LMFDB - Embedded newform 170.2.o.b.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(3,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([12, 1]))

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

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

chi := DirichletCharacter("170.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.o (of order $16$, 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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			73.2
Character	$\chi$	$=$	170.73
Dual form			170.2.o.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.923880 + 0.382683i) q^{2} +(-0.302197 + 1.51925i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-1.88843 + 1.19743i) q^{5} +(-0.860584 + 1.28795i) q^{6} +(-0.201119 - 0.134383i) q^{7} +(0.382683 + 0.923880i) q^{8} +(0.554854 + 0.229828i) q^{9} +O(q^{10})$	\(q+(0.923880 + 0.382683i) q^{2} +(-0.302197 + 1.51925i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-1.88843 + 1.19743i) q^{5} +(-0.860584 + 1.28795i) q^{6} +(-0.201119 - 0.134383i) q^{7} +(0.382683 + 0.923880i) q^{8} +(0.554854 + 0.229828i) q^{9} +(-2.20292 + 0.383608i) q^{10} +(1.18040 + 0.788717i) q^{11} +(-1.28795 + 0.860584i) q^{12} -0.250606i q^{13} +(-0.134383 - 0.201119i) q^{14} +(-1.24851 - 3.23085i) q^{15} +1.00000i q^{16} +(-2.28902 - 3.42934i) q^{17} +(0.424667 + 0.424667i) q^{18} +(5.56274 - 2.30416i) q^{19} +(-2.18203 - 0.488612i) q^{20} +(0.264939 - 0.264939i) q^{21} +(0.788717 + 1.18040i) q^{22} +(3.04284 - 0.605259i) q^{23} +(-1.51925 + 0.302197i) q^{24} +(2.13233 - 4.52252i) q^{25} +(0.0959029 - 0.231530i) q^{26} +(-3.09859 + 4.63737i) q^{27} +(-0.0471892 - 0.237236i) q^{28} +(-0.237131 + 1.19214i) q^{29} +(0.0829196 - 3.46270i) q^{30} +(4.24419 - 2.83588i) q^{31} +(-0.382683 + 0.923880i) q^{32} +(-1.55497 + 1.55497i) q^{33} +(-0.802430 - 4.04427i) q^{34} +(0.540714 + 0.0129482i) q^{35} +(0.229828 + 0.554854i) q^{36} +(-6.37360 - 1.26779i) q^{37} +6.02107 q^{38} +(0.380733 + 0.0757325i) q^{39} +(-1.82895 - 1.28645i) q^{40} +(0.171169 + 0.860522i) q^{41} +(0.346160 - 0.143384i) q^{42} +(8.17809 - 3.38747i) q^{43} +(0.276961 + 1.39237i) q^{44} +(-1.32300 + 0.230383i) q^{45} +(3.04284 + 0.605259i) q^{46} -10.2201 q^{47} +(-1.51925 - 0.302197i) q^{48} +(-2.65639 - 6.41310i) q^{49} +(3.70071 - 3.36225i) q^{50} +(5.90175 - 2.44125i) q^{51} +(0.177206 - 0.177206i) q^{52} +(-0.757188 + 1.82801i) q^{53} +(-4.63737 + 3.09859i) q^{54} +(-3.17353 - 0.0759951i) q^{55} +(0.0471892 - 0.237236i) q^{56} +(1.81955 + 9.14748i) q^{57} +(-0.675292 + 1.01065i) q^{58} +(-0.520057 + 1.25553i) q^{59} +(1.40172 - 3.16738i) q^{60} +(-8.99481 + 1.78918i) q^{61} +(5.00636 - 0.995828i) q^{62} +(-0.0807066 - 0.120786i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(0.300083 + 0.473253i) q^{65} +(-2.03166 + 0.841542i) q^{66} +(7.69457 + 7.69457i) q^{67} +(0.806326 - 4.04349i) q^{68} +4.80573i q^{69} +(0.494599 + 0.218885i) q^{70} +(-0.548870 - 0.821442i) q^{71} +0.600569i q^{72} +(-13.0293 + 8.70593i) q^{73} +(-5.40328 - 3.61035i) q^{74} +(6.22643 + 4.60623i) q^{75} +(5.56274 + 2.30416i) q^{76} +(-0.131410 - 0.317252i) q^{77} +(0.322770 + 0.215668i) q^{78} +(5.86124 - 8.77197i) q^{79} +(-1.19743 - 1.88843i) q^{80} +(-4.83492 - 4.83492i) q^{81} +(-0.171169 + 0.860522i) q^{82} +(-0.176383 - 0.0730601i) q^{83} +0.374680 q^{84} +(8.42905 + 3.73513i) q^{85} +8.85190 q^{86} +(-1.73949 - 0.720521i) q^{87} +(-0.276961 + 1.39237i) q^{88} +(-5.17953 - 5.17953i) q^{89} +(-1.31046 - 0.293446i) q^{90} +(-0.0336774 + 0.0504017i) q^{91} +(2.57960 + 1.72363i) q^{92} +(3.02581 + 7.30496i) q^{93} +(-9.44214 - 3.91106i) q^{94} +(-7.74578 + 11.0122i) q^{95} +(-1.28795 - 0.860584i) q^{96} +(7.88775 - 5.27043i) q^{97} -6.94149i q^{98} +(0.473679 + 0.708911i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q + 8 q^{10} - 8 q^{15} - 16 q^{18} - 16 q^{20} - 8 q^{25} - 8 q^{26} + 24 q^{27} + 8 q^{28} - 8 q^{29} - 16 q^{31} + 32 q^{33} - 8 q^{34} - 32 q^{35} + 16 q^{37} + 32 q^{39} + 8 q^{40} - 56 q^{41} - 8 q^{42} - 48 q^{43} - 16 q^{44} - 24 q^{45} - 96 q^{47} - 16 q^{49} - 32 q^{51} - 16 q^{52} - 40 q^{53} + 24 q^{54} + 8 q^{55} - 8 q^{56} - 8 q^{57} + 16 q^{58} + 24 q^{61} - 24 q^{62} - 24 q^{63} + 16 q^{65} - 16 q^{67} + 24 q^{68} + 8 q^{70} + 24 q^{71} + 16 q^{73} - 32 q^{74} + 184 q^{75} + 40 q^{77} + 16 q^{78} + 104 q^{79} + 8 q^{80} + 48 q^{81} + 56 q^{82} + 16 q^{83} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 16 q^{88} + 16 q^{89} + 40 q^{90} + 48 q^{91} + 8 q^{92} + 136 q^{93} + 8 q^{94} + 8 q^{95} + 144 q^{97} - 160 q^{99}+O(q^{100}) $ 40 * q + 8 * q^10 - 8 * q^15 - 16 * q^18 - 16 * q^20 - 8 * q^25 - 8 * q^26 + 24 * q^27 + 8 * q^28 - 8 * q^29 - 16 * q^31 + 32 * q^33 - 8 * q^34 - 32 * q^35 + 16 * q^37 + 32 * q^39 + 8 * q^40 - 56 * q^41 - 8 * q^42 - 48 * q^43 - 16 * q^44 - 24 * q^45 - 96 * q^47 - 16 * q^49 - 32 * q^51 - 16 * q^52 - 40 * q^53 + 24 * q^54 + 8 * q^55 - 8 * q^56 - 8 * q^57 + 16 * q^58 + 24 * q^61 - 24 * q^62 - 24 * q^63 + 16 * q^65 - 16 * q^67 + 24 * q^68 + 8 * q^70 + 24 * q^71 + 16 * q^73 - 32 * q^74 + 184 * q^75 + 40 * q^77 + 16 * q^78 + 104 * q^79 + 8 * q^80 + 48 * q^81 + 56 * q^82 + 16 * q^83 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 16 * q^88 + 16 * q^89 + 40 * q^90 + 48 * q^91 + 8 * q^92 + 136 * q^93 + 8 * q^94 + 8 * q^95 + 144 * q^97 - 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.923880	+	0.382683i	0.653281	+	0.270598i
$2$	0.923880	+	0.382683i	0.653281	+	0.270598i
$3$	−0.302197	+	1.51925i	−0.174473	+	0.877137i	0.790030	+	0.613068i	$0.210065\pi$
$3$	−0.302197	+	1.51925i	−0.174473	+	0.877137i	−0.964504	+	0.264069i	$0.914935\pi$
$4$	0.707107	+	0.707107i	0.353553	+	0.353553i
$5$	−1.88843	+	1.19743i	−0.844531	+	0.535506i
$5$	−1.88843	+	1.19743i	−0.844531	+	0.535506i
$6$	−0.860584	+	1.28795i	−0.351332	+	0.525805i
$7$	−0.201119	−	0.134383i	−0.0760159	−	0.0507922i	0.516982	−	0.855997i	$-0.327056\pi$
$7$	−0.201119	−	0.134383i	−0.0760159	−	0.0507922i	−0.592997	+	0.805204i	$0.702056\pi$
$8$	0.382683	+	0.923880i	0.135299	+	0.326641i
$9$	0.554854	+	0.229828i	0.184951	+	0.0766093i
$10$	−2.20292	+	0.383608i	−0.696624	+	0.121308i
$11$	1.18040	+	0.788717i	0.355904	+	0.237807i	0.720649	−	0.693300i	$-0.243844\pi$
$11$	1.18040	+	0.788717i	0.355904	+	0.237807i	−0.364745	+	0.931107i	$0.618844\pi$
$12$	−1.28795	+	0.860584i	−0.371800	+	0.248429i
$13$		−	0.250606i		−	0.0695057i	−0.999396	−	0.0347529i	$-0.988936\pi$
$13$		−	0.250606i		−	0.0695057i	0.999396	−	0.0347529i	$-0.0110644\pi$
$14$	−0.134383	−	0.201119i	−0.0359155	−	0.0537513i
$15$	−1.24851	−	3.23085i	−0.322364	−	0.834201i
$16$			1.00000i			0.250000i
$17$	−2.28902	−	3.42934i	−0.555170	−	0.831737i
$17$	−2.28902	−	3.42934i	−0.555170	−	0.831737i
$18$	0.424667	+	0.424667i	0.100095	+	0.100095i
$19$	5.56274	−	2.30416i	1.27618	−	0.528611i	0.361342	−	0.932433i	$-0.382319\pi$
$19$	5.56274	−	2.30416i	1.27618	−	0.528611i	0.914837	+	0.403822i	$0.132319\pi$
$20$	−2.18203	−	0.488612i	−0.487917	−	0.109257i
$21$	0.264939	−	0.264939i	0.0578144	−	0.0578144i
$22$	0.788717	+	1.18040i	0.168155	+	0.251662i
$23$	3.04284	−	0.605259i	0.634477	−	0.126205i	0.132635	−	0.991165i	$-0.457656\pi$
$23$	3.04284	−	0.605259i	0.634477	−	0.126205i	0.501841	+	0.864960i	$0.332656\pi$
$24$	−1.51925	+	0.302197i	−0.310115	+	0.0616857i
$25$	2.13233	−	4.52252i	0.426467	−	0.904503i
$26$	0.0959029	−	0.231530i	0.0188081	−	0.0454068i
$27$	−3.09859	+	4.63737i	−0.596324	+	0.892462i
$28$	−0.0471892	−	0.237236i	−0.00891792	−	0.0448334i
$29$	−0.237131	+	1.19214i	−0.0440342	+	0.221375i	−0.996536	−	0.0831567i	$-0.973500\pi$
$29$	−0.237131	+	1.19214i	−0.0440342	+	0.221375i	0.952502	+	0.304531i	$0.0984998\pi$
$30$	0.0829196	−	3.46270i	0.0151390	−	0.632199i
$31$	4.24419	−	2.83588i	0.762279	−	0.509339i	−0.112623	−	0.993638i	$-0.535925\pi$
$31$	4.24419	−	2.83588i	0.762279	−	0.509339i	0.874902	+	0.484299i	$0.160925\pi$
$32$	−0.382683	+	0.923880i	−0.0676495	+	0.163320i
$33$	−1.55497	+	1.55497i	−0.270685	+	0.270685i
$34$	−0.802430	−	4.04427i	−0.137616	−	0.693586i
$35$	0.540714	+	0.0129482i	0.0913973	+	0.00218865i
$36$	0.229828	+	0.554854i	0.0383047	+	0.0924756i
$37$	−6.37360	−	1.26779i	−1.04781	−	0.208423i	−0.358982	−	0.933345i	$-0.616876\pi$
$37$	−6.37360	−	1.26779i	−1.04781	−	0.208423i	−0.688832	+	0.724921i	$0.741876\pi$
$38$	6.02107			0.976746
$39$	0.380733	+	0.0757325i	0.0609660	+	0.0121269i
$40$	−1.82895	−	1.28645i	−0.289182	−	0.203405i
$41$	0.171169	+	0.860522i	0.0267320	+	0.134391i	0.991847	−	0.127436i	$-0.0406749\pi$
$41$	0.171169	+	0.860522i	0.0267320	+	0.134391i	−0.965115	+	0.261827i	$0.915675\pi$
$42$	0.346160	−	0.143384i	0.0534136	−	0.0221246i
$43$	8.17809	−	3.38747i	1.24715	−	0.516585i	0.341205	−	0.939989i	$-0.389165\pi$
$43$	8.17809	−	3.38747i	1.24715	−	0.516585i	0.905941	+	0.423404i	$0.139165\pi$
$44$	0.276961	+	1.39237i	0.0417534	+	0.209908i
$45$	−1.32300	+	0.230383i	−0.197222	+	0.0343435i
$46$	3.04284	+	0.605259i	0.448643	+	0.0892406i
$47$	−10.2201			−1.49075			−0.745377	−	0.666643i	$-0.767731\pi$
$47$	−10.2201			−1.49075			−0.745377	+	0.666643i	$0.767731\pi$
$48$	−1.51925	−	0.302197i	−0.219284	−	0.0436183i
$49$	−2.65639	−	6.41310i	−0.379485	−	0.916158i
$50$	3.70071	−	3.36225i	0.523360	−	0.475494i
$51$	5.90175	−	2.44125i	0.826410	−	0.341844i
$52$	0.177206	−	0.177206i	0.0245740	−	0.0245740i
$53$	−0.757188	+	1.82801i	−0.104008	+	0.251097i	−0.967313	−	0.253585i	$-0.918390\pi$
$53$	−0.757188	+	1.82801i	−0.104008	+	0.251097i	0.863305	+	0.504682i	$0.168390\pi$
$54$	−4.63737	+	3.09859i	−0.631066	+	0.421665i
$55$	−3.17353	−	0.0759951i	−0.427919	−	0.0102472i
$56$	0.0471892	−	0.237236i	0.00630592	−	0.0317020i
$57$	1.81955	+	9.14748i	0.241005	+	1.21161i
