LMFDB - Embedded newform 775.2.df.b.507.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(43,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 38]))

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

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

chi := DirichletCharacter("775.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.df (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$14$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			507.7
Character	$\chi$	$=$	775.507
Dual form			775.2.df.b.668.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0322043 + 0.0632044i) q^{2} +(-0.0569594 + 1.08685i) q^{3} +(1.17261 + 1.61396i) q^{4} +(-0.0668594 - 0.0386013i) q^{6} +(1.97885 - 2.44368i) q^{7} +(-0.279898 + 0.0443315i) q^{8} +(1.80557 + 0.189773i) q^{9} +O(q^{10})$	\(q+(-0.0322043 + 0.0632044i) q^{2} +(-0.0569594 + 1.08685i) q^{3} +(1.17261 + 1.61396i) q^{4} +(-0.0668594 - 0.0386013i) q^{6} +(1.97885 - 2.44368i) q^{7} +(-0.279898 + 0.0443315i) q^{8} +(1.80557 + 0.189773i) q^{9} +(1.77665 - 3.99042i) q^{11} +(-1.82093 + 1.18252i) q^{12} +(3.27771 + 2.12857i) q^{13} +(0.0907237 + 0.203769i) q^{14} +(-1.22675 + 3.77554i) q^{16} +(-0.623752 + 1.62493i) q^{17} +(-0.0701414 + 0.108008i) q^{18} +(1.46007 - 6.86910i) q^{19} +(2.54320 + 2.28990i) q^{21} +(0.194996 + 0.240801i) q^{22} +(-1.02696 - 6.48399i) q^{23} +(-0.0322389 - 0.306732i) q^{24} +(-0.240092 + 0.138617i) q^{26} +(-0.819861 + 5.17640i) q^{27} +(6.26443 + 0.328305i) q^{28} +(0.255441 + 0.786167i) q^{29} +(-3.11543 - 4.61455i) q^{31} +(-0.599894 - 0.599894i) q^{32} +(4.23579 + 2.15824i) q^{33} +(-0.0826153 - 0.0917536i) q^{34} +(1.81094 + 3.13665i) q^{36} +(0.291921 + 1.08947i) q^{37} +(0.387137 + 0.313497i) q^{38} +(-2.50014 + 3.44114i) q^{39} +(-6.74839 + 7.49485i) q^{41} +(-0.226634 + 0.0869965i) q^{42} +(5.01711 + 7.72567i) q^{43} +(8.52371 - 1.81177i) q^{44} +(0.442890 + 0.143904i) q^{46} +(-9.30187 + 4.73954i) q^{47} +(-4.03357 - 1.54834i) q^{48} +(-0.600323 - 2.82430i) q^{49} +(-1.73053 - 0.770481i) q^{51} +(0.408052 + 7.78610i) q^{52} +(-4.58094 + 3.70958i) q^{53} +(-0.300768 - 0.218521i) q^{54} +(-0.445544 + 0.771705i) q^{56} +(7.38251 + 1.97814i) q^{57} +(-0.0579155 - 0.00917292i) q^{58} +(0.435631 - 0.392244i) q^{59} +9.21086i q^{61} +(0.391990 - 0.0483010i) q^{62} +(4.03669 - 4.03669i) q^{63} +(-7.49384 + 2.43490i) q^{64} +(-0.272821 + 0.198216i) q^{66} +(1.70835 - 6.37563i) q^{67} +(-3.35400 + 0.898701i) q^{68} +(7.10563 - 0.746831i) q^{69} +(0.191176 - 1.81892i) q^{71} +(-0.513787 + 0.0269265i) q^{72} +(-0.0491467 - 0.128032i) q^{73} +(-0.0782601 - 0.0166347i) q^{74} +(12.7986 - 5.69829i) q^{76} +(-6.23557 - 12.2380i) q^{77} +(-0.136980 - 0.268839i) q^{78} +(-9.87826 + 4.39808i) q^{79} +(-0.251755 - 0.0535122i) q^{81} +(-0.256380 - 0.667894i) q^{82} +(2.79788 - 0.146631i) q^{83} +(-0.713636 + 6.78979i) q^{84} +(-0.649869 + 0.0683040i) q^{86} +(-0.868996 + 0.232847i) q^{87} +(-0.320379 + 1.19567i) q^{88} +(4.24416 - 3.08356i) q^{89} +(11.6876 - 3.79755i) q^{91} +(9.26070 - 9.26070i) q^{92} +(5.19278 - 3.12317i) q^{93} -0.740552i q^{94} +(0.686164 - 0.617825i) q^{96} +(-7.51144 - 1.18969i) q^{97} +(0.197841 + 0.0530113i) q^{98} +(3.96513 - 6.86781i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 12 q^{2} + 14 q^{3} - 36 q^{6} - 6 q^{7} + 40 q^{8}+O(q^{10}) $ 224 * q + 12 * q^2 + 14 * q^3 - 36 * q^6 - 6 * q^7 + 40 * q^8	$ 224 q + 12 q^{2} + 14 q^{3} - 36 q^{6} - 6 q^{7} + 40 q^{8} - 28 q^{11} + 40 q^{12} + 14 q^{13} + 24 q^{16} + 14 q^{17} + 40 q^{18} - 44 q^{21} - 30 q^{22} + 30 q^{23} - 48 q^{26} - 100 q^{27} + 48 q^{28} - 44 q^{31} - 28 q^{32} - 20 q^{33} + 16 q^{36} - 30 q^{37} - 38 q^{38} - 20 q^{41} + 130 q^{42} - 22 q^{43} + 28 q^{47} + 156 q^{48} - 36 q^{51} + 10 q^{52} - 26 q^{53} - 48 q^{56} + 20 q^{58} - 30 q^{62} - 152 q^{63} - 152 q^{66} - 38 q^{67} + 126 q^{68} - 128 q^{71} + 156 q^{72} + 30 q^{73} + 128 q^{76} - 30 q^{78} - 64 q^{81} - 8 q^{82} + 82 q^{83} - 28 q^{86} + 24 q^{87} - 252 q^{88} - 194 q^{93} + 60 q^{96} + 38 q^{97} - 174 q^{98}+O(q^{100}) $ 224 * q + 12 * q^2 + 14 * q^3 - 36 * q^6 - 6 * q^7 + 40 * q^8 - 28 * q^11 + 40 * q^12 + 14 * q^13 + 24 * q^16 + 14 * q^17 + 40 * q^18 - 44 * q^21 - 30 * q^22 + 30 * q^23 - 48 * q^26 - 100 * q^27 + 48 * q^28 - 44 * q^31 - 28 * q^32 - 20 * q^33 + 16 * q^36 - 30 * q^37 - 38 * q^38 - 20 * q^41 + 130 * q^42 - 22 * q^43 + 28 * q^47 + 156 * q^48 - 36 * q^51 + 10 * q^52 - 26 * q^53 - 48 * q^56 + 20 * q^58 - 30 * q^62 - 152 * q^63 - 152 * q^66 - 38 * q^67 + 126 * q^68 - 128 * q^71 + 156 * q^72 + 30 * q^73 + 128 * q^76 - 30 * q^78 - 64 * q^81 - 8 * q^82 + 82 * q^83 - 28 * q^86 + 24 * q^87 - 252 * q^88 - 194 * q^93 + 60 * q^96 + 38 * q^97 - 174 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.0322043	+	0.0632044i	−0.0227718	+	0.0446923i	−0.902112	−	0.431502i	$-0.857984\pi$
$2$	−0.0322043	+	0.0632044i	−0.0227718	+	0.0446923i	0.879340	+	0.476194i	$0.157984\pi$
$3$	−0.0569594	+	1.08685i	−0.0328855	+	0.627493i	0.931621	+	0.363433i	$0.118395\pi$
$3$	−0.0569594	+	1.08685i	−0.0328855	+	0.627493i	−0.964506	+	0.264061i	$0.914938\pi$
$4$	1.17261	+	1.61396i	0.586306	+	0.806982i
$5$		0			0
$5$		0			0
$6$	−0.0668594	−	0.0386013i	−0.0272952	−	0.0157589i
$7$	1.97885	−	2.44368i	0.747935	−	0.923622i	−0.251082	−	0.967966i	$-0.580786\pi$
$7$	1.97885	−	2.44368i	0.747935	−	0.923622i	0.999016	+	0.0443434i	$0.0141196\pi$
$8$	−0.279898	+	0.0443315i	−0.0989589	+	0.0156735i
$9$	1.80557	+	0.189773i	0.601856	+	0.0632576i
$10$		0			0
$11$	1.77665	−	3.99042i	0.535680	−	1.20316i	−0.419669	−	0.907677i	$-0.637854\pi$
$11$	1.77665	−	3.99042i	0.535680	−	1.20316i	0.955349	−	0.295479i	$-0.0954794\pi$
$12$	−1.82093	+	1.18252i	−0.525657	+	0.341365i
$13$	3.27771	+	2.12857i	0.909074	+	0.590360i	0.912249	−	0.409635i	$-0.134344\pi$
$13$	3.27771	+	2.12857i	0.909074	+	0.590360i	−0.00317504	+	0.999995i	$0.501011\pi$
$14$	0.0907237	+	0.203769i	0.0242469	+	0.0544595i
$15$		0			0
$16$	−1.22675	+	3.77554i	−0.306687	+	0.943884i
$17$	−0.623752	+	1.62493i	−0.151282	+	0.394104i	−0.988189	−	0.153242i	$-0.951028\pi$
$17$	−0.623752	+	1.62493i	−0.151282	+	0.394104i	0.836906	+	0.547346i	$0.184362\pi$
$18$	−0.0701414	+	0.108008i	−0.0165325	+	0.0254578i
$19$	1.46007	−	6.86910i	0.334963	−	1.57588i	−0.412108	−	0.911135i	$-0.635207\pi$
$19$	1.46007	−	6.86910i	0.334963	−	1.57588i	0.747071	−	0.664744i	$-0.231459\pi$
$20$		0			0
$21$	2.54320	+	2.28990i	0.554971	+	0.499698i
$22$	0.194996	+	0.240801i	0.0415734	+	0.0513388i
$23$	−1.02696	−	6.48399i	−0.214137	−	1.35201i	−0.827171	−	0.561950i	$-0.810051\pi$
$23$	−1.02696	−	6.48399i	−0.214137	−	1.35201i	0.613034	−	0.790056i	$-0.289949\pi$
$24$	−0.0322389	−	0.306732i	−0.00658073	−	0.0626115i
$25$		0			0
$26$	−0.240092	+	0.138617i	−0.0470858	+	0.0271850i
$27$	−0.819861	+	5.17640i	−0.157782	+	0.996198i
$28$	6.26443	+	0.328305i	1.18387	+	0.0620437i
$29$	0.255441	+	0.786167i	0.0474342	+	0.145988i	0.971968	−	0.235112i	$-0.0755456\pi$
$29$	0.255441	+	0.786167i	0.0474342	+	0.145988i	−0.924534	+	0.381099i	$0.875546\pi$
$30$		0			0
$31$	−3.11543	−	4.61455i	−0.559549	−	0.828798i
$31$	−3.11543	−	4.61455i	−0.559549	−	0.828798i
$32$	−0.599894	−	0.599894i	−0.106047	−	0.106047i
$33$	4.23579	+	2.15824i	0.737357	+	0.375702i
$34$	−0.0826153	−	0.0917536i	−0.0141684	−	0.0157356i
$35$		0			0
$36$	1.81094	+	3.13665i	0.301824	+	0.522775i
$37$	0.291921	+	1.08947i	0.0479916	+	0.179107i	0.985761	−	0.168151i	$-0.0537796\pi$
$37$	0.291921	+	1.08947i	0.0479916	+	0.179107i	−0.937770	+	0.347258i	$0.887113\pi$
$38$	0.387137	+	0.313497i	0.0628019	+	0.0508559i
$39$	−2.50014	+	3.44114i	−0.400342	+	0.551024i
$40$		0			0
$41$	−6.74839	+	7.49485i	−1.05392	+	1.17050i	−0.0689785	+	0.997618i	$0.521974\pi$
$41$	−6.74839	+	7.49485i	−1.05392	+	1.17050i	−0.984943	+	0.172880i	$0.944693\pi$
$42$	−0.226634	+	0.0869965i	−0.0349703	+	0.0134239i
$43$	5.01711	+	7.72567i	0.765102	+	1.17815i	0.979507	+	0.201409i	$0.0645521\pi$
$43$	5.01711	+	7.72567i	0.765102	+	1.17815i	−0.214405	+	0.976745i	$0.568781\pi$
$44$	8.52371	−	1.81177i	1.28500	−	0.273135i
$45$		0			0
$46$	0.442890	+	0.143904i	0.0653005	+	0.0212174i
$47$	−9.30187	+	4.73954i	−1.35682	+	0.691333i	−0.972725	−	0.231962i	$-0.925485\pi$
$47$	−9.30187	+	4.73954i	−1.35682	+	0.691333i	−0.384092	+	0.923295i	$0.625485\pi$
$48$	−4.03357	−	1.54834i	−0.582195	−	0.223484i
$49$	−0.600323	−	2.82430i	−0.0857604	−	0.403471i
$50$		0			0
$51$	−1.73053	−	0.770481i	−0.242322	−	0.107889i
$52$	0.408052	+	7.78610i	0.0565867	+	1.07974i
$53$	−4.58094	+	3.70958i	−0.629241	+	0.509549i	−0.890063	−	0.455838i	$-0.849340\pi$
$53$	−4.58094	+	3.70958i	−0.629241	+	0.509549i	0.260822	+	0.965387i	$0.416006\pi$
$54$	−0.300768	−	0.218521i	−0.0409294	−	0.0297369i
$55$		0			0
$56$	−0.445544	+	0.771705i	−0.0595383	+	0.103123i
$57$	7.38251	+	1.97814i	0.977838	+	0.262011i
$58$	−0.0579155	−	0.00917292i	−0.00760468	−	0.00120446i
