LMFDB - Embedded newform 201.2.d.a.200.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,2,Mod(200,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("201.200");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	201.d (of order $2$, degree $1$, 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:	$1.60499308063$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 7 x^{18} + 32 x^{16} + 128 x^{14} + 423 x^{12} + 1186 x^{10} + 3807 x^{8} + 10368 x^{6} + \cdots + 59049 $ x^20 + 7x^18 + 32x^16 + 128x^14 + 423x^12 + 1186x^10 + 3807x^8 + 10368x^6 + 23328x^4 + 45927*x^2 + 59049
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			200.6
Root			$-1.24906 - 1.19993i$ of defining polynomial
Character	$\chi$	$=$	201.200
Dual form			201.2.d.a.200.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.18817 q^{2} +(-1.24906 + 1.19993i) q^{3} -0.588256 q^{4} -2.08509 q^{5} +(1.48410 - 1.42572i) q^{6} +0.284155i q^{7} +3.07528 q^{8} +(0.120318 - 2.99759i) q^{9} +O(q^{10})$	\(q-1.18817 q^{2} +(-1.24906 + 1.19993i) q^{3} -0.588256 q^{4} -2.08509 q^{5} +(1.48410 - 1.42572i) q^{6} +0.284155i q^{7} +3.07528 q^{8} +(0.120318 - 2.99759i) q^{9} +2.47744 q^{10} +1.80373 q^{11} +(0.734769 - 0.705868i) q^{12} -5.82854i q^{13} -0.337624i q^{14} +(2.60442 - 2.50198i) q^{15} -2.47744 q^{16} +2.11827i q^{17} +(-0.142958 + 3.56164i) q^{18} +3.37994 q^{19} +1.22657 q^{20} +(-0.340967 - 0.354927i) q^{21} -2.14313 q^{22} -5.85449i q^{23} +(-3.84122 + 3.69014i) q^{24} -0.652380 q^{25} +6.92529i q^{26} +(3.44662 + 3.88855i) q^{27} -0.167156i q^{28} -1.18816i q^{29} +(-3.09448 + 2.97277i) q^{30} -9.35599i q^{31} -3.20695 q^{32} +(-2.25297 + 2.16435i) q^{33} -2.51687i q^{34} -0.592489i q^{35} +(-0.0707775 + 1.76335i) q^{36} -9.06621 q^{37} -4.01594 q^{38} +(6.99386 + 7.28021i) q^{39} -6.41226 q^{40} +6.14602 q^{41} +(0.405126 + 0.421713i) q^{42} +1.57889i q^{43} -1.06105 q^{44} +(-0.250874 + 6.25025i) q^{45} +6.95612i q^{46} +3.59553i q^{47} +(3.09448 - 2.97277i) q^{48} +6.91926 q^{49} +0.775137 q^{50} +(-2.54179 - 2.64586i) q^{51} +3.42867i q^{52} -5.90760 q^{53} +(-4.09517 - 4.62025i) q^{54} -3.76094 q^{55} +0.873856i q^{56} +(-4.22176 + 4.05570i) q^{57} +1.41174i q^{58} -8.92620i q^{59} +(-1.53206 + 1.47180i) q^{60} -3.69460i q^{61} +11.1165i q^{62} +(0.851778 + 0.0341888i) q^{63} +8.76528 q^{64} +12.1531i q^{65} +(2.67691 - 2.57162i) q^{66} +(-1.97202 + 7.94425i) q^{67} -1.24609i q^{68} +(7.02500 + 7.31263i) q^{69} +0.703977i q^{70} -12.9205i q^{71} +(0.370011 - 9.21843i) q^{72} +2.98669 q^{73} +10.7722 q^{74} +(0.814863 - 0.782812i) q^{75} -1.98827 q^{76} +0.512537i q^{77} +(-8.30988 - 8.65012i) q^{78} -2.32354i q^{79} +5.16571 q^{80} +(-8.97105 - 0.721325i) q^{81} -7.30251 q^{82} -10.4066i q^{83} +(0.200576 + 0.208788i) q^{84} -4.41680i q^{85} -1.87599i q^{86} +(1.42571 + 1.48409i) q^{87} +5.54697 q^{88} -4.96972i q^{89} +(0.298080 - 7.42635i) q^{90} +1.65621 q^{91} +3.44394i q^{92} +(11.2266 + 11.6862i) q^{93} -4.27210i q^{94} -7.04749 q^{95} +(4.00568 - 3.84812i) q^{96} -8.79672i q^{97} -8.22124 q^{98} +(0.217020 - 5.40683i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 12 q^{4} - 4 q^{6} - 14 q^{9}+O(q^{10}) $ 20 * q + 12 * q^4 - 4 * q^6 - 14 * q^9	$ 20 q + 12 q^{4} - 4 q^{6} - 14 q^{9} - 12 q^{10} + 2 q^{15} + 12 q^{16} + 24 q^{19} + 12 q^{21} - 28 q^{22} + 2 q^{24} - 4 q^{25} + 10 q^{33} - 44 q^{36} + 24 q^{37} - 8 q^{39} - 32 q^{40} - 48 q^{49} - 26 q^{54} - 8 q^{55} - 38 q^{60} - 16 q^{64} + 32 q^{67} + 4 q^{73} + 116 q^{76} - 30 q^{81} - 32 q^{82} + 90 q^{84} - 40 q^{88} + 74 q^{90} + 20 q^{91} - 2 q^{93} + 30 q^{96}+O(q^{100}) $ 20 * q + 12 * q^4 - 4 * q^6 - 14 * q^9 - 12 * q^10 + 2 * q^15 + 12 * q^16 + 24 * q^19 + 12 * q^21 - 28 * q^22 + 2 * q^24 - 4 * q^25 + 10 * q^33 - 44 * q^36 + 24 * q^37 - 8 * q^39 - 32 * q^40 - 48 * q^49 - 26 * q^54 - 8 * q^55 - 38 * q^60 - 16 * q^64 + 32 * q^67 + 4 * q^73 + 116 * q^76 - 30 * q^81 - 32 * q^82 + 90 * q^84 - 40 * q^88 + 74 * q^90 + 20 * q^91 - 2 * q^93 + 30 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.18817			−0.840162			−0.420081	−	0.907487i	$-0.637998\pi$
$2$	−1.18817			−0.840162			−0.420081	+	0.907487i	$0.637998\pi$
$3$	−1.24906	+	1.19993i	−0.721147	+	0.692782i
$3$	−1.24906	+	1.19993i	−0.721147	+	0.692782i
$4$	−0.588256			−0.294128
$5$	−2.08509			−0.932483			−0.466241	−	0.884658i	$-0.654392\pi$
$5$	−2.08509			−0.932483			−0.466241	+	0.884658i	$0.654392\pi$
$6$	1.48410	−	1.42572i	0.605880	−	0.582049i
$7$			0.284155i			0.107400i	0.998557	+	0.0537002i	$0.0171015\pi$
$7$			0.284155i			0.107400i	−0.998557	+	0.0537002i	$0.982898\pi$
$8$	3.07528			1.08728
$9$	0.120318	−	2.99759i	0.0401059	−	0.999195i
$10$	2.47744			0.783437
$11$	1.80373			0.543844			0.271922	−	0.962319i	$-0.412341\pi$
$11$	1.80373			0.543844			0.271922	+	0.962319i	$0.412341\pi$
$12$	0.734769	−	0.705868i	0.212109	−	0.203767i
$13$		−	5.82854i		−	1.61655i	−0.588808	−	0.808273i	$-0.700403\pi$
$13$		−	5.82854i		−	1.61655i	0.588808	−	0.808273i	$-0.299597\pi$
$14$		−	0.337624i		−	0.0902337i
$15$	2.60442	−	2.50198i	0.672457	−	0.646007i
$16$	−2.47744			−0.619361
$17$			2.11827i			0.513757i	0.966444	+	0.256878i	$0.0826940\pi$
$17$			2.11827i			0.513757i	−0.966444	+	0.256878i	$0.917306\pi$
$18$	−0.142958	+	3.56164i	−0.0336954	+	0.839486i
$19$	3.37994			0.775411			0.387706	−	0.921783i	$-0.373268\pi$
$19$	3.37994			0.775411			0.387706	+	0.921783i	$0.373268\pi$
$20$	1.22657			0.274269
$21$	−0.340967	−	0.354927i	−0.0744051	−	0.0774514i
$22$	−2.14313			−0.456917
$23$		−	5.85449i		−	1.22075i	−0.792114	−	0.610373i	$-0.791020\pi$
$23$		−	5.85449i		−	1.22075i	0.792114	−	0.610373i	$-0.208980\pi$
$24$	−3.84122	+	3.69014i	−0.784087	+	0.753246i
$25$	−0.652380			−0.130476
$26$			6.92529i			1.35816i
$27$	3.44662	+	3.88855i	0.663302	+	0.748351i
$28$		−	0.167156i		−	0.0315894i
$29$		−	1.18816i		−	0.220636i	−0.993896	−	0.110318i	$-0.964813\pi$
$29$		−	1.18816i		−	0.220636i	0.993896	−	0.110318i	$-0.0351869\pi$
$30$	−3.09448	+	2.97277i	−0.564973	+	0.542751i
$31$		−	9.35599i		−	1.68038i	−0.542288	−	0.840192i	$-0.682442\pi$
$31$		−	9.35599i		−	1.68038i	0.542288	−	0.840192i	$-0.317558\pi$
$32$	−3.20695			−0.566913
$33$	−2.25297	+	2.16435i	−0.392191	+	0.376765i
$34$		−	2.51687i		−	0.431639i
$35$		−	0.592489i		−	0.100149i
$36$	−0.0707775	+	1.76335i	−0.0117963	+	0.293891i
$37$	−9.06621			−1.49048			−0.745238	−	0.666798i	$-0.767664\pi$
$37$	−9.06621			−1.49048			−0.745238	+	0.666798i	$0.767664\pi$
$38$	−4.01594			−0.651471
$39$	6.99386	+	7.28021i	1.11991	+	1.16577i
$40$	−6.41226			−1.01387
$41$	6.14602			0.959847			0.479924	−	0.877310i	$-0.340664\pi$
$41$	6.14602			0.959847			0.479924	+	0.877310i	$0.340664\pi$
$42$	0.405126	+	0.421713i	0.0625123	+	0.0650718i
$43$			1.57889i			0.240779i	0.992727	+	0.120389i	$0.0384143\pi$
$43$			1.57889i			0.240779i	−0.992727	+	0.120389i	$0.961586\pi$
$44$	−1.06105			−0.159960
$45$	−0.250874	+	6.25025i	−0.0373980	+	0.931733i
$46$			6.95612i			1.02562i
$47$			3.59553i			0.524462i	0.965005	+	0.262231i	$0.0844583\pi$
$47$			3.59553i			0.524462i	−0.965005	+	0.262231i	$0.915542\pi$
$48$	3.09448	−	2.97277i	0.446650	−	0.429082i
$49$	6.91926			0.988465
$50$	0.775137			0.109621
$51$	−2.54179	−	2.64586i	−0.355922	−	0.370494i
$52$			3.42867i			0.475471i
$53$	−5.90760			−0.811471			−0.405736	−	0.913990i	$-0.632985\pi$
$53$	−5.90760			−0.811471			−0.405736	+	0.913990i	$0.632985\pi$
$54$	−4.09517	−	4.62025i	−0.557282	−	0.628736i
$55$	−3.76094			−0.507125
$56$			0.873856i			0.116774i
