LMFDB - Embedded newform 585.2.i.h.391.6

Newspace parameters

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.6
Character	$\chi$	$=$	585.391
Dual form			585.2.i.h.196.6

$q$-expansion

$f(q)$	$=$	$q+(-0.332241 - 0.575458i) q^{2} +(-0.727463 - 1.57188i) q^{3} +(0.779232 - 1.34967i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.662856 + 0.940866i) q^{6} +(-1.40460 - 2.43283i) q^{7} -2.36453 q^{8} +(-1.94159 + 2.28697i) q^{9} +O(q^{10})$	\(q+(-0.332241 - 0.575458i) q^{2} +(-0.727463 - 1.57188i) q^{3} +(0.779232 - 1.34967i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.662856 + 0.940866i) q^{6} +(-1.40460 - 2.43283i) q^{7} -2.36453 q^{8} +(-1.94159 + 2.28697i) q^{9} -0.664482 q^{10} +(-0.115146 - 0.199439i) q^{11} +(-2.68838 - 0.243022i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-0.933329 + 1.61657i) q^{14} +(-1.72502 - 0.155937i) q^{15} +(-0.772870 - 1.33865i) q^{16} -3.24172 q^{17} +(1.96113 + 0.357482i) q^{18} +3.80076 q^{19} +(-0.779232 - 1.34967i) q^{20} +(-2.80232 + 3.97765i) q^{21} +(-0.0765124 + 0.132523i) q^{22} +(1.25026 - 2.16552i) q^{23} +(1.72011 + 3.71676i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.664482 q^{26} +(5.00727 + 1.38826i) q^{27} -4.37803 q^{28} +(2.64853 + 4.58739i) q^{29} +(0.483386 + 1.04448i) q^{30} +(2.05661 - 3.56215i) q^{31} +(-2.87809 + 4.98500i) q^{32} +(-0.229728 + 0.326080i) q^{33} +(1.07703 + 1.86547i) q^{34} -2.80920 q^{35} +(1.57370 + 4.40259i) q^{36} +2.95700 q^{37} +(-1.26277 - 2.18718i) q^{38} +(1.72502 + 0.155937i) q^{39} +(-1.18227 + 2.04775i) q^{40} +(-1.74574 + 3.02371i) q^{41} +(3.22002 + 0.291080i) q^{42} +(-5.66677 - 9.81514i) q^{43} -0.358902 q^{44} +(1.00977 + 2.82495i) q^{45} -1.66155 q^{46} +(0.720625 + 1.24816i) q^{47} +(-1.54196 + 2.18867i) q^{48} +(-0.445790 + 0.772130i) q^{49} +(-0.332241 + 0.575458i) q^{50} +(2.35823 + 5.09558i) q^{51} +(0.779232 + 1.34967i) q^{52} -3.34833 q^{53} +(-0.864732 - 3.34271i) q^{54} -0.230292 q^{55} +(3.32122 + 5.75252i) q^{56} +(-2.76491 - 5.97432i) q^{57} +(1.75990 - 3.04823i) q^{58} +(-3.89632 + 6.74863i) q^{59} +(-1.55465 + 2.20669i) q^{60} +(-5.04095 - 8.73119i) q^{61} -2.73316 q^{62} +(8.29097 + 1.51131i) q^{63} +0.733399 q^{64} +(0.500000 + 0.866025i) q^{65} +(0.263970 + 0.0238621i) q^{66} +(-1.00966 + 1.74879i) q^{67} +(-2.52605 + 4.37525i) q^{68} +(-4.31345 - 0.389923i) q^{69} +(0.933329 + 1.61657i) q^{70} -3.51686 q^{71} +(4.59096 - 5.40761i) q^{72} -5.30003 q^{73} +(-0.982436 - 1.70163i) q^{74} +(-0.997554 + 1.41594i) q^{75} +(2.96167 - 5.12977i) q^{76} +(-0.323467 + 0.560262i) q^{77} +(-0.483386 - 1.04448i) q^{78} +(2.69870 + 4.67428i) q^{79} -1.54574 q^{80} +(-1.46043 - 8.88072i) q^{81} +2.32003 q^{82} +(-0.0501921 - 0.0869352i) q^{83} +(3.18486 + 6.88173i) q^{84} +(-1.62086 + 2.80741i) q^{85} +(-3.76547 + 6.52198i) q^{86} +(5.28410 - 7.50032i) q^{87} +(0.272266 + 0.471579i) q^{88} +7.04620 q^{89} +(1.29015 - 1.51965i) q^{90} +2.80920 q^{91} +(-1.94849 - 3.37488i) q^{92} +(-7.09538 - 0.641401i) q^{93} +(0.478842 - 0.829379i) q^{94} +(1.90038 - 3.29155i) q^{95} +(9.92951 + 0.897599i) q^{96} +(-1.63221 - 2.82707i) q^{97} +0.592438 q^{98} +(0.679676 + 0.123894i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) $ 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	−0.332241	−	0.575458i	−0.234930	−	0.406910i	0.724323	−	0.689461i	$-0.242153\pi$
$2$	−0.332241	−	0.575458i	−0.234930	−	0.406910i	−0.959252	+	0.282551i	$0.908819\pi$
$3$	−0.727463	−	1.57188i	−0.420001	−	0.907524i
$3$	−0.727463	−	1.57188i	−0.420001	−	0.907524i
$4$	0.779232	−	1.34967i	0.389616	−	0.674835i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.662856	+	0.940866i	−0.270610	+	0.384107i
$7$	−1.40460	−	2.43283i	−0.530888	−	0.919525i	−0.999350	−	0.0360416i	$-0.988525\pi$
$7$	−1.40460	−	2.43283i	−0.530888	−	0.919525i	0.468462	−	0.883484i	$-0.344808\pi$
$8$	−2.36453			−0.835989
$9$	−1.94159	+	2.28697i	−0.647198	+	0.762322i
$10$	−0.664482			−0.210128
$11$	−0.115146	−	0.199439i	−0.0347178	−	0.0601330i	0.848144	−	0.529765i	$-0.177720\pi$
$11$	−0.115146	−	0.199439i	−0.0347178	−	0.0601330i	−0.882862	+	0.469632i	$0.844387\pi$
$12$	−2.68838	−	0.243022i	−0.776068	−	0.0701543i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−0.933329	+	1.61657i	−0.249443	+	0.432048i
$15$	−1.72502	−	0.155937i	−0.445397	−	0.0402626i
$16$	−0.772870	−	1.33865i	−0.193217	−	0.334662i
$17$	−3.24172			−0.786232			−0.393116	−	0.919489i	$-0.628603\pi$
$17$	−3.24172			−0.786232			−0.393116	+	0.919489i	$0.628603\pi$
$18$	1.96113	+	0.357482i	0.462243	+	0.0842593i
$19$	3.80076			0.871954			0.435977	−	0.899958i	$-0.356403\pi$
$19$	3.80076			0.871954			0.435977	+	0.899958i	$0.356403\pi$
$20$	−0.779232	−	1.34967i	−0.174242	−	0.301795i
$21$	−2.80232	+	3.97765i	−0.611517	+	0.867995i
$22$	−0.0765124	+	0.132523i	−0.0163125	+	0.0282541i
$23$	1.25026	−	2.16552i	0.260698	−	0.451542i	−0.705730	−	0.708481i	$-0.749381\pi$
$23$	1.25026	−	2.16552i	0.260698	−	0.451542i	0.966428	+	0.256939i	$0.0827141\pi$
$24$	1.72011	+	3.71676i	0.351116	+	0.758680i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.664482			0.130316
$27$	5.00727	+	1.38826i	0.963649	+	0.267171i
$28$	−4.37803			−0.827370
$29$	2.64853	+	4.58739i	0.491820	+	0.851857i	0.999956	−	0.00942032i	$-0.00299862\pi$
$29$	2.64853	+	4.58739i	0.491820	+	0.851857i	−0.508136	+	0.861277i	$0.669665\pi$
$30$	0.483386	+	1.04448i	0.0882538	+	0.190696i
$31$	2.05661	−	3.56215i	0.369378	−	0.639782i	−0.620090	−	0.784530i	$-0.712904\pi$
$31$	2.05661	−	3.56215i	0.369378	−	0.639782i	0.989468	+	0.144749i	$0.0462374\pi$
$32$	−2.87809	+	4.98500i	−0.508780	+	0.881232i
$33$	−0.229728	+	0.326080i	−0.0399906	+	0.0567632i
$34$	1.07703	+	1.86547i	0.184709	+	0.319926i
$35$	−2.80920			−0.474841
$36$	1.57370	+	4.40259i	0.262283	+	0.733765i
$37$	2.95700			0.486128			0.243064	−	0.970010i	$-0.421848\pi$
$37$	2.95700			0.486128			0.243064	+	0.970010i	$0.421848\pi$
$38$	−1.26277	−	2.18718i	−0.204848	−	0.354807i
$39$	1.72502	+	0.155937i	0.276224	+	0.0249698i
$40$	−1.18227	+	2.04775i	−0.186933	+	0.323777i
$41$	−1.74574	+	3.02371i	−0.272639	+	0.472224i	−0.969537	−	0.244946i	$-0.921230\pi$
$41$	−1.74574	+	3.02371i	−0.272639	+	0.472224i	0.696898	+	0.717170i	$0.254563\pi$
$42$	3.22002	+	0.291080i	0.496860	+	0.0449147i
$43$	−5.66677	−	9.81514i	−0.864175	−	1.49679i	−0.867864	−	0.496801i	$-0.834508\pi$
$43$	−5.66677	−	9.81514i	−0.864175	−	1.49679i	0.00368958	−	0.999993i	$-0.498826\pi$
$44$	−0.358902			−0.0541065
$45$	1.00977	+	2.82495i	0.150528	+	0.421119i
$46$	−1.66155			−0.244983
$47$	0.720625	+	1.24816i	0.105114	+	0.182063i	0.913785	−	0.406199i	$-0.133146\pi$
$47$	0.720625	+	1.24816i	0.105114	+	0.182063i	−0.808671	+	0.588261i	$0.799813\pi$
$48$	−1.54196	+	2.18867i	−0.222562	+	0.315908i
$49$	−0.445790	+	0.772130i	−0.0636842	+	0.110304i
$50$	−0.332241	+	0.575458i	−0.0469859	+	0.0813820i
$51$	2.35823	+	5.09558i	0.330218	+	0.713524i
$52$	0.779232	+	1.34967i	0.108060	+	0.187165i
