LMFDB - Embedded newform 165.2.p.b.101.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(41,165)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("165.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.p (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.5
Character	$\chi$	$=$	165.101
Dual form			165.2.p.b.116.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.140144 + 0.431318i) q^{2} +(0.180419 + 1.72263i) q^{3} +(1.45164 + 1.05468i) q^{4} +(0.951057 - 0.309017i) q^{5} +(-0.768285 - 0.163597i) q^{6} +(2.72178 - 3.74621i) q^{7} +(-1.39214 + 1.01145i) q^{8} +(-2.93490 + 0.621591i) q^{9} +O(q^{10})$	\(q+(-0.140144 + 0.431318i) q^{2} +(0.180419 + 1.72263i) q^{3} +(1.45164 + 1.05468i) q^{4} +(0.951057 - 0.309017i) q^{5} +(-0.768285 - 0.163597i) q^{6} +(2.72178 - 3.74621i) q^{7} +(-1.39214 + 1.01145i) q^{8} +(-2.93490 + 0.621591i) q^{9} +0.453514i q^{10} +(-2.24032 + 2.44560i) q^{11} +(-1.55491 + 2.69092i) q^{12} +(-2.34827 - 0.762999i) q^{13} +(1.23437 + 1.69896i) q^{14} +(0.703911 + 1.58256i) q^{15} +(0.867797 + 2.67080i) q^{16} +(-0.465691 - 1.43325i) q^{17} +(0.143204 - 1.35299i) q^{18} +(-1.58515 - 2.18177i) q^{19} +(1.70650 + 0.554477i) q^{20} +(6.94438 + 4.01272i) q^{21} +(-0.740863 - 1.30903i) q^{22} -5.63898i q^{23} +(-1.99352 - 2.21566i) q^{24} +(0.809017 - 0.587785i) q^{25} +(0.658190 - 0.905921i) q^{26} +(-1.60028 - 4.94359i) q^{27} +(7.90208 - 2.56754i) q^{28} +(0.463093 + 0.336457i) q^{29} +(-0.781237 + 0.0818229i) q^{30} +(-2.36854 + 7.28961i) q^{31} -4.71514 q^{32} +(-4.61705 - 3.41801i) q^{33} +0.683450 q^{34} +(1.43092 - 4.40393i) q^{35} +(-4.91599 - 2.19304i) q^{36} +(0.396224 + 0.287874i) q^{37} +(1.16318 - 0.377941i) q^{38} +(0.890690 - 4.18285i) q^{39} +(-1.01145 + 1.39214i) q^{40} +(6.82953 - 4.96195i) q^{41} +(-2.70397 + 2.43288i) q^{42} +2.51824i q^{43} +(-5.83146 + 1.18731i) q^{44} +(-2.59917 + 1.49810i) q^{45} +(2.43219 + 0.790268i) q^{46} +(-1.96912 - 2.71027i) q^{47} +(-4.44424 + 1.97676i) q^{48} +(-4.46287 - 13.7353i) q^{49} +(0.140144 + 0.431318i) q^{50} +(2.38494 - 1.06080i) q^{51} +(-2.60412 - 3.58426i) q^{52} +(12.6599 + 4.11346i) q^{53} +(2.35653 + 0.00258193i) q^{54} +(-1.37494 + 3.01820i) q^{55} +7.96819i q^{56} +(3.47238 - 3.12425i) q^{57} +(-0.210019 + 0.152588i) q^{58} +(-2.21091 + 3.04306i) q^{59} +(-0.647271 + 3.03971i) q^{60} +(7.73467 - 2.51315i) q^{61} +(-2.81220 - 2.04319i) q^{62} +(-5.65953 + 12.6866i) q^{63} +(-1.07480 + 3.30788i) q^{64} -2.46912 q^{65} +(2.12130 - 1.51241i) q^{66} -7.19080 q^{67} +(0.835601 - 2.57172i) q^{68} +(9.71387 - 1.01738i) q^{69} +(1.69896 + 1.23437i) q^{70} +(-6.97057 + 2.26487i) q^{71} +(3.45708 - 3.83384i) q^{72} +(-3.93323 + 5.41362i) q^{73} +(-0.179693 + 0.130555i) q^{74} +(1.15850 + 1.28759i) q^{75} -4.83896i q^{76} +(3.06405 + 15.0491i) q^{77} +(1.67932 + 0.970371i) q^{78} +(3.68901 + 1.19863i) q^{79} +(1.65065 + 2.27192i) q^{80} +(8.22725 - 3.64861i) q^{81} +(1.18306 + 3.64109i) q^{82} +(-1.83123 - 5.63595i) q^{83} +(5.84861 + 13.1491i) q^{84} +(-0.885798 - 1.21920i) q^{85} +(-1.08616 - 0.352916i) q^{86} +(-0.496039 + 0.858440i) q^{87} +(0.645247 - 5.67059i) q^{88} -3.19518i q^{89} +(-0.281901 - 1.33102i) q^{90} +(-9.24982 + 6.72039i) q^{91} +(5.94731 - 8.18577i) q^{92} +(-12.9846 - 2.76492i) q^{93} +(1.44495 - 0.469491i) q^{94} +(-2.18177 - 1.58515i) q^{95} +(-0.850704 - 8.12244i) q^{96} +(-0.622669 + 1.91638i) q^{97} +6.54972 q^{98} +(5.05496 - 8.57015i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) $ 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9	$ 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9} + 8 q^{12} + 6 q^{15} + 32 q^{16} - 30 q^{18} - 100 q^{19} - 82 q^{22} + 100 q^{24} + 12 q^{25} + 14 q^{27} + 30 q^{28} + 10 q^{30} + 10 q^{31} - 46 q^{33} - 28 q^{34} + 14 q^{36} + 6 q^{37} - 50 q^{40} - 52 q^{42} + 32 q^{45} + 20 q^{46} - 80 q^{48} - 26 q^{49} - 30 q^{51} + 40 q^{52} + 6 q^{55} - 70 q^{57} + 92 q^{58} + 44 q^{60} + 70 q^{61} - 20 q^{63} + 18 q^{64} + 76 q^{66} + 20 q^{67} + 42 q^{69} - 4 q^{70} - 80 q^{72} + 90 q^{73} - 6 q^{75} - 108 q^{78} - 100 q^{79} + 38 q^{81} - 34 q^{82} + 70 q^{84} + 20 q^{85} + 74 q^{88} + 20 q^{90} - 86 q^{91} + 76 q^{93} + 10 q^{94} - 30 q^{96} + 6 q^{97} - 28 q^{99}+O(q^{100}) $ 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9 + 8 * q^12 + 6 * q^15 + 32 * q^16 - 30 * q^18 - 100 * q^19 - 82 * q^22 + 100 * q^24 + 12 * q^25 + 14 * q^27 + 30 * q^28 + 10 * q^30 + 10 * q^31 - 46 * q^33 - 28 * q^34 + 14 * q^36 + 6 * q^37 - 50 * q^40 - 52 * q^42 + 32 * q^45 + 20 * q^46 - 80 * q^48 - 26 * q^49 - 30 * q^51 + 40 * q^52 + 6 * q^55 - 70 * q^57 + 92 * q^58 + 44 * q^60 + 70 * q^61 - 20 * q^63 + 18 * q^64 + 76 * q^66 + 20 * q^67 + 42 * q^69 - 4 * q^70 - 80 * q^72 + 90 * q^73 - 6 * q^75 - 108 * q^78 - 100 * q^79 + 38 * q^81 - 34 * q^82 + 70 * q^84 + 20 * q^85 + 74 * q^88 + 20 * q^90 - 86 * q^91 + 76 * q^93 + 10 * q^94 - 30 * q^96 + 6 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$1$

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 $

$2$	−0.140144	+	0.431318i	−0.0990965	+	0.304988i	−0.988300	−	0.152525i	$-0.951260\pi$
$2$	−0.140144	+	0.431318i	−0.0990965	+	0.304988i	0.889203	+	0.457513i	$0.151260\pi$
$3$	0.180419	+	1.72263i	0.104165	+	0.994560i
$3$	0.180419	+	1.72263i	0.104165	+	0.994560i
$4$	1.45164	+	1.05468i	0.725820	+	0.527339i
$5$	0.951057	−	0.309017i	0.425325	−	0.138197i
$5$	0.951057	−	0.309017i	0.425325	−	0.138197i
$6$	−0.768285	−	0.163597i	−0.313651	−	0.0667883i
$7$	2.72178	−	3.74621i	1.02874	−	1.41593i	0.122843	−	0.992426i	$-0.460799\pi$
$7$	2.72178	−	3.74621i	1.02874	−	1.41593i	0.905893	−	0.423507i	$-0.139201\pi$
$8$	−1.39214	+	1.01145i	−0.492196	+	0.357602i
$9$	−2.93490	+	0.621591i	−0.978299	+	0.207197i
$10$			0.453514i			0.143414i
$11$	−2.24032	+	2.44560i	−0.675483	+	0.737376i
$11$	−2.24032	+	2.44560i	−0.675483	+	0.737376i
$12$	−1.55491	+	2.69092i	−0.448865	+	0.776801i
$13$	−2.34827	−	0.762999i	−0.651293	−	0.211618i	−0.0353085	−	0.999376i	$-0.511241\pi$
$13$	−2.34827	−	0.762999i	−0.651293	−	0.211618i	−0.615984	+	0.787759i	$0.711241\pi$
$14$	1.23437	+	1.69896i	0.329898	+	0.454066i
$15$	0.703911	+	1.58256i	0.181749	+	0.408616i
$16$	0.867797	+	2.67080i	0.216949	+	0.667701i
$17$	−0.465691	−	1.43325i	−0.112947	−	0.347614i	0.878567	−	0.477620i	$-0.158500\pi$
$17$	−0.465691	−	1.43325i	−0.112947	−	0.347614i	−0.991513	+	0.130006i	$0.958500\pi$
$18$	0.143204	−	1.35299i	0.0337535	−	0.318902i
$19$	−1.58515	−	2.18177i	−0.363658	−	0.500532i	0.587506	−	0.809220i	$-0.300110\pi$
$19$	−1.58515	−	2.18177i	−0.363658	−	0.500532i	−0.951163	+	0.308688i	$0.900110\pi$
$20$	1.70650	+	0.554477i	0.381586	+	0.123985i
$21$	6.94438	+	4.01272i	1.51539	+	0.875648i
$22$	−0.740863	−	1.30903i	−0.157953	−	0.279085i
$23$		−	5.63898i		−	1.17581i	−0.808930	−	0.587905i	$-0.799953\pi$
$23$		−	5.63898i		−	1.17581i	0.808930	−	0.587905i	$-0.200047\pi$
$24$	−1.99352	−	2.21566i	−0.406926	−	0.452269i
$25$	0.809017	−	0.587785i	0.161803	−	0.117557i
$26$	0.658190	−	0.905921i	0.129082	−	0.177666i
$27$	−1.60028	−	4.94359i	−0.307975	−	0.951395i
$28$	7.90208	−	2.56754i	1.49335	−	0.485220i
$29$	0.463093	+	0.336457i	0.0859942	+	0.0624784i	0.629952	−	0.776634i	$-0.283075\pi$
$29$	0.463093	+	0.336457i	0.0859942	+	0.0624784i	−0.543957	+	0.839113i	$0.683075\pi$
$30$	−0.781237	+	0.0818229i	−0.142634	+	0.0149387i
$31$	−2.36854	+	7.28961i	−0.425402	+	1.30925i	0.477207	+	0.878791i	$0.341649\pi$
$31$	−2.36854	+	7.28961i	−0.425402	+	1.30925i	−0.902609	+	0.430462i	$0.858351\pi$
$32$	−4.71514			−0.833528
$33$	−4.61705	−	3.41801i	−0.803726	−	0.594999i
$34$	0.683450			0.117211
$35$	1.43092	−	4.40393i	0.241870	−	0.744400i
$36$	−4.91599	−	2.19304i	−0.819332	−	0.365507i
$37$	0.396224	+	0.287874i	0.0651389	+	0.0473262i	0.619878	−	0.784698i	$-0.287182\pi$
$37$	0.396224	+	0.287874i	0.0651389	+	0.0473262i	−0.554739	+	0.832024i	$0.687182\pi$
$38$	1.16318	−	0.377941i	0.188693	−	0.0613102i
$39$	0.890690	−	4.18285i	0.142625	−	0.669793i
$40$	−1.01145	+	1.39214i	−0.159924	+	0.220117i
$41$	6.82953	−	4.96195i	1.06659	−	0.774926i	0.0912970	−	0.995824i	$-0.470899\pi$
$41$	6.82953	−	4.96195i	1.06659	−	0.774926i	0.975297	+	0.220898i	$0.0708988\pi$
$42$	−2.70397	+	2.43288i	−0.417232	+	0.375401i
$43$			2.51824i			0.384029i	0.981392	+	0.192014i	$0.0615020\pi$
$43$			2.51824i			0.384029i	−0.981392	+	0.192014i	$0.938498\pi$
$44$	−5.83146	+	1.18731i	−0.879125	+	0.178993i
$45$	−2.59917	+	1.49810i	−0.387462	+	0.223324i
$46$	2.43219	+	0.790268i	0.358607	+	0.116519i
$47$	−1.96912	−	2.71027i	−0.287226	−	0.395333i	0.640885	−	0.767637i	$-0.278568\pi$
$47$	−1.96912	−	2.71027i	−0.287226	−	0.395333i	−0.928111	+	0.372304i	$0.878568\pi$
$48$	−4.44424	+	1.97676i	−0.641470	+	0.285320i
$49$	−4.46287	−	13.7353i	−0.637552	−	1.96218i
$50$	0.140144	+	0.431318i	0.0198193	+	0.0609976i
$51$	2.38494	−	1.06080i	0.333958	−	0.148542i
$52$	−2.60412	−	3.58426i	−0.361127	−	0.497048i
$53$	12.6599	+	4.11346i	1.73898	+	0.565028i	0.994698	−	0.102842i	$-0.0327935\pi$
$53$	12.6599	+	4.11346i	1.73898	+	0.565028i	0.744279	+	0.667869i	$0.232793\pi$
$54$	2.35653	+	0.00258193i	0.320683	+	0.000351357i
$55$	−1.37494	+	3.01820i	−0.185397	+	0.406974i
$56$			7.96819i			1.06479i
$57$	3.47238	−	3.12425i	0.459929	−	0.413818i
$58$	−0.210019	+	0.152588i	−0.0275769	+	0.0200358i
$59$	−2.21091	+	3.04306i	−0.287837	+	0.396173i	−0.928310	−	0.371807i	$-0.878738\pi$
$59$	−2.21091	+	3.04306i	−0.287837	+	0.396173i	0.640473	+	0.767980i	$0.278738\pi$
$60$	−0.647271	+	3.03971i	−0.0835623	+	0.392425i