$58$	−0.675292	+	1.01065i	−0.0886702	+	0.132704i
$59$	−0.520057	+	1.25553i	−0.0677056	+	0.163456i	−0.954110	−	0.299455i	$-0.903195\pi$
$59$	−0.520057	+	1.25553i	−0.0677056	+	0.163456i	0.886405	+	0.462911i	$0.153195\pi$
$60$	1.40172	−	3.16738i	0.180962	−	0.408907i
$61$	−8.99481	+	1.78918i	−1.15167	+	0.229081i	−0.733760	−	0.679409i	$-0.762236\pi$
$61$	−8.99481	+	1.78918i	−1.15167	+	0.229081i	−0.417907	+	0.908490i	$0.637236\pi$
$62$	5.00636	−	0.995828i	0.635809	−	0.126470i
$63$	−0.0807066	−	0.120786i	−0.0101681	−	0.0152176i
$64$	−0.707107	+	0.707107i	−0.0883883	+	0.0883883i
$65$	0.300083	+	0.473253i	0.0372207	+	0.0586998i
$66$	−2.03166	+	0.841542i	−0.250080	+	0.103587i
$67$	7.69457	+	7.69457i	0.940041	+	0.940041i	0.998301	−	0.0582603i	$-0.0185553\pi$
$67$	7.69457	+	7.69457i	0.940041	+	0.940041i	−0.0582603	+	0.998301i	$0.518555\pi$
$68$	0.806326	−	4.04349i	0.0977814	−	0.490346i
$69$			4.80573i			0.578542i
$70$	0.494599	+	0.218885i	0.0591159	+	0.0261617i
$71$	−0.548870	−	0.821442i	−0.0651389	−	0.0974872i	0.797470	−	0.603358i	$-0.206171\pi$
$71$	−0.548870	−	0.821442i	−0.0651389	−	0.0974872i	−0.862609	+	0.505871i	$0.831171\pi$
$72$			0.600569i			0.0707778i
$73$	−13.0293	+	8.70593i	−1.52497	+	1.01895i	−0.540917	+	0.841076i	$0.681923\pi$
$73$	−13.0293	+	8.70593i	−1.52497	+	1.01895i	−0.984053	+	0.177876i	$0.943077\pi$
$74$	−5.40328	−	3.61035i	−0.628118	−	0.419695i
$75$	6.22643	+	4.60623i	0.718966	+	0.531882i
$76$	5.56274	+	2.30416i	0.638090	+	0.264306i
$77$	−0.131410	−	0.317252i	−0.0149756	−	0.0361542i
$78$	0.322770	+	0.215668i	0.0365465	+	0.0244196i
$79$	5.86124	−	8.77197i	0.659441	−	0.986924i	−0.339486	−	0.940611i	$-0.610253\pi$
$79$	5.86124	−	8.77197i	0.659441	−	0.986924i	0.998927	−	0.0463124i	$-0.0147470\pi$
$80$	−1.19743	−	1.88843i	−0.133876	−	0.211133i
$81$	−4.83492	−	4.83492i	−0.537213	−	0.537213i
$82$	−0.171169	+	0.860522i	−0.0189024	+	0.0950288i
$83$	−0.176383	−	0.0730601i	−0.0193605	−	0.00801939i	0.372982	−	0.927839i	$-0.378335\pi$
$83$	−0.176383	−	0.0730601i	−0.0193605	−	0.00801939i	−0.392343	+	0.919819i	$0.628335\pi$
$84$	0.374680			0.0408810
$85$	8.42905	+	3.73513i	0.914258	+	0.405132i
$86$	8.85190			0.954525
$87$	−1.73949	−	0.720521i	−0.186493	−	0.0772480i
$88$	−0.276961	+	1.39237i	−0.0295241	+	0.148428i
$89$	−5.17953	−	5.17953i	−0.549029	−	0.549029i	0.377131	−	0.926160i	$-0.376911\pi$
$89$	−5.17953	−	5.17953i	−0.549029	−	0.549029i	−0.926160	+	0.377131i	$0.876911\pi$
$90$	−1.31046	−	0.293446i	−0.138135	−	0.0309319i
$91$	−0.0336774	+	0.0504017i	−0.00353035	+	0.00528354i
$92$	2.57960	+	1.72363i	0.268942	+	0.179701i
$93$	3.02581	+	7.30496i	0.313762	+	0.757489i
$94$	−9.44214	−	3.91106i	−0.973882	−	0.403395i
$95$	−7.74578	+	11.0122i	−0.794700	+	1.12983i
$96$	−1.28795	−	0.860584i	−0.131451	−	0.0878329i
$97$	7.88775	−	5.27043i	0.800880	−	0.535131i	−0.0864553	−	0.996256i	$-0.527554\pi$
$97$	7.88775	−	5.27043i	0.800880	−	0.535131i	0.887335	+	0.461125i	$0.152554\pi$
$98$		−	6.94149i		−	0.701197i
$99$	0.473679	+	0.708911i	0.0476066	+	0.0712483i
$100$	4.70569	−	1.69011i	0.470569	−	0.169011i
$101$			16.9065i			1.68226i	0.540832	+	0.841131i	$0.318110\pi$
$101$			16.9065i			1.68226i	−0.540832	+	0.841131i	$0.681890\pi$
$102$	6.38673	+	0.00307642i	0.632380	+	0.000304611i
$103$	−2.75429	−	2.75429i	−0.271388	−	0.271388i	0.558271	−	0.829659i	$-0.311465\pi$
$103$	−2.75429	−	2.75429i	−0.271388	−	0.271388i	−0.829659	+	0.558271i	$0.811465\pi$
$104$	0.231530	−	0.0959029i	0.0227034	−	0.00940406i
$105$	−0.183073	+	0.817564i	−0.0178661	+	0.0797861i
$106$	−1.39910	+	1.39910i	−0.135893	+	0.135893i
$107$	−0.551617	−	0.825553i	−0.0533268	−	0.0798093i	0.803848	−	0.594835i	$-0.202782\pi$
$107$	−0.551617	−	0.825553i	−0.0533268	−	0.0798093i	−0.857175	+	0.515025i	$0.827782\pi$
$108$	−5.47015	+	1.08808i	−0.526365	+	0.104701i
$109$	6.16805	−	1.22690i	0.590792	−	0.117516i	0.109364	−	0.994002i	$-0.465119\pi$
$109$	6.16805	−	1.22690i	0.590792	−	0.117516i	0.481427	+	0.876486i	$0.340119\pi$
$110$	−2.90288	−	1.28467i	−0.276779	−	0.122488i
$111$	3.85216	−	9.29994i	0.365631	−	0.882712i
$112$	0.134383	−	0.201119i	0.0126980	−	0.0190040i
$113$	1.39524	+	7.01434i	0.131253	+	0.659854i	0.989254	+	0.146206i	$0.0467062\pi$
$113$	1.39524	+	7.01434i	0.131253	+	0.659854i	−0.858001	+	0.513648i	$0.828294\pi$
$114$	−1.81955	+	9.14748i	−0.170416	+	0.856740i
$115$	−5.02144	+	4.78657i	−0.468252	+	0.446350i
$116$	−1.01065	+	0.675292i	−0.0938362	+	0.0626993i
$117$	0.0575964	−	0.139050i	0.00532479	−	0.0128552i
$118$	−0.960940	+	0.960940i	−0.0884617	+	0.0884617i
$119$	−0.000480394		0.997313i	−4.40377e−5		0.0914235i
$120$	2.50713	−	2.38986i	0.228869	−	0.218164i
$121$	−3.43825	−	8.30067i	−0.312568	−	0.754607i
$122$	−8.99481	−	1.78918i	−0.814352	−	0.161985i
$123$	−1.35907			−0.122543
$124$	5.00636	+	0.995828i	0.449585	+	0.0894280i
$125$	1.38862	+	11.0938i	0.124202	+	0.992257i
$126$	−0.0283404	−	0.142477i	−0.00252476	−	0.0126928i
$127$	−14.4919	+	6.00272i	−1.28594	+	0.532655i	−0.917774	−	0.397103i	$-0.870016\pi$
$127$	−14.4919	+	6.00272i	−1.28594	+	0.532655i	−0.368170	+	0.929759i	$0.620016\pi$
$128$	−0.923880	+	0.382683i	−0.0816602	+	0.0338248i
$129$	2.67501	+	13.4482i	0.235522	+	1.18405i
$130$	0.0961346	+	0.552065i	0.00843157	+	0.0484193i
$131$	−5.73305	−	1.14038i	−0.500899	−	0.0996350i	−0.0618271	−	0.998087i	$-0.519693\pi$
$131$	−5.73305	−	1.14038i	−0.500899	−	0.0996350i	−0.439072	+	0.898452i	$0.644693\pi$
$132$	−2.19906			−0.191403
$133$	−1.42841	−	0.284129i	−0.123859	−	0.0246371i
$134$	4.16427	+	10.0534i	0.359738	+	0.868485i
$135$	0.298558	−	12.4677i	0.0256958	−	1.07305i
$136$	2.29233	−	3.42713i	0.196565	−	0.293874i
$137$	10.2123	−	10.2123i	0.872492	−	0.872492i	−0.120251	−	0.992744i	$-0.538370\pi$
$137$	10.2123	−	10.2123i	0.872492	−	0.872492i	0.992744	+	0.120251i	$0.0383700\pi$
$138$	−1.83907	+	4.43992i	−0.156552	+	0.377951i
$139$	16.7907	−	11.2192i	1.42417	−	0.951598i	0.425249	−	0.905076i	$-0.360186\pi$
$139$	16.7907	−	11.2192i	1.42417	−	0.951598i	0.998917	−	0.0465215i	$-0.0148136\pi$
$140$	0.373187	+	0.391498i	0.0315400	+	0.0330876i
$141$	3.08848	−	15.5268i	0.260097	−	1.30760i
$142$	−0.192737	−	0.968957i	−0.0161742	−	0.0813130i
$143$	0.197658	−	0.295815i	0.0165290	−	0.0247373i
$144$	−0.229828	+	0.554854i	−0.0191523	+	0.0462378i
$145$	−0.979694	−	2.53522i	−0.0813592	−	0.210538i
$146$	−15.3692	+	3.05712i	−1.27196	+	0.253009i
$147$	10.5458	−	2.09770i	0.869806	−	0.173015i
$148$	−3.61035	−	5.40328i	−0.296769	−	0.444147i
$149$	−9.07239	+	9.07239i	−0.743239	+	0.743239i	−0.973200	−	0.229961i	$-0.926140\pi$
$149$	−9.07239	+	9.07239i	−0.743239	+	0.743239i	0.229961	+	0.973200i	$0.426140\pi$
$150$	3.98974	+	6.63835i	0.325761	+	0.542019i
$151$	6.66259	−	2.75974i	0.542194	−	0.224584i	−0.0947404	−	0.995502i	$-0.530202\pi$
$151$	6.66259	−	2.75974i	0.542194	−	0.224584i	0.636935	+	0.770918i	$0.280202\pi$
$152$	4.25754	+	4.25754i	0.345332	+	0.345332i
$153$	−0.481915	−	2.42886i	−0.0389605	−	0.196362i
$154$		−	0.343391i		−	0.0276712i
$155$	−4.61910	+	10.4375i	−0.371015	+	0.838357i
$156$	0.215668	+	0.322770i	0.0172672	+	0.0258423i
$157$		−	24.9767i		−	1.99336i	−0.0814150	−	0.996680i	$-0.525944\pi$
$157$		−	24.9767i		−	1.99336i	0.0814150	−	0.996680i	$-0.474056\pi$
$158$	8.77197	−	5.86124i	0.697860	−	0.466295i
$159$	−2.54838	−	1.70277i	−0.202100	−	0.135039i
$160$	−0.383608	−	2.20292i	−0.0303269	−	0.174156i
$161$	−0.693311	−	0.287179i	−0.0546405	−	0.0226328i
$162$	−2.61664	−	6.31713i	−0.205583	−	0.496320i
$163$	−5.66535	−	3.78546i	−0.443744	−	0.296500i	0.313553	−	0.949571i	$-0.398481\pi$
$163$	−5.66535	−	3.78546i	−0.443744	−	0.296500i	−0.757297	+	0.653070i	$0.773481\pi$
$164$	−0.487447	+	0.729516i	−0.0380632	+	0.0569656i
$165$	1.07449	−	4.79841i	0.0836486	−	0.373556i
$166$	−0.134997	−	0.134997i	−0.0104778	−	0.0104778i
$167$	3.26312	−	16.4048i	0.252508	−	1.26944i	−0.621456	−	0.783449i	$-0.713458\pi$
$167$	3.26312	−	16.4048i	0.252508	−	1.26944i	0.873963	−	0.485992i	$-0.161542\pi$
$168$	0.346160	+	0.143384i	0.0267068	+	0.0110623i
$169$	12.9372			0.995169
$170$	6.35805	+	6.67647i	0.487640	+	0.512061i
$171$	3.61607			0.276528
$172$	8.17809	+	3.38747i	0.623573	+	0.258292i
$173$	2.15257	−	10.8217i	0.163657	−	0.822758i	−0.808513	−	0.588479i	$-0.799727\pi$
$173$	2.15257	−	10.8217i	0.163657	−	0.822758i	0.972169	−	0.234279i	$-0.0752729\pi$
$174$	−1.33135	−	1.33135i	−0.100929	−	0.100929i
$175$	−1.03660	+	0.623014i	−0.0783599	+	0.0470954i
$176$	−0.788717	+	1.18040i	−0.0594518	+	0.0889759i
$177$	−1.75030	−	1.16951i	−0.131560	−	0.0879058i
$178$	−2.80314	−	6.76738i	−0.210104	−	0.507236i
$179$	−13.8487	−	5.73630i	−1.03510	−	0.428751i	−0.200547	−	0.979684i	$-0.564272\pi$
$179$	−13.8487	−	5.73630i	−1.03510	−	0.428751i	−0.834550	+	0.550933i	$0.814272\pi$
$180$	−1.09841	−	0.772600i	−0.0818707	−	0.0575862i
$181$	−14.6146	−	9.76518i	−1.08630	−	0.725840i	−0.122498	−	0.992469i	$-0.539090\pi$
$181$	−14.6146	−	9.76518i	−1.08630	−	0.725840i	−0.963799	+	0.266628i	$0.914090\pi$
$182$	−0.0504017	+	0.0336774i	−0.00373603	+	0.00249633i
$183$		−	14.2060i		−	1.05014i
$184$	1.72363	+	2.57960i	0.127068	+	0.190170i
$185$	13.5542	−	5.23780i	0.996523	−	0.385090i
$186$			7.90683i			0.579757i
$187$	0.00281951	−	5.85338i	0.000206183	−	0.428041i
$188$	−7.22670	−	7.22670i	−0.527061	−	0.527061i
$189$	1.24637	−	0.516264i	0.0906602	−	0.0375527i
$190$	−11.3704	+	7.20979i	−0.824893	+	0.523053i
$191$	−6.51300	+	6.51300i	−0.471264	+	0.471264i	−0.902324	−	0.431059i	$-0.858140\pi$
$191$	−6.51300	+	6.51300i	−0.471264	+	0.471264i	0.431059	+	0.902324i	$0.358140\pi$
$192$	−0.860584	−	1.28795i	−0.0621073	−	0.0929501i
$193$	9.20405	−	1.83080i	0.662522	−	0.131784i	0.147635	−	0.989042i	$-0.452834\pi$
$193$	9.20405	−	1.83080i	0.662522	−	0.131784i	0.514887	+	0.857258i	$0.327834\pi$
