LMFDB - Embedded newform 260.2.j.a.31.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(31,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("260.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.j (of order $4$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.12
Character	$\chi$	$=$	260.31
Dual form			260.2.j.a.151.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.551623 - 1.30220i) q^{2} +0.224099i q^{3} +(-1.39142 + 1.43664i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.291821 - 0.123618i) q^{6} +(-0.228458 + 0.228458i) q^{7} +(2.63833 + 1.01942i) q^{8} +2.94978 q^{9} +O(q^{10})$	\(q+(-0.551623 - 1.30220i) q^{2} +0.224099i q^{3} +(-1.39142 + 1.43664i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.291821 - 0.123618i) q^{6} +(-0.228458 + 0.228458i) q^{7} +(2.63833 + 1.01942i) q^{8} +2.94978 q^{9} +(1.31085 + 0.530735i) q^{10} +(2.37131 - 2.37131i) q^{11} +(-0.321950 - 0.311817i) q^{12} +(3.08312 - 1.86932i) q^{13} +(0.423519 + 0.171474i) q^{14} +(-0.158462 - 0.158462i) q^{15} +(-0.127875 - 3.99796i) q^{16} -0.164659i q^{17} +(-1.62717 - 3.84119i) q^{18} +(5.57482 + 5.57482i) q^{19} +(-0.0319728 - 1.99974i) q^{20} +(-0.0511972 - 0.0511972i) q^{21} +(-4.39597 - 1.77984i) q^{22} -2.09657 q^{23} +(-0.228452 + 0.591247i) q^{24} -1.00000i q^{25} +(-4.13494 - 2.98366i) q^{26} +1.33334i q^{27} +(-0.0103300 - 0.646094i) q^{28} -4.19301 q^{29} +(-0.118937 + 0.293760i) q^{30} +(4.60655 + 4.60655i) q^{31} +(-5.13558 + 2.37188i) q^{32} +(0.531408 + 0.531408i) q^{33} +(-0.214418 + 0.0908294i) q^{34} -0.323088i q^{35} +(-4.10440 + 4.23777i) q^{36} +(-4.58248 - 4.58248i) q^{37} +(4.18430 - 10.3347i) q^{38} +(0.418914 + 0.690925i) q^{39} +(-2.58642 + 1.14474i) q^{40} +(6.09528 - 6.09528i) q^{41} +(-0.0384272 + 0.0949103i) q^{42} -7.98487 q^{43} +(0.107222 + 6.70621i) q^{44} +(-2.08581 + 2.08581i) q^{45} +(1.15652 + 2.73015i) q^{46} +(5.11715 - 5.11715i) q^{47} +(0.895939 - 0.0286566i) q^{48} +6.89561i q^{49} +(-1.30220 + 0.551623i) q^{50} +0.0368998 q^{51} +(-1.60439 + 7.03036i) q^{52} +1.03734 q^{53} +(1.73627 - 0.735501i) q^{54} +3.35353i q^{55} +(-0.835642 + 0.369852i) q^{56} +(-1.24931 + 1.24931i) q^{57} +(2.31296 + 5.46012i) q^{58} +(-3.19704 + 3.19704i) q^{59} +(0.448141 - 0.00716508i) q^{60} -12.4682 q^{61} +(3.45755 - 8.53970i) q^{62} +(-0.673900 + 0.673900i) q^{63} +(5.92155 + 5.37914i) q^{64} +(-0.858285 + 3.50191i) q^{65} +(0.398860 - 0.985133i) q^{66} +(4.65669 + 4.65669i) q^{67} +(0.236555 + 0.229110i) q^{68} -0.469841i q^{69} +(-0.420724 + 0.178223i) q^{70} +(0.687724 + 0.687724i) q^{71} +(7.78249 + 3.00707i) q^{72} +(6.28575 + 6.28575i) q^{73} +(-3.43949 + 8.49509i) q^{74} +0.224099 q^{75} +(-15.7659 + 0.252073i) q^{76} +1.08349i q^{77} +(0.668637 - 0.926637i) q^{78} +1.07573i q^{79} +(2.91740 + 2.73656i) q^{80} +8.55054 q^{81} +(-11.2995 - 4.57495i) q^{82} +(-12.4601 - 12.4601i) q^{83} +(0.144789 - 0.00231495i) q^{84} +(0.116431 + 0.116431i) q^{85} +(4.40464 + 10.3979i) q^{86} -0.939650i q^{87} +(8.67364 - 3.83892i) q^{88} +(-5.50207 - 5.50207i) q^{89} +(3.86671 + 1.56555i) q^{90} +(-0.277302 + 1.13142i) q^{91} +(2.91722 - 3.01202i) q^{92} +(-1.03232 + 1.03232i) q^{93} +(-9.48626 - 3.84079i) q^{94} -7.88398 q^{95} +(-0.531537 - 1.15088i) q^{96} +(3.45542 - 3.45542i) q^{97} +(8.97944 - 3.80378i) q^{98} +(6.99483 - 6.99483i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) $ 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9	$ 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 40 q^{24} - 16 q^{26} - 44 q^{28} + 40 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{41} + 8 q^{42} + 28 q^{44} - 12 q^{46} + 104 q^{48} + 56 q^{52} - 16 q^{53} + 20 q^{54} - 48 q^{57} - 4 q^{58} + 16 q^{61} - 8 q^{65} + 64 q^{66} + 24 q^{68} - 8 q^{70} - 32 q^{72} + 48 q^{73} - 136 q^{74} - 88 q^{76} + 52 q^{78} - 32 q^{80} + 56 q^{81} - 20 q^{84} - 64 q^{86} - 8 q^{89} - 88 q^{92} - 48 q^{93} - 16 q^{94} - 4 q^{96} - 32 q^{97} + 16 q^{98}+O(q^{100}) $ 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 40 * q^24 - 16 * q^26 - 44 * q^28 + 40 * q^32 - 4 * q^34 + 16 * q^37 + 8 * q^41 + 8 * q^42 + 28 * q^44 - 12 * q^46 + 104 * q^48 + 56 * q^52 - 16 * q^53 + 20 * q^54 - 48 * q^57 - 4 * q^58 + 16 * q^61 - 8 * q^65 + 64 * q^66 + 24 * q^68 - 8 * q^70 - 32 * q^72 + 48 * q^73 - 136 * q^74 - 88 * q^76 + 52 * q^78 - 32 * q^80 + 56 * q^81 - 20 * q^84 - 64 * q^86 - 8 * q^89 - 88 * q^92 - 48 * q^93 - 16 * q^94 - 4 * q^96 - 32 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.551623	−	1.30220i	−0.390056	−	0.920791i
$2$	−0.551623	−	1.30220i	−0.390056	−	0.920791i
$3$			0.224099i			0.129384i	0.997905	+	0.0646919i	$0.0206065\pi$
$3$			0.224099i			0.129384i	−0.997905	+	0.0646919i	$0.979394\pi$
$4$	−1.39142	+	1.43664i	−0.695712	+	0.718321i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	0.291821	−	0.123618i	0.119135	−	0.0504669i
$7$	−0.228458	+	0.228458i	−0.0863489	+	0.0863489i	−0.748962	−	0.662613i	$-0.769447\pi$
$7$	−0.228458	+	0.228458i	−0.0863489	+	0.0863489i	0.662613	+	0.748962i	$0.269447\pi$
$8$	2.63833	+	1.01942i	0.932790	+	0.360420i
$9$	2.94978			0.983260
$10$	1.31085	+	0.530735i	0.414526	+	0.167833i
$11$	2.37131	−	2.37131i	0.714975	−	0.714975i	−0.252596	−	0.967572i	$-0.581284\pi$
$11$	2.37131	−	2.37131i	0.714975	−	0.714975i	0.967572	+	0.252596i	$0.0812845\pi$
$12$	−0.321950	−	0.311817i	−0.0929390	−	0.0900139i
$13$	3.08312	−	1.86932i	0.855104	−	0.518457i
$13$	3.08312	−	1.86932i	0.855104	−	0.518457i
$14$	0.423519	+	0.171474i	0.113190	+	0.0458284i
$15$	−0.158462	−	0.158462i	−0.0409147	−	0.0409147i
$16$	−0.127875	−	3.99796i	−0.0319687	−	0.999489i
$17$		−	0.164659i		−	0.0399356i	−0.999801	−	0.0199678i	$-0.993644\pi$
$17$		−	0.164659i		−	0.0399356i	0.999801	−	0.0199678i	$-0.00635636\pi$
$18$	−1.62717	−	3.84119i	−0.383527	−	0.905377i
$19$	5.57482	+	5.57482i	1.27895	+	1.27895i	0.941256	+	0.337695i	$0.109647\pi$
$19$	5.57482	+	5.57482i	1.27895	+	1.27895i	0.337695	+	0.941256i	$0.390353\pi$
$20$	−0.0319728	−	1.99974i	−0.00714933	−	0.447156i
$21$	−0.0511972	−	0.0511972i	−0.0111721	−	0.0111721i
$22$	−4.39597	−	1.77984i	−0.937224	−	0.379462i
$23$	−2.09657			−0.437166			−0.218583	−	0.975818i	$-0.570143\pi$
$23$	−2.09657			−0.437166			−0.218583	+	0.975818i	$0.570143\pi$
$24$	−0.228452	+	0.591247i	−0.0466325	+	0.120688i
$25$		−	1.00000i		−	0.200000i
$26$	−4.13494	−	2.98366i	−0.810929	−	0.585145i
$27$			1.33334i			0.256602i
$28$	−0.0103300	−	0.646094i	−0.00195219	−	0.122100i
$29$	−4.19301			−0.778623			−0.389311	−	0.921106i	$-0.627287\pi$
$29$	−4.19301			−0.778623			−0.389311	+	0.921106i	$0.627287\pi$
$30$	−0.118937	+	0.293760i	−0.0217149	+	0.0536330i
$31$	4.60655	+	4.60655i	0.827360	+	0.827360i	0.987151	−	0.159791i	$-0.0510819\pi$
$31$	4.60655	+	4.60655i	0.827360	+	0.827360i	−0.159791	+	0.987151i	$0.551082\pi$
$32$	−5.13558	+	2.37188i	−0.907851	+	0.419293i
$33$	0.531408	+	0.531408i	0.0925062	+	0.0925062i
$34$	−0.214418	+	0.0908294i	−0.0367723	+	0.0155771i
$35$		−	0.323088i		−	0.0546119i
$36$	−4.10440	+	4.23777i	−0.684066	+	0.706296i
$37$	−4.58248	−	4.58248i	−0.753355	−	0.753355i	0.221748	−	0.975104i	$-0.428824\pi$
$37$	−4.58248	−	4.58248i	−0.753355	−	0.753355i	−0.975104	+	0.221748i	$0.928824\pi$
$38$	4.18430	−	10.3347i	0.678784	−	1.67651i
$39$	0.418914	+	0.690925i	0.0670799	+	0.110637i
$40$	−2.58642	+	1.14474i	−0.408949	+	0.180999i
$41$	6.09528	−	6.09528i	0.951924	−	0.951924i	−0.0469727	−	0.998896i	$-0.514957\pi$
$41$	6.09528	−	6.09528i	0.951924	−	0.951924i	0.998896	+	0.0469727i	$0.0149574\pi$
$42$	−0.0384272	+	0.0949103i	−0.00592945	+	0.0146450i
$43$	−7.98487			−1.21768			−0.608841	−	0.793293i	$-0.708365\pi$
$43$	−7.98487			−1.21768			−0.608841	+	0.793293i	$0.708365\pi$
$44$	0.107222	+	6.70621i	0.0161643	+	1.01100i
$45$	−2.08581	+	2.08581i	−0.310934	+	0.310934i
$46$	1.15652	+	2.73015i	0.170519	+	0.402538i
$47$	5.11715	−	5.11715i	0.746412	−	0.746412i	−0.227391	−	0.973804i	$-0.573020\pi$
$47$	5.11715	−	5.11715i	0.746412	−	0.746412i	0.973804	+	0.227391i	$0.0730196\pi$
$48$	0.895939	−	0.0286566i	0.129318	−	0.00413623i
$49$			6.89561i			0.985088i
$50$	−1.30220	+	0.551623i	−0.184158	+	0.0780112i
$51$	0.0368998			0.00516701
$52$	−1.60439	+	7.03036i	−0.222488	+	0.974935i
$53$	1.03734			0.142490			0.0712449	−	0.997459i	$-0.477303\pi$
$53$	1.03734			0.142490			0.0712449	+	0.997459i	$0.477303\pi$
$54$	1.73627	−	0.735501i	0.236276	−	0.100089i
$55$			3.35353i			0.452190i
$56$	−0.835642	+	0.369852i	−0.111667	+	0.0494235i
$57$	−1.24931	+	1.24931i	−0.165475	+	0.165475i
$58$	2.31296	+	5.46012i	0.303707	+	0.716949i
$59$	−3.19704	+	3.19704i	−0.416219	+	0.416219i	−0.883898	−	0.467680i	$-0.845090\pi$
$59$	−3.19704	+	3.19704i	−0.416219	+	0.416219i	0.467680	+	0.883898i	$0.345090\pi$
$60$	0.448141	−	0.00716508i	0.0578548	−	0.000925007i
$61$	−12.4682			−1.59639			−0.798193	−	0.602402i	$-0.794211\pi$
$61$	−12.4682			−1.59639			−0.798193	+	0.602402i	$0.794211\pi$
$62$	3.45755	−	8.53970i	0.439109	−	1.08454i
$63$	−0.673900	+	0.673900i	−0.0849034	+	0.0849034i
