LMFDB - Embedded newform 151.2.g.a.76.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [151,2,Mod(2,151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(151, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([14]))

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

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

chi := DirichletCharacter("151.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	151.g (of order $15$, 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:	$1.20574107052$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			76.5
Character	$\chi$	$=$	151.76
Dual form			151.2.g.a.2.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.465766 - 0.806731i) q^{2} +(-2.42147 - 1.75930i) q^{3} +(0.566123 - 0.980554i) q^{4} +(1.07846 - 1.19776i) q^{5} +(-0.291444 + 2.77290i) q^{6} +(-0.384809 + 0.427373i) q^{7} -2.91779 q^{8} +(1.84134 + 5.66705i) q^{9} +O(q^{10})$	\(q+(-0.465766 - 0.806731i) q^{2} +(-2.42147 - 1.75930i) q^{3} +(0.566123 - 0.980554i) q^{4} +(1.07846 - 1.19776i) q^{5} +(-0.291444 + 2.77290i) q^{6} +(-0.384809 + 0.427373i) q^{7} -2.91779 q^{8} +(1.84134 + 5.66705i) q^{9} +(-1.46858 - 0.312156i) q^{10} +(-1.96090 - 0.873048i) q^{11} +(-3.09595 + 1.37840i) q^{12} +(-0.715073 + 0.318371i) q^{13} +(0.524007 + 0.111381i) q^{14} +(-4.71869 + 1.00299i) q^{15} +(0.226763 + 0.392764i) q^{16} +(2.30510 - 0.489965i) q^{17} +(3.71415 - 4.12498i) q^{18} +1.37182 q^{19} +(-0.563921 - 1.73557i) q^{20} +(1.68368 - 0.357878i) q^{21} +(0.209005 + 1.98855i) q^{22} +(-3.95119 - 6.84365i) q^{23} +(7.06535 + 5.13328i) q^{24} +(0.251108 + 2.38913i) q^{25} +(0.589897 + 0.428585i) q^{26} +(2.73655 - 8.42223i) q^{27} +(0.201214 + 0.619272i) q^{28} +(3.76386 - 2.73461i) q^{29} +(3.00695 + 3.33956i) q^{30} +(8.86672 - 1.88468i) q^{31} +(-2.70655 + 4.68789i) q^{32} +(3.21231 + 5.56388i) q^{33} +(-1.46891 - 1.63139i) q^{34} +(0.0968866 + 0.921814i) q^{35} +(6.59927 + 1.40272i) q^{36} +(0.862247 - 8.20374i) q^{37} +(-0.638946 - 1.10669i) q^{38} +(2.29164 + 0.487104i) q^{39} +(-3.14673 + 3.49480i) q^{40} +(-9.49425 - 6.89797i) q^{41} +(-1.07292 - 1.19159i) q^{42} +(-1.99664 - 2.21750i) q^{43} +(-1.96618 + 1.42851i) q^{44} +(8.77355 + 3.90624i) q^{45} +(-3.68066 + 6.37509i) q^{46} +(-8.66953 + 3.85992i) q^{47} +(0.141892 - 1.35001i) q^{48} +(0.697129 + 6.63274i) q^{49} +(1.81043 - 1.31536i) q^{50} +(-6.44374 - 2.86894i) q^{51} +(-0.0926394 + 0.881405i) q^{52} +(10.5209 - 7.64391i) q^{53} +(-8.06907 + 1.71513i) q^{54} +(-3.16046 + 1.40713i) q^{55} +(1.12279 - 1.24699i) q^{56} +(-3.32182 - 2.41344i) q^{57} +(-3.95917 - 1.76274i) q^{58} +6.99848 q^{59} +(-1.68788 + 5.19475i) q^{60} +(0.271292 + 2.58117i) q^{61} +(-5.65025 - 6.27524i) q^{62} +(-3.13051 - 1.39379i) q^{63} +5.94954 q^{64} +(-0.389850 + 1.19983i) q^{65} +(2.99237 - 5.18294i) q^{66} +(1.87590 - 5.77342i) q^{67} +(0.824535 - 2.53766i) q^{68} +(-2.47237 + 23.5231i) q^{69} +(0.698530 - 0.507512i) q^{70} +(2.47292 + 0.525636i) q^{71} +(-5.37263 - 16.5353i) q^{72} +(4.29396 + 13.2155i) q^{73} +(-7.01981 + 3.12542i) q^{74} +(3.59516 - 6.22700i) q^{75} +(0.776617 - 1.34514i) q^{76} +(1.12769 - 0.502079i) q^{77} +(-0.674408 - 2.07562i) q^{78} +(-0.259696 - 0.799261i) q^{79} +(0.714991 + 0.151976i) q^{80} +(-6.98172 + 5.07251i) q^{81} +(-1.14271 + 10.8722i) q^{82} +(-2.36487 + 7.27833i) q^{83} +(0.602254 - 1.85355i) q^{84} +(1.89911 - 3.28936i) q^{85} +(-0.858954 + 2.64359i) q^{86} -13.9251 q^{87} +(5.72149 + 2.54737i) q^{88} +(0.285055 + 0.316585i) q^{89} +(-0.935143 - 8.89729i) q^{90} +(0.139103 - 0.428115i) q^{91} -8.94743 q^{92} +(-24.7863 - 11.0356i) q^{93} +(7.15189 + 5.19615i) q^{94} +(1.47946 - 1.64310i) q^{95} +(14.8013 - 6.58995i) q^{96} +(10.5066 - 2.23324i) q^{97} +(5.02614 - 3.65170i) q^{98} +(1.33693 - 12.7201i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) $ 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9	\( 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9} + 11 q^{10} - 7 q^{11} + 7 q^{12} - 8 q^{13} + 5 q^{14} + 10 q^{15} - 47 q^{16} - 26 q^{17} - 40 q^{18} - 20 q^{19} + 23 q^{20} - 2 q^{21} - 32 q^{22} - q^{23} + 95 q^{24} - 51 q^{25} + 41 q^{26} + 5 q^{27} - 2 q^{28} + 13 q^{29} + 19 q^{30} - 24 q^{31} - 60 q^{32} + 39 q^{33} + 47 q^{34} - 54 q^{35} + 11 q^{36} + 5 q^{37} + 8 q^{38} - 13 q^{39} - 74 q^{40} + 8 q^{41} + 166 q^{42} - 8 q^{43} + 18 q^{44} - 33 q^{45} + 21 q^{46} - 5 q^{47} + 8 q^{48} + 21 q^{49} - 72 q^{50} - 6 q^{51} + 96 q^{52} + 41 q^{53} - 60 q^{54} - 116 q^{55} - 85 q^{56} - 8 q^{57} - 58 q^{58} + 32 q^{59} - 6 q^{60} - 18 q^{61} + 38 q^{62} - 129 q^{63} + 160 q^{64} + 53 q^{65} + 43 q^{66} + 4 q^{67} + 10 q^{68} + 81 q^{69} + 33 q^{70} - 41 q^{71} - 40 q^{72} - 58 q^{73} - 20 q^{74} + 32 q^{75} - q^{76} - 22 q^{77} - 10 q^{78} + 32 q^{79} + 71 q^{80} - 66 q^{81} - 10 q^{82} + 80 q^{83} - 58 q^{84} - 2 q^{85} - 72 q^{86} + 72 q^{87} + 89 q^{88} + 9 q^{89} + 121 q^{90} - 138 q^{91} - 72 q^{92} - 85 q^{93} + 11 q^{94} - 47 q^{95} - 201 q^{96} + 54 q^{97} - 92 q^{98} - 21 q^{99}+O(q^{100}) \) 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9 + 11 * q^10 - 7 * q^11 + 7 * q^12 - 8 * q^13 + 5 * q^14 + 10 * q^15 - 47 * q^16 - 26 * q^17 - 40 * q^18 - 20 * q^19 + 23 * q^20 - 2 * q^21 - 32 * q^22 - q^23 + 95 * q^24 - 51 * q^25 + 41 * q^26 + 5 * q^27 - 2 * q^28 + 13 * q^29 + 19 * q^30 - 24 * q^31 - 60 * q^32 + 39 * q^33 + 47 * q^34 - 54 * q^35 + 11 * q^36 + 5 * q^37 + 8 * q^38 - 13 * q^39 - 74 * q^40 + 8 * q^41 + 166 * q^42 - 8 * q^43 + 18 * q^44 - 33 * q^45 + 21 * q^46 - 5 * q^47 + 8 * q^48 + 21 * q^49 - 72 * q^50 - 6 * q^51 + 96 * q^52 + 41 * q^53 - 60 * q^54 - 116 * q^55 - 85 * q^56 - 8 * q^57 - 58 * q^58 + 32 * q^59 - 6 * q^60 - 18 * q^61 + 38 * q^62 - 129 * q^63 + 160 * q^64 + 53 * q^65 + 43 * q^66 + 4 * q^67 + 10 * q^68 + 81 * q^69 + 33 * q^70 - 41 * q^71 - 40 * q^72 - 58 * q^73 - 20 * q^74 + 32 * q^75 - q^76 - 22 * q^77 - 10 * q^78 + 32 * q^79 + 71 * q^80 - 66 * q^81 - 10 * q^82 + 80 * q^83 - 58 * q^84 - 2 * q^85 - 72 * q^86 + 72 * q^87 + 89 * q^88 + 9 * q^89 + 121 * q^90 - 138 * q^91 - 72 * q^92 - 85 * q^93 + 11 * q^94 - 47 * q^95 - 201 * q^96 + 54 * q^97 - 92 * q^98 - 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/151\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{8}{15}\right)$

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 $

$2$	−0.465766	−	0.806731i	−0.329347	−	0.570445i	0.653036	−	0.757327i	$-0.273495\pi$
$2$	−0.465766	−	0.806731i	−0.329347	−	0.570445i	−0.982382	+	0.186882i	$0.940162\pi$
$3$	−2.42147	−	1.75930i	−1.39804	−	1.01573i	−0.994929	−	0.100583i	$-0.967929\pi$
$3$	−2.42147	−	1.75930i	−1.39804	−	1.01573i	−0.403110	−	0.915152i	$-0.632071\pi$
$4$	0.566123	−	0.980554i	0.283062	−	0.490277i
$5$	1.07846	−	1.19776i	0.482304	−	0.535653i	−0.452053	−	0.891991i	$-0.649308\pi$
$5$	1.07846	−	1.19776i	0.482304	−	0.535653i	0.934357	+	0.356338i	$0.115975\pi$
$6$	−0.291444	+	2.77290i	−0.118981	+	1.13203i
$7$	−0.384809	+	0.427373i	−0.145444	+	0.161532i	−0.811465	−	0.584401i	$-0.801329\pi$
$7$	−0.384809	+	0.427373i	−0.145444	+	0.161532i	0.666021	+	0.745933i	$0.267996\pi$
$8$	−2.91779			−1.03159
$9$	1.84134	+	5.66705i	0.613778	+	1.88902i
$10$	−1.46858	−	0.312156i	−0.464406	−	0.0987125i
$11$	−1.96090	−	0.873048i	−0.591233	−	0.263234i	0.0892363	−	0.996010i	$-0.471557\pi$
