LMFDB - Embedded newform 855.2.l.b.391.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(391,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 4]))

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

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

chi := DirichletCharacter("855.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.5
Character	$\chi$	$=$	855.391
Dual form			855.2.l.b.691.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.16307 q^{2} +(-1.36343 + 1.06821i) q^{3} +2.67885 q^{4} +(0.500000 + 0.866025i) q^{5} +(2.94918 - 2.31060i) q^{6} +(-2.59940 - 4.50229i) q^{7} -1.46840 q^{8} +(0.717865 - 2.91285i) q^{9} +O(q^{10})$	\(q-2.16307 q^{2} +(-1.36343 + 1.06821i) q^{3} +2.67885 q^{4} +(0.500000 + 0.866025i) q^{5} +(2.94918 - 2.31060i) q^{6} +(-2.59940 - 4.50229i) q^{7} -1.46840 q^{8} +(0.717865 - 2.91285i) q^{9} +(-1.08153 - 1.87327i) q^{10} +(-1.09289 - 1.89294i) q^{11} +(-3.65242 + 2.86157i) q^{12} -5.51113 q^{13} +(5.62267 + 9.73875i) q^{14} +(-1.60681 - 0.646658i) q^{15} -2.18145 q^{16} +(2.29805 - 3.98033i) q^{17} +(-1.55279 + 6.30068i) q^{18} +(1.96477 + 3.89097i) q^{19} +(1.33943 + 2.31995i) q^{20} +(8.35347 + 3.36185i) q^{21} +(2.36399 + 4.09455i) q^{22} -0.0138826 q^{23} +(2.00206 - 1.56856i) q^{24} +(-0.500000 + 0.866025i) q^{25} +11.9209 q^{26} +(2.13277 + 4.73828i) q^{27} +(-6.96341 - 12.0610i) q^{28} +(-0.758359 + 1.31352i) q^{29} +(3.47563 + 1.39876i) q^{30} +(2.58048 - 4.46952i) q^{31} +7.65543 q^{32} +(3.51213 + 1.41345i) q^{33} +(-4.97083 + 8.60973i) q^{34} +(2.59940 - 4.50229i) q^{35} +(1.92306 - 7.80309i) q^{36} -10.6205 q^{37} +(-4.24993 - 8.41643i) q^{38} +(7.51402 - 5.88703i) q^{39} +(-0.734202 - 1.27167i) q^{40} +(1.90901 + 3.30651i) q^{41} +(-18.0691 - 7.27189i) q^{42} +4.11097 q^{43} +(-2.92769 - 5.07091i) q^{44} +(2.88153 - 0.834733i) q^{45} +0.0300290 q^{46} +(0.222233 - 0.384919i) q^{47} +(2.97425 - 2.33024i) q^{48} +(-10.0137 + 17.3443i) q^{49} +(1.08153 - 1.87327i) q^{50} +(1.11860 + 7.88169i) q^{51} -14.7635 q^{52} +(5.54987 + 9.61265i) q^{53} +(-4.61332 - 10.2492i) q^{54} +(1.09289 - 1.89294i) q^{55} +(3.81697 + 6.61118i) q^{56} +(-6.83519 - 3.20627i) q^{57} +(1.64038 - 2.84122i) q^{58} +(-1.24097 - 2.14943i) q^{59} +(-4.30440 - 1.73230i) q^{60} +(2.23141 - 3.86492i) q^{61} +(-5.58175 + 9.66787i) q^{62} +(-14.9805 + 4.33961i) q^{63} -12.1963 q^{64} +(-2.75557 - 4.77278i) q^{65} +(-7.59696 - 3.05739i) q^{66} +4.85080 q^{67} +(6.15613 - 10.6627i) q^{68} +(0.0189279 - 0.0148295i) q^{69} +(-5.62267 + 9.73875i) q^{70} +(-0.669934 + 1.16036i) q^{71} +(-1.05412 + 4.27723i) q^{72} +(-5.38078 + 9.31979i) q^{73} +22.9729 q^{74} +(-0.243381 - 1.71487i) q^{75} +(5.26333 + 10.4233i) q^{76} +(-5.68171 + 9.84102i) q^{77} +(-16.2533 + 12.7340i) q^{78} -3.20925 q^{79} +(-1.09073 - 1.88919i) q^{80} +(-7.96934 - 4.18206i) q^{81} +(-4.12932 - 7.15219i) q^{82} +(0.202477 + 0.350701i) q^{83} +(22.3777 + 9.00589i) q^{84} +4.59609 q^{85} -8.89230 q^{86} +(-0.369141 - 2.60097i) q^{87} +(1.60480 + 2.77960i) q^{88} +(2.34580 + 4.06304i) q^{89} +(-6.23294 + 1.80558i) q^{90} +(14.3256 + 24.8127i) q^{91} -0.0371895 q^{92} +(1.25608 + 8.85036i) q^{93} +(-0.480705 + 0.832606i) q^{94} +(-2.38730 + 3.64703i) q^{95} +(-10.4376 + 8.17759i) q^{96} -11.3187 q^{97} +(21.6604 - 37.5169i) q^{98} +(-6.29839 + 1.82454i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} - 2 q^{3} + 80 q^{4} + 40 q^{5} + 2 q^{6} + q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q + 4 * q^2 - 2 * q^3 + 80 * q^4 + 40 * q^5 + 2 * q^6 + q^7 - 2 * q^9	\( 80 q + 4 q^{2} - 2 q^{3} + 80 q^{4} + 40 q^{5} + 2 q^{6} + q^{7} - 2 q^{9} + 2 q^{10} - q^{11} - 6 q^{12} - 18 q^{13} - q^{15} + 88 q^{16} + 6 q^{17} - 15 q^{18} + 9 q^{19} + 40 q^{20} - 4 q^{21} + 9 q^{22} - 30 q^{24} - 40 q^{25} - 8 q^{26} - 2 q^{27} + 13 q^{28} - 3 q^{29} + 7 q^{30} + 24 q^{31} + 4 q^{32} + q^{33} + q^{34} - q^{35} + 12 q^{36} - 40 q^{37} + 14 q^{38} + 23 q^{39} - 3 q^{41} - 29 q^{42} - 30 q^{43} - 34 q^{44} - q^{45} - 46 q^{46} + 6 q^{47} - 5 q^{48} - 33 q^{49} - 2 q^{50} + 37 q^{51} - 56 q^{52} - 16 q^{53} - 23 q^{54} + q^{55} + 20 q^{56} + 4 q^{58} - 2 q^{59} - 3 q^{60} + 7 q^{61} - 8 q^{62} - 41 q^{63} + 180 q^{64} - 9 q^{65} - 30 q^{66} - 102 q^{67} + 11 q^{68} - 24 q^{69} + 14 q^{71} + 22 q^{72} - 8 q^{73} + 24 q^{74} + q^{75} + 12 q^{76} + 10 q^{77} - q^{78} - 42 q^{79} + 44 q^{80} - 22 q^{81} + 5 q^{82} + 3 q^{83} - 131 q^{84} + 12 q^{85} + 14 q^{86} - 22 q^{87} + 46 q^{88} - 18 q^{89} - 15 q^{90} + 24 q^{91} - 54 q^{92} - 24 q^{93} + 42 q^{94} - 160 q^{96} - 42 q^{97} + 5 q^{98} + 32 q^{99}+O(q^{100}) \) 80 * q + 4 * q^2 - 2 * q^3 + 80 * q^4 + 40 * q^5 + 2 * q^6 + q^7 - 2 * q^9 + 2 * q^10 - q^11 - 6 * q^12 - 18 * q^13 - q^15 + 88 * q^16 + 6 * q^17 - 15 * q^18 + 9 * q^19 + 40 * q^20 - 4 * q^21 + 9 * q^22 - 30 * q^24 - 40 * q^25 - 8 * q^26 - 2 * q^27 + 13 * q^28 - 3 * q^29 + 7 * q^30 + 24 * q^31 + 4 * q^32 + q^33 + q^34 - q^35 + 12 * q^36 - 40 * q^37 + 14 * q^38 + 23 * q^39 - 3 * q^41 - 29 * q^42 - 30 * q^43 - 34 * q^44 - q^45 - 46 * q^46 + 6 * q^47 - 5 * q^48 - 33 * q^49 - 2 * q^50 + 37 * q^51 - 56 * q^52 - 16 * q^53 - 23 * q^54 + q^55 + 20 * q^56 + 4 * q^58 - 2 * q^59 - 3 * q^60 + 7 * q^61 - 8 * q^62 - 41 * q^63 + 180 * q^64 - 9 * q^65 - 30 * q^66 - 102 * q^67 + 11 * q^68 - 24 * q^69 + 14 * q^71 + 22 * q^72 - 8 * q^73 + 24 * q^74 + q^75 + 12 * q^76 + 10 * q^77 - q^78 - 42 * q^79 + 44 * q^80 - 22 * q^81 + 5 * q^82 + 3 * q^83 - 131 * q^84 + 12 * q^85 + 14 * q^86 - 22 * q^87 + 46 * q^88 - 18 * q^89 - 15 * q^90 + 24 * q^91 - 54 * q^92 - 24 * q^93 + 42 * q^94 - 160 * q^96 - 42 * q^97 + 5 * q^98 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−2.16307			−1.52952			−0.764759	−	0.644316i	$-0.777142\pi$
$2$	−2.16307			−1.52952			−0.764759	+	0.644316i	$0.777142\pi$
$3$	−1.36343	+	1.06821i	−0.787175	+	0.616730i
$3$	−1.36343	+	1.06821i	−0.787175	+	0.616730i
$4$	2.67885			1.33943
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	2.94918	−	2.31060i	1.20400	−	0.943300i
$7$	−2.59940	−	4.50229i	−0.982480	−	1.70171i	−0.652638	−	0.757670i	$-0.726338\pi$
$7$	−2.59940	−	4.50229i	−0.982480	−	1.70171i	−0.329843	−	0.944036i	$-0.606996\pi$
$8$	−1.46840			−0.519159
$9$	0.717865	−	2.91285i	0.239288	−	0.970949i
$10$	−1.08153	−	1.87327i	−0.342011	−	0.592380i
$11$	−1.09289	−	1.89294i	−0.329519	−	0.570743i	0.652898	−	0.757446i	$-0.273553\pi$
$11$	−1.09289	−	1.89294i	−0.329519	−	0.570743i	−0.982416	+	0.186703i	$0.940220\pi$
$12$	−3.65242	+	2.86157i	−1.05436	+	0.826064i
$13$	−5.51113			−1.52851			−0.764256	−	0.644913i	$-0.776894\pi$
$13$	−5.51113			−1.52851			−0.764256	+	0.644913i	$0.776894\pi$
$14$	5.62267	+	9.73875i	1.50272	+	2.60279i
$15$	−1.60681	−	0.646658i	−0.414876	−	0.166966i
$16$	−2.18145			−0.545363
$17$	2.29805	−	3.98033i	0.557358	−	0.965373i	−0.440357	−	0.897823i	$-0.645148\pi$
$17$	2.29805	−	3.98033i	0.557358	−	0.965373i	0.997716	−	0.0675505i	$-0.0215184\pi$
$18$	−1.55279	+	6.30068i	−0.365996	+	1.48508i
$19$	1.96477	+	3.89097i	0.450749	+	0.892651i
$19$	1.96477	+	3.89097i	0.450749	+	0.892651i
$20$	1.33943	+	2.31995i	0.299505	+	0.518758i
$21$	8.35347	+	3.36185i	1.82288	+	0.733615i
$22$	2.36399	+	4.09455i	0.504005	+	0.872962i
$23$	−0.0138826			−0.00289473			−0.00144736	−	0.999999i	$-0.500461\pi$
$23$	−0.0138826			−0.00289473			−0.00144736	+	0.999999i	$0.500461\pi$
$24$	2.00206	−	1.56856i	0.408669	−	0.320181i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	11.9209			2.33789
$27$	2.13277	+	4.73828i	0.410451	+	0.911883i
$28$	−6.96341	−	12.0610i	−1.31596	−	2.27931i
$29$	−0.758359	+	1.31352i	−0.140824	+	0.243914i	−0.927807	−	0.373060i	$-0.878308\pi$
$29$	−0.758359	+	1.31352i	−0.140824	+	0.243914i	0.786983	+	0.616974i	$0.211642\pi$
$30$	3.47563	+	1.39876i	0.634561	+	0.255378i
$31$	2.58048	−	4.46952i	0.463468	−	0.802750i	−0.535663	−	0.844432i	$-0.679938\pi$
$31$	2.58048	−	4.46952i	0.463468	−	0.802750i	0.999131	+	0.0416817i	$0.0132716\pi$
$32$	7.65543			1.35330
$33$	3.51213	+	1.41345i	0.611383	+	0.246051i
$34$	−4.97083	+	8.60973i	−0.852490	+	1.47656i
$35$	2.59940	−	4.50229i	0.439379	−	0.761026i
$36$	1.92306	−	7.80309i	0.320509	−	1.30051i
$37$	−10.6205			−1.74600			−0.873001	−	0.487718i	$-0.837830\pi$
$37$	−10.6205			−1.74600			−0.873001	+	0.487718i	$0.837830\pi$
$38$	−4.24993	−	8.41643i	−0.689429	−	1.36533i
$39$	7.51402	−	5.88703i	1.20321	−	0.942679i
$40$	−0.734202	−	1.27167i	−0.116087	−	0.201069i
$41$	1.90901	+	3.30651i	0.298138	+	0.516389i	0.975710	−	0.219067i	$-0.0703012\pi$
$41$	1.90901	+	3.30651i	0.298138	+	0.516389i	−0.677572	+	0.735456i	$0.736968\pi$
$42$	−18.0691	−	7.27189i	−2.78812	−	1.12208i
$43$	4.11097			0.626917			0.313459	−	0.949602i	$-0.398512\pi$
$43$	4.11097			0.626917			0.313459	+	0.949602i	$0.398512\pi$
$44$	−2.92769	−	5.07091i	−0.441366	−	0.764468i
$45$	2.88153	−	0.834733i	0.429553	−	0.124435i
$46$	0.0300290			0.00442754
$47$	0.222233	−	0.384919i	0.0324161	−	0.0561463i	−0.849362	−	0.527810i	$-0.823013\pi$
$47$	0.222233	−	0.384919i	0.0324161	−	0.0561463i	0.881778	+	0.471664i	$0.156347\pi$
$48$	2.97425	−	2.33024i	0.429296	−	0.336342i
$49$	−10.0137	+	17.3443i	−1.43054	+	2.47776i
$50$	1.08153	−	1.87327i	0.152952	−	0.264920i