$59$	0.435631	−	0.392244i	0.0567143	−	0.0510658i	−0.640286	−	0.768136i	$-0.721184\pi$
$59$	0.435631	−	0.392244i	0.0567143	−	0.0510658i	0.697000	+	0.717071i	$0.254518\pi$
$60$		0			0
$61$			9.21086i			1.17933i	0.807648	+	0.589665i	$0.200740\pi$
$61$			9.21086i			1.17933i	−0.807648	+	0.589665i	$0.799260\pi$
$62$	0.391990	−	0.0483010i	0.0497828	−	0.00613424i
$63$	4.03669	−	4.03669i	0.508575	−	0.508575i
$64$	−7.49384	+	2.43490i	−0.936730	+	0.304362i
$65$		0			0
$66$	−0.272821	+	0.198216i	−0.0335819	+	0.0243987i
$67$	1.70835	−	6.37563i	0.208708	−	0.778908i	−0.779580	−	0.626303i	$-0.784567\pi$
$67$	1.70835	−	6.37563i	0.208708	−	0.778908i	0.988287	−	0.152605i	$-0.0487661\pi$
$68$	−3.35400	+	0.898701i	−0.406732	+	0.108984i
$69$	7.10563	−	0.746831i	0.855417	−	0.0899079i
$70$		0			0
$71$	0.191176	−	1.81892i	0.0226885	−	0.215866i	−0.977303	−	0.211844i	$-0.932053\pi$
$71$	0.191176	−	1.81892i	0.0226885	−	0.215866i	0.999992	−	0.00402205i	$-0.00128026\pi$
$72$	−0.513787	+	0.0269265i	−0.0605504	+	0.00317331i
$73$	−0.0491467	−	0.128032i	−0.00575219	−	0.0149850i	0.930674	−	0.365849i	$-0.119221\pi$
$73$	−0.0491467	−	0.128032i	−0.00575219	−	0.0149850i	−0.936426	+	0.350864i	$0.885888\pi$
$74$	−0.0782601	−	0.0166347i	−0.00909755	−	0.00193374i
$75$		0			0
$76$	12.7986	−	5.69829i	1.46810	−	0.653639i
$77$	−6.23557	−	12.2380i	−0.710609	−	1.39465i
$78$	−0.136980	−	0.268839i	−0.0155100	−	0.0304400i
$79$	−9.87826	+	4.39808i	−1.11139	+	0.494823i	−0.878530	−	0.477687i	$-0.841475\pi$
$79$	−9.87826	+	4.39808i	−1.11139	+	0.494823i	−0.232861	+	0.972510i	$0.574809\pi$
$80$		0			0
$81$	−0.251755	−	0.0535122i	−0.0279728	−	0.00594580i
$82$	−0.256380	−	0.667894i	−0.0283125	−	0.0737565i
$83$	2.79788	−	0.146631i	0.307107	−	0.0160948i	0.101840	−	0.994801i	$-0.467527\pi$
$83$	2.79788	−	0.146631i	0.307107	−	0.0160948i	0.205267	+	0.978706i	$0.434194\pi$
$84$	−0.713636	+	6.78979i	−0.0778641	+	0.740827i
$85$		0			0
$86$	−0.649869	+	0.0683040i	−0.0700772	+	0.00736541i
$87$	−0.868996	+	0.232847i	−0.0931661	+	0.0249638i
$88$	−0.320379	+	1.19567i	−0.0341525	+	0.127459i
$89$	4.24416	−	3.08356i	0.449880	−	0.326857i	−0.339668	−	0.940545i	$-0.610315\pi$
$89$	4.24416	−	3.08356i	0.449880	−	0.326857i	0.789548	+	0.613688i	$0.210315\pi$
$90$		0			0
$91$	11.6876	−	3.79755i	1.22520	−	0.398091i
$92$	9.26070	−	9.26070i	0.965494	−	0.965494i
$93$	5.19278	−	3.12317i	0.538466	−	0.323857i
$94$		−	0.740552i		−	0.0763821i
$95$		0			0
$96$	0.686164	−	0.617825i	0.0700313	−	0.0630565i
$97$	−7.51144	−	1.18969i	−0.762671	−	0.120795i	−0.237031	−	0.971502i	$-0.576174\pi$
$97$	−7.51144	−	1.18969i	−0.762671	−	0.120795i	−0.525640	+	0.850707i	$0.676174\pi$
$98$	0.197841	+	0.0530113i	0.0199850	+	0.00535495i
$99$	3.96513	−	6.86781i	0.398511	−	0.690241i
$100$		0			0
$101$	−6.91369	−	5.02309i	−0.687938	−	0.499816i	0.188044	−	0.982161i	$-0.439785\pi$
$101$	−6.91369	−	5.02309i	−0.687938	−	0.499816i	−0.875982	+	0.482344i	$0.839785\pi$
$102$	0.104428	−	0.0845642i	0.0103399	−	0.00837311i
$103$	0.441485	+	8.42403i	0.0435008	+	0.830044i	0.930055	+	0.367420i	$0.119759\pi$
$103$	0.441485	+	8.42403i	0.0435008	+	0.830044i	−0.886554	+	0.462624i	$0.846908\pi$
$104$	−1.01179	−	0.450477i	−0.0992140	−	0.0441729i
$105$		0			0
$106$	−0.0869356	−	0.409000i	−0.00844394	−	0.0397256i
$107$	−11.1064	−	4.26334i	−1.07369	−	0.412153i	−0.243658	−	0.969861i	$-0.578347\pi$
$107$	−11.1064	−	4.26334i	−1.07369	−	0.412153i	−0.830037	+	0.557709i	$0.811681\pi$
$108$	−9.31590	+	4.74669i	−0.896423	+	0.456750i
$109$	1.90205	+	0.618012i	0.182183	+	0.0591948i	0.398688	−	0.917087i	$-0.369466\pi$
$109$	1.90205	+	0.618012i	0.182183	+	0.0591948i	−0.216505	+	0.976282i	$0.569466\pi$
$110$		0			0
$111$	−1.20071	+	0.255219i	−0.113967	+	0.0242244i
$112$	6.79864	+	10.4690i	0.642411	+	0.989226i
$113$	−4.22215	+	1.62073i	−0.397186	+	0.152465i	−0.548759	−	0.835981i	$-0.684900\pi$
$113$	−4.22215	+	1.62073i	−0.397186	+	0.152465i	0.151573	+	0.988446i	$0.451566\pi$
$114$	−0.362775	+	0.402903i	−0.0339770	+	0.0377353i
$115$		0			0
$116$	−0.969311	+	1.33414i	−0.0899983	+	0.123872i
$117$	5.51419	+	4.46530i	0.509787	+	0.412817i
$118$	0.0107624	+	0.0401657i	0.000990756	+	0.00369755i
$119$	2.73649	+	4.73974i	0.250854	+	0.434491i
$120$		0			0
$121$	−5.40652	−	6.00455i	−0.491502	−	0.545869i
$122$	−0.582167	−	0.296629i	−0.0527069	−	0.0268555i
$123$	−7.76139	−	7.76139i	−0.699821	−	0.699821i
$124$	3.79451	−	10.4393i	0.340757	−	0.937475i
$125$		0			0
$126$	0.125138	+	0.385135i	0.0111482	+	0.0343105i
$127$	11.3096	+	0.592711i	1.00356	+	0.0525946i	0.547032	−	0.837112i	$-0.315758\pi$
$127$	11.3096	+	0.592711i	1.00356	+	0.0525946i	0.456533	+	0.889706i	$0.349091\pi$
$128$	0.352868	−	2.22792i	0.0311895	−	0.196922i
$129$	−8.68242	+	5.01280i	−0.764444	+	0.441352i
$130$		0			0
$131$	−0.368745	−	3.50838i	−0.0322174	−	0.306528i	−0.998750	−	0.0499844i	$-0.984083\pi$
$131$	−0.368745	−	3.50838i	−0.0322174	−	0.306528i	0.966533	−	0.256544i	$-0.0825838\pi$
$132$	1.48362	+	9.36719i	0.129132	+	0.815310i
$133$	−13.8966	−	17.1608i	−1.20499	−	1.48803i
$134$	0.347952	+	0.313298i	0.0300585	+	0.0270648i
$135$		0			0
$136$	0.102551	−	0.482467i	0.00879372	−	0.0413712i
$137$	11.0095	−	16.9532i	0.940606	−	1.44841i	0.0473395	−	0.998879i	$-0.484926\pi$
$137$	11.0095	−	16.9532i	0.940606	−	1.44841i	0.893267	−	0.449527i	$-0.148408\pi$
$138$	−0.181628	+	0.473158i	−0.0154612	+	0.0402779i
$139$	−1.60733	+	4.94685i	−0.136332	+	0.419586i	−0.995795	−	0.0916117i	$-0.970798\pi$
$139$	−1.60733	+	4.94685i	−0.136332	+	0.419586i	0.859463	+	0.511198i	$0.170798\pi$
$140$		0			0
$141$	−4.62134	−	10.3797i	−0.389187	−	0.874128i
$142$	0.108807	+	0.0706602i	0.00913089	+	0.00592967i
$143$	14.3172	−	9.29773i	1.19727	−	0.777515i
$144$	−2.93147	+	6.58418i	−0.244289	+	0.548682i
$145$		0			0
$146$	0.00967490	+	0.00101687i	0.000800700	+	8.41570e-5i
$147$	3.10378	−	0.491591i	0.255996	−	0.0405457i
$148$	−1.41605	+	1.74867i	−0.116398	+	0.143740i
$149$	−2.31939	−	1.33910i	−0.190012	−	0.109703i	0.401976	−	0.915650i	$-0.368323\pi$
$149$	−2.31939	−	1.33910i	−0.190012	−	0.109703i	−0.591988	+	0.805947i	$0.701657\pi$
$150$		0			0
$151$	2.99962	+	4.12862i	0.244105	+	0.335982i	0.913436	−	0.406983i	$-0.133419\pi$
$151$	2.99962	+	4.12862i	0.244105	+	0.335982i	−0.669331	+	0.742965i	$0.733419\pi$
$152$	−0.104154	+	1.98737i	−0.00844799	+	0.161197i
$153$	−1.43459	+	2.81555i	−0.115980	+	0.227624i
$154$	0.974307			0.0785119
$155$		0			0
$156$	−8.48557			−0.679389
$157$	9.14360	−	17.9453i	0.729739	−	1.43219i	−0.165318	−	0.986240i	$-0.552865\pi$
$157$	9.14360	−	17.9453i	0.729739	−	1.43219i	0.895057	−	0.445952i	$-0.147135\pi$
$158$	0.0401437	−	0.765987i	0.00319366	−	0.0609386i
$159$	−3.77083	−	5.19010i	−0.299046	−	0.411601i
$160$		0			0
$161$	−17.8770	−	10.3213i	−1.40890	−	0.813431i
$162$	0.0114898	−	0.0141887i	0.000902723	−	0.00111477i
$163$	−2.24915	+	0.356231i	−0.176167	+	0.0279022i	−0.243895	−	0.969802i	$-0.578425\pi$
$163$	−2.24915	+	0.356231i	−0.176167	+	0.0279022i	0.0677274	+	0.997704i	$0.478425\pi$
$164$	−20.0097	−	2.10310i	−1.56249	−	0.164224i
$165$		0			0
$166$	−0.0808359	+	0.181560i	−0.00627408	+	0.0140918i
$167$	−10.2865	+	6.68015i	−0.795996	+	0.516926i	−0.877402	−	0.479755i	$-0.840725\pi$
$167$	−10.2865	+	6.68015i	−0.795996	+	0.516926i	0.0814066	+	0.996681i	$0.474059\pi$
$168$	−0.813350	−	0.528196i	−0.0627513	−	0.0407512i
$169$	0.925014	+	2.07762i	0.0711549	+	0.159817i
$170$		0			0
$171$	3.93982	−	12.1255i	0.301286	−	0.927262i
$172$	−6.58582	+	17.1567i	−0.502164	+	1.30818i
$173$	2.45795	−	3.78491i	0.186875	−	0.287762i	−0.732799	−	0.680445i	$-0.761787\pi$
$173$	2.45795	−	3.78491i	0.186875	−	0.287762i	0.919674	+	0.392683i	$0.128453\pi$
$174$	0.0132684	−	0.0624230i	0.00100588	−	0.00473228i
$175$		0			0
$176$	12.8865	+	11.6030i	0.971355	+	0.874612i
$177$	0.401497	+	0.495807i	0.0301784	+	0.0372672i
$178$	0.0582147	+	0.367553i	0.00436338	+	0.0275493i
$179$	1.07512	+	10.2291i	0.0803582	+	0.764557i	0.958295	+	0.285781i	$0.0922528\pi$
$179$	1.07512	+	10.2291i	0.0803582	+	0.764557i	−0.877937	+	0.478776i	$0.841081\pi$
$180$		0			0
$181$	−19.0168	+	10.9793i	−1.41351	+	0.816088i	−0.995717	−	0.0924557i	$-0.970528\pi$
$181$	−19.0168	+	10.9793i	−1.41351	+	0.816088i	−0.417789	+	0.908544i	$0.637195\pi$
$182$	−0.136370	+	0.861008i	−0.0101084	+	0.0638221i
$183$	−10.0108	−	0.524645i	−0.740022	−	0.0387829i
$184$	0.574890	+	1.76933i	0.0423815	+	0.130437i
$185$		0			0
$186$	0.0301685	+	0.428786i	0.00221206	+	0.0314401i
$187$	5.37597	+	5.37597i	0.393130	+	0.393130i
$188$	−18.5569	−	9.45523i	−1.35340	−	0.689593i
$189$	11.0271	+	12.2468i	0.802100	+	0.890823i
$190$		0			0
$191$	8.38581	+	14.5246i	0.606776	+	1.05097i	0.991768	+	0.128047i	$0.0408707\pi$
$191$	8.38581	+	14.5246i	0.606776	+	1.05097i	−0.384992	+	0.922920i	$0.625796\pi$
$192$	−2.21952	−	8.28337i	−0.160180	−	0.597801i
$193$	−7.75743	−	6.28185i	−0.558392	−	0.452177i	0.308110	−	0.951351i	$-0.400304\pi$
