LMFDB - Embedded newform 429.2.bi.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(5,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 8, 15]))

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

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

chi := DirichletCharacter("429.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bi (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	429.5
Dual form			429.2.bi.a.86.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15405 + 2.26495i) q^{2} +(-0.969560 + 1.43525i) q^{3} +(-2.62261 - 3.60971i) q^{4} +(2.77016 - 1.41147i) q^{5} +(-2.13186 - 3.85237i) q^{6} +(1.58890 + 0.251657i) q^{7} +(6.18102 - 0.978978i) q^{8} +(-1.11991 - 2.78313i) q^{9} +O(q^{10})$	\(q+(-1.15405 + 2.26495i) q^{2} +(-0.969560 + 1.43525i) q^{3} +(-2.62261 - 3.60971i) q^{4} +(2.77016 - 1.41147i) q^{5} +(-2.13186 - 3.85237i) q^{6} +(1.58890 + 0.251657i) q^{7} +(6.18102 - 0.978978i) q^{8} +(-1.11991 - 2.78313i) q^{9} +7.90318i q^{10} +(2.79215 + 1.78994i) q^{11} +(7.72363 - 0.264276i) q^{12} +(-3.05946 + 1.90781i) q^{13} +(-2.40366 + 3.30836i) q^{14} +(-0.660023 + 5.34438i) q^{15} +(-2.15830 + 6.64258i) q^{16} +(-2.22004 + 6.83258i) q^{17} +(7.59609 + 0.675341i) q^{18} +(6.54207 - 1.03616i) q^{19} +(-12.3600 - 6.29775i) q^{20} +(-1.90172 + 2.03648i) q^{21} +(-7.27642 + 4.25841i) q^{22} -3.95549 q^{23} +(-4.58779 + 9.82051i) q^{24} +(2.74261 - 3.77487i) q^{25} +(-0.790327 - 9.13124i) q^{26} +(5.08031 + 1.09106i) q^{27} +(-3.25865 - 6.39547i) q^{28} +(0.341238 + 0.469673i) q^{29} +(-11.3431 - 7.66261i) q^{30} +(4.25772 + 2.16942i) q^{31} +(-3.70409 - 3.70409i) q^{32} +(-5.27618 + 2.27199i) q^{33} +(-12.9134 - 12.9134i) q^{34} +(4.75670 - 1.54555i) q^{35} +(-7.10923 + 11.3416i) q^{36} +(9.55040 + 1.51263i) q^{37} +(-5.20303 + 16.0133i) q^{38} +(0.228139 - 6.24083i) q^{39} +(15.7406 - 11.4362i) q^{40} +(0.0258790 + 0.163394i) q^{41} +(-2.41783 - 6.65751i) q^{42} +1.56005i q^{43} +(-0.861546 - 14.7732i) q^{44} +(-7.03060 - 6.12900i) q^{45} +(4.56484 - 8.95900i) q^{46} +(-8.74504 + 1.38508i) q^{47} +(-7.44118 - 9.53810i) q^{48} +(-4.19613 - 1.36341i) q^{49} +(5.38480 + 10.5683i) q^{50} +(-7.65402 - 9.81092i) q^{51} +(14.9104 + 6.04032i) q^{52} +(-0.967701 + 0.314425i) q^{53} +(-8.33415 + 10.2475i) q^{54} +(10.2611 + 1.01740i) q^{55} +10.0674 q^{56} +(-4.85578 + 10.3942i) q^{57} +(-1.45759 + 0.230860i) q^{58} +(1.15746 - 7.30792i) q^{59} +(21.0227 - 11.6337i) q^{60} +(-0.521623 + 1.60539i) q^{61} +(-9.82726 + 7.13993i) q^{62} +(-1.07902 - 4.70394i) q^{63} +(-0.620846 + 0.201725i) q^{64} +(-5.78237 + 9.60324i) q^{65} +(0.943036 - 14.5723i) q^{66} +(-5.69702 + 5.69702i) q^{67} +(30.4860 - 9.90549i) q^{68} +(3.83509 - 5.67713i) q^{69} +(-1.98889 + 12.5573i) q^{70} +(11.0841 - 5.64765i) q^{71} +(-9.64679 - 16.1062i) q^{72} +(-0.653129 - 0.103445i) q^{73} +(-14.4477 + 19.8856i) q^{74} +(2.75878 + 7.59630i) q^{75} +(-20.8976 - 20.8976i) q^{76} +(3.98599 + 3.54670i) q^{77} +(13.8719 + 7.71896i) q^{78} +(0.857623 + 2.63949i) q^{79} +(3.39693 + 21.4474i) q^{80} +(-6.49162 + 6.23369i) q^{81} +(-0.399945 - 0.129950i) q^{82} +(0.842861 - 0.429459i) q^{83} +(12.3386 + 1.52380i) q^{84} +(3.49409 + 22.0608i) q^{85} +(-3.53344 - 1.80038i) q^{86} +(-1.00495 + 0.0343859i) q^{87} +(19.0107 + 8.33022i) q^{88} +(-4.46189 + 4.46189i) q^{89} +(21.9956 - 8.85082i) q^{90} +(-5.34128 + 2.26138i) q^{91} +(10.3737 + 14.2782i) q^{92} +(-7.24178 + 4.00753i) q^{93} +(6.95509 - 21.4056i) q^{94} +(16.6601 - 12.1042i) q^{95} +(8.90765 - 1.72497i) q^{96} +(3.90192 + 1.98813i) q^{97} +(7.93060 - 7.93060i) q^{98} +(1.85470 - 9.77548i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.15405	+	2.26495i	−0.816038	+	1.60156i	−0.0173265	+	0.999850i	$0.505515\pi$
$2$	−1.15405	+	2.26495i	−0.816038	+	1.60156i	−0.798711	+	0.601714i	$0.794485\pi$
$3$	−0.969560	+	1.43525i	−0.559776	+	0.828644i
$3$	−0.969560	+	1.43525i	−0.559776	+	0.828644i
$4$	−2.62261	−	3.60971i	−1.31131	−	1.80486i
$5$	2.77016	−	1.41147i	1.23885	−	0.631226i	0.293089	−	0.956085i	$-0.405317\pi$
$5$	2.77016	−	1.41147i	1.23885	−	0.631226i	0.945763	+	0.324859i	$0.105317\pi$
$6$	−2.13186	−	3.85237i	−0.870328	−	1.57272i
$7$	1.58890	+	0.251657i	0.600547	+	0.0951173i	0.449303	−	0.893379i	$-0.351672\pi$
$7$	1.58890	+	0.251657i	0.600547	+	0.0951173i	0.151244	+	0.988497i	$0.451672\pi$
$8$	6.18102	−	0.978978i	2.18532	−	0.346121i
$9$	−1.11991	−	2.78313i	−0.373302	−	0.927710i
$10$			7.90318i			2.49921i
$11$	2.79215	+	1.78994i	0.841865	+	0.539688i
$11$	2.79215	+	1.78994i	0.841865	+	0.539688i
$12$	7.72363	−	0.264276i	2.22962	−	0.0762899i
$13$	−3.05946	+	1.90781i	−0.848540	+	0.529131i
$13$	−3.05946	+	1.90781i	−0.848540	+	0.529131i
$14$	−2.40366	+	3.30836i	−0.642405	+	0.884195i
$15$	−0.660023	+	5.34438i	−0.170417	+	1.37991i
$16$	−2.15830	+	6.64258i	−0.539576	+	1.66064i
$17$	−2.22004	+	6.83258i	−0.538439	+	1.65714i	0.197661	+	0.980270i	$0.436665\pi$
$17$	−2.22004	+	6.83258i	−0.538439	+	1.65714i	−0.736100	+	0.676873i	$0.763335\pi$
$18$	7.59609	+	0.675341i	1.79042	+	0.159179i
$19$	6.54207	−	1.03616i	1.50085	−	0.237712i	0.648717	−	0.761030i	$-0.275306\pi$
$19$	6.54207	−	1.03616i	1.50085	−	0.237712i	0.852137	+	0.523318i	$0.175306\pi$
$20$	−12.3600	−	6.29775i	−2.76379	−	1.40822i
$21$	−1.90172	+	2.03648i	−0.414990	+	0.444395i
$22$	−7.27642	+	4.25841i	−1.55134	+	0.907896i
$23$	−3.95549			−0.824777			−0.412388	−	0.911008i	$-0.635305\pi$
$23$	−3.95549			−0.824777			−0.412388	+	0.911008i	$0.635305\pi$
$24$	−4.58779	+	9.82051i	−0.936480	+	2.00460i
$25$	2.74261	−	3.77487i	0.548521	−	0.754975i
$26$	−0.790327	−	9.13124i	−0.154996	−	1.79078i
$27$	5.08031	+	1.09106i	0.977707	+	0.209975i
$28$	−3.25865	−	6.39547i	−0.615827	−	1.20863i
$29$	0.341238	+	0.469673i	0.0633662	+	0.0872161i	0.839524	−	0.543323i	$-0.182834\pi$
$29$	0.341238	+	0.469673i	0.0633662	+	0.0872161i	−0.776158	+	0.630539i	$0.782834\pi$
$30$	−11.3431	−	7.66261i	−2.07095	−	1.39899i
$31$	4.25772	+	2.16942i	0.764710	+	0.389639i	0.792419	−	0.609977i	$-0.208821\pi$
$31$	4.25772	+	2.16942i	0.764710	+	0.389639i	−0.0277096	+	0.999616i	$0.508821\pi$
$32$	−3.70409	−	3.70409i	−0.654797	−	0.654797i
$33$	−5.27618	+	2.27199i	−0.918465	+	0.395502i
$34$	−12.9134	−	12.9134i	−2.21464	−	2.21464i
$35$	4.75670	−	1.54555i	0.804029	−	0.261245i
$36$	−7.10923	+	11.3416i	−1.18487	+	1.89027i
$37$	9.55040	+	1.51263i	1.57008	+	0.248676i	0.879969	−	0.475032i	$-0.157563\pi$
$37$	9.55040	+	1.51263i	1.57008	+	0.248676i	0.690107	+	0.723707i	$0.257563\pi$
$38$	−5.20303	+	16.0133i	−0.844043	+	2.59770i
$39$	0.228139	−	6.24083i	0.0365315	−	0.999333i
$40$	15.7406	−	11.4362i	2.48881	−	1.80823i
$41$	0.0258790	+	0.163394i	0.00404162	+	0.0255178i	0.989627	−	0.143663i	$-0.0458880\pi$
$41$	0.0258790	+	0.163394i	0.00404162	+	0.0255178i	−0.985585	+	0.169180i	$0.945888\pi$
$42$	−2.41783	−	6.65751i	−0.373080	−	1.02728i
$43$			1.56005i			0.237905i	0.992900	+	0.118953i	$0.0379537\pi$
$43$			1.56005i			0.237905i	−0.992900	+	0.118953i	$0.962046\pi$
$44$	−0.861546	−	14.7732i	−0.129883	−	2.22714i
$45$	−7.03060	−	6.12900i	−1.04806	−	0.913657i
$46$	4.56484	−	8.95900i	0.673049	−	1.32093i
$47$	−8.74504	+	1.38508i	−1.27560	+	0.202034i	−0.757243	−	0.653133i	$-0.773454\pi$
$47$	−8.74504	+	1.38508i	−1.27560	+	0.202034i	−0.518352	+	0.855167i	$0.673454\pi$
$48$	−7.44118	−	9.53810i	−1.07404	−	1.37671i
$49$	−4.19613	−	1.36341i	−0.599447	−	0.194772i
$50$	5.38480	+	10.5683i	0.761526	+	1.49458i
$51$	−7.65402	−	9.81092i	−1.07178	−	1.37380i
$52$	14.9104	+	6.04032i	2.06770	+	0.837642i
$53$	−0.967701	+	0.314425i	−0.132924	+	0.0431896i	−0.374723	−	0.927137i	$-0.622262\pi$
$53$	−0.967701	+	0.314425i	−0.132924	+	0.0431896i	0.241800	+	0.970326i	$0.422262\pi$
$54$	−8.33415	+	10.2475i	−1.13413	+	1.39451i
$55$	10.2611	+	1.01740i	1.38361	+	0.137186i
$56$	10.0674			1.34531
$57$	−4.85578	+	10.3942i	−0.643163	+	1.37674i
$58$	−1.45759	+	0.230860i	−0.191391	+	0.0303134i
$59$	1.15746	−	7.30792i	0.150689	−	0.951411i	−0.790238	−	0.612800i	$-0.790043\pi$
$59$	1.15746	−	7.30792i	0.150689	−	0.951411i	0.940927	−	0.338611i	$-0.109957\pi$
$60$	21.0227	−	11.6337i	2.71401	−	1.50191i
$61$	−0.521623	+	1.60539i	−0.0667870	+	0.205549i	−0.978881	−	0.204433i	$-0.934465\pi$
$61$	−0.521623	+	1.60539i	−0.0667870	+	0.205549i	0.912094	+	0.409982i	$0.134465\pi$
$62$	−9.82726	+	7.13993i	−1.24806	+	0.906771i
$63$	−1.07902	−	4.70394i	−0.135944	−	0.592641i
$64$	−0.620846	+	0.201725i	−0.0776057	+	0.0252156i
$65$	−5.78237	+	9.60324i	−0.717214	+	1.19114i
$66$	0.943036	−	14.5723i	0.116080	−	1.79373i
$67$	−5.69702	+	5.69702i	−0.696002	+	0.696002i	−0.963546	−	0.267544i	$-0.913788\pi$
$67$	−5.69702	+	5.69702i	−0.696002	+	0.696002i	0.267544	+	0.963546i	$0.413788\pi$
$68$	30.4860	−	9.90549i	3.69696	−	1.20122i
$69$	3.83509	−	5.67713i	0.461690	−	0.683446i
$70$	−1.98889	+	12.5573i	−0.237718	+	1.50089i
$71$	11.0841	−	5.64765i	1.31545	−	0.670253i	0.351459	−	0.936203i	$-0.385686\pi$
$71$	11.0841	−	5.64765i	1.31545	−	0.670253i	0.963987	+	0.265951i	$0.0856858\pi$
$72$	−9.64679	−	16.1062i	−1.13688	−	1.89814i
$73$	−0.653129	−	0.103445i	−0.0764430	−	0.0121074i	0.118096	−	0.993002i	$-0.462321\pi$
$73$	−0.653129	−	0.103445i	−0.0764430	−	0.0121074i	−0.194539	+	0.980895i	$0.562321\pi$