$53$	−3.34833			−0.459929			−0.229964	−	0.973199i	$-0.573861\pi$
$53$	−3.34833			−0.459929			−0.229964	+	0.973199i	$0.573861\pi$
$54$	−0.864732	−	3.34271i	−0.117675	−	0.454885i
$55$	−0.230292			−0.0310526
$56$	3.32122	+	5.75252i	0.443817	+	0.768713i
$57$	−2.76491	−	5.97432i	−0.366222	−	0.791318i
$58$	1.75990	−	3.04823i	0.231086	−	0.400253i
$59$	−3.89632	+	6.74863i	−0.507258	+	0.878596i	0.492707	+	0.870195i	$0.336007\pi$
$59$	−3.89632	+	6.74863i	−0.507258	+	0.878596i	−0.999965	+	0.00840088i	$0.997326\pi$
$60$	−1.55465	+	2.20669i	−0.200705	+	0.284883i
$61$	−5.04095	−	8.73119i	−0.645428	−	1.11791i	−0.984203	−	0.177046i	$-0.943346\pi$
$61$	−5.04095	−	8.73119i	−0.645428	−	1.11791i	0.338775	−	0.940868i	$-0.389988\pi$
$62$	−2.73316			−0.347112
$63$	8.29097	+	1.51131i	1.04456	+	0.190407i
$64$	0.733399			0.0916749
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$	0.263970	+	0.0238621i	0.0324925	+	0.00293723i
$67$	−1.00966	+	1.74879i	−0.123350	+	0.213649i	−0.921087	−	0.389357i	$-0.872697\pi$
$67$	−1.00966	+	1.74879i	−0.123350	+	0.213649i	0.797737	+	0.603006i	$0.206030\pi$
$68$	−2.52605	+	4.37525i	−0.306328	+	0.530576i
$69$	−4.31345	−	0.389923i	−0.519278	−	0.0469412i
$70$	0.933329	+	1.61657i	0.111554	+	0.193218i
$71$	−3.51686			−0.417375			−0.208687	−	0.977982i	$-0.566919\pi$
$71$	−3.51686			−0.417375			−0.208687	+	0.977982i	$0.566919\pi$
$72$	4.59096	−	5.40761i	0.541050	−	0.637293i
$73$	−5.30003			−0.620322			−0.310161	−	0.950684i	$-0.600383\pi$
$73$	−5.30003			−0.620322			−0.310161	+	0.950684i	$0.600383\pi$
$74$	−0.982436	−	1.70163i	−0.114206	−	0.197810i
$75$	−0.997554	+	1.41594i	−0.115188	+	0.163499i
$76$	2.96167	−	5.12977i	0.339727	−	0.588425i
$77$	−0.323467	+	0.560262i	−0.0368625	+	0.0638478i
$78$	−0.483386	−	1.04448i	−0.0547327	−	0.118264i
$79$	2.69870	+	4.67428i	0.303627	+	0.525898i	0.976955	−	0.213446i	$-0.0684689\pi$
$79$	2.69870	+	4.67428i	0.303627	+	0.525898i	−0.673327	+	0.739344i	$0.735136\pi$
$80$	−1.54574			−0.172819
$81$	−1.46043	−	8.88072i	−0.162270	−	0.986746i
$82$	2.32003			0.256204
$83$	−0.0501921	−	0.0869352i	−0.00550930	−	0.00954238i	0.863258	−	0.504764i	$-0.168420\pi$
$83$	−0.0501921	−	0.0869352i	−0.00550930	−	0.00954238i	−0.868767	+	0.495221i	$0.835087\pi$
$84$	3.18486	+	6.88173i	0.347496	+	0.750858i
$85$	−1.62086	+	2.80741i	−0.175807	+	0.304506i
$86$	−3.76547	+	6.52198i	−0.406041	+	0.703283i
$87$	5.28410	−	7.50032i	0.566515	−	0.804119i
$88$	0.272266	+	0.471579i	0.0290237	+	0.0502705i
$89$	7.04620			0.746896			0.373448	−	0.927651i	$-0.378175\pi$
$89$	7.04620			0.746896			0.373448	+	0.927651i	$0.378175\pi$
$90$	1.29015	−	1.51965i	0.135994	−	0.160185i
$91$	2.80920			0.294484
$92$	−1.94849	−	3.37488i	−0.203144	−	0.351856i
$93$	−7.09538	−	0.641401i	−0.735756	−	0.0665102i
$94$	0.478842	−	0.829379i	0.0493888	−	0.0855439i
$95$	1.90038	−	3.29155i	0.194975	−	0.337706i
$96$	9.92951	+	0.897599i	1.01343	+	0.0916109i
$97$	−1.63221	−	2.82707i	−0.165726	−	0.287046i	0.771187	−	0.636609i	$-0.219663\pi$
$97$	−1.63221	−	2.82707i	−0.165726	−	0.287046i	−0.936913	+	0.349563i	$0.886330\pi$
$98$	0.592438			0.0598453
$99$	0.679676	+	0.123894i	0.0683100	+	0.0124518i
$100$	−1.55846			−0.155846
$101$	−5.57900	−	9.66312i	−0.555132	−	0.961516i	−0.997893	−	0.0648769i	$-0.979335\pi$
$101$	−5.57900	−	9.66312i	−0.555132	−	0.961516i	0.442762	−	0.896639i	$-0.353999\pi$
$102$	2.14879	−	3.05002i	0.212762	−	0.301997i
$103$	6.33925	−	10.9799i	0.624625	−	1.08188i	−0.363988	−	0.931404i	$-0.618585\pi$
$103$	6.33925	−	10.9799i	0.624625	−	1.08188i	0.988613	−	0.150479i	$-0.0480815\pi$
$104$	1.18227	−	2.04775i	0.115931	−	0.200798i
$105$	2.04359	+	4.41571i	0.199434	+	0.430929i
$106$	1.11245	+	1.92682i	0.108051	+	0.187150i
$107$	4.15748			0.401919			0.200959	−	0.979600i	$-0.435594\pi$
$107$	4.15748			0.401919			0.200959	+	0.979600i	$0.435594\pi$
$108$	5.77552	−	5.67638i	0.555750	−	0.546210i
$109$	−4.90157			−0.469485			−0.234742	−	0.972058i	$-0.575425\pi$
$109$	−4.90157			−0.469485			−0.234742	+	0.972058i	$0.575425\pi$
$110$	0.0765124	+	0.132523i	0.00729517	+	0.0126356i
$111$	−2.15111	−	4.64804i	−0.204174	−	0.441172i
$112$	−2.17114	+	3.76053i	−0.205154	+	0.355336i
$113$	8.07368	−	13.9840i	0.759508	−	1.31551i	−0.183594	−	0.983002i	$-0.558773\pi$
$113$	8.07368	−	13.9840i	0.759508	−	1.31551i	0.943102	−	0.332504i	$-0.107894\pi$
$114$	−2.51935	+	3.57600i	−0.235959	+	0.334924i
$115$	−1.25026	−	2.16552i	−0.116588	−	0.201936i
$116$	8.25528			0.766483
$117$	−1.00977	−	2.82495i	−0.0933536	−	0.261167i
$118$	5.17807			0.476680
$119$	4.55331	+	7.88656i	0.417401	+	0.722960i
$120$	4.07886	+	0.368717i	0.372347	+	0.0336591i
$121$	5.47348	−	9.48035i	0.497589	−	0.861850i
$122$	−3.34962	+	5.80171i	−0.303260	+	0.525262i
$123$	6.02286	+	0.544450i	0.543063	+	0.0490914i
$124$	−3.20515	−	5.55149i	−0.287831	−	0.498538i
$125$	−1.00000			−0.0894427
$126$	−1.88490	−	5.27322i	−0.167921	−	0.469776i
$127$	17.7472			1.57481			0.787404	−	0.616438i	$-0.211425\pi$
$127$	17.7472			1.57481			0.787404	+	0.616438i	$0.211425\pi$
$128$	5.51252	+	9.54796i	0.487242	+	0.843929i
$129$	−11.3058	+	16.0476i	−0.995422	+	1.41291i
$130$	0.332241	−	0.575458i	0.0291394	−	0.0504710i
$131$	7.57097	−	13.1133i	0.661479	−	1.14571i	−0.318748	−	0.947839i	$-0.603262\pi$
$131$	7.57097	−	13.1133i	0.661479	−	1.14571i	0.980227	−	0.197876i	$-0.0634042\pi$
$132$	0.261088	+	0.564149i	0.0227248	+	0.0491029i
$133$	−5.33854	−	9.24661i	−0.462910	−	0.801783i
$134$	1.34181			0.115914
$135$	3.70590	−	3.64229i	0.318953	−	0.313478i
$136$	7.66515			0.657281
$137$	−10.4043	−	18.0207i	−0.888896	−	1.53961i	−0.841182	−	0.540752i	$-0.818140\pi$
$137$	−10.4043	−	18.0207i	−0.888896	−	1.53961i	−0.0477139	−	0.998861i	$-0.515194\pi$
$138$	1.20872	+	2.61176i	0.102893	+	0.222327i
$139$	3.36287	−	5.82466i	0.285235	−	0.494041i	−0.687431	−	0.726249i	$-0.741262\pi$
$139$	3.36287	−	5.82466i	0.285235	−	0.494041i	0.972666	+	0.232208i	$0.0745951\pi$
$140$	−2.18902	+	3.79149i	−0.185006	+	0.320439i
$141$	1.43772	−	2.04072i	0.121078	−	0.171860i
$142$	1.16844	+	2.02381i	0.0980537	+	0.169834i
$143$	0.230292			0.0192580
$144$	4.56204	+	0.831587i	0.380170	+	0.0692989i
$145$	5.29706			0.439897
$146$	1.76089	+	3.04995i	0.145732	+	0.252415i
$147$	1.53799	+	0.139030i	0.126851	+	0.0114670i
$148$	2.30419	−	3.99097i	0.189403	−	0.328056i
$149$	−11.0995	+	19.2249i	−0.909306	+	1.57496i	−0.0942751	+	0.995546i	$0.530053\pi$
$149$	−11.0995	+	19.2249i	−0.909306	+	1.57496i	−0.815031	+	0.579418i	$0.803280\pi$
$150$	1.14624	+	0.103617i	0.0935903	+	0.00846029i
$151$	−2.01163	−	3.48424i	−0.163704	−	0.283544i	0.772490	−	0.635027i	$-0.219011\pi$
$151$	−2.01163	−	3.48424i	−0.163704	−	0.283544i	−0.936194	+	0.351483i	$0.885678\pi$
$152$	−8.98702			−0.728944
$153$	6.29410	−	7.41369i	0.508847	−	0.599362i
$154$	0.429876			0.0346404
$155$	−2.05661	−	3.56215i	−0.165191	−	0.286119i
$156$	1.55465	−	2.20669i	0.124472	−	0.176677i
$157$	−10.9161	+	18.9073i	−0.871201	+	1.50896i	−0.0104452	+	0.999945i	$0.503325\pi$
