LMFDB - Embedded newform 585.2.i.e.196.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 $ x^16 - 5x^15 + 20x^14 - 44x^13 + 96x^12 - 107x^11 + 178x^10 - 19x^9 + 231x^8 + 326x^7 + 551x^6 + 859x^5 + 1118x^4 + 1215x^3 + 1103x^2 + 770*x + 268
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.3
Root			$-0.317019 - 1.12493i$ of defining polynomial
Character	$\chi$	$=$	585.196
Dual form			585.2.i.e.391.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.817019 + 1.41512i) q^{2} +(1.40359 + 1.01486i) q^{3} +(-0.335039 - 0.580304i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.58290 + 1.15709i) q^{6} +(-1.06506 + 1.84473i) q^{7} -2.17314 q^{8} +(0.940129 + 2.84889i) q^{9} +O(q^{10})$	\(q+(-0.817019 + 1.41512i) q^{2} +(1.40359 + 1.01486i) q^{3} +(-0.335039 - 0.580304i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.58290 + 1.15709i) q^{6} +(-1.06506 + 1.84473i) q^{7} -2.17314 q^{8} +(0.940129 + 2.84889i) q^{9} -1.63404 q^{10} +(0.0263229 - 0.0455925i) q^{11} +(0.118669 - 1.15453i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-1.74034 - 3.01437i) q^{14} +(-0.177097 + 1.72297i) q^{15} +(2.44558 - 4.23586i) q^{16} -2.48047 q^{17} +(-4.79961 - 0.997201i) q^{18} +2.13105 q^{19} +(0.335039 - 0.580304i) q^{20} +(-3.36705 + 1.50837i) q^{21} +(0.0430125 + 0.0744999i) q^{22} +(-2.46542 - 4.27023i) q^{23} +(-3.05020 - 2.20543i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.63404 q^{26} +(-1.57166 + 4.95277i) q^{27} +1.42734 q^{28} +(1.24347 - 2.15375i) q^{29} +(-2.29352 - 1.65831i) q^{30} +(4.08030 + 7.06728i) q^{31} +(1.82302 + 3.15756i) q^{32} +(0.0832164 - 0.0372793i) q^{33} +(2.02659 - 3.51016i) q^{34} -2.13012 q^{35} +(1.33824 - 1.50005i) q^{36} -1.11963 q^{37} +(-1.74110 + 3.01568i) q^{38} +(-0.177097 + 1.72297i) q^{39} +(-1.08657 - 1.88200i) q^{40} +(2.73708 + 4.74077i) q^{41} +(0.616421 - 5.99713i) q^{42} +(4.73861 - 8.20752i) q^{43} -0.0352767 q^{44} +(-1.99714 + 2.23862i) q^{45} +8.05716 q^{46} +(-4.88280 + 8.45726i) q^{47} +(7.73138 - 3.46350i) q^{48} +(1.23130 + 2.13268i) q^{49} +(-0.817019 - 1.41512i) q^{50} +(-3.48156 - 2.51732i) q^{51} +(0.335039 - 0.580304i) q^{52} -3.64091 q^{53} +(-5.72467 - 6.27058i) q^{54} +0.0526457 q^{55} +(2.31452 - 4.00887i) q^{56} +(2.99111 + 2.16271i) q^{57} +(2.03187 + 3.51931i) q^{58} +(-3.74544 - 6.48728i) q^{59} +(1.05918 - 0.474493i) q^{60} +(2.89202 - 5.00912i) q^{61} -13.3347 q^{62} +(-6.25673 - 1.29994i) q^{63} +3.82454 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-0.0152348 + 0.148219i) q^{66} +(3.11795 + 5.40045i) q^{67} +(0.831054 + 1.43943i) q^{68} +(0.873237 - 8.49569i) q^{69} +(1.74034 - 3.01437i) q^{70} +2.50050 q^{71} +(-2.04303 - 6.19104i) q^{72} -1.10245 q^{73} +(0.914759 - 1.58441i) q^{74} +(-1.58069 + 0.708116i) q^{75} +(-0.713983 - 1.23666i) q^{76} +(0.0560707 + 0.0971174i) q^{77} +(-2.29352 - 1.65831i) q^{78} +(7.80779 - 13.5235i) q^{79} +4.89115 q^{80} +(-7.23231 + 5.35664i) q^{81} -8.94500 q^{82} +(-0.244576 + 0.423618i) q^{83} +(2.00340 + 1.44855i) q^{84} +(-1.24024 - 2.14815i) q^{85} +(7.74307 + 13.4114i) q^{86} +(3.93107 - 1.76104i) q^{87} +(-0.0572033 + 0.0990790i) q^{88} -4.64901 q^{89} +(-1.53621 - 4.65519i) q^{90} -2.13012 q^{91} +(-1.65202 + 2.86138i) q^{92} +(-1.44522 + 14.0605i) q^{93} +(-7.97868 - 13.8195i) q^{94} +(1.06552 + 1.84554i) q^{95} +(-0.645704 + 6.28203i) q^{96} +(-3.67049 + 6.35747i) q^{97} -4.02399 q^{98} +(0.154635 + 0.0321280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 8 q^{13} - 10 q^{14} + 5 q^{15} - 11 q^{16} - 4 q^{17} + 5 q^{18} - 20 q^{19} + 9 q^{20} + 11 q^{21} - 3 q^{22} - 6 q^{23} - 57 q^{24} - 8 q^{25} - 6 q^{26} - 14 q^{27} - 68 q^{28} - 14 q^{29} + 7 q^{30} + 31 q^{31} - q^{32} - 31 q^{33} + 7 q^{34} + 22 q^{35} + 2 q^{36} + 2 q^{37} - 9 q^{38} + 5 q^{39} - 6 q^{40} + 12 q^{41} - 26 q^{42} - 15 q^{43} + 32 q^{44} - 16 q^{45} - 64 q^{46} + 18 q^{47} - 4 q^{48} - 17 q^{49} - 3 q^{50} + 32 q^{51} + 9 q^{52} + 4 q^{53} + 2 q^{54} - 12 q^{55} - 16 q^{56} + 45 q^{57} + 42 q^{58} - 24 q^{59} - 8 q^{60} + 9 q^{61} - 40 q^{62} + 47 q^{63} - 60 q^{64} - 8 q^{65} + 55 q^{66} + 18 q^{67} + 14 q^{68} - 12 q^{69} + 10 q^{70} + 20 q^{71} - 9 q^{72} + 12 q^{73} + 37 q^{74} + 4 q^{75} + 53 q^{76} + 34 q^{77} + 7 q^{78} + 3 q^{79} - 22 q^{80} + 13 q^{81} - 68 q^{82} + 10 q^{83} + 22 q^{84} - 2 q^{85} - 60 q^{86} + 11 q^{87} + 14 q^{88} - 26 q^{89} + 19 q^{90} + 22 q^{91} - 5 q^{92} + 74 q^{93} - 17 q^{94} - 10 q^{95} + 13 q^{96} + 34 q^{97} - 60 q^{98} - 43 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 8 * q^13 - 10 * q^14 + 5 * q^15 - 11 * q^16 - 4 * q^17 + 5 * q^18 - 20 * q^19 + 9 * q^20 + 11 * q^21 - 3 * q^22 - 6 * q^23 - 57 * q^24 - 8 * q^25 - 6 * q^26 - 14 * q^27 - 68 * q^28 - 14 * q^29 + 7 * q^30 + 31 * q^31 - q^32 - 31 * q^33 + 7 * q^34 + 22 * q^35 + 2 * q^36 + 2 * q^37 - 9 * q^38 + 5 * q^39 - 6 * q^40 + 12 * q^41 - 26 * q^42 - 15 * q^43 + 32 * q^44 - 16 * q^45 - 64 * q^46 + 18 * q^47 - 4 * q^48 - 17 * q^49 - 3 * q^50 + 32 * q^51 + 9 * q^52 + 4 * q^53 + 2 * q^54 - 12 * q^55 - 16 * q^56 + 45 * q^57 + 42 * q^58 - 24 * q^59 - 8 * q^60 + 9 * q^61 - 40 * q^62 + 47 * q^63 - 60 * q^64 - 8 * q^65 + 55 * q^66 + 18 * q^67 + 14 * q^68 - 12 * q^69 + 10 * q^70 + 20 * q^71 - 9 * q^72 + 12 * q^73 + 37 * q^74 + 4 * q^75 + 53 * q^76 + 34 * q^77 + 7 * q^78 + 3 * q^79 - 22 * q^80 + 13 * q^81 - 68 * q^82 + 10 * q^83 + 22 * q^84 - 2 * q^85 - 60 * q^86 + 11 * q^87 + 14 * q^88 - 26 * q^89 + 19 * q^90 + 22 * q^91 - 5 * q^92 + 74 * q^93 - 17 * q^94 - 10 * q^95 + 13 * q^96 + 34 * q^97 - 60 * q^98 - 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.817019	+	1.41512i	−0.577719	+	1.00064i	0.418021	+	0.908437i	$0.362724\pi$
$2$	−0.817019	+	1.41512i	−0.577719	+	1.00064i	−0.995740	+	0.0922020i	$0.970609\pi$
$3$	1.40359	+	1.01486i	0.810363	+	0.585928i
$3$	1.40359	+	1.01486i	0.810363	+	0.585928i
$4$	−0.335039	−	0.580304i	−0.167519	−	0.290152i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−2.58290	+	1.15709i	−1.05447	+	0.472379i
$7$	−1.06506	+	1.84473i	−0.402554	+	0.697244i	−0.994033	−	0.109076i	$-0.965211\pi$
$7$	−1.06506	+	1.84473i	−0.402554	+	0.697244i	0.591479	+	0.806320i	$0.298544\pi$
$8$	−2.17314			−0.768322
$9$	0.940129	+	2.84889i	0.313376	+	0.949629i
$10$	−1.63404			−0.516728
$11$	0.0263229	−	0.0455925i	0.00793664	−	0.0137467i	−0.862030	−	0.506858i	$-0.830807\pi$
$11$	0.0263229	−	0.0455925i	0.00793664	−	0.0137467i	0.869966	+	0.493111i	$0.164140\pi$
$12$	0.118669	−	1.15453i	0.0342568	−	0.333283i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	−1.74034	−	3.01437i	−0.465127	−	0.805623i
$15$	−0.177097	+	1.72297i	−0.0457263	+	0.444870i
$16$	2.44558	−	4.23586i	0.611394	−	1.05897i
$17$	−2.48047			−0.601603			−0.300801	−	0.953687i	$-0.597254\pi$
$17$	−2.48047			−0.601603			−0.300801	+	0.953687i	$0.597254\pi$
$18$	−4.79961	−	0.997201i	−1.13128	−	0.235042i
$19$	2.13105			0.488895			0.244448	−	0.969662i	$-0.421393\pi$
$19$	2.13105			0.488895			0.244448	+	0.969662i	$0.421393\pi$
$20$	0.335039	−	0.580304i	0.0749170	−	0.129760i
$21$	−3.36705	+	1.50837i	−0.734750	+	0.329153i
$22$	0.0430125	+	0.0744999i	0.00917030	+	0.0158834i
$23$	−2.46542	−	4.27023i	−0.514075	−	0.890404i	−0.999867	−	0.0163291i	$-0.994802\pi$
$23$	−2.46542	−	4.27023i	−0.514075	−	0.890404i	0.485792	−	0.874074i	$-0.338531\pi$
$24$	−3.05020	−	2.20543i	−0.622620	−	0.450181i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.63404			−0.320461
$27$	−1.57166	+	4.95277i	−0.302466	+	0.953160i
$28$	1.42734			0.269743
$29$	1.24347	−	2.15375i	0.230906	−	0.399941i	−0.727169	−	0.686459i	$-0.759164\pi$
$29$	1.24347	−	2.15375i	0.230906	−	0.399941i	0.958075	+	0.286517i	$0.0924976\pi$
$30$	−2.29352	−	1.65831i	−0.418737	−	0.302765i
$31$	4.08030	+	7.06728i	0.732843	+	1.26932i	0.955663	+	0.294462i	$0.0951404\pi$
$31$	4.08030	+	7.06728i	0.732843	+	1.26932i	−0.222820	+	0.974860i	$0.571526\pi$
$32$	1.82302	+	3.15756i	0.322267	+	0.558183i
$33$	0.0832164	−	0.0372793i	0.0144861	−	0.00648949i
$34$	2.02659	−	3.51016i	0.347558	−	0.601987i
$35$	−2.13012			−0.360055
$36$	1.33824	−	1.50005i	0.223040	−	0.250008i
$37$	−1.11963			−0.184066			−0.0920331	−	0.995756i	$-0.529337\pi$
$37$	−1.11963			−0.184066			−0.0920331	+	0.995756i	$0.529337\pi$
$38$	−1.74110	+	3.01568i	−0.282444	+	0.489208i
$39$	−0.177097	+	1.72297i	−0.0283583	+	0.275897i
$40$	−1.08657	−	1.88200i	−0.171802	−	0.297570i
$41$	2.73708	+	4.74077i	0.427461	+	0.740384i	0.996647	−	0.0818250i	$-0.0260749\pi$
$41$	2.73708	+	4.74077i	0.427461	+	0.740384i	−0.569186	+	0.822209i	$0.692742\pi$
$42$	0.616421	−	5.99713i	0.0951158	−	0.925378i
$43$	4.73861	−	8.20752i	0.722632	−	1.25163i	−0.237310	−	0.971434i	$-0.576266\pi$
$43$	4.73861	−	8.20752i	0.722632	−	1.25163i	0.959941	−	0.280201i	$-0.0904010\pi$
$44$	−0.0352767			−0.00531816
$45$	−1.99714	+	2.23862i	−0.297717	+	0.333714i
$46$	8.05716			1.18796
$47$	−4.88280	+	8.45726i	−0.712230	+	1.23362i	0.251789	+	0.967782i	$0.418981\pi$
$47$	−4.88280	+	8.45726i	−0.712230	+	1.23362i	−0.964018	+	0.265836i	$0.914352\pi$
$48$	7.73138	−	3.46350i	1.11593	−	0.499913i
$49$	1.23130	+	2.13268i	0.175900	+	0.304668i
$50$	−0.817019	−	1.41512i	−0.115544	−	0.200128i
$51$	−3.48156	−	2.51732i	−0.487516	−	0.352496i
