LMFDB - Embedded newform 731.2.m.c.87.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.14
Character	$\chi$	$=$	731.87
Dual form			731.2.m.c.689.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.177484 - 0.177484i) q^{2} +(0.604214 - 0.250274i) q^{3} -1.93700i q^{4} +(1.47313 + 3.55644i) q^{5} +(-0.151658 - 0.0628188i) q^{6} +(-0.253865 + 0.612883i) q^{7} +(-0.698755 + 0.698755i) q^{8} +(-1.81888 + 1.81888i) q^{9} +O(q^{10})$	\(q+(-0.177484 - 0.177484i) q^{2} +(0.604214 - 0.250274i) q^{3} -1.93700i q^{4} +(1.47313 + 3.55644i) q^{5} +(-0.151658 - 0.0628188i) q^{6} +(-0.253865 + 0.612883i) q^{7} +(-0.698755 + 0.698755i) q^{8} +(-1.81888 + 1.81888i) q^{9} +(0.369755 - 0.892669i) q^{10} +(-0.105411 - 0.0436628i) q^{11} +(-0.484780 - 1.17036i) q^{12} +3.75929i q^{13} +(0.153834 - 0.0637201i) q^{14} +(1.78017 + 1.78017i) q^{15} -3.62596 q^{16} +(-1.28043 + 3.91925i) q^{17} +0.645645 q^{18} +(2.22672 + 2.22672i) q^{19} +(6.88882 - 2.85344i) q^{20} +0.433849i q^{21} +(0.0109594 + 0.0264583i) q^{22} +(-1.63252 - 0.676210i) q^{23} +(-0.247318 + 0.597078i) q^{24} +(-6.94264 + 6.94264i) q^{25} +(0.667214 - 0.667214i) q^{26} +(-1.39460 + 3.36686i) q^{27} +(1.18715 + 0.491735i) q^{28} +(-2.58202 - 6.23354i) q^{29} -0.631903i q^{30} +(1.68458 - 0.697775i) q^{31} +(2.04106 + 2.04106i) q^{32} -0.0746187 q^{33} +(0.922860 - 0.468349i) q^{34} -2.55366 q^{35} +(3.52317 + 3.52317i) q^{36} +(2.01307 - 0.833839i) q^{37} -0.790415i q^{38} +(0.940851 + 2.27142i) q^{39} +(-3.51443 - 1.45573i) q^{40} +(3.49689 - 8.44224i) q^{41} +(0.0770012 - 0.0770012i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(-0.0845748 + 0.204182i) q^{44} +(-9.14819 - 3.78931i) q^{45} +(0.169729 + 0.409762i) q^{46} -0.580038i q^{47} +(-2.19086 + 0.907483i) q^{48} +(4.63857 + 4.63857i) q^{49} +2.46442 q^{50} +(0.207232 + 2.68852i) q^{51} +7.28174 q^{52} +(2.58071 + 2.58071i) q^{53} +(0.845083 - 0.350045i) q^{54} -0.439210i q^{55} +(-0.250866 - 0.605644i) q^{56} +(1.90271 + 0.788127i) q^{57} +(-0.648088 + 1.56462i) q^{58} +(9.08685 - 9.08685i) q^{59} +(3.44818 - 3.44818i) q^{60} +(-4.35633 + 10.5171i) q^{61} +(-0.422830 - 0.175142i) q^{62} +(-0.653013 - 1.57651i) q^{63} +6.52741i q^{64} +(-13.3697 + 5.53791i) q^{65} +(0.0132436 + 0.0132436i) q^{66} +8.10735 q^{67} +(7.59158 + 2.48019i) q^{68} -1.15563 q^{69} +(0.453234 + 0.453234i) q^{70} +(10.4370 - 4.32313i) q^{71} -2.54191i q^{72} +(0.675324 + 1.63038i) q^{73} +(-0.505281 - 0.209294i) q^{74} +(-2.45728 + 5.93241i) q^{75} +(4.31316 - 4.31316i) q^{76} +(0.0535204 - 0.0535204i) q^{77} +(0.236154 - 0.570126i) q^{78} +(10.6520 + 4.41221i) q^{79} +(-5.34150 - 12.8955i) q^{80} -5.33353i q^{81} +(-2.11901 + 0.877721i) q^{82} +(-3.05854 - 3.05854i) q^{83} +0.840364 q^{84} +(-15.8248 + 1.21978i) q^{85} +0.251000 q^{86} +(-3.12018 - 3.12018i) q^{87} +(0.104166 - 0.0431471i) q^{88} -8.74618i q^{89} +(0.951117 + 2.29620i) q^{90} +(-2.30400 - 0.954350i) q^{91} +(-1.30982 + 3.16218i) q^{92} +(0.843211 - 0.843211i) q^{93} +(-0.102948 + 0.102948i) q^{94} +(-4.63896 + 11.1994i) q^{95} +(1.74406 + 0.722414i) q^{96} +(2.48228 + 5.99275i) q^{97} -1.64654i q^{98} +(0.271148 - 0.112313i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.177484	−	0.177484i	−0.125500	−	0.125500i	0.641567	−	0.767067i	$-0.278285\pi$
$2$	−0.177484	−	0.177484i	−0.125500	−	0.125500i	−0.767067	+	0.641567i	$0.778285\pi$
$3$	0.604214	−	0.250274i	0.348843	−	0.144496i	−0.201380	−	0.979513i	$-0.564543\pi$
$3$	0.604214	−	0.250274i	0.348843	−	0.144496i	0.550223	+	0.835018i	$0.314543\pi$
$4$		−	1.93700i		−	0.968499i
$5$	1.47313	+	3.55644i	0.658802	+	1.59049i	0.799656	+	0.600459i	$0.205015\pi$
$5$	1.47313	+	3.55644i	0.658802	+	1.59049i	−0.140854	+	0.990030i	$0.544985\pi$
$6$	−0.151658	−	0.0628188i	−0.0619142	−	0.0256457i
$7$	−0.253865	+	0.612883i	−0.0959518	+	0.231648i	−0.964566	−	0.263840i	$-0.915011\pi$
$7$	−0.253865	+	0.612883i	−0.0959518	+	0.231648i	0.868615	+	0.495488i	$0.165011\pi$
$8$	−0.698755	+	0.698755i	−0.247047	+	0.247047i
$9$	−1.81888	+	1.81888i	−0.606294	+	0.606294i
$10$	0.369755	−	0.892669i	0.116927	−	0.282287i
$11$	−0.105411	−	0.0436628i	−0.0317827	−	0.0131648i	0.366735	−	0.930325i	$-0.380475\pi$
$11$	−0.105411	−	0.0436628i	−0.0317827	−	0.0131648i	−0.398518	+	0.917160i	$0.630475\pi$
$12$	−0.484780	−	1.17036i	−0.139944	−	0.337855i
$13$			3.75929i			1.04264i	0.853362	+	0.521319i	$0.174560\pi$
$13$			3.75929i			1.04264i	−0.853362	+	0.521319i	$0.825440\pi$
$14$	0.153834	−	0.0637201i	0.0411139	−	0.0170299i
$15$	1.78017	+	1.78017i	0.459637	+	0.459637i
$16$	−3.62596			−0.906490
$17$	−1.28043	+	3.91925i	−0.310549	+	0.950557i
$17$	−1.28043	+	3.91925i	−0.310549	+	0.950557i
$18$	0.645645			0.152180
$19$	2.22672	+	2.22672i	0.510845	+	0.510845i	0.914785	−	0.403940i	$-0.132360\pi$
$19$	2.22672	+	2.22672i	0.510845	+	0.510845i	−0.403940	+	0.914785i	$0.632360\pi$
$20$	6.88882	−	2.85344i	1.54039	−	0.638049i
$21$			0.433849i			0.0946735i
$22$	0.0109594	+	0.0264583i	0.00233655	+	0.00564093i
$23$	−1.63252	−	0.676210i	−0.340403	−	0.141000i	0.205932	−	0.978566i	$-0.433977\pi$
$23$	−1.63252	−	0.676210i	−0.340403	−	0.141000i	−0.546335	+	0.837567i	$0.683977\pi$
$24$	−0.247318	+	0.597078i	−0.0504835	+	0.121878i
$25$	−6.94264	+	6.94264i	−1.38853	+	1.38853i
$26$	0.667214	−	0.667214i	0.130851	−	0.130851i
$27$	−1.39460	+	3.36686i	−0.268390	+	0.647952i
$28$	1.18715	+	0.491735i	0.224351	+	0.0929293i
$29$	−2.58202	−	6.23354i	−0.479469	−	1.15754i	−0.959859	−	0.280485i	$-0.909505\pi$
$29$	−2.58202	−	6.23354i	−0.479469	−	1.15754i	0.480390	−	0.877055i	$-0.340495\pi$
$30$		−	0.631903i		−	0.115369i
$31$	1.68458	−	0.697775i	0.302559	−	0.125324i	−0.226239	−	0.974072i	$-0.572643\pi$
$31$	1.68458	−	0.697775i	0.302559	−	0.125324i	0.528798	+	0.848748i	$0.322643\pi$
$32$	2.04106	+	2.04106i	0.360812	+	0.360812i
$33$	−0.0746187			−0.0129895
$34$	0.922860	−	0.468349i	0.158269	−	0.0803211i
$35$	−2.55366			−0.431647
$36$	3.52317	+	3.52317i	0.587195	+	0.587195i
$37$	2.01307	−	0.833839i	0.330946	−	0.137082i	−0.211022	−	0.977481i	$-0.567679\pi$
$37$	2.01307	−	0.833839i	0.330946	−	0.137082i	0.541968	+	0.840399i	$0.317679\pi$
$38$		−	0.790415i		−	0.128222i
$39$	0.940851	+	2.27142i	0.150657	+	0.363718i
$40$	−3.51443	−	1.45573i	−0.555681	−	0.230171i
$41$	3.49689	−	8.44224i	0.546123	−	1.31846i	−0.374219	−	0.927340i	$-0.622089\pi$
$41$	3.49689	−	8.44224i	0.546123	−	1.31846i	0.920341	−	0.391116i	$-0.127911\pi$
$42$	0.0770012	−	0.0770012i	0.0118815	−	0.0118815i
$43$	−0.707107	+	0.707107i	−0.107833	+	0.107833i
$43$	−0.707107	+	0.707107i	−0.107833	+	0.107833i
$44$	−0.0845748	+	0.204182i	−0.0127501	+	0.0307815i
$45$	−9.14819	−	3.78931i	−1.36373	−	0.564876i
$46$	0.169729	+	0.409762i	0.0250252	+	0.0604161i
$47$		−	0.580038i		−	0.0846072i	−0.999105	−	0.0423036i	$-0.986530\pi$
$47$		−	0.580038i		−	0.0846072i	0.999105	−	0.0423036i	$-0.0134697\pi$
$48$	−2.19086	+	0.907483i	−0.316223	+	0.130984i
$49$	4.63857	+	4.63857i	0.662653	+	0.662653i
$50$	2.46442			0.348521
$51$	0.207232	+	2.68852i	0.0290183	+	0.376469i
$52$	7.28174			1.00980
$53$	2.58071	+	2.58071i	0.354488	+	0.354488i	0.861776	−	0.507288i	$-0.169352\pi$
$53$	2.58071	+	2.58071i	0.354488	+	0.354488i	−0.507288	+	0.861776i	$0.669352\pi$
$54$	0.845083	−	0.350045i	0.115001	−	0.0476350i
$55$		−	0.439210i		−	0.0592231i
$56$	−0.250866	−	0.605644i	−0.0335234	−	0.0809326i
$57$	1.90271	+	0.788127i	0.252020	+	0.104390i
$58$	−0.648088	+	1.56462i	−0.0850981	+	0.205445i
$59$	9.08685	−	9.08685i	1.18301	−	1.18301i	0.204045	−	0.978961i	$-0.434591\pi$
$59$	9.08685	−	9.08685i	1.18301	−	1.18301i	0.978961	−	0.204045i	$-0.0654089\pi$
$60$	3.44818	−	3.44818i	0.445159	−	0.445159i
$61$	−4.35633	+	10.5171i	−0.557771	+	1.34658i	0.353756	+	0.935338i	$0.384904\pi$
$61$	−4.35633	+	10.5171i	−0.557771	+	1.34658i	−0.911527	+	0.411241i	$0.865096\pi$
$62$	−0.422830	−	0.175142i	−0.0536994	−	0.0222430i
$63$	−0.653013	−	1.57651i	−0.0822719	−	0.198622i
$64$			6.52741i			0.815926i
$65$	−13.3697	+	5.53791i	−1.65831	+	0.686893i
$66$	0.0132436	+	0.0132436i	0.00163018	+	0.00163018i
$67$	8.10735			0.990470			0.495235	−	0.868759i	$-0.335082\pi$
$67$	8.10735			0.990470			0.495235	+	0.868759i	$0.335082\pi$
$68$	7.59158	+	2.48019i	0.920614	+	0.300767i
$69$	−1.15563			−0.139121
$70$	0.453234	+	0.453234i	0.0541718	+	0.0541718i
$71$	10.4370	−	4.32313i	1.23864	−	0.513061i	0.335350	−	0.942094i	$-0.391146\pi$
$71$	10.4370	−	4.32313i	1.23864	−	0.513061i	0.903289	+	0.429033i	$0.141146\pi$
$72$		−	2.54191i		−	0.299566i
$73$	0.675324	+	1.63038i	0.0790408	+	0.190821i	0.958460	−	0.285227i	$-0.0920689\pi$
$73$	0.675324	+	1.63038i	0.0790408	+	0.190821i	−0.879419	+	0.476048i	$0.842069\pi$
$74$	−0.505281	−	0.209294i	−0.0587377	−	0.0243299i
$75$	−2.45728	+	5.93241i	−0.283743	+	0.685015i
