LMFDB - Embedded newform 961.2.c.a.521.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(439,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.439"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-4,-2,4,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			521.1
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	961.521
Dual form			961.2.c.a.439.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.41421 q^{2} +(-1.20711 - 2.09077i) q^{3} +3.82843 q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.91421 + 5.04757i) q^{6} +(-1.20711 - 2.09077i) q^{7} -4.41421 q^{8} +(-1.41421 + 2.44949i) q^{9} +(1.20711 - 2.09077i) q^{10} +(-2.62132 + 4.54026i) q^{11} +(-4.62132 - 8.00436i) q^{12} +(0.914214 - 1.58346i) q^{13} +(2.91421 + 5.04757i) q^{14} +2.41421 q^{15} +3.00000 q^{16} +(-0.0857864 - 0.148586i) q^{17} +(3.41421 - 5.91359i) q^{18} +(-0.792893 - 1.37333i) q^{19} +(-1.91421 + 3.31552i) q^{20} +(-2.91421 + 5.04757i) q^{21} +(6.32843 - 10.9612i) q^{22} +4.00000 q^{23} +(5.32843 + 9.22911i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-2.20711 + 3.82282i) q^{26} -0.414214 q^{27} +(-4.62132 - 8.00436i) q^{28} +1.17157 q^{29} -5.82843 q^{30} +1.58579 q^{32} +12.6569 q^{33} +(0.207107 + 0.358719i) q^{34} +2.41421 q^{35} +(-5.41421 + 9.37769i) q^{36} +(0.500000 + 0.866025i) q^{37} +(1.91421 + 3.31552i) q^{38} -4.41421 q^{39} +(2.20711 - 3.82282i) q^{40} +(-4.74264 + 8.21449i) q^{41} +(7.03553 - 12.1859i) q^{42} +(4.44975 + 7.70719i) q^{43} +(-10.0355 + 17.3821i) q^{44} +(-1.41421 - 2.44949i) q^{45} -9.65685 q^{46} -1.65685 q^{47} +(-3.62132 - 6.27231i) q^{48} +(0.585786 - 1.01461i) q^{49} +(-4.82843 - 8.36308i) q^{50} +(-0.207107 + 0.358719i) q^{51} +(3.50000 - 6.06218i) q^{52} +(0.0857864 - 0.148586i) q^{53} +1.00000 q^{54} +(-2.62132 - 4.54026i) q^{55} +(5.32843 + 9.22911i) q^{56} +(-1.91421 + 3.31552i) q^{57} -2.82843 q^{58} +(5.03553 + 8.72180i) q^{59} +9.24264 q^{60} -2.82843 q^{61} +6.82843 q^{63} -9.82843 q^{64} +(0.914214 + 1.58346i) q^{65} -30.5563 q^{66} +(2.62132 - 4.54026i) q^{67} +(-0.328427 - 0.568852i) q^{68} +(-4.82843 - 8.36308i) q^{69} -5.82843 q^{70} +(7.03553 - 12.1859i) q^{71} +(6.24264 - 10.8126i) q^{72} +(1.91421 - 3.31552i) q^{73} +(-1.20711 - 2.09077i) q^{74} +(4.82843 - 8.36308i) q^{75} +(-3.03553 - 5.25770i) q^{76} +12.6569 q^{77} +10.6569 q^{78} +(-7.62132 - 13.2005i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(4.74264 + 8.21449i) q^{81} +(11.4497 - 19.8315i) q^{82} +(2.03553 - 3.52565i) q^{83} +(-11.1569 + 19.3242i) q^{84} +0.171573 q^{85} +(-10.7426 - 18.6068i) q^{86} +(-1.41421 - 2.44949i) q^{87} +(11.5711 - 20.0417i) q^{88} +12.4853 q^{89} +(3.41421 + 5.91359i) q^{90} -4.41421 q^{91} +15.3137 q^{92} +4.00000 q^{94} +1.58579 q^{95} +(-1.91421 - 3.31552i) q^{96} +10.8284 q^{97} +(-1.41421 + 2.44949i) q^{98} +(-7.41421 - 12.8418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 6 q^{6} - 2 q^{7} - 12 q^{8} + 2 q^{10} - 2 q^{11} - 10 q^{12} - 2 q^{13} + 6 q^{14} + 4 q^{15} + 12 q^{16} - 6 q^{17} + 8 q^{18} - 6 q^{19} - 2 q^{20} - 6 q^{21}+ \cdots - 24 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 6 * q^6 - 2 * q^7 - 12 * q^8 + 2 * q^10 - 2 * q^11 - 10 * q^12 - 2 * q^13 + 6 * q^14 + 4 * q^15 + 12 * q^16 - 6 * q^17 + 8 * q^18 - 6 * q^19 - 2 * q^20 - 6 * q^21 + 14 * q^22 + 16 * q^23 + 10 * q^24 + 8 * q^25 - 6 * q^26 + 4 * q^27 - 10 * q^28 + 16 * q^29 - 12 * q^30 + 12 * q^32 + 28 * q^33 - 2 * q^34 + 4 * q^35 - 16 * q^36 + 2 * q^37 + 2 * q^38 - 12 * q^39 + 6 * q^40 - 2 * q^41 + 14 * q^42 - 2 * q^43 - 26 * q^44 - 16 * q^46 + 16 * q^47 - 6 * q^48 + 8 * q^49 - 8 * q^50 + 2 * q^51 + 14 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 + 10 * q^56 - 2 * q^57 + 6 * q^59 + 20 * q^60 + 16 * q^63 - 28 * q^64 - 2 * q^65 - 60 * q^66 + 2 * q^67 + 10 * q^68 - 8 * q^69 - 12 * q^70 + 14 * q^71 + 8 * q^72 + 2 * q^73 - 2 * q^74 + 8 * q^75 + 2 * q^76 + 28 * q^77 + 20 * q^78 - 22 * q^79 - 6 * q^80 + 2 * q^81 + 26 * q^82 - 6 * q^83 - 22 * q^84 + 12 * q^85 - 26 * q^86 + 18 * q^88 + 16 * q^89 + 8 * q^90 - 12 * q^91 + 16 * q^92 + 16 * q^94 + 12 * q^95 - 2 * q^96 + 32 * q^97 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.41421			−1.70711			−0.853553	−	0.521005i	$-0.825557\pi$
$2$	−2.41421			−1.70711			−0.853553	+	0.521005i	$0.825557\pi$
$3$	−1.20711	−	2.09077i	−0.696923	−	1.20711i	−0.969528	−	0.244981i	$-0.921218\pi$
$3$	−1.20711	−	2.09077i	−0.696923	−	1.20711i	0.272605	−	0.962126i	$-0.412115\pi$
$4$	3.82843			1.91421
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	2.91421	+	5.04757i	1.18972	+	2.06066i
$7$	−1.20711	−	2.09077i	−0.456243	−	0.790237i	0.542515	−	0.840046i	$-0.317472\pi$
$7$	−1.20711	−	2.09077i	−0.456243	−	0.790237i	−0.998759	+	0.0498090i	$0.984139\pi$
$8$	−4.41421			−1.56066
$9$	−1.41421	+	2.44949i	−0.471405	+	0.816497i
$10$	1.20711	−	2.09077i	0.381721	−	0.661160i
$11$	−2.62132	+	4.54026i	−0.790358	+	1.36894i	0.135388	+	0.990793i	$0.456772\pi$
$11$	−2.62132	+	4.54026i	−0.790358	+	1.36894i	−0.925745	+	0.378147i	$0.876561\pi$
$12$	−4.62132	−	8.00436i	−1.33406	−	2.31066i
$13$	0.914214	−	1.58346i	0.253557	−	0.439174i	−0.710945	−	0.703247i	$-0.751733\pi$
$13$	0.914214	−	1.58346i	0.253557	−	0.439174i	0.964503	+	0.264073i	$0.0850661\pi$
$14$	2.91421	+	5.04757i	0.778856	+	1.34902i
$15$	2.41421			0.623347
$16$	3.00000			0.750000
$17$	−0.0857864	−	0.148586i	−0.0208063	−	0.0360375i	0.855435	−	0.517911i	$-0.173290\pi$
$17$	−0.0857864	−	0.148586i	−0.0208063	−	0.0360375i	−0.876241	+	0.481873i	$0.839957\pi$
$18$	3.41421	−	5.91359i	0.804738	−	1.39385i
$19$	−0.792893	−	1.37333i	−0.181902	−	0.315064i	0.760626	−	0.649190i	$-0.224892\pi$
$19$	−0.792893	−	1.37333i	−0.181902	−	0.315064i	−0.942528	+	0.334126i	$0.891559\pi$
$20$	−1.91421	+	3.31552i	−0.428031	+	0.741372i
$21$	−2.91421	+	5.04757i	−0.635934	+	1.10147i
$22$	6.32843	−	10.9612i	1.34923	−	2.33693i
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$	5.32843	+	9.22911i	1.08766	+	1.88388i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	−2.20711	+	3.82282i	−0.432849	+	0.749717i
$27$	−0.414214			−0.0797154
$28$	−4.62132	−	8.00436i	−0.873347	−	1.51268i
$29$	1.17157			0.217556			0.108778	−	0.994066i	$-0.465306\pi$
$29$	1.17157			0.217556			0.108778	+	0.994066i	$0.465306\pi$
$30$	−5.82843			−1.06412
$31$		0			0
$31$		0			0
$32$	1.58579			0.280330
$33$	12.6569			2.20328
$34$	0.207107	+	0.358719i	0.0355185	+	0.0615199i
$35$	2.41421			0.408077
$36$	−5.41421	+	9.37769i	−0.902369	+	1.56295i
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	1.91421	+	3.31552i	0.310526	+	0.537848i
$39$	−4.41421			−0.706840
$40$	2.20711	−	3.82282i	0.348974	−	0.604441i
$41$	−4.74264	+	8.21449i	−0.740676	+	1.28289i	0.211512	+	0.977375i	$0.432161\pi$
$41$	−4.74264	+	8.21449i	−0.740676	+	1.28289i	−0.952188	+	0.305513i	$0.901172\pi$
$42$	7.03553	−	12.1859i	1.08561	−	1.88033i
$43$	4.44975	+	7.70719i	0.678580	+	1.17534i	0.975409	+	0.220404i	$0.0707377\pi$
$43$	4.44975	+	7.70719i	0.678580	+	1.17534i	−0.296828	+	0.954931i	$0.595929\pi$
$44$	−10.0355	+	17.3821i	−1.51291	+	2.62044i
$45$	−1.41421	−	2.44949i	−0.210819	−	0.365148i
$46$	−9.65685			−1.42383
$47$	−1.65685			−0.241677			−0.120839	−	0.992672i	$-0.538558\pi$
$47$	−1.65685			−0.241677			−0.120839	+	0.992672i	$0.538558\pi$
$48$	−3.62132	−	6.27231i	−0.522693	−	0.905330i
$49$	0.585786	−	1.01461i	0.0836838	−	0.144945i
$50$	−4.82843	−	8.36308i	−0.682843	−	1.18272i
$51$	−0.207107	+	0.358719i	−0.0290008	+	0.0502308i
$52$	3.50000	−	6.06218i	0.485363	−	0.840673i
$53$	0.0857864	−	0.148586i	0.0117837	−	0.0204099i	−0.860073	−	0.510170i	$-0.829582\pi$
$53$	0.0857864	−	0.148586i	0.0117837	−	0.0204099i	0.871857	+	0.489760i	$0.162916\pi$
$54$	1.00000			0.136083
$55$	−2.62132	−	4.54026i	−0.353459	−	0.612209i
$56$	5.32843	+	9.22911i	0.712041	+	1.23329i
$57$	−1.91421	+	3.31552i	−0.253544	+	0.439151i
$58$	−2.82843			−0.371391
$59$	5.03553	+	8.72180i	0.655571	+	1.13548i	0.981750	+	0.190174i	$0.0609052\pi$
$59$	5.03553	+	8.72180i	0.655571	+	1.13548i	−0.326180	+	0.945308i	$0.605761\pi$
$60$	9.24264			1.19322
$61$	−2.82843			−0.362143			−0.181071	−	0.983470i	$-0.557957\pi$
$61$	−2.82843			−0.362143			−0.181071	+	0.983470i	$0.557957\pi$
$62$		0			0
$63$	6.82843			0.860301
$64$	−9.82843			−1.22855
$65$	0.914214	+	1.58346i	0.113394	+	0.196405i
$66$	−30.5563			−3.76123
$67$	2.62132	−	4.54026i	0.320245	−	0.554681i	−0.660293	−	0.751008i	$-0.729568\pi$
$67$	2.62132	−	4.54026i	0.320245	−	0.554681i	0.980539	+	0.196327i	$0.0629013\pi$
$68$	−0.328427	−	0.568852i	−0.0398276	−	0.0689835i
$69$	−4.82843	−	8.36308i	−0.581274	−	1.00680i
