LMFDB - Embedded newform 603.2.k.a.365.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(38,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("603.38");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.k (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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$66$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			365.14
Character	$\chi$	$=$	603.365
Dual form			603.2.k.a.38.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.912112 + 1.57982i) q^{2} +(1.09608 + 1.34112i) q^{3} +(-0.663895 - 1.14990i) q^{4} +(-0.255149 + 0.441931i) q^{5} +(-3.11848 + 0.508369i) q^{6} +3.55097i q^{7} -1.22626 q^{8} +(-0.597201 + 2.93996i) q^{9} +O(q^{10})$	\(q+(-0.912112 + 1.57982i) q^{2} +(1.09608 + 1.34112i) q^{3} +(-0.663895 - 1.14990i) q^{4} +(-0.255149 + 0.441931i) q^{5} +(-3.11848 + 0.508369i) q^{6} +3.55097i q^{7} -1.22626 q^{8} +(-0.597201 + 2.93996i) q^{9} +(-0.465449 - 0.806182i) q^{10} -1.16662 q^{11} +(0.814468 - 2.15075i) q^{12} +1.62982i q^{13} +(-5.60991 - 3.23888i) q^{14} +(-0.872348 + 0.142208i) q^{15} +(2.44628 - 4.23708i) q^{16} +(4.83825 - 2.79337i) q^{17} +(-4.09990 - 3.62504i) q^{18} +(1.00058 + 1.73306i) q^{19} +0.677569 q^{20} +(-4.76227 + 3.89216i) q^{21} +(1.06409 - 1.84306i) q^{22} -7.36612i q^{23} +(-1.34409 - 1.64456i) q^{24} +(2.36980 + 4.10461i) q^{25} +(-2.57483 - 1.48658i) q^{26} +(-4.59742 + 2.42152i) q^{27} +(4.08326 - 2.35747i) q^{28} +0.194041i q^{29} +(0.571014 - 1.50787i) q^{30} +(-6.71378 + 3.87620i) q^{31} +(3.23629 + 5.60542i) q^{32} +(-1.27872 - 1.56458i) q^{33} +10.1915i q^{34} +(-1.56929 - 0.906027i) q^{35} +(3.77713 - 1.26510i) q^{36} +(-2.71090 - 4.69542i) q^{37} -3.65057 q^{38} +(-2.18579 + 1.78642i) q^{39} +(0.312880 - 0.541923i) q^{40} +(-1.61652 - 2.79990i) q^{41} +(-1.80520 - 11.0736i) q^{42} +(2.13818 - 1.23448i) q^{43} +(0.774516 + 1.34150i) q^{44} +(-1.14688 - 1.01405i) q^{45} +(11.6372 + 6.71873i) q^{46} +4.05030i q^{47} +(8.36375 - 1.36344i) q^{48} -5.60939 q^{49} -8.64608 q^{50} +(9.04937 + 3.42691i) q^{51} +(1.87413 - 1.08203i) q^{52} -6.56266 q^{53} +(0.367777 - 9.47180i) q^{54} +(0.297663 - 0.515568i) q^{55} -4.35442i q^{56} +(-1.22752 + 3.24148i) q^{57} +(-0.306551 - 0.176987i) q^{58} +(2.90583 + 1.67768i) q^{59} +(0.742672 + 0.908701i) q^{60} +(12.4814 + 7.20616i) q^{61} -14.1421i q^{62} +(-10.4397 - 2.12064i) q^{63} -2.02233 q^{64} +(-0.720270 - 0.415848i) q^{65} +(3.63810 - 0.593075i) q^{66} +(1.34991 - 8.07327i) q^{67} +(-6.42419 - 3.70901i) q^{68} +(9.87885 - 8.07389i) q^{69} +(2.86273 - 1.65280i) q^{70} +(5.77105 + 3.33192i) q^{71} +(0.732324 - 3.60516i) q^{72} +(5.71957 + 9.90659i) q^{73} +9.89059 q^{74} +(-2.90727 + 7.67718i) q^{75} +(1.32856 - 2.30114i) q^{76} -4.14265i q^{77} +(-0.828551 - 5.08258i) q^{78} -12.5427i q^{79} +(1.24833 + 2.16217i) q^{80} +(-8.28670 - 3.51149i) q^{81} +5.89779 q^{82} +(-9.43396 - 5.44670i) q^{83} +(7.63724 + 2.89215i) q^{84} +2.85090i q^{85} +4.50394i q^{86} +(-0.260233 + 0.212686i) q^{87} +1.43059 q^{88} +15.9746i q^{89} +(2.64811 - 0.886949i) q^{90} -5.78745 q^{91} +(-8.47030 + 4.89033i) q^{92} +(-12.5573 - 4.75534i) q^{93} +(-6.39876 - 3.69432i) q^{94} -1.02119 q^{95} +(-3.97029 + 10.4843i) q^{96} +(9.31484 + 5.37792i) q^{97} +(5.11639 - 8.86184i) q^{98} +(0.696709 - 3.42982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 63 q^{4} + 3 q^{5} + 7 q^{6} + 12 q^{8} - 7 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 63 * q^4 + 3 * q^5 + 7 * q^6 + 12 * q^8 - 7 * q^9	$ 132 q - 3 q^{2} - 3 q^{3} - 63 q^{4} + 3 q^{5} + 7 q^{6} + 12 q^{8} - 7 q^{9} - 6 q^{11} + 6 q^{12} + 4 q^{15} - 57 q^{16} + 9 q^{17} - 4 q^{19} - 30 q^{20} - 6 q^{21} - 11 q^{24} - 57 q^{25} + 36 q^{26} - 24 q^{28} + 45 q^{30} + 15 q^{32} - q^{33} + 15 q^{35} - q^{36} - 4 q^{37} + 14 q^{39} - 12 q^{40} + 3 q^{41} + 42 q^{42} + 3 q^{43} + 6 q^{44} - 9 q^{45} - 24 q^{46} - 21 q^{48} - 120 q^{49} - 24 q^{50} + 18 q^{52} - 60 q^{53} - 16 q^{54} - 9 q^{57} + 12 q^{58} + 12 q^{59} - 13 q^{60} + 18 q^{61} + 24 q^{63} + 84 q^{64} + 18 q^{65} - 30 q^{66} - 14 q^{67} - 39 q^{68} - 18 q^{69} + 45 q^{70} - 30 q^{71} + 39 q^{72} + 14 q^{73} + 30 q^{74} + 24 q^{75} - 7 q^{76} - 21 q^{78} + 18 q^{80} - 3 q^{81} - 24 q^{82} - 63 q^{83} + 129 q^{84} - 18 q^{87} - 30 q^{88} - 35 q^{90} + 42 q^{91} - 12 q^{92} - 28 q^{93} - 6 q^{94} + 24 q^{95} + 120 q^{96} - 39 q^{97} + 21 q^{98} - 72 q^{99}+O(q^{100}) $ 132 * q - 3 * q^2 - 3 * q^3 - 63 * q^4 + 3 * q^5 + 7 * q^6 + 12 * q^8 - 7 * q^9 - 6 * q^11 + 6 * q^12 + 4 * q^15 - 57 * q^16 + 9 * q^17 - 4 * q^19 - 30 * q^20 - 6 * q^21 - 11 * q^24 - 57 * q^25 + 36 * q^26 - 24 * q^28 + 45 * q^30 + 15 * q^32 - q^33 + 15 * q^35 - q^36 - 4 * q^37 + 14 * q^39 - 12 * q^40 + 3 * q^41 + 42 * q^42 + 3 * q^43 + 6 * q^44 - 9 * q^45 - 24 * q^46 - 21 * q^48 - 120 * q^49 - 24 * q^50 + 18 * q^52 - 60 * q^53 - 16 * q^54 - 9 * q^57 + 12 * q^58 + 12 * q^59 - 13 * q^60 + 18 * q^61 + 24 * q^63 + 84 * q^64 + 18 * q^65 - 30 * q^66 - 14 * q^67 - 39 * q^68 - 18 * q^69 + 45 * q^70 - 30 * q^71 + 39 * q^72 + 14 * q^73 + 30 * q^74 + 24 * q^75 - 7 * q^76 - 21 * q^78 + 18 * q^80 - 3 * q^81 - 24 * q^82 - 63 * q^83 + 129 * q^84 - 18 * q^87 - 30 * q^88 - 35 * q^90 + 42 * q^91 - 12 * q^92 - 28 * q^93 - 6 * q^94 + 24 * q^95 + 120 * q^96 - 39 * q^97 + 21 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.912112	+	1.57982i	−0.644960	+	1.11710i	0.339350	+	0.940660i	$0.389793\pi$
$2$	−0.912112	+	1.57982i	−0.644960	+	1.11710i	−0.984311	+	0.176444i	$0.943541\pi$
$3$	1.09608	+	1.34112i	0.632824	+	0.774295i
$3$	1.09608	+	1.34112i	0.632824	+	0.774295i
$4$	−0.663895	−	1.14990i	−0.331947	−	0.574950i
$5$	−0.255149	+	0.441931i	−0.114106	+	0.197638i	−0.917422	−	0.397915i	$-0.869734\pi$
$5$	−0.255149	+	0.441931i	−0.114106	+	0.197638i	0.803316	+	0.595553i	$0.203067\pi$
$6$	−3.11848	+	0.508369i	−1.27311	+	0.207541i
$7$			3.55097i			1.34214i	0.741394	+	0.671070i	$0.234165\pi$
$7$			3.55097i			1.34214i	−0.741394	+	0.671070i	$0.765835\pi$
$8$	−1.22626			−0.433549
$9$	−0.597201	+	2.93996i	−0.199067	+	0.979986i
$10$	−0.465449	−	0.806182i	−0.147188	−	0.254937i
$11$	−1.16662			−0.351750			−0.175875	−	0.984412i	$-0.556276\pi$
$11$	−1.16662			−0.351750			−0.175875	+	0.984412i	$0.556276\pi$
$12$	0.814468	−	2.15075i	0.235117	−	0.620868i
$13$			1.62982i			0.452032i	0.974124	+	0.226016i	$0.0725701\pi$
$13$			1.62982i			0.452032i	−0.974124	+	0.226016i	$0.927430\pi$
$14$	−5.60991	−	3.23888i	−1.49931	−	0.865627i
$15$	−0.872348	+	0.142208i	−0.225239	+	0.0367180i
$16$	2.44628	−	4.23708i	0.611569	−	1.05927i
$17$	4.83825	−	2.79337i	1.17345	−	0.677491i	0.218959	−	0.975734i	$-0.429734\pi$
$17$	4.83825	−	2.79337i	1.17345	−	0.677491i	0.954490	+	0.298243i	$0.0964005\pi$
$18$	−4.09990	−	3.62504i	−0.966356	−	0.854430i
$19$	1.00058	+	1.73306i	0.229549	+	0.397591i	0.957675	−	0.287853i	$-0.0929415\pi$
$19$	1.00058	+	1.73306i	0.229549	+	0.397591i	−0.728125	+	0.685444i	$0.759608\pi$
$20$	0.677569			0.151509
$21$	−4.76227	+	3.89216i	−1.03921	+	0.849339i
$22$	1.06409	−	1.84306i	0.226865	−	0.392942i
$23$		−	7.36612i		−	1.53594i	−0.640484	−	0.767971i	$-0.721266\pi$
$23$		−	7.36612i		−	1.53594i	0.640484	−	0.767971i	$-0.278734\pi$
$24$	−1.34409	−	1.64456i	−0.274360	−	0.335695i
$25$	2.36980	+	4.10461i	0.473960	+	0.820922i
$26$	−2.57483	−	1.48658i	−0.504966	−	0.291542i
$27$	−4.59742	+	2.42152i	−0.884773	+	0.466022i
$28$	4.08326	−	2.35747i	0.771664	−	0.445520i
$29$			0.194041i			0.0360326i	0.999838	+	0.0180163i	$0.00573507\pi$
$29$			0.194041i			0.0360326i	−0.999838	+	0.0180163i	$0.994265\pi$
$30$	0.571014	−	1.50787i	0.104252	−	0.275297i
$31$	−6.71378	+	3.87620i	−1.20583	+	0.696187i	−0.961846	−	0.273592i	$-0.911788\pi$
$31$	−6.71378	+	3.87620i	−1.20583	+	0.696187i	−0.243985	+	0.969779i	$0.578455\pi$
$32$	3.23629	+	5.60542i	0.572101	+	0.990908i
$33$	−1.27872	−	1.56458i	−0.222596	−	0.272359i
$34$			10.1915i			1.74782i
$35$	−1.56929	−	0.906027i	−0.265258	−	0.153147i
$36$	3.77713	−	1.26510i	0.629522	−	0.210850i
$37$	−2.71090	−	4.69542i	−0.445670	−	0.771923i	0.552429	−	0.833560i	$-0.313701\pi$
$37$	−2.71090	−	4.69542i	−0.445670	−	0.771923i	−0.998099	+	0.0616373i	$0.980368\pi$
$38$	−3.65057			−0.592200
$39$	−2.18579	+	1.78642i	−0.350006	+	0.286057i
$40$	0.312880	−	0.541923i	0.0494706	−	0.0856856i
$41$	−1.61652	−	2.79990i	−0.252458	−	0.437271i	0.711744	−	0.702439i	$-0.247906\pi$
$41$	−1.61652	−	2.79990i	−0.252458	−	0.437271i	−0.964202	+	0.265169i	$0.914572\pi$
$42$	−1.80520	−	11.0736i	−0.278549	−	1.70870i
$43$	2.13818	−	1.23448i	0.326070	−	0.188257i	−0.328025	−	0.944669i	$-0.606383\pi$
$43$	2.13818	−	1.23448i	0.326070	−	0.188257i	0.654095	+	0.756412i	$0.273050\pi$
$44$	0.774516	+	1.34150i	0.116763	+	0.202239i
$45$	−1.14688	−	1.01405i	−0.170967	−	0.151166i
$46$	11.6372	+	6.71873i	1.71581	+	0.990622i
$47$			4.05030i			0.590797i	0.955374	+	0.295398i	$0.0954523\pi$
$47$			4.05030i			0.590797i	−0.955374	+	0.295398i	$0.904548\pi$
$48$	8.36375	−	1.36344i	1.20720	−	0.196796i
$49$	−5.60939			−0.801341
$50$	−8.64608			−1.22274
$51$	9.04937	+	3.42691i	1.26717	+	0.479863i
$52$	1.87413	−	1.08203i	0.259896	−	0.150051i
$53$	−6.56266			−0.901450			−0.450725	−	0.892663i	$-0.648835\pi$
