LMFDB - Embedded newform 560.2.bd.b.141.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(141,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 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("560.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bd (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.9
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.b.421.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.557588 + 1.29965i) q^{2} +(-2.40733 - 2.40733i) q^{3} +(-1.37819 - 1.44934i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(4.47099 - 1.78639i) q^{6} +1.00000i q^{7} +(2.65210 - 0.983032i) q^{8} +8.59045i q^{9} +O(q^{10})$	\(q+(-0.557588 + 1.29965i) q^{2} +(-2.40733 - 2.40733i) q^{3} +(-1.37819 - 1.44934i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(4.47099 - 1.78639i) q^{6} +1.00000i q^{7} +(2.65210 - 0.983032i) q^{8} +8.59045i q^{9} +(-0.524718 - 1.31327i) q^{10} +(-2.37243 + 2.37243i) q^{11} +(-0.171285 + 6.80680i) q^{12} +(-0.459738 - 0.459738i) q^{13} +(-1.29965 - 0.557588i) q^{14} +3.40448 q^{15} +(-0.201183 + 3.99494i) q^{16} +6.60890 q^{17} +(-11.1646 - 4.78994i) q^{18} +(-2.56181 - 2.56181i) q^{19} +(1.99937 + 0.0503116i) q^{20} +(2.40733 - 2.40733i) q^{21} +(-1.76049 - 4.40617i) q^{22} -7.04981i q^{23} +(-8.75096 - 4.01800i) q^{24} -1.00000i q^{25} +(0.853844 - 0.341155i) q^{26} +(13.4580 - 13.4580i) q^{27} +(1.44934 - 1.37819i) q^{28} +(-1.21927 - 1.21927i) q^{29} +(-1.89830 + 4.42463i) q^{30} +0.0789065 q^{31} +(-5.07985 - 2.48900i) q^{32} +11.4224 q^{33} +(-3.68505 + 8.58927i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(12.4505 - 11.8393i) q^{36} +(0.585796 - 0.585796i) q^{37} +(4.75791 - 1.90103i) q^{38} +2.21348i q^{39} +(-1.18021 + 2.57043i) q^{40} -0.548655i q^{41} +(1.78639 + 4.47099i) q^{42} +(-2.40716 + 2.40716i) q^{43} +(6.70812 + 0.168802i) q^{44} +(-6.07437 - 6.07437i) q^{45} +(9.16231 + 3.93090i) q^{46} +9.79702 q^{47} +(10.1014 - 9.13281i) q^{48} -1.00000 q^{49} +(1.29965 + 0.557588i) q^{50} +(-15.9098 - 15.9098i) q^{51} +(-0.0327110 + 1.29992i) q^{52} +(0.805532 - 0.805532i) q^{53} +(9.98673 + 24.9948i) q^{54} -3.35512i q^{55} +(0.983032 + 2.65210i) q^{56} +12.3343i q^{57} +(2.26448 - 0.904778i) q^{58} +(10.3251 - 10.3251i) q^{59} +(-4.69201 - 4.93425i) q^{60} +(5.24714 + 5.24714i) q^{61} +(-0.0439974 + 0.102551i) q^{62} -8.59045 q^{63} +(6.06730 - 5.21420i) q^{64} +0.650168 q^{65} +(-6.36902 + 14.8452i) q^{66} +(-1.05522 - 1.05522i) q^{67} +(-9.10832 - 9.57855i) q^{68} +(-16.9712 + 16.9712i) q^{69} +(1.31327 - 0.524718i) q^{70} +7.97855i q^{71} +(8.44469 + 22.7828i) q^{72} -13.8380i q^{73} +(0.434698 + 1.08796i) q^{74} +(-2.40733 + 2.40733i) q^{75} +(-0.182277 + 7.24361i) q^{76} +(-2.37243 - 2.37243i) q^{77} +(-2.87675 - 1.23421i) q^{78} +7.50113 q^{79} +(-2.68259 - 2.96711i) q^{80} -39.0245 q^{81} +(0.713061 + 0.305924i) q^{82} +(0.984319 + 0.984319i) q^{83} +(-6.80680 - 0.171285i) q^{84} +(-4.67320 + 4.67320i) q^{85} +(-1.78626 - 4.47067i) q^{86} +5.87038i q^{87} +(-3.95975 + 8.62410i) q^{88} -7.03304i q^{89} +(11.2816 - 4.50757i) q^{90} +(0.459738 - 0.459738i) q^{91} +(-10.2176 + 9.71599i) q^{92} +(-0.189954 - 0.189954i) q^{93} +(-5.46270 + 12.7327i) q^{94} +3.62295 q^{95} +(6.23703 + 18.2207i) q^{96} -6.77139 q^{97} +(0.557588 - 1.29965i) q^{98} +(-20.3802 - 20.3802i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) $ 52 * q - 8 * q^4 + 12 * q^6	$ 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) $ 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.557588	+	1.29965i	−0.394275	+	0.918993i
$2$	−0.557588	+	1.29965i	−0.394275	+	0.918993i
$3$	−2.40733	−	2.40733i	−1.38987	−	1.38987i	−0.825567	−	0.564304i	$-0.809144\pi$
$3$	−2.40733	−	2.40733i	−1.38987	−	1.38987i	−0.564304	−	0.825567i	$-0.690856\pi$
$4$	−1.37819	−	1.44934i	−0.689095	−	0.724671i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	4.47099	−	1.78639i	1.82527	−	0.729291i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.65210	−	0.983032i	0.937660	−	0.347554i
$9$			8.59045i			2.86348i
$10$	−0.524718	−	1.31327i	−0.165930	−	0.415292i
$11$	−2.37243	+	2.37243i	−0.715314	+	0.715314i	−0.967642	−	0.252327i	$-0.918804\pi$
$11$	−2.37243	+	2.37243i	−0.715314	+	0.715314i	0.252327	+	0.967642i	$0.418804\pi$
$12$	−0.171285	+	6.80680i	−0.0494456	+	1.96495i
$13$	−0.459738	−	0.459738i	−0.127508	−	0.127508i	0.640473	−	0.767981i	$-0.278738\pi$
$13$	−0.459738	−	0.459738i	−0.127508	−	0.127508i	−0.767981	+	0.640473i	$0.778738\pi$
$14$	−1.29965	−	0.557588i	−0.347347	−	0.149022i
$15$	3.40448			0.879032
$16$	−0.201183	+	3.99494i	−0.0502957	+	0.998734i
$17$	6.60890			1.60289			0.801447	−	0.598066i	$-0.204064\pi$
$17$	6.60890			1.60289			0.801447	+	0.598066i	$0.204064\pi$
$18$	−11.1646	−	4.78994i	−2.63152	−	1.12900i
$19$	−2.56181	−	2.56181i	−0.587721	−	0.587721i	0.349293	−	0.937014i	$-0.386422\pi$
$19$	−2.56181	−	2.56181i	−0.587721	−	0.587721i	−0.937014	+	0.349293i	$0.886422\pi$
$20$	1.99937	+	0.0503116i	0.447072	+	0.0112500i
$21$	2.40733	−	2.40733i	0.525322	−	0.525322i
$22$	−1.76049	−	4.40617i	−0.375338	−	0.939399i
$23$		−	7.04981i		−	1.46999i	−0.678074	−	0.734994i	$-0.737185\pi$
$23$		−	7.04981i		−	1.46999i	0.678074	−	0.734994i	$-0.262815\pi$
$24$	−8.75096	−	4.01800i	−1.78628	−	0.820171i
$25$		−	1.00000i		−	0.200000i
$26$	0.853844	−	0.341155i	0.167453	−	0.0669060i
$27$	13.4580	−	13.4580i	2.59000	−	2.59000i
$28$	1.44934	−	1.37819i	0.273900	−	0.260453i
$29$	−1.21927	−	1.21927i	−0.226413	−	0.226413i	0.584779	−	0.811192i	$-0.301181\pi$
$29$	−1.21927	−	1.21927i	−0.226413	−	0.226413i	−0.811192	+	0.584779i	$0.801181\pi$
$30$	−1.89830	+	4.42463i	−0.346580	+	0.807824i
$31$	0.0789065			0.0141720			0.00708601	−	0.999975i	$-0.497744\pi$
$31$	0.0789065			0.0141720			0.00708601	+	0.999975i	$0.497744\pi$
$32$	−5.07985	−	2.48900i	−0.897999	−	0.439997i
$33$	11.4224			1.98839
$34$	−3.68505	+	8.58927i	−0.631980	+	1.47305i
$35$	−0.707107	−	0.707107i	−0.119523	−	0.119523i
$36$	12.4505	−	11.8393i	2.07508	−	1.97321i
$37$	0.585796	−	0.585796i	0.0963043	−	0.0963043i	−0.657313	−	0.753617i	$-0.728307\pi$
$37$	0.585796	−	0.585796i	0.0963043	−	0.0963043i	0.753617	+	0.657313i	$0.228307\pi$
$38$	4.75791	−	1.90103i	0.771834	−	0.308388i
$39$			2.21348i			0.354440i
$40$	−1.18021	+	2.57043i	−0.186608	+	0.406420i
$41$		−	0.548655i		−	0.0856855i	−0.999082	−	0.0428428i	$-0.986359\pi$
$41$		−	0.548655i		−	0.0856855i	0.999082	−	0.0428428i	$-0.0136415\pi$
$42$	1.78639	+	4.47099i	0.275646	+	0.689888i
$43$	−2.40716	+	2.40716i	−0.367088	+	0.367088i	−0.866414	−	0.499326i	$-0.833581\pi$
$43$	−2.40716	+	2.40716i	−0.367088	+	0.367088i	0.499326	+	0.866414i	$0.333581\pi$
$44$	6.70812	+	0.168802i	1.01129	+	0.0254478i
$45$	−6.07437	−	6.07437i	−0.905513	−	0.905513i
$46$	9.16231	+	3.93090i	1.35091	+	0.579579i
$47$	9.79702			1.42904			0.714521	−	0.699614i	$-0.246645\pi$
$47$	9.79702			1.42904			0.714521	+	0.699614i	$0.246645\pi$
$48$	10.1014	−	9.13281i	1.45802	−	1.31821i
$49$	−1.00000			−0.142857
$50$	1.29965	+	0.557588i	0.183799	+	0.0788549i
$51$	−15.9098	−	15.9098i	−2.22782	−	2.22782i
$52$	−0.0327110	+	1.29992i	−0.00453620	+	0.180267i
$53$	0.805532	−	0.805532i	0.110648	−	0.110648i	−0.649615	−	0.760263i	$-0.725070\pi$
$53$	0.805532	−	0.805532i	0.110648	−	0.110648i	0.760263	+	0.649615i	$0.225070\pi$
$54$	9.98673	+	24.9948i	1.35902	+	3.40137i
$55$		−	3.35512i		−	0.452405i
$56$	0.983032	+	2.65210i	0.131363	+	0.354402i
$57$			12.3343i			1.63371i
$58$	2.26448	−	0.904778i	0.297341	−	0.118803i
$59$	10.3251	−	10.3251i	1.34421	−	1.34421i	0.452392	−	0.891819i	$-0.350571\pi$
$59$	10.3251	−	10.3251i	1.34421	−	1.34421i	0.891819	−	0.452392i	$-0.149429\pi$
$60$	−4.69201	−	4.93425i	−0.605737	−	0.637009i
$61$	5.24714	+	5.24714i	0.671828	+	0.671828i	0.958137	−	0.286309i	$-0.0924285\pi$
$61$	5.24714	+	5.24714i	0.671828	+	0.671828i	−0.286309	+	0.958137i	$0.592429\pi$
$62$	−0.0439974	+	0.102551i	−0.00558767	+	0.0130240i
$63$	−8.59045			−1.08230
$64$	6.06730	−	5.21420i	0.758412	−	0.651775i
$65$	0.650168			0.0806434
$66$	−6.36902	+	14.8452i	−0.783972	+	1.82732i
$67$	−1.05522	−	1.05522i	−0.128915	−	0.128915i	0.639705	−	0.768620i	$-0.279057\pi$
$67$	−1.05522	−	1.05522i	−0.128915	−	0.128915i	−0.768620	+	0.639705i	$0.779057\pi$
$68$	−9.10832	−	9.57855i	−1.10455	−	1.16157i
$69$	−16.9712	+	16.9712i	−2.04309	+	2.04309i
$70$	1.31327	−	0.524718i	0.156965	−	0.0627158i
$71$			7.97855i			0.946880i	0.880826	+	0.473440i	$0.156988\pi$
$71$			7.97855i			0.946880i	−0.880826	+	0.473440i	$0.843012\pi$
$72$	8.44469	+	22.7828i	0.995216	+	2.68497i
$73$		−	13.8380i		−	1.61962i	−0.586695	−	0.809808i	$-0.699571\pi$
