LMFDB - Embedded newform 1323.2.h.h.802.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(226,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			802.6
Character	$\chi$	$=$	1323.802
Dual form			1323.2.h.h.226.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0683740 q^{2} -1.99532 q^{4} +(-1.33190 + 2.30691i) q^{5} +0.273176 q^{8} +O(q^{10})$	\(q-0.0683740 q^{2} -1.99532 q^{4} +(-1.33190 + 2.30691i) q^{5} +0.273176 q^{8} +(0.0910670 - 0.157733i) q^{10} +(-0.799563 - 1.38488i) q^{11} +(-2.62690 - 4.54992i) q^{13} +3.97197 q^{16} +(-3.27360 + 5.67005i) q^{17} +(-0.950968 - 1.64713i) q^{19} +(2.65756 - 4.60304i) q^{20} +(0.0546693 + 0.0946900i) q^{22} +(-1.53419 + 2.65729i) q^{23} +(-1.04789 - 1.81500i) q^{25} +(0.179612 + 0.311096i) q^{26} +(3.19452 - 5.53306i) q^{29} +6.71923 q^{31} -0.817932 q^{32} +(0.223829 - 0.387684i) q^{34} +(-2.11477 - 3.66290i) q^{37} +(0.0650215 + 0.112621i) q^{38} +(-0.363842 + 0.630193i) q^{40} +(3.69648 + 6.40249i) q^{41} +(5.63176 - 9.75450i) q^{43} +(1.59539 + 2.76329i) q^{44} +(0.104898 - 0.181689i) q^{46} -3.79918 q^{47} +(0.0716485 + 0.124099i) q^{50} +(5.24152 + 9.07858i) q^{52} +(4.44931 - 7.70643i) q^{53} +4.25974 q^{55} +(-0.218422 + 0.378317i) q^{58} +10.8928 q^{59} +2.71386 q^{61} -0.459420 q^{62} -7.88802 q^{64} +13.9950 q^{65} -3.32533 q^{67} +(6.53190 - 11.3136i) q^{68} +12.3890 q^{71} +(-1.09932 + 1.90407i) q^{73} +(0.144596 + 0.250447i) q^{74} +(1.89749 + 3.28655i) q^{76} +0.813556 q^{79} +(-5.29025 + 9.16298i) q^{80} +(-0.252743 - 0.437764i) q^{82} +(3.41842 - 5.92088i) q^{83} +(-8.72020 - 15.1038i) q^{85} +(-0.385066 + 0.666954i) q^{86} +(-0.218422 - 0.378317i) q^{88} +(0.235286 + 0.407527i) q^{89} +(3.06120 - 5.30216i) q^{92} +0.259765 q^{94} +5.06636 q^{95} +(2.57623 - 4.46216i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 20 q^{11} + 24 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} + 96 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} + 120 q^{65} + 24 q^{67} + 112 q^{71} - 68 q^{74} - 24 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} + 128 q^{95}+O(q^{100}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 20 * q^11 + 24 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 + 96 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 + 120 * q^65 + 24 * q^67 + 112 * q^71 - 68 * q^74 - 24 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 + 128 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.0683740			−0.0483477			−0.0241739	−	0.999708i	$-0.507696\pi$
$2$	−0.0683740			−0.0483477			−0.0241739	+	0.999708i	$0.507696\pi$
$3$		0			0
$3$		0			0
$4$	−1.99532			−0.997662
$5$	−1.33190	+	2.30691i	−0.595642	+	1.03168i	0.397814	+	0.917466i	$0.369769\pi$
$5$	−1.33190	+	2.30691i	−0.595642	+	1.03168i	−0.993456	+	0.114216i	$0.963564\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	0.273176			0.0965824
$9$		0			0
$10$	0.0910670	−	0.157733i	0.0287979	−	0.0498794i
$11$	−0.799563	−	1.38488i	−0.241077	−	0.417558i	0.719944	−	0.694032i	$-0.244167\pi$
$11$	−0.799563	−	1.38488i	−0.241077	−	0.417558i	−0.961021	+	0.276474i	$0.910834\pi$
$12$		0			0
$13$	−2.62690	−	4.54992i	−0.728571	−	1.26192i	−0.957487	−	0.288476i	$-0.906852\pi$
$13$	−2.62690	−	4.54992i	−0.728571	−	1.26192i	0.228916	−	0.973446i	$-0.426482\pi$
$14$		0			0
$15$		0			0
$16$	3.97197			0.992993
$17$	−3.27360	+	5.67005i	−0.793966	+	1.37519i	0.129528	+	0.991576i	$0.458654\pi$
$17$	−3.27360	+	5.67005i	−0.793966	+	1.37519i	−0.923494	+	0.383613i	$0.874680\pi$
$18$		0			0
$19$	−0.950968	−	1.64713i	−0.218167	−	0.377877i	0.736081	−	0.676894i	$-0.236674\pi$
$19$	−0.950968	−	1.64713i	−0.218167	−	0.377877i	−0.954248	+	0.299017i	$0.903341\pi$
$20$	2.65756	−	4.60304i	0.594249	−	1.02927i
$21$		0			0
$22$	0.0546693	+	0.0946900i	0.0116555	+	0.0201880i
$23$	−1.53419	+	2.65729i	−0.319900	+	0.554083i	−0.980467	−	0.196684i	$-0.936983\pi$
$23$	−1.53419	+	2.65729i	−0.319900	+	0.554083i	0.660567	+	0.750767i	$0.270316\pi$
$24$		0			0
$25$	−1.04789	−	1.81500i	−0.209578	−	0.363000i
$26$	0.179612	+	0.311096i	0.0352247	+	0.0610110i
$27$		0			0
$28$		0			0
$29$	3.19452	−	5.53306i	0.593207	−	1.02746i	−0.400591	−	0.916257i	$-0.631195\pi$
$29$	3.19452	−	5.53306i	0.593207	−	1.02746i	0.993797	−	0.111207i	$-0.0354716\pi$
$30$		0			0
$31$	6.71923			1.20681			0.603405	−	0.797435i	$-0.293810\pi$
$31$	6.71923			1.20681			0.603405	+	0.797435i	$0.293810\pi$
$32$	−0.817932			−0.144591
$33$		0			0
$34$	0.223829	−	0.387684i	0.0383864	−	0.0664872i
$35$		0			0
$36$		0			0
$37$	−2.11477	−	3.66290i	−0.347667	−	0.602176i	0.638168	−	0.769897i	$-0.279693\pi$
$37$	−2.11477	−	3.66290i	−0.347667	−	0.602176i	−0.985835	+	0.167721i	$0.946359\pi$
$38$	0.0650215	+	0.112621i	0.0105479	+	0.0182695i
$39$		0			0
$40$	−0.363842	+	0.630193i	−0.0575285	+	0.0996423i
$41$	3.69648	+	6.40249i	0.577293	+	0.999901i	0.995788	+	0.0916820i	$0.0292243\pi$
$41$	3.69648	+	6.40249i	0.577293	+	0.999901i	−0.418495	+	0.908219i	$0.637442\pi$
$42$		0			0
$43$	5.63176	−	9.75450i	0.858836	−	1.48755i	−0.0142043	−	0.999899i	$-0.504522\pi$
$43$	5.63176	−	9.75450i	0.858836	−	1.48755i	0.873040	−	0.487648i	$-0.162145\pi$
$44$	1.59539	+	2.76329i	0.240514	+	0.416582i
$45$		0			0
$46$	0.104898	−	0.181689i	0.0154664	−	0.0267887i
$47$	−3.79918			−0.554167			−0.277083	−	0.960846i	$-0.589368\pi$
$47$	−3.79918			−0.554167			−0.277083	+	0.960846i	$0.589368\pi$
$48$		0			0
$49$		0			0
$50$	0.0716485	+	0.124099i	0.0101326	+	0.0175502i
$51$		0			0
$52$	5.24152	+	9.07858i	0.726868	+	1.25897i
$53$	4.44931	−	7.70643i	0.611160	−	1.05856i	−0.379885	−	0.925034i	$-0.624037\pi$
$53$	4.44931	−	7.70643i	0.611160	−	1.05856i	0.991045	−	0.133527i	$-0.0426301\pi$
$54$		0			0
$55$	4.25974			0.574383
$56$		0			0
$57$		0			0
$58$	−0.218422	+	0.378317i	−0.0286802	+	0.0496755i
$59$	10.8928			1.41812			0.709060	−	0.705148i	$-0.249120\pi$
$59$	10.8928			1.41812			0.709060	+	0.705148i	$0.249120\pi$
$60$		0			0
$61$	2.71386			0.347475			0.173737	−	0.984792i	$-0.444416\pi$
$61$	2.71386			0.347475			0.173737	+	0.984792i	$0.444416\pi$
$62$	−0.459420			−0.0583465
$63$		0			0
$64$	−7.88802			−0.986002
$65$	13.9950			1.73587
$66$		0			0
$67$	−3.32533			−0.406254			−0.203127	−	0.979152i	$-0.565110\pi$
$67$	−3.32533			−0.406254			−0.203127	+	0.979152i	$0.565110\pi$
$68$	6.53190	−	11.3136i	0.792110	−	1.37197i
$69$		0			0
$70$		0			0
$71$	12.3890			1.47031			0.735154	−	0.677900i	$-0.237110\pi$
$71$	12.3890			1.47031			0.735154	+	0.677900i	$0.237110\pi$
$72$		0			0
$73$	−1.09932	+	1.90407i	−0.128665	+	0.222855i	−0.923160	−	0.384417i	$-0.874403\pi$
$73$	−1.09932	+	1.90407i	−0.128665	+	0.222855i	0.794494	+	0.607271i	$0.207736\pi$
$74$	0.144596	+	0.250447i	0.0168089	+	0.0291138i
$75$		0			0
$76$	1.89749	+	3.28655i	0.217657	+	0.376993i
$77$		0			0
$78$		0			0
$79$	0.813556			0.0915322			0.0457661	−	0.998952i	$-0.485427\pi$
$79$	0.813556			0.0915322			0.0457661	+	0.998952i	$0.485427\pi$