$76$	4.31316	−	4.31316i	0.494753	−	0.494753i
$77$	0.0535204	−	0.0535204i	0.00609922	−	0.00609922i
$78$	0.236154	−	0.570126i	0.0267392	−	0.0645541i
$79$	10.6520	+	4.41221i	1.19844	+	0.496412i	0.890496	−	0.454991i	$-0.150357\pi$
$79$	10.6520	+	4.41221i	1.19844	+	0.496412i	0.307949	+	0.951403i	$0.400357\pi$
$80$	−5.34150	−	12.8955i	−0.597198	−	1.44176i
$81$		−	5.33353i		−	0.592614i
$82$	−2.11901	+	0.877721i	−0.234005	+	0.0969281i
$83$	−3.05854	−	3.05854i	−0.335718	−	0.335718i	0.519035	−	0.854753i	$-0.326291\pi$
$83$	−3.05854	−	3.05854i	−0.335718	−	0.335718i	−0.854753	+	0.519035i	$0.826291\pi$
$84$	0.840364			0.0916912
$85$	−15.8248	+	1.21978i	−1.71644	+	0.132304i
$86$	0.251000			0.0270661
$87$	−3.12018	−	3.12018i	−0.334519	−	0.334519i
$88$	0.104166	−	0.0431471i	0.0111042	−	0.00459950i
$89$		−	8.74618i		−	0.927093i	−0.886073	−	0.463547i	$-0.846577\pi$
$89$		−	8.74618i		−	0.927093i	0.886073	−	0.463547i	$-0.153423\pi$
$90$	0.951117	+	2.29620i	0.100257	+	0.242041i
$91$	−2.30400	−	0.954350i	−0.241525	−	0.100043i
$92$	−1.30982	+	3.16218i	−0.136558	+	0.329680i
$93$	0.843211	−	0.843211i	0.0874369	−	0.0874369i
$94$	−0.102948	+	0.102948i	−0.0106182	+	0.0106182i
$95$	−4.63896	+	11.1994i	−0.475948	+	1.14904i
$96$	1.74406	+	0.722414i	0.178003	+	0.0737311i
$97$	2.48228	+	5.99275i	0.252037	+	0.608472i	0.998368	−	0.0571033i	$-0.0181864\pi$
$97$	2.48228	+	5.99275i	0.252037	+	0.608472i	−0.746331	+	0.665575i	$0.768186\pi$
$98$		−	1.64654i		−	0.166326i
$99$	0.271148	−	0.112313i	0.0272514	−	0.0112879i
$100$	13.4479	+	13.4479i	1.34479	+	1.34479i
$101$	−3.04315			−0.302805			−0.151403	−	0.988472i	$-0.548379\pi$
$101$	−3.04315			−0.302805			−0.151403	+	0.988472i	$0.548379\pi$
$102$	0.440390	−	0.513951i	0.0436051	−	0.0508887i
$103$	−15.5734			−1.53449			−0.767245	−	0.641354i	$-0.778373\pi$
$103$	−15.5734			−1.53449			−0.767245	+	0.641354i	$0.778373\pi$
$104$	−2.62682	−	2.62682i	−0.257581	−	0.257581i
$105$	−1.54296	+	0.639114i	−0.150577	+	0.0623711i
$106$		−	0.916070i		−	0.0889766i
$107$	2.51318	+	6.06736i	0.242959	+	0.586554i	0.997574	−	0.0696133i	$-0.0221765\pi$
$107$	2.51318	+	6.06736i	0.242959	+	0.586554i	−0.754615	+	0.656167i	$0.772177\pi$
$108$	6.52160	+	2.70133i	0.627541	+	0.259936i
$109$	−2.85334	+	6.88858i	−0.273301	+	0.659806i	−0.999620	−	0.0275508i	$-0.991229\pi$
$109$	−2.85334	+	6.88858i	−0.273301	+	0.659806i	0.726320	+	0.687357i	$0.241229\pi$
$110$	−0.0779528	+	0.0779528i	−0.00743251	+	0.00743251i
$111$	1.00764	−	1.00764i	0.0956405	−	0.0956405i
$112$	0.920503	−	2.22229i	0.0869794	−	0.209987i
$113$	3.02139	+	1.25150i	0.284228	+	0.117731i	0.520243	−	0.854018i	$-0.325841\pi$
$113$	3.02139	+	1.25150i	0.284228	+	0.117731i	−0.236015	+	0.971749i	$0.575841\pi$
$114$	−0.197820	−	0.477580i	−0.0185276	−	0.0447295i
$115$		−	6.80209i		−	0.634298i
$116$	−12.0744	+	5.00136i	−1.12108	+	0.464365i
$117$	−6.83770	−	6.83770i	−0.632146	−	0.632146i
$118$	−3.22554			−0.296935
$119$	−2.07699	−	1.77971i	−0.190397	−	0.163146i
$120$	−2.48780			−0.227104
$121$	−7.76897	−	7.76897i	−0.706270	−	0.706270i
$122$	2.63980	−	1.09344i	0.238996	−	0.0989955i
$123$		−	5.97610i		−	0.538847i
$124$	−1.35159	−	3.26302i	−0.121376	−	0.293028i
$125$	−17.1363	−	7.09808i	−1.53272	−	0.634872i
$126$	−0.163907	+	0.395705i	−0.0146020	+	0.0352522i
$127$	5.37305	−	5.37305i	0.476781	−	0.476781i	−0.427320	−	0.904101i	$-0.640542\pi$
$127$	5.37305	−	5.37305i	0.476781	−	0.476781i	0.904101	+	0.427320i	$0.140542\pi$
$128$	5.24063	−	5.24063i	0.463211	−	0.463211i
$129$	−0.250274	+	0.604214i	−0.0220354	+	0.0531981i
$130$	3.35580	+	1.39002i	0.294323	+	0.121913i
$131$	−0.0180811	−	0.0436517i	−0.00157976	−	0.00381387i	0.923088	−	0.384590i	$-0.125657\pi$
$131$	−0.0180811	−	0.0436517i	−0.00157976	−	0.00381387i	−0.924667	+	0.380776i	$0.875657\pi$
$132$			0.144536i			0.0125803i
$133$	−1.93001	+	0.799435i	−0.167353	+	0.0693198i
$134$	−1.43893	−	1.43893i	−0.124304	−	0.124304i
$135$	−14.0284			−1.20738
$136$	−1.84389	−	3.63330i	−0.158112	−	0.311553i
$137$	−2.10692			−0.180006			−0.0900032	−	0.995941i	$-0.528688\pi$
$137$	−2.10692			−0.180006			−0.0900032	+	0.995941i	$0.528688\pi$
$138$	0.205105	+	0.205105i	0.0174597	+	0.0174597i
$139$	3.72932	−	1.54473i	0.316316	−	0.131023i	−0.218876	−	0.975753i	$-0.570239\pi$
$139$	3.72932	−	1.54473i	0.316316	−	0.131023i	0.535193	+	0.844730i	$0.320239\pi$
$140$			4.94643i			0.418050i
$141$	−0.145168	−	0.350467i	−0.0122254	−	0.0295147i
$142$	−2.61968	−	1.08511i	−0.219839	−	0.0910602i
$143$	0.164141	−	0.396272i	0.0137262	−	0.0331379i
$144$	6.59520	−	6.59520i	0.549600	−	0.549600i
$145$	18.3656	−	18.3656i	1.52518	−	1.52518i
$146$	0.169507	−	0.409226i	0.0140285	−	0.0338677i
$147$	3.96360	+	1.64178i	0.326912	+	0.135412i
$148$	−1.61515	−	3.89931i	−0.132764	−	0.320521i
$149$		−	13.1304i		−	1.07568i	−0.843046	−	0.537841i	$-0.819240\pi$
$149$		−	13.1304i		−	1.07568i	0.843046	−	0.537841i	$-0.180760\pi$
$150$	1.48904	−	0.616779i	0.121579	−	0.0503598i
$151$	4.00928	+	4.00928i	0.326271	+	0.326271i	0.851167	−	0.524896i	$-0.175896\pi$
$151$	4.00928	+	4.00928i	0.326271	+	0.326271i	−0.524896	+	0.851167i	$0.675896\pi$
$152$	−3.11186			−0.252406
$153$	−4.79970	−	9.45760i	−0.388033	−	0.764602i
$154$	−0.0189981			−0.00153091
$155$	4.96319	+	4.96319i	0.398653	+	0.398653i
$156$	4.39973	−	1.82243i	0.352260	−	0.145911i
$157$		−	21.0367i		−	1.67891i	−0.543431	−	0.839454i	$-0.682875\pi$
$157$		−	21.0367i		−	1.67891i	0.543431	−	0.839454i	$-0.317125\pi$
$158$	−1.10747	−	2.67366i	−0.0881053	−	0.212705i
$159$	2.20519	+	0.913418i	0.174883	+	0.0724388i
$160$	−4.25217	+	10.2657i	−0.336164	+	0.811571i
$161$	0.828876	−	0.828876i	0.0653245	−	0.0653245i
$162$	−0.946617	+	0.946617i	−0.0743732	+	0.0743732i
$163$	−7.43235	+	17.9433i	−0.582147	+	1.40543i	0.308716	+	0.951154i	$0.400101\pi$
$163$	−7.43235	+	17.9433i	−0.582147	+	1.40543i	−0.890863	+	0.454272i	$0.849899\pi$
$164$	−16.3526	−	6.77347i	−1.27692	−	0.528919i
$165$	−0.109923	−	0.265377i	−0.00855748	−	0.0206596i
$166$			1.08568i			0.0842654i
$167$	16.4528	−	6.81498i	1.27316	−	0.527359i	0.359235	−	0.933247i	$-0.383038\pi$
$167$	16.4528	−	6.81498i	1.27316	−	0.527359i	0.913923	+	0.405888i	$0.133038\pi$
$168$	−0.303154	−	0.303154i	−0.0233888	−	0.0233888i
$169$	−1.13224			−0.0870957
$170$	3.02514	+	2.59216i	0.232018	+	0.198810i
$171$	−8.10029			−0.619445
$172$	1.36966	+	1.36966i	0.104436	+	0.104436i
$173$	−3.63542	+	1.50584i	−0.276396	+	0.114487i	−0.516576	−	0.856241i	$-0.672794\pi$
$173$	−3.63542	+	1.50584i	−0.276396	+	0.114487i	0.240180	+	0.970728i	$0.422794\pi$
$174$			1.10757i			0.0839644i
$175$	−2.49254	−	6.01752i	−0.188418	−	0.454882i
$176$	0.382218	+	0.158320i	0.0288107	+	0.0119338i
$177$	3.21620	−	7.76460i	0.241745	−	0.583623i
$178$	−1.55231	+	1.55231i	−0.116350	+	0.116350i
$179$	−10.6978	+	10.6978i	−0.799593	+	0.799593i	−0.983031	−	0.183439i	$-0.941277\pi$
$179$	−10.6978	+	10.6978i	−0.799593	+	0.799593i	0.183439	+	0.983031i	$0.441277\pi$
$180$	−7.33988	+	17.7200i	−0.547082	+	1.32077i
$181$	9.17661	+	3.80108i	0.682092	+	0.282532i	0.696701	−	0.717362i	$-0.254650\pi$
$181$	9.17661	+	3.80108i	0.682092	+	0.282532i	−0.0146092	+	0.999893i	$0.504650\pi$
$182$	0.239542	+	0.578306i	0.0177561	+	0.0428669i
$183$			7.44487i			0.550340i
$184$	1.61323	−	0.668223i	0.118929	−	0.0492620i
$185$	5.93100	+	5.93100i	0.436056	+	0.436056i
$186$	−0.299313			−0.0219467
$187$	0.306097	−	0.357226i	0.0223840	−	0.0261230i
$188$	−1.12353			−0.0819420
$189$	−1.70945	−	1.70945i	−0.124344	−	0.124344i
$190$	2.81107	−	1.16438i	0.203936	−	0.0844731i
$191$			13.0184i			0.941978i	0.882139	+	0.470989i	$0.156103\pi$
$191$			13.0184i			0.941978i	−0.882139	+	0.470989i	$0.843897\pi$
$192$	1.63364	+	3.94396i	0.117898	+	0.284631i
$193$	−12.8443	−	5.32029i	−0.924555	−	0.382963i	−0.130945	−	0.991390i	$-0.541801\pi$
$193$	−12.8443	−	5.32029i	−0.924555	−	0.382963i	−0.793610	+	0.608427i	$0.791801\pi$
$194$	0.623053	−	1.50418i	0.0447326	−	0.107994i
$195$	−6.69216	+	6.69216i	−0.479236	+	0.479236i
$196$	8.98490	−	8.98490i	0.641779	−	0.641779i
$197$	0.783626	−	1.89184i	0.0558311	−	0.134788i	−0.893503	−	0.449058i	$-0.851760\pi$
$197$	0.783626	−	1.89184i	0.0558311	−	0.134788i	0.949334	+	0.314270i	$0.101760\pi$
$198$	−0.0680584	−	0.0281907i	−0.00483670	−	0.00200343i
$199$	−8.42809	−	20.3472i	−0.597452	−	1.44238i	−0.876170	−	0.482003i	$-0.839910\pi$
$199$	−8.42809	−	20.3472i	−0.597452	−	1.44238i	0.278718	−	0.960373i	$-0.410090\pi$
$200$		−	9.70241i		−	0.686064i
$201$	4.89858	−	2.02906i	0.345519	−	0.143119i
$202$	0.540112	+	0.540112i	0.0380021	+	0.0380021i
$203$	4.47592			0.314148
$204$	5.20767	−	0.401408i	0.364610	−	0.0281042i
$205$	35.1757			2.45678
$206$	2.76403	+	2.76403i	0.192579	+	0.192579i
$207$	4.19930	−	1.73941i	0.291871	−	0.120897i
$208$		−	13.6310i		−	0.945142i