$53$	−6.56266			−0.901450			−0.450725	+	0.892663i	$0.648835\pi$
$54$	0.367777	−	9.47180i	0.0500481	−	1.28895i
$55$	0.297663	−	0.515568i	0.0401369	−	0.0695191i
$56$		−	4.35442i		−	0.581884i
$57$	−1.22752	+	3.24148i	−0.162589	+	0.429344i
$58$	−0.306551	−	0.176987i	−0.0402521	−	0.0232396i
$59$	2.90583	+	1.67768i	0.378307	+	0.218416i	0.677081	−	0.735908i	$-0.263244\pi$
$59$	2.90583	+	1.67768i	0.378307	+	0.218416i	−0.298774	+	0.954324i	$0.596578\pi$
$60$	0.742672	+	0.908701i	0.0958786	+	0.117313i
$61$	12.4814	+	7.20616i	1.59808	+	0.922655i	0.991856	+	0.127364i	$0.0406518\pi$
$61$	12.4814	+	7.20616i	1.59808	+	0.922655i	0.606229	+	0.795290i	$0.292682\pi$
$62$		−	14.1421i		−	1.79605i
$63$	−10.4397	−	2.12064i	−1.31528	−	0.267176i
$64$	−2.02233			−0.252792
$65$	−0.720270	−	0.415848i	−0.0893385	−	0.0515796i
$66$	3.63810	−	0.593075i	0.447819	−	0.0730025i
$67$	1.34991	−	8.07327i	0.164917	−	0.986307i
$67$	1.34991	−	8.07327i	0.164917	−	0.986307i
$68$	−6.42419	−	3.70901i	−0.779047	−	0.449783i
$69$	9.87885	−	8.07389i	1.18927	−	0.971982i
$70$	2.86273	−	1.65280i	0.342161	−	0.197547i
$71$	5.77105	+	3.33192i	0.684898	+	0.395426i	0.801698	−	0.597730i	$-0.203930\pi$
$71$	5.77105	+	3.33192i	0.684898	+	0.395426i	−0.116800	+	0.993155i	$0.537264\pi$
$72$	0.732324	−	3.60516i	0.0863052	−	0.424872i
$73$	5.71957	+	9.90659i	0.669425	+	1.15948i	0.978065	+	0.208300i	$0.0667930\pi$
$73$	5.71957	+	9.90659i	0.669425	+	1.15948i	−0.308640	+	0.951179i	$0.599874\pi$
$74$	9.89059			1.14976
$75$	−2.90727	+	7.67718i	−0.335703	+	0.886484i
$76$	1.32856	−	2.30114i	0.152397	−	0.263959i
$77$		−	4.14265i		−	0.472098i
$78$	−0.828551	−	5.08258i	−0.0938150	−	0.575488i
$79$		−	12.5427i		−	1.41117i	−0.708628	−	0.705583i	$-0.750685\pi$
$79$		−	12.5427i		−	1.41117i	0.708628	−	0.705583i	$-0.249315\pi$
$80$	1.24833	+	2.16217i	0.139568	+	0.241738i
$81$	−8.28670	−	3.51149i	−0.920745	−	0.390166i
$82$	5.89779			0.651302
$83$	−9.43396	−	5.44670i	−1.03551	−	0.597853i	−0.116953	−	0.993137i	$-0.537313\pi$
$83$	−9.43396	−	5.44670i	−1.03551	−	0.597853i	−0.918559	+	0.395285i	$0.870646\pi$
$84$	7.63724	+	2.89215i	0.833292	+	0.315560i
$85$			2.85090i			0.309224i
$86$			4.50394i			0.485672i
$87$	−0.260233	+	0.212686i	−0.0278999	+	0.0228023i
$88$	1.43059			0.152501
$89$			15.9746i			1.69331i	0.532145	+	0.846653i	$0.321386\pi$
$89$			15.9746i			1.69331i	−0.532145	+	0.846653i	$0.678614\pi$
$90$	2.64811	−	0.886949i	0.279135	−	0.0934926i
$91$	−5.78745			−0.606690
$92$	−8.47030	+	4.89033i	−0.883090	+	0.509852i
$93$	−12.5573	−	4.75534i	−1.30213	−	0.493105i
$94$	−6.39876	−	3.69432i	−0.659981	−	0.381040i
$95$	−1.02119			−0.104772
$96$	−3.97029	+	10.4843i	−0.405216	+	1.07005i
$97$	9.31484	+	5.37792i	0.945778	+	0.546045i	0.891767	−	0.452495i	$-0.149466\pi$
$97$	9.31484	+	5.37792i	0.945778	+	0.546045i	0.0540114	+	0.998540i	$0.482799\pi$
$98$	5.11639	−	8.86184i	0.516833	−	0.895181i
$99$	0.696709	−	3.42982i	0.0700219	−	0.344710i
$100$	3.14659	−	5.45006i	0.314659	−	0.545006i
$101$	−6.87484			−0.684072			−0.342036	−	0.939687i	$-0.611117\pi$
$101$	−6.87484			−0.684072			−0.342036	+	0.939687i	$0.611117\pi$
$102$	−13.6679	+	11.1707i	−1.35333	+	1.10606i
$103$	−2.94165	−	5.09510i	−0.289850	−	0.502035i	0.683924	−	0.729553i	$-0.260272\pi$
$103$	−2.94165	−	5.09510i	−0.289850	−	0.502035i	−0.973774	+	0.227519i	$0.926939\pi$
$104$		−	1.99859i		−	0.195978i
$105$	−0.504978	−	3.09768i	−0.0492808	−	0.302303i
$106$	5.98588	−	10.3678i	0.581400	−	1.00701i
$107$		−	2.95179i		−	0.285361i	−0.989769	−	0.142680i	$-0.954428\pi$
$107$		−	2.95179i		−	0.285361i	0.989769	−	0.142680i	$-0.0455721\pi$
$108$	5.83671	+	3.67893i	0.561638	+	0.354005i
$109$			8.31094i			0.796044i	0.917376	+	0.398022i	$0.130303\pi$
$109$			8.31094i			0.796044i	−0.917376	+	0.398022i	$0.869697\pi$
$110$	0.543004	+	0.940511i	0.0517734	+	0.0896742i
$111$	3.32574	−	8.78222i	0.315666	−	0.833572i
$112$	15.0457	+	8.68666i	1.42169	+	0.820812i
$113$	5.70036	+	9.87331i	0.536245	+	0.928803i	0.999102	+	0.0423701i	$0.0134909\pi$
$113$	5.70036	+	9.87331i	0.536245	+	0.928803i	−0.462857	+	0.886433i	$0.653176\pi$
$114$	−4.00133	−	4.89585i	−0.374759	−	0.458538i
$115$	3.25532	+	1.87946i	0.303560	+	0.175261i
$116$	0.223128	−	0.128823i	0.0207169	−	0.0119609i
$117$	−4.79161	−	0.973332i	−0.442985	−	0.0899846i
$118$	−5.30089	+	3.06047i	−0.487986	+	0.281739i
$119$	9.91917	+	17.1805i	0.909288	+	1.57493i
$120$	1.06973	−	0.174385i	0.0976522	−	0.0159191i
$121$	−9.63899			−0.876272
$122$	−22.7689	+	13.1456i	−2.06140	+	1.19015i
$123$	1.98315	−	5.23687i	0.178815	−	0.472193i
$124$	8.91449	+	5.14678i	0.800545	+	0.462195i
$125$	−4.97010			−0.444539
$126$	12.8724	−	14.5586i	1.14677	−	1.29699i
$127$	−1.58371	+	2.74306i	−0.140531	+	0.243407i	−0.927697	−	0.373334i	$-0.878214\pi$
$127$	−1.58371	+	2.74306i	−0.140531	+	0.243407i	0.787166	+	0.616742i	$0.211548\pi$
$128$	−4.62799	+	8.01592i	−0.409061	+	0.708514i
$129$	3.99922	+	1.51447i	0.352111	+	0.133341i
$130$	1.31393	−	0.758600i	0.115240	−	0.0665336i
$131$	10.7307	+	6.19540i	0.937550	+	0.541295i	0.889191	−	0.457535i	$-0.151268\pi$
$131$	10.7307	+	6.19540i	0.937550	+	0.541295i	0.0483585	+	0.998830i	$0.484601\pi$
$132$	−0.950178	+	2.50911i	−0.0827024	+	0.218390i
$133$	−6.15404	+	3.55304i	−0.533623	+	0.308087i
$134$	11.5231	+	9.49634i	0.995443	+	0.820359i
$135$	0.102880	−	2.64959i	0.00885450	−	0.228041i
$136$	−5.93296	+	3.42540i	−0.508748	+	0.293726i
$137$	5.90288	+	10.2241i	0.504317	+	0.873503i	0.999988	+	0.00499255i	$0.00158918\pi$
$137$	5.90288	+	10.2241i	0.504317	+	0.873503i	−0.495670	+	0.868511i	$0.665077\pi$
$138$	3.74471	+	22.9711i	0.318771	+	1.95543i
$139$	−0.805297	−	0.464938i	−0.0683044	−	0.0394356i	0.465459	−	0.885070i	$-0.345889\pi$
$139$	−0.805297	−	0.464938i	−0.0683044	−	0.0394356i	−0.533763	+	0.845634i	$0.679223\pi$
$140$			2.40603i			0.203346i
$141$	−5.43193	+	4.43947i	−0.457451	+	0.373870i
$142$	−10.5277	+	6.07816i	−0.883464	+	0.510068i
$143$		−	1.90139i		−	0.159002i
$144$	10.9959	+	9.72234i	0.916325	+	0.810195i
$145$	−0.0857530	−	0.0495095i	−0.00712140	−	0.00411154i
$146$	−20.8676			−1.72701
$147$	−6.14836	−	7.52286i	−0.507108	−	0.620475i
$148$	−3.59951	+	6.23453i	−0.295878	+	0.512476i
$149$	13.5822	+	7.84168i	1.11270	+	0.642415i	0.939526	−	0.342476i	$-0.111266\pi$
$149$	13.5822	+	7.84168i	1.11270	+	0.642415i	0.173170	+	0.984892i	$0.444599\pi$
$150$	−9.47683	−	11.5954i	−0.773780	−	0.946762i
$151$	6.62465	−	11.4742i	0.539106	−	0.933760i	−0.459846	−	0.887999i	$-0.652095\pi$
$151$	6.62465	−	11.4742i	0.539106	−	0.933760i	0.998952	−	0.0457610i	$-0.0145713\pi$
$152$	−1.22697	−	2.12518i	−0.0995208	−	0.172375i
$153$	5.32297	+	15.8925i	0.430337	+	1.28483i
$154$	6.54465	+	3.77856i	0.527383	+	0.304485i
$155$		−	3.95604i		−	0.317757i
$156$	3.50534	+	1.32744i	0.280652	+	0.106280i
$157$	5.88956			0.470038			0.235019	−	0.971991i	$-0.424485\pi$
$157$	5.88956			0.470038			0.235019	+	0.971991i	$0.424485\pi$
$158$	19.8153	+	11.4404i	1.57642	+	0.910146i
$159$	−7.19322	−	8.80131i	−0.570460	−	0.697989i
$160$	−3.30295			−0.261121
$161$	26.1569			2.06145
$162$	13.1059	−	9.88866i	1.02970	−	0.776926i
$163$	−9.32967	+	16.1595i	−0.730756	+	1.26571i	0.225805	+	0.974173i	$0.427499\pi$
$163$	−9.32967	+	16.1595i	−0.730756	+	1.26571i	−0.956561	+	0.291534i	$0.905834\pi$
$164$	−2.14640	+	3.71768i	−0.167606	+	0.290302i
$165$	1.01770	−	0.165904i	0.0792280	−	0.0129156i
$166$	17.2096	−	9.93599i	1.33573	−	0.771183i
$167$	−7.05507	+	4.07324i	−0.545937	+	0.315197i	−0.747482	−	0.664282i	$-0.768737\pi$
$167$	−7.05507	+	4.07324i	−0.545937	+	0.315197i	0.201544	+	0.979479i	$0.435404\pi$
$168$	5.83979	−	4.77281i	0.450550	−	0.368230i
$169$	10.3437			0.795667
$170$	−4.50392	−	2.60034i	−0.345435	−	0.199437i
$171$	−5.69267	+	1.90668i	−0.435329	+	0.145808i
$172$	−2.83906	−	1.63913i	−0.216476	−	0.124983i
$173$	−14.7520	−	8.51708i	−1.12157	−	0.647541i	−0.179772	−	0.983708i	$-0.557536\pi$
$173$	−14.7520	−	8.51708i	−1.12157	−	0.647541i	−0.941802	+	0.336167i	$0.890869\pi$
$174$	−0.0986446	−	0.605114i	−0.00747822	−	0.0458736i
$175$	−14.5753	+	8.41508i	−1.10179	+	0.636120i
$176$	−2.85389	+	4.94307i	−0.215120	+	0.372598i
$177$	0.935063	+	5.73595i	0.0702836	+	0.431140i
$178$	−25.2371	−	14.5706i	−1.89160	−	1.09212i
$179$	6.28734			0.469938			0.234969	−	0.972003i	$-0.424501\pi$
$179$	6.28734			0.469938			0.234969	+	0.972003i	$0.424501\pi$
$180$	−0.404645	+	1.99202i	−0.0301604	+	0.148477i
$181$	7.49157	−	12.9758i	0.556844	−	0.964482i	−0.440913	−	0.897550i	$-0.645345\pi$
$181$	7.49157	−	12.9758i	0.556844	−	0.964482i	0.997758	−	0.0669325i	$-0.0213212\pi$
$182$	5.27880	−	9.14316i	0.391291	−	0.677736i
$183$	4.01638	+	24.6377i	0.296900	+	1.82127i
$184$			9.03279i			0.665906i
$185$	2.76674			0.203415
$186$	18.9663	−	15.5009i	1.39067	−	1.13658i
$187$	−5.64442	+	3.25881i	−0.412761	+	0.238308i
$188$	4.65744	−	2.68897i	0.339678	−	0.196113i
$189$	−8.59875	−	16.3253i	−0.625467	−	1.18749i
$190$	0.931440	−	1.61330i	0.0675737	−	0.117041i
$191$	−5.61338	+	9.72265i	−0.406170	+	0.703507i	−0.994457	−	0.105146i	$-0.966469\pi$
$191$	−5.61338	+	9.72265i	−0.406170	+	0.703507i	0.588287	+	0.808652i	$0.299802\pi$
$192$	−2.21665	−	2.71219i	−0.159973	−	0.195736i