$157$	−10.9161	+	18.9073i	−0.871201	+	1.50896i	−0.860756	+	0.509019i	$0.830008\pi$
$158$	1.79324	−	3.10598i	0.142662	−	0.247098i
$159$	2.43579	+	5.26317i	0.193171	+	0.417396i
$160$	2.87809	+	4.98500i	0.227533	+	0.394099i
$161$	−7.02446			−0.553605
$162$	−4.62527	+	3.79095i	−0.363395	+	0.297845i
$163$	10.4867			0.821381			0.410690	−	0.911775i	$-0.365288\pi$
$163$	10.4867			0.821381			0.410690	+	0.911775i	$0.365288\pi$
$164$	2.72067	+	4.71235i	0.212449	+	0.367972i
$165$	0.167529	+	0.361990i	0.0130421	+	0.0281809i
$166$	−0.0333517	+	0.0577669i	−0.00258859	+	0.00448358i
$167$	−3.30617	+	5.72645i	−0.255839	+	0.443126i	−0.965123	−	0.261797i	$-0.915685\pi$
$167$	−3.30617	+	5.72645i	−0.255839	+	0.443126i	0.709284	+	0.704923i	$0.249018\pi$
$168$	6.62619	−	9.40530i	0.511221	−	0.725634i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	2.15406			0.165209
$171$	−7.37953	+	8.69220i	−0.564327	+	0.664709i
$172$	−17.6629			−1.34679
$173$	−8.64411	−	14.9720i	−0.657200	−	1.13830i	−0.981338	−	0.192293i	$-0.938408\pi$
$173$	−8.64411	−	14.9720i	−0.657200	−	1.13830i	0.324138	−	0.946010i	$-0.394926\pi$
$174$	−6.07171	−	0.548865i	−0.460295	−	0.0416094i
$175$	−1.40460	+	2.43283i	−0.106178	+	0.183905i
$176$	−0.177986	+	0.308280i	−0.0134162	+	0.0232375i
$177$	13.4424	+	1.21516i	1.01040	+	0.0913368i
$178$	−2.34104	−	4.05479i	−0.175468	−	0.303920i
$179$	15.1868			1.13512			0.567558	−	0.823333i	$-0.307888\pi$
$179$	15.1868			1.13512			0.567558	+	0.823333i	$0.307888\pi$
$180$	4.59960	+	0.838433i	0.342834	+	0.0624931i
$181$	24.3392			1.80912			0.904559	−	0.426348i	$-0.140200\pi$
$181$	24.3392			1.80912			0.904559	+	0.426348i	$0.140200\pi$
$182$	−0.933329	−	1.61657i	−0.0691830	−	0.119828i
$183$	−10.0572	+	14.2754i	−0.743453	+	1.05527i
$184$	−2.95629	+	5.12044i	−0.217940	+	0.377484i
$185$	1.47850	−	2.56084i	0.108701	−	0.188276i
$186$	1.98827	+	4.29619i	0.145787	+	0.315012i
$187$	0.373270	+	0.646523i	0.0272962	+	0.0472785i
$188$	2.24614			0.163816
$189$	−3.65579	−	14.1318i	−0.265919	−	1.02794i
$190$	−2.52553			−0.183221
$191$	−7.13201	−	12.3530i	−0.516054	−	0.893832i	−0.999826	−	0.0186379i	$-0.994067\pi$
$191$	−7.13201	−	12.3530i	−0.516054	−	0.893832i	0.483772	−	0.875194i	$-0.339266\pi$
$192$	−0.533521	−	1.15281i	−0.0385036	−	0.0831971i
$193$	−12.7915	+	22.1556i	−0.920756	+	1.59480i	−0.122507	+	0.992468i	$0.539093\pi$
$193$	−12.7915	+	22.1556i	−0.920756	+	1.59480i	−0.798249	+	0.602328i	$0.794240\pi$
$194$	−1.08457	+	1.87854i	−0.0778679	+	0.134871i
$195$	0.997554	−	1.41594i	0.0714363	−	0.101398i
$196$	0.694747	+	1.20334i	0.0496248	+	0.0859527i
$197$	10.2976			0.733675			0.366838	−	0.930285i	$-0.380440\pi$
$197$	10.2976			0.733675			0.366838	+	0.930285i	$0.380440\pi$
$198$	−0.154520	−	0.432288i	−0.0109813	−	0.0307213i
$199$	3.31578			0.235049			0.117525	−	0.993070i	$-0.462504\pi$
$199$	3.31578			0.235049			0.117525	+	0.993070i	$0.462504\pi$
$200$	1.18227	+	2.04775i	0.0835989	+	0.144798i
$201$	3.48337	+	0.314887i	0.245698	+	0.0222104i
$202$	−3.70715	+	6.42096i	−0.260834	+	0.451777i
$203$	7.44024	−	12.8869i	0.522202	−	0.904481i
$204$	8.71496	+	0.787807i	0.610169	+	0.0551575i
$205$	1.74574	+	3.02371i	0.121928	+	0.211185i
$206$	−8.42463			−0.586972
$207$	2.52496	+	7.06386i	0.175497	+	0.490972i
$208$	1.54574			0.107178
$209$	−0.437642	−	0.758018i	−0.0302723	−	0.0524332i
$210$	1.86209	−	2.64308i	0.128497	−	0.182390i
$211$	−5.85961	+	10.1491i	−0.403392	+	0.698695i	−0.994133	−	0.108166i	$-0.965502\pi$
$211$	−5.85961	+	10.1491i	−0.403392	+	0.698695i	0.590741	+	0.806861i	$0.298836\pi$
$212$	−2.60913	+	4.51914i	−0.179196	+	0.310376i
$213$	2.55839	+	5.52807i	0.175298	+	0.378777i
$214$	−1.38128	−	2.39245i	−0.0944226	−	0.163545i
$215$	−11.3335			−0.772941
$216$	−11.8399	−	3.28259i	−0.805600	−	0.223352i
$217$	−11.5548			−0.784394
$218$	1.62850	+	2.82065i	0.110296	+	0.191038i
$219$	3.85558	+	8.33100i	0.260536	+	0.562957i
$220$	−0.179451	+	0.310818i	−0.0120986	+	0.0209553i
$221$	1.62086	−	2.80741i	0.109031	−	0.188847i
$222$	−1.96006	+	2.78214i	−0.131551	+	0.186725i
$223$	0.489654	+	0.848106i	0.0327897	+	0.0567934i	0.881955	−	0.471334i	$-0.156228\pi$
$223$	0.489654	+	0.848106i	0.0327897	+	0.0567934i	−0.849165	+	0.528128i	$0.822894\pi$
$224$	16.1702			1.08042
$225$	2.95137	+	0.537986i	0.196758	+	0.0358658i
$226$	−10.7296			−0.713724
$227$	−7.98509	−	13.8306i	−0.529989	−	0.917967i	−0.999388	−	0.0349814i	$-0.988863\pi$
$227$	−7.98509	−	13.8306i	−0.529989	−	0.917967i	0.469399	−	0.882986i	$-0.344471\pi$
$228$	−10.2179	−	0.923666i	−0.676695	−	0.0611713i
$229$	5.14710	−	8.91505i	0.340130	−	0.589123i	−0.644326	−	0.764751i	$-0.722862\pi$
$229$	5.14710	−	8.91505i	0.340130	−	0.589123i	0.984457	+	0.175628i	$0.0561955\pi$
$230$	−0.830776	+	1.43895i	−0.0547798	+	0.0948813i
$231$	1.11597	+	0.100881i	0.0734257	+	0.00663747i
$232$	−6.26254	−	10.8470i	−0.411156	−	0.712143i
$233$	7.73176			0.506524			0.253262	−	0.967398i	$-0.418496\pi$
$233$	7.73176			0.506524			0.253262	+	0.967398i	$0.418496\pi$
$234$	−1.29015	+	1.51965i	−0.0843400	+	0.0993424i
$235$	1.44125			0.0940168
$236$	6.07228	+	10.5175i	0.395272	+	0.684630i
$237$	5.38419	−	7.64240i	0.349741	−	0.496427i
$238$	3.02559	−	5.24047i	0.196120	−	0.339689i
$239$	−7.30932	+	12.6601i	−0.472801	+	0.818915i	−0.999515	−	0.0311272i	$-0.990090\pi$
$239$	−7.30932	+	12.6601i	−0.472801	+	0.818915i	0.526715	+	0.850042i	$0.323424\pi$
$240$	1.12447	+	2.42971i	0.0725842	+	0.156837i
$241$	−7.15642	−	12.3953i	−0.460985	−	0.798450i	0.538025	−	0.842929i	$-0.319171\pi$
$241$	−7.15642	−	12.3953i	−0.460985	−	0.798450i	−0.999010	+	0.0444789i	$0.985837\pi$
$242$	−7.27406			−0.467594
$243$	−12.8970	+	8.75601i	−0.827342	+	0.561698i
$244$	−15.7123			−1.00588
$245$	0.445790	+	0.772130i	0.0284805	+	0.0493296i
$246$	−1.68773	−	3.64679i	−0.107606	−	0.232511i
$247$	−1.90038	+	3.29155i	−0.120918	+	0.209436i
$248$	−4.86292	+	8.42283i	−0.308796	+	0.534850i
$249$	−0.100139	+	0.142138i	−0.00634602	+	0.00900763i
$250$	0.332241	+	0.575458i	0.0210128	+	0.0363952i
$251$	−19.0291			−1.20110			−0.600552	−	0.799586i	$-0.705052\pi$
$251$	−19.0291			−1.20110			−0.600552	+	0.799586i	$0.705052\pi$
$252$	8.50036	−	10.0124i	0.535472	−	0.630722i
$253$	−0.575851			−0.0362034
$254$	−5.89634	−	10.2128i	−0.369969	−	0.640805i
$255$	5.59202	+	0.505502i	0.350186	+	0.0316558i
$256$	4.39637	−	7.61473i	0.274773	−	0.475921i
$257$	6.97060	−	12.0734i	0.434814	−	0.753120i	−0.562467	−	0.826820i	$-0.690147\pi$
$257$	6.97060	−	12.0734i	0.434814	−	0.753120i	0.997280	+	0.0737002i	$0.0234808\pi$
$258$	12.9910	+	1.17435i	0.808783	+	0.0731117i
$259$	−4.15339	−	7.19389i	−0.258079	−	0.447007i
$260$	1.55846			0.0966518
$261$	−15.6336	−	2.84975i	−0.967694	−	0.176395i
$262$	−10.0615			−0.621604
$263$	5.97895	+	10.3558i	0.368678	+	0.638569i	0.989359	−	0.145494i	$-0.0464772\pi$
$263$	5.97895	+	10.3558i	0.368678	+	0.638569i	−0.620681	+	0.784063i	$0.713144\pi$