$74$	−14.4477	+	19.8856i	−1.67951	+	2.31165i
$75$	2.75878	+	7.59630i	0.318556	+	0.877145i
$76$	−20.8976	−	20.8976i	−2.39711	−	2.39711i
$77$	3.98599	+	3.54670i	0.454246	+	0.404184i
$78$	13.8719	+	7.71896i	1.57068	+	0.874001i
$79$	0.857623	+	2.63949i	0.0964901	+	0.296966i	0.987639	−	0.156745i	$-0.0501000\pi$
$79$	0.857623	+	2.63949i	0.0964901	+	0.296966i	−0.891149	+	0.453711i	$0.850100\pi$
$80$	3.39693	+	21.4474i	0.379788	+	2.39789i
$81$	−6.49162	+	6.23369i	−0.721291	+	0.692632i
$82$	−0.399945	−	0.129950i	−0.0441665	−	0.0143506i
$83$	0.842861	−	0.429459i	0.0925160	−	0.0471392i	−0.407120	−	0.913375i	$-0.633467\pi$
$83$	0.842861	−	0.429459i	0.0925160	−	0.0471392i	0.499636	+	0.866235i	$0.333467\pi$
$84$	12.3386	+	1.52380i	1.34625	+	0.166260i
$85$	3.49409	+	22.0608i	0.378987	+	2.39283i
$86$	−3.53344	−	1.80038i	−0.381020	−	0.194140i
$87$	−1.00495	+	0.0343859i	−0.107742	+	0.00368656i
$88$	19.0107	+	8.33022i	2.02654	+	0.888005i
$89$	−4.46189	+	4.46189i	−0.472960	+	0.472960i	−0.902871	−	0.429911i	$-0.858545\pi$
$89$	−4.46189	+	4.46189i	−0.472960	+	0.472960i	0.429911	+	0.902871i	$0.358545\pi$
$90$	21.9956	−	8.85082i	2.31854	−	0.932958i
$91$	−5.34128	+	2.26138i	−0.559918	+	0.237057i
$92$	10.3737	+	14.2782i	1.08153	+	1.48860i
$93$	−7.24178	+	4.00753i	−0.750938	+	0.415561i
$94$	6.95509	−	21.4056i	0.717363	−	2.20782i
$95$	16.6601	−	12.1042i	1.70929	−	1.24187i
$96$	8.90765	−	1.72497i	0.909133	−	0.176054i
$97$	3.90192	+	1.98813i	0.396180	+	0.201864i	0.640719	−	0.767776i	$-0.278636\pi$
$97$	3.90192	+	1.98813i	0.396180	+	0.201864i	−0.244539	+	0.969640i	$0.578636\pi$
$98$	7.93060	−	7.93060i	0.801112	−	0.801112i
$99$	1.85470	−	9.77548i	0.186404	−	0.982473i
$100$	−20.8190			−2.08190
$101$	0.389550	+	1.19891i	0.0387617	+	0.119296i	0.968565	−	0.248761i	$-0.0800232\pi$
$101$	0.389550	+	1.19891i	0.0387617	+	0.119296i	−0.929803	+	0.368057i	$0.880023\pi$
$102$	31.0544	−	6.01370i	3.07484	−	0.595445i
$103$	−7.82225	−	10.7664i	−0.770750	−	1.06085i	−0.996243	−	0.0866011i	$-0.972399\pi$
$103$	−7.82225	−	10.7664i	−0.770750	−	1.06085i	0.225494	−	0.974245i	$-0.427601\pi$
$104$	−17.0429	+	14.7873i	−1.67119	+	1.45002i
$105$	−2.39366	+	8.32557i	−0.233597	+	0.812492i
$106$	0.404619	−	2.55466i	0.0393000	−	0.248131i
$107$	6.85104	−	9.42965i	0.662315	−	0.911599i	−0.337240	−	0.941419i	$-0.609493\pi$
$107$	6.85104	−	9.42965i	0.662315	−	0.911599i	0.999555	+	0.0298198i	$0.00949334\pi$
$108$	−9.38526	−	21.1999i	−0.903097	−	2.03996i
$109$	−1.61834	+	1.61834i	−0.155009	+	0.155009i	−0.780351	−	0.625342i	$-0.784960\pi$
$109$	−1.61834	+	1.61834i	−0.155009	+	0.155009i	0.625342	+	0.780351i	$0.284960\pi$
$110$	−14.1462	+	22.0669i	−1.34879	+	2.10399i
$111$	−11.4307	+	12.2407i	−1.08495	+	1.16183i
$112$	−5.10098	+	10.0112i	−0.481997	+	0.945972i
$113$	1.22177	−	1.68162i	0.114934	−	0.158193i	−0.747674	−	0.664066i	$-0.768829\pi$
$113$	1.22177	−	1.68162i	0.114934	−	0.158193i	0.862608	+	0.505873i	$0.168829\pi$
$114$	−17.9385	−	22.9935i	−1.68009	−	2.15354i
$115$	−10.9573	+	5.58304i	−1.02178	+	0.520621i
$116$	0.800453	−	2.46354i	0.0743202	−	0.228734i
$117$	8.73598	+	6.37830i	0.807641	+	0.589674i
$118$	15.2163	+	11.0553i	1.40078	+	1.01772i
$119$	−5.24688	+	10.2976i	−0.480981	+	0.943978i
$120$	1.15241	+	33.6799i	0.105200	+	3.07454i
$121$	4.59221	+	9.99558i	0.417474	+	0.908689i
$122$	−3.03416	−	3.03416i	−0.274700	−	0.274700i
$123$	−0.259603	−	0.121277i	−0.0234076	−	0.0109352i
$124$	−3.33537	−	21.0587i	−0.299525	−	1.89113i
$125$	−0.162444	+	1.02563i	−0.0145294	+	0.0917351i
$126$	11.8995	+	2.98466i	1.06009	+	0.265894i
$127$	15.4437	+	5.01796i	1.37041	+	0.445272i	0.899504	−	0.436913i	$-0.143928\pi$
$127$	15.4437	+	5.01796i	1.37041	+	0.445272i	0.470903	+	0.882185i	$0.343928\pi$
$128$	1.89852	−	11.9868i	0.167807	−	1.05949i
$129$	−2.23907	−	1.51256i	−0.197139	−	0.133174i
$130$	−15.0777	−	24.1794i	−1.32241	−	2.12068i
$131$		−	3.73387i		−	0.326230i	−0.986607	−	0.163115i	$-0.947846\pi$
$131$		−	3.73387i		−	0.326230i	0.986607	−	0.163115i	$-0.0521542\pi$
$132$	22.0386	+	13.0870i	1.91821	+	1.13907i
$133$	10.6554			0.923944
$134$	−6.32884	−	19.4782i	−0.546728	−	1.68266i
$135$	15.6133	−	4.14827i	1.34378	−	0.357026i
$136$	−7.03317	+	44.4057i	−0.603089	+	3.80776i
$137$	−0.175099	−	0.343651i	−0.0149597	−	0.0293601i	0.883406	−	0.468609i	$-0.155245\pi$
$137$	−0.175099	−	0.343651i	−0.0149597	−	0.0293601i	−0.898365	+	0.439249i	$0.855245\pi$
$138$	8.43255	+	15.2380i	0.717827	+	1.29714i
$139$	12.6935	−	9.22234i	1.07665	−	0.782229i	0.0995503	−	0.995033i	$-0.468260\pi$
$139$	12.6935	−	9.22234i	1.07665	−	0.782229i	0.977095	+	0.212804i	$0.0682596\pi$
$140$	−18.0540	−	13.1170i	−1.52584	−	1.10859i
$141$	6.49091	−	13.8943i	0.546633	−	1.17011i
$142$			31.6227i			2.65372i
$143$	−11.9573	−	0.149361i	−0.999922	−	0.0124902i
$144$	20.9043	−	1.43222i	1.74202	−	0.119352i
$145$	1.60821	+	0.819423i	0.133554	+	0.0680494i
$146$	0.988044	−	1.35993i	0.0817711	−	0.112548i
$147$	6.02523	−	4.70061i	0.496953	−	0.387700i
$148$	−19.5868	−	38.4413i	−1.61002	−	3.15985i
$149$	−2.93589	+	1.49591i	−0.240517	+	0.122550i	−0.570095	−	0.821579i	$-0.693094\pi$
$149$	−2.93589	+	1.49591i	−0.240517	+	0.122550i	0.329578	+	0.944128i	$0.393094\pi$
$150$	−20.3890	−	2.51802i	−1.66476	−	0.205595i
$151$	−1.62273	−	10.2455i	−0.132056	−	0.833769i	−0.961425	−	0.275067i	$-0.911300\pi$
$151$	−1.62273	−	10.2455i	−0.132056	−	0.833769i	0.829369	−	0.558701i	$-0.188700\pi$
$152$	39.4223	−	12.8091i	3.19757	−	1.03895i
$153$	21.5022	−	1.47318i	1.73835	−	0.119100i
$154$	−12.6332	+	4.93501i	−1.01801	+	0.397675i
$155$	14.8566			1.19331
$156$	−23.1259	+	15.5438i	−1.85156	+	1.24450i
$157$	−9.52581	−	6.92091i	−0.760243	−	0.552349i	0.138742	−	0.990329i	$-0.455694\pi$
$157$	−9.52581	−	6.92091i	−0.760243	−	0.552349i	−0.898985	+	0.437980i	$0.855694\pi$
$158$	−6.96807	−	1.10363i	−0.554350	−	0.0878004i
$159$	0.486965	−	1.69375i	0.0386188	−	0.134323i
$160$	−15.4891	−	5.03272i	−1.22452	−	0.397871i
$161$	−6.28487	−	0.995426i	−0.495317	−	0.0784505i
$162$	−6.62734	−	21.8972i	−0.520693	−	1.72041i
$163$	6.16621	−	12.1019i	0.482975	−	0.947891i	−0.513011	−	0.858382i	$-0.671470\pi$
$163$	6.16621	−	12.1019i	0.482975	−	0.947891i	0.995986	−	0.0895093i	$-0.0285299\pi$
$164$	0.521934	−	0.521934i	0.0407562	−	0.0407562i
$165$	−11.4090	+	13.7409i	−0.888190	+	1.06973i
$166$			2.40466i			0.186638i
$167$	−10.7847	−	5.49508i	−0.834545	−	0.425222i	−0.0161441	−	0.999870i	$-0.505139\pi$
$167$	−10.7847	−	5.49508i	−0.834545	−	0.425222i	−0.818401	+	0.574648i	$0.805139\pi$
$168$	−9.76093	+	14.4492i	−0.753072	+	1.11478i
$169$	5.72054	−	11.6737i	0.440041	−	0.897977i
$170$	−53.9991	−	17.5454i	−4.14154	−	1.34567i
$171$	−10.2103	−	17.0470i	−0.780799	−	1.30362i
$172$	5.63133	−	4.09140i	0.429385	−	0.311966i
$173$	−10.1959	−	7.40779i	−0.775183	−	0.563204i	0.128346	−	0.991729i	$-0.459033\pi$
$173$	−10.1959	−	7.40779i	−0.775183	−	0.563204i	−0.903530	+	0.428526i	$0.859033\pi$
$174$	1.08188	−	2.31585i	0.0820173	−	0.175564i
$175$	5.30769	−	5.30769i	0.401224	−	0.401224i
$176$	−17.9161	+	14.6838i	−1.35048	+	1.10684i
$177$	9.36649	+	8.74672i	0.704029	+	0.657444i
$178$	−4.95673	−	15.2552i	−0.371523	−	1.14343i
$179$	−0.288124	−	0.209335i	−0.0215354	−	0.0156464i	0.576965	−	0.816769i	$-0.304237\pi$
$179$	−0.288124	−	0.209335i	−0.0215354	−	0.0156464i	−0.598501	+	0.801122i	$0.704237\pi$
$180$	−3.68539	+	41.4524i	−0.274693	+	3.08968i
$181$	−8.56512	−	2.78298i	−0.636640	−	0.206857i	−0.0271259	−	0.999632i	$-0.508635\pi$
$181$	−8.56512	−	2.78298i	−0.636640	−	0.206857i	−0.609514	+	0.792775i	$0.708635\pi$
$182$	1.04219	−	14.7075i	0.0772521	−	1.09019i
$183$	−1.79840	−	2.30519i	−0.132941	−	0.170404i
$184$	−24.4490	+	3.87234i	−1.80240	+	0.285473i
$185$	28.5911	−	9.28982i	2.10206	−	0.683001i
$186$	−0.719478	−	21.0272i	−0.0527547	−	1.54179i
$187$	−18.4286	+	15.1038i	−1.34763	+	1.10450i
$188$	27.9346	+	27.9346i	2.03734	+	2.03734i
$189$	7.79753	+	3.01208i	0.567186	+	0.219097i
$190$	8.18898	+	51.7032i	0.594091	+	3.75094i
$191$	−8.23638	−	11.3364i	−0.595964	−	0.820274i	0.399368	−	0.916791i	$-0.369230\pi$
$191$	−8.23638	−	11.3364i	−0.595964	−	0.820274i	−0.995331	+	0.0965172i	$0.969230\pi$
$192$	0.312421	−	1.08666i	0.0225470	−	0.0784226i
$193$	6.80303	−	3.46632i	0.489693	−	0.249511i	−0.191666	−	0.981460i	$-0.561389\pi$
$193$	6.80303	−	3.46632i	0.489693	−	0.249511i	0.681359	+	0.731949i	$0.261389\pi$
$194$	−9.00604	+	6.54327i	−0.646596	+	0.469779i
$195$	−8.17673	−	17.6101i	−0.585548	−	1.26108i
$196$	6.08331	+	18.7225i	0.434522	+	1.33732i
$197$	0.449971	+	0.449971i	0.0320591	+	0.0320591i	0.722955	−	0.690896i	$-0.242784\pi$
$197$	0.449971	+	0.449971i	0.0320591	+	0.0320591i	−0.690896	+	0.722955i	$0.742784\pi$
$198$	20.0006	+	15.4822i	1.42138	+	1.10027i
$199$		−	17.7089i		−	1.25535i	−0.778475	−	0.627675i	$-0.784007\pi$
$199$		−	17.7089i		−	1.25535i	0.778475	−	0.627675i	$-0.215993\pi$
$200$	13.2566	−	26.0175i	0.937383	−	1.83972i
$201$	−2.65307	−	13.7003i	−0.187133	−	0.966343i
$202$	−3.16504	−	0.501293i	−0.222692	−	0.0352709i
$203$	0.423995	+	0.832137i	0.0297586	+	0.0584046i
$204$	−15.3411	+	53.3590i	−1.07409	+	3.73588i
$205$	0.302313	+	0.416099i	0.0211145	+	0.0290616i
$206$	33.4127	−	5.29205i	2.32797	−	0.368715i
$207$	4.42978	+	11.0086i	0.307891	+	0.765154i
$208$	−6.06953	−	24.4403i	−0.420846	−	1.69463i
