LMFDB - Embedded newform 930.2.r.b.119.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(119,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("930.119");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.r (of order $6$, degree $2$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			119.9
Character	$\chi$	$=$	930.119
Dual form			930.2.r.b.719.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.12217 + 1.31937i) q^{3} +1.00000 q^{4} +(-1.92892 + 1.13105i) q^{5} +(-1.12217 + 1.31937i) q^{6} +(-0.996061 - 0.575076i) q^{7} +1.00000 q^{8} +(-0.481481 - 2.96111i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.12217 + 1.31937i) q^{3} +1.00000 q^{4} +(-1.92892 + 1.13105i) q^{5} +(-1.12217 + 1.31937i) q^{6} +(-0.996061 - 0.575076i) q^{7} +1.00000 q^{8} +(-0.481481 - 2.96111i) q^{9} +(-1.92892 + 1.13105i) q^{10} +(-1.18492 - 2.05235i) q^{11} +(-1.12217 + 1.31937i) q^{12} +(-2.12245 - 3.67620i) q^{13} +(-0.996061 - 0.575076i) q^{14} +(0.672286 - 3.81419i) q^{15} +1.00000 q^{16} +(-0.282061 - 0.162848i) q^{17} +(-0.481481 - 2.96111i) q^{18} +(2.95296 - 5.11467i) q^{19} +(-1.92892 + 1.13105i) q^{20} +(1.87649 - 0.668843i) q^{21} +(-1.18492 - 2.05235i) q^{22} +3.91946i q^{23} +(-1.12217 + 1.31937i) q^{24} +(2.44143 - 4.36342i) q^{25} +(-2.12245 - 3.67620i) q^{26} +(4.44711 + 2.68761i) q^{27} +(-0.996061 - 0.575076i) q^{28} +6.15260 q^{29} +(0.672286 - 3.81419i) q^{30} +(-5.18162 - 2.03737i) q^{31} +1.00000 q^{32} +(4.03749 + 0.739723i) q^{33} +(-0.282061 - 0.162848i) q^{34} +(2.57176 - 0.0173251i) q^{35} +(-0.481481 - 2.96111i) q^{36} +(-2.70854 + 4.69134i) q^{37} +(2.95296 - 5.11467i) q^{38} +(7.23202 + 1.32500i) q^{39} +(-1.92892 + 1.13105i) q^{40} +(6.40890 - 3.70018i) q^{41} +(1.87649 - 0.668843i) q^{42} +(2.92261 - 5.06211i) q^{43} +(-1.18492 - 2.05235i) q^{44} +(4.27791 + 5.16715i) q^{45} +3.91946i q^{46} -9.74464 q^{47} +(-1.12217 + 1.31937i) q^{48} +(-2.83858 - 4.91656i) q^{49} +(2.44143 - 4.36342i) q^{50} +(0.531377 - 0.189401i) q^{51} +(-2.12245 - 3.67620i) q^{52} +(-5.94982 + 3.43513i) q^{53} +(4.44711 + 2.68761i) q^{54} +(4.60693 + 2.61859i) q^{55} +(-0.996061 - 0.575076i) q^{56} +(3.43444 + 9.63557i) q^{57} +6.15260 q^{58} +(-6.72767 - 3.88422i) q^{59} +(0.672286 - 3.81419i) q^{60} -7.88942i q^{61} +(-5.18162 - 2.03737i) q^{62} +(-1.22328 + 3.22633i) q^{63} +1.00000 q^{64} +(8.25201 + 4.69047i) q^{65} +(4.03749 + 0.739723i) q^{66} +(5.51167 - 3.18217i) q^{67} +(-0.282061 - 0.162848i) q^{68} +(-5.17122 - 4.39829i) q^{69} +(2.57176 - 0.0173251i) q^{70} +(-5.90885 + 3.41147i) q^{71} +(-0.481481 - 2.96111i) q^{72} +(-7.91524 - 13.7096i) q^{73} +(-2.70854 + 4.69134i) q^{74} +(3.01727 + 8.11764i) q^{75} +(2.95296 - 5.11467i) q^{76} +2.72568i q^{77} +(7.23202 + 1.32500i) q^{78} +(-1.66882 - 0.963496i) q^{79} +(-1.92892 + 1.13105i) q^{80} +(-8.53635 + 2.85144i) q^{81} +(6.40890 - 3.70018i) q^{82} +(4.70315 - 2.71537i) q^{83} +(1.87649 - 0.668843i) q^{84} +(0.728262 - 0.00490607i) q^{85} +(2.92261 - 5.06211i) q^{86} +(-6.90424 + 8.11756i) q^{87} +(-1.18492 - 2.05235i) q^{88} -6.10143 q^{89} +(4.27791 + 5.16715i) q^{90} +4.88229i q^{91} +3.91946i q^{92} +(8.50268 - 4.55021i) q^{93} -9.74464 q^{94} +(0.0889628 + 13.2057i) q^{95} +(-1.12217 + 1.31937i) q^{96} +12.1521i q^{97} +(-2.83858 - 4.91656i) q^{98} +(-5.50671 + 4.49686i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) $ 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9	$ 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) $ 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 2 * q^25 + 18 * q^31 + 64 * q^32 - 8 * q^33 + 6 * q^34 + 16 * q^35 - 4 * q^36 + 4 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^45 - 4 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 + 6 * q^57 + 18 * q^62 + 12 * q^63 + 64 * q^64 - 8 * q^66 + 6 * q^68 - 10 * q^69 + 16 * q^70 - 4 * q^72 - 63 * q^75 + 4 * q^76 - 8 * q^78 - 30 * q^79 + 2 * q^80 - 12 * q^81 - 54 * q^83 - 16 * q^87 + 9 * q^90 - 18 * q^93 - 4 * q^94 - 56 * q^95 + 30 * q^98 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.12217	+	1.31937i	−0.647884	+	0.761739i
$3$	−1.12217	+	1.31937i	−0.647884	+	0.761739i
$4$	1.00000			0.500000
$5$	−1.92892	+	1.13105i	−0.862637	+	0.505823i
$5$	−1.92892	+	1.13105i	−0.862637	+	0.505823i
$6$	−1.12217	+	1.31937i	−0.458123	+	0.538631i
$7$	−0.996061	−	0.575076i	−0.376476	−	0.217358i	0.299808	−	0.954000i	$-0.403077\pi$
$7$	−0.996061	−	0.575076i	−0.376476	−	0.217358i	−0.676284	+	0.736641i	$0.736411\pi$
$8$	1.00000			0.353553
$9$	−0.481481	−	2.96111i	−0.160494	−	0.987037i
$10$	−1.92892	+	1.13105i	−0.609977	+	0.357671i
$11$	−1.18492	−	2.05235i	−0.357268	−	0.618806i	0.630235	−	0.776404i	$-0.282958\pi$
$11$	−1.18492	−	2.05235i	−0.357268	−	0.618806i	−0.987503	+	0.157598i	$0.949625\pi$
$12$	−1.12217	+	1.31937i	−0.323942	+	0.380870i
$13$	−2.12245	−	3.67620i	−0.588663	−	1.01959i	−0.994408	−	0.105608i	$-0.966321\pi$
$13$	−2.12245	−	3.67620i	−0.588663	−	1.01959i	0.405745	−	0.913986i	$-0.367012\pi$
$14$	−0.996061	−	0.575076i	−0.266208	−	0.153696i
$15$	0.672286	−	3.81419i	0.173584	−	0.984819i
$16$	1.00000			0.250000
$17$	−0.282061	−	0.162848i	−0.0684099	−	0.0394965i	0.465405	−	0.885098i	$-0.345909\pi$
$17$	−0.282061	−	0.162848i	−0.0684099	−	0.0394965i	−0.533815	+	0.845601i	$0.679242\pi$
$18$	−0.481481	−	2.96111i	−0.113486	−	0.697940i
$19$	2.95296	−	5.11467i	0.677455	−	1.17339i	−0.298290	−	0.954475i	$-0.596416\pi$
$19$	2.95296	−	5.11467i	0.677455	−	1.17339i	0.975745	−	0.218911i	$-0.0702505\pi$
$20$	−1.92892	+	1.13105i	−0.431319	+	0.252911i
$21$	1.87649	−	0.668843i	0.409483	−	0.145953i
$22$	−1.18492	−	2.05235i	−0.252627	−	0.437562i
$23$			3.91946i			0.817263i	0.912699	+	0.408632i	$0.133994\pi$
$23$			3.91946i			0.817263i	−0.912699	+	0.408632i	$0.866006\pi$
$24$	−1.12217	+	1.31937i	−0.229061	+	0.269316i
$25$	2.44143	−	4.36342i	0.488287	−	0.872683i
$26$	−2.12245	−	3.67620i	−0.416247	−	0.720962i
$27$	4.44711	+	2.68761i	0.855846	+	0.517231i
$28$	−0.996061	−	0.575076i	−0.188238	−	0.108679i
$29$	6.15260			1.14251			0.571254	−	0.820773i	$-0.306457\pi$
$29$	6.15260			1.14251			0.571254	+	0.820773i	$0.306457\pi$
$30$	0.672286	−	3.81419i	0.122742	−	0.696372i
$31$	−5.18162	−	2.03737i	−0.930646	−	0.365922i
$31$	−5.18162	−	2.03737i	−0.930646	−	0.365922i
$32$	1.00000			0.176777
$33$	4.03749	+	0.739723i	0.702837	+	0.128769i
$34$	−0.282061	−	0.162848i	−0.0483731	−	0.0279282i
$35$	2.57176	−	0.0173251i	0.434707	−	0.00292848i
$36$	−0.481481	−	2.96111i	−0.0802469	−	0.493518i
$37$	−2.70854	+	4.69134i	−0.445282	+	0.771251i	−0.998072	−	0.0620698i	$-0.980230\pi$
$37$	−2.70854	+	4.69134i	−0.445282	+	0.771251i	0.552790	+	0.833321i	$0.313563\pi$
$38$	2.95296	−	5.11467i	0.479033	−	0.829709i
$39$	7.23202	+	1.32500i	1.15805	+	0.212171i
$40$	−1.92892	+	1.13105i	−0.304988	+	0.178835i
$41$	6.40890	−	3.70018i	1.00090	−	0.577871i	0.0923864	−	0.995723i	$-0.470550\pi$
$41$	6.40890	−	3.70018i	1.00090	−	0.577871i	0.908515	+	0.417853i	$0.137217\pi$
$42$	1.87649	−	0.668843i	0.289548	−	0.103205i
$43$	2.92261	−	5.06211i	0.445694	−	0.771965i	−0.552406	−	0.833575i	$-0.686290\pi$
$43$	2.92261	−	5.06211i	0.445694	−	0.771965i	0.998100	+	0.0616100i	$0.0196235\pi$
$44$	−1.18492	−	2.05235i	−0.178634	−	0.309403i
$45$	4.27791	+	5.16715i	0.637714	+	0.770274i
$46$			3.91946i			0.577892i
$47$	−9.74464			−1.42140			−0.710701	−	0.703495i	$-0.751622\pi$
$47$	−9.74464			−1.42140			−0.710701	+	0.703495i	$0.751622\pi$
$48$	−1.12217	+	1.31937i	−0.161971	+	0.190435i
$49$	−2.83858	−	4.91656i	−0.405511	−	0.702365i
$50$	2.44143	−	4.36342i	0.345271	−	0.617080i
$51$	0.531377	−	0.189401i	0.0744076	−	0.0265214i
$52$	−2.12245	−	3.67620i	−0.294331	−	0.509797i
$53$	−5.94982	+	3.43513i	−0.817271	+	0.471852i	−0.849474	−	0.527630i	$-0.823081\pi$
$53$	−5.94982	+	3.43513i	−0.817271	+	0.471852i	0.0322036	+	0.999481i	$0.489748\pi$
$54$	4.44711	+	2.68761i	0.605175	+	0.365737i
$55$	4.60693	+	2.61859i	0.621199	+	0.353091i
$56$	−0.996061	−	0.575076i	−0.133104	−	0.0768478i
$57$	3.43444	+	9.63557i	0.454903	+	1.27626i
$58$	6.15260			0.807875
$59$	−6.72767	−	3.88422i	−0.875868	−	0.505683i	−0.00657435	−	0.999978i	$-0.502093\pi$
$59$	−6.72767	−	3.88422i	−0.875868	−	0.505683i	−0.869294	+	0.494296i	$0.835426\pi$
$60$	0.672286	−	3.81419i	0.0867918	−	0.492410i
$61$		−	7.88942i		−	1.01014i	−0.863079	−	0.505069i	$-0.831467\pi$
$61$		−	7.88942i		−	1.01014i	0.863079	−	0.505069i	$-0.168533\pi$
$62$	−5.18162	−	2.03737i	−0.658066	−	0.258746i
$63$	−1.22328	+	3.22633i	−0.154119	+	0.406480i
$64$	1.00000			0.125000
$65$	8.25201	+	4.69047i	1.02354	+	0.581781i
$66$	4.03749	+	0.739723i	0.496981	+	0.0910537i
$67$	5.51167	−	3.18217i	0.673358	−	0.388764i	−0.123990	−	0.992284i	$-0.539569\pi$
$67$	5.51167	−	3.18217i	0.673358	−	0.388764i	0.797348	+	0.603520i	$0.206236\pi$
$68$	−0.282061	−	0.162848i	−0.0342049	−	0.0197482i
$69$	−5.17122	−	4.39829i	−0.622542	−	0.529491i
$70$	2.57176	−	0.0173251i	0.307384	−	0.00207075i
$71$	−5.90885	+	3.41147i	−0.701251	+	0.404867i	−0.807813	−	0.589439i	$-0.799349\pi$