$264$	0.543201	−	0.771026i	0.0334317	−	0.0474534i
$265$	−1.67417	+	2.89974i	−0.102843	+	0.178130i
$266$	−3.54736	+	6.14421i	−0.217503	+	0.376725i
$267$	−5.12585	−	11.0758i	−0.313697	−	0.677826i
$268$	1.57352	+	2.72543i	0.0961183	+	0.166482i
$269$	2.54602			0.155234			0.0776168	−	0.996983i	$-0.475269\pi$
$269$	2.54602			0.155234			0.0776168	+	0.996983i	$0.475269\pi$
$270$	−3.32724	−	0.922474i	−0.202489	−	0.0561400i
$271$	16.6012			1.00845			0.504225	−	0.863572i	$-0.331778\pi$
$271$	16.6012			1.00845			0.504225	+	0.863572i	$0.331778\pi$
$272$	2.50542	+	4.33952i	0.151914	+	0.263122i
$273$	−2.04359	−	4.41571i	−0.123684	−	0.267251i
$274$	−6.91344	+	11.9744i	−0.417656	+	0.723402i
$275$	−0.115146	+	0.199439i	−0.00694356	+	0.0120266i
$276$	−3.88744	+	5.51789i	−0.233997	+	0.332138i
$277$	8.95287	+	15.5068i	0.537926	+	0.931714i	0.999016	+	0.0443610i	$0.0141252\pi$
$277$	8.95287	+	15.5068i	0.537926	+	0.931714i	−0.461090	+	0.887353i	$0.652541\pi$
$278$	−4.46913			−0.268041
$279$	4.15342	+	11.6197i	0.248659	+	0.695650i
$280$	6.64244			0.396962
$281$	−2.36433	−	4.09514i	−0.141044	−	0.244296i	0.786846	−	0.617149i	$-0.211713\pi$
$281$	−2.36433	−	4.09514i	−0.141044	−	0.244296i	−0.927890	+	0.372854i	$0.878379\pi$
$282$	−1.65202	−	0.149338i	−0.0983765	−	0.00889295i
$283$	2.98943	−	5.17785i	0.177703	−	0.307791i	−0.763390	−	0.645938i	$-0.776467\pi$
$283$	2.98943	−	5.17785i	0.177703	−	0.307791i	0.941094	+	0.338146i	$0.109800\pi$
$284$	−2.74045	+	4.74660i	−0.162616	+	0.281659i
$285$	−6.55637	−	0.592677i	−0.388366	−	0.0351072i
$286$	−0.0765124	−	0.132523i	−0.00452427	−	0.00783627i
$287$	9.80825			0.578963
$288$	−5.81244	−	16.2609i	−0.342502	−	0.958185i
$289$	−6.49128			−0.381840
$290$	−1.75990	−	3.04823i	−0.103345	−	0.178998i
$291$	−3.25644	+	4.62223i	−0.190896	+	0.270960i
$292$	−4.12996	+	7.15330i	−0.241687	+	0.418615i
$293$	7.80549	−	13.5195i	0.456002	−	0.789818i	−0.542744	−	0.839898i	$-0.682614\pi$
$293$	7.80549	−	13.5195i	0.456002	−	0.789818i	0.998745	+	0.0500805i	$0.0159478\pi$
$294$	−0.430977	−	0.931240i	−0.0251351	−	0.0543110i
$295$	3.89632	+	6.74863i	0.226853	+	0.392920i
$296$	−6.99193			−0.406397
$297$	−0.299694	−	1.15850i	−0.0173900	−	0.0672227i
$298$	14.7508			0.854492
$299$	1.25026	+	2.16552i	0.0723045	+	0.125235i
$300$	1.13373	+	2.44971i	0.0654557	+	0.141434i
$301$	−15.9191	+	27.5726i	−0.917560	+	1.58926i
$302$	−1.33669	+	2.31522i	−0.0769179	+	0.133226i
$303$	−11.1307	+	15.7991i	−0.639443	+	0.907633i
$304$	−2.93749	−	5.08788i	−0.168477	−	0.291810i
$305$	−10.0819			−0.577288
$306$	−6.35742	−	1.15886i	−0.363430	−	0.0662474i
$307$	23.7975			1.35819			0.679097	−	0.734048i	$-0.262371\pi$
$307$	23.7975			1.35819			0.679097	+	0.734048i	$0.262371\pi$
$308$	0.504112	+	0.873148i	0.0287245	+	0.0497523i
$309$	−21.8706	−	1.97704i	−1.24418	−	0.112470i
$310$	−1.36658	+	2.36699i	−0.0776165	+	0.134436i
$311$	−0.779514	+	1.35016i	−0.0442022	+	0.0765604i	−0.887280	−	0.461231i	$-0.847408\pi$
$311$	−0.779514	+	1.35016i	−0.0442022	+	0.0765604i	0.843078	+	0.537791i	$0.180741\pi$
$312$	−4.07886	−	0.368717i	−0.230920	−	0.0208745i
$313$	13.7455	+	23.8079i	0.776941	+	1.34570i	0.933697	+	0.358064i	$0.116563\pi$
$313$	13.7455	+	23.8079i	0.776941	+	1.34570i	−0.156756	+	0.987637i	$0.550104\pi$
$314$	14.5071			0.818684
$315$	5.45432	−	6.42453i	0.307316	−	0.361982i
$316$	8.41165			0.473192
$317$	7.65181	+	13.2533i	0.429768	+	0.744381i	0.996852	−	0.0792791i	$-0.0252618\pi$
$317$	7.65181	+	13.2533i	0.429768	+	0.744381i	−0.567084	+	0.823660i	$0.691929\pi$
$318$	2.21946	−	3.15033i	0.124461	−	0.176662i
$319$	0.609935	−	1.05644i	0.0341498	−	0.0591492i
$320$	0.366700	−	0.635142i	0.0204991	−	0.0355055i
$321$	−3.02441	−	6.53504i	−0.168806	−	0.364751i
$322$	2.33381	+	4.04228i	0.130058	+	0.225268i
$323$	−12.3210			−0.685557
$324$	−13.1240	−	4.94905i	−0.729114	−	0.274947i
$325$	1.00000			0.0554700
$326$	−3.48411	−	6.03465i	−0.192967	−	0.334228i
$327$	3.56571	+	7.70466i	0.197184	+	0.426069i
$328$	4.12786	−	7.14967i	0.227923	−	0.394774i
$329$	2.02438	−	3.50632i	0.111608	−	0.193310i
$330$	0.152650	−	0.216674i	0.00840313	−	0.0119275i
$331$	6.68506	+	11.5789i	0.367444	+	0.636432i	0.989165	−	0.146807i	$-0.0468995\pi$
$331$	6.68506	+	11.5789i	0.367444	+	0.636432i	−0.621721	+	0.783239i	$0.713566\pi$
$332$	−0.156445			−0.00858604
$333$	−5.74129	+	6.76256i	−0.314621	+	0.370586i
$334$	4.39377			0.240417
$335$	1.00966	+	1.74879i	0.0551638	+	0.0955466i
$336$	7.49051	+	0.677121i	0.408641	+	0.0369400i
$337$	−17.4801	+	30.2764i	−0.952200	+	1.64926i	−0.211552	+	0.977367i	$0.567852\pi$
$337$	−17.4801	+	30.2764i	−0.952200	+	1.64926i	−0.740648	+	0.671893i	$0.765481\pi$
$338$	−0.332241	+	0.575458i	−0.0180715	+	0.0313008i
$339$	−27.8545	−	2.51796i	−1.51285	−	0.136757i
$340$	2.52605	+	4.37525i	0.136994	+	0.237281i
$341$	−0.947241			−0.0512960
$342$	7.45378	+	1.35870i	0.403054	+	0.0734702i
$343$	−17.1597			−0.926539
$344$	13.3993	+	23.2082i	0.722441	+	1.25130i
$345$	−2.49441	+	3.54059i	−0.134294	+	0.190619i
$346$	−5.74385	+	9.94864i	−0.308791	+	0.534842i
$347$	12.1455	−	21.0367i	0.652007	−	1.12931i	−0.330629	−	0.943761i	$-0.607261\pi$
$347$	12.1455	−	21.0367i	0.652007	−	1.12931i	0.982635	−	0.185548i	$-0.0594059\pi$
$348$	−6.00541	−	12.9763i	−0.321924	−	0.695602i
$349$	−16.1586	−	27.9875i	−0.864951	−	1.49814i	−0.867096	−	0.498141i	$-0.834016\pi$
$349$	−16.1586	−	27.9875i	−0.864951	−	1.49814i	0.00214531	−	0.999998i	$-0.499317\pi$
$350$	1.86666			0.0997771
$351$	−3.70590	+	3.64229i	−0.197807	+	0.194411i
$352$	1.32560			0.0706548
$353$	17.0661	+	29.5593i	0.908334	+	1.57328i	0.816378	+	0.577518i	$0.195979\pi$
$353$	17.0661	+	29.5593i	0.908334	+	1.57328i	0.0919565	+	0.995763i	$0.470688\pi$
$354$	−3.76685	−	8.13928i	−0.200206	−	0.432598i
$355$	−1.75843	+	3.04569i	−0.0933278	+	0.161649i
$356$	5.49063	−	9.51004i	0.291003	−	0.504031i
$357$	9.08433	−	12.8944i	0.480794	−	0.682445i
$358$	−5.04568	−	8.73938i	−0.266673	−	0.461890i
$359$	25.3297			1.33685			0.668426	−	0.743779i	$-0.266968\pi$
$359$	25.3297			1.33685			0.668426	+	0.743779i	$0.266968\pi$
$360$	−2.38764	−	6.67970i	−0.125840	−	0.352051i
$361$	−4.55424			−0.239697
$362$	−8.08647	−	14.0062i	−0.425016	−	0.736149i
$363$	−18.8837	−	1.70703i	−0.991137	−	0.0895960i
$364$	2.18902	−	3.79149i	0.114736	−	0.198728i
$365$	−2.65002	+	4.58996i	−0.138708	+	0.240250i
$366$	11.5563	+	1.04466i	0.604058	+	0.0546051i
$367$	−1.79298	−	3.10554i	−0.0935930	−	0.162108i	0.815428	−	0.578859i	$-0.196502\pi$
$367$	−1.79298	−	3.10554i	−0.0935930	−	0.162108i	−0.909021	+	0.416751i	$0.863169\pi$
$368$	−3.86516			−0.201485
$369$	−3.52561	−	9.86327i	−0.183536	−	0.513461i
$370$	−1.96487			−0.102149
$371$	4.70306	+	8.14594i	0.244171	+	0.422916i
$372$	−6.39462	+	9.07661i	−0.331546	+	0.470600i
$373$	−0.717545	+	1.24282i	−0.0371531	+	0.0643510i	−0.884004	−	0.467479i	$-0.845162\pi$
$373$	−0.717545	+	1.24282i	−0.0371531	+	0.0643510i	0.846851	+	0.531830i	$0.178496\pi$
$374$	0.248031	−	0.429603i	0.0128254	−	0.0222142i
