LMFDB - Embedded newform 603.2.f.c.565.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(238,603)]

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([2, 2]))

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

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

chi := DirichletCharacter("603.238");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.f (of order $3$, 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:	$128$
Relative dimension:	$64$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			565.12
Character	$\chi$	$=$	603.565
Dual form			603.2.f.c.238.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.943426 - 1.63406i) q^{2} +(0.958630 + 1.44258i) q^{3} +(-0.780103 + 1.35118i) q^{4} +(0.159032 + 0.275451i) q^{5} +(1.45286 - 2.92742i) q^{6} -1.45939 q^{7} -0.829824 q^{8} +(-1.16206 + 2.76579i) q^{9} +O(q^{10})$	\(q+(-0.943426 - 1.63406i) q^{2} +(0.958630 + 1.44258i) q^{3} +(-0.780103 + 1.35118i) q^{4} +(0.159032 + 0.275451i) q^{5} +(1.45286 - 2.92742i) q^{6} -1.45939 q^{7} -0.829824 q^{8} +(-1.16206 + 2.76579i) q^{9} +(0.300070 - 0.519736i) q^{10} -3.03244 q^{11} +(-2.69701 + 0.169920i) q^{12} -1.46001 q^{13} +(1.37682 + 2.38472i) q^{14} +(-0.244907 + 0.493472i) q^{15} +(2.34308 + 4.05834i) q^{16} +(-1.94051 + 3.36106i) q^{17} +(5.61579 - 0.710446i) q^{18} +(1.37446 - 2.38064i) q^{19} -0.496245 q^{20} +(-1.39901 - 2.10528i) q^{21} +(2.86088 + 4.95519i) q^{22} -7.44385 q^{23} +(-0.795494 - 1.19709i) q^{24} +(2.44942 - 4.24252i) q^{25} +(1.37741 + 2.38574i) q^{26} +(-5.10386 + 0.975013i) q^{27} +(1.13847 - 1.97189i) q^{28} -1.85606 q^{29} +(1.03741 - 0.0653605i) q^{30} +(-3.54417 + 6.13868i) q^{31} +(3.59123 - 6.22019i) q^{32} +(-2.90699 - 4.37453i) q^{33} +7.32290 q^{34} +(-0.232089 - 0.401990i) q^{35} +(-2.83056 - 3.72775i) q^{36} +(-1.18608 + 2.05436i) q^{37} -5.18682 q^{38} +(-1.39961 - 2.10617i) q^{39} +(-0.131969 - 0.228576i) q^{40} +(-0.0648970 + 0.112405i) q^{41} +(-2.12029 + 4.27224i) q^{42} +(-0.906506 + 1.57011i) q^{43} +(2.36562 - 4.09737i) q^{44} +(-0.946647 + 0.119759i) q^{45} +(7.02272 + 12.1637i) q^{46} +1.62555 q^{47} +(-3.60832 + 7.27053i) q^{48} -4.87020 q^{49} -9.24337 q^{50} +(-6.70881 + 0.422677i) q^{51} +(1.13896 - 1.97273i) q^{52} -4.89462 q^{53} +(6.40834 + 7.42016i) q^{54} +(-0.482255 - 0.835290i) q^{55} +1.21103 q^{56} +(4.75186 - 0.299383i) q^{57} +(1.75106 + 3.03292i) q^{58} +(-1.17683 - 2.03834i) q^{59} +(-0.475716 - 0.715873i) q^{60} +(6.89393 + 11.9406i) q^{61} +13.3746 q^{62} +(1.69589 - 4.03636i) q^{63} -4.17988 q^{64} +(-0.232188 - 0.402161i) q^{65} +(-4.40572 + 8.87724i) q^{66} +(8.17753 + 0.357744i) q^{67} +(-3.02759 - 5.24395i) q^{68} +(-7.13590 - 10.7383i) q^{69} +(-0.437917 + 0.758495i) q^{70} +(1.28978 + 2.23396i) q^{71} +(0.964304 - 2.29512i) q^{72} +(3.45832 - 5.98999i) q^{73} +4.47593 q^{74} +(8.46824 - 0.533527i) q^{75} +(2.14445 + 3.71430i) q^{76} +4.42550 q^{77} +(-2.12119 + 4.27406i) q^{78} +8.24314 q^{79} +(-0.745250 + 1.29081i) q^{80} +(-6.29924 - 6.42803i) q^{81} +0.244902 q^{82} +(-1.61952 - 2.80509i) q^{83} +(3.93598 - 0.247979i) q^{84} -1.23441 q^{85} +3.42088 q^{86} +(-1.77928 - 2.67751i) q^{87} +2.51639 q^{88} -1.00664 q^{89} +(1.08878 + 1.43389i) q^{90} +2.13071 q^{91} +(5.80698 - 10.0580i) q^{92} +(-12.2531 + 0.771983i) q^{93} +(-1.53358 - 2.65624i) q^{94} +0.874335 q^{95} +(12.4158 - 0.782233i) q^{96} +(0.617090 + 1.06883i) q^{97} +(4.59467 + 7.95820i) q^{98} +(3.52387 - 8.38711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + q^{2} - 3 q^{3} - 65 q^{4} + 5 q^{5} + 3 q^{6} - 8 q^{7} - 36 q^{8} + 5 q^{9}+O(q^{10}) $ 128 * q + q^2 - 3 * q^3 - 65 * q^4 + 5 * q^5 + 3 * q^6 - 8 * q^7 - 36 * q^8 + 5 * q^9	\( 128 q + q^{2} - 3 q^{3} - 65 q^{4} + 5 q^{5} + 3 q^{6} - 8 q^{7} - 36 q^{8} + 5 q^{9} - 2 q^{10} - 30 q^{11} - 10 q^{12} + 12 q^{13} - 8 q^{14} + 12 q^{15} - 59 q^{16} - q^{17} + 8 q^{18} + 8 q^{19} - 6 q^{20} + 12 q^{21} - 20 q^{22} - 18 q^{23} - 39 q^{24} - 57 q^{25} + 8 q^{26} - 24 q^{27} - 16 q^{28} - 2 q^{29} + 23 q^{30} + 16 q^{31} + 27 q^{32} - 3 q^{33} - 4 q^{34} + 11 q^{35} + 45 q^{36} + 2 q^{37} - 4 q^{38} + 8 q^{39} - 6 q^{40} - 7 q^{41} + 18 q^{42} - 11 q^{43} - 18 q^{44} + 3 q^{45} - 4 q^{46} - 24 q^{47} + 71 q^{48} + 104 q^{49} + 44 q^{50} + 42 q^{51} - 6 q^{52} - 60 q^{53} + 48 q^{54} + 10 q^{55} - 28 q^{56} + 29 q^{57} + 6 q^{59} - 7 q^{60} - 6 q^{61} - 22 q^{62} + 20 q^{63} + 56 q^{64} - 26 q^{65} + 54 q^{66} - 19 q^{68} + 8 q^{69} + 25 q^{70} + 8 q^{71} + 11 q^{72} + 22 q^{73} - 42 q^{74} - 44 q^{75} - 5 q^{76} - 70 q^{77} + 15 q^{78} - 30 q^{79} + 14 q^{80} - 63 q^{81} - 24 q^{82} - 3 q^{83} - 77 q^{84} + 24 q^{85} + 20 q^{87} - 6 q^{88} + 116 q^{89} - q^{90} - 10 q^{91} + 4 q^{92} + 26 q^{93} + 4 q^{94} - 180 q^{95} - 56 q^{96} + 19 q^{97} - 49 q^{98} + 4 q^{99}+O(q^{100}) \) 128 * q + q^2 - 3 * q^3 - 65 * q^4 + 5 * q^5 + 3 * q^6 - 8 * q^7 - 36 * q^8 + 5 * q^9 - 2 * q^10 - 30 * q^11 - 10 * q^12 + 12 * q^13 - 8 * q^14 + 12 * q^15 - 59 * q^16 - q^17 + 8 * q^18 + 8 * q^19 - 6 * q^20 + 12 * q^21 - 20 * q^22 - 18 * q^23 - 39 * q^24 - 57 * q^25 + 8 * q^26 - 24 * q^27 - 16 * q^28 - 2 * q^29 + 23 * q^30 + 16 * q^31 + 27 * q^32 - 3 * q^33 - 4 * q^34 + 11 * q^35 + 45 * q^36 + 2 * q^37 - 4 * q^38 + 8 * q^39 - 6 * q^40 - 7 * q^41 + 18 * q^42 - 11 * q^43 - 18 * q^44 + 3 * q^45 - 4 * q^46 - 24 * q^47 + 71 * q^48 + 104 * q^49 + 44 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 48 * q^54 + 10 * q^55 - 28 * q^56 + 29 * q^57 + 6 * q^59 - 7 * q^60 - 6 * q^61 - 22 * q^62 + 20 * q^63 + 56 * q^64 - 26 * q^65 + 54 * q^66 - 19 * q^68 + 8 * q^69 + 25 * q^70 + 8 * q^71 + 11 * q^72 + 22 * q^73 - 42 * q^74 - 44 * q^75 - 5 * q^76 - 70 * q^77 + 15 * q^78 - 30 * q^79 + 14 * q^80 - 63 * q^81 - 24 * q^82 - 3 * q^83 - 77 * q^84 + 24 * q^85 + 20 * q^87 - 6 * q^88 + 116 * q^89 - q^90 - 10 * q^91 + 4 * q^92 + 26 * q^93 + 4 * q^94 - 180 * q^95 - 56 * q^96 + 19 * q^97 - 49 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.943426	−	1.63406i	−0.667103	−	1.15546i	−0.978711	−	0.205245i	$-0.934201\pi$
$2$	−0.943426	−	1.63406i	−0.667103	−	1.15546i	0.311608	−	0.950211i	$-0.399132\pi$
$3$	0.958630	+	1.44258i	0.553465	+	0.832872i
$3$	0.958630	+	1.44258i	0.553465	+	0.832872i
$4$	−0.780103	+	1.35118i	−0.390052	+	0.675589i
$5$	0.159032	+	0.275451i	0.0711213	+	0.123186i	0.899393	−	0.437141i	$-0.144009\pi$
$5$	0.159032	+	0.275451i	0.0711213	+	0.123186i	−0.828272	+	0.560327i	$0.810676\pi$
$6$	1.45286	−	2.92742i	0.593129	−	1.19512i
$7$	−1.45939			−0.551596			−0.275798	−	0.961216i	$-0.588942\pi$
$7$	−1.45939			−0.551596			−0.275798	+	0.961216i	$0.588942\pi$
$8$	−0.829824			−0.293387
$9$	−1.16206	+	2.76579i	−0.387353	+	0.921932i
$10$	0.300070	−	0.519736i	0.0948903	−	0.164355i
$11$	−3.03244			−0.914315			−0.457158	−	0.889386i	$-0.651132\pi$
$11$	−3.03244			−0.914315			−0.457158	+	0.889386i	$0.651132\pi$
$12$	−2.69701	+	0.169920i	−0.778560	+	0.0490518i
$13$	−1.46001			−0.404933			−0.202467	−	0.979289i	$-0.564896\pi$
$13$	−1.46001			−0.404933			−0.202467	+	0.979289i	$0.564896\pi$
$14$	1.37682	+	2.38472i	0.367971	+	0.637344i
$15$	−0.244907	+	0.493472i	−0.0632348	+	0.127414i
$16$	2.34308	+	4.05834i	0.585771	+	1.01459i
$17$	−1.94051	+	3.36106i	−0.470642	+	0.815176i	−0.999436	−	0.0335739i	$-0.989311\pi$
$17$	−1.94051	+	3.36106i	−0.470642	+	0.815176i	0.528794	+	0.848750i	$0.322644\pi$
$18$	5.61579	−	0.710446i	1.32366	−	0.167454i
$19$	1.37446	−	2.38064i	0.315324	−	0.546157i	−0.664182	−	0.747571i	$-0.731220\pi$
$19$	1.37446	−	2.38064i	0.315324	−	0.546157i	0.979506	+	0.201414i	$0.0645535\pi$
$20$	−0.496245			−0.110964
$21$	−1.39901	−	2.10528i	−0.305289	−	0.459409i
$22$	2.86088	+	4.95519i	0.609942	+	1.05645i
$23$	−7.44385			−1.55215			−0.776075	−	0.630640i	$-0.782792\pi$
$23$	−7.44385			−1.55215			−0.776075	+	0.630640i	$0.782792\pi$
$24$	−0.795494	−	1.19709i	−0.162380	−	0.244354i
$25$	2.44942	−	4.24252i	0.489884	−	0.848503i
$26$	1.37741	+	2.38574i	0.270132	+	0.467882i
$27$	−5.10386	+	0.975013i	−0.982238	+	0.187641i
$28$	1.13847	−	1.97189i	0.215151	−	0.372652i
$29$	−1.85606			−0.344662			−0.172331	−	0.985039i	$-0.555130\pi$
$29$	−1.85606			−0.344662			−0.172331	+	0.985039i	$0.555130\pi$
$30$	1.03741	−	0.0653605i	0.189405	−	0.0119331i
$31$	−3.54417	+	6.13868i	−0.636552	+	1.10254i	0.349632	+	0.936887i	$0.386306\pi$
$31$	−3.54417	+	6.13868i	−0.636552	+	1.10254i	−0.986184	+	0.165653i	$0.947027\pi$
$32$	3.59123	−	6.22019i	0.634845	−	1.09958i
$33$	−2.90699	−	4.37453i	−0.506042	−	0.761508i
$34$	7.32290			1.25587
$35$	−0.232089	−	0.401990i	−0.0392302	−	0.0679487i
$36$	−2.83056	−	3.72775i	−0.471759	−	0.621292i
$37$	−1.18608	+	2.05436i	−0.194991	+	0.337734i	−0.946898	−	0.321535i	$-0.895801\pi$
$37$	−1.18608	+	2.05436i	−0.194991	+	0.337734i	0.751907	+	0.659270i	$0.229134\pi$
$38$	−5.18682			−0.841413
$39$	−1.39961	−	2.10617i	−0.224116	−	0.337258i
$40$	−0.131969	−	0.228576i	−0.0208661	−	0.0361411i
$41$	−0.0648970	+	0.112405i	−0.0101352	+	0.0175547i	−0.871049	−	0.491197i	$-0.836560\pi$
$41$	−0.0648970	+	0.112405i	−0.0101352	+	0.0175547i	0.860913	+	0.508752i	$0.169893\pi$
$42$	−2.12029	+	4.27224i	−0.327167	+	0.659221i
$43$	−0.906506	+	1.57011i	−0.138241	+	0.239440i	−0.926831	−	0.375479i	$-0.877478\pi$
$43$	−0.906506	+	1.57011i	−0.138241	+	0.239440i	0.788590	+	0.614919i	$0.210811\pi$
