LMFDB - Embedded newform 546.2.bv.a.515.25

Newspace parameters

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			515.25
Character	$\chi$	$=$	546.515
Dual form			546.2.bv.a.317.25

$q$-expansion

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-1.01561 - 1.40305i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.935798 - 0.250746i) q^{5} +(-0.617867 - 1.61810i) q^{6} +(2.47599 - 0.932449i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.937080 + 2.84989i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-1.01561 - 1.40305i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.935798 - 0.250746i) q^{5} +(-0.617867 - 1.61810i) q^{6} +(2.47599 - 0.932449i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.937080 + 2.84989i) q^{9} +(-0.839013 - 0.484404i) q^{10} +(0.989868 - 0.265234i) q^{11} +(-0.178019 - 1.72288i) q^{12} +(1.28292 - 3.36959i) q^{13} +(2.63296 - 0.259843i) q^{14} +(0.598595 + 1.56763i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.05787 - 3.56434i) q^{17} +(-1.64276 + 2.51025i) q^{18} +(0.715871 - 2.67167i) q^{19} +(-0.685051 - 0.685051i) q^{20} +(-3.82291 - 2.52693i) q^{21} +1.02479 q^{22} +(-0.318592 - 0.551817i) q^{23} +(0.273960 - 1.71025i) q^{24} +(-3.51728 - 2.03070i) q^{25} +(2.11132 - 2.92273i) q^{26} +(4.95024 - 1.57961i) q^{27} +(2.61050 + 0.430471i) q^{28} -3.48270i q^{29} +(0.172467 + 1.66914i) q^{30} +(-2.41212 + 0.646325i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-1.37745 - 1.11946i) q^{33} +(2.91027 - 2.91027i) q^{34} +(-2.55084 + 0.251738i) q^{35} +(-2.23648 + 1.99954i) q^{36} +(2.79469 + 0.748834i) q^{37} +(1.38296 - 2.39535i) q^{38} +(-6.03063 + 1.62219i) q^{39} +(-0.484404 - 0.839013i) q^{40} +(-0.0484181 + 0.0484181i) q^{41} +(-3.03863 - 3.43027i) q^{42} +8.67865i q^{43} +(0.989868 + 0.265234i) q^{44} +(1.59152 - 2.43195i) q^{45} +(-0.164915 - 0.615472i) q^{46} +(-0.867903 + 3.23906i) q^{47} +(0.707270 - 1.58107i) q^{48} +(5.26108 - 4.61748i) q^{49} +(-2.87185 - 2.87185i) q^{50} +(-7.09092 + 0.732681i) q^{51} +(2.79583 - 2.27669i) q^{52} +(6.87259 + 3.96789i) q^{53} +(5.19039 - 0.244568i) q^{54} -0.992823 q^{55} +(2.41013 + 1.09145i) q^{56} +(-4.47551 + 1.70897i) q^{57} +(0.901389 - 3.36403i) q^{58} +(5.60584 - 1.50208i) q^{59} +(-0.265415 + 1.65690i) q^{60} +(0.594016 + 1.02887i) q^{61} -2.49721 q^{62} +(0.337178 + 7.93009i) q^{63} +1.00000i q^{64} +(-2.04546 + 2.83157i) q^{65} +(-1.04078 - 1.43782i) q^{66} +(1.62806 - 0.436237i) q^{67} +(3.56434 - 2.05787i) q^{68} +(-0.450660 + 1.00743i) q^{69} +(-2.52907 - 0.417044i) q^{70} +(-8.55610 + 8.55610i) q^{71} +(-2.67779 + 1.35256i) q^{72} +(3.42226 + 12.7721i) q^{73} +(2.50565 + 1.44664i) q^{74} +(0.723009 + 6.99731i) q^{75} +(1.95579 - 1.95579i) q^{76} +(2.20359 - 1.57972i) q^{77} +(-6.24500 + 0.00607038i) q^{78} +(-0.0157356 - 0.0272549i) q^{79} +(-0.250746 - 0.935798i) q^{80} +(-7.24376 - 5.34115i) q^{81} +(-0.0592998 + 0.0342367i) q^{82} +(-6.06316 + 6.06316i) q^{83} +(-2.04727 - 4.09984i) q^{84} +(-2.81950 + 2.81950i) q^{85} +(-2.24620 + 8.38293i) q^{86} +(-4.88639 + 3.53706i) q^{87} +(0.887491 + 0.512393i) q^{88} +(-1.67059 + 6.23472i) q^{89} +(2.16672 - 1.93717i) q^{90} +(0.0345255 - 9.53933i) q^{91} -0.637183i q^{92} +(3.35659 + 2.72790i) q^{93} +(-1.67666 + 2.90406i) q^{94} +(-1.33982 + 2.32064i) q^{95} +(1.09238 - 1.34414i) q^{96} +(-8.64212 - 8.64212i) q^{97} +(6.27690 - 3.09847i) q^{98} +(-0.171696 + 3.06956i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7} + O(q^{10}) $	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−1.01561	−	1.40305i	−0.586362	−	0.810049i
$3$	−1.01561	−	1.40305i	−0.586362	−	0.810049i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−0.935798	−	0.250746i	−0.418501	−	0.112137i	0.0434222	−	0.999057i	$-0.486174\pi$
$5$	−0.935798	−	0.250746i	−0.418501	−	0.112137i	−0.461924	+	0.886920i	$0.652841\pi$
$6$	−0.617867	−	1.61810i	−0.252243	−	0.660586i
$7$	2.47599	−	0.932449i	0.935837	−	0.352433i
$7$	2.47599	−	0.932449i	0.935837	−	0.352433i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.937080	+	2.84989i	−0.312360	+	0.949964i
$10$	−0.839013	−	0.484404i	−0.265319	−	0.153182i
$11$	0.989868	−	0.265234i	0.298456	−	0.0799712i	−0.106483	−	0.994314i	$-0.533959\pi$
$11$	0.989868	−	0.265234i	0.298456	−	0.0799712i	0.404940	+	0.914343i	$0.367292\pi$
$12$	−0.178019	−	1.72288i	−0.0513897	−	0.497352i
$13$	1.28292	−	3.36959i	0.355817	−	0.934555i
$13$	1.28292	−	3.36959i	0.355817	−	0.934555i
$14$	2.63296	−	0.259843i	0.703688	−	0.0694460i
$15$	0.598595	+	1.56763i	0.154557	+	0.404760i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.05787	−	3.56434i	0.499107	−	0.864479i	−0.500892	−	0.865510i	$-0.666995\pi$
$17$	2.05787	−	3.56434i	0.499107	−	0.864479i	0.999999	+	0.00103068i	$0.000328075\pi$
$18$	−1.64276	+	2.51025i	−0.387201	+	0.591672i
$19$	0.715871	−	2.67167i	0.164232	−	0.612922i	−0.833905	−	0.551908i	$-0.813900\pi$
$19$	0.715871	−	2.67167i	0.164232	−	0.612922i	0.998137	−	0.0610140i	$-0.0194334\pi$
$20$	−0.685051	−	0.685051i	−0.153182	−	0.153182i
$21$	−3.82291	−	2.52693i	−0.834227	−	0.551421i
$22$	1.02479			0.218485
$23$	−0.318592	−	0.551817i	−0.0664309	−	0.115062i	0.830897	−	0.556426i	$-0.187828\pi$
$23$	−0.318592	−	0.551817i	−0.0664309	−	0.115062i	−0.897328	+	0.441365i	$0.854495\pi$
$24$	0.273960	−	1.71025i	0.0559219	−	0.349103i
$25$	−3.51728	−	2.03070i	−0.703457	−	0.406141i
$26$	2.11132	−	2.92273i	0.414063	−	0.573194i
$27$	4.95024	−	1.57961i	0.952673	−	0.303996i
$28$	2.61050	+	0.430471i	0.493338	+	0.0813514i
$29$		−	3.48270i		−	0.646721i	−0.946276	−	0.323361i	$-0.895187\pi$
$29$		−	3.48270i		−	0.646721i	0.946276	−	0.323361i	$-0.104813\pi$
$30$	0.172467	+	1.66914i	0.0314880	+	0.304742i
$31$	−2.41212	+	0.646325i	−0.433229	+	0.116083i	−0.468841	−	0.883282i	$-0.655328\pi$
$31$	−2.41212	+	0.646325i	−0.433229	+	0.116083i	0.0356126	+	0.999366i	$0.488662\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−1.37745	−	1.11946i	−0.239784	−	0.194872i
$34$	2.91027	−	2.91027i	0.499107	−	0.499107i
$35$	−2.55084	+	0.251738i	−0.431170	+	0.0425515i
$36$	−2.23648	+	1.99954i	−0.372747	+	0.333256i
$37$	2.79469	+	0.748834i	0.459443	+	0.123107i	0.481115	−	0.876658i	$-0.340232\pi$
$37$	2.79469	+	0.748834i	0.459443	+	0.123107i	−0.0216713	+	0.999765i	$0.506899\pi$
$38$	1.38296	−	2.39535i	0.224345	−	0.388577i
$39$	−6.03063	+	1.62219i	−0.965674	+	0.259758i
$40$	−0.484404	−	0.839013i	−0.0765911	−	0.132660i
$41$	−0.0484181	+	0.0484181i	−0.00756163	+	0.00756163i	−0.710877	−	0.703316i	$-0.751702\pi$
$41$	−0.0484181	+	0.0484181i	−0.00756163	+	0.00756163i	0.703316	+	0.710877i	$0.251702\pi$
$42$	−3.03863	−	3.43027i	−0.468871	−	0.529302i
$43$			8.67865i			1.32348i	0.749733	+	0.661741i	$0.230182\pi$
$43$			8.67865i			1.32348i	−0.749733	+	0.661741i	$0.769818\pi$
$44$	0.989868	+	0.265234i	0.149228	+	0.0399856i
$45$	1.59152	−	2.43195i	0.237249	−	0.362534i
$46$	−0.164915	−	0.615472i	−0.0243154	−	0.0907463i
$47$	−0.867903	+	3.23906i	−0.126597	+	0.472465i	−0.999892	−	0.0147269i	$-0.995312\pi$
$47$	−0.867903	+	3.23906i	−0.126597	+	0.472465i	0.873295	+	0.487192i	$0.161979\pi$
$48$	0.707270	−	1.58107i	0.102086	−	0.228207i
$49$	5.26108	−	4.61748i	0.751582	−	0.659639i
$50$	−2.87185	−	2.87185i	−0.406141	−	0.406141i
$51$	−7.09092	+	0.732681i	−0.992928	+	0.102596i
$52$	2.79583	−	2.27669i	0.387712	−	0.315720i
