LMFDB - Embedded newform 165.2.p.b.101.3

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			101.3
Character	$\chi$	$=$	165.101
Dual form			165.2.p.b.116.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.491121 + 1.51151i) q^{2} +(-1.07720 - 1.35634i) q^{3} +(-0.425442 - 0.309102i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(2.57916 - 0.962071i) q^{6} +(-1.78891 + 2.46222i) q^{7} +(-1.89539 + 1.37708i) q^{8} +(-0.679300 + 2.92208i) q^{9} +O(q^{10})$	\(q+(-0.491121 + 1.51151i) q^{2} +(-1.07720 - 1.35634i) q^{3} +(-0.425442 - 0.309102i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(2.57916 - 0.962071i) q^{6} +(-1.78891 + 2.46222i) q^{7} +(-1.89539 + 1.37708i) q^{8} +(-0.679300 + 2.92208i) q^{9} -1.58930i q^{10} +(0.668870 + 3.24848i) q^{11} +(0.0390382 + 0.910006i) q^{12} +(-1.51385 - 0.491878i) q^{13} +(-2.84311 - 3.91320i) q^{14} +(1.44360 + 0.957081i) q^{15} +(-1.47562 - 4.54149i) q^{16} +(0.898365 + 2.76488i) q^{17} +(-4.08315 - 2.46187i) q^{18} +(-1.39211 - 1.91607i) q^{19} +(0.500137 + 0.162504i) q^{20} +(5.26660 - 0.225931i) q^{21} +(-5.23862 - 0.584388i) q^{22} -3.51389i q^{23} +(3.90949 + 1.08740i) q^{24} +(0.809017 - 0.587785i) q^{25} +(1.48696 - 2.04663i) q^{26} +(4.69506 - 2.22629i) q^{27} +(1.52215 - 0.494577i) q^{28} +(4.81478 + 3.49814i) q^{29} +(-2.15563 + 1.71199i) q^{30} +(0.0658086 - 0.202538i) q^{31} +2.90358 q^{32} +(3.68553 - 4.40646i) q^{33} -4.62037 q^{34} +(0.940483 - 2.89451i) q^{35} +(1.19222 - 1.03320i) q^{36} +(3.92798 + 2.85384i) q^{37} +(3.57986 - 1.16317i) q^{38} +(0.963555 + 2.58313i) q^{39} +(1.37708 - 1.89539i) q^{40} +(-1.89674 + 1.37806i) q^{41} +(-2.24504 + 8.07150i) q^{42} +11.8663i q^{43} +(0.719545 - 1.58879i) q^{44} +(-0.256920 - 2.98898i) q^{45} +(5.31129 + 1.72574i) q^{46} +(-7.63593 - 10.5100i) q^{47} +(-4.57026 + 6.89351i) q^{48} +(-0.699213 - 2.15196i) q^{49} +(0.491121 + 1.51151i) q^{50} +(2.78240 - 4.19681i) q^{51} +(0.492013 + 0.677198i) q^{52} +(11.2504 + 3.65547i) q^{53} +(1.05923 + 8.19003i) q^{54} +(-1.63997 - 2.88279i) q^{55} -7.13032i q^{56} +(-1.09927 + 3.95215i) q^{57} +(-7.65213 + 5.55960i) q^{58} +(0.196917 - 0.271033i) q^{59} +(-0.318335 - 0.853404i) q^{60} +(11.0521 - 3.59104i) q^{61} +(0.273819 + 0.198941i) q^{62} +(-5.97959 - 6.89991i) q^{63} +(1.52523 - 4.69417i) q^{64} +1.59175 q^{65} +(4.85039 + 7.73483i) q^{66} -8.55624 q^{67} +(0.472428 - 1.45398i) q^{68} +(-4.76602 + 3.78514i) q^{69} +(3.91320 + 2.84311i) q^{70} +(-8.16546 + 2.65312i) q^{71} +(-2.73640 - 6.47392i) q^{72} +(6.13509 - 8.44422i) q^{73} +(-6.24273 + 4.53561i) q^{74} +(-1.66870 - 0.464140i) q^{75} +1.24548i q^{76} +(-9.19501 - 4.16432i) q^{77} +(-4.37767 + 0.187797i) q^{78} +(-8.85108 - 2.87589i) q^{79} +(2.80680 + 3.86322i) q^{80} +(-8.07710 - 3.96994i) q^{81} +(-1.15143 - 3.54374i) q^{82} +(2.49987 + 7.69379i) q^{83} +(-2.31047 - 1.53179i) q^{84} +(-1.70879 - 2.35195i) q^{85} +(-17.9361 - 5.82780i) q^{86} +(-0.441800 - 10.2987i) q^{87} +(-5.74118 - 5.23604i) q^{88} +9.73184i q^{89} +(4.64406 + 1.07961i) q^{90} +(3.91924 - 2.84749i) q^{91} +(-1.08615 + 1.49496i) q^{92} +(-0.345598 + 0.128914i) q^{93} +(19.6361 - 6.38016i) q^{94} +(1.91607 + 1.39211i) q^{95} +(-3.12773 - 3.93824i) q^{96} +(-3.23762 + 9.96437i) q^{97} +3.59611 q^{98} +(-9.94668 - 0.252198i) 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 $

$2$	−0.491121	+	1.51151i	−0.347275	+	1.06880i	0.613080	+	0.790021i	$0.289930\pi$
$2$	−0.491121	+	1.51151i	−0.347275	+	1.06880i	−0.960355	+	0.278781i	$0.910070\pi$
$3$	−1.07720	−	1.35634i	−0.621919	−	0.783081i
$3$	−1.07720	−	1.35634i	−0.621919	−	0.783081i
$4$	−0.425442	−	0.309102i	−0.212721	−	0.154551i
$5$	−0.951057	+	0.309017i	−0.425325	+	0.138197i
$5$	−0.951057	+	0.309017i	−0.425325	+	0.138197i
$6$	2.57916	−	0.962071i	1.05294	−	0.392764i
$7$	−1.78891	+	2.46222i	−0.676143	+	0.930631i	−0.999880	−	0.0155164i	$-0.995061\pi$
$7$	−1.78891	+	2.46222i	−0.676143	+	0.930631i	0.323737	+	0.946147i	$0.395061\pi$
$8$	−1.89539	+	1.37708i	−0.670120	+	0.486871i
$9$	−0.679300	+	2.92208i	−0.226433	+	0.974027i
$10$		−	1.58930i		−	0.502581i
$11$	0.668870	+	3.24848i	0.201672	+	0.979453i
$11$	0.668870	+	3.24848i	0.201672	+	0.979453i
$12$	0.0390382	+	0.910006i	0.0112694	+	0.262696i
$13$	−1.51385	−	0.491878i	−0.419865	−	0.136423i	0.0914620	−	0.995809i	$-0.470846\pi$
$13$	−1.51385	−	0.491878i	−0.419865	−	0.136423i	−0.511327	+	0.859386i	$0.670846\pi$
$14$	−2.84311	−	3.91320i	−0.759853	−	1.04585i
$15$	1.44360	+	0.957081i	0.372737	+	0.247117i
$16$	−1.47562	−	4.54149i	−0.368905	−	1.13537i
$17$	0.898365	+	2.76488i	0.217885	+	0.670583i	0.998936	+	0.0461149i	$0.0146840\pi$
$17$	0.898365	+	2.76488i	0.217885	+	0.670583i	−0.781051	+	0.624468i	$0.785316\pi$
$18$	−4.08315	−	2.46187i	−0.962407	−	0.580267i
$19$	−1.39211	−	1.91607i	−0.319372	−	0.439577i	0.618904	−	0.785467i	$-0.287577\pi$
$19$	−1.39211	−	1.91607i	−0.319372	−	0.439577i	−0.938275	+	0.345890i	$0.887577\pi$
$20$	0.500137	+	0.162504i	0.111834	+	0.0363371i
$21$	5.26660	−	0.225931i	1.14927	−	0.0493022i
$22$	−5.23862	−	0.584388i	−1.11688	−	0.124592i
$23$		−	3.51389i		−	0.732696i	−0.930478	−	0.366348i	$-0.880608\pi$
$23$		−	3.51389i		−	0.732696i	0.930478	−	0.366348i	$-0.119392\pi$
$24$	3.90949	+	1.08740i	0.798020	+	0.221964i
$25$	0.809017	−	0.587785i	0.161803	−	0.117557i
$26$	1.48696	−	2.04663i	0.291617	−	0.401377i
$27$	4.69506	−	2.22629i	0.903565	−	0.428450i
$28$	1.52215	−	0.494577i	0.287660	−	0.0934663i
$29$	4.81478	+	3.49814i	0.894083	+	0.649589i	0.936939	−	0.349492i	$-0.113646\pi$
$29$	4.81478	+	3.49814i	0.894083	+	0.649589i	−0.0428566	+	0.999081i	$0.513646\pi$
$30$	−2.15563	+	1.71199i	−0.393562	+	0.312565i
$31$	0.0658086	−	0.202538i	0.0118196	−	0.0363769i	−0.944973	−	0.327149i	$-0.893912\pi$
$31$	0.0658086	−	0.202538i	0.0118196	−	0.0363769i	0.956792	+	0.290772i	$0.0939121\pi$
$32$	2.90358			0.513286
$33$	3.68553	−	4.40646i	0.641568	−	0.767066i
$34$	−4.62037			−0.792386
$35$	0.940483	−	2.89451i	0.158971	−	0.489262i
$36$	1.19222	−	1.03320i	0.198704	−	0.172201i
$37$	3.92798	+	2.85384i	0.645755	+	0.469169i	0.861823	−	0.507210i	$-0.169323\pi$
$37$	3.92798	+	2.85384i	0.645755	+	0.469169i	−0.216067	+	0.976378i	$0.569323\pi$
$38$	3.57986	−	1.16317i	0.580731	−	0.188691i
$39$	0.963555	+	2.58313i	0.154292	+	0.413633i
$40$	1.37708	−	1.89539i	0.217735	−	0.299687i
$41$	−1.89674	+	1.37806i	−0.296221	+	0.215217i	−0.725962	−	0.687735i	$-0.758605\pi$
$41$	−1.89674	+	1.37806i	−0.296221	+	0.215217i	0.429741	+	0.902952i	$0.358605\pi$
$42$	−2.24504	+	8.07150i	−0.346417	+	1.24546i
$43$			11.8663i			1.80960i	0.425838	+	0.904799i	$0.359979\pi$
$43$			11.8663i			1.80960i	−0.425838	+	0.904799i	$0.640021\pi$
$44$	0.719545	−	1.58879i	0.108475	−	0.239519i
$45$	−0.256920	−	2.98898i	−0.0382994	−	0.445571i
$46$	5.31129	+	1.72574i	0.783107	+	0.254447i
$47$	−7.63593	−	10.5100i	−1.11381	−	1.53303i	−0.815674	−	0.578512i	$-0.803633\pi$
$47$	−7.63593	−	10.5100i	−1.11381	−	1.53303i	−0.298141	−	0.954522i	$-0.596367\pi$
$48$	−4.57026	+	6.89351i	−0.659660	+	0.994993i
$49$	−0.699213	−	2.15196i	−0.0998875	−	0.307422i
$50$	0.491121	+	1.51151i	0.0694550	+	0.213760i
$51$	2.78240	−	4.19681i	0.389614	−	0.587670i
$52$	0.492013	+	0.677198i	0.0682300	+	0.0939105i
$53$	11.2504	+	3.65547i	1.54536	+	0.502117i	0.952849	−	0.303446i	$-0.0981373\pi$
$53$	11.2504	+	3.65547i	1.54536	+	0.502117i	0.592509	+	0.805564i	$0.298137\pi$
$54$	1.05923	+	8.19003i	0.144143	+	1.11452i
$55$	−1.63997	−	2.88279i	−0.221133	−	0.388716i
$56$		−	7.13032i		−	0.952829i
$57$	−1.09927	+	3.95215i	−0.145601	+	0.523475i
$58$	−7.65213	+	5.55960i	−1.00477	+	0.730011i
$59$	0.196917	−	0.271033i	0.0256365	−	0.0352855i	−0.796006	−	0.605288i	$-0.793058\pi$
$59$	0.196917	−	0.271033i	0.0256365	−	0.0352855i	0.821643	+	0.570003i	$0.193058\pi$
$60$	−0.318335	−	0.853404i	−0.0410968	−	0.110174i
$61$	11.0521	−	3.59104i	1.41507	−	0.459785i	0.501040	−	0.865424i	$-0.332951\pi$
$61$	11.0521	−	3.59104i	1.41507	−	0.459785i	0.914033	+	0.405639i	$0.132951\pi$
$62$	0.273819	+	0.198941i	0.0347751	+	0.0252656i
$63$	−5.97959	−	6.89991i	−0.753358	−	0.869307i
$64$	1.52523	−	4.69417i	0.190654	−	0.586772i
$65$	1.59175			0.197433
$66$	4.85039	+	7.73483i	0.597042	+	0.952092i
$67$	−8.55624			−1.04531			−0.522656	−	0.852544i	$-0.675059\pi$
$67$	−8.55624			−1.04531			−0.522656	+	0.852544i	$0.675059\pi$
$68$	0.472428	−	1.45398i	0.0572903	−	0.176321i
$69$	−4.76602	+	3.78514i	−0.573761	+	0.455678i
$70$	3.91320	+	2.84311i	0.467717	+	0.339816i
$71$	−8.16546	+	2.65312i	−0.969062	+	0.314867i	−0.750437	−	0.660942i	$-0.770157\pi$
$71$	−8.16546	+	2.65312i	−0.969062	+	0.314867i	−0.218625	+	0.975809i	$0.570157\pi$
$72$	−2.73640	−	6.47392i	−0.322488	−	0.762959i
$73$	6.13509	−	8.44422i	0.718058	−	0.988321i	−0.281529	−	0.959553i	$-0.590841\pi$
$73$	6.13509	−	8.44422i	0.718058	−	0.988321i	0.999586	−	0.0287686i	$-0.00915859\pi$
$74$	−6.24273	+	4.53561i	−0.725703	+	0.527254i
$75$	−1.66870	−	0.464140i	−0.192685	−	0.0535943i
$76$			1.24548i			0.142866i
$77$	−9.19501	−	4.16432i	−1.04787	−	0.474568i
$78$	−4.37767	+	0.187797i	−0.495673	+	0.0212638i
$79$	−8.85108	−	2.87589i	−0.995824	−	0.323563i	−0.234628	−	0.972085i	$-0.575387\pi$