$71$	−5.90885	+	3.41147i	−0.701251	+	0.404867i	0.106562	+	0.994306i	$0.466016\pi$
$72$	−0.481481	−	2.96111i	−0.0567431	−	0.348970i
$73$	−7.91524	−	13.7096i	−0.926409	−	1.60459i	−0.789280	−	0.614034i	$-0.789546\pi$
$73$	−7.91524	−	13.7096i	−0.926409	−	1.60459i	−0.137129	−	0.990553i	$-0.543788\pi$
$74$	−2.70854	+	4.69134i	−0.314862	+	0.545357i
$75$	3.01727	+	8.11764i	0.348404	+	0.937344i
$76$	2.95296	−	5.11467i	0.338727	−	0.586693i
$77$			2.72568i			0.310621i
$78$	7.23202	+	1.32500i	0.818865	+	0.150027i
$79$	−1.66882	−	0.963496i	−0.187757	−	0.108402i	0.403175	−	0.915123i	$-0.367907\pi$
$79$	−1.66882	−	0.963496i	−0.187757	−	0.108402i	−0.590932	+	0.806721i	$0.701240\pi$
$80$	−1.92892	+	1.13105i	−0.215659	+	0.126456i
$81$	−8.53635	+	2.85144i	−0.948484	+	0.316827i
$82$	6.40890	−	3.70018i	0.707744	−	0.408616i
$83$	4.70315	−	2.71537i	0.516238	−	0.298050i	−0.219156	−	0.975690i	$-0.570330\pi$
$83$	4.70315	−	2.71537i	0.516238	−	0.298050i	0.735394	+	0.677640i	$0.236997\pi$
$84$	1.87649	−	0.668843i	0.204741	−	0.0729767i
$85$	0.728262	−	0.00490607i	0.0789911	−	0.000532138i
$86$	2.92261	−	5.06211i	0.315154	−	0.545862i
$87$	−6.90424	+	8.11756i	−0.740212	+	0.870293i
$88$	−1.18492	−	2.05235i	−0.126313	−	0.218781i
$89$	−6.10143			−0.646751			−0.323375	−	0.946271i	$-0.604818\pi$
$89$	−6.10143			−0.646751			−0.323375	+	0.946271i	$0.604818\pi$
$90$	4.27791	+	5.16715i	0.450932	+	0.544666i
$91$			4.88229i			0.511803i
$92$			3.91946i			0.408632i
$93$	8.50268	−	4.55021i	0.881687	−	0.471835i
$94$	−9.74464			−1.00508
$95$	0.0889628	+	13.2057i	0.00912739	+	1.35488i
$96$	−1.12217	+	1.31937i	−0.114531	+	0.134658i
$97$			12.1521i			1.23385i	0.787020	+	0.616927i	$0.211623\pi$
$97$			12.1521i			1.23385i	−0.787020	+	0.616927i	$0.788377\pi$
$98$	−2.83858	−	4.91656i	−0.286739	−	0.496647i
$99$	−5.50671	+	4.49686i	−0.553445	+	0.451951i
$100$	2.44143	−	4.36342i	0.244143	−	0.436342i
$101$		−	9.75329i		−	0.970489i	−0.874379	−	0.485244i	$-0.838731\pi$
$101$		−	9.75329i		−	0.970489i	0.874379	−	0.485244i	$-0.161269\pi$
$102$	0.531377	−	0.189401i	0.0526141	−	0.0187535i
$103$	2.47328	−	1.42795i	0.243700	−	0.140700i	−0.373176	−	0.927760i	$-0.621731\pi$
$103$	2.47328	−	1.42795i	0.243700	−	0.140700i	0.616876	+	0.787060i	$0.288398\pi$
$104$	−2.12245	−	3.67620i	−0.208124	−	0.360481i
$105$	−2.86309	+	3.41255i	−0.279409	+	0.333031i
$106$	−5.94982	+	3.43513i	−0.577898	+	0.333649i
$107$	−8.09940	+	14.0286i	−0.782999	+	1.35619i	0.147188	+	0.989108i	$0.452978\pi$
$107$	−8.09940	+	14.0286i	−0.782999	+	1.35619i	−0.930187	+	0.367085i	$0.880356\pi$
$108$	4.44711	+	2.68761i	0.427923	+	0.258615i
$109$	11.4068			1.09257			0.546286	−	0.837599i	$-0.316041\pi$
$109$	11.4068			1.09257			0.546286	+	0.837599i	$0.316041\pi$
$110$	4.60693	+	2.61859i	0.439254	+	0.249673i
$111$	−3.15017	−	8.83804i	−0.299001	−	0.838869i
$112$	−0.996061	−	0.575076i	−0.0941189	−	0.0543396i
$113$	−5.70370	−	9.87909i	−0.536559	−	0.929347i	−0.999086	−	0.0427418i	$-0.986391\pi$
$113$	−5.70370	−	9.87909i	−0.536559	−	0.929347i	0.462528	−	0.886605i	$-0.346943\pi$
$114$	3.43444	+	9.63557i	0.321665	+	0.902453i
$115$	−4.43312	−	7.56030i	−0.413390	−	0.705002i
$116$	6.15260			0.571254
$117$	−9.86371	+	8.05484i	−0.911900	+	0.744670i
$118$	−6.72767	−	3.88422i	−0.619332	−	0.357572i
$119$	0.187300	+	0.324413i	0.0171698	+	0.0297389i
$120$	0.672286	−	3.81419i	0.0613711	−	0.348186i
$121$	2.69191	−	4.66253i	0.244719	−	0.423866i
$122$		−	7.88942i		−	0.714275i
$123$	−2.30994	+	12.6079i	−0.208281	+	1.13682i
$124$	−5.18162	−	2.03737i	−0.465323	−	0.182961i
$125$	0.225936	+	11.1781i	0.0202084	+	0.999796i
$126$	−1.22328	+	3.22633i	−0.108978	+	0.287425i
$127$	−6.22733	+	10.7860i	−0.552586	+	0.957107i	0.445501	+	0.895281i	$0.353026\pi$
$127$	−6.22733	+	10.7860i	−0.552586	+	0.957107i	−0.998087	+	0.0618254i	$0.980308\pi$
$128$	1.00000			0.0883883
$129$	3.39915	+	9.53655i	0.299278	+	0.839647i
$130$	8.25201	+	4.69047i	0.723749	+	0.411381i
$131$	−11.2712	−	6.50743i	−0.984770	−	0.568557i	−0.0810631	−	0.996709i	$-0.525832\pi$
$131$	−11.2712	−	6.50743i	−0.984770	−	0.568557i	−0.903707	+	0.428152i	$0.859165\pi$
$132$	4.03749	+	0.739723i	0.351419	+	0.0643847i
$133$	−5.88265	+	3.39635i	−0.510091	+	0.294501i
$134$	5.51167	−	3.18217i	0.476136	−	0.274897i
$135$	−11.6179	−	0.154254i	−0.999912	−	0.0132761i
$136$	−0.282061	−	0.162848i	−0.0241865	−	0.0139641i
$137$	4.03169	−	2.32769i	0.344450	−	0.198868i	−0.317788	−	0.948162i	$-0.602940\pi$
$137$	4.03169	−	2.32769i	0.344450	−	0.198868i	0.662238	+	0.749293i	$0.269607\pi$
$138$	−5.17122	−	4.39829i	−0.440203	−	0.374407i
$139$			13.6026i			1.15376i	0.816828	+	0.576881i	$0.195730\pi$
$139$			13.6026i			1.15376i	−0.816828	+	0.576881i	$0.804270\pi$
$140$	2.57176	−	0.0173251i	0.217353	−	0.00146424i
$141$	10.9351	−	12.8568i	0.920902	−	1.08274i
$142$	−5.90885	+	3.41147i	−0.495859	+	0.286285i
$143$	−5.02989	+	8.71203i	−0.420621	+	0.728536i
$144$	−0.481481	−	2.96111i	−0.0401234	−	0.246759i
$145$	−11.8678	+	6.95892i	−0.985570	+	0.577907i
$146$	−7.91524	−	13.7096i	−0.655070	−	1.13461i
$147$	9.67212	+	1.77206i	0.797743	+	0.146157i
$148$	−2.70854	+	4.69134i	−0.222641	+	0.385625i
$149$	20.5556	+	11.8678i	1.68398	+	0.972247i	0.958969	+	0.283510i	$0.0914989\pi$
$149$	20.5556	+	11.8678i	1.68398	+	0.972247i	0.725012	+	0.688737i	$0.241834\pi$
$150$	3.01727	+	8.11764i	0.246359	+	0.662803i
$151$			8.61990i			0.701478i	0.936473	+	0.350739i	$0.114069\pi$
$151$			8.61990i			0.701478i	−0.936473	+	0.350739i	$0.885931\pi$
$152$	2.95296	−	5.11467i	0.239516	−	0.414855i
$153$	−0.346404	+	0.913622i	−0.0280051	+	0.0738620i
$154$			2.72568i			0.219642i
$155$	12.2993	−	1.93078i	0.987901	−	0.155084i
$156$	7.23202	+	1.32500i	0.579025	+	0.106085i
$157$		−	16.1601i		−	1.28972i	−0.764301	−	0.644860i	$-0.776916\pi$
$157$		−	16.1601i		−	1.28972i	0.764301	−	0.644860i	$-0.223084\pi$
$158$	−1.66882	−	0.963496i	−0.132765	−	0.0766517i
$159$	2.14448	−	11.7048i	0.170068	−	0.928252i
$160$	−1.92892	+	1.13105i	−0.152494	+	0.0894177i
$161$	2.25399	−	3.90402i	0.177639	−	0.307680i
$162$	−8.53635	+	2.85144i	−0.670679	+	0.224030i
$163$		−	15.1298i		−	1.18506i	−0.805550	−	0.592528i	$-0.798130\pi$
$163$		−	15.1298i		−	1.18506i	0.805550	−	0.592528i	$-0.201870\pi$
$164$	6.40890	−	3.70018i	0.500451	−	0.288935i
$165$	−8.62465	+	3.13976i	−0.671428	+	0.244430i
$166$	4.70315	−	2.71537i	0.365035	−	0.210753i
$167$	12.3209	+	7.11348i	0.953420	+	0.550458i	0.894142	−	0.447784i	$-0.147787\pi$
$167$	12.3209	+	7.11348i	0.953420	+	0.550458i	0.0592786	+	0.998241i	$0.481120\pi$
$168$	1.87649	−	0.668843i	0.144774	−	0.0516023i
$169$	−2.50962	+	4.34679i	−0.193048	+	0.334369i
$170$	0.728262	−	0.00490607i	0.0558552	−	0.000376279i
$171$	−16.5669	−	6.28142i	−1.26690	−	0.480352i
$172$	2.92261	−	5.06211i	0.222847	−	0.385983i
$173$	−1.11273	−	1.92730i	−0.0845989	−	0.146530i	0.820621	−	0.571472i	$-0.193628\pi$
$173$	−1.11273	−	1.92730i	−0.0845989	−	0.146530i	−0.905220	+	0.424943i	$0.860294\pi$
$174$	−6.90424	+	8.11756i	−0.523409	+	0.615390i
$175$	−4.94111	+	2.94222i	−0.373513	+	0.222411i
$176$	−1.18492	−	2.05235i	−0.0893170	−	0.154702i
$177$	12.6743	−	4.51755i	0.952659	−	0.339560i
$178$	−6.10143			−0.457322
$179$	−4.88016	+	8.45268i	−0.364760	+	0.631783i	−0.988738	−	0.149659i	$-0.952182\pi$
$179$	−4.88016	+	8.45268i	−0.364760	+	0.631783i	0.623978	+	0.781442i	$0.285516\pi$
$180$	4.27791	+	5.16715i	0.318857	+	0.385137i
$181$	2.88528	−	1.66582i	0.214461	−	0.123819i	−0.388922	−	0.921271i	$-0.627152\pi$
$181$	2.88528	−	1.66582i	0.214461	−	0.123819i	0.603383	+	0.797452i	$0.293819\pi$
$182$			4.88229i			0.361899i
$183$	10.4091	+	8.85325i	0.769461	+	0.654451i
$184$			3.91946i			0.288946i
$185$	−0.0815994	−	12.1127i	−0.00599931	−	0.890544i
$186$	8.50268	−	4.55021i	0.623447	−	0.333638i
$187$			0.771850i			0.0564433i
$188$	−9.74464			−0.710701
$189$	−2.88401	−	5.23445i	−0.209781	−	0.380750i
$190$	0.0889628	+	13.2057i	0.00645404	+	0.958044i
$191$	4.71452	−	2.72193i	0.341130	−	0.196952i	−0.319641	−	0.947539i	$-0.603562\pi$
$191$	4.71452	−	2.72193i	0.341130	−	0.196952i	0.660772	+	0.750587i	$0.270229\pi$
$192$	−1.12217	+	1.31937i	−0.0809854	+	0.0952174i
$193$	−0.398168	−	0.229882i	−0.0286607	−	0.0165473i	0.485601	−	0.874180i	$-0.338601\pi$
$193$	−0.398168	−	0.229882i	−0.0286607	−	0.0165473i	−0.514262	+	0.857633i	$0.671934\pi$
$194$			12.1521i			0.872467i
$195$	−15.4486	+	5.62398i	−1.10630	+	0.402742i
$196$	−2.83858	−	4.91656i	−0.202755	−	0.351183i
$197$	12.8639	−	7.42698i	0.916515	−	0.529150i	0.0339935	−	0.999422i	$-0.489177\pi$
$197$	12.8639	−	7.42698i	0.916515	−	0.529150i	0.882522	+	0.470272i	$0.155844\pi$
$198$	−5.50671	+	4.49686i	−0.391345	+	0.319578i
$199$	−8.34879	+	4.82018i	−0.591830	+	0.341693i	−0.765821	−	0.643054i	$-0.777667\pi$
$199$	−8.34879	+	4.82018i	−0.591830	+	0.341693i	0.173991	+	0.984747i	$0.444334\pi$
$200$	2.44143	−	4.36342i	0.172635	−	0.308540i
$201$	−1.98656	+	10.8429i	−0.140121	+	0.764797i
$202$		−	9.75329i		−	0.686239i
$203$	−6.12836	−	3.53821i	−0.430126	−	0.248334i