$53$	6.87259	+	3.96789i	0.944023	+	0.545032i	0.891219	−	0.453573i	$-0.149851\pi$
$53$	6.87259	+	3.96789i	0.944023	+	0.545032i	0.0528037	+	0.998605i	$0.483184\pi$
$54$	5.19039	−	0.244568i	0.706323	−	0.0332814i
$55$	−0.992823			−0.133872
$56$	2.41013	+	1.09145i	0.322067	+	0.145851i
$57$	−4.47551	+	1.70897i	−0.592796	+	0.226358i
$58$	0.901389	−	3.36403i	0.118358	−	0.441719i
$59$	5.60584	−	1.50208i	0.729818	−	0.195554i	0.125270	−	0.992123i	$-0.460020\pi$
$59$	5.60584	−	1.50208i	0.729818	−	0.195554i	0.604548	+	0.796568i	$0.293354\pi$
$60$	−0.265415	+	1.65690i	−0.0342650	+	0.213905i
$61$	0.594016	+	1.02887i	0.0760560	+	0.131733i	0.901545	−	0.432685i	$-0.142434\pi$
$61$	0.594016	+	1.02887i	0.0760560	+	0.131733i	−0.825489	+	0.564418i	$0.809101\pi$
$62$	−2.49721			−0.317146
$63$	0.337178	+	7.93009i	0.0424804	+	0.999097i
$64$			1.00000i			0.125000i
$65$	−2.04546	+	2.83157i	−0.253708	+	0.351212i
$66$	−1.04078	−	1.43782i	−0.128111	−	0.176984i
$67$	1.62806	−	0.436237i	0.198899	−	0.0532948i	−0.157994	−	0.987440i	$-0.550503\pi$
$67$	1.62806	−	0.436237i	0.198899	−	0.0532948i	0.356893	+	0.934145i	$0.383836\pi$
$68$	3.56434	−	2.05787i	0.432239	−	0.249554i
$69$	−0.450660	+	1.00743i	−0.0542531	+	0.121280i
$70$	−2.52907	−	0.417044i	−0.302282	−	0.0498463i
$71$	−8.55610	+	8.55610i	−1.01542	+	1.01542i	−0.0155429	+	0.999879i	$0.504948\pi$
$71$	−8.55610	+	8.55610i	−1.01542	+	1.01542i	−0.999879	+	0.0155429i	$0.995052\pi$
$72$	−2.67779	+	1.35256i	−0.315581	+	0.159401i
$73$	3.42226	+	12.7721i	0.400545	+	1.49486i	0.812126	+	0.583482i	$0.198310\pi$
$73$	3.42226	+	12.7721i	0.400545	+	1.49486i	−0.411581	+	0.911373i	$0.635023\pi$
$74$	2.50565	+	1.44664i	0.291275	+	0.168168i
$75$	0.723009	+	6.99731i	0.0834859	+	0.807980i
$76$	1.95579	−	1.95579i	0.224345	−	0.224345i
$77$	2.20359	−	1.57972i	0.251122	−	0.180026i
$78$	−6.24500	+	0.00607038i	−0.707106	+	0.000687335i
$79$	−0.0157356	−	0.0272549i	−0.00177039	−	0.00306641i	0.865139	−	0.501532i	$-0.167230\pi$
$79$	−0.0157356	−	0.0272549i	−0.00177039	−	0.00306641i	−0.866909	+	0.498466i	$0.833897\pi$
$80$	−0.250746	−	0.935798i	−0.0280343	−	0.104625i
$81$	−7.24376	−	5.34115i	−0.804863	−	0.593461i
$82$	−0.0592998	+	0.0342367i	−0.00654856	+	0.00378082i
$83$	−6.06316	+	6.06316i	−0.665518	+	0.665518i	−0.956675	−	0.291157i	$-0.905960\pi$
$83$	−6.06316	+	6.06316i	−0.665518	+	0.665518i	0.291157	+	0.956675i	$0.405960\pi$
$84$	−2.04727	−	4.09984i	−0.223376	−	0.447329i
$85$	−2.81950	+	2.81950i	−0.305817	+	0.305817i
$86$	−2.24620	+	8.38293i	−0.242214	+	0.903955i
$87$	−4.88639	+	3.53706i	−0.523876	+	0.379213i
$88$	0.887491	+	0.512393i	0.0946069	+	0.0546213i
$89$	−1.67059	+	6.23472i	−0.177082	+	0.660879i	0.819106	+	0.573643i	$0.194470\pi$
$89$	−1.67059	+	6.23472i	−0.177082	+	0.660879i	−0.996188	+	0.0872363i	$0.972196\pi$
$90$	2.16672	−	1.93717i	0.228393	−	0.204196i
$91$	0.0345255	−	9.53933i	0.00361926	−	0.999993i
$92$		−	0.637183i		−	0.0664309i
$93$	3.35659	+	2.72790i	0.348062	+	0.282870i
$94$	−1.67666	+	2.90406i	−0.172934	+	0.299531i
$95$	−1.33982	+	2.32064i	−0.137463	+	0.238092i
$96$	1.09238	−	1.34414i	0.111491	−	0.137185i
$97$	−8.64212	−	8.64212i	−0.877475	−	0.877475i	0.115798	−	0.993273i	$-0.463057\pi$
$97$	−8.64212	−	8.64212i	−0.877475	−	0.877475i	−0.993273	+	0.115798i	$0.963057\pi$
$98$	6.27690	−	3.09847i	0.634063	−	0.312993i
$99$	−0.171696	+	3.06956i	−0.0172561	+	0.308503i
$100$	−2.03070	−	3.51728i	−0.203070	−	0.351728i
$101$	5.68164	−	9.84089i	0.565344	−	0.979205i	−0.431673	−	0.902030i	$-0.642077\pi$
$101$	5.68164	−	9.84089i	0.565344	−	0.979205i	0.997018	−	0.0771748i	$-0.0245900\pi$
$102$	−7.03894	−	1.12755i	−0.696959	−	0.111644i
$103$	−12.5991	+	7.27409i	−1.24143	+	0.716738i	−0.969385	−	0.245548i	$-0.921032\pi$
$103$	−12.5991	+	7.27409i	−1.24143	+	0.716738i	−0.272042	+	0.962285i	$0.587699\pi$
$104$	3.28982	−	1.47550i	0.322593	−	0.144685i
$105$	2.94385	+	3.32327i	0.287290	+	0.324318i
$106$	5.61145	+	5.61145i	0.545032	+	0.545032i
$107$	7.41867	−	4.28317i	0.717189	−	0.414070i	−0.0965279	−	0.995330i	$-0.530774\pi$
$107$	7.41867	−	4.28317i	0.717189	−	0.414070i	0.813717	+	0.581261i	$0.197440\pi$
$108$	5.07683	+	1.10714i	0.488519	+	0.106534i
$109$	0.938198	−	0.251389i	0.0898631	−	0.0240787i	−0.213607	−	0.976920i	$-0.568521\pi$
$109$	0.938198	−	0.251389i	0.0898631	−	0.0240787i	0.303470	+	0.952841i	$0.401855\pi$
$110$	−0.958993	−	0.256961i	−0.0914364	−	0.0245003i
$111$	−1.78766	−	4.68160i	−0.169677	−	0.444357i
$112$	2.04552	+	1.67805i	0.193284	+	0.158561i
$113$			8.13853i			0.765608i	0.923829	+	0.382804i	$0.125042\pi$
$113$			8.13853i			0.765608i	−0.923829	+	0.382804i	$0.874958\pi$
$114$	−4.76533	+	0.492385i	−0.446314	+	0.0461161i
$115$	0.159771	+	0.596274i	0.0148987	+	0.0556029i
$116$	1.74135	−	3.01611i	0.161680	−	0.280039i
$117$	8.40076	+	6.81375i	0.776651	+	0.629931i
$118$	5.80359			0.534264
$119$	1.77171	−	10.7441i	0.162412	−	0.984913i
$120$	−0.685209	+	1.53175i	−0.0625508	+	0.139829i
$121$	−8.61679	+	4.97491i	−0.783345	+	0.452264i
$122$	0.307485	+	1.14755i	0.0278384	+	0.103894i
$123$	0.117107	+	0.0187590i	0.0105591	+	0.00169144i
$124$	−2.41212	−	0.646325i	−0.216614	−	0.0580417i
$125$	6.20753	+	6.20753i	0.555218	+	0.555218i
$126$	−1.72677	+	7.74715i	−0.153833	+	0.690171i
$127$			20.2101i			1.79335i	0.442687	+	0.896676i	$0.354025\pi$
$127$			20.2101i			1.79335i	−0.442687	+	0.896676i	$0.645975\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	12.1766	−	8.81411i	1.07209	−	0.776039i
$130$	−2.70863	+	2.20568i	−0.237562	+	0.193451i
$131$	3.53443	−	2.04060i	0.308805	−	0.178288i	−0.337587	−	0.941294i	$-0.609611\pi$
$131$	3.53443	−	2.04060i	0.308805	−	0.178288i	0.646391	+	0.763006i	$0.276277\pi$
$132$	−0.633182	−	1.65820i	−0.0551114	−	0.144328i
$133$	−0.718703	−	7.28254i	−0.0623194	−	0.631476i
$134$	1.68549			0.145604
$135$	−5.02850	+	0.236939i	−0.432784	+	0.0203925i
$136$	3.97550	−	1.06523i	0.340897	−	0.0913429i
$137$	17.4258	−	4.66924i	1.48879	−	0.398920i	0.579462	−	0.814999i	$-0.303263\pi$
$137$	17.4258	−	4.66924i	1.48879	−	0.398920i	0.909328	+	0.416079i	$0.136596\pi$
$138$	−0.696046	+	0.856462i	−0.0592514	+	0.0729069i
$139$	−19.1544			−1.62465			−0.812326	−	0.583204i	$-0.801799\pi$
$139$	−19.1544			−1.62465			−0.812326	+	0.583204i	$0.801799\pi$
$140$	−2.33496	−	1.05741i	−0.197340	−	0.0893671i
$141$	5.42600	−	2.07190i	0.456951	−	0.174486i
$142$	−10.4790	+	6.05008i	−0.879381	+	0.507711i
$143$	0.376189	−	3.67572i	0.0314585	−	0.307379i
$144$	−2.93662	+	0.613411i	−0.244718	+	0.0511176i
$145$	−0.873274	+	3.25910i	−0.0725215	+	0.270654i
$146$			13.2226i			1.09431i
$147$	−11.8217	−	2.69199i	−0.975039	−	0.222032i
$148$	2.04585	+	2.04585i	0.168168	+	0.168168i
$149$	19.7448	+	5.29060i	1.61756	+	0.433423i	0.950282	−	0.311389i	$-0.100794\pi$
$149$	19.7448	+	5.29060i	1.61756	+	0.433423i	0.667274	+	0.744812i	$0.267461\pi$
$150$	−1.11266	+	6.94601i	−0.0908487	+	0.567140i
$151$	0.0427232	+	0.159445i	0.00347676	+	0.0129755i	0.967642	−	0.252325i	$-0.0811954\pi$
$151$	0.0427232	+	0.159445i	0.00347676	+	0.0129755i	−0.964166	+	0.265301i	$0.914529\pi$
$152$	2.39535	−	1.38296i	0.194289	−	0.112173i
$153$	8.22959	+	9.20478i	0.665323	+	0.744162i
$154$	2.53736	−	0.955562i	0.204467	−	0.0770014i
$155$	2.41932			0.194324
$156$	−6.03377	−	1.61046i	−0.483088	−	0.128940i
$157$	2.07855	−	3.60015i	0.165886	−	0.287323i	−0.771083	−	0.636734i	$-0.780285\pi$