$52$	0.335039	−	0.580304i	0.0464615	−	0.0804737i
$53$	−3.64091			−0.500118			−0.250059	−	0.968231i	$-0.580450\pi$
$53$	−3.64091			−0.500118			−0.250059	+	0.968231i	$0.580450\pi$
$54$	−5.72467	−	6.27058i	−0.779029	−	0.853318i
$55$	0.0526457			0.00709875
$56$	2.31452	−	4.00887i	0.309291	−	0.535708i
$57$	2.99111	+	2.16271i	0.396183	+	0.286458i
$58$	2.03187	+	3.51931i	0.266798	+	0.462108i
$59$	−3.74544	−	6.48728i	−0.487614	−	0.844572i	0.512284	−	0.858816i	$-0.328799\pi$
$59$	−3.74544	−	6.48728i	−0.487614	−	0.844572i	−0.999899	+	0.0142434i	$0.995466\pi$
$60$	1.05918	−	0.474493i	0.136740	−	0.0612567i
$61$	2.89202	−	5.00912i	0.370285	−	0.641352i	−0.619324	−	0.785135i	$-0.712593\pi$
$61$	2.89202	−	5.00912i	0.370285	−	0.641352i	0.989609	+	0.143783i	$0.0459267\pi$
$62$	−13.3347			−1.69351
$63$	−6.25673	−	1.29994i	−0.788274	−	0.163777i
$64$	3.82454			0.478067
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	−0.0152348	+	0.148219i	−0.00187527	+	0.0182445i
$67$	3.11795	+	5.40045i	0.380919	+	0.659770i	0.991194	−	0.132419i	$-0.0422745\pi$
$67$	3.11795	+	5.40045i	0.380919	+	0.659770i	−0.610275	+	0.792189i	$0.708941\pi$
$68$	0.831054	+	1.43943i	0.100780	+	0.174556i
$69$	0.873237	−	8.49569i	0.105125	−	1.02276i
$70$	1.74034	−	3.01437i	0.208011	−	0.360286i
$71$	2.50050			0.296755			0.148377	−	0.988931i	$-0.452595\pi$
$71$	2.50050			0.296755			0.148377	+	0.988931i	$0.452595\pi$
$72$	−2.04303	−	6.19104i	−0.240774	−	0.729621i
$73$	−1.10245			−0.129032			−0.0645159	−	0.997917i	$-0.520550\pi$
$73$	−1.10245			−0.129032			−0.0645159	+	0.997917i	$0.520550\pi$
$74$	0.914759	−	1.58441i	0.106339	−	0.184184i
$75$	−1.58069	+	0.708116i	−0.182522	+	0.0817662i
$76$	−0.713983	−	1.23666i	−0.0818995	−	0.141854i
$77$	0.0560707	+	0.0971174i	0.00638985	+	0.0110676i
$78$	−2.29352	−	1.65831i	−0.259690	−	0.187767i
$79$	7.80779	−	13.5235i	0.878445	−	1.52151i	0.0253969	−	0.999677i	$-0.491915\pi$
$79$	7.80779	−	13.5235i	0.878445	−	1.52151i	0.853048	−	0.521833i	$-0.174752\pi$
$80$	4.89115			0.546847
$81$	−7.23231	+	5.35664i	−0.803591	+	0.595183i
$82$	−8.94500			−0.987810
$83$	−0.244576	+	0.423618i	−0.0268457	+	0.0464981i	−0.879136	−	0.476571i	$-0.841880\pi$
$83$	−0.244576	+	0.423618i	−0.0268457	+	0.0464981i	0.852290	+	0.523069i	$0.175213\pi$
$84$	2.00340	+	1.44855i	0.218589	+	0.158050i
$85$	−1.24024	−	2.14815i	−0.134522	−	0.233000i
$86$	7.74307	+	13.4114i	0.834957	+	1.44619i
$87$	3.93107	−	1.76104i	0.421455	−	0.188803i
$88$	−0.0572033	+	0.0990790i	−0.00609789	+	0.0105619i
$89$	−4.64901			−0.492794			−0.246397	−	0.969169i	$-0.579247\pi$
$89$	−4.64901			−0.492794			−0.246397	+	0.969169i	$0.579247\pi$
$90$	−1.53621	−	4.65519i	−0.161930	−	0.490700i
$91$	−2.13012			−0.223297
$92$	−1.65202	+	2.86138i	−0.172235	+	0.298320i
$93$	−1.44522	+	14.0605i	−0.149862	+	1.45800i
$94$	−7.97868	−	13.8195i	−0.822938	−	1.42537i
$95$	1.06552	+	1.84554i	0.109320	+	0.189348i
$96$	−0.645704	+	6.28203i	−0.0659019	+	0.641157i
$97$	−3.67049	+	6.35747i	−0.372682	+	0.645503i	−0.989977	−	0.141228i	$-0.954895\pi$
$97$	−3.67049	+	6.35747i	−0.372682	+	0.645503i	0.617296	+	0.786731i	$0.288228\pi$
$98$	−4.02399			−0.406484
$99$	0.154635	+	0.0321280i	0.0155414	+	0.00322898i
$100$	0.670078			0.0670078
$101$	−0.276429	+	0.478790i	−0.0275058	+	0.0476414i	−0.879451	−	0.475990i	$-0.842090\pi$
$101$	−0.276429	+	0.478790i	−0.0275058	+	0.0476414i	0.851945	+	0.523632i	$0.175423\pi$
$102$	6.40681	−	2.87012i	0.634369	−	0.284184i
$103$	3.91898	+	6.78787i	0.386148	+	0.668828i	0.991928	−	0.126804i	$-0.0404720\pi$
$103$	3.91898	+	6.78787i	0.386148	+	0.668828i	−0.605780	+	0.795633i	$0.707139\pi$
$104$	−1.08657	−	1.88200i	−0.106547	−	0.184545i
$105$	−2.98981	−	2.16176i	−0.291776	−	0.210967i
$106$	2.97469	−	5.15232i	0.288928	−	0.500437i
$107$	19.4173			1.87714			0.938572	−	0.345084i	$-0.112149\pi$
$107$	19.4173			1.87714			0.938572	+	0.345084i	$0.112149\pi$
$108$	3.40068	−	0.747329i	0.327230	−	0.0719118i
$109$	−2.13502			−0.204498			−0.102249	−	0.994759i	$-0.532604\pi$
$109$	−2.13502			−0.204498			−0.102249	+	0.994759i	$0.532604\pi$
$110$	−0.0430125	+	0.0744999i	−0.00410108	+	0.00710328i
$111$	−1.57150	−	1.13627i	−0.149160	−	0.107850i
$112$	5.20936	+	9.02288i	0.492238	+	0.852582i
$113$	3.11765	+	5.39992i	0.293283	+	0.507982i	0.974584	−	0.224022i	$-0.0719187\pi$
$113$	3.11765	+	5.39992i	0.293283	+	0.507982i	−0.681301	+	0.732004i	$0.738585\pi$
$114$	−5.50428	+	2.46581i	−0.515523	+	0.230944i
$115$	2.46542	−	4.27023i	0.229901	−	0.398201i
$116$	−1.66644			−0.154725
$117$	−1.99714	+	2.23862i	−0.184636	+	0.206960i
$118$	12.2404			1.12682
$119$	2.64185	−	4.57581i	0.242178	−	0.419464i
$120$	0.384858	−	3.74427i	0.0351325	−	0.341803i
$121$	5.49861	+	9.52388i	0.499874	+	0.865807i
$122$	4.72567	+	8.18509i	0.427842	+	0.741043i
$123$	−0.969461	+	9.43185i	−0.0874133	+	0.850441i
$124$	2.73412	−	4.73563i	0.245531	−	0.425272i
$125$	−1.00000			−0.0894427
$126$	6.95144	−	7.79194i	0.619283	−	0.694161i
$127$	−10.6036			−0.940918			−0.470459	−	0.882422i	$-0.655912\pi$
$127$	−10.6036			−0.940918			−0.470459	+	0.882422i	$0.655912\pi$
$128$	−6.77076	+	11.7273i	−0.598456	+	1.03656i
$129$	14.9805	−	6.71097i	1.31896	−	0.590868i
$130$	−0.817019	−	1.41512i	−0.0716573	−	0.124114i
$131$	8.09616	+	14.0230i	0.707365	+	1.22519i	0.965831	+	0.259171i	$0.0834494\pi$
$131$	8.09616	+	14.0230i	0.707365	+	1.22519i	−0.258467	+	0.966020i	$0.583217\pi$
$132$	−0.0495140	−	0.0358008i	−0.00430964	−	0.00311606i
$133$	−2.26969	+	3.93121i	−0.196807	+	0.340880i
$134$	−10.1897			−0.880256
$135$	−5.07505	+	1.11529i	−0.436791	+	0.0959886i
$136$	5.39042			0.462224
$137$	10.3843	−	17.9861i	0.887189	−	1.53666i	0.0440058	−	0.999031i	$-0.485988\pi$
$137$	10.3843	−	17.9861i	0.887189	−	1.53666i	0.843184	−	0.537626i	$-0.180679\pi$
$138$	11.3090	+	8.17687i	0.962682	+	0.696062i
$139$	1.25038	+	2.16571i	0.106055	+	0.183693i	0.914169	−	0.405333i	$-0.132845\pi$
$139$	1.25038	+	2.16571i	0.106055	+	0.183693i	−0.808113	+	0.589027i	$0.799511\pi$
$140$	0.713672	+	1.23612i	0.0603163	+	0.104471i
$141$	−15.4364	+	6.91518i	−1.29998	+	0.582363i
$142$	−2.04295	+	3.53850i	−0.171441	+	0.296944i
$143$	0.0526457			0.00440245
$144$	14.3666	+	2.98491i	1.19722	+	0.248743i
$145$	2.48694			0.206529
$146$	0.900721	−	1.56009i	0.0745442	−	0.129114i
$147$	−0.436121	+	4.24300i	−0.0359706	+	0.349957i
$148$	0.375120	+	0.649727i	0.0308347	+	0.0534072i
$149$	0.945127	+	1.63701i	0.0774279	+	0.134109i	0.902139	−	0.431444i	$-0.141996\pi$
$149$	0.945127	+	1.63701i	0.0774279	+	0.134109i	−0.824712	+	0.565553i	$0.808663\pi$
$150$	0.289384	−	2.81540i	0.0236281	−	0.229877i
$151$	2.44343	−	4.23214i	0.198843	−	0.344406i	−0.749310	−	0.662219i	$-0.769615\pi$
$151$	2.44343	−	4.23214i	0.198843	−	0.344406i	0.948154	+	0.317812i	$0.102948\pi$
$152$	−4.63107			−0.375629
$153$	−2.33196	−	7.06658i	−0.188528	−	0.571299i
$154$	−0.183243			−0.0147662
$155$	−4.08030	+	7.06728i	−0.327737	+	0.567658i
$156$	1.05918	−	0.474493i	0.0848025	−	0.0379898i
$157$	8.99989	+	15.5883i	0.718269	+	1.24408i	0.961685	+	0.274157i	$0.0883987\pi$
$157$	8.99989	+	15.5883i	0.718269	+	1.24408i	−0.243416	+	0.969922i	$0.578268\pi$
$158$	12.7582	+	22.0979i	1.01499	+	1.75801i
$159$	−5.11035	−	3.69501i	−0.405277	−	0.293033i
$160$	−1.82302	+	3.15756i	−0.144122	+	0.249627i
$161$	10.5032			0.827772
$162$	−1.67134	−	14.6111i	−0.131313	−	1.14795i
$163$	9.41748			0.737634			0.368817	−	0.929502i	$-0.379763\pi$
$163$	9.41748			0.737634			0.368817	+	0.929502i	$0.379763\pi$
$164$	1.83406	−	3.17668i	0.143216	−	0.248057i
$165$	0.0738930	+	0.0534279i	0.00575256	+	0.00415935i
$166$	−0.399646	−	0.692207i	−0.0310185	−	0.0537257i
$167$	7.74523	+	13.4151i	0.599344	+	1.03809i	0.992918	+	0.118801i	$0.0379051\pi$
$167$	7.74523	+	13.4151i	0.599344	+	1.03809i	−0.393574	+	0.919293i	$0.628762\pi$
$168$	7.31707	−	3.27790i	0.564525	−	0.252896i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	4.05318			0.310865
$171$	2.00346	+	6.07111i	0.153208	+	0.464269i
$172$	−6.35048			−0.484219
$173$	4.83831	−	8.38021i	0.367850	−	0.637135i	−0.621379	−	0.783510i	$-0.713427\pi$
$173$	4.83831	−	8.38021i	0.367850	−	0.637135i	0.989229	+	0.146375i	$0.0467606\pi$
$174$	−0.719678	+	7.00172i	−0.0545587	+	0.530799i
$175$	−1.06506	−	1.84473i	−0.0805108	−	0.139449i
$176$	−0.128749	−	0.223000i	−0.00970482	−	0.0168092i
$177$	1.32661	−	12.9066i	0.0997143	−	0.970117i
$178$	3.79832	−	6.57889i	0.284696	−	0.493109i
$179$	−3.31630			−0.247872			−0.123936	−	0.992290i	$-0.539552\pi$
$179$	−3.31630			−0.247872			−0.123936	+	0.992290i	$0.539552\pi$
$180$	1.96820	+	0.408927i	0.146701	+	0.0304796i
$181$	−22.6189			−1.68125			−0.840623	−	0.541621i	$-0.817811\pi$
$181$	−22.6189			−1.68125			−0.840623	+	0.541621i	$0.817811\pi$
$182$	1.74034	−	3.01437i	0.129003	−	0.223440i
$183$	9.14275	−	4.09577i	0.675852	−	0.302768i
$184$	5.35770	+	9.27981i	0.394975	+	0.684117i
$185$	−0.559815	−	0.969629i	−0.0411585	−	0.0712885i
$186$	−18.7165	−	13.5328i	−1.37236	−	0.992276i
$187$	−0.0652931	+	0.113091i	−0.00477470	+	0.00827003i
$188$	6.54371			0.477249
$189$	−7.46263	−	8.17428i	−0.542827	−	0.594591i
$190$	−3.48221			−0.252626
$191$	−2.94105	+	5.09405i	−0.212807	+	0.368593i	−0.952592	−	0.304251i	$-0.901594\pi$
$191$	−2.94105	+	5.09405i	−0.212807	+	0.368593i	0.739785	+	0.672843i	$0.234927\pi$