$204$	0.531377	−	0.189401i	0.0372038	−	0.0132607i
$205$	−8.17712	+	14.3861i	−0.571115	+	1.00477i
$206$	2.47328	−	1.42795i	0.172322	−	0.0994900i
$207$	11.6059	−	1.88714i	0.806669	−	0.131166i
$208$	−2.12245	−	3.67620i	−0.147166	−	0.254898i
$209$	−13.9961			−0.968132
$210$	−2.86309	+	3.41255i	−0.197572	+	0.235488i
$211$	−11.6563	+	20.1893i	−0.802452	+	1.38989i	0.115546	+	0.993302i	$0.463138\pi$
$211$	−11.6563	+	20.1893i	−0.802452	+	1.38989i	−0.917998	+	0.396585i	$0.870195\pi$
$212$	−5.94982	+	3.43513i	−0.408635	+	0.235926i
$213$	2.12971	−	11.6242i	0.145926	−	0.796478i
$214$	−8.09940	+	14.0286i	−0.553664	+	0.958974i
$215$	0.0880486	+	13.0700i	0.00600487	+	0.891368i
$216$	4.44711	+	2.68761i	0.302587	+	0.182869i
$217$	3.98956	+	5.00916i	0.270829	+	0.340044i
$218$	11.4068			0.772565
$219$	26.9703	+	4.94132i	1.82248	+	0.333904i
$220$	4.60693	+	2.61859i	0.310599	+	0.176546i
$221$			1.38255i			0.0930004i
$222$	−3.15017	−	8.83804i	−0.211426	−	0.593170i
$223$	−3.51266	+	6.08411i	−0.235225	+	0.407422i	−0.959338	−	0.282260i	$-0.908916\pi$
$223$	−3.51266	+	6.08411i	−0.235225	+	0.407422i	0.724113	+	0.689681i	$0.242249\pi$
$224$	−0.996061	−	0.575076i	−0.0665521	−	0.0384239i
$225$	−14.0961	−	5.12845i	−0.939737	−	0.341897i
$226$	−5.70370	−	9.87909i	−0.379404	−	0.657147i
$227$	−1.06064	−	1.83708i	−0.0703972	−	0.121931i	0.828678	−	0.559725i	$-0.189093\pi$
$227$	−1.06064	−	1.83708i	−0.0703972	−	0.121931i	−0.899075	+	0.437794i	$0.855760\pi$
$228$	3.43444	+	9.63557i	0.227451	+	0.638131i
$229$	−16.2859	−	9.40267i	−1.07620	−	0.621346i	−0.146334	−	0.989235i	$-0.546747\pi$
$229$	−16.2859	−	9.40267i	−1.07620	−	0.621346i	−0.929870	+	0.367889i	$0.880081\pi$
$230$	−4.43312	−	7.56030i	−0.292311	−	0.498512i
$231$	−3.59619	−	3.05867i	−0.236612	−	0.201246i
$232$	6.15260			0.403938
$233$	−16.5941			−1.08711			−0.543556	−	0.839373i	$-0.682923\pi$
$233$	−16.5941			−1.08711			−0.543556	+	0.839373i	$0.682923\pi$
$234$	−9.86371	+	8.05484i	−0.644811	+	0.526561i
$235$	18.7966	−	11.0217i	1.22615	−	0.718977i
$236$	−6.72767	−	3.88422i	−0.437934	−	0.252841i
$237$	3.14391	−	1.12060i	0.204219	−	0.0727905i
$238$	0.187300	+	0.324413i	0.0121409	+	0.0210286i
$239$	5.63430	+	9.75890i	0.364453	+	0.631251i	0.988688	−	0.149986i	$-0.0479228\pi$
$239$	5.63430	+	9.75890i	0.364453	+	0.631251i	−0.624236	+	0.781236i	$0.714589\pi$
$240$	0.672286	−	3.81419i	0.0433959	−	0.246205i
$241$	19.8736	+	11.4740i	1.28017	+	0.739106i	0.976879	−	0.213792i	$-0.0685816\pi$
$241$	19.8736	+	11.4740i	1.28017	+	0.739106i	0.303290	+	0.952898i	$0.401915\pi$
$242$	2.69191	−	4.66253i	0.173043	−	0.299719i
$243$	5.81711	−	14.4624i	0.373168	−	0.927764i
$244$		−	7.88942i		−	0.505069i
$245$	11.0363	+	6.27304i	0.705081	+	0.400770i
$246$	−2.30994	+	12.6079i	−0.147277	+	0.803852i
$247$	−25.0701			−1.59517
$248$	−5.18162	−	2.03737i	−0.329033	−	0.129373i
$249$	−1.69515	+	9.25230i	−0.107426	+	0.586341i
$250$	0.225936	+	11.1781i	0.0142895	+	0.706962i
$251$	8.16084	−	14.1350i	0.515108	−	0.892193i	−0.484739	−	0.874659i	$-0.661085\pi$
$251$	8.16084	−	14.1350i	0.515108	−	0.892193i	0.999846	−	0.0175335i	$-0.00558138\pi$
$252$	−1.22328	+	3.22633i	−0.0770593	+	0.203240i
$253$	8.04409	−	4.64426i	0.505728	−	0.291982i
$254$	−6.22733	+	10.7860i	−0.390737	+	0.676777i
$255$	−0.810759	+	0.966354i	−0.0507717	+	0.0605154i
$256$	1.00000			0.0625000
$257$	1.66337	+	2.88103i	0.103758	+	0.179714i	0.913230	−	0.407444i	$-0.133580\pi$
$257$	1.66337	+	2.88103i	0.103758	+	0.179714i	−0.809472	+	0.587158i	$0.800247\pi$
$258$	3.39915	+	9.53655i	0.211622	+	0.593720i
$259$	5.39575	−	3.11524i	0.335276	−	0.193571i
$260$	8.25201	+	4.69047i	0.511768	+	0.290890i
$261$	−2.96236	−	18.2185i	−0.183365	−	1.12770i
$262$	−11.2712	−	6.50743i	−0.696337	−	0.402031i
$263$		−	3.51416i		−	0.216692i	−0.994113	−	0.108346i	$-0.965444\pi$
$263$		−	3.51416i		−	0.216692i	0.994113	−	0.108346i	$-0.0345555\pi$
$264$	4.03749	+	0.739723i	0.248490	+	0.0455268i
$265$	7.59139	−	13.3556i	0.466335	−	0.820431i
$266$	−5.88265	+	3.39635i	−0.360688	+	0.208244i
$267$	6.84683	−	8.05006i	0.419019	−	0.492656i
$268$	5.51167	−	3.18217i	0.336679	−	0.194382i
$269$	14.5882	+	25.2676i	0.889461	+	1.54059i	0.840514	+	0.541790i	$0.182253\pi$
$269$	14.5882	+	25.2676i	0.889461	+	1.54059i	0.0489471	+	0.998801i	$0.484413\pi$
$270$	−11.6179	−	0.154254i	−0.707044	−	0.00938763i
$271$			17.4293i			1.05876i	0.848386	+	0.529378i	$0.177575\pi$
$271$			17.4293i			1.05876i	−0.848386	+	0.529378i	$0.822425\pi$
$272$	−0.282061	−	0.162848i	−0.0171025	−	0.00987411i
$273$	−6.44155	−	5.47875i	−0.389860	−	0.331589i
$274$	4.03169	−	2.32769i	0.243563	−	0.140621i
$275$	−11.8482	+	0.159642i	−0.714471	+	0.00962677i
$276$	−5.17122	−	4.39829i	−0.311271	−	0.264746i
$277$	−3.05552			−0.183588			−0.0917942	−	0.995778i	$-0.529260\pi$
$277$	−3.05552			−0.183588			−0.0917942	+	0.995778i	$0.529260\pi$
$278$			13.6026i			0.815833i
$279$	−3.53802	+	16.3243i	−0.211815	+	0.977310i
$280$	2.57176	−	0.0173251i	0.153692	−	0.00103537i
$281$			13.7415i			0.819749i	0.912142	+	0.409874i	$0.134427\pi$
$281$			13.7415i			0.819749i	−0.912142	+	0.409874i	$0.865573\pi$
$282$	10.9351	−	12.8568i	0.651176	−	0.765611i
$283$			5.87010i			0.348941i	0.984662	+	0.174471i	$0.0558214\pi$
$283$			5.87010i			0.348941i	−0.984662	+	0.174471i	$0.944179\pi$
$284$	−5.90885	+	3.41147i	−0.350626	+	0.202434i
$285$	−17.5231	−	14.7017i	−1.03798	−	0.870851i
$286$	−5.02989	+	8.71203i	−0.297424	+	0.515153i
$287$	−8.51153			−0.502420
$288$	−0.481481	−	2.96111i	−0.0283716	−	0.174485i
$289$	−8.44696	−	14.6306i	−0.496880	−	0.860622i
$290$	−11.8678	+	6.95892i	−0.696904	+	0.408642i
$291$	−16.0331	−	13.6366i	−0.939875	−	0.799394i
$292$	−7.91524	−	13.7096i	−0.463204	−	0.802294i
$293$	16.3181	−	28.2638i	0.953313	−	1.65119i	0.215130	−	0.976585i	$-0.430982\pi$
$293$	16.3181	−	28.2638i	0.953313	−	1.65119i	0.738183	−	0.674601i	$-0.235684\pi$
$294$	9.67212	+	1.77206i	0.564089	+	0.103349i
$295$	17.3704	−	0.117019i	1.01134	−	0.00681309i
$296$	−2.70854	+	4.69134i	−0.157431	+	0.272678i
$297$	0.246426	−	12.3116i	0.0142991	−	0.714393i
$298$	20.5556	+	11.8678i	1.19075	+	0.687482i
$299$	14.4087	−	8.31887i	0.833277	−	0.481092i
$300$	3.01727	+	8.11764i	0.174202	+	0.468672i
$301$	−5.82220	+	3.36145i	−0.335586	+	0.193751i
$302$			8.61990i			0.496020i
$303$	12.8682	+	10.9448i	0.739259	+	0.628764i
$304$	2.95296	−	5.11467i	0.169364	−	0.293347i
$305$	8.92336	+	15.2180i	0.510950	+	0.871382i
$306$	−0.346404	+	0.913622i	−0.0198026	+	0.0522283i
$307$	8.09277	+	4.67236i	0.461879	+	0.266666i	0.712834	−	0.701333i	$-0.247411\pi$
$307$	8.09277	+	4.67236i	0.461879	+	0.266666i	−0.250955	+	0.967999i	$0.580745\pi$
$308$			2.72568i			0.155310i
$309$	−0.891440	+	4.86558i	−0.0507123	+	0.276793i
$310$	12.2993	−	1.93078i	0.698552	−	0.109661i
$311$		−	11.9460i		−	0.677393i	−0.940896	−	0.338697i	$-0.890014\pi$
$311$		−	11.9460i		−	0.677393i	0.940896	−	0.338697i	$-0.109986\pi$
$312$	7.23202	+	1.32500i	0.409432	+	0.0750136i
$313$	−5.17715	+	8.96708i	−0.292630	+	0.506849i	−0.974431	−	0.224688i	$-0.927864\pi$
$313$	−5.17715	+	8.96708i	−0.292630	+	0.506849i	0.681801	+	0.731538i	$0.261197\pi$
$314$		−	16.1601i		−	0.911970i
$315$	−1.28956	−	7.60692i	−0.0726582	−	0.428602i
$316$	−1.66882	−	0.963496i	−0.0938787	−	0.0542009i
$317$	17.1526	−	29.7092i	0.963387	−	1.66864i	0.249500	−	0.968375i	$-0.419734\pi$
$317$	17.1526	−	29.7092i	0.963387	−	1.66864i	0.713888	−	0.700260i	$-0.246933\pi$
$318$	2.14448	−	11.7048i	0.120257	−	0.656373i
$319$	−7.29036	−	12.6273i	−0.408182	−	0.706991i
$320$	−1.92892	+	1.13105i	−0.107830	+	0.0632278i
$321$	−9.42002	−	26.4285i	−0.525774	−	1.47510i
$322$	2.25399	−	3.90402i	0.125610	−	0.217562i
$323$	−1.66583	+	0.961767i	−0.0926892	+	0.0535141i
$324$	−8.53635	+	2.85144i	−0.474242	+	0.158413i
$325$	−21.2226	+	0.285953i	−1.17722	+	0.0158618i
$326$		−	15.1298i		−	0.837962i
$327$	−12.8003	+	15.0498i	−0.707859	+	0.832255i
$328$	6.40890	−	3.70018i	0.353872	−	0.204308i
$329$	9.70625	+	5.60391i	0.535123	+	0.308953i
$330$	−8.62465	+	3.13976i	−0.474771	+	0.172838i
$331$	15.4178	−	8.90148i	0.847440	−	0.489270i	−0.0123462	−	0.999924i	$-0.503930\pi$
$331$	15.4178	−	8.90148i	0.847440	−	0.489270i	0.859786	+	0.510654i	$0.170597\pi$
$332$	4.70315	−	2.71537i	0.258119	−	0.149025i
$333$	15.1957	+	5.76151i	0.832718	+	0.315729i
$334$	12.3209	+	7.11348i	0.674170	+	0.389232i
$335$	−7.03236	+	12.3721i	−0.384219	+	0.675962i
$336$	1.87649	−	0.668843i	0.102371	−	0.0364884i
$337$	17.1276			0.932999			0.466500	−	0.884521i	$-0.345515\pi$
$337$	17.1276			0.932999			0.466500	+	0.884521i	$0.345515\pi$
$338$	−2.50962	+	4.34679i	−0.136505	+	0.236434i
$339$	19.4347	+	3.56070i	1.05555	+	0.193391i
$340$	0.728262	−	0.00490607i	0.0394956	−	0.000266069i
$341$	1.95843	+	13.0486i	0.106055	+	0.706621i
$342$	−16.5669	−	6.28142i	−0.895836	−	0.339660i
$343$			14.5806i			0.787281i
$344$	2.92261	−	5.06211i	0.157577	−	0.272931i
$345$	14.9495	+	2.63500i	0.804856	+	0.141864i
$346$	−1.11273	−	1.92730i	−0.0598205	−	0.103612i