$73$		−	13.8380i		−	1.61962i	0.586695	−	0.809808i	$-0.300429\pi$
$74$	0.434698	+	1.08796i	0.0505326	+	0.126473i
$75$	−2.40733	+	2.40733i	−0.277974	+	0.277974i
$76$	−0.182277	+	7.24361i	−0.0209086	+	0.830899i
$77$	−2.37243	−	2.37243i	−0.270363	−	0.270363i
$78$	−2.87675	−	1.23421i	−0.325728	−	0.139747i
$79$	7.50113			0.843943			0.421971	−	0.906609i	$-0.361338\pi$
$79$	7.50113			0.843943			0.421971	+	0.906609i	$0.361338\pi$
$80$	−2.68259	−	2.96711i	−0.299923	−	0.331732i
$81$	−39.0245			−4.33606
$82$	0.713061	+	0.305924i	0.0787444	+	0.0337836i
$83$	0.984319	+	0.984319i	0.108043	+	0.108043i	0.759062	−	0.651019i	$-0.225658\pi$
$83$	0.984319	+	0.984319i	0.108043	+	0.108043i	−0.651019	+	0.759062i	$0.725658\pi$
$84$	−6.80680	−	0.171285i	−0.742682	−	0.0186887i
$85$	−4.67320	+	4.67320i	−0.506879	+	0.506879i
$86$	−1.78626	−	4.47067i	−0.192618	−	0.482084i
$87$			5.87038i			0.629371i
$88$	−3.95975	+	8.62410i	−0.422111	+	0.919332i
$89$		−	7.03304i		−	0.745501i	−0.927932	−	0.372751i	$-0.878415\pi$
$89$		−	7.03304i		−	0.745501i	0.927932	−	0.372751i	$-0.121585\pi$
$90$	11.2816	−	4.50757i	1.18918	−	0.475139i
$91$	0.459738	−	0.459738i	0.0481936	−	0.0481936i
$92$	−10.2176	+	9.71599i	−1.06526	+	1.01296i
$93$	−0.189954	−	0.189954i	−0.0196973	−	0.0196973i
$94$	−5.46270	+	12.7327i	−0.563435	+	1.31328i
$95$	3.62295			0.371707
$96$	6.23703	+	18.2207i	0.636564	+	1.85964i
$97$	−6.77139			−0.687531			−0.343765	−	0.939056i	$-0.611703\pi$
$97$	−6.77139			−0.687531			−0.343765	+	0.939056i	$0.611703\pi$
$98$	0.557588	−	1.29965i	0.0563249	−	0.131285i
$99$	−20.3802	−	20.3802i	−2.04829	−	2.04829i
$100$	−1.44934	+	1.37819i	−0.144934	+	0.137819i
$101$	5.49510	−	5.49510i	0.546783	−	0.546783i	−0.378726	−	0.925509i	$-0.623638\pi$
$101$	5.49510	−	5.49510i	0.546783	−	0.546783i	0.925509	+	0.378726i	$0.123638\pi$
$102$	29.5483	−	11.8061i	2.92572	−	1.16898i
$103$		−	0.602751i		−	0.0593908i	−0.999559	−	0.0296954i	$-0.990546\pi$
$103$		−	0.602751i		−	0.0593908i	0.999559	−	0.0296954i	$-0.00945373\pi$
$104$	−1.67121	−	0.767335i	−0.163876	−	0.0752434i
$105$			3.40448i			0.332243i
$106$	0.597756	+	1.49607i	0.0580592	+	0.145311i
$107$	9.56811	−	9.56811i	0.924984	−	0.924984i	−0.0723925	−	0.997376i	$-0.523063\pi$
$107$	9.56811	−	9.56811i	0.924984	−	0.924984i	0.997376	+	0.0723925i	$0.0230634\pi$
$108$	−38.0531	−	0.957559i	−3.66166	−	0.0921411i
$109$	14.7149	+	14.7149i	1.40944	+	1.40944i	0.762789	+	0.646647i	$0.223829\pi$
$109$	14.7149	+	14.7149i	1.40944	+	1.40944i	0.646647	+	0.762789i	$0.276171\pi$
$110$	4.36049	+	1.87078i	0.415757	+	0.178372i
$111$	−2.82041			−0.267701
$112$	−3.99494	−	0.201183i	−0.377486	−	0.0190100i
$113$	15.5240			1.46038			0.730189	−	0.683245i	$-0.239432\pi$
$113$	15.5240			1.46038			0.730189	+	0.683245i	$0.239432\pi$
$114$	−16.0302	−	6.87744i	−1.50137	−	0.644131i
$115$	4.98497	+	4.98497i	0.464851	+	0.464851i
$116$	−0.0867529	+	3.44753i	−0.00805481	+	0.320095i
$117$	3.94936	−	3.94936i	0.365118	−	0.365118i
$118$	7.66187	+	19.1762i	0.705332	+	1.76531i
$119$			6.60890i			0.605837i
$120$	9.02902	−	3.34671i	0.824233	−	0.305511i
$121$		−	0.256846i		−	0.0233496i
$122$	−9.74521	+	3.89371i	−0.882290	+	0.352520i
$123$	−1.32079	+	1.32079i	−0.119092	+	0.119092i
$124$	−0.108748	−	0.114362i	−0.00976587	−	0.0102701i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	4.78994	−	11.1646i	0.426721	−	0.994621i
$127$	−12.4812			−1.10752			−0.553762	−	0.832675i	$-0.686808\pi$
$127$	−12.4812			−1.10752			−0.553762	+	0.832675i	$0.686808\pi$
$128$	3.39359	+	10.7928i	0.299954	+	0.953954i
$129$	11.5896			1.02041
$130$	−0.362526	+	0.844992i	−0.0317956	+	0.0741107i
$131$	−0.940145	−	0.940145i	−0.0821408	−	0.0821408i	0.664843	−	0.746983i	$-0.268499\pi$
$131$	−0.940145	−	0.940145i	−0.0821408	−	0.0821408i	−0.746983	+	0.664843i	$0.768499\pi$
$132$	−15.7423	−	16.5550i	−1.37019	−	1.44093i
$133$	2.56181	−	2.56181i	0.222137	−	0.222137i
$134$	1.95979	−	0.783039i	0.169300	−	0.0676443i
$135$			19.0326i			1.63806i
$136$	17.5275	−	6.49676i	1.50297	−	0.557092i
$137$		−	6.37076i		−	0.544291i	−0.962256	−	0.272145i	$-0.912267\pi$
$137$		−	6.37076i		−	0.544291i	0.962256	−	0.272145i	$-0.0877332\pi$
$138$	−12.5937	−	31.5196i	−1.07205	−	2.68313i
$139$	−0.486651	+	0.486651i	−0.0412772	+	0.0412772i	−0.727444	−	0.686167i	$-0.759292\pi$
$139$	−0.486651	+	0.486651i	−0.0412772	+	0.0412772i	0.686167	+	0.727444i	$0.259292\pi$
$140$	−0.0503116	+	1.99937i	−0.00425211	+	0.168977i
$141$	−23.5846	−	23.5846i	−1.98618	−	1.98618i
$142$	−10.3693	−	4.44875i	−0.870176	−	0.373331i
$143$	2.18139			0.182417
$144$	−34.3183	−	1.72825i	−2.85986	−	0.144021i
$145$	1.72431			0.143196
$146$	17.9846	+	7.71591i	1.48841	+	0.638573i
$147$	2.40733	+	2.40733i	0.198553	+	0.198553i
$148$	−1.65636	−	0.0416802i	−0.136152	−	0.00342609i
$149$	11.4185	−	11.4185i	0.935443	−	0.935443i	−0.0625964	−	0.998039i	$-0.519938\pi$
$149$	11.4185	−	11.4185i	0.935443	−	0.935443i	0.998039	+	0.0625964i	$0.0199381\pi$
$150$	−1.78639	−	4.47099i	−0.145858	−	0.365054i
$151$			11.2483i			0.915377i	0.889113	+	0.457689i	$0.151323\pi$
$151$			11.2483i			0.915377i	−0.889113	+	0.457689i	$0.848677\pi$
$152$	−9.31254	−	4.27585i	−0.755347	−	0.346817i
$153$			56.7734i			4.58986i
$154$	4.40617	−	1.76049i	0.355059	−	0.141865i
$155$	−0.0557953	+	0.0557953i	−0.00448159	+	0.00448159i
$156$	3.20809	−	3.05060i	0.256853	−	0.244243i
$157$	−7.65513	−	7.65513i	−0.610946	−	0.610946i	0.332247	−	0.943193i	$-0.392193\pi$
$157$	−7.65513	−	7.65513i	−0.610946	−	0.610946i	−0.943193	+	0.332247i	$0.892193\pi$
$158$	−4.18254	+	9.74886i	−0.332745	+	0.775577i
$159$	−3.87836			−0.307574
$160$	5.35198	−	1.83201i	0.423112	−	0.144833i
$161$	7.04981			0.555603
$162$	21.7596	−	50.7183i	1.70960	−	3.98480i
$163$	8.49444	+	8.49444i	0.665336	+	0.665336i	0.956633	−	0.291297i	$-0.0940868\pi$
$163$	8.49444	+	8.49444i	0.665336	+	0.665336i	−0.291297	+	0.956633i	$0.594087\pi$
$164$	−0.795189	+	0.756151i	−0.0620938	+	0.0590455i
$165$	−8.07688	+	8.07688i	−0.628784	+	0.628784i
$166$	−1.82812	+	0.730427i	−0.141889	+	0.0566921i
$167$			10.1424i			0.784843i	0.919785	+	0.392422i	$0.128363\pi$
$167$			10.1424i			0.784843i	−0.919785	+	0.392422i	$0.871637\pi$
$168$	4.01800	−	8.75096i	0.309996	−	0.675151i
$169$		−	12.5773i		−	0.967483i
$170$	−3.46781	−	8.67925i	−0.265969	−	0.665668i
$171$	22.0071	−	22.0071i	1.68293	−	1.68293i
$172$	6.80631	+	0.171272i	0.518976	+	0.0130594i
$173$	3.05165	+	3.05165i	0.232013	+	0.232013i	0.813532	−	0.581520i	$-0.197542\pi$
$173$	3.05165	+	3.05165i	0.232013	+	0.232013i	−0.581520	+	0.813532i	$0.697542\pi$
$174$	−7.62945	−	3.27325i	−0.578387	−	0.248145i
$175$	1.00000			0.0755929
$176$	−9.00042	−	9.95500i	−0.678432	−	0.750386i
$177$	−49.7117			−3.73656
$178$	9.14051	+	3.92154i	0.685110	+	0.293932i
$179$	−3.38310	−	3.38310i	−0.252865	−	0.252865i	0.569279	−	0.822144i	$-0.307222\pi$
$179$	−3.38310	−	3.38310i	−0.252865	−	0.252865i	−0.822144	+	0.569279i	$0.807222\pi$
$180$	−0.432200	+	17.1755i	−0.0322143	+	1.28018i
$181$	6.90132	−	6.90132i	0.512971	−	0.512971i	−0.402465	−	0.915436i	$-0.631846\pi$
$181$	6.90132	−	6.90132i	0.512971	−	0.512971i	0.915436	+	0.402465i	$0.131846\pi$
$182$	0.341155	+	0.853844i	0.0252881	+	0.0632911i
$183$		−	25.2632i		−	1.86751i
$184$	−6.93019	−	18.6968i	−0.510900	−	1.37835i
$185$			0.828441i			0.0609082i
$186$	0.352790	−	0.140958i	0.0258678	−	0.0103355i
$187$	−15.6791	+	15.6791i	−1.14657	+	1.14657i
$188$	−13.5022	−	14.1992i	−0.984746	−	1.03558i
$189$	13.4580	+	13.4580i	0.978929	+	0.978929i
$190$	−2.02012	+	4.70858i	−0.146555	+	0.341596i
$191$	−9.25297			−0.669522			−0.334761	−	0.942303i	$-0.608656\pi$
$191$	−9.25297			−0.669522			−0.334761	+	0.942303i	$0.608656\pi$
$192$	−27.1583	−	2.05368i	−1.95998	−	0.148212i
$193$	−18.2876			−1.31637			−0.658185	−	0.752856i	$-0.728675\pi$
$193$	−18.2876			−1.31637			−0.658185	+	0.752856i	$0.728675\pi$
$194$	3.77565	−	8.80046i	0.271076	−	0.631836i
$195$	−1.56517	−	1.56517i	−0.112084	−	0.112084i
$196$	1.37819	+	1.44934i	0.0984422	+	0.103524i
$197$	4.05457	−	4.05457i	0.288876	−	0.288876i	−0.547760	−	0.836636i	$-0.684519\pi$
$197$	4.05457	−	4.05457i	0.288876	−	0.288876i	0.836636	+	0.547760i	$0.184519\pi$
$198$	37.8510	−	15.1234i	2.68995	−	1.07478i
$199$			8.19764i			0.581115i	0.956858	+	0.290558i	$0.0938408\pi$
$199$			8.19764i			0.581115i	−0.956858	+	0.290558i	$0.906159\pi$
$200$	−0.983032	−	2.65210i	−0.0695108	−	0.187532i
$201$			5.08051i			0.358352i
$202$	4.07771	+	10.2057i	0.286907	+	0.718072i
$203$	1.21927	−	1.21927i	0.0855762	−	0.0855762i
$204$	−1.13200	+	44.9854i	−0.0792561	+	3.14961i
$205$	0.387958	+	0.387958i	0.0270961	+	0.0270961i