$44$	2.36562	−	4.09737i	0.356630	−	0.617702i
$45$	−0.946647	+	0.119759i	−0.141118	+	0.0178526i
$46$	7.02272	+	12.1637i	1.03544	+	1.79344i
$47$	1.62555			0.237110			0.118555	−	0.992947i	$-0.462174\pi$
$47$	1.62555			0.237110			0.118555	+	0.992947i	$0.462174\pi$
$48$	−3.60832	+	7.27053i	−0.520816	+	1.04941i
$49$	−4.87020			−0.695742
$50$	−9.24337			−1.30721
$51$	−6.70881	+	0.422677i	−0.939422	+	0.0591866i
$52$	1.13896	−	1.97273i	0.157945	−	0.273569i
$53$	−4.89462			−0.672328			−0.336164	−	0.941803i	$-0.609130\pi$
$53$	−4.89462			−0.672328			−0.336164	+	0.941803i	$0.609130\pi$
$54$	6.40834	+	7.42016i	0.872064	+	1.00976i
$55$	−0.482255	−	0.835290i	−0.0650272	−	0.112630i
$56$	1.21103			0.161831
$57$	4.75186	−	0.299383i	0.629400	−	0.0396542i
$58$	1.75106	+	3.03292i	0.229925	+	0.398242i
$59$	−1.17683	−	2.03834i	−0.153211	−	0.265369i	0.779195	−	0.626781i	$-0.215628\pi$
$59$	−1.17683	−	2.03834i	−0.153211	−	0.265369i	−0.932406	+	0.361412i	$0.882295\pi$
$60$	−0.475716	−	0.715873i	−0.0614146	−	0.0924187i
$61$	6.89393	+	11.9406i	0.882678	+	1.52884i	0.848352	+	0.529432i	$0.177595\pi$
$61$	6.89393	+	11.9406i	0.882678	+	1.52884i	0.0343257	+	0.999411i	$0.489072\pi$
$62$	13.3746			1.69858
$63$	1.69589	−	4.03636i	0.213662	−	0.508533i
$64$	−4.17988			−0.522485
$65$	−0.232188	−	0.402161i	−0.0287994	−	0.0498820i
$66$	−4.40572	+	8.87724i	−0.542307	+	1.09271i
$67$	8.17753	+	0.357744i	0.999044	+	0.0437054i
$67$	8.17753	+	0.357744i	0.999044	+	0.0437054i
$68$	−3.02759	−	5.24395i	−0.367150	−	0.635922i
$69$	−7.13590	−	10.7383i	−0.859061	−	1.29274i
$70$	−0.437917	+	0.758495i	−0.0523411	+	0.0906575i
$71$	1.28978	+	2.23396i	0.153068	+	0.265122i	0.932354	−	0.361547i	$-0.117751\pi$
$71$	1.28978	+	2.23396i	0.153068	+	0.265122i	−0.779286	+	0.626669i	$0.784418\pi$
$72$	0.964304	−	2.29512i	0.113644	−	0.270483i
$73$	3.45832	−	5.98999i	0.404766	−	0.701075i	−0.589528	−	0.807748i	$-0.700686\pi$
$73$	3.45832	−	5.98999i	0.404766	−	0.701075i	0.994294	+	0.106673i	$0.0340198\pi$
$74$	4.47593			0.520316
$75$	8.46824	−	0.533527i	0.977828	−	0.0616064i
$76$	2.14445	+	3.71430i	0.245985	+	0.426059i
$77$	4.42550			0.504332
$78$	−2.12119	+	4.27406i	−0.240178	+	0.483942i
$79$	8.24314			0.927426			0.463713	−	0.885985i	$-0.346517\pi$
$79$	8.24314			0.927426			0.463713	+	0.885985i	$0.346517\pi$
$80$	−0.745250	+	1.29081i	−0.0833215	+	0.144317i
$81$	−6.29924	−	6.42803i	−0.699915	−	0.714226i
$82$	0.244902			0.0270449
$83$	−1.61952	−	2.80509i	−0.177765	−	0.307898i	0.763350	−	0.645986i	$-0.223553\pi$
$83$	−1.61952	−	2.80509i	−0.177765	−	0.307898i	−0.941115	+	0.338087i	$0.890220\pi$
$84$	3.93598	−	0.247979i	0.429450	−	0.0270568i
$85$	−1.23441			−0.133891
$86$	3.42088			0.368883
$87$	−1.77928	−	2.67751i	−0.190758	−	0.287060i
$88$	2.51639			0.268248
$89$	−1.00664			−0.106703			−0.0533516	−	0.998576i	$-0.516990\pi$
$89$	−1.00664			−0.106703			−0.0533516	+	0.998576i	$0.516990\pi$
$90$	1.08878	+	1.43389i	0.114768	+	0.151146i
$91$	2.13071			0.223359
$92$	5.80698	−	10.0580i	0.605419	−	1.04862i
$93$	−12.2531	+	0.771983i	−1.27058	+	0.0800509i
$94$	−1.53358	−	2.65624i	−0.158177	−	0.273970i
$95$	0.874335			0.0897049
$96$	12.4158	−	0.782233i	1.26718	−	0.0798363i
$97$	0.617090	+	1.06883i	0.0626559	+	0.108523i	0.895652	−	0.444756i	$-0.146710\pi$
$97$	0.617090	+	1.06883i	0.0626559	+	0.108523i	−0.832996	+	0.553279i	$0.813376\pi$
$98$	4.59467	+	7.95820i	0.464131	+	0.803899i
$99$	3.52387	−	8.38711i	0.354163	−	0.842936i
$100$	3.82160	+	6.61920i	0.382160	+	0.661920i
$101$	15.2168			1.51413			0.757066	−	0.653338i	$-0.226632\pi$
$101$	15.2168			1.51413			0.757066	+	0.653338i	$0.226632\pi$
$102$	7.01995	+	10.5638i	0.695078	+	1.04598i
$103$	−9.89613	+	17.1406i	−0.975095	+	1.68891i	−0.295473	+	0.955351i	$0.595477\pi$
$103$	−9.89613	+	17.1406i	−0.975095	+	1.68891i	−0.679622	+	0.733563i	$0.737856\pi$
$104$	1.21155			0.118802
$105$	0.357414	−	0.720165i	0.0348800	−	0.0702809i
$106$	4.61771	+	7.99811i	0.448512	+	0.776845i
$107$	−13.1742			−1.27360			−0.636798	−	0.771031i	$-0.719741\pi$
$107$	−13.1742			−1.27360			−0.636798	+	0.771031i	$0.719741\pi$
$108$	2.66412	−	7.65683i	0.256355	−	0.736779i
$109$	11.9797			1.14744			0.573722	−	0.819050i	$-0.305499\pi$
$109$	11.9797			1.14744			0.573722	+	0.819050i	$0.305499\pi$
$110$	−0.909943	+	1.57607i	−0.0867597	+	0.150272i
$111$	−4.10058	+	0.258350i	−0.389210	+	0.0245215i
$112$	−3.41946	−	5.92268i	−0.323109	−	0.559641i
$113$	−0.466255	+	0.807577i	−0.0438616	+	0.0759704i	−0.887123	−	0.461534i	$-0.847299\pi$
$113$	−0.466255	+	0.807577i	−0.0438616	+	0.0759704i	0.843261	+	0.537504i	$0.180633\pi$
$114$	−4.97224	−	7.48239i	−0.465693	−	0.700790i
$115$	−1.18381	−	2.05042i	−0.110391	−	0.191203i
$116$	1.44792	−	2.50787i	0.134436	−	0.232850i
$117$	1.69661	−	4.03808i	0.156852	−	0.373321i
$118$	−2.22051	+	3.84603i	−0.204414	+	0.354056i
$119$	2.83195	−	4.90508i	0.259604	−	0.449648i
$120$	0.203230	−	0.409495i	0.0185523	−	0.0373816i
$121$	−1.80430			−0.164028
$122$	13.0078	−	22.5302i	1.17767	−	2.03979i
$123$	−0.224365	+	0.0141357i	−0.0202303	+	0.00127457i
$124$	−5.52964	−	9.57761i	−0.496576	−	0.860095i
$125$	3.14846			0.281607
$126$	−8.19560	+	1.03681i	−0.730122	+	0.0923668i
$127$	−3.50347	−	6.06819i	−0.310883	−	0.538465i	0.667671	−	0.744456i	$-0.267291\pi$
$127$	−3.50347	−	6.06819i	−0.310883	−	0.538465i	−0.978554	+	0.205992i	$0.933958\pi$
$128$	−3.23904	−	5.61019i	−0.286294	−	0.495875i
$129$	−3.13401	+	0.197453i	−0.275935	+	0.0173848i
$130$	−0.438104	+	0.758818i	−0.0384243	+	0.0665528i
$131$	−1.12366	−	1.94623i	−0.0981745	−	0.170043i	0.812755	−	0.582606i	$-0.197967\pi$
$131$	−1.12366	−	1.94623i	−0.0981745	−	0.170043i	−0.910929	+	0.412563i	$0.864634\pi$
$132$	8.17852	−	0.515273i	0.711849	−	0.0448488i
$133$	−2.00587	+	3.47427i	−0.173931	+	0.301258i
$134$	−7.13032	−	13.7001i	−0.615966	−	1.18351i
$135$	−1.08024	−	1.25081i	−0.0929727	−	0.107652i
$136$	1.61028	−	2.78909i	0.138080	−	0.239162i
$137$	−5.03998	+	8.72950i	−0.430595	+	0.745812i	−0.996925	−	0.0783669i	$-0.975029\pi$
$137$	−5.03998	+	8.72950i	−0.430595	+	0.745812i	0.566330	+	0.824179i	$0.308363\pi$
$138$	−10.8149	+	21.7913i	−0.920626	+	1.85500i
$139$	−2.17660	−	3.76997i	−0.184616	−	0.319765i	0.758831	−	0.651288i	$-0.225771\pi$
$139$	−2.17660	−	3.76997i	−0.184616	−	0.319765i	−0.943447	+	0.331523i	$0.892438\pi$
$140$	0.724213			0.0612072
$141$	1.55830	+	2.34497i	0.131232	+	0.197482i
$142$	2.43361	−	4.21514i	0.204224	−	0.353727i
$143$	4.42739			0.370237
$144$	−13.9473	+	1.76446i	−1.16228	+	0.147038i
$145$	−0.295173	−	0.511255i	−0.0245128	−	0.0424574i
$146$	−13.0507			−1.08008
$147$	−4.66871	−	7.02563i	−0.385069	−	0.579464i
$148$	−1.85054	−	3.20522i	−0.152113	−	0.263468i
$149$	2.50795	+	4.34390i	0.205459	+	0.355866i	0.950279	−	0.311400i	$-0.100798\pi$
$149$	2.50795	+	4.34390i	0.205459	+	0.355866i	−0.744820	+	0.667266i	$0.767464\pi$
$150$	−8.86097	−	13.3343i	−0.723495	−	1.08874i
$151$	−12.1779	−	21.0928i	−0.991026	−	1.71651i	−0.611272	−	0.791420i	$-0.709342\pi$
$151$	−12.1779	−	21.0928i	−0.991026	−	1.71651i	−0.379754	−	0.925088i	$-0.623991\pi$
$152$	−1.14056	+	1.97551i	−0.0925120	+	0.160235i
$153$	−7.04101	−	9.27279i	−0.569232	−	0.749661i
$154$	−4.17513	−	7.23153i	−0.336441	−	0.582734i
$155$	−2.25455			−0.181089
$156$	3.93766	−	0.248085i	0.315265	−	0.0198627i
$157$	5.34207			0.426344			0.213172	−	0.977015i	$-0.431621\pi$
$157$	5.34207			0.426344			0.213172	+	0.977015i	$0.431621\pi$
$158$	−7.77679	−	13.4698i	−0.618688	−	1.07160i
$159$	−4.69213	−	7.06087i	−0.372110	−	0.559963i
$160$	2.28448			0.180604
$161$	10.8634			0.856160
$162$	−4.56093	+	16.3577i	−0.358341	+	1.28518i
$163$	−10.6857	−	18.5082i	−0.836969	−	1.44967i	−0.892417	−	0.451211i	$-0.850992\pi$
$163$	−10.6857	−	18.5082i	−0.836969	−	1.44967i	0.0554486	−	0.998462i	$-0.482341\pi$
$164$	−0.101253	−	0.175375i	−0.00790651	−	0.0136945i
$165$	0.742667	−	1.49642i	0.0578165	−	0.116496i
$166$	−3.05579	+	5.29278i	−0.237175	+	0.410799i
$167$	9.93859	−	17.2141i	0.769071	−	1.33207i	−0.168996	−	0.985617i	$-0.554052\pi$
$167$	9.93859	−	17.2141i	0.769071	−	1.33207i	0.938067	−	0.346454i	$-0.112614\pi$
$168$	1.16093	+	1.74701i	0.0895678	+	0.134785i
$169$	−10.8684			−0.836029
$170$	1.16457	+	2.01710i	0.0893188	+	0.154705i
$171$	4.98716	+	6.56793i	0.381378	+	0.502263i
$172$	−1.41434	−	2.44970i	−0.107842	−	0.186788i
$173$	7.79057	+	13.4937i	0.592306	+	1.02590i	0.993921	+	0.110095i	$0.0351156\pi$
$173$	7.79057	+	13.4937i	0.592306	+	1.02590i	−0.401615	+	0.915808i	$0.631551\pi$
$174$	−2.69661	+	5.43348i	−0.204429	+	0.411911i
$175$	−3.57464	+	6.19146i	−0.270218	+	0.468031i
$176$	−7.10526	−	12.3067i	−0.535579	−	0.927651i
$177$	1.81231	−	3.65168i	0.136221	−	0.274477i
$178$	0.949686	+	1.64490i	0.0711819	+	0.123291i
$179$	−6.21370			−0.464434			−0.232217	−	0.972664i	$-0.574598\pi$
$179$	−6.21370			−0.464434			−0.232217	+	0.972664i	$0.574598\pi$
$180$	0.576666	−	1.37251i	0.0429822	−	0.102301i
$181$	−8.70375	−	15.0753i	−0.646945	−	1.12054i	−0.983849	−	0.179002i	$-0.942713\pi$
$181$	−8.70375	−	15.0753i	−0.646945	−	1.12054i	0.336904	−	0.941539i	$-0.390620\pi$
$182$	−2.01017	−	3.48172i	−0.149004	−	0.258082i
$183$	−10.6166	+	21.3917i	−0.784800	+	1.58132i
$184$	6.17709			0.455381
$185$	−0.754501			−0.0554720
$186$	12.8213	+	19.2940i	0.940105	+	1.41470i
$187$	5.88447	−	10.1922i	0.430315	−	0.745328i