$347$	2.68079	+	1.54776i	0.143912	+	0.0830879i	0.570227	−	0.821487i	$-0.306855\pi$
$347$	2.68079	+	1.54776i	0.143912	+	0.0830879i	−0.426315	+	0.904575i	$0.640188\pi$
$348$	−6.90424	+	8.11756i	−0.370106	+	0.435147i
$349$	5.53280			0.296164			0.148082	−	0.988975i	$-0.452690\pi$
$349$	5.53280			0.296164			0.148082	+	0.988975i	$0.452690\pi$
$350$	−4.94111	+	2.94222i	−0.264114	+	0.157268i
$351$	0.441403	−	22.0528i	0.0235603	−	1.17709i
$352$	−1.18492	−	2.05235i	−0.0631566	−	0.109391i
$353$	10.3291	+	5.96353i	0.549765	+	0.317407i	0.749027	−	0.662539i	$-0.230521\pi$
$353$	10.3291	+	5.96353i	0.549765	+	0.317407i	−0.199262	+	0.979946i	$0.563855\pi$
$354$	12.6743	−	4.51755i	0.673632	−	0.240105i
$355$	7.53911	−	13.2637i	0.400134	−	0.703963i
$356$	−6.10143			−0.323375
$357$	−0.638203	−	0.116928i	−0.0337773	−	0.00618846i
$358$	−4.88016	+	8.45268i	−0.257924	+	0.446738i
$359$	−6.38325	+	3.68537i	−0.336895	+	0.194507i	−0.658898	−	0.752232i	$-0.728977\pi$
$359$	−6.38325	+	3.68537i	−0.336895	+	0.194507i	0.322003	+	0.946739i	$0.395644\pi$
$360$	4.27791	+	5.16715i	0.225466	+	0.272333i
$361$	−7.93992	−	13.7523i	−0.417890	−	0.723807i
$362$	2.88528	−	1.66582i	0.151647	−	0.0875534i
$363$	3.13083	+	8.78377i	0.164326	+	0.461028i
$364$			4.88229i			0.255901i
$365$	30.7741	+	17.4921i	1.61079	+	0.915578i
$366$	10.4091	+	8.85325i	0.544091	+	0.462767i
$367$	−2.44646	−	4.23739i	−0.127704	−	0.221190i	0.795083	−	0.606501i	$-0.207427\pi$
$367$	−2.44646	−	4.23739i	−0.127704	−	0.221190i	−0.922787	+	0.385311i	$0.874094\pi$
$368$			3.91946i			0.204316i
$369$	−14.0424	−	17.1959i	−0.731018	−	0.895182i
$370$	−0.0815994	−	12.1127i	−0.00424215	−	0.629709i
$371$	7.90185			0.410243
$372$	8.50268	−	4.55021i	0.440844	−	0.235917i
$373$		−	25.5466i		−	1.32276i	−0.750053	−	0.661378i	$-0.769972\pi$
$373$		−	25.5466i		−	1.32276i	0.750053	−	0.661378i	$-0.230028\pi$
$374$			0.771850i			0.0399114i
$375$	−15.0015	−	12.2456i	−0.774676	−	0.632358i
$376$	−9.74464			−0.502541
$377$	−13.0586	−	22.6182i	−0.672552	−	1.16489i
$378$	−2.88401	−	5.23445i	−0.148337	−	0.269231i
$379$	0.132403	−	0.229328i	0.00680108	−	0.0117798i	−0.862605	−	0.505878i	$-0.831168\pi$
$379$	0.132403	−	0.229328i	0.00680108	−	0.0117798i	0.869406	+	0.494099i	$0.164502\pi$
$380$	0.0889628	+	13.2057i	0.00456370	+	0.677440i
$381$	−7.24270	−	20.3199i	−0.371055	−	1.04102i
$382$	4.71452	−	2.72193i	0.241216	−	0.139266i
$383$	−33.2231	+	19.1814i	−1.69762	+	0.980122i	−0.749612	+	0.661878i	$0.769760\pi$
$383$	−33.2231	+	19.1814i	−1.69762	+	0.980122i	−0.948009	+	0.318244i	$0.896907\pi$
$384$	−1.12217	+	1.31937i	−0.0572654	+	0.0673289i
$385$	−3.08290	−	5.25762i	−0.157119	−	0.267953i
$386$	−0.398168	−	0.229882i	−0.0202662	−	0.0117007i
$387$	−16.3967	−	6.21687i	−0.833489	−	0.316021i
$388$			12.1521i			0.616927i
$389$	7.96052	−	13.7880i	0.403614	−	0.699080i	−0.590545	−	0.807005i	$-0.701087\pi$
$389$	7.96052	−	13.7880i	0.403614	−	0.699080i	0.994159	+	0.107924i	$0.0344205\pi$
$390$	−15.4486	+	5.62398i	−0.782271	+	0.284781i
$391$	0.638276	−	1.10553i	0.0322790	−	0.0559089i
$392$	−2.83858	−	4.91656i	−0.143370	−	0.248324i
$393$	21.2339	−	7.56848i	1.07111	−	0.381779i
$394$	12.8639	−	7.42698i	0.648074	−	0.374166i
$395$	4.30879	−	0.0290269i	0.216799	−	0.00146050i
$396$	−5.50671	+	4.49686i	−0.276723	+	0.225976i
$397$	16.2347	+	9.37313i	0.814798	+	0.470424i	0.848619	−	0.529004i	$-0.177434\pi$
$397$	16.2347	+	9.37313i	0.814798	+	0.470424i	−0.0338214	+	0.999428i	$0.510768\pi$
$398$	−8.34879	+	4.82018i	−0.418487	+	0.241614i
$399$	2.12027	−	11.5727i	0.106146	−	0.579358i
$400$	2.44143	−	4.36342i	0.122072	−	0.218171i
$401$	7.69817			0.384428			0.192214	−	0.981353i	$-0.438433\pi$
$401$	7.69817			0.384428			0.192214	+	0.981353i	$0.438433\pi$
$402$	−1.98656	+	10.8429i	−0.0990807	+	0.540793i
$403$	3.50798	+	23.3729i	0.174745	+	1.16429i
$404$		−	9.75329i		−	0.485244i
$405$	13.2408	−	15.1553i	0.657939	−	0.753071i
$406$	−6.12836	−	3.53821i	−0.304145	−	0.175598i
$407$	12.8377			0.636340
$408$	0.531377	−	0.189401i	0.0263071	−	0.00937673i
$409$	−1.71414	−	0.989662i	−0.0847590	−	0.0489356i	0.457021	−	0.889456i	$-0.348916\pi$
$409$	−1.71414	−	0.989662i	−0.0847590	−	0.0489356i	−0.541780	+	0.840520i	$0.682250\pi$
$410$	−8.17712	+	14.3861i	−0.403839	+	0.710481i
$411$	−1.45313	+	7.93135i	−0.0716777	+	0.391225i
$412$	2.47328	−	1.42795i	0.121850	−	0.0703501i
$413$	4.46745	+	7.73784i	0.219829	+	0.380754i
$414$	11.6059	−	1.88714i	0.570401	−	0.0927481i
$415$	−6.00076	+	10.5572i	−0.294566	+	0.518234i
$416$	−2.12245	−	3.67620i	−0.104062	−	0.180240i
$417$	−17.9469	−	15.2644i	−0.878866	−	0.747503i
$418$	−13.9961			−0.684572
$419$			3.70987i			0.181239i	0.995886	+	0.0906196i	$0.0288847\pi$
$419$			3.70987i			0.181239i	−0.995886	+	0.0906196i	$0.971115\pi$
$420$	−2.86309	+	3.41255i	−0.139704	+	0.166515i
$421$	2.92363	+	5.06387i	0.142489	+	0.246798i	0.928433	−	0.371499i	$-0.121156\pi$
$421$	2.92363	+	5.06387i	0.142489	+	0.246798i	−0.785944	+	0.618297i	$0.787823\pi$
$422$	−11.6563	+	20.1893i	−0.567419	+	0.982799i
$423$	4.69186	+	28.8549i	0.228126	+	1.40298i
$424$	−5.94982	+	3.43513i	−0.288949	+	0.166825i
$425$	−1.39921	+	0.833167i	−0.0678715	+	0.0404145i
$426$	2.12971	−	11.6242i	0.103185	−	0.563195i
$427$	−4.53702	+	7.85834i	−0.219562	+	0.380292i
$428$	−8.09940	+	14.0286i	−0.391499	+	0.678097i
$429$	−5.85002	−	16.4126i	−0.282442	−	0.792410i
$430$	0.0880486	+	13.0700i	0.00424608	+	0.630293i
$431$	0.535714	+	0.309295i	0.0258044	+	0.0148982i	0.512847	−	0.858480i	$-0.328591\pi$
$431$	0.535714	+	0.309295i	0.0258044	+	0.0148982i	−0.487042	+	0.873378i	$0.661924\pi$
$432$	4.44711	+	2.68761i	0.213962	+	0.129308i
$433$	−19.8014			−0.951597			−0.475798	−	0.879554i	$-0.657841\pi$
$433$	−19.8014			−0.951597			−0.475798	+	0.879554i	$0.657841\pi$
$434$	3.98956	+	5.00916i	0.191505	+	0.240448i
$435$	4.13631	−	23.4672i	0.198321	−	1.12516i
$436$	11.4068			0.546286
$437$	20.0467	+	11.5740i	0.958966	+	0.553659i
$438$	26.9703	+	4.94132i	1.28869	+	0.236105i
$439$	−17.6243	−	30.5262i	−0.841161	−	1.45693i	−0.888914	−	0.458075i	$-0.848539\pi$
$439$	−17.6243	−	30.5262i	−0.841161	−	1.45693i	0.0477523	−	0.998859i	$-0.484794\pi$
$440$	4.60693	+	2.61859i	0.219627	+	0.124837i
$441$	−13.1917	+	10.7726i	−0.628178	+	0.512979i
$442$			1.38255i			0.0657612i
$443$	−10.2043	−	17.6744i	−0.484822	−	0.839736i	0.515026	−	0.857174i	$-0.327782\pi$
$443$	−10.2043	−	17.6744i	−0.484822	−	0.839736i	−0.999848	+	0.0174385i	$0.994449\pi$
$444$	−3.15017	−	8.83804i	−0.149501	−	0.419435i
$445$	11.7692	−	6.90105i	0.557911	−	0.327141i
$446$	−3.51266	+	6.08411i	−0.166329	+	0.288091i
$447$	−38.7248	+	13.8028i	−1.83162	+	0.652852i
$448$	−0.996061	−	0.575076i	−0.0470595	−	0.0271698i
$449$	−32.2841			−1.52358			−0.761791	−	0.647823i	$-0.775680\pi$
$449$	−32.2841			−1.52358			−0.761791	+	0.647823i	$0.775680\pi$
$450$	−14.0961	−	5.12845i	−0.664495	−	0.241758i
$451$	−15.1881	−	8.76885i	−0.715180	−	0.412909i
$452$	−5.70370	−	9.87909i	−0.268279	−	0.464673i
$453$	−11.3728	−	9.67297i	−0.534343	−	0.454476i
$454$	−1.06064	−	1.83708i	−0.0497783	−	0.0862186i
$455$	−5.52213	−	9.41753i	−0.258882	−	0.441500i
$456$	3.43444	+	9.63557i	0.160832	+	0.451227i
$457$	0.447328			0.0209251			0.0104626	−	0.999945i	$-0.496670\pi$
$457$	0.447328			0.0209251			0.0104626	+	0.999945i	$0.496670\pi$
$458$	−16.2859	−	9.40267i	−0.760991	−	0.439358i
$459$	−0.816684	−	1.48227i	−0.0381195	−	0.0691866i
$460$	−4.43312	−	7.56030i	−0.206695	−	0.352501i
$461$	5.05183			0.235287			0.117644	−	0.993056i	$-0.462466\pi$
$461$	5.05183			0.235287			0.117644	+	0.993056i	$0.462466\pi$
$462$	−3.59619	−	3.05867i	−0.167310	−	0.142302i
$463$	13.8424			0.643310			0.321655	−	0.946857i	$-0.395761\pi$
$463$	13.8424			0.643310			0.321655	+	0.946857i	$0.395761\pi$
$464$	6.15260			0.285627
$465$	−11.2544	+	18.3940i	−0.521912	+	0.853000i
$466$	−16.5941			−0.768705
$467$	16.8843			0.781315			0.390657	−	0.920536i	$-0.372248\pi$
$467$	16.8843			0.781315			0.390657	+	0.920536i	$0.372248\pi$
$468$	−9.86371	+	8.05484i	−0.455950	+	0.372335i
$469$	−7.31995			−0.338004
$470$	18.7966	−	11.0217i	0.867022	−	0.508393i
$471$	21.3212	+	18.1344i	0.982431	+	0.835589i
$472$	−6.72767	−	3.88422i	−0.309666	−	0.178786i
$473$	−13.8523			−0.636929
$474$	3.14391	−	1.12060i	0.144405	−	0.0514706i
$475$	−15.1080	−	25.3721i	−0.693202	−	1.16415i
$476$	0.187300	+	0.324413i	0.00858488	+	0.0148695i
$477$	13.0365	+	15.9641i	0.596902	+	0.730947i
$478$	5.63430	+	9.75890i	0.257707	+	0.446362i
$479$	−12.1074	−	6.99019i	−0.553200	−	0.319390i	0.197212	−	0.980361i	$-0.436811\pi$
$479$	−12.1074	−	6.99019i	−0.553200	−	0.319390i	−0.750412	+	0.660971i	$0.770145\pi$
$480$	0.672286	−	3.81419i	0.0306855	−	0.174093i
$481$	22.9950			1.04848
$482$	19.8736	+	11.4740i	0.905216	+	0.522627i
$483$	2.62150	+	7.35480i	0.119282	+	0.334655i
$484$	2.69191	−	4.66253i	0.122360	−	0.211933i
$485$	−13.7446	−	23.4403i	−0.624111	−	1.06437i
$486$	5.81711	−	14.4624i	0.263869	−	0.656028i
$487$	2.36047	+	4.08845i	0.106963	+	0.185265i	0.914538	−	0.404499i	$-0.132554\pi$