$192$	5.36809	+	3.88136i	0.387408	+	0.280113i
$193$	0.229769	+	0.397972i	0.0165392	+	0.0286467i	0.874177	−	0.485608i	$-0.161402\pi$
$193$	0.229769	+	0.397972i	0.0165392	+	0.0286467i	−0.857637	+	0.514255i	$0.828069\pi$
$194$	−5.99771	−	10.3883i	−0.430611	−	0.745840i
$195$	−1.58069	+	0.708116i	−0.113195	+	0.0507092i
$196$	0.825068	−	1.42906i	0.0589335	−	0.102076i
$197$	−2.31119			−0.164665			−0.0823326	−	0.996605i	$-0.526237\pi$
$197$	−2.31119			−0.164665			−0.0823326	+	0.996605i	$0.526237\pi$
$198$	−0.171804	+	0.192577i	−0.0122096	+	0.0136859i
$199$	24.3734			1.72779			0.863893	−	0.503675i	$-0.168019\pi$
$199$	24.3734			1.72779			0.863893	+	0.503675i	$0.168019\pi$
$200$	1.08657	−	1.88200i	0.0768322	−	0.133077i
$201$	−1.10436	+	10.7443i	−0.0778957	+	0.757844i
$202$	−0.451696	−	0.782360i	−0.0317812	−	0.0550467i
$203$	2.64873	+	4.58774i	0.185904	+	0.321996i
$204$	−0.294355	+	2.86377i	−0.0206090	+	0.200504i
$205$	−2.73708	+	4.74077i	−0.191166	+	0.331110i
$206$	−12.8075			−0.892341
$207$	9.84758	−	11.0383i	0.684454	−	0.767212i
$208$	4.89115			0.339140
$209$	0.0560952	−	0.0971597i	0.00388019	−	0.00672068i
$210$	5.50188	−	2.46473i	0.379666	−	0.170083i
$211$	−13.6969	−	23.7237i	−0.942934	−	1.63321i	−0.759836	−	0.650114i	$-0.774721\pi$
$211$	−13.6969	−	23.7237i	−0.942934	−	1.63321i	−0.183097	−	0.983095i	$-0.558612\pi$
$212$	1.21985	+	2.11284i	0.0837794	+	0.145110i
$213$	3.50967	+	2.53765i	0.240479	+	0.173877i
$214$	−15.8643	+	27.4778i	−1.08446	+	1.87834i
$215$	9.47722			0.646341
$216$	3.41544	−	10.7631i	0.232391	−	0.732334i
$217$	−17.3830			−1.18004
$218$	1.74435	−	3.02131i	0.118142	−	0.204629i
$219$	−1.54739	−	1.11883i	−0.104563	−	0.0756034i
$220$	−0.0176384	−	0.0305505i	−0.00118918	−	0.00205972i
$221$	−1.24024	−	2.14815i	−0.0834273	−	0.144500i
$222$	2.89190	−	1.29551i	0.194091	−	0.0869490i
$223$	−12.6679	+	21.9415i	−0.848307	+	1.46931i	0.0344101	+	0.999408i	$0.489045\pi$
$223$	−12.6679	+	21.9415i	−0.848307	+	1.46931i	−0.882718	+	0.469904i	$0.844289\pi$
$224$	−7.76649			−0.518920
$225$	−2.93727	−	0.610268i	−0.195818	−	0.0406845i
$226$	−10.1887			−0.677742
$227$	10.6209	−	18.3959i	0.704931	−	1.22098i	−0.261785	−	0.965126i	$-0.584311\pi$
$227$	10.6209	−	18.3959i	0.704931	−	1.22098i	0.966716	−	0.255850i	$-0.0823554\pi$
$228$	0.252889	−	2.46035i	0.0167480	−	0.162941i
$229$	−6.11686	−	10.5947i	−0.404214	−	0.700119i	0.590016	−	0.807392i	$-0.299121\pi$
$229$	−6.11686	−	10.5947i	−0.404214	−	0.700119i	−0.994230	+	0.107273i	$0.965788\pi$
$230$	4.02858	+	6.97771i	0.265637	+	0.460096i
$231$	−0.0198600	+	0.193217i	−0.00130669	+	0.0127127i
$232$	−2.70223	+	4.68040i	−0.177410	+	0.307284i
$233$	11.4048			0.747154			0.373577	−	0.927599i	$-0.378131\pi$
$233$	11.4048			0.747154			0.373577	+	0.927599i	$0.378131\pi$
$234$	−1.53621	−	4.65519i	−0.100425	−	0.304319i
$235$	−9.76560			−0.637038
$236$	−2.50973	+	4.34698i	−0.163370	+	0.282965i
$237$	24.6833	−	11.0576i	1.60335	−	0.718270i
$238$	4.31687	+	7.47705i	0.279821	+	0.484665i
$239$	−7.42854	−	12.8666i	−0.480512	−	0.832272i	0.519238	−	0.854630i	$-0.326216\pi$
$239$	−7.42854	−	12.8666i	−0.480512	−	0.832272i	−0.999750	+	0.0223581i	$0.992883\pi$
$240$	6.86517	+	4.96382i	0.443145	+	0.320413i
$241$	9.29538	−	16.1001i	0.598768	−	1.03710i	−0.394235	−	0.919010i	$-0.628990\pi$
$241$	9.29538	−	16.1001i	0.598768	−	1.03710i	0.993003	−	0.118087i	$-0.0376763\pi$
$242$	−17.9699			−1.15515
$243$	−15.5874	+	0.178762i	−0.999934	+	0.0114676i
$244$	−3.87575			−0.248120
$245$	−1.23130	+	2.13268i	−0.0786650	+	0.136252i
$246$	−12.5551	−	9.07790i	−0.800484	−	0.578786i
$247$	1.06552	+	1.84554i	0.0677976	+	0.117429i
$248$	−8.86707	−	15.3582i	−0.563059	−	0.975247i
$249$	−0.773196	+	0.346376i	−0.0489993	+	0.0219507i
$250$	0.817019	−	1.41512i	0.0516728	−	0.0894999i
$251$	30.0723			1.89815			0.949073	−	0.315058i	$-0.102024\pi$
$251$	30.0723			1.89815			0.949073	+	0.315058i	$0.102024\pi$
$252$	1.34189	+	4.06634i	0.0845309	+	0.256155i
$253$	−0.259587			−0.0163201
$254$	8.66334	−	15.0054i	0.543587	−	0.941520i
$255$	0.439285	−	4.27379i	0.0275091	−	0.267635i
$256$	−7.23913	−	12.5385i	−0.452446	−	0.783659i
$257$	−1.52032	−	2.63327i	−0.0948348	−	0.164259i	0.814705	−	0.579876i	$-0.196899\pi$
$257$	−1.52032	−	2.63327i	−0.0948348	−	0.164259i	−0.909540	+	0.415617i	$0.863566\pi$
$258$	−2.74255	+	26.6822i	−0.170744	+	1.66116i
$259$	1.19247	−	2.06542i	0.0740966	−	0.128339i
$260$	0.670078			0.0415565
$261$	7.30481	+	1.51770i	0.452156	+	0.0939431i
$262$	−26.4588			−1.63463
$263$	2.40051	−	4.15780i	0.148022	−	0.256381i	−0.782474	−	0.622683i	$-0.786043\pi$
$263$	2.40051	−	4.15780i	0.148022	−	0.256381i	0.930496	+	0.366301i	$0.119376\pi$
$264$	−0.180841	+	0.0810131i	−0.0111300	+	0.00498601i
$265$	−1.82046	−	3.15312i	−0.111830	−	0.193695i
$266$	−3.70875	−	6.42375i	−0.227398	−	0.393865i
$267$	−6.52530	−	4.71808i	−0.399342	−	0.288742i
$268$	2.08927	−	3.61872i	0.127623	−	0.221049i
$269$	−16.8723			−1.02873			−0.514363	−	0.857573i	$-0.671971\pi$
$269$	−16.8723			−1.02873			−0.514363	+	0.857573i	$0.671971\pi$
$270$	2.56815	−	8.09300i	0.156293	−	0.492525i
$271$	−2.34099			−0.142205			−0.0711026	−	0.997469i	$-0.522652\pi$
$271$	−2.34099			−0.142205			−0.0711026	+	0.997469i	$0.522652\pi$
$272$	−6.06618	+	10.5069i	−0.367816	+	0.637076i
$273$	−2.98981	−	2.16176i	−0.180952	−	0.130836i
$274$	16.9683	+	29.3900i	1.02509	+	1.77551i
$275$	0.0263229	+	0.0455925i	0.00158733	+	0.00274933i
$276$	−5.22266	+	2.33964i	−0.314367	+	0.140830i
$277$	1.88617	−	3.26693i	0.113329	−	0.196291i	−0.803782	−	0.594924i	$-0.797182\pi$
$277$	1.88617	−	3.26693i	0.113329	−	0.196291i	0.917110	+	0.398633i	$0.130515\pi$
$278$	−4.08632			−0.245081
$279$	−16.2979	+	18.2685i	−0.975729	+	1.09370i
$280$	4.62905			0.276638
$281$	−5.47798	+	9.48813i	−0.326789	+	0.566015i	−0.981873	−	0.189541i	$-0.939300\pi$
$281$	−5.47798	+	9.48813i	−0.326789	+	0.566015i	0.655084	+	0.755556i	$0.272633\pi$
$282$	2.82601	−	27.4941i	0.168286	−	1.63725i
$283$	−8.78483	−	15.2158i	−0.522204	−	0.904484i	−0.999666	−	0.0258318i	$-0.991777\pi$
$283$	−8.78483	−	15.2158i	−0.522204	−	0.904484i	0.477462	−	0.878652i	$-0.341557\pi$
$284$	−0.837764	−	1.45105i	−0.0497122	−	0.0861040i
$285$	−0.377403	+	3.67173i	−0.0223554	+	0.217495i
$286$	−0.0430125	+	0.0744999i	−0.00254338	+	0.00440527i
$287$	−11.6606			−0.688305
$288$	−7.28166	+	8.16209i	−0.429076	+	0.480956i
$289$	−10.8473			−0.638074
$290$	−2.03187	+	3.51931i	−0.119316	+	0.206661i
$291$	−11.6038	+	5.19826i	−0.680226	+	0.304727i
$292$	0.369363	+	0.639756i	0.0216153	+	0.0374389i
$293$	−12.2723	−	21.2562i	−0.716953	−	1.24180i	−0.962202	−	0.272338i	$-0.912203\pi$
$293$	−12.2723	−	21.2562i	−0.716953	−	1.24180i	0.245249	−	0.969460i	$-0.421130\pi$
$294$	−5.64803	−	4.08377i	−0.329400	−	0.238171i
$295$	3.74544	−	6.48728i	0.218068	−	0.377704i
$296$	2.43312			0.141422
$297$	0.184439	+	0.202027i	0.0107022	+	0.0117228i
$298$	−3.08875			−0.178926
$299$	2.46542	−	4.27023i	0.142579	−	0.246954i
$300$	0.940514	+	0.680033i	0.0543006	+	0.0392617i
$301$	10.0938	+	17.4830i	0.581797	+	1.00770i
$302$	3.99265	+	6.91547i	0.229751	+	0.397941i
$303$	−0.873897	+	0.391488i	−0.0502041	+	0.0224904i
$304$	5.21163	−	9.02681i	0.298908	−	0.517723i
$305$	5.78404			0.331193
$306$	11.9053	+	2.47353i	0.680581	+	0.141402i
$307$	−11.0689			−0.631735			−0.315868	−	0.948803i	$-0.602296\pi$
$307$	−11.0689			−0.631735			−0.315868	+	0.948803i	$0.602296\pi$
$308$	0.0375718	−	0.0650762i	0.00214085	−	0.00370806i
$309$	−1.38808	+	13.5046i	−0.0789651	+	0.768249i
$310$	−6.66736	−	11.5482i	−0.378680	−	0.655894i
$311$	−7.39666	−	12.8114i	−0.419426	−	0.726468i	0.576456	−	0.817129i	$-0.304435\pi$
$311$	−7.39666	−	12.8114i	−0.419426	−	0.726468i	−0.995882	+	0.0906608i	$0.971102\pi$
$312$	0.384858	−	3.74427i	0.0217883	−	0.211977i
$313$	−13.5262	+	23.4281i	−0.764548	+	1.32424i	0.175937	+	0.984401i	$0.443704\pi$
$313$	−13.5262	+	23.4281i	−0.764548	+	1.32424i	−0.940485	+	0.339834i	$0.889629\pi$
$314$	−29.4123			−1.65983
$315$	−2.00258	−	6.06846i	−0.112833	−	0.341919i
$316$	−10.4636			−0.588626
$317$	−0.288999	+	0.500561i	−0.0162318	+	0.0281143i	−0.874027	−	0.485877i	$-0.838500\pi$
$317$	−0.288999	+	0.500561i	−0.0162318	+	0.0281143i	0.857795	+	0.513991i	$0.171834\pi$
$318$	9.40412	−	4.21285i	0.527357	−	0.236245i
$319$	−0.0654632	−	0.113386i	−0.00366524	−	0.00634838i
$320$	1.91227	+	3.31215i	0.106899	+	0.185155i
$321$	27.2540	+	19.7058i	1.52117	+	1.09987i
$322$	−8.58135	+	14.8633i	−0.478220	+	0.828301i
$323$	−5.28600			−0.294121
$324$	5.53159	+	2.40226i	0.307311	+	0.133459i
$325$	−1.00000			−0.0554700
$326$	−7.69425	+	13.3268i	−0.426145	+	0.738105i
$327$	−2.99669	−	2.16674i	−0.165718	−	0.119821i
$328$	−5.94808	−	10.3024i	−0.328428	−	0.568853i
$329$	−10.4009	−	18.0149i	−0.573422	−	0.993196i
$330$	−0.135979	+	0.0609157i	−0.00748538	+	0.00335330i
$331$	12.0570	−	20.8833i	0.662712	−	1.14785i	−0.317188	−	0.948363i	$-0.602739\pi$
$331$	12.0570	−	20.8833i	0.662712	−	1.14785i	0.979900	−	0.199489i	$-0.0639281\pi$
$332$	0.327770			0.0179887
$333$	−1.05260	−	3.18970i	−0.0576820	−	0.174795i
$334$	−25.3120			−1.38501
$335$	−3.11795	+	5.40045i	−0.170352	+	0.295058i
$336$	−1.84513	+	17.9512i	−0.100660	+	0.979317i
$337$	−3.06746	−	5.31299i	−0.167095	−	0.289417i	0.770302	−	0.637679i	$-0.220105\pi$
