LMFDB - Embedded newform 1232.2.bi.b.527.12

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			527.12
Character	$\chi$	$=$	1232.527
Dual form			1232.2.bi.b.879.12

$q$-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	−0.0705073	−	0.997511i	$-0.522462\pi$
$3$	1.31308	−	0.758109i	0.758109	−	0.437694i	0.828616	+	0.559817i	$0.189128\pi$
$4$		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	$-0.607507\pi$
$19$	2.83947	−	4.91811i	0.651419	−	1.12829i	0.982779	−	0.184787i	$-0.0591594\pi$
$20$		0			0
$21$	2.13603	−	3.39556i	0.466120	−	0.740971i
$22$		0			0
$23$	7.10168	+	4.10016i	1.48080	+	0.854942i	0.999763	−	0.0217573i	$-0.00692610\pi$
$23$	7.10168	+	4.10016i	1.48080	+	0.854942i	0.481039	+	0.876699i	$0.340259\pi$
$24$		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	−0.766958	−	0.641698i	$-0.778230\pi$
$31$	−3.31121	+	1.91173i	−0.594710	+	0.343356i	0.172248	+	0.985054i	$0.444897\pi$
$32$		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	$-0.159905\pi$
$43$	11.4945			1.75290			0.876450	+	0.481493i	$0.159905\pi$
$44$		0			0
$45$	−0.155871	−	0.269977i	−0.0232359	−	0.0402457i
$46$		0			0
$47$	−1.79602	−	1.03693i	−0.261976	−	0.151252i	0.363259	−	0.931688i	$-0.381664\pi$
$47$	−1.79602	−	1.03693i	−0.261976	−	0.151252i	−0.625236	+	0.780436i	$0.714997\pi$
$48$		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	−0.999874	−	0.0158836i	$-0.994944\pi$
$59$	−11.4146	+	6.59023i	−1.48606	+	0.857974i	−0.486181	+	0.873858i	$0.661611\pi$
$60$		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	−0.404933	−	0.914346i	$-0.632705\pi$
$67$	1.50977	−	0.871668i	0.184448	−	0.106491i	0.589381	+	0.807855i	$0.299372\pi$
$68$		0			0
$69$	12.4335			1.49681
$70$		0			0
$71$		−	2.53120i		−	0.300398i	−0.988656	−	0.150199i	$-0.952009\pi$
$71$		−	2.53120i		−	0.300398i	0.988656	−	0.150199i	$-0.0479915\pi$
$72$		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	−0.962062	−	0.272832i	$-0.912040\pi$
$79$	−2.17540	+	3.76790i	−0.244751	+	0.423921i	0.717310	+	0.696754i	$0.245373\pi$
$80$		0			0
$81$	3.20262	+	5.54710i	0.355846	+	0.616344i
$82$		0			0
$83$	14.8881			1.63418			0.817092	−	0.576507i	$-0.195585\pi$
$83$	14.8881			1.63418			0.817092	+	0.576507i	$0.195585\pi$
$84$		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	0.449319	−	0.893371i	$-0.351667\pi$
$103$	−1.01188	−	0.584209i	−0.0997035	−	0.0575638i	−0.549023	+	0.835807i	$0.685000\pi$
$104$		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	$0.478302\pi$
$107$	−8.58515	+	14.8699i	−0.829958	+	1.43753i	−0.898070	+	0.439852i	$0.855031\pi$
$108$		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	$-0.257760\pi$
$127$	15.5441			1.37932			0.689659	+	0.724134i	$0.257760\pi$
$128$		0			0
$129$	15.0933	−	8.71411i	1.32889	−	0.767235i
$130$		0			0
$131$	−0.826984	+	1.43238i	−0.0722539	+	0.125147i	−0.899889	−	0.436119i	$-0.856353\pi$
$131$	−0.826984	+	1.43238i	−0.0722539	+	0.125147i	0.827635	+	0.561267i	$0.189686\pi$
$132$		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	$-0.499133\pi$
$139$	0.0641939			0.00544485			0.00272243	+	0.999996i	$0.499133\pi$
$140$		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	$-0.837466\pi$