$64$	5.92155	+	5.37914i	0.740194	+	0.672393i
$65$	−0.858285	+	3.50191i	−0.106457	+	0.434358i
$66$	0.398860	−	0.985133i	0.0490963	−	0.121262i
$67$	4.65669	+	4.65669i	0.568905	+	0.568905i	0.931822	−	0.362916i	$-0.118219\pi$
$67$	4.65669	+	4.65669i	0.568905	+	0.568905i	−0.362916	+	0.931822i	$0.618219\pi$
$68$	0.236555	+	0.229110i	0.0286865	+	0.0277837i
$69$		−	0.469841i		−	0.0565622i
$70$	−0.420724	+	0.178223i	−0.0502861	+	0.0213017i
$71$	0.687724	+	0.687724i	0.0816178	+	0.0816178i	0.746737	−	0.665119i	$-0.231619\pi$
$71$	0.687724	+	0.687724i	0.0816178	+	0.0816178i	−0.665119	+	0.746737i	$0.731619\pi$
$72$	7.78249	+	3.00707i	0.917175	+	0.354387i
$73$	6.28575	+	6.28575i	0.735692	+	0.735692i	0.971741	−	0.236049i	$-0.0758527\pi$
$73$	6.28575	+	6.28575i	0.735692	+	0.735692i	−0.236049	+	0.971741i	$0.575853\pi$
$74$	−3.43949	+	8.49509i	−0.399832	+	0.987534i
$75$	0.224099			0.0258767
$76$	−15.7659	+	0.252073i	−1.80848	+	0.0289147i
$77$			1.08349i			0.123475i
$78$	0.668637	−	0.926637i	0.0757082	−	0.104921i
$79$			1.07573i			0.121029i	0.998167	+	0.0605147i	$0.0192742\pi$
$79$			1.07573i			0.121029i	−0.998167	+	0.0605147i	$0.980726\pi$
$80$	2.91740	+	2.73656i	0.326176	+	0.305957i
$81$	8.55054			0.950060
$82$	−11.2995	−	4.57495i	−1.24783	−	0.505219i
$83$	−12.4601	−	12.4601i	−1.36767	−	1.36767i	−0.863749	−	0.503923i	$-0.831890\pi$
$83$	−12.4601	−	12.4601i	−1.36767	−	1.36767i	−0.503923	−	0.863749i	$-0.668110\pi$
$84$	0.144789	−	0.00231495i	0.0157978	−	0.000252582i
$85$	0.116431	+	0.116431i	0.0126287	+	0.0126287i
$86$	4.40464	+	10.3979i	0.474964	+	1.12123i
$87$		−	0.939650i		−	0.100741i
$88$	8.67364	−	3.83892i	0.924614	−	0.409230i
$89$	−5.50207	−	5.50207i	−0.583218	−	0.583218i	0.352568	−	0.935786i	$-0.385308\pi$
$89$	−5.50207	−	5.50207i	−0.583218	−	0.583218i	−0.935786	+	0.352568i	$0.885308\pi$
$90$	3.86671	+	1.56555i	0.407587	+	0.165024i
$91$	−0.277302	+	1.13142i	−0.0290691	+	0.118605i
$92$	2.91722	−	3.01202i	0.304142	−	0.314025i
$93$	−1.03232	+	1.03232i	−0.107047	+	0.107047i
$94$	−9.48626	−	3.84079i	−0.978433	−	0.396147i
$95$	−7.88398			−0.808879
$96$	−0.531537	−	1.15088i	−0.0542497	−	0.117461i
$97$	3.45542	−	3.45542i	0.350844	−	0.350844i	−0.509579	−	0.860424i	$-0.670199\pi$
$97$	3.45542	−	3.45542i	0.350844	−	0.350844i	0.860424	+	0.509579i	$0.170199\pi$
$98$	8.97944	−	3.80378i	0.907060	−	0.384240i
$99$	6.99483	−	6.99483i	0.703007	−	0.703007i
$100$	1.43664	+	1.39142i	0.143664	+	0.139142i
$101$		−	3.09206i		−	0.307671i	−0.988096	−	0.153836i	$-0.950837\pi$
$101$		−	3.09206i		−	0.307671i	0.988096	−	0.153836i	$-0.0491626\pi$
$102$	−0.0203548	−	0.0480508i	−0.00201543	−	0.00475774i
$103$	−14.7346			−1.45184			−0.725922	−	0.687777i	$-0.758587\pi$
$103$	−14.7346			−1.45184			−0.725922	+	0.687777i	$0.758587\pi$
$104$	10.0399	−	1.78888i	0.984495	−	0.175414i
$105$	0.0724038			0.00706589
$106$	−0.572221	−	1.35082i	−0.0555790	−	0.131203i
$107$		−	6.66169i		−	0.644010i	−0.946738	−	0.322005i	$-0.895643\pi$
$107$		−	6.66169i		−	0.644010i	0.946738	−	0.322005i	$-0.104357\pi$
$108$	−1.91553	−	1.85524i	−0.184322	−	0.178521i
$109$	−5.91330	+	5.91330i	−0.566392	+	0.566392i	−0.931116	−	0.364724i	$-0.881163\pi$
$109$	−5.91330	+	5.91330i	−0.566392	+	0.566392i	0.364724	+	0.931116i	$0.381163\pi$
$110$	4.36695	−	1.84988i	0.416373	−	0.176380i
$111$	1.02693	−	1.02693i	0.0974720	−	0.0974720i
$112$	0.942578	+	0.884150i	0.0890653	+	0.0835443i
$113$	−11.2658			−1.05980			−0.529899	−	0.848061i	$-0.677770\pi$
$113$	−11.2658			−1.05980			−0.529899	+	0.848061i	$0.677770\pi$
$114$	2.31600	+	0.937699i	0.216913	+	0.0878236i
$115$	1.48250	−	1.48250i	0.138244	−	0.138244i
$116$	5.83426	−	6.02385i	0.541697	−	0.559301i
$117$	9.09453	−	5.51409i	0.840789	−	0.509778i
$118$	5.92672	+	2.39961i	0.545599	+	0.220902i
$119$	0.0376175	+	0.0376175i	0.00344839	+	0.00344839i
$120$	−0.256535	−	0.579615i	−0.0234184	−	0.0529114i
$121$		−	0.246178i		−	0.0223798i
$122$	6.87773	+	16.2360i	0.622680	+	1.46994i
$123$	1.36595	+	1.36595i	0.123163	+	0.123163i
$124$	−13.0276	+	0.208291i	−1.16991	+	0.0187051i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	1.24929	+	0.505811i	0.111295	+	0.0450612i
$127$	0.519464			0.0460950			0.0230475	−	0.999734i	$-0.492663\pi$
$127$	0.519464			0.0460950			0.0230475	+	0.999734i	$0.492663\pi$
$128$	3.73823	−	10.6783i	0.330416	−	0.943835i
$129$		−	1.78940i		−	0.157548i
$130$	5.03361	−	0.814076i	0.441477	−	0.0713992i
$131$		−	18.4347i		−	1.61065i	−0.592836	−	0.805323i	$-0.701992\pi$
$131$		−	18.4347i		−	1.61065i	0.592836	−	0.805323i	$-0.298008\pi$
$132$	−1.50286	+	0.0240283i	−0.130807	+	0.00209140i
$133$	−2.54722			−0.220872
$134$	3.49518	−	8.63266i	0.301938	−	0.745748i
$135$	−0.942814	−	0.942814i	−0.0811445	−	0.0811445i
$136$	0.167857	−	0.434423i	0.0143936	−	0.0372515i
$137$	10.5127	+	10.5127i	0.898159	+	0.898159i	0.995273	−	0.0971146i	$-0.0309613\pi$
$137$	10.5127	+	10.5127i	0.898159	+	0.898159i	−0.0971146	+	0.995273i	$0.530961\pi$
$138$	−0.611824	+	0.259175i	−0.0520819	+	0.0220624i
$139$		−	7.86798i		−	0.667354i	−0.942688	−	0.333677i	$-0.891711\pi$
$139$		−	7.86798i		−	0.667354i	0.942688	−	0.333677i	$-0.108289\pi$
$140$	0.464162	+	0.449553i	0.0392288	+	0.0379941i
$141$	1.14675	+	1.14675i	0.0965736	+	0.0965736i
$142$	0.516187	−	1.27492i	0.0433174	−	0.106988i
$143$	2.87829	−	11.7438i	0.240694	−	0.982062i
$144$	−0.377203	−	11.7931i	−0.0314335	−	0.982757i
$145$	2.96491	−	2.96491i	0.246222	−	0.246222i
$146$	4.71791	−	11.6526i	0.390457	−	0.964379i
$147$	−1.54530			−0.127454
$148$	12.9596	−	0.207203i	1.06527	−	0.0170320i
$149$	−8.95831	+	8.95831i	−0.733893	+	0.733893i	−0.971389	−	0.237496i	$-0.923673\pi$
$149$	−8.95831	+	8.95831i	−0.733893	+	0.733893i	0.237496	+	0.971389i	$0.423673\pi$
$150$	−0.123618	−	0.291821i	−0.0100934	−	0.0238271i
$151$	13.8579	−	13.8579i	1.12774	−	1.12774i	0.137198	−	0.990544i	$-0.456190\pi$
$151$	13.8579	−	13.8579i	1.12774	−	1.12774i	0.990544	−	0.137198i	$-0.0438095\pi$
$152$	9.02510	+	20.3913i	0.732032	+	1.65395i
$153$		−	0.485706i		−	0.0392670i
$154$	1.41091	−	0.597676i	0.113694	−	0.0481621i
$155$	−6.51464			−0.523269
$156$	−1.57550	−	0.359541i	−0.126141	−	0.0287864i
$157$	−2.66626			−0.212791			−0.106395	−	0.994324i	$-0.533931\pi$
$157$	−2.66626			−0.212791			−0.106395	+	0.994324i	$0.533931\pi$
$158$	1.40081	−	0.593399i	0.111443	−	0.0472083i
$159$			0.232467i			0.0184359i
$160$	1.95423	−	5.30858i	0.154495	−	0.419680i
$161$	0.478979	−	0.478979i	0.0377488	−	0.0377488i
$162$	−4.71667	−	11.1345i	−0.370577	−	0.874807i
$163$	−12.3748	+	12.3748i	−0.969272	+	0.969272i	−0.999542	−	0.0302694i	$-0.990363\pi$
$163$	−12.3748	+	12.3748i	−0.969272	+	0.969272i	0.0302694	+	0.999542i	$0.490363\pi$
$164$	0.275607	+	17.2379i	0.0215213	+	1.34605i
$165$	−0.751524			−0.0585061
$166$	−9.35219	+	23.0987i	−0.725871	+	1.79281i
$167$	−9.87966	+	9.87966i	−0.764511	+	0.764511i	−0.977134	−	0.212623i	$-0.931799\pi$
$167$	−9.87966	+	9.87966i	−0.764511	+	0.764511i	0.212623	+	0.977134i	$0.431799\pi$
$168$	−0.0828835	−	0.187267i	−0.00639460	−	0.0144479i
$169$	6.01127	−	11.5267i	0.462405	−	0.886669i
$170$	0.0873900	−	0.215842i	0.00670251	−	0.0165543i
$171$	16.4445	+	16.4445i	1.25754	+	1.25754i
$172$	11.1103	−	11.4714i	0.847156	−	0.874685i
$173$			0.797525i			0.0606347i	0.999540	+	0.0303174i	$0.00965180\pi$
$173$			0.797525i			0.0606347i	−0.999540	+	0.0303174i	$0.990348\pi$
$174$	−1.22361	+	0.518333i	−0.0927615	+	0.0392947i
$175$	0.228458	+	0.228458i	0.0172698	+	0.0172698i
$176$	−9.78360	−	9.17714i	−0.737467	−	0.691753i
$177$	−0.716453	−	0.716453i	−0.0538519	−	0.0538519i
$178$	−4.12970	+	10.1998i	−0.309534	+	0.764509i
$179$	−2.59885			−0.194247			−0.0971236	−	0.995272i	$-0.530964\pi$
$179$	−2.59885			−0.194247			−0.0971236	+	0.995272i	$0.530964\pi$
$180$	−0.0943127	−	5.89881i	−0.00702965	−	0.439671i
$181$		−	3.15511i		−	0.234518i	−0.993101	−	0.117259i	$-0.962589\pi$
$181$		−	3.15511i		−	0.234518i	0.993101	−	0.117259i	$-0.0374107\pi$
$182$	1.62630	−	0.263018i	0.120549	−	0.0194962i
$183$		−	2.79411i		−	0.206546i
$184$	−5.53145	−	2.13729i	−0.407784	−	0.157563i
$185$	6.48061			0.476464
$186$	1.91374	+	0.774834i	0.140322	+	0.0568136i
$187$	−0.390456	−	0.390456i	−0.0285529	−	0.0285529i
$188$	0.231379	+	14.4716i	0.0168750	+	1.05545i
$189$	−0.304612	−	0.304612i	−0.0221573	−	0.0221573i
$190$	4.34898	+	10.2665i	0.315508	+	0.744809i
$191$			1.72613i			0.124898i	0.998048	+	0.0624490i	$0.0198911\pi$
$191$			1.72613i			0.124898i	−0.998048	+	0.0624490i	$0.980109\pi$
$192$	−1.20546	+	1.32702i	−0.0869967	+	0.0957691i
$193$	3.43647	+	3.43647i	0.247362	+	0.247362i	0.819887	−	0.572525i	$-0.194036\pi$
$193$	3.43647	+	3.43647i	0.247362	+	0.247362i	−0.572525	+	0.819887i	$0.694036\pi$
$194$	−6.40571	−	2.59354i	−0.459903	−	0.186205i
$195$	−0.784774	−	0.192341i	−0.0561989	−	0.0137738i
$196$	−9.90652	−	9.59473i	−0.707609	−	0.685338i
$197$	−8.75367	+	8.75367i	−0.623673	+	0.623673i	−0.946469	−	0.322795i	$-0.895377\pi$
$197$	−8.75367	+	8.75367i	−0.623673	+	0.623673i	0.322795	+	0.946469i	$0.395377\pi$