$11$	−1.96090	−	0.873048i	−0.591233	−	0.263234i	−0.680469	+	0.732777i	$0.738224\pi$
$12$	−3.09595	+	1.37840i	−0.893722	+	0.397911i
$13$	−0.715073	+	0.318371i	−0.198326	+	0.0883002i	−0.503496	−	0.863997i	$-0.667953\pi$
$13$	−0.715073	+	0.318371i	−0.198326	+	0.0883002i	0.305171	+	0.952298i	$0.401287\pi$
$14$	0.524007	+	0.111381i	0.140047	+	0.0297678i
$15$	−4.71869	+	1.00299i	−1.21836	+	0.258971i
$16$	0.226763	+	0.392764i	0.0566906	+	0.0981910i
$17$	2.30510	−	0.489965i	0.559069	−	0.118834i	0.0802939	−	0.996771i	$-0.474414\pi$
$17$	2.30510	−	0.489965i	0.559069	−	0.118834i	0.478776	+	0.877937i	$0.341081\pi$
$18$	3.71415	−	4.12498i	0.875434	−	0.972268i
$19$	1.37182			0.314716			0.157358	−	0.987542i	$-0.449702\pi$
$19$	1.37182			0.314716			0.157358	+	0.987542i	$0.449702\pi$
$20$	−0.563921	−	1.73557i	−0.126097	−	0.388085i
$21$	1.68368	−	0.357878i	0.367410	−	0.0780954i
$22$	0.209005	+	1.98855i	0.0445601	+	0.423961i
$23$	−3.95119	−	6.84365i	−0.823879	−	1.42700i	−0.902773	−	0.430117i	$-0.858472\pi$
$23$	−3.95119	−	6.84365i	−0.823879	−	1.42700i	0.0788939	−	0.996883i	$-0.474861\pi$
$24$	7.06535	+	5.13328i	1.44221	+	1.04783i
$25$	0.251108	+	2.38913i	0.0502216	+	0.477827i
$26$	0.589897	+	0.428585i	0.115688	+	0.0840525i
$27$	2.73655	−	8.42223i	0.526649	−	1.62086i
$28$	0.201214	+	0.619272i	0.0380258	+	0.117031i
$29$	3.76386	−	2.73461i	0.698932	−	0.507804i	−0.180652	−	0.983547i	$-0.557821\pi$
$29$	3.76386	−	2.73461i	0.698932	−	0.507804i	0.879584	+	0.475743i	$0.157821\pi$
$30$	3.00695	+	3.33956i	0.548991	+	0.609717i
$31$	8.86672	−	1.88468i	1.59251	−	0.338499i	0.675500	−	0.737360i	$-0.263928\pi$
$31$	8.86672	−	1.88468i	1.59251	−	0.338499i	0.917011	+	0.398862i	$0.130595\pi$
$32$	−2.70655	+	4.68789i	−0.478456	+	0.828709i
$33$	3.21231	+	5.56388i	0.559191	+	0.968547i
$34$	−1.46891	−	1.63139i	−0.251916	−	0.279781i
$35$	0.0968866	+	0.921814i	0.0163768	+	0.155815i
$36$	6.59927	+	1.40272i	1.09988	+	0.233786i
$37$	0.862247	−	8.20374i	0.141753	−	1.34869i	−0.660106	−	0.751172i	$-0.729489\pi$
$37$	0.862247	−	8.20374i	0.141753	−	1.34869i	0.801859	−	0.597514i	$-0.203845\pi$
$38$	−0.638946	−	1.10669i	−0.103651	−	0.179528i
$39$	2.29164	+	0.487104i	0.366956	+	0.0779990i
$40$	−3.14673	+	3.49480i	−0.497542	+	0.552577i
$41$	−9.49425	−	6.89797i	−1.48275	−	1.07728i	−0.976657	−	0.214805i	$-0.931088\pi$
$41$	−9.49425	−	6.89797i	−1.48275	−	1.07728i	−0.506095	−	0.862477i	$-0.668912\pi$
$42$	−1.07292	−	1.19159i	−0.165554	−	0.183867i
$43$	−1.99664	−	2.21750i	−0.304485	−	0.338165i	0.571412	−	0.820664i	$-0.306396\pi$
$43$	−1.99664	−	2.21750i	−0.304485	−	0.338165i	−0.875897	+	0.482499i	$0.839729\pi$
$44$	−1.96618	+	1.42851i	−0.296413	+	0.215357i
$45$	8.77355	+	3.90624i	1.30788	+	0.582308i
$46$	−3.68066	+	6.37509i	−0.542684	+	0.939956i
$47$	−8.66953	+	3.85992i	−1.26458	+	0.563027i	−0.925862	−	0.377861i	$-0.876660\pi$
$47$	−8.66953	+	3.85992i	−1.26458	+	0.563027i	−0.338718	+	0.940888i	$0.609993\pi$
$48$	0.141892	−	1.35001i	0.0204803	−	0.194857i
$49$	0.697129	+	6.63274i	0.0995899	+	0.947534i
$50$	1.81043	−	1.31536i	0.256034	−	0.186019i
$51$	−6.44374	−	2.86894i	−0.902304	−	0.401732i
$52$	−0.0926394	+	0.881405i	−0.0128468	+	0.122229i
$53$	10.5209	−	7.64391i	1.44516	−	1.04997i	0.458231	−	0.888833i	$-0.348483\pi$
$53$	10.5209	−	7.64391i	1.44516	−	1.04997i	0.986932	−	0.161139i	$-0.0515166\pi$
$54$	−8.06907	+	1.71513i	−1.09806	+	0.233400i
$55$	−3.16046	+	1.40713i	−0.426156	+	0.189737i
$56$	1.12279	−	1.24699i	0.150039	−	0.166636i
$57$	−3.32182	−	2.41344i	−0.439986	−	0.319668i
$58$	−3.95917	−	1.76274i	−0.519865	−	0.231459i
$59$	6.99848			0.911124			0.455562	−	0.890204i	$-0.349438\pi$
$59$	6.99848			0.911124			0.455562	+	0.890204i	$0.349438\pi$