$61$	7.73467	−	2.51315i	0.990323	−	0.321776i	0.231331	−	0.972875i	$-0.425692\pi$
$61$	7.73467	−	2.51315i	0.990323	−	0.321776i	0.758992	+	0.651099i	$0.225692\pi$
$62$	−2.81220	−	2.04319i	−0.357150	−	0.259485i
$63$	−5.65953	+	12.6866i	−0.713034	+	1.59836i
$64$	−1.07480	+	3.30788i	−0.134350	+	0.413485i
$65$	−2.46912			−0.306256
$66$	2.12130	−	1.51241i	0.261114	−	0.186164i
$67$	−7.19080			−0.878496			−0.439248	−	0.898366i	$-0.644755\pi$
$67$	−7.19080			−0.878496			−0.439248	+	0.898366i	$0.644755\pi$
$68$	0.835601	−	2.57172i	0.101332	−	0.311866i
$69$	9.71387	−	1.01738i	1.16941	−	0.122478i
$70$	1.69896	+	1.23437i	0.203064	+	0.147535i
$71$	−6.97057	+	2.26487i	−0.827254	+	0.268791i	−0.691888	−	0.722005i	$-0.743221\pi$
$71$	−6.97057	+	2.26487i	−0.827254	+	0.268791i	−0.135366	+	0.990796i	$0.543221\pi$
$72$	3.45708	−	3.83384i	0.407421	−	0.451823i
$73$	−3.93323	+	5.41362i	−0.460349	+	0.633617i	−0.974581	−	0.224035i	$-0.928077\pi$
$73$	−3.93323	+	5.41362i	−0.460349	+	0.633617i	0.514232	+	0.857651i	$0.328077\pi$
$74$	−0.179693	+	0.130555i	−0.0208889	+	0.0151767i
$75$	1.15850	+	1.28759i	0.133772	+	0.148678i
$76$		−	4.83896i		−	0.555067i
$77$	3.06405	+	15.0491i	0.349181	+	1.71500i
$78$	1.67932	+	0.970371i	0.190145	+	0.109873i
$79$	3.68901	+	1.19863i	0.415047	+	0.134857i	0.509094	−	0.860711i	$-0.329981\pi$
$79$	3.68901	+	1.19863i	0.415047	+	0.134857i	−0.0940474	+	0.995568i	$0.529981\pi$
$80$	1.65065	+	2.27192i	0.184548	+	0.254009i
$81$	8.22725	−	3.64861i	0.914139	−	0.405402i
$82$	1.18306	+	3.64109i	0.130647	+	0.402091i
$83$	−1.83123	−	5.63595i	−0.201004	−	0.618626i	−0.999854	−	0.0170958i	$-0.994558\pi$
$83$	−1.83123	−	5.63595i	−0.201004	−	0.618626i	0.798850	−	0.601530i	$-0.205442\pi$
$84$	5.84861	+	13.1491i	0.638136	+	1.43469i
$85$	−0.885798	−	1.21920i	−0.0960782	−	0.132240i
$86$	−1.08616	−	0.352916i	−0.117124	−	0.0380559i
$87$	−0.496039	+	0.858440i	−0.0531809	+	0.0920344i
$88$	0.645247	−	5.67059i	0.0687836	−	0.604487i
$89$		−	3.19518i		−	0.338688i	−0.985557	−	0.169344i	$-0.945835\pi$
$89$		−	3.19518i		−	0.338688i	0.985557	−	0.169344i	$-0.0541650\pi$
$90$	−0.281901	−	1.33102i	−0.0297149	−	0.140302i
$91$	−9.24982	+	6.72039i	−0.969644	+	0.704488i
$92$	5.94731	−	8.18577i	0.620050	−	0.853425i
$93$	−12.9846	−	2.76492i	−1.34644	−	0.286709i
$94$	1.44495	−	0.469491i	0.149035	−	0.0484243i
$95$	−2.18177	−	1.58515i	−0.223845	−	0.162633i
$96$	−0.850704	−	8.12244i	−0.0868246	−	0.828993i
$97$	−0.622669	+	1.91638i	−0.0632224	+	0.194579i	−0.977678	−	0.210107i	$-0.932619\pi$
$97$	−0.622669	+	1.91638i	−0.0632224	+	0.194579i	0.914456	+	0.404685i	$0.132619\pi$
$98$	6.54972			0.661622
$99$	5.05496	−	8.57015i	0.508042	−	0.861332i
$100$	1.79432			0.179432
$101$	−3.85644	+	11.8689i	−0.383730	+	1.18100i	0.553667	+	0.832738i	$0.313228\pi$
$101$	−3.85644	+	11.8689i	−0.383730	+	1.18100i	−0.937397	+	0.348262i	$0.886772\pi$
$102$	0.123308	+	1.17733i	0.0122093	+	0.116573i
$103$	1.89303	+	1.37537i	0.186526	+	0.135519i	0.677130	−	0.735864i	$-0.263224\pi$
$103$	1.89303	+	1.37537i	0.186526	+	0.135519i	−0.490604	+	0.871383i	$0.663224\pi$
$104$	4.04086	−	1.31295i	0.396239	−	0.128746i
$105$	7.84450	+	1.67039i	0.765545	+	0.163014i
$106$	−3.54842	+	4.88398i	−0.344653	+	0.474374i
$107$	−14.6054	+	10.6114i	−1.41196	+	1.02585i	−0.418923	+	0.908022i	$0.637592\pi$
$107$	−14.6054	+	10.6114i	−1.41196	+	1.02585i	−0.993034	+	0.117826i	$0.962408\pi$
$108$	2.89086	−	8.86409i	0.278173	−	0.852948i
$109$			19.0666i			1.82625i	0.407679	+	0.913126i	$0.366338\pi$
$109$			19.0666i			1.82625i	−0.407679	+	0.913126i	$0.633662\pi$
$110$	−1.10911	−	1.01602i	−0.105750	−	0.0968736i
$111$	−0.424413	+	0.734485i	−0.0402835	+	0.0697143i
$112$	12.3673	+	4.01839i	1.16860	+	0.379702i
$113$	−1.01840	−	1.40170i	−0.0958027	−	0.131861i	0.758425	−	0.651761i	$-0.225969\pi$
$113$	−1.01840	−	1.40170i	−0.0958027	−	0.131861i	−0.854227	+	0.519900i	$0.825969\pi$
$114$	0.860914	+	1.93555i	0.0806320	+	0.181281i
$115$	−1.74254	−	5.36299i	−0.162493	−	0.500101i
$116$	0.317390	+	0.976827i	0.0294690	+	0.0906961i
$117$	7.36620	+	0.779659i	0.681006	+	0.0720795i
$118$	−1.00268	−	1.38007i	−0.0923044	−	0.127046i
$119$	−6.63676	−	2.15641i	−0.608391	−	0.197678i
$120$	−2.58063	−	1.49118i	−0.235578	−	0.136126i
$121$	−0.961900	−	10.9579i	−0.0874455	−	0.996169i
$122$			3.68831i			0.333923i
$123$	9.77977	+	10.8695i	0.881812	+	0.980071i
$124$	−11.1265	+	8.08384i	−0.999185	+	0.725950i
$125$	0.587785	−	0.809017i	0.0525731	−	0.0723607i
$126$	−4.67880	−	4.21900i	−0.416820	−	0.375858i
$127$	−10.1051	+	3.28335i	−0.896683	+	0.291350i	−0.720867	−	0.693073i	$-0.756256\pi$
$127$	−10.1051	+	3.28335i	−0.896683	+	0.291350i	−0.175815	+	0.984423i	$0.556256\pi$
$128$	−8.90539	−	6.47014i	−0.787132	−	0.571885i
$129$	−4.33800	+	0.454340i	−0.381940	+	0.0400024i
$130$	0.346031	−	1.06497i	0.0303489	−	0.0934044i
$131$	3.21711			0.281081			0.140540	−	0.990075i	$-0.455116\pi$
$131$	3.21711			0.281081			0.140540	+	0.990075i	$0.455116\pi$
$132$	−3.09740	−	9.83122i	−0.269594	−	0.855698i
$133$	−12.4878			−1.08283
$134$	1.00775	−	3.10152i	0.0870559	−	0.267931i
$135$	−3.04961	−	4.20712i	−0.262469	−	0.362091i
$136$	2.09797	+	1.52426i	0.179899	+	0.130705i
$137$	15.1500	−	4.92255i	1.29436	−	0.420562i	0.420742	−	0.907181i	$-0.361770\pi$
$137$	15.1500	−	4.92255i	1.29436	−	0.420562i	0.873614	+	0.486619i	$0.161770\pi$
$138$	−0.922522	+	4.33235i	−0.0785303	+	0.368794i
$139$	6.56849	−	9.04075i	0.557132	−	0.766827i	−0.433826	−	0.900997i	$-0.642837\pi$
$139$	6.56849	−	9.04075i	0.557132	−	0.766827i	0.990958	+	0.134170i	$0.0428368\pi$
$140$	6.72191	−	4.88375i	0.568105	−	0.412753i
$141$	4.31351	−	3.88105i	0.363263	−	0.326844i
$142$		−	3.32394i		−	0.278939i
$143$	7.12687	−	4.03356i	0.595979	−	0.337303i
$144$	−4.20704	−	7.29912i	−0.350587	−	0.608260i
$145$	0.544398	+	0.176886i	0.0452098	+	0.0146896i
$146$	−1.78378	−	2.45516i	−0.147626	−	0.203190i
$147$	22.8556	−	10.1660i	1.88510	−	0.838475i
$148$	0.271561	+	0.835778i	0.0223221	+	0.0687005i
$149$	−5.22728	−	16.0879i	−0.428236	−	1.31797i	−0.899862	−	0.436175i	$-0.856333\pi$
$149$	−5.22728	−	16.0879i	−0.428236	−	1.31797i	0.471626	−	0.881799i	$-0.343667\pi$
$150$	−0.717716	+	0.319234i	−0.0586013	+	0.0260653i
$151$	−11.3593	−	15.6347i	−0.924405	−	1.27233i	−0.962002	−	0.273041i	$-0.911970\pi$
$151$	−11.3593	−	15.6347i	−0.924405	−	1.27233i	0.0375975	−	0.999293i	$-0.488030\pi$
$152$	4.41350	+	1.43403i	0.357982	+	0.116315i
$153$	2.25765	+	3.91697i	0.182520	+	0.316669i
$154$	−6.92035	−	0.787455i	−0.557658	−	0.0634549i
$155$			7.66475i			0.615648i
$156$	5.70452	−	5.13260i	0.456727	−	0.410937i
$157$	4.25532	−	3.09167i	0.339611	−	0.246742i	−0.404887	−	0.914367i	$-0.632689\pi$
$157$	4.25532	−	3.09167i	0.339611	−	0.246742i	0.744498	+	0.667625i	$0.232689\pi$
$158$	−1.03398	+	1.42316i	−0.0822594	+	0.113220i
$159$	−4.80187	+	22.5505i	−0.380813	+	1.78837i
$160$	−4.48437	+	1.45706i	−0.354520	+	0.115191i
$161$	−21.1248	−	15.3481i	−1.66487	−	1.20960i
$162$	0.420716	+	4.05989i	0.0330546	+	0.318975i
$163$	−5.41702	+	16.6719i	−0.424294	+	1.30584i	0.479375	+	0.877610i	$0.340863\pi$
$163$	−5.41702	+	16.6719i	−0.424294	+	1.30584i	−0.903669	+	0.428232i	$0.859137\pi$
$164$	15.1473			1.18280
$165$	−5.44730	−	1.82397i	−0.424072	−	0.141996i
$166$	2.68752			0.208592
$167$	0.269161	−	0.828392i	0.0208283	−	0.0641029i	−0.940102	−	0.340893i	$-0.889271\pi$
$167$	0.269161	−	0.828392i	0.0208283	−	0.0641029i	0.960930	+	0.276790i	$0.0892706\pi$
$168$	−13.7262	+	1.43762i	−1.05900	+	0.110915i
$169$	−5.58502	−	4.05776i	−0.429617	−	0.312135i
$170$	0.650000	−	0.211198i	0.0498527	−	0.0161981i
$171$	6.00841	+	5.41795i	0.459475	+	0.414321i
$172$	−2.65594	+	3.65558i	−0.202513	+	0.278736i
$173$	13.1394	−	9.54634i	0.998971	−	0.725795i	0.0371035	−	0.999311i	$-0.488187\pi$
$173$	13.1394	−	9.54634i	0.998971	−	0.725795i	0.961867	+	0.273517i	$0.0881869\pi$
$174$	−0.300744	−	0.334255i	−0.0227993	−	0.0253398i
$175$		−	4.63057i		−	0.350038i
$176$	−8.47586	−	3.86118i	−0.638892	−	0.291048i
$177$	−5.64096	−	3.25956i	−0.424000	−	0.245003i
$178$	1.37814	+	0.447784i	0.103296	+	0.0335629i
$179$	10.9962	+	15.1350i	0.821894	+	1.13124i	0.989378	+	0.145365i	$0.0464356\pi$
$179$	10.9962	+	15.1350i	0.821894	+	1.13124i	−0.167484	+	0.985875i	$0.553564\pi$
$180$	−5.35307	−	0.566584i	−0.398994	−	0.0422307i
$181$	2.57484	+	7.92454i	0.191386	+	0.589027i	1.00000		0.000686228i	$0.000218433\pi$
$181$	2.57484	+	7.92454i	0.191386	+	0.589027i	−0.808613	+	0.588340i	$0.799782\pi$
$182$	−1.60232	−	4.93143i	−0.118772	−	0.365542i
$183$	5.72471	+	12.8705i	0.423182	+	0.951418i
$184$	5.70355	+	7.85026i	0.420471	+	0.578729i
$185$	0.465790	+	0.151344i	0.0342455	+	0.0111270i
$186$	3.01227	−	5.21301i	0.220871	−	0.382237i
$187$	4.54845	+	2.07205i	0.332616	+	0.151523i
$188$		−	6.01112i		−	0.438406i
$189$	−22.8753	−	7.46036i	−1.66394	−	0.542662i
$190$	0.989464	−	0.718887i	0.0717832	−	0.0521536i
$191$	−11.9113	+	16.3946i	−0.861874	+	1.18627i	0.119245	+	0.992865i	$0.461953\pi$
$191$	−11.9113	+	16.3946i	−0.861874	+	1.18627i	−0.981119	+	0.193403i	$0.938047\pi$
$192$	−5.89217	−	1.25467i	−0.425231	−	0.0905479i
$193$	7.08949	−	2.30351i	0.510312	−	0.165811i	−0.0425319	−	0.999095i	$-0.513542\pi$
$193$	7.08949	−	2.30351i	0.510312	−	0.165811i	0.552844	+	0.833285i	$0.313542\pi$
$194$	−0.739305	−	0.537136i	−0.0530790	−	0.0385641i
$195$	−0.445477	−	4.25337i	−0.0319012	−	0.304590i
$196$	8.00783	−	24.6456i	0.571988	−	1.76040i
$197$	−13.6689			−0.973868			−0.486934	−	0.873439i	$-0.661885\pi$
$197$	−13.6689			−0.973868			−0.486934	+	0.873439i	$0.661885\pi$
