LMFDB - Embedded newform 841.2.e.j.270.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			270.1
Character	$\chi$	$=$	841.270
Dual form			841.2.e.j.651.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.702039 - 1.45780i) q^{2} +(1.26503 - 1.00883i) q^{3} +(-0.385338 + 0.483198i) q^{4} +(-2.57146 + 1.23835i) q^{5} +(-2.35877 - 1.13592i) q^{6} +(1.39417 + 1.74823i) q^{7} +(-2.18001 - 0.497572i) q^{8} +(-0.0849954 + 0.372389i) q^{9} +O(q^{10})$	\(q+(-0.702039 - 1.45780i) q^{2} +(1.26503 - 1.00883i) q^{3} +(-0.385338 + 0.483198i) q^{4} +(-2.57146 + 1.23835i) q^{5} +(-2.35877 - 1.13592i) q^{6} +(1.39417 + 1.74823i) q^{7} +(-2.18001 - 0.497572i) q^{8} +(-0.0849954 + 0.372389i) q^{9} +(3.61052 + 2.87930i) q^{10} +(3.52732 - 0.805088i) q^{11} +1.00000i q^{12} +(0.942614 + 4.12986i) q^{13} +(1.56981 - 3.25974i) q^{14} +(-2.00369 + 4.16070i) q^{15} +(1.08014 + 4.73240i) q^{16} +6.61803i q^{17} +(0.602539 - 0.137526i) q^{18} +(-1.44960 - 1.15601i) q^{19} +(0.392512 - 1.71971i) q^{20} +(3.52732 + 0.805088i) q^{21} +(-3.64997 - 4.57692i) q^{22} +(-2.91560 - 1.40408i) q^{23} +(-3.25974 + 1.56981i) q^{24} +(1.96144 - 2.45956i) q^{25} +(5.35875 - 4.27346i) q^{26} +(2.37427 + 4.93022i) q^{27} -1.38197 q^{28} +7.47214 q^{30} +(0.473007 + 0.982209i) q^{31} +(2.64413 - 2.10862i) q^{32} +(3.64997 - 4.57692i) q^{33} +(9.64776 - 4.64612i) q^{34} +(-5.74995 - 2.76903i) q^{35} +(-0.147186 - 0.184565i) q^{36} +(8.48987 + 1.93776i) q^{37} +(-0.667563 + 2.92478i) q^{38} +(5.35875 + 4.27346i) q^{39} +(6.22196 - 1.42012i) q^{40} -2.85410i q^{41} +(-1.30266 - 5.70733i) q^{42} +(1.19923 - 2.49022i) q^{43} +(-0.970194 + 2.01463i) q^{44} +(-0.242586 - 1.06284i) q^{45} +5.23607i q^{46} +(-6.82450 + 1.55765i) q^{47} +(6.14058 + 4.89695i) q^{48} +(0.445042 - 1.94986i) q^{49} +(-4.96255 - 1.13267i) q^{50} +(6.67646 + 8.37201i) q^{51} +(-2.35877 - 1.13592i) q^{52} +(1.80194 - 0.867767i) q^{53} +(5.52044 - 6.92242i) q^{54} +(-8.07338 + 6.43830i) q^{55} +(-2.16942 - 4.50484i) q^{56} -3.00000 q^{57} -5.09017 q^{59} +(-1.23835 - 2.57146i) q^{60} +(1.26503 - 1.00883i) q^{61} +(1.09979 - 1.37910i) q^{62} +(-0.769519 + 0.370581i) q^{63} +(3.81657 + 1.83796i) q^{64} +(-7.53810 - 9.45248i) q^{65} +(-9.23465 - 2.10775i) q^{66} +(-2.33027 + 10.2096i) q^{67} +(-3.19782 - 2.55018i) q^{68} +(-5.10479 + 1.16513i) q^{69} +10.3262i q^{70} +(0.339982 + 1.48956i) q^{71} +(0.370581 - 0.769519i) q^{72} +(-0.126606 + 0.262899i) q^{73} +(-3.13536 - 13.7369i) q^{74} -5.09017i q^{75} +(1.11717 - 0.254986i) q^{76} +(6.32515 + 5.04414i) q^{77} +(2.46779 - 10.8121i) q^{78} +(4.96255 + 1.13267i) q^{79} +(-8.63789 - 10.8316i) q^{80} +(6.94485 + 3.34446i) q^{81} +(-4.16070 + 2.00369i) q^{82} +(4.95317 - 6.21108i) q^{83} +(-1.74823 + 1.39417i) q^{84} +(-8.19543 - 17.0180i) q^{85} -4.47214 q^{86} -8.09017 q^{88} +(-3.77835 - 7.84582i) q^{89} +(-1.37910 + 1.09979i) q^{90} +(-5.90578 + 7.40561i) q^{91} +(1.80194 - 0.867767i) q^{92} +(1.58925 + 0.765341i) q^{93} +(7.06179 + 8.85521i) q^{94} +(5.15912 + 1.17754i) q^{95} +(1.21766 - 5.33494i) q^{96} +(-12.9489 - 10.3264i) q^{97} +(-3.15493 + 0.720093i) q^{98} +1.38197i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9	$ 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9} + 8 q^{13} + 6 q^{16} + 16 q^{20} + 10 q^{22} - 4 q^{23} - 10 q^{24} - 26 q^{25} - 60 q^{28} + 72 q^{30} - 10 q^{33} + 16 q^{34} - 30 q^{35} - 8 q^{36} - 12 q^{38} - 10 q^{42} + 18 q^{45} + 8 q^{49} - 16 q^{51} - 6 q^{52} + 8 q^{53} - 22 q^{54} - 72 q^{57} + 12 q^{59} - 16 q^{62} + 10 q^{63} + 8 q^{64} + 26 q^{65} - 24 q^{67} + 24 q^{71} - 34 q^{74} + 22 q^{78} + 42 q^{80} + 4 q^{81} - 14 q^{82} + 4 q^{83} - 60 q^{88} + 20 q^{91} + 8 q^{92} + 16 q^{93} - 14 q^{94} + 4 q^{96}+O(q^{100}) $ 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9 + 8 * q^13 + 6 * q^16 + 16 * q^20 + 10 * q^22 - 4 * q^23 - 10 * q^24 - 26 * q^25 - 60 * q^28 + 72 * q^30 - 10 * q^33 + 16 * q^34 - 30 * q^35 - 8 * q^36 - 12 * q^38 - 10 * q^42 + 18 * q^45 + 8 * q^49 - 16 * q^51 - 6 * q^52 + 8 * q^53 - 22 * q^54 - 72 * q^57 + 12 * q^59 - 16 * q^62 + 10 * q^63 + 8 * q^64 + 26 * q^65 - 24 * q^67 + 24 * q^71 - 34 * q^74 + 22 * q^78 + 42 * q^80 + 4 * q^81 - 14 * q^82 + 4 * q^83 - 60 * q^88 + 20 * q^91 + 8 * q^92 + 16 * q^93 - 14 * q^94 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{14}\right)$

Coefficient data

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

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

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

$2$	−0.702039	−	1.45780i	−0.496416	−	1.03082i	−0.987193	−	0.159533i	$-0.949001\pi$
$2$	−0.702039	−	1.45780i	−0.496416	−	1.03082i	0.490776	−	0.871286i	$-0.336713\pi$
$3$	1.26503	−	1.00883i	0.730365	−	0.582447i	−0.186114	−	0.982528i	$-0.559589\pi$
$3$	1.26503	−	1.00883i	0.730365	−	0.582447i	0.916480	+	0.400081i	$0.131018\pi$
$4$	−0.385338	+	0.483198i	−0.192669	+	0.241599i
$5$	−2.57146	+	1.23835i	−1.14999	+	0.553806i	−0.909031	−	0.416729i	$-0.863176\pi$
$5$	−2.57146	+	1.23835i	−1.14999	+	0.553806i	−0.240960	+	0.970535i	$0.577462\pi$
$6$	−2.35877	−	1.13592i	−0.962963	−	0.463738i
$7$	1.39417	+	1.74823i	0.526945	+	0.660768i	0.972067	−	0.234702i	$-0.0754113\pi$
$7$	1.39417	+	1.74823i	0.526945	+	0.660768i	−0.445122	+	0.895470i	$0.646840\pi$
$8$	−2.18001	−	0.497572i	−0.770748	−	0.175918i
$9$	−0.0849954	+	0.372389i	−0.0283318	+	0.124130i
$10$	3.61052	+	2.87930i	1.14175	+	0.910514i
$11$	3.52732	−	0.805088i	1.06353	−	0.242743i	0.345258	−	0.938508i	$-0.387791\pi$
$11$	3.52732	−	0.805088i	1.06353	−	0.242743i	0.718270	+	0.695765i	$0.244934\pi$
$12$			1.00000i			0.288675i
$13$	0.942614	+	4.12986i	0.261434	+	1.14542i	0.919697	+	0.392629i	$0.128434\pi$
$13$	0.942614	+	4.12986i	0.261434	+	1.14542i	−0.658263	+	0.752788i	$0.728708\pi$
$14$	1.56981	−	3.25974i	0.419548	−	0.871201i
$15$	−2.00369	+	4.16070i	−0.517350	+	1.07429i
$16$	1.08014	+	4.73240i	0.270035	+	1.18310i
$17$			6.61803i			1.60511i	0.596579	+	0.802555i	$0.296526\pi$
$17$			6.61803i			1.60511i	−0.596579	+	0.802555i	$0.703474\pi$
$18$	0.602539	−	0.137526i	0.142020	−	0.0324151i
$19$	−1.44960	−	1.15601i	−0.332560	−	0.265208i	0.442946	−	0.896549i	$-0.353933\pi$
$19$	−1.44960	−	1.15601i	−0.332560	−	0.265208i	−0.775506	+	0.631341i	$0.782505\pi$
$20$	0.392512	−	1.71971i	0.0877683	−	0.384538i
$21$	3.52732	+	0.805088i	0.769725	+	0.175685i
$22$	−3.64997	−	4.57692i	−0.778177	−	0.975803i
$23$	−2.91560	−	1.40408i	−0.607944	−	0.292770i	0.104472	−	0.994528i	$-0.466685\pi$
$23$	−2.91560	−	1.40408i	−0.607944	−	0.292770i	−0.712416	+	0.701757i	$0.752399\pi$
$24$	−3.25974	+	1.56981i	−0.665391	+	0.320435i
$25$	1.96144	−	2.45956i	0.392287	−	0.491912i
$26$	5.35875	−	4.27346i	1.05094	−	0.838095i
$27$	2.37427	+	4.93022i	0.456929	+	0.948822i
$28$	−1.38197			−0.261167
$29$		0			0
$29$		0			0
$30$	7.47214			1.36422
$31$	0.473007	+	0.982209i	0.0849546	+	0.176410i	0.939118	−	0.343594i	$-0.111645\pi$
$31$	0.473007	+	0.982209i	0.0849546	+	0.176410i	−0.854164	+	0.520004i	$0.825930\pi$
$32$	2.64413	−	2.10862i	0.467420	−	0.372755i
$33$	3.64997	−	4.57692i	0.635379	−	0.796740i
$34$	9.64776	−	4.64612i	1.65458	−	0.796802i
$35$	−5.74995	−	2.76903i	−0.971919	−	0.468052i
$36$	−0.147186	−	0.184565i	−0.0245310	−	0.0307609i
$37$	8.48987	+	1.93776i	1.39573	+	0.318565i	0.853248	−	0.521505i	$-0.174629\pi$
