LMFDB - Embedded newform 850.2.v.c.193.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(107,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("850.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.v (of order $16$, degree $8$, 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:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			193.4
Character	$\chi$	$=$	850.193
Dual form			850.2.v.c.207.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.923880 - 0.382683i) q^{2} +(1.19858 + 0.800867i) q^{3} +(0.707107 - 0.707107i) q^{4} +(1.41382 + 0.281227i) q^{6} +(3.32261 + 0.660909i) q^{7} +(0.382683 - 0.923880i) q^{8} +(-0.352840 - 0.851831i) q^{9} +O(q^{10})$	\(q+(0.923880 - 0.382683i) q^{2} +(1.19858 + 0.800867i) q^{3} +(0.707107 - 0.707107i) q^{4} +(1.41382 + 0.281227i) q^{6} +(3.32261 + 0.660909i) q^{7} +(0.382683 - 0.923880i) q^{8} +(-0.352840 - 0.851831i) q^{9} +(0.778556 - 3.91407i) q^{11} +(1.41382 - 0.281227i) q^{12} -4.10923 q^{13} +(3.32261 - 0.660909i) q^{14} -1.00000i q^{16} +(3.10352 + 2.71444i) q^{17} +(-0.651963 - 0.651963i) q^{18} +(2.45357 - 5.92345i) q^{19} +(3.45312 + 3.45312i) q^{21} +(-0.778556 - 3.91407i) q^{22} +(1.82418 + 2.73008i) q^{23} +(1.19858 - 0.800867i) q^{24} +(-3.79643 + 1.57253i) q^{26} +(1.10298 - 5.54504i) q^{27} +(2.81678 - 1.88211i) q^{28} +(-4.93652 + 7.38803i) q^{29} +(2.05047 + 10.3084i) q^{31} +(-0.382683 - 0.923880i) q^{32} +(4.06781 - 4.06781i) q^{33} +(3.90605 + 1.32015i) q^{34} +(-0.851831 - 0.352840i) q^{36} +(-3.51957 + 5.26741i) q^{37} -6.41149i q^{38} +(-4.92525 - 3.29095i) q^{39} +(0.637150 + 0.953562i) q^{41} +(4.51172 + 1.86882i) q^{42} +(-4.26901 - 1.76828i) q^{43} +(-2.21714 - 3.31818i) q^{44} +(2.73008 + 1.82418i) q^{46} +0.236401i q^{47} +(0.800867 - 1.19858i) q^{48} +(4.13581 + 1.71311i) q^{49} +(1.54592 + 5.73898i) q^{51} +(-2.90567 + 2.90567i) q^{52} +(-0.352066 - 0.849962i) q^{53} +(-1.10298 - 5.54504i) q^{54} +(1.88211 - 2.81678i) q^{56} +(7.68469 - 5.13475i) q^{57} +(-1.73348 + 8.71477i) q^{58} +(-3.06957 + 1.27146i) q^{59} +(0.930398 - 0.621672i) q^{61} +(5.83924 + 8.73903i) q^{62} +(-0.609368 - 3.06350i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(2.20148 - 5.31485i) q^{66} +(-6.65464 - 6.65464i) q^{67} +(4.11392 - 0.275124i) q^{68} +4.73315i q^{69} +(6.11118 - 1.21559i) q^{71} -0.922015 q^{72} +(-2.06953 + 0.411656i) q^{73} +(-1.23591 + 6.21333i) q^{74} +(-2.45357 - 5.92345i) q^{76} +(5.17368 - 12.4904i) q^{77} +(-5.80973 - 1.15563i) q^{78} +(-0.0457198 - 0.00909423i) q^{79} +(3.80695 - 3.80695i) q^{81} +(0.953562 + 0.637150i) q^{82} +(0.909194 - 0.376601i) q^{83} +4.88345 q^{84} -4.62074 q^{86} +(-11.8337 + 4.90166i) q^{87} +(-3.31818 - 2.21714i) q^{88} +(6.70937 - 6.70937i) q^{89} +(-13.6534 - 2.71583i) q^{91} +(3.22035 + 0.640567i) q^{92} +(-5.79800 + 13.9976i) q^{93} +(0.0904666 + 0.218406i) q^{94} +(0.281227 - 1.41382i) q^{96} +(-6.84757 + 1.36207i) q^{97} +4.47657 q^{98} +(-3.60883 + 0.717841i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 16 q^{18} + 8 q^{26} - 24 q^{27} + 8 q^{28} - 8 q^{29} - 16 q^{31} - 64 q^{33} + 24 q^{34} + 32 q^{37} - 32 q^{39} + 16 q^{41} + 24 q^{42} + 16 q^{43} - 16 q^{44} - 16 q^{49} + 32 q^{51} + 16 q^{52} - 16 q^{53} + 24 q^{54} + 8 q^{56} + 24 q^{57} + 16 q^{58} - 64 q^{59} - 24 q^{61} + 40 q^{62} + 24 q^{63} - 16 q^{67} + 8 q^{71} + 16 q^{72} - 32 q^{73} + 8 q^{74} - 24 q^{77} - 32 q^{78} + 72 q^{79} + 48 q^{81} - 48 q^{82} - 16 q^{83} - 64 q^{86} - 40 q^{87} - 32 q^{88} + 16 q^{89} + 48 q^{91} - 24 q^{92} + 8 q^{93} + 8 q^{94} + 48 q^{97} - 64 q^{99}+O(q^{100}) $ 32 * q - 16 * q^18 + 8 * q^26 - 24 * q^27 + 8 * q^28 - 8 * q^29 - 16 * q^31 - 64 * q^33 + 24 * q^34 + 32 * q^37 - 32 * q^39 + 16 * q^41 + 24 * q^42 + 16 * q^43 - 16 * q^44 - 16 * q^49 + 32 * q^51 + 16 * q^52 - 16 * q^53 + 24 * q^54 + 8 * q^56 + 24 * q^57 + 16 * q^58 - 64 * q^59 - 24 * q^61 + 40 * q^62 + 24 * q^63 - 16 * q^67 + 8 * q^71 + 16 * q^72 - 32 * q^73 + 8 * q^74 - 24 * q^77 - 32 * q^78 + 72 * q^79 + 48 * q^81 - 48 * q^82 - 16 * q^83 - 64 * q^86 - 40 * q^87 - 32 * q^88 + 16 * q^89 + 48 * q^91 - 24 * q^92 + 8 * q^93 + 8 * q^94 + 48 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{15}{16}\right)$

Coefficient data

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

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

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

$2$	0.923880	−	0.382683i	0.653281	−	0.270598i
$2$	0.923880	−	0.382683i	0.653281	−	0.270598i
$3$	1.19858	+	0.800867i	0.692001	+	0.462381i	0.851183	−	0.524869i	$-0.175886\pi$
$3$	1.19858	+	0.800867i	0.692001	+	0.462381i	−0.159182	+	0.987249i	$0.550886\pi$
$4$	0.707107	−	0.707107i	0.353553	−	0.353553i
$5$		0			0
$5$		0			0
$6$	1.41382	+	0.281227i	0.577191	+	0.114810i
$7$	3.32261	+	0.660909i	1.25583	+	0.249800i	0.777782	−	0.628534i	$-0.216345\pi$
$7$	3.32261	+	0.660909i	1.25583	+	0.249800i	0.478048	+	0.878334i	$0.341345\pi$
$8$	0.382683	−	0.923880i	0.135299	−	0.326641i
$9$	−0.352840	−	0.851831i	−0.117613	−	0.283944i
$10$		0			0
$11$	0.778556	−	3.91407i	0.234743	−	1.18014i	−0.666057	−	0.745901i	$-0.732019\pi$
$11$	0.778556	−	3.91407i	0.234743	−	1.18014i	0.900800	−	0.434234i	$-0.142981\pi$
$12$	1.41382	−	0.281227i	0.408136	−	0.0811832i
$13$	−4.10923			−1.13970			−0.569848	−	0.821750i	$-0.692998\pi$
$13$	−4.10923			−1.13970			−0.569848	+	0.821750i	$0.692998\pi$
$14$	3.32261	−	0.660909i	0.888006	−	0.176635i
$15$		0			0
$16$		−	1.00000i		−	0.250000i
$17$	3.10352	+	2.71444i	0.752714	+	0.658348i
$17$	3.10352	+	2.71444i	0.752714	+	0.658348i
$18$	−0.651963	−	0.651963i	−0.153669	−	0.153669i
$19$	2.45357	−	5.92345i	0.562888	−	1.35893i	−0.344559	−	0.938765i	$-0.611972\pi$
$19$	2.45357	−	5.92345i	0.562888	−	1.35893i	0.907447	−	0.420167i	$-0.138028\pi$
$20$		0			0
$21$	3.45312	+	3.45312i	0.753533	+	0.753533i
$22$	−0.778556	−	3.91407i	−0.165989	−	0.834482i
$23$	1.82418	+	2.73008i	0.380368	+	0.569261i	0.971418	−	0.237374i	$-0.0762866\pi$
$23$	1.82418	+	2.73008i	0.380368	+	0.569261i	−0.591050	+	0.806635i	$0.701287\pi$
$24$	1.19858	−	0.800867i	0.244659	−	0.163476i
$25$		0			0
$26$	−3.79643	+	1.57253i	−0.744542	+	0.308399i
$27$	1.10298	−	5.54504i	0.212268	−	1.06714i
$28$	2.81678	−	1.88211i	0.532321	−	0.355685i
$29$	−4.93652	+	7.38803i	−0.916689	+	1.37192i	0.0115476	+	0.999933i	$0.496324\pi$
$29$	−4.93652	+	7.38803i	−0.916689	+	1.37192i	−0.928237	+	0.371989i	$0.878676\pi$
$30$		0			0
$31$	2.05047	+	10.3084i	0.368275	+	1.85144i	0.508144	+	0.861272i	$0.330332\pi$
$31$	2.05047	+	10.3084i	0.368275	+	1.85144i	−0.139869	+	0.990170i	$0.544668\pi$
$32$	−0.382683	−	0.923880i	−0.0676495	−	0.163320i
$33$	4.06781	−	4.06781i	0.708114	−	0.708114i
$34$	3.90605	+	1.32015i	0.669882	+	0.226403i
$35$		0			0
$36$	−0.851831	−	0.352840i	−0.141972	−	0.0588067i
$37$	−3.51957	+	5.26741i	−0.578614	+	0.865957i	−0.999146	−	0.0413208i	$-0.986843\pi$
$37$	−3.51957	+	5.26741i	−0.578614	+	0.865957i	0.420532	+	0.907278i	$0.361843\pi$
$38$		−	6.41149i		−	1.04008i
$39$	−4.92525	−	3.29095i	−0.788671	−	0.526973i
$40$		0			0
$41$	0.637150	+	0.953562i	0.0995060	+	0.148921i	0.877882	−	0.478877i	$-0.158956\pi$
$41$	0.637150	+	0.953562i	0.0995060	+	0.148921i	−0.778376	+	0.627799i	$0.783956\pi$
$42$	4.51172	+	1.86882i	0.696174	+	0.288365i
$43$	−4.26901	−	1.76828i	−0.651017	−	0.269660i	0.0326358	−	0.999467i	$-0.489610\pi$
$43$	−4.26901	−	1.76828i	−0.651017	−	0.269660i	−0.683653	+	0.729807i	$0.739610\pi$
$44$	−2.21714	−	3.31818i	−0.334246	−	0.500235i
$45$		0			0
$46$	2.73008	+	1.82418i	0.402528	+	0.268961i
$47$			0.236401i			0.0344826i	0.999851	+	0.0172413i	$0.00548834\pi$
$47$			0.236401i			0.0344826i	−0.999851	+	0.0172413i	$0.994512\pi$
$48$	0.800867	−	1.19858i	0.115595	−	0.173000i
$49$	4.13581	+	1.71311i	0.590830	+	0.244730i
$50$		0			0
$51$	1.54592	+	5.73898i	0.216472	+	0.803618i
$52$	−2.90567	+	2.90567i	−0.402943	+	0.402943i
$53$	−0.352066	−	0.849962i	−0.0483600	−	0.116751i	0.897853	−	0.440294i	$-0.145126\pi$
$53$	−0.352066	−	0.849962i	−0.0483600	−	0.116751i	−0.946213	+	0.323543i	$0.895126\pi$
$54$	−1.10298	−	5.54504i	−0.150096	−	0.754584i
$55$		0			0
$56$	1.88211	−	2.81678i	0.251507	−	0.376408i
$57$	7.68469	−	5.13475i	1.01786	−	0.680114i
$58$	−1.73348	+	8.71477i	−0.227617	+	1.14431i
$59$	−3.06957	+	1.27146i	−0.399625	+	0.165530i	−0.573439	−	0.819249i	$-0.694391\pi$
$59$	−3.06957	+	1.27146i	−0.399625	+	0.165530i	0.173814	+	0.984779i	$0.444391\pi$
$60$		0			0
$61$	0.930398	−	0.621672i	0.119125	−	0.0795970i	−0.494580	−	0.869132i	$-0.664678\pi$
