448$		0			0
$449$	−8.23955			−0.388848			−0.194424	−	0.980918i	$-0.562284\pi$
$449$	−8.23955			−0.388848			−0.194424	+	0.980918i	$0.562284\pi$
$450$		0			0
$451$	−7.11957	−	2.95392i	−0.335247	−	0.139095i
$452$		0			0
$453$	−27.7356	−	16.0131i	−1.30313	−	0.752363i
$454$		0			0
$455$	4.33345	+	0.164399i	0.203155	+	0.00770715i
$456$		0			0
$457$	−17.4987	−	10.1029i	−0.818554	−	0.472592i	0.0313638	−	0.999508i	$-0.490015\pi$
$457$	−17.4987	−	10.1029i	−0.818554	−	0.472592i	−0.849917	+	0.526916i	$0.823348\pi$
$458$		0			0
$459$	−6.05013	−	10.4791i	−0.282396	−	0.489124i
$460$		0			0
$461$			13.4160i			0.624848i	0.949943	+	0.312424i	$0.101141\pi$
$461$			13.4160i			0.624848i	−0.949943	+	0.312424i	$0.898859\pi$
$462$		0			0
$463$		−	31.6735i		−	1.47199i	−0.676986	−	0.735996i	$-0.736714\pi$
$463$		−	31.6735i		−	1.47199i	0.676986	−	0.735996i	$-0.263286\pi$
$464$		0			0
$465$	−1.28888	−	2.23241i	−0.0597705	−	0.103526i
$466$		0			0
$467$	−2.27799	−	1.31520i	−0.105413	−	0.0608602i	0.446367	−	0.894850i	$-0.352718\pi$
$467$	−2.27799	−	1.31520i	−0.105413	−	0.0608602i	−0.551780	+	0.833990i	$0.686051\pi$
$468$		0			0
$469$	2.45599	−	3.90418i	0.113407	−	0.180278i
$470$		0			0
$471$	23.2616	+	13.4301i	1.07184	+	0.618825i
$472$		0			0
$473$	−14.6097	+	35.2126i	−0.671756	+	1.61907i
$474$		0			0
$475$	−27.2719			−1.25132
$476$		0			0
$477$	7.43183			0.340280
$478$		0			0
$479$	−14.4995	−	25.1139i	−0.662500	−	1.14748i	−0.979957	−	0.199211i	$-0.936162\pi$
$479$	−14.4995	−	25.1139i	−0.662500	−	1.14748i	0.317457	−	0.948273i	$-0.397171\pi$
$480$		0			0
$481$	3.33350	+	1.92460i	0.151995	+	0.0877542i
$482$		0			0
$483$	−29.0917	+	15.3561i	−1.32372	+	0.698727i
$484$		0			0
$485$	−2.72982	+	4.72818i	−0.123955	+	0.214696i
$486$		0			0
$487$	−27.4060	+	15.8229i	−1.24189	+	0.717003i	−0.969478	−	0.245179i	$-0.921153\pi$
$487$	−27.4060	+	15.8229i	−1.24189	+	0.717003i	−0.272408	+	0.962182i	$0.587820\pi$
$488$		0			0
$489$	24.2866			1.09828
$490$		0			0
$491$	0.790237			0.0356629			0.0178314	−	0.999841i	$-0.494324\pi$
$491$	0.790237			0.0356629			0.0178314	+	0.999841i	$0.494324\pi$
$492$		0			0
$493$	−4.41273	−	7.64307i	−0.198739	−	0.344227i
$494$		0			0
$495$	−1.02516	+	0.134354i	−0.0460777	+	0.00603874i
$496$		0			0
$497$	−3.12619	−	5.92248i	−0.140229	−	0.265660i
$498$		0			0
$499$	−14.7657	−	8.52496i	−0.661002	−	0.381630i	0.131657	−	0.991295i	$-0.457970\pi$
$499$	−14.7657	−	8.52496i	−0.661002	−	0.381630i	−0.792659	+	0.609666i	$0.791304\pi$
$500$		0			0
$501$	−11.9157	+	6.87953i	−0.532354	+	0.307355i
$502$		0			0
$503$	−18.2695			−0.814597			−0.407299	−	0.913295i	$-0.633529\pi$
$503$	−18.2695			−0.814597			−0.407299	+	0.913295i	$0.633529\pi$
$504$		0			0
$505$		−	7.34491i		−	0.326844i
$506$		0			0
$507$	0.771531	−	0.445443i	0.0342649	−	0.0197828i
$508$		0			0
$509$	−0.836386	+	1.44866i	−0.0370722	+	0.0642109i	−0.883966	−	0.467551i	$-0.845136\pi$
$509$	−0.836386	+	1.44866i	−0.0370722	+	0.0642109i	0.846894	+	0.531762i	$0.178470\pi$
$510$		0			0
$511$	−11.6418	+	18.5065i	−0.515004	+	0.818680i
$512$		0			0
$513$	27.5987	+	15.9341i	1.21851	+	0.703508i
$514$		0			0
$515$	−0.449941	+	0.259773i	−0.0198268	+	0.0114470i
$516$		0			0
$517$	5.45933	−	4.18400i	0.240101	−	0.184012i
$518$		0			0
$519$	−10.2799			−0.451240
$520$		0			0
$521$	−12.4684	−	21.5958i	−0.546249	−	0.946131i	−0.998527	−	0.0542543i	$-0.982722\pi$
$521$	−12.4684	−	21.5958i	−0.546249	−	0.946131i	0.452278	−	0.891877i	$-0.350611\pi$
$522$		0			0