$193$	5.25286	−	9.09822i	0.378109	−	0.654904i	−0.612678	−	0.790333i	$-0.709908\pi$
$193$	5.25286	−	9.09822i	0.378109	−	0.654904i	0.990787	+	0.135428i	$0.0432411\pi$
$194$	−16.9923	+	9.81053i	−1.21998	+	0.704355i
$195$	−0.231775	−	1.42177i	−0.0165977	−	0.101815i
$196$	3.72404	+	6.45023i	0.266003	+	0.460731i
$197$	7.71542	−	13.3635i	0.549701	−	0.952109i	−0.448594	−	0.893736i	$-0.648075\pi$
$197$	7.71542	−	13.3635i	0.549701	−	0.952109i	0.998295	−	0.0583738i	$-0.0185915\pi$
$198$	4.78304	+	4.22906i	0.339916	+	0.300546i
$199$	7.37051	+	12.7661i	0.522481	+	0.904964i	0.999658	+	0.0261568i	$0.00832691\pi$
$199$	7.37051	+	12.7661i	0.522481	+	0.904964i	−0.477176	+	0.878807i	$0.658340\pi$
$200$	−2.90599	−	5.03332i	−0.205485	−	0.355910i
$201$	12.3068	−	7.03860i	0.868057	−	0.496465i
$202$	6.27062	−	10.8610i	0.441200	−	0.764180i
$203$	−0.689035			−0.0483608
$204$	−2.06723	−	12.6810i	−0.144735	−	0.887846i
$205$	1.64982			0.115228
$206$	10.7325			0.747767
$207$	21.6561	+	4.39905i	1.50520	+	0.305755i
$208$	6.90569	+	3.98700i	0.478823	+	0.276449i
$209$	−1.16730	−	2.02183i	−0.0807440	−	0.139853i
$210$	5.35438	+	2.02765i	0.369488	+	0.139921i
$211$	5.06892			0.348959			0.174480	−	0.984661i	$-0.444176\pi$
$211$	5.06892			0.348959			0.174480	+	0.984661i	$0.444176\pi$
$212$	4.35691	+	7.54640i	0.299234	+	0.518289i
$213$	1.85706	+	11.3917i	0.127243	+	0.780548i
$214$	4.66331	+	2.69236i	0.318777	+	0.184046i
$215$			1.25991i			0.0859250i
$216$	5.63763	−	2.96942i	0.383592	−	0.202043i
$217$	−13.7643	−	23.8404i	−0.934380	−	1.61839i
$218$	−13.1298	−	7.58051i	−0.889264	−	0.513417i
$219$	−7.01679	+	18.5291i	−0.474151	+	1.25208i
$220$	−0.790468			−0.0532934
$221$	4.55270	+	7.88550i	0.306247	+	0.530436i
$222$	10.8409	+	13.2645i	0.727594	+	0.890252i
$223$	−7.57834	−	13.1261i	−0.507483	−	0.878987i	−0.999962	−	0.00866271i	$-0.997243\pi$
$223$	−7.57834	−	13.1261i	−0.507483	−	0.878987i	0.492479	−	0.870324i	$-0.336091\pi$
$224$	−19.9047	+	11.4920i	−1.32994	+	0.767840i
$225$	−13.4826	+	4.51583i	−0.898842	+	0.301055i
$226$	−20.7975			−1.38343
$227$		−	23.0862i		−	1.53229i	−0.642669	−	0.766144i	$-0.722173\pi$
$227$		−	23.0862i		−	1.53229i	0.642669	−	0.766144i	$-0.277827\pi$
$228$	4.54231	−	0.740479i	0.300822	−	0.0490394i
$229$			26.3803i			1.74326i	0.490163	+	0.871631i	$0.336937\pi$
$229$			26.3803i			1.74326i	−0.490163	+	0.871631i	$0.663063\pi$
$230$	−5.93843	+	3.42856i	−0.391569	+	0.226072i
$231$	5.55578	−	4.54069i	0.365544	−	0.298755i
$232$		−	0.237945i		−	0.0156219i
$233$	−11.9364	+	20.6745i	−0.781982	+	1.35443i	0.148804	+	0.988867i	$0.452458\pi$
$233$	−11.9364	+	20.6745i	−0.781982	+	1.35443i	−0.930786	+	0.365565i	$0.880876\pi$
$234$	5.90818	−	6.68211i	0.386230	−	0.436823i
$235$	−1.78995	−	1.03343i	−0.116764	−	0.0674136i
$236$		−	4.45522i		−	0.290010i
$237$	16.8213	−	13.7479i	1.09266	−	0.893020i
$238$	−36.1895			−2.34582
$239$	−5.65972	−	9.80292i	−0.366097	−	0.634098i	0.622855	−	0.782338i	$-0.285973\pi$
$239$	−5.65972	−	9.80292i	−0.366097	−	0.634098i	−0.988952	+	0.148239i	$0.952639\pi$
$240$	−1.53146	+	4.04408i	−0.0988551	+	0.261045i
$241$	−2.87792	−	4.98471i	−0.185383	−	0.321094i	0.758322	−	0.651880i	$-0.226019\pi$
$241$	−2.87792	−	4.98471i	−0.185383	−	0.321094i	−0.943706	+	0.330786i	$0.892686\pi$
$242$	8.79183	−	15.2279i	0.565160	−	0.978887i
$243$	−4.37359	−	14.9623i	−0.280566	−	0.959835i
$244$		−	19.1365i		−	1.22509i
$245$	1.43123	−	2.47897i	0.0914380	−	0.158375i
$246$	6.46448	+	7.90964i	0.412160	+	0.504301i
$247$	−2.82458	+	1.63077i	−0.179724	+	0.103764i
$248$	8.23285	−	4.75324i	0.522786	−	0.301831i
$249$	−3.03574	−	18.6221i	−0.192382	−	1.18013i
$250$	4.53329	−	7.85188i	0.286710	−	0.496597i
$251$	2.31432	+	4.00852i	0.146079	+	0.253015i	0.929775	−	0.368129i	$-0.120001\pi$
$251$	2.31432	+	4.00852i	0.146079	+	0.253015i	−0.783696	+	0.621144i	$0.786668\pi$
$252$	4.49234	+	13.4125i	0.282991	+	0.844908i
$253$			8.59350i			0.540268i
$254$	−2.88904	−	5.00396i	−0.181274	−	0.313976i
$255$	−3.82340	+	3.12483i	−0.239431	+	0.195684i
$256$	−10.4648	−	18.1256i	−0.654052	−	1.13285i
$257$	13.4301	−	7.75389i	0.837748	−	0.483674i	−0.0187499	−	0.999824i	$-0.505969\pi$
$257$	13.4301	−	7.75389i	0.837748	−	0.483674i	0.856498	+	0.516150i	$0.172635\pi$
$258$	−6.04032	+	4.93670i	−0.376054	+	0.307345i
$259$	16.6733	−	9.62634i	1.03603	−	0.598152i
$260$			1.10432i			0.0684869i
$261$	−0.570473	−	0.115882i	−0.0353114	−	0.00717289i
$262$	−19.5753	+	11.3018i	−1.20936	+	0.698227i
$263$	17.9627	−	10.3708i	1.10763	−	0.639489i	0.169413	−	0.985545i	$-0.445813\pi$
$263$	17.9627	−	10.3708i	1.10763	−	0.639489i	0.938214	+	0.346056i	$0.112479\pi$
$264$	1.56804	+	1.91859i	0.0965063	+	0.118081i
$265$	1.67446	−	2.90024i	0.102861	−	0.178161i
$266$		−	12.9631i		−	0.794816i
$267$	−21.4239	+	17.5095i	−1.31112	+	1.07157i
$268$	−10.1797	+	3.80755i	−0.621821	+	0.232583i
$269$			2.13863i			0.130394i	0.997872	+	0.0651972i	$0.0207676\pi$
$269$			2.13863i			0.130394i	−0.997872	+	0.0651972i	$0.979232\pi$
$270$	4.09205	+	2.57926i	0.249034	+	0.156969i
$271$			4.66908i			0.283626i	0.989893	+	0.141813i	$0.0452932\pi$
$271$			4.66908i			0.283626i	−0.989893	+	0.141813i	$0.954707\pi$
$272$		−	27.3334i		−	1.65733i
$273$	−6.34353	−	7.76167i	−0.383928	−	0.469757i
$274$	−21.5364			−1.30106
$275$	−2.76466	−	4.78854i	−0.166715	−	0.288760i
$276$	−15.8427	−	5.99947i	−0.953617	−	0.361126i
$277$	−5.81737	−	10.0760i	−0.349532	−	0.605407i	0.636634	−	0.771166i	$-0.280326\pi$
$277$	−5.81737	−	10.0760i	−0.349532	−	0.605407i	−0.986166	+	0.165758i	$0.946993\pi$
$278$	1.46904	−	0.848151i	0.0881072	−	0.0508687i
$279$	−7.38640	−	22.0531i	−0.442212	−	1.32028i
$280$	1.92435	+	1.11103i	0.115002	+	0.0663965i
$281$	2.20110	−	3.81242i	0.131307	−	0.227430i	−0.792874	−	0.609386i	$-0.791416\pi$
$281$	2.20110	−	3.81242i	0.131307	−	0.227430i	0.924180	+	0.381956i	$0.124749\pi$
$282$	−2.05904	−	12.6308i	−0.122614	−	0.752152i
$283$	−6.27107	+	10.8618i	−0.372776	+	0.645667i	−0.989992	−	0.141127i	$-0.954927\pi$
$283$	−6.27107	+	10.8618i	−0.372776	+	0.645667i	0.617215	+	0.786794i	$0.288261\pi$
$284$		−	8.84817i		−	0.525043i
$285$	−1.11931	−	1.36954i	−0.0663022	−	0.0811245i
$286$	3.00386	+	1.73428i	0.177622	+	0.102550i
$287$	9.94236	−	5.74022i	0.586879	−	0.338835i
$288$	−18.4124	+	6.16700i	−1.08496	+	0.363394i
$289$	7.10581	−	12.3076i	0.417989	−	0.723977i
$290$	0.156433	−	0.0903164i	0.00918604	−	0.00530356i
$291$	2.99741	+	18.3870i	0.175711	+	1.07786i
$292$	7.59439	−	13.1539i	0.444428	−	0.769772i
$293$	−0.833707	−	0.481341i	−0.0487057	−	0.0281202i	0.475449	−	0.879743i	$-0.342285\pi$
$293$	−0.833707	−	0.481341i	−0.0487057	−	0.0281202i	−0.524155	+	0.851623i	$0.675619\pi$
$294$	17.4928	−	2.85164i	1.02020	−	0.166311i
$295$	−1.48284	+	0.856119i	−0.0863344	+	0.0498452i
$296$	3.32428	+	5.75782i	0.193220	+	0.334666i
$297$	5.36345	−	2.82501i	0.311219	−	0.163923i
$298$	−24.7769	+	14.3050i	−1.43529	+	0.828665i
$299$	12.0055			0.694295
$300$	10.7581	−	1.75377i	0.621120	−	0.101254i
$301$	4.38361	+	7.59263i	0.252667	+	0.437632i
$302$	12.0848	+	20.9316i	0.695404	+	1.20448i
$303$	−7.53540	−	9.21998i	−0.432898	−	0.529674i
$304$	9.79080			0.561541
$305$	−6.36926	+	3.67729i	−0.364703	+	0.210561i
$306$	−29.9624	−	6.08634i	−1.71284	−	0.347933i
$307$	−3.78150	−	6.54975i	−0.215822	−	0.373814i	0.737705	−	0.675123i	$-0.235910\pi$
$307$	−3.78150	−	6.54975i	−0.215822	−	0.373814i	−0.953526	+	0.301309i	$0.902576\pi$
$308$	−4.76363	+	2.75028i	−0.271433	+	0.156712i
$309$	3.60883	−	9.52976i	0.205299	−	0.542129i
$310$	6.24985	+	3.60835i	0.354967	+	0.204941i
$311$	−2.88517	+	4.99726i	−0.163603	+	0.283368i	−0.936158	−	0.351579i	$-0.885645\pi$
$311$	−2.88517	+	4.99726i	−0.163603	+	0.283368i	0.772555	+	0.634947i	$0.218978\pi$
$312$	2.68035	−	2.19062i	0.151745	−	0.124020i
$313$	−7.91880	+	4.57192i	−0.447597	+	0.258420i	−0.706815	−	0.707399i	$-0.749869\pi$
$313$	−7.91880	+	4.57192i	−0.447597	+	0.258420i	0.259218	+	0.965819i	$0.416535\pi$
$314$	−5.37194	+	9.30447i	−0.303156	+	0.525082i
$315$	3.60086	−	4.07255i	0.202885	−	0.229462i
$316$	−14.4229	+	8.32704i	−0.811349	+	0.468433i
$317$	−14.1230	−	8.15391i	−0.793226	−	0.457969i	0.0478711	−	0.998854i	$-0.484756\pi$
$317$	−14.1230	−	8.15391i	−0.793226	−	0.457969i	−0.841097	+	0.540884i	$0.818090\pi$
$318$	20.4655	−	3.33625i	1.14765	−	0.187088i
$319$		−	0.226373i		−	0.0126745i
$320$	0.515997	−	0.893733i	0.0288451	−	0.0499612i
$321$	3.95871	−	3.23541i	0.220953	−	0.180583i
$322$	−23.8580	+	41.3233i	−1.32955	+	2.30286i
$323$	9.68214	+	5.58999i	0.538729	+	0.311035i
$324$	1.46364	+	11.8601i	0.0813133	+	0.658896i
$325$	−6.68979	+	3.86235i	−0.371083	+	0.214245i
$326$	−17.0194	−	29.4784i	−0.942617	−	1.63266i
$327$	−11.1460	+	9.10949i	−0.616373	+	0.503756i
$328$	1.98228	+	3.43341i	0.109453	+	0.189578i
$329$	−14.3825			−0.792932
$330$	−0.666159	+	1.75911i	−0.0366708	+	0.0968359i
$331$		−	9.20942i		−	0.506195i	−0.967441	−	0.253098i	$-0.918551\pi$
$331$		−	9.20942i		−	0.506195i	0.967441	−	0.253098i	$-0.0814494\pi$
$332$			14.4641i			0.793823i
$333$	15.4233	−	5.16583i	0.845192	−	0.283086i
$334$		−	14.8610i		−	0.813158i
$335$	3.22341	+	2.65646i	0.176113	+	0.145138i
$336$	4.84154	+	29.6994i	0.264128	+	1.62024i