$194$	9.30424	−	1.85073i	0.668005	−	0.132875i
$195$	−0.809671	+	0.312885i	−0.0579818	+	0.0224061i
$196$	2.65639	−	6.41310i	0.189742	−	0.458079i
$197$	3.72400	−	5.57335i	0.265324	−	0.397085i	−0.674755	−	0.738041i	$-0.735751\pi$
$197$	3.72400	−	5.57335i	0.265324	−	0.397085i	0.940079	+	0.340956i	$0.110751\pi$
$198$	0.166334	+	0.836218i	0.0118208	+	0.0594274i
$199$	−4.92775	+	24.7735i	−0.349319	+	1.75614i	0.262294	+	0.964988i	$0.415521\pi$
$199$	−4.92775	+	24.7735i	−0.349319	+	1.75614i	−0.611613	+	0.791157i	$0.709479\pi$
$200$	4.99427	+	0.239328i	0.353148	+	0.0169231i
$201$	−14.0152	+	9.36467i	−0.988557	+	0.660533i
$202$	−6.46985	+	15.6196i	−0.455217	+	1.09899i
$203$	0.207895	−	0.207895i	0.0145914	−	0.0145914i
$204$	5.89939	+	2.44694i	0.413040	+	0.171320i
$205$	−1.35365	−	1.42007i	−0.0945432	−	0.0991823i
$206$	−1.49061	−	3.59866i	−0.103856	−	0.250730i
$207$	1.82744	+	0.363500i	0.127016	+	0.0252650i
$208$	0.250606			0.0173764
$209$	8.38358	+	1.66760i	0.579904	+	0.115350i
$210$	−0.482006	+	0.685272i	−0.0332616	+	0.0472882i
$211$	4.01313	+	20.1754i	0.276275	+	1.38893i	0.830711	+	0.556704i	$0.187934\pi$
$211$	4.01313	+	20.1754i	0.276275	+	1.38893i	−0.554436	+	0.832227i	$0.687066\pi$
$212$	−1.82801	+	0.757188i	−0.125548	+	0.0520039i
$213$	1.41384	−	0.585631i	0.0968746	−	0.0401268i
$214$	−0.193702	−	0.973807i	−0.0132412	−	0.0665681i
$215$	−11.3875	+	16.1897i	−0.776620	+	1.10413i
$216$	−5.47015	−	1.08808i	−0.372197	−	0.0740345i
$217$	−1.23468			−0.0838157
$218$	6.16805	+	1.22690i	0.417753	+	0.0830962i
$219$	−9.28902	−	22.4257i	−0.627694	−	1.51539i
$220$	−2.19029	−	2.29776i	−0.147669	−	0.154915i
$221$	−0.859415	+	0.573644i	−0.0578105	+	0.0385875i
$222$	7.11787	−	7.11787i	0.477720	−	0.477720i
$223$	−1.75687	+	4.24146i	−0.117649	+	0.284029i	−0.971724	−	0.236121i	$-0.924124\pi$
$223$	−1.75687	+	4.24146i	−0.117649	+	0.284029i	0.854075	+	0.520150i	$0.174124\pi$
$224$	0.201119	−	0.134383i	0.0134378	−	0.00897887i
$225$	2.22253	−	2.01927i	0.148169	−	0.134618i
$226$	−1.39524	+	7.01434i	−0.0928100	+	0.466587i
$227$	3.68065	+	18.5039i	0.244293	+	1.22815i	0.886904	+	0.461953i	$0.152851\pi$
$227$	3.68065	+	18.5039i	0.244293	+	1.22815i	−0.642611	+	0.766193i	$0.722149\pi$
$228$	−5.18163	+	7.75486i	−0.343162	+	0.513578i
$229$	−7.85190	+	18.9562i	−0.518868	+	1.25266i	0.419731	+	0.907649i	$0.362124\pi$
$229$	−7.85190	+	18.9562i	−0.518868	+	1.25266i	−0.938599	+	0.345010i	$0.887876\pi$
$230$	−6.47095	+	2.50059i	−0.426682	+	0.164884i
$231$	0.521696	−	0.103772i	0.0343250	−	0.00682768i
$232$	−1.19214	+	0.237131i	−0.0782677	+	0.0155684i
$233$	−6.03405	−	9.03059i	−0.395304	−	0.591614i	0.579420	−	0.815029i	$-0.303279\pi$
$233$	−6.03405	−	9.03059i	−0.395304	−	0.591614i	−0.974723	+	0.223416i	$0.928279\pi$
$234$	0.106424	−	0.106424i	0.00695717	−	0.00695717i
$235$	19.2999	−	12.2378i	1.25899	−	0.798308i
$236$	−1.25553	+	0.520057i	−0.0817279	+	0.0338528i
$237$	11.5555	+	11.5555i	0.750612	+	0.750612i
$238$	−0.382099	+	0.921213i	−0.0247678	+	0.0597134i
$239$			7.02173i			0.454198i	0.973872	+	0.227099i	$0.0729241\pi$
$239$			7.02173i			0.454198i	−0.973872	+	0.227099i	$0.927076\pi$
$240$	3.23085	−	1.24851i	0.208550	−	0.0805909i
$241$	−9.37504	−	14.0307i	−0.603900	−	0.903800i	0.395996	−	0.918252i	$-0.370399\pi$
$241$	−9.37504	−	14.0307i	−0.603900	−	0.903800i	−0.999896	+	0.0144526i	$0.995399\pi$
$242$		−	8.98458i		−	0.577551i
$243$	−5.10558	+	3.41144i	−0.327523	+	0.218844i
$244$	−7.62543	−	5.09515i	−0.488168	−	0.326184i
$245$	12.6956	+	8.92985i	0.811095	+	0.570507i
$246$	−1.25562	−	0.520094i	−0.0800553	−	0.0331600i
$247$	−0.577438	−	1.39406i	−0.0367415	−	0.0887018i
$248$	4.24419	+	2.83588i	0.269506	+	0.180078i
$249$	0.164299	−	0.245890i	0.0104120	−	0.0155827i
$250$	−2.96248	+	10.7807i	−0.187364	+	0.681832i
$251$	19.5290	+	19.5290i	1.23266	+	1.23266i	0.962939	+	0.269721i	$0.0869313\pi$
$251$	19.5290	+	19.5290i	1.23266	+	1.23266i	0.269721	+	0.962939i	$0.413069\pi$
$252$	0.0283404	−	0.142477i	0.00178528	−	0.00897519i
$253$	4.06915	+	1.68550i	0.255825	+	0.105966i
$254$	−15.6859			−0.984219
$255$	−8.22181	+	11.6770i	−0.514870	+	0.731245i
$256$	−1.00000			−0.0625000
$257$	0.738606	+	0.305941i	0.0460730	+	0.0190841i	0.405601	−	0.914050i	$-0.367062\pi$
$257$	0.738606	+	0.305941i	0.0460730	+	0.0190841i	−0.359528	+	0.933134i	$0.617062\pi$
$258$	−2.67501	+	13.4482i	−0.166539	+	0.837249i
$259$	1.11148	+	1.11148i	0.0690642	+	0.0690642i
$260$	−0.122449	+	0.546831i	−0.00759399	+	0.0339130i
$261$	−0.405560	+	0.606963i	−0.0251035	+	0.0375701i
$262$	−4.86025	−	3.24751i	−0.300267	−	0.200632i
$263$	−2.85697	−	6.89733i	−0.176168	−	0.425308i	0.810989	−	0.585062i	$-0.198930\pi$
$263$	−2.85697	−	6.89733i	−0.176168	−	0.425308i	−0.987157	+	0.159754i	$0.948930\pi$
$264$	−2.03166	−	0.841542i	−0.125040	−	0.0517934i
$265$	−0.759017	−	4.35875i	−0.0466260	−	0.267756i
$266$	−1.21095	−	0.809132i	−0.0742482	−	0.0496110i
$267$	9.43421	−	6.30374i	0.577364	−	0.385782i
$268$			10.8818i			0.664709i
$269$	−11.5222	−	17.2442i	−0.702519	−	1.05139i	−0.995452	−	0.0952616i	$-0.969631\pi$
$269$	−11.5222	−	17.2442i	−0.702519	−	1.05139i	0.292933	−	0.956133i	$-0.405369\pi$
$270$	5.04701	−	11.4044i	0.307151	−	0.694049i
$271$			20.6843i			1.25648i	0.778018	+	0.628242i	$0.216225\pi$
$271$			20.6843i			1.25648i	−0.778018	+	0.628242i	$0.783775\pi$
$272$	3.42934	−	2.28902i	0.207934	−	0.138792i
$273$	−0.0663954	−	0.0663954i	−0.00401843	−	0.00401843i
$274$	13.3430	−	5.52684i	0.806078	−	0.333888i
$275$	6.08399	−	3.65656i	0.366878	−	0.220499i
$276$	−3.39817	+	3.39817i	−0.204546	+	0.204546i
$277$	11.4016	+	17.0637i	0.685054	+	1.02526i	0.997168	+	0.0752111i	$0.0239631\pi$
$277$	11.4016	+	17.0637i	0.685054	+	1.02526i	−0.312114	+	0.950045i	$0.601037\pi$
$278$	19.8060	−	3.93965i	1.18788	−	0.236284i
$279$	3.00667	−	0.598064i	0.180005	−	0.0358051i
$280$	0.194960	+	0.504509i	0.0116511	+	0.0301502i
$281$	−8.90415	+	21.4965i	−0.531177	+	1.28237i	0.399568	+	0.916704i	$0.369160\pi$
$281$	−8.90415	+	21.4965i	−0.531177	+	1.28237i	−0.930744	+	0.365671i	$0.880840\pi$
$282$	8.79525	−	13.1630i	0.523749	−	0.783846i
$283$	3.33557	+	16.7691i	0.198279	+	0.996817i	0.943846	+	0.330386i	$0.107179\pi$
$283$	3.33557	+	16.7691i	0.198279	+	0.996817i	−0.745567	+	0.666431i	$0.767821\pi$
$284$	0.192737	−	0.968957i	0.0114369	−	0.0574970i
$285$	−14.3895	−	15.0956i	−0.852362	−	0.894186i
$286$	0.295815	−	0.197658i	0.0174919	−	0.0116877i
$287$	0.0812147	−	0.196070i	0.00479395	−	0.0115736i
$288$	−0.424667	+	0.424667i	−0.0250237	+	0.0250237i
$289$	−6.52075	+	15.6997i	−0.383573	+	0.923510i
$290$	0.0650663	−	2.71715i	0.00382083	−	0.159556i
$291$	5.62342	+	13.5761i	0.329651	+	0.795847i
$292$	−15.3692	−	3.05712i	−0.899412	−	0.178904i
$293$	31.7214			1.85318			0.926591	−	0.376071i	$-0.122725\pi$
$293$	31.7214			1.85318			0.926591	+	0.376071i	$0.122725\pi$
$294$	10.5458	+	2.09770i	0.615045	+	0.122340i
$295$	−0.521313	−	2.99371i	−0.0303520	−	0.174300i
$296$	−1.26779	−	6.37360i	−0.0736887	−	0.370458i
$297$	−7.31514	+	3.03003i	−0.424468	+	0.175820i
$298$	−11.8536	+	4.90994i	−0.686663	+	0.284425i
$299$	−0.151682	−	0.762556i	−0.00877199	−	0.0440998i
$300$	1.14565	+	7.65985i	0.0661443	+	0.442241i
$301$	−2.09999	−	0.417714i	−0.121041	−	0.0240766i
$302$	7.21154			0.414977
$303$	−25.6852	−	5.10910i	−1.47557	−	0.293510i
$304$	2.30416	+	5.56274i	0.132153	+	0.319045i
$305$	14.8437	−	14.1494i	0.849945	−	0.810191i
$306$	0.484255	−	2.42840i	0.0276830	−	0.138822i
$307$	−10.0231	+	10.0231i	−0.572047	+	0.572047i	−0.932700	−	0.360653i	$-0.882554\pi$
$307$	−10.0231	+	10.0231i	−0.572047	+	0.572047i	0.360653	+	0.932700i	$0.382554\pi$
$308$	0.131410	−	0.317252i	0.00748779	−	0.0180771i
$309$	5.01679	−	3.35211i	0.285395	−	0.190695i
$310$	−8.26173	+	7.87531i	−0.469235	+	0.447287i
$311$	5.82573	−	29.2879i	0.330347	−	1.66077i	−0.356750	−	0.934200i	$-0.616115\pi$
$311$	5.82573	−	29.2879i	0.330347	−	1.66077i	0.687097	−	0.726566i	$-0.258885\pi$
$312$	0.0757325	+	0.380733i	0.00428751	+	0.0215548i
$313$	0.526834	−	0.788463i	0.0297784	−	0.0445666i	−0.816282	−	0.577654i	$-0.803968\pi$
$313$	0.526834	−	0.788463i	0.0297784	−	0.0445666i	0.846060	+	0.533087i	$0.178968\pi$
$314$	9.55818	−	23.0755i	0.539399	−	1.30223i
$315$	0.297041	+	0.131456i	0.0167364	+	0.00740668i
$316$	10.3472	−	2.05819i	0.582078	−	0.115782i
$317$	−9.03747	+	1.79766i	−0.507595	+	0.100967i	−0.442243	−	0.896895i	$-0.645817\pi$
$317$	−9.03747	+	1.79766i	−0.507595	+	0.100967i	−0.0653519	+	0.997862i	$0.520817\pi$
$318$	−1.70277	−	2.54838i	−0.0954868	−	0.142906i
$319$	−1.22017	+	1.22017i	−0.0683164	+	0.0683164i
$320$	0.488612	−	2.18203i	0.0273143	−	0.121979i
$321$	1.42092	−	0.588562i	0.0793078	−	0.0328504i
$322$	−0.530637	−	0.530637i	−0.0295712	−	0.0295712i
$323$	−20.6350	−	13.8022i	−1.14816	−	0.767977i
$324$		−	6.83761i		−	0.379867i
$325$	−1.13337	−	0.534377i	−0.0628682	−	0.0296419i
$326$	−3.78546	−	5.66535i	−0.209657	−	0.313775i
$327$			9.74154i			0.538708i
$328$	−0.729516	+	0.487447i	−0.0402808	+	0.0269147i
$329$	2.05546	+	1.37341i	0.113321	+	0.0757187i
$330$	2.82897	−	4.02196i	0.155730	−	0.221402i
$331$	−14.0014	−	5.79957i	−0.769587	−	0.318773i	−0.0368818	−	0.999320i	$-0.511743\pi$
$331$	−14.0014	−	5.79957i	−0.769587	−	0.318773i	−0.732705	+	0.680546i	$0.761743\pi$
$332$	−0.0730601	−	0.176383i	−0.00400969	−	0.00968026i
$333$	−3.24504	−	2.16827i	−0.177827	−	0.118820i
$334$	9.29257	−	13.9073i	0.508467	−	0.760975i
$335$	−23.7443	−	5.31696i	−1.29729	−	0.290497i
$336$	0.264939	+	0.264939i	0.0144536	+	0.0144536i
$337$	−2.99672	+	15.0655i	−0.163242	+	0.820671i	0.809202	+	0.587531i	$0.199900\pi$
$337$	−2.99672	+	15.0655i	−0.163242	+	0.820671i	−0.972443	+	0.233140i	$0.925100\pi$
$338$	11.9524	+	4.95085i	0.650125	+	0.269291i
$339$	−11.0781			−0.601682