$198$	−12.9671	−	5.25013i	−0.921534	−	0.373110i
$199$	−4.53732			−0.321642			−0.160821	−	0.986984i	$-0.551414\pi$
$199$	−4.53732			−0.321642			−0.160821	+	0.986984i	$0.551414\pi$
$200$	1.01942	−	2.63833i	0.0720841	−	0.186558i
$201$	−1.04356	+	1.04356i	−0.0736071	+	0.0736071i
$202$	−4.02646	+	1.70565i	−0.283301	+	0.120009i
$203$	0.957926	−	0.957926i	0.0672332	−	0.0672332i
$204$	−0.0513434	+	0.0530118i	−0.00359475	+	0.00371157i
$205$			8.62003i			0.602049i
$206$	8.12795	+	19.1873i	0.566301	+	1.33685i
$207$	−6.18443			−0.429848
$208$	−7.86772	−	12.0871i	−0.545528	−	0.838092i
$209$	26.4392			1.82884
$210$	−0.0399396	−	0.0942839i	−0.00275609	−	0.00650621i
$211$			23.5229i			1.61938i	0.586857	+	0.809691i	$0.300365\pi$
$211$			23.5229i			1.61938i	−0.586857	+	0.809691i	$0.699635\pi$
$212$	−1.44338	+	1.49029i	−0.0991319	+	0.102353i
$213$	−0.154118	+	0.154118i	−0.0105600	+	0.0105600i
$214$	−8.67482	+	3.67474i	−0.592999	+	0.251200i
$215$	5.64616	−	5.64616i	0.385065	−	0.385065i
$216$	−1.35924	+	3.51779i	−0.0924844	+	0.239355i
$217$	−2.10480			−0.142883
$218$	10.9622	+	4.43836i	0.742453	+	0.300604i
$219$	−1.40863	+	1.40863i	−0.0951866	+	0.0951866i
$220$	−4.81782	−	4.66619i	−0.324817	−	0.314594i
$221$	−0.307800	−	0.507662i	−0.0207049	−	0.0341491i
$222$	−1.90374	−	0.770786i	−0.127771	−	0.0517318i
$223$	10.1925	+	10.1925i	0.682541	+	0.682541i	0.960572	−	0.278031i	$-0.0896818\pi$
$223$	10.1925	+	10.1925i	0.682541	+	0.682541i	−0.278031	+	0.960572i	$0.589682\pi$
$224$	0.631389	−	1.71514i	0.0421864	−	0.114597i
$225$		−	2.94978i		−	0.196652i
$226$	6.21448	+	14.6703i	0.413381	+	0.975853i
$227$	7.37422	+	7.37422i	0.489444	+	0.489444i	0.908131	−	0.418687i	$-0.137509\pi$
$227$	7.37422	+	7.37422i	0.489444	+	0.489444i	−0.418687	+	0.908131i	$0.637509\pi$
$228$	−0.0564893	−	3.53314i	−0.00374110	−	0.233988i
$229$	−13.2054	−	13.2054i	−0.872636	−	0.872636i	0.120123	−	0.992759i	$-0.461671\pi$
$229$	−13.2054	−	13.2054i	−0.872636	−	0.872636i	−0.992759	+	0.120123i	$0.961671\pi$
$230$	−2.74829	−	1.11272i	−0.181217	−	0.0733709i
$231$	−0.242808			−0.0159756
$232$	−11.0625	−	4.27445i	−0.726291	−	0.280631i
$233$			19.5570i			1.28122i	0.767864	+	0.640612i	$0.221319\pi$
$233$			19.5570i			1.28122i	−0.767864	+	0.640612i	$0.778681\pi$
$234$	−12.1972	−	8.80115i	−0.797354	−	0.575349i
$235$			7.23674i			0.472073i
$236$	−0.144558	−	9.04143i	−0.00940994	−	0.588547i
$237$	−0.241071			−0.0156592
$238$	0.0282347	−	0.0697360i	0.00183018	−	0.00452032i
$239$	−9.65315	−	9.65315i	−0.624411	−	0.624411i	0.322245	−	0.946656i	$-0.395562\pi$
$239$	−9.65315	−	9.65315i	−0.624411	−	0.624411i	−0.946656	+	0.322245i	$0.895562\pi$
$240$	−0.613261	+	0.653788i	−0.0395858	+	0.0422018i
$241$	−14.8881	−	14.8881i	−0.959028	−	0.959028i	0.0401650	−	0.999193i	$-0.487212\pi$
$241$	−14.8881	−	14.8881i	−0.959028	−	0.959028i	−0.999193	+	0.0401650i	$0.987212\pi$
$242$	−0.320572	+	0.135797i	−0.0206071	+	0.00872938i
$243$			5.91619i			0.379524i
$244$	17.3485	−	17.9123i	1.11063	−	1.14672i
$245$	−4.87594	−	4.87594i	−0.311512	−	0.311512i
$246$	1.02524	−	2.53222i	0.0653671	−	0.161448i
$247$	27.6090	+	6.76670i	1.75672	+	0.430555i
$248$	7.45757	+	16.8496i	0.473556	+	1.06995i
$249$	2.79229	−	2.79229i	0.176954	−	0.176954i
$250$	0.530735	−	1.31085i	0.0335666	−	0.0829053i
$251$	0.886900			0.0559806			0.0279903	−	0.999608i	$-0.491089\pi$
$251$	0.886900			0.0559806			0.0279903	+	0.999608i	$0.491089\pi$
$252$	−0.0304713	−	1.90583i	−0.00191951	−	0.120056i
$253$	−4.97162	+	4.97162i	−0.312563	+	0.312563i
$254$	−0.286548	−	0.676444i	−0.0179796	−	0.0424439i
$255$	−0.0260921	+	0.0260921i	−0.00163395	+	0.00163395i
$256$	−15.9673	+	1.02248i	−0.997956	+	0.0639047i
$257$		−	14.2727i		−	0.890304i	−0.895455	−	0.445152i	$-0.853150\pi$
$257$		−	14.2727i		−	0.890304i	0.895455	−	0.445152i	$-0.146850\pi$
$258$	−2.33015	+	0.987075i	−0.145069	+	0.0614526i
$259$	2.09381			0.130103
$260$	−3.83674	−	6.10569i	−0.237945	−	0.378659i
$261$	−12.3685			−0.765588
$262$	−24.0056	+	10.1690i	−1.48307	+	0.628242i
$263$			20.9249i			1.29028i	0.764064	+	0.645141i	$0.223201\pi$
$263$			20.9249i			1.29028i	−0.764064	+	0.645141i	$0.776799\pi$
$264$	0.860299	+	1.94376i	0.0529477	+	0.119630i
$265$	−0.733511	+	0.733511i	−0.0450592	+	0.0450592i
$266$	1.40510	+	3.31698i	0.0861525	+	0.203377i
$267$	1.23301	−	1.23301i	0.0754589	−	0.0754589i
$268$	−13.1694	+	0.210559i	−0.804451	+	0.0128619i
$269$	−2.07606			−0.126580			−0.0632898	−	0.997995i	$-0.520159\pi$
$269$	−2.07606			−0.126580			−0.0632898	+	0.997995i	$0.520159\pi$
$270$	−0.707651	+	1.74781i	−0.0430662	+	0.106368i
$271$	−3.27856	+	3.27856i	−0.199158	+	0.199158i	−0.799639	−	0.600481i	$-0.794976\pi$
$271$	−3.27856	+	3.27856i	−0.199158	+	0.199158i	0.600481	+	0.799639i	$0.294976\pi$
$272$	−0.658297	+	0.0210557i	−0.0399151	+	0.00127669i
$273$	−0.253551	−	0.0621431i	−0.0153456	−	0.00376107i
$274$	7.89053	−	19.4886i	0.476684	−	1.17735i
$275$	−2.37131	−	2.37131i	−0.142995	−	0.142995i
$276$	0.674992	+	0.653748i	0.0406298	+	0.0393510i
$277$		−	25.5435i		−	1.53476i	−0.641192	−	0.767381i	$-0.721560\pi$
$277$		−	25.5435i		−	1.53476i	0.641192	−	0.767381i	$-0.278440\pi$
$278$	−10.2456	+	4.34016i	−0.614493	+	0.260305i
$279$	13.5883	+	13.5883i	0.813510	+	0.813510i
$280$	0.329363	−	0.852413i	0.0196832	−	0.0509414i
$281$	11.1794	+	11.1794i	0.666905	+	0.666905i	0.956998	−	0.290093i	$-0.0936862\pi$
$281$	11.1794	+	11.1794i	0.666905	+	0.666905i	−0.290093	+	0.956998i	$0.593686\pi$
$282$	0.860718	−	2.12586i	0.0512550	−	0.126593i
$283$	23.5698			1.40108			0.700541	−	0.713613i	$-0.252942\pi$
$283$	23.5698			1.40108			0.700541	+	0.713613i	$0.252942\pi$
$284$	−1.94493	+	0.0310964i	−0.115410	+	0.00184523i
$285$		−	1.76679i		−	0.104656i
$286$	−16.8804	+	2.73003i	−0.998158	+	0.161430i
$287$			2.78503i			0.164395i
$288$	−15.1488	+	6.99653i	−0.892653	+	0.412274i
$289$	16.9729			0.998405
$290$	−5.49640	−	2.22538i	−0.322760	−	0.130679i
$291$	0.774356	+	0.774356i	0.0453936	+	0.0453936i
$292$	−17.7765	+	0.284219i	−1.04029	+	0.0166326i
$293$	−7.01195	−	7.01195i	−0.409643	−	0.409643i	0.471971	−	0.881614i	$-0.343543\pi$
$293$	−7.01195	−	7.01195i	−0.409643	−	0.409643i	−0.881614	+	0.471971i	$0.843543\pi$
$294$	0.852424	+	2.01228i	0.0497144	+	0.117359i
$295$		−	4.52129i		−	0.263240i
$296$	−7.41861	−	16.7616i	−0.431198	−	0.974247i
$297$	3.16176	+	3.16176i	0.183464	+	0.183464i
$298$	16.6071	+	6.72386i	0.962022	+	0.389503i
$299$	−6.46399	+	3.91917i	−0.373822	+	0.226652i
$300$	−0.311817	+	0.321950i	−0.0180028	+	0.0185878i
$301$	1.82421	−	1.82421i	0.105145	−	0.105145i
$302$	−25.6901	−	10.4014i	−1.47830	−	0.598532i
$303$	0.692927			0.0398076
$304$	21.5750	−	23.0007i	1.23741	−	1.31918i
$305$	8.81633	−	8.81633i	0.504822	−	0.504822i
$306$	−0.632485	+	0.267927i	−0.0361567	+	0.0153163i
$307$	16.2942	−	16.2942i	0.929960	−	0.929960i	−0.0677424	−	0.997703i	$-0.521580\pi$
$307$	16.2942	−	16.2942i	0.929960	−	0.929960i	0.997703	+	0.0677424i	$0.0215796\pi$
$308$	−1.55658	−	1.50759i	−0.0886944	−	0.0859029i
$309$		−	3.30202i		−	0.187845i
$310$	3.59362	+	8.48333i	0.204104	+	0.481821i
$311$	−18.2463			−1.03465			−0.517325	−	0.855789i	$-0.673072\pi$
$311$	−18.2463			−1.03465			−0.517325	+	0.855789i	$0.673072\pi$
$312$	0.400887	+	2.24994i	0.0226958	+	0.127378i
$313$	−0.300863			−0.0170058			−0.00850289	−	0.999964i	$-0.502707\pi$
$313$	−0.300863			−0.0170058			−0.00850289	+	0.999964i	$0.502707\pi$
$314$	1.47077	+	3.47199i	0.0830003	+	0.195936i
$315$		−	0.953039i		−	0.0536977i
$316$	−1.54544	−	1.49680i	−0.0869379	−	0.0842017i
$317$	−20.1567	+	20.1567i	−1.13211	+	1.13211i	−0.142284	+	0.989826i	$0.545445\pi$
$317$	−20.1567	+	20.1567i	−1.13211	+	1.13211i	−0.989826	+	0.142284i	$0.954555\pi$
$318$	0.302718	−	0.128234i	0.0169756	−	0.00719102i
$319$	−9.94291	+	9.94291i	−0.556696	+	0.556696i
$320$	−7.99080	+	0.383543i	−0.446699	+	0.0214407i
$321$	1.49288			0.0833244
$322$	−0.887939	−	0.359508i	−0.0494829	−	0.0200346i
$323$	0.917941	−	0.917941i	0.0510756	−	0.0510756i
$324$	−11.8974	+	12.2841i	−0.660968	+	0.682447i
$325$	−1.86932	−	3.08312i	−0.103691	−	0.171021i
$326$	22.9407	+	9.28821i	1.27057	+	0.514427i
$327$	−1.32517	−	1.32517i	−0.0732819	−	0.0732819i
$328$	22.2950	−	9.86769i	1.23104	−	0.544852i
$329$			2.33810i			0.128904i
$330$	0.414558	+	0.978631i	0.0228207	+	0.0538719i
$331$	−2.00558	−	2.00558i	−0.110237	−	0.110237i	0.649837	−	0.760074i	$-0.274837\pi$
$331$	−2.00558	−	2.00558i	−0.110237	−	0.110237i	−0.760074	+	0.649837i	$0.774837\pi$
$332$	35.2379	−	0.563399i	1.93393	−	0.0309206i
$333$	−13.5173	−	13.5173i	−0.740744	−	0.740744i
$334$	18.3151	+	7.41540i	1.00216	+	0.405753i
$335$	−6.58556			−0.359807
$336$	−0.198137	+	0.211231i	−0.0108093	+	0.0115236i
$337$			0.349964i			0.0190638i	0.999955	+	0.00953188i	$0.00303414\pi$
$337$			0.349964i			0.0190638i	−0.999955	+	0.00953188i	$0.996966\pi$
$338$	−18.3260	−	1.46946i	−0.996801	−	0.0799280i
$339$		−	2.52466i		−	0.137121i
$340$	−0.329275	+	0.00526459i	−0.0178574	+	0.000285513i
$341$	21.8471			1.18308