$79$	−8.85108	−	2.87589i	−0.995824	−	0.323563i	−0.761196	+	0.648522i	$0.775387\pi$
$80$	2.80680	+	3.86322i	0.313809	+	0.431921i
$81$	−8.07710	−	3.96994i	−0.897456	−	0.441104i
$82$	−1.15143	−	3.54374i	−0.127154	−	0.391341i
$83$	2.49987	+	7.69379i	0.274396	+	0.844504i	0.989379	+	0.145362i	$0.0464345\pi$
$83$	2.49987	+	7.69379i	0.274396	+	0.844504i	−0.714983	+	0.699142i	$0.753565\pi$
$84$	−2.31047	−	1.53179i	−0.252093	−	0.167132i
$85$	−1.70879	−	2.35195i	−0.185344	−	0.255105i
$86$	−17.9361	−	5.82780i	−1.93410	−	0.628428i
$87$	−0.441800	−	10.2987i	−0.0473659	−	1.10413i
$88$	−5.74118	−	5.23604i	−0.612012	−	0.558163i
$89$			9.73184i			1.03157i	0.856717	+	0.515787i	$0.172500\pi$
$89$			9.73184i			1.03157i	−0.856717	+	0.515787i	$0.827500\pi$
$90$	4.64406	+	1.07961i	0.489527	+	0.113801i
$91$	3.91924	−	2.84749i	0.410848	−	0.298499i
$92$	−1.08615	+	1.49496i	−0.113239	+	0.155860i
$93$	−0.345598	+	0.128914i	−0.0358369	+	0.0133678i
$94$	19.6361	−	6.38016i	2.02531	−	0.658063i
$95$	1.91607	+	1.39211i	0.196585	+	0.142827i
$96$	−3.12773	−	3.93824i	−0.319222	−	0.401945i
$97$	−3.23762	+	9.96437i	−0.328731	+	1.01173i	0.640998	+	0.767543i	$0.278521\pi$
$97$	−3.23762	+	9.96437i	−0.328731	+	1.01173i	−0.969728	+	0.244186i	$0.921479\pi$
$98$	3.59611			0.363262
$99$	−9.94668	−	0.252198i	−0.999679	−	0.0253468i
$100$	−0.525875			−0.0525875
$101$	0.359909	−	1.10769i	0.0358123	−	0.110219i	−0.931552	−	0.363607i	$-0.881545\pi$
$101$	0.359909	−	1.10769i	0.0358123	−	0.110219i	0.967365	+	0.253388i	$0.0815450\pi$
$102$	4.97704	+	6.26677i	0.492800	+	0.620503i
$103$	15.6128	+	11.3434i	1.53838	+	1.11770i	0.951344	+	0.308131i	$0.0997035\pi$
$103$	15.6128	+	11.3434i	1.53838	+	1.11770i	0.587032	+	0.809564i	$0.300296\pi$
$104$	3.54668	−	1.15239i	0.347780	−	0.113001i
$105$	−4.93902	+	1.84234i	−0.481999	+	0.179794i
$106$	−11.0506	+	15.2098i	−1.07333	+	1.47731i
$107$	6.40161	−	4.65105i	0.618867	−	0.449634i	−0.233658	−	0.972319i	$-0.575070\pi$
$107$	6.40161	−	4.65105i	0.618867	−	0.449634i	0.852526	+	0.522685i	$0.175070\pi$
$108$	−2.68563	−	0.504094i	−0.258425	−	0.0485065i
$109$			11.6570i			1.11654i	0.829659	+	0.558270i	$0.188535\pi$
$109$			11.6570i			1.11654i	−0.829659	+	0.558270i	$0.811465\pi$
$110$	5.16281	−	1.06304i	0.492254	−	0.101356i
$111$	−0.360428	−	8.40181i	−0.0342103	−	0.797464i
$112$	13.8219	+	4.49100i	1.30605	+	0.424360i
$113$	1.98009	+	2.72536i	0.186271	+	0.256381i	0.891932	−	0.452169i	$-0.149350\pi$
$113$	1.98009	+	2.72536i	0.186271	+	0.256381i	−0.705661	+	0.708550i	$0.749350\pi$
$114$	−5.43386	−	3.60254i	−0.508928	−	0.337409i
$115$	1.08585	+	3.34191i	0.101256	+	0.311634i
$116$	−0.967129	−	2.97652i	−0.0897956	−	0.276363i
$117$	2.46566	−	4.08945i	0.227951	−	0.378069i
$118$	0.312961	+	0.430754i	0.0288104	+	0.0396541i
$119$	−8.41483	−	2.73415i	−0.771387	−	0.250639i
$120$	−4.05417	+	0.173919i	−0.370093	+	0.0158766i
$121$	−10.1052	+	4.34562i	−0.918657	+	0.395056i
$122$			18.4690i			1.67210i
$123$	3.91227	+	1.08818i	0.352758	+	0.0981174i
$124$	−0.0906026	+	0.0658266i	−0.00813635	+	0.00591140i
$125$	−0.587785	+	0.809017i	−0.0525731	+	0.0723607i
$126$	13.3660	−	5.64955i	1.19074	−	0.503302i
$127$	10.3510	−	3.36324i	0.918501	−	0.298439i	0.188649	−	0.982045i	$-0.439589\pi$
$127$	10.3510	−	3.36324i	0.918501	−	0.298439i	0.729852	+	0.683606i	$0.239589\pi$
$128$	11.0443	+	8.02418i	0.976191	+	0.709244i
$129$	16.0947	−	12.7824i	1.41706	−	1.12542i
$130$	−0.781742	+	2.40596i	−0.0685633	+	0.211016i
$131$	−16.8888			−1.47558			−0.737792	−	0.675028i	$-0.764131\pi$
$131$	−16.8888			−1.47558			−0.737792	+	0.675028i	$0.764131\pi$
$132$	−2.93002	+	0.735491i	−0.255026	+	0.0640162i
$133$	7.20814			0.625025
$134$	4.20215	−	12.9329i	0.363010	−	1.11723i
$135$	−3.77731	+	3.56818i	−0.325099	+	0.307100i
$136$	−5.51021	−	4.00340i	−0.472497	−	0.343289i
$137$	−7.55832	+	2.45585i	−0.645751	+	0.209817i	−0.613540	−	0.789664i	$-0.710255\pi$
$137$	−7.55832	+	2.45585i	−0.645751	+	0.209817i	−0.0322111	+	0.999481i	$0.510255\pi$
$138$	−3.38061	−	9.06287i	−0.287777	−	0.771482i
$139$	−6.88820	+	9.48080i	−0.584250	+	0.804151i	−0.994153	−	0.107978i	$-0.965562\pi$
$139$	−6.88820	+	9.48080i	−0.584250	+	0.804151i	0.409904	+	0.912129i	$0.365562\pi$
$140$	−1.29482	+	0.940741i	−0.109432	+	0.0795072i
$141$	−6.02965	+	21.6782i	−0.507788	+	1.82563i
$142$		−	13.6452i		−	1.14508i
$143$	0.585290	−	5.24670i	0.0489444	−	0.438751i
$144$	14.2730	−	1.22685i	1.18942	−	0.102237i
$145$	−5.66012	−	1.83908i	−0.470047	−	0.152728i
$146$	9.75049	+	13.4204i	0.806957	+	1.11068i
$147$	−2.16559	+	3.26645i	−0.178615	+	0.269412i
$148$	−0.788999	−	2.42829i	−0.0648553	−	0.199604i
$149$	−1.13405	−	3.49024i	−0.0929048	−	0.285932i	0.893797	−	0.448471i	$-0.148031\pi$
$149$	−1.13405	−	3.49024i	−0.0929048	−	0.285932i	−0.986702	+	0.162540i	$0.948031\pi$
$150$	1.52109	−	2.29432i	0.124196	−	0.187331i
$151$	8.58173	+	11.8117i	0.698371	+	0.961225i	0.999970	+	0.00779041i	$0.00247979\pi$
$151$	8.58173	+	11.8117i	0.698371	+	0.961225i	−0.301598	+	0.953435i	$0.597520\pi$
$152$	5.27717	+	1.71466i	0.428035	+	0.139077i
$153$	−8.68947	+	0.746911i	−0.702502	+	0.0603841i
$154$	10.8103	−	11.8532i	0.871118	−	0.955158i
$155$			0.212961i			0.0171054i
$156$	0.388514	−	1.39681i	0.0311060	−	0.111834i
$157$	13.7640	−	10.0001i	1.09848	−	0.798095i	0.117672	−	0.993053i	$-0.462457\pi$
$157$	13.7640	−	10.0001i	1.09848	−	0.798095i	0.980812	+	0.194958i	$0.0624569\pi$
$158$	8.69389	−	11.9661i	0.691649	−	0.951973i
$159$	−7.16081	−	19.1970i	−0.567889	−	1.52242i
$160$	−2.76147	+	0.897256i	−0.218313	+	0.0709343i
$161$	8.65196	+	6.28602i	0.681870	+	0.495407i
$162$	9.96745	−	10.2589i	0.783117	−	0.806019i
$163$	4.55634	−	14.0230i	0.356880	−	1.09836i	−0.598032	−	0.801473i	$-0.704050\pi$
$163$	4.55634	−	14.0230i	0.356880	−	1.09836i	0.954911	−	0.296891i	$-0.0959497\pi$
$164$	1.23291			0.0962744
$165$	−2.14347	+	5.32968i	−0.166869	+	0.414915i
$166$	−12.8570			−0.997898
$167$	1.98620	−	6.11289i	0.153697	−	0.473030i	−0.844330	−	0.535824i	$-0.820001\pi$
$167$	1.98620	−	6.11289i	0.153697	−	0.473030i	0.998027	+	0.0627939i	$0.0200011\pi$
$168$	−9.67111	+	7.68075i	−0.746143	+	0.592583i
$169$	−8.46744	−	6.15195i	−0.651341	−	0.473227i
$170$	4.39423	−	1.42777i	0.337022	−	0.109505i
$171$	6.54458	−	2.76626i	0.500476	−	0.211542i
$172$	3.66790	−	5.04844i	0.279675	−	0.384940i
$173$	5.48478	−	3.98492i	0.417000	−	0.302968i	−0.359430	−	0.933172i	$-0.617029\pi$
$173$	5.48478	−	3.98492i	0.417000	−	0.302968i	0.776430	+	0.630204i	$0.217029\pi$
$174$	15.7835	+	4.39010i	1.19655	+	0.332812i
$175$			3.04347i			0.230065i
$176$	13.7659	−	7.83119i	1.03765	−	0.590298i
$177$	−0.579731	+	0.0248698i	−0.0435753	+	0.00186933i
$178$	−14.7098	−	4.77951i	−1.10255	−	0.358239i
$179$	4.76489	+	6.55831i	0.356145	+	0.490191i	0.949070	−	0.315067i	$-0.102027\pi$
$179$	4.76489	+	6.55831i	0.356145	+	0.490191i	−0.592925	+	0.805258i	$0.702027\pi$
$180$	−0.814594	+	1.35105i	−0.0607162	+	0.100701i
$181$	−2.68396	−	8.26039i	−0.199497	−	0.613990i	−0.999895	−	0.0145198i	$-0.995378\pi$
$181$	−2.68396	−	8.26039i	−0.199497	−	0.613990i	0.800397	−	0.599470i	$-0.204622\pi$
$182$	2.37921	+	7.32245i	0.176359	+	0.542776i
$183$	−16.7759	−	11.1221i	−1.24011	−	0.822168i
$184$	4.83890	+	6.66018i	0.356729	+	0.490995i
$185$	−4.61761	−	1.50035i	−0.339494	−	0.110308i
$186$	−0.0251254	−	0.585689i	−0.00184228	−	0.0429448i
$187$	−8.38077	+	4.76767i	−0.612863	+	0.348646i
$188$			6.83166i			0.498250i
$189$	−2.91741	+	15.5429i	−0.212210	+	1.13058i
$190$	−3.04521	+	2.21248i	−0.220923	+	0.160510i
$191$	11.6704	−	16.0629i	0.844440	−	1.16227i	−0.140621	−	0.990064i	$-0.544910\pi$
$191$	11.6704	−	16.0629i	0.844440	−	1.16227i	0.985061	−	0.172208i	$-0.0550901\pi$
$192$	−8.00985	+	2.98782i	−0.578061	+	0.215627i
$193$	−20.6715	+	6.71657i	−1.48797	+	0.483469i	−0.936482	−	0.350717i	$-0.885938\pi$
$193$	−20.6715	+	6.71657i	−1.48797	+	0.483469i	−0.551483	+	0.834186i	$0.685938\pi$
$194$	−13.4712	−	9.78742i	−0.967178	−	0.702696i
$195$	−1.71463	−	2.15895i	−0.122787	−	0.154606i
$196$	−0.367699	+	1.13166i	−0.0262642	+	0.0808329i
$197$	4.82294			0.343620			0.171810	−	0.985130i	$-0.445038\pi$
$197$	4.82294			0.343620			0.171810	+	0.985130i	$0.445038\pi$
$198$	5.26622	−	14.9107i	0.374254	−	1.05966i
$199$	8.28921			0.587607			0.293803	−	0.955866i	$-0.405079\pi$
$199$	8.28921			0.587607			0.293803	+	0.955866i	$0.405079\pi$
$200$	−0.723973	+	2.22816i	−0.0511926	+	0.157555i
$201$	9.21675	+	11.6051i	0.650099	+	0.818564i
$202$	1.49752	+	1.08801i	0.105365	+	0.0765525i
$203$	−17.2264	+	5.59719i	−1.20906	+	0.392846i
$204$	−2.48099	+	0.925453i	−0.173704	+	0.0647947i
$205$	1.37806	−	1.89674i	0.0962480	−	0.132474i
$206$	−24.8134	+	18.0280i	−1.72883	+	1.25607i
$207$	10.2679	+	2.38698i	0.713666	+	0.165907i
$208$			7.60094i			0.527031i
$209$	5.29318	−	5.80384i	0.366137	−	0.401460i
$210$	−0.359072	−	8.37021i	−0.0247783	−	0.577599i
$211$	−0.355560	−	0.115528i	−0.0244778	−	0.00795331i	0.296753	−	0.954954i	$-0.404096\pi$
$211$	−0.355560	−	0.115528i	−0.0244778	−	0.00795331i	−0.321230	+	0.947001i	$0.604096\pi$
$212$	−3.65647	−	5.03270i	−0.251127	−	0.345647i