$188$	−1.26809	+	2.19640i	−0.0924852	+	0.160189i
$189$	7.44849	−	1.42292i	0.541798	−	0.103502i
$190$	−0.824870	−	1.42872i	−0.0598424	−	0.103650i
$191$	9.11848	+	15.7937i	0.659790	+	1.14279i	0.980670	+	0.195670i	$0.0626880\pi$
$191$	9.11848	+	15.7937i	0.659790	+	1.14279i	−0.320880	+	0.947120i	$0.603979\pi$
$192$	−4.00696	−	6.02980i	−0.289177	−	0.435164i
$193$	5.28535	+	9.15449i	0.380448	+	0.658955i	0.991126	−	0.132924i	$-0.0424365\pi$
$193$	5.28535	+	9.15449i	0.380448	+	0.658955i	−0.610678	+	0.791879i	$0.709103\pi$
$194$	1.16436	−	2.01672i	0.0835959	−	0.144792i
$195$	0.357566	−	0.720473i	0.0256059	−	0.0515941i
$196$	3.79926	−	6.58050i	0.271375	−	0.470036i
$197$	5.87354	+	10.1733i	0.418472	+	0.724815i	0.995786	−	0.0917073i	$-0.0292324\pi$
$197$	5.87354	+	10.1733i	0.418472	+	0.724815i	−0.577314	+	0.816522i	$0.695899\pi$
$198$	−17.0296	+	2.15439i	−1.21024	+	0.153106i
$199$	5.92349	−	10.2598i	0.419905	−	0.727296i	−0.576025	−	0.817432i	$-0.695397\pi$
$199$	5.92349	−	10.2598i	0.419905	−	0.727296i	0.995929	+	0.0901359i	$0.0287301\pi$
$200$	−2.03259	+	3.52054i	−0.143726	+	0.248940i
$201$	7.32315	+	12.1397i	0.516535	+	0.856266i
$202$	−14.3560	−	24.8652i	−1.01008	−	1.74951i
$203$	2.70871			0.190114
$204$	4.66246	−	9.39454i	0.326437	−	0.657749i
$205$	−0.0412828			−0.00288331
$206$	37.3451			2.60195
$207$	8.65020	−	20.5882i	0.601230	−	1.43098i
$208$	−3.42092	−	5.92521i	−0.237198	−	0.410839i
$209$	−4.16798	+	7.21916i	−0.288305	+	0.499360i
$210$	−1.51399	+	0.0953861i	−0.104475	+	0.00658227i
$211$	−6.58277			−0.453177			−0.226588	−	0.973991i	$-0.572757\pi$
$211$	−6.58277			−0.453177			−0.226588	+	0.973991i	$0.572757\pi$
$212$	3.81831	−	6.61351i	0.262243	−	0.454218i
$213$	−1.98624	+	4.00214i	−0.136095	+	0.274222i
$214$	12.4289	+	21.5274i	0.849619	+	1.47158i
$215$	−0.576654			−0.0393274
$216$	4.23530	−	0.809089i	0.288176	−	0.0550515i
$217$	5.17231	−	8.95870i	0.351119	−	0.608156i
$218$	−11.3019	−	19.5755i	−0.765463	−	1.32582i
$219$	11.9563	−	0.753283i	0.807929	−	0.0509022i
$220$	1.50484			0.101456
$221$	2.83316	−	4.90717i	0.190579	−	0.330092i
$222$	4.29075	+	6.45687i	0.287977	+	0.433357i
$223$	−5.97346	+	10.3463i	−0.400013	+	0.692842i	−0.993727	−	0.111834i	$-0.964328\pi$
$223$	−5.97346	+	10.3463i	−0.400013	+	0.692842i	0.593714	+	0.804676i	$0.297661\pi$
$224$	−5.24098	+	9.07765i	−0.350178	+	0.606526i
$225$	8.88756	+	11.7046i	0.592504	+	0.780309i
$226$	1.75951			0.117041
$227$	10.5194			0.698198			0.349099	−	0.937086i	$-0.386488\pi$
$227$	10.5194			0.698198			0.349099	+	0.937086i	$0.386488\pi$
$228$	−3.30243	+	6.65417i	−0.218709	+	0.440683i
$229$	4.06274			0.268474			0.134237	−	0.990949i	$-0.457142\pi$
$229$	4.06274			0.268474			0.134237	+	0.990949i	$0.457142\pi$
$230$	−2.23367	+	3.86884i	−0.147284	+	0.255104i
$231$	4.24241	+	6.38412i	0.279130	+	0.420045i
$232$	1.54021			0.101119
$233$	−8.87762	−	15.3765i	−0.581593	−	1.00735i	−0.995291	−	0.0969338i	$-0.969096\pi$
$233$	−8.87762	−	15.3765i	−0.581593	−	1.00735i	0.413698	−	0.910414i	$-0.364237\pi$
$234$	−8.19910	+	1.03726i	−0.535992	+	0.0678076i
$235$	0.258514	+	0.447759i	0.0168636	+	0.0292086i
$236$	3.67221			0.239040
$237$	7.90212	+	11.8914i	0.513298	+	0.772428i
$238$	−10.6869			−0.692731
$239$	−6.41942	+	11.1188i	−0.415238	+	0.719213i	−0.995453	−	0.0952497i	$-0.969635\pi$
$239$	−6.41942	+	11.1188i	−0.415238	+	0.719213i	0.580215	+	0.814463i	$0.302968\pi$
$240$	−2.57651	+	0.162329i	−0.166313	+	0.0104783i
$241$	−2.92657	+	5.06897i	−0.188517	+	0.326521i	−0.944756	−	0.327775i	$-0.893701\pi$
$241$	−2.92657	+	5.06897i	−0.188517	+	0.326521i	0.756239	+	0.654295i	$0.227035\pi$
$242$	1.70223	+	2.94834i	0.109423	+	0.189527i
$243$	3.23430	−	15.2492i	0.207480	−	0.978239i
$244$	−21.5119			−1.37716
$245$	−0.774517	−	1.34150i	−0.0494821	−	0.0857054i
$246$	0.234770	+	0.353290i	0.0149684	+	0.0225249i
$247$	−2.00673	+	3.47576i	−0.127685	+	0.221157i
$248$	2.94104	−	5.09403i	0.186756	−	0.323471i
$249$	2.49404	−	5.02532i	0.158053	−	0.318467i
$250$	−2.97034	−	5.14478i	−0.187861	−	0.325384i
$251$	−11.1604	+	19.3305i	−0.704441	+	1.22013i	0.262452	+	0.964945i	$0.415469\pi$
$251$	−11.1604	+	19.3305i	−0.704441	+	1.22013i	−0.966893	+	0.255183i	$0.917864\pi$
$252$	4.13087	+	5.44023i	0.260221	+	0.342702i
$253$	22.5730			1.41916
$254$	−6.61052	+	11.4498i	−0.414781	+	0.718422i
$255$	−1.18334	−	1.78073i	−0.0741038	−	0.111514i
$256$	−10.2915	+	17.8254i	−0.643217	+	1.11409i
$257$	10.6249	−	18.4029i	0.662766	−	1.14794i	−0.317120	−	0.948385i	$-0.602716\pi$
$257$	10.6249	−	18.4029i	0.662766	−	1.14794i	0.979886	−	0.199559i	$-0.0639508\pi$
$258$	3.27936	+	4.93489i	0.204164	+	0.307233i
$259$	1.73095	−	2.99810i	0.107556	−	0.186293i
$260$	0.724522			0.0449330
$261$	2.15685	−	5.13349i	0.133506	−	0.317755i
$262$	−2.12018	+	3.67225i	−0.130985	+	0.226873i
$263$	−7.25494	+	12.5659i	−0.447359	+	0.774848i	−0.998213	−	0.0597530i	$-0.980969\pi$
$263$	−7.25494	+	12.5659i	−0.447359	+	0.774848i	0.550854	+	0.834601i	$0.314302\pi$
$264$	2.41229	+	3.63009i	0.148466	+	0.223417i
$265$	−0.778401	−	1.34823i	−0.0478168	−	0.0828211i
$266$	7.56957			0.464120
$267$	−0.964991	−	1.45215i	−0.0590565	−	0.0888701i
$268$	−6.86270	+	10.7702i	−0.419206	+	0.657896i
$269$	18.8421			1.14882			0.574410	−	0.818568i	$-0.305231\pi$
$269$	18.8421			1.14882			0.574410	+	0.818568i	$0.305231\pi$
$270$	−1.02476	+	2.94523i	−0.0623651	+	0.179241i
$271$	20.7396			1.25984			0.629919	−	0.776661i	$-0.283088\pi$
$271$	20.7396			1.25984			0.629919	+	0.776661i	$0.283088\pi$
$272$	−18.1871			−1.10275
$273$	2.04256	+	3.07372i	0.123622	+	0.186030i
$274$	19.0194			1.14900
$275$	−7.42771	+	12.8652i	−0.447908	+	0.775799i
$276$	20.0761	−	1.26486i	1.20844	−	0.0761358i
$277$	−7.54434	+	13.0672i	−0.453296	+	0.785131i	−0.998588	−	0.0531147i	$-0.983085\pi$
$277$	−7.54434	+	13.0672i	−0.453296	+	0.785131i	0.545293	+	0.838246i	$0.316418\pi$
$278$	−4.10691	+	7.11338i	−0.246316	+	0.426632i
$279$	−12.8598	−	16.9360i	−0.769896	−	1.01393i
$280$	0.192593	+	0.333581i	0.0115096	+	0.0199353i
$281$	5.65291	+	9.79112i	0.337224	+	0.584089i	0.983909	−	0.178668i	$-0.0571787\pi$
$281$	5.65291	+	9.79112i	0.337224	+	0.584089i	−0.646685	+	0.762757i	$0.723845\pi$
$282$	2.36170	−	4.75866i	0.140637	−	0.283374i
$283$	−8.06799	−	13.9742i	−0.479592	−	0.830678i	0.520134	−	0.854085i	$-0.325882\pi$
$283$	−8.06799	−	13.9742i	−0.479592	−	0.830678i	−0.999726	+	0.0234070i	$0.992549\pi$
$284$	−4.02463			−0.238818
$285$	0.838164	+	1.26130i	0.0496485	+	0.0747127i
$286$	−4.17691	−	7.23462i	−0.246986	−	0.427792i
$287$	0.0947097	−	0.164042i	0.00559054	−	0.00968309i
$288$	13.0305	+	17.1608i	0.767832	+	1.01121i
$289$	0.968859	+	1.67811i	0.0569917	+	0.0987125i
$290$	−0.556948	+	0.964662i	−0.0327051	+	0.0566469i
$291$	−0.950310	+	1.91481i	−0.0557082	+	0.112248i
$292$	5.39569	+	9.34562i	0.315759	+	0.546911i
$293$	1.40654	+	2.43619i	0.0821707	+	0.142324i	0.904182	−	0.427147i	$-0.140481\pi$
$293$	1.40654	+	2.43619i	0.0821707	+	0.142324i	−0.822011	+	0.569471i	$0.807148\pi$
$294$	−7.07573	+	14.2571i	−0.412665	+	0.831492i
$295$	0.374308	−	0.648321i	0.0217931	−	0.0377467i
$296$	0.984241	−	1.70475i	0.0572078	−	0.0990869i
$297$	15.4771	−	2.95667i	0.898075	−	0.171563i
$298$	4.73213	−	8.19629i	0.274125	−	0.474799i
$299$	10.8681			0.628518
$300$	−5.88521	+	11.8583i	−0.339783	+	0.684640i
$301$	1.32294	−	2.29140i	0.0762531	−	0.132074i
$302$	−22.9779	+	39.7990i	−1.32223	+	2.29017i
$303$	14.5873	+	21.9515i	0.838019	+	1.26108i
$304$	12.8819			0.738830
$305$	−2.19271	+	3.79789i	−0.125554	+	0.217466i
$306$	−8.50964	+	20.2536i	−0.486464	+	1.15782i
$307$	−10.3955	+	18.0055i	−0.593301	+	1.02763i	0.400483	+	0.916304i	$0.368842\pi$
$307$	−10.3955	+	18.0055i	−0.593301	+	1.02763i	−0.993784	+	0.111324i	$0.964491\pi$
$308$	−3.45235	+	5.97964i	−0.196716	+	0.340722i
$309$	−34.2134	+	2.15555i	−1.94633	+	0.122625i
$310$	2.12700	+	3.68406i	0.120805	+	0.209241i
$311$	−0.624601	−	1.08184i	−0.0354179	−	0.0613456i	0.847773	−	0.530359i	$-0.177943\pi$
$311$	−0.624601	−	1.08184i	−0.0354179	−	0.0613456i	−0.883191	+	0.469014i	$0.844610\pi$
$312$	1.16143	+	1.74775i	0.0657529	+	0.0989471i
$313$	1.29699	−	2.24644i	0.0733099	−	0.126977i	−0.827040	−	0.562143i	$-0.809977\pi$
$313$	1.29699	−	2.24644i	0.0733099	−	0.126977i	0.900350	+	0.435166i	$0.143310\pi$
$314$	−5.03985	−	8.72927i	−0.284415	−	0.492621i
$315$	1.38152	−	0.174774i	0.0778399	−	0.00984742i
$316$	−6.43050	+	11.1380i	−0.361744	+	0.626559i
$317$	3.64578	+	6.31468i	0.204768	+	0.354668i	0.950059	−	0.312071i	$-0.101023\pi$
$317$	3.64578	+	6.31468i	0.204768	+	0.354668i	−0.745291	+	0.666739i	$0.767689\pi$
$318$	−7.11122	+	14.3286i	−0.398777	+	0.803510i
$319$	5.62840			0.315130
$320$	−0.664735	−	1.15135i	−0.0371598	−	0.0643627i
$321$	−12.6292	−	19.0048i	−0.704891	−	1.06074i
$322$	−10.2489	−	17.7515i	−0.571146	−	0.989254i
$323$	5.33432	+	9.23931i	0.296809	+	0.514089i
$324$	13.5995	−	3.49687i	0.755527	−	0.194270i
$325$	−3.57617	+	6.19411i	−0.198370	+	0.343587i
$326$	−20.1623	+	34.9222i	−1.11669	+	1.93416i
$327$	11.4841	+	17.2816i	0.635070	+	0.955675i
$328$	0.0538531	−	0.0932763i	0.00297354	−	0.00515032i
$329$	−2.37230			−0.130789
$330$	−3.14590	+	0.198202i	−0.173176	+	0.0109107i
$331$	−15.8965			−0.873750			−0.436875	−	0.899522i	$-0.643915\pi$
$331$	−15.8965			−0.873750			−0.436875	+	0.899522i	$0.643915\pi$
$332$	5.05356			0.277350