$157$	2.07855	−	3.60015i	0.165886	−	0.287323i	0.936970	+	0.349411i	$0.113618\pi$
$158$	−0.00814535	−	0.0303989i	−0.000648009	−	0.00241840i
$159$	−1.41272	−	13.6724i	−0.112036	−	1.08429i
$160$		−	0.968809i		−	0.0765911i
$161$	−1.30337	−	1.06922i	−0.102720	−	0.0842666i
$162$	−5.61455	−	7.03398i	−0.441120	−	0.552642i
$163$	−9.85619	−	2.64096i	−0.771997	−	0.206856i	−0.148743	−	0.988876i	$-0.547523\pi$
$163$	−9.85619	−	2.64096i	−0.771997	−	0.206856i	−0.623253	+	0.782020i	$0.714189\pi$
$164$	−0.0661403	+	0.0177222i	−0.00516469	+	0.00138387i
$165$	1.00832	+	1.39298i	0.0784975	+	0.108443i
$166$	−7.42583	+	4.28730i	−0.576356	+	0.332759i
$167$	−18.0695	−	18.0695i	−1.39826	−	1.39826i	−0.805040	−	0.593220i	$-0.797856\pi$
$167$	−18.0695	−	18.0695i	−1.39826	−	1.39826i	−0.593220	−	0.805040i	$-0.702144\pi$
$168$	−0.916395	−	4.49001i	−0.0707014	−	0.346412i
$169$	−9.70824	−	8.64581i	−0.746788	−	0.665062i
$170$	−3.45316	+	1.99368i	−0.264845	+	0.152909i
$171$	6.94313	+	4.54372i	0.530954	+	0.347467i
$172$	−4.33933	+	7.51593i	−0.330870	+	0.573084i
$173$	2.51736	+	4.36020i	0.191392	+	0.331500i	0.945712	−	0.325007i	$-0.105367\pi$
$173$	2.51736	+	4.36020i	0.191392	+	0.331500i	−0.754320	+	0.656507i	$0.772033\pi$
$174$	−5.63535	+	2.15185i	−0.427215	+	0.163131i
$175$	−10.6023	−	1.74832i	−0.801458	−	0.132161i
$176$	0.724634	+	0.724634i	0.0546213	+	0.0546213i
$177$	−7.80083	−	6.33973i	−0.586346	−	0.476523i
$178$	−3.22733	+	5.58990i	−0.241898	+	0.418980i
$179$	−1.24867	+	2.16277i	−0.0933302	+	0.161653i	−0.908910	−	0.416991i	$-0.863085\pi$
$179$	−1.24867	+	2.16277i	−0.0933302	+	0.161653i	0.815580	+	0.578644i	$0.196418\pi$
$180$	2.59427	−	1.31037i	0.193365	−	0.0976695i
$181$			0.778086i			0.0578347i	0.999582	+	0.0289173i	$0.00920596\pi$
$181$			0.778086i			0.0578347i	−0.999582	+	0.0289173i	$0.990794\pi$
$182$	2.50231	−	9.20535i	0.185484	−	0.682346i
$183$	0.840259	−	1.87836i	0.0621138	−	0.138852i
$184$	0.164915	−	0.615472i	0.0121577	−	0.0453732i
$185$	−2.42749	−	1.40151i	−0.178473	−	0.103041i
$186$	2.53618	+	3.50370i	0.185962	+	0.256904i
$187$	1.09164	−	4.07404i	0.0798283	−	0.297923i
$188$	−2.37115	+	2.37115i	−0.172934	+	0.172934i
$189$	10.7838	−	8.52694i	0.784409	−	0.620244i
$190$	−1.89479	+	1.89479i	−0.137463	+	0.137463i
$191$	−18.0065	+	10.3961i	−1.30291	+	0.752234i	−0.980902	−	0.194503i	$-0.937690\pi$
$191$	−18.0065	+	10.3961i	−1.30291	+	0.752234i	−0.322006	+	0.946738i	$0.604357\pi$
$192$	1.40305	−	1.01561i	0.101256	−	0.0732952i
$193$	−5.49236	−	20.4978i	−0.395349	−	1.47546i	−0.821185	−	0.570662i	$-0.806687\pi$
$193$	−5.49236	−	20.4978i	−0.395349	−	1.47546i	0.425837	−	0.904800i	$-0.359980\pi$
$194$	−6.11090	−	10.5844i	−0.438737	−	0.759915i
$195$	6.05021	−	0.00588104i	0.433264	−	0.000421150i
$196$	6.86496	−	1.36831i	0.490355	−	0.0977366i
$197$	2.00709	−	2.00709i	0.142999	−	0.142999i	−0.631983	−	0.774982i	$-0.717759\pi$
$197$	2.00709	−	2.00709i	0.142999	−	0.142999i	0.774982	+	0.631983i	$0.217759\pi$
$198$	−0.960307	+	2.92053i	−0.0682460	+	0.207553i
$199$	11.4097	+	6.58738i	0.808811	+	0.466967i	0.846543	−	0.532321i	$-0.178680\pi$
$199$	11.4097	+	6.58738i	0.808811	+	0.466967i	−0.0377317	+	0.999288i	$0.512013\pi$
$200$	−1.05117	−	3.92302i	−0.0743289	−	0.277399i
$201$	−2.26553	−	1.84119i	−0.159798	−	0.129868i
$202$	8.03505	−	8.03505i	0.565344	−	0.565344i
$203$	−3.24744	−	8.62314i	−0.227926	−	0.605226i
$204$	−6.50726	−	2.91094i	−0.455599	−	0.203807i
$205$	0.0574501	−	0.0331689i	0.00401249	−	0.00231661i
$206$	−14.0525	+	3.76535i	−0.979082	+	0.262344i
$207$	1.87116	−	0.390855i	0.130055	−	0.0271663i
$208$	3.55961	−	0.573754i	0.246814	−	0.0397827i
$209$		−	2.83447i		−	0.196064i
$210$	1.98341	+	3.97196i	0.136869	+	0.274091i
$211$	14.0500			0.967244			0.483622	−	0.875277i	$-0.339321\pi$
$211$	14.0500			0.967244			0.483622	+	0.875277i	$0.339321\pi$
$212$	3.96789	+	6.87259i	0.272516	+	0.472011i
$213$	20.6943	+	3.31496i	1.41795	+	0.227137i
$214$	8.27445	−	2.21713i	0.565629	−	0.151560i
$215$	2.17614	−	8.12146i	0.148411	−	0.553879i
$216$	4.61730	+	2.38340i	0.314167	+	0.162169i
$217$	−5.36972	+	3.84947i	−0.364520	+	0.261319i
$218$	0.971294			0.0657843
$219$	14.4441	−	17.7730i	0.976042	−	1.20099i
$220$	−0.859810	−	0.496411i	−0.0579683	−	0.0334680i
$221$	−9.37027	−	11.5069i	−0.630312	−	0.774040i
$222$	−0.515058	−	4.98475i	−0.0345684	−	0.334555i
$223$	3.20158	+	3.20158i	0.214394	+	0.214394i	0.806131	−	0.591737i	$-0.201558\pi$
$223$	3.20158	+	3.20158i	0.214394	+	0.214394i	−0.591737	+	0.806131i	$0.701558\pi$
$224$	1.54151	+	2.15029i	0.102997	+	0.143672i
$225$	9.08326	−	8.12094i	0.605551	−	0.541396i
$226$	−2.10641	+	7.86122i	−0.140116	+	0.522920i
$227$	5.74340	+	21.4347i	0.381203	+	1.42267i	0.844066	+	0.536239i	$0.180155\pi$
$227$	5.74340	+	21.4347i	0.381203	+	1.42267i	−0.462863	+	0.886430i	$0.653178\pi$
$228$	−4.73039	−	0.757750i	−0.313278	−	0.0501832i
$229$	0.206162	+	0.0552409i	0.0136236	+	0.00365042i	0.265624	−	0.964077i	$-0.414422\pi$
$229$	0.206162	+	0.0552409i	0.0136236	+	0.00365042i	−0.252001	+	0.967727i	$0.581089\pi$
$230$			0.617309i			0.0407041i
$231$	−4.45440	−	1.48736i	−0.293078	−	0.0978611i
$232$	2.46264	−	2.46264i	0.161680	−	0.161680i
$233$	2.96602	+	5.13730i	0.194310	+	0.336556i	0.946674	−	0.322192i	$-0.104420\pi$
$233$	2.96602	+	5.13730i	0.194310	+	0.336556i	−0.752364	+	0.658748i	$0.771086\pi$
$234$	6.35099	+	8.75585i	0.415177	+	0.572388i
$235$	1.62436	−	2.81348i	0.105962	−	0.183531i
$236$	5.60584	+	1.50208i	0.364909	+	0.0977771i
$237$	−0.0222586	+	0.0497581i	−0.00144585	+	0.00323213i
$238$	4.49213	−	9.91948i	0.291181	−	0.642985i
$239$	16.2577	−	16.2577i	1.05162	−	1.05162i	0.0530291	−	0.998593i	$-0.483112\pi$
$239$	16.2577	−	16.2577i	1.05162	−	1.05162i	0.998593	−	0.0530291i	$-0.0168876\pi$
$240$	−1.05831	+	1.30221i	−0.0683135	+	0.0840575i
$241$	−1.02561	−	3.82763i	−0.0660653	−	0.246559i	0.924994	−	0.379982i	$-0.124070\pi$
$241$	−1.02561	−	3.82763i	−0.0660653	−	0.246559i	−0.991059	+	0.133423i	$0.957403\pi$
$242$	−9.61078	+	2.57520i	−0.617804	+	0.165540i
$243$	−0.137057	+	15.5879i	−0.00879224	+	0.999961i
$244$			1.18803i			0.0760560i
$245$	−6.08112	+	3.00183i	−0.388508	+	0.191780i
$246$	0.108261	+	0.0484292i	0.00690247	+	0.00308773i
$247$	−8.08401	−	5.83972i	−0.514373	−	0.371572i
$248$	−2.16264	−	1.24860i	−0.137328	−	0.0792864i
$249$	14.6647	+	2.34910i	0.929337	+	0.148868i
$250$	4.38939	+	7.60264i	0.277609	+	0.480833i
$251$	−25.5203			−1.61082			−0.805412	−	0.592715i	$-0.798056\pi$
$251$	−25.5203			−1.61082			−0.805412	+	0.592715i	$0.798056\pi$
$252$	−3.67304	+	7.03625i	−0.231380	+	0.443242i
$253$	−0.461724	−	0.461724i	−0.0290284	−	0.0290284i
$254$	−5.23075	+	19.5214i	−0.328206	+	1.22488i
$255$	6.81939	+	1.09238i	0.427047	+	0.0684075i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.41632	+	9.38134i	0.337861	+	0.585192i	0.984030	−	0.178002i	$-0.0569634\pi$
$257$	5.41632	+	9.38134i	0.337861	+	0.585192i	−0.646169	+	0.763194i	$0.723630\pi$
$258$	14.0429	−	5.36225i	0.874273	−	0.333839i
$259$	7.61787	−	0.751796i	0.473351	−	0.0467143i
$260$	−3.18721	+	1.42948i	−0.197662	+	0.0886523i
$261$	9.92532	+	3.26357i	0.614362	+	0.202010i
$262$	3.94215	−	1.05629i	0.243547	−	0.0652581i
$263$	−1.97029	−	1.13755i	−0.121493	−	0.0701440i	0.438022	−	0.898964i	$-0.355679\pi$
$263$	−1.97029	−	1.13755i	−0.121493	−	0.0701440i	−0.559515	+	0.828820i	$0.689013\pi$
$264$	−0.182432	−	1.76558i	−0.0112279	−	0.108664i