$37$	8.48987	+	1.93776i	1.39573	+	0.318565i	0.542478	+	0.840070i	$0.317486\pi$
$38$	−0.667563	+	2.92478i	−0.108293	+	0.474463i
$39$	5.35875	+	4.27346i	0.858087	+	0.684302i
$40$	6.22196	−	1.42012i	0.983778	−	0.224541i
$41$		−	2.85410i		−	0.445736i	−0.974849	−	0.222868i	$-0.928458\pi$
$41$		−	2.85410i		−	0.445736i	0.974849	−	0.222868i	$-0.0715419\pi$
$42$	−1.30266	−	5.70733i	−0.201005	−	0.880660i
$43$	1.19923	−	2.49022i	0.182880	−	0.379754i	−0.789293	−	0.614016i	$-0.789553\pi$
$43$	1.19923	−	2.49022i	0.182880	−	0.379754i	0.972174	+	0.234262i	$0.0752672\pi$
$44$	−0.970194	+	2.01463i	−0.146262	+	0.303717i
$45$	−0.242586	−	1.06284i	−0.0361625	−	0.158438i
$46$			5.23607i			0.772016i
$47$	−6.82450	+	1.55765i	−0.995455	+	0.227206i	−0.689065	−	0.724700i	$-0.741978\pi$
$47$	−6.82450	+	1.55765i	−0.995455	+	0.227206i	−0.306390	+	0.951906i	$0.599121\pi$
$48$	6.14058	+	4.89695i	0.886317	+	0.706814i
$49$	0.445042	−	1.94986i	0.0635774	−	0.278551i
$50$	−4.96255	−	1.13267i	−0.701810	−	0.160184i
$51$	6.67646	+	8.37201i	0.934891	+	1.17232i
$52$	−2.35877	−	1.13592i	−0.327102	−	0.157524i
$53$	1.80194	−	0.867767i	0.247515	−	0.119197i	−0.306013	−	0.952027i	$-0.598995\pi$
$53$	1.80194	−	0.867767i	0.247515	−	0.119197i	0.553529	+	0.832830i	$0.313281\pi$
$54$	5.52044	−	6.92242i	0.751237	−	0.942021i
$55$	−8.07338	+	6.43830i	−1.08861	+	0.868141i
$56$	−2.16942	−	4.50484i	−0.289901	−	0.601985i
$57$	−3.00000			−0.397360
$58$		0			0
$59$	−5.09017			−0.662684			−0.331342	−	0.943511i	$-0.607501\pi$
$59$	−5.09017			−0.662684			−0.331342	+	0.943511i	$0.607501\pi$
$60$	−1.23835	−	2.57146i	−0.159870	−	0.331974i
$61$	1.26503	−	1.00883i	0.161970	−	0.129167i	−0.539151	−	0.842209i	$-0.681255\pi$
$61$	1.26503	−	1.00883i	0.161970	−	0.129167i	0.701121	+	0.713042i	$0.252683\pi$
$62$	1.09979	−	1.37910i	0.139674	−	0.175146i
$63$	−0.769519	+	0.370581i	−0.0969503	+	0.0466888i
$64$	3.81657	+	1.83796i	0.477071	+	0.229745i
$65$	−7.53810	−	9.45248i	−0.934986	−	1.17244i
$66$	−9.23465	−	2.10775i	−1.13671	−	0.259446i
$67$	−2.33027	+	10.2096i	−0.284688	+	1.24730i	0.607020	+	0.794687i	$0.292365\pi$
$67$	−2.33027	+	10.2096i	−0.284688	+	1.24730i	−0.891708	+	0.452612i	$0.850492\pi$
$68$	−3.19782	−	2.55018i	−0.387793	−	0.309255i
$69$	−5.10479	+	1.16513i	−0.614544	+	0.140266i
$70$			10.3262i			1.23422i
$71$	0.339982	+	1.48956i	0.0403484	+	0.176778i	0.991087	−	0.133216i	$-0.0425303\pi$
$71$	0.339982	+	1.48956i	0.0403484	+	0.176778i	−0.950739	+	0.309993i	$0.899673\pi$
$72$	0.370581	−	0.769519i	0.0436734	−	0.0906887i
$73$	−0.126606	+	0.262899i	−0.0148181	+	0.0307700i	−0.908247	−	0.418435i	$-0.862579\pi$
$73$	−0.126606	+	0.262899i	−0.0148181	+	0.0307700i	0.893428	+	0.449205i	$0.148293\pi$
$74$	−3.13536	−	13.7369i	−0.364478	−	1.59688i
$75$		−	5.09017i		−	0.587762i
$76$	1.11717	−	0.254986i	0.128148	−	0.0292489i
$77$	6.32515	+	5.04414i	0.720818	+	0.574833i
$78$	2.46779	−	10.8121i	0.279423	−	1.22423i
$79$	4.96255	+	1.13267i	0.558330	+	0.127435i	0.492368	−	0.870387i	$-0.336131\pi$
$79$	4.96255	+	1.13267i	0.558330	+	0.127435i	0.0659619	+	0.997822i	$0.478988\pi$
$80$	−8.63789	−	10.8316i	−0.965746	−	1.21101i
$81$	6.94485	+	3.34446i	0.771650	+	0.371607i
$82$	−4.16070	+	2.00369i	−0.459473	+	0.221271i
$83$	4.95317	−	6.21108i	0.543681	−	0.681755i	−0.431767	−	0.901985i	$-0.642110\pi$
$83$	4.95317	−	6.21108i	0.543681	−	0.681755i	0.975448	+	0.220231i	$0.0706810\pi$
$84$	−1.74823	+	1.39417i	−0.190747	+	0.152116i
$85$	−8.19543	−	17.0180i	−0.888919	−	1.84586i
$86$	−4.47214			−0.482243
$87$		0			0
$88$	−8.09017			−0.862415
$89$	−3.77835	−	7.84582i	−0.400504	−	0.831655i	−0.999522	−	0.0309196i	$-0.990156\pi$
$89$	−3.77835	−	7.84582i	−0.400504	−	0.831655i	0.599018	−	0.800736i	$-0.295558\pi$
$90$	−1.37910	+	1.09979i	−0.145370	+	0.115928i
$91$	−5.90578	+	7.40561i	−0.619094	+	0.776319i
$92$	1.80194	−	0.867767i	0.187865	−	0.0904710i
$93$	1.58925	+	0.765341i	0.164797	+	0.0793622i
$94$	7.06179	+	8.85521i	0.728368	+	0.913345i
$95$	5.15912	+	1.17754i	0.529315	+	0.120813i
$96$	1.21766	−	5.33494i	0.124277	−	0.544495i
$97$	−12.9489	−	10.3264i	−1.31476	−	1.04849i	−0.994883	−	0.101033i	$-0.967785\pi$
$97$	−12.9489	−	10.3264i	−1.31476	−	1.04849i	−0.319882	−	0.947457i	$-0.603643\pi$
$98$	−3.15493	+	0.720093i	−0.318696	+	0.0727404i
$99$			1.38197i			0.138893i
$100$	0.432641	+	1.89552i	0.0432641	+	0.189552i
$101$	−0.702039	+	1.45780i	−0.0698555	+	0.145056i	−0.932973	−	0.359947i	$-0.882795\pi$
$101$	−0.702039	+	1.45780i	−0.0698555	+	0.145056i	0.863117	+	0.505004i	$0.168509\pi$
$102$	7.51757	−	15.6104i	0.744351	−	1.54566i
$103$	2.93290	+	12.8499i	0.288987	+	1.26614i	0.885917	+	0.463843i	$0.153530\pi$
$103$	2.93290	+	12.8499i	0.288987	+	1.26614i	−0.596930	+	0.802293i	$0.703613\pi$
$104$		−	9.47214i		−	0.928819i
$105$	−10.0673	+	2.29780i	−0.982472	+	0.224243i
$106$	−2.53006	−	2.01766i	−0.245741	−	0.195972i
$107$	−2.50026	+	10.9544i	−0.241709	+	1.05900i	0.697751	+	0.716340i	$0.254184\pi$
$107$	−2.50026	+	10.9544i	−0.241709	+	1.05900i	−0.939460	+	0.342657i	$0.888673\pi$
$108$	−3.29717	−	0.752558i	−0.317271	−	0.0724149i
$109$	10.3612	+	12.9925i	0.992421	+	1.24446i	0.969595	+	0.244717i	$0.0786949\pi$
$109$	10.3612	+	12.9925i	0.992421	+	1.24446i	0.0228259	+	0.999739i	$0.492734\pi$
$110$	15.0536	+	7.24942i	1.43530	+	0.691205i
$111$	12.6948	−	6.11350i	1.20494	−	0.580267i
$112$	−6.76742	+	8.48608i	−0.639461	+	0.801859i
$113$	7.77474	−	6.20015i	0.731386	−	0.583261i	−0.185389	−	0.982665i	$-0.559354\pi$
$113$	7.77474	−	6.20015i	0.731386	−	0.583261i	0.916775	+	0.399404i	$0.130783\pi$
$114$	2.10612	+	4.37339i	0.197256	+	0.409606i
$115$	9.23607			0.861268
$116$		0			0
$117$	−1.61803			−0.149587
$118$	3.57350	+	7.42044i	0.328967	+	0.683107i
$119$	−11.5698	+	9.22664i	−1.06060	+	0.845804i
$120$	6.43830	−	8.07338i	0.587734	−	0.736995i
$121$	1.88318	−	0.906891i	0.171198	−	0.0824446i
$122$	−2.35877	−	1.13592i	−0.213553	−	0.102842i
$123$	−2.87930	−	3.61052i	−0.259617	−	0.325550i
$124$	−0.656869	−	0.149926i	−0.0589886	−	0.0134638i
$125$	1.17754	−	5.15912i	0.105322	−	0.461446i
$126$	1.08046	+	0.861642i	0.0962554	+	0.0767611i
$127$	1.89552	−	0.432641i	0.168201	−	0.0383907i	−0.137591	−	0.990489i	$-0.543936\pi$
$127$	1.89552	−	0.432641i	0.168201	−	0.0383907i	0.305792	+	0.952098i	$0.401079\pi$
$128$		−	13.6180i		−	1.20368i
$129$	−0.995144	−	4.36001i	−0.0876175	−	0.383877i
$130$	−8.48777	+	17.6250i	−0.744426	+	1.54582i
$131$	−0.575433	+	1.19490i	−0.0502758	+	0.104399i	−0.924593	−	0.380956i	$-0.875595\pi$
$131$	−0.575433	+	1.19490i	−0.0502758	+	0.104399i	0.874318	+	0.485354i	$0.161309\pi$
$132$	0.805088	+	3.52732i	0.0700739	+	0.307014i
$133$		−	4.14590i		−	0.359495i
$134$	16.5194	−	3.77046i	1.42706	−	0.325718i
$135$	−12.2107	−	9.73768i	−1.05093	−	0.838086i
$136$	3.29295	−	14.4273i	0.282368	−	1.23713i
$137$	13.5068	+	3.08283i	1.15396	+	0.263384i	0.756348	−	0.654170i	$-0.226982\pi$
$137$	13.5068	+	3.08283i	1.15396	+	0.263384i	0.397612	+	0.917554i	$0.369839\pi$
$138$	5.28229	+	6.62378i	0.449658	+	0.563854i
$139$	−13.2516	−	6.38165i	−1.12399	−	0.541285i	−0.222866	−	0.974849i	$-0.571541\pi$
$139$	−13.2516	−	6.38165i	−1.12399	−	0.541285i	−0.901123	+	0.433564i	$0.857256\pi$
$140$	3.55367	−	1.71136i	0.300340	−	0.144636i
$141$	−7.06179	+	8.85521i	−0.594710	+	0.745743i
$142$	1.93279	−	1.54135i	0.162196	−	0.129347i
$143$	6.64981	+	13.8085i	0.556085	+	1.15472i