$80$	−5.29025	+	9.16298i	−0.591468	+	1.02445i
$81$		0			0
$82$	−0.252743	−	0.437764i	−0.0279108	−	0.0483429i
$83$	3.41842	−	5.92088i	0.375220	−	0.649901i	−0.615140	−	0.788418i	$-0.710900\pi$
$83$	3.41842	−	5.92088i	0.375220	−	0.649901i	0.990360	+	0.138517i	$0.0442337\pi$
$84$		0			0
$85$	−8.72020	−	15.1038i	−0.945838	−	1.63824i
$86$	−0.385066	+	0.666954i	−0.0415227	+	0.0719195i
$87$		0			0
$88$	−0.218422	−	0.378317i	−0.0232838	−	0.0403288i
$89$	0.235286	+	0.407527i	0.0249403	+	0.0431978i	0.878226	−	0.478246i	$-0.158727\pi$
$89$	0.235286	+	0.407527i	0.0249403	+	0.0431978i	−0.853286	+	0.521443i	$0.825394\pi$
$90$		0			0
$91$		0			0
$92$	3.06120	−	5.30216i	0.319152	−	0.552788i
$93$		0			0
$94$	0.259765			0.0267927
$95$	5.06636			0.519798
$96$		0			0
$97$	2.57623	−	4.46216i	0.261576	−	0.453064i	−0.705085	−	0.709123i	$-0.749091\pi$
$97$	2.57623	−	4.46216i	0.261576	−	0.453064i	0.966661	+	0.256059i	$0.0824243\pi$
$98$		0			0
$99$		0			0
$100$	2.09088	+	3.62152i	0.209088	+	0.362152i
$101$	−0.922440	−	1.59771i	−0.0917862	−	0.158978i	0.816477	−	0.577379i	$-0.195924\pi$
$101$	−0.922440	−	1.59771i	−0.0917862	−	0.158978i	−0.908263	+	0.418400i	$0.862591\pi$
$102$		0			0
$103$	−2.58901	+	4.48430i	−0.255103	+	0.441851i	−0.964923	−	0.262531i	$-0.915443\pi$
$103$	−2.58901	+	4.48430i	−0.255103	+	0.441851i	0.709821	+	0.704383i	$0.248776\pi$
$104$	−0.717607	−	1.24293i	−0.0703671	−	0.121879i
$105$		0			0
$106$	−0.304217	+	0.526920i	−0.0295482	+	0.0511790i
$107$	−8.47445	−	14.6782i	−0.819256	−	1.41899i	−0.906231	−	0.422782i	$-0.861054\pi$
$107$	−8.47445	−	14.6782i	−0.819256	−	1.41899i	0.0869755	−	0.996210i	$-0.472280\pi$
$108$		0			0
$109$	4.24996	−	7.36115i	0.407073	−	0.705070i	−0.587488	−	0.809233i	$-0.699883\pi$
$109$	4.24996	−	7.36115i	0.407073	−	0.705070i	0.994560	+	0.104163i	$0.0332163\pi$
$110$	−0.291255			−0.0277701
$111$		0			0
$112$		0			0
$113$	1.95196	+	3.38089i	0.183625	+	0.318048i	0.943112	−	0.332474i	$-0.107884\pi$
$113$	1.95196	+	3.38089i	0.183625	+	0.318048i	−0.759487	+	0.650522i	$0.774550\pi$
$114$		0			0
$115$	−4.08675	−	7.07847i	−0.381092	−	0.660070i
$116$	−6.37410	+	11.0403i	−0.591820	+	1.02506i
$117$		0			0
$118$	−0.744783			−0.0685628
$119$		0			0
$120$		0			0
$121$	4.22140	−	7.31167i	0.383763	−	0.664698i
$122$	−0.185558			−0.0167996
$123$		0			0
$124$	−13.4070			−1.20399
$125$	−7.73623			−0.691949
$126$		0			0
$127$	10.9533			0.971946			0.485973	−	0.873974i	$-0.338465\pi$
$127$	10.9533			0.971946			0.485973	+	0.873974i	$0.338465\pi$
$128$	2.17520			0.192262
$129$		0			0
$130$	−0.956896			−0.0839253
$131$	−2.22671	+	3.85678i	−0.194549	+	0.336968i	−0.946752	−	0.321962i	$-0.895658\pi$
$131$	−2.22671	+	3.85678i	−0.194549	+	0.336968i	0.752204	+	0.658931i	$0.228991\pi$
$132$		0			0
$133$		0			0
$134$	0.227366			0.0196414
$135$		0			0
$136$	−0.894271	+	1.54892i	−0.0766831	+	0.132819i
$137$	−9.76800	−	16.9187i	−0.834537	−	1.44546i	−0.894407	−	0.447254i	$-0.852402\pi$
$137$	−9.76800	−	16.9187i	−0.834537	−	1.44546i	0.0598699	−	0.998206i	$-0.480931\pi$
$138$		0			0
$139$	−1.31540	−	2.27833i	−0.111570	−	0.193246i	0.804833	−	0.593501i	$-0.202255\pi$
$139$	−1.31540	−	2.27833i	−0.111570	−	0.193246i	−0.916404	+	0.400256i	$0.868921\pi$
$140$		0			0
$141$		0			0
$142$	−0.847087			−0.0710860
$143$	−4.20075	+	7.27590i	−0.351284	+	0.608442i
$144$		0			0
$145$	8.50952	+	14.7389i	0.706677	+	1.22400i
$146$	0.0751647	−	0.130189i	0.00622067	−	0.0107745i
$147$		0			0
$148$	4.21966	+	7.30867i	0.346854	+	0.600769i
$149$	−4.40640	+	7.63212i	−0.360987	+	0.625247i	−0.988124	−	0.153662i	$-0.950893\pi$
$149$	−4.40640	+	7.63212i	−0.360987	+	0.625247i	0.627137	+	0.778909i	$0.284227\pi$
$150$		0			0
$151$	−2.33211	−	4.03933i	−0.189784	−	0.328716i	0.755394	−	0.655271i	$-0.227446\pi$
$151$	−2.33211	−	4.03933i	−0.189784	−	0.328716i	−0.945178	+	0.326555i	$0.894112\pi$
$152$	−0.259782	−	0.449956i	−0.0210711	−	0.0364962i
$153$		0			0
$154$		0			0
$155$	−8.94931	+	15.5007i	−0.718826	+	1.24504i
$156$		0			0
$157$	−4.07294			−0.325056			−0.162528	−	0.986704i	$-0.551965\pi$
$157$	−4.07294			−0.325056			−0.162528	+	0.986704i	$0.551965\pi$
$158$	−0.0556261			−0.00442537
$159$		0			0
$160$	1.08940	−	1.88690i	0.0861246	−	0.149172i
$161$		0			0
$162$		0			0
$163$	6.06112	+	10.4982i	0.474744	+	0.822280i	0.999582	−	0.0289220i	$-0.00920745\pi$
$163$	6.06112	+	10.4982i	0.474744	+	0.822280i	−0.524838	+	0.851202i	$0.675874\pi$
$164$	−7.37568	−	12.7750i	−0.575944	−	0.997564i
$165$		0			0
$166$	−0.233731	+	0.404834i	−0.0181410	+	0.0314212i
$167$	−2.39951	−	4.15608i	−0.185680	−	0.321607i	0.758126	−	0.652109i	$-0.226115\pi$
$167$	−2.39951	−	4.15608i	−0.185680	−	0.321607i	−0.943805	+	0.330502i	$0.892782\pi$
$168$		0			0
$169$	−7.30121	+	12.6461i	−0.561631	+	0.972774i
$170$	0.596235	+	1.03271i	0.0457291	+	0.0792051i
$171$		0			0
$172$	−11.2372	+	19.4634i	−0.856828	+	1.48407i
$173$	−5.03171			−0.382554			−0.191277	−	0.981536i	$-0.561263\pi$
$173$	−5.03171			−0.382554			−0.191277	+	0.981536i	$0.561263\pi$
$174$		0			0
$175$		0			0
$176$	−3.17584	−	5.50072i	−0.239388	−	0.414632i
$177$		0			0
$178$	−0.0160874	−	0.0278642i	−0.00120580	−	0.00208851i
$179$	−8.19896	+	14.2010i	−0.612819	+	1.06143i	0.377944	+	0.925828i	$0.376631\pi$
$179$	−8.19896	+	14.2010i	−0.612819	+	1.06143i	−0.990763	+	0.135605i	$0.956702\pi$
$180$		0			0
$181$	−14.4345			−1.07291			−0.536454	−	0.843930i	$-0.680237\pi$
$181$	−14.4345			−1.07291			−0.536454	+	0.843930i	$0.680237\pi$
$182$		0			0
$183$		0			0
$184$	−0.419103	+	0.725908i	−0.0308967	+	0.0535147i
$185$	11.2666			0.828339
$186$		0			0
$187$	10.4698			0.765629
$188$	7.58059			0.552871
$189$		0			0
$190$	−0.346407			−0.0251310
$191$	−2.84131			−0.205590			−0.102795	−	0.994703i	$-0.532779\pi$
$191$	−2.84131			−0.205590			−0.102795	+	0.994703i	$0.532779\pi$
$192$		0			0
$193$	8.82886			0.635515			0.317758	−	0.948172i	$-0.397070\pi$
$193$	8.82886			0.635515			0.317758	+	0.948172i	$0.397070\pi$
$194$	−0.176147	+	0.305096i	−0.0126466	+	0.0219046i
$195$		0			0
$196$		0			0
$197$	−5.72354			−0.407785			−0.203893	−	0.978993i	$-0.565359\pi$
$197$	−5.72354			−0.407785			−0.203893	+	0.978993i	$0.565359\pi$
$198$		0			0
$199$	5.70752	−	9.88572i	0.404596	−	0.700780i	−0.589679	−	0.807638i	$-0.700746\pi$
$199$	5.70752	−	9.88572i	0.404596	−	0.700780i	0.994274	+	0.106858i	$0.0340789\pi$
$200$	−0.286259	−	0.495815i	−0.0202416	−	0.0350594i
$201$		0			0
$202$	0.0630709	+	0.109242i	0.00443765	+	0.00768624i
$203$		0			0
$204$		0			0
$205$	−19.6933			−1.37544
$206$	0.177021	−	0.306609i	0.0123336	−	0.0213625i
$207$		0			0
$208$	−10.4340	−	18.0722i	−0.723466	−	1.25308i
$209$	−1.52072	+	2.63396i	−0.105190	+	0.182195i
$210$		0			0
$211$	10.6919	+	18.5189i	0.736059	+	1.27489i	0.954257	+	0.298986i	$0.0966486\pi$
$211$	10.6919	+	18.5189i	0.736059	+	1.27489i	−0.218199	+	0.975904i	$0.570018\pi$