$57$	−4.22176	+	4.05570i	−0.559185	+	0.537191i
$58$			1.41174i			0.185370i
$59$		−	8.92620i		−	1.16209i	−0.813871	−	0.581046i	$-0.802644\pi$
$59$		−	8.92620i		−	1.16209i	0.813871	−	0.581046i	$-0.197356\pi$
$60$	−1.53206	+	1.47180i	−0.197788	+	0.190009i
$61$		−	3.69460i		−	0.473046i	−0.971626	−	0.236523i	$-0.923992\pi$
$61$		−	3.69460i		−	0.473046i	0.971626	−	0.236523i	$-0.0760078\pi$
$62$			11.1165i			1.41180i
$63$	0.851778	+	0.0341888i	0.107314	+	0.00430739i
$64$	8.76528			1.09566
$65$			12.1531i			1.50740i
$66$	2.67691	−	2.57162i	0.329504	−	0.316544i
$67$	−1.97202	+	7.94425i	−0.240921	+	0.970545i
$67$	−1.97202	+	7.94425i	−0.240921	+	0.970545i
$68$		−	1.24609i		−	0.151110i
$69$	7.02500	+	7.31263i	0.845711	+	0.880337i
$70$			0.703977i			0.0841414i
$71$		−	12.9205i		−	1.53338i	−0.642020	−	0.766688i	$-0.721903\pi$
$71$		−	12.9205i		−	1.53338i	0.642020	−	0.766688i	$-0.278097\pi$
$72$	0.370011	−	9.21843i	0.0436062	−	1.08640i
$73$	2.98669			0.349566			0.174783	−	0.984607i	$-0.444078\pi$
$73$	2.98669			0.349566			0.174783	+	0.984607i	$0.444078\pi$
$74$	10.7722			1.25224
$75$	0.814863	−	0.782812i	0.0940923	−	0.0903914i
$76$	−1.98827			−0.228070
$77$			0.512537i			0.0584090i
$78$	−8.30988	−	8.65012i	−0.940909	−	0.979433i
$79$		−	2.32354i		−	0.261419i	−0.991421	−	0.130709i	$-0.958275\pi$
$79$		−	2.32354i		−	0.261419i	0.991421	−	0.130709i	$-0.0417255\pi$
$80$	5.16571			0.577543
$81$	−8.97105	−	0.721325i	−0.996783	−	0.0801472i
$82$	−7.30251			−0.806427
$83$		−	10.4066i		−	1.14228i	−0.820854	−	0.571138i	$-0.806502\pi$
$83$		−	10.4066i		−	1.14228i	0.820854	−	0.571138i	$-0.193498\pi$
$84$	0.200576	+	0.208788i	0.0218846	+	0.0227806i
$85$		−	4.41680i		−	0.479070i
$86$		−	1.87599i		−	0.202293i
$87$	1.42571	+	1.48409i	0.152853	+	0.159111i
$88$	5.54697			0.591309
$89$		−	4.96972i		−	0.526789i	−0.964688	−	0.263395i	$-0.915158\pi$
$89$		−	4.96972i		−	0.526789i	0.964688	−	0.263395i	$-0.0848422\pi$
$90$	0.298080	−	7.42635i	0.0314204	−	0.782806i
$91$	1.65621			0.173618
$92$			3.44394i			0.359055i
$93$	11.2266	+	11.6862i	1.16414	+	1.21180i
$94$		−	4.27210i		−	0.440633i
$95$	−7.04749			−0.723058
$96$	4.00568	−	3.84812i	0.408828	−	0.392748i
$97$		−	8.79672i		−	0.893171i	−0.894741	−	0.446586i	$-0.852640\pi$
$97$		−	8.79672i		−	0.893171i	0.894741	−	0.446586i	$-0.147360\pi$
$98$	−8.22124			−0.830471
$99$	0.217020	−	5.40683i	0.0218113	−	0.543406i
$100$	0.383766			0.0383766
$101$	−8.83225			−0.878842			−0.439421	−	0.898281i	$-0.644816\pi$
$101$	−8.83225			−0.878842			−0.439421	+	0.898281i	$0.644816\pi$
$102$	3.02007	+	3.14373i	0.299032	+	0.311275i
$103$	14.5531			1.43396			0.716982	−	0.697092i	$-0.245523\pi$
$103$	14.5531			1.43396			0.716982	+	0.697092i	$0.245523\pi$
$104$		−	17.9244i		−	1.75763i
$105$	0.710948	+	0.740057i	0.0693814	+	0.0722221i
$106$	7.01922			0.681767
$107$		−	2.82813i		−	0.273406i	−0.990612	−	0.136703i	$-0.956349\pi$
$107$		−	2.82813i		−	0.273406i	0.990612	−	0.136703i	$-0.0436505\pi$
$108$	−2.02749	−	2.28746i	−0.195096	−	0.220111i
$109$			14.9319i			1.43021i	0.699016	+	0.715106i	$0.253622\pi$
$109$			14.9319i			1.43021i	−0.699016	+	0.715106i	$0.746378\pi$
$110$	4.46863			0.426067
$111$	11.3243	−	10.8789i	1.07485	−	1.03258i
$112$		−	0.703977i		−	0.0665196i
$113$	−6.11810			−0.575543			−0.287771	−	0.957699i	$-0.592914\pi$
$113$	−6.11810			−0.575543			−0.287771	+	0.957699i	$0.592914\pi$
$114$	5.01616	−	4.81886i	0.469806	−	0.451328i
$115$			12.2072i			1.13832i
$116$			0.698943i			0.0648952i
$117$	−17.4715	−	0.701276i	−1.61525	−	0.0648330i
$118$			10.6058i			0.976345i
$119$	−0.601918			−0.0551777
$120$	8.00932	−	7.69429i	0.731147	−	0.702389i
$121$	−7.74657			−0.704234
$122$			4.38981i			0.397435i
$123$	−7.67677	+	7.37482i	−0.692191	+	0.664965i
$124$			5.50371i			0.494248i
$125$	11.7857			1.05415
$126$	−1.01206	−	0.0406221i	−0.0901611	−	0.00361890i
$127$	2.89301			0.256714			0.128357	−	0.991728i	$-0.459030\pi$
$127$	2.89301			0.256714			0.128357	+	0.991728i	$0.459030\pi$
$128$	−4.00074			−0.353619
$129$	−1.89457	−	1.97214i	−0.166807	−	0.173637i
$130$		−	14.4399i		−	1.26646i
$131$			11.7543i			1.02698i	0.858096	+	0.513490i	$0.171648\pi$
$131$			11.7543i			1.02698i	−0.858096	+	0.513490i	$0.828352\pi$
$132$	1.32532	−	1.27319i	0.115354	−	0.110817i
$133$			0.960426i			0.0832795i
$134$	2.34309	−	9.43911i	0.202412	−	0.815415i
$135$	−7.18653	−	8.10799i	−0.618518	−	0.697825i
$136$			6.51429i			0.558596i
$137$	5.72373			0.489011			0.244505	−	0.969648i	$-0.421374\pi$
$137$	5.72373			0.489011			0.244505	+	0.969648i	$0.421374\pi$
$138$	−8.34688	−	8.68863i	−0.710534	−	0.739626i
$139$		−	9.17061i		−	0.777841i	−0.921271	−	0.388921i	$-0.872848\pi$
$139$		−	9.17061i		−	0.777841i	0.921271	−	0.388921i	$-0.127152\pi$
$140$			0.348535i			0.0294566i
$141$	−4.31440	−	4.49105i	−0.363338	−	0.378214i
$142$			15.3517i			1.28828i
$143$		−	10.5131i		−	0.879149i
$144$	−0.298080	+	7.42635i	−0.0248400	+	0.618863i
$145$			2.47743i			0.205739i
$146$	−3.54869			−0.293692
$147$	−8.64259	+	8.30265i	−0.712829	+	0.684791i
$148$	5.33325			0.438391
$149$			12.8862i			1.05568i	0.849344	+	0.527840i	$0.176998\pi$
$149$			12.8862i			1.05568i	−0.849344	+	0.527840i	$0.823002\pi$
$150$	−0.968195	+	0.930113i	−0.0790528	+	0.0759434i
$151$	13.2071			1.07478			0.537389	−	0.843334i	$-0.319411\pi$
$151$	13.2071			1.07478			0.537389	+	0.843334i	$0.319411\pi$
$152$	10.3943			0.843087
$153$	6.34971	+	0.254866i	0.513344	+	0.0206047i
$154$		−	0.608981i		−	0.0490731i
$155$			19.5081i			1.56693i
$156$	−4.11418	−	4.28263i	−0.329398	−	0.342885i
$157$	−11.7999			−0.941731			−0.470865	−	0.882205i	$-0.656058\pi$
$157$	−11.7999			−0.941731			−0.470865	+	0.882205i	$0.656058\pi$
$158$			2.76076i			0.219634i
$159$	7.37896	−	7.08873i	0.585190	−	0.562173i
$160$	6.68679			0.528637
$161$	1.66358			0.131109
$162$	10.6591	+	0.857056i	0.837459	+	0.0673367i
$163$	−4.07931			−0.319516			−0.159758	−	0.987156i	$-0.551071\pi$
$163$	−4.07931			−0.319516			−0.159758	+	0.987156i	$0.551071\pi$
$164$	−3.61543			−0.282318
$165$	4.69765	−	4.51288i	0.365712	−	0.351327i
$166$			12.3648i			0.959697i
$167$			5.34158i			0.413343i	0.978410	+	0.206672i	$0.0662632\pi$
$167$			5.34158i			0.413343i	−0.978410	+	0.206672i	$0.933737\pi$
$168$	−1.04857	−	1.09150i	−0.0808989	−	0.0842112i
$169$	−20.9719			−1.61322
$170$			5.24791i			0.402496i
$171$	0.406666	−	10.1317i	0.0310986	−	0.774787i
$172$		−	0.928792i		−	0.0708197i
$173$			24.8155i			1.88668i	0.331821	+	0.943342i	$0.392337\pi$
$173$			24.8155i			1.88668i	−0.331821	+	0.943342i	$0.607663\pi$
$174$	−1.69399	−	1.76335i	−0.128421	−	0.133679i
$175$		−	0.185377i		−	0.0140132i
$176$	−4.46863			−0.336836
$177$	10.7108	+	11.1494i	0.805076	+	0.838039i
$178$			5.90487i			0.442588i
$179$	−15.4421			−1.15420			−0.577098	−	0.816675i	$-0.695815\pi$
$179$	−15.4421			−1.15420			−0.577098	+	0.816675i	$0.695815\pi$
$180$	0.147578	−	3.67675i	0.0109998	−	0.274048i
$181$	−6.79326			−0.504939			−0.252469	−	0.967605i	$-0.581243\pi$
$181$	−6.79326			−0.504939			−0.252469	+	0.967605i	$0.581243\pi$
$182$	−1.96785			−0.145867
$183$	4.43328	+	4.61479i	0.327718	+	0.341135i
$184$		−	18.0042i		−	1.32729i
$185$	18.9039			1.38984
$186$	−13.3391	−	13.8852i	−0.978067	−	1.01811i
$187$			3.82079i			0.279404i
$188$		−	2.11509i		−	0.154259i
$189$	−1.10495	+	0.979373i	−0.0803732	+	0.0712389i
$190$	8.37361			0.607486
$191$	22.3294			1.61570			0.807849	−	0.589390i	$-0.200632\pi$
$191$	22.3294			1.61570			0.807849	+	0.589390i	$0.200632\pi$