$193$	−7.75743	−	6.28185i	−0.558392	−	0.452177i	−0.866502	+	0.499174i	$0.833637\pi$
$194$	0.317094	−	0.436443i	0.0227660	−	0.0313348i
$195$		0			0
$196$	3.85437	−	4.28071i	0.275312	−	0.305765i
$197$	−4.75155	+	1.82395i	−0.338534	+	0.129951i	−0.521695	−	0.853132i	$-0.674700\pi$
$197$	−4.75155	+	1.82395i	−0.338534	+	0.129951i	0.183161	+	0.983083i	$0.441367\pi$
$198$	0.306382	+	0.471786i	0.0217736	+	0.0335284i
$199$	6.18725	−	1.31514i	0.438602	−	0.0932278i	0.0166822	−	0.999861i	$-0.494690\pi$
$199$	6.18725	−	1.31514i	0.438602	−	0.0932278i	0.421920	+	0.906633i	$0.361356\pi$
$200$		0			0
$201$	6.83205	+	2.21987i	0.481896	+	0.156577i
$202$	0.540132	−	0.275211i	0.0380035	−	0.0193638i
$203$	2.42662	+	0.931491i	0.170315	+	0.0653779i
$204$	−0.785712	−	3.69648i	−0.0550108	−	0.258806i
$205$		0			0
$206$	−0.546653	−	0.243386i	−0.0380872	−	0.0169575i
$207$	−0.623766	−	11.9022i	−0.0433548	−	0.827258i
$208$	−12.0574	+	9.76391i	−0.836032	+	0.677005i
$209$	−24.8165	−	18.0303i	−1.71660	−	1.24718i
$210$		0			0
$211$	1.17473	−	2.03470i	0.0808719	−	0.140074i	−0.822753	−	0.568399i	$-0.807563\pi$
$211$	1.17473	−	2.03470i	0.0808719	−	0.140074i	0.903625	+	0.428325i	$0.140896\pi$
$212$	−11.3588	−	3.04358i	−0.780125	−	0.209034i
$213$	1.96601	+	0.311385i	0.134708	+	0.0213357i
$214$	0.627135	−	0.564675i	0.0428701	−	0.0386004i
$215$		0			0
$216$		−	1.48521i		−	0.101056i
$217$	−17.4414	−	1.51839i	−1.18400	−	0.103075i
$218$	−0.100315	+	0.100315i	−0.00679419	+	0.00679419i
$219$	0.141951	−	0.0461225i	0.00959213	−	0.00311667i
$220$		0			0
$221$	−5.50327	+	3.99836i	−0.370190	+	0.268959i
$222$	0.0225371	−	0.0841095i	0.00151259	−	0.00564506i
$223$	13.8894	−	3.72164i	0.930100	−	0.249220i	0.238203	−	0.971215i	$-0.423442\pi$
$223$	13.8894	−	3.72164i	0.930100	−	0.249220i	0.691897	+	0.721996i	$0.256775\pi$
$224$	−2.65304	+	0.278846i	−0.177264	+	0.0186312i
$225$		0			0
$226$	0.0335338	−	0.319053i	0.00223063	−	0.0212231i
$227$	−15.6647	+	0.820953i	−1.03970	+	0.0544886i	−0.564538	−	0.825407i	$-0.690945\pi$
$227$	−15.6647	+	0.820953i	−1.03970	+	0.0544886i	−0.475166	+	0.879896i	$0.657612\pi$
$228$	5.46419	+	14.2347i	0.361875	+	0.942716i
$229$	2.87355	+	0.610792i	0.189890	+	0.0403623i	0.301875	−	0.953348i	$-0.402388\pi$
$229$	2.87355	+	0.610792i	0.189890	+	0.0403623i	−0.111985	+	0.993710i	$0.535721\pi$
$230$		0			0
$231$	13.6560	−	6.08006i	0.898501	−	0.400039i
$232$	−0.106349	−	0.208723i	−0.00698218	−	0.0137033i
$233$	2.07455	+	4.07154i	0.135908	+	0.266735i	0.948923	−	0.315508i	$-0.102175\pi$
$233$	2.07455	+	4.07154i	0.135908	+	0.266735i	−0.813014	+	0.582244i	$0.802175\pi$
$234$	−0.459807	+	0.204719i	−0.0300585	+	0.0133829i
$235$		0			0
$236$	1.14389	+	0.243142i	0.0744611	+	0.0158272i
$237$	−4.21740	−	10.9867i	−0.273950	−	0.713663i
$238$	−0.387699	+	0.0203185i	−0.0251308	+	0.00131705i
$239$	0.653633	−	6.21891i	0.0422800	−	0.402268i	−0.952831	−	0.303502i	$-0.901844\pi$
$239$	0.653633	−	6.21891i	0.0422800	−	0.402268i	0.995111	−	0.0987654i	$-0.0314893\pi$
$240$		0			0
$241$	21.8619	−	2.29778i	1.40825	−	0.148013i	0.630305	−	0.776348i	$-0.282930\pi$
$241$	21.8619	−	2.29778i	1.40825	−	0.148013i	0.777943	+	0.628335i	$0.216263\pi$
$242$	0.553627	−	0.148344i	0.0355885	−	0.00953591i
$243$	−3.99685	+	14.9165i	−0.256398	+	0.956891i
$244$	−14.8660	+	10.8008i	−0.951697	+	0.691449i
$245$		0			0
$246$	0.740504	−	0.240604i	0.0472128	−	0.0153404i
$247$	19.4071	−	19.4071i	1.23484	−	1.23484i
$248$	1.07657	+	1.15349i	0.0683625	+	0.0732468i
$249$			3.04923i			0.193237i
$250$		0			0
$251$	−8.29972	+	7.47310i	−0.523873	+	0.471698i	−0.888124	−	0.459603i	$-0.847992\pi$
$251$	−8.29972	+	7.47310i	−0.523873	+	0.471698i	0.364251	+	0.931301i	$0.381325\pi$
$252$	11.2485	+	1.78159i	0.708591	+	0.112230i
$253$	−27.6984	−	7.42177i	−1.74138	−	0.466602i
$254$	−0.401679	+	0.695729i	−0.0252036	+	0.0436539i
$255$		0			0
$256$	−12.6198	−	9.16884i	−0.788739	−	0.573053i
$257$	13.4951	−	10.9282i	0.841804	−	0.681679i	−0.108128	−	0.994137i	$-0.534486\pi$
$257$	13.4951	−	10.9282i	0.841804	−	0.681679i	0.949932	+	0.312458i	$0.101152\pi$
$258$	−0.0372200	−	0.710201i	−0.00231722	−	0.0442152i
$259$	3.23997	+	1.44253i	0.201322	+	0.0896342i
$260$		0			0
$261$	0.312023	+	1.46795i	0.0193137	+	0.0908640i
$262$	0.233620	+	0.0896784i	0.0144331	+	0.00554035i
$263$	22.6855	−	11.5588i	1.39885	−	0.712749i	0.418168	−	0.908370i	$-0.362672\pi$
$263$	22.6855	−	11.5588i	1.39885	−	0.712749i	0.980680	+	0.195621i	$0.0626722\pi$
$264$	−1.28127	−	0.416309i	−0.0788566	−	0.0256220i
$265$		0			0
$266$	1.53217	−	0.325673i	0.0939434	−	0.0199683i
$267$	3.10963	+	4.78840i	0.190306	+	0.293045i
$268$	12.2933	−	4.71894i	0.750931	−	0.288255i
$269$	5.25465	−	5.83588i	0.320382	−	0.355820i	−0.561344	−	0.827583i	$-0.689715\pi$
$269$	5.25465	−	5.83588i	0.320382	−	0.355820i	0.881726	+	0.471763i	$0.156382\pi$
$270$		0			0
$271$	−6.45006	+	8.87774i	−0.391813	+	0.539285i	−0.958666	−	0.284535i	$-0.908161\pi$
$271$	−6.45006	+	8.87774i	−0.391813	+	0.539285i	0.566853	+	0.823819i	$0.308161\pi$
$272$	−5.36980	−	4.34838i	−0.325592	−	0.263659i
$273$	3.46164	+	12.9190i	0.209508	+	0.781895i
$274$	0.716961	+	1.24181i	0.0433132	+	0.0750207i
$275$		0			0
$276$	9.53751	+	10.5925i	0.574090	+	0.637592i
$277$	−6.95592	−	3.54422i	−0.417941	−	0.212951i	0.232358	−	0.972630i	$-0.425356\pi$
$277$	−6.95592	−	3.54422i	−0.417941	−	0.212951i	−0.650298	+	0.759679i	$0.725356\pi$
$278$	−0.260900	−	0.260900i	−0.0156477	−	0.0156477i
$279$	−4.74941	−	8.92310i	−0.284340	−	0.534212i
$280$		0			0
$281$	−2.64976	−	8.15512i	−0.158071	−	0.486494i	0.840388	−	0.541986i	$-0.182327\pi$
$281$	−2.64976	−	8.15512i	−0.158071	−	0.486494i	−0.998459	+	0.0554920i	$0.982327\pi$
$282$	0.804870	+	0.0421814i	0.0479293	+	0.00251187i
$283$	2.42354	−	15.3017i	0.144065	−	0.909589i	−0.804717	−	0.593658i	$-0.797683\pi$
$283$	2.42354	−	15.3017i	0.144065	−	0.909589i	0.948782	−	0.315931i	$-0.102317\pi$
$284$	3.15985	−	1.82434i	0.187502	−	0.108255i
$285$		0			0
$286$	0.126581	+	1.20434i	0.00748490	+	0.0712141i
$287$	4.96092	+	31.3220i	0.292834	+	1.84888i
$288$	−0.969305	−	1.19699i	−0.0571168	−	0.0705334i
$289$	10.3821	+	9.34811i	0.610713	+	0.549889i
$290$		0			0
$291$	1.72087	−	8.09604i	0.100879	−	0.474598i
$292$	0.149008	−	0.229453i	0.00872005	−	0.0134277i
$293$	−9.06430	+	23.6133i	−0.529542	+	1.37950i	0.364367	+	0.931255i	$0.381285\pi$
$293$	−9.06430	+	23.6133i	−0.529542	+	1.37950i	−0.893909	+	0.448248i	$0.852048\pi$
$294$	−0.0688843	+	0.212004i	−0.00401741	+	0.0123643i
$295$		0			0
$296$	−0.130006	−	0.291998i	−0.00755643	−	0.0169720i
$297$	19.1994	+	12.4682i	1.11406	+	0.723480i
$298$	0.159331	−	0.103471i	0.00922982	−	0.00599392i
$299$	10.4356	−	23.4386i	0.603504	−	1.35549i
$300$		0			0
$301$	28.8071	+	3.02775i	1.66042	+	0.174517i
$302$	−0.357547	+	0.0566299i	−0.0205745	+	0.00325869i
$303$	5.85315	−	7.22804i	0.336255	−	0.415240i
$304$	24.1434	+	13.9392i	1.38472	+	0.799467i
$305$		0			0
$306$	−0.131755	−	0.181345i	−0.00753194	−	0.0103668i
$307$	−0.627633	+	11.9760i	−0.0358209	+	0.683504i	0.920421	+	0.390928i	$0.127846\pi$
$307$	−0.627633	+	11.9760i	−0.0358209	+	0.683504i	−0.956242	+	0.292576i	$0.905488\pi$
$308$	12.4398	−	24.4144i	0.708821	−	1.39114i
$309$	−9.18080			−0.522278
$310$		0			0
$311$	−12.9477			−0.734199			−0.367099	−	0.930182i	$-0.619649\pi$
$311$	−12.9477			−0.734199			−0.367099	+	0.930182i	$0.619649\pi$
$312$	0.547232	−	1.07400i	0.0309809	−	0.0608035i
$313$	−1.75047	+	33.4009i	−0.0989424	+	1.88793i	0.276394	+	0.961044i	$0.410861\pi$
$313$	−1.75047	+	33.4009i	−0.0989424	+	1.88793i	−0.375336	+	0.926889i	$0.622473\pi$
$314$	0.839761	+	1.15583i	0.0473904	+	0.0652274i
$315$		0			0
$316$	−18.6817	−	10.7859i	−1.05093	−	0.606754i
$317$	−7.58334	+	9.36464i	−0.425923	+	0.525971i	−0.944258	−	0.329207i	$-0.893219\pi$
$317$	−7.58334	+	9.36464i	−0.425923	+	0.525971i	0.518335	+	0.855178i	$0.326552\pi$
$318$	0.449474	−	0.0711896i	0.0252052	−	0.00399212i
$319$	3.59097	+	0.377426i	0.201055	+	0.0211318i
$320$		0			0
$321$	5.26623	−	11.8281i	0.293932	−	0.660182i
$322$	1.22807	−	0.797515i	0.0684374	−	0.0444438i
$323$	10.2511	+	6.65713i	0.570385	+	0.370413i
$324$	−0.208844	−	0.469072i	−0.0116025	−	0.0260596i
$325$		0			0
$326$	0.0499170	−	0.153629i	0.00276465	−	0.00850870i
$327$	−0.780026	+	2.03204i	−0.0431355	+	0.112372i
$328$	1.55660	−	2.39696i	0.0859490	−	0.132350i
$329$	−6.82510	+	32.1096i	−0.376280	+	1.77026i
$330$		0			0
$331$	−4.13010	−	3.71876i	−0.227011	−	0.204402i	0.547774	−	0.836626i	$-0.315475\pi$
$331$	−4.13010	−	3.71876i	−0.227011	−	0.204402i	−0.774785	+	0.632225i	$0.782142\pi$
$332$	3.51748	+	4.34373i	0.193047	+	0.238393i
$333$	0.320333	+	2.02250i	0.0175541	+	0.110832i
$334$	−0.0909450	−	0.865283i	−0.00497629	−	0.0473462i
$335$		0			0
$336$	−11.7655	+	6.79280i	−0.641859	+	0.370577i
$337$	−0.506327	+	3.19682i	−0.0275814	+	0.174142i	−0.997634	−	0.0687544i	$-0.978098\pi$
$337$	−0.506327	+	3.19682i	−0.0275814	+	0.174142i	0.970052	+	0.242896i	$0.0780975\pi$
