LMFDB - Embedded newform 287.2.n.a.64.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(64,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("287.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.n (of order $10$, degree $4$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.15
Character	$\chi$	$=$	287.64
Dual form			287.2.n.a.148.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.239839 + 0.738150i) q^{2} -2.56947i q^{3} +(1.13069 - 0.821496i) q^{4} +(0.320630 - 0.232952i) q^{5} +(1.89665 - 0.616259i) q^{6} +(0.951057 + 0.309017i) q^{7} +(2.13339 + 1.55000i) q^{8} -3.60216 q^{9} +O(q^{10})$	\(q+(0.239839 + 0.738150i) q^{2} -2.56947i q^{3} +(1.13069 - 0.821496i) q^{4} +(0.320630 - 0.232952i) q^{5} +(1.89665 - 0.616259i) q^{6} +(0.951057 + 0.309017i) q^{7} +(2.13339 + 1.55000i) q^{8} -3.60216 q^{9} +(0.248853 + 0.180802i) q^{10} +(0.206004 - 0.283540i) q^{11} +(-2.11081 - 2.90528i) q^{12} +(-3.61230 + 1.17371i) q^{13} +0.776136i q^{14} +(-0.598562 - 0.823849i) q^{15} +(0.231313 - 0.711908i) q^{16} +(1.49711 - 2.06060i) q^{17} +(-0.863941 - 2.65894i) q^{18} +(-0.965702 - 0.313776i) q^{19} +(0.171165 - 0.526793i) q^{20} +(0.794009 - 2.44371i) q^{21} +(0.258703 + 0.0840576i) q^{22} +(-0.684214 - 2.10579i) q^{23} +(3.98266 - 5.48167i) q^{24} +(-1.49655 + 4.60590i) q^{25} +(-1.73274 - 2.38491i) q^{26} +1.54724i q^{27} +(1.32921 - 0.431886i) q^{28} +(4.72480 + 6.50313i) q^{29} +(0.464565 - 0.639420i) q^{30} +(-4.19849 - 3.05038i) q^{31} +5.85499 q^{32} +(-0.728547 - 0.529320i) q^{33} +(1.88010 + 0.610880i) q^{34} +(0.376924 - 0.122470i) q^{35} +(-4.07294 + 2.95916i) q^{36} +(-4.79777 + 3.48578i) q^{37} -0.788088i q^{38} +(3.01580 + 9.28168i) q^{39} +1.04510 q^{40} +(2.47872 + 5.90389i) q^{41} +1.99426 q^{42} +(2.02860 + 6.24340i) q^{43} -0.489828i q^{44} +(-1.15496 + 0.839130i) q^{45} +(1.39029 - 1.01010i) q^{46} +(6.93974 - 2.25486i) q^{47} +(-1.82922 - 0.594351i) q^{48} +(0.809017 + 0.587785i) q^{49} -3.75877 q^{50} +(-5.29464 - 3.84678i) q^{51} +(-3.12020 + 4.29459i) q^{52} +(-3.10400 - 4.27229i) q^{53} +(-1.14210 + 0.371089i) q^{54} -0.138900i q^{55} +(1.55000 + 2.13339i) q^{56} +(-0.806236 + 2.48134i) q^{57} +(-3.66709 + 5.04731i) q^{58} +(2.40866 + 7.41310i) q^{59} +(-1.35358 - 0.439804i) q^{60} +(1.36765 - 4.20918i) q^{61} +(1.24468 - 3.83072i) q^{62} +(-3.42586 - 1.11313i) q^{63} +(0.941632 + 2.89805i) q^{64} +(-0.884795 + 1.21782i) q^{65} +(0.215983 - 0.664728i) q^{66} +(3.78227 + 5.20584i) q^{67} -3.55977i q^{68} +(-5.41077 + 1.75807i) q^{69} +(0.180802 + 0.248853i) q^{70} +(3.63175 - 4.99868i) q^{71} +(-7.68481 - 5.58334i) q^{72} -8.89270 q^{73} +(-3.72372 - 2.70544i) q^{74} +(11.8347 + 3.84533i) q^{75} +(-1.34968 + 0.438537i) q^{76} +(0.283540 - 0.206004i) q^{77} +(-6.12796 + 4.45222i) q^{78} +4.32293i q^{79} +(-0.0916742 - 0.282144i) q^{80} -6.83091 q^{81} +(-3.76346 + 3.24565i) q^{82} -1.61137 q^{83} +(-1.10972 - 3.41536i) q^{84} -1.00944i q^{85} +(-4.12203 + 2.99483i) q^{86} +(16.7096 - 12.1402i) q^{87} +(0.878971 - 0.285595i) q^{88} +(2.95730 + 0.960884i) q^{89} +(-0.896409 - 0.651279i) q^{90} -3.79819 q^{91} +(-2.50354 - 1.81893i) q^{92} +(-7.83786 + 10.7879i) q^{93} +(3.32884 + 4.58176i) q^{94} +(-0.382728 + 0.124356i) q^{95} -15.0442i q^{96} +(-9.40522 - 12.9452i) q^{97} +(-0.239839 + 0.738150i) q^{98} +(-0.742059 + 1.02136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9}+O(q^{10}) $ 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9	$ 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9} + 36 q^{10} - 10 q^{11} + 20 q^{15} - 12 q^{16} - 10 q^{17} + 20 q^{18} + 30 q^{19} - 30 q^{20} + 4 q^{21} - 20 q^{22} - 12 q^{23} + 60 q^{24} - 50 q^{25} - 30 q^{26} + 2 q^{31} + 24 q^{32} - 46 q^{33} + 50 q^{34} + 86 q^{36} - 48 q^{37} + 16 q^{39} - 60 q^{40} - 24 q^{41} - 4 q^{42} + 22 q^{43} - 16 q^{45} + 20 q^{46} + 20 q^{48} + 22 q^{49} - 16 q^{50} + 8 q^{51} + 70 q^{52} - 30 q^{54} + 8 q^{57} - 90 q^{58} - 4 q^{59} - 50 q^{60} - 64 q^{61} - 44 q^{62} + 14 q^{64} + 80 q^{65} - 26 q^{66} + 10 q^{67} + 40 q^{71} + 18 q^{72} + 124 q^{73} + 80 q^{74} + 70 q^{75} - 190 q^{76} + 8 q^{77} + 74 q^{78} + 26 q^{80} + 144 q^{81} - 58 q^{82} - 60 q^{83} + 26 q^{84} + 10 q^{86} + 8 q^{87} + 160 q^{88} - 164 q^{90} - 40 q^{91} - 156 q^{92} - 20 q^{93} + 10 q^{94} + 80 q^{95} - 90 q^{97} - 40 q^{99}+O(q^{100}) $ 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9 + 36 * q^10 - 10 * q^11 + 20 * q^15 - 12 * q^16 - 10 * q^17 + 20 * q^18 + 30 * q^19 - 30 * q^20 + 4 * q^21 - 20 * q^22 - 12 * q^23 + 60 * q^24 - 50 * q^25 - 30 * q^26 + 2 * q^31 + 24 * q^32 - 46 * q^33 + 50 * q^34 + 86 * q^36 - 48 * q^37 + 16 * q^39 - 60 * q^40 - 24 * q^41 - 4 * q^42 + 22 * q^43 - 16 * q^45 + 20 * q^46 + 20 * q^48 + 22 * q^49 - 16 * q^50 + 8 * q^51 + 70 * q^52 - 30 * q^54 + 8 * q^57 - 90 * q^58 - 4 * q^59 - 50 * q^60 - 64 * q^61 - 44 * q^62 + 14 * q^64 + 80 * q^65 - 26 * q^66 + 10 * q^67 + 40 * q^71 + 18 * q^72 + 124 * q^73 + 80 * q^74 + 70 * q^75 - 190 * q^76 + 8 * q^77 + 74 * q^78 + 26 * q^80 + 144 * q^81 - 58 * q^82 - 60 * q^83 + 26 * q^84 + 10 * q^86 + 8 * q^87 + 160 * q^88 - 164 * q^90 - 40 * q^91 - 156 * q^92 - 20 * q^93 + 10 * q^94 + 80 * q^95 - 90 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.239839	+	0.738150i	0.169592	+	0.521951i	0.999345	−	0.0361798i	$-0.0115189\pi$
$2$	0.239839	+	0.738150i	0.169592	+	0.521951i	−0.829753	+	0.558130i	$0.811519\pi$
$3$		−	2.56947i		−	1.48348i	−0.670686	−	0.741741i	$-0.734000\pi$
$3$		−	2.56947i		−	1.48348i	0.670686	−	0.741741i	$-0.266000\pi$
$4$	1.13069	−	0.821496i	0.565346	−	0.410748i
$5$	0.320630	−	0.232952i	0.143390	−	0.104179i	−0.513777	−	0.857923i	$-0.671754\pi$
$5$	0.320630	−	0.232952i	0.143390	−	0.104179i	0.657168	+	0.753744i	$0.271754\pi$
$6$	1.89665	−	0.616259i	0.774305	−	0.251587i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$8$	2.13339	+	1.55000i	0.754266	+	0.548006i
$9$	−3.60216			−1.20072
$10$	0.248853	+	0.180802i	0.0786942	+	0.0571747i
$11$	0.206004	−	0.283540i	0.0621125	−	0.0854905i	−0.776831	−	0.629709i	$-0.783174\pi$
$11$	0.206004	−	0.283540i	0.0621125	−	0.0854905i	0.838943	+	0.544219i	$0.183174\pi$
$12$	−2.11081	−	2.90528i	−0.609338	−	0.838681i
$13$	−3.61230	+	1.17371i	−1.00187	+	0.325527i	−0.763613	−	0.645675i	$-0.776576\pi$
$13$	−3.61230	+	1.17371i	−1.00187	+	0.325527i	−0.238258	+	0.971202i	$0.576576\pi$
$14$			0.776136i			0.207431i
$15$	−0.598562	−	0.823849i	−0.154548	−	0.212717i
$16$	0.231313	−	0.711908i	0.0578282	−	0.177977i
$17$	1.49711	−	2.06060i	0.363103	−	0.499768i	−0.587907	−	0.808929i	$-0.700048\pi$
$17$	1.49711	−	2.06060i	0.363103	−	0.499768i	0.951010	+	0.309160i	$0.100048\pi$
$18$	−0.863941	−	2.65894i	−0.203633	−	0.626717i
$19$	−0.965702	−	0.313776i	−0.221547	−	0.0719851i	0.196140	−	0.980576i	$-0.437159\pi$
$19$	−0.965702	−	0.313776i	−0.221547	−	0.0719851i	−0.417687	+	0.908591i	$0.637159\pi$
$20$	0.171165	−	0.526793i	0.0382738	−	0.117795i
$21$	0.794009	−	2.44371i	0.173267	−	0.533261i
$22$	0.258703	+	0.0840576i	0.0551556	+	0.0179211i
$23$	−0.684214	−	2.10579i	−0.142668	−	0.439088i	0.854035	−	0.520215i	$-0.174148\pi$
$23$	−0.684214	−	2.10579i	−0.142668	−	0.439088i	−0.996704	+	0.0811266i	$0.974148\pi$
$24$	3.98266	−	5.48167i	0.812958	−	1.11894i
$25$	−1.49655	+	4.60590i	−0.299310	+	0.921180i
$26$	−1.73274	−	2.38491i	−0.339818	−	0.467720i
$27$			1.54724i			0.297767i
$28$	1.32921	−	0.431886i	0.251197	−	0.0816188i
$29$	4.72480	+	6.50313i	0.877373	+	1.20760i	0.977142	+	0.212590i	$0.0681898\pi$
$29$	4.72480	+	6.50313i	0.877373	+	1.20760i	−0.0997684	+	0.995011i	$0.531810\pi$
$30$	0.464565	−	0.639420i	0.0848177	−	0.116741i
$31$	−4.19849	−	3.05038i	−0.754072	−	0.547865i	0.143015	−	0.989721i	$-0.454320\pi$
$31$	−4.19849	−	3.05038i	−0.754072	−	0.547865i	−0.897086	+	0.441856i	$0.854320\pi$
$32$	5.85499			1.03503
$33$	−0.728547	−	0.529320i	−0.126824	−	0.0921428i
$34$	1.88010	+	0.610880i	0.322434	+	0.104765i
$35$	0.376924	−	0.122470i	0.0637117	−	0.0207012i
$36$	−4.07294	+	2.95916i	−0.678823	+	0.493194i
$37$	−4.79777	+	3.48578i	−0.788748	+	0.573059i	−0.907592	−	0.419854i	$-0.862081\pi$
$37$	−4.79777	+	3.48578i	−0.788748	+	0.573059i	0.118844	+	0.992913i	$0.462081\pi$
$38$		−	0.788088i		−	0.127845i
$39$	3.01580	+	9.28168i	0.482914	+	1.48626i
$40$	1.04510			0.165245
$41$	2.47872	+	5.90389i	0.387110	+	0.922033i
$41$	2.47872	+	5.90389i	0.387110	+	0.922033i
$42$	1.99426			0.307721
$43$	2.02860	+	6.24340i	0.309359	+	0.952110i	0.978014	+	0.208537i	$0.0668703\pi$
$43$	2.02860	+	6.24340i	0.309359	+	0.952110i	−0.668655	+	0.743573i	$0.733130\pi$
$44$		−	0.489828i		−	0.0738443i
$45$	−1.15496	+	0.839130i	−0.172172	+	0.125090i
$46$	1.39029	−	1.01010i	0.204987	−	0.148932i
$47$	6.93974	−	2.25486i	1.01226	−	0.328905i	0.244509	−	0.969647i	$-0.421373\pi$
$47$	6.93974	−	2.25486i	1.01226	−	0.328905i	0.767756	+	0.640742i	$0.221373\pi$
$48$	−1.82922	−	0.594351i	−0.264026	−	0.0857872i
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	−3.75877			−0.531571
$51$	−5.29464	−	3.84678i	−0.741398	−	0.538657i
$52$	−3.12020	+	4.29459i	−0.432694	+	0.595552i
$53$	−3.10400	−	4.27229i	−0.426368	−	0.586845i	0.540747	−	0.841185i	$-0.318142\pi$
$53$	−3.10400	−	4.27229i	−0.426368	−	0.586845i	−0.967115	+	0.254341i	$0.918142\pi$
$54$	−1.14210	+	0.371089i	−0.155420	+	0.0504989i