$209$	20.1211	+	8.81681i	1.39181	+	0.609871i
$210$	−16.0946	−	15.0297i	−1.11063	−	1.03715i
$211$	5.62025	+	17.2973i	0.386914	+	1.19080i	0.935082	+	0.354430i	$0.115325\pi$
$211$	5.62025	+	17.2973i	0.386914	+	1.19080i	−0.548169	+	0.836368i	$0.684675\pi$
$212$	3.67289	+	2.66851i	0.252255	+	0.183274i
$213$	−2.64093	+	21.3843i	−0.180954	+	1.46523i
$214$	13.4513	+	26.3996i	0.919510	+	1.80464i
$215$	2.20195	+	4.32158i	0.150172	+	0.294729i
$216$	32.4697	+	1.77038i	2.20928	+	0.120459i
$217$	6.21914	+	4.51847i	0.422183	+	0.306734i
$218$	−1.79782	−	5.53312i	−0.121764	−	0.374750i
$219$	0.781718	−	0.837109i	0.0528236	−	0.0565666i
$220$	−23.2385	−	39.7080i	−1.56674	−	2.67711i
$221$	−6.24313	−	25.1394i	−0.419959	−	1.69106i
$222$	−14.5329	−	40.0164i	−0.975384	−	2.68572i
$223$	9.44826	−	1.49646i	0.632702	−	0.100210i	0.168158	−	0.985760i	$-0.446218\pi$
$223$	9.44826	−	1.49646i	0.632702	−	0.100210i	0.464544	+	0.885550i	$0.346218\pi$
$224$	−4.95326	−	6.81758i	−0.330954	−	0.455519i
$225$	−13.5774	−	3.40553i	−0.905161	−	0.227035i
$226$	2.39881	+	4.70792i	0.159566	+	0.313166i
$227$	−2.29760	−	0.363904i	−0.152497	−	0.0241532i	0.0797191	−	0.996817i	$-0.474598\pi$
$227$	−2.29760	−	0.363904i	−0.152497	−	0.0241532i	−0.232216	+	0.972664i	$0.574598\pi$
$228$	50.2547	−	9.73185i	3.32820	−	0.644508i
$229$	−8.99502	+	17.6537i	−0.594407	+	1.16659i	0.376339	+	0.926482i	$0.377183\pi$
$229$	−8.99502	+	17.6537i	−0.594407	+	1.16659i	−0.970746	+	0.240108i	$0.922817\pi$
$230$		−	31.2610i		−	2.06129i
$231$	−8.95507	+	2.28217i	−0.589200	+	0.150156i
$232$	2.56900	+	2.56900i	0.168663	+	0.168663i
$233$	−1.93313	−	5.94957i	−0.126644	−	0.389769i	0.867553	−	0.497344i	$-0.165691\pi$
$233$	−1.93313	−	5.94957i	−0.126644	−	0.389769i	−0.994197	+	0.107575i	$0.965691\pi$
$234$	−24.5283	+	12.4257i	−1.60347	+	0.812294i
$235$	−22.2701	+	16.1802i	−1.45274	+	1.05548i
$236$	−29.4151	+	14.9877i	−1.91476	+	0.975619i
$237$	−4.61986	−	1.32824i	−0.300092	−	0.0862785i
$238$	−17.2684	−	23.7679i	−1.11934	−	1.54064i
$239$	2.87346	+	18.1423i	0.185869	+	1.17353i	0.887438	+	0.460928i	$0.152483\pi$
$239$	2.87346	+	18.1423i	0.185869	+	1.17353i	−0.701569	+	0.712602i	$0.747517\pi$
$240$	−34.0759	−	15.9191i	−2.19959	−	1.02757i
$241$	15.9623	+	15.9623i	1.02822	+	1.02822i	0.999590	+	0.0286307i	$0.00911467\pi$
$241$	15.9623	+	15.9623i	1.02822	+	1.02822i	0.0286307	+	0.999590i	$0.490885\pi$
$242$	−27.9392	−	1.13426i	−1.79600	−	0.0729129i
$243$	−2.65290	−	15.3611i	−0.170184	−	0.985412i
$244$	7.16302	−	2.32741i	0.458565	−	0.148997i
$245$	−13.5483	+	2.14585i	−0.865571	+	0.137093i
$246$	0.574282	−	0.448028i	0.0366149	−	0.0285652i
$247$	−18.0384	+	15.6511i	−1.14775	+	0.995856i
$248$	28.4409	+	9.24101i	1.80600	+	0.586805i
$249$	−0.200822	+	1.62610i	−0.0127266	+	0.103050i
$250$	−2.13553	−	1.55156i	−0.135063	−	0.0981291i
$251$	6.65414	+	20.4793i	0.420006	+	1.29264i	0.907696	+	0.419628i	$0.137839\pi$
$251$	6.65414	+	20.4793i	0.420006	+	1.29264i	−0.487691	+	0.873016i	$0.662161\pi$
$252$	−14.1500	+	16.2316i	−0.891368	+	1.02249i
$253$	−11.0443	−	7.08010i	−0.694351	−	0.445122i
$254$	−29.1883	+	29.1883i	−1.83144	+	1.83144i
$255$	−35.0506	−	16.3744i	−2.19495	−	1.02540i
$256$	23.9022	+	17.3660i	1.49389	+	1.08537i
$257$	1.00994	−	0.733767i	0.0629986	−	0.0457711i	−0.555840	−	0.831289i	$-0.687603\pi$
$257$	1.00994	−	0.733767i	0.0629986	−	0.0457711i	0.618839	+	0.785518i	$0.287603\pi$
$258$	6.00988	−	3.32581i	0.374159	−	0.207056i
$259$	14.7939	+	4.80684i	0.919251	+	0.298683i
$260$	49.8299	−	4.31287i	3.09032	−	0.267473i
$261$	0.925008	−	1.47570i	0.0572565	−	0.0913434i
$262$	8.45705	+	4.30908i	0.522478	+	0.266216i
$263$		−	12.5968i		−	0.776749i	−0.921502	−	0.388374i	$-0.873037\pi$
$263$		−	12.5968i		−	0.776749i	0.921502	−	0.388374i	$-0.126963\pi$
$264$	−30.3880	+	19.2085i	−1.87025	+	1.18220i
$265$	−2.23688	+	2.23688i	−0.137411	+	0.137411i
$266$	−12.2969	+	24.1341i	−0.753973	+	1.47976i
$267$	−2.07787	−	10.7300i	−0.127164	−	0.656667i
$268$	35.5057	+	5.62355i	2.16886	+	0.343513i
$269$	−13.1174	−	4.26209i	−0.799779	−	0.259864i	−0.119516	−	0.992832i	$-0.538134\pi$
$269$	−13.1174	−	4.26209i	−0.799779	−	0.259864i	−0.680263	+	0.732968i	$0.738134\pi$
$270$	−8.62287	+	40.1506i	−0.524771	+	2.44349i
$271$	−3.34745	−	0.530184i	−0.203343	−	0.0322064i	0.0539319	−	0.998545i	$-0.482825\pi$
$271$	−3.34745	−	0.530184i	−0.203343	−	0.0322064i	−0.257275	+	0.966338i	$0.582825\pi$
$272$	−40.5944	−	29.4936i	−2.46140	−	1.78831i
$273$	1.93304	−	9.85863i	0.116993	−	0.596671i
$274$	0.980428			0.0592298
$275$	14.4146	−	5.63091i	0.869231	−	0.339557i
$276$	−30.5508	+	1.04534i	−1.83894	+	0.0629221i
$277$	−22.6448	+	7.35775i	−1.36060	+	0.442084i	−0.896242	−	0.443565i	$-0.853713\pi$
$277$	−22.6448	+	7.35775i	−1.36060	+	0.442084i	−0.464354	+	0.885650i	$0.653713\pi$
$278$	6.23926	+	39.3932i	0.374206	+	2.36264i
$279$	1.26952	−	14.2793i	0.0760045	−	0.854882i
$280$	27.8882	−	14.2098i	1.66664	−	0.849196i
$281$	−7.94327	−	15.5896i	−0.473856	−	0.929995i	−0.996974	−	0.0777345i	$-0.975231\pi$
$281$	−7.94327	−	15.5896i	−0.473856	−	0.929995i	0.523118	−	0.852260i	$-0.324769\pi$
$282$	23.9790	+	30.7363i	1.42793	+	1.83032i
$283$	9.43293	−	12.9833i	0.560730	−	0.771778i	−0.430689	−	0.902500i	$-0.641730\pi$
$283$	9.43293	−	12.9833i	0.560730	−	0.771778i	0.991419	+	0.130722i	$0.0417295\pi$
$284$	−49.4558	−	25.1990i	−2.93466	−	1.49528i
$285$	1.21972	+	35.6472i	0.0722502	+	2.11156i
$286$	14.1377	−	26.9104i	0.835978	−	1.59125i
$287$			0.266128i			0.0157091i
$288$	−6.16074	+	14.4572i	−0.363025	+	0.851899i
$289$	−28.0023	−	20.3448i	−1.64719	−	1.19675i
$290$	−3.71191	+	2.69686i	−0.217971	+	0.158365i
$291$	−6.63662	+	3.67264i	−0.389045	+	0.215294i
$292$	1.33949	+	2.62891i	0.0783880	+	0.153845i
$293$	4.66070	−	29.4265i	0.272281	−	1.71911i	−0.350368	−	0.936612i	$-0.613944\pi$
$293$	4.66070	−	29.4265i	0.272281	−	1.71911i	0.622649	−	0.782501i	$-0.286056\pi$
$294$	3.69323	+	19.0716i	0.215393	+	1.11228i
$295$	−7.10853	−	21.8778i	−0.413875	−	1.27378i
$296$	60.5121			3.51719
$297$	12.2321	+	12.1399i	0.709776	+	0.704427i
$298$		−	8.37600i		−	0.485209i
$299$	12.1016	−	7.54631i	0.699856	−	0.436415i
$300$	20.1853	−	29.8805i	1.16540	−	1.72515i
$301$	−0.392597	+	2.47876i	−0.0226289	+	0.142873i
$302$	25.0783	+	8.14845i	1.44310	+	0.468891i
$303$	−2.09844	−	0.603314i	−0.120552	−	0.0346595i
$304$	−7.23699	+	45.6926i	−0.415070	+	2.62065i
$305$	0.820976	+	5.18344i	0.0470090	+	0.296803i
$306$	−21.4779	+	50.4016i	−1.22781	+	2.88127i
$307$	−2.45065	−	2.45065i	−0.139866	−	0.139866i	0.633707	−	0.773573i	$-0.281532\pi$
$307$	−2.45065	−	2.45065i	−0.139866	−	0.139866i	−0.773573	+	0.633707i	$0.781532\pi$
$308$	2.34886	−	23.6899i	0.133839	−	1.34986i
$309$	23.0367	−	0.788235i	1.31051	−	0.0448411i
$310$	−17.1453	+	33.6495i	−0.973788	+	1.91117i
$311$	25.7301	+	18.6940i	1.45902	+	1.06004i	0.983617	+	0.180270i	$0.0576971\pi$
$311$	25.7301	+	18.6940i	1.45902	+	1.06004i	0.475401	+	0.879769i	$0.342303\pi$
$312$	−4.69950	−	38.7981i	−0.266057	−	2.19651i
$313$	7.84214	−	24.1356i	0.443264	−	1.36423i	−0.441112	−	0.897452i	$-0.645416\pi$
$313$	7.84214	−	24.1356i	0.443264	−	1.36423i	0.884376	−	0.466774i	$-0.154584\pi$
$314$	26.6688	−	13.5884i	1.50501	−	0.766840i
$315$	−9.62851	−	11.5076i	−0.542505	−	0.648383i
$316$	7.27860	−	10.0181i	0.409453	−	0.563564i
$317$	10.7286	−	21.0562i	0.602581	−	1.18263i	−0.365221	−	0.930921i	$-0.619007\pi$
$317$	10.7286	−	21.0562i	0.602581	−	1.18263i	0.967802	−	0.251711i	$-0.0809933\pi$
$318$	3.27428	+	3.05763i	0.183613	+	0.171463i
$319$	0.112099	+	1.92219i	0.00627633	+	0.107622i
$320$	−1.43511	+	1.43511i	−0.0802252	+	0.0802252i
$321$	6.89144	+	18.9756i	0.384643	+	1.05911i
$322$	9.50766	−	13.0862i	0.529841	−	0.729264i
$323$	−7.44400	+	46.9995i	−0.414195	+	2.61512i
$324$	39.5268	+	7.08437i	2.19593	+	0.393576i
$325$	−1.18915	+	16.7814i	−0.0659621	+	0.930866i
$326$	20.2940	+	27.9324i	1.12398	+	1.54703i
$327$	−0.753650	−	3.89181i	−0.0416770	−	0.215217i
$328$	0.319918	+	0.984605i	0.0176645	+	0.0543657i
$329$	−14.2435			−0.785272
$330$	−17.9559	−	41.6986i	−0.988441	−	2.29543i
$331$	−2.53756	+	2.53756i	−0.139477	+	0.139477i	−0.773398	−	0.633921i	$-0.781444\pi$
$331$	−2.53756	+	2.53756i	−0.139477	+	0.139477i	0.633921	+	0.773398i	$0.281444\pi$
$332$	−3.76072	−	1.91618i	−0.206396	−	0.105164i
$333$	−6.48569	−	28.2740i	−0.355413	−	1.54941i
$334$	24.8922	−	18.0852i	1.36204	−	0.989580i
$335$	−7.74050	+	23.8228i	−0.422908	+	1.30158i
$336$	−9.42295	−	17.0277i	−0.514064	−	0.928936i
$337$	−2.46546	−	3.39342i	−0.134302	−	0.184851i	0.736569	−	0.676362i	$-0.236445\pi$
$337$	−2.46546	−	3.39342i	−0.134302	−	0.184851i	−0.870871	+	0.491511i	$0.836445\pi$
$338$	19.8386	+	26.4288i	1.07908	+	1.43754i
$339$	1.22897	+	3.38398i	0.0667486	+	0.183792i
$340$	70.4696	−	70.4696i	3.82175	−	3.82175i
$341$	8.00507	+	13.6784i	0.433499	+	0.740728i
$342$	50.3939	−	3.45265i	2.72499	−	0.186698i
$343$	−16.3577	−	8.33465i	−0.883231	−	0.450029i
$344$	1.52725	+	9.64270i	0.0823440	+	0.519899i
$345$	2.61072	−	21.1396i	0.140556	−	1.13812i
$346$	28.5449	−	14.5444i	1.53459	−	0.781910i
$347$	0.317526	+	0.103170i	0.0170457	+	0.00553847i	0.317527	−	0.948249i	$-0.397147\pi$
$347$	0.317526	+	0.103170i	0.0170457	+	0.00553847i	−0.300482	+	0.953788i	$0.597147\pi$