$70$	−5.82843			−0.696630
$71$	7.03553	−	12.1859i	0.834964	−	1.44620i	−0.0590953	−	0.998252i	$-0.518822\pi$
$71$	7.03553	−	12.1859i	0.834964	−	1.44620i	0.894060	−	0.447948i	$-0.147845\pi$
$72$	6.24264	−	10.8126i	0.735702	−	1.27427i
$73$	1.91421	−	3.31552i	0.224042	−	0.388052i	−0.731990	−	0.681316i	$-0.761408\pi$
$73$	1.91421	−	3.31552i	0.224042	−	0.388052i	0.956032	+	0.293264i	$0.0947415\pi$
$74$	−1.20711	−	2.09077i	−0.140323	−	0.243047i
$75$	4.82843	−	8.36308i	0.557539	−	0.965685i
$76$	−3.03553	−	5.25770i	−0.348200	−	0.603099i
$77$	12.6569			1.44238
$78$	10.6569			1.20665
$79$	−7.62132	−	13.2005i	−0.857466	−	1.48517i	−0.874339	−	0.485316i	$-0.838704\pi$
$79$	−7.62132	−	13.2005i	−0.857466	−	1.48517i	0.0168732	−	0.999858i	$-0.494629\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$	4.74264	+	8.21449i	0.526960	+	0.912722i
$82$	11.4497	−	19.8315i	1.26441	−	2.19003i
$83$	2.03553	−	3.52565i	0.223429	−	0.386990i	−0.732418	−	0.680855i	$-0.761608\pi$
$83$	2.03553	−	3.52565i	0.223429	−	0.386990i	0.955847	+	0.293865i	$0.0949416\pi$
$84$	−11.1569	+	19.3242i	−1.21731	+	2.10845i
$85$	0.171573			0.0186097
$86$	−10.7426	−	18.6068i	−1.15841	−	2.00642i
$87$	−1.41421	−	2.44949i	−0.151620	−	0.262613i
$88$	11.5711	−	20.0417i	1.23348	−	2.13645i
$89$	12.4853			1.32344			0.661719	−	0.749752i	$-0.269827\pi$
$89$	12.4853			1.32344			0.661719	+	0.749752i	$0.269827\pi$
$90$	3.41421	+	5.91359i	0.359890	+	0.623347i
$91$	−4.41421			−0.462735
$92$	15.3137			1.59656
$93$		0			0
$94$	4.00000			0.412568
$95$	1.58579			0.162698
$96$	−1.91421	−	3.31552i	−0.195369	−	0.338388i
$97$	10.8284			1.09946			0.549730	−	0.835342i	$-0.314731\pi$
$97$	10.8284			1.09946			0.549730	+	0.835342i	$0.314731\pi$
$98$	−1.41421	+	2.44949i	−0.142857	+	0.247436i
$99$	−7.41421	−	12.8418i	−0.745157	−	1.29065i
$100$	7.65685	+	13.2621i	0.765685	+	1.32621i
$101$	8.48528			0.844317			0.422159	−	0.906522i	$-0.361273\pi$
$101$	8.48528			0.844317			0.422159	+	0.906522i	$0.361273\pi$
$102$	0.500000	−	0.866025i	0.0495074	−	0.0857493i
$103$	6.03553	−	10.4539i	0.594699	−	1.03005i	−0.398890	−	0.916999i	$-0.630605\pi$
$103$	6.03553	−	10.4539i	0.594699	−	1.03005i	0.993589	−	0.113050i	$-0.0360620\pi$
$104$	−4.03553	+	6.98975i	−0.395717	+	0.685401i
$105$	−2.91421	−	5.04757i	−0.284398	−	0.492592i
$106$	−0.207107	+	0.358719i	−0.0201160	+	0.0348419i
$107$	−4.79289	−	8.30153i	−0.463346	−	0.802540i	0.535779	−	0.844358i	$-0.320018\pi$
$107$	−4.79289	−	8.30153i	−0.463346	−	0.802540i	−0.999125	+	0.0418188i	$0.986685\pi$
$108$	−1.58579			−0.152592
$109$	−5.17157			−0.495347			−0.247673	−	0.968844i	$-0.579666\pi$
$109$	−5.17157			−0.495347			−0.247673	+	0.968844i	$0.579666\pi$
$110$	6.32843	+	10.9612i	0.603392	+	1.04511i
$111$	1.20711	−	2.09077i	0.114574	−	0.198447i
$112$	−3.62132	−	6.27231i	−0.342183	−	0.592678i
$113$	−2.67157	+	4.62730i	−0.251320	+	0.435300i	−0.963890	−	0.266302i	$-0.914198\pi$
$113$	−2.67157	+	4.62730i	−0.251320	+	0.435300i	0.712569	+	0.701602i	$0.247531\pi$
$114$	4.62132	−	8.00436i	0.432826	−	0.749677i
$115$	−2.00000	+	3.46410i	−0.186501	+	0.323029i
$116$	4.48528			0.416448
$117$	2.58579	+	4.47871i	0.239056	+	0.414057i
$118$	−12.1569	−	21.0563i	−1.11913	−	1.93839i
$119$	−0.207107	+	0.358719i	−0.0189854	+	0.0328838i
$120$	−10.6569			−0.972833
$121$	−8.24264	−	14.2767i	−0.749331	−	1.29788i
$122$	6.82843			0.618217
$123$	22.8995			2.06478
$124$		0			0
$125$	−9.00000			−0.804984
$126$	−16.4853			−1.46863
$127$	−5.44975	−	9.43924i	−0.483587	−	0.837597i	0.516235	−	0.856447i	$-0.327333\pi$
$127$	−5.44975	−	9.43924i	−0.483587	−	0.837597i	−0.999822	+	0.0188496i	$0.994000\pi$
$128$	20.5563			1.81694
$129$	10.7426	−	18.6068i	0.945837	−	1.63824i
$130$	−2.20711	−	3.82282i	−0.193576	−	0.335284i
$131$	2.37868	+	4.11999i	0.207826	+	0.359966i	0.951030	−	0.309100i	$-0.100028\pi$
$131$	2.37868	+	4.11999i	0.207826	+	0.359966i	−0.743203	+	0.669066i	$0.766694\pi$
$132$	48.4558			4.21754
$133$	−1.91421	+	3.31552i	−0.165983	+	0.287492i
$134$	−6.32843	+	10.9612i	−0.546693	+	0.946900i
$135$	0.207107	−	0.358719i	0.0178249	−	0.0308737i
$136$	0.378680	+	0.655892i	0.0324715	+	0.0562423i
$137$	−3.74264	+	6.48244i	−0.319755	+	0.553833i	−0.980437	−	0.196834i	$-0.936934\pi$
$137$	−3.74264	+	6.48244i	−0.319755	+	0.553833i	0.660681	+	0.750666i	$0.270267\pi$
$138$	11.6569	+	20.1903i	0.992297	+	1.71871i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	9.24264			0.781146
$141$	2.00000	+	3.46410i	0.168430	+	0.291730i
$142$	−16.9853	+	29.4194i	−1.42537	+	2.46882i
$143$	4.79289	+	8.30153i	0.400802	+	0.694209i
$144$	−4.24264	+	7.34847i	−0.353553	+	0.612372i
$145$	−0.585786	+	1.01461i	−0.0486469	+	0.0842589i
$146$	−4.62132	+	8.00436i	−0.382463	+	0.662446i
$147$	−2.82843			−0.233285
$148$	1.91421	+	3.31552i	0.157347	+	0.272534i
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	0.844818	−	0.535054i	$-0.179709\pi$
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	−0.885779	+	0.464107i	$0.846375\pi$
$150$	−11.6569	+	20.1903i	−0.951778	+	1.64853i
$151$	17.3137			1.40897			0.704485	−	0.709719i	$-0.251178\pi$
$151$	17.3137			1.40897			0.704485	+	0.709719i	$0.251178\pi$
$152$	3.50000	+	6.06218i	0.283887	+	0.491708i
$153$	0.485281			0.0392327
$154$	−30.5563			−2.46230
$155$		0			0
$156$	−16.8995			−1.35304
$157$	14.8284			1.18344			0.591719	−	0.806145i	$-0.298450\pi$
$157$	14.8284			1.18344			0.591719	+	0.806145i	$0.298450\pi$
$158$	18.3995	+	31.8689i	1.46379	+	2.53535i
$159$	−0.414214			−0.0328493
$160$	−0.792893	+	1.37333i	−0.0626837	+	0.108571i
$161$	−4.82843	−	8.36308i	−0.380533	−	0.659103i
$162$	−11.4497	−	19.8315i	−0.899577	−	1.55811i
$163$	−12.9706			−1.01593			−0.507966	−	0.861377i	$-0.669603\pi$
$163$	−12.9706			−1.01593			−0.507966	+	0.861377i	$0.669603\pi$
$164$	−18.1569	+	31.4486i	−1.41781	+	2.45572i
$165$	−6.32843	+	10.9612i	−0.492667	+	0.853325i
$166$	−4.91421	+	8.51167i	−0.381417	+	0.660634i
$167$	−4.27817	−	7.41002i	−0.331055	−	0.573404i	0.651664	−	0.758508i	$-0.274071\pi$
$167$	−4.27817	−	7.41002i	−0.331055	−	0.573404i	−0.982719	+	0.185104i	$0.940738\pi$
$168$	12.8640	−	22.2810i	0.992476	−	1.71902i
$169$	4.82843	+	8.36308i	0.371417	+	0.643314i
$170$	−0.414214			−0.0317687
$171$	4.48528			0.342998
$172$	17.0355	+	29.5064i	1.29895	+	2.24984i
$173$	7.15685	−	12.3960i	0.544126	−	0.942453i	−0.454536	−	0.890728i	$-0.650195\pi$
$173$	7.15685	−	12.3960i	0.544126	−	0.942453i	0.998661	−	0.0517246i	$-0.0164718\pi$
$174$	3.41421	+	5.91359i	0.258831	+	0.448308i
$175$	4.82843	−	8.36308i	0.364995	−	0.632190i
$176$	−7.86396	+	13.6208i	−0.592768	+	1.02670i
$177$	12.1569	−	21.0563i	0.913765	−	1.58269i
$178$	−30.1421			−2.25925
$179$	−3.37868	−	5.85204i	−0.252534	−	0.437402i	0.711689	−	0.702495i	$-0.247931\pi$
$179$	−3.37868	−	5.85204i	−0.252534	−	0.437402i	−0.964223	+	0.265093i	$0.914597\pi$
$180$	−5.41421	−	9.37769i	−0.403552	−	0.698972i
$181$	−5.15685	+	8.93193i	−0.383306	+	0.663905i	−0.991533	−	0.129858i	$-0.958548\pi$
$181$	−5.15685	+	8.93193i	−0.383306	+	0.663905i	0.608227	+	0.793763i	$0.291881\pi$
$182$	10.6569			0.789939
$183$	3.41421	+	5.91359i	0.252386	+	0.437145i
$184$	−17.6569			−1.30168
$185$	−1.00000			−0.0735215
$186$		0			0
$187$	0.899495			0.0657776
$188$	−6.34315			−0.462621
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$	−3.82843			−0.277743
$191$	0.550253	−	0.953065i	0.0398149	−	0.0689614i	−0.845431	−	0.534084i	$-0.820657\pi$
$191$	0.550253	−	0.953065i	0.0398149	−	0.0689614i	0.885246	+	0.465123i	$0.153990\pi$
$192$	11.8640	+	20.5490i	0.856208	+	1.48300i
$193$	10.5711	+	18.3096i	0.760922	+	1.31796i	0.942376	+	0.334556i	$0.108586\pi$
$193$	10.5711	+	18.3096i	0.760922	+	1.31796i	−0.181454	+	0.983399i	$0.558080\pi$
$194$	−26.1421			−1.87690
$195$	2.20711	−	3.82282i	0.158054	−	0.273758i
$196$	2.24264	−	3.88437i	0.160189	−	0.277455i
$197$	1.74264	−	3.01834i	0.124158	−	0.215048i	−0.797245	−	0.603655i	$-0.793710\pi$
$197$	1.74264	−	3.01834i	0.124158	−	0.215048i	0.921404	+	0.388607i	$0.127044\pi$
$198$	17.8995	+	31.0028i	1.27206	+	2.20328i
$199$	7.79289	−	13.4977i	0.552424	−	0.956826i	−0.445675	−	0.895195i	$-0.647036\pi$
$199$	7.79289	−	13.4977i	0.552424	−	0.956826i	0.998099	−	0.0616310i	$-0.0196302\pi$
$200$	−8.82843	−	15.2913i	−0.624264	−	1.08126i
$201$	−12.6569			−0.892746
$202$	−20.4853			−1.44134
$203$	−1.41421	−	2.44949i	−0.0992583	−	0.171920i
$204$	−0.792893	+	1.37333i	−0.0555136	+	0.0961524i
$205$	−4.74264	−	8.21449i	−0.331240	−	0.573725i
$206$	−14.5711	+	25.2378i	−1.01521	+	1.75840i
$207$	−5.65685	+	9.79796i	−0.393179	+	0.681005i
$208$	2.74264	−	4.75039i	0.190168	−	0.329380i
$209$	8.31371			0.575071