$265$	−5.43642	−	5.43642i	−0.333957	−	0.333957i
$266$	1.19065	−	7.22040i	0.0730032	−	0.442711i
$267$	10.4443	−	3.98812i	0.639179	−	0.244069i
$268$	1.62806	+	0.436237i	0.0994494	+	0.0266474i
$269$	−14.0370	−	8.10427i	−0.855852	−	0.494126i	0.00676921	−	0.999977i	$-0.497845\pi$
$269$	−14.0370	−	8.10427i	−0.855852	−	0.494126i	−0.862621	+	0.505851i	$0.831179\pi$
$270$	−4.91848	−	1.07261i	−0.299329	−	0.0652767i
$271$	31.3351	+	8.39621i	1.90347	+	0.510033i	0.995937	+	0.0900530i	$0.0287036\pi$
$271$	31.3351	+	8.39621i	1.90347	+	0.510033i	0.907533	+	0.419980i	$0.137963\pi$
$272$	4.11574			0.249554
$273$	−13.4192	+	9.63978i	−0.812166	+	0.583426i
$274$	18.0406			1.08987
$275$	−4.02026	−	1.07723i	−0.242431	−	0.0649591i
$276$	−0.893998	+	0.647128i	−0.0538123	+	0.0389526i
$277$	−24.4046	−	14.0900i	−1.46633	−	0.846585i	−0.467037	−	0.884238i	$-0.654679\pi$
$277$	−24.4046	−	14.0900i	−1.46633	−	0.846585i	−0.999291	+	0.0376525i	$0.988012\pi$
$278$	−18.5017	−	4.95751i	−1.10966	−	0.297332i
$279$	0.418390	−	7.47993i	0.0250484	−	0.447812i
$280$	−1.98172	−	1.62571i	−0.118430	−	0.0971546i
$281$	13.0253	+	13.0253i	0.777021	+	0.777021i	0.979323	−	0.202302i	$-0.0648422\pi$
$281$	13.0253	+	13.0253i	0.777021	+	0.777021i	−0.202302	+	0.979323i	$0.564842\pi$
$282$	5.77736	−	0.596955i	0.344037	−	0.0355482i
$283$	17.8732	+	10.3191i	1.06245	+	0.613408i	0.926110	−	0.377254i	$-0.123132\pi$
$283$	17.8732	+	10.3191i	1.06245	+	0.613408i	0.136344	+	0.990662i	$0.456465\pi$
$284$	−11.6878	+	3.13175i	−0.693546	+	0.185835i
$285$	4.61669	−	0.477027i	0.273469	−	0.0282567i
$286$	1.31472	−	3.45311i	0.0777409	−	0.204187i
$287$	−0.0747354	+	0.165030i	−0.00441149	+	0.00974142i
$288$	−2.99532	−	0.167543i	−0.176501	−	0.00987258i
$289$	0.0303301	+	0.0525333i	0.00178413	+	0.00309020i
$290$	−1.68704	+	2.92203i	−0.0990662	+	0.171588i
$291$	−3.34829	+	20.9023i	−0.196280	+	1.22532i
$292$	−3.42226	+	12.7721i	−0.200273	+	0.747428i
$293$	−21.8967	−	21.8967i	−1.27922	−	1.27922i	−0.941104	−	0.338117i	$-0.890210\pi$
$293$	−21.8967	−	21.8967i	−1.27922	−	1.27922i	−0.338117	−	0.941104i	$-0.609790\pi$
$294$	−10.7222	−	5.65995i	−0.625330	−	0.330095i
$295$	−5.62257			−0.327359
$296$	1.44664	+	2.50565i	0.0840840	+	0.145638i
$297$	4.48111	−	2.87657i	0.260021	−	0.166916i
$298$	17.7027	+	10.2207i	1.02549	+	0.592067i
$299$	−2.26812	+	0.365586i	−0.131169	+	0.0211424i
$300$	−2.87251	+	6.42136i	−0.165845	+	0.370737i
$301$	8.09240	+	21.4883i	0.466438	+	1.23856i
$302$			0.165070i			0.00949869i
$303$	−19.5775	+	2.02288i	−1.12470	+	0.116212i
$304$	2.67167	−	0.715871i	0.153231	−	0.0410580i
$305$	−0.297895	−	1.11176i	−0.0170574	−	0.0636591i
$306$	5.56680	+	11.0211i	0.318233	+	0.630035i
$307$	11.4023	−	11.4023i	0.650764	−	0.650764i	−0.302413	−	0.953177i	$-0.597792\pi$
$307$	11.4023	−	11.4023i	0.650764	−	0.650764i	0.953177	+	0.302413i	$0.0977921\pi$
$308$	2.69822	−	0.266284i	0.153746	−	0.0151729i
$309$	23.0016	+	10.2895i	1.30852	+	0.585349i
$310$	2.33688	+	0.626165i	0.132726	+	0.0355638i
$311$	−8.76323	+	15.1784i	−0.496917	+	0.860686i	−0.999994	−	0.00355622i	$-0.998868\pi$
$311$	−8.76323	+	15.1784i	−0.496917	+	0.860686i	0.503077	+	0.864242i	$0.332201\pi$
$312$	−5.41136	−	3.11724i	−0.306358	−	0.176479i
$313$	2.56506	+	4.44282i	0.144986	+	0.251123i	0.929368	−	0.369155i	$-0.120353\pi$
$313$	2.56506	+	4.44282i	0.144986	+	0.251123i	−0.784382	+	0.620278i	$0.787020\pi$
$314$	2.93951	−	2.93951i	0.165886	−	0.165886i
$315$	1.67291	−	7.50550i	0.0942578	−	0.422887i
$316$		−	0.0314712i		−	0.00177039i
$317$	26.0000	+	6.96668i	1.46031	+	0.391288i	0.899596	−	0.436724i	$-0.143861\pi$
$317$	26.0000	+	6.96668i	1.46031	+	0.391288i	0.560711	+	0.828012i	$0.310528\pi$
$318$	2.17409	−	13.5722i	0.121917	−	0.761088i
$319$	−0.923732	−	3.44741i	−0.0517191	−	0.193018i
$320$	0.250746	−	0.935798i	0.0140171	−	0.0523127i
$321$	−13.5439	−	6.05871i	−0.755949	−	0.338164i
$322$	−0.982225	−	1.37013i	−0.0547372	−	0.0763542i
$323$	−8.04955	−	8.04955i	−0.447889	−	0.447889i
$324$	−3.60271	−	8.24745i	−0.200150	−	0.458192i
$325$	−11.3550	+	9.24657i	−0.629863	+	0.512907i
$326$	−8.83682	−	5.10194i	−0.489426	−	0.282570i
$327$	−1.30555	−	1.06102i	−0.0721972	−	0.0586747i
$328$	−0.0684735			−0.00378082
$329$	0.871336	+	8.82915i	0.0480383	+	0.486767i
$330$	0.613432	+	1.60648i	0.0337683	+	0.0884340i
$331$	1.39711	−	5.21409i	0.0767922	−	0.286592i	−0.916841	−	0.399251i	$-0.869270\pi$
$331$	1.39711	−	5.21409i	0.0767922	−	0.286592i	0.993634	+	0.112659i	$0.0359367\pi$
$332$	−8.28243	+	2.21927i	−0.454557	+	0.121798i
$333$	−4.75294	+	7.26283i	−0.260459	+	0.398001i
$334$	−12.7771	−	22.1305i	−0.699130	−	1.21093i
$335$	−1.63292			−0.0892158
$336$	0.276931	−	4.57420i	0.0151078	−	0.249543i
$337$		−	24.6635i		−	1.34350i	−0.740776	−	0.671752i	$-0.765542\pi$
$337$		−	24.6635i		−	1.34350i	0.740776	−	0.671752i	$-0.234458\pi$
$338$	−7.13974	−	10.8639i	−0.388351	−	0.590918i
$339$	11.4187	−	8.26556i	0.620181	−	0.448923i
$340$	−3.85150	+	1.03201i	−0.208877	+	0.0559684i
$341$	−2.21625	+	1.27955i	−0.120017	+	0.0692916i
$342$	5.53055	+	6.18591i	0.299058	+	0.334496i
$343$	8.72082	−	16.3385i	0.470880	−	0.882197i
$344$	−6.13673	+	6.13673i	−0.330870	+	0.330870i
$345$	0.674336	−	0.829748i	0.0363050	−	0.0446721i
$346$	1.30308	+	4.86317i	0.0700542	+	0.261446i
$347$	22.4958	+	12.9880i	1.20764	+	0.697230i	0.962243	−	0.272193i	$-0.0877489\pi$
$347$	22.4958	+	12.9880i	1.20764	+	0.697230i	0.245395	+	0.969423i	$0.421082\pi$
$348$	−6.00027	+	0.619988i	−0.321648	+	0.0332348i
$349$	20.0901	−	20.0901i	1.07540	−	1.07540i	0.0784823	−	0.996916i	$-0.474993\pi$
$349$	20.0901	−	20.0901i	1.07540	−	1.07540i	0.996916	−	0.0784823i	$-0.0250074\pi$
$350$	−9.78853	−	4.43282i	−0.523219	−	0.236944i
$351$	1.02812	−	18.7068i	0.0548772	−	0.998493i
$352$	0.512393	+	0.887491i	0.0273107	+	0.0473034i
$353$	3.41201	+	12.7338i	0.181603	+	0.677752i	0.995332	+	0.0965075i	$0.0307672\pi$
$353$	3.41201	+	12.7338i	0.181603	+	0.677752i	−0.813729	+	0.581244i	$0.802566\pi$
$354$	−5.89418	−	8.14271i	−0.313272	−	0.432780i
$355$	10.1522	−	5.86137i	0.538822	−	0.311089i
$356$	−4.56413	+	4.56413i	−0.241898	+	0.241898i
$357$	−16.8739	+	8.42604i	−0.893061	+	0.445953i
$358$	−1.76589	+	1.76589i	−0.0933302	+	0.0933302i
$359$	2.37583	−	8.86671i	0.125391	−	0.467967i	−0.874462	−	0.485094i	$-0.838785\pi$
$359$	2.37583	−	8.86671i	0.125391	−	0.467967i	0.999853	+	0.0171272i	$0.00545203\pi$
$360$	2.84502	−	0.594278i	0.149946	−	0.0313212i
$361$	9.82916	+	5.67487i	0.517324	+	0.298677i
$362$	−0.201384	+	0.751574i	−0.0105845	+	0.0395018i
$363$	15.7313	+	7.03720i	0.825680	+	0.369357i
$364$	4.79956	−	8.24404i	0.251566	−	0.432105i
$365$		−	12.8102i		−	0.670515i
$366$	1.29778	−	1.59688i	0.0678362	−	0.0834702i
$367$	−7.46508	+	12.9299i	−0.389674	+	0.674935i	−0.992406	−	0.123009i	$-0.960746\pi$
$367$	−7.46508	+	12.9299i	−0.389674	+	0.674935i	0.602732	+	0.797944i	$0.294079\pi$
$368$	0.318592	−	0.551817i	0.0166077	−	0.0287654i
$369$	−0.0926146	−	0.183358i	−0.00482133	−	0.00954523i
$370$	−1.98204	−	1.98204i	−0.103041	−	0.103041i
$371$	20.7163	+	3.41613i	1.07554	+	0.177356i
$372$	1.54294	+	4.04072i	0.0799978	+	0.209502i
$373$	−10.8093	−	18.7223i	−0.559686	−	0.969404i	−0.997522	−	0.0703493i	$-0.977589\pi$
$373$	−10.8093	−	18.7223i	−0.559686	−	0.969404i	0.437837	−	0.899054i	$-0.355745\pi$
$374$	2.10888	−	3.65269i	0.109048	−	0.188876i