$333$	−4.30363	−	5.66775i	−0.235837	−	0.310591i
$334$	−37.5053			−2.05220
$335$	1.20195	+	2.30941i	0.0656694	+	0.126176i
$336$	5.26593	−	10.6105i	0.287280	−	0.578850i
$337$	−15.4824			−0.843383			−0.421691	−	0.906739i	$-0.638563\pi$
$337$	−15.4824			−0.843383			−0.421691	+	0.906739i	$0.638563\pi$
$338$	10.2535	+	17.7596i	0.557717	+	0.965994i
$339$	−1.61196	+	0.101559i	−0.0875495	+	0.00551590i
$340$	0.962968	−	1.66791i	0.0522243	−	0.0904551i
$341$	10.7475	−	18.6152i	0.582009	−	1.00807i
$342$	6.02739	−	14.3457i	0.325924	−	0.775726i
$343$	17.3232			0.935364
$344$	0.752240	−	1.30292i	0.0405581	−	0.0702487i
$345$	1.82305	−	3.67333i	0.0981499	−	0.197766i
$346$	14.6996	−	25.4605i	0.790257	−	1.36877i
$347$	−0.865421	+	1.49895i	−0.0464582	+	0.0804680i	−0.888319	−	0.459226i	$-0.848127\pi$
$347$	−0.865421	+	1.49895i	−0.0464582	+	0.0804680i	0.841861	+	0.539694i	$0.181460\pi$
$348$	5.00582	−	0.315383i	0.268340	−	0.0169063i
$349$	−15.7202	+	27.2282i	−0.841483	+	1.45749i	0.0471569	+	0.998887i	$0.484984\pi$
$349$	−15.7202	+	27.2282i	−0.841483	+	1.45749i	−0.888640	+	0.458605i	$0.848349\pi$
$350$	13.4896			0.721052
$351$	7.45167	−	1.42353i	0.397741	−	0.0759822i
$352$	−10.8902	+	18.8623i	−0.580449	+	1.00537i
$353$	−1.79574	−	3.11032i	−0.0955778	−	0.165546i	0.814272	−	0.580484i	$-0.197137\pi$
$353$	−1.79574	−	3.11032i	−0.0955778	−	0.165546i	−0.909850	+	0.414938i	$0.863803\pi$
$354$	−7.67685	+	0.483666i	−0.408020	+	0.0257066i
$355$	−0.410231	+	0.710541i	−0.0217728	+	0.0377116i
$356$	0.785280	−	1.36014i	0.0416197	−	0.0720875i
$357$	9.79074	−	0.616849i	0.518181	−	0.0326471i
$358$	5.86216	+	10.1536i	0.309825	+	0.536633i
$359$	26.0009			1.37228			0.686139	−	0.727471i	$-0.259304\pi$
$359$	26.0009			1.37228			0.686139	+	0.727471i	$0.259304\pi$
$360$	0.785550	−	0.0993789i	0.0414021	−	0.00523773i
$361$	5.72169	+	9.91026i	0.301142	+	0.521593i
$362$	−16.4227	+	28.4449i	−0.863157	+	1.49503i
$363$	−1.72966	−	2.60285i	−0.0907835	−	0.136614i
$364$	−1.66218	+	2.87897i	−0.0871217	+	0.150899i
$365$	2.19993			0.115150
$366$	44.9713	−	2.83334i	2.35069	−	0.148101i
$367$	−0.482150			−0.0251680			−0.0125840	−	0.999921i	$-0.504006\pi$
$367$	−0.482150			−0.0251680			−0.0125840	+	0.999921i	$0.504006\pi$
$368$	−17.4416	−	30.2097i	−0.909205	−	1.57479i
$369$	−0.235475	−	0.310113i	−0.0122583	−	0.0161438i
$370$	0.711815	+	1.23290i	0.0370055	+	0.0640954i
$371$	7.14314			0.370853
$372$	8.51558	−	17.1583i	0.441512	−	0.889617i
$373$	−11.2721	+	19.5238i	−0.583646	+	1.01091i	0.411396	+	0.911457i	$0.365041\pi$
$373$	−11.2721	+	19.5238i	−0.583646	+	1.01091i	−0.995043	+	0.0994487i	$0.968292\pi$
$374$	−22.2063			−1.14826
$375$	3.01821	+	4.54190i	0.155860	+	0.234543i
$376$	−1.34892			−0.0695651
$377$	2.70987			0.139565
$378$	−9.35223	−	10.8289i	−0.481027	−	0.556977i
$379$	−1.99786	+	3.46040i	−0.102623	+	0.177749i	−0.912765	−	0.408486i	$-0.866057\pi$
$379$	−1.99786	+	3.46040i	−0.102623	+	0.177749i	0.810141	+	0.586235i	$0.199390\pi$
$380$	−0.682072	+	1.18138i	−0.0349896	+	0.0606037i
$381$	5.39530	−	10.8712i	0.276410	−	0.556947i
$382$	17.2052	−	29.8003i	0.880295	−	1.52472i
$383$	−22.0747			−1.12797			−0.563983	−	0.825786i	$-0.690732\pi$
$383$	−22.0747			−1.12797			−0.563983	+	0.825786i	$0.690732\pi$
$384$	4.98809	−	10.0507i	0.254547	−	0.512896i
$385$	0.703796	+	1.21901i	0.0358687	+	0.0621265i
$386$	9.97267	−	17.2732i	0.507595	−	0.879181i
$387$	−3.28920	−	4.33177i	−0.167199	−	0.220196i
$388$	−1.92557			−0.0977562
$389$	−9.87583	−	17.1054i	−0.500725	−	0.867280i	−1.00000		0.000836849i	$-0.999734\pi$
$389$	−9.87583	−	17.1054i	−0.500725	−	0.867280i	0.499275	−	0.866444i	$-0.333600\pi$
$390$	−1.51463	+	0.0954268i	−0.0766964	+	0.00483212i
$391$	14.4449	−	25.0192i	0.730508	−	1.26528i
$392$	4.04141			0.204122
$393$	1.73042	−	3.48668i	0.0872882	−	0.175880i
$394$	11.0825	−	19.1954i	0.558328	−	0.967052i
$395$	1.31092	+	2.27059i	0.0659597	+	0.114246i
$396$	8.58350	+	11.3042i	0.431337	+	0.568057i
$397$	−14.5379			−0.729639			−0.364819	−	0.931078i	$-0.618869\pi$
$397$	−14.5379			−0.729639			−0.364819	+	0.931078i	$0.618869\pi$
$398$	−22.3535			−1.12048
$399$	−6.93480	+	0.436915i	−0.347174	+	0.0218731i
$400$	22.9568			1.14784
$401$	16.0878	+	27.8648i	0.803384	+	1.39150i	0.917376	+	0.398021i	$0.130303\pi$
$401$	16.0878	+	27.8648i	0.803384	+	1.39150i	−0.113992	+	0.993482i	$0.536364\pi$
$402$	12.9281	−	23.4193i	0.644795	−	1.16805i
$403$	5.17452	−	8.96252i	0.257761	−	0.446455i
$404$	−11.8707	+	20.5607i	−0.590590	+	1.02293i
$405$	0.768830	−	2.75740i	0.0382035	−	0.137016i
$406$	−2.55547	−	4.42620i	−0.126826	−	0.219668i
$407$	3.59673	−	6.22972i	0.178283	−	0.308796i
$408$	5.56714	−	0.350748i	0.275614	−	0.0173646i
$409$	5.81936	−	10.0794i	0.287749	−	0.498396i	−0.685523	−	0.728051i	$-0.740426\pi$
$409$	5.81936	−	10.0794i	0.287749	−	0.498396i	0.973272	+	0.229655i	$0.0737598\pi$
$410$	0.0389472	+	0.0674586i	0.00192347	+	0.00333154i
$411$	−17.4245	+	1.09780i	−0.859485	+	0.0541503i
$412$	−15.4400	−	26.7429i	−0.760675	−	1.31753i
$413$	1.71745	+	2.97472i	0.0845103	+	0.146376i
$414$	−41.8031	+	5.28846i	−2.05451	+	0.259914i
$415$	0.515110	−	0.892197i	0.0252858	−	0.0437962i
$416$	−5.24322	+	9.08152i	−0.257070	+	0.445258i
$417$	3.35193	−	6.75392i	0.164145	−	0.330741i
$418$	15.7287			0.769317
$419$	−34.6935			−1.69489			−0.847443	−	0.530886i	$-0.821859\pi$
$419$	−34.6935			−1.69489			−0.847443	+	0.530886i	$0.821859\pi$
$420$	0.694252	+	1.04473i	0.0338760	+	0.0509778i
$421$	1.62628	+	2.81680i	0.0792601	+	0.137283i	0.902931	−	0.429786i	$-0.141411\pi$
$421$	1.62628	+	2.81680i	0.0792601	+	0.137283i	−0.823671	+	0.567068i	$0.808078\pi$
$422$	6.21036	+	10.7567i	0.302315	+	0.523626i
$423$	−1.88898	+	4.49592i	−0.0918453	+	0.218599i
$424$	4.06167			0.197252
$425$	9.50623	+	16.4653i	0.461120	+	0.798683i
$426$	8.41361	−	0.530085i	0.407641	−	0.0256827i
$427$	−10.0609	−	17.4260i	−0.486881	−	0.843303i
$428$	10.2772	−	17.8007i	0.496768	−	0.860428i
$429$	4.24422	+	6.38685i	0.204913	+	0.308360i
$430$	0.544030	+	0.942287i	0.0262354	+	0.0454411i
$431$	−11.3518	−	19.6619i	−0.546797	−	0.947080i	−0.998491	−	0.0549077i	$-0.982514\pi$
$431$	−11.3518	−	19.6619i	−0.546797	−	0.947080i	0.451694	−	0.892173i	$-0.350820\pi$
$432$	−15.9157	−	18.4287i	−0.765744	−	0.886649i
$433$	−4.82122	−	8.35060i	−0.231693	−	0.401304i	0.726613	−	0.687047i	$-0.241093\pi$
$433$	−4.82122	−	8.35060i	−0.231693	−	0.401304i	−0.958306	+	0.285742i	$0.907760\pi$
$434$	−19.5188			−0.936930
$435$	0.454563	−	0.915914i	0.0217946	−	0.0439147i
$436$	−9.34538	+	16.1867i	−0.447563	+	0.775201i
$437$	−10.2313	+	17.7212i	−0.489430	+	0.847718i
$438$	−12.5108	−	18.8266i	−0.597787	−	0.899570i
$439$	17.4869	+	30.2882i	0.834604	+	1.44558i	0.894353	+	0.447363i	$0.147637\pi$
$439$	17.4869	+	30.2882i	0.834604	+	1.44558i	−0.0597489	+	0.998213i	$0.519030\pi$
$440$	0.400187	+	0.693144i	0.0190782	+	0.0330443i
$441$	5.65945	−	13.4700i	0.269498	−	0.641427i
$442$	−10.6915			−0.508542
$443$	−36.2604			−1.72278			−0.861392	−	0.507941i	$-0.830407\pi$
$443$	−36.2604			−1.72278			−0.861392	+	0.507941i	$0.830407\pi$
$444$	2.84980	−	5.74216i	0.135246	−	0.272511i
$445$	−0.160087	−	0.277279i	−0.00758886	−	0.0131443i
$446$	22.5421			1.06740
$447$	−3.86222	+	7.78211i	−0.182677	+	0.368081i
$448$	6.10006			0.288201
$449$	2.78797	+	4.82891i	0.131573	+	0.227890i	0.924283	−	0.381708i	$-0.124664\pi$
$449$	2.78797	+	4.82891i	0.131573	+	0.227890i	−0.792710	+	0.609598i	$0.791331\pi$
$450$	10.7413	−	25.5653i	0.506352	−	1.20516i
$451$	0.196796	−	0.340861i	0.00926677	−	0.0160505i
$452$	−0.727454	−	1.25999i	−0.0342165	−	0.0592648i
$453$	18.7539	−	37.7878i	0.881134	−	1.77543i
$454$	−9.92428	−	17.1894i	−0.465770	−	0.806737i
$455$	0.338852	+	0.586908i	0.0158856	+	0.0275147i
$456$	−3.94321	+	0.248435i	−0.184658	+	0.0116340i
$457$	−11.2929			−0.528260			−0.264130	−	0.964487i	$-0.585085\pi$
$457$	−11.2929			−0.528260			−0.264130	+	0.964487i	$0.585085\pi$
$458$	−3.83290	−	6.63877i	−0.179099	−	0.310209i
$459$	6.62700	−	19.0464i	0.309322	−	0.889009i
$460$	3.69398			0.172233
$461$	8.58172	−	14.8640i	0.399691	−	0.692284i	−0.593997	−	0.804467i	$-0.702451\pi$
$461$	8.58172	−	14.8640i	0.399691	−	0.692284i	0.993688	+	0.112183i	$0.0357843\pi$
$462$	6.42965	−	12.9553i	0.299134	−	0.602735i
$463$	−38.8777			−1.80680			−0.903401	−	0.428798i	$-0.858937\pi$
$463$	−38.8777			−1.80680			−0.903401	+	0.428798i	$0.858937\pi$
$464$	−4.34891	−	7.53253i	−0.201893	−	0.349689i
$465$	−2.16127	−	3.25236i	−0.100227	−	0.150824i
$466$	−16.7508	+	29.0132i	−0.775964	+	1.34401i
$467$	−13.3944	+	23.1997i	−0.619817	+	1.07355i	0.369702	+	0.929151i	$0.379460\pi$
$467$	−13.3944	+	23.1997i	−0.619817	+	1.07355i	−0.989519	+	0.144404i	$0.953873\pi$
$468$	4.13263	+	5.44255i	0.191031	+	0.251582i
$469$	−11.9342	−	0.522086i	−0.551069	−	0.0241077i
$470$	0.487777	−	0.844854i	0.0224995	−	0.0389702i
$471$	5.12107	+	7.70635i	0.235966	+	0.355090i
$472$	0.976565	+	1.69146i	0.0449500	+	0.0778557i
$473$	2.74893	−	4.76128i	0.126396	−	0.218924i
$474$	11.9762	−	24.1312i	0.550083	−	1.10838i
$475$	−6.73328	−	11.6624i	−0.308944	−	0.535107i
$476$	4.41843	+	7.65294i	0.202518	+	0.350772i
$477$	5.68784	−	13.5375i	0.260428	−	0.619840i
$478$	24.2250			1.10803
$479$	1.00095	+	1.73370i	0.0457346	+	0.0792146i	0.887987	−	0.459870i	$-0.152104\pi$