$348$	2.75972	+	3.53740i	0.147936	+	0.189625i
$349$	−1.29166	−	8.15521i	−0.0691409	−	0.436539i	−0.997839	−	0.0657025i	$-0.979071\pi$
$349$	−1.29166	−	8.15521i	−0.0691409	−	0.436539i	0.928698	−	0.370836i	$-0.120929\pi$
$350$	5.89633	+	18.1470i	0.315172	+	0.970000i
$351$	−17.6245	+	6.35420i	−0.940728	+	0.339162i
$352$	−3.71227	−	16.9725i	−0.197865	−	0.904637i
$353$	9.69885	+	9.69885i	0.516218	+	0.516218i	0.916425	−	0.400207i	$-0.131062\pi$
$353$	9.69885	+	9.69885i	0.516218	+	0.516218i	−0.400207	+	0.916425i	$0.631062\pi$
$354$	−30.6203	+	11.1205i	−1.62745	+	0.591048i
$355$	22.7333	−	31.2897i	1.20656	−	1.66069i
$356$	27.8080	+	4.40435i	1.47382	+	0.233430i
$357$	−9.69247	−	17.5147i	−0.512980	−	0.926978i
$358$	0.806644	−	0.411005i	0.0426324	−	0.0217223i
$359$	−1.29697	+	8.18878i	−0.0684517	+	0.432187i	0.929533	+	0.368738i	$0.120210\pi$
$359$	−1.29697	+	8.18878i	−0.0684517	+	0.432187i	−0.997985	+	0.0634491i	$0.979790\pi$
$360$	−49.4565	−	31.0007i	−2.60659	−	1.63388i
$361$	23.6550	−	7.68597i	1.24500	−	0.404525i
$362$	16.1879	−	16.1879i	0.850817	−	0.850817i
$363$	−18.7986	−	3.10032i	−0.986672	−	0.162725i
$364$	22.1710	+	13.3498i	1.16208	+	0.699718i
$365$	−1.95528	+	0.635309i	−0.102344	+	0.0332536i
$366$	7.29659	−	1.41299i	0.381399	−	0.0738580i
$367$	3.24347	−	2.35652i	0.169308	−	0.123009i	−0.499905	−	0.866080i	$-0.666632\pi$
$367$	3.24347	−	2.35652i	0.169308	−	0.123009i	0.669212	+	0.743071i	$0.266632\pi$
$368$	8.53715	−	26.2747i	0.445030	−	1.36966i
$369$	0.425764	−	0.255010i	0.0221644	−	0.0132753i
$370$	−11.9546	+	75.4785i	−0.621491	+	3.92394i
$371$	−1.61671	+	0.256061i	−0.0839351	+	0.0132940i
$372$	33.4584	+	15.6306i	1.73474	+	0.810408i
$373$	−17.7809			−0.920661			−0.460331	−	0.887748i	$-0.652269\pi$
$373$	−17.7809			−0.920661			−0.460331	+	0.887748i	$0.652269\pi$
$374$	−12.9420	−	59.1706i	−0.669213	−	3.05964i
$375$	−1.31454	−	1.22756i	−0.0678825	−	0.0633908i
$376$	−52.6974	+	17.1224i	−2.71766	+	0.883021i
$377$	−1.94005	−	0.785929i	−0.0999175	−	0.0404774i
$378$	−15.8210	+	14.1849i	−0.813743	+	0.729594i
$379$	1.54217	+	3.02667i	0.0792157	+	0.155470i	0.927217	−	0.374525i	$-0.122194\pi$
$379$	1.54217	+	3.02667i	0.0792157	+	0.155470i	−0.848001	+	0.529994i	$0.822194\pi$
$380$	−87.3857	−	28.3933i	−4.48279	−	1.45655i
$381$	−22.1756	+	17.3004i	−1.13609	+	0.886326i
$382$	35.1817	−	5.57223i	1.80005	−	0.285100i
$383$	8.63664	−	16.9504i	0.441311	−	0.866123i	−0.558029	−	0.829821i	$-0.688442\pi$
$383$	8.63664	−	16.9504i	0.441311	−	0.866123i	0.999341	−	0.0363014i	$-0.0115576\pi$
$384$	15.3633	+	14.3467i	0.784006	+	0.732129i
$385$	16.0479	+	4.19882i	0.817875	+	0.213992i
$386$			19.4089i			0.987885i
$387$	4.34182	−	1.74711i	0.220707	−	0.0888104i
$388$	−3.05665	−	19.2989i	−0.155178	−	0.979754i
$389$	−3.60558	+	2.61961i	−0.182810	+	0.132819i	−0.675427	−	0.737427i	$-0.736041\pi$
$389$	−3.60558	+	2.61961i	−0.182810	+	0.132819i	0.492617	+	0.870247i	$0.336041\pi$
$390$	49.3224	+	1.80302i	2.49754	+	0.0912996i
$391$	8.78134	−	27.0262i	0.444092	−	1.36677i
$392$	−27.2711	−	4.31932i	−1.37740	−	0.218159i
$393$	5.35905	+	3.62022i	0.270329	+	0.182616i
$394$	−1.53845	+	0.499873i	−0.0775061	+	0.0251833i
$395$	6.10130	+	6.10130i	0.306990	+	0.306990i
$396$	−40.1509	+	18.9424i	−2.01766	+	0.951890i
$397$	−0.413088	−	0.413088i	−0.0207323	−	0.0207323i	0.696665	−	0.717397i	$-0.254667\pi$
$397$	−0.413088	−	0.413088i	−0.0207323	−	0.0207323i	−0.717397	+	0.696665i	$0.754667\pi$
$398$	40.1098	+	20.4370i	2.01052	+	1.02441i
$399$	−10.3311	+	15.2933i	−0.517202	+	0.765621i
$400$	19.1555	+	26.3653i	0.957776	+	1.31827i
$401$	−13.6876	−	26.8634i	−0.683526	−	1.34149i	−0.928270	−	0.371907i	$-0.878704\pi$
$401$	−13.6876	−	26.8634i	−0.683526	−	1.34149i	0.244744	−	0.969588i	$-0.421296\pi$
$402$	34.0923	+	9.80176i	1.70037	+	0.488868i
$403$	−17.1651	+	1.48568i	−0.855057	+	0.0740069i
$404$	3.30609	−	4.55045i	0.164484	−	0.226393i
$405$	−9.18418	+	26.4310i	−0.456366	+	1.31337i
$406$	−2.37407			−0.117823
$407$	23.9586	+	21.3182i	1.18758	+	1.05670i
$408$	−56.9143	−	53.1484i	−2.81768	−	2.63124i
$409$	−6.07806	−	3.09692i	−0.300541	−	0.153133i	0.297217	−	0.954810i	$-0.403941\pi$
$409$	−6.07806	−	3.09692i	−0.300541	−	0.153133i	−0.597758	+	0.801677i	$0.703941\pi$
$410$	−1.29133	+	0.204527i	−0.0637742	+	0.0101008i
$411$	0.662996	+	0.0818791i	0.0327032	+	0.00403880i
$412$	−18.3489	+	56.4722i	−0.903987	+	2.78219i
$413$	3.67818	−	11.3203i	0.180991	−	0.557034i
$414$	−30.0463	−	2.67131i	−1.47669	−	0.131287i
$415$	1.72869	−	2.37934i	0.0848580	−	0.116797i
$416$	18.3992	+	4.26581i	0.902095	+	0.209149i
$417$	0.929319	+	27.1599i	0.0455089	+	1.33003i
$418$	−43.1905	+	35.3984i	−2.11252	+	1.73139i
$419$			0.616611i			0.0301234i	0.999887	+	0.0150617i	$0.00479447\pi$
$419$			0.616611i			0.0301234i	−0.999887	+	0.0150617i	$0.995206\pi$
$420$	36.3306	−	13.1943i	1.77275	−	0.643816i
$421$	4.01648	−	0.636148i	0.195751	−	0.0310039i	−0.0577889	−	0.998329i	$-0.518405\pi$
$421$	4.01648	−	0.636148i	0.195751	−	0.0310039i	0.253540	+	0.967325i	$0.418405\pi$
$422$	−45.6637	−	7.23243i	−2.22288	−	0.352069i
$423$	13.6485	+	22.7874i	0.663612	+	1.10796i
$424$	−5.67357	+	2.89083i	−0.275533	+	0.140391i
$425$	19.7034	+	27.1194i	0.955756	+	1.31549i
$426$	−45.3867	−	30.6602i	−2.19899	−	1.48549i
$427$	−1.23281	+	2.41953i	−0.0596601	+	0.117089i
$428$	−52.0060			−2.51380
$429$	11.8077	−	17.0170i	0.570082	−	0.821588i
$430$	−12.3293			−0.594574
$431$	15.5271	−	30.4736i	0.747913	−	1.46786i	−0.131255	−	0.991349i	$-0.541901\pi$
$431$	15.5271	−	30.4736i	0.747913	−	1.46786i	0.879167	−	0.476513i	$-0.158099\pi$
$432$	−18.2123	+	31.3915i	−0.876242	+	1.51033i
$433$	−4.93245	−	6.78894i	−0.237039	−	0.326256i	0.673881	−	0.738840i	$-0.264626\pi$
$433$	−4.93245	−	6.78894i	−0.237039	−	0.326256i	−0.910919	+	0.412585i	$0.864626\pi$
$434$	−17.4113	+	8.87152i	−0.835771	+	0.425846i
$435$	−2.73534	+	1.51371i	−0.131149	+	0.0725767i
$436$	10.0860	+	1.59747i	0.483033	+	0.0765049i
$437$	−25.8771	+	4.09853i	−1.23787	+	0.196059i
$438$	0.993870	+	2.73662i	0.0474889	+	0.130761i
$439$			26.1701i			1.24903i	0.781013	+	0.624515i	$0.214703\pi$
$439$			26.1701i			1.24903i	−0.781013	+	0.624515i	$0.785297\pi$
$440$	64.4203	−	3.75688i	3.07112	−	0.179102i
$441$	0.904736	+	13.2053i	0.0430826	+	0.628822i
$442$	64.1444	+	14.8717i	3.05104	+	0.707376i
$443$	10.0679	−	13.8573i	0.478341	−	0.658380i	−0.499844	−	0.866116i	$-0.666609\pi$
$443$	10.0679	−	13.8573i	0.478341	−	0.658380i	0.978185	+	0.207735i	$0.0666092\pi$
$444$	74.1635	+	9.15909i	3.51965	+	0.434671i
$445$	−6.06234	+	18.6580i	−0.287382	+	0.884472i
$446$	−7.51437	+	23.1269i	−0.355816	+	1.09509i
$447$	0.699510	−	5.66411i	0.0330857	−	0.267903i
$448$	−1.03723	+	0.164280i	−0.0490043	+	0.00776152i
$449$	5.90092	+	3.00667i	0.278482	+	0.141894i	0.587654	−	0.809113i	$-0.300052\pi$
$449$	5.90092	+	3.00667i	0.278482	+	0.141894i	−0.309172	+	0.951006i	$0.600052\pi$
$450$	23.3824	−	26.8221i	1.10226	−	1.26440i
$451$	−0.220207	+	0.502542i	−0.0103691	+	0.0236638i
$452$	−9.27438			−0.436230
$453$	16.2783	+	7.60462i	0.764819	+	0.357296i
$454$	3.47577	−	4.78399i	0.163126	−	0.224524i
$455$	−11.6043	+	13.8034i	−0.544018	+	0.647113i
$456$	−19.8380	+	69.0002i	−0.929001	+	3.23123i
$457$	8.48602	+	16.6547i	0.396959	+	0.779076i	0.999824	−	0.0187672i	$-0.00597414\pi$
$457$	8.48602	+	16.6547i	0.396959	+	0.779076i	−0.602865	+	0.797843i	$0.705974\pi$
$458$	−29.6041	−	40.7466i	−1.38331	−	1.90396i
$459$	−18.7333	+	32.2894i	−0.874394	+	1.50714i
$460$	48.8900	+	24.9107i	2.27951	+	1.16147i
$461$	−24.5004	−	24.5004i	−1.14110	−	1.14110i	−0.988250	−	0.152847i	$-0.951156\pi$
$461$	−24.5004	−	24.5004i	−1.14110	−	1.14110i	−0.152847	−	0.988250i	$-0.548844\pi$
$462$	5.16560	−	22.9166i	0.240326	−	1.06618i
$463$	11.2060	+	11.2060i	0.520785	+	0.520785i	0.917809	−	0.397023i	$-0.129957\pi$
$463$	11.2060	+	11.2060i	0.520785	+	0.520785i	−0.397023	+	0.917809i	$0.629957\pi$
$464$	−3.85634	+	1.25300i	−0.179026	+	0.0581690i
$465$	−14.4044	+	21.3230i	−0.667987	+	0.988831i
$466$	15.7064	+	2.48766i	0.727587	+	0.115238i
$467$	6.36855	−	19.6004i	0.294702	−	0.906998i	−0.688620	−	0.725122i	$-0.741783\pi$
$467$	6.36855	−	19.6004i	0.294702	−	0.906998i	0.983322	−	0.181876i	$-0.0582168\pi$
$468$	0.112761	−	48.2622i	0.00521238	−	2.23092i
$469$	−10.4857	+	7.61830i	−0.484184	+	0.351780i
$470$	−10.9465	−	69.1136i	−0.504926	−	3.18797i
$471$	19.1691	−	6.96172i	0.883266	−	0.320779i
$472$		−	46.3036i		−	2.13130i
$473$	−2.79240	+	4.35589i	−0.128395	+	0.200284i
$474$	8.33996	−	8.93091i	0.383067	−	0.410210i
$475$	14.0309	−	27.5373i	0.643784	−	1.26350i
$476$	50.9318	−	8.06681i	2.33446	−	0.369742i
$477$	1.95882	+	2.34111i	0.0896882	+	0.107192i
$478$	−44.4077	−	14.4289i	−2.03116	−	0.659963i
$479$	−1.98985	−	3.90530i	−0.0909185	−	0.178438i	0.841069	−	0.540928i	$-0.181927\pi$
$479$	−1.98985	−	3.90530i	−0.0909185	−	0.178438i	−0.931988	+	0.362490i	$0.881927\pi$
$480$	22.2409	−	17.3513i	1.01515	−	0.791974i
$481$	−32.1048	+	13.5925i	−1.46385	+	0.619764i
$482$	−54.5751	+	17.7325i	−2.48583	+	0.807695i
$483$	7.52225	−	8.05526i	0.342274	−	0.366527i
$484$	24.0376	−	42.7911i	1.09262	−	1.94505i
$485$	13.6151			0.618230
$486$	37.8537	+	11.7188i	1.71708	+	0.531574i
$487$	−13.0720	+	2.07040i	−0.592349	+	0.0938188i	−0.445410	−	0.895327i	$-0.646942\pi$