$337$		−	29.1700i		−	1.58899i	−0.607270	−	0.794495i	$-0.707736\pi$
$337$		−	29.1700i		−	1.58899i	0.607270	−	0.794495i	$-0.292264\pi$
$338$	−9.43459	+	16.3412i	−0.513174	+	0.888843i
$339$	−6.99321	+	18.4668i	−0.379819	+	1.00298i
$340$	3.27825	−	1.89270i	0.177788	−	0.102646i
$341$	7.83246	−	4.52207i	0.424151	−	0.244884i
$342$	2.18012	−	10.7325i	0.117888	−	0.580348i
$343$			4.93802i			0.266628i
$344$	−2.62197	+	1.51380i	−0.141367	+	0.0816185i
$345$	1.04752	+	6.42582i	0.0563968	+	0.345955i
$346$	26.9110	−	15.5371i	1.44674	−	0.835277i
$347$	−0.503146	−	0.871475i	−0.0270103	−	0.0467832i	0.852204	−	0.523209i	$-0.175265\pi$
$347$	−0.503146	−	0.871475i	−0.0270103	−	0.0467832i	−0.879215	+	0.476426i	$0.841932\pi$
$348$	0.417334	+	0.158040i	0.0223715	+	0.00847186i
$349$	−3.52383	−	6.10346i	−0.188626	−	0.326711i	0.756166	−	0.654380i	$-0.227070\pi$
$349$	−3.52383	−	6.10346i	−0.188626	−	0.326711i	−0.944793	+	0.327669i	$0.893737\pi$
$350$		−	30.7020i		−	1.64109i
$351$	−3.94665	−	7.49298i	−0.210657	−	0.399945i
$352$	−3.77554	−	6.53942i	−0.201237	−	0.348552i
$353$	−0.744982	+	1.29035i	−0.0396514	+	0.0686782i	−0.885170	−	0.465268i	$-0.845958\pi$
$353$	−0.744982	+	1.29035i	−0.0396514	+	0.0686782i	0.845519	+	0.533946i	$0.179291\pi$
$354$	−9.91467	−	3.75459i	−0.526959	−	0.199554i
$355$	−2.94496	+	1.70027i	−0.156302	+	0.0902411i
$356$	18.3692	−	10.6055i	0.973566	−	0.562089i
$357$	−12.1689	+	32.1340i	−0.644044	+	1.70071i
$358$	−5.73475	+	9.93288i	−0.303091	+	0.524969i
$359$		−	11.6651i		−	0.615659i	−0.951441	−	0.307830i	$-0.900397\pi$
$359$		−	11.6651i		−	0.615659i	0.951441	−	0.307830i	$-0.0996027\pi$
$360$	1.40638	+	1.24349i	0.0741227	+	0.0655377i
$361$	7.49767	−	12.9863i	0.394614	−	0.683492i
$362$	13.6663	+	23.6707i	0.718285	+	1.24411i
$363$	−10.5651	−	12.9270i	−0.554526	−	0.678493i
$364$	3.84226	+	6.65499i	0.201389	+	0.348816i
$365$	−5.83738			−0.305542
$366$	−42.5865	−	16.1271i	−2.22603	−	0.842978i
$367$		−	35.9890i		−	1.87861i	−0.343086	−	0.939304i	$-0.611472\pi$
$367$		−	35.9890i		−	1.87861i	0.343086	−	0.939304i	$-0.388528\pi$
$368$	−31.2108	−	18.0196i	−1.62698	−	0.939335i
$369$	9.19697	−	3.08041i	0.478775	−	0.160360i
$370$	−2.52358	+	4.37096i	−0.131194	+	0.227235i
$371$		−	23.3038i		−	1.20987i
$372$	2.86858	+	17.5967i	0.148729	+	0.912346i
$373$	7.81584	−	4.51248i	0.404689	−	0.233647i	−0.283816	−	0.958879i	$-0.591601\pi$
$373$	7.81584	−	4.51248i	0.404689	−	0.233647i	0.688505	+	0.725231i	$0.258267\pi$
$374$		−	11.8896i		−	0.614796i
$375$	−5.44765	−	6.66550i	−0.281315	−	0.344205i
$376$		−	4.96672i		−	0.256139i
$377$	−0.316253			−0.0162879
$378$	33.6341	+	1.30597i	1.72995	+	0.0671716i
$379$	10.1477	−	5.85877i	0.521252	−	0.300945i	−0.216195	−	0.976350i	$-0.569365\pi$
$379$	10.1477	−	5.85877i	0.521252	−	0.300945i	0.737447	+	0.675405i	$0.236031\pi$
$380$	0.677963	+	1.17427i	0.0347788	+	0.0602386i
$381$	−5.41465	+	0.882685i	−0.277401	+	0.0452213i
$382$	−10.2401	−	17.7363i	−0.523927	−	0.907468i
$383$	−26.2565			−1.34165			−0.670823	−	0.741618i	$-0.734059\pi$
$383$	−26.2565			−1.34165			−0.670823	+	0.741618i	$0.734059\pi$
$384$	−15.8230	+	2.57943i	−0.807462	+	0.131631i
$385$	1.83077	+	1.05699i	0.0933045	+	0.0538694i
$386$	9.58239	+	16.5972i	0.487731	+	0.844774i
$387$	2.35240	+	7.02341i	0.119579	+	0.357020i
$388$		−	14.2815i		−	0.725034i
$389$	23.3248	+	13.4666i	1.18261	+	0.682781i	0.956617	−	0.291347i	$-0.0941035\pi$
$389$	23.3248	+	13.4666i	1.18261	+	0.682781i	0.225995	+	0.974129i	$0.427437\pi$
$390$	2.45755	+	0.930652i	0.124443	+	0.0471254i
$391$	−20.5763	−	35.6392i	−1.04059	−	1.80235i
$392$	6.87858			0.347421
$393$	3.45303	+	21.1819i	0.174182	+	1.06849i
$394$	14.0746	+	24.3780i	0.709070	+	1.22815i
$395$	5.54302	+	3.20026i	0.278900	+	0.161023i
$396$	−4.40650	+	1.47590i	−0.221435	+	0.0741667i
$397$	19.4779			0.977567			0.488784	−	0.872405i	$-0.337441\pi$
$397$	19.4779			0.977567			0.488784	+	0.872405i	$0.337441\pi$
$398$	−26.8909			−1.34792
$399$	−11.5104	−	4.35887i	−0.576240	−	0.218217i
$400$	23.1887			1.15944
$401$	11.8043	−	20.4457i	0.589481	−	1.02101i	−0.404820	−	0.914397i	$-0.632666\pi$
$401$	11.8043	−	20.4457i	0.589481	−	1.02101i	0.994300	−	0.106614i	$-0.0340010\pi$
$402$	−0.105458	+	25.8626i	−0.00525979	+	1.28991i
$403$	−6.31753	−	10.9423i	−0.314698	−	0.545074i
$404$	4.56417	+	7.90538i	0.227076	+	0.393307i
$405$	3.66618	−	2.76620i	0.182174	−	0.137454i
$406$	0.628477	−	1.08855i	0.0311908	−	0.0540240i
$407$	3.16261	+	5.47779i	0.156765	+	0.271524i
$408$	−11.0969	−	4.20229i	−0.549378	−	0.208044i
$409$	4.79871	−	2.77054i	0.237281	−	0.136994i	−0.376645	−	0.926357i	$-0.622922\pi$
$409$	4.79871	−	2.77054i	0.237281	−	0.136994i	0.613926	+	0.789363i	$0.289589\pi$
$410$	−1.50482	+	2.60642i	−0.0743177	+	0.128722i
$411$	−7.24167	+	19.1229i	−0.357205	+	0.943265i
$412$	−3.90590	+	6.76522i	−0.192430	+	0.333298i
$413$	−5.95740	+	10.3185i	−0.293145	+	0.507741i
$414$	−26.7025	+	30.2004i	−1.31236	+	1.48427i
$415$	4.81413	−	2.77944i	0.236317	−	0.136437i
$416$	−9.13585	+	5.27459i	−0.447922	+	0.258608i
$417$	−0.259135	−	1.58961i	−0.0126899	−	0.0778435i
$418$	4.25884			0.208307
$419$			18.5149i			0.904511i	0.891888	+	0.452256i	$0.149380\pi$
$419$			18.5149i			0.904511i	−0.891888	+	0.452256i	$0.850620\pi$
$420$	−3.22677	+	2.63721i	−0.157450	+	0.128683i
$421$	10.3441	−	17.9164i	0.504138	−	0.873193i	−0.495850	−	0.868408i	$-0.665144\pi$
$421$	10.3441	−	17.9164i	0.504138	−	0.873193i	0.999989	−	0.00478511i	$-0.00152315\pi$
$422$	−4.62342	+	8.00800i	−0.225065	+	0.389824i
$423$	−11.9077	−	2.41884i	−0.578972	−	0.117608i
$424$	8.04753			0.390823
$425$	22.9314	+	13.2394i	1.11233	+	0.642207i
$426$	−19.6908	−	7.45670i	−0.954021	−	0.361279i
$427$	−25.5889	+	44.3212i	−1.23833	+	2.14485i
$428$	−3.39427	+	1.95968i	−0.164068	+	0.0947247i
$429$	2.54999	−	2.08408i	0.123115	−	0.100621i
$430$	−1.99043	−	1.14918i	−0.0959872	−	0.0554182i
$431$	30.7054	+	17.7278i	1.47903	+	0.853916i	0.999718	−	0.0237314i	$-0.00755465\pi$
$431$	30.7054	+	17.7278i	1.47903	+	0.853916i	0.479307	+	0.877647i	$0.340888\pi$
$432$	−0.986376	+	25.4033i	−0.0474570	+	1.22222i
$433$	32.6560	+	18.8539i	1.56935	+	0.906062i	0.996245	+	0.0865770i	$0.0275929\pi$
$433$	32.6560	+	18.8539i	1.56935	+	0.906062i	0.573100	+	0.819485i	$0.305740\pi$
$434$	50.2182			2.41055
$435$	−0.0275943	−	0.169272i	−0.00132305	−	0.00811595i
$436$	9.55675	−	5.51759i	0.457685	−	0.264245i
$437$	12.7659	−	7.37041i	0.610677	−	0.352574i
$438$	−22.8726	−	27.9859i	−1.09289	−	1.33722i
$439$	−18.0595	+	31.2800i	−0.861933	+	1.49291i	0.00812806	+	0.999967i	$0.497413\pi$
$439$	−18.0595	+	31.2800i	−0.861933	+	1.49291i	−0.870061	+	0.492944i	$0.835921\pi$
$440$	−0.365013	+	0.632221i	−0.0174013	+	0.0301399i
$441$	3.34993	−	16.4914i	0.159521	−	0.785303i
$442$	−16.6103			−0.790070
$443$	38.6339			1.83555			0.917777	−	0.397096i	$-0.129982\pi$
$443$	38.6339			1.83555			0.917777	+	0.397096i	$0.129982\pi$
$444$	−12.3066	+	2.00620i	−0.584046	+	0.0952101i
$445$	−7.05969	−	4.07591i	−0.334661	−	0.193217i
$446$	27.6492			1.30923
$447$	4.37059	+	26.8105i	0.206722	+	1.26809i
$448$		−	7.18125i		−	0.339282i
$449$	−18.5372	−	10.7024i	−0.874824	−	0.505080i	−0.00587557	−	0.999983i	$-0.501870\pi$
$449$	−18.5372	−	10.7024i	−0.874824	−	0.505080i	−0.868948	+	0.494903i	$0.835204\pi$
$450$	5.16344	−	25.4191i	0.243407	−	1.19827i
$451$	1.88587	+	3.26643i	0.0888023	+	0.153810i
$452$	7.56888	−	13.1097i	0.356010	−	0.616628i
$453$	22.6495	−	3.69227i	1.06417	−	0.173478i
$454$	36.4722	+	21.0572i	1.71172	+	0.988265i
$455$	1.47666	−	2.55766i	0.0692271	−	0.119905i
$456$	1.50526	−	3.97490i	0.0704901	−	0.186142i
$457$	8.96041			0.419150			0.209575	−	0.977793i	$-0.432792\pi$
$457$	8.96041			0.419150			0.209575	+	0.977793i	$0.432792\pi$
$458$	−41.6763	−	24.0618i	−1.94740	−	1.12433i
$459$	−15.4793	+	24.5582i	−0.722510	+	1.14628i
$460$		−	4.99106i		−	0.232709i
$461$	16.9576	−	9.79046i	0.789793	−	0.455987i	−0.0500967	−	0.998744i	$-0.515953\pi$
$461$	16.9576	−	9.79046i	0.789793	−	0.455987i	0.839890	+	0.542757i	$0.182620\pi$
$462$	2.10599	+	12.9188i	0.0979796	+	0.601036i
$463$			23.7547i			1.10398i	0.833852	+	0.551988i	$0.186131\pi$
$463$			23.7547i			1.10398i	−0.833852	+	0.551988i	$0.813869\pi$
$464$	0.822168	+	0.474679i	0.0381682	+	0.0220364i
$465$	5.30552	−	4.33615i	0.246038	−	0.201084i
$466$	−21.7747	−	37.7149i	−1.00869	−	1.74711i
$467$	5.13562	−	2.96505i	0.237648	−	0.137206i	−0.376447	−	0.926438i	$-0.622854\pi$
$467$	5.13562	−	2.96505i	0.237648	−	0.137206i	0.614095	+	0.789232i	$0.289521\pi$
$468$	2.06189	+	6.15606i	0.0953110	+	0.284564i
$469$	28.6680	+	4.79348i	1.32376	+	0.221342i
$470$	3.26528	−	1.88521i	0.150616	−	0.0869581i
$471$	6.45546	+	7.89861i	0.297452	+	0.363949i
$472$	−3.56331	−	2.05728i	−0.164015	−	0.0946939i
$473$	−2.49446	+	1.44018i	−0.114695	+	0.0662194i
$474$	6.37632	+	39.1142i	0.292874	+	1.79658i
$475$	−4.74235	+	8.21400i	−0.217594	+	0.376884i
$476$	13.1706	−	22.8121i	0.603672	−	1.04559i
$477$	3.91922	−	19.2939i	0.179449	−	0.883409i
$478$	20.6492			0.944472
$479$	−16.8210	−	9.71159i	−0.768570	−	0.443734i	0.0637945	−	0.997963i	$-0.479680\pi$
$479$	−16.8210	−	9.71159i	−0.768570	−	0.443734i	−0.832364	+	0.554229i	$0.813013\pi$
$480$	−3.62031	−	4.42965i	−0.165244	−	0.202185i