$198$	2.98804	+	3.38135i	0.212351	+	0.240302i
$199$	11.7105			0.830133			0.415067	−	0.909791i	$-0.363758\pi$
$199$	11.7105			0.830133			0.415067	+	0.909791i	$0.363758\pi$
$200$	−0.531751	+	1.63656i	−0.0376004	+	0.115722i
$201$	−1.29736	−	12.3871i	−0.0915088	−	0.873717i
$202$	−4.57881	−	3.32670i	−0.322164	−	0.234066i
$203$	2.52087	−	0.819081i	0.176930	−	0.0574882i
$204$	4.58087	+	0.975443i	0.320725	+	0.0682947i
$205$	4.96195	−	6.82953i	0.346557	−	0.476995i
$206$	−0.858518	+	0.623750i	−0.0598158	+	0.0434587i
$207$	3.50514	+	16.5498i	0.243624	+	1.15029i
$208$		−	6.93389i		−	0.480779i
$209$	8.88697	+	1.01123i	0.614725	+	0.0699485i
$210$	−1.81983	+	3.14938i	−0.125580	+	0.217328i
$211$	−3.66580	−	1.19109i	−0.252364	−	0.0819982i	0.180103	−	0.983648i	$-0.442357\pi$
$211$	−3.66580	−	1.19109i	−0.252364	−	0.0819982i	−0.432467	+	0.901650i	$0.642357\pi$
$212$	14.0393	+	19.3234i	0.964222	+	1.32714i
$213$	−5.15916	−	11.5991i	−0.353500	−	0.794755i
$214$	−2.53005	−	7.78670i	−0.172951	−	0.532288i
$215$	0.778180	+	2.39499i	0.0530715	+	0.163337i
$216$	7.22802	+	5.26357i	0.491804	+	0.358141i
$217$	20.8618	+	28.7137i	1.41619	+	1.94922i
$218$	−8.22377	−	2.67207i	−0.556984	−	0.180975i
$219$	−10.0353	−	5.79877i	−0.678122	−	0.391844i
$220$	−5.17915	+	2.93122i	−0.349178	+	0.197623i
$221$			3.72098i			0.250300i
$222$	−0.257318	−	0.285990i	−0.0172700	−	0.0191944i
$223$	18.9238	−	13.7489i	1.26723	−	0.920698i	0.268143	−	0.963379i	$-0.413590\pi$
$223$	18.9238	−	13.7489i	1.26723	−	0.920698i	0.999089	+	0.0426814i	$0.0135900\pi$
$224$	−12.8336	+	17.6639i	−0.857479	+	1.18022i
$225$	−2.00902	+	2.22797i	−0.133935	+	0.148531i
$226$	0.747302	−	0.242813i	0.0497098	−	0.0161517i
$227$	−5.59908	−	4.06797i	−0.371624	−	0.270001i	0.386260	−	0.922390i	$-0.373767\pi$
$227$	−5.59908	−	4.06797i	−0.371624	−	0.270001i	−0.757884	+	0.652389i	$0.773767\pi$
$228$	8.33573	−	0.873043i	0.552047	−	0.0578187i
$229$	−0.201744	+	0.620905i	−0.0133316	+	0.0410306i	−0.957501	−	0.288430i	$-0.906867\pi$
$229$	−0.201744	+	0.620905i	−0.0133316	+	0.0410306i	0.944169	+	0.329460i	$0.106867\pi$
$230$	2.55736			0.168627
$231$	−25.3712	+	7.99337i	−1.66930	+	0.525925i
$232$	−0.984999			−0.0646684
$233$	−5.70562	+	17.5601i	−0.373788	+	1.15040i	0.570505	+	0.821294i	$0.306747\pi$
$233$	−5.70562	+	17.5601i	−0.373788	+	1.15040i	−0.944293	+	0.329106i	$0.893253\pi$
$234$	−1.36861	+	3.06791i	−0.0894687	+	0.200556i
$235$	−2.71027	−	1.96912i	−0.176798	−	0.128451i
$236$	−6.41890	+	2.08563i	−0.417835	+	0.135763i
$237$	−1.39923	+	6.57106i	−0.0908898	+	0.426836i
$238$	1.86020	−	2.56035i	0.120579	−	0.165963i
$239$	−0.484930	+	0.352322i	−0.0313675	+	0.0227898i	−0.603359	−	0.797470i	$-0.706171\pi$
$239$	−0.484930	+	0.352322i	−0.0313675	+	0.0227898i	0.571991	+	0.820260i	$0.306171\pi$
$240$	−3.61587	+	3.25335i	−0.233403	+	0.210003i
$241$		−	3.10234i		−	0.199839i	−0.994996	−	0.0999195i	$-0.968141\pi$
$241$		−	3.10234i		−	0.199839i	0.994996	−	0.0999195i	$-0.0318585\pi$
$242$	4.86113	+	1.12079i	0.312485	+	0.0720471i
$243$	7.76956	+	13.5142i	0.498418	+	0.866937i
$244$	13.8785	+	4.50940i	0.888481	+	0.288685i
$245$	−8.48888	−	11.6839i	−0.542334	−	0.746459i
$246$	−6.05879	+	2.69490i	−0.386294	+	0.171820i
$247$	2.05767	+	6.33284i	0.130926	+	0.402949i
$248$	−4.07574	−	12.5438i	−0.258809	−	0.796534i
$249$	9.37826	−	4.17137i	0.594323	−	0.264350i
$250$	0.266569	+	0.366901i	0.0168593	+	0.0232049i
$251$	25.4210	+	8.25979i	1.60456	+	0.521353i	0.968230	−	0.250063i	$-0.0804513\pi$
$251$	25.4210	+	8.25979i	1.60456	+	0.521353i	0.636331	+	0.771416i	$0.280451\pi$
$252$	−21.5958	+	12.4473i	−1.36041	+	0.784108i
$253$	13.7907	+	12.6331i	0.867013	+	0.794239i
$254$		−	4.81865i		−	0.302349i
$255$	1.94041	−	1.74587i	0.121513	−	0.109330i
$256$	−1.58898	+	1.15446i	−0.0993115	+	0.0721540i
$257$	−7.94749	+	10.9388i	−0.495751	+	0.682343i	−0.981436	−	0.191791i	$-0.938570\pi$
$257$	−7.94749	+	10.9388i	−0.495751	+	0.682343i	0.485685	+	0.874134i	$0.338570\pi$
$258$	0.411978	−	1.93473i	0.0256486	−	0.120451i
$259$	2.15687	−	0.700809i	0.134021	−	0.0435462i
$260$	−3.58426	−	2.60412i	−0.222287	−	0.161501i
$261$	−1.56827	−	0.699611i	−0.0970734	−	0.0433048i
$262$	−0.450858	+	1.38760i	−0.0278541	+	0.0857262i
$263$	6.67606			0.411664			0.205832	−	0.978587i	$-0.434010\pi$
$263$	6.67606			0.411664			0.205832	+	0.978587i	$0.434010\pi$
$264$	9.88474	+	0.0884356i	0.608364	+	0.00544283i
$265$	13.3114			0.817716
$266$	1.75008	−	5.38620i	0.107304	−	0.330249i
$267$	5.50411	−	0.576473i	0.336846	−	0.0352796i
$268$	−10.4384	−	7.58398i	−0.637630	−	0.463265i
$269$	17.3312	−	5.63123i	1.05670	−	0.343342i	0.271405	−	0.962465i	$-0.412512\pi$
$269$	17.3312	−	5.63123i	1.05670	−	0.343342i	0.785294	+	0.619123i	$0.212512\pi$
$270$	2.24199	−	0.725752i	0.136443	−	0.0441679i
$271$	−0.952566	+	1.31109i	−0.0578643	+	0.0796433i	−0.836968	−	0.547251i	$-0.815674\pi$
$271$	−0.952566	+	1.31109i	−0.0578643	+	0.0796433i	0.779104	+	0.626894i	$0.215674\pi$
$272$	3.42381	−	2.48754i	0.207599	−	0.150829i
$273$	−13.2456	−	14.7215i	−0.801659	−	0.890986i
$274$			7.22435i			0.436439i
$275$	−0.374973	+	3.29536i	−0.0226117	+	0.198718i
$276$	15.1740	+	8.76813i	0.913370	+	0.527779i
$277$	−22.7632	−	7.39621i	−1.36771	−	0.444395i	−0.469098	−	0.883146i	$-0.655421\pi$
$277$	−22.7632	−	7.39621i	−1.36771	−	0.444395i	−0.898609	+	0.438751i	$0.855421\pi$
$278$	2.97891	+	4.10011i	0.178663	+	0.245908i
$279$	2.42026	−	22.8665i	0.144897	−	1.36898i
$280$	2.46231	+	7.57820i	0.147151	+	0.452884i
$281$	5.75748	+	17.7197i	0.343462	+	1.05707i	0.962402	+	0.271630i	$0.0875627\pi$
$281$	5.75748	+	17.7197i	0.343462	+	1.05707i	−0.618939	+	0.785439i	$0.712437\pi$
$282$	1.06946	+	2.40440i	0.0636852	+	0.143180i
$283$	−11.7112	−	16.1191i	−0.696158	−	0.958179i	−0.999985	−	0.00545200i	$-0.998265\pi$
$283$	−11.7112	−	16.1191i	−0.696158	−	0.958179i	0.303827	−	0.952727i	$-0.401735\pi$
$284$	−12.5075	−	4.06392i	−0.742181	−	0.241149i
$285$	2.33699	−	4.04437i	0.138431	−	0.239568i
$286$	0.740960	+	3.63922i	0.0438139	+	0.215192i
$287$		−	39.0902i		−	2.30742i
$288$	13.8385	−	2.93089i	0.815439	−	0.172705i
$289$	11.9160	−	8.65744i	0.700938	−	0.509261i
$290$	−0.152588	+	0.210019i	−0.00896027	+	0.0123328i
$291$	−3.41355	−	0.726875i	−0.200106	−	0.0426102i
$292$	−11.4193	+	3.71034i	−0.668261	+	0.217131i
$293$	16.9197	+	12.2929i	0.988459	+	0.718158i	0.959583	−	0.281425i	$-0.0908071\pi$
$293$	16.9197	+	12.2929i	0.988459	+	0.718158i	0.0288762	+	0.999583i	$0.490807\pi$
$294$	1.18170	+	11.2827i	0.0689180	+	0.658022i
$295$	−1.16235	+	3.57734i	−0.0676744	+	0.208281i
$296$	−0.842770			−0.0489850
$297$	15.6752	+	7.16159i	0.909567	+	0.415558i
$298$	7.67158			0.444403
$299$	−4.30254	+	13.2418i	−0.248822	+	0.765796i
$300$	0.323731	+	3.09095i	0.0186906	+	0.178456i
$301$	9.43386	+	6.85410i	0.543759	+	0.395064i
$302$	8.33546	−	2.70835i	0.479652	−	0.155848i
$303$	−21.1415	−	4.50183i	−1.21455	−	0.258623i
$304$	4.45149	−	6.12695i	0.255310	−	0.351405i
$305$	6.57951	−	4.78029i	0.376741	−	0.273719i
$306$	−2.00586	+	0.424827i	−0.114667	+	0.0242857i
$307$		−	16.5273i		−	0.943264i	−0.881795	−	0.471632i	$-0.843665\pi$
$307$		−	16.5273i		−	0.943264i	0.881795	−	0.471632i	$-0.156335\pi$
$308$	−11.4240	+	25.0774i	−0.650945	+	1.42892i
$309$	−2.02771	+	3.50914i	−0.115352	+	0.199628i
$310$	−3.30594	−	1.07417i	−0.187765	−	0.0610085i
$311$	−0.466958	−	0.642713i	−0.0264788	−	0.0364449i	0.795572	−	0.605859i	$-0.207170\pi$
$311$	−0.466958	−	0.642713i	−0.0264788	−	0.0364449i	−0.822051	+	0.569414i	$0.807170\pi$
$312$	2.99078	+	6.72401i	0.169320	+	0.380672i
$313$	0.394809	+	1.21510i	0.0223159	+	0.0686814i	0.961594	−	0.274475i	$-0.0885040\pi$
$313$	0.394809	+	1.21510i	0.0223159	+	0.0686814i	−0.939278	+	0.343156i	$0.888504\pi$
$314$	0.737136	+	2.26867i	0.0415990	+	0.128029i
$315$	−1.46217	+	13.8145i	−0.0823839	+	0.778361i
$316$	4.09095	+	5.63070i	0.230134	+	0.316752i
$317$	−13.3749	−	4.34577i	−0.751210	−	0.244083i	−0.0917080	−	0.995786i	$-0.529233\pi$
$317$	−13.3749	−	4.34577i	−0.751210	−	0.244083i	−0.659502	+	0.751703i	$0.729233\pi$
$318$	−9.05349	−	5.23145i	−0.507695	−	0.293365i
$319$	−1.86032	+	0.378767i	−0.104158	+	0.0212069i
$320$			3.47811i			0.194432i
$321$	−20.9147	−	23.2452i	−1.16734	−	1.29742i
$322$	9.58040	−	6.96057i	0.533895	−	0.387897i
$323$	−2.38883	+	3.28794i	−0.132918	+	0.182946i
$324$	15.7911	+	3.38062i	0.877284	+	0.187812i
$325$	−2.34827	+	0.762999i	−0.130259	+	0.0423236i
$326$	−6.43172	−	4.67292i	−0.356220	−	0.258809i
$327$	−32.8447	+	3.43999i	−1.81632	+	0.190232i
$328$	−4.48892	+	13.8155i	−0.247859	+	0.762831i
$329$	−15.5127			−0.855244
$330$	1.55012	−	2.09390i	0.0853312	−	0.115265i
$331$	6.38930			0.351188			0.175594	−	0.984463i	$-0.443815\pi$
$331$	6.38930			0.351188			0.175594	+	0.984463i	$0.443815\pi$
$332$	3.28582	−	10.1127i	0.180333	−	0.555008i
$333$	−1.34182	−	0.598590i	−0.0735311	−	0.0328026i
$334$	0.319579	+	0.232188i	0.0174866	+	0.0127047i
$335$	−6.83886	+	2.22208i	−0.373647	+	0.121405i
$336$	−4.69089	+	22.0293i	−0.255909	+	1.20180i
$337$	4.07913	−	5.61443i	0.222204	−	0.305838i	−0.683331	−	0.730108i	$-0.739470\pi$
$337$	4.07913	−	5.61443i	0.222204	−	0.305838i	0.905535	+	0.424271i	$0.139470\pi$
$338$	2.53289	−	1.84025i	0.137771	−	0.100096i
$339$	2.23087	−	2.00721i	0.121164	−	0.109017i
$340$		−	2.70406i		−	0.146648i
$341$	−12.5212	−	22.1236i	−0.678059	−	1.19806i
$342$	−3.17890	+	1.83224i	−0.171895	+	0.0990765i
$343$	−32.7747	−	10.6491i	−1.76967	−	0.574999i
$344$	−2.54708	−	3.50575i	−0.137329	−	0.189017i
$345$	8.92405	−	3.96934i	0.480455	−	0.213702i