$212$	−8.87782	+	15.3768i	−0.609731	+	1.05609i
$213$		0			0
$214$	0.579432	+	1.00361i	0.0396091	+	0.0686050i
$215$	15.0018	+	25.9840i	1.02312	+	1.77209i
$216$		0			0
$217$		0			0
$218$	−0.290587	+	0.503311i	−0.0196810	+	0.0340885i
$219$		0			0
$220$	−8.49956			−0.573041
$221$	34.3977			2.31384
$222$		0			0
$223$	−3.58387	+	6.20744i	−0.239994	+	0.415681i	−0.960712	−	0.277547i	$-0.910479\pi$
$223$	−3.58387	+	6.20744i	−0.239994	+	0.415681i	0.720719	+	0.693228i	$0.243812\pi$
$224$		0			0
$225$		0			0
$226$	−0.133463	−	0.231165i	−0.00887784	−	0.0153769i
$227$	−6.89434	−	11.9413i	−0.457593	−	0.792575i	0.541240	−	0.840868i	$-0.317955\pi$
$227$	−6.89434	−	11.9413i	−0.457593	−	0.792575i	−0.998833	+	0.0482933i	$0.984622\pi$
$228$		0			0
$229$	13.1972	−	22.8581i	0.872092	−	1.51051i	0.0122645	−	0.999925i	$-0.496096\pi$
$229$	13.1972	−	22.8581i	0.872092	−	1.51051i	0.859828	−	0.510584i	$-0.170571\pi$
$230$	0.279428	+	0.483983i	0.0184249	+	0.0319129i
$231$		0			0
$232$	0.872666	−	1.51150i	0.0572933	−	0.0992349i
$233$	−6.32230	−	10.9505i	−0.414187	−	0.717394i	0.581155	−	0.813793i	$-0.302601\pi$
$233$	−6.32230	−	10.9505i	−0.414187	−	0.717394i	−0.995343	+	0.0963989i	$0.969268\pi$
$234$		0			0
$235$	5.06010	−	8.76436i	0.330085	−	0.571724i
$236$	−21.7346			−1.41481
$237$		0			0
$238$		0			0
$239$	−7.71640	−	13.3652i	−0.499133	−	0.864523i	0.500867	−	0.865524i	$-0.333015\pi$
$239$	−7.71640	−	13.3652i	−0.499133	−	0.864523i	−0.999999	+	0.00100121i	$0.999681\pi$
$240$		0			0
$241$	−0.589942	−	1.02181i	−0.0380015	−	0.0658205i	0.846399	−	0.532549i	$-0.178766\pi$
$241$	−0.589942	−	1.02181i	−0.0380015	−	0.0658205i	−0.884401	+	0.466729i	$0.845432\pi$
$242$	−0.288634	+	0.499928i	−0.0185541	+	0.0321366i
$243$		0			0
$244$	−5.41504			−0.346662
$245$		0			0
$246$		0			0
$247$	−4.99620	+	8.65367i	−0.317900	+	0.550620i
$248$	1.83553			0.116557
$249$		0			0
$250$	0.528957			0.0334542
$251$	−5.54970			−0.350294			−0.175147	−	0.984542i	$-0.556040\pi$
$251$	−5.54970			−0.350294			−0.175147	+	0.984542i	$0.556040\pi$
$252$		0			0
$253$	4.90672			0.308483
$254$	−0.748919			−0.0469913
$255$		0			0
$256$	15.6273			0.976707
$257$	4.91538	−	8.51369i	0.306613	−	0.531069i	−0.671006	−	0.741452i	$-0.734138\pi$
$257$	4.91538	−	8.51369i	0.306613	−	0.531069i	0.977619	+	0.210382i	$0.0674709\pi$
$258$		0			0
$259$		0			0
$260$	−27.9246			−1.73181
$261$		0			0
$262$	0.152249	−	0.263703i	0.00940598	−	0.0162916i
$263$	5.96612	+	10.3336i	0.367887	+	0.637199i	0.989235	−	0.146336i	$-0.0467480\pi$
$263$	5.96612	+	10.3336i	0.367887	+	0.637199i	−0.621348	+	0.783535i	$0.713415\pi$
$264$		0			0
$265$	11.8520	+	20.5283i	0.728065	+	1.26105i
$266$		0			0
$267$		0			0
$268$	6.63512			0.405304
$269$	14.9824	−	25.9503i	0.913494	−	1.58222i	0.104401	−	0.994535i	$-0.466707\pi$
$269$	14.9824	−	25.9503i	0.913494	−	1.58222i	0.809092	−	0.587682i	$-0.199959\pi$
$270$		0			0
$271$	3.54825	+	6.14575i	0.215541	+	0.373328i	0.953440	−	0.301584i	$-0.0975152\pi$
$271$	3.54825	+	6.14575i	0.215541	+	0.373328i	−0.737899	+	0.674911i	$0.764182\pi$
$272$	−13.0027	+	22.5213i	−0.788402	+	1.36555i
$273$		0			0
$274$	0.667877	+	1.15680i	0.0403479	+	0.0698847i
$275$	−1.67571	+	2.90242i	−0.101049	+	0.175022i
$276$		0			0
$277$	4.91175	+	8.50741i	0.295119	+	0.511161i	0.975013	−	0.222150i	$-0.0713075\pi$
$277$	4.91175	+	8.50741i	0.295119	+	0.511161i	−0.679894	+	0.733311i	$0.737974\pi$
$278$	0.0899388	+	0.155779i	0.00539417	+	0.00934298i
$279$		0			0
$280$		0			0
$281$	−11.9389	+	20.6787i	−0.712213	+	1.23359i	0.251812	+	0.967776i	$0.418974\pi$
$281$	−11.9389	+	20.6787i	−0.712213	+	1.23359i	−0.964025	+	0.265813i	$0.914360\pi$
$282$		0			0
$283$	−3.01595			−0.179280			−0.0896399	−	0.995974i	$-0.528572\pi$
$283$	−3.01595			−0.179280			−0.0896399	+	0.995974i	$0.528572\pi$
$284$	−24.7201			−1.46687
$285$		0			0
$286$	0.287222	−	0.497483i	0.0169838	−	0.0294168i
$287$		0			0
$288$		0			0
$289$	−12.9330	−	22.4006i	−0.760763	−	1.31768i
$290$	−0.581830	−	1.00776i	−0.0341662	−	0.0591776i
$291$		0			0
$292$	2.19350	−	3.79925i	0.128365	−	0.222334i
$293$	8.52913	+	14.7729i	0.498277	+	0.863041i	0.999998	−	0.00198814i	$-0.000632845\pi$
$293$	8.52913	+	14.7729i	0.498277	+	0.863041i	−0.501721	+	0.865030i	$0.667300\pi$
$294$		0			0
$295$	−14.5081	+	25.1287i	−0.844692	+	1.46305i
$296$	−0.577706	−	1.00062i	−0.0335785	−	0.0581596i
$297$		0			0
$298$	0.301283	−	0.521838i	0.0174529	−	0.0302293i
$299$	16.1206			0.932280
$300$		0			0
$301$		0			0
$302$	0.159456	+	0.276185i	0.00917564	+	0.0158927i
$303$		0			0
$304$	−3.77722	−	6.54234i	−0.216638	−	0.375229i
$305$	−3.61458	+	6.26064i	−0.206970	+	0.358483i
$306$		0			0
$307$	23.2178			1.32511			0.662554	−	0.749014i	$-0.269473\pi$
$307$	23.2178			1.32511			0.662554	+	0.749014i	$0.269473\pi$
$308$		0			0
$309$		0			0
$310$	0.611900	−	1.05984i	0.0347536	−	0.0601950i
$311$	−1.79093			−0.101555			−0.0507773	−	0.998710i	$-0.516170\pi$
$311$	−1.79093			−0.101555			−0.0507773	+	0.998710i	$0.516170\pi$
$312$		0			0
$313$	4.60917			0.260526			0.130263	−	0.991480i	$-0.458418\pi$
$313$	4.60917			0.260526			0.130263	+	0.991480i	$0.458418\pi$
$314$	0.278483			0.0157157
$315$		0			0
$316$	−1.62331			−0.0913183
$317$	25.8841			1.45380			0.726898	−	0.686745i	$-0.240961\pi$
$317$	25.8841			1.45380			0.726898	+	0.686745i	$0.240961\pi$
$318$		0			0
$319$	−10.2169			−0.572035
$320$	10.5060	−	18.1970i	0.587304	−	1.01724i
$321$		0			0
$322$		0			0
$323$	12.4524			0.692869
$324$		0			0
$325$	−5.50541	+	9.53566i	−0.305385	+	0.528943i
$326$	−0.414423	−	0.717802i	−0.0229528	−	0.0397554i
$327$		0			0
$328$	1.00979	+	1.74901i	0.0557563	+	0.0965728i
$329$		0			0
$330$		0			0
$331$	0.161323			0.00886714			0.00443357	−	0.999990i	$-0.498589\pi$
$331$	0.161323			0.00886714			0.00443357	+	0.999990i	$0.498589\pi$
$332$	−6.82086	+	11.8141i	−0.374343	+	0.648382i
$333$		0			0
$334$	0.164064	+	0.284168i	0.00897719	+	0.0155490i
$335$	4.42899	−	7.67124i	0.241982	−	0.419125i
$336$		0			0
$337$	4.52675	+	7.84057i	0.246588	+	0.427103i	0.962577	−	0.271009i	$-0.0873572\pi$
$337$	4.52675	+	7.84057i	0.246588	+	0.427103i	−0.715989	+	0.698112i	$0.754024\pi$
$338$	0.499213	−	0.864662i	0.0271536	−	0.0470314i
$339$		0			0
$340$	17.3996	+	30.1370i	0.943627	+	1.63441i
$341$	−5.37245	−	9.30535i	−0.290934	−	0.503913i
$342$		0			0
$343$		0			0
$344$	1.53846	−	2.66470i	0.0829484	−	0.143671i
$345$		0			0
$346$	0.344038			0.0184956
$347$	5.81968			0.312417			0.156208	−	0.987724i	$-0.450073\pi$
$347$	5.81968			0.312417			0.156208	+	0.987724i	$0.450073\pi$
$348$		0			0
$349$	−13.6310	+	23.6095i	−0.729648	+	1.26379i	0.227384	+	0.973805i	$0.426983\pi$
$349$	−13.6310	+	23.6095i	−0.729648	+	1.26379i	−0.957032	+	0.289983i	$0.906350\pi$
$350$		0			0
$351$		0			0
$352$	0.653988	+	1.13274i	0.0348577	+	0.0603753i
$353$	−12.0948	−	20.9488i	−0.643741	−	1.11499i	−0.984591	−	0.174874i	$-0.944048\pi$
$353$	−12.0948	−	20.9488i	−0.643741	−	1.11499i	0.340850	−	0.940118i	$-0.389285\pi$