$479$	1.00095	+	1.73370i	0.0457346	+	0.0792146i	−0.842252	+	0.539084i	$0.818770\pi$
$480$	2.18997	+	3.29554i	0.0999580	+	0.150420i
$481$	1.73169	−	2.99938i	0.0789583	−	0.136760i
$482$	11.0440			0.503041
$483$	10.4140	+	15.6714i	0.473854	+	0.713072i
$484$	1.40754	−	2.43794i	0.0639792	−	0.110815i
$485$	−0.196274	+	0.339956i	−0.00891234	+	0.0154366i
$486$	−27.9695	+	9.10149i	−1.26872	+	0.412852i
$487$	−11.2879	+	19.5513i	−0.511505	+	0.885953i	0.488406	+	0.872617i	$0.337579\pi$
$487$	−11.2879	+	19.5513i	−0.511505	+	0.885953i	−0.999911	+	0.0133366i	$0.995755\pi$
$488$	−5.72075	−	9.90864i	−0.258966	−	0.448543i
$489$	16.4558	−	33.1574i	0.744159	−	1.49943i
$490$	−1.46140	+	2.53121i	−0.0660192	+	0.114349i
$491$	7.46622	+	12.9319i	0.336946	+	0.583607i	0.983857	−	0.178958i	$-0.0572728\pi$
$491$	7.46622	+	12.9319i	0.336946	+	0.583607i	−0.646911	+	0.762566i	$0.723939\pi$
$492$	0.155928	−	0.314184i	0.00702977	−	0.0141645i
$493$	3.60170	−	6.23833i	0.162213	−	0.280960i
$494$	7.57280			0.340716
$495$	2.87065	−	0.363162i	0.129026	−	0.0163229i
$496$	−33.2172			−1.49149
$497$	−1.88228	−	3.26020i	−0.0844318	−	0.146240i
$498$	−10.5646	+	0.665605i	−0.473412	+	0.0298265i
$499$	8.45885			0.378670			0.189335	−	0.981913i	$-0.439367\pi$
$499$	8.45885			0.378670			0.189335	+	0.981913i	$0.439367\pi$
$500$	−2.45613	+	4.25414i	−0.109841	+	0.190251i
$501$	34.3602	−	2.16480i	1.53510	−	0.0967162i
$502$	42.1162			1.87974
$503$	−6.54928	−	11.3437i	−0.292018	−	0.505790i	0.682269	−	0.731102i	$-0.260993\pi$
$503$	−6.54928	−	11.3437i	−0.292018	−	0.505790i	−0.974287	+	0.225311i	$0.927660\pi$
$504$	−1.40729	+	3.34947i	−0.0626857	+	0.149197i
$505$	2.41996	+	4.19150i	0.107687	+	0.186519i
$506$	−21.2960	−	36.8857i	−0.946722	−	1.63977i
$507$	−10.4187	−	15.6785i	−0.462713	−	0.696306i
$508$	10.9323			0.485041
$509$	10.6080	+	18.3735i	0.470190	+	0.814393i	0.999419	−	0.0340860i	$-0.0108520\pi$
$509$	10.6080	+	18.3735i	0.470190	+	0.814393i	−0.529229	+	0.848479i	$0.677519\pi$
$510$	−1.79343	+	3.61364i	−0.0794145	+	0.160015i
$511$	−5.04702	+	8.74169i	−0.223267	+	0.386710i
$512$	25.8808			1.14378
$513$	−4.69391	+	13.4906i	−0.207241	+	0.595624i
$514$	−40.0954			−1.76853
$515$	−6.29520			−0.277400
$516$	2.17806	−	4.38865i	0.0958838	−	0.193199i
$517$	−4.92937			−0.216793
$518$	−6.53210			−0.287004
$519$	−11.9974	+	24.1739i	−0.526626	+	1.06112i
$520$	0.192675	+	0.333723i	0.00844936	+	0.0146347i
$521$	21.5778			0.945341			0.472670	−	0.881239i	$-0.343290\pi$
$521$	21.5778			0.945341			0.472670	+	0.881239i	$0.343290\pi$
$522$	−10.4233	+	1.31863i	−0.456214	+	0.0577150i
$523$	−14.1779	+	24.5568i	−0.619956	+	1.07379i	0.369538	+	0.929216i	$0.379516\pi$
$523$	−14.1779	+	24.5568i	−0.619956	+	1.07379i	−0.989493	+	0.144579i	$0.953817\pi$
$524$	3.50628			0.153173
$525$	−12.3584	+	0.778621i	−0.539366	+	0.0339818i
$526$	27.3780			1.19374
$527$	−13.7550	−	23.8243i	−0.599176	−	1.03780i
$528$	10.9420	−	22.0474i	0.476190	−	0.959492i
$529$	32.4110			1.40917
$530$	−1.46873	+	2.54391i	−0.0637974	+	0.110500i
$531$	7.00517	−	0.886214i	0.303998	−	0.0384584i
$532$	−3.12958	−	5.42059i	−0.135684	−	0.235012i
$533$	0.0947501	−	0.164112i	0.00410408	−	0.00710848i
$534$	−1.46250	+	2.94685i	−0.0632887	+	0.127523i
$535$	−2.09512	−	3.62885i	−0.0905797	−	0.156889i
$536$	−6.78591	−	0.296864i	−0.293107	−	0.0128226i
$537$	−5.95664	−	8.96375i	−0.257048	−	0.386814i
$538$	−17.7761	−	30.7891i	−0.766381	−	1.32741i
$539$	14.7686			0.636128
$540$	2.53277	−	0.483846i	0.108993	−	0.0208214i
$541$	20.8232			0.895260			0.447630	−	0.894219i	$-0.352268\pi$
$541$	20.8232			0.895260			0.447630	+	0.894219i	$0.352268\pi$
$542$	−19.5662	−	33.8897i	−0.840441	−	1.45569i
$543$	13.4037	−	27.0075i	0.575206	−	1.15900i
$544$	13.9376	+	24.1406i	0.597570	+	1.03502i
$545$	1.90515	+	3.29982i	0.0816077	+	0.141349i
$546$	3.09564	−	6.23750i	0.132481	−	0.266940i
$547$	−9.17858			−0.392448			−0.196224	−	0.980559i	$-0.562868\pi$
$547$	−9.17858			−0.392448			−0.196224	+	0.980559i	$0.562868\pi$
$548$	−7.86341	−	13.6198i	−0.335908	−	0.581810i
$549$	−41.0365	+	5.19148i	−1.75140	+	0.221567i
$550$	28.0300			1.19520
$551$	−2.55109	+	4.41862i	−0.108680	+	0.188240i
$552$	5.92154	+	8.91093i	0.252037	+	0.379274i
$553$	−12.0299			−0.511564
$554$	28.4701			1.20958
$555$	−0.723287	−	1.08843i	−0.0307018	−	0.0462011i
$556$	6.79188			0.288040
$557$	−6.48032	−	11.2243i	−0.274580	−	0.475587i	0.695449	−	0.718576i	$-0.255206\pi$
$557$	−6.48032	−	11.2243i	−0.274580	−	0.475587i	−0.970029	+	0.242989i	$0.921872\pi$
$558$	−15.5421	+	36.9915i	−0.657950	+	1.56598i
$559$	1.32351	−	2.29238i	0.0559783	−	0.0969573i
$560$	1.08761	−	1.88379i	0.0459598	−	0.0796047i
$561$	20.3441	−	1.28174i	0.858928	−	0.0541152i
$562$	10.6662	−	18.4744i	0.449926	−	0.779295i
$563$	−20.4144	−	35.3588i	−0.860365	−	1.49020i	−0.871577	−	0.490258i	$-0.836903\pi$
$563$	−20.4144	−	35.3588i	−0.860365	−	1.49020i	0.0112128	−	0.999937i	$-0.496431\pi$
$564$	−4.38411	+	0.276213i	−0.184604	+	0.0116307i
$565$	−0.296598			−0.0124780
$566$	−15.2231	+	26.3672i	−0.639874	+	1.10829i
$567$	9.19302	+	9.38097i	0.386070	+	0.393964i
$568$	−1.07029	−	1.85379i	−0.0449082	−	0.0777834i
$569$	−13.5100			−0.566367			−0.283183	−	0.959066i	$-0.591391\pi$
$569$	−13.5100			−0.566367			−0.283183	+	0.959066i	$0.591391\pi$
$570$	1.27029	−	2.55955i	0.0532066	−	0.107208i
$571$	16.9031	−	29.2770i	0.707371	−	1.22520i	−0.258458	−	0.966023i	$-0.583214\pi$
$571$	16.9031	−	29.2770i	0.707371	−	1.22520i	0.965829	−	0.259180i	$-0.0834524\pi$
$572$	−3.45382	+	5.98219i	−0.144411	+	0.250128i
$573$	−14.0423	+	28.2944i	−0.586627	+	1.18201i
$574$	−0.357406			−0.0149178
$575$	−18.2331	+	31.5807i	−0.760373	+	1.31700i
$576$	4.85727	−	11.5607i	0.202386	−	0.481696i
$577$	19.6536	+	34.0411i	0.818192	+	1.41715i	0.907013	+	0.421103i	$0.138357\pi$
$577$	19.6536	+	34.0411i	0.818192	+	1.41715i	−0.0888209	+	0.996048i	$0.528310\pi$
$578$	1.82809	−	3.16635i	0.0760386	−	0.131703i
$579$	−8.13937	+	16.4003i	−0.338261	+	0.681573i
$580$	0.921063			0.0382450
$581$	2.36350	+	4.09370i	0.0980545	+	0.169835i
$582$	4.02547	−	0.253617i	0.166861	−	0.0105128i
$583$	14.8426			0.614720
$584$	−2.86980	+	4.97063i	−0.118753	+	0.205686i
$585$	1.38211	−	0.174849i	0.0571433	−	0.00722912i
$586$	2.65392	−	4.59673i	0.109633	−	0.189889i
$587$	21.8131	+	37.7815i	0.900325	+	1.55941i	0.827073	+	0.562094i	$0.190004\pi$
$587$	21.8131	+	37.7815i	0.900325	+	1.55941i	0.0732515	+	0.997314i	$0.476662\pi$
$588$	13.1350	−	0.827545i	0.541677	−	0.0341274i
$589$	9.74267	+	16.8748i	0.401440	+	0.695314i
$590$	−1.41253			−0.0581528
$591$	−9.04517	+	18.2254i	−0.372069	+	0.749694i
$592$	−11.1164			−0.456880
$593$	12.5834	−	21.7950i	0.516737	−	0.895014i	−0.483074	−	0.875579i	$-0.660480\pi$
$593$	12.5834	−	21.7950i	0.516737	−	0.895014i	0.999811	−	0.0194349i	$-0.00618670\pi$
$594$	−19.4329	−	22.5012i	−0.797342	−	0.923235i
$595$	1.80148			0.0738535
$596$	−7.82585			−0.320559
$597$	20.4790	−	1.29024i	0.838148	−	0.0528060i
$598$	−10.2532	−	17.7591i	−0.419286	−	0.726224i
$599$	−10.4122	+	18.0345i	−0.425431	+	0.736869i	−0.996461	−	0.0840610i	$-0.973211\pi$
$599$	−10.4122	+	18.0345i	−0.425431	+	0.736869i	0.571029	+	0.820930i	$0.306544\pi$
$600$	−7.02715	+	0.442733i	−0.286882	+	0.0180745i
$601$	−3.18150	−	5.51052i	−0.129776	−	0.224779i	0.793814	−	0.608161i	$-0.208093\pi$
$601$	−3.18150	−	5.51052i	−0.129776	−	0.224779i	−0.923590	+	0.383382i	$0.874759\pi$
$602$	−4.99239			−0.203474
$603$	−10.4922	+	22.2017i	−0.427276	+	0.904121i
$604$	38.0002			1.54621
$605$	−0.286942	−	0.496998i	−0.0116658	−	0.0202058i
$606$	22.1080	−	44.5461i	0.898076	−	1.80956i
$607$	−2.69227	+	4.66315i	−0.109276	+	0.189271i	−0.915477	−	0.402370i	$-0.868187\pi$
$607$	−2.69227	+	4.66315i	−0.109276	+	0.189271i	0.806201	+	0.591641i	$0.201520\pi$
$608$	−9.87203	−	17.0989i	−0.400364	−	0.693450i
$609$	2.59665	+	3.90752i	0.105222	+	0.158341i
$610$	8.27464			0.335030
$611$	−2.37331			−0.0960138
$612$	18.0219	−	2.27993i	0.728493	−	0.0921607i
$613$	−10.2710	+	17.7899i	−0.414843	+	0.718529i	−0.995412	−	0.0956823i	$-0.969497\pi$
$613$	−10.2710	+	17.7899i	−0.414843	+	0.718529i	0.580569	+	0.814211i	$0.302830\pi$
$614$	39.2294			1.58317
$615$	−0.0395749	−	0.0595536i	−0.00159581	−	0.00240143i
$616$	−3.67239			−0.147965
$617$	−0.874913	−	1.51539i	−0.0352227	−	0.0610074i	0.847877	−	0.530193i	$-0.177881\pi$
$617$	−0.874913	−	1.51539i	−0.0352227	−	0.0610074i	−0.883099	+	0.469186i	$0.844547\pi$
$618$	35.8001	+	53.8731i	1.44009	+	2.16709i
$619$	−5.40267	−	9.35770i	−0.217152	−	0.376118i	0.736784	−	0.676128i	$-0.236343\pi$
$619$	−5.40267	−	9.35770i	−0.217152	−	0.376118i	−0.953936	+	0.300010i	$0.903010\pi$
$620$	1.75878	−	3.04629i	0.0706342	−	0.122342i
$621$	37.9924	−	7.25785i	1.52458	−	0.291248i
$622$	−1.17853	+	2.04127i	−0.0472547	+	0.0818476i
$623$	1.46907			0.0588570
$624$	5.26818	−	10.6150i	0.210896	−	0.424941i
$625$	−11.7464	−	20.3453i	−0.469855	−	0.813813i
$626$	−4.89444			−0.195621
$627$	−14.4097	+	0.907861i	−0.575470	+	0.0362565i
$628$	−4.16737	+	7.21810i	−0.166296	+	0.288033i
$629$	−4.60321	−	7.97299i	−0.183542	−	0.317904i
$630$	−1.58896	−	2.09260i	−0.0633055	−	0.0833713i
$631$	−10.3021	+	17.8437i	−0.410120	+	0.710348i	−0.994902	−	0.100842i	$-0.967846\pi$
$631$	−10.3021	+	17.8437i	−0.410120	+	0.710348i	0.584783	+	0.811190i	$0.301180\pi$
$632$	−6.84036			−0.272095
$633$	−6.31044	−	9.49616i	−0.250818	−	0.377438i