$51$	1.11860	+	7.88169i	0.156636	+	1.10366i
$52$	−14.7635			−2.04733
$53$	5.54987	+	9.61265i	0.762333	+	1.32040i	0.941645	+	0.336607i	$0.109280\pi$
$53$	5.54987	+	9.61265i	0.762333	+	1.32040i	−0.179312	+	0.983792i	$0.557387\pi$
$54$	−4.61332	−	10.2492i	−0.627793	−	1.39474i
$55$	1.09289	−	1.89294i	0.147365	−	0.255244i
$56$	3.81697	+	6.61118i	0.510064	+	0.883456i
$57$	−6.83519	−	3.20627i	−0.905343	−	0.424681i
$58$	1.64038	−	2.84122i	0.215392	−	0.373071i
$59$	−1.24097	−	2.14943i	−0.161561	−	0.279832i	0.773868	−	0.633347i	$-0.218320\pi$
$59$	−1.24097	−	2.14943i	−0.161561	−	0.279832i	−0.935429	+	0.353515i	$0.884986\pi$
$60$	−4.30440	−	1.73230i	−0.555696	−	0.223639i
$61$	2.23141	−	3.86492i	0.285703	−	0.494852i	−0.687076	−	0.726585i	$-0.741106\pi$
$61$	2.23141	−	3.86492i	0.285703	−	0.494852i	0.972779	+	0.231733i	$0.0744395\pi$
$62$	−5.58175	+	9.66787i	−0.708883	+	1.22782i
$63$	−14.9805	+	4.33961i	−1.88737	+	0.546739i
$64$	−12.1963			−1.52454
$65$	−2.75557	−	4.77278i	−0.341786	−	0.591990i
$66$	−7.59696	−	3.05739i	−0.935122	−	0.376339i
$67$	4.85080			0.592619			0.296310	−	0.955092i	$-0.404244\pi$
$67$	4.85080			0.592619			0.296310	+	0.955092i	$0.404244\pi$
$68$	6.15613	−	10.6627i	0.746541	−	1.29305i
$69$	0.0189279	−	0.0148295i	0.00227866	−	0.00178527i
$70$	−5.62267	+	9.73875i	−0.672038	+	1.16400i
$71$	−0.669934	+	1.16036i	−0.0795066	+	0.137709i	−0.903037	−	0.429562i	$-0.858668\pi$
$71$	−0.669934	+	1.16036i	−0.0795066	+	0.137709i	0.823531	+	0.567272i	$0.192001\pi$
$72$	−1.05412	+	4.27723i	−0.124229	+	0.504077i
$73$	−5.38078	+	9.31979i	−0.629773	+	1.09080i	0.357824	+	0.933789i	$0.383519\pi$
$73$	−5.38078	+	9.31979i	−0.629773	+	1.09080i	−0.987597	+	0.157010i	$0.949815\pi$
$74$	22.9729			2.67054
$75$	−0.243381	−	1.71487i	−0.0281033	−	0.198016i
$76$	5.26333	+	10.4233i	0.603746	+	1.19564i
$77$	−5.68171	+	9.84102i	−0.647491	+	1.12149i
$78$	−16.2533	+	12.7340i	−1.84033	+	1.44185i
$79$	−3.20925			−0.361068			−0.180534	−	0.983569i	$-0.557783\pi$
$79$	−3.20925			−0.361068			−0.180534	+	0.983569i	$0.557783\pi$
$80$	−1.09073	−	1.88919i	−0.121947	−	0.211218i
$81$	−7.96934	−	4.18206i	−0.885482	−	0.464673i
$82$	−4.12932	−	7.15219i	−0.456007	−	0.789827i
$83$	0.202477	+	0.350701i	0.0222248	+	0.0384944i	0.876924	−	0.480629i	$-0.159592\pi$
$83$	0.202477	+	0.350701i	0.0222248	+	0.0384944i	−0.854699	+	0.519124i	$0.826258\pi$
$84$	22.3777	+	9.00589i	2.44161	+	0.982623i
$85$	4.59609			0.498516
$86$	−8.89230			−0.958882
$87$	−0.369141	−	2.60097i	−0.0395761	−	0.278853i
$88$	1.60480	+	2.77960i	0.171073	+	0.296306i
$89$	2.34580	+	4.06304i	0.248654	+	0.430681i	0.963153	−	0.268956i	$-0.0866785\pi$
$89$	2.34580	+	4.06304i	0.248654	+	0.430681i	−0.714499	+	0.699637i	$0.753345\pi$
$90$	−6.23294	+	1.80558i	−0.657010	+	0.190325i
$91$	14.3256	+	24.8127i	1.50173	+	2.60108i
$92$	−0.0371895			−0.00387727
$93$	1.25608	+	8.85036i	0.130250	+	0.917739i
$94$	−0.480705	+	0.832606i	−0.0495810	+	0.0858767i
$95$	−2.38730	+	3.64703i	−0.244931	+	0.374177i
$96$	−10.4376	+	8.17759i	−1.06529	+	0.834622i
$97$	−11.3187			−1.14924			−0.574620	−	0.818420i	$-0.694850\pi$
$97$	−11.3187			−1.14924			−0.574620	+	0.818420i	$0.694850\pi$
$98$	21.6604	−	37.5169i	2.18803	−	3.78978i
$99$	−6.29839	+	1.82454i	−0.633012	+	0.183373i
$100$	−1.33943	+	2.31995i	−0.133943	+	0.231995i
$101$	−8.55339	+	14.8149i	−0.851094	+	1.47414i	0.0291275	+	0.999576i	$0.490727\pi$
$101$	−8.55339	+	14.8149i	−0.851094	+	1.47414i	−0.880222	+	0.474563i	$0.842606\pi$
$102$	−2.41961	−	17.0486i	−0.239578	−	1.68806i
$103$	0.591048	−	1.02372i	0.0582377	−	0.100871i	−0.835437	−	0.549587i	$-0.814785\pi$
$103$	0.591048	−	1.02372i	0.0582377	−	0.100871i	0.893674	+	0.448716i	$0.148119\pi$
$104$	8.09256			0.793541
$105$	1.26529	+	8.91524i	0.123480	+	0.870039i
$106$	−12.0047	−	20.7928i	−1.16600	−	2.01958i
$107$	5.86354			0.566850			0.283425	−	0.958994i	$-0.408529\pi$
$107$	5.86354			0.566850			0.283425	+	0.958994i	$0.408529\pi$
$108$	5.71337	+	12.6932i	0.549769	+	1.22140i
$109$	2.26312	−	3.91983i	0.216767	−	0.375452i	−0.737051	−	0.675838i	$-0.763782\pi$
$109$	2.26312	−	3.91983i	0.216767	−	0.375452i	0.953818	+	0.300386i	$0.0971154\pi$
$110$	−2.36399	+	4.09455i	−0.225398	+	0.390400i
$111$	14.4803	−	11.3449i	1.37441	−	1.07681i
$112$	5.67047	+	9.82153i	0.535809	+	0.928048i
$113$	−8.04625	+	13.9365i	−0.756927	+	1.31104i	0.187483	+	0.982268i	$0.439967\pi$
$113$	−8.04625	+	13.9365i	−0.756927	+	1.31104i	−0.944410	+	0.328769i	$0.893366\pi$
$114$	14.7850	+	6.93538i	1.38474	+	0.649558i
$115$	−0.00694131	−	0.0120227i	−0.000647281	−	0.00112112i
$116$	−2.03153	+	3.51872i	−0.188623	+	0.326705i
$117$	−3.95625	+	16.0531i	−0.365755	+	1.48411i
$118$	2.68431	+	4.64936i	0.247111	+	0.428008i
$119$	−23.8942			−2.19037
$120$	2.35944	+	0.949556i	0.215387	+	0.0866822i
$121$	3.11118	−	5.38873i	0.282835	−	0.489884i
$122$	−4.82669	+	8.36008i	−0.436988	+	0.756886i
$123$	−6.13483	−	2.46896i	−0.553159	−	0.222618i
$124$	6.91273	−	11.9732i	0.620781	−	1.07522i
$125$	−1.00000			−0.0894427
$126$	32.4038	−	9.38686i	2.88676	−	0.836248i
$127$	−2.83877	−	4.91689i	−0.251900	−	0.436303i	0.712149	−	0.702028i	$-0.247722\pi$
$127$	−2.83877	−	4.91689i	−0.251900	−	0.436303i	−0.964049	+	0.265725i	$0.914389\pi$
$128$	11.0705			0.978506
$129$	−5.60501	+	4.39137i	−0.493494	+	0.386639i
$130$	5.96047	+	10.3238i	0.522768	+	0.905460i
$131$	1.47311	+	2.55151i	0.128707	+	0.222926i	0.923176	−	0.384378i	$-0.125584\pi$
$131$	1.47311	+	2.55151i	0.128707	+	0.222926i	−0.794469	+	0.607305i	$0.792251\pi$
$132$	9.40848	+	3.78643i	0.818903	+	0.329567i
$133$	12.4111	−	18.9602i	1.07618	−	1.64405i
$134$	−10.4926			−0.906422
$135$	−3.03709	+	4.21617i	−0.261391	+	0.362870i
$136$	−3.37446	+	5.84474i	−0.289358	+	0.501182i
$137$	−8.10938	+	14.0459i	−0.692831	+	1.20002i	0.278075	+	0.960559i	$0.410304\pi$
$137$	−8.10938	+	14.0459i	−0.692831	+	1.20002i	−0.970906	+	0.239460i	$0.923030\pi$
$138$	−0.0409424	+	0.0320772i	−0.00348525	+	0.00273060i
$139$	−0.872271			−0.0739850			−0.0369925	−	0.999316i	$-0.511778\pi$
$139$	−0.872271			−0.0739850			−0.0369925	+	0.999316i	$0.511778\pi$
$140$	6.96341	−	12.0610i	0.588515	−	1.01934i
$141$	0.108175	+	0.762201i	0.00910997	+	0.0641889i
$142$	1.44911	−	2.50994i	0.121607	−	0.210629i
$143$	6.02306	+	10.4322i	0.503673	+	0.872388i
$144$	−1.56599	+	6.35423i	−0.130499	+	0.529520i
$145$	−1.51672			−0.125957
$146$	11.6390	−	20.1593i	0.963249	−	1.66840i
$147$	−4.87432	−	34.3445i	−0.402027	−	2.83268i
$148$	−28.4508			−2.33864
$149$	−8.57348	−	14.8497i	−0.702367	−	1.21654i	−0.967633	−	0.252360i	$-0.918793\pi$
$149$	−8.57348	−	14.8497i	−0.702367	−	1.21654i	0.265266	−	0.964175i	$-0.414540\pi$
$150$	0.526450	+	3.70937i	0.0429845	+	0.302869i
$151$	−9.50161	−	16.4573i	−0.773230	−	1.33927i	−0.935784	−	0.352574i	$-0.885306\pi$
$151$	−9.50161	−	16.4573i	−0.773230	−	1.33927i	0.162554	−	0.986700i	$-0.448027\pi$
$152$	−2.88508	−	5.71352i	−0.234011	−	0.463428i
$153$	−9.94441	−	9.55120i	−0.803958	−	0.772169i
$154$	12.2899	−	21.2868i	0.990350	−	1.71534i
$155$	5.16096			0.414538
$156$	20.1290	−	15.7705i	1.61161	−	1.26265i
$157$	−2.37897	−	4.12050i	−0.189863	−	0.328852i	0.755342	−	0.655331i	$-0.227471\pi$
$157$	−2.37897	−	4.12050i	−0.189863	−	0.328852i	−0.945204	+	0.326479i	$0.894138\pi$
$158$	6.94181			0.552261
$159$	−17.8351	−	7.17774i	−1.41442	−	0.569232i
$160$	3.82772	+	6.62980i	0.302608	+	0.524132i
$161$	0.0360865	+	0.0625036i	0.00284401	+	0.00492598i
$162$	17.2382	+	9.04607i	1.35436	+	0.710727i
$163$	−14.2483			−1.11601			−0.558006	−	0.829837i	$-0.688433\pi$
$163$	−14.2483			−1.11601			−0.558006	+	0.829837i	$0.688433\pi$
$164$	5.11396	+	8.85764i	0.399333	+	0.691666i
$165$	0.531978	+	3.74832i	0.0414145	+	0.291806i
$166$	−0.437971	−	0.758589i	−0.0339932	−	0.0588779i
$167$	11.2409			0.869846			0.434923	−	0.900468i	$-0.356776\pi$
$167$	11.2409			0.869846			0.434923	+	0.900468i	$0.356776\pi$
$168$	−12.2663	−	4.93655i	−0.946363	−	0.380863i
$169$	17.3726			1.33635
$170$	−9.94165			−0.762490
$171$	12.7442	−	2.92988i	0.974577	−	0.224053i
$172$	11.0127			0.839710
$173$	21.6308			1.64456			0.822279	−	0.569085i	$-0.192702\pi$
$173$	21.6308			1.64456			0.822279	+	0.569085i	$0.192702\pi$
$174$	0.798476	+	5.62606i	0.0605323	+	0.426511i
$175$	5.19880			0.392992
$176$	2.38409	+	4.12936i	0.179707	+	0.311262i
$177$	3.98802	+	1.60497i	0.299758	+	0.120637i
$178$	−5.07411	−	8.78861i	−0.380321	−	0.658735i
$179$	−7.90754			−0.591037			−0.295519	−	0.955337i	$-0.595492\pi$
$179$	−7.90754			−0.591037			−0.295519	+	0.955337i	$0.595492\pi$
$180$	7.71920	−	2.23613i	0.575355	−	0.166671i
$181$	8.61786	+	14.9266i	0.640560	+	1.10948i	0.985308	+	0.170788i	$0.0546313\pi$
$181$	8.61786	+	14.9266i	0.640560	+	1.10948i	−0.344747	+	0.938696i	$0.612035\pi$
$182$	−30.9873	−	53.6715i	−2.29693	−	3.97840i
$183$	1.08617	+	7.65315i	0.0802919	+	0.565737i
$184$	0.0203853			0.00150282
$185$	−5.31026	−	9.19764i	−0.390418	−	0.676224i
$186$	−2.71699	−	19.1439i	−0.199219	−	1.40370i
$187$	−10.0461			−0.734640
$188$	0.595330	−	1.03114i	0.0434189	−	0.0752038i
$189$	15.7892	−	21.9190i	1.14850	−	1.59437i
$190$	5.16388	−	7.88876i	0.374627	−	0.572311i
$191$	1.75485	+	3.03949i	0.126976	+	0.219930i	0.922504	−	0.385988i	$-0.126139\pi$
$191$	1.75485	+	3.03949i	0.126976	+	0.219930i	−0.795527	+	0.605918i	$0.792806\pi$