$206$	0.783366	+	0.336087i	0.0545797	+	0.0234163i
$207$	60.5611			4.20929
$208$	1.92912	−	1.74413i	0.133760	−	0.120934i
$209$	12.1555			0.840810
$210$	−4.42463	−	1.89830i	−0.305329	−	0.130995i
$211$	8.21521	+	8.21521i	0.565558	+	0.565558i	0.930881	−	0.365323i	$-0.119041\pi$
$211$	8.21521	+	8.21521i	0.565558	+	0.565558i	−0.365323	+	0.930881i	$0.619041\pi$
$212$	−2.27767	−	0.0573147i	−0.156431	−	0.00393639i
$213$	19.2070	−	19.2070i	1.31604	−	1.31604i
$214$	7.10014	+	17.7703i	0.485356	+	1.21475i
$215$		−	3.40423i		−	0.232167i
$216$	22.4624	−	48.9218i	1.52838	−	3.32871i
$217$			0.0789065i			0.00535652i
$218$	−27.3292	+	10.9194i	−1.85097	+	0.739557i
$219$	−33.3126	+	33.3126i	−2.25106	+	2.25106i
$220$	−4.86272	+	4.62400i	−0.327844	+	0.311750i
$221$	−3.03836	−	3.03836i	−0.204382	−	0.204382i
$222$	1.57263	−	3.66555i	0.105548	−	0.246015i
$223$	22.1333			1.48215			0.741077	−	0.671420i	$-0.234315\pi$
$223$	22.1333			1.48215			0.741077	+	0.671420i	$0.234315\pi$
$224$	2.48900	−	5.07985i	0.166303	−	0.339412i
$225$	8.59045			0.572697
$226$	−8.65602	+	20.1758i	−0.575790	+	1.34208i
$227$	−13.4268	−	13.4268i	−0.891169	−	0.891169i	0.103464	−	0.994633i	$-0.467007\pi$
$227$	−13.4268	−	13.4268i	−0.891169	−	0.891169i	−0.994633	+	0.103464i	$0.967007\pi$
$228$	17.8765	−	16.9989i	1.18390	−	1.12578i
$229$	−15.1501	+	15.1501i	−1.00115	+	1.00115i	−0.00114841	+	0.999999i	$0.500366\pi$
$229$	−15.1501	+	15.1501i	−1.00115	+	1.00115i	−0.999999	+	0.00114841i	$0.999634\pi$
$230$	−9.25829	+	3.69917i	−0.610474	+	0.243916i
$231$			11.4224i			0.751541i
$232$	−4.43222	−	2.03505i	−0.290990	−	0.133608i
$233$			2.07514i			0.135947i	0.997687	+	0.0679735i	$0.0216533\pi$
$233$			2.07514i			0.135947i	−0.997687	+	0.0679735i	$0.978347\pi$
$234$	2.93067	+	7.33491i	0.191584	+	0.479498i
$235$	−6.92754	+	6.92754i	−0.451903	+	0.451903i
$236$	−29.1945	−	0.734644i	−1.90040	−	0.0478212i
$237$	−18.0577	−	18.0577i	−1.17297	−	1.17297i
$238$	−8.58927	−	3.68505i	−0.556760	−	0.238866i
$239$	−14.9463			−0.966795			−0.483397	−	0.875401i	$-0.660597\pi$
$239$	−14.9463			−0.966795			−0.483397	+	0.875401i	$0.660597\pi$
$240$	−0.684922	+	13.6007i	−0.0442115	+	0.877919i
$241$	8.77461			0.565222			0.282611	−	0.959235i	$-0.408799\pi$
$241$	8.77461			0.565222			0.282611	+	0.959235i	$0.408799\pi$
$242$	0.333810	+	0.143214i	0.0214581	+	0.00920615i
$243$	53.5706	+	53.5706i	3.43656	+	3.43656i
$244$	0.373341	−	14.8365i	0.0239007	−	0.949807i
$245$	0.707107	−	0.707107i	0.0451754	−	0.0451754i
$246$	−0.980112	−	2.45303i	−0.0624897	−	0.156399i
$247$			2.35553i			0.149879i
$248$	0.209268	−	0.0775676i	0.0132885	−	0.00492555i
$249$		−	4.73916i		−	0.300332i
$250$	−1.31327	+	0.524718i	−0.0830583	+	0.0331861i
$251$	−15.3667	+	15.3667i	−0.969937	+	0.969937i	−0.999561	−	0.0296242i	$-0.990569\pi$
$251$	−15.3667	+	15.3667i	−0.969937	+	0.969937i	0.0296242	+	0.999561i	$0.490569\pi$
$252$	11.8393	+	12.4505i	0.745804	+	0.784308i
$253$	16.7252	+	16.7252i	1.05150	+	1.05150i
$254$	6.95935	−	16.2212i	0.436668	−	1.01781i
$255$	22.4998			1.40899
$256$	−15.9191	−	1.60743i	−0.994941	−	0.100464i
$257$	12.1822			0.759907			0.379954	−	0.925006i	$-0.375940\pi$
$257$	12.1822			0.759907			0.379954	+	0.925006i	$0.375940\pi$
$258$	−6.46224	+	15.0625i	−0.402322	+	0.937749i
$259$	0.585796	+	0.585796i	0.0363996	+	0.0363996i
$260$	−0.896055	−	0.942315i	−0.0555710	−	0.0584399i
$261$	10.4741	−	10.4741i	0.648331	−	0.648331i
$262$	1.74608	−	0.697647i	0.107873	−	0.0431008i
$263$		−	18.4787i		−	1.13944i	−0.821837	−	0.569722i	$-0.807051\pi$
$263$		−	18.4787i		−	1.13944i	0.821837	−	0.569722i	$-0.192949\pi$
$264$	30.2935	−	11.2286i	1.86443	−	0.691073i
$265$			1.13919i			0.0699801i
$266$	1.90103	+	4.75791i	0.116560	+	0.291726i
$267$	−16.9308	+	16.9308i	−1.03615	+	1.03615i
$268$	−0.0750802	+	2.98366i	−0.00458626	+	0.182256i
$269$	18.2057	+	18.2057i	1.11002	+	1.11002i	0.993147	+	0.116875i	$0.0372877\pi$
$269$	18.2057	+	18.2057i	1.11002	+	1.11002i	0.116875	+	0.993147i	$0.462712\pi$
$270$	−24.7357	−	10.6123i	−1.50537	−	0.645846i
$271$	7.57219			0.459978			0.229989	−	0.973193i	$-0.426131\pi$
$271$	7.57219			0.459978			0.229989	+	0.973193i	$0.426131\pi$
$272$	−1.32960	+	26.4021i	−0.0806187	+	1.60086i
$273$	−2.21348			−0.133966
$274$	8.27977	+	3.55226i	0.500199	+	0.214600i
$275$	2.37243	+	2.37243i	0.143063	+	0.143063i
$276$	47.9867	+	1.20753i	2.88846	+	0.0726845i
$277$	9.62303	−	9.62303i	0.578192	−	0.578192i	−0.356213	−	0.934405i	$-0.615932\pi$
$277$	9.62303	−	9.62303i	0.578192	−	0.578192i	0.934405	+	0.356213i	$0.115932\pi$
$278$	−0.361126	−	0.903828i	−0.0216589	−	0.0542080i
$279$			0.677843i			0.0405814i
$280$	−2.57043	−	1.18021i	−0.153612	−	0.0705311i
$281$		−	22.1150i		−	1.31927i	−0.751585	−	0.659637i	$-0.770710\pi$
$281$		−	22.1150i		−	1.31927i	0.751585	−	0.659637i	$-0.229290\pi$
$282$	43.8023	−	17.5013i	2.60839	−	1.04219i
$283$	8.73247	−	8.73247i	0.519091	−	0.519091i	−0.398205	−	0.917296i	$-0.630367\pi$
$283$	8.73247	−	8.73247i	0.519091	−	0.519091i	0.917296	+	0.398205i	$0.130367\pi$
$284$	11.5637	−	10.9960i	0.686176	−	0.652491i
$285$	−8.72163	−	8.72163i	−0.516625	−	0.516625i
$286$	−1.21632	+	2.83505i	−0.0719225	+	0.167640i
$287$	0.548655			0.0323861
$288$	21.3816	−	43.6382i	1.25992	−	2.57141i
$289$	26.6776			1.56927
$290$	−0.961456	+	2.24101i	−0.0564587	+	0.131596i
$291$	16.3010	+	16.3010i	0.955579	+	0.955579i
$292$	−20.0560	+	19.0714i	−1.17369	+	1.11607i
$293$	0.540807	−	0.540807i	0.0315943	−	0.0315943i	−0.691133	−	0.722727i	$-0.742888\pi$
$293$	0.540807	−	0.540807i	0.0315943	−	0.0315943i	0.722727	+	0.691133i	$0.242888\pi$
$294$	−4.47099	+	1.78639i	−0.260753	+	0.104184i
$295$			14.6019i			0.850154i
$296$	0.977735	−	2.12945i	0.0568297	−	0.123772i
$297$			63.8566i			3.70533i
$298$	8.47328	+	21.2070i	0.490844	+	1.22849i
$299$	−3.24107	+	3.24107i	−0.187436	+	0.187436i
$300$	6.80680	+	0.171285i	0.392991	+	0.00988913i
$301$	−2.40716	−	2.40716i	−0.138746	−	0.138746i
$302$	−14.6189	−	6.27195i	−0.841225	−	0.360910i
$303$	−26.4570			−1.51992
$304$	10.7497	−	9.71890i	0.616537	−	0.557417i
$305$	−7.42058			−0.424901
$306$	−73.7857	−	31.6562i	−4.21805	−	1.80967i
$307$	−8.07455	−	8.07455i	−0.460839	−	0.460839i	0.438092	−	0.898930i	$-0.355655\pi$
$307$	−8.07455	−	8.07455i	−0.460839	−	0.460839i	−0.898930	+	0.438092i	$0.855655\pi$
$308$	−0.168802	+	6.70812i	−0.00961837	+	0.382231i
$309$	−1.45102	+	1.45102i	−0.0825456	+	0.0825456i
$310$	−0.0414037	−	0.103625i	−0.00235157	−	0.00588552i
$311$		−	30.3239i		−	1.71951i	−0.510708	−	0.859754i	$-0.670617\pi$
$311$		−	30.3239i		−	1.71951i	0.510708	−	0.859754i	$-0.329383\pi$
$312$	2.17592	+	5.87038i	0.123187	+	0.332345i
$313$			8.12409i			0.459201i	0.973285	+	0.229600i	$0.0737419\pi$
$313$			8.12409i			0.459201i	−0.973285	+	0.229600i	$0.926258\pi$
$314$	14.2174	−	5.68059i	0.802335	−	0.320574i
$315$	6.07437	−	6.07437i	0.342252	−	0.342252i
$316$	−10.3380	−	10.8717i	−0.581557	−	0.611581i
$317$	19.7163	+	19.7163i	1.10738	+	1.10738i	0.993494	+	0.113885i	$0.0363296\pi$
$317$	19.7163	+	19.7163i	1.10738	+	1.10738i	0.113885	+	0.993494i	$0.463670\pi$
$318$	2.16253	−	5.04052i	0.121269	−	0.282658i
$319$	5.78528			0.323913
$320$	−0.603230	+	7.97722i	−0.0337216	+	0.445940i
$321$	−46.0671			−2.57122
$322$	−3.93090	+	9.16231i	−0.219060	+	0.510595i
$323$	−16.9308	−	16.9308i	−0.942054	−	0.942054i
$324$	53.7832	+	56.5598i	2.98796	+	3.14221i
$325$	−0.459738	+	0.459738i	−0.0255017	+	0.0255017i
$326$	−15.7762	+	6.30341i	−0.873764	+	0.349114i
$327$		−	70.8474i		−	3.91787i
$328$	−0.539345	−	1.45509i	−0.0297804	−	0.0803439i
$329$			9.79702i			0.540127i
$330$	−5.99356	−	15.0007i	−0.329934	−	0.825762i
$331$	2.96634	−	2.96634i	0.163045	−	0.163045i	−0.620869	−	0.783914i	$-0.713220\pi$
$331$	2.96634	−	2.96634i	0.163045	−	0.163045i	0.783914	+	0.620869i	$0.213220\pi$
$332$	0.0700356	−	2.78319i	0.00384371	−	0.152748i
$333$	5.03225	+	5.03225i	0.275766	+	0.275766i
$334$	−13.1816	−	5.65529i	−0.721265	−	0.309444i
$335$	1.49230			0.0815333
$336$	9.13281	+	10.1014i	0.498236	+	0.551079i
$337$	−8.40709			−0.457964			−0.228982	−	0.973431i	$-0.573540\pi$
$337$	−8.40709			−0.457964			−0.228982	+	0.973431i	$0.573540\pi$
$338$	16.3461	+	7.01295i	0.889110	+	0.381454i
$339$	−37.3714	−	37.3714i	−2.02974	−	2.02974i
$340$	13.2136	+	0.332504i	0.716609	+	0.0180326i
$341$	−0.187200	+	0.187200i	−0.0101375	+	0.0101375i
$342$	16.3307	+	40.8726i	0.883063	+	2.21013i
$343$		−	1.00000i		−	0.0539949i
$344$	−4.01771	+	8.75034i	−0.216621	+	0.471786i
$345$		−	24.0009i		−	1.29217i
$346$	−5.66765	+	2.26452i	−0.304695	+	0.121741i
$347$	3.86718	−	3.86718i	0.207601	−	0.207601i	−0.595646	−	0.803247i	$-0.703104\pi$