$342$	12.3428	−	30.4851i	0.667421	−	1.64844i
$343$	−3.17456	−	3.17456i	−0.171410	−	0.171410i
$344$	−21.0667	−	8.13996i	−1.13584	−	0.438877i
$345$	0.332227	+	0.332227i	0.0178865	+	0.0178865i
$346$	1.03853	−	0.439933i	0.0558319	−	0.0236510i
$347$		−	0.551711i		−	0.0296174i	−0.999890	−	0.0148087i	$-0.995286\pi$
$347$		−	0.551711i		−	0.0296174i	0.999890	−	0.0148087i	$-0.00471393\pi$
$348$	1.34994	+	1.30745i	0.0723644	+	0.0700868i
$349$	12.0863	+	12.0863i	0.646965	+	0.646965i	0.952258	−	0.305293i	$-0.0987544\pi$
$349$	12.0863	+	12.0863i	0.646965	+	0.646965i	−0.305293	+	0.952258i	$0.598754\pi$
$350$	0.171474	−	0.423519i	0.00916568	−	0.0226381i
$351$	2.49244	+	4.11085i	0.133037	+	0.219421i
$352$	−6.55357	+	17.8025i	−0.349307	+	0.948875i
$353$	4.95955	−	4.95955i	0.263970	−	0.263970i	−0.562695	−	0.826665i	$-0.690235\pi$
$353$	4.95955	−	4.95955i	0.263970	−	0.263970i	0.826665	+	0.562695i	$0.190235\pi$
$354$	−0.537750	+	1.32817i	−0.0285811	+	0.0705916i
$355$	−0.972589			−0.0516196
$356$	15.5602	−	0.248783i	0.824689	−	0.0131855i
$357$	−0.00843006	+	0.00843006i	−0.000446166	+	0.000446166i
$358$	1.43359	+	3.38421i	0.0757674	+	0.178861i
$359$	22.5202	−	22.5202i	1.18857	−	1.18857i	0.211111	−	0.977462i	$-0.432292\pi$
$359$	22.5202	−	22.5202i	1.18857	−	1.18857i	0.977462	−	0.211111i	$-0.0677082\pi$
$360$	−7.62937	+	3.37673i	−0.402103	+	0.177969i
$361$			43.1571i			2.27143i
$362$	−4.10857	+	1.74043i	−0.215942	+	0.0914750i
$363$	0.0551683			0.00289558
$364$	−1.23961	−	1.97267i	−0.0649730	−	0.103396i
$365$	−8.88940			−0.465292
$366$	−3.63847	+	1.54129i	−0.190186	+	0.0805647i
$367$		−	6.16314i		−	0.321713i	−0.986978	−	0.160857i	$-0.948574\pi$
$367$		−	6.16314i		−	0.321713i	0.986978	−	0.160857i	$-0.0514257\pi$
$368$	0.268099	+	8.38201i	0.0139756	+	0.436942i
$369$	17.9797	−	17.9797i	0.935988	−	0.935988i
$370$	−3.57485	−	8.43902i	−0.185848	−	0.438724i
$371$	−0.236989	+	0.236989i	−0.0123038	+	0.0123038i
$372$	−0.0466779	−	2.91948i	−0.00242014	−	0.151368i
$373$	22.4004			1.15985			0.579925	−	0.814670i	$-0.303082\pi$
$373$	22.4004			1.15985			0.579925	+	0.814670i	$0.303082\pi$
$374$	−0.293065	+	0.723834i	−0.0151540	+	0.0374286i
$375$	−0.158462	+	0.158462i	−0.00818295	+	0.00818295i
$376$	18.7172	−	8.28418i	0.965268	−	0.427224i
$377$	−12.9276	+	7.83809i	−0.665803	+	0.403682i
$378$	−0.228633	+	0.564695i	−0.0117596	+	0.0290448i
$379$	−26.1939	−	26.1939i	−1.34549	−	1.34549i	−0.890493	−	0.454997i	$-0.849640\pi$
$379$	−26.1939	−	26.1939i	−1.34549	−	1.34549i	−0.454997	−	0.890493i	$-0.650360\pi$
$380$	10.9700	−	11.3264i	0.562747	−	0.581035i
$381$			0.116412i			0.00596395i
$382$	2.24775	−	0.952170i	0.115005	−	0.0487173i
$383$	7.07988	+	7.07988i	0.361765	+	0.361765i	0.864462	−	0.502697i	$-0.167659\pi$
$383$	7.07988	+	7.07988i	0.361765	+	0.361765i	−0.502697	+	0.864462i	$0.667659\pi$
$384$	2.39299	+	0.837735i	0.122117	+	0.0427505i
$385$	−0.766141	−	0.766141i	−0.0390461	−	0.0390461i
$386$	2.57932	−	6.37058i	0.131284	−	0.324254i
$387$	−23.5536			−1.19730
$388$	0.156241	+	9.77214i	0.00793195	+	0.496105i
$389$			5.29134i			0.268282i	0.990962	+	0.134141i	$0.0428274\pi$
$389$			5.29134i			0.268282i	−0.990962	+	0.134141i	$0.957173\pi$
$390$	0.182434	+	1.12803i	0.00923790	+	0.0571200i
$391$			0.345219i			0.0174585i
$392$	−7.02955	+	18.1929i	−0.355046	+	0.918880i
$393$	4.13120			0.208391
$394$	16.2277	+	6.57027i	0.817540	+	0.331005i
$395$	−0.760658	−	0.760658i	−0.0382729	−	0.0382729i
$396$	0.316281	+	19.7818i	0.0158937	+	0.994074i
$397$	21.3250	+	21.3250i	1.07027	+	1.07027i	0.997337	+	0.0729334i	$0.0232360\pi$
$397$	21.3250	+	21.3250i	1.07027	+	1.07027i	0.0729334	+	0.997337i	$0.476764\pi$
$398$	2.50289	+	5.90848i	0.125458	+	0.296165i
$399$		−	0.570830i		−	0.0285773i
$400$	−3.99796	+	0.127875i	−0.199898	+	0.00639374i
$401$	−14.8325	−	14.8325i	−0.740699	−	0.740699i	0.232013	−	0.972713i	$-0.425469\pi$
$401$	−14.8325	−	14.8325i	−0.740699	−	0.740699i	−0.972713	+	0.232013i	$0.925469\pi$
$402$	1.93457	+	0.783268i	0.0964877	+	0.0390659i
$403$	22.8137	+	5.59142i	1.13643	+	0.278528i
$404$	4.44217	+	4.30236i	0.221006	+	0.214051i
$405$	−6.04614	+	6.04614i	−0.300435	+	0.300435i
$406$	−1.77582	−	0.718993i	−0.0881325	−	0.0356830i
$407$	−21.7329			−1.07726
$408$	0.0973539	+	0.0376165i	0.00481974	+	0.00186230i
$409$	6.50458	−	6.50458i	0.321631	−	0.321631i	−0.527762	−	0.849392i	$-0.676969\pi$
$409$	6.50458	−	6.50458i	0.321631	−	0.321631i	0.849392	+	0.527762i	$0.176969\pi$
$410$	11.2250	−	4.75501i	0.554362	−	0.234833i
$411$	−2.35588	+	2.35588i	−0.116207	+	0.116207i
$412$	20.5021	−	21.1684i	1.01007	−	1.04289i
$413$		−	1.46078i		−	0.0718801i
$414$	3.41147	+	8.05334i	0.167665	+	0.395800i
$415$	17.6212			0.864991
$416$	−11.3998	+	16.9129i	−0.558921	+	0.829221i
$417$	1.76321			0.0863447
$418$	−14.5845	−	34.4290i	−0.713349	−	1.68398i
$419$			36.3853i			1.77754i	0.458354	+	0.888770i	$0.348439\pi$
$419$			36.3853i			1.77754i	−0.458354	+	0.888770i	$0.651561\pi$
$420$	−0.100744	+	0.104018i	−0.00491582	+	0.00507557i
$421$	8.63430	−	8.63430i	0.420810	−	0.420810i	−0.464673	−	0.885483i	$-0.653828\pi$
$421$	8.63430	−	8.63430i	0.420810	−	0.420810i	0.885483	+	0.464673i	$0.153828\pi$
$422$	30.6314	−	12.9758i	1.49111	−	0.631650i
$423$	15.0945	−	15.0945i	0.733917	−	0.733917i
$424$	2.73685	+	1.05749i	0.132913	+	0.0513562i
$425$	−0.164659			−0.00798711
$426$	0.285707	+	0.115677i	0.0138426	+	0.00560457i
$427$	2.84845	−	2.84845i	0.137846	−	0.137846i
$428$	9.57046	+	9.26924i	0.462606	+	0.448046i
$429$	2.63177	+	0.645022i	0.127063	+	0.0311419i
$430$	−10.4669	−	4.23785i	−0.504761	−	0.204367i
$431$	−1.25160	−	1.25160i	−0.0602875	−	0.0602875i	0.676320	−	0.736608i	$-0.263574\pi$
$431$	−1.25160	−	1.25160i	−0.0602875	−	0.0602875i	−0.736608	+	0.676320i	$0.763574\pi$
$432$	5.33064	−	0.170501i	0.256470	−	0.00820322i
$433$		−	10.0447i		−	0.482717i	−0.970436	−	0.241358i	$-0.922407\pi$
$433$		−	10.0447i		−	0.482717i	0.970436	−	0.241358i	$-0.0775930\pi$
$434$	1.16106	+	2.74086i	0.0557325	+	0.131566i
$435$	0.664433	+	0.664433i	0.0318571	+	0.0318571i
$436$	−0.267378	−	16.7232i	−0.0128051	−	0.800896i
$437$	−11.6880	−	11.6880i	−0.559114	−	0.559114i
$438$	2.61135	+	1.05728i	0.124775	+	0.0505188i
$439$	−19.6265			−0.936722			−0.468361	−	0.883537i	$-0.655155\pi$
$439$	−19.6265			−0.936722			−0.468361	+	0.883537i	$0.655155\pi$
$440$	−3.41867	+	8.84772i	−0.162979	+	0.421798i
$441$			20.3405i			0.968597i
$442$	−0.491286	+	0.680854i	−0.0233681	+	0.0323849i
$443$		−	19.9052i		−	0.945723i	−0.881137	−	0.472861i	$-0.843221\pi$
$443$		−	19.9052i		−	0.945723i	0.881137	−	0.472861i	$-0.156779\pi$
$444$	0.0464341	+	2.90423i	0.00220366	+	0.137829i
$445$	7.78110			0.368859
$446$	7.65022	−	18.8951i	0.362248	−	0.894707i
$447$	−2.00755	−	2.00755i	−0.0949538	−	0.0949538i
$448$	−2.58173	+	0.123918i	−0.121975	+	0.00585458i
$449$	−5.24140	−	5.24140i	−0.247357	−	0.247357i	0.572528	−	0.819885i	$-0.305963\pi$
$449$	−5.24140	−	5.24140i	−0.247357	−	0.247357i	−0.819885	+	0.572528i	$0.805963\pi$
$450$	−3.84119	+	1.62717i	−0.181075	+	0.0767053i
$451$		−	28.9076i		−	1.36120i
$452$	15.6755	−	16.1849i	0.737315	−	0.761275i
$453$	3.10555	+	3.10555i	0.145911	+	0.145911i
$454$	5.53488	−	13.6705i	0.259765	−	0.641586i
$455$	−0.603956	−	0.996120i	−0.0283139	−	0.0466988i
$456$	−4.56967	+	2.02252i	−0.213995	+	0.0947131i
$457$	−5.96344	+	5.96344i	−0.278958	+	0.278958i	−0.832693	−	0.553735i	$-0.813202\pi$
$457$	−5.96344	+	5.96344i	−0.278958	+	0.278958i	0.553735	+	0.832693i	$0.313202\pi$
$458$	−9.91159	+	24.4804i	−0.463138	+	1.14389i
$459$	0.219546			0.0102475
$460$	0.0670333	+	4.19261i	0.00312544	+	0.195482i
$461$	6.76103	−	6.76103i	0.314892	−	0.314892i	−0.531909	−	0.846802i	$-0.678525\pi$
$461$	6.76103	−	6.76103i	0.314892	−	0.314892i	0.846802	+	0.531909i	$0.178525\pi$
$462$	0.133939	+	0.316184i	0.00623139	+	0.0147102i
$463$	−11.5279	+	11.5279i	−0.535746	+	0.535746i	−0.922277	−	0.386530i	$-0.873673\pi$
$463$	−11.5279	+	11.5279i	−0.535746	+	0.535746i	0.386530	+	0.922277i	$0.373673\pi$
$464$	0.536180	+	16.7635i	0.0248916	+	0.778225i
$465$		−	1.45993i		−	0.0677024i
$466$	25.4671	−	10.7881i	1.17974	−	0.499750i
$467$	−33.6340			−1.55640			−0.778198	−	0.628019i	$-0.783866\pi$
$467$	−33.6340			−1.55640			−0.778198	+	0.628019i	$0.783866\pi$
$468$	−4.73258	+	20.7380i	−0.218764	+	0.958615i
$469$	−2.12771			−0.0982487
$470$	9.42364	−	3.99195i	0.434680	−	0.184135i
$471$		−	0.597506i		−	0.0275316i
$472$	−11.6940	+	5.17570i	−0.538258	+	0.238231i
$473$	−18.9346	+	18.9346i	−0.870612	+	0.870612i
$474$	0.132980	+	0.313922i	0.00610799	+	0.0144189i
$475$	5.57482	−	5.57482i	0.255790	−	0.255790i
$476$	−0.106385	+	0.00170093i	−0.00487614	+	7.79619e-5i
$477$	3.05993			0.140104
$478$	−7.24539	+	17.8952i	−0.331396	+	0.818507i
$479$	27.9469	−	27.9469i	1.27693	−	1.27693i	0.334549	−	0.942378i	$-0.391416\pi$
$479$	27.9469	−	27.9469i	1.27693	−	1.27693i	0.942378	−	0.334549i	$-0.108584\pi$
$480$	1.18965	+	0.437941i	0.0542997	+	0.0199892i
$481$	−22.6945	−	5.56221i	−1.03478	−	0.253615i
$482$	−11.1746	+	27.5999i	−0.508990	+	1.25714i
