LMFDB - Embedded newform 1170.2.q.c.629.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(359,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.359"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.q (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,0,0,0,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			629.2
Character	$\chi$	$=$	1170.629
Dual form			1170.2.q.c.359.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.23186 - 0.137134i) q^{5} +(-3.64075 + 3.64075i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.67513 - 1.48119i) q^{10} +(0.550376 - 0.550376i) q^{11} +(-2.57644 + 2.52229i) q^{13} -5.14880i q^{14} -1.00000 q^{16} -3.92461i q^{17} +(-0.0343813 + 0.0343813i) q^{19} +(-0.137134 + 2.23186i) q^{20} +0.778350i q^{22} -5.25738i q^{23} +(4.96239 + 0.612127i) q^{25} +(0.0382937 - 3.60535i) q^{26} +(3.64075 + 3.64075i) q^{28} +2.61043i q^{29} +(-1.75191 + 1.75191i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.77512 + 2.77512i) q^{34} +(8.62491 - 7.62637i) q^{35} +(-3.40442 + 3.40442i) q^{37} -0.0486226i q^{38} +(-1.48119 - 1.67513i) q^{40} +(2.00378 + 2.00378i) q^{41} +8.65410 q^{43} +(-0.550376 - 0.550376i) q^{44} +(3.71753 + 3.71753i) q^{46} +(-3.70662 - 3.70662i) q^{47} -19.5101i q^{49} +(-3.94178 + 3.07610i) q^{50} +(2.52229 + 2.57644i) q^{52} +7.17150 q^{53} +(-1.30384 + 1.15289i) q^{55} -5.14880 q^{56} +(-1.84586 - 1.84586i) q^{58} +(6.80629 - 6.80629i) q^{59} +10.8249 q^{61} -2.47757i q^{62} +1.00000i q^{64} +(6.09615 - 5.27607i) q^{65} +(-9.45160 - 9.45160i) q^{67} -3.92461 q^{68} +(-0.706074 + 11.4914i) q^{70} +(-7.43355 - 7.43355i) q^{71} +(6.06238 - 6.06238i) q^{73} -4.81457i q^{74} +(0.0343813 + 0.0343813i) q^{76} +4.00757i q^{77} -1.13946 q^{79} +(2.23186 + 0.137134i) q^{80} -2.83378 q^{82} +(6.10358 - 6.10358i) q^{83} +(-0.538197 + 8.75918i) q^{85} +(-6.11937 + 6.11937i) q^{86} +0.778350 q^{88} +(-5.69461 + 5.69461i) q^{89} +(0.197167 - 18.5632i) q^{91} -5.25738 q^{92} +5.24195 q^{94} +(0.0814492 - 0.0720195i) q^{95} +(-0.250273 - 0.250273i) q^{97} +(13.7957 + 13.7957i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{13} - 24 q^{16} - 48 q^{19} + 32 q^{25} - 8 q^{31} + 16 q^{34} - 32 q^{37} + 8 q^{40} + 80 q^{43} + 8 q^{46} - 12 q^{52} + 16 q^{55} - 24 q^{58} - 16 q^{61} - 8 q^{67} - 24 q^{70} + 48 q^{73}+ \cdots + 64 q^{97}+O(q^{100}) $ 24 * q - 20 * q^13 - 24 * q^16 - 48 * q^19 + 32 * q^25 - 8 * q^31 + 16 * q^34 - 32 * q^37 + 8 * q^40 + 80 * q^43 + 8 * q^46 - 12 * q^52 + 16 * q^55 - 24 * q^58 - 16 * q^61 - 8 * q^67 - 24 * q^70 + 48 * q^73 + 48 * q^76 - 96 * q^79 - 72 * q^82 + 8 * q^85 + 8 * q^88 + 48 * q^91 - 16 * q^94 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−2.23186	−	0.137134i	−0.998118	−	0.0613281i
$5$	−2.23186	−	0.137134i	−0.998118	−	0.0613281i
$6$		0			0
$7$	−3.64075	+	3.64075i	−1.37607	+	1.37607i	−0.524926	+	0.851148i	$0.675907\pi$
$7$	−3.64075	+	3.64075i	−1.37607	+	1.37607i	−0.851148	+	0.524926i	$0.824093\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	1.67513	−	1.48119i	0.529723	−	0.468395i
$11$	0.550376	−	0.550376i	0.165945	−	0.165945i	−0.619250	−	0.785194i	$-0.712563\pi$
$11$	0.550376	−	0.550376i	0.165945	−	0.165945i	0.785194	+	0.619250i	$0.212563\pi$
$12$		0			0
$13$	−2.57644	+	2.52229i	−0.714577	+	0.699557i
$13$	−2.57644	+	2.52229i	−0.714577	+	0.699557i
$14$		−	5.14880i		−	1.37607i
$15$		0			0
$16$	−1.00000			−0.250000
$17$		−	3.92461i		−	0.951858i	−0.879484	−	0.475929i	$-0.842112\pi$
$17$		−	3.92461i		−	0.951858i	0.879484	−	0.475929i	$-0.157888\pi$
$18$		0			0
$19$	−0.0343813	+	0.0343813i	−0.00788762	+	0.00788762i	−0.711040	−	0.703152i	$-0.751775\pi$
$19$	−0.0343813	+	0.0343813i	−0.00788762	+	0.00788762i	0.703152	+	0.711040i	$0.251775\pi$
$20$	−0.137134	+	2.23186i	−0.0306641	+	0.499059i
$21$		0			0
$22$			0.778350i			0.165945i
$23$		−	5.25738i		−	1.09624i	−0.836400	−	0.548119i	$-0.815344\pi$
$23$		−	5.25738i		−	1.09624i	0.836400	−	0.548119i	$-0.184656\pi$
$24$		0			0
$25$	4.96239	+	0.612127i	0.992478	+	0.122425i
$26$	0.0382937	−	3.60535i	0.00751002	−	0.707067i
$27$		0			0
$28$	3.64075	+	3.64075i	0.688037	+	0.688037i
$29$			2.61043i			0.484745i	0.970183	+	0.242373i	$0.0779257\pi$
$29$			2.61043i			0.484745i	−0.970183	+	0.242373i	$0.922074\pi$
$30$		0			0
$31$	−1.75191	+	1.75191i	−0.314652	+	0.314652i	−0.846709	−	0.532057i	$-0.821419\pi$
$31$	−1.75191	+	1.75191i	−0.314652	+	0.314652i	0.532057	+	0.846709i	$0.321419\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	2.77512	+	2.77512i	0.475929	+	0.475929i
$35$	8.62491	−	7.62637i	1.45788	−	1.28909i
$36$		0			0
$37$	−3.40442	+	3.40442i	−0.559683	+	0.559683i	−0.929217	−	0.369534i	$-0.879517\pi$
$37$	−3.40442	+	3.40442i	−0.559683	+	0.559683i	0.369534	+	0.929217i	$0.379517\pi$
$38$		−	0.0486226i		−	0.00788762i
$39$		0			0
$40$	−1.48119	−	1.67513i	−0.234197	−	0.264861i
$41$	2.00378	+	2.00378i	0.312938	+	0.312938i	0.846047	−	0.533109i	$-0.178976\pi$
$41$	2.00378	+	2.00378i	0.312938	+	0.312938i	−0.533109	+	0.846047i	$0.678976\pi$
$42$		0			0
$43$	8.65410			1.31974			0.659869	−	0.751381i	$-0.270612\pi$
$43$	8.65410			1.31974			0.659869	+	0.751381i	$0.270612\pi$
$44$	−0.550376	−	0.550376i	−0.0829724	−	0.0829724i
$45$		0			0
$46$	3.71753	+	3.71753i	0.548119	+	0.548119i
$47$	−3.70662	−	3.70662i	−0.540666	−	0.540666i	0.383058	−	0.923724i	$-0.374871\pi$
$47$	−3.70662	−	3.70662i	−0.540666	−	0.540666i	−0.923724	+	0.383058i	$0.874871\pi$
$48$		0			0
$49$		−	19.5101i		−	2.78716i
$50$	−3.94178	+	3.07610i	−0.557452	+	0.435026i
$51$		0			0
$52$	2.52229	+	2.57644i	0.349778	+	0.357288i
$53$	7.17150			0.985082			0.492541	−	0.870289i	$-0.336068\pi$
$53$	7.17150			0.985082			0.492541	+	0.870289i	$0.336068\pi$
$54$		0			0
$55$	−1.30384	+	1.15289i	−0.175809	+	0.155455i
$56$	−5.14880			−0.688037
$57$		0			0
$58$	−1.84586	−	1.84586i	−0.242373	−	0.242373i
$59$	6.80629	−	6.80629i	0.886104	−	0.886104i	−0.108042	−	0.994146i	$-0.534458\pi$
$59$	6.80629	−	6.80629i	0.886104	−	0.886104i	0.994146	+	0.108042i	$0.0344582\pi$
$60$		0			0
$61$	10.8249			1.38598			0.692991	−	0.720946i	$-0.256293\pi$
$61$	10.8249			1.38598			0.692991	+	0.720946i	$0.256293\pi$
$62$		−	2.47757i		−	0.314652i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	6.09615	−	5.27607i	0.756134	−	0.654416i
$66$		0			0
$67$	−9.45160	−	9.45160i	−1.15470	−	1.15470i	−0.985599	−	0.169097i	$-0.945915\pi$
$67$	−9.45160	−	9.45160i	−1.15470	−	1.15470i	−0.169097	−	0.985599i	$-0.554085\pi$
$68$	−3.92461			−0.475929
$69$		0			0
$70$	−0.706074	+	11.4914i	−0.0843920	+	1.37348i
$71$	−7.43355	−	7.43355i	−0.882200	−	0.882200i	0.111558	−	0.993758i	$-0.464416\pi$
$71$	−7.43355	−	7.43355i	−0.882200	−	0.882200i	−0.993758	+	0.111558i	$0.964416\pi$
$72$		0			0
$73$	6.06238	−	6.06238i	0.709548	−	0.709548i	−0.256892	−	0.966440i	$-0.582699\pi$
$73$	6.06238	−	6.06238i	0.709548	−	0.709548i	0.966440	+	0.256892i	$0.0826986\pi$
$74$		−	4.81457i		−	0.559683i
$75$		0			0
$76$	0.0343813	+	0.0343813i	0.00394381	+	0.00394381i