$337$	−3.06746	−	5.31299i	−0.167095	−	0.289417i	−0.937397	+	0.348262i	$0.886772\pi$
$338$	−0.817019	−	1.41512i	−0.0444400	−	0.0769723i
$339$	−1.10425	+	10.7432i	−0.0599748	+	0.583493i
$340$	−0.831054	+	1.43943i	−0.0450702	+	0.0780640i
$341$	0.429620			0.0232652
$342$	−10.2282	−	2.12508i	−0.553078	−	0.114911i
$343$	−20.1564			−1.08835
$344$	−10.2977	+	17.8361i	−0.555214	+	0.961658i
$345$	7.79410	−	3.49160i	0.419620	−	0.187981i
$346$	7.90599	+	13.6936i	0.425028	+	0.736171i
$347$	1.86200	+	3.22507i	0.0999572	+	0.173131i	0.911667	−	0.410930i	$-0.134796\pi$
$347$	1.86200	+	3.22507i	0.0999572	+	0.173131i	−0.811710	+	0.584061i	$0.801463\pi$
$348$	−2.33900	−	1.69120i	−0.125383	−	0.0906578i
$349$	1.67433	−	2.90002i	0.0896246	−	0.155234i	−0.817728	−	0.575605i	$-0.804767\pi$
$349$	1.67433	−	2.90002i	0.0896246	−	0.155234i	0.907352	+	0.420371i	$0.138100\pi$
$350$	3.48069			0.186051
$351$	−5.07505	+	1.11529i	−0.270886	+	0.0595296i
$352$	0.191948			0.0102309
$353$	17.7813	−	30.7981i	0.946403	−	1.63922i	0.193486	−	0.981103i	$-0.438021\pi$
$353$	17.7813	−	30.7981i	0.946403	−	1.63922i	0.752917	−	0.658115i	$-0.228646\pi$
$354$	17.1804	+	12.4222i	0.913130	+	0.660234i
$355$	1.25025	+	2.16550i	0.0663563	+	0.114933i
$356$	1.55760	+	2.69784i	0.0825525	+	0.142985i
$357$	8.35186	−	3.74147i	0.442028	−	0.198019i
$358$	2.70948	−	4.69296i	0.143200	−	0.248030i
$359$	9.06902			0.478645			0.239322	−	0.970940i	$-0.423075\pi$
$359$	9.06902			0.478645			0.239322	+	0.970940i	$0.423075\pi$
$360$	4.34008	−	4.86484i	0.228742	−	0.256399i
$361$	−14.4586			−0.760981
$362$	18.4800	−	32.0083i	0.971289	−	1.68232i
$363$	−1.94758	+	18.9479i	−0.102221	+	0.994508i
$364$	0.713672	+	1.23612i	0.0374066	+	0.0647901i
$365$	−0.551224	−	0.954749i	−0.0288524	−	0.0499738i
$366$	−1.67381	+	16.2844i	−0.0874912	+	0.851199i
$367$	12.3093	−	21.3203i	0.642541	−	1.11291i	−0.342323	−	0.939582i	$-0.611214\pi$
$367$	12.3093	−	21.3203i	0.642541	−	1.11291i	0.984864	−	0.173331i	$-0.0554529\pi$
$368$	−24.1174			−1.25721
$369$	−10.9327	+	12.2546i	−0.569134	+	0.637948i
$370$	1.82952			0.0951121
$371$	3.87778	−	6.71652i	0.201324	−	0.348704i
$372$	8.64357	−	3.87214i	0.448148	−	0.200761i
$373$	−13.4879	−	23.3617i	−0.698376	−	1.20962i	−0.969029	−	0.246946i	$-0.920573\pi$
$373$	−13.4879	−	23.3617i	−0.698376	−	1.20962i	0.270653	−	0.962677i	$-0.412760\pi$
$374$	−0.106691	−	0.184795i	−0.00551688	−	0.00955551i
$375$	−1.40359	−	1.01486i	−0.0724811	−	0.0524070i
$376$	10.6110	−	18.3788i	0.547222	−	0.947816i
$377$	2.48694			0.128084
$378$	17.6647	−	3.88197i	0.908573	−	0.199667i
$379$	14.2429			0.731611			0.365805	−	0.930691i	$-0.380794\pi$
$379$	14.2429			0.731611			0.365805	+	0.930691i	$0.380794\pi$
$380$	0.713983	−	1.23666i	0.0366266	−	0.0634391i
$381$	−14.8831	−	10.7611i	−0.762485	−	0.551310i
$382$	−4.80579	−	8.32387i	−0.245886	−	0.425886i
$383$	−12.9868	−	22.4938i	−0.663595	−	1.14938i	−0.979664	−	0.200644i	$-0.935697\pi$
$383$	−12.9868	−	22.4938i	−0.663595	−	1.14938i	0.316070	−	0.948736i	$-0.397637\pi$
$384$	−21.4049	+	9.58896i	−1.09231	+	0.489335i
$385$	−0.0560707	+	0.0971174i	−0.00285763	+	0.00494956i
$386$	−0.750903			−0.0382200
$387$	27.8372	+	5.78365i	1.41504	+	0.293999i
$388$	4.91902			0.249726
$389$	−12.8953	+	22.3354i	−0.653819	+	1.13245i	0.328370	+	0.944549i	$0.393501\pi$
$389$	−12.8953	+	22.3354i	−0.653819	+	1.13245i	−0.982189	+	0.187898i	$0.939832\pi$
$390$	0.289384	−	2.81540i	0.0146535	−	0.142563i
$391$	6.11539	+	10.5922i	0.309269	+	0.535669i
$392$	−2.67580	−	4.63461i	−0.135148	−	0.234083i
$393$	−2.86762	+	27.8989i	−0.144652	+	1.40731i
$394$	1.88828	−	3.27060i	0.0951303	−	0.164771i
$395$	15.6156			0.785705
$396$	−0.0331647	−	0.100499i	−0.00166659	−	0.00505028i
$397$	−19.2890			−0.968086			−0.484043	−	0.875044i	$-0.660832\pi$
$397$	−19.2890			−0.968086			−0.484043	+	0.875044i	$0.660832\pi$
$398$	−19.9135	+	34.4913i	−0.998176	+	1.72889i
$399$	−7.17533	+	3.21440i	−0.359216	+	0.160921i
$400$	2.44558	+	4.23586i	0.122279	+	0.211793i
$401$	8.23155	+	14.2575i	0.411064	+	0.711983i	0.995006	−	0.0998116i	$-0.0318240\pi$
$401$	8.23155	+	14.2575i	0.411064	+	0.711983i	−0.583943	+	0.811795i	$0.698491\pi$
$402$	−14.3022	−	10.3411i	−0.713327	−	0.515767i
$403$	−4.08030	+	7.06728i	−0.203254	+	0.352046i
$404$	0.370458			0.0184310
$405$	−8.25515	−	3.58505i	−0.410202	−	0.178142i
$406$	−8.65625			−0.429602
$407$	−0.0294719	+	0.0510468i	−0.00146087	+	0.00253030i
$408$	7.56593	+	5.47050i	0.374570	+	0.270830i
$409$	9.87631	+	17.1063i	0.488352	+	0.845850i	0.999910	−	0.0133982i	$-0.00426491\pi$
$409$	9.87631	+	17.1063i	0.488352	+	0.845850i	−0.511558	+	0.859249i	$0.670932\pi$
$410$	−4.47250	−	7.74660i	−0.220881	−	0.382577i
$411$	32.8286	−	14.7066i	1.61932	−	0.725421i
$412$	2.62602	−	4.54840i	0.129375	−	0.224084i
$413$	15.9564			0.785164
$414$	7.57477	+	22.9539i	0.372280	+	1.12812i
$415$	−0.489152			−0.0240115
$416$	−1.82302	+	3.15756i	−0.0893809	+	0.154812i
$417$	−0.442876	+	4.30873i	−0.0216877	+	0.210999i
$418$	0.0916617	+	0.158763i	0.00448332	+	0.00776533i
$419$	8.72915	+	15.1193i	0.426447	+	0.738628i	0.996554	−	0.0829423i	$-0.0264317\pi$
$419$	8.72915	+	15.1193i	0.426447	+	0.738628i	−0.570107	+	0.821570i	$0.693098\pi$
$420$	−0.252779	+	2.45927i	−0.0123343	+	0.120000i
$421$	3.70798	−	6.42241i	0.180716	−	0.313009i	−0.761409	−	0.648272i	$-0.775492\pi$
$421$	3.70798	−	6.42241i	0.180716	−	0.313009i	0.942125	+	0.335263i	$0.108825\pi$
$422$	44.7625			2.17900
$423$	−28.6842	−	5.95963i	−1.39468	−	0.289767i
$424$	7.91222			0.384251
$425$	1.24024	−	2.14815i	0.0601603	−	0.104201i
$426$	−6.45854	+	2.89330i	−0.312917	+	0.140181i
$427$	6.16034	+	10.6700i	0.298120	+	0.516358i
$428$	−6.50556	−	11.2680i	−0.314458	−	0.544657i
$429$	0.0738930	+	0.0534279i	0.00356759	+	0.00257952i
$430$	−7.74307	+	13.4114i	−0.373404	+	0.646755i
$431$	33.6097			1.61892			0.809461	−	0.587174i	$-0.199760\pi$
$431$	33.6097			1.61892			0.809461	+	0.587174i	$0.199760\pi$
$432$	17.1356	+	18.7697i	0.824438	+	0.903057i
$433$	30.2826			1.45529			0.727644	−	0.685955i	$-0.240615\pi$
$433$	30.2826			1.45529			0.727644	+	0.685955i	$0.240615\pi$
$434$	14.2022	−	24.5990i	0.681730	−	1.18079i
$435$	3.49064	+	2.52388i	0.167363	+	0.121011i
$436$	0.715315	+	1.23896i	0.0342574	+	0.0593355i
$437$	−5.25391	−	9.10005i	−0.251329	−	0.435314i
$438$	2.84752	−	1.27563i	0.136060	−	0.0609520i
$439$	14.3685	−	24.8870i	0.685772	−	1.18779i	−0.287422	−	0.957804i	$-0.592798\pi$
$439$	14.3685	−	24.8870i	0.685772	−	1.18779i	0.973194	−	0.229987i	$-0.0738685\pi$
$440$	−0.114407			−0.00545412
$441$	−4.91818	+	5.51283i	−0.234199	+	0.262516i
$442$	4.05318			0.192790
$443$	11.2109	−	19.4179i	0.532646	−	0.922570i	−0.466627	−	0.884454i	$-0.654531\pi$
$443$	11.2109	−	19.4179i	0.532646	−	0.922570i	0.999273	−	0.0381159i	$-0.0121356\pi$
$444$	−0.132865	+	1.29264i	−0.00630552	+	0.0613461i
$445$	−2.32450	−	4.02616i	−0.110192	−	0.190858i
$446$	−20.6999	−	35.8532i	−0.980167	−	1.69770i
$447$	−0.334759	+	3.25686i	−0.0158336	+	0.154044i
$448$	−4.07336	+	7.05526i	−0.192448	+	0.333330i
$449$	16.0149			0.755791			0.377895	−	0.925848i	$-0.376648\pi$
$449$	16.0149			0.755791			0.377895	+	0.925848i	$0.376648\pi$
$450$	3.26341	−	3.65799i	0.153839	−	0.172439i
$451$	0.288192			0.0135704
$452$	2.08907	−	3.61837i	0.0982614	−	0.170194i
$453$	7.72458	−	3.46046i	0.362933	−	0.162586i
$454$	17.3549	+	30.0595i	0.814505	+	1.41076i
$455$	−1.06506	−	1.84473i	−0.0499307	−	0.0864825i
$456$	−6.50012	−	4.69987i	−0.304396	−	0.220092i
$457$	−0.532780	+	0.922803i	−0.0249224	+	0.0431669i	−0.878218	−	0.478261i	$-0.841267\pi$
$457$	−0.532780	+	0.922803i	−0.0249224	+	0.0431669i	0.853295	+	0.521428i	$0.174601\pi$
$458$	19.9904			0.934089
$459$	3.89845	−	12.2852i	0.181964	−	0.573424i
$460$	−3.30404			−0.154052
$461$	−12.3193	+	21.3377i	−0.573769	+	0.993798i	0.422405	+	0.906407i	$0.361186\pi$
$461$	−12.3193	+	21.3377i	−0.573769	+	0.993798i	−0.996174	+	0.0873903i	$0.972147\pi$
$462$	−0.257198	−	0.185966i	−0.0119660	−	0.00865191i
$463$	−3.56164	−	6.16895i	−0.165524	−	0.286695i	0.771318	−	0.636451i	$-0.219598\pi$
$463$	−3.56164	−	6.16895i	−0.165524	−	0.286695i	−0.936841	+	0.349755i	$0.886265\pi$
$464$	−6.08199	−	10.5343i	−0.282349	−	0.489043i
$465$	−12.8993	+	5.77865i	−0.598193	+	0.267978i
$466$	−9.31794	+	16.1391i	−0.431645	+	0.747631i
$467$	20.4662			0.947063			0.473531	−	0.880777i	$-0.342979\pi$
$467$	20.4662			0.947063			0.473531	+	0.880777i	$0.342979\pi$
$468$	1.96820	+	0.408927i	0.0909801	+	0.0189027i
$469$	−13.2832			−0.613361
$470$	7.97868	−	13.8195i	0.368029	−	0.637445i
$471$	−3.18771	+	31.0131i	−0.146882	+	1.42901i
$472$	8.13936	+	14.0978i	0.374645	+	0.648903i
$473$	−0.249468	−	0.432090i	−0.0114705	−	0.0198675i
$474$	−4.51889	+	43.9641i	−0.207560	+	2.01934i
$475$	−1.06552	+	1.84554i	−0.0488895	+	0.0846792i
$476$	−3.54048			−0.162278
$477$	−3.42293	−	10.3725i	−0.156725	−	0.474926i
$478$	24.2770			1.11041
$479$	7.23493	−	12.5313i	0.330573	−	0.572568i	−0.652052	−	0.758175i	$-0.726092\pi$
$479$	7.23493	−	12.5313i	0.330573	−	0.572568i	0.982624	+	0.185606i	$0.0594248\pi$
$480$	−5.76325	+	2.58182i	−0.263055	+	0.117843i
$481$	−0.559815	−	0.969629i	−0.0255254	−	0.0442113i
$482$	15.1890	+	26.3081i	0.691840	+	1.19830i
$483$	14.7422	+	10.6593i	0.670796	+	0.485015i