$483$	0.107339	+	0.107339i	0.00488408	+	0.00488408i
$484$	0.353669	+	0.342538i	0.0160759	+	0.0155699i
$485$			4.88670i			0.221893i
$486$	7.70404	−	3.26351i	0.349462	−	0.148036i
$487$	−20.7972	−	20.7972i	−0.942410	−	0.942410i	0.0560194	−	0.998430i	$-0.482159\pi$
$487$	−20.7972	−	20.7972i	−0.942410	−	0.942410i	−0.998430	+	0.0560194i	$0.982159\pi$
$488$	−32.8951	−	12.7103i	−1.48909	−	0.575370i
$489$	−2.77319	−	2.77319i	−0.125408	−	0.125408i
$490$	−3.65974	+	9.03910i	−0.165330	+	0.408345i
$491$	−28.6510			−1.29300			−0.646500	−	0.762914i	$-0.723768\pi$
$491$	−28.6510			−1.29300			−0.646500	+	0.762914i	$0.723768\pi$
$492$	−3.86299	+	0.0617632i	−0.174157	+	0.00278450i
$493$			0.690415i			0.0310947i
$494$	−6.41816	−	39.6849i	−0.288767	−	1.78551i
$495$			9.89218i			0.444620i
$496$	17.8277	−	19.0058i	0.800488	−	0.853387i
$497$	−0.314232			−0.0140952
$498$	−5.17641	−	2.09582i	−0.231960	−	0.0939159i
$499$	−10.9680	−	10.9680i	−0.490996	−	0.490996i	0.417624	−	0.908620i	$-0.362863\pi$
$499$	−10.9680	−	10.9680i	−0.490996	−	0.490996i	−0.908620	+	0.417624i	$0.862863\pi$
$500$	−1.99974	+	0.0319728i	−0.0894313	+	0.00142987i
$501$	−2.21402	−	2.21402i	−0.0989153	−	0.0989153i
$502$	−0.489234	−	1.15492i	−0.0218356	−	0.0515465i
$503$		−	10.3885i		−	0.463201i	−0.972811	−	0.231601i	$-0.925604\pi$
$503$		−	10.3885i		−	0.463201i	0.972811	−	0.231601i	$-0.0743962\pi$
$504$	−2.46496	+	1.09098i	−0.109798	+	0.0485962i
$505$	2.18641	+	2.18641i	0.0972941	+	0.0972941i
$506$	9.21647	+	3.73156i	0.409722	+	0.165888i
$507$	2.58312	+	1.34712i	0.114721	+	0.0598277i
$508$	−0.722796	+	0.746284i	−0.0320689	+	0.0331110i
$509$	−26.9432	+	26.9432i	−1.19424	+	1.19424i	−0.218372	+	0.975866i	$0.570075\pi$
$509$	−26.9432	+	26.9432i	−1.19424	+	1.19424i	−0.975866	+	0.218372i	$0.929925\pi$
$510$	0.0483701	+	0.0195840i	0.00214186	+	0.000867196i
$511$	−2.87206			−0.127052
$512$	10.1394	+	20.2285i	0.448102	+	0.893983i
$513$	−7.43313	+	7.43313i	−0.328181	+	0.328181i
$514$	−18.5858	+	7.87312i	−0.819784	+	0.347269i
$515$	10.4189	−	10.4189i	0.459114	−	0.459114i
$516$	2.57073	+	2.48982i	0.113170	+	0.109608i
$517$		−	24.2686i		−	1.06733i
$518$	−1.15499	−	2.72655i	−0.0507474	−	0.119798i
$519$	−0.178725			−0.00784515
$520$	−5.83436	+	8.36422i	−0.255854	+	0.366795i
$521$	−7.58386			−0.332255			−0.166128	−	0.986104i	$-0.553126\pi$
$521$	−7.58386			−0.332255			−0.166128	+	0.986104i	$0.553126\pi$
$522$	6.82272	+	16.1061i	0.298622	+	0.704947i
$523$		−	8.28154i		−	0.362126i	−0.983471	−	0.181063i	$-0.942046\pi$
$523$		−	8.28154i		−	0.362126i	0.983471	−	0.181063i	$-0.0579539\pi$
$524$	26.4840	+	25.6505i	1.15696	+	1.12055i
$525$	−0.0511972	+	0.0511972i	−0.00223443	+	0.00223443i
$526$	27.2482	−	11.5426i	1.18808	−	0.503282i
$527$	0.758507	−	0.758507i	0.0330411	−	0.0330411i
$528$	2.05659	−	2.19250i	0.0895016	−	0.0954162i
$529$	−18.6044			−0.808886
$530$	1.35980	+	0.550553i	0.0590658	+	0.0239145i
$531$	−9.43055	+	9.43055i	−0.409251	+	0.409251i
$532$	3.54427	−	3.65944i	0.153663	−	0.158657i
$533$	7.39845	−	30.1865i	0.320462	−	1.30752i
$534$	−2.28577	−	0.925462i	−0.0989151	−	0.0400487i
$535$	4.71053	+	4.71053i	0.203654	+	0.203654i
$536$	7.53875	+	17.0330i	0.325624	+	0.735714i
$537$		−	0.582401i		−	0.0251324i
$538$	1.14520	+	2.70344i	0.0493732	+	0.116553i
$539$	16.3516	+	16.3516i	0.704314	+	0.704314i
$540$	2.66634	−	0.0426306i	0.114741	−	0.00183453i
$541$	3.89526	+	3.89526i	0.167470	+	0.167470i	0.785866	−	0.618396i	$-0.212217\pi$
$541$	3.89526	+	3.89526i	0.167470	+	0.167470i	−0.618396	+	0.785866i	$0.712217\pi$
$542$	6.07786	+	2.46080i	0.261066	+	0.105700i
$543$	0.707058			0.0303428
$544$	0.390550	+	0.845617i	0.0167447	+	0.0362555i
$545$		−	8.36267i		−	0.358218i
$546$	0.0589422	+	0.364453i	0.00252249	+	0.0155971i
$547$			34.5232i			1.47611i	0.674742	+	0.738054i	$0.264255\pi$
$547$			34.5232i			1.47611i	−0.674742	+	0.738054i	$0.735745\pi$
$548$	−29.7305	+	0.475345i	−1.27003	+	0.0203057i
$549$	−36.7784			−1.56966
$550$	−1.77984	+	4.39597i	−0.0758925	+	0.187445i
$551$	−23.3753	−	23.3753i	−0.995820	−	0.995820i
$552$	0.478966	−	1.23959i	0.0203862	−	0.0527606i
$553$	−0.245760	−	0.245760i	−0.0104508	−	0.0104508i
$554$	−33.2627	+	14.0904i	−1.41319	+	0.598643i
$555$			1.45230i			0.0616467i
$556$	11.3035	+	10.9477i	0.479374	+	0.464286i
$557$	12.4411	+	12.4411i	0.527148	+	0.527148i	0.919721	−	0.392573i	$-0.128415\pi$
$557$	12.4411	+	12.4411i	0.527148	+	0.527148i	−0.392573	+	0.919721i	$0.628415\pi$
$558$	10.1990	−	25.1902i	0.431758	−	1.06639i
$559$	−24.6183	+	14.9263i	−1.04124	+	0.631315i
$560$	−1.29169	+	0.0413148i	−0.0545839	+	0.00174587i
$561$	0.0875008	−	0.0875008i	0.00369429	−	0.00369429i
$562$	8.39093	−	20.7245i	0.353950	−	0.874211i
$563$	42.1244			1.77533			0.887666	−	0.460487i	$-0.152325\pi$
$563$	42.1244			1.77533			0.887666	+	0.460487i	$0.152325\pi$
$564$	−3.24308	+	0.0518518i	−0.136558	+	0.00218335i
$565$	7.96613	−	7.96613i	0.335138	−	0.335138i
$566$	−13.0017	−	30.6925i	−0.546500	−	1.29010i
$567$	−1.95344	+	1.95344i	−0.0820366	+	0.0820366i
$568$	1.11336	+	2.51552i	0.0467156	+	0.105549i
$569$		−	21.1026i		−	0.884667i	−0.896851	−	0.442333i	$-0.854151\pi$
$569$		−	21.1026i		−	0.884667i	0.896851	−	0.442333i	$-0.145849\pi$
$570$	−2.30071	+	0.974604i	−0.0963662	+	0.0408217i
$571$	−14.7651			−0.617900			−0.308950	−	0.951078i	$-0.599978\pi$
$571$	−14.7651			−0.617900			−0.308950	+	0.951078i	$0.599978\pi$
$572$	12.8666	+	20.4756i	0.537981	+	0.856128i
$573$	−0.386823			−0.0161598
$574$	3.62665	−	1.53629i	0.151374	−	0.0641234i
$575$			2.09657i			0.0874332i
$576$	17.4673	+	15.8673i	0.727803	+	0.661137i
$577$	6.01577	−	6.01577i	0.250440	−	0.250440i	−0.570711	−	0.821151i	$-0.693332\pi$
$577$	6.01577	−	6.01577i	0.250440	−	0.250440i	0.821151	+	0.570711i	$0.193332\pi$
$578$	−9.36263	−	22.1020i	−0.389434	−	0.919323i
$579$	−0.770110	+	0.770110i	−0.0320047	+	0.0320047i
$580$	0.134062	+	8.38495i	0.00556663	+	0.348166i
$581$	5.69321			0.236194
$582$	0.581210	−	1.43552i	0.0240919	−	0.0595040i
$583$	2.45985	−	2.45985i	0.101877	−	0.101877i
$584$	10.1760	+	22.9917i	0.421088	+	0.951404i
$585$	−2.53175	+	10.3299i	−0.104675	+	0.427087i
$586$	−5.26298	+	12.9989i	−0.217412	+	0.536979i
$587$	13.2253	+	13.2253i	0.545866	+	0.545866i	0.925242	−	0.379377i	$-0.123862\pi$
$587$	13.2253	+	13.2253i	0.545866	+	0.545866i	−0.379377	+	0.925242i	$0.623862\pi$
$588$	2.15017	−	2.22004i	0.0886716	−	0.0915531i
$589$			51.3613i			2.11631i
$590$	−5.88760	+	2.49405i	−0.242389	+	0.102678i
$591$	−1.96169	−	1.96169i	−0.0806932	−	0.0806932i
$592$	−17.7346	+	18.9065i	−0.728887	+	0.777054i
$593$	−15.5899	−	15.5899i	−0.640202	−	0.640202i	0.310403	−	0.950605i	$-0.399536\pi$
$593$	−15.5899	−	15.5899i	−0.640202	−	0.640202i	−0.950605	+	0.310403i	$0.899536\pi$
$594$	2.37313	−	5.86132i	0.0973707	−	0.240493i
$595$	−0.0531992			−0.00218096
$596$	−0.405062	−	25.3347i	−0.0165920	−	1.03775i
$597$		−	1.01681i		−	0.0416153i
$598$	8.66921	+	6.25547i	0.354510	+	0.255805i
$599$			29.6137i			1.20998i	0.796233	+	0.604991i	$0.206823\pi$
$599$			29.6137i			1.20998i	−0.796233	+	0.604991i	$0.793177\pi$
$600$	0.591247	+	0.228452i	0.0241376	+	0.00932651i
$601$	−16.2938			−0.664640			−0.332320	−	0.943167i	$-0.607831\pi$
$601$	−16.2938			−0.664640			−0.332320	+	0.943167i	$0.607831\pi$
$602$	−3.38175	−	1.36920i	−0.137830	−	0.0558044i
$603$	13.7362	+	13.7362i	0.559382	+	0.559382i
$604$	0.626604	+	39.1911i	0.0254962	+	1.59466i
$605$	0.174074	+	0.174074i	0.00707711	+	0.00707711i
$606$	−0.382234	−	0.902327i	−0.0155272	−	0.0366545i
$607$		−	5.26587i		−	0.213735i	−0.994273	−	0.106868i	$-0.965918\pi$
$607$		−	5.26587i		−	0.213735i	0.994273	−	0.106868i	$-0.0340821\pi$
$608$	−41.8527	−	15.4071i	−1.69735	−	0.624841i
$609$	0.214670	+	0.214670i	0.00869889	+	0.00869889i
$610$	−16.3439	−	6.61730i	−0.661744	−	0.267926i
$611$	6.21118	−	25.3424i	0.251278	−	1.02524i
$612$	0.697786	+	0.675824i	0.0282063	+	0.0273186i
$613$	29.4327	−	29.4327i	1.18877	−	1.18877i	0.211368	−	0.977407i	$-0.432208\pi$
$613$	29.4327	−	29.4327i	1.18877	−	1.18877i	0.977407	−	0.211368i	$-0.0677918\pi$
$614$	−30.2065	−	12.2300i	−1.21904	−	0.493562i
$615$	−1.93174			−0.0778954
$616$	−1.10453	+	2.85859i	−0.0445028	+	0.115176i
$617$	8.36048	−	8.36048i	0.336580	−	0.336580i	−0.518498	−	0.855079i	$-0.673509\pi$
$617$	8.36048	−	8.36048i	0.336580	−	0.336580i	0.855079	+	0.518498i	$0.173509\pi$
$618$	−4.29987	+	1.82147i	−0.172966	+	0.0732702i
$619$	5.74153	−	5.74153i	0.230772	−	0.230772i	−0.582243	−	0.813015i	$-0.697825\pi$
$619$	5.74153	−	5.74153i	0.230772	−	0.230772i	0.813015	+	0.582243i	$0.197825\pi$
$620$	9.06463	−	9.35920i	0.364044	−	0.375875i
$621$		−	2.79545i		−	0.112177i
$622$	10.0650	+	23.7602i	0.403572	+	0.952697i
$623$	2.51398			0.100720
$624$	2.70872	−	1.76315i	0.108436	−	0.0705825i
$625$	−1.00000			−0.0400000
$626$	0.165963	+	0.391782i	0.00663321	+	0.0156588i
$627$			5.92500i			0.236622i
$628$	3.70990	−	3.83046i	0.148041	−	0.152852i
$629$	−0.754545	+	0.754545i	−0.0300857	+	0.0300857i
