LMFDB - Embedded newform 570.2.s.a.521.3

Newspace parameters

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.s (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.3
Character	$\chi$	$=$	570.521
Dual form			570.2.s.a.221.3

$q$-expansion

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.01463 + 1.40375i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.708367 - 1.58057i) q^{6} +2.73284 q^{7} +1.00000 q^{8} +(-0.941036 - 2.84859i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.01463 + 1.40375i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.708367 - 1.58057i) q^{6} +2.73284 q^{7} +1.00000 q^{8} +(-0.941036 - 2.84859i) q^{9} +(0.866025 - 0.500000i) q^{10} -0.361598i q^{11} +(1.72300 + 0.176823i) q^{12} +(2.32225 - 1.34075i) q^{13} +(-1.36642 + 2.36671i) q^{14} +(1.58057 - 0.708367i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.37205 + 0.792151i) q^{17} +(2.93747 + 0.609333i) q^{18} +(2.26593 - 3.72365i) q^{19} +1.00000i q^{20} +(-2.77283 + 3.83623i) q^{21} +(0.313153 + 0.180799i) q^{22} +(3.44153 - 1.98697i) q^{23} +(-1.01463 + 1.40375i) q^{24} +(0.500000 + 0.866025i) q^{25} +2.68150i q^{26} +(4.95352 + 1.56929i) q^{27} +(-1.36642 - 2.36671i) q^{28} +(1.24989 + 2.16488i) q^{29} +(-0.176823 + 1.72300i) q^{30} +5.44068i q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.507593 + 0.366889i) q^{33} +(-1.37205 + 0.792151i) q^{34} +(-2.36671 - 1.36642i) q^{35} +(-1.99643 + 2.23925i) q^{36} +7.93595i q^{37} +(2.09181 + 3.82417i) q^{38} +(-0.474151 + 4.62022i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(-2.12250 + 3.67627i) q^{41} +(-1.93585 - 4.31946i) q^{42} +(1.23694 - 2.14245i) q^{43} +(-0.313153 + 0.180799i) q^{44} +(-0.609333 + 2.93747i) q^{45} +3.97393i q^{46} +(6.62319 - 3.82390i) q^{47} +(-0.708367 - 1.58057i) q^{48} +0.468410 q^{49} -1.00000 q^{50} +(-2.50411 + 1.12227i) q^{51} +(-2.32225 - 1.34075i) q^{52} +(-1.37459 - 2.38085i) q^{53} +(-3.83581 + 3.50522i) q^{54} +(-0.180799 + 0.313153i) q^{55} +2.73284 q^{56} +(2.92800 + 6.95894i) q^{57} -2.49978 q^{58} +(-1.56849 + 2.71671i) q^{59} +(-1.40375 - 1.01463i) q^{60} +(3.73492 + 6.46907i) q^{61} +(-4.71176 - 2.72034i) q^{62} +(-2.57170 - 7.78473i) q^{63} +1.00000 q^{64} -2.68150 q^{65} +(-0.571532 + 0.256144i) q^{66} +(-0.731797 + 0.422503i) q^{67} -1.58430i q^{68} +(-0.702683 + 6.84709i) q^{69} +(2.36671 - 1.36642i) q^{70} +(4.22259 - 7.31374i) q^{71} +(-0.941036 - 2.84859i) q^{72} +(6.07501 - 10.5222i) q^{73} +(-6.87273 - 3.96797i) q^{74} +(-1.72300 - 0.176823i) q^{75} +(-4.35774 - 0.100523i) q^{76} -0.988188i q^{77} +(-3.76416 - 2.72074i) q^{78} +(3.57112 + 2.06179i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-7.22890 + 5.36125i) q^{81} +(-2.12250 - 3.67627i) q^{82} +0.651818i q^{83} +(4.70869 + 0.483229i) q^{84} +(-0.792151 - 1.37205i) q^{85} +(1.23694 + 2.14245i) q^{86} +(-4.30713 - 0.442019i) q^{87} -0.361598i q^{88} +(-5.47514 - 9.48321i) q^{89} +(-2.23925 - 1.99643i) q^{90} +(6.34632 - 3.66405i) q^{91} +(-3.44153 - 1.98697i) q^{92} +(-7.63736 - 5.52029i) q^{93} +7.64780i q^{94} +(-3.82417 + 2.09181i) q^{95} +(1.72300 + 0.176823i) q^{96} +(15.3033 + 8.83538i) q^{97} +(-0.234205 + 0.405655i) q^{98} +(-1.03004 + 0.340276i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24q - 12q^{2} + 4q^{3} - 12q^{4} - 2q^{6} - 12q^{7} + 24q^{8} - 4q^{9} + O(q^{10}) $	$ 24q - 12q^{2} + 4q^{3} - 12q^{4} - 2q^{6} - 12q^{7} + 24q^{8} - 4q^{9} - 2q^{12} + 18q^{13} + 6q^{14} - 12q^{16} + 12q^{17} + 2q^{18} + 6q^{19} - 6q^{21} + 18q^{22} + 4q^{24} + 12q^{25} + 28q^{27} + 6q^{28} - 12q^{32} - 22q^{33} - 12q^{34} + 2q^{36} + 6q^{38} + 40q^{39} + 6q^{41} - 6q^{42} - 22q^{43} - 18q^{44} + 8q^{45} + 12q^{47} - 2q^{48} + 12q^{49} - 24q^{50} - 20q^{51} - 18q^{52} + 8q^{53} + 4q^{54} - 12q^{56} + 26q^{59} + 22q^{61} - 18q^{62} + 6q^{63} + 24q^{64} + 8q^{65} + 8q^{66} - 48q^{67} - 64q^{69} + 24q^{71} - 4q^{72} - 8q^{73} + 30q^{74} + 2q^{75} - 12q^{76} - 38q^{78} + 18q^{79} - 12q^{81} + 6q^{82} + 12q^{84} - 22q^{86} - 24q^{87} + 28q^{89} + 8q^{90} + 18q^{91} + 2q^{93} - 2q^{96} + 6q^{97} - 6q^{98} + 2q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.01463	+	1.40375i	−0.585799	+	0.810456i
$3$	−1.01463	+	1.40375i	−0.585799	+	0.810456i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−0.708367	−	1.58057i	−0.289190	−	0.645267i
$7$	2.73284			1.03292			0.516458	−	0.856312i	$-0.327250\pi$
$7$	2.73284			1.03292			0.516458	+	0.856312i	$0.327250\pi$
$8$	1.00000			0.353553
$9$	−0.941036	−	2.84859i	−0.313679	−	0.949529i
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$		−	0.361598i		−	0.109026i	−0.998513	−	0.0545129i	$-0.982639\pi$
$11$		−	0.361598i		−	0.109026i	0.998513	−	0.0545129i	$-0.0173606\pi$
$12$	1.72300	+	0.176823i	0.497388	+	0.0510444i
$13$	2.32225	−	1.34075i	0.644075	−	0.371857i	−0.142108	−	0.989851i	$-0.545388\pi$
$13$	2.32225	−	1.34075i	0.644075	−	0.371857i	0.786183	+	0.617994i	$0.212055\pi$
$14$	−1.36642	+	2.36671i	−0.365191	+	0.632529i
$15$	1.58057	−	0.708367i	0.408103	−	0.182900i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.37205	+	0.792151i	0.332770	+	0.192125i	0.657070	−	0.753829i	$-0.271795\pi$
$17$	1.37205	+	0.792151i	0.332770	+	0.192125i	−0.324300	+	0.945954i	$0.605129\pi$
$18$	2.93747	+	0.609333i	0.692368	+	0.143621i
$19$	2.26593	−	3.72365i	0.519839	−	0.854264i
$19$	2.26593	−	3.72365i	0.519839	−	0.854264i
$20$			1.00000i			0.223607i
$21$	−2.77283	+	3.83623i	−0.605081	+	0.837133i
$22$	0.313153	+	0.180799i	0.0667644	+	0.0385464i
$23$	3.44153	−	1.98697i	0.717608	−	0.414311i	−0.0962636	−	0.995356i	$-0.530689\pi$
$23$	3.44153	−	1.98697i	0.717608	−	0.414311i	0.813872	+	0.581045i	$0.197356\pi$
$24$	−1.01463	+	1.40375i	−0.207111	+	0.286540i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$			2.68150i			0.525885i
$27$	4.95352	+	1.56929i	0.953305	+	0.302011i
$28$	−1.36642	−	2.36671i	−0.258229	−	0.447266i
$29$	1.24989	+	2.16488i	0.232099	+	0.402007i	0.958426	−	0.285342i	$-0.0921073\pi$
$29$	1.24989	+	2.16488i	0.232099	+	0.402007i	−0.726327	+	0.687350i	$0.758774\pi$
$30$	−0.176823	+	1.72300i	−0.0322833	+	0.314576i
$31$			5.44068i			0.977174i	0.872515	+	0.488587i	$0.162488\pi$
$31$			5.44068i			0.977174i	−0.872515	+	0.488587i	$0.837512\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.507593	+	0.366889i	0.0883606	+	0.0638672i
$34$	−1.37205	+	0.792151i	−0.235304	+	0.135853i
$35$	−2.36671	−	1.36642i	−0.400047	−	0.230967i
$36$	−1.99643	+	2.23925i	−0.332739	+	0.373209i
$37$			7.93595i			1.30466i	0.757934	+	0.652331i	$0.226209\pi$
$37$			7.93595i			1.30466i	−0.757934	+	0.652331i	$0.773791\pi$
$38$	2.09181	+	3.82417i	0.339337	+	0.620363i
$39$	−0.474151	+	4.62022i	−0.0759249	+	0.739828i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	−2.12250	+	3.67627i	−0.331478	+	0.574137i	−0.982802	−	0.184663i	$-0.940881\pi$
$41$	−2.12250	+	3.67627i	−0.331478	+	0.574137i	0.651324	+	0.758800i	$0.274214\pi$
$42$	−1.93585	−	4.31946i	−0.298709	−	0.666507i
$43$	1.23694	−	2.14245i	0.188632	−	0.326720i	−0.756162	−	0.654384i	$-0.772928\pi$
$43$	1.23694	−	2.14245i	0.188632	−	0.326720i	0.944794	+	0.327664i	$0.106261\pi$
$44$	−0.313153	+	0.180799i	−0.0472095	+	0.0272564i