$151$	−10.5612	−	18.2926i	−0.859461	−	1.48863i	0.0129820	−	0.999916i	$-0.495868\pi$
$152$		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	0.932651	−	0.360780i	$-0.117489\pi$
$163$	13.8719	+	8.00895i	1.08653	+	0.627309i	0.153881	+	0.988089i	$0.450823\pi$
$164$		0			0
$165$	−2.06535	−	0.856917i	−0.160787	−	0.0667109i
$166$		0			0
$167$	−9.07459			−0.702213			−0.351106	−	0.936336i	$-0.614194\pi$
$167$	−9.07459			−0.702213			−0.351106	+	0.936336i	$0.614194\pi$
$168$		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	−0.406176	−	0.913795i	$-0.633138\pi$
$179$	2.43639	−	1.40665i	0.182105	−	0.105138i	0.588281	+	0.808656i	$0.299805\pi$
$180$		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	0.713413	−	0.700744i	$-0.247148\pi$
$191$	6.40235	+	3.69640i	0.463258	+	0.267462i	−0.250155	+	0.968206i	$0.580482\pi$
$192$		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	−0.414254	−	0.910161i	$-0.635958\pi$
$199$	2.35358	−	1.35884i	0.166841	−	0.0963258i	0.581096	+	0.813835i	$0.302624\pi$
$200$		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	$-0.687377\pi$
$211$	−16.1309			−1.11050			−0.555248	+	0.831685i	$0.687377\pi$
$212$		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	$-0.960488\pi$
$223$		−	3.69783i		−	0.247625i	0.992306	−	0.123812i	$-0.0395121\pi$
$224$		0			0
$225$	−3.36679			−0.224453
$226$		0			0
$227$	−10.4176	−	18.0438i	−0.691439	−	1.19761i	−0.971366	−	0.237586i	$-0.923644\pi$
$227$	−10.4176	−	18.0438i	−0.691439	−	1.19761i	0.279927	−	0.960021i	$-0.409690\pi$
$228$		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	$-0.532447\pi$
$239$	−3.14626			−0.203515			−0.101757	+	0.994809i	$0.532447\pi$
$240$		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	$-0.600255\pi$
$251$		−	30.1273i		−	1.90162i	0.309779	−	0.950809i	$-0.399745\pi$
$252$		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	0.959855	−	0.280496i	$-0.0904989\pi$
$263$	3.84367	+	6.65744i	0.237011	+	0.410515i	−0.722844	+	0.691011i	$0.757166\pi$
$264$		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	$-0.601346\pi$
$271$	10.9634	−	18.9892i	0.665982	−	1.15351i	0.979018	−	0.203773i	$-0.0653205\pi$
$272$		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	$-0.925633\pi$
$283$	−11.5556	−	20.0149i	−0.686910	−	1.18976i	0.285922	−	0.958253i	$-0.407700\pi$
$284$		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	$-0.582430\pi$
$307$	−8.97370			−0.512156			−0.256078	+	0.966656i	$0.582430\pi$
$308$		0			0
$309$	−1.77158			−0.100782
$310$		0			0
$311$	−16.8641	+	9.73650i	−0.956276	+	0.552106i	−0.895025	−	0.446016i	$-0.852842\pi$
$311$	−16.8641	+	9.73650i	−0.956276	+	0.552106i	−0.0612509	+	0.998122i	$0.519509\pi$
$312$		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	0.198953	−	0.980009i	$-0.436246\pi$
$331$	−10.0115	−	5.78015i	−0.550283	−	0.317706i	−0.749236	+	0.662303i	$0.769579\pi$
$332$		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	0.997663	−	0.0683209i	$-0.0217642\pi$
$347$	8.19003	+	14.1856i	0.439664	+	0.761521i	−0.557999	+	0.829841i	$0.688431\pi$
$348$		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	−0.767141	−	0.641478i	$-0.778322\pi$