$213$	12.3943	+	8.21719i	0.849245	+	0.563032i
$214$	3.88616	+	11.9604i	0.265652	+	0.817593i
$215$	−3.66690	−	11.2856i	−0.250080	−	0.769668i
$216$	−5.83318	+	10.6852i	−0.396898	+	0.727033i
$217$	0.380967	+	0.524356i	0.0258617	+	0.0355956i
$218$	−17.6198	−	5.72500i	−1.19336	−	0.387746i
$219$	−18.0619	+	0.774834i	−1.22051	+	0.0523584i
$220$	−0.193365	+	1.73338i	−0.0130367	+	0.116864i
$221$		−	4.62749i		−	0.311279i
$222$	12.8765	+	3.58151i	0.864212	+	0.240375i
$223$	3.46085	−	2.51446i	0.231756	−	0.168381i	−0.465847	−	0.884865i	$-0.654250\pi$
$223$	3.46085	−	2.51446i	0.231756	−	0.168381i	0.697603	+	0.716485i	$0.254250\pi$
$224$	−5.19424	+	7.14925i	−0.347054	+	0.477679i
$225$	1.16799	+	2.76329i	0.0778660	+	0.184220i
$226$	−5.09189	+	1.65446i	−0.338708	+	0.110053i
$227$	−0.550593	−	0.400030i	−0.0365442	−	0.0265509i	0.569363	−	0.822086i	$-0.307190\pi$
$227$	−0.550593	−	0.400030i	−0.0365442	−	0.0265509i	−0.605907	+	0.795535i	$0.707190\pi$
$228$	1.68929	−	1.34163i	0.111876	−	0.0888514i
$229$	−0.805914	+	2.48035i	−0.0532563	+	0.163906i	−0.974147	−	0.225915i	$-0.927463\pi$
$229$	−0.805914	+	2.48035i	−0.0532563	+	0.163906i	0.920891	+	0.389821i	$0.127463\pi$
$230$	−5.58462			−0.368239
$231$	4.25660	+	16.9573i	0.280064	+	1.11571i
$232$	−13.9431			−0.915409
$233$	−1.07815	+	3.31822i	−0.0706323	+	0.217384i	−0.980141	−	0.198300i	$-0.936458\pi$
$233$	−1.07815	+	3.31822i	−0.0706323	+	0.217384i	0.909509	+	0.415684i	$0.136458\pi$
$234$	4.97032	+	5.73530i	0.324920	+	0.374928i
$235$	10.5100	+	7.63593i	0.685594	+	0.498113i
$236$	−0.167554	+	0.0544415i	−0.0109068	+	0.00354384i
$237$	5.63366	+	15.1029i	0.365946	+	0.981041i
$238$	8.26540	−	11.3763i	0.535766	−	0.737419i
$239$	11.5507	−	8.39209i	0.747154	−	0.542839i	−0.147789	−	0.989019i	$-0.547216\pi$
$239$	11.5507	−	8.39209i	0.747154	−	0.542839i	0.894943	+	0.446179i	$0.147216\pi$
$240$	2.21636	−	7.96841i	0.143066	−	0.514358i
$241$		−	8.26022i		−	0.532088i	−0.963961	−	0.266044i	$-0.914283\pi$
$241$		−	8.26022i		−	0.532088i	0.963961	−	0.266044i	$-0.0857166\pi$
$242$	−1.60558	−	17.4084i	−0.103211	−	1.11906i
$243$	3.31605	+	15.2317i	0.212725	+	0.977112i
$244$	−5.81201	−	1.88844i	−0.372076	−	0.120895i
$245$	1.32998	+	1.83056i	0.0849694	+	0.116950i
$246$	−3.56619	+	5.37903i	−0.227372	+	0.342955i
$247$	1.16496	+	3.58539i	0.0741248	+	0.228133i
$248$	0.154178	+	0.474511i	0.00979032	+	0.0301315i
$249$	7.74253	−	11.6784i	0.490663	−	0.740087i
$250$	−0.934167	−	1.28577i	−0.0590819	−	0.0813193i
$251$	21.3330	+	6.93151i	1.34653	+	0.437513i	0.891523	−	0.452976i	$-0.149638\pi$
$251$	21.3330	+	6.93151i	1.34653	+	0.437513i	0.455004	+	0.890489i	$0.349638\pi$
$252$	0.411197	+	4.78382i	0.0259030	+	0.301352i
$253$	11.4148	−	2.35034i	0.717642	−	0.147764i
$254$			17.2974i			1.08534i
$255$	−1.34933	+	4.85121i	−0.0844986	+	0.303794i
$256$	−9.56656	+	6.95051i	−0.597910	+	0.434407i
$257$	−2.69265	+	3.70611i	−0.167963	+	0.231181i	−0.884698	−	0.466164i	$-0.845636\pi$
$257$	−2.69265	+	3.70611i	−0.167963	+	0.231181i	0.716735	+	0.697345i	$0.245636\pi$
$258$	11.4163	+	30.6051i	0.710745	+	1.90539i
$259$	−14.0536	+	4.56628i	−0.873246	+	0.283735i
$260$	−0.677198	−	0.492013i	−0.0419981	−	0.0305134i
$261$	−13.4925	+	11.6929i	−0.835167	+	0.723772i
$262$	8.29445	−	25.5277i	0.512433	−	1.57711i
$263$	−9.61697			−0.593008			−0.296504	−	0.955032i	$-0.595821\pi$
$263$	−9.61697			−0.593008			−0.296504	+	0.955032i	$0.595821\pi$
$264$	−0.917456	+	13.4272i	−0.0564655	+	0.826387i
$265$	−11.8293			−0.726671
$266$	−3.54007	+	10.8952i	−0.217055	+	0.668028i
$267$	13.1997	−	10.4831i	0.807806	−	0.641555i
$268$	3.64019	+	2.64475i	0.222360	+	0.161554i
$269$	−13.7292	+	4.46087i	−0.837082	+	0.271984i	−0.696025	−	0.718017i	$-0.745050\pi$
$269$	−13.7292	+	4.46087i	−0.837082	+	0.271984i	−0.141056	+	0.990002i	$0.545050\pi$
$270$	−3.53825	−	7.46187i	−0.215331	−	0.454115i
$271$	0.189591	−	0.260949i	0.0115168	−	0.0158515i	−0.803220	−	0.595683i	$-0.796882\pi$
$271$	0.189591	−	0.260949i	0.0115168	−	0.0158515i	0.814737	+	0.579831i	$0.196882\pi$
$272$	11.2310	−	8.15983i	0.680982	−	0.494762i
$273$	−8.08395	−	2.24850i	−0.489263	−	0.136085i
$274$		−	12.6306i		−	0.763044i
$275$	2.45054	+	2.23492i	0.147773	+	0.134771i
$276$	3.19766	−	0.137176i	0.192476	−	0.00825701i
$277$	−3.72833	−	1.21141i	−0.224014	−	0.0727865i	0.194860	−	0.980831i	$-0.437575\pi$
$277$	−3.72833	−	1.21141i	−0.224014	−	0.0727865i	−0.418873	+	0.908045i	$0.637575\pi$
$278$	−10.9474	−	15.0678i	−0.656583	−	0.903708i
$279$	0.547128	+	0.329882i	0.0327557	+	0.0197495i
$280$	2.20339	+	6.78134i	0.131678	+	0.405262i
$281$	−8.45874	−	26.0333i	−0.504606	−	1.55302i	−0.801431	−	0.598087i	$-0.795928\pi$
$281$	−8.45874	−	26.0333i	−0.504606	−	1.55302i	0.296825	−	0.954932i	$-0.404072\pi$
$282$	−29.8056	−	19.7605i	−1.77490	−	1.17672i
$283$	−14.0410	−	19.3258i	−0.834651	−	1.14880i	−0.987039	−	0.160478i	$-0.948696\pi$
$283$	−14.0410	−	19.3258i	−0.834651	−	1.14880i	0.152388	−	0.988321i	$-0.451304\pi$
$284$	4.29401	+	1.39521i	0.254803	+	0.0827905i
$285$	−0.175817	−	4.09841i	−0.0104145	−	0.242769i
$286$	7.64301	+	3.46144i	0.451941	+	0.204679i
$287$		−	7.13540i		−	0.421190i
$288$	−1.97240	+	8.48450i	−0.116225	+	0.499954i
$289$	6.91577	−	5.02460i	0.406810	−	0.295565i
$290$	5.55960	−	7.65213i	0.326471	−	0.449349i
$291$	17.0026	−	6.34227i	0.996710	−	0.371791i
$292$	−5.22025	+	1.69616i	−0.305492	+	0.0992603i
$293$	20.0524	+	14.5689i	1.17147	+	0.851124i	0.991184	−	0.132490i	$-0.0422973\pi$
$293$	20.0524	+	14.5689i	1.17147	+	0.851124i	0.180287	+	0.983614i	$0.442297\pi$
$294$	−3.87371	−	4.87754i	−0.225920	−	0.284464i
$295$	−0.103526	+	0.318619i	−0.00602749	+	0.0185507i
$296$	−11.3750			−0.661158
$297$	10.3725	+	13.7627i	0.601871	+	0.798594i
$298$	5.83250			0.337868
$299$	−1.72841	+	5.31949i	−0.0999563	+	0.307634i
$300$	0.566471	+	0.713264i	0.0327052	+	0.0411803i
$301$	−29.2175	−	21.2277i	−1.68407	−	1.22355i
$302$	−22.0683	+	7.17042i	−1.26989	+	0.412611i
$303$	−1.89009	+	0.705036i	−0.108583	+	0.0405033i
$304$	−6.64760	+	9.14964i	−0.381266	+	0.524768i
$305$	−9.40145	+	6.83056i	−0.538326	+	0.391117i
$306$	3.13861	−	13.5011i	0.179423	−	0.771805i
$307$			2.25061i			0.128449i	0.997935	+	0.0642245i	$0.0204574\pi$
$307$			2.25061i			0.128449i	−0.997935	+	0.0642245i	$0.979543\pi$
$308$	2.62474	+	4.61387i	0.149559	+	0.262900i
$309$	−1.43262	−	33.3952i	−0.0814987	−	1.89979i
$310$	−0.321894	−	0.104590i	−0.0182823	−	0.00594029i
$311$	2.07841	+	2.86069i	0.117856	+	0.162215i	0.863869	−	0.503717i	$-0.168034\pi$
$311$	2.07841	+	2.86069i	0.117856	+	0.162215i	−0.746013	+	0.665931i	$0.768034\pi$
$312$	−5.38349	−	3.56915i	−0.304780	−	0.202063i
$313$	−5.43345	−	16.7225i	−0.307117	−	0.945209i	−0.978879	−	0.204442i	$-0.934462\pi$
$313$	−5.43345	−	16.7225i	−0.307117	−	0.945209i	0.671762	−	0.740767i	$-0.265538\pi$
$314$	8.35553	+	25.7157i	0.471530	+	1.45122i
$315$	7.81912	+	4.71441i	0.440558	+	0.265627i
$316$	2.87668	+	3.95941i	0.161826	+	0.222734i
$317$	−1.22050	−	0.396564i	−0.0685500	−	0.0222732i	0.274541	−	0.961575i	$-0.411474\pi$
$317$	−1.22050	−	0.396564i	−0.0685500	−	0.0222732i	−0.343091	+	0.939302i	$0.611474\pi$
$318$	32.5333	−	1.39564i	1.82438	−	0.0782636i
$319$	−8.14318	+	17.9805i	−0.455931	+	1.00672i
$320$			4.93575i			0.275917i
$321$	−13.2042	−	3.67266i	−0.736985	−	0.204988i
$322$	−13.7506	+	9.99037i	−0.766289	+	0.556741i
$323$	4.04710	−	5.57035i	0.225186	−	0.309942i
$324$	2.20923	+	4.18562i	0.122735	+	0.232535i
$325$	−1.51385	+	0.491878i	−0.0839731	+	0.0272845i
$326$	18.9582	+	13.7739i	1.05000	+	0.762868i
$327$	15.8108	−	12.5569i	0.874342	−	0.694398i
$328$	1.69735	−	5.22392i	0.0937207	−	0.288443i
$329$	39.5377			2.17979
$330$	−7.00319	−	5.85741i	−0.385513	−	0.322440i
$331$	25.3583			1.39382			0.696910	−	0.717158i	$-0.254558\pi$
$331$	25.3583			1.39382			0.696910	+	0.717158i	$0.254558\pi$
$332$	1.31462	−	4.04598i	0.0721490	−	0.222052i
$333$	−11.0074	+	9.53925i	−0.603203	+	0.522748i
$334$	8.26426	+	6.00434i	0.452200	+	0.328543i
$335$	8.13747	−	2.64402i	0.444597	−	0.144458i
$336$	−8.79756	−	23.5848i	−0.479946	−	1.28666i
$337$	−0.947444	+	1.30404i	−0.0516106	+	0.0710358i	−0.834042	−	0.551701i	$-0.813979\pi$
$337$	−0.947444	+	1.30404i	−0.0516106	+	0.0710358i	0.782432	+	0.622736i	$0.213979\pi$
$338$	13.4573	−	9.77730i	0.731980	−	0.531815i
$339$	1.56356	−	5.62142i	0.0849212	−	0.305314i
$340$			1.52881i			0.0829113i
$341$	0.701957	+	0.0783061i	0.0380131	+	0.00424051i
$342$	0.967071	+	11.2508i	0.0522932	+	0.608373i
$343$	−13.7122	−	4.45535i	−0.740387	−	0.240566i
$344$	−16.3409	−	22.4913i	−0.881041	−	1.21265i
$345$	3.36308	−	5.07267i	0.181062	−	0.273103i
$346$	3.32958	+	10.2474i	0.178999	+	0.550904i
$347$	9.14722	+	28.1522i	0.491048	+	1.51129i	0.823026	+	0.568004i	$0.192284\pi$
$347$	9.14722	+	28.1522i	0.491048	+	1.51129i	−0.331978	+	0.943287i	$0.607716\pi$
$348$	−2.99537	+	4.51804i	−0.160569	+	0.242192i
$349$	5.41242	+	7.44955i	0.289720	+	0.398765i	0.928923	−	0.370272i	$-0.120736\pi$
$349$	5.41242	+	7.44955i	0.289720	+	0.398765i	−0.639203	+	0.769038i	$0.720736\pi$
$350$	−4.60025	−	1.49471i	−0.245894	−	0.0798956i
$351$	−8.20267	+	1.06086i	−0.437826	+	0.0566247i