$77$			4.00757i			0.456705i
$78$		0			0
$79$	−1.13946			−0.128200			−0.0640998	−	0.997943i	$-0.520418\pi$
$79$	−1.13946			−0.128200			−0.0640998	+	0.997943i	$0.520418\pi$
$80$	2.23186	+	0.137134i	0.249529	+	0.0153320i
$81$		0			0
$82$	−2.83378			−0.312938
$83$	6.10358	−	6.10358i	0.669955	−	0.669955i	−0.287751	−	0.957705i	$-0.592907\pi$
$83$	6.10358	−	6.10358i	0.669955	−	0.669955i	0.957705	+	0.287751i	$0.0929075\pi$
$84$		0			0
$85$	−0.538197	+	8.75918i	−0.0583757	+	0.950067i
$86$	−6.11937	+	6.11937i	−0.659869	+	0.659869i
$87$		0			0
$88$	0.778350			0.0829724
$89$	−5.69461	+	5.69461i	−0.603627	+	0.603627i	−0.941273	−	0.337646i	$-0.890369\pi$
$89$	−5.69461	+	5.69461i	−0.603627	+	0.603627i	0.337646	+	0.941273i	$0.390369\pi$
$90$		0			0
$91$	0.197167	−	18.5632i	0.0206687	−	1.94595i
$92$	−5.25738			−0.548119
$93$		0			0
$94$	5.24195			0.540666
$95$	0.0814492	−	0.0720195i	0.00835651	−	0.00738904i
$96$		0			0
$97$	−0.250273	−	0.250273i	−0.0254113	−	0.0254113i	0.694287	−	0.719698i	$-0.255720\pi$
$97$	−0.250273	−	0.250273i	−0.0254113	−	0.0254113i	−0.719698	+	0.694287i	$0.755720\pi$
$98$	13.7957	+	13.7957i	1.39358	+	1.39358i
$99$		0			0
$100$	0.612127	−	4.96239i	0.0612127	−	0.496239i
$101$	−11.5281			−1.14709			−0.573547	−	0.819173i	$-0.694433\pi$
$101$	−11.5281			−1.14709			−0.573547	+	0.819173i	$0.694433\pi$
$102$		0			0
$103$	−8.51648			−0.839154			−0.419577	−	0.907720i	$-0.637822\pi$
$103$	−8.51648			−0.839154			−0.419577	+	0.907720i	$0.637822\pi$
$104$	−3.60535	−	0.0382937i	−0.353533	−	0.00375501i
$105$		0			0
$106$	−5.07102	+	5.07102i	−0.492541	+	0.492541i
$107$	−6.03336			−0.583266			−0.291633	−	0.956530i	$-0.594199\pi$
$107$	−6.03336			−0.583266			−0.291633	+	0.956530i	$0.594199\pi$
$108$		0			0
$109$	10.1500	−	10.1500i	0.972191	−	0.972191i	−0.0274323	−	0.999624i	$-0.508733\pi$
$109$	10.1500	−	10.1500i	0.972191	−	0.972191i	0.999624	+	0.0274323i	$0.00873306\pi$
$110$	0.106738	−	1.73717i	0.0101771	−	0.165632i
$111$		0			0
$112$	3.64075	−	3.64075i	0.344018	−	0.344018i
$113$	−4.19034			−0.394194			−0.197097	−	0.980384i	$-0.563151\pi$
$113$	−4.19034			−0.394194			−0.197097	+	0.980384i	$0.563151\pi$
$114$		0			0
$115$	−0.720964	+	11.7337i	−0.0672303	+	1.09418i
$116$	2.61043			0.242373
$117$		0			0
$118$			9.62555i			0.886104i
$119$	14.2885	+	14.2885i	1.30983	+	1.30983i
$120$		0			0
$121$			10.3942i			0.944925i
$122$	−7.65433	+	7.65433i	−0.692991	+	0.692991i
$123$		0			0
$124$	1.75191	+	1.75191i	0.157326	+	0.157326i
$125$	−10.9914	−	2.04669i	−0.983101	−	0.183062i
$126$		0			0
$127$	10.5948			0.940138			0.470069	−	0.882630i	$-0.344229\pi$
$127$	10.5948			0.940138			0.470069	+	0.882630i	$0.344229\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−0.579881	+	8.04138i	−0.0508590	+	0.705275i
$131$		−	17.6938i		−	1.54591i	−0.634461	−	0.772955i	$-0.718778\pi$
$131$		−	17.6938i		−	1.54591i	0.634461	−	0.772955i	$-0.281222\pi$
$132$		0			0
$133$		−	0.250348i		−	0.0217079i
$134$	13.3666			1.15470
$135$		0			0
$136$	2.77512	−	2.77512i	0.237965	−	0.237965i
$137$	5.98471	+	5.98471i	0.511308	+	0.511308i	0.914927	−	0.403619i	$-0.132248\pi$
$137$	5.98471	+	5.98471i	0.511308	+	0.511308i	−0.403619	+	0.914927i	$0.632248\pi$
$138$		0			0
$139$	−5.33438			−0.452456			−0.226228	−	0.974074i	$-0.572640\pi$
$139$	−5.33438			−0.452456			−0.226228	+	0.974074i	$0.572640\pi$
$140$	−7.62637	−	8.62491i	−0.644546	−	0.728938i
$141$		0			0
$142$	10.5126			0.882200
$143$	−0.0298059	+	2.80622i	−0.00249250	+	0.234668i
$144$		0			0
$145$	0.357979	−	5.82612i	0.0297285	−	0.483833i
$146$			8.57350i			0.709548i
$147$		0			0
$148$	3.40442	+	3.40442i	0.279841	+	0.279841i
$149$	4.85113	+	4.85113i	0.397420	+	0.397420i	0.877322	−	0.479902i	$-0.159328\pi$
$149$	4.85113	+	4.85113i	0.397420	+	0.397420i	−0.479902	+	0.877322i	$0.659328\pi$
$150$		0			0
$151$	11.1353	+	11.1353i	0.906174	+	0.906174i	0.995961	−	0.0897866i	$-0.0286185\pi$
$151$	11.1353	+	11.1353i	0.906174	+	0.906174i	−0.0897866	+	0.995961i	$0.528618\pi$
$152$	−0.0486226			−0.00394381
$153$		0			0
$154$	−2.83378	−	2.83378i	−0.228352	−	0.228352i
$155$	4.15026	−	3.66977i	0.333357	−	0.294763i
$156$		0			0
$157$		−	16.1859i		−	1.29177i	−0.763434	−	0.645886i	$-0.776488\pi$
$157$		−	16.1859i		−	1.29177i	0.763434	−	0.645886i	$-0.223512\pi$
$158$	0.805722	−	0.805722i	0.0640998	−	0.0640998i
$159$		0			0
$160$	−1.67513	+	1.48119i	−0.132431	+	0.117099i
$161$	19.1408	+	19.1408i	1.50851	+	1.50851i
$162$		0			0
$163$	−12.1521	+	12.1521i	−0.951828	+	0.951828i	−0.998892	−	0.0470643i	$-0.985013\pi$
$163$	−12.1521	+	12.1521i	−0.951828	+	0.951828i	0.0470643	+	0.998892i	$0.485013\pi$
$164$	2.00378	−	2.00378i	0.156469	−	0.156469i
$165$		0			0
$166$			8.63176i			0.669955i
$167$	8.78603	+	8.78603i	0.679883	+	0.679883i	0.959974	−	0.280090i	$-0.0903644\pi$
$167$	8.78603	+	8.78603i	0.679883	+	0.679883i	−0.280090	+	0.959974i	$0.590364\pi$
$168$		0			0
$169$	0.276124	−	12.9971i	0.0212403	−	0.999774i
$170$	−5.81311	−	6.57424i	−0.445845	−	0.504221i
$171$		0			0
$172$		−	8.65410i		−	0.659869i
$173$		−	24.1950i		−	1.83951i	−0.392488	−	0.919757i	$-0.628386\pi$
$173$		−	24.1950i		−	1.83951i	0.392488	−	0.919757i	$-0.371614\pi$
$174$		0			0
$175$	−20.2954	+	15.8382i	−1.53419	+	1.19726i
$176$	−0.550376	+	0.550376i	−0.0414862	+	0.0414862i
$177$		0			0
$178$		−	8.05339i		−	0.603627i
$179$	5.43792			0.406449			0.203225	−	0.979132i	$-0.434858\pi$
$179$	5.43792			0.406449			0.203225	+	0.979132i	$0.434858\pi$
$180$		0			0
$181$			21.7408i			1.61598i	0.589194	+	0.807992i	$0.299445\pi$
$181$			21.7408i			1.61598i	−0.589194	+	0.807992i	$0.700555\pi$
$182$	12.9868	+	13.2656i	0.962642	+	0.983311i
$183$		0			0
$184$	3.71753	−	3.71753i	0.274060	−	0.274060i
$185$	8.06504	−	7.13132i	0.592954	−	0.524305i
$186$		0			0
$187$	−2.16001	−	2.16001i	−0.157956	−	0.157956i
$188$	−3.70662	+	3.70662i	−0.270333	+	0.270333i
$189$		0			0
$190$	−0.00666780	+	0.108519i	−0.000483733	+	0.00787277i
$191$			5.73164i			0.414727i	0.978264	+	0.207364i	$0.0664883\pi$
$191$			5.73164i			0.414727i	−0.978264	+	0.207364i	$0.933512\pi$
$192$		0			0
$193$	7.41222	−	7.41222i	0.533544	−	0.533544i	−0.388082	−	0.921625i	$-0.626862\pi$
$193$	7.41222	−	7.41222i	0.533544	−	0.533544i	0.921625	+	0.388082i	$0.126862\pi$
$194$	0.353939			0.0254113
$195$		0			0
$196$	−19.5101			−1.39358
$197$	−2.70779	+	2.70779i	−0.192922	+	0.192922i	−0.796957	−	0.604036i	$-0.793558\pi$
$197$	−2.70779	+	2.70779i	−0.192922	+	0.192922i	0.604036	+	0.796957i	$0.293558\pi$
$198$		0			0
$199$		−	1.40527i		−	0.0996172i	−0.998759	−	0.0498086i	$-0.984139\pi$
$199$		−	1.40527i		−	0.0996172i	0.998759	−	0.0498086i	$-0.0158611\pi$
$200$	3.07610	+	3.94178i	0.217513	+	0.278726i
$201$		0			0
$202$	8.15163	−	8.15163i	0.573547	−	0.573547i
$203$	−9.50394	−	9.50394i	−0.667046	−	0.667046i
$204$		0			0
$205$	−4.19737	−	4.74695i	−0.293157	−	0.331541i
$206$	6.02206	−	6.02206i	0.419577	−	0.419577i
$207$		0			0
$208$	2.57644	−	2.52229i	0.178644	−	0.174889i