$347$	3.86718	−	3.86718i	0.207601	−	0.207601i	0.803247	+	0.595646i	$0.203104\pi$
$348$	8.50818	−	8.09050i	0.456087	−	0.433696i
$349$	−18.4321	−	18.4321i	−0.986646	−	0.986646i	0.0132656	−	0.999912i	$-0.495777\pi$
$349$	−18.4321	−	18.4321i	−0.986646	−	0.986646i	−0.999912	+	0.0132656i	$0.995777\pi$
$350$	−0.557588	+	1.29965i	−0.0298044	+	0.0694693i
$351$	−12.3744			−0.660494
$352$	17.9566	−	6.14662i	0.957088	−	0.327616i
$353$	−31.9993			−1.70315			−0.851574	−	0.524234i	$-0.824352\pi$
$353$	−31.9993			−1.70315			−0.851574	+	0.524234i	$0.824352\pi$
$354$	27.7187	−	64.6079i	1.47323	−	3.43387i
$355$	−5.64169	−	5.64169i	−0.299430	−	0.299430i
$356$	−10.1933	+	9.69287i	−0.540243	+	0.513721i
$357$	15.9098	−	15.9098i	0.842035	−	0.842035i
$358$	6.28324	−	2.51048i	0.332079	−	0.132683i
$359$			37.0569i			1.95579i	0.209100	+	0.977894i	$0.432946\pi$
$359$			37.0569i			1.95579i	−0.209100	+	0.977894i	$0.567054\pi$
$360$	−22.0811	−	10.1386i	−1.16378	−	0.534349i
$361$		−	5.87421i		−	0.309169i
$362$	5.12122	+	12.8174i	0.269165	+	0.673668i
$363$	−0.618311	+	0.618311i	−0.0324529	+	0.0324529i
$364$	−1.29992	−	0.0327110i	−0.0681345	−	0.00171452i
$365$	9.78495	+	9.78495i	0.512167	+	0.512167i
$366$	32.8333	+	14.0865i	1.71623	+	0.736311i
$367$	−17.0503			−0.890019			−0.445010	−	0.895526i	$-0.646800\pi$
$367$	−17.0503			−0.890019			−0.445010	+	0.895526i	$0.646800\pi$
$368$	28.1636	+	1.41830i	1.46813	+	0.0739341i
$369$	4.71319			0.245359
$370$	−1.07668	−	0.461929i	−0.0559742	−	0.0240145i
$371$	0.805532	+	0.805532i	0.0418211	+	0.0418211i
$372$	−0.0135155	+	0.537100i	−0.000700745	+	0.0278474i
$373$	4.54035	−	4.54035i	0.235090	−	0.235090i	−0.579723	−	0.814814i	$-0.696839\pi$
$373$	4.54035	−	4.54035i	0.235090	−	0.235090i	0.814814	+	0.579723i	$0.196839\pi$
$374$	−11.6349	−	29.1199i	−0.601628	−	1.50576i
$375$		−	3.40448i		−	0.175806i
$376$	25.9827	−	9.63078i	1.33996	−	0.496669i
$377$			1.12109i			0.0577392i
$378$	−24.9948	+	9.98673i	−1.28560	+	0.513662i
$379$	−13.9534	+	13.9534i	−0.716736	+	0.716736i	−0.967935	−	0.251199i	$-0.919175\pi$
$379$	−13.9534	+	13.9534i	−0.716736	+	0.716736i	0.251199	+	0.967935i	$0.419175\pi$
$380$	−4.99312	−	5.25090i	−0.256142	−	0.269365i
$381$	30.0462	+	30.0462i	1.53931	+	1.53931i
$382$	5.15935	−	12.0256i	0.263975	−	0.615285i
$383$	−22.7548			−1.16272			−0.581358	−	0.813648i	$-0.697479\pi$
$383$	−22.7548			−1.16272			−0.581358	+	0.813648i	$0.697479\pi$
$384$	17.8122	−	34.1512i	0.908975	−	1.74277i
$385$	3.35512			0.170993
$386$	10.1969	−	23.7675i	0.519011	−	1.20973i
$387$	−20.6786	−	20.6786i	−1.05115	−	1.05115i
$388$	9.33227	+	9.81406i	0.473774	+	0.498234i
$389$	0.289788	−	0.289788i	0.0146928	−	0.0146928i	−0.699722	−	0.714415i	$-0.746693\pi$
$389$	0.289788	−	0.289788i	0.0146928	−	0.0146928i	0.714415	+	0.699722i	$0.246693\pi$
$390$	2.90689	−	1.16145i	0.147196	−	0.0588125i
$391$		−	46.5915i		−	2.35623i
$392$	−2.65210	+	0.983032i	−0.133951	+	0.0496506i
$393$			4.52647i			0.228330i
$394$	3.00875	+	7.53031i	0.151579	+	0.379372i
$395$	−5.30410	+	5.30410i	−0.266878	+	0.266878i
$396$	−1.45008	+	57.6258i	−0.0728694	+	2.89580i
$397$	−16.1773	−	16.1773i	−0.811914	−	0.811914i	0.173006	−	0.984921i	$-0.444652\pi$
$397$	−16.1773	−	16.1773i	−0.811914	−	0.811914i	−0.984921	+	0.173006i	$0.944652\pi$
$398$	−10.6541	−	4.57091i	−0.534041	−	0.229119i
$399$	−12.3343			−0.617485
$400$	3.99494	+	0.201183i	0.199747	+	0.0100591i
$401$	12.1093			0.604709			0.302355	−	0.953196i	$-0.402227\pi$
$401$	12.1093			0.604709			0.302355	+	0.953196i	$0.402227\pi$
$402$	−6.60290	−	2.83283i	−0.329323	−	0.141289i
$403$	−0.0362763	−	0.0362763i	−0.00180705	−	0.00180705i
$404$	−15.5376	−	0.390984i	−0.773023	−	0.0194522i
$405$	27.5945	−	27.5945i	1.37118	−	1.37118i
$406$	0.904778	+	2.26448i	0.0449034	+	0.112384i
$407$			2.77952i			0.137776i
$408$	−57.8342	−	26.5546i	−2.86322	−	1.31465i
$409$		−	14.9655i		−	0.739998i	−0.929032	−	0.369999i	$-0.879358\pi$
$409$		−	14.9655i		−	0.739998i	0.929032	−	0.369999i	$-0.120642\pi$
$410$	−0.720531	+	0.287889i	−0.0355845	+	0.0142178i
$411$	−15.3365	+	15.3365i	−0.756494	+	0.756494i
$412$	−0.873592	+	0.830706i	−0.0430388	+	0.0409259i
$413$	10.3251	+	10.3251i	0.508064	+	0.508064i
$414$	−33.7682	+	78.7083i	−1.65961	+	3.86830i
$415$	−1.39204			−0.0683324
$416$	1.19111	+	3.47969i	0.0583991	+	0.170606i
$417$	2.34306			0.114740
$418$	−6.77774	+	15.7979i	−0.331510	+	0.772698i
$419$	−15.4782	−	15.4782i	−0.756159	−	0.756159i	0.219462	−	0.975621i	$-0.429570\pi$
$419$	−15.4782	−	15.4782i	−0.756159	−	0.756159i	−0.975621	+	0.219462i	$0.929570\pi$
$420$	4.93425	−	4.69201i	0.240767	−	0.228947i
$421$	−4.06993	+	4.06993i	−0.198356	+	0.198356i	−0.799295	−	0.600939i	$-0.794794\pi$
$421$	−4.06993	+	4.06993i	−0.198356	+	0.198356i	0.600939	+	0.799295i	$0.294794\pi$
$422$	−15.2576	+	6.09621i	−0.742729	+	0.296759i
$423$			84.1608i			4.09204i
$424$	1.34449	−	2.92822i	0.0652942	−	0.142207i
$425$		−	6.60890i		−	0.320579i
$426$	14.2528	+	35.6720i	0.690551	+	1.72831i
$427$	−5.24714	+	5.24714i	−0.253927	+	0.253927i
$428$	−27.0541	−	0.680784i	−1.30771	−	0.0329069i
$429$	−5.25133	−	5.25133i	−0.253536	−	0.253536i
$430$	4.42432	+	1.89816i	0.213360	+	0.0915374i
$431$	25.4099			1.22395			0.611975	−	0.790877i	$-0.290375\pi$
$431$	25.4099			1.22395			0.611975	+	0.790877i	$0.290375\pi$
$432$	51.0565	+	56.4716i	2.45646	+	2.71699i
$433$	−8.25231			−0.396581			−0.198290	−	0.980143i	$-0.563539\pi$
$433$	−8.25231			−0.396581			−0.198290	+	0.980143i	$0.563539\pi$
$434$	−0.102551	−	0.0439974i	−0.00492261	−	0.00211194i
$435$	−4.15098	−	4.15098i	−0.199024	−	0.199024i
$436$	1.04699	−	41.6070i	0.0501417	−	1.99261i
$437$	−18.0603	+	18.0603i	−0.863942	+	0.863942i
$438$	−24.7201	−	61.8695i	−1.18117	−	2.95624i
$439$		−	21.2883i		−	1.01603i	−0.861347	−	0.508017i	$-0.830379\pi$
$439$		−	21.2883i		−	1.01603i	0.861347	−	0.508017i	$-0.169621\pi$
$440$	−3.29819	−	8.89813i	−0.157235	−	0.424202i
$441$		−	8.59045i		−	0.409069i
$442$	5.64297	−	2.25466i	0.268409	−	0.107243i
$443$	2.23347	−	2.23347i	0.106115	−	0.106115i	−0.652056	−	0.758171i	$-0.726093\pi$
$443$	2.23347	−	2.23347i	0.106115	−	0.106115i	0.758171	+	0.652056i	$0.226093\pi$
$444$	3.88706	+	4.08773i	0.184471	+	0.193995i
$445$	4.97311	+	4.97311i	0.235748	+	0.235748i
$446$	−12.3413	+	28.7656i	−0.584376	+	1.36209i
$447$	−54.9763			−2.60029
$448$	5.21420	+	6.06730i	0.246348	+	0.286653i
$449$	14.8424			0.700457			0.350229	−	0.936664i	$-0.386104\pi$
$449$	14.8424			0.700457			0.350229	+	0.936664i	$0.386104\pi$
$450$	−4.78994	+	11.1646i	−0.225800	+	0.526304i
$451$	1.30165	+	1.30165i	0.0612921	+	0.0612921i
$452$	−21.3951	−	22.4996i	−1.00634	−	1.05829i
$453$	27.0785	−	27.0785i	1.27226	−	1.27226i
$454$	24.9368	−	9.96355i	1.17034	−	0.467613i
$455$			0.650168i			0.0304803i
$456$	12.1250	+	32.7117i	0.567803	+	1.53187i
$457$		−	14.1926i		−	0.663903i	−0.943296	−	0.331952i	$-0.892293\pi$
$457$		−	14.1926i		−	0.663903i	0.943296	−	0.331952i	$-0.107707\pi$
$458$	−11.2423	−	28.1374i	−0.525320	−	1.31477i
$459$	88.9429	−	88.9429i	4.15150	−	4.15150i
$460$	0.354688	−	14.0952i	0.0165374	−	0.657191i
$461$	19.2200	+	19.2200i	0.895167	+	0.895167i	0.995004	−	0.0998372i	$-0.0318322\pi$
$461$	19.2200	+	19.2200i	0.895167	+	0.895167i	−0.0998372	+	0.995004i	$0.531832\pi$
$462$	−14.8452	−	6.36902i	−0.690660	−	0.296313i
$463$	8.06592			0.374855			0.187428	−	0.982278i	$-0.439985\pi$
$463$	8.06592			0.374855			0.187428	+	0.982278i	$0.439985\pi$
$464$	5.11622	−	4.62562i	0.237514	−	0.214739i
$465$	0.268635			0.0124577
$466$	−2.69696	−	1.15708i	−0.124934	−	0.0536005i
$467$	−7.83411	−	7.83411i	−0.362520	−	0.362520i	0.502220	−	0.864740i	$-0.332517\pi$
$467$	−7.83411	−	7.83411i	−0.362520	−	0.362520i	−0.864740	+	0.502220i	$0.832517\pi$
$468$	−11.1669	−	0.281002i	−0.516192	−	0.0129893i
$469$	1.05522	−	1.05522i	0.0487255	−	0.0487255i
$470$	−5.14067	−	12.8661i	−0.237122	−	0.593469i
$471$			36.8568i			1.69827i
$472$	17.2333	−	37.5331i	0.793227	−	1.72760i
$473$		−	11.4216i		−	0.525167i
$474$	33.5374	−	13.3999i	1.54043	−	0.615480i
$475$	−2.56181	+	2.56181i	−0.117544	+	0.117544i
$476$	9.57855	−	9.10832i	0.439032	−	0.417479i
$477$	6.91988	+	6.91988i	0.316840	+	0.316840i
$478$	8.33388	−	19.4250i	0.381183	−	0.888477i
$479$	22.0416			1.00711			0.503554	−	0.863964i	$-0.332026\pi$
$479$	22.0416			1.00711			0.503554	+	0.863964i	$0.332026\pi$
$480$	−17.2942	−	8.47373i	−0.789370	−	0.386771i
$481$	−0.538625			−0.0245592
$482$	−4.89262	+	11.4039i	−0.222853	+	0.519435i
$483$	−16.9712	−	16.9712i	−0.772217	−	0.772217i
$484$	−0.372257	+	0.353982i	−0.0169208	+	0.0160901i