$192$	16.6288	−	13.0282i	1.20008	−	0.940228i
$193$	9.88932	+	17.1288i	0.711849	+	1.23296i	0.964162	+	0.265313i	$0.0854754\pi$
$193$	9.88932	+	17.1288i	0.711849	+	1.23296i	−0.252313	+	0.967646i	$0.581191\pi$
$194$	24.4831			1.75778
$195$	8.85533	+	3.56382i	0.634143	+	0.255210i
$196$	−26.8254	+	46.4629i	−1.91610	+	3.31878i
$197$	14.3469			1.02218			0.511088	−	0.859528i	$-0.329243\pi$
$197$	14.3469			1.02218			0.511088	+	0.859528i	$0.329243\pi$
$198$	13.6238	−	3.94661i	0.968204	−	0.280473i
$199$	0.766527	+	1.32766i	0.0543377	+	0.0941156i	0.891915	−	0.452204i	$-0.149362\pi$
$199$	0.766527	+	1.32766i	0.0543377	+	0.0941156i	−0.837577	+	0.546319i	$0.816029\pi$
$200$	0.734202	−	1.27167i	0.0519159	−	0.0899210i
$201$	−6.61371	+	5.18166i	−0.466495	+	0.365486i
$202$	18.5015	−	32.0456i	1.30176	−	2.25472i
$203$	7.88511			0.553426
$204$	2.99658	+	21.1139i	0.209802	+	1.47827i
$205$	−1.90901	+	3.30651i	−0.133331	+	0.230936i
$206$	−1.27848	+	2.21438i	−0.0890756	+	0.154283i
$207$	−0.00996585	+	0.0404379i	−0.000692675	+	0.00281063i
$208$	12.0223			0.833594
$209$	5.21810	−	7.97160i	0.360944	−	0.551407i
$210$	−2.73691	−	19.2843i	−0.188865	−	1.33074i
$211$	−7.15094	−	12.3858i	−0.492291	−	0.852673i	0.507670	−	0.861552i	$-0.330507\pi$
$211$	−7.15094	−	12.3858i	−0.492291	−	0.852673i	−0.999961	+	0.00887901i	$0.997174\pi$
$212$	14.8673	+	25.7509i	1.02109	+	1.76858i
$213$	−0.326099	−	2.29770i	−0.0223440	−	0.157435i
$214$	−12.6832			−0.867008
$215$	2.05549	+	3.56021i	0.140183	+	0.242804i
$216$	−3.13176	−	6.95771i	−0.213089	−	0.473412i
$217$	−26.8308			−1.82139
$218$	−4.89527	+	8.47885i	−0.331549	+	0.574260i
$219$	−2.61917	−	18.4546i	−0.176987	−	1.24705i
$220$	2.92769	−	5.07091i	0.197385	−	0.341881i
$221$	−12.6648	+	21.9361i	−0.851929	+	1.47558i
$222$	−31.3218	+	24.5398i	−2.10218	+	1.64700i
$223$	17.2738			1.15674			0.578369	−	0.815775i	$-0.303689\pi$
$223$	17.2738			1.15674			0.578369	+	0.815775i	$0.303689\pi$
$224$	−19.8995	−	34.4670i	−1.32959	−	2.30292i
$225$	2.16367	+	2.07811i	0.144244	+	0.138541i
$226$	17.4046	−	30.1456i	1.15773	−	2.00525i
$227$	3.14386	+	5.44533i	0.208666	+	0.361419i	0.951294	−	0.308284i	$-0.0997547\pi$
$227$	3.14386	+	5.44533i	0.208666	+	0.361419i	−0.742629	+	0.669703i	$0.766421\pi$
$228$	−18.3105	−	8.58914i	−1.21264	−	0.568830i
$229$	7.99113	−	13.8410i	0.528069	−	0.914642i	−0.471396	−	0.881922i	$-0.656250\pi$
$229$	7.99113	−	13.8410i	0.528069	−	0.914642i	0.999465	−	0.0327203i	$-0.0104170\pi$
$230$	0.0150145	+	0.0260059i	0.000990028	+	0.00171478i
$231$	−2.76565	−	19.4868i	−0.181966	−	1.28213i
$232$	1.11358	−	1.92877i	0.0731099	−	0.126630i
$233$	10.0348	−	17.3807i	0.657398	−	1.13865i	−0.323888	−	0.946095i	$-0.604990\pi$
$233$	10.0348	−	17.3807i	0.657398	−	1.13865i	0.981287	−	0.192552i	$-0.0616765\pi$
$234$	8.55763	−	34.7238i	0.559429	−	2.26997i
$235$	0.444467			0.0289938
$236$	−3.32439	−	5.75801i	−0.216399	−	0.374815i
$237$	4.37557	−	3.42814i	0.284224	−	0.222682i
$238$	51.6847			3.35022
$239$	−8.66261	+	15.0041i	−0.560338	+	0.970533i	0.437129	+	0.899399i	$0.355995\pi$
$239$	−8.66261	+	15.0041i	−0.560338	+	0.970533i	−0.997467	+	0.0711345i	$0.977338\pi$
$240$	3.50518	+	1.41065i	0.226258	+	0.0910574i
$241$	−7.79604	+	13.5031i	−0.502187	+	0.869813i	0.497810	+	0.867286i	$0.334138\pi$
$241$	−7.79604	+	13.5031i	−0.502187	+	0.869813i	−0.999997	+	0.00252720i	$0.999196\pi$
$242$	−6.72969	+	11.6562i	−0.432601	+	0.749287i
$243$	15.3329	−	2.81097i	0.983607	−	0.180324i
$244$	5.97763	−	10.3536i	0.382678	−	0.662818i
$245$	−20.0275			−1.27951
$246$	13.2700	+	5.34052i	0.846067	+	0.340499i
$247$	−10.8281	−	21.4437i	−0.688976	−	1.36443i
$248$	−3.78919	+	6.56306i	−0.240614	+	0.416755i
$249$	−0.650684	−	0.261867i	−0.0412354	−	0.0165952i
$250$	2.16307			0.136804
$251$	3.45345	+	5.98156i	0.217980	+	0.377553i	0.954190	−	0.299200i	$-0.0967199\pi$
$251$	3.45345	+	5.98156i	0.217980	+	0.377553i	−0.736210	+	0.676753i	$0.763387\pi$
$252$	−40.1305	+	11.6252i	−2.52799	+	0.732317i
$253$	0.0151722	+	0.0262790i	0.000953867	+	0.00165215i
$254$	6.14044	+	10.6355i	0.385285	+	0.667334i
$255$	−6.26644	+	4.90958i	−0.392420	+	0.307450i
$256$	0.446318			0.0278949
$257$	−19.0505			−1.18834			−0.594169	−	0.804340i	$-0.702519\pi$
$257$	−19.0505			−1.18834			−0.594169	+	0.804340i	$0.702519\pi$
$258$	12.1240	−	9.49882i	0.754807	−	0.591371i
$259$	27.6070	+	47.8167i	1.71541	+	2.97118i
$260$	−7.38175	−	12.7856i	−0.457797	−	0.792928i
$261$	3.28167	+	3.15191i	0.203130	+	0.195098i
$262$	−3.18644	−	5.51908i	−0.196859	−	0.340970i
$263$	−6.43907			−0.397050			−0.198525	−	0.980096i	$-0.563615\pi$
$263$	−6.43907			−0.397050			−0.198525	+	0.980096i	$0.563615\pi$
$264$	−5.15722	−	2.07552i	−0.317405	−	0.127739i
$265$	−5.54987	+	9.61265i	−0.340926	+	0.590501i
$266$	−26.8460	+	41.0121i	−1.64603	+	2.51461i
$267$	−7.53849	−	3.03386i	−0.461348	−	0.185669i
$268$	12.9946			0.793770
$269$	−9.87331	+	17.1011i	−0.601987	+	1.04267i	0.390533	+	0.920589i	$0.372291\pi$
$269$	−9.87331	+	17.1011i	−0.601987	+	1.04267i	−0.992520	+	0.122083i	$0.961043\pi$
$270$	6.56942	−	9.11985i	0.399802	−	0.555017i
$271$	−6.26407	+	10.8497i	−0.380515	+	0.659072i	−0.991136	−	0.132852i	$-0.957587\pi$
$271$	−6.26407	+	10.8497i	−0.380515	+	0.659072i	0.610621	+	0.791923i	$0.290920\pi$
$272$	−5.01308	+	8.68291i	−0.303963	+	0.526479i
$273$	−46.0371	−	18.5276i	−2.78629	−	1.12134i
$274$	17.5411	−	30.3821i	1.05970	−	1.83545i
$275$	2.18578			0.131807
$276$	0.0507052	−	0.0397261i	0.00305209	−	0.00239123i
$277$	10.3605	+	17.9450i	0.622505	+	1.07821i	0.989018	+	0.147797i	$0.0472183\pi$
$277$	10.3605	+	17.9450i	0.622505	+	1.07821i	−0.366513	+	0.930413i	$0.619448\pi$
$278$	1.88678			0.113161
$279$	−11.1666	−	10.7251i	−0.668527	−	0.642092i
$280$	−3.81697	+	6.61118i	−0.228107	+	0.395094i
$281$	−12.4863	+	21.6269i	−0.744868	+	1.29015i	0.205388	+	0.978681i	$0.434154\pi$
$281$	−12.4863	+	21.6269i	−0.744868	+	1.29015i	−0.950256	+	0.311469i	$0.899179\pi$
$282$	−0.233989	−	1.64869i	−0.0139339	−	0.0981781i
$283$	9.72183	+	16.8387i	0.577903	+	1.00096i	0.995720	+	0.0924259i	$0.0294621\pi$
$283$	9.72183	+	16.8387i	0.577903	+	1.00096i	−0.417817	+	0.908531i	$0.637205\pi$
$284$	−1.79466	+	3.10843i	−0.106493	+	0.184452i
$285$	−0.640879	−	7.52258i	−0.0379624	−	0.445599i
$286$	−13.0283	−	22.5656i	−0.770378	−	1.33433i
$287$	9.92457	−	17.1899i	0.585829	−	1.01469i
$288$	5.49557	−	22.2991i	0.323829	−	1.31399i
$289$	−2.06204	−	3.57156i	−0.121297	−	0.210092i
$290$	3.28076			0.192653
$291$	15.4322	−	12.0907i	0.904653	−	0.708771i
$292$	−14.4143	+	24.9663i	−0.843534	+	1.46104i
$293$	9.32332	−	16.1485i	0.544674	−	0.943404i	−0.453953	−	0.891026i	$-0.649987\pi$
$293$	9.32332	−	16.1485i	0.544674	−	0.943404i	0.998627	−	0.0523779i	$-0.0166800\pi$
$294$	10.5435	+	74.2894i	0.614908	+	4.33264i
$295$	1.24097	−	2.14943i	0.0722523	−	0.125145i
$296$	15.5952			0.906453
$297$	6.63840	−	9.21562i	0.385199	−	0.534745i
$298$	18.5450	+	32.1209i	1.07428	+	1.86071i
$299$	0.0765090			0.00442463
$300$	−0.651983	−	4.59387i	−0.0376423	−	0.265227i
$301$	−10.6861	−	18.5088i	−0.615934	−	1.06683i
$302$	20.5526	+	35.5982i	1.18267	+	2.04844i
$303$	−4.16347	−	29.3358i	−0.239185	−	1.68530i
$304$	−4.28605	−	8.48797i	−0.245822	−	0.486819i
$305$	4.46283			0.255541
$306$	21.5104	+	20.6599i	1.22967	+	1.18105i
$307$	−6.88169	+	11.9194i	−0.392759	+	0.680278i	−0.992812	−	0.119682i	$-0.961813\pi$
$307$	−6.88169	+	11.9194i	−0.392759	+	0.680278i	0.600053	+	0.799960i	$0.295146\pi$
$308$	−15.2205	+	26.3626i	−0.867267	+	1.50215i
$309$	0.287700	+	2.02714i	0.0163667	+	0.115320i
$310$	−11.1635			−0.634044
$311$	14.8795	−	25.7721i	0.843741	−	1.46140i	−0.0429682	−	0.999076i	$-0.513681\pi$
$311$	14.8795	−	25.7721i	0.843741	−	1.46140i	0.886710	−	0.462327i	$-0.152985\pi$
$312$	−11.0336	+	8.64454i	−0.624656	+	0.489401i
$313$	3.02956	−	5.24735i	0.171241	−	0.296598i	−0.767613	−	0.640914i	$-0.778556\pi$
$313$	3.02956	−	5.24735i	0.171241	−	0.296598i	0.938854	+	0.344316i	$0.111889\pi$
$314$	5.14587	+	8.91291i	0.290398	+	0.502985i
$315$	−11.2485	−	10.8037i	−0.633779	−	0.608719i
$316$	−8.59710			−0.483625
$317$	−9.05834	+	15.6895i	−0.508767	+	0.881210i	0.491181	+	0.871057i	$0.336565\pi$
$317$	−9.05834	+	15.6895i	−0.508767	+	0.881210i	−0.999948	+	0.0101531i	$0.996768\pi$
$318$	38.5786	+	15.5259i	2.16338	+	0.870650i
$319$	3.31521			0.185616
$320$	−6.09815	−	10.5623i	−0.340897	−	0.590451i
$321$	−7.99451	+	6.26348i	−0.446210	+	0.349593i
$322$	−0.0780574	−	0.135199i	−0.00434997	−	0.00753437i
$323$	20.0025	+	1.12120i	1.11297	+	0.0623851i
$324$	−21.3487	−	11.2031i	−1.18604	−	0.622396i
$325$	2.75557	−	4.77278i	0.152851	−	0.264746i
$326$	30.8200			1.70696
$327$	1.10160	+	7.76188i	0.0609187	+	0.429233i
$328$	−2.80320	−	4.85528i	−0.154781	−	0.268088i
$329$	−2.31069			−0.127393
$330$	−1.15070	−	8.10786i	−0.0633442	−	0.446323i
$331$	11.2122	+	19.4201i	0.616277	+	1.06742i	0.990159	+	0.139947i	$0.0446932\pi$
$331$	11.2122	+	19.4201i	0.616277	+	1.06742i	−0.373882	+	0.927476i	$0.621973\pi$
$332$	0.542407	+	0.939476i	0.0297684	+	0.0515604i
$333$	−7.62410	+	30.9359i	−0.417798	+	1.69528i
$334$	−24.3148			−1.33045
$335$	2.42540	+	4.20092i	0.132514	+	0.229521i
$336$	−18.2227	−	7.33371i	−0.994130	−	0.400087i