$634$	6.87905	−	11.9149i	0.273202	−	0.473200i
$635$	1.11433	−	1.93007i	0.0442207	−	0.0765925i
$636$	13.2008	−	0.831696i	0.523447	−	0.0329789i
$637$	7.11052			0.281729
$638$	−5.30997	−	9.19715i	−0.210224	−	0.364119i
$639$	−7.67746	+	0.971265i	−0.303716	+	0.0384227i
$640$	1.03022	−	1.78440i	0.0407232	−	0.0705346i
$641$	43.3860			1.71364			0.856821	−	0.515613i	$-0.172436\pi$
$641$	43.3860			1.71364			0.856821	+	0.515613i	$0.172436\pi$
$642$	−19.1403	+	38.5664i	−0.755407	+	1.52209i
$643$	−3.74673	−	6.48953i	−0.147757	−	0.255922i	0.782641	−	0.622473i	$-0.213872\pi$
$643$	−3.74673	−	6.48953i	−0.147757	−	0.255922i	−0.930398	+	0.366551i	$0.880539\pi$
$644$	−8.47461	+	14.6785i	−0.333947	+	0.578412i
$645$	−0.552797	−	0.831867i	−0.0217664	−	0.0327547i
$646$	10.0651	−	17.4332i	0.396005	−	0.685900i
$647$	−15.9329	+	27.5966i	−0.626386	+	1.08493i	0.361885	+	0.932223i	$0.382133\pi$
$647$	−15.9329	+	27.5966i	−0.626386	+	1.08493i	−0.988271	+	0.152710i	$0.951200\pi$
$648$	5.22726	+	5.33414i	0.205346	+	0.209545i
$649$	3.56868	+	6.18113i	0.140083	+	0.242631i
$650$	13.4954			0.529333
$651$	17.8819	−	1.12662i	0.700849	−	0.0441557i
$652$	33.3438			1.30584
$653$	4.39491			0.171986			0.0859932	−	0.996296i	$-0.472594\pi$
$653$	4.39491			0.171986			0.0859932	+	0.996296i	$0.472594\pi$
$654$	17.4048	−	35.0696i	0.680583	−	1.37133i
$655$	0.357395	−	0.619027i	0.0139646	−	0.0241874i
$656$	−0.608236			−0.0237476
$657$	12.5483	+	16.5257i	0.489556	+	0.644730i
$658$	2.23808	+	3.87648i	0.0872496	+	0.151121i
$659$	26.4937			1.03205			0.516023	−	0.856575i	$-0.327412\pi$
$659$	26.4937			1.03205			0.516023	+	0.856575i	$0.327412\pi$
$660$	1.44258	+	2.17084i	0.0561523	+	0.0844999i
$661$	−4.26876	−	7.39371i	−0.166036	−	0.287582i	0.770987	−	0.636851i	$-0.219763\pi$
$661$	−4.26876	−	7.39371i	−0.166036	−	0.287582i	−0.937023	+	0.349269i	$0.886430\pi$
$662$	14.9972	+	25.9758i	0.582881	+	1.00958i
$663$	9.79492	−	0.617112i	0.380403	−	0.0239666i
$664$	1.34391	+	2.32773i	0.0521540	+	0.0903334i
$665$	−1.27599			−0.0494808
$666$	−5.20129	+	12.3795i	−0.201546	+	0.479696i
$667$	13.8163			0.534968
$668$	15.5063	+	26.8576i	0.599955	+	1.03915i
$669$	−20.6517	+	1.30113i	−0.798442	+	0.0503044i
$670$	2.63976	−	4.14281i	0.101983	−	0.160051i
$671$	−20.9054	−	36.2093i	−0.807046	−	1.39784i
$672$	−18.1194	+	1.14158i	−0.698970	+	0.0440374i
$673$	3.78897	−	6.56268i	0.146054	−	0.252973i	−0.783712	−	0.621125i	$-0.786676\pi$
$673$	3.78897	−	6.56268i	0.146054	−	0.252973i	0.929766	+	0.368152i	$0.120009\pi$
$674$	14.6065	+	25.2993i	0.562623	+	0.974491i
$675$	−8.36497	+	24.0414i	−0.321968	+	0.925354i
$676$	8.47846	−	14.6851i	0.326095	−	0.564812i
$677$	−0.521765			−0.0200531			−0.0100265	−	0.999950i	$-0.503192\pi$
$677$	−0.521765			−0.0200531			−0.0100265	+	0.999950i	$0.503192\pi$
$678$	1.68671	+	2.53822i	0.0647779	+	0.0974799i
$679$	−0.900571	−	1.55984i	−0.0345608	−	0.0598610i
$680$	1.02434			0.0392818
$681$	10.0842	+	15.1751i	0.386428	+	0.581510i
$682$	−40.5578			−1.55304
$683$	−8.19703	+	14.1977i	−0.313651	+	0.543259i	−0.979150	−	0.203140i	$-0.934885\pi$
$683$	−8.19703	+	14.1977i	−0.313651	+	0.543259i	0.665499	+	0.746399i	$0.268219\pi$
$684$	−12.7650	+	1.61488i	−0.488080	+	0.0617464i
$685$	−3.20607			−0.122498
$686$	−16.3431	−	28.3071i	−0.623984	−	1.08077i
$687$	3.89467	+	5.86082i	0.148591	+	0.223604i
$688$	−8.49608			−0.323910
$689$	7.14619			0.272248
$690$	−7.72236	+	0.486534i	−0.293985	+	0.0185220i
$691$	−10.7484			−0.408889			−0.204445	−	0.978878i	$-0.565539\pi$
$691$	−10.7484			−0.408889			−0.204445	+	0.978878i	$0.565539\pi$
$692$	−24.3098			−0.924120
$693$	−5.14269	+	12.2400i	−0.195355	+	0.464960i
$694$	3.26584			0.123970
$695$	0.692296	−	1.19909i	0.0262603	−	0.0454842i
$696$	1.47649	+	2.22187i	0.0559661	+	0.0842196i
$697$	−0.251866	−	0.436245i	−0.00954011	−	0.0165240i
$698$	59.3234			2.24542
$699$	13.6714	−	27.5470i	0.517101	−	1.04192i
$700$	−5.57718	−	9.65997i	−0.210798	−	0.365112i
$701$	−0.836919	−	1.44959i	−0.0316100	−	0.0547501i	0.849788	−	0.527125i	$-0.176730\pi$
$701$	−0.836919	−	1.44959i	−0.0316100	−	0.0547501i	−0.881398	+	0.472375i	$0.843397\pi$
$702$	−9.35622	−	10.8335i	−0.353128	−	0.408884i
$703$	3.26046	+	5.64728i	0.122971	+	0.212991i
$704$	12.6752			0.477716
$705$	−0.398108	+	0.802161i	−0.0149936	+	0.0302111i
$706$	−3.38830	+	5.86871i	−0.127520	+	0.220872i
$707$	−22.2072			−0.835189
$708$	3.52029	+	5.29744i	0.132300	+	0.199090i
$709$	1.08039	+	1.87129i	0.0405749	+	0.0702778i	0.885600	−	0.464449i	$-0.153748\pi$
$709$	1.08039	+	1.87129i	0.0405749	+	0.0702778i	−0.845025	+	0.534727i	$0.820414\pi$
$710$	1.54809			0.0580988
$711$	−9.57902	+	22.7988i	−0.359241	+	0.855023i
$712$	0.835330			0.0313053
$713$	26.3823	−	45.6955i	0.988024	−	1.71131i
$714$	−10.2448	−	15.4167i	−0.383402	−	0.576956i
$715$	0.704096	+	1.21953i	0.0263317	+	0.0456078i
$716$	4.84733	−	8.39582i	0.181153	−	0.313767i
$717$	−22.1935	+	1.39826i	−0.828833	+	0.0522191i
$718$	−24.5300	−	42.4871i	−0.915450	−	1.58561i
$719$	−12.5363	+	21.7135i	−0.467525	+	0.809776i	−0.999311	−	0.0371018i	$-0.988187\pi$
$719$	−12.5363	+	21.7135i	−0.467525	+	0.809776i	0.531787	+	0.846878i	$0.321521\pi$
$720$	−2.70410	−	3.56121i	−0.100776	−	0.132718i
$721$	14.4423	−	25.0147i	0.537858	−	0.931598i
$722$	10.7960	−	18.6992i	0.401785	−	0.695912i
$723$	−10.1179	+	0.637459i	−0.376288	+	0.0237074i
$724$	27.1593			1.00937
$725$	−4.54627	+	7.87437i	−0.168844	+	0.292447i
$726$	−2.62141	+	5.28196i	−0.0972895	+	0.196032i
$727$	−7.71792	−	13.3678i	−0.286242	−	0.495785i	0.686668	−	0.726971i	$-0.259073\pi$
$727$	−7.71792	−	13.3678i	−0.286242	−	0.495785i	−0.972910	+	0.231186i	$0.925739\pi$
$728$	−1.76812			−0.0655308
$729$	25.0987	−	9.95265i	0.929581	−	0.368617i
$730$	−2.07547	−	3.59483i	−0.0768167	−	0.133050i
$731$	−3.51816	−	6.09364i	−0.130124	−	0.225381i
$732$	−20.6220	−	31.0326i	−0.762210	−	1.14700i
$733$	−23.6972	+	41.0448i	−0.875276	+	1.51602i	−0.0188085	+	0.999823i	$0.505987\pi$
$733$	−23.6972	+	41.0448i	−0.875276	+	1.51602i	−0.856468	+	0.516200i	$0.827346\pi$
$734$	0.454873	+	0.787863i	0.0167897	+	0.0290805i
$735$	1.19275	−	2.40330i	0.0439951	−	0.0886472i
$736$	−26.7326	+	46.3022i	−0.985375	+	1.70672i
$737$	−24.7979	−	1.08484i	−0.913442	−	0.0399605i
$738$	−0.284590	+	0.677348i	−0.0104759	+	0.0249335i
$739$	−3.05255	+	5.28718i	−0.112290	+	0.194492i	−0.916693	−	0.399592i	$-0.869152\pi$
$739$	−3.05255	+	5.28718i	−0.112290	+	0.194492i	0.804403	+	0.594084i	$0.202485\pi$
$740$	0.588589	−	1.01947i	0.0216369	−	0.0374763i
$741$	−6.93776	+	0.437101i	−0.254865	+	0.0160573i
$742$	−6.73902	−	11.6723i	−0.247397	−	0.428504i
$743$	32.6211			1.19675			0.598377	−	0.801215i	$-0.295813\pi$
$743$	32.6211			1.19675			0.598377	+	0.801215i	$0.295813\pi$
$744$	10.1679	−	0.640610i	0.372773	−	0.0234859i
$745$	−0.797689	+	1.38164i	−0.0292251	+	0.0506193i
$746$	42.5375			1.55741
$747$	9.64027	−	1.21958i	0.352719	−	0.0446220i
$748$	9.18100	+	15.9020i	0.335691	+	0.581433i
$749$	19.2262			0.702510
$750$	4.57429	−	9.21688i	0.167029	−	0.336553i
$751$	18.9832	+	32.8798i	0.692705	+	1.19980i	0.970948	+	0.239290i	$0.0769147\pi$
$751$	18.9832	+	32.8798i	0.692705	+	1.19980i	−0.278243	+	0.960511i	$0.589752\pi$
$752$	3.80879	+	6.59702i	0.138892	+	0.240568i
$753$	−38.5844	+	2.43094i	−1.40609	+	0.0885885i
$754$	−2.55656	−	4.42808i	−0.0931043	−	0.161261i
$755$	3.87336	−	6.70886i	0.140966	−	0.244160i
$756$	−3.88798	+	11.1743i	−0.141404	+	0.406404i
$757$	−5.73261	−	9.92918i	−0.208355	−	0.360882i	0.742841	−	0.669468i	$-0.233478\pi$
$757$	−5.73261	−	9.92918i	−0.208355	−	0.360882i	−0.951197	+	0.308586i	$0.900144\pi$
$758$	7.53934			0.273841
$759$	21.6392	+	32.5634i	0.785453	+	1.18198i
$760$	−0.725545			−0.0263183
$761$	19.1574	+	33.1816i	0.694455	+	1.20283i	0.970364	+	0.241647i	$0.0776876\pi$
$761$	19.1574	+	33.1816i	0.694455	+	1.20283i	−0.275910	+	0.961184i	$0.588979\pi$
$762$	−22.8542	+	1.43989i	−0.827921	+	0.0521617i
$763$	−17.4830			−0.632926
$764$	−28.4534			−1.02941
$765$	1.43446	−	3.41413i	0.0518629	−	0.123438i
$766$	20.8259	+	36.0715i	0.752469	+	1.30332i
$767$	1.71819	+	2.97598i	0.0620401	+	0.107457i
$768$	−35.5802	+	2.24167i	−1.28389	+	0.0808892i
$769$	22.3426	−	38.6986i	0.805696	−	1.39551i	−0.110124	−	0.993918i	$-0.535125\pi$
$769$	22.3426	−	38.6986i	0.805696	−	1.39551i	0.915820	−	0.401588i	$-0.131542\pi$
$770$	1.32796	−	2.30009i	0.0478563	−	0.0828895i
$771$	36.7331	−	2.31430i	1.32291	−	0.0833475i
$772$	−16.4925			−0.593577
$773$	−20.6140	−	35.7046i	−0.741436	−	1.28420i	−0.951842	−	0.306590i	$-0.900812\pi$
$773$	−20.6140	−	35.7046i	−0.741436	−	1.28420i	0.210406	−	0.977614i	$-0.432521\pi$
$774$	−3.97527	+	9.46146i	−0.142888	+	0.340085i
$775$	17.3623	+	30.0724i	0.623672	+	1.08023i
$776$	−0.512076	−	0.886941i	−0.0183824	−	0.0318393i
$777$	5.98433	−	0.377032i	0.214687	−	0.0135260i
$778$	−18.6342	+	32.2754i	−0.668069	+	1.15713i
$779$	0.178397	+	0.308993i	0.00639174	+	0.0110708i
$780$	0.694548	+	1.04518i	0.0248688	+	0.0374234i
$781$	−3.91117	−	6.77434i	−0.139953	−	0.242405i
$782$	−54.5106			−1.94929
$783$	9.47307	−	1.80968i	0.338540	−	0.0646728i
$784$	−11.4113	−	19.7649i	−0.407546	−	0.705890i
$785$	0.849560	+	1.47148i	0.0303221	+	0.0525194i
$786$	−7.32997	+	0.461812i	−0.261451	+	0.0164723i
$787$	−4.35927			−0.155391			−0.0776956	−	0.996977i	$-0.524756\pi$