$209$			0.0378454i			0.00261782i
$210$		0			0
$211$	−15.8923			−1.09407			−0.547034	−	0.837110i	$-0.684243\pi$
$211$	−15.8923			−1.09407			−0.547034	+	0.837110i	$0.684243\pi$
$212$		−	7.17150i		−	0.492541i
$213$		0			0
$214$	4.26623	−	4.26623i	0.291633	−	0.291633i
$215$	−19.3147	−	1.18677i	−1.31725	−	0.0809370i
$216$		0			0
$217$		−	12.7565i		−	0.865969i
$218$			14.3542i			0.972191i
$219$		0			0
$220$	1.15289	+	1.30384i	0.0777277	+	0.0879047i
$221$	9.89900	+	10.1115i	0.665879	+	0.680176i
$222$		0			0
$223$	−9.11780	−	9.11780i	−0.610573	−	0.610573i	0.332522	−	0.943095i	$-0.392100\pi$
$223$	−9.11780	−	9.11780i	−0.610573	−	0.610573i	−0.943095	+	0.332522i	$0.892100\pi$
$224$			5.14880i			0.344018i
$225$		0			0
$226$	2.96302	−	2.96302i	0.197097	−	0.197097i
$227$	−19.2800	+	19.2800i	−1.27966	+	1.27966i	−0.338802	+	0.940858i	$0.610022\pi$
$227$	−19.2800	+	19.2800i	−1.27966	+	1.27966i	−0.940858	+	0.338802i	$0.889978\pi$
$228$		0			0
$229$	−0.641799	−	0.641799i	−0.0424113	−	0.0424113i	0.685583	−	0.727994i	$-0.259547\pi$
$229$	−0.641799	−	0.641799i	−0.0424113	−	0.0424113i	−0.727994	+	0.685583i	$0.759547\pi$
$230$	−7.78720	−	8.80679i	−0.513473	−	0.580703i
$231$		0			0
$232$	−1.84586	+	1.84586i	−0.121186	+	0.121186i
$233$			21.1428i			1.38511i	0.721363	+	0.692557i	$0.243516\pi$
$233$			21.1428i			1.38511i	−0.721363	+	0.692557i	$0.756484\pi$
$234$		0			0
$235$	7.76435	+	8.78095i	0.506490	+	0.572806i
$236$	−6.80629	−	6.80629i	−0.443052	−	0.443052i
$237$		0			0
$238$	−20.2070			−1.30983
$239$	10.7555	+	10.7555i	0.695718	+	0.695718i	0.963484	−	0.267766i	$-0.0862853\pi$
$239$	10.7555	+	10.7555i	0.695718	+	0.695718i	−0.267766	+	0.963484i	$0.586285\pi$
$240$		0			0
$241$	−3.91857	−	3.91857i	−0.252417	−	0.252417i	0.569544	−	0.821961i	$-0.307120\pi$
$241$	−3.91857	−	3.91857i	−0.252417	−	0.252417i	−0.821961	+	0.569544i	$0.807120\pi$
$242$	−7.34979	−	7.34979i	−0.472462	−	0.472462i
$243$		0			0
$244$		−	10.8249i		−	0.692991i
$245$	−2.67550	+	43.5438i	−0.170931	+	2.78191i
$246$		0			0
$247$	0.00186194	−	0.175301i	0.000118472	−	0.0111542i
$248$	−2.47757			−0.157326
$249$		0			0
$250$	9.21933	−	6.32487i	0.583082	−	0.400020i
$251$	−10.5128			−0.663565			−0.331783	−	0.943356i	$-0.607650\pi$
$251$	−10.5128			−0.663565			−0.331783	+	0.943356i	$0.607650\pi$
$252$		0			0
$253$	−2.89354	−	2.89354i	−0.181915	−	0.181915i
$254$	−7.49167	+	7.49167i	−0.470069	+	0.470069i
$255$		0			0
$256$	1.00000			0.0625000
$257$			16.1542i			1.00767i	0.863799	+	0.503836i	$0.168079\pi$
$257$			16.1542i			1.00767i	−0.863799	+	0.503836i	$0.831921\pi$
$258$		0			0
$259$		−	24.7893i		−	1.54033i
$260$	−5.27607	−	6.09615i	−0.327208	−	0.378067i
$261$		0			0
$262$	12.5114	+	12.5114i	0.772955	+	0.772955i
$263$	−26.6515			−1.64340			−0.821702	−	0.569918i	$-0.806975\pi$
$263$	−26.6515			−1.64340			−0.821702	+	0.569918i	$0.806975\pi$
$264$		0			0
$265$	−16.0058	−	0.983456i	−0.983227	−	0.0604132i
$266$	0.177023	+	0.177023i	0.0108540	+	0.0108540i
$267$		0			0
$268$	−9.45160	+	9.45160i	−0.577348	+	0.577348i
$269$		−	14.5851i		−	0.889271i	−0.895712	−	0.444635i	$-0.853333\pi$
$269$		−	14.5851i		−	0.889271i	0.895712	−	0.444635i	$-0.146667\pi$
$270$		0			0
$271$	−22.3588	−	22.3588i	−1.35820	−	1.35820i	−0.876134	−	0.482067i	$-0.839886\pi$
$271$	−22.3588	−	22.3588i	−1.35820	−	1.35820i	−0.482067	−	0.876134i	$-0.660114\pi$
$272$			3.92461i			0.237965i
$273$		0			0
$274$	−8.46366			−0.511308
$275$	3.06808	−	2.39428i	0.185012	−	0.144381i
$276$		0			0
$277$	−8.71213			−0.523461			−0.261731	−	0.965141i	$-0.584293\pi$
$277$	−8.71213			−0.523461			−0.261731	+	0.965141i	$0.584293\pi$
$278$	3.77198	−	3.77198i	0.226228	−	0.226228i
$279$		0			0
$280$	11.4914	+	0.706074i	0.686742	+	0.0421960i
$281$	8.78056	−	8.78056i	0.523805	−	0.523805i	−0.394914	−	0.918718i	$-0.629226\pi$
$281$	8.78056	−	8.78056i	0.523805	−	0.523805i	0.918718	+	0.394914i	$0.129226\pi$
$282$		0			0
$283$	4.42996			0.263334			0.131667	−	0.991294i	$-0.457967\pi$
$283$	4.42996			0.263334			0.131667	+	0.991294i	$0.457967\pi$
$284$	−7.43355	+	7.43355i	−0.441100	+	0.441100i
$285$		0			0
$286$	−1.96322	−	2.00537i	−0.116088	−	0.118580i
$287$	−14.5905			−0.861253
$288$		0			0
$289$	1.59742			0.0939659
$290$	3.86656	+	4.37282i	0.227052	+	0.256781i
$291$		0			0
$292$	−6.06238	−	6.06238i	−0.354774	−	0.354774i
$293$	−21.7172	−	21.7172i	−1.26873	−	1.26873i	−0.946743	−	0.321991i	$-0.895648\pi$
$293$	−21.7172	−	21.7172i	−1.26873	−	1.26873i	−0.321991	−	0.946743i	$-0.604352\pi$
$294$		0			0
$295$	−16.1241	+	14.2573i	−0.938779	+	0.830093i
$296$	−4.81457			−0.279841
$297$		0			0
$298$	−6.86054			−0.397420
$299$	13.2606	+	13.5453i	0.766881	+	0.783347i
$300$		0			0
$301$	−31.5074	+	31.5074i	−1.81606	+	1.81606i
$302$	−15.7476			−0.906174
$303$		0			0
$304$	0.0343813	−	0.0343813i	0.00197191	−	0.00197191i
$305$	−24.1596	−	1.48446i	−1.38337	−	0.0849997i
$306$		0			0
$307$	−0.222982	+	0.222982i	−0.0127263	+	0.0127263i	−0.713441	−	0.700715i	$-0.752864\pi$
$307$	−0.222982	+	0.222982i	−0.0127263	+	0.0127263i	0.700715	+	0.713441i	$0.252864\pi$
$308$	4.00757			0.228352
$309$		0			0
$310$	−0.339759	+	5.52959i	−0.0192970	+	0.314060i
$311$	−7.31599			−0.414852			−0.207426	−	0.978251i	$-0.566509\pi$
$311$	−7.31599			−0.414852			−0.207426	+	0.978251i	$0.566509\pi$
$312$		0			0
$313$		−	11.8892i		−	0.672016i	−0.941859	−	0.336008i	$-0.890923\pi$
$313$		−	11.8892i		−	0.672016i	0.941859	−	0.336008i	$-0.109077\pi$
$314$	11.4451	+	11.4451i	0.645886	+	0.645886i
$315$		0			0
$316$			1.13946i			0.0640998i
$317$	23.9626	−	23.9626i	1.34587	−	1.34587i	0.455784	−	0.890090i	$-0.349359\pi$
$317$	23.9626	−	23.9626i	1.34587	−	1.34587i	0.890090	−	0.455784i	$-0.150641\pi$
$318$		0			0
$319$	1.43672	+	1.43672i	0.0804410	+	0.0804410i
$320$	0.137134	−	2.23186i	0.00766602	−	0.124765i
$321$		0			0
$322$	−27.0692			−1.50851
$323$	0.134933	+	0.134933i	0.00750790	+	0.00750790i
$324$		0			0
$325$	−14.3293	+	10.9395i	−0.794845	+	0.606812i
$326$		−	17.1857i		−	0.951828i
$327$		0			0
$328$			2.83378i			0.156469i
$329$	26.9897			1.48799
$330$		0			0
$331$	20.2559	−	20.2559i	1.11337	−	1.11337i	0.120674	−	0.992692i	$-0.461494\pi$
$331$	20.2559	−	20.2559i	1.11337	−	1.11337i	0.992692	−	0.120674i	$-0.0385057\pi$
$332$	−6.10358	−	6.10358i	−0.334977	−	0.334977i
$333$		0			0
$334$	−12.4253			−0.679883
$335$	19.7985	+	22.3908i	1.08171	+	1.22334i
$336$		0			0
$337$	18.3122			0.997531			0.498765	−	0.866737i	$-0.333787\pi$
$337$	18.3122			0.997531			0.498765	+	0.866737i	$0.333787\pi$
$338$	8.99506	+	9.38556i	0.489267	+	0.510507i
$339$		0			0
$340$	8.75918	+	0.538197i	0.475033	+	0.0291878i
$341$			1.92842i			0.104430i
$342$		0			0
$343$	45.5462	+	45.5462i	2.45926	+	2.45926i
$344$	6.11937	+	6.11937i	0.329934	+	0.329934i
$345$		0			0
$346$	17.1085	+	17.1085i	0.919757	+	0.919757i
$347$	−19.3467			−1.03859			−0.519293	−	0.854596i	$-0.673805\pi$
$347$	−19.3467			−1.03859			−0.519293	+	0.854596i	$0.673805\pi$
$348$		0			0
$349$	12.5378	+	12.5378i	0.671136	+	0.671136i	0.957978	−	0.286842i	$-0.0926055\pi$