$192$	−10.9484	+	10.5178i	−0.790132	+	0.759054i
$193$	−23.6517			−1.70248			−0.851242	−	0.524773i	$-0.824150\pi$
$193$	−23.6517			−1.70248			−0.851242	+	0.524773i	$0.824150\pi$
$194$			10.4520i			0.750408i
$195$	−14.5829	−	15.1799i	−1.04430	−	1.08706i
$196$	−4.07029			−0.290735
$197$	−19.5884			−1.39562			−0.697809	−	0.716284i	$-0.745842\pi$
$197$	−19.5884			−1.39562			−0.697809	+	0.716284i	$0.745842\pi$
$198$	−0.257856	+	6.42422i	−0.0183251	+	0.456549i
$199$	12.8766			0.912798			0.456399	−	0.889775i	$-0.349139\pi$
$199$	12.8766			0.912798			0.456399	+	0.889775i	$0.349139\pi$
$200$	−2.00625			−0.141863
$201$	−7.06940	−	12.2892i	−0.498637	−	0.866811i
$202$	10.4942			0.738370
$203$	0.337622			0.0236964
$204$	1.49522	+	1.55644i	0.104686	+	0.108973i
$205$	−12.8150			−0.895041
$206$	−17.2916			−1.20476
$207$	−17.5493	−	0.704398i	−1.21976	−	0.0489591i
$208$			14.4399i			1.00123i
$209$	6.09649			0.421703
$210$	−0.844726	−	0.879312i	−0.0582916	−	0.0606783i
$211$	−9.41052			−0.647847			−0.323923	−	0.946083i	$-0.605002\pi$
$211$	−9.41052			−0.647847			−0.323923	+	0.946083i	$0.605002\pi$
$212$	3.47518			0.238676
$213$	15.5037	+	16.1385i	1.06230	+	1.10579i
$214$			3.36029i			0.229705i
$215$		−	3.29214i		−	0.224522i
$216$	10.5993	+	11.9584i	0.721194	+	0.813665i
$217$	2.65855			0.180474
$218$		−	17.7416i		−	1.20161i
$219$	−3.73057	+	3.58383i	−0.252088	+	0.242173i
$220$	2.21239			0.149160
$221$	12.3464			0.830512
$222$	−13.4551	+	12.9259i	−0.903050	+	0.867531i
$223$	−4.29838			−0.287841			−0.143920	−	0.989589i	$-0.545971\pi$
$223$	−4.29838			−0.287841			−0.143920	+	0.989589i	$0.545971\pi$
$224$		−	0.911269i		−	0.0608867i
$225$	−0.0784928	+	1.95556i	−0.00523285	+	0.130371i
$226$	7.26934			0.483549
$227$			18.7640i			1.24541i	0.782456	+	0.622706i	$0.213967\pi$
$227$			18.7640i			1.24541i	−0.782456	+	0.622706i	$0.786033\pi$
$228$	2.48347	−	2.38579i	0.164472	−	0.158003i
$229$		−	18.5224i		−	1.22399i	−0.790861	−	0.611996i	$-0.790367\pi$
$229$		−	18.5224i		−	1.22399i	0.790861	−	0.611996i	$-0.209633\pi$
$230$		−	14.5042i		−	0.956377i
$231$	−0.615011	−	0.640191i	−0.0404647	−	0.0421215i
$232$		−	3.65393i		−	0.239892i
$233$	5.72185			0.374851			0.187426	−	0.982279i	$-0.439986\pi$
$233$	5.72185			0.374851			0.187426	+	0.982279i	$0.439986\pi$
$234$	20.7591	+	0.833234i	1.35707	+	0.0544702i
$235$		−	7.49702i		−	0.489052i
$236$			5.25088i			0.341803i
$237$	2.78809	+	2.90225i	0.181106	+	0.188521i
$238$	0.715179			0.0463582
$239$	−10.2059			−0.660163			−0.330082	−	0.943952i	$-0.607076\pi$
$239$	−10.2059			−0.660163			−0.330082	+	0.943952i	$0.607076\pi$
$240$	−6.45229	+	6.19850i	−0.416494	+	0.400112i
$241$	24.4388			1.57424			0.787120	−	0.616800i	$-0.211571\pi$
$241$	24.4388			1.57424			0.787120	+	0.616800i	$0.211571\pi$
$242$	9.20423			0.591670
$243$	12.0709	−	9.86368i	0.774352	−	0.632756i
$244$			2.17337i			0.139136i
$245$	−14.4273			−0.921727
$246$	9.12129	−	8.76253i	0.581552	−	0.558678i
$247$		−	19.7001i		−	1.25349i
$248$		−	28.7723i		−	1.82704i
$249$	12.4873	+	12.9985i	0.791349	+	0.823749i
$250$	−14.0035			−0.885656
$251$	19.6684			1.24146			0.620730	−	0.784025i	$-0.286836\pi$
$251$	19.6684			1.24146			0.620730	+	0.784025i	$0.286836\pi$
$252$	−0.501063	−	0.0201118i	−0.0315640	−	0.00126692i
$253$		−	10.5599i		−	0.663895i
$254$	−3.43739			−0.215681
$255$	5.29987	+	5.51687i	0.331891	+	0.345480i
$256$	−12.7770			−0.798563
$257$			16.0646i			1.00208i	0.865424	+	0.501040i	$0.167049\pi$
$257$			16.0646i			1.00208i	−0.865424	+	0.501040i	$0.832951\pi$
$258$	2.25106	+	2.34323i	0.140145	+	0.145883i
$259$		−	2.57621i		−	0.160078i
$260$		−	7.14910i		−	0.443369i
$261$	−3.56162	−	0.142957i	−0.220458	−	0.00884880i
$262$		−	13.9661i		−	0.862830i
$263$		−	25.0924i		−	1.54726i	−0.633637	−	0.773631i	$-0.718439\pi$
$263$		−	25.0924i		−	1.54726i	0.633637	−	0.773631i	$-0.281561\pi$
$264$	−6.92852	+	6.65600i	−0.426421	+	0.409648i
$265$	12.3179			0.756683
$266$		−	1.14115i		−	0.0699682i
$267$	5.96334	+	6.20750i	0.364950	+	0.379893i
$268$	1.16005	−	4.67325i	0.0708615	−	0.285464i
$269$		−	32.6631i		−	1.99151i	−0.0920625	−	0.995753i	$-0.529346\pi$
$269$		−	32.6631i		−	1.99151i	0.0920625	−	0.995753i	$-0.470654\pi$
$270$	8.53881	+	9.63366i	0.519655	+	0.586286i
$271$			29.8679i			1.81434i	0.420759	+	0.907172i	$0.361764\pi$
$271$			29.8679i			1.81434i	−0.420759	+	0.907172i	$0.638236\pi$
$272$		−	5.24791i		−	0.318201i
$273$	−2.06871	+	1.98734i	−0.125204	+	0.120279i
$274$	−6.80075			−0.410848
$275$	−1.17671			−0.0709585
$276$	−4.13250	−	4.30169i	−0.248747	−	0.258932i
$277$	4.29277			0.257927			0.128964	−	0.991649i	$-0.458835\pi$
$277$	4.29277			0.257927			0.128964	+	0.991649i	$0.458835\pi$
$278$			10.8962i			0.653512i
$279$	−28.0454	−	1.12569i	−1.67903	−	0.0673933i
$280$		−	1.82207i		−	0.108890i
$281$	27.5062			1.64088			0.820442	−	0.571730i	$-0.193727\pi$
$281$	27.5062			1.64088			0.820442	+	0.571730i	$0.193727\pi$
$282$	5.12623	+	5.33612i	0.305263	+	0.317761i
$283$	1.67756			0.0997205			0.0498603	−	0.998756i	$-0.484122\pi$
$283$	1.67756			0.0997205			0.0498603	+	0.998756i	$0.484122\pi$
$284$			7.60053i			0.451009i
$285$	8.80277	−	8.45653i	0.521431	−	0.500921i
$286$			12.4913i			0.738627i
$287$			1.74642i			0.103088i
$288$	−0.385852	+	9.61310i	−0.0227366	+	0.566457i
$289$	12.5129			0.736054
$290$		−	2.94360i		−	0.172854i
$291$	10.5555	+	10.9877i	0.618773	+	0.644108i
$292$	−1.75694			−0.102817
$293$		−	18.4716i		−	1.07912i	−0.841947	−	0.539560i	$-0.818591\pi$
$293$		−	18.4716i		−	1.07912i	0.841947	−	0.539560i	$-0.181409\pi$
$294$	10.2689	−	9.86495i	0.598892	−	0.575335i
$295$			18.6120i			1.08363i
$296$	−27.8812			−1.62056
$297$	6.21676	+	7.01388i	0.360733	+	0.406986i
$298$		−	15.3110i		−	0.886943i
$299$	−34.1231			−1.97339
$300$	−0.479348	+	0.460494i	−0.0276752	+	0.0265866i
$301$	−0.448649			−0.0258597
$302$	−15.6923			−0.902988
$303$	11.0320	−	10.5981i	0.633774	−	0.608846i
$304$	−8.37361			−0.480259
$305$			7.70360i			0.441107i
$306$	−7.54453	−	0.302824i	−0.431292	−	0.0173113i
$307$	7.26092			0.414403			0.207201	−	0.978298i	$-0.433564\pi$
$307$	7.26092			0.414403			0.207201	+	0.978298i	$0.433564\pi$
$308$		−	0.301503i		−	0.0171797i
$309$	−18.1778	+	17.4628i	−1.03410	+	0.993424i
$310$		−	23.1789i		−	1.31647i
$311$	−21.0740			−1.19500			−0.597499	−	0.801870i	$-0.703839\pi$
$311$	−21.0740			−1.19500			−0.597499	+	0.801870i	$0.703839\pi$
$312$	21.5081	+	22.3887i	1.21766	+	1.26751i
$313$		−	15.0937i		−	0.853146i	−0.904453	−	0.426573i	$-0.859721\pi$
$313$		−	15.0937i		−	0.853146i	0.904453	−	0.426573i	$-0.140279\pi$
$314$	14.0202			0.791206
$315$	−1.77604	−	0.0712869i	−0.100068	−	0.00401656i
$316$			1.36684i			0.0768905i
$317$			8.49323i			0.477028i	0.971139	+	0.238514i	$0.0766602\pi$
$317$			8.49323i			0.477028i	−0.971139	+	0.238514i	$0.923340\pi$
$318$	−8.76745	+	8.42260i	−0.491654	+	0.472316i
$319$		−	2.14312i		−	0.119992i
$320$	−18.2764			−1.02168
$321$	3.39357	+	3.53251i	0.189410	+	0.197166i
$322$	−1.97661			−0.110152
$323$			7.15964i			0.398373i
$324$	5.27727	+	0.424324i	0.293182	+	0.0235735i
$325$			3.80242i			0.210920i
$326$	4.84691			0.268445
$327$	−17.9172	−	18.6508i	−0.990826	−	1.03139i
$328$	18.9008			1.04362
$329$	−1.02169			−0.0563274
$330$	−5.58160	+	5.36206i	−0.307257	+	0.295172i
$331$		−	14.3805i		−	0.790426i	−0.918590	−	0.395213i	$-0.870671\pi$
$331$		−	14.3805i		−	0.790426i	0.918590	−	0.395213i	$-0.129329\pi$
$332$			6.12176i			0.335975i
$333$	−1.09083	+	27.1768i	−0.0597769	+	1.48928i
$334$		−	6.34669i		−	0.347275i