$337$	−0.848151	−	1.46904i	−0.0462017	−	0.0800237i	0.842000	−	0.539478i	$-0.181378\pi$
$337$	−0.848151	−	1.46904i	−0.0462017	−	0.0800237i	−0.888201	+	0.459454i	$0.848045\pi$
$338$	−37.5780			−2.04397
$339$	−3.91662	−	27.5965i	−0.212721	−	1.49883i
$340$	12.3123			0.667726
$341$	−11.2807			−0.610885
$342$	−27.5666	+	6.33752i	−1.49063	+	0.342694i
$343$	67.7273			3.65693
$344$	−6.03657			−0.325470
$345$	0.0223067	+	0.00897732i	0.00120095	+	0.000483322i
$346$	−46.7888			−2.51538
$347$	16.8022	+	29.1023i	0.901991	+	1.56229i	0.824907	+	0.565269i	$0.191228\pi$
$347$	16.8022	+	29.1023i	0.901991	+	1.56229i	0.0770839	+	0.997025i	$0.475439\pi$
$348$	−0.988874	−	6.96761i	−0.0530092	−	0.373503i
$349$	7.43017	+	12.8694i	0.397728	+	0.688885i	0.993445	−	0.114309i	$-0.0364655\pi$
$349$	7.43017	+	12.8694i	0.397728	+	0.688885i	−0.595717	+	0.803194i	$0.703132\pi$
$350$	−11.2453			−0.601089
$351$	−11.7540	−	26.1133i	−0.627380	−	1.39382i
$352$	−8.36654	−	14.4913i	−0.445938	−	0.772388i
$353$	−13.1296	−	22.7411i	−0.698818	−	1.21039i	−0.968876	−	0.247545i	$-0.920376\pi$
$353$	−13.1296	−	22.7411i	−0.698818	−	1.21039i	0.270058	−	0.962844i	$-0.412957\pi$
$354$	−8.62634	−	3.47166i	−0.458485	−	0.184517i
$355$	−1.33987			−0.0711128
$356$	6.28404	+	10.8843i	0.333053	+	0.576866i
$357$	32.5779	−	25.5239i	1.72421	−	1.35087i
$358$	17.1045			0.904002
$359$	10.6075	−	18.3728i	0.559844	−	0.969679i	−0.437665	−	0.899138i	$-0.644194\pi$
$359$	10.6075	−	18.3728i	0.559844	−	0.969679i	0.997509	−	0.0705403i	$-0.0224723\pi$
$360$	−4.23125	+	1.22573i	−0.223006	+	0.0646014i
$361$	−11.2794	+	15.2897i	−0.593650	+	0.804723i
$362$	−18.6410	−	32.2872i	−0.979749	−	1.69698i
$363$	1.51441	+	10.6705i	0.0794859	+	0.560057i
$364$	38.3762	+	66.4696i	2.01146	+	3.48395i
$365$	−10.7616			−0.563286
$366$	−2.34946	−	16.5543i	−0.122808	−	0.865305i
$367$	−9.42736	+	16.3287i	−0.492104	+	0.852350i	−0.999959	−	0.00909332i	$-0.997105\pi$
$367$	−9.42736	+	16.3287i	−0.492104	+	0.852350i	0.507854	+	0.861443i	$0.330439\pi$
$368$	0.0302843			0.00157868
$369$	11.0018	−	3.18703i	0.572728	−	0.165910i
$370$	11.4864	+	19.8951i	0.597152	+	1.03430i
$371$	28.8526	−	49.9742i	1.49795	−	2.59453i
$372$	3.36486	+	23.7088i	0.174460	+	1.22924i
$373$	0.964009	−	1.66971i	0.0499145	−	0.0864544i	−0.839989	−	0.542604i	$-0.817438\pi$
$373$	0.964009	−	1.66971i	0.0499145	−	0.0864544i	0.889903	+	0.456150i	$0.150772\pi$
$374$	21.7303			1.12365
$375$	1.36343	−	1.06821i	0.0704071	−	0.0551620i
$376$	−0.326328	+	0.565217i	−0.0168291	+	0.0291488i
$377$	4.17941	−	7.23896i	0.215251	−	0.372825i
$378$	−34.1531	+	47.4123i	−1.75665	+	2.43862i
$379$	−10.1827			−0.523051			−0.261525	−	0.965197i	$-0.584226\pi$
$379$	−10.1827			−0.523051			−0.261525	+	0.965197i	$0.584226\pi$
$380$	−6.39522	+	9.76985i	−0.328068	+	0.501183i
$381$	9.12271	+	3.67142i	0.467370	+	0.188093i
$382$	−3.79585	−	6.57461i	−0.194213	−	0.336386i
$383$	−10.6697	−	18.4804i	−0.545195	−	0.944305i	−0.998595	−	0.0529978i	$-0.983122\pi$
$383$	−10.6697	−	18.4804i	−0.545195	−	0.944305i	0.453400	−	0.891307i	$-0.350211\pi$
$384$	−15.0939	+	11.8256i	−0.770255	+	0.603474i
$385$	−11.3634			−0.579134
$386$	−21.3913	−	37.0507i	−1.08879	−	1.88583i
$387$	2.95112	−	11.9746i	0.150014	−	0.608704i
$388$	−30.3211			−1.53932
$389$	−4.09771	+	7.09744i	−0.207762	+	0.359854i	−0.951009	−	0.309163i	$-0.899951\pi$
$389$	−4.09771	+	7.09744i	−0.207762	+	0.359854i	0.743247	+	0.669017i	$0.233285\pi$
$390$	−19.1547	−	7.70877i	−0.969934	−	0.390349i
$391$	−0.0319029	+	0.0552575i	−0.00161340	+	0.00279449i
$392$	14.7042	−	25.4685i	0.742676	−	1.28635i
$393$	−4.73402	−	1.90520i	−0.238800	−	0.0961048i
$394$	−31.0333			−1.56344
$395$	−1.60462	−	2.77929i	−0.0807374	−	0.139841i
$396$	−16.8725	+	4.88768i	−0.847873	+	0.245615i
$397$	−2.59934	+	4.50219i	−0.130457	+	0.225958i	−0.923853	−	0.382748i	$-0.874978\pi$
$397$	−2.59934	+	4.50219i	−0.130457	+	0.225958i	0.793396	+	0.608706i	$0.208311\pi$
$398$	−1.65805	−	2.87182i	−0.0831104	−	0.143952i
$399$	3.33180	+	39.1084i	0.166799	+	1.95787i
$400$	1.09073	−	1.88919i	0.0545363	−	0.0944597i
$401$	−11.6318	−	20.1468i	−0.580864	−	1.00609i	−0.995377	−	0.0960423i	$-0.969382\pi$
$401$	−11.6318	−	20.1468i	−0.580864	−	1.00609i	0.414514	−	0.910043i	$-0.363952\pi$
$402$	14.3059	−	11.2083i	0.713513	−	0.559018i
$403$	−14.2214	+	24.6321i	−0.708417	+	1.22701i
$404$	−22.9133	+	39.6870i	−1.13998	+	1.97450i
$405$	−0.362899	−	8.99268i	−0.0180326	−	0.446850i
$406$	−17.0560			−0.846475
$407$	11.6071	+	20.1040i	0.575341	+	0.996519i
$408$	−1.64256	−	11.5735i	−0.0813190	−	0.572973i
$409$	−5.20492			−0.257367			−0.128683	−	0.991686i	$-0.541075\pi$
$409$	−5.20492			−0.257367			−0.128683	+	0.991686i	$0.541075\pi$
$410$	4.12932	−	7.15219i	0.203933	−	0.353221i
$411$	−3.94735	−	27.8130i	−0.194708	−	1.37191i
$412$	1.58333	−	2.74241i	0.0780051	−	0.135109i
$413$	−6.45158	+	11.1745i	−0.317461	+	0.549859i
$414$	0.0215568	−	0.0874699i	0.00105946	−	0.00429891i
$415$	−0.202477	+	0.350701i	−0.00993921	+	0.0172152i
$416$	−42.1901			−2.06854
$417$	1.18928	−	0.931766i	0.0582392	−	0.0456288i
$418$	−11.2871	+	17.2431i	−0.552070	+	0.843387i
$419$	9.33779	−	16.1735i	0.456181	−	0.790129i	−0.542574	−	0.840008i	$-0.682550\pi$
$419$	9.33779	−	16.1735i	0.456181	−	0.790129i	0.998755	+	0.0498792i	$0.0158836\pi$
$420$	3.38953	+	23.8826i	0.165392	+	1.16535i
$421$	−9.27264			−0.451921			−0.225960	−	0.974137i	$-0.572552\pi$
$421$	−9.27264			−0.451921			−0.225960	+	0.974137i	$0.572552\pi$
$422$	15.4679	+	26.7913i	0.752968	+	1.30418i
$423$	−0.961677	−	0.923651i	−0.0467583	−	0.0449095i
$424$	−8.14945	−	14.1153i	−0.395772	−	0.685497i
$425$	2.29805	+	3.98033i	0.111472	+	0.193075i
$426$	0.705374	+	4.97007i	0.0341755	+	0.240800i
$427$	−23.2013			−1.12279
$428$	15.7076			0.759254
$429$	−19.3558	−	7.78972i	−0.934507	−	0.376091i
$430$	−4.44615	−	7.70096i	−0.214412	−	0.371373i
$431$	11.3630	+	19.6813i	0.547335	+	0.948013i	0.998456	+	0.0555496i	$0.0176911\pi$
$431$	11.3630	+	19.6813i	0.547335	+	0.948013i	−0.451121	+	0.892463i	$0.648976\pi$
$432$	−4.65253	−	10.3363i	−0.223845	−	0.497307i
$433$	−18.0471	−	31.2585i	−0.867290	−	1.50219i	−0.864755	−	0.502193i	$-0.832527\pi$
$433$	−18.0471	−	31.2585i	−0.867290	−	1.50219i	−0.00253437	−	0.999997i	$-0.500807\pi$
$434$	58.0368			2.78585
$435$	2.06793	−	1.62017i	0.0991498	−	0.0776811i
$436$	6.06256	−	10.5007i	0.290344	−	0.502890i
$437$	−0.0272762	−	0.0540169i	−0.00130480	−	0.00258398i
$438$	5.66543	+	39.9186i	0.270705	+	1.90738i
$439$	−29.5573			−1.41069			−0.705346	−	0.708863i	$-0.749209\pi$
$439$	−29.5573			−1.41069			−0.705346	+	0.708863i	$0.749209\pi$
$440$	−1.60480	+	2.77960i	−0.0765060	+	0.132512i
$441$	43.3328	+	41.6194i	2.06347	+	1.98188i
$442$	27.3949	−	47.4493i	1.30304	−	2.25693i
$443$	−20.6919	+	35.8394i	−0.983101	+	1.70278i	−0.333010	+	0.942923i	$0.608064\pi$
$443$	−20.6919	+	35.8394i	−0.983101	+	1.70278i	−0.650090	+	0.759857i	$0.725269\pi$
$444$	38.7906	−	30.3914i	1.84092	−	1.44231i
$445$	−2.34580	+	4.06304i	−0.111201	+	0.192606i
$446$	−37.3644			−1.76925
$447$	27.5519	+	11.0882i	1.30316	+	0.524455i
$448$	31.7030	+	54.9113i	1.49783	+	2.59431i
$449$	−16.6979			−0.788023			−0.394011	−	0.919106i	$-0.628913\pi$
$449$	−16.6979			−0.788023			−0.394011	+	0.919106i	$0.628913\pi$
$450$	−4.68015	−	4.49509i	−0.220624	−	0.211901i
$451$	4.17268	−	7.22729i	0.196484	−	0.340320i
$452$	−21.5547	+	37.3339i	−1.01385	+	1.75604i
$453$	30.5345	+	12.2886i	1.43464	+	0.577368i
$454$	−6.80038	−	11.7786i	−0.319158	−	0.552797i
$455$	−14.3256	+	24.8127i	−0.671596	+	1.16324i
$456$	10.0368	+	4.70811i	0.470017	+	0.220477i
$457$	3.31090	+	5.73465i	0.154877	+	0.268256i	0.933014	−	0.359839i	$-0.117168\pi$
$457$	3.31090	+	5.73465i	0.154877	+	0.268256i	−0.778137	+	0.628095i	$0.783835\pi$
$458$	−17.2853	+	29.9391i	−0.807691	+	1.39896i
$459$	23.7611	+	2.39967i	1.10908	+	0.112007i
$460$	−0.0185948	−	0.0322071i	−0.000866985	−	0.00150166i
$461$	9.79745			0.456313			0.228156	−	0.973624i	$-0.426730\pi$
$461$	9.79745			0.456313			0.228156	+	0.973624i	$0.426730\pi$
$462$	5.98228	+	42.1511i	0.278321	+	1.96105i
$463$	−10.7443	+	18.6097i	−0.499332	+	0.864868i	−1.00000		0.000771637i	$-0.999754\pi$
$463$	−10.7443	+	18.6097i	−0.499332	+	0.864868i	0.500668	+	0.865639i	$0.333088\pi$
$464$	1.65432	−	2.86537i	0.0768000	−	0.133022i
$465$	−7.03659	+	5.51298i	−0.326314	+	0.255658i
$466$	−21.7058	+	37.5956i	−1.00550	+	1.74158i
$467$	21.0465			0.973917			0.486958	−	0.873425i	$-0.338106\pi$
$467$	21.0465			0.973917			0.486958	+	0.873425i	$0.338106\pi$
$468$	−10.5982	+	43.0038i	−0.489902	+	1.98785i
$469$	−12.6092	−	21.8397i	−0.582237	−	1.00846i
$470$	−0.961410			−0.0443466
$471$	7.64510	+	3.07676i	0.352268	+	0.141770i
$472$	1.82225	+	3.15623i	0.0838759	+	0.145277i
$473$	−4.49284	−	7.78183i	−0.206581	−	0.357809i
$474$	−9.46465	+	7.41530i	−0.434726	+	0.340596i
$475$	−4.35207	−	0.243946i	−0.199687	−	0.0111930i
$476$	−64.0090			−2.93385
$477$	31.9842	−	9.26532i	1.46446	−	0.424230i
$478$	18.7378	−	32.4548i	0.857047	−	1.48445i
$479$	12.6104	−	21.8418i	0.576182	−	0.997977i	−0.419730	−	0.907649i	$-0.637875\pi$
$479$	12.6104	−	21.8418i	0.576182	−	0.997977i	0.995912	−	0.0903277i	$-0.0287915\pi$
$480$	−12.3008	−	4.95045i	−0.561453	−	0.225956i
$481$	58.5311			2.66879