$346$	2.27610	+	7.00512i	0.122364	+	0.376598i
$347$	−0.0255237	−	0.0785538i	−0.00137018	−	0.00421699i	0.950369	−	0.311125i	$-0.100706\pi$
$347$	−0.0255237	−	0.0785538i	−0.00137018	−	0.00421699i	−0.951739	+	0.306908i	$0.900706\pi$
$348$	−1.62545	+	0.722984i	−0.0871331	+	0.0387560i
$349$	3.42615	+	4.71569i	0.183398	+	0.252425i	0.890810	−	0.454376i	$-0.150138\pi$
$349$	3.42615	+	4.71569i	0.183398	+	0.252425i	−0.707413	+	0.706801i	$0.750138\pi$
$350$	1.99725	+	0.648945i	0.106757	+	0.0346875i
$351$	−0.0140571	+	12.8299i	−0.000750312	+	0.684809i
$352$	10.5634	−	11.5313i	0.563034	−	0.614623i
$353$		−	7.24504i		−	0.385615i	−0.981237	−	0.192807i	$-0.938241\pi$
$353$		−	7.24504i		−	0.385615i	0.981237	−	0.192807i	$-0.0617593\pi$
$354$	2.19645	−	1.97624i	0.116740	−	0.105036i
$355$	−5.92952	+	4.30805i	−0.314706	+	0.228647i
$356$	3.36989	−	4.63825i	0.178604	−	0.245827i
$357$	2.51730	−	11.8217i	0.133230	−	0.625672i
$358$	−8.06902	+	2.62178i	−0.426461	+	0.138566i
$359$	−12.0084	−	8.72460i	−0.633778	−	0.460467i	0.223929	−	0.974605i	$-0.428112\pi$
$359$	−12.0084	−	8.72460i	−0.633778	−	0.460467i	−0.857707	+	0.514139i	$0.828112\pi$
$360$	2.10316	−	4.71450i	0.110846	−	0.248476i
$361$	3.62390	−	11.1532i	0.190732	−	0.587012i
$362$	−3.77884			−0.198612
$363$	18.7028	−	3.63401i	0.981641	−	0.190736i
$364$	−20.5152			−1.07529
$365$	−2.06782	+	6.36410i	−0.108235	+	0.333112i
$366$	−6.35358	+	0.665442i	−0.332107	+	0.0347832i
$367$	0.811381	+	0.589503i	0.0423538	+	0.0307718i	0.608761	−	0.793354i	$-0.291667\pi$
$367$	0.811381	+	0.589503i	0.0423538	+	0.0307718i	−0.566407	+	0.824126i	$0.691667\pi$
$368$	15.0606	−	4.89349i	0.785089	−	0.255091i
$369$	−16.9597	+	18.8080i	−0.882886	+	0.979105i
$370$	−0.130555	+	0.179693i	−0.00678723	+	0.00934182i
$371$	49.8674	−	36.2308i	2.58899	−	1.88101i
$372$	−15.9329	−	17.7083i	−0.826081	−	0.918130i
$373$			13.6417i			0.706340i	0.935559	+	0.353170i	$0.114896\pi$
$373$			13.6417i			0.706340i	−0.935559	+	0.353170i	$0.885104\pi$
$374$	−1.53115	+	1.67144i	−0.0791739	+	0.0864283i
$375$	1.49968	+	0.866573i	0.0774433	+	0.0447496i
$376$	5.48259	+	1.78140i	0.282743	+	0.0918688i
$377$	−0.830750	−	1.14343i	−0.0427858	−	0.0588896i
$378$	6.42362	−	8.82102i	0.330395	−	0.453704i
$379$	0.307672	+	0.946918i	0.0158041	+	0.0486399i	0.958648	−	0.284596i	$-0.0918594\pi$
$379$	0.307672	+	0.946918i	0.0158041	+	0.0486399i	−0.942843	+	0.333236i	$0.891859\pi$
$380$	−1.49532	−	4.60212i	−0.0767083	−	0.236084i
$381$	−7.47914	−	16.8150i	−0.383168	−	0.861456i
$382$	−5.40197	−	7.43517i	−0.276389	−	0.380416i
$383$	−34.7798	−	11.3006i	−1.77716	−	0.577435i	−0.778428	−	0.627733i	$-0.783983\pi$
$383$	−34.7798	−	11.3006i	−1.77716	−	0.577435i	−0.998734	+	0.0502982i	$0.983983\pi$
$384$	9.53895	−	16.5080i	0.486782	−	0.842421i
$385$	7.56451	+	13.3657i	0.385523	+	0.681179i
$386$			3.38065i			0.172070i
$387$	−1.56532	−	7.39079i	−0.0795696	−	0.375695i
$388$	−2.92505	+	2.12517i	−0.148497	+	0.107889i
$389$	10.7749	−	14.8303i	0.546308	−	0.751928i	−0.443198	−	0.896424i	$-0.646156\pi$
$389$	10.7749	−	14.8303i	0.546308	−	0.751928i	0.989505	+	0.144496i	$0.0461560\pi$
$390$	1.89698	+	0.403941i	0.0960576	+	0.0204543i
$391$	−8.08207	+	2.62602i	−0.408728	+	0.132804i
$392$	20.1055	+	14.6075i	1.01548	+	0.737790i
$393$	0.580430	+	5.54189i	0.0292788	+	0.279552i
$394$	1.91561	−	5.89564i	0.0965070	−	0.297018i
$395$	3.87886			0.195167
$396$	16.3767	−	7.10941i	0.822961	−	0.357261i
$397$	1.52698			0.0766371			0.0383185	−	0.999266i	$-0.487800\pi$
$397$	1.52698			0.0766371			0.0383185	+	0.999266i	$0.487800\pi$
$398$	−1.64115	+	5.05094i	−0.0822633	+	0.253181i
$399$	−2.25304	−	21.5118i	−0.112793	−	1.07694i
$400$	2.27192	+	1.65065i	0.113596	+	0.0825324i
$401$	11.6056	−	3.77088i	0.579555	−	0.188309i	−0.00454647	−	0.999990i	$-0.501447\pi$
$401$	11.6056	−	3.77088i	0.579555	−	0.188309i	0.584101	+	0.811681i	$0.301447\pi$
$402$	5.52459	+	1.17640i	0.275541	+	0.0586733i
$403$	11.1239	−	15.3108i	0.554122	−	0.762684i
$404$	−18.1160	+	13.1621i	−0.901306	+	0.654837i
$405$	6.69709	−	6.01240i	0.332781	−	0.298758i
$406$			1.20209i			0.0596585i
$407$	−1.59169	+	0.324075i	−0.0788974	+	0.0160638i
$408$	−2.24723	+	3.88903i	−0.111254	+	0.192536i
$409$	−5.27054	−	1.71250i	−0.260611	−	0.0846777i	0.175797	−	0.984426i	$-0.443750\pi$
$409$	−5.27054	−	1.71250i	−0.260611	−	0.0846777i	−0.436408	+	0.899749i	$0.643750\pi$
$410$	2.25031	+	3.09729i	0.111135	+	0.152964i
$411$	11.2131	+	25.2098i	0.553101	+	1.24351i
$412$	1.29743	+	3.99308i	0.0639198	+	0.196725i
$413$	5.38232	+	16.5651i	0.264847	+	0.815115i
$414$	−7.62946	−	0.807524i	−0.374968	−	0.0396876i
$415$	−3.48321	−	4.79423i	−0.170984	−	0.235339i
$416$	11.0724	+	3.59765i	0.542870	+	0.176389i
$417$	16.7589	+	9.68394i	0.820689	+	0.474225i
$418$	−1.68162	+	3.69139i	−0.0822505	+	0.180552i
$419$		−	17.0119i		−	0.831087i	−0.909573	−	0.415543i	$-0.863591\pi$
$419$		−	17.0119i		−	0.831087i	0.909573	−	0.415543i	$-0.136409\pi$
$420$	9.62566	+	10.6982i	0.469684	+	0.522020i
$421$	−15.0983	+	10.9696i	−0.735847	+	0.534624i	−0.891408	−	0.453202i	$-0.850282\pi$
$421$	−15.0983	+	10.9696i	−0.735847	+	0.534624i	0.155561	+	0.987826i	$0.450282\pi$
$422$	1.02748	−	1.41420i	0.0500169	−	0.0688423i
$423$	7.46385	+	6.73036i	0.362905	+	0.327241i
$424$	−21.7850	+	7.07837i	−1.05797	+	0.343756i
$425$	−1.21920	−	0.885798i	−0.0591397	−	0.0429675i
$426$	5.72591	−	0.599703i	0.277421	−	0.0290557i
$427$	11.6373	−	35.8159i	0.563168	−	1.73325i
$428$	−32.3934			−1.56580
$429$	8.23415	+	11.5492i	0.397548	+	0.557601i
$430$	−1.14206			−0.0550750
$431$	−2.01436	+	6.19956i	−0.0970283	+	0.298623i	−0.987777	−	0.155874i	$-0.950181\pi$
$431$	−2.01436	+	6.19956i	−0.0970283	+	0.298623i	0.890749	+	0.454496i	$0.150181\pi$
$432$	11.8146	−	8.56408i	0.568432	−	0.412039i
$433$	11.2188	+	8.15095i	0.539142	+	0.391710i	0.823766	−	0.566929i	$-0.191869\pi$
$433$	11.2188	+	8.15095i	0.539142	+	0.391710i	−0.284624	+	0.958639i	$0.591869\pi$
$434$	−15.3084	+	4.97400i	−0.734826	+	0.238760i
$435$	−0.206488	+	0.969709i	−0.00990035	+	0.0464940i
$436$	−20.1091	+	27.6779i	−0.963053	+	1.32553i
$437$	−12.3030	+	8.93862i	−0.588530	+	0.427592i
$438$	3.90749	−	3.51574i	0.186707	−	0.167989i
$439$		−	18.8386i		−	0.899117i	−0.893251	−	0.449558i	$-0.851581\pi$
$439$		−	18.8386i		−	0.899117i	0.893251	−	0.449558i	$-0.148419\pi$
$440$	−1.13864	−	5.59245i	−0.0542827	−	0.266609i
$441$	21.6358	+	37.5376i	1.03028	+	1.78750i
$442$	−1.60492	−	0.521472i	−0.0763385	−	0.0248039i
$443$	3.93907	+	5.42166i	0.187151	+	0.257591i	0.892274	−	0.451493i	$-0.149109\pi$
$443$	3.93907	+	5.42166i	0.187151	+	0.257591i	−0.705124	+	0.709084i	$0.749109\pi$
$444$	−1.39074	+	0.618589i	−0.0660016	+	0.0293569i
$445$	−0.987365	−	3.03880i	−0.0468056	−	0.144053i
$446$	3.27812	+	10.0890i	0.155223	+	0.477728i
$447$	26.7704	−	11.9072i	1.26620	−	0.563193i
$448$	9.46665	+	13.0297i	0.447257	+	0.615597i
$449$	22.2745	+	7.23741i	1.05120	+	0.341555i	0.783138	−	0.621848i	$-0.213618\pi$
$449$	22.2745	+	7.23741i	1.05120	+	0.341555i	0.268059	+	0.963402i	$0.413618\pi$
$450$	−0.679411	−	1.17876i	−0.0320277	−	0.0555674i
$451$	−3.16544	+	27.8187i	−0.149055	+	1.30993i
$452$		−	3.10885i		−	0.146228i
$453$	24.8834	−	22.3886i	1.16912	−	1.05191i
$454$	2.53926	−	1.84488i	0.119174	−	0.0865847i
$455$	−6.72039	+	9.24982i	−0.315057	+	0.433638i
$456$	−1.67402	+	7.86155i	−0.0783934	+	0.368151i
$457$	−31.5191	+	10.2412i	−1.47440	+	0.479062i	−0.932434	−	0.361339i	$-0.882320\pi$
$457$	−31.5191	+	10.2412i	−1.47440	+	0.479062i	−0.541966	+	0.840401i	$0.682320\pi$
$458$	−0.239534	−	0.174032i	−0.0111927	−	0.00813197i
$459$	−6.34017	+	4.59579i	−0.295934	+	0.214513i
$460$	3.12668	−	9.62295i	0.145782	−	0.448672i
$461$	24.1258			1.12365			0.561824	−	0.827257i	$-0.310100\pi$
$461$	24.1258			1.12365			0.561824	+	0.827257i	$0.310100\pi$
$462$	0.107926	−	12.0633i	0.00502118	−	0.561234i
$463$	21.5425			1.00117			0.500584	−	0.865688i	$-0.333119\pi$
$463$	21.5425			1.00117			0.500584	+	0.865688i	$0.333119\pi$
$464$	−0.496739	+	1.52881i	−0.0230605	+	0.0709730i
$465$	−13.2035	+	1.38287i	−0.612298	+	0.0641291i
$466$	−6.77438	−	4.92187i	−0.313817	−	0.228001i
$467$	2.27085	−	0.737843i	0.105082	−	0.0341433i	−0.256004	−	0.966676i	$-0.582406\pi$
$467$	2.27085	−	0.737843i	0.105082	−	0.0341433i	0.361086	+	0.932532i	$0.382406\pi$
$468$	9.87078	+	8.90075i	0.456277	+	0.411437i
$469$	−19.5718	+	26.9382i	−0.903740	+	1.24389i
$470$	1.22914	−	0.893026i	0.0566962	−	0.0411922i
$471$	6.09354	+	6.77253i	0.280775	+	0.312062i
$472$		−	6.47260i		−	0.297926i
$473$	−6.15861	−	5.64168i	−0.283173	−	0.259405i
$474$	−2.63812	−	1.52441i	−0.121173	−	0.0700183i
$475$	−2.56482	−	0.833361i	−0.117682	−	0.0382372i
$476$	−7.35986	−	10.1300i	−0.337339	−	0.464307i
$477$	−39.7125	−	4.20328i	−1.81831	−	0.192455i
$478$	−0.0840030	−	0.258535i	−0.00384221	−	0.0118251i
$479$	5.76419	+	17.7403i	0.263372	+	0.810577i	0.992064	+	0.125735i	$0.0401289\pi$
$479$	5.76419	+	17.7403i	0.263372	+	0.810577i	−0.728691	+	0.684842i	$0.759871\pi$
$480$	−3.31904	−	7.46202i	−0.151493	−	0.340593i
$481$	−0.710794	−	0.978324i	−0.0324094	−	0.0446077i
$482$	1.33809	+	0.434773i	0.0609485	+	0.0198034i
$483$	22.6277	−	39.1593i	1.02960	−	1.78181i
$484$	10.1607	−	16.9214i	0.461849	−	0.769153i
$485$			2.01500i			0.0914964i
$486$	−6.91778	+	1.45722i	−0.313797	+	0.0661009i
$487$	4.03161	−	2.92914i	0.182690	−	0.132732i	−0.492682	−	0.870210i	$-0.663983\pi$
$487$	4.03161	−	2.92914i	0.182690	−	0.132732i	0.675371	+	0.737478i	$0.263983\pi$
$488$	−8.22584	+	11.3219i	−0.372366	+	0.512518i
$489$	−29.6968	−	6.32358i	−1.34294	−	0.285962i