$55$		−	0.138900i		−	0.0187293i
$56$	1.55000	+	2.13339i	0.207127	+	0.285086i
$57$	−0.806236	+	2.48134i	−0.106789	+	0.328662i
$58$	−3.66709	+	5.04731i	−0.481512	+	0.662745i
$59$	2.40866	+	7.41310i	0.313581	+	0.965103i	0.976335	+	0.216265i	$0.0693877\pi$
$59$	2.40866	+	7.41310i	0.313581	+	0.965103i	−0.662754	+	0.748838i	$0.730612\pi$
$60$	−1.35358	−	0.439804i	−0.174746	−	0.0567785i
$61$	1.36765	−	4.20918i	0.175109	−	0.538930i	−0.824529	−	0.565819i	$-0.808560\pi$
$61$	1.36765	−	4.20918i	0.175109	−	0.538930i	0.999638	+	0.0268889i	$0.00856002\pi$
$62$	1.24468	−	3.83072i	0.158074	−	0.486502i
$63$	−3.42586	−	1.11313i	−0.431618	−	0.140241i
$64$	0.941632	+	2.89805i	0.117704	+	0.362256i
$65$	−0.884795	+	1.21782i	−0.109745	+	0.151051i
$66$	0.215983	−	0.664728i	0.0265857	−	0.0818224i
$67$	3.78227	+	5.20584i	0.462077	+	0.635995i	0.974938	−	0.222477i	$-0.0714142\pi$
$67$	3.78227	+	5.20584i	0.462077	+	0.635995i	−0.512860	+	0.858472i	$0.671414\pi$
$68$		−	3.55977i		−	0.431686i
$69$	−5.41077	+	1.75807i	−0.651380	+	0.211646i
$70$	0.180802	+	0.248853i	0.0216100	+	0.0297436i
$71$	3.63175	−	4.99868i	0.431010	−	0.593234i	−0.537175	−	0.843471i	$-0.680509\pi$
$71$	3.63175	−	4.99868i	0.431010	−	0.593234i	0.968185	+	0.250237i	$0.0805086\pi$
$72$	−7.68481	−	5.58334i	−0.905663	−	0.658003i
$73$	−8.89270			−1.04081			−0.520406	−	0.853919i	$-0.674219\pi$
$73$	−8.89270			−1.04081			−0.520406	+	0.853919i	$0.674219\pi$
$74$	−3.72372	−	2.70544i	−0.432874	−	0.314501i
$75$	11.8347	+	3.84533i	1.36655	+	0.444021i
$76$	−1.34968	+	0.438537i	−0.154819	+	0.0503036i
$77$	0.283540	−	0.206004i	0.0323124	−	0.0234763i
$78$	−6.12796	+	4.45222i	−0.693855	+	0.504115i
$79$			4.32293i			0.486367i	0.969980	+	0.243184i	$0.0781917\pi$
$79$			4.32293i			0.486367i	−0.969980	+	0.243184i	$0.921808\pi$
$80$	−0.0916742	−	0.282144i	−0.0102495	−	0.0315447i
$81$	−6.83091			−0.758990
$82$	−3.76346	+	3.24565i	−0.415605	+	0.358422i
$83$	−1.61137			−0.176871			−0.0884355	−	0.996082i	$-0.528187\pi$
$83$	−1.61137			−0.176871			−0.0884355	+	0.996082i	$0.528187\pi$
$84$	−1.10972	−	3.41536i	−0.121080	−	0.372646i
$85$		−	1.00944i		−	0.109490i
$86$	−4.12203	+	2.99483i	−0.444490	+	0.322941i
$87$	16.7096	−	12.1402i	1.79145	−	1.30157i
$88$	0.878971	−	0.285595i	0.0936987	−	0.0304445i
$89$	2.95730	+	0.960884i	0.313473	+	0.101853i	0.461528	−	0.887126i	$-0.347301\pi$
$89$	2.95730	+	0.960884i	0.313473	+	0.101853i	−0.148055	+	0.988979i	$0.547301\pi$
$90$	−0.896409	−	0.651279i	−0.0944898	−	0.0686509i
$91$	−3.79819			−0.398159
$92$	−2.50354	−	1.81893i	−0.261012	−	0.189636i
$93$	−7.83786	+	10.7879i	−0.812748	+	1.11865i
$94$	3.32884	+	4.58176i	0.343344	+	0.472573i
$95$	−0.382728	+	0.124356i	−0.0392671	+	0.0127586i
$96$		−	15.0442i		−	1.53544i
$97$	−9.40522	−	12.9452i	−0.954955	−	1.31438i	−0.949291	−	0.314399i	$-0.898197\pi$
$97$	−9.40522	−	12.9452i	−0.954955	−	1.31438i	−0.00566466	−	0.999984i	$-0.501803\pi$
$98$	−0.239839	+	0.738150i	−0.0242274	+	0.0745644i
$99$	−0.742059	+	1.02136i	−0.0745798	+	0.102650i
$100$	2.09159	+	6.43726i	0.209159	+	0.643726i
$101$	−1.67645	−	0.544713i	−0.166813	−	0.0542010i	0.224420	−	0.974493i	$-0.427951\pi$
$101$	−1.67645	−	0.544713i	−0.166813	−	0.0542010i	−0.391233	+	0.920292i	$0.627951\pi$
$102$	1.56964	−	4.83085i	0.155417	−	0.478325i
$103$	−2.07739	+	6.39354i	−0.204691	+	0.629975i	0.795035	+	0.606564i	$0.207453\pi$
$103$	−2.07739	+	6.39354i	−0.204691	+	0.629975i	−0.999726	+	0.0234107i	$0.992547\pi$
$104$	−9.52566	−	3.09508i	−0.934068	−	0.303497i
$105$	−0.314682	−	0.968493i	−0.0307099	−	0.0945152i
$106$	2.40913	−	3.31588i	0.233995	−	0.322067i
$107$	−2.84963	+	8.77026i	−0.275484	+	0.847853i	0.713607	+	0.700546i	$0.247060\pi$
$107$	−2.84963	+	8.77026i	−0.275484	+	0.847853i	−0.989091	+	0.147306i	$0.952940\pi$
$108$	1.27105	+	1.74945i	0.122307	+	0.168341i
$109$		−	15.5431i		−	1.48876i	−0.667758	−	0.744379i	$-0.732746\pi$
$109$		−	15.5431i		−	1.48876i	0.667758	−	0.744379i	$-0.267254\pi$
$110$	0.102529	−	0.0333138i	0.00977578	−	0.00317634i
$111$	8.95660	+	12.3277i	0.850123	+	1.17009i
$112$	0.439983	−	0.605585i	0.0415745	−	0.0572224i
$113$	−7.34716	−	5.33802i	−0.691163	−	0.502159i	0.185880	−	0.982573i	$-0.440487\pi$
$113$	−7.34716	−	5.33802i	−0.691163	−	0.502159i	−0.877042	+	0.480414i	$0.840487\pi$
$114$	−2.02497			−0.189656
$115$	−0.709928	−	0.515793i	−0.0662011	−	0.0480979i
$116$	10.6846	+	3.47163i	0.992039	+	0.322333i
$117$	13.0121	−	4.22788i	1.20297	−	0.390868i
$118$	−4.89428	+	3.55590i	−0.450555	+	0.327348i
$119$	2.06060	−	1.49711i	0.188895	−	0.137240i
$120$		−	2.68536i		−	0.245138i
$121$	3.36123	+	10.3448i	0.305566	+	0.940436i
$122$	3.43502			0.310992
$123$	15.1699	−	6.36898i	1.36782	−	0.574272i
$124$	−7.25308			−0.651346
$125$	1.20546	+	3.71003i	0.107820	+	0.331835i
$126$		−	2.79577i		−	0.249067i
$127$	9.57943	−	6.95986i	0.850037	−	0.617588i	−0.0751195	−	0.997175i	$-0.523934\pi$
$127$	9.57943	−	6.95986i	0.850037	−	0.617588i	0.925156	+	0.379587i	$0.123934\pi$
$128$	7.56023	−	5.49283i	0.668236	−	0.485502i
$129$	16.0422	−	5.21243i	1.41244	−	0.458929i
$130$	−1.11114	−	0.361031i	−0.0974533	−	0.0316645i
$131$	15.1093	+	10.9775i	1.32010	+	0.959111i	0.999931	+	0.0117511i	$0.00374058\pi$
$131$	15.1093	+	10.9775i	1.32010	+	0.959111i	0.320172	+	0.947360i	$0.396259\pi$
$132$	−1.25860			−0.109547
$133$	−0.821475	−	0.596837i	−0.0712309	−	0.0517523i
$134$	−2.93556	+	4.04045i	−0.253593	+	0.349041i
$135$	0.360432	+	0.496092i	0.0310211	+	0.0426968i
$136$	6.38784	−	2.07553i	0.547752	−	0.177976i
$137$		−	5.37439i		−	0.459165i	−0.973289	−	0.229583i	$-0.926264\pi$
$137$		−	5.37439i		−	0.459165i	0.973289	−	0.229583i	$-0.0737361\pi$
$138$	−2.59543	−	3.57230i	−0.220938	−	0.304095i
$139$	−3.43964	+	10.5861i	−0.291747	+	0.897905i	0.692548	+	0.721372i	$0.256488\pi$
$139$	−3.43964	+	10.5861i	−0.291747	+	0.897905i	−0.984295	+	0.176533i	$0.943512\pi$
$140$	0.325576	−	0.448117i	0.0275162	−	0.0378728i
$141$	−5.79378	−	17.8314i	−0.487925	−	1.50168i
$142$	4.56081	+	1.48190i	0.382734	+	0.124358i
$143$	−0.411354	+	1.26602i	−0.0343992	+	0.105870i
$144$	−0.833227	+	2.56441i	−0.0694356	+	0.213701i
$145$	3.02983	+	0.984451i	0.251614	+	0.0817542i
$146$	−2.13282	−	6.56414i	−0.176513	−	0.543252i
$147$	1.51030	−	2.07874i	0.124567	−	0.171452i
$148$	−2.56124	+	7.88269i	−0.210533	+	0.647953i
$149$	1.85501	+	2.55320i	0.151968	+	0.209166i	0.878213	−	0.478270i	$-0.158736\pi$
$149$	1.85501	+	2.55320i	0.151968	+	0.209166i	−0.726245	+	0.687436i	$0.758736\pi$
$150$			9.65805i			0.788576i
$151$	13.6885	−	4.44766i	1.11395	−	0.361946i	0.306497	−	0.951872i	$-0.400843\pi$
$151$	13.6885	−	4.44766i	1.11395	−	0.361946i	0.807457	+	0.589926i	$0.200843\pi$
$152$	−1.57386	−	2.16624i	−0.127657	−	0.175705i
$153$	−5.39284	+	7.42261i	−0.435985	+	0.600083i
$154$	0.220066	+	0.159887i	0.0177334	+	0.0128841i
$155$	−2.05676			−0.165203
$156$	11.0348	+	8.01725i	0.883491	+	0.641894i
$157$	2.26675	+	0.736510i	0.180906	+	0.0587799i	0.398069	−	0.917355i	$-0.369680\pi$
$157$	2.26675	+	0.736510i	0.180906	+	0.0587799i	−0.217163	+	0.976135i	$0.569680\pi$
$158$	−3.19097	+	1.03681i	−0.253860	+	0.0824840i
$159$	−10.9775	+	7.97564i	−0.870574	+	0.632509i
$160$	1.87729	−	1.36393i	0.148413	−	0.107828i
$161$		−	2.21416i		−	0.174500i
$162$	−1.63832	−	5.04223i	−0.128719	−	0.396155i
$163$	−21.1104			−1.65349			−0.826747	−	0.562573i	$-0.809811\pi$
$163$	−21.1104			−1.65349			−0.826747	+	0.562573i	$0.809811\pi$
$164$	7.65269	+	4.63923i	0.597575	+	0.362263i
$165$	−0.356900			−0.0277846
$166$	−0.386470	−	1.18943i	−0.0299959	−	0.0923180i
$167$		−	19.4055i		−	1.50165i	−0.660504	−	0.750823i	$-0.729657\pi$
$167$		−	19.4055i		−	1.50165i	0.660504	−	0.750823i	$-0.270343\pi$
$168$	5.48167	−	3.98266i	0.422920	−	0.307269i
$169$	1.15387	−	0.838337i	0.0887594	−	0.0644874i
$170$	0.745121	−	0.242105i	0.0571482	−	0.0185686i
$171$	3.47862	+	1.13027i	0.266016	+	0.0864340i
$172$	7.42266	+	5.39288i	0.565972	+	0.411203i
$173$	−13.3983			−1.01865			−0.509326	−	0.860574i	$-0.670105\pi$
$173$	−13.3983			−1.01865			−0.509326	+	0.860574i	$0.670105\pi$
$174$	12.9689	+	9.42247i	0.983171	+	0.714315i
$175$	−2.84660	+	3.91801i	−0.215183	+	0.296174i
$176$	−0.154203	−	0.212242i	−0.0116235	−	0.0159984i
$177$	19.0477	−	6.18898i	1.43171	−	0.465192i
$178$			2.41338i			0.180891i
$179$	−8.49838	−	11.6970i	−0.635199	−	0.874276i	0.363150	−	0.931731i	$-0.381701\pi$
$179$	−8.49838	−	11.6970i	−0.635199	−	0.874276i	−0.998348	+	0.0574551i	$0.981701\pi$
$180$	−0.616566	+	1.89759i	−0.0459561	+	0.141438i
$181$	−10.3564	+	14.2544i	−0.769787	+	1.05952i	0.226549	+	0.974000i	$0.427256\pi$
$181$	−10.3564	+	14.2544i	−0.769787	+	1.05952i	−0.996336	+	0.0855212i	$0.972744\pi$
$182$	−0.910956	−	2.80363i	−0.0675245	−	0.207819i
$183$	−10.8154	−	3.51412i	−0.799494	−	0.259771i
$184$	1.80428	−	5.55300i	0.133013	−	0.409373i
$185$	−0.726291	+	2.23530i	−0.0533980	+	0.164342i
$186$	−9.84290	−	3.19815i	−0.721717	−	0.234500i
$187$	−0.275851	−	0.848982i	−0.0201722	−	0.0620837i
$188$	5.99435	−	8.25051i	0.437183	−	0.601731i
$189$	−0.478124	+	1.47151i	−0.0347784	+	0.107037i
$190$	−0.183586	−	0.252685i	−0.0133188	−	0.0183317i
$191$		−	16.7934i		−	1.21513i	−0.794270	−	0.607565i	$-0.792146\pi$
$191$		−	16.7934i		−	1.21513i	0.794270	−	0.607565i	$-0.207854\pi$
$192$	7.44643	−	2.41949i	0.537400	−	0.174612i