$60$	−1.68788	+	5.19475i	−0.217904	+	0.670639i
$61$	0.271292	+	2.58117i	0.0347354	+	0.330486i	0.998066	+	0.0621673i	$0.0198012\pi$
$61$	0.271292	+	2.58117i	0.0347354	+	0.330486i	−0.963330	+	0.268318i	$0.913532\pi$
$62$	−5.65025	−	6.27524i	−0.717583	−	0.796957i
$63$	−3.13051	−	1.39379i	−0.394407	−	0.175601i
$64$	5.94954			0.743692
$65$	−0.389850	+	1.19983i	−0.0483549	+	0.148821i
$66$	2.99237	−	5.18294i	0.368335	−	0.637975i
$67$	1.87590	−	5.77342i	0.229177	−	0.705336i	−0.768663	−	0.639654i	$-0.779078\pi$
$67$	1.87590	−	5.77342i	0.229177	−	0.705336i	0.997841	−	0.0656818i	$-0.0209222\pi$
$68$	0.824535	−	2.53766i	0.0999896	−	0.307736i
$69$	−2.47237	+	23.5231i	−0.297639	+	2.83184i
$70$	0.698530	−	0.507512i	0.0834903	−	0.0606592i
$71$	2.47292	+	0.525636i	0.293482	+	0.0623815i	0.352300	−	0.935887i	$-0.385400\pi$
$71$	2.47292	+	0.525636i	0.293482	+	0.0623815i	−0.0588179	+	0.998269i	$0.518733\pi$
$72$	−5.37263	−	16.5353i	−0.633171	−	1.94870i
$73$	4.29396	+	13.2155i	0.502570	+	1.54675i	0.804817	+	0.593523i	$0.202263\pi$
$73$	4.29396	+	13.2155i	0.502570	+	1.54675i	−0.302246	+	0.953230i	$0.597737\pi$
$74$	−7.01981	+	3.12542i	−0.816037	+	0.363323i
$75$	3.59516	−	6.22700i	0.415134	−	0.719032i
$76$	0.776617	−	1.34514i	0.0890841	−	0.154298i
$77$	1.12769	−	0.502079i	0.128512	−	0.0572172i
$78$	−0.674408	−	2.07562i	−0.0763617	−	0.235017i
$79$	−0.259696	−	0.799261i	−0.0292180	−	0.0899239i	0.935384	−	0.353633i	$-0.115054\pi$
$79$	−0.259696	−	0.799261i	−0.0292180	−	0.0899239i	−0.964602	+	0.263710i	$0.915054\pi$
$80$	0.714991	+	0.151976i	0.0799384	+	0.0169914i
$81$	−6.98172	+	5.07251i	−0.775746	+	0.563613i
$82$	−1.14271	+	10.8722i	−0.126191	+	1.20063i
$83$	−2.36487	+	7.27833i	−0.259579	+	0.798901i	0.733314	+	0.679890i	$0.237972\pi$
$83$	−2.36487	+	7.27833i	−0.259579	+	0.798901i	−0.992893	+	0.119011i	$0.962028\pi$
$84$	0.602254	−	1.85355i	0.0657113	−	0.202239i
$85$	1.89911	−	3.28936i	0.205988	−	0.356781i
$86$	−0.858954	+	2.64359i	−0.0926234	+	0.285065i
$87$	−13.9251			−1.49293
$88$	5.72149	+	2.54737i	0.609913	+	0.271551i
$89$	0.285055	+	0.316585i	0.0302157	+	0.0335580i	0.758063	−	0.652181i	$-0.226146\pi$
$89$	0.285055	+	0.316585i	0.0302157	+	0.0335580i	−0.727848	+	0.685739i	$0.759479\pi$
$90$	−0.935143	−	8.89729i	−0.0985728	−	0.937857i
$91$	0.139103	−	0.428115i	0.0145820	−	0.0448787i
$92$	−8.94743			−0.932834
$93$	−24.7863	−	11.0356i	−2.57022	−	1.14433i
$94$	7.15189	+	5.19615i	0.737661	+	0.535942i
$95$	1.47946	−	1.64310i	0.151789	−	0.168579i
$96$	14.8013	−	6.58995i	1.51065	−	0.672584i
$97$	10.5066	−	2.23324i	1.06678	−	0.226751i	0.359110	−	0.933295i	$-0.383080\pi$
$97$	10.5066	−	2.23324i	1.06678	−	0.226751i	0.707669	+	0.706544i	$0.249747\pi$
$98$	5.02614	−	3.65170i	0.507717	−	0.368878i
$99$	1.33693	−	12.7201i	0.134367	−	1.27842i
$100$	2.48483	+	1.10632i	0.248483	+	0.110632i
$101$	−3.28230	+	2.38473i	−0.326601	+	0.237290i	−0.738987	−	0.673720i	$-0.764696\pi$
$101$	−3.28230	+	2.38473i	−0.326601	+	0.237290i	0.412386	+	0.911009i	$0.364696\pi$
$102$	0.686817	+	6.53462i	0.0680050	+	0.647024i
$103$	−1.19795	+	11.3978i	−0.118038	+	1.12305i	0.761810	+	0.647800i	$0.224311\pi$
$103$	−1.19795	+	11.3978i	−0.118038	+	1.12305i	−0.879848	+	0.475255i	$0.842356\pi$
$104$	2.08643	−	0.928940i	0.204592	−	0.0910901i
$105$	1.38714	−	2.40260i	0.135371	−	0.234470i
$106$	−11.0669	−	4.92729i	−1.07491	−	0.478581i
$107$	9.79688	−	7.11785i	0.947100	−	0.688109i	−0.00301898	−	0.999995i	$-0.500961\pi$
$107$	9.79688	−	7.11785i	0.947100	−	0.688109i	0.950119	+	0.311887i	$0.100961\pi$
$108$	−6.70923	−	7.45136i	−0.645596	−	0.717007i
$109$	2.47758	+	2.75163i	0.237309	+	0.263559i	0.850022	−	0.526747i	$-0.176588\pi$