$485$	4.78810	−	4.78810i	0.217416	−	0.217416i
$486$	−99.4935	+	39.7528i	−4.51312	+	1.80322i
$487$			38.4601i			1.74279i	0.490580	+	0.871396i	$0.336785\pi$
$487$			38.4601i			1.74279i	−0.490580	+	0.871396i	$0.663215\pi$
$488$	19.0741	+	8.75786i	0.863443	+	0.396449i
$489$		−	40.8978i		−	1.84946i
$490$	0.524718	+	1.31327i	0.0237044	+	0.0593274i
$491$	−11.7492	+	11.7492i	−0.530232	+	0.530232i	−0.920641	−	0.390409i	$-0.872334\pi$
$491$	−11.7492	+	11.7492i	−0.530232	+	0.530232i	0.390409	+	0.920641i	$0.372334\pi$
$492$	3.73458	+	0.0939762i	0.168368	+	0.00423677i
$493$	−8.05805	−	8.05805i	−0.362916	−	0.362916i
$494$	−3.06137	−	1.31341i	−0.137737	−	0.0590933i
$495$	28.8220			1.29545
$496$	−0.0158746	+	0.315227i	−0.000712792	+	0.0141541i
$497$	−7.97855			−0.357887
$498$	6.15925	+	2.64250i	0.276003	+	0.118413i
$499$	7.05189	+	7.05189i	0.315686	+	0.315686i	0.847108	−	0.531421i	$-0.178342\pi$
$499$	7.05189	+	7.05189i	0.315686	+	0.315686i	−0.531421	+	0.847108i	$0.678342\pi$
$500$	0.0503116	−	1.99937i	0.00225000	−	0.0894144i
$501$	24.4161	−	24.4161i	1.09083	−	1.09083i
$502$	−11.4031	−	28.5396i	−0.508944	−	1.27379i
$503$		−	22.3743i		−	0.997621i	−0.866711	−	0.498811i	$-0.833770\pi$
$503$		−	22.3743i		−	0.997621i	0.866711	−	0.498811i	$-0.166230\pi$
$504$	−22.7828	+	8.44469i	−1.01482	+	0.376156i
$505$			7.77124i			0.345816i
$506$	−31.0627	+	12.4112i	−1.38091	+	0.551743i
$507$	−30.2776	+	30.2776i	−1.34468	+	1.34468i
$508$	17.2014	+	18.0895i	0.763189	+	0.802590i
$509$	13.7297	+	13.7297i	0.608560	+	0.608560i	0.942570	−	0.334009i	$-0.108402\pi$
$509$	13.7297	+	13.7297i	0.608560	+	0.608560i	−0.334009	+	0.942570i	$0.608402\pi$
$510$	−12.5456	+	29.2420i	−0.555531	+	1.29486i
$511$	13.8380			0.612157
$512$	10.9654	−	19.7929i	0.484606	−	0.874733i
$513$	−68.9541			−3.04440
$514$	−6.79268	+	15.8327i	−0.299612	+	0.698349i
$515$	0.426209	+	0.426209i	0.0187810	+	0.0187810i
$516$	−15.9727	−	16.7973i	−0.703159	−	0.739461i
$517$	−23.2427	+	23.2427i	−1.02221	+	1.02221i
$518$	−1.08796	+	0.434698i	−0.0478024	+	0.0190995i
$519$		−	14.6927i		−	0.644936i
$520$	1.72431	−	0.639135i	0.0756161	−	0.0280279i
$521$		−	29.6617i		−	1.29950i	−0.760147	−	0.649751i	$-0.774873\pi$
$521$		−	29.6617i		−	1.29950i	0.760147	−	0.649751i	$-0.225127\pi$
$522$	7.77245	+	19.4529i	0.340191	+	0.851432i
$523$	4.26196	−	4.26196i	0.186362	−	0.186362i	−0.607759	−	0.794121i	$-0.707931\pi$
$523$	4.26196	−	4.26196i	0.186362	−	0.186362i	0.794121	+	0.607759i	$0.207931\pi$
$524$	−0.0668926	+	2.65829i	−0.00292222	+	0.116128i
$525$	−2.40733	−	2.40733i	−0.105064	−	0.105064i
$526$	24.0159	+	10.3035i	1.04714	+	0.449254i
$527$	0.521485			0.0227163
$528$	−2.29800	+	45.6319i	−0.100007	+	1.98587i
$529$	−26.6999			−1.16086
$530$	−1.48056	−	0.635201i	−0.0643112	−	0.0275914i
$531$	88.6971	+	88.6971i	3.84913	+	3.84913i
$532$	−7.24361	−	0.182277i	−0.314050	−	0.00790269i
$533$	−0.252238	+	0.252238i	−0.0109256	+	0.0109256i
$534$	−12.5638	−	31.4446i	−0.543687	−	1.36074i
$535$			13.5313i			0.585011i
$536$	−3.83586	−	1.76123i	−0.165684	−	0.0760737i
$537$			16.2885i			0.702900i
$538$	−33.8124	+	13.5098i	−1.45776	+	0.582449i
$539$	2.37243	−	2.37243i	0.102188	−	0.102188i
$540$	27.5847	−	26.2305i	1.18706	−	1.12878i
$541$	−21.2903	−	21.2903i	−0.915342	−	0.915342i	0.0813437	−	0.996686i	$-0.474079\pi$
$541$	−21.2903	−	21.2903i	−0.915342	−	0.915342i	−0.996686	+	0.0813437i	$0.974079\pi$
$542$	−4.22217	+	9.84122i	−0.181358	+	0.422716i
$543$	−33.2275			−1.42593
$544$	−33.5722	−	16.4495i	−1.43940	−	0.705268i
$545$	−20.8101			−0.891406
$546$	1.23421	−	2.87675i	0.0528193	−	0.123114i
$547$	14.5737	+	14.5737i	0.623126	+	0.623126i	0.946329	−	0.323204i	$-0.104760\pi$
$547$	14.5737	+	14.5737i	0.623126	+	0.623126i	−0.323204	+	0.946329i	$0.604760\pi$
$548$	−9.23341	+	8.78012i	−0.394432	+	0.375068i
$549$	−45.0753	+	45.0753i	−1.92377	+	1.92377i
$550$	−4.40617	+	1.76049i	−0.187880	+	0.0750677i
$551$			6.24710i			0.266135i
$552$	−28.3262	+	61.6926i	−1.20564	+	2.62581i
$553$			7.50113i			0.318980i
$554$	7.14090	+	17.8723i	0.303388	+	0.759320i
$555$	1.99433	−	1.99433i	0.0846545	−	0.0846545i
$556$	1.37602	+	0.0346259i	0.0583563	+	0.00146846i
$557$	−3.63217	−	3.63217i	−0.153900	−	0.153900i	0.625957	−	0.779857i	$-0.284708\pi$
$557$	−3.63217	−	3.63217i	−0.153900	−	0.153900i	−0.779857	+	0.625957i	$0.784708\pi$
$558$	−0.880959	−	0.377957i	−0.0372940	−	0.0160002i
$559$	2.21332			0.0936136
$560$	2.96711	−	2.68259i	0.125383	−	0.113360i
$561$	75.4897			3.18718
$562$	28.7419	+	12.3311i	1.21240	+	0.520156i
$563$	8.01210	+	8.01210i	0.337670	+	0.337670i	0.855490	−	0.517820i	$-0.173256\pi$
$563$	8.01210	+	8.01210i	0.337670	+	0.337670i	−0.517820	+	0.855490i	$0.673256\pi$
$564$	−1.67808	+	66.6863i	−0.0706599	+	2.80800i
$565$	−10.9771	+	10.9771i	−0.461812	+	0.461812i
$566$	6.48004	+	16.2183i	0.272377	+	0.681706i
$567$		−	39.0245i		−	1.63888i
$568$	7.84317	+	21.1599i	0.329092	+	0.887852i
$569$		−	22.6007i		−	0.947469i	−0.880668	−	0.473735i	$-0.842906\pi$
$569$		−	22.6007i		−	0.947469i	0.880668	−	0.473735i	$-0.157094\pi$
$570$	16.1982	−	6.47201i	0.678467	−	0.271083i
$571$	−23.3563	+	23.3563i	−0.977432	+	0.977432i	−0.999751	−	0.0223187i	$-0.992895\pi$
$571$	−23.3563	+	23.3563i	−0.977432	+	0.977432i	0.0223187	+	0.999751i	$0.492895\pi$
$572$	−3.00637	−	3.16158i	−0.125703	−	0.132192i
$573$	22.2749	+	22.2749i	0.930549	+	0.930549i
$574$	−0.305924	+	0.713061i	−0.0127690	+	0.0297626i
$575$	−7.04981			−0.293998
$576$	44.7923	+	52.1208i	1.86635	+	2.17170i
$577$	−0.618797			−0.0257609			−0.0128804	−	0.999917i	$-0.504100\pi$
$577$	−0.618797			−0.0257609			−0.0128804	+	0.999917i	$0.504100\pi$
$578$	−14.8751	+	34.6715i	−0.618722	+	1.44215i
$579$	44.0242	+	44.0242i	1.82958	+	1.82958i
$580$	−2.37643	−	2.49912i	−0.0986759	−	0.103770i
$581$	−0.984319	+	0.984319i	−0.0408364	+	0.0408364i
$582$	−30.2748	+	12.0964i	−1.25493	+	0.501410i
$583$			3.82214i			0.158297i
$584$	−13.6032	−	36.6998i	−0.562904	−	1.51865i
$585$			5.58523i			0.230921i
$586$	0.401313	+	1.00441i	0.0165781	+	0.0414917i
$587$	−7.04144	+	7.04144i	−0.290631	+	0.290631i	−0.837330	−	0.546698i	$-0.815884\pi$
$587$	−7.04144	+	7.04144i	−0.290631	+	0.290631i	0.546698	+	0.837330i	$0.315884\pi$
$588$	0.171285	−	6.80680i	0.00706366	−	0.280708i
$589$	−0.202144	−	0.202144i	−0.00832919	−	0.00832919i
$590$	−18.9773	−	8.14183i	−0.781285	−	0.335194i
$591$	−19.5214			−0.803001
$592$	2.22237	+	2.45807i	0.0913387	+	0.101026i
$593$	27.9722			1.14868			0.574340	−	0.818617i	$-0.305259\pi$
$593$	27.9722			1.14868			0.574340	+	0.818617i	$0.305259\pi$
$594$	−82.9913	−	35.6057i	−3.40517	−	1.46092i
$595$	−4.67320	−	4.67320i	−0.191582	−	0.191582i
$596$	−32.2863	−	0.812444i	−1.32250	−	0.0332790i
$597$	19.7344	−	19.7344i	0.807675	−	0.807675i
$598$	−2.40508	−	6.01944i	−0.0983510	−	0.246153i
$599$			27.6858i			1.13121i	0.824676	+	0.565605i	$0.191357\pi$
$599$			27.6858i			1.13121i	−0.824676	+	0.565605i	$0.808643\pi$
$600$	−4.01800	+	8.75096i	−0.164034	+	0.357256i
$601$		−	23.9255i		−	0.975942i	−0.872860	−	0.487971i	$-0.837737\pi$
$601$		−	23.9255i		−	0.975942i	0.872860	−	0.487971i	$-0.162263\pi$
$602$	4.47067	−	1.78626i	0.182211	−	0.0728026i
$603$	9.06480	−	9.06480i	0.369147	−	0.369147i
$604$	16.3027	−	15.5024i	0.663347	−	0.630782i
$605$	0.181617	+	0.181617i	0.00738379	+	0.00738379i
$606$	14.7521	−	34.3849i	0.599264	−	1.39679i
$607$	−7.11335			−0.288722			−0.144361	−	0.989525i	$-0.546113\pi$
$607$	−7.11335			−0.288722			−0.144361	+	0.989525i	$0.546113\pi$
$608$	6.63728	+	19.3900i	0.269177	+	0.786368i
$609$	−5.87038			−0.237880
$610$	4.13763	−	9.64417i	0.167528	−	0.390481i
$611$	−4.50406	−	4.50406i	−0.182215	−	0.182215i
$612$	82.2841	−	78.2446i	3.32614	−	3.16285i
$613$	−12.2698	+	12.2698i	−0.495571	+	0.495571i	−0.910056	−	0.414485i	$-0.863962\pi$
$613$	−12.2698	+	12.2698i	−0.495571	+	0.495571i	0.414485	+	0.910056i	$0.363962\pi$
$614$	14.9964	−	5.99183i	0.605205	−	0.241810i
$615$		−	1.86788i		−	0.0753203i
$616$	−8.62410	−	3.95975i	−0.347475	−	0.159543i
$617$			26.2983i			1.05873i	0.848394	+	0.529366i	$0.177570\pi$
$617$			26.2983i			1.05873i	−0.848394	+	0.529366i	$0.822430\pi$
$618$	−1.07675	−	2.69489i	−0.0433132	−	0.108404i
$619$	7.29239	−	7.29239i	0.293106	−	0.293106i	−0.545200	−	0.838306i	$-0.683546\pi$
$619$	7.29239	−	7.29239i	0.293106	−	0.293106i	0.838306	+	0.545200i	$0.183546\pi$
$620$	0.157763	+	0.00396991i	0.00633592	+	0.000159436i
$621$	−94.8768	−	94.8768i	−3.80727	−	3.80727i
$622$	39.4105	+	16.9082i	1.58022	+	0.677958i
$623$	7.03304			0.281773
$624$	−8.84271	−	0.445314i	−0.353992	−	0.0178268i
$625$	−1.00000			−0.0400000
$626$	−10.5585	−	4.52990i	−0.422002	−	0.181051i