$193$	−14.7434	−	20.2926i	−1.06126	−	1.46069i	−0.878625	−	0.477512i	$-0.841539\pi$
$193$	−14.7434	−	20.2926i	−1.06126	−	1.46069i	−0.182631	−	0.983182i	$-0.558461\pi$
$194$	7.29973	−	10.0472i	0.524090	−	0.721349i
$195$	3.12914	+	2.27345i	0.224082	+	0.162805i
$196$	1.39761			0.0998294
$197$	−9.38800	−	6.82078i	−0.668867	−	0.485961i	0.200779	−	0.979637i	$-0.435653\pi$
$197$	−9.38800	−	6.82078i	−0.668867	−	0.485961i	−0.869646	+	0.493676i	$0.835653\pi$
$198$	−0.931889	−	0.302789i	−0.0662265	−	0.0215183i
$199$	7.68470	−	2.49691i	0.544754	−	0.177001i	−0.0236960	−	0.999719i	$-0.507543\pi$
$199$	7.68470	−	2.49691i	0.544754	−	0.177001i	0.568450	+	0.822718i	$0.307543\pi$
$200$	−10.3318	+	7.50652i	−0.730571	+	0.530791i
$201$	13.3762	−	9.71841i	0.943488	−	0.685484i
$202$		−	1.36812i		−	0.0962604i
$203$	2.48397	+	7.64489i	0.174341	+	0.536566i
$204$	−9.14672			−0.640399
$205$	2.17007	+	1.31555i	0.151564	+	0.0918818i
$206$	−5.21763			−0.363530
$207$	2.46465	+	7.58541i	0.171305	+	0.527223i
$208$			2.84312i			0.197135i
$209$	−0.287906	+	0.209176i	−0.0199149	+	0.0144690i
$210$	0.639420	−	0.464565i	0.0441241	−	0.0320581i
$211$	−11.5151	+	3.74147i	−0.792729	+	0.257573i	−0.677266	−	0.735739i	$-0.736835\pi$
$211$	−11.5151	+	3.74147i	−0.792729	+	0.257573i	−0.115463	+	0.993312i	$0.536835\pi$
$212$	−7.01934	−	2.28072i	−0.482091	−	0.156641i
$213$	−12.8439	−	9.33167i	−0.880052	−	0.639395i
$214$	−7.15721			−0.489257
$215$	2.10484	+	1.52926i	0.143549	+	0.104295i
$216$	−2.39822	+	3.30086i	−0.163178	+	0.224595i
$217$	−3.05038	−	4.19849i	−0.207074	−	0.285012i
$218$	11.4731	−	3.72784i	0.777058	−	0.252481i
$219$			22.8495i			1.54403i
$220$	−0.114106	−	0.157054i	−0.00769303	−	0.0105886i
$221$	−2.98947	+	9.20066i	−0.201094	+	0.618903i
$222$	−6.95155	+	9.56798i	−0.466557	+	0.642161i
$223$	−8.04885	−	24.7718i	−0.538991	−	1.65884i	−0.734864	−	0.678214i	$-0.762754\pi$
$223$	−8.04885	−	24.7718i	−0.538991	−	1.65884i	0.195873	−	0.980629i	$-0.437246\pi$
$224$	5.56843	+	1.80929i	0.372056	+	0.120888i
$225$	5.39081	−	16.5912i	0.359387	−	1.10608i
$226$	2.17812	−	6.70357i	0.144887	−	0.445915i
$227$	−20.8453	−	6.77305i	−1.38355	−	0.449543i	−0.479716	−	0.877424i	$-0.659260\pi$
$227$	−20.8453	−	6.77305i	−1.38355	−	0.449543i	−0.903835	+	0.427880i	$0.859260\pi$
$228$	1.12681	+	3.46795i	0.0746245	+	0.229671i
$229$	3.97134	−	5.46607i	0.262433	−	0.361208i	−0.657384	−	0.753556i	$-0.728337\pi$
$229$	3.97134	−	5.46607i	0.262433	−	0.361208i	0.919817	+	0.392348i	$0.128337\pi$
$230$	0.210464	−	0.647740i	0.0138776	−	0.0427107i
$231$	−0.529320	−	0.728547i	−0.0348267	−	0.0479348i
$232$			21.1971i			1.39166i
$233$	−6.85304	+	2.22669i	−0.448957	+	0.145875i	−0.524765	−	0.851247i	$-0.675847\pi$
$233$	−6.85304	+	2.22669i	−0.448957	+	0.145875i	0.0758072	+	0.997122i	$0.475847\pi$
$234$	6.24162	+	8.59085i	0.408027	+	0.561601i
$235$	1.69982	−	2.33960i	0.110884	−	0.152619i
$236$	8.81328	+	6.40322i	0.573696	+	0.416814i
$237$	11.1076			0.721517
$238$	1.59931	+	1.16196i	0.103668	+	0.0753189i
$239$	0.361289	+	0.117390i	0.0233698	+	0.00759332i	0.320679	−	0.947188i	$-0.396089\pi$
$239$	0.361289	+	0.117390i	0.0233698	+	0.00759332i	−0.297309	+	0.954781i	$0.596089\pi$
$240$	−0.724960	+	0.235554i	−0.0467960	+	0.0152049i
$241$	−17.8040	+	12.9354i	−1.14686	+	0.833240i	−0.988060	−	0.154071i	$-0.950762\pi$
$241$	−17.8040	+	12.9354i	−1.14686	+	0.833240i	−0.158797	+	0.987311i	$0.550762\pi$
$242$	−6.82986	+	4.96218i	−0.439040	+	0.318981i
$243$			22.1935i			1.42371i
$244$	−1.91144	−	5.88280i	−0.122367	−	0.376608i
$245$	0.396321			0.0253200
$246$	8.33959	+	9.67010i	0.531713	+	0.616543i
$247$	3.85668			0.245395
$248$	−4.22893	−	13.0153i	−0.268537	−	0.826472i
$249$			4.14037i			0.262385i
$250$	−2.44944	+	1.77962i	−0.154916	+	0.112553i
$251$	6.89143	−	5.00691i	0.434983	−	0.316034i	−0.348655	−	0.937251i	$-0.613362\pi$
$251$	6.89143	−	5.00691i	0.434983	−	0.316034i	0.783638	+	0.621217i	$0.213362\pi$
$252$	−4.78803	+	1.55572i	−0.301617	+	0.0980014i
$253$	−0.738027	−	0.239800i	−0.0463994	−	0.0150761i
$254$	7.43494	+	5.40180i	0.466510	+	0.338939i
$255$	−2.59374			−0.162426
$256$	10.7982	+	7.84536i	0.674889	+	0.490335i
$257$	−12.6513	+	17.4130i	−0.789163	+	1.08619i	0.205048	+	0.978752i	$0.434265\pi$
$257$	−12.6513	+	17.4130i	−0.789163	+	1.08619i	−0.994212	+	0.107438i	$0.965735\pi$
$258$	7.69511	+	10.5914i	0.479077	+	0.659393i
$259$	−5.64011	+	1.83258i	−0.350460	+	0.113871i
$260$			2.10383i			0.130474i
$261$	−17.0195	−	23.4253i	−1.05348	−	1.44999i
$262$	−4.47926	+	13.7857i	−0.276730	+	0.851686i
$263$	−0.459851	+	0.632930i	−0.0283556	+	0.0390282i	−0.822959	−	0.568100i	$-0.807679\pi$
$263$	−0.459851	+	0.632930i	−0.0283556	+	0.0390282i	0.794604	+	0.607128i	$0.207679\pi$
$264$	−0.733827	−	2.25849i	−0.0451640	−	0.139000i
$265$	−1.99048	−	0.646745i	−0.122274	−	0.0397292i
$266$	0.243533	−	0.749517i	0.0149319	−	0.0459558i
$267$	2.46896	−	7.59868i	0.151098	−	0.465031i
$268$	8.55316	+	2.77909i	0.522467	+	0.169760i
$269$	0.564962	+	1.73877i	0.0344463	+	0.106015i	0.966801	−	0.255529i	$-0.0822497\pi$
$269$	0.564962	+	1.73877i	0.0344463	+	0.106015i	−0.932355	+	0.361544i	$0.882250\pi$
$270$	−0.279745	+	0.385035i	−0.0170247	+	0.0234325i
$271$	4.10878	−	12.6455i	0.249591	−	0.768161i	−0.745257	−	0.666778i	$-0.767673\pi$
$271$	4.10878	−	12.6455i	0.249591	−	0.768161i	0.994847	−	0.101384i	$-0.0323269\pi$
$272$	−1.12065	−	1.54245i	−0.0679497	−	0.0935247i
$273$			9.75933i			0.590662i
$274$	3.96711	−	1.28899i	0.239662	−	0.0778708i
$275$	0.997662	+	1.37316i	0.0601613	+	0.0828049i
$276$	−4.67367	+	6.43275i	−0.281322	+	0.387206i
$277$	5.58948	+	4.06100i	0.335839	+	0.244002i	0.742904	−	0.669398i	$-0.233448\pi$
$277$	5.58948	+	4.06100i	0.335839	+	0.244002i	−0.407065	+	0.913399i	$0.633448\pi$
$278$	−8.63912			−0.518140
$279$	15.1237	+	10.9880i	0.905430	+	0.657833i
$280$	0.993952	+	0.322954i	0.0594000	+	0.0193002i
$281$	29.1959	−	9.48631i	1.74168	−	0.565906i	0.746625	−	0.665245i	$-0.231673\pi$
$281$	29.1959	−	9.48631i	1.74168	−	0.565906i	0.995054	+	0.0993389i	$0.0316728\pi$
$282$	11.7727	−	8.55336i	0.701053	−	0.509345i
$283$	16.3683	−	11.8923i	0.972996	−	0.706923i	0.0168637	−	0.999858i	$-0.494632\pi$
$283$	16.3683	−	11.8923i	0.972996	−	0.706923i	0.956132	+	0.292935i	$0.0946319\pi$
$284$		−	8.63543i		−	0.512419i
$285$	0.319528	+	0.983407i	0.0189272	+	0.0582520i
$286$	−1.03317			−0.0610926
$287$	0.532995	+	6.38090i	0.0314617	+	0.376653i
$288$	−21.0906			−1.24278
$289$	3.24857	+	9.99807i	0.191092	+	0.588122i
$290$			2.47258i			0.145195i
$291$	−33.2622	+	24.1664i	−1.94987	+	1.41666i
$292$	−10.0549	+	7.30531i	−0.588419	+	0.427511i
$293$	−12.6551	+	4.11190i	−0.739321	+	0.240220i	−0.654380	−	0.756166i	$-0.727070\pi$
$293$	−12.6551	+	4.11190i	−0.739321	+	0.240220i	−0.0849410	+	0.996386i	$0.527070\pi$
$294$	1.89665	+	0.616259i	0.110615	+	0.0359410i
$295$	2.49918	+	1.81576i	0.145508	+	0.105718i
$296$	−15.6384			−0.908966
$297$	0.438705	+	0.318738i	0.0254562	+	0.0184950i
$298$	−1.43974	+	1.98163i	−0.0834018	+	0.114793i
$299$	4.94317	+	6.80368i	0.285871	+	0.393467i
$300$	16.5403	−	5.37428i	0.954957	−	0.310284i
$301$			6.56470i			0.378383i
$302$	6.56608	+	9.03743i	0.377835	+	0.520046i
$303$	−1.39962	+	4.30759i	−0.0804062	+	0.247465i
$304$	−0.446759	+	0.614911i	−0.0256234	+	0.0352675i
$305$	−0.542027	−	1.66819i	−0.0310364	−	0.0955201i
$306$	−6.77241	−	2.20049i	−0.387153	−	0.125794i
$307$	−4.99112	+	15.3611i	−0.284858	+	0.876703i	0.701583	+	0.712588i	$0.252477\pi$
$307$	−4.99112	+	15.3611i	−0.284858	+	0.876703i	−0.986441	+	0.164115i	$0.947523\pi$
$308$	0.151365	−	0.465854i	0.00862482	−	0.0265445i
$309$	16.4280	+	5.33778i	0.934556	+	0.303656i
$310$	−0.493291	−	1.51819i	−0.0280170	−	0.0862276i
$311$	0.964173	−	1.32707i	0.0546732	−	0.0752513i	−0.780805	−	0.624775i	$-0.785191\pi$
$311$	0.964173	−	1.32707i	0.0546732	−	0.0752513i	0.835478	+	0.549524i	$0.185191\pi$
$312$	−7.95270	+	24.4759i	−0.450233	+	1.38567i
$313$	3.78017	+	5.20295i	0.213668	+	0.294088i	0.902375	−	0.430951i	$-0.141822\pi$
$313$	3.78017	+	5.20295i	0.213668	+	0.294088i	−0.688708	+	0.725039i	$0.741822\pi$
$314$			1.84984i			0.104393i
$315$	−1.35774	+	0.441157i	−0.0765000	+	0.0248564i
$316$	3.55127	+	4.88790i	0.199774	+	0.274966i
$317$	14.5099	−	19.9712i	0.814958	−	1.12169i	−0.175582	−	0.984465i	$-0.556181\pi$
$317$	14.5099	−	19.9712i	0.814958	−	1.12169i	0.990539	−	0.137228i	$-0.0438193\pi$
$318$	−8.52005	−	6.19018i	−0.477781	−	0.347128i
$319$	2.81722			0.157734
$320$	0.977020	+	0.709847i	0.0546171	+	0.0396816i
$321$	22.5349	+	7.32203i	1.25777	+	0.408676i
$322$	1.63438	−	0.531043i	0.0910806	−	0.0295939i
$323$	−2.09233	+	1.52017i	−0.116420	+	0.0845843i
$324$	−7.72365	+	5.61156i	−0.429092	+	0.311753i
$325$		−	18.3944i		−	1.02034i
$326$	−5.06311	−	15.5826i	−0.280420	−	0.863043i
$327$	−39.9374			−2.20855
$328$	−3.86295	+	16.4373i	−0.213296	+	0.907597i
$329$	7.29687			0.402290
$330$	−0.0855987	−	0.263446i	−0.00471205	−	0.0145022i
$331$			7.26062i			0.399080i	0.979890	+	0.199540i	$0.0639447\pi$
$331$			7.26062i			0.399080i	−0.979890	+	0.199540i	$0.936055\pi$
$332$	−1.82197	+	1.32374i	−0.0999933	+	0.0726494i
$333$	17.2823	−	12.5564i	0.947067	−	0.688084i
$334$	14.3242	−	4.65421i	0.783785	−	0.254667i
$335$	2.42542	+	0.788067i	0.132515	+	0.0430567i
$336$	−1.55603	−	1.13052i	−0.0848885	−	0.0616751i
$337$	14.9801			0.816019			0.408009	−	0.912978i	$-0.366223\pi$