$490$	6.22915	−	2.02397i	0.281404	−	0.0914339i
$491$	3.19395	+	2.32054i	0.144141	+	0.104725i	0.657519	−	0.753438i	$-0.271606\pi$
$491$	3.19395	+	2.32054i	0.144141	+	0.104725i	−0.513378	+	0.858163i	$0.671606\pi$
$492$	2.73286	+	26.0931i	0.123207	+	1.17637i
$493$	0.266568	−	0.820413i	0.0120056	−	0.0369495i
$494$	−3.01984			−0.135869
$495$	2.15923	−	9.71276i	0.0970501	−	0.436556i
$496$	−21.5245			−0.966480
$497$	−10.4876	+	32.2777i	−0.470435	+	1.44785i
$498$	0.484881	+	4.62960i	0.0217281	+	0.207457i
$499$	5.50314	+	3.99827i	0.246354	+	0.178987i	0.704110	−	0.710091i	$-0.251346\pi$
$499$	5.50314	+	3.99827i	0.246354	+	0.178987i	−0.457755	+	0.889078i	$0.651346\pi$
$500$	1.70650	−	0.554477i	0.0763172	−	0.0247970i
$501$	1.47557	+	0.314206i	0.0659237	+	0.0140377i
$502$	−7.12519	+	9.80698i	−0.318013	+	0.437707i
$503$	−20.7847	+	15.1010i	−0.926745	+	0.673319i	−0.945194	−	0.326510i	$-0.894127\pi$
$503$	−20.7847	+	15.1010i	−0.926745	+	0.673319i	0.0184489	+	0.999830i	$0.494127\pi$
$504$	−4.95296	−	23.3858i	−0.220622	−	1.04169i
$505$			12.4797i			0.555339i
$506$	−7.38158	+	4.17771i	−0.328151	+	0.185722i
$507$	5.98236	−	10.3530i	0.265686	−	0.459794i
$508$	−18.1318	−	5.89139i	−0.804470	−	0.261388i
$509$	−9.25404	−	12.7371i	−0.410178	−	0.564562i	0.553084	−	0.833126i	$-0.313451\pi$
$509$	−9.25404	−	12.7371i	−0.410178	−	0.564562i	−0.963262	+	0.268564i	$0.913451\pi$
$510$	0.481088	+	1.08160i	0.0213029	+	0.0478942i
$511$	9.57518	+	29.4694i	0.423581	+	1.30365i
$512$	−7.07837	−	21.7850i	−0.312823	−	0.962769i
$513$	−8.24908	+	11.3278i	−0.364206	+	0.500133i
$514$	−3.60430	−	4.96090i	−0.158979	−	0.218816i
$515$	2.22539	+	0.723074i	0.0980625	+	0.0318625i
$516$	−6.77639	−	3.91565i	−0.298314	−	0.172377i
$517$	11.0397	+	1.25619i	0.485525	+	0.0552471i
$518$			1.02851i			0.0451901i
$519$	18.8154	+	20.9120i	0.825904	+	0.917934i
$520$	3.43736	−	2.49739i	0.150738	−	0.109518i
$521$	−5.56842	+	7.66428i	−0.243957	+	0.335778i	−0.913383	−	0.407100i	$-0.866540\pi$
$521$	−5.56842	+	7.66428i	−0.243957	+	0.335778i	0.669426	+	0.742878i	$0.266540\pi$
$522$	0.521538	−	0.578376i	0.0228271	−	0.0253148i
$523$	0.218761	−	0.0710796i	0.00956574	−	0.00310810i	−0.304230	−	0.952599i	$-0.598399\pi$
$523$	0.218761	−	0.0710796i	0.00956574	−	0.00310810i	0.313796	+	0.949490i	$0.398399\pi$
$524$	4.67009	+	3.39302i	0.204014	+	0.148225i
$525$	7.97674	−	0.835444i	0.348134	−	0.0364618i
$526$	−0.935608	+	2.87951i	−0.0407945	+	0.125552i
$527$	11.5508			0.503163
$528$	5.12217	−	15.2974i	0.222914	−	0.665734i
$529$	−8.79812			−0.382527
$530$	−1.86552	+	5.74147i	−0.0810328	+	0.249393i
$531$	4.59727	−	10.3054i	0.199504	−	0.447215i
$532$	−18.1277	−	13.1706i	−0.785937	−	0.571017i
$533$	−19.8235	+	6.44106i	−0.858653	+	0.278993i
$534$	−0.522723	+	2.45481i	−0.0226204	+	0.106230i
$535$	−10.6114	+	14.6054i	−0.458773	+	0.631447i
$536$	10.0106	−	7.27313i	0.432393	−	0.314152i
$537$	−24.0880	+	21.6730i	−1.03947	+	0.935258i
$538$			8.26442i			0.356304i
$539$	43.5893	+	19.8571i	1.87752	+	0.855307i
$540$	0.0102154	−	9.32358i	0.000439600	−	0.401223i
$541$	38.9280	+	12.6485i	1.67365	+	0.543801i	0.983662	−	0.180024i	$-0.0576176\pi$
$541$	38.9280	+	12.6485i	1.67365	+	0.543801i	0.689984	+	0.723825i	$0.257618\pi$
$542$	−0.432002	−	0.594600i	−0.0185561	−	0.0255403i
$543$	−13.1865	+	5.86523i	−0.565886	+	0.251701i
$544$	2.19580	+	6.75798i	0.0941442	+	0.289746i
$545$	5.89191	+	18.1334i	0.252382	+	0.776751i
$546$	8.20593	−	3.64993i	0.351182	−	0.156202i
$547$	16.0943	+	22.1519i	0.688142	+	0.947147i	0.999996	−	0.00298372i	$-0.000949749\pi$
$547$	16.0943	+	22.1519i	0.688142	+	0.947147i	−0.311853	+	0.950130i	$0.600950\pi$
$548$	27.1841	+	8.83265i	1.16125	+	0.377312i
$549$	−21.1383	+	12.1836i	−0.902162	+	0.519985i
$550$	−1.36880	−	0.623557i	−0.0583657	−	0.0265885i
$551$		−	1.54369i		−	0.0657636i
$552$	−12.4940	+	11.2414i	−0.531782	+	0.478467i
$553$	14.5310	−	10.5574i	0.617921	−	0.448946i
$554$	6.38023	−	8.78164i	0.271070	−	0.373096i
$555$	−0.176672	+	0.829688i	−0.00749932	+	0.0352183i
$556$	19.0702	−	6.19627i	0.808755	−	0.262780i
$557$	−11.5944	−	8.42382i	−0.491270	−	0.356929i	0.314402	−	0.949290i	$-0.398196\pi$
$557$	−11.5944	−	8.42382i	−0.491270	−	0.356929i	−0.805673	+	0.592361i	$0.798196\pi$
$558$	9.52356	+	4.24850i	0.403164	+	0.179853i
$559$	1.92142	−	5.91351i	0.0812673	−	0.250115i
$560$	13.0038			0.549510
$561$	−2.74874	+	8.20913i	−0.116052	+	0.346590i
$562$	−8.44970			−0.356429
$563$	6.17839	−	19.0151i	0.260388	−	0.801392i	−0.732332	−	0.680948i	$-0.761568\pi$
$563$	6.17839	−	19.0151i	0.260388	−	0.801392i	0.992720	−	0.120444i	$-0.0384319\pi$
$564$	10.3549	−	1.08452i	0.436021	−	0.0456666i
$565$	−1.40170	−	1.01840i	−0.0589701	−	0.0428443i
$566$	8.59369	−	2.79226i	0.361220	−	0.117367i
$567$	8.72428	−	40.7517i	0.366385	−	1.71141i
$568$	7.41320	−	10.2034i	0.311051	−	0.428125i
$569$	−4.88308	+	3.54777i	−0.204709	+	0.148730i	−0.685417	−	0.728151i	$-0.740380\pi$
$569$	−4.88308	+	3.54777i	−0.204709	+	0.148730i	0.480707	+	0.876881i	$0.340380\pi$
$570$	1.41689	+	1.57478i	0.0593472	+	0.0659601i
$571$		−	42.5140i		−	1.77916i	−0.456784	−	0.889578i	$-0.650999\pi$
$571$		−	42.5140i		−	1.77916i	0.456784	−	0.889578i	$-0.349001\pi$
$572$	14.5997	+	1.66128i	0.610446	+	0.0694616i
$573$	−30.3908	−	17.5609i	−1.26959	−	0.733618i
$574$	16.8603	+	5.47824i	0.703735	+	0.228657i
$575$	−3.31451	−	4.56203i	−0.138225	−	0.190250i
$576$	1.09827	−	10.3764i	0.0457611	−	0.432349i
$577$	−4.53707	−	13.9637i	−0.188881	−	0.581315i	0.811113	−	0.584890i	$-0.198862\pi$
$577$	−4.53707	−	13.9637i	−0.188881	−	0.581315i	−0.999994	+	0.00357457i	$0.998862\pi$
$578$	2.06417	+	6.35285i	0.0858580	+	0.264244i
$579$	5.24718	+	11.7970i	0.218065	+	0.490265i
$580$	0.603712	+	0.830939i	0.0250678	+	0.0345028i
$581$	−26.0976	−	8.47964i	−1.08271	−	0.351795i
$582$	0.791901	−	1.37046i	0.0328254	−	0.0568073i
$583$	−38.4222	+	21.7456i	−1.59129	+	0.900612i
$584$		−	11.5148i		−	0.476485i
$585$	7.24660	−	1.53478i	0.299610	−	0.0634554i
$586$	−7.67333	+	5.57500i	−0.316982	+	0.230301i
$587$	1.89042	−	2.60194i	0.0780260	−	0.107394i	−0.768220	−	0.640186i	$-0.778857\pi$
$587$	1.89042	−	2.60194i	0.0780260	−	0.107394i	0.846246	+	0.532792i	$0.178857\pi$
$588$	43.8999	+	9.34798i	1.81040	+	0.385504i
$589$	19.6587	−	6.38751i	0.810024	−	0.263193i
$590$	−1.38007	−	1.00268i	−0.0568167	−	0.0412798i
$591$	−2.46613	−	23.5464i	−0.101443	−	0.968570i
$592$	−0.425012	+	1.30805i	−0.0174679	+	0.0537607i
$593$	−29.0168			−1.19158			−0.595789	−	0.803141i	$-0.703161\pi$
$593$	−29.0168			−1.19158			−0.595789	+	0.803141i	$0.703161\pi$
$594$	−5.28570	+	5.75734i	−0.216875	+	0.236226i
$595$	−6.97830			−0.286083
$596$	9.37944	−	28.8670i	0.384197	−	1.18244i
$597$	2.11280	+	20.1728i	0.0864710	+	0.825617i
$598$	−5.10847	−	3.71152i	−0.208901	−	0.151775i
$599$	38.5104	−	12.5128i	1.57349	−	0.511258i	0.613121	−	0.789989i	$-0.289914\pi$
$599$	38.5104	−	12.5128i	1.57349	−	0.511258i	0.960369	+	0.278731i	$0.0899137\pi$
$600$	−2.91512	−	0.620741i	−0.119009	−	0.0253417i
$601$	7.61646	−	10.4832i	0.310682	−	0.427617i	−0.624912	−	0.780695i	$-0.714865\pi$
$601$	7.61646	−	10.4832i	0.310682	−	0.427617i	0.935594	+	0.353079i	$0.114865\pi$
$602$	−4.27839	+	3.10843i	−0.174374	+	0.126690i
$603$	21.1043	−	4.46974i	0.859432	−	0.182022i
$604$		−	34.6763i		−	1.41096i
$605$	−4.30099	−	10.1243i	−0.174860	−	0.411611i
$606$	4.90457	−	8.48780i	0.199234	−	0.344793i
$607$	20.3324	+	6.60640i	0.825266	+	0.268145i	0.691050	−	0.722807i	$-0.257148\pi$
$607$	20.3324	+	6.60640i	0.825266	+	0.268145i	0.134216	+	0.990952i	$0.457148\pi$
$608$	7.47420	+	10.2874i	0.303119	+	0.417207i
$609$	1.86579	+	4.19475i	0.0756055	+	0.169980i
$610$	1.13975	+	3.50779i	0.0461471	+	0.142026i
$611$	2.55610	+	7.86687i	0.103409	+	0.318259i
$612$	−0.853847	+	8.06713i	−0.0345147	+	0.326094i
$613$	3.24415	+	4.46519i	0.131030	+	0.180347i	0.869491	−	0.493949i	$-0.164447\pi$
$613$	3.24415	+	4.46519i	0.131030	+	0.180347i	−0.738461	+	0.674296i	$0.764447\pi$
$614$	7.12853	+	2.31620i	0.287684	+	0.0934742i
$615$	12.6600	+	7.31541i	0.510500	+	0.294986i
$616$	−19.4870	−	17.8513i	−0.785153	−	0.719250i
$617$		−	6.89327i		−	0.277512i	−0.990327	−	0.138756i	$-0.955690\pi$
$617$		−	6.89327i		−	0.277512i	0.990327	−	0.138756i	$-0.0443105\pi$
$618$	−1.22938	−	1.36637i	−0.0494530	−	0.0549635i
$619$	−24.6829	+	17.9332i	−0.992089	+	0.720795i	−0.960378	−	0.278702i	$-0.910096\pi$
$619$	−24.6829	+	17.9332i	−0.992089	+	0.720795i	−0.0317113	+	0.999497i	$0.510096\pi$
$620$	−8.08384	+	11.1265i	−0.324655	+	0.446849i
$621$	−27.8768	+	9.02397i	−1.11866	+	0.362120i
$622$	0.342655	−	0.111335i	0.0137392	−	0.00446414i
$623$	−11.9698	−	8.69657i	−0.479560	−	0.348421i
$624$	11.9445	−	1.25101i	0.478164	−	0.0500805i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	−0.579423			−0.0231584
$627$	−0.138597	+	15.4914i	−0.00553501	+	0.618667i
$628$	9.43789			0.376613
$629$	0.228077	−	0.701949i	0.00909403	−	0.0279885i
$630$	−5.75354	−	2.56668i	−0.229227	−	0.102259i
$631$	−26.1345	−	18.9879i	−1.04040	−	0.755895i	−0.0700363	−	0.997544i	$-0.522312\pi$
$631$	−26.1345	−	18.9879i	−1.04040	−	0.755895i	−0.970364	+	0.241650i	$0.922312\pi$
$632$	−6.34799	+	2.06259i	−0.252509	+	0.0820453i
$633$	1.39043	−	6.52971i	0.0552645	−	0.259533i
$634$	3.74882	−	5.15980i	0.148885	−	0.204922i
$635$	−8.59591	+	6.24529i	−0.341118	+	0.247837i
$636$	−30.7541	+	27.6708i	−1.21948	+	1.09722i
$637$			35.6593i			1.41287i
$638$	0.0973424	−	0.855469i	0.00385382	−	0.0338683i
$639$	19.0501	−	10.9800i	0.753609	−	0.434363i
$640$	−10.4689	−	3.40156i	−0.413820	−	0.134458i