$209$	−0.137497	−	0.331947i	−0.00951085	−	0.0229612i
$210$	0.387283	+	0.160418i	0.0267251	+	0.0110699i
$211$	2.78522	−	6.72411i	0.191742	−	0.462907i	−0.798546	−	0.601933i	$-0.794397\pi$
$211$	2.78522	−	6.72411i	0.191742	−	0.462907i	0.990289	+	0.139026i	$0.0443973\pi$
$212$	4.99883	−	4.99883i	0.343321	−	0.343321i
$213$	5.22419	−	5.22419i	0.357956	−	0.357956i
$214$	0.630810	−	1.52291i	0.0431213	−	0.104104i
$215$	−3.55644	−	1.47313i	−0.242547	−	0.100466i
$216$	−1.37813	−	3.32709i	−0.0937696	−	0.226380i
$217$			1.20959i			0.0821123i
$218$	1.72904	−	0.716190i	0.117105	−	0.0485065i
$219$	0.816081	+	0.816081i	0.0551457	+	0.0551457i
$220$	−0.850750			−0.0573575
$221$	−14.7336	−	4.81350i	−0.991088	−	0.323791i
$222$	−0.357679			−0.0240058
$223$	9.77468	+	9.77468i	0.654561	+	0.654561i	0.954088	−	0.299527i	$-0.0968287\pi$
$223$	9.77468	+	9.77468i	0.654561	+	0.654561i	−0.299527	+	0.954088i	$0.596829\pi$
$224$	−1.76908	+	0.732779i	−0.118202	+	0.0489608i
$225$		−	25.2557i		−	1.68371i
$226$	−0.314127	−	0.758370i	−0.0208954	−	0.0504460i
$227$	−10.2430	−	4.24278i	−0.679850	−	0.281603i	0.0159141	−	0.999873i	$-0.494934\pi$
$227$	−10.2430	−	4.24278i	−0.679850	−	0.281603i	−0.695764	+	0.718270i	$0.744934\pi$
$228$	1.52660	−	3.68554i	0.101102	−	0.244081i
$229$	−9.59172	+	9.59172i	−0.633839	+	0.633839i	−0.949029	−	0.315190i	$-0.897932\pi$
$229$	−9.59172	+	9.59172i	−0.633839	+	0.633839i	0.315190	+	0.949029i	$0.397932\pi$
$230$	−1.20726	+	1.20726i	−0.0796045	+	0.0796045i
$231$	0.0189430	−	0.0457326i	0.00124636	−	0.00300898i
$232$	6.15991	+	2.55152i	0.404418	+	0.167515i
$233$	−0.536021	−	1.29407i	−0.0351159	−	0.0847773i	0.905349	−	0.424669i	$-0.139610\pi$
$233$	−0.536021	−	1.29407i	−0.0351159	−	0.0847773i	−0.940465	+	0.339892i	$0.889610\pi$
$234$			2.42717i			0.158669i
$235$	2.06287	−	0.854469i	0.134567	−	0.0557394i
$236$	−17.6012	−	17.6012i	−1.14574	−	1.14574i
$237$	7.54036			0.489799
$238$	0.0527616	+	0.684503i	0.00342003	+	0.0443697i
$239$	14.5730			0.942647			0.471324	−	0.881960i	$-0.343776\pi$
$239$	14.5730			0.942647			0.471324	+	0.881960i	$0.343776\pi$
$240$	−6.45482	−	6.45482i	−0.416657	−	0.416657i
$241$	−4.59013	+	1.90129i	−0.295676	+	0.122473i	−0.525590	−	0.850738i	$-0.676155\pi$
$241$	−4.59013	+	1.90129i	−0.295676	+	0.122473i	0.229914	+	0.973211i	$0.426155\pi$
$242$			2.75774i			0.177274i
$243$	−5.51864	−	13.3232i	−0.354021	−	0.854681i
$244$	20.3716	+	8.43821i	1.30416	+	0.540201i
$245$	−9.66360	+	23.3300i	−0.617385	+	1.49050i
$246$	−1.06066	+	1.06066i	−0.0676254	+	0.0676254i
$247$	−8.37089	+	8.37089i	−0.532627	+	0.532627i
$248$	−0.689533	+	1.66468i	−0.0437854	+	0.105707i
$249$	−2.61348	−	1.08254i	−0.165623	−	0.0686032i
$250$	1.78162	+	4.30122i	0.112680	+	0.272033i
$251$		−	17.5640i		−	1.10863i	−0.832308	−	0.554314i	$-0.812981\pi$
$251$		−	17.5640i		−	1.10863i	0.832308	−	0.554314i	$-0.187019\pi$
$252$	−3.05370	+	1.26489i	−0.192365	+	0.0796803i
$253$	0.142560	+	0.142560i	0.00896270	+	0.00896270i
$254$	−1.90726			−0.119672
$255$	−9.25630	+	4.69754i	−0.579652	+	0.294172i
$256$	11.1946			0.699660
$257$	7.33243	+	7.33243i	0.457384	+	0.457384i	0.897796	−	0.440412i	$-0.145167\pi$
$257$	7.33243	+	7.33243i	0.457384	+	0.457384i	−0.440412	+	0.897796i	$0.645167\pi$
$258$	0.151658	−	0.0628188i	0.00944182	−	0.00391093i
$259$			1.44546i			0.0898163i
$260$	10.7269	+	25.8971i	0.665255	+	1.60607i
$261$	16.0345	+	6.64169i	0.992508	+	0.411110i
$262$	−0.00453838	+	0.0109566i	−0.000280382	+	0.000676901i
$263$	−12.1451	+	12.1451i	−0.748897	+	0.748897i	−0.974272	−	0.225375i	$-0.927639\pi$
$263$	−12.1451	+	12.1451i	−0.748897	+	0.748897i	0.225375	+	0.974272i	$0.427639\pi$
$264$	0.0521402	−	0.0521402i	0.00320901	−	0.00320901i
$265$	−5.37643	+	12.9799i	−0.330272	+	0.797346i
$266$	0.484432	+	0.200658i	0.0297025	+	0.0123032i
$267$	−2.18894	−	5.28457i	−0.133961	−	0.323410i
$268$		−	15.7039i		−	0.959270i
$269$	−28.2066	+	11.6836i	−1.71979	+	0.712359i	−0.719955	+	0.694021i	$0.755837\pi$
$269$	−28.2066	+	11.6836i	−1.71979	+	0.712359i	−0.999832	+	0.0183377i	$0.994163\pi$
$270$	2.48983	+	2.48983i	0.151526	+	0.151526i
$271$	9.25373			0.562124			0.281062	−	0.959690i	$-0.409313\pi$
$271$	9.25373			0.562124			0.281062	+	0.959690i	$0.409313\pi$
$272$	4.64278	−	14.2110i	0.281510	−	0.861671i
$273$	−1.63096			−0.0987103
$274$	0.373945	+	0.373945i	0.0225908	+	0.0225908i
$275$	1.03497	−	0.428698i	0.0624110	−	0.0258515i
$276$			2.23845i			0.134739i
$277$	8.93004	+	21.5590i	0.536554	+	1.29536i	0.927114	+	0.374779i	$0.122281\pi$
$277$	8.93004	+	21.5590i	0.536554	+	1.29536i	−0.390560	+	0.920578i	$0.627719\pi$
$278$	−0.936060	−	0.387729i	−0.0561412	−	0.0232544i
$279$	−1.79488	+	4.33322i	−0.107456	+	0.259423i
$280$	1.78438	−	1.78438i	0.106637	−	0.106637i
$281$	4.94600	−	4.94600i	0.295053	−	0.295053i	−0.544019	−	0.839073i	$-0.683098\pi$
$281$	4.94600	−	4.94600i	0.295053	−	0.295053i	0.839073	+	0.544019i	$0.183098\pi$
$282$	−0.0364373	+	0.0879674i	−0.00216981	+	0.00523838i
$283$	−22.7457	−	9.42156i	−1.35209	−	0.560054i	−0.415216	−	0.909723i	$-0.636294\pi$
$283$	−22.7457	−	9.42156i	−1.35209	−	0.560054i	−0.936873	+	0.349669i	$0.886294\pi$
$284$	−8.37389	−	20.2164i	−0.496899	−	1.19962i
$285$			7.92788i			0.469607i
$286$	−0.0994644	+	0.0411995i	−0.00588145	+	0.00243618i
$287$	4.28637	+	4.28637i	0.253017	+	0.253017i
$288$	−7.42490			−0.437516
$289$	−13.7210	−	10.0366i	−0.807118	−	0.590390i
$290$	−6.51920			−0.382821
$291$	2.99966	+	2.99966i	0.175843	+	0.175843i
$292$	3.15804	−	1.30810i	0.184810	−	0.0765509i
$293$			24.3177i			1.42065i	0.703872	+	0.710326i	$0.251453\pi$
$293$			24.3177i			1.42065i	−0.703872	+	0.710326i	$0.748547\pi$
$294$	−0.412087	−	0.994866i	−0.0240334	−	0.0580218i
$295$	45.7029	+	18.9308i	2.66093	+	1.10219i
$296$	−0.823990	+	1.98929i	−0.0478935	+	0.115625i
$297$	0.294013	−	0.294013i	0.0170604	−	0.0170604i
$298$	−2.33043	+	2.33043i	−0.134998	+	0.134998i
$299$	2.54207	−	6.13709i	0.147012	−	0.354917i
$300$	11.4911	+	4.75975i	0.663437	+	0.274805i
$301$	−0.253865	−	0.612883i	−0.0146325	−	0.0353260i
$302$		−	1.42317i		−	0.0818941i
$303$	−1.83872	+	0.761622i	−0.105632	+	0.0437540i
$304$	−8.07401	−	8.07401i	−0.463076	−	0.463076i
$305$	−43.8209			−2.50918
$306$	−0.826703	+	2.53044i	−0.0472594	+	0.144656i
$307$	27.8152			1.58750			0.793749	−	0.608246i	$-0.208126\pi$
$307$	27.8152			1.58750			0.793749	+	0.608246i	$0.208126\pi$
$308$	−0.103669	−	0.103669i	−0.00590709	−	0.00590709i
$309$	−9.40966	+	3.89761i	−0.535297	+	0.221727i
$310$		−	1.76177i		−	0.100062i
$311$	−6.15968	−	14.8708i	−0.349284	−	0.843245i	−0.996705	−	0.0811130i	$-0.974153\pi$
$311$	−6.15968	−	14.8708i	−0.349284	−	0.843245i	0.647421	−	0.762132i	$-0.275847\pi$
$312$	−2.24459	−	0.929738i	−0.127075	−	0.0526361i
$313$	2.34916	−	5.67137i	0.132782	−	0.320565i	−0.843479	−	0.537163i	$-0.819496\pi$
$313$	2.34916	−	5.67137i	0.132782	−	0.320565i	0.976261	+	0.216598i	$0.0694961\pi$
$314$	−3.73367	+	3.73367i	−0.210703	+	0.210703i
$315$	4.64480	−	4.64480i	0.261705	−	0.261705i
$316$	8.54644	−	20.6329i	0.480775	−	1.16069i
$317$	19.4129	+	8.04108i	1.09034	+	0.451632i	0.854124	−	0.520070i	$-0.174094\pi$
$317$	19.4129	+	8.04108i	1.09034	+	0.451632i	0.236212	+	0.971702i	$0.424094\pi$
$318$	−0.229268	−	0.553503i	−0.0128567	−	0.0310389i
$319$			0.769824i			0.0431019i
$320$	−23.2144	+	9.61570i	−1.29772	+	0.537534i
$321$	3.03700	+	3.03700i	0.169509	+	0.169509i
$322$	−0.294224			−0.0163965
$323$	−11.5782	+	5.87592i	−0.644230	+	0.326945i
$324$	−10.3310			−0.573947
$325$	−26.0994	−	26.0994i	−1.44773	−	1.44773i
$326$	4.50377	−	1.86552i	0.249441	−	0.103322i
$327$			4.87630i			0.269660i
$328$	3.45559	+	8.34253i	0.190803	+	0.460639i
$329$	0.355496	+	0.147251i	0.0195991	+	0.00811821i
$330$	−0.0275907	+	0.0666098i	−0.00151882	+	0.00366675i
$331$	−10.6599	+	10.6599i	−0.585923	+	0.585923i	−0.936525	−	0.350602i	$-0.885977\pi$
$331$	−10.6599	+	10.6599i	−0.585923	+	0.585923i	0.350602	+	0.936525i	$0.385977\pi$
$332$	−5.92439	+	5.92439i	−0.325143	+	0.325143i
$333$	−2.14487	+	5.17819i	−0.117538	+	0.283763i
$334$	−4.12967	−	1.71056i	−0.225965	−	0.0935979i
$335$	11.9432	+	28.8333i	0.652524	+	1.57533i
$336$		−	1.57312i		−	0.0858206i
$337$	18.8753	−	7.81842i	1.02821	−	0.425896i	0.196141	−	0.980576i	$-0.437159\pi$
$337$	18.8753	−	7.81842i	1.02821	−	0.425896i	0.832064	+	0.554679i	$0.187159\pi$
$338$	0.200955	+	0.200955i	0.0109305	+	0.0109305i
$339$	2.13878			0.116163
$340$	2.36271	+	30.6526i	0.128136	+	1.66237i
$341$	−0.208040			−0.0112660
$342$	1.43767	+	1.43767i	0.0777404	+	0.0777404i
$343$	−8.31065	+	3.44239i	−0.448733	+	0.185871i
$344$		−	0.988189i		−	0.0532796i
$345$	−1.70238	−	4.10992i	−0.0916533	−	0.221271i
$346$	0.912493	+	0.377967i	0.0490559	+	0.0203196i
$347$	−9.29912	+	22.4501i	−0.499203	+	1.20518i	0.450711	+	0.892670i	$0.351171\pi$