$630$	−1.24104	+	0.525718i	−0.0494443	+	0.0209451i
$631$	−19.5606	+	19.5606i	−0.778695	+	0.778695i	−0.979609	−	0.200914i	$-0.935609\pi$
$631$	−19.5606	+	19.5606i	−0.778695	+	0.778695i	0.200914	+	0.979609i	$0.435609\pi$
$632$	−1.09663	+	2.83814i	−0.0436215	+	0.112895i
$633$	−5.27146			−0.209522
$634$	37.3668	+	15.1290i	1.48402	+	0.600850i
$635$	−0.367317	+	0.367317i	−0.0145765	+	0.0145765i
$636$	−0.333972	−	0.323461i	−0.0132429	−	0.0128261i
$637$	12.8901	+	21.2600i	0.510725	+	0.842352i
$638$	18.4323	+	7.46287i	0.729743	+	0.295458i
$639$	2.02863	+	2.02863i	0.0802515	+	0.0802515i
$640$	4.90736	+	10.1940i	0.193980	+	0.402954i
$641$			23.4477i			0.926127i	0.886325	+	0.463064i	$0.153250\pi$
$641$			23.4477i			0.926127i	−0.886325	+	0.463064i	$0.846750\pi$
$642$	−0.823506	−	1.94402i	−0.0325012	−	0.0767244i
$643$	−18.3793	−	18.3793i	−0.724809	−	0.724809i	0.244771	−	0.969581i	$-0.421287\pi$
$643$	−18.3793	−	18.3793i	−0.724809	−	0.724809i	−0.969581	+	0.244771i	$0.921287\pi$
$644$	0.0216577	+	1.35458i	0.000853432	+	0.0533781i
$645$	1.26530	+	1.26530i	0.0498211	+	0.0498211i
$646$	−1.70170	−	0.688981i	−0.0669523	−	0.0271076i
$647$	30.3560			1.19342			0.596709	−	0.802458i	$-0.296475\pi$
$647$	30.3560			1.19342			0.596709	+	0.802458i	$0.296475\pi$
$648$	22.5591	+	8.71661i	0.886206	+	0.342421i
$649$			15.1623i			0.595172i
$650$	−2.98366	+	4.13494i	−0.117029	+	0.162186i
$651$		−	0.471685i		−	0.0184868i
$652$	−0.559545	−	34.9969i	−0.0219135	−	1.37058i
$653$	8.48844			0.332178			0.166089	−	0.986111i	$-0.446886\pi$
$653$	8.48844			0.332178			0.166089	+	0.986111i	$0.446886\pi$
$654$	−0.994633	+	2.45662i	−0.0388932	+	0.0960613i
$655$	13.0353	+	13.0353i	0.509331	+	0.509331i
$656$	−25.1481	−	23.5892i	−0.981869	−	0.921005i
$657$	18.5416	+	18.5416i	0.723376	+	0.723376i
$658$	3.04467	−	1.28975i	0.118694	−	0.0502797i
$659$		−	13.5240i		−	0.526822i	−0.964684	−	0.263411i	$-0.915152\pi$
$659$		−	13.5240i		−	0.526822i	0.964684	−	0.263411i	$-0.0848476\pi$
$660$	1.04569	−	1.07967i	0.0407034	−	0.0420261i
$661$	30.8594	+	30.8594i	1.20029	+	1.20029i	0.974077	+	0.226215i	$0.0726353\pi$
$661$	30.8594	+	30.8594i	1.20029	+	1.20029i	0.226215	+	0.974077i	$0.427365\pi$
$662$	−1.50534	+	3.71799i	−0.0585065	+	0.144504i
$663$	0.113767	−	0.0689777i	0.00441833	−	0.00267887i
$664$	−20.1717	−	45.5759i	−0.782814	−	1.76869i
$665$	1.80116	−	1.80116i	0.0698459	−	0.0698459i
$666$	−10.1457	+	25.0586i	−0.393139	+	0.971002i
$667$	8.79096			0.340387
$668$	−0.446722	−	27.9403i	−0.0172842	−	1.08104i
$669$	−2.28413	+	2.28413i	−0.0883097	+	0.0883097i
$670$	3.63274	+	8.57568i	0.140345	+	0.331307i
$671$	−29.5659	+	29.5659i	−1.14138	+	1.14138i
$672$	0.384361	+	0.141494i	0.0148271	+	0.00545824i
$673$		−	2.85413i		−	0.110019i	−0.998486	−	0.0550093i	$-0.982481\pi$
$673$		−	2.85413i		−	0.110019i	0.998486	−	0.0550093i	$-0.0175189\pi$
$674$	0.455722	−	0.193048i	0.0175537	−	0.00743594i
$675$	1.33334			0.0513203
$676$	8.19549	+	24.6746i	0.315211	+	0.949022i
$677$	−29.6713			−1.14036			−0.570180	−	0.821520i	$-0.693126\pi$
$677$	−29.6713			−1.14036			−0.570180	+	0.821520i	$0.693126\pi$
$678$	−3.28760	+	1.39266i	−0.126260	+	0.0534848i
$679$			1.57883i			0.0605901i
$680$	0.188491	+	0.425876i	0.00722830	+	0.0163316i
$681$	−1.65256	+	1.65256i	−0.0633261	+	0.0633261i
$682$	−12.0513	−	28.4491i	−0.461469	−	1.08937i
$683$	−29.2450	+	29.2450i	−1.11903	+	1.11903i	−0.127145	+	0.991884i	$0.540581\pi$
$683$	−29.2450	+	29.2450i	−1.11903	+	1.11903i	−0.991884	+	0.127145i	$0.959419\pi$
$684$	−46.5061	+	0.743559i	−1.77820	+	0.0284307i
$685$	−14.8672			−0.568045
$686$	−2.38274	+	5.88506i	−0.0909734	+	0.224693i
$687$	2.95932	−	2.95932i	0.112905	−	0.112905i
$688$	1.02106	+	31.9232i	0.0389277	+	1.21706i
$689$	3.19825	−	1.93913i	0.121844	−	0.0738748i
$690$	0.249361	−	0.615889i	0.00949300	−	0.0234465i
$691$	3.12363	+	3.12363i	0.118828	+	0.118828i	0.764020	−	0.645192i	$-0.223223\pi$
$691$	3.12363	+	3.12363i	0.118828	+	0.118828i	−0.645192	+	0.764020i	$0.723223\pi$
$692$	−1.14576	−	1.10970i	−0.0435552	−	0.0421843i
$693$			3.19605i			0.121408i
$694$	−0.718435	+	0.304336i	−0.0272714	+	0.0115524i
$695$	5.56350	+	5.56350i	0.211036	+	0.211036i
$696$	0.957901	−	2.47911i	0.0363091	−	0.0939703i
$697$	−1.00364	−	1.00364i	−0.0380156	−	0.0380156i
$698$	9.07165	−	22.4058i	0.343367	−	0.848073i
$699$	−4.38272			−0.165770
$700$	−0.646094	+	0.0103300i	−0.0244200	+	0.000390438i
$701$		−	35.1266i		−	1.32671i	−0.748304	−	0.663356i	$-0.769132\pi$
$701$		−	35.1266i		−	1.32671i	0.748304	−	0.663356i	$-0.230868\pi$
$702$	3.97824	−	5.51329i	0.150149	−	0.208086i
$703$		−	51.0930i		−	1.92701i
$704$	26.7974	−	1.28622i	1.00997	−	0.0484763i
$705$	−1.62175			−0.0610785
$706$	−9.19411	−	3.72250i	−0.346025	−	0.140098i
$707$	0.706404	+	0.706404i	0.0265671	+	0.0265671i
$708$	2.02618	−	0.0323954i	0.0761484	−	0.00121749i
$709$	−25.4419	−	25.4419i	−0.955492	−	0.955492i	0.0435590	−	0.999051i	$-0.486130\pi$
$709$	−25.4419	−	25.4419i	−0.955492	−	0.955492i	−0.999051	+	0.0435590i	$0.986130\pi$
$710$	0.536502	+	1.26650i	0.0201346	+	0.0475309i
$711$			3.17318i			0.119003i
$712$	−8.90733	−	20.1252i	−0.333816	−	0.754223i
$713$	−9.65797	−	9.65797i	−0.361694	−	0.361694i
$714$	0.0156278	+	0.00632737i	0.000584855	+	0.000236796i
$715$	6.26883	+	10.3393i	0.234441	+	0.386670i
$716$	3.61611	−	3.73362i	0.135140	−	0.139532i
$717$	2.16326	−	2.16326i	0.0807886	−	0.0807886i
$718$	−41.7484	−	16.9031i	−1.55804	−	0.630817i
$719$	24.5308			0.914845			0.457423	−	0.889249i	$-0.348773\pi$
$719$	24.5308			0.914845			0.457423	+	0.889249i	$0.348773\pi$
$720$	8.60569	+	8.07225i	0.320715	+	0.300835i
$721$	3.36624	−	3.36624i	0.125365	−	0.125365i
$722$	56.1990	−	23.8065i	2.09151	−	0.885985i
$723$	3.33642	−	3.33642i	0.124083	−	0.124083i
$724$	4.53276	+	4.39010i	0.168459	+	0.163157i
$725$			4.19301i			0.155725i
$726$	−0.0304321	−	0.0718398i	−0.00112944	−	0.00266623i
$727$	−4.57535			−0.169690			−0.0848452	−	0.996394i	$-0.527040\pi$
$727$	−4.57535			−0.169690			−0.0848452	+	0.996394i	$0.527040\pi$
$728$	−1.88501	+	2.70238i	−0.0698632	+	0.100157i
$729$	24.3258			0.900956
$730$	4.90359	+	11.5757i	0.181490	+	0.428437i
$731$			1.31478i			0.0486288i
$732$	4.01413	+	3.88779i	0.148367	+	0.143697i
$733$	32.1976	−	32.1976i	1.18924	−	1.18924i	0.211968	−	0.977277i	$-0.432013\pi$
$733$	32.1976	−	32.1976i	1.18924	−	1.18924i	0.977277	−	0.211968i	$-0.0679874\pi$
$734$	−8.02561	+	3.39973i	−0.296231	+	0.125486i
$735$	1.09269	−	1.09269i	0.0403046	−	0.0403046i
$736$	10.7671	−	4.97282i	0.396881	−	0.183301i
$737$	22.0849			0.813507
$738$	−33.3312	−	13.4951i	−1.22694	−	0.496762i
$739$	−1.88057	+	1.88057i	−0.0691779	+	0.0691779i	−0.740849	−	0.671671i	$-0.765577\pi$
$739$	−1.88057	+	1.88057i	−0.0691779	+	0.0691779i	0.671671	+	0.740849i	$0.265577\pi$
$740$	−9.01728	+	9.31031i	−0.331482	+	0.342254i
$741$	−1.51641	+	6.18715i	−0.0557068	+	0.227291i
$742$	0.439334	+	0.177877i	0.0161285	+	0.00653008i
$743$	32.0605	+	32.0605i	1.17619	+	1.17619i	0.980708	+	0.195478i	$0.0626258\pi$
$743$	32.0605	+	32.0605i	1.17619	+	1.17619i	0.195478	+	0.980708i	$0.437374\pi$
$744$	−3.77598	+	1.67123i	−0.138434	+	0.0612704i
$745$		−	12.6690i		−	0.464155i
$746$	−12.3566	−	29.1697i	−0.452407	−	1.06798i
$747$	−36.7545	−	36.7545i	−1.34478	−	1.34478i
$748$	1.10423	−	0.0176550i	0.0403748	−	0.000645530i
$749$	1.52192	+	1.52192i	0.0556096	+	0.0556096i
$750$	0.293760	+	0.118937i	0.0107266	+	0.00434297i
$751$	17.7183			0.646550			0.323275	−	0.946305i	$-0.395216\pi$
$751$	17.7183			0.646550			0.323275	+	0.946305i	$0.395216\pi$
$752$	−21.1125	−	19.8038i	−0.769893	−	0.722169i
$753$			0.198754i			0.00724298i
$754$	17.3379	+	12.5105i	0.631408	+	0.455607i
$755$			19.5981i			0.713246i
$756$	0.861463	−	0.0137735i	0.0313311	−	0.000500936i
$757$	36.3086			1.31966			0.659829	−	0.751416i	$-0.270629\pi$
$757$	36.3086			1.31966			0.659829	+	0.751416i	$0.270629\pi$
$758$	−19.6604	+	48.5587i	−0.714099	+	1.76373i
$759$	−1.11414	−	1.11414i	−0.0404406	−	0.0404406i
$760$	−20.8005	−	8.03711i	−0.754515	−	0.291537i
$761$	15.5979	+	15.5979i	0.565424	+	0.565424i	0.930843	−	0.365419i	$-0.119074\pi$
$761$	15.5979	+	15.5979i	0.565424	+	0.565424i	−0.365419	+	0.930843i	$0.619074\pi$
$762$	0.151591	−	0.0642153i	0.00549155	−	0.00232627i
$763$		−	2.70188i		−	0.0978146i
$764$	−2.47982	−	2.40177i	−0.0897168	−	0.0868931i
$765$	0.343446	+	0.343446i	0.0124173	+	0.0124173i
$766$	5.31396	−	13.1248i	0.192001	−	0.474219i
$767$	−3.88056	+	15.8331i	−0.140119	+	0.571701i
$768$	−0.229136	−	3.57826i	−0.00826823	−	0.129119i
$769$	18.4721	−	18.4721i	0.666121	−	0.666121i	−0.290695	−	0.956816i	$-0.593887\pi$
$769$	18.4721	−	18.4721i	0.666121	−	0.666121i	0.956816	+	0.290695i	$0.0938865\pi$
$770$	−0.575044	+	1.42029i	−0.0207231	+	0.0511835i
$771$	3.19849			0.115191
$772$	−9.71855	+	0.155385i	−0.349778	+	0.00559241i
$773$	12.9611	−	12.9611i	0.466177	−	0.466177i	−0.434497	−	0.900673i	$-0.643074\pi$
$773$	12.9611	−	12.9611i	0.466177	−	0.466177i	0.900673	+	0.434497i	$0.143074\pi$
$774$	12.9927	+	30.6714i	0.467013	+	1.10246i