$482$	16.8633	−	29.2082i	0.768104	−	1.33040i
$483$	−0.115968	−	0.0466713i	−0.00527673	−	0.00212362i
$484$	8.33440	−	14.4356i	0.378837	−	0.656164i
$485$	−5.65935	−	9.80228i	−0.256978	−	0.445099i
$486$	−33.1661	+	6.08032i	−1.50445	+	0.275809i
$487$	12.8807			0.583678			0.291839	−	0.956467i	$-0.405733\pi$
$487$	12.8807			0.583678			0.291839	+	0.956467i	$0.405733\pi$
$488$	−3.27661	+	5.67526i	−0.148325	+	0.256907i
$489$	19.4265	−	15.2201i	0.878496	−	0.688278i
$490$	43.3208			1.95703
$491$	18.3931	+	31.8577i	0.830067	+	1.43772i	0.897984	+	0.440028i	$0.145031\pi$
$491$	18.3931	+	31.8577i	0.830067	+	1.43772i	−0.0679171	+	0.997691i	$0.521635\pi$
$492$	−16.4343	−	6.61397i	−0.740916	−	0.298181i
$493$	3.48549	+	6.03704i	0.156978	+	0.271895i
$494$	23.4219	+	46.3841i	1.05380	+	2.08692i
$495$	−4.72930	−	4.54230i	−0.212566	−	0.204161i
$496$	−5.62920	+	9.75005i	−0.252758	+	0.437790i
$497$	6.96571			0.312455
$498$	1.40747	+	0.566436i	0.0630703	+	0.0253826i
$499$	−8.56969	−	14.8431i	−0.383632	−	0.664470i	0.607946	−	0.793978i	$-0.291994\pi$
$499$	−8.56969	−	14.8431i	−0.383632	−	0.664470i	−0.991578	+	0.129508i	$0.958660\pi$
$500$	−2.67885			−0.119802
$501$	−15.3261	+	12.0076i	−0.684721	+	0.536460i
$502$	−7.47005	−	12.9385i	−0.333405	−	0.577474i
$503$	−13.6175	−	23.5861i	−0.607172	−	1.05165i	−0.991704	−	0.128542i	$-0.958970\pi$
$503$	−13.6175	−	23.5861i	−0.607172	−	1.05165i	0.384532	−	0.923112i	$-0.374363\pi$
$504$	21.9974	−	6.37230i	0.979843	−	0.283845i
$505$	−17.1068			−0.761242
$506$	−0.0328184	−	0.0568432i	−0.00145896	−	0.00252699i
$507$	−23.6862	+	18.5575i	−1.05194	+	0.824167i
$508$	−7.60464	−	13.1716i	−0.337401	−	0.584396i
$509$	−0.249520			−0.0110598			−0.00552989	−	0.999985i	$-0.501760\pi$
$509$	−0.249520			−0.0110598			−0.00552989	+	0.999985i	$0.501760\pi$
$510$	13.5547	−	10.6198i	0.600213	−	0.470250i
$511$	55.9472			2.47496
$512$	−23.1065			−1.02117
$513$	−14.2461	+	17.6082i	−0.628982	+	0.777420i
$514$	41.2075			1.81758
$515$	1.18210			0.0520894
$516$	−15.0150	+	11.7638i	−0.660998	+	0.517874i
$517$	−0.971506			−0.0427268
$518$	−59.7157	−	103.431i	−2.62376	−	4.54448i
$519$	−29.4920	+	23.1062i	−1.29455	+	1.01425i
$520$	4.04628	+	7.00837i	0.177441	+	0.307337i
$521$	15.2359			0.667497			0.333748	−	0.942662i	$-0.391686\pi$
$521$	15.2359			0.667497			0.333748	+	0.942662i	$0.391686\pi$
$522$	−7.09847	−	6.81779i	−0.310691	−	0.298406i
$523$	−3.88449	−	6.72814i	−0.169857	−	0.294201i	0.768512	−	0.639835i	$-0.220997\pi$
$523$	−3.88449	−	6.72814i	−0.169857	−	0.294201i	−0.938369	+	0.345634i	$0.887664\pi$
$524$	3.94626	+	6.83512i	0.172393	+	0.298593i
$525$	−7.08818	+	5.55340i	−0.309354	+	0.242370i
$526$	13.9281			0.607295
$527$	−11.8601	−	20.5424i	−0.516636	−	0.894839i
$528$	−7.66154	−	3.08338i	−0.333426	−	0.134187i
$529$	−22.9998			−0.999992
$530$	12.0047	−	20.7928i	0.521452	−	0.903182i
$531$	−7.15181	+	2.07177i	−0.310362	+	0.0899070i
$532$	33.2474	−	50.7915i	1.44146	−	2.20209i
$533$	−10.5208	−	18.2226i	−0.455707	−	0.789308i
$534$	16.3062	+	6.56243i	0.705640	+	0.283984i
$535$	2.93177	+	5.07798i	0.126752	+	0.219540i
$536$	−7.12293			−0.307664
$537$	10.7813	−	8.44689i	0.465250	−	0.364510i
$538$	21.3566	−	36.9908i	0.920749	−	1.59478i
$539$	43.7757			1.88555
$540$	−8.13591	+	11.2945i	−0.350114	+	0.486038i
$541$	−17.1369	−	29.6819i	−0.736771	−	1.27612i	−0.953942	−	0.299991i	$-0.903016\pi$
$541$	−17.1369	−	29.6819i	−0.736771	−	1.27612i	0.217171	−	0.976134i	$-0.430317\pi$
$542$	13.5496	−	23.4686i	0.582005	−	1.00806i
$543$	−27.6945	−	11.1456i	−1.18848	−	0.478305i
$544$	17.5925	−	30.4712i	0.754274	−	1.30644i
$545$	4.52623			0.193882
$546$	99.5812	+	40.0764i	4.26168	+	1.71511i
$547$	13.5627	−	23.4912i	0.579897	−	1.00441i	−0.415594	−	0.909550i	$-0.636426\pi$
$547$	13.5627	−	23.4912i	0.579897	−	1.00441i	0.995491	−	0.0948607i	$-0.0302406\pi$
$548$	−21.7238	+	37.6268i	−0.927997	+	1.60734i
$549$	−9.65606	−	9.27425i	−0.412111	−	0.395815i
$550$	−4.72798			−0.201602
$551$	−6.60086	−	0.369996i	−0.281206	−	0.0157624i
$552$	−0.0277939	+	0.0217757i	−0.00118299	+	0.000926837i
$553$	8.34211	+	14.4490i	0.354743	+	0.614432i
$554$	−22.4105	−	38.8162i	−0.952133	−	1.64914i
$555$	17.0651	+	6.86785i	0.724375	+	0.291524i
$556$	−2.33668			−0.0990975
$557$	1.60490	+	2.77977i	0.0680018	+	0.117783i	0.898022	−	0.439951i	$-0.145004\pi$
$557$	1.60490	+	2.77977i	0.0680018	+	0.117783i	−0.830020	+	0.557734i	$0.811671\pi$
$558$	24.1541	+	23.1990i	1.02252	+	0.982092i
$559$	−22.6561			−0.958251
$560$	−5.67047	+	9.82153i	−0.239621	+	0.415036i
$561$	13.6971	−	10.7313i	0.578290	−	0.453074i
$562$	27.0086	−	46.7803i	1.13929	−	1.97331i
$563$	−8.51953	+	14.7563i	−0.359055	+	0.621902i	−0.987803	−	0.155707i	$-0.950234\pi$
$563$	−8.51953	+	14.7563i	−0.359055	+	0.621902i	0.628748	+	0.777609i	$0.283568\pi$
$564$	0.289785	+	2.04182i	0.0122021	+	0.0859763i
$565$	−16.0925			−0.677016
$566$	−21.0290	−	36.4232i	−0.883913	−	1.53098i
$567$	1.88664	+	46.7511i	0.0792313	+	1.96336i
$568$	0.983734	−	1.70388i	0.0412766	−	0.0714931i
$569$	9.08257	+	15.7315i	0.380761	+	0.659497i	0.991171	−	0.132588i	$-0.0423287\pi$
$569$	9.08257	+	15.7315i	0.380761	+	0.659497i	−0.610410	+	0.792085i	$0.708995\pi$
$570$	1.38626	+	16.2718i	0.0580642	+	0.681553i
$571$	−12.0964	+	20.9515i	−0.506217	+	0.876793i	0.493757	+	0.869600i	$0.335623\pi$
$571$	−12.0964	+	20.9515i	−0.506217	+	0.876793i	−0.999974	+	0.00719332i	$0.997710\pi$
$572$	16.1349	+	27.9464i	0.674634	+	1.16850i
$573$	−5.63941	−	2.26958i	−0.235590	−	0.0948129i
$574$	−21.4675	+	37.1828i	−0.896036	+	1.55198i
$575$	0.00694131	−	0.0120227i	0.000289473	−	0.000501382i
$576$	−8.75530	+	35.5259i	−0.364804	+	1.48025i
$577$	3.50898			0.146081			0.0730403	−	0.997329i	$-0.476730\pi$
$577$	3.50898			0.146081			0.0730403	+	0.997329i	$0.476730\pi$
$578$	4.46034	+	7.72553i	0.185526	+	0.321340i
$579$	−31.7805	−	12.7900i	−1.32075	−	0.531535i
$580$	−4.06306			−0.168709
$581$	1.05264	−	1.82322i	0.0436708	−	0.0756400i
$582$	−33.3809	+	26.1530i	−1.38368	+	1.08408i
$583$	12.1308	−	21.0111i	0.502406	−	0.870193i
$584$	7.90116	−	13.6852i	0.326952	−	0.566298i
$585$	−15.8805	+	4.60032i	−0.656578	+	0.190200i
$586$	−20.1670	+	34.9302i	−0.833089	+	1.44295i
$587$	18.3480			0.757303			0.378652	−	0.925539i	$-0.376388\pi$
$587$	18.3480			0.757303			0.378652	+	0.925539i	$0.376388\pi$
$588$	−13.0576	−	92.0038i	−0.538486	−	3.79417i
$589$	22.4609	+	1.25899i	0.925483	+	0.0518759i
$590$	−2.68431	+	4.64936i	−0.110511	+	0.191411i
$591$	−19.5610	+	15.3255i	−0.804632	+	0.630407i
$592$	23.1682			0.952206
$593$	−9.76643	−	16.9159i	−0.401059	−	0.694655i	0.592795	−	0.805353i	$-0.298024\pi$
$593$	−9.76643	−	16.9159i	−0.401059	−	0.694655i	−0.993854	+	0.110699i	$0.964691\pi$
$594$	−14.3593	+	19.9340i	−0.589169	+	0.817902i
$595$	−11.9471	−	20.6930i	−0.489783	−	0.848329i
$596$	−22.9671	−	39.7802i	−0.940769	−	1.62946i
$597$	−2.46332	−	0.991362i	−0.100817	−	0.0405738i
$598$	−0.165494			−0.00676755
$599$	−10.6255			−0.434146			−0.217073	−	0.976155i	$-0.569651\pi$
$599$	−10.6255			−0.434146			−0.217073	+	0.976155i	$0.569651\pi$
$600$	0.357382	+	2.51812i	0.0145901	+	0.102802i
$601$	10.1311	+	17.5475i	0.413255	+	0.715778i	0.995243	−	0.0974186i	$-0.0310586\pi$
$601$	10.1311	+	17.5475i	0.413255	+	0.715778i	−0.581989	+	0.813197i	$0.697725\pi$
$602$	23.1146	+	40.0357i	0.942082	+	1.63173i
$603$	3.48222	−	14.1296i	0.141807	−	0.575403i
$604$	−25.4534	−	44.0866i	−1.03568	−	1.79386i
$605$	6.22237			0.252975
$606$	9.00587	+	63.4553i	0.365838	+	2.57770i
$607$	1.71800	−	2.97566i	0.0697313	−	0.120778i	−0.829052	−	0.559172i	$-0.811119\pi$
$607$	1.71800	−	2.97566i	0.0697313	−	0.120778i	0.898783	+	0.438394i	$0.144452\pi$
$608$	15.0412	+	29.7871i	0.610000	+	1.20803i
$609$	−10.7508	+	8.42293i	−0.435643	+	0.341314i
$610$	−9.65338			−0.390854
$611$	−1.22476	+	2.12134i	−0.0495483	+	0.0858203i
$612$	−26.6396	−	25.5863i	−1.07684	−	1.03426i
$613$	−15.3156	+	26.5274i	−0.618591	+	1.07143i	0.371152	+	0.928572i	$0.378963\pi$
$613$	−15.3156	+	26.5274i	−0.618591	+	1.07143i	−0.989743	+	0.142859i	$0.954370\pi$
$614$	14.8856	−	25.7825i	0.600732	−	1.04050i
$615$	−0.929236	−	6.54740i	−0.0374704	−	0.264017i
$616$	8.34305	−	14.4506i	0.336151	−	0.582231i
$617$	4.72377			0.190172			0.0950858	−	0.995469i	$-0.469687\pi$
$617$	4.72377			0.190172			0.0950858	+	0.995469i	$0.469687\pi$
$618$	−0.622314	−	4.38483i	−0.0250332	−	0.176384i
$619$	−0.634139	−	1.09836i	−0.0254882	−	0.0441469i	0.853000	−	0.521911i	$-0.174781\pi$
$619$	−0.634139	−	1.09836i	−0.0254882	−	0.0441469i	−0.878488	+	0.477764i	$0.841447\pi$
$620$	13.8255			0.555244
$621$	−0.0296084	−	0.0657798i	−0.00118814	−	0.00263965i
$622$	−32.1854	+	55.7468i	−1.29052	+	2.23524i
$623$	12.1953	−	21.1229i	0.488595	−	0.846271i
$624$	−16.3915	+	12.8423i	−0.656185	+	0.514103i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−6.55314	+	11.3504i	−0.261916	+	0.453652i
$627$	1.40082	+	16.4427i	0.0559434	+	0.656659i
$628$	−6.37292	−	11.0382i	−0.254307	−	0.440473i
$629$	−24.4065	+	42.2732i	−0.973149	+	1.68554i
$630$	24.3312	+	23.3691i	0.969377	+	0.931047i
$631$	−15.9552	−	27.6352i	−0.635166	−	1.10014i	−0.986480	−	0.163882i	$-0.947598\pi$
$631$	−15.9552	−	27.6352i	−0.635166	−	1.10014i	0.351314	−	0.936258i	$-0.385735\pi$
$632$	4.71247			0.187452
