LMFDB - Embedded newform 390.2.l.c.287.3

Newspace parameters

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.l (of order $4$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
Defining polynomial:	$ x^{20} + 2 x^{18} - 12 x^{17} + 6 x^{16} - 24 x^{15} + 72 x^{14} - 112 x^{13} + 189 x^{12} - 356 x^{11} + 908 x^{10} - 1068 x^{9} + 1701 x^{8} - 3024 x^{7} + 5832 x^{6} - 5832 x^{5} + \cdots + 59049 $ x^20 + 2x^18 - 12x^17 + 6x^16 - 24x^15 + 72x^14 - 112x^13 + 189x^12 - 356x^11 + 908x^10 - 1068x^9 + 1701x^8 - 3024x^7 + 5832x^6 - 5832x^5 + 4374x^4 - 26244x^3 + 13122*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			287.3
Root			$-0.807075 - 1.53252i$ of defining polynomial
Character	$\chi$	$=$	390.287
Dual form			390.2.l.c.53.3

$q$-expansion

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.807075 - 1.53252i) q^{3} -1.00000i q^{4} +(-2.02552 - 0.947239i) q^{5} +(1.65435 + 0.512970i) q^{6} +(-1.59729 - 1.59729i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.69726 + 2.47372i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.807075 - 1.53252i) q^{3} -1.00000i q^{4} +(-2.02552 - 0.947239i) q^{5} +(1.65435 + 0.512970i) q^{6} +(-1.59729 - 1.59729i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.69726 + 2.47372i) q^{9} +(2.10206 - 0.762461i) q^{10} +2.58997i q^{11} +(-1.53252 + 0.807075i) q^{12} +(0.707107 - 0.707107i) q^{13} +2.25891 q^{14} +(0.183080 + 3.86865i) q^{15} -1.00000 q^{16} +(-0.155426 + 0.155426i) q^{17} +(-0.549041 - 2.94933i) q^{18} +6.77461i q^{19} +(-0.947239 + 2.02552i) q^{20} +(-1.15876 + 3.73703i) q^{21} +(-1.83139 - 1.83139i) q^{22} +(1.81338 + 1.81338i) q^{23} +(0.512970 - 1.65435i) q^{24} +(3.20547 + 3.83731i) q^{25} +1.00000i q^{26} +(5.16086 + 0.604615i) q^{27} +(-1.59729 + 1.59729i) q^{28} -0.890831 q^{29} +(-2.86501 - 2.60609i) q^{30} -9.39662 q^{31} +(0.707107 - 0.707107i) q^{32} +(3.96919 - 2.09030i) q^{33} -0.219806i q^{34} +(1.72233 + 4.74837i) q^{35} +(2.47372 + 1.69726i) q^{36} +(-2.88699 - 2.88699i) q^{37} +(-4.79037 - 4.79037i) q^{38} +(-1.65435 - 0.512970i) q^{39} +(-0.762461 - 2.10206i) q^{40} +2.11082i q^{41} +(-1.82311 - 3.46184i) q^{42} +(-4.38869 + 4.38869i) q^{43} +2.58997 q^{44} +(5.78105 - 3.40287i) q^{45} -2.56451 q^{46} +(-3.71800 + 3.71800i) q^{47} +(0.807075 + 1.53252i) q^{48} -1.89731i q^{49} +(-4.98000 - 0.446773i) q^{50} +(0.363635 + 0.112754i) q^{51} +(-0.707107 - 0.707107i) q^{52} +(-2.24202 - 2.24202i) q^{53} +(-4.07680 + 3.22175i) q^{54} +(2.45332 - 5.24604i) q^{55} -2.25891i q^{56} +(10.3823 - 5.46761i) q^{57} +(0.629912 - 0.629912i) q^{58} +2.75114 q^{59} +(3.86865 - 0.183080i) q^{60} -2.28989 q^{61} +(6.64441 - 6.64441i) q^{62} +(6.66228 - 1.24024i) q^{63} +1.00000i q^{64} +(-2.10206 + 0.762461i) q^{65} +(-1.32858 + 4.28471i) q^{66} +(-10.9926 - 10.9926i) q^{67} +(0.155426 + 0.155426i) q^{68} +(1.31552 - 4.24259i) q^{69} +(-4.57548 - 2.13973i) q^{70} +9.60806i q^{71} +(-2.94933 + 0.549041i) q^{72} +(-1.65186 + 1.65186i) q^{73} +4.08282 q^{74} +(3.29371 - 8.00946i) q^{75} +6.77461 q^{76} +(4.13694 - 4.13694i) q^{77} +(1.53252 - 0.807075i) q^{78} +12.1165i q^{79} +(2.02552 + 0.947239i) q^{80} +(-3.23861 - 8.39711i) q^{81} +(-1.49257 - 1.49257i) q^{82} +(-5.93928 - 5.93928i) q^{83} +(3.73703 + 1.15876i) q^{84} +(0.462045 - 0.167593i) q^{85} -6.20654i q^{86} +(0.718967 + 1.36522i) q^{87} +(-1.83139 + 1.83139i) q^{88} +6.43585 q^{89} +(-1.68163 + 6.49401i) q^{90} -2.25891 q^{91} +(1.81338 - 1.81338i) q^{92} +(7.58377 + 14.4005i) q^{93} -5.25805i q^{94} +(6.41718 - 13.7221i) q^{95} +(-1.65435 - 0.512970i) q^{96} +(8.84860 + 8.84860i) q^{97} +(1.34160 + 1.34160i) q^{98} +(-6.40687 - 4.39585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 20 * q - 4 * q^7 - 4 * q^9	$ 20 q - 4 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} + 16 q^{14} + 4 q^{15} - 20 q^{16} - 12 q^{17} + 8 q^{18} - 16 q^{21} + 4 q^{22} - 16 q^{23} - 4 q^{24} + 32 q^{25} + 36 q^{27} - 4 q^{28} + 24 q^{29} - 4 q^{30} - 8 q^{31} + 36 q^{33} + 20 q^{35} - 4 q^{36} - 16 q^{37} - 24 q^{38} - 8 q^{40} + 4 q^{42} - 20 q^{43} - 16 q^{44} + 24 q^{45} - 40 q^{46} - 16 q^{47} + 12 q^{51} - 32 q^{53} - 28 q^{54} - 4 q^{55} + 16 q^{57} + 28 q^{58} - 16 q^{60} + 24 q^{61} - 40 q^{62} + 36 q^{63} + 8 q^{65} + 12 q^{68} - 72 q^{69} + 20 q^{70} + 8 q^{72} + 28 q^{73} + 48 q^{74} - 52 q^{75} + 16 q^{76} - 8 q^{77} + 4 q^{78} - 16 q^{81} - 112 q^{83} - 8 q^{85} + 4 q^{87} + 4 q^{88} + 88 q^{89} - 4 q^{90} - 16 q^{91} - 16 q^{92} + 40 q^{93} + 8 q^{95} + 36 q^{97} - 40 q^{99}+O(q^{100}) $ 20 * q - 4 * q^7 - 4 * q^9 - 8 * q^10 - 4 * q^12 + 16 * q^14 + 4 * q^15 - 20 * q^16 - 12 * q^17 + 8 * q^18 - 16 * q^21 + 4 * q^22 - 16 * q^23 - 4 * q^24 + 32 * q^25 + 36 * q^27 - 4 * q^28 + 24 * q^29 - 4 * q^30 - 8 * q^31 + 36 * q^33 + 20 * q^35 - 4 * q^36 - 16 * q^37 - 24 * q^38 - 8 * q^40 + 4 * q^42 - 20 * q^43 - 16 * q^44 + 24 * q^45 - 40 * q^46 - 16 * q^47 + 12 * q^51 - 32 * q^53 - 28 * q^54 - 4 * q^55 + 16 * q^57 + 28 * q^58 - 16 * q^60 + 24 * q^61 - 40 * q^62 + 36 * q^63 + 8 * q^65 + 12 * q^68 - 72 * q^69 + 20 * q^70 + 8 * q^72 + 28 * q^73 + 48 * q^74 - 52 * q^75 + 16 * q^76 - 8 * q^77 + 4 * q^78 - 16 * q^81 - 112 * q^83 - 8 * q^85 + 4 * q^87 + 4 * q^88 + 88 * q^89 - 4 * q^90 - 16 * q^91 - 16 * q^92 + 40 * q^93 + 8 * q^95 + 36 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.807075	−	1.53252i	−0.465965	−	0.884803i
$3$	−0.807075	−	1.53252i	−0.465965	−	0.884803i
$4$		−	1.00000i		−	0.500000i
$5$	−2.02552	−	0.947239i	−0.905841	−	0.423618i
$5$	−2.02552	−	0.947239i	−0.905841	−	0.423618i
$6$	1.65435	+	0.512970i	0.675384	+	0.209419i
$7$	−1.59729	−	1.59729i	−0.603720	−	0.603720i	0.337578	−	0.941298i	$-0.390392\pi$
$7$	−1.59729	−	1.59729i	−0.603720	−	0.603720i	−0.941298	+	0.337578i	$0.890392\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.69726	+	2.47372i	−0.565754	+	0.824574i
$10$	2.10206	−	0.762461i	0.664730	−	0.241111i
$11$			2.58997i			0.780905i	0.920623	+	0.390453i	$0.127681\pi$
$11$			2.58997i			0.780905i	−0.920623	+	0.390453i	$0.872319\pi$
$12$	−1.53252	+	0.807075i	−0.442402	+	0.232982i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$14$	2.25891			0.603720
$15$	0.183080	+	3.86865i	0.0472710	+	0.998882i
$16$	−1.00000			−0.250000
$17$	−0.155426	+	0.155426i	−0.0376964	+	0.0376964i	−0.725704	−	0.688007i	$-0.758486\pi$
$17$	−0.155426	+	0.155426i	−0.0376964	+	0.0376964i	0.688007	+	0.725704i	$0.258486\pi$
$18$	−0.549041	−	2.94933i	−0.129410	−	0.695164i
$19$			6.77461i			1.55420i	0.629376	+	0.777101i	$0.283311\pi$
$19$			6.77461i			1.55420i	−0.629376	+	0.777101i	$0.716689\pi$
$20$	−0.947239	+	2.02552i	−0.211809	+	0.452920i
$21$	−1.15876	+	3.73703i	−0.252861	+	0.815486i
$22$	−1.83139	−	1.83139i	−0.390453	−	0.390453i
$23$	1.81338	+	1.81338i	0.378116	+	0.378116i	0.870422	−	0.492306i	$-0.163846\pi$
$23$	1.81338	+	1.81338i	0.378116	+	0.378116i	−0.492306	+	0.870422i	$0.663846\pi$
$24$	0.512970	−	1.65435i	0.104710	−	0.337692i
$25$	3.20547	+	3.83731i	0.641095	+	0.767462i
$26$			1.00000i			0.196116i
$27$	5.16086	+	0.604615i	0.993207	+	0.116358i
$28$	−1.59729	+	1.59729i	−0.301860	+	0.301860i
$29$	−0.890831			−0.165423			−0.0827115	−	0.996574i	$-0.526358\pi$
$29$	−0.890831			−0.165423			−0.0827115	+	0.996574i	$0.526358\pi$