$487$	2.36047	+	4.08845i	0.106963	+	0.185265i	−0.807576	+	0.589764i	$0.799221\pi$
$488$		−	7.88942i		−	0.357137i
$489$	19.9618	+	16.9782i	0.902704	+	0.767779i
$490$	11.0363	+	6.27304i	0.498568	+	0.283387i
$491$	5.00068	+	8.66143i	0.225677	+	0.390885i	0.956522	−	0.291659i	$-0.0942071\pi$
$491$	5.00068	+	8.66143i	0.225677	+	0.390885i	−0.730845	+	0.682543i	$0.760874\pi$
$492$	−2.30994	+	12.6079i	−0.104140	+	0.568409i
$493$	−1.73541	−	1.00194i	−0.0781588	−	0.0451250i
$494$	−25.0701			−1.12796
$495$	5.53579	−	14.9024i	0.248815	−	0.669815i
$496$	−5.18162	−	2.03737i	−0.232661	−	0.0914804i
$497$	7.84743			0.352005
$498$	−1.69515	+	9.25230i	−0.0759614	+	0.414605i
$499$	31.3741	+	18.1139i	1.40450	+	0.810888i	0.994850	−	0.101355i	$-0.0323177\pi$
$499$	31.3741	+	18.1139i	1.40450	+	0.810888i	0.409649	+	0.912243i	$0.365651\pi$
$500$	0.225936	+	11.1781i	0.0101042	+	0.499898i
$501$	−23.2114	+	8.27334i	−1.03701	+	0.369625i
$502$	8.16084	−	14.1350i	0.364236	−	0.630875i
$503$	−0.284981	+	0.493601i	−0.0127067	+	0.0220086i	−0.872309	−	0.488955i	$-0.837378\pi$
$503$	−0.284981	+	0.493601i	−0.0127067	+	0.0220086i	0.859602	+	0.510964i	$0.170711\pi$
$504$	−1.22328	+	3.22633i	−0.0544892	+	0.143712i
$505$	11.0315	+	18.8133i	0.490895	+	0.837180i
$506$	8.04409	−	4.64426i	0.357603	−	0.206462i
$507$	−2.91882	−	8.18895i	−0.129629	−	0.363684i
$508$	−6.22733	+	10.7860i	−0.276293	+	0.478553i
$509$	10.3917	+	17.9989i	0.460603	+	0.797788i	0.998991	−	0.0449089i	$-0.0142997\pi$
$509$	10.3917	+	17.9989i	0.460603	+	0.797788i	−0.538388	+	0.842697i	$0.680966\pi$
$510$	−0.810759	+	0.966354i	−0.0359010	+	0.0427909i
$511$			18.2075i			0.805451i
$512$	1.00000			0.0441942
$513$	26.8784	−	14.8091i	1.18671	−	0.653838i
$514$	1.66337	+	2.88103i	0.0733679	+	0.127077i
$515$	−3.15567	+	5.55181i	−0.139055	+	0.244642i
$516$	3.39915	+	9.53655i	0.149639	+	0.419823i
$517$	11.5466	+	19.9994i	0.507821	+	0.879572i
$518$	5.39575	−	3.11524i	0.237076	−	0.136876i
$519$	3.79148	+	0.694652i	0.166428	+	0.0304918i
$520$	8.25201	+	4.69047i	0.361875	+	0.205691i
$521$	−21.4810	−	12.4021i	−0.941102	−	0.543345i	−0.0507962	−	0.998709i	$-0.516176\pi$
$521$	−21.4810	−	12.4021i	−0.941102	−	0.543345i	−0.890306	+	0.455364i	$0.849509\pi$
$522$	−2.96236	−	18.2185i	−0.129659	−	0.797403i
$523$	−8.92818			−0.390402			−0.195201	−	0.980763i	$-0.562536\pi$
$523$	−8.92818			−0.390402			−0.195201	+	0.980763i	$0.562536\pi$
$524$	−11.2712	−	6.50743i	−0.492385	−	0.284279i
$525$	1.66288	−	9.82082i	0.0725739	−	0.428616i
$526$		−	3.51416i		−	0.153225i
$527$	1.12975	+	1.41848i	0.0492127	+	0.0617899i
$528$	4.03749	+	0.739723i	0.175709	+	0.0321923i
$529$	7.63786			0.332081
$530$	7.59139	−	13.3556i	0.329749	−	0.580132i
$531$	−8.26237	+	21.7916i	−0.358556	+	0.945673i
$532$	−5.88265	+	3.39635i	−0.255045	+	0.147250i
$533$	−27.2052	−	15.7069i	−1.17839	−	0.680342i
$534$	6.84683	−	8.05006i	0.296291	−	0.348360i
$535$	−0.244008	−	36.2208i	−0.0105494	−	1.56596i
$536$	5.51167	−	3.18217i	0.238068	−	0.137449i
$537$	−5.67587	−	15.9241i	−0.244932	−	0.687174i
$538$	14.5882	+	25.2676i	0.628944	+	1.08936i
$539$	−6.72699	+	11.6515i	−0.289752	+	0.501865i
$540$	−11.6179	−	0.154254i	−0.499956	−	0.00663805i
$541$	20.8884	−	36.1798i	0.898062	−	1.55549i	0.0680933	−	0.997679i	$-0.478308\pi$
$541$	20.8884	−	36.1798i	0.898062	−	1.55549i	0.829969	−	0.557810i	$-0.188358\pi$
$542$			17.4293i			0.748654i
$543$	−1.03993	+	5.67608i	−0.0446279	+	0.243584i
$544$	−0.282061	−	0.162848i	−0.0120933	−	0.00698205i
$545$	−22.0027	+	12.9017i	−0.942493	+	0.552647i
$546$	−6.44155	−	5.47875i	−0.275673	−	0.234469i
$547$	−16.7262	+	9.65685i	−0.715159	+	0.412897i	−0.812968	−	0.582308i	$-0.802150\pi$
$547$	−16.7262	+	9.65685i	−0.715159	+	0.412897i	0.0978095	+	0.995205i	$0.468816\pi$
$548$	4.03169	−	2.32769i	0.172225	−	0.0994342i
$549$	−23.3615	+	3.79861i	−0.997042	+	0.162121i
$550$	−11.8482	+	0.159642i	−0.505207	+	0.00680715i
$551$	18.1684	−	31.4685i	0.773998	−	1.34060i
$552$	−5.17122	−	4.39829i	−0.220102	−	0.187203i
$553$	1.10817	+	1.91940i	0.0471241	+	0.0816213i
$554$	−3.05552			−0.129817
$555$	16.0727	+	13.4848i	0.682249	+	0.572399i
$556$			13.6026i			0.576881i
$557$			5.32274i			0.225532i	0.993622	+	0.112766i	$0.0359710\pi$
$557$			5.32274i			0.225532i	−0.993622	+	0.112766i	$0.964029\pi$
$558$	−3.53802	+	16.3243i	−0.149776	+	0.691062i
$559$	−24.8125			−1.04945
$560$	2.57176	−	0.0173251i	0.108677	−	0.000732120i
$561$	−1.01836	−	0.866145i	−0.0429951	−	0.0365687i
$562$			13.7415i			0.579650i
$563$	−15.2215	−	26.3644i	−0.641510	−	1.11113i	−0.985096	−	0.172006i	$-0.944975\pi$
$563$	−15.2215	−	26.3644i	−0.641510	−	1.11113i	0.343586	−	0.939121i	$-0.388358\pi$
$564$	10.9351	−	12.8568i	0.460451	−	0.541369i
$565$	22.1757	+	12.6047i	0.932940	+	0.530286i
$566$			5.87010i			0.246739i
$567$	10.1425	+	2.06884i	0.425946	+	0.0868833i
$568$	−5.90885	+	3.41147i	−0.247930	+	0.143142i
$569$	−20.1762	−	34.9463i	−0.845832	−	1.46502i	−0.884897	−	0.465787i	$-0.845771\pi$
$569$	−20.1762	−	34.9463i	−0.845832	−	1.46502i	0.0390654	−	0.999237i	$-0.487562\pi$
$570$	−17.5231	−	14.7017i	−0.733962	−	0.615785i
$571$	25.4693	−	14.7047i	1.06586	−	0.615372i	0.138809	−	0.990319i	$-0.455673\pi$
$571$	25.4693	−	14.7047i	1.06586	−	0.615372i	0.927046	+	0.374948i	$0.122339\pi$
$572$	−5.02989	+	8.71203i	−0.210310	+	0.364268i
$573$	−1.69924	+	9.27465i	−0.0709869	+	0.387454i
$574$	−8.51153			−0.355265
$575$	17.1022	+	9.56910i	0.713212	+	0.399059i
$576$	−0.481481	−	2.96111i	−0.0200617	−	0.123380i
$577$	9.45915	+	5.46124i	0.393790	+	0.227355i	0.683801	−	0.729669i	$-0.260326\pi$
$577$	9.45915	+	5.46124i	0.393790	+	0.227355i	−0.290011	+	0.957023i	$0.593659\pi$
$578$	−8.44696	−	14.6306i	−0.351347	−	0.608551i
$579$	0.750111	−	0.267365i	0.0311736	−	0.0111113i
$580$	−11.8678	+	6.95892i	−0.492785	+	0.288953i
$581$	−6.24617			−0.259135
$582$	−16.0331	−	13.6366i	−0.664592	−	0.565257i
$583$	14.1002	+	8.14074i	0.583969	+	0.337155i
$584$	−7.91524	−	13.7096i	−0.327535	−	0.567307i
$585$	9.91580	−	26.6935i	0.409968	−	1.10364i
$586$	16.3181	−	28.2638i	0.674094	−	1.16757i
$587$		−	26.1714i		−	1.08021i	−0.841598	−	0.540104i	$-0.818385\pi$
$587$		−	26.1714i		−	1.08021i	0.841598	−	0.540104i	$-0.181615\pi$
$588$	9.67212	+	1.77206i	0.398871	+	0.0730787i
$589$	−25.7216	+	20.4860i	−1.05984	+	0.844111i
$590$	17.3704	−	0.117019i	0.715127	−	0.00481759i
$591$	−4.63651	+	25.3066i	−0.190720	+	1.04097i
$592$	−2.70854	+	4.69134i	−0.111320	+	0.192813i
$593$	4.63363			0.190280			0.0951402	−	0.995464i	$-0.469670\pi$
$593$	4.63363			0.190280			0.0951402	+	0.995464i	$0.469670\pi$
$594$	0.246426	−	12.3116i	0.0101110	−	0.505152i
$595$	−0.728215	−	0.413919i	−0.0298539	−	0.0169690i
$596$	20.5556	+	11.8678i	0.841990	+	0.486123i
$597$	3.00914	−	16.4242i	0.123156	−	0.672198i
$598$	14.4087	−	8.31887i	0.589216	−	0.340184i
$599$	−20.4399	+	11.8010i	−0.835152	+	0.482175i	−0.855613	−	0.517615i	$-0.826820\pi$
$599$	−20.4399	+	11.8010i	−0.835152	+	0.482175i	0.0204614	+	0.999791i	$0.493486\pi$
$600$	3.01727	+	8.11764i	0.123179	+	0.331401i
$601$	−11.3744	−	6.56699i	−0.463970	−	0.267873i	0.249742	−	0.968312i	$-0.419654\pi$
$601$	−11.3744	−	6.56699i	−0.463970	−	0.267873i	−0.713712	+	0.700439i	$0.752987\pi$
$602$	−5.82220	+	3.36145i	−0.237295	+	0.137002i
$603$	−12.0765	−	14.7885i	−0.491794	−	0.602235i
$604$			8.61990i			0.350739i
$605$	0.0810984	+	12.0383i	0.00329712	+	0.489427i
$606$	12.8682	+	10.9448i	0.522735	+	0.444603i
$607$	34.9531	−	20.1802i	1.41870	−	0.819088i	0.422516	−	0.906355i	$-0.361147\pi$
$607$	34.9531	−	20.1802i	1.41870	−	0.819088i	0.996185	+	0.0872676i	$0.0278135\pi$
$608$	2.95296	−	5.11467i	0.119758	−	0.207427i
$609$	11.5453	−	4.11512i	0.467837	−	0.166753i
$610$	8.92336	+	15.2180i	0.361296	+	0.616160i
$611$	20.6825	+	35.8232i	0.836726	+	1.44925i
$612$	−0.346404	+	0.913622i	−0.0140026	+	0.0369310i
$613$	−14.1359	+	24.4841i	−0.570944	+	0.988903i	0.425526	+	0.904946i	$0.360089\pi$
$613$	−14.1359	+	24.4841i	−0.570944	+	0.988903i	−0.996469	+	0.0839570i	$0.973244\pi$
$614$	8.09277	+	4.67236i	0.326597	+	0.188561i
$615$	−9.80456	−	26.9323i	−0.395358	−	1.08602i
$616$			2.72568i			0.109821i
$617$	7.37685	−	12.7771i	0.296981	−	0.514386i	−0.678463	−	0.734635i	$-0.737354\pi$
$617$	7.37685	−	12.7771i	0.296981	−	0.514386i	0.975444	+	0.220249i	$0.0706869\pi$
$618$	−0.891440	+	4.86558i	−0.0358590	+	0.195722i
$619$		−	29.8573i		−	1.20007i	−0.799975	−	0.600033i	$-0.795154\pi$
$619$		−	29.8573i		−	1.20007i	0.799975	−	0.600033i	$-0.204846\pi$
$620$	12.2993	−	1.93078i	0.493951	−	0.0775419i
$621$	−10.5340	+	17.4302i	−0.422713	+	0.699452i
$622$		−	11.9460i		−	0.478989i
$623$	6.07740	+	3.50879i	0.243486	+	0.140577i
$624$	7.23202	+	1.32500i	0.289512	+	0.0530426i
$625$	−13.0788	−	21.3060i	−0.523152	−	0.852239i
$626$	−5.17715	+	8.96708i	−0.206920	+	0.358397i
$627$	15.7060	−	18.4661i	0.627237	−	0.737464i
$628$		−	16.1601i		−	0.644860i
$629$	1.52795	−	0.882162i	0.0609234	−	0.0351741i
$630$	−1.28956	−	7.60692i	−0.0513771	−	0.303067i
$631$	28.4375	−	16.4184i	1.13208	−	0.653606i	0.187622	−	0.982241i	$-0.439922\pi$