$45$	−0.609333	+	2.93747i	−0.0908340	+	0.437892i
$46$			3.97393i			0.585925i
$47$	6.62319	−	3.82390i	0.966092	−	0.557773i	0.0680494	−	0.997682i	$-0.478322\pi$
$47$	6.62319	−	3.82390i	0.966092	−	0.557773i	0.898043	+	0.439908i	$0.144989\pi$
$48$	−0.708367	−	1.58057i	−0.102244	−	0.228136i
$49$	0.468410			0.0669158
$50$	−1.00000			−0.141421
$51$	−2.50411	+	1.12227i	−0.350645	+	0.157149i
$52$	−2.32225	−	1.34075i	−0.322037	−	0.185928i
$53$	−1.37459	−	2.38085i	−0.188814	−	0.327035i	0.756041	−	0.654524i	$-0.227131\pi$
$53$	−1.37459	−	2.38085i	−0.188814	−	0.327035i	−0.944855	+	0.327489i	$0.893798\pi$
$54$	−3.83581	+	3.50522i	−0.521987	+	0.477001i
$55$	−0.180799	+	0.313153i	−0.0243789	+	0.0422255i
$56$	2.73284			0.365191
$57$	2.92800	+	6.95894i	0.387822	+	0.921734i
$58$	−2.49978			−0.328238
$59$	−1.56849	+	2.71671i	−0.204200	+	0.353685i	−0.949878	−	0.312622i	$-0.898793\pi$
$59$	−1.56849	+	2.71671i	−0.204200	+	0.353685i	0.745677	+	0.666307i	$0.232126\pi$
$60$	−1.40375	−	1.01463i	−0.181224	−	0.130989i
$61$	3.73492	+	6.46907i	0.478208	+	0.828280i	0.999688	−	0.0249834i	$-0.00795330\pi$
$61$	3.73492	+	6.46907i	0.478208	+	0.828280i	−0.521480	+	0.853263i	$0.674620\pi$
$62$	−4.71176	−	2.72034i	−0.598395	−	0.345483i
$63$	−2.57170	−	7.78473i	−0.324004	−	0.980784i
$64$	1.00000			0.125000
$65$	−2.68150			−0.332599
$66$	−0.571532	+	0.256144i	−0.0703507	+	0.0315291i
$67$	−0.731797	+	0.422503i	−0.0894032	+	0.0516170i	−0.544035	−	0.839062i	$-0.683104\pi$
$67$	−0.731797	+	0.422503i	−0.0894032	+	0.0516170i	0.454632	+	0.890679i	$0.349771\pi$
$68$		−	1.58430i		−	0.192125i
$69$	−0.702683	+	6.84709i	−0.0845931	+	0.824293i
$70$	2.36671	−	1.36642i	0.282876	−	0.163318i
$71$	4.22259	−	7.31374i	0.501129	−	0.867981i	−0.498870	−	0.866677i	$-0.666251\pi$
$71$	4.22259	−	7.31374i	0.501129	−	0.867981i	0.999999	−	0.00130440i	$-0.000415204\pi$
$72$	−0.941036	−	2.84859i	−0.110902	−	0.335709i
$73$	6.07501	−	10.5222i	0.711026	−	1.23153i	−0.253447	−	0.967349i	$-0.581564\pi$
$73$	6.07501	−	10.5222i	0.711026	−	1.23153i	0.964472	−	0.264184i	$-0.0851025\pi$
$74$	−6.87273	−	3.96797i	−0.798939	−	0.461268i
$75$	−1.72300	−	0.176823i	−0.198955	−	0.0204178i
$76$	−4.35774	−	0.100523i	−0.499867	−	0.0115308i
$77$		−	0.988188i		−	0.112614i
$78$	−3.76416	−	2.72074i	−0.426207	−	0.308063i
$79$	3.57112	+	2.06179i	0.401783	+	0.231969i	0.687253	−	0.726418i	$-0.258816\pi$
$79$	3.57112	+	2.06179i	0.401783	+	0.231969i	−0.285470	+	0.958388i	$0.592150\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	−7.22890	+	5.36125i	−0.803211	+	0.595694i
$82$	−2.12250	−	3.67627i	−0.234391	−	0.405976i
$83$			0.651818i			0.0715463i	0.999360	+	0.0357732i	$0.0113894\pi$
$83$			0.651818i			0.0715463i	−0.999360	+	0.0357732i	$0.988611\pi$
$84$	4.70869	+	0.483229i	0.513760	+	0.0527246i
$85$	−0.792151	−	1.37205i	−0.0859208	−	0.148819i
$86$	1.23694	+	2.14245i	0.133383	+	0.231026i
$87$	−4.30713	−	0.442019i	−0.461773	−	0.0473895i
$88$		−	0.361598i		−	0.0385464i
$89$	−5.47514	−	9.48321i	−0.580363	−	1.00522i	−0.995436	−	0.0954304i	$-0.969577\pi$
$89$	−5.47514	−	9.48321i	−0.580363	−	1.00522i	0.415073	−	0.909788i	$-0.363756\pi$
$90$	−2.23925	−	1.99643i	−0.236038	−	0.210442i
$91$	6.34632	−	3.66405i	0.665275	−	0.384097i
$92$	−3.44153	−	1.98697i	−0.358804	−	0.207156i
$93$	−7.63736	−	5.52029i	−0.791957	−	0.572428i
$94$			7.64780i			0.788811i
$95$	−3.82417	+	2.09181i	−0.392352	+	0.214616i
$96$	1.72300	+	0.176823i	0.175853	+	0.0180469i
$97$	15.3033	+	8.83538i	1.55382	+	0.897097i	0.997826	+	0.0659098i	$0.0209950\pi$
$97$	15.3033	+	8.83538i	1.55382	+	0.897097i	0.555992	+	0.831187i	$0.312338\pi$
$98$	−0.234205	+	0.405655i	−0.0236583	+	0.0409774i
$99$	−1.03004	+	0.340276i	−0.103523	+	0.0341990i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	0.597354	−	0.344883i	0.0594390	−	0.0343171i	−0.469986	−	0.882674i	$-0.655741\pi$
$101$	0.597354	−	0.344883i	0.0594390	−	0.0343171i	0.529425	+	0.848357i	$0.322408\pi$
$102$	0.280141	−	2.72975i	0.0277381	−	0.270286i
$103$		−	15.3946i		−	1.51688i	−0.651744	−	0.758439i	$-0.725962\pi$
$103$		−	15.3946i		−	1.51688i	0.651744	−	0.758439i	$-0.274038\pi$
$104$	2.32225	−	1.34075i	0.227715	−	0.131471i
$105$	4.31946	−	1.93585i	0.421536	−	0.188920i
$106$	2.74917			0.267023
$107$	0.902808			0.0872778			0.0436389	−	0.999047i	$-0.486105\pi$
$107$	0.902808			0.0872778			0.0436389	+	0.999047i	$0.486105\pi$
$108$	−1.11771	−	5.07452i	−0.107552	−	0.488296i
$109$	8.27239	+	4.77607i	0.792351	+	0.457464i	0.840790	−	0.541362i	$-0.182091\pi$
$109$	8.27239	+	4.77607i	0.792351	+	0.457464i	−0.0484384	+	0.998826i	$0.515424\pi$
$110$	−0.180799	−	0.313153i	−0.0172385	−	0.0298579i
$111$	−11.1401	−	8.05208i	−1.05737	−	0.764270i
$112$	−1.36642	+	2.36671i	−0.129115	+	0.223633i
$113$	18.0868			1.70146			0.850731	−	0.525602i	$-0.176160\pi$
$113$	18.0868			1.70146			0.850731	+	0.525602i	$0.176160\pi$
$114$	−7.49062	−	0.943751i	−0.701561	−	0.0883904i
$115$	−3.97393			−0.370571
$116$	1.24989	−	2.16488i	0.116050	−	0.201004i
$117$	−6.00456	−	5.35343i	−0.555121	−	0.494924i
$118$	−1.56849	−	2.71671i	−0.144391	−	0.250093i
$119$	3.74958	+	2.16482i	0.343723	+	0.198449i
$120$	1.58057	−	0.708367i	0.144286	−	0.0646648i
$121$	10.8692			0.988113
$122$	−7.46984			−0.676288
$123$	−3.00702	−	6.70953i	−0.271133	−	0.604978i
$124$	4.71176	−	2.72034i	0.423129	−	0.244294i
$125$		−	1.00000i		−	0.0894427i
$126$	8.02763	+	1.66521i	0.715158	+	0.148349i
$127$	−3.08394	+	1.78051i	−0.273655	+	0.157995i	−0.630548	−	0.776151i	$-0.717170\pi$
$127$	−3.08394	+	1.78051i	−0.273655	+	0.157995i	0.356892	+	0.934145i	$0.383836\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	1.75242	+	3.91016i	0.154292	+	0.344271i
$130$	1.34075	−	2.32225i	0.117591	−	0.203674i
$131$	−4.10014	−	2.36722i	−0.358231	−	0.206825i	0.310073	−	0.950713i	$-0.399646\pi$
$131$	−4.10014	−	2.36722i	−0.358231	−	0.206825i	−0.668305	+	0.743888i	$0.732980\pi$
$132$	0.0639388	−	0.623033i	0.00556516	−	0.0542281i
$133$	6.19241	−	10.1761i	0.536950	−	0.882383i
$134$		−	0.845006i		−	0.0729974i
$135$	−3.50522	−	3.83581i	−0.301682	−	0.330134i
$136$	1.37205	+	0.792151i	0.117652	+	0.0679264i
$137$	−4.07740	+	2.35409i	−0.348356	+	0.201123i	−0.663961	−	0.747767i	$-0.731126\pi$
$137$	−4.07740	+	2.35409i	−0.348356	+	0.201123i	0.315605	+	0.948891i	$0.397793\pi$
$138$	−5.57841	−	4.03209i	−0.474866	−	0.343234i
$139$	−7.46724	−	12.9336i	−0.633363	−	1.09702i	−0.986860	−	0.161581i	$-0.948341\pi$
$139$	−7.46724	−	12.9336i	−0.633363	−	1.09702i	0.353497	−	0.935436i	$-0.384993\pi$
$140$			2.73284i			0.230967i
$141$	−1.35231	+	13.1772i	−0.113885	+	1.10972i
$142$	4.22259	+	7.31374i	0.354352	+	0.613755i
$143$	−0.484812	−	0.839718i	−0.0405420	−	0.0702208i
$144$	2.93747	+	0.609333i	0.244789	+	0.0507777i
$145$		−	2.49978i		−	0.207596i
$146$	6.07501	+	10.5222i	0.502771	+	0.870825i
$147$	−0.475265	+	0.657532i	−0.0391992	+	0.0542323i
$148$	6.87273	−	3.96797i	0.564935	−	0.326165i
$149$	−19.6035	−	11.3181i	−1.60598	−	0.927215i	−0.990257	−	0.139254i	$-0.955529\pi$
$149$	−19.6035	−	11.3181i	−1.60598	−	0.927215i	−0.615726	−	0.787960i	$-0.711137\pi$
$150$	1.01463	−	1.40375i	0.0828445	−	0.114616i
$151$			3.63440i			0.295763i	0.989005	+	0.147882i	$0.0472455\pi$
$151$			3.63440i			0.295763i	−0.989005	+	0.147882i	$0.952755\pi$