$352$	1.94212	+	9.43223i	0.103515	+	0.502739i
$353$		−	15.4022i		−	0.819775i	−0.912136	−	0.409888i	$-0.865568\pi$
$353$		−	15.4022i		−	0.819775i	0.912136	−	0.409888i	$-0.134432\pi$
$354$	0.247127	−	0.888486i	0.0131346	−	0.0472225i
$355$	6.94595	−	5.04653i	0.368653	−	0.267842i
$356$	3.00813	−	4.14034i	0.159431	−	0.219437i
$357$	5.35600	+	14.3586i	0.283470	+	0.759936i
$358$	−12.2531	+	3.98128i	−0.647598	+	0.210417i
$359$	−10.4761	−	7.61136i	−0.552910	−	0.401712i	0.275947	−	0.961173i	$-0.411008\pi$
$359$	−10.4761	−	7.61136i	−0.552910	−	0.401712i	−0.828857	+	0.559460i	$0.811008\pi$
$360$	4.60302	+	5.31147i	0.242601	+	0.279939i
$361$	4.13795	−	12.7353i	0.217787	−	0.670280i
$362$	13.8038			0.725514
$363$	16.7794	+	9.02501i	0.880692	+	0.473690i
$364$	−2.54758			−0.133529
$365$	−3.22541	+	9.92678i	−0.168825	+	0.519591i
$366$	25.0502	−	19.8947i	1.30939	−	1.03991i
$367$	−23.0215	−	16.7261i	−1.20171	−	0.873094i	−0.207259	−	0.978286i	$-0.566454\pi$
$367$	−23.0215	−	16.7261i	−1.20171	−	0.873094i	−0.994452	+	0.105192i	$0.966454\pi$
$368$	−15.9583	+	5.18516i	−0.831883	+	0.270295i
$369$	−2.73835	−	6.47854i	−0.142553	−	0.337259i
$370$	4.53561	−	6.24273i	0.235795	−	0.324544i
$371$	−29.1264	+	21.1616i	−1.51217	+	1.09865i
$372$	0.186880	+	0.0519795i	0.00968926	+	0.00269501i
$373$			11.4932i			0.595096i	0.954707	+	0.297548i	$0.0961689\pi$
$373$			11.4932i			0.595096i	−0.954707	+	0.297548i	$0.903831\pi$
$374$	−3.09043	−	15.0092i	−0.159802	−	0.776105i
$375$	1.73046	−	0.0742347i	0.0893605	−	0.00383346i
$376$	28.9461	+	9.40515i	1.49278	+	0.485034i
$377$	−5.56818	−	7.66394i	−0.286776	−	0.394713i
$378$	−22.0605	−	12.0431i	−1.13467	−	0.619433i
$379$	3.59704	+	11.0705i	0.184767	+	0.568656i	0.999944	−	0.0105564i	$-0.00336028\pi$
$379$	3.59704	+	11.0705i	0.184767	+	0.568656i	−0.815177	+	0.579212i	$0.803360\pi$
$380$	−0.384875	−	1.18452i	−0.0197437	−	0.0607647i
$381$	−15.7117	−	10.4165i	−0.804935	−	0.533656i
$382$	18.5478	+	25.5288i	0.948986	+	1.30617i
$383$	18.8527	+	6.12562i	0.963329	+	0.313005i	0.748120	−	0.663563i	$-0.230957\pi$
$383$	18.8527	+	6.12562i	0.963329	+	0.313005i	0.215209	+	0.976568i	$0.430957\pi$
$384$	−1.01342	−	23.6234i	−0.0517158	−	1.20553i
$385$	10.0318	+	1.11909i	0.511269	+	0.0570340i
$386$		−	34.5439i		−	1.75824i
$387$	−34.6744	−	8.06079i	−1.76260	−	0.409753i
$388$	4.45743	−	3.23851i	0.226292	−	0.164410i
$389$	0.772281	−	1.06295i	0.0391562	−	0.0538939i	−0.788990	−	0.614406i	$-0.789396\pi$
$389$	0.772281	−	1.06295i	0.0391562	−	0.0538939i	0.828146	+	0.560512i	$0.189396\pi$
$390$	4.10538	−	1.53138i	0.207884	−	0.0775444i
$391$	9.71549	−	3.15675i	0.491333	−	0.159644i
$392$	4.28869	+	3.11592i	0.216612	+	0.157378i
$393$	18.1926	+	22.9069i	0.917694	+	1.15550i
$394$	−2.36865	+	7.28994i	−0.119331	+	0.367262i
$395$	9.30657			0.468264
$396$	4.15378	+	3.18183i	0.208735	+	0.159893i
$397$	12.7850			0.641659			0.320830	−	0.947137i	$-0.396038\pi$
$397$	12.7850			0.641659			0.320830	+	0.947137i	$0.396038\pi$
$398$	−4.07101	+	12.5293i	−0.204061	+	0.628035i
$399$	−7.76457	−	9.77666i	−0.388715	−	0.489445i
$400$	−3.86322	−	2.80680i	−0.193161	−	0.140340i
$401$	25.7286	−	8.35973i	1.28482	−	0.417465i	0.414548	−	0.910027i	$-0.363940\pi$
$401$	25.7286	−	8.35973i	1.28482	−	0.417465i	0.870277	+	0.492563i	$0.163940\pi$
$402$	−22.0679	+	8.23172i	−1.10065	+	0.410561i
$403$	−0.199248	+	0.274241i	−0.00992525	+	0.0136609i
$404$	−0.495508	+	0.360008i	−0.0246524	+	0.0179110i
$405$	8.90856	+	1.27967i	0.442670	+	0.0635873i
$406$		−	28.7868i		−	1.42867i
$407$	−6.64334	+	14.6688i	−0.329298	+	0.727105i
$408$	0.505612	+	11.7861i	0.0250315	+	0.583501i
$409$	6.65344	+	2.16183i	0.328992	+	0.106896i	0.468855	−	0.883275i	$-0.344667\pi$
$409$	6.65344	+	2.16183i	0.328992	+	0.106896i	−0.139864	+	0.990171i	$0.544667\pi$
$410$	2.19015	+	3.01449i	0.108164	+	0.148875i
$411$	11.4727	+	7.60620i	0.565909	+	0.375186i
$412$	−3.13609	−	9.65189i	−0.154504	−	0.475515i
$413$	0.315077	+	0.969707i	0.0155039	+	0.0477161i
$414$	−8.65072	+	14.3477i	−0.425160	+	0.705152i
$415$	−4.75503	−	6.54473i	−0.233415	−	0.321268i
$416$	−4.39558	−	1.42821i	−0.215511	−	0.0700237i
$417$	20.2791	−	0.869949i	0.993071	−	0.0426016i
$418$	6.17299	+	10.8511i	0.301931	+	0.530745i
$419$			28.2365i			1.37945i	0.724074	+	0.689723i	$0.242268\pi$
$419$			28.2365i			1.37945i	−0.724074	+	0.689723i	$0.757732\pi$
$420$	2.67074	+	0.742849i	0.130319	+	0.0362473i
$421$	18.1757	−	13.2054i	0.885830	−	0.643593i	−0.0489576	−	0.998801i	$-0.515590\pi$
$421$	18.1757	−	13.2054i	0.885830	−	0.643593i	0.934787	+	0.355208i	$0.115590\pi$
$422$	0.349246	−	0.480696i	0.0170010	−	0.0233999i
$423$	35.8980	−	15.1734i	1.74542	−	0.737755i
$424$	−26.3577	+	8.56413i	−1.28004	+	0.415911i
$425$	2.35195	+	1.70879i	0.114086	+	0.0828886i
$426$	−18.5075	+	14.6986i	−0.896691	+	0.712148i
$427$	−10.9292	+	33.6366i	−0.528901	+	1.62779i
$428$	−4.16116			−0.201137
$429$	−7.74676	+	4.85787i	−0.374017	+	0.234540i
$430$	18.8592			0.909470
$431$	1.72486	−	5.30857i	0.0830836	−	0.255705i	−0.900882	−	0.434064i	$-0.857079\pi$
$431$	1.72486	−	5.30857i	0.0830836	−	0.255705i	0.983965	+	0.178360i	$0.0570790\pi$
$432$	−17.0388	−	18.0374i	−0.819780	−	0.867826i
$433$	16.5209	+	12.0032i	0.793946	+	0.576836i	0.909132	−	0.416508i	$-0.136746\pi$
$433$	16.5209	+	12.0032i	0.793946	+	0.576836i	−0.115186	+	0.993344i	$0.536746\pi$
$434$	−0.979673	+	0.318315i	−0.0470258	+	0.0152796i
$435$	3.60264	+	9.65808i	0.172733	+	0.463069i
$436$	3.60321	−	4.95939i	0.172562	−	0.237512i
$437$	−6.73287	+	4.89171i	−0.322077	+	0.234002i
$438$	7.69940	−	27.6814i	0.367892	−	1.32267i
$439$		−	14.2557i		−	0.680390i	−0.940355	−	0.340195i	$-0.889507\pi$
$439$		−	14.2557i		−	0.680390i	0.940355	−	0.340195i	$-0.110493\pi$
$440$	7.07821	+	3.20564i	0.337440	+	0.152823i
$441$	6.76316	−	0.581333i	0.322055	−	0.0276825i
$442$	6.99452	+	2.27266i	0.332696	+	0.108099i
$443$	−3.73118	−	5.13552i	−0.177274	−	0.243996i	0.711129	−	0.703062i	$-0.248184\pi$
$443$	−3.73118	−	5.13552i	−0.177274	−	0.243996i	−0.888402	+	0.459066i	$0.848184\pi$
$444$	−2.44367	+	3.68589i	−0.115972	+	0.174925i
$445$	−3.00730	−	9.25553i	−0.142560	−	0.438754i
$446$	2.10094	+	6.46603i	0.0994824	+	0.306175i
$447$	−3.51235	+	5.29782i	−0.166128	+	0.250578i
$448$	8.82959	+	12.1529i	0.417159	+	0.574170i
$449$	−11.9393	−	3.87932i	−0.563451	−	0.183076i	0.0134222	−	0.999910i	$-0.495727\pi$
$449$	−11.9393	−	3.87932i	−0.563451	−	0.183076i	−0.576874	+	0.816833i	$0.695727\pi$
$450$	−4.75038	+	0.408323i	−0.223935	+	0.0192485i
$451$	−5.74527	−	5.23977i	−0.270534	−	0.246731i
$452$		−	1.77153i		−	0.0833260i
$453$	6.77649	−	24.3633i	0.318387	−	1.14469i
$454$	0.875058	−	0.635767i	0.0410685	−	0.0298380i
$455$	−2.84749	+	3.91924i	−0.133493	+	0.183737i
$456$	−3.35889	−	9.00464i	−0.157294	−	0.421681i
$457$	−9.89688	+	3.21569i	−0.462956	+	0.150424i	−0.531203	−	0.847245i	$-0.678260\pi$
$457$	−9.89688	+	3.21569i	−0.462956	+	0.150424i	0.0682462	+	0.997669i	$0.478260\pi$
$458$	−3.35328	−	2.43630i	−0.156689	−	0.113841i
$459$	10.3733	+	10.9813i	0.484185	+	0.512562i
$460$	0.571022	−	1.75743i	0.0266241	−	0.0819404i
$461$	−9.45198			−0.440223			−0.220111	−	0.975475i	$-0.570642\pi$
$461$	−9.45198			−0.440223			−0.220111	+	0.975475i	$0.570642\pi$
$462$	−27.7217	−	1.89417i	−1.28973	−	0.0881249i
$463$	10.6325			0.494133			0.247067	−	0.968999i	$-0.420533\pi$
$463$	10.6325			0.494133			0.247067	+	0.968999i	$0.420533\pi$
$464$	8.78200	−	27.0282i	0.407694	−	1.25475i
$465$	0.288847	−	0.229401i	0.0133950	−	0.0106382i
$466$	−4.48603	−	3.25929i	−0.207811	−	0.150984i
$467$	−7.68583	+	2.49728i	−0.355658	+	0.115560i	−0.481396	−	0.876503i	$-0.659870\pi$
$467$	−7.68583	+	2.49728i	−0.355658	+	0.115560i	0.125738	+	0.992063i	$0.459870\pi$
$468$	−2.31305	+	0.977682i	−0.106921	+	0.0451934i
$469$	15.3063	−	21.0673i	0.706780	−	0.972799i
$470$	−16.7035	+	12.1358i	−0.770474	+	0.559782i
$471$	−28.3900	−	7.89650i	−1.30814	−	0.363852i
$472$			0.784884i			0.0361272i
$473$	−38.5475	+	7.93704i	−1.77242	+	0.364945i
$474$	−25.5951	+	1.09800i	−1.17562	+	0.0504328i
$475$	−2.25248	−	0.731875i	−0.103351	−	0.0335807i
$476$	2.73490	+	3.76426i	0.125354	+	0.172535i
$477$	−18.3239	+	30.3913i	−0.838996	+	1.39152i
$478$	7.01197	+	21.5806i	0.320720	+	0.987075i
$479$	−3.27929	−	10.0926i	−0.149835	−	0.461143i	0.847766	−	0.530370i	$-0.177947\pi$
$479$	−3.27929	−	10.0926i	−0.149835	−	0.461143i	−0.997601	+	0.0692265i	$0.977947\pi$
$480$	4.19163	+	2.77896i	0.191321	+	0.126842i
$481$	−4.54261	−	6.25236i	−0.207125	−	0.285083i
$482$	12.4854	+	4.05677i	0.568697	+	0.184781i
$483$	−0.793896	−	18.5062i	−0.0361235	−	0.842063i
$484$	5.64243	+	1.27473i	0.256474	+	0.0579424i
$485$		−	10.4772i		−	0.475743i
$486$	−24.6515	−	2.46833i	−1.11821	−	0.111966i
$487$	−17.5357	+	12.7404i	−0.794619	+	0.577324i	−0.909330	−	0.416075i	$-0.863406\pi$
$487$	−17.5357	+	12.7404i	−0.794619	+	0.577324i	0.114712	+	0.993399i	$0.463406\pi$
$488$	−16.0028	+	22.0260i	−0.724413	+	0.997069i
$489$	−23.9279	+	8.92555i	−1.08206	+	0.403627i
$490$	−3.42010	+	1.11126i	−0.154505	+	0.0502016i
$491$	29.7049	+	21.5819i	1.34056	+	0.973975i	0.999423	+	0.0339626i	$0.0108127\pi$
$491$	29.7049	+	21.5819i	1.34056	+	0.973975i	0.341139	+	0.940013i	$0.389187\pi$