$627$	−29.2622	−	29.2622i	−1.16862	−	1.16862i
$628$	−0.544673	+	21.6451i	−0.0217348	+	0.863735i
$629$	3.87147	−	3.87147i	0.154365	−	0.154365i
$630$	4.50757	+	11.2816i	0.179586	+	0.449468i
$631$			2.05090i			0.0816448i	0.999166	+	0.0408224i	$0.0129978\pi$
$631$			2.05090i			0.0816448i	−0.999166	+	0.0408224i	$0.987002\pi$
$632$	19.8938	−	7.37385i	0.791331	−	0.293316i
$633$		−	39.5534i		−	1.57211i
$634$	−36.6180	+	14.6308i	−1.45428	+	0.581062i
$635$	8.82551	−	8.82551i	0.350230	−	0.350230i
$636$	5.34512	+	5.62107i	0.211948	+	0.222890i
$637$	0.459738	+	0.459738i	0.0182155	+	0.0182155i
$638$	−3.22580	+	7.51885i	−0.127711	+	0.297674i
$639$	−68.5394			−2.71138
$640$	−10.0313	−	5.23200i	−0.396520	−	0.206813i
$641$	−20.8338			−0.822884			−0.411442	−	0.911436i	$-0.634975\pi$
$641$	−20.8338			−0.822884			−0.411442	+	0.911436i	$0.634975\pi$
$642$	25.6865	−	59.8712i	1.01377	−	2.36293i
$643$	−11.2607	−	11.2607i	−0.444079	−	0.444079i	0.449301	−	0.893380i	$-0.351673\pi$
$643$	−11.2607	−	11.2607i	−0.444079	−	0.444079i	−0.893380	+	0.449301i	$0.851673\pi$
$644$	−9.71599	−	10.2176i	−0.382864	−	0.402629i
$645$	−8.19510	+	8.19510i	−0.322682	+	0.322682i
$646$	31.4445	−	12.5637i	1.23717	−	0.494313i
$647$			25.3682i			0.997326i	0.866796	+	0.498663i	$0.166175\pi$
$647$			25.3682i			0.997326i	−0.866796	+	0.498663i	$0.833825\pi$
$648$	−103.497	+	38.3623i	−4.06575	+	1.50701i
$649$			48.9911i			1.92307i
$650$	−0.341155	−	0.853844i	−0.0133812	−	0.0334905i
$651$	0.189954	−	0.189954i	0.00744488	−	0.00744488i
$652$	0.604391	−	24.0183i	0.0236698	−	0.940629i
$653$	5.67998	+	5.67998i	0.222275	+	0.222275i	0.809456	−	0.587181i	$-0.199762\pi$
$653$	5.67998	+	5.67998i	0.222275	+	0.222275i	−0.587181	+	0.809456i	$0.699762\pi$
$654$	92.0770	+	39.5037i	3.60049	+	1.54472i
$655$	1.32957			0.0519504
$656$	2.19184	+	0.110380i	0.0855771	+	0.00430961i
$657$	118.875			4.63774
$658$	−12.7327	−	5.46270i	−0.496373	−	0.212958i
$659$	21.2237	+	21.2237i	0.826759	+	0.826759i	0.987067	−	0.160308i	$-0.0512487\pi$
$659$	21.2237	+	21.2237i	0.826759	+	0.826759i	−0.160308	+	0.987067i	$0.551249\pi$
$660$	22.8376	+	0.574681i	0.888954	+	0.0223694i
$661$	10.8284	−	10.8284i	0.421176	−	0.421176i	−0.464433	−	0.885608i	$-0.653742\pi$
$661$	10.8284	−	10.8284i	0.421176	−	0.421176i	0.885608	+	0.464433i	$0.153742\pi$
$662$	2.20122	+	5.50921i	0.0855527	+	0.214122i
$663$			14.6287i			0.568130i
$664$	3.57813	+	1.64290i	0.138858	+	0.0637568i
$665$			3.62295i			0.140492i
$666$	−9.34610	+	3.73425i	−0.362154	+	0.144699i
$667$	−8.59565	+	8.59565i	−0.332825	+	0.332825i
$668$	14.6998	−	13.9782i	0.568753	−	0.540832i
$669$	−53.2821	−	53.2821i	−2.06000	−	2.06000i
$670$	−0.832091	+	1.93948i	−0.0321465	+	0.0749285i
$671$	−24.8970			−0.961136
$672$	−18.2207	+	6.23703i	−0.702879	+	0.240599i
$673$	−6.30782			−0.243148			−0.121574	−	0.992582i	$-0.538794\pi$
$673$	−6.30782			−0.243148			−0.121574	+	0.992582i	$0.538794\pi$
$674$	4.68770	−	10.9263i	0.180563	−	0.420865i
$675$	−13.4580	−	13.4580i	−0.518001	−	0.518001i
$676$	−18.2288	+	17.3339i	−0.701107	+	0.666688i
$677$	22.7752	−	22.7752i	0.875320	−	0.875320i	−0.117726	−	0.993046i	$-0.537560\pi$
$677$	22.7752	−	22.7752i	0.875320	−	0.875320i	0.993046	+	0.117726i	$0.0375604\pi$
$678$	69.4077	−	27.7320i	2.66559	−	1.06504i
$679$		−	6.77139i		−	0.259862i
$680$	−7.79990	+	16.9877i	−0.299112	+	0.651449i
$681$			64.6455i			2.47722i
$682$	−0.138914	−	0.347676i	−0.00531931	−	0.0133132i
$683$	27.3383	−	27.3383i	1.04607	−	1.04607i	0.0471834	−	0.998886i	$-0.484975\pi$
$683$	27.3383	−	27.3383i	1.04607	−	1.04607i	0.998886	−	0.0471834i	$-0.0150245\pi$
$684$	−62.2259	−	1.56584i	−2.37927	−	0.0598713i
$685$	4.50481	+	4.50481i	0.172120	+	0.172120i
$686$	1.29965	+	0.557588i	0.0496209	+	0.0212888i
$687$	72.9426			2.78293
$688$	−9.13216	−	10.1007i	−0.348160	−	0.385086i
$689$	−0.740667			−0.0282172
$690$	31.1928	+	13.3826i	1.18749	+	0.509468i
$691$	1.72857	+	1.72857i	0.0657578	+	0.0657578i	0.739221	−	0.673463i	$-0.235194\pi$
$691$	1.72857	+	1.72857i	0.0657578	+	0.0657578i	−0.673463	+	0.739221i	$0.735194\pi$
$692$	0.217129	−	8.62864i	0.00825402	−	0.328012i
$693$	20.3802	−	20.3802i	0.774181	−	0.774181i
$694$	2.86969	+	7.18228i	0.108932	+	0.272636i
$695$		−	0.688228i		−	0.0261060i
$696$	5.77077	+	15.5688i	0.218740	+	0.590136i
$697$		−	3.62601i		−	0.137345i
$698$	34.2328	−	13.6778i	1.29573	−	0.517711i
$699$	4.99555	−	4.99555i	0.188949	−	0.188949i
$700$	−1.37819	−	1.44934i	−0.0520907	−	0.0547800i
$701$	−11.7717	−	11.7717i	−0.444609	−	0.444609i	0.448948	−	0.893558i	$-0.351799\pi$
$701$	−11.7717	−	11.7717i	−0.444609	−	0.444609i	−0.893558	+	0.448948i	$0.851799\pi$
$702$	6.89980	−	16.0824i	0.260416	−	0.606989i
$703$	−3.00140			−0.113200
$704$	−2.02391	+	26.7646i	−0.0762790	+	1.00873i
$705$	33.3537			1.25617
$706$	17.8424	−	41.5879i	0.671508	−	1.56518i
$707$	5.49510	+	5.49510i	0.206664	+	0.206664i
$708$	68.5122	+	72.0493i	2.57485	+	2.70778i
$709$	−10.0291	+	10.0291i	−0.376652	+	0.376652i	−0.869893	−	0.493241i	$-0.835812\pi$
$709$	−10.0291	+	10.0291i	−0.376652	+	0.376652i	0.493241	+	0.869893i	$0.335812\pi$
$710$	10.4780	−	4.18649i	0.393231	−	0.157116i
$711$			64.4381i			2.41662i
$712$	−6.91370	−	18.6524i	−0.259102	−	0.699027i
$713$		−	0.556276i		−	0.0208327i
$714$	11.8061	+	29.5483i	0.441831	+	1.10582i
$715$	−1.54248	+	1.54248i	−0.0576854	+	0.0576854i
$716$	−0.240713	+	9.56584i	−0.00899585	+	0.357492i
$717$	35.9806	+	35.9806i	1.34372	+	1.34372i
$718$	−48.1611	−	20.6625i	−1.79736	−	0.771118i
$719$	29.4371			1.09782			0.548909	−	0.835882i	$-0.315043\pi$
$719$	29.4371			1.09782			0.548909	+	0.835882i	$0.315043\pi$
$720$	25.4888	−	23.0447i	0.949911	−	0.858824i
$721$	0.602751			0.0224476
$722$	7.63443	+	3.27539i	0.284124	+	0.121897i
$723$	−21.1234	−	21.1234i	−0.785586	−	0.785586i
$724$	−19.5137	−	0.491038i	−0.725221	−	0.0182493i
$725$	−1.21927	+	1.21927i	−0.0452827	+	0.0452827i
$726$	−0.458826	−	1.14835i	−0.0170286	−	0.0426194i
$727$		−	29.1709i		−	1.08189i	−0.841058	−	0.540945i	$-0.818067\pi$
$727$		−	29.1709i		−	1.08189i	0.841058	−	0.540945i	$-0.181933\pi$
$728$	0.767335	−	1.67121i	0.0284393	−	0.0619391i
$729$		−	140.851i		−	5.21669i
$730$	−18.1730	+	7.26105i	−0.672613	+	0.268744i
$731$	−15.9087	+	15.9087i	−0.588403	+	0.588403i
$732$	−36.6150	+	34.8175i	−1.35333	+	1.28689i
$733$	−7.03839	−	7.03839i	−0.259969	−	0.259969i	0.565072	−	0.825041i	$-0.308848\pi$
$733$	−7.03839	−	7.03839i	−0.259969	−	0.259969i	−0.825041	+	0.565072i	$0.808848\pi$
$734$	9.50706	−	22.1595i	0.350912	−	0.817921i
$735$	−3.40448			−0.125576
$736$	−17.5470	+	35.8120i	−0.646790	+	1.32005i
$737$	5.00686			0.184430
$738$	−2.62802	+	6.12551i	−0.0967389	+	0.225483i
$739$	−9.63082	−	9.63082i	−0.354276	−	0.354276i	0.507422	−	0.861698i	$-0.330599\pi$
$739$	−9.63082	−	9.63082i	−0.354276	−	0.354276i	−0.861698	+	0.507422i	$0.830599\pi$
$740$	1.20069	−	1.14175i	0.0441384	−	0.0419715i
$741$	5.67053	−	5.67053i	0.208312	−	0.208312i
$742$	−1.49607	+	0.597756i	−0.0549223	+	0.0219443i
$743$		−	1.94893i		−	0.0714992i	−0.999361	−	0.0357496i	$-0.988618\pi$
$743$		−	1.94893i		−	0.0714992i	0.999361	−	0.0357496i	$-0.0113819\pi$
$744$	−0.690508	−	0.317046i	−0.0253152	−	0.0116235i
$745$			16.1482i			0.591626i
$746$	3.36923	+	8.43252i	0.123356	+	0.308737i
$747$	−8.45574	+	8.45574i	−0.309379	+	0.309379i
$748$	44.3333	+	1.11559i	1.62099	+	0.0407901i
$749$	9.56811	+	9.56811i	0.349611	+	0.349611i
$750$	4.42463	+	1.89830i	0.161565	+	0.0693160i
$751$	35.1964			1.28434			0.642168	−	0.766564i	$-0.278035\pi$
$751$	35.1964			1.28434			0.642168	+	0.766564i	$0.278035\pi$
$752$	−1.97099	+	39.1385i	−0.0718747	+	1.42723i
$753$	73.9853			2.69617
$754$	−1.45703	−	0.625108i	−0.0530619	−	0.0227651i
$755$	−7.95378	−	7.95378i	−0.289468	−	0.289468i
$756$	0.957559	−	38.0531i	0.0348261	−	1.38398i
$757$	−15.7315	+	15.7315i	−0.571772	+	0.571772i	−0.932623	−	0.360852i	$-0.882486\pi$
$757$	−15.7315	+	15.7315i	−0.571772	+	0.571772i	0.360852	+	0.932623i	$0.382486\pi$
$758$	−10.3543	−	25.9148i	−0.376084	−	0.941266i
$759$		−	80.5260i		−	2.92291i
$760$	9.60844	−	3.56148i	0.348535	−	0.129188i
$761$		−	3.53285i		−	0.128066i	−0.997948	−	0.0640329i	$-0.979604\pi$
$761$		−	3.53285i		−	0.128066i	0.997948	−	0.0640329i	$-0.0203963\pi$
$762$	−55.8031	+	22.2962i	−2.02153	+	0.807707i
$763$	−14.7149	+	14.7149i	−0.532717	+	0.532717i
$764$	12.7524	+	13.4107i	0.461364	+	0.485183i
$765$	−40.1449	−	40.1449i	−1.45144	−	1.45144i
$766$	12.6878	−	29.5733i	0.458430	−	1.06853i
$767$	−9.49367			−0.342796
$768$	34.4528	+	42.1920i	1.24321	+	1.52247i
$769$	8.78487			0.316791			0.158395	−	0.987376i	$-0.449368\pi$