$347$	−9.29912	+	22.4501i	−0.499203	+	1.20518i	−0.949914	+	0.312512i	$0.898829\pi$
$348$	−6.04379	+	6.04379i	−0.323981	+	0.323981i
$349$	−6.65512	+	6.65512i	−0.356240	+	0.356240i	−0.862425	−	0.506185i	$-0.831055\pi$
$349$	−6.65512	+	6.65512i	−0.356240	+	0.356240i	0.506185	+	0.862425i	$0.331055\pi$
$350$	−0.625628	+	1.51040i	−0.0334412	+	0.0807343i
$351$	−12.6570	−	5.24269i	−0.675580	−	0.279834i
$352$	−0.126032	−	0.304269i	−0.00671755	−	0.0162176i
$353$		−	23.5757i		−	1.25481i	−0.778694	−	0.627403i	$-0.784118\pi$
$353$		−	23.5757i		−	1.25481i	0.778694	−	0.627403i	$-0.215882\pi$
$354$	−1.94892	+	0.807269i	−0.103584	+	0.0429058i
$355$	30.7499	+	30.7499i	1.63204	+	1.63204i
$356$	−16.9413			−0.897889
$357$	−1.70036	−	0.555512i	−0.0899926	−	0.0294008i
$358$	3.79739			0.200698
$359$	−5.62282	−	5.62282i	−0.296761	−	0.296761i	0.542983	−	0.839744i	$-0.317295\pi$
$359$	−5.62282	−	5.62282i	−0.296761	−	0.296761i	−0.839744	+	0.542983i	$0.817295\pi$
$360$	9.04014	−	3.74455i	0.476457	−	0.197355i
$361$		−	9.08342i		−	0.478075i
$362$	−0.954072	−	2.30333i	−0.0501449	−	0.121060i
$363$	−6.63849	−	2.74975i	−0.348430	−	0.144325i
$364$	−1.84857	+	4.46285i	−0.0968916	+	0.233917i
$365$	−4.80350	+	4.80350i	−0.251427	+	0.251427i
$366$	1.32135	−	1.32135i	0.0690679	−	0.0690679i
$367$	−2.67501	+	6.45804i	−0.139634	+	0.337107i	−0.978191	−	0.207707i	$-0.933400\pi$
$367$	−2.67501	+	6.45804i	−0.139634	+	0.337107i	0.838557	+	0.544814i	$0.183400\pi$
$368$	5.91944	+	2.45191i	0.308572	+	0.127815i
$369$	8.99501	+	21.7159i	0.468262	+	1.13048i
$370$		−	2.10532i		−	0.109450i
$371$	−2.23683	+	0.926523i	−0.116130	+	0.0481027i
$372$	−1.63330	−	1.63330i	−0.0846826	−	0.0846826i
$373$	31.2985			1.62058			0.810288	−	0.586032i	$-0.199311\pi$
$373$	31.2985			1.62058			0.810288	+	0.586032i	$0.199311\pi$
$374$	−0.117729	+	0.00907460i	−0.00608764	+	0.000469236i
$375$	−12.1305			−0.626414
$376$	0.405304	+	0.405304i	0.0209020	+	0.0209020i
$377$	23.4337	−	9.70655i	1.20690	−	0.499913i
$378$			0.606801i			0.0312105i
$379$	2.01414	+	4.86255i	0.103459	+	0.249773i	0.967129	−	0.254285i	$-0.0818400\pi$
$379$	2.01414	+	4.86255i	0.103459	+	0.249773i	−0.863670	+	0.504057i	$0.831840\pi$
$380$	21.6933	+	8.98567i	1.11284	+	0.460955i
$381$	1.90174	−	4.59120i	0.0974290	−	0.235214i
$382$	2.31056	−	2.31056i	0.118218	−	0.118218i
$383$	−4.07871	+	4.07871i	−0.208413	+	0.208413i	−0.803592	−	0.595180i	$-0.797081\pi$
$383$	−4.07871	+	4.07871i	−0.208413	+	0.208413i	0.595180	+	0.803592i	$0.297081\pi$
$384$	1.85487	−	4.47806i	0.0946561	−	0.228520i
$385$	0.269185	+	0.111500i	0.0137189	+	0.00568256i
$386$	1.33540	+	3.22393i	0.0679699	+	0.164094i
$387$		−	2.57229i		−	0.130757i
$388$	11.6079	−	4.80817i	0.589304	−	0.244098i
$389$	26.9021	+	26.9021i	1.36399	+	1.36399i	0.868764	+	0.495226i	$0.164915\pi$
$389$	26.9021	+	26.9021i	1.36399	+	1.36399i	0.495226	+	0.868764i	$0.335085\pi$
$390$	2.37551			0.120288
$391$	4.74055	−	5.53239i	0.239740	−	0.279785i
$392$	−6.48244			−0.327413
$393$	−0.0218498	−	0.0218498i	−0.00110218	−	0.00110218i
$394$	−0.474853	+	0.196691i	−0.0239227	+	0.00990913i
$395$			44.3830i			2.23315i
$396$	−0.217551	−	0.525214i	−0.0109323	−	0.0263930i
$397$	13.8979	+	5.75669i	0.697514	+	0.288920i	0.703127	−	0.711064i	$-0.251787\pi$
$397$	13.8979	+	5.75669i	0.697514	+	0.288920i	−0.00561271	+	0.999984i	$0.501787\pi$
$398$	−2.11545	+	5.10716i	−0.106038	+	0.255999i
$399$	−0.966060	+	0.966060i	−0.0483635	+	0.0483635i
$400$	25.1738	−	25.1738i	1.25869	−	1.25869i
$401$	0.265619	−	0.641262i	0.0132644	−	0.0320231i	−0.917109	−	0.398637i	$-0.869483\pi$
$401$	0.265619	−	0.641262i	0.0132644	−	0.0320231i	0.930373	+	0.366614i	$0.119483\pi$
$402$	−1.22955	−	0.509294i	−0.0613241	−	0.0254013i
$403$	2.62314	+	6.33281i	0.130668	+	0.315460i
$404$			5.89459i			0.293267i
$405$	18.9684	−	7.85696i	0.942547	−	0.390416i
$406$	−0.794404	−	0.794404i	−0.0394256	−	0.0394256i
$407$	−0.248608			−0.0123230
$408$	−2.02342	−	1.73381i	−0.100174	−	0.0858366i
$409$	26.0506			1.28812			0.644060	−	0.764975i	$-0.277249\pi$
$409$	26.0506			1.28812			0.644060	+	0.764975i	$0.277249\pi$
$410$	−6.24313	−	6.24313i	−0.308326	−	0.308326i
$411$	−1.27303	+	0.527307i	−0.0627940	+	0.0260101i
$412$			30.1656i			1.48615i
$413$	3.26235	+	7.87600i	0.160530	+	0.387553i
$414$	−1.05403	−	0.436592i	−0.0518026	−	0.0214573i
$415$	6.37190	−	15.3831i	0.312784	−	0.755128i
$416$	−7.67293	+	7.67293i	−0.376196	+	0.376196i
$417$	1.86670	−	1.86670i	0.0914127	−	0.0914127i
$418$	−0.0345118	+	0.0833188i	−0.00168803	+	0.00407525i
$419$	17.7814	+	7.36530i	0.868678	+	0.359818i	0.772095	−	0.635507i	$-0.219209\pi$
$419$	17.7814	+	7.36530i	0.868678	+	0.359818i	0.0965829	+	0.995325i	$0.469209\pi$
$420$	1.23796	+	2.98871i	0.0604064	+	0.145834i
$421$		−	26.1036i		−	1.27221i	−0.771601	−	0.636107i	$-0.780544\pi$
$421$		−	26.1036i		−	1.27221i	0.771601	−	0.636107i	$-0.219456\pi$
$422$	−1.68775	+	0.699091i	−0.0821586	+	0.0340312i
$423$	1.05502	+	1.05502i	0.0512969	+	0.0512969i
$424$	−3.60657			−0.175150
$425$	−18.3204	−	36.0995i	−0.888669	−	1.75108i
$426$	−1.85442			−0.0898470
$427$	−5.33985	−	5.33985i	−0.258413	−	0.258413i
$428$	11.7525	−	4.86803i	0.568077	−	0.235305i
$429$		−	0.280513i		−	0.0135433i
$430$	0.369755	+	0.892669i	0.0178312	+	0.0430483i
$431$	35.7528	+	14.8093i	1.72215	+	0.713339i	0.999761	+	0.0218543i	$0.00695699\pi$
$431$	35.7528	+	14.8093i	1.72215	+	0.713339i	0.722391	+	0.691485i	$0.243043\pi$
$432$	5.05676	−	12.2081i	0.243293	−	0.587362i
$433$	−7.11630	+	7.11630i	−0.341988	+	0.341988i	−0.857114	−	0.515126i	$-0.827745\pi$
$433$	−7.11630	+	7.11630i	−0.341988	+	0.341988i	0.515126	+	0.857114i	$0.327745\pi$
$434$	0.214683	−	0.214683i	0.0103051	−	0.0103051i
$435$	6.50033	−	15.6932i	0.311667	−	0.752430i
$436$	13.3432	+	5.52692i	0.639022	+	0.264692i
$437$	−2.12943	−	5.14089i	−0.101864	−	0.245922i
$438$		−	0.289683i		−	0.0138416i
$439$	−15.0238	+	6.22306i	−0.717046	+	0.297010i	−0.711217	−	0.702973i	$-0.751856\pi$
$439$	−15.0238	+	6.22306i	−0.717046	+	0.297010i	−0.00582955	+	0.999983i	$0.501856\pi$
$440$	0.306900	+	0.306900i	0.0146309	+	0.0146309i
$441$	−16.8740			−0.803525
$442$	1.76066	+	3.46930i	0.0837459	+	0.165018i
$443$	−7.65206			−0.363560			−0.181780	−	0.983339i	$-0.558186\pi$
$443$	−7.65206			−0.363560			−0.181780	+	0.983339i	$0.558186\pi$
$444$	−1.95179	−	1.95179i	−0.0926278	−	0.0926278i
$445$	31.1053	−	12.8842i	1.47453	−	0.610771i
$446$		−	3.46970i		−	0.164295i
$447$	−3.28619	−	7.93356i	−0.155431	−	0.375245i
$448$	−4.00054	−	1.65708i	−0.189008	−	0.0782896i
$449$	11.9882	−	28.9420i	0.565757	−	1.36586i	−0.339344	−	0.940662i	$-0.610205\pi$
$449$	11.9882	−	28.9420i	0.565757	−	1.36586i	0.905101	−	0.425197i	$-0.139795\pi$
$450$	−4.48249	+	4.48249i	−0.211306	+	0.211306i
$451$	−0.737224	+	0.737224i	−0.0347145	+	0.0347145i
$452$	2.42415	−	5.85243i	0.114023	−	0.275275i
$453$	3.42588	+	1.41905i	0.160962	+	0.0666727i
$454$	1.06494	+	2.57099i	0.0499801	+	0.120663i
$455$		−	9.59994i		−	0.450052i
$456$	−1.88023	+	0.778818i	−0.0880500	+	0.0364715i
$457$	−6.41507	−	6.41507i	−0.300084	−	0.300084i	0.540963	−	0.841047i	$-0.318060\pi$
$457$	−6.41507	−	6.41507i	−0.300084	−	0.300084i	−0.841047	+	0.540963i	$0.818060\pi$
$458$	3.40476			0.159094
$459$	−11.4099	−	9.77679i	−0.532567	−	0.456342i
$460$	−13.1756			−0.614317
$461$	4.56218	+	4.56218i	0.212482	+	0.212482i	0.805321	−	0.592839i	$-0.201993\pi$
$461$	4.56218	+	4.56218i	0.212482	+	0.212482i	−0.592839	+	0.805321i	$0.701993\pi$
$462$	−0.0114789	+	0.00475471i	−0.000534047	+	0.000221209i
$463$			27.8576i			1.29465i	0.762213	+	0.647326i	$0.224113\pi$
$463$			27.8576i			1.29465i	−0.762213	+	0.647326i	$0.775887\pi$
$464$	9.36230	+	22.6026i	0.434634	+	1.04930i
$465$	4.24099	+	1.75667i	0.196671	+	0.0814638i
$466$	−0.134541	+	0.324812i	−0.00623251	+	0.0150466i
$467$	28.1437	−	28.1437i	1.30233	−	1.30233i	0.375521	−	0.926814i	$-0.377464\pi$
$467$	28.1437	−	28.1437i	1.30233	−	1.30233i	0.926814	−	0.375521i	$-0.122536\pi$
$468$	−13.2446	+	13.2446i	−0.612233	+	0.612233i
$469$	−2.05817	+	4.96886i	−0.0950374	+	0.229441i
$470$	−0.517782	−	0.214472i	−0.0238835	−	0.00989286i
$471$	−5.26492	−	12.7106i	−0.242595	−	0.585676i
$472$			12.6990i			0.584517i
$473$	0.105411	−	0.0436628i	0.00484682	−	0.00200762i
$474$	−1.33829	−	1.33829i	−0.0614699	−	0.0614699i
$475$	−30.9187			−1.41865
$476$	−3.44730	+	4.02312i	−0.158007	+	0.184399i
$477$	−9.38802			−0.429848
$478$	−2.58647	−	2.58647i	−0.118302	−	0.118302i
$479$	−15.3894	+	6.37449i	−0.703159	+	0.291258i	−0.705470	−	0.708739i	$-0.749264\pi$
$479$	−15.3894	+	6.37449i	−0.703159	+	0.291258i	0.00231143	+	0.999997i	$0.499264\pi$
$480$			7.26686i			0.331685i
$481$	3.13464	+	7.56769i	0.142927	+	0.345057i
$482$	1.15212	+	0.477225i	0.0524778	+	0.0217370i
$483$	0.293373	−	0.708264i	0.0133489	−	0.0322271i