$523$	−12.0685	+	20.9033i	−0.527720	+	0.914038i	0.471758	+	0.881728i	$0.343620\pi$
$523$	−12.0685	+	20.9033i	−0.527720	+	0.914038i	−0.999478	+	0.0323095i	$0.989714\pi$
$524$		0			0
$525$	19.2507	+	0.730317i	0.840168	+	0.0318736i
$526$		0			0
$527$	4.12221	−	7.13988i	0.179566	−	0.311018i
$528$		0			0
$529$	22.1226	+	38.3174i	0.961851	+	1.66597i
$530$		0			0
$531$			9.24058i			0.401007i
$532$		0			0
$533$	8.56680			0.371069
$534$		0			0
$535$	3.81746	+	6.61203i	0.165043	+	0.285863i
$536$		0			0
$537$	2.13279	−	3.69410i	0.0920368	−	0.159412i
$538$		0			0
$539$	−12.6857	−	19.4441i	−0.546412	−	0.837517i
$540$		0			0
$541$	−19.9721	−	11.5309i	−0.858666	−	0.495751i	0.00489930	−	0.999988i	$-0.498440\pi$
$541$	−19.9721	−	11.5309i	−0.858666	−	0.495751i	−0.863565	+	0.504237i	$0.831774\pi$
$542$		0			0
$543$	14.7389	−	8.50952i	0.632507	−	0.365178i
$544$		0			0
$545$			1.10211i			0.0472092i
$546$		0			0
$547$	−1.71106			−0.0731596			−0.0365798	−	0.999331i	$-0.511646\pi$
$547$	−1.71106			−0.0731596			−0.0365798	+	0.999331i	$0.511646\pi$
$548$		0			0
$549$	7.24888	−	4.18514i	0.309375	−	0.178618i
$550$		0			0
$551$	20.1294	+	11.6217i	0.857541	+	0.495101i
$552$		0			0
$553$	−0.436386	+	11.5028i	−0.0185570	+	0.489150i
$554$		0			0
$555$	−0.609702	−	0.352012i	−0.0258804	−	0.0149421i
$556$		0			0
$557$	29.4941	−	17.0284i	1.24971	−	0.721518i	0.278655	−	0.960391i	$-0.410111\pi$
$557$	29.4941	−	17.0284i	1.24971	−	0.721518i	0.971051	+	0.238873i	$0.0767781\pi$
$558$		0			0
$559$		−	42.3704i		−	1.79208i
$560$		0			0
$561$	6.59595	+	8.60646i	0.278481	+	0.363365i
$562$		0			0
$563$	−3.72091	−	6.44480i	−0.156817	−	0.271616i	0.776902	−	0.629622i	$-0.216790\pi$
$563$	−3.72091	−	6.44480i	−0.156817	−	0.271616i	−0.933719	+	0.358006i	$0.883457\pi$
$564$		0			0
$565$	3.57238	−	6.18755i	0.150291	−	0.260312i
$566$		0			0
$567$	−14.3445	−	9.02361i	−0.602411	−	0.378956i
$568$		0			0
$569$	4.34931	+	2.51108i	0.182333	+	0.105270i	0.588388	−	0.808579i	$-0.299763\pi$
$569$	4.34931	+	2.51108i	0.182333	+	0.105270i	−0.406055	+	0.913848i	$0.633096\pi$
$570$		0			0
$571$	4.28733	+	7.42587i	0.179419	+	0.310763i	0.941682	−	0.336505i	$-0.109245\pi$
$571$	4.28733	+	7.42587i	0.179419	+	0.310763i	−0.762263	+	0.647268i	$0.775911\pi$
$572$		0			0
$573$	11.2091			0.468266
$574$		0			0
$575$		−	39.3802i		−	1.64227i
$576$		0			0
$577$	−6.36472	−	11.0240i	−0.264967	−	0.458936i	0.702588	−	0.711597i	$-0.252028\pi$
$577$	−6.36472	−	11.0240i	−0.264967	−	0.458936i	−0.967555	+	0.252661i	$0.918694\pi$
$578$		0			0
$579$	15.5900	−	27.0027i	0.647898	−	1.12219i
$580$		0			0
$581$	34.8351	−	18.3878i	1.44520	−	0.762853i
$582$		0			0
$583$	−34.8598	+	4.56857i	−1.44375	+	0.189211i
$584$		0			0
$585$	0.995169	−	0.574561i	0.0411452	−	0.0237552i
$586$		0			0
$587$		−	1.65362i		−	0.0682520i	−0.999418	−	0.0341260i	$-0.989135\pi$
$587$		−	1.65362i		−	0.0682520i	0.999418	−	0.0341260i	$-0.0108648\pi$
$588$		0			0
$589$			21.7132i			0.894675i
$590$		0			0
$591$	1.10773	+	1.91865i	0.0455661	+	0.0789228i
$592$		0			0
$593$	16.4070	+	9.47258i	0.673754	+	0.388992i	0.797498	−	0.603322i	$-0.206157\pi$
$593$	16.4070	+	9.47258i	0.673754	+	0.388992i	−0.123743	+	0.992314i	$0.539490\pi$
$594$		0			0
$595$	−1.18419	−	2.24341i	−0.0485469	−	0.0919707i
$596$		0			0
$597$	2.06030	−	3.56855i	0.0843225	−	0.146051i
$598$		0			0
$599$	29.9830	−	17.3107i	1.22507	−	0.707296i	0.259077	−	0.965857i	$-0.416582\pi$
$599$	29.9830	−	17.3107i	1.22507	−	0.707296i	0.965995	+	0.258561i	$0.0832483\pi$