$340$	3.31910	+	8.60137i	0.180004	+	0.466475i
$341$	7.24654			0.392422
$342$	3.34081	+	1.38381i	0.180650	+	0.0748278i
$343$	−0.657888	+	3.30743i	−0.0355226	+	0.178584i
$344$	6.25924	+	6.25924i	0.337475	+	0.337475i
$345$	−5.75452	−	9.07529i	−0.309813	−	0.488597i
$346$	6.12999	−	9.17418i	0.329550	−	0.493207i
$347$	−17.3930	−	11.6216i	−0.933706	−	0.623883i	−0.00712393	−	0.999975i	$-0.502268\pi$
$347$	−17.3930	−	11.6216i	−0.933706	−	0.623883i	−0.926582	+	0.376092i	$0.877268\pi$
$348$	−0.720521	−	1.73949i	−0.0386240	−	0.0932465i
$349$	2.52921	+	1.04763i	0.135386	+	0.0560785i	0.449348	−	0.893357i	$-0.351656\pi$
$349$	2.52921	+	1.04763i	0.135386	+	0.0560785i	−0.313962	+	0.949436i	$0.601656\pi$
$350$	−1.19611	+	0.178898i	−0.0639350	+	0.00956251i
$351$	1.16215	+	0.776527i	0.0620312	+	0.0414479i
$352$	−1.18040	+	0.788717i	−0.0629154	+	0.0420388i
$353$			10.1837i			0.542025i	0.962576	+	0.271013i	$0.0873585\pi$
$353$			10.1837i			0.542025i	−0.962576	+	0.271013i	$0.912642\pi$
$354$	−1.16951	−	1.75030i	−0.0621588	−	0.0930272i
$355$	2.02012	+	0.894003i	0.107217	+	0.0474488i
$356$		−	7.32495i		−	0.388222i
$357$	−1.51502	−	0.302114i	−0.0801832	−	0.0159896i
$358$	−10.5993	−	10.5993i	−0.560190	−	0.560190i
$359$	−20.3347	+	8.42291i	−1.07322	+	0.444544i	−0.848128	−	0.529792i	$-0.822270\pi$
$359$	−20.3347	+	8.42291i	−1.07322	+	0.444544i	−0.225097	+	0.974336i	$0.572270\pi$
$360$	−0.719138	−	1.13413i	−0.0379019	−	0.0597741i
$361$	12.1999	−	12.1999i	0.642099	−	0.642099i
$362$	−9.76518	−	14.6146i	−0.513247	−	0.768128i
$363$	13.6498	−	2.71511i	0.716428	−	0.142506i
$364$	−0.0594529	+	0.0118259i	−0.00311618	+	0.000619847i
$365$	14.1803	−	32.0422i	0.742230	−	1.67717i
$366$	5.43641	−	13.1246i	0.284165	−	0.686036i
$367$	−1.05658	+	1.58128i	−0.0551529	+	0.0825421i	−0.858021	−	0.513614i	$-0.828306\pi$
$367$	−1.05658	+	1.58128i	−0.0551529	+	0.0825421i	0.802868	+	0.596156i	$0.203306\pi$
$368$	0.605259	+	3.04284i	0.0315513	+	0.158619i
$369$	−0.102799	+	0.516803i	−0.00535148	+	0.0269037i
$370$	14.5268	+	0.347868i	0.755215	+	0.0180848i
$371$	0.397940	−	0.265895i	0.0206600	−	0.0138046i
$372$	−3.02581	+	7.30496i	−0.156881	+	0.378745i
$373$	−4.01050	+	4.01050i	−0.207656	+	0.207656i	−0.803270	−	0.595615i	$-0.796909\pi$
$373$	−4.01050	+	4.01050i	−0.207656	+	0.207656i	0.595615	+	0.803270i	$0.296909\pi$
$374$	2.24260	−	5.40674i	0.115962	−	0.279576i
$375$	−17.2738	−	1.24284i	−0.892015	−	0.0641802i
$376$	−3.91106	−	9.44214i	−0.201698	−	0.486941i
$377$	0.298758	+	0.0594266i	0.0153868	+	0.00306063i
$378$	1.34906			0.0693883
$379$	1.89732	+	0.377400i	0.0974587	+	0.0193857i	0.243579	−	0.969881i	$-0.421679\pi$
$379$	1.89732	+	0.377400i	0.0974587	+	0.0193857i	−0.146120	+	0.989267i	$0.546679\pi$
$380$	−13.2639	+	2.30973i	−0.680424	+	0.118487i
$381$	−4.74022	−	23.8307i	−0.242849	−	1.22088i
$382$	−8.50965	+	3.52481i	−0.435392	+	0.180345i
$383$	26.3105	−	10.8982i	1.34440	−	0.556870i	0.409674	−	0.912232i	$-0.365642\pi$
$383$	26.3105	−	10.8982i	1.34440	−	0.556870i	0.934729	+	0.355362i	$0.115642\pi$
$384$	−0.302197	−	1.51925i	−0.0154214	−	0.0775287i
$385$	0.628045	+	0.441754i	0.0320081	+	0.0225139i
$386$	9.20405	+	1.83080i	0.468474	+	0.0931852i
$387$	5.31618			0.270237
$388$	9.30424	+	1.85073i	0.472351	+	0.0939565i
$389$	−9.59778	−	23.1711i	−0.486627	−	1.17482i	−0.956407	−	0.292038i	$-0.905667\pi$
$389$	−9.59778	−	23.1711i	−0.486627	−	1.17482i	0.469780	−	0.882784i	$-0.344333\pi$
$390$	−0.867774	−	0.0207802i	−0.0439415	−	0.00105225i
$391$	−9.04078	−	9.04949i	−0.457212	−	0.457652i
$392$	4.90838	−	4.90838i	0.247910	−	0.247910i
$393$	3.46502	−	8.36530i	0.174787	−	0.421973i
$394$	5.57335	−	3.72400i	0.280781	−	0.187612i
$395$	−0.564747	+	23.5837i	−0.0284155	+	1.18662i
$396$	−0.166334	+	0.836218i	−0.00835860	+	0.0420215i
$397$	0.897961	+	4.51435i	0.0450674	+	0.226569i	0.996755	−	0.0805001i	$-0.0256517\pi$
$397$	0.897961	+	4.51435i	0.0450674	+	0.226569i	−0.951687	+	0.307069i	$0.900652\pi$
$398$	−14.0330	+	21.0019i	−0.703413	+	1.05273i
$399$	0.863324	−	2.08425i	0.0432203	−	0.104343i
$400$	4.52252	+	2.13233i	0.226126	+	0.106617i
$401$	36.0272	−	7.16626i	1.79911	−	0.357866i	0.821818	−	0.569750i	$-0.192960\pi$
$401$	36.0272	−	7.16626i	1.79911	−	0.357866i	0.977295	+	0.211884i	$0.0679600\pi$
$402$	−16.5321	+	3.28843i	−0.824545	+	0.164012i
$403$	−0.710689	−	1.06362i	−0.0354019	−	0.0529828i
$404$	−11.9547	+	11.9547i	−0.594769	+	0.594769i
$405$	14.9199	+	3.34094i	0.741374	+	0.166013i
$406$	0.271628	−	0.112512i	0.0134807	−	0.00558388i
$407$	−6.52346	−	6.52346i	−0.323356	−	0.323356i
$408$	4.51392	+	4.51827i	0.223473	+	0.223688i
$409$			37.5509i			1.85677i	0.371618	+	0.928386i	$0.378803\pi$
$409$			37.5509i			1.85677i	−0.371618	+	0.928386i	$0.621197\pi$
$410$	−0.707173	−	1.83000i	−0.0349248	−	0.0903771i
$411$	12.4288	+	18.6010i	0.613069	+	0.917522i
$412$		−	3.89516i		−	0.191901i
$413$	0.273316	−	0.182624i	0.0134490	−	0.00898632i
$414$	1.54923	+	1.03516i	0.0761404	+	0.0508754i
$415$	0.420571	−	0.0732366i	0.0206450	−	0.00359504i
$416$	0.231530	+	0.0959029i	0.0113517	+	0.00470203i
$417$	11.9706	+	28.8996i	0.586202	+	1.41522i
$418$	7.10726	+	4.74892i	0.347627	+	0.232277i
$419$	14.3243	−	21.4378i	0.699787	−	1.04731i	−0.295962	−	0.955200i	$-0.595640\pi$
$419$	14.3243	−	21.4378i	0.699787	−	1.04731i	0.995749	−	0.0921057i	$-0.0293598\pi$
$420$	−0.707558	+	0.448653i	−0.0345253	+	0.0218920i
$421$	3.63694	+	3.63694i	0.177254	+	0.177254i	0.790158	−	0.612904i	$-0.209999\pi$
$421$	3.63694	+	3.63694i	0.177254	+	0.177254i	−0.612904	+	0.790158i	$0.709999\pi$
$422$	−4.01313	+	20.1754i	−0.195356	+	0.982122i
$423$	−5.67066	−	2.34886i	−0.275717	−	0.114206i
$424$	−1.97863			−0.0960906
$425$	−20.3902	+	3.03964i	−0.989070	+	0.147444i
$426$	1.53033			0.0741446
$427$	2.04946	+	0.848916i	0.0991805	+	0.0410819i
$428$	0.193702	−	0.973807i	0.00936295	−	0.0470707i
$429$	0.389685	+	0.389685i	0.0188142	+	0.0188142i
$430$	−16.7162	+	10.5995i	−0.806126	+	0.511154i
$431$	2.44173	−	3.65430i	0.117614	−	0.176022i	−0.767992	−	0.640460i	$-0.778744\pi$
$431$	2.44173	−	3.65430i	0.117614	−	0.176022i	0.885605	+	0.464438i	$0.153744\pi$
$432$	−4.63737	−	3.09859i	−0.223116	−	0.149081i
$433$	8.88880	+	21.4595i	0.427169	+	1.03128i	0.980181	+	0.198103i	$0.0634782\pi$
$433$	8.88880	+	21.4595i	0.427169	+	1.03128i	−0.553013	+	0.833173i	$0.686522\pi$
$434$	−1.14070	−	0.472493i	−0.0547552	−	0.0226804i
$435$	4.14768	−	0.722262i	0.198866	−	0.0346298i
$436$	5.22902	+	3.49392i	0.250424	+	0.167328i
$437$	15.5319	−	10.3781i	0.742993	−	0.496452i
$438$		−	24.2734i		−	1.15983i
$439$	−5.19233	−	7.77087i	−0.247816	−	0.370883i	0.686618	−	0.727018i	$-0.259094\pi$
$439$	−5.19233	−	7.77087i	−0.247816	−	0.370883i	−0.934435	+	0.356135i	$0.884094\pi$
$440$	−1.14425	−	2.96104i	−0.0545499	−	0.141162i
$441$		−	4.16885i		−	0.198517i
$442$	−1.01352	+	0.201094i	−0.0482082	+	0.00956507i
$443$	−0.680053	−	0.680053i	−0.0323103	−	0.0323103i	0.690767	−	0.723077i	$-0.257273\pi$
$443$	−0.680053	−	0.680053i	−0.0323103	−	0.0323103i	−0.723077	+	0.690767i	$0.757273\pi$
$444$	9.29994	−	3.85216i	0.441356	−	0.182816i
$445$	15.9833	+	3.57906i	0.757680	+	0.169664i
$446$	−3.24627	+	3.24627i	−0.153715	+	0.153715i
$447$	−11.0415	−	16.5248i	−0.522247	−	0.781598i
$448$	0.237236	−	0.0471892i	0.0112084	−	0.00222948i
$449$	1.16763	−	0.232256i	0.0551039	−	0.0109609i	−0.167461	−	0.985879i	$-0.553557\pi$
$449$	1.16763	−	0.232256i	0.0551039	−	0.0109609i	0.222565	+	0.974918i	$0.428557\pi$
$450$	2.82609	−	1.01503i	0.133223	−	0.0478490i
$451$	−0.476661	+	1.15076i	−0.0224451	+	0.0541873i
$452$	−3.97331	+	5.94647i	−0.186889	+	0.279699i
$453$	2.17930	+	10.9561i	0.102393	+	0.514762i
$454$	−3.68065	+	18.5039i	−0.172742	+	0.868430i
$455$	0.00324491	−	0.135506i	0.000152124	−	0.00635264i
$456$	−7.75486	+	5.18163i	−0.363154	+	0.242652i
$457$	−6.83836	+	16.5093i	−0.319885	+	0.772270i	0.679375	+	0.733792i	$0.262251\pi$
$457$	−6.83836	+	16.5093i	−0.319885	+	0.772270i	−0.999259	+	0.0384787i	$0.987749\pi$
$458$	−14.5084	+	14.5084i	−0.677934	+	0.677934i
$459$	22.9959	+	0.0110768i	1.07335	+	0.000517023i
$460$	−6.93531	−	0.166077i	−0.323361	−	0.00774337i
$461$	1.95502	+	4.71984i	0.0910545	+	0.219825i	0.962845	−	0.270053i	$-0.0870413\pi$
$461$	1.95502	+	4.71984i	0.0910545	+	0.219825i	−0.871791	+	0.489878i	$0.837041\pi$
$462$	0.521696	+	0.103772i	0.0242715	+	0.00482790i
$463$	−30.5132			−1.41807			−0.709034	−	0.705174i	$-0.750869\pi$
$463$	−30.5132			−1.41807			−0.709034	+	0.705174i	$0.750869\pi$
$464$	−1.19214	−	0.237131i	−0.0553437	−	0.0110085i
$465$	−14.4612	−	10.1717i	−0.670622	−	0.471702i
$466$	−2.11888	−	10.6523i	−0.0981550	−	0.493459i
$467$	−10.9852	+	4.55023i	−0.508335	+	0.210559i	−0.622084	−	0.782950i	$-0.713714\pi$
$467$	−10.9852	+	4.55023i	−0.508335	+	0.210559i	0.113749	+	0.993509i	$0.463714\pi$
$468$	0.139050	−	0.0575964i	0.00642759	−	0.00266239i
$469$	−0.513502	−	2.58155i	−0.0237113	−	0.119205i
$470$	22.5140	−	3.92051i	1.03849	−	0.180840i
$471$	37.9458	+	7.54789i	1.74845	+	0.347788i
$472$	−1.35897			−0.0625518
$473$	12.3252	+	2.45163i	0.566711	+	0.112726i
$474$	6.25381	+	15.0980i	0.287247	+	0.693475i
$475$	1.44101	−	30.0708i	0.0661181	−	1.37974i
$476$	−0.705546	+	0.704867i	−0.0323387	+	0.0323075i
$477$	−0.840257	+	0.840257i	−0.0384727	+	0.0384727i
$478$	−2.68710	+	6.48723i	−0.122905	+	0.296719i
$479$	−3.46289	+	2.31383i	−0.158223	+	0.105722i	−0.632161	−	0.774837i	$-0.717832\pi$
$479$	−3.46289	+	2.31383i	−0.158223	+	0.105722i	0.473938	+	0.880558i	$0.342832\pi$
$480$	3.46270	+	0.0829196i	0.158050	+	0.00378475i
$481$	−0.317716	+	1.59727i	−0.0144866	+	0.0728290i
$482$	−3.29208	−	16.5504i	−0.149950	−	0.753850i
$483$	0.645811	−	0.966525i	0.0293854	−	0.0439784i
$484$	3.43825	−	8.30067i	0.156284	−	0.377303i