$30$	−2.86501	−	2.60609i	−0.523077	−	0.475806i
$31$	−9.39662			−1.68768			−0.843841	−	0.536593i	$-0.819711\pi$
$31$	−9.39662			−1.68768			−0.843841	+	0.536593i	$0.819711\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	3.96919	−	2.09030i	0.690947	−	0.363874i
$34$		−	0.219806i		−	0.0376964i
$35$	1.72233	+	4.74837i	0.291127	+	0.802621i
$36$	2.47372	+	1.69726i	0.412287	+	0.282877i
$37$	−2.88699	−	2.88699i	−0.474618	−	0.474618i	0.428788	−	0.903405i	$-0.358941\pi$
$37$	−2.88699	−	2.88699i	−0.474618	−	0.474618i	−0.903405	+	0.428788i	$0.858941\pi$
$38$	−4.79037	−	4.79037i	−0.777101	−	0.777101i
$39$	−1.65435	−	0.512970i	−0.264907	−	0.0821410i
$40$	−0.762461	−	2.10206i	−0.120556	−	0.332365i
$41$			2.11082i			0.329654i	0.986322	+	0.164827i	$0.0527067\pi$
$41$			2.11082i			0.329654i	−0.986322	+	0.164827i	$0.947293\pi$
$42$	−1.82311	−	3.46184i	−0.281312	−	0.534174i
$43$	−4.38869	+	4.38869i	−0.669269	+	0.669269i	−0.957547	−	0.288278i	$-0.906917\pi$
$43$	−4.38869	+	4.38869i	−0.669269	+	0.669269i	0.288278	+	0.957547i	$0.406917\pi$
$44$	2.58997			0.390453
$45$	5.78105	−	3.40287i	0.861788	−	0.507269i
$46$	−2.56451			−0.378116
$47$	−3.71800	+	3.71800i	−0.542326	+	0.542326i	−0.924210	−	0.381884i	$-0.875275\pi$
$47$	−3.71800	+	3.71800i	−0.542326	+	0.542326i	0.381884	+	0.924210i	$0.375275\pi$
$48$	0.807075	+	1.53252i	0.116491	+	0.221201i
$49$		−	1.89731i		−	0.271044i
$50$	−4.98000	−	0.446773i	−0.704278	−	0.0631833i
$51$	0.363635	+	0.112754i	0.0509191	+	0.0157887i
$52$	−0.707107	−	0.707107i	−0.0980581	−	0.0980581i
$53$	−2.24202	−	2.24202i	−0.307965	−	0.307965i	0.536155	−	0.844120i	$-0.319876\pi$
$53$	−2.24202	−	2.24202i	−0.307965	−	0.307965i	−0.844120	+	0.536155i	$0.819876\pi$
$54$	−4.07680	+	3.22175i	−0.554783	+	0.438425i
$55$	2.45332	−	5.24604i	0.330806	−	0.707376i
$56$		−	2.25891i		−	0.301860i
$57$	10.3823	−	5.46761i	1.37516	−	0.724203i
$58$	0.629912	−	0.629912i	0.0827115	−	0.0827115i
$59$	2.75114			0.358169			0.179084	−	0.983834i	$-0.442687\pi$
$59$	2.75114			0.358169			0.179084	+	0.983834i	$0.442687\pi$
$60$	3.86865	−	0.183080i	0.499441	−	0.0236355i
$61$	−2.28989			−0.293191			−0.146595	−	0.989197i	$-0.546831\pi$
$61$	−2.28989			−0.293191			−0.146595	+	0.989197i	$0.546831\pi$
$62$	6.64441	−	6.64441i	0.843841	−	0.843841i
$63$	6.66228	−	1.24024i	0.839369	−	0.156255i
$64$			1.00000i			0.125000i
$65$	−2.10206	+	0.762461i	−0.260728	+	0.0945716i
$66$	−1.32858	+	4.28471i	−0.163537	+	0.527411i
$67$	−10.9926	−	10.9926i	−1.34295	−	1.34295i	−0.893104	−	0.449850i	$-0.851477\pi$
$67$	−10.9926	−	10.9926i	−1.34295	−	1.34295i	−0.449850	−	0.893104i	$-0.648523\pi$
$68$	0.155426	+	0.155426i	0.0188482	+	0.0188482i
$69$	1.31552	−	4.24259i	0.158370	−	0.510747i
$70$	−4.57548	−	2.13973i	−0.546874	−	0.255747i
$71$			9.60806i			1.14027i	0.821552	+	0.570134i	$0.193109\pi$
$71$			9.60806i			1.14027i	−0.821552	+	0.570134i	$0.806891\pi$
$72$	−2.94933	+	0.549041i	−0.347582	+	0.0647052i
$73$	−1.65186	+	1.65186i	−0.193336	+	0.193336i	−0.797136	−	0.603800i	$-0.793653\pi$
$73$	−1.65186	+	1.65186i	−0.193336	+	0.193336i	0.603800	+	0.797136i	$0.293653\pi$
$74$	4.08282			0.474618
$75$	3.29371	−	8.00946i	0.380325	−	0.924853i
$76$	6.77461			0.777101
$77$	4.13694	−	4.13694i	0.471448	−	0.471448i
$78$	1.53252	−	0.807075i	0.173524	−	0.0913832i
$79$			12.1165i			1.36321i	0.731721	+	0.681605i	$0.238718\pi$
$79$			12.1165i			1.36321i	−0.731721	+	0.681605i	$0.761282\pi$
$80$	2.02552	+	0.947239i	0.226460	+	0.105905i
$81$	−3.23861	−	8.39711i	−0.359846	−	0.933012i
$82$	−1.49257	−	1.49257i	−0.164827	−	0.164827i
$83$	−5.93928	−	5.93928i	−0.651921	−	0.651921i	0.301534	−	0.953455i	$-0.402501\pi$
$83$	−5.93928	−	5.93928i	−0.651921	−	0.651921i	−0.953455	+	0.301534i	$0.902501\pi$
$84$	3.73703	+	1.15876i	0.407743	+	0.126431i
$85$	0.462045	−	0.167593i	0.0501158	−	0.0181780i
$86$		−	6.20654i		−	0.669269i
$87$	0.718967	+	1.36522i	0.0770813	+	0.146367i
$88$	−1.83139	+	1.83139i	−0.195226	+	0.195226i
$89$	6.43585			0.682199			0.341099	−	0.940027i	$-0.389201\pi$
$89$	6.43585			0.682199			0.341099	+	0.940027i	$0.389201\pi$
$90$	−1.68163	+	6.49401i	−0.177259	+	0.684528i
$91$	−2.25891			−0.236798
$92$	1.81338	−	1.81338i	0.189058	−	0.189058i
$93$	7.58377	+	14.4005i	0.786400	+	1.49327i
$94$		−	5.25805i		−	0.542326i
$95$	6.41718	−	13.7221i	0.658388	−	1.40786i
$96$	−1.65435	−	0.512970i	−0.168846	−	0.0523548i
$97$	8.84860	+	8.84860i	0.898439	+	0.898439i	0.995298	−	0.0968592i	$-0.0308796\pi$
$97$	8.84860	+	8.84860i	0.898439	+	0.898439i	−0.0968592	+	0.995298i	$0.530880\pi$
$98$	1.34160	+	1.34160i	0.135522	+	0.135522i
$99$	−6.40687	−	4.39585i	−0.643914	−	0.441800i
$100$	3.83731	−	3.20547i	0.383731	−	0.320547i
$101$		−	16.1955i		−	1.61151i	−0.592246	−	0.805757i	$-0.701759\pi$
$101$		−	16.1955i		−	1.61151i	0.592246	−	0.805757i	$-0.298241\pi$
$102$	−0.336858	+	0.177400i	−0.0333539	+	0.0175652i
$103$	11.4202	−	11.4202i	1.12526	−	1.12526i	0.134326	−	0.990937i	$-0.457113\pi$
$103$	11.4202	−	11.4202i	1.12526	−	1.12526i	0.990937	−	0.134326i	$-0.0428869\pi$
$104$	1.00000			0.0980581
$105$	5.88694	−	6.47181i	0.574507	−	0.631584i
$106$	3.17070			0.307965
$107$	−10.0756	+	10.0756i	−0.974043	+	0.974043i	−0.999672	−	0.0256290i	$-0.991841\pi$
$107$	−10.0756	+	10.0756i	−0.974043	+	0.974043i	0.0256290	+	0.999672i	$0.491841\pi$
$108$	0.604615	−	5.16086i	0.0581791	−	0.496604i
$109$			9.17905i			0.879194i	0.898195	+	0.439597i	$0.144879\pi$
$109$			9.17905i			0.879194i	−0.898195	+	0.439597i	$0.855121\pi$
$110$	1.97475	+	5.44427i	0.188285	+	0.519091i
$111$	−2.09436	+	6.75439i	−0.198788	+	0.641098i
$112$	1.59729	+	1.59729i	0.150930	+	0.150930i
$113$	7.84170	+	7.84170i	0.737685	+	0.737685i	0.972130	−	0.234444i	$-0.0753271\pi$
$113$	7.84170	+	7.84170i	0.737685	+	0.737685i	−0.234444	+	0.972130i	$0.575327\pi$
$114$	−3.47517	+	11.2075i	−0.325480	+	1.04968i
$115$	−1.95534	−	5.39075i	−0.182336	−	0.502690i
$116$			0.890831i			0.0827115i
$117$	0.549041	+	2.94933i	0.0507589	+	0.272666i
$118$	−1.94535	+	1.94535i	−0.179084	+	0.179084i
$119$	0.496523			0.0455161
$120$	−2.60609	+	2.86501i	−0.237903	+	0.261538i
$121$	4.29206			0.390187
$122$	1.61920	−	1.61920i	0.146595	−	0.146595i
$123$	3.23488	−	1.70359i	0.291679	−	0.153607i
$124$			9.39662i			0.843841i
$125$	−2.85791	−	10.8089i	−0.255619	−	0.966778i
$126$	−3.83397	+	5.58793i	−0.341557	+	0.497812i
$127$	−8.05797	−	8.05797i	−0.715029	−	0.715029i	0.252554	−	0.967583i	$-0.418729\pi$
$127$	−8.05797	−	8.05797i	−0.715029	−	0.715029i	−0.967583	+	0.252554i	$0.918729\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	10.2678	+	3.18377i	0.904027	+	0.280315i
$130$	0.947239	−	2.02552i	0.0830784	−	0.177650i
$131$		−	14.2078i		−	1.24134i	−0.784071	−	0.620671i	$-0.786860\pi$
$131$		−	14.2078i		−	1.24134i	0.784071	−	0.620671i	$-0.213140\pi$
$132$	−2.09030	−	3.96919i	−0.181937	−	0.345474i
$133$	10.8210	−	10.8210i	0.938303	−	0.938303i
$134$	15.5458			1.34295
$135$	−9.88071	−	6.11323i	−0.850396	−	0.526143i
$136$	−0.219806			−0.0188482
$137$	−10.9549	+	10.9549i	−0.935939	+	0.935939i	−0.998068	−	0.0621288i	$-0.980211\pi$
$137$	−10.9549	+	10.9549i	−0.935939	+	0.935939i	0.0621288	+	0.998068i	$0.480211\pi$
$138$	2.06975	+	3.93017i	0.176189	+	0.334558i