$61$	0.930398	−	0.621672i	0.119125	−	0.0795970i	0.613706	+	0.789535i	$0.289678\pi$
$62$	5.83924	+	8.73903i	0.741584	+	1.10986i
$63$	−0.609368	−	3.06350i	−0.0767732	−	0.385965i
$64$	−0.707107	−	0.707107i	−0.0883883	−	0.0883883i
$65$		0			0
$66$	2.20148	−	5.31485i	0.270984	−	0.654212i
$67$	−6.65464	−	6.65464i	−0.812994	−	0.812994i	0.172088	−	0.985082i	$-0.444949\pi$
$67$	−6.65464	−	6.65464i	−0.812994	−	0.812994i	−0.985082	+	0.172088i	$0.944949\pi$
$68$	4.11392	−	0.275124i	0.498886	−	0.0333636i
$69$			4.73315i			0.569804i
$70$		0			0
$71$	6.11118	−	1.21559i	0.725264	−	0.144264i	0.181366	−	0.983416i	$-0.441948\pi$
$71$	6.11118	−	1.21559i	0.725264	−	0.144264i	0.543897	+	0.839152i	$0.316948\pi$
$72$	−0.922015			−0.108661
$73$	−2.06953	+	0.411656i	−0.242220	+	0.0481806i	−0.314707	−	0.949189i	$-0.601906\pi$
$73$	−2.06953	+	0.411656i	−0.242220	+	0.0481806i	0.0724870	+	0.997369i	$0.476906\pi$
$74$	−1.23591	+	6.21333i	−0.143671	+	0.722285i
$75$		0			0
$76$	−2.45357	−	5.92345i	−0.281444	−	0.679466i
$77$	5.17368	−	12.4904i	0.589596	−	1.42341i
$78$	−5.80973	−	1.15563i	−0.657822	−	0.130849i
$79$	−0.0457198	−	0.00909423i	−0.00514388	−	0.00102318i	0.192518	−	0.981293i	$-0.438335\pi$
$79$	−0.0457198	−	0.00909423i	−0.00514388	−	0.00102318i	−0.197662	+	0.980270i	$0.563335\pi$
$80$		0			0
$81$	3.80695	−	3.80695i	0.422995	−	0.422995i
$82$	0.953562	+	0.637150i	0.105303	+	0.0703614i
$83$	0.909194	−	0.376601i	0.0997970	−	0.0413373i	−0.332226	−	0.943200i	$-0.607800\pi$
$83$	0.909194	−	0.376601i	0.0997970	−	0.0413373i	0.432023	+	0.901862i	$0.357800\pi$
$84$	4.88345			0.532829
$85$		0			0
$86$	−4.62074			−0.498267
$87$	−11.8337	+	4.90166i	−1.26870	+	0.525513i
$88$	−3.31818	−	2.21714i	−0.353720	−	0.236348i
$89$	6.70937	−	6.70937i	0.711191	−	0.711191i	−0.255593	−	0.966784i	$-0.582271\pi$
$89$	6.70937	−	6.70937i	0.711191	−	0.711191i	0.966784	+	0.255593i	$0.0822708\pi$
$90$		0			0
$91$	−13.6534	−	2.71583i	−1.43126	−	0.284696i
$92$	3.22035	+	0.640567i	0.335745	+	0.0667838i
$93$	−5.79800	+	13.9976i	−0.601224	+	1.45148i
$94$	0.0904666	+	0.218406i	0.00933091	+	0.0225268i
$95$		0			0
$96$	0.281227	−	1.41382i	0.0287026	−	0.144298i
$97$	−6.84757	+	1.36207i	−0.695265	+	0.138297i	−0.530057	−	0.847962i	$-0.677830\pi$
$97$	−6.84757	+	1.36207i	−0.695265	+	0.138297i	−0.165208	+	0.986259i	$0.552830\pi$
$98$	4.47657			0.452201
$99$	−3.60883	+	0.717841i	−0.362701	+	0.0721457i
$100$		0			0
$101$			0.274817i			0.0273453i	0.999907	+	0.0136727i	$0.00435228\pi$
$101$			0.274817i			0.0273453i	−0.999907	+	0.0136727i	$0.995648\pi$
$102$	3.62446	+	4.71053i	0.358875	+	0.466412i
$103$	−2.76147	−	2.76147i	−0.272096	−	0.272096i	0.557848	−	0.829943i	$-0.311627\pi$
$103$	−2.76147	−	2.76147i	−0.272096	−	0.272096i	−0.829943	+	0.557848i	$0.811627\pi$
$104$	−1.57253	+	3.79643i	−0.154200	+	0.372271i
$105$		0			0
$106$	−0.650533	−	0.650533i	−0.0631854	−	0.0631854i
$107$	2.36785	+	11.9040i	0.228909	+	1.15080i	0.908717	+	0.417414i	$0.137063\pi$
$107$	2.36785	+	11.9040i	0.228909	+	1.15080i	−0.679807	+	0.733391i	$0.737937\pi$
$108$	−3.14101	−	4.70085i	−0.302244	−	0.452340i
$109$	−15.8475	+	10.5890i	−1.51792	+	1.01424i	−0.532048	+	0.846714i	$0.678577\pi$
$109$	−15.8475	+	10.5890i	−1.51792	+	1.01424i	−0.985868	+	0.167525i	$0.946423\pi$
$110$		0			0
$111$	−8.43698	+	3.49471i	−0.800803	+	0.331704i
$112$	0.660909	−	3.32261i	0.0624500	−	0.313958i
$113$	5.19185	−	3.46908i	0.488408	−	0.326344i	−0.286864	−	0.957971i	$-0.592613\pi$
$113$	5.19185	−	3.46908i	0.488408	−	0.326344i	0.775272	+	0.631628i	$0.217613\pi$
$114$	5.13475	−	7.68469i	0.480913	−	0.719738i
$115$		0			0
$116$	1.73348	+	8.71477i	0.160949	+	0.809147i
$117$	1.44990	+	3.50037i	0.134043	+	0.323609i
$118$	−2.34935	+	2.34935i	−0.216275	+	0.216275i
$119$	8.51780	+	11.0702i	0.780826	+	1.01480i
$120$		0			0
$121$	−4.55109	−	1.88512i	−0.413735	−	0.171375i
$122$	0.621672	−	0.930398i	0.0562836	−	0.0842343i
$123$			1.65319i			0.149063i
$124$	8.73903	+	5.83924i	0.784788	+	0.524379i
$125$		0			0
$126$	−1.73533	−	2.59711i	−0.154596	−	0.231369i
$127$	−5.21517	−	2.16020i	−0.462772	−	0.191686i	0.139101	−	0.990278i	$-0.455579\pi$
$127$	−5.21517	−	2.16020i	−0.462772	−	0.191686i	−0.601873	+	0.798592i	$0.705579\pi$
$128$	−0.923880	−	0.382683i	−0.0816602	−	0.0338248i
$129$	−3.70059	−	5.53833i	−0.325819	−	0.487623i
$130$		0			0
$131$	−9.76948	−	6.52776i	−0.853563	−	0.570333i	0.0500185	−	0.998748i	$-0.484072\pi$
$131$	−9.76948	−	6.52776i	−0.853563	−	0.570333i	−0.903582	+	0.428415i	$0.859072\pi$
$132$		−	5.75275i		−	0.500712i
$133$	12.0671	−	18.0597i	1.04635	−	1.56598i
$134$	−8.69471	−	3.60147i	−0.751108	−	0.311119i
$135$		0			0
$136$	3.69548	−	1.82851i	0.316885	−	0.156793i
$137$	−6.69914	+	6.69914i	−0.572346	+	0.572346i	−0.932783	−	0.360438i	$-0.882627\pi$
$137$	−6.69914	+	6.69914i	−0.572346	+	0.572346i	0.360438	+	0.932783i	$0.382627\pi$
$138$	1.81130	+	4.37286i	0.154188	+	0.372243i
$139$	0.949096	+	4.77143i	0.0805013	+	0.404707i	0.999934	+	0.0114607i	$0.00364813\pi$
$139$	0.949096	+	4.77143i	0.0805013	+	0.404707i	−0.919433	+	0.393247i	$0.871352\pi$
$140$		0			0
$141$	−0.189325	+	0.283345i	−0.0159441	+	0.0238620i
$142$	5.18081	−	3.46171i	0.434764	−	0.290500i
$143$	−3.19927	+	16.0838i	−0.267536	+	1.34500i
$144$	−0.851831	+	0.352840i	−0.0709859	+	0.0294033i
$145$		0			0
$146$	−1.75446	+	1.17230i	−0.145201	+	0.0970199i
$147$	3.58513	+	5.36553i	0.295697	+	0.442541i
$148$	1.23591	+	6.21333i	0.101591	+	0.510733i
$149$	0.853790	+	0.853790i	0.0699452	+	0.0699452i	0.741214	−	0.671269i	$-0.234250\pi$
$149$	0.853790	+	0.853790i	0.0699452	+	0.0699452i	−0.671269	+	0.741214i	$0.734250\pi$
$150$		0			0
$151$	2.75046	−	6.64020i	0.223829	−	0.540372i	−0.771574	−	0.636139i	$-0.780530\pi$
$151$	2.75046	−	6.64020i	0.223829	−	0.540372i	0.995404	+	0.0957674i	$0.0305305\pi$
$152$	−4.53361	−	4.53361i	−0.367724	−	0.367724i
$153$	1.21720	−	3.60144i	0.0984044	−	0.291159i
$154$		−	13.5195i		−	1.08943i
$155$		0			0
$156$	−5.80973	+	1.15563i	−0.465150	+	0.0925242i
$157$	−22.3932			−1.78717			−0.893587	−	0.448889i	$-0.851820\pi$
$157$	−22.3932			−1.78717			−0.893587	+	0.448889i	$0.851820\pi$
$158$	−0.0457198	+	0.00909423i	−0.00363727	+	0.000723498i
$159$	0.258727	−	1.30071i	0.0205184	−	0.103153i
$160$		0			0
$161$	4.25672	+	10.2766i	0.335476	+	0.809911i
$162$	2.06031	−	4.97402i	0.161873	−	0.390796i
$163$	2.72119	+	0.541279i	0.213140	+	0.0423962i	0.300505	−	0.953780i	$-0.402845\pi$
$163$	2.72119	+	0.541279i	0.213140	+	0.0423962i	−0.0873651	+	0.996176i	$0.527845\pi$
$164$	1.12480	+	0.223737i	0.0878323	+	0.0174709i
$165$		0			0
$166$	0.695867	−	0.695867i	0.0540098	−	0.0540098i
$167$	−3.35489	−	2.24166i	−0.259609	−	0.173465i	0.418954	−	0.908008i	$-0.362397\pi$
$167$	−3.35489	−	2.24166i	−0.259609	−	0.173465i	−0.678563	+	0.734542i	$0.737397\pi$
$168$	4.51172	−	1.86882i	0.348087	−	0.144182i
$169$	3.88578			0.298906
$170$		0			0
$171$	−5.91149			−0.452063
$172$	−4.26901	+	1.76828i	−0.325509	+	0.134830i
$173$	9.10954	+	6.08680i	0.692585	+	0.462771i	0.851386	−	0.524540i	$-0.175763\pi$
$173$	9.10954	+	6.08680i	0.692585	+	0.462771i	−0.158801	+	0.987311i	$0.550763\pi$
$174$	−9.05708	+	9.05708i	−0.686616	+	0.686616i
$175$		0			0
$176$	−3.91407	−	0.778556i	−0.295034	−	0.0586859i
$177$	−4.69740	−	0.934372i	−0.353079	−	0.0702317i
$178$	3.63108	−	8.76621i	0.272161	−	0.657055i
$179$	1.74304	+	4.20808i	0.130281	+	0.314527i	0.975537	−	0.219835i	$-0.0705519\pi$
$179$	1.74304	+	4.20808i	0.130281	+	0.314527i	−0.845256	+	0.534362i	$0.820552\pi$
$180$		0			0
$181$	4.89042	−	24.5858i	0.363502	−	1.82745i	−0.174688	−	0.984624i	$-0.555892\pi$
$181$	4.89042	−	24.5858i	0.363502	−	1.82745i	0.538190	−	0.842823i	$-0.319108\pi$
$182$	−13.6534	+	2.71583i	−1.01206	+	0.201311i
$183$	1.61303			0.119239
$184$	3.22035	−	0.640567i	0.237407	−	0.0472232i
$185$		0			0
$186$			15.1509i			1.11092i
$187$	13.0407	−	10.0340i	0.953634	−	0.733762i
$188$	0.167160	+	0.167160i	0.0121914	+	0.0121914i
$189$	7.32953	−	17.6950i	0.533145	−	1.28713i
$190$		0			0
$191$	14.3864	+	14.3864i	1.04096	+	1.04096i	0.999124	+	0.0418392i	$0.0133217\pi$
$191$	14.3864	+	14.3864i	1.04096	+	1.04096i	0.0418392	+	0.999124i	$0.486678\pi$
$192$	−0.281227	−	1.41382i	−0.0202958	−	0.102034i
$193$	−0.455950	−	0.682377i	−0.0328200	−	0.0491186i	0.814697	−	0.579887i	$-0.196903\pi$
$193$	−0.455950	−	0.682377i	−0.0328200	−	0.0491186i	−0.847517	+	0.530769i	$0.821903\pi$
$194$	−5.80509	+	3.87883i	−0.416781	+	0.278484i
$195$		0			0
$196$	4.13581	−	1.71311i	0.295415	−	0.122365i