$787$	−4.35927			−0.155391			−0.0776956	+	0.996977i	$0.524756\pi$
$788$	−18.3279			−0.652903
$789$	−25.0821	+	1.58026i	−0.892947	+	0.0562586i
$790$	2.47352	−	4.28426i	0.0880038	−	0.152427i
$791$	0.680445	−	1.17857i	0.0241938	−	0.0419050i
$792$	−2.92420	+	6.95982i	−0.103907	+	0.247307i
$793$	−10.0652	−	17.4334i	−0.357426	−	0.619079i
$794$	13.7155	+	23.7559i	0.486744	+	0.843065i
$795$	1.19873	−	2.41536i	0.0425145	−	0.0856639i
$796$	9.24186	+	16.0074i	0.327569	+	0.567366i
$797$	7.43993	−	12.8863i	0.263536	−	0.456457i	−0.703643	−	0.710554i	$-0.748445\pi$
$797$	7.43993	−	12.8863i	0.263536	−	0.456457i	0.967179	+	0.254096i	$0.0817779\pi$
$798$	7.25641	+	10.9197i	0.256874	+	0.386553i
$799$	−3.15438	+	5.46355i	−0.111594	+	0.193287i
$800$	−17.5928	−	30.4717i	−0.622000	−	1.07734i
$801$	1.16977	−	2.78415i	0.0413318	−	0.0983730i
$802$	30.3552	−	52.5767i	1.07188	−	1.85655i
$803$	−10.4871	+	18.1643i	−0.370083	+	0.641003i
$804$	−22.1157	+	0.424691i	−0.779960	+	0.0149777i
$805$	1.72764	+	2.99235i	0.0608911	+	0.105467i
$806$	−19.5271			−0.687812
$807$	18.0626	+	27.1811i	0.635832	+	0.956821i
$808$	−12.6273			−0.444227
$809$	−10.5965			−0.372553			−0.186277	−	0.982497i	$-0.559642\pi$
$809$	−10.5965			−0.372553			−0.186277	+	0.982497i	$0.559642\pi$
$810$	−5.23109	+	1.34508i	−0.183802	+	0.0472614i
$811$	−24.2718	−	42.0401i	−0.852300	−	1.47623i	−0.879128	−	0.476586i	$-0.841874\pi$
$811$	−24.2718	−	42.0401i	−0.852300	−	1.47623i	0.0268280	−	0.999640i	$-0.491459\pi$
$812$	−2.11307	+	3.65995i	−0.0741543	+	0.128439i
$813$	19.8815	+	29.9184i	0.697276	+	1.04928i
$814$	−13.5730			−0.475733
$815$	3.39874	−	5.88678i	0.119053	−	0.206205i
$816$	−17.4347	−	26.2363i	−0.610336	−	0.918454i
$817$	2.49192	+	4.31613i	0.0871813	+	0.151002i
$818$	−21.9605			−0.767833
$819$	−2.47601	+	5.89312i	−0.0865189	+	0.205922i
$820$	0.0322048	−	0.0557804i	0.00112464	−	0.00194794i
$821$	−19.3951	−	33.5933i	−0.676893	−	1.17241i	−0.975912	−	0.218166i	$-0.929992\pi$
$821$	−19.3951	−	33.5933i	−0.676893	−	1.17241i	0.299018	−	0.954247i	$-0.403341\pi$
$822$	18.2325	+	27.4369i	0.635933	+	0.956973i
$823$	−46.1104			−1.60731			−0.803654	−	0.595096i	$-0.797114\pi$
$823$	−46.1104			−1.60731			−0.803654	+	0.595096i	$0.797114\pi$
$824$	8.21205	−	14.2237i	0.286080	−	0.495506i
$825$	−25.6794	+	1.61789i	−0.894043	+	0.0563276i
$826$	3.24058	−	5.61285i	0.112754	−	0.195296i
$827$	20.0307	−	34.6941i	0.696534	−	1.20643i	−0.273126	−	0.961978i	$-0.588058\pi$
$827$	20.0307	−	34.6941i	0.696534	−	1.20643i	0.969661	−	0.244455i	$-0.0786090\pi$
$828$	21.0703	+	27.7489i	0.732242	+	0.964340i
$829$	−38.0528			−1.32163			−0.660815	−	0.750549i	$-0.729789\pi$
$829$	−38.0528			−1.32163			−0.660815	+	0.750549i	$0.729789\pi$
$830$	−1.94387			−0.0674728
$831$	−26.0827	+	1.64329i	−0.904797	+	0.0570052i
$832$	6.10266			0.211572
$833$	9.45065	−	16.3690i	0.327446	−	0.567153i
$834$	−14.1986	+	0.894558i	−0.491657	+	0.0309760i
$835$	6.32222			0.218789
$836$	−6.50292	−	11.2634i	−0.224908	−	0.389552i
$837$	12.1036	−	34.7866i	0.418363	−	1.20240i
$838$	32.7307	+	56.6912i	1.13066	+	1.95837i
$839$	−3.64116			−0.125707			−0.0628534	−	0.998023i	$-0.520020\pi$
$839$	−3.64116			−0.125707			−0.0628534	+	0.998023i	$0.520020\pi$
$840$	−0.296591	+	0.597611i	−0.0102334	+	0.0206195i
$841$	−25.5550			−0.881208
$842$	3.06855	−	5.31489i	0.105749	−	0.183163i
$843$	−8.70540	+	17.5408i	−0.299830	+	0.604138i
$844$	5.13524	−	8.89450i	0.176762	−	0.306161i
$845$	−1.72842	−	2.99371i	−0.0594594	−	0.102987i
$846$	9.12872	−	1.15486i	0.313852	−	0.0397050i
$847$	2.63317			0.0904769
$848$	−11.4685	−	19.8640i	−0.393830	−	0.682134i
$849$	12.4246	−	25.0347i	0.426411	−	0.859190i
$850$	17.9368	−	31.0675i	0.615228	−	1.06561i
$851$	8.82903	−	15.2923i	0.302655	−	0.524214i
$852$	−3.85813	−	5.80585i	−0.132177	−	0.198905i
$853$	5.42226	+	9.39163i	0.185655	+	0.321563i	0.943797	−	0.330526i	$-0.107226\pi$
$853$	5.42226	+	9.39163i	0.185655	+	0.321563i	−0.758142	+	0.652089i	$0.773893\pi$
$854$	−18.9834	+	32.8803i	−0.649600	+	1.12514i
$855$	−1.01603	+	2.41823i	−0.0347475	+	0.0827018i
$856$	10.9323			0.373657
$857$	9.36685	−	16.2239i	0.319965	−	0.554196i	−0.660515	−	0.750813i	$-0.729662\pi$
$857$	9.36685	−	16.2239i	0.319965	−	0.554196i	0.980480	+	0.196617i	$0.0629954\pi$
$858$	6.43239	−	12.9608i	0.219598	−	0.442476i
$859$	10.7353	−	18.5941i	0.366284	−	0.634423i	−0.622697	−	0.782463i	$-0.713963\pi$
$859$	10.7353	−	18.5941i	0.366284	−	0.634423i	0.988981	+	0.148040i	$0.0472964\pi$
$860$	0.449849	−	0.779162i	0.0153397	−	0.0265692i
$861$	0.327435	−	0.0206295i	0.0111589	−	0.000703050i
$862$	−21.4192	+	37.0991i	−0.729540	+	1.26360i
$863$	27.8084			0.946608			0.473304	−	0.880899i	$-0.343061\pi$
$863$	27.8084			0.946608			0.473304	+	0.880899i	$0.343061\pi$
$864$	−12.2643	+	35.2484i	−0.417241	+	1.19918i
$865$	−2.47790	+	4.29184i	−0.0842511	+	0.145927i
$866$	−9.09692	+	15.7563i	−0.309126	+	0.535422i
$867$	−1.49203	+	3.00634i	−0.0506720	+	0.102101i
$868$	8.06987	+	13.9774i	0.273909	+	0.474425i
$869$	−24.9968			−0.847960
$870$	−1.92551	+	0.121313i	−0.0652808	+	0.00411290i
$871$	−11.9393	−	0.522309i	−0.404546	−	0.0176978i
$872$	−9.94102			−0.336645
$873$	−3.67326	+	0.464699i	−0.124321	+	0.0157277i
$874$	38.6099			1.30600
$875$	−4.59482			−0.155333
$876$	−8.30930	+	16.7427i	−0.280745	+	0.565683i
$877$	18.9646			0.640390			0.320195	−	0.947352i	$-0.396252\pi$
$877$	18.9646			0.640390			0.320195	+	0.947352i	$0.396252\pi$
$878$	32.9952	−	57.1493i	1.11353	−	1.92870i
$879$	−2.16605	+	4.36444i	−0.0730590	+	0.147209i
$880$	2.25993	−	3.91431i	0.0761822	−	0.131951i
$881$	19.8332	−	34.3522i	0.668199	−	1.15735i	−0.310208	−	0.950669i	$-0.600399\pi$
$881$	19.8332	−	34.3522i	0.668199	−	1.15735i	0.978407	−	0.206686i	$-0.0662679\pi$
$882$	−27.3500	+	3.46001i	−0.920923	+	0.116505i
$883$	3.42964	+	5.94031i	0.115416	+	0.199907i	0.917946	−	0.396705i	$-0.129846\pi$
$883$	3.42964	+	5.94031i	0.115416	+	0.199907i	−0.802530	+	0.596612i	$0.796513\pi$
$884$	4.42031	+	7.65620i	0.148671	+	0.257506i
$885$	1.29408	−	0.0815310i	0.0434999	−	0.00274063i
$886$	34.2090	+	59.2517i	1.14927	+	1.99060i
$887$	−7.90505			−0.265425			−0.132713	−	0.991155i	$-0.542369\pi$
$887$	−7.90505			−0.265425			−0.132713	+	0.991155i	$0.542369\pi$
$888$	3.40276	−	0.214385i	0.114189	−	0.00719429i
$889$	5.11291	+	8.85582i	0.171482	+	0.297015i
$890$	−0.302061	+	0.523185i	−0.0101251	+	0.0175372i
$891$	19.1021	+	19.4926i	0.639943	+	0.653027i
$892$	−9.31983	−	16.1424i	−0.312051	−	0.540488i
$893$	2.23425	−	3.86984i	0.0747665	−	0.129499i
$894$	16.3601	−	1.03074i	0.547165	−	0.0344732i
$895$	−0.988177	−	1.71157i	−0.0330311	−	0.0572116i
$896$	4.72701	+	8.18743i	0.157918	+	0.273523i
$897$	10.4185	+	15.6781i	0.347862	+	0.523475i
$898$	5.26049	−	9.11143i	0.175545	−	0.304052i
$899$	6.57820	−	11.3938i	0.219395	−	0.380004i
$900$	−22.7483	+	2.87785i	−0.758276	+	0.0959285i
$901$	9.49805	−	16.4511i	0.316426	−	0.548066i
$902$	−0.742650			−0.0247276
$903$	4.57373	−	0.288160i	0.152204	−	0.00958937i
$904$	0.386909	−	0.670147i	0.0128684	−	0.0222887i
$905$	2.76835	−	4.79492i	0.0920230	−	0.159389i
$906$	−79.4404	+	5.00501i	−2.63923	+	0.166280i
$907$	−50.2685			−1.66914			−0.834570	−	0.550902i	$-0.814284\pi$
$907$	−50.2685			−1.66914			−0.834570	+	0.550902i	$0.814284\pi$
$908$	−8.20623	+	14.2136i	−0.272333	+	0.471695i
$909$	−17.6829	+	42.0867i	−0.586504	+	1.39593i
$910$	0.639362	−	1.10741i	0.0211947	−	0.0367102i
$911$	0.522959	−	0.905791i	0.0173264	−	0.0300102i	−0.857232	−	0.514930i	$-0.827818\pi$
$911$	0.522959	−	0.905791i	0.0173264	−	0.0300102i	0.874559	+	0.484920i	$0.161151\pi$
$912$	12.3490	+	18.5832i	0.408917	+	0.615351i
$913$	4.91109	+	8.50626i	0.162533	+	0.281516i
$914$	10.6540	+	18.4533i	0.352403	+	0.610381i
$915$	−7.58075	+	0.477612i	−0.250612	+	0.0157894i
$916$	−3.16936	+	5.48949i	−0.104719	+	0.181378i
$917$	1.63985	+	2.84030i	0.0541526	+	0.0937951i
$918$	−37.3750	+	7.13992i	−1.23356	+	0.235652i
$919$	24.2350	−	41.9763i	0.799440	−	1.38467i	−0.120542	−	0.992708i	$-0.538463\pi$
$919$	24.2350	−	41.9763i	0.799440	−	1.38467i	0.919982	−	0.391962i	$-0.128203\pi$
$920$	0.982355	+	1.70149i	0.0323873	+	0.0560964i
$921$	−35.9397	+	2.26432i	−1.18425	+	0.0746119i
$922$	−32.3849			−1.06654
$923$	−1.88308	−	3.26159i	−0.0619824	−	0.107357i
$924$	−11.9356	+	0.751982i	−0.392653	+	0.0247384i
$925$	5.81043	+	10.0640i	0.191046	+	0.330901i
$926$	36.6782	+	63.5286i	1.20532	+	2.08768i
$927$	−35.9075	−	47.2891i	−1.17936	−	1.55318i
$928$	−6.66554	+	11.5451i	−0.218807	+	0.378985i
$929$	17.0995	−	29.6171i	0.561015	−	0.971707i	−0.436393	−	0.899756i	$-0.643744\pi$
$929$	17.0995	−	29.6171i	0.561015	−	0.971707i	0.997408	−	0.0719505i	$-0.0229224\pi$
$930$	−3.27555	+	6.60001i	−0.107409	+	0.216423i
$931$	−6.69391	+	11.5942i	−0.219384	+	0.379984i
$932$	27.7019			0.907405
$933$	0.961878	−	1.93812i	0.0314905	−	0.0634512i
$934$	50.5463			1.65393
$935$	3.74328			0.122418
$936$	−1.40789	+	3.35090i	−0.0460184	+	0.109528i
$937$	−49.3790			−1.61314			−0.806571	−	0.591138i	$-0.798679\pi$
$937$	−49.3790			−1.61314			−0.806571	+	0.591138i	$0.798679\pi$
$938$	10.4059	+	19.9937i	0.339764	+	0.652818i
$939$	4.48400	−	0.282506i	0.146330	−	0.00921925i
$940$	−0.806669			−0.0263107
$941$	26.0776	+	45.1678i	0.850106	+	1.47243i	0.881112	+	0.472908i	$0.156796\pi$
$941$	26.0776	+	45.1678i	0.850106	+	1.47243i	−0.0310053	+	0.999519i	$0.509871\pi$