$139$			15.0559i			1.27703i	0.769611	+	0.638513i	$0.220450\pi$
$139$			15.0559i			1.27703i	−0.769611	+	0.638513i	$0.779550\pi$
$140$	4.74837	−	1.72233i	0.401311	−	0.145564i
$141$	8.69863	+	2.69722i	0.732557	+	0.227147i
$142$	−6.79393	−	6.79393i	−0.570134	−	0.570134i
$143$	1.83139	+	1.83139i	0.153148	+	0.153148i
$144$	1.69726	−	2.47372i	0.141438	−	0.206144i
$145$	1.80440	+	0.843830i	0.149847	+	0.0700763i
$146$		−	2.33609i		−	0.193336i
$147$	−2.90767	+	1.53127i	−0.239821	+	0.126297i
$148$	−2.88699	+	2.88699i	−0.237309	+	0.237309i
$149$	−15.7204			−1.28787			−0.643934	−	0.765081i	$-0.722699\pi$
$149$	−15.7204			−1.28787			−0.643934	+	0.765081i	$0.722699\pi$
$150$	3.33454	+	7.99255i	0.272264	+	0.652589i
$151$	−14.3294			−1.16611			−0.583056	−	0.812432i	$-0.698143\pi$
$151$	−14.3294			−1.16611			−0.583056	+	0.812432i	$0.698143\pi$
$152$	−4.79037	+	4.79037i	−0.388550	+	0.388550i
$153$	−0.120683	−	0.648280i	−0.00975661	−	0.0524104i
$154$			5.85052i			0.471448i
$155$	19.0330	+	8.90085i	1.52877	+	0.714933i
$156$	−0.512970	+	1.65435i	−0.0410705	+	0.132454i
$157$	−9.89671	−	9.89671i	−0.789843	−	0.789843i	0.191625	−	0.981468i	$-0.438624\pi$
$157$	−9.89671	−	9.89671i	−0.789843	−	0.789843i	−0.981468	+	0.191625i	$0.938624\pi$
$158$	−8.56764	−	8.56764i	−0.681605	−	0.681605i
$159$	−1.62647	+	5.24543i	−0.128988	+	0.415990i
$160$	−2.10206	+	0.762461i	−0.166182	+	0.0602778i
$161$		−	5.79300i		−	0.456553i
$162$	8.22769	+	3.64761i	0.646429	+	0.286583i
$163$	−9.12788	+	9.12788i	−0.714951	+	0.714951i	−0.967567	−	0.252616i	$-0.918709\pi$
$163$	−9.12788	+	9.12788i	−0.714951	+	0.714951i	0.252616	+	0.967567i	$0.418709\pi$
$164$	2.11082			0.164827
$165$	−10.0197	+	0.474171i	−0.780032	+	0.0369141i
$166$	8.39941			0.651921
$167$	−13.1748	+	13.1748i	−1.01950	+	1.01950i	−0.0196916	+	0.999806i	$0.506268\pi$
$167$	−13.1748	+	13.1748i	−1.01950	+	1.01950i	−0.999806	+	0.0196916i	$0.993732\pi$
$168$	−3.46184	+	1.82311i	−0.267087	+	0.140656i
$169$		−	1.00000i		−	0.0769231i
$170$	−0.208209	+	0.445222i	−0.0159689	+	0.0341469i
$171$	−16.7585	−	11.4983i	−1.28155	−	0.879295i
$172$	4.38869	+	4.38869i	0.334634	+	0.334634i
$173$	−11.0567	−	11.0567i	−0.840628	−	0.840628i	0.148312	−	0.988941i	$-0.452616\pi$
$173$	−11.0567	−	11.0567i	−0.840628	−	0.840628i	−0.988941	+	0.148312i	$0.952616\pi$
$174$	−1.47374	−	0.456970i	−0.111724	−	0.0346428i
$175$	1.00922	−	11.2494i	0.0762900	−	0.850374i
$176$		−	2.58997i		−	0.195226i
$177$	−2.22038	−	4.21620i	−0.166894	−	0.316909i
$178$	−4.55083	+	4.55083i	−0.341099	+	0.341099i
$179$	−11.4964			−0.859281			−0.429641	−	0.903000i	$-0.641360\pi$
$179$	−11.4964			−0.859281			−0.429641	+	0.903000i	$0.641360\pi$
$180$	−3.40287	−	5.78105i	−0.253635	−	0.430894i
$181$	17.6773			1.31394			0.656970	−	0.753917i	$-0.271838\pi$
$181$	17.6773			1.31394			0.656970	+	0.753917i	$0.271838\pi$
$182$	1.59729	−	1.59729i	0.118399	−	0.118399i
$183$	1.84811	+	3.50931i	0.136616	+	0.259416i
$184$			2.56451i			0.189058i
$185$	3.11299	+	8.58232i	0.228871	+	0.630985i
$186$	−15.5453	−	4.82019i	−1.13983	−	0.353433i
$187$	−0.402549	−	0.402549i	−0.0294373	−	0.0294373i
$188$	3.71800	+	3.71800i	0.271163	+	0.271163i
$189$	−7.27765	−	9.20915i	−0.529371	−	0.669867i
$190$	5.16537	+	14.2406i	0.374735	+	1.03312i
$191$			18.0153i			1.30354i	0.758416	+	0.651771i	$0.225974\pi$
$191$			18.0153i			1.30354i	−0.758416	+	0.651771i	$0.774026\pi$
$192$	1.53252	−	0.807075i	0.110600	−	0.0582456i
$193$	3.58559	−	3.58559i	0.258097	−	0.258097i	−0.566183	−	0.824280i	$-0.691580\pi$
$193$	3.58559	−	3.58559i	0.258097	−	0.258097i	0.824280	+	0.566183i	$0.191580\pi$
$194$	−12.5138			−0.898439
$195$	2.86501	+	2.60609i	0.205167	+	0.186626i
$196$	−1.89731			−0.135522
$197$	−11.8377	+	11.8377i	−0.843398	+	0.843398i	−0.989299	−	0.145901i	$-0.953392\pi$
$197$	−11.8377	+	11.8377i	−0.843398	+	0.843398i	0.145901	+	0.989299i	$0.453392\pi$
$198$	7.63868	−	1.42200i	0.542857	−	0.101057i
$199$		−	6.88147i		−	0.487814i	−0.969799	−	0.243907i	$-0.921571\pi$
$199$		−	6.88147i		−	0.487814i	0.969799	−	0.243907i	$-0.0784292\pi$
$200$	−0.446773	+	4.98000i	−0.0315916	+	0.352139i
$201$	−7.97454	+	25.7182i	−0.562481	+	1.81402i
$202$	11.4520	+	11.4520i	0.805757	+	0.805757i
$203$	1.42292	+	1.42292i	0.0998692	+	0.0998692i
$204$	0.112754	−	0.363635i	0.00789435	−	0.0254595i
$205$	1.99945	−	4.27551i	0.139648	−	0.298614i
$206$			16.1506i			1.12526i
$207$	−7.56358	+	1.40802i	−0.525705	+	0.0978643i
$208$	−0.707107	+	0.707107i	−0.0490290	+	0.0490290i
$209$	−17.5460			−1.21368
$210$	0.413561	+	8.73895i	0.0285384	+	0.603045i
$211$	−7.30339			−0.502786			−0.251393	−	0.967885i	$-0.580889\pi$
$211$	−7.30339			−0.502786			−0.251393	+	0.967885i	$0.580889\pi$
$212$	−2.24202	+	2.24202i	−0.153983	+	0.153983i
$213$	14.7246	−	7.75442i	1.00891	−	0.531324i
$214$		−	14.2490i		−	0.974043i
$215$	13.0465	−	4.73224i	0.889765	−	0.322736i
$216$	3.22175	+	4.07680i	0.219212	+	0.277391i
$217$	15.0092	+	15.0092i	1.01889	+	1.01889i
$218$	−6.49057	−	6.49057i	−0.439597	−	0.439597i
$219$	3.86470	+	1.19834i	0.261152	+	0.0809765i
$220$	−5.24604	−	2.45332i	−0.353688	−	0.165403i
$221$			0.219806i			0.0147857i
$222$	−3.29514	−	6.25701i	−0.221155	−	0.419943i
$223$	16.1979	−	16.1979i	1.08469	−	1.08469i	0.0886232	−	0.996065i	$-0.471753\pi$
$223$	16.1979	−	16.1979i	1.08469	−	1.08469i	0.996065	−	0.0886232i	$-0.0282467\pi$
$224$	−2.25891			−0.150930
$225$	−14.9330	+	1.41654i	−0.995531	+	0.0944362i
$226$	−11.0898			−0.737685
$227$	−17.2226	+	17.2226i	−1.14310	+	1.14310i	−0.155223	+	0.987879i	$0.549610\pi$
$227$	−17.2226	+	17.2226i	−1.14310	+	1.14310i	−0.987879	+	0.155223i	$0.950390\pi$
$228$	−5.46761	−	10.3823i	−0.362102	−	0.687581i
$229$		−	23.5974i		−	1.55936i	−0.626177	−	0.779681i	$-0.715381\pi$
$229$		−	23.5974i		−	1.55936i	0.626177	−	0.779681i	$-0.284619\pi$
$230$	5.19447	+	2.42920i	0.342513	+	0.160177i
$231$	−9.67878	−	3.00114i	−0.636817	−	0.197461i
$232$	−0.629912	−	0.629912i	−0.0413558	−	0.0413558i
$233$	−7.44530	−	7.44530i	−0.487758	−	0.487758i	0.419840	−	0.907598i	$-0.362086\pi$
$233$	−7.44530	−	7.44530i	−0.487758	−	0.487758i	−0.907598	+	0.419840i	$0.862086\pi$
$234$	−2.47372	−	1.69726i	−0.161712	−	0.110953i
$235$	11.0527	−	4.00905i	0.721000	−	0.261522i
$236$		−	2.75114i		−	0.179084i
$237$	18.5688	−	9.77889i	1.20617	−	0.635207i
$238$	−0.351094	+	0.351094i	−0.0227581	+	0.0227581i
$239$	19.2221			1.24337			0.621687	−	0.783266i	$-0.286448\pi$
$239$	19.2221			1.24337			0.621687	+	0.783266i	$0.286448\pi$
$240$	−0.183080	−	3.86865i	−0.0118177	−	0.249721i
$241$	16.0808			1.03586			0.517928	−	0.855424i	$-0.326704\pi$
$241$	16.0808			1.03586			0.517928	+	0.855424i	$0.326704\pi$
$242$	−3.03494	+	3.03494i	−0.195094	+	0.195094i
$243$	−10.2550	+	11.7403i	−0.657857	+	0.753143i
$244$			2.28989i			0.146595i
$245$	−1.79721	+	3.84304i	−0.114819	+	0.245523i
$246$	−1.08279	+	3.49202i	−0.0690360	+	0.222643i
$247$	4.79037	+	4.79037i	0.304804	+	0.304804i
$248$	−6.64441	−	6.64441i	−0.421921	−	0.421921i
$249$	−4.30865	+	13.8955i	−0.273050	+	0.880594i
$250$	9.66389	+	5.62220i	0.611198	+	0.355579i
$251$		−	25.4480i		−	1.60626i	−0.595801	−	0.803132i	$-0.703165\pi$
$251$		−	25.4480i		−	1.60626i	0.595801	−	0.803132i	$-0.296835\pi$
$252$	−1.24024	−	6.66228i	−0.0781276	−	0.419684i
$253$	−4.69660	+	4.69660i	−0.295273	+	0.295273i