$144$	−1.85410			−0.154508
$145$		0			0
$146$	0.472136			0.0390742
$147$	−1.40408	−	2.91560i	−0.115806	−	0.240474i
$148$	−4.20779	+	3.35560i	−0.345878	+	0.275829i
$149$	−4.60258	+	5.77145i	−0.377058	+	0.472816i	−0.933762	−	0.357895i	$-0.883494\pi$
$149$	−4.60258	+	5.77145i	−0.377058	+	0.472816i	0.556704	+	0.830711i	$0.312066\pi$
$150$	−7.42044	+	3.57350i	−0.605876	+	0.291775i
$151$	16.5114	+	7.95146i	1.34368	+	0.647080i	0.960935	−	0.276775i	$-0.0892657\pi$
$151$	16.5114	+	7.95146i	1.34368	+	0.647080i	0.382742	+	0.923855i	$0.374980\pi$
$152$	2.58493	+	3.24139i	0.209665	+	0.262912i
$153$	−2.46449	−	0.562503i	−0.199242	−	0.0454756i
$154$	2.91284	−	12.7620i	0.234723	−	1.02839i
$155$	−2.43263	−	1.93996i	−0.195394	−	0.155821i
$156$	−4.12986	+	0.942614i	−0.330654	+	0.0754695i
$157$		−	5.56231i		−	0.443920i	−0.975056	−	0.221960i	$-0.928755\pi$
$157$		−	5.56231i		−	0.443920i	0.975056	−	0.221960i	$-0.0712455\pi$
$158$	−1.83270	−	8.02957i	−0.145802	−	0.638798i
$159$	1.40408	−	2.91560i	0.111351	−	0.231222i
$160$	−4.18805	+	8.69658i	−0.331095	+	0.687525i
$161$	−1.61018	−	7.05464i	−0.126900	−	0.555984i
$162$		−	12.4721i		−	0.979904i
$163$	22.4569	−	5.12565i	1.75896	−	0.401472i	0.783456	−	0.621447i	$-0.213455\pi$
$163$	22.4569	−	5.12565i	1.75896	−	0.401472i	0.975505	+	0.219975i	$0.0705977\pi$
$164$	1.37910	+	1.09979i	0.107689	+	0.0858795i
$165$	−3.71793	+	16.2893i	−0.289440	+	1.26812i
$166$	−12.5318	−	2.86031i	−0.972658	−	0.222003i
$167$	−12.1407	−	15.2239i	−0.939474	−	1.17806i	−0.983840	−	0.179048i	$-0.942698\pi$
$167$	−12.1407	−	15.2239i	−0.939474	−	1.17806i	0.0443665	−	0.999015i	$-0.485873\pi$
$168$	−7.28899	−	3.51019i	−0.562358	−	0.270817i
$169$	−4.45464	+	2.14524i	−0.342664	+	0.165018i
$170$	−19.0553	+	23.8946i	−1.46147	+	1.83263i
$171$	0.553696	−	0.441558i	0.0423422	−	0.0337668i
$172$	0.741162	+	1.53904i	0.0565131	+	0.117351i
$173$	7.09017			0.539056			0.269528	−	0.962993i	$-0.413132\pi$
$173$	7.09017			0.539056			0.269528	+	0.962993i	$0.413132\pi$
$174$		0			0
$175$	7.03444			0.531754
$176$	7.62000	+	15.8231i	0.574379	+	1.19271i
$177$	−6.43922	+	5.13510i	−0.484001	+	0.385978i
$178$	−8.78508	+	11.0161i	−0.658469	+	0.825694i
$179$	−14.4155	+	6.94214i	−1.07747	+	0.518880i	−0.886506	−	0.462718i	$-0.846874\pi$
$179$	−14.4155	+	6.94214i	−1.07747	+	0.518880i	−0.190960	+	0.981598i	$0.561160\pi$
$180$	0.607039	+	0.292334i	0.0452460	+	0.0217893i
$181$	−7.44713	−	9.33841i	−0.553541	−	0.694118i	0.423808	−	0.905752i	$-0.360693\pi$
$181$	−7.44713	−	9.33841i	−0.553541	−	0.694118i	−0.977349	+	0.211634i	$0.932122\pi$
$182$	14.9420	+	3.41041i	1.10757	+	0.252796i
$183$	0.582567	−	2.55239i	0.0430646	−	0.188678i
$184$	5.65739	+	4.51161i	0.417068	+	0.332601i
$185$	−24.2310	+	5.53056i	−1.78150	+	0.406615i
$186$		−	2.85410i		−	0.209273i
$187$	5.32810	+	23.3439i	0.389629	+	1.70708i
$188$	1.87708	−	3.89781i	0.136900	−	0.284277i
$189$	−5.30903	+	11.0243i	−0.386175	+	0.801901i
$190$	−1.90529	−	8.34763i	−0.138224	−	0.605601i
$191$			12.0344i			0.870782i	0.900242	+	0.435391i	$0.143390\pi$
$191$			12.0344i			0.870782i	−0.900242	+	0.435391i	$0.856610\pi$
$192$	6.68226	−	1.52518i	0.482250	−	0.110070i
$193$	−2.75820	−	2.19959i	−0.198539	−	0.158330i	0.519174	−	0.854669i	$-0.326240\pi$
$193$	−2.75820	−	2.19959i	−0.198539	−	0.158330i	−0.717713	+	0.696339i	$0.754811\pi$
$194$	−5.96320	+	26.1265i	−0.428133	+	1.87577i
$195$	−19.0718	−	4.35302i	−1.36576	−	0.311726i
$196$	0.770676	+	0.966397i	0.0550483	+	0.0690283i
$197$	17.7565	+	8.55107i	1.26510	+	0.609238i	0.941518	−	0.336963i	$-0.109400\pi$
$197$	17.7565	+	8.55107i	1.26510	+	0.609238i	0.323579	+	0.946201i	$0.395114\pi$
$198$	2.01463	−	0.970194i	0.143173	−	0.0689487i
$199$	0.532524	−	0.667764i	0.0377496	−	0.0473365i	−0.762598	−	0.646872i	$-0.776077\pi$
$199$	0.532524	−	0.667764i	0.0377496	−	0.0473365i	0.800348	+	0.599536i	$0.204648\pi$
$200$	−5.49975	+	4.38590i	−0.388891	+	0.310130i
$201$	7.35184	+	15.2663i	0.518559	+	1.07680i
$202$	2.61803			0.184204
$203$		0			0
$204$	−6.61803			−0.463355
$205$	3.53437	+	7.33920i	0.246851	+	0.512592i
$206$	16.6735	−	13.2967i	1.16170	−	0.926424i
$207$	0.770676	−	0.966397i	0.0535657	−	0.0671692i
$208$	−18.5260	+	8.92165i	−1.28455	+	0.618605i
$209$	−6.04388	−	2.91058i	−0.418064	−	0.201329i
$210$	10.4174	+	13.0630i	0.718869	+	0.901433i
$211$	−19.1597	−	4.37309i	−1.31901	−	0.301056i	−0.495625	−	0.868537i	$-0.665061\pi$
$211$	−19.1597	−	4.37309i	−1.31901	−	0.301056i	−0.823387	+	0.567481i	$0.807918\pi$
$212$	−0.275051	+	1.20508i	−0.0188906	+	0.0827650i
$213$	1.93279	+	1.54135i	0.132433	+	0.105612i
$214$	17.7245	−	4.04551i	1.21162	−	0.276545i
$215$			7.88854i			0.537994i
$216$	−2.72278	−	11.9293i	−0.185262	−	0.811685i
$217$	−1.05768	+	2.19629i	−0.0717997	+	0.149094i
$218$	11.6665	−	24.2257i	0.790155	−	1.64077i
$219$	0.105060	+	0.460299i	0.00709931	+	0.0311041i
$220$		−	6.38197i		−	0.430272i
$221$	−27.3316	+	6.23825i	−1.83852	+	0.419630i
$222$	−17.8245	−	14.2146i	−1.19630	−	0.954018i
$223$	−4.07797	+	17.8668i	−0.273081	+	1.19645i	0.633273	+	0.773928i	$0.281711\pi$
$223$	−4.07797	+	17.8668i	−0.273081	+	1.19645i	−0.906354	+	0.422518i	$0.861146\pi$
$224$	7.37270	+	1.68277i	0.492609	+	0.112435i
$225$	0.749202	+	0.939469i	0.0499468	+	0.0626313i
$226$	−14.4967	−	6.98126i	−0.964309	−	0.464387i
$227$	−13.4141	+	6.45990i	−0.890326	+	0.428758i	−0.822385	−	0.568931i	$-0.807357\pi$
$227$	−13.4141	+	6.45990i	−0.890326	+	0.428758i	−0.0679407	+	0.997689i	$0.521643\pi$
$228$	1.15601	−	1.44960i	0.0765589	−	0.0960018i
$229$	−12.2812	+	9.79390i	−0.811562	+	0.647199i	−0.938719	−	0.344683i	$-0.887986\pi$
$229$	−12.2812	+	9.79390i	−0.811562	+	0.647199i	0.127157	+	0.991883i	$0.459415\pi$
$230$	−6.48408	−	13.4643i	−0.427547	−	0.887811i
$231$	13.0902			0.861270
$232$		0			0
$233$	10.7639			0.705169			0.352584	−	0.935780i	$-0.385303\pi$
$233$	10.7639			0.705169			0.352584	+	0.935780i	$0.385303\pi$
$234$	1.13592	+	2.35877i	0.0742576	+	0.154197i
$235$	15.6200	−	12.4565i	1.01894	−	0.812574i
$236$	1.96144	−	2.45956i	0.127679	−	0.160104i
$237$	7.42044	−	3.57350i	0.482009	−	0.232124i
$238$	21.5730	+	10.3890i	1.39837	+	0.673421i
$239$	9.19189	+	11.5263i	0.594574	+	0.745572i	0.984521	−	0.175265i	$-0.0560782\pi$
$239$	9.19189	+	11.5263i	0.594574	+	0.745572i	−0.389947	+	0.920837i	$0.627507\pi$
$240$	−21.8544	−	4.98812i	−1.41069	−	0.321982i
$241$	5.93073	−	25.9842i	0.382032	−	1.67379i	−0.309073	−	0.951038i	$-0.600019\pi$
$241$	5.93073	−	25.9842i	0.382032	−	1.67379i	0.691105	−	0.722754i	$-0.257124\pi$
$242$	−2.64413	−	2.10862i	−0.169971	−	0.135547i
$243$	−3.84538	+	0.877683i	−0.246681	+	0.0563034i
$244$			1.00000i			0.0640184i
$245$	1.27019	+	5.56509i	0.0811498	+	0.355540i
$246$	−3.24204	+	6.73216i	−0.206705	+	0.429227i
$247$	3.40777	−	7.07630i	0.216831	−	0.450254i
$248$	−0.542438	−	2.37658i	−0.0344448	−	0.150913i
$249$		−	12.8541i		−	0.814596i
$250$	−8.34763	+	1.90529i	−0.527951	+	0.120501i
$251$	−9.11027	−	7.26520i	−0.575035	−	0.458575i	0.292281	−	0.956332i	$-0.405586\pi$
$251$	−9.11027	−	7.26520i	−0.575035	−	0.458575i	−0.867316	+	0.497757i	$0.834157\pi$
$252$	0.117461	−	0.514629i	0.00739933	−	0.0324186i
$253$	−11.4147	−	2.60532i	−0.717633	−	0.163795i
$254$	−1.96144	−	2.45956i	−0.123071	−	0.154327i
$255$	−27.5357	−	13.2605i	−1.72435	−	0.830404i
$256$	−12.2192	+	5.88446i	−0.763701	+	0.367779i