$633$	22.9804	+	9.24843i	0.913388	+	0.367592i
$634$	19.5938	−	33.9374i	0.778169	−	1.34783i
$635$	2.83877	−	4.91689i	0.112653	−	0.195121i
$636$	−47.7777	−	19.2281i	−1.89451	−	0.762444i
$637$	55.1871	−	95.5868i	2.18659	−	3.78729i
$638$	−7.17102			−0.283903
$639$	2.89903	+	2.78440i	0.114684	+	0.110149i
$640$	5.53526	+	9.58736i	0.218801	+	0.378974i
$641$	17.5154			0.691816			0.345908	−	0.938268i	$-0.387571\pi$
$641$	17.5154			0.691816			0.345908	+	0.938268i	$0.387571\pi$
$642$	17.2927	−	13.5483i	0.682487	−	0.534710i
$643$	−8.47372	−	14.6769i	−0.334171	−	0.578801i	0.649154	−	0.760657i	$-0.275123\pi$
$643$	−8.47372	−	14.6769i	−0.334171	−	0.578801i	−0.983325	+	0.181856i	$0.941790\pi$
$644$	0.0966704	+	0.167438i	0.00380935	+	0.00659798i
$645$	−6.60554	−	2.65839i	−0.260093	−	0.104674i
$646$	−43.2668	−	2.42522i	−1.70231	−	0.0954191i
$647$	7.17073			0.281911			0.140955	−	0.990016i	$-0.454983\pi$
$647$	7.17073			0.281911			0.140955	+	0.990016i	$0.454983\pi$
$648$	11.7022	+	6.14095i	0.459706	+	0.241239i
$649$	−2.71250	+	4.69818i	−0.106475	+	0.184420i
$650$	−5.96047	+	10.3238i	−0.233789	+	0.404934i
$651$	36.5818	−	28.6609i	1.43375	−	1.12331i
$652$	−38.1691			−1.49482
$653$	24.9697	−	43.2488i	0.977140	−	1.69246i	0.304455	−	0.952527i	$-0.401526\pi$
$653$	24.9697	−	43.2488i	0.977140	−	1.69246i	0.672684	−	0.739929i	$-0.265141\pi$
$654$	−2.38284	−	16.7895i	−0.0931762	−	0.656520i
$655$	−1.47311	+	2.55151i	−0.0575593	+	0.0996957i
$656$	−4.16442	−	7.21299i	−0.162593	−	0.281620i
$657$	23.2844	+	22.3637i	0.908412	+	0.872492i
$658$	4.99818			0.194849
$659$	−18.7883	+	32.5423i	−0.731889	+	1.26767i	0.224186	+	0.974546i	$0.428028\pi$
$659$	−18.7883	+	32.5423i	−0.731889	+	1.26767i	−0.956075	+	0.293122i	$0.905306\pi$
$660$	1.42509	+	10.0412i	0.0554716	+	0.390853i
$661$	−34.5261			−1.34291			−0.671455	−	0.741046i	$-0.734330\pi$
$661$	−34.5261			−1.34291			−0.671455	+	0.741046i	$0.734330\pi$
$662$	−24.2527	−	42.0069i	−0.942607	−	1.63264i
$663$	−6.16477	−	43.4370i	−0.239420	−	1.68695i
$664$	−0.297318	−	0.514970i	−0.0115382	−	0.0199847i
$665$	22.6255	+	1.26822i	0.877380	+	0.0491796i
$666$	16.4914	−	66.9165i	0.639030	−	2.59296i
$667$	0.0105280	−	0.0182350i	0.000407646	−	0.000706064i
$668$	30.1127			1.16509
$669$	−23.5516	+	18.4520i	−0.910556	+	0.713395i
$670$	−5.24630	−	9.08686i	−0.202682	−	0.351056i
$671$	−9.75475			−0.376578
$672$	63.9494	+	25.7364i	2.46690	+	0.992803i
$673$	4.19456	+	7.26520i	0.161689	+	0.280053i	0.935474	−	0.353394i	$-0.114973\pi$
$673$	4.19456	+	7.26520i	0.161689	+	0.280053i	−0.773786	+	0.633447i	$0.781639\pi$
$674$	1.83461	+	3.17763i	0.0706664	+	0.122398i
$675$	−5.16986	−	0.522110i	−0.198988	−	0.0200960i
$676$	46.5385			1.78994
$677$	−17.5779	−	30.4458i	−0.675574	−	1.17013i	−0.976301	−	0.216418i	$-0.930563\pi$
$677$	−17.5779	−	30.4458i	−0.675574	−	1.17013i	0.300727	−	0.953710i	$-0.402771\pi$
$678$	8.47190	+	59.6930i	0.325361	+	2.29250i
$679$	29.4218	+	50.9601i	1.12911	+	1.95567i
$680$	−6.74892			−0.258809
$681$	−10.1032	−	4.06601i	−0.387154	−	0.155810i
$682$	24.4009			0.934361
$683$	−41.8769			−1.60238			−0.801188	−	0.598413i	$-0.795798\pi$
$683$	−41.8769			−1.60238			−0.801188	+	0.598413i	$0.795798\pi$
$684$	34.1400	−	7.84872i	1.30537	−	0.300103i
$685$	−16.2188			−0.619687
$686$	−146.499			−5.59335
$687$	3.88979	+	27.4074i	0.148405	+	1.04566i
$688$	−8.96789			−0.341898
$689$	−30.5861	−	52.9766i	−1.16524	−	2.01825i
$690$	−0.0482509	−	0.0194185i	−0.00183688	−	0.000739251i
$691$	−18.0138	−	31.2009i	−0.685279	−	1.18694i	−0.973349	−	0.229328i	$-0.926347\pi$
$691$	−18.0138	−	31.2009i	−0.685279	−	1.18694i	0.288071	−	0.957609i	$-0.406986\pi$
$692$	57.9457			2.20276
$693$	24.5867	+	23.6145i	0.933970	+	0.897040i
$694$	−36.3443	−	62.9502i	−1.37961	−	2.38956i
$695$	−0.436135	−	0.755409i	−0.0165436	−	0.0286543i
$696$	0.542048	+	3.81927i	0.0205463	+	0.144769i
$697$	17.5480			0.664678
$698$	−16.0719	−	27.8374i	−0.608332	−	1.05366i
$699$	4.88455	+	34.4165i	0.184750	+	1.30175i
$700$	13.9268			0.526384
$701$	−7.49983	+	12.9901i	−0.283265	+	0.490629i	−0.972187	−	0.234207i	$-0.924751\pi$
$701$	−7.49983	+	12.9901i	−0.283265	+	0.490629i	0.688922	+	0.724835i	$0.258084\pi$
$702$	25.4246	+	56.4847i	0.959589	+	2.13188i
$703$	−20.8669	−	41.3242i	−0.787010	−	1.55857i
$704$	13.3292	+	23.0869i	0.502363	+	0.870119i
$705$	−0.605998	+	0.474783i	−0.0228232	+	0.0178813i
$706$	28.4002	+	49.1906i	1.06886	+	1.85131i
$707$	88.9347			3.34473
$708$	10.6833	+	4.29949i	0.401503	+	0.161585i
$709$	10.6478	−	18.4425i	0.399887	−	0.692624i	−0.593825	−	0.804594i	$-0.702383\pi$
$709$	10.6478	−	18.4425i	0.399887	−	0.692624i	0.993712	+	0.111970i	$0.0357162\pi$
$710$	2.89822			0.108768
$711$	−2.30381	+	9.34804i	−0.0863995	+	0.350579i
$712$	−3.44457	−	5.96618i	−0.129091	−	0.223592i
$713$	−0.0358238	+	0.0620487i	−0.00134161	+	0.00232374i
$714$	−70.4682	+	55.2099i	−2.63721	+	2.06618i
$715$	−6.02306	+	10.4322i	−0.225250	+	0.390144i
$716$	−21.1831			−0.791651
$717$	−4.21664	−	29.7104i	−0.157473	−	1.10956i
$718$	−22.9448	+	39.7415i	−0.856292	+	1.48314i
$719$	−1.66353	+	2.88132i	−0.0620392	+	0.107455i	−0.895377	−	0.445309i	$-0.853094\pi$
$719$	−1.66353	+	2.88132i	−0.0620392	+	0.107455i	0.833338	+	0.552764i	$0.186427\pi$
$720$	−6.28592	+	1.82093i	−0.234263	+	0.0678621i
$721$	−6.14548			−0.228869
$722$	24.3980	−	33.0727i	0.907999	−	1.23084i
$723$	−3.79482	−	26.7383i	−0.141131	−	0.994409i
$724$	23.0860	+	39.9861i	0.857984	+	1.48607i
$725$	−0.758359	−	1.31352i	−0.0281647	−	0.0487827i
$726$	−3.27577	−	23.0810i	−0.121575	−	0.856618i
$727$	−35.8107			−1.32814			−0.664072	−	0.747668i	$-0.731173\pi$
$727$	−35.8107			−1.32814			−0.664072	+	0.747668i	$0.731173\pi$
$728$	−21.0358	−	36.4351i	−0.779639	−	1.35037i
$729$	−17.9026	+	20.2113i	−0.663060	+	0.748567i
$730$	23.2780			0.861556
$731$	9.44721	−	16.3630i	0.349418	−	0.605209i
$732$	2.90969	+	20.5017i	0.107545	+	0.757763i
$733$	17.5423	−	30.3842i	0.647941	−	1.12227i	−0.335673	−	0.941979i	$-0.608964\pi$
$733$	17.5423	−	30.3842i	0.647941	−	1.12227i	0.983614	−	0.180288i	$-0.0577031\pi$
$734$	20.3920	−	35.3200i	0.752683	−	1.30368i
$735$	27.3060	−	21.3935i	1.00720	−	0.789112i
$736$	−0.106278			−0.00391744
$737$	−5.30139	−	9.18228i	−0.195279	−	0.338233i
$738$	−23.7975	+	6.89376i	−0.875999	+	0.253763i
$739$	17.4626	−	30.2461i	0.642373	−	1.11262i	−0.342529	−	0.939507i	$-0.611283\pi$
$739$	17.4626	−	30.2461i	0.642373	−	1.11262i	0.984902	−	0.173115i	$-0.0553832\pi$
$740$	−14.2254	−	24.6391i	−0.522936	−	0.905752i
$741$	37.6696	+	17.6702i	1.38383	+	0.649131i
$742$	−62.4102	+	108.098i	−2.29115	+	3.96839i
$743$	−7.67999	−	13.3021i	−0.281751	−	0.488008i	0.690065	−	0.723748i	$-0.257582\pi$
$743$	−7.67999	−	13.3021i	−0.281751	−	0.488008i	−0.971816	+	0.235740i	$0.924249\pi$
$744$	−1.84444	−	12.9959i	−0.0676203	−	0.476453i
$745$	8.57348	−	14.8497i	0.314108	−	0.544051i
$746$	−2.08521	+	3.61170i	−0.0763451	+	0.132234i
$747$	1.16689	−	0.338029i	0.0426942	−	0.0123678i
$748$	−26.9119			−0.983996
$749$	−15.2417	−	26.3994i	−0.556919	−	0.964612i
$750$	−2.94918	+	2.31060i	−0.107689	+	0.0843713i
$751$	−20.5951			−0.751528			−0.375764	−	0.926715i	$-0.622620\pi$
$751$	−20.5951			−0.751528			−0.375764	+	0.926715i	$0.622620\pi$
$752$	−0.484791	+	0.839683i	−0.0176785	+	0.0306201i
$753$	−11.0981	−	4.46641i	−0.404436	−	0.162765i
$754$	−9.04035	+	15.6583i	−0.329230	+	0.570243i
$755$	9.50161	−	16.4573i	0.345799	−	0.598941i
$756$	42.2970	−	58.7178i	1.53833	−	2.13555i
$757$	−5.12464	+	8.87614i	−0.186258	+	0.322609i	−0.944000	−	0.329946i	$-0.892969\pi$
$757$	−5.12464	+	8.87614i	−0.186258	+	0.322609i	0.757741	+	0.652555i	$0.226303\pi$
$758$	22.0259			0.800016
$759$	−0.0487576	−	0.0196224i	−0.00176979	−	0.000712249i
$760$	3.50551	−	5.35531i	0.127158	−	0.194257i
$761$	−15.5137	+	26.8706i	−0.562372	+	0.974057i	0.434917	+	0.900471i	$0.356778\pi$
$761$	−15.5137	+	26.8706i	−0.562372	+	0.974057i	−0.997289	+	0.0735863i	$0.976556\pi$
$762$	−19.7330	−	7.94153i	−0.714852	−	0.287691i
$763$	−23.5310			−0.851878
$764$	4.70098	+	8.14234i	0.170076	+	0.294580i
$765$	3.29938	−	13.3877i	0.119289	−	0.484034i
$766$	23.0792	+	39.9743i	0.833885	+	1.44433i
$767$	6.83917	+	11.8458i	0.246948	+	0.427727i
$768$	−0.608522	+	0.476760i	−0.0219581	+	0.0172036i
$769$	37.5626			1.35454			0.677271	−	0.735734i	$-0.263162\pi$
$769$	37.5626			1.35454			0.677271	+	0.735734i	$0.263162\pi$
$770$	24.5798			0.885796
$771$	25.9740	−	20.3499i	0.935430	−	0.732884i
$772$	26.4920	+	45.8856i	0.953470	+	1.65146i
$773$	−2.90427	−	5.03034i	−0.104459	−	0.180929i	0.809058	−	0.587729i	$-0.199978\pi$
$773$	−2.90427	−	5.03034i	−0.104459	−	0.180929i	−0.913517	+	0.406800i	$0.866645\pi$
$774$	−6.38347	+	25.9019i	−0.229449	+	0.931025i
$775$	2.58048	+	4.46952i	0.0926936	+	0.160550i
$776$	16.6204			0.596638
$777$	−88.7182	−	35.7046i	−3.18275	−	1.28089i
$778$	8.86361	−	15.3522i	0.317776	−	0.550404i
$779$	−9.11476	+	13.9244i	−0.326570	+	0.498895i
$780$	23.7221	+	9.54695i	0.849388	+	0.341836i
$781$	2.92866			0.104796
$782$	0.0690081	−	0.119526i	0.00246773	−	0.00427423i
$783$	−7.84121	−	0.791893i	−0.280222	−	0.0282999i
$784$	21.8445	−	37.8358i	0.780161	−	1.35128i
$785$	2.37897	−	4.12050i	0.0849091	−	0.147067i
$786$	10.2400	+	4.12108i	0.365249	+	0.146994i
