LMFDB - Embedded newform 41.2.g.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,2,Mod(2,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("41.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	41.g (of order $20$, degree $8$, 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:	$0.327386648287$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			8.1
Character	$\chi$	$=$	41.8
Dual form			41.2.g.a.36.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61018 + 2.21623i) q^{2} +(1.24382 + 1.24382i) q^{3} +(-1.70094 - 5.23496i) q^{4} +(-1.15434 + 0.375067i) q^{5} +(-4.75938 + 0.753811i) q^{6} +(1.19485 + 0.189245i) q^{7} +(9.13005 + 2.96653i) q^{8} +0.0941838i q^{9} +O(q^{10})$	\(q+(-1.61018 + 2.21623i) q^{2} +(1.24382 + 1.24382i) q^{3} +(-1.70094 - 5.23496i) q^{4} +(-1.15434 + 0.375067i) q^{5} +(-4.75938 + 0.753811i) q^{6} +(1.19485 + 0.189245i) q^{7} +(9.13005 + 2.96653i) q^{8} +0.0941838i q^{9} +(1.02746 - 3.16221i) q^{10} +(0.836104 - 0.426016i) q^{11} +(4.39569 - 8.62703i) q^{12} +(0.289312 + 1.82664i) q^{13} +(-2.34333 + 2.34333i) q^{14} +(-1.90231 - 0.969274i) q^{15} +(-12.3693 + 8.98684i) q^{16} +(-1.02572 - 2.01309i) q^{17} +(-0.208733 - 0.151653i) q^{18} +(0.815977 - 5.15188i) q^{19} +(3.92693 + 5.40495i) q^{20} +(1.25079 + 1.72156i) q^{21} +(-0.402132 + 2.53896i) q^{22} +(-5.31348 - 3.86047i) q^{23} +(7.66631 + 15.0460i) q^{24} +(-2.85326 + 2.07302i) q^{25} +(-4.51411 - 2.30005i) q^{26} +(3.61432 - 3.61432i) q^{27} +(-1.04167 - 6.57687i) q^{28} +(-0.689088 + 1.35241i) q^{29} +(5.21120 - 2.65524i) q^{30} +(-0.515703 + 1.58717i) q^{31} -22.6839i q^{32} +(1.56985 + 0.510076i) q^{33} +(6.11308 + 0.968216i) q^{34} +(-1.45024 + 0.229695i) q^{35} +(0.493049 - 0.160201i) q^{36} +(1.97146 + 6.06752i) q^{37} +(10.1039 + 10.1039i) q^{38} +(-1.91217 + 2.63187i) q^{39} -11.6518 q^{40} +(4.89143 + 4.13206i) q^{41} -5.82938 q^{42} +(0.714124 - 0.982908i) q^{43} +(-3.65235 - 3.65235i) q^{44} +(-0.0353253 - 0.108720i) q^{45} +(17.1114 - 5.55982i) q^{46} +(-5.36365 + 0.849519i) q^{47} +(-26.5633 - 4.20721i) q^{48} +(-5.26555 - 1.71088i) q^{49} -9.66143i q^{50} +(1.22811 - 3.77974i) q^{51} +(9.07032 - 4.62156i) q^{52} +(-4.56121 + 8.95188i) q^{53} +(2.19044 + 13.8299i) q^{54} +(-0.805362 + 0.805362i) q^{55} +(10.3476 + 5.27237i) q^{56} +(7.42295 - 5.39309i) q^{57} +(-1.88770 - 3.70481i) q^{58} +(-6.23053 - 4.52674i) q^{59} +(-1.83840 + 11.6072i) q^{60} +(0.982392 + 1.35215i) q^{61} +(-2.68716 - 3.69855i) q^{62} +(-0.0178238 + 0.112535i) q^{63} +(25.5342 + 18.5517i) q^{64} +(-1.01908 - 2.00005i) q^{65} +(-3.65820 + 2.65784i) q^{66} +(13.1161 + 6.68301i) q^{67} +(-8.79377 + 8.79377i) q^{68} +(-1.80728 - 11.4107i) q^{69} +(1.82609 - 3.58391i) q^{70} +(2.77828 - 1.41561i) q^{71} +(-0.279399 + 0.859903i) q^{72} -0.596826i q^{73} +(-16.6214 - 5.40063i) q^{74} +(-6.12741 - 0.970487i) q^{75} +(-28.3578 + 4.49144i) q^{76} +(1.07964 - 0.350796i) q^{77} +(-2.75389 - 8.47560i) q^{78} +(-5.89711 - 5.89711i) q^{79} +(10.9077 - 15.0132i) q^{80} +9.27368 q^{81} +(-17.0337 + 4.18715i) q^{82} +11.1844 q^{83} +(6.88480 - 9.47611i) q^{84} +(1.93908 + 1.93908i) q^{85} +(1.02848 + 3.16533i) q^{86} +(-2.53926 + 0.825056i) q^{87} +(8.89746 - 1.40922i) q^{88} +(6.08909 + 0.964418i) q^{89} +(0.297829 + 0.0967704i) q^{90} +2.23731i q^{91} +(-11.1715 + 34.3823i) q^{92} +(-2.61560 + 1.33271i) q^{93} +(6.75374 - 13.2550i) q^{94} +(0.990387 + 6.25306i) q^{95} +(28.2148 - 28.2148i) q^{96} +(-15.0243 - 7.65525i) q^{97} +(12.2702 - 8.91483i) q^{98} +(0.0401238 + 0.0787475i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) $ 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{19}{20}\right)$

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 $

$2$	−1.61018	+	2.21623i	−1.13857	+	1.56711i	−0.367917	+	0.929858i	$0.619929\pi$
$2$	−1.61018	+	2.21623i	−1.13857	+	1.56711i	−0.770655	+	0.637252i	$0.780071\pi$
$3$	1.24382	+	1.24382i	0.718121	+	0.718121i	0.968220	−	0.250099i	$-0.0804633\pi$
$3$	1.24382	+	1.24382i	0.718121	+	0.718121i	−0.250099	+	0.968220i	$0.580463\pi$
$4$	−1.70094	−	5.23496i	−0.850472	−	2.61748i
$5$	−1.15434	+	0.375067i	−0.516236	+	0.167735i	−0.555536	−	0.831492i	$-0.687487\pi$
$5$	−1.15434	+	0.375067i	−0.516236	+	0.167735i	0.0393006	+	0.999227i	$0.487487\pi$
$6$	−4.75938	+	0.753811i	−1.94301	+	0.307742i
$7$	1.19485	+	0.189245i	0.451609	+	0.0715279i	0.378096	−	0.925766i	$-0.376579\pi$
$7$	1.19485	+	0.189245i	0.451609	+	0.0715279i	0.0735133	+	0.997294i	$0.476579\pi$
$8$	9.13005	+	2.96653i	3.22796	+	1.04883i
$9$			0.0941838i			0.0313946i
$10$	1.02746	−	3.16221i	0.324912	−	0.999977i
$11$	0.836104	−	0.426016i	0.252095	−	0.128449i	−0.323377	−	0.946270i	$-0.604818\pi$
$11$	0.836104	−	0.426016i	0.252095	−	0.128449i	0.575472	+	0.817821i	$0.304818\pi$
$12$	4.39569	−	8.62703i	1.26893	−	2.49041i
$13$	0.289312	+	1.82664i	0.0802407	+	0.506620i	0.994773	+	0.102108i	$0.0325587\pi$
$13$	0.289312	+	1.82664i	0.0802407	+	0.506620i	−0.914533	+	0.404512i	$0.867441\pi$
$14$	−2.34333	+	2.34333i	−0.626282	+	0.626282i
$15$	−1.90231	−	0.969274i	−0.491174	−	0.250265i
$16$	−12.3693	+	8.98684i	−3.09233	+	2.24671i
$17$	−1.02572	−	2.01309i	−0.248774	−	0.488247i	0.732524	−	0.680741i	$-0.238342\pi$
$17$	−1.02572	−	2.01309i	−0.248774	−	0.488247i	−0.981298	+	0.192495i	$0.938342\pi$
$18$	−0.208733	−	0.151653i	−0.0491988	−	0.0357450i
$19$	0.815977	−	5.15188i	0.187198	−	1.18192i	−0.697788	−	0.716304i	$-0.745832\pi$
$19$	0.815977	−	5.15188i	0.187198	−	1.18192i	0.884986	−	0.465618i	$-0.154168\pi$
$20$	3.92693	+	5.40495i	0.878088	+	1.20858i
$21$	1.25079	+	1.72156i	0.272944	+	0.375676i
$22$	−0.402132	+	2.53896i	−0.0857349	+	0.541309i
$23$	−5.31348	−	3.86047i	−1.10794	−	0.804963i	−0.125599	−	0.992081i	$-0.540085\pi$
$23$	−5.31348	−	3.86047i	−1.10794	−	0.804963i	−0.982337	+	0.187118i	$0.940085\pi$
$24$	7.66631	+	15.0460i	1.56488	+	3.07125i
$25$	−2.85326	+	2.07302i	−0.570653	+	0.414603i
$26$	−4.51411	−	2.30005i	−0.885290	−	0.451078i
$27$	3.61432	−	3.61432i	0.695576	−	0.695576i
$28$	−1.04167	−	6.57687i	−0.196858	−	1.24291i
$29$	−0.689088	+	1.35241i	−0.127961	+	0.251137i	−0.946094	−	0.323891i	$-0.895009\pi$
$29$	−0.689088	+	1.35241i	−0.127961	+	0.251137i	0.818134	+	0.575028i	$0.195009\pi$
$30$	5.21120	−	2.65524i	0.951431	−	0.484778i
$31$	−0.515703	+	1.58717i	−0.0926230	+	0.285064i	−0.986627	−	0.162995i	$-0.947885\pi$
$31$	−0.515703	+	1.58717i	−0.0926230	+	0.285064i	0.894004	+	0.448059i	$0.147885\pi$
$32$		−	22.6839i		−	4.00999i
$33$	1.56985	+	0.510076i	0.273276	+	0.0887928i
$34$	6.11308	+	0.968216i	1.04838	+	0.166048i
$35$	−1.45024	+	0.229695i	−0.245135	+	0.0388255i
$36$	0.493049	−	0.160201i	0.0821748	−	0.0267002i
$37$	1.97146	+	6.06752i	0.324105	+	0.997494i	0.971843	+	0.235630i	$0.0757154\pi$
$37$	1.97146	+	6.06752i	0.324105	+	0.997494i	−0.647737	+	0.761864i	$0.724285\pi$
$38$	10.1039	+	10.1039i	1.63906	+	1.63906i
$39$	−1.91217	+	2.63187i	−0.306192	+	0.421437i
$40$	−11.6518			−1.84231
$41$	4.89143	+	4.13206i	0.763913	+	0.645319i
$41$	4.89143	+	4.13206i	0.763913	+	0.645319i
$42$	−5.82938			−0.899493
$43$	0.714124	−	0.982908i	0.108903	−	0.149892i	−0.751087	−	0.660204i	$-0.770470\pi$
$43$	0.714124	−	0.982908i	0.108903	−	0.149892i	0.859990	+	0.510312i	$0.170470\pi$
$44$	−3.65235	−	3.65235i	−0.550612	−	0.550612i
$45$	−0.0353253	−	0.108720i	−0.00526598	−	0.0162070i
$46$	17.1114	−	5.55982i	2.52293	−	0.819750i
$47$	−5.36365	+	0.849519i	−0.782369	+	0.123915i	−0.534826	−	0.844962i	$-0.679623\pi$
$47$	−5.36365	+	0.849519i	−0.782369	+	0.123915i	−0.247542	+	0.968877i	$0.579623\pi$
$48$	−26.5633	−	4.20721i	−3.83408	−	0.607258i
$49$	−5.26555	−	1.71088i	−0.752222	−	0.244412i
$50$		−	9.66143i		−	1.36633i
$51$	1.22811	−	3.77974i	0.171970	−	0.529270i
$52$	9.07032	−	4.62156i	1.25783	−	0.640895i
$53$	−4.56121	+	8.95188i	−0.626530	+	1.22963i	0.331632	+	0.943409i	$0.392401\pi$
$53$	−4.56121	+	8.95188i	−0.626530	+	1.22963i	−0.958162	+	0.286226i	$0.907599\pi$
$54$	2.19044	+	13.8299i	0.298081	+	1.88201i
$55$	−0.805362	+	0.805362i	−0.108595	+	0.108595i
$56$	10.3476	+	5.27237i	1.38276	+	0.704550i
$57$	7.42295	−	5.39309i	0.983193	−	0.714332i
$58$	−1.88770	−	3.70481i	−0.247867	−	0.486466i
$59$	−6.23053	−	4.52674i	−0.811146	−	0.589332i	0.103017	−	0.994680i	$-0.467150\pi$
$59$	−6.23053	−	4.52674i	−0.811146	−	0.589332i	−0.914163	+	0.405348i	$0.867150\pi$
$60$	−1.83840	+	11.6072i	−0.237336	+	1.49848i
$61$	0.982392	+	1.35215i	0.125782	+	0.173125i	0.867264	−	0.497849i	$-0.165876\pi$
$61$	0.982392	+	1.35215i	0.125782	+	0.173125i	−0.741481	+	0.670973i	$0.765876\pi$
$62$	−2.68716	−	3.69855i	−0.341269	−	0.469717i
$63$	−0.0178238	+	0.112535i	−0.00224559	+	0.0141781i
$64$	25.5342	+	18.5517i	3.19177	+	2.31896i
$65$	−1.01908	−	2.00005i	−0.126401	−	0.248076i
$66$	−3.65820	+	2.65784i	−0.450293	+	0.327157i
$67$	13.1161	+	6.68301i	1.60239	+	0.816460i	0.999831	+	0.0183870i	$0.00585310\pi$
$67$	13.1161	+	6.68301i	1.60239	+	0.816460i	0.602561	+	0.798073i	$0.294147\pi$
$68$	−8.79377	+	8.79377i	−1.06640	+	1.06640i
$69$	−1.80728	−	11.4107i	−0.217571	−	1.37369i
$70$	1.82609	−	3.58391i	0.218260	−	0.428359i
$71$	2.77828	−	1.41561i	0.329722	−	0.168001i	−0.281291	−	0.959623i	$-0.590763\pi$