$375$	2.40504	−	15.0139i	0.124196	−	0.775313i
$376$	−2.90406	+	1.67666i	−0.149765	+	0.0864671i
$377$	−11.7353	−	4.46802i	−0.604397	−	0.230115i
$378$	12.6233	−	5.44533i	0.649274	−	0.280077i
$379$	14.4640	+	14.4640i	0.742967	+	0.742967i	0.973148	−	0.230181i	$-0.0739318\pi$
$379$	14.4640	+	14.4640i	0.742967	+	0.742967i	−0.230181	+	0.973148i	$0.573932\pi$
$380$	−2.32064	+	1.33982i	−0.119046	+	0.0687313i
$381$	28.3557	−	20.5255i	1.45270	−	1.05155i
$382$	−20.0837	+	5.38141i	−1.02757	+	0.275337i
$383$	−27.8016	−	7.44941i	−1.42059	−	0.380647i	−0.534900	−	0.844915i	$-0.679651\pi$
$383$	−27.8016	−	7.44941i	−1.42059	−	0.380647i	−0.885695	+	0.464268i	$0.846317\pi$
$384$	1.61810	−	0.617867i	0.0825732	−	0.0315304i
$385$	−2.45822	+	0.925757i	−0.125283	+	0.0471809i
$386$		−	21.2209i		−	1.08011i
$387$	−24.7332	−	8.13259i	−1.25726	−	0.413403i
$388$	−3.16324	−	11.8054i	−0.160589	−	0.599326i
$389$	2.90415	−	5.03013i	0.147246	−	0.255038i	−0.782963	−	0.622069i	$-0.786292\pi$
$389$	2.90415	−	5.03013i	0.147246	−	0.255038i	0.930209	+	0.367031i	$0.119626\pi$
$390$	5.84557	+	1.56023i	0.296002	+	0.0790052i
$391$	−2.62248			−0.132625
$392$	6.98519	+	0.455095i	0.352805	+	0.0229858i
$393$	−6.45266	−	2.88652i	−0.325494	−	0.145605i
$394$	2.45817	−	1.41923i	0.123841	−	0.0714997i
$395$	0.00789129	+	0.0294507i	0.000397054	+	0.00148183i
$396$	−1.68347	+	2.57247i	−0.0845978	+	0.129272i
$397$	−20.5855	−	5.51587i	−1.03316	−	0.276834i	−0.297882	−	0.954603i	$-0.596280\pi$
$397$	−20.5855	−	5.51587i	−1.03316	−	0.276834i	−0.735275	+	0.677769i	$0.762947\pi$
$398$	9.31597	+	9.31597i	0.466967	+	0.466967i
$399$	−9.48782	+	8.40458i	−0.474985	+	0.420755i
$400$		−	4.06141i		−	0.203070i
$401$	1.52226	−	5.68116i	0.0760181	−	0.283703i	−0.917444	−	0.397865i	$-0.869751\pi$
$401$	1.52226	−	5.68116i	0.0760181	−	0.283703i	0.993462	+	0.114161i	$0.0364180\pi$
$402$	−1.71180	−	2.36482i	−0.0853766	−	0.117946i
$403$	−0.916700	+	8.95702i	−0.0456641	+	0.446181i
$404$	9.84089	−	5.68164i	0.489602	−	0.282672i
$405$	5.43942	+	6.81458i	0.270287	+	0.338619i
$406$	−0.904955	−	9.16981i	−0.0449122	−	0.455090i
$407$	2.96499			0.146969
$408$	−5.53212	−	4.49596i	−0.273881	−	0.222583i
$409$	0.349927	−	0.0937626i	0.0173028	−	0.00463626i	−0.250157	−	0.968205i	$-0.580482\pi$
$409$	0.349927	−	0.0937626i	0.0173028	−	0.00463626i	0.267460	+	0.963569i	$0.413816\pi$
$410$	0.0640773	−	0.0171695i	0.00316455	−	0.000847939i
$411$	−24.2490	−	19.7072i	−1.19611	−	0.972082i
$412$	−14.5482			−0.716738
$413$	12.4794	−	8.94630i	0.614071	−	0.440219i
$414$	1.90857	+	0.106756i	0.0938009	+	0.00524676i
$415$	7.19421	−	4.15358i	0.353150	−	0.203891i
$416$	3.58682	+	0.367090i	0.175858	+	0.0179981i
$417$	19.4533	+	26.8745i	0.952634	+	1.31605i
$418$	0.733615	−	2.73789i	0.0358823	−	0.133914i
$419$		−	4.19355i		−	0.204869i	−0.994740	−	0.102434i	$-0.967337\pi$
$419$		−	4.19355i		−	0.204869i	0.994740	−	0.102434i	$-0.0326631\pi$
$420$	0.887812	+	4.34997i	0.0433208	+	0.212257i
$421$	−1.34291	−	1.34291i	−0.0654495	−	0.0654495i	0.673624	−	0.739074i	$-0.264737\pi$
$421$	−1.34291	−	1.34291i	−0.0654495	−	0.0654495i	−0.739074	+	0.673624i	$0.764737\pi$
$422$	13.5713	+	3.63642i	0.660640	+	0.177018i
$423$	−8.41767	−	5.50868i	−0.409281	−	0.267841i
$424$	2.05393	+	7.66538i	0.0997477	+	0.372264i
$425$	−14.4762	+	8.35786i	−0.702201	+	0.405416i
$426$	19.1311	+	8.55807i	0.926907	+	0.414640i
$427$	2.43015	+	1.99357i	0.117603	+	0.0964758i
$428$	8.56634			0.414070
$429$	−5.53927	+	3.20528i	−0.267438	+	0.154752i
$430$	4.20398	−	7.28150i	0.202734	−	0.351145i
$431$	−8.43634	−	31.4848i	−0.406364	−	1.51657i	−0.801526	−	0.597960i	$-0.795978\pi$
$431$	−8.43634	−	31.4848i	−0.406364	−	1.51657i	0.395162	−	0.918611i	$-0.370688\pi$
$432$	3.84310	+	3.49723i	0.184901	+	0.168260i
$433$			21.9098i			1.05292i	0.850201	+	0.526458i	$0.176480\pi$
$433$			21.9098i			1.05292i	−0.850201	+	0.526458i	$0.823520\pi$
$434$	−6.18306	+	2.32852i	−0.296797	+	0.111772i
$435$	5.45958	−	2.08473i	0.261767	−	0.0999551i
$436$	0.938198	+	0.251389i	0.0449315	+	0.0120394i
$437$	−1.70234	+	0.456141i	−0.0814340	+	0.0218202i
$438$	18.5519	−	13.4290i	0.886445	−	0.641662i
$439$	−5.86906	+	3.38851i	−0.280115	+	0.161725i	−0.633476	−	0.773763i	$-0.718372\pi$
$439$	−5.86906	+	3.38851i	−0.280115	+	0.161725i	0.353360	+	0.935487i	$0.385039\pi$
$440$	−0.702032	−	0.702032i	−0.0334680	−	0.0334680i
$441$	8.22926	+	19.3204i	0.391869	+	0.920021i
$442$	−6.07277	−	13.5400i	−0.288852	−	0.644034i
$443$	−30.3397	+	17.5166i	−1.44148	+	0.832240i	−0.997949	−	0.0640182i	$-0.979608\pi$
$443$	−30.3397	+	17.5166i	−1.44148	+	0.832240i	−0.443533	+	0.896258i	$0.646275\pi$
$444$	0.792641	−	4.94821i	0.0376171	−	0.234832i
$445$	3.12666	−	5.41554i	0.148218	−	0.256721i
$446$	2.26386	+	3.92112i	0.107197	+	0.185671i
$447$	−12.6300	−	33.0760i	−0.597379	−	1.56444i
$448$	0.932449	+	2.47599i	0.0440541	+	0.116980i
$449$	−2.14151	−	2.14151i	−0.101064	−	0.101064i	0.654767	−	0.755831i	$-0.272767\pi$
$449$	−2.14151	−	2.14151i	−0.101064	−	0.101064i	−0.755831	+	0.654767i	$0.772767\pi$
$450$	10.8756	−	5.49331i	0.512681	−	0.258957i
$451$	−0.0350854	+	0.0607696i	−0.00165210	+	0.00286153i
$452$	−4.06926	+	7.04817i	−0.191402	+	0.331518i
$453$	0.180319	−	0.221876i	0.00847212	−	0.0104247i
$454$			22.1908i			1.04147i
$455$	−2.42426	+	8.91822i	−0.113651	+	0.418093i
$456$	−4.37309	−	1.95625i	−0.204789	−	0.0916096i
$457$	−8.21302	+	30.6514i	−0.384189	+	1.43381i	0.455252	+	0.890363i	$0.349549\pi$
$457$	−8.21302	+	30.6514i	−0.384189	+	1.43381i	−0.839441	+	0.543451i	$0.817118\pi$
$458$	0.184840	+	0.106717i	0.00863698	+	0.00498657i
$459$	4.55670	−	20.8949i	0.212688	−	0.975292i
$460$	−0.159771	+	0.596274i	−0.00744937	+	0.0278014i
$461$	−11.2027	+	11.2027i	−0.521764	+	0.521764i	−0.918104	−	0.396340i	$-0.870280\pi$
$461$	−11.2027	+	11.2027i	−0.521764	+	0.521764i	0.396340	+	0.918104i	$0.370280\pi$
$462$	−3.91767	−	2.58956i	−0.182266	−	0.120477i
$463$	−17.5213	+	17.5213i	−0.814284	+	0.814284i	−0.985273	−	0.170989i	$-0.945304\pi$
$463$	−17.5213	+	17.5213i	−0.814284	+	0.814284i	0.170989	+	0.985273i	$0.445304\pi$
$464$	3.01611	−	1.74135i	0.140019	−	0.0808402i
$465$	−2.45708	−	3.39441i	−0.113944	−	0.157412i
$466$	1.53533	+	5.72991i	0.0711226	+	0.265433i
$467$	17.3288	+	30.0144i	0.801882	+	1.38890i	0.918376	+	0.395708i	$0.129501\pi$
$467$	17.3288	+	30.0144i	0.801882	+	1.38890i	−0.116495	+	0.993191i	$0.537166\pi$
$468$	3.86840	+	10.1013i	0.178817	+	0.466931i
$469$	3.62429	−	2.59820i	0.167354	−	0.119974i
$470$	2.29720	−	2.29720i	0.105962	−	0.105962i
$471$	−7.16217	+	0.740043i	−0.330015	+	0.0340994i
$472$	5.02606	+	2.90180i	0.231343	+	0.133566i
$473$	2.30188	+	8.59072i	0.105840	+	0.395002i
$474$	−0.0343785	+	0.0423016i	−0.00157906	+	0.00194298i
$475$	−7.94328	+	7.94328i	−0.364463	+	0.364463i
$476$	6.90641	−	8.41884i	0.316555	−	0.385877i
$477$	−17.7482	+	15.8679i	−0.812635	+	0.726541i
$478$	19.9115	−	11.4959i	0.910731	−	0.525811i
$479$	5.30314	−	1.42097i	0.242307	−	0.0649259i	−0.135622	−	0.990761i	$-0.543303\pi$
$479$	5.30314	−	1.42097i	0.242307	−	0.0649259i	0.377929	+	0.925835i	$0.376637\pi$
$480$	−1.35928	+	0.983930i	−0.0620425	+	0.0449101i
$481$	6.10861	−	8.45624i	0.278529	−	0.385572i
$482$		−	3.96265i		−	0.180494i
$483$	−0.176456	+	2.91460i	−0.00802901	+	0.132619i
$484$	−9.94981			−0.452264
$485$	5.92030	+	10.2543i	0.268827	+	0.465622i
$486$	−4.16682	+	15.0212i	−0.189011	+	0.681377i