$481$	7.65271	−	4.41829i	0.348934	−	0.201457i
$482$	10.5000			0.478260
$483$	28.6701	+	35.0795i	1.30454	+	1.59617i
$484$	6.39928	+	11.0839i	0.290876	+	0.503812i
$485$	−4.75335	+	2.74435i	−0.215838	+	0.124614i
$486$	27.6271	+	6.73782i	1.25319	+	0.305634i
$487$	−2.56602	+	1.48149i	−0.116277	+	0.0671327i	−0.557011	−	0.830505i	$-0.688052\pi$
$487$	−2.56602	+	1.48149i	−0.116277	+	0.0671327i	0.440733	+	0.897638i	$0.354718\pi$
$488$	−15.3055	−	8.83664i	−0.692848	−	0.400016i
$489$	−31.8978	+	5.19992i	−1.44247	+	0.235149i
$490$	2.61089	+	4.52219i	0.117948	+	0.204292i
$491$	−32.4933	−	18.7600i	−1.46640	−	0.846626i	−0.467106	−	0.884201i	$-0.654703\pi$
$491$	−32.4933	−	18.7600i	−1.46640	−	0.846626i	−0.999294	+	0.0375749i	$0.988037\pi$
$492$	−7.33848	+	1.19631i	−0.330844	+	0.0539336i
$493$	0.542029	+	0.938821i	0.0244118	+	0.0422824i
$494$		−	5.94978i		−	0.267693i
$495$	1.33798	+	1.18301i	0.0601379	+	0.0531726i
$496$			37.9291i			1.70307i
$497$	−11.8315	+	20.4928i	−0.530717	+	0.919229i
$498$	32.1886	+	12.1895i	1.44240	+	0.546225i
$499$		−	7.30222i		−	0.326892i	−0.986552	−	0.163446i	$-0.947739\pi$
$499$		−	7.30222i		−	0.326892i	0.986552	−	0.163446i	$-0.0522610\pi$
$500$	3.29962	+	5.71512i	0.147564	+	0.255588i
$501$	−13.1956	−	4.99707i	−0.589538	−	0.223252i
$502$	−8.44367			−0.376859
$503$	15.0987	−	26.1517i	0.673217	−	1.16605i	−0.303769	−	0.952746i	$-0.598245\pi$
$503$	15.0987	−	26.1517i	0.673217	−	1.16605i	0.976987	−	0.213301i	$-0.0684215\pi$
$504$	12.8018	+	2.60046i	0.570238	+	0.115834i
$505$	1.75411	−	3.03821i	0.0780569	−	0.135199i
$506$	−13.5762	−	7.83823i	−0.603536	−	0.348452i
$507$	11.3375	+	13.8721i	0.503518	+	0.616082i
$508$	4.20566			0.186596
$509$	14.3827	+	8.30387i	0.637503	+	0.368062i	0.783652	−	0.621200i	$-0.213355\pi$
$509$	14.3827	+	8.30387i	0.637503	+	0.368062i	−0.146149	+	0.989263i	$0.546688\pi$
$510$	−1.44931	−	8.89049i	−0.0641765	−	0.393677i
$511$	−35.1780	+	20.3100i	−1.55618	+	0.898463i
$512$	19.6684			0.869228
$513$	−8.79673	−	5.54466i	−0.388385	−	0.244803i
$514$			28.2896i			1.24780i
$515$	3.00224			0.132295
$516$	−0.913576	−	5.60414i	−0.0402180	−	0.246709i
$517$		−	4.72517i		−	0.207813i
$518$			35.1212i			1.54314i
$519$	−4.74703	−	29.1196i	−0.208371	−	1.27821i
$520$	0.883240	+	0.509939i	0.0387326	+	0.0223623i
$521$	31.1418			1.36435			0.682174	−	0.731190i	$-0.261035\pi$
$521$	31.1418			1.36435			0.682174	+	0.731190i	$0.261035\pi$
$522$	0.703408	−	0.795550i	0.0307873	−	0.0348203i
$523$	−16.6013	−	28.7543i	−0.725924	−	1.25734i	−0.958593	−	0.284781i	$-0.908079\pi$
$523$	−16.6013	−	28.7543i	−0.725924	−	1.25734i	0.232669	−	0.972556i	$-0.425254\pi$
$524$		−	16.4524i		−	0.718726i
$525$	−27.2614	−	10.3236i	−1.18979	−	0.450561i
$526$			37.8372i			1.64978i
$527$	−21.6553	+	37.5081i	−0.943321	+	1.63388i
$528$	−9.75735	+	1.59062i	−0.424634	+	0.0692230i
$529$	−31.2598			−1.35912
$530$	3.05458	+	5.29069i	0.132683	+	0.229813i
$531$	−6.66768	+	7.54111i	−0.289353	+	0.327256i
$532$	8.17127	+	4.71769i	0.354269	+	0.204538i
$533$	4.56334	−	2.63465i	0.197660	−	0.114119i
$534$	−8.12100	−	49.8166i	−0.351430	−	2.15577i
$535$	1.30449	+	0.753148i	0.0563980	+	0.0325614i
$536$	−1.65534	+	9.89994i	−0.0714997	+	0.427612i
$537$	6.89145	+	8.43207i	0.297388	+	0.363871i
$538$	−3.37865	−	1.95067i	−0.145664	−	0.0840992i
$539$	6.54405			0.281872
$540$	−3.11507	+	1.64075i	−0.134051	+	0.0706066i
$541$		−	24.2771i		−	1.04375i	−0.853021	−	0.521876i	$-0.825232\pi$
$541$		−	24.2771i		−	1.04375i	0.853021	−	0.521876i	$-0.174768\pi$
$542$	−7.37632	−	4.25872i	−0.316840	−	0.182928i
$543$	25.6135	−	4.17545i	1.09918	−	0.179186i
$544$	31.3160	+	18.0803i	1.34266	+	0.775187i
$545$	−3.67287	−	2.12053i	−0.157328	−	0.0908336i
$546$	18.0481	−	2.94216i	0.772386	−	0.125913i
$547$			16.9551i			0.724948i	0.931994	+	0.362474i	$0.118068\pi$
$547$			16.9551i			0.724948i	−0.931994	+	0.362474i	$0.881932\pi$
$548$	7.83779	−	13.5754i	0.334814	−	0.579914i
$549$	−28.6397	+	32.3914i	−1.22231	+	1.38243i
$550$	10.0867			0.430099
$551$	−0.336285	+	0.194154i	−0.0143262	+	0.00827125i
$552$	−12.1141	+	9.90070i	−0.515608	+	0.421402i
$553$	44.5388			1.89398
$554$	21.2244			0.901737
$555$	3.03258	+	3.71053i	0.128726	+	0.157503i
$556$			1.23468i			0.0523621i
$557$	−28.4428	−	16.4215i	−1.20516	−	0.695800i	−0.243463	−	0.969910i	$-0.578283\pi$
$557$	−28.4428	−	16.4215i	−1.20516	−	0.695800i	−0.961698	+	0.274110i	$0.911617\pi$
$558$	41.5772	+	8.44568i	1.76010	+	0.357534i
$559$	2.01199	+	3.48486i	0.0850980	+	0.147394i
$560$	−7.67781	+	4.43279i	−0.324447	+	0.187319i
$561$	−10.5572	−	3.99792i	−0.445726	−	0.168792i
$562$	4.01530	+	6.95470i	0.169375	+	0.293366i
$563$	−1.88573	+	3.26618i	−0.0794741	+	0.137653i	−0.903023	−	0.429592i	$-0.858657\pi$
$563$	−1.88573	+	3.26618i	−0.0794741	+	0.137653i	0.823549	+	0.567245i	$0.191991\pi$
$564$	8.71117	+	3.29884i	0.366806	+	0.138906i
$565$	−5.81777			−0.244755
$566$	−11.4398	−	19.8144i	−0.480852	−	0.832860i
$567$	12.4692	−	29.4258i	0.523657	−	1.23577i
$568$	−7.07682	−	4.08580i	−0.296937	−	0.171436i
$569$			2.05287i			0.0860608i	0.999074	+	0.0430304i	$0.0137012\pi$
$569$			2.05287i			0.0860608i	−0.999074	+	0.0430304i	$0.986299\pi$
$570$	3.18456	−	0.519141i	0.133387	−	0.0217444i
$571$	−9.99667	−	17.3147i	−0.418348	−	0.724599i	0.577426	−	0.816443i	$-0.304057\pi$
$571$	−9.99667	−	17.3147i	−0.418348	−	0.724599i	−0.995773	+	0.0918438i	$0.970724\pi$
$572$	−2.18641	+	1.26232i	−0.0914183	+	0.0527804i
$573$	−19.1920	+	3.12864i	−0.801756	+	0.130701i
$574$			20.9429i			0.874139i
$575$	30.2351	−	17.4562i	1.26089	−	0.727975i
$576$	1.20774	−	5.94558i	0.0503225	−	0.247732i
$577$	−15.7958	−	9.11973i	−0.657589	−	0.379659i	0.133769	−	0.991013i	$-0.457292\pi$
$577$	−15.7958	−	9.11973i	−0.657589	−	0.379659i	−0.791358	+	0.611353i	$0.790625\pi$
$578$	12.9626	+	22.4518i	0.539172	+	0.933873i
$579$	17.9594	−	2.92770i	0.746366	−	0.121671i
$580$			0.131476i			0.00545926i
$581$	19.3411	−	33.4997i	0.802402	−	1.38980i
$582$	−31.7821	−	12.0356i	−1.31741	−	0.498891i
$583$	7.65615			0.317085
$584$	−7.01369	−	12.1481i	−0.290229	−	0.502691i
$585$	1.65272	−	1.86922i	0.0683316	−	0.0772827i
$586$	1.52087	−	0.878074i	0.0628265	−	0.0362729i
$587$	−16.2844	+	28.2054i	−0.672130	+	1.16416i	0.305169	+	0.952298i	$0.401287\pi$
$587$	−16.2844	+	28.2054i	−0.672130	+	1.16416i	−0.977299	+	0.211865i	$0.932046\pi$
$588$	−4.56867	+	12.0644i	−0.188409	+	0.497527i
$589$	−13.4354	−	7.75692i	−0.553595	−	0.319618i
$590$		−	3.12350i		−	0.128593i
$591$	26.3788	−	4.30022i	1.08508	−	0.176887i
$592$	−26.5265			−1.09023
$593$	−1.52565	−	2.64250i	−0.0626509	−	0.108514i	0.832999	−	0.553275i	$-0.186622\pi$
$593$	−1.52565	−	2.64250i	−0.0626509	−	0.108514i	−0.895650	+	0.444761i	$0.853289\pi$
$594$	−0.429058	+	11.0500i	−0.0176044	+	0.453388i
$595$	−10.1235			−0.415022
$596$		−	20.8242i		−	0.852993i
$597$	−9.04216	+	23.8774i	−0.370071	+	0.977238i
$598$	−10.9503	+	18.9665i	−0.447793	+	0.775600i
$599$	−10.5920	−	18.3459i	−0.432779	−	0.749595i	0.564333	−	0.825548i	$-0.309134\pi$
$599$	−10.5920	−	18.3459i	−0.432779	−	0.749595i	−0.997111	+	0.0759525i	$0.975800\pi$
$600$	3.56508	−	9.41423i	0.145544	−	0.384334i
$601$	20.3331	−	35.2179i	0.829404	−	1.43657i	−0.0691024	−	0.997610i	$-0.522014\pi$
$601$	20.3331	−	35.2179i	0.829404	−	1.43657i	0.898506	−	0.438960i	$-0.144653\pi$
$602$	−15.9934			−0.651841
$603$	22.9289	+	8.79003i	0.933738	+	0.357958i
$604$	−17.5923			−0.715820
$605$	2.45938	−	4.25977i	0.0999880	−	0.173184i
$606$	21.4391	−	3.49496i	0.870903	−	0.141973i
$607$	16.4249	+	28.4488i	0.666667	+	1.15470i	0.978831	+	0.204672i	$0.0656129\pi$
$607$	16.4249	+	28.4488i	0.666667	+	1.15470i	−0.312164	+	0.950028i	$0.601054\pi$
$608$	−6.47635	+	11.2174i	−0.262651	+	0.454924i
$609$	−0.755240	−	0.924078i	−0.0306039	−	0.0374455i
$610$		−	13.4164i		−	0.543215i
$611$	−6.60127			−0.267059
$612$	14.7408	−	16.6718i	0.595863	−	0.673918i
$613$	1.52870	+	2.64778i	0.0617434	+	0.106943i	0.895245	−	0.445575i	$-0.147001\pi$
$613$	1.52870	+	2.64778i	0.0617434	+	0.106943i	−0.833501	+	0.552517i	$0.813667\pi$
$614$	13.7966			0.556785
$615$	1.80834	+	2.21260i	0.0729192	+	0.0892207i
$616$			5.07997i			0.204678i
$617$	11.7199	+	6.76650i	0.471827	+	0.272409i	0.717004	−	0.697069i	$-0.245513\pi$
$617$	11.7199	+	6.76650i	0.471827	+	0.272409i	−0.245177	+	0.969478i	$0.578846\pi$
$618$	11.7637	+	14.3935i	0.473205	+	0.578992i
$619$	−22.6717	+	39.2685i	−0.911252	+	1.57833i	−0.0989539	+	0.995092i	$0.531550\pi$
$619$	−22.6717	+	39.2685i	−0.911252	+	1.57833i	−0.812298	+	0.583243i	$0.801784\pi$
$620$	−4.54905	+	2.62640i	−0.182694	+	0.105479i
$621$	17.8372	+	33.8651i	0.715784	+	1.35896i
$622$	−5.26319	−	9.11611i	−0.211035	−	0.365523i
$623$	−56.7254			−2.27265
$624$	2.22217	+	13.6314i	0.0889580	+	0.545694i
$625$	−10.5809	+	18.3266i	−0.423235	+	0.733064i
$626$		−	16.6804i		−	0.666683i
$627$	1.43205	−	3.78158i	0.0571906	−	0.151022i
$628$	−3.91005	−	6.77241i	−0.156028	−	0.270248i
$629$	−26.2321	−	15.1451i	−1.04594	−	0.603875i
$630$	3.14953	+	9.40335i	0.125480	+	0.374638i
$631$	1.81541	−	1.04813i	0.0722702	−	0.0417252i	−0.463429	−	0.886134i	$-0.653381\pi$
$631$	1.81541	−	1.04813i	0.0722702	−	0.0417252i	0.535700	+	0.844409i	$0.320048\pi$