$257$	−0.511050	+	0.640836i	−0.0318784	+	0.0399743i	−0.797515	−	0.603299i	$-0.793853\pi$
$257$	−0.511050	+	0.640836i	−0.0318784	+	0.0399743i	0.765637	+	0.643273i	$0.222424\pi$
$258$	−5.65739	+	4.51161i	−0.352213	+	0.280881i
$259$	8.44864	+	17.5438i	0.524973	+	1.09012i
$260$	7.47214			0.463402
$261$		0			0
$262$	2.14590			0.132574
$263$	−1.42826	−	2.96581i	−0.0880701	−	0.182879i	0.852282	−	0.523083i	$-0.175218\pi$
$263$	−1.42826	−	2.96581i	−0.0880701	−	0.182879i	−0.940352	+	0.340204i	$0.889504\pi$
$264$	−10.2343	+	8.16159i	−0.629878	+	0.502311i
$265$	−3.55901	+	4.46285i	−0.218628	+	0.274151i
$266$	−6.04388	+	2.91058i	−0.370574	+	0.178459i
$267$	−12.6948	−	6.11350i	−0.776909	−	0.374140i
$268$	−4.03531	−	5.06012i	−0.246496	−	0.309096i
$269$	5.84957	+	1.33513i	0.356654	+	0.0814040i	0.397094	−	0.917778i	$-0.370019\pi$
$269$	5.84957	+	1.33513i	0.356654	+	0.0814040i	−0.0404396	+	0.999182i	$0.512876\pi$
$270$	−5.62322	+	24.6369i	−0.342218	+	1.49936i
$271$	−9.52297	−	7.59432i	−0.578479	−	0.461322i	0.290014	−	0.957022i	$-0.406340\pi$
$271$	−9.52297	−	7.59432i	−0.578479	−	0.461322i	−0.868494	+	0.495700i	$0.834911\pi$
$272$	−31.3192	+	7.14840i	−1.89900	+	0.433435i
$273$			15.3262i			0.927586i
$274$	−4.98812	−	21.8544i	−0.301343	−	1.32027i
$275$	4.93845	−	10.2548i	0.297800	−	0.618388i
$276$	1.40408	−	2.91560i	0.0845155	−	0.175498i
$277$	5.25551	+	23.0259i	0.315773	+	1.38349i	0.844889	+	0.534942i	$0.179666\pi$
$277$	5.25551	+	23.0259i	0.315773	+	1.38349i	−0.529116	+	0.848549i	$0.677476\pi$
$278$			23.7984i			1.42733i
$279$	−0.405968	+	0.0926595i	−0.0243046	+	0.00554738i
$280$	11.1571	+	8.89752i	0.666766	+	0.531728i
$281$	3.81058	−	16.6953i	0.227320	−	0.995956i	−0.724494	−	0.689281i	$-0.757926\pi$
$281$	3.81058	−	16.6953i	0.227320	−	0.995956i	0.951814	−	0.306675i	$-0.0992164\pi$
$282$	17.8668	+	4.07797i	1.06395	+	0.242840i
$283$	0.476304	+	0.597266i	0.0283133	+	0.0355038i	0.795787	−	0.605577i	$-0.207058\pi$
$283$	0.476304	+	0.597266i	0.0283133	+	0.0355038i	−0.767473	+	0.641081i	$0.778486\pi$
$284$	−0.850760	−	0.409704i	−0.0504833	−	0.0243115i
$285$	7.71437	−	3.71505i	0.456960	−	0.220060i
$286$	15.4615	−	19.3881i	0.914260	−	1.14645i
$287$	4.98962	−	3.97909i	0.294528	−	0.234878i
$288$	0.560489	+	1.16387i	0.0330271	+	0.0685816i
$289$	−26.7984			−1.57637
$290$		0			0
$291$	−26.7984			−1.57095
$292$	−0.0782465	−	0.162481i	−0.00457903	−	0.00950846i
$293$	13.6603	−	10.8937i	0.798041	−	0.636417i	−0.137154	−	0.990550i	$-0.543795\pi$
$293$	13.6603	−	10.8937i	0.798041	−	0.636417i	0.935195	+	0.354133i	$0.115224\pi$
$294$	−3.26463	+	4.09372i	−0.190397	+	0.238751i
$295$	13.0892	−	6.30340i	0.762080	−	0.366998i
$296$	−17.5438	−	8.44864i	−1.01971	−	0.491067i
$297$	12.3441	+	15.4790i	0.716276	+	0.898182i
$298$	11.6448	+	2.65785i	0.674565	+	0.153965i
$299$	3.05036	−	13.3645i	0.176407	−	0.772890i
$300$	2.45956	+	1.96144i	0.142003	+	0.113244i
$301$	6.02539	−	1.37526i	0.347297	−	0.0792684i
$302$		−	29.6525i		−	1.70631i
$303$	0.582567	+	2.55239i	0.0334676	+	0.146631i
$304$	3.90495	−	8.10872i	0.223964	−	0.465067i
$305$	−2.00369	+	4.16070i	−0.114731	+	0.238241i
$306$	0.910148	+	3.98762i	0.0520297	+	0.227957i
$307$		−	3.18034i		−	0.181512i	−0.995873	−	0.0907558i	$-0.971072\pi$
$307$		−	3.18034i		−	0.181512i	0.995873	−	0.0907558i	$-0.0289283\pi$
$308$	−4.87464	+	1.11260i	−0.277758	+	0.0633965i
$309$	16.6735	+	13.2967i	0.948524	+	0.756422i
$310$	−1.12027	+	4.90822i	−0.0636270	+	0.278768i
$311$	−8.86226	−	2.02275i	−0.502533	−	0.114700i	−0.0362627	−	0.999342i	$-0.511545\pi$
$311$	−8.86226	−	2.02275i	−0.502533	−	0.114700i	−0.466270	+	0.884642i	$0.654402\pi$
$312$	−9.55575	−	11.9825i	−0.540988	−	0.678377i
$313$	21.7045	+	10.4523i	1.22681	+	0.590801i	0.931200	−	0.364508i	$-0.118763\pi$
$313$	21.7045	+	10.4523i	1.22681	+	0.590801i	0.295610	+	0.955309i	$0.404477\pi$
$314$	−8.10872	+	3.90495i	−0.457602	+	0.220369i
$315$	1.51988	−	1.90587i	0.0856354	−	0.107383i
$316$	−2.45956	+	1.96144i	−0.138361	+	0.110339i
$317$	−6.20098	−	12.8765i	−0.348282	−	0.723214i	0.651077	−	0.759011i	$-0.274317\pi$
$317$	−6.20098	−	12.8765i	−0.348282	−	0.723214i	−0.999359	+	0.0357971i	$0.988603\pi$
$318$	−5.23607			−0.293624
$319$		0			0
$320$	−12.0902			−0.675861
$321$	7.88815	+	16.3799i	0.440274	+	0.914238i
$322$	−9.15384	+	7.29995i	−0.510124	+	0.406810i
$323$	7.65054	−	9.59347i	0.425687	−	0.533795i
$324$	−4.29215	+	2.06699i	−0.238453	+	0.114833i
$325$	12.0065	+	5.78204i	0.666002	+	0.320730i
$326$	−23.2378	−	29.1393i	−1.28702	−	1.61387i
$327$	26.2144	+	5.98326i	1.44966	+	0.330875i
$328$	−1.42012	+	6.22196i	−0.0784131	+	0.343550i
$329$	−12.2376	−	9.75916i	−0.674681	−	0.538040i
$330$	26.3566	−	6.01573i	1.45088	−	0.331155i
$331$		−	1.18034i		−	0.0648773i	−0.999474	−	0.0324387i	$-0.989673\pi$
$331$		−	1.18034i		−	0.0648773i	0.999474	−	0.0324387i	$-0.0103274\pi$
$332$	1.09254	+	4.78673i	0.0599609	+	0.262706i
$333$	−1.44320	+	2.99684i	−0.0790869	+	0.164226i
$334$	−13.6702	+	28.3864i	−0.748000	+	1.55324i
$335$	−6.65083	−	29.1392i	−0.363373	−	1.59204i
$336$			17.5623i			0.958102i
$337$	23.4654	−	5.35583i	1.27824	−	0.291751i	0.471086	−	0.882087i	$-0.343862\pi$
$337$	23.4654	−	5.35583i	1.27824	−	0.291751i	0.807157	+	0.590337i	$0.201005\pi$
$338$	6.25465	+	4.98792i	0.340208	+	0.271307i
$339$	3.58040	−	15.6868i	0.194461	−	0.851988i
$340$	11.3811	+	2.59766i	0.617226	+	0.140878i
$341$	2.45921	+	3.08376i	0.133174	+	0.166995i
$342$	−1.03242	−	0.497187i	−0.0558268	−	0.0268848i
$343$	18.1316	−	8.73174i	0.979017	−	0.471470i
$344$	−3.85338	+	4.83198i	−0.207760	+	0.260523i
$345$	11.6839	−	9.31760i	0.629040	−	0.501643i
$346$	−4.97757	−	10.3360i	−0.267596	−	0.555669i
$347$	−8.12461			−0.436152			−0.218076	−	0.975932i	$-0.569978\pi$
$347$	−8.12461			−0.436152			−0.218076	+	0.975932i	$0.569978\pi$
$348$		0			0
$349$	13.4721			0.721147			0.360573	−	0.932731i	$-0.382581\pi$
$349$	13.4721			0.721147			0.360573	+	0.932731i	$0.382581\pi$
$350$	−4.93845	−	10.2548i	−0.263971	−	0.548142i
$351$	−18.1231	+	14.4527i	−0.967341	+	0.771428i
$352$	7.62906	−	9.56654i	0.406630	−	0.509898i
$353$	19.0326	−	9.16563i	1.01300	−	0.487837i	0.147672	−	0.989036i	$-0.452822\pi$
$353$	19.0326	−	9.16563i	1.01300	−	0.487837i	0.865332	+	0.501199i	$0.167108\pi$
$354$	12.0065	+	5.78204i	0.638140	+	0.307312i
$355$	−2.71884	−	3.40932i	−0.144301	−	0.180948i
$356$	5.24703	+	1.19760i	0.278092	+	0.0634727i
$357$	−5.32810	+	23.3439i	−0.281993	+	1.23549i
$358$	20.2405	+	16.1412i	1.06974	+	0.853091i
$359$	27.5281	−	6.28312i	1.45288	−	0.331610i	0.578034	−	0.816013i	$-0.303820\pi$
$359$	27.5281	−	6.28312i	1.45288	−	0.331610i	0.874845	+	0.484403i	$0.160963\pi$
$360$			2.43769i			0.128478i
$361$	−3.46294	−	15.1721i	−0.182260	−	0.798533i
$362$	−8.38534	+	17.4123i	−0.440724	+	0.915172i
$363$	1.46738	−	3.04705i	0.0770175	−	0.159928i
$364$	−1.30266	−	5.70733i	−0.0682779	−	0.299145i
$365$		−	0.832816i		−	0.0435916i
$366$	−4.12986	+	0.942614i	−0.215871	+	0.0492712i
$367$	4.90248	+	3.90960i	0.255907	+	0.204079i	0.743037	−	0.669250i	$-0.233385\pi$
$367$	4.90248	+	3.90960i	0.255907	+	0.204079i	−0.487130	+	0.873330i	$0.661956\pi$
$368$	3.49540	−	15.3144i	0.182211	−	0.798317i
$369$	1.06284	+	0.242586i	0.0553291	+	0.0126285i
$370$	25.0735	+	31.4412i	1.30351	+	1.63455i
$371$	4.02926	+	1.94039i	0.209189	+	0.100740i
$372$	−0.982209	+	0.473007i	−0.0509252	+	0.0245243i