$338$	−0.161104	−	0.00844309i	−0.00876289	−	0.000459244i
$339$	−1.52100	−	4.68116i	−0.0826094	−	0.254246i
$340$		0			0
$341$	−23.9490	+	4.23345i	−1.29691	+	0.229254i
$342$	0.639508	+	0.639508i	0.0345806	+	0.0345806i
$343$	11.5223	+	5.87090i	0.622145	+	0.316999i
$344$	−1.74677	−	1.93998i	−0.0941795	−	0.104597i
$345$		0			0
$346$	0.160067	+	0.277244i	0.00860524	+	0.0149047i
$347$	−3.81647	−	14.2433i	−0.204879	−	0.764618i	−0.989486	−	0.144626i	$-0.953802\pi$
$347$	−3.81647	−	14.2433i	−0.204879	−	0.764618i	0.784608	−	0.619993i	$-0.212864\pi$
$348$	−1.39480	−	1.12949i	−0.0747692	−	0.0605469i
$349$	18.9330	−	26.0590i	1.01346	−	1.39491i	0.0967705	−	0.995307i	$-0.469149\pi$
$349$	18.9330	−	26.0590i	1.01346	−	1.39491i	0.916689	−	0.399601i	$-0.130851\pi$
$350$		0			0
$351$	−13.7056	+	15.2216i	−0.731551	+	0.812470i
$352$	−3.45963	+	1.32803i	−0.184399	+	0.0707841i
$353$	−4.26423	−	6.56633i	−0.226962	−	0.349491i	0.706783	−	0.707431i	$-0.250146\pi$
$353$	−4.26423	−	6.56633i	−0.226962	−	0.349491i	−0.933745	+	0.357940i	$0.883479\pi$
$354$	−0.0442671	+	0.00940927i	−0.00235277	+	0.000500097i
$355$		0			0
$356$	9.95351	+	3.23409i	0.527535	+	0.171407i
$357$	−5.30726	+	2.70418i	−0.280890	+	0.143121i
$358$	−0.681146	−	0.261467i	−0.0359997	−	0.0138190i
$359$	−3.43650	−	16.1675i	−0.181371	−	0.853286i	−0.970884	−	0.239551i	$-0.923000\pi$
$359$	−3.43650	−	16.1675i	−0.181371	−	0.853286i	0.789512	−	0.613735i	$-0.210334\pi$
$360$		0			0
$361$	−27.6953	−	12.3307i	−1.45765	−	0.648987i
$362$	−0.0815217	−	1.55553i	−0.00428468	−	0.0817566i
$363$	6.83400	−	5.53407i	0.358692	−	0.290463i
$364$	19.8342	+	14.4104i	1.03959	+	0.755309i
$365$		0			0
$366$	0.355551	−	0.615833i	0.0185850	−	0.0321901i
$367$	−2.68949	−	0.720646i	−0.140390	−	0.0376174i	0.187940	−	0.982181i	$-0.439819\pi$
$367$	−2.68949	−	0.720646i	−0.140390	−	0.0376174i	−0.328330	+	0.944563i	$0.606486\pi$
$368$	25.7404	+	4.07688i	1.34181	+	0.212522i
$369$	−13.6070	+	12.2518i	−0.708351	+	0.637802i
$370$		0			0
$371$			18.5350i			0.962291i
$372$	11.1298	+	4.71868i	0.577053	+	0.244652i
$373$	0.754454	−	0.754454i	0.0390641	−	0.0390641i	−0.687305	−	0.726369i	$-0.741206\pi$
$373$	0.754454	−	0.754454i	0.0390641	−	0.0390641i	0.726369	+	0.687305i	$0.241206\pi$
$374$	−0.512914	+	0.166656i	−0.0265221	+	0.00861756i
$375$		0			0
$376$	2.39346	−	1.73895i	0.123433	−	0.0896796i
$377$	−0.836151	+	3.12056i	−0.0430640	+	0.160717i
$378$	−1.12917	+	0.302560i	−0.0580782	+	0.0155620i
$379$	−0.0287978	+	0.00302677i	−0.00147924	+	0.000155475i	−0.105268	−	0.994444i	$-0.533570\pi$
$379$	−0.0287978	+	0.00302677i	−0.00147924	+	0.000155475i	0.103789	+	0.994599i	$0.466903\pi$
$380$		0			0
$381$	−1.28838	+	12.2581i	−0.0660055	+	0.628001i
$382$	−1.18808	+	0.0622647i	−0.0607875	+	0.00318574i
$383$	8.53091	+	22.2238i	0.435909	+	1.13558i	0.959025	+	0.283321i	$0.0914362\pi$
$383$	8.53091	+	22.2238i	0.435909	+	1.13558i	−0.523116	+	0.852262i	$0.675230\pi$
$384$	2.40132	+	0.510416i	0.122542	+	0.0260471i
$385$		0			0
$386$	0.646863	−	0.288002i	0.0329244	−	0.0146589i
$387$	7.59260	+	14.9013i	0.385954	+	0.757477i
$388$	−6.88788	−	13.5182i	−0.349679	−	0.686284i
$389$	14.1713	−	6.30947i	0.718514	−	0.319903i	−0.0147088	−	0.999892i	$-0.504682\pi$
$389$	14.1713	−	6.30947i	0.718514	−	0.319903i	0.733222	+	0.679989i	$0.238015\pi$
$390$		0			0
$391$	11.1766	+	2.37566i	0.565226	+	0.120142i
$392$	0.293235	+	0.763902i	0.0148106	+	0.0385829i
$393$	3.83408	−	0.200936i	0.193404	−	0.0101359i
$394$	0.0377385	−	0.359058i	0.00190124	−	0.0180891i
$395$		0			0
$396$	15.7340	−	1.65370i	0.790661	−	0.0831018i
$397$	−5.81855	+	1.55908i	−0.292025	+	0.0782477i	−0.401857	−	0.915702i	$-0.631635\pi$
$397$	−5.81855	+	1.55908i	−0.292025	+	0.0782477i	0.109833	+	0.993950i	$0.464969\pi$
$398$	−0.116133	+	0.433414i	−0.00582122	+	0.0217251i
$399$	19.4428	−	14.1260i	0.973358	−	0.707186i
$400$		0			0
$401$	34.1154	−	11.0848i	1.70364	−	0.553546i	0.714386	−	0.699752i	$-0.246706\pi$
$401$	34.1154	−	11.0848i	1.70364	−	0.553546i	0.989254	+	0.146205i	$0.0467060\pi$
$402$	−0.360327	+	0.360327i	−0.0179715	+	0.0179715i
$403$	−0.389100	−	21.7566i	−0.0193824	−	1.08377i
$404$		−	17.0486i		−	0.848199i
$405$		0			0
$406$	−0.137022	+	0.123375i	−0.00680028	+	0.00612300i
$407$	4.86606	+	0.770709i	0.241202	+	0.0382026i
$408$	0.518528	+	0.138939i	0.0256710	+	0.00687851i
$409$	−10.0701	+	17.4419i	−0.497933	+	0.862446i	−0.999997	−	0.00238475i	$-0.999241\pi$
$409$	−10.0701	+	17.4419i	−0.497933	+	0.862446i	0.502064	+	0.864831i	$0.332574\pi$
$410$		0			0
$411$	17.7985	+	12.9313i	0.877933	+	0.637856i
$412$	−13.0784	+	10.5907i	−0.644326	+	0.521765i
$413$	−0.0964686	−	1.84073i	−0.00474691	−	0.0905765i
$414$	0.772358	+	0.343876i	0.0379593	+	0.0169006i
$415$		0			0
$416$	−0.689363	−	3.24320i	−0.0337988	−	0.159011i
$417$	−5.28493	−	2.02870i	−0.258804	−	0.0993457i
$418$	1.93879	−	0.987863i	0.0948294	−	0.0483180i
$419$	−11.7746	−	3.82578i	−0.575225	−	0.186902i	0.00693557	−	0.999976i	$-0.497792\pi$
$419$	−11.7746	−	3.82578i	−0.575225	−	0.186902i	−0.582160	+	0.813074i	$0.697792\pi$
$420$		0			0
$421$	21.0885	−	4.48249i	1.02779	−	0.218463i	0.336988	−	0.941509i	$-0.390592\pi$
$421$	21.0885	−	4.48249i	1.02779	−	0.218463i	0.690800	+	0.723046i	$0.257258\pi$
$422$	0.0907704	+	0.139774i	0.00441864	+	0.00680410i
$423$	−17.6946	+	6.79231i	−0.860340	+	0.330253i
$424$	1.11775	−	1.24138i	0.0542825	−	0.0602869i
$425$		0			0
$426$	−0.0829946	+	0.114232i	−0.00402110	+	0.00553457i
$427$	22.5084	+	18.2269i	1.08926	+	0.882062i
$428$	−6.14261	−	22.9245i	−0.296914	−	1.10810i
$429$	9.28974	+	16.0903i	0.448513	+	0.776847i
$430$		0			0
$431$	−15.6686	−	17.4017i	−0.754728	−	0.838211i	0.236326	−	0.971674i	$-0.424057\pi$
$431$	−15.6686	−	17.4017i	−0.754728	−	0.838211i	−0.991054	+	0.133463i	$0.957390\pi$
$432$	−18.5379	−	9.44554i	−0.891906	−	0.454449i
$433$	6.71039	+	6.71039i	0.322481	+	0.322481i	0.849718	−	0.527237i	$-0.176772\pi$
$433$	6.71039	+	6.71039i	0.322481	+	0.322481i	−0.527237	+	0.849718i	$0.676772\pi$
$434$	0.657657	−	1.05348i	0.0315686	−	0.0505685i
$435$		0			0
$436$	1.23291	+	3.79452i	0.0590459	+	0.181725i
$437$	−46.0386	−	2.41278i	−2.20233	−	0.115419i
$438$	−0.00165626	+	0.0104572i	−7.91394e−5	+	0.000499666i
$439$	−1.70220	+	0.982765i	−0.0812415	+	0.0469048i	−0.540070	−	0.841620i	$-0.681602\pi$
$439$	−1.70220	+	0.982765i	−0.0812415	+	0.0469048i	0.458829	+	0.888525i	$0.348269\pi$
$440$		0			0
$441$	−0.547949	−	5.21338i	−0.0260928	−	0.248256i
$442$	−0.0754852	−	0.476595i	−0.00359046	−	0.0226693i
$443$	−1.95404	−	2.41304i	−0.0928393	−	0.114647i	0.728609	−	0.684930i	$-0.240167\pi$
$443$	−1.95404	−	2.41304i	−0.0928393	−	0.114647i	−0.821449	+	0.570283i	$0.806834\pi$
$444$	−1.81989	−	1.63863i	−0.0863680	−	0.0777661i
$445$		0			0
$446$	−0.212072	+	0.997721i	−0.0100419	+	0.0472435i
$447$	1.58751	−	2.44456i	0.0750869	−	0.115624i
$448$	−8.87908	+	23.1308i	−0.419497	+	1.09283i
$449$	2.12388	−	6.53664i	0.100232	−	0.308483i	−0.888350	−	0.459167i	$-0.848148\pi$
$449$	2.12388	−	6.53664i	0.100232	−	0.308483i	0.988582	+	0.150685i	$0.0481478\pi$
$450$		0			0
$451$	17.9181	+	40.2446i	0.843728	+	1.89504i
$452$	−7.56674	−	4.91390i	−0.355910	−	0.231130i
$453$	−4.65805	+	3.02497i	−0.218854	+	0.142125i
$454$	0.452583	−	1.01652i	0.0212408	−	0.0477075i
$455$		0			0
$456$	−2.15404	−	0.226399i	−0.100872	−	0.0106021i
$457$	−4.64490	+	0.735680i	−0.217279	+	0.0344137i	−0.264125	−	0.964488i	$-0.585083\pi$
$457$	−4.64490	+	0.735680i	−0.217279	+	0.0344137i	0.0468456	+	0.998902i	$0.485083\pi$
$458$	−0.131145	+	0.161951i	−0.00612802	+	0.00756748i
$459$	−7.89990	−	4.56101i	−0.368736	−	0.212890i
$460$		0			0
$461$	−11.7940	−	16.2331i	−0.549302	−	0.756049i	0.440615	−	0.897696i	$-0.354760\pi$
$461$	−11.7940	−	16.2331i	−0.549302	−	0.756049i	−0.989917	+	0.141647i	$0.954760\pi$
$462$	−0.0554959	+	1.05893i	−0.00258190	+	0.0492657i
$463$	−1.44162	+	2.82935i	−0.0669979	+	0.131491i	−0.922077	−	0.387007i	$-0.873509\pi$
$463$	−1.44162	+	2.82935i	−0.0669979	+	0.131491i	0.855079	+	0.518498i	$0.173509\pi$
$464$	−3.28156			−0.152343
$465$		0			0
$466$	−0.324149			−0.0150159
$467$	10.7271	−	21.0530i	0.496389	−	0.974218i	−0.497874	−	0.867250i	$-0.665886\pi$
$467$	10.7271	−	21.0530i	0.496389	−	0.974218i	0.994262	−	0.106968i	$-0.0341143\pi$
$468$	−0.740824	+	14.1358i	−0.0342446	+	0.653426i
$469$	−12.1994	−	16.7911i	−0.563317	−	0.775339i
$470$		0			0
$471$	18.9831	+	10.9599i	0.874693	+	0.505005i
$472$	−0.104543	+	0.129100i	−0.00481200	+	0.00594233i
$473$	39.7423	−	6.29456i	1.82735	−	0.289424i
$474$	0.830226	+	0.0872603i	0.0381335	+	0.00400800i
$475$		0			0
$476$	−4.44092	+	9.97448i	−0.203549	+	0.457179i
$477$	−8.97518	+	5.82855i	−0.410945	+	0.266871i
$478$	0.372013	+	0.241588i	0.0170155	+	0.0110500i
$479$	12.0698	+	27.1092i	0.551482	+	1.23865i	0.947308	+	0.320324i	$0.103792\pi$
$479$	12.0698	+	27.1092i	0.551482	+	1.23865i	−0.395826	+	0.918326i	$0.629542\pi$
$480$		0			0
$481$	−1.36217	+	4.19233i	−0.0621097	+	0.191154i