$197$	4.87199	−	24.4932i	0.347115	−	1.74507i	−0.274355	−	0.961628i	$-0.588464\pi$
$197$	4.87199	−	24.4932i	0.347115	−	1.74507i	0.621470	−	0.783438i	$-0.286536\pi$
$198$	−3.05942	+	2.04424i	−0.217423	+	0.145278i
$199$	9.38195	−	14.0411i	0.665069	−	0.995346i	−0.333546	−	0.942734i	$-0.608245\pi$
$199$	9.38195	−	14.0411i	0.665069	−	0.995346i	0.998615	−	0.0526122i	$-0.0167547\pi$
$200$		0			0
$201$	−2.64665	−	13.3056i	−0.186680	−	0.938505i
$202$	0.105168	+	0.253898i	0.00739959	+	0.0178642i
$203$	−21.2850	+	21.2850i	−1.49391	+	1.49391i
$204$	5.15120	+	2.96494i	0.360656	+	0.207587i
$205$		0			0
$206$	−3.60803	−	1.49450i	−0.251384	−	0.104126i
$207$	1.68192	−	2.51718i	0.116902	−	0.174956i
$208$			4.10923i			0.284924i
$209$	−21.2745	−	14.2152i	−1.47159	−	0.983284i
$210$		0			0
$211$	11.6479	+	17.4323i	0.801875	+	1.20009i	0.976513	+	0.215457i	$0.0691243\pi$
$211$	11.6479	+	17.4323i	0.801875	+	1.20009i	−0.174639	+	0.984633i	$0.555876\pi$
$212$	−0.849962	−	0.352066i	−0.0583757	−	0.0241800i
$213$	8.29827	+	3.43726i	0.568588	+	0.235517i
$214$	6.74308	+	10.0917i	0.460947	+	0.689857i
$215$		0			0
$216$	−4.70085	−	3.14101i	−0.319853	−	0.213719i
$217$			35.6060i			2.41709i
$218$	−10.5890	+	15.8475i	−0.717175	+	1.07333i
$219$	−2.81018	−	1.16402i	−0.189895	−	0.0786569i
$220$		0			0
$221$	−12.7531	−	11.1542i	−0.857865	−	0.750316i
$222$	−6.45739	+	6.45739i	−0.433392	+	0.433392i
$223$	−1.10412	−	2.66557i	−0.0739371	−	0.178500i	0.882590	−	0.470144i	$-0.155798\pi$
$223$	−1.10412	−	2.66557i	−0.0739371	−	0.178500i	−0.956527	+	0.291644i	$0.905798\pi$
$224$	−0.660909	−	3.32261i	−0.0441588	−	0.222001i
$225$		0			0
$226$	3.46908	−	5.19185i	0.230760	−	0.345356i
$227$	4.08992	−	2.73280i	0.271458	−	0.181382i	−0.412389	−	0.911008i	$-0.635306\pi$
$227$	4.08992	−	2.73280i	0.271458	−	0.181382i	0.683847	+	0.729625i	$0.260306\pi$
$228$	1.80308	−	9.06472i	0.119412	−	0.600325i
$229$	−12.9587	+	5.36767i	−0.856336	+	0.354706i	−0.767273	−	0.641320i	$-0.778387\pi$
$229$	−12.9587	+	5.36767i	−0.856336	+	0.354706i	−0.0890622	+	0.996026i	$0.528387\pi$
$230$		0			0
$231$	16.2042	−	10.8273i	1.06616	−	0.712384i
$232$	4.93652	+	7.38803i	0.324099	+	0.485048i
$233$	−0.900329	−	4.52626i	−0.0589825	−	0.296525i	0.940023	−	0.341111i	$-0.110803\pi$
$233$	−0.900329	−	4.52626i	−0.0589825	−	0.296525i	−0.999006	+	0.0445858i	$0.985803\pi$
$234$	2.67907	+	2.67907i	0.175136	+	0.175136i
$235$		0			0
$236$	−1.27146	+	3.06957i	−0.0827650	+	0.199812i
$237$	−0.0475156	−	0.0475156i	−0.00308647	−	0.00308647i
$238$	12.1058	+	6.96788i	0.784702	+	0.451661i
$239$			15.9839i			1.03391i	0.856011	+	0.516957i	$0.172935\pi$
$239$			15.9839i			1.03391i	−0.856011	+	0.516957i	$0.827065\pi$
$240$		0			0
$241$	−9.99768	+	1.98866i	−0.644007	+	0.128101i	−0.506280	−	0.862369i	$-0.668980\pi$
$241$	−9.99768	+	1.98866i	−0.644007	+	0.128101i	−0.137727	+	0.990470i	$0.543980\pi$
$242$	−4.92606			−0.316659
$243$	−9.02331	+	1.79485i	−0.578845	+	0.115140i
$244$	0.218302	−	1.09748i	0.0139754	−	0.0702589i
$245$		0			0
$246$	0.632650	+	1.52735i	0.0403363	+	0.0973804i
$247$	−10.0823	+	24.3408i	−0.641521	+	1.54877i
$248$	10.3084	+	2.05047i	0.654584	+	0.130205i
$249$	1.39135	+	0.276757i	0.0881732	+	0.0175387i
$250$		0			0
$251$	−11.9830	+	11.9830i	−0.756361	+	0.756361i	−0.975658	−	0.219297i	$-0.929623\pi$
$251$	−11.9830	+	11.9830i	−0.756361	+	0.756361i	0.219297	+	0.975658i	$0.429623\pi$
$252$	−2.59711	−	1.73533i	−0.163603	−	0.109316i
$253$	12.1059	−	5.01444i	0.761094	−	0.315255i
$254$	−5.64486			−0.354190
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	7.46649	−	3.09272i	0.465747	−	0.192919i	−0.137454	−	0.990508i	$-0.543892\pi$
$257$	7.46649	−	3.09272i	0.465747	−	0.192919i	0.603200	+	0.797590i	$0.293892\pi$
$258$	−5.53833	−	3.70059i	−0.344801	−	0.230389i
$259$	−15.1755	+	15.1755i	−0.942957	+	0.942957i
$260$		0			0
$261$	8.03516	+	1.59829i	0.497364	+	0.0989318i
$262$	−11.5239	−	2.29224i	−0.711948	−	0.141615i
$263$	−0.764104	+	1.84471i	−0.0471167	+	0.113750i	−0.945686	−	0.325083i	$-0.894608\pi$
$263$	−0.764104	+	1.84471i	−0.0471167	+	0.113750i	0.898569	+	0.438832i	$0.144608\pi$
$264$	−2.20148	−	5.31485i	−0.135492	−	0.327106i
$265$		0			0
$266$	4.23741	−	21.3029i	0.259812	−	1.30617i
$267$	13.4150	−	2.66841i	0.820986	−	0.163304i
$268$	−9.41108			−0.574873
$269$	19.6028	−	3.89924i	1.19520	−	0.237741i	0.442908	−	0.896567i	$-0.353947\pi$
$269$	19.6028	−	3.89924i	1.19520	−	0.237741i	0.752295	+	0.658826i	$0.228947\pi$
$270$		0			0
$271$		−	4.71454i		−	0.286388i	−0.989695	−	0.143194i	$-0.954263\pi$
$271$		−	4.71454i		−	0.286388i	0.989695	−	0.143194i	$-0.0457373\pi$
$272$	2.71444	−	3.10352i	0.164587	−	0.188179i
$273$	−14.1897	−	14.1897i	−0.858799	−	0.858799i
$274$	−3.62555	+	8.75284i	−0.219027	+	0.528779i
$275$		0			0
$276$	3.34684	+	3.34684i	0.201456	+	0.201456i
$277$	−1.56666	−	7.87611i	−0.0941312	−	0.473229i	−0.998881	−	0.0472868i	$-0.984943\pi$
$277$	−1.56666	−	7.87611i	−0.0941312	−	0.473229i	0.904750	−	0.425943i	$-0.140057\pi$
$278$	2.70280	+	4.04502i	0.162103	+	0.242604i
$279$	8.05752	−	5.38387i	0.482391	−	0.322324i
$280$		0			0
$281$	−2.47998	+	1.02724i	−0.147943	+	0.0612800i	−0.455426	−	0.890273i	$-0.650513\pi$
$281$	−2.47998	+	1.02724i	−0.147943	+	0.0612800i	0.307483	+	0.951553i	$0.400513\pi$
$282$	−0.0664822	+	0.334229i	−0.00395896	+	0.0199030i
$283$	−11.9901	+	8.01151i	−0.712736	+	0.476235i	−0.858323	−	0.513111i	$-0.828493\pi$
$283$	−11.9901	+	8.01151i	−0.712736	+	0.476235i	0.145586	+	0.989346i	$0.453493\pi$
$284$	3.46171	−	5.18081i	0.205414	−	0.307424i
$285$		0			0
$286$	3.19927	+	16.0838i	0.189177	+	0.951055i
$287$	1.48678	+	3.58942i	0.0877621	+	0.211876i
$288$	−0.651963	+	0.651963i	−0.0384173	+	0.0384173i
$289$	2.26367	+	16.8486i	0.133157	+	0.991095i
$290$		0			0
$291$	−9.29820	−	3.85144i	−0.545070	−	0.225775i
$292$	−1.17230	+	1.75446i	−0.0686034	+	0.102672i
$293$			25.4534i			1.48700i	0.668734	+	0.743502i	$0.266836\pi$
$293$			25.4534i			1.48700i	−0.668734	+	0.743502i	$0.733164\pi$
$294$	5.36553	+	3.58513i	0.312924	+	0.209089i
$295$		0			0
$296$	3.51957	+	5.26741i	0.204571	+	0.306162i
$297$	−20.8449	−	8.63424i	−1.20954	−	0.501010i
$298$	1.11553	+	0.462068i	0.0646209	+	0.0267669i
$299$	−7.49598	−	11.2185i	−0.433504	−	0.648784i
$300$		0			0
$301$	−13.0156	−	8.69674i	−0.750206	−	0.501272i
$302$		−	7.18730i		−	0.413583i
$303$	−0.220092	+	0.329391i	−0.0126439	+	0.0189230i
$304$	−5.92345	−	2.45357i	−0.339733	−	0.140722i
$305$		0			0
$306$	−0.253668	−	3.79309i	−0.0145012	−	0.216837i
$307$	20.6197	−	20.6197i	1.17683	−	1.17683i	0.196278	−	0.980548i	$-0.437114\pi$
$307$	20.6197	−	20.6197i	1.17683	−	1.17683i	0.980548	−	0.196278i	$-0.0628856\pi$
$308$	−5.17368	−	12.4904i	−0.294798	−	0.711705i
$309$	−1.09828	−	5.52141i	−0.0624788	−	0.314102i
$310$		0			0
$311$	4.37580	−	6.54884i	0.248129	−	0.371351i	−0.686409	−	0.727216i	$-0.740814\pi$
$311$	4.37580	−	6.54884i	0.248129	−	0.371351i	0.934537	+	0.355865i	$0.115814\pi$
$312$	−4.92525	+	3.29095i	−0.278837	+	0.186313i
$313$	−3.59937	+	18.0953i	−0.203449	+	1.02280i	0.735179	+	0.677873i	$0.237098\pi$
$313$	−3.59937	+	18.0953i	−0.203449	+	1.02280i	−0.938628	+	0.344932i	$0.887902\pi$
$314$	−20.6887	+	8.56952i	−1.16753	+	0.483606i
$315$		0			0
$316$	−0.0387593	+	0.0258982i	−0.00218038	+	0.00145689i
$317$	−7.57932	−	11.3432i	−0.425697	−	0.637100i	0.555180	−	0.831730i	$-0.312649\pi$
$317$	−7.57932	−	11.3432i	−0.425697	−	0.637100i	−0.980877	+	0.194630i	$0.937649\pi$
$318$	−0.258727	−	1.30071i	−0.0145087	−	0.0729400i
$319$	25.0739	+	25.0739i	1.40387	+	1.40387i
$320$		0			0
$321$	−6.69546	+	16.1643i	−0.373704	+	0.902201i
$322$	7.86539	+	7.86539i	0.438321	+	0.438321i
$323$	23.6935	−	11.7235i	1.31834	−	0.652311i
$324$		−	5.38384i		−	0.299102i
$325$		0			0
$326$	2.72119	−	0.541279i	0.150713	−	0.0299787i
$327$	−27.4749			−1.51936
$328$	1.12480	−	0.223737i	0.0621068	−	0.0123538i
$329$	−0.156239	+	0.785468i	−0.00861375	+	0.0433042i
$330$		0			0
$331$	4.14619	+	10.0098i	0.227895	+	0.550188i	0.995921	−	0.0902314i	$-0.0287607\pi$
$331$	4.14619	+	10.0098i	0.227895	+	0.550188i	−0.768026	+	0.640419i	$0.778761\pi$
$332$	0.376601	−	0.909194i	0.0206686	−	0.0498985i
$333$	5.72879	+	1.13953i	0.313936	+	0.0624457i
$334$	−3.95736	−	0.787168i	−0.216537	−	0.0430719i
$335$		0			0
$336$	3.45312	−	3.45312i	0.188383	−	0.188383i
$337$	20.7479	+	13.8633i	1.13021	+	0.755182i	0.972638	−	0.232325i	$-0.0746334\pi$
$337$	20.7479	+	13.8633i	1.13021	+	0.755182i	0.157572	+	0.987507i	$0.449633\pi$
$338$	3.58999	−	1.48702i	0.195270	−	0.0808834i