$487$	−13.0720	+	2.07040i	−0.592349	+	0.0938188i	−0.146939	+	0.989146i	$0.546942\pi$
$488$	−1.65252	+	10.4336i	−0.0748062	+	0.472308i
$489$	11.3907	+	20.5836i	0.515107	+	0.930821i
$490$	10.7752	−	33.1628i	0.486776	−	1.49814i
$491$	−29.6719	+	21.5579i	−1.33908	+	0.972895i	−0.339598	+	0.940571i	$0.610291\pi$
$491$	−29.6719	+	21.5579i	−1.33908	+	0.972895i	−0.999477	+	0.0323244i	$0.989709\pi$
$492$	0.243061	+	1.25515i	0.0109580	+	0.0565867i
$493$	−3.96664	+	1.28884i	−0.178648	+	0.0580464i
$494$	−14.6318	−	58.9183i	−0.658317	−	2.65086i
$495$	−8.65996	−	29.6975i	−0.389236	−	1.33480i
$496$	−23.6000	+	23.6000i	−1.05967	+	1.05967i
$497$	19.0328	−	6.18414i	0.853739	−	0.277397i
$498$	−3.45129	−	2.33146i	−0.154656	−	0.104475i
$499$	5.40708	−	34.1389i	0.242054	−	1.52827i	−0.504774	−	0.863251i	$-0.668424\pi$
$499$	5.40708	−	34.1389i	0.242054	−	1.52827i	0.746828	−	0.665017i	$-0.231576\pi$
$500$	4.12826	−	2.10345i	0.184621	−	0.0940692i
$501$	18.3432	−	10.1510i	0.819516	−	0.453512i
$502$	−54.0640	−	8.56289i	−2.41299	−	0.382181i
$503$	−18.0099	+	24.7885i	−0.803022	+	1.10526i	0.189341	+	0.981911i	$0.439365\pi$
$503$	−18.0099	+	24.7885i	−0.803022	+	1.10526i	−0.992363	+	0.123353i	$0.960635\pi$
$504$	−11.2745	−	28.0188i	−0.502207	−	1.24806i
$505$	2.77134	+	2.77134i	0.123323	+	0.123323i
$506$	28.7818	−	16.8441i	1.27951	−	0.748811i
$507$	11.2083	+	19.5288i	0.497779	+	0.867304i
$508$	−22.3894	−	68.9075i	−0.993369	−	3.05728i
$509$	−0.317026	−	2.00162i	−0.0140519	−	0.0887204i	0.979666	−	0.200637i	$-0.0643011\pi$
$509$	−0.317026	−	2.00162i	−0.0140519	−	0.0887204i	−0.993718	+	0.111916i	$0.964301\pi$
$510$	77.5374	−	60.4911i	3.43342	−	2.67859i
$511$	−1.01172	−	0.328729i	−0.0447560	−	0.0145421i
$512$	−45.2907	+	23.0768i	−2.00159	+	1.01986i
$513$	34.3663	+	1.87379i	1.51731	+	0.0827298i
$514$	0.496422	+	3.13428i	0.0218962	+	0.138247i
$515$	−36.8653	−	18.7838i	−1.62448	−	0.827713i
$516$	0.412283	+	12.0492i	0.0181498	+	0.530438i
$517$	−26.8967	−	11.7858i	−1.18292	−	0.518338i
$518$	−27.9603	+	27.9603i	−1.22850	+	1.22850i
$519$	20.5176	−	7.45147i	0.900624	−	0.327083i
$520$	−26.3396	+	65.0187i	−1.15507	+	2.85126i
$521$	5.23235	+	7.20171i	0.229233	+	0.315513i	0.908104	−	0.418746i	$-0.137530\pi$
$521$	5.23235	+	7.20171i	0.229233	+	0.315513i	−0.678870	+	0.734258i	$0.737530\pi$
$522$	2.27488	+	3.79813i	0.0995689	+	0.166240i
$523$	−9.76077	+	30.0406i	−0.426809	+	1.31358i	0.474443	+	0.880286i	$0.342649\pi$
$523$	−9.76077	+	30.0406i	−0.426809	+	1.31358i	−0.901252	+	0.433296i	$0.857351\pi$
$524$	−13.4782	+	9.79250i	−0.588799	+	0.427787i
$525$	2.47176	+	12.7640i	0.107876	+	0.557067i
$526$	28.5311	+	14.5373i	1.24401	+	0.633856i
$527$	−24.2750	+	24.2750i	−1.05744	+	1.05744i
$528$	−3.70426	−	39.9511i	−0.161207	−	1.73865i
$529$	−7.35410			−0.319743
$530$	−2.48496	−	7.64791i	−0.107940	−	0.332204i
$531$	−21.6351	+	4.96282i	−0.938885	+	0.215368i
$532$	−27.9451	−	38.4631i	−1.21157	−	1.66759i
$533$	−0.390899	−	0.450524i	−0.0169317	−	0.0195143i
$534$	26.7010	+	7.67672i	1.15546	+	0.332204i
$535$	5.66884	−	35.7916i	0.245085	−	1.54741i
$536$	−29.6362	+	40.7907i	−1.28009	+	1.76189i
$537$	0.579802	−	0.210569i	0.0250203	−	0.00908672i
$538$	24.7915	−	24.7915i	1.06884	−	1.06884i
$539$	−9.27581	−	11.3177i	−0.399538	−	0.487486i
$540$	−55.9216	−	45.4801i	−2.40648	−	1.95715i
$541$	4.09245	−	8.03188i	0.175948	−	0.345317i	−0.786144	−	0.618044i	$-0.787925\pi$
$541$	4.09245	−	8.03188i	0.175948	−	0.345317i	0.962092	+	0.272726i	$0.0879254\pi$
$542$	5.06397	−	6.96996i	0.217516	−	0.299386i
$543$	12.2987	−	9.59485i	0.527787	−	0.411755i
$544$	33.5317	−	17.0853i	1.43766	−	0.732525i
$545$	−2.19883	+	6.76729i	−0.0941873	+	0.289879i
$546$	20.0985	+	15.7556i	0.860137	+	0.674278i
$547$	−21.0952	−	15.3266i	−0.901968	−	0.655318i	0.0370031	−	0.999315i	$-0.488219\pi$
$547$	−21.0952	−	15.3266i	−0.901968	−	0.655318i	−0.938971	+	0.343997i	$0.888219\pi$
$548$	−0.781266	+	1.53332i	−0.0333740	+	0.0655003i
$549$	5.05218	−	0.346142i	0.215622	−	0.0147730i
$550$	−3.88141	+	39.1467i	−0.165504	+	1.66922i
$551$	2.71906	+	2.71906i	0.115836	+	0.115836i
$552$	18.1470	−	38.8449i	0.772386	−	1.65335i
$553$	0.698430	+	4.40971i	0.0297002	+	0.187520i
$554$	9.46834	−	59.7807i	0.402271	−	2.53984i
$555$	−14.3876	+	50.0426i	−0.610718	+	2.12419i
$556$	−66.5800	−	21.6332i	−2.82362	−	0.917450i
$557$	5.73490	−	36.2087i	0.242995	−	1.53421i	−0.500656	−	0.865646i	$-0.666908\pi$
$557$	5.73490	−	36.2087i	0.242995	−	1.53421i	0.743652	−	0.668567i	$-0.233092\pi$
$558$	30.8769	+	19.3545i	1.30713	+	0.819342i
$559$	−2.97627	−	4.77290i	−0.125883	−	0.201872i
$560$			34.9325i			1.47617i
$561$	−3.81021	−	41.0938i	−0.160867	−	1.73498i
$562$	44.4766			1.87613
$563$	8.80189	+	27.0894i	0.370955	+	1.14168i	0.946167	+	0.323679i	$0.104920\pi$
$563$	8.80189	+	27.0894i	0.370955	+	1.14168i	−0.575212	+	0.818005i	$0.695080\pi$
$564$	−67.1775	+	13.0089i	−2.82868	+	0.547775i
$565$	1.01094	−	6.38283i	0.0425306	−	0.268528i
$566$	18.5205	+	36.3486i	0.778476	+	1.52785i
$567$	−11.8833	+	8.27103i	−0.499051	+	0.347351i
$568$	62.9824	−	45.7594i	2.64268	−	1.92002i
$569$	22.9086	+	16.6440i	0.960376	+	0.697754i	0.953238	−	0.302220i	$-0.0977278\pi$
$569$	22.9086	+	16.6440i	0.960376	+	0.697754i	0.00713834	+	0.999975i	$0.497728\pi$
$570$	−82.1469	−	38.3761i	−3.44075	−	1.60740i
$571$			11.8679i			0.496657i	0.968676	+	0.248329i	$0.0798813\pi$
$571$			11.8679i			0.496657i	−0.968676	+	0.248329i	$0.920119\pi$
$572$	30.8203	+	43.5543i	1.28866	+	1.82109i
$573$	24.2563	−	0.829966i	1.01332	−	0.0346723i
$574$	−0.602769	−	0.307126i	−0.0251591	−	0.0128192i
$575$	−10.8483	+	14.9315i	−0.452407	+	0.622685i
$576$	1.25672	+	1.50198i	0.0523631	+	0.0625825i
$577$	−10.0905	−	19.8038i	−0.420075	−	0.824443i	−0.999953	−	0.00973945i	$-0.996900\pi$
$577$	−10.0905	−	19.8038i	−0.420075	−	0.824443i	0.579878	−	0.814703i	$-0.303100\pi$
$578$	78.3962	−	39.9448i	3.26085	−	1.66149i
$579$	−1.62090	+	13.1249i	−0.0673625	+	0.545451i
$580$	−1.25982	−	7.95420i	−0.0523113	−	0.330280i
$581$	1.44730	−	0.470255i	0.0600439	−	0.0195095i
$582$	−0.659354	−	19.2700i	−0.0273311	−	0.798769i
$583$	−3.26477	−	0.854206i	−0.135213	−	0.0353776i
$584$	−4.13828			−0.171243
$585$	33.2028	+	5.33835i	1.37277	+	0.220714i
$586$	61.2709	+	44.5159i	2.53108	+	1.83894i
$587$	−19.0550	−	3.01801i	−0.786483	−	0.124567i	−0.249740	−	0.968313i	$-0.580345\pi$
$587$	−19.0550	−	3.01801i	−0.786483	−	0.124567i	−0.536742	+	0.843746i	$0.680345\pi$
$588$	−32.7697	−	9.42151i	−1.35140	−	0.388536i
$589$	30.1022	+	9.78080i	1.24034	+	0.403011i
$590$	57.7558	+	9.14763i	2.37777	+	0.376602i
$591$	−1.08210	+	0.209548i	−0.0445115	+	0.00861966i
$592$	−30.6605	+	60.1745i	−1.26014	+	2.47316i
$593$	−22.9715	+	22.9715i	−0.943327	+	0.943327i	−0.998478	−	0.0551514i	$-0.982436\pi$
$593$	−22.9715	+	22.9715i	−0.943327	+	0.943327i	0.0551514	+	0.998478i	$0.482436\pi$
$594$	−41.6127	+	13.6950i	−1.70739	+	0.561913i
$595$			35.9317i			1.47306i
$596$	13.0995	+	6.67452i	0.536576	+	0.273399i
$597$	25.4168	+	17.1698i	1.04024	+	0.702715i
$598$	3.12613	+	36.1185i	0.127837	+	1.47700i
$599$	−18.7307	−	6.08597i	−0.765316	−	0.248666i	−0.0997573	−	0.995012i	$-0.531807\pi$
$599$	−18.7307	−	6.08597i	−0.765316	−	0.248666i	−0.665559	+	0.746346i	$0.731807\pi$
$600$	24.4887	+	44.2521i	0.999746	+	1.80659i
$601$	−23.3295	+	16.9499i	−0.951629	+	0.691399i	−0.951192	−	0.308601i	$-0.900139\pi$
$601$	−23.3295	+	16.9499i	−0.951629	+	0.691399i	−0.000437615		1.00000i	$0.500139\pi$
$602$	−5.16120	−	3.74983i	−0.210355	−	0.152832i
$603$	22.2357	+	9.47543i	0.905507	+	0.385869i
$604$	−32.7276	+	32.7276i	−1.33167	+	1.33167i
$605$	26.8296	+	21.2076i	1.09078	+	0.862210i
$606$	3.78818	−	4.05660i	0.153884	−	0.164788i
$607$	−0.0253566	−	0.0780396i	−0.00102919	−	0.00316753i	0.950541	−	0.310600i	$-0.100530\pi$
$607$	−0.0253566	−	0.0780396i	−0.00102919	−	0.00316753i	−0.951570	+	0.307433i	$0.900530\pi$
$608$	−28.0705	−	20.3944i	−1.13841	−	0.827102i
$609$	−1.60542	−	0.198267i	−0.0650548	−	0.00803418i
$610$	−12.6877	−	4.12248i	−0.513710	−	0.166915i
$611$	24.1126	−	20.9214i	0.975492	−	0.846391i
$612$	−61.7096	−	73.7532i	−2.49446	−	2.98129i
$613$	−17.2089	+	2.72562i	−0.695061	+	0.110087i	−0.493961	−	0.869484i	$-0.664452\pi$
$613$	−17.2089	+	2.72562i	−0.695061	+	0.110087i	−0.201100	+	0.979571i	$0.564452\pi$
$614$	8.37879	−	2.72243i	0.338141	−	0.109869i
$615$	−0.890318	+	0.0304636i	−0.0359011	+	0.00122841i
$616$	28.1097	+	18.0200i	1.13257	+	0.726048i
$617$	27.3493	+	27.3493i	1.10104	+	1.10104i	0.994285	+	0.106754i	$0.0340458\pi$
$617$	27.3493	+	27.3493i	1.10104	+	1.10104i	0.106754	+	0.994285i	$0.465954\pi$
$618$	−24.8002	+	53.0867i	−0.997610	+	2.13546i
$619$	−5.53829	−	34.9674i	−0.222603	−	1.40546i	−0.805348	−	0.592803i	$-0.798021\pi$
$619$	−5.53829	−	34.9674i	−0.222603	−	1.40546i	0.582745	−	0.812655i	$-0.301979\pi$
$620$	−38.9631	−	53.6281i	−1.56480	−	2.15376i
$621$	−20.0951	−	4.31569i	−0.806390	−	0.173183i
$622$	−72.0349	+	36.7036i	−2.88833	+	1.47168i
$623$	−8.21236	+	5.96663i	−0.329021	+	0.239048i
$624$	40.9628	+	14.9850i	1.63982	+	0.599882i
$625$	8.20701	+	25.2586i	0.328280	+	1.01034i
$626$	45.6159	+	45.6159i	1.82318	+	1.82318i
$627$	−32.1630	+	20.3305i	−1.28447	+	0.811921i
$628$			52.5363i			2.09643i
$629$	−31.5374	+	61.8957i	−1.25748	+	2.46794i