$335$	4.11185	−	16.5645i	0.224654	−	0.905016i
$336$	0.844726	+	0.879312i	0.0460836	+	0.0479704i
$337$		−	12.0321i		−	0.655428i	−0.944777	−	0.327714i	$-0.893722\pi$
$337$		−	12.0321i		−	0.655428i	0.944777	−	0.327714i	$-0.106278\pi$
$338$	24.9181			1.35537
$339$	7.64190	−	7.34132i	0.415051	−	0.398726i
$340$			2.59821i			0.140908i
$341$		−	16.8756i		−	0.913867i
$342$	−0.483188	+	12.0381i	−0.0261278	+	0.650947i
$343$			3.95522i			0.213562i
$344$			4.85554i			0.261793i
$345$	−14.6478	−	15.2475i	−0.788611	−	0.820899i
$346$		−	29.4850i		−	1.58512i
$347$	10.7604			0.577650			0.288825	−	0.957382i	$-0.406735\pi$
$347$	10.7604			0.577650			0.288825	+	0.957382i	$0.406735\pi$
$348$	−0.838685	−	0.873023i	−0.0449582	−	0.0467990i
$349$	18.9659			1.01522			0.507612	−	0.861586i	$-0.330528\pi$
$349$	18.9659			1.01522			0.507612	+	0.861586i	$0.330528\pi$
$350$			0.220259i			0.0117733i
$351$	22.6646	−	20.0888i	1.20974	−	1.07226i
$352$	−5.78445			−0.308312
$353$	−3.90528			−0.207857			−0.103929	−	0.994585i	$-0.533141\pi$
$353$	−3.90528			−0.207857			−0.103929	+	0.994585i	$0.533141\pi$
$354$	−12.7263	−	13.2473i	−0.676394	−	0.704088i
$355$			26.9404i			1.42985i
$356$			2.92347i			0.154943i
$357$	0.751833	−	0.722261i	0.0397912	−	0.0382261i
$358$	18.3478			0.969711
$359$			5.81988i			0.307162i	0.988136	+	0.153581i	$0.0490805\pi$
$359$			5.81988i			0.307162i	−0.988136	+	0.153581i	$0.950919\pi$
$360$	−0.771508	+	19.2213i	−0.0406620	+	1.01305i
$361$	−7.57601			−0.398737
$362$	8.07154			0.424231
$363$	9.67596	−	9.29537i	0.507856	−	0.487881i
$364$	−0.974273			−0.0510658
$365$	−6.22754			−0.325964
$366$	−5.26748	−	5.48315i	−0.275336	−	0.286609i
$367$		−	18.1437i		−	0.947092i	−0.880769	−	0.473546i	$-0.842974\pi$
$367$		−	18.1437i		−	0.947092i	0.880769	−	0.473546i	$-0.157026\pi$
$368$			14.5042i			0.756082i
$369$	0.739475	−	18.4232i	0.0384955	−	0.959075i
$370$	−22.4610			−1.16769
$371$		−	1.67867i		−	0.0871523i
$372$	−6.60409	−	6.87448i	−0.342406	−	0.356425i
$373$		−	32.9179i		−	1.70442i	−0.523198	−	0.852211i	$-0.675261\pi$
$373$		−	32.9179i		−	1.70442i	0.523198	−	0.852211i	$-0.324739\pi$
$374$		−	4.53974i		−	0.234744i
$375$	−14.7211	+	14.1421i	−0.760197	+	0.730296i
$376$			11.0573i			0.570236i
$377$	−6.92524			−0.356668
$378$	1.31287	−	1.16366i	0.0675265	−	0.0598522i
$379$			27.1075i			1.39242i	0.717838	+	0.696210i	$0.245132\pi$
$379$			27.1075i			1.39242i	−0.717838	+	0.696210i	$0.754868\pi$
$380$	4.14573			0.212671
$381$	−3.61356	+	3.47143i	−0.185128	+	0.177847i
$382$	−26.5311			−1.35745
$383$	16.2915			0.832458			0.416229	−	0.909260i	$-0.363352\pi$
$383$	16.2915			0.832458			0.416229	+	0.909260i	$0.363352\pi$
$384$	4.99717	−	4.80062i	0.255011	−	0.244981i
$385$		−	1.06869i		−	0.0544654i
$386$	28.1022			1.43036
$387$	4.73286	+	0.189969i	0.240585	+	0.00965664i
$388$			5.17472i			0.262706i
$389$			11.6479i			0.590570i	0.955409	+	0.295285i	$0.0954147\pi$
$389$			11.6479i			0.590570i	−0.955409	+	0.295285i	$0.904585\pi$
$390$	17.3269	+	18.0363i	0.877382	+	0.913305i
$391$	12.4014			0.627166
$392$	21.2787			1.07474
$393$	−14.1044	−	14.6819i	−0.711473	−	0.740604i
$394$	23.2744			1.17255
$395$			4.84480i			0.243768i
$396$	−0.127663	+	3.18060i	−0.00641532	+	0.159831i
$397$	−22.5704			−1.13278			−0.566388	−	0.824139i	$-0.691660\pi$
$397$	−22.5704			−1.13278			−0.566388	+	0.824139i	$0.691660\pi$
$398$	−15.2996			−0.766899
$399$	−1.15245	−	1.19963i	−0.0576945	−	0.0600567i
$400$	1.61623			0.0808117
$401$	−22.4255			−1.11987			−0.559937	−	0.828535i	$-0.689175\pi$
$401$	−22.4255			−1.11987			−0.559937	+	0.828535i	$0.689175\pi$
$402$	8.39963	+	14.6016i	0.418936	+	0.728262i
$403$	−54.5317			−2.71642
$404$	5.19562			0.258492
$405$	18.7055	+	1.50403i	0.929483	+	0.0747359i
$406$	−0.401151			−0.0199088
$407$	−16.3530			−0.810587
$408$	−7.81672	−	8.13677i	−0.386985	−	0.402830i
$409$			5.36804i			0.265433i	0.991154	+	0.132716i	$0.0423699\pi$
$409$			5.36804i			0.265433i	−0.991154	+	0.132716i	$0.957630\pi$
$410$	15.2264			0.751979
$411$	−7.14930	+	6.86809i	−0.352649	+	0.338778i
$412$	−8.56097			−0.421769
$413$	2.53642			0.124809
$414$	20.8516	+	0.836944i	1.02480	+	0.0411336i
$415$			21.6988i			1.06515i
$416$			18.6918i			0.916442i
$417$	11.0041	+	11.4547i	0.538874	+	0.560938i
$418$	−7.24365			−0.354299
$419$			25.3733i			1.23957i	0.784772	+	0.619785i	$0.212780\pi$
$419$			25.3733i			1.23957i	−0.784772	+	0.619785i	$0.787220\pi$
$420$	−0.418219	−	0.435343i	−0.0204070	−	0.0212425i
$421$	23.4937			1.14501			0.572505	−	0.819901i	$-0.305972\pi$
$421$	23.4937			1.14501			0.572505	+	0.819901i	$0.305972\pi$
$422$	11.1813			0.544296
$423$	10.7779	+	0.432606i	0.524040	+	0.0210340i
$424$	−18.1675			−0.882294
$425$		−	1.38192i		−	0.0670329i
$426$	−18.4210	−	19.1752i	−0.892500	−	0.929042i
$427$	1.04984			0.0508053
$428$			1.66366i			0.0804162i
$429$	12.6150	+	13.1315i	0.609058	+	0.633995i
$430$			3.91161i			0.188635i
$431$			13.7134i			0.660554i	0.943884	+	0.330277i	$0.107142\pi$
$431$			13.7134i			0.660554i	−0.943884	+	0.330277i	$0.892858\pi$
$432$	−8.53881	−	9.63366i	−0.410824	−	0.463500i
$433$		−	5.71949i		−	0.274861i	−0.990511	−	0.137431i	$-0.956116\pi$
$433$		−	5.71949i		−	0.274861i	0.990511	−	0.137431i	$-0.0438844\pi$
$434$	−3.15880			−0.151627
$435$	−2.97275	−	3.09447i	−0.142532	−	0.148368i
$436$		−	8.78375i		−	0.420665i
$437$		−	19.7878i		−	0.946580i
$438$	4.43254	−	4.25820i	0.211795	−	0.203465i
$439$	20.4267			0.974912			0.487456	−	0.873148i	$-0.337925\pi$
$439$	20.4267			0.974912			0.487456	+	0.873148i	$0.337925\pi$
$440$	−11.5660			−0.551385
$441$	0.832509	−	20.7411i	0.0396433	−	0.987670i
$442$	−14.6697			−0.697764
$443$	32.1851			1.52916			0.764580	−	0.644529i	$-0.222947\pi$
$443$	32.1851			1.52916			0.764580	+	0.644529i	$0.222947\pi$
$444$	−6.66157	+	6.39955i	−0.316144	+	0.303709i
$445$			10.3623i			0.491222i
$446$	5.10720			0.241833
$447$	−15.4626	−	16.0957i	−0.731357	−	0.761301i
$448$			2.49070i			0.117674i
$449$		−	2.60431i		−	0.122905i	−0.998110	−	0.0614525i	$-0.980427\pi$
$449$		−	2.60431i		−	0.122905i	0.998110	−	0.0614525i	$-0.0195733\pi$
$450$	0.0932627	−	2.32354i	0.00439644	−	0.109533i
$451$	11.0857			0.522007
$452$	3.59901			0.169283
$453$	−16.4965	+	15.8476i	−0.775073	+	0.744587i
$454$		−	22.2948i		−	1.04635i
$455$	−3.45335			−0.161895
$456$	−12.9831	+	12.4724i	−0.607990	+	0.584075i
$457$	−2.03308			−0.0951034			−0.0475517	−	0.998869i	$-0.515142\pi$
$457$	−2.03308			−0.0951034			−0.0475517	+	0.998869i	$0.515142\pi$
$458$			22.0077i			1.02835i
$459$	−8.23701	+	7.30089i	−0.384471	+	0.340776i
$460$		−	7.18093i		−	0.334813i
$461$		−	7.30863i		−	0.340397i	−0.985410	−	0.170198i	$-0.945559\pi$
$461$		−	7.30863i		−	0.340397i	0.985410	−	0.170198i	$-0.0544409\pi$
$462$	0.730736	+	0.760655i	0.0339969	+	0.0353889i
$463$			18.7222i			0.870097i	0.900407	+	0.435048i	$0.143269\pi$
$463$			18.7222i			0.870097i	−0.900407	+	0.435048i	$0.856731\pi$
$464$			2.94360i			0.136653i
$465$	−23.4085	−	24.3669i	−1.08554	−	1.12999i
$466$	−6.79853			−0.314936
$467$			12.4044i			0.574005i	0.957930	+	0.287003i	$0.0926589\pi$
$467$			12.4044i			0.574005i	−0.957930	+	0.287003i	$0.907341\pi$
$468$	10.2777	+	0.412530i	0.475089	+	0.0190692i
$469$	−2.25740	−	0.560359i	−0.104237	−	0.0258750i
$470$			8.90773i			0.410883i
$471$	14.7388	−	14.1590i	0.679126	−	0.652414i
$472$		−	27.4506i		−	1.26352i
$473$			2.84789i			0.130946i
$474$	−3.31273	−	3.44836i	−0.152159	−	0.158388i
$475$	−2.20500			−0.101173
$476$	0.354081			0.0162293
$477$	−0.710789	+	17.7085i	−0.0325448	+	0.810818i