$492$	−1.32809	−	1.67225i	−0.0598749	−	0.0753907i
$493$	−5.34653	+	16.4549i	−0.240795	+	0.741092i
$494$	−5.99150			−0.269570
$495$	9.53779	−	2.83384i	0.428692	−	0.127372i
$496$	−1.01693			−0.0456616
$497$	8.07468	−	24.8513i	0.362199	−	1.11473i
$498$	13.8495	+	17.4384i	0.620612	+	0.781436i
$499$	−7.67254	−	5.57443i	−0.343470	−	0.249546i	0.402654	−	0.915352i	$-0.368088\pi$
$499$	−7.67254	−	5.57443i	−0.343470	−	0.249546i	−0.746125	+	0.665806i	$0.768088\pi$
$500$	0.500137	−	0.162504i	0.0223668	−	0.00726742i
$501$	−10.4307	+	3.89083i	−0.466008	+	0.173829i
$502$	−20.9542	+	28.8409i	−0.935230	+	1.28723i
$503$	−9.57117	+	6.95386i	−0.426757	+	0.310057i	−0.780351	−	0.625342i	$-0.784960\pi$
$503$	−9.57117	+	6.95386i	−0.426757	+	0.310057i	0.353594	+	0.935399i	$0.384960\pi$
$504$	20.8354	+	4.84362i	0.928081	+	0.215752i
$505$			1.16469i			0.0518280i
$506$	−2.05348	+	18.4079i	−0.0912881	+	0.818332i
$507$	0.776964	+	18.1116i	0.0345062	+	0.804362i
$508$	−5.44332	−	1.76864i	−0.241508	−	0.0784709i
$509$	−4.93798	−	6.79654i	−0.218872	−	0.301251i	0.685435	−	0.728134i	$-0.259612\pi$
$509$	−4.93798	−	6.79654i	−0.218872	−	0.301251i	−0.904307	+	0.426882i	$0.859612\pi$
$510$	−6.66998	−	4.42207i	−0.295352	−	0.195812i
$511$	9.81642	+	30.2118i	0.434253	+	1.33649i
$512$	2.62966	+	8.09326i	0.116216	+	0.357675i
$513$	−10.8018	−	5.89684i	−0.476910	−	0.260352i
$514$	−4.27943	−	5.89013i	−0.188758	−	0.259802i
$515$	−18.3540	−	5.96356i	−0.808772	−	0.262786i
$516$	−10.7984	+	0.463240i	−0.475374	+	0.0203930i
$517$	29.0339	−	31.8349i	1.27691	−	1.40010i
$518$		−	23.4848i		−	1.03186i
$519$	−11.3131	−	3.14666i	−0.496589	−	0.138123i
$520$	−3.01699	+	2.19197i	−0.132304	+	0.0961242i
$521$	−5.37246	+	7.39456i	−0.235372	+	0.323962i	−0.910321	−	0.413902i	$-0.864165\pi$
$521$	−5.37246	+	7.39456i	−0.235372	+	0.323962i	0.674949	+	0.737864i	$0.264165\pi$
$522$	−11.0475	−	26.1368i	−0.483536	−	1.14398i
$523$	−27.4836	+	8.92996i	−1.20177	+	0.390480i	−0.840413	−	0.541947i	$-0.817688\pi$
$523$	−27.4836	+	8.92996i	−1.20177	+	0.390480i	−0.361360	+	0.932426i	$0.617688\pi$
$524$	7.18522	+	5.22037i	0.313888	+	0.228053i
$525$	4.12797	−	3.27841i	0.180159	−	0.143082i
$526$	4.72309	−	14.5362i	0.205937	−	0.633808i
$527$	0.619114			0.0269690
$528$	−25.4503	−	10.2355i	−1.10758	−	0.445444i
$529$	10.6526			0.463156
$530$	5.80964	−	17.8802i	0.252355	−	0.776667i
$531$	0.658216	+	0.759521i	0.0285641	+	0.0329604i
$532$	−3.06665	−	2.22805i	−0.132956	−	0.0965981i
$533$	3.54921	−	1.15321i	0.153733	−	0.0499510i
$534$	9.36273	+	25.0999i	0.405165	+	1.08618i
$535$	−4.65105	+	6.40161i	−0.201082	+	0.276766i
$536$	16.2174	−	11.7826i	0.700484	−	0.508932i
$537$	3.76256	−	13.5274i	0.162366	−	0.583750i
$538$		−	22.9427i		−	0.989128i
$539$	6.52290	−	3.71076i	0.280961	−	0.159834i
$540$	2.70996	−	0.350483i	0.116618	−	0.0150824i
$541$	−5.00380	−	1.62583i	−0.215130	−	0.0699000i	0.199469	−	0.979904i	$-0.436078\pi$
$541$	−5.00380	−	1.62583i	−0.215130	−	0.0699000i	−0.414599	+	0.910004i	$0.636078\pi$
$542$	0.301317	+	0.414727i	0.0129427	+	0.0178140i
$543$	−8.31272	+	12.5384i	−0.356733	+	0.538075i
$544$	2.60848	+	8.02807i	0.111838	+	0.344200i
$545$	−3.60222	−	11.0865i	−0.154302	−	0.474893i
$546$	7.36884	−	11.1147i	0.315357	−	0.475666i
$547$	−17.6182	−	24.2494i	−0.753302	−	1.03683i	−0.997742	−	0.0671662i	$-0.978604\pi$
$547$	−17.6182	−	24.2494i	−0.753302	−	1.03683i	0.244440	−	0.969664i	$-0.421396\pi$
$548$	3.97473	+	1.29147i	0.169792	+	0.0551688i
$549$	2.98563	+	34.7344i	0.127423	+	1.48243i
$550$	−4.58163	+	2.60640i	−0.195361	+	0.111137i
$551$		−	14.0953i		−	0.600479i
$552$	3.82100	−	13.7375i	0.162633	−	0.584707i
$553$	22.9148	−	16.6486i	0.974437	−	0.707970i
$554$	3.66212	−	5.04048i	0.155589	−	0.214149i
$555$	2.93909	+	7.87921i	0.124757	+	0.334454i
$556$	5.86106	−	1.90437i	0.248564	−	0.0807635i
$557$	−12.0834	−	8.77912i	−0.511991	−	0.371983i	0.301587	−	0.953439i	$-0.402483\pi$
$557$	−12.0834	−	8.77912i	−0.511991	−	0.371983i	−0.813578	+	0.581455i	$0.802483\pi$
$558$	−0.767327	+	0.664980i	−0.0324836	+	0.0281509i
$559$	5.83679	−	17.9638i	0.246870	−	0.759788i
$560$	−14.5332			−0.614139
$561$	15.4943	+	6.23144i	0.654170	+	0.263092i
$562$	43.5040			1.83511
$563$	7.64925	−	23.5420i	0.322377	−	0.992175i	−0.650233	−	0.759735i	$-0.725329\pi$
$563$	7.64925	−	23.5420i	0.322377	−	0.992175i	0.972611	−	0.232441i	$-0.0746711\pi$
$564$	9.26603	−	7.35903i	0.390170	−	0.309871i
$565$	−2.72536	−	1.98009i	−0.114657	−	0.0833031i
$566$	36.1070	−	11.7319i	1.51769	−	0.493128i
$567$	24.2240	−	12.7857i	1.01731	−	0.536951i
$568$	11.8231	−	16.2732i	0.496088	−	0.682807i
$569$	−24.2146	+	17.5929i	−1.01513	+	0.737534i	−0.965279	−	0.261223i	$-0.915874\pi$
$569$	−24.2146	+	17.5929i	−1.01513	+	0.737534i	−0.0498501	+	0.998757i	$0.515874\pi$
$570$	6.28116	+	1.74707i	0.263089	+	0.0731765i
$571$			10.8730i			0.455021i	0.973776	+	0.227510i	$0.0730585\pi$
$571$			10.8730i			0.455021i	−0.973776	+	0.227510i	$0.926941\pi$
$572$	−1.87077	+	2.05125i	−0.0782209	+	0.0857672i
$573$	−34.3580	+	1.47392i	−1.43533	+	0.0615738i
$574$	10.7853	+	3.50435i	0.450168	+	0.146269i
$575$	−2.06541	−	2.84280i	−0.0861336	−	0.118553i
$576$	12.6807	+	7.64559i	0.528361	+	0.318566i
$577$	13.4875	+	41.5102i	0.561491	+	1.72809i	0.678155	+	0.734919i	$0.262780\pi$
$577$	13.4875	+	41.5102i	0.561491	+	1.72809i	−0.116664	+	0.993171i	$0.537220\pi$
$578$	4.19828	+	12.9210i	0.174625	+	0.537442i
$579$	31.3771	+	20.8024i	1.30399	+	0.864519i
$580$	1.83959	+	2.53198i	0.0763847	+	0.105135i
$581$	−23.4158	−	7.60826i	−0.971452	−	0.315644i
$582$	1.23611	+	28.8145i	0.0512383	+	1.19440i
$583$	−4.34967	+	38.9916i	−0.180145	+	1.61487i
$584$			24.4536i			1.01190i
$585$	−1.08128	+	4.65123i	−0.0447053	+	0.192305i
$586$	−31.8692	+	23.1543i	−1.31651	+	0.956497i
$587$	17.0454	−	23.4609i	0.703537	−	0.968336i	−0.296375	−	0.955072i	$-0.595778\pi$
$587$	17.0454	−	23.4609i	0.703537	−	0.968336i	0.999912	−	0.0132641i	$-0.00422221\pi$
$588$	1.93100	−	0.720296i	0.0796329	−	0.0297045i
$589$	−0.479690	+	0.155861i	−0.0197653	+	0.00642213i
$590$	−0.430754	−	0.312961i	−0.0177338	−	0.0128844i
$591$	−5.19525	−	6.54153i	−0.213704	−	0.269083i
$592$	7.16450	−	22.0501i	0.294459	−	0.906252i
$593$	−28.6616			−1.17699			−0.588495	−	0.808501i	$-0.700279\pi$
$593$	−28.6616			−1.17699			−0.588495	+	0.808501i	$0.700279\pi$
$594$	−25.8967	+	8.91896i	−1.06255	+	0.365949i
$595$	8.84788			0.362728
$596$	−0.596368	+	1.83543i	−0.0244282	+	0.0751822i
$597$	−8.92910	−	11.2430i	−0.365444	−	0.460144i
$598$	−7.19162	−	5.22502i	−0.294087	−	0.213667i
$599$	18.2372	−	5.92563i	0.745152	−	0.242115i	0.0882581	−	0.996098i	$-0.471870\pi$
$599$	18.2372	−	5.92563i	0.745152	−	0.242115i	0.656894	+	0.753983i	$0.271870\pi$
$600$	3.80200	−	1.41821i	0.155216	−	0.0578983i
$601$	2.53456	−	3.48853i	0.103387	−	0.142300i	−0.754189	−	0.656658i	$-0.771970\pi$
$601$	2.53456	−	3.48853i	0.103387	−	0.142300i	0.857576	+	0.514358i	$0.171970\pi$
$602$	46.4354	−	33.7373i	1.89256	−	1.37503i
$603$	5.81225	−	25.0020i	0.236693	−	1.01816i
$604$		−	7.67784i		−	0.312407i
$605$	8.26777	−	7.25562i	0.336133	−	0.294983i
$606$	−0.137411	−	3.20315i	−0.00558196	−	0.130119i
$607$	−14.3024	−	4.64714i	−0.580518	−	0.188622i	0.00401479	−	0.999992i	$-0.498722\pi$
$607$	−14.3024	−	4.64714i	−0.580518	−	0.188622i	−0.584532	+	0.811370i	$0.698722\pi$
$608$	−4.04210	−	5.56347i	−0.163929	−	0.225629i
$609$	26.1479	+	17.3355i	1.05956	+	0.702470i
$610$	−5.70723	−	17.5651i	−0.231079	−	0.711189i
$611$	6.39000	+	19.6664i	0.258512	+	0.795617i
$612$	3.92774	+	2.36816i	0.158769	+	0.0957273i
$613$	−15.6048	−	21.4782i	−0.630273	−	0.867496i	0.367777	−	0.929914i	$-0.380119\pi$
$613$	−15.6048	−	21.4782i	−0.630273	−	0.867496i	−0.998050	+	0.0624178i	$0.980119\pi$
$614$	−3.40182	−	1.10532i	−0.137286	−	0.0446071i
$615$	−4.05706	+	0.174043i	−0.163596	+	0.00701809i
$616$	23.1627	−	4.76926i	0.933251	−	0.192159i
$617$			35.6545i			1.43540i	0.696354	+	0.717698i	$0.254804\pi$
$617$			35.6545i			1.43540i	−0.696354	+	0.717698i	$0.745196\pi$
$618$	51.1810	+	14.2357i	2.05880	+	0.572643i
$619$	−6.78360	+	4.92857i	−0.272656	+	0.198096i	−0.715708	−	0.698400i	$-0.753896\pi$
$619$	−6.78360	+	4.92857i	−0.272656	+	0.198096i	0.443052	+	0.896496i	$0.353896\pi$
$620$	0.0658266	−	0.0906026i	0.00264366	−	0.00363869i
$621$	−7.82294	−	16.4979i	−0.313924	−	0.662039i
$622$	−5.34472	+	1.73661i	−0.214304	+	0.0696316i
$623$	−23.9619	−	17.4094i	−0.960014	−	0.697491i
$624$	10.3094	−	8.18770i	0.412708	−	0.327770i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	27.9447			1.11690
$627$	−13.5738	−	0.927469i	−0.542083	−	0.0370395i
$628$	−8.94682			−0.357017
$629$	−4.36178	+	13.4242i	−0.173916	+	0.535257i
$630$	−10.9660	+	9.50337i	−0.436897	+	0.378623i
$631$	27.7751	+	20.1798i	1.10571	+	0.803346i	0.981983	−	0.188970i	$-0.0605149\pi$
$631$	27.7751	+	20.1798i	1.10571	+	0.803346i	0.123728	+	0.992316i	$0.460515\pi$
$632$	20.7365	−	6.73771i	0.824855	−	0.268012i
$633$	0.226312	+	0.606706i	0.00899510	+	0.0241144i
$634$	1.19882	−	1.65004i	0.0476113	−	0.0655314i
$635$	−8.80507	+	6.39726i	−0.349418	+	0.253867i
$636$	−2.88730	+	10.3806i	−0.114489	+	0.411618i