$152$	2.26593	−	3.72365i	0.183791	−	0.302028i
$153$	0.965367	−	4.65383i	0.0780453	−	0.376240i
$154$	0.855796	+	0.494094i	0.0689620	+	0.0398152i
$155$	2.72034	−	4.71176i	0.218503	−	0.378458i
$156$	4.23831	−	1.89949i	0.339336	−	0.152081i
$157$	−6.76442	+	11.7163i	−0.539859	+	0.935064i	0.459052	+	0.888410i	$0.348189\pi$
$157$	−6.76442	+	11.7163i	−0.539859	+	0.935064i	−0.998911	+	0.0466542i	$0.985144\pi$
$158$	−3.57112	+	2.06179i	−0.284103	+	0.164027i
$159$	4.73683	+	0.486117i	0.375655	+	0.0385516i
$160$			1.00000i			0.0790569i
$161$	9.40514	−	5.43006i	0.741229	−	0.427949i
$162$	−1.02852	−	8.94104i	−0.0808084	−	0.702474i
$163$	−18.9557			−1.48472			−0.742361	−	0.670000i	$-0.766294\pi$
$163$	−18.9557			−1.48472			−0.742361	+	0.670000i	$0.766294\pi$
$164$	4.24499			0.331478
$165$	−0.256144	−	0.571532i	−0.0199408	−	0.0444937i
$166$	−0.564491	−	0.325909i	−0.0438130	−	0.0252954i
$167$	−2.66087	−	4.60877i	−0.205905	−	0.356637i	0.744516	−	0.667605i	$-0.232680\pi$
$167$	−2.66087	−	4.60877i	−0.205905	−	0.356637i	−0.950421	+	0.310967i	$0.899347\pi$
$168$	−2.77283	+	3.83623i	−0.213929	+	0.295971i
$169$	−2.90478	+	5.03123i	−0.223445	+	0.387018i
$170$	1.58430			0.121510
$171$	−12.7395	−	2.95060i	−0.974211	−	0.225638i
$172$	−2.47389			−0.188632
$173$	−5.01989	+	8.69470i	−0.381655	+	0.661046i	−0.991299	−	0.131630i	$-0.957979\pi$
$173$	−5.01989	+	8.69470i	−0.381655	+	0.661046i	0.609644	+	0.792675i	$0.291312\pi$
$174$	2.53636	−	3.50907i	0.192281	−	0.266022i
$175$	1.36642	+	2.36671i	0.103292	+	0.178906i
$176$	0.313153	+	0.180799i	0.0236048	+	0.0136282i
$177$	−2.22214	−	4.95824i	−0.167026	−	0.372684i
$178$	10.9503			0.820757
$179$	−6.28120			−0.469479			−0.234739	−	0.972058i	$-0.575424\pi$
$179$	−6.28120			−0.469479			−0.234739	+	0.972058i	$0.575424\pi$
$180$	2.84859	−	0.941036i	0.212321	−	0.0701407i
$181$	−21.3026	+	12.2990i	−1.58341	+	0.914180i	−0.589049	+	0.808097i	$0.700498\pi$
$181$	−21.3026	+	12.2990i	−1.58341	+	0.914180i	−0.994357	+	0.106083i	$0.966169\pi$
$182$			7.32810i			0.543195i
$183$	−12.8705	−	1.32084i	−0.951418	−	0.0976394i
$184$	3.44153	−	1.98697i	0.253713	−	0.146481i
$185$	3.96797	−	6.87273i	0.291731	−	0.505293i
$186$	8.59939	−	3.85400i	0.630538	−	0.282589i
$187$	0.286440	−	0.496128i	0.0209466	−	0.0362805i
$188$	−6.62319	−	3.82390i	−0.483046	−	0.278887i
$189$	13.5372	+	4.28863i	0.984684	+	0.311952i
$190$	0.100523	−	4.35774i	0.00729274	−	0.316144i
$191$		−	25.6046i		−	1.85268i	−0.376683	−	0.926342i	$-0.622935\pi$
$191$		−	25.6046i		−	1.85268i	0.376683	−	0.926342i	$-0.377065\pi$
$192$	−1.01463	+	1.40375i	−0.0732249	+	0.101307i
$193$	2.59120	+	1.49603i	0.186519	+	0.107687i	0.590352	−	0.807146i	$-0.298989\pi$
$193$	2.59120	+	1.49603i	0.186519	+	0.107687i	−0.403833	+	0.914833i	$0.632322\pi$
$194$	−15.3033	+	8.83538i	−1.09872	+	0.634344i
$195$	2.72074	−	3.76416i	0.194836	−	0.269557i
$196$	−0.234205	−	0.405655i	−0.0167289	−	0.0289754i
$197$			17.7186i			1.26240i	0.775620	+	0.631201i	$0.217438\pi$
$197$			17.7186i			1.26240i	−0.775620	+	0.631201i	$0.782562\pi$
$198$	0.220333	−	1.06218i	0.0156584	−	0.0754859i
$199$	−10.2862	−	17.8162i	−0.729170	−	1.26296i	−0.957235	−	0.289313i	$-0.906573\pi$
$199$	−10.2862	−	17.8162i	−0.729170	−	1.26296i	0.228065	−	0.973646i	$-0.426760\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	0.149417	−	1.45595i	0.0105390	−	0.102695i
$202$			0.689765i			0.0485317i
$203$	3.41575	+	5.91626i	0.239739	+	0.415240i
$204$	2.22397	+	1.60749i	0.155709	+	0.112547i
$205$	3.67627	−	2.12250i	0.256762	−	0.148242i
$206$	13.3321	+	7.69731i	0.928894	+	0.536297i
$207$	−8.89865	−	7.93369i	−0.618499	−	0.551429i
$208$			2.68150i			0.185928i
$209$	−1.34646	−	0.819353i	−0.0931368	−	0.0566758i
$210$	−0.483229	+	4.70869i	−0.0333460	+	0.324930i
$211$	0.240924	+	0.139098i	0.0165859	+	0.00957587i	0.508270	−	0.861198i	$-0.330285\pi$
$211$	0.240924	+	0.139098i	0.0165859	+	0.00957587i	−0.491684	+	0.870774i	$0.663619\pi$
$212$	−1.37459	+	2.38085i	−0.0944069	+	0.163518i
$213$	5.98229	+	13.3482i	0.409900	+	0.914606i
$214$	−0.451404	+	0.781855i	−0.0308573	+	0.0534465i
$215$	−2.14245	+	1.23694i	−0.146114	+	0.0843588i
$216$	4.95352	+	1.56929i	0.337044	+	0.106777i
$217$			14.8685i			1.00934i
$218$	−8.27239	+	4.77607i	−0.560277	+	0.323476i
$219$	8.60667	+	19.2040i	0.581585	+	1.29769i
$220$	0.361598			0.0243789
$221$	4.24830			0.285772
$222$	12.5434	−	5.62157i	0.841855	−	0.377295i
$223$	4.55894	+	2.63211i	0.305290	+	0.176259i	0.644817	−	0.764337i	$-0.276934\pi$
$223$	4.55894	+	2.63211i	0.305290	+	0.176259i	−0.339527	+	0.940596i	$0.610267\pi$
$224$	−1.36642	−	2.36671i	−0.0912978	−	0.158132i
$225$	1.99643	−	2.23925i	0.133095	−	0.149284i
$226$	−9.04339	+	15.6636i	−0.601557	+	1.04193i
$227$	18.1853			1.20700			0.603500	−	0.797363i	$-0.293773\pi$
$227$	18.1853			1.20700			0.603500	+	0.797363i	$0.293773\pi$
$228$	4.56262	−	6.01519i	0.302167	−	0.398366i
$229$	−0.0923898			−0.00610529			−0.00305265	−	0.999995i	$-0.500972\pi$
$229$	−0.0923898			−0.00610529			−0.00305265	+	0.999995i	$0.500972\pi$
$230$	1.98697	−	3.44153i	0.131017	−	0.226928i
$231$	1.38717	+	1.00265i	0.0912691	+	0.0659695i
$232$	1.24989	+	2.16488i	0.0820594	+	0.142131i
$233$	12.3845	+	7.15019i	0.811335	+	0.468425i	0.847419	−	0.530924i	$-0.178155\pi$
$233$	12.3845	+	7.15019i	0.811335	+	0.468425i	−0.0360842	+	0.999349i	$0.511488\pi$
$234$	7.63848	−	2.52339i	0.499343	−	0.164959i
$235$	−7.64780			−0.498888
$236$	3.13699			0.204200
$237$	−6.51762	+	2.92101i	−0.423365	+	0.189740i
$238$	−3.74958	+	2.16482i	−0.243049	+	0.140324i
$239$			26.1968i			1.69453i	0.531172	+	0.847264i	$0.321752\pi$
$239$			26.1968i			1.69453i	−0.531172	+	0.847264i	$0.678248\pi$
$240$	−0.176823	+	1.72300i	−0.0114139	+	0.111219i
$241$	−16.7185	+	9.65242i	−1.07693	+	0.621767i	−0.930067	−	0.367390i	$-0.880251\pi$
$241$	−16.7185	+	9.65242i	−1.07693	+	0.621767i	−0.146865	+	0.989157i	$0.546918\pi$
$242$	−5.43462	+	9.41304i	−0.349351	+	0.605093i
$243$	−0.191165	−	15.5873i	−0.0122632	−	0.999925i
$244$	3.73492	−	6.46907i	0.239104	−	0.414140i
$245$	−0.405655	−	0.234205i	−0.0259164	−	0.0149628i
$246$	7.31413	+	0.750613i	0.466332	+	0.0478573i
$247$	0.269553	−	11.6853i	0.0171513	−	0.743516i
$248$			5.44068i			0.345483i
$249$	−0.914990	−	0.661357i	−0.0579852	−	0.0419118i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	−9.65147	+	5.57228i	−0.609195	+	0.351719i	−0.772650	−	0.634832i	$-0.781069\pi$
$251$	−9.65147	+	5.57228i	−0.609195	+	0.351719i	0.163455	+	0.986551i	$0.447736\pi$
$252$	−5.45593	+	6.11952i	−0.343691	+	0.385494i
$253$	−0.718482	−	1.24445i	−0.0451706	−	0.0782378i
$254$		−	3.56102i		−	0.223438i
$255$	2.72975	+	0.280141i	0.170944	+	0.0175431i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.98490	+	6.90205i	0.248571	+	0.430538i	0.963130	−	0.269038i	$-0.0867057\pi$
$257$	3.98490	+	6.90205i	0.248571	+	0.430538i	−0.714558	+	0.699576i	$0.753372\pi$
$258$	−4.26251	−	0.437440i	−0.265372	−	0.0272338i
$259$			21.6877i			1.34761i
$260$	1.34075	+	2.32225i	0.0831497	+	0.144020i
$261$	4.99064	−	5.59765i	0.308913	−	0.346486i
$262$	4.10014	−	2.36722i	0.253308	−	0.146247i
$263$	14.1470	+	8.16779i	0.872343	+	0.503647i	0.868126	−	0.496344i	$-0.165324\pi$