$359$	3.25828	−	5.64352i	0.171966	−	0.297853i	0.939107	+	0.343625i	$0.111655\pi$
$360$		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	−0.0269210	−	0.999638i	$-0.508570\pi$
$367$	15.8110	−	9.12851i	0.825330	−	0.476505i	0.852251	+	0.523133i	$0.175237\pi$
$368$		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	$0.152738\pi$
$379$			17.9742i			0.923274i	−0.887069	+	0.461637i	$0.847262\pi$
$380$		0			0
$381$	20.4107	−	11.7841i	1.04567	−	0.603720i
$382$		0			0
$383$	10.9906	+	6.34544i	0.561595	+	0.324237i	0.753785	−	0.657121i	$-0.228226\pi$
$383$	10.9906	+	6.34544i	0.561595	+	0.324237i	−0.192191	+	0.981358i	$0.561559\pi$
$384$		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	$0.00332872\pi$
$419$			0.428111i			0.0209146i	−0.999945	+	0.0104573i	$0.996671\pi$
$420$		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	0.920865	−	0.389882i	$-0.127484\pi$
$431$	2.54908	+	4.41514i	0.122785	+	0.212670i	−0.798080	+	0.602551i	$0.794151\pi$
$432$		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	−0.890337	−	0.455302i	$-0.849531\pi$
$439$	−1.06575	+	1.84593i	−0.0508653	+	0.0881012i	0.839472	+	0.543403i	$0.182865\pi$
$440$		0			0
$441$	2.12473	+	4.42378i	0.101177	+	0.210656i
$442$		0			0
$443$	4.89496	+	2.82611i	0.232567	+	0.134272i	0.611756	−	0.791047i	$-0.290464\pi$
$443$	4.89496	+	2.82611i	0.232567	+	0.134272i	−0.379189	+	0.925319i	$0.623797\pi$
$444$		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	$0.263286\pi$
$463$			31.6735i			1.47199i	−0.676986	+	0.735996i	$0.736714\pi$
$464$		0			0
$465$	−1.28888	−	2.23241i	−0.0597705	−	0.103526i
$466$		0			0
$467$	2.27799	+	1.31520i	0.105413	+	0.0608602i	0.551780	−	0.833990i	$-0.313949\pi$
$467$	2.27799	+	1.31520i	0.105413	+	0.0608602i	−0.446367	+	0.894850i	$0.647282\pi$
$468$		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	$0.0638378\pi$
$479$	14.4995	+	25.1139i	0.662500	+	1.14748i	−0.317457	+	0.948273i	$0.602829\pi$
$480$		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	0.272408	−	0.962182i	$-0.412180\pi$
$487$	27.4060	−	15.8229i	1.24189	−	0.717003i	0.969478	+	0.245179i	$0.0788466\pi$
$488$		0			0
$489$	24.2866			1.09828
$490$		0			0
$491$	−0.790237			−0.0356629			−0.0178314	−	0.999841i	$-0.505676\pi$
$491$	−0.790237			−0.0356629			−0.0178314	+	0.999841i	$0.505676\pi$
$492$		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	0.792659	−	0.609666i	$-0.208696\pi$
$499$	14.7657	+	8.52496i	0.661002	+	0.381630i	−0.131657	+	0.991295i	$0.542030\pi$
$500$		0			0
$501$	−11.9157	+	6.87953i	−0.532354	+	0.307355i
$502$		0			0
$503$	18.2695			0.814597			0.407299	−	0.913295i	$-0.366471\pi$
$503$	18.2695			0.814597			0.407299	+	0.913295i	$0.366471\pi$
$504$		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	$-0.656380\pi$
$523$	12.0685	−	20.9033i	0.527720	−	0.914038i	0.999478	−	0.0323095i	$-0.0102862\pi$
$524$		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	$-0.488354\pi$
$547$	1.71106			0.0731596			0.0365798	+	0.999331i	$0.488354\pi$
$548$		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	0.933719	−	0.358006i	$-0.116543\pi$
$563$	3.72091	+	6.44480i	0.156817	+	0.271616i	−0.776902	+	0.629622i	$0.783210\pi$