$354$		0			0
$355$	−16.5009	+	28.5804i	−0.875777	+	1.51689i
$356$	−0.469472	−	0.813149i	−0.0248820	−	0.0430968i
$357$		0			0
$358$	0.560595	−	0.970979i	0.0296284	−	0.0513179i
$359$	−10.5188	−	18.2191i	−0.555161	−	0.961567i	−0.997891	−	0.0649124i	$-0.979323\pi$
$359$	−10.5188	−	18.2191i	−0.555161	−	0.961567i	0.442730	−	0.896655i	$-0.354010\pi$
$360$		0			0
$361$	7.69132	−	13.3218i	0.404806	−	0.701145i
$362$	0.986944			0.0518726
$363$		0			0
$364$		0			0
$365$	−2.92835	−	5.07205i	−0.153277	−	0.265483i
$366$		0			0
$367$	−17.5190	−	30.3438i	−0.914485	−	1.58393i	−0.807654	−	0.589657i	$-0.799263\pi$
$367$	−17.5190	−	30.3438i	−0.914485	−	1.58393i	−0.106831	−	0.994277i	$-0.534070\pi$
$368$	−6.09375	+	10.5547i	−0.317659	+	0.550201i
$369$		0			0
$370$	−0.770345			−0.0400483
$371$		0			0
$372$		0			0
$373$	−0.564310	+	0.977414i	−0.0292189	+	0.0506086i	−0.880265	−	0.474482i	$-0.842635\pi$
$373$	−0.564310	+	0.977414i	−0.0292189	+	0.0506086i	0.851046	+	0.525091i	$0.175969\pi$
$374$	−0.715863			−0.0370164
$375$		0			0
$376$	−1.03784			−0.0535227
$377$	−33.5667			−1.72877
$378$		0			0
$379$	−21.9619			−1.12811			−0.564054	−	0.825738i	$-0.690759\pi$
$379$	−21.9619			−1.12811			−0.564054	+	0.825738i	$0.690759\pi$
$380$	−10.1090			−0.518583
$381$		0			0
$382$	0.194272			0.00993981
$383$	−11.5200	+	19.9533i	−0.588647	+	1.01957i	0.405763	+	0.913978i	$0.367006\pi$
$383$	−11.5200	+	19.9533i	−0.588647	+	1.01957i	−0.994410	+	0.105588i	$0.966328\pi$
$384$		0			0
$385$		0			0
$386$	−0.603664			−0.0307257
$387$		0			0
$388$	−5.14042	+	8.90346i	−0.260965	+	0.452005i
$389$	7.88753	+	13.6616i	0.399914	+	0.692671i	0.993715	−	0.111941i	$-0.0357067\pi$
$389$	7.88753	+	13.6616i	0.399914	+	0.692671i	−0.593801	+	0.804612i	$0.702373\pi$
$390$		0			0
$391$	−10.0446	−	17.3978i	−0.507979	−	0.879846i
$392$		0			0
$393$		0			0
$394$	0.391341			0.0197155
$395$	−1.08357	+	1.87680i	−0.0545204	+	0.0944321i
$396$		0			0
$397$	−8.25277	−	14.2942i	−0.414195	−	0.717406i	0.581149	−	0.813797i	$-0.302603\pi$
$397$	−8.25277	−	14.2942i	−0.414195	−	0.717406i	−0.995344	+	0.0963911i	$0.969270\pi$
$398$	−0.390246	+	0.675926i	−0.0195613	+	0.0338811i
$399$		0			0
$400$	−4.16220	−	7.20914i	−0.208110	−	0.360457i
$401$	10.8300	−	18.7581i	0.540823	−	0.936733i	−0.458034	−	0.888935i	$-0.651446\pi$
$401$	10.8300	−	18.7581i	0.540823	−	0.936733i	0.998857	−	0.0477986i	$-0.0152206\pi$
$402$		0			0
$403$	−17.6507	−	30.5720i	−0.879246	−	1.52290i
$404$	1.84057	+	3.18796i	0.0915716	+	0.158607i
$405$		0			0
$406$		0			0
$407$	−3.38179	+	5.85743i	−0.167629	+	0.290342i
$408$		0			0
$409$	−30.5721			−1.51169			−0.755846	−	0.654750i	$-0.772774\pi$
$409$	−30.5721			−1.51169			−0.755846	+	0.654750i	$0.772774\pi$
$410$	1.34651			0.0664993
$411$		0			0
$412$	5.16592	−	8.94763i	0.254507	−	0.440818i
$413$		0			0
$414$		0			0
$415$	9.10596	+	15.7720i	0.446994	+	0.774216i
$416$	2.14863	+	3.72153i	0.105345	+	0.182463i
$417$		0			0
$418$	0.103978	−	0.180094i	0.00508571	−	0.00880871i
$419$	−10.8081	−	18.7202i	−0.528011	−	0.914542i	−0.999467	−	0.0326524i	$-0.989605\pi$
$419$	−10.8081	−	18.7202i	−0.528011	−	0.914542i	0.471456	−	0.881890i	$-0.343729\pi$
$420$		0			0
$421$	13.6217	−	23.5935i	0.663881	−	1.14988i	−0.315706	−	0.948857i	$-0.602241\pi$
$421$	13.6217	−	23.5935i	0.663881	−	1.14988i	0.979587	−	0.201019i	$-0.0644252\pi$
$422$	−0.731046	−	1.26621i	−0.0355867	−	0.0616380i
$423$		0			0
$424$	1.21545	−	2.10521i	0.0590273	−	0.102238i
$425$	13.7215			0.665592
$426$		0			0
$427$		0			0
$428$	16.9093	+	29.2877i	0.817341	+	1.41568i
$429$		0			0
$430$	−1.02574	−	1.77663i	−0.0494654	−	0.0856765i
$431$	4.09843	−	7.09869i	0.197415	−	0.341932i	−0.750275	−	0.661126i	$-0.770079\pi$
$431$	4.09843	−	7.09869i	0.197415	−	0.341932i	0.947689	+	0.319194i	$0.103412\pi$
$432$		0			0
$433$	3.41468			0.164099			0.0820494	−	0.996628i	$-0.473853\pi$
$433$	3.41468			0.164099			0.0820494	+	0.996628i	$0.473853\pi$
$434$		0			0
$435$		0			0
$436$	−8.48005	+	14.6879i	−0.406121	+	0.703422i
$437$	5.83585			0.279167
$438$		0			0
$439$	6.58831			0.314443			0.157221	−	0.987563i	$-0.449746\pi$
$439$	6.58831			0.314443			0.157221	+	0.987563i	$0.449746\pi$
$440$	1.16366			0.0554753
$441$		0			0
$442$	−2.35191			−0.111869
$443$	−28.6912			−1.36316			−0.681581	−	0.731743i	$-0.738707\pi$
$443$	−28.6912			−1.36316			−0.681581	+	0.731743i	$0.738707\pi$
$444$		0			0
$445$	−1.25350			−0.0594218
$446$	0.245043	−	0.424428i	0.0116031	−	0.0200972i
$447$		0			0
$448$		0			0
$449$	−0.457724			−0.0216013			−0.0108007	−	0.999942i	$-0.503438\pi$
$449$	−0.457724			−0.0216013			−0.0108007	+	0.999942i	$0.503438\pi$
$450$		0			0
$451$	5.91114	−	10.2384i	0.278345	−	0.482107i
$452$	−3.89479	−	6.74598i	−0.183196	−	0.317304i
$453$		0			0
$454$	0.471393	+	0.816477i	0.0221236	+	0.0383192i
$455$		0			0
$456$		0			0
$457$	20.2210			0.945900			0.472950	−	0.881089i	$-0.343189\pi$
$457$	20.2210			0.945900			0.472950	+	0.881089i	$0.343189\pi$
$458$	−0.902342	+	1.56290i	−0.0421637	+	0.0730296i
$459$		0			0
$460$	8.15440	+	14.1238i	0.380201	+	0.658527i
$461$	12.1036	−	20.9640i	0.563719	−	0.976390i	−0.433449	−	0.901178i	$-0.642703\pi$
$461$	12.1036	−	20.9640i	0.563719	−	0.976390i	0.997168	−	0.0752117i	$-0.0239633\pi$
$462$		0			0
$463$	2.40242	+	4.16111i	0.111650	+	0.193383i	0.916436	−	0.400182i	$-0.131053\pi$
$463$	2.40242	+	4.16111i	0.111650	+	0.193383i	−0.804786	+	0.593565i	$0.797720\pi$
$464$	12.6885	−	21.9772i	0.589050	−	1.02026i
$465$		0			0
$466$	0.432281	+	0.748732i	0.0200250	+	0.0346843i
$467$	−13.6228	−	23.5954i	−0.630389	−	1.09187i	−0.987472	−	0.157793i	$-0.949562\pi$
$467$	−13.6228	−	23.5954i	−0.630389	−	1.09187i	0.357083	−	0.934073i	$-0.383771\pi$
$468$		0			0
$469$		0			0
$470$	−0.345979	+	0.599254i	−0.0159588	+	0.0276415i
$471$		0			0
$472$	2.97565			0.136965
$473$	−18.0118			−0.828184
$474$		0			0
$475$	−1.99302	+	3.45202i	−0.0914462	+	0.158389i
$476$		0			0
$477$		0			0
$478$	0.527601	+	0.913832i	0.0241319	+	0.0417977i
$479$	10.2628	+	17.7756i	0.468917	+	0.812188i	0.999369	−	0.0355269i	$-0.0113109\pi$
$479$	10.2628	+	17.7756i	0.468917	+	0.812188i	−0.530452	+	0.847715i	$0.677978\pi$
$480$		0			0
$481$	−11.1106	+	19.2441i	−0.506600	+	0.877457i
$482$	0.0403366	+	0.0698651i	0.00183728	+	0.00318227i
$483$		0			0
$484$	−8.42306	+	14.5892i	−0.382866	+	0.663144i
$485$	6.86254	+	11.8863i	0.311612	+	0.539727i
$486$		0			0
$487$	−12.9224	+	22.3823i	−0.585571	+	1.01424i	0.409233	+	0.912430i	$0.365796\pi$
$487$	−12.9224	+	22.3823i	−0.585571	+	1.01424i	−0.994804	+	0.101809i	$0.967537\pi$
$488$	0.741363			0.0335599
$489$		0			0
$490$		0			0
$491$	7.80775	+	13.5234i	0.352359	+	0.610303i	0.986662	−	0.162781i	$-0.0520463\pi$
$491$	7.80775	+	13.5234i	0.352359	+	0.610303i	−0.634303	+	0.773084i	$0.718713\pi$
$492$		0			0
$493$	20.9152	+	36.2261i	0.941971	+	1.63154i
$494$	0.341610	−	0.591686i	0.0153698	−	0.0266212i