$349$	12.5378	+	12.5378i	0.671136	+	0.671136i	−0.286842	+	0.957978i	$0.592606\pi$
$350$	3.15172	−	25.5503i	0.168466	−	1.36572i
$351$		0			0
$352$		−	0.778350i		−	0.0414862i
$353$	18.1171	−	18.1171i	0.964275	−	0.964275i	−0.0351088	−	0.999383i	$-0.511178\pi$
$353$	18.1171	−	18.1171i	0.964275	−	0.964275i	0.999383	+	0.0351088i	$0.0111778\pi$
$354$		0			0
$355$	15.5712	+	17.6100i	0.826436	+	0.934643i
$356$	5.69461	+	5.69461i	0.301814	+	0.301814i
$357$		0			0
$358$	−3.84519	+	3.84519i	−0.203225	+	0.203225i
$359$	19.1639	−	19.1639i	1.01143	−	1.01143i	0.0114978	−	0.999934i	$-0.496340\pi$
$359$	19.1639	−	19.1639i	1.01143	−	1.01143i	0.999934	−	0.0114978i	$-0.00365993\pi$
$360$		0			0
$361$			18.9976i			0.999876i
$362$	−15.3731	−	15.3731i	−0.807992	−	0.807992i
$363$		0			0
$364$	−18.5632	−	0.197167i	−0.972976	−	0.0103343i
$365$	−14.3617	+	12.6990i	−0.751727	+	0.664697i
$366$		0			0
$367$			24.3950i			1.27341i	0.771108	+	0.636704i	$0.219703\pi$
$367$			24.3950i			1.27341i	−0.771108	+	0.636704i	$0.780297\pi$
$368$			5.25738i			0.274060i
$369$		0			0
$370$	−0.660241	+	10.7454i	−0.0343243	+	0.558629i
$371$	−26.1096	+	26.1096i	−1.35555	+	1.35555i
$372$		0			0
$373$		−	34.3966i		−	1.78099i	−0.454994	−	0.890495i	$-0.650359\pi$
$373$		−	34.3966i		−	1.78099i	0.454994	−	0.890495i	$-0.349641\pi$
$374$	3.05472			0.157956
$375$		0			0
$376$		−	5.24195i		−	0.270333i
$377$	−6.58427	−	6.72564i	−0.339107	−	0.346388i
$378$		0			0
$379$	13.6574	−	13.6574i	0.701535	−	0.701535i	−0.263205	−	0.964740i	$-0.584780\pi$
$379$	13.6574	−	13.6574i	0.701535	−	0.701535i	0.964740	+	0.263205i	$0.0847797\pi$
$380$	−0.0720195	−	0.0814492i	−0.00369452	−	0.00417825i
$381$		0			0
$382$	−4.05288	−	4.05288i	−0.207364	−	0.207364i
$383$	8.78211	−	8.78211i	0.448745	−	0.448745i	−0.446192	−	0.894937i	$-0.647220\pi$
$383$	8.78211	−	8.78211i	0.448745	−	0.448745i	0.894937	+	0.446192i	$0.147220\pi$
$384$		0			0
$385$	0.549573	−	8.94432i	0.0280088	−	0.455845i
$386$			10.4825i			0.533544i
$387$		0			0
$388$	−0.250273	+	0.250273i	−0.0127057	+	0.0127057i
$389$	7.51513			0.381032			0.190516	−	0.981684i	$-0.438984\pi$
$389$	7.51513			0.381032			0.190516	+	0.981684i	$0.438984\pi$
$390$		0			0
$391$	−20.6332			−1.04346
$392$	13.7957	−	13.7957i	0.696790	−	0.696790i
$393$		0			0
$394$		−	3.82939i		−	0.192922i
$395$	2.54312	+	0.156259i	0.127958	+	0.00786224i
$396$		0			0
$397$	−12.6929	+	12.6929i	−0.637037	+	0.637037i	−0.949824	−	0.312786i	$-0.898738\pi$
$397$	−12.6929	+	12.6929i	−0.637037	+	0.637037i	0.312786	+	0.949824i	$0.398738\pi$
$398$	0.993678	+	0.993678i	0.0498086	+	0.0498086i
$399$		0			0
$400$	−4.96239	−	0.612127i	−0.248119	−	0.0306063i
$401$	18.0961	−	18.0961i	0.903674	−	0.903674i	−0.0920776	−	0.995752i	$-0.529351\pi$
$401$	18.0961	−	18.0961i	0.903674	−	0.903674i	0.995752	+	0.0920776i	$0.0293508\pi$
$402$		0			0
$403$	0.0948755	−	8.93251i	0.00472608	−	0.444960i
$404$			11.5281i			0.573547i
$405$		0			0
$406$	13.4406			0.667046
$407$			3.74742i			0.185753i
$408$		0			0
$409$	−5.08597	+	5.08597i	−0.251485	+	0.251485i	−0.821579	−	0.570094i	$-0.806907\pi$
$409$	−5.08597	+	5.08597i	−0.251485	+	0.251485i	0.570094	+	0.821579i	$0.306907\pi$
$410$	6.32459	+	0.388607i	0.312349	+	0.0191919i
$411$		0			0
$412$			8.51648i			0.419577i
$413$			49.5600i			2.43869i
$414$		0			0
$415$	−14.4593	+	12.7853i	−0.709781	+	0.627606i
$416$	−0.0382937	+	3.60535i	−0.00187750	+	0.176767i
$417$		0			0
$418$	−0.0267607	−	0.0267607i	−0.00130891	−	0.00130891i
$419$		−	29.1668i		−	1.42489i	−0.701727	−	0.712446i	$-0.747587\pi$
$419$		−	29.1668i		−	1.42489i	0.701727	−	0.712446i	$-0.252413\pi$
$420$		0			0
$421$	6.59073	−	6.59073i	0.321213	−	0.321213i	−0.528020	−	0.849232i	$-0.677065\pi$
$421$	6.59073	−	6.59073i	0.321213	−	0.321213i	0.849232	+	0.528020i	$0.177065\pi$
$422$	11.2375	−	11.2375i	0.547034	−	0.547034i
$423$		0			0
$424$	5.07102	+	5.07102i	0.246270	+	0.246270i
$425$	2.40236	−	19.4755i	0.116532	−	0.944698i
$426$		0			0
$427$	−39.4106	+	39.4106i	−1.90721	+	1.90721i
$428$			6.03336i			0.291633i
$429$		0			0
$430$	14.4967	−	12.8184i	0.699095	−	0.618158i
$431$	−29.2398	−	29.2398i	−1.40843	−	1.40843i	−0.768088	−	0.640344i	$-0.778792\pi$
$431$	−29.2398	−	29.2398i	−1.40843	−	1.40843i	−0.640344	−	0.768088i	$-0.721208\pi$
$432$		0			0
$433$	16.1132			0.774353			0.387176	−	0.922006i	$-0.373450\pi$
$433$	16.1132			0.774353			0.387176	+	0.922006i	$0.373450\pi$
$434$	9.02022	+	9.02022i	0.432984	+	0.432984i
$435$		0			0
$436$	−10.1500	−	10.1500i	−0.486096	−	0.486096i
$437$	0.180756	+	0.180756i	0.00864672	+	0.00864672i
$438$		0			0
$439$		−	27.6716i		−	1.32069i	−0.750962	−	0.660346i	$-0.770410\pi$
$439$		−	27.6716i		−	1.32069i	0.750962	−	0.660346i	$-0.229590\pi$
$440$	−1.73717	−	0.106738i	−0.0828162	−	0.00508854i
$441$		0			0
$442$	−14.1496	−	0.150288i	−0.673027	−	0.00714847i
$443$	−11.2000			−0.532126			−0.266063	−	0.963956i	$-0.585723\pi$
$443$	−11.2000			−0.532126			−0.266063	+	0.963956i	$0.585723\pi$
$444$		0			0
$445$	13.4905	−	11.9286i	0.639510	−	0.565471i
$446$	12.8945			0.610573
$447$		0			0
$448$	−3.64075	−	3.64075i	−0.172009	−	0.172009i
$449$	−29.0434	+	29.0434i	−1.37064	+	1.37064i	−0.511157	+	0.859487i	$0.670783\pi$
$449$	−29.0434	+	29.0434i	−1.37064	+	1.37064i	−0.859487	+	0.511157i	$0.829217\pi$
$450$		0			0
$451$	2.20567			0.103861
$452$			4.19034i			0.197097i
$453$		0			0
$454$		−	27.2661i		−	1.27966i
$455$	−2.98569	+	41.4034i	−0.139971	+	1.94102i
$456$		0			0
$457$	−7.84694	−	7.84694i	−0.367064	−	0.367064i	0.499341	−	0.866405i	$-0.333575\pi$
$457$	−7.84694	−	7.84694i	−0.367064	−	0.367064i	−0.866405	+	0.499341i	$0.833575\pi$
$458$	0.907641			0.0424113
$459$		0			0
$460$	11.7337	+	0.720964i	0.547088	+	0.0336151i
$461$	−12.0214	−	12.0214i	−0.559890	−	0.559890i	0.369386	−	0.929276i	$-0.379568\pi$
$461$	−12.0214	−	12.0214i	−0.559890	−	0.559890i	−0.929276	+	0.369386i	$0.879568\pi$
$462$		0			0
$463$	15.7642	−	15.7642i	0.732627	−	0.732627i	−0.238513	−	0.971139i	$-0.576660\pi$
$463$	15.7642	−	15.7642i	0.732627	−	0.732627i	0.971139	+	0.238513i	$0.0766599\pi$
$464$		−	2.61043i		−	0.121186i
$465$		0			0
$466$	−14.9502	−	14.9502i	−0.692557	−	0.692557i
$467$		−	18.8621i		−	0.872832i	−0.899745	−	0.436416i	$-0.856248\pi$
$467$		−	18.8621i		−	0.872832i	0.899745	−	0.436416i	$-0.143752\pi$
$468$		0			0
$469$	68.8218			3.17790
$470$	−11.6993	−	0.718849i	−0.539648	−	0.0331580i
$471$		0			0
$472$	9.62555			0.443052
$473$	4.76301	−	4.76301i	0.219004	−	0.219004i
$474$		0			0
$475$	−0.191659	+	0.149568i	−0.00879393	+	0.00686264i
$476$	14.2885	−	14.2885i	0.654914	−	0.654914i
$477$		0			0
$478$	−15.2106			−0.695718
$479$	−5.19594	+	5.19594i	−0.237408	+	0.237408i	−0.815776	−	0.578368i	$-0.803690\pi$
$479$	−5.19594	+	5.19594i	−0.237408	+	0.237408i	0.578368	+	0.815776i	$0.303690\pi$
$480$		0			0
$481$	0.184368	−	17.3582i	0.00840645	−	0.791466i
$482$	5.54169			0.252417
$483$		0			0
$484$	10.3942			0.472462