$210$	7.03553	+	12.1859i	0.485498	+	0.840907i
$211$	−3.79289	−	6.56948i	−0.261114	−	0.452262i	0.705425	−	0.708785i	$-0.250756\pi$
$211$	−3.79289	−	6.56948i	−0.261114	−	0.452262i	−0.966538	+	0.256523i	$0.917423\pi$
$212$	0.328427	−	0.568852i	0.0225565	−	0.0390689i
$213$	−33.9706			−2.32762
$214$	11.5711	+	20.0417i	0.790982	+	1.37002i
$215$	−8.89949			−0.606941
$216$	1.82843			0.124409
$217$		0			0
$218$	12.4853			0.845610
$219$	−9.24264			−0.624560
$220$	−10.0355	−	17.3821i	−0.676596	−	1.17190i
$221$	−0.313708			−0.0211023
$222$	−2.91421	+	5.04757i	−0.195589	+	0.338770i
$223$	0.863961	+	1.49642i	0.0578551	+	0.100208i	0.893502	−	0.449059i	$-0.148241\pi$
$223$	0.863961	+	1.49642i	0.0578551	+	0.100208i	−0.835647	+	0.549266i	$0.814907\pi$
$224$	−1.91421	−	3.31552i	−0.127899	−	0.221527i
$225$	−11.3137			−0.754247
$226$	6.44975	−	11.1713i	0.429031	−	0.743103i
$227$	7.79289	−	13.4977i	0.517232	−	0.895873i	−0.482567	−	0.875859i	$-0.660296\pi$
$227$	7.79289	−	13.4977i	0.517232	−	0.895873i	0.999800	−	0.0200140i	$-0.00637108\pi$
$228$	−7.32843	+	12.6932i	−0.485337	+	0.840628i
$229$	5.74264	+	9.94655i	0.379484	+	0.657286i	0.990987	−	0.133956i	$-0.0427681\pi$
$229$	5.74264	+	9.94655i	0.379484	+	0.657286i	−0.611503	+	0.791242i	$0.709435\pi$
$230$	4.82843	−	8.36308i	0.318377	−	0.551445i
$231$	−15.2782	−	26.4626i	−1.00523	−	1.74111i
$232$	−5.17157			−0.339530
$233$	−14.8284			−0.971443			−0.485721	−	0.874114i	$-0.661443\pi$
$233$	−14.8284			−0.971443			−0.485721	+	0.874114i	$0.661443\pi$
$234$	−6.24264	−	10.8126i	−0.408094	−	0.706840i
$235$	0.828427	−	1.43488i	0.0540406	−	0.0936011i
$236$	19.2782	+	33.3908i	1.25490	+	2.17355i
$237$	−18.3995	+	31.8689i	−1.19518	+	2.07010i
$238$	0.500000	−	0.866025i	0.0324102	−	0.0561361i
$239$	−6.37868	+	11.0482i	−0.412602	+	0.714648i	−0.995173	−	0.0981314i	$-0.968713\pi$
$239$	−6.37868	+	11.0482i	−0.412602	+	0.714648i	0.582571	+	0.812780i	$0.302047\pi$
$240$	7.24264			0.467510
$241$	12.3284	+	21.3535i	0.794144	+	1.37550i	0.923381	+	0.383884i	$0.125414\pi$
$241$	12.3284	+	21.3535i	0.794144	+	1.37550i	−0.129238	+	0.991614i	$0.541253\pi$
$242$	19.8995	+	34.4669i	1.27919	+	2.21562i
$243$	10.8284	−	18.7554i	0.694644	−	1.20316i
$244$	−10.8284			−0.693219
$245$	0.585786	+	1.01461i	0.0374245	+	0.0648212i
$246$	−55.2843			−3.52480
$247$	−2.89949			−0.184490
$248$		0			0
$249$	−9.82843			−0.622851
$250$	21.7279			1.37419
$251$	1.79289	+	3.10538i	0.113166	+	0.196010i	0.917045	−	0.398783i	$-0.130567\pi$
$251$	1.79289	+	3.10538i	0.113166	+	0.196010i	−0.803879	+	0.594793i	$0.797234\pi$
$252$	26.1421			1.64680
$253$	−10.4853	+	18.1610i	−0.659204	+	1.14177i
$254$	13.1569	+	22.7883i	0.825534	+	1.42987i
$255$	−0.207107	−	0.358719i	−0.0129695	−	0.0224639i
$256$	−29.9706			−1.87316
$257$	0.156854	−	0.271680i	0.00978430	−	0.0169469i	−0.861092	−	0.508450i	$-0.830219\pi$
$257$	0.156854	−	0.271680i	0.00978430	−	0.0169469i	0.870876	+	0.491503i	$0.163552\pi$
$258$	−25.9350	+	44.9208i	−1.61464	+	2.79665i
$259$	1.20711	−	2.09077i	0.0750060	−	0.129914i
$260$	3.50000	+	6.06218i	0.217061	+	0.375960i
$261$	−1.65685	+	2.86976i	−0.102557	+	0.177633i
$262$	−5.74264	−	9.94655i	−0.354782	−	0.614500i
$263$	0.686292			0.0423185			0.0211593	−	0.999776i	$-0.493264\pi$
$263$	0.686292			0.0423185			0.0211593	+	0.999776i	$0.493264\pi$
$264$	−55.8701			−3.43856
$265$	0.0857864	+	0.148586i	0.00526982	+	0.00912759i
$266$	4.62132	−	8.00436i	0.283351	−	0.490779i
$267$	−15.0711	−	26.1039i	−0.922334	−	1.59753i
$268$	10.0355	−	17.3821i	0.613018	−	1.06178i
$269$	−15.9142	+	27.5642i	−0.970307	+	1.68062i	−0.275681	+	0.961249i	$0.588903\pi$
$269$	−15.9142	+	27.5642i	−0.970307	+	1.68062i	−0.694626	+	0.719371i	$0.744430\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	23.3137			1.41621			0.708103	−	0.706109i	$-0.249551\pi$
$271$	23.3137			1.41621			0.708103	+	0.706109i	$0.249551\pi$
$272$	−0.257359	−	0.445759i	−0.0156047	−	0.0270281i
$273$	5.32843	+	9.22911i	0.322491	+	0.558571i
$274$	9.03553	−	15.6500i	0.545857	−	0.945451i
$275$	−20.9706			−1.26457
$276$	−18.4853	−	32.0174i	−1.11268	−	1.92722i
$277$	14.1421			0.849719			0.424859	−	0.905259i	$-0.360324\pi$
$277$	14.1421			0.849719			0.424859	+	0.905259i	$0.360324\pi$
$278$		0			0
$279$		0			0
$280$	−10.6569			−0.636869
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$	−4.82843	−	8.36308i	−0.287529	−	0.498014i
$283$	−2.34315			−0.139286			−0.0696428	−	0.997572i	$-0.522186\pi$
$283$	−2.34315			−0.139286			−0.0696428	+	0.997572i	$0.522186\pi$
$284$	26.9350	−	46.6528i	1.59830	−	2.76834i
$285$	−1.91421	−	3.31552i	−0.113388	−	0.196394i
$286$	−11.5711	−	20.0417i	−0.684212	−	1.18509i
$287$	22.8995			1.35171
$288$	−2.24264	+	3.88437i	−0.132149	+	0.228889i
$289$	8.48528	−	14.6969i	0.499134	−	0.864526i
$290$	1.41421	−	2.44949i	0.0830455	−	0.143839i
$291$	−13.0711	−	22.6398i	−0.766240	−	1.32717i
$292$	7.32843	−	12.6932i	0.428864	−	0.742814i
$293$	12.3995	+	21.4766i	0.724386	+	1.25467i	0.959226	+	0.282640i	$0.0912101\pi$
$293$	12.3995	+	21.4766i	0.724386	+	1.25467i	−0.234840	+	0.972034i	$0.575457\pi$
$294$	6.82843			0.398242
$295$	−10.0711			−0.586360
$296$	−2.20711	−	3.82282i	−0.128285	−	0.222197i
$297$	1.08579	−	1.88064i	0.0630037	−	0.109126i
$298$	1.20711	+	2.09077i	0.0699258	+	0.121115i
$299$	3.65685	−	6.33386i	0.211481	−	0.366296i
$300$	18.4853	−	32.0174i	1.06725	−	1.84853i
$301$	10.7426	−	18.6068i	0.619196	−	1.07248i
$302$	−41.7990			−2.40526
$303$	−10.2426	−	17.7408i	−0.588424	−	1.01918i
$304$	−2.37868	−	4.11999i	−0.136427	−	0.236298i
$305$	1.41421	−	2.44949i	0.0809776	−	0.140257i
$306$	−1.17157			−0.0669744
$307$	1.37868	+	2.38794i	0.0786854	+	0.136287i	0.902683	−	0.430306i	$-0.141594\pi$
$307$	1.37868	+	2.38794i	0.0786854	+	0.136287i	−0.823998	+	0.566593i	$0.808261\pi$
$308$	48.4558			2.76103
$309$	−29.1421			−1.65784
$310$		0			0
$311$	−11.3137			−0.641542			−0.320771	−	0.947157i	$-0.603942\pi$
$311$	−11.3137			−0.641542			−0.320771	+	0.947157i	$0.603942\pi$
$312$	19.4853			1.10314
$313$	1.91421	+	3.31552i	0.108198	+	0.187404i	0.915040	−	0.403363i	$-0.132159\pi$
$313$	1.91421	+	3.31552i	0.108198	+	0.187404i	−0.806842	+	0.590767i	$0.798825\pi$
$314$	−35.7990			−2.02025
$315$	−3.41421	+	5.91359i	−0.192369	+	0.333193i
$316$	−29.1777	−	50.5372i	−1.64137	−	2.84294i
$317$	1.08579	+	1.88064i	0.0609838	+	0.105627i	0.894905	−	0.446256i	$-0.147243\pi$
$317$	1.08579	+	1.88064i	0.0609838	+	0.105627i	−0.833922	+	0.551883i	$0.813910\pi$
$318$	1.00000			0.0560772
$319$	−3.07107	+	5.31925i	−0.171947	+	0.297821i
$320$	4.91421	−	8.51167i	0.274713	−	0.475817i
$321$	−11.5711	+	20.0417i	−0.645834	+	1.11862i
$322$	11.6569	+	20.1903i	0.649611	+	1.12516i
$323$	−0.136039	+	0.235626i	−0.00756941	+	0.0131106i
$324$	18.1569	+	31.4486i	1.00871	+	1.74714i
$325$	7.31371			0.405692
$326$	31.3137			1.73431
$327$	6.24264	+	10.8126i	0.345219	+	0.597937i
$328$	20.9350	−	36.2605i	1.15594	−	2.00215i
$329$	2.00000	+	3.46410i	0.110264	+	0.190982i
$330$	15.2782	−	26.4626i	0.841036	−	1.45672i
$331$	0.378680	−	0.655892i	0.0208141	−	0.0360511i	−0.855431	−	0.517917i	$-0.826708\pi$
$331$	0.378680	−	0.655892i	0.0208141	−	0.0360511i	0.876245	+	0.481866i	$0.160041\pi$
$332$	7.79289	−	13.4977i	0.427691	−	0.740782i
$333$	−2.82843			−0.154997
$334$	10.3284	+	17.8894i	0.565146	+	0.978862i
$335$	2.62132	+	4.54026i	0.143218	+	0.248061i
$336$	−8.74264	+	15.1427i	−0.476950	+	0.826102i
$337$	13.3137			0.725244			0.362622	−	0.931936i	$-0.381882\pi$
$337$	13.3137			0.725244			0.362622	+	0.931936i	$0.381882\pi$
$338$	−11.6569	−	20.1903i	−0.634049	−	1.09821i
$339$	12.8995			0.700604
$340$	0.656854			0.0356229
$341$		0			0
$342$	−10.8284			−0.585534
$343$	−19.7279			−1.06521
$344$	−19.6421	−	34.0212i	−1.05903	−	1.83430i
$345$	9.65685			0.519908
$346$	−17.2782	+	29.9267i	−0.928880	+	1.60887i
$347$	11.2782	+	19.5344i	0.605444	+	1.04866i	0.991981	+	0.126386i	$0.0403378\pi$
$347$	11.2782	+	19.5344i	0.605444	+	1.04866i	−0.386537	+	0.922274i	$0.626329\pi$
$348$	−5.41421	−	9.37769i	−0.290232	−	0.502697i
$349$	35.1127			1.87954			0.939770	−	0.341808i	$-0.111039\pi$
$349$	35.1127			1.87954			0.939770	+	0.341808i	$0.111039\pi$
$350$	−11.6569	+	20.1903i	−0.623085	+	1.07921i
$351$	−0.378680	+	0.655892i	−0.0202124	+	0.0350089i
$352$	−4.15685	+	7.19988i	−0.221561	+	0.383755i
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	0.903179	−	0.429263i	$-0.141227\pi$
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	−0.823343	+	0.567545i	$0.807893\pi$
$354$	−29.3492	+	50.8344i	−1.55989	+	2.70182i
$355$	7.03553	+	12.1859i	0.373407	+	0.646761i
$356$	47.7990			2.53334