$373$	11.4610	−	14.3716i	0.593426	−	0.744133i	−0.390911	−	0.920429i	$-0.627840\pi$
$373$	11.4610	−	14.3716i	0.593426	−	0.744133i	0.984337	+	0.176295i	$0.0564114\pi$
$374$	30.2902	−	24.1556i	1.56627	−	1.24906i
$375$	−3.71505	−	7.71437i	−0.191844	−	0.398368i
$376$	15.6525			0.807215
$377$		0			0
$378$	19.7984			1.01832
$379$	−16.3610	−	33.9739i	−0.840407	−	1.74512i	−0.644661	−	0.764468i	$-0.723002\pi$
$379$	−16.3610	−	33.9739i	−0.840407	−	1.74512i	−0.195745	−	0.980655i	$-0.562713\pi$
$380$	−2.55699	+	2.03913i	−0.131171	+	0.104605i
$381$	1.96144	−	2.45956i	0.100487	−	0.126007i
$382$	17.5438	−	8.44864i	0.897618	−	0.432270i
$383$	−19.9528	−	9.60875i	−1.01954	−	0.490984i	−0.152014	−	0.988378i	$-0.548576\pi$
$383$	−19.9528	−	9.60875i	−1.01954	−	0.490984i	−0.867525	+	0.497394i	$0.834290\pi$
$384$	−13.7382	−	17.2272i	−0.701077	−	0.879123i
$385$	−22.5113	−	5.13805i	−1.14728	−	0.261859i
$386$	−1.27019	+	5.56509i	−0.0646512	+	0.283255i
$387$	0.825401	+	0.658236i	0.0419575	+	0.0334600i
$388$	9.97943	−	2.27774i	0.506629	−	0.115635i
$389$			21.1246i			1.07106i	0.844516	+	0.535530i	$0.179888\pi$
$389$			21.1246i			1.07106i	−0.844516	+	0.535530i	$0.820112\pi$
$390$	7.04334	+	30.8589i	0.356653	+	1.56260i
$391$	9.29223	−	19.2955i	0.469928	−	0.975816i
$392$	−1.94039	+	4.02926i	−0.0980043	+	0.203508i
$393$	0.477507	+	2.09210i	0.0240871	+	0.105532i
$394$		−	31.8885i		−	1.60652i
$395$	−14.1636	+	3.23275i	−0.712649	+	0.162658i
$396$	−0.667764	−	0.532524i	−0.0335564	−	0.0267603i
$397$	7.10827	−	31.1434i	0.356754	−	1.56304i	−0.404470	−	0.914551i	$-0.632544\pi$
$397$	7.10827	−	31.1434i	0.356754	−	1.56304i	0.761224	−	0.648489i	$-0.224599\pi$
$398$	−1.34732	−	0.307516i	−0.0675349	−	0.0154144i
$399$	−4.18250	−	5.24469i	−0.209387	−	0.262563i
$400$	13.7583	+	6.62563i	0.687913	+	0.331281i
$401$	29.7940	−	14.3481i	1.48784	−	0.716507i	0.499158	−	0.866511i	$-0.333643\pi$
$401$	29.7940	−	14.3481i	1.48784	−	0.716507i	0.988685	+	0.150004i	$0.0479286\pi$
$402$	17.0939	−	21.4350i	0.852564	−	1.06908i
$403$	−3.61052	+	2.87930i	−0.179853	+	0.143428i
$404$	−0.433884	−	0.900969i	−0.0215865	−	0.0448249i
$405$	−22.0000			−1.09319
$406$		0			0
$407$	31.5066			1.56172
$408$	−10.3890	−	21.5730i	−0.514334	−	1.06802i
$409$	0.456271	−	0.363864i	0.0225611	−	0.0179919i	−0.612144	−	0.790746i	$-0.709693\pi$
$409$	0.456271	−	0.363864i	0.0225611	−	0.0179919i	0.634705	+	0.772754i	$0.281121\pi$
$410$	8.21781	−	10.3048i	0.405849	−	0.508918i
$411$	20.1965	−	9.72611i	0.996219	−	0.479754i
$412$	−7.33920	−	3.53437i	−0.361576	−	0.174126i
$413$	−7.09654	−	8.89878i	−0.349198	−	0.437880i
$414$	−1.94986	−	0.445042i	−0.0958302	−	0.0218726i
$415$	−5.04539	+	22.1053i	−0.247668	+	1.08511i
$416$	11.2007	+	8.93226i	0.549160	+	0.437940i
$417$	−23.2017	+	5.29564i	−1.13619	+	0.259328i
$418$			10.8541i			0.530891i
$419$	0.570167	+	2.49806i	0.0278545	+	0.122038i	0.986944	−	0.161065i	$-0.0514930\pi$
$419$	0.570167	+	2.49806i	0.0278545	+	0.122038i	−0.959089	+	0.283104i	$0.908636\pi$
$420$	2.76903	−	5.74995i	0.135115	−	0.280569i
$421$	−0.852824	+	1.77091i	−0.0415641	+	0.0863087i	−0.920717	−	0.390231i	$-0.872395\pi$
$421$	−0.852824	+	1.77091i	−0.0415641	+	0.0863087i	0.879153	+	0.476540i	$0.158109\pi$
$422$	7.07580	+	31.0011i	0.344445	+	1.50911i
$423$		−	2.67376i		−	0.130003i
$424$	−4.36001	+	0.995144i	−0.211741	+	0.0483285i
$425$	16.2775	+	12.9808i	0.789573	+	0.629664i
$426$	0.890084	−	3.89971i	0.0431247	−	0.188942i
$427$	3.52732	+	0.805088i	0.170699	+	0.0389610i
$428$	−4.32968	−	5.42925i	−0.209283	−	0.262433i
$429$	22.3426	+	10.7596i	1.07871	+	0.519479i
$430$	11.4999	−	5.53806i	0.554575	−	0.267069i
$431$	−21.5707	+	27.0488i	−1.03902	+	1.30290i	−0.0872211	+	0.996189i	$0.527799\pi$
$431$	−21.5707	+	27.0488i	−1.03902	+	1.30290i	−0.951804	+	0.306707i	$0.900773\pi$
$432$	−20.7672	+	16.5613i	−0.999165	+	0.796807i
$433$	−5.47476	−	11.3685i	−0.263100	−	0.546333i	0.727010	−	0.686627i	$-0.240909\pi$
$433$	−5.47476	−	11.3685i	−0.263100	−	0.546333i	−0.990110	+	0.140294i	$0.955195\pi$
$434$	3.94427			0.189331
$435$		0			0
$436$	−10.2705			−0.491868
$437$	2.60330	+	5.40581i	0.124533	+	0.258595i
$438$	0.597266	−	0.476304i	0.0285385	−	0.0227587i
$439$	1.90522	−	2.38906i	0.0909310	−	0.114024i	−0.734285	−	0.678842i	$-0.762482\pi$
$439$	1.90522	−	2.38906i	0.0909310	−	0.114024i	0.825216	+	0.564818i	$0.191054\pi$
$440$	20.8035	−	10.0184i	0.991769	−	0.477611i
$441$	0.688279	+	0.331458i	0.0327752	+	0.0157837i
$442$	28.2819	+	35.4644i	1.34523	+	1.68687i
$443$	12.7620	+	2.91284i	0.606340	+	0.138393i	0.514658	−	0.857395i	$-0.327919\pi$
$443$	12.7620	+	2.91284i	0.606340	+	0.138393i	0.0916812	+	0.995788i	$0.470776\pi$
$444$	−1.93776	+	8.48987i	−0.0919619	+	0.402911i
$445$	19.4317	+	15.4963i	0.921152	+	0.734594i
$446$	28.9090	−	6.59830i	1.36888	−	0.312438i
$447$			11.9443i			0.564945i
$448$	2.10775	+	9.23465i	0.0995818	+	0.436296i
$449$	−6.12844	+	12.7258i	−0.289219	+	0.600569i	−0.994065	−	0.108791i	$-0.965302\pi$
$449$	−6.12844	+	12.7258i	−0.289219	+	0.600569i	0.704846	+	0.709361i	$0.251016\pi$
$450$	0.843588	−	1.75173i	0.0397671	−	0.0825773i
$451$	−2.29780	−	10.0673i	−0.108199	−	0.474052i
$452$			6.14590i			0.289079i
$453$	28.9090	−	6.59830i	1.35826	−	0.310015i
$454$	18.8345	+	15.0200i	0.883945	+	0.704922i
$455$	6.01573	−	26.3566i	0.282022	−	1.23562i
$456$	6.54002	+	1.49272i	0.306264	+	0.0699028i
$457$	−3.29938	−	4.13729i	−0.154339	−	0.193534i	0.698651	−	0.715463i	$-0.253784\pi$
$457$	−3.29938	−	4.13729i	−0.154339	−	0.193534i	−0.852989	+	0.521929i	$0.825213\pi$
$458$	22.8994	+	11.0278i	1.07002	+	0.515294i
$459$	−32.6284	+	15.7130i	−1.52296	+	0.733420i
$460$	−3.55901	+	4.46285i	−0.165940	+	0.208082i
$461$	−6.23801	+	4.97465i	−0.290533	+	0.231692i	−0.757900	−	0.652371i	$-0.773774\pi$
$461$	−6.23801	+	4.97465i	−0.290533	+	0.231692i	0.467366	+	0.884064i	$0.345203\pi$
$462$	−9.18981	−	19.0828i	−0.427548	−	0.887813i
$463$	2.70820			0.125861			0.0629305	−	0.998018i	$-0.479955\pi$
$463$	2.70820			0.125861			0.0629305	+	0.998018i	$0.479955\pi$
$464$		0			0
$465$	−5.03444			−0.233467
$466$	−7.55670	−	15.6916i	−0.350057	−	0.726901i
$467$	−0.0435700	+	0.0347459i	−0.00201618	+	0.00160785i	−0.624497	−	0.781027i	$-0.714696\pi$
$467$	−0.0435700	+	0.0347459i	−0.00201618	+	0.00160785i	0.622481	+	0.782635i	$0.286125\pi$
$468$	0.623490	−	0.781831i	0.0288208	−	0.0361402i
$469$	−21.0975	+	10.1600i	−0.974190	+	0.469145i
$470$	−29.1249	−	14.0258i	−1.34343	−	0.646963i
$471$	−5.61141	−	7.03648i	−0.258560	−	0.324224i
$472$	11.0966	+	2.53273i	0.510762	+	0.116578i
$473$	2.22521	−	9.74928i	0.102315	−	0.448272i
$474$	−10.4189	−	8.30877i	−0.478555	−	0.381635i
$475$	−5.68657	+	1.29792i	−0.260918	+	0.0595528i
$476$		−	9.14590i		−	0.419202i
$477$	0.169991	+	0.744779i	0.00778335	+	0.0341011i
$478$	10.3499	−	21.4918i	0.473394	−	0.983012i
$479$	4.85097	−	10.0731i	0.221646	−	0.460253i	−0.760260	−	0.649618i	$-0.774929\pi$
$479$	4.85097	−	10.0731i	0.221646	−	0.460253i	0.981907	+	0.189365i	$0.0606429\pi$
$480$	3.47534	+	15.2265i	0.158627	+	0.694990i
$481$			36.8885i			1.68197i
$482$	−42.0434	+	9.59613i	−1.91502	+	0.437092i
$483$	−9.15384	−	7.29995i	−0.416514	−	0.332159i
$484$	−0.287452	+	1.25941i	−0.0130660	+	0.0572458i
$485$	46.0853	+	10.5187i	2.09263	+	0.477629i
$486$	3.97909	+	4.98962i	0.180495	+	0.226334i