$375$	0.727463	+	1.57188i	0.0375661	+	0.0811714i
$376$	−1.70394	−	2.95132i	−0.0878741	−	0.152202i
$377$	−5.29706			−0.272812
$378$	−6.91766	+	6.79891i	−0.355806	+	0.349698i
$379$	34.5139			1.77286			0.886429	−	0.462864i	$-0.153178\pi$
$379$	34.5139			1.77286			0.886429	+	0.462864i	$0.153178\pi$
$380$	−2.96167	−	5.12977i	−0.151931	−	0.263151i
$381$	−12.9104	−	27.8964i	−0.661421	−	1.42917i
$382$	−4.73909	+	8.20834i	−0.242473	+	0.419975i
$383$	−3.32127	+	5.75260i	−0.169709	+	0.293944i	−0.938317	−	0.345775i	$-0.887616\pi$
$383$	−3.32127	+	5.75260i	−0.169709	+	0.293944i	0.768609	+	0.639719i	$0.220949\pi$
$384$	10.9981	−	15.6108i	0.561243	−	0.796635i
$385$	0.323467	+	0.560262i	0.0164854	+	0.0285536i
$386$	16.9995			0.865251
$387$	33.4495	+	6.09729i	1.70033	+	0.309943i
$388$	−5.08748			−0.258278
$389$	−15.0663	−	26.0956i	−0.763893	−	1.32310i	−0.940830	−	0.338879i	$-0.889952\pi$
$389$	−15.0663	−	26.0956i	−0.763893	−	1.32310i	0.176937	−	0.984222i	$-0.443381\pi$
$390$	−1.14624	−	0.103617i	−0.0580422	−	0.00524685i
$391$	−4.05300	+	7.01999i	−0.204969	+	0.355016i
$392$	1.05408	−	1.82573i	0.0532393	−	0.0922132i
$393$	−26.1201	−	2.36118i	−1.31759	−	0.119106i
$394$	−3.42129	−	5.92585i	−0.172362	−	0.298540i
$395$	5.39740			0.271573
$396$	0.696841	−	0.820796i	0.0350176	−	0.0412465i
$397$	25.4593			1.27777			0.638883	−	0.769304i	$-0.279397\pi$
$397$	25.4593			1.27777			0.638883	+	0.769304i	$0.279397\pi$
$398$	−1.10164	−	1.90809i	−0.0552201	−	0.0956440i
$399$	−10.6510	+	15.1181i	−0.533214	+	0.756851i
$400$	−0.772870	+	1.33865i	−0.0386435	+	0.0669325i
$401$	5.17727	−	8.96730i	0.258541	−	0.447805i	−0.707311	−	0.706903i	$-0.750092\pi$
$401$	5.17727	−	8.96730i	0.258541	−	0.447805i	0.965851	+	0.259097i	$0.0834251\pi$
$402$	−0.976115	−	2.10915i	−0.0486842	−	0.105195i
$403$	2.05661	+	3.56215i	0.102447	+	0.177444i
$404$	−17.3894			−0.865153
$405$	−8.42114	−	3.17559i	−0.418450	−	0.157796i
$406$	−9.88780			−0.490723
$407$	−0.340486	−	0.589740i	−0.0168773	−	0.0292323i
$408$	−5.57611	−	12.0487i	−0.276059	−	0.596498i
$409$	−14.1797	+	24.5600i	−0.701142	+	1.21441i	0.266923	+	0.963718i	$0.413993\pi$
$409$	−14.1797	+	24.5600i	−0.701142	+	1.21441i	−0.968066	+	0.250696i	$0.919340\pi$
$410$	1.16001	−	2.00920i	0.0572889	−	0.0992273i
$411$	−20.7576	+	29.4636i	−1.02390	+	1.45333i
$412$	−9.87950	−	17.1118i	−0.486728	−	0.843037i
$413$	21.8911			1.07719
$414$	3.22606	−	3.79991i	0.158552	−	0.186756i
$415$	−0.100384			−0.00492766
$416$	−2.87809	−	4.98500i	−0.141110	−	0.244410i
$417$	−11.6020	−	1.04879i	−0.568153	−	0.0513594i
$418$	−0.290805	+	0.503689i	−0.0142237	+	0.0246362i
$419$	5.32788	−	9.22817i	0.260284	−	0.450825i	−0.706033	−	0.708179i	$-0.749517\pi$
$419$	5.32788	−	9.22817i	0.260284	−	0.450825i	0.966317	+	0.257353i	$0.0828504\pi$
$420$	7.55218	+	0.682695i	0.368509	+	0.0333121i
$421$	−2.97812	−	5.15826i	−0.145145	−	0.251398i	0.784282	−	0.620404i	$-0.213031\pi$
$421$	−2.97812	−	5.15826i	−0.145145	−	0.251398i	−0.929427	+	0.369006i	$0.879698\pi$
$422$	7.78720			0.379075
$423$	−4.25366	−	0.775373i	−0.206820	−	0.0376999i
$424$	7.91724			0.384495
$425$	1.62086	+	2.80741i	0.0786232	+	0.136179i
$426$	2.33117	−	3.30890i	0.112946	−	0.160317i
$427$	−14.1610	+	24.5276i	−0.685300	+	1.18697i
$428$	3.23964	−	5.61122i	0.156594	−	0.271229i
$429$	−0.167529	−	0.361990i	−0.00808837	−	0.0174771i
$430$	3.76547	+	6.52198i	0.181587	+	0.314518i
$431$	−29.7924			−1.43505			−0.717524	−	0.696534i	$-0.754725\pi$
$431$	−29.7924			−1.43505			−0.717524	+	0.696534i	$0.754725\pi$
$432$	−2.01157	−	7.77592i	−0.0967817	−	0.374119i
$433$	−18.3601			−0.882332			−0.441166	−	0.897426i	$-0.645435\pi$
$433$	−18.3601			−0.882332			−0.441166	+	0.897426i	$0.645435\pi$
$434$	3.83899	+	6.64932i	0.184277	+	0.319178i
$435$	−3.85342	−	8.32632i	−0.184757	−	0.399217i
$436$	−3.81946	+	6.61550i	−0.182919	+	0.316825i
$437$	4.75194	−	8.23061i	0.227316	−	0.393723i
$438$	3.51316	−	4.98662i	0.167865	−	0.238270i
$439$	−7.50668	−	13.0020i	−0.358274	−	0.620549i	0.629398	−	0.777083i	$-0.283301\pi$
$439$	−7.50668	−	13.0020i	−0.358274	−	0.620549i	−0.987673	+	0.156534i	$0.949968\pi$
$440$	0.544533			0.0259596
$441$	−0.900294	−	2.51867i	−0.0428711	−	0.119937i
$442$	−2.15406			−0.102458
$443$	9.83816	+	17.0402i	0.467425	+	0.809604i	0.999307	−	0.0372145i	$-0.0118485\pi$
$443$	9.83816	+	17.0402i	0.467425	+	0.809604i	−0.531882	+	0.846818i	$0.678515\pi$
$444$	−7.94953	−	0.718615i	−0.377268	−	0.0341039i
$445$	3.52310	−	6.10219i	0.167011	−	0.289272i
$446$	0.325366	−	0.563551i	0.0154065	−	0.0266849i
$447$	38.2936	+	3.46163i	1.81123	+	0.163730i
$448$	−1.03013	−	1.78424i	−0.0486691	−	0.0842974i
$449$	22.3106			1.05290			0.526452	−	0.850205i	$-0.323522\pi$
$449$	22.3106			1.05290			0.526452	+	0.850205i	$0.323522\pi$
$450$	−0.670976	−	1.87713i	−0.0316301	−	0.0884887i
$451$	0.804060			0.0378617
$452$	−12.5825	−	21.7936i	−0.591833	−	1.02508i
$453$	−4.01342	+	5.69669i	−0.188567	+	0.267654i
$454$	−5.30594	+	9.19016i	−0.249020	+	0.431316i
$455$	1.40460	−	2.43283i	0.0658486	−	0.114053i
$456$	6.53773	+	14.1265i	0.306157	+	0.661533i
$457$	17.5884	+	30.4640i	0.822751	+	1.42505i	0.903626	+	0.428323i	$0.140895\pi$
$457$	17.5884	+	30.4640i	0.822751	+	1.42505i	−0.0808747	+	0.996724i	$0.525771\pi$
$458$	−6.84031			−0.319627
$459$	−16.2321	−	4.50035i	−0.757651	−	0.210058i
$460$	−3.89698			−0.181698
$461$	19.8328	+	34.3514i	0.923706	+	1.59991i	0.793629	+	0.608402i	$0.208189\pi$
$461$	19.8328	+	34.3514i	0.923706	+	1.59991i	0.130077	+	0.991504i	$0.458478\pi$
$462$	−0.312719	−	0.675713i	−0.0145490	−	0.0314370i
$463$	−2.66388	+	4.61398i	−0.123801	+	0.214430i	−0.921264	−	0.388939i	$-0.872842\pi$
$463$	−2.66388	+	4.61398i	−0.123801	+	0.214430i	0.797463	+	0.603369i	$0.206175\pi$
$464$	4.09394	−	7.09090i	0.190056	−	0.329187i
$465$	−4.10316	+	5.82407i	−0.190279	+	0.270085i
$466$	−2.56880	−	4.44930i	−0.118998	−	0.206110i
$467$	6.02093			0.278615			0.139308	−	0.990249i	$-0.455512\pi$
$467$	6.02093			0.278615			0.139308	+	0.990249i	$0.455512\pi$
$468$	−4.59960	−	0.838433i	−0.212617	−	0.0387566i
$469$	5.67269			0.261940
$470$	−0.478842	−	0.829379i	−0.0220873	−	0.0382564i
$471$	37.6610	+	3.40444i	1.73533	+	0.156868i
$472$	9.21298	−	15.9574i	0.424062	−	0.734497i
$473$	−1.30501	+	2.26035i	−0.0600045	+	0.103931i
$474$	−6.18673	−	0.559262i	−0.284166	−	0.0256878i
$475$	−1.90038	−	3.29155i	−0.0871954	−	0.151027i
$476$	14.1923			0.650504
$477$	6.50110	−	7.65752i	0.297665	−	0.350614i
$478$	9.71382			0.444300
$479$	10.2229	+	17.7066i	0.467098	+	0.809037i	0.999293	−	0.0375843i	$-0.0119663\pi$
$479$	10.2229	+	17.7066i	0.467098	+	0.809037i	−0.532196	+	0.846621i	$0.678633\pi$
$480$	5.74210	−	8.15041i	0.262090	−	0.372014i
$481$	−1.47850	+	2.56084i	−0.0674138	+	0.116764i
$482$	−4.75531	+	8.23643i	−0.216598	+	0.375159i
$483$	5.11004	+	11.0416i	0.232515	+	0.502410i
$484$	−8.53023	−	14.7748i	−0.387738	−	0.671581i
$485$	−3.26442			−0.148230
$486$	9.32362	+	4.51257i	0.422928	+	0.204694i