$357$	1.00000			0.0529256
$358$	8.15685	+	14.1281i	0.431103	+	0.746693i
$359$	−13.4497	+	23.2956i	−0.709851	+	1.22950i	0.255062	+	0.966925i	$0.417904\pi$
$359$	−13.4497	+	23.2956i	−0.709851	+	1.22950i	−0.964912	+	0.262572i	$0.915429\pi$
$360$	6.24264	+	10.8126i	0.329016	+	0.569873i
$361$	8.24264	−	14.2767i	0.433823	−	0.751404i
$362$	12.4497	−	21.5636i	0.654344	−	1.13336i
$363$	−19.8995	+	34.4669i	−1.04445	+	1.80904i
$364$	−16.8995			−0.885774
$365$	1.91421	+	3.31552i	0.100195	+	0.173542i
$366$	−8.24264	−	14.2767i	−0.430850	−	0.746254i
$367$	9.10660	−	15.7731i	0.475361	−	0.823349i	−0.524241	−	0.851570i	$-0.675651\pi$
$367$	9.10660	−	15.7731i	0.475361	−	0.823349i	0.999602	+	0.0282210i	$0.00898422\pi$
$368$	12.0000			0.625543
$369$	−13.4142	−	23.2341i	−0.698316	−	1.20952i
$370$	2.41421			0.125509
$371$	−0.414214			−0.0215049
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	−2.17157			−0.112289
$375$	10.8640	+	18.8169i	0.561013	+	0.971702i
$376$	7.31371			0.377176
$377$	1.07107	−	1.85514i	0.0551628	−	0.0955448i
$378$	−1.20711	−	2.09077i	−0.0620869	−	0.107538i
$379$	14.6924	+	25.4480i	0.754697	+	1.30717i	0.945525	+	0.325550i	$0.105550\pi$
$379$	14.6924	+	25.4480i	0.754697	+	1.30717i	−0.190827	+	0.981624i	$0.561117\pi$
$380$	6.07107			0.311439
$381$	−13.1569	+	22.7883i	−0.674046	+	1.16748i
$382$	−1.32843	+	2.30090i	−0.0679682	+	0.117724i
$383$	12.4497	−	21.5636i	0.636152	−	1.10185i	−0.350117	−	0.936706i	$-0.613858\pi$
$383$	12.4497	−	21.5636i	0.636152	−	1.10185i	0.986270	−	0.165142i	$-0.0528084\pi$
$384$	−24.8137	−	42.9786i	−1.26627	−	2.19324i
$385$	−6.32843	+	10.9612i	−0.322527	+	0.558632i
$386$	−25.5208	−	44.2033i	−1.29898	−	2.24989i
$387$	−25.1716			−1.27954
$388$	41.4558			2.10460
$389$	8.57107	+	14.8455i	0.434570	+	0.752698i	0.997260	−	0.0739699i	$-0.0235669\pi$
$389$	8.57107	+	14.8455i	0.434570	+	0.752698i	−0.562690	+	0.826668i	$0.690234\pi$
$390$	−5.32843	+	9.22911i	−0.269815	+	0.467334i
$391$	−0.343146	−	0.594346i	−0.0173536	−	0.0300574i
$392$	−2.58579	+	4.47871i	−0.130602	+	0.226209i
$393$	5.74264	−	9.94655i	0.289678	−	0.501737i
$394$	−4.20711	+	7.28692i	−0.211951	+	0.367110i
$395$	15.2426			0.766940
$396$	−28.3848	−	49.1639i	−1.42639	−	2.47058i
$397$	8.25736	+	14.3022i	0.414425	+	0.717805i	0.995368	−	0.0961392i	$-0.0306494\pi$
$397$	8.25736	+	14.3022i	0.414425	+	0.717805i	−0.580943	+	0.813944i	$0.697316\pi$
$398$	−18.8137	+	32.5863i	−0.943046	+	1.63340i
$399$	9.24264			0.462711
$400$	6.00000	+	10.3923i	0.300000	+	0.519615i
$401$	21.1716			1.05726			0.528629	−	0.848853i	$-0.322706\pi$
$401$	21.1716			1.05726			0.528629	+	0.848853i	$0.322706\pi$
$402$	30.5563			1.52401
$403$		0			0
$404$	32.4853			1.61620
$405$	−9.48528			−0.471327
$406$	3.41421	+	5.91359i	0.169445	+	0.293487i
$407$	−5.24264			−0.259868
$408$	0.914214	−	1.58346i	0.0452603	−	0.0783932i
$409$	4.67157	+	8.09140i	0.230994	+	0.400094i	0.958101	−	0.286431i	$-0.0924688\pi$
$409$	4.67157	+	8.09140i	0.230994	+	0.400094i	−0.727107	+	0.686525i	$0.759135\pi$
$410$	11.4497	+	19.8315i	0.565463	+	0.979410i
$411$	18.0711			0.891380
$412$	23.1066	−	40.0218i	1.13838	−	1.97173i
$413$	12.1569	−	21.0563i	0.598200	−	1.03611i
$414$	13.6569	−	23.6544i	0.671198	−	1.16255i
$415$	2.03553	+	3.52565i	0.0999204	+	0.173067i
$416$	1.44975	−	2.51104i	0.0710797	−	0.123114i
$417$		0			0
$418$	−20.0711			−0.981708
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$	−11.1569	−	19.3242i	−0.544399	−	0.942926i
$421$	1.42893	−	2.47498i	0.0696419	−	0.120623i	−0.829102	−	0.559098i	$-0.811148\pi$
$421$	1.42893	−	2.47498i	0.0696419	−	0.120623i	0.898744	+	0.438474i	$0.144481\pi$
$422$	9.15685	+	15.8601i	0.445749	+	0.772059i
$423$	2.34315	−	4.05845i	0.113928	−	0.197328i
$424$	−0.378680	+	0.655892i	−0.0183903	+	0.0318530i
$425$	0.343146	−	0.594346i	0.0166450	−	0.0288300i
$426$	82.0122			3.97350
$427$	3.41421	+	5.91359i	0.165225	+	0.286179i
$428$	−18.3492	−	31.7818i	−0.886944	−	1.53623i
$429$	11.5711	−	20.0417i	0.558656	−	0.967621i
$430$	21.4853			1.03611
$431$	12.6213	+	21.8608i	0.607948	+	1.05300i	0.991578	+	0.129510i	$0.0413403\pi$
$431$	12.6213	+	21.8608i	0.607948	+	1.05300i	−0.383631	+	0.923487i	$0.625326\pi$
$432$	−1.24264			−0.0597866
$433$	35.1127			1.68741			0.843704	−	0.536808i	$-0.180370\pi$
$433$	35.1127			1.68741			0.843704	+	0.536808i	$0.180370\pi$
$434$		0			0
$435$	2.82843			0.135613
$436$	−19.7990			−0.948200
$437$	−3.17157	−	5.49333i	−0.151717	−	0.262781i
$438$	22.3137			1.06619
$439$	6.03553	−	10.4539i	0.288060	−	0.498935i	−0.685286	−	0.728274i	$-0.740323\pi$
$439$	6.03553	−	10.4539i	0.288060	−	0.498935i	0.973347	+	0.229339i	$0.0736563\pi$
$440$	11.5711	+	20.0417i	0.551629	+	0.955449i
$441$	1.65685	+	2.86976i	0.0788978	+	0.136655i
$442$	0.757359			0.0360239
$443$	6.62132	−	11.4685i	0.314588	−	0.544883i	−0.664761	−	0.747056i	$-0.731467\pi$
$443$	6.62132	−	11.4685i	0.314588	−	0.544883i	0.979350	+	0.202173i	$0.0648002\pi$
$444$	4.62132	−	8.00436i	0.219318	−	0.379870i
$445$	−6.24264	+	10.8126i	−0.295930	+	0.512565i
$446$	−2.08579	−	3.61269i	−0.0987649	−	0.171066i
$447$	−1.20711	+	2.09077i	−0.0570942	+	0.0988900i
$448$	11.8640	+	20.5490i	0.560519	+	0.970848i
$449$	−4.62742			−0.218381			−0.109191	−	0.994021i	$-0.534826\pi$
$449$	−4.62742			−0.218381			−0.109191	+	0.994021i	$0.534826\pi$
$450$	27.3137			1.28758
$451$	−24.8640	−	43.0656i	−1.17080	−	2.02788i
$452$	−10.2279	+	17.7153i	−0.481081	+	0.833257i
$453$	−20.8995	−	36.1990i	−0.981944	−	1.70078i
$454$	−18.8137	+	32.5863i	−0.882971	+	1.52935i
$455$	2.20711	−	3.82282i	0.103471	−	0.179217i
$456$	8.44975	−	14.6354i	0.395696	−	0.685365i
$457$	−31.1127			−1.45539			−0.727695	−	0.685901i	$-0.759409\pi$
$457$	−31.1127			−1.45539			−0.727695	+	0.685901i	$0.759409\pi$
$458$	−13.8640	−	24.0131i	−0.647820	−	1.12206i
$459$	0.0355339	+	0.0615465i	0.00165858	+	0.00287275i
$460$	−7.65685	+	13.2621i	−0.357003	+	0.618347i
$461$	−26.1421			−1.21756			−0.608780	−	0.793339i	$-0.708341\pi$
$461$	−26.1421			−1.21756			−0.608780	+	0.793339i	$0.708341\pi$
$462$	36.8848	+	63.8863i	1.71604	+	2.97226i
$463$	−24.9706			−1.16048			−0.580240	−	0.814445i	$-0.697041\pi$
$463$	−24.9706			−1.16048			−0.580240	+	0.814445i	$0.697041\pi$
$464$	3.51472			0.163167
$465$		0			0
$466$	35.7990			1.65836
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$	9.89949	+	17.1464i	0.457604	+	0.792594i
$469$	−12.6569			−0.584439
$470$	−2.00000	+	3.46410i	−0.0922531	+	0.159787i
$471$	−17.8995	−	31.0028i	−0.824765	−	1.42854i
$472$	−22.2279	−	38.4999i	−1.02312	−	1.77210i
$473$	−46.6569			−2.14528
$474$	44.4203	−	76.9382i	2.04029	−	3.53389i
$475$	3.17157	−	5.49333i	0.145522	−	0.252051i
$476$	−0.792893	+	1.37333i	−0.0363422	+	0.0629465i
$477$	0.242641	+	0.420266i	0.0111098	+	0.0192427i
$478$	15.3995	−	26.6727i	0.704357	−	1.21998i
$479$	−4.86396	−	8.42463i	−0.222240	−	0.384931i	0.733248	−	0.679962i	$-0.238004\pi$
$479$	−4.86396	−	8.42463i	−0.222240	−	0.384931i	−0.955488	+	0.295030i	$0.904670\pi$
$480$	3.82843			0.174743
$481$	1.82843			0.0833691
$482$	−29.7635	−	51.5518i	−1.35569	−	2.34812i
$483$	−11.6569	+	20.1903i	−0.530405	+	0.918689i
$484$	−31.5563	−	54.6572i	−1.43438	−	2.48442i
$485$	−5.41421	+	9.37769i	−0.245847	+	0.425819i
$486$	−26.1421	+	45.2795i	−1.18583	+	2.05392i
$487$	−8.69239	+	15.0557i	−0.393890	+	0.682237i	−0.992959	−	0.118460i	$-0.962204\pi$
$487$	−8.69239	+	15.0557i	−0.393890	+	0.682237i	0.599069	+	0.800697i	$0.295537\pi$
$488$	12.4853			0.565182
$489$	15.6569	+	27.1185i	0.708027	+	1.22634i
$490$	−1.41421	−	2.44949i	−0.0638877	−	0.110657i
$491$	2.20711	−	3.82282i	0.0996053	−	0.172522i	−0.811916	−	0.583774i	$-0.801575\pi$
$491$	2.20711	−	3.82282i	0.0996053	−	0.172522i	0.911521	+	0.411253i	$0.134909\pi$
$492$	87.6690			3.95243
$493$	−0.100505	−	0.174080i	−0.00452652	−	0.00784016i
$494$	7.00000			0.314945
$495$	14.8284			0.666488
$496$		0			0
$497$	−33.9706			−1.52379
$498$	23.7279			1.06327
$499$	20.1066	+	34.8257i	0.900095	+	1.55901i	0.827369	+	0.561659i	$0.189837\pi$
$499$	20.1066	+	34.8257i	0.900095	+	1.55901i	0.0727259	+	0.997352i	$0.476830\pi$
$500$	−34.4558			−1.54091
$501$	−10.3284	+	17.8894i	−0.461440	+	0.799238i
$502$	−4.32843	−	7.49706i	−0.193187	−	0.334610i
$503$	−11.6924	−	20.2518i	−0.521338	−	0.902984i	−0.999692	−	0.0248166i	$-0.992100\pi$
$503$	−11.6924	−	20.2518i	−0.521338	−	0.902984i	0.478354	−	0.878167i	$-0.341234\pi$
$504$	−30.1421			−1.34264
$505$	−4.24264	+	7.34847i	−0.188795	+	0.327003i
$506$	25.3137	−	43.8446i	1.12533	−	1.94913i
$507$	11.6569	−	20.1903i	0.517699	−	0.896681i
$508$	−20.8640	−	36.1374i	−0.925689	−	1.60334i