$630$	37.1761	−	8.52771i	1.48113	−	0.339752i
$631$	−34.8901	−	5.52605i	−1.38895	−	0.219988i	−0.583242	−	0.812298i	$-0.698216\pi$
$631$	−34.8901	−	5.52605i	−1.38895	−	0.219988i	−0.805710	+	0.592310i	$0.798216\pi$
$632$	7.88499	+	15.4752i	0.313648	+	0.615569i
$633$	−30.2752	−	8.70434i	−1.20333	−	0.345966i
$634$	35.3098	+	48.5998i	1.40233	+	1.93014i
$635$	49.8641	−	7.89770i	1.97880	−	0.313411i
$636$	−7.39107	+	2.68424i	−0.293075	+	0.106437i
$637$	15.4390	−	3.83413i	0.611715	−	0.151914i
$638$	−4.48305	−	1.96441i	−0.177486	−	0.0777718i
$639$	−28.1313	−	24.5238i	−1.11286	−	0.970145i
$640$	−11.6597	−	35.8849i	−0.460890	−	1.41847i
$641$	−36.8513	−	26.7740i	−1.45554	−	1.05751i	−0.984498	−	0.175397i	$-0.943879\pi$
$641$	−36.8513	−	26.7740i	−1.45554	−	1.05751i	−0.471039	−	0.882112i	$-0.656121\pi$
$642$	−50.9320	−	6.29003i	−2.01012	−	0.248248i
$643$	10.3692	+	20.3507i	0.408921	+	0.802553i	0.999992	−	0.00406704i	$-0.00129458\pi$
$643$	10.3692	+	20.3507i	0.408921	+	0.802553i	−0.591071	+	0.806620i	$0.701295\pi$
$644$	12.8896	+	25.2972i	0.507920	+	0.996849i
$645$	−8.33749	−	1.02967i	−0.328288	−	0.0405432i
$646$	−97.8610	−	71.1002i	−3.85029	−	2.79740i
$647$	2.28245	+	7.02466i	0.0897324	+	0.276168i	0.985845	−	0.167659i	$-0.0536206\pi$
$647$	2.28245	+	7.02466i	0.0897324	+	0.276168i	−0.896113	+	0.443827i	$0.853621\pi$
$648$	−34.0222	+	44.8857i	−1.33652	+	1.76328i
$649$	16.3126	−	18.3330i	0.640324	−	0.719635i
$650$	−36.6368	−	22.0600i	−1.43701	−	0.865264i
$651$	−12.5150	+	4.54511i	−0.490501	+	0.178137i
$652$	−59.8558	+	9.48023i	−2.34414	+	0.371275i
$653$	3.53791	+	4.86952i	0.138449	+	0.190559i	0.872611	−	0.488415i	$-0.162425\pi$
$653$	3.53791	+	4.86952i	0.138449	+	0.190559i	−0.734162	+	0.678974i	$0.762425\pi$
$654$	9.68452	+	2.78436i	0.378695	+	0.108877i
$655$	−5.27023	−	10.3434i	−0.205925	−	0.404151i
$656$	−1.14121	−	0.180750i	−0.0445568	−	0.00705710i
$657$	0.443541	+	1.93359i	0.0173042	+	0.0754366i
$658$	16.4378	−	32.2610i	0.640812	−	1.25766i
$659$			18.0420i			0.702815i	0.936223	+	0.351408i	$0.114297\pi$
$659$			18.0420i			0.702815i	−0.936223	+	0.351408i	$0.885703\pi$
$660$	79.5221	+	5.14622i	3.09539	+	0.200316i
$661$	−8.74427	−	8.74427i	−0.340113	−	0.340113i	0.516297	−	0.856410i	$-0.327310\pi$
$661$	−8.74427	−	8.74427i	−0.340113	−	0.340113i	−0.856410	+	0.516297i	$0.827310\pi$
$662$	−2.81898	−	8.67593i	−0.109563	−	0.337200i
$663$	42.1345	+	15.4137i	1.63637	+	0.598617i
$664$	4.78931	−	3.47964i	0.185861	−	0.135036i
$665$	29.5172	−	15.0398i	1.14463	−	0.583218i
$666$	71.5241	+	17.9399i	2.77150	+	0.695156i
$667$	−1.34976	−	1.85779i	−0.0522630	−	0.0719338i
$668$	8.44840	+	53.3411i	0.326879	+	2.06383i
$669$	−7.01286	+	15.0116i	−0.271133	+	0.580380i
$670$	−45.0246	−	45.0246i	−1.73945	−	1.73945i
$671$	−4.33001	+	3.54882i	−0.167158	+	0.137001i
$672$	14.5875	−	0.499132i	0.562723	−	0.0192544i
$673$	45.8348	−	14.8926i	1.76680	−	0.574069i	0.768934	−	0.639328i	$-0.220787\pi$
$673$	45.8348	−	14.8926i	1.76680	−	0.574069i	0.997868	+	0.0652589i	$0.0207873\pi$
$674$	10.5312	−	1.66798i	0.405647	−	0.0642481i
$675$	18.0519	−	16.1852i	0.694819	−	0.622968i
$676$	−57.1415	+	9.96608i	−2.19775	+	0.383311i
$677$	−3.59240	−	1.16724i	−0.138067	−	0.0448607i	0.239168	−	0.970978i	$-0.423125\pi$
$677$	−3.59240	−	1.16724i	−0.138067	−	0.0448607i	−0.377235	+	0.926117i	$0.623125\pi$
$678$	−9.08285	−	1.12172i	−0.348825	−	0.0430794i
$679$	5.69943	+	4.14088i	0.218724	+	0.158912i
$680$	43.1941	+	132.938i	1.65642	+	5.09793i
$681$	2.74996	−	2.94481i	0.105379	−	0.112845i
$682$	−40.2193	+	2.34552i	−1.54007	+	0.0898144i
$683$	33.1020	−	33.1020i	1.26661	−	1.26661i	0.318784	−	0.947827i	$-0.396725\pi$
$683$	33.1020	−	33.1020i	1.26661	−	1.26661i	0.947827	−	0.318784i	$-0.103275\pi$
$684$	−34.7573	+	81.5639i	−1.32898	+	3.11867i
$685$	−0.970104	−	0.704822i	−0.0370658	−	0.0269299i
$686$	37.7552	−	27.4308i	1.44150	−	1.04731i
$687$	−16.6163	−	30.0265i	−0.633953	−	1.14558i
$688$	−10.3627	−	3.36706i	−0.395076	−	0.128368i
$689$	2.36078	−	2.80816i	0.0899384	−	0.106982i
$690$	44.8674	+	30.3094i	1.70807	+	1.15386i
$691$	10.6757	+	5.43955i	0.406123	+	0.206930i	0.645105	−	0.764094i	$-0.276814\pi$
$691$	10.6757	+	5.43955i	0.406123	+	0.206930i	−0.238982	+	0.971024i	$0.576814\pi$
$692$			56.2322i			2.13763i
$693$	5.40699	−	15.0655i	0.205395	−	0.572291i
$694$	−0.600117	+	0.600117i	−0.0227801	+	0.0227801i
$695$	22.1459	−	43.4637i	0.840040	−	1.64867i
$696$	−6.17796	+	1.19636i	−0.234175	+	0.0453481i
$697$	−1.17385	−	0.185920i	−0.0444628	−	0.00704222i
$698$	19.9618	+	6.48599i	0.755566	+	0.245498i
$699$	10.4134	+	2.99393i	0.393872	+	0.113241i
$700$	−33.0793	−	5.23924i	−1.25028	−	0.198025i
$701$	−22.9603	−	16.6816i	−0.867198	−	0.630056i	0.0626355	−	0.998036i	$-0.480049\pi$
$701$	−22.9603	−	16.6816i	−0.867198	−	0.630056i	−0.929834	+	0.367980i	$0.880049\pi$
$702$	5.94765	−	47.2518i	0.224480	−	1.78341i
$703$	64.0467			2.41557
$704$	−2.09457	−	0.548031i	−0.0789421	−	0.0206547i
$705$	−1.63045	−	47.6510i	−0.0614063	−	1.79464i
$706$	−33.1604	+	10.7745i	−1.24801	+	0.405503i
$707$	0.317241	+	2.00298i	0.0119311	+	0.0753299i
$708$	7.00850	−	56.7496i	0.263396	−	2.13278i
$709$	21.1072	−	10.7546i	0.792697	−	0.403899i	−0.0102516	−	0.999947i	$-0.503263\pi$
$709$	21.1072	−	10.7546i	0.792697	−	0.403899i	0.802949	+	0.596048i	$0.203263\pi$
$710$	44.6344	+	87.5999i	1.67510	+	3.28757i
$711$	6.38559	−	5.34286i	0.239478	−	0.200373i
$712$	−23.2110	+	31.9472i	−0.869868	+	1.19727i
$713$	−16.8414	−	8.58111i	−0.630715	−	0.321365i
$714$	50.8557	−	1.74010i	1.90323	−	0.0651218i
$715$	−33.3345	+	16.4636i	−1.24664	+	0.615704i
$716$			1.58905i			0.0593856i
$717$	−28.8248	−	13.4659i	−1.07648	−	0.502894i
$718$	−17.0504	−	12.3879i	−0.636316	−	0.462311i
$719$	32.6424	−	23.7161i	1.21736	−	0.884462i	0.221480	−	0.975165i	$-0.428911\pi$
$719$	32.6424	−	23.7161i	1.21736	−	0.884462i	0.995878	+	0.0907027i	$0.0289113\pi$
$720$	55.8865	−	33.4731i	2.08277	−	1.24747i
$721$	−9.71932	−	19.0752i	−0.361967	−	0.710399i
$722$	−9.89071	+	62.4475i	−0.368094	+	2.32406i
$723$	−38.3863	+	7.43353i	−1.42760	+	0.276456i
$724$	12.4172	+	38.2163i	0.461483	+	1.42030i
$725$	2.70884			0.100604
$726$	28.7167	−	39.0001i	1.06578	−	1.44743i
$727$		−	24.1069i		−	0.894074i	−0.894515	−	0.447037i	$-0.852479\pi$
$727$		−	24.1069i		−	0.894074i	0.894515	−	0.447037i	$-0.147521\pi$
$728$	−30.8007	+	19.2066i	−1.14155	+	0.711845i
$729$	24.6192	+	11.0859i	0.911821	+	0.410589i
$730$	0.817548	−	5.16180i	0.0302588	−	0.191047i
$731$	−10.6592	−	3.46337i	−0.394243	−	0.128097i
$732$	−3.60456	+	12.5373i	−0.133228	+	0.463392i
$733$	−7.61560	+	48.0830i	−0.281288	+	1.77599i	0.291787	+	0.956483i	$0.405750\pi$
$733$	−7.61560	+	48.0830i	−0.281288	+	1.77599i	−0.573076	+	0.819502i	$0.694250\pi$
$734$	1.59428	+	10.0659i	0.0588458	+	0.371538i
$735$	10.0561	−	21.5258i	0.370925	−	0.793992i
$736$	14.6515	+	14.6515i	0.540061	+	0.540061i
$737$	−26.1043	+	5.70961i	−0.961564	+	0.210316i
$738$	0.0862329	+	1.25863i	0.00317428	+	0.0463308i
$739$	−10.4767	+	20.5616i	−0.385390	+	0.756371i	−0.999459	−	0.0328815i	$-0.989532\pi$
$739$	−10.4767	+	20.5616i	−0.385390	+	0.756371i	0.614069	+	0.789252i	$0.289532\pi$
$740$	−108.517	−	78.8422i	−3.98916	−	2.89830i
$741$	−4.97401	−	41.0643i	−0.182725	−	1.50854i
$742$	1.28580	−	3.95727i	0.0472030	−	0.145276i
$743$	−9.09995	+	4.63666i	−0.333845	+	0.170102i	−0.612875	−	0.790180i	$-0.709987\pi$
$743$	−9.09995	+	4.63666i	−0.333845	+	0.170102i	0.279030	+	0.960282i	$0.409987\pi$
$744$	−40.8384	+	31.8602i	−1.49721	+	1.16805i
$745$	−6.02144	+	8.28780i	−0.220608	+	0.303642i
$746$	20.5201	−	40.2730i	0.751294	−	1.47450i
$747$	−2.13916	−	1.86484i	−0.0782679	−	0.0682308i
$748$	102.852	+	26.9105i	3.76063	+	0.983944i
$749$	13.2586	−	13.2586i	0.484460	−	0.484460i
$750$	4.29741	−	1.56071i	0.156919	−	0.0569889i
$751$	22.2640	−	30.6437i	0.812424	−	1.11821i	−0.178521	−	0.983936i	$-0.557131\pi$
$751$	22.2640	−	30.6437i	0.812424	−	1.11821i	0.990945	−	0.134269i	$-0.0428687\pi$
$752$	9.67397	−	61.0791i	0.352773	−	2.22732i
$753$	−35.8446	−	10.3056i	−1.30625	−	0.375556i
$754$	4.01901	−	3.48712i	0.146364	−	0.126993i
$755$	−18.9564	−	26.0913i	−0.689894	−	0.949558i
$756$	−9.57711	−	36.0464i	−0.348316	−	1.31099i
$757$	2.88506	+	8.87930i	0.104859	+	0.322724i	0.989697	−	0.143175i	$-0.0457311\pi$
$757$	2.88506	+	8.87930i	0.104859	+	0.322724i	−0.884838	+	0.465899i	$0.845731\pi$
$758$	−8.63501			−0.313638
$759$	20.8699	−	8.98682i	0.757528	−	0.326201i
$760$	91.1264	−	91.1264i	3.30550	−	3.30550i
$761$	−7.07931	−	3.60709i	−0.256625	−	0.130757i	0.320946	−	0.947098i	$-0.395999\pi$
$761$	−7.07931	−	3.60709i	−0.256625	−	0.130757i	−0.577571	+	0.816341i	$0.695999\pi$
$762$	−13.5928	−	70.1924i	−0.492415	−	2.54280i
$763$	−2.97864	+	2.16411i	−0.107834	+	0.0783461i
$764$	−19.3204	+	59.4620i	−0.698986	+	2.15126i
$765$	57.4851	−	34.4305i	2.07838	−	1.24484i
$766$	28.4246	+	39.1232i	1.02702	+	1.41358i
$767$	10.4009	+	24.5665i	0.375555	+	0.887044i
$768$	−48.0992	+	17.4684i	−1.73563	+	0.630336i
$769$	−35.0404	+	35.0404i	−1.26359	+	1.26359i	−0.314247	+	0.949341i	$0.601752\pi$
$769$	−35.0404	+	35.0404i	−1.26359	+	1.26359i	−0.949341	+	0.314247i	$0.898248\pi$
$770$	−28.0302	+	31.5020i	−1.01014	+	1.13525i
$771$	0.0739405	+	2.16096i	0.00266290	+	0.0778250i