$337$	14.9801			0.816019			0.408009	+	0.912978i	$0.366223\pi$
$338$	0.895562	+	0.650664i	0.0487121	+	0.0353914i
$339$	−13.7159	+	18.8783i	−0.744944	+	1.02533i
$340$	−0.829255	−	1.14137i	−0.0449727	−	0.0618995i
$341$	−1.72981	+	0.562050i	−0.0936745	+	0.0304367i
$342$			2.83882i			0.153506i
$343$	0.587785	+	0.809017i	0.0317374	+	0.0436828i
$344$	−5.34945	+	16.4639i	−0.288423	+	0.887675i
$345$	−1.32531	+	1.82414i	−0.0713524	+	0.0982082i
$346$	−3.21343	−	9.88993i	−0.172755	−	0.531686i
$347$	10.6257	+	3.45250i	0.570418	+	0.185340i	0.580003	−	0.814614i	$-0.303051\pi$
$347$	10.6257	+	3.45250i	0.570418	+	0.185340i	−0.00958561	+	0.999954i	$0.503051\pi$
$348$	8.92025	−	27.4537i	0.478175	−	1.47167i
$349$	−4.61214	+	14.1947i	−0.246882	+	0.759825i	0.748439	+	0.663204i	$0.230804\pi$
$349$	−4.61214	+	14.1947i	−0.246882	+	0.759825i	−0.995321	+	0.0966217i	$0.969196\pi$
$350$	−3.57481	−	1.16153i	−0.191081	−	0.0620861i
$351$	−1.81601	−	5.58909i	−0.0969312	−	0.298324i
$352$	1.20615	−	1.66012i	0.0642881	−	0.0884849i
$353$	4.79282	−	14.7508i	0.255096	−	0.785105i	−0.738714	−	0.674018i	$-0.764567\pi$
$353$	4.79282	−	14.7508i	0.255096	−	0.785105i	0.993811	−	0.111087i	$-0.0354332\pi$
$354$	9.13678	+	12.5757i	0.485614	+	0.668391i
$355$		−	2.44875i		−	0.129966i
$356$	4.13315	−	1.34294i	0.219057	−	0.0711758i
$357$	−3.84678	−	5.29464i	−0.203593	−	0.280222i
$358$	6.59590	−	9.07848i	0.348604	−	0.479812i
$359$	−5.16917	−	3.75562i	−0.272818	−	0.198214i	0.442961	−	0.896541i	$-0.353928\pi$
$359$	−5.16917	−	3.75562i	−0.272818	−	0.198214i	−0.715779	+	0.698327i	$0.753928\pi$
$360$	−3.76463			−0.198413
$361$	−14.5372	−	10.5619i	−0.765116	−	0.555889i
$362$	−13.0058	−	4.22583i	−0.683567	−	0.222104i
$363$	26.5806	−	8.63657i	1.39512	−	0.453302i
$364$	−4.29459	+	3.12020i	−0.225097	+	0.163543i
$365$	−2.85127	+	2.07157i	−0.149242	+	0.108431i
$366$		−	8.82617i		−	0.461351i
$367$	−3.61715	−	11.1324i	−0.188813	−	0.581108i	0.811180	−	0.584797i	$-0.198826\pi$
$367$	−3.61715	−	11.1324i	−0.188813	−	0.581108i	−0.999993	+	0.00368878i	$0.998826\pi$
$368$	−1.65740			−0.0863979
$369$	−8.92874	−	21.2668i	−0.464812	−	1.10711i
$370$	−1.82418			−0.0948344
$371$	−1.63187	−	5.02238i	−0.0847225	−	0.260749i
$372$			18.6366i			0.966260i
$373$	23.7815	−	17.2783i	1.23136	−	0.894634i	0.234367	−	0.972148i	$-0.424698\pi$
$373$	23.7815	−	17.2783i	1.23136	−	0.894634i	0.996991	+	0.0775136i	$0.0246981\pi$
$374$	0.560516	−	0.407239i	0.0289836	−	0.0210578i
$375$	9.53281	−	3.09740i	0.492272	−	0.159949i
$376$	18.3002	+	5.94608i	0.943759	+	0.306646i
$377$	−24.7001	−	17.9457i	−1.27212	−	0.924250i
$378$	−1.20087			−0.0617661
$379$	−10.8467	−	7.88056i	−0.557155	−	0.404797i	0.273261	−	0.961940i	$-0.411898\pi$
$379$	−10.8467	−	7.88056i	−0.557155	−	0.404797i	−0.830417	+	0.557143i	$0.811898\pi$
$380$	−0.330590	+	0.455018i	−0.0169589	+	0.0233419i
$381$	−17.8831	−	24.6140i	−0.916181	−	1.26101i
$382$	12.3961	−	4.02773i	0.634238	−	0.206076i
$383$			20.9813i			1.07210i	0.844187	+	0.536048i	$0.180083\pi$
$383$			20.9813i			1.07210i	−0.844187	+	0.536048i	$0.819917\pi$
$384$	−14.1136	−	19.4258i	−0.720234	−	0.991317i
$385$	0.0429226	−	0.132102i	0.00218754	−	0.00673255i
$386$	11.4429	−	15.7498i	0.582429	−	0.801645i
$387$	−7.30737	−	22.4898i	−0.371454	−	1.14322i
$388$	−21.2688	−	6.91066i	−1.07976	−	0.350835i
$389$	−1.65313	+	5.08782i	−0.0838172	+	0.257963i	−0.984178	−	0.177181i	$-0.943302\pi$
$389$	−1.65313	+	5.08782i	−0.0838172	+	0.257963i	0.900361	+	0.435143i	$0.143302\pi$
$390$	−0.927657	+	2.85504i	−0.0469738	+	0.144570i
$391$	−5.36354	−	1.74272i	−0.271246	−	0.0881331i
$392$	0.814881	+	2.50795i	0.0411577	+	0.126670i
$393$	28.2064	−	38.8228i	1.42282	−	1.95835i
$394$	2.78315	−	8.56564i	0.140213	−	0.431531i
$395$	1.00703	+	1.38606i	0.0506693	+	0.0697403i
$396$			1.76444i			0.0886664i
$397$	−6.07722	+	1.97461i	−0.305007	+	0.0991027i	−0.457522	−	0.889198i	$-0.651263\pi$
$397$	−6.07722	+	1.97461i	−0.305007	+	0.0991027i	0.152515	+	0.988301i	$0.451263\pi$
$398$	3.68619	+	5.07360i	0.184772	+	0.254317i
$399$	−1.53355	+	2.11075i	−0.0767737	+	0.105670i
$400$	2.93281	+	2.13081i	0.146640	+	0.106540i
$401$	−0.977652			−0.0488216			−0.0244108	−	0.999702i	$-0.507771\pi$
$401$	−0.977652			−0.0488216			−0.0244108	+	0.999702i	$0.507771\pi$
$402$	10.3818	+	7.54281i	0.517797	+	0.376201i
$403$	18.7464	+	6.09109i	0.933827	+	0.303419i
$404$	−2.34303	+	0.761297i	−0.116570	+	0.0378760i
$405$	−2.19020	+	1.59127i	−0.108832	+	0.0790709i
$406$	−5.04731	+	3.66709i	−0.250494	+	0.181995i
$407$			2.07844i			0.103025i
$408$	−5.33302	−	16.4133i	−0.264024	−	0.812581i
$409$	−15.6293			−0.772818			−0.386409	−	0.922328i	$-0.626285\pi$
$409$	−15.6293			−0.772818			−0.386409	+	0.922328i	$0.626285\pi$
$410$	−0.450602	+	1.91736i	−0.0222536	+	0.0946916i
$411$	−13.8093			−0.681164
$412$	2.90338	+	8.93569i	0.143039	+	0.440230i
$413$			7.79459i			0.383547i
$414$	−5.00805	+	3.63856i	−0.246132	+	0.178826i
$415$	−0.516655	+	0.375372i	−0.0253616	+	0.0184263i
$416$	−21.1500	+	6.87204i	−1.03696	+	0.336930i
$417$	27.2007	+	8.83806i	1.33203	+	0.432801i
$418$	−0.223454	−	0.162349i	−0.0109295	−	0.00794076i
$419$	31.1506			1.52181			0.760904	−	0.648865i	$-0.224756\pi$
$419$	31.1506			1.52181			0.760904	+	0.648865i	$0.224756\pi$
$420$	−1.15142	−	0.836557i	−0.0561836	−	0.0408198i
$421$	−15.3767	+	21.1642i	−0.749415	+	1.03148i	0.248606	+	0.968605i	$0.420028\pi$
$421$	−15.3767	+	21.1642i	−0.749415	+	1.03148i	−0.998021	+	0.0628769i	$0.979972\pi$
$422$	−5.52352	−	7.60248i	−0.268881	−	0.370083i
$423$	−24.9981	+	8.12237i	−1.21545	+	0.394923i
$424$		−	13.9256i		−	0.676289i
$425$	7.25041	+	9.97933i	0.351696	+	0.484069i
$426$	3.80768	−	11.7188i	0.184483	−	0.567780i
$427$	2.60142	−	3.58054i	0.125891	−	0.173275i
$428$	3.98268	+	12.2574i	0.192510	+	0.592485i
$429$	3.25299	+	1.05696i	0.157056	+	0.0510306i
$430$	−0.623997	+	1.92047i	−0.0300918	+	0.0926131i
$431$	−10.5494	+	32.4677i	−0.508146	+	1.56391i	0.287271	+	0.957849i	$0.407252\pi$
$431$	−10.5494	+	32.4677i	−0.508146	+	1.56391i	−0.795417	+	0.606063i	$0.792748\pi$
$432$	1.10149	+	0.357897i	0.0529956	+	0.0172193i
$433$	−2.97040	−	9.14194i	−0.142748	−	0.439334i	0.853966	−	0.520328i	$-0.174190\pi$
$433$	−2.97040	−	9.14194i	−0.142748	−	0.439334i	−0.996715	+	0.0809946i	$0.974190\pi$
$434$	2.36751	−	3.25860i	0.113644	−	0.156418i
$435$	2.52951	−	7.78505i	0.121281	−	0.373264i
$436$	−12.7686	−	17.5744i	−0.611504	−	0.841663i
$437$			2.24826i			0.107549i
$438$	−16.8663	+	5.48021i	−0.805905	+	0.261854i
$439$	−1.83806	−	2.52987i	−0.0877258	−	0.120744i	0.762898	−	0.646518i	$-0.223776\pi$
$439$	−1.83806	−	2.52987i	−0.0877258	−	0.120744i	−0.850624	+	0.525774i	$0.823776\pi$
$440$	0.215295	−	0.296328i	0.0102638	−	0.0141269i
$441$	−2.91421	−	2.11730i	−0.138772	−	0.100824i
$442$	−7.50846			−0.357141
$443$	33.3990	+	24.2658i	1.58683	+	1.15290i	0.908291	+	0.418339i	$0.137388\pi$
$443$	33.3990	+	24.2658i	1.58683	+	1.15290i	0.678542	+	0.734562i	$0.262612\pi$
$444$	20.2543	+	6.58103i	0.961228	+	0.312322i
$445$	1.17204	−	0.380818i	0.0555599	−	0.0180525i
$446$	16.3549	−	11.8825i	0.774426	−	0.562653i
$447$	6.56036	−	4.76638i	0.310294	−	0.225442i
$448$			3.04719i			0.143966i
$449$	2.88407	+	8.87625i	0.136108	+	0.418896i	0.995761	−	0.0919821i	$-0.0293203\pi$
$449$	2.88407	+	8.87625i	0.136108	+	0.418896i	−0.859653	+	0.510878i	$0.829320\pi$
$450$	13.5397			0.638269
$451$	2.18461	+	0.513410i	0.102869	+	0.0241755i
$452$	−12.6925			−0.597007
$453$	−11.4281	−	35.1721i	−0.536940	−	1.65253i
$454$		−	17.0114i		−	0.798385i
$455$	−1.21782	+	0.884795i	−0.0570921	+	0.0414798i
$456$	−5.56608	+	4.04399i	−0.260656	+	0.189377i
$457$	37.6206	−	12.2237i	1.75982	−	0.571800i	0.762637	−	0.646827i	$-0.223904\pi$
$457$	37.6206	−	12.2237i	1.75982	−	0.571800i	0.997181	+	0.0750273i	$0.0239044\pi$
$458$	4.98726	+	1.62046i	0.233040	+	0.0757191i
$459$	3.18824	+	2.31639i	0.148814	+	0.108120i
$460$	−1.22643			−0.0571827
$461$	−17.6654	−	12.8347i	−0.822760	−	0.597770i	0.0947417	−	0.995502i	$-0.469797\pi$
$461$	−17.6654	−	12.8347i	−0.822760	−	0.597770i	−0.917502	+	0.397732i	$0.869797\pi$
$462$	0.410825	−	0.565452i	0.0191133	−	0.0263072i
$463$	−4.24771	−	5.84647i	−0.197408	−	0.271709i	0.698825	−	0.715293i	$-0.253707\pi$
$463$	−4.24771	−	5.84647i	−0.197408	−	0.271709i	−0.896233	+	0.443584i	$0.853707\pi$
$464$	5.72254	−	1.85936i	0.265662	−	0.0863188i
$465$			5.28477i			0.245075i
$466$	−3.28726	−	4.52452i	−0.152279	−	0.209594i
$467$	−8.81402	+	27.1268i	−0.407864	+	1.25528i	0.510615	+	0.859809i	$0.329418\pi$
$467$	−8.81402	+	27.1268i	−0.407864	+	1.25528i	−0.918480	+	0.395468i	$0.870582\pi$
$468$	11.2395	−	15.4698i	0.519545	−	0.715092i
$469$	1.98846	+	6.11984i	0.0918183	+	0.282588i
$470$	2.13466	+	0.693592i	0.0984644	+	0.0319930i
$471$	1.89244	−	5.82433i	0.0871990	−	0.268371i
$472$	−6.35166	+	19.5484i	−0.292359	+	0.899789i
$473$	2.18815	+	0.710974i	0.100611	+	0.0326906i
$474$	2.66404	+	8.19908i	0.122364	+	0.376596i
$475$	2.89044	−	3.97835i	0.132622	−	0.182539i
$476$	1.10003	−	3.38555i	0.0504198	−	0.155176i
$477$	11.1811	+	15.3895i	0.511949	+	0.704637i
$478$			0.294840i			0.0134857i
$479$	32.0731	−	10.4212i	1.46546	−	0.476156i	0.535724	−	0.844393i	$-0.320039\pi$
$479$	32.0731	−	10.4212i	1.46546	−	0.476156i	0.929732	+	0.368237i	$0.120039\pi$