$478$	12.1263			0.554644
$479$		−	26.6194i		−	1.21627i	−0.793832	−	0.608137i	$-0.791917\pi$
$479$		−	26.6194i		−	1.21627i	0.793832	−	0.608137i	$-0.208083\pi$
$480$	−8.35222	+	8.02370i	−0.381225	+	0.366230i
$481$			52.8428i			2.40942i
$482$	−29.0374			−1.32262
$483$	−2.07792	+	1.99619i	−0.0945485	+	0.0908296i
$484$	4.55696			0.207135
$485$			18.3420i			0.832867i
$486$	−14.3423	+	11.7197i	−0.650581	+	0.531617i
$487$		−	1.99331i		−	0.0903256i	−0.998980	−	0.0451628i	$-0.985619\pi$
$487$		−	1.99331i		−	0.0903256i	0.998980	−	0.0451628i	$-0.0143807\pi$
$488$		−	11.3620i		−	0.514332i
$489$	5.09531	−	4.89490i	0.230418	−	0.221355i
$490$	17.1421			0.774400
$491$			5.02744i			0.226885i	0.993545	+	0.113443i	$0.0361878\pi$
$491$			5.02744i			0.226885i	−0.993545	+	0.113443i	$0.963812\pi$
$492$	4.51590	−	4.33828i	0.203593	−	0.195585i
$493$	2.51685			0.113353
$494$			23.4070i			1.05313i
$495$	−0.452508	+	11.2737i	−0.0203387	+	0.506717i
$496$			23.1789i			1.04076i
$497$	3.67141			0.164685
$498$	−14.8370	−	15.4445i	−0.664861	−	0.692083i
$499$			16.1557i			0.723227i	0.932328	+	0.361614i	$0.117774\pi$
$499$			16.1557i			0.723227i	−0.932328	+	0.361614i	$0.882226\pi$
$500$	−6.93303			−0.310055
$501$	−6.40954	−	6.67196i	−0.286357	−	0.298081i
$502$	−23.3694			−1.04303
$503$	−30.1953			−1.34634			−0.673170	−	0.739488i	$-0.735068\pi$
$503$	−30.1953			−1.34634			−0.673170	+	0.739488i	$0.735068\pi$
$504$	2.61946	+	0.105140i	0.116680	+	0.00468332i
$505$	18.4161			0.819505
$506$			12.5469i			0.557779i
$507$	26.1952	−	25.1648i	1.16337	−	1.11761i
$508$	−1.70183			−0.0755066
$509$			26.3273i			1.16694i	0.812135	+	0.583469i	$0.198305\pi$
$509$			26.3273i			1.16694i	−0.812135	+	0.583469i	$0.801695\pi$
$510$	−6.29714	−	6.55497i	−0.278842	−	0.290259i
$511$			0.848683i			0.0375435i
$512$	23.1827			1.02454
$513$	11.6494	+	13.1431i	0.514332	+	0.580280i
$514$		−	19.0874i		−	0.841909i
$515$	−30.3447			−1.33715
$516$	1.11449	+	1.16012i	0.0490626	+	0.0510714i
$517$			6.48535i			0.285226i
$518$			3.06097i			0.134491i
$519$	−29.7769	−	30.9961i	−1.30706	−	1.36058i
$520$			37.3741i			1.63896i
$521$	−29.4500			−1.29023			−0.645113	−	0.764087i	$-0.723190\pi$
$521$	−29.4500			−1.29023			−0.645113	+	0.764087i	$0.723190\pi$
$522$	4.23180	+	0.169857i	0.185221	+	0.00743443i
$523$	30.4914			1.33329			0.666647	−	0.745373i	$-0.267729\pi$
$523$	30.4914			1.33329			0.666647	+	0.745373i	$0.267729\pi$
$524$		−	6.91455i		−	0.302063i
$525$	0.222440	+	0.231547i	0.00970807	+	0.0101055i
$526$			29.8139i			1.29995i
$527$	19.8185			0.863309
$528$	5.58160	−	5.36206i	0.242908	−	0.233354i
$529$	−11.2750			−0.490219
$530$	−14.6357			−0.635736
$531$	−26.7570	−	1.07398i	−1.16116	−	0.0466067i
$532$		−	0.564976i		−	0.0244948i
$533$		−	35.8223i		−	1.55164i
$534$	−7.08545	−	7.37555i	−0.306617	−	0.319171i
$535$			5.89692i			0.254946i
$536$	−6.06453	+	24.4308i	−0.261948	+	1.05525i
$537$	19.2881	−	18.5295i	0.832345	−	0.799606i
$538$			38.8093i			1.67319i
$539$	12.4804			0.537571
$540$	4.22752	+	4.76957i	0.181923	+	0.205250i
$541$		−	28.7585i		−	1.23643i	−0.786011	−	0.618213i	$-0.787857\pi$
$541$		−	28.7585i		−	1.23643i	0.786011	−	0.618213i	$-0.212143\pi$
$542$		−	35.4881i		−	1.52434i
$543$	8.48521	−	8.15146i	0.364135	−	0.349813i
$544$		−	6.79319i		−	0.291256i
$545$		−	31.1343i		−	1.33365i
$546$	2.45797	−	2.36129i	0.105191	−	0.101054i
$547$		−	11.4401i		−	0.489142i	−0.969631	−	0.244571i	$-0.921353\pi$
$547$		−	11.4401i		−	0.489142i	0.969631	−	0.244571i	$-0.0786471\pi$
$548$	−3.36701			−0.143832
$549$	−11.0749	−	0.444526i	−0.472665	−	0.0189719i
$550$	1.39813			0.0596167
$551$		−	4.01591i		−	0.171084i
$552$	21.6039	+	22.4884i	0.919522	+	0.957170i
$553$	0.660245			0.0280765
$554$	−5.10053			−0.216701
$555$	−23.6122	+	22.6834i	−1.00228	+	0.962859i
$556$			5.39466i			0.228785i
$557$		−	23.2899i		−	0.986823i	−0.869796	−	0.493411i	$-0.835750\pi$
$557$		−	23.2899i		−	0.986823i	0.869796	−	0.493411i	$-0.164250\pi$
$558$	33.3226	+	1.33751i	1.41066	+	0.0566213i
$559$	9.20263			0.389230
$560$			1.46786i			0.0620284i
$561$	−4.58469	−	4.77240i	−0.193566	−	0.201491i
$562$	−32.6820			−1.37861
$563$	32.6882			1.37764			0.688822	−	0.724930i	$-0.258128\pi$
$563$	32.6882			1.37764			0.688822	+	0.724930i	$0.258128\pi$
$564$	2.53797	+	2.64188i	0.106868	+	0.111243i
$565$	12.7568			0.536684
$566$	−1.99322			−0.0837814
$567$	0.204968	−	2.54916i	0.00860784	−	0.107055i
$568$		−	39.7341i		−	1.66720i
$569$		−	27.4431i		−	1.15047i	−0.817987	−	0.575237i	$-0.804910\pi$
$569$		−	27.4431i		−	1.15047i	0.817987	−	0.575237i	$-0.195090\pi$
$570$	−10.4592	+	10.0478i	−0.438086	+	0.420855i
$571$	−6.20555			−0.259694			−0.129847	−	0.991534i	$-0.541449\pi$
$571$	−6.20555			−0.259694			−0.129847	+	0.991534i	$0.541449\pi$
$572$			6.18438i			0.258582i
$573$	−27.8908	+	26.7938i	−1.16516	+	1.11933i
$574$		−	2.07504i		−	0.0866106i
$575$			3.81935i			0.159278i
$576$	1.05462	−	26.2747i	0.0439424	−	1.09478i
$577$			21.8157i			0.908198i	0.890951	+	0.454099i	$0.150039\pi$
$577$			21.8157i			0.908198i	−0.890951	+	0.454099i	$0.849961\pi$
$578$	−14.8675			−0.618404
$579$	29.5424	−	28.3804i	1.22774	−	1.17945i
$580$		−	1.45736i		−	0.0605136i
$581$	2.95709			0.122681
$582$	−12.5417	−	13.0552i	−0.519870	−	0.541155i
$583$	−10.6557			−0.441314
$584$	9.18493			0.380075
$585$	36.4298	+	1.46223i	1.50619	+	0.0604557i
$586$			21.9473i			0.906635i
$587$	22.8171			0.941761			0.470881	−	0.882197i	$-0.343936\pi$
$587$	22.8171			0.941761			0.470881	+	0.882197i	$0.343936\pi$
$588$	5.08405	−	4.88408i	0.209663	−	0.201416i
$589$		−	31.6227i		−	1.30299i
$590$		−	22.1141i		−	0.910425i
$591$	24.4672	−	23.5048i	1.00645	−	0.966860i
$592$	22.4610			0.923143
$593$	23.2240			0.953695			0.476847	−	0.878986i	$-0.341779\pi$
$593$	23.2240			0.953695			0.476847	+	0.878986i	$0.341779\pi$
$594$	−7.38656	−	8.33367i	−0.303074	−	0.341934i
$595$	1.25506			0.0514522
$596$		−	7.58040i		−	0.310505i
$597$	−16.0837	+	15.4511i	−0.658262	+	0.632370i
$598$	40.5440			1.65797
$599$	18.3890			0.751355			0.375678	−	0.926750i	$-0.377410\pi$
$599$	18.3890			0.751355			0.375678	+	0.926750i	$0.377410\pi$
$600$	2.50594	−	2.40737i	0.102304	−	0.0982805i
$601$	16.5923			0.676814			0.338407	−	0.941000i	$-0.390112\pi$
$601$	16.5923			0.676814			0.338407	+	0.941000i	$0.390112\pi$
$602$	0.533071			0.0217264
$603$	23.5763	+	6.86714i	0.960102	+	0.279652i
$604$	−7.76915			−0.316122
$605$	16.1523			0.656686
$606$	−13.1079	+	12.5924i	−0.532473	+	0.511529i
$607$	21.3350			0.865961			0.432981	−	0.901403i	$-0.357462\pi$
$607$	21.3350			0.865961			0.432981	+	0.901403i	$0.357462\pi$
$608$	−10.8393			−0.439591
$609$	−0.421711	+	0.405124i	−0.0170886	+	0.0164164i
$610$		−	9.15318i		−	0.370601i
$611$	20.9567			0.847817
$612$	−3.73525	−	0.149926i	−0.150989	−	0.00606041i
$613$	23.0971			0.932884			0.466442	−	0.884552i	$-0.345536\pi$
$613$	23.0971			0.932884			0.466442	+	0.884552i	$0.345536\pi$
$614$	−8.62720			−0.348165
$615$	16.0068	−	15.3772i	0.645456	−	0.620068i
$616$			1.57620i			0.0635068i
$617$			15.1138i			0.608460i	0.952599	+	0.304230i	$0.0983991\pi$
$617$			15.1138i			0.608460i	−0.952599	+	0.304230i	$0.901601\pi$
$618$	21.5983	−	20.7488i	0.868810	−	0.834637i
$619$	−29.4064			−1.18194			−0.590972	−	0.806692i	$-0.701256\pi$
$619$	−29.4064			−1.18194			−0.590972	+	0.806692i	$0.701256\pi$
$620$		−	11.4758i		−	0.460878i
$621$	22.7655	−	20.1782i	0.913547	−	0.809723i
$622$	25.0395			1.00399
$623$	1.41217			0.0565774
$624$	−17.3269	−	18.0363i	−0.693631	−	0.722031i