$339$	9.00112			0.488874
$340$		0			0
$341$	41.9441			2.27140
$342$	−5.46151	+	2.26223i	−0.295324	+	0.122327i
$343$	−7.10795	−	4.74938i	−0.383793	−	0.256442i
$344$	−3.26736	+	3.26736i	−0.176164	+	0.176164i
$345$		0			0
$346$	10.7454	+	2.13740i	0.577678	+	0.114907i
$347$	14.5581	+	2.89578i	0.781519	+	0.155454i	0.569697	−	0.821855i	$-0.307060\pi$
$347$	14.5581	+	2.89578i	0.781519	+	0.155454i	0.211821	+	0.977308i	$0.432060\pi$
$348$	−4.90166	+	11.8337i	−0.262756	+	0.634350i
$349$	−9.23718	−	22.3005i	−0.494455	−	1.19372i	−0.952431	−	0.304756i	$-0.901425\pi$
$349$	−9.23718	−	22.3005i	−0.494455	−	1.19372i	0.457975	−	0.888965i	$-0.348575\pi$
$350$		0			0
$351$	−4.53238	+	22.7858i	−0.241921	+	1.21622i
$352$	−3.91407	+	0.778556i	−0.208620	+	0.0414972i
$353$	28.6326			1.52396			0.761979	−	0.647601i	$-0.224228\pi$
$353$	28.6326			1.52396			0.761979	+	0.647601i	$0.224228\pi$
$354$	−4.69740	+	0.934372i	−0.249664	+	0.0496613i
$355$		0			0
$356$		−	9.48848i		−	0.502888i
$357$	1.34355	+	20.0901i	0.0711084	+	1.06328i
$358$	3.22073	+	3.22073i	0.170221	+	0.170221i
$359$	0.934800	−	2.25681i	0.0493369	−	0.119110i	−0.897290	−	0.441442i	$-0.854467\pi$
$359$	0.934800	−	2.25681i	0.0493369	−	0.119110i	0.946626	+	0.322333i	$0.104467\pi$
$360$		0			0
$361$	−15.6322	−	15.6322i	−0.822746	−	0.822746i
$362$	−4.89042	−	24.5858i	−0.257035	−	1.29220i
$363$	−3.94512	−	5.90428i	−0.207065	−	0.309895i
$364$	−11.5748	+	7.73402i	−0.606684	+	0.405373i
$365$		0			0
$366$	1.49025	−	0.617282i	0.0778966	−	0.0322658i
$367$	0.610498	−	3.06918i	0.0318677	−	0.160210i	−0.961575	−	0.274543i	$-0.911473\pi$
$367$	0.610498	−	3.06918i	0.0318677	−	0.160210i	0.993442	+	0.114334i	$0.0364733\pi$
$368$	2.73008	−	1.82418i	0.142315	−	0.0950920i
$369$	0.587462	−	0.879198i	0.0305820	−	0.0457692i
$370$		0			0
$371$	−0.608031	−	3.05678i	−0.0315674	−	0.158700i
$372$	5.79800	+	13.9976i	0.300612	+	0.725742i
$373$	26.0461	−	26.0461i	1.34861	−	1.34861i	0.461447	−	0.887168i	$-0.347331\pi$
$373$	26.0461	−	26.0461i	1.34861	−	1.34861i	0.887168	−	0.461447i	$-0.152669\pi$
$374$	8.20822	−	14.2607i	0.424437	−	0.737404i
$375$		0			0
$376$	0.218406	+	0.0904666i	0.0112634	+	0.00466546i
$377$	20.2853	−	30.3591i	1.04475	−	1.56357i
$378$		−	19.1530i		−	0.985123i
$379$	−12.5653	−	8.39587i	−0.645437	−	0.431267i	0.189298	−	0.981920i	$-0.439379\pi$
$379$	−12.5653	−	8.39587i	−0.645437	−	0.431267i	−0.834734	+	0.550653i	$0.814379\pi$
$380$		0			0
$381$	−4.52078	−	6.76583i	−0.231607	−	0.346624i
$382$	18.7967	+	7.78586i	0.961725	+	0.398360i
$383$	−12.3842	−	5.12969i	−0.632802	−	0.262115i	0.0431413	−	0.999069i	$-0.486263\pi$
$383$	−12.3842	−	5.12969i	−0.632802	−	0.262115i	−0.675943	+	0.736954i	$0.736263\pi$
$384$	−0.800867	−	1.19858i	−0.0408690	−	0.0611649i
$385$		0			0
$386$	−0.682377	−	0.455950i	−0.0347321	−	0.0232072i
$387$			4.26039i			0.216568i
$388$	−3.87883	+	5.80509i	−0.196918	+	0.294709i
$389$	26.7298	+	11.0719i	1.35526	+	0.561366i	0.937751	−	0.347308i	$-0.112904\pi$
$389$	26.7298	+	11.0719i	1.35526	+	0.561366i	0.417506	+	0.908674i	$0.362904\pi$
$390$		0			0
$391$	−1.74925	+	13.4245i	−0.0884632	+	0.678905i
$392$	3.16541	−	3.16541i	0.159877	−	0.159877i
$393$	−6.48165	−	15.6481i	−0.326956	−	0.789342i
$394$	−4.87199	−	24.4932i	−0.245448	−	1.23395i
$395$		0			0
$396$	−2.04424	+	3.05942i	−0.102727	+	0.153741i
$397$	6.44614	−	4.30718i	0.323523	−	0.216171i	−0.383194	−	0.923668i	$-0.625176\pi$
$397$	6.44614	−	4.30718i	0.323523	−	0.216171i	0.706716	+	0.707497i	$0.250176\pi$
$398$	3.29450	−	16.5626i	0.165139	−	0.830207i
$399$	28.9269	−	11.9819i	1.44816	−	0.599845i
$400$		0			0
$401$	−18.0601	+	12.0674i	−0.901881	+	0.602618i	−0.917707	−	0.397257i	$-0.869962\pi$
$401$	−18.0601	+	12.0674i	−0.901881	+	0.602618i	0.0158265	+	0.999875i	$0.494962\pi$
$402$	−7.53702	−	11.2799i	−0.375912	−	0.562593i
$403$	−8.42584	−	42.3596i	−0.419721	−	2.11008i
$404$	0.194325	+	0.194325i	0.00966803	+	0.00966803i
$405$		0			0
$406$	−11.5193	+	27.8102i	−0.571696	+	1.38020i
$407$	17.8768	+	17.8768i	0.886120	+	0.886120i
$408$	5.89372	+	0.767968i	0.291783	+	0.0380201i
$409$		−	23.8104i		−	1.17735i	−0.808371	−	0.588673i	$-0.799650\pi$
$409$		−	23.8104i		−	1.17735i	0.808371	−	0.588673i	$-0.200350\pi$
$410$		0			0
$411$	−13.3946	+	2.66435i	−0.660706	+	0.131423i
$412$	−3.90531			−0.192401
$413$	−11.0393	+	2.19586i	−0.543210	+	0.108051i
$414$	0.590613	−	2.96921i	0.0290270	−	0.145929i
$415$		0			0
$416$	1.57253	+	3.79643i	0.0770999	+	0.186136i
$417$	−2.68371	+	6.47905i	−0.131422	+	0.317280i
$418$	−25.0950	−	4.99171i	−1.22744	−	0.244152i
$419$	26.4209	+	5.25544i	1.29074	+	0.256745i	0.792276	−	0.610163i	$-0.208896\pi$
$419$	26.4209	+	5.25544i	1.29074	+	0.256745i	0.498468	+	0.866908i	$0.333896\pi$
$420$		0			0
$421$	5.64041	−	5.64041i	0.274897	−	0.274897i	−0.556171	−	0.831068i	$-0.687730\pi$
$421$	5.64041	−	5.64041i	0.274897	−	0.274897i	0.831068	+	0.556171i	$0.187730\pi$
$422$	17.4323	+	11.6479i	0.848592	+	0.567011i
$423$	0.201373	−	0.0834116i	0.00979111	−	0.00405561i
$424$	−0.919993			−0.0446788
$425$		0			0
$426$	8.98199			0.435179
$427$	3.50222	−	1.45067i	0.169484	−	0.0702028i
$428$	10.0917	+	6.74308i	0.487802	+	0.325939i
$429$	−16.7156	+	16.7156i	−0.807035	+	0.807035i
$430$		0			0
$431$	15.3057	+	3.04448i	0.737247	+	0.146648i	0.549410	−	0.835553i	$-0.314852\pi$
$431$	15.3057	+	3.04448i	0.737247	+	0.146648i	0.187837	+	0.982200i	$0.439852\pi$
$432$	−5.54504	−	1.10298i	−0.266786	−	0.0530670i
$433$	8.12458	−	19.6145i	0.390443	−	0.942612i	−0.599401	−	0.800449i	$-0.704594\pi$
$433$	8.12458	−	19.6145i	0.390443	−	0.942612i	0.989843	−	0.142163i	$-0.0454056\pi$
$434$	13.6258	+	32.8956i	0.654060	+	1.57904i
$435$		0			0
$436$	−3.71835	+	18.6934i	−0.178077	+	0.895252i
$437$	20.6472	−	4.10699i	0.987691	−	0.196464i
$438$	−3.04172			−0.145339
$439$	−6.00338	+	1.19415i	−0.286526	+	0.0569935i	−0.336261	−	0.941769i	$-0.609162\pi$
$439$	−6.00338	+	1.19415i	−0.286526	+	0.0569935i	0.0497351	+	0.998762i	$0.484162\pi$
$440$		0			0
$441$		−	4.12746i		−	0.196546i
$442$	−16.0509	−	5.42479i	−0.763461	−	0.258031i
$443$	−9.63227	−	9.63227i	−0.457643	−	0.457643i	0.440238	−	0.897881i	$-0.354894\pi$
$443$	−9.63227	−	9.63227i	−0.457643	−	0.457643i	−0.897881	+	0.440238i	$0.854894\pi$
$444$	−3.49471	+	8.43698i	−0.165852	+	0.400402i
$445$		0			0
$446$	−2.04014	−	2.04014i	−0.0966035	−	0.0966035i
$447$	0.339565	+	1.70711i	0.0160609	+	0.0807434i
$448$	−1.88211	−	2.81678i	−0.0889213	−	0.133080i
$449$	−14.9345	+	9.97891i	−0.704803	+	0.470934i	−0.855605	−	0.517630i	$-0.826814\pi$
$449$	−14.9345	+	9.97891i	−0.704803	+	0.470934i	0.150802	+	0.988564i	$0.451814\pi$
$450$		0			0
$451$	4.22836	−	1.75144i	0.199106	−	0.0824723i
$452$	1.21818	−	6.12420i	0.0572983	−	0.288058i
$453$	8.61456	−	5.75607i	0.404747	−	0.270444i
$454$	2.73280	−	4.08992i	0.128257	−	0.191950i
$455$		0			0
$456$	−1.80308	−	9.06472i	−0.0844371	−	0.424494i
$457$	−5.40111	−	13.0394i	−0.252653	−	0.609959i	0.745763	−	0.666211i	$-0.232085\pi$
$457$	−5.40111	−	13.0394i	−0.252653	−	0.609959i	−0.998417	+	0.0562522i	$0.982085\pi$
$458$	−9.91817	+	9.91817i	−0.463445	+	0.463445i
$459$	18.4748	−	14.2152i	0.862328	−	0.663507i
$460$		0			0
$461$	−0.0278421	−	0.0115326i	−0.00129673	−	0.000537125i	0.382035	−	0.924148i	$-0.375223\pi$
$461$	−0.0278421	−	0.0115326i	−0.00129673	−	0.000537125i	−0.383332	+	0.923611i	$0.625223\pi$
$462$	10.8273	−	16.2042i	0.503732	−	0.753888i
$463$			1.59180i			0.0739771i	0.999316	+	0.0369885i	$0.0117765\pi$
$463$			1.59180i			0.0739771i	−0.999316	+	0.0369885i	$0.988223\pi$
$464$	7.38803	+	4.93652i	0.342981	+	0.229172i
$465$		0			0
$466$	−2.56392	−	3.83718i	−0.118771	−	0.177754i
$467$	7.40647	+	3.06786i	0.342730	+	0.141964i	0.547408	−	0.836866i	$-0.315615\pi$
$467$	7.40647	+	3.06786i	0.342730	+	0.141964i	−0.204678	+	0.978829i	$0.565615\pi$
$468$	3.50037	+	1.44990i	0.161805	+	0.0670217i
$469$	−17.7127	−	26.5089i	−0.817896	−	1.22407i
$470$		0			0
$471$	−26.8401	−	17.9340i	−1.23673	−	0.826355i
$472$			3.32248i			0.152930i
$473$	−10.2448	+	15.3325i	−0.471058	+	0.704987i
$474$	−0.0620821	−	0.0257153i	−0.00285153	−	0.00118114i
$475$		0			0
$476$	13.8508	+	1.80480i	0.634850	+	0.0827227i
$477$	−0.599801	+	0.599801i	−0.0274630	+	0.0274630i
$478$	6.11678	+	14.7672i	0.279775	+	0.675437i
$479$	−4.90199	−	24.6439i	−0.223977	−	1.12601i	−0.915086	−	0.403259i	$-0.867877\pi$
$479$	−4.90199	−	24.6439i	−0.223977	−	1.12601i	0.691108	−	0.722751i	$-0.257123\pi$
$480$		0			0
$481$	14.4627	−	21.6450i	0.659444	−	0.986927i
$482$	−8.47562	+	5.66323i	−0.386054	+	0.257953i