$769$	8.78487			0.316791			0.158395	+	0.987376i	$0.449368\pi$
$770$	−1.87078	+	4.36049i	−0.0674181	+	0.157141i
$771$	−29.3266	−	29.3266i	−1.05617	−	1.05617i
$772$	25.2038	+	26.5050i	0.907104	+	0.953935i
$773$	12.0940	−	12.0940i	0.434991	−	0.434991i	−0.455331	−	0.890322i	$-0.650479\pi$
$773$	12.0940	−	12.0940i	0.434991	−	0.434991i	0.890322	+	0.455331i	$0.150479\pi$
$774$	38.4051	−	15.3448i	1.38044	−	0.551558i
$775$		−	0.0789065i		−	0.00283441i
$776$	−17.9584	+	6.65649i	−0.644670	+	0.238954i
$777$		−	2.82041i		−	0.101181i
$778$	0.215041	+	0.538206i	0.00770960	+	0.0192956i
$779$	−1.40555	+	1.40555i	−0.0503591	+	0.0503591i
$780$	−0.111364	+	4.42556i	−0.00398746	+	0.158460i
$781$	−18.9286	−	18.9286i	−0.677317	−	0.677317i
$782$	60.5528	+	25.9789i	2.16536	+	0.929003i
$783$	−32.8181			−1.17282
$784$	0.201183	−	3.99494i	0.00718510	−	0.142676i
$785$	10.8260			0.386396
$786$	−5.88284	−	2.52391i	−0.209834	−	0.0900249i
$787$	2.37139	+	2.37139i	0.0845310	+	0.0845310i	0.748108	−	0.663577i	$-0.230963\pi$
$787$	2.37139	+	2.37139i	0.0845310	+	0.0845310i	−0.663577	+	0.748108i	$0.730963\pi$
$788$	−11.4644	−	0.288488i	−0.408403	−	0.0102770i
$789$	−44.4842	+	44.4842i	−1.58368	+	1.58368i
$790$	−3.93598	−	9.85099i	−0.140036	−	0.350482i
$791$			15.5240i			0.551971i
$792$	−74.0849	−	34.0161i	−2.63249	−	1.20871i
$793$		−	4.82462i		−	0.171327i
$794$	30.0451	−	12.0046i	1.06626	−	0.426026i
$795$	2.74241	−	2.74241i	0.0972634	−	0.0972634i
$796$	11.8812	−	11.2979i	0.421117	−	0.400444i
$797$	−1.17474	−	1.17474i	−0.0416113	−	0.0416113i	0.685995	−	0.727606i	$-0.259367\pi$
$797$	−1.17474	−	1.17474i	−0.0416113	−	0.0416113i	−0.727606	+	0.685995i	$0.759367\pi$
$798$	6.87744	−	16.0302i	0.243459	−	0.567464i
$799$	64.7475			2.29060
$800$	−2.48900	+	5.07985i	−0.0879994	+	0.179600i
$801$	60.4170			2.13473
$802$	−6.75200	+	15.7379i	−0.238421	+	0.555723i
$803$	32.8297	+	32.8297i	1.15853	+	1.15853i
$804$	7.36340	−	7.00191i	0.259687	−	0.246938i
$805$	−4.98497	+	4.98497i	−0.175697	+	0.175697i
$806$	0.0673738	−	0.0269193i	0.00237314	−	0.000948193i
$807$		−	87.6542i		−	3.08557i
$808$	9.17171	−	19.9754i	0.322660	−	0.702733i
$809$		−	5.70645i		−	0.200628i	−0.994956	−	0.100314i	$-0.968015\pi$
$809$		−	5.70645i		−	0.200628i	0.994956	−	0.100314i	$-0.0319848\pi$
$810$	20.4769	+	51.2496i	0.719484	+	1.80073i
$811$	−26.8909	+	26.8909i	−0.944266	+	0.944266i	−0.998527	−	0.0542609i	$-0.982720\pi$
$811$	−26.8909	+	26.8909i	−0.944266	+	0.944266i	0.0542609	+	0.998527i	$0.482720\pi$
$812$	−3.44753	−	0.0867529i	−0.120985	−	0.00304443i
$813$	−18.2287	−	18.2287i	−0.639310	−	0.639310i
$814$	−3.61241	−	1.54983i	−0.126615	−	0.0543214i
$815$	−12.0129			−0.420795
$816$	66.7594	−	60.3578i	2.33705	−	2.11295i
$817$	12.3334			0.431490
$818$	19.4500	+	8.34461i	0.680053	+	0.291762i
$819$	3.94936	+	3.94936i	0.138002	+	0.138002i
$820$	0.0276037	−	1.09696i	0.000963964	−	0.0383076i
$821$	−36.8377	+	36.8377i	−1.28564	+	1.28564i	−0.348238	+	0.937406i	$0.613220\pi$
$821$	−36.8377	+	36.8377i	−1.28564	+	1.28564i	−0.937406	+	0.348238i	$0.886780\pi$
$822$	−11.3807	−	28.4836i	−0.396946	−	0.993479i
$823$			26.3035i			0.916883i	0.888725	+	0.458442i	$0.151592\pi$
$823$			26.3035i			0.916883i	−0.888725	+	0.458442i	$0.848408\pi$
$824$	−0.592523	−	1.59856i	−0.0206415	−	0.0556884i
$825$		−	11.4224i		−	0.397678i
$826$	−19.1762	+	7.66187i	−0.667224	+	0.266590i
$827$	−6.37770	+	6.37770i	−0.221774	+	0.221774i	−0.809245	−	0.587471i	$-0.800124\pi$
$827$	−6.37770	+	6.37770i	−0.221774	+	0.221774i	0.587471	+	0.809245i	$0.300124\pi$
$828$	−83.4647	−	87.7737i	−2.90060	−	3.05035i
$829$	−23.0074	−	23.0074i	−0.799079	−	0.799079i	0.183871	−	0.982950i	$-0.441137\pi$
$829$	−23.0074	−	23.0074i	−0.799079	−	0.799079i	−0.982950	+	0.183871i	$0.941137\pi$
$830$	0.776184	−	1.80916i	0.0269417	−	0.0627970i
$831$	−46.3316			−1.60722
$832$	−5.18653	−	0.392201i	−0.179811	−	0.0135971i
$833$	−6.60890			−0.228985
$834$	−1.30646	+	3.04516i	−0.0452390	+	0.105445i
$835$	−7.17177	−	7.17177i	−0.248189	−	0.248189i
$836$	−16.7525	−	17.6174i	−0.579398	−	0.609311i
$837$	1.06193	−	1.06193i	0.0367056	−	0.0367056i
$838$	28.7467	−	11.4858i	0.993039	−	0.396770i
$839$			55.5878i			1.91910i	0.281531	+	0.959552i	$0.409158\pi$
$839$			55.5878i			1.91910i	−0.281531	+	0.959552i	$0.590842\pi$
$840$	3.34671	+	9.02902i	0.115472	+	0.311531i
$841$		−	26.0267i		−	0.897474i
$842$	−3.02015	−	7.55883i	−0.104081	−	0.260495i
$843$	−53.2382	+	53.2382i	−1.83362	+	1.83362i
$844$	0.584523	−	23.2288i	0.0201201	−	0.799567i
$845$	8.89348	+	8.89348i	0.305945	+	0.305945i
$846$	−109.380	−	46.9271i	−3.76055	−	1.61339i
$847$	0.256846			0.00882532
$848$	3.05599	+	3.38011i	0.104943	+	0.116073i
$849$	−42.0438			−1.44294
$850$	8.58927	+	3.68505i	0.294610	+	0.126396i
$851$	−4.12975	−	4.12975i	−0.141566	−	0.141566i
$852$	−54.3084	−	1.36660i	−1.86057	−	0.0468191i
$853$	−17.7059	+	17.7059i	−0.606238	+	0.606238i	−0.941961	−	0.335723i	$-0.891020\pi$
$853$	−17.7059	+	17.7059i	−0.606238	+	0.606238i	0.335723	+	0.941961i	$0.391020\pi$
$854$	−3.89371	−	9.74521i	−0.133240	−	0.333474i
$855$			31.1228i			1.06438i
$856$	15.9699	−	34.7814i	0.545838	−	1.18880i
$857$		−	32.2502i		−	1.10165i	−0.834622	−	0.550823i	$-0.814314\pi$
$857$		−	32.2502i		−	1.10165i	0.834622	−	0.550823i	$-0.185686\pi$
$858$	9.75297	−	3.89682i	0.332961	−	0.133035i
$859$	1.87487	−	1.87487i	0.0639696	−	0.0639696i	−0.674398	−	0.738368i	$-0.735597\pi$
$859$	1.87487	−	1.87487i	0.0639696	−	0.0639696i	0.738368	+	0.674398i	$0.235597\pi$
$860$	−4.93390	+	4.69168i	−0.168244	+	0.159985i
$861$	−1.32079	−	1.32079i	−0.0450125	−	0.0450125i
$862$	−14.1682	+	33.0240i	−0.482572	+	1.12480i
$863$	3.59902			0.122512			0.0612560	−	0.998122i	$-0.480489\pi$
$863$	3.59902			0.122512			0.0612560	+	0.998122i	$0.480489\pi$
$864$	−101.862	+	34.8678i	−3.46541	+	1.18623i
$865$	−4.31569			−0.146738
$866$	4.60139	−	10.7251i	0.156362	−	0.364455i
$867$	−64.2216	−	64.2216i	−2.18108	−	2.18108i
$868$	0.114362	−	0.108748i	0.00388172	−	0.00369115i
$869$	−17.7959	+	17.7959i	−0.603685	+	0.603685i
$870$	7.70938	−	3.08029i	0.261372	−	0.104432i
$871$			0.970248i			0.0328756i
$872$	53.4908	+	24.5603i	1.81143	+	0.831717i
$873$		−	58.1693i		−	1.96873i
$874$	−13.4019	−	33.5424i	−0.453326	−	1.13459i
$875$	−0.707107	+	0.707107i	−0.0239046	+	0.0239046i
$876$	94.1925	+	2.37024i	3.18247	+	0.0800829i
$877$	0.572209	+	0.572209i	0.0193221	+	0.0193221i	0.716702	−	0.697380i	$-0.245651\pi$
$877$	0.572209	+	0.572209i	0.0193221	+	0.0193221i	−0.697380	+	0.716702i	$0.745651\pi$
$878$	27.6673	+	11.8701i	0.933727	+	0.400596i
$879$	−2.60380			−0.0878239
$880$	13.4035	+	0.674993i	0.451832	+	0.0227540i
$881$	−25.7619			−0.867940			−0.433970	−	0.900927i	$-0.642888\pi$
$881$	−25.7619			−0.867940			−0.433970	+	0.900927i	$0.642888\pi$
$882$	11.1646	+	4.78994i	0.375932	+	0.161286i
$883$	−21.9261	−	21.9261i	−0.737871	−	0.737871i	0.234294	−	0.972166i	$-0.424722\pi$
$883$	−21.9261	−	21.9261i	−0.737871	−	0.737871i	−0.972166	+	0.234294i	$0.924722\pi$
$884$	−0.216184	+	8.59107i	−0.00727104	+	0.288949i
$885$	35.1515	−	35.1515i	1.18160	−	1.18160i
$886$	1.65737	+	4.14808i	0.0556806	+	0.139358i
$887$			10.1484i			0.340749i	0.985379	+	0.170374i	$0.0544977\pi$
$887$			10.1484i			0.340749i	−0.985379	+	0.170374i	$0.945502\pi$
$888$	−7.48001	+	2.77255i	−0.251013	+	0.0930406i
$889$		−	12.4812i		−	0.418605i
$890$	−9.23627	+	3.69037i	−0.309600	+	0.123701i
$891$	92.5829	−	92.5829i	3.10164	−	3.10164i
$892$	−30.5039	−	32.0787i	−1.02135	−	1.07407i
$893$	−25.0981	−	25.0981i	−0.839877	−	0.839877i
$894$	30.6541	−	71.4500i	1.02523	−	2.38965i
$895$	4.78443			0.159926
$896$	−10.7928	+	3.39359i	−0.360561	+	0.113372i
$897$	15.6046			0.521023
$898$	−8.27596	+	19.2900i	−0.276172	+	0.643715i
$899$	−0.0962086	−	0.0962086i	−0.00320873	−	0.00320873i
$900$	−11.8393	−	12.4505i	−0.394643	−	0.415017i
$901$	5.32368	−	5.32368i	0.177357	−	0.177357i
$902$	−2.41747	+	0.965904i	−0.0804929	+	0.0321611i
$903$			11.5896i			0.385679i
$904$	41.1713	−	15.2606i	1.36934	−	0.507560i
$905$			9.75994i			0.324431i
$906$	20.0939	+	50.2912i	0.667576	+	1.67081i
$907$	24.4321	−	24.4321i	0.811253	−	0.811253i	−0.173568	−	0.984822i	$-0.555530\pi$
$907$	24.4321	−	24.4321i	0.811253	−	0.811253i	0.984822	+	0.173568i	$0.0555298\pi$
$908$	−0.955336	+	37.9647i	−0.0317040	+	1.25990i
$909$	47.2054	+	47.2054i	1.56570	+	1.56570i
$910$	−0.844992	−	0.362526i	−0.0280112	−	0.0120176i
$911$	−17.2393			−0.571163			−0.285581	−	0.958354i	$-0.592187\pi$
$911$	−17.2393			−0.571163			−0.285581	+	0.958354i	$0.592187\pi$
$912$	−49.2746	−	2.48144i	−1.63164	−	0.0821687i
$913$	−4.67045			−0.154569