$254$	11.3957			0.715029
$255$	−0.629746	−	0.572835i	−0.0394362	−	0.0358723i
$256$	1.00000			0.0625000
$257$	12.1316	−	12.1316i	0.756749	−	0.756749i	−0.218980	−	0.975729i	$-0.570273\pi$
$257$	12.1316	−	12.1316i	0.756749	−	0.756749i	0.975729	+	0.218980i	$0.0702731\pi$
$258$	−9.51167	+	5.00914i	−0.592171	+	0.311856i
$259$			9.22273i			0.573073i
$260$	0.762461	+	2.10206i	0.0472858	+	0.130364i
$261$	1.51197	−	2.20367i	0.0935887	−	0.136404i
$262$	10.0464	+	10.0464i	0.620671	+	0.620671i
$263$	3.81582	+	3.81582i	0.235294	+	0.235294i	0.814898	−	0.579604i	$-0.196793\pi$
$263$	3.81582	+	3.81582i	0.235294	+	0.235294i	−0.579604	+	0.814898i	$0.696793\pi$
$264$	4.28471	+	1.32858i	0.263705	+	0.0817683i
$265$	2.41753	+	6.66499i	0.148508	+	0.409427i
$266$			15.3033i			0.938303i
$267$	−5.19421	−	9.86310i	−0.317881	−	0.603612i
$268$	−10.9926	+	10.9926i	−0.671477	+	0.671477i
$269$	−2.98732			−0.182140			−0.0910701	−	0.995844i	$-0.529029\pi$
$269$	−2.98732			−0.182140			−0.0910701	+	0.995844i	$0.529029\pi$
$270$	11.3094	−	2.66401i	0.688270	−	0.162127i
$271$	17.9161			1.08832			0.544162	−	0.838980i	$-0.316848\pi$
$271$	17.9161			1.08832			0.544162	+	0.838980i	$0.316848\pi$
$272$	0.155426	−	0.155426i	0.00942410	−	0.00942410i
$273$	1.82311	+	3.46184i	0.110340	+	0.209520i
$274$		−	15.4926i		−	0.935939i
$275$	−9.93851	+	8.30208i	−0.599315	+	0.500634i
$276$	−4.24259	−	1.31552i	−0.255374	−	0.0791848i
$277$	11.8188	+	11.8188i	0.710120	+	0.710120i	0.966560	−	0.256440i	$-0.0825496\pi$
$277$	11.8188	+	11.8188i	0.710120	+	0.710120i	−0.256440	+	0.966560i	$0.582550\pi$
$278$	−10.6461	−	10.6461i	−0.638513	−	0.638513i
$279$	15.9485	−	23.2446i	0.954812	−	1.39162i
$280$	−2.13973	+	4.57548i	−0.127873	+	0.273437i
$281$		−	0.763857i		−	0.0455679i	−0.999740	−	0.0227839i	$-0.992747\pi$
$281$		−	0.763857i		−	0.0455679i	0.999740	−	0.0227839i	$-0.00725298\pi$
$282$	−8.05808	+	4.24364i	−0.479852	+	0.252705i
$283$	−3.73216	+	3.73216i	−0.221854	+	0.221854i	−0.809279	−	0.587425i	$-0.800142\pi$
$283$	−3.73216	+	3.73216i	−0.221854	+	0.221854i	0.587425	+	0.809279i	$0.300142\pi$
$284$	9.60806			0.570134
$285$	−26.2086	+	1.24029i	−1.55246	+	0.0734686i
$286$	−2.58997			−0.153148
$287$	3.37160	−	3.37160i	0.199019	−	0.199019i
$288$	0.549041	+	2.94933i	0.0323526	+	0.173791i
$289$			16.9517i			0.997158i
$290$	−1.87258	+	0.679223i	−0.109962	+	0.0398854i
$291$	6.41921	−	20.7022i	0.376301	−	1.21358i
$292$	1.65186	+	1.65186i	0.0966680	+	0.0966680i
$293$	22.4543	+	22.4543i	1.31180	+	1.31180i	0.920091	+	0.391704i	$0.128114\pi$
$293$	22.4543	+	22.4543i	1.31180	+	1.31180i	0.391704	+	0.920091i	$0.371886\pi$
$294$	0.973263	−	3.13881i	0.0567619	−	0.183059i
$295$	−5.57250	−	2.60599i	−0.324444	−	0.151727i
$296$		−	4.08282i		−	0.237309i
$297$	−1.56593	+	13.3665i	−0.0908647	+	0.775601i
$298$	11.1160	−	11.1160i	0.643934	−	0.643934i
$299$	2.56451			0.148309
$300$	−8.00946	−	3.29371i	−0.462426	−	0.190162i
$301$	14.0200			0.808102
$302$	10.1324	−	10.1324i	0.583056	−	0.583056i
$303$	−24.8200	+	13.0710i	−1.42587	+	0.750909i
$304$		−	6.77461i		−	0.388550i
$305$	4.63822	+	2.16908i	0.265584	+	0.124201i
$306$	0.543739	+	0.373068i	0.0310835	+	0.0213269i
$307$	4.92117	+	4.92117i	0.280866	+	0.280866i	0.833454	−	0.552588i	$-0.186360\pi$
$307$	4.92117	+	4.92117i	0.280866	+	0.280866i	−0.552588	+	0.833454i	$0.686360\pi$
$308$	−4.13694	−	4.13694i	−0.235724	−	0.235724i
$309$	−26.7186	−	8.28476i	−1.51997	−	0.471304i
$310$	−19.7522	+	7.16455i	−1.12185	+	0.406919i
$311$			2.99483i			0.169821i	0.996389	+	0.0849107i	$0.0270605\pi$
$311$			2.99483i			0.169821i	−0.996389	+	0.0849107i	$0.972940\pi$
$312$	−0.807075	−	1.53252i	−0.0456916	−	0.0867621i
$313$	−22.8829	+	22.8829i	−1.29342	+	1.29342i	−0.360759	+	0.932659i	$0.617482\pi$
$313$	−22.8829	+	22.8829i	−1.29342	+	1.29342i	−0.932659	+	0.360759i	$0.882518\pi$
$314$	13.9961			0.789843
$315$	−14.6694	−	3.79865i	−0.826527	−	0.214030i
$316$	12.1165			0.681605
$317$	14.7717	−	14.7717i	0.829659	−	0.829659i	−0.157810	−	0.987469i	$-0.550444\pi$
$317$	14.7717	−	14.7717i	0.829659	−	0.829659i	0.987469	+	0.157810i	$0.0504435\pi$
$318$	−2.55899	−	4.85917i	−0.143501	−	0.272489i
$319$		−	2.30722i		−	0.129180i
$320$	0.947239	−	2.02552i	0.0529523	−	0.113230i
$321$	23.5728	+	7.30932i	1.31571	+	0.407967i
$322$	4.09627	+	4.09627i	0.228276	+	0.228276i
$323$	−1.05295	−	1.05295i	−0.0585878	−	0.0585878i
$324$	−8.39711	+	3.23861i	−0.466506	+	0.179923i
$325$	4.98000	+	0.446773i	0.276241	+	0.0247825i
$326$		−	12.9088i		−	0.714951i
$327$	14.0671	−	7.40818i	0.777914	−	0.409673i
$328$	−1.49257	+	1.49257i	−0.0824136	+	0.0824136i
$329$	11.8775			0.654826
$330$	6.74971	−	7.42028i	0.371559	−	0.408473i
$331$	−0.111775			−0.00614372			−0.00307186	−	0.999995i	$-0.500978\pi$
$331$	−0.111775			−0.00614372			−0.00307186	+	0.999995i	$0.500978\pi$
$332$	−5.93928	+	5.93928i	−0.325960	+	0.325960i
$333$	12.0416	−	2.24164i	0.659874	−	0.122841i
$334$		−	18.6320i		−	1.01950i
$335$	11.8531	+	32.6782i	0.647603	+	1.78540i
$336$	1.15876	−	3.73703i	0.0632153	−	0.203871i
$337$	−8.54851	−	8.54851i	−0.465667	−	0.465667i	0.434840	−	0.900508i	$-0.356805\pi$
$337$	−8.54851	−	8.54851i	−0.465667	−	0.465667i	−0.900508	+	0.434840i	$0.856805\pi$
$338$	0.707107	+	0.707107i	0.0384615	+	0.0384615i
$339$	5.68876	−	18.3464i	0.308971	−	0.996442i
$340$	−0.167593	−	0.462045i	−0.00908902	−	0.0250579i
$341$		−	24.3370i		−	1.31792i
$342$	19.9806	−	3.71954i	1.08043	−	0.201130i
$343$	−14.2116	+	14.2116i	−0.767355	+	0.767355i
$344$	−6.20654			−0.334634
$345$	−6.68335	+	7.34734i	−0.359820	+	0.395567i
$346$	15.6366			0.840628
$347$	6.09851	−	6.09851i	0.327385	−	0.327385i	−0.524206	−	0.851591i	$-0.675638\pi$
$347$	6.09851	−	6.09851i	0.327385	−	0.327385i	0.851591	+	0.524206i	$0.175638\pi$
$348$	1.36522	−	0.718967i	0.0731834	−	0.0385407i
$349$		−	4.89335i		−	0.261935i	−0.991387	−	0.130967i	$-0.958192\pi$
$349$		−	4.89335i		−	0.261935i	0.991387	−	0.130967i	$-0.0418083\pi$
$350$	7.24089	+	8.66815i	0.387042	+	0.463332i
$351$	4.07680	−	3.22175i	0.217604	−	0.171964i
$352$	1.83139	+	1.83139i	0.0976132	+	0.0976132i
$353$	8.68950	+	8.68950i	0.462495	+	0.462495i	0.899473	−	0.436977i	$-0.143951\pi$
$353$	8.68950	+	8.68950i	0.462495	+	0.462495i	−0.436977	+	0.899473i	$0.643951\pi$
$354$	4.55135	+	1.41126i	0.241901	+	0.0750074i
$355$	9.10114	−	19.4613i	0.483038	−	1.03290i
$356$		−	6.43585i		−	0.341099i
$357$	−0.400731	−	0.760933i	−0.0212089	−	0.0402728i
$358$	8.12918	−	8.12918i	0.429641	−	0.429641i
$359$	31.8464			1.68079			0.840394	−	0.541975i	$-0.182323\pi$
$359$	31.8464			1.68079			0.840394	+	0.541975i	$0.182323\pi$
$360$	6.49401	+	1.68163i	0.342264	+	0.0886296i
$361$	−26.8953			−1.41554
$362$	−12.4997	+	12.4997i	−0.656970	+	0.656970i
$363$	−3.46401	−	6.57768i	−0.181813	−	0.345239i
$364$			2.25891i			0.118399i
$365$	4.91059	−	1.78117i	0.257032	−	0.0932309i
$366$	−3.78827	−	1.17465i	−0.198016	−	0.0613997i
$367$	14.9797	+	14.9797i	0.781935	+	0.781935i	0.980157	−	0.198222i	$-0.0635167\pi$
$367$	14.9797	+	14.9797i	0.781935	+	0.781935i	−0.198222	+	0.980157i	$0.563517\pi$
$368$	−1.81338	−	1.81338i	−0.0945290	−	0.0945290i
$369$	−5.22158	−	3.58261i	−0.271825	−	0.186503i
$370$	−8.26983	−	3.86740i	−0.429928	−	0.201057i
$371$			7.16233i			0.371850i