$600$		0			0
$601$		−	41.5339i		−	1.69420i	−0.531431	−	0.847102i	$-0.678345\pi$
$601$		−	41.5339i		−	1.69420i	0.531431	−	0.847102i	$-0.321655\pi$
$602$		0			0
$603$		−	1.22222i		−	0.0497727i
$604$		0			0
$605$	4.72606	−	1.26040i	0.192142	−	0.0512425i
$606$		0			0
$607$	−13.7473	+	23.8111i	−0.557987	+	0.966462i	0.439677	+	0.898156i	$0.355093\pi$
$607$	−13.7473	+	23.8111i	−0.557987	+	0.966462i	−0.997664	+	0.0683062i	$0.978241\pi$
$608$		0			0
$609$	−13.8977	−	8.74258i	−0.563164	−	0.354267i
$610$		0			0
$611$	−3.82227	+	6.62037i	−0.154633	+	0.267831i
$612$		0			0
$613$	26.1804	−	15.1153i	1.05742	−	0.610500i	0.132701	−	0.991156i	$-0.457635\pi$
$613$	26.1804	−	15.1153i	1.05742	−	0.610500i	0.924717	+	0.380656i	$0.124302\pi$
$614$		0			0
$615$	−1.56688			−0.0631827
$616$		0			0
$617$	−4.81946			−0.194024			−0.0970122	−	0.995283i	$-0.530929\pi$
$617$	−4.81946			−0.194024			−0.0970122	+	0.995283i	$0.530929\pi$
$618$		0			0
$619$	7.44195	−	4.29661i	0.299117	−	0.172695i	−0.342929	−	0.939361i	$-0.611419\pi$
$619$	7.44195	−	4.29661i	0.299117	−	0.172695i	0.642046	+	0.766666i	$0.278086\pi$
$620$		0			0
$621$	−23.0086	+	39.8521i	−0.923305	+	1.59921i
$622$		0			0
$623$	−0.525863	+	13.8614i	−0.0210683	+	0.555345i
$624$		0			0
$625$	−11.0366	+	19.1160i	−0.441466	+	0.764641i
$626$		0			0
$627$	−26.3776	−	10.9441i	−1.05342	−	0.437065i
$628$		0			0
$629$		−	2.25167i		−	0.0897798i
$630$		0			0
$631$		−	23.1184i		−	0.920327i	−0.887834	−	0.460164i	$-0.847791\pi$
$631$		−	23.1184i		−	0.920327i	0.887834	−	0.460164i	$-0.152209\pi$
$632$		0			0
$633$	−21.1812	+	12.2290i	−0.841877	+	0.486058i
$634$		0			0
$635$	3.45591	−	5.98581i	0.137144	−	0.237540i
$636$		0			0
$637$	21.3043	+	14.5574i	0.844106	+	0.576786i
$638$		0			0
$639$	−1.53683	−	0.887290i	−0.0607961	−	0.0351007i
$640$		0			0
$641$	15.1069	+	26.1659i	0.596685	+	1.03349i	0.993307	+	0.115507i	$0.0368492\pi$
$641$	15.1069	+	26.1659i	0.596685	+	1.03349i	−0.396621	+	0.917982i	$0.629817\pi$
$642$		0			0
$643$			10.4763i			0.413145i	0.978431	+	0.206572i	$0.0662309\pi$
$643$			10.4763i			0.413145i	−0.978431	+	0.206572i	$0.933769\pi$
$644$		0			0
$645$			7.74960i			0.305140i
$646$		0			0
$647$	−26.7841	+	15.4638i	−1.05299	+	0.607944i	−0.923485	−	0.383634i	$-0.874672\pi$
$647$	−26.7841	+	15.4638i	−1.05299	+	0.607944i	−0.129506	+	0.991579i	$0.541339\pi$
$648$		0			0
$649$	−5.68047	−	43.3440i	−0.222978	−	1.70140i
$650$		0			0
$651$	0.581459	−	15.3269i	0.0227892	−	0.600708i
$652$		0			0
$653$	−12.7611	+	22.1029i	−0.499381	+	0.864954i	−1.00000		0.000714266i	$-0.999773\pi$
$653$	−12.7611	+	22.1029i	−0.499381	+	0.864954i	0.500618	+	0.865668i	$0.333106\pi$
$654$		0			0
$655$	0.367725	+	0.636918i	0.0143682	+	0.0248865i
$656$		0			0
$657$			5.79355i			0.226028i
$658$		0			0
$659$	−9.28212			−0.361580			−0.180790	−	0.983522i	$-0.557865\pi$
$659$	−9.28212			−0.361580			−0.180790	+	0.983522i	$0.557865\pi$
$660$		0			0
$661$	−12.8440	−	22.2465i	−0.499575	−	0.865289i	0.500425	−	0.865780i	$-0.333177\pi$
$661$	−12.8440	−	22.2465i	−0.499575	−	0.865289i	−1.00000		0.000491031i	$0.999844\pi$
$662$		0			0
$663$	−10.4368	−	6.02570i	−0.405332	−	0.234019i
$664$		0			0
$665$	5.65513	+	3.55745i	0.219297	+	0.137952i
$666$		0			0
$667$	−16.7816	+	29.0666i	−0.649786	+	1.12546i
$668$		0			0
$669$	−2.80336	−	4.85556i	−0.108384	−	0.187727i
$670$		0			0
$671$	−31.4289	+	24.0870i	−1.21330	+	0.929868i
$672$		0			0
$673$			14.9138i			0.574886i	0.957798	+	0.287443i	$0.0928053\pi$