$487$	−23.9967	+	6.42991i	−1.08740	+	0.291367i	−0.757622	−	0.652693i	$-0.773639\pi$
$487$	−23.9967	+	6.42991i	−1.08740	+	0.291367i	−0.329774	+	0.944060i	$0.606972\pi$
$488$	−0.307485	+	1.14755i	−0.0139192	+	0.0519472i
$489$	6.30464	+	16.5109i	0.285106	+	0.746648i
$490$	−6.65084	+	1.32563i	−0.300454	+	0.0598860i
$491$	−13.7326			−0.619744			−0.309872	−	0.950778i	$-0.600286\pi$
$491$	−13.7326			−0.619744			−0.309872	+	0.950778i	$0.600286\pi$
$492$	0.0920378	+	0.0747991i	0.00414938	+	0.00337220i
$493$	−12.4135	−	7.16695i	−0.559077	−	0.322783i
$494$	−6.29712	−	7.73303i	−0.283321	−	0.347925i
$495$	0.930354	−	2.82944i	0.0418163	−	0.127174i
$496$	−1.76579	−	1.76579i	−0.0792864	−	0.0792864i
$497$	−13.2067	+	29.1630i	−0.592402	+	1.30814i
$498$	13.5570	+	6.06456i	0.607504	+	0.271759i
$499$	6.69439	−	24.9838i	0.299682	−	1.11843i	−0.637745	−	0.770247i	$-0.720133\pi$
$499$	6.69439	−	24.9838i	0.299682	−	1.11843i	0.937427	−	0.348181i	$-0.113201\pi$
$500$	2.27211	+	8.47965i	0.101612	+	0.379221i
$501$	−7.00082	+	43.7039i	−0.312774	+	1.95255i
$502$	−24.6507	−	6.60513i	−1.10021	−	0.294801i
$503$		−	23.5158i		−	1.04852i	−0.851559	−	0.524260i	$-0.824342\pi$
$503$		−	23.5158i		−	1.04852i	0.851559	−	0.524260i	$-0.175658\pi$
$504$	−5.36900	+	5.84584i	−0.239154	+	0.260394i
$505$	−7.78443	+	7.78443i	−0.346403	+	0.346403i
$506$	−0.326488	−	0.565494i	−0.0145142	−	0.0251393i
$507$	−2.27070	+	22.4019i	−0.100845	+	0.994902i
$508$	−10.1050	+	17.5024i	−0.448338	+	0.776544i
$509$	−36.3055	−	9.72802i	−1.60921	−	0.431187i	−0.661404	−	0.750030i	$-0.730039\pi$
$509$	−36.3055	−	9.72802i	−1.60921	−	0.431187i	−0.947808	+	0.318843i	$0.896706\pi$
$510$	6.30429	+	2.82015i	0.279159	+	0.124878i
$511$	20.3828	+	28.4324i	0.901681	+	1.25778i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−0.676453	−	14.3562i	−0.0298661	−	0.633840i
$514$	2.80369	+	10.4635i	0.123666	+	0.461526i
$515$	13.6142	−	3.64790i	0.599912	−	0.160746i
$516$	14.9523	−	1.54497i	0.658236	−	0.0680134i
$517$			3.43644i			0.151134i
$518$	7.55288	+	1.24547i	0.331854	+	0.0547228i
$519$	3.56091	−	7.96024i	0.156307	−	0.349416i
$520$	−3.44858	+	0.555858i	−0.151230	+	0.0243760i
$521$	−35.6395	−	20.5765i	−1.56139	−	0.901472i	−0.997116	−	0.0758870i	$-0.975821\pi$
$521$	−35.6395	−	20.5765i	−1.56139	−	0.901472i	−0.564278	−	0.825585i	$-0.690845\pi$
$522$	8.74245	+	5.72123i	0.382647	+	0.250411i
$523$	14.4894	+	25.0964i	0.633578	+	1.09739i	0.986814	+	0.161855i	$0.0517478\pi$
$523$	14.4894	+	25.0964i	0.633578	+	1.09739i	−0.353236	+	0.935534i	$0.614919\pi$
$524$	4.08121			0.178288
$525$	8.31481	+	16.6511i	0.362888	+	0.726715i
$526$	−1.60873	−	1.60873i	−0.0701440	−	0.0701440i
$527$	−2.66011	+	9.92765i	−0.115876	+	0.432455i
$528$	0.280751	−	1.75264i	0.0122181	−	0.0762738i
$529$	11.2970	−	19.5670i	0.491174	−	0.850738i
$530$	−3.84413	−	6.65823i	−0.166978	−	0.289215i
$531$	−0.972353	+	17.3836i	−0.0421965	+	0.754384i
$532$	3.01885	−	6.66621i	0.130884	−	0.289017i
$533$	0.101032	+	0.225265i	0.00437620	+	0.00975732i
$534$	11.1206	−	1.14905i	0.481235	−	0.0497244i
$535$	−8.01636	+	2.14798i	−0.346577	+	0.0928651i
$536$	1.45968	+	0.842744i	0.0630484	+	0.0364010i
$537$	4.30262	−	0.444576i	0.185672	−	0.0191849i
$538$	−11.4612	−	11.4612i	−0.494126	−	0.494126i
$539$	3.98306	−	5.96611i	0.171562	−	0.256978i
$540$	−4.47328	−	2.30905i	−0.192499	−	0.0993659i
$541$	6.93022	+	1.85695i	0.297953	+	0.0798364i	0.404699	−	0.914450i	$-0.367376\pi$
$541$	6.93022	+	1.85695i	0.297953	+	0.0798364i	−0.106745	+	0.994286i	$0.534043\pi$
$542$	28.0943	+	16.2202i	1.20675	+	0.696718i
$543$	1.09169	−	0.790231i	0.0468490	−	0.0339121i
$544$	3.97550	+	1.06523i	0.170448	+	0.0456715i
$545$	−0.940998			−0.0403079
$546$	−15.4569	+	5.83817i	−0.661494	+	0.249851i
$547$	3.41524			0.146025			0.0730126	−	0.997331i	$-0.476739\pi$
$547$	3.41524			0.146025			0.0730126	+	0.997331i	$0.476739\pi$
$548$	17.4258	+	4.66924i	0.744395	+	0.199460i
$549$	−3.48880	+	0.728752i	−0.148898	+	0.0311024i
$550$	−3.60447	−	2.08104i	−0.153695	−	0.0887358i
$551$	−9.30461	−	2.49316i	−0.396390	−	0.106212i
$552$	−1.03102	+	0.393694i	−0.0438833	+	0.0167567i
$553$	−0.0643750	−	0.0528102i	−0.00273751	−	0.00224572i
$554$	−19.9262	−	19.9262i	−0.846585	−	0.846585i
$555$	0.498993	+	4.82927i	0.0211811	+	0.204991i
$556$	−16.5882	−	9.57718i	−0.703495	−	0.406163i
$557$	4.28820	−	1.14902i	0.181697	−	0.0486855i	−0.166823	−	0.985987i	$-0.553351\pi$
$557$	4.28820	−	1.14902i	0.181697	−	0.0486855i	0.348520	+	0.937301i	$0.386684\pi$
$558$	2.34008	−	7.11677i	0.0990636	−	0.301277i
$559$	29.2435	+	11.1340i	1.23687	+	0.470918i
$560$	−1.49343	−	2.08322i	−0.0631089	−	0.0880321i
$561$	−6.82475	+	2.60601i	−0.288141	+	0.110026i
$562$	9.21024	+	15.9526i	0.388511	+	0.672920i
$563$	−11.0361	+	19.1151i	−0.465116	+	0.805605i	−0.999207	−	0.0398220i	$-0.987321\pi$
$563$	−11.0361	+	19.1151i	−0.465116	+	0.805605i	0.534090	+	0.845427i	$0.320654\pi$
$564$	5.73500	+	0.918676i	0.241487	+	0.0386832i
$565$	2.04071	−	7.61602i	0.0858531	−	0.320408i
$566$	14.5934	+	14.5934i	0.613408	+	0.613408i
$567$	−22.9159	−	6.47021i	−0.962375	−	0.271723i
$568$	−12.1002			−0.507711
$569$	21.7766	+	37.7183i	0.912925	+	1.58123i	0.809912	+	0.586552i	$0.199515\pi$
$569$	21.7766	+	37.7183i	0.912925	+	1.58123i	0.103013	+	0.994680i	$0.467152\pi$
$570$	4.58285	+	0.734115i	0.191954	+	0.0307487i
$571$	29.0000	+	16.7431i	1.21361	+	0.700678i	0.963544	−	0.267550i	$-0.0862142\pi$
$571$	29.0000	+	16.7431i	1.21361	+	0.700678i	0.250067	+	0.968229i	$0.419548\pi$
$572$	2.16365	−	2.99517i	0.0904667	−	0.125234i
$573$	32.8738	+	14.7057i	1.37332	+	0.614338i
$574$	−0.114902	+	0.140064i	−0.00479591	+	0.00584616i
$575$			2.58786i			0.107921i
$576$	−2.84989	−	0.937080i	−0.118745	−	0.0390450i
$577$	−13.5027	+	3.61803i	−0.562124	+	0.150621i	−0.528682	−	0.848820i	$-0.677314\pi$
$577$	−13.5027	+	3.61803i	−0.562124	+	0.150621i	−0.0334420	+	0.999441i	$0.510647\pi$
$578$	0.0157000	+	0.0585933i	0.000653035	+	0.00243716i
$579$	−23.1812	+	28.5237i	−0.963379	+	1.18541i
$580$	−2.38583	+	2.38583i	−0.0990662	+	0.0990662i
$581$	−9.35875	+	20.6659i	−0.388266	+	0.857367i
$582$	−8.64412	+	19.3235i	−0.358310	+	0.800984i
$583$	7.85538	+	2.10484i	0.325336	+	0.0871736i
$584$	−6.61130	+	11.4511i	−0.273578	+	0.473850i
$585$	−6.15289	−	8.48275i	−0.254391	−	0.350719i
$586$	−15.4833	−	26.8179i	−0.639610	−	1.10784i
$587$	16.7060	−	16.7060i	0.689531	−	0.689531i	−0.272597	−	0.962128i	$-0.587883\pi$
$587$	16.7060	−	16.7060i	0.689531	−	0.689531i	0.962128	+	0.272597i	$0.0878826\pi$
$588$	−8.89192	−	8.24219i	−0.366697	−	0.339902i
$589$			6.90705i			0.284600i
$590$	−5.43099	−	1.45523i	−0.223590	−	0.0599108i
$591$	−4.85446	−	0.777624i	−0.199686	−	0.0319872i
$592$	0.748834	+	2.79469i	0.0307769	+	0.114861i
$593$	6.86959	−	25.6377i	0.282100	−	1.05281i	−0.668832	−	0.743413i	$-0.733205\pi$
$593$	6.86959	−	25.6377i	0.282100	−	1.05281i	0.950932	−	0.309399i	$-0.100128\pi$
$594$	5.07294	−	1.61876i	0.208145	−	0.0664185i
$595$	−4.35201	+	9.61009i	−0.178415	+	0.393975i
$596$	14.4542	+	14.4542i	0.592067	+	0.592067i
$597$	−2.34536	−	22.6985i	−0.0959893	−	0.928989i
$598$	−2.28546	−	0.233904i	−0.0934593	−	0.00956503i
$599$	−32.0100	−	18.4810i	−1.30789	−	0.755112i	−0.326148	−	0.945319i	$-0.605751\pi$
$599$	−32.0100	−	18.4810i	−1.30789	−	0.755112i	−0.981744	+	0.190206i	$0.939084\pi$
$600$	−4.43660	+	5.45909i	−0.181124	+	0.222867i