$632$			15.3806i			0.611809i
$633$	5.55597	+	6.79803i	0.220830	+	0.270197i
$634$	25.7635	−	14.8745i	1.02320	−	0.590744i
$635$	−0.808164	−	1.39978i	−0.0320710	−	0.0555486i
$636$	−5.34507	+	14.1146i	−0.211946	+	0.559681i
$637$		−	9.14231i		−	0.362232i
$638$	0.357630	+	0.206478i	0.0141587	+	0.00817453i
$639$	−13.2422	+	14.9768i	−0.523852	+	0.592474i
$640$	−2.36166	−	4.09051i	−0.0933527	−	0.161692i
$641$	24.1369			0.953351			0.476676	−	0.879079i	$-0.341842\pi$
$641$	24.1369			0.953351			0.476676	+	0.879079i	$0.341842\pi$
$642$	1.50060	+	9.20511i	0.0592239	+	0.363297i
$643$	24.7398	−	42.8506i	0.975643	−	1.68986i	0.297847	−	0.954614i	$-0.403732\pi$
$643$	24.7398	−	42.8506i	0.975643	−	1.68986i	0.677796	−	0.735250i	$-0.262935\pi$
$644$	−17.3654	−	30.0778i	−0.684294	−	1.18523i
$645$	−1.68969	+	1.38096i	−0.0665314	+	0.0543754i
$646$	−17.6624	+	10.1974i	−0.694917	+	0.401211i
$647$	3.12728	+	5.41660i	0.122946	+	0.212949i	0.920928	−	0.389732i	$-0.127432\pi$
$647$	3.12728	+	5.41660i	0.122946	+	0.212949i	−0.797982	+	0.602681i	$0.794099\pi$
$648$	10.1617	+	4.30600i	0.399188	+	0.169156i
$649$	−3.39001	−	1.95723i	−0.133070	−	0.0768278i
$650$		−	14.0916i		−	0.552717i
$651$	16.8861	−	44.5907i	0.661817	−	1.74765i
$652$	24.7757			0.970290
$653$	−44.1130			−1.72628			−0.863138	−	0.504968i	$-0.831504\pi$
$653$	−44.1130			−1.72628			−0.863138	+	0.504968i	$0.831504\pi$
$654$	−4.22502	−	25.9175i	−0.165212	−	1.01346i
$655$	−5.47588	+	3.16150i	−0.213961	+	0.123530i
$656$	−15.8178			−0.617583
$657$	−32.5407	+	10.8991i	−1.26953	+	0.425214i
$658$	13.1184	−	22.7218i	0.511410	−	0.885788i
$659$		−	17.6438i		−	0.687304i	−0.939097	−	0.343652i	$-0.888336\pi$
$659$		−	17.6438i		−	0.687304i	0.939097	−	0.343652i	$-0.111664\pi$
$660$	−0.866419	−	1.06011i	−0.0337253	−	0.0412648i
$661$	−36.2727	−	20.9421i	−1.41085	−	0.814552i	−0.415378	−	0.909649i	$-0.636351\pi$
$661$	−36.2727	−	20.9421i	−1.41085	−	0.814552i	−0.995468	+	0.0950963i	$0.969684\pi$
$662$	14.5493	+	8.40001i	0.565473	+	0.326476i
$663$	−5.58526	+	14.7489i	−0.216914	+	0.572799i
$664$	11.5685	+	6.67908i	0.448945	+	0.259198i
$665$		−	3.62622i		−	0.140619i
$666$	−5.90667	+	29.0779i	−0.228879	+	1.12675i
$667$	1.42933			0.0553440
$668$	9.36764	+	5.40841i	0.362445	+	0.209258i
$669$	9.29713	−	24.5507i	0.359448	−	0.949186i
$670$	−7.13684	+	2.66943i	−0.275720	+	0.103129i
$671$	−14.5611	−	8.40688i	−0.562127	−	0.324544i
$672$	−37.2293	−	14.0984i	−1.43615	−	0.543857i
$673$	25.4150	−	14.6734i	0.979676	−	0.565616i	0.0775039	−	0.996992i	$-0.475305\pi$
$673$	25.4150	−	14.6734i	0.979676	−	0.565616i	0.902172	+	0.431376i	$0.141972\pi$
$674$	46.0834	+	26.6063i	1.77507	+	1.02484i
$675$	−20.8344	−	13.1321i	−0.801915	−	0.505454i
$676$	−6.86711	−	11.8942i	−0.264120	−	0.457469i
$677$	−31.2840			−1.20234			−0.601171	−	0.799120i	$-0.705299\pi$
$677$	−31.2840			−1.20234			−0.601171	+	0.799120i	$0.705299\pi$
$678$	−22.7957	−	27.8919i	−0.875465	−	1.07118i
$679$	−19.0968	+	33.0767i	−0.732870	+	1.26937i
$680$		−	3.49595i		−	0.134064i
$681$	30.9614	−	25.3045i	1.18644	−	0.969669i
$682$			16.4985i			0.631761i
$683$	6.60763	+	11.4447i	0.252834	+	0.437921i	0.964305	−	0.264794i	$-0.0853041\pi$
$683$	6.60763	+	11.4447i	0.252834	+	0.437921i	−0.711471	+	0.702715i	$0.751971\pi$
$684$	5.97183	+	5.28016i	0.228339	+	0.201892i
$685$	−6.02447			−0.230183
$686$	−7.80120	−	4.50402i	−0.297851	−	0.171964i
$687$	−35.3792	+	28.9151i	−1.34980	+	1.10318i
$688$		−	12.0795i		−	0.460528i
$689$		−	10.6960i		−	0.407484i
$690$	−11.1071	−	4.20616i	−0.422841	−	0.160126i
$691$	−1.20560			−0.0458631			−0.0229316	−	0.999737i	$-0.507300\pi$
$691$	−1.20560			−0.0458631			−0.0229316	+	0.999737i	$0.507300\pi$
$692$			22.6178i			0.859799i
$693$	12.1792	+	2.47399i	0.462650	+	0.0939792i
$694$	1.83570			0.0696823
$695$	0.410942	−	0.237257i	0.0155879	−	0.00899968i
$696$	0.319113	−	0.260808i	0.0120960	−	0.00988591i
$697$	−15.6423	−	9.03108i	−0.592494	−	0.342077i
$698$	12.8565			0.486626
$699$	−40.8103	+	6.65282i	−1.54359	+	0.251633i
$700$	19.3530	+	11.1735i	0.731475	+	0.422317i
$701$	−17.4995	+	30.3100i	−0.660946	+	1.14479i	0.319422	+	0.947613i	$0.396511\pi$
$701$	−17.4995	+	30.3100i	−0.660946	+	1.14479i	−0.980367	+	0.197179i	$0.936822\pi$
$702$	15.4374	+	0.599412i	0.582646	+	0.0226233i
$703$	5.42496	−	9.39631i	0.204606	−	0.354389i
$704$	2.35930			0.0889196
$705$	−0.575986	−	3.53327i	−0.0216929	−	0.133071i
$706$	−1.35901	−	2.35388i	−0.0511471	−	0.0885894i
$707$		−	24.4124i		−	0.918121i
$708$	5.97498	−	4.88330i	0.224554	−	0.183525i
$709$	5.80602	−	10.0563i	0.218050	−	0.377673i	−0.736162	−	0.676805i	$-0.763364\pi$
$709$	5.80602	−	10.0563i	0.218050	−	0.377673i	0.954212	+	0.299132i	$0.0966972\pi$
$710$		−	6.20335i		−	0.232808i
$711$	36.8750	+	7.49052i	1.38292	+	0.280916i
$712$		−	19.5891i		−	0.734131i
$713$	28.5526	+	49.4545i	1.06930	+	1.85209i
$714$	−39.6668	−	48.5345i	−1.48449	−	1.81636i
$715$	0.840284	+	0.485138i	0.0314249	+	0.0181431i
$716$	−4.17413	−	7.22981i	−0.155995	−	0.270191i
$717$	6.94336	−	18.3352i	0.259305	−	0.684740i
$718$	18.4288	+	10.6399i	0.687756	+	0.397076i
$719$	−32.7839	+	18.9278i	−1.22263	+	0.705887i	−0.965478	−	0.260484i	$-0.916118\pi$
$719$	−32.7839	+	18.9278i	−1.22263	+	0.705887i	−0.257153	+	0.966371i	$0.582785\pi$
$720$	−7.10220	+	2.37879i	−0.264683	+	0.0886523i
$721$	18.0925	−	10.4457i	0.673801	−	0.389019i
$722$	13.6774	+	23.6900i	0.509021	+	0.881650i
$723$	3.53065	−	9.32330i	0.131306	−	0.346737i
$724$	−19.8945			−0.739372
$725$	−0.796464	+	0.459839i	−0.0295799	+	0.0170780i
$726$	30.0590	−	4.90016i	1.11559	−	0.181862i
$727$	27.5706	+	15.9179i	1.02254	+	0.590362i	0.914838	−	0.403822i	$-0.132318\pi$
$727$	27.5706	+	15.9179i	1.02254	+	0.590362i	0.107699	+	0.994184i	$0.465652\pi$
$728$	7.09693			0.263030
$729$	15.2725	−	22.2655i	0.565647	−	0.824648i
$730$	5.32434	−	9.22203i	0.197063	−	0.341323i
$731$	6.89672	−	11.9455i	0.255084	−	0.441819i
$732$	25.6644	−	20.9753i	0.948583	−	0.775268i
$733$	32.4030	−	18.7079i	1.19683	−	0.690991i	0.236985	−	0.971513i	$-0.423841\pi$
$733$	32.4030	−	18.7079i	1.19683	−	0.690991i	0.959848	+	0.280522i	$0.0905075\pi$
$734$	56.8562	+	32.8259i	2.09860	+	1.21163i
$735$	4.89334	−	0.797702i	0.180493	−	0.0294237i
$736$	41.2903	−	23.8389i	1.52198	−	0.878715i
$737$	−1.57483	+	9.41847i	−0.0580097	+	0.346934i
$738$	−3.52217	+	17.3393i	−0.129653	+	0.638267i
$739$	28.2280	−	16.2975i	1.03839	−	0.599512i	0.119010	−	0.992893i	$-0.462028\pi$
$739$	28.2280	−	16.2975i	1.03839	−	0.599512i	0.919375	+	0.393381i	$0.128695\pi$
$740$	−1.83682	−	3.18147i	−0.0675230	−	0.116953i
$741$	−5.28303	−	2.00063i	−0.194077	−	0.0734952i
$742$	36.8159	+	21.2557i	1.35155	+	0.780320i
$743$		−	34.5096i		−	1.26603i	−0.774138	−	0.633017i	$-0.781816\pi$
$743$		−	34.5096i		−	1.26603i	0.774138	−	0.633017i	$-0.218184\pi$
$744$	15.3986	+	5.83128i	0.564538	+	0.213785i
$745$	−6.93097	+	4.00160i	−0.253931	+	0.146607i
$746$			16.4635i			0.602773i
$747$	21.6470	−	24.4827i	0.792023	−	0.895774i
$748$	7.49461	+	4.32701i	0.274030	+	0.158211i
$749$	10.4817			0.382994
$750$	15.4992	−	2.52664i	0.565950	−	0.0922600i
$751$	−8.43843	+	14.6158i	−0.307923	+	0.533338i	−0.977908	−	0.209037i	$-0.932967\pi$
$751$	−8.43843	+	14.6158i	−0.307923	+	0.533338i	0.669985	+	0.742375i	$0.266301\pi$
$752$	17.1614	+	9.90815i	0.625813	+	0.361313i
$753$	−2.83921	+	7.49745i	−0.103467	+	0.273222i
$754$	0.288458	−	0.499624i	0.0105050	−	0.0181952i
$755$	3.38055	+	5.85528i	0.123031	+	0.213096i
$756$	−13.0638	+	20.7260i	−0.475125	+	0.753797i
$757$	−36.6818	−	21.1783i	−1.33322	−	0.769737i	−0.347432	−	0.937705i	$-0.612946\pi$
$757$	−36.6818	−	21.1783i	−1.33322	−	0.769737i	−0.985792	+	0.167968i	$0.946279\pi$
$758$			21.3754i			0.776390i
$759$	−11.5249	+	9.41919i	−0.418327	+	0.341895i
$760$	1.25225			0.0454238
$761$	22.3774	+	12.9196i	0.811180	+	0.468335i	0.847365	−	0.531010i	$-0.178187\pi$
$761$	22.3774	+	12.9196i	0.811180	+	0.468335i	−0.0361858	+	0.999345i	$0.511521\pi$
$762$	3.54428	−	9.35930i	0.128396	−	0.339052i
$763$	−29.5119			−1.06840
$764$	14.9068			0.539308
$765$	−8.38153	−	1.70256i	−0.303035	−	0.0615562i
$766$	23.9489	−	41.4807i	0.865308	−	1.49876i
$767$	−2.73433	+	4.73599i	−0.0987308	+	0.171007i
$768$	12.8383	−	33.9018i	0.463261	−	1.22332i
$769$	5.07847	−	2.93206i	0.183134	−	0.105733i	−0.405630	−	0.914037i	$-0.632948\pi$
$769$	5.07847	−	2.93206i	0.183134	−	0.105733i	0.588764	+	0.808305i	$0.299615\pi$
$770$	−3.33973	+	1.92819i	−0.120355	+	0.0694872i
$771$	25.1194	+	9.51249i	0.904654	+	0.342584i
$772$	−13.9494			−0.502049
$773$	−0.625384	−	0.361065i	−0.0224935	−	0.0129866i	0.488711	−	0.872446i	$-0.337467\pi$
$773$	−0.625384	−	0.361065i	−0.0224935	−	0.0129866i	−0.511205	+	0.859459i	$0.670801\pi$
$774$	−13.2414	−	2.68976i	−0.475952	−	0.0966813i
$775$	−31.8206	−	18.3716i	−1.14303	−	0.659929i
$776$	−11.4224	−	6.59474i	−0.410041	−	0.236737i
$777$	31.1854	+	11.8096i	1.11877	+	0.423668i
$778$	−42.5496	+	24.5660i	−1.52548	+	0.880734i
$779$	3.23493	−	5.60306i	0.115903	−	0.200750i
$780$	−1.48102	+	1.21043i	−0.0530291	+	0.0433402i
$781$	−6.73265	−	3.88710i	−0.240913	−	0.139091i
$782$	75.0715			2.68455
$783$	−0.469876	−	0.892089i	−0.0167920	−	0.0318806i
$784$	−13.7221	+	23.7674i	−0.490076	+	0.848836i