$487$	−11.8179			−0.535518			−0.267759	−	0.963486i	$-0.586283\pi$
$487$	−11.8179			−0.535518			−0.267759	+	0.963486i	$0.586283\pi$
$488$	11.9195	+	20.6452i	0.539571	+	0.934564i
$489$	−7.62868	−	16.4838i	−0.344981	−	0.745422i
$490$	0.296219	−	0.513066i	0.0133818	−	0.0231780i
$491$	21.0956	−	36.5387i	0.952031	−	1.64897i	0.211011	−	0.977484i	$-0.432324\pi$
$491$	21.0956	−	36.5387i	0.952031	−	1.64897i	0.741020	−	0.671483i	$-0.234342\pi$
$492$	5.42804	−	7.70463i	0.244715	−	0.347351i
$493$	−8.58578	−	14.8710i	−0.386684	−	0.669756i
$494$	2.52553			0.113629
$495$	0.447133	−	0.526670i	0.0200971	−	0.0236720i
$496$	−6.35797			−0.285481
$497$	4.93978	+	8.55594i	0.221579	+	0.383787i
$498$	0.115065	+	0.0104015i	0.00515617	+	0.000466102i
$499$	18.8086	−	32.5775i	0.841989	−	1.45837i	−0.0462216	−	0.998931i	$-0.514718\pi$
$499$	18.8086	−	32.5775i	0.841989	−	1.45837i	0.888211	−	0.459437i	$-0.151949\pi$
$500$	−0.779232	+	1.34967i	−0.0348483	+	0.0603591i
$501$	11.4064	+	1.03110i	0.509600	+	0.0460663i
$502$	6.32223	+	10.9504i	0.282175	+	0.488741i
$503$	29.4702			1.31401			0.657005	−	0.753886i	$-0.271823\pi$
$503$	29.4702			1.31401			0.657005	+	0.753886i	$0.271823\pi$
$504$	−19.6043	−	3.57354i	−0.873244	−	0.159178i
$505$	−11.1580			−0.496525
$506$	0.191321	+	0.331378i	0.00850526	+	0.0147315i
$507$	−0.997554	+	1.41594i	−0.0443029	+	0.0628841i
$508$	13.8292	−	23.9528i	0.613570	−	1.06273i
$509$	10.5176	−	18.2170i	0.466185	−	0.807456i	−0.533069	−	0.846071i	$-0.678962\pi$
$509$	10.5176	−	18.2170i	0.466185	−	0.807456i	0.999254	+	0.0386160i	$0.0122949\pi$
$510$	−1.56700	−	3.38592i	−0.0693879	−	0.149931i
$511$	7.44442	+	12.8941i	0.329322	+	0.570402i
$512$	16.2075			0.716275
$513$	19.0314	+	5.27645i	0.840257	+	0.232961i
$514$	−9.26367			−0.408603
$515$	−6.33925	−	10.9799i	−0.279341	−	0.483833i
$516$	12.8491	+	27.7639i	0.565652	+	1.22224i
$517$	0.165954	−	0.287441i	0.00729865	−	0.0126416i
$518$	−2.75985	+	4.78021i	−0.121261	+	0.210030i
$519$	−17.2459	+	24.4791i	−0.757012	+	1.07451i
$520$	−1.18227	−	2.04775i	−0.0518458	−	0.0897996i
$521$	30.7616			1.34769			0.673845	−	0.738873i	$-0.264642\pi$
$521$	30.7616			1.34769			0.673845	+	0.738873i	$0.264642\pi$
$522$	3.55420	+	9.94326i	0.155563	+	0.435205i
$523$	−14.0570			−0.614672			−0.307336	−	0.951601i	$-0.599438\pi$
$523$	−14.0570			−0.614672			−0.307336	+	0.951601i	$0.599438\pi$
$524$	−11.7991	−	20.4366i	−0.515446	−	0.892778i
$525$	4.84591	+	0.438056i	0.211493	+	0.0191183i
$526$	3.97290	−	6.88127i	0.173227	−	0.300038i
$527$	−6.66695	+	11.5475i	−0.290417	+	0.503017i
$528$	0.614056	+	0.0555089i	0.0267234	+	0.00241572i
$529$	8.37369	+	14.5037i	0.364073	+	0.630594i
$530$	2.22491			0.0966437
$531$	−7.86881	−	22.0138i	−0.341477	−	0.955319i
$532$	−16.6398			−0.721428
$533$	−1.74574	−	3.02371i	−0.0756164	−	0.130971i
$534$	−4.67062	+	6.62953i	−0.202117	+	0.286888i
$535$	2.07874	−	3.60048i	0.0898717	−	0.155662i
$536$	2.38738	−	4.13507i	0.103119	−	0.178608i
$537$	−11.0479	−	23.8718i	−0.476750	−	1.03014i
$538$	−0.845892	−	1.46513i	−0.0364690	−	0.0631661i
$539$	0.205324			0.00884391
$540$	−2.02813	−	7.83994i	−0.0872768	−	0.337377i
$541$	16.4764			0.708374			0.354187	−	0.935175i	$-0.384758\pi$
$541$	16.4764			0.708374			0.354187	+	0.935175i	$0.384758\pi$
$542$	−5.51559	−	9.55328i	−0.236915	−	0.410349i
$543$	−17.7059	−	38.2582i	−0.759832	−	1.64182i
$544$	9.32996	−	16.1600i	0.400019	−	0.692852i
$545$	−2.45078	+	4.24488i	−0.104980	+	0.181831i
$546$	−1.86209	+	2.64308i	−0.0796902	+	0.113113i
$547$	23.0919	+	39.9964i	0.987339	+	1.71012i	0.631044	+	0.775747i	$0.282627\pi$
$547$	23.0919	+	39.9964i	0.987339	+	1.71012i	0.356295	+	0.934374i	$0.384040\pi$
$548$	−32.4293			−1.38531
$549$	29.7554	+	5.42393i	1.26993	+	0.231488i
$550$	0.153025			0.00652500
$551$	10.0664	+	17.4355i	0.428844	+	0.742779i
$552$	10.1993	+	0.921987i	0.434111	+	0.0392424i
$553$	7.58117	−	13.1310i	0.322384	−	0.558386i
$554$	5.94901	−	10.3040i	0.252749	−	0.437775i
$555$	−5.10087	−	0.461104i	−0.216520	−	0.0195728i
$556$	−5.24091	−	9.07752i	−0.222264	−	0.384973i
$557$	−38.2914			−1.62246			−0.811229	−	0.584728i	$-0.801201\pi$
$557$	−38.2914			−1.62246			−0.811229	+	0.584728i	$0.801201\pi$
$558$	5.30668	−	6.25064i	0.224650	−	0.264611i
$559$	11.3335			0.479358
$560$	2.17114	+	3.76053i	0.0917475	+	0.158911i
$561$	0.744715	−	1.05706i	0.0314419	−	0.0446290i
$562$	−1.57105	+	2.72115i	−0.0662709	+	0.114785i
$563$	5.14550	−	8.91227i	0.216857	−	0.375607i	−0.736988	−	0.675905i	$-0.763753\pi$
$563$	5.14550	−	8.91227i	0.216857	−	0.375607i	0.953845	+	0.300298i	$0.0970861\pi$
$564$	−1.63398	−	3.53065i	−0.0688031	−	0.148667i
$565$	−8.07368	−	13.9840i	−0.339662	−	0.588312i
$566$	−3.97285			−0.166991
$567$	−19.5540	+	16.0268i	−0.821191	+	0.673063i
$568$	8.31574			0.348921
$569$	6.01983	+	10.4266i	0.252364	+	0.437108i	0.964176	−	0.265262i	$-0.0854586\pi$
$569$	6.01983	+	10.4266i	0.252364	+	0.437108i	−0.711812	+	0.702370i	$0.752125\pi$
$570$	1.83723	+	3.96983i	0.0769532	+	0.166278i
$571$	−10.2247	+	17.7097i	−0.427890	+	0.741127i	−0.996685	−	0.0813519i	$-0.974076\pi$
$571$	−10.2247	+	17.7097i	−0.427890	+	0.741127i	0.568796	+	0.822479i	$0.307410\pi$
$572$	0.179451	−	0.310818i	0.00750322	−	0.0129960i
$573$	−14.2291	+	20.1970i	−0.594430	+	0.843742i
$574$	−3.25870	−	5.64424i	−0.136016	−	0.235586i
$575$	−2.50052			−0.104279
$576$	−1.42396	+	1.67726i	−0.0593318	+	0.0698858i
$577$	8.66059			0.360545			0.180273	−	0.983617i	$-0.442302\pi$
$577$	8.66059			0.360545			0.180273	+	0.983617i	$0.442302\pi$
$578$	2.15667	+	3.73546i	0.0897055	+	0.155375i
$579$	44.1313	+	3.98934i	1.83403	+	0.165791i
$580$	4.12764	−	7.14928i	0.171391	−	0.296858i
$581$	−0.140999	+	0.244218i	−0.00584964	+	0.0101319i
$582$	3.74182	+	0.338250i	0.155103	+	0.0140209i
$583$	0.385547	+	0.667787i	0.0159677	+	0.0276569i
$584$	12.5321			0.518582
$585$	−2.95137	−	0.537986i	−0.122024	−	0.0222430i
$586$	−10.3732			−0.428513
$587$	−19.6997	−	34.1208i	−0.813092	−	1.40832i	−0.910690	−	0.413091i	$-0.864449\pi$
$587$	−19.6997	−	34.1208i	−0.813092	−	1.40832i	0.0975972	−	0.995226i	$-0.468884\pi$
$588$	1.38610	−	1.96744i	0.0571616	−	0.0811359i
$589$	7.81668	−	13.5389i	0.322081	−	0.557860i
$590$	2.58903	−	4.48434i	0.106589	−	0.184617i
$591$	−7.49114	−	16.1866i	−0.308145	−	0.665828i
$592$	−2.28537	−	3.95839i	−0.0939283	−	0.162689i
$593$	4.26159			0.175002			0.0875012	−	0.996164i	$-0.472112\pi$
$593$	4.26159			0.175002			0.0875012	+	0.996164i	$0.472112\pi$
$594$	−0.567095	+	0.557360i	−0.0232682	+	0.0228688i
$595$	9.10661			0.373335
$596$	17.2982	+	29.9613i	0.708560	+	1.22726i
$597$	−2.41211	−	5.21200i	−0.0987211	−	0.213313i
$598$	0.830776	−	1.43895i	0.0339730	−	0.0588429i
$599$	13.3206	−	23.0720i	0.544266	−	0.942696i	−0.454387	−	0.890805i	$-0.650142\pi$
$599$	13.3206	−	23.0720i	0.544266	−	0.942696i	0.998653	−	0.0518919i	$-0.0165251\pi$
$600$	2.35875	−	3.34804i	0.0962955	−	0.136683i
$601$	−21.2732	−	36.8462i	−0.867751	−	1.50299i	−0.864289	−	0.502995i	$-0.832231\pi$