$631$	28.4375	−	16.4184i	1.13208	−	0.653606i	0.944457	+	0.328636i	$0.106589\pi$
$632$	−1.66882	−	0.963496i	−0.0663823	−	0.0383258i
$633$	−13.5569	−	38.0347i	−0.538837	−	1.51174i
$634$	17.1526	−	29.7092i	0.681218	−	1.17990i
$635$	−0.187609	−	27.8488i	−0.00744502	−	1.10515i
$636$	2.14448	−	11.7048i	0.0850342	−	0.464126i
$637$	−12.0495	+	20.8703i	−0.477418	+	0.826913i
$638$	−7.29036	−	12.6273i	−0.288628	−	0.499918i
$639$	12.9468	+	15.8542i	0.512166	+	0.627182i
$640$	−1.92892	+	1.13105i	−0.0762471	+	0.0447088i
$641$	−15.4302	−	26.7259i	−0.609456	−	1.05561i	−0.991330	−	0.131395i	$-0.958054\pi$
$641$	−15.4302	−	26.7259i	−0.609456	−	1.05561i	0.381874	−	0.924214i	$-0.375279\pi$
$642$	−9.42002	−	26.4285i	−0.371778	−	1.04305i
$643$	38.0016			1.49864			0.749318	−	0.662210i	$-0.230381\pi$
$643$	38.0016			1.49864			0.749318	+	0.662210i	$0.230381\pi$
$644$	2.25399	−	3.90402i	0.0888195	−	0.153840i
$645$	−17.3430	−	14.5506i	−0.682881	−	0.572929i
$646$	−1.66583	+	0.961767i	−0.0655412	+	0.0378402i
$647$			48.3294i			1.90003i	0.312209	+	0.950013i	$0.398931\pi$
$647$			48.3294i			1.90003i	−0.312209	+	0.950013i	$0.601069\pi$
$648$	−8.53635	+	2.85144i	−0.335340	+	0.112015i
$649$			18.4100i			0.722657i
$650$	−21.2226	+	0.285953i	−0.832419	+	0.0112160i
$651$	−11.0859	−	0.357403i	−0.434491	−	0.0140077i
$652$		−	15.1298i		−	0.592528i
$653$	−6.14945			−0.240647			−0.120323	−	0.992735i	$-0.538393\pi$
$653$	−6.14945			−0.240647			−0.120323	+	0.992735i	$0.538393\pi$
$654$	−12.8003	+	15.0498i	−0.500532	+	0.588493i
$655$	29.1015	−	0.196047i	1.13709	−	0.00766021i
$656$	6.40890	−	3.70018i	0.250225	−	0.144468i
$657$	−36.7846	+	30.0388i	−1.43510	+	1.17193i
$658$	9.70625	+	5.60391i	0.378389	+	0.218463i
$659$		−	5.11790i		−	0.199365i	−0.995019	−	0.0996825i	$-0.968217\pi$
$659$		−	5.11790i		−	0.199365i	0.995019	−	0.0996825i	$-0.0317827\pi$
$660$	−8.62465	+	3.13976i	−0.335714	+	0.122215i
$661$	−0.623086	−	1.07922i	−0.0242353	−	0.0419767i	0.853653	−	0.520841i	$-0.174382\pi$
$661$	−0.623086	−	1.07922i	−0.0242353	−	0.0419767i	−0.877889	+	0.478865i	$0.841048\pi$
$662$	15.4178	−	8.90148i	0.599231	−	0.345966i
$663$	−1.82410	−	1.55145i	−0.0708421	−	0.0602534i
$664$	4.70315	−	2.71537i	0.182518	−	0.105377i
$665$	7.50569	−	13.2049i	0.291058	−	0.512063i
$666$	15.1957	+	5.76151i	0.588821	+	0.223254i
$667$			24.1148i			0.933730i
$668$	12.3209	+	7.11348i	0.476710	+	0.275229i
$669$	−4.08540	−	11.4619i	−0.157951	−	0.443142i
$670$	−7.03236	+	12.3721i	−0.271684	+	0.477977i
$671$	−16.1918	+	9.34836i	−0.625079	+	0.360890i
$672$	1.87649	−	0.668843i	0.0723870	−	0.0258012i
$673$	9.47126	+	16.4047i	0.365090	+	0.632355i	0.988791	−	0.149309i	$-0.0477048\pi$
$673$	9.47126	+	16.4047i	0.365090	+	0.632355i	−0.623700	+	0.781663i	$0.714371\pi$
$674$	17.1276			0.659730
$675$	22.5845	−	12.8430i	0.869277	−	0.494326i
$676$	−2.50962	+	4.34679i	−0.0965239	+	0.167184i
$677$	−19.0799	+	11.0158i	−0.733299	+	0.423370i	−0.819628	−	0.572897i	$-0.805820\pi$
$677$	−19.0799	+	11.0158i	−0.733299	+	0.423370i	0.0863292	+	0.996267i	$0.472486\pi$
$678$	19.4347	+	3.56070i	0.746385	+	0.136748i
$679$	6.98835	−	12.1042i	0.268188	−	0.464516i
$680$	0.728262	−	0.00490607i	0.0279276	−	0.000188139i
$681$	3.61401	+	0.662136i	0.138489	+	0.0253731i
$682$	1.95843	+	13.0486i	0.0749923	+	0.499657i
$683$	15.0523			0.575960			0.287980	−	0.957636i	$-0.407016\pi$
$683$	15.0523			0.575960			0.287980	+	0.957636i	$0.407016\pi$
$684$	−16.5669	−	6.28142i	−0.633451	−	0.240176i
$685$	−5.14403	+	9.04998i	−0.196543	+	0.345782i
$686$			14.5806i			0.556692i
$687$	30.6811	−	10.9358i	1.17056	−	0.417226i
$688$	2.92261	−	5.06211i	0.111424	−	0.192991i
$689$	25.2564	+	14.5818i	0.962194	+	0.555523i
$690$	14.9495	+	2.63500i	0.569119	+	0.100313i
$691$	7.32478	+	12.6869i	0.278648	+	0.482632i	0.971049	−	0.238881i	$-0.0767805\pi$
$691$	7.32478	+	12.6869i	0.278648	+	0.482632i	−0.692401	+	0.721513i	$0.743447\pi$
$692$	−1.11273	−	1.92730i	−0.0422995	−	0.0732648i
$693$	8.07105	−	1.31237i	0.306594	−	0.0498527i
$694$	2.68079	+	1.54776i	0.101761	+	0.0587520i
$695$	−15.3853	−	26.2384i	−0.583599	−	0.995278i
$696$	−6.90424	+	8.11756i	−0.261705	+	0.307695i
$697$	−2.41027			−0.0912954
$698$	5.53280			0.209419
$699$	18.6213	−	21.8937i	0.704322	−	0.828097i
$700$	−4.94111	+	2.94222i	−0.186757	+	0.111205i
$701$	−6.92391	−	3.99752i	−0.261513	−	0.150984i	0.363512	−	0.931590i	$-0.381578\pi$
$701$	−6.92391	−	3.99752i	−0.261513	−	0.150984i	−0.625024	+	0.780605i	$0.714911\pi$
$702$	0.441403	−	22.0528i	0.0166597	−	0.832328i
$703$	15.9964	+	27.7066i	0.603317	+	1.04498i
$704$	−1.18492	−	2.05235i	−0.0446585	−	0.0773508i
$705$	−6.55119	+	37.1679i	−0.246732	+	1.39982i
$706$	10.3291	+	5.96353i	0.388742	+	0.224441i
$707$	−5.60888	+	9.71487i	−0.210944	+	0.365365i
$708$	12.6743	−	4.51755i	0.476330	−	0.169780i
$709$			15.2414i			0.572404i	0.958169	+	0.286202i	$0.0923928\pi$
$709$			15.2414i			0.572404i	−0.958169	+	0.286202i	$0.907607\pi$
$710$	7.53911	−	13.2637i	0.282938	−	0.497777i
$711$	−2.04951	+	5.40548i	−0.0768627	+	0.202721i
$712$	−6.10143			−0.228661
$713$	7.98537	−	20.3091i	0.299054	−	0.760582i
$714$	−0.638203	−	0.116928i	−0.0238842	−	0.00437590i
$715$	−0.151534	−	22.4938i	−0.00566705	−	0.841222i
$716$	−4.88016	+	8.45268i	−0.182380	+	0.315891i
$717$	−19.1982	−	3.51738i	−0.716971	−	0.131359i
$718$	−6.38325	+	3.68537i	−0.238221	+	0.137537i
$719$	22.2214	−	38.4886i	0.828718	−	1.43538i	−0.0703260	−	0.997524i	$-0.522404\pi$
$719$	22.2214	−	38.4886i	0.828718	−	1.43538i	0.899044	−	0.437858i	$-0.144263\pi$
$720$	4.27791	+	5.16715i	0.159428	+	0.192568i
$721$	−3.28472			−0.122329
$722$	−7.93992	−	13.7523i	−0.295493	−	0.511809i
$723$	−37.4400	+	13.3449i	−1.39241	+	0.496301i
$724$	2.88528	−	1.66582i	0.107231	−	0.0619096i
$725$	15.0212	−	26.8463i	0.557872	−	0.997048i
$726$	3.13083	+	8.78377i	0.116196	+	0.325996i
$727$	15.5130	+	8.95646i	0.575347	+	0.332177i	0.759282	−	0.650762i	$-0.225550\pi$
$727$	15.5130	+	8.95646i	0.575347	+	0.332177i	−0.183935	+	0.982938i	$0.558884\pi$
$728$			4.88229i			0.180950i
$729$	12.5535	+	23.9042i	0.464945	+	0.885340i
$730$	30.7741	+	17.4921i	1.13900	+	0.647412i
$731$	−1.64871	+	0.951884i	−0.0609798	+	0.0352067i
$732$	10.4091	+	8.85325i	0.384731	+	0.327226i
$733$	33.6135	−	19.4068i	1.24154	−	0.716805i	0.272135	−	0.962259i	$-0.412270\pi$
$733$	33.6135	−	19.4068i	1.24154	−	0.716805i	0.969408	+	0.245454i	$0.0789370\pi$
$734$	−2.44646	−	4.23739i	−0.0903004	−	0.156405i
$735$	−20.6610	+	7.52153i	−0.762093	+	0.277436i
$736$			3.91946i			0.144473i
$737$	−13.0618	−	7.54125i	−0.481139	−	0.277785i
$738$	−14.0424	−	17.1959i	−0.516908	−	0.632989i
$739$	−26.1751	+	15.1122i	−0.962868	+	0.555912i	−0.897054	−	0.441920i	$-0.854297\pi$
$739$	−26.1751	+	15.1122i	−0.962868	+	0.555912i	−0.0658132	+	0.997832i	$0.520964\pi$
$740$	−0.0815994	−	12.1127i	−0.00299966	−	0.445272i
$741$	28.1328	−	33.0767i	1.03348	−	1.21510i
$742$	7.90185			0.290086
$743$		−	14.3870i		−	0.527807i	−0.964549	−	0.263904i	$-0.914990\pi$
$743$		−	14.3870i		−	0.527807i	0.964549	−	0.263904i	$-0.0850101\pi$
$744$	8.50268	−	4.55021i	0.311723	−	0.166819i
$745$	−53.0731	+	0.357537i	−1.94445	+	0.0130991i
$746$		−	25.5466i		−	0.935329i
$747$	−10.3050	−	12.6192i	−0.377039	−	0.461711i
$748$			0.771850i			0.0282216i
$749$	16.1350	−	9.31554i	0.589560	−	0.340383i
$750$	−15.0015	−	12.2456i	−0.547779	−	0.447144i
$751$	−17.8664	+	30.9455i	−0.651954	+	1.12922i	0.330694	+	0.943738i	$0.392717\pi$
$751$	−17.8664	+	30.9455i	−0.651954	+	1.12922i	−0.982648	+	0.185480i	$0.940616\pi$
$752$	−9.74464			−0.355350
$753$	9.49147	+	26.6290i	0.345888	+	0.970415i
$754$	−13.0586	−	22.6182i	−0.475566	−	0.823705i
$755$	−9.74957	−	16.6271i	−0.354823	−	0.605121i
$756$	−2.88401	−	5.23445i	−0.104890	−	0.190375i
$757$	13.4198	+	23.2438i	0.487751	+	0.844810i	0.999901	−	0.0140863i	$-0.00448397\pi$
$757$	13.4198	+	23.2438i	0.487751	+	0.844810i	−0.512150	+	0.858896i	$0.671151\pi$
$758$	0.132403	−	0.229328i	0.00480909	−	0.00832958i
$759$	−2.89931	+	15.8248i	−0.105238	+	0.574403i
$760$	0.0889628	+	13.2057i	0.00322702	+	0.479022i
$761$	−18.3229	+	31.7361i	−0.664203	+	1.15043i	0.315298	+	0.948993i	$0.397896\pi$
$761$	−18.3229	+	31.7361i	−0.664203	+	1.15043i	−0.979501	+	0.201441i	$0.935438\pi$
$762$	−7.24270	−	20.3199i	−0.262375	−	0.736112i
$763$	−11.3618	−	6.55976i	−0.411326	−	0.237479i
$764$	4.71452	−	2.72193i	0.170565	−	0.0984758i
$765$	−0.365172	−	2.15410i	−0.0132028	−	0.0778817i
$766$	−33.2231	+	19.1814i	−1.20040	+	0.693051i
$767$			32.9763i			1.19071i
$768$	−1.12217	+	1.31937i	−0.0404927	+	0.0476087i
$769$	2.03601	−	3.52648i	0.0734205	−	0.127168i	−0.826978	−	0.562235i	$-0.809942\pi$
$769$	2.03601	−	3.52648i	0.0734205	−	0.127168i	0.900398	+	0.435067i	$0.143275\pi$
$770$	−3.08290	−	5.25762i	−0.111100	−	0.189471i
$771$	−5.66773	−	1.03840i	−0.204118	−	0.0373972i
$772$	−0.398168	−	0.229882i	−0.0143304	−	0.00827365i
$773$		−	37.5422i		−	1.35030i	−0.737681	−	0.675149i	$-0.764079\pi$
$773$		−	37.5422i		−	1.35030i	0.737681	−	0.675149i	$-0.235921\pi$