$637$			3.60166i			0.142703i
$638$	−23.1785	−	21.1391i	−0.917647	−	0.836907i
$639$	−2.20583	−	25.6624i	−0.0872614	−	1.01519i
$640$	−12.9834	−	4.21856i	−0.513214	−	0.166753i
$641$	16.2846	+	22.4138i	0.643202	+	0.885292i	0.998781	−	0.0493544i	$-0.0157164\pi$
$641$	16.2846	+	22.4138i	0.643202	+	0.885292i	−0.355579	+	0.934646i	$0.615716\pi$
$642$	12.0361	−	18.1546i	0.475028	−	0.716504i
$643$	−0.171595	−	0.528115i	−0.00676704	−	0.0208268i	0.947616	−	0.319412i	$-0.103485\pi$
$643$	−0.171595	−	0.528115i	−0.00676704	−	0.0208268i	−0.954383	+	0.298585i	$0.903485\pi$
$644$	−1.73789	−	5.34867i	−0.0684824	−	0.210767i
$645$	−11.3570	+	17.1303i	−0.447183	+	0.674505i
$646$	6.43205	+	8.85296i	0.253066	+	0.348315i
$647$	7.37805	+	2.39727i	0.290061	+	0.0942466i	0.450433	−	0.892810i	$-0.351269\pi$
$647$	7.37805	+	2.39727i	0.290061	+	0.0942466i	−0.160372	+	0.987057i	$0.551269\pi$
$648$	20.7761	−	3.59825i	0.816164	−	0.141353i
$649$	1.01216	+	0.458395i	0.0397307	+	0.0179936i
$650$		−	2.52977i		−	0.0992258i
$651$	0.300828	−	1.08155i	0.0117904	−	0.0423894i
$652$	−6.27298	+	4.55759i	−0.245669	+	0.178489i
$653$	6.73420	−	9.26883i	0.263530	−	0.362717i	−0.656662	−	0.754185i	$-0.728032\pi$
$653$	6.73420	−	9.26883i	0.263530	−	0.362717i	0.920192	+	0.391467i	$0.128032\pi$
$654$	11.2149	+	30.0653i	0.438537	+	1.17565i
$655$	16.0622	−	5.21894i	0.627603	−	0.203921i
$656$	9.05732	+	6.58053i	0.353629	+	0.256926i
$657$	20.5071	+	23.6634i	0.800059	+	0.923196i
$658$	−19.4178	+	59.7619i	−0.756985	+	2.32976i
$659$	36.4244			1.41889			0.709447	−	0.704759i	$-0.248945\pi$
$659$	36.4244			1.41889			0.709447	+	0.704759i	$0.248945\pi$
$660$	2.55934	−	1.60492i	0.0996221	−	0.0624714i
$661$	−45.3470			−1.76379			−0.881896	−	0.471444i	$-0.843733\pi$
$661$	−45.3470			−1.76379			−0.881896	+	0.471444i	$0.843733\pi$
$662$	−12.4540	+	38.3295i	−0.484039	+	1.48972i
$663$	−6.27644	+	4.98472i	−0.243757	+	0.193590i
$664$	−15.3332	−	11.1402i	−0.595043	−	0.432324i
$665$	−6.85535	+	2.22744i	−0.265839	+	0.0863763i
$666$	−9.01274	−	21.3228i	−0.349236	−	0.826242i
$667$	12.2921	−	16.9186i	0.475952	−	0.655091i
$668$	−2.73452	+	1.98674i	−0.105802	+	0.0768695i
$669$	−7.13847	−	1.98552i	−0.275989	−	0.0767647i
$670$			13.5984i			0.525353i
$671$	19.0578	+	33.5005i	0.735718	+	1.29327i
$672$	15.2920	−	0.656009i	0.589902	−	0.0253061i
$673$	5.85381	+	1.90202i	0.225648	+	0.0733174i	0.419659	−	0.907682i	$-0.362150\pi$
$673$	5.85381	+	1.90202i	0.225648	+	0.0733174i	−0.194011	+	0.980999i	$0.562150\pi$
$674$	−1.50577	−	2.07252i	−0.0580002	−	0.0798304i
$675$	2.48980	−	4.56080i	0.0958326	−	0.175545i
$676$	1.70082	+	5.23460i	0.0654163	+	0.201331i
$677$	−13.9585	−	42.9598i	−0.536469	−	1.65108i	−0.740454	−	0.672107i	$-0.765390\pi$
$677$	−13.9585	−	42.9598i	−0.536469	−	1.65108i	0.203986	−	0.978974i	$-0.434610\pi$
$678$	7.72896	+	5.12415i	0.296829	+	0.196792i
$679$	−18.7427	−	25.7971i	−0.719277	−	0.990000i
$680$	6.47764	+	2.10471i	0.248406	+	0.0807121i
$681$	0.0505220	+	1.17770i	0.00193601	+	0.0451296i
$682$	−0.463107	+	1.02256i	−0.0177333	+	0.0391559i
$683$			16.8793i			0.645869i	0.946421	+	0.322934i	$0.104669\pi$
$683$			16.8793i			0.645869i	−0.946421	+	0.322934i	$0.895331\pi$
$684$	−3.63940	−	0.846055i	−0.139156	−	0.0323497i
$685$	6.42949	−	4.67130i	0.245658	−	0.178481i
$686$	13.4687	−	18.5380i	0.514236	−	0.707785i
$687$	4.23232	−	1.57873i	0.161473	−	0.0602323i
$688$	53.8908	−	17.5102i	2.05457	−	0.667570i
$689$	−15.2333	−	11.0676i	−0.580342	−	0.421643i
$690$	6.01573	+	7.57463i	0.229015	+	0.288361i
$691$	−1.86744	+	5.74738i	−0.0710406	+	0.218641i	−0.980273	−	0.197648i	$-0.936670\pi$
$691$	−1.86744	+	5.74738i	−0.0710406	+	0.218641i	0.909232	+	0.416289i	$0.136670\pi$
$692$	−3.56520			−0.135529
$693$	18.4146	−	24.0397i	0.699514	−	0.913194i
$694$	−47.0449			−1.78580
$695$	3.62134	−	11.1453i	0.137365	−	0.422767i
$696$	15.0194	+	18.9115i	0.569310	+	0.716840i
$697$	−5.51414	−	4.00626i	−0.208863	−	0.151748i
$698$	−13.9183	+	4.52232i	−0.526814	+	0.171172i
$699$	5.66201	−	2.11203i	0.214157	−	0.0798843i
$700$	0.940741	−	1.29482i	0.0355567	−	0.0489396i
$701$	5.09950	−	3.70500i	0.192605	−	0.139936i	−0.487303	−	0.873233i	$-0.662019\pi$
$701$	5.09950	−	3.70500i	0.192605	−	0.139936i	0.679909	+	0.733297i	$0.262019\pi$
$702$	2.42499	−	12.9195i	0.0915253	−	0.487614i
$703$		−	11.4991i		−	0.433699i
$704$	16.2691	+	1.81488i	0.613165	+	0.0684010i
$705$	−0.964384	−	22.4804i	−0.0363208	−	0.846662i
$706$	23.2806	+	7.56433i	0.876177	+	0.284687i
$707$	2.08352	+	2.86772i	0.0783588	+	0.107852i
$708$	0.254329	+	0.168615i	0.00955828	+	0.00633695i
$709$	−14.9012	−	45.8611i	−0.559625	−	1.72235i	−0.683405	−	0.730040i	$-0.739502\pi$
$709$	−14.9012	−	45.8611i	−0.559625	−	1.72235i	0.123779	−	0.992310i	$-0.460498\pi$
$710$	4.21660	+	12.9774i	0.158246	+	0.487032i
$711$	14.4161	−	23.9100i	0.540646	−	0.896694i
$712$	−13.4015	−	18.4456i	−0.502243	−	0.691278i
$713$	−0.711696	−	0.231244i	−0.0266532	−	0.00866015i
$714$	−24.3336	+	1.04388i	−0.910662	+	0.0390664i
$715$	1.06468	+	5.17077i	0.0398166	+	0.193376i
$716$		−	4.26302i		−	0.159317i
$717$	−23.8249	−	6.62675i	−0.889757	−	0.247481i
$718$	16.6497	−	12.0967i	0.621363	−	0.451446i
$719$	−17.4277	+	23.9872i	−0.649944	+	0.894572i	−0.999097	−	0.0424943i	$-0.986470\pi$
$719$	−17.4277	+	23.9872i	−0.649944	+	0.894572i	0.349152	+	0.937066i	$0.386470\pi$
$720$	−13.1953	+	5.57740i	−0.491760	+	0.207857i
$721$	−55.8597	+	18.1499i	−2.08032	+	0.675938i
$722$	17.2174	+	12.5092i	0.640764	+	0.465542i
$723$	−11.2036	+	8.89788i	−0.416668	+	0.330916i
$724$	−1.41143	+	4.34393i	−0.0524554	+	0.161441i
$725$	5.95140			0.221029
$726$	−21.8822	+	20.9300i	−0.812123	+	0.776784i
$727$	−10.1214			−0.375381			−0.187690	−	0.982228i	$-0.560100\pi$
$727$	−10.1214			−0.375381			−0.187690	+	0.982228i	$0.560100\pi$
$728$	−3.50725	+	10.7942i	−0.129987	+	0.400060i
$729$	17.0872	−	20.9052i	0.632861	−	0.774266i
$730$	−13.4204	−	9.75049i	−0.496711	−	0.360882i
$731$	−32.8090	+	10.6603i	−1.21349	+	0.394285i
$732$	3.69932	+	9.91726i	0.136731	+	0.366553i
$733$	−13.7673	+	18.9490i	−0.508505	+	0.699898i	−0.983666	−	0.180001i	$-0.942390\pi$
$733$	−13.7673	+	18.9490i	−0.508505	+	0.699898i	0.475161	+	0.879899i	$0.342390\pi$
$734$	36.5880	−	26.5828i	1.35049	−	0.981187i
$735$	1.05021	−	3.77578i	0.0387376	−	0.139272i
$736$		−	10.2029i		−	0.376083i
$737$	−5.72302	−	27.7948i	−0.210810	−	1.02383i
$738$	11.1373	−	0.957313i	0.409968	−	0.0352392i
$739$	44.8541	+	14.5740i	1.64999	+	0.536113i	0.978737	−	0.205119i	$-0.0657581\pi$
$739$	44.8541	+	14.5740i	1.64999	+	0.536113i	0.671249	+	0.741232i	$0.265758\pi$
$740$	1.50077	+	2.06563i	0.0551692	+	0.0759339i
$741$	3.60810	−	5.44224i	0.132547	−	0.199926i
$742$	−17.6814	−	54.4179i	−0.649106	−	1.99774i
$743$	−3.42039	−	10.5269i	−0.125482	−	0.386194i	0.868507	−	0.495678i	$-0.165080\pi$
$743$	−3.42039	−	10.5269i	−0.125482	−	0.386194i	−0.993989	+	0.109484i	$0.965080\pi$
$744$	0.477517	−	0.720259i	0.0175066	−	0.0264060i
$745$	2.15709	+	2.96898i	0.0790295	+	0.108775i
$746$	−17.3722	−	5.64456i	−0.636040	−	0.206662i
$747$	−24.1800	+	2.07842i	−0.884701	+	0.0760453i
$748$	5.03923	+	0.562146i	0.184252	+	0.0205541i
$749$			24.0825i			0.879954i
$750$	−0.737658	+	2.65207i	−0.0269355	+	0.0968400i
$751$	−34.7053	+	25.2149i	−1.26641	+	0.920104i	−0.999054	−	0.0434928i	$-0.986151\pi$
$751$	−34.7053	+	25.2149i	−1.26641	+	0.920104i	−0.267360	+	0.963597i	$0.586151\pi$
$752$	−36.4631	+	50.1872i	−1.32967	+	1.83014i
$753$	−13.5783	−	36.4013i	−0.494822	−	1.32654i
$754$	14.3188	−	4.65246i	0.521460	−	0.169433i
$755$	−11.8117	−	8.58173i	−0.429873	−	0.312321i
$756$	6.04553	−	5.71083i	0.219874	−	0.207701i
$757$	1.91385	−	5.89022i	0.0695600	−	0.214084i	−0.910233	−	0.414095i	$-0.864098\pi$
$757$	1.91385	−	5.89022i	0.0695600	−	0.214084i	0.979794	+	0.200012i	$0.0640980\pi$
$758$	−18.4999			−0.671946
$759$	−15.4838	−	12.9505i	−0.562027	−	0.470074i
$760$	−5.54874			−0.201274
$761$	6.59766	−	20.3055i	0.239165	−	0.736074i	−0.757377	−	0.652978i	$-0.773519\pi$
$761$	6.59766	−	20.3055i	0.239165	−	0.736074i	0.996542	−	0.0830958i	$-0.0264808\pi$
$762$	23.4611	−	18.6327i	0.849906	−	0.674991i
$763$	−28.7021	−	20.8533i	−1.03909	−	0.754940i
$764$	−9.93015	+	3.22650i	−0.359260	+	0.116731i
$765$	8.03337	−	3.39555i	0.290447	−	0.122766i
$766$	−18.5179	+	25.4878i	−0.669080	+	0.920910i
$767$	−0.431418	+	0.313444i	−0.0155776	+	0.0113178i
$768$	19.7323	+	5.48842i	0.712028	+	0.198046i
$769$		−	13.2364i		−	0.477317i	−0.971104	−	0.238658i	$-0.923292\pi$
$769$		−	13.2364i		−	0.477317i	0.971104	−	0.238658i	$-0.0767077\pi$
$770$	−6.61835	+	14.6136i	−0.238509	+	0.526639i
$771$	7.92725	−	0.340070i	0.285493	−	0.0122473i
$772$	10.8706	+	3.53208i	0.391242	+	0.127122i
$773$	14.5283	+	19.9965i	0.522547	+	0.719224i	0.985972	−	0.166912i	$-0.0533796\pi$
$773$	14.5283	+	19.9965i	0.522547	+	0.719224i	−0.463425	+	0.886136i	$0.653380\pi$
$774$	29.2133	−	48.4520i	1.05005	−	1.74157i
$775$	−0.0658086	−	0.202538i	−0.00236391	−	0.00727538i
$776$	−7.58519	−	23.3448i	−0.272292	−	0.838030i
$777$	21.3318	+	14.1426i	0.765276	+	0.507363i
$778$	1.22739	+	1.68935i	0.0440039	+	0.0605662i