$485$	0.524253	+	0.592894i	0.0238051	+	0.0269219i
$486$		0			0
$487$	1.60126	+	1.60126i	0.0725601	+	0.0725601i	0.742455	−	0.669895i	$-0.233661\pi$
$487$	1.60126	+	1.60126i	0.0725601	+	0.0725601i	−0.669895	+	0.742455i	$0.733661\pi$
$488$	7.65433	+	7.65433i	0.346495	+	0.346495i
$489$		0			0
$490$	−28.8983	−	32.6820i	−1.30549	−	1.47642i
$491$	−17.5496			−0.792003			−0.396001	−	0.918250i	$-0.629602\pi$
$491$	−17.5496			−0.792003			−0.396001	+	0.918250i	$0.629602\pi$
$492$		0			0
$493$	10.2449			0.461409
$494$	0.122640	+	0.125273i	0.00551784	+	0.00563631i
$495$		0			0
$496$	1.75191	−	1.75191i	0.0786630	−	0.0786630i
$497$	54.1274			2.42795
$498$		0			0
$499$	−16.6757	+	16.6757i	−0.746507	+	0.746507i	−0.973821	−	0.227314i	$-0.927006\pi$
$499$	−16.6757	+	16.6757i	−0.746507	+	0.746507i	0.227314	+	0.973821i	$0.427006\pi$
$500$	−2.04669	+	10.9914i	−0.0915309	+	0.491551i
$501$		0			0
$502$	7.43371	−	7.43371i	0.331783	−	0.331783i
$503$	−0.137436			−0.00612796			−0.00306398	−	0.999995i	$-0.500975\pi$
$503$	−0.137436			−0.00612796			−0.00306398	+	0.999995i	$0.500975\pi$
$504$		0			0
$505$	25.7292	+	1.58090i	1.14493	+	0.0703491i
$506$	4.09208			0.181915
$507$		0			0
$508$		−	10.5948i		−	0.470069i
$509$	−30.0672	−	30.0672i	−1.33271	−	1.33271i	−0.902940	−	0.429767i	$-0.858596\pi$
$509$	−30.0672	−	30.0672i	−1.33271	−	1.33271i	−0.429767	−	0.902940i	$-0.641404\pi$
$510$		0			0
$511$			44.1432i			1.95278i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−11.4228	−	11.4228i	−0.503836	−	0.503836i
$515$	19.0076	+	1.16790i	0.837575	+	0.0514638i
$516$		0			0
$517$	−4.08007			−0.179441
$518$	17.5287	+	17.5287i	0.770165	+	0.770165i
$519$		0			0
$520$	8.04138	+	0.579881i	0.352638	+	0.0254295i
$521$			2.76003i			0.120919i	0.998171	+	0.0604597i	$0.0192567\pi$
$521$			2.76003i			0.120919i	−0.998171	+	0.0604597i	$0.980743\pi$
$522$		0			0
$523$		−	10.3526i		−	0.452688i	−0.974047	−	0.226344i	$-0.927323\pi$
$523$		−	10.3526i		−	0.452688i	0.974047	−	0.226344i	$-0.0726774\pi$
$524$	−17.6938			−0.772955
$525$		0			0
$526$	18.8455	−	18.8455i	0.821702	−	0.821702i
$527$	6.87556	+	6.87556i	0.299504	+	0.299504i
$528$		0			0
$529$	−4.64001			−0.201739
$530$	12.0132	−	10.6224i	0.521820	−	0.461407i
$531$		0			0
$532$	−0.250348			−0.0108540
$533$	−10.2168	−	0.108516i	−0.442537	−	0.00470034i
$534$		0			0
$535$	13.4656	+	0.827377i	0.582169	+	0.0357706i
$536$		−	13.3666i		−	0.577348i
$537$		0			0
$538$	10.3132	+	10.3132i	0.444635	+	0.444635i
$539$	−10.7379	−	10.7379i	−0.462514	−	0.462514i
$540$		0			0
$541$	13.3717	+	13.3717i	0.574894	+	0.574894i	0.933492	−	0.358598i	$-0.116745\pi$
$541$	13.3717	+	13.3717i	0.574894	+	0.574894i	−0.358598	+	0.933492i	$0.616745\pi$
$542$	31.6201			1.35820
$543$		0			0
$544$	−2.77512	−	2.77512i	−0.118982	−	0.118982i
$545$	−24.0452	+	21.2614i	−1.02998	+	0.910739i
$546$		0			0
$547$		−	24.2164i		−	1.03542i	−0.855556	−	0.517710i	$-0.826785\pi$
$547$		−	24.2164i		−	1.03542i	0.855556	−	0.517710i	$-0.173215\pi$
$548$	5.98471	−	5.98471i	0.255654	−	0.255654i
$549$		0			0
$550$	−0.476449	+	3.86247i	−0.0203158	+	0.164696i
$551$	−0.0897502	−	0.0897502i	−0.00382349	−	0.00382349i
$552$		0			0
$553$	4.14850	−	4.14850i	0.176412	−	0.176412i
$554$	6.16041	−	6.16041i	0.261731	−	0.261731i
$555$		0			0
$556$			5.33438i			0.226228i
$557$	7.37044	+	7.37044i	0.312296	+	0.312296i	0.845798	−	0.533503i	$-0.179125\pi$
$557$	7.37044	+	7.37044i	0.312296	+	0.312296i	−0.533503	+	0.845798i	$0.679125\pi$
$558$		0			0
$559$	−22.2968	+	21.8281i	−0.943054	+	0.923232i
$560$	−8.62491	+	7.62637i	−0.364469	+	0.322273i
$561$		0			0
$562$			12.4176i			0.523805i
$563$		−	16.7767i		−	0.707052i	−0.935425	−	0.353526i	$-0.884983\pi$
$563$		−	16.7767i		−	0.707052i	0.935425	−	0.353526i	$-0.115017\pi$
$564$		0			0
$565$	9.35224	+	0.574637i	0.393452	+	0.0241752i
$566$	−3.13246	+	3.13246i	−0.131667	+	0.131667i
$567$		0			0
$568$		−	10.5126i		−	0.441100i
$569$	4.58148			0.192066			0.0960329	−	0.995378i	$-0.469385\pi$
$569$	4.58148			0.192066			0.0960329	+	0.995378i	$0.469385\pi$
$570$		0			0
$571$		−	5.28925i		−	0.221348i	−0.993857	−	0.110674i	$-0.964699\pi$
$571$		−	5.28925i		−	0.221348i	0.993857	−	0.110674i	$-0.0353010\pi$
$572$	2.80622	+	0.0298059i	0.117334	+	0.00124625i
$573$		0			0
$574$	10.3171	−	10.3171i	0.430626	−	0.430626i
$575$	3.21818	−	26.0891i	0.134207	−	1.08799i
$576$		0			0
$577$	30.7653	+	30.7653i	1.28078	+	1.28078i	0.940226	+	0.340551i	$0.110613\pi$
$577$	30.7653	+	30.7653i	1.28078	+	1.28078i	0.340551	+	0.940226i	$0.389387\pi$
$578$	−1.12955	+	1.12955i	−0.0469829	+	0.0469829i
$579$		0			0
$580$	−5.82612	−	0.357979i	−0.241916	−	0.0148643i
$581$			44.4432i			1.84381i
$582$		0			0
$583$	3.94703	−	3.94703i	0.163469	−	0.163469i
$584$	8.57350			0.354774
$585$		0			0
$586$	30.7128			1.26873
$587$	4.67233	−	4.67233i	0.192848	−	0.192848i	−0.604078	−	0.796925i	$-0.706458\pi$
$587$	4.67233	−	4.67233i	0.192848	−	0.192848i	0.796925	+	0.604078i	$0.206458\pi$
$588$		0			0
$589$		−	0.120466i		−	0.00496371i
$590$	1.31999	−	21.4829i	0.0543431	−	0.884436i
$591$		0			0
$592$	3.40442	−	3.40442i	0.139921	−	0.139921i
$593$	−16.5930	−	16.5930i	−0.681395	−	0.681395i	0.278920	−	0.960314i	$-0.410024\pi$
$593$	−16.5930	−	16.5930i	−0.681395	−	0.681395i	−0.960314	+	0.278920i	$0.910024\pi$
$594$		0			0
$595$	−29.9305	−	33.8494i	−1.22703	−	1.38769i
$596$	4.85113	−	4.85113i	0.198710	−	0.198710i
$597$		0			0
$598$	−18.9547	−	0.201325i	−0.775114	−	0.00823277i
$599$		−	5.00194i		−	0.204374i	−0.994765	−	0.102187i	$-0.967416\pi$
$599$		−	5.00194i		−	0.204374i	0.994765	−	0.102187i	$-0.0325840\pi$
$600$		0			0
$601$	40.9490			1.67034			0.835172	−	0.549988i	$-0.185368\pi$
$601$	40.9490			1.67034			0.835172	+	0.549988i	$0.185368\pi$
$602$		−	44.5582i		−	1.81606i
$603$		0			0
$604$	11.1353	−	11.1353i	0.453087	−	0.453087i
$605$	1.42539	−	23.1983i	0.0579505	−	0.943146i
$606$		0			0
$607$		−	10.8468i		−	0.440259i	−0.975471	−	0.220130i	$-0.929352\pi$
$607$		−	10.8468i		−	0.440259i	0.975471	−	0.220130i	$-0.0706481\pi$
$608$			0.0486226i			0.00197191i
$609$		0			0
$610$	18.1331	−	16.0337i	0.734186	−	0.649187i
$611$	18.8991	+	0.200734i	0.764574	+	0.00812082i
$612$		0			0
$613$	29.3943	+	29.3943i	1.18723	+	1.18723i	0.977831	+	0.209394i	$0.0671492\pi$
$613$	29.3943	+	29.3943i	1.18723	+	1.18723i	0.209394	+	0.977831i	$0.432851\pi$
$614$		−	0.315344i		−	0.0127263i
$615$		0			0
$616$	−2.83378	+	2.83378i	−0.114176	+	0.114176i
$617$	22.8438	−	22.8438i	0.919655	−	0.919655i	−0.0773490	−	0.997004i	$-0.524646\pi$
$617$	22.8438	−	22.8438i	0.919655	−	0.919655i	0.997004	+	0.0773490i	$0.0246456\pi$
$618$		0			0
$619$	−0.357348	−	0.357348i	−0.0143630	−	0.0143630i	0.699889	−	0.714252i	$-0.253233\pi$
$619$	−0.357348	−	0.357348i	−0.0143630	−	0.0143630i	−0.714252	+	0.699889i	$0.753233\pi$
$620$	−3.66977	−	4.15026i	−0.147381	−	0.166678i
$621$		0			0
$622$	5.17319	−	5.17319i	0.207426	−	0.207426i
$623$		−	41.4653i		−	1.66127i
$624$		0			0
$625$	24.2506	+	6.07522i	0.970024	+	0.243009i