$625$	−21.3125			−0.852500
$626$			17.9339i			0.716781i
$627$	−7.61490	+	7.31538i	−0.304110	+	0.292148i
$628$	6.94133			0.276989
$629$		−	19.2047i		−	0.765743i
$630$	2.11023	+	0.0847009i	0.0840737	+	0.00337456i
$631$			38.5932i			1.53637i	0.640227	+	0.768186i	$0.278840\pi$
$631$			38.5932i			1.53637i	−0.640227	+	0.768186i	$0.721160\pi$
$632$		−	7.14554i		−	0.284234i
$633$	11.7543	−	11.2920i	0.467193	−	0.448817i
$634$		−	10.0914i		−	0.400780i
$635$	−6.03221			−0.239381
$636$	−4.34072	+	4.16998i	−0.172121	+	0.165351i
$637$		−	40.3292i		−	1.59790i
$638$			2.54638i			0.100812i
$639$	−38.7302	−	1.55456i	−1.53214	−	0.0614974i
$640$	8.34192			0.329743
$641$	−44.8759			−1.77249			−0.886245	−	0.463216i	$-0.846695\pi$
$641$	−44.8759			−1.77249			−0.886245	+	0.463216i	$0.846695\pi$
$642$	−4.03213	−	4.19722i	−0.159135	−	0.165651i
$643$	−0.785522			−0.0309780			−0.0154890	−	0.999880i	$-0.504930\pi$
$643$	−0.785522			−0.0309780			−0.0154890	+	0.999880i	$0.504930\pi$
$644$	−0.978611			−0.0385627
$645$	3.95035	+	4.11209i	0.155545	+	0.161913i
$646$		−	8.50686i		−	0.334698i
$647$	7.38168			0.290204			0.145102	−	0.989417i	$-0.453649\pi$
$647$	7.38168			0.290204			0.145102	+	0.989417i	$0.453649\pi$
$648$	−27.5885	−	2.21828i	−1.08378	−	0.0871422i
$649$		−	16.1004i		−	0.631996i
$650$		−	4.51792i		−	0.177207i
$651$	−3.32069	+	3.19008i	−0.130148	+	0.125029i
$652$	2.39968			0.0939786
$653$	−32.4608			−1.27029			−0.635144	−	0.772394i	$-0.719059\pi$
$653$	−32.4608			−1.27029			−0.635144	+	0.772394i	$0.719059\pi$
$654$	21.2887	+	22.1603i	0.832454	+	0.866538i
$655$		−	24.5089i		−	0.957641i
$656$	−15.2264			−0.594492
$657$	0.359352	−	8.95287i	0.0140197	−	0.349285i
$658$	1.21394			0.0473242
$659$		−	25.2488i		−	0.983554i	−0.870721	−	0.491777i	$-0.836348\pi$
$659$		−	25.2488i		−	0.983554i	0.870721	−	0.491777i	$-0.163652\pi$
$660$	−2.76342	+	2.65473i	−0.107566	+	0.103335i
$661$			34.1358i			1.32773i	0.747854	+	0.663863i	$0.231084\pi$
$661$			34.1358i			1.32773i	−0.747854	+	0.663863i	$0.768916\pi$
$662$			17.0865i			0.664086i
$663$	−15.4215	+	14.8149i	−0.598921	+	0.575364i
$664$		−	32.0034i		−	1.24197i
$665$		−	2.00258i		−	0.0776567i
$666$	1.29608	−	32.2906i	0.0502223	−	1.25123i
$667$	−6.95608			−0.269340
$668$		−	3.14221i		−	0.121576i
$669$	5.36895	−	5.15777i	0.207575	−	0.199411i
$670$	−4.88557	+	19.6814i	−0.188746	+	0.760360i
$671$		−	6.66405i		−	0.257263i
$672$	1.09346	+	1.13823i	0.0421812	+	0.0439083i
$673$			36.3860i			1.40258i	0.712878	+	0.701288i	$0.247391\pi$
$673$			36.3860i			1.40258i	−0.712878	+	0.701288i	$0.752609\pi$
$674$			14.2961i			0.550666i
$675$	−2.24851	−	2.53681i	−0.0865450	−	0.0976418i
$676$	12.3368			0.474493
$677$	28.0827			1.07931			0.539654	−	0.841887i	$-0.318555\pi$
$677$	28.0827			1.07931			0.539654	+	0.841887i	$0.318555\pi$
$678$	−9.07986	+	8.72273i	−0.348710	+	0.334994i
$679$	2.49963			0.0959269
$680$		−	13.5829i		−	0.520881i
$681$	−22.5156	−	23.4375i	−0.862800	−	0.898126i
$682$			20.0511i			0.767796i
$683$	33.9446			1.29885			0.649427	−	0.760424i	$-0.275009\pi$
$683$	33.9446			1.29885			0.649427	+	0.760424i	$0.275009\pi$
$684$	−0.239224	+	5.96001i	−0.00914695	+	0.227887i
$685$	−11.9345			−0.455994
$686$		−	4.69947i		−	0.179427i
$687$	22.2256	+	23.1356i	0.847960	+	0.882679i
$688$		−	3.91161i		−	0.149129i
$689$			34.4327i			1.31178i
$690$	17.4040	+	18.1166i	0.662561	+	0.689688i
$691$	−46.2852			−1.76077			−0.880387	−	0.474257i	$-0.842717\pi$
$691$	−46.2852			−1.76077			−0.880387	+	0.474257i	$0.842717\pi$
$692$		−	14.5978i		−	0.554927i
$693$	1.53637	+	0.0616673i	0.0583620	+	0.00234255i
$694$	−12.7852			−0.485319
$695$			19.1216i			0.725323i
$696$	4.38448	+	4.56399i	0.166193	+	0.172998i
$697$			13.0190i			0.493128i
$698$	−22.5347			−0.852952
$699$	−7.14696	+	6.86585i	−0.270323	+	0.259690i
$700$			0.109049i			0.00412166i
$701$	−12.1107			−0.457415			−0.228707	−	0.973495i	$-0.573450\pi$
$701$	−12.1107			−0.457415			−0.228707	+	0.973495i	$0.573450\pi$
$702$	−26.9293	+	23.8688i	−1.01638	+	0.900871i
$703$	−30.6433			−1.15573
$704$	15.8102			0.595868
$705$	8.99593	+	9.36426i	0.338806	+	0.352678i
$706$	4.64013			0.174634
$707$		−	2.50973i		−	0.0943880i
$708$	−6.30071	−	6.55869i	−0.236795	−	0.246491i
$709$	24.5566			0.922242			0.461121	−	0.887337i	$-0.347447\pi$
$709$	24.5566			0.922242			0.461121	+	0.887337i	$0.347447\pi$
$710$		−	32.0097i		−	1.20130i
$711$	−6.96501	−	0.279563i	−0.261208	−	0.0104844i
$712$		−	15.2833i		−	0.572766i
$713$	−54.7745			−2.05132
$714$	−0.893304	+	0.858168i	−0.0334311	+	0.0321161i
$715$			21.9208i			0.819791i
$716$	9.08389			0.339481
$717$	12.7478	−	12.2464i	0.476075	−	0.457349i
$718$		−	6.91500i		−	0.258066i
$719$		−	0.813125i		−	0.0303244i	−0.999885	−	0.0151622i	$-0.995174\pi$
$719$		−	0.813125i		−	0.0303244i	0.999885	−	0.0151622i	$-0.00482647\pi$
$720$	0.621526	−	15.4846i	0.0231629	−	0.577079i
$721$			4.13534i			0.154008i
$722$	9.00158			0.335004
$723$	−30.5256	+	29.3249i	−1.13526	+	1.09060i
$724$	3.99617			0.148517
$725$			0.775132i			0.0287877i
$726$	−11.4967	+	11.0445i	−0.426681	+	0.409899i
$727$			3.76568i			0.139661i	0.997559	+	0.0698306i	$0.0222459\pi$
$727$			3.76568i			0.139661i	−0.997559	+	0.0698306i	$0.977754\pi$
$728$	5.09330			0.188770
$729$	−3.24161	+	26.8047i	−0.120060	+	0.992767i
$730$	7.39936			0.273863
$731$	−3.34452			−0.123702
$732$	−2.60790	−	2.71468i	−0.0963909	−	0.100337i
$733$			13.3040i			0.491396i	0.969346	+	0.245698i	$0.0790172\pi$
$733$			13.3040i			0.491396i	−0.969346	+	0.245698i	$0.920983\pi$
$734$			21.5577i			0.795710i
$735$	18.0206	−	17.3118i	0.664700	−	0.638556i
$736$			18.7750i			0.692057i
$737$	−3.55699	+	14.3293i	−0.131023	+	0.527825i
$738$	−0.878621	+	21.8899i	−0.0323425	+	0.805778i
$739$			31.3888i			1.15466i	0.816512	+	0.577328i	$0.195905\pi$
$739$			31.3888i			1.15466i	−0.816512	+	0.577328i	$0.804095\pi$
$740$	−11.1203			−0.408792
$741$	23.6388	+	24.6067i	0.868394	+	0.903949i
$742$			1.99455i			0.0732221i
$743$			44.9992i			1.65086i	0.564504	+	0.825430i	$0.309068\pi$
$743$			44.9992i			1.65086i	−0.564504	+	0.825430i	$0.690932\pi$
$744$	34.5249	+	35.9384i	1.26574	+	1.31757i
$745$		−	26.8690i		−	0.984404i
$746$			39.1120i			1.43199i
$747$	−31.1948	−	1.25210i	−1.14136	−	0.0458120i
$748$		−	2.24760i		−	0.0821804i
$749$	0.803626			0.0293639
$750$	17.4912	−	16.8032i	0.638688	−	0.613567i
$751$	13.1434			0.479611			0.239805	−	0.970821i	$-0.422916\pi$
$751$	13.1434			0.479611			0.239805	+	0.970821i	$0.422916\pi$
$752$		−	8.90773i		−	0.324831i
$753$	−24.5671	+	23.6008i	−0.895275	+	0.860061i
$754$	8.22836			0.299659
$755$	−27.5380			−1.00221
$756$	0.649993	−	0.576122i	0.0236400	−	0.0209534i
$757$		−	10.0377i		−	0.364825i	−0.983222	−	0.182412i	$-0.941609\pi$
$757$		−	10.0377i		−	0.364825i	0.983222	−	0.182412i	$-0.0583906\pi$
$758$		−	32.2083i		−	1.16986i
$759$	12.6712	+	13.1900i	0.459935	+	0.478766i
$760$	−21.6730			−0.786164
$761$		−	27.5790i		−	0.999739i	−0.866101	−	0.499869i	$-0.833381\pi$
$761$		−	27.5790i		−	0.999739i	0.866101	−	0.499869i	$-0.166619\pi$
$762$	4.29352	−	4.12464i	0.155538	−	0.149420i
$763$	−4.24296			−0.153605
$764$	−13.1354			−0.475222
$765$	−13.2397	−	0.531419i	−0.478684	−	0.0192135i
$766$	−19.3571			−0.699399
$767$	−52.0267			−1.87857
$768$	15.9593	−	15.3316i	0.575881	−	0.553230i
$769$			46.2944i			1.66942i	0.550690	+	0.834710i	$0.314365\pi$
$769$			46.2944i			1.66942i	−0.550690	+	0.834710i	$0.685635\pi$
$770$			1.26978i			0.0457598i
$771$	−19.2764	−	20.0657i	−0.694223	−	0.722647i
$772$	13.9132			0.500748