$942$	7.76130	−	15.6385i	0.252877	−	0.509530i
$943$	0.483084	−	0.836725i	0.0157314	−	0.0272475i
$944$	5.51484	−	9.55198i	0.179493	−	0.310891i
$945$	1.57649	+	1.82541i	0.0512833	+	0.0593805i
$946$	−10.3736			−0.337276
$947$	14.6482	−	25.3714i	0.476002	−	0.824460i	−0.523620	−	0.851952i	$-0.675419\pi$
$947$	14.6482	−	25.3714i	0.476002	−	0.824460i	0.999622	+	0.0274921i	$0.00875211\pi$
$948$	−22.2318	+	1.40068i	−0.722057	+	0.0454919i
$949$	−5.04917	+	8.74542i	−0.163903	+	0.283888i
$950$	−12.7047	+	22.0052i	−0.412195	+	0.713942i
$951$	−5.61446	+	11.3128i	−0.182061	+	0.366842i
$952$	−2.35002	+	4.07035i	−0.0761645	+	0.131921i
$953$	54.6555			1.77046			0.885232	−	0.465150i	$-0.154000\pi$
$953$	54.6555			1.77046			0.885232	+	0.465150i	$0.154000\pi$
$954$	−27.4872	+	3.47737i	−0.889930	+	0.112584i
$955$	−2.90026	+	5.02339i	−0.0938501	+	0.162553i
$956$	−10.0156	−	17.3476i	−0.323929	−	0.561061i
$957$	5.39555	+	8.11940i	0.174413	+	0.262463i
$958$	1.88864	−	3.27123i	0.0610193	−	0.105689i
$959$	7.35527	−	12.7397i	0.237514	−	0.411387i
$960$	1.02368	−	2.06265i	0.0330392	−	0.0665719i
$961$	−9.62228	−	16.6663i	−0.310396	−	0.537622i
$962$	−6.53489			−0.210693
$963$	15.3092	−	36.4371i	0.493331	−	1.17417i
$964$	−4.56605	−	7.90864i	−0.147063	−	0.254720i
$965$	−1.68108	+	2.91171i	−0.0541158	+	0.0937314i
$966$	15.7831	−	31.8019i	0.507813	−	1.02321i
$967$	4.14402	−	7.17765i	0.133263	−	0.230818i	−0.791670	−	0.610949i	$-0.790788\pi$
$967$	4.14402	−	7.17765i	0.133263	−	0.230818i	0.924932	+	0.380132i	$0.124121\pi$
$968$	1.49725			0.0481236
$969$	−8.21479	+	16.5522i	−0.263897	+	0.531735i
$970$	0.740679			0.0237818
$971$	−11.2262	−	19.4443i	−0.360265	−	0.623998i	0.627739	−	0.778424i	$-0.283980\pi$
$971$	−11.2262	−	19.4443i	−0.360265	−	0.623998i	−0.988004	+	0.154426i	$0.950647\pi$
$972$	18.0814	+	16.2661i	0.579960	+	0.521735i
$973$	3.17649	+	5.50184i	0.101834	+	0.176381i
$974$	42.5973			1.36491
$975$	−12.3637	+	0.778953i	−0.395955	+	0.0249465i
$976$	−32.3061	+	55.9559i	−1.03409	+	1.79110i
$977$	45.5566			1.45748			0.728742	−	0.684788i	$-0.240105\pi$
$977$	45.5566			1.45748			0.728742	+	0.684788i	$0.240105\pi$
$978$	−69.7061	+	4.39171i	−2.22896	+	0.140431i
$979$	3.05256			0.0975603
$980$	2.41681			0.0772022
$981$	−13.9211	+	33.1333i	−0.444466	+	1.05787i
$982$	14.0876	−	24.4005i	0.449555	−	0.778652i
$983$	19.0768	−	33.0421i	0.608457	−	1.05388i	−0.383038	−	0.923733i	$-0.625122\pi$
$983$	19.0768	−	33.0421i	0.608457	−	1.05388i	0.991495	−	0.130146i	$-0.0415445\pi$
$984$	0.186183	−	0.0117302i	0.00593531	−	0.000373944i
$985$	−1.86816	+	3.23575i	−0.0595245	+	0.103100i
$986$	−13.5918			−0.432850
$987$	−2.27415	−	3.42222i	−0.0723871	−	0.108930i
$988$	−3.13091	−	5.42290i	−0.0996076	−	0.172525i
$989$	6.74790	−	11.6877i	0.214571	−	0.371647i
$990$	−3.30167	−	4.34820i	−0.104934	−	0.138195i
$991$	32.8103			1.04225			0.521127	−	0.853479i	$-0.325512\pi$
$991$	32.8103			1.04225			0.521127	+	0.853479i	$0.325512\pi$
$992$	25.4558	+	44.0908i	0.808224	+	1.39988i
$993$	−15.2388	−	22.9319i	−0.483590	−	0.727722i
$994$	−3.55158	+	6.15152i	−0.112649	+	0.195114i
$995$	3.76809			0.119457
$996$	4.84450	+	7.29016i	0.153504	+	0.230997i
$997$	−18.0565	+	31.2747i	−0.571854	+	0.990481i	0.424521	+	0.905418i	$0.360442\pi$
$997$	−18.0565	+	31.2747i	−0.571854	+	0.990481i	−0.996376	+	0.0850628i	$0.972891\pi$
$998$	−7.98030	−	13.8223i	−0.252612	−	0.437537i
$999$	4.05058	−	11.6416i	0.128155	−	0.368324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.f.c.565.12	yes	128
9.4	even	3		603.2.h.c.364.53	yes	128
67.37	even	3		603.2.h.c.439.53	yes	128
603.238	even	3	inner	603.2.f.c.238.12	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.f.c.238.12	✓	128	603.238	even	3	inner
603.2.f.c.565.12	yes	128	1.1	even	1	trivial
603.2.h.c.364.53	yes	128	9.4	even	3
603.2.h.c.439.53	yes	128	67.37	even	3

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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.943426 - 1.63406i) q^{2} +(0.958630 + 1.44258i) q^{3} +(-0.780103 + 1.35118i) q^{4} +(0.159032 + 0.275451i) q^{5} +(1.45286 - 2.92742i) q^{6} -1.45939 q^{7} -0.829824 q^{8} +(-1.16206 + 2.76579i) q^{9} +O(q^{10})\)	\(q+(-0.943426 - 1.63406i) q^{2} +(0.958630 + 1.44258i) q^{3} +(-0.780103 + 1.35118i) q^{4} +(0.159032 + 0.275451i) q^{5} +(1.45286 - 2.92742i) q^{6} -1.45939 q^{7} -0.829824 q^{8} +(-1.16206 + 2.76579i) q^{9} +(0.300070 - 0.519736i) q^{10} -3.03244 q^{11} +(-2.69701 + 0.169920i) q^{12} -1.46001 q^{13} +(1.37682 + 2.38472i) q^{14} +(-0.244907 + 0.493472i) q^{15} +(2.34308 + 4.05834i) q^{16} +(-1.94051 + 3.36106i) q^{17} +(5.61579 - 0.710446i) q^{18} +(1.37446 - 2.38064i) q^{19} -0.496245 q^{20} +(-1.39901 - 2.10528i) q^{21} +(2.86088 + 4.95519i) q^{22} -7.44385 q^{23} +(-0.795494 - 1.19709i) q^{24} +(2.44942 - 4.24252i) q^{25} +(1.37741 + 2.38574i) q^{26} +(-5.10386 + 0.975013i) q^{27} +(1.13847 - 1.97189i) q^{28} -1.85606 q^{29} +(1.03741 - 0.0653605i) q^{30} +(-3.54417 + 6.13868i) q^{31} +(3.59123 - 6.22019i) q^{32} +(-2.90699 - 4.37453i) q^{33} +7.32290 q^{34} +(-0.232089 - 0.401990i) q^{35} +(-2.83056 - 3.72775i) q^{36} +(-1.18608 + 2.05436i) q^{37} -5.18682 q^{38} +(-1.39961 - 2.10617i) q^{39} +(-0.131969 - 0.228576i) q^{40} +(-0.0648970 + 0.112405i) q^{41} +(-2.12029 + 4.27224i) q^{42} +(-0.906506 + 1.57011i) q^{43} +(2.36562 - 4.09737i) q^{44} +(-0.946647 + 0.119759i) q^{45} +(7.02272 + 12.1637i) q^{46} +1.62555 q^{47} +(-3.60832 + 7.27053i) q^{48} -4.87020 q^{49} -9.24337 q^{50} +(-6.70881 + 0.422677i) q^{51} +(1.13896 - 1.97273i) q^{52} -4.89462 q^{53} +(6.40834 + 7.42016i) q^{54} +(-0.482255 - 0.835290i) q^{55} +1.21103 q^{56} +(4.75186 - 0.299383i) q^{57} +(1.75106 + 3.03292i) q^{58} +(-1.17683 - 2.03834i) q^{59} +(-0.475716 - 0.715873i) q^{60} +(6.89393 + 11.9406i) q^{61} +13.3746 q^{62} +(1.69589 - 4.03636i) q^{63} -4.17988 q^{64} +(-0.232188 - 0.402161i) q^{65} +(-4.40572 + 8.87724i) q^{66} +(8.17753 + 0.357744i) q^{67} +(-3.02759 - 5.24395i) q^{68} +(-7.13590 - 10.7383i) q^{69} +(-0.437917 + 0.758495i) q^{70} +(1.28978 + 2.23396i) q^{71} +(0.964304 - 2.29512i) q^{72} +(3.45832 - 5.98999i) q^{73} +4.47593 q^{74} +(8.46824 - 0.533527i) q^{75} +(2.14445 + 3.71430i) q^{76} +4.42550 q^{77} +(-2.12119 + 4.27406i) q^{78} +8.24314 q^{79} +(-0.745250 + 1.29081i) q^{80} +(-6.29924 - 6.42803i) q^{81} +0.244902 q^{82} +(-1.61952 - 2.80509i) q^{83} +(3.93598 - 0.247979i) q^{84} -1.23441 q^{85} +3.42088 q^{86} +(-1.77928 - 2.67751i) q^{87} +2.51639 q^{88} -1.00664 q^{89} +(1.08878 + 1.43389i) q^{90} +2.13071 q^{91} +(5.80698 - 10.0580i) q^{92} +(-12.2531 + 0.771983i) q^{93} +(-1.53358 - 2.65624i) q^{94} +0.874335 q^{95} +(12.4158 - 0.782233i) q^{96} +(0.617090 + 1.06883i) q^{97} +(4.59467 + 7.95820i) q^{98} +(3.52387 - 8.38711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + q^{2} - 3 q^{3} - 65 q^{4} + 5 q^{5} + 3 q^{6} - 8 q^{7} - 36 q^{8} + 5 q^{9}+O(q^{10}) \) 128 * q + q^2 - 3 * q^3 - 65 * q^4 + 5 * q^5 + 3 * q^6 - 8 * q^7 - 36 * q^8 + 5 * q^9	\( 128 q + q^{2} - 3 q^{3} - 65 q^{4} + 5 q^{5} + 3 q^{6} - 8 q^{7} - 36 q^{8} + 5 q^{9} - 2 q^{10} - 30 q^{11} - 10 q^{12} + 12 q^{13} - 8 q^{14} + 12 q^{15} - 59 q^{16} - q^{17} + 8 q^{18} + 8 q^{19} - 6 q^{20} + 12 q^{21} - 20 q^{22} - 18 q^{23} - 39 q^{24} - 57 q^{25} + 8 q^{26} - 24 q^{27} - 16 q^{28} - 2 q^{29} + 23 q^{30} + 16 q^{31} + 27 q^{32} - 3 q^{33} - 4 q^{34} + 11 q^{35} + 45 q^{36} + 2 q^{37} - 4 q^{38} + 8 q^{39} - 6 q^{40} - 7 q^{41} + 18 q^{42} - 11 q^{43} - 18 q^{44} + 3 q^{45} - 4 q^{46} - 24 q^{47} + 71 q^{48} + 104 q^{49} + 44 q^{50} + 42 q^{51} - 6 q^{52} - 60 q^{53} + 48 q^{54} + 10 q^{55} - 28 q^{56} + 29 q^{57} + 6 q^{59} - 7 q^{60} - 6 q^{61} - 22 q^{62} + 20 q^{63} + 56 q^{64} - 26 q^{65} + 54 q^{66} - 19 q^{68} + 8 q^{69} + 25 q^{70} + 8 q^{71} + 11 q^{72} + 22 q^{73} - 42 q^{74} - 44 q^{75} - 5 q^{76} - 70 q^{77} + 15 q^{78} - 30 q^{79} + 14 q^{80} - 63 q^{81} - 24 q^{82} - 3 q^{83} - 77 q^{84} + 24 q^{85} + 20 q^{87} - 6 q^{88} + 116 q^{89} - q^{90} - 10 q^{91} + 4 q^{92} + 26 q^{93} + 4 q^{94} - 180 q^{95} - 56 q^{96} + 19 q^{97} - 49 q^{98} + 4 q^{99}+O(q^{100}) \) 128 * q + q^2 - 3 * q^3 - 65 * q^4 + 5 * q^5 + 3 * q^6 - 8 * q^7 - 36 * q^8 + 5 * q^9 - 2 * q^10 - 30 * q^11 - 10 * q^12 + 12 * q^13 - 8 * q^14 + 12 * q^15 - 59 * q^16 - q^17 + 8 * q^18 + 8 * q^19 - 6 * q^20 + 12 * q^21 - 20 * q^22 - 18 * q^23 - 39 * q^24 - 57 * q^25 + 8 * q^26 - 24 * q^27 - 16 * q^28 - 2 * q^29 + 23 * q^30 + 16 * q^31 + 27 * q^32 - 3 * q^33 - 4 * q^34 + 11 * q^35 + 45 * q^36 + 2 * q^37 - 4 * q^38 + 8 * q^39 - 6 * q^40 - 7 * q^41 + 18 * q^42 - 11 * q^43 - 18 * q^44 + 3 * q^45 - 4 * q^46 - 24 * q^47 + 71 * q^48 + 104 * q^49 + 44 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 48 * q^54 + 10 * q^55 - 28 * q^56 + 29 * q^57 + 6 * q^59 - 7 * q^60 - 6 * q^61 - 22 * q^62 + 20 * q^63 + 56 * q^64 - 26 * q^65 + 54 * q^66 - 19 * q^68 + 8 * q^69 + 25 * q^70 + 8 * q^71 + 11 * q^72 + 22 * q^73 - 42 * q^74 - 44 * q^75 - 5 * q^76 - 70 * q^77 + 15 * q^78 - 30 * q^79 + 14 * q^80 - 63 * q^81 - 24 * q^82 - 3 * q^83 - 77 * q^84 + 24 * q^85 + 20 * q^87 - 6 * q^88 + 116 * q^89 - q^90 - 10 * q^91 + 4 * q^92 + 26 * q^93 + 4 * q^94 - 180 * q^95 - 56 * q^96 + 19 * q^97 - 49 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more