$495$		0			0
$496$	26.6886			1.19835
$497$		0			0
$498$		0			0
$499$	−10.6345	+	18.4195i	−0.476066	+	0.824571i	−0.999624	−	0.0274192i	$-0.991271\pi$
$499$	−10.6345	+	18.4195i	−0.476066	+	0.824571i	0.523558	+	0.851990i	$0.324604\pi$
$500$	15.4363			0.690332
$501$		0			0
$502$	0.379455			0.0169359
$503$	16.3298			0.728110			0.364055	−	0.931377i	$-0.381392\pi$
$503$	16.3298			0.728110			0.364055	+	0.931377i	$0.381392\pi$
$504$		0			0
$505$	4.91437			0.218687
$506$	−0.335492			−0.0149144
$507$		0			0
$508$	−21.8553			−0.969674
$509$	−6.73089	+	11.6582i	−0.298342	+	0.516743i	−0.975757	−	0.218858i	$-0.929767\pi$
$509$	−6.73089	+	11.6582i	−0.298342	+	0.516743i	0.677415	+	0.735601i	$0.263100\pi$
$510$		0			0
$511$		0			0
$512$	−5.41890			−0.239484
$513$		0			0
$514$	−0.336084	+	0.582115i	−0.0148240	+	0.0256760i
$515$	−6.89659	−	11.9452i	−0.303900	−	0.526370i
$516$		0			0
$517$	3.03768	+	5.26142i	0.133597	+	0.231397i
$518$		0			0
$519$		0			0
$520$	3.82311			0.167654
$521$	−0.713095	+	1.23512i	−0.0312413	+	0.0541115i	−0.881223	−	0.472700i	$-0.843279\pi$
$521$	−0.713095	+	1.23512i	−0.0312413	+	0.0541115i	0.849982	+	0.526812i	$0.176613\pi$
$522$		0			0
$523$	3.85530	+	6.67758i	0.168581	+	0.291990i	0.937921	−	0.346849i	$-0.112748\pi$
$523$	3.85530	+	6.67758i	0.168581	+	0.291990i	−0.769340	+	0.638839i	$0.779415\pi$
$524$	4.44301	−	7.69553i	0.194094	−	0.336181i
$525$		0			0
$526$	−0.407928	−	0.706551i	−0.0177865	−	0.0308071i
$527$	−21.9961	+	38.0984i	−0.958165	+	1.65959i
$528$		0			0
$529$	6.79254	+	11.7650i	0.295328	+	0.511523i
$530$	−0.810371	−	1.40360i	−0.0352003	−	0.0609686i
$531$		0			0
$532$		0			0
$533$	19.4206	−	33.6374i	0.841198	−	1.45700i
$534$		0			0
$535$	45.1483			1.95193
$536$	−0.908402			−0.0392370
$537$		0			0
$538$	−1.02441	+	1.77432i	−0.0441653	+	0.0764966i
$539$		0			0
$540$		0			0
$541$	−14.0228	−	24.2882i	−0.602886	−	1.04423i	−0.992382	−	0.123201i	$-0.960684\pi$
$541$	−14.0228	−	24.2882i	−0.602886	−	1.04423i	0.389495	−	0.921028i	$-0.372649\pi$
$542$	−0.242608	−	0.420209i	−0.0104209	−	0.0180495i
$543$		0			0
$544$	2.67759	−	4.63771i	0.114801	−	0.198840i
$545$	11.3210	+	19.6086i	0.484939	+	0.839939i
$546$		0			0
$547$	17.7305	−	30.7101i	0.758101	−	1.31307i	−0.185717	−	0.982603i	$-0.559461\pi$
$547$	17.7305	−	30.7101i	0.758101	−	1.31307i	0.943818	−	0.330466i	$-0.107206\pi$
$548$	19.4903	+	33.7583i	0.832586	+	1.44208i
$549$		0			0
$550$	0.114575	−	0.198450i	0.00488550	−	0.00846193i
$551$	−12.1515			−0.517673
$552$		0			0
$553$		0			0
$554$	−0.335836	−	0.581685i	−0.0142683	−	0.0247134i
$555$		0			0
$556$	2.62464	+	4.54601i	0.111310	+	0.192794i
$557$	17.5209	−	30.3472i	0.742386	−	1.28585i	−0.209019	−	0.977911i	$-0.567027\pi$
$557$	17.5209	−	30.3472i	0.742386	−	1.28585i	0.951406	−	0.307940i	$-0.0996395\pi$
$558$		0			0
$559$	−59.1763			−2.50289
$560$		0			0
$561$		0			0
$562$	0.816308	−	1.41389i	0.0344339	−	0.0596412i
$563$	−16.0262			−0.675425			−0.337712	−	0.941249i	$-0.609653\pi$
$563$	−16.0262			−0.675425			−0.337712	+	0.941249i	$0.609653\pi$
$564$		0			0
$565$	−10.3992			−0.437499
$566$	0.206213			0.00866776
$567$		0			0
$568$	3.38439			0.142006
$569$	−0.371302			−0.0155658			−0.00778290	−	0.999970i	$-0.502477\pi$
$569$	−0.371302			−0.0155658			−0.00778290	+	0.999970i	$0.502477\pi$
$570$		0			0
$571$	29.2304			1.22325			0.611626	−	0.791147i	$-0.290516\pi$
$571$	29.2304			1.22325			0.611626	+	0.791147i	$0.290516\pi$
$572$	8.38185	−	14.5178i	0.350463	−	0.607019i
$573$		0			0
$574$		0			0
$575$	6.43065			0.268177
$576$		0			0
$577$	7.52852	−	13.0398i	0.313417	−	0.542853i	−0.665683	−	0.746235i	$-0.731860\pi$
$577$	7.52852	−	13.0398i	0.313417	−	0.542853i	0.979100	+	0.203381i	$0.0651930\pi$
$578$	0.884279	+	1.53162i	0.0367811	+	0.0637068i
$579$		0			0
$580$	−16.9793	−	29.4089i	−0.705025	−	1.22114i
$581$		0			0
$582$		0			0
$583$	−14.2300			−0.589347
$584$	−0.300307	+	0.520148i	−0.0124268	+	0.0215239i
$585$		0			0
$586$	−0.583171	−	1.01008i	−0.0240906	−	0.0417261i
$587$	0.835901	−	1.44782i	0.0345013	−	0.0597580i	−0.848259	−	0.529581i	$-0.822349\pi$
$587$	0.835901	−	1.44782i	0.0345013	−	0.0597580i	0.882760	+	0.469823i	$0.155682\pi$
$588$		0			0
$589$	−6.38977	−	11.0674i	−0.263286	−	0.456025i
$590$	0.991973	−	1.71815i	0.0408389	−	0.0707350i
$591$		0			0
$592$	−8.39982	−	14.5489i	−0.345231	−	0.597957i
$593$	−5.40871	−	9.36816i	−0.222109	−	0.384704i	0.733339	−	0.679863i	$-0.237961\pi$
$593$	−5.40871	−	9.36816i	−0.222109	−	0.384704i	−0.955448	+	0.295159i	$0.904627\pi$
$594$		0			0
$595$		0			0
$596$	8.79221	−	15.2286i	0.360143	−	0.623786i
$597$		0			0
$598$	−1.10223			−0.0450736
$599$	−16.6401			−0.679898			−0.339949	−	0.940444i	$-0.610410\pi$
$599$	−16.6401			−0.679898			−0.339949	+	0.940444i	$0.610410\pi$
$600$		0			0
$601$	12.9011	−	22.3453i	0.526246	−	0.911485i	−0.473286	−	0.880909i	$-0.656932\pi$
$601$	12.9011	−	22.3453i	0.526246	−	0.911485i	0.999532	−	0.0305765i	$-0.00973432\pi$
$602$		0			0
$603$		0			0
$604$	4.65332	+	8.05978i	0.189341	+	0.327948i
$605$	11.2449	+	19.4768i	0.457171	+	0.791843i
$606$		0			0
$607$	18.9025	−	32.7400i	0.767227	−	1.32888i	−0.171834	−	0.985126i	$-0.554969\pi$
$607$	18.9025	−	32.7400i	0.767227	−	1.32888i	0.939061	−	0.343750i	$-0.111697\pi$
$608$	0.777828	+	1.34724i	0.0315451	+	0.0546377i
$609$		0			0
$610$	0.247143	−	0.428065i	0.0100065	−	0.0173318i
$611$	9.98005	+	17.2860i	0.403750	+	0.699315i
$612$		0			0
$613$	6.47719	−	11.2188i	0.261611	−	0.453124i	−0.705059	−	0.709149i	$-0.749080\pi$
$613$	6.47719	−	11.2188i	0.261611	−	0.453124i	0.966670	+	0.256025i	$0.0824129\pi$
$614$	−1.58749			−0.0640659
$615$		0			0
$616$		0			0
$617$	−16.2202	−	28.0941i	−0.652999	−	1.13103i	−0.982391	−	0.186834i	$-0.940177\pi$
$617$	−16.2202	−	28.0941i	−0.652999	−	1.13103i	0.329393	−	0.944193i	$-0.393156\pi$
$618$		0			0
$619$	16.5987	+	28.7498i	0.667157	+	1.15555i	0.978696	+	0.205317i	$0.0658224\pi$
$619$	16.5987	+	28.7498i	0.667157	+	1.15555i	−0.311538	+	0.950234i	$0.600844\pi$
$620$	17.8568	−	30.9289i	0.717146	−	1.24213i
$621$		0			0
$622$	0.122453			0.00490993
$623$		0			0
$624$		0			0
$625$	15.5433	−	26.9218i	0.621732	−	1.07687i
$626$	−0.315147			−0.0125958
$627$		0			0
$628$	8.12683			0.324296
$629$	27.6917			1.10414
$630$		0			0
$631$	32.2773			1.28494			0.642470	−	0.766311i	$-0.277910\pi$
$631$	32.2773			1.28494			0.642470	+	0.766311i	$0.277910\pi$
$632$	0.222244			0.00884040
$633$		0			0
$634$	−1.76980			−0.0702877
$635$	−14.5886	+	25.2682i	−0.578931	+	1.00274i
$636$		0			0
$637$		0			0
$638$	0.698568			0.0276566
$639$		0			0
$640$	−2.89714	+	5.01799i	−0.114519	+	0.198353i
$641$	21.5407	+	37.3096i	0.850806	+	1.47364i	0.880482	+	0.474079i	$0.157219\pi$
$641$	21.5407	+	37.3096i	0.850806	+	1.47364i	−0.0296762	+	0.999560i	$0.509448\pi$
$642$		0			0
$643$	3.20088	+	5.54409i	0.126230	+	0.218638i	0.922213	−	0.386682i	$-0.126379\pi$