$485$	−8.58451	+	19.3978i	−0.389803	+	0.880811i
$486$	−6.02244	+	1.19794i	−0.273184	+	0.0543396i
$487$	9.97377	−	1.98391i	0.451955	−	0.0898994i	0.0361360	−	0.999347i	$-0.488495\pi$
$487$	9.97377	−	1.98391i	0.451955	−	0.0898994i	0.415819	+	0.909447i	$0.363495\pi$
$488$	−5.09515	−	7.62543i	−0.230647	−	0.345187i
$489$	7.46310	−	7.46310i	0.337493	−	0.337493i
$490$	8.31193	+	13.1085i	0.375495	+	0.592183i
$491$	−9.31628	+	3.85893i	−0.420438	+	0.174151i	−0.582864	−	0.812570i	$-0.698068\pi$
$491$	−9.31628	+	3.85893i	−0.420438	+	0.174151i	0.162426	+	0.986721i	$0.448068\pi$
$492$	−0.961009	−	0.961009i	−0.0433256	−	0.0433256i
$493$	4.63105	−	1.91563i	0.208572	−	0.0862756i
$494$		−	1.50892i		−	0.0678894i
$495$	−1.74338	−	0.771532i	−0.0783591	−	0.0346778i
$496$	2.83588	+	4.24419i	0.127335	+	0.190570i
$497$			0.238967i			0.0107191i
$498$	0.245890	−	0.164299i	0.0110186	−	0.00736239i
$499$	−25.8286	−	17.2581i	−1.15624	−	0.772578i	−0.178824	−	0.983881i	$-0.557229\pi$
$499$	−25.8286	−	17.2581i	−1.15624	−	0.772578i	−0.977421	+	0.211303i	$0.932229\pi$
$500$	−6.86258	+	8.82638i	−0.306904	+	0.394728i
$501$	23.9368	+	9.91495i	1.06942	+	0.442967i
$502$	10.5690	+	25.5159i	0.471718	+	1.13883i
$503$	4.63404	+	3.09637i	0.206622	+	0.138060i	0.654576	−	0.755996i	$-0.272847\pi$
$503$	4.63404	+	3.09637i	0.206622	+	0.138060i	−0.447954	+	0.894056i	$0.647847\pi$
$504$	0.0807066	−	0.120786i	0.00359496	−	0.00538023i
$505$	−20.2443	−	31.9268i	−0.900861	−	1.42072i
$506$	3.11439	+	3.11439i	0.138451	+	0.138451i
$507$	−3.90958	+	19.6548i	−0.173630	+	0.872899i
$508$	−14.4919	−	6.00272i	−0.642972	−	0.266328i
$509$	−44.5099			−1.97287			−0.986433	−	0.164167i	$-0.947506\pi$
$509$	−44.5099			−1.97287			−0.986433	+	0.164167i	$0.947506\pi$
$510$	−12.0646	+	7.64184i	−0.534228	+	0.338386i
$511$	3.79038			0.167677
$512$	−0.923880	−	0.382683i	−0.0408301	−	0.0169124i
$513$	−6.55140	+	32.9361i	−0.289252	+	1.45417i
$514$	0.565305	+	0.565305i	0.0249345	+	0.0249345i
$515$	8.49935	+	1.90322i	0.374526	+	0.0838660i
$516$	−7.61780	+	11.4008i	−0.335355	+	0.501894i
$517$	−12.0638	−	8.06076i	−0.530565	−	0.354512i
$518$	0.601530	+	1.45222i	0.0264297	+	0.0638070i
$519$	15.7903	+	6.54056i	0.693117	+	0.287099i
$520$	−0.322392	+	0.458347i	−0.0141378	+	0.0200998i
$521$	−18.5333	−	12.3835i	−0.811957	−	0.542533i	0.0788644	−	0.996885i	$-0.474871\pi$
$521$	−18.5333	−	12.3835i	−0.811957	−	0.542533i	−0.890822	+	0.454353i	$0.849871\pi$
$522$	−0.606963	+	0.405560i	−0.0265661	+	0.0177509i
$523$			15.7551i			0.688922i	0.938801	+	0.344461i	$0.111938\pi$
$523$			15.7551i			0.688922i	−0.938801	+	0.344461i	$0.888062\pi$
$524$	−3.24751	−	4.86025i	−0.141868	−	0.212321i
$525$	−0.633252	−	1.76313i	−0.0276374	−	0.0769493i
$526$		−	7.46562i		−	0.325516i
$527$	−19.4402	−	8.06338i	−0.846830	−	0.351246i
$528$	−1.55497	−	1.55497i	−0.0676713	−	0.0676713i
$529$	−12.3567	+	5.11830i	−0.537247	+	0.222535i
$530$	0.966781	−	4.31742i	0.0419943	−	0.187537i
$531$	−0.577111	+	0.577111i	−0.0250445	+	0.0250445i
$532$	−0.809132	−	1.21095i	−0.0350803	−	0.0525014i
$533$	0.215652	−	0.0428959i	0.00934094	−	0.00185803i
$534$	11.1284	−	2.21358i	0.481573	−	0.0957909i
$535$	2.03023	+	0.898478i	0.0877745	+	0.0388446i
$536$	−4.16427	+	10.0534i	−0.179869	+	0.434242i
$537$	12.8999	−	19.3060i	0.556670	−	0.833116i
$538$	−4.04605	−	20.3409i	−0.174438	−	0.876957i
$539$	1.92252	−	9.66516i	0.0828088	−	0.416308i
$540$	9.02710	−	8.60487i	0.388464	−	0.370295i
$541$	−30.9603	+	20.6870i	−1.33109	+	0.889404i	−0.998558	−	0.0536885i	$-0.982902\pi$
$541$	−30.9603	+	20.6870i	−1.33109	+	0.889404i	−0.332530	+	0.943093i	$0.607902\pi$
$542$	−7.91555	+	19.1098i	−0.340002	+	0.820838i
$543$	19.2522	−	19.2522i	0.826191	−	0.826191i
$544$	4.04427	−	0.802430i	0.173397	−	0.0344039i
$545$	−10.1788	+	9.70270i	−0.436012	+	0.415618i
$546$	−0.0359330	−	0.0867498i	−0.00153779	−	0.00371255i
$547$	17.3622	+	3.45355i	0.742352	+	0.147663i	0.551756	−	0.834005i	$-0.313958\pi$
$547$	17.3622	+	3.45355i	0.742352	+	0.147663i	0.190596	+	0.981669i	$0.438958\pi$
$548$	14.4423			0.616945
$549$	−5.40201	−	1.07453i	−0.230552	−	0.0458597i
$550$	7.02018	−	1.04998i	0.299341	−	0.0447713i
$551$	1.42778	+	7.17795i	0.0608256	+	0.305791i
$552$	−4.43992	+	1.83907i	−0.188976	+	0.0782762i
$553$	−2.35762	+	0.976556i	−0.100256	+	0.0415274i
$554$	4.00370	+	20.1280i	0.170101	+	0.855155i
$555$	3.86147	+	22.1750i	0.163910	+	0.941275i
$556$	19.8060	+	3.93965i	0.839960	+	0.167078i
$557$	18.8677			0.799448			0.399724	−	0.916636i	$-0.369106\pi$
$557$	18.8677			0.799448			0.399724	+	0.916636i	$0.369106\pi$
$558$	3.00667	+	0.598064i	0.127282	+	0.0253181i
$559$	−0.848923	−	2.04948i	−0.0359056	−	0.0866838i
$560$	−0.0129482	+	0.540714i	−0.000547162	+	0.0228493i
$561$	8.89187	+	1.77316i	0.375415	+	0.0748627i
$562$	−16.4527	+	16.4527i	−0.694016	+	0.694016i
$563$	2.93238	−	7.07939i	0.123585	−	0.298361i	−0.849963	−	0.526842i	$-0.823376\pi$
$563$	2.93238	−	7.07939i	0.123585	−	0.298361i	0.973548	+	0.228481i	$0.0733760\pi$
$564$	13.1630	−	8.79525i	0.554263	−	0.370347i
$565$	−11.0340	−	11.5754i	−0.464203	−	0.486981i
$566$	−3.33557	+	16.7691i	−0.140205	+	0.704856i
$567$	0.322661	+	1.62213i	0.0135505	+	0.0681230i
$568$	0.548870	−	0.821442i	0.0230301	−	0.0344669i
$569$	12.8952	−	31.1318i	0.540596	−	1.30511i	−0.383707	−	0.923455i	$-0.625353\pi$
$569$	12.8952	−	31.1318i	0.540596	−	1.30511i	0.924303	−	0.381660i	$-0.124647\pi$
$570$	−7.51736	−	19.4531i	−0.314867	−	0.814803i
$571$	−1.88068	+	0.374090i	−0.0787038	+	0.0156552i	−0.234285	−	0.972168i	$-0.575275\pi$
$571$	−1.88068	+	0.374090i	−0.0787038	+	0.0156552i	0.155581	+	0.987823i	$0.450275\pi$
$572$	0.348938	−	0.0694081i	0.0145898	−	0.00290210i
$573$	−7.92664	−	11.8631i	−0.331140	−	0.495586i
$574$	0.150065	−	0.150065i	0.00626360	−	0.00626360i
$575$	3.75106	−	15.0519i	0.156430	−	0.627708i
$576$	−0.554854	+	0.229828i	−0.0231189	+	0.00957617i
$577$	−9.67382	−	9.67382i	−0.402726	−	0.402726i	0.476466	−	0.879193i	$-0.341917\pi$
$577$	−9.67382	−	9.67382i	−0.402726	−	0.402726i	−0.879193	+	0.476466i	$0.841917\pi$
$578$	−12.0324	+	12.0092i	−0.500481	+	0.499518i
$579$			14.5365i			0.604115i
$580$	1.09992	−	2.48542i	0.0456717	−	0.103201i
$581$	0.0256559	+	0.0383967i	0.00106438	+	0.00159296i
$582$			14.6947i			0.609115i
$583$	−2.33557	+	1.56058i	−0.0967293	+	0.0646325i
$584$	−13.0293	−	8.70593i	−0.539158	−	0.360254i
$585$	0.0577355	+	0.331554i	0.00238707	+	0.0137081i
$586$	29.3067	+	12.1392i	1.21065	+	0.501467i
$587$	4.75599	+	11.4820i	0.196301	+	0.473912i	0.991126	−	0.132926i	$-0.0424374\pi$
$587$	4.75599	+	11.4820i	0.196301	+	0.473912i	−0.794825	+	0.606839i	$0.792437\pi$
$588$	8.94033	+	5.97373i	0.368693	+	0.246353i
$589$	17.0750	−	25.5545i	0.703563	−	1.05296i
$590$	0.664012	−	2.96532i	0.0273369	−	0.122080i
$591$	7.34191	+	7.34191i	0.302006	+	0.302006i
$592$	1.26779	−	6.37360i	0.0521058	−	0.261953i
$593$	27.6385	+	11.4482i	1.13498	+	0.470122i	0.869470	−	0.493987i	$-0.164461\pi$
$593$	27.6385	+	11.4482i	1.13498	+	0.470122i	0.265507	+	0.964109i	$0.414461\pi$
$594$	−7.91785			−0.324874
$595$	−1.19330	−	1.88393i	−0.0489206	−	0.0772336i
$596$	−12.8303			−0.525549
$597$	−36.1478	−	14.9729i	−1.47943	−	0.612801i
$598$	0.151682	−	0.762556i	0.00620273	−	0.0311832i
$599$	11.2916	+	11.2916i	0.461360	+	0.461360i	0.899101	−	0.437741i	$-0.144221\pi$
$599$	11.2916	+	11.2916i	0.461360	+	0.461360i	−0.437741	+	0.899101i	$0.644221\pi$
$600$	−1.87285	+	7.51520i	−0.0764588	+	0.306807i
$601$	9.39260	−	14.0570i	0.383132	−	0.573398i	−0.588912	−	0.808197i	$-0.700443\pi$
$601$	9.39260	−	14.0570i	0.383132	−	0.573398i	0.972044	+	0.234800i	$0.0754434\pi$
$602$	−1.78029	−	1.18955i	−0.0725590	−	0.0484824i
$603$	2.50093	+	6.03779i	0.101846	+	0.245878i
$604$	6.66259	+	2.75974i	0.271097	+	0.112292i
$605$	16.4324	+	11.5582i	0.668070	+	0.469907i
$606$	−21.7748	−	14.5495i	−0.884542	−	0.591032i
$607$	36.3070	−	24.2596i	1.47366	−	0.984666i	0.479405	−	0.877594i	$-0.340852\pi$
$607$	36.3070	−	24.2596i	1.47366	−	0.984666i	0.994251	−	0.107072i	$-0.0341475\pi$
$608$			6.02107i			0.244186i
$609$	0.253019	+	0.378669i	0.0102528	+	0.0153445i
$610$	19.1285	−	7.39190i	0.774490	−	0.299289i
$611$			2.56122i			0.103616i
$612$	1.37670	−	2.05823i	0.0556498	−	0.0831991i
$613$	14.2688	+	14.2688i	0.576311	+	0.576311i	0.933885	−	0.357574i	$-0.116396\pi$
$613$	14.2688	+	14.2688i	0.576311	+	0.576311i	−0.357574	+	0.933885i	$0.616396\pi$
$614$	−13.0958	+	5.42445i	−0.528503	+	0.218913i
$615$	2.56651	−	1.62739i	0.103492	−	0.0656227i
$616$	0.242814	−	0.242814i	0.00978326	−	0.00978326i
$617$	9.61423	+	14.3887i	0.387054	+	0.579268i	0.972921	−	0.231140i	$-0.0742455\pi$
$617$	9.61423	+	14.3887i	0.387054	+	0.579268i	−0.585866	+	0.810408i	$0.699246\pi$
$618$	5.91770	−	1.17710i	0.238045	−	0.0473501i
$619$	1.23501	−	0.245658i	0.0496392	−	0.00987384i	−0.170208	−	0.985408i	$-0.554444\pi$
$619$	1.23501	−	0.245658i	0.0496392	−	0.00987384i	0.219847	+	0.975534i	$0.429444\pi$
$620$	−10.6466	+	4.11421i	−0.427578	+	0.165231i
$621$	−6.62172	+	15.9862i	−0.265720	+	0.641506i
$622$	16.5903	−	24.8291i	0.665209	−	0.995556i
$623$	0.345659	+	1.73774i	0.0138485	+	0.0696212i
$624$	−0.0757325	+	0.380733i	−0.00303172	+	0.0152415i
$625$	−15.9063	−	19.2870i	−0.636252	−	0.771481i
$626$	0.788463	−	0.526834i	0.0315133	−	0.0210565i
$627$	−5.06698	+	12.2328i	−0.202356	+	0.488530i
$628$	17.6612	−	17.6612i	0.704759	−	0.704759i
$629$	10.2416	+	24.7592i	0.408361	+	0.987216i
$630$	0.224124	+	0.235122i	0.00892933	+	0.00936748i
$631$	−3.78090	−	9.12791i	−0.150515	−	0.363376i	0.830580	−	0.556899i	$-0.188009\pi$
$631$	−3.78090	−	9.12791i	−0.150515	−	0.363376i	−0.981096	+	0.193522i	$0.938009\pi$
$632$	10.3472	+	2.05819i	0.411591	+	0.0818706i
$633$	−31.8641			−1.26649
$634$	−9.03747	−	1.79766i	−0.358924	−	0.0713943i