$785$	−1.50272	+	2.60278i	−0.0536343	+	0.0928973i
$786$	−36.6132	−	13.8651i	−1.30595	−	0.494551i
$787$		−	31.8701i		−	1.13605i	−0.823013	−	0.568023i	$-0.807708\pi$
$787$		−	31.8701i		−	1.13605i	0.823013	−	0.568023i	$-0.192292\pi$
$788$	−20.4889			−0.729887
$789$	33.5971	+	12.7229i	1.19609	+	0.452947i
$790$	−10.1117	+	5.83800i	−0.359758	+	0.207707i
$791$	−35.0598	+	20.2418i	−1.24658	+	0.719716i
$792$	−0.854347	+	4.20586i	−0.0303579	+	0.149449i
$793$	−11.7448	+	20.3425i	−0.417069	+	0.722385i
$794$	−17.7660	+	30.7716i	−0.630492	+	1.09204i
$795$	5.72492	−	0.933265i	0.203042	−	0.0330995i
$796$	9.78648	−	16.9507i	0.346873	−	0.600801i
$797$	22.7167	−	13.1155i	0.804666	−	0.464574i	−0.0404341	−	0.999182i	$-0.512874\pi$
$797$	22.7167	−	13.1155i	0.804666	−	0.464574i	0.845100	+	0.534608i	$0.179541\pi$
$798$	17.3850	−	14.2086i	0.615423	−	0.502979i
$799$	11.3140	+	19.5964i	0.400259	+	0.693270i
$800$	−15.3387	+	26.5674i	−0.542306	+	0.939301i
$801$	−46.9647	−	9.54005i	−1.65942	−	0.337081i
$802$	21.5338	+	37.2976i	0.760384	+	1.31702i
$803$	−6.67259	−	11.5573i	−0.235471	−	0.407847i
$804$	−16.2641	−	9.47873i	−0.573592	−	0.334289i
$805$	−6.67391	+	11.5595i	−0.235224	+	0.407421i
$806$	23.0492			0.811872
$807$	−2.86815	+	2.34411i	−0.100964	+	0.0825167i
$808$	8.43035			0.296579
$809$	−21.2595			−0.747445			−0.373722	−	0.927541i	$-0.621919\pi$
$809$	−21.2595			−0.747445			−0.373722	+	0.927541i	$0.621919\pi$
$810$	1.02614	+	8.31501i	0.0360549	+	0.292160i
$811$	5.22670	+	3.01763i	0.183534	+	0.105963i	0.588952	−	0.808168i	$-0.299541\pi$
$811$	5.22670	+	3.01763i	0.183534	+	0.105963i	−0.405418	+	0.914131i	$0.632874\pi$
$812$	0.457447	+	0.792321i	0.0160532	+	0.0278050i
$813$	−6.26179	+	5.11770i	−0.219611	+	0.179486i
$814$	−11.5386			−0.404428
$815$	−4.76091	−	8.24614i	−0.166768	−	0.288850i
$816$	36.6573	−	29.9597i	1.28326	−	1.04880i
$817$	4.27886	+	2.47040i	0.149698	+	0.0864283i
$818$			10.1082i			0.353423i
$819$	3.45627	−	17.0149i	0.120772	−	0.594548i
$820$	−1.09531	−	1.89712i	−0.0382497	−	0.0662505i
$821$	37.9136	+	21.8894i	1.32319	+	0.763947i	0.984237	−	0.176855i	$-0.0565923\pi$
$821$	37.9136	+	21.8894i	1.32319	+	0.763947i	0.338958	+	0.940802i	$0.389926\pi$
$822$	−23.6056	−	28.8828i	−0.823342	−	1.00740i
$823$	−41.3231			−1.44043			−0.720216	−	0.693750i	$-0.755957\pi$
$823$	−41.3231			−1.44043			−0.720216	+	0.693750i	$0.755957\pi$
$824$	3.60724	+	6.24792i	0.125664	+	0.217657i
$825$	3.39170	−	8.95638i	0.118084	−	0.311821i
$826$	−10.8676	−	18.8233i	−0.378133	−	0.654946i
$827$	−6.82478	+	3.94029i	−0.237321	+	0.137017i	−0.613945	−	0.789349i	$-0.710418\pi$
$827$	−6.82478	+	3.94029i	−0.237321	+	0.137017i	0.376624	+	0.926366i	$0.377085\pi$
$828$	−9.31890	−	27.8228i	−0.323854	−	0.966911i
$829$	19.7521			0.686020			0.343010	−	0.939332i	$-0.388554\pi$
$829$	19.7521			0.686020			0.343010	+	0.939332i	$0.388554\pi$
$830$			10.1406i			0.351987i
$831$	7.13677	−	18.8459i	0.247572	−	0.653758i
$832$		−	3.29605i		−	0.114270i
$833$	−27.1397	+	15.6691i	−0.940333	+	0.542902i
$834$	2.74766	+	1.04051i	0.0951438	+	0.0360301i
$835$		−	4.15714i		−	0.143864i
$836$	−1.54993	+	2.68456i	−0.0536055	+	0.0928475i
$837$	21.4797	−	34.0781i	0.742448	−	1.17791i
$838$	−29.2502	−	16.8876i	−1.01043	−	0.583374i
$839$		−	28.1612i		−	0.972231i	−0.873895	−	0.486115i	$-0.838413\pi$
$839$		−	28.1612i		−	0.972231i	0.873895	−	0.486115i	$-0.161587\pi$
$840$	0.619235	+	3.79857i	0.0213656	+	0.131063i
$841$	28.9623			0.998702
$842$	18.8699	+	32.6836i	0.650298	+	1.12635i
$843$	7.52549	−	1.22679i	0.259192	−	0.0422529i
$844$	−3.36523	−	5.82875i	−0.115836	−	0.200634i
$845$	−2.63918	+	4.57120i	−0.0907906	+	0.157254i
$846$	14.6825	−	16.6058i	0.504795	−	0.570920i
$847$		−	34.2278i		−	1.17608i
$848$	−16.0541	+	27.8065i	−0.551299	+	0.954878i
$849$	−21.4406	+	3.49520i	−0.735839	+	0.119955i
$850$	−41.8319	+	24.1517i	−1.43482	+	0.828396i
$851$	−34.5871	+	19.9689i	−1.18563	+	0.684523i
$852$	11.8665	−	9.69834i	0.406538	−	0.332260i
$853$	10.6791	−	18.4968i	0.365646	−	0.633318i	−0.623233	−	0.782036i	$-0.714181\pi$
$853$	10.6791	−	18.4968i	0.365646	−	0.633318i	0.988880	+	0.148718i	$0.0475147\pi$
$854$	−46.6798	−	80.8518i	−1.59735	−	2.76669i
$855$	0.609856	−	3.00226i	0.0208566	−	0.102675i
$856$			3.61967i			0.123718i
$857$	−18.6339	−	32.2749i	−0.636523	−	1.10249i	−0.986190	−	0.165616i	$-0.947039\pi$
$857$	−18.6339	−	32.2749i	−0.636523	−	1.10249i	0.349667	−	0.936874i	$-0.386295\pi$
$858$	0.966608	+	5.92945i	0.0329994	+	0.202428i
$859$	−12.3753	−	21.4347i	−0.422240	−	0.731341i	0.573918	−	0.818913i	$-0.305423\pi$
$859$	−12.3753	−	21.4347i	−0.422240	−	0.731341i	−0.996158	+	0.0875714i	$0.972089\pi$
$860$	1.44877	−	0.836447i	0.0494026	−	0.0285226i
$861$	18.5960	+	7.04212i	0.633749	+	0.239995i
$862$	−56.0134	+	32.3394i	−1.90783	+	1.10148i
$863$			21.9229i			0.746265i	0.927778	+	0.373133i	$0.121716\pi$
$863$			21.9229i			0.746265i	−0.927778	+	0.373133i	$0.878284\pi$
$864$	−28.4522	−	17.9337i	−0.967965	−	0.610117i
$865$	7.52793	−	4.34625i	0.255957	−	0.147777i
$866$	−59.5718	+	34.3938i	−2.02433	+	1.16875i
$867$	24.2945	−	3.96045i	0.825086	−	0.134504i
$868$	−18.2761	+	31.6551i	−0.620330	+	1.07444i
$869$			14.6326i			0.496378i
$870$	0.292588	+	0.110800i	0.00991967	+	0.00375648i
$871$	13.1580	+	2.20011i	0.445842	+	0.0745478i
$872$		−	10.1914i		−	0.345124i
$873$	−21.3737	+	24.1735i	−0.723390	+	0.818150i
$874$			26.8905i			0.909586i
$875$		−	17.6487i		−	0.596634i
$876$	25.9650	−	4.23276i	0.877276	−	0.143012i
$877$	13.8207			0.466692			0.233346	−	0.972394i	$-0.425033\pi$
$877$	13.8207			0.466692			0.233346	+	0.972394i	$0.425033\pi$
$878$	−32.9446	−	57.0616i	−1.11182	−	1.92574i
$879$	−0.268277	−	1.64569i	−0.00904877	−	0.0555078i
$880$	−1.45633	−	2.52244i	−0.0490930	−	0.0850315i
$881$	2.99847	−	1.73116i	0.101021	−	0.0583244i	−0.448638	−	0.893713i	$-0.648091\pi$
$881$	2.99847	−	1.73116i	0.101021	−	0.0583244i	0.549659	+	0.835389i	$0.314758\pi$
$882$	22.9979	+	20.3343i	0.774381	+	0.684690i
$883$	28.6754	+	16.5557i	0.965003	+	0.557145i	0.897709	−	0.440588i	$-0.145230\pi$
$883$	28.6754	+	16.5557i	0.965003	+	0.557145i	0.0672938	+	0.997733i	$0.478564\pi$
$884$	6.04502	−	10.4703i	0.203316	−	0.352154i
$885$	−2.77348	−	1.05029i	−0.0932294	−	0.0353051i
$886$	−35.2385	+	61.0348i	−1.18386	+	2.05050i
$887$			31.2101i			1.04793i	0.851739	+	0.523966i	$0.175548\pi$
$887$			31.2101i			1.04793i	−0.851739	+	0.523966i	$0.824452\pi$
$888$	−4.07823	+	10.7693i	−0.136856	+	0.361394i
$889$	−9.74053	−	5.62370i	−0.326687	−	0.188613i
$890$	12.8784	−	7.43537i	0.431686	−	0.249234i
$891$	9.66747	+	4.09659i	0.323872	+	0.137241i
$892$	−10.0624	+	17.4287i	−0.336916	+	0.583555i
$893$	−7.01940	+	4.05265i	−0.234895	+	0.135617i
$894$	−46.3423	−	17.5494i	−1.54992	−	0.586939i
$895$	−1.60421	+	2.77857i	−0.0536228	+	0.0928774i
$896$	−28.4643	−	16.4339i	−0.950925	−	0.549017i
$897$	13.1590	+	16.1008i	0.439367	+	0.537589i
$898$	33.8160	−	19.5237i	1.12845	−	0.651513i
$899$	−0.752144	−	1.30275i	−0.0250854	−	0.0434492i
$900$	14.1438	+	12.5056i	0.471460	+	0.416854i
$901$	−31.7518	+	18.3319i	−1.05781	+	0.610725i
$902$	−6.88051			−0.229096
$903$	−5.37782	+	14.2011i	−0.178963	+	0.472583i
$904$	−6.99013	−	12.1073i	−0.232488	−	0.402681i
$905$	3.82294	+	6.62152i	0.127079	+	0.220107i
$906$	−14.8257	+	39.1499i	−0.492551	+	1.30067i
$907$	7.21080			0.239431			0.119715	−	0.992808i	$-0.461802\pi$
$907$	7.21080			0.239431			0.119715	+	0.992808i	$0.461802\pi$
$908$	−26.5469	+	15.3268i	−0.880989	+	0.508639i
$909$	4.10566	−	20.2117i	0.136176	−	0.670381i
$910$	2.69377	+	4.66574i	0.0892975	+	0.154668i
$911$	−26.6333	+	15.3767i	−0.882401	+	0.509454i	−0.871449	−	0.490486i	$-0.836819\pi$
$911$	−26.6333	+	15.3767i	−0.882401	+	0.509454i	−0.0109515	+	0.999940i	$0.503486\pi$
$912$	10.7315	+	13.1306i	0.355357	+	0.434799i
$913$	11.0059	+	6.35425i	0.364241	+	0.210295i
$914$	−8.17289	+	14.1559i	−0.270335	+	0.468234i
$915$	−11.9129	−	4.51131i	−0.393829	−	0.149139i
$916$	30.3347	−	17.5138i	1.00229	−	0.578671i
$917$	−21.9997	+	38.1046i	−0.726494	+	1.25832i
$918$	−24.6788	−	46.8543i	−0.814523	−	1.54642i
$919$	−11.8099	+	6.81846i	−0.389573	+	0.224920i	−0.681975	−	0.731375i	$-0.738879\pi$
$919$	−11.8099	+	6.81846i	−0.389573	+	0.224920i	0.292402	+	0.956296i	$0.405545\pi$
$920$	−3.99188	−	2.30471i	−0.131608	−	0.0759840i
$921$	4.63915	−	12.2505i	0.152865	−	0.403668i
$922$			35.7200i			1.17637i
$923$	−5.43044	+	9.40580i	−0.178745	+	0.309596i
$924$	−8.90979	−	3.37405i	−0.293111	−	0.110998i
$925$	12.8486	−	22.2544i	0.422459	−	0.731720i
$926$	−37.5283	−	21.6670i	−1.23326	−	0.712021i
$927$	16.7361	−	5.60555i	0.549686	−	0.184110i
$928$	−1.08768	+	0.627975i	−0.0357050	+	0.0206143i
$929$	18.4197	+	31.9038i	0.604331	+	1.04673i	0.992157	+	0.124999i	$0.0398927\pi$
$929$	18.4197	+	31.9038i	0.604331	+	1.04673i	−0.387826	+	0.921732i	$0.626774\pi$
$930$	2.01113	+	12.3368i	0.0659475	+	0.404541i
$931$	−5.61265	−	9.72140i	−0.183947	−	0.318606i
$932$	31.6981			1.03831
$933$	−9.86430	+	1.60806i	−0.322943	+	0.0526455i
$934$			10.8178i			0.353971i
$935$		−	3.32593i		−	0.108770i
$936$	5.87577	+	1.19356i	0.192056	+	0.0390127i
$937$			40.8513i			1.33455i	0.744810	+	0.667276i	$0.232540\pi$