$787$	22.4048	−	38.8063i	0.798646	−	1.38330i	−0.121852	−	0.992548i	$-0.538883\pi$
$787$	22.4048	−	38.8063i	0.798646	−	1.38330i	0.920498	−	0.390747i	$-0.127783\pi$
$788$	38.4333			1.36913
$789$	8.77920	−	6.87826i	0.312548	−	0.244873i
$790$	3.47091	+	6.01179i	0.123489	+	0.213890i
$791$	83.6616			2.97467
$792$	9.24858	−	2.67917i	0.328634	−	0.0952000i
$793$	−12.2976	+	21.3001i	−0.436701	+	0.756388i
$794$	5.62254	−	9.73853i	0.199537	−	0.345608i
$795$	−2.70147	−	19.0346i	−0.0958113	−	0.675086i
$796$	2.05341	+	3.55662i	0.0727813	+	0.126061i
$797$	−27.8678	+	48.2685i	−0.987129	+	1.70976i	−0.355064	+	0.934842i	$0.615541\pi$
$797$	−27.8678	+	48.2685i	−0.987129	+	1.70976i	−0.632065	+	0.774916i	$0.717792\pi$
$798$	−7.20690	−	84.5940i	−0.255122	−	2.99460i
$799$	−1.02141	−	1.76913i	−0.0361347	−	0.0625872i
$800$	−3.82772	+	6.62980i	−0.135330	+	0.234399i
$801$	13.5190	−	3.91623i	0.477669	−	0.138373i
$802$	25.1603	+	43.5790i	0.888442	+	1.53883i
$803$	23.5224			0.830088
$804$	−17.7172	+	13.8809i	−0.624836	+	0.489542i
$805$	−0.0360865	+	0.0625036i	−0.00127188	+	0.00220296i
$806$	30.7617	−	53.2809i	1.08354	−	1.87674i
$807$	−4.80596	−	33.8628i	−0.169178	−	1.19203i
$808$	12.5598	−	21.7543i	0.441853	−	0.765312i
$809$	15.0375			0.528689			0.264345	−	0.964428i	$-0.414844\pi$
$809$	15.0375			0.528689			0.264345	+	0.964428i	$0.414844\pi$
$810$	0.784973	+	19.4518i	0.0275812	+	0.683465i
$811$	10.5183	+	18.2182i	0.369346	+	0.639727i	0.989463	−	0.144783i	$-0.0462483\pi$
$811$	10.5183	+	18.2182i	0.369346	+	0.639727i	−0.620117	+	0.784509i	$0.712915\pi$
$812$	21.1230			0.741273
$813$	−3.04912	−	21.4841i	−0.106937	−	0.753480i
$814$	−25.1068	−	43.4863i	−0.879994	−	1.52419i
$815$	−7.12414	−	12.3394i	−0.249548	−	0.432229i
$816$	−2.44018	−	17.1935i	−0.0854235	−	0.601894i
$817$	8.07712	+	15.9957i	0.282583	+	0.559618i
$818$	11.2586			0.393647
$819$	82.5595	−	23.9162i	2.88486	−	0.835698i
$820$	−5.11396	+	8.85764i	−0.178587	+	0.309322i
$821$	−0.265136	+	0.459228i	−0.00925329	+	0.0160272i	−0.870615	−	0.491965i	$-0.836279\pi$
$821$	−0.265136	+	0.459228i	−0.00925329	+	0.0160272i	0.861362	+	0.507992i	$0.169612\pi$
$822$	8.53837	+	60.1614i	0.297810	+	2.09837i
$823$	−26.9685			−0.940062			−0.470031	−	0.882650i	$-0.655757\pi$
$823$	−26.9685			−0.940062			−0.470031	+	0.882650i	$0.655757\pi$
$824$	−0.867897	+	1.50324i	−0.0302346	+	0.0523679i
$825$	−2.98015	+	2.33487i	−0.103756	+	0.0812896i
$826$	13.9552	−	24.1711i	0.485563	−	0.841020i
$827$	0.981481	+	1.69997i	0.0341294	+	0.0591139i	0.882586	−	0.470152i	$-0.155801\pi$
$827$	0.981481	+	1.69997i	0.0341294	+	0.0591139i	−0.848456	+	0.529266i	$0.822467\pi$
$828$	−0.0266971	+	0.108327i	−0.000927787	+	0.00376463i
$829$	22.6952			0.788238			0.394119	−	0.919060i	$-0.371050\pi$
$829$	22.6952			0.788238			0.394119	+	0.919060i	$0.371050\pi$
$830$	0.437971	−	0.758589i	0.0152022	−	0.0263310i
$831$	−33.2948	−	13.3995i	−1.15498	−	0.464823i
$832$	67.2154			2.33027
$833$	46.0241	+	79.7162i	1.59464	+	2.76200i
$834$	−2.57248	+	2.01547i	−0.0890779	+	0.0697901i
$835$	5.62044	+	9.73489i	0.194503	+	0.336890i
$836$	13.9785	−	21.3547i	0.483458	−	0.738569i
$837$	26.6814	+	2.69459i	0.922245	+	0.0931386i
$838$	−20.1983	+	34.9844i	−0.697737	+	1.20852i
$839$	−30.9025			−1.06687			−0.533436	−	0.845840i	$-0.679100\pi$
$839$	−30.9025			−1.06687			−0.533436	+	0.845840i	$0.679100\pi$
$840$	−1.85796	−	13.0912i	−0.0641056	−	0.451688i
$841$	13.3498	+	23.1225i	0.460337	+	0.797328i
$842$	20.0573			0.691221
$843$	−6.07785	−	42.8246i	−0.209332	−	1.47496i
$844$	−19.1563	−	33.1797i	−0.659387	−	1.14209i
$845$	8.68628	+	15.0451i	0.298817	+	0.517566i
$846$	2.08017	+	1.99792i	0.0715177	+	0.0686899i
$847$	−32.3488			−1.11152
$848$	−12.1068	−	20.9696i	−0.415748	−	0.720097i
$849$	−31.2422	−	12.5734i	−1.07223	−	0.431518i
$850$	−4.97083	−	8.60973i	−0.170498	−	0.295311i
$851$	0.147441			0.00505420
$852$	−0.873572	−	6.15519i	−0.0299281	−	0.210873i
$853$	−23.8027			−0.814989			−0.407494	−	0.913208i	$-0.633597\pi$
$853$	−23.8027			−0.814989			−0.407494	+	0.913208i	$0.633597\pi$
$854$	50.1860			1.71733
$855$	8.90947	+	9.57190i	0.304698	+	0.327352i
$856$	−8.61005			−0.294285
$857$	19.7270			0.673862			0.336931	−	0.941529i	$-0.390611\pi$
$857$	19.7270			0.673862			0.336931	+	0.941529i	$0.390611\pi$
$858$	41.8679	+	16.8497i	1.42935	+	0.575239i
$859$	−16.2736			−0.555249			−0.277624	−	0.960690i	$-0.589547\pi$
$859$	−16.2736			−0.555249			−0.277624	+	0.960690i	$0.589547\pi$
$860$	5.50634	+	9.53727i	0.187765	+	0.325218i
$861$	4.83091	+	34.0386i	0.164637	+	1.16003i
$862$	−24.5789	−	42.5718i	−0.837159	−	1.45000i
$863$	−47.9702			−1.63293			−0.816463	−	0.577398i	$-0.804068\pi$
$863$	−47.9702			−1.63293			−0.816463	+	0.577398i	$0.804068\pi$
$864$	16.3273	+	36.2736i	0.555464	+	1.23405i
$865$	10.8154	+	18.7328i	0.367734	+	0.636934i
$866$	39.0371	+	67.6143i	1.32654	+	2.29763i
$867$	6.62662	+	2.66688i	0.225052	+	0.0905719i
$868$	−71.8758			−2.43962
$869$	3.50735	+	6.07491i	0.118979	+	0.206077i
$870$	−4.47307	+	3.50453i	−0.151651	+	0.118815i
$871$	−26.7334			−0.905826
$872$	−3.32317	+	5.75590i	−0.112537	+	0.194919i
$873$	−8.12530	+	32.9696i	−0.275000	+	1.11585i
$874$	0.0590002	+	0.116842i	0.00199571	+	0.00395225i
$875$	2.59940	+	4.50229i	0.0878757	+	0.152205i
$876$	−7.01636	−	49.4373i	−0.237061	−	1.67033i
$877$	−6.43603	−	11.1475i	−0.217329	−	0.376426i	0.736661	−	0.676262i	$-0.236401\pi$
$877$	−6.43603	−	11.1475i	−0.217329	−	0.376426i	−0.953991	+	0.299836i	$0.903068\pi$
$878$	63.9344			2.15768
$879$	4.53825	+	31.9765i	0.153071	+	1.07854i
$880$	−2.38409	+	4.12936i	−0.0803676	+	0.139201i
$881$	12.1659			0.409881			0.204941	−	0.978774i	$-0.434300\pi$
$881$	12.1659			0.409881			0.204941	+	0.978774i	$0.434300\pi$
$882$	−93.7317	−	90.0255i	−3.15611	−	3.03132i
$883$	23.2680	+	40.3014i	0.783031	+	1.35625i	0.930168	+	0.367133i	$0.119661\pi$
$883$	23.2680	+	40.3014i	0.783031	+	1.35625i	−0.147138	+	0.989116i	$0.547006\pi$
$884$	−33.9272	+	58.7637i	−1.14110	+	1.97644i
$885$	0.604061	+	4.25621i	0.0203053	+	0.143071i
$886$	44.7579	−	77.5229i	1.50367	−	2.60443i
$887$	−52.3235			−1.75685			−0.878426	−	0.477879i	$-0.841406\pi$
$887$	−52.3235			−1.75685			−0.878426	+	0.477879i	$0.841406\pi$
$888$	−21.2629	+	16.6589i	−0.713537	+	0.559037i
$889$	−14.7582	+	25.5619i	−0.494973	+	0.857319i
$890$	5.07411	−	8.78861i	0.170085	−	0.294595i
$891$	0.793216	+	19.6560i	0.0265737	+	0.658501i
$892$	46.2740			1.54937
$893$	1.93435	+	0.108426i	0.0647305	+	0.00362833i
$894$	−59.5965	−	23.9846i	−1.99321	−	0.802164i
$895$	−3.95377	−	6.84813i	−0.132160	−	0.228908i
$896$	−28.7767	−	49.8427i	−0.961363	−	1.66513i
$897$	−0.104314	+	0.0817274i	−0.00348296	+	0.00272880i
$898$	36.1187			1.20530
$899$	3.91386	+	6.77900i	0.130535	+	0.226092i
$900$	5.79614	+	5.56696i	0.193205	+	0.185565i
$901$	51.0154			1.69957
$902$	−9.02578	+	15.6331i	−0.300526	+	0.520526i
$903$	34.3409	+	13.8205i	1.14279	+	0.459916i
$904$	11.8151	−	20.4644i	0.392966	−	0.680636i
$905$	−8.61786	+	14.9266i	−0.286467	+	0.496176i
$906$	−66.0482	−	26.5810i	−2.19430	−	0.883096i
$907$	34.2580			1.13752			0.568760	−	0.822504i	$-0.307423\pi$
$907$	34.2580			1.13752			0.568760	+	0.822504i	$0.307423\pi$
$908$	8.42195	+	14.5872i	0.279492	+	0.484095i
$909$	37.0134	+	35.5498i	1.22766	+	1.17911i
$910$	30.9873	−	53.6715i	1.02722	−	1.77919i
$911$	18.9284	+	32.7849i	0.627126	+	1.08621i	0.988126	+	0.153648i	$0.0491021\pi$
$911$	18.9284	+	32.7849i	0.627126	+	1.08621i	−0.361000	+	0.932566i	$0.617565\pi$
$912$	14.9106	+	6.99434i	0.493741	+	0.231606i
$913$	0.442571	−	0.766555i	0.0146469	−	0.0253693i
$914$	−7.16170	−	12.4044i	−0.236888	−	0.410302i
$915$	−6.08474	+	4.76722i	−0.201155	+	0.157600i
$916$	21.4071	−	37.0781i	0.707309	−	1.22510i
$917$	7.65842	−	13.2648i	0.252903	−	0.438042i
$918$	−51.3969	−	5.19064i	−1.69635	−	0.171317i
$919$	−19.5846			−0.646036			−0.323018	−	0.946393i	$-0.604697\pi$
$919$	−19.5846			−0.646036			−0.323018	+	0.946393i	$0.604697\pi$
$920$	0.0101926	+	0.0176542i	0.000336042	+	0.000582041i
$921$	−3.34975	−	23.6024i	−0.110378	−	0.777724i
$922$	−21.1925			−0.697939
$923$	3.69210	−	6.39490i	0.121527	−	0.210491i
$924$	−7.40876	−	52.2021i	−0.243730	−	1.71732i
$925$	5.31026	−	9.19764i	0.174600	−	0.302417i
$926$	23.2407	−	40.2541i	0.763737	−	1.32283i
$927$	−2.55766	−	2.45653i	−0.0840046	−	0.0806829i
$928$	−5.80556	+	10.0555i	−0.190577	+	0.330089i
$929$	6.65837			0.218454			0.109227	−	0.994017i	$-0.465162\pi$
$929$	6.65837			0.218454			0.109227	+	0.994017i	$0.465162\pi$
$930$	15.2206	−	11.9249i	0.499104	−	0.391034i
$931$	−87.1610	−	4.88562i	−2.85659	−	0.160120i
$932$	26.8816	−	46.5603i	0.880537	−	1.52513i
$933$	7.24281	+	51.0328i	0.237119	+	1.67074i
$934$	−45.5250			−1.48962
$935$	−5.02303	−	8.70013i	−0.164270	−	0.284525i
$936$	5.80937	−	23.5724i	0.189885	−	0.770488i
$937$	1.91312	+	3.31362i	0.0624989	+	0.108251i	0.895582	−	0.444897i	$-0.146760\pi$
$937$	1.91312	+	3.31362i	0.0624989	+	0.108251i	−0.833083	+	0.553148i	$0.813426\pi$
$938$	27.2744	+	47.2407i	0.890542	+	1.54246i
$939$	1.47468	+	10.3906i	0.0481243	+	0.339084i
$940$	1.19066			0.0388351
$941$	−31.0885			−1.01346			−0.506728	−	0.862106i	$-0.669145\pi$
$941$	−31.0885			−1.01346			−0.506728	+	0.862106i	$0.669145\pi$
$942$	−16.5369	−	6.65524i	−0.538800	−	0.216840i