$484$	3.68450	−	6.38174i	0.167477	−	0.290079i
$485$	−7.34097			−0.333336
$486$	12.4823	−	22.2041i	0.566207	−	1.00720i
$487$	29.8595			1.35306			0.676531	−	0.736414i	$-0.263483\pi$
$487$	29.8595			1.35306			0.676531	+	0.736414i	$0.263483\pi$
$488$	−6.28477	+	10.8855i	−0.284498	+	0.492765i
$489$	13.2183	+	9.55740i	0.597751	+	0.432200i
$490$	−2.01199	−	3.48488i	−0.0908926	−	0.157431i
$491$	−11.0235	−	19.0932i	−0.497483	−	0.861665i	0.502513	−	0.864570i	$-0.332409\pi$
$491$	−11.0235	−	19.0932i	−0.497483	−	0.861665i	−0.999996	+	0.00290444i	$0.999075\pi$
$492$	5.79815	−	2.59745i	0.261401	−	0.117102i
$493$	−3.08439	+	5.34231i	−0.138914	+	0.240606i
$494$	−3.48221			−0.156672
$495$	0.0494938	+	0.149982i	0.00222458	+	0.00674117i
$496$	39.9147			1.79222
$497$	−2.66318	+	4.61276i	−0.119460	+	0.206910i
$498$	0.141552	−	1.37716i	0.00634312	−	0.0617119i
$499$	−10.5861	−	18.3357i	−0.473901	−	0.820820i	0.525653	−	0.850699i	$-0.323821\pi$
$499$	−10.5861	−	18.3357i	−0.473901	−	0.820820i	−0.999554	+	0.0298789i	$0.990488\pi$
$500$	0.335039	+	0.580304i	0.0149834	+	0.0259520i
$501$	−2.74332	+	26.6896i	−0.122562	+	1.19241i
$502$	−24.5696	+	42.5558i	−1.09660	+	1.89936i
$503$	−40.3143			−1.79752			−0.898762	−	0.438436i	$-0.855533\pi$
$503$	−40.3143			−1.79752			−0.898762	+	0.438436i	$0.855533\pi$
$504$	13.5968	+	2.82496i	0.605648	+	0.125834i
$505$	−0.552859			−0.0246019
$506$	0.212088	−	0.367346i	0.00942844	−	0.0163305i
$507$	−1.58069	+	0.708116i	−0.0702008	+	0.0314485i
$508$	3.55262	+	6.15332i	0.157622	+	0.273009i
$509$	−9.50834	−	16.4689i	−0.421450	−	0.729973i	0.574632	−	0.818412i	$-0.305145\pi$
$509$	−9.50834	−	16.4689i	−0.421450	−	0.729973i	−0.996082	+	0.0884396i	$0.971812\pi$
$510$	5.68901	+	4.11340i	0.251913	+	0.182144i
$511$	1.17417	−	2.03373i	0.0519423	−	0.0899667i
$512$	−3.42501			−0.151366
$513$	−3.34928	+	10.5546i	−0.147874	+	0.465996i
$514$	4.96851			0.219152
$515$	−3.91898	+	6.78787i	−0.172691	+	0.299109i
$516$	−8.91347	−	6.44483i	−0.392393	−	0.283718i
$517$	0.257059	+	0.445238i	0.0113054	+	0.0195816i
$518$	1.94854	+	3.37498i	0.0856141	+	0.148288i
$519$	15.2957	−	6.85217i	0.671408	−	0.300777i
$520$	1.08657	−	1.88200i	0.0476493	−	0.0825310i
$521$	−33.4407			−1.46507			−0.732533	−	0.680732i	$-0.761662\pi$
$521$	−33.4407			−1.46507			−0.732533	+	0.680732i	$0.761662\pi$
$522$	−8.11588	+	9.09718i	−0.355223	+	0.398173i
$523$	−6.40250			−0.279962			−0.139981	−	0.990154i	$-0.544704\pi$
$523$	−6.40250			−0.279962			−0.139981	+	0.990154i	$0.544704\pi$
$524$	5.42505	−	9.39647i	0.236995	−	0.410487i
$525$	0.377238	−	3.67013i	0.0164640	−	0.160178i
$526$	3.92252	+	6.79401i	0.171030	+	0.296233i
$527$	−10.1211	−	17.5302i	−0.440880	−	0.763627i
$528$	0.0456022	−	0.443662i	0.00198458	−	0.0193079i
$529$	−0.656552	+	1.13718i	−0.0285457	+	0.0494426i
$530$	5.94939			0.258425
$531$	14.9603	−	16.7692i	0.649224	−	0.727722i
$532$	3.04173			0.131876
$533$	−2.73708	+	4.74077i	−0.118556	+	0.205346i
$534$	12.0079	−	5.37931i	0.519634	−	0.232785i
$535$	9.70866	+	16.8159i	0.419742	+	0.727015i
$536$	−6.77576	−	11.7360i	−0.292668	−	0.506916i
$537$	−4.65473	−	3.36557i	−0.200866	−	0.145235i
$538$	13.7850	−	23.8764i	0.594315	−	1.02938i
$539$	0.129646			0.00558423
$540$	2.34755	+	2.57141i	0.101022	+	0.110656i
$541$	−17.4745			−0.751286			−0.375643	−	0.926764i	$-0.622578\pi$
$541$	−17.4745			−0.751286			−0.375643	+	0.926764i	$0.622578\pi$
$542$	1.91264	−	3.31278i	0.0821547	−	0.142296i
$543$	−31.7476	−	22.9549i	−1.36242	−	0.985089i
$544$	−4.52195	−	7.83224i	−0.193877	−	0.335805i
$545$	−1.06751	−	1.84898i	−0.0457271	−	0.0792017i
$546$	5.50188	−	2.46473i	0.235459	−	0.105481i
$547$	5.03733	−	8.72491i	0.215381	−	0.373050i	−0.738010	−	0.674790i	$-0.764234\pi$
$547$	5.03733	−	8.72491i	0.215381	−	0.373050i	0.953390	+	0.301740i	$0.0975675\pi$
$548$	−13.9166			−0.594486
$549$	16.9893	+	3.52981i	0.725085	+	0.150649i
$550$	−0.0860250			−0.00366812
$551$	2.64989	−	4.58974i	0.112889	−	0.195529i
$552$	−1.89767	+	18.4623i	−0.0807701	+	0.785810i
$553$	16.6315	+	28.8066i	0.707243	+	1.22498i
$554$	3.08206	+	5.33829i	0.130944	+	0.226802i
$555$	0.198284	−	1.92909i	0.00841667	−	0.0818855i
$556$	0.837849	−	1.45120i	0.0355327	−	0.0615444i
$557$	21.2315			0.899607			0.449804	−	0.893127i	$-0.351494\pi$
$557$	21.2315			0.899607			0.449804	+	0.893127i	$0.351494\pi$
$558$	−12.5364	−	37.9891i	−0.530706	−	1.60821i
$559$	9.47722			0.400844
$560$	−5.20936	+	9.02288i	−0.220136	+	0.381286i
$561$	−0.206416	+	0.0924701i	−0.00871488	+	0.00390409i
$562$	−8.95122	−	15.5040i	−0.377584	−	0.653995i
$563$	−6.17245	−	10.6910i	−0.260138	−	0.450572i	0.706140	−	0.708072i	$-0.250435\pi$
$563$	−6.17245	−	10.6910i	−0.260138	−	0.450572i	−0.966278	+	0.257500i	$0.917101\pi$
$564$	9.18469	+	6.64094i	0.386745	+	0.279634i
$565$	−3.11765	+	5.39992i	−0.131160	+	0.227176i
$566$	28.7095			1.20675
$567$	−2.17875	−	19.0468i	−0.0914989	−	0.799892i
$568$	−5.43394			−0.228003
$569$	−3.87874	+	6.71817i	−0.162605	+	0.281640i	−0.935802	−	0.352526i	$-0.885323\pi$
$569$	−3.87874	+	6.71817i	−0.162605	+	0.281640i	0.773197	+	0.634166i	$0.218656\pi$
$570$	−4.88759	−	3.53394i	−0.204719	−	0.148021i
$571$	5.10696	+	8.84552i	0.213720	+	0.370173i	0.952876	−	0.303361i	$-0.0981087\pi$
$571$	5.10696	+	8.84552i	0.213720	+	0.370173i	−0.739156	+	0.673534i	$0.764775\pi$
$572$	−0.0176384	−	0.0305505i	−0.000737497	−	0.00127738i
$573$	−9.29777	+	4.16521i	−0.388420	+	0.174004i
$574$	9.52694	−	16.5011i	0.397647	−	0.688745i
$575$	4.93083			0.205630
$576$	3.59556	+	10.8957i	0.149815	+	0.453987i
$577$	−44.5539			−1.85480			−0.927402	−	0.374065i	$-0.877964\pi$
$577$	−44.5539			−1.85480			−0.927402	+	0.374065i	$0.877964\pi$
$578$	8.86242	−	15.3502i	0.368628	−	0.638482i
$579$	−0.0813831	+	0.791773i	−0.00338217	+	0.0329050i
$580$	−0.833220	−	1.44318i	−0.0345976	−	0.0599248i
$581$	−0.520975	−	0.902355i	−0.0216137	−	0.0374360i
$582$	2.12436	−	20.6678i	0.0880575	−	0.856708i
$583$	−0.0958392	+	0.165998i	−0.00396925	+	0.00687495i
$584$	2.39578			0.0991380
$585$	−2.93727	−	0.610268i	−0.121441	−	0.0252315i
$586$	40.1066			1.65679
$587$	−10.4535	+	18.1059i	−0.431461	+	0.747312i	−0.996999	−	0.0774099i	$-0.975335\pi$
$587$	−10.4535	+	18.1059i	−0.431461	+	0.747312i	0.565539	+	0.824722i	$0.308668\pi$
$588$	2.60835	−	1.16849i	0.107567	−	0.0481876i
$589$	8.69530	+	15.0607i	0.358284	+	0.620565i
$590$	6.12018	+	10.6005i	0.251964	+	0.436414i
$591$	−3.24396	−	2.34553i	−0.133439	−	0.0964820i
$592$	−2.73814	+	4.74260i	−0.112537	+	0.194920i
$593$	−7.48843			−0.307513			−0.153756	−	0.988109i	$-0.549137\pi$
$593$	−7.48843			−0.307513			−0.153756	+	0.988109i	$0.549137\pi$
$594$	−0.436581	+	0.0959426i	−0.0179132	+	0.00393657i
$595$	5.28369			0.216610
$596$	0.633309	−	1.09692i	0.0259413	−	0.0449317i
$597$	34.2103	+	24.7356i	1.40013	+	1.01236i
$598$	4.02858	+	6.97771i	0.164741	+	0.285340i
$599$	13.9657	+	24.1893i	0.570623	+	0.988349i	0.996502	+	0.0835684i	$0.0266317\pi$
$599$	13.9657	+	24.1893i	0.570623	+	0.988349i	−0.425879	+	0.904780i	$0.640035\pi$
$600$	3.43506	−	1.53884i	0.140236	−	0.0628227i
$601$	−16.3890	+	28.3866i	−0.668521	+	1.15791i	0.309796	+	0.950803i	$0.399739\pi$
$601$	−16.3890	+	28.3866i	−0.668521	+	1.15791i	−0.978318	+	0.207110i	$0.933594\pi$
$602$	−32.9873			−1.34446
$603$	−12.4540	+	13.9598i	−0.507166	+	0.568488i
$604$	−3.27457			−0.133240
$605$	−5.49861	+	9.52388i	−0.223550	+	0.387201i
$606$	0.159988	−	1.55652i	0.00649908	−	0.0632293i
$607$	−19.5852	−	33.9226i	−0.794940	−	1.37688i	−0.922878	−	0.385093i	$-0.874169\pi$
$607$	−19.5852	−	33.9226i	−0.794940	−	1.37688i	0.127938	−	0.991782i	$-0.459164\pi$
$608$	3.88494	+	6.72891i	0.157555	+	0.272893i
$609$	−0.938166	+	9.12738i	−0.0380164	+	0.369860i
$610$	−4.72567	+	8.18509i	−0.191337	+	0.331405i
$611$	−9.76560			−0.395074
$612$	−3.31947	+	3.72083i	−0.134182	+	0.150406i
$613$	−10.2019			−0.412051			−0.206026	−	0.978547i	$-0.566053\pi$
$613$	−10.2019			−0.412051			−0.206026	+	0.978547i	$0.566053\pi$
$614$	9.04350	−	15.6638i	0.364966	−	0.632139i
$615$	−8.65295	+	3.87635i	−0.348921	+	0.156309i
$616$	−0.121850	−	0.211050i	−0.00490946	−	0.00850344i
$617$	4.84474	+	8.39133i	0.195042	+	0.337822i	0.946914	−	0.321486i	$-0.104182\pi$
$617$	4.84474	+	8.39133i	0.195042	+	0.337822i	−0.751872	+	0.659309i	$0.770849\pi$
$618$	−17.9765	−	12.9978i	−0.723120	−	0.522848i
$619$	9.93748	−	17.2122i	0.399421	−	0.691818i	−0.594233	−	0.804293i	$-0.702544\pi$
$619$	9.93748	−	17.2122i	0.399421	−	0.691818i	0.993655	+	0.112475i	$0.0358778\pi$
$620$	5.46823			0.219610
$621$	25.0242	−	5.49929i	1.00419	−	0.220679i
$622$	24.1728			0.969243
$623$	4.95146	−	8.57618i	0.198376	−	0.343598i
$624$	6.86517	+	4.96382i	0.274827	+	0.198712i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−22.1024	−	38.2824i	−0.883388	−	1.53007i
$627$	0.177338	−	0.0794438i	0.00708219	−	0.00317268i
$628$	6.03062	−	10.4453i	0.240648	−	0.416815i
$629$	2.77721			0.110735
$630$	10.2237	+	2.12415i	0.407323	+	0.0846283i
$631$	−38.9270			−1.54966			−0.774830	−	0.632170i	$-0.782165\pi$
$631$	−38.9270			−1.54966			−0.774830	+	0.632170i	$0.782165\pi$
$632$	−16.9674	+	29.3885i	−0.674928	+	1.16901i
$633$	4.85137	−	47.1988i	0.192825	−	1.87598i
$634$	−0.472235	−	0.817935i	−0.0187548	−	0.0324843i
$635$	−5.30180	−	9.18299i	−0.210396	−	0.364416i