$775$	4.60655	−	4.60655i	0.165472	−	0.165472i
$776$	12.6391	−	5.59399i	0.453716	−	0.200813i
$777$			0.469221i			0.0168332i
$778$	6.89036	−	2.91882i	0.247031	−	0.104645i
$779$	67.9602			2.43493
$780$	1.36828	−	0.859811i	0.0489923	−	0.0307862i
$781$	3.26161			0.116709
$782$	0.449542	−	0.190431i	0.0160756	−	0.00680978i
$783$		−	5.59071i		−	0.199796i
$784$	27.5684	−	0.881775i	0.984584	−	0.0314920i
$785$	1.88533	−	1.88533i	0.0672903	−	0.0672903i
$786$	−2.27886	−	5.37963i	−0.0812844	−	0.191885i
$787$	36.4039	−	36.4039i	1.29766	−	1.29766i	0.367721	−	0.929936i	$-0.380138\pi$
$787$	36.4039	−	36.4039i	1.29766	−	1.29766i	0.929936	−	0.367721i	$-0.119862\pi$
$788$	−0.395809	−	24.7560i	−0.0141001	−	0.881895i
$789$	−4.68924			−0.166941
$790$	−0.570929	+	1.41012i	−0.0203128	+	0.0501699i
$791$	2.57376	−	2.57376i	0.0915125	−	0.0915125i
$792$	25.5853	−	11.3240i	0.909135	−	0.402380i
$793$	−38.4409	+	23.3070i	−1.36508	+	0.827657i
$794$	16.0059	−	39.5326i	0.568030	−	1.40296i
$795$	−0.164379	−	0.164379i	−0.00582993	−	0.00582993i
$796$	6.31334	−	6.51850i	0.223770	−	0.231042i
$797$			8.72336i			0.308997i	0.987993	+	0.154499i	$0.0493762\pi$
$797$			8.72336i			0.308997i	−0.987993	+	0.154499i	$0.950624\pi$
$798$	−0.743332	+	0.314883i	−0.0263137	+	0.0111467i
$799$	−0.842582	−	0.842582i	−0.0298084	−	0.0298084i
$800$	2.37188	+	5.13558i	0.0838587	+	0.181570i
$801$	−16.2299	−	16.2299i	−0.573455	−	0.573455i
$802$	−11.1329	+	27.4967i	−0.393115	+	0.970944i
$803$	29.8109			1.05200
$804$	−0.0471860	−	2.95126i	−0.00166412	−	0.104083i
$805$			0.677378i			0.0238744i
$806$	−5.30341	−	32.7922i	−0.186805	−	1.15506i
$807$		−	0.465244i		−	0.0163774i
$808$	3.15211	−	8.15786i	0.110891	−	0.286992i
$809$	−26.9629			−0.947966			−0.473983	−	0.880534i	$-0.657184\pi$
$809$	−26.9629			−0.947966			−0.473983	+	0.880534i	$0.657184\pi$
$810$	11.2084	+	4.53807i	0.393825	+	0.159451i
$811$	−12.8980	−	12.8980i	−0.452912	−	0.452912i	0.443408	−	0.896320i	$-0.353769\pi$
$811$	−12.8980	−	12.8980i	−0.452912	−	0.452912i	−0.896320	+	0.443408i	$0.853769\pi$
$812$	0.0433139	+	2.70908i	0.00152002	+	0.0950700i
$813$	−0.734723	−	0.734723i	−0.0257679	−	0.0257679i
$814$	11.9884	+	28.3005i	0.420192	+	0.991933i
$815$		−	17.5007i		−	0.613022i
$816$	−0.00471856	−	0.147524i	−0.000165183	−	0.00516437i
$817$	−44.5142	−	44.5142i	−1.55735	−	1.55735i
$818$	−12.0583	−	4.88216i	−0.421609	−	0.170701i
$819$	−0.817979	+	3.33745i	−0.0285825	+	0.116620i
$820$	−12.3839	−	11.9941i	−0.432464	−	0.418853i
$821$	39.8989	−	39.8989i	1.39248	−	1.39248i	0.572753	−	0.819728i	$-0.305875\pi$
$821$	39.8989	−	39.8989i	1.39248	−	1.39248i	0.819728	−	0.572753i	$-0.194125\pi$
$822$	4.36738	+	1.76826i	0.152330	+	0.0616752i
$823$	38.8491			1.35420			0.677098	−	0.735893i	$-0.263237\pi$
$823$	38.8491			1.35420			0.677098	+	0.735893i	$0.263237\pi$
$824$	−38.8748	−	15.0208i	−1.35427	−	0.523274i
$825$	0.531408	−	0.531408i	0.0185012	−	0.0185012i
$826$	−1.90221	+	0.805797i	−0.0661865	+	0.0280373i
$827$	−35.1605	+	35.1605i	−1.22265	+	1.22265i	−0.255966	+	0.966686i	$0.582393\pi$
$827$	−35.1605	+	35.1605i	−1.22265	+	1.22265i	−0.966686	+	0.255966i	$0.917607\pi$
$828$	8.60517	−	8.88481i	0.299050	−	0.308768i
$829$			42.3908i			1.47229i	0.676823	+	0.736146i	$0.263356\pi$
$829$			42.3908i			1.47229i	−0.676823	+	0.736146i	$0.736644\pi$
$830$	−9.72026	−	22.9463i	−0.337395	−	0.796476i
$831$	5.72428			0.198573
$832$	28.3122	+	5.51525i	0.981550	+	0.191207i
$833$	1.13542			0.0393400
$834$	−0.972626	−	2.29604i	−0.0336793	−	0.0795054i
$835$		−	13.9719i		−	0.483519i
$836$	−36.7881	+	37.9836i	−1.27234	+	1.31369i
$837$	−6.14210	+	6.14210i	−0.212302	+	0.212302i
$838$	47.3808	−	20.0710i	1.63674	−	0.693340i
$839$	−15.6788	+	15.6788i	−0.541292	+	0.541292i	−0.923908	−	0.382616i	$-0.875023\pi$
$839$	−15.6788	+	15.6788i	−0.541292	+	0.541292i	0.382616	+	0.923908i	$0.375023\pi$
$840$	0.191025	+	0.0738101i	0.00659099	+	0.00254669i
$841$	−11.4187			−0.393747
$842$	−16.0064	−	6.48067i	−0.551618	−	0.223339i
$843$	−2.50529	+	2.50529i	−0.0862867	+	0.0862867i
$844$	−33.7939	−	32.7303i	−1.16323	−	1.12662i
$845$	3.89999	+	12.4012i	0.134164	+	0.426615i
$846$	−27.9824	−	11.3295i	−0.962054	−	0.389516i
$847$	0.0562412	+	0.0562412i	0.00193247	+	0.00193247i
$848$	−0.132650	−	4.14724i	−0.00455521	−	0.142417i
$849$			5.28198i			0.181277i
$850$	0.0908294	+	0.214418i	0.00311542	+	0.00735446i
$851$	9.60751	+	9.60751i	0.329341	+	0.329341i
$852$	−0.00696867	−	0.435857i	−0.000238743	−	0.0149322i
$853$	34.8149	+	34.8149i	1.19204	+	1.19204i	0.976494	+	0.215545i	$0.0691526\pi$
$853$	34.8149	+	34.8149i	1.19204	+	1.19204i	0.215545	+	0.976494i	$0.430847\pi$
$854$	−5.28051	−	2.13797i	−0.180695	−	0.0731598i
$855$	−23.2560			−0.795339
$856$	6.79108	−	17.5757i	0.232114	−	0.600726i
$857$			16.1849i			0.552867i	0.961033	+	0.276433i	$0.0891525\pi$
$857$			16.1849i			0.552867i	−0.961033	+	0.276433i	$0.910847\pi$
$858$	−0.611798	−	3.78288i	−0.0208864	−	0.129145i
$859$			40.5410i			1.38324i	0.722261	+	0.691621i	$0.243103\pi$
$859$			40.5410i			1.38324i	−0.722261	+	0.691621i	$0.756897\pi$
$860$	0.255299	+	15.9677i	0.00870561	+	0.544494i
$861$	−0.624123			−0.0212701
$862$	−0.939418	+	2.32024i	−0.0319967	+	0.0790278i
$863$	3.51814	+	3.51814i	0.119759	+	0.119759i	0.764446	−	0.644687i	$-0.223012\pi$
$863$	3.51814	+	3.51814i	0.119759	+	0.119759i	−0.644687	+	0.764446i	$0.723012\pi$
$864$	−3.16253	−	6.84748i	−0.107591	−	0.232956i
$865$	−0.563936	−	0.563936i	−0.0191744	−	0.0191744i
$866$	−13.0801	+	5.54088i	−0.444481	+	0.188287i
$867$			3.80361i			0.129177i
$868$	2.92867	−	3.02385i	0.0994057	−	0.102636i
$869$	2.55089	+	2.55089i	0.0865331	+	0.0865331i
$870$	0.498705	−	1.23174i	0.0169077	−	0.0417598i
$871$	23.0620	+	5.65228i	0.781426	+	0.191520i
$872$	−21.6294	+	9.57308i	−0.732464	+	0.324185i
$873$	10.1927	−	10.1927i	0.344971	−	0.344971i
$874$	−8.77270	+	21.6675i	−0.296741	+	0.732912i
$875$	−0.323088			−0.0109224
$876$	−0.0636932	−	3.98370i	−0.00215199	−	0.134597i
$877$	16.0057	−	16.0057i	0.540475	−	0.540475i	−0.383193	−	0.923668i	$-0.625176\pi$
$877$	16.0057	−	16.0057i	0.540475	−	0.540475i	0.923668	+	0.383193i	$0.125176\pi$
$878$	10.8264	+	25.5575i	0.365374	+	0.862525i
$879$	1.57137	−	1.57137i	0.0530011	−	0.0530011i
$880$	13.4073	−	0.428832i	0.451959	−	0.0144559i
$881$		−	32.7679i		−	1.10398i	−0.833851	−	0.551990i	$-0.813869\pi$
$881$		−	32.7679i		−	1.10398i	0.833851	−	0.551990i	$-0.186131\pi$
$882$	26.4874	−	11.2203i	0.891876	−	0.377807i
$883$	−50.7712			−1.70859			−0.854294	−	0.519790i	$-0.826010\pi$
$883$	−50.7712			−1.70859			−0.854294	+	0.519790i	$0.826010\pi$
$884$	1.15761	+	0.264176i	0.0389346	+	0.00888519i
$885$	1.01322			0.0340589
$886$	−25.9204	+	10.9801i	−0.870813	+	0.368885i
$887$			6.74108i			0.226343i	0.993575	+	0.113172i	$0.0361010\pi$
$887$			6.74108i			0.226343i	−0.993575	+	0.113172i	$0.963899\pi$
$888$	3.75626	−	1.66250i	0.126052	−	0.0557900i
$889$	−0.118676	+	0.118676i	−0.00398025	+	0.00398025i
$890$	−4.29223	−	10.1325i	−0.143876	−	0.339642i
$891$	20.2759	−	20.2759i	0.679269	−	0.679269i
$892$	−28.8251	+	0.460868i	−0.965135	+	0.0154310i
$893$	57.0543			1.90925
$894$	−1.50681	+	3.72163i	−0.0503953	+	0.124470i
$895$	1.83767	−	1.83767i	0.0614264	−	0.0614264i
$896$	1.58551	+	3.29356i	0.0529681	+	0.110030i
$897$	−0.878283	−	1.44858i	−0.0293250	−	0.0483665i
$898$	−3.93405	+	9.71660i	−0.131281	+	0.324247i
$899$	−19.3153	−	19.3153i	−0.644201	−	0.644201i
$900$	4.23777	+	4.10440i	0.141259	+	0.136813i
$901$		−	0.170807i		−	0.00569041i
$902$	−37.6433	+	15.9461i	−1.25338	+	0.530946i
$903$	0.408803	+	0.408803i	0.0136041	+	0.0136041i
$904$	−29.7229	−	11.4846i	−0.988570	−	0.381973i
$905$	2.23100	+	2.23100i	0.0741610	+	0.0741610i
$906$	2.33094	−	5.75712i	0.0774403	−	0.191268i
$907$	17.9464			0.595899			0.297949	−	0.954582i	$-0.403697\pi$
$907$	17.9464			0.595899			0.297949	+	0.954582i	$0.403697\pi$
$908$	−20.8548	+	0.333435i	−0.692090	+	0.0110654i
$909$		−	9.12088i		−	0.302521i
$910$	−0.963987	+	1.33595i	−0.0319558	+	0.0442863i
$911$		−	14.9948i		−	0.496801i	−0.968657	−	0.248400i	$-0.920095\pi$
$911$		−	14.9948i		−	0.496801i	0.968657	−	0.248400i	$-0.0799049\pi$
$912$	5.15445	+	4.83494i	0.170681	+	0.160101i
$913$	−59.0933			−1.95570
$914$	11.0551	+	4.47600i	0.365671	+	0.148053i
$915$	1.97573	+	1.97573i	0.0653157	+	0.0653157i
$916$	37.3457	−	0.597099i	1.23394	−	0.0197287i
$917$	4.21155	+	4.21155i	0.139078	+	0.139078i
$918$	−0.121107	−	0.285892i	−0.00399711	−	0.00943583i
$919$			5.71668i			0.188576i	0.995545	+	0.0942879i	$0.0300574\pi$
$919$			5.71668i			0.188576i	−0.995545	+	0.0942879i	$0.969943\pi$
$920$	5.42262	−	2.40003i	0.178779	−	0.0791267i
$921$	3.65152	+	3.65152i	0.120322	+	0.120322i
$922$	−12.5337	−	5.07464i	−0.412776	−	0.167124i
$923$	3.40591	+	0.834758i	0.112107	+	0.0274764i
$924$	0.337850	−	0.348829i	0.0111144	−	0.0114756i
$925$	−4.58248	+	4.58248i	−0.150671	+	0.150671i
$926$	21.3706	+	8.65251i	0.702281	+	0.284339i
$927$	−43.4639			−1.42754
$928$	21.5335	−	9.94532i	0.706873	−	0.326471i