$372$	14.4005	−	7.58377i	0.746633	−	0.393200i
$373$	16.2983	−	16.2983i	0.843893	−	0.843893i	−0.145470	−	0.989363i	$-0.546469\pi$
$373$	16.2983	−	16.2983i	0.843893	−	0.843893i	0.989363	+	0.145470i	$0.0464693\pi$
$374$	0.569291			0.0294373
$375$	−14.2584	+	13.1034i	−0.736298	+	0.676657i
$376$	−5.25805			−0.271163
$377$	−0.629912	+	0.629912i	−0.0324421	+	0.0324421i
$378$	11.6579	+	1.36577i	0.599619	+	0.0702478i
$379$		−	6.82263i		−	0.350455i	−0.984528	−	0.175228i	$-0.943934\pi$
$379$		−	6.82263i		−	0.350455i	0.984528	−	0.175228i	$-0.0560661\pi$
$380$	−13.7221	−	6.41718i	−0.703930	−	0.329194i
$381$	−5.84565	+	18.8524i	−0.299482	+	0.965838i
$382$	−12.7388	−	12.7388i	−0.651771	−	0.651771i
$383$	−15.1912	−	15.1912i	−0.776235	−	0.776235i	0.202953	−	0.979188i	$-0.434946\pi$
$383$	−15.1912	−	15.1912i	−0.776235	−	0.776235i	−0.979188	+	0.202953i	$0.934946\pi$
$384$	−0.512970	+	1.65435i	−0.0261774	+	0.0844230i
$385$	−12.2981	+	4.46079i	−0.626771	+	0.227343i
$386$			5.07079i			0.258097i
$387$	−3.40765	−	18.3051i	−0.173220	−	0.930503i
$388$	8.84860	−	8.84860i	0.449219	−	0.449219i
$389$	−2.88396			−0.146222			−0.0731112	−	0.997324i	$-0.523293\pi$
$389$	−2.88396			−0.146222			−0.0731112	+	0.997324i	$0.523293\pi$
$390$	−3.86865	+	0.183080i	−0.195897	+	0.00927060i
$391$	−0.563694			−0.0285072
$392$	1.34160	−	1.34160i	0.0677610	−	0.0677610i
$393$	−21.7738	+	11.4668i	−1.09834	+	0.578422i
$394$		−	16.7410i		−	0.843398i
$395$	11.4772	−	24.5422i	0.577480	−	1.23485i
$396$	−4.39585	+	6.40687i	−0.220900	+	0.321957i
$397$	−26.9155	−	26.9155i	−1.35085	−	1.35085i	−0.884712	−	0.466137i	$-0.845645\pi$
$397$	−26.9155	−	26.9155i	−1.35085	−	1.35085i	−0.466137	−	0.884712i	$-0.654355\pi$
$398$	4.86593	+	4.86593i	0.243907	+	0.243907i
$399$	−25.3169	−	7.85012i	−1.26743	−	0.392997i
$400$	−3.20547	−	3.83731i	−0.160274	−	0.191865i
$401$		−	29.6662i		−	1.48146i	−0.671803	−	0.740729i	$-0.734480\pi$
$401$		−	29.6662i		−	1.48146i	0.671803	−	0.740729i	$-0.265520\pi$
$402$	−12.5466	−	23.8243i	−0.625769	−	1.18825i
$403$	−6.64441	+	6.64441i	−0.330982	+	0.330982i
$404$	−16.1955			−0.805757
$405$	−1.39420	+	20.0763i	−0.0692782	+	0.997597i
$406$	−2.01231			−0.0998692
$407$	7.47721	−	7.47721i	0.370631	−	0.370631i
$408$	0.177400	+	0.336858i	0.00878260	+	0.0166769i
$409$		−	3.05276i		−	0.150949i	−0.997148	−	0.0754747i	$-0.975953\pi$
$409$		−	3.05276i		−	0.150949i	0.997148	−	0.0754747i	$-0.0240472\pi$
$410$	1.60942	+	4.43707i	0.0794834	+	0.219131i
$411$	25.6300	+	7.94722i	1.26424	+	0.392007i
$412$	−11.4202	−	11.4202i	−0.562632	−	0.562632i
$413$	−4.39438	−	4.39438i	−0.216234	−	0.216234i
$414$	4.35264	−	6.34388i	0.213921	−	0.311785i
$415$	6.40422	+	17.6561i	0.314371	+	0.866702i
$416$		−	1.00000i		−	0.0490290i
$417$	23.0736	−	12.1513i	1.12992	−	0.595049i
$418$	12.4069	−	12.4069i	0.606842	−	0.606842i
$419$	6.17929			0.301878			0.150939	−	0.988543i	$-0.451770\pi$
$419$	6.17929			0.301878			0.150939	+	0.988543i	$0.451770\pi$
$420$	−6.47181	−	5.88694i	−0.315792	−	0.287253i
$421$	2.65347			0.129322			0.0646610	−	0.997907i	$-0.479403\pi$
$421$	2.65347			0.129322			0.0646610	+	0.997907i	$0.479403\pi$
$422$	5.16428	−	5.16428i	0.251393	−	0.251393i
$423$	−2.88688	−	15.5077i	−0.140365	−	0.754011i
$424$		−	3.17070i		−	0.153983i
$425$	−1.09463	−	0.0982034i	−0.0530975	−	0.00476357i
$426$	−4.92865	+	15.8951i	−0.238794	+	0.770118i
$427$	3.65763	+	3.65763i	0.177005	+	0.177005i
$428$	10.0756	+	10.0756i	0.487021	+	0.487021i
$429$	1.32858	−	4.28471i	0.0641443	−	0.206868i
$430$	−5.87908	+	12.5715i	−0.283514	+	0.606251i
$431$		−	35.9248i		−	1.73043i	−0.501397	−	0.865217i	$-0.667180\pi$
$431$		−	35.9248i		−	1.73043i	0.501397	−	0.865217i	$-0.332820\pi$
$432$	−5.16086	−	0.604615i	−0.248302	−	0.0290895i
$433$	−8.25075	+	8.25075i	−0.396506	+	0.396506i	−0.876999	−	0.480493i	$-0.840458\pi$
$433$	−8.25075	+	8.25075i	−0.396506	+	0.396506i	0.480493	+	0.876999i	$0.340458\pi$
$434$	−21.2261			−1.01889
$435$	−0.163093	−	3.44632i	−0.00781971	−	0.165238i
$436$	9.17905			0.439597
$437$	−12.2849	+	12.2849i	−0.587669	+	0.587669i
$438$	−3.58011	+	1.88540i	−0.171064	+	0.0900877i
$439$		−	5.36829i		−	0.256215i	−0.991760	−	0.128107i	$-0.959110\pi$
$439$		−	5.36829i		−	0.256215i	0.991760	−	0.128107i	$-0.0408902\pi$
$440$	5.44427	−	1.97475i	0.259545	−	0.0941425i
$441$	4.69342	+	3.22023i	0.223496	+	0.153344i
$442$	−0.155426	−	0.155426i	−0.00739287	−	0.00739287i
$443$	11.3450	+	11.3450i	0.539018	+	0.539018i	0.923241	−	0.384223i	$-0.125530\pi$
$443$	11.3450	+	11.3450i	0.539018	+	0.539018i	−0.384223	+	0.923241i	$0.625530\pi$
$444$	6.75439	+	2.09436i	0.320549	+	0.0993941i
$445$	−13.0360	−	6.09629i	−0.617964	−	0.288992i
$446$			22.9072i			1.08469i
$447$	12.6876	+	24.0920i	0.600102	+	1.13951i
$448$	1.59729	−	1.59729i	0.0754650	−	0.0754650i
$449$	−16.0281			−0.756412			−0.378206	−	0.925721i	$-0.623459\pi$
$449$	−16.0281			−0.756412			−0.378206	+	0.925721i	$0.623459\pi$
$450$	9.55755	−	11.5608i	0.450547	−	0.544984i
$451$	−5.46696			−0.257429
$452$	7.84170	−	7.84170i	0.368843	−	0.368843i
$453$	11.5649	+	21.9602i	0.543367	+	1.03178i
$454$		−	24.3564i		−	1.14310i
$455$	4.57548	+	2.13973i	0.214502	+	0.100312i
$456$	11.2075	+	3.47517i	0.524842	+	0.162740i
$457$	0.963319	+	0.963319i	0.0450621	+	0.0450621i	0.729279	−	0.684217i	$-0.239856\pi$
$457$	0.963319	+	0.963319i	0.0450621	+	0.0450621i	−0.684217	+	0.729279i	$0.739856\pi$
$458$	16.6859	+	16.6859i	0.779681	+	0.779681i
$459$	−0.896106	+	0.708160i	−0.0418266	+	0.0330541i
$460$	−5.39075	+	1.95534i	−0.251345	+	0.0911680i
$461$			17.4655i			0.813447i	0.913551	+	0.406724i	$0.133329\pi$
$461$			17.4655i			0.813447i	−0.913551	+	0.406724i	$0.866671\pi$
$462$	8.96606	−	4.72180i	0.417139	−	0.219678i
$463$	−0.256369	+	0.256369i	−0.0119145	+	0.0119145i	−0.713039	−	0.701124i	$-0.752682\pi$
$463$	−0.256369	+	0.256369i	−0.0119145	+	0.0119145i	0.701124	+	0.713039i	$0.252682\pi$
$464$	0.890831			0.0413558
$465$	−1.72033	−	36.3523i	−0.0797784	−	1.68580i
$466$	10.5292			0.487758
$467$	−17.7653	+	17.7653i	−0.822079	+	0.822079i	−0.986406	−	0.164327i	$-0.947455\pi$
$467$	−17.7653	+	17.7653i	−0.822079	+	0.822079i	0.164327	+	0.986406i	$0.447455\pi$
$468$	2.94933	−	0.549041i	0.136333	−	0.0253794i
$469$			35.1167i			1.62154i
$470$	−4.98063	+	10.6503i	−0.229739	+	0.491261i
$471$	−7.17956	+	23.1543i	−0.330817	+	1.06690i
$472$	1.94535	+	1.94535i	0.0895421	+	0.0895421i
$473$	−11.3666	−	11.3666i	−0.522635	−	0.522635i
$474$	−6.21539	+	20.0448i	−0.285482	+	0.920690i
$475$	−25.9963	+	21.7158i	−1.19279	+	0.996391i
$476$		−	0.496523i		−	0.0227581i
$477$	9.35144	−	1.74084i	0.428173	−	0.0797078i
$478$	−13.5921	+	13.5921i	−0.621687	+	0.621687i
$479$	21.2442			0.970671			0.485336	−	0.874328i	$-0.338697\pi$
$479$	21.2442			0.970671			0.485336	+	0.874328i	$0.338697\pi$
$480$	2.86501	+	2.60609i	0.130769	+	0.118951i
$481$	−4.08282			−0.186160
$482$	−11.3708	+	11.3708i	−0.517928	+	0.517928i
$483$	−8.87792	+	4.67539i	−0.403959	+	0.212737i
$484$		−	4.29206i		−	0.195094i
$485$	−9.54128	−	26.3048i	−0.433247	−	1.19444i
$486$	−1.05032	−	15.5530i	−0.0476433	−	0.705500i
$487$	10.4620	+	10.4620i	0.474077	+	0.474077i	0.903231	−	0.429154i	$-0.141188\pi$
$487$	10.4620	+	10.4620i	0.474077	+	0.474077i	−0.429154	+	0.903231i	$0.641188\pi$