$774$	−16.3967	−	6.21687i	−0.589366	−	0.223461i
$775$	−21.5404	+	17.6354i	−0.773756	+	0.633484i
$776$			12.1521i			0.436233i
$777$	−1.94478	+	10.6148i	−0.0697685	+	0.380804i
$778$	7.96052	−	13.7880i	0.285398	−	0.494324i
$779$		−	43.7059i		−	1.56593i
$780$	−15.4486	+	5.62398i	−0.553149	+	0.201371i
$781$	14.0031	+	8.08467i	0.501069	+	0.289292i
$782$	0.638276	−	1.10553i	0.0228247	−	0.0395335i
$783$	27.3612	+	16.5358i	0.977811	+	0.590940i
$784$	−2.83858	−	4.91656i	−0.101378	−	0.175591i
$785$	18.2780	+	31.1716i	0.652370	+	1.11256i
$786$	21.2339	−	7.56848i	0.757388	−	0.269959i
$787$	10.7430	−	18.6075i	0.382948	−	0.663286i	−0.608534	−	0.793528i	$-0.708242\pi$
$787$	10.7430	−	18.6075i	0.382948	−	0.663286i	0.991482	+	0.130242i	$0.0415755\pi$
$788$	12.8639	−	7.42698i	0.458258	−	0.264575i
$789$	4.63648	+	3.94348i	0.165063	+	0.140391i
$790$	4.30879	−	0.0290269i	0.153300	−	0.00103273i
$791$			13.1202i			0.466502i
$792$	−5.50671	+	4.49686i	−0.195672	+	0.159789i
$793$	−29.0031	+	16.7449i	−1.02993	+	0.594630i
$794$	16.2347	+	9.37313i	0.576149	+	0.332640i
$795$	9.10225	+	25.0031i	0.322824	+	0.886770i
$796$	−8.34879	+	4.82018i	−0.295915	+	0.170847i
$797$	−17.7187	+	10.2299i	−0.627628	+	0.362361i	−0.779833	−	0.625988i	$-0.784696\pi$
$797$	−17.7187	+	10.2299i	−0.627628	+	0.362361i	0.152205	+	0.988349i	$0.451363\pi$
$798$	2.12027	−	11.5727i	0.0750568	−	0.409668i
$799$	2.74858	+	1.58690i	0.0972379	+	0.0561403i
$800$	2.44143	−	4.36342i	0.0863177	−	0.154270i
$801$	2.93773	+	18.0670i	0.103799	+	0.638367i
$802$	7.69817			0.271832
$803$	−18.7579	+	32.4897i	−0.661952	+	1.14653i
$804$	−1.98656	+	10.8429i	−0.0700606	+	0.382399i
$805$	0.0679051	+	10.0799i	0.00239334	+	0.355270i
$806$	3.50798	+	23.3729i	0.123563	+	0.823274i
$807$	−49.7078	−	9.10714i	−1.74980	−	0.320587i
$808$		−	9.75329i		−	0.343120i
$809$	−6.68909	+	11.5858i	−0.235176	+	0.407337i	−0.959324	−	0.282308i	$-0.908900\pi$
$809$	−6.68909	+	11.5858i	−0.235176	+	0.407337i	0.724148	+	0.689645i	$0.242233\pi$
$810$	13.2408	−	15.1553i	0.465233	−	0.532502i
$811$	12.3459	+	21.3837i	0.433524	+	0.750885i	0.997174	−	0.0751287i	$-0.0239368\pi$
$811$	12.3459	+	21.3837i	0.433524	+	0.750885i	−0.563650	+	0.826014i	$0.690603\pi$
$812$	−6.12836	−	3.53821i	−0.215063	−	0.124167i
$813$	−22.9958	−	19.5586i	−0.806497	−	0.685951i
$814$	12.8377			0.449960
$815$	17.1126	+	29.1841i	0.599429	+	1.02227i
$816$	0.531377	−	0.189401i	0.0186019	−	0.00663035i
$817$	−17.2607	−	29.8964i	−0.603876	−	1.04594i
$818$	−1.71414	−	0.989662i	−0.0599337	−	0.0346027i
$819$	14.4570	−	2.35073i	0.505168	−	0.0821412i
$820$	−8.17712	+	14.3861i	−0.285557	+	0.502386i
$821$	20.6876			0.722004			0.361002	−	0.932565i	$-0.382435\pi$
$821$	20.6876			0.722004			0.361002	+	0.932565i	$0.382435\pi$
$822$	−1.45313	+	7.93135i	−0.0506838	+	0.276638i
$823$	6.00138	−	10.3947i	0.209195	−	0.362337i	−0.742266	−	0.670105i	$-0.766249\pi$
$823$	6.00138	−	10.3947i	0.209195	−	0.362337i	0.951461	+	0.307769i	$0.0995823\pi$
$824$	2.47328	−	1.42795i	0.0861609	−	0.0497450i
$825$	13.0850	−	15.8113i	0.455561	−	0.550478i
$826$	4.46745	+	7.73784i	0.155442	+	0.269234i
$827$	48.4395	−	27.9666i	1.68441	−	0.972493i	0.725738	−	0.687971i	$-0.241498\pi$
$827$	48.4395	−	27.9666i	1.68441	−	0.972493i	0.958669	−	0.284522i	$-0.0918350\pi$
$828$	11.6059	−	1.88714i	0.403334	−	0.0655828i
$829$			33.5302i			1.16455i	0.812991	+	0.582277i	$0.197838\pi$
$829$			33.5302i			1.16455i	−0.812991	+	0.582277i	$0.802162\pi$
$830$	−6.00076	+	10.5572i	−0.208289	+	0.366447i
$831$	3.42881	−	4.03137i	0.118944	−	0.139847i
$832$	−2.12245	−	3.67620i	−0.0735829	−	0.127449i
$833$			1.84903i			0.0640650i
$834$	−17.9469	−	15.2644i	−0.621452	−	0.528565i
$835$	−31.8117	+	0.214306i	−1.10089	+	0.00741635i
$836$	−13.9961			−0.484066
$837$	−17.5676	−	22.9865i	−0.607224	−	0.794531i
$838$			3.70987i			0.128155i
$839$			7.25474i			0.250462i	0.992128	+	0.125231i	$0.0399671\pi$
$839$			7.25474i			0.250462i	−0.992128	+	0.125231i	$0.960033\pi$
$840$	−2.86309	+	3.41255i	−0.0987859	+	0.117744i
$841$	8.85443			0.305325
$842$	2.92363	+	5.06387i	0.100755	+	0.174512i
$843$	−18.1301	−	15.4203i	−0.624435	−	0.531102i
$844$	−11.6563	+	20.1893i	−0.401226	+	0.694944i
$845$	−0.0756066	−	11.2231i	−0.00260095	−	0.386087i
$846$	4.69186	+	28.8549i	0.161309	+	0.992053i
$847$	−5.36262	+	3.09611i	−0.184262	+	0.106384i
$848$	−5.94982	+	3.43513i	−0.204318	+	0.117963i
$849$	−7.74484	−	6.58724i	−0.265802	−	0.226073i
$850$	−1.39921	+	0.833167i	−0.0479924	+	0.0285774i
$851$	−18.3875	−	10.6160i	−0.630315	−	0.363912i
$852$	2.12971	−	11.6242i	0.0729628	−	0.398239i
$853$		−	36.3991i		−	1.24628i	−0.782109	−	0.623141i	$-0.785856\pi$
$853$		−	36.3991i		−	1.24628i	0.782109	−	0.623141i	$-0.214144\pi$
$854$	−4.53702	+	7.85834i	−0.155254	+	0.268907i
$855$	39.0608	−	6.62174i	1.33585	−	0.226459i
$856$	−8.09940	+	14.0286i	−0.276832	+	0.479487i
$857$	28.8592	+	49.9856i	0.985811	+	1.70748i	0.638274	+	0.769809i	$0.279649\pi$
$857$	28.8592	+	49.9856i	0.985811	+	1.70748i	0.347537	+	0.937666i	$0.387018\pi$
$858$	−5.85002	−	16.4126i	−0.199716	−	0.560319i
$859$	−29.8935	+	17.2590i	−1.01995	+	0.588870i	−0.914090	−	0.405511i	$-0.867094\pi$
$859$	−29.8935	+	17.2590i	−1.01995	+	0.588870i	−0.105862	+	0.994381i	$0.533760\pi$
$860$	0.0880486	+	13.0700i	0.00300243	+	0.445684i
$861$	9.55136	−	11.2299i	0.325510	−	0.382713i
$862$	0.535714	+	0.309295i	0.0182465	+	0.0105346i
$863$	−12.1829	+	7.03381i	−0.414711	+	0.239434i	−0.692812	−	0.721118i	$-0.743628\pi$
$863$	−12.1829	+	7.03381i	−0.414711	+	0.239434i	0.278101	+	0.960552i	$0.410295\pi$
$864$	4.44711	+	2.68761i	0.151294	+	0.0914343i
$865$	4.32623	+	2.45904i	0.147096	+	0.0836099i
$866$	−19.8014			−0.672880
$867$	28.7821	+	5.27326i	0.977490	+	0.179089i
$868$	3.98956	+	5.00916i	0.135415	+	0.170022i
$869$			4.56668i			0.154914i
$870$	4.13631	−	23.4672i	0.140234	−	0.795611i
$871$	−23.3966	−	13.5080i	−0.792762	−	0.457701i
$872$	11.4068			0.386282
$873$	35.9836	−	5.85099i	1.21786	−	0.198026i
$874$	20.0467	+	11.5740i	0.678091	+	0.391496i
$875$	6.20319	−	11.2640i	0.209706	−	0.380791i
$876$	26.9703	+	4.94132i	0.911241	+	0.166952i
$877$	−21.8930	+	12.6399i	−0.739274	+	0.426820i	−0.821805	−	0.569768i	$-0.807033\pi$
$877$	−21.8930	+	12.6399i	−0.739274	+	0.426820i	0.0825311	+	0.996588i	$0.473700\pi$
$878$	−17.6243	−	30.5262i	−0.594791	−	1.03021i
$879$	18.9788	+	53.2463i	0.640138	+	1.79595i
$880$	4.60693	+	2.61859i	0.155300	+	0.0882728i
$881$	28.8559	+	49.9798i	0.972179	+	1.68386i	0.688947	+	0.724812i	$0.258073\pi$
$881$	28.8559	+	49.9798i	0.972179	+	1.68386i	0.283232	+	0.959051i	$0.408593\pi$
$882$	−13.1917	+	10.7726i	−0.444189	+	0.362731i
$883$	−33.2470			−1.11885			−0.559425	−	0.828881i	$-0.688978\pi$
$883$	−33.2470			−1.11885			−0.559425	+	0.828881i	$0.688978\pi$
$884$			1.38255i			0.0465002i
$885$	−19.3381	+	23.0493i	−0.650042	+	0.774794i
$886$	−10.2043	−	17.6744i	−0.342821	−	0.593783i
$887$	−8.24124	+	14.2742i	−0.276714	+	0.479282i	−0.970566	−	0.240835i	$-0.922579\pi$
$887$	−8.24124	+	14.2742i	−0.276714	+	0.479282i	0.693852	+	0.720117i	$0.255912\pi$
$888$	−3.15017	−	8.83804i	−0.105713	−	0.296585i
$889$	12.4056	−	7.16237i	0.416070	−	0.240218i
$890$	11.7692	−	6.90105i	0.394503	−	0.231324i
$891$	15.9671	+	14.1408i	0.534917	+	0.473736i
$892$	−3.51266	+	6.08411i	−0.117613	+	0.203711i
$893$	−28.7755	+	49.8406i	−0.962935	+	1.66785i
$894$	−38.7248	+	13.8028i	−1.29515	+	0.461636i
$895$	−0.147023	−	21.8242i	−0.00491443	−	0.729504i
$896$	−0.996061	−	0.575076i	−0.0332761	−	0.0192119i
$897$	−5.19330	+	28.3456i	−0.173399	+	0.946432i
$898$	−32.2841			−1.07734
$899$	−31.8804	−	12.5351i	−1.06327	−	0.418069i
$900$	−14.0961	−	5.12845i	−0.469869	−	0.170948i
$901$	2.23762			0.0745459
$902$	−15.1881	−	8.76885i	−0.505708	−	0.291971i
$903$	2.09848	−	11.4538i	0.0698332	−	0.381157i
$904$	−5.70370	−	9.87909i	−0.189702	−	0.328574i
$905$	−3.68133	+	6.47662i	−0.122372	+	0.215290i
$906$	−11.3728	−	9.67297i	−0.377838	−	0.321363i
$907$			43.5648i			1.44655i	0.690562	+	0.723274i	$0.257363\pi$
$907$			43.5648i			1.44655i	−0.690562	+	0.723274i	$0.742637\pi$
$908$	−1.06064	−	1.83708i	−0.0351986	−	0.0609657i
$909$	−28.8806	+	4.69603i	−0.957908	+	0.155757i
$910$	−5.52213	−	9.41753i	−0.183057	−	0.312188i
$911$	0.529754	−	0.917560i	0.0175515	−	0.0304001i	−0.857116	−	0.515123i	$-0.827746\pi$
$911$	0.529754	−	0.917560i	0.0175515	−	0.0304001i	0.874668	+	0.484723i	$0.161080\pi$
$912$	3.43444	+	9.63557i	0.113726	+	0.319065i
$913$	−11.1458	−	6.43500i	−0.368871	−	0.212967i
$914$	0.447328			0.0147963
$915$	−30.0917	−	5.30395i	−0.994802	−	0.175343i
$916$	−16.2859	−	9.40267i	−0.538102	−	0.310673i
$917$	7.48454	+	12.9636i	0.247161	+	0.428096i
$918$	−0.816684	−	1.48227i	−0.0269546	−	0.0489223i
$919$	−9.67021	−	16.7493i	−0.318991	−	0.552508i	0.661287	−	0.750133i	$-0.270011\pi$
$919$	−9.67021	−	16.7493i	−0.318991	−	0.552508i	−0.980278	+	0.197625i	$0.936677\pi$
$920$	−4.43312	−	7.56030i	−0.146156	−	0.249256i
$921$	−15.2460	+	5.43419i	−0.502373	+	0.179063i