$482$	−0.558816	+	1.45577i	−0.0254534	+	0.0663083i
$483$	12.2359	−	18.8417i	0.556755	−	0.857327i
$484$	3.35137	−	15.7669i	0.152335	−	0.716679i
$485$		0			0
$486$	−0.814070	−	0.732992i	−0.0369270	−	0.0332492i
$487$	4.21927	+	5.21037i	0.191193	+	0.236104i	0.863724	−	0.503965i	$-0.168126\pi$
$487$	4.21927	+	5.21037i	0.191193	+	0.236104i	−0.672531	+	0.740069i	$0.734793\pi$
$488$	−0.408331	−	2.57810i	−0.0184843	−	0.116705i
$489$	−0.259059	−	2.46478i	−0.0117151	−	0.111461i
$490$		0			0
$491$	9.78893	−	5.65164i	0.441768	−	0.255055i	−0.262579	−	0.964910i	$-0.584573\pi$
$491$	9.78893	−	5.65164i	0.441768	−	0.255055i	0.704347	+	0.709856i	$0.251240\pi$
$492$	3.42549	−	21.6277i	0.154433	−	0.975052i
$493$	−1.43680	−	0.0752995i	−0.0647102	−	0.00339132i
$494$	0.601622	+	1.85160i	0.0270683	+	0.0833075i
$495$		0			0
$496$	21.2442	−	6.10155i	0.953895	−	0.273968i
$497$	−4.06654	−	4.06654i	−0.182409	−	0.182409i
$498$	−0.192725	−	0.0981980i	−0.00863619	−	0.00440036i
$499$	−6.18041	−	6.86404i	−0.276673	−	0.307276i	0.588753	−	0.808313i	$-0.299619\pi$
$499$	−6.18041	−	6.86404i	−0.276673	−	0.307276i	−0.865426	+	0.501036i	$0.832952\pi$
$500$		0			0
$501$	−6.67441	−	11.5604i	−0.298191	−	0.516481i
$502$	−0.205047	−	0.765244i	−0.00915168	−	0.0341545i
$503$	−5.61310	−	4.54540i	−0.250276	−	0.202669i	0.495970	−	0.868339i	$-0.334812\pi$
$503$	−5.61310	−	4.54540i	−0.250276	−	0.202669i	−0.746246	+	0.665670i	$0.768146\pi$
$504$	−0.950908	+	1.30881i	−0.0423568	+	0.0582992i
$505$		0			0
$506$	1.36109	−	1.51165i	0.0605080	−	0.0672010i
$507$	−2.31075	+	0.887012i	−0.102624	+	0.0393936i
$508$	12.3052	+	18.9483i	0.545954	+	0.840695i
$509$	23.3136	−	4.95545i	1.03336	−	0.219646i	0.340138	−	0.940375i	$-0.389526\pi$
$509$	23.3136	−	4.95545i	1.03336	−	0.219646i	0.693217	+	0.720729i	$0.256193\pi$
$510$		0			0
$511$	−0.410122	−	0.133257i	−0.0181427	−	0.00589493i
$512$	5.00560	−	2.55048i	0.221218	−	0.112716i
$513$	34.3601	+	13.1896i	1.51704	+	0.582336i
$514$	0.256106	+	1.20489i	0.0112964	+	0.0531452i
$515$		0			0
$516$	−18.2716	−	8.13503i	−0.804362	−	0.358125i
$517$	2.38659	+	45.5388i	0.104962	+	2.00280i
$518$	−0.195515	+	0.158325i	−0.00859043	+	0.00695639i
$519$	3.97363	+	2.88701i	0.174423	+	0.126726i
$520$		0			0
$521$	−12.3861	+	21.4533i	−0.542643	+	0.939885i	0.456108	+	0.889924i	$0.349243\pi$
$521$	−12.3861	+	21.4533i	−0.542643	+	0.939885i	−0.998751	+	0.0499607i	$0.984090\pi$
$522$	−0.102830	−	0.0275531i	−0.00450073	−	0.00120597i
$523$	−22.6713	−	3.59079i	−0.991348	−	0.157014i	−0.360366	−	0.932811i	$-0.617348\pi$
$523$	−22.6713	−	3.59079i	−0.991348	−	0.157014i	−0.630983	+	0.775797i	$0.717348\pi$
$524$	5.23000	−	4.70911i	0.228473	−	0.205718i
$525$		0			0
$526$			1.80607i			0.0787483i
$527$	9.44158	−	2.18403i	0.411282	−	0.0951378i
$528$	−13.3448	+	13.3448i	−0.580756	+	0.580756i
$529$	−19.1132	+	6.21026i	−0.831010	+	0.270011i
$530$		0			0
$531$	0.860997	−	0.625551i	0.0373641	−	0.0271466i
$532$	11.4017	−	42.5516i	0.494325	−	1.84485i
$533$	−38.0726	+	10.2015i	−1.64911	+	0.441877i
$534$	−0.402791	+	0.0423351i	−0.0174305	+	0.00183202i
$535$		0			0
$536$	−0.195521	+	1.86026i	−0.00844523	+	0.0803510i
$537$	−11.1787	+	0.585851i	−0.482397	+	0.0252813i
$538$	0.199631	+	0.520057i	0.00860672	+	0.0224213i
$539$	−12.3367	−	2.62225i	−0.531379	−	0.112948i
$540$		0			0
$541$	−37.6189	+	16.7490i	−1.61736	+	0.720097i	−0.997890	−	0.0649202i	$-0.979321\pi$
$541$	−37.6189	+	16.7490i	−1.61736	+	0.720097i	−0.619474	+	0.785017i	$0.712654\pi$
$542$	−0.353393	−	0.693573i	−0.0151795	−	0.0297915i
$543$	−10.8497	−	21.2938i	−0.465606	−	0.913803i
$544$	1.34897	−	0.600601i	0.0578367	−	0.0257505i
$545$		0			0
$546$	−0.928019	−	0.197257i	−0.0397155	−	0.00844180i
$547$	−6.16273	−	16.0545i	−0.263499	−	0.686440i	−0.999951	−	0.00994870i	$-0.996833\pi$
$547$	−6.16273	−	16.0545i	−0.263499	−	0.686440i	0.736451	−	0.676491i	$-0.236500\pi$
$548$	40.2717	−	2.11055i	1.72032	−	0.0901582i
$549$	−1.74797	+	16.6308i	−0.0746015	+	0.709786i
$550$		0			0
$551$	5.77322	−	0.606790i	0.245947	−	0.0258501i
$552$	−1.95574	+	0.524040i	−0.0832419	+	0.0223046i
$553$	−8.80010	+	32.8424i	−0.374218	+	1.39660i
$554$	0.448020	−	0.325506i	0.0190346	−	0.0138294i
$555$		0			0
$556$	−9.86881	+	3.20657i	−0.418531	+	0.135989i
$557$	−16.6477	+	16.6477i	−0.705388	+	0.705388i	−0.965562	−	0.260174i	$-0.916220\pi$
$557$	−16.6477	+	16.6477i	−0.705388	+	0.705388i	0.260174	+	0.965562i	$0.416220\pi$
$558$	0.716931	−	0.0128217i	0.0303501	−	0.000542787i
$559$			36.0018i			1.52272i
$560$		0			0
$561$	−6.14908	+	5.53666i	−0.259614	+	0.233758i
$562$	0.600773	+	0.0951531i	0.0253421	+	0.00401379i
$563$	−15.4538	−	4.14083i	−0.651300	−	0.174515i	−0.0819834	−	0.996634i	$-0.526125\pi$
$563$	−15.4538	−	4.14083i	−0.651300	−	0.174515i	−0.569317	+	0.822118i	$0.692792\pi$
$564$	11.3334	−	19.6300i	0.477223	−	0.826574i
$565$		0			0
$566$	0.889084	+	0.645957i	0.0373710	+	0.0271516i
$567$	−0.628952	+	0.509315i	−0.0264135	+	0.0213892i
$568$	0.0271256	+	0.517587i	0.00113817	+	0.0217175i
$569$	34.1914	+	15.2230i	1.43338	+	0.638181i	0.968911	−	0.247409i	$-0.0795791\pi$
$569$	34.1914	+	15.2230i	1.43338	+	0.638181i	0.464467	+	0.885590i	$0.346246\pi$
$570$		0			0
$571$	−3.81748	−	17.9598i	−0.159757	−	0.751596i	−0.982956	−	0.183843i	$-0.941146\pi$
$571$	−3.81748	−	17.9598i	−0.159757	−	0.751596i	0.823199	−	0.567753i	$-0.192187\pi$
$572$	31.7948	+	12.2049i	1.32941	+	0.510311i
$573$	−16.2638	+	8.28680i	−0.679429	+	0.346186i
$574$	−2.13945	−	0.695151i	−0.0892991	−	0.0290150i
$575$		0			0
$576$	−13.9927	+	2.97424i	−0.583029	+	0.123927i
$577$	13.8136	+	21.2711i	0.575069	+	0.885529i	0.999804	−	0.0197889i	$-0.00629940\pi$
$577$	13.8136	+	21.2711i	0.575069	+	0.885529i	−0.424735	+	0.905318i	$0.639633\pi$
$578$	−0.925191	+	0.355147i	−0.0384829	+	0.0147722i
$579$	7.26928	−	8.07336i	0.302101	−	0.335517i
$580$		0			0
$581$	5.17826	−	7.12726i	0.214830	−	0.295689i
$582$	0.456286	+	0.369493i	0.0189137	+	0.0153160i
$583$	6.66403	+	24.8705i	0.275996	+	1.03003i
$584$	0.0194319	+	0.0336570i	0.000804098	+	0.00139274i
$585$		0			0
$586$	−1.20056	−	1.33335i	−0.0495945	−	0.0550803i
$587$	34.5874	+	17.6232i	1.42758	+	0.727386i	0.985513	−	0.169598i	$-0.0542470\pi$
$587$	34.5874	+	17.6232i	1.42758	+	0.727386i	0.442062	+	0.896984i	$0.354247\pi$
$588$	4.43295	+	4.43295i	0.182812	+	0.182812i
$589$	−36.2465	+	14.6626i	−1.49351	+	0.604164i
$590$		0			0
$591$	−1.71171	−	5.26812i	−0.0704105	−	0.216701i
$592$	−4.47143	−	0.234338i	−0.183775	−	0.00963122i
$593$	1.41530	−	8.93582i	0.0581192	−	0.366950i	−0.941438	−	0.337187i	$-0.890525\pi$
$593$	1.41530	−	8.93582i	0.0581192	−	0.366950i	0.999557	−	0.0297635i	$-0.00947541\pi$
$594$	−1.40635	+	0.811956i	−0.0577032	+	0.0333150i
$595$		0			0
$596$	−0.558488	−	5.31366i	−0.0228766	−	0.217656i
$597$	1.07694	+	6.79952i	0.0440761	+	0.278286i
$598$	1.14536	+	1.41440i	0.0468371	+	0.0578390i
$599$	−8.90857	−	8.02132i	−0.363994	−	0.327742i	0.466757	−	0.884386i	$-0.345422\pi$
$599$	−8.90857	−	8.02132i	−0.363994	−	0.327742i	−0.830751	+	0.556644i	$0.812089\pi$
$600$		0			0
$601$	1.72168	−	8.09988i	0.0702289	−	0.330401i	−0.928982	−	0.370125i	$-0.879315\pi$
$601$	1.72168	−	8.09988i	0.0702289	−	0.330401i	0.999211	+	0.0397246i	$0.0126481\pi$
$602$	−1.11908	+	1.72323i	−0.0456103	+	0.0702337i
$603$	4.29445	−	11.1874i	0.174884	−	0.455588i
$604$	−3.14605	+	9.68254i	−0.128011	+	0.393977i
$605$		0			0
$606$	0.268347	+	0.602718i	0.0109009	+	0.0244838i
$607$	17.4236	+	11.3150i	0.707201	+	0.459262i	0.847464	−	0.530853i	$-0.178128\pi$
$607$	17.4236	+	11.3150i	0.707201	+	0.459262i	−0.140263	+	0.990114i	$0.544795\pi$
$608$	−4.99662	+	3.24484i	−0.202640	+	0.131596i
$609$	−1.15061	+	2.58431i	−0.0466251	+	0.104722i
$610$		0			0
$611$	−40.5773	−	4.26485i	−1.64158	−	0.172537i
$612$	−6.22642	+	0.986167i	−0.251688	+	0.0398635i
$613$	21.8414	−	26.9719i	0.882166	−	1.08938i	−0.113233	−	0.993568i	$-0.536121\pi$
$613$	21.8414	−	26.9719i	0.882166	−	1.08938i	0.995399	−	0.0958160i	$-0.0305460\pi$
$614$	−0.736721	−	0.425346i	−0.0297316	−	0.0171656i
$615$		0			0
$616$	2.28785	+	3.14896i	0.0921801	+	0.126875i
$617$	1.92743	−	36.7775i	0.0775953	−	1.48061i	−0.631435	−	0.775429i	$-0.717534\pi$
$617$	1.92743	−	36.7775i	0.0775953	−	1.48061i	0.709030	−	0.705178i	$-0.249133\pi$
$618$	0.295661	−	0.580267i	0.0118932	−	0.0233418i
$619$	−25.1386			−1.01041			−0.505203	−	0.863000i	$-0.668582\pi$
$619$	−25.1386			−1.01041			−0.505203	+	0.863000i	$0.668582\pi$
$620$		0			0
$621$	34.4057			1.38065
$622$	0.416972	−	0.818354i	0.0167191	−	0.0328130i
$623$	0.863326	−	16.4733i	0.0345884	−	0.659987i
$624$	−9.92513	−	13.6608i	−0.397323	−	0.546868i
$625$		0			0
$626$	−2.05471	−	1.18629i	−0.0821229	−	0.0474137i
$627$	21.0097	−	25.9449i	0.839048	−	1.03614i
$628$	39.6850	−	6.28549i	1.58360	−	0.250818i
$629$	−1.95239	−	0.205205i	−0.0778470	−	0.00818205i
$630$		0			0
$631$	−2.80677	+	6.30411i	−0.111736	+	0.250963i	−0.960754	−	0.277400i	$-0.910527\pi$