$483$	−3.12818	+	15.7264i	−0.142337	+	0.715577i
$484$	−4.55109	+	1.88512i	−0.206868	+	0.0856873i
$485$		0			0
$486$	−7.64959	+	5.11129i	−0.346993	+	0.231853i
$487$	16.5862	+	24.8229i	0.751591	+	1.12483i	0.988191	+	0.153228i	$0.0489668\pi$
$487$	16.5862	+	24.8229i	0.751591	+	1.12483i	−0.236600	+	0.971607i	$0.576033\pi$
$488$	−0.218302	−	1.09748i	−0.00988208	−	0.0496806i
$489$	2.82808	+	2.82808i	0.127890	+	0.127890i
$490$		0			0
$491$	4.99913	−	12.0690i	0.225608	−	0.544665i	−0.770026	−	0.638013i	$-0.779757\pi$
$491$	4.99913	−	12.0690i	0.225608	−	0.544665i	0.995634	+	0.0933475i	$0.0297568\pi$
$492$	1.16898	+	1.16898i	0.0527019	+	0.0527019i
$493$	−35.3749	+	9.52902i	−1.59321	+	0.429165i
$494$			26.3463i			1.18538i
$495$		0			0
$496$	10.3084	−	2.05047i	0.462861	−	0.0920687i
$497$	21.1085			0.946845
$498$	1.39135	−	0.276757i	0.0623479	−	0.0124018i
$499$	0.263630	−	1.32536i	0.0118017	−	0.0593312i	−0.974436	−	0.224667i	$-0.927871\pi$
$499$	0.263630	−	1.32536i	0.0118017	−	0.0593312i	0.986237	+	0.165335i	$0.0528707\pi$
$500$		0			0
$501$	−2.22583	−	5.37364i	−0.0994429	−	0.240076i
$502$	−6.48516	+	15.6566i	−0.289447	+	0.698786i
$503$	−11.3171	−	2.25111i	−0.504604	−	0.100372i	−0.0637774	−	0.997964i	$-0.520315\pi$
$503$	−11.3171	−	2.25111i	−0.504604	−	0.100372i	−0.440827	+	0.897592i	$0.645315\pi$
$504$	−3.06350	−	0.609368i	−0.136459	−	0.0271434i
$505$		0			0
$506$	9.26549	−	9.26549i	0.411901	−	0.411901i
$507$	4.65743	+	3.11199i	0.206844	+	0.138208i
$508$	−5.21517	+	2.16020i	−0.231386	+	0.0958432i
$509$	−14.1673			−0.627955			−0.313978	−	0.949430i	$-0.601662\pi$
$509$	−14.1673			−0.627955			−0.313978	+	0.949430i	$0.601662\pi$
$510$		0			0
$511$	−7.14832			−0.316223
$512$	−0.923880	+	0.382683i	−0.0408301	+	0.0169124i
$513$	−30.1395	−	20.1386i	−1.33069	−	0.889139i
$514$	5.71460	−	5.71460i	0.252060	−	0.252060i
$515$		0			0
$516$	−6.53291	−	1.29948i	−0.287595	−	0.0572062i
$517$	0.925287	+	0.184051i	0.0406941	+	0.00809456i
$518$	−8.21290	+	19.8277i	−0.360854	+	0.871179i
$519$	6.04381	+	14.5910i	0.265294	+	0.640476i
$520$		0			0
$521$	4.56636	−	22.9566i	0.200056	−	1.00575i	−0.742028	−	0.670369i	$-0.766136\pi$
$521$	4.56636	−	22.9566i	0.200056	−	1.00575i	0.942083	−	0.335379i	$-0.108864\pi$
$522$	8.03516	−	1.59829i	0.351689	−	0.0699553i
$523$	9.20697			0.402593			0.201296	−	0.979530i	$-0.435485\pi$
$523$	9.20697			0.402593			0.201296	+	0.979530i	$0.435485\pi$
$524$	−11.5239	+	2.29224i	−0.503423	+	0.100137i
$525$		0			0
$526$			1.99670i			0.0870602i
$527$	−21.6178	+	37.5582i	−0.941687	+	1.63606i
$528$	−4.06781	−	4.06781i	−0.177029	−	0.177029i
$529$	4.67602	−	11.2889i	0.203305	−	0.490822i
$530$		0			0
$531$	2.16614	+	2.16614i	0.0940023	+	0.0940023i
$532$	−4.23741	−	21.3029i	−0.183715	−	0.923598i
$533$	−2.61819	−	3.91841i	−0.113407	−	0.169725i
$534$	11.3727	−	7.59900i	0.492145	−	0.328841i
$535$		0			0
$536$	−8.69471	+	3.60147i	−0.375554	+	0.155560i
$537$	−1.28093	+	6.43968i	−0.0552763	+	0.277893i
$538$	16.6184	−	11.1041i	0.716472	−	0.478731i
$539$	9.92517	−	14.8541i	0.427507	−	0.639810i
$540$		0			0
$541$	−2.15895	−	10.8538i	−0.0928205	−	0.466640i	−0.999039	−	0.0438305i	$-0.986044\pi$
$541$	−2.15895	−	10.8538i	−0.0928205	−	0.466640i	0.906218	−	0.422810i	$-0.138956\pi$
$542$	−1.80418	−	4.35567i	−0.0774961	−	0.187092i
$543$	25.5515	−	25.5515i	1.09652	−	1.09652i
$544$	1.32015	−	3.90605i	0.0566008	−	0.167470i
$545$		0			0
$546$	−18.5397	−	7.67940i	−0.793427	−	0.328648i
$547$	12.8978	−	19.3029i	0.551471	−	0.825334i	−0.446101	−	0.894983i	$-0.647188\pi$
$547$	12.8978	−	19.3029i	0.551471	−	0.825334i	0.997572	+	0.0696486i	$0.0221878\pi$
$548$			9.47401i			0.404710i
$549$	−0.857841	−	0.573191i	−0.0366118	−	0.0244632i
$550$		0			0
$551$	31.6505	+	47.3683i	1.34836	+	2.01796i
$552$	4.37286	+	1.81130i	0.186121	+	0.0770940i
$553$	−0.145899	−	0.0604332i	−0.00620424	−	0.00256988i
$554$	−4.46146	−	6.67704i	−0.189549	−	0.283680i
$555$		0			0
$556$	4.04502	+	2.70280i	0.171547	+	0.114624i
$557$		−	2.59243i		−	0.109845i	−0.998491	−	0.0549225i	$-0.982509\pi$
$557$		−	2.59243i		−	0.109845i	0.998491	−	0.0549225i	$-0.0174912\pi$
$558$	5.38387	−	8.05752i	0.227917	−	0.341102i
$559$	17.5423	+	7.26627i	0.741962	+	0.307331i
$560$		0			0
$561$	23.6663	−	1.58272i	0.999193	−	0.0668223i
$562$	−1.89809	+	1.89809i	−0.0800662	+	0.0800662i
$563$	15.5244	+	37.4793i	0.654277	+	1.57957i	0.806510	+	0.591221i	$0.201354\pi$
$563$	15.5244	+	37.4793i	0.654277	+	1.57957i	−0.152232	+	0.988345i	$0.548646\pi$
$564$	0.0664822	+	0.334229i	0.00279941	+	0.0140736i
$565$		0			0
$566$	−8.01151	+	11.9901i	−0.336749	+	0.503981i
$567$	15.1651	−	10.1330i	0.636873	−	0.425545i
$568$	1.21559	−	6.11118i	0.0510050	−	0.256419i
$569$	7.73559	−	3.20419i	0.324293	−	0.134326i	−0.214597	−	0.976703i	$-0.568844\pi$
$569$	7.73559	−	3.20419i	0.324293	−	0.134326i	0.538890	+	0.842376i	$0.318844\pi$
$570$		0			0
$571$	−21.0371	+	14.0565i	−0.880375	+	0.588248i	−0.911515	−	0.411267i	$-0.865086\pi$
$571$	−21.0371	+	14.0565i	−0.880375	+	0.588248i	0.0311396	+	0.999515i	$0.490086\pi$
$572$	9.11074	+	13.6352i	0.380939	+	0.570116i
$573$	5.72169	+	28.7649i	0.239027	+	1.20167i
$574$	2.74722	+	2.74722i	0.114667	+	0.114667i
$575$		0			0
$576$	−0.352840	+	0.851831i	−0.0147017	+	0.0354930i
$577$	−18.6006	−	18.6006i	−0.774352	−	0.774352i	0.204512	−	0.978864i	$-0.434439\pi$
$577$	−18.6006	−	18.6006i	−0.774352	−	0.774352i	−0.978864	+	0.204512i	$0.934439\pi$
$578$	8.53904	+	14.6998i	0.355177	+	0.611432i
$579$		−	1.18304i		−	0.0491654i
$580$		0			0
$581$	3.26980	−	0.650404i	0.135654	−	0.0269833i
$582$	−10.0643			−0.417179
$583$	−3.60091	+	0.716266i	−0.149135	+	0.0296647i
$584$	−0.411656	+	2.06953i	−0.0170344	+	0.0856378i
$585$		0			0
$586$	9.74059	+	23.5159i	0.402380	+	0.971432i
$587$	−16.0085	+	38.6479i	−0.660740	+	1.59517i	0.135906	+	0.990722i	$0.456606\pi$
$587$	−16.0085	+	38.6479i	−0.660740	+	1.59517i	−0.796646	+	0.604446i	$0.793394\pi$
$588$	6.32907	+	1.25893i	0.261007	+	0.0519174i
$589$	66.0922	+	13.1466i	2.72328	+	0.541694i
$590$		0			0
$591$	25.4552	−	25.4552i	1.04709	−	1.04709i
$592$	5.26741	+	3.51957i	0.216489	+	0.144653i
$593$	23.9894	−	9.93672i	0.985125	−	0.408052i	0.168804	−	0.985650i	$-0.446010\pi$
$593$	23.9894	−	9.93672i	0.985125	−	0.408052i	0.816322	+	0.577597i	$0.196010\pi$
$594$	−22.5624			−0.925745
$595$		0			0
$596$	1.20744			0.0494587
$597$	22.4901	−	9.31569i	0.920457	−	0.381266i
$598$	−11.2185	−	7.49598i	−0.458760	−	0.306534i
$599$	−26.4954	+	26.4954i	−1.08257	+	1.08257i	−0.0863049	+	0.996269i	$0.527506\pi$
$599$	−26.4954	+	26.4954i	−1.08257	+	1.08257i	−0.996269	+	0.0863049i	$0.972494\pi$
$600$		0			0
$601$	40.1212	+	7.98061i	1.63658	+	0.325536i	0.925839	−	0.377919i	$-0.123360\pi$
$601$	40.1212	+	7.98061i	1.63658	+	0.325536i	0.710740	+	0.703455i	$0.248360\pi$
$602$	−15.3529	−	3.05389i	−0.625739	−	0.124467i
$603$	−3.32061	+	8.01665i	−0.135226	+	0.326463i
$604$	−2.75046	−	6.64020i	−0.111915	−	0.270186i
$605$		0			0
$606$	−0.0772859	+	0.388543i	−0.00313953	+	0.0157835i
$607$	−13.3146	+	2.64843i	−0.540422	+	0.107497i	−0.457751	−	0.889080i	$-0.651345\pi$
$607$	−13.3146	+	2.64843i	−0.540422	+	0.107497i	−0.0826705	+	0.996577i	$0.526345\pi$
$608$	−6.41149			−0.260020
$609$	−42.5582	+	8.46535i	−1.72455	+	0.343033i
$610$		0			0
$611$		−	0.971424i		−	0.0392996i
$612$	−1.68591	−	3.40729i	−0.0681490	−	0.137731i
$613$	21.4097	+	21.4097i	0.864728	+	0.864728i	0.991883	−	0.127154i	$-0.0405844\pi$
$613$	21.4097	+	21.4097i	0.864728	+	0.864728i	−0.127154	+	0.991883i	$0.540584\pi$
$614$	11.1593	−	26.9409i	0.450352	−	1.08725i
$615$		0			0
$616$	−9.55972	−	9.55972i	−0.385172	−	0.385172i
$617$	−6.59622	−	33.1615i	−0.265554	−	1.33503i	−0.851361	−	0.524580i	$-0.824223\pi$
$617$	−6.59622	−	33.1615i	−0.265554	−	1.33503i	0.585807	−	0.810450i	$-0.300777\pi$
$618$	−3.12763	−	4.68083i	−0.125812	−	0.188291i
$619$	−13.5554	+	9.05744i	−0.544838	+	0.364049i	−0.797324	−	0.603551i	$-0.793752\pi$
$619$	−13.5554	+	9.05744i	−0.544838	+	0.364049i	0.252486	+	0.967601i	$0.418752\pi$
$620$		0			0
$621$	17.1504	−	7.10394i	0.688223	−	0.285071i
$622$	1.53658	−	7.72489i	0.0616111	−	0.309740i
$623$	26.7269	−	17.8584i	1.07079	−	0.715480i
$624$	−3.29095	+	4.92525i	−0.131743	+	0.197168i
$625$		0			0
$626$	3.59937	+	18.0953i	0.143860	+	0.723232i
$627$	−14.1148	−	34.0761i	−0.563690	−	1.36087i
$628$	−15.8344	+	15.8344i	−0.631862	+	0.631862i
$629$	−25.2211	+	6.79386i	−1.00563	+	0.270889i
$630$		0			0
$631$	−37.9013	−	15.6992i	−1.50883	−	0.624976i	−0.533510	−	0.845794i	$-0.679127\pi$