$626$	8.40692	+	8.40692i	0.336008	+	0.336008i
$627$		0			0
$628$	−16.1859			−0.645886
$629$	13.3610	+	13.3610i	0.532739	+	0.532739i
$630$		0			0
$631$	8.71866	+	8.71866i	0.347084	+	0.347084i	0.859022	−	0.511938i	$-0.171072\pi$
$631$	8.71866	+	8.71866i	0.347084	+	0.347084i	−0.511938	+	0.859022i	$0.671072\pi$
$632$	−0.805722	−	0.805722i	−0.0320499	−	0.0320499i
$633$		0			0
$634$			33.8883i			1.34587i
$635$	−23.6461	−	1.45291i	−0.938368	−	0.0576569i
$636$		0			0
$637$	49.2101	+	50.2667i	1.94978	+	1.99164i
$638$	−2.03183			−0.0804410
$639$		0			0
$640$	1.48119	+	1.67513i	0.0585493	+	0.0662154i
$641$	−7.76922			−0.306866			−0.153433	−	0.988159i	$-0.549033\pi$
$641$	−7.76922			−0.306866			−0.153433	+	0.988159i	$0.549033\pi$
$642$		0			0
$643$	−19.4383	−	19.4383i	−0.766570	−	0.766570i	0.210931	−	0.977501i	$-0.432351\pi$
$643$	−19.4383	−	19.4383i	−0.766570	−	0.766570i	−0.977501	+	0.210931i	$0.932351\pi$
$644$	19.1408	−	19.1408i	0.754253	−	0.754253i
$645$		0			0
$646$	−0.190825			−0.00750790
$647$			41.2049i			1.61993i	0.586476	+	0.809967i	$0.300515\pi$
$647$			41.2049i			1.61993i	−0.586476	+	0.809967i	$0.699485\pi$
$648$		0			0
$649$		−	7.49205i		−	0.294089i
$650$	2.39696	−	17.8677i	0.0940165	−	0.700829i
$651$		0			0
$652$	12.1521	+	12.1521i	0.475914	+	0.475914i
$653$	19.6236			0.767932			0.383966	−	0.923347i	$-0.374558\pi$
$653$	19.6236			0.767932			0.383966	+	0.923347i	$0.374558\pi$
$654$		0			0
$655$	−2.42641	+	39.4900i	−0.0948078	+	1.54300i
$656$	−2.00378	−	2.00378i	−0.0782346	−	0.0782346i
$657$		0			0
$658$	−19.0846	+	19.0846i	−0.743996	+	0.743996i
$659$		−	23.2139i		−	0.904286i	−0.891945	−	0.452143i	$-0.850660\pi$
$659$		−	23.2139i		−	0.904286i	0.891945	−	0.452143i	$-0.149340\pi$
$660$		0			0
$661$	−18.6638	−	18.6638i	−0.725937	−	0.725937i	0.243871	−	0.969808i	$-0.421583\pi$
$661$	−18.6638	−	18.6638i	−0.725937	−	0.725937i	−0.969808	+	0.243871i	$0.921583\pi$
$662$			28.6462i			1.11337i
$663$		0			0
$664$	8.63176			0.334977
$665$	−0.0343312	+	0.558741i	−0.00133131	+	0.0216670i
$666$		0			0
$667$	13.7240			0.531397
$668$	8.78603	−	8.78603i	0.339942	−	0.339942i
$669$		0			0
$670$	−29.8323	−	1.83301i	−1.15252	−	0.0708154i
$671$	5.95775	−	5.95775i	0.229996	−	0.229996i
$672$		0			0
$673$	−5.34372			−0.205985			−0.102993	−	0.994682i	$-0.532842\pi$
$673$	−5.34372			−0.205985			−0.102993	+	0.994682i	$0.532842\pi$
$674$	−12.9487	+	12.9487i	−0.498765	+	0.498765i
$675$		0			0
$676$	−12.9971	−	0.276124i	−0.499887	−	0.0106202i
$677$	−0.745860			−0.0286657			−0.0143329	−	0.999897i	$-0.504562\pi$
$677$	−0.745860			−0.0286657			−0.0143329	+	0.999897i	$0.504562\pi$
$678$		0			0
$679$	1.82236			0.0699358
$680$	−6.57424	+	5.81311i	−0.252111	+	0.222923i
$681$		0			0
$682$	−1.36360	−	1.36360i	−0.0522148	−	0.0522148i
$683$	9.43828	+	9.43828i	0.361146	+	0.361146i	0.864235	−	0.503089i	$-0.167803\pi$
$683$	9.43828	+	9.43828i	0.361146	+	0.361146i	−0.503089	+	0.864235i	$0.667803\pi$
$684$		0			0
$685$	−12.5363	−	14.1777i	−0.478988	−	0.541704i
$686$	−64.4120			−2.45926
$687$		0			0
$688$	−8.65410			−0.329934
$689$	−18.4770	+	18.0886i	−0.703917	+	0.689121i
$690$		0			0
$691$	−24.6463	+	24.6463i	−0.937591	+	0.937591i	−0.998164	−	0.0605726i	$-0.980707\pi$
$691$	−24.6463	+	24.6463i	−0.937591	+	0.937591i	0.0605726	+	0.998164i	$0.480707\pi$
$692$	−24.1950			−0.919757
$693$		0			0
$694$	13.6802	−	13.6802i	0.519293	−	0.519293i
$695$	11.9056	+	0.731525i	0.451605	+	0.0277483i
$696$		0			0
$697$	7.86407	−	7.86407i	0.297873	−	0.297873i
$698$	−17.7312			−0.671136
$699$		0			0
$700$	15.8382	+	20.2954i	0.598628	+	0.767095i
$701$	31.1027			1.17473			0.587367	−	0.809321i	$-0.300165\pi$
$701$	31.1027			1.17473			0.587367	+	0.809321i	$0.300165\pi$
$702$		0			0
$703$		−	0.234097i		−	0.00882913i
$704$	0.550376	+	0.550376i	0.0207431	+	0.0207431i
$705$		0			0
$706$			25.6214i			0.964275i
$707$	41.9711	−	41.9711i	1.57849	−	1.57849i
$708$		0			0
$709$	−2.74683	−	2.74683i	−0.103159	−	0.103159i	0.653643	−	0.756803i	$-0.273240\pi$
$709$	−2.74683	−	2.74683i	−0.103159	−	0.103159i	−0.756803	+	0.653643i	$0.773240\pi$
$710$	−23.4627	−	1.44164i	−0.880540	−	0.0541037i
$711$		0			0
$712$	−8.05339			−0.301814
$713$	9.21044	+	9.21044i	0.344934	+	0.344934i
$714$		0			0
$715$	0.451351	−	6.25900i	0.0168796	−	0.234073i
$716$		−	5.43792i		−	0.203225i
$717$		0			0
$718$			27.1018i			1.01143i
$719$	−34.1555			−1.27379			−0.636893	−	0.770952i	$-0.719781\pi$
$719$	−34.1555			−1.27379			−0.636893	+	0.770952i	$0.719781\pi$
$720$		0			0
$721$	31.0064	−	31.0064i	1.15474	−	1.15474i
$722$	−13.4334	−	13.4334i	−0.499938	−	0.499938i
$723$		0			0
$724$	21.7408			0.807992
$725$	−1.59792	+	12.9540i	−0.0593451	+	0.481099i
$726$		0			0
$727$	43.2743			1.60495			0.802477	−	0.596684i	$-0.203515\pi$
$727$	43.2743			1.60495			0.802477	+	0.596684i	$0.203515\pi$
$728$	13.2656	−	12.9868i	0.491655	−	0.481321i
$729$		0			0
$730$	1.17572	−	19.1348i	0.0435152	−	0.708212i
$731$		−	33.9640i		−	1.25620i
$732$		0			0
$733$	−19.2236	−	19.2236i	−0.710039	−	0.710039i	0.256504	−	0.966543i	$-0.417429\pi$
$733$	−19.2236	−	19.2236i	−0.710039	−	0.710039i	−0.966543	+	0.256504i	$0.917429\pi$
$734$	−17.2499	−	17.2499i	−0.636704	−	0.636704i
$735$		0			0
$736$	−3.71753	−	3.71753i	−0.137030	−	0.137030i
$737$	−10.4039			−0.383232
$738$		0			0
$739$	−22.5897	−	22.5897i	−0.830977	−	0.830977i	0.156673	−	0.987650i	$-0.449923\pi$
$739$	−22.5897	−	22.5897i	−0.830977	−	0.830977i	−0.987650	+	0.156673i	$0.949923\pi$
$740$	−7.13132	−	8.06504i	−0.262152	−	0.296477i
$741$		0			0
$742$		−	36.9246i		−	1.35555i
$743$	−8.51811	+	8.51811i	−0.312499	+	0.312499i	−0.845877	−	0.533378i	$-0.820922\pi$
$743$	−8.51811	+	8.51811i	−0.312499	+	0.312499i	0.533378	+	0.845877i	$0.320922\pi$
$744$		0			0
$745$	−10.1618	−	11.4923i	−0.372299	−	0.421045i
$746$	24.3221	+	24.3221i	0.890495	+	0.890495i
$747$		0			0
$748$	−2.16001	+	2.16001i	−0.0789779	+	0.0789779i
$749$	21.9659	−	21.9659i	0.802618	−	0.802618i
$750$		0			0
$751$		−	10.4080i		−	0.379795i	−0.981804	−	0.189897i	$-0.939184\pi$
$751$		−	10.4080i		−	0.379795i	0.981804	−	0.189897i	$-0.0608155\pi$
$752$	3.70662	+	3.70662i	0.135166	+	0.135166i
$753$		0			0
$754$	9.41152	+	0.0999632i	0.342747	+	0.00364045i
$755$	−23.3253	−	26.3793i	−0.848895	−	0.960043i
$756$		0			0
$757$		−	27.2934i		−	0.991995i	−0.868324	−	0.495998i	$-0.834802\pi$
$757$		−	27.2934i		−	0.991995i	0.868324	−	0.495998i	$-0.165198\pi$
$758$			19.3145i			0.701535i
$759$		0			0
$760$	0.108519	+	0.00666780i	0.00393639	+	0.000241867i
$761$	−3.37998	+	3.37998i	−0.122524	+	0.122524i	−0.765710	−	0.643186i	$-0.777612\pi$
$761$	−3.37998	+	3.37998i	−0.122524	+	0.122524i	0.643186	+	0.765710i	$0.277612\pi$
$762$		0			0
$763$			73.9070i			2.67561i
$764$	5.73164			0.207364
$765$		0			0
$766$			12.4198i			0.448745i
$767$	−0.368598	+	34.7035i	−0.0133093	+	1.25307i
$768$		0			0
$769$	−27.6564	+	27.6564i	−0.997316	+	0.997316i	−0.999996	−	0.00268029i	$-0.999147\pi$
$769$	−27.6564	+	27.6564i	−0.997316	+	0.997316i	0.00268029	+	0.999996i	$0.499147\pi$