$631$	−2.80677	+	6.30411i	−0.111736	+	0.250963i	0.849019	+	0.528363i	$0.177194\pi$
$632$	2.56993	−	1.66893i	0.102226	−	0.0663866i
$633$	2.14450	+	1.39265i	0.0852362	+	0.0553530i
$634$	−0.347671	−	0.780882i	−0.0138078	−	0.0310128i
$635$		0			0
$636$	3.95490	−	12.1719i	0.156822	−	0.482649i
$637$	4.04404	−	10.5351i	0.160231	−	0.417415i
$638$	−0.139499	+	0.214810i	−0.00552283	+	0.00850442i
$639$	0.690363	−	3.24790i	0.0273103	−	0.128485i
$640$		0			0
$641$	13.2567	+	11.9364i	0.523609	+	0.471459i	0.888037	−	0.459772i	$-0.152069\pi$
$641$	13.2567	+	11.9364i	0.523609	+	0.471459i	−0.364428	+	0.931231i	$0.618736\pi$
$642$	0.577996	+	0.713765i	0.0228117	+	0.0281701i
$643$	−6.08654	−	38.4289i	−0.240030	−	1.51549i	−0.753538	−	0.657404i	$-0.771654\pi$
$643$	−6.08654	−	38.4289i	−0.240030	−	1.51549i	0.513508	−	0.858085i	$-0.328346\pi$
$644$	−4.30461	−	40.9557i	−0.169626	−	1.61388i
$645$		0			0
$646$	−0.750889	+	0.433526i	−0.0295433	+	0.0170568i
$647$	−2.56058	+	16.1669i	−0.100667	+	0.635586i	0.884833	+	0.465909i	$0.154272\pi$
$647$	−2.56058	+	16.1669i	−0.100667	+	0.635586i	−0.985500	+	0.169677i	$0.945728\pi$
$648$	0.0728380	+	0.00381728i	0.00286135	+	0.000149957i
$649$	−0.791254	−	2.43523i	−0.0310594	−	0.0955911i
$650$		0			0
$651$	2.64371	−	18.8697i	0.103615	−	0.739564i
$652$	−3.21233	−	3.21233i	−0.125805	−	0.125805i
$653$	−25.7100	−	13.0999i	−1.00611	−	0.512638i	−0.128344	−	0.991730i	$-0.540966\pi$
$653$	−25.7100	−	13.0999i	−1.00611	−	0.512638i	−0.877765	+	0.479091i	$0.840966\pi$
$654$	−0.103314	−	0.114741i	−0.00403988	−	0.00448674i
$655$		0			0
$656$	−20.0185	−	34.6731i	−0.781591	−	1.35376i
$657$	−0.0644408	−	0.240496i	−0.00251407	−	0.00938266i
$658$	−1.80967	−	1.46544i	−0.0705483	−	0.0571289i
$659$	25.9081	−	35.6594i	1.00923	−	1.38909i	0.0897506	−	0.995964i	$-0.471393\pi$
$659$	25.9081	−	35.6594i	1.00923	−	1.38909i	0.919484	−	0.393128i	$-0.128607\pi$
$660$		0			0
$661$	2.48122	−	2.75568i	0.0965083	−	0.107183i	−0.692956	−	0.720980i	$-0.743692\pi$
$661$	2.48122	−	2.75568i	0.0965083	−	0.107183i	0.789464	+	0.613797i	$0.210359\pi$
$662$	0.368049	−	0.141281i	0.0143046	−	0.00549103i
$663$	−4.03215	−	6.20897i	−0.156596	−	0.241136i
$664$	−0.776620	+	0.165076i	−0.0301387	+	0.00640618i
$665$		0			0
$666$	−0.138147	−	0.0448867i	−0.00535309	−	0.00173932i
$667$	4.83517	−	2.46364i	0.187219	−	0.0953927i
$668$	−22.8436	−	8.76885i	−0.883847	−	0.339277i
$669$	3.25374	+	15.3076i	0.125797	+	0.591827i
$670$		0			0
$671$	36.7552	+	16.3645i	1.41892	+	0.631743i
$672$	−0.151948	−	2.89935i	−0.00586153	−	0.111845i
$673$	−13.5882	+	11.0035i	−0.523786	+	0.424153i	−0.854403	−	0.519612i	$-0.826077\pi$
$673$	−13.5882	+	11.0035i	−0.523786	+	0.424153i	0.330617	+	0.943765i	$0.392743\pi$
$674$	−0.185747	−	0.134953i	−0.00715472	−	0.00519821i
$675$		0			0
$676$	−2.26851	+	3.92918i	−0.0872504	+	0.151122i
$677$	−29.3867	−	7.87414i	−1.12942	−	0.302628i	−0.354732	−	0.934968i	$-0.615428\pi$
$677$	−29.3867	−	7.87414i	−1.12942	−	0.302628i	−0.774691	+	0.632340i	$0.782094\pi$
$678$	0.344852	+	0.0546193i	0.0132440	+	0.00209764i
$679$	−17.7712	+	16.0013i	−0.681997	+	0.614073i
$680$		0			0
$681$		−	17.0720i		−	0.654199i
$682$	0.503687	−	1.65002i	0.0192872	−	0.0631825i
$683$	−2.77195	+	2.77195i	−0.106066	+	0.106066i	−0.758148	−	0.652082i	$-0.773896\pi$
$683$	−2.77195	+	2.77195i	−0.106066	+	0.106066i	0.652082	+	0.758148i	$0.273896\pi$
$684$	24.1900	−	7.85982i	0.924929	−	0.300528i
$685$		0			0
$686$	−0.742134	+	0.539192i	−0.0283348	+	0.0205864i
$687$	−0.827516	+	3.08833i	−0.0315717	+	0.117827i
$688$	−35.3233	+	9.46484i	−1.34669	+	0.360844i
$689$	−22.9111	+	2.40806i	−0.872844	+	0.0917397i
$690$		0			0
$691$	3.10919	−	29.5819i	0.118279	−	1.12535i	−0.760904	−	0.648865i	$-0.775244\pi$
$691$	3.10919	−	29.5819i	0.118279	−	1.12535i	0.879183	−	0.476485i	$-0.158089\pi$
$692$	8.99093	−	0.471195i	0.341784	−	0.0179121i
$693$	−8.93630	−	23.2798i	−0.339462	−	0.884328i
$694$	1.02314	+	0.217476i	0.0388380	+	0.00825527i
$695$		0			0
$696$	0.232908	−	0.103697i	0.00882834	−	0.00393063i
$697$	−7.96928	−	15.6406i	−0.301858	−	0.592430i
$698$	1.03732	+	2.03586i	0.0392632	+	0.0770584i
$699$	−4.54332	+	2.02282i	−0.171844	+	0.0765099i
$700$		0			0
$701$	12.9670	+	2.75622i	0.489756	+	0.104101i	0.446169	−	0.894949i	$-0.352788\pi$
$701$	12.9670	+	2.75622i	0.489756	+	0.104101i	0.0435872	+	0.999050i	$0.486121\pi$
$702$	−0.520695	−	1.35646i	−0.0196524	−	0.0511961i
$703$	7.90987	−	0.414539i	0.298326	−	0.0156346i
$704$	−3.59767	+	34.2295i	−0.135592	+	1.29007i
$705$		0			0
$706$	0.552348	−	0.0580541i	0.0207879	−	0.00218489i
$707$	−25.9560	+	6.95488i	−0.976174	+	0.261565i
$708$	−0.329414	+	1.22939i	−0.0123802	+	0.0462033i
$709$	19.0689	−	13.8544i	0.716147	−	0.520311i	−0.169004	−	0.985615i	$-0.554055\pi$
$709$	19.0689	−	13.8544i	0.716147	−	0.520311i	0.885151	+	0.465304i	$0.154055\pi$
$710$		0			0
$711$	−18.6705	+	6.06641i	−0.700198	+	0.227508i
$712$	−1.05123	+	1.05123i	−0.0393966	+	0.0393966i
$713$	−26.7213	+	24.9394i	−1.00072	+	0.933989i
$714$		−	0.422528i		−	0.0158127i
$715$		0			0
$716$	−15.2486	+	13.7299i	−0.569869	+	0.513112i
$717$	6.72179	+	1.06463i	0.251030	+	0.0397592i
$718$	1.13252	+	0.303459i	0.0422654	+	0.0113250i
$719$	−16.6609	+	28.8576i	−0.621348	+	1.07621i	0.367887	+	0.929871i	$0.380081\pi$
$719$	−16.6609	+	28.8576i	−0.621348	+	1.07621i	−0.989235	+	0.146336i	$0.953252\pi$
$720$		0			0
$721$	21.4592	+	15.5910i	0.799183	+	0.580641i
$722$	1.67126	−	1.35336i	0.0621980	−	0.0503670i
$723$	1.25210	+	23.8915i	0.0465661	+	0.888534i
$724$	−40.0196	−	17.8179i	−1.48732	−	0.662196i
$725$		0			0
$726$	0.129693	+	0.610160i	0.00481338	+	0.0226451i
$727$	−8.79366	−	3.37557i	−0.326139	−	0.125193i	0.189789	−	0.981825i	$-0.439220\pi$
$727$	−8.79366	−	3.37557i	−0.326139	−	0.125193i	−0.515928	+	0.856632i	$0.672553\pi$
$728$	−3.10300	+	1.58106i	−0.115005	+	0.0585978i
$729$	−16.7186	−	5.43222i	−0.619209	−	0.201193i
$730$		0			0
$731$	−15.6831	+	3.33355i	−0.580061	+	0.123296i
$732$	−10.8921	−	16.7723i	−0.402582	−	0.619922i
$733$	−13.5871	+	5.21562i	−0.501853	+	0.192643i	−0.596107	−	0.802905i	$-0.703287\pi$
$733$	−13.5871	+	5.21562i	−0.501853	+	0.192643i	0.0942544	+	0.995548i	$0.469953\pi$
$734$	0.132161	−	0.146780i	0.00487815	−	0.00541773i
$735$		0			0
$736$	−3.27364	+	4.50578i	−0.120668	+	0.166085i
$737$	−22.4063	−	18.1443i	−0.825347	−	0.668353i
$738$	−0.336164	−	1.25458i	−0.0123744	−	0.0461818i
$739$	−4.75149	−	8.22982i	−0.174786	−	0.302739i	0.765301	−	0.643673i	$-0.222590\pi$
$739$	−4.75149	−	8.22982i	−0.174786	−	0.302739i	−0.940087	+	0.340934i	$0.889257\pi$
$740$		0			0
$741$	19.9872	+	22.1980i	0.734247	+	0.815464i
$742$	−1.17150	−	0.596907i	−0.0430070	−	0.0219131i
$743$	−32.7625	−	32.7625i	−1.20194	−	1.20194i	−0.973576	−	0.228365i	$-0.926662\pi$
$743$	−32.7625	−	32.7625i	−1.20194	−	1.20194i	−0.228365	−	0.973576i	$-0.573338\pi$
$744$	−1.31499	+	1.10437i	−0.0482100	+	0.0404882i
$745$		0			0
$746$	0.0233882	+	0.0719814i	0.000856302	+	0.00263543i
$747$	5.07958	+	0.266210i	0.185852	+	0.00974010i
$748$	−2.37268	+	14.9805i	−0.0867539	+	0.547743i
$749$	−32.3961	+	18.7039i	−1.18373	+	0.683425i
$750$		0			0
$751$	−3.79985	−	36.1531i	−0.138658	−	1.31925i	−0.813622	−	0.581395i	$-0.802507\pi$
$751$	−3.79985	−	36.1531i	−0.138658	−	1.31925i	0.674963	−	0.737851i	$-0.264159\pi$
$752$	−6.48327	−	40.9338i	−0.236420	−	1.49270i
$753$	−7.64939	−	9.44621i	−0.278759	−	0.344239i
$754$	−0.170305	−	0.153344i	−0.00620215	−	0.00558445i
$755$		0			0
$756$	−6.83539	+	32.1580i	−0.248601	+	1.16958i
$757$	−27.8317	+	42.8570i	−1.01156	+	1.55766i	−0.194669	+	0.980869i	$0.562363\pi$
$757$	−27.8317	+	42.8570i	−1.01156	+	1.55766i	−0.816889	+	0.576795i	$0.804303\pi$
$758$	0.000736106	−	0.00191762i	2.67366e−5	−	6.96511e-5i
$759$	9.64403	−	29.6813i	0.350056	−	1.07736i
$760$		0			0
$761$	−7.18623	−	16.1405i	−0.260501	−	0.585094i	0.735187	−	0.677865i	$-0.237094\pi$
$761$	−7.18623	−	16.1405i	−0.260501	−	0.585094i	−0.995688	+	0.0927703i	$0.970428\pi$
$762$	−0.733274	−	0.476194i	−0.0265637	−	0.0172507i
$763$	5.27408	−	3.42503i	0.190935	−	0.123994i
$764$	−13.6089	+	30.5662i	−0.492354	+	1.10585i
$765$		0			0
$766$	−1.67937	−	0.176509i	−0.0606782	−	0.00637754i
$767$	2.26279	−	0.358391i	0.0817047	−	0.0129408i
$768$	10.6840	−	13.1936i	0.385525	−	0.476083i
$769$	22.9067	+	13.2252i	0.826037	+	0.476913i	0.852494	−	0.522737i	$-0.175089\pi$
$769$	22.9067	+	13.2252i	0.826037	+	0.476913i	−0.0264567	+	0.999650i	$0.508422\pi$
$770$		0			0
$771$	11.1086	+	15.2897i	0.400066	+	0.550644i
$772$	1.04220	−	19.8864i	0.0375096	−	0.715727i
$773$	12.6350	−	24.7975i	0.454448	−	0.891904i	−0.544151	−	0.838987i	$-0.683148\pi$
$773$	12.6350	−	24.7975i	0.454448	−	0.891904i	0.998599	−	0.0529167i	$-0.0168518\pi$
$774$	−1.18634			−0.0426422
$775$		0			0
$776$	2.15518			0.0773663
$777$	−1.75236	+	3.43919i	−0.0628655	+	0.123380i
$778$	−0.0575899	+	1.09888i	−0.00206470	+	0.0393968i
$779$	41.6297	+	57.2983i	1.49154	+	2.05293i