$773$			5.77454i			0.207696i	0.994593	+	0.103848i	$0.0331155\pi$
$773$			5.77454i			0.207696i	−0.994593	+	0.103848i	$0.966885\pi$
$774$	−5.62344	−	0.225715i	−0.202130	−	0.00811314i
$775$			6.10366i			0.219250i
$776$		−	27.0524i		−	0.971124i
$777$	3.09128	+	3.21785i	0.110899	+	0.115440i
$778$		−	13.8396i		−	0.496175i
$779$	20.7732			0.744276
$780$	8.57845	+	8.92968i	0.307158	+	0.319734i
$781$		−	23.3050i		−	0.833917i
$782$	−14.7350			−0.526921
$783$	4.62022	−	4.09514i	0.165113	−	0.146348i
$784$	−17.1421			−0.612217
$785$	24.6038			0.878148
$786$	16.7584	+	17.4446i	0.597753	+	0.622227i
$787$		−	36.7066i		−	1.30845i	−0.756301	−	0.654224i	$-0.772995\pi$
$787$		−	36.7066i		−	1.30845i	0.756301	−	0.654224i	$-0.227005\pi$
$788$	11.5230			0.410490
$789$	30.1092	+	31.3419i	1.07191	+	1.11580i
$790$		−	5.75644i		−	0.204805i
$791$		−	1.73849i		−	0.0618135i
$792$	0.667398	−	16.6275i	0.0237150	−	0.590833i
$793$	−21.5341			−0.764700
$794$	26.8175			0.951716
$795$	−15.3858	+	14.7807i	−0.545680	+	0.524216i
$796$	−7.57474			−0.268479
$797$		−	28.5045i		−	1.00968i	−0.863213	−	0.504840i	$-0.831551\pi$
$797$		−	28.5045i		−	1.00968i	0.863213	−	0.504840i	$-0.168449\pi$
$798$	1.36930	+	1.42537i	0.0484727	+	0.0504574i
$799$	−7.61632			−0.269446
$800$	2.09215			0.0739686
$801$	−14.8972	−	0.597945i	−0.526366	−	0.0211274i
$802$	26.6452			0.940876
$803$	5.38718			0.190109
$804$	4.15861	+	7.22917i	0.146663	+	0.254953i
$805$	−3.46872			−0.122256
$806$	64.7929			2.28223
$807$	39.1936	+	40.7983i	1.37968	+	1.43617i
$808$	−27.1617			−0.955545
$809$	−10.3307			−0.363209			−0.181605	−	0.983372i	$-0.558129\pi$
$809$	−10.3307			−0.363209			−0.181605	+	0.983372i	$0.558129\pi$
$810$	−22.2253	−	1.78704i	−0.780916	−	0.0627903i
$811$		−	5.53520i		−	0.194367i	−0.995266	−	0.0971836i	$-0.969017\pi$
$811$		−	5.53520i		−	0.194367i	0.995266	−	0.0971836i	$-0.0309834\pi$
$812$	−0.198608			−0.00696977
$813$	−35.8395	−	37.3069i	−1.25695	−	1.30841i
$814$	19.4301			0.681024
$815$	8.50575			0.297943
$816$	6.29714	+	6.55497i	0.220444	+	0.229470i
$817$			5.33656i			0.186702i
$818$		−	6.37814i		−	0.223006i
$819$	0.199271	−	4.96462i	0.00696309	−	0.173478i
$820$	7.53852			0.263256
$821$			49.4968i			1.72745i	0.503964	+	0.863725i	$0.331875\pi$
$821$			49.4968i			1.72745i	−0.503964	+	0.863725i	$0.668125\pi$
$822$	8.49457	−	8.16045i	0.296282	−	0.284628i
$823$	−20.7084			−0.721851			−0.360925	−	0.932595i	$-0.617539\pi$
$823$	−20.7084			−0.721851			−0.360925	+	0.932595i	$0.617539\pi$
$824$	44.7550			1.55912
$825$	1.46979	−	1.41198i	0.0511715	−	0.0491588i
$826$	−3.01369			−0.104860
$827$			21.2556i			0.739131i	0.929205	+	0.369565i	$0.120493\pi$
$827$			21.2556i			0.739131i	−0.929205	+	0.369565i	$0.879507\pi$
$828$	10.3235	+	0.414366i	0.358766	+	0.0144002i
$829$	−20.3605			−0.707150			−0.353575	−	0.935406i	$-0.615034\pi$
$829$	−20.3605			−0.707150			−0.353575	+	0.935406i	$0.615034\pi$
$830$		−	25.7819i		−	0.894901i
$831$	−5.36193	+	5.15103i	−0.186003	+	0.178687i
$832$		−	51.0888i		−	1.77118i
$833$			14.6569i			0.507831i
$834$	−13.0748	−	13.6101i	−0.452742	−	0.471279i
$835$		−	11.1377i		−	0.385436i
$836$	−3.58629			−0.124035
$837$	36.3812	−	32.2465i	1.25752	−	1.11460i
$838$		−	30.1478i		−	1.04144i
$839$			14.1993i			0.490215i	0.969496	+	0.245107i	$0.0788232\pi$
$839$			14.1993i			0.490215i	−0.969496	+	0.245107i	$0.921177\pi$
$840$	2.18637	+	2.27588i	0.0754368	+	0.0785255i
$841$	27.5883			0.951320
$842$	−27.9144			−0.961995
$843$	−34.3570	+	33.0057i	−1.18332	+	1.13678i
$844$	5.53579			0.190550
$845$	43.7283			1.50430
$846$	−12.8060	−	0.514009i	−0.440279	−	0.0176720i
$847$		−	2.20122i		−	0.0756350i
$848$	14.6357			0.502594
$849$	−2.09538	+	2.01296i	−0.0719132	+	0.0690846i
$850$			1.64195i			0.0563185i
$851$			53.0780i			1.81949i
$852$	−9.12014	−	9.49355i	−0.312451	−	0.325244i
$853$	−42.0998			−1.44147			−0.720735	−	0.693210i	$-0.756196\pi$
$853$	−42.0998			−1.44147			−0.720735	+	0.693210i	$0.756196\pi$
$854$	−1.24739			−0.0426847
$855$	−0.847938	+	21.1255i	−0.0289989	+	0.722476i
$856$		−	8.69730i		−	0.297268i
$857$	4.49937			0.153695			0.0768477	−	0.997043i	$-0.475514\pi$
$857$	4.49937			0.153695			0.0768477	+	0.997043i	$0.475514\pi$
$858$	−14.9888	−	15.6024i	−0.511708	−	0.532659i
$859$	−54.3034			−1.85281			−0.926404	−	0.376530i	$-0.877117\pi$
$859$	−54.3034			−1.85281			−0.926404	+	0.376530i	$0.877117\pi$
$860$			1.93662i			0.0660382i
$861$	−2.09559	−	2.18139i	−0.0714175	−	0.0743416i
$862$		−	16.2939i		−	0.554972i
$863$			19.2335i			0.654716i	0.944900	+	0.327358i	$0.106158\pi$
$863$			19.2335i			0.654716i	−0.944900	+	0.327358i	$0.893842\pi$
$864$	−11.0531	−	12.4704i	−0.376035	−	0.424250i
$865$		−	51.7426i		−	1.75930i
$866$			6.79572i			0.230928i
$867$	−15.6294	+	15.0147i	−0.530803	+	0.509925i
$868$	−1.56391			−0.0530824
$869$		−	4.19103i		−	0.142171i
$870$	3.53213	+	3.67675i	0.119750	+	0.124653i
$871$	46.3034	+	11.4940i	1.56893	+	0.389459i
$872$			45.9197i			1.55504i
$873$	−26.3689	−	1.05840i	−0.892453	−	0.0358214i
$874$			23.5113i			0.795280i
$875$			3.34898i			0.113216i
$876$	2.19453	−	2.10821i	0.0741462	−	0.0712298i
$877$	24.1312			0.814854			0.407427	−	0.913238i	$-0.366426\pi$
$877$	24.1312			0.814854			0.407427	+	0.913238i	$0.366426\pi$
$878$	−24.2703			−0.819084
$879$	22.1646	+	23.0721i	0.747595	+	0.778204i
$880$	9.31752			0.314093
$881$			5.93369i			0.199911i	0.994992	+	0.0999555i	$0.0318700\pi$
$881$			5.93369i			0.199911i	−0.994992	+	0.0999555i	$0.968130\pi$
$882$	−0.989161	+	24.6439i	−0.0333068	+	0.829803i
$883$			10.8852i			0.366315i	0.983084	+	0.183158i	$0.0586319\pi$
$883$			10.8852i			0.366315i	−0.983084	+	0.183158i	$0.941368\pi$
$884$	−7.26287			−0.244277
$885$	−22.3331	−	23.2475i	−0.750720	−	0.781457i
$886$	−38.2413			−1.28474
$887$		−	26.3504i		−	0.884761i	−0.896827	−	0.442381i	$-0.854134\pi$
$887$		−	26.3504i		−	0.884761i	0.896827	−	0.442381i	$-0.145866\pi$
$888$	34.8254	−	33.4556i	1.16866	−	1.12270i
$889$			0.822064i			0.0275711i
$890$		−	12.3122i		−	0.412706i
$891$	−16.1813	−	1.30107i	−0.542094	−	0.0435876i
$892$	2.52855			0.0846620
$893$			12.1527i			0.406674i
$894$	18.3722	+	19.1244i	0.614458	+	0.639616i
$895$	32.1982			1.07627
$896$		−	1.13683i		−	0.0379788i
$897$	42.6219	−	40.9455i	1.42310	−	1.36713i
$898$			3.09436i			0.103260i
$899$	−11.1164			−0.370753
$900$	0.0461738	−	1.15037i	0.00153913	−	0.0383457i
$901$		−	12.5139i		−	0.416899i
$902$	−13.1717			−0.438571
$903$	0.560391	−	0.538350i	0.0186487	−	0.0179151i
$904$	−18.8149			−0.625775
$905$	14.1646			0.470847
$906$	19.6006	−	18.8297i	0.651187	−	0.625574i
$907$	37.8798			1.25778			0.628889	−	0.777495i	$-0.283510\pi$
$907$	37.8798			1.25778			0.628889	+	0.777495i	$0.283510\pi$
$908$		−	11.0381i		−	0.366311i
$909$	−1.06268	+	26.4754i	−0.0352467	+	0.878135i
$910$	4.10316			0.136018
$911$		−	8.16988i		−	0.270680i	−0.990799	−	0.135340i	$-0.956787\pi$
$911$		−	8.16988i		−	0.270680i	0.990799	−	0.135340i	$-0.0432127\pi$
$912$	10.4592	−	10.0478i	0.346338	−	0.332715i
$913$		−	18.7707i		−	0.621220i
$914$	2.41564			0.0799023
$915$	−9.24381	−	9.62228i	−0.305591	−	0.318103i
$916$			10.8959i			0.360010i
$917$	−3.34005			−0.110298
$918$	9.78696	−	8.67469i	0.323018	−	0.286307i
$919$			16.7633i			0.552969i	0.961018	+	0.276485i	$0.0891695\pi$
$919$			16.7633i			0.552969i	−0.961018	+	0.276485i	$0.910831\pi$
$920$			37.5405i			1.23767i
$921$	−9.06935	+	8.71262i	−0.298845	+	0.287091i
$922$			8.68389i			0.285989i
$923$	−75.3074			−2.47877
$924$	0.361784	+	0.376596i	0.0119018	+	0.0123891i