$487$	−20.2157	−	9.73535i	−0.916059	−	0.441151i	−0.0843966	−	0.996432i	$-0.526896\pi$
$487$	−20.2157	−	9.73535i	−0.916059	−	0.441151i	−0.831663	+	0.555281i	$0.812611\pi$
$488$	−3.25974	+	1.56981i	−0.147561	+	0.0710618i
$489$	23.2378	−	29.1393i	1.05085	−	1.31772i
$490$	7.22105	−	5.75859i	0.326214	−	0.260147i
$491$	−10.9012	−	22.6365i	−0.491962	−	1.02157i	−0.988169	−	0.153366i	$-0.950989\pi$
$491$	−10.9012	−	22.6365i	−0.491962	−	1.02157i	0.496207	−	0.868204i	$-0.334726\pi$
$492$	2.85410			0.128673
$493$		0			0
$494$	−12.7082			−0.571769
$495$	−1.71136	−	3.55367i	−0.0769197	−	0.159725i
$496$	−4.13729	+	3.29938i	−0.185770	+	0.148147i
$497$	−2.13010	+	2.67106i	−0.0955478	+	0.119813i
$498$	−18.7387	+	9.02408i	−0.839701	+	0.404379i
$499$	−32.1528	−	15.4840i	−1.43936	−	0.693158i	−0.458646	−	0.888619i	$-0.651665\pi$
$499$	−32.1528	−	15.4840i	−1.43936	−	0.693158i	−0.980711	+	0.195461i	$0.937380\pi$
$500$	2.03913	+	2.55699i	0.0911926	+	0.114352i
$501$	−30.7166	−	7.01087i	−1.37232	−	0.313223i
$502$	−4.19543	+	18.3814i	−0.187251	+	0.820402i
$503$	−15.0663	−	12.0150i	−0.671773	−	0.535721i	0.227133	−	0.973864i	$-0.427065\pi$
$503$	−15.0663	−	12.0150i	−0.671773	−	0.535721i	−0.898905	+	0.438143i	$0.855636\pi$
$504$	1.86195	−	0.424977i	0.0829377	−	0.0189300i
$505$		−	4.61803i		−	0.205500i
$506$	4.21550	+	18.4693i	0.187402	+	0.821061i
$507$	−3.47107	+	7.20775i	−0.154156	+	0.320107i
$508$	−0.521366	+	1.08263i	−0.0231319	+	0.0480338i
$509$	−2.54513	−	11.1509i	−0.112811	−	0.494256i	−0.999492	−	0.0318747i	$-0.989852\pi$
$509$	−2.54513	−	11.1509i	−0.112811	−	0.494256i	0.886681	−	0.462381i	$-0.153005\pi$
$510$			49.4508i			2.18972i
$511$	−0.636117	+	0.145190i	−0.0281402	+	0.00642281i
$512$	−4.13729	−	3.29938i	−0.182844	−	0.145813i
$513$	2.25767	−	9.89152i	0.0996788	−	0.436721i
$514$	1.29299	+	0.295116i	0.0570312	+	0.0130170i
$515$	−23.4545	−	29.4110i	−1.03353	−	1.29600i
$516$	2.49022	+	1.19923i	0.109626	+	0.0527929i
$517$	−22.8182	+	10.9886i	−1.00354	+	0.483280i
$518$	19.6440	−	24.6328i	0.863109	−	1.08230i
$519$	8.96928	−	7.15276i	0.393708	−	0.313971i
$520$	11.7298	+	24.3572i	0.514386	+	1.06813i
$521$	7.09017			0.310626			0.155313	−	0.987865i	$-0.450361\pi$
$521$	7.09017			0.310626			0.155313	+	0.987865i	$0.450361\pi$
$522$		0			0
$523$	−22.6180			−0.989018			−0.494509	−	0.869173i	$-0.664652\pi$
$523$	−22.6180			−0.989018			−0.494509	+	0.869173i	$0.664652\pi$
$524$	−0.355637	−	0.738488i	−0.0155361	−	0.0322610i
$525$	8.89878	−	7.09654i	0.388375	−	0.309718i
$526$	−3.32086	+	4.16422i	−0.144796	+	0.181569i
$527$	−6.50029	+	3.13038i	−0.283157	+	0.136361i
$528$	25.6023	+	12.3294i	1.11420	+	0.536569i
$529$	−7.81100	−	9.79468i	−0.339608	−	0.425856i
$530$	9.00450	+	2.05522i	0.391131	+	0.0892730i
$531$	0.432641	−	1.89552i	0.0187750	−	0.0822588i
$532$	2.00329	+	1.59757i	0.0868537	+	0.0692635i
$533$	11.7870	−	2.69032i	0.510554	−	0.116531i
$534$			22.7984i			0.986582i
$535$	−7.13600	−	31.2648i	−0.308516	−	1.35170i
$536$	10.1600	−	21.0975i	0.438845	−	0.911271i
$537$	−11.2326	+	23.3248i	−0.484723	+	1.00654i
$538$	−2.16028	−	9.46480i	−0.0931362	−	0.408056i
$539$		−	7.23607i		−	0.311680i
$540$	9.41047	−	2.14788i	0.404962	−	0.0924299i
$541$	−27.0488	−	21.5707i	−1.16292	−	0.927398i	−0.164659	−	0.986351i	$-0.552652\pi$
$541$	−27.0488	−	21.5707i	−1.16292	−	0.927398i	−0.998261	+	0.0589529i	$0.981224\pi$
$542$	−4.38549	+	19.2141i	−0.188373	+	0.825315i
$543$	−18.8417	−	4.30049i	−0.808574	−	0.184552i
$544$	13.9549	+	17.4989i	0.598313	+	0.750260i
$545$	−42.7326	−	20.5789i	−1.83046	−	0.881504i
$546$	22.3426	−	10.7596i	0.956173	−	0.460469i
$547$	5.99675	−	7.51968i	0.256402	−	0.321518i	−0.636924	−	0.770926i	$-0.719794\pi$
$547$	5.99675	−	7.51968i	0.256402	−	0.321518i	0.893327	+	0.449408i	$0.148365\pi$
$548$	−6.69428	+	5.33851i	−0.285965	+	0.228050i
$549$	0.268155	+	0.556829i	0.0114446	+	0.0237649i
$550$	−18.4164			−0.785278
$551$		0			0
$552$	11.7082			0.498334
$553$	4.93845	+	10.2548i	0.210004	+	0.436078i
$554$	29.8775	−	23.8265i	1.26937	−	1.01229i
$555$	−25.0735	+	31.4412i	−1.06431	+	1.33460i
$556$	8.18996	−	3.94408i	0.347332	−	0.167266i
$557$	29.2874	+	14.1041i	1.24095	+	0.597609i	0.935070	−	0.354462i	$-0.115336\pi$
$557$	29.2874	+	14.1041i	1.24095	+	0.597609i	0.305877	+	0.952071i	$0.401050\pi$
$558$	0.420084	+	0.526768i	0.0177836	+	0.0222999i
$559$	11.4147	+	2.60532i	0.482788	+	0.110193i
$560$	6.89341	−	30.2020i	0.291300	−	1.27627i
$561$	30.2902	+	24.1556i	1.27885	+	1.01985i
$562$	−27.0135	+	6.16566i	−1.13950	+	0.260082i
$563$		−	45.3951i		−	1.91318i	−0.291443	−	0.956588i	$-0.594135\pi$
$563$		−	45.3951i		−	1.91318i	0.291443	−	0.956588i	$-0.405865\pi$
$564$	−1.55765	−	6.82450i	−0.0655888	−	0.287363i
$565$	−12.3145	+	25.5713i	−0.518074	+	1.07579i
$566$	0.536310	−	1.11366i	0.0225428	−	0.0468106i
$567$	3.83539	+	16.8039i	0.161071	+	0.705698i
$568$		−	3.41641i		−	0.143349i
$569$	15.5445	−	3.54793i	0.651660	−	0.148737i	0.116104	−	0.993237i	$-0.462959\pi$
$569$	15.5445	−	3.54793i	0.651660	−	0.148737i	0.535556	+	0.844500i	$0.320102\pi$
$570$	−10.8316	−	8.63789i	−0.453685	−	0.361801i
$571$	−0.780287	+	3.41866i	−0.0326540	+	0.143066i	−0.988627	−	0.150388i	$-0.951948\pi$
$571$	−0.780287	+	3.41866i	−0.0326540	+	0.143066i	0.955973	+	0.293454i	$0.0948049\pi$
$572$	−9.23465	−	2.10775i	−0.386120	−	0.0881294i
$573$	12.1407	+	15.2239i	0.507184	+	0.635989i
$574$	−9.30362	−	4.48039i	−0.388326	−	0.187008i
$575$	−9.17217	+	4.41708i	−0.382506	+	0.184205i
$576$	−1.00883	+	1.26503i	−0.0420345	+	0.0527096i
$577$	5.65739	−	4.51161i	0.235520	−	0.187821i	−0.498617	−	0.866823i	$-0.666158\pi$
$577$	5.65739	−	4.51161i	0.235520	−	0.187821i	0.734137	+	0.679002i	$0.237587\pi$
$578$	18.8135	+	39.0666i	0.782538	+	1.62496i
$579$	−5.70820			−0.237225
$580$		0			0
$581$	17.7639			0.736972
$582$	18.8135	+	39.0666i	0.779844	+	1.61936i
$583$	5.65739	−	4.51161i	0.234305	−	0.186852i
$584$	0.406812	−	0.510126i	0.0168340	−	0.0211092i
$585$	4.16070	−	2.00369i	0.172024	−	0.0828424i
$586$	−25.4708	−	12.2661i	−1.05219	−	0.506709i
$587$	27.6717	+	34.6992i	1.14213	+	1.43219i	0.884863	+	0.465850i	$0.154252\pi$
$587$	27.6717	+	34.6992i	1.14213	+	1.43219i	0.257270	+	0.966340i	$0.417177\pi$
$588$	1.94986	+	0.445042i	0.0804107	+	0.0183532i
$589$	0.449779	−	1.97061i	0.0185328	−	0.0811975i
$590$	−18.3782	−	14.6561i	−0.756618	−	0.603383i
$591$	31.0890	−	7.09587i	1.27883	−	0.291885i
$592$			42.2705i			1.73731i
$593$	−7.69084	−	33.6958i	−0.315825	−	1.38372i	−0.844800	−	0.535082i	$-0.820281\pi$
$593$	−7.69084	−	33.6958i	−0.315825	−	1.38372i	0.528975	−	0.848637i	$-0.322576\pi$
$594$	13.8992	−	28.8620i	0.570292	−	1.18422i
$595$	18.3255	−	38.0534i	0.751274	−	1.56004i
$596$	−1.01521	−	4.44792i	−0.0415846	−	0.182194i
$597$		−	1.38197i		−	0.0565601i
$598$	−21.6242	+	4.93559i	−0.884281	+	0.201831i
$599$	35.2363	+	28.1000i	1.43972	+	1.14813i	0.963140	+	0.269001i	$0.0866934\pi$
$599$	35.2363	+	28.1000i	1.43972	+	1.14813i	0.476575	+	0.879134i	$0.341878\pi$
$600$	−2.53273	+	11.0966i	−0.103398	+	0.453017i
$601$	−39.1522	−	8.93623i	−1.59705	−	0.364516i	−0.670864	−	0.741581i	$-0.734076\pi$
$601$	−39.1522	−	8.93623i	−1.59705	−	0.364516i	−0.926187	+	0.377064i	$0.876934\pi$
$602$	−6.23490	−	7.81831i	−0.254115	−	0.318651i
$603$	−3.60388	−	1.73553i	−0.146761	−	0.0706764i
$604$	−10.2046	+	4.91427i	−0.415219	+	0.199959i