$601$	−21.2732	−	36.8462i	−0.867751	−	1.50299i	−0.00346220	−	0.999994i	$-0.501102\pi$
$602$	21.1559			0.862249
$603$	−2.03906	−	5.70450i	−0.0830371	−	0.232305i
$604$	−6.27010			−0.255127
$605$	−5.47348	−	9.48035i	−0.222529	−	0.385431i
$606$	12.7898	+	1.15616i	0.519549	+	0.0469657i
$607$	−5.14131	+	8.90502i	−0.208679	+	0.361443i	−0.951299	−	0.308270i	$-0.900250\pi$
$607$	−5.14131	+	8.90502i	−0.208679	+	0.361443i	0.742619	+	0.669714i	$0.233583\pi$
$608$	−10.9389	+	18.9468i	−0.443632	+	0.768393i
$609$	−25.6691	−	2.32041i	−1.04016	−	0.0940278i
$610$	3.34962	+	5.80171i	0.135622	+	0.234904i
$611$	−1.44125			−0.0583067
$612$	−5.10148	−	14.2719i	−0.206215	−	0.576909i
$613$	2.78688			0.112561			0.0562804	−	0.998415i	$-0.482076\pi$
$613$	2.78688			0.112561			0.0562804	+	0.998415i	$0.482076\pi$
$614$	−7.90650	−	13.6945i	−0.319080	−	0.552663i
$615$	3.48294	−	4.94373i	0.140446	−	0.199350i
$616$	0.764850	−	1.32476i	0.0308167	−	0.0533761i
$617$	−21.4024	+	37.0700i	−0.861627	+	1.49238i	0.00873099	+	0.999962i	$0.497221\pi$
$617$	−21.4024	+	37.0700i	−0.861627	+	1.49238i	−0.870358	+	0.492420i	$0.836113\pi$
$618$	6.12861	+	13.2425i	0.246529	+	0.532691i
$619$	−3.74849	−	6.49257i	−0.150664	−	0.260958i	0.780807	−	0.624772i	$-0.214808\pi$
$619$	−3.74849	−	6.49257i	−0.150664	−	0.260958i	−0.931472	+	0.363813i	$0.881475\pi$
$620$	−6.41031			−0.257444
$621$	9.26670	−	9.10764i	0.371860	−	0.365477i
$622$	1.03594			0.0415376
$623$	−9.89708	−	17.1422i	−0.396518	−	0.686790i
$624$	−1.12447	−	2.42971i	−0.0450148	−	0.0972663i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	9.13363	−	15.8199i	0.365053	−	0.632291i
$627$	−0.873142	+	1.23935i	−0.0348699	+	0.0494948i
$628$	17.0124	+	29.4663i	0.678868	+	1.17583i
$629$	−9.58575			−0.382209
$630$	−5.50920	−	1.00424i	−0.219492	−	0.0400098i
$631$	2.02620			0.0806619			0.0403310	−	0.999186i	$-0.487159\pi$
$631$	2.02620			0.0806619			0.0403310	+	0.999186i	$0.487159\pi$
$632$	−6.38117	−	11.0525i	−0.253829	−	0.439645i
$633$	20.2158	+	1.82745i	0.803507	+	0.0726348i
$634$	5.08449	−	8.80659i	0.201931	−	0.349754i
$635$	8.87359	−	15.3695i	0.352138	−	0.609920i
$636$	9.00158	+	0.813717i	0.356936	+	0.0322660i
$637$	−0.445790	−	0.772130i	−0.0176628	−	0.0305929i
$638$	−0.810581			−0.0320912
$639$	6.82832	−	8.04294i	0.270124	−	0.318174i
$640$	11.0250			0.435803
$641$	−2.06080	−	3.56940i	−0.0813965	−	0.140983i	0.822453	−	0.568832i	$-0.192605\pi$
$641$	−2.06080	−	3.56940i	−0.0813965	−	0.140983i	−0.903850	+	0.427849i	$0.859271\pi$
$642$	−2.75581	+	3.91163i	−0.108763	+	0.154380i
$643$	10.1784	−	17.6295i	0.401396	−	0.695239i	−0.592499	−	0.805572i	$-0.701858\pi$
$643$	10.1784	−	17.6295i	0.401396	−	0.695239i	0.993895	+	0.110333i	$0.0351917\pi$
$644$	−5.47369	+	9.48070i	−0.215693	+	0.373592i
$645$	8.24474	+	17.8149i	0.324636	+	0.701462i
$646$	4.09353	+	7.09020i	0.161058	+	0.278960i
$647$	−9.76640			−0.383957			−0.191978	−	0.981399i	$-0.561490\pi$
$647$	−9.76640			−0.383957			−0.191978	+	0.981399i	$0.561490\pi$
$648$	3.45323	+	20.9988i	0.135656	+	0.824909i
$649$	1.79458			0.0704435
$650$	−0.332241	−	0.575458i	−0.0130316	−	0.0225713i
$651$	8.40572	+	18.1628i	0.329446	+	0.711856i
$652$	8.17156	−	14.1536i	0.320023	−	0.554296i
$653$	−24.6834	+	42.7529i	−0.965937	+	1.67305i	−0.258861	+	0.965915i	$0.583347\pi$
$653$	−24.6834	+	42.7529i	−0.965937	+	1.67305i	−0.707076	+	0.707137i	$0.749986\pi$
$654$	3.24903	−	4.61172i	0.127047	−	0.180332i
$655$	−7.57097	−	13.1133i	−0.295822	−	0.512379i
$656$	5.39692			0.210714
$657$	10.2905	−	12.1210i	0.401471	−	0.472885i
$658$	−2.69032			−0.104880
$659$	3.52180	+	6.09994i	0.137190	+	0.237620i	0.926432	−	0.376462i	$-0.122860\pi$
$659$	3.52180	+	6.09994i	0.137190	+	0.237620i	−0.789242	+	0.614082i	$0.789526\pi$
$660$	0.619112	+	0.0559659i	0.0240989	+	0.00217847i
$661$	11.1100	−	19.2430i	0.432128	−	0.748467i	−0.564929	−	0.825140i	$-0.691096\pi$
$661$	11.1100	−	19.2430i	0.432128	−	0.748467i	0.997056	+	0.0766727i	$0.0244296\pi$
$662$	4.44210	−	7.69394i	0.172647	−	0.299034i
$663$	−5.59202	−	0.505502i	−0.217176	−	0.0196321i
$664$	0.118681	+	0.205561i	0.00460571	+	0.00797733i
$665$	−10.6771			−0.414039
$666$	5.79906	+	1.05707i	0.224709	+	0.0409608i
$667$	13.2454			0.512865
$668$	5.15254	+	8.92446i	0.199358	+	0.345298i
$669$	0.976913	−	1.38664i	0.0377696	−	0.0536107i
$670$	0.670903	−	1.16204i	0.0259192	−	0.0448934i
$671$	−1.16089	+	2.01072i	−0.0448157	+	0.0776230i
$672$	−11.7633	−	25.4176i	−0.453778	−	0.980506i
$673$	5.46905	+	9.47267i	0.210816	+	0.365145i	0.951970	−	0.306191i	$-0.0990545\pi$
$673$	5.46905	+	9.47267i	0.210816	+	0.365145i	−0.741154	+	0.671335i	$0.765721\pi$
$674$	23.2304			0.894801
$675$	−1.30136	−	5.03055i	−0.0500895	−	0.193626i
$676$	−1.55846			−0.0599409
$677$	−4.35062	−	7.53550i	−0.167208	−	0.289613i	0.770229	−	0.637767i	$-0.220142\pi$
$677$	−4.35062	−	7.53550i	−0.167208	−	0.289613i	−0.937437	+	0.348154i	$0.886808\pi$
$678$	7.80541	+	16.8656i	0.299765	+	0.647721i
$679$	−4.58520	+	7.94180i	−0.175964	+	0.304778i
$680$	3.83257	−	6.63821i	0.146972	−	0.254564i
$681$	−15.9311	+	22.6128i	−0.610481	+	0.866525i
$682$	0.314712	+	0.545098i	0.0120510	+	0.0208729i
$683$	7.83468			0.299786			0.149893	−	0.988702i	$-0.452107\pi$
$683$	7.83468			0.299786			0.149893	+	0.988702i	$0.452107\pi$
$684$	5.98124	+	16.7332i	0.228698	+	0.639809i
$685$	−20.8085			−0.795053
$686$	5.70117	+	9.87471i	0.217672	+	0.377018i
$687$	−17.7577	−	1.60524i	−0.677498	−	0.0612439i
$688$	−8.75935	+	15.1716i	−0.333947	+	0.578413i
$689$	1.67417	−	2.89974i	0.0637806	−	0.110471i
$690$	2.86621	+	0.259097i	0.109115	+	0.00986365i
$691$	18.7536	+	32.4822i	0.713420	+	1.23568i	0.963566	+	0.267472i	$0.0861882\pi$
$691$	18.7536	+	32.4822i	0.713420	+	1.23568i	−0.250145	+	0.968208i	$0.580478\pi$
$692$	−26.9431			−1.02422
$693$	−0.653258	−	1.82756i	−0.0248152	−	0.0694233i
$694$	−16.1410			−0.612703
$695$	−3.36287	−	5.82466i	−0.127561	−	0.220942i
$696$	−12.4944	+	17.7348i	−0.473600	+	0.672234i
$697$	5.65920	−	9.80201i	0.214357	−	0.371278i
$698$	−10.7371	+	18.5972i	−0.406405	+	0.703915i
$699$	−5.62457	−	12.1534i	−0.212741	−	0.459683i
$700$	2.18902	+	3.79149i	0.0827370	+	0.143305i
$701$	−34.0001			−1.28416			−0.642082	−	0.766636i	$-0.721929\pi$
$701$	−34.0001			−1.28416			−0.642082	+	0.766636i	$0.721929\pi$
$702$	3.32724	+	0.922474i	0.125578	+	0.0348166i
$703$	11.2388			0.423881
$704$	−0.0844479	−	0.146268i	−0.00318275	−	0.00551269i
$705$	−1.04846	−	2.26547i	−0.0394872	−	0.0853225i
$706$	11.3401	−	19.6416i	0.426789	−	0.739221i
$707$	−15.6725	+	27.1456i	−0.589426	+	1.02091i
$708$	12.1148	−	17.1960i	0.455304	−	0.646264i
$709$	20.4335	+	35.3919i	0.767397	+	1.32917i	0.938970	+	0.343999i	$0.111782\pi$
$709$	20.4335	+	35.3919i	0.767397	+	1.32917i	−0.171573	+	0.985171i	$0.554885\pi$
$710$	2.33689			0.0877019
$711$	−15.9297	−	2.90373i	−0.597411	−	0.108898i
$712$	−16.6610			−0.624397
$713$	−5.14260	−	8.90725i	−0.192592	−	0.333579i