$770$	5.93598	+	6.71320i	0.213918	+	0.241927i
$771$		0			0
$772$	−7.41222	−	7.41222i	−0.266772	−	0.266772i
$773$	4.31423	−	4.31423i	0.155172	−	0.155172i	−0.625251	−	0.780423i	$-0.715004\pi$
$773$	4.31423	−	4.31423i	0.155172	−	0.155172i	0.780423	+	0.625251i	$0.215004\pi$
$774$		0			0
$775$	−9.76604	+	7.62126i	−0.350806	+	0.273764i
$776$		−	0.353939i		−	0.0127057i
$777$		0			0
$778$	−5.31400	+	5.31400i	−0.190516	+	0.190516i
$779$	−0.137786			−0.00493668
$780$		0			0
$781$	−8.18250			−0.292793
$782$	14.5898	−	14.5898i	0.521732	−	0.521732i
$783$		0			0
$784$			19.5101i			0.696790i
$785$	−2.21963	+	36.1245i	−0.0792220	+	1.28934i
$786$		0			0
$787$	−3.35404	+	3.35404i	−0.119558	+	0.119558i	−0.764355	−	0.644796i	$-0.776942\pi$
$787$	−3.35404	+	3.35404i	−0.119558	+	0.119558i	0.644796	+	0.764355i	$0.276942\pi$
$788$	2.70779	+	2.70779i	0.0964608	+	0.0964608i
$789$		0			0
$790$	−1.90875	+	1.68777i	−0.0679102	+	0.0600480i
$791$	15.2560	−	15.2560i	0.542440	−	0.542440i
$792$		0			0
$793$	−27.8897	+	27.3034i	−0.990391	+	0.969573i
$794$		−	17.9504i		−	0.637037i
$795$		0			0
$796$	−1.40527			−0.0498086
$797$		−	10.1658i		−	0.360092i	−0.983658	−	0.180046i	$-0.942375\pi$
$797$		−	10.1658i		−	0.360092i	0.983658	−	0.180046i	$-0.0576247\pi$
$798$		0			0
$799$	−14.5470	+	14.5470i	−0.514637	+	0.514637i
$800$	3.94178	−	3.07610i	0.139363	−	0.108757i
$801$		0			0
$802$			25.5917i			0.903674i
$803$		−	6.67318i		−	0.235491i
$804$		0			0
$805$	−40.0947	−	45.3444i	−1.41315	−	1.59818i
$806$	6.24915	+	6.38332i	0.220117	+	0.224843i
$807$		0			0
$808$	−8.15163	−	8.15163i	−0.286773	−	0.286773i
$809$			46.6723i			1.64091i	0.571710	+	0.820456i	$0.306280\pi$
$809$			46.6723i			1.64091i	−0.571710	+	0.820456i	$0.693720\pi$
$810$		0			0
$811$	13.7747	−	13.7747i	0.483695	−	0.483695i	−0.422614	−	0.906310i	$-0.638888\pi$
$811$	13.7747	−	13.7747i	0.483695	−	0.483695i	0.906310	+	0.422614i	$0.138888\pi$
$812$	−9.50394	+	9.50394i	−0.333523	+	0.333523i
$813$		0			0
$814$	−2.64983	−	2.64983i	−0.0928764	−	0.0928764i
$815$	28.7883	−	25.4554i	1.00841	−	0.891662i
$816$		0			0
$817$	−0.297540	+	0.297540i	−0.0104096	+	0.0104096i
$818$		−	7.19265i		−	0.251485i
$819$		0			0
$820$	−4.74695	+	4.19737i	−0.165771	+	0.146579i
$821$	−18.0751	−	18.0751i	−0.630826	−	0.630826i	0.317449	−	0.948275i	$-0.397174\pi$
$821$	−18.0751	−	18.0751i	−0.630826	−	0.630826i	−0.948275	+	0.317449i	$0.897174\pi$
$822$		0			0
$823$	17.1420			0.597531			0.298766	−	0.954327i	$-0.403425\pi$
$823$	17.1420			0.597531			0.298766	+	0.954327i	$0.403425\pi$
$824$	−6.02206	−	6.02206i	−0.209789	−	0.209789i
$825$		0			0
$826$	−35.0442	−	35.0442i	−1.21934	−	1.21934i
$827$	9.42298	+	9.42298i	0.327669	+	0.327669i	0.851700	−	0.524030i	$-0.175572\pi$
$827$	9.42298	+	9.42298i	0.327669	+	0.327669i	−0.524030	+	0.851700i	$0.675572\pi$
$828$		0			0
$829$		−	7.00109i		−	0.243158i	−0.992582	−	0.121579i	$-0.961204\pi$
$829$		−	7.00109i		−	0.243158i	0.992582	−	0.121579i	$-0.0387958\pi$
$830$	1.18371	−	19.2649i	0.0410871	−	0.668693i
$831$		0			0
$832$	−2.52229	−	2.57644i	−0.0874446	−	0.0893221i
$833$	−76.5696			−2.65298
$834$		0			0
$835$	−18.4043	−	20.8140i	−0.636908	−	0.720300i
$836$	0.0378454			0.00130891
$837$		0			0
$838$	20.6240	+	20.6240i	0.712446	+	0.712446i
$839$	−14.9675	+	14.9675i	−0.516737	+	0.516737i	−0.916582	−	0.399846i	$-0.869064\pi$
$839$	−14.9675	+	14.9675i	−0.516737	+	0.516737i	0.399846	+	0.916582i	$0.369064\pi$
$840$		0			0
$841$	22.1856			0.765022
$842$			9.32070i			0.321213i
$843$		0			0
$844$			15.8923i			0.547034i
$845$	−2.39861	+	28.9698i	−0.0825146	+	0.996590i
$846$		0			0
$847$	−37.8426	−	37.8426i	−1.30029	−	1.30029i
$848$	−7.17150			−0.246270
$849$		0			0
$850$	12.0725	+	15.4699i	0.414083	+	0.530615i
$851$	17.8983	+	17.8983i	0.613546	+	0.613546i
$852$		0			0
$853$	34.6315	−	34.6315i	1.18576	−	1.18576i	0.207532	−	0.978228i	$-0.433457\pi$
$853$	34.6315	−	34.6315i	1.18576	−	1.18576i	0.978228	−	0.207532i	$-0.0665430\pi$
$854$		−	55.7350i		−	1.90721i
$855$		0			0
$856$	−4.26623	−	4.26623i	−0.145817	−	0.145817i
$857$			29.6038i			1.01125i	0.862755	+	0.505623i	$0.168737\pi$
$857$			29.6038i			1.01125i	−0.862755	+	0.505623i	$0.831263\pi$
$858$		0			0
$859$	−6.02088			−0.205430			−0.102715	−	0.994711i	$-0.532753\pi$
$859$	−6.02088			−0.205430			−0.102715	+	0.994711i	$0.532753\pi$
$860$	−1.18677	+	19.3147i	−0.0404685	+	0.658627i
$861$		0			0
$862$	41.3513			1.40843
$863$	−7.08031	+	7.08031i	−0.241017	+	0.241017i	−0.817271	−	0.576254i	$-0.804514\pi$
$863$	−7.08031	+	7.08031i	−0.241017	+	0.241017i	0.576254	+	0.817271i	$0.304514\pi$
$864$		0			0
$865$	−3.31796	+	53.9999i	−0.112814	+	1.83605i
$866$	−11.3938	+	11.3938i	−0.387176	+	0.387176i
$867$		0			0
$868$	−12.7565			−0.432984
$869$	−0.627133	+	0.627133i	−0.0212740	+	0.0212740i
$870$		0			0
$871$	48.1912	+	0.511856i	1.63290	+	0.0173436i
$872$	14.3542			0.486096
$873$		0			0
$874$	−0.255627			−0.00864672
$875$	47.4685	−	32.5655i	1.60473	−	1.10091i
$876$		0			0
$877$	14.2730	+	14.2730i	0.481966	+	0.481966i	0.905759	−	0.423793i	$-0.139302\pi$
$877$	14.2730	+	14.2730i	0.481966	+	0.481966i	−0.423793	+	0.905759i	$0.639302\pi$
$878$	19.5667	+	19.5667i	0.660346	+	0.660346i
$879$		0			0
$880$	1.30384	−	1.15289i	0.0439524	−	0.0388638i
$881$	−48.2389			−1.62521			−0.812605	−	0.582815i	$-0.801951\pi$
$881$	−48.2389			−1.62521			−0.812605	+	0.582815i	$0.801951\pi$
$882$		0			0
$883$	−44.8686			−1.50995			−0.754974	−	0.655755i	$-0.772350\pi$
$883$	−44.8686			−1.50995			−0.754974	+	0.655755i	$0.772350\pi$
$884$	10.1115	−	9.89900i	0.340088	−	0.332939i
$885$		0			0
$886$	7.91957	−	7.91957i	0.266063	−	0.266063i
$887$	−52.8307			−1.77388			−0.886940	−	0.461885i	$-0.847173\pi$
$887$	−52.8307			−1.77388			−0.886940	+	0.461885i	$0.847173\pi$
$888$		0			0
$889$	−38.5731	+	38.5731i	−1.29370	+	1.29370i
$890$	−1.10439	+	17.9740i	−0.0370193	+	0.602491i
$891$		0			0
$892$	−9.11780	+	9.11780i	−0.305287	+	0.305287i
$893$	0.254877			0.00852914
$894$		0			0
$895$	−12.1367	−	0.745723i	−0.405684	−	0.0249268i
$896$	5.14880			0.172009
$897$		0			0
$898$		−	41.0736i		−	1.37064i
$899$	−4.57324	−	4.57324i	−0.152526	−	0.152526i
$900$		0			0
$901$		−	28.1454i		−	0.937658i
$902$	−1.55964	+	1.55964i	−0.0519305	+	0.0519305i
$903$		0			0
$904$	−2.96302	−	2.96302i	−0.0985484	−	0.0985484i
$905$	2.98140	−	48.5225i	0.0991052	−	1.61294i
$906$		0			0
$907$	3.58033			0.118883			0.0594414	−	0.998232i	$-0.481068\pi$
$907$	3.58033			0.118883			0.0594414	+	0.998232i	$0.481068\pi$
$908$	19.2800	+	19.2800i	0.639830	+	0.639830i
$909$		0			0
$910$	−27.1654	−	31.3878i	−0.900525	−	1.04050i
$911$		−	10.5533i		−	0.349647i	−0.984600	−	0.174823i	$-0.944065\pi$
$911$		−	10.5533i		−	0.349647i	0.984600	−	0.174823i	$-0.0559355\pi$
$912$		0			0
$913$		−	6.71853i		−	0.222351i
$914$	11.0972			0.367064
$915$		0			0
$916$	−0.641799	+	0.641799i	−0.0212056	+	0.0212056i
$917$	64.4185	+	64.4185i	2.12729	+	2.12729i
$918$		0			0