$488$	−1.61920	−	1.61920i	−0.0732976	−	0.0732976i
$489$	21.3556	+	6.62182i	0.965733	+	0.299449i
$490$	−1.44662	−	3.98826i	−0.0653518	−	0.180171i
$491$			16.1195i			0.727462i	0.931504	+	0.363731i	$0.118497\pi$
$491$			16.1195i			0.727462i	−0.931504	+	0.363731i	$0.881503\pi$
$492$	−1.70359	−	3.23488i	−0.0768037	−	0.145840i
$493$	0.138458	−	0.138458i	0.00623586	−	0.00623586i
$494$	−6.77461			−0.304804
$495$	8.81332	+	14.9727i	0.396129	+	0.672974i
$496$	9.39662			0.421921
$497$	15.3469	−	15.3469i	0.688402	−	0.688402i
$498$	−6.77895	−	12.8723i	−0.303772	−	0.576822i
$499$		−	0.297723i		−	0.0133279i	−0.999978	−	0.00666395i	$-0.997879\pi$
$499$		−	0.297723i		−	0.0133279i	0.999978	−	0.00666395i	$-0.00212122\pi$
$500$	−10.8089	+	2.85791i	−0.483389	+	0.127810i
$501$	30.8238	+	9.55766i	1.37710	+	0.427005i
$502$	17.9945	+	17.9945i	0.803132	+	0.803132i
$503$	−7.46751	−	7.46751i	−0.332960	−	0.332960i	0.520750	−	0.853709i	$-0.325653\pi$
$503$	−7.46751	−	7.46751i	−0.332960	−	0.332960i	−0.853709	+	0.520750i	$0.825653\pi$
$504$	5.58793	+	3.83397i	0.248906	+	0.170778i
$505$	−15.3410	+	32.8044i	−0.682667	+	1.45978i
$506$		−	6.64200i		−	0.295273i
$507$	−1.53252	+	0.807075i	−0.0680618	+	0.0358434i
$508$	−8.05797	+	8.05797i	−0.357514	+	0.357514i
$509$	−9.67667			−0.428911			−0.214456	−	0.976734i	$-0.568798\pi$
$509$	−9.67667			−0.428911			−0.214456	+	0.976734i	$0.568798\pi$
$510$	0.850353	−	0.0402420i	0.0376543	−	0.00178195i
$511$	5.27702			0.233442
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−4.09603	+	34.9628i	−0.180844	+	1.54364i
$514$			17.1567i			0.756749i
$515$	−33.9494	+	12.3142i	−1.49599	+	0.542627i
$516$	3.18377	−	10.2678i	0.140158	−	0.452013i
$517$	−9.62951	−	9.62951i	−0.423505	−	0.423505i
$518$	−6.52145	−	6.52145i	−0.286536	−	0.286536i
$519$	−8.02111	+	25.8683i	−0.352088	+	1.13549i
$520$	−2.02552	−	0.947239i	−0.0888250	−	0.0415392i
$521$			24.0972i			1.05572i	0.849332	+	0.527860i	$0.177005\pi$
$521$			24.0972i			1.05572i	−0.849332	+	0.527860i	$0.822995\pi$
$522$	0.489103	+	2.62735i	0.0214075	+	0.114996i
$523$	2.67631	−	2.67631i	0.117027	−	0.117027i	−0.646168	−	0.763195i	$-0.723630\pi$
$523$	2.67631	−	2.67631i	0.117027	−	0.117027i	0.763195	+	0.646168i	$0.223630\pi$
$524$	−14.2078			−0.620671
$525$	−18.0545	+	7.53244i	−0.787962	+	0.328743i
$526$	−5.39638			−0.235294
$527$	1.46048	−	1.46048i	0.0636195	−	0.0636195i
$528$	−3.96919	+	2.09030i	−0.172737	+	0.0909686i
$529$		−	16.4233i		−	0.714056i
$530$	−6.42232	−	3.00341i	−0.278968	−	0.130460i
$531$	−4.66941	+	6.80557i	−0.202635	+	0.295337i
$532$	−10.8210	−	10.8210i	−0.469151	−	0.469151i
$533$	1.49257	+	1.49257i	0.0646506	+	0.0646506i
$534$	10.6471	+	3.30140i	0.460746	+	0.142866i
$535$	29.9523	−	10.8643i	1.29495	−	0.469705i
$536$		−	15.5458i		−	0.671477i
$537$	9.27845	+	17.6185i	0.400395	+	0.760295i
$538$	2.11235	−	2.11235i	0.0910701	−	0.0910701i
$539$	4.91397			0.211660
$540$	−6.11323	+	9.88071i	−0.263071	+	0.425198i
$541$	−31.9887			−1.37530			−0.687650	−	0.726042i	$-0.741358\pi$
$541$	−31.9887			−1.37530			−0.687650	+	0.726042i	$0.741358\pi$
$542$	−12.6686	+	12.6686i	−0.544162	+	0.544162i
$543$	−14.2669	−	27.0908i	−0.612250	−	1.16258i
$544$			0.219806i			0.00942410i
$545$	8.69476	−	18.5924i	0.372443	−	0.796410i
$546$	−3.73703	−	1.15876i	−0.159930	−	0.0495902i
$547$	6.13891	+	6.13891i	0.262481	+	0.262481i	0.826061	−	0.563580i	$-0.190576\pi$
$547$	6.13891	+	6.13891i	0.262481	+	0.262481i	−0.563580	+	0.826061i	$0.690576\pi$
$548$	10.9549	+	10.9549i	0.467970	+	0.467970i
$549$	3.88654	−	5.66456i	0.165874	−	0.241757i
$550$	1.15713	−	12.8980i	0.0493402	−	0.549975i
$551$		−	6.03503i		−	0.257101i
$552$	3.93017	−	2.06975i	0.167279	−	0.0880944i
$553$	19.3536	−	19.3536i	0.822997	−	0.822997i
$554$	−16.7142			−0.710120
$555$	10.6402	−	11.6973i	0.451652	−	0.496523i
$556$	15.0559			0.638513
$557$	6.14058	−	6.14058i	0.260185	−	0.260185i	−0.564944	−	0.825129i	$-0.691102\pi$
$557$	6.14058	−	6.14058i	0.260185	−	0.260185i	0.825129	+	0.564944i	$0.191102\pi$
$558$	5.15913	+	27.7137i	0.218403	+	1.17322i
$559$			6.20654i			0.262509i
$560$	−1.72233	−	4.74837i	−0.0727818	−	0.200655i
$561$	−0.292029	+	0.941804i	−0.0123295	+	0.0397630i
$562$	0.540129	+	0.540129i	0.0227839	+	0.0227839i
$563$	24.9348	+	24.9348i	1.05088	+	1.05088i	0.998634	+	0.0522422i	$0.0166368\pi$
$563$	24.9348	+	24.9348i	1.05088	+	1.05088i	0.0522422	+	0.998634i	$0.483363\pi$
$564$	2.69722	−	8.69863i	0.113574	−	0.366278i
$565$	−8.45557	−	23.3115i	−0.355728	−	0.980722i
$566$		−	5.27807i		−	0.221854i
$567$	−8.23963	+	18.5857i	−0.346032	+	0.780524i
$568$	−6.79393	+	6.79393i	−0.285067	+	0.285067i
$569$	−5.56111			−0.233134			−0.116567	−	0.993183i	$-0.537189\pi$
$569$	−5.56111			−0.233134			−0.116567	+	0.993183i	$0.537189\pi$
$570$	17.6553	−	19.4093i	0.739498	−	0.812966i
$571$	33.8131			1.41503			0.707517	−	0.706697i	$-0.249815\pi$
$571$	33.8131			1.41503			0.707517	+	0.706697i	$0.249815\pi$
$572$	1.83139	−	1.83139i	0.0765741	−	0.0765741i
$573$	27.6089	−	14.5397i	1.15338	−	0.607405i
$574$			4.76816i			0.199019i
$575$	−1.14575	+	12.7713i	−0.0477812	+	0.532598i
$576$	−2.47372	−	1.69726i	−0.103072	−	0.0707192i
$577$	0.174550	+	0.174550i	0.00726661	+	0.00726661i	0.710731	−	0.703464i	$-0.248364\pi$
$577$	0.174550	+	0.174550i	0.00726661	+	0.00726661i	−0.703464	+	0.710731i	$0.748364\pi$
$578$	−11.9867	−	11.9867i	−0.498579	−	0.498579i
$579$	−8.38885	−	2.60117i	−0.348629	−	0.108101i
$580$	0.843830	−	1.80440i	0.0350381	−	0.0749235i
$581$			18.9736i			0.787156i
$582$	10.0996	+	19.1777i	0.418641	+	0.794942i
$583$	5.80677	−	5.80677i	0.240492	−	0.240492i
$584$	−2.33609			−0.0966680
$585$	1.68163	−	6.49401i	0.0695267	−	0.268494i
$586$	−31.7552			−1.31180
$587$	6.55064	−	6.55064i	0.270374	−	0.270374i	−0.558877	−	0.829251i	$-0.688768\pi$
$587$	6.55064	−	6.55064i	0.270374	−	0.270374i	0.829251	+	0.558877i	$0.188768\pi$
$588$	1.53127	+	2.90767i	0.0631485	+	0.119910i
$589$		−	63.6584i		−	2.62300i
$590$	5.78307	−	2.09764i	0.238085	−	0.0863584i
$591$	27.6954	+	8.58762i	1.13924	+	0.353248i
$592$	2.88699	+	2.88699i	0.118654	+	0.118654i
$593$	−17.9410	−	17.9410i	−0.736747	−	0.736747i	0.235200	−	0.971947i	$-0.424425\pi$
$593$	−17.9410	−	17.9410i	−0.736747	−	0.736747i	−0.971947	+	0.235200i	$0.924425\pi$
$594$	−8.34423	−	10.5588i	−0.342368	−	0.433233i
$595$	−1.00572	−	0.470326i	−0.0412304	−	0.0192815i
$596$			15.7204i			0.643934i
$597$	−10.5460	+	5.55386i	−0.431620	+	0.227304i
$598$	−1.81338	+	1.81338i	−0.0741547	+	0.0741547i
$599$	−41.6634			−1.70232			−0.851161	−	0.524905i	$-0.824101\pi$
$599$	−41.6634			−1.70232			−0.851161	+	0.524905i	$0.824101\pi$
$600$	7.99255	−	3.33454i	0.326294	−	0.136132i
$601$	−22.6630			−0.924444			−0.462222	−	0.886764i	$-0.652948\pi$
$601$	−22.6630			−0.924444			−0.462222	+	0.886764i	$0.652948\pi$
$602$	−9.91367	+	9.91367i	−0.404051	+	0.404051i
$603$	45.8498	−	8.53530i	1.86715	−	0.347584i
$604$			14.3294i			0.583056i
$605$	−8.69365	−	4.06561i	−0.353447	−	0.165290i
$606$	8.30782	−	26.7930i	0.337482	−	1.08839i
$607$	11.2274	+	11.2274i	0.455706	+	0.455706i	0.897243	−	0.441537i	$-0.145567\pi$
$607$	11.2274	+	11.2274i	0.455706	+	0.455706i	−0.441537	+	0.897243i	$0.645567\pi$
$608$	4.79037	+	4.79037i	0.194275	+	0.194275i