$109$	2.47758	+	2.75163i	0.237309	+	0.263559i	−0.612713	+	0.790306i	$0.709922\pi$
$110$	2.60721	+	1.89425i	0.248588	+	0.180609i
$111$	−16.5208	+	18.3482i	−1.56808	+	1.74153i
$112$	−0.255117	−	0.0542268i	−0.0241063	−	0.00512395i
$113$	1.35055	+	2.33922i	0.127049	+	0.220055i	0.922532	−	0.385921i	$-0.126116\pi$
$113$	1.35055	+	2.33922i	0.127049	+	0.220055i	−0.795483	+	0.605976i	$0.792783\pi$
$114$	−0.399808	+	3.80392i	−0.0374454	+	0.356269i
$115$	−12.4582	−	2.64808i	−1.16174	−	0.246935i
$116$	−0.550620	−	5.23880i	−0.0511238	−	0.486410i
$117$	−3.12091	−	3.46612i	−0.288528	−	0.320443i
$118$	−3.25966	−	5.64589i	−0.300076	−	0.519746i
$119$	−0.677626	+	1.17368i	−0.0621179	+	0.107591i
$120$	13.7682	−	2.92651i	1.25685	−	0.267153i
$121$	−4.27753	−	4.75068i	−0.388866	−	0.431880i
$122$	1.95596	−	1.42108i	0.177084	−	0.128659i
$123$	10.8544	+	33.4065i	0.978712	+	3.01217i
$124$	3.17163	−	9.76127i	0.284821	−	0.876587i
$125$	9.65204	+	7.01261i	0.863304	+	0.627227i
$126$	0.333670	+	3.17466i	0.0297257	+	0.282821i
$127$	−0.703927	−	0.511433i	−0.0624634	−	0.0453823i	0.556115	−	0.831105i	$-0.312291\pi$
$127$	−0.703927	−	0.511433i	−0.0624634	−	0.0453823i	−0.618579	+	0.785723i	$0.712291\pi$
$128$	2.64201	+	4.57610i	0.233523	+	0.404474i
$129$	0.933568	+	8.88231i	0.0821961	+	0.782043i
$130$	1.14952	−	0.244339i	0.100820	−	0.0214299i
$131$	0.220706	+	0.679263i	0.0192832	+	0.0593474i	0.960235	−	0.279193i	$-0.0900669\pi$
$131$	0.220706	+	0.679263i	0.0192832	+	0.0593474i	−0.940952	+	0.338540i	$0.890067\pi$
$132$	7.27425			0.633142
$133$	−0.527887	+	0.586278i	−0.0457736	+	0.0508368i
$134$	−5.53133	+	1.17572i	−0.477834	+	0.101567i
$135$	−7.13651	−	12.3608i	−0.614213	−	1.06385i
$136$	−6.72581	+	1.42961i	−0.576733	+	0.122588i
$137$	6.15273	+	1.30780i	0.525663	+	0.111733i	0.463097	−	0.886308i	$-0.346738\pi$
$137$	6.15273	+	1.30780i	0.525663	+	0.111733i	0.0625663	+	0.998041i	$0.480072\pi$
$138$	20.1283	−	8.96171i	1.71344	−	0.762872i
$139$	11.6088	−	5.16855i	0.984642	−	0.438391i	0.149702	−	0.988731i	$-0.452169\pi$
$139$	11.6088	−	5.16855i	0.984642	−	0.438391i	0.834940	+	0.550340i	$0.185502\pi$
$140$	0.958739	+	0.426858i	0.0810282	+	0.0360761i
$141$	27.7838	+	5.90563i	2.33982	+	0.497344i
$142$	−0.727757	−	2.23981i	−0.0610720	−	0.187960i
$143$	1.68014			0.140500
$144$	−1.80827	+	2.00828i	−0.150689	+	0.167357i
$145$	0.783801	−	7.45737i	0.0650911	−	0.619301i
$146$	8.66134	−	9.61939i	0.716818	−	0.796107i
$147$	9.98092	−	17.2875i	0.823213	−	1.42585i
$148$	−7.55607	−	5.48981i	−0.621105	−	0.451259i
$149$	−7.04426	−	12.2010i	−0.577088	−	0.999546i	−0.995811	−	0.0914323i	$-0.970855\pi$
$149$	−7.04426	−	12.2010i	−0.577088	−	0.999546i	0.418723	−	0.908114i	$-0.362478\pi$
$150$	−6.69802			−0.546891
$151$	8.84181	+	8.53360i	0.719536	+	0.694455i
$151$	8.84181	+	8.53360i	0.719536	+	0.694455i
$152$	−4.00267			−0.324660
$153$	7.02112	+	12.1609i	0.567624	+	0.983153i
$154$	−0.930282	−	0.675890i	−0.0749643	−	0.0544647i
$155$	7.30506	−	12.6527i	0.586756	−	1.01629i
$156$	1.77498	−	1.97132i	0.142112	−	0.157832i
$157$	2.19102	−	20.8462i	0.174863	−	1.66371i	−0.457631	−	0.889142i	$-0.651302\pi$
$157$	2.19102	−	20.8462i	0.174863	−	1.66371i	0.632494	−	0.774566i	$-0.282031\pi$
$158$	−0.523831	+	0.581773i	−0.0416738	+	0.0462834i
$159$	−38.9241			−3.08689
$160$	2.69603	+	8.29751i	0.213140	+	0.655976i
$161$	4.44525	+	0.944866i	0.350335	+	0.0744659i
$162$	7.34400	+	3.26976i	0.576999	+	0.256897i
$163$	−1.37071	+	0.610278i	−0.107362	+	0.0478006i	−0.459715	−	0.888067i	$-0.652048\pi$
$163$	−1.37071	+	0.610278i	−0.107362	+	0.0478006i	0.352353	+	0.935867i	$0.385382\pi$
$164$	−12.1388	+	5.40452i	−0.947877	+	0.422022i
$165$	10.1285	+	2.15289i	0.788505	+	0.167602i