$263$	14.1470	+	8.16779i	0.872343	+	0.503647i	0.00421689	+	0.999991i	$0.498658\pi$
$264$	0.507593	+	0.366889i	0.0312402	+	0.0225805i
$265$			2.74917i			0.168880i
$266$	5.71659	+	10.4509i	0.350507	+	0.640783i
$267$	18.8673	+	1.93626i	1.15466	+	0.118497i
$268$	0.731797	+	0.422503i	0.0447016	+	0.0258085i
$269$	15.6050	−	27.0287i	0.951456	−	1.64797i	0.209179	−	0.977877i	$-0.432921\pi$
$269$	15.6050	−	27.0287i	0.951456	−	1.64797i	0.742277	−	0.670093i	$-0.233746\pi$
$270$	5.07452	−	1.11771i	0.308825	−	0.0680216i
$271$	15.8830	−	27.5101i	0.964823	−	1.67112i	0.254733	−	0.967011i	$-0.418012\pi$
$271$	15.8830	−	27.5101i	0.964823	−	1.67112i	0.710090	−	0.704111i	$-0.248654\pi$
$272$	−1.37205	+	0.792151i	−0.0831925	+	0.0480312i
$273$	−1.29578	+	12.6263i	−0.0784241	+	0.764180i
$274$		−	4.70818i		−	0.284431i
$275$	0.313153	−	0.180799i	0.0188838	−	0.0109026i
$276$	6.28110	−	2.81500i	0.378078	−	0.169443i
$277$	−20.8653			−1.25367			−0.626836	−	0.779151i	$-0.715651\pi$
$277$	−20.8653			−1.25367			−0.626836	+	0.779151i	$0.715651\pi$
$278$	14.9345			0.895710
$279$	15.4982	−	5.11987i	0.927855	−	0.306519i
$280$	−2.36671	−	1.36642i	−0.141438	−	0.0816592i
$281$	0.194045	+	0.336095i	0.0115757	+	0.0200498i	0.871755	−	0.489942i	$-0.162982\pi$
$281$	0.194045	+	0.336095i	0.0115757	+	0.0200498i	−0.860180	+	0.509991i	$0.829649\pi$
$282$	−10.7356	−	7.75972i	−0.639297	−	0.462085i
$283$	−10.8411	+	18.7773i	−0.644434	+	1.11619i	0.339997	+	0.940426i	$0.389574\pi$
$283$	−10.8411	+	18.7773i	−0.644434	+	1.11619i	−0.984432	+	0.175767i	$0.943760\pi$
$284$	−8.44518			−0.501129
$285$	0.943751	−	7.49062i	0.0559030	−	0.443706i
$286$	0.969623			0.0573350
$287$	−5.80044	+	10.0467i	−0.342389	+	0.593036i
$288$	−1.99643	+	2.23925i	−0.117641	+	0.131949i
$289$	−7.24499	−	12.5487i	−0.426176	−	0.738159i
$290$	2.16488	+	1.24989i	0.127126	+	0.0733961i
$291$	−27.9300	+	12.5174i	−1.63728	+	0.733783i
$292$	−12.1500			−0.711026
$293$	−32.2855			−1.88614			−0.943069	−	0.332596i	$-0.892076\pi$
$293$	−32.2855			−1.88614			−0.943069	+	0.332596i	$0.892076\pi$
$294$	−0.331807	−	0.740357i	−0.0193514	−	0.0431785i
$295$	2.71671	−	1.56849i	0.158173	−	0.0913212i
$296$			7.93595i			0.461268i
$297$	0.567453	−	1.79118i	0.0329269	−	0.103935i
$298$	19.6035	−	11.3181i	1.13560	−	0.655640i
$299$	5.32805	−	9.22845i	0.308129	−	0.533695i
$300$	0.708367	+	1.58057i	0.0408976	+	0.0912545i
$301$	3.38037	−	5.85497i	0.194841	−	0.337475i
$302$	−3.14748	−	1.81720i	−0.181117	−	0.104568i
$303$	−0.121966	+	1.18847i	−0.00700679	+	0.0682756i
$304$	2.09181	+	3.82417i	0.119974	+	0.219331i
$305$		−	7.46984i		−	0.427722i
$306$	3.54765	+	3.16295i	0.202806	+	0.180814i
$307$	−16.9205	−	9.76906i	−0.965705	−	0.557550i	−0.0677805	−	0.997700i	$-0.521592\pi$
$307$	−16.9205	−	9.76906i	−0.965705	−	0.557550i	−0.897924	+	0.440150i	$0.854925\pi$
$308$	−0.855796	+	0.494094i	−0.0487635	+	0.0281536i
$309$	21.6102	+	15.6199i	1.22936	+	0.888586i
$310$	2.72034	+	4.71176i	0.154505	+	0.267610i
$311$			30.7306i			1.74257i	0.490775	+	0.871287i	$0.336714\pi$
$311$			30.7306i			1.74257i	−0.490775	+	0.871287i	$0.663286\pi$
$312$	−0.474151	+	4.62022i	−0.0268435	+	0.261569i
$313$	−5.11644	−	8.86194i	−0.289198	−	0.500906i	0.684420	−	0.729088i	$-0.260055\pi$
$313$	−5.11644	−	8.86194i	−0.289198	−	0.500906i	−0.973619	+	0.228181i	$0.926722\pi$
$314$	−6.76442	−	11.7163i	−0.381738	−	0.661190i
$315$	−1.66521	+	8.02763i	−0.0938239	+	0.452305i
$316$		−	4.12358i		−	0.231969i
$317$	0.252084	+	0.436622i	0.0141584	+	0.0245231i	0.873018	−	0.487688i	$-0.162160\pi$
$317$	0.252084	+	0.436622i	0.0141584	+	0.0245231i	−0.858859	+	0.512211i	$0.828826\pi$
$318$	−2.78940	+	3.85915i	−0.156422	+	0.216411i
$319$	0.782814	−	0.451958i	0.0438291	−	0.0253048i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	−0.916020	+	1.26732i	−0.0511272	+	0.0707348i
$322$			10.8601i			0.605211i
$323$	6.05865	−	3.31406i	0.337112	−	0.184399i
$324$	8.25743	+	3.57979i	0.458746	+	0.198877i
$325$	2.32225	+	1.34075i	0.128815	+	0.0743714i
$326$	9.47783	−	16.4161i	0.524929	−	0.909203i
$327$	−15.0979	+	6.76642i	−0.834913	+	0.374184i
$328$	−2.12250	+	3.67627i	−0.117195	+	0.202988i
$329$	18.1001	−	10.4501i	0.997892	−	0.576133i
$330$	0.623033	+	0.0639388i	0.0342968	+	0.00351972i
$331$			16.7161i			0.918800i	0.888229	+	0.459400i	$0.151936\pi$
$331$			16.7161i			0.918800i	−0.888229	+	0.459400i	$0.848064\pi$
$332$	0.564491	−	0.325909i	0.0309805	−	0.0178866i
$333$	22.6062	−	7.46801i	1.23881	−	0.409244i
$334$	5.32175			0.291193
$335$	0.845006			0.0461676
$336$	−1.93585	−	4.31946i	−0.105609	−	0.235646i
$337$	5.81314	+	3.35622i	0.316662	+	0.182825i	0.649904	−	0.760017i	$-0.274809\pi$
$337$	5.81314	+	3.35622i	0.316662	+	0.182825i	−0.333242	+	0.942841i	$0.608143\pi$
$338$	−2.90478	−	5.03123i	−0.157999	−	0.273663i
$339$	−18.3515	+	25.3893i	−0.996715	+	1.37896i
$340$	−0.792151	+	1.37205i	−0.0429604	+	0.0744096i
$341$	1.96733			0.106537
$342$	8.92503	−	9.55740i	0.482610	−	0.516805i
$343$	−17.8498			−0.963798
$344$	1.23694	−	2.14245i	0.0666915	−	0.115513i
$345$	4.03209	−	5.57841i	0.217080	−	0.300332i
$346$	−5.01989	−	8.69470i	−0.269871	−	0.467430i
$347$	28.1207	+	16.2355i	1.50960	+	0.871566i	0.999937	+	0.0111900i	$0.00356197\pi$
$347$	28.1207	+	16.2355i	1.50960	+	0.871566i	0.509660	+	0.860376i	$0.329771\pi$
$348$	1.77076	+	3.95109i	0.0949229	+	0.211801i
$349$	2.90700			0.155608			0.0778040	−	0.996969i	$-0.475209\pi$
$349$	2.90700			0.155608			0.0778040	+	0.996969i	$0.475209\pi$
$350$	−2.73284			−0.146076
$351$	13.6073	−	2.99714i	0.726304	−	0.159975i
$352$	−0.313153	+	0.180799i	−0.0166911	+	0.00963661i
$353$			10.7325i			0.571233i	0.958344	+	0.285616i	$0.0921983\pi$
$353$			10.7325i			0.571233i	−0.958344	+	0.285616i	$0.907802\pi$
$354$	5.40503	+	0.554692i	0.287274	+	0.0294815i
$355$	−7.31374	+	4.22259i	−0.388173	+	0.224112i
$356$	−5.47514	+	9.48321i	−0.290182	+	0.502609i
$357$	−6.84332	+	3.06698i	−0.362187	+	0.162322i
$358$	3.14060	−	5.43967i	0.165986	−	0.287496i
$359$	1.09849	+	0.634215i	0.0579762	+	0.0334726i	0.528708	−	0.848804i	$-0.322677\pi$
$359$	1.09849	+	0.634215i	0.0579762	+	0.0334726i	−0.470732	+	0.882276i	$0.656010\pi$
$360$	−0.609333	+	2.93747i	−0.0321147	+	0.154818i
$361$	−8.73116	−	16.8750i	−0.459535	−	0.888160i
$362$		−	24.5981i		−	1.29285i
$363$	−11.0283	+	15.2577i	−0.578836	+	0.800823i
$364$	−6.34632	−	3.66405i	−0.332638	−	0.192048i
$365$	−10.5222	+	6.07501i	−0.550758	+	0.317980i
$366$	7.57916	−	10.4858i	0.396169	−	0.548102i
$367$	−4.80585	−	8.32397i	−0.250863	−	0.434508i	0.712900	−	0.701265i	$-0.247381\pi$
$367$	−4.80585	−	8.32397i	−0.250863	−	0.434508i	−0.963764	+	0.266757i	$0.914048\pi$
$368$			3.97393i			0.207156i
$369$	12.4695	+	2.58661i	0.649138	+	0.134654i
$370$	3.96797	+	6.87273i	0.206285	+	0.357296i
$371$	−3.75652	−	6.50649i	−0.195029	−	0.337800i
$372$	−0.962037	+	9.37429i	−0.0498793	+	0.486034i
$373$			13.3101i			0.689173i	0.938755	+	0.344586i	$0.111981\pi$
$373$			13.3101i			0.689173i	−0.938755	+	0.344586i	$0.888019\pi$
$374$	0.286440	+	0.496128i	0.0148114	+	0.0256542i
$375$	1.40375	+	1.01463i	0.0724894	+	0.0523955i
$376$	6.62319	−	3.82390i	0.341565	−	0.197203i
$377$	5.80511	+	3.35158i	0.298978	+	0.172615i
$378$	−10.4826	+	9.57921i	−0.539169	+	0.492702i