$484$	−15.0485	+	15.0485i	−0.684022	+	0.684022i
$485$	−17.6562	+	17.6562i	−0.801725	+	0.801725i
$486$	−1.38518	+	3.34412i	−0.0628330	+	0.151692i
$487$	23.4362	+	9.70758i	1.06199	+	0.439893i	0.844159	−	0.536093i	$-0.180100\pi$
$487$	23.4362	+	9.70758i	1.06199	+	0.439893i	0.217836	+	0.975985i	$0.430100\pi$
$488$	−4.30488	−	10.3929i	−0.194873	−	0.470464i
$489$			12.7017i			0.574391i
$490$	5.85584	−	2.42557i	0.264540	−	0.109576i
$491$	7.87339	+	7.87339i	0.355321	+	0.355321i	0.862085	−	0.506764i	$-0.169158\pi$
$491$	7.87339	+	7.87339i	0.355321	+	0.355321i	−0.506764	+	0.862085i	$0.669158\pi$
$492$	−11.5757			−0.521873
$493$	27.7369	−	2.13796i	1.24921	−	0.0962890i
$494$	2.97140			0.133690
$495$	0.798872	+	0.798872i	0.0359066	+	0.0359066i
$496$	−6.10821	+	2.53010i	−0.274267	+	0.113605i
$497$			7.49412i			0.336157i
$498$	0.271718	+	0.655986i	0.0121760	+	0.0293954i
$499$	−1.37354	−	0.568940i	−0.0614882	−	0.0254692i	0.351727	−	0.936102i	$-0.385594\pi$
$499$	−1.37354	−	0.568940i	−0.0614882	−	0.0254692i	−0.413216	+	0.910633i	$0.635594\pi$
$500$	−13.7490	+	33.1930i	−0.614873	+	1.48443i
$501$	8.23542	−	8.23542i	0.367931	−	0.367931i
$502$	−3.11733	+	3.11733i	−0.139133	+	0.139133i
$503$	1.71526	−	4.14099i	0.0764795	−	0.184638i	−0.881016	−	0.473087i	$-0.843140\pi$
$503$	1.71526	−	4.14099i	0.0764795	−	0.184638i	0.957495	+	0.288449i	$0.0931396\pi$
$504$	1.55789	+	0.645300i	0.0693940	+	0.0287439i
$505$	−4.48295	−	10.8228i	−0.199489	−	0.481608i
$506$		−	0.0506044i		−	0.00224964i
$507$	−0.684118	+	0.283371i	−0.0303827	+	0.0125849i
$508$	−10.4076	−	10.4076i	−0.461762	−	0.461762i
$509$	19.4795			0.863412			0.431706	−	0.902014i	$-0.357912\pi$
$509$	19.4795			0.863412			0.431706	+	0.902014i	$0.357912\pi$
$510$	2.47659	+	0.809107i	0.109665	+	0.0358278i
$511$	−1.17067			−0.0517875
$512$	−12.4681	−	12.4681i	−0.551018	−	0.551018i
$513$	−10.6024	+	4.39167i	−0.468109	+	0.193897i
$514$		−	2.60278i		−	0.114804i
$515$	−22.9415	−	55.3858i	−1.01093	−	2.44059i
$516$	1.17036	+	0.484780i	0.0515223	+	0.0213412i
$517$	−0.0253261	+	0.0611426i	−0.00111384	+	0.00268905i
$518$	0.256546	−	0.256546i	0.0112720	−	0.0112720i
$519$	−1.81970	+	1.81970i	−0.0798761	+	0.0798761i
$520$	5.47250	−	13.2118i	0.239985	−	0.579375i
$521$	−11.1504	−	4.61863i	−0.488506	−	0.202346i	0.124814	−	0.992180i	$-0.460166\pi$
$521$	−11.1504	−	4.61863i	−0.488506	−	0.202346i	−0.613320	+	0.789834i	$0.710166\pi$
$522$	−1.66707	−	4.02466i	−0.0729656	−	0.176154i
$523$		−	29.1524i		−	1.27475i	−0.770555	−	0.637374i	$-0.780021\pi$
$523$		−	29.1524i		−	1.27475i	0.770555	−	0.637374i	$-0.219979\pi$
$524$	−0.0845534	+	0.0350232i	−0.00369373	+	0.00152999i
$525$	−3.01206	−	3.01206i	−0.131457	−	0.131457i
$526$	4.31111			0.187973
$527$	0.577772	+	7.49572i	0.0251681	+	0.326519i
$528$	0.270565			0.0117748
$529$	−14.0556	−	14.0556i	−0.611113	−	0.611113i
$530$	3.25795	−	1.34949i	0.141516	−	0.0586180i
$531$			33.0558i			1.43450i
$532$	1.54850	+	3.73842i	0.0671362	+	0.162081i
$533$	31.7368	+	13.1458i	1.37467	+	0.569409i
$534$	−0.549425	+	1.32643i	−0.0237759	+	0.0574002i
$535$	−17.8760	+	17.8760i	−0.772846	+	0.772846i
$536$	−5.66505	+	5.66505i	−0.244693	+	0.244693i
$537$	−3.78639	+	9.14116i	−0.163395	+	0.394470i
$538$	7.07987	+	2.93258i	0.305235	+	0.126432i
$539$	−0.286425	−	0.691491i	−0.0123372	−	0.0297846i
$540$			27.1731i			1.16934i
$541$	−36.6919	+	15.1983i	−1.57751	+	0.653425i	−0.988016	−	0.154350i	$-0.950672\pi$
$541$	−36.6919	+	15.1983i	−1.57751	+	0.653425i	−0.589491	+	0.807775i	$0.700672\pi$
$542$	−1.64239	−	1.64239i	−0.0705467	−	0.0705467i
$543$	6.49595			0.278768
$544$	−10.6129	+	5.38599i	−0.455022	+	0.230922i
$545$	−28.7022			−1.22947
$546$	0.289470	+	0.289470i	0.0123882	+	0.0123882i
$547$	−25.0608	+	10.3805i	−1.07152	+	0.443840i	−0.847528	−	0.530750i	$-0.821910\pi$
$547$	−25.0608	+	10.3805i	−1.07152	+	0.443840i	−0.223996	+	0.974590i	$0.571910\pi$
$548$			4.08110i			0.174336i
$549$	−11.2057	−	27.0530i	−0.478249	−	1.15460i
$550$	−0.259778	−	0.107603i	−0.0110770	−	0.00458822i
$551$	8.13093	−	19.6298i	0.346389	−	0.836257i
$552$	0.807500	−	0.807500i	0.0343695	−	0.0343695i
$553$	−5.40834	+	5.40834i	−0.229986	+	0.229986i
$554$	2.24144	−	5.41133i	0.0952299	−	0.229905i
$555$	5.06797	+	2.09922i	0.215123	+	0.0891070i
$556$	−2.99215	−	7.22368i	−0.126895	−	0.306352i
$557$		−	19.8456i		−	0.840887i	−0.907319	−	0.420443i	$-0.861875\pi$
$557$		−	19.8456i		−	0.840887i	0.907319	−	0.420443i	$-0.138125\pi$
$558$	1.08764	−	0.450515i	0.0460434	−	0.0190718i
$559$	−2.65822	−	2.65822i	−0.112431	−	0.112431i
$560$	9.25947			0.391284
$561$	0.0955439	−	0.292449i	0.00403387	−	0.0123472i
$562$	−1.75567			−0.0740585
$563$	−9.14652	−	9.14652i	−0.385480	−	0.385480i	0.487592	−	0.873072i	$-0.337875\pi$
$563$	−9.14652	−	9.14652i	−0.385480	−	0.385480i	−0.873072	+	0.487592i	$0.837875\pi$
$564$	−0.678855	+	0.281191i	−0.0285849	+	0.0118403i
$565$			12.5890i			0.529624i
$566$	2.36482	+	5.70917i	0.0994007	+	0.239974i
$567$	3.26883	+	1.35399i	0.137278	+	0.0568624i
$568$	−4.27206	+	10.3137i	−0.179252	+	0.432752i
$569$	−7.76611	+	7.76611i	−0.325572	+	0.325572i	−0.850900	−	0.525328i	$-0.823943\pi$
$569$	−7.76611	+	7.76611i	−0.325572	+	0.325572i	0.525328	+	0.850900i	$0.323943\pi$
$570$	1.40707	−	1.40707i	0.0589358	−	0.0589358i
$571$	−6.38200	+	15.4075i	−0.267078	+	0.644784i	−0.999343	−	0.0362357i	$-0.988463\pi$
$571$	−6.38200	+	15.4075i	−0.267078	+	0.644784i	0.732265	+	0.681020i	$0.238463\pi$
$572$	−0.767578	−	0.317941i	−0.0320940	−	0.0132938i
$573$	3.25816	+	7.86590i	0.136112	+	0.328603i
$574$		−	1.52153i		−	0.0635073i
$575$	16.0287	−	6.63929i	0.668441	−	0.276877i
$576$	−11.8726	−	11.8726i	−0.494691	−	0.494691i
$577$	16.6270			0.692191			0.346095	−	0.938199i	$-0.387507\pi$
$577$	16.6270			0.692191			0.346095	+	0.938199i	$0.387507\pi$
$578$	0.653918	+	4.21660i	0.0271994	+	0.175388i
$579$	−9.09225			−0.377861
$580$	−35.5741	−	35.5741i	−1.47714	−	1.47714i
$581$	2.65098	−	1.09807i	0.109981	−	0.0455557i
$582$		−	1.06478i		−	0.0441367i
$583$	−0.159355	−	0.384717i	−0.00659981	−	0.0159334i
$584$	−1.61112	−	0.667348i	−0.0666686	−	0.0276151i
$585$	14.2451	−	34.3907i	0.588962	−	1.42188i
$586$	4.31600	−	4.31600i	0.178292	−	0.178292i
$587$	−4.05767	+	4.05767i	−0.167478	+	0.167478i	−0.785870	−	0.618392i	$-0.787784\pi$
$587$	−4.05767	+	4.05767i	−0.167478	+	0.167478i	0.618392	+	0.785870i	$0.287784\pi$
$588$	3.18012	−	7.67749i	0.131146	−	0.316614i
$589$	5.30483	+	2.19733i	0.218582	+	0.0905396i
$590$	−4.75163	−	11.4715i	−0.195622	−	0.472272i
$591$		−	1.33920i		−	0.0550873i
$592$	−7.29930	+	3.02347i	−0.299999	+	0.124264i
$593$	−24.3343	−	24.3343i	−0.999291	−	0.999291i	0.000708947	−	1.00000i	$-0.499774\pi$
$593$	−24.3343	−	24.3343i	−0.999291	−	0.999291i	−1.00000		0.000708947i	$0.999774\pi$
$594$	−0.104365			−0.00428216
$595$	3.26978	−	10.0084i	0.134048	−	0.410305i
$596$	−25.4335			−1.04180
$597$	−10.1847	−	10.1847i	−0.416834	−	0.416834i
$598$	−1.54041	+	0.638060i	−0.0629922	+	0.0260922i
$599$		−	48.5421i		−	1.98338i	−0.128665	−	0.991688i	$-0.541069\pi$
$599$		−	48.5421i		−	1.98338i	0.128665	−	0.991688i	$-0.458931\pi$
$600$	−2.42826	−	5.86234i	−0.0991332	−	0.239329i
$601$	−35.1729	−	14.5691i	−1.43473	−	0.594286i	−0.476219	−	0.879327i	$-0.657993\pi$
$601$	−35.1729	−	14.5691i	−1.43473	−	0.594286i	−0.958515	+	0.285040i	$0.907993\pi$
$602$	−0.0637201	+	0.153834i	−0.00259704	+	0.00626981i
$603$	−14.7463	+	14.7463i	−0.600516	+	0.600516i
$604$	7.76598	−	7.76598i	0.315993	−	0.315993i
$605$	16.1852	−	39.0746i	0.658022	−	1.58861i
$606$	0.461519	+	0.191167i	0.0187479	+	0.00776565i
$607$	9.62008	+	23.2249i	0.390467	+	0.942671i	0.989838	+	0.142199i	$0.0454174\pi$
$607$	9.62008	+	23.2249i	0.390467	+	0.942671i	−0.599371	+	0.800471i	$0.704583\pi$
$608$			9.08975i			0.368638i
$609$	2.70441	−	1.12020i	0.109588	−	0.0453930i
$610$	7.77752	+	7.77752i	0.314903	+	0.314903i
$611$	2.18053			0.0882148
$612$	−18.3194	+	9.29702i	−0.740516	+	0.375810i
$613$	39.8851			1.61094			0.805471	−	0.592635i	$-0.201912\pi$
$613$	39.8851			1.61094			0.805471	+	0.592635i	$0.201912\pi$
$614$	−4.93676	−	4.93676i	−0.199231	−	0.199231i
$615$	21.2537	−	8.80356i	0.857030	−	0.354994i
$616$			0.0747953i			0.00301359i
$617$	−4.52770	−	10.9308i	−0.182278	−	0.440059i	0.806157	−	0.591702i	$-0.201544\pi$
$617$	−4.52770	−	10.9308i	−0.182278	−	0.440059i	−0.988435	+	0.151643i	$0.951544\pi$
$618$	2.36183	+	0.978301i	0.0950067	+	0.0393530i
$619$	−12.2216	+	29.5055i	−0.491226	+	1.18592i	0.462871	+	0.886426i	$0.346819\pi$
$619$	−12.2216	+	29.5055i	−0.491226	+	1.18592i	−0.954097	+	0.299499i	$0.903181\pi$
$620$	9.61369	−	9.61369i	0.386095	−	0.386095i
$621$	4.55340	−	4.55340i	0.182722	−	0.182722i
$622$	−1.54608	+	3.73258i	−0.0619923	+	0.149663i
$623$	5.36039	+	2.22034i	0.214759	+	0.0889562i