$631$	−37.9013	−	15.6992i	−1.50883	−	0.624976i	−0.975315	+	0.220818i	$0.929127\pi$
$632$	−0.0258982	+	0.0387593i	−0.00103017	+	0.00154176i
$633$			30.2225i			1.20124i
$634$	−11.3432	−	7.57932i	−0.450498	−	0.301013i
$635$		0			0
$636$	−0.736791	−	1.10269i	−0.0292157	−	0.0437243i
$637$	−16.9950	−	7.03955i	−0.673366	−	0.278917i
$638$	32.7606	+	13.5699i	1.29700	+	0.537237i
$639$	−3.19175	−	4.77679i	−0.126264	−	0.188967i
$640$		0			0
$641$	27.6769	+	18.4931i	1.09317	+	0.730433i	0.965244	−	0.261351i	$-0.0841679\pi$
$641$	27.6769	+	18.4931i	1.09317	+	0.730433i	0.127926	+	0.991784i	$0.459168\pi$
$642$			17.4961i			0.690515i
$643$	17.3317	−	25.9387i	0.683495	−	1.02292i	−0.313805	−	0.949487i	$-0.601604\pi$
$643$	17.3317	−	25.9387i	0.683495	−	1.02292i	0.997300	−	0.0734351i	$-0.0233962\pi$
$644$	10.2766	+	4.25672i	0.404956	+	0.167738i
$645$		0			0
$646$	17.4036	−	19.8982i	0.684735	−	0.782884i
$647$	12.0824	−	12.0824i	0.475009	−	0.475009i	−0.428522	−	0.903531i	$-0.640966\pi$
$647$	12.0824	−	12.0824i	0.475009	−	0.475009i	0.903531	+	0.428522i	$0.140966\pi$
$648$	−2.06031	−	4.97402i	−0.0809365	−	0.195398i
$649$	2.58674	+	13.0044i	0.101538	+	0.510468i
$650$		0			0
$651$	−28.5156	+	42.6767i	−1.11762	+	1.67263i
$652$	2.30691	−	1.54143i	0.0903458	−	0.0603671i
$653$	5.03733	−	25.3244i	0.197126	−	0.991019i	−0.747847	−	0.663871i	$-0.768912\pi$
$653$	5.03733	−	25.3244i	0.197126	−	0.991019i	0.944973	−	0.327148i	$-0.106088\pi$
$654$	−25.3835	+	10.5142i	−0.992572	+	0.411137i
$655$		0			0
$656$	0.953562	−	0.637150i	0.0372303	−	0.0248765i
$657$	1.08087	+	1.61764i	0.0421689	+	0.0631103i
$658$	0.156239	+	0.785468i	0.00609084	+	0.0306207i
$659$	−14.3607	−	14.3607i	−0.559413	−	0.559413i	0.369727	−	0.929140i	$-0.379451\pi$
$659$	−14.3607	−	14.3607i	−0.559413	−	0.559413i	−0.929140	+	0.369727i	$0.879451\pi$
$660$		0			0
$661$	−15.4896	+	37.3951i	−0.602474	+	1.45450i	0.268553	+	0.963265i	$0.413455\pi$
$661$	−15.4896	+	37.3951i	−0.602474	+	1.45450i	−0.871027	+	0.491236i	$0.836545\pi$
$662$	7.66116	+	7.66116i	0.297759	+	0.297759i
$663$	−6.35254	−	23.5828i	−0.246712	−	0.915880i
$664$		−	0.984105i		−	0.0381907i
$665$		0			0
$666$	5.72879	−	1.13953i	0.221986	−	0.0441558i
$667$	−29.1750			−1.12966
$668$	−3.95736	+	0.787168i	−0.153115	+	0.0304564i
$669$	0.811395	−	4.07916i	0.0313703	−	0.157709i
$670$		0			0
$671$	−1.70890	−	4.12565i	−0.0659713	−	0.159269i
$672$	1.86882	−	4.51172i	0.0720912	−	0.174044i
$673$	−24.4315	−	4.85972i	−0.941763	−	0.187328i	−0.299746	−	0.954019i	$-0.596902\pi$
$673$	−24.4315	−	4.85972i	−0.941763	−	0.187328i	−0.642017	+	0.766691i	$0.721902\pi$
$674$	24.4738	+	4.86815i	0.942696	+	0.187514i
$675$		0			0
$676$	2.74766	−	2.74766i	0.105679	−	0.105679i
$677$	−15.3618	−	10.2644i	−0.590400	−	0.394493i	0.224176	−	0.974549i	$-0.428031\pi$
$677$	−15.3618	−	10.2644i	−0.590400	−	0.394493i	−0.814577	+	0.580056i	$0.803031\pi$
$678$	8.31595	−	3.44458i	0.319372	−	0.132288i
$679$	−23.6520			−0.907681
$680$		0			0
$681$	7.09071			0.271717
$682$	38.7513	−	16.0513i	1.48387	−	0.614637i
$683$	28.0572	+	18.7472i	1.07358	+	0.717342i	0.961069	−	0.276309i	$-0.0891112\pi$
$683$	28.0572	+	18.7472i	1.07358	+	0.717342i	0.112509	+	0.993651i	$0.464111\pi$
$684$	−4.18006	+	4.18006i	−0.159828	+	0.159828i
$685$		0			0
$686$	−8.38440	−	1.66776i	−0.320118	−	0.0636754i
$687$	−19.8309	−	3.94460i	−0.756594	−	0.150496i
$688$	−1.76828	+	4.26901i	−0.0674150	+	0.162754i
$689$	1.44672	+	3.49269i	0.0551157	+	0.133061i
$690$		0			0
$691$	0.992781	−	4.99105i	0.0377672	−	0.189868i	−0.957296	−	0.289108i	$-0.906641\pi$
$691$	0.992781	−	4.99105i	0.0377672	−	0.189868i	0.995064	+	0.0992401i	$0.0316412\pi$
$692$	10.7454	−	2.13740i	0.408480	−	0.0812517i
$693$	−12.4652			−0.473513
$694$	14.5581	−	2.89578i	0.552617	−	0.109922i
$695$		0			0
$696$			12.8087i			0.485511i
$697$	−0.610976	+	4.68890i	−0.0231424	+	0.177605i
$698$	−17.0681	−	17.0681i	−0.646037	−	0.646037i
$699$	2.54581	−	6.14614i	0.0962915	−	0.232468i
$700$		0			0
$701$	4.66511	+	4.66511i	0.176199	+	0.176199i	0.789696	−	0.613498i	$-0.210238\pi$
$701$	4.66511	+	4.66511i	0.176199	+	0.176199i	−0.613498	+	0.789696i	$0.710238\pi$
$702$	4.53238	+	22.7858i	0.171064	+	0.859996i
$703$	22.5657	+	33.7720i	0.851081	+	1.27373i
$704$	−3.31818	+	2.21714i	−0.125059	+	0.0835616i
$705$		0			0
$706$	26.4531	−	10.9572i	0.995574	−	0.412380i
$707$	−0.181629	+	0.913111i	−0.00683086	+	0.0343411i
$708$	−3.98227	+	2.66087i	−0.149663	+	0.100001i
$709$	6.35644	−	9.51308i	0.238721	−	0.357271i	−0.692693	−	0.721233i	$-0.743576\pi$
$709$	6.35644	−	9.51308i	0.238721	−	0.357271i	0.931414	+	0.363961i	$0.118576\pi$
$710$		0			0
$711$	0.00838502	+	0.0421543i	0.000314463	+	0.00158091i
$712$	−3.63108	−	8.76621i	−0.136081	−	0.328528i
$713$	−24.4023	+	24.4023i	−0.913874	+	0.913874i
$714$	8.92944	+	18.0467i	0.334176	+	0.675381i
$715$		0			0
$716$	4.20808	+	1.74304i	0.157263	+	0.0651406i
$717$	−12.8010	+	19.1580i	−0.478062	+	0.715470i
$718$		−	2.44275i		−	0.0911626i
$719$	2.07623	+	1.38730i	0.0774305	+	0.0517374i	0.593683	−	0.804699i	$-0.297673\pi$
$719$	2.07623	+	1.38730i	0.0774305	+	0.0517374i	−0.516252	+	0.856436i	$0.672673\pi$
$720$		0			0
$721$	−7.35022	−	11.0004i	−0.273736	−	0.409675i
$722$	−20.4244	−	8.46007i	−0.760118	−	0.314851i
$723$	−13.5757	−	5.62323i	−0.504885	−	0.209130i
$724$	−13.9267	−	20.8428i	−0.517583	−	0.774617i
$725$		0			0
$726$	−5.90428	−	3.94512i	−0.219129	−	0.146417i
$727$		−	3.46425i		−	0.128482i	−0.997934	−	0.0642410i	$-0.979537\pi$
$727$		−	3.46425i		−	0.128482i	0.997934	−	0.0642410i	$-0.0204626\pi$
$728$	−7.73402	+	11.5748i	−0.286642	+	0.428990i
$729$	−27.1747	−	11.2561i	−1.00647	−	0.416893i
$730$		0			0
$731$	−8.44906	−	17.0758i	−0.312500	−	0.631573i
$732$	1.14059	−	1.14059i	0.0421573	−	0.0421573i
$733$	1.45266	+	3.50704i	0.0536554	+	0.129536i	0.948434	−	0.316974i	$-0.102667\pi$
$733$	1.45266	+	3.50704i	0.0536554	+	0.129536i	−0.894779	+	0.446510i	$0.852667\pi$
$734$	−0.610498	−	3.06918i	−0.0225339	−	0.113285i
$735$		0			0
$736$	1.82418	−	2.73008i	0.0672402	−	0.100632i
$737$	−31.2277	+	20.8657i	−1.15029	+	0.768598i
$738$	0.206289	−	1.03709i	0.00759361	−	0.0381756i
$739$	1.03602	−	0.429133i	0.0381105	−	0.0157859i	−0.363547	−	0.931576i	$-0.618434\pi$
$739$	1.03602	−	0.429133i	0.0381105	−	0.0157859i	0.401657	+	0.915790i	$0.368434\pi$
$740$		0			0
$741$	−31.5782	+	21.0999i	−1.16005	+	0.775123i
$742$	−1.73153	−	2.59141i	−0.0635664	−	0.0951338i
$743$	6.53046	+	32.8308i	0.239579	+	1.20445i	0.893913	+	0.448241i	$0.147949\pi$
$743$	6.53046	+	32.8308i	0.239579	+	1.20445i	−0.654334	+	0.756206i	$0.727051\pi$
$744$	10.7133	+	10.7133i	0.392769	+	0.392769i
$745$		0			0
$746$	14.0960	−	34.0308i	0.516093	−	1.24596i
$747$	−0.641600	−	0.641600i	−0.0234749	−	0.0234749i
$748$	2.12606	−	16.3163i	0.0777366	−	0.596584i
$749$			41.1174i			1.50240i
$750$		0			0
$751$	−48.2534	+	9.59819i	−1.76079	+	0.350243i	−0.966376	−	0.257133i	$-0.917222\pi$
$751$	−48.2534	+	9.59819i	−1.76079	+	0.350243i	−0.794415	+	0.607376i	$0.792222\pi$
$752$	0.236401			0.00862064
$753$	−23.9594	+	4.76582i	−0.873129	+	0.173676i
$754$	7.12326	−	35.8110i	0.259414	−	1.30416i
$755$		0			0
$756$	−7.32953	−	17.6950i	−0.266572	−	0.643563i
$757$	−0.354617	+	0.856120i	−0.0128888	+	0.0311162i	−0.930193	−	0.367071i	$-0.880361\pi$
$757$	−0.354617	+	0.856120i	−0.0128888	+	0.0311162i	0.917304	+	0.398187i	$0.130361\pi$
$758$	−14.8218	−	2.94824i	−0.538352	−	0.107085i
$759$	18.5259	+	3.68502i	0.672446	+	0.133758i
$760$		0			0
$761$	−10.7310	+	10.7310i	−0.388999	+	0.388999i	−0.874330	−	0.485331i	$-0.838699\pi$
$761$	−10.7310	+	10.7310i	−0.388999	+	0.388999i	0.485331	+	0.874330i	$0.338699\pi$
$762$	−6.76583	−	4.52078i	−0.245100	−	0.163771i
$763$	−59.6535	+	24.7093i	−2.15960	+	0.894536i
$764$	20.3454			0.736072
$765$		0			0
$766$	−13.4045			−0.484325
$767$	12.6136	−	5.22472i	0.455450	−	0.188654i
$768$	−1.19858	−	0.800867i	−0.0432501	−	0.0288988i
$769$	3.05558	−	3.05558i	0.110187	−	0.110187i	−0.649864	−	0.760051i	$-0.725174\pi$
$769$	3.05558	−	3.05558i	0.110187	−	0.110187i	0.760051	+	0.649864i	$0.225174\pi$
$770$		0			0
$771$	11.4260	+	2.27278i	0.411499	+	0.0818522i
$772$	−0.804919	−	0.160108i	−0.0289697	−	0.00576242i
$773$	18.4025	−	44.4276i	0.661893	−	1.59795i	−0.132942	−	0.991124i	$-0.542442\pi$
$773$	18.4025	−	44.4276i	0.661893	−	1.59795i	0.794834	−	0.606826i	$-0.207558\pi$
$774$	1.63038	+	3.93609i	0.0586028	+	0.141480i
$775$		0			0
$776$	−1.36207	+	6.84757i	−0.0488953	+	0.245813i
$777$	−30.3425	+	6.03550i	−1.08853	+	0.216523i
$778$	28.9322			1.03727