$780$		0			0
$781$	−6.91860	−	3.99446i	−0.247567	−	0.142933i
$782$	−0.510087	+	0.629905i	−0.0182407	+	0.0225253i
$783$	−4.27894	+	0.677718i	−0.152917	+	0.0242197i
$784$	11.3997	+	1.19815i	0.407132	+	0.0427912i
$785$		0			0
$786$	−0.110774	+	0.248802i	−0.00395117	+	0.00887447i
$787$	27.0679	−	17.5781i	0.964868	−	0.626593i	0.0369263	−	0.999318i	$-0.488243\pi$
$787$	27.0679	−	17.5781i	0.964868	−	0.626593i	0.927942	+	0.372725i	$0.121577\pi$
$788$	−8.51552	−	5.53004i	−0.303353	−	0.197000i
$789$	11.2706	+	25.3141i	0.401243	+	0.901207i
$790$		0			0
$791$	−4.39445	+	13.5247i	−0.156249	+	0.480884i
$792$	−0.805372	+	2.09807i	−0.0286176	+	0.0745515i
$793$	−19.6060	+	30.1906i	−0.696229	+	1.07210i
$794$	0.0888416	−	0.417967i	0.00315287	−	0.0148331i
$795$		0			0
$796$	9.37783	+	8.44384i	0.332388	+	0.299284i
$797$	−9.59133	−	11.8443i	−0.339742	−	0.419547i	0.578428	−	0.815734i	$-0.303667\pi$
$797$	−9.59133	−	11.8443i	−0.339742	−	0.419547i	−0.918170	+	0.396187i	$0.870333\pi$
$798$	0.266686	+	1.68379i	0.00944059	+	0.0596055i
$799$	−1.89936	−	18.0712i	−0.0671945	−	0.639313i
$800$		0			0
$801$	8.24829	−	4.76215i	0.291439	−	0.168262i
$802$	−0.398055	+	2.51322i	−0.0140558	+	0.0887448i
$803$	−0.598216	−	0.0313512i	−0.0211106	−	0.00110636i
$804$	4.42857	+	13.6297i	0.156184	+	0.480683i
$805$		0			0
$806$	1.38764	+	0.676062i	0.0488777	+	0.0238133i
$807$	6.04343	+	6.04343i	0.212739	+	0.212739i
$808$	2.15781	+	1.09946i	0.0759115	+	0.0386788i
$809$	−21.1268	−	23.4637i	−0.742779	−	0.824940i	0.246779	−	0.969072i	$-0.420628\pi$
$809$	−21.1268	−	23.4637i	−0.742779	−	0.824940i	−0.989559	+	0.144132i	$0.953961\pi$
$810$		0			0
$811$	−5.96240	−	10.3272i	−0.209368	−	0.362636i	0.742148	−	0.670237i	$-0.233807\pi$
$811$	−5.96240	−	10.3272i	−0.209368	−	0.362636i	−0.951516	+	0.307600i	$0.900474\pi$
$812$	1.34209	+	5.00875i	0.0470981	+	0.175773i
$813$	−9.28139	−	7.51592i	−0.325512	−	0.263595i
$814$	−0.205420	+	0.282737i	−0.00719997	+	0.00990991i
$815$		0			0
$816$	5.03190	−	5.58849i	0.176152	−	0.195636i
$817$	60.3937	−	23.1830i	2.11291	−	0.811070i
$818$	−0.778105	−	1.19818i	−0.0272058	−	0.0418933i
$819$	21.8235	−	4.63873i	0.762574	−	0.162090i
$820$		0			0
$821$	−2.83114	−	0.919893i	−0.0988075	−	0.0321045i	0.259196	−	0.965825i	$-0.416542\pi$
$821$	−2.83114	−	0.919893i	−0.0988075	−	0.0321045i	−0.358004	+	0.933720i	$0.616542\pi$
$822$	−1.39050	+	0.708497i	−0.0484994	+	0.0247117i
$823$	−14.9624	−	5.74352i	−0.521555	−	0.200206i	0.0833254	−	0.996522i	$-0.473446\pi$
$823$	−14.9624	−	5.74352i	−0.521555	−	0.200206i	−0.604881	+	0.796316i	$0.706779\pi$
$824$	−0.497020	−	2.33830i	−0.0173145	−	0.0814584i
$825$		0			0
$826$	0.119449	+	0.0531821i	0.00415616	+	0.00185044i
$827$	1.30266	+	24.8563i	0.0452980	+	0.864338i	0.922922	+	0.384987i	$0.125794\pi$
$827$	1.30266	+	24.8563i	0.0452980	+	0.864338i	−0.877624	+	0.479350i	$0.840872\pi$
$828$	18.4782	−	14.9634i	0.642163	−	0.520013i
$829$	−17.0408	−	12.3808i	−0.591850	−	0.430004i	0.251127	−	0.967954i	$-0.419199\pi$
$829$	−17.0408	−	12.3808i	−0.591850	−	0.430004i	−0.842977	+	0.537950i	$0.819199\pi$
$830$		0			0
$831$	4.24824	−	7.35817i	0.147370	−	0.255252i
$832$	−29.7455	−	7.97029i	−1.03124	−	0.276320i
$833$	4.96374	+	0.786179i	0.171983	+	0.0272395i
$834$	0.298420	−	0.268698i	0.0103334	−	0.00930427i
$835$		0			0
$836$		−	61.1955i		−	2.11649i
$837$	26.4410	−	12.3434i	0.913934	−	0.426652i
$838$	0.620997	−	0.620997i	0.0214520	−	0.0214520i
$839$	−36.6120	+	11.8960i	−1.26399	+	0.410694i	−0.862913	−	0.505352i	$-0.831363\pi$
$839$	−36.6120	+	11.8960i	−1.26399	+	0.410694i	−0.401073	+	0.916046i	$0.631363\pi$
$840$		0			0
$841$	22.9087	−	16.6441i	0.789955	−	0.573936i
$842$	−0.395825	+	1.47724i	−0.0136410	+	0.0509090i
$843$	9.01432	−	2.41538i	0.310470	−	0.0831901i
$844$	4.66143	−	0.489936i	0.160453	−	0.0168643i
$845$		0			0
$846$	0.140537	−	1.33712i	0.00483175	−	0.0459710i
$847$	−25.3719	+	1.32968i	−0.871788	+	0.0456885i
$848$	−8.38598	−	21.8462i	−0.287976	−	0.750203i
$849$	16.4926	+	3.50560i	0.566023	+	0.120312i
$850$		0			0
$851$	6.76429	−	3.01166i	0.231877	−	0.103238i
$852$	1.80280	+	3.53819i	0.0617629	+	0.121217i
$853$	−15.2409	−	29.9120i	−0.521839	−	1.02417i	−0.990072	−	0.140561i	$-0.955109\pi$
$853$	−15.2409	−	29.9120i	−0.521839	−	1.02417i	0.468233	−	0.883605i	$-0.344891\pi$
$854$	−1.87689	+	0.835643i	−0.0642257	+	0.0285951i
$855$		0			0
$856$	3.29765	+	0.700938i	0.112712	+	0.0239576i
$857$	17.4061	+	45.3445i	0.594582	+	1.54894i	0.818606	+	0.574356i	$0.194747\pi$
$857$	17.4061	+	45.3445i	0.594582	+	1.54894i	−0.224024	+	0.974584i	$0.571919\pi$
$858$	−1.31615	+	0.0689763i	−0.0449325	+	0.00235481i
$859$	4.61635	−	43.9216i	0.157508	−	1.49859i	−0.575183	−	0.818025i	$-0.695069\pi$
$859$	4.61635	−	43.9216i	0.157508	−	1.49859i	0.732691	−	0.680562i	$-0.238264\pi$
$860$		0			0
$861$	−34.3249	+	3.60770i	−1.16979	+	0.122950i
$862$	1.60446	−	0.429913i	0.0546481	−	0.0146429i
$863$	−12.1041	+	45.1731i	−0.412028	+	1.53771i	0.378686	+	0.925525i	$0.376376\pi$
$863$	−12.1041	+	45.1731i	−0.412028	+	1.53771i	−0.790714	+	0.612185i	$0.790291\pi$
$864$	3.59712	−	2.61346i	0.122376	−	0.0889117i
$865$		0			0
$866$	−0.640229	+	0.208023i	−0.0217559	+	0.00706891i
$867$	−10.7514	+	10.7514i	−0.365135	+	0.365135i
$868$	−18.0014	−	29.9303i	−0.611008	−	1.01590i
$869$			47.2322i			1.60224i
$870$		0			0
$871$	19.1705	−	17.2612i	0.649567	−	0.584872i
$872$	−0.559776	−	0.0886598i	−0.0189564	−	0.00300240i
$873$	−13.3366	−	3.57354i	−0.451376	−	0.120946i
$874$	1.63514	−	2.83214i	0.0553094	−	0.0957986i
$875$		0			0
$876$	0.240893	+	0.175019i	0.00813902	+	0.00591335i
$877$	34.9799	−	28.3262i	1.18119	−	0.956506i	0.181548	−	0.983382i	$-0.441889\pi$
$877$	34.9799	−	28.3262i	1.18119	−	0.956506i	0.999639	+	0.0268759i	$0.00855590\pi$
$878$	−0.00729703	−	0.139236i	−0.000246263	−	0.00469898i
$879$	−25.1478	−	11.1965i	−0.848215	−	0.377650i
$880$		0			0
$881$	6.53922	+	30.7646i	0.220312	+	1.03649i	0.939732	+	0.341911i	$0.111074\pi$
$881$	6.53922	+	30.7646i	0.220312	+	1.03649i	−0.719420	+	0.694575i	$0.755592\pi$
$882$	0.347155	+	0.133260i	0.0116893	+	0.00448711i
$883$	49.6709	−	25.3086i	1.67156	−	0.851702i	0.678431	−	0.734664i	$-0.262660\pi$
$883$	49.6709	−	25.3086i	1.67156	−	0.851702i	0.993127	−	0.117038i	$-0.0373399\pi$
$884$	−12.9064	−	4.19354i	−0.434089	−	0.141044i
$885$		0			0
$886$	0.215443	−	0.0457939i	0.00723796	−	0.00153848i
$887$	−2.77750	−	4.27697i	−0.0932593	−	0.143607i	0.788962	−	0.614443i	$-0.210619\pi$
$887$	−2.77750	−	4.27697i	−0.0932593	−	0.143607i	−0.882221	+	0.470836i	$0.843952\pi$
$888$	0.324763	−	0.124665i	0.0108983	−	0.00418348i
$889$	23.8284	−	26.4641i	0.799179	−	0.887578i
$890$		0			0
$891$	−0.660816	+	0.909535i	−0.0221382	+	0.0304706i
$892$	22.2934	+	18.0529i	0.746439	+	0.604455i
$893$	18.9750	+	70.8155i	0.634973	+	2.36975i
$894$	0.103382	+	0.179063i	0.00345762	+	0.00598877i
$895$		0			0
$896$	−4.74605	−	5.27102i	−0.158554	−	0.176092i
$897$	24.8799	+	12.6769i	0.830716	+	0.423271i
$898$	0.344746	+	0.344746i	0.0115043	+	0.0115043i
$899$	2.83200	−	3.62800i	0.0944524	−	0.121001i
$900$		0			0
$901$	−3.17043	−	9.75757i	−0.105622	−	0.325072i
$902$	−3.12067	−	0.163548i	−0.103907	−	0.00544554i
$903$	−4.93155	+	31.1366i	−0.164112	+	1.03616i
$904$	1.10992	−	0.640813i	0.0369154	−	0.0213131i
$905$		0			0
$906$	−0.0411826	−	0.391826i	−0.00136820	−	0.0130175i
$907$	−1.35145	−	8.53270i	−0.0448740	−	0.283323i	0.955039	−	0.296479i	$-0.0958124\pi$
$907$	−1.35145	−	8.53270i	−0.0448740	−	0.283323i	−0.999913	+	0.0131553i	$0.995812\pi$
$908$	−19.6936	−	24.3196i	−0.653556	−	0.807075i
$909$	−11.5299	−	10.3816i	−0.382422	−	0.344334i
$910$		0			0
$911$	−10.0627	+	47.3411i	−0.333391	+	1.56848i	0.417890	+	0.908497i	$0.362770\pi$
$911$	−10.0627	+	47.3411i	−0.333391	+	1.56848i	−0.751281	+	0.659982i	$0.770564\pi$
$912$	−16.5250	+	25.4463i	−0.547198	+	0.842610i
$913$	4.38573	−	11.4252i	0.145146	−	0.378119i
$914$	0.103087	−	0.317270i	0.00340983	−	0.0104944i
$915$		0			0
$916$	2.38377	+	5.35403i	0.0787619	+	0.176902i
$917$	−9.30303	−	6.04146i	−0.307213	−	0.199506i
$918$	0.542686	−	0.352425i	0.0179113	−	0.0116317i
$919$	−18.7765	+	42.1726i	−0.619378	+	1.39115i	0.282547	+	0.959253i	$0.408821\pi$
$919$	−18.7765	+	42.1726i	−0.619378	+	1.39115i	−0.901925	+	0.431892i	$0.857846\pi$
$920$		0			0
$921$	−12.9803	−	1.36429i	−0.427716	−	0.0449548i
$922$	1.40582	−	0.222660i	0.0462982	−	0.00733291i
$923$	4.49833	−	5.55497i	0.148064	−	0.182844i
$924$	25.8262	+	14.9108i	0.849621	+	0.490529i
$925$		0			0
$926$	−0.132401	−	0.182234i	−0.00435096	−	0.00598858i
$927$	−0.801521	+	15.2939i	−0.0263254	+	0.502318i
$928$	0.318379	−	0.624854i	0.0104513	−	0.0205119i
$929$	21.3673			0.701037			0.350519	−	0.936556i	$-0.386005\pi$
$929$	21.3673			0.701037			0.350519	+	0.936556i	$0.386005\pi$
$930$		0			0
$931$	−20.2769			−0.664548
$932$	−4.13867	+	8.12259i	−0.135567	+	0.266064i
$933$	0.737495	−	14.0722i	0.0241445	−	0.460705i