$624$	−3.41149	−	8.23607i	−0.136569	−	0.329707i
$625$		−	22.3087i		−	0.892347i
$626$	−1.42352	+	0.589640i	−0.0568951	+	0.0235667i
$627$	−0.166155	−	0.166155i	−0.00663560	−	0.00663560i
$628$	−40.7480			−1.62602
$629$	0.690436	+	8.95738i	0.0275295	+	0.357154i
$630$	−1.64876			−0.0656881
$631$	−15.3050	−	15.3050i	−0.609283	−	0.609283i	0.333475	−	0.942759i	$-0.391779\pi$
$631$	−15.3050	−	15.3050i	−0.609283	−	0.609283i	−0.942759	+	0.333475i	$0.891779\pi$
$632$	−10.5262	+	4.36009i	−0.418710	+	0.173435i
$633$		−	4.75987i		−	0.189188i
$634$	−2.01831	−	4.87264i	−0.0801575	−	0.193517i
$635$	27.0241	+	11.1937i	1.07242	+	0.444210i
$636$	1.76929	−	4.27144i	0.0701569	−	0.169374i
$637$	−17.4377	+	17.4377i	−0.690907	+	0.690907i
$638$	0.136632	−	0.136632i	0.00540930	−	0.00540930i
$639$	−11.1203	+	26.8468i	−0.439913	+	1.06204i
$640$	26.3581	+	10.9179i	1.04190	+	0.431568i
$641$	7.06508	+	17.0566i	0.279054	+	0.673695i	0.999810	−	0.0194932i	$-0.00620528\pi$
$641$	7.06508	+	17.0566i	0.279054	+	0.673695i	−0.720756	+	0.693189i	$0.756205\pi$
$642$		−	1.07804i		−	0.0425468i
$643$	33.5459	−	13.8951i	1.32292	−	0.547971i	0.394292	−	0.918985i	$-0.370990\pi$
$643$	33.5459	−	13.8951i	1.32292	−	0.547971i	0.928627	+	0.371014i	$0.120990\pi$
$644$	−1.60553	−	1.60553i	−0.0632668	−	0.0632668i
$645$	−2.51754			−0.0991280
$646$	3.09783	+	1.01207i	0.121883	+	0.0398194i
$647$	36.5783			1.43804			0.719021	−	0.694989i	$-0.244591\pi$
$647$	36.5783			1.43804			0.719021	+	0.694989i	$0.244591\pi$
$648$	3.72683	+	3.72683i	0.146404	+	0.146404i
$649$	−1.35461	+	0.561099i	−0.0531733	+	0.0220251i
$650$			9.26446i			0.363382i
$651$	0.302728	+	0.730851i	0.0118649	+	0.0286443i
$652$	34.7561	+	14.3965i	1.36115	+	0.563809i
$653$	18.0584	−	43.5969i	0.706680	−	1.70608i	−0.00145316	−	0.999999i	$-0.500463\pi$
$653$	18.0584	−	43.5969i	0.706680	−	1.70608i	0.708134	−	0.706078i	$-0.249537\pi$
$654$	0.865465	−	0.865465i	0.0338424	−	0.0338424i
$655$	0.128609	−	0.128609i	0.00502517	−	0.00502517i
$656$	−12.6796	+	30.6112i	−0.495055	+	1.19517i
$657$	−4.19380	−	1.73713i	−0.163616	−	0.0677719i
$658$	−0.0369601	−	0.0892296i	−0.00144085	−	0.00347853i
$659$		−	43.2318i		−	1.68407i	−0.539423	−	0.842035i	$-0.681357\pi$
$659$		−	43.2318i		−	1.68407i	0.539423	−	0.842035i	$-0.318643\pi$
$660$	−0.514035	+	0.212920i	−0.0200088	+	0.00828791i
$661$	−28.1662	−	28.1662i	−1.09554	−	1.09554i	−0.994926	−	0.100611i	$-0.967920\pi$
$661$	−28.1662	−	28.1662i	−1.09554	−	1.09554i	−0.100611	−	0.994926i	$-0.532080\pi$
$662$	3.78394			0.147067
$663$	−10.1069	+	0.779044i	−0.392521	+	0.0302556i
$664$	4.27434			0.165876
$665$	−5.68629	−	5.68629i	−0.220505	−	0.220505i
$666$	1.29973	−	0.538365i	0.0503634	−	0.0208612i
$667$			11.9223i			0.461635i
$668$	−13.2006	−	31.8691i	−0.510747	−	1.23305i
$669$	8.35235	+	3.45966i	0.322921	+	0.133758i
$670$	2.99774	−	7.23718i	0.115813	−	0.279596i
$671$	0.918414	−	0.918414i	0.0354550	−	0.0354550i
$672$	−0.885511	+	0.885511i	−0.0341593	+	0.0341593i
$673$	−13.2063	+	31.8827i	−0.509064	+	1.22899i	0.435360	+	0.900257i	$0.356621\pi$
$673$	−13.2063	+	31.8827i	−0.509064	+	1.22899i	−0.944423	+	0.328732i	$0.893379\pi$
$674$	−4.73772	−	1.96243i	−0.182490	−	0.0755899i
$675$	−13.6927	−	33.0571i	−0.527032	−	1.27237i
$676$			2.19315i			0.0843521i
$677$	10.7636	−	4.45843i	0.413679	−	0.171351i	−0.166130	−	0.986104i	$-0.553127\pi$
$677$	10.7636	−	4.45843i	0.413679	−	0.171351i	0.579809	+	0.814752i	$0.303127\pi$
$678$	−0.379600	−	0.379600i	−0.0145785	−	0.0145785i
$679$	−4.30302			−0.165135
$680$	10.2053	−	11.9100i	0.391357	−	0.456727i
$681$	−7.25081			−0.277852
$682$	0.0369239	+	0.0369239i	0.00141389	+	0.00141389i
$683$	−9.84793	+	4.07914i	−0.376820	+	0.156084i	−0.563051	−	0.826422i	$-0.690373\pi$
$683$	−9.84793	+	4.07914i	−0.376820	+	0.156084i	0.186231	+	0.982506i	$0.440373\pi$
$684$			15.6902i			0.599932i
$685$	−3.10376	−	7.49314i	−0.118589	−	0.286298i
$686$	2.08598	+	0.864040i	0.0796430	+	0.0329892i
$687$	−3.39490	+	8.19601i	−0.129523	+	0.312697i
$688$	2.56394	−	2.56394i	0.0977494	−	0.0977494i
$689$	−9.70163	+	9.70163i	−0.369603	+	0.369603i
$690$	−0.427299	+	1.03159i	−0.0162670	+	0.0392720i
$691$	24.3593	+	10.0899i	0.926670	+	0.383839i	0.794414	−	0.607376i	$-0.207778\pi$
$691$	24.3593	+	10.0899i	0.926670	+	0.383839i	0.132256	+	0.991216i	$0.457778\pi$
$692$	2.91681	+	7.04181i	0.110881	+	0.267689i
$693$			0.194695i			0.00739584i
$694$	5.63497	−	2.33408i	0.213901	−	0.0886006i
$695$	10.9875	+	10.9875i	0.416780	+	0.416780i
$696$	4.36049			0.165284
$697$	28.6097	+	24.5149i	1.08367	+	0.928567i
$698$	2.36236			0.0894165
$699$	−0.647743	−	0.647743i	−0.0244999	−	0.0244999i
$700$	−11.6559	+	4.82804i	−0.440553	+	0.182483i
$701$			27.5402i			1.04018i	0.854111	+	0.520090i	$0.174102\pi$
$701$			27.5402i			1.04018i	−0.854111	+	0.520090i	$0.825898\pi$
$702$	1.31592	+	3.17691i	0.0496661	+	0.119905i
$703$	6.33927	+	2.62581i	0.239090	+	0.0990343i
$704$	0.285005	−	0.688063i	0.0107415	−	0.0259324i
$705$	1.03257	−	1.03257i	0.0388887	−	0.0388887i
$706$	−4.18431	+	4.18431i	−0.157479	+	0.157479i
$707$	0.772549	−	1.86510i	0.0290547	−	0.0701443i
$708$	−15.0400	−	6.22978i	−0.565239	−	0.234130i
$709$	−11.1363	−	26.8855i	−0.418234	−	1.00971i	−0.982859	−	0.184359i	$-0.940979\pi$
$709$	−11.1363	−	26.8855i	−0.418234	−	1.00971i	0.564625	−	0.825348i	$-0.309021\pi$
$710$		−	10.9152i		−	0.409642i
$711$	−27.4000	+	11.3495i	−1.02758	+	0.425638i
$712$	6.11143	+	6.11143i	0.229036	+	0.229036i
$713$	−3.22194			−0.120663
$714$	0.203192	+	0.400381i	0.00760428	+	0.0149839i
$715$	1.65112			0.0617483
$716$	20.7217	+	20.7217i	0.774405	+	0.774405i
$717$	8.80520	−	3.64723i	0.328836	−	0.136208i
$718$			1.99592i			0.0744872i
$719$	−17.4170	−	42.0484i	−0.649546	−	1.56814i	−0.813430	−	0.581663i	$-0.802402\pi$
$719$	−17.4170	−	42.0484i	−0.649546	−	1.56814i	0.163885	−	0.986480i	$-0.447598\pi$
$720$	33.1710	+	13.7399i	1.23621	+	0.512055i
$721$	3.95353	−	9.54466i	0.147237	−	0.355462i
$722$	−1.61216	+	1.61216i	−0.0599985	+	0.0599985i
$723$	−2.29758	+	2.29758i	−0.0854478	+	0.0854478i
$724$	7.36268	−	17.7751i	0.273632	−	0.660606i
$725$	61.2033	+	25.3512i	2.27303	+	0.941521i
$726$	0.690189	+	1.66626i	0.0256153	+	0.0618409i
$727$		−	39.4092i		−	1.46161i	−0.682588	−	0.730803i	$-0.739146\pi$
$727$		−	39.4092i		−	1.46161i	0.682588	−	0.730803i	$-0.260854\pi$
$728$	2.27679	−	0.943078i	0.0843835	−	0.0349528i
$729$	4.64525	+	4.64525i	0.172046	+	0.172046i
$730$	1.70509			0.0631083
$731$	−1.86593	−	3.67673i	−0.0690138	−	0.135989i
$732$	14.4207			0.533004
$733$	−10.5713	−	10.5713i	−0.390462	−	0.390462i	0.484390	−	0.874852i	$-0.339041\pi$
$733$	−10.5713	−	10.5713i	−0.390462	−	0.390462i	−0.874852	+	0.484390i	$0.839041\pi$
$734$	1.62097	−	0.671428i	0.0598311	−	0.0247829i
$735$			16.5149i			0.609160i
$736$	−1.95188	−	4.71225i	−0.0719471	−	0.173696i
$737$	−0.854607	−	0.353990i	−0.0314798	−	0.0130394i
$738$	2.25775	−	5.45070i	0.0831090	−	0.200643i
$739$	−20.5627	+	20.5627i	−0.756412	+	0.756412i	−0.975667	−	0.219256i	$-0.929637\pi$
$739$	−20.5627	+	20.5627i	−0.756412	+	0.756412i	0.219256	+	0.975667i	$0.429637\pi$
$740$	11.4883	−	11.4883i	0.422320	−	0.422320i
$741$	−2.96280	+	7.15282i	−0.108841	+	0.262766i
$742$	0.561444	+	0.232558i	0.0206113	+	0.00853747i
$743$	−9.75831	−	23.5586i	−0.357998	−	0.864283i	−0.995581	−	0.0939018i	$-0.970066\pi$
$743$	−9.75831	−	23.5586i	−0.357998	−	0.864283i	0.637584	−	0.770381i	$-0.279934\pi$
$744$			1.17840i			0.0432021i
$745$	46.6974	−	19.3427i	1.71086	−	0.708662i
$746$	−5.55499	−	5.55499i	−0.203383	−	0.203383i
$747$	11.1262			0.407088
$748$	−0.691947	−	0.592910i	−0.0253001	−	0.0216789i
$749$	−4.35659			−0.159186
$750$	2.15296	+	2.15296i	0.0786151	+	0.0786151i
$751$	1.19019	−	0.492995i	0.0434308	−	0.0179896i	−0.360862	−	0.932619i	$-0.617518\pi$
$751$	1.19019	−	0.492995i	0.0434308	−	0.0179896i	0.404293	+	0.914629i	$0.367518\pi$
$752$			2.10320i			0.0766956i
$753$	−4.39580	−	10.6124i	−0.160192	−	0.386737i
$754$	−5.88186	−	2.43635i	−0.214205	−	0.0887265i
$755$	−8.35260	+	20.1650i	−0.303982	+	0.733878i
$756$	−3.31120	+	3.31120i	−0.120427	+	0.120427i
$757$	−6.16340	+	6.16340i	−0.224012	+	0.224012i	−0.810186	−	0.586173i	$-0.800634\pi$
$757$	−6.16340	+	6.16340i	−0.224012	+	0.224012i	0.586173	+	0.810186i	$0.300634\pi$
$758$	0.505549	−	1.22050i	0.0183624	−	0.0443307i
$759$	0.121816	+	0.0504579i	0.00442165	+	0.00183151i
$760$	−4.58417	−	11.0672i	−0.166285	−	0.401448i
$761$			2.25689i			0.0818122i	0.999163	+	0.0409061i	$0.0130245\pi$
$761$			2.25689i			0.0818122i	−0.999163	+	0.0409061i	$0.986976\pi$
$762$	−1.15239	+	0.477337i	−0.0417468	+	0.0172921i
$763$	−3.49753	−	3.49753i	−0.126619	−	0.126619i
$764$	25.2166			0.912305
$765$	26.5648	−	31.0021i	0.960453	−	1.12088i
$766$	1.44781			0.0523117
$767$	34.1601	+	34.1601i	1.23345	+	1.23345i