$779$	7.21166	−	1.43449i	0.258385	−	0.0513959i
$780$		0			0
$781$		−	24.8660i		−	0.889774i
$782$	3.52123	+	13.0720i	0.125919	+	0.467454i
$783$	35.5220	+	35.5220i	1.26945	+	1.26945i
$784$	1.71311	−	4.13581i	0.0611824	−	0.147707i
$785$		0			0
$786$	−11.9765	−	11.9765i	−0.427189	−	0.427189i
$787$	−4.23720	−	21.3018i	−0.151040	−	0.759329i	−0.979840	−	0.199784i	$-0.935976\pi$
$787$	−4.23720	−	21.3018i	−0.151040	−	0.759329i	0.828800	−	0.559545i	$-0.189024\pi$
$788$	−13.8743	−	20.7643i	−0.494250	−	0.739698i
$789$	−2.39321	+	1.59909i	−0.0852004	+	0.0569291i
$790$		0			0
$791$	19.5432	−	8.09508i	0.694878	−	0.287828i
$792$	−0.717841	+	3.60883i	−0.0255074	+	0.128234i
$793$	−3.82322	+	2.55459i	−0.135767	+	0.0907163i
$794$	4.30718	−	6.44614i	0.152856	−	0.228765i
$795$		0			0
$796$	−3.29450	−	16.5626i	−0.116771	−	0.587045i
$797$	18.1709	+	43.8685i	0.643647	+	1.55390i	0.821725	+	0.569884i	$0.193012\pi$
$797$	18.1709	+	43.8685i	0.643647	+	1.55390i	−0.178078	+	0.984016i	$0.556988\pi$
$798$	22.1397	−	22.1397i	0.783736	−	0.783736i
$799$	−0.641694	+	0.733674i	−0.0227015	+	0.0259555i
$800$		0			0
$801$	−8.08258	−	3.34791i	−0.285584	−	0.118293i
$802$	−12.0674	+	18.0601i	−0.426115	+	0.637726i
$803$			8.42078i			0.297163i
$804$	−11.2799	−	7.53702i	−0.397813	−	0.265810i
$805$		0			0
$806$	−23.9948	−	35.9107i	−0.845180	−	1.26490i
$807$	26.6183	+	11.0257i	0.937009	+	0.388122i
$808$	0.253898	+	0.105168i	0.00893209	+	0.00369979i
$809$	12.2131	+	18.2782i	0.429389	+	0.642626i	0.981571	−	0.191098i	$-0.0612047\pi$
$809$	12.2131	+	18.2782i	0.429389	+	0.642626i	−0.552182	+	0.833724i	$0.686205\pi$
$810$		0			0
$811$	4.88955	+	3.26709i	0.171695	+	0.114723i	0.638449	−	0.769664i	$-0.279576\pi$
$811$	4.88955	+	3.26709i	0.171695	+	0.114723i	−0.466753	+	0.884387i	$0.654576\pi$
$812$			30.1015i			1.05636i
$813$	3.77572	−	5.65077i	0.132420	−	0.198181i
$814$	23.3572	+	9.67486i	0.818668	+	0.339104i
$815$		0			0
$816$	5.73898	−	1.54592i	0.200904	−	0.0541180i
$817$	−20.9486	+	20.9486i	−0.732900	+	0.732900i
$818$	−9.11183	−	21.9979i	−0.318588	−	0.769139i
$819$	2.50404	+	12.5886i	0.0874981	+	0.439882i
$820$		0			0
$821$	−24.8776	+	37.2319i	−0.868234	+	1.29940i	0.0847559	+	0.996402i	$0.472989\pi$
$821$	−24.8776	+	37.2319i	−0.868234	+	1.29940i	−0.952990	+	0.303002i	$0.902011\pi$
$822$	−11.3554	+	7.58742i	−0.396064	+	0.264642i
$823$	−6.32796	+	31.8128i	−0.220579	+	1.10892i	0.698730	+	0.715386i	$0.253749\pi$
$823$	−6.32796	+	31.8128i	−0.220579	+	1.10892i	−0.919308	+	0.393538i	$0.871251\pi$
$824$	−3.60803	+	1.49450i	−0.125692	+	0.0520632i
$825$		0			0
$826$	−9.35869	+	6.25328i	−0.325631	+	0.217579i
$827$	−19.7136	−	29.5034i	−0.685508	−	1.02594i	−0.997128	−	0.0757284i	$-0.975872\pi$
$827$	−19.7136	−	29.5034i	−0.685508	−	1.02594i	0.311621	−	0.950207i	$-0.399128\pi$
$828$	−0.590613	−	2.96921i	−0.0205252	−	0.103187i
$829$	37.4477	+	37.4477i	1.30061	+	1.30061i	0.927978	+	0.372634i	$0.121545\pi$
$829$	37.4477	+	37.4477i	1.30061	+	1.30061i	0.372634	+	0.927978i	$0.378455\pi$
$830$		0			0
$831$	4.42995	−	10.6948i	0.153673	−	0.371000i
$832$	2.90567	+	2.90567i	0.100736	+	0.100736i
$833$	8.18544	+	16.5430i	0.283609	+	0.573183i
$834$			7.01287i			0.242836i
$835$		0			0
$836$	−25.0950	+	4.99171i	−0.867929	+	0.172642i
$837$	59.4220			2.05393
$838$	26.4209	−	5.25544i	0.912694	−	0.181546i
$839$	−1.12143	+	5.63782i	−0.0387161	+	0.194639i	−0.995303	−	0.0968079i	$-0.969137\pi$
$839$	−1.12143	+	5.63782i	−0.0387161	+	0.194639i	0.956587	+	0.291447i	$0.0941367\pi$
$840$		0			0
$841$	−19.1159	−	46.1499i	−0.659169	−	1.59137i
$842$	3.05257	−	7.36955i	0.105198	−	0.253972i
$843$	−3.79514	−	0.754899i	−0.130711	−	0.0260001i
$844$	20.5628	+	4.09020i	0.707801	+	0.140790i
$845$		0			0
$846$	0.154124	−	0.154124i	0.00529891	−	0.00529891i
$847$	−13.8756	−	9.27138i	−0.476772	−	0.318569i
$848$	−0.849962	+	0.352066i	−0.0291878	+	0.0120900i
$849$	−20.7872			−0.713416
$850$		0			0
$851$	−20.8008			−0.713042
$852$	8.29827	−	3.43726i	0.284294	−	0.117758i
$853$	−42.9088	−	28.6707i	−1.46917	−	0.981667i	−0.994855	−	0.101312i	$-0.967696\pi$
$853$	−42.9088	−	28.6707i	−1.46917	−	0.981667i	−0.474314	−	0.880356i	$-0.657304\pi$
$854$	2.68049	−	2.68049i	0.0917243	−	0.0917243i
$855$		0			0
$856$	11.9040	+	2.36785i	0.406871	+	0.0809316i
$857$	−41.4056	−	8.23610i	−1.41439	−	0.281340i	−0.572020	−	0.820240i	$-0.693840\pi$
$857$	−41.4056	−	8.23610i	−1.41439	−	0.281340i	−0.842370	+	0.538900i	$0.818840\pi$
$858$	−9.04640	+	21.8399i	−0.308839	+	0.745603i
$859$	−15.3248	−	36.9973i	−0.522874	−	1.26233i	−0.936110	−	0.351706i	$-0.885602\pi$
$859$	−15.3248	−	36.9973i	−0.522874	−	1.26233i	0.413236	−	0.910624i	$-0.364398\pi$
$860$		0			0
$861$	−1.09261	+	5.49292i	−0.0372361	+	0.187198i
$862$	15.3057	−	3.04448i	0.521313	−	0.103696i
$863$	−18.5491			−0.631417			−0.315709	−	0.948856i	$-0.602242\pi$
$863$	−18.5491			−0.631417			−0.315709	+	0.948856i	$0.602242\pi$
$864$	−5.54504	+	1.10298i	−0.188646	+	0.0375240i
$865$		0			0
$866$		−	21.2306i		−	0.721444i
$867$	−10.7803	+	22.0073i	−0.366118	+	0.747408i
$868$	25.1772	+	25.1772i	0.854571	+	0.854571i
$869$	−0.0711908	+	0.171870i	−0.00241498	+	0.00583028i
$870$		0			0
$871$	27.3455	+	27.3455i	0.926565	+	0.926565i
$872$	3.71835	+	18.6934i	0.125919	+	0.633039i
$873$	3.57634	+	5.35238i	0.121041	+	0.181151i
$874$	17.5039	−	11.6957i	0.592078	−	0.395614i
$875$		0			0
$876$	−2.81018	+	1.16402i	−0.0949473	+	0.0393285i
$877$	3.03337	−	15.2498i	0.102430	−	0.514949i	−0.895171	−	0.445722i	$-0.852947\pi$
$877$	3.03337	−	15.2498i	0.102430	−	0.514949i	0.997601	−	0.0692263i	$-0.0220531\pi$
$878$	−5.08942	+	3.40064i	−0.171760	+	0.114766i
$879$	−20.3848	+	30.5080i	−0.687561	+	1.02901i
$880$		0			0
$881$	−8.46141	−	42.5384i	−0.285072	−	1.43316i	−0.812205	−	0.583372i	$-0.801733\pi$
$881$	−8.46141	−	42.5384i	−0.285072	−	1.43316i	0.527133	−	0.849783i	$-0.323267\pi$
$882$	−1.57951	−	3.81328i	−0.0531849	−	0.128400i
$883$	8.26816	−	8.26816i	0.278246	−	0.278246i	−0.554163	−	0.832408i	$-0.686961\pi$
$883$	8.26816	−	8.26816i	0.278246	−	0.278246i	0.832408	+	0.554163i	$0.186961\pi$
$884$	−16.9050	+	1.13055i	−0.568578	+	0.0380244i
$885$		0			0
$886$	−12.5852	−	5.21295i	−0.422807	−	0.175132i
$887$	2.11844	−	3.17047i	0.0711304	−	0.106454i	−0.794199	−	0.607658i	$-0.792109\pi$
$887$	2.11844	−	3.17047i	0.0711304	−	0.106454i	0.865329	+	0.501204i	$0.167109\pi$
$888$			9.13213i			0.306454i
$889$	−15.9003	−	10.6243i	−0.533280	−	0.356326i
$890$		0			0
$891$	−11.9367	−	17.8646i	−0.399896	−	0.598486i
$892$	−2.66557	−	1.10412i	−0.0892500	−	0.0369686i
$893$	1.40031	+	0.580026i	0.0468594	+	0.0194098i
$894$	0.966999	+	1.44722i	0.0323413	+	0.0484021i
$895$		0			0
$896$	−2.81678	−	1.88211i	−0.0941019	−	0.0628769i
$897$		−	19.4496i		−	0.649403i
$898$	−9.97891	+	14.9345i	−0.333001	+	0.498371i
$899$	−86.2809	−	35.7387i	−2.87763	−	1.19195i
$900$		0			0
$901$	1.21453	−	3.59354i	0.0404617	−	0.119718i
$902$	3.23625	−	3.23625i	0.107755	−	0.107755i
$903$	−8.63532	−	20.8475i	−0.287365	−	0.693761i
$904$	−1.21818	−	6.12420i	−0.0405160	−	0.203688i
$905$		0			0
$906$	5.75607	−	8.61456i	0.191233	−	0.286200i
$907$	−35.2429	+	23.5486i	−1.17022	+	0.781917i	−0.979838	−	0.199793i	$-0.935973\pi$
$907$	−35.2429	+	23.5486i	−1.17022	+	0.781917i	−0.190384	+	0.981710i	$0.560973\pi$
$908$	0.959632	−	4.82439i	0.0318465	−	0.160103i
$909$	0.234098	−	0.0969664i	0.00776453	−	0.00321617i
$910$		0			0
$911$	49.6433	−	33.1706i	1.64476	−	1.09899i	0.740448	−	0.672113i	$-0.234613\pi$
$911$	49.6433	−	33.1706i	1.64476	−	1.09899i	0.904309	−	0.426879i	$-0.140387\pi$
$912$	−5.13475	−	7.68469i	−0.170029	−	0.254466i
$913$	−0.766181	−	3.85185i	−0.0253569	−	0.127478i
$914$	−9.97995	−	9.97995i	−0.330107	−	0.330107i
$915$		0			0
$916$	−5.36767	+	12.9587i	−0.177353	+	0.428168i
$917$	−28.1460	−	28.1460i	−0.929461	−	0.929461i
$918$	11.6285	−	20.2031i	0.383799	−	0.666801i
$919$		−	14.6741i		−	0.484053i	−0.970270	−	0.242026i	$-0.922188\pi$
$919$		−	14.6741i		−	0.484053i	0.970270	−	0.242026i	$-0.0778120\pi$
$920$		0			0
$921$	41.2280	−	8.20075i	1.35851	−	0.270224i
$922$	−0.0301360			−0.000992478
$923$	−25.1123	+	4.99514i	−0.826580	+	0.164417i
$924$	3.80204	−	19.1142i	0.125078	−	0.628810i
$925$		0			0
$926$	0.609154	+	1.47063i	0.0200181	+	0.0483279i
$927$	−1.37795	+	3.32666i	−0.0452578	+	0.109262i
$928$	8.71477	+	1.73348i	0.286077	+	0.0569042i
$929$	2.76873	+	0.550734i	0.0908391	+	0.0180690i	0.240301	−	0.970699i	$-0.422754\pi$
$929$	2.76873	+	0.550734i	0.0908391	+	0.0180690i	−0.149461	+	0.988768i	$0.547754\pi$