$509$	3.39949	−	5.88810i	0.150680	−	0.260985i	−0.780798	−	0.624784i	$-0.785187\pi$
$509$	3.39949	−	5.88810i	0.150680	−	0.260985i	0.931478	+	0.363799i	$0.118520\pi$
$510$	0.500000	+	0.866025i	0.0221404	+	0.0383482i
$511$	−9.24264			−0.408870
$512$	31.2426			1.38074
$513$	0.328427	+	0.568852i	0.0145004	+	0.0251154i
$514$	−0.378680	+	0.655892i	−0.0167028	+	0.0289302i
$515$	6.03553	+	10.4539i	0.265957	+	0.460652i
$516$	41.1274	−	71.2348i	1.81053	−	3.13594i
$517$	4.34315	−	7.52255i	0.191011	−	0.330841i
$518$	−2.91421	+	5.04757i	−0.128043	+	0.221777i
$519$	−34.5563			−1.51686
$520$	−4.03553	−	6.98975i	−0.176970	−	0.306521i
$521$	−15.2279	−	26.3755i	−0.667147	−	1.15553i	−0.978698	−	0.205304i	$-0.934182\pi$
$521$	−15.2279	−	26.3755i	−0.667147	−	1.15553i	0.311551	−	0.950229i	$-0.399152\pi$
$522$	4.00000	−	6.92820i	0.175075	−	0.303239i
$523$	8.00000			0.349816			0.174908	−	0.984585i	$-0.444037\pi$
$523$	8.00000			0.349816			0.174908	+	0.984585i	$0.444037\pi$
$524$	9.10660	+	15.7731i	0.397824	+	0.689051i
$525$	−23.3137			−1.01749
$526$	−1.65685			−0.0722423
$527$		0			0
$528$	37.9706			1.65246
$529$	−7.00000			−0.304348
$530$	−0.207107	−	0.358719i	−0.00899614	−	0.0155818i
$531$	−28.4853			−1.23616
$532$	−7.32843	+	12.6932i	−0.317728	+	0.550320i
$533$	8.67157	+	15.0196i	0.375608	+	0.650571i
$534$	36.3848	+	63.0203i	1.57452	+	2.72715i
$535$	9.58579			0.414430
$536$	−11.5711	+	20.0417i	−0.499794	+	0.865669i
$537$	−8.15685	+	14.1281i	−0.351994	+	0.609672i
$538$	38.4203	−	66.5459i	1.65642	−	2.86900i
$539$	3.07107	+	5.31925i	0.132280	+	0.229116i
$540$	0.792893	−	1.37333i	0.0341207	−	0.0590988i
$541$	−12.6421	−	21.8968i	−0.543528	−	0.941418i	−0.998698	−	0.0510134i	$-0.983755\pi$
$541$	−12.6421	−	21.8968i	−0.543528	−	0.941418i	0.455170	−	0.890405i	$-0.349578\pi$
$542$	−56.2843			−2.41762
$543$	24.8995			1.06854
$544$	−0.136039	−	0.235626i	−0.00583262	−	0.0101024i
$545$	2.58579	−	4.47871i	0.110763	−	0.191847i
$546$	−12.8640	−	22.2810i	−0.550527	−	0.953540i
$547$	−2.86396	+	4.96053i	−0.122454	+	0.212097i	−0.920735	−	0.390189i	$-0.872410\pi$
$547$	−2.86396	+	4.96053i	−0.122454	+	0.212097i	0.798281	+	0.602285i	$0.205743\pi$
$548$	−14.3284	+	24.8176i	−0.612080	+	1.06015i
$549$	4.00000	−	6.92820i	0.170716	−	0.295689i
$550$	50.6274			2.15876
$551$	−0.928932	−	1.60896i	−0.0395738	−	0.0685439i
$552$	21.3137	+	36.9164i	0.907172	+	1.57127i
$553$	−18.3995	+	31.8689i	−0.782426	+	1.35520i
$554$	−34.1421			−1.45056
$555$	1.20711	+	2.09077i	0.0512388	+	0.0887483i
$556$		0			0
$557$	−44.4853			−1.88490			−0.942451	−	0.334344i	$-0.891485\pi$
$557$	−44.4853			−1.88490			−0.942451	+	0.334344i	$0.891485\pi$
$558$		0			0
$559$	16.2721			0.688236
$560$	7.24264			0.306057
$561$	−1.08579	−	1.88064i	−0.0458419	−	0.0794006i
$562$	−4.82843			−0.203675
$563$	−2.37868	+	4.11999i	−0.100249	+	0.173637i	−0.911787	−	0.410663i	$-0.865297\pi$
$563$	−2.37868	+	4.11999i	−0.100249	+	0.173637i	0.811538	+	0.584300i	$0.198631\pi$
$564$	7.65685	+	13.2621i	0.322412	+	0.558433i
$565$	−2.67157	−	4.62730i	−0.112394	−	0.194672i
$566$	5.65685			0.237775
$567$	11.4497	−	19.8315i	0.480844	−	0.832847i
$568$	−31.0563	+	53.7912i	−1.30310	+	2.25703i
$569$	7.57107	−	13.1135i	0.317396	−	0.549745i	−0.662548	−	0.749019i	$-0.730525\pi$
$569$	7.57107	−	13.1135i	0.317396	−	0.549745i	0.979944	+	0.199274i	$0.0638583\pi$
$570$	4.62132	+	8.00436i	0.193566	+	0.335266i
$571$	−20.4497	+	35.4200i	−0.855795	+	1.48228i	0.0201099	+	0.999798i	$0.493598\pi$
$571$	−20.4497	+	35.4200i	−0.855795	+	1.48228i	−0.875905	+	0.482483i	$0.839735\pi$
$572$	18.3492	+	31.7818i	0.767220	+	1.32886i
$573$	−2.65685			−0.110992
$574$	−55.2843			−2.30752
$575$	8.00000	+	13.8564i	0.333623	+	0.577852i
$576$	13.8995	−	24.0746i	0.579146	−	1.00311i
$577$	16.9853	+	29.4194i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833332\pi$
$577$	16.9853	+	29.4194i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$578$	−20.4853	+	35.4815i	−0.852075	+	1.47584i
$579$	25.5208	−	44.2033i	1.06061	−	1.83703i
$580$	−2.24264	+	3.88437i	−0.0931206	+	0.161290i
$581$	−9.82843			−0.407752
$582$	31.5563	+	54.6572i	1.30805	+	2.26561i
$583$	0.449747	+	0.778985i	0.0186266	+	0.0322623i
$584$	−8.44975	+	14.6354i	−0.349653	+	0.605617i
$585$	−5.17157			−0.213818
$586$	−29.9350	−	51.8490i	−1.23660	−	2.14186i
$587$	20.3431			0.839651			0.419826	−	0.907605i	$-0.362091\pi$
$587$	20.3431			0.839651			0.419826	+	0.907605i	$0.362091\pi$
$588$	−10.8284			−0.446557
$589$		0			0
$590$	24.3137			1.00098
$591$	−8.41421			−0.346114
$592$	1.50000	+	2.59808i	0.0616496	+	0.106780i
$593$	21.3137			0.875249			0.437625	−	0.899158i	$-0.355820\pi$
$593$	21.3137			0.875249			0.437625	+	0.899158i	$0.355820\pi$
$594$	−2.62132	+	4.54026i	−0.107554	+	0.186289i
$595$	−0.207107	−	0.358719i	−0.00849055	−	0.0147061i
$596$	−1.91421	−	3.31552i	−0.0784092	−	0.135809i
$597$	−37.6274			−1.53999
$598$	−8.82843	+	15.2913i	−0.361021	+	0.625307i
$599$	−17.4497	+	30.2238i	−0.712977	+	1.23491i	0.250757	+	0.968050i	$0.419320\pi$
$599$	−17.4497	+	30.2238i	−0.712977	+	1.23491i	−0.963734	+	0.266863i	$0.914013\pi$
$600$	−21.3137	+	36.9164i	−0.870129	+	1.50711i
$601$	−11.7426	−	20.3389i	−0.478992	−	0.829639i	0.520717	−	0.853729i	$-0.325664\pi$
$601$	−11.7426	−	20.3389i	−0.478992	−	0.829639i	−0.999710	+	0.0240900i	$0.992331\pi$
$602$	−25.9350	+	44.9208i	−1.05703	+	1.83083i
$603$	7.41421	+	12.8418i	0.301930	+	0.522958i
$604$	66.2843			2.69707
$605$	16.4853			0.670222
$606$	24.7279	+	42.8300i	1.00450	+	1.73985i
$607$	2.20711	−	3.82282i	0.0895837	−	0.155164i	−0.817752	−	0.575571i	$-0.804780\pi$
$607$	2.20711	−	3.82282i	0.0895837	−	0.155164i	0.907335	+	0.420408i	$0.138113\pi$
$608$	−1.25736	−	2.17781i	−0.0509927	−	0.0883219i
$609$	−3.41421	+	5.91359i	−0.138351	+	0.239631i
$610$	−3.41421	+	5.91359i	−0.138237	+	0.239434i
$611$	−1.51472	+	2.62357i	−0.0612790	+	0.106138i
$612$	1.85786			0.0750997
$613$	−5.15685	−	8.93193i	−0.208283	−	0.360757i	0.742890	−	0.669413i	$-0.233454\pi$
$613$	−5.15685	−	8.93193i	−0.208283	−	0.360757i	−0.951174	+	0.308656i	$0.900121\pi$
$614$	−3.32843	−	5.76500i	−0.134324	−	0.232657i
$615$	−11.4497	+	19.8315i	−0.461698	+	0.799685i
$616$	−55.8701			−2.25107
$617$	−11.6421	−	20.1648i	−0.468695	−	0.811803i	0.530665	−	0.847582i	$-0.321942\pi$
$617$	−11.6421	−	20.1648i	−0.468695	−	0.811803i	−0.999360	+	0.0357786i	$0.988609\pi$
$618$	70.3553			2.83011
$619$	31.6569			1.27240			0.636198	−	0.771526i	$-0.280506\pi$
$619$	31.6569			1.27240			0.636198	+	0.771526i	$0.280506\pi$
$620$		0			0
$621$	−1.65685			−0.0664873
$622$	27.3137			1.09518
$623$	−15.0711	−	26.1039i	−0.603810	−	1.04583i
$624$	−13.2426			−0.530130
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−4.62132	−	8.00436i	−0.184705	−	0.319919i
$627$	−10.0355	−	17.3821i	−0.400781	−	0.694172i
$628$	56.7696			2.26535
$629$	0.0857864	−	0.148586i	0.00342053	−	0.00592453i
$630$	8.24264	−	14.2767i	0.328395	−	0.568796i
$631$	−16.0061	+	27.7234i	−0.637193	+	1.10365i	0.348853	+	0.937177i	$0.386571\pi$
$631$	−16.0061	+	27.7234i	−0.637193	+	1.10365i	−0.986046	+	0.166473i	$0.946762\pi$
$632$	33.6421	+	58.2699i	1.33821	+	2.31785i
$633$	−9.15685	+	15.8601i	−0.363952	+	0.630384i
$634$	−2.62132	−	4.54026i	−0.104106	−	0.180317i
$635$	10.8995			0.432533
$636$	−1.58579			−0.0628805
$637$	−1.07107	−	1.85514i	−0.0424373	−	0.0735035i
$638$	7.41421	−	12.8418i	0.293532	−	0.508412i
$639$	19.8995	+	34.4669i	0.787212	+	1.36349i
$640$	−10.2782	+	17.8023i	−0.406281	+	0.703699i
$641$	9.98528	−	17.2950i	0.394395	−	0.683112i	−0.598629	−	0.801027i	$-0.704288\pi$
$641$	9.98528	−	17.2950i	0.394395	−	0.683112i	0.993024	+	0.117915i	$0.0376209\pi$
$642$	27.9350	−	48.3849i	1.10251	−	1.90960i
$643$	−12.6863			−0.500298			−0.250149	−	0.968207i	$-0.580480\pi$
$643$	−12.6863			−0.500298			−0.250149	+	0.968207i	$0.580480\pi$
$644$	−18.4853	−	32.0174i	−0.728422	−	1.26166i
$645$	10.7426	+	18.6068i	0.422991	+	0.732642i
$646$	0.328427	−	0.568852i	0.0129218	−	0.0223812i
$647$	22.6863			0.891890			0.445945	−	0.895060i	$-0.352868\pi$
$647$	22.6863			0.891890			0.445945	+	0.895060i	$0.352868\pi$
$648$	−20.9350	−	36.2605i	−0.822406	−	1.42445i
$649$	−52.7990			−2.07254
$650$	−17.6569			−0.692559
$651$		0			0
$652$	−49.6569			−1.94471
$653$	22.1421			0.866489			0.433244	−	0.901276i	$-0.357369\pi$
$653$	22.1421			0.866489			0.433244	+	0.901276i	$0.357369\pi$
$654$	−15.0711	−	26.1039i	−0.589325	−	1.02074i
$655$	−4.75736			−0.185885
$656$	−14.2279	+	24.6435i	−0.555507	+	0.962166i
$657$	5.41421	+	9.37769i	0.211229	+	0.365859i
$658$	−4.82843	−	8.36308i	−0.188232	−	0.326027i
$659$	9.65685			0.376178			0.188089	−	0.982152i	$-0.439771\pi$