$379$		−	6.83849i		−	0.351270i	−0.984455	−	0.175635i	$-0.943802\pi$
$379$		−	6.83849i		−	0.351270i	0.984455	−	0.175635i	$-0.0561978\pi$
$380$	3.72365	+	2.26593i	0.191019	+	0.116240i
$381$	0.629671	−	6.13565i	0.0322590	−	0.314339i
$382$	22.1742	+	12.8023i	1.13453	+	0.655023i
$383$	10.2329	−	17.7238i	0.522874	−	0.905645i	−0.476771	−	0.879027i	$-0.658193\pi$
$383$	10.2329	−	17.7238i	0.522874	−	0.905645i	0.999646	−	0.0266177i	$-0.00847367\pi$
$384$	−0.708367	−	1.58057i	−0.0361487	−	0.0806584i
$385$	−0.494094	+	0.855796i	−0.0251814	+	0.0436154i
$386$	−2.59120	+	1.49603i	−0.131889	+	0.0761460i
$387$	−7.26696	−	1.50742i	−0.369400	−	0.0766265i
$388$		−	17.6708i		−	0.897097i
$389$	−9.69169	+	5.59550i	−0.491388	+	0.283703i	−0.725150	−	0.688591i	$-0.758230\pi$
$389$	−9.69169	+	5.59550i	−0.491388	+	0.283703i	0.233762	+	0.972294i	$0.424896\pi$
$390$	1.89949	+	4.23831i	0.0961842	+	0.214615i
$391$	6.29591			0.318398
$392$	0.468410			0.0236583
$393$	7.48313	−	3.35372i	0.377474	−	0.169173i
$394$	−15.3448	−	8.85932i	−0.773060	−	0.446326i
$395$	−2.06179	−	3.57112i	−0.103740	−	0.179683i
$396$	0.809709	+	0.721905i	0.0406894	+	0.0362771i
$397$	19.4671	−	33.7181i	0.977028	−	1.69226i	0.303953	−	0.952687i	$-0.401693\pi$
$397$	19.4671	−	33.7181i	0.977028	−	1.69226i	0.673074	−	0.739575i	$-0.264973\pi$
$398$	20.5724			1.03120
$399$	8.00174	+	19.0177i	0.400588	+	0.952074i
$400$	−1.00000			−0.0500000
$401$	−14.6051	+	25.2968i	−0.729345	+	1.26326i	0.227815	+	0.973704i	$0.426842\pi$
$401$	−14.6051	+	25.2968i	−0.729345	+	1.26326i	−0.957160	+	0.289559i	$0.906492\pi$
$402$	1.18618	+	0.857372i	0.0591612	+	0.0427618i
$403$	7.29458	+	12.6346i	0.363369	+	0.629373i
$404$	−0.597354	−	0.344883i	−0.0297195	−	0.0171586i
$405$	8.94104	−	1.02852i	0.444284	−	0.0511077i
$406$	−6.83150			−0.339042
$407$	2.86962			0.142242
$408$	−2.50411	+	1.12227i	−0.123972	+	0.0555605i
$409$	−13.1471	+	7.59047i	−0.650081	+	0.375325i	−0.788487	−	0.615051i	$-0.789135\pi$
$409$	−13.1471	+	7.59047i	−0.650081	+	0.375325i	0.138406	+	0.990376i	$0.455802\pi$
$410$			4.24499i			0.209645i
$411$	0.832515	−	8.11220i	0.0410649	−	0.400145i
$412$	−13.3321	+	7.69731i	−0.656827	+	0.379219i
$413$	−4.28644	+	7.42433i	−0.210922	+	0.365327i
$414$	11.3201	−	3.73961i	0.556352	−	0.183792i
$415$	0.325909	−	0.564491i	0.0159982	−	0.0277098i
$416$	−2.32225	−	1.34075i	−0.113857	−	0.0657356i
$417$	25.7321	+	2.64076i	1.26011	+	0.129319i
$418$	1.38281	−	0.756395i	0.0676356	−	0.0369965i
$419$		−	18.6245i		−	0.909864i	−0.890526	−	0.454932i	$-0.849663\pi$
$419$		−	18.6245i		−	0.909864i	0.890526	−	0.454932i	$-0.150337\pi$
$420$	−3.83623	−	2.77283i	−0.187189	−	0.135300i
$421$	0.995150	+	0.574550i	0.0485006	+	0.0280019i	0.524054	−	0.851685i	$-0.324419\pi$
$421$	0.995150	+	0.574550i	0.0485006	+	0.0280019i	−0.475554	+	0.879687i	$0.657752\pi$
$422$	−0.240924	+	0.139098i	−0.0117280	+	0.00677117i
$423$	−17.1254	−	15.2683i	−0.832665	−	0.742371i
$424$	−1.37459	−	2.38085i	−0.0667558	−	0.115624i
$425$			1.58430i			0.0768499i
$426$	−14.5511	−	1.49330i	−0.705001	−	0.0723508i
$427$	10.2069	+	17.6789i	0.493948	+	0.855544i
$428$	−0.451404	−	0.781855i	−0.0218194	−	0.0377924i
$429$	1.67066	+	0.171452i	0.0806603	+	0.00827777i
$430$		−	2.47389i		−	0.119301i
$431$	−0.361329	−	0.625840i	−0.0174046	−	0.0301457i	0.857192	−	0.514997i	$-0.172207\pi$
$431$	−0.361329	−	0.625840i	−0.0174046	−	0.0301457i	−0.874597	+	0.484851i	$0.838874\pi$
$432$	−3.83581	+	3.50522i	−0.184550	+	0.168645i
$433$	−20.1778	+	11.6497i	−0.969684	+	0.559847i	−0.899140	−	0.437662i	$-0.855807\pi$
$433$	−20.1778	+	11.6497i	−0.969684	+	0.559847i	−0.0705439	+	0.997509i	$0.522473\pi$
$434$	−12.8765	−	7.43425i	−0.618091	−	0.356855i
$435$	3.50907	+	2.53636i	0.168247	+	0.121609i
$436$		−	9.55213i		−	0.457464i
$437$	0.399474	−	17.3174i	0.0191094	−	0.828402i
$438$	−20.9345	−	2.14840i	−1.00029	−	0.102655i
$439$	4.96102	+	2.86425i	0.236776	+	0.136703i	0.613694	−	0.789544i	$-0.289683\pi$
$439$	4.96102	+	2.86425i	0.236776	+	0.136703i	−0.376918	+	0.926247i	$0.623016\pi$
$440$	−0.180799	+	0.313153i	−0.00861924	+	0.0149290i
$441$	−0.440791	−	1.33431i	−0.0209900	−	0.0635385i
$442$	−2.12415	+	3.67914i	−0.101036	+	0.174999i
$443$	−20.0773	+	11.5917i	−0.953903	+	0.550736i	−0.894291	−	0.447486i	$-0.852320\pi$
$443$	−20.0773	+	11.5917i	−0.953903	+	0.550736i	−0.0596116	+	0.998222i	$0.518986\pi$
$444$	−1.40326	+	13.6736i	−0.0665957	+	0.648923i
$445$			10.9503i			0.519093i
$446$	−4.55894	+	2.63211i	−0.215872	+	0.124634i
$447$	35.7782	−	16.0347i	1.69225	−	0.758417i
$448$	2.73284			0.129115
$449$	−12.0455			−0.568464			−0.284232	−	0.958755i	$-0.591739\pi$
$449$	−12.0455			−0.568464			−0.284232	+	0.958755i	$0.591739\pi$
$450$	0.941036	+	2.84859i	0.0443609	+	0.134284i
$451$	1.32933	+	0.767490i	0.0625958	+	0.0361397i
$452$	−9.04339	−	15.6636i	−0.425365	−	0.736754i
$453$	−5.10179	−	3.68759i	−0.239703	−	0.173258i
$454$	−9.09264	+	15.7489i	−0.426739	+	0.739133i
$455$	−7.32810			−0.343547
$456$	2.92800	+	6.95894i	0.137116	+	0.325882i
$457$	30.1464			1.41019			0.705094	−	0.709113i	$-0.250905\pi$
$457$	30.1464			1.41019			0.705094	+	0.709113i	$0.250905\pi$
$458$	0.0461949	−	0.0800119i	0.00215855	−	0.00373871i
$459$	5.55333	+	6.07707i	0.259207	+	0.283653i
$460$	1.98697	+	3.44153i	0.0926428	+	0.160462i
$461$	−34.0561	−	19.6623i	−1.58615	−	0.915765i	−0.993933	−	0.109987i	$-0.964919\pi$
$461$	−34.0561	−	19.6623i	−1.58615	−	0.915765i	−0.592218	−	0.805778i	$-0.701748\pi$
$462$	−1.56190	+	0.700000i	−0.0726664	+	0.0325670i
$463$	−16.6034			−0.771624			−0.385812	−	0.922577i	$-0.626079\pi$
$463$	−16.6034			−0.771624			−0.385812	+	0.922577i	$0.626079\pi$
$464$	−2.49978			−0.116050
$465$	3.85400	+	8.59939i	0.178725	+	0.398787i
$466$	−12.3845	+	7.15019i	−0.573701	+	0.331226i
$467$		−	17.0263i		−	0.787884i	−0.919135	−	0.393942i	$-0.871111\pi$
$467$		−	17.0263i		−	0.787884i	0.919135	−	0.393942i	$-0.128889\pi$
$468$	−1.63393	+	7.87681i	−0.0755282	+	0.364106i
$469$	−1.99988	+	1.15463i	−0.0923460	+	0.0533160i
$470$	3.82390	−	6.62319i	0.176383	−	0.305505i
$471$	−9.58338	−	21.3833i	−0.441579	−	0.985292i
$472$	−1.56849	+	2.71671i	−0.0721957	+	0.125047i
$473$	−0.774704	−	0.447276i	−0.0356209	−	0.0205658i
$474$	0.729144	−	7.10493i	0.0334907	−	0.326340i
$475$	4.35774	+	0.100523i	0.199947	+	0.00461233i
$476$		−	4.32964i		−	0.198449i
$477$	−5.48853	+	6.15610i	−0.251303	+	0.281868i
$478$	−22.6871	−	13.0984i	−1.03768	−	0.599106i
$479$	−10.9769	+	6.33750i	−0.501546	+	0.289568i	−0.729352	−	0.684139i	$-0.760178\pi$
$479$	−10.9769	+	6.33750i	−0.501546	+	0.289568i	0.227806	+	0.973707i	$0.426845\pi$
$480$	−1.40375	−	1.01463i	−0.0640722	−	0.0463115i
$481$	10.6401	+	18.4292i	0.485147	+	0.840300i
$482$		−	19.3048i		−	0.879311i
$483$	−1.92032	+	18.7120i	−0.0873776	+	0.851426i
$484$	−5.43462	−	9.41304i	−0.247028	−	0.427866i
$485$	−8.83538	−	15.3033i	−0.401194	−	0.694889i
$486$	13.5946	+	7.62809i	0.616662	+	0.346017i
$487$		−	32.6229i		−	1.47829i	−0.673549	−	0.739143i	$-0.735231\pi$
$487$		−	32.6229i		−	1.47829i	0.673549	−	0.739143i	$-0.264769\pi$
$488$	3.73492	+	6.46907i	0.169072	+	0.292841i
$489$	19.2331	−	26.6090i	0.869749	−	1.20330i
$490$	0.405655	−	0.234205i	0.0183256	−	0.0105803i