$673$			14.9138i			0.574886i	−0.957798	+	0.287443i	$0.907195\pi$
$674$		0			0
$675$	23.3383	−	13.4744i	0.898290	−	0.518628i
$676$		0			0
$677$	−21.0008	−	12.1248i	−0.807127	−	0.465995i	0.0388304	−	0.999246i	$-0.487637\pi$
$677$	−21.0008	−	12.1248i	−0.807127	−	0.465995i	−0.845957	+	0.533251i	$0.820970\pi$
$678$		0			0
$679$	−28.7286	+	15.1644i	−1.10250	+	0.581957i
$680$		0			0
$681$	−27.3583	−	15.7953i	−1.04837	−	0.605278i
$682$		0			0
$683$	−4.76035	+	2.74839i	−0.182150	+	0.105164i	−0.588302	−	0.808641i	$-0.700203\pi$
$683$	−4.76035	+	2.74839i	−0.182150	+	0.105164i	0.406153	+	0.913805i	$0.366870\pi$
$684$		0			0
$685$	−7.01095			−0.267875
$686$		0			0
$687$		−	23.4551i		−	0.894867i
$688$		0			0
$689$	33.8398	−	19.5374i	1.28919	−	0.744317i
$690$		0			0
$691$	−41.7407	−	24.0990i	−1.58789	−	0.916770i	−0.993654	−	0.112481i	$-0.964120\pi$
$691$	−41.7407	−	24.0990i	−1.58789	−	0.916770i	−0.594238	−	0.804289i	$-0.702546\pi$
$692$		0			0
$693$	−5.58884	−	2.57131i	−0.212302	−	0.0976762i
$694$		0			0
$695$	0.0142722	−	0.0247201i	0.000541374	−	0.000937687i
$696$		0			0
$697$	−2.50566	−	4.33993i	−0.0949087	−	0.164387i
$698$		0			0
$699$	−9.51849			−0.360022
$700$		0			0
$701$		−	39.1877i		−	1.48010i	−0.672553	−	0.740049i	$-0.734802\pi$
$701$		−	39.1877i		−	1.48010i	0.672553	−	0.740049i	$-0.265198\pi$
$702$		0			0
$703$	2.96508	+	5.13567i	0.111830	+	0.193696i
$704$		0			0
$705$	0.699099	−	1.21087i	0.0263296	−	0.0456042i
$706$		0			0
$707$	23.2705	−	36.9922i	0.875178	−	1.39123i
$708$		0			0
$709$	−5.52544	+	9.57035i	−0.207512	+	0.359422i	−0.950930	−	0.309405i	$-0.899870\pi$
$709$	−5.52544	+	9.57035i	−0.207512	+	0.359422i	0.743418	+	0.668827i	$0.233203\pi$
$710$		0			0
$711$	1.52513	+	2.64161i	0.0571969	+	0.0990680i
$712$		0			0
$713$	−31.3535			−1.17420
$714$		0			0
$715$	−4.31475	+	3.30680i	−0.161362	+	0.123667i
$716$		0			0
$717$	−4.13130	+	2.38521i	−0.154286	+	0.0890772i
$718$		0			0
$719$	15.6902	+	9.05875i	0.585146	+	0.337834i	0.763176	−	0.646191i	$-0.223639\pi$
$719$	15.6902	+	9.05875i	0.585146	+	0.337834i	−0.178030	+	0.984025i	$0.556972\pi$
$720$		0			0
$721$	−3.08912	−	0.117193i	−0.115045	−	0.00436448i
$722$		0			0
$723$	−15.6698	+	27.1409i	−0.582766	+	1.00938i
$724$		0			0
$725$	17.0220	−	9.82766i	0.632181	−	0.364990i
$726$		0			0
$727$			33.5442i			1.24408i	0.782984	+	0.622042i	$0.213697\pi$
$727$			33.5442i			1.24408i	−0.782984	+	0.622042i	$0.786303\pi$
$728$		0			0
$729$	−30.0160			−1.11171
$730$		0			0
$731$	−21.4648	+	12.3927i	−0.793904	+	0.458361i
$732$		0			0
$733$	29.5991	+	17.0891i	1.09327	+	0.631199i	0.934445	−	0.356108i	$-0.115896\pi$
$733$	29.5991	+	17.0891i	1.09327	+	0.631199i	0.158824	+	0.987307i	$0.449230\pi$
$734$		0			0
$735$	−3.89658	−	2.66257i	−0.143728	−	0.0982105i
$736$		0			0
$737$	0.751337	+	5.73297i	0.0276759	+	0.211177i
$738$		0			0
$739$	−16.8587	−	29.2002i	−0.620159	−	1.07415i	−0.989456	−	0.144835i	$-0.953735\pi$
$739$	−16.8587	−	29.2002i	−0.620159	−	1.07415i	0.369297	−	0.929311i	$-0.379598\pi$
$740$		0			0
$741$	31.7395			1.16598
$742$		0			0
$743$	46.4286			1.70330			0.851650	−	0.524112i	$-0.175603\pi$
$743$	46.4286			1.70330			0.851650	+	0.524112i	$0.175603\pi$
$744$		0			0
$745$	3.16556	−	1.82764i	0.115977	−	0.0669595i
$746$		0			0
$747$	5.21890	−	9.03941i	0.190950	−	0.330735i
$748$		0			0
$749$	−1.72219	+	45.3957i	−0.0629273	+	1.65872i
$750$		0			0
$751$	−14.6089	−	8.43447i	−0.533088	−	0.307778i	0.209185	−	0.977876i	$-0.432919\pi$