$641$	−29.0114	−	39.9308i	−1.14588	−	1.57717i	−0.753608	−	0.657325i	$-0.771688\pi$
$641$	−29.0114	−	39.9308i	−1.14588	−	1.57717i	−0.392275	−	0.919848i	$-0.628312\pi$
$642$	12.9571	−	5.76321i	0.511377	−	0.227456i
$643$	−10.6022	−	32.6304i	−0.418112	−	1.28682i	−0.909438	−	0.415840i	$-0.863488\pi$
$643$	−10.6022	−	32.6304i	−0.418112	−	1.28682i	0.491326	−	0.870976i	$-0.336512\pi$
$644$	−14.4783	−	44.5597i	−0.570526	−	1.75590i
$645$	−3.98528	+	1.77262i	−0.156920	+	0.0697968i
$646$	−1.08337	−	1.49113i	−0.0426246	−	0.0586677i
$647$	−28.9866	−	9.41831i	−1.13958	−	0.370272i	−0.322371	−	0.946613i	$-0.604480\pi$
$647$	−28.9866	−	9.41831i	−1.13958	−	0.370272i	−0.817209	+	0.576341i	$0.804480\pi$
$648$	−7.76310	+	13.4008i	−0.304963	+	0.526435i
$649$	−2.48894	−	12.2245i	−0.0976996	−	0.479852i
$650$		−	1.11978i		−	0.0439214i
$651$	−45.6992	+	41.1176i	−1.79109	+	1.61152i
$652$	−25.4470	+	18.4883i	−0.996582	+	0.724059i
$653$	2.62689	−	3.61560i	0.102798	−	0.141489i	−0.754519	−	0.656278i	$-0.772130\pi$
$653$	2.62689	−	3.61560i	0.102798	−	0.141489i	0.857317	+	0.514789i	$0.172130\pi$
$654$	3.11925	−	14.6486i	0.121972	−	0.572806i
$655$	3.05966	−	0.994143i	0.119551	−	0.0388444i
$656$	19.1790	+	13.9344i	0.748816	+	0.544046i
$657$	8.17856	−	18.3333i	0.319076	−	0.715250i
$658$	2.17401	−	6.69092i	0.0847518	−	0.260839i
$659$	−14.0453			−0.547129			−0.273564	−	0.961854i	$-0.588203\pi$
$659$	−14.0453			−0.547129			−0.273564	+	0.961854i	$0.588203\pi$
$660$	−5.98382	−	8.39290i	−0.232920	−	0.326693i
$661$	45.1181			1.75489			0.877445	−	0.479678i	$-0.159246\pi$
$661$	45.1181			1.75489			0.877445	+	0.479678i	$0.159246\pi$
$662$	−0.895420	+	2.75582i	−0.0348015	+	0.107108i
$663$	−6.40986	+	0.671337i	−0.248938	+	0.0260726i
$664$	8.24981	+	5.99384i	0.320155	+	0.232606i
$665$	−11.8766	+	3.85893i	−0.460554	+	0.149643i
$666$	0.446230	−	0.494861i	0.0172911	−	0.0191755i
$667$	1.89727	−	2.61137i	0.0734627	−	0.101113i
$668$	1.26441	−	0.918648i	0.0489215	−	0.0355436i
$669$	27.0986	+	30.1181i	1.04769	+	1.16443i
$670$		−	3.26113i		−	0.125989i
$671$	−11.1820	+	24.5462i	−0.431677	+	0.947594i
$672$	−32.7438	−	18.9206i	−1.26312	−	0.729877i
$673$	−7.97155	−	2.59011i	−0.307280	−	0.0998415i	0.151318	−	0.988485i	$-0.451648\pi$
$673$	−7.97155	−	2.59011i	−0.307280	−	0.0998415i	−0.458598	+	0.888644i	$0.651648\pi$
$674$	1.84994	+	2.54623i	0.0712571	+	0.0980770i
$675$	−4.20043	−	3.05883i	−0.161675	−	0.117734i
$676$	−3.82781	−	11.7808i	−0.147224	−	0.453108i
$677$	−3.12592	−	9.62060i	−0.120139	−	0.369750i	0.872845	−	0.487997i	$-0.162272\pi$
$677$	−3.12592	−	9.62060i	−0.120139	−	0.369750i	−0.992984	+	0.118247i	$0.962272\pi$
$678$	0.553104	+	1.24351i	0.0212418	+	0.0477569i
$679$	5.48438	+	7.54860i	0.210471	+	0.289689i
$680$	2.46631	+	0.801353i	0.0945787	+	0.0307305i
$681$	5.99742	−	10.3791i	0.229822	−	0.397727i
$682$	11.2971	−	2.30012i	0.432587	−	0.0880763i
$683$			8.59190i			0.328760i	0.986397	+	0.164380i	$0.0525623\pi$
$683$			8.59190i			0.328760i	−0.986397	+	0.164380i	$0.947438\pi$
$684$	3.00786	+	14.2019i	0.115008	+	0.543021i
$685$	12.8874	−	9.36325i	0.492402	−	0.357751i
$686$	9.18632	−	12.6439i	0.350735	−	0.482746i
$687$	−1.10599	−	0.235507i	−0.0421960	−	0.00898515i
$688$	−6.72574	+	2.18532i	−0.256416	+	0.0833147i
$689$	−26.5904	−	19.3190i	−1.01301	−	0.735997i
$690$	0.461398	+	4.40538i	0.0175651	+	0.167710i
$691$	5.53165	−	17.0247i	0.210434	−	0.647649i	−0.789012	−	0.614377i	$-0.789407\pi$
$691$	5.53165	−	17.0247i	0.210434	−	0.647649i	0.999446	−	0.0332717i	$-0.0105927\pi$
$692$	29.1420			1.10781
$693$	−18.3471	−	42.2630i	−0.696947	−	1.60544i
$694$	0.0374587			0.00142191
$695$	3.45326	−	10.6280i	0.130990	−	0.403145i
$696$	−0.177713	−	1.69679i	−0.00673620	−	0.0643166i
$697$	−10.2922	−	7.47770i	−0.389844	−	0.283238i
$698$	−2.51411	+	0.816885i	−0.0951606	+	0.0309196i
$699$	−31.2789	−	6.66048i	−1.18308	−	0.251923i
$700$	4.88375	−	6.72191i	0.184589	−	0.254064i
$701$	3.94980	−	2.86970i	0.149182	−	0.108387i	−0.510691	−	0.859765i	$-0.670610\pi$
$701$	3.94980	−	2.86970i	0.149182	−	0.108387i	0.659873	+	0.751378i	$0.270610\pi$
$702$	−5.53179	−	1.80409i	−0.208784	−	0.0680910i
$703$		−	1.32079i		−	0.0498146i
$704$	−5.68186	−	10.0392i	−0.214143	−	0.378368i
$705$	2.90308	−	5.02405i	0.109336	−	0.189217i
$706$	3.12492	+	1.01535i	0.117608	+	0.0382131i
$707$	33.9670	+	46.7515i	1.27746	+	1.75827i
$708$	−4.75086	−	10.6811i	−0.178548	−	0.401420i
$709$	8.05063	+	24.7773i	0.302348	+	0.930531i	0.980654	+	0.195751i	$0.0627144\pi$
$709$	8.05063	+	24.7773i	0.302348	+	0.930531i	−0.678306	+	0.734780i	$0.737286\pi$
$710$	−1.02715	−	3.16125i	−0.0385484	−	0.118640i
$711$	−11.5719	−	1.22481i	−0.433982	−	0.0459338i
$712$	3.23176	+	4.44814i	0.121116	+	0.166701i
$713$	41.1060	+	13.3561i	1.53943	+	0.500192i
$714$	4.74614	+	2.74250i	0.177620	+	0.102635i
$715$	5.53162	−	6.03846i	0.206871	−	0.225826i
$716$			33.5679i			1.25449i
$717$	−0.694411	−	0.771788i	−0.0259333	−	0.0288230i
$718$	5.44598	−	3.95673i	0.203242	−	0.147664i
$719$	19.3848	−	26.6809i	0.722933	−	0.995032i	−0.276489	−	0.961017i	$-0.589171\pi$
$719$	19.3848	−	26.6809i	0.722933	−	0.995032i	0.999421	−	0.0340143i	$-0.0108292\pi$
$720$	−6.25669	−	5.64183i	−0.233173	−	0.210259i
$721$	10.3048	−	3.34824i	0.383772	−	0.124695i
$722$	4.30272	+	3.12611i	0.160131	+	0.116342i
$723$	5.34417	−	0.559722i	0.198752	−	0.0208163i
$724$	−4.62010	+	14.2192i	−0.171705	+	0.528452i
$725$	0.572414			0.0212589
$726$	−1.05366	+	8.57613i	−0.0391051	+	0.318290i
$727$	6.67220			0.247458			0.123729	−	0.992316i	$-0.460515\pi$
$727$	6.67220			0.247458			0.123729	+	0.992316i	$0.460515\pi$
$728$	6.07972	−	18.7115i	0.225329	−	0.693493i
$729$	−21.8782	+	15.8223i	−0.810303	+	0.586011i
$730$	−2.45516	−	1.78378i	−0.0908694	−	0.0660205i
$731$	3.60927	−	1.17272i	0.133494	−	0.0433748i
$732$	−5.26407	+	24.7211i	−0.194566	+	0.913719i
$733$	19.9176	−	27.4142i	0.735673	−	1.01257i	−0.263183	−	0.964746i	$-0.584772\pi$
$733$	19.9176	−	27.4142i	0.735673	−	1.01257i	0.998856	−	0.0478213i	$-0.0152278\pi$
$734$	−0.367973	+	0.267348i	−0.0135821	+	0.00986800i
$735$	18.5955	−	16.7312i	0.685906	−	0.617139i
$736$			26.5886i			0.980069i
$737$	16.1097	−	17.5858i	0.593409	−	0.647782i
$738$	−5.73543	−	9.95083i	−0.211124	−	0.366295i
$739$	−25.7910	−	8.37999i	−0.948736	−	0.308263i	−0.206534	−	0.978439i	$-0.566218\pi$
$739$	−25.7910	−	8.37999i	−0.948736	−	0.308263i	−0.742202	+	0.670176i	$0.766218\pi$
$740$	0.516539	+	0.710955i	0.0189884	+	0.0261352i
$741$	−10.5379	+	4.68716i	−0.387119	+	0.172187i
$742$	8.63839	+	26.5862i	0.317125	+	0.976011i
$743$	6.03306	+	18.5678i	0.221331	+	0.681188i	0.998643	+	0.0520726i	$0.0165827\pi$
$743$	6.03306	+	18.5678i	0.221331	+	0.681188i	−0.777312	+	0.629115i	$0.783417\pi$
$744$	20.8730	−	9.28413i	0.765242	−	0.340373i
$745$	−9.94288	−	13.6852i	−0.364279	−	0.501387i
$746$	−5.88390	−	1.91180i	−0.215425	−	0.0699958i
$747$	8.87774	+	15.4027i	0.324819	+	0.563554i
$748$	4.41737	+	7.80502i	0.161515	+	0.285380i
$749$			83.5969i			3.05456i
$750$	−0.583940	+	0.525396i	−0.0213225	+	0.0191847i
$751$	−23.0149	+	16.7213i	−0.839825	+	0.610168i	−0.922322	−	0.386423i	$-0.873711\pi$
$751$	−23.0149	+	16.7213i	−0.839825	+	0.610168i	0.0824969	+	0.996591i	$0.473711\pi$
$752$	5.52979	−	7.61110i	0.201651	−	0.277548i
$753$	−9.64210	+	45.2812i	−0.351378	+	1.65014i
$754$	0.609606	−	0.198073i	0.0222005	−	0.00721339i
$755$	−15.6347	−	11.3593i	−0.569005	−	0.413406i
$756$	−25.3384	−	34.9559i	−0.921550	−	1.27133i
$757$	−5.72745	+	17.6273i	−0.208168	+	0.640674i	0.791401	+	0.611298i	$0.209352\pi$
$757$	−5.72745	+	17.6273i	−0.208168	+	0.640674i	−0.999568	+	0.0293764i	$0.990648\pi$
$758$	−0.451541			−0.0164007
$759$	−19.2741	+	26.0355i	−0.699606	+	0.945028i
$760$	4.64063			0.168333
$761$	5.18255	−	15.9502i	0.187867	−	0.578196i	−0.812119	−	0.583492i	$-0.801686\pi$
$761$	5.18255	−	15.9502i	0.187867	−	0.578196i	0.999986	+	0.00529635i	$0.00168589\pi$
$762$	8.30074	−	0.869378i	0.300704	−	0.0314943i
$763$	71.4275	+	51.8951i	2.58585	+	1.87873i
$764$	−34.5819	+	11.2364i	−1.25113	+	0.406517i
$765$	3.35757	+	3.02761i	0.121393	+	0.109463i
$766$	9.74833	−	13.4174i	0.352221	−	0.484791i
$767$	7.51367	−	5.45900i	0.271303	−	0.197113i
$768$	−2.27540	−	2.52894i	−0.0821063	−	0.0912553i
$769$			22.0263i			0.794289i	0.917756	+	0.397145i	$0.129999\pi$
$769$			22.0263i			0.794289i	−0.917756	+	0.397145i	$0.870001\pi$
$770$	−6.82498	+	1.38959i	−0.245955	+	0.0500774i
$771$	−20.2773	−	11.7170i	−0.730271	−	0.421978i
$772$	12.7208	+	4.13325i	0.457833	+	0.148759i
$773$	−1.75385	−	2.41397i	−0.0630818	−	0.0868246i	0.776311	−	0.630351i	$-0.217089\pi$
$773$	−1.75385	−	2.41397i	−0.0630818	−	0.0868246i	−0.839392	+	0.543526i	$0.817089\pi$
$774$	3.40715	+	0.360622i	0.122467	+	0.0129623i
$775$	2.36854	+	7.28961i	0.0850804	+	0.261851i
$776$	−1.07148	−	3.29767i	−0.0384638	−	0.118379i
$777$	1.59638	+	3.58904i	0.0572696	+	0.128756i
$778$	4.88656	+	6.72578i	0.175192	+	0.241131i
$779$	−21.6516	−	7.03504i	−0.775750	−	0.252057i
$780$	3.83926	−	6.64419i	0.137468	−	0.237900i
$781$	10.0774	−	22.1213i	0.360596	−	0.791561i
$782$		−	3.85396i		−	0.137817i
$783$	0.922224	−	2.82777i	0.0329576	−	0.101056i
$784$	32.8114	−	23.8389i	1.17184	−	0.851389i
$785$	3.09167	−	4.25532i	0.110346	−	0.151879i
$786$	−2.47166	−	0.526311i	−0.0881612	−	0.0187729i
$787$	51.0596	−	16.5903i	1.82008	−	0.591380i	0.820268	−	0.571980i	$-0.193824\pi$
$787$	51.0596	−	16.5903i	1.82008	−	0.591380i	0.999812	−	0.0193999i	$-0.00617557\pi$
$788$	−19.8423	−	14.4163i	−0.706852	−	0.513558i