$564$		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	0.762263	−	0.647268i	$-0.224089\pi$
$571$	−4.28733	−	7.42587i	−0.179419	−	0.310763i	−0.941682	+	0.336505i	$0.890755\pi$
$572$		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	$0.0108648\pi$
$587$			1.65362i			0.0682520i	−0.999418	+	0.0341260i	$0.989135\pi$
$588$		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	−0.965995	−	0.258561i	$-0.916752\pi$
$599$	−29.9830	+	17.3107i	−1.22507	+	0.707296i	−0.259077	+	0.965857i	$0.583418\pi$
$600$		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	$-0.644907\pi$
$607$	13.7473	−	23.8111i	0.557987	−	0.966462i	0.997664	−	0.0683062i	$-0.0217595\pi$
$608$		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	−0.642046	−	0.766666i	$-0.721914\pi$
$619$	−7.44195	+	4.29661i	−0.299117	+	0.172695i	0.342929	+	0.939361i	$0.388581\pi$
$620$		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	$0.152209\pi$
$631$			23.1184i			0.920327i	−0.887834	+	0.460164i	$0.847791\pi$
$632$		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	$-0.933769\pi$
$643$		−	10.4763i		−	0.413145i	0.978431	−	0.206572i	$-0.0662309\pi$
$644$		0			0
$645$			7.74960i			0.305140i
$646$		0			0
$647$	26.7841	−	15.4638i	1.05299	−	0.607944i	0.129506	−	0.991579i	$-0.458661\pi$
$647$	26.7841	−	15.4638i	1.05299	−	0.607944i	0.923485	+	0.383634i	$0.125328\pi$
$648$		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	$-0.442135\pi$
$659$	9.28212			0.361580			0.180790	+	0.983522i	$0.442135\pi$
$660$		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	−0.406153	−	0.913805i	$-0.633130\pi$
$683$	4.76035	−	2.74839i	0.182150	−	0.105164i	0.588302	+	0.808641i	$0.299797\pi$
$684$		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	$0.0358797\pi$
$691$	41.7407	+	24.0990i	1.58789	+	0.916770i	0.594238	+	0.804289i	$0.297454\pi$
$692$		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	0.178030	−	0.984025i	$-0.443028\pi$
$719$	−15.6902	−	9.05875i	−0.585146	−	0.337834i	−0.763176	+	0.646191i	$0.776361\pi$
$720$		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	$-0.786303\pi$
$727$		−	33.5442i		−	1.24408i	0.782984	−	0.622042i	$-0.213697\pi$
$728$		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	$0.0462651\pi$
$739$	16.8587	+	29.2002i	0.620159	+	1.07415i	−0.369297	+	0.929311i	$0.620402\pi$
$740$		0			0
$741$	31.7395			1.16598
$742$		0			0
$743$	−46.4286			−1.70330			−0.851650	−	0.524112i	$-0.824397\pi$
$743$	−46.4286			−1.70330			−0.851650	+	0.524112i	$0.824397\pi$
$744$		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	0.742273	−	0.670098i	$-0.233748\pi$
$751$	14.6089	+	8.43447i	0.533088	+	0.307778i	−0.209185	+	0.977876i	$0.567081\pi$
$752$		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	0.901730	−	0.432300i	$-0.142298\pi$
$787$	2.14558	+	3.71626i	0.0764818	+	0.132470i	−0.825248	+	0.564771i	$0.808965\pi$
$788$		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	$-0.449438\pi$
$811$	9.00928			0.316359			0.158179	+	0.987410i	$0.449438\pi$
$812$		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	−0.415152	−	0.909752i	$-0.636272\pi$
$823$	4.73756	−	2.73523i	0.165141	−	0.0953442i	0.580293	+	0.814408i	$0.302938\pi$