$635$	20.1790	−	28.6887i	0.800780	−	1.13847i
$636$	−0.597935	−	3.00602i	−0.0237096	−	0.119196i
$637$	−1.60716	+	0.665710i	−0.0636782	+	0.0263764i
$638$	−1.59423	+	0.660351i	−0.0631161	+	0.0261435i
$639$	−0.115752	−	0.581926i	−0.00457909	−	0.0230206i
$640$	1.28645	−	1.82895i	0.0508512	−	0.0722956i
$641$	−21.2165	−	4.22022i	−0.838001	−	0.166689i	−0.242609	−	0.970124i	$-0.578003\pi$
$641$	−21.2165	−	4.22022i	−0.838001	−	0.166689i	−0.595392	+	0.803435i	$0.703003\pi$
$642$	1.53799			0.0606995
$643$	44.2123	+	8.79438i	1.74356	+	0.346816i	0.961168	−	0.275965i	$-0.0889973\pi$
$643$	44.2123	+	8.79438i	1.74356	+	0.346816i	0.782396	+	0.622781i	$0.213997\pi$
$644$	−0.287179	−	0.693311i	−0.0113164	−	0.0273203i
$645$	−21.1548	−	22.1929i	−0.832971	−	0.873843i
$646$	−13.7824	−	20.6483i	−0.542260	−	0.812396i
$647$	3.89261	−	3.89261i	0.153034	−	0.153034i	−0.626438	−	0.779472i	$-0.715488\pi$
$647$	3.89261	−	3.89261i	0.153034	−	0.153034i	0.779472	+	0.626438i	$0.215488\pi$
$648$	2.61664	−	6.31713i	0.102791	−	0.248160i
$649$	−1.60413	+	1.07185i	−0.0629676	+	0.0420736i
$650$	−0.842602	−	0.927422i	−0.0330496	−	0.0363765i
$651$	0.373117	−	1.87579i	0.0146236	−	0.0735179i
$652$	−1.32928	−	6.68273i	−0.0520586	−	0.261716i
$653$	15.2280	−	22.7903i	0.595918	−	0.891854i	−0.403818	−	0.914839i	$-0.632317\pi$
$653$	15.2280	−	22.7903i	0.595918	−	0.891854i	0.999736	+	0.0229854i	$0.00731712\pi$
$654$	−3.72793	+	9.00001i	−0.145773	+	0.351928i
$655$	12.1920	−	4.71140i	0.476380	−	0.184090i
$656$	−0.860522	+	0.171169i	−0.0335977	+	0.00668301i
$657$	−9.23025	+	1.83601i	−0.360106	+	0.0716296i
$658$	1.37341	+	2.05546i	0.0535412	+	0.0801300i
$659$	−1.15499	+	1.15499i	−0.0449919	+	0.0449919i	−0.729245	−	0.684253i	$-0.760128\pi$
$659$	−1.15499	+	1.15499i	−0.0449919	+	0.0449919i	0.684253	+	0.729245i	$0.260128\pi$
$660$	4.15276	−	2.63321i	0.161646	−	0.102498i
$661$	−19.9073	+	8.24587i	−0.774303	+	0.320727i	−0.734614	−	0.678485i	$-0.762637\pi$
$661$	−19.9073	+	8.24587i	−0.774303	+	0.320727i	−0.0396893	+	0.999212i	$0.512637\pi$
$662$	−10.7162	−	10.7162i	−0.416497	−	0.416497i
$663$	−0.611794	−	1.47902i	−0.0237601	−	0.0574402i
$664$		−	0.190915i		−	0.00740895i
$665$	3.03768	−	1.17386i	0.117796	−	0.0455205i
$666$	−2.16827	−	3.24504i	−0.0840187	−	0.125743i
$667$			3.77102i			0.146014i
$668$	13.9073	−	9.29257i	0.538090	−	0.359540i
$669$	−5.91290	−	3.95087i	−0.228606	−	0.152749i
$670$	−19.9022	−	13.9988i	−0.768889	−	0.540821i
$671$	−12.0286	−	4.98242i	−0.464360	−	0.192344i
$672$	0.143384	+	0.346160i	0.00553116	+	0.0133534i
$673$	−34.8788	−	23.3052i	−1.34448	−	0.898351i	−0.345284	−	0.938498i	$-0.612217\pi$
$673$	−34.8788	−	23.3052i	−1.34448	−	0.898351i	−0.999194	+	0.0401469i	$0.987217\pi$
$674$	−8.53393	+	12.7719i	−0.328715	+	0.491956i
$675$	14.3653	+	23.9018i	0.552922	+	0.919983i
$676$	9.14798	+	9.14798i	0.351845	+	0.351845i
$677$	−2.35700	+	11.8494i	−0.0905869	+	0.455411i	0.908693	+	0.417465i	$0.137081\pi$
$677$	−2.35700	+	11.8494i	−0.0905869	+	0.455411i	−0.999280	+	0.0379458i	$0.987919\pi$
$678$	−10.2349	−	4.23942i	−0.393068	−	0.162814i
$679$	−2.29464			−0.0880600
$680$	−0.225153	+	9.21679i	−0.00863421	+	0.353448i
$681$	−29.2242			−1.11987
$682$	6.69493	+	2.77313i	0.256362	+	0.106189i
$683$	4.55614	−	22.9053i	0.174336	−	0.876446i	−0.790272	−	0.612757i	$-0.790061\pi$
$683$	4.55614	−	22.9053i	0.174336	−	0.876446i	0.964608	−	0.263689i	$-0.0849394\pi$
$684$	2.55695	+	2.55695i	0.0977673	+	0.0977673i
$685$	−7.05670	+	31.5136i	−0.269622	+	1.20407i
$686$	−1.87351	+	2.80390i	−0.0715308	+	0.107053i
$687$	−26.4262	−	17.6575i	−1.00822	−	0.673674i
$688$	3.38747	+	8.17809i	0.129146	+	0.311787i
$689$	0.458112	+	0.189756i	0.0174527	+	0.00722913i
$690$	−1.84352	−	10.5866i	−0.0701815	−	0.403026i
$691$	−23.0135	−	15.3771i	−0.875474	−	0.584973i	0.0346081	−	0.999401i	$-0.488982\pi$
$691$	−23.0135	−	15.3771i	−0.875474	−	0.584973i	−0.910082	+	0.414428i	$0.863982\pi$
$692$	9.17418	−	6.12999i	0.348750	−	0.233027i
$693$		−	0.206230i		−	0.00783404i
$694$	−11.6216	−	17.3930i	−0.441152	−	0.660230i
$695$	−18.2739	+	41.2922i	−0.693167	+	1.56630i
$696$		−	1.88281i		−	0.0713678i
$697$	2.55921	−	2.55675i	0.0969372	−	0.0968438i
$698$	1.93577	+	1.93577i	0.0732701	+	0.0732701i
$699$	15.5432	−	6.43819i	0.587896	−	0.243515i
$700$	−1.17353	−	0.292453i	−0.0443552	−	0.0110537i
$701$	4.84755	−	4.84755i	0.183089	−	0.183089i	−0.609611	−	0.792701i	$-0.708674\pi$
$701$	4.84755	−	4.84755i	0.183089	−	0.183089i	0.792701	+	0.609611i	$0.208674\pi$
$702$	0.776527	+	1.16215i	0.0293081	+	0.0438627i
$703$	−38.3759	+	7.63343i	−1.44737	+	0.287900i
$704$	−1.39237	+	0.276961i	−0.0524771	+	0.0104383i
$705$	12.7599	+	33.0196i	0.480565	+	1.24359i
$706$	−3.89714	+	9.40854i	−0.146671	+	0.354095i
$707$	2.27196	−	3.40022i	0.0854457	−	0.127879i
$708$	−0.410678	−	2.06462i	−0.0154342	−	0.0775930i
$709$	−8.65704	+	43.5219i	−0.325122	+	1.63450i	0.379696	+	0.925111i	$0.376028\pi$
$709$	−8.65704	+	43.5219i	−0.325122	+	1.63450i	−0.704818	+	0.709388i	$0.748972\pi$
$710$	1.52423	+	1.59902i	0.0572032	+	0.0600101i
$711$	5.26818	−	3.52008i	0.197572	−	0.132013i
$712$	2.80314	−	6.76738i	0.105052	−	0.253618i
$713$	11.1980	−	11.1980i	0.419367	−	0.419367i
$714$	−1.28408	−	0.858890i	−0.0480555	−	0.0321431i
$715$	−0.0190449	+	0.795307i	−0.000712238	+	0.0297428i
$716$	−5.73630	−	13.8487i	−0.214376	−	0.517548i
$717$	−10.6677	−	2.12194i	−0.398394	−	0.0792454i
$718$	−22.0101			−0.821411
$719$	45.6966	+	9.08963i	1.70420	+	0.338986i	0.948703	−	0.316169i	$-0.102397\pi$
$719$	45.6966	+	9.08963i	1.70420	+	0.338986i	0.755494	+	0.655155i	$0.227397\pi$
$720$	−0.230383	−	1.32300i	−0.00858588	−	0.0493055i
$721$	0.183809	+	0.924072i	0.00684542	+	0.0344142i
$722$	15.9399	−	6.60252i	0.593222	−	0.245721i
$723$	24.1493	−	10.0029i	0.898121	−	0.372014i
$724$	−3.42908	−	17.2391i	−0.127441	−	0.640687i
$725$	4.88582	+	3.61447i	0.181455	+	0.134238i
$726$	13.6498	+	2.71511i	0.506591	+	0.100767i
$727$	43.0062			1.59501			0.797506	−	0.603311i	$-0.206152\pi$
$727$	43.0062			1.59501			0.797506	+	0.603311i	$0.206152\pi$
$728$	−0.0594529	−	0.0118259i	−0.00220347	−	0.000438298i
$729$	−11.4898	−	27.7389i	−0.425550	−	1.02737i
$730$	25.3629	−	24.1766i	0.938723	−	0.894816i
$731$	−30.3366	−	20.2914i	−1.12204	−	0.750506i
$732$	10.0452	−	10.0452i	0.371280	−	0.371280i
$733$	10.8031	−	26.0810i	0.399022	−	0.963325i	−0.588876	−	0.808223i	$-0.700429\pi$
$733$	10.8031	−	26.0810i	0.399022	−	0.963325i	0.987898	−	0.155102i	$-0.0495706\pi$
$734$	−1.58128	+	1.05658i	−0.0583661	+	0.0389990i
$735$	−17.4032	+	16.5892i	−0.641928	+	0.611903i
$736$	−0.605259	+	3.04284i	−0.0223101	+	0.112161i
$737$	3.01382	+	15.1515i	0.111015	+	0.558112i
$738$	−0.292746	+	0.438125i	−0.0107761	+	0.0161276i
$739$	2.98911	−	7.21635i	0.109956	−	0.265458i	−0.859317	−	0.511443i	$-0.829111\pi$
$739$	2.98911	−	7.21635i	0.109956	−	0.265458i	0.969274	+	0.245985i	$0.0791113\pi$
$740$	13.2879	+	5.88057i	0.488474	+	0.216174i
$741$	2.29242	−	0.455990i	0.0842140	−	0.0167512i
$742$	0.469402	−	0.0933698i	0.0172323	−	0.00342771i
$743$	1.97661	+	2.95821i	0.0725149	+	0.108526i	0.865955	−	0.500123i	$-0.166712\pi$
$743$	1.97661	+	2.95821i	0.0725149	+	0.108526i	−0.793440	+	0.608649i	$0.791712\pi$
$744$	−5.59097	+	5.59097i	−0.204975	+	0.204975i
$745$	6.26904	−	27.9961i	0.229680	−	1.02570i
$746$	−5.23997	+	2.17046i	−0.191849	+	0.0794664i
$747$	−0.0810754	−	0.0810754i	−0.00296639	−	0.00296639i
$748$	4.14096	−	4.13697i	0.151408	−	0.151263i
$749$			0.240163i			0.00877536i
$750$	−15.4833	−	7.75864i	−0.565370	−	0.283305i
$751$	7.02525	+	10.5140i	0.256355	+	0.383663i	0.937216	−	0.348751i	$-0.113394\pi$
$751$	7.02525	+	10.5140i	0.256355	+	0.383663i	−0.680860	+	0.732413i	$0.738394\pi$
$752$		−	10.2201i		−	0.372689i
$753$	−35.5709	+	23.7677i	−1.29628	+	0.866145i
$754$	0.253275	+	0.169233i	0.00922371	+	0.00616309i
$755$	−9.27726	+	13.1895i	−0.337634	+	0.480017i
$756$	1.24637	+	0.516264i	0.0453301	+	0.0187763i
$757$	−6.31920	−	15.2559i	−0.229675	−	0.554485i	0.766463	−	0.642289i	$-0.222015\pi$
$757$	−6.31920	−	15.2559i	−0.229675	−	0.554485i	−0.996138	+	0.0878041i	$0.972015\pi$
$758$	1.60847	+	1.07474i	0.0584222	+	0.0390365i
$759$	−3.79036	+	5.67268i	−0.137581	+	0.205905i
$760$	−13.1381	−	2.94197i	−0.476571	−	0.106716i
$761$	4.49157	+	4.49157i	0.162819	+	0.162819i	0.783814	−	0.620995i	$-0.213271\pi$
$761$	4.49157	+	4.49157i	0.162819	+	0.162819i	−0.620995	+	0.783814i	$0.713271\pi$
$762$	4.74022	−	23.8307i	0.171720	−	0.863295i
$763$	−1.40539	−	0.582130i	−0.0508784	−	0.0210745i
$764$	−9.21078			−0.333234
$765$	3.81845	+	4.00968i	0.138056	+	0.144970i
$766$	28.4783			1.02896
$767$	0.314644	+	0.130330i	0.0113611	+	0.00470593i
$768$	0.302197	−	1.51925i	0.0109046	−	0.0548211i
$769$	10.8129	+	10.8129i	0.389923	+	0.389923i	0.874660	−	0.484737i	$-0.161085\pi$
$769$	10.8129	+	10.8129i	0.389923	+	0.389923i	−0.484737	+	0.874660i	$0.661085\pi$
$770$	0.411186	+	0.648470i	0.0148181	+	0.0233692i
$771$	−0.688003	+	1.02967i	−0.0247778	+	0.0370827i
$772$	7.80281	+	5.21367i	0.280829	+	0.187644i
$773$	−2.50130	−	6.03868i	−0.0899656	−	0.217196i	0.872492	−	0.488629i	$-0.162503\pi$
$773$	−2.50130	−	6.03868i	−0.0899656	−	0.217196i	−0.962458	+	0.271432i	$0.912503\pi$
$774$	4.91151	+	2.03441i	0.176541	+	0.0731255i
$775$	−3.77527	−	25.2415i	−0.135612	−	0.906700i
$776$	7.88775	+	5.27043i	0.283154	+	0.189197i
$777$	−2.02450	+	1.35273i	−0.0726286	+	0.0485289i
$778$		−	25.0802i		−	0.899169i
$779$	2.93495	+	4.39246i	0.105155	+	0.157376i
$780$	−0.793767	−	0.351281i	−0.0284214	−	0.0125779i
$781$		−	1.40253i		−	0.0501865i
$782$	−4.88950	−	11.8204i	−0.174848	−	0.422696i
$783$	−4.79362	−	4.79362i	−0.171310	−	0.171310i
$784$	6.41310	−	2.65639i	0.229039	−	0.0948712i
$785$	29.9078	+	47.1668i	1.06746	+	1.68346i