$789$	1.20449	+	11.5004i	0.0428810	+	0.409424i
$790$	−0.543598	+	1.67302i	−0.0193403	+	0.0595234i
$791$	−8.02292			−0.285262
$792$	1.63106	+	17.0437i	0.0579571	+	0.605621i
$793$	−20.0806			−0.713084
$794$	−0.213997	+	0.658615i	−0.00759447	+	0.0233734i
$795$	2.40164	+	22.9307i	0.0851776	+	0.813267i
$796$	16.9994	+	12.3508i	0.602527	+	0.437761i
$797$	7.42838	−	2.41363i	0.263127	−	0.0854950i	−0.174483	−	0.984660i	$-0.555825\pi$
$797$	7.42838	−	2.41363i	0.263127	−	0.0854950i	0.437609	+	0.899165i	$0.355825\pi$
$798$	9.59417	+	2.04297i	0.339630	+	0.0723202i
$799$	−2.96749	+	4.08439i	−0.104982	+	0.144495i
$800$	−3.81463	+	2.77149i	−0.134868	+	0.0979871i
$801$	1.98610	+	9.37753i	0.0701753	+	0.331339i
$802$			5.53416i			0.195418i
$803$	−4.42784	−	21.7474i	−0.156255	−	0.767448i
$804$	11.1811	−	19.3499i	0.394326	−	0.682417i
$805$	−24.8337	−	8.06895i	−0.875272	−	0.284393i
$806$	5.04486	+	6.94366i	0.177698	+	0.244580i
$807$	12.8274	+	28.8392i	0.451546	+	1.01519i
$808$	−6.63609	−	20.4238i	−0.233457	−	0.718506i
$809$	11.3173	+	34.8310i	0.397894	+	1.22459i	0.926684	+	0.375840i	$0.122646\pi$
$809$	11.3173	+	34.8310i	0.397894	+	1.22459i	−0.528790	+	0.848753i	$0.677354\pi$
$810$	1.65470	+	3.73118i	0.0581402	+	0.131100i
$811$	−19.5752	−	26.9430i	−0.687380	−	0.946097i	0.312613	−	0.949881i	$-0.398796\pi$
$811$	−19.5752	−	26.9430i	−0.687380	−	0.946097i	−0.999993	+	0.00378328i	$0.998796\pi$
$812$	4.52326	+	1.46970i	0.158735	+	0.0515762i
$813$	−2.43039	−	1.40437i	−0.0852375	−	0.0492534i
$814$	0.0832866	−	0.731943i	0.00291919	−	0.0256546i
$815$			17.5299i			0.614044i
$816$	4.90283	+	5.44915i	0.171633	+	0.190758i
$817$	5.49423	−	3.99179i	0.192219	−	0.139655i
$818$	1.47727	−	2.03328i	0.0516514	−	0.0710920i
$819$	22.9699	−	25.4733i	0.802634	−	0.890107i
$820$	14.4059	−	4.68076i	0.503076	−	0.163459i
$821$	−12.1588	−	8.83389i	−0.424345	−	0.308305i	0.355039	−	0.934852i	$-0.384468\pi$
$821$	−12.1588	−	8.83389i	−0.424345	−	0.308305i	−0.779384	+	0.626547i	$0.784468\pi$
$822$	−12.4449	+	1.30341i	−0.434065	+	0.0454618i
$823$	−4.74885	+	14.6155i	−0.165534	+	0.509463i	−0.999075	−	0.0429952i	$-0.986310\pi$
$823$	−4.74885	+	14.6155i	−0.165534	+	0.509463i	0.833541	+	0.552458i	$0.186310\pi$
$824$	−4.02648			−0.140269
$825$	−5.74433	−	0.0513927i	−0.199992	−	0.00178926i
$826$	−7.89912			−0.274845
$827$	−0.194359	+	0.598176i	−0.00675853	+	0.0208006i	−0.954379	−	0.298598i	$-0.903481\pi$
$827$	−0.194359	+	0.598176i	−0.00675853	+	0.0208006i	0.947620	+	0.319399i	$0.103481\pi$
$828$	−12.3665	+	27.7212i	−0.429767	+	0.963378i
$829$	3.81422	+	2.77119i	0.132473	+	0.0962474i	0.652049	−	0.758177i	$-0.273910\pi$
$829$	3.81422	+	2.77119i	0.132473	+	0.0962474i	−0.519575	+	0.854425i	$0.673910\pi$
$830$	2.55599	−	0.830490i	0.0887196	−	0.0288267i
$831$	8.63399	−	40.5469i	0.299510	−	1.40656i
$832$	5.04782	−	6.94773i	0.175002	−	0.240869i
$833$	−17.6078	+	12.7928i	−0.610074	+	0.443245i
$834$	−6.52552	+	5.87129i	−0.225960	+	0.203306i
$835$		−	0.871023i		−	0.0301430i
$836$	11.8342	+	10.8408i	0.409293	+	0.374938i
$837$	39.8272	+	0.0436367i	1.37663	+	0.00150830i
$838$	7.33755	+	2.38411i	0.253471	+	0.0823578i
$839$	−11.6844	−	16.0822i	−0.403391	−	0.555220i	0.558200	−	0.829706i	$-0.311492\pi$
$839$	−11.6844	−	16.0822i	−0.403391	−	0.555220i	−0.961591	+	0.274486i	$0.911492\pi$
$840$	−12.6102	+	5.60889i	−0.435092	+	0.193525i
$841$	−8.86024	−	27.2690i	−0.305526	−	0.940311i
$842$	−2.61544	−	8.04949i	−0.0901340	−	0.277404i
$843$	−29.4857	+	13.1150i	−1.01554	+	0.451704i
$844$	−4.06521	−	5.59528i	−0.139930	−	0.192597i
$845$	−6.56559	−	2.13329i	−0.225863	−	0.0733874i
$846$	−3.94894	+	2.27608i	−0.135767	+	0.0782531i
$847$	−43.6685	−	26.2214i	−1.50047	−	0.900978i
$848$			37.3819i			1.28370i
$849$	25.6542	−	23.0822i	0.880451	−	0.792180i
$850$	0.552923	−	0.401722i	0.0189651	−	0.0137790i
$851$	1.62332	−	2.23430i	0.0556465	−	0.0765909i
$852$	4.74403	−	22.2789i	0.162528	−	0.763263i
$853$	−24.4464	+	7.94313i	−0.837030	+	0.271967i	−0.696004	−	0.718038i	$-0.745040\pi$
$853$	−24.4464	+	7.94313i	−0.837030	+	0.271967i	−0.141026	+	0.990006i	$0.545040\pi$
$854$	13.8172	+	10.0387i	0.472813	+	0.343519i
$855$	7.38858	+	3.29608i	0.252684	+	0.112723i
$856$	9.59984	−	29.5453i	0.328116	−	1.00984i
$857$	−7.26084			−0.248026			−0.124013	−	0.992281i	$-0.539576\pi$
$857$	−7.26084			−0.248026			−0.124013	+	0.992281i	$0.539576\pi$
$858$	−6.13535	+	1.93299i	−0.209457	+	0.0659910i
$859$	−45.4614			−1.55112			−0.775561	−	0.631273i	$-0.782533\pi$
$859$	−45.4614			−1.55112			−0.775561	+	0.631273i	$0.782533\pi$
$860$	−1.39631	+	4.29739i	−0.0476137	+	0.146540i
$861$	67.3378	−	7.05263i	2.29487	−	0.240353i
$862$	−2.39168	−	1.73766i	−0.0814611	−	0.0591849i
$863$	2.62923	−	0.854289i	0.0895000	−	0.0290803i	−0.263925	−	0.964543i	$-0.585017\pi$
$863$	2.62923	−	0.854289i	0.0895000	−	0.0290803i	0.353425	+	0.935463i	$0.385017\pi$
$864$	7.54557	+	23.3097i	0.256705	+	0.793014i
$865$	9.54634	−	13.1394i	0.324585	−	0.446753i
$866$	−5.08790	+	3.69658i	−0.172894	+	0.125615i
$867$	17.0634	+	18.9648i	0.579504	+	0.644078i
$868$			63.6844i			2.16159i
$869$	−11.1960	+	6.33652i	−0.379797	+	0.214952i
$870$	−0.389315	−	0.224961i	−0.0131990	−	0.00762688i
$871$	16.8859	+	5.48657i	0.572158	+	0.185905i
$872$	−19.2849	−	26.5434i	−0.653070	−	0.898874i
$873$	0.636265	−	6.01142i	0.0215343	−	0.203456i
$874$	−2.13121	−	6.55917i	−0.0720891	−	0.221867i
$875$	−1.43092	−	4.40393i	−0.0483740	−	0.148880i
$876$	−8.45179	−	19.0017i	−0.285560	−	0.642008i
$877$	−6.47691	−	8.91471i	−0.218710	−	0.301028i	0.685537	−	0.728037i	$-0.259567\pi$
$877$	−6.47691	−	8.91471i	−0.218710	−	0.301028i	−0.904247	+	0.427009i	$0.859567\pi$
$878$	8.12542	+	2.64011i	0.274220	+	0.0890994i
$879$	−18.1234	+	31.3642i	−0.611288	+	1.05789i
$880$	−9.25419	−	1.05302i	−0.311959	−	0.0354973i
$881$			10.5939i			0.356918i	0.983947	+	0.178459i	$0.0571113\pi$
$881$			10.5939i			0.356918i	−0.983947	+	0.178459i	$0.942889\pi$
$882$	−19.2228	+	4.07125i	−0.647264	+	0.137086i
$883$	20.9215	−	15.2003i	0.704064	−	0.511532i	−0.177189	−	0.984177i	$-0.556701\pi$
$883$	20.9215	−	15.2003i	0.704064	−	0.511532i	0.881253	+	0.472645i	$0.156701\pi$
$884$	−3.92443	+	5.40152i	−0.131993	+	0.181673i
$885$	−6.37213	−	1.35687i	−0.214197	−	0.0456107i
$886$	−2.89049	+	0.939179i	−0.0971081	+	0.0315523i
$887$	45.6484	+	33.1655i	1.53272	+	1.11359i	0.954701	+	0.297567i	$0.0961751\pi$
$887$	45.6484	+	33.1655i	1.53272	+	1.11359i	0.578022	+	0.816021i	$0.303825\pi$
$888$	−0.152052	−	1.45178i	−0.00510254	−	0.0487185i
$889$	−15.2037	+	46.7923i	−0.509917	+	1.56936i
$890$	1.44906			0.0485726
$891$	−9.50865	+	28.2946i	−0.318552	+	0.947905i
$892$	41.9712			1.40530
$893$	−2.79182	+	8.59234i	−0.0934247	+	0.287532i
$894$	1.38410	+	13.2153i	0.0462913	+	0.441985i
$895$	15.1350	+	10.9962i	0.505906	+	0.367562i
$896$	−48.4770	+	15.7511i	−1.61950	+	0.526208i
$897$	−23.5870	−	5.02258i	−0.787548	−	0.167699i
$898$	−6.24325	+	8.59310i	−0.208340	+	0.286755i
$899$	−3.54949	+	2.57886i	−0.118382	+	0.0860096i
$900$	−5.26616	+	1.11534i	−0.175539	+	0.0371779i
$901$		−	20.0605i		−	0.668311i
$902$	−11.5551	−	5.26392i	−0.384742	−	0.175269i
$903$	−10.1050	+	17.4877i	−0.336274	+	0.581953i
$904$	2.83550	+	0.921311i	0.0943075	+	0.0306424i
$905$	4.89764	+	6.74102i	0.162803	+	0.224079i
$906$	6.16937	+	13.8703i	0.204964	+	0.460808i
$907$	−12.4636	−	38.3589i	−0.413846	−	1.27369i	−0.913279	−	0.407334i	$-0.866459\pi$
$907$	−12.4636	−	38.3589i	−0.413846	−	1.27369i	0.499434	−	0.866352i	$-0.333541\pi$
$908$	−3.83745	−	11.8105i	−0.127350	−	0.391944i
$909$	3.94065	−	37.2311i	0.130703	−	1.23488i
$910$	−3.04779	−	4.19493i	−0.101033	−	0.139060i
$911$	14.8092	+	4.81180i	0.490651	+	0.159422i	0.543885	−	0.839160i	$-0.316953\pi$
$911$	14.8092	+	4.81180i	0.490651	+	0.159422i	−0.0532340	+	0.998582i	$0.516953\pi$
$912$	11.3576	+	6.56284i	0.376088	+	0.217317i
$913$	17.8858	+	8.14790i	0.591934	+	0.269656i
$914$		−	15.0300i		−	0.497147i
$915$	9.42174	+	10.4716i	0.311473	+	0.346180i
$916$	−0.947714	+	0.688555i	−0.0313134	+	0.0227505i
$917$	8.75627	−	12.0520i	0.289158	−	0.397991i
$918$	−1.09371	−	3.37870i	−0.0360980	−	0.111514i
$919$	48.0102	−	15.5995i	1.58371	−	0.514579i	0.620702	−	0.784047i	$-0.286848\pi$
$919$	48.0102	−	15.5995i	1.58371	−	0.514579i	0.963009	+	0.269467i	$0.0868477\pi$
$920$	7.85026	+	5.70355i	0.258815	+	0.188040i
$921$	28.4704	−	2.98185i	0.938133	−	0.0982553i
$922$	−3.38107	+	10.4059i	−0.111350	+	0.342699i
$923$	18.0969			0.595665
$924$	−45.2602	−	15.1549i	−1.48895	−	0.498560i
$925$	0.489760			0.0161032
$926$	−3.01905	+	9.29169i	−0.0992122	+	0.305344i
$927$	−6.41077	−	2.85987i	−0.210557	−	0.0939306i
$928$	−2.18355	−	1.58644i	−0.0716785	−	0.0520775i
$929$	10.6157	−	3.44924i	0.348288	−	0.113166i	−0.129648	−	0.991560i	$-0.541385\pi$
$929$	10.6157	−	3.44924i	0.348288	−	0.113166i	0.477937	+	0.878394i	$0.341385\pi$
$930$	1.25393	−	5.88871i	0.0411181	−	0.193099i
$931$	−22.8929	+	31.5094i	−0.750285	+	1.03268i
$932$	−26.8028	+	19.4733i	−0.877953	+	0.637870i
$933$	1.02291	−	0.920354i	0.0334885	−	0.0301310i
$934$			1.08286i			0.0354323i
$935$	4.96614	+	0.565088i	0.162410	+	0.0184804i
$936$	−11.0434	+	6.36515i	−0.360964	+	0.208051i
$937$	15.4065	+	5.00587i	0.503308	+	0.163535i	0.549657	−	0.835391i	$-0.314759\pi$
$937$	15.4065	+	5.00587i	0.503308	+	0.163535i	−0.0463487	+	0.998925i	$0.514759\pi$
$938$	−8.87608	−	12.2169i	−0.289814	−	0.398895i
$939$	−2.02193	+	0.899336i	−0.0659832	+	0.0293487i
$940$	−1.85754	−	5.71691i	−0.0605862	−	0.186465i
$941$	−9.27963	−	28.5598i	−0.302507	−	0.931022i	−0.980596	−	0.196042i	$-0.937191\pi$