$779$	5.28093	+	1.71588i	0.189209	+	0.0614777i
$780$	0.0621391	+	1.44850i	0.00222494	+	0.0518647i
$781$	−14.0802	−	24.7507i	−0.503830	−	0.885651i
$782$			16.2354i			0.580579i
$783$	30.3936	+	5.70489i	1.08618	+	0.203876i
$784$	−8.74131	+	6.35094i	−0.312190	+	0.226819i
$785$	−10.0001	+	13.7640i	−0.356919	+	0.491257i
$786$	−43.5589	+	16.2483i	−1.55370	+	0.579556i
$787$	32.3269	−	10.5036i	1.15233	−	0.374414i	0.330308	−	0.943873i	$-0.392847\pi$
$787$	32.3269	−	10.5036i	1.15233	−	0.374414i	0.822020	+	0.569459i	$0.192847\pi$
$788$	−2.05188	−	1.49078i	−0.0730952	−	0.0531068i
$789$	10.3594	+	13.0438i	0.368803	+	0.464373i
$790$	−4.57065	+	14.0670i	−0.162616	+	0.500482i
$791$	−10.2526			−0.364542
$792$	19.2001	−	13.2193i	0.682246	−	0.469729i
$793$	−18.4975			−0.656865
$794$	−6.27897	+	19.3247i	−0.222832	+	0.685807i
$795$	12.7425	+	16.0446i	0.451931	+	0.569043i
$796$	−3.52658	−	2.56221i	−0.124996	−	0.0908152i
$797$	−2.80711	+	0.912085i	−0.0994329	+	0.0323077i	−0.358311	−	0.933602i	$-0.616647\pi$
$797$	−2.80711	+	0.912085i	−0.0994329	+	0.0323077i	0.258878	+	0.965910i	$0.416647\pi$
$798$	18.5909	−	6.93474i	0.658111	−	0.245487i
$799$	22.1989	−	30.5542i	0.785342	−	1.08093i
$800$	2.34905	−	1.70668i	0.0830514	−	0.0603404i
$801$	−28.4372	−	6.61084i	−1.00478	−	0.233582i
$802$			42.9948i			1.51820i
$803$	31.5345	+	14.2816i	1.11283	+	0.503987i
$804$	−0.334020	−	7.78623i	−0.0117800	−	0.274599i
$805$	−10.1710	−	3.30475i	−0.358480	−	0.116477i
$806$	−0.316665	−	0.435852i	−0.0111540	−	0.0153522i
$807$	20.8394	+	13.8161i	0.733583	+	0.486351i
$808$	0.843204	+	2.59512i	0.0296638	+	0.0912958i
$809$	−3.54281	−	10.9036i	−0.124558	−	0.383352i	0.869262	−	0.494352i	$-0.164595\pi$
$809$	−3.54281	−	10.9036i	−0.124558	−	0.383352i	−0.993820	+	0.111000i	$0.964595\pi$
$810$	−6.30942	+	12.8369i	−0.221690	+	0.451044i
$811$	−8.37444	−	11.5264i	−0.294066	−	0.404748i	0.636263	−	0.771472i	$-0.280479\pi$
$811$	−8.37444	−	11.5264i	−0.294066	−	0.404748i	−0.930330	+	0.366724i	$0.880479\pi$
$812$	9.05893	+	2.94343i	0.317906	+	0.103294i
$813$	−0.558162	+	0.0239445i	−0.0195756	+	0.000839770i
$814$	−18.9094	−	17.2457i	−0.662775	−	0.604460i
$815$			14.7446i			0.516481i
$816$	−23.1655	−	6.44335i	−0.810955	−	0.225562i
$817$	22.7368	−	16.5192i	0.795458	−	0.577934i
$818$	−6.53529	+	8.99505i	−0.228501	+	0.314505i
$819$	5.65827	+	13.3866i	0.197716	+	0.467767i
$820$	−1.17257	+	0.380991i	−0.0409479	+	0.0133048i
$821$	−23.5738	−	17.1273i	−0.822730	−	0.597748i	0.0947631	−	0.995500i	$-0.469791\pi$
$821$	−23.5738	−	17.1273i	−0.822730	−	0.597748i	−0.917493	+	0.397751i	$0.869791\pi$
$822$	−17.1314	+	13.6057i	−0.597526	+	0.474552i
$823$	−14.0968	+	43.3854i	−0.491382	+	1.51232i	0.331138	+	0.943582i	$0.392568\pi$
$823$	−14.0968	+	43.3854i	−0.491382	+	1.51232i	−0.822520	+	0.568736i	$0.807432\pi$
$824$	−45.2130			−1.57507
$825$	0.391602	−	5.73120i	0.0136338	−	0.199535i
$826$	−1.62047			−0.0563832
$827$	−10.7557	+	33.1027i	−0.374013	+	1.15109i	0.570130	+	0.821555i	$0.306893\pi$
$827$	−10.7557	+	33.1027i	−0.374013	+	1.15109i	−0.944142	+	0.329538i	$0.893107\pi$
$828$	−3.63056	−	4.18934i	−0.126171	−	0.145590i
$829$	33.6792	+	24.4694i	1.16973	+	0.849856i	0.990976	−	0.134039i	$-0.0427947\pi$
$829$	33.6792	+	24.4694i	1.16973	+	0.849856i	0.178750	+	0.983895i	$0.442795\pi$
$830$	12.2278	−	3.97304i	0.424431	−	0.137906i
$831$	2.37306	+	6.36180i	0.0823207	+	0.220688i
$832$	−4.61793	+	6.35603i	−0.160098	+	0.220356i
$833$	5.32176	−	3.86648i	0.184388	−	0.133966i
$834$	−8.64454	+	31.0794i	−0.299336	+	1.07619i
$835$			6.42748i			0.222432i
$836$	−4.04592	+	0.833065i	−0.139931	+	0.0288122i
$837$	−0.141933	−	1.09744i	−0.00490593	−	0.0379330i
$838$	−42.6799	−	13.8676i	−1.47435	−	0.479047i
$839$	28.0890	+	38.6612i	0.969740	+	1.33473i	0.942178	+	0.335112i	$0.108774\pi$
$839$	28.0890	+	38.6612i	0.969740	+	1.33473i	0.0275618	+	0.999620i	$0.491226\pi$
$840$	6.82430	−	10.2934i	0.235461	−	0.355155i
$841$	1.98362	+	6.10497i	0.0684008	+	0.210516i
$842$	11.0337	+	33.9583i	0.380247	+	1.17028i
$843$	−26.1983	+	39.5159i	−0.902316	+	1.36100i
$844$	0.115560	+	0.159055i	0.00397774	+	0.00547490i
$845$	9.95407	+	3.23427i	0.342430	+	0.111262i
$846$	5.30453	+	61.7123i	0.182374	+	2.12171i
$847$	7.37743	−	32.6552i	0.253492	−	1.12204i
$848$		−	56.4876i		−	1.93979i
$849$	−11.0874	+	39.8620i	−0.380518	+	1.36806i
$850$	−3.73795	+	2.71578i	−0.128211	+	0.0931506i
$851$	10.0281	−	13.8025i	0.343758	−	0.473143i
$852$	−2.73312	−	7.32704i	−0.0936351	−	0.251020i
$853$	46.5373	−	15.1209i	1.59341	−	0.517730i	0.627942	−	0.778260i	$-0.283897\pi$
$853$	46.5373	−	15.1209i	1.59341	−	0.517730i	0.965466	+	0.260531i	$0.0838975\pi$
$854$	−45.4747	−	33.0393i	−1.55611	−	1.13058i
$855$	−5.36944	+	4.65326i	−0.183631	+	0.159138i
$856$	−5.72868	+	17.6311i	−0.195802	+	0.602617i
$857$	−10.2473			−0.350041			−0.175021	−	0.984565i	$-0.555999\pi$
$857$	−10.2473			−0.350041			−0.175021	+	0.984565i	$0.555999\pi$
$858$	−3.53814	−	14.0951i	−0.120790	−	0.481200i
$859$	54.2237			1.85009			0.925044	−	0.379861i	$-0.124028\pi$
$859$	54.2237			1.85009			0.925044	+	0.379861i	$0.124028\pi$
$860$	−1.92833	+	5.93479i	−0.0657556	+	0.202375i
$861$	−9.67801	+	7.68623i	−0.329826	+	0.261946i
$862$	7.17687	+	5.21430i	0.244445	+	0.177600i
$863$	10.9114	−	3.54532i	0.371427	−	0.120684i	−0.117355	−	0.993090i	$-0.537441\pi$
$863$	10.9114	−	3.54532i	0.371427	−	0.120684i	0.488782	+	0.872406i	$0.337441\pi$
$864$	13.6325	−	6.46422i	0.463787	−	0.219917i
$865$	−3.98492	+	5.48478i	−0.135491	+	0.186488i
$866$	−26.2567	+	19.0766i	−0.892241	+	0.648251i
$867$	−14.2647	−	3.96764i	−0.484454	−	0.134748i
$868$		−	0.340841i		−	0.0115689i
$869$	3.42204	−	30.6761i	0.116085	−	1.04062i
$870$	−16.3677	+	0.702153i	−0.554915	+	0.0238052i
$871$	12.9528	+	4.20863i	0.438890	+	0.142604i
$872$	−16.0526	−	22.0946i	−0.543611	−	0.748216i
$873$	−26.9174	−	16.2294i	−0.911015	−	0.549281i
$874$	−4.08724	−	12.5792i	−0.138253	−	0.425499i
$875$	−0.940483	−	2.89451i	−0.0317941	−	0.0978523i
$876$	7.92379	+	5.25332i	0.267720	+	0.177493i
$877$	20.0266	+	27.5642i	0.676249	+	0.930776i	0.999881	−	0.0154064i	$-0.00490421\pi$
$877$	20.0266	+	27.5642i	0.676249	+	0.930776i	−0.323633	+	0.946183i	$0.604904\pi$
$878$	21.5478	+	7.00129i	0.727202	+	0.236282i
$879$	−1.83999	−	42.8913i	−0.0620612	−	1.44669i
$880$	−10.6722	+	11.7018i	−0.359760	+	0.394468i
$881$		−	7.35780i		−	0.247890i	−0.992289	−	0.123945i	$-0.960445\pi$
$881$		−	7.35780i		−	0.247890i	0.992289	−	0.123945i	$-0.0395547\pi$
$882$	−2.44284	+	10.5081i	−0.0822546	+	0.353827i
$883$	9.10208	−	6.61305i	0.306310	−	0.222547i	−0.424002	−	0.905661i	$-0.639375\pi$
$883$	9.10208	−	6.61305i	0.306310	−	0.222547i	0.730311	+	0.683114i	$0.239375\pi$
$884$	−1.43037	+	1.96873i	−0.0481084	+	0.0662156i
$885$	0.543672	−	0.202799i	0.0182753	−	0.00681702i
$886$	9.59487	−	3.11756i	0.322346	−	0.104737i
$887$	−43.4380	−	31.5596i	−1.45851	−	1.05967i	−0.983749	−	0.179549i	$-0.942536\pi$
$887$	−43.4380	−	31.5596i	−1.45851	−	1.05967i	−0.474756	−	0.880117i	$-0.657464\pi$
$888$	12.2531	+	15.4283i	0.411187	+	0.517741i
$889$	−10.2359	+	31.5029i	−0.343301	+	1.05657i
$890$	15.4668			0.518449
$891$	7.49372	−	28.8937i	0.251049	−	0.967974i
$892$	−2.24962			−0.0753227
$893$	−9.50780	+	29.2620i	−0.318166	+	0.979215i
$894$	−6.28275	−	7.91084i	−0.210126	−	0.264578i
$895$	−6.55831	−	4.76489i	−0.219220	−	0.159273i
$896$	−39.5146	+	12.8391i	−1.32009	+	0.428923i
$897$	9.07685	−	3.38583i	0.303067	−	0.113049i
$898$	11.7273	−	16.1412i	0.391345	−	0.538640i
$899$	1.02536	−	0.744968i	0.0341977	−	0.0248461i
$900$	0.357227	−	1.53665i	0.0119076	−	0.0512217i
$901$			34.3899i			1.14569i
$902$	10.7416	−	6.11070i	0.357657	−	0.203464i
$903$	2.68097	+	62.4952i	0.0892171	+	2.07971i
$904$	−7.50608	−	2.43887i	−0.249649	−	0.0811157i
$905$	5.10520	+	7.02671i	0.169703	+	0.233576i
$906$	33.4973	+	22.2081i	1.11287	+	0.737814i
$907$	0.304175	+	0.936155i	0.0101000	+	0.0310845i	0.955979	−	0.293433i	$-0.0947979\pi$
$907$	0.304175	+	0.936155i	0.0101000	+	0.0310845i	−0.945880	+	0.324518i	$0.894798\pi$
$908$	0.110596	+	0.340379i	0.00367025	+	0.0112959i
$909$	2.99226	+	1.80413i	0.0992470	+	0.0598393i
$910$	−4.52552	−	6.22885i	−0.150020	−	0.206484i
$911$	28.6805	+	9.31885i	0.950227	+	0.308747i	0.742808	−	0.669505i	$-0.233494\pi$
$911$	28.6805	+	9.31885i	0.950227	+	0.308747i	0.207419	+	0.978252i	$0.433494\pi$
$912$	19.5708	−	0.839563i	0.648053	−	0.0278007i
$913$	−23.3210	+	13.2669i	−0.771814	+	0.439071i
$914$		−	16.5386i		−	0.547047i
$915$	19.3917	+	5.39369i	0.641071	+	0.178310i
$916$	1.10955	−	0.806136i	0.0366606	−	0.0266355i
$917$	30.2125	−	41.5840i	0.997705	−	1.37322i
$918$	−21.6929	+	10.2863i	−0.715973	+	0.339498i
$919$	−18.0078	+	5.85110i	−0.594023	+	0.193010i	−0.590573	−	0.806984i	$-0.701098\pi$
$919$	−18.0078	+	5.85110i	−0.594023	+	0.193010i	−0.00345021	+	0.999994i	$0.501098\pi$
$920$	−6.66018	−	4.83890i	−0.219580	−	0.159534i
$921$	3.05258	−	2.42434i	0.100586	−	0.0798848i
$922$	4.64206	−	14.2868i	0.152878	−	0.470511i
$923$	13.6663			0.449830
$924$	3.43060	−	8.53008i	0.112858	−	0.280619i
$925$	4.85525			0.159640
$926$	−5.22183	+	16.0711i	−0.171600	+	0.528130i