$480$	−3.50457	−	4.82363i	−0.159961	−	0.220168i
$481$	13.2397	−	18.2228i	0.603677	−	0.830890i
$482$	−13.8183	−	10.0396i	−0.629408	−	0.457292i
$483$	−5.68922			−0.258868
$484$	12.2987	+	8.93555i	0.559033	+	0.406161i
$485$	−6.03120	−	1.95966i	−0.273863	−	0.0889834i
$486$	−16.3821	+	5.32288i	−0.743109	+	0.241451i
$487$	24.9405	−	18.1203i	1.13016	−	0.821110i	0.144443	−	0.989513i	$-0.453861\pi$
$487$	24.9405	−	18.1203i	1.13016	−	0.821110i	0.985718	+	0.168403i	$0.0538609\pi$
$488$	9.44193	−	6.85996i	0.427416	−	0.310536i
$489$			54.2425i			2.45293i
$490$	0.0950534	+	0.292544i	0.00429407	+	0.0132158i
$491$	−32.0652			−1.44708			−0.723542	−	0.690280i	$-0.757487\pi$
$491$	−32.0652			−1.44708			−0.723542	+	0.690280i	$0.757487\pi$
$492$	11.9204	−	19.6633i	0.537411	−	0.886492i
$493$	20.4739			0.922097
$494$	0.924984	+	2.84681i	0.0416170	+	0.128084i
$495$			0.500342i			0.0224887i
$496$	−3.14276	+	2.28335i	−0.141114	+	0.102525i
$497$	4.99868	−	3.63175i	0.224221	−	0.162906i
$498$	−3.05621	+	0.993023i	−0.136952	+	0.0444984i
$499$	16.8693	+	5.48118i	0.755175	+	0.245371i	0.661206	−	0.750204i	$-0.270045\pi$
$499$	16.8693	+	5.48118i	0.755175	+	0.245371i	0.0939683	+	0.995575i	$0.470045\pi$
$500$	4.41078	+	3.20462i	0.197256	+	0.143315i
$501$	−49.8619			−2.22766
$502$	5.34869	+	3.88605i	0.238724	+	0.173443i
$503$	24.7714	−	34.0948i	1.10450	−	1.52021i	0.275220	−	0.961381i	$-0.411249\pi$
$503$	24.7714	−	34.0948i	1.10450	−	1.52021i	0.829280	−	0.558833i	$-0.188751\pi$
$504$	−5.58334	−	7.68481i	−0.248702	−	0.342309i
$505$	−0.664414	+	0.215881i	−0.0295660	+	0.00960658i
$506$		−	0.602288i		−	0.0267750i
$507$	−2.15408	−	2.96484i	−0.0956660	−	0.131673i
$508$	5.11388	−	15.7389i	0.226892	−	0.698302i
$509$	−21.0678	+	28.9973i	−0.933813	+	1.28528i	0.0245403	+	0.999699i	$0.492188\pi$
$509$	−21.0678	+	28.9973i	−0.933813	+	1.28528i	−0.958353	+	0.285585i	$0.907812\pi$
$510$	−0.622080	−	1.91457i	−0.0275462	−	0.0847784i
$511$	−8.45746	−	2.74799i	−0.374136	−	0.121564i
$512$	2.57429	−	7.92284i	0.113768	−	0.350143i
$513$	0.485487	−	1.49417i	0.0214348	−	0.0659694i
$514$	−15.8876	−	5.16220i	−0.700773	−	0.227695i
$515$	0.823312	+	2.53389i	0.0362795	+	0.111657i
$516$	13.8568	−	19.0723i	0.610013	−	0.839610i
$517$	0.790270	−	2.43220i	0.0347560	−	0.106968i
$518$	−2.70544	−	3.72372i	−0.118870	−	0.163611i
$519$			34.4264i			1.51115i
$520$	−3.77522	+	1.22664i	−0.165554	+	0.0537919i
$521$	17.8466	+	24.5638i	0.781876	+	1.07616i	0.995072	+	0.0991502i	$0.0316124\pi$
$521$	17.8466	+	24.5638i	0.781876	+	1.07616i	−0.213197	+	0.977009i	$0.568388\pi$
$522$	13.2095	−	18.1813i	0.578162	−	0.795772i
$523$	12.9334	+	9.39668i	0.565539	+	0.410888i	0.833482	−	0.552547i	$-0.186344\pi$
$523$	12.9334	+	9.39668i	0.565539	+	0.410888i	−0.267943	+	0.963435i	$0.586344\pi$
$524$	26.1019			1.14027
$525$	10.0672	+	7.31425i	0.439369	+	0.319220i
$526$	−0.577488	−	0.187637i	−0.0251797	−	0.00818137i
$527$	−12.5712	+	4.08464i	−0.547611	+	0.177930i
$528$	−0.545350	+	0.396220i	−0.0237333	+	0.0172432i
$529$	14.6412	−	10.6374i	0.636573	−	0.462497i
$530$		−	1.62438i		−	0.0705587i
$531$	−8.67639	−	26.7032i	−0.376523	−	1.15882i
$532$	−1.41913			−0.0615273
$533$	−15.8833	−	18.4173i	−0.687982	−	0.797743i
$534$	6.20111			0.268348
$535$	1.12937	+	3.47584i	0.0488268	+	0.150274i
$536$			16.9686i			0.732931i
$537$	−30.0551	+	21.8363i	−1.29697	+	0.942306i
$538$	−1.14798	+	0.834053i	−0.0494927	+	0.0359586i
$539$	0.333321	−	0.108303i	0.0143572	−	0.00466492i
$540$	0.815076	+	0.264834i	0.0350753	+	0.0113966i
$541$	16.9915	+	12.3450i	0.730521	+	0.530755i	0.889728	−	0.456490i	$-0.150894\pi$
$541$	16.9915	+	12.3450i	0.730521	+	0.530755i	−0.159207	+	0.987245i	$0.550894\pi$
$542$	10.3197			0.443271
$543$	36.6262	+	26.6105i	1.57178	+	1.14197i
$544$	8.76558	−	12.0648i	0.375821	−	0.517273i
$545$	−3.62079	−	4.98358i	−0.155097	−	0.213473i
$546$	−7.20385	+	2.34067i	−0.308296	+	0.100172i
$547$			10.7640i			0.460235i	0.973163	+	0.230118i	$0.0739111\pi$
$547$			10.7640i			0.460235i	−0.973163	+	0.230118i	$0.926089\pi$
$548$	−4.41504	−	6.07678i	−0.188601	−	0.259587i
$549$	−4.92648	+	15.1622i	−0.210257	+	0.647105i
$550$	−0.774322	+	1.06576i	−0.0330172	+	0.0454443i
$551$	−2.52222	−	7.76261i	−0.107450	−	0.330698i
$552$	−14.2683	−	4.63604i	−0.607297	−	0.197323i
$553$	−1.33586	+	4.11135i	−0.0568064	+	0.174832i
$554$	−1.65705	+	5.09986i	−0.0704011	+	0.216672i
$555$	5.74352	+	1.86618i	0.243799	+	0.0792150i
$556$	4.80729	+	14.7953i	0.203874	+	0.627461i
$557$	−21.7010	+	29.8688i	−0.919499	+	1.26558i	0.0443177	+	0.999017i	$0.485889\pi$
$557$	−21.7010	+	29.8688i	−0.919499	+	1.26558i	−0.963817	+	0.266565i	$0.914111\pi$
$558$	−4.48353	+	13.7989i	−0.189803	+	0.584153i
$559$	−14.6558	−	20.1720i	−0.619876	−	0.853186i
$560$		−	0.296664i		−	0.0125363i
$561$	−2.18143	+	0.708790i	−0.0921001	+	0.0299251i
$562$	14.0046	+	19.2757i	0.590750	+	0.813097i
$563$	−16.2118	+	22.3136i	−0.683244	+	0.940405i	−0.999967	−	0.00811333i	$-0.997417\pi$
$563$	−16.2118	+	22.3136i	−0.683244	+	0.940405i	0.316723	+	0.948518i	$0.397417\pi$
$564$	−21.1994	−	15.4023i	−0.892657	−	0.648553i
$565$	−3.59922			−0.151420
$566$	12.7041	+	9.23004i	0.533991	+	0.387967i
$567$	−6.49658	−	2.11087i	−0.272831	−	0.0886480i
$568$	15.4959	−	5.03491i	0.650192	−	0.211260i
$569$	31.4383	−	22.8413i	1.31796	−	0.957556i	0.318008	−	0.948088i	$-0.396986\pi$
$569$	31.4383	−	22.8413i	1.31796	−	0.957556i	0.999955	−	0.00946795i	$-0.00301379\pi$
$570$	−0.649266	+	0.471719i	−0.0271948	+	0.0197582i
$571$		−	41.8453i		−	1.75117i	−0.483064	−	0.875585i	$-0.660476\pi$
$571$		−	41.8453i		−	1.75117i	0.483064	−	0.875585i	$-0.339524\pi$
$572$	0.574914	+	1.76940i	0.0240383	+	0.0739824i
$573$	−43.1502			−1.80263
$574$	−4.58223	+	1.92382i	−0.191258	+	0.0802988i
$575$	10.7230			0.447181
$576$	−3.39191	−	10.4392i	−0.141330	−	0.434968i
$577$			36.3544i			1.51345i	0.653730	+	0.756727i	$0.273203\pi$
$577$			36.3544i			1.51345i	−0.653730	+	0.756727i	$0.726797\pi$
$578$	−6.60094	+	4.79586i	−0.274563	+	0.199482i
$579$	−52.1412	+	37.8828i	−2.16691	+	1.57436i
$580$	4.23452	−	1.37588i	0.175829	−	0.0571303i
$581$	−1.53251	−	0.497941i	−0.0635791	−	0.0206581i
$582$	−25.8160	−	18.7564i	−1.07011	−	0.777479i
$583$	−1.85080			−0.0766524
$584$	−18.9716	−	13.7836i	−0.785049	−	0.570371i
$585$	3.18718	−	4.38677i	0.131774	−	0.181371i
$586$	−6.07040	−	8.35519i	−0.250766	−	0.345150i
$587$	−24.0785	+	7.82358i	−0.993826	+	0.322914i	−0.760396	−	0.649460i	$-0.774995\pi$
$587$	−24.0785	+	7.82358i	−0.993826	+	0.322914i	−0.233430	+	0.972374i	$0.574995\pi$
$588$		−	3.59112i		−	0.148095i
$589$	3.09736	+	4.26315i	0.127624	+	0.175660i
$590$	−0.740902	+	2.28026i	−0.0305025	+	0.0938769i
$591$	−17.5258	+	24.1222i	−0.720914	+	0.992253i
$592$	1.37177	+	4.22188i	0.0563794	+	0.173518i
$593$	8.69175	+	2.82412i	0.356927	+	0.115973i	0.481991	−	0.876176i	$-0.339914\pi$
$593$	8.69175	+	2.82412i	0.356927	+	0.115973i	−0.125064	+	0.992149i	$0.539914\pi$
$594$	−0.130057	+	0.400275i	−0.00533632	+	0.0164235i
$595$	0.311936	−	0.960039i	0.0127881	−	0.0393578i
$596$	4.19488	+	1.36300i	0.171829	+	0.0558307i
$597$	−6.41573	−	19.7456i	−0.262578	−	0.808133i
$598$	−3.83657	+	5.28059i	−0.156889	+	0.215939i
$599$	−11.9177	+	36.6789i	−0.486944	+	1.49866i	0.342201	+	0.939627i	$0.388828\pi$
$599$	−11.9177	+	36.6789i	−0.486944	+	1.49866i	−0.829145	+	0.559034i	$0.811172\pi$
$600$	19.2878	+	26.5473i	0.787420	+	1.08379i
$601$			14.0728i			0.574042i	0.957924	+	0.287021i	$0.0926650\pi$
$601$			14.0728i			0.574042i	−0.957924	+	0.287021i	$0.907335\pi$
$602$	−4.84573	+	1.57447i	−0.197497	+	0.0641708i
$603$	−13.6243	−	18.7523i	−0.554826	−	0.763653i
$604$	11.8237	−	16.2740i	0.481101	−	0.662179i
$605$	3.48755	+	2.53385i	0.141789	+	0.103016i
$606$	−3.51533			−0.142801
$607$	−35.8078	−	26.0159i	−1.45339	−	1.05595i	−0.985024	−	0.172418i	$-0.944842\pi$
$607$	−35.8078	−	26.0159i	−1.45339	−	1.05595i	−0.468369	−	0.883533i	$-0.655158\pi$
$608$	−5.65418	−	1.83715i	−0.229307	−	0.0745064i
$609$	19.6433	−	6.38249i	0.795986	−	0.258632i
$610$	1.10137	−	0.800193i	0.0445932	−	0.0323989i
$611$	−22.4218	+	16.2904i	−0.907091	+	0.659040i
$612$			12.8229i			0.518334i
$613$	−13.2253	−	40.7032i	−0.534164	−	1.64399i	−0.745448	−	0.666563i	$-0.767765\pi$
$613$	−13.2253	−	40.7032i	−0.534164	−	1.64399i	0.211284	−	0.977425i	$-0.432235\pi$
$614$	−12.5358			−0.505905
$615$	3.38026	−	5.57593i	0.136305	−	0.224843i
$616$	0.924205			0.0372373
$617$	4.36263	+	13.4268i	0.175633	+	0.540543i	0.999662	−	0.0260050i	$-0.00827858\pi$
$617$	4.36263	+	13.4268i	0.175633	+	0.540543i	−0.824029	+	0.566548i	$0.808279\pi$
$618$			13.4065i			0.539290i
$619$	23.2116	−	16.8642i	0.932954	−	0.677831i	−0.0137606	−	0.999905i	$-0.504380\pi$
$619$	23.2116	−	16.8642i	0.932954	−	0.677831i	0.946714	+	0.322075i	$0.104380\pi$
$620$	−2.32556	+	1.68962i	−0.0933966	+	0.0678566i
$621$	3.25817	−	1.05864i	0.130746	−	0.0424819i
$622$	1.21082	+	0.393420i	0.0485496	+	0.0157747i
$623$	2.51563	+	1.82771i	0.100786	+	0.0732256i
$624$	7.30529			0.292446
$625$	−18.3393	−	13.3243i	−0.733572	−	0.532971i
$626$	−2.93393	+	4.03820i	−0.117263	+	0.161399i
$627$	0.537471	+	0.739766i	0.0214645	+	0.0295434i
$628$	3.16803	−	1.02936i	0.126418	−	0.0410758i
$629$			15.1049i			0.602271i
$630$	−0.651279	−	0.896409i	−0.0259476	−	0.0357138i
$631$	13.8667	−	42.6774i	0.552026	−	1.69896i	−0.151644	−	0.988435i	$-0.548457\pi$