$71$	2.77828	−	1.41561i	0.329722	−	0.168001i	0.611012	+	0.791621i	$0.290763\pi$
$72$	−0.279399	+	0.859903i	−0.0329275	+	0.101340i
$73$		−	0.596826i		−	0.0698532i	−0.999390	−	0.0349266i	$-0.988880\pi$
$73$		−	0.596826i		−	0.0698532i	0.999390	−	0.0349266i	$-0.0111197\pi$
$74$	−16.6214	−	5.40063i	−1.93220	−	0.627810i
$75$	−6.12741	−	0.970487i	−0.707533	−	0.112062i
$76$	−28.3578	+	4.49144i	−3.25287	+	0.515203i
$77$	1.07964	−	0.350796i	0.123036	−	0.0399769i
$78$	−2.75389	−	8.47560i	−0.311817	−	0.959673i
$79$	−5.89711	−	5.89711i	−0.663477	−	0.663477i	0.292721	−	0.956198i	$-0.405439\pi$
$79$	−5.89711	−	5.89711i	−0.663477	−	0.663477i	−0.956198	+	0.292721i	$0.905439\pi$
$80$	10.9077	−	15.0132i	1.21952	−	1.67853i
$81$	9.27368			1.03041
$82$	−17.0337	+	4.18715i	−1.88106	+	0.462394i
$83$	11.1844			1.22765			0.613823	−	0.789443i	$-0.289631\pi$
$83$	11.1844			1.22765			0.613823	+	0.789443i	$0.289631\pi$
$84$	6.88480	−	9.47611i	0.751193	−	1.03393i
$85$	1.93908	+	1.93908i	0.210322	+	0.210322i
$86$	1.02848	+	3.16533i	0.110903	+	0.341326i
$87$	−2.53926	+	0.825056i	−0.272238	+	0.0884553i
$88$	8.89746	−	1.40922i	0.948473	−	0.150223i
$89$	6.08909	+	0.964418i	0.645443	+	0.102228i	0.470570	−	0.882363i	$-0.344048\pi$
$89$	6.08909	+	0.964418i	0.645443	+	0.102228i	0.174873	+	0.984591i	$0.444048\pi$
$90$	0.297829	+	0.0967704i	0.0313939	+	0.0102005i
$91$			2.23731i			0.234534i
$92$	−11.1715	+	34.3823i	−1.16471	+	3.58460i
$93$	−2.61560	+	1.33271i	−0.271225	+	0.138196i
$94$	6.75374	−	13.2550i	0.696595	−	1.36714i
$95$	0.990387	+	6.25306i	0.101612	+	0.641550i
$96$	28.2148	−	28.2148i	2.87966	−	2.87966i
$97$	−15.0243	−	7.65525i	−1.52548	−	0.777273i	−0.528074	−	0.849198i	$-0.677086\pi$
$97$	−15.0243	−	7.65525i	−1.52548	−	0.777273i	−0.997410	+	0.0719256i	$0.977086\pi$
$98$	12.2702	−	8.91483i	1.23948	−	0.900534i
$99$	0.0401238	+	0.0787475i	0.00403260	+	0.00791442i
$100$	15.7054	+	11.4106i	1.57054	+	1.14106i
$101$	1.46960	−	9.27866i	0.146230	−	0.923262i	−0.800055	−	0.599927i	$-0.795196\pi$
$101$	1.46960	−	9.27866i	0.146230	−	0.923262i	0.946285	−	0.323334i	$-0.104804\pi$
$102$	6.39929	+	8.80787i	0.633624	+	0.872109i
$103$	6.15464	+	8.47113i	0.606435	+	0.834686i	0.996278	−	0.0861955i	$-0.0274710\pi$
$103$	6.15464	+	8.47113i	0.606435	+	0.834686i	−0.389844	+	0.920881i	$0.627471\pi$
$104$	−2.77737	+	17.5356i	−0.272343	+	1.71951i
$105$	−2.08953	−	1.51814i	−0.203918	−	0.148155i
$106$	−12.4950	−	24.5229i	−1.21362	−	2.38187i
$107$	4.04469	−	2.93864i	0.391014	−	0.284089i	−0.374857	−	0.927083i	$-0.622308\pi$
$107$	4.04469	−	2.93864i	0.391014	−	0.284089i	0.765871	+	0.642994i	$0.222308\pi$
$108$	−25.0686	−	12.7731i	−2.41222	−	1.22909i
$109$	−5.70768	+	5.70768i	−0.546697	+	0.546697i	−0.925484	−	0.378787i	$-0.876341\pi$
$109$	−5.70768	+	5.70768i	−0.546697	+	0.546697i	0.378787	+	0.925484i	$0.376341\pi$
$110$	−0.488085	−	3.08165i	−0.0465371	−	0.293824i
$111$	−5.09477	+	9.99905i	−0.483574	+	0.949068i
$112$	−16.4802	+	8.39706i	−1.55723	+	0.793448i
$113$	0.593004	−	1.82508i	0.0557851	−	0.171689i	−0.919282	−	0.393600i	$-0.871229\pi$
$113$	0.593004	−	1.82508i	0.0557851	−	0.171689i	0.975067	+	0.221911i	$0.0712295\pi$
$114$			25.1348i			2.35409i
$115$	7.58148	+	2.46337i	0.706977	+	0.229711i
$116$	8.25193	+	1.30698i	0.766173	+	0.121350i
$117$	−0.172040	+	0.0272485i	−0.0159051	+	0.00251913i
$118$	20.0646	−	6.51939i	1.84710	−	0.600158i
$119$	−0.844612	−	2.59945i	−0.0774255	−	0.238291i
$120$	−14.4928	−	14.4928i	−1.32300	−	1.32300i
$121$	−5.94806	+	8.18680i	−0.540733	+	0.744254i
$122$	−4.57850			−0.414518
$123$	0.944523	+	11.2236i	0.0851648	+	1.01200i
$124$	9.18597			0.824924
$125$	6.08321	−	8.37282i	0.544099	−	0.748888i
$126$	−0.220704	−	0.220704i	−0.0196619	−	0.0196619i
$127$	1.11004	+	3.41634i	0.0984997	+	0.303151i	0.988150	−	0.153492i	$-0.0490518\pi$
$127$	1.11004	+	3.41634i	0.0984997	+	0.303151i	−0.889650	+	0.456643i	$0.849052\pi$
$128$	−39.0820	+	12.6985i	−3.45439	+	1.12240i
$129$	2.11080	−	0.334319i	0.185846	−	0.0294351i
$130$	6.07348	+	0.961945i	0.532680	+	0.0843682i
$131$	7.54778	+	2.45242i	0.659453	+	0.214269i	0.619578	−	0.784935i	$-0.287304\pi$
$131$	7.54778	+	2.45242i	0.659453	+	0.214269i	0.0398754	+	0.999205i	$0.487304\pi$
$132$		−	9.08573i		−	0.790812i
$133$	1.94994	−	6.00128i	0.169081	−	0.520377i
$134$	−35.9305	+	18.3075i	−3.10392	+	1.58153i
$135$	−2.81653	+	5.52776i	−0.242408	+	0.475753i
$136$	−3.39299	−	21.4225i	−0.290946	−	1.83696i
$137$	−5.27127	+	5.27127i	−0.450355	+	0.450355i	−0.895472	−	0.445117i	$-0.853162\pi$
$137$	−5.27127	+	5.27127i	−0.450355	+	0.450355i	0.445117	+	0.895472i	$0.353162\pi$
$138$	28.1989	+	14.3681i	2.40045	+	1.22309i
$139$	−1.71214	+	1.24394i	−0.145221	+	0.105510i	−0.658024	−	0.752997i	$-0.728607\pi$
$139$	−1.71214	+	1.24394i	−0.145221	+	0.105510i	0.512802	+	0.858507i	$0.328607\pi$
$140$	3.66921	+	7.20124i	0.310105	+	0.608616i
$141$	−7.72807	−	5.61477i	−0.650821	−	0.472849i
$142$	−1.33624	+	8.43670i	−0.112135	+	0.707992i
$143$	1.02008	+	1.40401i	0.0853030	+	0.117409i
$144$	−0.846415	−	1.16499i	−0.0705346	−	0.0970825i
$145$	0.288196	−	1.81960i	0.0239333	−	0.151109i
$146$	1.32270	+	0.961000i	0.109468	+	0.0795329i
$147$	−4.42137	−	8.67744i	−0.364669	−	0.715703i
$148$	28.4099	−	20.6410i	2.33528	−	1.69668i
$149$	7.89085	+	4.02059i	0.646444	+	0.329379i	0.746288	−	0.665624i	$-0.231834\pi$
$149$	7.89085	+	4.02059i	0.646444	+	0.329379i	−0.0998440	+	0.995003i	$0.531834\pi$
$150$	12.0171	−	12.0171i	0.981191	−	0.981191i
$151$	−0.837422	−	5.28728i	−0.0681485	−	0.430272i	−0.998048	−	0.0624578i	$-0.980106\pi$
$151$	−0.837422	−	5.28728i	−0.0681485	−	0.430272i	0.929899	−	0.367815i	$-0.119894\pi$
$152$	22.7331	−	44.6163i	1.84390	−	3.61886i
$153$	0.189601	−	0.0966064i	0.0153283	−	0.00781016i
$154$	−0.960973	+	2.95757i	−0.0774374	+	0.238328i
$155$		−	2.02556i		−	0.162697i
$156$	17.0302	+	5.53346i	1.36351	+	0.443032i
$157$	−8.26051	−	1.30834i	−0.659260	−	0.104417i	−0.182165	−	0.983268i	$-0.558310\pi$
$157$	−8.26051	−	1.30834i	−0.659260	−	0.104417i	−0.477095	+	0.878851i	$0.658310\pi$
$158$	22.5648	−	3.57391i	1.79516	−	0.284325i
$159$	−16.8079	+	5.46121i	−1.33295	+	0.433102i
$160$	8.50800	+	26.1849i	0.672617	+	2.07010i
$161$	−5.61821	−	5.61821i	−0.442777	−	0.442777i
$162$	−14.9323	+	20.5526i	−1.17320	+	1.61477i
$163$	−0.165656			−0.0129752			−0.00648760	−	0.999979i	$-0.502065\pi$
$163$	−0.165656			−0.0129752			−0.00648760	+	0.999979i	$0.502065\pi$
$164$	13.3111	−	32.6349i	1.03943	−	2.54835i
$165$	−2.00345			−0.155969
$166$	−18.0089	+	24.7872i	−1.39776	+	1.92386i
$167$	4.32550	+	4.32550i	0.334717	+	0.334717i	0.854375	−	0.519657i	$-0.173940\pi$
$167$	4.32550	+	4.32550i	0.334717	+	0.334717i	−0.519657	+	0.854375i	$0.673940\pi$
$168$	6.31269	+	19.4285i	0.487034	+	1.49894i
$169$	9.11081	−	2.96028i	0.700831	−	0.227714i
$170$	−7.41971	+	1.17517i	−0.569065	+	0.0901311i
$171$	0.485224	+	0.0768519i	0.0371060	+	0.00587701i
$172$	−6.36017	−	2.06654i	−0.484959	−	0.157573i
$173$		−	19.1289i		−	1.45434i	−0.686456	−	0.727171i	$-0.740835\pi$
$173$		−	19.1289i		−	1.45434i	0.686456	−	0.727171i	$-0.259165\pi$
$174$	2.26017	−	6.95608i	0.171343	−	0.527339i
$175$	−3.80152	+	1.93697i	−0.287368	+	0.146421i
$176$	−6.51350	+	12.7835i	−0.490974	+	0.963590i
$177$	−2.11920	−	13.3801i	−0.159289	−	1.00571i
$178$	−11.9419	+	11.9419i	−0.895086	+	0.895086i
$179$	−11.6175	−	5.91943i	−0.868335	−	0.442439i	−0.0377216	−	0.999288i	$-0.512010\pi$
$179$	−11.6175	−	5.91943i	−0.868335	−	0.442439i	−0.830613	+	0.556850i	$0.812010\pi$
$180$	−0.509059	+	0.369853i	−0.0379430	+	0.0275672i
$181$	−5.39400	−	10.5863i	−0.400933	−	0.786875i	0.598971	−	0.800771i	$-0.295577\pi$
$181$	−5.39400	−	10.5863i	−0.400933	−	0.786875i	−0.999903	+	0.0138960i	$0.995577\pi$
$182$	−4.95839	−	3.60248i	−0.367541	−	0.267034i
$183$	−0.459909	+	2.90375i	−0.0339974	+	0.214651i
$184$	−37.0601	−	51.0088i	−2.73211	−	3.76042i
$185$	−4.55145	−	6.26454i	−0.334630	−	0.460578i
$186$	1.25800	−	7.94269i	0.0922409	−	0.582386i
$187$	−1.71522	−	1.24618i	−0.125429	−	0.0911298i
$188$	13.5705	+	26.6335i	0.989728	+	1.94245i
$189$	5.00254	−	3.63456i	0.363882	−	0.264375i
$190$	−15.4529	−	7.87365i	−1.12107	−	0.571215i
$191$	−0.305210	+	0.305210i	−0.0220842	+	0.0220842i	−0.718063	−	0.695978i	$-0.754971\pi$
$191$	−0.305210	+	0.305210i	−0.0220842	+	0.0220842i	0.695978	+	0.718063i	$0.254971\pi$
$192$	8.68499	+	54.8349i	0.626785	+	3.95737i
$193$	−9.62661	+	18.8933i	−0.692938	+	1.35997i	0.229304	+	0.973355i	$0.426355\pi$
$193$	−9.62661	+	18.8933i	−0.692938	+	1.35997i	−0.922242	+	0.386613i	$0.873645\pi$
$194$	41.1576	−	20.9709i	2.95495	−	1.50562i
$195$	1.22016	−	3.75526i	0.0873774	−	0.268920i
$196$			30.4751i			2.17679i
$197$	22.2882	+	7.24188i	1.58797	+	0.515963i	0.964094	−	0.265561i	$-0.0855572\pi$
$197$	22.2882	+	7.24188i	1.58797	+	0.515963i	0.623876	+	0.781524i	$0.285557\pi$
$198$	−0.239129	−	0.0378744i	−0.0169942	−	0.00269161i
$199$	5.20701	−	0.824709i	0.369115	−	0.0584621i	0.0308784	−	0.999523i	$-0.490170\pi$
$199$	5.20701	−	0.824709i	0.369115	−	0.0584621i	0.338237	+	0.941061i	$0.390170\pi$
$200$	−32.2001	+	10.4624i	−2.27689	+	0.739807i
$201$	8.00167	+	24.6266i	0.564394	+	1.73703i
$202$	18.1973	+	18.1973i	1.28036	+	1.28036i
$203$	−1.07929	+	1.48552i	−0.0757515	+	0.104263i