$768$	6.76392	−	2.80171i	0.244072	−	0.101098i
$769$		−	8.16534i		−	0.294450i	−0.989103	−	0.147225i	$-0.952966\pi$
$769$		−	8.16534i		−	0.294450i	0.989103	−	0.147225i	$-0.0470341\pi$
$770$	−0.0279865	−	0.0675655i	−0.00100856	−	0.00243489i
$771$	6.26547	+	2.59524i	0.225646	+	0.0934654i
$772$	−10.3054	+	24.8794i	−0.370900	+	0.895431i
$773$	−1.08537	+	1.08537i	−0.0390379	+	0.0390379i	−0.726356	−	0.687318i	$-0.758788\pi$
$773$	−1.08537	+	1.08537i	−0.0390379	+	0.0390379i	0.687318	+	0.726356i	$0.258788\pi$
$774$	−0.456540	+	0.456540i	−0.0164100	+	0.0164100i
$775$	−6.85101	+	16.5398i	−0.246096	+	0.594128i
$776$	−5.92197	−	2.45296i	−0.212586	−	0.0880561i
$777$	0.361760	+	0.873366i	0.0129781	+	0.0313318i
$778$		−	9.54939i		−	0.342362i
$779$	26.5851	−	11.0119i	0.952511	−	0.394543i
$780$	12.9627	+	12.9627i	0.464140	+	0.464140i
$781$	−1.28893			−0.0461217
$782$	−1.82328	+	0.140539i	−0.0652005	+	0.00502567i
$783$	24.5883			0.878715
$784$	−16.8193	−	16.8193i	−0.600688	−	0.600688i
$785$	74.8156	−	30.9896i	2.67028	−	1.10607i
$786$			0.00775598i			0.000276647i
$787$	−12.9545	−	31.2748i	−0.461776	−	1.11483i	−0.967667	−	0.252230i	$-0.918836\pi$
$787$	−12.9545	−	31.2748i	−0.461776	−	1.11483i	0.505891	−	0.862597i	$-0.331164\pi$
$788$	−3.66449	−	1.51788i	−0.130542	−	0.0540723i
$789$	−4.29863	+	10.3778i	−0.153035	+	0.369460i
$790$	7.87728	−	7.87728i	0.280261	−	0.280261i
$791$	−1.53405	+	1.53405i	−0.0545444	+	0.0545444i
$792$	−0.110987	+	0.267946i	−0.00394374	+	0.00952104i
$793$	−39.5369	−	16.3767i	−1.40400	−	0.581554i
$794$	−1.44493	−	3.48837i	−0.0512787	−	0.123798i
$795$			9.18820i			0.325872i
$796$	−39.4125	+	16.3252i	−1.39694	+	0.578631i
$797$	−25.3968	−	25.3968i	−0.899602	−	0.899602i	0.0957986	−	0.995401i	$-0.469460\pi$
$797$	−25.3968	−	25.3968i	−0.899602	−	0.899602i	−0.995401	+	0.0957986i	$0.969460\pi$
$798$	0.342921			0.0121393
$799$	2.27331	+	0.742697i	0.0804240	+	0.0262747i
$800$	−28.3407			−1.00200
$801$	15.9083	+	15.9083i	0.562091	+	0.562091i
$802$	−0.160957	+	0.0666706i	−0.00568359	+	0.00235422i
$803$		−	0.201347i		−	0.00710538i
$804$	−3.93028	−	9.48854i	−0.138610	−	0.334635i
$805$	4.16889	+	1.72681i	0.146934	+	0.0608620i
$806$	0.658408	−	1.58954i	0.0231914	−	0.0559891i
$807$	−14.1187	+	14.1187i	−0.497003	+	0.497003i
$808$	2.12642	−	2.12642i	0.0748072	−	0.0748072i
$809$	−12.1636	+	29.3654i	−0.427648	+	1.03243i	0.552383	+	0.833590i	$0.313719\pi$
$809$	−12.1636	+	29.3654i	−0.427648	+	1.03243i	−0.980031	+	0.198843i	$0.936281\pi$
$810$	−4.76107	−	1.97210i	−0.167287	−	0.0692926i
$811$	6.42990	+	15.5231i	0.225784	+	0.545091i	0.995656	−	0.0931071i	$-0.0296799\pi$
$811$	6.42990	+	15.5231i	0.225784	+	0.545091i	−0.769872	+	0.638198i	$0.779680\pi$
$812$		−	8.66984i		−	0.304252i
$813$	5.59124	−	2.31597i	0.196093	−	0.0812245i
$814$	0.0441239	+	0.0441239i	0.00154654	+	0.00154654i
$815$	−74.7630			−2.61884
$816$	−0.751415	−	9.74848i	−0.0263048	−	0.341265i
$817$	−3.14906			−0.110172
$818$	−4.62357	−	4.62357i	−0.161659	−	0.161659i
$819$	5.92656	−	2.45486i	0.207091	−	0.0857799i
$820$		−	68.1353i		−	2.37939i
$821$	10.1345	+	24.4669i	0.353698	+	0.853902i	0.996157	+	0.0875826i	$0.0279142\pi$
$821$	10.1345	+	24.4669i	0.353698	+	0.853902i	−0.642459	+	0.766320i	$0.722086\pi$
$822$	0.319532	+	0.132354i	0.0111449	+	0.00461639i
$823$	−9.96845	+	24.0660i	−0.347478	+	0.838887i	0.649438	+	0.760415i	$0.275004\pi$
$823$	−9.96845	+	24.0660i	−0.347478	+	0.838887i	−0.996916	+	0.0784724i	$0.974996\pi$
$824$	10.8820	−	10.8820i	0.379091	−	0.379091i
$825$	0.518051	−	0.518051i	0.0180362	−	0.0180362i
$826$	0.818851	−	1.97688i	0.0284915	−	0.0687845i
$827$	40.2781	+	16.6838i	1.40061	+	0.580151i	0.949909	−	0.312525i	$-0.101175\pi$
$827$	40.2781	+	16.6838i	1.40061	+	0.580151i	0.450699	+	0.892676i	$0.351175\pi$
$828$	−3.36923	−	8.13404i	−0.117089	−	0.282677i
$829$		−	36.0349i		−	1.25154i	−0.780006	−	0.625772i	$-0.784784\pi$
$829$		−	36.0349i		−	1.25154i	0.780006	−	0.625772i	$-0.215216\pi$
$830$	−3.86117	+	1.59935i	−0.134023	+	0.0555142i
$831$	10.7913	+	10.7913i	0.374347	+	0.374347i
$832$	−24.5384			−0.850717
$833$	−24.1191	+	12.2403i	−0.835676	+	0.424103i
$834$	−0.662619			−0.0229446
$835$	48.4742	+	48.4742i	1.67752	+	1.67752i
$836$	−0.642980	+	0.266331i	−0.0222379	+	0.00921126i
$837$			6.64484i			0.229679i
$838$	−1.84869	−	4.46314i	−0.0638620	−	0.154177i
$839$	−15.6681	−	6.48992i	−0.540921	−	0.224057i	0.0954577	−	0.995433i	$-0.469569\pi$
$839$	−15.6681	−	6.48992i	−0.540921	−	0.224057i	−0.636379	+	0.771377i	$0.719569\pi$
$840$	0.631565	−	1.52473i	0.0217911	−	0.0526083i
$841$	−11.6841	+	11.6841i	−0.402901	+	0.402901i
$842$	−4.63298	+	4.63298i	−0.159663	+	0.159663i
$843$	1.75059	−	4.22630i	0.0602935	−	0.145561i
$844$	−13.0246	−	5.39496i	−0.448325	−	0.185702i
$845$	−1.66794	−	4.02676i	−0.0573788	−	0.138525i
$846$		−	0.374499i		−	0.0128755i
$847$	6.73374	−	2.78921i	0.231374	−	0.0958382i
$848$	−9.35756	−	9.35756i	−0.321340	−	0.321340i
$849$	−16.1012			−0.552593
$850$	−3.15551	+	9.65866i	−0.108233	+	0.331289i
$851$	−3.85021			−0.131984
$852$	−10.1193	−	10.1193i	−0.346680	−	0.346680i
$853$	−38.5677	+	15.9753i	−1.32053	+	0.546983i	−0.927940	−	0.372730i	$-0.878422\pi$
$853$	−38.5677	+	15.9753i	−1.32053	+	0.546983i	−0.392593	+	0.919712i	$0.628422\pi$
$854$			1.89548i			0.0648618i
$855$	−11.9327	−	28.8082i	−0.408091	−	0.985220i
$856$	−5.99570	−	2.48350i	−0.204929	−	0.0848843i
$857$	−3.07960	+	7.43481i	−0.105197	+	0.253968i	−0.967710	−	0.252067i	$-0.918890\pi$
$857$	−3.07960	+	7.43481i	−0.105197	+	0.253968i	0.862513	+	0.506036i	$0.168890\pi$
$858$	−0.0497866	+	0.0497866i	−0.00169969	+	0.00169969i
$859$	0.914394	−	0.914394i	0.0311987	−	0.0311987i	−0.691335	−	0.722534i	$-0.742977\pi$
$859$	0.914394	−	0.914394i	0.0311987	−	0.0311987i	0.722534	+	0.691335i	$0.242977\pi$
$860$	−2.85344	+	6.88882i	−0.0973016	+	0.234907i
$861$	3.66265	+	1.51712i	0.124823	+	0.0517033i
$862$	−3.71714	−	8.97397i	−0.126606	−	0.305655i
$863$			32.8239i			1.11734i	0.829391	+	0.558669i	$0.188688\pi$
$863$			32.8239i			1.11734i	−0.829391	+	0.558669i	$0.811312\pi$
$864$	−9.71841	+	4.02550i	−0.330627	+	0.136950i
$865$	−10.7109	−	10.7109i	−0.364181	−	0.364181i
$866$	2.52606			0.0858391
$867$	−10.8023	−	2.63027i	−0.366867	−	0.0893286i
$868$	2.34297			0.0795257
$869$	−0.930193	−	0.930193i	−0.0315547	−	0.0315547i
$870$	−3.93899	+	1.63159i	−0.133544	+	0.0553159i
$871$			30.4779i			1.03270i
$872$	−2.81964	−	6.80722i	−0.0954851	−	0.230521i
$873$	−15.4151	−	6.38514i	−0.521721	−	0.216104i
$874$	−0.534487	+	1.29037i	−0.0180793	+	0.0436473i
$875$	8.70059	−	8.70059i	0.294134	−	0.294134i
$876$	1.58075	−	1.58075i	0.0534086	−	0.0534086i
$877$	−0.0572862	+	0.138301i	−0.00193442	+	0.00467010i	−0.924844	−	0.380347i	$-0.875805\pi$
$877$	−0.0572862	+	0.138301i	−0.00193442	+	0.00467010i	0.922909	+	0.385017i	$0.125805\pi$
$878$	3.77098	+	1.56199i	0.127264	+	0.0527146i
$879$	6.08607	+	14.6931i	0.205278	+	0.495585i
$880$			1.59256i			0.0536852i
$881$	21.2499	−	8.80199i	0.715927	−	0.296546i	0.00517205	−	0.999987i	$-0.498354\pi$
$881$	21.2499	−	8.80199i	0.715927	−	0.296546i	0.710755	+	0.703440i	$0.248354\pi$
$882$	2.99487	+	2.99487i	0.100843	+	0.100843i
$883$	−7.86626			−0.264721			−0.132360	−	0.991202i	$-0.542256\pi$
$883$	−7.86626			−0.264721			−0.132360	+	0.991202i	$0.542256\pi$
$884$	−9.32374	+	28.5389i	−0.313591	+	0.959868i
$885$	32.3522			1.08751
$886$	1.35812	+	1.35812i	0.0456269	+	0.0456269i
$887$	23.9740	−	9.93036i	0.804968	−	0.333429i	0.0580239	−	0.998315i	$-0.481520\pi$
$887$	23.9740	−	9.93036i	0.804968	−	0.333429i	0.746945	+	0.664886i	$0.231520\pi$
$888$			1.40818i			0.0472554i
$889$	1.92902	+	4.65708i	0.0646974	+	0.156193i
$890$	−7.80744	−	3.23395i	−0.261706	−	0.108402i
$891$	−0.232877	+	0.562215i	−0.00780167	+	0.0188349i
$892$	18.9336	−	18.9336i	0.633942	−	0.633942i
$893$	1.29158	−	1.29158i	0.0432212	−	0.0432212i
$894$	−0.824835	+	1.99133i	−0.0275866	+	0.0666000i
$895$	−53.8054	−	22.2869i	−1.79852	−	0.744970i
$896$	1.88149	+	4.54231i	0.0628560	+	0.151748i
$897$		−	4.34433i		−	0.145053i
$898$	−7.26446	+	3.00904i	−0.242418	+	0.100413i
$899$	−8.69921	−	8.69921i	−0.290135	−	0.290135i
$900$	−48.9203			−1.63068
$901$	−13.4189	+	6.81003i	−0.447047	+	0.226875i
$902$	0.261691			0.00871336
$903$	−0.306777	−	0.306777i	−0.0102089	−	0.0102089i
$904$	−2.98570	+	1.23672i	−0.0993029	+	0.0411326i
$905$			38.2355i			1.27099i
$906$	−0.356182	−	0.859899i	−0.0118333	−	0.0285682i
$907$	35.3307	+	14.6345i	1.17314	+	0.485929i	0.882228	−	0.470822i	$-0.156043\pi$
$907$	35.3307	+	14.6345i	1.17314	+	0.485929i	0.290908	+	0.956751i	$0.406043\pi$
$908$	−8.21826	+	19.8406i	−0.272732	+	0.658434i
$909$	5.53514	−	5.53514i	0.183589	−	0.183589i
$910$	−1.70384	+	1.70384i	−0.0564816	+	0.0564816i