$772$	−30.3541	−	15.4662i	−1.09247	−	0.556640i
$773$	1.20906	+	7.63372i	0.0434869	+	0.274566i	0.999845	−	0.0176331i	$-0.00561309\pi$
$773$	1.20906	+	7.63372i	0.0434869	+	0.274566i	−0.956358	+	0.292199i	$0.905613\pi$
$774$	−1.05356	+	11.8503i	−0.0378696	+	0.425949i
$775$	19.8665	−	10.1225i	0.713627	−	0.363611i
$776$	26.0642	+	8.46877i	0.935650	+	0.304011i
$777$	−21.2427	+	16.5725i	−0.762076	+	0.594536i
$778$	−1.77226	−	11.1896i	−0.0635388	−	0.401168i
$779$	0.338605	+	1.04212i	0.0121318	+	0.0373378i
$780$	−42.1230	+	75.7001i	−1.50824	+	2.71050i
$781$	41.0576	+	4.07087i	1.46915	+	0.145667i
$782$	51.0790	+	51.0790i	1.82658	+	1.82658i
$783$	1.22115	+	2.75840i	0.0436403	+	0.0985771i
$784$	18.1131	−	24.9305i	0.646895	−	0.890374i
$785$	−36.1566	−	5.72664i	−1.29048	−	0.204393i
$786$	−14.3842	+	7.96010i	−0.513069	+	0.283927i
$787$	−23.2206	+	11.8315i	−0.827723	+	0.421746i	−0.815906	−	0.578184i	$-0.803762\pi$
$787$	−23.2206	+	11.8315i	−0.827723	+	0.421746i	−0.0118170	+	0.999930i	$0.503762\pi$
$788$	0.444167	−	2.80436i	0.0158228	−	0.0999013i
$789$	18.0795	+	12.2133i	0.643648	+	0.434805i
$790$	−20.8604	+	6.77795i	−0.742179	+	0.241149i
$791$	2.36445	−	2.36445i	0.0840703	−	0.0840703i
$792$	1.89393	−	62.2382i	0.0672980	−	2.21154i
$793$	−1.46690	−	5.90678i	−0.0520910	−	0.209756i
$794$	1.41235	−	0.458901i	0.0501225	−	0.0162858i
$795$	−1.04170	−	5.37929i	−0.0369453	−	0.190784i
$796$	−63.9240	+	46.4435i	−2.26573	+	1.64615i
$797$	−5.51819	+	16.9832i	−0.195464	+	0.601577i	0.804507	+	0.593944i	$0.202430\pi$
$797$	−5.51819	+	16.9832i	−0.195464	+	0.601577i	−0.999971	+	0.00763323i	$0.997570\pi$
$798$	−22.7159	−	41.0487i	−0.804135	−	1.45311i
$799$	9.95068	−	62.8261i	0.352030	−	2.22263i
$800$	−24.1413	+	3.82361i	−0.853525	+	0.135185i
$801$	17.4149	+	7.42113i	0.615326	+	0.262213i
$802$	76.6406			2.70627
$803$	−1.63847	−	1.45790i	−0.0578205	−	0.0514481i
$804$	−42.4961	+	45.5073i	−1.49872	+	1.60492i
$805$	−18.8151	+	6.11339i	−0.663144	+	0.215469i
$806$	16.4445	−	40.5928i	0.579232	−	1.42982i
$807$	18.8352	−	14.6944i	0.663032	−	0.517267i
$808$	3.58153	+	7.02914i	0.125998	+	0.247284i
$809$	−36.1329	−	11.7403i	−1.27037	−	0.412767i	−0.405188	−	0.914233i	$-0.632794\pi$
$809$	−36.1329	−	11.7403i	−1.27037	−	0.412767i	−0.865177	+	0.501467i	$0.832794\pi$
$810$	−49.2659	−	51.3045i	−1.73103	−	1.80266i
$811$	19.6938	−	3.11919i	0.691542	−	0.109529i	0.199236	−	0.979952i	$-0.436154\pi$
$811$	19.6938	−	3.11919i	0.691542	−	0.109529i	0.492306	+	0.870422i	$0.336154\pi$
$812$	1.89180	−	3.71287i	0.0663893	−	0.130296i
$813$	4.00650	−	4.29040i	0.140514	−	0.150471i
$814$	−75.9341	+	29.6629i	−2.66149	+	1.03968i
$815$		−	42.2274i		−	1.47916i
$816$	81.6895	−	29.6675i	2.85970	−	1.03857i
$817$	1.61646	+	10.2060i	0.0565529	+	0.357061i
$818$	14.0288	−	10.1925i	0.490505	−	0.356373i
$819$	12.2754	+	12.3329i	0.428938	+	0.430948i
$820$	0.709147	−	2.18253i	0.0247645	−	0.0762173i
$821$	−26.2958	−	4.16484i	−0.917729	−	0.145354i	−0.320337	−	0.947304i	$-0.603796\pi$
$821$	−26.2958	−	4.16484i	−0.917729	−	0.145354i	−0.597392	+	0.801950i	$0.703796\pi$
$822$	−0.950584	+	1.40716i	−0.0331554	+	0.0490804i
$823$	−26.2948	+	8.54371i	−0.916581	+	0.297815i	−0.729063	−	0.684446i	$-0.760044\pi$
$823$	−26.2948	+	8.54371i	−0.916581	+	0.297815i	−0.187517	+	0.982261i	$0.560044\pi$
$824$	−58.8896	−	58.8896i	−2.05152	−	2.05152i
$825$	−5.89402	+	26.1481i	−0.205203	+	0.910359i
$826$	21.3951	+	21.3951i	0.744430	+	0.744430i
$827$	36.8067	+	18.7540i	1.27990	+	0.652139i	0.955837	−	0.293898i	$-0.0949526\pi$
$827$	36.8067	+	18.7540i	1.27990	+	0.652139i	0.324058	+	0.946037i	$0.394953\pi$
$828$	28.1205	−	44.8616i	0.977254	−	1.55905i
$829$	27.5400	+	37.9055i	0.956503	+	1.31651i	0.948577	+	0.316545i	$0.102523\pi$
$829$	27.5400	+	37.9055i	0.956503	+	1.31651i	0.00792601	+	0.999969i	$0.497477\pi$
$830$	3.39409	+	6.66128i	0.117811	+	0.231216i
$831$	11.3953	−	39.6349i	0.395298	−	1.37492i
$832$	1.51460	−	1.80162i	0.0525092	−	0.0624600i
$833$	18.6311	−	25.6436i	0.645531	−	0.888497i
$834$	−62.5885	−	29.2391i	−2.16726	−	1.01247i
$835$	−37.6314			−1.30229
$836$	−20.9437	−	95.7546i	−0.724354	−	3.31174i
$837$	19.2636	+	15.6668i	0.665847	+	0.541523i
$838$	−1.39660	−	0.711601i	−0.0482446	−	0.0245819i
$839$	52.4518	−	8.30755i	1.81084	−	0.286809i	0.842914	−	0.538049i	$-0.180838\pi$
$839$	52.4518	−	8.30755i	1.81084	−	0.286809i	0.967925	+	0.251240i	$0.0808384\pi$
$840$	−6.64471	+	53.8039i	−0.229264	+	1.85641i
$841$	8.85734	−	27.2601i	0.305426	−	0.940003i
$842$	−3.19438	+	9.83129i	−0.110086	+	0.338808i
$843$	30.0764	+	3.71440i	1.03589	+	0.127931i
$844$	47.6987	−	65.6517i	1.64186	−	2.25982i
$845$	−0.630243	−	40.4123i	−0.0216810	−	1.39023i
$846$	−67.3635	+	4.61530i	−2.31601	+	0.158677i
$847$	4.78111	+	17.0376i	0.164281	+	0.585419i
$848$		−	7.10666i		−	0.244044i
$849$	9.48856	+	26.1268i	0.325646	+	0.896668i
$850$	−84.1630	+	13.3301i	−2.88677	+	0.457219i
$851$	−37.7765	−	5.98321i	−1.29496	−	0.205102i
$852$	84.1173	−	46.5497i	2.88181	−	1.59477i
$853$	12.1758	−	6.20387i	0.416891	−	0.212416i	−0.232947	−	0.972489i	$-0.574837\pi$
$853$	12.1758	−	6.20387i	0.416891	−	0.212416i	0.649838	+	0.760073i	$0.274837\pi$
$854$	−4.05740	−	5.58453i	−0.138841	−	0.191099i
$855$	−52.3454	−	32.8115i	−1.79017	−	1.12213i
$856$	33.1150	−	64.9919i	1.13185	−	2.22138i
$857$	53.7599			1.83640			0.918201	−	0.396115i	$-0.129642\pi$
$857$	53.7599			1.83640			0.918201	+	0.396115i	$0.129642\pi$
$858$	24.9160	+	46.3824i	0.850617	+	1.58347i
$859$	−22.3199			−0.761544			−0.380772	−	0.924669i	$-0.624342\pi$
$859$	−22.3199			−0.761544			−0.380772	+	0.924669i	$0.624342\pi$
$860$	9.82479	−	19.2822i	0.335023	−	0.657519i
$861$	−0.381962	−	0.258028i	−0.0130172	−	0.00879356i
$862$	51.1023	+	70.3362i	1.74055	+	2.39566i
$863$	31.9206	−	16.2643i	1.08659	−	0.553645i	0.183466	−	0.983026i	$-0.441268\pi$
$863$	31.9206	−	16.2643i	1.08659	−	0.553645i	0.903123	+	0.429382i	$0.141268\pi$
$864$	−14.7765	−	22.8593i	−0.502708	−	0.777691i
$865$	−38.7002	−	6.12951i	−1.31585	−	0.208410i
$866$	21.0689	−	3.33699i	0.715952	−	0.113396i
$867$	56.3499	−	20.4648i	1.91374	−	0.695021i
$868$		−	34.2995i		−	1.16420i
$869$	−2.32993	+	8.90496i	−0.0790373	+	0.302080i
$870$	−0.271758	−	7.94230i	−0.00921346	−	0.269269i
$871$	6.56097	−	28.2986i	0.222310	−	0.958862i
$872$	−8.41868	+	11.5873i	−0.285093	+	0.392396i
$873$	1.16344	−	13.0861i	0.0393763	−	0.442896i
$874$	20.5805	−	63.3404i	0.696147	−	2.14252i
$875$	−0.516213	+	1.58874i	−0.0174512	+	0.0537092i
$876$	−5.07187	−	0.626369i	−0.171363	−	0.0211630i
$877$	55.7095	−	8.82352i	1.88118	−	0.297949i	0.892856	−	0.450342i	$-0.148698\pi$
$877$	55.7095	−	8.82352i	1.88118	−	0.297949i	0.988320	+	0.152393i	$0.0486979\pi$
$878$	−59.2740	−	30.2016i	−2.00040	−	1.01925i
$879$	37.7156	+	35.2200i	1.27212	+	1.18794i
$880$	−28.9048	+	65.9646i	−0.974380	+	2.22366i
$881$	−15.2996			−0.515458			−0.257729	−	0.966217i	$-0.582974\pi$
$881$	−15.2996			−0.515458			−0.257729	+	0.966217i	$0.582974\pi$
$882$	−30.9534	−	13.1904i	−1.04226	−	0.444143i
$883$	−22.9096	+	31.5323i	−0.770969	+	1.06115i	0.225253	+	0.974300i	$0.427679\pi$
$883$	−22.9096	+	31.5323i	−0.770969	+	1.06115i	−0.996222	+	0.0868475i	$0.972321\pi$
$884$	−74.3727	+	88.4667i	−2.50142	+	2.97546i
$885$	38.2924	+	11.0093i	1.28718	+	0.370074i
$886$	19.7673	+	38.7954i	0.664094	+	1.30336i
$887$	−7.30017	−	10.0478i	−0.245116	−	0.337373i	0.668678	−	0.743553i	$-0.266861\pi$
$887$	−7.30017	−	10.0478i	−0.245116	−	0.337373i	−0.913793	+	0.406180i	$0.866861\pi$
$888$	−58.6701	+	86.8502i	−1.96884	+	2.91450i
$889$	23.2757	+	11.8595i	0.780640	+	0.397756i
$890$	−35.2632	−	35.2632i	−1.18202	−	1.18202i
$891$	−29.2835	+	5.78576i	−0.981035	+	0.193830i
$892$	−30.1809	−	30.1809i	−1.01053	−	1.01053i
$893$	−55.7755	+	18.1226i	−1.86646	+	0.606449i
$894$	12.0217	+	8.12104i	0.402065	+	0.271608i
$895$	−1.09362	−	0.173212i	−0.0365556	−	0.00578984i
$896$	6.03310	−	18.5680i	0.201552	−	0.620312i
$897$	−0.902401	+	24.6855i	−0.0301303	+	0.824226i
$898$	−13.6199	+	9.89547i	−0.454503	+	0.330216i
$899$	0.433977	+	2.74002i	0.0144740	+	0.0913849i
$900$	23.3153	+	57.9420i	0.777177	+	1.93140i
$901$		−	7.30993i		−	0.243529i
$902$	−0.884104	−	1.07872i	−0.0294374	−	0.0359174i
$903$	−3.17700	−	2.96678i	−0.105724	−	0.0987283i
$904$	5.90550	−	11.5902i	0.196414	−	0.385484i
$905$	−27.6548	+	4.38009i	−0.919276	+	0.145599i
$906$	−36.0101	+	28.0934i	−1.19635	+	0.933340i
$907$	15.4716	+	5.02704i	0.513728	+	0.166920i	0.554397	−	0.832252i	$-0.312949\pi$
$907$	15.4716	+	5.02704i	0.513728	+	0.166920i	−0.0406693	+	0.999173i	$0.512949\pi$
$908$	4.71212	+	9.24805i	0.156377	+	0.306907i
$909$	2.90047	−	2.42684i	0.0962025	−	0.0804931i
$910$	−17.8721	−	42.2131i	−0.592454	−	1.39935i
$911$	25.6642	−	8.33879i	0.850291	−	0.276276i	0.148723	−	0.988879i	$-0.452484\pi$
$911$	25.6642	−	8.33879i	0.850291	−	0.276276i	0.701568	+	0.712602i	$0.252484\pi$
$912$	−58.5637	−	54.6886i	−1.93924	−	1.81092i
$913$	3.12210	+	0.309558i	0.103326	+	0.0102449i
$914$	−47.5155			−1.57167
$915$	−8.23554	−	3.84735i	−0.272258	−	0.127189i
$916$	87.3153	−	13.8294i	2.88498	−	0.456936i
$917$	0.939654	−	5.93274i	0.0310301	−	0.195916i
$918$	−51.5149	−	79.6937i	−1.70025	−	2.63028i
$919$	0.228272	−	0.702549i	0.00753000	−	0.0231749i	−0.947221	−	0.320582i	$-0.896122\pi$