$204$	−21.8758			−1.53161
$205$	−7.19617	−	2.93518i	−0.502602	−	0.205002i
$206$	−28.6841			−1.99851
$207$	0.363593	−	0.500443i	0.0252715	−	0.0347832i
$208$	−19.9944	−	19.9944i	−1.38636	−	1.38636i
$209$	−1.51254	−	4.65513i	−0.104625	−	0.322002i
$210$	6.72907	−	2.18641i	0.464350	−	0.150877i
$211$	21.8950	−	3.46783i	1.50731	−	0.238735i	0.652547	−	0.757748i	$-0.273701\pi$
$211$	21.8950	−	3.46783i	1.50731	−	0.238735i	0.854766	+	0.519013i	$0.173701\pi$
$212$	54.6211	+	8.65113i	3.75139	+	0.594162i
$213$	5.21645	+	1.69493i	0.357425	+	0.116134i
$214$			13.6957i			0.936219i
$215$	−0.455684	+	1.40245i	−0.0310774	+	0.0956465i
$216$	43.7209	−	22.2769i	2.97483	−	1.51575i
$217$	−0.916550	+	1.79883i	−0.0622195	+	0.122113i
$218$	−3.45911	−	21.8400i	−0.234280	−	1.47919i
$219$	0.742345	−	0.742345i	0.0501630	−	0.0501630i
$220$	5.58592	+	2.84617i	0.376603	+	0.191889i
$221$	3.38045	−	2.45604i	0.227394	−	0.165211i
$222$	−13.9567	−	27.3915i	−0.936710	−	1.83840i
$223$	−19.1614	−	13.9216i	−1.28314	−	0.932258i	−0.283500	−	0.958972i	$-0.591496\pi$
$223$	−19.1614	−	13.9216i	−1.28314	−	0.932258i	−0.999643	+	0.0267138i	$0.991496\pi$
$224$	4.29282	−	27.1038i	0.286826	−	1.81095i
$225$	−0.195245	−	0.268731i	−0.0130163	−	0.0179154i
$226$	3.08995	+	4.25295i	0.205540	+	0.282902i
$227$	−2.24211	+	14.1561i	−0.148814	+	0.939575i	0.794401	+	0.607393i	$0.207785\pi$
$227$	−2.24211	+	14.1561i	−0.148814	+	0.939575i	−0.943215	+	0.332182i	$0.892215\pi$
$228$	−40.8586	−	29.6855i	−2.70593	−	1.96597i
$229$	9.37117	+	18.3920i	0.619264	+	1.21537i	0.961252	+	0.275670i	$0.0888997\pi$
$229$	9.37117	+	18.3920i	0.619264	+	1.21537i	−0.341988	+	0.939704i	$0.611100\pi$
$230$	−17.6670	+	12.8358i	−1.16493	+	0.846369i
$231$	1.77920	+	0.906549i	0.117063	+	0.0596466i
$232$	−10.3034	+	10.3034i	−0.676450	+	0.676450i
$233$	2.82151	+	17.8143i	0.184843	+	1.16705i	0.889306	+	0.457313i	$0.151188\pi$
$233$	2.82151	+	17.8143i	0.184843	+	1.16705i	−0.704462	+	0.709741i	$0.748812\pi$
$234$	0.216628	−	0.425156i	0.0141614	−	0.0277933i
$235$	5.87284	−	2.99236i	0.383102	−	0.195200i
$236$	−13.0996	+	40.3163i	−0.852709	+	2.62437i
$237$		−	14.6699i		−	0.952913i
$238$	7.12096	+	2.31374i	0.461583	+	0.149977i
$239$	−22.4231	−	3.55147i	−1.45043	−	0.229725i	−0.619015	−	0.785379i	$-0.712468\pi$
$239$	−22.4231	−	3.55147i	−1.45043	−	0.229725i	−0.831414	+	0.555653i	$0.812468\pi$
$240$	32.2410	−	5.10647i	2.08115	−	0.329621i
$241$	−2.97068	+	0.965234i	−0.191359	+	0.0621762i	−0.403129	−	0.915143i	$-0.632077\pi$
$241$	−2.97068	+	0.965234i	−0.191359	+	0.0621762i	0.211770	+	0.977320i	$0.432077\pi$
$242$	−8.56635	−	26.3645i	−0.550666	−	1.69478i
$243$	0.691854	+	0.691854i	0.0443824	+	0.0443824i
$244$	5.40745	−	7.44271i	0.346176	−	0.476471i
$245$	6.71992			0.429320
$246$	−26.3949	−	15.9788i	−1.68288	−	1.01877i
$247$	9.64672			0.613806
$248$	−9.41679	+	12.9611i	−0.597967	+	0.823030i
$249$	13.9114	+	13.9114i	0.881598	+	0.881598i
$250$	8.76100	+	26.9636i	0.554094	+	1.70533i
$251$	6.26375	−	2.03521i	0.395364	−	0.128462i	−0.104586	−	0.994516i	$-0.533352\pi$
$251$	6.26375	−	2.03521i	0.395364	−	0.128462i	0.499950	+	0.866054i	$0.333352\pi$
$252$	0.619435	−	0.0981089i	0.0390207	−	0.00618028i
$253$	−6.08724	−	0.964124i	−0.382702	−	0.0606140i
$254$	−9.35875	−	3.04084i	−0.587220	−	0.190799i
$255$			4.82373i			0.302074i
$256$	15.2801	−	47.0273i	0.955005	−	2.93920i
$257$	−6.08184	+	3.09885i	−0.379375	+	0.193301i	−0.633270	−	0.773931i	$-0.718288\pi$
$257$	−6.08184	+	3.09885i	−0.379375	+	0.193301i	0.253896	+	0.967232i	$0.418288\pi$
$258$	−2.65786	+	5.21634i	−0.165471	+	0.324755i
$259$	1.20734	+	7.62284i	0.0750204	+	0.473660i
$260$	−8.73682	+	8.73682i	−0.541834	+	0.541834i
$261$	−0.127375	−	0.0649010i	−0.00788433	−	0.00401727i
$262$	−17.5885	+	12.7788i	−1.08662	+	0.789475i
$263$	5.84108	+	11.4638i	0.360177	+	0.706887i	0.997995	−	0.0633007i	$-0.0201627\pi$
$263$	5.84108	+	11.4638i	0.360177	+	0.706887i	−0.637818	+	0.770187i	$0.720163\pi$
$264$	12.8197	+	9.31404i	0.788996	+	0.573239i
$265$	1.90762	−	12.0443i	0.117184	−	0.739873i
$266$	10.1605	+	13.9847i	0.622978	+	0.857456i
$267$	6.37418	+	8.77331i	0.390094	+	0.536918i
$268$	12.6755	−	80.0300i	0.774280	−	4.88861i
$269$	13.0297	+	9.46664i	0.794435	+	0.577191i	0.909276	−	0.416193i	$-0.136636\pi$
$269$	13.0297	+	9.46664i	0.794435	+	0.577191i	−0.114841	+	0.993384i	$0.536636\pi$
$270$	−7.71564	−	15.1428i	−0.469559	−	0.921561i
$271$	16.7793	−	12.1909i	1.01927	−	0.740544i	0.0531382	−	0.998587i	$-0.483078\pi$
$271$	16.7793	−	12.1909i	1.01927	−	0.740544i	0.966133	+	0.258043i	$0.0830776\pi$
$272$	30.7788	+	15.6826i	1.86624	+	0.950897i
$273$	−2.78281	+	2.78281i	−0.168424	+	0.168424i
$274$	−3.19463	−	20.1701i	−0.192994	−	1.21852i
$275$	−1.50249	+	2.94880i	−0.0906033	+	0.177819i
$276$	−56.6608	+	28.8701i	−3.41058	+	1.73778i
$277$	1.50210	−	4.62298i	0.0902524	−	0.277768i	−0.895735	−	0.444588i	$-0.853350\pi$
$277$	1.50210	−	4.62298i	0.0902524	−	0.277768i	0.985987	+	0.166820i	$0.0533499\pi$
$278$		−	5.79746i		−	0.347708i
$279$	−0.149486	−	0.0485709i	−0.00894948	−	0.00290786i
$280$	−13.9221	−	2.20505i	−0.832006	−	0.131777i
$281$	5.74924	−	0.910591i	0.342971	−	0.0543213i	0.0174270	−	0.999848i	$-0.494453\pi$
$281$	5.74924	−	0.910591i	0.342971	−	0.0543213i	0.325544	+	0.945527i	$0.394453\pi$
$282$	24.8873	−	8.08636i	1.48201	−	0.481536i
$283$	−4.46953	−	13.7558i	−0.265686	−	0.817697i	−0.991535	−	0.129843i	$-0.958553\pi$
$283$	−4.46953	−	13.7558i	−0.265686	−	0.817697i	0.725849	−	0.687854i	$-0.241447\pi$
$284$	−12.1363	−	12.1363i	−0.720160	−	0.720160i
$285$	−6.54582	+	9.00955i	−0.387741	+	0.533680i
$286$	−4.75413			−0.281117
$287$	5.06254	+	5.86285i	0.298832	+	0.346073i
$288$	2.13646			0.125892
$289$	6.99191	−	9.62354i	0.411289	−	0.566091i
$290$	3.56859	+	3.56859i	0.209555	+	0.209555i
$291$	−9.16575	−	28.2093i	−0.537306	−	1.65366i
$292$	−3.12436	+	1.01517i	−0.182839	+	0.0594081i
$293$	−19.4615	+	3.08239i	−1.13695	+	0.180075i	−0.696401	−	0.717653i	$-0.745216\pi$
$293$	−19.4615	+	3.08239i	−1.13695	+	0.180075i	−0.440550	+	0.897728i	$0.645216\pi$
$294$	26.3504	+	4.17350i	1.53679	+	0.243403i
$295$	8.88997	+	2.88853i	0.517594	+	0.168177i
$296$			61.2451i			3.55980i
$297$	1.48219	−	4.56170i	0.0860052	−	0.264697i
$298$	−21.6163	+	11.0140i	−1.25220	+	0.638026i
$299$	5.51445	−	10.8227i	0.318909	−	0.625893i
$300$	5.34192	+	33.7275i	0.308416	+	1.94726i
$301$	1.03928	−	1.03928i	0.0599031	−	0.0599031i
$302$	13.0662	+	6.65757i	0.751877	+	0.383100i
$303$	13.3689	−	9.71309i	0.768024	−	0.558002i
$304$	36.2060	+	71.0583i	2.07656	+	4.07547i
$305$	−1.64116	−	1.19237i	−0.0939725	−	0.0682750i
$306$	−0.0911903	+	0.575753i	−0.00521300	+	0.0329136i
$307$	5.79055	+	7.97001i	0.330484	+	0.454872i	0.941632	−	0.336644i	$-0.109292\pi$
$307$	5.79055	+	7.97001i	0.330484	+	0.454872i	−0.611148	+	0.791516i	$0.709292\pi$
$308$	−3.67280	−	5.05518i	−0.209277	−	0.288046i
$309$	−2.88131	+	18.1918i	−0.163912	+	1.03490i
$310$	4.48910	+	3.26152i	0.254963	+	0.185242i
$311$	−11.5241	−	22.6173i	−0.653472	−	1.28251i	−0.945351	−	0.326056i	$-0.894280\pi$
$311$	−11.5241	−	22.6173i	−0.653472	−	1.28251i	0.291879	−	0.956455i	$-0.405720\pi$
$312$	−25.2657	+	18.3566i	−1.43039	+	1.03924i
$313$	−23.3678	−	11.9065i	−1.32083	−	0.672995i	−0.355656	−	0.934617i	$-0.615743\pi$
$313$	−23.3678	−	11.9065i	−1.32083	−	0.672995i	−0.965170	+	0.261622i	$0.915743\pi$
$314$	16.2005	−	16.2005i	0.914248	−	0.914248i
$315$	−0.0216335	−	0.136589i	−0.00121891	−	0.00769591i
$316$	−20.8405	+	40.9018i	−1.17237	+	2.30091i
$317$	−18.5064	+	9.42948i	−1.03942	+	0.529612i	−0.888473	−	0.458929i	$-0.848233\pi$
$317$	−18.5064	+	9.42948i	−1.03942	+	0.529612i	−0.150950	+	0.988541i	$0.548233\pi$
$318$	14.9605	−	46.0436i	0.838942	−	2.58200i
$319$			1.42432i			0.0797466i
$320$	−36.4332	−	11.8379i	−2.03668	−	0.661756i
$321$	8.68601	+	1.37573i	0.484806	+	0.0767857i
$322$	21.4976	−	3.40489i	1.19801	−	0.189747i
$323$	−11.2082	+	3.64176i	−0.623640	+	0.202633i
$324$	−15.7740	−	48.5474i	−0.876334	−	2.69708i
$325$	−4.61215	−	4.61215i	−0.255836	−	0.255836i
$326$	0.266737	−	0.367132i	0.0147732	−	0.0203336i
$327$	−14.1987			−0.785188
$328$	32.4011	+	52.2365i	1.78905	+	2.88428i
$329$	−6.56951			−0.362189
$330$	3.22593	−	4.44011i	0.177582	−	0.244420i
$331$	−4.50312	−	4.50312i	−0.247514	−	0.247514i	0.572436	−	0.819949i	$-0.305999\pi$
$331$	−4.50312	−	4.50312i	−0.247514	−	0.247514i	−0.819949	+	0.572436i	$0.805999\pi$
$332$	−19.0240	−	58.5499i	−1.04408	−	3.21334i
$333$	−0.571462	+	0.185679i	−0.0313159	+	0.0101752i
$334$	−16.5512	+	2.62145i	−0.905639	+	0.143439i
$335$	−17.6470	−	2.79502i	−0.964161	−	0.152708i
$336$	−30.9428	−	10.0539i	−1.68807	−	0.548487i
$337$		−	11.0639i		−	0.602688i	−0.953515	−	0.301344i	$-0.902565\pi$
$337$		−	11.0639i		−	0.602688i	0.953515	−	0.301344i	$-0.0974353\pi$
$338$	−8.10942	+	24.9582i	−0.441094	+	1.35755i
$339$	3.00766	−	1.53248i	0.163354	−	0.0832329i
$340$	6.85273	−	13.4492i	0.371642	−	0.729388i
$341$	0.244979	+	1.54674i	0.0132664	+	0.0837606i
$342$	−0.951621	+	0.951621i	−0.0514578	+	0.0514578i
$343$	−13.5130	−	6.88519i	−0.729631	−	0.371766i
$344$	9.43581	−	6.85552i	0.508745	−	0.369625i
$345$	6.36601	+	12.4940i	0.342735	+	0.672655i