$930$		0			0
$931$	20.2950	−	20.2950i	0.665142	−	0.665142i
$932$	−3.83718	−	2.56392i	−0.125691	−	0.0839840i
$933$	10.4895	−	4.34489i	0.343411	−	0.142245i
$934$	8.01670			0.262314
$935$		0			0
$936$	3.78877			0.123840
$937$	−6.17591	+	2.55815i	−0.201758	+	0.0835710i	−0.481274	−	0.876570i	$-0.659826\pi$
$937$	−6.17591	+	2.55815i	−0.201758	+	0.0835710i	0.279516	+	0.960141i	$0.409826\pi$
$938$	−26.5089	−	17.7127i	−0.865547	−	0.578340i
$939$	−18.8060	+	18.8060i	−0.613712	+	0.613712i
$940$		0			0
$941$	−40.1031	−	7.97701i	−1.30733	−	0.260043i	−0.508216	−	0.861229i	$-0.669695\pi$
$941$	−40.1031	−	7.97701i	−1.30733	−	0.260043i	−0.799109	+	0.601186i	$0.794695\pi$
$942$	−31.6601	−	6.29758i	−1.03154	−	0.205186i
$943$	−1.44102	+	3.47894i	−0.0469262	+	0.113290i
$944$	1.27146	+	3.06957i	0.0413825	+	0.0999061i
$945$		0			0
$946$	−3.59750	+	18.0859i	−0.116965	+	0.588023i
$947$	31.4810	−	6.26196i	1.02299	−	0.203486i	0.345038	−	0.938589i	$-0.387866\pi$
$947$	31.4810	−	6.26196i	1.02299	−	0.203486i	0.677956	+	0.735102i	$0.262866\pi$
$948$	−0.0671972			−0.00218246
$949$	8.50419	−	1.69159i	0.276058	−	0.0549113i
$950$		0			0
$951$		−	19.6658i		−	0.637708i
$952$	13.4871	−	3.63305i	0.437120	−	0.117748i
$953$	9.45879	+	9.45879i	0.306400	+	0.306400i	0.843511	−	0.537111i	$-0.180484\pi$
$953$	9.45879	+	9.45879i	0.306400	+	0.306400i	−0.537111	+	0.843511i	$0.680484\pi$
$954$	−0.324610	+	0.783678i	−0.0105096	+	0.0253725i
$955$		0			0
$956$	11.3023	+	11.3023i	0.365544	+	0.365544i
$957$	9.97225	+	50.1339i	0.322357	+	1.62060i
$958$	−13.9597	−	20.8921i	−0.451017	−	0.674994i
$959$	−26.6862	+	17.8311i	−0.861741	+	0.575797i
$960$		0			0
$961$	−73.4183	+	30.4109i	−2.36833	+	0.980995i
$962$	5.07864	−	25.5320i	0.163742	−	0.823186i
$963$	9.30473	−	6.21722i	0.299841	−	0.200347i
$964$	−5.66323	+	8.47562i	−0.182400	+	0.272981i
$965$		0			0
$966$	3.12818	+	15.7264i	0.100648	+	0.505990i
$967$	−3.82200	−	9.22713i	−0.122907	−	0.296725i	0.850436	−	0.526079i	$-0.176338\pi$
$967$	−3.82200	−	9.22713i	−0.122907	−	0.296725i	−0.973343	+	0.229355i	$0.926338\pi$
$968$	−3.48325	+	3.48325i	−0.111956	+	0.111956i
$969$	37.7876	+	4.92382i	1.21391	+	0.158176i
$970$		0			0
$971$	3.40320	+	1.40965i	0.109214	+	0.0452379i	0.436621	−	0.899645i	$-0.356175\pi$
$971$	3.40320	+	1.40965i	0.109214	+	0.0452379i	−0.327407	+	0.944883i	$0.606175\pi$
$972$	−5.11129	+	7.64959i	−0.163945	+	0.245361i
$973$			16.4809i			0.528353i
$974$	24.8229	+	16.5862i	0.795378	+	0.531455i
$975$		0			0
$976$	−0.621672	−	0.930398i	−0.0198992	−	0.0297813i
$977$	4.18309	+	1.73269i	0.133829	+	0.0554338i	0.448593	−	0.893736i	$-0.351925\pi$
$977$	4.18309	+	1.73269i	0.133829	+	0.0554338i	−0.314764	+	0.949170i	$0.601925\pi$
$978$	3.69506	+	1.53054i	0.118155	+	0.0489414i
$979$	−21.0373	−	31.4845i	−0.672354	−	1.00625i
$980$		0			0
$981$	14.6116	+	9.76319i	0.466514	+	0.311715i
$982$		−	13.0634i		−	0.416869i
$983$	19.9641	−	29.8783i	0.636755	−	0.952971i	−0.363021	−	0.931781i	$-0.618255\pi$
$983$	19.9641	−	29.8783i	0.636755	−	0.952971i	0.999775	−	0.0211897i	$-0.00674539\pi$
$984$	1.52735	+	0.632650i	0.0486902	+	0.0201681i
$985$		0			0
$986$	−29.0356	+	22.3411i	−0.924681	+	0.711484i
$987$	−0.816320	+	0.816320i	−0.0259838	+	0.0259838i
$988$	10.0823	+	24.3408i	0.320760	+	0.774384i
$989$	−2.95989	−	14.8804i	−0.0941192	−	0.473169i
$990$		0			0
$991$	8.74298	−	13.0848i	0.277730	−	0.415652i	−0.666213	−	0.745762i	$-0.732086\pi$
$991$	8.74298	−	13.0848i	0.277730	−	0.415652i	0.943943	+	0.330110i	$0.107086\pi$
$992$	8.73903	−	5.83924i	0.277465	−	0.185396i
$993$	−3.04696	+	15.3181i	−0.0966923	+	0.486105i
$994$	19.5017	−	8.07787i	0.618556	−	0.256214i
$995$		0			0
$996$	1.17953	−	0.788137i	0.0373748	−	0.0249731i
$997$	13.1987	+	19.7532i	0.418007	+	0.625591i	0.979393	−	0.201963i	$-0.0647319\pi$
$997$	13.1987	+	19.7532i	0.418007	+	0.625591i	−0.561387	+	0.827554i	$0.689732\pi$
$998$	−0.263630	−	1.32536i	−0.00834507	−	0.0419535i
$999$	25.3260	+	25.3260i	0.801278	+	0.801278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.v.c.193.4		32
5.2	odd	4		850.2.s.c.57.4		32
5.3	odd	4		170.2.o.a.57.1	yes	32
5.4	even	2		170.2.r.a.23.1	yes	32
17.3	odd	16		850.2.s.c.343.4		32
85.3	even	16		170.2.r.a.37.1	yes	32
85.37	even	16	inner	850.2.v.c.207.4		32
85.54	odd	16		170.2.o.a.3.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.a.3.1	✓	32	85.54	odd	16
170.2.o.a.57.1	yes	32	5.3	odd	4
170.2.r.a.23.1	yes	32	5.4	even	2
170.2.r.a.37.1	yes	32	85.3	even	16
850.2.s.c.57.4		32	5.2	odd	4
850.2.s.c.343.4		32	17.3	odd	16
850.2.v.c.193.4		32	1.1	even	1	trivial
850.2.v.c.207.4		32	85.37	even	16	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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.v (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.923880 - 0.382683i) q^{2} +(1.19858 + 0.800867i) q^{3} +(0.707107 - 0.707107i) q^{4} +(1.41382 + 0.281227i) q^{6} +(3.32261 + 0.660909i) q^{7} +(0.382683 - 0.923880i) q^{8} +(-0.352840 - 0.851831i) q^{9} +O(q^{10})\)	\(q+(0.923880 - 0.382683i) q^{2} +(1.19858 + 0.800867i) q^{3} +(0.707107 - 0.707107i) q^{4} +(1.41382 + 0.281227i) q^{6} +(3.32261 + 0.660909i) q^{7} +(0.382683 - 0.923880i) q^{8} +(-0.352840 - 0.851831i) q^{9} +(0.778556 - 3.91407i) q^{11} +(1.41382 - 0.281227i) q^{12} -4.10923 q^{13} +(3.32261 - 0.660909i) q^{14} -1.00000i q^{16} +(3.10352 + 2.71444i) q^{17} +(-0.651963 - 0.651963i) q^{18} +(2.45357 - 5.92345i) q^{19} +(3.45312 + 3.45312i) q^{21} +(-0.778556 - 3.91407i) q^{22} +(1.82418 + 2.73008i) q^{23} +(1.19858 - 0.800867i) q^{24} +(-3.79643 + 1.57253i) q^{26} +(1.10298 - 5.54504i) q^{27} +(2.81678 - 1.88211i) q^{28} +(-4.93652 + 7.38803i) q^{29} +(2.05047 + 10.3084i) q^{31} +(-0.382683 - 0.923880i) q^{32} +(4.06781 - 4.06781i) q^{33} +(3.90605 + 1.32015i) q^{34} +(-0.851831 - 0.352840i) q^{36} +(-3.51957 + 5.26741i) q^{37} -6.41149i q^{38} +(-4.92525 - 3.29095i) q^{39} +(0.637150 + 0.953562i) q^{41} +(4.51172 + 1.86882i) q^{42} +(-4.26901 - 1.76828i) q^{43} +(-2.21714 - 3.31818i) q^{44} +(2.73008 + 1.82418i) q^{46} +0.236401i q^{47} +(0.800867 - 1.19858i) q^{48} +(4.13581 + 1.71311i) q^{49} +(1.54592 + 5.73898i) q^{51} +(-2.90567 + 2.90567i) q^{52} +(-0.352066 - 0.849962i) q^{53} +(-1.10298 - 5.54504i) q^{54} +(1.88211 - 2.81678i) q^{56} +(7.68469 - 5.13475i) q^{57} +(-1.73348 + 8.71477i) q^{58} +(-3.06957 + 1.27146i) q^{59} +(0.930398 - 0.621672i) q^{61} +(5.83924 + 8.73903i) q^{62} +(-0.609368 - 3.06350i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(2.20148 - 5.31485i) q^{66} +(-6.65464 - 6.65464i) q^{67} +(4.11392 - 0.275124i) q^{68} +4.73315i q^{69} +(6.11118 - 1.21559i) q^{71} -0.922015 q^{72} +(-2.06953 + 0.411656i) q^{73} +(-1.23591 + 6.21333i) q^{74} +(-2.45357 - 5.92345i) q^{76} +(5.17368 - 12.4904i) q^{77} +(-5.80973 - 1.15563i) q^{78} +(-0.0457198 - 0.00909423i) q^{79} +(3.80695 - 3.80695i) q^{81} +(0.953562 + 0.637150i) q^{82} +(0.909194 - 0.376601i) q^{83} +4.88345 q^{84} -4.62074 q^{86} +(-11.8337 + 4.90166i) q^{87} +(-3.31818 - 2.21714i) q^{88} +(6.70937 - 6.70937i) q^{89} +(-13.6534 - 2.71583i) q^{91} +(3.22035 + 0.640567i) q^{92} +(-5.79800 + 13.9976i) q^{93} +(0.0904666 + 0.218406i) q^{94} +(0.281227 - 1.41382i) q^{96} +(-6.84757 + 1.36207i) q^{97} +4.47657 q^{98} +(-3.60883 + 0.717841i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 16 q^{18} + 8 q^{26} - 24 q^{27} + 8 q^{28} - 8 q^{29} - 16 q^{31} - 64 q^{33} + 24 q^{34} + 32 q^{37} - 32 q^{39} + 16 q^{41} + 24 q^{42} + 16 q^{43} - 16 q^{44} - 16 q^{49} + 32 q^{51} + 16 q^{52} - 16 q^{53} + 24 q^{54} + 8 q^{56} + 24 q^{57} + 16 q^{58} - 64 q^{59} - 24 q^{61} + 40 q^{62} + 24 q^{63} - 16 q^{67} + 8 q^{71} + 16 q^{72} - 32 q^{73} + 8 q^{74} - 24 q^{77} - 32 q^{78} + 72 q^{79} + 48 q^{81} - 48 q^{82} - 16 q^{83} - 64 q^{86} - 40 q^{87} - 32 q^{88} + 16 q^{89} + 48 q^{91} - 24 q^{92} + 8 q^{93} + 8 q^{94} + 48 q^{97} - 64 q^{99}+O(q^{100}) \) 32 * q - 16 * q^18 + 8 * q^26 - 24 * q^27 + 8 * q^28 - 8 * q^29 - 16 * q^31 - 64 * q^33 + 24 * q^34 + 32 * q^37 - 32 * q^39 + 16 * q^41 + 24 * q^42 + 16 * q^43 - 16 * q^44 - 16 * q^49 + 32 * q^51 + 16 * q^52 - 16 * q^53 + 24 * q^54 + 8 * q^56 + 24 * q^57 + 16 * q^58 - 64 * q^59 - 24 * q^61 + 40 * q^62 + 24 * q^63 - 16 * q^67 + 8 * q^71 + 16 * q^72 - 32 * q^73 + 8 * q^74 - 24 * q^77 - 32 * q^78 + 72 * q^79 + 48 * q^81 - 48 * q^82 - 16 * q^83 - 64 * q^86 - 40 * q^87 - 32 * q^88 + 16 * q^89 + 48 * q^91 - 24 * q^92 + 8 * q^93 + 8 * q^94 + 48 * q^97 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more