$943$	−0.0265021	−	0.0459030i	−0.000863027	−	0.00149481i
$944$	2.70713	+	4.68888i	0.0881095	+	0.152610i
$945$	26.8770	+	2.71434i	0.874310	+	0.0882976i
$946$	9.71831	+	16.8326i	0.315969	+	0.547275i
$947$	−13.2761			−0.431417			−0.215708	−	0.976458i	$-0.569206\pi$
$947$	−13.2761			−0.431417			−0.215708	+	0.976458i	$0.569206\pi$
$948$	11.7215	−	9.18349i	0.380697	−	0.298266i
$949$	29.6542	−	51.3626i	0.962616	−	1.66730i
$950$	9.41381	+	0.527670i	0.305424	+	0.0171199i
$951$	−4.40926	−	31.0677i	−0.142980	−	1.00744i
$952$	35.0863			1.13715
$953$	1.82550	−	3.16187i	0.0591339	−	0.102423i	−0.834943	−	0.550336i	$-0.814499\pi$
$953$	1.82550	−	3.16187i	0.0591339	−	0.102423i	0.894077	+	0.447914i	$0.147833\pi$
$954$	−69.1840	+	20.0415i	−2.23991	+	0.648867i
$955$	−1.75485	+	3.03949i	−0.0567856	+	0.0983555i
$956$	−23.2059	+	40.1937i	−0.750531	+	1.29996i
$957$	−4.52005	+	3.54133i	−0.146112	+	0.114475i
$958$	−27.2770	+	47.2452i	−0.881281	+	1.52642i
$959$	84.3181			2.72277
$960$	19.5971	+	7.88684i	0.632494	+	0.254547i
$961$	2.18224	+	3.77975i	0.0703948	+	0.121927i
$962$	−126.607			−4.08196
$963$	4.20923	−	17.0796i	0.135641	−	0.550382i
$964$	−20.8844	+	36.1729i	−0.672643	+	1.16505i
$965$	−9.88932	+	17.1288i	−0.318349	+	0.551396i
$966$	0.250847	+	0.100953i	0.00807086	+	0.00324811i
$967$	−12.9794	−	22.4810i	−0.417389	−	0.722939i	0.578287	−	0.815834i	$-0.303722\pi$
$967$	−12.9794	−	22.4810i	−0.417389	−	0.722939i	−0.995676	+	0.0928942i	$0.970388\pi$
$968$	−4.56847	+	7.91283i	−0.146836	+	0.254328i
$969$	−28.4696	+	19.8382i	−0.914576	+	0.637294i
$970$	12.2415	+	21.2030i	0.393052	+	0.680787i
$971$	7.67882	−	13.3001i	0.246425	−	0.426821i	−0.716106	−	0.697991i	$-0.754077\pi$
$971$	7.67882	−	13.3001i	0.246425	−	0.426821i	0.962531	+	0.271171i	$0.0874108\pi$
$972$	41.0746	−	7.53019i	1.31747	−	0.241531i
$973$	2.26738	+	3.92722i	0.0726889	+	0.125901i
$974$	−27.8617			−0.892747
$975$	1.34131	+	9.45085i	0.0429562	+	0.302669i
$976$	−4.86772	+	8.43114i	−0.155812	+	0.269874i
$977$	−18.9522	+	32.8261i	−0.606333	+	1.05020i	0.385506	+	0.922705i	$0.374027\pi$
$977$	−18.9522	+	32.8261i	−0.606333	+	1.05020i	−0.991839	+	0.127495i	$0.959306\pi$
$978$	−42.0208	+	32.9221i	−1.34368	+	1.05273i
$979$	5.12739	−	8.88090i	0.163872	−	0.283835i
$980$	−53.6507			−1.71381
$981$	−9.79325	−	9.40602i	−0.312675	−	0.300311i
$982$	−39.7854	−	68.9103i	−1.26960	−	2.19902i
$983$	34.6049			1.10372			0.551862	−	0.833935i	$-0.313917\pi$
$983$	34.6049			1.10372			0.551862	+	0.833935i	$0.313917\pi$
$984$	9.00841	+	3.62543i	0.287178	+	0.115574i
$985$	7.17346	+	12.4248i	0.228566	+	0.395887i
$986$	−7.53934	−	13.0585i	−0.240101	−	0.415868i
$987$	3.15046	−	2.46830i	0.100280	−	0.0785668i
$988$	−29.0069	−	57.4444i	−0.922833	−	1.82755i
$989$	−0.0570711			−0.00181475
$990$	10.2298	+	9.82528i	0.325124	+	0.312268i
$991$	−13.1231	+	22.7298i	−0.416868	+	0.722037i	−0.995623	−	0.0934649i	$-0.970206\pi$
$991$	−13.1231	+	22.7298i	−0.416868	+	0.722037i	0.578754	+	0.815502i	$0.303539\pi$
$992$	19.7547	−	34.2161i	0.627212	−	1.08636i
$993$	−36.0316	−	14.5009i	−1.14343	−	0.460172i
$994$	−15.0673			−0.477905
$995$	−0.766527	+	1.32766i	−0.0243005	+	0.0420898i
$996$	−1.74309	−	0.701504i	−0.0552318	−	0.0222280i
$997$	−19.7970	+	34.2894i	−0.626976	+	1.08595i	0.361179	+	0.932497i	$0.382374\pi$
$997$	−19.7970	+	34.2894i	−0.626976	+	1.08595i	−0.988155	+	0.153458i	$0.950959\pi$
$998$	18.5368	+	32.1067i	0.586772	+	1.01632i
$999$	−22.6511	−	50.3230i	−0.716649	−	1.59215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.l.b.391.5	yes	80
9.7	even	3		855.2.j.a.106.36	✓	80
19.7	even	3		855.2.j.a.121.36	yes	80
171.7	even	3	inner	855.2.l.b.691.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.j.a.106.36	✓	80	9.7	even	3
855.2.j.a.121.36	yes	80	19.7	even	3
855.2.l.b.391.5	yes	80	1.1	even	1	trivial
855.2.l.b.691.5	yes	80	171.7	even	3	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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.16307 q^{2} +(-1.36343 + 1.06821i) q^{3} +2.67885 q^{4} +(0.500000 + 0.866025i) q^{5} +(2.94918 - 2.31060i) q^{6} +(-2.59940 - 4.50229i) q^{7} -1.46840 q^{8} +(0.717865 - 2.91285i) q^{9} +O(q^{10})\)	\(q-2.16307 q^{2} +(-1.36343 + 1.06821i) q^{3} +2.67885 q^{4} +(0.500000 + 0.866025i) q^{5} +(2.94918 - 2.31060i) q^{6} +(-2.59940 - 4.50229i) q^{7} -1.46840 q^{8} +(0.717865 - 2.91285i) q^{9} +(-1.08153 - 1.87327i) q^{10} +(-1.09289 - 1.89294i) q^{11} +(-3.65242 + 2.86157i) q^{12} -5.51113 q^{13} +(5.62267 + 9.73875i) q^{14} +(-1.60681 - 0.646658i) q^{15} -2.18145 q^{16} +(2.29805 - 3.98033i) q^{17} +(-1.55279 + 6.30068i) q^{18} +(1.96477 + 3.89097i) q^{19} +(1.33943 + 2.31995i) q^{20} +(8.35347 + 3.36185i) q^{21} +(2.36399 + 4.09455i) q^{22} -0.0138826 q^{23} +(2.00206 - 1.56856i) q^{24} +(-0.500000 + 0.866025i) q^{25} +11.9209 q^{26} +(2.13277 + 4.73828i) q^{27} +(-6.96341 - 12.0610i) q^{28} +(-0.758359 + 1.31352i) q^{29} +(3.47563 + 1.39876i) q^{30} +(2.58048 - 4.46952i) q^{31} +7.65543 q^{32} +(3.51213 + 1.41345i) q^{33} +(-4.97083 + 8.60973i) q^{34} +(2.59940 - 4.50229i) q^{35} +(1.92306 - 7.80309i) q^{36} -10.6205 q^{37} +(-4.24993 - 8.41643i) q^{38} +(7.51402 - 5.88703i) q^{39} +(-0.734202 - 1.27167i) q^{40} +(1.90901 + 3.30651i) q^{41} +(-18.0691 - 7.27189i) q^{42} +4.11097 q^{43} +(-2.92769 - 5.07091i) q^{44} +(2.88153 - 0.834733i) q^{45} +0.0300290 q^{46} +(0.222233 - 0.384919i) q^{47} +(2.97425 - 2.33024i) q^{48} +(-10.0137 + 17.3443i) q^{49} +(1.08153 - 1.87327i) q^{50} +(1.11860 + 7.88169i) q^{51} -14.7635 q^{52} +(5.54987 + 9.61265i) q^{53} +(-4.61332 - 10.2492i) q^{54} +(1.09289 - 1.89294i) q^{55} +(3.81697 + 6.61118i) q^{56} +(-6.83519 - 3.20627i) q^{57} +(1.64038 - 2.84122i) q^{58} +(-1.24097 - 2.14943i) q^{59} +(-4.30440 - 1.73230i) q^{60} +(2.23141 - 3.86492i) q^{61} +(-5.58175 + 9.66787i) q^{62} +(-14.9805 + 4.33961i) q^{63} -12.1963 q^{64} +(-2.75557 - 4.77278i) q^{65} +(-7.59696 - 3.05739i) q^{66} +4.85080 q^{67} +(6.15613 - 10.6627i) q^{68} +(0.0189279 - 0.0148295i) q^{69} +(-5.62267 + 9.73875i) q^{70} +(-0.669934 + 1.16036i) q^{71} +(-1.05412 + 4.27723i) q^{72} +(-5.38078 + 9.31979i) q^{73} +22.9729 q^{74} +(-0.243381 - 1.71487i) q^{75} +(5.26333 + 10.4233i) q^{76} +(-5.68171 + 9.84102i) q^{77} +(-16.2533 + 12.7340i) q^{78} -3.20925 q^{79} +(-1.09073 - 1.88919i) q^{80} +(-7.96934 - 4.18206i) q^{81} +(-4.12932 - 7.15219i) q^{82} +(0.202477 + 0.350701i) q^{83} +(22.3777 + 9.00589i) q^{84} +4.59609 q^{85} -8.89230 q^{86} +(-0.369141 - 2.60097i) q^{87} +(1.60480 + 2.77960i) q^{88} +(2.34580 + 4.06304i) q^{89} +(-6.23294 + 1.80558i) q^{90} +(14.3256 + 24.8127i) q^{91} -0.0371895 q^{92} +(1.25608 + 8.85036i) q^{93} +(-0.480705 + 0.832606i) q^{94} +(-2.38730 + 3.64703i) q^{95} +(-10.4376 + 8.17759i) q^{96} -11.3187 q^{97} +(21.6604 - 37.5169i) q^{98} +(-6.29839 + 1.82454i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} - 2 q^{3} + 80 q^{4} + 40 q^{5} + 2 q^{6} + q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q + 4 * q^2 - 2 * q^3 + 80 * q^4 + 40 * q^5 + 2 * q^6 + q^7 - 2 * q^9	\( 80 q + 4 q^{2} - 2 q^{3} + 80 q^{4} + 40 q^{5} + 2 q^{6} + q^{7} - 2 q^{9} + 2 q^{10} - q^{11} - 6 q^{12} - 18 q^{13} - q^{15} + 88 q^{16} + 6 q^{17} - 15 q^{18} + 9 q^{19} + 40 q^{20} - 4 q^{21} + 9 q^{22} - 30 q^{24} - 40 q^{25} - 8 q^{26} - 2 q^{27} + 13 q^{28} - 3 q^{29} + 7 q^{30} + 24 q^{31} + 4 q^{32} + q^{33} + q^{34} - q^{35} + 12 q^{36} - 40 q^{37} + 14 q^{38} + 23 q^{39} - 3 q^{41} - 29 q^{42} - 30 q^{43} - 34 q^{44} - q^{45} - 46 q^{46} + 6 q^{47} - 5 q^{48} - 33 q^{49} - 2 q^{50} + 37 q^{51} - 56 q^{52} - 16 q^{53} - 23 q^{54} + q^{55} + 20 q^{56} + 4 q^{58} - 2 q^{59} - 3 q^{60} + 7 q^{61} - 8 q^{62} - 41 q^{63} + 180 q^{64} - 9 q^{65} - 30 q^{66} - 102 q^{67} + 11 q^{68} - 24 q^{69} + 14 q^{71} + 22 q^{72} - 8 q^{73} + 24 q^{74} + q^{75} + 12 q^{76} + 10 q^{77} - q^{78} - 42 q^{79} + 44 q^{80} - 22 q^{81} + 5 q^{82} + 3 q^{83} - 131 q^{84} + 12 q^{85} + 14 q^{86} - 22 q^{87} + 46 q^{88} - 18 q^{89} - 15 q^{90} + 24 q^{91} - 54 q^{92} - 24 q^{93} + 42 q^{94} - 160 q^{96} - 42 q^{97} + 5 q^{98} + 32 q^{99}+O(q^{100}) \) 80 * q + 4 * q^2 - 2 * q^3 + 80 * q^4 + 40 * q^5 + 2 * q^6 + q^7 - 2 * q^9 + 2 * q^10 - q^11 - 6 * q^12 - 18 * q^13 - q^15 + 88 * q^16 + 6 * q^17 - 15 * q^18 + 9 * q^19 + 40 * q^20 - 4 * q^21 + 9 * q^22 - 30 * q^24 - 40 * q^25 - 8 * q^26 - 2 * q^27 + 13 * q^28 - 3 * q^29 + 7 * q^30 + 24 * q^31 + 4 * q^32 + q^33 + q^34 - q^35 + 12 * q^36 - 40 * q^37 + 14 * q^38 + 23 * q^39 - 3 * q^41 - 29 * q^42 - 30 * q^43 - 34 * q^44 - q^45 - 46 * q^46 + 6 * q^47 - 5 * q^48 - 33 * q^49 - 2 * q^50 + 37 * q^51 - 56 * q^52 - 16 * q^53 - 23 * q^54 + q^55 + 20 * q^56 + 4 * q^58 - 2 * q^59 - 3 * q^60 + 7 * q^61 - 8 * q^62 - 41 * q^63 + 180 * q^64 - 9 * q^65 - 30 * q^66 - 102 * q^67 + 11 * q^68 - 24 * q^69 + 14 * q^71 + 22 * q^72 - 8 * q^73 + 24 * q^74 + q^75 + 12 * q^76 + 10 * q^77 - q^78 - 42 * q^79 + 44 * q^80 - 22 * q^81 + 5 * q^82 + 3 * q^83 - 131 * q^84 + 12 * q^85 + 14 * q^86 - 22 * q^87 + 46 * q^88 - 18 * q^89 - 15 * q^90 + 24 * q^91 - 54 * q^92 - 24 * q^93 + 42 * q^94 - 160 * q^96 - 42 * q^97 + 5 * q^98 + 32 * q^99

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