$346$	42.3940	+	30.8010i	2.27912	+	1.65587i
$347$	0.198212	−	1.25146i	0.0106406	−	0.0671819i	−0.981797	−	0.189935i	$-0.939172\pi$
$347$	0.198212	−	1.25146i	0.0106406	−	0.0671819i	0.992437	+	0.122753i	$0.0391723\pi$
$348$	8.63828	+	11.8896i	0.463061	+	0.637348i
$349$	−8.34115	−	11.4806i	−0.446491	−	0.614543i	0.525148	−	0.851011i	$-0.324010\pi$
$349$	−8.34115	−	11.4806i	−0.446491	−	0.614543i	−0.971639	+	0.236468i	$0.924010\pi$
$350$	1.82838	−	11.5439i	0.0977309	−	0.617049i
$351$	7.64774	+	5.55641i	0.408206	+	0.296579i
$352$	−9.66373	−	18.9661i	−0.515078	−	1.01090i
$353$	−0.827363	+	0.601115i	−0.0440361	+	0.0319941i	−0.609586	−	0.792720i	$-0.708664\pi$
$353$	−0.827363	+	0.601115i	−0.0440361	+	0.0319941i	0.565549	+	0.824714i	$0.308664\pi$
$354$	33.0657	+	16.8478i	1.75742	+	0.895452i
$355$	−2.67613	+	2.67613i	−0.142034	+	0.142034i
$356$	−5.30851	−	33.5166i	−0.281350	−	1.77638i
$357$	2.18270	−	4.28380i	0.115521	−	0.226723i
$358$	31.8252	−	16.2157i	1.68201	−	0.857028i
$359$	−3.46550	+	10.6657i	−0.182902	+	0.562915i	−0.999906	−	0.0137176i	$-0.995633\pi$
$359$	−3.46550	+	10.6657i	−0.182902	+	0.562915i	0.817004	+	0.576632i	$0.195633\pi$
$360$		−	1.09741i		−	0.0578387i
$361$	−7.80596	−	2.53631i	−0.410840	−	0.133490i
$362$	32.1471	+	5.09159i	1.68961	+	0.267608i
$363$	−17.5812	+	2.78459i	−0.922776	+	0.146153i
$364$	11.7122	−	3.80554i	0.613888	−	0.199464i
$365$	0.223850	+	0.688939i	0.0117168	+	0.0360607i
$366$	−5.69484	−	5.69484i	−0.297674	−	0.297674i
$367$	16.8756	−	23.2272i	0.880897	−	1.21245i	−0.0952746	−	0.995451i	$-0.530373\pi$
$367$	16.8756	−	23.2272i	0.880897	−	1.21245i	0.976172	−	0.217000i	$-0.0696271\pi$
$368$	100.417			5.23462
$369$	−0.389173	+	0.460694i	−0.0202595	+	0.0239827i
$370$	21.2123			1.10278
$371$	−7.14404	+	9.83293i	−0.370900	+	0.510500i
$372$	11.4257	+	11.4257i	0.592395	+	0.592395i
$373$	10.5118	+	32.3520i	0.544281	+	1.67512i	0.722694	+	0.691168i	$0.242903\pi$
$373$	10.5118	+	32.3520i	0.544281	+	1.67512i	−0.178414	+	0.983956i	$0.557097\pi$
$374$	5.52365	−	1.79474i	0.285621	−	0.0928039i
$375$	17.9807	−	2.84787i	0.928521	−	0.147063i
$376$	−51.4905	−	8.15530i	−2.65542	−	0.420577i
$377$	−2.66974	−	0.867450i	−0.137498	−	0.0446760i
$378$			16.9391i			0.871253i
$379$	−2.16181	+	6.65338i	−0.111045	+	0.341761i	−0.991102	−	0.133108i	$-0.957504\pi$
$379$	−2.16181	+	6.65338i	−0.111045	+	0.341761i	0.880057	+	0.474869i	$0.157504\pi$
$380$	31.0499	−	15.8207i	1.59283	−	0.811587i
$381$	−2.86863	+	5.63000i	−0.146964	+	0.288434i
$382$	−0.184971	−	1.16786i	−0.00946392	−	0.0597528i
$383$	13.4809	−	13.4809i	0.688840	−	0.688840i	−0.273136	−	0.961976i	$-0.588061\pi$
$383$	13.4809	−	13.4809i	0.688840	−	0.688840i	0.961976	+	0.273136i	$0.0880608\pi$
$384$	−64.4057	−	32.8164i	−3.28669	−	1.67465i
$385$	−1.11470	+	0.809873i	−0.0568101	+	0.0412750i
$386$	−26.3712	−	51.7564i	−1.34226	−	2.63433i
$387$	0.0925740	+	0.0672589i	0.00470580	+	0.00341896i
$388$	−14.5195	+	91.6727i	−0.737117	+	4.65398i
$389$	10.7762	+	14.8322i	0.546377	+	0.752024i	0.989515	−	0.144430i	$-0.0461348\pi$
$389$	10.7762	+	14.8322i	0.546377	+	0.752024i	−0.443138	+	0.896453i	$0.646135\pi$
$390$	6.35784	+	8.75082i	0.321942	+	0.443115i
$391$	−2.32133	+	14.6563i	−0.117395	+	0.741200i
$392$	−42.9994	−	31.2409i	−2.17180	−	1.57790i
$393$	6.33772	+	12.4385i	0.319696	+	0.627438i
$394$	−51.9378	+	37.7350i	−2.61659	+	1.90106i
$395$	9.01908	+	4.59545i	0.453799	+	0.231222i
$396$	0.343992	−	0.343992i	0.0172862	−	0.0172862i
$397$	−1.30237	−	8.22286i	−0.0653642	−	0.412694i	−0.998575	−	0.0533644i	$-0.983006\pi$
$397$	−1.30237	−	8.22286i	−0.0653642	−	0.412694i	0.933211	−	0.359329i	$-0.116994\pi$
$398$	−6.55650	+	12.8679i	−0.328648	+	0.645008i
$399$	9.88990	−	5.03915i	0.495114	−	0.252273i
$400$	16.6631	−	51.2837i	0.833153	−	2.56418i
$401$		−	4.20180i		−	0.209828i	−0.994481	−	0.104914i	$-0.966543\pi$
$401$		−	4.20180i		−	0.209828i	0.994481	−	0.104914i	$-0.0334567\pi$
$402$	−67.4624	−	21.9199i	−3.36472	−	1.09326i
$403$	−3.04840	−	0.482819i	−0.151851	−	0.0240509i
$404$	−51.0732	+	8.08920i	−2.54099	+	0.402453i
$405$	−10.7050	+	3.47825i	−0.531934	+	0.172836i
$406$	−1.55439	−	4.78392i	−0.0771430	−	0.237422i
$407$	4.23321	+	4.23321i	0.209832	+	0.209832i
$408$	22.4255	−	30.8660i	1.11023	−	1.52809i
$409$	38.6631			1.91177			0.955883	−	0.293746i	$-0.0949020\pi$
$409$	38.6631			1.91177			0.955883	+	0.293746i	$0.0949020\pi$
$410$	18.0922	−	11.2222i	0.893509	−	0.554224i
$411$	−13.1130			−0.646819
$412$	33.8774	−	46.6282i	1.66902	−	2.29721i
$413$	−6.58786	−	6.58786i	−0.324167	−	0.324167i
$414$	0.523645	+	1.61161i	0.0257357	+	0.0792064i
$415$	−12.9106	+	4.19490i	−0.633755	+	0.205919i
$416$	41.4355	−	6.56274i	2.03154	−	0.321765i
$417$	−3.67683	−	0.582353i	−0.180055	−	0.0285179i
$418$	12.7523	+	4.14347i	0.623735	+	0.202664i
$419$		−	8.92254i		−	0.435895i	−0.975961	−	0.217947i	$-0.930064\pi$
$419$		−	8.92254i		−	0.435895i	0.975961	−	0.217947i	$-0.0699361\pi$
$420$	−4.39321	+	13.5209i	−0.214367	+	0.659753i
$421$	17.2160	−	8.77197i	0.839054	−	0.427520i	0.0190099	−	0.999819i	$-0.493949\pi$
$421$	17.2160	−	8.77197i	0.839054	−	0.427520i	0.820045	+	0.572300i	$0.193949\pi$
$422$	−27.5695	+	54.1081i	−1.34206	+	2.63394i
$423$	−0.0800109	−	0.505169i	−0.00389026	−	0.0245622i
$424$	−68.2001	+	68.2001i	−3.31209	+	3.31209i
$425$	7.09983	+	3.61754i	0.344392	+	0.175477i
$426$	−12.1558	+	8.83170i	−0.588950	+	0.427897i
$427$	0.917921	+	1.80152i	0.0444213	+	0.0871817i
$428$	−22.2634	−	16.1753i	−1.07614	−	0.781864i
$429$	−0.477550	+	3.01513i	−0.0230563	+	0.145572i
$430$	−2.37442	−	3.26811i	−0.114505	−	0.157602i
$431$	11.6004	+	15.9666i	0.558773	+	0.769085i	0.991170	−	0.132598i	$-0.0423320\pi$
$431$	11.6004	+	15.9666i	0.558773	+	0.769085i	−0.432397	+	0.901683i	$0.642332\pi$
$432$	−12.2254	+	77.1880i	−0.588193	+	3.71371i
$433$	−8.46295	−	6.14869i	−0.406703	−	0.295487i	0.365562	−	0.930787i	$-0.380877\pi$
$433$	−8.46295	−	6.14869i	−0.406703	−	0.295487i	−0.772266	+	0.635299i	$0.780877\pi$
$434$	−2.51081	−	4.92774i	−0.120523	−	0.236539i
$435$	2.62172	−	1.90479i	0.125702	−	0.0913276i
$436$	39.5880	+	20.1711i	1.89592	+	0.966019i
$437$	−24.2243	+	24.2243i	−1.15881	+	1.15881i
$438$	0.449894	+	2.84052i	0.0214968	+	0.135725i
$439$	13.6513	−	26.7922i	0.651540	−	1.27872i	−0.294803	−	0.955558i	$-0.595254\pi$
$439$	13.6513	−	26.7922i	0.651540	−	1.27872i	0.946344	−	0.323162i	$-0.104746\pi$
$440$	−9.74213	+	4.96386i	−0.464438	+	0.236643i
$441$	0.161137	−	0.495930i	0.00767321	−	0.0236157i
$442$			11.4465i			0.544456i
$443$	−20.8472	−	6.77365i	−0.990479	−	0.321826i	−0.231424	−	0.972853i	$-0.574338\pi$
$443$	−20.8472	−	6.77365i	−0.990479	−	0.321826i	−0.759055	+	0.651027i	$0.774338\pi$
$444$	61.0106	+	9.66313i	2.89543	+	0.458592i
$445$	−7.39059	+	1.17056i	−0.350348	+	0.0554896i
$446$	61.7069	−	20.0498i	2.92190	−	0.949384i
$447$	4.81391	+	14.8157i	0.227690	+	0.700759i
$448$	26.9986	+	26.9986i	1.27556	+	1.27556i
$449$	−2.93496	+	4.03963i	−0.138509	+	0.190642i	−0.872637	−	0.488370i	$-0.837592\pi$
$449$	−2.93496	+	4.03963i	−0.138509	+	0.190642i	0.734127	+	0.679012i	$0.237592\pi$
$450$	0.909950			0.0428955
$451$	5.85007	+	1.37100i	0.275469	+	0.0645580i
$452$	−10.5629			−0.496836
$453$	5.53482	−	7.61803i	0.260049	−	0.357926i
$454$	−27.7630	−	27.7630i	−1.30298	−	1.30298i
$455$	−0.839142	−	2.58261i	−0.0393396	−	0.121075i
$456$	83.7706	−	27.2187i	3.92292	−	1.27463i
$457$	12.1280	−	1.92089i	0.567326	−	0.0898556i	0.133819	−	0.991006i	$-0.457276\pi$
$457$	12.1280	−	1.92089i	0.567326	−	0.0898556i	0.433507	+	0.901150i	$0.357276\pi$
$458$	−55.8501	−	8.84579i	−2.60970	−	0.413336i
$459$	−10.9832	−	3.56867i	−0.512654	−	0.166571i
$460$		−	43.8788i		−	2.04586i
$461$	9.09708	−	27.9979i	0.423693	−	1.30399i	−0.480547	−	0.876969i	$-0.659562\pi$
$461$	9.09708	−	27.9979i	0.423693	−	1.30399i	0.904240	−	0.427025i	$-0.140438\pi$
$462$	−4.87397	+	2.48341i	−0.226758	+	0.115539i
$463$	8.27308	−	16.2368i	0.384483	−	0.754590i	−0.614940	−	0.788574i	$-0.710820\pi$
$463$	8.27308	−	16.2368i	0.384483	−	0.754590i	0.999422	+	0.0339843i	$0.0108196\pi$
$464$	−3.63035	−	22.9212i	−0.168535	−	1.06409i
$465$	2.51943	−	2.51943i	0.116836	−	0.116836i
$466$	−44.0238	−	22.4312i	−2.03936	−	1.03911i
$467$	−13.9475	+	10.1335i	−0.645414	+	0.468921i	−0.861706	−	0.507408i	$-0.830604\pi$
$467$	−13.9475	+	10.1335i	−0.645414	+	0.468921i	0.216292	+	0.976329i	$0.430604\pi$
$468$	0.435276	+	0.854277i	0.0201206	+	0.0394890i
$469$	14.4071	+	10.4673i	0.665256	+	0.483337i
$470$	−2.82460	+	17.8338i	−0.130289	+	0.822613i
$471$	−8.64726	−	11.9019i	−0.398445	−	0.548412i
$472$	−43.4563	−	59.8125i	−2.00024	−	2.75309i
$473$	0.178347	−	1.12604i	0.00820043	−	0.0517755i
$474$	32.5119	+	23.6213i	1.49332	+	1.08496i
$475$	8.35174	+	16.3912i	0.383204	+	0.752080i
$476$	−12.1714	+	8.84303i	−0.557875	+	0.405320i
$477$	−0.843122	−	0.429592i	−0.0386039	−	0.0196697i
$478$	43.9762	−	43.9762i	2.01142	−	2.01142i
$479$	3.50656	+	22.1396i	0.160219	+	1.01158i	0.928463	+	0.371425i	$0.121131\pi$
$479$	3.50656	+	22.1396i	0.160219	+	1.01158i	−0.768244	+	0.640157i	$0.778869\pi$
$480$	−21.9870	+	43.1518i	−1.00356	+	1.96960i
$481$	−10.5128	+	5.35656i	−0.479344	+	0.244238i
$482$	2.64417	−	8.13792i	0.120439	−	0.370672i
$483$		−	13.9761i		−	0.635935i