$166$	6.97314	−	1.48219i	0.541220	−	0.115040i
$167$	10.9025	+	18.8837i	0.843661	+	1.46126i	0.886779	+	0.462194i	$0.152938\pi$
$167$	10.9025	+	18.8837i	0.843661	+	1.46126i	−0.0431176	+	0.999070i	$0.513729\pi$
$168$	−4.91264	+	1.04421i	−0.379018	+	0.0805628i
$169$	−8.28873	+	9.20557i	−0.637595	+	0.708120i
$170$	−3.53817			−0.271365
$171$	2.52597	+	7.77415i	0.193166	+	0.594504i
$172$	−3.30472	+	0.702440i	−0.251982	+	0.0535605i
$173$	2.41812	+	23.0069i	0.183846	+	1.74918i	0.565385	+	0.824827i	$0.308728\pi$
$173$	2.41812	+	23.0069i	0.183846	+	1.74918i	−0.381539	+	0.924353i	$0.624606\pi$
$174$	6.48584	+	11.2338i	0.491691	+	0.851633i
$175$	−1.11768	−	0.812043i	−0.0844888	−	0.0613847i
$176$	−0.101756	−	0.968145i	−0.00767016	−	0.0729767i
$177$	−16.9466	−	12.3125i	−1.27379	−	0.925460i
$178$	0.122630	−	0.377417i	0.00919153	−	0.0282886i
$179$	1.52475	+	4.69271i	0.113965	+	0.350750i	0.991730	−	0.128343i	$-0.0409658\pi$
$179$	1.52475	+	4.69271i	0.113965	+	0.350750i	−0.877764	+	0.479093i	$0.840966\pi$
$180$	8.79719	−	6.39153i	0.655704	−	0.476397i
$181$	−14.2954	−	15.8767i	−1.06257	−	1.18011i	−0.983062	−	0.183272i	$-0.941331\pi$
$181$	−14.2954	−	15.8767i	−1.06257	−	1.18011i	−0.0795101	−	0.996834i	$-0.525336\pi$
$182$	−0.410163	+	0.0871829i	−0.0304033	+	0.00646243i
$183$	3.88414	−	6.72753i	0.287124	−	0.497314i
$184$	11.5287	+	19.9683i	0.849909	+	1.47209i
$185$	−8.89617	−	9.88020i	−0.654060	−	0.726407i
$186$	2.64188	+	25.1358i	0.193712	+	1.84305i
$187$	−4.94783	−	1.05169i	−0.361821	−	0.0769075i
$188$	−1.12316	+	10.6861i	−0.0819147	+	0.779366i
$189$	2.54639	+	4.41048i	0.185223	+	0.320815i
$190$	−2.01462	−	0.428221i	−0.146156	−	0.0310664i
$191$	8.17257	−	9.07656i	0.591346	−	0.656757i	−0.370984	−	0.928639i	$-0.620980\pi$
$191$	8.17257	−	9.07656i	0.591346	−	0.656757i	0.962330	+	0.271883i	$0.0876462\pi$
$192$	−14.4067	−	10.4670i	−1.03971	−	0.755394i
$193$	−15.1072	−	16.7782i	−1.08744	−	1.20772i	−0.976866	−	0.213853i	$-0.931399\pi$
$193$	−15.1072	−	16.7782i	−1.08744	−	1.20772i	−0.110571	−	0.993868i	$-0.535268\pi$
$194$	−6.69522	−	7.43580i	−0.480689	−	0.533859i
$195$	3.05489	−	2.21950i	0.218765	−	0.158942i
$196$	6.89842	+	3.07137i	0.492744	+	0.219384i
$197$	−7.35338	+	12.7364i	−0.523906	+	0.907433i	0.475706	+	0.879604i	$0.342193\pi$
$197$	−7.35338	+	12.7364i	−0.523906	+	0.907433i	−0.999613	+	0.0278283i	$0.991141\pi$
$198$	−10.8844	+	4.84604i	−0.773519	+	0.344393i
$199$	−1.33466	+	12.6984i	−0.0946113	+	0.900167i	0.839542	+	0.543295i	$0.182823\pi$
$199$	−1.33466	+	12.6984i	−0.0946113	+	0.900167i	−0.934153	+	0.356872i	$0.883843\pi$
$200$	−0.732681	−	6.97100i	−0.0518084	−	0.492924i
$201$	−14.6996	+	10.6799i	−1.03683	+	0.753303i
$202$	3.45262	+	1.53721i	0.242926	+	0.108157i
$203$	−0.279669	+	2.66088i	−0.0196289	+	0.186757i
$204$	−6.46110	+	4.69427i	−0.452368	+	0.328664i
$205$	−18.5013	+	3.93257i	−1.29219	+	0.274663i
$206$	9.75290	−	4.34227i	0.679516	−	0.302540i
$207$	31.5078	−	34.9930i	2.18995	−	2.43218i
$208$	−0.287196	−	0.208660i	−0.0199135	−	0.0144680i
$209$	−2.68999	−	1.19766i	−0.186071	−	0.0828440i
$210$	−2.58434			−0.178336
$211$	−1.65056	+	5.07990i	−0.113629	+	0.349715i	−0.991659	−	0.128892i	$-0.958858\pi$
$211$	−1.65056	+	5.07990i	−0.113629	+	0.349715i	0.878029	+	0.478607i	$0.158858\pi$
$212$	−1.53912	−	14.6437i	−0.105707	−	1.00574i
$213$	−5.06336	−	5.62343i	−0.346936	−	0.385311i
$214$	−10.3053	−	4.58819i	−0.704452	−	0.313642i
$215$	−4.80933			−0.327993
$216$	−7.98468	+	24.5743i	−0.543289	+	1.67207i
$217$	−2.60653	+	4.51464i	−0.176943	+	0.306474i
$218$	1.06585	−	3.28036i	0.0721887	−	0.222174i
$219$	12.8523	−	39.5553i	0.868477	−	2.67290i
$220$	−0.409445	+	3.89561i	−0.0276048	+	0.262642i