$643$	3.20088	+	5.54409i	0.126230	+	0.218638i	−0.795983	+	0.605319i	$0.793045\pi$
$644$		0			0
$645$		0			0
$646$	−0.851419			−0.0334986
$647$	−1.94403	+	3.36716i	−0.0764278	+	0.132377i	−0.901706	−	0.432349i	$-0.857685\pi$
$647$	−1.94403	+	3.36716i	−0.0764278	+	0.132377i	0.825278	+	0.564726i	$0.191018\pi$
$648$		0			0
$649$	−8.70947	−	15.0852i	−0.341877	−	0.592148i
$650$	0.376427	−	0.651991i	0.0147647	−	0.0255732i
$651$		0			0
$652$	−12.0939	−	20.9473i	−0.473634	−	0.820358i
$653$	7.55174	−	13.0800i	0.295522	−	0.511860i	−0.679584	−	0.733598i	$-0.737840\pi$
$653$	7.55174	−	13.0800i	0.295522	−	0.511860i	0.975106	+	0.221738i	$0.0711730\pi$
$654$		0			0
$655$	−5.93150	−	10.2737i	−0.231763	−	0.401425i
$656$	14.6823	+	25.4305i	0.573248	+	0.992895i
$657$		0			0
$658$		0			0
$659$	7.13002	−	12.3496i	0.277746	−	0.481070i	−0.693078	−	0.720862i	$-0.743746\pi$
$659$	7.13002	−	12.3496i	0.277746	−	0.481070i	0.970824	+	0.239792i	$0.0770793\pi$
$660$		0			0
$661$	19.4193			0.755323			0.377662	−	0.925944i	$-0.376728\pi$
$661$	19.4193			0.755323			0.377662	+	0.925944i	$0.376728\pi$
$662$	−0.0110303			−0.000428706
$663$		0			0
$664$	0.933832	−	1.61744i	0.0362397	−	0.0627690i
$665$		0			0
$666$		0			0
$667$	9.80197	+	16.9775i	0.379534	+	0.657372i
$668$	4.78781	+	8.29273i	0.185246	+	0.320855i
$669$		0			0
$670$	−0.302828	+	0.524513i	−0.0116993	+	0.0202637i
$671$	−2.16991	−	3.75839i	−0.0837683	−	0.145091i
$672$		0			0
$673$	−2.96563	+	5.13663i	−0.114317	+	0.198002i	−0.917506	−	0.397721i	$-0.869801\pi$
$673$	−2.96563	+	5.13663i	−0.114317	+	0.198002i	0.803190	+	0.595723i	$0.203135\pi$
$674$	−0.309512	−	0.536091i	−0.0119220	−	0.0206494i
$675$		0			0
$676$	14.5683	−	25.2330i	0.560318	−	0.970500i
$677$	36.9826			1.42136			0.710678	−	0.703518i	$-0.248388\pi$
$677$	36.9826			1.42136			0.710678	+	0.703518i	$0.248388\pi$
$678$		0			0
$679$		0			0
$680$	−2.38215	−	4.12601i	−0.0913513	−	0.158225i
$681$		0			0
$682$	0.367336	+	0.636244i	0.0140660	+	0.0243630i
$683$	6.56800	−	11.3761i	0.251317	−	0.435294i	−0.712571	−	0.701600i	$-0.752470\pi$
$683$	6.56800	−	11.3761i	0.251317	−	0.435294i	0.963889	+	0.266305i	$0.0858029\pi$
$684$		0			0
$685$	52.0398			1.98834
$686$		0			0
$687$		0			0
$688$	22.3692	−	38.7446i	0.852818	−	1.47712i
$689$	−46.7516			−1.78109
$690$		0			0
$691$	−14.7658			−0.561719			−0.280860	−	0.959749i	$-0.590620\pi$
$691$	−14.7658			−0.561719			−0.280860	+	0.959749i	$0.590620\pi$
$692$	10.0399			0.381659
$693$		0			0
$694$	−0.397915			−0.0151046
$695$	7.00788			0.265824
$696$		0			0
$697$	−48.4032			−1.83340
$698$	0.932003	−	1.61428i	0.0352768	−	0.0611012i
$699$		0			0
$700$		0			0
$701$	30.4627			1.15056			0.575281	−	0.817956i	$-0.304893\pi$
$701$	30.4627			1.15056			0.575281	+	0.817956i	$0.304893\pi$
$702$		0			0
$703$	−4.02217	+	6.96660i	−0.151699	+	0.262750i
$704$	6.30697	+	10.9240i	0.237703	+	0.411713i
$705$		0			0
$706$	0.826969	+	1.43235i	0.0311234	+	0.0539073i
$707$		0			0
$708$		0			0
$709$	14.1030			0.529650			0.264825	−	0.964296i	$-0.414686\pi$
$709$	14.1030			0.529650			0.264825	+	0.964296i	$0.414686\pi$
$710$	1.12823	−	1.95415i	0.0423418	−	0.0733381i
$711$		0			0
$712$	0.0642745	+	0.111327i	0.00240879	+	0.00417215i
$713$	−10.3086	+	17.8549i	−0.386058	+	0.668673i
$714$		0			0
$715$	−11.1899	−	19.3815i	−0.418479	−	0.724827i
$716$	16.3596	−	28.3356i	0.611386	−	1.05895i
$717$		0			0
$718$	0.719212	+	1.24571i	0.0268408	+	0.0464896i
$719$	−7.49790	−	12.9867i	−0.279624	−	0.484324i	0.691667	−	0.722217i	$-0.256877\pi$
$719$	−7.49790	−	12.9867i	−0.279624	−	0.484324i	−0.971291	+	0.237893i	$0.923543\pi$
$720$		0			0
$721$		0			0
$722$	−0.525886	+	0.910861i	−0.0195715	+	0.0338987i
$723$		0			0
$724$	28.8015			1.07040
$725$	−13.3900			−0.497293
$726$		0			0
$727$	13.0527	−	22.6080i	0.484099	−	0.838485i	−0.515734	−	0.856749i	$-0.672481\pi$
$727$	13.0527	−	22.6080i	0.484099	−	0.838485i	0.999833	+	0.0182642i	$0.00581399\pi$
$728$		0			0
$729$		0			0
$730$	0.200223	+	0.346796i	0.00741059	+	0.0128355i
$731$	36.8723	+	63.8648i	1.36377	+	2.36212i
$732$		0			0
$733$	14.1911	−	24.5796i	0.524159	−	0.907869i	−0.475446	−	0.879745i	$-0.657713\pi$
$733$	14.1911	−	24.5796i	0.524159	−	0.907869i	0.999604	−	0.0281244i	$-0.00895345\pi$
$734$	1.19784	+	2.07473i	0.0442132	+	0.0765796i
$735$		0			0
$736$	1.25486	−	2.17348i	0.0462548	−	0.0801156i
$737$	2.65881	+	4.60520i	0.0979386	+	0.169635i
$738$		0			0
$739$	−23.2933	+	40.3451i	−0.856857	+	1.48412i	0.0180552	+	0.999837i	$0.494253\pi$
$739$	−23.2933	+	40.3451i	−0.856857	+	1.48412i	−0.874912	+	0.484282i	$0.839081\pi$
$740$	−22.4806			−0.826403
$741$		0			0
$742$		0			0
$743$	0.169513	+	0.293606i	0.00621884	+	0.0107713i	0.869118	−	0.494605i	$-0.164687\pi$
$743$	0.169513	+	0.293606i	0.00621884	+	0.0107713i	−0.862899	+	0.505376i	$0.831354\pi$
$744$		0			0
$745$	−11.7377	−	20.3304i	−0.430038	−	0.744847i
$746$	0.0385841	−	0.0668297i	0.00141267	−	0.00244681i
$747$		0			0
$748$	−20.8907			−0.763839
$749$		0			0
$750$		0			0
$751$	18.1831	−	31.4940i	0.663510	−	1.14923i	−0.316177	−	0.948700i	$-0.602399\pi$
$751$	18.1831	−	31.4940i	0.663510	−	1.14923i	0.979687	−	0.200533i	$-0.0642673\pi$
$752$	−15.0902			−0.550284
$753$		0			0
$754$	2.29509			0.0835822
$755$	12.4245			0.452174
$756$		0			0
$757$	−27.4703			−0.998424			−0.499212	−	0.866480i	$-0.666377\pi$
$757$	−27.4703			−0.998424			−0.499212	+	0.866480i	$0.666377\pi$
$758$	1.50162			0.0545415
$759$		0			0
$760$	1.38401			0.0502033
$761$	−16.5178	+	28.6097i	−0.598771	+	1.03710i	0.394232	+	0.919011i	$0.371011\pi$
$761$	−16.5178	+	28.6097i	−0.598771	+	1.03710i	−0.993003	+	0.118091i	$0.962323\pi$
$762$		0			0
$763$		0			0
$764$	5.66934			0.205110
$765$		0			0
$766$	0.787671	−	1.36429i	0.0284597	−	0.0492937i
$767$	−28.6143	−	49.5614i	−1.03320	−	1.78956i
$768$		0			0
$769$	1.28876	+	2.23219i	0.0464738	+	0.0804949i	0.888327	−	0.459212i	$-0.151868\pi$
$769$	1.28876	+	2.23219i	0.0464738	+	0.0804949i	−0.841853	+	0.539707i	$0.818535\pi$
$770$		0			0
$771$		0			0
$772$	−17.6164			−0.634030
$773$	−3.36486	+	5.82811i	−0.121026	+	0.209623i	−0.920172	−	0.391513i	$-0.871952\pi$
$773$	−3.36486	+	5.82811i	−0.121026	+	0.209623i	0.799147	+	0.601136i	$0.205285\pi$
$774$		0			0
$775$	−7.04102	−	12.1954i	−0.252921	−	0.438072i
$776$	0.703765	−	1.21896i	0.0252637	−	0.0437580i
$777$		0			0
$778$	−0.539302	−	0.934099i	−0.0193349	−	0.0334891i
$779$	7.03047	−	12.1771i	0.251893	−	0.436291i
$780$		0			0
$781$	−9.90581	−	17.1574i	−0.354458	−	0.613939i
$782$	0.686792	+	1.18956i	0.0245596	+	0.0425385i
$783$		0			0
$784$		0			0
$785$	5.42473	−	9.39590i	0.193617	−	0.335354i
$786$		0			0
$787$	−28.6683			−1.02191			−0.510956	−	0.859607i	$-0.670709\pi$
$787$	−28.6683			−1.02191			−0.510956	+	0.859607i	$0.670709\pi$
$788$	11.4203			0.406832
$789$		0			0
$790$	0.0740881	−	0.128324i	0.00263594	−	0.00456558i
$791$		0			0
$792$		0			0
$793$	−7.12905	−	12.3479i	−0.253160	−	0.438486i