$714$	−10.4384	−	0.943600i	−0.390647	−	0.0353133i
$715$	0.115146	−	0.199439i	0.00430621	−	0.00745858i
$716$	11.8341	−	20.4972i	0.442260	−	0.766016i
$717$	25.2174	+	2.27958i	0.941761	+	0.0851325i
$718$	−8.41556	−	14.5762i	−0.314066	−	0.543978i
$719$	−33.2593			−1.24036			−0.620181	−	0.784459i	$-0.712941\pi$
$719$	−33.2593			−1.24036			−0.620181	+	0.784459i	$0.712941\pi$
$720$	3.00120	−	3.53505i	0.111848	−	0.131744i
$721$	−35.6164			−1.32642
$722$	1.51310	+	2.62077i	0.0563119	+	0.0975351i
$723$	−14.2778	+	20.2661i	−0.530998	+	0.753705i
$724$	18.9659	−	32.8499i	0.704862	−	1.22086i
$725$	2.64853	−	4.58739i	0.0983639	−	0.170371i
$726$	5.29161	+	11.4339i	0.196390	+	0.424353i
$727$	−7.54471	−	13.0678i	−0.279818	−	0.484659i	0.691521	−	0.722356i	$-0.256941\pi$
$727$	−7.54471	−	13.0678i	−0.279818	−	0.484659i	−0.971339	+	0.237697i	$0.923607\pi$
$728$	−6.64244			−0.246185
$729$	23.1455	+	13.9028i	0.857239	+	0.514918i
$730$	3.52178			0.130347
$731$	18.3701	+	31.8179i	0.679441	+	1.17683i
$732$	11.4301	+	24.6978i	0.422469	+	0.912856i
$733$	3.43481	−	5.94926i	0.126867	−	0.219741i	−0.795594	−	0.605830i	$-0.792841\pi$
$733$	3.43481	−	5.94926i	0.126867	−	0.219741i	0.922461	+	0.386089i	$0.126174\pi$
$734$	−1.19140	+	2.06357i	−0.0439756	+	0.0761679i
$735$	0.889398	−	1.26242i	0.0328059	−	0.0465652i
$736$	7.19674	+	12.4651i	0.265275	+	0.459470i
$737$	0.465035			0.0171298
$738$	−4.50455	+	5.30582i	−0.165815	+	0.195310i
$739$	53.1537			1.95529			0.977645	−	0.210265i	$-0.0674326\pi$
$739$	53.1537			1.95529			0.977645	+	0.210265i	$0.0674326\pi$
$740$	−2.30419	−	3.99097i	−0.0847037	−	0.146711i
$741$	6.55637	+	0.592677i	0.240854	+	0.0217725i
$742$	3.12510	−	5.41283i	0.114726	−	0.198711i
$743$	−21.3602	+	36.9969i	−0.783629	+	1.35729i	0.146185	+	0.989257i	$0.453300\pi$
$743$	−21.3602	+	36.9969i	−0.783629	+	1.35729i	−0.929815	+	0.368028i	$0.880033\pi$
$744$	16.7773	+	1.51662i	0.615084	+	0.0556018i
$745$	11.0995	+	19.2249i	0.406654	+	0.704345i
$746$	0.953590			0.0349134
$747$	0.296271	+	0.0540053i	0.0108400	+	0.00197595i
$748$	1.16346			0.0425402
$749$	−5.83959	−	10.1145i	−0.213374	−	0.369574i
$750$	0.662856	−	0.940866i	0.0242041	−	0.0343556i
$751$	−8.29029	+	14.3592i	−0.302517	+	0.523975i	−0.976705	−	0.214585i	$-0.931160\pi$
$751$	−8.29029	+	14.3592i	−0.302517	+	0.523975i	0.674188	+	0.738559i	$0.264494\pi$
$752$	1.11390	−	1.92933i	0.0406197	−	0.0703554i
$753$	13.8429	+	29.9113i	0.504465	+	1.09003i
$754$	1.75990	+	3.04823i	0.0640917	+	0.111010i
$755$	−4.02326			−0.146421
$756$	−21.9220	−	6.07785i	−0.797294	−	0.221049i
$757$	−28.7091			−1.04345			−0.521725	−	0.853114i	$-0.674711\pi$
$757$	−28.7091			−1.04345			−0.521725	+	0.853114i	$0.674711\pi$
$758$	−11.4669	−	19.8613i	−0.416497	−	0.721394i
$759$	0.418910	+	0.905166i	0.0152055	+	0.0328555i
$760$	−4.49351	+	7.78299i	−0.162997	+	0.282319i
$761$	3.37843	−	5.85160i	0.122468	−	0.212121i	−0.798272	−	0.602296i	$-0.794253\pi$
$761$	3.37843	−	5.85160i	0.122468	−	0.212121i	0.920740	+	0.390176i	$0.127586\pi$
$762$	−11.7638	+	16.6977i	−0.426158	+	0.604895i
$763$	6.88473	+	11.9247i	0.249244	+	0.431703i
$764$	−22.2300			−0.804252
$765$	−3.27340	−	9.15769i	−0.118350	−	0.331097i
$766$	4.41384			0.159479
$767$	−3.89632	−	6.74863i	−0.140688	−	0.243679i
$768$	−15.1676	−	1.37111i	−0.547314	−	0.0494756i
$769$	14.3441	−	24.8447i	0.517262	−	0.895923i	−0.482537	−	0.875875i	$-0.660285\pi$
$769$	14.3441	−	24.8447i	0.517262	−	0.895923i	0.999799	−	0.0200481i	$-0.00638193\pi$
$770$	0.214938	−	0.372284i	0.00774583	−	0.0134162i
$771$	−24.0488	−	2.17394i	−0.866096	−	0.0782926i
$772$	19.9352	+	34.5287i	0.717482	+	1.24272i
$773$	33.4431			1.20286			0.601432	−	0.798924i	$-0.294597\pi$
$773$	33.4431			1.20286			0.601432	+	0.798924i	$0.294597\pi$
$774$	−7.60454	−	21.2745i	−0.273339	−	0.764697i

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.332241 - 0.575458i) q^{2} +(-0.727463 - 1.57188i) q^{3} +(0.779232 - 1.34967i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.662856 + 0.940866i) q^{6} +(-1.40460 - 2.43283i) q^{7} -2.36453 q^{8} +(-1.94159 + 2.28697i) q^{9} +O(q^{10})\)	\(q+(-0.332241 - 0.575458i) q^{2} +(-0.727463 - 1.57188i) q^{3} +(0.779232 - 1.34967i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.662856 + 0.940866i) q^{6} +(-1.40460 - 2.43283i) q^{7} -2.36453 q^{8} +(-1.94159 + 2.28697i) q^{9} -0.664482 q^{10} +(-0.115146 - 0.199439i) q^{11} +(-2.68838 - 0.243022i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-0.933329 + 1.61657i) q^{14} +(-1.72502 - 0.155937i) q^{15} +(-0.772870 - 1.33865i) q^{16} -3.24172 q^{17} +(1.96113 + 0.357482i) q^{18} +3.80076 q^{19} +(-0.779232 - 1.34967i) q^{20} +(-2.80232 + 3.97765i) q^{21} +(-0.0765124 + 0.132523i) q^{22} +(1.25026 - 2.16552i) q^{23} +(1.72011 + 3.71676i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.664482 q^{26} +(5.00727 + 1.38826i) q^{27} -4.37803 q^{28} +(2.64853 + 4.58739i) q^{29} +(0.483386 + 1.04448i) q^{30} +(2.05661 - 3.56215i) q^{31} +(-2.87809 + 4.98500i) q^{32} +(-0.229728 + 0.326080i) q^{33} +(1.07703 + 1.86547i) q^{34} -2.80920 q^{35} +(1.57370 + 4.40259i) q^{36} +2.95700 q^{37} +(-1.26277 - 2.18718i) q^{38} +(1.72502 + 0.155937i) q^{39} +(-1.18227 + 2.04775i) q^{40} +(-1.74574 + 3.02371i) q^{41} +(3.22002 + 0.291080i) q^{42} +(-5.66677 - 9.81514i) q^{43} -0.358902 q^{44} +(1.00977 + 2.82495i) q^{45} -1.66155 q^{46} +(0.720625 + 1.24816i) q^{47} +(-1.54196 + 2.18867i) q^{48} +(-0.445790 + 0.772130i) q^{49} +(-0.332241 + 0.575458i) q^{50} +(2.35823 + 5.09558i) q^{51} +(0.779232 + 1.34967i) q^{52} -3.34833 q^{53} +(-0.864732 - 3.34271i) q^{54} -0.230292 q^{55} +(3.32122 + 5.75252i) q^{56} +(-2.76491 - 5.97432i) q^{57} +(1.75990 - 3.04823i) q^{58} +(-3.89632 + 6.74863i) q^{59} +(-1.55465 + 2.20669i) q^{60} +(-5.04095 - 8.73119i) q^{61} -2.73316 q^{62} +(8.29097 + 1.51131i) q^{63} +0.733399 q^{64} +(0.500000 + 0.866025i) q^{65} +(0.263970 + 0.0238621i) q^{66} +(-1.00966 + 1.74879i) q^{67} +(-2.52605 + 4.37525i) q^{68} +(-4.31345 - 0.389923i) q^{69} +(0.933329 + 1.61657i) q^{70} -3.51686 q^{71} +(4.59096 - 5.40761i) q^{72} -5.30003 q^{73} +(-0.982436 - 1.70163i) q^{74} +(-0.997554 + 1.41594i) q^{75} +(2.96167 - 5.12977i) q^{76} +(-0.323467 + 0.560262i) q^{77} +(-0.483386 - 1.04448i) q^{78} +(2.69870 + 4.67428i) q^{79} -1.54574 q^{80} +(-1.46043 - 8.88072i) q^{81} +2.32003 q^{82} +(-0.0501921 - 0.0869352i) q^{83} +(3.18486 + 6.88173i) q^{84} +(-1.62086 + 2.80741i) q^{85} +(-3.76547 + 6.52198i) q^{86} +(5.28410 - 7.50032i) q^{87} +(0.272266 + 0.471579i) q^{88} +7.04620 q^{89} +(1.29015 - 1.51965i) q^{90} +2.80920 q^{91} +(-1.94849 - 3.37488i) q^{92} +(-7.09538 - 0.641401i) q^{93} +(0.478842 - 0.829379i) q^{94} +(1.90038 - 3.29155i) q^{95} +(9.92951 + 0.897599i) q^{96} +(-1.63221 - 2.82707i) q^{97} +0.592438 q^{98} +(0.679676 + 0.123894i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Introduction

L-functions

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