$919$	0.228272	−	0.702549i	0.00753000	−	0.0231749i	0.954751	+	0.297407i	$0.0961217\pi$
$920$	−62.2618	+	45.2359i	−2.05271	+	1.49138i
$921$	5.89336	−	1.14125i	0.194193	−	0.0376055i
$922$	83.7670	−	27.2175i	2.75872	−	0.896362i
$923$	−23.1368	+	38.4251i	−0.761557	+	1.26478i
$924$	31.7237	+	26.3400i	1.04363	+	0.866523i
$925$	31.9030	−	31.9030i	1.04896	−	1.04896i
$926$	−38.3132	+	12.4487i	−1.25905	+	0.409091i
$927$	−21.2041	+	33.8277i	−0.696435	+	1.11105i
$928$	0.475737	−	3.00369i	0.0156168	−	0.0986009i
$929$	8.14627	−	4.15073i	0.267270	−	0.136181i	−0.315220	−	0.949019i	$-0.602078\pi$
$929$	8.14627	−	4.15073i	0.267270	−	0.136181i	0.582490	+	0.812838i	$0.302078\pi$
$930$	−31.6722	−	57.2331i	−1.03857	−	1.87675i
$931$	−28.8641	−	4.57162i	−0.945982	−	0.149829i
$932$	−16.4064	+	22.5815i	−0.537410	+	0.739681i
$933$	−51.7775	+	18.8042i	−1.69512	+	0.615623i
$934$	37.0444	+	37.0444i	1.21213	+	1.21213i
$935$	−29.7316	+	67.8513i	−0.972326	+	2.21898i
$936$	60.2415	+	30.8721i	1.96906	+	1.00909i
$937$	9.56446	+	29.4364i	0.312457	+	0.961644i	0.976789	+	0.214206i	$0.0687164\pi$
$937$	9.56446	+	29.4364i	0.312457	+	0.961644i	−0.664331	+	0.747438i	$0.731284\pi$
$938$	−5.15407	−	32.5415i	−0.168286	−	1.06252i
$939$	27.0373	+	34.6564i	0.882329	+	1.13097i
$940$	116.812	+	37.9545i	3.80998	+	1.23794i
$941$	−45.3385	+	23.1011i	−1.47799	+	0.753075i	−0.992624	−	0.121235i	$-0.961314\pi$
$941$	−45.3385	+	23.1011i	−1.47799	+	0.753075i	−0.485368	+	0.874310i	$0.661314\pi$
$942$	−6.35417	+	51.4513i	−0.207030	+	1.67637i
$943$	−0.102364	−	0.646302i	−0.00333344	−	0.0210465i
$944$	46.0453	+	23.4613i	1.49865	+	0.763599i
$945$	25.8518	−	2.66199i	0.840960	−	0.0865946i
$946$	−6.64332	−	11.3516i	−0.215993	−	0.369072i
$947$	15.7438	−	15.7438i	0.511605	−	0.511605i	−0.403413	−	0.915018i	$-0.632176\pi$
$947$	15.7438	−	15.7438i	0.511605	−	0.511605i	0.915018	+	0.403413i	$0.132176\pi$
$948$	7.32152	+	20.1598i	0.237792	+	0.654761i
$949$	2.19557	−	0.929558i	0.0712713	−	0.0301747i
$950$	46.1782	+	63.5589i	1.49822	+	2.06212i
$951$	19.8189	+	35.8136i	0.642670	+	1.16133i
$952$	−22.3500	+	68.7862i	−0.724367	+	2.22937i
$953$	28.2589	−	20.5313i	0.915396	−	0.665074i	−0.0269775	−	0.999636i	$-0.508588\pi$
$953$	28.2589	−	20.5313i	0.915396	−	0.665074i	0.942374	+	0.334562i	$0.108588\pi$
$954$	−7.56309	+	1.73487i	−0.244864	+	0.0561686i
$955$	−38.8170	−	19.7783i	−1.25609	−	0.640009i
$956$	57.9526	−	57.9526i	1.87432	−	1.87432i
$957$	−2.86752	−	1.70279i	−0.0926938	−	0.0550435i
$958$	11.1417			0.359972
$959$	−0.191732	−	0.590092i	−0.00619136	−	0.0190551i
$960$	−0.668322	−	3.45118i	−0.0215700	−	0.111386i
$961$	−4.79952	−	6.60597i	−0.154823	−	0.213096i
$962$	6.26429	−	88.4024i	0.201969	−	2.85021i
$963$	−33.9165	−	8.50702i	−1.09294	−	0.274135i
$964$	15.7564	−	99.4821i	0.507480	−	3.20410i
$965$	13.9529	−	19.2045i	0.449159	−	0.618214i
$966$	9.56372	+	26.3337i	0.307708	+	0.847274i
$967$	−19.9440	+	19.9440i	−0.641357	+	0.641357i	−0.950889	−	0.309532i	$-0.899828\pi$
$967$	−19.9440	+	19.9440i	−0.641357	+	0.641357i	0.309532	+	0.950889i	$0.399828\pi$
$968$	38.1700	+	57.2872i	1.22683	+	1.84128i
$969$	−60.2388	−	56.2529i	−1.93515	−	1.80710i
$970$	−15.7125	+	30.8376i	−0.504499	+	0.990135i
$971$	−20.7250	+	28.5256i	−0.665098	+	0.915429i	−0.999637	−	0.0269532i	$-0.991419\pi$
$971$	−20.7250	+	28.5256i	−0.665098	+	0.915429i	0.334539	+	0.942382i	$0.391419\pi$
$972$	−48.4915	+	49.8623i	−1.55537	+	1.59933i
$973$	22.4895	−	11.4590i	0.720979	−	0.367357i
$974$	10.3964	−	31.9968i	0.333122	−	1.02524i
$975$	−22.9326	−	17.9773i	−0.734432	−	0.575735i
$976$	−9.53812	−	6.92985i	−0.305308	−	0.221819i
$977$	−4.56285	+	8.95511i	−0.145979	+	0.286499i	−0.952405	−	0.304835i	$-0.901399\pi$
$977$	−4.56285	+	8.95511i	−0.145979	+	0.286499i	0.806426	+	0.591334i	$0.201399\pi$
$978$	−59.7663	+	2.04500i	−1.91112	+	0.0653917i
$979$	−20.4448	+	4.47175i	−0.653419	+	0.142918i
$980$	43.2779	+	43.2779i	1.38246	+	1.38246i
$981$	6.31644	+	2.69166i	0.201668	+	0.0859382i
$982$	−14.5848	−	92.0845i	−0.465418	−	2.93853i
$983$	4.42682	−	27.9498i	0.141194	−	0.891461i	−0.810796	−	0.585329i	$-0.800965\pi$
$983$	4.42682	−	27.9498i	0.141194	−	0.891461i	0.951989	−	0.306132i	$-0.0990347\pi$
$984$	−1.72334	−	0.495471i	−0.0549380	−	0.0157950i
$985$	1.88161	+	0.611371i	0.0599530	+	0.0194799i
$986$	1.65855	−	10.4716i	0.0528188	−	0.333485i
$987$	13.8100	−	20.4431i	0.439576	−	0.650711i
$988$	103.804	+	24.0666i	3.30244	+	0.765662i
$989$		−	6.17076i		−	0.196219i
$990$	77.2574	+	14.6580i	2.45540	+	0.465862i
$991$	18.5935			0.590641			0.295320	−	0.955398i	$-0.404574\pi$
$991$	18.5935			0.590641			0.295320	+	0.955398i	$0.404574\pi$
$992$	−7.73527	−	23.8067i	−0.245595	−	0.755864i
$993$	−1.18172	−	6.10236i	−0.0375009	−	0.193652i
$994$	−7.95808	+	50.2453i	−0.252415	+	1.59368i
$995$	−24.9955	−	49.0564i	−0.792410	−	1.55519i
$996$	6.39645	−	3.53973i	0.202679	−	0.112161i
$997$	−0.680338	+	0.494294i	−0.0215465	+	0.0156545i	−0.598506	−	0.801118i	$-0.704239\pi$
$997$	−0.680338	+	0.494294i	−0.0215465	+	0.0156545i	0.576960	+	0.816772i	$0.304239\pi$
$998$	71.0831	+	51.6449i	2.25010	+	1.63479i
$999$	46.8686	+	18.1047i	1.48286	+	0.572809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bi.a.5.4	✓	416
3.2	odd	2	inner	429.2.bi.a.5.49	yes	416
11.9	even	5	inner	429.2.bi.a.317.49	yes	416
13.8	odd	4	inner	429.2.bi.a.203.4	yes	416
33.20	odd	10	inner	429.2.bi.a.317.4	yes	416
39.8	even	4	inner	429.2.bi.a.203.49	yes	416
143.86	odd	20	inner	429.2.bi.a.86.49	yes	416
429.86	even	20	inner	429.2.bi.a.86.4	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bi.a.5.4	✓	416	1.1	even	1	trivial
429.2.bi.a.5.49	yes	416	3.2	odd	2	inner
429.2.bi.a.86.4	yes	416	429.86	even	20	inner
429.2.bi.a.86.49	yes	416	143.86	odd	20	inner
429.2.bi.a.203.4	yes	416	13.8	odd	4	inner
429.2.bi.a.203.49	yes	416	39.8	even	4	inner
429.2.bi.a.317.4	yes	416	33.20	odd	10	inner
429.2.bi.a.317.49	yes	416	11.9	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15405 + 2.26495i) q^{2} +(-0.969560 + 1.43525i) q^{3} +(-2.62261 - 3.60971i) q^{4} +(2.77016 - 1.41147i) q^{5} +(-2.13186 - 3.85237i) q^{6} +(1.58890 + 0.251657i) q^{7} +(6.18102 - 0.978978i) q^{8} +(-1.11991 - 2.78313i) q^{9} +O(q^{10})\)	\(q+(-1.15405 + 2.26495i) q^{2} +(-0.969560 + 1.43525i) q^{3} +(-2.62261 - 3.60971i) q^{4} +(2.77016 - 1.41147i) q^{5} +(-2.13186 - 3.85237i) q^{6} +(1.58890 + 0.251657i) q^{7} +(6.18102 - 0.978978i) q^{8} +(-1.11991 - 2.78313i) q^{9} +7.90318i q^{10} +(2.79215 + 1.78994i) q^{11} +(7.72363 - 0.264276i) q^{12} +(-3.05946 + 1.90781i) q^{13} +(-2.40366 + 3.30836i) q^{14} +(-0.660023 + 5.34438i) q^{15} +(-2.15830 + 6.64258i) q^{16} +(-2.22004 + 6.83258i) q^{17} +(7.59609 + 0.675341i) q^{18} +(6.54207 - 1.03616i) q^{19} +(-12.3600 - 6.29775i) q^{20} +(-1.90172 + 2.03648i) q^{21} +(-7.27642 + 4.25841i) q^{22} -3.95549 q^{23} +(-4.58779 + 9.82051i) q^{24} +(2.74261 - 3.77487i) q^{25} +(-0.790327 - 9.13124i) q^{26} +(5.08031 + 1.09106i) q^{27} +(-3.25865 - 6.39547i) q^{28} +(0.341238 + 0.469673i) q^{29} +(-11.3431 - 7.66261i) q^{30} +(4.25772 + 2.16942i) q^{31} +(-3.70409 - 3.70409i) q^{32} +(-5.27618 + 2.27199i) q^{33} +(-12.9134 - 12.9134i) q^{34} +(4.75670 - 1.54555i) q^{35} +(-7.10923 + 11.3416i) q^{36} +(9.55040 + 1.51263i) q^{37} +(-5.20303 + 16.0133i) q^{38} +(0.228139 - 6.24083i) q^{39} +(15.7406 - 11.4362i) q^{40} +(0.0258790 + 0.163394i) q^{41} +(-2.41783 - 6.65751i) q^{42} +1.56005i q^{43} +(-0.861546 - 14.7732i) q^{44} +(-7.03060 - 6.12900i) q^{45} +(4.56484 - 8.95900i) q^{46} +(-8.74504 + 1.38508i) q^{47} +(-7.44118 - 9.53810i) q^{48} +(-4.19613 - 1.36341i) q^{49} +(5.38480 + 10.5683i) q^{50} +(-7.65402 - 9.81092i) q^{51} +(14.9104 + 6.04032i) q^{52} +(-0.967701 + 0.314425i) q^{53} +(-8.33415 + 10.2475i) q^{54} +(10.2611 + 1.01740i) q^{55} +10.0674 q^{56} +(-4.85578 + 10.3942i) q^{57} +(-1.45759 + 0.230860i) q^{58} +(1.15746 - 7.30792i) q^{59} +(21.0227 - 11.6337i) q^{60} +(-0.521623 + 1.60539i) q^{61} +(-9.82726 + 7.13993i) q^{62} +(-1.07902 - 4.70394i) q^{63} +(-0.620846 + 0.201725i) q^{64} +(-5.78237 + 9.60324i) q^{65} +(0.943036 - 14.5723i) q^{66} +(-5.69702 + 5.69702i) q^{67} +(30.4860 - 9.90549i) q^{68} +(3.83509 - 5.67713i) q^{69} +(-1.98889 + 12.5573i) q^{70} +(11.0841 - 5.64765i) q^{71} +(-9.64679 - 16.1062i) q^{72} +(-0.653129 - 0.103445i) q^{73} +(-14.4477 + 19.8856i) q^{74} +(2.75878 + 7.59630i) q^{75} +(-20.8976 - 20.8976i) q^{76} +(3.98599 + 3.54670i) q^{77} +(13.8719 + 7.71896i) q^{78} +(0.857623 + 2.63949i) q^{79} +(3.39693 + 21.4474i) q^{80} +(-6.49162 + 6.23369i) q^{81} +(-0.399945 - 0.129950i) q^{82} +(0.842861 - 0.429459i) q^{83} +(12.3386 + 1.52380i) q^{84} +(3.49409 + 22.0608i) q^{85} +(-3.53344 - 1.80038i) q^{86} +(-1.00495 + 0.0343859i) q^{87} +(19.0107 + 8.33022i) q^{88} +(-4.46189 + 4.46189i) q^{89} +(21.9956 - 8.85082i) q^{90} +(-5.34128 + 2.26138i) q^{91} +(10.3737 + 14.2782i) q^{92} +(-7.24178 + 4.00753i) q^{93} +(6.95509 - 21.4056i) q^{94} +(16.6601 - 12.1042i) q^{95} +(8.90765 - 1.72497i) q^{96} +(3.90192 + 1.98813i) q^{97} +(7.93060 - 7.93060i) q^{98} +(1.85470 - 9.77548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Introduction

L-functions

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