$631$	13.8667	−	42.6774i	0.552026	−	1.69896i	0.703670	−	0.710526i	$-0.251543\pi$
$632$	−6.70052	+	9.22247i	−0.266532	+	0.366850i
$633$	9.61358	+	29.5876i	0.382105	+	1.17600i
$634$	18.2218	+	5.92061i	0.723679	+	0.235137i
$635$	1.45014	−	4.46309i	0.0575472	−	0.177112i
$636$	−5.86024	+	18.0360i	−0.232374	+	0.715173i
$637$	−3.61230	−	1.17371i	−0.143124	−	0.0465039i
$638$	0.675681	+	2.07953i	0.0267505	+	0.0823295i
$639$	−13.0822	+	18.0061i	−0.517522	+	0.712308i
$640$	1.14448	−	3.52233i	0.0452394	−	0.139233i
$641$	14.8877	+	20.4912i	0.588030	+	0.809354i	0.994547	−	0.104289i	$-0.0332567\pi$
$641$	14.8877	+	20.4912i	0.588030	+	0.809354i	−0.406517	+	0.913643i	$0.633257\pi$
$642$			18.3902i			0.725805i
$643$	1.17043	−	0.380296i	0.0461573	−	0.0149974i	−0.285847	−	0.958275i	$-0.592275\pi$
$643$	1.17043	−	0.380296i	0.0461573	−	0.0149974i	0.332005	+	0.943278i	$0.392275\pi$
$644$	−1.81893	−	2.50354i	−0.0716757	−	0.0986531i
$645$	3.92938	−	5.40833i	0.154719	−	0.212953i
$646$	−1.62393	−	1.17986i	−0.0638928	−	0.0464208i
$647$	48.2296			1.89610			0.948051	−	0.318118i	$-0.103051\pi$
$647$	48.2296			1.89610			0.948051	+	0.318118i	$0.103051\pi$
$648$	−14.5730	−	10.5879i	−0.572480	−	0.415931i
$649$	2.59810	+	0.844174i	0.101984	+	0.0331367i
$650$	13.5778	−	4.41170i	0.532565	−	0.173041i
$651$	−10.7879	+	7.83786i	−0.422811	+	0.307190i
$652$	−23.8694	+	17.3421i	−0.934797	+	0.679170i
$653$		−	12.2884i		−	0.480881i	−0.970664	−	0.240440i	$-0.922708\pi$
$653$		−	12.2884i		−	0.480881i	0.970664	−	0.240440i	$-0.0772918\pi$
$654$	−9.57857	−	29.4798i	−0.374552	−	1.15275i
$655$	7.40172			0.289209
$656$	4.77639	−	0.398971i	0.186487	−	0.0155772i
$657$	32.0330			1.24972
$658$	1.75008	+	5.38618i	0.0682251	+	0.209975i
$659$		−	38.8355i		−	1.51281i	−0.654101	−	0.756407i	$-0.726953\pi$
$659$		−	38.8355i		−	1.51281i	0.654101	−	0.756407i	$-0.273047\pi$
$660$	−0.403544	+	0.293192i	−0.0157079	+	0.0114125i
$661$	−13.0187	+	9.45863i	−0.506368	+	0.367898i	−0.811444	−	0.584430i	$-0.801318\pi$
$661$	−13.0187	+	9.45863i	−0.506368	+	0.367898i	0.305076	+	0.952328i	$0.401318\pi$
$662$	−5.35942	+	1.74138i	−0.208300	+	0.0676808i
$663$	23.6408	+	7.68136i	0.918132	+	0.298319i
$664$	−3.43768	−	2.49762i	−0.133408	−	0.0969265i
$665$	−0.402424			−0.0156053
$666$	13.4135	+	9.74545i	0.519761	+	0.377628i
$667$	10.4615	−	14.3990i	0.405070	−	0.557531i
$668$	−15.9416	−	21.9417i	−0.616798	−	0.848949i
$669$	−63.6504	+	20.6813i	−2.46087	+	0.799584i
$670$			1.97933i			0.0764683i
$671$	−0.911730	−	1.25489i	−0.0351970	−	0.0484445i
$672$	4.64892	−	14.3079i	0.179336	−	0.551939i
$673$	−11.2881	+	15.5367i	−0.435123	+	0.598896i	−0.969120	−	0.246591i	$-0.920690\pi$
$673$	−11.2881	+	15.5367i	−0.435123	+	0.598896i	0.533996	+	0.845487i	$0.320690\pi$
$674$	3.59282	+	11.0576i	0.138390	+	0.425922i
$675$	−7.12644	−	2.31552i	−0.274297	−	0.0891244i
$676$	0.615983	−	1.89580i	0.0236917	−	0.0729154i
$677$	2.72787	−	8.39554i	0.104841	−	0.322667i	−0.884852	−	0.465872i	$-0.845741\pi$
$677$	2.72787	−	8.39554i	0.104841	−	0.322667i	0.989693	+	0.143205i	$0.0457408\pi$
$678$	−17.2246	−	5.59661i	−0.661507	−	0.214937i
$679$	−4.94462	−	15.2180i	−0.189757	−	0.584012i
$680$	1.56464	−	2.15354i	0.0600010	−	0.0825843i
$681$	−17.4031	+	53.5613i	−0.666890	+	2.05248i
$682$	−0.829753	−	1.14206i	−0.0317729	−	0.0437316i
$683$		−	10.9781i		−	0.420065i	−0.977694	−	0.210032i	$-0.932643\pi$
$683$		−	10.9781i		−	0.420065i	0.977694	−	0.210032i	$-0.0673569\pi$
$684$	4.86176	−	1.57968i	0.185894	−	0.0604006i
$685$	−1.25197	−	1.72319i	−0.0478354	−	0.0658398i
$686$	−0.456202	+	0.627908i	−0.0174179	+	0.0239736i
$687$	−14.0449	−	10.2042i	−0.535846	−	0.389315i
$688$	4.91397			0.187343
$689$	16.2270	+	11.7896i	0.618199	+	0.449148i
$690$	−1.66435	−	0.540779i	−0.0633606	−	0.0205871i
$691$	19.1409	−	6.21925i	0.728153	−	0.236591i	0.0785986	−	0.996906i	$-0.474955\pi$
$691$	19.1409	−	6.21925i	0.728153	−	0.236591i	0.649554	+	0.760315i	$0.274955\pi$
$692$	−15.1493	+	11.0066i	−0.575891	+	0.418409i
$693$	−1.02136	+	0.742059i	−0.0387982	+	0.0281885i
$694$			8.67141i			0.329162i
$695$	1.36320	+	4.19551i	0.0517092	+	0.159145i
$696$	54.4653			2.06450
$697$	15.8765	+	3.73115i	0.601364	+	0.141328i
$698$	−11.5840			−0.438461
$699$	5.72140	+	17.6087i	0.216403	+	0.666020i
$700$			6.76854i			0.255827i
$701$	−8.10597	+	5.88933i	−0.306158	+	0.222437i	−0.730246	−	0.683184i	$-0.760595\pi$
$701$	−8.10597	+	5.88933i	−0.306158	+	0.222437i	0.424088	+	0.905621i	$0.360595\pi$
$702$	3.69004	−	2.68097i	0.139271	−	0.101187i
$703$	5.72697	−	1.86080i	0.215997	−	0.0701816i
$704$	1.01569	+	0.330018i	0.0382803	+	0.0124380i
$705$	−6.01152	−	4.36763i	−0.226407	−	0.164494i
$706$	12.0378			0.453049
$707$	−1.42608	−	1.03611i	−0.0536331	−	0.0389668i
$708$	16.4529	−	22.6454i	0.618337	−	0.851068i
$709$	5.66454	+	7.79656i	0.212736	+	0.292806i	0.902028	−	0.431678i	$-0.142078\pi$
$709$	5.66454	+	7.79656i	0.212736	+	0.292806i	−0.689292	+	0.724484i	$0.742078\pi$
$710$	1.80754	−	0.587306i	0.0678359	−	0.0220412i
$711$		−	15.5719i		−	0.583991i
$712$	4.81969	+	6.63373i	0.180626	+	0.248610i
$713$	−3.55081	+	10.9283i	−0.132979	+	0.409267i
$714$	2.98563	−	4.10936i	0.111734	−	0.153789i
$715$	0.163028	+	0.501749i	0.00609691	+	0.0187644i
$716$	−19.2181	−	6.24434i	−0.718214	−	0.233362i
$717$	0.301629	−	0.928320i	0.0112646	−	0.0346687i
$718$	1.53244	−	4.71636i	0.0571901	−	0.176013i
$719$	−12.8331	−	4.16971i	−0.478592	−	0.155504i	0.0597794	−	0.998212i	$-0.480960\pi$
$719$	−12.8331	−	4.16971i	−0.478592	−	0.155504i	−0.538372	+	0.842708i	$0.680960\pi$
$720$	0.330225	+	1.01633i	0.0123068	+	0.0378764i
$721$	−3.95143	+	5.43867i	−0.147159	+	0.202547i
$722$	4.30966	−	13.2638i	0.160389	−	0.493627i
$723$	33.2370	+	45.7468i	1.23610	+	1.70134i
$724$			24.6251i			0.915184i
$725$	−37.0236	+	12.0297i	−1.37502	+	0.446772i
$726$	12.7502	+	17.5491i	0.473203	+	0.651308i
$727$	−27.2667	+	37.5294i	−1.01127	+	1.39189i	−0.0931159	+	0.995655i	$0.529683\pi$
$727$	−27.2667	+	37.5294i	−1.01127	+	1.39189i	−0.918150	+	0.396233i	$0.870317\pi$
$728$	−8.10301	−	5.88718i	−0.300318	−	0.218194i
$729$	36.5328			1.35307
$730$	−2.21297	−	1.60782i	−0.0819058	−	0.0595081i
$731$	15.9022	+	5.16694i	0.588164	+	0.191106i
$732$	−15.1157	+	4.91138i	−0.558691	+	0.181530i
$733$	24.5546	−	17.8400i	0.906945	−	0.658934i	−0.0332952	−	0.999446i	$-0.510600\pi$
$733$	24.5546	−	17.8400i	0.906945	−	0.658934i	0.940240	+	0.340511i	$0.110600\pi$
$734$	7.34987	−	5.33999i	0.271289	−	0.197103i
$735$		−	1.01833i		−	0.0375618i
$736$	−4.00607	−	12.3294i	−0.147666	−	0.454468i
$737$	2.25523			0.0830723
$738$	13.5566	−	11.6914i	0.499026	−	0.430365i
$739$	8.75409			0.322024			0.161012	−	0.986952i	$-0.448524\pi$
$739$	8.75409			0.322024			0.161012	+	0.986952i	$0.448524\pi$
$740$	1.01507	+	3.12408i	0.0373149	+	0.114843i
$741$		−	9.90962i		−	0.364039i
$742$	3.31588	−	2.40913i	0.121730	−	0.0884419i
$743$	−8.90892	+	6.47271i	−0.326837	+	0.237461i	−0.739087	−	0.673610i	$-0.764743\pi$
$743$	−8.90892	+	6.47271i	−0.326837	+	0.237461i	0.412251	+	0.911071i	$0.364743\pi$
$744$	−33.4424	+	10.8661i	−1.22606	+	0.398370i
$745$	1.18954	+	0.386506i	0.0435815	+	0.0141605i
$746$	18.4577	+	13.4103i	0.675784	+	0.490986i
$747$	5.80443			0.212373
$748$	−1.00934	−	0.733327i	−0.0369050	−	0.0268131i
$749$	−5.42032	+	7.46043i	−0.198054	+	0.272598i
$750$	4.57269	+	6.29376i	0.166971	+	0.229816i
$751$	−23.8855	+	7.76085i	−0.871592	+	0.283198i	−0.710462	−	0.703736i	$-0.751514\pi$
$751$	−23.8855	+	7.76085i	−0.871592	+	0.283198i	−0.161130	+	0.986933i	$0.551514\pi$
$752$		−	5.46203i		−	0.199180i
$753$	−12.8651	−	17.7073i	−0.468830	−	0.645290i
$754$	7.32254	−	22.5365i	0.266671	−	0.820730i
$755$	3.35286	−	4.61481i	0.122023	−	0.167950i
$756$	0.668232	+	2.05661i	0.0243034	+	0.0747980i
$757$	−8.32883	−	2.70620i	−0.302717	−	0.0983586i	0.153720	−	0.988114i	$-0.450875\pi$
$757$	−8.32883	−	2.70620i	−0.302717	−	0.0983586i	−0.456437	+	0.889756i	$0.650875\pi$
$758$	3.21557	−	9.89652i	0.116795	−	0.359458i
$759$	−0.616157	+	1.89634i	−0.0223651	+	0.0688327i
$760$	−1.00926	−	0.327928i	−0.0366096	−	0.0118952i
$761$	−0.272366	−	0.838255i	−0.00987325	−	0.0303867i	0.945999	−	0.324171i	$-0.105085\pi$
$761$	−0.272366	−	0.838255i	−0.00987325	−	0.0303867i	−0.955872	+	0.293784i	$0.905085\pi$
$762$	13.8798	−	19.1038i	0.502810	−	0.692059i
$763$	4.80308	−	14.7824i	0.173883	−	0.535157i
$764$	−13.7957	−	18.9882i	−0.499112	−	0.686969i
$765$			3.63619i			0.131467i
$766$	−15.4874	+	5.03215i	−0.559581	+	0.181819i
$767$	−17.4016	−	23.9512i	−0.628335	−	0.864829i
$768$	20.1584	−	27.7457i	0.727404	−	1.00119i
$769$	0.509880	+	0.370450i	0.0183868	+	0.0133588i	0.596941	−	0.802285i	$-0.296383\pi$
$769$	0.509880	+	0.370450i	0.0183868	+	0.0133588i	−0.578554	+	0.815644i	$0.696383\pi$
$770$	0.107806			0.00388505
$771$	44.7420	+	32.5070i	1.61134	+	1.17071i
$772$	−33.3406	−	10.8330i	−1.19995	−	0.389889i
$773$	37.7819	−	12.2761i	1.35892	−	0.441540i	0.463238	−	0.886234i	$-0.346688\pi$
$773$	37.7819	−	12.2761i	1.35892	−	0.441540i	0.895682	+	0.444694i	$0.146688\pi$
$774$	14.8482	−	10.7879i	0.533708	−	0.387762i
$775$	20.3330	−	14.7728i	0.730383	−	0.530654i
$776$		−	42.1951i		−	1.51472i
$777$	4.70877	+	14.4921i	0.168926	+	0.519901i
$778$	−4.15206			−0.148858
$779$	−0.541203	−	6.47916i	−0.0193906	−	0.232140i
$780$	5.40572			0.193556