$751$	−14.6089	−	8.43447i	−0.533088	−	0.307778i	−0.742273	+	0.670098i	$0.766252\pi$
$752$		0			0
$753$	−22.8398	−	39.5596i	−0.832327	−	1.44163i
$754$		0			0
$755$	−9.39228			−0.341820
$756$		0			0
$757$	42.2078			1.53407			0.767035	−	0.641605i	$-0.221731\pi$
$757$	42.2078			1.53407			0.767035	+	0.641605i	$0.221731\pi$
$758$		0			0
$759$	15.8031	−	38.0889i	0.573617	−	1.38254i
$760$		0			0
$761$	5.35266	+	3.09036i	0.194034	+	0.112026i	0.593870	−	0.804561i	$-0.297599\pi$
$761$	5.35266	+	3.09036i	0.194034	+	0.112026i	−0.399836	+	0.916587i	$0.630933\pi$
$762$		0			0
$763$	−3.49176	+	5.55071i	−0.126410	+	0.200949i
$764$		0			0
$765$	−0.582144	−	0.336101i	−0.0210475	−	0.0121518i
$766$		0			0
$767$	24.2924	+	42.0757i	0.877149	+	1.51927i
$768$		0			0
$769$			4.19742i			0.151363i	0.997132	+	0.0756815i	$0.0241132\pi$
$769$			4.19742i			0.151363i	−0.997132	+	0.0756815i	$0.975887\pi$
$770$		0			0
$771$		−	32.8658i		−	1.18363i
$772$		0			0
$773$	−2.20163	−	3.81334i	−0.0791873	−	0.137156i	0.823712	−	0.567008i	$-0.191899\pi$
$773$	−2.20163	−	3.81334i	−0.0791873	−	0.137156i	−0.902900	+	0.429852i	$0.858566\pi$
$774$		0			0
$775$	15.9013	+	9.18064i	0.571193	+	0.329778i
$776$		0			0
$777$	−1.95546	−	3.70457i	−0.0701519	−	0.132901i
$778$		0			0
$779$	11.4300	+	6.59910i	0.409522	+	0.236437i
$780$		0			0
$781$	7.75412	+	3.21719i	0.277464	+	0.115120i
$782$		0			0
$783$	−22.9680			−0.820809
$784$		0			0
$785$	7.87722			0.281150
$786$		0			0
$787$	−2.14558	−	3.71626i	−0.0764818	−	0.132470i	0.825248	−	0.564771i	$-0.191035\pi$
$787$	−2.14558	−	3.71626i	−0.0764818	−	0.132470i	−0.901730	+	0.432300i	$0.857702\pi$
$788$		0			0
$789$	10.0941	+	5.82785i	0.359360	+	0.207477i
$790$		0			0
$791$	37.5958	−	19.8450i	1.33675	−	0.705606i
$792$		0			0
$793$	22.0045	−	38.1130i	0.781404	−	1.35343i
$794$		0			0
$795$	−6.18935	+	3.57342i	−0.219514	+	0.126736i
$796$		0			0
$797$	34.2668			1.21379			0.606896	−	0.794781i	$-0.292415\pi$
$797$	34.2668			1.21379			0.606896	+	0.794781i	$0.292415\pi$
$798$		0			0
$799$	4.47183			0.158202
$800$		0			0
$801$	1.83785	+	3.18325i	0.0649372	+	0.112474i
$802$		0			0
$803$	−3.56147	−	27.1753i	−0.125681	−	0.958994i
$804$		0			0
$805$	−5.13691	+	8.16593i	−0.181052	+	0.287811i
$806$		0			0
$807$	18.4366	+	10.6444i	0.648998	+	0.374699i
$808$		0			0
$809$	−29.0755	+	16.7868i	−1.02224	+	0.590192i	−0.914753	−	0.404015i	$-0.867614\pi$
$809$	−29.0755	+	16.7868i	−1.02224	+	0.590192i	−0.107489	+	0.994206i	$0.534281\pi$
$810$		0			0
$811$	−9.00928			−0.316359			−0.158179	−	0.987410i	$-0.550562\pi$
$811$	−9.00928			−0.316359			−0.158179	+	0.987410i	$0.550562\pi$
$812$		0			0
$813$		−	33.2459i		−	1.16599i
$814$		0			0
$815$	6.16826	−	3.56124i	0.216065	−	0.124745i
$816$		0			0
$817$	32.6384	−	56.5314i	1.14187	−	1.97778i
$818$		0			0
$819$	6.83246	+	0.259204i	0.238745	+	0.00905733i
$820$		0			0
$821$	−42.5864	−	24.5873i	−1.48627	−	0.858101i	−0.486397	−	0.873738i	$-0.661689\pi$
$821$	−42.5864	−	24.5873i	−1.48627	−	0.858101i	−0.999878	+	0.0156370i	$0.995022\pi$
$822$		0			0
$823$	−4.73756	+	2.73523i	−0.165141	+	0.0953442i	−0.580293	−	0.814408i	$-0.697062\pi$
$823$	−4.73756	+	2.73523i	−0.165141	+	0.0953442i	0.415152	+	0.909752i	$0.363728\pi$
$824$		0			0
$825$	−19.1676	+	14.6899i	−0.667330	+	0.511438i
$826$		0			0
$827$	−28.4857			−0.990544			−0.495272	−	0.868738i	$-0.664932\pi$
$827$	−28.4857			−0.990544			−0.495272	+	0.868738i	$0.664932\pi$
$828$		0			0
$829$	13.5693	+	23.5027i	0.471281	+	0.816283i	0.999460	−	0.0328498i	$-0.0104583\pi$