$601$	10.4935			0.428041			0.214020	−	0.976829i	$-0.431344\pi$
$601$	10.4935			0.428041			0.214020	+	0.976829i	$0.431344\pi$
$602$	2.25509	+	22.8505i	0.0919105	+	0.931319i
$603$	−0.282392	+	5.04857i	−0.0114999	+	0.205594i
$604$	−0.0427232	+	0.159445i	−0.00173838	+	0.00648773i
$605$	9.31101	−	2.49488i	0.378546	−	0.101431i
$606$	−19.4340	−	3.11309i	−0.789453	−	0.126460i
$607$	13.3739	+	23.1642i	0.542829	+	0.940207i	0.998740	+	0.0501821i	$0.0159802\pi$
$607$	13.3739	+	23.1642i	0.542829	+	0.940207i	−0.455911	+	0.890025i	$0.650686\pi$
$608$	2.76591			0.112173
$609$	−8.80054	+	13.3140i	−0.356616	+	0.539512i
$610$		−	1.15098i		−	0.0466017i
$611$	9.80084	+	7.07992i	0.396499	+	0.286423i
$612$	2.52464	+	12.0864i	0.102053	+	0.488562i
$613$	5.79912	−	1.55387i	0.234224	−	0.0627602i	−0.139798	−	0.990180i	$-0.544645\pi$
$613$	5.79912	−	1.55387i	0.234224	−	0.0627602i	0.374022	+	0.927420i	$0.377979\pi$
$614$	13.9649	−	8.06265i	0.563578	−	0.325382i
$615$	−0.104884	−	0.0469187i	−0.00422934	−	0.00189194i
$616$	2.67520	+	0.441141i	0.107787	+	0.0177741i
$617$	−18.6670	+	18.6670i	−0.751503	+	0.751503i	−0.974760	−	0.223257i	$-0.928331\pi$
$617$	−18.6670	+	18.6670i	−0.751503	+	0.751503i	0.223257	+	0.974760i	$0.428331\pi$
$618$	19.5548	+	15.8922i	0.786608	+	0.639276i
$619$	−5.95707	−	22.2321i	−0.239435	−	0.893583i	−0.976099	−	0.217324i	$-0.930267\pi$
$619$	−5.95707	−	22.2321i	−0.239435	−	0.893583i	0.736665	−	0.676258i	$-0.236400\pi$
$620$	2.09519	+	1.20966i	0.0841448	+	0.0485810i
$621$	−2.44876	−	2.22837i	−0.0982652	−	0.0894216i
$622$	−12.3931	+	12.3931i	−0.496917	+	0.496917i
$623$	1.67720	+	16.9949i	0.0671955	+	0.680885i
$624$	−4.42017	−	4.41159i	−0.176948	−	0.176605i
$625$	5.90105	+	10.2209i	0.236042	+	0.408836i
$626$	1.32777	+	4.95532i	0.0530686	+	0.198055i
$627$	−3.97689	+	2.87871i	−0.158822	+	0.114965i
$628$	3.60015	−	2.07855i	0.143662	−	0.0829431i
$629$	8.42020	−	8.42020i	0.335735	−	0.335735i
$630$	3.55847	−	6.81678i	0.141773	−	0.271587i
$631$	1.85070	−	1.85070i	0.0736750	−	0.0736750i	−0.669309	−	0.742984i	$-0.733410\pi$
$631$	1.85070	−	1.85070i	0.0736750	−	0.0736750i	0.742984	+	0.669309i	$0.233410\pi$
$632$	0.00814535	−	0.0303989i	0.000324005	−	0.00120920i
$633$	−14.2693	−	19.7128i	−0.567155	−	0.783515i
$634$	23.3110	+	13.4586i	0.925797	+	0.534509i
$635$	5.06760	−	18.9125i	0.201101	−	0.750521i
$636$	5.61274	−	12.5470i	0.222560	−	0.497521i
$637$	−8.80946	−	23.6515i	−0.349043	−	0.937107i
$638$		−	3.56903i		−	0.141299i
$639$	−16.3662	−	32.4017i	−0.647437	−	1.28179i
$640$	0.484404	−	0.839013i	0.0191478	−	0.0331649i
$641$	16.8365	−	29.1616i	0.665001	−	1.15181i	−0.314285	−	0.949329i	$-0.601765\pi$
$641$	16.8365	−	29.1616i	0.665001	−	1.15181i	0.979285	−	0.202486i	$-0.0649021\pi$
$642$	−11.5143	−	9.35770i	−0.454435	−	0.369319i
$643$	−2.15687	−	2.15687i	−0.0850587	−	0.0850587i	0.663297	−	0.748356i	$-0.269157\pi$
$643$	−2.15687	−	2.15687i	−0.0850587	−	0.0850587i	−0.748356	+	0.663297i	$0.769157\pi$
$644$	−0.594141	−	1.57766i	−0.0234124	−	0.0621685i
$645$	−13.6049	+	5.19500i	−0.535692	+	0.204553i
$646$	−5.69189	−	9.85864i	−0.223944	−	0.387883i
$647$	−20.9209	+	36.2361i	−0.822487	+	1.42459i	0.0813383	+	0.996687i	$0.474081\pi$
$647$	−20.9209	+	36.2361i	−0.822487	+	1.42459i	−0.903825	+	0.427902i	$0.859253\pi$
$648$	−1.34535	−	8.89888i	−0.0528504	−	0.349581i
$649$	5.15064	−	2.97372i	0.202180	−	0.116729i
$650$	−13.3613	+	5.99260i	−0.524073	+	0.235049i
$651$	10.8545	+	3.62441i	0.425422	+	0.142052i
$652$	−7.21523	−	7.21523i	−0.282570	−	0.282570i
$653$	11.1683	−	6.44801i	0.437049	−	0.252330i	−0.265296	−	0.964167i	$-0.585470\pi$
$653$	11.1683	−	6.44801i	0.437049	−	0.252330i	0.702345	+	0.711837i	$0.252136\pi$
$654$	−0.986454	−	1.36277i	−0.0385734	−	0.0532886i
$655$	−3.81919	+	1.02335i	−0.149228	+	0.0399855i
$656$	−0.0661403	−	0.0177222i	−0.00258234	−	0.000691937i
$657$	−39.6059	−	2.21536i	−1.54517	−	0.0864293i
$658$	−1.44351	+	8.75383i	−0.0562738	+	0.341260i
$659$			39.5546i			1.54083i	0.637543	+	0.770415i	$0.279951\pi$
$659$			39.5546i			1.54083i	−0.637543	+	0.770415i	$0.720049\pi$
$660$	0.176742	+	1.71051i	0.00687965	+	0.0665816i
$661$	−11.1046	−	41.4429i	−0.431919	−	1.61194i	−0.748333	−	0.663323i	$-0.769146\pi$
$661$	−11.1046	−	41.4429i	−0.431919	−	1.61194i	0.316414	−	0.948621i	$-0.397521\pi$
$662$	2.69901	−	4.67483i	0.104900	−	0.181692i
$663$	−6.62824	+	24.8335i	−0.257420	+	0.964452i
$664$	−8.57460			−0.332759
$665$	−1.15351	+	6.99519i	−0.0447311	+	0.271262i
$666$	−6.47074	+	5.78521i	−0.250736	+	0.224172i
$667$	−1.92181	+	1.10956i	−0.0744129	+	0.0429623i
$668$	−6.61390	−	24.6834i	−0.255899	−	0.955030i
$669$	1.24042	−	7.74353i	0.0479573	−	0.299382i
$670$	−1.57728	−	0.422630i	−0.0609355	−	0.0163276i
$671$	0.860888	+	0.860888i	0.0332342	+	0.0332342i
$672$	1.45138	−	4.34666i	0.0559884	−	0.167676i
$673$		−	17.9661i		−	0.692541i	−0.938135	−	0.346271i	$-0.887448\pi$
$673$		−	17.9661i		−	0.692541i	0.938135	−	0.346271i	$-0.112552\pi$
$674$	6.38338	−	23.8231i	0.245878	−	0.917631i
$675$	−20.6191	−	4.49654i	−0.793630	−	0.173072i
$676$	−4.08468	−	12.3416i	−0.157103	−	0.474677i
$677$	4.04856	−	2.33744i	0.155599	−	0.0898350i	−0.420179	−	0.907441i	$-0.638033\pi$
$677$	4.04856	−	2.33744i	0.155599	−	0.0898350i	0.575778	+	0.817606i	$0.304699\pi$
$678$	13.1689	−	5.02853i	0.505750	−	0.193119i
$679$	−29.4562	−	13.3395i	−1.13042	−	0.511923i
$680$	−3.98737			−0.152909
$681$	24.2408	−	29.8275i	0.928909	−	1.14299i
$682$	−2.47190	+	0.662345i	−0.0946541	+	0.0253625i
$683$	49.3429	−	13.2214i	1.88805	−	0.505902i	0.889227	−	0.457466i	$-0.151243\pi$
$683$	49.3429	−	13.2214i	1.88805	−	0.505902i	0.998826	−	0.0484369i	$-0.0154240\pi$
$684$	3.74107	+	7.40654i	0.143043	+	0.283196i
$685$	−17.4779			−0.667795
$686$	12.6524	−	13.5247i	0.483070	−	0.516375i
$687$	−0.131874	−	0.345358i	−0.00503131	−	0.0131762i
$688$	−7.51593	+	4.33933i	−0.286542	+	0.165435i
$689$	22.1871	−	18.0673i	0.845262	−	0.688310i
$690$	0.866113	−	0.626944i	0.0329724	−	0.0238673i
$691$	−3.35934	+	12.5372i	−0.127795	+	0.476938i	−0.999924	−	0.0123385i	$-0.996072\pi$
$691$	−3.35934	+	12.5372i	−0.127795	+	0.476938i	0.872129	+	0.489277i	$0.162739\pi$
$692$			5.03473i			0.191392i
$693$	2.43709	+	7.76031i	0.0925775	+	0.294790i
$694$	18.3677	+	18.3677i	0.697230	+	0.697230i
$695$	17.9246	+	4.80288i	0.679919	+	0.182184i
$696$	−5.95628	−	0.954122i	−0.225772	−	0.0361659i
$697$	0.0729402	+	0.272216i	0.00276281	+	0.0103109i
$698$	24.6052	−	14.2058i	0.931322	−	0.537699i
$699$	4.19555	−	9.37895i	0.158690	−	0.354744i
$700$	−8.30770	−	6.81524i	−0.314001	−	0.257592i
$701$	−34.1302			−1.28908			−0.644541	−	0.764570i	$-0.722951\pi$
$701$	−34.1302			−1.28908			−0.644541	+	0.764570i	$0.722951\pi$
$702$	5.83476	−	17.8032i	0.220219	−	0.671940i
$703$	4.00127	−	6.93040i	0.150911	−	0.261385i
$704$	0.265234	+	0.989868i	0.00999639	+	0.0373071i
$705$	−5.59716	+	0.578336i	−0.210801	+	0.0217814i
$706$			13.1830i			0.496149i
$707$	4.89156	−	29.6638i	0.183966	−	1.11562i
$708$	−3.58585	−	9.39078i	−0.134764	−	0.352927i
$709$	26.0559	+	6.98166i	0.978550	+	0.262202i	0.712434	−	0.701739i	$-0.247593\pi$
$709$	26.0559	+	6.98166i	0.978550	+	0.262202i	0.266116	+	0.963941i	$0.414259\pi$
$710$	11.3233	−	3.03407i	0.424956	−	0.113867i
$711$	0.0924190	−	0.0193048i	0.00346598	−	0.000723986i
$712$	−5.58990	+	3.22733i	−0.209490	+	0.120949i
$713$	1.12513	+	1.12513i	0.0421365	+	0.0421365i