$937$			40.8513i			1.33455i	−0.744810	+	0.667276i	$0.767460\pi$
$938$	−33.7212	+	40.9181i	−1.10104	+	1.33602i
$939$	−14.8112	−	5.60884i	−0.483344	−	0.183038i
$940$			2.74436i			0.0895110i
$941$	14.7130	−	25.4837i	0.479630	−	0.830744i	−0.520097	−	0.854107i	$-0.674104\pi$
$941$	14.7130	−	25.4837i	0.479630	−	0.830744i	0.999727	+	0.0233632i	$0.00743741\pi$
$942$	−18.3665	+	2.99407i	−0.598413	+	0.0975521i
$943$	−20.6244	+	11.9075i	−0.671623	+	0.387762i
$944$	14.2169	−	8.20815i	0.462722	−	0.267153i
$945$	9.40862	+	0.365324i	0.306063	+	0.0118840i
$946$		−	5.25440i		−	0.170835i
$947$	−20.5462	+	11.8623i	−0.667661	+	0.385474i	−0.795190	−	0.606361i	$-0.792629\pi$
$947$	−20.5462	+	11.8623i	−0.667661	+	0.385474i	0.127529	+	0.991835i	$0.459295\pi$
$948$	−26.9762	−	10.2156i	−0.876147	−	0.331789i
$949$	−16.1460	+	9.32190i	−0.524121	+	0.302602i
$950$	−8.65111	−	14.9842i	−0.280679	−	0.486150i
$951$	−4.54461	−	27.8780i	−0.147369	−	0.904005i
$952$	−12.1635	−	21.0678i	−0.394221	−	0.682811i
$953$			42.2453i			1.36846i	0.729267	+	0.684229i	$0.239861\pi$
$953$			42.2453i			1.36846i	−0.729267	+	0.684229i	$0.760139\pi$
$954$	26.9062	+	23.7899i	0.871122	+	0.770227i
$955$	−2.86450	−	4.96146i	−0.0926930	−	0.160549i
$956$	−7.51492	+	13.0162i	−0.243050	+	0.420975i
$957$	0.303594	−	0.248124i	0.00981378	−	0.00802071i
$958$	30.6852	−	17.7161i	0.991394	−	0.572381i
$959$	−36.3055	+	20.9610i	−1.17236	+	0.676865i
$960$	1.76418	−	0.287593i	0.0569386	−	0.00928202i
$961$	14.5499	−	25.2012i	0.469352	−	0.812941i
$962$			16.1199i			0.519727i
$963$	8.67815	+	1.76281i	0.279649	+	0.0568058i
$964$	−3.82128	+	6.61865i	−0.123075	+	0.213172i
$965$	2.68053	+	4.64281i	0.0862892	+	0.149457i
$966$	−81.5698	+	13.2973i	−2.62446	+	0.427835i
$967$	−8.32249	−	14.4150i	−0.267633	−	0.463554i	0.700617	−	0.713538i	$-0.252908\pi$
$967$	−8.32249	−	14.4150i	−0.267633	−	0.463554i	−0.968250	+	0.249983i	$0.919575\pi$
$968$	11.8199			0.379907
$969$	3.11560	+	19.1120i	0.100087	+	0.613966i
$970$		−	10.0126i		−	0.321485i
$971$	35.3288	+	20.3971i	1.13376	+	0.654574i	0.944877	−	0.327427i	$-0.106181\pi$
$971$	35.3288	+	20.3971i	1.13376	+	0.654574i	0.188879	+	0.982000i	$0.439515\pi$
$972$	−14.3016	+	14.9626i	−0.458724	+	0.479926i
$973$	1.65098	−	2.85958i	0.0529281	−	0.0916741i
$974$		−	5.40514i		−	0.173192i
$975$	−12.5124	−	4.73834i	−0.400719	−	0.151748i
$976$	61.0661	−	35.2565i	1.95468	−	1.12853i
$977$			32.4872i			1.03936i	0.854362	+	0.519678i	$0.173948\pi$
$977$			32.4872i			1.03936i	−0.854362	+	0.519678i	$0.826052\pi$
$978$	20.8794	−	55.1359i	0.667651	−	1.76305i
$979$		−	18.6364i		−	0.595621i
$980$	−3.80075			−0.121410
$981$	−24.4338	−	4.96330i	−0.780112	−	0.158466i
$982$	59.2749	−	34.2224i	1.89154	−	1.09208i
$983$	4.05911	+	7.03059i	0.129466	+	0.224241i	0.923470	−	0.383671i	$-0.125340\pi$
$983$	4.05911	+	7.03059i	0.129466	+	0.224241i	−0.794004	+	0.607912i	$0.792007\pi$
$984$	−2.43186	+	6.42177i	−0.0775250	+	0.204719i
$985$	3.93716	+	6.81937i	0.125448	+	0.217283i
$986$	−1.97756			−0.0629784
$987$	−15.7644	−	19.2886i	−0.501787	−	0.613964i
$988$	3.75045	+	2.16532i	0.119318	+	0.0688881i
$989$	−9.09334	−	15.7501i	−0.289152	−	0.500825i
$990$	−3.08934	+	1.03474i	−0.0981858	+	0.0328860i
$991$			5.63715i			0.179070i	0.995984	+	0.0895350i	$0.0285381\pi$
$991$			5.63715i			0.179070i	−0.995984	+	0.0895350i	$0.971462\pi$
$992$	−43.4555	−	25.0891i	−1.37971	−	0.796578i
$993$	12.3509	−	10.0943i	0.391945	−	0.320333i
$994$	−21.5834	−	37.3835i	−0.684583	−	1.18573i
$995$	−7.52232			−0.238473
$996$	−19.3981	+	15.8539i	−0.614653	+	0.502350i
$997$	−26.0381	−	45.0993i	−0.824635	−	1.42831i	−0.902198	−	0.431323i	$-0.858047\pi$
$997$	−26.0381	−	45.0993i	−0.824635	−	1.42831i	0.0775621	−	0.996988i	$-0.475286\pi$
$998$	11.5362	+	6.66044i	0.365173	+	0.210833i
$999$	23.8332	+	15.0223i	0.754050	+	0.475284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.k.a.365.14	yes	132
9.2	odd	6		603.2.t.a.164.14	yes	132
67.38	odd	6		603.2.t.a.239.14	yes	132
603.38	even	6	inner	603.2.k.a.38.14	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.k.a.38.14	✓	132	603.38	even	6	inner
603.2.k.a.365.14	yes	132	1.1	even	1	trivial
603.2.t.a.164.14	yes	132	9.2	odd	6
603.2.t.a.239.14	yes	132	67.38	odd	6

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.912112 + 1.57982i) q^{2} +(1.09608 + 1.34112i) q^{3} +(-0.663895 - 1.14990i) q^{4} +(-0.255149 + 0.441931i) q^{5} +(-3.11848 + 0.508369i) q^{6} +3.55097i q^{7} -1.22626 q^{8} +(-0.597201 + 2.93996i) q^{9} +O(q^{10})\)	\(q+(-0.912112 + 1.57982i) q^{2} +(1.09608 + 1.34112i) q^{3} +(-0.663895 - 1.14990i) q^{4} +(-0.255149 + 0.441931i) q^{5} +(-3.11848 + 0.508369i) q^{6} +3.55097i q^{7} -1.22626 q^{8} +(-0.597201 + 2.93996i) q^{9} +(-0.465449 - 0.806182i) q^{10} -1.16662 q^{11} +(0.814468 - 2.15075i) q^{12} +1.62982i q^{13} +(-5.60991 - 3.23888i) q^{14} +(-0.872348 + 0.142208i) q^{15} +(2.44628 - 4.23708i) q^{16} +(4.83825 - 2.79337i) q^{17} +(-4.09990 - 3.62504i) q^{18} +(1.00058 + 1.73306i) q^{19} +0.677569 q^{20} +(-4.76227 + 3.89216i) q^{21} +(1.06409 - 1.84306i) q^{22} -7.36612i q^{23} +(-1.34409 - 1.64456i) q^{24} +(2.36980 + 4.10461i) q^{25} +(-2.57483 - 1.48658i) q^{26} +(-4.59742 + 2.42152i) q^{27} +(4.08326 - 2.35747i) q^{28} +0.194041i q^{29} +(0.571014 - 1.50787i) q^{30} +(-6.71378 + 3.87620i) q^{31} +(3.23629 + 5.60542i) q^{32} +(-1.27872 - 1.56458i) q^{33} +10.1915i q^{34} +(-1.56929 - 0.906027i) q^{35} +(3.77713 - 1.26510i) q^{36} +(-2.71090 - 4.69542i) q^{37} -3.65057 q^{38} +(-2.18579 + 1.78642i) q^{39} +(0.312880 - 0.541923i) q^{40} +(-1.61652 - 2.79990i) q^{41} +(-1.80520 - 11.0736i) q^{42} +(2.13818 - 1.23448i) q^{43} +(0.774516 + 1.34150i) q^{44} +(-1.14688 - 1.01405i) q^{45} +(11.6372 + 6.71873i) q^{46} +4.05030i q^{47} +(8.36375 - 1.36344i) q^{48} -5.60939 q^{49} -8.64608 q^{50} +(9.04937 + 3.42691i) q^{51} +(1.87413 - 1.08203i) q^{52} -6.56266 q^{53} +(0.367777 - 9.47180i) q^{54} +(0.297663 - 0.515568i) q^{55} -4.35442i q^{56} +(-1.22752 + 3.24148i) q^{57} +(-0.306551 - 0.176987i) q^{58} +(2.90583 + 1.67768i) q^{59} +(0.742672 + 0.908701i) q^{60} +(12.4814 + 7.20616i) q^{61} -14.1421i q^{62} +(-10.4397 - 2.12064i) q^{63} -2.02233 q^{64} +(-0.720270 - 0.415848i) q^{65} +(3.63810 - 0.593075i) q^{66} +(1.34991 - 8.07327i) q^{67} +(-6.42419 - 3.70901i) q^{68} +(9.87885 - 8.07389i) q^{69} +(2.86273 - 1.65280i) q^{70} +(5.77105 + 3.33192i) q^{71} +(0.732324 - 3.60516i) q^{72} +(5.71957 + 9.90659i) q^{73} +9.89059 q^{74} +(-2.90727 + 7.67718i) q^{75} +(1.32856 - 2.30114i) q^{76} -4.14265i q^{77} +(-0.828551 - 5.08258i) q^{78} -12.5427i q^{79} +(1.24833 + 2.16217i) q^{80} +(-8.28670 - 3.51149i) q^{81} +5.89779 q^{82} +(-9.43396 - 5.44670i) q^{83} +(7.63724 + 2.89215i) q^{84} +2.85090i q^{85} +4.50394i q^{86} +(-0.260233 + 0.212686i) q^{87} +1.43059 q^{88} +15.9746i q^{89} +(2.64811 - 0.886949i) q^{90} -5.78745 q^{91} +(-8.47030 + 4.89033i) q^{92} +(-12.5573 - 4.75534i) q^{93} +(-6.39876 - 3.69432i) q^{94} -1.02119 q^{95} +(-3.97029 + 10.4843i) q^{96} +(9.31484 + 5.37792i) q^{97} +(5.11639 - 8.86184i) q^{98} +(0.696709 - 3.42982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 63 q^{4} + 3 q^{5} + 7 q^{6} + 12 q^{8} - 7 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 63 * q^4 + 3 * q^5 + 7 * q^6 + 12 * q^8 - 7 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 63 q^{4} + 3 q^{5} + 7 q^{6} + 12 q^{8} - 7 q^{9} - 6 q^{11} + 6 q^{12} + 4 q^{15} - 57 q^{16} + 9 q^{17} - 4 q^{19} - 30 q^{20} - 6 q^{21} - 11 q^{24} - 57 q^{25} + 36 q^{26} - 24 q^{28} + 45 q^{30} + 15 q^{32} - q^{33} + 15 q^{35} - q^{36} - 4 q^{37} + 14 q^{39} - 12 q^{40} + 3 q^{41} + 42 q^{42} + 3 q^{43} + 6 q^{44} - 9 q^{45} - 24 q^{46} - 21 q^{48} - 120 q^{49} - 24 q^{50} + 18 q^{52} - 60 q^{53} - 16 q^{54} - 9 q^{57} + 12 q^{58} + 12 q^{59} - 13 q^{60} + 18 q^{61} + 24 q^{63} + 84 q^{64} + 18 q^{65} - 30 q^{66} - 14 q^{67} - 39 q^{68} - 18 q^{69} + 45 q^{70} - 30 q^{71} + 39 q^{72} + 14 q^{73} + 30 q^{74} + 24 q^{75} - 7 q^{76} - 21 q^{78} + 18 q^{80} - 3 q^{81} - 24 q^{82} - 63 q^{83} + 129 q^{84} - 18 q^{87} - 30 q^{88} - 35 q^{90} + 42 q^{91} - 12 q^{92} - 28 q^{93} - 6 q^{94} + 24 q^{95} + 120 q^{96} - 39 q^{97} + 21 q^{98} - 72 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 63 * q^4 + 3 * q^5 + 7 * q^6 + 12 * q^8 - 7 * q^9 - 6 * q^11 + 6 * q^12 + 4 * q^15 - 57 * q^16 + 9 * q^17 - 4 * q^19 - 30 * q^20 - 6 * q^21 - 11 * q^24 - 57 * q^25 + 36 * q^26 - 24 * q^28 + 45 * q^30 + 15 * q^32 - q^33 + 15 * q^35 - q^36 - 4 * q^37 + 14 * q^39 - 12 * q^40 + 3 * q^41 + 42 * q^42 + 3 * q^43 + 6 * q^44 - 9 * q^45 - 24 * q^46 - 21 * q^48 - 120 * q^49 - 24 * q^50 + 18 * q^52 - 60 * q^53 - 16 * q^54 - 9 * q^57 + 12 * q^58 + 12 * q^59 - 13 * q^60 + 18 * q^61 + 24 * q^63 + 84 * q^64 + 18 * q^65 - 30 * q^66 - 14 * q^67 - 39 * q^68 - 18 * q^69 + 45 * q^70 - 30 * q^71 + 39 * q^72 + 14 * q^73 + 30 * q^74 + 24 * q^75 - 7 * q^76 - 21 * q^78 + 18 * q^80 - 3 * q^81 - 24 * q^82 - 63 * q^83 + 129 * q^84 - 18 * q^87 - 30 * q^88 - 35 * q^90 + 42 * q^91 - 12 * q^92 - 28 * q^93 - 6 * q^94 + 24 * q^95 + 120 * q^96 - 39 * q^97 + 21 * q^98 - 72 * q^99

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