$824$		0			0
$825$	−19.1676	+	14.6899i	−0.667330	+	0.511438i
$826$		0			0
$827$	28.4857			0.990544			0.495272	−	0.868738i	$-0.335068\pi$
$827$	28.4857			0.990544			0.495272	+	0.868738i	$0.335068\pi$
$828$		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	$-0.956153\pi$
$839$		−	7.95474i		−	0.274628i	0.990528	−	0.137314i	$-0.0438469\pi$
$840$		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	0.865507	−	0.500897i	$-0.166997\pi$
$859$	25.3365	+	14.6280i	0.864470	+	0.499102i	−0.00103656	+	0.999999i	$0.500330\pi$
$860$		0			0
$861$	−7.89148	−	4.96426i	−0.268941	−	0.169182i
$862$		0			0
$863$	−2.89963	−	1.67410i	−0.0987046	−	0.0569871i	0.449835	−	0.893112i	$-0.351483\pi$
$863$	−2.89963	−	1.67410i	−0.0987046	−	0.0569871i	−0.548540	+	0.836124i	$0.684816\pi$
$864$		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	$-0.774087\pi$
$883$		−	38.7266i		−	1.30325i	0.758540	−	0.651626i	$-0.225913\pi$
$884$		0			0
$885$	−4.44312	−	7.69571i	−0.149354	−	0.258689i
$886$		0			0
$887$	8.35475	−	14.4709i	0.280525	−	0.485884i	−0.690989	−	0.722865i	$-0.742825\pi$
$887$	8.35475	−	14.4709i	0.280525	−	0.485884i	0.971514	+	0.236982i	$0.0761581\pi$
$888$		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	−0.986572	−	0.163328i	$-0.947777\pi$
$907$	−40.3082	+	23.2719i	−1.33841	+	0.772732i	−0.351840	+	0.936060i	$0.614444\pi$
$908$		0			0
$909$		−	11.5806i		−	0.384103i
$910$		0			0
$911$		−	45.8951i		−	1.52057i	−0.649589	−	0.760286i	$-0.725059\pi$
$911$		−	45.8951i		−	1.52057i	0.649589	−	0.760286i	$-0.274941\pi$
$912$		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	$0.385912\pi$
$919$	−19.2681	+	33.3733i	−0.635596	+	1.10088i	−0.986389	+	0.164431i	$0.947421\pi$
$920$		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	0.632144	−	0.774851i	$-0.282175\pi$
$947$	8.52964	+	4.92459i	0.277176	+	0.160028i	−0.354968	+	0.934878i	$0.615508\pi$
$948$		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	$-0.685622\pi$
$967$	−34.2470			−1.10131			−0.550655	+	0.834733i	$0.685622\pi$
$968$		0			0
$969$	−9.28333	−	16.0792i	−0.298223	−	0.516538i
$970$		0			0
$971$	−16.1644	−	9.33252i	−0.518740	−	0.299495i	0.217679	−	0.976020i	$-0.430151\pi$
$971$	−16.1644	−	9.33252i	−0.518740	−	0.299495i	−0.736419	+	0.676526i	$0.763485\pi$
$972$		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	0.364213	−	0.931315i	$-0.381338\pi$
$983$	42.4161	−	24.4889i	1.35286	−	0.781076i	0.988650	+	0.150240i	$0.0480045\pi$
$984$		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	−0.214014	−	0.976831i	$-0.568654\pi$
$991$	16.5251	−	9.54080i	0.524938	−	0.303073i	0.738953	+	0.673757i	$0.235321\pi$
$992$		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.b.527.12	yes	32
4.3	odd	2		1232.2.bi.a.527.5	✓	32
7.4	even	3		1232.2.bi.a.879.6	yes	32
11.10	odd	2	inner	1232.2.bi.b.527.11	yes	32
28.11	odd	6	inner	1232.2.bi.b.879.11	yes	32
44.43	even	2		1232.2.bi.a.527.6	yes	32
77.32	odd	6		1232.2.bi.a.879.5	yes	32
308.263	even	6	inner	1232.2.bi.b.879.12	yes	32

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

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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