$781$	−0.669170	−	2.05949i	−0.0239448	−	0.0736944i
$782$		−	4.37707i		−	0.156524i
$783$	−10.0619	+	7.31040i	−0.359583	+	0.261252i
$784$	0.605585	−	0.439983i	0.0216280	−	0.0157137i
$785$	0.898359	−	0.291894i	0.0320638	−	0.0104182i
$786$	35.4220	+	11.5093i	1.26346	+	0.410523i
$787$	−29.2933	−	21.2828i	−1.04419	−	0.758651i	−0.0730934	−	0.997325i	$-0.523287\pi$
$787$	−29.2933	−	21.2828i	−1.04419	−	0.758651i	−0.971100	+	0.238674i	$0.923287\pi$
$788$	−16.2182			−0.577749
$789$	1.62629	+	1.18157i	0.0578976	+	0.0420651i
$790$	−0.781594	+	1.07577i	−0.0278079	+	0.0382743i
$791$	−5.33802	−	7.34716i	−0.189798	−	0.261235i
$792$	−3.16620	+	1.02876i	−0.112506	+	0.0365554i
$793$			16.8100i			0.596941i
$794$	−2.91511	−	4.01231i	−0.103453	−	0.142391i
$795$	−1.66179	+	5.11446i	−0.0589376	+	0.181391i
$796$	6.63783	−	9.13618i	0.235272	−	0.323823i
$797$	4.93395	+	15.1851i	0.174769	+	0.537885i	0.999623	−	0.0274616i	$-0.00874240\pi$
$797$	4.93395	+	15.1851i	0.174769	+	0.537885i	−0.824853	+	0.565347i	$0.808742\pi$
$798$	−1.92586	−	0.625749i	−0.0681746	−	0.0221513i
$799$	5.74321	−	17.6758i	0.203180	−	0.625324i
$800$	−8.76228	+	26.9675i	−0.309793	+	0.953446i
$801$	−10.6527	−	3.46126i	−0.376393	−	0.122298i
$802$	−0.234479	−	0.721653i	−0.00827976	−	0.0254825i
$803$	−1.83193	+	2.52143i	−0.0646474	+	0.0889795i
$804$	7.14078	−	21.9771i	0.251836	−	0.775071i
$805$	−0.515793	−	0.709928i	−0.0181793	−	0.0250217i
$806$			15.2986i			0.538869i
$807$	4.46772	−	1.45165i	0.157271	−	0.0511006i
$808$	−2.73222	−	3.76058i	−0.0961192	−	0.132297i
$809$	30.1021	−	41.4320i	1.05833	−	1.45667i	0.176981	−	0.984214i	$-0.443367\pi$
$809$	30.1021	−	41.4320i	1.05833	−	1.45667i	0.881353	−	0.472458i	$-0.156633\pi$
$810$	−1.69989	−	1.23504i	−0.0597281	−	0.0433950i
$811$	37.0753			1.30189			0.650945	−	0.759125i	$-0.274373\pi$
$811$	37.0753			1.30189			0.650945	+	0.759125i	$0.274373\pi$
$812$	9.08885	+	6.60344i	0.318956	+	0.231735i
$813$	−32.4923	−	10.5574i	−1.13955	−	0.370264i
$814$	−1.53420	+	0.498492i	−0.0537737	+	0.0174721i
$815$	−6.76864	+	4.91770i	−0.237095	+	0.172260i
$816$	−3.96327	+	2.87949i	−0.138742	+	0.100802i
$817$		−	6.66579i		−	0.233207i
$818$	−3.74852	−	11.5367i	−0.131064	−	0.403373i
$819$	13.6817			0.478078
$820$	3.53440	−	0.295228i	0.123427	−	0.0103098i
$821$	−14.9231			−0.520819			−0.260410	−	0.965498i	$-0.583858\pi$
$821$	−14.9231			−0.520819			−0.260410	+	0.965498i	$0.583858\pi$
$822$	−3.31202	−	10.1934i	−0.115520	−	0.355534i
$823$		−	31.3365i		−	1.09232i	−0.837681	−	0.546160i	$-0.816089\pi$
$823$		−	31.3365i		−	1.09232i	0.837681	−	0.546160i	$-0.183911\pi$
$824$	−14.3418	+	10.4200i	−0.499622	+	0.362996i
$825$	3.52830	−	2.56346i	0.122840	−	0.0892482i
$826$	−5.75357	+	1.86945i	−0.200192	+	0.0650465i
$827$	−0.411192	−	0.133604i	−0.0142986	−	0.00464588i	0.301859	−	0.953353i	$-0.402393\pi$
$827$	−0.411192	−	0.133604i	−0.0142986	−	0.00464588i	−0.316158	+	0.948707i	$0.602393\pi$
$828$	9.01815	+	6.55207i	0.313402	+	0.227700i
$829$	41.3196			1.43509			0.717544	−	0.696513i	$-0.245266\pi$
$829$	41.3196			1.43509			0.717544	+	0.696513i	$0.245266\pi$
$830$	−0.400995	−	0.291340i	−0.0139187	−	0.0101125i
$831$	10.4346	−	14.3620i	0.361972	−	0.498212i
$832$	−6.80291	−	9.36340i	−0.235848	−	0.324617i
$833$	2.42238	−	0.787078i	0.0839304	−	0.0272706i
$834$			22.1979i			0.768651i
$835$	−4.52055	−	6.22200i	−0.156440	−	0.215321i
$836$	−0.153696	+	0.473027i	−0.00531569	+	0.0163600i
$837$	4.71968	−	6.49608i	0.163136	−	0.224537i
$838$	7.47114	+	22.9938i	0.258086	+	0.794308i
$839$	7.69893	+	2.50153i	0.265797	+	0.0863626i	0.438883	−	0.898544i	$-0.355374\pi$
$839$	7.69893	+	2.50153i	0.265797	+	0.0863626i	−0.173087	+	0.984907i	$0.555374\pi$
$840$	0.829821	−	2.55393i	0.0286315	−	0.0881188i
$841$	−11.0055	+	33.8713i	−0.379498	+	1.16798i
$842$	−19.3103	−	6.27430i	−0.665477	−	0.216227i
$843$	−24.3748	−	75.0178i	−0.839512	−	2.58375i
$844$	−9.94638	+	13.6900i	−0.342368	+	0.471230i
$845$	0.174674	−	0.537592i	0.00600898	−	0.0184937i
$846$	−11.9910	−	16.5043i	−0.412261	−	0.567428i
$847$			10.8772i			0.373744i
$848$	−3.75948	+	1.22153i	−0.129101	+	0.0419474i
$849$	−30.5568	−	42.0579i	−1.04871	−	1.44342i
$850$	−5.62731	+	7.74532i	−0.193015	+	0.265662i
$851$	10.6230	+	7.71809i	0.364153	+	0.264573i
$852$	−22.1885			−0.760164
$853$	18.0551	+	13.1178i	0.618196	+	0.449146i	0.852291	−	0.523068i	$-0.175213\pi$
$853$	18.0551	+	13.1178i	0.618196	+	0.449146i	−0.234095	+	0.972214i	$0.575213\pi$
$854$	3.26690	+	1.06148i	0.111791	+	0.0363231i
$855$	1.37865	−	0.447950i	0.0471488	−	0.0153196i
$856$	−19.6732	+	14.2934i	−0.672417	+	0.488539i
$857$	−25.2150	+	18.3198i	−0.861329	+	0.625792i	−0.928246	−	0.371966i	$-0.878684\pi$
$857$	−25.2150	+	18.3198i	−0.861329	+	0.625792i	0.0669171	+	0.997759i	$0.478684\pi$
$858$			2.65470i			0.0906298i
$859$	−13.9929	−	43.0657i	−0.477431	−	1.46938i	−0.842651	−	0.538461i	$-0.819006\pi$
$859$	−13.9929	−	43.0657i	−0.477431	−	1.46938i	0.365219	−	0.930922i	$-0.380994\pi$
$860$	3.63621			0.123994
$861$	16.3955	−	1.36951i	0.558758	−	0.0466729i
$862$	−26.4961			−0.902462
$863$	−5.20397	−	16.0162i	−0.177145	−	0.545197i	0.822580	−	0.568650i	$-0.192534\pi$
$863$	−5.20397	−	16.0162i	−0.177145	−	0.545197i	−0.999725	+	0.0234527i	$0.992534\pi$
$864$			9.05909i			0.308196i
$865$	−4.29589	+	3.12115i	−0.146065	+	0.106122i
$866$	6.03570	−	4.38519i	0.205101	−	0.149015i
$867$	25.6897	−	8.34710i	0.872469	−	0.283482i
$868$	−6.89809	−	2.24132i	−0.234136	−	0.0760755i
$869$	1.22572	+	0.890539i	0.0415798	+	0.0302095i
$870$	6.35321			0.215394
$871$	−19.7728	−	14.3658i	−0.669976	−	0.486766i
$872$	24.0917	−	33.1594i	0.815848	−	1.12292i
$873$	33.8791	+	46.6306i	1.14664	+	1.57821i
$874$	−1.65955	+	0.539221i	−0.0561352	+	0.0182394i
$875$			3.90096i			0.131876i
$876$	18.7708	+	25.8357i	0.634205	+	0.872909i
$877$	4.08369	−	12.5683i	0.137896	−	0.424401i	−0.858133	−	0.513427i	$-0.828376\pi$
$877$	4.08369	−	12.5683i	0.137896	−	0.424401i	0.996029	+	0.0890264i	$0.0283755\pi$
$878$	1.42659	−	1.96353i	0.0481449	−	0.0662658i
$879$	10.5654	+	32.5170i	0.356362	+	1.09677i
$880$	−0.0988843	−	0.0321295i	−0.00333339	−	0.00108308i
$881$	−12.1915	+	37.5217i	−0.410743	+	1.26414i	0.505260	+	0.862967i	$0.331397\pi$
$881$	−12.1915	+	37.5217i	−0.410743	+	1.26414i	−0.916003	+	0.401171i	$0.868603\pi$
$882$	0.863941	−	2.65894i	0.0290904	−	0.0895310i
$883$	−42.9861	−	13.9670i	−1.44660	−	0.470029i	−0.522651	−	0.852547i	$-0.675057\pi$
$883$	−42.9861	−	13.9670i	−1.44660	−	0.470029i	−0.923948	+	0.382518i	$0.875057\pi$
$884$	4.17813	+	12.8590i	0.140526	+	0.432493i
$885$	4.66554	−	6.42157i	0.156831	−	0.215859i
$886$	−9.90138	+	30.4733i	−0.332643	+	1.02377i
$887$	1.56632	+	2.15586i	0.0525919	+	0.0723866i	0.834503	−	0.551003i	$-0.185755\pi$
$887$	1.56632	+	2.15586i	0.0525919	+	0.0723866i	−0.781911	+	0.623390i	$0.785755\pi$
$888$			40.1825i			1.34844i
$889$	11.2613	−	3.65902i	0.377692	−	0.122719i
$890$	0.562202	+	0.773804i	0.0188450	+	0.0259380i
$891$	−1.40719	+	1.93683i	−0.0471427	+	0.0648864i
$892$	−29.4507	−	21.3972i	−0.986083	−	0.716431i
$893$	−7.40924			−0.247941
$894$	5.09174	+	3.69936i	0.170293	+	0.123725i
$895$	−5.44968	−	1.77071i	−0.182163	−	0.0591882i
$896$	8.88758	−	2.88775i	0.296913	−	0.0964730i
$897$	17.4818	−	12.7013i	0.583702	−	0.424084i
$898$	−5.86029	+	4.25775i	−0.195560	+	0.142083i
$899$		−	41.7158i		−	1.39130i
$900$	−7.53426	−	23.1881i	−0.251142	−	0.772936i
$901$	−13.4505			−0.448102
$902$	0.144983	+	1.73571i	0.00482741	+	0.0577928i
$903$	16.8678			0.561325
$904$	−7.40041	−	22.7761i	−0.246134	−	0.757523i
$905$			6.98294i			0.232121i
$906$	23.2214	−	16.8713i	0.771479	−	0.560512i
$907$	0.269666	−	0.195924i	0.00895412	−	0.00650555i	−0.583299	−	0.812257i	$-0.698238\pi$
$907$	0.269666	−	0.195924i	0.00895412	−	0.00650555i	0.592253	+	0.805752i	$0.298238\pi$
$908$	−29.1337	+	9.46610i	−0.966834	+	0.314144i
$909$	6.03886	+	1.96215i	0.200296	+	0.0650802i
$910$	−0.945191	−	0.686722i	−0.0313328	−	0.0227646i
$911$	20.8986			0.692402			0.346201	−	0.938160i	$-0.387472\pi$
$911$	20.8986			0.692402			0.346201	+	0.938160i	$0.387472\pi$
$912$	1.57999	+	1.14793i	0.0523188	+	0.0380118i
$913$	−0.331949	+	0.456888i	−0.0109859	+	0.0151208i
$914$	18.0458	+	24.8379i	0.596902	+	0.821566i
$915$	−4.28635	+	1.39272i	−0.141702	+	0.0460419i
$916$		−	9.44288i		−	0.312002i
$917$	10.9775	+	15.1093i	0.362510	+	0.498952i
$918$	−0.945179	+	2.90896i	−0.0311956	+	0.0960100i
$919$	−0.0700241	+	0.0963799i	−0.00230988	+	0.00317928i	−0.810170	−	0.586194i	$-0.800625\pi$
$919$	−0.0700241	+	0.0963799i	−0.00230988	+	0.00317928i	0.807860	+	0.589374i	$0.200625\pi$
$920$	−0.715074	−	2.20077i	−0.0235753	−	0.0725572i
$921$	39.4698	+	12.8245i	1.30057	+	0.422582i
$922$	5.23705	−	16.1180i	0.172473	−	0.530817i
$923$	−7.25198	+	22.3193i	−0.238702	+	0.734649i
$924$	−1.19700	−	0.388928i	−0.0393783	−	0.0127948i
$925$	−8.87508	−	27.3147i	−0.291811	−	0.898101i
$926$	3.29680	−	4.53766i	0.108340	−	0.149117i
$927$	7.48309	−	23.0306i	0.245777	−	0.756424i
$928$	27.6637	+	38.0758i	0.908104	+	1.24990i
$929$		−	14.8040i		−	0.485703i	−0.970063	−	0.242852i	$-0.921917\pi$
$929$		−	14.8040i		−	0.485703i	0.970063	−	0.242852i	$-0.0780828\pi$
$930$	−3.90095	+	1.26750i	−0.127917	+	0.0415628i
$931$	−0.596837	−	0.821475i	−0.0195605	−	0.0269228i
$932$	−5.91946	+	8.14744i	−0.193898	+	0.266878i