$609$	1.03226	−	3.32906i	0.0418291	−	0.134900i
$610$	−4.81349	+	1.74595i	−0.194892	+	0.0706915i
$611$			5.25805i			0.212718i
$612$	−0.648280	+	0.120683i	−0.0262052	+	0.00487830i
$613$	6.53782	−	6.53782i	0.264060	−	0.264060i	−0.562641	−	0.826701i	$-0.690215\pi$
$613$	6.53782	−	6.53782i	0.264060	−	0.264060i	0.826701	+	0.562641i	$0.190215\pi$
$614$	−6.95958			−0.280866
$615$	−8.16603	+	0.386448i	−0.329286	+	0.0155831i
$616$	5.85052			0.235724
$617$	22.7714	−	22.7714i	0.916744	−	0.916744i	−0.0800471	−	0.996791i	$-0.525507\pi$
$617$	22.7714	−	22.7714i	0.916744	−	0.916744i	0.996791	+	0.0800471i	$0.0255071\pi$
$618$	24.7511	−	13.0347i	0.995636	−	0.524333i
$619$			5.97955i			0.240338i	0.992753	+	0.120169i	$0.0383437\pi$
$619$			5.97955i			0.240338i	−0.992753	+	0.120169i	$0.961656\pi$
$620$	8.90085	−	19.0330i	0.357467	−	0.764386i
$621$	8.26220	+	10.4550i	0.331551	+	0.419545i
$622$	−2.11767	−	2.11767i	−0.0849107	−	0.0849107i
$623$	−10.2799	−	10.2799i	−0.411857	−	0.411857i
$624$	1.65435	+	0.512970i	0.0662269	+	0.0205352i
$625$	−4.44986	+	24.6008i	−0.177994	+	0.984031i
$626$		−	32.3613i		−	1.29342i
$627$	14.1610	+	26.8897i	0.565534	+	1.07387i
$628$	−9.89671	+	9.89671i	−0.394922	+	0.394922i
$629$	0.897427			0.0357828
$630$	13.0589	−	7.68678i	0.520278	−	0.306249i
$631$	−13.0508			−0.519544			−0.259772	−	0.965670i	$-0.583647\pi$
$631$	−13.0508			−0.519544			−0.259772	+	0.965670i	$0.583647\pi$
$632$	−8.56764	+	8.56764i	−0.340802	+	0.340802i
$633$	5.89438	+	11.1926i	0.234281	+	0.444867i
$634$			20.8903i			0.829659i
$635$	8.68876	+	23.9544i	0.344803	+	0.950602i
$636$	5.24543	+	1.62647i	0.207995	+	0.0644939i
$637$	−1.34160	−	1.34160i	−0.0531561	−	0.0531561i
$638$	1.63145	+	1.63145i	0.0645899	+	0.0645899i
$639$	−23.7677	−	16.3074i	−0.940235	−	0.645111i
$640$	0.762461	+	2.10206i	0.0301389	+	0.0830912i
$641$			24.2560i			0.958055i	0.877800	+	0.479027i	$0.159011\pi$
$641$			24.2560i			0.958055i	−0.877800	+	0.479027i	$0.840989\pi$
$642$	−21.8370	+	11.5000i	−0.861836	+	0.453870i
$643$	−13.2221	+	13.2221i	−0.521429	+	0.521429i	−0.918003	−	0.396574i	$-0.870199\pi$
$643$	−13.2221	+	13.2221i	−0.521429	+	0.521429i	0.396574	+	0.918003i	$0.370199\pi$
$644$	−5.79300			−0.228276
$645$	−17.7818	−	16.1748i	−0.700157	−	0.636883i
$646$	1.48910			0.0585878
$647$	−8.17921	+	8.17921i	−0.321558	+	0.321558i	−0.849365	−	0.527807i	$-0.823015\pi$
$647$	−8.17921	+	8.17921i	−0.321558	+	0.321558i	0.527807	+	0.849365i	$0.323015\pi$
$648$	3.64761	−	8.22769i	0.143292	−	0.323214i
$649$			7.12538i			0.279696i
$650$	−3.83731	+	3.20547i	−0.150512	+	0.125729i
$651$	10.8884	−	35.1154i	0.426749	−	1.37628i
$652$	9.12788	+	9.12788i	0.357476	+	0.357476i
$653$	12.1320	+	12.1320i	0.474763	+	0.474763i	0.903452	−	0.428689i	$-0.141024\pi$
$653$	12.1320	+	12.1320i	0.474763	+	0.474763i	−0.428689	+	0.903452i	$0.641024\pi$
$654$	−4.70858	+	15.1853i	−0.184120	+	0.593793i
$655$	−13.4582	+	28.7782i	−0.525855	+	1.12446i
$656$		−	2.11082i		−	0.0824136i
$657$	−1.28261	−	6.88989i	−0.0500393	−	0.268800i
$658$	−8.39864	+	8.39864i	−0.327413	+	0.327413i
$659$	13.1366			0.511731			0.255865	−	0.966712i	$-0.417640\pi$
$659$	13.1366			0.511731			0.255865	+	0.966712i	$0.417640\pi$
$660$	0.474171	+	10.0197i	0.0184571	+	0.390016i
$661$	−34.2832			−1.33346			−0.666731	−	0.745298i	$-0.732307\pi$
$661$	−34.2832			−1.33346			−0.666731	+	0.745298i	$0.732307\pi$
$662$	0.0790370	−	0.0790370i	0.00307186	−	0.00307186i
$663$	0.336858	−	0.177400i	0.0130825	−	0.00688964i
$664$		−	8.39941i		−	0.325960i
$665$	−32.1684	+	11.6681i	−1.24744	+	0.452471i
$666$	−6.92960	+	10.0998i	−0.268517	+	0.391358i
$667$	−1.61542	−	1.61542i	−0.0625491	−	0.0625491i
$668$	13.1748	+	13.1748i	0.509749	+	0.509749i
$669$	−37.8965	−	11.7507i	−1.46516	−	0.454309i
$670$	−31.4884	−	14.7256i	−1.21650	−	0.568900i
$671$		−	5.93075i		−	0.228954i
$672$	1.82311	+	3.46184i	0.0703281	+	0.133543i
$673$	0.645929	−	0.645929i	0.0248987	−	0.0248987i	−0.694548	−	0.719447i	$-0.744396\pi$
$673$	0.645929	−	0.645929i	0.0248987	−	0.0248987i	0.719447	+	0.694548i	$0.244396\pi$
$674$	12.0894			0.465667
$675$	14.2229	+	21.7419i	0.547440	+	0.836845i
$676$	−1.00000			−0.0384615
$677$	10.5020	−	10.5020i	0.403624	−	0.403624i	−0.475884	−	0.879508i	$-0.657872\pi$
$677$	10.5020	−	10.5020i	0.403624	−	0.403624i	0.879508	+	0.475884i	$0.157872\pi$
$678$	8.95033	+	16.9954i	0.343735	+	0.652706i
$679$		−	28.2676i		−	1.08481i
$680$	0.445222	+	0.208209i	0.0170735	+	0.00798444i
$681$	40.2939	+	12.4941i	1.54407	+	0.478775i
$682$	17.2088	+	17.2088i	0.658960	+	0.658960i
$683$	−19.5328	−	19.5328i	−0.747401	−	0.747401i	0.226590	−	0.973990i	$-0.427242\pi$
$683$	−19.5328	−	19.5328i	−0.747401	−	0.747401i	−0.973990	+	0.226590i	$0.927242\pi$
$684$	−11.4983	+	16.7585i	−0.439648	+	0.640777i
$685$	32.5663	−	11.8125i	1.24429	−	0.451331i
$686$		−	20.0983i		−	0.767355i
$687$	−36.1636	+	19.0449i	−1.37973	+	0.726608i
$688$	4.38869	−	4.38869i	0.167317	−	0.167317i
$689$	−3.17070			−0.120794
$690$	−0.469509	−	9.92120i	−0.0178739	−	0.377693i
$691$	7.28568			0.277160			0.138580	−	0.990351i	$-0.455746\pi$
$691$	7.28568			0.277160			0.138580	+	0.990351i	$0.455746\pi$
$692$	−11.0567	+	11.0567i	−0.420314	+	0.420314i
$693$	3.21218	+	17.2551i	0.122021	+	0.655468i
$694$			8.62460i			0.327385i
$695$	14.2616	−	30.4961i	0.540972	−	1.15678i
$696$	−0.456970	+	1.47374i	−0.0173214	+	0.0558621i
$697$	−0.328077	−	0.328077i	−0.0124268	−	0.0124268i
$698$	3.46012	+	3.46012i	0.130967	+	0.130967i
$699$	−5.40119	+	17.4190i	−0.204292	+	0.658848i
$700$	−11.2494	−	1.00922i	−0.425187	−	0.0381450i
$701$			16.4241i			0.620330i	0.950683	+	0.310165i	$0.100384\pi$
$701$			16.4241i			0.620330i	−0.950683	+	0.310165i	$0.899616\pi$
$702$	−0.604615	+	5.16086i	−0.0228197	+	0.194784i
$703$	19.5582	−	19.5582i	0.737652	−	0.737652i
$704$	−2.58997			−0.0976132
$705$	−15.0643	−	13.7030i	−0.567356	−	0.516083i
$706$	−12.2888			−0.462495
$707$	−25.8690	+	25.8690i	−0.972903	+	0.972903i
$708$	−4.21620	+	2.22038i	−0.158454	+	0.0834470i
$709$			25.9013i			0.972742i	0.873752	+	0.486371i	$0.161680\pi$
$709$			25.9013i			0.972742i	−0.873752	+	0.486371i	$0.838320\pi$
$710$	7.32577	+	20.1967i	0.274931	+	0.757969i
$711$	−29.9728	−	20.5648i	−1.12407	−	0.771241i
$712$	4.55083	+	4.55083i	0.170550	+	0.170550i
$713$	−17.0396	−	17.0396i	−0.638140	−	0.638140i
$714$	0.821420	+	0.254701i	0.0307409	+	0.00953196i
$715$	−1.97475	−	5.44427i	−0.0738515	−	0.203604i
$716$			11.4964i			0.429641i
$717$	−15.5137	−	29.4583i	−0.579368	−	1.10014i
$718$	−22.5188	+	22.5188i	−0.840394	+	0.840394i
$719$	7.92976			0.295730			0.147865	−	0.989008i	$-0.452760\pi$
$719$	7.92976			0.295730			0.147865	+	0.989008i	$0.452760\pi$
$720$	−5.78105	+	3.40287i	−0.215447	+	0.126817i
$721$	−36.4827			−1.35869
$722$	19.0179	−	19.0179i	0.707772	−	0.707772i
$723$	−12.9784	−	24.6442i	−0.482672	−	0.916529i
$724$		−	17.6773i		−	0.656970i
$725$	−2.85554	−	3.41839i	−0.106052	−	0.126956i
$726$	7.10055	+	2.20170i	0.263526	+	0.0817127i
$727$	−13.1739	−	13.1739i	−0.488594	−	0.488594i	0.419268	−	0.907862i	$-0.362287\pi$
$727$	−13.1739	−	13.1739i	−0.488594	−	0.488594i	−0.907862	+	0.419268i	$0.862287\pi$
$728$	−1.59729	−	1.59729i	−0.0591996	−	0.0591996i
$729$	26.2689	+	6.24066i	0.972922	+	0.231136i
$730$	−2.21283	+	4.73180i	−0.0819007	+	0.175132i