$925$	5.91461			0.194471
$926$		−	22.2452i		−	0.731022i
$927$	1.75100	−	43.6243i	0.0575104	−	1.43281i
$928$			3.81037i			0.125082i
$929$	28.7510			0.943289			0.471644	−	0.881789i	$-0.343661\pi$
$929$	28.7510			0.943289			0.471644	+	0.881789i	$0.343661\pi$
$930$	27.8132	+	28.9520i	0.912030	+	0.949372i
$931$	23.3867			0.766467
$932$	−3.36591			−0.110254
$933$	26.3228	−	25.2874i	0.861768	−	0.827873i
$934$		−	14.7385i		−	0.482258i
$935$		−	7.96670i		−	0.260539i
$936$	−53.7300	−	2.15662i	−1.75622	−	0.0704914i
$937$		−	32.1691i		−	1.05092i	−0.850818	−	0.525460i	$-0.823893\pi$
$937$		−	32.1691i		−	1.05092i	0.850818	−	0.525460i	$-0.176107\pi$
$938$	2.68217	+	0.665801i	0.0875759	+	0.0217392i
$939$	18.1114	+	18.8530i	0.591044	+	0.615244i
$940$			4.41017i			0.143844i
$941$	−14.8956			−0.485581			−0.242791	−	0.970079i	$-0.578063\pi$
$941$	−14.8956			−0.485581			−0.242791	+	0.970079i	$0.578063\pi$
$942$	−17.5121	+	16.8233i	−0.570576	+	0.548134i
$943$		−	35.9818i		−	1.17173i
$944$			22.1141i			0.719754i
$945$	2.30392	−	2.04209i	0.0749466	−	0.0664291i
$946$		−	3.38377i		−	0.110016i
$947$			49.1528i			1.59725i	0.601828	+	0.798626i	$0.294439\pi$
$947$			49.1528i			1.59725i	−0.601828	+	0.798626i	$0.705561\pi$
$948$	−1.64011	−	1.70726i	−0.0532684	−	0.0554494i
$949$		−	17.4081i		−	0.565089i
$950$	2.61992			0.0850013
$951$	−10.1913	−	10.6086i	−0.330476	−	0.344007i
$952$	−1.85107			−0.0599934
$953$			26.4663i			0.857329i	0.903464	+	0.428664i	$0.141016\pi$
$953$			26.4663i			0.857329i	−0.903464	+	0.428664i	$0.858984\pi$
$954$	0.844537	−	21.0407i	0.0273429	−	0.681219i
$955$	−46.5589			−1.50661
$956$	6.00366			0.194172
$957$	2.57160	+	2.67689i	0.0831280	+	0.0865315i
$958$			31.6284i			1.02187i
$959$			1.62642i			0.0525200i
$960$	22.8284	−	21.9305i	0.736784	−	0.707805i
$961$	−56.5345			−1.82369
$962$		−	62.7861i		−	2.02431i
$963$	−8.47756	−	0.340274i	−0.273186	−	0.0109652i
$964$	−14.3762			−0.463028
$965$	49.3160			1.58754
$966$	2.46892	−	2.37181i	0.0794361	−	0.0763116i
$967$	−10.0427			−0.322951			−0.161476	−	0.986877i	$-0.551625\pi$
$967$	−10.0427			−0.322951			−0.161476	+	0.986877i	$0.551625\pi$
$968$	−23.8229			−0.765697
$969$	−8.59109	−	8.94284i	−0.275986	−	0.287285i
$970$		−	21.7934i		−	0.699743i
$971$		−	46.2031i		−	1.48273i	−0.671103	−	0.741365i	$-0.734179\pi$
$971$		−	46.2031i		−	1.48273i	0.671103	−	0.741365i	$-0.265821\pi$
$972$	−7.10080	+	5.80237i	−0.227758	+	0.186111i
$973$	2.60587			0.0835404
$974$			2.36839i			0.0758881i
$975$	−4.56265	−	4.74946i	−0.146122	−	0.152105i
$976$			9.15318i			0.292986i
$977$		−	53.6359i		−	1.71597i	−0.513679	−	0.857983i	$-0.671718\pi$
$977$		−	53.6359i		−	1.71597i	0.513679	−	0.857983i	$-0.328282\pi$
$978$	−6.05409	+	5.81597i	−0.193589	+	0.185974i
$979$		−	8.96402i		−	0.286491i
$980$	8.48694			0.271105
$981$	44.7595	+	1.79657i	1.42906	+	0.0573599i
$982$		−	5.97345i		−	0.190620i
$983$	10.0426			0.320308			0.160154	−	0.987092i	$-0.448801\pi$
$983$	10.0426			0.320308			0.160154	+	0.987092i	$0.448801\pi$
$984$	−23.6082	+	22.6797i	−0.752603	+	0.723001i
$985$	40.8438			1.30139
$986$	−2.99044			−0.0952351
$987$	1.27615	−	1.22596i	0.0406204	−	0.0390226i
$988$			11.5887i			0.368686i
$989$	9.24360			0.293929
$990$	0.537655	−	13.3951i	0.0170878	−	0.425724i
$991$		−	21.7474i		−	0.690830i	−0.938450	−	0.345415i	$-0.887738\pi$
$991$		−	21.7474i		−	0.690830i	0.938450	−	0.345415i	$-0.112262\pi$
$992$			30.0042i			0.952633i
$993$	17.2557	+	17.9622i	0.547593	+	0.570013i
$994$	−4.36225			−0.138362
$995$	−26.8489			−0.851169
$996$	−7.34571	−	7.64647i	−0.232758	−	0.242288i
$997$	30.6083			0.969374			0.484687	−	0.874688i	$-0.338933\pi$
$997$	30.6083			0.969374			0.484687	+	0.874688i	$0.338933\pi$
$998$		−	19.1957i		−	0.607628i
$999$	−31.2478	−	35.2544i	−0.988637	−	1.11540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.d.a.200.6	yes	20
3.2	odd	2	inner	201.2.d.a.200.16	yes	20
67.66	odd	2	inner	201.2.d.a.200.15	yes	20
201.200	even	2	inner	201.2.d.a.200.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.d.a.200.5	✓	20	201.200	even	2	inner
201.2.d.a.200.6	yes	20	1.1	even	1	trivial
201.2.d.a.200.15	yes	20	67.66	odd	2	inner
201.2.d.a.200.16	yes	20	3.2	odd	2	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.18817 q^{2} +(-1.24906 + 1.19993i) q^{3} -0.588256 q^{4} -2.08509 q^{5} +(1.48410 - 1.42572i) q^{6} +0.284155i q^{7} +3.07528 q^{8} +(0.120318 - 2.99759i) q^{9} +O(q^{10})\)	\(q-1.18817 q^{2} +(-1.24906 + 1.19993i) q^{3} -0.588256 q^{4} -2.08509 q^{5} +(1.48410 - 1.42572i) q^{6} +0.284155i q^{7} +3.07528 q^{8} +(0.120318 - 2.99759i) q^{9} +2.47744 q^{10} +1.80373 q^{11} +(0.734769 - 0.705868i) q^{12} -5.82854i q^{13} -0.337624i q^{14} +(2.60442 - 2.50198i) q^{15} -2.47744 q^{16} +2.11827i q^{17} +(-0.142958 + 3.56164i) q^{18} +3.37994 q^{19} +1.22657 q^{20} +(-0.340967 - 0.354927i) q^{21} -2.14313 q^{22} -5.85449i q^{23} +(-3.84122 + 3.69014i) q^{24} -0.652380 q^{25} +6.92529i q^{26} +(3.44662 + 3.88855i) q^{27} -0.167156i q^{28} -1.18816i q^{29} +(-3.09448 + 2.97277i) q^{30} -9.35599i q^{31} -3.20695 q^{32} +(-2.25297 + 2.16435i) q^{33} -2.51687i q^{34} -0.592489i q^{35} +(-0.0707775 + 1.76335i) q^{36} -9.06621 q^{37} -4.01594 q^{38} +(6.99386 + 7.28021i) q^{39} -6.41226 q^{40} +6.14602 q^{41} +(0.405126 + 0.421713i) q^{42} +1.57889i q^{43} -1.06105 q^{44} +(-0.250874 + 6.25025i) q^{45} +6.95612i q^{46} +3.59553i q^{47} +(3.09448 - 2.97277i) q^{48} +6.91926 q^{49} +0.775137 q^{50} +(-2.54179 - 2.64586i) q^{51} +3.42867i q^{52} -5.90760 q^{53} +(-4.09517 - 4.62025i) q^{54} -3.76094 q^{55} +0.873856i q^{56} +(-4.22176 + 4.05570i) q^{57} +1.41174i q^{58} -8.92620i q^{59} +(-1.53206 + 1.47180i) q^{60} -3.69460i q^{61} +11.1165i q^{62} +(0.851778 + 0.0341888i) q^{63} +8.76528 q^{64} +12.1531i q^{65} +(2.67691 - 2.57162i) q^{66} +(-1.97202 + 7.94425i) q^{67} -1.24609i q^{68} +(7.02500 + 7.31263i) q^{69} +0.703977i q^{70} -12.9205i q^{71} +(0.370011 - 9.21843i) q^{72} +2.98669 q^{73} +10.7722 q^{74} +(0.814863 - 0.782812i) q^{75} -1.98827 q^{76} +0.512537i q^{77} +(-8.30988 - 8.65012i) q^{78} -2.32354i q^{79} +5.16571 q^{80} +(-8.97105 - 0.721325i) q^{81} -7.30251 q^{82} -10.4066i q^{83} +(0.200576 + 0.208788i) q^{84} -4.41680i q^{85} -1.87599i q^{86} +(1.42571 + 1.48409i) q^{87} +5.54697 q^{88} -4.96972i q^{89} +(0.298080 - 7.42635i) q^{90} +1.65621 q^{91} +3.44394i q^{92} +(11.2266 + 11.6862i) q^{93} -4.27210i q^{94} -7.04749 q^{95} +(4.00568 - 3.84812i) q^{96} -8.79672i q^{97} -8.22124 q^{98} +(0.217020 - 5.40683i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 12 q^{4} - 4 q^{6} - 14 q^{9}+O(q^{10}) \) 20 * q + 12 * q^4 - 4 * q^6 - 14 * q^9	\( 20 q + 12 q^{4} - 4 q^{6} - 14 q^{9} - 12 q^{10} + 2 q^{15} + 12 q^{16} + 24 q^{19} + 12 q^{21} - 28 q^{22} + 2 q^{24} - 4 q^{25} + 10 q^{33} - 44 q^{36} + 24 q^{37} - 8 q^{39} - 32 q^{40} - 48 q^{49} - 26 q^{54} - 8 q^{55} - 38 q^{60} - 16 q^{64} + 32 q^{67} + 4 q^{73} + 116 q^{76} - 30 q^{81} - 32 q^{82} + 90 q^{84} - 40 q^{88} + 74 q^{90} + 20 q^{91} - 2 q^{93} + 30 q^{96}+O(q^{100}) \) 20 * q + 12 * q^4 - 4 * q^6 - 14 * q^9 - 12 * q^10 + 2 * q^15 + 12 * q^16 + 24 * q^19 + 12 * q^21 - 28 * q^22 + 2 * q^24 - 4 * q^25 + 10 * q^33 - 44 * q^36 + 24 * q^37 - 8 * q^39 - 32 * q^40 - 48 * q^49 - 26 * q^54 - 8 * q^55 - 38 * q^60 - 16 * q^64 + 32 * q^67 + 4 * q^73 + 116 * q^76 - 30 * q^81 - 32 * q^82 + 90 * q^84 - 40 * q^88 + 74 * q^90 + 20 * q^91 - 2 * q^93 + 30 * q^96

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