$929$	24.4668	−	24.4668i	0.802729	−	0.802729i	−0.180793	−	0.983521i	$-0.557866\pi$
$929$	24.4668	−	24.4668i	0.802729	−	0.802729i	0.983521	+	0.180793i	$0.0578662\pi$
$930$	−1.90111	+	0.805328i	−0.0623398	+	0.0264078i
$931$	−38.4418	+	38.4418i	−1.25988	+	1.25988i
$932$	−28.0965	−	27.2122i	−0.920330	−	0.891364i
$933$		−	4.08897i		−	0.133867i
$934$	18.5533	+	43.7981i	0.607082	+	1.43312i
$935$	0.552188			0.0180585
$936$	29.6155	−	5.27681i	0.968014	−	0.172478i
$937$	−46.5707			−1.52140			−0.760699	−	0.649105i	$-0.775144\pi$
$937$	−46.5707			−1.52140			−0.760699	+	0.649105i	$0.775144\pi$
$938$	1.17370	+	2.77070i	0.0383225	+	0.0904666i
$939$		−	0.0674232i		−	0.00220027i
$940$	−10.3966	−	10.0694i	−0.339100	−	0.328427i
$941$	−23.7060	+	23.7060i	−0.772793	+	0.772793i	−0.978594	−	0.205801i	$-0.934020\pi$
$941$	−23.7060	+	23.7060i	−0.772793	+	0.772793i	0.205801	+	0.978594i	$0.434020\pi$
$942$	−0.778070	+	0.329598i	−0.0253509	+	0.0107389i
$943$	−12.7792	+	12.7792i	−0.416148	+	0.416148i
$944$	13.1904	+	12.3728i	0.429312	+	0.402700i
$945$	0.430787			0.0140135
$946$	35.1012	+	14.2118i	1.14124	+	0.462064i
$947$	10.5116	−	10.5116i	0.341580	−	0.341580i	−0.515381	−	0.856961i	$-0.672350\pi$
$947$	10.5116	−	10.5116i	0.341580	−	0.341580i	0.856961	+	0.515381i	$0.172350\pi$
$948$	0.335432	−	0.346333i	0.0108943	−	0.0112484i
$949$	31.1298	+	7.62964i	1.01052	+	0.247669i
$950$	−10.3347	−	4.18430i	−0.335302	−	0.135757i
$951$	−4.51709	−	4.51709i	−0.146477	−	0.146477i
$952$	0.0608992	+	0.137596i	0.00197376	+	0.00445950i
$953$			24.9099i			0.806912i	0.914999	+	0.403456i	$0.132191\pi$
$953$			24.9099i			0.806912i	−0.914999	+	0.403456i	$0.867809\pi$
$954$	−1.68793	−	3.98462i	−0.0546486	−	0.129007i
$955$	−1.22055	−	1.22055i	−0.0394962	−	0.0394962i
$956$	27.2998	−	0.436480i	0.882937	−	0.0141168i
$957$	−2.22820	−	2.22820i	−0.0720274	−	0.0720274i
$958$	−51.8085	−	20.9762i	−1.67386	−	0.677710i
$959$	−4.80341			−0.155110
$960$	−0.0859516	−	1.79073i	−0.00277408	−	0.0577956i
$961$			11.4405i			0.369050i
$962$	5.27571	+	32.6209i	0.170096	+	1.05174i
$963$		−	19.6505i		−	0.633229i
$964$	42.1046	−	0.673186i	1.35610	−	0.0216819i
$965$	−4.85990			−0.156446
$966$	0.0805655	−	0.198986i	0.00259215	−	0.00640229i
$967$	27.5864	+	27.5864i	0.887119	+	0.887119i	0.994245	−	0.107126i	$-0.0341649\pi$
$967$	27.5864	+	27.5864i	0.887119	+	0.887119i	−0.107126	+	0.994245i	$0.534165\pi$
$968$	0.250959	−	0.649498i	0.00806614	−	0.0208757i
$969$	0.205710	+	0.205710i	0.00660835	+	0.00660835i
$970$	6.36343	−	2.69561i	0.204317	−	0.0865509i
$971$			36.9190i			1.18479i	0.805649	+	0.592393i	$0.201817\pi$
$971$			36.9190i			1.18479i	−0.805649	+	0.592393i	$0.798183\pi$
$972$	−8.49944	−	8.23194i	−0.272620	−	0.264039i
$973$	1.79750	+	1.79750i	0.0576253	+	0.0576253i
$974$	−15.6098	+	38.5542i	−0.500170	+	1.23536i
$975$	0.690925	−	0.418914i	0.0221273	−	0.0134160i
$976$	1.59437	+	49.8472i	0.0510344	+	1.59557i
$977$	−32.2117	+	32.2117i	−1.03054	+	1.03054i	−0.0310249	+	0.999519i	$0.509877\pi$
$977$	−32.2117	+	32.2117i	−1.03054	+	1.03054i	−0.999519	+	0.0310249i	$0.990123\pi$
$978$	−2.08148	+	5.14099i	−0.0665584	+	0.164391i
$979$	−26.0942			−0.833973
$980$	13.7895	−	0.220472i	0.440488	−	0.00704272i
$981$	−17.4429	+	17.4429i	−0.556910	+	0.556910i
$982$	15.8045	+	37.3091i	0.504342	+	1.19058i
$983$	−22.4651	+	22.4651i	−0.716526	+	0.716526i	−0.967892	−	0.251366i	$-0.919120\pi$
$983$	−22.4651	+	22.4651i	−0.716526	+	0.716526i	0.251366	+	0.967892i	$0.419120\pi$
$984$	2.21134	+	4.99630i	0.0704950	+	0.159276i
$985$		−	12.3796i		−	0.394446i
$986$	0.899055	−	0.380849i	0.0286317	−	0.0121287i
$987$	−0.523967			−0.0166781
$988$	−48.1371	+	30.2488i	−1.53145	+	0.962343i
$989$	16.7409			0.532329
$990$	12.8815	−	5.45675i	0.409403	−	0.173427i
$991$		−	48.1265i		−	1.52879i	−0.644749	−	0.764394i	$-0.723038\pi$
$991$		−	48.1265i		−	1.52879i	0.644749	−	0.764394i	$-0.276962\pi$
$992$	−34.5835	−	12.7311i	−1.09803	−	0.404213i
$993$	0.449450	−	0.449450i	0.0142629	−	0.0142629i
$994$	0.173337	+	0.409191i	0.00549793	+	0.0129788i
$995$	3.20837	−	3.20837i	0.101712	−	0.101712i
$996$	0.126257	+	7.89679i	0.00400062	+	0.250219i
$997$	13.7707			0.436123			0.218062	−	0.975935i	$-0.430027\pi$
$997$	13.7707			0.436123			0.218062	+	0.975935i	$0.430027\pi$
$998$	−8.23229	+	20.3327i	−0.260589	+	0.643621i
$999$	6.11001	−	6.11001i	0.193312	−	0.193312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.j.a.31.12	✓	56
4.3	odd	2	inner	260.2.j.a.31.24	yes	56
13.8	odd	4	inner	260.2.j.a.151.24	yes	56
52.47	even	4	inner	260.2.j.a.151.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.j.a.31.12	✓	56	1.1	even	1	trivial
260.2.j.a.31.24	yes	56	4.3	odd	2	inner
260.2.j.a.151.12	yes	56	52.47	even	4	inner
260.2.j.a.151.24	yes	56	13.8	odd	4	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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.551623 - 1.30220i) q^{2} +0.224099i q^{3} +(-1.39142 + 1.43664i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.291821 - 0.123618i) q^{6} +(-0.228458 + 0.228458i) q^{7} +(2.63833 + 1.01942i) q^{8} +2.94978 q^{9} +O(q^{10})\)	\(q+(-0.551623 - 1.30220i) q^{2} +0.224099i q^{3} +(-1.39142 + 1.43664i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.291821 - 0.123618i) q^{6} +(-0.228458 + 0.228458i) q^{7} +(2.63833 + 1.01942i) q^{8} +2.94978 q^{9} +(1.31085 + 0.530735i) q^{10} +(2.37131 - 2.37131i) q^{11} +(-0.321950 - 0.311817i) q^{12} +(3.08312 - 1.86932i) q^{13} +(0.423519 + 0.171474i) q^{14} +(-0.158462 - 0.158462i) q^{15} +(-0.127875 - 3.99796i) q^{16} -0.164659i q^{17} +(-1.62717 - 3.84119i) q^{18} +(5.57482 + 5.57482i) q^{19} +(-0.0319728 - 1.99974i) q^{20} +(-0.0511972 - 0.0511972i) q^{21} +(-4.39597 - 1.77984i) q^{22} -2.09657 q^{23} +(-0.228452 + 0.591247i) q^{24} -1.00000i q^{25} +(-4.13494 - 2.98366i) q^{26} +1.33334i q^{27} +(-0.0103300 - 0.646094i) q^{28} -4.19301 q^{29} +(-0.118937 + 0.293760i) q^{30} +(4.60655 + 4.60655i) q^{31} +(-5.13558 + 2.37188i) q^{32} +(0.531408 + 0.531408i) q^{33} +(-0.214418 + 0.0908294i) q^{34} -0.323088i q^{35} +(-4.10440 + 4.23777i) q^{36} +(-4.58248 - 4.58248i) q^{37} +(4.18430 - 10.3347i) q^{38} +(0.418914 + 0.690925i) q^{39} +(-2.58642 + 1.14474i) q^{40} +(6.09528 - 6.09528i) q^{41} +(-0.0384272 + 0.0949103i) q^{42} -7.98487 q^{43} +(0.107222 + 6.70621i) q^{44} +(-2.08581 + 2.08581i) q^{45} +(1.15652 + 2.73015i) q^{46} +(5.11715 - 5.11715i) q^{47} +(0.895939 - 0.0286566i) q^{48} +6.89561i q^{49} +(-1.30220 + 0.551623i) q^{50} +0.0368998 q^{51} +(-1.60439 + 7.03036i) q^{52} +1.03734 q^{53} +(1.73627 - 0.735501i) q^{54} +3.35353i q^{55} +(-0.835642 + 0.369852i) q^{56} +(-1.24931 + 1.24931i) q^{57} +(2.31296 + 5.46012i) q^{58} +(-3.19704 + 3.19704i) q^{59} +(0.448141 - 0.00716508i) q^{60} -12.4682 q^{61} +(3.45755 - 8.53970i) q^{62} +(-0.673900 + 0.673900i) q^{63} +(5.92155 + 5.37914i) q^{64} +(-0.858285 + 3.50191i) q^{65} +(0.398860 - 0.985133i) q^{66} +(4.65669 + 4.65669i) q^{67} +(0.236555 + 0.229110i) q^{68} -0.469841i q^{69} +(-0.420724 + 0.178223i) q^{70} +(0.687724 + 0.687724i) q^{71} +(7.78249 + 3.00707i) q^{72} +(6.28575 + 6.28575i) q^{73} +(-3.43949 + 8.49509i) q^{74} +0.224099 q^{75} +(-15.7659 + 0.252073i) q^{76} +1.08349i q^{77} +(0.668637 - 0.926637i) q^{78} +1.07573i q^{79} +(2.91740 + 2.73656i) q^{80} +8.55054 q^{81} +(-11.2995 - 4.57495i) q^{82} +(-12.4601 - 12.4601i) q^{83} +(0.144789 - 0.00231495i) q^{84} +(0.116431 + 0.116431i) q^{85} +(4.40464 + 10.3979i) q^{86} -0.939650i q^{87} +(8.67364 - 3.83892i) q^{88} +(-5.50207 - 5.50207i) q^{89} +(3.86671 + 1.56555i) q^{90} +(-0.277302 + 1.13142i) q^{91} +(2.91722 - 3.01202i) q^{92} +(-1.03232 + 1.03232i) q^{93} +(-9.48626 - 3.84079i) q^{94} -7.88398 q^{95} +(-0.531537 - 1.15088i) q^{96} +(3.45542 - 3.45542i) q^{97} +(8.97944 - 3.80378i) q^{98} +(6.99483 - 6.99483i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) \) 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9	\( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 40 q^{24} - 16 q^{26} - 44 q^{28} + 40 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{41} + 8 q^{42} + 28 q^{44} - 12 q^{46} + 104 q^{48} + 56 q^{52} - 16 q^{53} + 20 q^{54} - 48 q^{57} - 4 q^{58} + 16 q^{61} - 8 q^{65} + 64 q^{66} + 24 q^{68} - 8 q^{70} - 32 q^{72} + 48 q^{73} - 136 q^{74} - 88 q^{76} + 52 q^{78} - 32 q^{80} + 56 q^{81} - 20 q^{84} - 64 q^{86} - 8 q^{89} - 88 q^{92} - 48 q^{93} - 16 q^{94} - 4 q^{96} - 32 q^{97} + 16 q^{98}+O(q^{100}) \) 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 40 * q^24 - 16 * q^26 - 44 * q^28 + 40 * q^32 - 4 * q^34 + 16 * q^37 + 8 * q^41 + 8 * q^42 + 28 * q^44 - 12 * q^46 + 104 * q^48 + 56 * q^52 - 16 * q^53 + 20 * q^54 - 48 * q^57 - 4 * q^58 + 16 * q^61 - 8 * q^65 + 64 * q^66 + 24 * q^68 - 8 * q^70 - 32 * q^72 + 48 * q^73 - 136 * q^74 - 88 * q^76 + 52 * q^78 - 32 * q^80 + 56 * q^81 - 20 * q^84 - 64 * q^86 - 8 * q^89 - 88 * q^92 - 48 * q^93 - 16 * q^94 - 4 * q^96 - 32 * q^97 + 16 * q^98

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