$794$	0.564275	+	0.977352i	0.0200254	+	0.0346849i
$795$		0			0
$796$	−11.3884	+	19.7252i	−0.403650	+	0.699142i
$797$	11.4913	+	19.9035i	0.407042	+	0.705017i	0.994557	−	0.104196i	$-0.0332270\pi$
$797$	11.4913	+	19.9035i	0.407042	+	0.705017i	−0.587515	+	0.809213i	$0.699894\pi$
$798$		0			0
$799$	12.4370	−	21.5415i	0.439989	−	0.762084i
$800$	0.857104	+	1.48455i	0.0303032	+	0.0524867i
$801$		0			0
$802$	−0.740489	+	1.28256i	−0.0261476	+	0.0452889i
$803$	3.51589			0.124073
$804$		0			0
$805$		0			0
$806$	1.20685	+	2.09033i	0.0425095	+	0.0736287i
$807$		0			0
$808$	−0.251989	−	0.436457i	−0.00886493	−	0.0153545i
$809$	−8.23894	+	14.2703i	−0.289666	+	0.501716i	−0.973730	−	0.227706i	$-0.926878\pi$
$809$	−8.23894	+	14.2703i	−0.289666	+	0.501716i	0.684064	+	0.729422i	$0.260211\pi$
$810$		0			0
$811$	−40.4318			−1.41975			−0.709876	−	0.704326i	$-0.751249\pi$
$811$	−40.4318			−1.41975			−0.709876	+	0.704326i	$0.751249\pi$
$812$		0			0
$813$		0			0
$814$	0.231227	−	0.400496i	0.00810449	−	0.0140374i
$815$	−32.2911			−1.13111
$816$		0			0
$817$	−21.4225			−0.749479
$818$	2.09033			0.0730868
$819$		0			0
$820$	39.2945			1.37222
$821$	28.1086			0.980998			0.490499	−	0.871442i	$-0.336814\pi$
$821$	28.1086			0.980998			0.490499	+	0.871442i	$0.336814\pi$
$822$		0			0
$823$	25.9058			0.903019			0.451510	−	0.892266i	$-0.350886\pi$
$823$	25.9058			0.903019			0.451510	+	0.892266i	$0.350886\pi$
$824$	−0.707256	+	1.22500i	−0.0246384	+	0.0426750i
$825$		0			0
$826$		0			0
$827$	17.7998			0.618961			0.309480	−	0.950906i	$-0.399845\pi$
$827$	17.7998			0.618961			0.309480	+	0.950906i	$0.399845\pi$
$828$		0			0
$829$	−7.85344	+	13.6026i	−0.272761	+	0.472436i	−0.969568	−	0.244823i	$-0.921270\pi$
$829$	−7.85344	+	13.6026i	−0.272761	+	0.472436i	0.696807	+	0.717259i	$0.254604\pi$
$830$	−0.622611	−	1.07839i	−0.0216111	−	0.0374316i
$831$		0			0
$832$	20.7210	+	35.8899i	0.718373	+	1.24426i
$833$		0			0
$834$		0			0
$835$	12.7836			0.442395
$836$	3.03433	−	5.25561i	0.104944	−	0.181769i
$837$		0			0
$838$	0.738994	+	1.27998i	0.0255281	+	0.0442160i
$839$	−3.69822	+	6.40550i	−0.127677	+	0.221142i	−0.922776	−	0.385337i	$-0.874085\pi$
$839$	−3.69822	+	6.40550i	−0.127677	+	0.221142i	0.795099	+	0.606479i	$0.207419\pi$
$840$		0			0
$841$	−5.90986	−	10.2362i	−0.203788	−	0.352971i
$842$	−0.931370	+	1.61318i	−0.0320971	+	0.0555938i
$843$		0			0
$844$	−21.3338	−	36.9511i	−0.734338	−	1.27191i
$845$	−19.4489	−	33.6865i	−0.669062	−	1.15885i
$846$		0			0
$847$		0			0
$848$	17.6725	−	30.6097i	0.606878	−	1.05114i
$849$		0			0
$850$	−0.938196			−0.0321798
$851$	12.9778			0.444874
$852$		0			0
$853$	26.5631	−	46.0086i	0.909503	−	1.57530i	0.0947464	−	0.995501i	$-0.469796\pi$
$853$	26.5631	−	46.0086i	0.909503	−	1.57530i	0.814756	−	0.579804i	$-0.196871\pi$
$854$		0			0
$855$		0			0
$856$	−2.31502	−	4.00973i	−0.0791257	−	0.137050i
$857$	−1.90765	−	3.30414i	−0.0651640	−	0.112867i	0.831603	−	0.555371i	$-0.187424\pi$
$857$	−1.90765	−	3.30414i	−0.0651640	−	0.112867i	−0.896767	+	0.442504i	$0.854090\pi$
$858$		0			0
$859$	−19.4884	+	33.7549i	−0.664936	+	1.15170i	0.314367	+	0.949301i	$0.398208\pi$
$859$	−19.4884	+	33.7549i	−0.664936	+	1.15170i	−0.979303	+	0.202401i	$0.935126\pi$
$860$	−29.9336	−	51.8464i	−1.02073	−	1.76795i
$861$		0			0
$862$	−0.280226	+	0.485366i	−0.00954454	+	0.0165316i
$863$	13.3368	+	23.1000i	0.453989	+	0.786332i	0.998629	−	0.0523375i	$-0.0166672\pi$
$863$	13.3368	+	23.1000i	0.453989	+	0.786332i	−0.544640	+	0.838670i	$0.683334\pi$
$864$		0			0
$865$	6.70171	−	11.6077i	0.227865	−	0.394674i
$866$	−0.233475			−0.00793380
$867$		0			0
$868$		0			0
$869$	−0.650490	−	1.12668i	−0.0220664	−	0.0382200i
$870$		0			0
$871$	8.73531	+	15.1300i	0.295985	+	0.512661i
$872$	1.16099	−	2.01089i	0.0393160	−	0.0680974i
$873$		0			0
$874$	−0.399020			−0.0134971
$875$		0			0
$876$		0			0
$877$	−12.0068	+	20.7963i	−0.405440	+	0.702242i	−0.994373	−	0.105940i	$-0.966215\pi$
$877$	−12.0068	+	20.7963i	−0.405440	+	0.702242i	0.588933	+	0.808182i	$0.299548\pi$
$878$	−0.450469			−0.0152026
$879$		0			0
$880$	16.9196			0.570358
$881$	4.67326			0.157446			0.0787231	−	0.996897i	$-0.474916\pi$
$881$	4.67326			0.157446			0.0787231	+	0.996897i	$0.474916\pi$
$882$		0			0
$883$	−35.6948			−1.20122			−0.600612	−	0.799541i	$-0.705076\pi$
$883$	−35.6948			−1.20122			−0.600612	+	0.799541i	$0.705076\pi$
$884$	−68.6346			−2.30843
$885$		0			0
$886$	1.96173			0.0659058
$887$	14.5516	−	25.2041i	0.488596	−	0.846272i	−0.511318	−	0.859391i	$-0.670843\pi$
$887$	14.5516	−	25.2041i	0.488596	−	0.846272i	0.999914	+	0.0131191i	$0.00417605\pi$
$888$		0			0
$889$		0			0
$890$	0.0857071			0.00287291
$891$		0			0
$892$	7.15098	−	12.3859i	0.239433	−	0.414710i
$893$	3.61290	+	6.25772i	0.120901	+	0.209407i
$894$		0			0
$895$	−21.8403	−	37.8285i	−0.730041	−	1.26447i
$896$		0			0
$897$		0			0
$898$	0.0312964			0.00104437
$899$	21.4647	−	37.1779i	0.715887	−	1.23995i
$900$		0			0
$901$	29.1306	+	50.4556i	0.970480	+	1.68092i
$902$	−0.404168	+	0.700040i	−0.0134573	+	0.0233088i
$903$		0			0
$904$	0.533229	+	0.923579i	0.0177349	+	0.0307178i
$905$	19.2252	−	33.2991i	0.639069	−	1.10690i
$906$		0			0
$907$	20.6071	+	35.6925i	0.684247	+	1.18515i	0.973673	+	0.227950i	$0.0732024\pi$
$907$	20.6071	+	35.6925i	0.684247	+	1.18515i	−0.289426	+	0.957201i	$0.593464\pi$
$908$	13.7564	+	23.8269i	0.456524	+	0.790722i
$909$		0			0
$910$		0			0
$911$	−28.8619	+	49.9903i	−0.956239	+	1.65625i	−0.224731	+	0.974421i	$0.572150\pi$
$911$	−28.8619	+	49.9903i	−0.956239	+	1.65625i	−0.731508	+	0.681833i	$0.761183\pi$
$912$		0			0
$913$	−10.9330			−0.361829
$914$	−1.38259			−0.0457321
$915$		0			0
$916$	−26.3326	+	45.6094i	−0.870054	+	1.50698i
$917$		0			0
$918$		0			0
$919$	25.7799	+	44.6521i	0.850400	+	1.47294i	0.880848	+	0.473400i	$0.156973\pi$
$919$	25.7799	+	44.6521i	0.850400	+	1.47294i	−0.0304476	+	0.999536i	$0.509693\pi$
$920$	−1.11640	−	1.93367i	−0.0368068	−	0.0637512i
$921$		0			0
$922$	−0.827569	+	1.43339i	−0.0272545	+	0.0472062i
$923$	−32.5447	−	56.3691i	−1.07122	−	1.85541i
$924$		0			0
$925$	−4.43211	+	7.67664i	−0.145727	+	0.252406i
$926$	−0.164263	−	0.284511i	−0.00539801	−	0.00934962i
$927$		0			0
$928$	−2.61290	+	4.52567i	−0.0857725	+	0.148562i
$929$	50.2824			1.64971			0.824856	−	0.565343i	$-0.191256\pi$
$929$	50.2824			1.64971			0.824856	+	0.565343i	$0.191256\pi$
$930$		0			0
$931$		0			0
$932$	12.6150	+	21.8499i	0.413219	+	0.715717i
$933$		0			0
$934$	0.931446	+	1.61331i	0.0304779	+	0.0527892i
$935$	−13.9447	+	24.1529i	−0.456040	+	0.789885i
$936$		0			0
$937$	18.1400			0.592607			0.296303	−	0.955094i	$-0.404246\pi$
$937$	18.1400			0.592607			0.296303	+	0.955094i	$0.404246\pi$
$938$		0			0
$939$		0			0
$940$	−10.0966	+	17.4877i	−0.329313	+	0.570387i
$941$	17.0332			0.555267			0.277633	−	0.960687i	$-0.410450\pi$
$941$	17.0332			0.555267			0.277633	+	0.960687i	$0.410450\pi$
$942$		0			0