$605$	−3.71946	+	4.66406i	−0.151218	+	0.189621i
$606$	3.31189	−	2.64115i	0.134536	−	0.107289i
$607$	15.6106	+	32.4157i	0.633614	+	1.31571i	0.932412	+	0.361396i	$0.117700\pi$
$607$	15.6106	+	32.4157i	0.633614	+	1.31571i	−0.298798	+	0.954316i	$0.596586\pi$
$608$	−6.27051			−0.254303
$609$		0			0
$610$	7.47214			0.302538
$611$	−12.8657	−	26.7160i	−0.520492	−	1.08081i
$612$	1.22146	−	0.974082i	0.0493746	−	0.0393749i
$613$	24.6534	−	30.9144i	0.995742	−	1.24862i	0.0272369	−	0.999629i	$-0.491329\pi$
$613$	24.6534	−	30.9144i	0.995742	−	1.24862i	0.968505	−	0.248992i	$-0.0800994\pi$
$614$	−4.63629	+	2.23272i	−0.187106	+	0.0901053i
$615$	11.8751	+	5.71874i	0.478849	+	0.230602i
$616$	−11.2790	−	14.1435i	−0.454445	−	0.569856i
$617$	−7.97524	−	1.82030i	−0.321071	−	0.0732824i	0.0589479	−	0.998261i	$-0.481225\pi$
$617$	−7.97524	−	1.82030i	−0.321071	−	0.0732824i	−0.380019	+	0.924979i	$0.624083\pi$
$618$	7.67844	−	33.6414i	0.308872	−	1.35326i
$619$	19.5022	+	15.5525i	0.783860	+	0.625108i	0.931420	−	0.363945i	$-0.118571\pi$
$619$	19.5022	+	15.5525i	0.783860	+	0.625108i	−0.147560	+	0.989053i	$0.547142\pi$
$620$	1.87477	−	0.427905i	0.0752927	−	0.0171851i
$621$		−	17.7082i		−	0.710606i
$622$	3.27288	+	14.3394i	0.131231	+	0.574959i
$623$	8.44864	−	17.5438i	0.338488	−	0.702877i
$624$	−14.4355	+	29.9757i	−0.577884	+	1.19999i
$625$	6.86095	+	30.0598i	0.274438	+	1.20239i
$626$		−	38.9787i		−	1.55790i
$627$	−10.5820	+	2.41526i	−0.422603	+	0.0964564i
$628$	2.68770	+	2.14337i	0.107251	+	0.0855297i
$629$	−12.8241	+	56.1863i	−0.511332	+	2.24029i
$630$	−3.84538	−	0.877683i	−0.153204	−	0.0349677i
$631$	−14.4742	−	18.1500i	−0.576208	−	0.722542i	0.405253	−	0.914205i	$-0.367183\pi$
$631$	−14.4742	−	18.1500i	−0.576208	−	0.722542i	−0.981461	+	0.191663i	$0.938612\pi$
$632$	−10.2548	−	4.93845i	−0.407914	−	0.196441i
$633$	−28.6493	+	13.7968i	−1.13871	+	0.548373i
$634$	−14.4180	+	18.0795i	−0.572610	+	0.718031i
$635$	−4.33850	+	3.45984i	−0.172168	+	0.137300i
$636$	0.867767	+	1.80194i	0.0344092	+	0.0714515i
$637$	8.47214			0.335678
$638$		0			0
$639$	−0.583592			−0.0230865
$640$	16.8639	+	35.0182i	0.666603	+	1.38422i
$641$	22.6295	−	18.0465i	0.893813	−	0.712792i	−0.0646805	−	0.997906i	$-0.520603\pi$
$641$	22.6295	−	18.0465i	0.893813	−	0.712792i	0.958494	+	0.285114i	$0.0920314\pi$
$642$	18.3408	−	22.9987i	0.723855	−	0.907685i
$643$	−9.53549	+	4.59205i	−0.376043	+	0.181093i	−0.612352	−	0.790585i	$-0.709776\pi$
$643$	−9.53549	+	4.59205i	−0.376043	+	0.181093i	0.236309	+	0.971678i	$0.424062\pi$
$644$	4.02926	+	1.94039i	0.158775	+	0.0764620i
$645$	7.95818	+	9.97924i	0.313353	+	0.392932i
$646$	−19.3563	−	4.41795i	−0.761564	−	0.173822i
$647$	−8.78338	+	38.4825i	−0.345310	+	1.51290i	0.442378	+	0.896829i	$0.354135\pi$
$647$	−8.78338	+	38.4825i	−0.345310	+	1.51290i	−0.787688	+	0.616074i	$0.788722\pi$
$648$	−13.4757	−	10.7465i	−0.529376	−	0.422163i
$649$	−17.9547	+	4.09804i	−0.704782	+	0.160862i
$650$		−	21.5623i		−	0.845743i
$651$	0.877683	+	3.84538i	0.0343991	+	0.150712i
$652$	−6.17680	+	12.8263i	−0.241902	+	0.502315i
$653$	−12.1545	+	25.2390i	−0.475640	+	0.987678i	0.515750	+	0.856739i	$0.327513\pi$
$653$	−12.1545	+	25.2390i	−0.475640	+	0.987678i	−0.991390	+	0.130939i	$0.958201\pi$
$654$	−9.68112	−	42.4158i	−0.378562	−	1.65859i
$655$		−	3.78522i		−	0.147901i
$656$	13.5068	−	3.08283i	0.527350	−	0.120364i
$657$	−0.0871400	−	0.0694918i	−0.00339965	−	0.00271113i
$658$	−5.63562	+	24.6913i	−0.219699	+	0.962565i
$659$	−24.3189	−	5.55062i	−0.947329	−	0.216222i	−0.279171	−	0.960241i	$-0.590060\pi$
$659$	−24.3189	−	5.55062i	−0.947329	−	0.216222i	−0.668158	+	0.744020i	$0.732917\pi$
$660$	−6.43830	−	8.07338i	−0.250611	−	0.314256i
$661$	−16.6236	−	8.00552i	−0.646585	−	0.311379i	0.0816964	−	0.996657i	$-0.473966\pi$
$661$	−16.6236	−	8.00552i	−0.646585	−	0.311379i	−0.728281	+	0.685278i	$0.759680\pi$
$662$	−1.72070	+	0.828644i	−0.0668768	+	0.0322062i
$663$	−28.2819	+	35.4644i	−1.09838	+	1.37732i
$664$	−13.8884	+	11.0756i	−0.538974	+	0.429818i
$665$	5.13407	+	10.6610i	0.199091	+	0.413416i
$666$	5.38197			0.208547
$667$		0			0
$668$	12.0344			0.465627
$669$	12.8657	+	26.7160i	0.497418	+	1.03290i
$670$	−37.8099	+	30.1524i	−1.46072	+	1.16489i
$671$	3.64997	−	4.57692i	0.140906	−	0.176690i
$672$	11.0243	−	5.30903i	0.425272	−	0.204800i
$673$	2.22732	+	1.07262i	0.0858568	+	0.0413464i	0.476319	−	0.879272i	$-0.341971\pi$
$673$	2.22732	+	1.07262i	0.0858568	+	0.0413464i	−0.390463	+	0.920619i	$0.627685\pi$
$674$	−24.2814	−	30.4479i	−0.935283	−	1.17281i
$675$	16.7832	+	3.83065i	0.645985	+	0.147442i
$676$	0.679963	−	2.97911i	0.0261524	−	0.114581i
$677$	10.0331	+	8.00113i	0.385603	+	0.307508i	0.797036	−	0.603932i	$-0.206400\pi$
$677$	10.0331	+	8.00113i	0.385603	+	0.307508i	−0.411433	+	0.911440i	$0.634971\pi$
$678$	−25.3817	+	5.79321i	−0.974778	+	0.222487i
$679$		−	37.0344i		−	1.42125i
$680$	9.39841	+	41.1771i	0.360413	+	1.57907i
$681$	−10.4523	+	21.7045i	−0.400534	+	0.831718i
$682$	2.76903	−	5.74995i	0.106032	−	0.220177i
$683$	−3.14776	−	13.7912i	−0.120446	−	0.527707i	−0.998767	−	0.0496367i	$-0.984194\pi$
$683$	−3.14776	−	13.7912i	−0.120446	−	0.527707i	0.878322	−	0.478070i	$-0.158663\pi$
$684$			0.437694i			0.0167357i
$685$	−38.5496	+	8.79870i	−1.47291	+	0.336181i
$686$	−25.4582	−	20.3023i	−0.972000	−	0.775144i
$687$	−5.65568	+	24.7792i	−0.215778	+	0.945384i
$688$	13.0800	+	2.98543i	0.498671	+	0.113819i
$689$	5.28229	+	6.62378i	0.201239	+	0.252346i
$690$	−21.7857	−	10.4915i	−0.829369	−	0.399403i
$691$	37.6901	−	18.1506i	1.43380	−	0.690481i	0.454098	−	0.890952i	$-0.349962\pi$
$691$	37.6901	−	18.1506i	1.43380	−	0.690481i	0.979700	+	0.200471i	$0.0642473\pi$
$692$	−2.73211	+	3.42596i	−0.103859	+	0.130235i
$693$	−2.41599	+	1.92669i	−0.0917760	+	0.0731889i
$694$	5.70379	+	11.8440i	0.216513	+	0.449594i
$695$	41.9787			1.59234
$696$		0			0
$697$	18.8885			0.715455
$698$	−9.45796	−	19.6397i	−0.357989	−	0.743372i
$699$	13.6167	−	10.8590i	0.515031	−	0.410723i
$700$	−2.71064	+	3.39903i	−0.102452	+	0.128471i
$701$	−35.0876	+	16.8973i	−1.32524	+	0.638202i	−0.956609	−	0.291374i	$-0.905887\pi$
$701$	−35.0876	+	16.8973i	−1.32524	+	0.638202i	−0.368630	+	0.929576i	$0.620173\pi$
$702$	33.7923	+	16.2735i	1.27541	+	0.614203i
$703$	−10.0668	−	12.6234i	−0.379677	−	0.476099i
$704$	14.9420	+	3.41041i	0.563147	+	0.128535i
$705$	7.19326	−	31.5158i	0.270914	−	1.18695i
$706$	−26.7233	−	21.3111i	−1.00574	−	0.802054i
$707$	−3.52732	+	0.805088i	−0.132659	+	0.0302785i
$708$		−	5.09017i		−	0.191300i
$709$	−0.777360	−	3.40583i	−0.0291944	−	0.127909i	0.958231	−	0.285996i	$-0.0923244\pi$
$709$	−0.777360	−	3.40583i	−0.0291944	−	0.127909i	−0.987425	+	0.158087i	$0.949467\pi$
$710$	−3.06137	+	6.35699i	−0.114891	+	0.238574i
$711$	−0.843588	+	1.75173i	−0.0316370	+	0.0656949i
$712$	4.33296	+	18.9839i	0.162384	+	0.711453i
$713$		−	3.52786i		−	0.132120i
$714$	37.7713	−	8.62105i	1.41355	−	0.322635i
$715$	−34.1994	−	27.2731i	−1.27898	−	1.01996i
$716$	2.20041	−	9.64062i	0.0822331	−	0.360287i
$717$	23.2560	+	5.30804i	0.868512	+	0.198232i
$718$	−28.4853	−	35.7195i	−1.06306	−	1.33304i
$719$	26.5845	+	12.8024i	0.991435	+	0.477450i	0.858023	−	0.513611i	$-0.171692\pi$
$719$	26.5845	+	12.8024i	0.991435	+	0.477450i	0.133412	+	0.991061i	$0.457407\pi$
$720$	4.76774	−	2.29602i	0.177683	−	0.0855678i
$721$	−18.3756	+	23.0422i	−0.684342	+	0.858138i