$829$	13.5693	+	23.5027i	0.471281	+	0.816283i	−0.528179	+	0.849133i	$0.677125\pi$
$830$		0			0
$831$	23.6294	−	40.9274i	0.819695	−	1.41975i
$832$		0			0
$833$	1.14360	−	15.0506i	0.0396233	−	0.521471i
$834$		0			0
$835$	−2.01754	+	3.49449i	−0.0698200	+	0.120932i
$836$		0			0
$837$	−10.7279	−	18.5813i	−0.370812	−	0.642264i
$838$		0			0
$839$			7.95474i			0.274628i	0.990528	+	0.137314i	$0.0438469\pi$
$839$			7.95474i			0.274628i	−0.990528	+	0.137314i	$0.956153\pi$
$840$		0			0
$841$	12.2481			0.422347
$842$		0			0
$843$	9.57301	+	16.5809i	0.329712	+	0.571078i
$844$		0			0
$845$	0.130634	−	0.226265i	0.00449396	−	0.00778376i
$846$		0			0
$847$	27.7957	+	8.62540i	0.955072	+	0.296372i
$848$		0			0
$849$	−30.3470	−	17.5208i	−1.04151	−	0.601313i
$850$		0			0
$851$	−7.41584	+	4.28154i	−0.254212	+	0.146769i
$852$		0			0
$853$			27.6690i			0.947370i	0.880694	+	0.473685i	$0.157077\pi$
$853$			27.6690i			0.947370i	−0.880694	+	0.473685i	$0.842923\pi$
$854$		0			0
$855$	1.77036			0.0605452
$856$		0			0
$857$	−21.2087	+	12.2449i	−0.724477	+	0.418277i	−0.816398	−	0.577489i	$-0.804033\pi$
$857$	−21.2087	+	12.2449i	−0.724477	+	0.418277i	0.0919213	+	0.995766i	$0.470699\pi$
$858$		0			0
$859$	−25.3365	−	14.6280i	−0.864470	−	0.499102i	0.00103656	−	0.999999i	$-0.499670\pi$
$859$	−25.3365	−	14.6280i	−0.864470	−	0.499102i	−0.865507	+	0.500897i	$0.833003\pi$
$860$		0			0
$861$	−7.89148	−	4.96426i	−0.268941	−	0.169182i
$862$		0			0
$863$	2.89963	+	1.67410i	0.0987046	+	0.0569871i	0.548540	−	0.836124i	$-0.315184\pi$
$863$	2.89963	+	1.67410i	0.0987046	+	0.0569871i	−0.449835	+	0.893112i	$0.648517\pi$
$864$		0			0
$865$	−2.61087	+	1.50739i	−0.0887724	+	0.0512528i
$866$		0			0
$867$		−	18.7260i		−	0.635968i
$868$		0			0
$869$	−8.77767	−	11.4532i	−0.297762	−	0.388523i
$870$		0			0
$871$	−3.21308	−	5.56522i	−0.108871	−	0.188570i
$872$		0			0
$873$	−4.30404	+	7.45482i	−0.145670	+	0.252307i
$874$		0			0
$875$	10.1984	−	5.38322i	0.344767	−	0.181986i
$876$		0			0
$877$	22.9223	+	13.2342i	0.774031	+	0.446887i	0.834311	−	0.551295i	$-0.185866\pi$
$877$	22.9223	+	13.2342i	0.774031	+	0.446887i	−0.0602800	+	0.998182i	$0.519199\pi$
$878$		0			0
$879$	−7.94897	−	13.7680i	−0.268112	−	0.464384i
$880$		0			0
$881$	10.7302			0.361509			0.180754	−	0.983528i	$-0.442146\pi$
$881$	10.7302			0.361509			0.180754	+	0.983528i	$0.442146\pi$
$882$		0			0
$883$			38.7266i			1.30325i	0.758540	+	0.651626i	$0.225913\pi$
$883$			38.7266i			1.30325i	−0.758540	+	0.651626i	$0.774087\pi$
$884$		0			0
$885$	−4.44312	−	7.69571i	−0.149354	−	0.258689i
$886$		0			0
$887$	−8.35475	+	14.4709i	−0.280525	+	0.485884i	−0.971514	−	0.236982i	$-0.923842\pi$
$887$	−8.35475	+	14.4709i	−0.280525	+	0.485884i	0.690989	+	0.722865i	$0.257175\pi$
$888$		0			0
$889$	36.3700	−	19.1980i	1.21981	−	0.643879i
$890$		0			0
$891$	21.0636	−	2.76051i	0.705659	−	0.0924805i
$892$		0			0
$893$	−10.1995	+	5.88868i	−0.341313	+	0.197057i
$894$		0			0
$895$		−	1.25096i		−	0.0418149i
$896$		0			0
$897$			45.8314i			1.53027i
$898$		0			0
$899$	−7.82453	−	13.5525i	−0.260963	−	0.452001i
$900$		0			0
$901$	−19.7953	−	11.4288i	−0.659477	−	0.380749i
$902$		0			0
$903$	−24.5527	+	39.0303i	−0.817061	+	1.29885i
$904$		0			0
$905$	2.49557	−	4.32245i	0.0829555	−	0.143683i
$906$		0			0
$907$	40.3082	−	23.2719i	1.33841	−	0.772732i	0.351840	−	0.936060i	$-0.385556\pi$
$907$	40.3082	−	23.2719i	1.33841	−	0.772732i	0.986572	+	0.163328i	$0.0522229\pi$
$908$		0			0
$909$		−	11.5806i		−	0.384103i