$731$		−	1.36423i		−	0.0504580i
$732$	3.50931	−	1.84811i	0.129708	−	0.0683082i
$733$	−4.39131	+	4.39131i	−0.162197	+	0.162197i	−0.783539	−	0.621342i	$-0.786588\pi$
$733$	−4.39131	+	4.39131i	−0.162197	+	0.162197i	0.621342	+	0.783539i	$0.286588\pi$
$734$	−21.1845			−0.781935
$735$	7.34003	−	0.347359i	0.270741	−	0.0128125i
$736$	2.56451			0.0945290
$737$	28.4704	−	28.4704i	1.04872	−	1.04872i
$738$	6.22550	−	1.15893i	0.229164	−	0.0426607i
$739$			13.4115i			0.493350i	0.969098	+	0.246675i	$0.0793380\pi$
$739$			13.4115i			0.493350i	−0.969098	+	0.246675i	$0.920662\pi$
$740$	8.58232	−	3.11299i	0.315492	−	0.114436i
$741$	3.47517	−	11.2075i	0.127664	−	0.411720i
$742$	−5.06453	−	5.06453i	−0.185925	−	0.185925i
$743$	6.99293	+	6.99293i	0.256546	+	0.256546i	0.823648	−	0.567102i	$-0.191935\pi$
$743$	6.99293	+	6.99293i	0.256546	+	0.256546i	−0.567102	+	0.823648i	$0.691935\pi$
$744$	−4.82019	+	15.5453i	−0.176717	+	0.569917i
$745$	31.8421	+	14.8910i	1.16660	+	0.545565i
$746$			23.0492i			0.843893i
$747$	24.7727	−	4.61163i	0.906384	−	0.168731i
$748$	−0.402549	+	0.402549i	−0.0147187	+	0.0147187i
$749$	32.1873			1.17610
$750$	0.816675	−	19.3477i	0.0298207	−	0.706478i
$751$	−11.5511			−0.421507			−0.210754	−	0.977539i	$-0.567592\pi$
$751$	−11.5511			−0.421507			−0.210754	+	0.977539i	$0.567592\pi$
$752$	3.71800	−	3.71800i	0.135581	−	0.135581i
$753$	−38.9997	+	20.5384i	−1.42123	+	0.748462i
$754$		−	0.890831i		−	0.0324421i
$755$	29.0245	+	13.5734i	1.05631	+	0.493986i
$756$	−9.20915	+	7.27765i	−0.334933	+	0.264686i
$757$	−5.58355	−	5.58355i	−0.202938	−	0.202938i	0.598320	−	0.801257i	$-0.295835\pi$
$757$	−5.58355	−	5.58355i	−0.202938	−	0.202938i	−0.801257	+	0.598320i	$0.795835\pi$
$758$	4.82433	+	4.82433i	0.175228	+	0.175228i
$759$	10.9882	+	3.40715i	0.398845	+	0.123672i
$760$	14.2406	−	5.16537i	0.516562	−	0.187368i
$761$		−	37.4923i		−	1.35909i	−0.733632	−	0.679547i	$-0.762176\pi$
$761$		−	37.4923i		−	1.35909i	0.733632	−	0.679547i	$-0.237824\pi$
$762$	−9.19717	−	17.4642i	−0.333178	−	0.632660i
$763$	14.6616	−	14.6616i	0.530787	−	0.530787i
$764$	18.0153			0.651771
$765$	−0.369632	+	1.42742i	−0.0133641	+	0.0516085i
$766$	21.4836			0.776235
$767$	1.94535	−	1.94535i	0.0702426	−	0.0702426i
$768$	−0.807075	−	1.53252i	−0.0291228	−	0.0553002i
$769$		−	25.0653i		−	0.903880i	−0.892048	−	0.451940i	$-0.850732\pi$
$769$		−	25.0653i		−	0.903880i	0.892048	−	0.451940i	$-0.149268\pi$
$770$	5.54184	−	11.8503i	0.199714	−	0.427057i
$771$	−28.3831	−	8.80087i	−1.02219	−	0.316956i
$772$	−3.58559	−	3.58559i	−0.129048	−	0.129048i
$773$	2.54918	+	2.54918i

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.807075 - 1.53252i) q^{3} -1.00000i q^{4} +(-2.02552 - 0.947239i) q^{5} +(1.65435 + 0.512970i) q^{6} +(-1.59729 - 1.59729i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.69726 + 2.47372i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.807075 - 1.53252i) q^{3} -1.00000i q^{4} +(-2.02552 - 0.947239i) q^{5} +(1.65435 + 0.512970i) q^{6} +(-1.59729 - 1.59729i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.69726 + 2.47372i) q^{9} +(2.10206 - 0.762461i) q^{10} +2.58997i q^{11} +(-1.53252 + 0.807075i) q^{12} +(0.707107 - 0.707107i) q^{13} +2.25891 q^{14} +(0.183080 + 3.86865i) q^{15} -1.00000 q^{16} +(-0.155426 + 0.155426i) q^{17} +(-0.549041 - 2.94933i) q^{18} +6.77461i q^{19} +(-0.947239 + 2.02552i) q^{20} +(-1.15876 + 3.73703i) q^{21} +(-1.83139 - 1.83139i) q^{22} +(1.81338 + 1.81338i) q^{23} +(0.512970 - 1.65435i) q^{24} +(3.20547 + 3.83731i) q^{25} +1.00000i q^{26} +(5.16086 + 0.604615i) q^{27} +(-1.59729 + 1.59729i) q^{28} -0.890831 q^{29} +(-2.86501 - 2.60609i) q^{30} -9.39662 q^{31} +(0.707107 - 0.707107i) q^{32} +(3.96919 - 2.09030i) q^{33} -0.219806i q^{34} +(1.72233 + 4.74837i) q^{35} +(2.47372 + 1.69726i) q^{36} +(-2.88699 - 2.88699i) q^{37} +(-4.79037 - 4.79037i) q^{38} +(-1.65435 - 0.512970i) q^{39} +(-0.762461 - 2.10206i) q^{40} +2.11082i q^{41} +(-1.82311 - 3.46184i) q^{42} +(-4.38869 + 4.38869i) q^{43} +2.58997 q^{44} +(5.78105 - 3.40287i) q^{45} -2.56451 q^{46} +(-3.71800 + 3.71800i) q^{47} +(0.807075 + 1.53252i) q^{48} -1.89731i q^{49} +(-4.98000 - 0.446773i) q^{50} +(0.363635 + 0.112754i) q^{51} +(-0.707107 - 0.707107i) q^{52} +(-2.24202 - 2.24202i) q^{53} +(-4.07680 + 3.22175i) q^{54} +(2.45332 - 5.24604i) q^{55} -2.25891i q^{56} +(10.3823 - 5.46761i) q^{57} +(0.629912 - 0.629912i) q^{58} +2.75114 q^{59} +(3.86865 - 0.183080i) q^{60} -2.28989 q^{61} +(6.64441 - 6.64441i) q^{62} +(6.66228 - 1.24024i) q^{63} +1.00000i q^{64} +(-2.10206 + 0.762461i) q^{65} +(-1.32858 + 4.28471i) q^{66} +(-10.9926 - 10.9926i) q^{67} +(0.155426 + 0.155426i) q^{68} +(1.31552 - 4.24259i) q^{69} +(-4.57548 - 2.13973i) q^{70} +9.60806i q^{71} +(-2.94933 + 0.549041i) q^{72} +(-1.65186 + 1.65186i) q^{73} +4.08282 q^{74} +(3.29371 - 8.00946i) q^{75} +6.77461 q^{76} +(4.13694 - 4.13694i) q^{77} +(1.53252 - 0.807075i) q^{78} +12.1165i q^{79} +(2.02552 + 0.947239i) q^{80} +(-3.23861 - 8.39711i) q^{81} +(-1.49257 - 1.49257i) q^{82} +(-5.93928 - 5.93928i) q^{83} +(3.73703 + 1.15876i) q^{84} +(0.462045 - 0.167593i) q^{85} -6.20654i q^{86} +(0.718967 + 1.36522i) q^{87} +(-1.83139 + 1.83139i) q^{88} +6.43585 q^{89} +(-1.68163 + 6.49401i) q^{90} -2.25891 q^{91} +(1.81338 - 1.81338i) q^{92} +(7.58377 + 14.4005i) q^{93} -5.25805i q^{94} +(6.41718 - 13.7221i) q^{95} +(-1.65435 - 0.512970i) q^{96} +(8.84860 + 8.84860i) q^{97} +(1.34160 + 1.34160i) q^{98} +(-6.40687 - 4.39585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 20 * q - 4 * q^7 - 4 * q^9	\( 20 q - 4 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} + 16 q^{14} + 4 q^{15} - 20 q^{16} - 12 q^{17} + 8 q^{18} - 16 q^{21} + 4 q^{22} - 16 q^{23} - 4 q^{24} + 32 q^{25} + 36 q^{27} - 4 q^{28} + 24 q^{29} - 4 q^{30} - 8 q^{31} + 36 q^{33} + 20 q^{35} - 4 q^{36} - 16 q^{37} - 24 q^{38} - 8 q^{40} + 4 q^{42} - 20 q^{43} - 16 q^{44} + 24 q^{45} - 40 q^{46} - 16 q^{47} + 12 q^{51} - 32 q^{53} - 28 q^{54} - 4 q^{55} + 16 q^{57} + 28 q^{58} - 16 q^{60} + 24 q^{61} - 40 q^{62} + 36 q^{63} + 8 q^{65} + 12 q^{68} - 72 q^{69} + 20 q^{70} + 8 q^{72} + 28 q^{73} + 48 q^{74} - 52 q^{75} + 16 q^{76} - 8 q^{77} + 4 q^{78} - 16 q^{81} - 112 q^{83} - 8 q^{85} + 4 q^{87} + 4 q^{88} + 88 q^{89} - 4 q^{90} - 16 q^{91} - 16 q^{92} + 40 q^{93} + 8 q^{95} + 36 q^{97} - 40 q^{99}+O(q^{100}) \) 20 * q - 4 * q^7 - 4 * q^9 - 8 * q^10 - 4 * q^12 + 16 * q^14 + 4 * q^15 - 20 * q^16 - 12 * q^17 + 8 * q^18 - 16 * q^21 + 4 * q^22 - 16 * q^23 - 4 * q^24 + 32 * q^25 + 36 * q^27 - 4 * q^28 + 24 * q^29 - 4 * q^30 - 8 * q^31 + 36 * q^33 + 20 * q^35 - 4 * q^36 - 16 * q^37 - 24 * q^38 - 8 * q^40 + 4 * q^42 - 20 * q^43 - 16 * q^44 + 24 * q^45 - 40 * q^46 - 16 * q^47 + 12 * q^51 - 32 * q^53 - 28 * q^54 - 4 * q^55 + 16 * q^57 + 28 * q^58 - 16 * q^60 + 24 * q^61 - 40 * q^62 + 36 * q^63 + 8 * q^65 + 12 * q^68 - 72 * q^69 + 20 * q^70 + 8 * q^72 + 28 * q^73 + 48 * q^74 - 52 * q^75 + 16 * q^76 - 8 * q^77 + 4 * q^78 - 16 * q^81 - 112 * q^83 - 8 * q^85 + 4 * q^87 + 4 * q^88 + 88 * q^89 - 4 * q^90 - 16 * q^91 - 16 * q^92 + 40 * q^93 + 8 * q^95 + 36 * q^97 - 40 * q^99

Introduction

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