$722$	−19.6868	+	15.6997i	−0.732666	+	0.584282i
$723$	−18.7111	−	38.8539i	−0.695872	−	1.44499i
$724$	7.38197			0.274349
$725$		0			0
$726$	−5.47214			−0.203090
$727$	19.9345	+	41.3944i	0.739329	+	1.53523i	0.841375	+	0.540452i	$0.181747\pi$
$727$	19.9345	+	41.3944i	0.739329	+	1.53523i	−0.102046	+	0.994780i	$0.532539\pi$
$728$	16.5595	−	13.2057i	0.613734	−	0.489437i
$729$	−18.3971	+	23.0692i	−0.681372	+	0.854414i
$730$	−1.21408	+	0.584669i	−0.0449350	+	0.0216396i
$731$	16.4803	+	7.93651i	0.609547	+	0.293543i
$732$	1.00883	+	1.26503i	0.0372873	+	0.0467569i
$733$	−36.2482	−	8.27340i	−1.33886	−	0.305585i	−0.507657	−	0.861560i	$-0.669488\pi$
$733$	−36.2482	−	8.27340i	−1.33886	−	0.305585i	−0.831199	+	0.555974i	$0.812345\pi$
$734$	2.25767	−	9.89152i	0.0833323	−	0.365103i
$735$	7.22105	+	5.75859i	0.266352	+	0.212409i
$736$	−10.6699	+	2.43533i	−0.393297	+	0.0897674i
$737$			37.8885i			1.39564i
$738$	−0.392512	−	1.71971i	−0.0144486	−	0.0633033i
$739$	−3.50096	+	7.26981i	−0.128785	+	0.267424i	−0.955384	−	0.295367i	$-0.904558\pi$
$739$	−3.50096	+	7.26981i	−0.128785	+	0.267424i	0.826599	+	0.562791i	$0.190272\pi$
$740$	6.66475	−	13.8395i	0.245001	−	0.508750i
$741$	−2.82784	−	12.3896i	−0.103883	−	0.455143i
$742$		−	7.23607i		−	0.265644i
$743$	29.9926	−	6.84562i	1.10032	−	0.251141i	0.366456	−	0.930435i	$-0.380571\pi$
$743$	29.9926	−	6.84562i	1.10032	−	0.251141i	0.733866	+	0.679294i	$0.237714\pi$
$744$	−3.08376	−	2.45921i	−0.113056	−	0.0901591i
$745$	4.68827	−	20.5406i	0.171765	−	0.752551i
$746$	−28.9969	−	6.61836i	−1.06165	−	0.242315i
$747$	1.89194	+	2.37242i	0.0692226	+	0.0868024i
$748$	−13.3329	−	6.42077i	−0.487498	−	0.234767i
$749$	−22.6365	+	10.9012i	−0.827119	+	0.398320i
$750$	−8.63789	+	10.8316i	−0.315411	+	0.395513i
$751$	21.4786	−	17.1286i	0.783765	−	0.625031i	−0.147630	−	0.989043i	$-0.547164\pi$
$751$	21.4786	−	17.1286i	0.783765	−	0.625031i	0.931395	+	0.364011i	$0.118593\pi$
$752$	−14.7428	−	30.6138i	−0.537615	−	1.11637i
$753$	−18.8541			−0.687082
$754$		0			0
$755$	−52.3050			−1.90357
$756$	−3.28116	−	6.81340i	−0.119335	−	0.247801i
$757$	−36.7294	+	29.2907i	−1.33495	+	1.06459i	−0.342821	+	0.939401i	$0.611383\pi$
$757$	−36.7294	+	29.2907i	−1.33495	+	1.06459i	−0.992133	+	0.125190i	$0.960046\pi$
$758$	−38.0411	+	47.7020i	−1.38171	+	1.73261i
$759$	−17.0682	+	8.21961i	−0.619536	+	0.298353i
$760$	−10.6610	−	5.13407i	−0.386715	−	0.186232i
$761$	31.0488	+	38.9339i	1.12552	+	1.41135i	0.899330	+	0.437270i	$0.144055\pi$
$761$	31.0488	+	38.9339i	1.12552	+	1.41135i	0.226187	+	0.974084i	$0.427374\pi$
$762$	−4.96255	−	1.13267i	−0.179774	−	0.0410323i
$763$	−8.26867	+	36.2274i	−0.299346	+	1.31152i
$764$	−5.81502	−	4.63733i	−0.210380	−	0.167773i
$765$	7.03389	−	1.60544i	0.254311	−	0.0580448i
$766$			35.8328i			1.29469i
$767$	−4.79806	−	21.0217i	−0.173248	−	0.759049i
$768$	−9.52126	+	19.7711i	−0.343569	+	0.713428i
$769$	11.0036	−	22.8492i	0.396799	−	0.823963i	−0.602859	−	0.797847i	$-0.705972\pi$
$769$	11.0036	−	22.8492i	0.396799	−	0.823963i	0.999659	−	0.0261152i	$-0.00831368\pi$
$770$	8.31353	+	36.4240i	0.299599	+	1.31263i

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.702039 - 1.45780i) q^{2} +(1.26503 - 1.00883i) q^{3} +(-0.385338 + 0.483198i) q^{4} +(-2.57146 + 1.23835i) q^{5} +(-2.35877 - 1.13592i) q^{6} +(1.39417 + 1.74823i) q^{7} +(-2.18001 - 0.497572i) q^{8} +(-0.0849954 + 0.372389i) q^{9} +O(q^{10})\)	\(q+(-0.702039 - 1.45780i) q^{2} +(1.26503 - 1.00883i) q^{3} +(-0.385338 + 0.483198i) q^{4} +(-2.57146 + 1.23835i) q^{5} +(-2.35877 - 1.13592i) q^{6} +(1.39417 + 1.74823i) q^{7} +(-2.18001 - 0.497572i) q^{8} +(-0.0849954 + 0.372389i) q^{9} +(3.61052 + 2.87930i) q^{10} +(3.52732 - 0.805088i) q^{11} +1.00000i q^{12} +(0.942614 + 4.12986i) q^{13} +(1.56981 - 3.25974i) q^{14} +(-2.00369 + 4.16070i) q^{15} +(1.08014 + 4.73240i) q^{16} +6.61803i q^{17} +(0.602539 - 0.137526i) q^{18} +(-1.44960 - 1.15601i) q^{19} +(0.392512 - 1.71971i) q^{20} +(3.52732 + 0.805088i) q^{21} +(-3.64997 - 4.57692i) q^{22} +(-2.91560 - 1.40408i) q^{23} +(-3.25974 + 1.56981i) q^{24} +(1.96144 - 2.45956i) q^{25} +(5.35875 - 4.27346i) q^{26} +(2.37427 + 4.93022i) q^{27} -1.38197 q^{28} +7.47214 q^{30} +(0.473007 + 0.982209i) q^{31} +(2.64413 - 2.10862i) q^{32} +(3.64997 - 4.57692i) q^{33} +(9.64776 - 4.64612i) q^{34} +(-5.74995 - 2.76903i) q^{35} +(-0.147186 - 0.184565i) q^{36} +(8.48987 + 1.93776i) q^{37} +(-0.667563 + 2.92478i) q^{38} +(5.35875 + 4.27346i) q^{39} +(6.22196 - 1.42012i) q^{40} -2.85410i q^{41} +(-1.30266 - 5.70733i) q^{42} +(1.19923 - 2.49022i) q^{43} +(-0.970194 + 2.01463i) q^{44} +(-0.242586 - 1.06284i) q^{45} +5.23607i q^{46} +(-6.82450 + 1.55765i) q^{47} +(6.14058 + 4.89695i) q^{48} +(0.445042 - 1.94986i) q^{49} +(-4.96255 - 1.13267i) q^{50} +(6.67646 + 8.37201i) q^{51} +(-2.35877 - 1.13592i) q^{52} +(1.80194 - 0.867767i) q^{53} +(5.52044 - 6.92242i) q^{54} +(-8.07338 + 6.43830i) q^{55} +(-2.16942 - 4.50484i) q^{56} -3.00000 q^{57} -5.09017 q^{59} +(-1.23835 - 2.57146i) q^{60} +(1.26503 - 1.00883i) q^{61} +(1.09979 - 1.37910i) q^{62} +(-0.769519 + 0.370581i) q^{63} +(3.81657 + 1.83796i) q^{64} +(-7.53810 - 9.45248i) q^{65} +(-9.23465 - 2.10775i) q^{66} +(-2.33027 + 10.2096i) q^{67} +(-3.19782 - 2.55018i) q^{68} +(-5.10479 + 1.16513i) q^{69} +10.3262i q^{70} +(0.339982 + 1.48956i) q^{71} +(0.370581 - 0.769519i) q^{72} +(-0.126606 + 0.262899i) q^{73} +(-3.13536 - 13.7369i) q^{74} -5.09017i q^{75} +(1.11717 - 0.254986i) q^{76} +(6.32515 + 5.04414i) q^{77} +(2.46779 - 10.8121i) q^{78} +(4.96255 + 1.13267i) q^{79} +(-8.63789 - 10.8316i) q^{80} +(6.94485 + 3.34446i) q^{81} +(-4.16070 + 2.00369i) q^{82} +(4.95317 - 6.21108i) q^{83} +(-1.74823 + 1.39417i) q^{84} +(-8.19543 - 17.0180i) q^{85} -4.47214 q^{86} -8.09017 q^{88} +(-3.77835 - 7.84582i) q^{89} +(-1.37910 + 1.09979i) q^{90} +(-5.90578 + 7.40561i) q^{91} +(1.80194 - 0.867767i) q^{92} +(1.58925 + 0.765341i) q^{93} +(7.06179 + 8.85521i) q^{94} +(5.15912 + 1.17754i) q^{95} +(1.21766 - 5.33494i) q^{96} +(-12.9489 - 10.3264i) q^{97} +(-3.15493 + 0.720093i) q^{98} +1.38197i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9	\( 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9} + 8 q^{13} + 6 q^{16} + 16 q^{20} + 10 q^{22} - 4 q^{23} - 10 q^{24} - 26 q^{25} - 60 q^{28} + 72 q^{30} - 10 q^{33} + 16 q^{34} - 30 q^{35} - 8 q^{36} - 12 q^{38} - 10 q^{42} + 18 q^{45} + 8 q^{49} - 16 q^{51} - 6 q^{52} + 8 q^{53} - 22 q^{54} - 72 q^{57} + 12 q^{59} - 16 q^{62} + 10 q^{63} + 8 q^{64} + 26 q^{65} - 24 q^{67} + 24 q^{71} - 34 q^{74} + 22 q^{78} + 42 q^{80} + 4 q^{81} - 14 q^{82} + 4 q^{83} - 60 q^{88} + 20 q^{91} + 8 q^{92} + 16 q^{93} - 14 q^{94} + 4 q^{96}+O(q^{100}) \) 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9 + 8 * q^13 + 6 * q^16 + 16 * q^20 + 10 * q^22 - 4 * q^23 - 10 * q^24 - 26 * q^25 - 60 * q^28 + 72 * q^30 - 10 * q^33 + 16 * q^34 - 30 * q^35 - 8 * q^36 - 12 * q^38 - 10 * q^42 + 18 * q^45 + 8 * q^49 - 16 * q^51 - 6 * q^52 + 8 * q^53 - 22 * q^54 - 72 * q^57 + 12 * q^59 - 16 * q^62 + 10 * q^63 + 8 * q^64 + 26 * q^65 - 24 * q^67 + 24 * q^71 - 34 * q^74 + 22 * q^78 + 42 * q^80 + 4 * q^81 - 14 * q^82 + 4 * q^83 - 60 * q^88 + 20 * q^91 + 8 * q^92 + 16 * q^93 - 14 * q^94 + 4 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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