$221$	−1.49233	+	1.08424i	−0.100385	+	0.0729338i
$222$	22.4969	+	4.78186i	1.50989	+	0.320937i
$223$	−4.75773	−	14.6428i	−0.318601	−	0.980553i	−0.974247	−	0.225484i	$-0.927604\pi$
$223$	−4.75773	−	14.6428i	−0.318601	−	0.980553i	0.655646	−	0.755069i	$-0.272396\pi$
$224$	−0.961974	−	2.96065i	−0.0642746	−	0.197817i
$225$	−13.0770	+	5.82224i	−0.871798	+	0.388149i
$226$	1.25808	−	2.17906i	0.0836862	−	0.144949i
$227$	−5.14041	+	8.90345i	−0.341181	+	0.590943i	−0.984652	−	0.174527i	$-0.944160\pi$
$227$	−5.14041	+	8.90345i	−0.341181	+	0.590943i	0.643471	+	0.765470i	$0.277494\pi$
$228$	−4.24707	+	1.89092i	−0.281269	+	0.125229i
$229$	0.439804	+	1.35358i	0.0290631	+	0.0894469i	0.964536	−	0.263952i	$-0.0850259\pi$
$229$	0.439804	+	1.35358i	0.0290631	+	0.0894469i	−0.935473	+	0.353399i	$0.885026\pi$
$230$	3.66634	+	11.2838i	0.241751	+	0.744034i
$231$	−3.61398	−	0.768175i	−0.237782	−	0.0505422i
$232$	−10.9822	+	7.97901i	−0.721014	+	0.523848i
$233$	−0.0982009	+	0.934319i	−0.00643336	+	0.0612093i	−0.997268	−	0.0738743i	$-0.976464\pi$
$233$	−0.0982009	+	0.934319i	−0.00643336	+	0.0612093i	0.990834	+	0.135084i	$0.0431303\pi$
$234$	−1.34261	+	4.13214i	−0.0877694	+	0.270127i
$235$	−4.72653	+	14.5468i	−0.308325	+	0.948926i
$236$	3.96200	−	6.86239i	0.257904	−	0.446703i
$237$	−0.777297	+	2.39227i	−0.0504908	+	0.155395i
$238$	1.26246			0.0818332
$239$	−3.77005	−	1.67854i	−0.243864	−	0.108575i	0.281165	−	0.959659i	$-0.409279\pi$
$239$	−3.77005	−	1.67854i	−0.243864	−	0.108575i	−0.525030	+	0.851084i	$0.675946\pi$
$240$	−1.46396	−	1.62589i	−0.0944982	−	0.104951i
$241$	−2.76099	−	26.2691i	−0.177851	−	1.69214i	−0.611648	−	0.791130i	$-0.709493\pi$
$241$	−2.76099	−	26.2691i	−0.177851	−	1.69214i	0.433796	−	0.901011i	$-0.357174\pi$
$242$	−1.84019	+	5.66352i	−0.118292	+	0.364065i
$243$	−0.736844			−0.0472686
$244$	2.68457	+	1.19525i	0.171862	+	0.0765178i
$245$	8.69623	+	6.31818i	0.555582	+	0.403654i
$246$	21.8945	−	24.3163i	1.39594	−	1.55035i
$247$	−0.980949	+	0.436747i	−0.0624163	+	0.0277895i
$248$	−25.8712	+	5.49910i	−1.64283	+	0.349193i
$249$	18.5313	−	13.4638i	1.17437	−	0.853231i
$250$	1.16170	−	11.0528i	0.0734724	−	0.699043i
$251$	−0.569488	−	0.253552i	−0.0359458	−	0.0160041i	0.388685	−	0.921371i	$-0.372929\pi$
$251$	−0.569488	−	0.253552i	−0.0359458	−	0.0160041i	−0.424631	+	0.905367i	$0.639596\pi$
$252$	−3.13894	+	2.28057i	−0.197735	+	0.143663i
$253$	1.77303	+	16.8693i	0.111470	+	1.06056i
$254$	−0.0847233	+	0.806088i	−0.00531601	+	0.0505785i
$255$	−10.3856	+	4.62398i	−0.650374	+	0.289565i
$256$	8.41066	−	14.5677i	0.525666	−	0.910481i
$257$	5.12519	+	2.28188i	0.319701	+	0.142340i	0.560312	−	0.828282i	$-0.310681\pi$
$257$	5.12519	+	2.28188i	0.319701	+	0.142340i	−0.240611	+	0.970622i	$0.577348\pi$
$258$	6.73081	−	4.89022i	0.419042	−	0.304452i
$259$	3.17426	+	3.52537i	0.197239	+	0.219056i
$260$	0.955800	+	1.06152i	0.0592762	+	0.0658329i
$261$	22.4277	+	16.2947i	1.38824	+	1.00861i
$262$	0.445185	−	0.494428i	0.0275036	−	0.0305459i
$263$	19.2088	+	4.08297i	1.18447	+	0.251767i	0.757705	−	0.652597i	$-0.226320\pi$
$263$	19.2088	+	4.08297i	1.18447	+	0.251767i	0.426763	+	0.904363i	$0.359654\pi$
$264$	−9.37284	−	16.2342i	−0.576858	−	0.999148i
$265$	2.19092	−	20.8452i	0.134587	−	1.28051i
$266$	0.718841	+	0.152794i	0.0440750	+	0.00936842i
$267$	−0.133283	−	1.26810i	−0.00815677	−	0.0776065i
$268$	−4.59916	−	5.10789i	−0.280939	−	0.312014i
$269$	3.36964	+	5.83639i	0.205451	+	0.355851i	0.950276	−	0.311408i	$-0.100801\pi$
$269$	3.36964	+	5.83639i	0.205451	+	0.355851i	−0.744825	+	0.667259i	$0.767467\pi$
$270$	−6.64789	+	11.5145i	−0.404578	+	0.700750i
$271$	−4.04218	+	0.859193i	−0.245545	+	0.0521922i	−0.329040	−	0.944316i	$-0.606725\pi$