$659$	9.65685			0.376178			0.188089	+	0.982152i	$0.439771\pi$
$660$	−24.2279	+	41.9640i	−0.943071	+	1.63345i
$661$	−16.5711	+	28.7019i	−0.644540	+	1.11638i	0.339868	+	0.940473i	$0.389618\pi$
$661$	−16.5711	+	28.7019i	−0.644540	+	1.11638i	−0.984408	+	0.175903i	$0.943716\pi$
$662$	−0.914214	+	1.58346i	−0.0355319	+	0.0615431i
$663$	0.378680	+	0.655892i	0.0147067	+	0.0254728i
$664$	−8.98528	+	15.5630i	−0.348697	+	0.603960i
$665$	−1.91421	−	3.31552i	−0.0742300	−	0.128570i
$666$	6.82843			0.264596
$667$	4.68629			0.181454
$668$	−16.3787	−	28.3687i	−0.633710	−	1.09762i
$669$	2.08579	−	3.61269i	0.0806412	−	0.139675i
$670$	−6.32843	−	10.9612i	−0.244488	−	0.423466i
$671$	7.41421	−	12.8418i	0.286223	−	0.495752i
$672$	−4.62132	+	8.00436i	−0.178271	+	0.308775i
$673$	10.3284	−	17.8894i	0.398132	−	0.689584i	−0.595364	−	0.803456i	$-0.702992\pi$
$673$	10.3284	−	17.8894i	0.398132	−	0.689584i	0.993495	+	0.113872i	$0.0363254\pi$
$674$	−32.1421			−1.23807
$675$	−0.828427	−	1.43488i	−0.0318862	−	0.0552285i
$676$	18.4853	+	32.0174i	0.710972	+	1.23144i
$677$	20.2990	−	35.1589i	0.780154	−	1.35127i	−0.151698	−	0.988427i	$-0.548474\pi$
$677$	20.2990	−	35.1589i	0.780154	−	1.35127i	0.931852	−	0.362839i	$-0.118192\pi$
$678$	−31.1421			−1.19601
$679$	−13.0711	−	22.6398i	−0.501622	−	0.868834i
$680$	−0.757359			−0.0290434
$681$	−37.6274			−1.44189
$682$		0			0
$683$	−46.6274			−1.78415			−0.892074	−	0.451889i	$-0.850750\pi$
$683$	−46.6274			−1.78415			−0.892074	+	0.451889i	$0.850750\pi$
$684$	17.1716			0.656571
$685$	−3.74264	−	6.48244i	−0.142999	−	0.247681i
$686$	47.6274			1.81842
$687$	13.8640	−	24.0131i	0.528943	−	0.916156i
$688$	13.3492	+	23.1216i	0.508935	+	0.881501i
$689$	−0.156854	−	0.271680i	−0.00597567	−	0.0103502i
$690$	−23.3137			−0.887538
$691$	−7.03553	+	12.1859i	−0.267644	+	0.463574i	−0.968253	−	0.249972i	$-0.919579\pi$
$691$	−7.03553	+	12.1859i	−0.267644	+	0.463574i	0.700609	+	0.713546i	$0.252912\pi$
$692$	27.3995	−	47.4573i	1.04157	−	1.80406i
$693$	−17.8995	+	31.0028i	−0.679946	+	1.17770i
$694$	−27.2279	−	47.1601i	−1.03356	−	1.79017i
$695$		0			0
$696$	6.24264	+	10.8126i	0.236627	+	0.409849i
$697$	1.62742			0.0616428
$698$	−84.7696			−3.20857
$699$	17.8995	+	31.0028i	0.677021	+	1.17263i
$700$	18.4853	−	32.0174i	0.698678	−	1.21015i
$701$	−1.74264	−	3.01834i	−0.0658186	−	0.114001i	0.831238	−	0.555916i	$-0.187633\pi$
$701$	−1.74264	−	3.01834i	−0.0658186	−	0.114001i	−0.897057	+	0.441915i	$0.854299\pi$
$702$	0.914214	−	1.58346i	0.0345048	−	0.0597640i
$703$	0.792893	−	1.37333i	0.0299045	−	0.0517962i
$704$	25.7635	−	44.6236i	0.970997	−	1.68182i
$705$	−4.00000			−0.150649
$706$	−3.62132	−	6.27231i	−0.136290	−	0.236062i
$707$	−10.2426	−	17.7408i	−0.385214	−	0.667210i
$708$	46.5416	−	80.6125i	1.74914	−	3.02960i
$709$	5.31371			0.199561			0.0997803	−	0.995009i	$-0.468186\pi$
$709$	5.31371			0.199561			0.0997803	+	0.995009i	$0.468186\pi$
$710$	−16.9853	−	29.4194i	−0.637446	−	1.10409i
$711$	43.1127			1.61685
$712$	−55.1127			−2.06544
$713$		0			0
$714$	−2.41421			−0.0903497
$715$	−9.58579			−0.358488
$716$	−12.9350	−	22.4041i	−0.483405	−	0.837282i
$717$	30.7990			1.15021
$718$	32.4706	−	56.2407i	1.21179	−	2.09888i
$719$	3.03553	+	5.25770i	0.113206	+	0.196079i	0.917061	−	0.398746i	$-0.130555\pi$
$719$	3.03553	+	5.25770i	0.113206	+	0.196079i	−0.803855	+	0.594825i	$0.797221\pi$
$720$	−4.24264	−	7.34847i	−0.158114	−	0.273861i
$721$	−29.1421			−1.08531
$722$	−19.8995	+	34.4669i	−0.740583	+	1.28273i
$723$	29.7635	−	51.5518i	1.10691	−	1.91723i
$724$	−19.7426	+	34.1953i	−0.733729	+	1.27086i
$725$	2.34315	+	4.05845i	0.0870222	+	0.150727i
$726$	48.0416	−	83.2105i	1.78299	−	3.08823i
$727$	23.4203	+	40.5652i	0.868611	+	1.50448i	0.863416	+	0.504492i	$0.168320\pi$
$727$	23.4203	+	40.5652i	0.868611	+	1.50448i	0.00519502	+	0.999987i	$0.498346\pi$
$728$	19.4853			0.722173
$729$	−23.8284			−0.882534
$730$	−4.62132	−	8.00436i	−0.171043	−	0.296255i
$731$	0.763456	−	1.32234i	0.0282374	−	0.0489087i
$732$	13.0711	+	22.6398i	0.483121	+	0.836789i
$733$	14.8137	−	25.6581i	0.547157	−	0.947703i	−0.451311	−	0.892367i	$-0.649043\pi$
$733$	14.8137	−	25.6581i	0.547157	−	0.947703i	0.998468	−	0.0553366i	$-0.0176232\pi$
$734$	−21.9853	+	38.0796i	−0.811492	+	1.40554i
$735$	1.41421	−	2.44949i	0.0521641	−	0.0903508i
$736$	6.34315			0.233811
$737$	13.7426	+	23.8030i	0.506217	+	0.876793i
$738$	32.3848	+	56.0921i	1.19210	+	2.06478i
$739$	−3.93503	+	6.81567i	−0.144752	+	0.250718i	−0.929281	−	0.369375i	$-0.879572\pi$
$739$	−3.93503	+	6.81567i	−0.144752	+	0.250718i	0.784528	+	0.620093i	$0.212905\pi$
$740$	−3.82843			−0.140736
$741$	3.50000	+	6.06218i	0.128576	+	0.222700i
$742$	1.00000			0.0367112
$743$	5.65685			0.207530			0.103765	−	0.994602i	$-0.466911\pi$
$743$	5.65685			0.207530			0.103765	+	0.994602i	$0.466911\pi$
$744$		0			0
$745$	1.00000			0.0366372
$746$	−24.1421			−0.883906
$747$	5.75736	+	9.97204i	0.210651	+	0.364858i
$748$	3.44365			0.125912
$749$	−11.5711	+	20.0417i	−0.422798	+	0.732307i
$750$	−26.2279	−	45.4281i	−0.957708	−	1.65880i
$751$	0.621320	+	1.07616i	0.0226723	+	0.0392696i	0.877139	−	0.480237i	$-0.159449\pi$
$751$	0.621320	+	1.07616i	0.0226723	+	0.0392696i	−0.854467	+	0.519506i	$0.826116\pi$
$752$	−4.97056			−0.181258
$753$	4.32843	−	7.49706i	0.157737	−	0.273208i
$754$	−2.58579	+	4.47871i	−0.0941688	+	0.163105i
$755$	−8.65685	+	14.9941i	−0.315055	+	0.545692i
$756$	1.91421	+	3.31552i	0.0696193	+	0.120584i
$757$	17.3284	−	30.0137i	0.629812	−	1.09087i	−0.357777	−	0.933807i	$-0.616465\pi$
$757$	17.3284	−	30.0137i	0.629812	−	1.09087i	0.987589	−	0.157060i	$-0.0502016\pi$
$758$	−35.4706	−	61.4368i	−1.28835	−	2.23149i
$759$	50.6274			1.83766
$760$	−7.00000			−0.253917
$761$	−10.2279	−	17.7153i	−0.370762	−	0.642178i	0.618921	−	0.785453i	$-0.287570\pi$
$761$	−10.2279	−	17.7153i	−0.370762	−	0.642178i	−0.989683	+	0.143275i	$0.954237\pi$
$762$	31.7635	−	55.0159i	1.15067	−	1.99302i
$763$	6.24264	+	10.8126i	0.225999	+	0.391441i
$764$	2.10660	−	3.64874i	0.0762142	−	0.132007i
$765$	−0.242641	+	0.420266i	−0.00877269	+	0.0151947i
$766$	−30.0563	+	52.0591i	−1.08598	+	1.88097i
$767$	18.4142			0.664899
$768$	36.1777	+	62.6616i	1.30545	+	2.26110i
$769$	13.0563	+	22.6143i	0.470824	+	0.815491i	0.999443	−	0.0333680i	$-0.0106233\pi$
$769$	13.0563	+	22.6143i	0.470824	+	0.815491i	−0.528619	+	0.848859i	$0.677290\pi$
$770$	15.2782	−	26.4626i	0.550587	−	0.953645i
$771$	−0.757359			−0.0272756
$772$	40.4706	+	70.0971i	1.45657	+	2.52285i
$773$	−18.0000			−0.647415			−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000			−0.647415			−0.323708	+	0.946157i	$0.604929\pi$
$774$	60.7696			2.18432
$775$		0			0
$776$	−47.7990			−1.71588
$777$	−5.82843			−0.209094
$778$	−20.6924	−	35.8403i	−0.741858	−	1.28494i
$779$	15.0416			0.538922
$780$	8.44975	−	14.6354i	0.302549	−	0.524031i
$781$	36.8848	+	63.8863i	1.31984	+	2.28603i
$782$	0.828427	+	1.43488i	0.0296245	+	0.0513111i
$783$	−0.485281			−0.0173425
$784$	1.75736	−	3.04384i	0.0627628	−	0.108708i
$785$	−7.41421	+	12.8418i	−0.264625	+	0.458343i
$786$	−13.8640	+	24.0131i	−0.494511	+	0.856518i
$787$	19.7929	+	34.2823i	0.705540	+	1.22203i	0.966496	+	0.256681i	$0.0826290\pi$
$787$	19.7929	+	34.2823i	0.705540	+	1.22203i	−0.260956	+	0.965351i	$0.584038\pi$
$788$	6.67157	−	11.5555i	0.237665	−	0.411648i
$789$	−0.828427	−	1.43488i	−0.0294928	−	0.0510830i
$790$	−36.7990			−1.30925
$791$	12.8995			0.458653
$792$	32.7279	+	56.6864i	1.16294	+	2.01426i
$793$	−2.58579	+	4.47871i	−0.0918240	+	0.159044i
$794$	−19.9350	−	34.5285i	−0.707468	−	1.22537i
$795$	0.207107	−	0.358719i	0.00734532	−	0.0127225i
$796$	29.8345	−	51.6749i	1.05746	−	1.83157i
$797$	−11.2279	+	19.4473i	−0.397713	+	0.688860i	−0.993443	−	0.114325i	$-0.963529\pi$
$797$	−11.2279	+	19.4473i	−0.397713	+	0.688860i	0.595730	+	0.803185i	$0.296863\pi$
$798$	−22.3137			−0.789897
$799$	0.142136	+	0.246186i	0.00502840	+	0.00870944i
$800$	3.17157	+	5.49333i	0.112132	+	0.194218i
$801$	−17.6569	+	30.5826i	−0.623874	+	1.08058i
$802$	−51.1127			−1.80485
$803$	10.0355	+	17.3821i	0.354146	+	0.613399i
$804$	−48.4558			−1.70891
$805$	9.65685			0.340359
$806$		0			0
$807$	76.8406			2.70492
$808$	−37.4558			−1.31769
$809$	−22.9853	−	39.8117i	−0.808119	−	1.39970i	−0.914165	−	0.405343i	$-0.867152\pi$
$809$	−22.9853	−	39.8117i	−0.808119	−	1.39970i	0.106045	−	0.994361i	$-0.466181\pi$
$810$	22.8995			0.804606
$811$	−5.86396	+	10.1567i	−0.205912	+	0.356649i	−0.950423	−	0.310961i	$-0.899349\pi$
$811$	−5.86396	+	10.1567i	−0.205912	+	0.356649i	0.744511	+	0.667610i	$0.232683\pi$
$812$	−5.41421	−	9.37769i	−0.190002	−	0.329093i