$914$	18.4455	+	7.91365i	0.610122	+	0.261760i
$915$	17.8638	+	17.8638i	0.590558	+	0.590558i
$916$	42.8374	+	1.07795i	1.41539	+	0.0356165i
$917$	0.940145	−	0.940145i	0.0310463	−	0.0310463i
$918$	66.0013	+	165.188i	2.17837	+	5.45203i
$919$			18.0423i			0.595162i	0.954697	+	0.297581i	$0.0961798\pi$
$919$			18.0423i			0.595162i	−0.954697	+	0.297581i	$0.903820\pi$
$920$	18.1210	+	8.32027i	0.597433	+	0.274311i
$921$			38.8762i			1.28101i
$922$	−35.6962	+	14.2625i	−1.17559	+	0.469710i
$923$	3.66804	−	3.66804i	0.120735	−	0.120735i
$924$	16.5550	−	15.7423i	0.544620	−	0.517883i
$925$	−0.585796	−	0.585796i	−0.0192609	−	0.0192609i
$926$	−4.49747	+	10.4829i	−0.147796	+	0.344489i
$927$	5.17790			0.170065
$928$	3.15896	+	9.22849i	0.103698	+	0.302940i
$929$	0.815553			0.0267574			0.0133787	−	0.999911i	$-0.495741\pi$
$929$	0.815553			0.0267574			0.0133787	+	0.999911i	$0.495741\pi$
$930$	−0.149788	+	0.349132i	−0.00491174	+	0.0114485i
$931$	2.56181	+	2.56181i	0.0839601	+	0.0839601i
$932$	3.00759	−	2.85994i	0.0985169	−	0.0936805i
$933$	−72.9995	+	72.9995i	−2.38989	+	2.38989i
$934$	14.5498	−	5.81341i	0.476085	−	0.190221i
$935$		−	22.1737i		−	0.725156i
$936$	6.59176	−	14.3564i	0.215458	−	0.469255i
$937$			7.51159i			0.245393i	0.992444	+	0.122696i	$0.0391542\pi$
$937$			7.51159i			0.245393i	−0.992444	+	0.122696i	$0.960846\pi$
$938$	0.783039	+	1.95979i	0.0255671	+	0.0639895i
$939$	19.5573	−	19.5573i	0.638230	−	0.638230i
$940$	19.5878	+	0.492904i	0.638885	+	0.0160767i
$941$	20.2850	+	20.2850i	0.661273	+	0.661273i	0.955680	−	0.294407i	$-0.0951221\pi$
$941$	20.2850	+	20.2850i	0.661273	+	0.661273i	−0.294407	+	0.955680i	$0.595122\pi$
$942$	−47.9010	−	20.5509i	−1.56070	−	0.669586i
$943$	−3.86792			−0.125957
$944$	39.1708	+	43.3253i	1.27490	+	1.41012i
$945$	−19.0326			−0.619129
$946$	14.8441	+	6.36856i	0.482624	+	0.207060i
$947$	36.6209	+	36.6209i	1.19002	+	1.19002i	0.977061	+	0.212959i	$0.0683099\pi$
$947$	36.6209	+	36.6209i	1.19002	+	1.19002i	0.212959	+	0.977061i	$0.431690\pi$
$948$	−1.28483	+	51.0586i	−0.0417293	+	1.65831i
$949$	−6.36186	+	6.36186i	−0.206515	+	0.206515i
$950$	−1.90103	−	4.75791i	−0.0616775	−	0.154367i
$951$		−	94.9273i		−	3.07823i
$952$	6.49676	+	17.5275i	0.210561	+	0.568069i
$953$			33.0932i			1.07199i	0.844220	+	0.535996i	$0.180064\pi$
$953$			33.0932i			1.07199i	−0.844220	+	0.535996i	$0.819936\pi$
$954$	−12.8519	+	5.13499i	−0.416095	+	0.166252i
$955$	6.54284	−	6.54284i	0.211721	−	0.211721i
$956$	20.5988	+	21.6623i	0.666214	+	0.700608i
$957$	−13.9271	−	13.9271i	−0.450198	−	0.450198i
$958$	−12.2902	+	28.6464i	−0.397077	+	0.925525i
$959$	6.37076			0.205723
$960$	20.6560	−	17.7516i	0.666668	−	0.572931i
$961$	−30.9938			−0.999799
$962$	0.300331	−	0.700026i	0.00968307	−	0.0225697i
$963$	82.1944	+	82.1944i	2.64868	+	2.64868i
$964$	−12.0931	−	12.7174i	−0.389492	−	0.409600i
$965$	12.9313	−	12.9313i	0.416273	−	0.416273i
$966$	31.5196	−	12.5937i	1.01413	−	0.405196i
$967$		−	13.4306i		−	0.431899i	−0.976404	−	0.215950i	$-0.930715\pi$
$967$		−	13.4306i		−	0.431899i	0.976404	−	0.215950i	$-0.0692847\pi$
$968$	−0.252487	−	0.681181i	−0.00811525	−	0.0218940i
$969$			81.5158i			2.61867i
$970$	3.55307	+	8.89265i	0.114082	+	0.285526i
$971$	23.6365	−	23.6365i	0.758532	−	0.758532i	−0.217524	−	0.976055i	$-0.569798\pi$
$971$	23.6365	−	23.6365i	0.758532	−	0.758532i	0.976055	+	0.217524i	$0.0697979\pi$
$972$	3.81162	−	151.473i	0.122258	−	4.85849i
$973$	−0.486651	−	0.486651i	−0.0156013	−	0.0156013i
$974$	−49.9847	−	21.4449i	−1.60161	−	0.687139i
$975$	2.21348			0.0708881
$976$	−22.0176	+	19.9064i	−0.704768	+	0.637188i
$977$	33.7394			1.07942			0.539710	−	0.841851i	$-0.318534\pi$
$977$	33.7394			1.07942			0.539710	+	0.841851i	$0.318534\pi$
$978$	53.1529	+	22.8041i	1.69964	+	0.729196i
$979$	16.6854	+	16.6854i	0.533268	+	0.533268i
$980$	−1.99937	−	0.0503116i	−0.0638674	−	0.00160715i
$981$	−126.408	+	126.408i	−4.03590	+	4.03590i
$982$	−8.71862	−	21.8210i	−0.278222	−	0.696337i
$983$			10.1795i			0.324677i	0.986735	+	0.162338i	$0.0519036\pi$
$983$			10.1795i			0.324677i	−0.986735	+	0.162338i	$0.948096\pi$
$984$	−2.20450	+	4.80126i	−0.0702768	+	0.153059i
$985$			5.73403i			0.182701i
$986$	14.9657	−	5.97959i	0.476606	−	0.190429i
$987$	23.5846	−	23.5846i	0.750707	−	0.750707i
$988$	3.41396	−	3.24636i	0.108613	−	0.103281i
$989$	16.9700	+	16.9700i	0.539615	+	0.539615i
$990$	−16.0708	+	37.4586i	−0.510764	+	1.19051i
$991$	28.5540			0.907049			0.453525	−	0.891244i	$-0.350166\pi$
$991$	28.5540			0.907049			0.453525	+	0.891244i	$0.350166\pi$
$992$	−0.400833	−	0.196398i	−0.0127265	−	0.00623565i
$993$	−14.2819			−0.453223
$994$	4.44875	−	10.3693i	0.141106	−	0.328896i
$995$	−5.79660	−	5.79660i	−0.183765	−	0.183765i
$996$	−6.86866	+	6.53146i	−0.217642	+	0.206957i
$997$	−3.48225	+	3.48225i	−0.110284	+	0.110284i	−0.760096	−	0.649811i	$-0.774848\pi$
$997$	−3.48225	+	3.48225i	−0.110284	+	0.110284i	0.649811	+	0.760096i	$0.274848\pi$
$998$	−13.0971	+	5.23295i	−0.414580	+	0.165646i
$999$		−	15.7673i		−	0.498857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.b.141.9	✓	52
4.3	odd	2		2240.2.bd.b.1681.26		52
16.5	even	4	inner	560.2.bd.b.421.9	yes	52
16.11	odd	4		2240.2.bd.b.561.26		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.b.141.9	✓	52	1.1	even	1	trivial
560.2.bd.b.421.9	yes	52	16.5	even	4	inner
2240.2.bd.b.561.26		52	16.11	odd	4
2240.2.bd.b.1681.26		52	4.3	odd	2

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.557588 + 1.29965i) q^{2} +(-2.40733 - 2.40733i) q^{3} +(-1.37819 - 1.44934i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(4.47099 - 1.78639i) q^{6} +1.00000i q^{7} +(2.65210 - 0.983032i) q^{8} +8.59045i q^{9} +O(q^{10})\)	\(q+(-0.557588 + 1.29965i) q^{2} +(-2.40733 - 2.40733i) q^{3} +(-1.37819 - 1.44934i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(4.47099 - 1.78639i) q^{6} +1.00000i q^{7} +(2.65210 - 0.983032i) q^{8} +8.59045i q^{9} +(-0.524718 - 1.31327i) q^{10} +(-2.37243 + 2.37243i) q^{11} +(-0.171285 + 6.80680i) q^{12} +(-0.459738 - 0.459738i) q^{13} +(-1.29965 - 0.557588i) q^{14} +3.40448 q^{15} +(-0.201183 + 3.99494i) q^{16} +6.60890 q^{17} +(-11.1646 - 4.78994i) q^{18} +(-2.56181 - 2.56181i) q^{19} +(1.99937 + 0.0503116i) q^{20} +(2.40733 - 2.40733i) q^{21} +(-1.76049 - 4.40617i) q^{22} -7.04981i q^{23} +(-8.75096 - 4.01800i) q^{24} -1.00000i q^{25} +(0.853844 - 0.341155i) q^{26} +(13.4580 - 13.4580i) q^{27} +(1.44934 - 1.37819i) q^{28} +(-1.21927 - 1.21927i) q^{29} +(-1.89830 + 4.42463i) q^{30} +0.0789065 q^{31} +(-5.07985 - 2.48900i) q^{32} +11.4224 q^{33} +(-3.68505 + 8.58927i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(12.4505 - 11.8393i) q^{36} +(0.585796 - 0.585796i) q^{37} +(4.75791 - 1.90103i) q^{38} +2.21348i q^{39} +(-1.18021 + 2.57043i) q^{40} -0.548655i q^{41} +(1.78639 + 4.47099i) q^{42} +(-2.40716 + 2.40716i) q^{43} +(6.70812 + 0.168802i) q^{44} +(-6.07437 - 6.07437i) q^{45} +(9.16231 + 3.93090i) q^{46} +9.79702 q^{47} +(10.1014 - 9.13281i) q^{48} -1.00000 q^{49} +(1.29965 + 0.557588i) q^{50} +(-15.9098 - 15.9098i) q^{51} +(-0.0327110 + 1.29992i) q^{52} +(0.805532 - 0.805532i) q^{53} +(9.98673 + 24.9948i) q^{54} -3.35512i q^{55} +(0.983032 + 2.65210i) q^{56} +12.3343i q^{57} +(2.26448 - 0.904778i) q^{58} +(10.3251 - 10.3251i) q^{59} +(-4.69201 - 4.93425i) q^{60} +(5.24714 + 5.24714i) q^{61} +(-0.0439974 + 0.102551i) q^{62} -8.59045 q^{63} +(6.06730 - 5.21420i) q^{64} +0.650168 q^{65} +(-6.36902 + 14.8452i) q^{66} +(-1.05522 - 1.05522i) q^{67} +(-9.10832 - 9.57855i) q^{68} +(-16.9712 + 16.9712i) q^{69} +(1.31327 - 0.524718i) q^{70} +7.97855i q^{71} +(8.44469 + 22.7828i) q^{72} -13.8380i q^{73} +(0.434698 + 1.08796i) q^{74} +(-2.40733 + 2.40733i) q^{75} +(-0.182277 + 7.24361i) q^{76} +(-2.37243 - 2.37243i) q^{77} +(-2.87675 - 1.23421i) q^{78} +7.50113 q^{79} +(-2.68259 - 2.96711i) q^{80} -39.0245 q^{81} +(0.713061 + 0.305924i) q^{82} +(0.984319 + 0.984319i) q^{83} +(-6.80680 - 0.171285i) q^{84} +(-4.67320 + 4.67320i) q^{85} +(-1.78626 - 4.47067i) q^{86} +5.87038i q^{87} +(-3.95975 + 8.62410i) q^{88} -7.03304i q^{89} +(11.2816 - 4.50757i) q^{90} +(0.459738 - 0.459738i) q^{91} +(-10.2176 + 9.71599i) q^{92} +(-0.189954 - 0.189954i) q^{93} +(-5.46270 + 12.7327i) q^{94} +3.62295 q^{95} +(6.23703 + 18.2207i) q^{96} -6.77139 q^{97} +(0.557588 - 1.29965i) q^{98} +(-20.3802 - 20.3802i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) \) 52 * q - 8 * q^4 + 12 * q^6	\( 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) \) 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * q^99

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