$484$	52.9749	+	17.2126i	2.40795	+	0.782391i
$485$	20.2143	+	3.20163i	0.917885	+	0.145379i
$486$	−2.64732	+	0.419294i	−0.120085	+	0.0190196i
$487$	−0.367574	+	0.119432i	−0.0166564	+	0.00541198i	−0.317333	−	0.948314i	$-0.602787\pi$
$487$	−0.367574	+	0.119432i	−0.0166564	+	0.00541198i	0.300677	+	0.953726i	$0.402787\pi$
$488$	4.95810	+	15.2595i	0.224443	+	0.690764i
$489$	−0.206047	−	0.206047i	−0.00931776	−	0.00931776i
$490$	−10.8203	+	14.8929i	−0.488812	+	0.672792i
$491$	−26.9030			−1.21411			−0.607057	−	0.794658i	$-0.707650\pi$
$491$	−26.9030			−1.21411			−0.607057	+	0.794658i	$0.707650\pi$
$492$	57.1486	−	24.0353i	2.57646	−	1.08359i
$493$	3.42934			0.154450
$494$	−15.5330	+	21.3793i	−0.698863	+	0.961902i
$495$	−0.0758521	−	0.0758521i	−0.00340930	−	0.00340930i
$496$	−7.88475	−	24.2668i	−0.354036	−	1.08961i
$497$	3.58752	−	1.16566i	0.160922	−	0.0522868i
$498$	−53.2307	+	8.43092i	−2.38533	+	0.377799i
$499$	−9.04346	−	1.43234i	−0.404841	−	0.0641205i	−0.0493065	−	0.998784i	$-0.515701\pi$
$499$	−9.04346	−	1.43234i	−0.404841	−	0.0641205i	−0.355534	+	0.934663i	$0.615701\pi$
$500$	−54.1786	−	17.6037i	−2.42294	−	0.787262i
$501$			10.7603i			0.480735i
$502$	−5.57529	+	17.1590i	−0.248837	+	0.765842i
$503$	8.04239	−	4.09780i	0.358592	−	0.182712i	−0.265408	−	0.964136i	$-0.585507\pi$
$503$	8.04239	−	4.09780i	0.358592	−	0.182712i	0.624000	+	0.781424i	$0.285507\pi$
$504$	−0.496572	+	0.974577i	−0.0221191	+	0.0434111i
$505$	1.78371	+	11.2619i	0.0793741	+	0.501149i
$506$	11.9383	−	11.9383i	0.530722	−	0.530722i
$507$	15.0143	+	7.65016i	0.666807	+	0.339755i
$508$	15.9963	−	11.6220i	0.709721	−	0.515643i
$509$	5.82573	+	11.4336i	0.258221	+	0.506787i	0.983326	−	0.181851i	$-0.0582088\pi$
$509$	5.82573	+	11.4336i	0.258221	+	0.506787i	−0.725105	+	0.688638i	$0.758209\pi$
$510$	−10.6905	−	7.76709i	−0.473383	−	0.343933i
$511$	0.112946	−	0.713115i	0.00499645	−	0.0315463i
$512$	31.3114	+	43.0965i	1.38378	+	1.90461i
$513$	−15.6713	−	21.5697i	−0.691906	−	0.952326i
$514$	2.92512	−	18.4685i	0.129021	−	0.814609i
$515$	−10.2818	−	7.47015i	−0.453069	−	0.329174i
$516$	−5.34050	−	10.4813i	−0.235103	−	0.461415i
$517$	−4.12266	+	2.99529i	−0.181314	+	0.131733i
$518$	−18.8380	−	9.59844i	−0.827694	−	0.421731i
$519$	23.7929	−	23.7929i	1.04439	−	1.04439i
$520$	−3.37101	−	21.2837i	−0.147829	−	0.933353i
$521$	17.5110	−	34.3672i	0.767169	−	1.50565i	−0.0930117	−	0.995665i	$-0.529649\pi$
$521$	17.5110	−	34.3672i	0.767169	−	1.50565i	0.860181	−	0.509989i	$-0.170351\pi$
$522$	0.348933	−	0.177790i	0.0152724	−	0.00778167i
$523$	−5.49317	+	16.9063i	−0.240200	+	0.739259i	0.756189	+	0.654353i	$0.227059\pi$
$523$	−5.49317	+	16.9063i	−0.240200	+	0.739259i	−0.996389	+	0.0849058i	$0.972941\pi$
$524$		−	43.6838i		−	1.90834i
$525$	−7.13766	−	2.31917i	−0.311513	−	0.101217i
$526$	−34.8116	−	5.51361i	−1.51786	−	0.240405i
$527$	3.72409	−	0.589838i	0.162224	−	0.0256937i
$528$	−24.0020	+	7.79872i	−1.04455	+	0.339396i
$529$	6.22243	+	19.1507i	0.270541	+	0.832638i
$530$	23.6212	+	23.6212i	1.02604	+	1.02604i
$531$	0.426346	−	0.586815i	0.0185018	−	0.0254656i
$532$	−34.7332			−1.50588
$533$	−6.13265	+	10.1304i	−0.265635	+	0.438795i
$534$	−29.7073			−1.28556
$535$	−3.56675	+	4.90921i	−0.154204	+	0.212244i
$536$	99.9257	+	99.9257i	4.31613	+	4.31613i
$537$	−7.08742	−	21.8128i	−0.305845	−	0.941294i
$538$	−41.9605	+	13.6338i	−1.80904	+	0.587794i
$539$	−5.13141	+	0.812736i	−0.221026	+	0.0350070i
$540$	33.7284	+	5.34205i	1.45144	+	0.229885i
$541$	−23.9953	−	7.79656i	−1.03164	−	0.335200i	−0.256202	−	0.966623i	$-0.582471\pi$
$541$	−23.9953	−	7.79656i	−1.03164	−	0.335200i	−0.775439	+	0.631423i	$0.782471\pi$
$542$			56.8164i			2.44047i
$543$	6.45832	−	19.8767i	0.277153	−	0.852989i
$544$	−45.6649	+	23.2674i	−1.95787	+	0.997582i
$545$	4.44783	−	8.72936i	0.190524	−	0.373925i
$546$	−1.68651	−	10.6482i	−0.0721759	−	0.455701i
$547$	2.04384	−	2.04384i	0.0873882	−	0.0873882i	−0.662061	−	0.749450i	$-0.730318\pi$
$547$	2.04384	−	2.04384i	0.0873882	−	0.0873882i	0.749450	+	0.662061i	$0.230318\pi$
$548$	36.5611	+	18.6288i	1.56181	+	0.795783i
$549$	−0.127350	+	0.0925254i	−0.00543518	+	0.00394889i
$550$	−4.11593	−	8.07796i	−0.175504	−	0.344445i
$551$	6.40518	+	4.65364i	0.272870	+	0.198252i
$552$	17.3497	−	109.542i	0.738454	−	4.66242i
$553$	−5.93014	−	8.16214i	−0.252175	−	0.347090i
$554$	7.82694	+	10.7729i	0.332535	+	0.457695i
$555$	2.13077	−	13.4532i	0.0904462	−	0.571055i
$556$	9.42423	+	6.84710i	0.399676	+	0.290382i
$557$	2.79864	+	5.49264i	0.118582	+	0.232731i	0.942666	−	0.333737i	$-0.108310\pi$
$557$	2.79864	+	5.49264i	0.118582	+	0.232731i	−0.824084	+	0.566468i	$0.808310\pi$
$558$	0.348344	−	0.253087i	0.0147466	−	0.0107140i
$559$	2.00203	+	1.02008i	0.0846767	+	0.0431450i
$560$	15.8742	−	15.8742i	0.670808	−	0.670808i
$561$	−0.583402	−	3.68346i	−0.0246313	−	0.155516i
$562$	−7.23927	+	14.2079i	−0.305370	+	0.599323i
$563$	−26.9664	+	13.7401i	−1.13650	+	0.579075i	−0.917928	−	0.396746i	$-0.870139\pi$
$563$	−26.9664	+	13.7401i	−1.13650	+	0.579075i	−0.218570	+	0.975821i	$0.570139\pi$
$564$	−16.2481	+	50.0066i	−0.684170	+	2.10566i
$565$			2.32917i			0.0979891i
$566$	37.6828	+	12.2439i	1.58392	+	0.514648i
$567$	11.0806	+	1.75500i	0.465342	+	0.0737030i
$568$	29.5653	−	4.68268i	1.24053	−	0.196481i
$569$	19.3960	−	6.30213i	0.813121	−	0.264199i	0.127202	−	0.991877i	$-0.459400\pi$
$569$	19.3960	−	6.30213i	0.813121	−	0.264199i	0.685919	+	0.727678i	$0.259400\pi$
$570$	−9.42725	−	29.0141i	−0.394864	−	1.21527i
$571$	20.9716	+	20.9716i	0.877633	+	0.877633i	0.993289	−	0.115656i	$-0.0368971\pi$
$571$	20.9716	+	20.9716i	0.877633	+	0.877633i	−0.115656	+	0.993289i	$0.536897\pi$
$572$	5.61487	−	7.72821i	0.234770	−	0.323133i
$573$	−0.759253			−0.0317182
$574$	−21.1450	+	1.77946i	−0.882577	+	0.0742733i
$575$	23.1636			0.965987
$576$	−1.74727	+	2.40490i	−0.0728027	+	0.100204i
$577$	−22.9911	−	22.9911i	−0.957132	−	0.957132i	0.0419858	−	0.999118i	$-0.486632\pi$
$577$	−22.9911	−	22.9911i	−0.957132	−	0.957132i	−0.999118	+	0.0419858i	$0.986632\pi$
$578$	10.0697	+	30.9914i	0.418844	+	1.28907i
$579$	−35.4736	+	11.5261i	−1.47423	+	0.479008i
$580$	−10.0157	+	1.58633i	−0.415880	+	0.0658690i
$581$	13.3636	+	2.11659i	0.554417	+	0.0878110i
$582$	77.2768	+	25.1087i	3.20323	+	1.04079i
$583$			9.42785i			0.390462i
$584$	1.77050	−	5.44905i	0.0732639	−	0.225483i
$585$	0.188373	−	0.0959807i	0.00778825	−	0.00396831i
$586$	24.5053	−	48.0943i	1.01230	−	1.98676i
$587$	3.81641	+	24.0959i	0.157520	+	0.994543i	0.932135	+	0.362110i	$0.117944\pi$
$587$	3.81641	+	24.0959i	0.157520	+	0.994543i	−0.774615	+	0.632433i	$0.782056\pi$
$588$	−37.9056	+	37.9056i	−1.56320	+	1.56320i
$589$	7.75611	+	3.95194i	0.319585	+	0.162837i
$590$	−20.7161	+	15.0512i	−0.852870	+	0.619646i
$591$	18.7150	+	36.7302i	0.769830	+	1.51088i
$592$	−78.9134	−	57.3340i	−3.24332	−	2.35641i
$593$	2.72495	−	17.2047i	0.111900	−	0.706512i	−0.866405	−	0.499342i	$-0.833575\pi$
$593$	2.72495	−	17.2047i	0.111900	−	0.706512i	0.978305	−	0.207169i	$-0.0664250\pi$
$594$	7.72319	+	10.6301i	0.316886	+	0.436156i
$595$	1.94994	+	2.68386i	0.0799396	+	0.110027i
$596$	7.62575	−	48.1471i	0.312363	−	1.97218i
$597$	7.50238	+	5.45080i	0.307052	+	0.223086i
$598$	15.1063	+	29.6478i	0.617744	+	1.21239i
$599$	11.5445	−	8.38758i	0.471696	−	0.342707i	−0.326406	−	0.945230i	$-0.605838\pi$
$599$	11.5445	−	8.38758i	0.471696	−	0.342707i	0.798102	+	0.602522i	$0.205838\pi$
$600$	−53.0646	−	27.0378i	−2.16635	−	1.10381i
$601$	−28.1452	+	28.1452i	−1.14807	+	1.14807i	−0.161133	+	0.986933i	$0.551515\pi$
$601$	−28.1452	+	28.1452i	−1.14807	+	1.14807i	−0.986933	+	0.161133i	$0.948485\pi$
$602$	0.629849	+	3.97671i	0.0256707	+	0.162079i
$603$	−0.629431	+	1.23533i	−0.0256324	+	0.0503065i
$604$	−26.2543	+	13.3772i	−1.06827	+	0.544312i
$605$	3.79547	−	11.6813i	0.154308	−	0.474911i
$606$			45.2685i			1.83891i
$607$	−10.7097	−	3.47978i	−0.434691	−	0.141240i	0.0834937	−	0.996508i	$-0.473392\pi$
$607$	−10.7097	−	3.47978i	−0.434691	−	0.141240i	−0.518185	+	0.855269i	$0.673392\pi$
$608$	−116.865	−	18.5096i	−4.73950	−	0.750663i
$609$	−3.19017	+	0.505273i	−0.129272	+	0.0204747i
$610$	5.28514	−	1.71725i	0.213989	−	0.0695292i
$611$	−3.10354	−	9.55171i	−0.125556	−	0.386421i
$612$	−0.828231	−	0.828231i	−0.0334793	−	0.0334793i
$613$	22.6203	−	31.1342i	0.913625	−	1.25750i	−0.0522884	−	0.998632i	$-0.516652\pi$
$613$	22.6203	−	31.1342i	0.913625	−	1.25750i	0.965913	−	0.258865i	$-0.0833485\pi$
$614$	−26.9872			−1.08912
$615$	−5.29991	−	12.6016i	−0.213713	−	0.508145i
$616$	10.8978			0.439084
$617$	−12.9147	+	17.7756i	−0.519928	+	0.715619i	−0.985554	−	0.169362i	$-0.945829\pi$
$617$	−12.9147	+	17.7756i	−0.519928	+	0.715619i	0.465626	+	0.884982i	$0.345829\pi$
$618$	−35.6779	−	35.6779i	−1.43517	−	1.43517i
$619$	6.35485	+	19.5582i	0.255423	+	0.786111i	0.993746	+	0.111664i	$0.0356180\pi$
$619$	6.35485	+	19.5582i	0.255423	+	0.786111i	−0.738323	+	0.674447i	$0.764382\pi$
$620$	−10.6037	+	3.44535i	−0.425855	+	0.138369i
$621$	−33.1575	+	5.25164i	−1.33057	+	0.210741i
$622$	68.6811	+	10.8780i	2.75386	+	0.436169i
$623$	7.09302	+	2.30466i	0.284176	+	0.0923343i
$624$		−	49.7388i		−	1.99115i
$625$	1.56754	−	4.82438i	0.0627014	−	0.192975i
$626$	64.0140	−	32.6168i	2.55851	−	1.30363i