$813$	−28.1421	−	48.7436i	−0.986988	−	1.70951i
$814$	12.6569			0.443623
$815$	6.48528	−	11.2328i	0.227169	−	0.393469i
$816$	−0.621320	+	1.07616i	−0.0217506	+	0.0376731i
$817$	7.05635	−	12.2220i	0.246870	−	0.427592i
$818$	−11.2782	−	19.5344i	−0.394332	−	0.683003i
$819$	6.24264	−	10.8126i	0.218136	−	0.377822i
$820$	−18.1569	−	31.4486i	−0.634065	−	1.09823i
$821$	8.48528			0.296138			0.148069	−	0.988977i	$-0.452694\pi$
$821$	8.48528			0.296138			0.148069	+	0.988977i	$0.452694\pi$
$822$	−43.6274			−1.52168
$823$	−3.10660	−	5.38079i	−0.108289	−	0.187563i	0.806788	−	0.590841i	$-0.201204\pi$
$823$	−3.10660	−	5.38079i	−0.108289	−	0.187563i	−0.915077	+	0.403278i	$0.867871\pi$
$824$	−26.6421	+	46.1455i	−0.928123	+	1.60756i
$825$	25.3137	+	43.8446i	0.881310	+	1.52647i
$826$	−29.3492	+	50.8344i	−1.02119	+	1.76875i
$827$	8.55025	−	14.8095i	0.297321	−	0.514976i	−0.678201	−	0.734877i	$-0.737240\pi$
$827$	8.55025	−	14.8095i	0.297321	−	0.514976i	0.975522	+	0.219901i	$0.0705734\pi$
$828$	−21.6569	+	37.5108i	−0.752628	+	1.30359i
$829$	46.4264			1.61246			0.806228	−	0.591605i	$-0.201506\pi$
$829$	46.4264			1.61246			0.806228	+	0.591605i	$0.201506\pi$
$830$	−4.91421	−	8.51167i	−0.170575	−	0.295444i
$831$	−17.0711	−	29.5680i	−0.592189	−	1.02570i
$832$	−8.98528	+	15.5630i	−0.311509	+	0.539549i
$833$	−0.201010			−0.00696459
$834$		0			0
$835$	8.55635			0.296105
$836$	31.8284			1.10081
$837$		0			0
$838$	−67.5980			−2.33513
$839$	30.6274			1.05738			0.528688	−	0.848816i	$-0.322684\pi$
$839$	30.6274			1.05738			0.528688	+	0.848816i	$0.322684\pi$
$840$	12.8640	+	22.2810i	0.443849	+	0.768769i
$841$	−27.6274			−0.952670
$842$	−3.44975	+	5.97514i	−0.118886	+	0.205917i
$843$	−2.41421	−	4.18154i	−0.0831499	−	0.144020i
$844$	−14.5208	−	25.1508i	−0.499827	−	0.865726i
$845$	−9.65685			−0.332206
$846$	−5.65685	+	9.79796i	−0.194487	+	0.336861i
$847$	−19.8995	+	34.4669i	−0.683755	+	1.18430i
$848$	0.257359	−	0.445759i	0.00883776	−	0.0153074i
$849$	2.82843	+	4.89898i	0.0970714	+	0.168133i
$850$	−0.828427	+	1.43488i	−0.0284148	+	0.0492159i
$851$	2.00000	+	3.46410i	0.0685591	+	0.118748i
$852$	−130.054			−4.45557
$853$	−32.4853			−1.11227			−0.556137	−	0.831090i	$-0.687717\pi$
$853$	−32.4853			−1.11227			−0.556137	+	0.831090i	$0.687717\pi$
$854$	−8.24264	−	14.2767i	−0.282057	−	0.488538i
$855$	−2.24264	+	3.88437i	−0.0766967	+	0.132843i
$856$	21.1569	+	36.6447i	0.723126	+	1.25249i
$857$	1.25736	−	2.17781i	0.0429506	−	0.0743926i	−0.843751	−	0.536735i	$-0.819658\pi$
$857$	1.25736	−	2.17781i	0.0429506	−	0.0743926i	0.886702	+	0.462342i	$0.152991\pi$
$858$	−27.9350	+	48.3849i	−0.953686	+	1.65183i
$859$	−6.30761	+	10.9251i	−0.215213	+	0.372760i	−0.953338	−	0.301904i	$-0.902378\pi$
$859$	−6.30761	+	10.9251i	−0.215213	+	0.372760i	0.738125	+	0.674663i	$0.235711\pi$
$860$	−34.0711			−1.16181
$861$	−27.6421	−	47.8776i	−0.942041	−	1.63166i
$862$	−30.4706	−	52.7766i	−1.03783	−	1.79758i
$863$	−19.6924	+	34.1082i	−0.670337	+	1.16106i	0.307472	+	0.951557i	$0.400517\pi$
$863$	−19.6924	+	34.1082i	−0.670337	+	1.16106i	−0.977809	+	0.209500i	$0.932816\pi$
$864$	−0.656854			−0.0223466
$865$	7.15685	+	12.3960i	0.243340	+	0.421478i
$866$	−84.7696			−2.88059
$867$	−40.9706			−1.39143
$868$		0			0
$869$	79.9117			2.71082
$870$	−6.82843			−0.231505
$871$	−4.79289	−	8.30153i	−0.162401	−	0.281287i
$872$	22.8284			0.773068
$873$	−15.3137	+	26.5241i	−0.518291	+	0.897705i
$874$	7.65685	+	13.2621i	0.258997	+	0.448596i
$875$	10.8640	+	18.8169i	0.367269	+	0.636128i
$876$	−35.3848			−1.19554
$877$	−24.0858	+	41.7178i	−0.813319	+	1.40871i	0.0972093	+	0.995264i	$0.469008\pi$
$877$	−24.0858	+	41.7178i	−0.813319	+	1.40871i	−0.910529	+	0.413446i	$0.864325\pi$
$878$	−14.5711	+	25.2378i	−0.491750	+	0.851735i
$879$	29.9350	−	51.8490i	1.00968	−	1.74882i
$880$	−7.86396	−	13.6208i	−0.265094	−	0.459156i
$881$	17.1569	−	29.7165i	0.578029	−	1.00118i	−0.417676	−	0.908596i	$-0.637155\pi$
$881$	17.1569	−	29.7165i	0.578029	−	1.00118i	0.995705	−	0.0925798i	$-0.0295113\pi$
$882$	−4.00000	−	6.92820i	−0.134687	−	0.233285i
$883$	−26.2843			−0.884536			−0.442268	−	0.896883i	$-0.645826\pi$
$883$	−26.2843			−0.884536			−0.442268	+	0.896883i	$0.645826\pi$
$884$	−1.20101			−0.0403943
$885$	12.1569	+	21.0563i	0.408648	+	0.707799i
$886$	−15.9853	+	27.6873i	−0.537036	+	0.930174i
$887$	−26.6630	−	46.1816i	−0.895254	−	1.55063i	−0.833490	−	0.552535i	$-0.813661\pi$
$887$	−26.6630	−	46.1816i	−0.895254	−	1.55063i	−0.0617647	−	0.998091i	$-0.519673\pi$
$888$	−5.32843	+	9.22911i	−0.178810	+	0.309709i
$889$	−13.1569	+	22.7883i	−0.441267	+	0.764296i
$890$	15.0711	−	26.1039i	0.505183	−	0.875003i
$891$	−49.7279			−1.66595
$892$	3.30761	+	5.72895i	0.110747	+	0.191819i
$893$	1.31371	+	2.27541i	0.0439616	+	0.0761437i
$894$	2.91421	−	5.04757i	0.0974659	−	0.168816i
$895$	6.75736			0.225874
$896$	−24.8137	−	42.9786i	−0.828968	−	1.43581i
$897$	−17.6569			−0.589545
$898$	11.1716			0.372800
$899$		0			0
$900$	−43.3137			−1.44379
$901$	−0.0294373			−0.000980697
$902$	60.0269	+	103.970i	1.99868	+	3.46181i
$903$	−51.8701			−1.72613
$904$	11.7929	−	20.4259i	0.392226	−	0.679355i
$905$	−5.15685	−	8.93193i	−0.171420	−	0.296908i
$906$	50.4558	+	87.3921i	1.67628	+	2.90341i
$907$	55.3137			1.83666			0.918331	−	0.395814i	$-0.129537\pi$
$907$	55.3137			1.83666			0.918331	+	0.395814i	$0.129537\pi$
$908$	29.8345	−	51.6749i	0.990093	−	1.71489i
$909$	−12.0000	+	20.7846i	−0.398015	+	0.689382i
$910$	−5.32843	+	9.22911i	−0.176636	+	0.305942i
$911$	24.5208	+	42.4713i	0.812411	+	1.40714i	0.911172	+	0.412026i	$0.135179\pi$
$911$	24.5208	+	42.4713i	0.812411	+	1.40714i	−0.0987614	+	0.995111i	$0.531488\pi$
$912$	−5.74264	+	9.94655i	−0.190158	+	0.329363i
$913$	10.6716	+	18.4837i	0.353178	+	0.611721i
$914$	75.1127			2.48451
$915$	−6.82843			−0.225741
$916$	21.9853	+	38.0796i	0.726414	+	1.25819i
$917$	5.74264	−	9.94655i	0.189639	−	0.328464i
$918$	−0.0857864	−	0.148586i	−0.00283137	−	0.00490408i
$919$	7.55025	−	13.0774i	0.249060	−	0.431384i	−0.714205	−	0.699936i	$-0.753212\pi$
$919$	7.55025	−	13.0774i	0.249060	−	0.431384i	0.963265	+	0.268552i	$0.0865451\pi$
$920$	8.82843	−	15.2913i	0.291065	−	0.504139i
$921$	3.32843	−	5.76500i	0.109675	−	0.189963i
$922$	63.1127			2.07851
$923$	−12.8640	−	22.2810i	−0.423422	−	0.733389i
$924$	−58.4914	−	101.310i	−1.92423	−	3.33286i
$925$	−2.00000	+	3.46410i	−0.0657596	+	0.113899i
$926$	60.2843			1.98106
$927$	17.0711	+	29.5680i	0.560687	+	0.971139i
$928$	1.85786			0.0609874
$929$	−24.4853			−0.803336			−0.401668	−	0.915785i	$-0.631569\pi$
$929$	−24.4853			−0.803336			−0.401668	+	0.915785i	$0.631569\pi$
$930$		0			0
$931$	−1.85786			−0.0608890
$932$	−56.7696			−1.85955
$933$	13.6569	+	23.6544i	0.447105	+	0.774409i
$934$	19.3137			0.631964
$935$	−0.449747	+	0.778985i	−0.0147083	+	0.0254755i
$936$	−11.4142	−	19.7700i	−0.373085	−	0.646203i
$937$	−19.1569	−	33.1806i	−0.625827	−	1.08396i	−0.988380	−	0.152001i	$-0.951428\pi$
$937$	−19.1569	−	33.1806i	−0.625827	−	1.08396i	0.362553	−	0.931963i	$-0.381905\pi$
$938$	30.5563			0.997700
$939$	4.62132	−	8.00436i	0.150811	−	0.261212i
$940$	3.17157	−	5.49333i	0.103445	−	0.179173i
$941$	−17.5000	+	30.3109i	−0.570484	+	0.988107i	0.426033	+	0.904708i	$0.359911\pi$
$941$	−17.5000	+	30.3109i	−0.570484	+	0.988107i	−0.996516	+	0.0833989i	$0.973422\pi$
$942$	43.2132	+	74.8475i	1.40796	+	2.43866i
$943$	−18.9706	+	32.8580i	−0.617767	+	1.07000i
$944$	15.1066	+	26.1654i	0.491678	+	0.851611i
$945$	−1.00000			−0.0325300
$946$	112.640			3.66223
$947$	19.4497	+	33.6880i	0.632032	+	1.09471i	0.987136	+	0.159884i	$0.0511122\pi$
$947$	19.4497	+	33.6880i	0.632032	+	1.09471i	−0.355104	+	0.934827i	$0.615555\pi$
$948$	−70.4411	+	122.008i	−2.28782	+	3.96262i
$949$	−3.50000	−	6.06218i	−0.113615	−	0.196787i
$950$	−7.65685	+	13.2621i	−0.248421	+	0.430278i
$951$	2.62132	−	4.54026i	0.0850021	−	0.147228i
$952$	0.914214	−	1.58346i	0.0296298	−	0.0513204i
$953$	−20.4853			−0.663583			−0.331792	−	0.943353i	$-0.607653\pi$
$953$	−20.4853			−0.663583			−0.331792	+	0.943353i	$0.607653\pi$
$954$	−0.585786	−	1.01461i	−0.0189655	−	0.0328493i
$955$	0.550253	+	0.953065i	0.0178058	+	0.0308405i
$956$	−24.4203	+	42.2972i	−0.789809	+	1.36799i
$957$	14.8284			0.479335
$958$	11.7426	+	20.3389i	0.379387	+	0.657118i
$959$	18.0711			0.583545
$960$	−23.7279			−0.765815
$961$		0			0
$962$	−4.41421			−0.142320
$963$	27.1127			0.873694
$964$	47.1985	+	81.7502i	1.52016	+	2.63300i
$965$	−21.1421			−0.680589
$966$	28.1421	−	48.7436i	0.905458	−	1.56830i
$967$	−23.2782	−	40.3190i	−0.748576	−	1.29657i	−0.948505	−	0.316761i	$-0.897405\pi$
$967$	−23.2782	−	40.3190i	−0.748576	−	1.29657i	0.199930	−	0.979810i	$-0.435929\pi$