$491$	6.27240	+	3.62137i	0.283070	+	0.163430i	0.634812	−	0.772666i	$-0.281077\pi$
$491$	6.27240	+	3.62137i	0.283070	+	0.163430i	−0.351743	+	0.936097i	$0.614411\pi$
$492$	−4.30712	+	5.95892i	−0.194180	+	0.268649i
$493$			3.96041i			0.178368i
$494$	9.98496	+	6.07608i	0.449245	+	0.273376i
$495$	1.06218	+	0.220333i	0.0477415	+	0.00990325i
$496$	−4.71176	−	2.72034i	−0.211564	−	0.122147i
$497$	11.5397	−	19.9873i	0.517624	−	0.896552i
$498$	1.03025	−	0.461727i	0.0461665	−	0.0206905i
$499$	8.51878	−	14.7550i	0.381353	−	0.660522i	−0.609903	−	0.792476i	$-0.708792\pi$
$499$	8.51878	−	14.7550i	0.381353	−	0.660522i	0.991256	+	0.131954i	$0.0421250\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	9.16938	+	0.941008i	0.409658	+	0.0420412i
$502$		−	11.1446i		−	0.497406i
$503$	24.2478	−	13.9995i	1.08115	−	0.624205i	0.149947	−	0.988694i	$-0.452090\pi$
$503$	24.2478	−	13.9995i	1.08115	−	0.624205i	0.931208	+	0.364489i	$0.118756\pi$
$504$	−2.57170	−	7.78473i	−0.114553	−	0.346760i
$505$	−0.689765			−0.0306942
$506$	1.43696			0.0638809
$507$	−4.11531	−	9.18246i	−0.182767	−	0.407807i
$508$	3.08394	+	1.78051i	0.136828	+	0.0789974i
$509$	−16.1465	−	27.9666i	−0.715683	−	1.23960i	−0.962695	−	0.270587i	$-0.912782\pi$
$509$	−16.1465	−	27.9666i	−0.715683	−	1.23960i	0.247012	−	0.969012i	$-0.420551\pi$
$510$	−1.60749	+	2.22397i	−0.0711807	+	0.0984788i
$511$	16.6020	−	28.7555i	0.734430	−	1.27207i
$512$	1.00000			0.0441942
$513$	17.0678	−	14.8893i	0.753562	−	0.657377i
$514$	−7.96980			−0.351533
$515$	−7.69731	+	13.3321i	−0.339184	+	0.587484i
$516$	2.51009	−	3.47272i	0.110501	−	0.152878i
$517$	−1.38271	−	2.39493i	−0.0608117	−	0.105329i
$518$	−18.7821	−	10.8438i	−0.825237	−	0.476451i
$519$	−7.11185	−	15.8686i	−0.312175	−	0.696555i
$520$	−2.68150			−0.117591
$521$	−32.0134			−1.40253			−0.701266	−	0.712900i	$-0.747381\pi$
$521$	−32.0134			−1.40253			−0.701266	+	0.712900i	$0.747381\pi$
$522$	2.35238	+	7.12085i	0.102961	+	0.311671i
$523$	−15.0870	+	8.71046i	−0.659707	+	0.380882i	−0.792165	−	0.610307i	$-0.791046\pi$
$523$	−15.0870	+	8.71046i	−0.659707	+	0.380882i	0.132458	+	0.991189i	$0.457713\pi$
$524$			4.73444i			0.206825i
$525$	−4.70869	−	0.483229i	−0.205504	−	0.0210899i
$526$	−14.1470	+	8.16779i	−0.616840	+	0.356133i
$527$	−4.30984	+	7.46485i	−0.187739	+	0.325174i
$528$	−0.571532	+	0.256144i	−0.0248727	+	0.0111472i
$529$	−3.60393	+	6.24218i	−0.156692	+	0.271399i
$530$	−2.38085	−	1.37459i	−0.103418	−	0.0597082i
$531$	9.21479	+	1.91147i	0.399888	+	0.0829507i
$532$	−11.9090	−	0.274714i	−0.516321	−	0.0119104i
$533$			11.3829i			0.493050i
$534$	−11.1105	+	15.3715i	−0.480799	+	0.665188i
$535$	−0.781855	−	0.451404i	−0.0338025	−	0.0195159i
$536$	−0.731797	+	0.422503i	−0.0316088	+	0.0182494i
$537$	6.37311	−	8.81724i	0.275020	−	0.380492i
$538$	15.6050	+	27.0287i	0.672781	+	1.16529i
$539$		−	0.169376i		−	0.00729554i
$540$	−1.56929	+	4.95352i	−0.0675316	+	0.213165i
$541$	−14.8276	−	25.6821i	−0.637487	−	1.10416i	−0.985982	−	0.166850i	$-0.946641\pi$
$541$	−14.8276	−	25.6821i	−0.637487	−	1.10416i	0.348495	−	0.937311i	$-0.386693\pi$
$542$	15.8830	+	27.5101i	0.682233	+	1.18166i
$543$	4.34951	−	42.3825i	0.186655	−	1.81881i
$544$		−	1.58430i		−	0.0679264i
$545$	−4.77607	−	8.27239i	−0.204584	−	0.354350i
$546$	−10.2868	−	7.43534i	−0.440236	−	0.318203i
$547$	−20.9812	+	12.1135i	−0.897093	+	0.517937i	−0.876256	−	0.481846i	$-0.839967\pi$
$547$	−20.9812	+	12.1135i	−0.897093	+	0.517937i	−0.0208373	+	0.999783i	$0.506633\pi$
$548$	4.07740	+	2.35409i	0.174178	+	0.100562i
$549$	14.9130	−	16.7269i	0.636473	−	0.713886i
$550$			0.361598i			0.0154186i
$551$	10.8934	+	0.251287i	0.464075	+	0.0107052i
$552$	−0.702683	+	6.84709i	−0.0299082	+	0.291432i
$553$	9.75931	+	5.63454i	0.415008	+	0.239605i
$554$	10.4326	−	18.0699i	0.443240	−	0.767715i
$555$	5.62157	+	12.5434i	0.238622	+	0.532436i
$556$	−7.46724	+	12.9336i	−0.316681	+	0.548508i
$557$	16.2011	−	9.35371i	0.686463	−	0.396329i	−0.115823	−	0.993270i	$-0.536951\pi$
$557$	16.2011	−	9.35371i	0.686463	−	0.396329i	0.802285	+	0.596941i	$0.203617\pi$
$558$	−3.31518	+	15.9818i	−0.140343	+	0.676564i
$559$		−	6.63372i		−	0.280577i
$560$	2.36671	−	1.36642i	0.100012	−	0.0577418i
$561$	0.405809	+	0.905479i	0.0171333	+	0.0382293i
$562$	−0.388089			−0.0163706
$563$	37.5624			1.58307			0.791534	−	0.611125i	$-0.209283\pi$
$563$	37.5624			1.58307			0.791534	+	0.611125i	$0.209283\pi$
$564$	12.0879	−	5.41746i	0.508993	−	0.228116i
$565$	−15.6636	−	9.04339i	−0.658973	−	0.380458i
$566$	−10.8411	−	18.7773i	−0.455684	−	0.789268i
$567$	−19.7554	+	14.6514i	−0.829650	+	0.615302i
$568$	4.22259	−	7.31374i	0.177176	−	0.306878i
$569$	−21.0817			−0.883790			−0.441895	−	0.897067i	$-0.645694\pi$
$569$	−21.0817			−0.883790			−0.441895	+	0.897067i	$0.645694\pi$
$570$	6.01519	+	4.56262i	0.251949	+	0.191107i
$571$	23.5374			0.985009			0.492505	−	0.870310i	$-0.336082\pi$
$571$	23.5374			0.985009			0.492505	+	0.870310i	$0.336082\pi$
$572$	−0.484812	+	0.839718i	−0.0202710	+	0.0351104i
$573$	35.9425	+	25.9793i	1.50152	+	1.08530i
$574$	−5.80044	−	10.0467i	−0.242106	−	0.419340i
$575$	3.44153	+	1.98697i	0.143522	+	0.0828622i
$576$	−0.941036	−	2.84859i	−0.0392098	−	0.118691i
$577$	−7.74252			−0.322325			−0.161163	−	0.986928i	$-0.551524\pi$
$577$	−7.74252			−0.322325			−0.161163	+	0.986928i	$0.551524\pi$
$578$	14.4900			0.602704
$579$	−4.72918	+	2.11948i	−0.196538	+	0.0880825i
$580$	−2.16488	+	1.24989i	−0.0898916	+	0.0518989i
$581$			1.78131i			0.0739014i
$582$	3.12460	−	30.4468i	0.129519	−	1.26206i
$583$	−0.860910	+	0.497047i	−0.0356553	+	0.0205856i
$584$	6.07501	−	10.5222i	0.251386	−	0.435413i
$585$	2.52339	+	7.63848i	0.104329	+	0.315812i
$586$	16.1427	−	27.9601i	0.666851	−	1.15502i
$587$	−33.6896	−	19.4507i	−1.39052	−	0.802816i	−0.397146	−	0.917755i	$-0.629999\pi$
$587$	−33.6896	−	19.4507i	−1.39052	−	0.802816i	−0.993373	+	0.114939i	$0.963333\pi$
$588$	0.807072	+	0.0828258i	0.0332831	+	0.00341568i
$589$	20.2592	+	12.3282i	0.834765	+	0.507973i
$590$			3.13699i			0.129148i
$591$	−24.8726	−	17.9779i	−1.02312	−	0.739514i
$592$	−6.87273	−	3.96797i	−0.282468	−	0.163083i
$593$	7.33331	−	4.23389i	0.301143	−	0.173865i	−0.341813	−	0.939768i	$-0.611041\pi$
$593$	7.33331	−	4.23389i	0.301143	−	0.173865i	0.642956	+	0.765903i	$0.277708\pi$
$594$	1.26748	+	1.38702i	0.0520053	+	0.0569100i
$595$	−2.16482	−	3.74958i	−0.0887490	−	0.153718i
$596$			22.6362i			0.927215i
$597$	35.4463	+	3.63768i	1.45072	+	0.148880i
$598$	5.32805	+	9.22845i	0.217880	+	0.377379i
$599$	18.3405	+	31.7667i	0.749372	+	1.29795i	0.948124	+	0.317901i	$0.102978\pi$
$599$	18.3405	+	31.7667i	0.749372	+	1.29795i	−0.198752	+	0.980050i	$0.563689\pi$
$600$	−1.72300	−	0.176823i	−0.0703412	−	0.00721877i
$601$		−	9.79356i		−	0.399488i	−0.979848	−	0.199744i	$-0.935989\pi$
$601$		−	9.79356i		−	0.399488i	0.979848	−	0.199744i	$-0.0640110\pi$
$602$	3.38037	+	5.85497i	0.137773	+	0.238631i
$603$	1.89218	+	1.68700i	0.0770557	+	0.0686998i
$604$	3.14748	−	1.81720i	0.128069	−	0.0739408i
$605$	−9.41304	−	5.43462i	−0.382695	−	0.220949i
$606$	−0.968259	−	0.699860i	−0.0393328	−	0.0284298i
$607$		−	12.9985i		−	0.527593i	−0.964578	−	0.263796i	$-0.915025\pi$
$607$		−	12.9985i		−	0.527593i	0.964578	−	0.263796i	$-0.0849747\pi$