$922$	5.05183			0.166373
$923$	25.0825	+	14.4814i	0.825601	+	0.476661i
$924$	−3.59619	−	3.05867i	−0.118306	−	0.100623i
$925$	13.8575	+	23.2721i	0.455632	+	0.765182i
$926$	13.8424			0.454889
$927$	−5.41916	−	6.63613i	−0.177989	−	0.217959i
$928$	6.15260			0.201969
$929$	6.90820			0.226651			0.113325	−	0.993558i	$-0.463850\pi$
$929$	6.90820			0.226651			0.113325	+	0.993558i	$0.463850\pi$
$930$	−11.2544	+	18.3940i	−0.369047	+	0.603162i
$931$	−33.5288			−1.09886
$932$	−16.5941			−0.543556
$933$	15.7612	+	13.4054i	0.515997	+	0.438872i
$934$	16.8843			0.552473
$935$	−0.873004	−	1.48883i	−0.0285503	−	0.0486901i
$936$	−9.86371	+	8.05484i	−0.322405	+	0.263281i
$937$	−9.60104	−	5.54316i	−0.313652	−	0.181087i	0.334907	−	0.942251i	$-0.391295\pi$
$937$	−9.60104	−	5.54316i	−0.313652	−	0.181087i	−0.648560	+	0.761164i	$0.724628\pi$
$938$	−7.31995			−0.239005
$939$	−6.02129	−	16.8931i	−0.196497	−	0.551287i
$940$	18.7966	−	11.0217i	0.613077	−	0.359488i
$941$	5.61701	+	9.72894i	0.183109	+	0.317154i	0.942938	−	0.332969i	$-0.108050\pi$
$941$	5.61701	+	9.72894i	0.183109	+	0.317154i	−0.759829	+	0.650124i	$0.774717\pi$
$942$	21.3212	+	18.1344i	0.694683	+	0.590850i
$943$	14.5027	+	25.1194i	0.472272	+	0.818000i
$944$	−6.72767	−	3.88422i	−0.218967	−	0.126421i
$945$	11.4835	+	6.83484i	0.373557	+	0.222337i
$946$	−13.8523			−0.450377
$947$	−35.7758	−	20.6552i	−1.16256	−	0.671203i	−0.210642	−	0.977563i	$-0.567555\pi$
$947$	−35.7758	−	20.6552i	−1.16256	−	0.671203i	−0.951916	+	0.306360i	$0.900889\pi$
$948$	3.14391	−	1.12060i	0.102109	−	0.0363952i
$949$	−33.5995	+	58.1960i	−1.09068	+	1.88912i
$950$	−15.1080	−	25.3721i	−0.490168	−	0.823180i
$951$	19.9494	+	55.9694i	0.646903	+	1.81493i
$952$	0.187300	+	0.324413i	0.00607043	+	0.0105143i
$953$			1.55758i			0.0504550i	0.999682	+	0.0252275i	$0.00803101\pi$
$953$			1.55758i			0.0504550i	−0.999682	+	0.0252275i	$0.991969\pi$
$954$	13.0365	+	15.9641i	0.422073	+	0.516858i
$955$	−6.01526	+	10.5827i	−0.194649	+	0.342449i
$956$	5.63430	+	9.75890i	0.182226	+	0.315625i
$957$	24.8410	+	4.55122i	0.802997	+	0.147120i
$958$	−12.1074	−	6.99019i	−0.391171	−	0.225843i
$959$	−5.35440			−0.172903
$960$	0.672286	−	3.81419i	0.0216980	−	0.123102i
$961$	22.6983	+	21.1137i	0.732203	+	0.681087i
$962$	22.9950			0.741390
$963$	45.4399	+	17.2287i	1.46428	+	0.555188i
$964$	19.8736	+	11.4740i	0.640085	+	0.369553i
$965$	1.02804	−	0.00692559i	0.0330938	−	0.000222943i
$966$	2.62150	+	7.35480i	0.0843454	+	0.236637i
$967$	12.5116	−	21.6708i	0.402347	−	0.696885i	−0.591662	−	0.806186i	$-0.701528\pi$
$967$	12.5116	−	21.6708i	0.402347	−	0.696885i	0.994009	+	0.109301i	$0.0348614\pi$
$968$	2.69191	−	4.66253i	0.0865213	−	0.149859i
$969$	0.600411	−	3.27711i	0.0192880	−	0.105276i
$970$	−13.7446	−	23.4403i	−0.441313	−	0.752622i
$971$	−48.1883	+	27.8215i	−1.54644	+	0.892836i	−0.548028	+	0.836460i	$0.684621\pi$
$971$	−48.1883	+	27.8215i	−1.54644	+	0.892836i	−0.998410	+	0.0563756i	$0.982046\pi$
$972$	5.81711	−	14.4624i	0.186584	−	0.463882i
$973$	7.82256	−	13.5491i	0.250780	−	0.434363i
$974$	2.36047	+	4.08845i	0.0756342	+	0.131002i
$975$	23.4380	−	28.3214i	0.750618	−	0.907011i
$976$		−	7.88942i		−	0.252534i
$977$	−58.0437			−1.85698			−0.928491	−	0.371356i	$-0.878893\pi$
$977$	−58.0437			−1.85698			−0.928491	+	0.371356i	$0.878893\pi$
$978$	19.9618	+	16.9782i	0.638308	+	0.542902i
$979$	7.22973	+	12.5223i	0.231063	+	0.400213i
$980$	11.0363	+	6.27304i	0.352541	+	0.200385i
$981$	−5.49215	−	33.7767i	−0.175351	−	1.07841i
$982$	5.00068	+	8.66143i	0.159578	+	0.276397i
$983$	−16.8719	+	9.74099i	−0.538130	+	0.310689i	−0.744321	−	0.667822i	$-0.767227\pi$
$983$	−16.8719	+	9.74099i	−0.538130	+	0.310689i	0.206191	+	0.978512i	$0.433893\pi$
$984$	−2.30994	+	12.6079i	−0.0736383	+	0.401926i
$985$	−16.4131	+	28.8758i	−0.522964	+	0.920059i
$986$	−1.73541	−	1.00194i	−0.0552666	−	0.0319082i
$987$	−18.2857	+	6.51763i	−0.582039	+	0.207458i
$988$	−25.0701			−0.797585
$989$	19.8407	+	11.4551i	0.630899	+	0.364250i
$990$	5.53579	−	14.9024i	0.175939	−	0.473631i
$991$			8.39172i			0.266572i	0.991078	+	0.133286i	$0.0425528\pi$
$991$			8.39172i			0.266572i	−0.991078	+	0.133286i	$0.957447\pi$
$992$	−5.18162	−	2.03737i	−0.164516	−	0.0646864i
$993$	−5.55701	+	30.3308i	−0.176346	+	0.962518i
$994$	7.84743			0.248905
$995$	10.6522	−	18.7407i	0.337699	−	0.594119i
$996$	−1.69515	+	9.25230i	−0.0537128	+	0.293170i
$997$	−53.4544	+	30.8619i	−1.69292	+	0.977407i	−0.740775	+	0.671753i	$0.765542\pi$
$997$	−53.4544	+	30.8619i	−1.69292	+	0.977407i	−0.952143	+	0.305654i	$0.901125\pi$
$998$	31.3741	+	18.1139i	0.993131	+	0.573385i
$999$	−24.6537	+	13.5834i	−0.780007	+	0.429759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.r.b.119.9	yes	64
3.2	odd	2		930.2.r.a.119.12	✓	64
5.4	even	2		930.2.r.a.119.24	yes	64
15.14	odd	2	inner	930.2.r.b.119.21	yes	64
31.6	odd	6	inner	930.2.r.b.719.21	yes	64
93.68	even	6		930.2.r.a.719.24	yes	64
155.99	odd	6		930.2.r.a.719.12	yes	64
465.254	even	6	inner	930.2.r.b.719.9	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.r.a.119.12	✓	64	3.2	odd	2
930.2.r.a.119.24	yes	64	5.4	even	2
930.2.r.a.719.12	yes	64	155.99	odd	6
930.2.r.a.719.24	yes	64	93.68	even	6
930.2.r.b.119.9	yes	64	1.1	even	1	trivial
930.2.r.b.119.21	yes	64	15.14	odd	2	inner
930.2.r.b.719.9	yes	64	465.254	even	6	inner
930.2.r.b.719.21	yes	64	31.6	odd	6	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.12217 + 1.31937i) q^{3} +1.00000 q^{4} +(-1.92892 + 1.13105i) q^{5} +(-1.12217 + 1.31937i) q^{6} +(-0.996061 - 0.575076i) q^{7} +1.00000 q^{8} +(-0.481481 - 2.96111i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.12217 + 1.31937i) q^{3} +1.00000 q^{4} +(-1.92892 + 1.13105i) q^{5} +(-1.12217 + 1.31937i) q^{6} +(-0.996061 - 0.575076i) q^{7} +1.00000 q^{8} +(-0.481481 - 2.96111i) q^{9} +(-1.92892 + 1.13105i) q^{10} +(-1.18492 - 2.05235i) q^{11} +(-1.12217 + 1.31937i) q^{12} +(-2.12245 - 3.67620i) q^{13} +(-0.996061 - 0.575076i) q^{14} +(0.672286 - 3.81419i) q^{15} +1.00000 q^{16} +(-0.282061 - 0.162848i) q^{17} +(-0.481481 - 2.96111i) q^{18} +(2.95296 - 5.11467i) q^{19} +(-1.92892 + 1.13105i) q^{20} +(1.87649 - 0.668843i) q^{21} +(-1.18492 - 2.05235i) q^{22} +3.91946i q^{23} +(-1.12217 + 1.31937i) q^{24} +(2.44143 - 4.36342i) q^{25} +(-2.12245 - 3.67620i) q^{26} +(4.44711 + 2.68761i) q^{27} +(-0.996061 - 0.575076i) q^{28} +6.15260 q^{29} +(0.672286 - 3.81419i) q^{30} +(-5.18162 - 2.03737i) q^{31} +1.00000 q^{32} +(4.03749 + 0.739723i) q^{33} +(-0.282061 - 0.162848i) q^{34} +(2.57176 - 0.0173251i) q^{35} +(-0.481481 - 2.96111i) q^{36} +(-2.70854 + 4.69134i) q^{37} +(2.95296 - 5.11467i) q^{38} +(7.23202 + 1.32500i) q^{39} +(-1.92892 + 1.13105i) q^{40} +(6.40890 - 3.70018i) q^{41} +(1.87649 - 0.668843i) q^{42} +(2.92261 - 5.06211i) q^{43} +(-1.18492 - 2.05235i) q^{44} +(4.27791 + 5.16715i) q^{45} +3.91946i q^{46} -9.74464 q^{47} +(-1.12217 + 1.31937i) q^{48} +(-2.83858 - 4.91656i) q^{49} +(2.44143 - 4.36342i) q^{50} +(0.531377 - 0.189401i) q^{51} +(-2.12245 - 3.67620i) q^{52} +(-5.94982 + 3.43513i) q^{53} +(4.44711 + 2.68761i) q^{54} +(4.60693 + 2.61859i) q^{55} +(-0.996061 - 0.575076i) q^{56} +(3.43444 + 9.63557i) q^{57} +6.15260 q^{58} +(-6.72767 - 3.88422i) q^{59} +(0.672286 - 3.81419i) q^{60} -7.88942i q^{61} +(-5.18162 - 2.03737i) q^{62} +(-1.22328 + 3.22633i) q^{63} +1.00000 q^{64} +(8.25201 + 4.69047i) q^{65} +(4.03749 + 0.739723i) q^{66} +(5.51167 - 3.18217i) q^{67} +(-0.282061 - 0.162848i) q^{68} +(-5.17122 - 4.39829i) q^{69} +(2.57176 - 0.0173251i) q^{70} +(-5.90885 + 3.41147i) q^{71} +(-0.481481 - 2.96111i) q^{72} +(-7.91524 - 13.7096i) q^{73} +(-2.70854 + 4.69134i) q^{74} +(3.01727 + 8.11764i) q^{75} +(2.95296 - 5.11467i) q^{76} +2.72568i q^{77} +(7.23202 + 1.32500i) q^{78} +(-1.66882 - 0.963496i) q^{79} +(-1.92892 + 1.13105i) q^{80} +(-8.53635 + 2.85144i) q^{81} +(6.40890 - 3.70018i) q^{82} +(4.70315 - 2.71537i) q^{83} +(1.87649 - 0.668843i) q^{84} +(0.728262 - 0.00490607i) q^{85} +(2.92261 - 5.06211i) q^{86} +(-6.90424 + 8.11756i) q^{87} +(-1.18492 - 2.05235i) q^{88} -6.10143 q^{89} +(4.27791 + 5.16715i) q^{90} +4.88229i q^{91} +3.91946i q^{92} +(8.50268 - 4.55021i) q^{93} -9.74464 q^{94} +(0.0889628 + 13.2057i) q^{95} +(-1.12217 + 1.31937i) q^{96} +12.1521i q^{97} +(-2.83858 - 4.91656i) q^{98} +(-5.50671 + 4.49686i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) \) 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) \) 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 2 * q^25 + 18 * q^31 + 64 * q^32 - 8 * q^33 + 6 * q^34 + 16 * q^35 - 4 * q^36 + 4 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^45 - 4 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 + 6 * q^57 + 18 * q^62 + 12 * q^63 + 64 * q^64 - 8 * q^66 + 6 * q^68 - 10 * q^69 + 16 * q^70 - 4 * q^72 - 63 * q^75 + 4 * q^76 - 8 * q^78 - 30 * q^79 + 2 * q^80 - 12 * q^81 - 54 * q^83 - 16 * q^87 + 9 * q^90 - 18 * q^93 - 4 * q^94 - 56 * q^95 + 30 * q^98 - 102 * q^99

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