$714$	−18.4797	+	3.77165i	−0.691587	+	0.141150i
$715$	−1.27371	+	3.34540i	−0.0476341	+	0.125111i
$716$	−2.16277	+	1.24867i	−0.0808263	+	0.0466651i
$717$	−39.3217	−	6.29885i	−1.46850	−	0.235235i
$718$	4.58974	−	7.94967i	0.171288	−	0.296679i
$719$	0.115201	+	0.199534i	0.00429627	+	0.00744135i	0.868166	−	0.496275i	$-0.165299\pi$
$719$	0.115201	+	0.199534i	0.00429627	+	0.00744135i	−0.863869	+	0.503716i	$0.831966\pi$
$720$	2.90189	+	0.162317i	0.108147	+	0.00604921i
$721$	−24.4126	+	29.7586i	−0.909171	+	1.10827i
$722$	8.02547	+	8.02547i	0.298677	+	0.298677i
$723$	−4.32872	+	5.32635i	−0.160987	+	0.198089i
$724$	−0.389043	+	0.673842i	−0.0144587	+	0.0250432i
$725$	−7.07234	+	12.2496i	−0.262660	+	0.454940i
$726$	13.3739	+	10.8690i	0.496353	+	0.403386i
$727$			19.6490i			0.728740i	0.931254	+	0.364370i	$0.118716\pi$
$727$			19.6490i			0.728740i	−0.931254	+	0.364370i	$0.881284\pi$
$728$	6.76974	−	6.72091i	0.250903	−	0.249094i
$729$	22.0097	−	15.6389i	0.815173	−	0.579217i
$730$	3.31552	−	12.3737i	0.122713	−	0.457970i
$731$	30.9336	+	17.8595i	1.14412	+	0.660559i
$732$	1.66686	−	1.20658i	0.0616091	−	0.0445963i
$733$	−2.63809	+	9.84548i	−0.0974401	+	0.363651i	−0.997378	−	0.0723665i	$-0.976945\pi$
$733$	−2.63809	+	9.84548i	−0.0974401	+	0.363651i	0.899938	+	0.436018i	$0.143612\pi$
$734$	−10.5572	+	10.5572i	−0.389674	+	0.389674i
$735$	10.3877	+	5.48341i	0.383157	+	0.202259i
$736$	0.450556	−	0.450556i	0.0166077	−	0.0166077i
$737$	1.49586	−	0.863633i	0.0551006	−	0.0318123i
$738$	−0.0420024	−	0.201080i	−0.00154613	−	0.00740187i
$739$	−6.99720	−	26.1139i	−0.257396	−	0.960616i	−0.966742	−	0.255755i	$-0.917676\pi$
$739$	−6.99720	−	26.1139i	−0.257396	−	0.960616i	0.709345	−	0.704861i	$-0.248991\pi$
$740$	−1.40151	−	2.42749i	−0.0515207	−	0.0892364i
$741$	0.0167901	+	17.2731i	0.000616801	+	0.634543i
$742$	19.1263	+	8.66151i	0.702148	+	0.317974i
$743$	19.6477	−	19.6477i	0.720804	−	0.720804i	−0.247965	−	0.968769i	$-0.579762\pi$
$743$	19.6477	−	19.6477i	0.720804	−	0.720804i	0.968769	+	0.247965i	$0.0797618\pi$
$744$	0.444551	+	4.30238i	0.0162980	+	0.157733i
$745$	−17.1505	−	9.90187i	−0.628347	−	0.362776i
$746$	−5.59532	−	20.8820i	−0.204859	−	0.764545i
$747$	−11.5977	−	22.9610i	−0.424337	−	0.840100i
$748$	2.98241	−	2.98241i	0.109048	−	0.109048i
$749$	14.3747	−	17.5226i	0.525241	−	0.640263i
$750$	6.20896	−	13.8798i	0.226719	−	0.506819i
$751$	29.8497	−	17.2337i	1.08923	−	0.628867i	0.155859	−	0.987779i	$-0.450185\pi$
$751$	29.8497	−	17.2337i	1.08923	−	0.628867i	0.933371	+	0.358912i	$0.116852\pi$
$752$	−3.23906	+	0.867903i	−0.118116	+	0.0316492i
$753$	25.9186	+	35.8061i	0.944526	+	1.30485i
$754$	−10.1790	−	7.35309i	−0.370697	−	0.267784i
$755$		−	0.159921i		−	0.00582012i
$756$	13.6026	−	1.99262i	0.494720	−	0.0724710i
$757$	17.4476			0.634144			0.317072	−	0.948401i	$-0.397300\pi$
$757$	17.4476			0.634144			0.317072	+	0.948401i	$0.397300\pi$
$758$	10.2276	+	17.7147i	0.371483	+	0.643428i
$759$	−0.178890	+	1.11675i	−0.00649328	+	0.0405355i
$760$	−2.58833	+	0.693542i	−0.0938887	+	0.0251574i
$761$	12.8087	−	47.8027i	0.464314	−	1.73284i	−0.194838	−	0.980835i	$-0.562418\pi$
$761$	12.8087	−	47.8027i	0.464314	−	1.73284i	0.659152	−	0.752009i	$-0.270915\pi$
$762$	32.7018	−	12.4871i	1.18466	−	0.452361i
$763$	2.08856	−	1.49726i	0.0756111	−	0.0542045i
$764$	−20.7922			−0.752234
$765$	−5.39316	−	10.6773i	−0.194990	−	0.386040i
$766$	−24.9262	−	14.3912i	−0.900621	−	0.519974i
$767$	2.13044	−	20.8164i	0.0769258	−	0.751637i
$768$	1.72288	−	0.178019i	0.0621690	−	0.00642372i
$769$	16.7245	+	16.7245i	0.603100	+	0.603100i	0.941134	−	0.338034i	$-0.109762\pi$
$769$	16.7245	+	16.7245i	0.603100	+	0.603100i	−0.338034	+	0.941134i	$0.609762\pi$
$770$	−2.61406	+	0.257978i	−0.0942043	+	0.00929688i
$771$	7.66160	−	17.1271i	0.275926	−	0.616818i
$772$	5.49236	−	20.4978i	0.197674	−	0.737731i
$773$	−2.65097	−	9.89355i	−0.0953487	−	0.355846i	0.901723	−	0.432313i	$-0.142303\pi$
$773$	−2.65097	−	9.89355i	−0.0953487	−	0.355846i	−0.997072	+

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.01561 - 1.40305i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.935798 - 0.250746i) q^{5} +(-0.617867 - 1.61810i) q^{6} +(2.47599 - 0.932449i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.937080 + 2.84989i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.01561 - 1.40305i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.935798 - 0.250746i) q^{5} +(-0.617867 - 1.61810i) q^{6} +(2.47599 - 0.932449i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.937080 + 2.84989i) q^{9} +(-0.839013 - 0.484404i) q^{10} +(0.989868 - 0.265234i) q^{11} +(-0.178019 - 1.72288i) q^{12} +(1.28292 - 3.36959i) q^{13} +(2.63296 - 0.259843i) q^{14} +(0.598595 + 1.56763i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.05787 - 3.56434i) q^{17} +(-1.64276 + 2.51025i) q^{18} +(0.715871 - 2.67167i) q^{19} +(-0.685051 - 0.685051i) q^{20} +(-3.82291 - 2.52693i) q^{21} +1.02479 q^{22} +(-0.318592 - 0.551817i) q^{23} +(0.273960 - 1.71025i) q^{24} +(-3.51728 - 2.03070i) q^{25} +(2.11132 - 2.92273i) q^{26} +(4.95024 - 1.57961i) q^{27} +(2.61050 + 0.430471i) q^{28} -3.48270i q^{29} +(0.172467 + 1.66914i) q^{30} +(-2.41212 + 0.646325i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-1.37745 - 1.11946i) q^{33} +(2.91027 - 2.91027i) q^{34} +(-2.55084 + 0.251738i) q^{35} +(-2.23648 + 1.99954i) q^{36} +(2.79469 + 0.748834i) q^{37} +(1.38296 - 2.39535i) q^{38} +(-6.03063 + 1.62219i) q^{39} +(-0.484404 - 0.839013i) q^{40} +(-0.0484181 + 0.0484181i) q^{41} +(-3.03863 - 3.43027i) q^{42} +8.67865i q^{43} +(0.989868 + 0.265234i) q^{44} +(1.59152 - 2.43195i) q^{45} +(-0.164915 - 0.615472i) q^{46} +(-0.867903 + 3.23906i) q^{47} +(0.707270 - 1.58107i) q^{48} +(5.26108 - 4.61748i) q^{49} +(-2.87185 - 2.87185i) q^{50} +(-7.09092 + 0.732681i) q^{51} +(2.79583 - 2.27669i) q^{52} +(6.87259 + 3.96789i) q^{53} +(5.19039 - 0.244568i) q^{54} -0.992823 q^{55} +(2.41013 + 1.09145i) q^{56} +(-4.47551 + 1.70897i) q^{57} +(0.901389 - 3.36403i) q^{58} +(5.60584 - 1.50208i) q^{59} +(-0.265415 + 1.65690i) q^{60} +(0.594016 + 1.02887i) q^{61} -2.49721 q^{62} +(0.337178 + 7.93009i) q^{63} +1.00000i q^{64} +(-2.04546 + 2.83157i) q^{65} +(-1.04078 - 1.43782i) q^{66} +(1.62806 - 0.436237i) q^{67} +(3.56434 - 2.05787i) q^{68} +(-0.450660 + 1.00743i) q^{69} +(-2.52907 - 0.417044i) q^{70} +(-8.55610 + 8.55610i) q^{71} +(-2.67779 + 1.35256i) q^{72} +(3.42226 + 12.7721i) q^{73} +(2.50565 + 1.44664i) q^{74} +(0.723009 + 6.99731i) q^{75} +(1.95579 - 1.95579i) q^{76} +(2.20359 - 1.57972i) q^{77} +(-6.24500 + 0.00607038i) q^{78} +(-0.0157356 - 0.0272549i) q^{79} +(-0.250746 - 0.935798i) q^{80} +(-7.24376 - 5.34115i) q^{81} +(-0.0592998 + 0.0342367i) q^{82} +(-6.06316 + 6.06316i) q^{83} +(-2.04727 - 4.09984i) q^{84} +(-2.81950 + 2.81950i) q^{85} +(-2.24620 + 8.38293i) q^{86} +(-4.88639 + 3.53706i) q^{87} +(0.887491 + 0.512393i) q^{88} +(-1.67059 + 6.23472i) q^{89} +(2.16672 - 1.93717i) q^{90} +(0.0345255 - 9.53933i) q^{91} -0.637183i q^{92} +(3.35659 + 2.72790i) q^{93} +(-1.67666 + 2.90406i) q^{94} +(-1.33982 + 2.32064i) q^{95} +(1.09238 - 1.34414i) q^{96} +(-8.64212 - 8.64212i) q^{97} +(6.27690 - 3.09847i) q^{98} +(-0.171696 + 3.06956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7} + O(q^{10}) \)	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more