$919$	4.85905			0.160285			0.0801427	−	0.996783i	$-0.474462\pi$
$919$	4.85905			0.160285			0.0801427	+	0.996783i	$0.474462\pi$
$920$	−8.80679	+	7.78720i	−0.290351	+	0.256736i
$921$		0			0
$922$	17.0008			0.559890
$923$	37.9017	+	0.402568i	1.24755	+	0.0132507i
$924$		0			0
$925$	−18.9780	+	14.8101i	−0.623992	+	0.486953i
$926$			22.2940i			0.732627i
$927$		0			0
$928$	1.84586	+	1.84586i	0.0605932	+	0.0605932i
$929$	20.1241	+	20.1241i	0.660249	+	0.660249i	0.955439	−	0.295190i	$-0.0953828\pi$
$929$	20.1241	+	20.1241i	0.660249	+	0.660249i	−0.295190	+	0.955439i	$0.595383\pi$
$930$		0			0
$931$	0.670784	+	0.670784i	0.0219841	+	0.0219841i
$932$	21.1428			0.692557
$933$		0			0
$934$	13.3375	+	13.3375i	0.436416	+	0.436416i
$935$	4.52464	+	5.11706i	0.147971	+	0.167346i
$936$		0			0
$937$			11.5338i			0.376792i	0.982093	+	0.188396i	$0.0603288\pi$
$937$			11.5338i			0.376792i	−0.982093	+	0.188396i	$0.939671\pi$
$938$	−48.6644	+	48.6644i	−1.58895	+	1.58895i
$939$		0			0
$940$	8.78095	−	7.76435i	0.286403	−	0.253245i
$941$	2.25205	+	2.25205i	0.0734148	+	0.0734148i	0.742861	−	0.669446i	$-0.233468\pi$
$941$	2.25205	+	2.25205i	0.0734148	+	0.0734148i	−0.669446	+	0.742861i	$0.733468\pi$
$942$		0			0
$943$	10.5346	−	10.5346i	0.343055	−	0.343055i
$944$	−6.80629	+	6.80629i	−0.221526	+	0.221526i
$945$		0			0
$946$			6.73592i			0.219004i
$947$	−32.8141	−	32.8141i	−1.06631	−	1.06631i	−0.997639	−	0.0686747i	$-0.978123\pi$
$947$	−32.8141	−	32.8141i	−1.06631	−	1.06631i	−0.0686747	−	0.997639i	$-0.521877\pi$
$948$		0			0
$949$	−0.328311	+	30.9104i	−0.0106574	+	1.00340i
$950$	0.0297632	−	0.241284i	0.000965645	−	0.00782829i
$951$		0			0
$952$			20.2070i			0.654914i
$953$		−	26.9212i		−	0.872062i	−0.899932	−	0.436031i	$-0.856384\pi$
$953$		−	26.9212i		−	0.872062i	0.899932	−	0.436031i	$-0.143616\pi$
$954$		0			0
$955$	0.786002	−	12.7922i	0.0254344	−	0.413947i
$956$	10.7555	−	10.7555i	0.347859	−	0.347859i
$957$		0			0
$958$		−	7.34816i		−	0.237408i
$959$	−43.5777			−1.40720
$960$		0			0
$961$			24.8616i			0.801988i
$962$	12.1437	+	12.4045i	0.391530	+	0.399936i
$963$		0			0
$964$	−3.91857	+	3.91857i	−0.126209	+	0.126209i
$965$	−17.5595	+	15.5266i	−0.565260	+	0.499818i
$966$		0			0
$967$	−14.6599	−	14.6599i	−0.471431	−	0.471431i	0.430947	−	0.902377i	$-0.358180\pi$
$967$	−14.6599	−	14.6599i	−0.471431	−	0.471431i	−0.902377	+	0.430947i	$0.858180\pi$
$968$	−7.34979	+	7.34979i	−0.236231	+	0.236231i
$969$		0			0
$970$	−0.789942	−	0.0485370i	−0.0253635	−	0.00155843i
$971$			29.0063i			0.930858i	0.885085	+	0.465429i	$0.154100\pi$
$971$			29.0063i			0.930858i	−0.885085	+	0.465429i	$0.845900\pi$
$972$		0			0
$973$	19.4212	−	19.4212i	0.622614	−	0.622614i
$974$	−2.26453			−0.0725601
$975$		0			0
$976$	−10.8249			−0.346495
$977$	−0.784623	+	0.784623i	−0.0251023	+	0.0251023i	−0.719547	−	0.694444i	$-0.755650\pi$
$977$	−0.784623	+	0.784623i	−0.0251023	+	0.0251023i	0.694444	+	0.719547i	$0.255650\pi$
$978$		0			0
$979$			6.26835i			0.200337i
$980$	43.5438	+	2.67550i	1.39096	+	0.0854656i
$981$		0			0
$982$	12.4094	−	12.4094i	0.396001	−	0.396001i
$983$	−10.0476	−	10.0476i	−0.320469	−	0.320469i	0.528478	−	0.848947i	$-0.322763\pi$
$983$	−10.0476	−	10.0476i	−0.320469	−	0.320469i	−0.848947	+	0.528478i	$0.822763\pi$
$984$		0			0
$985$	6.41472	−	5.67207i	0.204390	−	0.180727i
$986$	−7.24427	+	7.24427i	−0.230704	+	0.230704i
$987$		0			0
$988$	−0.175301	−	0.00186194i	−0.00557708	−	5.92362e-5i
$989$		−	45.4979i		−	1.44675i
$990$		0			0
$991$	−45.2765			−1.43825			−0.719127	−	0.694878i	$-0.755458\pi$
$991$	−45.2765			−1.43825			−0.719127	+	0.694878i	$0.755458\pi$
$992$			2.47757i			0.0786630i
$993$		0			0
$994$	−38.2738	+	38.2738i	−1.21397	+	1.21397i
$995$	−0.192711	+	3.13637i	−0.00610934	+	0.0994297i
$996$		0			0
$997$			10.2589i			0.324903i	0.986717	+	0.162451i	$0.0519401\pi$
$997$			10.2589i			0.324903i	−0.986717	+	0.162451i	$0.948060\pi$
$998$		−	23.5830i		−	0.746507i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.q.c.629.2	yes	24
3.2	odd	2	inner	1170.2.q.c.629.10	yes	24
5.4	even	2		1170.2.q.d.629.11	yes	24
13.8	odd	4		1170.2.q.d.359.3	yes	24
15.14	odd	2		1170.2.q.d.629.3	yes	24
39.8	even	4		1170.2.q.d.359.11	yes	24
65.34	odd	4	inner	1170.2.q.c.359.10	yes	24
195.164	even	4	inner	1170.2.q.c.359.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.q.c.359.2	✓	24	195.164	even	4	inner
1170.2.q.c.359.10	yes	24	65.34	odd	4	inner
1170.2.q.c.629.2	yes	24	1.1	even	1	trivial
1170.2.q.c.629.10	yes	24	3.2	odd	2	inner
1170.2.q.d.359.3	yes	24	13.8	odd	4
1170.2.q.d.359.11	yes	24	39.8	even	4
1170.2.q.d.629.3	yes	24	15.14	odd	2
1170.2.q.d.629.11	yes	24	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-2.23186 - 0.137134i) q^{5} +(-3.64075 + 3.64075i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.67513 - 1.48119i) q^{10} +(0.550376 - 0.550376i) q^{11} +(-2.57644 + 2.52229i) q^{13} -5.14880i q^{14} -1.00000 q^{16} -3.92461i q^{17} +(-0.0343813 + 0.0343813i) q^{19} +(-0.137134 + 2.23186i) q^{20} +0.778350i q^{22} -5.25738i q^{23} +(4.96239 + 0.612127i) q^{25} +(0.0382937 - 3.60535i) q^{26} +(3.64075 + 3.64075i) q^{28} +2.61043i q^{29} +(-1.75191 + 1.75191i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.77512 + 2.77512i) q^{34} +(8.62491 - 7.62637i) q^{35} +(-3.40442 + 3.40442i) q^{37} -0.0486226i q^{38} +(-1.48119 - 1.67513i) q^{40} +(2.00378 + 2.00378i) q^{41} +8.65410 q^{43} +(-0.550376 - 0.550376i) q^{44} +(3.71753 + 3.71753i) q^{46} +(-3.70662 - 3.70662i) q^{47} -19.5101i q^{49} +(-3.94178 + 3.07610i) q^{50} +(2.52229 + 2.57644i) q^{52} +7.17150 q^{53} +(-1.30384 + 1.15289i) q^{55} -5.14880 q^{56} +(-1.84586 - 1.84586i) q^{58} +(6.80629 - 6.80629i) q^{59} +10.8249 q^{61} -2.47757i q^{62} +1.00000i q^{64} +(6.09615 - 5.27607i) q^{65} +(-9.45160 - 9.45160i) q^{67} -3.92461 q^{68} +(-0.706074 + 11.4914i) q^{70} +(-7.43355 - 7.43355i) q^{71} +(6.06238 - 6.06238i) q^{73} -4.81457i q^{74} +(0.0343813 + 0.0343813i) q^{76} +4.00757i q^{77} -1.13946 q^{79} +(2.23186 + 0.137134i) q^{80} -2.83378 q^{82} +(6.10358 - 6.10358i) q^{83} +(-0.538197 + 8.75918i) q^{85} +(-6.11937 + 6.11937i) q^{86} +0.778350 q^{88} +(-5.69461 + 5.69461i) q^{89} +(0.197167 - 18.5632i) q^{91} -5.25738 q^{92} +5.24195 q^{94} +(0.0814492 - 0.0720195i) q^{95} +(-0.250273 - 0.250273i) q^{97} +(13.7957 + 13.7957i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{13} - 24 q^{16} - 48 q^{19} + 32 q^{25} - 8 q^{31} + 16 q^{34} - 32 q^{37} + 8 q^{40} + 80 q^{43} + 8 q^{46} - 12 q^{52} + 16 q^{55} - 24 q^{58} - 16 q^{61} - 8 q^{67} - 24 q^{70} + 48 q^{73}+ \cdots + 64 q^{97}+O(q^{100}) \) 24 * q - 20 * q^13 - 24 * q^16 - 48 * q^19 + 32 * q^25 - 8 * q^31 + 16 * q^34 - 32 * q^37 + 8 * q^40 + 80 * q^43 + 8 * q^46 - 12 * q^52 + 16 * q^55 - 24 * q^58 - 16 * q^61 - 8 * q^67 - 24 * q^70 + 48 * q^73 + 48 * q^76 - 96 * q^79 - 72 * q^82 + 8 * q^85 + 8 * q^88 + 48 * q^91 - 16 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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