$786$	6.40252	−	6.40252i	0.228370	−	0.228370i
$787$	−2.81586	−	4.21424i	−0.100375	−	0.150221i	0.777883	−	0.628409i	$-0.216294\pi$
$787$	−2.81586	−	4.21424i	−0.100375	−	0.150221i	−0.878257	+	0.478188i	$0.841294\pi$
$788$	6.57422	−	1.30769i	0.234197	−	0.0465846i
$789$	11.3421	−	2.25609i	0.403790	−	0.0803188i
$790$	−9.54684	+	21.5723i	−0.339661	+	0.767510i
$791$	0.662002	−	1.59822i	0.0235381	−	0.0568260i
$792$	−0.473679	+	0.708911i	−0.0168315	+	0.0251901i
$793$	0.448380	+	2.25416i	0.0159224	+	0.0800475i
$794$	−0.897961	+	4.51435i	−0.0318674	+	0.160208i
$795$	6.85139	+	0.164067i	0.242994	+	0.00581886i
$796$	−21.0019	+	14.0330i	−0.744394	+	0.497388i
$797$	2.75805	−	6.65852i	0.0976951	−	0.235857i	−0.867475	−	0.497482i	$-0.834258\pi$
$797$	2.75805	−	6.65852i	0.0976951	−	0.235857i	0.965170	+	0.261625i	$0.0842582\pi$
$798$	1.59522	−	1.59522i	0.0564700	−	0.0564700i
$799$	23.3940	+	35.0482i	0.827622	+	1.23992i
$800$	3.36225	+	3.70071i	0.118874	+	0.130840i
$801$	−1.68348	−	4.06428i	−0.0594828	−	0.143604i
$802$	36.0272	+	7.16626i	1.27216	+	0.253049i
$803$	−22.2463			−0.785056
$804$	−16.5321	−	3.28843i	−0.583041	−	0.115974i
$805$	1.65314	−	0.287872i	0.0582657	−	0.0101462i
$806$	−0.249561	−	1.25463i	−0.00879040	−	0.0441923i
$807$	29.6801	−	12.2939i	1.04479	−	0.432765i
$808$	−15.6196	+	6.46985i	−0.549495	+	0.227608i
$809$	0.369390	+	1.85705i	0.0129871	+	0.0652904i	0.986735	−	0.162337i	$-0.0519032\pi$
$809$	0.369390	+	1.85705i	0.0129871	+	0.0652904i	−0.973748	+	0.227627i	$0.926903\pi$
$810$	12.5056	+	8.79621i	0.439403	+	0.309067i
$811$	19.7489	+	3.92829i	0.693476	+	0.137941i	0.529230	−	0.848478i	$-0.322481\pi$
$811$	19.7489	+	3.92829i	0.693476	+	0.137941i	0.164246	+	0.986419i	$0.447481\pi$
$812$	0.294008			0.0103177
$813$	−31.4246	−	6.25074i	−1.10211	−	0.219223i
$814$	−3.53047	−	8.52331i	−0.123743	−	0.298742i
$815$	15.2314	+	0.364740i	0.533534	+	0.0127763i
$816$	2.44125	+	5.90175i	0.0854610	+	0.206602i
$817$	37.6873	−	37.6873i	1.31851	−	1.31851i
$818$	−14.3701	+	34.6925i	−0.502439	+	1.21299i
$819$	−0.0302697	+	0.0202256i	−0.00105771	+	0.000706740i
$820$	0.0469669	−	1.96132i	0.00164015	−	0.0684923i
$821$	−1.61477	+	8.11799i	−0.0563558	+	0.283320i	−0.998679	−	0.0513847i	$-0.983637\pi$
$821$	−1.61477	+	8.11799i	−0.0563558	+	0.283320i	0.942323	+	0.334705i	$0.108637\pi$
$822$	4.36442	+	21.9414i	0.152227	+	0.765295i
$823$	0.0215627	−	0.0322708i	0.000751627	−	0.00112489i	−0.831094	−	0.556133i	$-0.812285\pi$
$823$	0.0215627	−	0.0322708i	0.000751627	−	0.00112489i	0.831845	+	0.555008i	$0.187285\pi$
$824$	1.49061	−	3.59866i	0.0519279	−	0.125365i
$825$	3.71665	+	10.3481i	0.129397	+	0.360274i
$826$	0.322398	−	0.0641289i	0.0112177	−	0.00223133i
$827$	−50.9885	+	10.1422i	−1.77304	+	0.352680i	−0.969974	−	0.243207i	$-0.921801\pi$
$827$	−50.9885	+	10.1422i	−1.77304	+	0.352680i	−0.803068	+	0.595887i	$0.796801\pi$
$828$	1.03516	+	1.54923i	0.0359743	+	0.0538394i
$829$	0.678814	−	0.678814i	0.0235762	−	0.0235762i	−0.695220	−	0.718797i	$-0.744693\pi$
$829$	0.678814	−	0.678814i	0.0235762	−	0.0235762i	0.718797	+	0.695220i	$0.244693\pi$
$830$	0.416583	+	0.0932836i	0.0144598	+	0.00323792i
$831$	−29.3694	+	12.1652i	−1.01881	+	0.422006i
$832$	0.177206	+	0.177206i	0.00614350	+	0.00614350i
$833$	−15.9122	+	23.7894i	−0.551324	+	0.824255i
$834$			31.2807i			1.08316i
$835$	13.4814	+	34.8867i	0.466543	+	1.20730i
$836$	4.74892	+	7.10726i	0.164245	+	0.245810i
$837$			28.4691i			0.984036i
$838$	21.4378	−	14.3243i	0.740557	−	0.494824i
$839$	24.5010	+	16.3711i	0.845870	+	0.565192i	0.901263	−	0.433273i	$-0.142641\pi$
$839$	24.5010	+	16.3711i	0.845870	+	0.565192i	−0.0553933	+	0.998465i	$0.517641\pi$
$840$	−0.825390	+	0.143730i	−0.0284787	+	0.00495917i
$841$	25.4275	+	10.5324i	0.876812	+	0.363187i
$842$	1.96830	+	4.75190i	0.0678321	+	0.163761i
$843$	−29.9677	−	20.0238i	−1.03214	−	0.689655i
$844$	−11.4284	+	17.1039i	−0.393383	+	0.588739i
$845$	−24.4310	+	15.4914i	−0.840452	+	0.532919i
$846$	−4.34013	−	4.34013i	−0.149217	−	0.149217i
$847$	−0.423975	+	2.13147i	−0.0145680	+	0.0732381i
$848$	−1.82801	−	0.757188i	−0.0627742	−	0.0260019i
$849$	−26.4843			−0.908940
$850$	−20.0013	−	4.99473i	−0.686040	−	0.171318i
$851$	−20.1612			−0.691117
$852$	1.41384	+	0.585631i	0.0484373	+	0.0200634i
$853$	−2.52953	+	12.7168i	−0.0866093	+	0.435414i	0.913013	+	0.407931i	$0.133749\pi$
$853$	−2.52953	+	12.7168i	−0.0866093	+	0.435414i	−0.999622	+	0.0274838i	$0.991251\pi$
$854$	1.56859	+	1.56859i	0.0536761	+	0.0536761i
$855$	−6.82869	+	4.32998i	−0.233536	+	0.148082i
$856$	0.551617	−	0.825553i	0.0188539	−	0.0282168i
$857$	−21.7128	−	14.5080i	−0.741694	−	0.495584i	0.126403	−	0.991979i	$-0.459657\pi$
$857$	−21.7128	−	14.5080i	−0.741694	−	0.495584i	−0.868097	+	0.496395i	$0.834657\pi$
$858$	0.210896	+	0.509148i	0.00719987	+	0.0173820i
$859$	−39.8276	−	16.4971i	−1.35890	−	0.562874i	−0.420143	−	0.907458i	$-0.638020\pi$
$859$	−39.8276	−	16.4971i	−1.35890	−	0.562874i	−0.938756	+	0.344583i	$0.888020\pi$
$860$	−19.5000	+	3.39566i	−0.664944	+	0.115791i
$861$	0.273335	+	0.182637i	0.00931524	+	0.00622424i
$862$	3.65430	−	2.44173i	0.124466	−	0.0831655i
$863$			23.8428i			0.811618i	0.913958	+	0.405809i	$0.133010\pi$
$863$			23.8428i			0.811618i	−0.913958	+	0.405809i	$0.866990\pi$
$864$	−3.09859	−	4.63737i	−0.105416	−	0.157767i
$865$	8.89321	+	23.0135i	0.302378	+	0.782484i
$866$			23.2276i			0.789305i
$867$	−21.8811	−	14.6510i	−0.743122	−	0.497574i
$868$	−0.873052	−	0.873052i	−0.0296333	−	0.0296333i
$869$	13.8372	−	5.73156i	0.469395	−	0.194430i
$870$	4.10835	+	0.919965i	0.139286	+	0.0311897i
$871$	1.92831	−	1.92831i	0.0653382	−	0.0653382i
$872$	3.49392	+	5.22902i	0.118319	+	0.177077i
$873$	5.58784	−	1.11149i	0.189120	−	0.0376183i
$874$	18.3212	−	3.64430i	0.619722	−	0.123270i
$875$	1.21154	−	2.41778i	0.0409576	−	0.0817358i
$876$	9.28902	−	22.4257i	0.313847	−	0.757694i
$877$	13.1347	−	19.6574i	0.443527	−	0.663785i	−0.540594	−	0.841283i	$-0.681801\pi$
$877$	13.1347	−	19.6574i	0.443527	−	0.663785i	0.984121	+	0.177499i	$0.0568005\pi$
$878$	−1.82330	−	9.16636i	−0.0615335	−	0.309350i
$879$	−9.58609	+	48.1925i	−0.323331	+	1.62549i
$880$	0.0759951	−	3.17353i	0.00256179	−	0.106980i
$881$	2.09659	−	1.40090i	0.0706359	−	0.0471974i	−0.519751	−	0.854318i	$-0.673975\pi$
$881$	2.09659	−	1.40090i	0.0706359	−	0.0471974i	0.590387	+	0.807120i	$0.298975\pi$
$882$	1.59535	−	3.85151i	0.0537182	−	0.129687i
$883$	14.0335	−	14.0335i	0.472267	−	0.472267i	−0.430381	−	0.902647i	$-0.641621\pi$
$883$	14.0335	−	14.0335i	0.472267	−	0.472267i	0.902647	+	0.430381i	$0.141621\pi$
$884$	−1.01333	−	0.202070i	−0.0340818	−	0.00679636i
$885$	4.70572	+	0.112686i	0.158181	+	0.00378789i
$886$	−0.368042	−	0.888533i	−0.0123646	−	0.0298508i
$887$	−12.7222	−	2.53061i	−0.427171	−	0.0849697i	−0.0231775	−	0.999731i	$-0.507378\pi$
$887$	−12.7222	−	2.53061i	−0.427171	−	0.0849697i	−0.403994	+	0.914762i	$0.632378\pi$
$888$	10.0662			0.337799
$889$	3.72125	+	0.740203i	0.124807	+	0.0248256i
$890$	13.3970	+	9.42316i	0.449068	+	0.315865i
$891$	−1.89375	−	9.52051i	−0.0634429	−	0.318949i
$892$	−4.24146	+	1.75687i	−0.142014	+	0.0588243i
$893$	−56.8517	+	23.5488i	−1.90247	+	0.788029i
$894$	−3.87727	−	19.4924i	−0.129675	−	0.651923i
$895$	33.0210	−	5.75016i	1.10377	−	0.192207i
$896$	0.237236	+	0.0471892i	0.00792550	+	0.00157648i
$897$	1.20435			0.0402120
$898$	1.16763	+	0.232256i	0.0389644	+	0.00775049i
$899$	2.37433	+	5.73214i	0.0791883	+	0.191178i
$900$	2.99941	+	0.143733i	0.0999802	+	0.00479111i
$901$	8.00210	−	1.58771i	0.266588	−	0.0528943i
$902$	−0.880756	+	0.880756i	−0.0293260	+	0.0293260i
$903$	1.26922	−	3.06417i	0.0422370	−	0.101969i
$904$	−5.94647	+	3.97331i	−0.197777	+	0.132150i
$905$	39.2918	+	0.940903i	1.30610	+	0.0312767i
$906$	−2.17930	+	10.9561i	−0.0724025	+	0.363992i
$907$	0.514531	+	2.58672i	0.0170847	+	0.0858907i	0.988387	−	0.151958i	$-0.0485578\pi$
$907$	0.514531	+	2.58672i	0.0170847	+	0.0858907i	−0.971302	+	0.237849i	$0.923558\pi$
$908$	−10.4816	+	15.6868i	−0.347844	+	0.520586i
$909$	−3.88559	+	9.38065i	−0.128877	+	0.311136i
$910$	0.0548539	−	0.123950i	0.00181839	−	0.00410889i
$911$	56.7789	−	11.2940i	1.88117	−	0.374188i	0.885302	−	0.465016i	$-0.153952\pi$
$911$	56.7789	−	11.2940i	1.88117	−	0.374188i	0.995867	+	0.0908286i	$0.0289516\pi$
$912$	−9.14748	+	1.81955i	−0.302903	+	0.0602512i
$913$	−0.150578	−	0.225356i	−0.00498341	−	0.00745820i
$914$	−12.6356	+	12.6356i	−0.417950	+	0.417950i
$915$	17.0107	+	26.8271i	0.562355	+	0.886875i
$916$	−18.9562	+	7.85190i	−0.626329	+	0.259434i
$917$	0.999779	+	0.999779i	0.0330156	+	0.0330156i
$918$	21.2412	+	8.81037i	0.701063	+	0.290786i
$919$		−	38.7156i		−	1.27711i	−0.769576	−	0.638556i	$-0.779532\pi$
$919$		−	38.7156i		−	1.27711i	0.769576	−	0.638556i	$-0.220468\pi$
$920$	−6.34384	−	2.80746i	−0.209150	−	0.0925594i
$921$	−12.1986	−	18.2565i	−0.401957	−	0.601571i
$922$			5.10872i			0.168247i
$923$	−0.205859	+	0.137550i	−0.00677592	+	0.00452752i
$924$	0.442272	+	0.295517i	0.0145497	+	0.00972179i
$925$	−19.3242	+	26.1214i	−0.635377	+	0.858865i
$926$	−28.1905	−	11.6769i	−0.926398	−	0.383727i
$927$	−0.895216	−	2.16124i	−0.0294028	−	0.0709845i
$928$	−1.01065	−	0.675292i	−0.0331761	−	0.0221676i
$929$	−7.38689	+	11.0553i	−0.242356	+	0.362711i	−0.932628	−	0.360838i	$-0.882491\pi$
$929$	−7.38689	+	11.0553i	−0.242356	+	0.362711i	0.690272	+	0.723550i	$0.257491\pi$
$930$	−9.46786	−	14.9315i	−0.310463	−	0.489623i
$931$	−29.5537	−	29.5537i	−0.968582	−	0.968582i
$932$	2.11888	−	10.6523i	0.0694061	−	0.348928i
$933$	42.7350	+	17.7014i	1.39908	+	0.579519i
$934$	−11.8903			−0.389063
$935$	7.00367	+	11.0571i	0.229045	+	0.361605i
$936$	0.150507			0.00491946
$937$	−7.51556	−	3.11305i	−0.245523	−	0.101699i	0.256529	−	0.966537i	$-0.417421\pi$