$636$	−0.432063	+	4.20353i	−0.0171324	+	0.166681i
$637$	−1.23130	+	2.13268i	−0.0487860	+	0.0844998i
$638$	0.213939			0.00846991
$639$	2.35079	+	7.12364i	0.0929959	+	0.281807i
$640$	−13.5415			−0.535275
$641$	3.94706	−	6.83651i	0.155899	−	0.270026i	−0.777487	−	0.628899i	$-0.783506\pi$
$641$	3.94706	−	6.83651i	0.155899	−	0.270026i	0.933386	+	0.358874i	$0.116839\pi$
$642$	−50.1531	+	22.4675i	−1.97938	+	0.886723i
$643$	−17.8875	−	30.9821i	−0.705415	−	1.22182i	−0.966541	−	0.256511i	$-0.917427\pi$
$643$	−17.8875	−	30.9821i	−0.705415	−	1.22182i	0.261126	−	0.965305i	$-0.415906\pi$
$644$	−3.51900	−	6.09508i	−0.138668	−	0.240180i
$645$	13.3021	+	9.61803i	0.523771	+	0.378710i
$646$	4.31876	−	7.48031i	0.169919	−	0.294309i
$647$	−1.47889			−0.0581412			−0.0290706	−	0.999577i	$-0.509255\pi$
$647$	−1.47889			−0.0581412			−0.0290706	+	0.999577i	$0.509255\pi$
$648$	15.7169	−	11.6407i	0.617416	−	0.457292i
$649$	−0.394362			−0.0154801
$650$	0.817019	−	1.41512i	0.0320461	−	0.0555055i
$651$	−24.3986	−	17.6413i	−0.956258	−	0.691416i
$652$	−3.15522	−	5.46500i	−0.123568	−	0.214026i
$653$	3.47523	+	6.01927i	0.135996	+	0.235552i	0.925978	−	0.377579i	$-0.123243\pi$
$653$	3.47523	+	6.01927i	0.135996	+	0.235552i	−0.789981	+	0.613131i	$0.789910\pi$
$654$	5.51455	−	2.47041i	0.215636	−	0.0966005i
$655$	−8.09616	+	14.0230i	−0.316343	+	0.547922i
$656$	26.7750			1.04539
$657$	−1.03644	−	3.14075i	−0.0404355	−	0.122532i
$658$	33.9910			1.32511
$659$	−15.4773	+	26.8075i	−0.602910	+	1.04427i	0.389469	+	0.921040i	$0.372659\pi$
$659$	−15.4773	+	26.8075i	−0.602910	+	1.04427i	−0.992378	+	0.123230i	$0.960675\pi$
$660$	0.00624741	−	0.0607808i	0.000243180	−	0.00236589i
$661$	−1.78839	−	3.09758i	−0.0695603	−	0.120482i	0.829147	−	0.559030i	$-0.188826\pi$
$661$	−1.78839	−	3.09758i	−0.0695603	−	0.120482i	−0.898708	+	0.438548i	$0.855493\pi$
$662$	19.7016	+	34.1241i	0.765724	+	1.32627i
$663$	0.439285	−	4.27379i	0.0170604	−	0.165980i
$664$	0.531498	−	0.920582i	0.0206261	−	0.0357255i
$665$	−4.53938			−0.176029
$666$	5.37380	+	1.11650i	0.208230	+	0.0432634i
$667$	−12.2627			−0.474812
$668$	5.18991	−	8.98918i	0.200804	−	0.347802i
$669$	−40.0481	+	17.9407i	−1.54835	+	0.693629i
$670$	−5.09485	−	8.82454i	−0.196831	−	0.340922i
$671$	−0.152252	−	0.263709i	−0.00587764	−	0.0101804i
$672$	−10.9010	−	7.88188i	−0.420514	−	0.304050i
$673$	14.0497	−	24.3347i	0.541575	−	0.938035i	−0.457239	−	0.889344i	$-0.651162\pi$
$673$	14.0497	−	24.3347i	0.541575	−	0.938035i	0.998814	−	0.0486913i	$-0.0155051\pi$
$674$	10.0247			0.386136
$675$	−3.50339	−	3.83748i	−0.134846	−	0.147705i
$676$	0.670078			0.0257722
$677$	−22.1467	+	38.3592i	−0.851167	+	1.47426i	0.0289890	+	0.999580i	$0.490771\pi$
$677$	−22.1467	+	38.3592i	−0.851167	+	1.47426i	−0.880156	+	0.474685i	$0.842562\pi$
$678$	−14.3008	−	10.3401i	−0.549217	−	0.397108i
$679$	−7.81856	−	13.5422i	−0.300049	−	0.519700i
$680$	2.69521	+	4.66824i	0.103357	+	0.179019i
$681$	33.5765	−	15.0416i	1.28665	−	0.576395i
$682$	−0.351008	+	0.607963i	−0.0134408	+	0.0232801i
$683$	−1.69041			−0.0646816			−0.0323408	−	0.999477i	$-0.510296\pi$
$683$	−1.69041			−0.0646816			−0.0323408	+	0.999477i	$0.510296\pi$
$684$	2.85185	−	3.19667i	0.109043	−	0.122228i
$685$	20.7686			0.793526
$686$	16.4682	−	28.5237i	0.628759	−	1.08904i
$687$	2.16656	−	21.0784i	0.0826594	−	0.804191i
$688$	−23.1773	−	40.1442i	−0.883625	−	1.53048i
$689$	−1.82046	−	3.15312i	−0.0693538	−	0.120124i
$690$	−1.42690	+	13.8823i	−0.0543212	+	0.528489i
$691$	5.40719	−	9.36552i	0.205699	−	0.356281i	−0.744656	−	0.667448i	$-0.767387\pi$
$691$	5.40719	−	9.36552i	0.205699	−	0.356281i	0.950355	+	0.311167i	$0.100720\pi$
$692$	−6.48409			−0.246488
$693$	−0.223963	+	0.251042i	−0.00850764	+	0.00953630i
$694$	−6.08514			−0.230989
$695$	−1.25038	+	2.16571i	−0.0474294	+	0.0821502i
$696$	−8.54277	+	3.82699i	−0.323813	+	0.145062i
$697$	−6.78926	−	11.7593i	−0.257162	−	0.445417i
$698$	2.73591	+	4.73874i	0.103556	+	0.179364i
$699$	16.0077	+	11.5743i	0.605466	+	0.437778i
$700$	−0.713672	+	1.23612i	−0.0269743	+	0.0467208i
$701$	−32.1755			−1.21525			−0.607626	−	0.794224i	$-0.707878\pi$
$701$	−32.1755			−1.21525			−0.607626	+	0.794224i	$0.707878\pi$
$702$	2.56815	−	8.09300i	0.0969285	−	0.305451i
$703$	−2.38598			−0.0899891
$704$	0.100673	−	0.174370i	0.00379425	−	0.00657183i
$705$	−13.7069	−	9.91069i	−0.516232	−	0.373258i
$706$	29.0553	+	50.3253i	1.09351	+	1.89402i
$707$	−0.588827	−	1.01988i	−0.0221451	−	0.0383565i
$708$	−7.93421	+	3.55436i	−0.298186	+	0.133581i
$709$	−15.9560	+	27.6366i	−0.599240	+	1.03791i	0.393694	+	0.919242i	$0.371197\pi$
$709$	−15.9560	+	27.6366i	−0.599240	+	1.03791i	−0.992934	+	0.118672i	$0.962136\pi$
$710$	−4.08591			−0.153341
$711$	45.8672	+	9.52968i	1.72015	+	0.357391i
$712$	10.1030			0.378624
$713$	20.1193	−	34.8476i	0.753472	−	1.30505i
$714$	−1.52901	+	14.8757i	−0.0572219	+	0.556710i
$715$	0.0263229	+	0.0455925i	0.000984419	+	0.00170506i
$716$	1.11109	+	1.92446i	0.0415234	+	0.0719206i
$717$	2.63115	−	25.5984i	0.0982621	−	0.955988i
$718$	−7.40956	+	12.8337i	−0.276522	+	0.478951i
$719$	20.6891			0.771572			0.385786	−	0.922588i	$-0.373930\pi$
$719$	20.6891			0.771572			0.385786	+	0.922588i	$0.373930\pi$
$720$	4.59831	+	13.9343i	0.171369	+	0.519302i
$721$	−16.6958			−0.621782
$722$	11.8130	−	20.4607i	0.439634	−	0.761468i
$723$	29.3862	−	13.1644i	1.09288	−	0.489590i
$724$	7.57820	+	13.1258i	0.281641	+	0.487817i
$725$	1.24347	+	2.15375i	0.0461812	+	0.0799882i
$726$	−25.2223	−	18.2369i	−0.936089	−	0.676834i
$727$	12.3396	−	21.3728i	0.457649	−	0.792672i	−0.541187	−	0.840902i	$-0.682025\pi$
$727$	12.3396	−	21.3728i	0.457649	−	0.792672i	0.998836	+	0.0482305i	$0.0153582\pi$
$728$	4.62905			0.171564
$729$	−22.0598	−	15.5681i	−0.817029	−	0.576597i
$730$	1.80144			0.0666744
$731$	−11.7540	+	20.3585i	−0.434737	+	0.752987i
$732$	−5.43997	−	3.93334i	−0.201067	−	0.145380i
$733$	10.8729	+	18.8325i	0.401602	+	0.695594i	0.993919	−	0.110110i	$-0.0351203\pi$
$733$	10.8729	+	18.8325i	0.401602	+	0.695594i	−0.592318	+	0.805704i	$0.701787\pi$
$734$	20.1139	+	34.8382i	0.742416	+	1.28590i
$735$	−3.89261	+	1.74381i	−0.143581	+	0.0643214i
$736$	8.98900	−	15.5694i	0.331339	−	0.573896i
$737$	0.328294			0.0120929
$738$	−8.40945	−	25.4833i	−0.309556	−	0.938053i
$739$	43.0460			1.58347			0.791736	−	0.610864i	$-0.209178\pi$
$739$	43.0460			1.58347			0.791736	+	0.610864i	$0.209178\pi$
$740$	−0.375120	+	0.649727i	−0.0137897	+	0.0238844i
$741$	−0.377403	+	3.67173i	−0.0138642	+	0.134885i
$742$	6.33644	+	10.9750i	0.232618	+	0.402906i
$743$	−3.94908	−	6.84001i	−0.144878	−	0.250936i	0.784450	−	0.620193i	$-0.212946\pi$
$743$	−3.94908	−	6.84001i	−0.144878	−	0.250936i	−0.929327	+	0.369257i	$0.879612\pi$
$744$	3.14067	−	30.5554i	0.115142	−	1.12022i
$745$	−0.945127	+	1.63701i	−0.0346268	+	0.0599754i
$746$	44.0794			1.61386
$747$	−1.43677	−	0.298513i	−0.0525687	−	0.0109220i
$748$	0.0875029			0.00319942
$749$	−20.6806	+	35.8198i	−0.755652	+	1.30883i
$750$	2.58290	−	1.15709i	0.0943142	−	0.0422509i
$751$	−19.3225	−	33.4676i	−0.705089	−	1.22125i	−0.966660	−	0.256065i	$-0.917574\pi$
$751$	−19.3225	−	33.4676i	−0.705089	−	1.22125i	0.261571	−	0.965184i	$-0.415759\pi$
$752$	23.8825	+	41.3657i	0.870906	+	1.50845i
$753$	42.2091	+	30.5191i	1.53819	+	1.11218i
$754$	−2.03187	+	3.51931i	−0.0739964	+	0.128166i
$755$	4.88685			0.177851
$756$	−2.24330	+	7.06930i	−0.0815879	+	0.257108i
$757$	−15.3437			−0.557678			−0.278839	−	0.960338i	$-0.589950\pi$
$757$	−15.3437			−0.557678			−0.278839	+	0.960338i	$0.589950\pi$
$758$	−11.6367	+	20.1554i	−0.422666	+	0.732078i
$759$	−0.364354	−	0.263444i	−0.0132252	−	0.00956241i
$760$	−2.31553	−	4.01062i	−0.0839932	−	0.145481i
$761$	−24.3585	−	42.1902i	−0.882995	−	1.52939i	−0.847994	−	0.530005i	$-0.822190\pi$
$761$	−24.3585	−	42.1902i	−0.882995	−	1.52939i	−0.0350009	−	0.999387i	$-0.511143\pi$
$762$	27.3881	−	12.2693i	0.992165	−	0.444470i
$763$	2.27392	−	3.93855i	0.0823215	−	0.142585i
$764$	3.94147			0.142597
$765$	4.95386	−	5.55283i	0.179107	−	0.200763i
$766$	42.4418			1.53349
$767$	3.74544	−	6.48728i	0.135240	−	0.234242i
$768$	2.56406	−	24.9457i	0.0925226	−	0.900149i
$769$	−3.18555	−	5.51753i	−0.114874	−	0.198967i	0.802856	−	0.596174i	$-0.203313\pi$
$769$	−3.18555	−	5.51753i	−0.114874	−	0.198967i	−0.917729	+	0.397206i	$0.869980\pi$
$770$	−0.0916217	−	0.158693i	−0.00330182	−	0.00571891i
$771$	0.538488	−	5.23893i	0.0193932	−	0.188676i
$772$	0.153963	−	0.266672i	0.00554126	−	0.00959775i
$773$	29.8732			1.07446			0.537232	−	0.843435i	$-0.319470\pi$
$773$	29.8732			1.07446			0.537232	+	0.843435i	$0.319470\pi$
$774$	−30.9280	+	34.6676i	−1.11169	+	1.24610i
$775$	−8.16059			−0.293137
$776$	7.97649	−	13.8157i	0.286339	−	0.495954i
$777$	3.76985	−	1.68882i	0.135243	−	0.0605860i
$778$	−21.0714	−	36.4968i	−0.755448	−	1.30847i
$779$	5.83285	+	10.1028i	0.208984	+	0.361970i
$780$	0.940514	+	0.680033i	0.0336758	+	0.0243491i
$781$	0.0658203	−	0.114004i	0.00235523	−	0.00407938i
$782$	−19.9856			−0.714682
$783$	8.71271	+	9.54356i	0.311367	+	0.341059i
$784$	12.0450			0.430178
$785$	−8.99989	+	15.5883i	−0.321220	+	0.556369i
$786$	−37.1374	−	26.8520i	−1.32465	−	0.957777i
$787$	11.8278	+	20.4864i	0.421616	+	0.730261i	0.996098	−	0.0882568i	$-0.0281296\pi$