$608$	−4.35774	−	0.100523i	−0.176730	−	0.00407676i
$609$	−11.7707	−	1.20797i	−0.476972	−	0.0489493i
$610$	6.46907	+	3.73492i	0.261925	+	0.151223i
$611$	10.2538	−	17.7601i	0.414824	−	0.718496i
$612$	−4.51302	+	1.49088i	−0.182428	+	0.0602654i
$613$	−14.8471	+	25.7160i	−0.599669	+	1.03866i	0.393200	+	0.919453i	$0.371368\pi$
$613$	−14.8471	+	25.7160i	−0.599669	+	1.03866i	−0.992870	+	0.119205i	$0.961965\pi$
$614$	16.9205	−	9.76906i	0.682856	−	0.394247i
$615$	−0.750613	+	7.31413i	−0.0302676	+	0.294934i
$616$		−	0.988188i		−	0.0398152i
$617$	−11.7412	+	6.77878i	−0.472683	+	0.272904i	−0.717362	−	0.696700i	$-0.754651\pi$
$617$	−11.7412	+	6.77878i	−0.472683	+	0.272904i	0.244679	+	0.969604i	$0.421317\pi$
$618$	−24.3324	+	10.9051i	−0.978791	+	0.438666i
$619$	11.0205			0.442953			0.221476	−	0.975166i	$-0.428912\pi$
$619$	11.0205			0.442953			0.221476	+	0.975166i	$0.428912\pi$
$620$	−5.44068			−0.218503
$621$	20.1658	−	4.44170i	0.809225	−	0.178239i
$622$	−26.6135	−	15.3653i	−1.06710	−	0.616093i
$623$	−14.9627	−	25.9161i	−0.599466	−	1.03831i
$624$	−3.76416	−	2.72074i	−0.150687	−	0.108917i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	10.2329			0.408988
$627$	2.51634	−	1.05876i	0.100493	−	0.0422826i
$628$	13.5288			0.539859
$629$	−6.28647	+	10.8885i	−0.250658	+	0.434152i
$630$	−6.11952	−	5.45593i	−0.243808	−	0.217369i
$631$	4.03125	+	6.98234i	0.160482	+	0.277962i	0.935042	−	0.354538i	$-0.115362\pi$
$631$	4.03125	+	6.98234i	0.160482	+	0.277962i	−0.774560	+	0.632501i	$0.782029\pi$
$632$	3.57112	+	2.06179i	0.142052	+	0.0820136i
$633$	−0.439708	+	0.197064i	−0.0174768	+	0.00783261i
$634$	−0.504167			−0.0200230
$635$	3.56102			0.141315
$636$	−1.94742	−	4.34527i	−0.0772204	−	0.172301i
$637$	1.08776	−	0.628021i	0.0430988	−	0.0248831i
$638$			0.903915i			0.0357864i
$639$	−24.8074	−	5.14593i	−0.981367	−	0.203570i
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$	2.77035	−	4.79838i	0.109422	−	0.189525i	−0.806114	−	0.591760i	$-0.798433\pi$
$641$	2.77035	−	4.79838i	0.109422	−	0.189525i	0.915536	+	0.402235i	$0.131767\pi$
$642$	−0.639520	−	1.42696i	−0.0252398	−	0.0563174i
$643$	−20.2446	+	35.0647i	−0.798369	+	1.38282i	0.122308	+	0.992492i	$0.460970\pi$
$643$	−20.2446	+	35.0647i	−0.798369	+	1.38282i	−0.920678	+	0.390324i	$0.872363\pi$
$644$	−9.40514	−	5.43006i	−0.370614	−	0.213974i
$645$	0.437440	−	4.26251i	0.0172242	−	0.167836i
$646$	−0.159259	+	6.90397i	−0.00626598	+	0.271633i
$647$			13.7403i			0.540185i	0.962834	+	0.270093i	$0.0870543\pi$
$647$			13.7403i			0.540185i	−0.962834	+	0.270093i	$0.912946\pi$
$648$	−7.22890	+	5.36125i	−0.283978	+	0.210610i
$649$	0.982355	+	0.567163i	0.0385608	+	0.0222631i
$650$	−2.32225	+	1.34075i	−0.0910860	+	0.0525885i
$651$	−20.8717	−	15.0861i	−0.818025	−	0.591270i
$652$	9.47783	+	16.4161i	0.371181	+	0.642904i
$653$			16.0733i			0.628997i	0.949258	+	0.314498i	$0.101836\pi$
$653$			16.0733i			0.628997i	−0.949258	+	0.314498i	$0.898164\pi$
$654$	1.68904	−	16.4583i	0.0660466	−	0.643572i
$655$	2.36722	+	4.10014i	0.0924949	+	0.160206i
$656$	−2.12250	−	3.67627i	−0.0828696	−	0.143534i
$657$	−35.6903	−	7.40340i	−1.39241	−	0.288834i
$658$			20.9002i			0.814775i
$659$	−0.00725277	−	0.0125622i	−0.000282528	−	0.000489352i	0.865884	−	0.500245i	$-0.166757\pi$
$659$	−0.00725277	−	0.0125622i	−0.000282528	−	0.000489352i	−0.866167	+	0.499755i	$0.833423\pi$
$660$	−0.366889	+	0.507593i	−0.0142811	+	0.0197580i
$661$	1.46214	−	0.844167i	0.0568706	−	0.0328343i	−0.471295	−	0.881976i	$-0.656213\pi$
$661$	1.46214	−	0.844167i	0.0568706	−	0.0328343i	0.528166	+	0.849141i	$0.322880\pi$
$662$	−14.4766	−	8.35805i	−0.562648	−	0.324845i
$663$	−4.31047	+	5.96356i	−0.167405	+	0.231605i
$664$			0.651818i			0.0252954i
$665$	−10.4509	+	5.71659i	−0.405267	+	0.221680i
$666$	−4.83563	+	23.3116i	−0.187377	+	0.903306i
$667$	8.60307	+	4.96699i	0.333112	+	0.192322i
$668$	−2.66087	+	4.60877i	−0.102952	+	0.178319i
$669$	−8.32049	+	3.72900i	−0.321689	+	0.144171i
$670$	−0.422503	+	0.731797i	−0.0163227	+	0.0282718i
$671$	2.33920	−	1.35054i	0.0903039	−	0.0521370i
$672$	4.70869	+	0.483229i	0.181641	+	0.0186410i
$673$			23.2047i			0.894476i	0.894415	+	0.447238i	$0.147592\pi$
$673$			23.2047i			0.894476i	−0.894415	+	0.447238i	$0.852408\pi$
$674$	−5.81314	+	3.35622i	−0.223914	+	0.129277i
$675$	1.11771	+	5.07452i	0.0430207	+	0.195318i
$676$	5.80957			0.223445
$677$	−41.7346			−1.60399			−0.801995	−	0.597330i	$-0.796228\pi$
$677$	−41.7346			−1.60399			−0.801995	+	0.597330i	$0.796228\pi$
$678$	−12.8121	−	28.5875i	−0.492045	−	1.09790i
$679$	41.8215	+	24.1457i	1.60496	+	0.926626i
$680$	−0.792151	−	1.37205i	−0.0303776	−	0.0526155i
$681$	−18.4514	+	25.5276i	−0.707059	+	0.978220i
$682$	−0.983667	+	1.70376i	−0.0376666	+	0.0652404i
$683$	38.4483			1.47118			0.735592	−	0.677424i	$-0.236904\pi$
$683$	38.4483			1.47118			0.735592	+	0.677424i	$0.236904\pi$
$684$	3.81444	+	12.5080i	0.145849	+	0.478255i
$685$	4.70818			0.179890
$686$	8.92489	−	15.4584i	0.340754	−	0.590203i
$687$	0.0937418	−	0.129692i	0.00357647	−	0.00494807i
$688$	1.23694	+	2.14245i	0.0471580	+	0.0816801i
$689$	−6.38425	−	3.68595i	−0.243221	−	0.140423i
$690$	2.81500	+	6.28110i	0.107165	+	0.239117i
$691$	−6.15004			−0.233958			−0.116979	−	0.993134i	$-0.537321\pi$
$691$	−6.15004			−0.233958			−0.116979	+	0.993134i	$0.537321\pi$
$692$	10.0398			0.381655
$693$	−2.81494	+	0.929920i	−0.106931	+	0.0353247i
$694$	−28.1207	+	16.2355i	−1.06745	+	0.616290i
$695$			14.9345i			0.566497i
$696$	−4.30713	−	0.442019i	−0.163261	−	0.0167547i
$697$	−5.82432	+	3.36268i	−0.220612	+	0.127370i
$698$	−1.45350	+	2.51753i	−0.0550157	+	0.0952900i
$699$	−22.6028	+	10.1299i	−0.854917	+	0.383149i
$700$	1.36642	−	2.36671i	0.0516458	−	0.0894532i
$701$	11.7642	+	6.79204i	0.444326	+	0.256532i	0.705431	−	0.708779i	$-0.250753\pi$
$701$	11.7642	+	6.79204i	0.444326	+	0.256532i	−0.261105	+	0.965310i	$0.584087\pi$
$702$	−4.20806	+	13.2828i	−0.158823	+	0.501329i
$703$	29.5507	+	17.9823i	1.11453	+	0.678214i
$704$		−	0.361598i		−	0.0136282i
$705$	7.75972	−	10.7356i	0.292248	−	0.404327i
$706$	−9.29461	−	5.36625i	−0.349807	−	0.201961i
$707$	1.63247	−	0.942509i	0.0613955	−	0.0354467i
$708$	−3.18289	+	4.40355i	−0.119620	+	0.165495i
$709$	6.74259	+	11.6785i	0.253223	+	0.438596i	0.964411	−	0.264406i	$-0.0851759\pi$
$709$	6.74259	+	11.6785i	0.253223	+	0.438596i	−0.711188	+	0.703002i	$0.751843\pi$
$710$		−	8.44518i		−	0.316942i
$711$	2.51263	−	12.1129i	0.0942311	−	0.454268i
$712$	−5.47514	−	9.48321i	−0.205189	−	0.355398i
$713$	10.8104	+	18.7242i	0.404854	+	0.701228i
$714$	0.765581	−	7.45998i	0.0286511	−	0.279183i
$715$			0.969623i			0.0362618i
$716$	3.14060	+	5.43967i	0.117370	+	0.203290i
$717$	−36.7738	−	26.5801i	−1.37334	−	0.992653i
$718$	−1.09849	+	0.634215i	−0.0409954	+	0.0236687i
$719$	−33.3719	−	19.2672i	−1.24456	−	0.718547i	−0.274541	−	0.961575i	$-0.588526\pi$
$719$	−33.3719	−	19.2672i	−1.24456	−	0.718547i	−0.970019	+	0.243028i	$0.921859\pi$
$720$	−2.23925	−	1.99643i	−0.0834521	−	0.0744026i
$721$		−	42.0710i		−	1.56681i
$722$	18.9798	+	0.876110i	0.706355	+	0.0326054i
$723$	3.41354	−	33.2622i	0.126951	−	1.23704i
$724$	21.3026	+	12.2990i	0.791703	+	0.457090i
$725$	−1.24989	+	2.16488i	−0.0464198	+	0.0804015i