$933$	−3.40986	−	2.47741i	−0.111634	−	0.0811068i
$934$	−22.1376			−0.724363
$935$	−0.286218	−	0.207949i	−0.00936033	−	0.00680067i
$936$	34.3130	+	11.1490i	1.12156	+	0.364415i
$937$	1.72675	−	0.561056i	0.0564106	−	0.0183289i	−0.280676	−	0.959803i	$-0.590559\pi$
$937$	1.72675	−	0.561056i	0.0564106	−	0.0183289i	0.337086	+	0.941474i	$0.390559\pi$
$938$	−4.04045	+	2.93556i	−0.131925	+	0.0958493i
$939$	13.3688	−	9.71302i	0.436275	−	0.316972i
$940$		−	4.04176i		−	0.131828i
$941$	7.73709	+	23.8123i	0.252222	+	0.776260i	0.994364	+	0.106017i	$0.0338099\pi$
$941$	7.73709	+	23.8123i	0.252222	+	0.776260i	−0.742142	+	0.670242i	$0.766190\pi$
$942$	4.75311			0.154865
$943$	10.7364	−	9.25919i	0.349626	−	0.301521i
$944$	5.83460			0.189900
$945$	0.189490	+	0.583192i	0.00616413	+	0.0189712i
$946$			1.78571i			0.0580583i
$947$	31.6414	−	22.9888i	1.02821	−	0.747036i	0.0602580	−	0.998183i	$-0.480808\pi$
$947$	31.6414	−	22.9888i	1.02821	−	0.747036i	0.967949	+	0.251147i	$0.0808077\pi$
$948$	12.5593	−	9.12486i	0.407907	−	0.296362i
$949$	32.1230	−	10.4374i	1.04276	−	0.338813i
$950$	3.62986	+	1.17941i	0.117768	+	0.0382652i
$951$	−51.3153	−	37.2827i	−1.66401	−	1.20898i
$952$	6.71657			0.217685
$953$	−10.7951	−	7.84310i	−0.349688	−	0.254063i	0.399050	−	0.916929i	$-0.369340\pi$
$953$	−10.7951	−	7.84310i	−0.349688	−	0.254063i	−0.748738	+	0.662866i	$0.769340\pi$
$954$	−8.67808	+	11.9444i	−0.280963	+	0.386713i
$955$	−3.91206	−	5.38449i	−0.126591	−	0.174238i
$956$	0.504942	−	0.164066i	0.0163310	−	0.00530626i
$957$		−	7.23876i		−	0.233996i
$958$	15.3848	+	21.1753i	0.497059	+	0.684143i
$959$	1.66078	−	5.11135i	0.0536293	−	0.165054i
$960$	1.82393	−	2.51042i	0.0588670	−	0.0810235i
$961$	−1.25703	−	3.86873i	−0.0405492	−	0.124798i
$962$	16.6266	+	5.40230i	0.536062	+	0.174177i
$963$	10.2648	−	31.5919i	0.330780	−	1.01803i
$964$	−9.50450	+	29.2518i	−0.306119	+	0.942138i
$965$	−9.45439	−	3.07192i	−0.304348	−	0.0988885i
$966$	−1.36450	−	4.19949i	−0.0439020	−	0.135117i
$967$	−21.7978	+	30.0021i	−0.700971	+	0.964804i	0.298973	+	0.954261i	$0.403356\pi$
$967$	−21.7978	+	30.0021i	−0.700971	+	0.964804i	−0.999944	+	0.0105423i	$0.996644\pi$
$968$	−8.86360	+	27.2794i	−0.284887	+	0.876792i
$969$	3.90602	+	5.37617i	0.125479	+	0.172708i
$970$		−	4.92193i		−	0.158034i
$971$	19.3604	−	6.29056i	0.621303	−	0.201874i	0.0185845	−	0.999827i	$-0.494084\pi$
$971$	19.3604	−	6.29056i	0.621303	−	0.201874i	0.602719	+	0.797954i	$0.294084\pi$
$972$	18.2319	+	25.0940i	0.584788	+	0.804891i
$973$	−6.54259	+	9.00511i	−0.209746	+	0.288690i
$974$	19.3572	+	14.0638i	0.620246	+	0.450635i
$975$	−47.2638			−1.51365
$976$	−2.68020	−	1.94728i	−0.0857910	−	0.0623308i
$977$	−40.7940	−	13.2548i	−1.30512	−	0.424058i	−0.427758	−	0.903893i	$-0.640697\pi$
$977$	−40.7940	−	13.2548i	−1.30512	−	0.424058i	−0.877359	+	0.479835i	$0.840697\pi$
$978$	−40.0391	+	13.0095i	−1.28031	+	0.415998i
$979$	0.881663	−	0.640566i	0.0281781	−	0.0204726i
$980$	0.448117	−	0.325576i	0.0143146	−	0.0104001i
$981$			55.9887i			1.78758i
$982$	−7.69051	−	23.6689i	−0.245414	−	0.755306i
$983$	28.6806			0.914770			0.457385	−	0.889269i	$-0.348786\pi$
$983$	28.6806			0.914770			0.457385	+	0.889269i	$0.348786\pi$
$984$	42.2351	+	9.92573i	1.34641	+	0.316421i
$985$	−4.59899			−0.146536
$986$	4.91044	+	15.1128i	0.156380	+	0.481289i
$987$		−	18.7491i		−	0.596790i
$988$	4.36072	−	3.16825i	0.138733	−	0.100795i
$989$	11.7593	−	8.54365i	0.373925	−	0.271672i
$990$	−0.369327	+	0.120002i	−0.0117380	+	0.00381390i
$991$	3.56731	+	1.15909i	0.113319	+	0.0368197i	0.365128	−	0.930957i	$-0.381025\pi$
$991$	3.56731	+	1.15909i	0.113319	+	0.0368197i	−0.251808	+	0.967777i	$0.581025\pi$
$992$	−24.5821	−	17.8600i	−0.780484	−	0.567055i
$993$	18.6559			0.592028
$994$	3.87965	+	2.81873i	0.123055	+	0.0894048i
$995$	1.88229	−	2.59075i	0.0596726	−	0.0821322i
$996$	3.40130	+	4.68148i	0.107774	+	0.148338i
$997$	−4.43462	+	1.44090i	−0.140446	+	0.0456336i	−0.378396	−	0.925644i	$-0.623524\pi$
$997$	−4.43462	+	1.44090i	−0.140446	+	0.0456336i	0.237951	+	0.971277i	$0.423524\pi$
$998$			13.7667i			0.435777i
$999$	−5.39335	−	7.42330i	−0.170638	−	0.234863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.n.a.64.15	✓	88
41.25	even	10	inner	287.2.n.a.148.15	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.n.a.64.15	✓	88	1.1	even	1	trivial
287.2.n.a.148.15	yes	88	41.25	even	10	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.239839 + 0.738150i) q^{2} -2.56947i q^{3} +(1.13069 - 0.821496i) q^{4} +(0.320630 - 0.232952i) q^{5} +(1.89665 - 0.616259i) q^{6} +(0.951057 + 0.309017i) q^{7} +(2.13339 + 1.55000i) q^{8} -3.60216 q^{9} +O(q^{10})\)	\(q+(0.239839 + 0.738150i) q^{2} -2.56947i q^{3} +(1.13069 - 0.821496i) q^{4} +(0.320630 - 0.232952i) q^{5} +(1.89665 - 0.616259i) q^{6} +(0.951057 + 0.309017i) q^{7} +(2.13339 + 1.55000i) q^{8} -3.60216 q^{9} +(0.248853 + 0.180802i) q^{10} +(0.206004 - 0.283540i) q^{11} +(-2.11081 - 2.90528i) q^{12} +(-3.61230 + 1.17371i) q^{13} +0.776136i q^{14} +(-0.598562 - 0.823849i) q^{15} +(0.231313 - 0.711908i) q^{16} +(1.49711 - 2.06060i) q^{17} +(-0.863941 - 2.65894i) q^{18} +(-0.965702 - 0.313776i) q^{19} +(0.171165 - 0.526793i) q^{20} +(0.794009 - 2.44371i) q^{21} +(0.258703 + 0.0840576i) q^{22} +(-0.684214 - 2.10579i) q^{23} +(3.98266 - 5.48167i) q^{24} +(-1.49655 + 4.60590i) q^{25} +(-1.73274 - 2.38491i) q^{26} +1.54724i q^{27} +(1.32921 - 0.431886i) q^{28} +(4.72480 + 6.50313i) q^{29} +(0.464565 - 0.639420i) q^{30} +(-4.19849 - 3.05038i) q^{31} +5.85499 q^{32} +(-0.728547 - 0.529320i) q^{33} +(1.88010 + 0.610880i) q^{34} +(0.376924 - 0.122470i) q^{35} +(-4.07294 + 2.95916i) q^{36} +(-4.79777 + 3.48578i) q^{37} -0.788088i q^{38} +(3.01580 + 9.28168i) q^{39} +1.04510 q^{40} +(2.47872 + 5.90389i) q^{41} +1.99426 q^{42} +(2.02860 + 6.24340i) q^{43} -0.489828i q^{44} +(-1.15496 + 0.839130i) q^{45} +(1.39029 - 1.01010i) q^{46} +(6.93974 - 2.25486i) q^{47} +(-1.82922 - 0.594351i) q^{48} +(0.809017 + 0.587785i) q^{49} -3.75877 q^{50} +(-5.29464 - 3.84678i) q^{51} +(-3.12020 + 4.29459i) q^{52} +(-3.10400 - 4.27229i) q^{53} +(-1.14210 + 0.371089i) q^{54} -0.138900i q^{55} +(1.55000 + 2.13339i) q^{56} +(-0.806236 + 2.48134i) q^{57} +(-3.66709 + 5.04731i) q^{58} +(2.40866 + 7.41310i) q^{59} +(-1.35358 - 0.439804i) q^{60} +(1.36765 - 4.20918i) q^{61} +(1.24468 - 3.83072i) q^{62} +(-3.42586 - 1.11313i) q^{63} +(0.941632 + 2.89805i) q^{64} +(-0.884795 + 1.21782i) q^{65} +(0.215983 - 0.664728i) q^{66} +(3.78227 + 5.20584i) q^{67} -3.55977i q^{68} +(-5.41077 + 1.75807i) q^{69} +(0.180802 + 0.248853i) q^{70} +(3.63175 - 4.99868i) q^{71} +(-7.68481 - 5.58334i) q^{72} -8.89270 q^{73} +(-3.72372 - 2.70544i) q^{74} +(11.8347 + 3.84533i) q^{75} +(-1.34968 + 0.438537i) q^{76} +(0.283540 - 0.206004i) q^{77} +(-6.12796 + 4.45222i) q^{78} +4.32293i q^{79} +(-0.0916742 - 0.282144i) q^{80} -6.83091 q^{81} +(-3.76346 + 3.24565i) q^{82} -1.61137 q^{83} +(-1.10972 - 3.41536i) q^{84} -1.00944i q^{85} +(-4.12203 + 2.99483i) q^{86} +(16.7096 - 12.1402i) q^{87} +(0.878971 - 0.285595i) q^{88} +(2.95730 + 0.960884i) q^{89} +(-0.896409 - 0.651279i) q^{90} -3.79819 q^{91} +(-2.50354 - 1.81893i) q^{92} +(-7.83786 + 10.7879i) q^{93} +(3.32884 + 4.58176i) q^{94} +(-0.382728 + 0.124356i) q^{95} -15.0442i q^{96} +(-9.40522 - 12.9452i) q^{97} +(-0.239839 + 0.738150i) q^{98} +(-0.742059 + 1.02136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9}+O(q^{10}) \) 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9	\( 88 q - 24 q^{4} + 8 q^{5} + 10 q^{6} - 18 q^{8} - 116 q^{9} + 36 q^{10} - 10 q^{11} + 20 q^{15} - 12 q^{16} - 10 q^{17} + 20 q^{18} + 30 q^{19} - 30 q^{20} + 4 q^{21} - 20 q^{22} - 12 q^{23} + 60 q^{24} - 50 q^{25} - 30 q^{26} + 2 q^{31} + 24 q^{32} - 46 q^{33} + 50 q^{34} + 86 q^{36} - 48 q^{37} + 16 q^{39} - 60 q^{40} - 24 q^{41} - 4 q^{42} + 22 q^{43} - 16 q^{45} + 20 q^{46} + 20 q^{48} + 22 q^{49} - 16 q^{50} + 8 q^{51} + 70 q^{52} - 30 q^{54} + 8 q^{57} - 90 q^{58} - 4 q^{59} - 50 q^{60} - 64 q^{61} - 44 q^{62} + 14 q^{64} + 80 q^{65} - 26 q^{66} + 10 q^{67} + 40 q^{71} + 18 q^{72} + 124 q^{73} + 80 q^{74} + 70 q^{75} - 190 q^{76} + 8 q^{77} + 74 q^{78} + 26 q^{80} + 144 q^{81} - 58 q^{82} - 60 q^{83} + 26 q^{84} + 10 q^{86} + 8 q^{87} + 160 q^{88} - 164 q^{90} - 40 q^{91} - 156 q^{92} - 20 q^{93} + 10 q^{94} + 80 q^{95} - 90 q^{97} - 40 q^{99}+O(q^{100}) \) 88 * q - 24 * q^4 + 8 * q^5 + 10 * q^6 - 18 * q^8 - 116 * q^9 + 36 * q^10 - 10 * q^11 + 20 * q^15 - 12 * q^16 - 10 * q^17 + 20 * q^18 + 30 * q^19 - 30 * q^20 + 4 * q^21 - 20 * q^22 - 12 * q^23 + 60 * q^24 - 50 * q^25 - 30 * q^26 + 2 * q^31 + 24 * q^32 - 46 * q^33 + 50 * q^34 + 86 * q^36 - 48 * q^37 + 16 * q^39 - 60 * q^40 - 24 * q^41 - 4 * q^42 + 22 * q^43 - 16 * q^45 + 20 * q^46 + 20 * q^48 + 22 * q^49 - 16 * q^50 + 8 * q^51 + 70 * q^52 - 30 * q^54 + 8 * q^57 - 90 * q^58 - 4 * q^59 - 50 * q^60 - 64 * q^61 - 44 * q^62 + 14 * q^64 + 80 * q^65 - 26 * q^66 + 10 * q^67 + 40 * q^71 + 18 * q^72 + 124 * q^73 + 80 * q^74 + 70 * q^75 - 190 * q^76 + 8 * q^77 + 74 * q^78 + 26 * q^80 + 144 * q^81 - 58 * q^82 - 60 * q^83 + 26 * q^84 + 10 * q^86 + 8 * q^87 + 160 * q^88 - 164 * q^90 - 40 * q^91 - 156 * q^92 - 20 * q^93 + 10 * q^94 + 80 * q^95 - 90 * q^97 - 40 * q^99

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