$787$	11.8278	+	20.4864i	0.421616	+	0.730261i	−0.574482	+	0.818518i	$0.694796\pi$
$788$	0.774338	+	1.34119i	0.0275846	+	0.0477780i
$789$	7.58891	−	3.39968i	0.270172	−	0.121032i
$790$	−12.7582	+	22.0979i	−0.453917	+	0.786207i
$791$	−13.2819			−0.472250
$792$	−0.336043	−	0.0698187i	−0.0119408	−	0.00248090i
$793$	5.78404			0.205397
$794$	15.7594	−	27.2962i	0.559282	−	0.968705i
$795$	0.644796	−	6.27319i	0.0228686	−	0.222487i
$796$	−8.16605	−	14.1440i	−0.289438	−	0.501321i
$797$	15.0003	+	25.9813i	0.531339	+	0.920305i	0.999331	+	0.0365729i	$0.0116441\pi$
$797$	15.0003	+	25.9813i	0.531339	+	0.920305i	−0.467992	+	0.883732i	$0.655023\pi$
$798$	1.31362	−	12.7802i	0.0465017	−	0.452413i
$799$	12.1116	−	20.9780i	0.428479	−	0.742148i
$800$	−3.64604			−0.128907
$801$	−4.37067	−	13.2445i	−0.154430	−	0.467971i
$802$	−26.9013			−0.949918
$803$	−0.0290196	+	0.0502634i	−0.00102408	+	0.00177376i
$804$	6.60497	−	2.95889i	0.232939	−	0.104352i
$805$	5.25162	+	9.09608i	0.185095	+	0.320595i
$806$	−6.66736	−	11.5482i	−0.234848	−	0.406768i
$807$	−23.6819	−	17.1230i	−0.833641	−	0.602759i
$808$	0.600720	−	1.04048i	0.0211333	−	0.0366039i
$809$	37.0787			1.30362			0.651808	−	0.758384i	$-0.274011\pi$
$809$	37.0787			1.30362			0.651808	+	0.758384i	$0.274011\pi$
$810$	11.8179	−	8.75295i	0.415238	−	0.307547i
$811$	−42.7582			−1.50144			−0.750722	−	0.660618i	$-0.770294\pi$
$811$	−42.7582			−1.50144			−0.750722	+	0.660618i	$0.770294\pi$
$812$	1.77486	−	3.07414i	0.0622852	−	0.107881i
$813$	−3.28579	−	2.37577i	−0.115238	−	0.0833220i
$814$	−0.0481581	−	0.0834124i	−0.00168794	−	0.00292360i
$815$	4.70874	+	8.15577i	0.164940	+	0.285684i
$816$	−19.1775	+	8.59112i	−0.671346	+	0.300749i
$817$	10.0982	−	17.4906i	0.353291	−	0.611918i
$818$	−32.2765			−1.12852
$819$	−2.00258	−	6.06846i	−0.0699760	−	0.212049i
$820$	3.66812			0.128096
$821$	−14.2835	+	24.7397i	−0.498496	+	0.863421i	−0.999998	−	0.00173559i	$-0.999448\pi$
$821$	−14.2835	+	24.7397i	−0.498496	+	0.863421i	0.501502	+	0.865156i	$0.332781\pi$
$822$	−6.01008	+	58.4719i	−0.209626	+	2.03944i
$823$	−16.0021	−	27.7164i	−0.557797	−	0.966133i	−0.997680	−	0.0680777i	$-0.978313\pi$
$823$	−16.0021	−	27.7164i	−0.557797	−	0.966133i	0.439883	−	0.898055i	$-0.355020\pi$
$824$	−8.51649	−	14.7510i	−0.296686	−	0.513875i
$825$	−0.00932341	+	0.0907071i	−0.000324600	+	0.00315802i
$826$	−13.0367	+	22.5802i	−0.453605	+	0.785666i
$827$	31.4986			1.09531			0.547657	−	0.836703i	$-0.315520\pi$
$827$	31.4986			1.09531			0.547657	+	0.836703i	$0.315520\pi$
$828$	−9.70487	−	2.01635i	−0.337268	−	0.0700730i
$829$	32.3851			1.12478			0.562390	−	0.826872i	$-0.309882\pi$
$829$	32.3851			1.12478			0.562390	+	0.826872i	$0.309882\pi$
$830$	0.399646	−	0.692207i	0.0138719	−	0.0240269i
$831$	5.96287	−	2.67125i	0.206850	−	0.0926645i
$832$	1.91227	+	3.31215i	0.0662960	+	0.114828i
$833$	−3.05421	−	5.29005i	−0.105822	−	0.183289i
$834$	−5.73552	−	4.14703i	−0.198605	−	0.143600i
$835$	−7.74523	+	13.4151i	−0.268035	+	0.464250i
$836$	−0.0751763			−0.00260003
$837$	−41.4154	+	9.10140i	−1.43153	+	0.314591i
$838$	−28.5275			−0.985467
$839$	−23.0381	+	39.9032i	−0.795365	+	1.37761i	0.127242	+	0.991872i	$0.459388\pi$
$839$	−23.0381	+	39.9032i	−0.795365	+	1.37761i	−0.922607	+	0.385741i	$0.873946\pi$
$840$	6.49728	+	4.69782i	0.224178	+	0.162090i
$841$	11.4076	+	19.7585i	0.393365	+	0.681328i
$842$	6.05898	+	10.4945i	0.208806	+	0.361663i
$843$	−17.3179	+	7.75808i	−0.596461	+	0.267203i
$844$	−9.17799	+	15.8967i	−0.315919	+	0.547189i
$845$	−1.00000			−0.0344010
$846$	31.8691	−	35.7224i	1.09568	−	1.22816i
$847$	−23.4254			−0.804905
$848$	−8.90413	+	15.4224i	−0.305769	+	0.529607i
$849$	3.11154	−	30.2721i	0.106788	−	1.03893i
$850$	2.02659	+	3.51016i	0.0695115	+	0.120397i
$851$	2.76036	+	4.78108i	0.0946238	+	0.163893i
$852$	0.296732	−	2.88689i	0.0101659	−	0.0989032i
$853$	−24.3786	+	42.2250i	−0.834709	+	1.44576i	0.0595585	+	0.998225i	$0.481031\pi$
$853$	−24.3786	+	42.2250i	−0.834709	+	1.44576i	−0.894267	+	0.447533i	$0.852303\pi$
$854$	−20.1324			−0.688918
$855$	−4.25601	+	4.77060i	−0.145552	+	0.163151i
$856$	−42.1966			−1.44225
$857$	−15.9740	+	27.6677i	−0.545660	+	0.945111i	0.452905	+	0.891559i	$0.350388\pi$
$857$	−15.9740	+	27.6677i	−0.545660	+	0.945111i	−0.998565	+	0.0535519i	$0.982946\pi$
$858$	−0.135979	+	0.0609157i	−0.00464224	+	0.00207963i
$859$	3.66749	+	6.35229i	0.125133	+	0.216737i	0.921785	−	0.387701i	$-0.126731\pi$
$859$	3.66749	+	6.35229i	0.125133	+	0.216737i	−0.796652	+	0.604439i	$0.793397\pi$
$860$	−3.17524	−	5.49967i	−0.108275	−	0.187537i
$861$	−16.3667	−	11.8339i	−0.557777	−	0.403297i
$862$	−27.4597	+	47.5617i	−0.935282	+	1.61996i
$863$	28.4742			0.969273			0.484637	−	0.874716i	$-0.338952\pi$
$863$	28.4742			0.969273			0.484637	+	0.874716i	$0.338952\pi$
$864$	−18.5038	+	4.06638i	−0.629513	+	0.138341i
$865$	9.67663			0.329015
$866$	−24.7414	+	42.8534i	−0.840748	+	1.45622i
$867$	−15.2251	−	11.0084i	−0.517072	−	0.373866i
$868$	5.82399	+	10.0874i	0.197679	+	0.342390i
$869$	−0.411046	−	0.711953i	−0.0139438	−	0.0241514i
$870$	−6.42351	+	2.87760i	−0.217777	+	0.0975598i
$871$	−3.11795	+	5.40045i	−0.105648	+	0.182987i
$872$	4.63970			0.157120
$873$	−21.5624	−	4.47996i	−0.729778	−	0.151624i
$874$	17.1702			0.580790
$875$	1.06506	−	1.84473i	0.0360055	−	0.0623634i
$876$	−0.130826	+	1.27281i	−0.00442022	+	0.0430041i
$877$	−22.9264	−	39.7098i	−0.774171	−	1.34090i	−0.935259	−	0.353963i	$-0.884834\pi$
$877$	−22.9264	−	39.7098i	−0.774171	−	1.34090i	0.161089	−	0.986940i	$-0.448499\pi$
$878$	23.4787	+	40.6663i	0.792367	+	1.37242i
$879$	4.34677	−	42.2895i	0.146613	−	1.42639i
$880$	0.128749	−	0.223000i	0.00434013	−	0.00751732i
$881$	−37.4454			−1.26157			−0.630784	−	0.775959i	$-0.717267\pi$
$881$	−37.4454			−1.26157			−0.630784	+	0.775959i	$0.717267\pi$
$882$	−3.78307	−	11.4639i	−0.127383	−	0.386009i
$883$	50.8068			1.70978			0.854892	−	0.518805i	$-0.173623\pi$
$883$	50.8068			1.70978			0.854892	+	0.518805i	$0.173623\pi$
$884$	−0.831054	+	1.43943i	−0.0279514	+	0.0484132i
$885$	11.8407	−	5.30440i	0.398022	−	0.178306i
$886$	18.3190	+	31.7295i	0.615440	+	1.06597i
$887$	22.6484	+	39.2282i	0.760459	+	1.31715i	0.942614	+	0.333884i	$0.108359\pi$
$887$	22.6484	+	39.2282i	0.760459	+	1.31715i	−0.182155	+	0.983270i	$0.558307\pi$
$888$	3.41510	+	2.46927i	0.114603	+	0.0828632i
$889$	11.2935	−	19.5608i	0.378770	−	0.656050i
$890$	7.59665			0.254640
$891$	0.0538477	+	0.470742i	0.00180396	+	0.0157704i
$892$	16.9770			0.568432
$893$	−10.4055	+	18.0228i	−0.348206	+	0.603110i
$894$	−4.33533	−	3.13464i	−0.144995	−	0.104838i
$895$	−1.65815	−	2.87200i	−0.0554258	−	0.0960004i
$896$	−14.4225	−	24.9805i	−0.481822	−	0.834540i
$897$	7.79410	−	3.49160i	0.260238	−	0.116581i
$898$	−13.0845	+	22.6630i	−0.436635	+	0.756274i
$899$	20.2949			0.676872
$900$	0.629960	+	1.90898i	0.0209987	+	0.0636325i
$901$	9.03118			0.300872
$902$	−0.235458	+	0.407825i	−0.00783989	+	0.0135791i
$903$	−3.57517	+	34.7827i	−0.118974	+	1.15749i
$904$	−6.77509	−	11.7348i	−0.225336	−	0.390294i
$905$	−11.3094	−	19.5885i	−0.375938	−	0.651144i
$906$	−1.41417	+	13.7585i	−0.0469828	+	0.457094i
$907$	−7.18452	+	12.4439i	−0.238558	+	0.413195i	−0.960301	−	0.278967i	$-0.910008\pi$
$907$	−7.18452	+	12.4439i	−0.238558	+	0.413195i	0.721743	+	0.692161i	$0.243341\pi$
$908$	−14.2336			−0.472359
$909$	−1.62390	−	0.337392i	−0.0538613	−	0.0111906i
$910$	3.48069			0.115384
$911$	−26.9532	+	46.6843i	−0.892998	+	1.54672i	−0.0567359	+	0.998389i	$0.518069\pi$
$911$	−26.9532	+	46.6843i	−0.892998	+	1.54672i	−0.836262	+	0.548329i	$0.815264\pi$
$912$	16.4759	−	7.38088i	0.545572	−	0.244405i
$913$	0.0128759	+	0.0223017i	0.000426129	+	0.000738077i
$914$	−0.870583	−	1.50789i	−0.0287963	−	0.0498767i
$915$	8.11842	+	5.86997i	0.268387	+	0.194055i
$916$	−4.09877	+	7.09929i	−0.135427	+	0.234567i
$917$	−34.4915			−1.13901
$918$	14.1999	+	15.5540i	0.468666	+	0.513359i
$919$	−15.6573			−0.516487			−0.258244	−	0.966080i	$-0.583144\pi$
$919$	−15.6573			−0.516487			−0.258244	+	0.966080i	$0.583144\pi$
$920$	−5.35770	+	9.27981i	−0.176638	+	0.305946i
$921$	−15.5362	−	11.2334i	−0.511935	−	0.370152i
$922$	−20.1303	−	34.8667i	−0.662955	−	1.14827i
$923$	1.25025	+	2.16550i	0.0411525	+	0.0712781i
$924$	0.118778	−	0.0532103i	0.00390752	−	0.00175049i
$925$	0.559815	−	0.969629i	0.0184066	−	0.0318812i
$926$	11.6397			0.382505
$927$	−15.6535	+	17.5462i	−0.514129	+	0.576293i
$928$	9.06746			0.297654
$929$	11.5720	−	20.0432i	0.379664	−	0.657597i	−0.611350	−	0.791361i	$-0.709373\pi$
$929$	11.5720	−	20.0432i	0.379664	−	0.657597i	0.991013	+	0.133764i	$0.0427064\pi$
$930$	2.36154	−	22.9754i	0.0774380	−	0.753392i
$931$	2.62396	+	4.54483i	0.0859969	+	0.148951i
$932$	−3.82105	−	6.61826i	−0.125163	−	0.216788i
$933$	2.61986	−	25.4885i	0.0857703	−	0.834456i
$934$	−16.7213	+	28.9621i	−0.547137	+	0.947668i
$935$	−0.130586			−0.00427062
$936$	4.34008	−	4.86484i	0.141860	−	0.159012i
$937$	14.6354			0.478118			0.239059	−	0.971005i	$-0.423161\pi$
$937$	14.6354			0.478118			0.239059	+	0.971005i	$0.423161\pi$
$938$	10.8526	−	18.7973i	0.354351	−	0.613754i
$939$	−42.7615	+	19.1563i	−1.39547	+	0.625142i
$940$	3.27186	+	5.66702i	0.106716	+	0.184838i
$941$	11.0197	+	19.0866i	0.359231	+	0.622206i	0.987833	−	0.155521i	$-0.0497057\pi$