$910$		0			0
$911$			45.8951i			1.52057i	0.649589	+	0.760286i	$0.274941\pi$
$911$			45.8951i			1.52057i	−0.649589	+	0.760286i	$0.725059\pi$
$912$		0			0
$913$	−18.9230	+	45.6085i	−0.626261	+	1.50942i
$914$		0			0
$915$	−4.02466	+	6.97092i	−0.133051	+	0.230451i
$916$		0			0
$917$	−0.165893	+	4.37284i	−0.00547828	+	0.144404i
$918$		0			0
$919$	19.2681	−	33.3733i	0.635596	−	1.10088i	−0.350793	−	0.936453i	$-0.614088\pi$
$919$	19.2681	−	33.3733i	0.635596	−	1.10088i	0.986389	−	0.164431i	$-0.0525789\pi$
$920$		0			0
$921$	−11.7832	+	6.80304i	−0.388270	+	0.224168i
$922$		0			0
$923$	−9.33034			−0.307112
$924$		0			0
$925$	5.01472			0.164883
$926$		0			0
$927$	−0.709411	+	0.409579i	−0.0233001	+	0.0134523i
$928$		0			0
$929$	−24.1911	+	41.9003i	−0.793686	+	1.37470i	0.129984	+	0.991516i	$0.458507\pi$
$929$	−24.1911	+	41.9003i	−0.793686	+	1.37470i	−0.923670	+	0.383188i	$0.874826\pi$
$930$		0			0
$931$	17.2108	+	35.8337i	0.564061	+	1.17440i
$932$		0			0
$933$	−14.7627	+	25.5697i	−0.483308	+	0.837113i
$934$		0			0
$935$	2.93722	+	1.21866i	0.0960574	+	0.0398544i
$936$		0			0
$937$		−	37.0707i		−	1.21105i	−0.795827	−	0.605523i	$-0.792964\pi$
$937$		−	37.0707i		−	1.21105i	0.795827	−	0.605523i	$-0.207036\pi$
$938$		0			0
$939$			15.6365i			0.510276i
$940$		0			0
$941$	17.4067	−	10.0498i	0.567443	−	0.327613i	−0.188684	−	0.982038i	$-0.560422\pi$
$941$	17.4067	−	10.0498i	0.567443	−	0.327613i	0.756127	+	0.654424i	$0.227089\pi$
$942$		0			0
$943$	−9.52902	+	16.5047i	−0.310307	+	0.537468i
$944$		0			0
$945$	−6.59710	−	0.250276i	−0.214604	−	0.00814147i
$946$		0			0
$947$	−8.52964	−	4.92459i	−0.277176	−	0.160028i	0.354968	−	0.934878i	$-0.384492\pi$
$947$	−8.52964	−	4.92459i	−0.277176	−	0.160028i	−0.632144	+	0.774851i	$0.717825\pi$
$948$		0			0
$949$	15.2306	+	26.3801i	0.494405	+	0.856335i
$950$		0			0
$951$		−	17.2826i		−	0.560425i
$952$		0			0
$953$		−	9.43881i		−	0.305753i	−0.988245	−	0.152877i	$-0.951146\pi$
$953$		−	9.43881i		−	0.305753i	0.988245	−	0.152877i	$-0.0488537\pi$
$954$		0			0
$955$	2.84686	−	1.64363i	0.0921221	−	0.0531867i
$956$		0			0
$957$	20.4076	−	2.67453i	0.659685	−	0.0864554i
$958$		0			0
$959$	−35.3102	−	22.2124i	−1.14023	−	0.717277i
$960$		0			0
$961$	−8.19061	+	14.1866i	−0.264213	+	0.457631i
$962$		0			0
$963$	6.01890	+	10.4250i	0.193956	+	0.335942i
$964$		0			0
$965$		−	9.14409i		−	0.294359i
$966$		0			0
$967$	34.2470			1.10131			0.550655	−	0.834733i	$-0.314378\pi$
$967$	34.2470			1.10131			0.550655	+	0.834733i	$0.314378\pi$
$968$		0			0
$969$	−9.28333	−	16.0792i	−0.298223	−	0.516538i
$970$		0			0
$971$	16.1644	+	9.33252i	0.518740	+	0.299495i	0.736419	−	0.676526i	$-0.236515\pi$
$971$	16.1644	+	9.33252i	0.518740	+	0.299495i	−0.217679	+	0.976020i	$0.569849\pi$
$972$		0			0
$973$	0.150200	−	0.0792834i	0.00481520	−	0.00254171i
$974$		0			0
$975$	13.4199	−	23.2440i	0.429781	−	0.744403i
$976$		0			0
$977$	−14.6425	−	25.3615i	−0.468455	−	0.811387i	0.530895	−	0.847437i	$-0.321856\pi$
$977$	−14.6425	−	25.3615i	−0.468455	−	0.811387i	−0.999350	+	0.0360501i	$0.988522\pi$
$978$		0			0
$979$	−10.5775	−	13.8016i	−0.338057	−	0.441100i
$980$		0			0
$981$			1.73767i			0.0554797i
$982$		0			0
$983$	−42.4161	+	24.4889i	−1.35286	+	0.781076i	−0.988650	−	0.150240i	$-0.951995\pi$
$983$	−42.4161	+	24.4889i	−1.35286	+	0.781076i	−0.364213	+	0.931315i	$0.618662\pi$
$984$		0			0
$985$	0.562679	+	0.324863i	0.0179285	+	0.0103510i
$986$		0			0
$987$	7.35731	−	3.88357i	0.234186	−	0.123615i
$988$		0			0