$627$	3.90881	−	7.67148i	0.156103	−	0.306369i
$628$	7.20156	+	45.4689i	0.287374	+	1.81440i
$629$	10.1923	−	10.1923i	0.406394	−	0.406394i
$630$	0.337546	+	0.171988i	0.0134482	+	0.00685218i
$631$	−29.0459	+	21.1031i	−1.15630	+	0.840102i	−0.989306	−	0.145856i	$-0.953406\pi$
$631$	−29.0459	+	21.1031i	−1.15630	+	0.840102i	−0.166995	+	0.985958i	$0.553406\pi$
$632$	−36.3469	−	71.3349i	−1.44580	−	2.83755i
$633$	31.5468	+	22.9201i	1.25387	+	0.910992i
$634$	8.90083	−	56.1976i	0.353497	−	2.23189i
$635$	−2.56271	−	3.52727i	−0.101698	−	0.139976i
$636$	57.1784	+	78.6994i	2.26727	+	3.12063i
$637$	1.60178	−	10.1133i	0.0634650	−	0.400702i
$638$	−3.15662	−	2.29342i	−0.124972	−	0.0907973i
$639$	0.133327	+	0.261669i	0.00527434	+	0.0103515i
$640$	40.3511	−	29.3168i	1.59502	−	1.15885i
$641$	−23.1194	−	11.7799i	−0.913160	−	0.465278i	−0.0667257	−	0.997771i	$-0.521255\pi$
$641$	−23.1194	−	11.7799i	−0.913160	−	0.465278i	−0.846434	+	0.532493i	$0.821255\pi$
$642$	−17.0350	+	17.0350i	−0.672318	+	0.672318i
$643$	6.58370	+	41.5679i	0.259636	+	1.63928i	0.680927	+	0.732351i	$0.261577\pi$
$643$	6.58370	+	41.5679i	0.259636	+	1.63928i	−0.421291	+	0.906926i	$0.638423\pi$
$644$	−19.8549	+	38.9674i	−0.782392	+	1.53553i
$645$	−2.31119	+	1.17761i	−0.0910030	+	0.0463684i
$646$	9.97627	−	30.7038i	0.392511	−	1.20802i
$647$			25.3408i			0.996251i	0.867105	+	0.498125i	$0.165978\pi$
$647$			25.3408i			0.996251i	−0.867105	+	0.498125i	$0.834022\pi$
$648$	84.6691	+	27.5107i	3.32612	+	1.08072i
$649$	−7.13784	−	1.13052i	−0.280185	−	0.0443769i
$650$	17.6480	−	2.79517i	0.692211	−	0.109635i
$651$	−3.37745	+	1.09740i	−0.132373	+	0.0430105i
$652$	0.281772	+	0.867204i	0.0110350	+	0.0339623i
$653$	−10.0983	−	10.0983i	−0.395178	−	0.395178i	0.481350	−	0.876528i	$-0.340147\pi$
$653$	−10.0983	−	10.0983i	−0.395178	−	0.395178i	−0.876528	+	0.481350i	$0.840147\pi$
$654$	22.8625	−	31.4675i	0.893994	−	1.23048i
$655$	−9.63252			−0.376374
$656$	−97.6379	−	7.15227i	−3.81212	−	0.279249i
$657$	0.0562113			0.00219301
$658$	10.5781	−	14.5595i	0.412378	−	0.567590i
$659$	3.30690	+	3.30690i	0.128818	+	0.128818i	0.768576	−	0.639758i	$-0.220965\pi$
$659$	3.30690	+	3.30690i	0.128818	+	0.128818i	−0.639758	+	0.768576i	$0.720965\pi$
$660$	3.40776	+	10.4880i	0.132647	+	0.408245i
$661$	−16.5128	+	5.36534i	−0.642274	+	0.208688i	−0.612005	−	0.790854i	$-0.709637\pi$
$661$	−16.5128	+	5.36534i	−0.642274	+	0.208688i	−0.0302696	+	0.999542i	$0.509637\pi$
$662$	17.2308	−	2.72909i	0.669693	−	0.106069i
$663$	7.25955	+	1.14980i	0.281938	+	0.0446546i
$664$	102.114	+	33.1789i	3.96279	+	1.28759i
$665$			7.65887i			0.296998i
$666$	0.508652	−	1.56547i	0.0197098	−	0.0606607i
$667$	8.88240	−	4.52581i	0.343928	−	0.175240i
$668$	15.2864	−	30.0013i	0.591449	−	1.16078i
$669$	−6.51742	−	41.1494i	−0.251978	−	1.59093i
$670$	34.6094	−	34.6094i	1.33708	−	1.33708i
$671$	1.39742	+	0.712021i	0.0539468	+	0.0274872i
$672$	39.0518	−	28.3728i	1.50646	−	1.09450i
$673$	−1.92976	−	3.78737i	−0.0743869	−	0.145992i	0.850818	−	0.525461i	$-0.176107\pi$
$673$	−1.92976	−	3.78737i	−0.0743869	−	0.145992i	−0.925205	+	0.379468i	$0.876107\pi$
$674$	24.5201	+	17.8149i	0.944479	+	0.686205i
$675$	−2.82006	+	17.8051i	−0.108544	+	0.685320i
$676$	−30.9939	−	42.6595i	−1.19207	−	1.64075i
$677$	−20.9582	−	28.8465i	−0.805490	−	1.10866i	−0.992004	−	0.126209i	$-0.959719\pi$
$677$	−20.9582	−	28.8465i	−0.805490	−	1.10866i	0.186514	−	0.982452i	$-0.440281\pi$
$678$	−1.44656	+	9.13324i	−0.0555550	+	0.350760i
$679$	−16.5030	−	11.9901i	−0.633326	−	0.460138i
$680$	11.9515	+	23.4562i	0.458320	+	0.899503i
$681$	−20.3965	+	14.8189i	−0.781595	+	0.567862i
$682$	−3.82239	−	1.94760i	−0.146367	−	0.0745776i
$683$	33.1183	−	33.1183i	1.26724	−	1.26724i	0.319726	−	0.947510i	$-0.396409\pi$
$683$	33.1183	−	33.1183i	1.26724	−	1.26724i	0.947510	−	0.319726i	$-0.103591\pi$
$684$	−0.423021	−	2.67085i	−0.0161746	−	0.102122i
$685$	4.10775	−	8.06191i	0.156949	−	0.308030i
$686$	37.0175	−	18.8614i	1.41334	−	0.720130i
$687$	−11.2202	+	34.5324i	−0.428079	+	1.31749i
$688$			18.5756i			0.708189i
$689$	−17.6715	−	5.74182i	−0.673231	−	0.218746i
$690$	−37.9400	−	6.00911i	−1.44435	−	0.228763i
$691$	−33.4395	+	5.29630i	−1.27210	+	0.201481i	−0.755729	−	0.654884i	$-0.772717\pi$
$691$	−33.4395	+	5.29630i	−1.27210	+	0.201481i	−0.516371	+	0.856365i	$0.672717\pi$
$692$	−100.139	+	32.5371i	−3.80672	+	1.23688i
$693$	0.0330393	+	0.101684i	0.00125506	+	0.00386267i
$694$	2.45436	+	2.45436i	0.0931664	+	0.0931664i
$695$	1.50982	−	2.07809i	0.0572708	−	0.0788266i
$696$	−25.6311			−0.971546
$697$	3.30097	−	14.0852i	0.125033	−	0.533517i
$698$	38.8744			1.47142
$699$	−18.6484	+	25.6673i	−0.705346	+	0.970826i
$700$	16.6061	+	16.6061i	0.627653	+	0.627653i
$701$	−2.77956	−	8.55460i	−0.104982	−	0.323103i	0.884744	−	0.466078i	$-0.154333\pi$
$701$	−2.77956	−	8.55460i	−0.104982	−	0.323103i	−0.989726	+	0.142975i	$0.954333\pi$
$702$	−24.6285	+	8.00230i	−0.929544	+	0.302027i
$703$	32.8678	−	5.20575i	1.23963	−	0.196338i
$704$	29.2525	+	4.63314i	1.10250	+	0.174618i
$705$	11.0267	+	3.58280i	0.415291	+	0.134936i
$706$		−	2.80153i		−	0.105437i
$707$	3.51188	−	10.8085i	0.132078	−	0.406494i
$708$	−66.4398	+	33.8528i	−2.49696	+	1.27227i
$709$	−6.86482	+	13.4730i	−0.257814	+	0.505988i	−0.983241	−	0.182311i	$-0.941642\pi$
$709$	−6.86482	+	13.4730i	−0.257814	+	0.505988i	0.725427	+	0.688299i	$0.241642\pi$
$710$	−1.62185	−	10.2400i	−0.0608671	−	0.384300i
$711$	0.555413	−	0.555413i	0.0208296	−	0.0208296i
$712$	52.7327	+	26.8687i	1.97624	+	1.00695i
$713$	8.86739	−	6.44254i	0.332087	−	0.241275i
$714$	5.97932	+	11.7351i	0.223770	+	0.439174i
$715$	−1.70411	−	1.23811i	−0.0637302	−	0.0463027i
$716$	−11.2272	+	70.8860i	−0.419581	+	2.64913i
$717$	−23.4729	−	32.3077i	−0.876613	−	1.20655i
$718$	−18.0576	−	24.8541i	−0.673902	−	0.927547i
$719$	6.05643	−	38.2388i	0.225867	−	1.42607i	−0.570522	−	0.821282i	$-0.693259\pi$
$719$	6.05643	−	38.2388i	0.225867	−	1.42607i	0.796389	−	0.604785i	$-0.206741\pi$
$720$	1.41400	+	1.02733i	0.0526966	+	0.0382863i
$721$	5.75073	+	11.2864i	0.214168	+	0.420329i
$722$	18.1901	−	13.2159i	0.676965	−	0.491844i
$723$	−4.89558	−	2.49442i	−0.182069	−	0.0927686i
$724$	−46.2441	+	46.2441i	−1.71865	+	1.71865i
$725$	−0.837423	−	5.28728i	−0.0311011	−	0.196365i
$726$	22.1377	−	43.4478i	0.821609	−	1.61250i
$727$	23.9407	−	12.1984i	0.887912	−	0.452414i	0.0503346	−	0.998732i	$-0.483971\pi$
$727$	23.9407	−	12.1984i	0.887912	−	0.452414i	0.837577	+	0.546319i	$0.183971\pi$
$728$	−6.63705	+	20.4268i	−0.245986	+	0.757066i
$729$		−	26.1000i		−	0.966665i
$730$	−1.88729	−	0.613216i	−0.0698516	−	0.0226962i
$731$	−2.71118	−	0.429408i	−0.100277	−	0.0158822i
$732$	15.9833	−	2.53151i	0.590760	−	0.0935672i
$733$	4.87811	−	1.58499i	0.180177	−	0.0585431i	−0.217539	−	0.976052i	$-0.569803\pi$
$733$	4.87811	−	1.58499i	0.180177	−	0.0585431i	0.397716	+	0.917509i	$0.369803\pi$
$734$	24.3041	+	74.8002i	0.897079	+	2.76093i
$735$	8.35838	+	8.35838i	0.308304	+	0.308304i
$736$	−87.5706	+	120.531i	−3.22789	+	4.44281i
$737$	13.8135			0.508828
$738$	−0.394362	−	1.60430i	−0.0145167	−	0.0590550i
$739$	1.40461			0.0516695			0.0258348	−	0.999666i	$-0.491776\pi$
$739$	1.40461			0.0516695			0.0258348	+	0.999666i	$0.491776\pi$
$740$	−25.0529	+	34.4823i	−0.920962	+	1.26760i
$741$	11.9988	+	11.9988i	0.440787	+	0.440787i
$742$	−10.2888	−	31.6657i	−0.377714	−	1.16248i
$743$	−8.77872	+	2.85238i	−0.322060	+	0.104644i	−0.465585	−	0.885003i	$-0.654156\pi$
$743$	−8.77872	+	2.85238i	−0.322060	+	0.104644i	0.143525	+	0.989647i	$0.454156\pi$
$744$	−27.8341	+	4.40849i	−1.02045	+	0.161623i
$745$	−10.6167	−	1.68152i	−0.388966	−	0.0616061i
$746$	−88.6254	−	28.7961i	−3.24481	−	1.05430i
$747$			1.05339i			0.0385415i
$748$	−3.60622	+	11.0988i	−0.131856	+	0.405812i
$749$	5.38890	−	2.74578i	0.196906	−	0.100329i
$750$	−22.6408	+	44.4350i	−0.826724	+	1.62254i
$751$	−4.42188	−	27.9186i	−0.161357	−	1.01877i	−0.926880	−	0.375358i	$-0.877520\pi$
$751$	−4.42188	−	27.9186i	−0.161357	−	1.01877i	0.765523	−	0.643408i	$-0.222480\pi$
$752$	58.7103	−	58.7103i	2.14094	−	2.14094i
$753$	10.3224	+	5.25954i	0.376170	+	0.191668i
$754$	6.22124	−	4.52000i	0.226564	−	0.164609i
$755$	2.94975	+	5.78922i	0.107352	+	0.210691i
$756$	−27.5358	−	20.0060i	−1.00147	−	0.727610i
$757$	2.19110	−	13.8341i	0.0796371	−	0.502809i	−0.915338	−	0.402686i	$-0.868077\pi$
$757$	2.19110	−	13.8341i	0.0796371	−	0.502809i	0.994975	−	0.100122i	$-0.0319234\pi$
$758$	−11.2645	−	15.5042i	−0.409145	−	0.563139i
$759$	−6.37224	−	8.77064i	−0.231298	−	0.318354i
$760$	−9.50762	+	60.0287i	−0.344877	+	2.17747i
$761$	38.0493	+	27.6444i	1.37929	+	1.00211i	0.996946	+	0.0780880i	$0.0248815\pi$
$761$	38.0493	+	27.6444i	1.37929	+	1.00211i	0.382339	+	0.924022i	$0.375119\pi$
$762$	−7.85835	−	15.4229i	−0.284678	−	0.558712i
$763$	−7.89995	+	5.73965i	−0.285998	+	0.207789i
$764$	2.11691	+	1.07862i	0.0765870	+	0.0390230i
$765$	−0.182629	+	0.182629i	−0.00660298	+	0.00660298i
$766$	8.17000	+	51.5834i	0.295194	+	1.86378i
$767$	6.46619	−	12.6906i	0.233480	−	0.458231i
$768$	77.4992	−	39.4878i	2.79651	−	1.42489i
$769$	−6.58433	+	20.2645i	−0.237437	+	0.730756i	0.759352	+	0.650680i	$0.225516\pi$