$941$	11.0197	+	19.0866i	0.359231	+	0.622206i	−0.628602	+	0.777727i	$0.716372\pi$
$942$	−41.2828	−	29.8493i	−1.34507	−	0.972542i
$943$	13.4961	−	23.3759i	0.439494	−	0.761225i
$944$	−36.6390			−1.19250
$945$	3.34782	−	10.5500i	0.108904	−	0.343190i
$946$	0.815279			0.0265070
$947$	25.1953	−	43.6396i	0.818737	−	1.41809i	−0.0878754	−	0.996131i	$-0.528008\pi$
$947$	25.1953	−	43.6396i	0.818737	−	1.41809i	0.906613	−	0.421963i	$-0.138659\pi$
$948$	−14.6867	−	10.6191i	−0.477001	−	0.344893i
$949$	−0.551224	−	0.954749i	−0.0178935	−	0.0309925i
$950$	−1.74110	−	3.01568i	−0.0564889	−	0.0978416i
$951$	−0.913633	+	0.409289i	−0.0296266	+	0.0132721i
$952$	−5.74111	+	9.94389i	−0.186070	+	0.322283i
$953$	−7.28058			−0.235841			−0.117921	−	0.993023i	$-0.537623\pi$
$953$	−7.28058			−0.235841			−0.117921	+	0.993023i	$0.537623\pi$
$954$	17.4750	+	3.63072i	0.565773	+	0.117549i
$955$	−5.88211			−0.190340
$956$	−4.97770	+	8.62163i	−0.160990	+	0.278843i
$957$	0.0231867	−	0.225583i	0.000749520	−	0.00729206i
$958$	11.8222	+	20.4766i	0.381956	+	0.661568i
$959$	22.1197	+	38.3125i	0.714283	+	1.23718i
$960$	−0.677316	+	6.58958i	−0.0218603	+	0.212678i
$961$	−17.7977	+	30.8264i	−0.574118	+	0.994401i
$962$	1.82952			0.0589861
$963$	18.2548	+	55.3178i	0.588253	+	1.78259i
$964$	−12.4573			−0.401221
$965$	−0.229769	+	0.397972i	−0.00739654	+	0.0128112i
$966$	−27.1289	+	12.1532i	−0.872856	+	0.391022i
$967$	−0.821636	−	1.42312i	−0.0264220	−	0.0457643i	0.852512	−	0.522708i	$-0.175078\pi$
$967$	−0.821636	−	1.42312i	−0.0264220	−	0.0457643i	−0.878934	+	0.476943i	$0.841745\pi$
$968$	−11.9493	−	20.6967i	−0.384064	−	0.665219i
$969$	−7.41937	−	5.36453i	−0.238345	−	0.172334i
$970$	5.99771	−	10.3883i	0.192575	−	0.333550i
$971$	59.5135			1.90988			0.954939	−	0.296803i	$-0.0959204\pi$
$971$	59.5135			1.90988			0.954939	+	0.296803i	$0.0959204\pi$
$972$	5.32613	+	8.98556i	0.170836	+	0.288212i
$973$	−5.32689			−0.170772
$974$	−24.3957	+	42.2547i	−0.781690	+	1.35393i
$975$	−1.40359	−	1.01486i	−0.0449509	−	0.0325014i
$976$	−14.1453	−	24.5004i	−0.452780	−	0.784238i
$977$	7.66363	+	13.2738i	0.245181	+	0.424666i	0.962183	−	0.272405i	$-0.0878192\pi$
$977$	7.66363	+	13.2738i	0.245181	+	0.424666i	−0.717001	+	0.697072i	$0.754486\pi$
$978$	−24.3244	+	10.8968i	−0.777809	+	0.348443i
$979$	−0.122375	+	0.211960i	−0.00391112	+	0.00677427i
$980$	1.65014			0.0527117
$981$	−2.00719	−	6.08243i	−0.0640848	−	0.194197i
$982$	36.0255			1.14962
$983$	1.63477	−	2.83150i	0.0521411	−	0.0903110i	−0.838777	−	0.544475i	$-0.816729\pi$
$983$	1.63477	−	2.83150i	0.0521411	−	0.0903110i	0.890918	+	0.454164i	$0.150062\pi$
$984$	2.10678	−	20.4967i	0.0671616	−	0.653412i
$985$	−1.15559	−	2.00155i	−0.0368203	−	0.0637746i
$986$	−5.04000	−	8.72954i	−0.160506	−	0.278005i
$987$	3.68396	−	35.8411i	0.117262	−	1.14083i
$988$	0.713983	−	1.23666i	0.0227148	−	0.0393432i
$989$	−46.7306			−1.48595
$990$	−0.252679	−	0.0524983i	−0.00803067	−	0.00166851i
$991$	−39.2309			−1.24621			−0.623106	−	0.782138i	$-0.714129\pi$
$991$	−39.2309			−1.24621			−0.623106	+	0.782138i	$0.714129\pi$
$992$	−14.8769	+	25.7676i	−0.472343	+	0.818122i
$993$	38.1167	−	17.0755i	1.20960	−	0.541874i
$994$	−4.35173	−	7.53742i	−0.138028	−	0.239072i
$995$	12.1867	+	21.1080i	0.386345	+	0.669169i
$996$	0.460054	+	0.332639i	0.0145774	+	0.0105401i
$997$	16.4127	−	28.4276i	0.519795	−	0.900312i	−0.479940	−	0.877301i	$-0.659342\pi$
$997$	16.4127	−	28.4276i	0.519795	−	0.900312i	0.999735	−	0.0230105i	$-0.00732513\pi$
$998$	34.5963			1.09513
$999$	1.75968	−	5.54527i	0.0556737	−	0.175445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.e.196.3	✓	16
3.2	odd	2		1755.2.i.f.586.6		16
9.2	odd	6		5265.2.a.ba.1.3		8
9.4	even	3	inner	585.2.i.e.391.3	yes	16
9.5	odd	6		1755.2.i.f.1171.6		16
9.7	even	3		5265.2.a.bf.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.e.196.3	✓	16	1.1	even	1	trivial
585.2.i.e.391.3	yes	16	9.4	even	3	inner
1755.2.i.f.586.6		16	3.2	odd	2
1755.2.i.f.1171.6		16	9.5	odd	6
5265.2.a.ba.1.3		8	9.2	odd	6
5265.2.a.bf.1.6		8	9.7	even	3

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.817019 + 1.41512i) q^{2} +(1.40359 + 1.01486i) q^{3} +(-0.335039 - 0.580304i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.58290 + 1.15709i) q^{6} +(-1.06506 + 1.84473i) q^{7} -2.17314 q^{8} +(0.940129 + 2.84889i) q^{9} +O(q^{10})\)	\(q+(-0.817019 + 1.41512i) q^{2} +(1.40359 + 1.01486i) q^{3} +(-0.335039 - 0.580304i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.58290 + 1.15709i) q^{6} +(-1.06506 + 1.84473i) q^{7} -2.17314 q^{8} +(0.940129 + 2.84889i) q^{9} -1.63404 q^{10} +(0.0263229 - 0.0455925i) q^{11} +(0.118669 - 1.15453i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-1.74034 - 3.01437i) q^{14} +(-0.177097 + 1.72297i) q^{15} +(2.44558 - 4.23586i) q^{16} -2.48047 q^{17} +(-4.79961 - 0.997201i) q^{18} +2.13105 q^{19} +(0.335039 - 0.580304i) q^{20} +(-3.36705 + 1.50837i) q^{21} +(0.0430125 + 0.0744999i) q^{22} +(-2.46542 - 4.27023i) q^{23} +(-3.05020 - 2.20543i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.63404 q^{26} +(-1.57166 + 4.95277i) q^{27} +1.42734 q^{28} +(1.24347 - 2.15375i) q^{29} +(-2.29352 - 1.65831i) q^{30} +(4.08030 + 7.06728i) q^{31} +(1.82302 + 3.15756i) q^{32} +(0.0832164 - 0.0372793i) q^{33} +(2.02659 - 3.51016i) q^{34} -2.13012 q^{35} +(1.33824 - 1.50005i) q^{36} -1.11963 q^{37} +(-1.74110 + 3.01568i) q^{38} +(-0.177097 + 1.72297i) q^{39} +(-1.08657 - 1.88200i) q^{40} +(2.73708 + 4.74077i) q^{41} +(0.616421 - 5.99713i) q^{42} +(4.73861 - 8.20752i) q^{43} -0.0352767 q^{44} +(-1.99714 + 2.23862i) q^{45} +8.05716 q^{46} +(-4.88280 + 8.45726i) q^{47} +(7.73138 - 3.46350i) q^{48} +(1.23130 + 2.13268i) q^{49} +(-0.817019 - 1.41512i) q^{50} +(-3.48156 - 2.51732i) q^{51} +(0.335039 - 0.580304i) q^{52} -3.64091 q^{53} +(-5.72467 - 6.27058i) q^{54} +0.0526457 q^{55} +(2.31452 - 4.00887i) q^{56} +(2.99111 + 2.16271i) q^{57} +(2.03187 + 3.51931i) q^{58} +(-3.74544 - 6.48728i) q^{59} +(1.05918 - 0.474493i) q^{60} +(2.89202 - 5.00912i) q^{61} -13.3347 q^{62} +(-6.25673 - 1.29994i) q^{63} +3.82454 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-0.0152348 + 0.148219i) q^{66} +(3.11795 + 5.40045i) q^{67} +(0.831054 + 1.43943i) q^{68} +(0.873237 - 8.49569i) q^{69} +(1.74034 - 3.01437i) q^{70} +2.50050 q^{71} +(-2.04303 - 6.19104i) q^{72} -1.10245 q^{73} +(0.914759 - 1.58441i) q^{74} +(-1.58069 + 0.708116i) q^{75} +(-0.713983 - 1.23666i) q^{76} +(0.0560707 + 0.0971174i) q^{77} +(-2.29352 - 1.65831i) q^{78} +(7.80779 - 13.5235i) q^{79} +4.89115 q^{80} +(-7.23231 + 5.35664i) q^{81} -8.94500 q^{82} +(-0.244576 + 0.423618i) q^{83} +(2.00340 + 1.44855i) q^{84} +(-1.24024 - 2.14815i) q^{85} +(7.74307 + 13.4114i) q^{86} +(3.93107 - 1.76104i) q^{87} +(-0.0572033 + 0.0990790i) q^{88} -4.64901 q^{89} +(-1.53621 - 4.65519i) q^{90} -2.13012 q^{91} +(-1.65202 + 2.86138i) q^{92} +(-1.44522 + 14.0605i) q^{93} +(-7.97868 - 13.8195i) q^{94} +(1.06552 + 1.84554i) q^{95} +(-0.645704 + 6.28203i) q^{96} +(-3.67049 + 6.35747i) q^{97} -4.02399 q^{98} +(0.154635 + 0.0321280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 8 q^{13} - 10 q^{14} + 5 q^{15} - 11 q^{16} - 4 q^{17} + 5 q^{18} - 20 q^{19} + 9 q^{20} + 11 q^{21} - 3 q^{22} - 6 q^{23} - 57 q^{24} - 8 q^{25} - 6 q^{26} - 14 q^{27} - 68 q^{28} - 14 q^{29} + 7 q^{30} + 31 q^{31} - q^{32} - 31 q^{33} + 7 q^{34} + 22 q^{35} + 2 q^{36} + 2 q^{37} - 9 q^{38} + 5 q^{39} - 6 q^{40} + 12 q^{41} - 26 q^{42} - 15 q^{43} + 32 q^{44} - 16 q^{45} - 64 q^{46} + 18 q^{47} - 4 q^{48} - 17 q^{49} - 3 q^{50} + 32 q^{51} + 9 q^{52} + 4 q^{53} + 2 q^{54} - 12 q^{55} - 16 q^{56} + 45 q^{57} + 42 q^{58} - 24 q^{59} - 8 q^{60} + 9 q^{61} - 40 q^{62} + 47 q^{63} - 60 q^{64} - 8 q^{65} + 55 q^{66} + 18 q^{67} + 14 q^{68} - 12 q^{69} + 10 q^{70} + 20 q^{71} - 9 q^{72} + 12 q^{73} + 37 q^{74} + 4 q^{75} + 53 q^{76} + 34 q^{77} + 7 q^{78} + 3 q^{79} - 22 q^{80} + 13 q^{81} - 68 q^{82} + 10 q^{83} + 22 q^{84} - 2 q^{85} - 60 q^{86} + 11 q^{87} + 14 q^{88} - 26 q^{89} + 19 q^{90} + 22 q^{91} - 5 q^{92} + 74 q^{93} - 17 q^{94} - 10 q^{95} + 13 q^{96} + 34 q^{97} - 60 q^{98} - 43 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 8 * q^13 - 10 * q^14 + 5 * q^15 - 11 * q^16 - 4 * q^17 + 5 * q^18 - 20 * q^19 + 9 * q^20 + 11 * q^21 - 3 * q^22 - 6 * q^23 - 57 * q^24 - 8 * q^25 - 6 * q^26 - 14 * q^27 - 68 * q^28 - 14 * q^29 + 7 * q^30 + 31 * q^31 - q^32 - 31 * q^33 + 7 * q^34 + 22 * q^35 + 2 * q^36 + 2 * q^37 - 9 * q^38 + 5 * q^39 - 6 * q^40 + 12 * q^41 - 26 * q^42 - 15 * q^43 + 32 * q^44 - 16 * q^45 - 64 * q^46 + 18 * q^47 - 4 * q^48 - 17 * q^49 - 3 * q^50 + 32 * q^51 + 9 * q^52 + 4 * q^53 + 2 * q^54 - 12 * q^55 - 16 * q^56 + 45 * q^57 + 42 * q^58 - 24 * q^59 - 8 * q^60 + 9 * q^61 - 40 * q^62 + 47 * q^63 - 60 * q^64 - 8 * q^65 + 55 * q^66 + 18 * q^67 + 14 * q^68 - 12 * q^69 + 10 * q^70 + 20 * q^71 - 9 * q^72 + 12 * q^73 + 37 * q^74 + 4 * q^75 + 53 * q^76 + 34 * q^77 + 7 * q^78 + 3 * q^79 - 22 * q^80 + 13 * q^81 - 68 * q^82 + 10 * q^83 + 22 * q^84 - 2 * q^85 - 60 * q^86 + 11 * q^87 + 14 * q^88 - 26 * q^89 + 19 * q^90 + 22 * q^91 - 5 * q^92 + 74 * q^93 - 17 * q^94 - 10 * q^95 + 13 * q^96 + 34 * q^97 - 60 * q^98 - 43 * q^99

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