$911$	21.4675	−	51.8271i	0.711250	−	1.71711i	0.0143952	−	0.999896i	$-0.495418\pi$
$911$	21.4675	−	51.8271i	0.711250	−	1.71711i	0.696855	−	0.717212i	$-0.254582\pi$
$912$	−6.89914	−	2.85772i	−0.228453	−	0.0946285i
$913$	0.188860	+	0.455949i	0.00625036	+	0.0150897i
$914$			2.27714i			0.0753213i
$915$	−26.4772	+	10.9672i	−0.875310	+	0.362565i
$916$	18.5791	+	18.5791i	0.613872	+	0.613872i
$917$	0.0313436			0.00103506
$918$	0.289844	+	3.76029i	0.00956628	+	0.124108i
$919$	−17.2293			−0.568342			−0.284171	−	0.958774i	$-0.591718\pi$
$919$	−17.2293			−0.568342			−0.284171	+	0.958774i	$0.591718\pi$
$920$	4.75299	+	4.75299i	0.156701	+	0.156701i
$921$	16.8063	−	6.96142i	0.553788	−	0.229386i
$922$		−	1.61943i		−	0.0533331i
$923$	16.2519	+	39.2355i	0.534937	+	1.29145i
$924$	−0.0885839	−	0.0366927i	−0.00291420	−	0.00120710i
$925$	−8.18695	+	19.7650i	−0.269185	+	0.649871i
$926$	4.94428	−	4.94428i	0.162479	−	0.162479i
$927$	28.3261	−	28.3261i	0.930352	−	0.930352i
$928$	7.45298	−	17.9931i	0.244656	−	0.590652i
$929$	−15.6429	−	6.47952i	−0.513228	−	0.212586i	0.111011	−	0.993819i	$-0.464591\pi$
$929$	−15.6429	−	6.47952i	−0.513228	−	0.212586i	−0.624239	+	0.781233i	$0.714591\pi$
$930$	−0.440926	−	1.06449i	−0.0144585	−	0.0349060i
$931$			20.6576i			0.677026i
$932$	−2.50661	+	1.03827i	−0.0821067	+	0.0340097i
$933$	−7.44354	−	7.44354i	−0.243691	−	0.243691i
$934$	−9.99012			−0.326887
$935$	1.72137	+	0.562377i	0.0562949	+	0.0183917i
$936$	9.55575			0.312340
$937$	17.3271	+	17.3271i	0.566053	+	0.566053i	0.931020	−	0.364968i	$-0.118920\pi$
$937$	17.3271	+	17.3271i	0.566053	+	0.566053i	−0.364968	+	0.931020i	$0.618920\pi$
$938$	1.24719	−	0.516601i	0.0407221	−	0.0168676i
$939$		−	4.01465i		−	0.131013i
$940$	−1.65511	−	3.99578i	−0.0539836	−	0.130328i
$941$	−29.0442	−	12.0305i	−0.946812	−	0.392182i	−0.144780	−	0.989464i	$-0.546248\pi$
$941$	−29.0442	−	12.0305i	−0.946812	−	0.392182i	−0.802032	+	0.597281i	$0.796248\pi$
$942$	−1.32150	+	3.19038i	−0.0430567	+	0.103948i
$943$	−11.4175	+	11.4175i	−0.371803	+	0.371803i
$944$	−32.9486	+	32.9486i	−1.07238	+	1.07238i
$945$	3.56133	−	8.59780i	0.115850	−	0.279686i
$946$	−0.0264583	−	0.0109594i	−0.000860234	−	0.000356320i
$947$	1.65496	+	3.99543i	0.0537790	+	0.129834i	0.948486	−	0.316821i	$-0.102615\pi$
$947$	1.65496	+	3.99543i	0.0537790	+	0.129834i	−0.894706	+	0.446655i	$0.852615\pi$
$948$		−	14.6057i		−	0.474370i
$949$	−6.12906	+	2.53874i	−0.198958	+	0.0824110i
$950$	5.48757	+	5.48757i	0.178040	+	0.178040i
$951$	13.7420			0.445615
$952$	2.69489	−	0.207722i	0.0873418	−	0.00673232i
$953$	−59.3502			−1.92254			−0.961271	−	0.275606i	$-0.911122\pi$
$953$	−59.3502			−1.92254			−0.961271	+	0.275606i	$0.911122\pi$
$954$	1.66622	+	1.66622i	0.0539460	+	0.0539460i
$955$	−46.2992	+	19.1777i	−1.49821	+	0.620577i
$956$		−	28.2278i		−	0.912953i
$957$	0.192667	+	0.465139i	0.00622803	+	0.0150358i
$958$	3.86274	+	1.60000i	0.124800	+	0.0516937i
$959$	0.534873	−	1.29130i	0.0172719	−	0.0416981i
$960$	−11.6199	+	11.6199i	−0.375030	+	0.375030i
$961$	−19.5694	+	19.5694i	−0.631271	+	0.631271i
$962$	0.786797	−	1.89949i	0.0253673	−	0.0612422i
$963$	−15.6070	−	6.46463i	−0.502929	−	0.208320i
$964$	3.68280	+	8.89107i	0.118615	+	0.286362i
$965$		−	53.5176i		−	1.72279i
$966$	−0.177775	+	0.0736367i	−0.00571981	+	0.00236922i
$967$	33.5651	+	33.5651i	1.07938	+	1.07938i	0.996565	+	0.0828168i	$0.0263916\pi$
$967$	33.5651	+	33.5651i	1.07938	+	1.07938i	0.0828168	+	0.996565i	$0.473608\pi$
$968$	10.8572			0.348964
$969$	−5.52515	+	6.44804i	−0.177493	+	0.207141i
$970$	6.26738			0.201233
$971$	−39.7979	−	39.7979i	−1.27717	−	1.27717i	−0.942242	−	0.334932i	$-0.891287\pi$
$971$	−39.7979	−	39.7979i	−1.27717	−	1.27717i	−0.334932	−	0.942242i	$-0.608713\pi$
$972$	−25.8070	+	10.6896i	−0.827758	+	0.342869i
$973$			2.67779i			0.0858460i
$974$	−2.43661	−	5.88249i	−0.0780740	−	0.188487i
$975$	−22.3016	−	9.23763i	−0.714223	−	0.295841i
$976$	15.7959	−	38.1347i	0.505614	−	1.22066i
$977$	15.4141	−	15.4141i	0.493140	−	0.493140i	−0.416154	−	0.909294i	$-0.636622\pi$
$977$	15.4141	−	15.4141i	0.493140	−	0.493140i	0.909294	+	0.416154i	$0.136622\pi$
$978$	2.25435	−	2.25435i	0.0720862	−	0.0720862i
$979$	−0.381883	+	0.921947i	−0.0122050	+	0.0294655i
$980$	45.1902	+	18.7184i	1.44355	+	0.597937i
$981$	−7.33962	−	17.7194i	−0.234336	−	0.565737i
$982$		−	2.79480i		−	0.0891858i
$983$	34.4560	−	14.2722i	1.09898	−	0.455211i	0.241848	−	0.970314i	$-0.422246\pi$
$983$	34.4560	−	14.2722i	1.09898	−	0.455211i	0.857128	+	0.515103i	$0.172246\pi$
$984$	4.17583	+	4.17583i	0.133121	+	0.133121i
$985$	7.88260			0.251161
$986$	−5.30231	−	4.54340i	−0.168860	−	0.144691i
$987$	0.251649			0.00801006
$988$	16.2144	+	16.2144i	0.515849	+	0.515849i
$989$	1.63252	−	0.676210i	0.0519110	−	0.0215022i
$990$		−	0.283574i		−	0.00901258i
$991$	21.3918	+	51.6444i	0.679533	+	1.64054i	0.764869	+	0.644186i	$0.222804\pi$
$991$	21.3918	+	51.6444i	0.679533	+	1.64054i	−0.0853356	+	0.996352i	$0.527196\pi$
$992$	4.86252	+	2.01412i	0.154385	+	0.0639485i
$993$	−3.77298	+	9.10878i	−0.119732	+	0.289059i
$994$	1.33009	−	1.33009i	0.0421878	−	0.0421878i
$995$	59.9480	−	59.9480i	1.90048	−	1.90048i
$996$	−2.09688	+	5.06232i	−0.0664422	+	0.160406i
$997$	17.2933	+	7.16313i	0.547685	+	0.226859i	0.639329	−	0.768933i	$-0.279212\pi$
$997$	17.2933	+	7.16313i	0.547685	+	0.226859i	−0.0916440	+	0.995792i	$0.529212\pi$
$998$	0.142804	+	0.344760i	0.00452039	+	0.0109132i
$999$			7.94058i			0.251229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.87.14	✓	128
17.9	even	8	inner	731.2.m.c.689.14	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.14	✓	128	1.1	even	1	trivial
731.2.m.c.689.14	yes	128	17.9	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.177484 - 0.177484i) q^{2} +(0.604214 - 0.250274i) q^{3} -1.93700i q^{4} +(1.47313 + 3.55644i) q^{5} +(-0.151658 - 0.0628188i) q^{6} +(-0.253865 + 0.612883i) q^{7} +(-0.698755 + 0.698755i) q^{8} +(-1.81888 + 1.81888i) q^{9} +O(q^{10})\)	\(q+(-0.177484 - 0.177484i) q^{2} +(0.604214 - 0.250274i) q^{3} -1.93700i q^{4} +(1.47313 + 3.55644i) q^{5} +(-0.151658 - 0.0628188i) q^{6} +(-0.253865 + 0.612883i) q^{7} +(-0.698755 + 0.698755i) q^{8} +(-1.81888 + 1.81888i) q^{9} +(0.369755 - 0.892669i) q^{10} +(-0.105411 - 0.0436628i) q^{11} +(-0.484780 - 1.17036i) q^{12} +3.75929i q^{13} +(0.153834 - 0.0637201i) q^{14} +(1.78017 + 1.78017i) q^{15} -3.62596 q^{16} +(-1.28043 + 3.91925i) q^{17} +0.645645 q^{18} +(2.22672 + 2.22672i) q^{19} +(6.88882 - 2.85344i) q^{20} +0.433849i q^{21} +(0.0109594 + 0.0264583i) q^{22} +(-1.63252 - 0.676210i) q^{23} +(-0.247318 + 0.597078i) q^{24} +(-6.94264 + 6.94264i) q^{25} +(0.667214 - 0.667214i) q^{26} +(-1.39460 + 3.36686i) q^{27} +(1.18715 + 0.491735i) q^{28} +(-2.58202 - 6.23354i) q^{29} -0.631903i q^{30} +(1.68458 - 0.697775i) q^{31} +(2.04106 + 2.04106i) q^{32} -0.0746187 q^{33} +(0.922860 - 0.468349i) q^{34} -2.55366 q^{35} +(3.52317 + 3.52317i) q^{36} +(2.01307 - 0.833839i) q^{37} -0.790415i q^{38} +(0.940851 + 2.27142i) q^{39} +(-3.51443 - 1.45573i) q^{40} +(3.49689 - 8.44224i) q^{41} +(0.0770012 - 0.0770012i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(-0.0845748 + 0.204182i) q^{44} +(-9.14819 - 3.78931i) q^{45} +(0.169729 + 0.409762i) q^{46} -0.580038i q^{47} +(-2.19086 + 0.907483i) q^{48} +(4.63857 + 4.63857i) q^{49} +2.46442 q^{50} +(0.207232 + 2.68852i) q^{51} +7.28174 q^{52} +(2.58071 + 2.58071i) q^{53} +(0.845083 - 0.350045i) q^{54} -0.439210i q^{55} +(-0.250866 - 0.605644i) q^{56} +(1.90271 + 0.788127i) q^{57} +(-0.648088 + 1.56462i) q^{58} +(9.08685 - 9.08685i) q^{59} +(3.44818 - 3.44818i) q^{60} +(-4.35633 + 10.5171i) q^{61} +(-0.422830 - 0.175142i) q^{62} +(-0.653013 - 1.57651i) q^{63} +6.52741i q^{64} +(-13.3697 + 5.53791i) q^{65} +(0.0132436 + 0.0132436i) q^{66} +8.10735 q^{67} +(7.59158 + 2.48019i) q^{68} -1.15563 q^{69} +(0.453234 + 0.453234i) q^{70} +(10.4370 - 4.32313i) q^{71} -2.54191i q^{72} +(0.675324 + 1.63038i) q^{73} +(-0.505281 - 0.209294i) q^{74} +(-2.45728 + 5.93241i) q^{75} +(4.31316 - 4.31316i) q^{76} +(0.0535204 - 0.0535204i) q^{77} +(0.236154 - 0.570126i) q^{78} +(10.6520 + 4.41221i) q^{79} +(-5.34150 - 12.8955i) q^{80} -5.33353i q^{81} +(-2.11901 + 0.877721i) q^{82} +(-3.05854 - 3.05854i) q^{83} +0.840364 q^{84} +(-15.8248 + 1.21978i) q^{85} +0.251000 q^{86} +(-3.12018 - 3.12018i) q^{87} +(0.104166 - 0.0431471i) q^{88} -8.74618i q^{89} +(0.951117 + 2.29620i) q^{90} +(-2.30400 - 0.954350i) q^{91} +(-1.30982 + 3.16218i) q^{92} +(0.843211 - 0.843211i) q^{93} +(-0.102948 + 0.102948i) q^{94} +(-4.63896 + 11.1994i) q^{95} +(1.74406 + 0.722414i) q^{96} +(2.48228 + 5.99275i) q^{97} -1.64654i q^{98} +(0.271148 - 0.112313i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

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