$943$	−22.6844			−0.738704
$944$	43.2658			1.40818
$945$		0			0
$946$	1.23154			0.0400408
$947$	−31.5059			−1.02381			−0.511903	−	0.859044i	$-0.671059\pi$
$947$	−31.5059			−1.02381			−0.511903	+	0.859044i	$0.671059\pi$
$948$		0			0
$949$	11.5512			0.374967
$950$	0.136271	−	0.236028i	0.00442121	−	0.00765777i
$951$		0			0
$952$		0			0
$953$	−16.0677			−0.520485			−0.260242	−	0.965543i	$-0.583803\pi$
$953$	−16.0677			−0.520485			−0.260242	+	0.965543i	$0.583803\pi$
$954$		0			0
$955$	3.78433	−	6.55465i	0.122458	−	0.212104i
$956$	15.3967	+	26.6679i	0.497966	+	0.862502i
$957$		0			0
$958$	−0.701705	−	1.21539i	−0.0226711	−	0.0392674i
$959$		0			0
$960$		0			0
$961$	14.1480			0.456388
$962$	0.759676	−	1.31580i	0.0244929	−	0.0424230i
$963$		0			0
$964$	1.17713	+	2.03884i	0.0379126	+	0.0656666i
$965$	−11.7591	+	20.3674i	−0.378539	+	0.655649i
$966$		0			0
$967$	13.3049	+	23.0448i	0.427857	+	0.741069i	0.996682	−	0.0813886i	$-0.0259355\pi$
$967$	13.3049	+	23.0448i	0.427857	+	0.741069i	−0.568826	+	0.822458i	$0.692602\pi$
$968$	1.15319	−	1.99738i	0.0370648	−	0.0641981i
$969$		0			0
$970$	−0.469219	−	0.812711i	−0.0150657	−	0.0260946i
$971$	−28.2839	−	48.9892i	−0.907674	−	1.57214i	−0.817287	−	0.576231i	$-0.804523\pi$
$971$	−28.2839	−	48.9892i	−0.907674	−	1.57214i	−0.0903867	−	0.995907i	$-0.528810\pi$
$972$		0			0
$973$		0			0
$974$	0.883558	−	1.53037i	0.0283110	−	0.0490361i
$975$		0			0
$976$	10.7794			0.345040
$977$	−53.7560			−1.71981			−0.859904	−	0.510456i	$-0.829477\pi$
$977$	−53.7560			−1.71981			−0.859904	+	0.510456i	$0.829477\pi$
$978$		0			0
$979$	0.376252	−	0.651687i	0.0120251	−	0.0208280i
$980$		0			0
$981$		0			0
$982$	−0.533847	−	0.924650i	−0.0170357	−	0.0295068i
$983$	13.7051	+	23.7379i	0.437125	+	0.757122i	0.997466	−	0.0711394i	$-0.0226635\pi$
$983$	13.7051	+	23.7379i	0.437125	+	0.757122i	−0.560342	+	0.828262i	$0.689330\pi$
$984$		0			0
$985$	7.62316	−	13.2037i	0.242894	−	0.420705i
$986$	−1.43005	−	2.47692i	−0.0455421	−	0.0788813i
$987$		0			0
$988$	9.96904	−	17.2669i	0.317157	−	0.549333i
$989$	17.2804	+	29.9305i	0.549483	+	0.951733i
$990$		0			0
$991$	8.66869	−	15.0146i	0.275370	−	0.476955i	−0.694858	−	0.719147i	$-0.744533\pi$
$991$	8.66869	−	15.0146i	0.275370	−	0.476955i	0.970228	+	0.242192i	$0.0778663\pi$
$992$	−5.49587			−0.174494
$993$		0			0
$994$		0			0
$995$	15.2037	+	26.3335i	0.481988	+	0.834828i
$996$		0			0
$997$	17.8319	+	30.8858i	0.564742	+	0.978162i	0.997074	+	0.0764472i	$0.0243576\pi$
$997$	17.8319	+	30.8858i	0.564742	+	0.978162i	−0.432332	+	0.901715i	$0.642309\pi$
$998$	0.727124	−	1.25942i	0.0230167	−	0.0398661i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.h.h.802.6		24
3.2	odd	2		441.2.h.h.214.7		24
7.2	even	3		1323.2.g.h.667.8		24
7.3	odd	6		1323.2.f.h.883.8		24
7.4	even	3		1323.2.f.h.883.7		24
7.5	odd	6		1323.2.g.h.667.7		24
7.6	odd	2	inner	1323.2.h.h.802.5		24
9.4	even	3		1323.2.g.h.361.8		24
9.5	odd	6		441.2.g.h.67.5		24
21.2	odd	6		441.2.g.h.79.5		24
21.5	even	6		441.2.g.h.79.6		24
21.11	odd	6		441.2.f.h.295.6	yes	24
21.17	even	6		441.2.f.h.295.5	yes	24
21.20	even	2		441.2.h.h.214.8		24
63.4	even	3		1323.2.f.h.442.7		24
63.5	even	6		441.2.h.h.373.8		24
63.11	odd	6		3969.2.a.bh.1.7		12
63.13	odd	6		1323.2.g.h.361.7		24
63.23	odd	6		441.2.h.h.373.7		24
63.25	even	3		3969.2.a.bi.1.6		12
63.31	odd	6		1323.2.f.h.442.8		24
63.32	odd	6		441.2.f.h.148.6	yes	24
63.38	even	6		3969.2.a.bh.1.8		12
63.40	odd	6	inner	1323.2.h.h.226.5		24
63.41	even	6		441.2.g.h.67.6		24
63.52	odd	6		3969.2.a.bi.1.5		12
63.58	even	3	inner	1323.2.h.h.226.6		24
63.59	even	6		441.2.f.h.148.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.5	✓	24	63.59	even	6
441.2.f.h.148.6	yes	24	63.32	odd	6
441.2.f.h.295.5	yes	24	21.17	even	6
441.2.f.h.295.6	yes	24	21.11	odd	6
441.2.g.h.67.5		24	9.5	odd	6
441.2.g.h.67.6		24	63.41	even	6
441.2.g.h.79.5		24	21.2	odd	6
441.2.g.h.79.6		24	21.5	even	6
441.2.h.h.214.7		24	3.2	odd	2
441.2.h.h.214.8		24	21.20	even	2
441.2.h.h.373.7		24	63.23	odd	6
441.2.h.h.373.8		24	63.5	even	6
1323.2.f.h.442.7		24	63.4	even	3
1323.2.f.h.442.8		24	63.31	odd	6
1323.2.f.h.883.7		24	7.4	even	3
1323.2.f.h.883.8		24	7.3	odd	6
1323.2.g.h.361.7		24	63.13	odd	6
1323.2.g.h.361.8		24	9.4	even	3
1323.2.g.h.667.7		24	7.5	odd	6
1323.2.g.h.667.8		24	7.2	even	3
1323.2.h.h.226.5		24	63.40	odd	6	inner
1323.2.h.h.226.6		24	63.58	even	3	inner
1323.2.h.h.802.5		24	7.6	odd	2	inner
1323.2.h.h.802.6		24	1.1	even	1	trivial
3969.2.a.bh.1.7		12	63.11	odd	6
3969.2.a.bh.1.8		12	63.38	even	6
3969.2.a.bi.1.5		12	63.52	odd	6
3969.2.a.bi.1.6		12	63.25	even	3

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.0683740 q^{2} -1.99532 q^{4} +(-1.33190 + 2.30691i) q^{5} +0.273176 q^{8} +O(q^{10})\)	\(q-0.0683740 q^{2} -1.99532 q^{4} +(-1.33190 + 2.30691i) q^{5} +0.273176 q^{8} +(0.0910670 - 0.157733i) q^{10} +(-0.799563 - 1.38488i) q^{11} +(-2.62690 - 4.54992i) q^{13} +3.97197 q^{16} +(-3.27360 + 5.67005i) q^{17} +(-0.950968 - 1.64713i) q^{19} +(2.65756 - 4.60304i) q^{20} +(0.0546693 + 0.0946900i) q^{22} +(-1.53419 + 2.65729i) q^{23} +(-1.04789 - 1.81500i) q^{25} +(0.179612 + 0.311096i) q^{26} +(3.19452 - 5.53306i) q^{29} +6.71923 q^{31} -0.817932 q^{32} +(0.223829 - 0.387684i) q^{34} +(-2.11477 - 3.66290i) q^{37} +(0.0650215 + 0.112621i) q^{38} +(-0.363842 + 0.630193i) q^{40} +(3.69648 + 6.40249i) q^{41} +(5.63176 - 9.75450i) q^{43} +(1.59539 + 2.76329i) q^{44} +(0.104898 - 0.181689i) q^{46} -3.79918 q^{47} +(0.0716485 + 0.124099i) q^{50} +(5.24152 + 9.07858i) q^{52} +(4.44931 - 7.70643i) q^{53} +4.25974 q^{55} +(-0.218422 + 0.378317i) q^{58} +10.8928 q^{59} +2.71386 q^{61} -0.459420 q^{62} -7.88802 q^{64} +13.9950 q^{65} -3.32533 q^{67} +(6.53190 - 11.3136i) q^{68} +12.3890 q^{71} +(-1.09932 + 1.90407i) q^{73} +(0.144596 + 0.250447i) q^{74} +(1.89749 + 3.28655i) q^{76} +0.813556 q^{79} +(-5.29025 + 9.16298i) q^{80} +(-0.252743 - 0.437764i) q^{82} +(3.41842 - 5.92088i) q^{83} +(-8.72020 - 15.1038i) q^{85} +(-0.385066 + 0.666954i) q^{86} +(-0.218422 - 0.378317i) q^{88} +(0.235286 + 0.407527i) q^{89} +(3.06120 - 5.30216i) q^{92} +0.259765 q^{94} +5.06636 q^{95} +(2.57623 - 4.46216i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 20 q^{11} + 24 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} + 96 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} + 120 q^{65} + 24 q^{67} + 112 q^{71} - 68 q^{74} - 24 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} + 128 q^{95}+O(q^{100}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 20 * q^11 + 24 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 + 96 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 + 120 * q^65 + 24 * q^67 + 112 * q^71 - 68 * q^74 - 24 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 + 128 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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