$968$	36.3848	+	63.0203i	1.16945	+	2.02555i
$969$	0.656854			0.0211012
$970$	13.0711	−	22.6398i	0.419687	−	0.726919i
$971$	−29.3492	+	50.8344i	−0.941862	+	1.63135i	−0.179947	+	0.983676i	$0.557592\pi$
$971$	−29.3492	+	50.8344i	−0.941862	+	1.63135i	−0.761915	+	0.647676i	$0.775741\pi$
$972$	41.4558	−	71.8036i	1.32970	−	2.30310i
$973$		0			0
$974$	20.9853	−	36.3476i	0.672412	−	1.16465i
$975$	−8.82843	−	15.2913i	−0.282736	−	0.489713i
$976$	−8.48528			−0.271607
$977$	16.4853			0.527411			0.263705	−	0.964603i	$-0.415055\pi$
$977$	16.4853			0.527411			0.263705	+	0.964603i	$0.415055\pi$
$978$	−37.7990	−	65.4698i	−1.20868	−	2.09349i
$979$	−32.7279	+	56.6864i	−1.04599	+	1.81171i
$980$	2.24264	+	3.88437i	0.0716385	+	0.124082i
$981$	7.31371	−	12.6677i	0.233509	−	0.404449i
$982$	−5.32843	+	9.22911i	−0.170037	+	0.294513i
$983$	24.4203	−	42.2972i	0.778887	−	1.34907i	−0.153697	−	0.988118i	$-0.549118\pi$
$983$	24.4203	−	42.2972i	0.778887	−	1.34907i	0.932584	−	0.360954i	$-0.117549\pi$
$984$	−101.083			−3.22242
$985$	1.74264	+	3.01834i	0.0555251	+	0.0961724i
$986$	0.242641	+	0.420266i	0.00772725	+	0.0133840i
$987$	4.82843	−	8.36308i	0.153691	−	0.266200i
$988$	−11.1005			−0.353154
$989$	17.7990	+	30.8288i	0.565975	+	0.980297i
$990$	−35.7990			−1.13777
$991$	19.9411			0.633451			0.316725	−	0.948517i	$-0.397417\pi$
$991$	19.9411			0.633451			0.316725	+	0.948517i	$0.397417\pi$
$992$		0			0
$993$	−1.82843			−0.0580234
$994$	82.0122			2.60127
$995$	7.79289	+	13.4977i	0.247051	+	0.427905i
$996$	−37.6274			−1.19227
$997$	23.2990	−	40.3550i	0.737886	−	1.27806i	−0.215559	−	0.976491i	$-0.569157\pi$
$997$	23.2990	−	40.3550i	0.737886	−	1.27806i	0.953445	−	0.301566i	$-0.0975093\pi$
$998$	−48.5416	−	84.0766i	−1.53656	−	2.66140i
$999$	−0.207107	−	0.358719i	−0.00655257	−	0.0113494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.a.521.1		4
31.2	even	5		961.2.g.r.844.1		16
31.3	odd	30		961.2.d.l.628.1		8
31.4	even	5		961.2.g.r.338.2		16
31.5	even	3	inner	961.2.c.a.439.1		4
31.6	odd	6		961.2.a.a.1.1		2
31.7	even	15		961.2.d.i.388.2		8
31.8	even	5		961.2.g.r.732.2		16
31.9	even	15		961.2.g.r.816.2		16
31.10	even	15		961.2.g.r.547.1		16
31.11	odd	30		961.2.g.o.235.2		16
31.12	odd	30		961.2.d.l.531.1		8
31.13	odd	30		961.2.g.o.846.1		16
31.14	even	15		961.2.d.i.374.2		8
31.15	odd	10		961.2.g.o.448.1		16
31.16	even	5		961.2.g.r.448.1		16
31.17	odd	30		961.2.d.l.374.2		8
31.18	even	15		961.2.g.r.846.1		16
31.19	even	15		961.2.d.i.531.1		8
31.20	even	15		961.2.g.r.235.2		16
31.21	odd	30		961.2.g.o.547.1		16
31.22	odd	30		961.2.g.o.816.2		16
31.23	odd	10		961.2.g.o.732.2		16
31.24	odd	30		961.2.d.l.388.2		8
31.25	even	3		961.2.a.c.1.1		2
31.26	odd	6		31.2.c.a.5.1	✓	4
31.27	odd	10		961.2.g.o.338.2		16
31.28	even	15		961.2.d.i.628.1		8
31.29	odd	10		961.2.g.o.844.1		16
31.30	odd	2		31.2.c.a.25.1	yes	4
93.26	even	6		279.2.h.c.253.2		4
93.56	odd	6		8649.2.a.k.1.2		2
93.68	even	6		8649.2.a.l.1.2		2
93.92	even	2		279.2.h.c.118.2		4
124.119	even	6		496.2.i.h.129.1		4
124.123	even	2		496.2.i.h.273.1		4
155.57	even	12		775.2.o.d.749.1		8
155.88	even	12		775.2.o.d.749.4		8
155.92	even	4		775.2.o.d.149.1		8
155.119	odd	6		775.2.e.e.501.2		4
155.123	even	4		775.2.o.d.149.4		8
155.154	odd	2		775.2.e.e.676.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.1	✓	4	31.26	odd	6
31.2.c.a.25.1	yes	4	31.30	odd	2
279.2.h.c.118.2		4	93.92	even	2
279.2.h.c.253.2		4	93.26	even	6
496.2.i.h.129.1		4	124.119	even	6
496.2.i.h.273.1		4	124.123	even	2
775.2.e.e.501.2		4	155.119	odd	6
775.2.e.e.676.2		4	155.154	odd	2
775.2.o.d.149.1		8	155.92	even	4
775.2.o.d.149.4		8	155.123	even	4
775.2.o.d.749.1		8	155.57	even	12
775.2.o.d.749.4		8	155.88	even	12
961.2.a.a.1.1		2	31.6	odd	6
961.2.a.c.1.1		2	31.25	even	3
961.2.c.a.439.1		4	31.5	even	3	inner
961.2.c.a.521.1		4	1.1	even	1	trivial
961.2.d.i.374.2		8	31.14	even	15
961.2.d.i.388.2		8	31.7	even	15
961.2.d.i.531.1		8	31.19	even	15
961.2.d.i.628.1		8	31.28	even	15
961.2.d.l.374.2		8	31.17	odd	30
961.2.d.l.388.2		8	31.24	odd	30
961.2.d.l.531.1		8	31.12	odd	30
961.2.d.l.628.1		8	31.3	odd	30
961.2.g.o.235.2		16	31.11	odd	30
961.2.g.o.338.2		16	31.27	odd	10
961.2.g.o.448.1		16	31.15	odd	10
961.2.g.o.547.1		16	31.21	odd	30
961.2.g.o.732.2		16	31.23	odd	10
961.2.g.o.816.2		16	31.22	odd	30
961.2.g.o.844.1		16	31.29	odd	10
961.2.g.o.846.1		16	31.13	odd	30
961.2.g.r.235.2		16	31.20	even	15
961.2.g.r.338.2		16	31.4	even	5
961.2.g.r.448.1		16	31.16	even	5
961.2.g.r.547.1		16	31.10	even	15
961.2.g.r.732.2		16	31.8	even	5
961.2.g.r.816.2		16	31.9	even	15
961.2.g.r.844.1		16	31.2	even	5
961.2.g.r.846.1		16	31.18	even	15
8649.2.a.k.1.2		2	93.56	odd	6
8649.2.a.l.1.2		2	93.68	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.41421 q^{2} +(-1.20711 - 2.09077i) q^{3} +3.82843 q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.91421 + 5.04757i) q^{6} +(-1.20711 - 2.09077i) q^{7} -4.41421 q^{8} +(-1.41421 + 2.44949i) q^{9} +(1.20711 - 2.09077i) q^{10} +(-2.62132 + 4.54026i) q^{11} +(-4.62132 - 8.00436i) q^{12} +(0.914214 - 1.58346i) q^{13} +(2.91421 + 5.04757i) q^{14} +2.41421 q^{15} +3.00000 q^{16} +(-0.0857864 - 0.148586i) q^{17} +(3.41421 - 5.91359i) q^{18} +(-0.792893 - 1.37333i) q^{19} +(-1.91421 + 3.31552i) q^{20} +(-2.91421 + 5.04757i) q^{21} +(6.32843 - 10.9612i) q^{22} +4.00000 q^{23} +(5.32843 + 9.22911i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-2.20711 + 3.82282i) q^{26} -0.414214 q^{27} +(-4.62132 - 8.00436i) q^{28} +1.17157 q^{29} -5.82843 q^{30} +1.58579 q^{32} +12.6569 q^{33} +(0.207107 + 0.358719i) q^{34} +2.41421 q^{35} +(-5.41421 + 9.37769i) q^{36} +(0.500000 + 0.866025i) q^{37} +(1.91421 + 3.31552i) q^{38} -4.41421 q^{39} +(2.20711 - 3.82282i) q^{40} +(-4.74264 + 8.21449i) q^{41} +(7.03553 - 12.1859i) q^{42} +(4.44975 + 7.70719i) q^{43} +(-10.0355 + 17.3821i) q^{44} +(-1.41421 - 2.44949i) q^{45} -9.65685 q^{46} -1.65685 q^{47} +(-3.62132 - 6.27231i) q^{48} +(0.585786 - 1.01461i) q^{49} +(-4.82843 - 8.36308i) q^{50} +(-0.207107 + 0.358719i) q^{51} +(3.50000 - 6.06218i) q^{52} +(0.0857864 - 0.148586i) q^{53} +1.00000 q^{54} +(-2.62132 - 4.54026i) q^{55} +(5.32843 + 9.22911i) q^{56} +(-1.91421 + 3.31552i) q^{57} -2.82843 q^{58} +(5.03553 + 8.72180i) q^{59} +9.24264 q^{60} -2.82843 q^{61} +6.82843 q^{63} -9.82843 q^{64} +(0.914214 + 1.58346i) q^{65} -30.5563 q^{66} +(2.62132 - 4.54026i) q^{67} +(-0.328427 - 0.568852i) q^{68} +(-4.82843 - 8.36308i) q^{69} -5.82843 q^{70} +(7.03553 - 12.1859i) q^{71} +(6.24264 - 10.8126i) q^{72} +(1.91421 - 3.31552i) q^{73} +(-1.20711 - 2.09077i) q^{74} +(4.82843 - 8.36308i) q^{75} +(-3.03553 - 5.25770i) q^{76} +12.6569 q^{77} +10.6569 q^{78} +(-7.62132 - 13.2005i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(4.74264 + 8.21449i) q^{81} +(11.4497 - 19.8315i) q^{82} +(2.03553 - 3.52565i) q^{83} +(-11.1569 + 19.3242i) q^{84} +0.171573 q^{85} +(-10.7426 - 18.6068i) q^{86} +(-1.41421 - 2.44949i) q^{87} +(11.5711 - 20.0417i) q^{88} +12.4853 q^{89} +(3.41421 + 5.91359i) q^{90} -4.41421 q^{91} +15.3137 q^{92} +4.00000 q^{94} +1.58579 q^{95} +(-1.91421 - 3.31552i) q^{96} +10.8284 q^{97} +(-1.41421 + 2.44949i) q^{98} +(-7.41421 - 12.8418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} + 6 q^{6} - 2 q^{7} - 12 q^{8} + 2 q^{10} - 2 q^{11} - 10 q^{12} - 2 q^{13} + 6 q^{14} + 4 q^{15} + 12 q^{16} - 6 q^{17} + 8 q^{18} - 6 q^{19} - 2 q^{20} - 6 q^{21}+ \cdots - 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 + 6 * q^6 - 2 * q^7 - 12 * q^8 + 2 * q^10 - 2 * q^11 - 10 * q^12 - 2 * q^13 + 6 * q^14 + 4 * q^15 + 12 * q^16 - 6 * q^17 + 8 * q^18 - 6 * q^19 - 2 * q^20 - 6 * q^21 + 14 * q^22 + 16 * q^23 + 10 * q^24 + 8 * q^25 - 6 * q^26 + 4 * q^27 - 10 * q^28 + 16 * q^29 - 12 * q^30 + 12 * q^32 + 28 * q^33 - 2 * q^34 + 4 * q^35 - 16 * q^36 + 2 * q^37 + 2 * q^38 - 12 * q^39 + 6 * q^40 - 2 * q^41 + 14 * q^42 - 2 * q^43 - 26 * q^44 - 16 * q^46 + 16 * q^47 - 6 * q^48 + 8 * q^49 - 8 * q^50 + 2 * q^51 + 14 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 + 10 * q^56 - 2 * q^57 + 6 * q^59 + 20 * q^60 + 16 * q^63 - 28 * q^64 - 2 * q^65 - 60 * q^66 + 2 * q^67 + 10 * q^68 - 8 * q^69 - 12 * q^70 + 14 * q^71 + 8 * q^72 + 2 * q^73 - 2 * q^74 + 8 * q^75 + 2 * q^76 + 28 * q^77 + 20 * q^78 - 22 * q^79 - 6 * q^80 + 2 * q^81 + 26 * q^82 - 6 * q^83 - 22 * q^84 + 12 * q^85 - 26 * q^86 + 18 * q^88 + 16 * q^89 + 8 * q^90 - 12 * q^91 + 16 * q^92 + 16 * q^94 + 12 * q^95 - 2 * q^96 + 32 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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