$937$	−7.51556	−	3.11305i	−0.245523	−	0.101699i	−0.502051	+	0.864838i	$0.667421\pi$
$938$	0.513502	−	2.58155i	0.0167664	−	0.0842905i
$939$	1.03866	+	1.03866i	0.0338954	+	0.0338954i
$940$	22.3006	+	4.99367i	0.727364	+	0.162875i
$941$	6.66132	−	9.96938i	0.217153	−	0.324992i	−0.706860	−	0.707353i	$-0.749889\pi$
$941$	6.66132	−	9.96938i	0.217153	−	0.324992i	0.924013	+	0.382361i	$0.124889\pi$
$942$	32.1689	+	21.4946i	1.04812	+	0.700331i
$943$	1.04168	+	2.51483i	0.0339217	+	0.0818942i
$944$	−1.25553	−	0.520057i	−0.0408640	−	0.0169264i
$945$	−1.73550	+	2.46737i	−0.0564557	+	0.0802635i
$946$	10.4488	+	6.98164i	0.339719	+	0.226993i
$947$	26.2868	−	17.5643i	0.854207	−	0.570763i	−0.0495681	−	0.998771i	$-0.515784\pi$
$947$	26.2868	−	17.5643i	0.854207	−	0.570763i	0.903775	+	0.428008i	$0.140784\pi$
$948$			16.3420i			0.530763i
$949$	2.18176	+	3.26524i	0.0708230	+	0.105994i
$950$	12.8389	−	27.2304i	0.416550	−	0.883470i
$951$		−	14.2734i		−	0.462846i
$952$	−0.921580	+	0.381211i	−0.0298686	+	0.0123551i
$953$	−35.4000	−	35.4000i	−1.14672	−	1.14672i	−0.987194	−	0.159524i	$-0.949004\pi$
$953$	−35.4000	−	35.4000i	−1.14672	−	1.14672i	−0.159524	−	0.987194i	$-0.550996\pi$
$954$	−1.09785	+	0.454744i	−0.0355442	+	0.0147229i
$955$	4.50050	−	20.0982i	0.145633	−	0.650362i
$956$	−4.96511	+	4.96511i	−0.160583	+	0.160583i
$957$	−1.48501	−	2.22247i	−0.0480034	−	0.0718422i
$958$	−4.08476	+	0.812508i	−0.131972	+	0.0262510i
$959$	−3.42624	+	0.681521i	−0.110639	+	0.0220075i
$960$	3.16738	+	1.40172i	0.102227	+	0.0452405i
$961$	−1.89224	+	4.56827i	−0.0610399	+	0.147363i
$962$	−0.904778	+	1.35410i	−0.0291712	+	0.0436578i
$963$	−0.116332	−	0.584839i	−0.00374873	−	0.0188462i
$964$	3.29208	−	16.5504i	0.106031	−	0.533052i
$965$	−15.1889	+	14.4785i	−0.488950	+	0.466080i
$966$	0.966525	−	0.645811i	0.0310974	−	0.0207786i
$967$	−2.55575	+	6.17012i	−0.0821873	+	0.198418i	−0.959631	−	0.281262i	$-0.909247\pi$
$967$	−2.55575	+	6.17012i	−0.0821873	+	0.198418i	0.877444	+	0.479680i	$0.159247\pi$
$968$	6.35306	−	6.35306i	0.204195	−	0.204195i
$969$	27.2048	−	27.1786i	0.873945	−	0.873103i
$970$	−15.3543	+	14.6361i	−0.492997	+	0.469938i
$971$	−0.716696	−	1.73026i	−0.0229999	−	0.0555266i	0.911962	−	0.410274i	$-0.134567\pi$
$971$	−0.716696	−	1.73026i	−0.0229999	−	0.0555266i	−0.934962	+	0.354747i	$0.884567\pi$
$972$	−6.02244	−	1.19794i	−0.193170	−	0.0384239i
$973$	−4.88460			−0.156593
$974$	9.97377	+	1.98391i	0.319580	+	0.0635685i
$975$	1.15435	−	1.56038i	0.0369688	−	0.0499723i
$976$	−1.78918	−	8.99481i	−0.0572702	−	0.287917i
$977$	19.1898	−	7.94869i	0.613938	−	0.254301i	−0.0539735	−	0.998542i	$-0.517189\pi$
$977$	19.1898	−	7.94869i	0.613938	−	0.254301i	0.667911	+	0.744241i	$0.267189\pi$
$978$	9.75101	−	4.03900i	0.311803	−	0.129153i
$979$	−2.02872	−	10.1991i	−0.0648383	−	0.325964i
$980$	2.66281	+	15.2915i	0.0850604	+	0.488470i
$981$	3.70434	+	0.736839i	0.118270	+	0.0235255i
$982$	−10.0839			−0.321789
$983$	−10.0810	−	2.00524i	−0.321534	−	0.0639571i	0.0316845	−	0.999498i	$-0.489913\pi$
$983$	−10.0810	−	2.00524i	−0.321534	−	0.0639571i	−0.353219	+	0.935541i	$0.614913\pi$
$984$	−0.520094	−	1.25562i	−0.0165800	−	0.0400276i
$985$	−0.358817	+	14.9841i	−0.0114329	+	0.477433i
$986$	5.01161	+	0.00241404i	0.159602	+	7.68786e-5i
$987$	−2.70770	+	2.70770i	−0.0861871	+	0.0861871i
$988$	0.577438	−	1.39406i	0.0183707	−	0.0443509i
$989$	22.8343	−	15.2574i	0.726090	−	0.485157i
$990$	−1.31542	−	1.37997i	−0.0418068	−	0.0438582i
$991$	3.19987	−	16.0868i	0.101647	−	0.511015i	−0.896095	−	0.443861i	$-0.853608\pi$
$991$	3.19987	−	16.0868i	0.101647	−	0.511015i	0.997743	−	0.0671536i	$-0.0213918\pi$
$992$	0.995828	+	5.00636i	0.0316176	+	0.158952i
$993$	13.0422	−	19.5190i	0.413880	−	0.619416i
$994$	−0.0914486	+	0.220776i	−0.00290057	+	0.00700260i
$995$	−20.3587	−	52.6836i	−0.645415	−	1.67018i
$996$	0.290047	−	0.0576940i	0.00919050	−	0.00182810i
$997$	−15.7026	+	3.12344i	−0.497306	+	0.0989204i	−0.437370	−	0.899282i	$-0.644090\pi$
$997$	−15.7026	+	3.12344i	−0.497306	+	0.0989204i	−0.0599366	+	0.998202i	$0.519090\pi$
$998$	−17.2581	−	25.8286i	−0.546295	−	0.817588i
$999$	25.6284	−	25.6284i	0.810846	−	0.810846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.o.b.73.2	yes	40
5.2	odd	4		170.2.r.b.107.4	yes	40
5.3	odd	4		850.2.v.d.107.2		40
5.4	even	2		850.2.s.d.243.4		40
17.7	odd	16		170.2.r.b.143.4	yes	40
85.7	even	16	inner	170.2.o.b.7.2	✓	40
85.24	odd	16		850.2.v.d.143.2		40
85.58	even	16		850.2.s.d.7.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.b.7.2	✓	40	85.7	even	16	inner
170.2.o.b.73.2	yes	40	1.1	even	1	trivial
170.2.r.b.107.4	yes	40	5.2	odd	4
170.2.r.b.143.4	yes	40	17.7	odd	16
850.2.s.d.7.4		40	85.58	even	16
850.2.s.d.243.4		40	5.4	even	2
850.2.v.d.107.2		40	5.3	odd	4
850.2.v.d.143.2		40	85.24	odd	16

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.o (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.923880 + 0.382683i) q^{2} +(-0.302197 + 1.51925i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-1.88843 + 1.19743i) q^{5} +(-0.860584 + 1.28795i) q^{6} +(-0.201119 - 0.134383i) q^{7} +(0.382683 + 0.923880i) q^{8} +(0.554854 + 0.229828i) q^{9} +O(q^{10})\)	\(q+(0.923880 + 0.382683i) q^{2} +(-0.302197 + 1.51925i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-1.88843 + 1.19743i) q^{5} +(-0.860584 + 1.28795i) q^{6} +(-0.201119 - 0.134383i) q^{7} +(0.382683 + 0.923880i) q^{8} +(0.554854 + 0.229828i) q^{9} +(-2.20292 + 0.383608i) q^{10} +(1.18040 + 0.788717i) q^{11} +(-1.28795 + 0.860584i) q^{12} -0.250606i q^{13} +(-0.134383 - 0.201119i) q^{14} +(-1.24851 - 3.23085i) q^{15} +1.00000i q^{16} +(-2.28902 - 3.42934i) q^{17} +(0.424667 + 0.424667i) q^{18} +(5.56274 - 2.30416i) q^{19} +(-2.18203 - 0.488612i) q^{20} +(0.264939 - 0.264939i) q^{21} +(0.788717 + 1.18040i) q^{22} +(3.04284 - 0.605259i) q^{23} +(-1.51925 + 0.302197i) q^{24} +(2.13233 - 4.52252i) q^{25} +(0.0959029 - 0.231530i) q^{26} +(-3.09859 + 4.63737i) q^{27} +(-0.0471892 - 0.237236i) q^{28} +(-0.237131 + 1.19214i) q^{29} +(0.0829196 - 3.46270i) q^{30} +(4.24419 - 2.83588i) q^{31} +(-0.382683 + 0.923880i) q^{32} +(-1.55497 + 1.55497i) q^{33} +(-0.802430 - 4.04427i) q^{34} +(0.540714 + 0.0129482i) q^{35} +(0.229828 + 0.554854i) q^{36} +(-6.37360 - 1.26779i) q^{37} +6.02107 q^{38} +(0.380733 + 0.0757325i) q^{39} +(-1.82895 - 1.28645i) q^{40} +(0.171169 + 0.860522i) q^{41} +(0.346160 - 0.143384i) q^{42} +(8.17809 - 3.38747i) q^{43} +(0.276961 + 1.39237i) q^{44} +(-1.32300 + 0.230383i) q^{45} +(3.04284 + 0.605259i) q^{46} -10.2201 q^{47} +(-1.51925 - 0.302197i) q^{48} +(-2.65639 - 6.41310i) q^{49} +(3.70071 - 3.36225i) q^{50} +(5.90175 - 2.44125i) q^{51} +(0.177206 - 0.177206i) q^{52} +(-0.757188 + 1.82801i) q^{53} +(-4.63737 + 3.09859i) q^{54} +(-3.17353 - 0.0759951i) q^{55} +(0.0471892 - 0.237236i) q^{56} +(1.81955 + 9.14748i) q^{57} +(-0.675292 + 1.01065i) q^{58} +(-0.520057 + 1.25553i) q^{59} +(1.40172 - 3.16738i) q^{60} +(-8.99481 + 1.78918i) q^{61} +(5.00636 - 0.995828i) q^{62} +(-0.0807066 - 0.120786i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(0.300083 + 0.473253i) q^{65} +(-2.03166 + 0.841542i) q^{66} +(7.69457 + 7.69457i) q^{67} +(0.806326 - 4.04349i) q^{68} +4.80573i q^{69} +(0.494599 + 0.218885i) q^{70} +(-0.548870 - 0.821442i) q^{71} +0.600569i q^{72} +(-13.0293 + 8.70593i) q^{73} +(-5.40328 - 3.61035i) q^{74} +(6.22643 + 4.60623i) q^{75} +(5.56274 + 2.30416i) q^{76} +(-0.131410 - 0.317252i) q^{77} +(0.322770 + 0.215668i) q^{78} +(5.86124 - 8.77197i) q^{79} +(-1.19743 - 1.88843i) q^{80} +(-4.83492 - 4.83492i) q^{81} +(-0.171169 + 0.860522i) q^{82} +(-0.176383 - 0.0730601i) q^{83} +0.374680 q^{84} +(8.42905 + 3.73513i) q^{85} +8.85190 q^{86} +(-1.73949 - 0.720521i) q^{87} +(-0.276961 + 1.39237i) q^{88} +(-5.17953 - 5.17953i) q^{89} +(-1.31046 - 0.293446i) q^{90} +(-0.0336774 + 0.0504017i) q^{91} +(2.57960 + 1.72363i) q^{92} +(3.02581 + 7.30496i) q^{93} +(-9.44214 - 3.91106i) q^{94} +(-7.74578 + 11.0122i) q^{95} +(-1.28795 - 0.860584i) q^{96} +(7.88775 - 5.27043i) q^{97} -6.94149i q^{98} +(0.473679 + 0.708911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q + 8 q^{10} - 8 q^{15} - 16 q^{18} - 16 q^{20} - 8 q^{25} - 8 q^{26} + 24 q^{27} + 8 q^{28} - 8 q^{29} - 16 q^{31} + 32 q^{33} - 8 q^{34} - 32 q^{35} + 16 q^{37} + 32 q^{39} + 8 q^{40} - 56 q^{41} - 8 q^{42} - 48 q^{43} - 16 q^{44} - 24 q^{45} - 96 q^{47} - 16 q^{49} - 32 q^{51} - 16 q^{52} - 40 q^{53} + 24 q^{54} + 8 q^{55} - 8 q^{56} - 8 q^{57} + 16 q^{58} + 24 q^{61} - 24 q^{62} - 24 q^{63} + 16 q^{65} - 16 q^{67} + 24 q^{68} + 8 q^{70} + 24 q^{71} + 16 q^{73} - 32 q^{74} + 184 q^{75} + 40 q^{77} + 16 q^{78} + 104 q^{79} + 8 q^{80} + 48 q^{81} + 56 q^{82} + 16 q^{83} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 16 q^{88} + 16 q^{89} + 40 q^{90} + 48 q^{91} + 8 q^{92} + 136 q^{93} + 8 q^{94} + 8 q^{95} + 144 q^{97} - 160 q^{99}+O(q^{100}) \) 40 * q + 8 * q^10 - 8 * q^15 - 16 * q^18 - 16 * q^20 - 8 * q^25 - 8 * q^26 + 24 * q^27 + 8 * q^28 - 8 * q^29 - 16 * q^31 + 32 * q^33 - 8 * q^34 - 32 * q^35 + 16 * q^37 + 32 * q^39 + 8 * q^40 - 56 * q^41 - 8 * q^42 - 48 * q^43 - 16 * q^44 - 24 * q^45 - 96 * q^47 - 16 * q^49 - 32 * q^51 - 16 * q^52 - 40 * q^53 + 24 * q^54 + 8 * q^55 - 8 * q^56 - 8 * q^57 + 16 * q^58 + 24 * q^61 - 24 * q^62 - 24 * q^63 + 16 * q^65 - 16 * q^67 + 24 * q^68 + 8 * q^70 + 24 * q^71 + 16 * q^73 - 32 * q^74 + 184 * q^75 + 40 * q^77 + 16 * q^78 + 104 * q^79 + 8 * q^80 + 48 * q^81 + 56 * q^82 + 16 * q^83 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 16 * q^88 + 16 * q^89 + 40 * q^90 + 48 * q^91 + 8 * q^92 + 136 * q^93 + 8 * q^94 + 8 * q^95 + 144 * q^97 - 160 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more