$927$	−43.7520	+	37.9163i	−1.43700	+	1.24534i
$928$	13.9801	+	10.1572i	0.458920	+	0.333425i
$929$	24.8929	−	8.08819i	0.816709	−	0.265365i	0.129272	−	0.991609i	$-0.458736\pi$
$929$	24.8929	−	8.08819i	0.816709	−	0.265365i	0.687437	+	0.726244i	$0.258736\pi$
$930$	0.204884	+	0.549260i	0.00671840	+	0.0180109i
$931$	−3.14992	+	4.33550i	−0.103235	+	0.142090i
$932$	1.48436	−	1.07845i	0.0486218	−	0.0353258i
$933$	1.64120	−	5.90055i	0.0537305	−	0.193175i
$934$		−	12.8437i		−	0.420259i
$935$	6.49730	−	7.12412i	0.212484	−	0.232984i
$936$	0.958106	+	11.1465i	0.0313167	+	0.364335i
$937$	4.51000	+	1.46539i	0.147335	+	0.0478722i	0.381756	−	0.924263i	$-0.375319\pi$
$937$	4.51000	+	1.46539i	0.147335	+	0.0478722i	−0.234421	+	0.972135i	$0.575319\pi$
$938$	24.3263	+	33.4823i	0.794283	+	1.09324i
$939$	−16.8284	+	25.3829i	−0.549174	+	0.828341i
$940$	−2.11110	−	6.49729i	−0.0688564	−	0.211918i
$941$	−5.25228	−	16.1649i	−0.171220	−	0.526960i	0.828221	−	0.560401i	$-0.189353\pi$
$941$	−5.25228	−	16.1649i	−0.171220	−	0.526960i	−0.999441	+	0.0334418i	$0.989353\pi$
$942$	25.8786	−	39.0337i	0.843170	−	1.27179i
$943$	4.84235	+	6.66493i	0.157689	+	0.217040i
$944$	−1.52147	−	0.494356i	−0.0495197	−	0.0160899i
$945$	−2.02840	−	15.6837i	−0.0659838	−	0.510191i
$946$	6.93455	−	62.1632i	0.225462	−	2.02110i
$947$			1.86000i			0.0604419i	0.999543	+	0.0302209i	$0.00962109\pi$
$947$			1.86000i			0.0604419i	−0.999543	+	0.0302209i	$0.990379\pi$
$948$	2.27155	−	8.16680i	0.0737764	−	0.265245i
$949$	−13.4411	+	9.76554i	−0.436317	+	0.317003i
$950$	2.21248	−	3.04521i	0.0717823	−	0.0987998i
$951$	0.776840	+	2.08258i	0.0251908	+	0.0675323i
$952$	19.7145	−	6.40563i	0.638951	−	0.207608i
$953$	26.1749	+	19.0172i	0.847889	+	0.616027i	0.924563	−	0.381029i	$-0.124430\pi$
$953$	26.1749	+	19.0172i	0.847889	+	0.616027i	−0.0766743	+	0.997056i	$0.524430\pi$
$954$	−36.9377	−	42.6227i	−1.19590	−	1.37996i
$955$	−6.13549	+	18.8831i	−0.198540	+	0.611042i
$956$	−7.50818			−0.242832
$957$	33.1594	−	8.32364i	1.07189	−	0.269065i
$958$	16.8657			0.544905
$959$	7.47429	−	23.0035i	0.241357	−	0.742822i
$960$	6.69454	−	5.31676i	0.216065	−	0.171598i
$961$	25.0428	+	18.1947i	0.807833	+	0.586925i
$962$	11.6815	−	3.79555i	0.376627	−	0.122374i
$963$	9.24211	+	21.8655i	0.297823	+	0.704605i
$964$	−2.55325	+	3.51425i	−0.0822346	+	0.113186i
$965$	17.5842	−	12.7757i	0.566056	−	0.411263i
$966$	28.3623	+	7.88881i	0.912543	+	0.253818i
$967$		−	2.05040i		−	0.0659365i	−0.999456	−	0.0329683i	$-0.989504\pi$
$967$		−	2.05040i		−	0.0659365i	0.999456	−	0.0329683i	$-0.0104960\pi$
$968$	13.1690	−	22.1523i	0.423269	−	0.712003i
$969$	−11.9148	+	0.511130i	−0.382758	+	0.0164199i
$970$	15.8364	+	5.14555i	0.508476	+	0.165214i
$971$	−18.1758	−	25.0168i	−0.583289	−	0.802829i	0.410762	−	0.911743i	$-0.365263\pi$
$971$	−18.1758	−	25.0168i	−0.583289	−	0.802829i	−0.994051	+	0.108914i	$0.965263\pi$
$972$	3.29735	−	7.50519i	0.105763	−	0.240729i
$973$	−11.0214	−	33.9205i	−0.353331	−	1.08744i
$974$	−10.6452	−	32.7626i	−0.341094	−	1.04978i
$975$	2.29786	+	1.52344i	0.0735904	+	0.0487890i
$976$	−32.6173	−	44.8939i	−1.04405	−	1.43702i
$977$	14.4482	+	4.69449i	0.462238	+	0.150190i	0.530872	−	0.847452i	$-0.321864\pi$
$977$	14.4482	+	4.69449i	0.462238	+	0.150190i	−0.0686348	+	0.997642i	$0.521864\pi$
$978$	−1.73959	−	40.5509i	−0.0556259	−	1.29668i
$979$	−31.6137	+	6.50934i	−1.01038	+	0.208039i
$980$		−	1.18990i		−	0.0380099i
$981$	−34.0627	−	7.91861i	−1.08754	−	0.252822i
$982$	−47.2100	+	34.3000i	−1.50653	+	1.09456i
$983$	33.4163	−	45.9936i	1.06581	−	1.46697i	0.191571	−	0.981479i	$-0.438642\pi$
$983$	33.4163	−	45.9936i	1.06581	−	1.46697i	0.874243	−	0.485488i	$-0.161358\pi$
$984$	−8.91377	+	3.32500i	−0.284161	+	0.105997i
$985$	−4.58689	+	1.49037i	−0.146150	+	0.0474871i
$986$	−22.2461	−	16.1627i	−0.708459	−	0.514725i
$987$	−42.5899	−	53.6265i	−1.35565	−	1.70695i
$988$	0.612625	−	1.88547i	0.0194902	−	0.0599847i
$989$	41.6970			1.32589
$990$	−0.400818	+	15.8083i	−0.0127388	+	0.502419i
$991$	20.9129			0.664321			0.332160	−	0.943223i	$-0.392222\pi$
$991$	20.9129			0.664321			0.332160	+	0.943223i	$0.392222\pi$
$992$	0.191081	−	0.588086i	0.00606681	−	0.0186717i
$993$	−27.3159	−	34.3945i	−0.866844	−	1.09148i
$994$	33.5975	+	24.4100i	1.06565	+	0.774238i
$995$	−7.88351	+	2.56151i	−0.249924	+	0.0812053i
$996$	−6.90381	+	2.57524i	−0.218756	+	0.0815997i
$997$	0.881034	−	1.21264i	0.0279026	−	0.0384047i	−0.794838	−	0.606822i	$-0.792444\pi$
$997$	0.881034	−	1.21264i	0.0279026	−	0.0384047i	0.822740	+	0.568417i	$0.192444\pi$
$998$	12.1940	−	8.85944i	0.385993	−	0.280441i
$999$	24.7956	+	4.65414i	0.784498	+	0.147251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.p.b.101.3	✓	48
3.2	odd	2	inner	165.2.p.b.101.10	yes	48
5.2	odd	4		825.2.bs.g.299.4		48
5.3	odd	4		825.2.bs.h.299.9		48
5.4	even	2		825.2.bi.e.101.10		48
11.6	odd	10	inner	165.2.p.b.116.10	yes	48
15.2	even	4		825.2.bs.h.299.10		48
15.8	even	4		825.2.bs.g.299.3		48
15.14	odd	2		825.2.bi.e.101.3		48
33.17	even	10	inner	165.2.p.b.116.3	yes	48
55.17	even	20		825.2.bs.g.149.3		48
55.28	even	20		825.2.bs.h.149.10		48
55.39	odd	10		825.2.bi.e.776.3		48
165.17	odd	20		825.2.bs.h.149.9		48
165.83	odd	20		825.2.bs.g.149.4		48
165.149	even	10		825.2.bi.e.776.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.p.b.101.3	✓	48	1.1	even	1	trivial
165.2.p.b.101.10	yes	48	3.2	odd	2	inner
165.2.p.b.116.3	yes	48	33.17	even	10	inner
165.2.p.b.116.10	yes	48	11.6	odd	10	inner
825.2.bi.e.101.3		48	15.14	odd	2
825.2.bi.e.101.10		48	5.4	even	2
825.2.bi.e.776.3		48	55.39	odd	10
825.2.bi.e.776.10		48	165.149	even	10
825.2.bs.g.149.3		48	55.17	even	20
825.2.bs.g.149.4		48	165.83	odd	20
825.2.bs.g.299.3		48	15.8	even	4
825.2.bs.g.299.4		48	5.2	odd	4
825.2.bs.h.149.9		48	165.17	odd	20
825.2.bs.h.149.10		48	55.28	even	20
825.2.bs.h.299.9		48	5.3	odd	4
825.2.bs.h.299.10		48	15.2	even	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)

\(f(q)\)	\(=\)	\(q+(-0.491121 + 1.51151i) q^{2} +(-1.07720 - 1.35634i) q^{3} +(-0.425442 - 0.309102i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(2.57916 - 0.962071i) q^{6} +(-1.78891 + 2.46222i) q^{7} +(-1.89539 + 1.37708i) q^{8} +(-0.679300 + 2.92208i) q^{9} +O(q^{10})\)	\(q+(-0.491121 + 1.51151i) q^{2} +(-1.07720 - 1.35634i) q^{3} +(-0.425442 - 0.309102i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(2.57916 - 0.962071i) q^{6} +(-1.78891 + 2.46222i) q^{7} +(-1.89539 + 1.37708i) q^{8} +(-0.679300 + 2.92208i) q^{9} -1.58930i q^{10} +(0.668870 + 3.24848i) q^{11} +(0.0390382 + 0.910006i) q^{12} +(-1.51385 - 0.491878i) q^{13} +(-2.84311 - 3.91320i) q^{14} +(1.44360 + 0.957081i) q^{15} +(-1.47562 - 4.54149i) q^{16} +(0.898365 + 2.76488i) q^{17} +(-4.08315 - 2.46187i) q^{18} +(-1.39211 - 1.91607i) q^{19} +(0.500137 + 0.162504i) q^{20} +(5.26660 - 0.225931i) q^{21} +(-5.23862 - 0.584388i) q^{22} -3.51389i q^{23} +(3.90949 + 1.08740i) q^{24} +(0.809017 - 0.587785i) q^{25} +(1.48696 - 2.04663i) q^{26} +(4.69506 - 2.22629i) q^{27} +(1.52215 - 0.494577i) q^{28} +(4.81478 + 3.49814i) q^{29} +(-2.15563 + 1.71199i) q^{30} +(0.0658086 - 0.202538i) q^{31} +2.90358 q^{32} +(3.68553 - 4.40646i) q^{33} -4.62037 q^{34} +(0.940483 - 2.89451i) q^{35} +(1.19222 - 1.03320i) q^{36} +(3.92798 + 2.85384i) q^{37} +(3.57986 - 1.16317i) q^{38} +(0.963555 + 2.58313i) q^{39} +(1.37708 - 1.89539i) q^{40} +(-1.89674 + 1.37806i) q^{41} +(-2.24504 + 8.07150i) q^{42} +11.8663i q^{43} +(0.719545 - 1.58879i) q^{44} +(-0.256920 - 2.98898i) q^{45} +(5.31129 + 1.72574i) q^{46} +(-7.63593 - 10.5100i) q^{47} +(-4.57026 + 6.89351i) q^{48} +(-0.699213 - 2.15196i) q^{49} +(0.491121 + 1.51151i) q^{50} +(2.78240 - 4.19681i) q^{51} +(0.492013 + 0.677198i) q^{52} +(11.2504 + 3.65547i) q^{53} +(1.05923 + 8.19003i) q^{54} +(-1.63997 - 2.88279i) q^{55} -7.13032i q^{56} +(-1.09927 + 3.95215i) q^{57} +(-7.65213 + 5.55960i) q^{58} +(0.196917 - 0.271033i) q^{59} +(-0.318335 - 0.853404i) q^{60} +(11.0521 - 3.59104i) q^{61} +(0.273819 + 0.198941i) q^{62} +(-5.97959 - 6.89991i) q^{63} +(1.52523 - 4.69417i) q^{64} +1.59175 q^{65} +(4.85039 + 7.73483i) q^{66} -8.55624 q^{67} +(0.472428 - 1.45398i) q^{68} +(-4.76602 + 3.78514i) q^{69} +(3.91320 + 2.84311i) q^{70} +(-8.16546 + 2.65312i) q^{71} +(-2.73640 - 6.47392i) q^{72} +(6.13509 - 8.44422i) q^{73} +(-6.24273 + 4.53561i) q^{74} +(-1.66870 - 0.464140i) q^{75} +1.24548i q^{76} +(-9.19501 - 4.16432i) q^{77} +(-4.37767 + 0.187797i) q^{78} +(-8.85108 - 2.87589i) q^{79} +(2.80680 + 3.86322i) q^{80} +(-8.07710 - 3.96994i) q^{81} +(-1.15143 - 3.54374i) q^{82} +(2.49987 + 7.69379i) q^{83} +(-2.31047 - 1.53179i) q^{84} +(-1.70879 - 2.35195i) q^{85} +(-17.9361 - 5.82780i) q^{86} +(-0.441800 - 10.2987i) q^{87} +(-5.74118 - 5.23604i) q^{88} +9.73184i q^{89} +(4.64406 + 1.07961i) q^{90} +(3.91924 - 2.84749i) q^{91} +(-1.08615 + 1.49496i) q^{92} +(-0.345598 + 0.128914i) q^{93} +(19.6361 - 6.38016i) q^{94} +(1.91607 + 1.39211i) q^{95} +(-3.12773 - 3.93824i) q^{96} +(-3.23762 + 9.96437i) q^{97} +3.59611 q^{98} +(-9.94668 - 0.252198i) 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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