$934$	0.985187	+	1.35599i	0.0322363	+	0.0443695i
$935$		0			0
$936$	−1.74136	−	1.00538i	−0.0569182	−	0.0328618i
$937$	6.09698	−	7.52914i	0.199180	−	0.245966i	−0.667763	−	0.744374i	$-0.732748\pi$
$937$	6.09698	−	7.52914i	0.199180	−	0.245966i	0.866943	+	0.498407i	$0.166082\pi$
$938$	1.45414	−	0.230314i	0.0474794	−	0.00752000i
$939$	−36.2021	−	3.80500i	−1.18141	−	0.124171i
$940$		0			0
$941$	−14.9445	+	33.5659i	−0.487176	+	1.09422i	0.488012	+	0.872837i	$0.337722\pi$
$941$	−14.9445	+	33.5659i	−0.487176	+	1.09422i	−0.975188	+	0.221378i	$0.928944\pi$
$942$	−1.30405	+	0.846859i	−0.0424882	+	0.0275921i
$943$	55.5269	+	36.0596i	1.80820	+	1.17426i
$944$	0.946522	+	2.12592i	0.0308067	+	0.0691929i
$945$		0			0
$946$	−0.882027	+	2.71460i	−0.0286772	+	0.0882593i
$947$	14.7611	−	38.4540i	0.479672	−	1.24959i	−0.453853	−	0.891076i	$-0.649951\pi$
$947$	14.7611	−	38.4540i	0.479672	−	1.24959i	0.933525	−	0.358512i	$-0.116716\pi$
$948$	12.7868	−	19.6899i	0.415294	−	0.639497i
$949$	0.111436	−	0.524263i	0.00361735	−	0.0170183i
$950$		0			0
$951$	−9.74602	−	8.77536i	−0.316036	−	0.284560i
$952$	−0.976058	−	1.20533i	−0.0316342	−	0.0390650i
$953$	7.33861	+	46.3342i	0.237721	+	1.50091i	0.761001	+	0.648751i	$0.224708\pi$
$953$	7.33861	+	46.3342i	0.237721	+	1.50091i	−0.523280	+	0.852161i	$0.675292\pi$
$954$	−0.0793510	−	0.754975i	−0.00256908	−	0.0244432i
$955$		0			0
$956$	10.8035	−	6.23743i	0.349412	−	0.201733i
$957$	−0.614745	+	3.88134i	−0.0198719	+	0.125466i
$958$	−2.10212	−	0.110167i	−0.0679163	−	0.00355934i
$959$	−19.6419	−	60.4514i	−0.634269	−	1.95208i
$960$		0			0
$961$	−11.5881	+	28.7527i	−0.373811	+	0.927505i
$962$	−0.221106	−	0.221106i	−0.00712875	−	0.00712875i
$963$	−19.2442	−	9.80543i	−0.620137	−	0.315976i
$964$	29.3441	+	32.5899i	0.945108	+	1.04965i
$965$		0			0
$966$	0.796830	+	1.38015i	0.0256376	+	0.0444056i
$967$	−4.72727	−	17.6424i	−0.152019	−	0.567342i	−0.999342	−	0.0362647i	$-0.988454\pi$
$967$	−4.72727	−	17.6424i	−0.152019	−	0.567342i	0.847323	−	0.531077i	$-0.178213\pi$
$968$	1.77947	+	1.44098i	0.0571942	+	0.0463150i
$969$	−7.81920	+	10.7622i	−0.251189	+	0.345732i
$970$		0			0
$971$	2.67405	−	2.96984i	0.0858145	−	0.0953066i	−0.698708	−	0.715407i	$-0.746241\pi$
$971$	2.67405	−	2.96984i	0.0858145	−	0.0953066i	0.784523	+	0.620100i	$0.212908\pi$
$972$	−28.7614	+	11.0405i	−0.922521	+	0.354123i
$973$	8.90783	+	13.7169i	0.285572	+	0.439742i
$974$	−0.465197	+	0.0988806i	−0.0149059	+	0.00316834i
$975$		0			0
$976$	−34.7759	−	11.2994i	−1.11315	−	0.361685i
$977$	38.7586	−	19.7485i	1.24000	−	0.631811i	0.293946	−	0.955822i	$-0.405031\pi$
$977$	38.7586	−	19.7485i	1.24000	−	0.631811i	0.946053	+	0.324011i	$0.105031\pi$
$978$	0.164128	+	0.0630029i	0.00524824	+	0.00201461i
$979$	−4.76432	−	22.4144i	−0.152268	−	0.716367i
$980$		0			0
$981$	3.31699	+	1.47682i	0.105903	+	0.0471512i
$982$	0.0419634	+	0.800710i	0.00133911	+	0.0255517i
$983$	−42.5077	+	34.4221i	−1.35579	+	1.09789i	−0.370157	+	0.928969i	$0.620696\pi$
$983$	−42.5077	+	34.4221i	−1.35579	+	1.09789i	−0.985629	+	0.168925i	$0.945971\pi$
$984$	2.51647	+	1.82832i	0.0802222	+	0.0582848i
$985$		0			0
$986$	0.0510303	−	0.0883871i	0.00162514	−	0.00281482i
$987$	−34.5095	−	9.24681i	−1.09845	−	0.294329i
$988$	54.0793	+	8.56531i	1.72049	+	0.272499i
$989$	44.9408	−	40.4649i	1.42903	−	1.28671i
$990$		0			0
$991$		−	56.3648i		−	1.79049i	−0.445577	−	0.895244i	$-0.647001\pi$
$991$		−	56.3648i		−	1.79049i	0.445577	−	0.895244i	$-0.352999\pi$
$992$	−0.899310	+	4.63717i	−0.0285531	+	0.147230i
$993$	4.27699	−	4.27699i	0.135726	−	0.135726i
$994$	0.387983	−	0.126063i	0.0123061	−	0.00399849i
$995$		0			0
$996$	−4.92134	+	3.57556i	−0.155939	+	0.113296i
$997$	−13.7298	+	51.2402i	−0.434826	+	1.62279i	0.306655	+	0.951821i	$0.400790\pi$
$997$	−13.7298	+	51.2402i	−0.434826	+	1.62279i	−0.741482	+	0.670973i	$0.765877\pi$
$998$	0.632873	−	0.169578i	0.0200332	−	0.00536789i
$999$	−5.87884	+	0.617891i	−0.185998	+	0.0195492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.df.b.507.7		224
5.2	odd	4		155.2.x.a.73.7	yes	224
5.3	odd	4	inner	775.2.df.b.693.8		224
5.4	even	2		155.2.x.a.42.8	yes	224
31.17	odd	30	inner	775.2.df.b.482.8		224
155.17	even	60		155.2.x.a.48.8	yes	224
155.48	even	60	inner	775.2.df.b.668.7		224
155.79	odd	30		155.2.x.a.17.7	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.x.a.17.7	✓	224	155.79	odd	30
155.2.x.a.42.8	yes	224	5.4	even	2
155.2.x.a.48.8	yes	224	155.17	even	60
155.2.x.a.73.7	yes	224	5.2	odd	4
775.2.df.b.482.8		224	31.17	odd	30	inner
775.2.df.b.507.7		224	1.1	even	1	trivial
775.2.df.b.668.7		224	155.48	even	60	inner
775.2.df.b.693.8		224	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.df (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0322043 + 0.0632044i) q^{2} +(-0.0569594 + 1.08685i) q^{3} +(1.17261 + 1.61396i) q^{4} +(-0.0668594 - 0.0386013i) q^{6} +(1.97885 - 2.44368i) q^{7} +(-0.279898 + 0.0443315i) q^{8} +(1.80557 + 0.189773i) q^{9} +O(q^{10})\)	\(q+(-0.0322043 + 0.0632044i) q^{2} +(-0.0569594 + 1.08685i) q^{3} +(1.17261 + 1.61396i) q^{4} +(-0.0668594 - 0.0386013i) q^{6} +(1.97885 - 2.44368i) q^{7} +(-0.279898 + 0.0443315i) q^{8} +(1.80557 + 0.189773i) q^{9} +(1.77665 - 3.99042i) q^{11} +(-1.82093 + 1.18252i) q^{12} +(3.27771 + 2.12857i) q^{13} +(0.0907237 + 0.203769i) q^{14} +(-1.22675 + 3.77554i) q^{16} +(-0.623752 + 1.62493i) q^{17} +(-0.0701414 + 0.108008i) q^{18} +(1.46007 - 6.86910i) q^{19} +(2.54320 + 2.28990i) q^{21} +(0.194996 + 0.240801i) q^{22} +(-1.02696 - 6.48399i) q^{23} +(-0.0322389 - 0.306732i) q^{24} +(-0.240092 + 0.138617i) q^{26} +(-0.819861 + 5.17640i) q^{27} +(6.26443 + 0.328305i) q^{28} +(0.255441 + 0.786167i) q^{29} +(-3.11543 - 4.61455i) q^{31} +(-0.599894 - 0.599894i) q^{32} +(4.23579 + 2.15824i) q^{33} +(-0.0826153 - 0.0917536i) q^{34} +(1.81094 + 3.13665i) q^{36} +(0.291921 + 1.08947i) q^{37} +(0.387137 + 0.313497i) q^{38} +(-2.50014 + 3.44114i) q^{39} +(-6.74839 + 7.49485i) q^{41} +(-0.226634 + 0.0869965i) q^{42} +(5.01711 + 7.72567i) q^{43} +(8.52371 - 1.81177i) q^{44} +(0.442890 + 0.143904i) q^{46} +(-9.30187 + 4.73954i) q^{47} +(-4.03357 - 1.54834i) q^{48} +(-0.600323 - 2.82430i) q^{49} +(-1.73053 - 0.770481i) q^{51} +(0.408052 + 7.78610i) q^{52} +(-4.58094 + 3.70958i) q^{53} +(-0.300768 - 0.218521i) q^{54} +(-0.445544 + 0.771705i) q^{56} +(7.38251 + 1.97814i) q^{57} +(-0.0579155 - 0.00917292i) q^{58} +(0.435631 - 0.392244i) q^{59} +9.21086i q^{61} +(0.391990 - 0.0483010i) q^{62} +(4.03669 - 4.03669i) q^{63} +(-7.49384 + 2.43490i) q^{64} +(-0.272821 + 0.198216i) q^{66} +(1.70835 - 6.37563i) q^{67} +(-3.35400 + 0.898701i) q^{68} +(7.10563 - 0.746831i) q^{69} +(0.191176 - 1.81892i) q^{71} +(-0.513787 + 0.0269265i) q^{72} +(-0.0491467 - 0.128032i) q^{73} +(-0.0782601 - 0.0166347i) q^{74} +(12.7986 - 5.69829i) q^{76} +(-6.23557 - 12.2380i) q^{77} +(-0.136980 - 0.268839i) q^{78} +(-9.87826 + 4.39808i) q^{79} +(-0.251755 - 0.0535122i) q^{81} +(-0.256380 - 0.667894i) q^{82} +(2.79788 - 0.146631i) q^{83} +(-0.713636 + 6.78979i) q^{84} +(-0.649869 + 0.0683040i) q^{86} +(-0.868996 + 0.232847i) q^{87} +(-0.320379 + 1.19567i) q^{88} +(4.24416 - 3.08356i) q^{89} +(11.6876 - 3.79755i) q^{91} +(9.26070 - 9.26070i) q^{92} +(5.19278 - 3.12317i) q^{93} -0.740552i q^{94} +(0.686164 - 0.617825i) q^{96} +(-7.51144 - 1.18969i) q^{97} +(0.197841 + 0.0530113i) q^{98} +(3.96513 - 6.86781i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 12 q^{2} + 14 q^{3} - 36 q^{6} - 6 q^{7} + 40 q^{8}+O(q^{10}) \) 224 * q + 12 * q^2 + 14 * q^3 - 36 * q^6 - 6 * q^7 + 40 * q^8	\( 224 q + 12 q^{2} + 14 q^{3} - 36 q^{6} - 6 q^{7} + 40 q^{8} - 28 q^{11} + 40 q^{12} + 14 q^{13} + 24 q^{16} + 14 q^{17} + 40 q^{18} - 44 q^{21} - 30 q^{22} + 30 q^{23} - 48 q^{26} - 100 q^{27} + 48 q^{28} - 44 q^{31} - 28 q^{32} - 20 q^{33} + 16 q^{36} - 30 q^{37} - 38 q^{38} - 20 q^{41} + 130 q^{42} - 22 q^{43} + 28 q^{47} + 156 q^{48} - 36 q^{51} + 10 q^{52} - 26 q^{53} - 48 q^{56} + 20 q^{58} - 30 q^{62} - 152 q^{63} - 152 q^{66} - 38 q^{67} + 126 q^{68} - 128 q^{71} + 156 q^{72} + 30 q^{73} + 128 q^{76} - 30 q^{78} - 64 q^{81} - 8 q^{82} + 82 q^{83} - 28 q^{86} + 24 q^{87} - 252 q^{88} - 194 q^{93} + 60 q^{96} + 38 q^{97} - 174 q^{98}+O(q^{100}) \) 224 * q + 12 * q^2 + 14 * q^3 - 36 * q^6 - 6 * q^7 + 40 * q^8 - 28 * q^11 + 40 * q^12 + 14 * q^13 + 24 * q^16 + 14 * q^17 + 40 * q^18 - 44 * q^21 - 30 * q^22 + 30 * q^23 - 48 * q^26 - 100 * q^27 + 48 * q^28 - 44 * q^31 - 28 * q^32 - 20 * q^33 + 16 * q^36 - 30 * q^37 - 38 * q^38 - 20 * q^41 + 130 * q^42 - 22 * q^43 + 28 * q^47 + 156 * q^48 - 36 * q^51 + 10 * q^52 - 26 * q^53 - 48 * q^56 + 20 * q^58 - 30 * q^62 - 152 * q^63 - 152 * q^66 - 38 * q^67 + 126 * q^68 - 128 * q^71 + 156 * q^72 + 30 * q^73 + 128 * q^76 - 30 * q^78 - 64 * q^81 - 8 * q^82 + 82 * q^83 - 28 * q^86 + 24 * q^87 - 252 * q^88 - 194 * q^93 + 60 * q^96 + 38 * q^97 - 174 * q^98

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