$941$	−9.27963	−	28.5598i	−0.302507	−	0.931022i	0.678088	−	0.734981i	$-0.262809\pi$
$942$	−3.77508	+	1.67912i	−0.122999	+	0.0547088i
$943$	−27.9803	−	38.5116i	−0.911165	−	1.25411i
$944$	−10.0461	−	3.26416i	−0.326971	−	0.106239i
$945$	−24.0611	−	0.0263626i	−0.782708	−	0.000857575i
$946$	3.29645	−	1.86567i	0.107177	−	0.0606583i
$947$		−	0.626343i		−	0.0203534i	−0.999948	−	0.0101767i	$-0.996761\pi$
$947$		−	0.626343i		−	0.0203534i	0.999948	−	0.0101767i	$-0.00323940\pi$
$948$	−8.96153	+	8.06307i	−0.291057	+	0.261876i
$949$	13.3669	−	9.71159i	0.433907	−	0.315252i
$950$	0.718887	−	0.989464i	0.0233238	−	0.0321024i
$951$	5.07305	−	23.8241i	0.164505	−	0.772548i
$952$	11.4204	−	3.71072i	0.370138	−	0.120265i
$953$	44.3750	+	32.2403i	1.43745	+	1.04437i	0.988569	+	0.150772i	$0.0481759\pi$
$953$	44.3750	+	32.2403i	1.43745	+	1.04437i	0.448877	+	0.893594i	$0.351824\pi$
$954$	7.37841	−	16.5397i	0.238885	−	0.535491i
$955$	−6.26216	+	19.2730i	−0.202639	+	0.623658i
$956$	−1.07553			−0.0347851
$957$	−0.988112	−	3.13629i	−0.0319411	−	0.101382i
$958$	−8.45954			−0.273315
$959$	22.7942	−	70.1533i	0.736063	−	2.26537i
$960$	−5.99150	+	0.627520i	−0.193375	+	0.0202531i
$961$	−22.4489	−	16.3101i	−0.724159	−	0.526132i
$962$	0.521582	−	0.169472i	0.0168165	−	0.00546400i
$963$	36.2694	−	40.2221i	1.16876	−	1.29614i
$964$	3.27196	−	4.50347i	0.105383	−	0.145047i
$965$	6.03068	−	4.38154i	0.194134	−	0.141047i
$966$	13.7190	+	15.2476i	0.441400	+	0.490585i
$967$			41.1782i			1.32420i	0.749414	+	0.662102i	$0.230335\pi$
$967$			41.1782i			1.32420i	−0.749414	+	0.662102i	$0.769665\pi$
$968$	12.4224	+	14.2820i	0.399272	+	0.459040i
$969$	−6.09490	−	3.52186i	−0.195796	−	0.113138i
$970$	−0.869105	−	0.282389i	−0.0279053	−	0.00906697i
$971$	15.3366	+	21.1090i	0.492174	+	0.677420i	0.980787	−	0.195081i	$-0.0624970\pi$
$971$	15.3366	+	21.1090i	0.492174	+	0.677420i	−0.488613	+	0.872501i	$0.662497\pi$
$972$	−2.97453	+	27.8121i	−0.0954082	+	0.892075i
$973$	−15.9906	−	49.2139i	−0.512634	−	1.57772i
$974$	0.698385	+	2.14941i	0.0223777	+	0.0688714i
$975$	−1.73804	−	3.90753i	−0.0556617	−	0.125141i
$976$	13.4243	+	18.4769i	0.429700	+	0.591431i
$977$	6.62796	+	2.15356i	0.212047	+	0.0688983i	0.413114	−	0.910679i	$-0.364441\pi$
$977$	6.62796	+	2.15356i	0.212047	+	0.0688983i	−0.201067	+	0.979577i	$0.564441\pi$
$978$	6.88929	−	11.9225i	0.220295	−	0.381241i
$979$	7.81413	+	7.15824i	0.249741	+	0.228778i
$980$		−	25.9139i		−	0.827789i
$981$	−11.8516	−	55.9586i	−0.378394	−	1.78662i
$982$	−1.44850	+	1.05240i	−0.0462236	+	0.0335834i
$983$	9.92256	−	13.6572i	0.316481	−	0.435598i	−0.620908	−	0.783883i	$-0.713236\pi$
$983$	9.92256	−	13.6572i	0.316481	−	0.435598i	0.937389	+	0.348285i	$0.113236\pi$
$984$	−24.6088	−	5.24015i	−0.784500	−	0.167050i
$985$	−12.9999	+	4.22392i	−0.414211	+	0.134585i
$986$	0.316501	+	0.229951i	0.0100794	+	0.00732314i
$987$	−2.79880	−	26.7227i	−0.0890867	−	0.850592i
$988$	−3.69212	+	11.3632i	−0.117462	+	0.361511i
$989$	14.2003			0.451544
$990$	3.88669	+	2.29250i	0.123527	+	0.0728603i
$991$	−42.9031			−1.36286			−0.681432	−	0.731882i	$-0.738642\pi$
$991$	−42.9031			−1.36286			−0.681432	+	0.731882i	$0.738642\pi$
$992$	11.1680	−	34.3716i	0.354584	−	1.09130i
$993$	1.15275	+	11.0064i	0.0365816	+	0.349277i
$994$	−12.4522	−	9.04702i	−0.394958	−	0.286954i
$995$	11.1373	−	3.61873i	0.353077	−	0.114722i
$996$	18.0133	+	3.83572i	0.570773	+	0.121539i
$997$	−29.3710	+	40.4257i	−0.930189	+	1.28030i	0.0295967	+	0.999562i	$0.490578\pi$
$997$	−29.3710	+	40.4257i	−0.930189	+	1.28030i	−0.959786	+	0.280734i	$0.909422\pi$
$998$	−2.49575	+	1.81327i	−0.0790017	+	0.0573981i
$999$	0.789059	−	2.41945i	0.0249647	−	0.0765480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.p.b.101.5	✓	48
3.2	odd	2	inner	165.2.p.b.101.8	yes	48
5.2	odd	4		825.2.bs.h.299.6		48
5.3	odd	4		825.2.bs.g.299.7		48
5.4	even	2		825.2.bi.e.101.8		48
11.6	odd	10	inner	165.2.p.b.116.8	yes	48
15.2	even	4		825.2.bs.g.299.8		48
15.8	even	4		825.2.bs.h.299.5		48
15.14	odd	2		825.2.bi.e.101.5		48
33.17	even	10	inner	165.2.p.b.116.5	yes	48
55.17	even	20		825.2.bs.h.149.5		48
55.28	even	20		825.2.bs.g.149.8		48
55.39	odd	10		825.2.bi.e.776.5		48
165.17	odd	20		825.2.bs.g.149.7		48
165.83	odd	20		825.2.bs.h.149.6		48
165.149	even	10		825.2.bi.e.776.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.p.b.101.5	✓	48	1.1	even	1	trivial
165.2.p.b.101.8	yes	48	3.2	odd	2	inner
165.2.p.b.116.5	yes	48	33.17	even	10	inner
165.2.p.b.116.8	yes	48	11.6	odd	10	inner
825.2.bi.e.101.5		48	15.14	odd	2
825.2.bi.e.101.8		48	5.4	even	2
825.2.bi.e.776.5		48	55.39	odd	10
825.2.bi.e.776.8		48	165.149	even	10
825.2.bs.g.149.7		48	165.17	odd	20
825.2.bs.g.149.8		48	55.28	even	20
825.2.bs.g.299.7		48	5.3	odd	4
825.2.bs.g.299.8		48	15.2	even	4
825.2.bs.h.149.5		48	55.17	even	20
825.2.bs.h.149.6		48	165.83	odd	20
825.2.bs.h.299.5		48	15.8	even	4
825.2.bs.h.299.6		48	5.2	odd	4

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.140144 + 0.431318i) q^{2} +(0.180419 + 1.72263i) q^{3} +(1.45164 + 1.05468i) q^{4} +(0.951057 - 0.309017i) q^{5} +(-0.768285 - 0.163597i) q^{6} +(2.72178 - 3.74621i) q^{7} +(-1.39214 + 1.01145i) q^{8} +(-2.93490 + 0.621591i) q^{9} +O(q^{10})\)	\(q+(-0.140144 + 0.431318i) q^{2} +(0.180419 + 1.72263i) q^{3} +(1.45164 + 1.05468i) q^{4} +(0.951057 - 0.309017i) q^{5} +(-0.768285 - 0.163597i) q^{6} +(2.72178 - 3.74621i) q^{7} +(-1.39214 + 1.01145i) q^{8} +(-2.93490 + 0.621591i) q^{9} +0.453514i q^{10} +(-2.24032 + 2.44560i) q^{11} +(-1.55491 + 2.69092i) q^{12} +(-2.34827 - 0.762999i) q^{13} +(1.23437 + 1.69896i) q^{14} +(0.703911 + 1.58256i) q^{15} +(0.867797 + 2.67080i) q^{16} +(-0.465691 - 1.43325i) q^{17} +(0.143204 - 1.35299i) q^{18} +(-1.58515 - 2.18177i) q^{19} +(1.70650 + 0.554477i) q^{20} +(6.94438 + 4.01272i) q^{21} +(-0.740863 - 1.30903i) q^{22} -5.63898i q^{23} +(-1.99352 - 2.21566i) q^{24} +(0.809017 - 0.587785i) q^{25} +(0.658190 - 0.905921i) q^{26} +(-1.60028 - 4.94359i) q^{27} +(7.90208 - 2.56754i) q^{28} +(0.463093 + 0.336457i) q^{29} +(-0.781237 + 0.0818229i) q^{30} +(-2.36854 + 7.28961i) q^{31} -4.71514 q^{32} +(-4.61705 - 3.41801i) q^{33} +0.683450 q^{34} +(1.43092 - 4.40393i) q^{35} +(-4.91599 - 2.19304i) q^{36} +(0.396224 + 0.287874i) q^{37} +(1.16318 - 0.377941i) q^{38} +(0.890690 - 4.18285i) q^{39} +(-1.01145 + 1.39214i) q^{40} +(6.82953 - 4.96195i) q^{41} +(-2.70397 + 2.43288i) q^{42} +2.51824i q^{43} +(-5.83146 + 1.18731i) q^{44} +(-2.59917 + 1.49810i) q^{45} +(2.43219 + 0.790268i) q^{46} +(-1.96912 - 2.71027i) q^{47} +(-4.44424 + 1.97676i) q^{48} +(-4.46287 - 13.7353i) q^{49} +(0.140144 + 0.431318i) q^{50} +(2.38494 - 1.06080i) q^{51} +(-2.60412 - 3.58426i) q^{52} +(12.6599 + 4.11346i) q^{53} +(2.35653 + 0.00258193i) q^{54} +(-1.37494 + 3.01820i) q^{55} +7.96819i q^{56} +(3.47238 - 3.12425i) q^{57} +(-0.210019 + 0.152588i) q^{58} +(-2.21091 + 3.04306i) q^{59} +(-0.647271 + 3.03971i) q^{60} +(7.73467 - 2.51315i) q^{61} +(-2.81220 - 2.04319i) q^{62} +(-5.65953 + 12.6866i) q^{63} +(-1.07480 + 3.30788i) q^{64} -2.46912 q^{65} +(2.12130 - 1.51241i) q^{66} -7.19080 q^{67} +(0.835601 - 2.57172i) q^{68} +(9.71387 - 1.01738i) q^{69} +(1.69896 + 1.23437i) q^{70} +(-6.97057 + 2.26487i) q^{71} +(3.45708 - 3.83384i) q^{72} +(-3.93323 + 5.41362i) q^{73} +(-0.179693 + 0.130555i) q^{74} +(1.15850 + 1.28759i) q^{75} -4.83896i q^{76} +(3.06405 + 15.0491i) q^{77} +(1.67932 + 0.970371i) q^{78} +(3.68901 + 1.19863i) q^{79} +(1.65065 + 2.27192i) q^{80} +(8.22725 - 3.64861i) q^{81} +(1.18306 + 3.64109i) q^{82} +(-1.83123 - 5.63595i) q^{83} +(5.84861 + 13.1491i) q^{84} +(-0.885798 - 1.21920i) q^{85} +(-1.08616 - 0.352916i) q^{86} +(-0.496039 + 0.858440i) q^{87} +(0.645247 - 5.67059i) q^{88} -3.19518i q^{89} +(-0.281901 - 1.33102i) q^{90} +(-9.24982 + 6.72039i) q^{91} +(5.94731 - 8.18577i) q^{92} +(-12.9846 - 2.76492i) q^{93} +(1.44495 - 0.469491i) q^{94} +(-2.18177 - 1.58515i) q^{95} +(-0.850704 - 8.12244i) q^{96} +(-0.622669 + 1.91638i) q^{97} +6.54972 q^{98} +(5.05496 - 8.57015i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9	\( 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9} + 8 q^{12} + 6 q^{15} + 32 q^{16} - 30 q^{18} - 100 q^{19} - 82 q^{22} + 100 q^{24} + 12 q^{25} + 14 q^{27} + 30 q^{28} + 10 q^{30} + 10 q^{31} - 46 q^{33} - 28 q^{34} + 14 q^{36} + 6 q^{37} - 50 q^{40} - 52 q^{42} + 32 q^{45} + 20 q^{46} - 80 q^{48} - 26 q^{49} - 30 q^{51} + 40 q^{52} + 6 q^{55} - 70 q^{57} + 92 q^{58} + 44 q^{60} + 70 q^{61} - 20 q^{63} + 18 q^{64} + 76 q^{66} + 20 q^{67} + 42 q^{69} - 4 q^{70} - 80 q^{72} + 90 q^{73} - 6 q^{75} - 108 q^{78} - 100 q^{79} + 38 q^{81} - 34 q^{82} + 70 q^{84} + 20 q^{85} + 74 q^{88} + 20 q^{90} - 86 q^{91} + 76 q^{93} + 10 q^{94} - 30 q^{96} + 6 q^{97} - 28 q^{99}+O(q^{100}) \) 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9 + 8 * q^12 + 6 * q^15 + 32 * q^16 - 30 * q^18 - 100 * q^19 - 82 * q^22 + 100 * q^24 + 12 * q^25 + 14 * q^27 + 30 * q^28 + 10 * q^30 + 10 * q^31 - 46 * q^33 - 28 * q^34 + 14 * q^36 + 6 * q^37 - 50 * q^40 - 52 * q^42 + 32 * q^45 + 20 * q^46 - 80 * q^48 - 26 * q^49 - 30 * q^51 + 40 * q^52 + 6 * q^55 - 70 * q^57 + 92 * q^58 + 44 * q^60 + 70 * q^61 - 20 * q^63 + 18 * q^64 + 76 * q^66 + 20 * q^67 + 42 * q^69 - 4 * q^70 - 80 * q^72 + 90 * q^73 - 6 * q^75 - 108 * q^78 - 100 * q^79 + 38 * q^81 - 34 * q^82 + 70 * q^84 + 20 * q^85 + 74 * q^88 + 20 * q^90 - 86 * q^91 + 76 * q^93 + 10 * q^94 - 30 * q^96 + 6 * q^97 - 28 * q^99

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