$769$	−6.58433	+	20.2645i	−0.237437	+	0.730756i	−0.996789	+	0.0800756i	$0.974484\pi$
$770$		−	3.77447i		−	0.136022i
$771$	−11.4191	−	3.71030i	−0.411250	−	0.133623i
$772$	115.280	+	18.2586i	4.14902	+	0.657140i
$773$	39.6933	−	6.28681i	1.42767	−	0.226121i	0.605719	−	0.795679i	$-0.292886\pi$
$773$	39.6933	−	6.28681i	1.42767	−	0.226121i	0.821951	+	0.569558i	$0.192886\pi$
$774$	−0.298122	+	0.0968658i	−0.0107158	+	0.00348177i
$775$	−1.81880	−	5.59768i	−0.0653331	−	0.201075i
$776$	−114.463	−	114.463i	−4.10897	−	4.10897i
$777$	−7.97974	+	10.9832i	−0.286272	+	0.394019i
$778$	−50.2234			−1.80059
$779$	25.2792	−	21.8284i	0.905720	−	0.782083i
$780$	−21.7341			−0.778205
$781$	1.71986	−	2.36719i	0.0615415	−	0.0847046i
$782$	−28.7439	−	28.7439i	−1.02788	−	1.02788i
$783$	2.39746	+	7.37863i	0.0856783	+	0.263691i
$784$	80.5067	−	26.1582i	2.87524	−	0.934222i
$785$	10.0261	−	1.58798i	0.357848	−	0.0566775i
$786$	−37.7714	−	5.98240i	−1.34726	−	0.213385i
$787$	−16.3451	−	5.31086i	−0.582642	−	0.189312i	0.00284204	−	0.999996i	$-0.499095\pi$
$787$	−16.3451	−	5.31086i	−0.582642	−	0.189312i	−0.585484	+	0.810684i	$0.699095\pi$
$788$		−	128.996i		−	4.59529i
$789$	−6.99362	+	21.5242i	−0.248980	+	0.766280i
$790$	−24.7070	+	12.5888i	−0.879034	+	0.447890i
$791$	1.05394	−	2.06846i	0.0374736	−	0.0735461i
$792$	0.132726	+	0.837997i	0.00471620	+	0.0297769i
$793$	−2.18567	+	2.18567i	−0.0776156	+	0.0776156i
$794$	20.3208	+	10.3540i	0.721158	+	0.367449i
$795$	17.3536	−	12.6082i	0.615470	−	0.447165i
$796$	−13.1742	−	25.8557i	−0.466946	−	0.916432i
$797$	26.3389	+	19.1363i	0.932971	+	0.677843i	0.946719	−	0.322062i	$-0.104376\pi$
$797$	26.3389	+	19.1363i	0.932971	+	0.677843i	−0.0137472	+	0.999906i	$0.504376\pi$
$798$	−4.75664	+	30.0323i	−0.168383	+	1.06313i
$799$	7.21177	+	9.92616i	0.255134	+	0.351162i
$800$	47.0242	+	64.7233i	1.66256	+	2.28831i
$801$	−0.0908325	+	0.573494i	−0.00320941	+	0.0202634i
$802$	9.31216	+	6.76568i	0.328824	+	0.238904i
$803$	−0.254257	−	0.499008i	−0.00897255	−	0.0176096i
$804$	115.309	−	83.7769i	4.06664	−	2.95459i
$805$	8.59253	+	4.37811i	0.302847	+	0.154308i
$806$	5.97852	−	5.97852i	0.210584	−	0.210584i
$807$	4.43182	+	27.9814i	0.156008	+	0.984993i
$808$	40.9429	−	80.3550i	1.44037	−	2.82688i
$809$	−29.0682	+	14.8110i	−1.02198	+	0.520727i	−0.882904	−	0.469554i	$-0.844415\pi$
$809$	−29.0682	+	14.8110i	−1.02198	+	0.520727i	−0.139081	+	0.990281i	$0.544415\pi$
$810$	9.52836	−	29.3253i	0.334793	−	1.03039i
$811$			7.47871i			0.262613i	0.991342	+	0.131306i	$0.0419172\pi$
$811$			7.47871i			0.262613i	−0.991342	+	0.131306i	$0.958083\pi$
$812$	9.61245	+	3.12327i	0.337331	+	0.109605i
$813$	36.0338	+	5.70719i	1.26376	+	0.200160i
$814$	−16.1980	+	2.56551i	−0.567739	+	0.0899211i
$815$	0.191223	−	0.0621322i	0.00669826	−	0.00217640i
$816$	18.7770	+	57.7897i	0.657327	+	2.02305i
$817$	−4.48111	−	4.48111i	−0.156774	−	0.156774i
$818$	−62.2547	+	85.6863i	−2.17669	+	2.99595i
$819$	−0.210718			−0.00736310
$820$	−3.12529	+	42.6642i	−0.109140	+	1.48990i
$821$	−31.8344			−1.11103			−0.555514	−	0.831507i	$-0.687479\pi$
$821$	−31.8344			−1.11103			−0.555514	+	0.831507i	$0.687479\pi$
$822$	21.1144	−	29.0615i	0.736450	−	1.01364i
$823$	−26.9979	−	26.9979i	−0.941087	−	0.941087i	0.0572719	−	0.998359i	$-0.481760\pi$
$823$	−26.9979	−	26.9979i	−0.941087	−	0.941087i	−0.998359	+	0.0572719i	$0.981760\pi$
$824$	31.0623	+	95.5998i	1.08210	+	3.33038i
$825$	−5.53660	+	1.79895i	−0.192760	+	0.0626314i
$826$	25.2079	−	3.99254i	0.877094	−	0.138918i
$827$	−26.4709	−	4.19258i	−0.920485	−	0.145790i	−0.321830	−	0.946798i	$-0.604298\pi$
$827$	−26.4709	−	4.19258i	−0.920485	−	0.145790i	−0.598655	+	0.801007i	$0.704298\pi$
$828$	−3.23825	−	1.05217i	−0.112537	−	0.0365655i
$829$			38.1519i			1.32507i	0.749031	+	0.662535i	$0.230519\pi$
$829$			38.1519i			1.32507i	−0.749031	+	0.662535i	$0.769481\pi$
$830$	11.4915	−	35.3674i	0.398877	−	1.22762i
$831$	7.61851	−	3.88182i	0.264283	−	0.134659i
$832$	−26.4999	+	52.0090i	−0.918720	+	1.80309i
$833$	1.95683	+	12.3549i	0.0678001	+	0.428073i
$834$	7.21100	−	7.21100i	0.249697	−	0.249697i
$835$	−6.61544	−	3.37074i	−0.228937	−	0.116649i
$836$	−21.7967	+	15.8362i	−0.753854	+	0.547707i
$837$	3.87262	+	7.60045i	0.133857	+	0.262710i
$838$	19.7744	+	14.3669i	0.683095	+	0.496298i
$839$	−8.25907	+	52.1457i	−0.285135	+	1.80027i	0.263986	+	0.964527i	$0.414963\pi$
$839$	−8.25907	+	52.1457i	−0.285135	+	1.80027i	−0.549120	+	0.835743i	$0.685037\pi$
$840$	−14.5740	−	20.0593i	−0.502849	−	0.692112i
$841$	15.6916	+	21.5976i	0.541090	+	0.744746i
$842$	−8.28018	+	52.2790i	−0.285354	+	1.80165i
$843$	8.28365	+	6.01842i	0.285304	+	0.207285i
$844$	−55.3961	−	108.721i	−1.90681	−	3.74233i
$845$	−9.40665	+	6.83433i	−0.323599	+	0.235108i
$846$	1.24840	+	0.636093i	0.0429210	+	0.0218693i
$847$	−8.65633	+	8.65633i	−0.297435	+	0.297435i
$848$	−24.0300	−	151.720i	−0.825194	−	5.21007i
$849$	11.5505	−	22.6690i	0.396411	−	0.777999i
$850$	−19.4494	+	9.90994i	−0.667107	+	0.339908i
$851$	12.9482	−	39.8503i	0.443857	−	1.36605i
$852$		−	30.1909i		−	1.03432i
$853$	10.6787	+	3.46971i	0.365631	+	0.118801i	0.486069	−	0.873920i	$-0.338430\pi$
$853$	10.6787	+	3.46971i	0.365631	+	0.118801i	−0.120439	+	0.992721i	$0.538430\pi$
$854$	−5.47061	−	0.866459i	−0.187200	−	0.0296496i
$855$	−0.588937	+	0.0932784i	−0.0201412	+	0.00319005i
$856$	45.6457	−	14.8312i	1.56014	−	0.506920i
$857$	−2.69200	−	8.28512i	−0.0919569	−	0.283014i	0.894492	−	0.447084i	$-0.147538\pi$
$857$	−2.69200	−	8.28512i	−0.0919569	−	0.283014i	−0.986449	+	0.164070i	$0.947538\pi$
$858$	−5.91328	−	5.91328i	−0.201876	−	0.201876i
$859$	16.6627	−	22.9343i	0.568525	−	0.782508i	−0.423854	−	0.905731i	$-0.639323\pi$
$859$	16.6627	−	22.9343i	0.568525	−	0.782508i	0.992379	+	0.123223i	$0.0393230\pi$
$860$	8.11688			0.276783
$861$	−0.995453	+	13.5892i	−0.0339249	+	0.463120i
$862$	−54.0645			−1.84145
$863$	21.9985	−	30.2783i	0.748836	−	1.03068i	−0.249225	−	0.968446i	$-0.580176\pi$
$863$	21.9985	−	30.2783i	0.748836	−	1.03068i	0.998061	−	0.0622388i	$-0.0198241\pi$
$864$	−81.9869	−	81.9869i	−2.78925	−	2.78925i
$865$	7.17462	+	22.0812i	0.243944	+	0.750784i
$866$	27.2538	−	8.85531i	0.926123	−	0.300916i
$867$	20.6667	−	3.27328i	0.701877	−	0.111166i
$868$	10.9758	+	1.73840i	0.372544	+	0.0590051i
$869$	−7.44287	−	2.41833i	−0.252482	−	0.0820364i
$870$			8.87739i			0.300972i
$871$	−8.41282	+	25.8920i	−0.285058	+	0.877317i
$872$	−69.0434	+	35.1794i	−2.33811	+	1.19132i
$873$	0.721000	−	1.41504i	0.0244022	−	0.0478920i
$874$	−14.6810	−	92.6923i	−0.496593	−	3.13536i
$875$	8.85302	−	8.85302i	0.299287	−	0.299287i
$876$	−5.14883	−	2.62346i	−0.173963	−	0.0886386i
$877$	−23.6500	+	17.1827i	−0.798604	+	0.580219i	−0.910504	−	0.413500i	$-0.864306\pi$
$877$	−23.6500	+	17.1827i	−0.798604	+	0.580219i	0.111901	+	0.993719i	$0.464306\pi$
$878$	37.3965	+	73.3947i	1.26207	+	2.47695i
$879$	−28.0405	−	20.3726i	−0.945784	−	0.687152i
$880$	2.72413	−	17.1995i	0.0918303	−	0.579793i
$881$	−10.9101	−	15.0165i	−0.367571	−	0.505918i	0.584668	−	0.811273i	$-0.301225\pi$
$881$	−10.9101	−	15.0165i	−0.367571	−	0.505918i	−0.952239	+	0.305355i	$0.901225\pi$
$882$	0.839633	+	1.15566i	0.0282719	+	0.0389129i
$883$	−7.30514	+	46.1228i	−0.245838	+	1.55216i	0.488007	+	0.872840i	$0.337724\pi$
$883$	−7.30514	+	46.1228i	−0.245838	+	1.55216i	−0.733844	+	0.679318i	$0.762276\pi$
$884$	−18.6072	−	13.5190i	−0.625829	−	0.454692i
$885$	7.46473	+	14.6503i	0.250924	+	0.492466i
$886$	48.5798	−	35.2953i	1.63207	−	1.18577i
$887$	−0.882451	−	0.449631i	−0.0296298	−	0.0150971i	0.439113	−	0.898432i	$-0.355293\pi$
$887$	−0.882451	−	0.449631i	−0.0296298	−	0.0150971i	−0.468743	+	0.883335i	$0.655293\pi$
$888$	−76.1780	+	76.1780i	−2.55637	+	2.55637i
$889$	0.679797	+	4.29207i	0.0227997	+	0.143951i
$890$	9.30600	−	18.2641i	0.311938	−	0.612213i
$891$	7.75376	−	3.95074i	0.259761	−	0.132355i
$892$	−40.2865	+	123.989i	−1.34889	+	4.15146i
$893$			28.3261i			0.947896i
$894$	−40.5863	−	13.1873i	−1.35741	−	0.441049i
$895$	15.6307	+	2.47567i	0.522478	+	0.0827524i
$896$	−49.1001	+	7.77670i	−1.64032	+	0.259801i
$897$	20.3205	−	6.60253i	0.678482	−	0.220452i
$898$	−4.22691	−	13.0091i	−0.141054	−	0.434119i
$899$	−1.79114	−	1.79114i	−0.0597380	−	0.0597380i
$900$	−1.07470	+	1.47920i	−0.0358233	+	0.0493065i
$901$	22.6995			0.756230
$902$	−12.4581	+	10.7575i	−0.414811	+	0.358187i
$903$	2.58536			0.0860352
$904$	10.8283	−	14.9039i	0.360144	−	0.495696i
$905$	10.1971	+	10.1971i	0.338962	+	0.338962i
$906$	7.97121	+	24.5329i	0.264826	+	0.815050i
$907$	−5.02782	+	1.63364i	−0.166946	+	0.0542440i	−0.391297	−	0.920264i	$-0.627974\pi$
$907$	−5.02782	+	1.63364i	−0.166946	+	0.0542440i	0.224352	+	0.974508i	$0.427974\pi$
$908$	77.9205	−	12.3414i	2.58588	−	0.409564i
$909$	0.873900	+	0.138412i	0.0289854	+	0.00459084i
$910$	7.07484	+	2.29875i	0.234529	+	0.0762029i
$911$			16.7723i			0.555691i	0.960626	+	0.277845i	$0.0896203\pi$
$911$			16.7723i			0.555691i	−0.960626	+	0.277845i	$0.910380\pi$
$912$	−43.3500	+	133.418i	−1.43546	+	4.41790i
$913$	9.35132	−	4.76473i	0.309483	−	0.157690i
$914$	−15.2713	+	29.9715i	−0.505128	+	0.991370i
$915$	−0.558211	−	3.52441i	−0.0184539	−	0.116513i
$916$	80.3414	−	80.3414i	2.65455	−	2.65455i
$917$	8.55433	+	4.35865i	0.282489	+	0.143935i
$918$	25.5940	−	18.5952i	0.844729	−	0.613732i