$726$	−7.69942	−	17.1797i	−0.285752	−	0.637597i
$727$	−0.428190	+	0.741646i	−0.0158807	+	0.0275061i	−0.873857	−	0.486184i	$-0.838389\pi$
$727$	−0.428190	+	0.741646i	−0.0158807	+	0.0275061i	0.857976	+	0.513690i	$0.171722\pi$
$728$	6.34632	−	3.66405i	0.235210	−	0.135799i
$729$	22.0746	+	15.5470i	0.817579	+	0.575816i
$730$		−	12.1500i		−	0.449692i
$731$	3.39428	−	1.95969i	0.125542	−	0.0724818i
$732$	5.29139	+	11.8066i	0.195575	+	0.436386i
$733$	4.85312			0.179254			0.0896270	−	0.995975i	$-0.471432\pi$
$733$	4.85312			0.179254			0.0896270	+	0.995975i	$0.471432\pi$
$734$	9.61170			0.354774
$735$	0.740357	−	0.331807i	0.0273085	−	0.0122389i
$736$	−3.44153	−	1.98697i	−0.126856	−	0.0732406i
$737$	0.152776	+	0.264616i	0.00562758	+	0.00974725i
$738$	−8.47484	+	9.50562i	−0.311963	+	0.349907i
$739$	−6.25405	+	10.8323i	−0.230059	+	0.398474i	−0.957825	−	0.287352i	$-0.907225\pi$
$739$	−6.25405	+	10.8323i	−0.230059	+	0.398474i	0.727766	+	0.685825i	$0.240559\pi$
$740$	−7.93595			−0.291731
$741$	16.1297	+	12.2347i	0.592540	+	0.449451i
$742$	7.51304			0.275813
$743$	−8.87174	+	15.3663i	−0.325473	+	0.563735i	−0.981608	−	0.190908i	$-0.938857\pi$
$743$	−8.87174	+	15.3663i	−0.325473	+	0.563735i	0.656135	+	0.754643i	$0.272190\pi$
$744$	−7.63736	−	5.52029i	−0.279999	−	0.202384i
$745$	11.3181	+	19.6035i	0.414663	+	0.718217i
$746$	−11.5269	−	6.65507i	−0.422030	−	0.243659i
$747$	1.85676	−	0.613384i	0.0679353	−	0.0224425i
$748$	−0.572880			−0.0209466
$749$	2.46723			0.0901506
$750$	−1.58057	+	0.708367i	−0.0577144	+	0.0258659i
$751$	14.7151	−	8.49577i	0.536962	−	0.310015i	−0.206885	−	0.978365i	$-0.566333\pi$
$751$	14.7151	−	8.49577i	0.536962	−	0.310015i	0.743847	+	0.668350i	$0.232999\pi$
$752$			7.64780i			0.278887i
$753$	1.97062	−	19.2021i	0.0718132	−	0.699763i
$754$	−5.80511	+	3.35158i	−0.211410	+	0.122057i
$755$	1.81720	−	3.14748i	0.0661347	−	0.114549i
$756$	−3.05452	−	13.8678i	−0.111092	−	0.504368i
$757$	27.1732	−	47.0654i	0.987628	−	1.71062i	0.358008	−	0.933719i	$-0.383456\pi$
$757$	27.1732	−	47.0654i	0.987628	−	1.71062i	0.629620	−	0.776903i	$-0.283211\pi$
$758$	5.92231	+	3.41925i	0.215108	+	0.124193i
$759$	2.47589	+	0.254089i	0.0898692	+	0.00922283i
$760$	−3.82417	+	2.09181i	−0.138717	+	0.0758781i
$761$			14.7061i			0.533095i	0.963822	+	0.266547i	$0.0858829\pi$
$761$			14.7061i			0.533095i	−0.963822	+	0.266547i	$0.914117\pi$
$762$	4.99879	+	3.61314i	0.181087	+	0.130890i
$763$	22.6071	+	13.0522i	0.818432	+	0.472522i
$764$	−22.1742	+	12.8023i	−0.802236	+	0.463171i
$765$	−3.16295	+	3.54765i	−0.114357	+	0.128266i
$766$	10.2329	+	17.7238i	0.369728	+	0.640388i
$767$			8.41182i			0.303733i
$768$	1.72300	+	0.176823i	0.0621735	+	0.00638056i
$769$	−16.8290	−	29.1487i	−0.606869	−	1.05113i	−0.991753	−	0.128164i	$-0.959092\pi$
$769$	−16.8290	−	29.1487i	−0.606869	−	1.05113i	0.384884	−	0.922965i	$-0.374242\pi$
$770$	−0.494094	−	0.855796i	−0.0178059	−	0.0308407i
$771$	−13.7320	−	1.40924i	−0.494545	−	0.0507527i
$772$		−	2.99206i		−	0.107687i
$773$	21.1817	+	36.6877i	0.761851	+	1.31957i	0.941895	+	0.335907i	$0.109043\pi$
$773$	21.1817	+	36.6877i	0.761851	+	1.31957i	−0.180044	+	0.983659i	$0.557624\pi$
$774$	4.93894	−	5.53966i	0.177527	−	0.199119i
$775$	−4.71176	+	2.72034i	−0.169252

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.01463 + 1.40375i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.708367 - 1.58057i) q^{6} +2.73284 q^{7} +1.00000 q^{8} +(-0.941036 - 2.84859i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.01463 + 1.40375i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.708367 - 1.58057i) q^{6} +2.73284 q^{7} +1.00000 q^{8} +(-0.941036 - 2.84859i) q^{9} +(0.866025 - 0.500000i) q^{10} -0.361598i q^{11} +(1.72300 + 0.176823i) q^{12} +(2.32225 - 1.34075i) q^{13} +(-1.36642 + 2.36671i) q^{14} +(1.58057 - 0.708367i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.37205 + 0.792151i) q^{17} +(2.93747 + 0.609333i) q^{18} +(2.26593 - 3.72365i) q^{19} +1.00000i q^{20} +(-2.77283 + 3.83623i) q^{21} +(0.313153 + 0.180799i) q^{22} +(3.44153 - 1.98697i) q^{23} +(-1.01463 + 1.40375i) q^{24} +(0.500000 + 0.866025i) q^{25} +2.68150i q^{26} +(4.95352 + 1.56929i) q^{27} +(-1.36642 - 2.36671i) q^{28} +(1.24989 + 2.16488i) q^{29} +(-0.176823 + 1.72300i) q^{30} +5.44068i q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.507593 + 0.366889i) q^{33} +(-1.37205 + 0.792151i) q^{34} +(-2.36671 - 1.36642i) q^{35} +(-1.99643 + 2.23925i) q^{36} +7.93595i q^{37} +(2.09181 + 3.82417i) q^{38} +(-0.474151 + 4.62022i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(-2.12250 + 3.67627i) q^{41} +(-1.93585 - 4.31946i) q^{42} +(1.23694 - 2.14245i) q^{43} +(-0.313153 + 0.180799i) q^{44} +(-0.609333 + 2.93747i) q^{45} +3.97393i q^{46} +(6.62319 - 3.82390i) q^{47} +(-0.708367 - 1.58057i) q^{48} +0.468410 q^{49} -1.00000 q^{50} +(-2.50411 + 1.12227i) q^{51} +(-2.32225 - 1.34075i) q^{52} +(-1.37459 - 2.38085i) q^{53} +(-3.83581 + 3.50522i) q^{54} +(-0.180799 + 0.313153i) q^{55} +2.73284 q^{56} +(2.92800 + 6.95894i) q^{57} -2.49978 q^{58} +(-1.56849 + 2.71671i) q^{59} +(-1.40375 - 1.01463i) q^{60} +(3.73492 + 6.46907i) q^{61} +(-4.71176 - 2.72034i) q^{62} +(-2.57170 - 7.78473i) q^{63} +1.00000 q^{64} -2.68150 q^{65} +(-0.571532 + 0.256144i) q^{66} +(-0.731797 + 0.422503i) q^{67} -1.58430i q^{68} +(-0.702683 + 6.84709i) q^{69} +(2.36671 - 1.36642i) q^{70} +(4.22259 - 7.31374i) q^{71} +(-0.941036 - 2.84859i) q^{72} +(6.07501 - 10.5222i) q^{73} +(-6.87273 - 3.96797i) q^{74} +(-1.72300 - 0.176823i) q^{75} +(-4.35774 - 0.100523i) q^{76} -0.988188i q^{77} +(-3.76416 - 2.72074i) q^{78} +(3.57112 + 2.06179i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-7.22890 + 5.36125i) q^{81} +(-2.12250 - 3.67627i) q^{82} +0.651818i q^{83} +(4.70869 + 0.483229i) q^{84} +(-0.792151 - 1.37205i) q^{85} +(1.23694 + 2.14245i) q^{86} +(-4.30713 - 0.442019i) q^{87} -0.361598i q^{88} +(-5.47514 - 9.48321i) q^{89} +(-2.23925 - 1.99643i) q^{90} +(6.34632 - 3.66405i) q^{91} +(-3.44153 - 1.98697i) q^{92} +(-7.63736 - 5.52029i) q^{93} +7.64780i q^{94} +(-3.82417 + 2.09181i) q^{95} +(1.72300 + 0.176823i) q^{96} +(15.3033 + 8.83538i) q^{97} +(-0.234205 + 0.405655i) q^{98} +(-1.03004 + 0.340276i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24q - 12q^{2} + 4q^{3} - 12q^{4} - 2q^{6} - 12q^{7} + 24q^{8} - 4q^{9} + O(q^{10}) \)	\( 24q - 12q^{2} + 4q^{3} - 12q^{4} - 2q^{6} - 12q^{7} + 24q^{8} - 4q^{9} - 2q^{12} + 18q^{13} + 6q^{14} - 12q^{16} + 12q^{17} + 2q^{18} + 6q^{19} - 6q^{21} + 18q^{22} + 4q^{24} + 12q^{25} + 28q^{27} + 6q^{28} - 12q^{32} - 22q^{33} - 12q^{34} + 2q^{36} + 6q^{38} + 40q^{39} + 6q^{41} - 6q^{42} - 22q^{43} - 18q^{44} + 8q^{45} + 12q^{47} - 2q^{48} + 12q^{49} - 24q^{50} - 20q^{51} - 18q^{52} + 8q^{53} + 4q^{54} - 12q^{56} + 26q^{59} + 22q^{61} - 18q^{62} + 6q^{63} + 24q^{64} + 8q^{65} + 8q^{66} - 48q^{67} - 64q^{69} + 24q^{71} - 4q^{72} - 8q^{73} + 30q^{74} + 2q^{75} - 12q^{76} - 38q^{78} + 18q^{79} - 12q^{81} + 6q^{82} + 12q^{84} - 22q^{86} - 24q^{87} + 28q^{89} + 8q^{90} + 18q^{91} + 2q^{93} - 2q^{96} + 6q^{97} - 6q^{98} + 2q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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