$989$	81.6305	+	47.1294i	2.59570	+	1.49863i
$990$		0			0
$991$	−16.5251	+	9.54080i	−0.524938	+	0.303073i	−0.738953	−	0.673757i	$-0.764679\pi$
$991$	−16.5251	+	9.54080i	−0.524938	+	0.303073i	0.214014	+	0.976831i	$0.431346\pi$
$992$		0			0
$993$	−17.5279			−0.556233
$994$		0			0
$995$		−	1.20844i		−	0.0383101i
$996$		0			0
$997$	20.9673	−	12.1055i	0.664042	−	0.383385i	−0.129774	−	0.991544i	$-0.541425\pi$
$997$	20.9673	−	12.1055i	0.664042	−	0.383385i	0.793815	+	0.608159i	$0.208092\pi$
$998$		0			0
$999$	−5.07482	−	2.92995i	−0.160560	−	0.0926995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.bi.a.527.5	✓	32
4.3	odd	2		1232.2.bi.b.527.12	yes	32
7.4	even	3		1232.2.bi.b.879.11	yes	32
11.10	odd	2	inner	1232.2.bi.a.527.6	yes	32
28.11	odd	6	inner	1232.2.bi.a.879.6	yes	32
44.43	even	2		1232.2.bi.b.527.11	yes	32
77.32	odd	6		1232.2.bi.b.879.12	yes	32
308.263	even	6	inner	1232.2.bi.a.879.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1232.2.bi.a.527.5	✓	32	1.1	even	1	trivial
1232.2.bi.a.527.6	yes	32	11.10	odd	2	inner
1232.2.bi.a.879.5	yes	32	308.263	even	6	inner
1232.2.bi.a.879.6	yes	32	28.11	odd	6	inner
1232.2.bi.b.527.11	yes	32	44.43	even	2
1232.2.bi.b.527.12	yes	32	4.3	odd	2
1232.2.bi.b.879.11	yes	32	7.4	even	3
1232.2.bi.b.879.12	yes	32	77.32	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31308 + 0.758109i) q^{3} +(-0.222329 + 0.385085i) q^{5} +(-2.33979 + 1.23506i) q^{7} +(-0.350541 + 0.607155i) q^{9} +O(q^{10})\)	\(q+(-1.31308 + 0.758109i) q^{3} +(-0.222329 + 0.385085i) q^{5} +(-2.33979 + 1.23506i) q^{7} +(-0.350541 + 0.607155i) q^{9} +(1.27102 - 3.06342i) q^{11} +3.68613i q^{13} -0.674199i q^{15} +(1.86739 - 1.07814i) q^{17} +(-2.83947 + 4.91811i) q^{19} +(2.13603 - 3.39556i) q^{21} +(-7.10168 - 4.10016i) q^{23} +(2.40114 + 4.15890i) q^{25} -5.61165i q^{27} -4.09291i q^{29} +(3.31121 - 1.91173i) q^{31} +(0.653455 + 4.98609i) q^{33} +(0.0445993 - 1.17561i) q^{35} +(0.522119 - 0.904337i) q^{37} +(-2.79449 - 4.84020i) q^{39} -2.32406i q^{41} -11.4945 q^{43} +(-0.155871 - 0.269977i) q^{45} +(1.79602 + 1.03693i) q^{47} +(3.94924 - 5.77957i) q^{49} +(-1.63469 + 2.83137i) q^{51} +(-5.30025 - 9.18031i) q^{53} +(0.897093 + 1.17054i) q^{55} -8.61051i q^{57} +(11.4146 - 6.59023i) q^{59} +(-10.3396 - 5.96955i) q^{61} +(0.0703188 - 1.85356i) q^{63} +(-1.41948 - 0.819534i) q^{65} +(-1.50977 + 0.871668i) q^{67} +12.4335 q^{69} +2.53120i q^{71} +(7.15659 - 4.13186i) q^{73} +(-6.30579 - 3.64065i) q^{75} +(0.809599 + 8.73754i) q^{77} +(2.17540 - 3.76790i) q^{79} +(3.20262 + 5.54710i) q^{81} -14.8881 q^{83} +0.958806i q^{85} +(3.10288 + 5.37434i) q^{87} +(2.62144 - 4.54047i) q^{89} +(-4.55260 - 8.62478i) q^{91} +(-2.89859 + 5.02051i) q^{93} +(-1.26259 - 2.18688i) q^{95} +12.2783 q^{97} +(1.41443 + 1.84556i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{5} + 12 q^{9}+O(q^{10}) \) 32 * q - 2 * q^5 + 12 * q^9	\( 32 q - 2 q^{5} + 12 q^{9} - 9 q^{11} - 18 q^{23} - 6 q^{25} + 5 q^{33} - 6 q^{37} - 10 q^{45} - 36 q^{47} - 32 q^{49} - 42 q^{59} - 18 q^{67} - 24 q^{69} - 78 q^{75} - 19 q^{77} - 24 q^{81} - 8 q^{89} - 18 q^{91} + 2 q^{93} + 12 q^{97}+O(q^{100}) \) 32 * q - 2 * q^5 + 12 * q^9 - 9 * q^11 - 18 * q^23 - 6 * q^25 + 5 * q^33 - 6 * q^37 - 10 * q^45 - 36 * q^47 - 32 * q^49 - 42 * q^59 - 18 * q^67 - 24 * q^69 - 78 * q^75 - 19 * q^77 - 24 * q^81 - 8 * q^89 - 18 * q^91 + 2 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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