$919$	−20.4457	−	40.1269i	−0.674440	−	1.32366i	−0.933770	−	0.357874i	$-0.883502\pi$
$919$	−20.4457	−	40.1269i	−0.674440	−	1.32366i	0.259330	−	0.965789i	$-0.416498\pi$
$920$	61.9116	+	44.9814i	2.04117	+	1.48299i
$921$	−2.71086	+	17.1157i	−0.0893258	+	0.563981i
$922$	47.4019	+	65.2431i	1.56110	+	2.14867i
$923$	3.38960	+	4.66538i	0.111570	+	0.153563i
$924$	1.71943	−	10.8561i	0.0565651	−	0.357138i
$925$	−18.2032	−	13.2254i	−0.598516	−	0.434847i
$926$	22.6634	+	44.4794i	0.744764	+	1.46168i
$927$	−0.797844	+	0.579667i	−0.0262046	+	0.0190388i
$928$	30.6780	+	15.6312i	1.00706	+	0.513121i
$929$	−9.65576	+	9.65576i	−0.316795	+	0.316795i	−0.847535	−	0.530740i	$-0.821914\pi$
$929$	−9.65576	+	9.65576i	−0.316795	+	0.316795i	0.530740	+	0.847535i	$0.321914\pi$
$930$	1.52689	+	9.64038i	0.0500686	+	0.316121i
$931$	−13.1108	+	25.7314i	−0.429690	+	0.843314i
$932$	88.4581	−	45.0717i	2.89754	−	1.47637i
$933$	13.7980	−	42.4658i	0.451726	−	1.39027i
$934$		−	47.2276i		−	1.54533i
$935$	2.44735	+	0.795191i	0.0800368	+	0.0260055i
$936$	−1.65157	−	0.261583i	−0.0539832	−	0.00855011i
$937$	18.4731	−	2.92586i	0.603491	−	0.0955836i	0.152790	−	0.988259i	$-0.451174\pi$
$937$	18.4731	−	2.92586i	0.603491	−	0.0955836i	0.450701	+	0.892675i	$0.351174\pi$
$938$	−46.3960	+	15.0750i	−1.51488	+	0.492216i
$939$	−14.2558	−	43.8749i	−0.465222	−	1.43180i
$940$	−25.6543	−	25.6543i	−0.836750	−	0.836750i
$941$	16.6302	−	22.8895i	0.542129	−	0.746176i	−0.446789	−	0.894639i	$-0.647433\pi$
$941$	16.6302	−	22.8895i	0.542129	−	0.746176i	0.988918	+	0.148463i	$0.0474326\pi$
$942$	40.3011			1.31308
$943$	−10.0388	−	40.8388i	−0.326909	−	1.32989i
$944$	117.749			3.83239
$945$	−4.41142	+	6.07180i	−0.143504	+	0.197516i
$946$	2.20839	+	2.20839i	0.0718011	+	0.0718011i
$947$	−3.74796	−	11.5350i	−0.121792	−	0.374839i	0.871511	−	0.490377i	$-0.163141\pi$
$947$	−3.74796	−	11.5350i	−0.121792	−	0.374839i	−0.993303	+	0.115538i	$0.963141\pi$
$948$	−76.7965	+	24.9527i	−2.49423	+	0.810426i
$949$	1.09019	−	0.172669i	0.0353890	−	0.00560507i
$950$	−49.7745	−	7.88351i	−1.61490	−	0.255775i
$951$	−34.7472	−	11.2901i	−1.12676	−	0.366105i
$952$		−	26.2387i		−	0.850400i
$953$	−9.89902	+	30.4661i	−0.320661	+	0.986892i	0.652701	+	0.757616i	$0.273636\pi$
$953$	−9.89902	+	30.4661i	−0.320661	+	0.986892i	−0.973361	+	0.229276i	$0.926364\pi$
$954$	2.30966	−	1.17683i	0.0747779	−	0.0381012i
$955$	0.237841	−	0.466789i	0.00769636	−	0.0151049i
$956$	19.5486	+	123.425i	0.632247	+	3.99185i
$957$	−1.77160	+	1.77160i	−0.0572677	+	0.0572677i
$958$	−54.7125	−	27.8774i	−1.76768	−	0.900679i
$959$	−7.29592	+	5.30080i	−0.235598	+	0.171172i
$960$	−30.5922	−	60.0405i	−0.987359	−	1.93780i
$961$	22.8264	+	16.5843i	0.736334	+	0.534978i
$962$	5.05625	−	31.9239i	0.163020	−	1.02927i
$963$	0.276772	+	0.380944i	0.00891885	+	0.0122757i
$964$	10.1059	+	13.9096i	0.325490	+	0.447999i
$965$	4.02611	−	25.4199i	0.129605	−	0.818294i
$966$	30.9743	+	22.5041i	0.996580	+	0.724058i
$967$	−18.5414	−	36.3896i	−0.596252	−	1.17021i	−0.970097	−	0.242719i	$-0.921961\pi$
$967$	−18.5414	−	36.3896i	−0.596252	−	1.17021i	0.373845	−	0.927491i	$-0.378039\pi$
$968$	−78.5925	+	57.1008i	−2.52606	+	1.83529i
$969$	−18.4707	−	9.41127i	−0.593363	−	0.302334i
$970$	−39.6444	+	39.6444i	−1.27290	+	1.27290i
$971$	−2.17456	−	13.7297i	−0.0697851	−	0.440606i	−0.997698	−	0.0678093i	$-0.978399\pi$
$971$	−2.17456	−	13.7297i	−0.0697851	−	0.440606i	0.927913	−	0.372796i	$-0.121601\pi$
$972$	2.44503	−	4.79863i	0.0784242	−	0.153916i
$973$	−2.28115	+	1.16230i	−0.0731303	+	0.0372617i
$974$	0.327173	−	1.00694i	0.0104833	−	0.0322643i
$975$		−	11.4734i		−	0.367442i
$976$	−24.3031	−	7.89654i	−0.777922	−	0.252762i
$977$	−45.5148	−	7.20884i	−1.45615	−	0.230631i	−0.622367	−	0.782726i	$-0.713829\pi$
$977$	−45.5148	−	7.20884i	−1.45615	−	0.230631i	−0.833781	+	0.552095i	$0.813829\pi$
$978$	0.788420	−	0.124873i	0.0252109	−	0.00399301i
$979$	5.50197	−	1.78770i	0.175844	−	0.0571351i
$980$	−11.4302	−	35.1786i	−0.365125	−	1.12374i
$981$	−0.537571	−	0.537571i	−0.0171633	−	0.0171633i
$982$	43.3188	−	59.6232i	1.38236	−	1.90265i
$983$	−25.4016			−0.810185			−0.405093	−	0.914276i	$-0.632761\pi$
$983$	−25.4016			−0.810185			−0.405093	+	0.914276i	$0.632761\pi$
$984$	−24.6717	+	105.274i	−0.786504	+	3.35601i
$985$	−28.4443			−0.906312
$986$	−5.52188	+	7.60021i	−0.175852	+	0.242040i
$987$	−8.17129	−	8.17129i	−0.260095	−	0.260095i
$988$	−16.4085	−	50.5003i	−0.522025	−	1.60663i
$989$	−7.58896	+	2.46580i	−0.241315	+	0.0784080i
$990$	0.290241	−	0.0459697i	0.00922448	−	0.00146101i
$991$	27.6423	+	4.37811i	0.878087	+	0.139075i	0.579173	−	0.815205i	$-0.303376\pi$
$991$	27.6423	+	4.37811i	0.878087	+	0.139075i	0.298914	+	0.954280i	$0.403376\pi$
$992$	36.0033	+	11.6982i	1.14311	+	0.371418i
$993$		−	11.2021i		−	0.355489i
$994$	−3.19321	+	9.82768i	−0.101282	+	0.311715i
$995$	−5.70133	+	2.90497i	−0.180744	+	0.0920938i
$996$	49.1631	−	96.4881i	1.55779	−	3.05734i
$997$	−4.76664	−	30.0954i	−0.150961	−	0.953130i	−0.940590	−	0.339545i	$-0.889727\pi$
$997$	−4.76664	−	30.0954i	−0.150961	−	0.953130i	0.789629	−	0.613585i	$-0.210273\pi$
$998$	17.7360	−	17.7360i	0.561425	−	0.561425i
$999$	29.0554	+	14.8045i	0.919272	+	0.468393i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.2.g.a.8.1	✓	24
3.2	odd	2		369.2.u.a.172.3		24
4.3	odd	2		656.2.bs.d.49.1		24
41.6	odd	40		1681.2.a.m.1.23		24
41.35	odd	40		1681.2.a.m.1.24		24
41.36	even	20	inner	41.2.g.a.36.1	yes	24
123.77	odd	20		369.2.u.a.118.3		24
164.159	odd	20		656.2.bs.d.241.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.8.1	✓	24	1.1	even	1	trivial
41.2.g.a.36.1	yes	24	41.36	even	20	inner
369.2.u.a.118.3		24	123.77	odd	20
369.2.u.a.172.3		24	3.2	odd	2
656.2.bs.d.49.1		24	4.3	odd	2
656.2.bs.d.241.1		24	164.159	odd	20
1681.2.a.m.1.23		24	41.6	odd	40
1681.2.a.m.1.24		24	41.35	odd	40

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:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	41.g (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61018 + 2.21623i) q^{2} +(1.24382 + 1.24382i) q^{3} +(-1.70094 - 5.23496i) q^{4} +(-1.15434 + 0.375067i) q^{5} +(-4.75938 + 0.753811i) q^{6} +(1.19485 + 0.189245i) q^{7} +(9.13005 + 2.96653i) q^{8} +0.0941838i q^{9} +O(q^{10})\)	\(q+(-1.61018 + 2.21623i) q^{2} +(1.24382 + 1.24382i) q^{3} +(-1.70094 - 5.23496i) q^{4} +(-1.15434 + 0.375067i) q^{5} +(-4.75938 + 0.753811i) q^{6} +(1.19485 + 0.189245i) q^{7} +(9.13005 + 2.96653i) q^{8} +0.0941838i q^{9} +(1.02746 - 3.16221i) q^{10} +(0.836104 - 0.426016i) q^{11} +(4.39569 - 8.62703i) q^{12} +(0.289312 + 1.82664i) q^{13} +(-2.34333 + 2.34333i) q^{14} +(-1.90231 - 0.969274i) q^{15} +(-12.3693 + 8.98684i) q^{16} +(-1.02572 - 2.01309i) q^{17} +(-0.208733 - 0.151653i) q^{18} +(0.815977 - 5.15188i) q^{19} +(3.92693 + 5.40495i) q^{20} +(1.25079 + 1.72156i) q^{21} +(-0.402132 + 2.53896i) q^{22} +(-5.31348 - 3.86047i) q^{23} +(7.66631 + 15.0460i) q^{24} +(-2.85326 + 2.07302i) q^{25} +(-4.51411 - 2.30005i) q^{26} +(3.61432 - 3.61432i) q^{27} +(-1.04167 - 6.57687i) q^{28} +(-0.689088 + 1.35241i) q^{29} +(5.21120 - 2.65524i) q^{30} +(-0.515703 + 1.58717i) q^{31} -22.6839i q^{32} +(1.56985 + 0.510076i) q^{33} +(6.11308 + 0.968216i) q^{34} +(-1.45024 + 0.229695i) q^{35} +(0.493049 - 0.160201i) q^{36} +(1.97146 + 6.06752i) q^{37} +(10.1039 + 10.1039i) q^{38} +(-1.91217 + 2.63187i) q^{39} -11.6518 q^{40} +(4.89143 + 4.13206i) q^{41} -5.82938 q^{42} +(0.714124 - 0.982908i) q^{43} +(-3.65235 - 3.65235i) q^{44} +(-0.0353253 - 0.108720i) q^{45} +(17.1114 - 5.55982i) q^{46} +(-5.36365 + 0.849519i) q^{47} +(-26.5633 - 4.20721i) q^{48} +(-5.26555 - 1.71088i) q^{49} -9.66143i q^{50} +(1.22811 - 3.77974i) q^{51} +(9.07032 - 4.62156i) q^{52} +(-4.56121 + 8.95188i) q^{53} +(2.19044 + 13.8299i) q^{54} +(-0.805362 + 0.805362i) q^{55} +(10.3476 + 5.27237i) q^{56} +(7.42295 - 5.39309i) q^{57} +(-1.88770 - 3.70481i) q^{58} +(-6.23053 - 4.52674i) q^{59} +(-1.83840 + 11.6072i) q^{60} +(0.982392 + 1.35215i) q^{61} +(-2.68716 - 3.69855i) q^{62} +(-0.0178238 + 0.112535i) q^{63} +(25.5342 + 18.5517i) q^{64} +(-1.01908 - 2.00005i) q^{65} +(-3.65820 + 2.65784i) q^{66} +(13.1161 + 6.68301i) q^{67} +(-8.79377 + 8.79377i) q^{68} +(-1.80728 - 11.4107i) q^{69} +(1.82609 - 3.58391i) q^{70} +(2.77828 - 1.41561i) q^{71} +(-0.279399 + 0.859903i) q^{72} -0.596826i q^{73} +(-16.6214 - 5.40063i) q^{74} +(-6.12741 - 0.970487i) q^{75} +(-28.3578 + 4.49144i) q^{76} +(1.07964 - 0.350796i) q^{77} +(-2.75389 - 8.47560i) q^{78} +(-5.89711 - 5.89711i) q^{79} +(10.9077 - 15.0132i) q^{80} +9.27368 q^{81} +(-17.0337 + 4.18715i) q^{82} +11.1844 q^{83} +(6.88480 - 9.47611i) q^{84} +(1.93908 + 1.93908i) q^{85} +(1.02848 + 3.16533i) q^{86} +(-2.53926 + 0.825056i) q^{87} +(8.89746 - 1.40922i) q^{88} +(6.08909 + 0.964418i) q^{89} +(0.297829 + 0.0967704i) q^{90} +2.23731i q^{91} +(-11.1715 + 34.3823i) q^{92} +(-2.61560 + 1.33271i) q^{93} +(6.75374 - 13.2550i) q^{94} +(0.990387 + 6.25306i) q^{95} +(28.2148 - 28.2148i) q^{96} +(-15.0243 - 7.65525i) q^{97} +(12.2702 - 8.91483i) q^{98} +(0.0401238 + 0.0787475i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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