$271$	−4.04218	+	0.859193i	−0.245545	+	0.0521922i	0.0834949	+	0.996508i	$0.473392\pi$
$272$	0.715151	+	0.794256i	0.0433624	+	0.0481588i
$273$	−1.09002	+	0.791945i	−0.0659710	+	0.0479307i
$274$	−1.81069	−	5.57273i	−0.109388	−	0.336661i
$275$	1.59343	−	4.90408i	0.0960876	−	0.295727i
$276$	21.6660	+	15.7412i	1.30414	+	0.947512i
$277$	1.54774	+	14.7258i	0.0929950	+	0.884788i	0.937206	+	0.348777i	$0.113403\pi$
$277$	1.54774	+	14.7258i	0.0929950	+	0.884788i	−0.844211	+	0.536011i	$0.819930\pi$
$278$	−9.57660	−	6.95781i	−0.574366	−	0.417302i
$279$	27.0072	+	46.7778i	1.61688	+	2.80051i
$280$	−0.282695	−	2.68966i	−0.0168942	−	0.160738i
$281$	−16.0967	+	3.42146i	−0.960250	+	0.204107i	−0.661267	−	0.750151i	$-0.729981\pi$
$281$	−16.0967	+	3.42146i	−0.960250	+	0.204107i	−0.298983	+	0.954258i	$0.596647\pi$
$282$	−8.17651	−	25.1647i	−0.486904	−	1.49854i
$283$	11.8070			0.701854			0.350927	−	0.936403i	$-0.385866\pi$
$283$	11.8070			0.701854			0.350927	+	0.936403i	$0.385866\pi$
$284$	1.91539	−	2.12726i	0.113658	−	0.126230i
$285$	−6.47318	+	1.37592i	−0.383438	+	0.0815023i
$286$	−0.782552	−	1.35542i	−0.0462733	−	0.0801477i
$287$	6.60148	−	1.40319i	0.389673	−	0.0828276i
$288$	−31.5502	−	6.70619i	−1.85911	−	0.395166i
$289$	−10.4568	+	4.65569i	−0.615108	+	0.273864i
$290$	−6.38116	+	2.84107i	−0.374714	+	0.166834i
$291$	−29.3703	−	13.0765i	−1.72172	−	0.766558i
$292$	15.3894	+	3.27112i	0.900596	+	0.191428i
$293$	1.21027	+	3.72482i	0.0707045	+	0.217606i	0.980165	−	0.198185i	$-0.0635047\pi$
$293$	1.21027	+	3.72482i	0.0707045	+	0.217606i	−0.909460	+	0.415791i	$0.863505\pi$
$294$	−18.5951			−1.08449
$295$	7.54761	−	8.38247i	0.439439	−	0.488046i
$296$	−2.51586	+	23.9368i	−0.146231	+	1.39130i
$297$	−12.7191	+	14.1260i	−0.738038	+	0.819674i
$298$	−6.56196	+	11.3657i	−0.380124	+	0.658394i
$299$	5.00421	+	3.63577i	0.289401	+	0.210262i
$300$	−4.07061	−	7.05050i	−0.235017	−	0.407061i
$301$	1.71602			0.0989100
$302$	2.76610	−	11.1076i	0.159171	−	0.639172i
$303$	12.1435			0.697624
$304$	0.311077	+	0.538801i	0.0178415	+	0.0309023i
$305$	3.38420	+	2.45876i	0.193779	+	0.140788i
$306$	6.54040	−	11.3283i	0.373890	−	0.647596i
$307$	−11.3030	+	12.5533i	−0.645098	+	0.716454i	−0.973654	−	0.228031i	$-0.926771\pi$
$307$	−11.3030	+	12.5533i	−0.645098	+	0.716454i	0.328556	+	0.944484i	$0.393438\pi$
$308$	0.146095	−	1.39000i	0.00832452	−	0.0792025i
$309$	22.9529	−	25.4918i	1.30575	−	1.45018i
$310$	−13.6098			−0.772985
$311$	2.40598	+	7.40484i	0.136430	+	0.419890i	0.995810	−	0.0914488i	$-0.0291498\pi$
$311$	2.40598	+	7.40484i	0.136430	+	0.419890i	−0.859379	+	0.511339i	$0.829150\pi$
$312$	−6.68653	−	1.42127i	−0.378550	−	0.0804633i
$313$	28.5354	+	12.7048i	1.61292	+	0.718116i	0.997539	−	0.0701174i	$-0.0223374\pi$
$313$	28.5354	+	12.7048i	1.61292	+	0.718116i	0.615376	+	0.788233i	$0.289004\pi$
$314$	−17.8378	+	7.94189i	−1.00664	+	0.448187i
$315$	−5.04556	+	2.24643i	−0.284285	+	0.126572i
$316$	−0.930738	−	0.197835i	−0.0523581	−	0.0111291i
$317$	−13.6293	+	2.89700i	−0.765498	+	0.162712i	−0.574083	−	0.818797i	$-0.694641\pi$
$317$	−13.6293	+	2.89700i	−0.765498	+	0.162712i	−0.191416	+	0.981509i	$0.561308\pi$
$318$	18.1296	+	31.4013i	1.01666	+	1.76090i
$319$	−9.76800	+	2.07625i	−0.546903	+	0.116248i
$320$	6.41637	−	7.12610i	0.358686	−	0.398361i
$321$	−36.2454			−2.02302
$322$	−1.30819	−	4.02621i	−0.0729028	−	0.224372i
$323$	3.16218	−	0.672142i	0.175948	−	0.0373990i
$324$	1.02136	+	9.71762i	0.0567424	+	0.539868i
$325$	−0.940192	−	1.62846i	−0.0521525	−	0.0903307i
$326$	1.13076	+	0.821545i	0.0626270	+	0.0455011i
$327$	−1.15844	−	11.0218i	−0.0640619	−	0.609508i
$328$	27.7022	+	20.1268i	1.52960	+	1.11132i
$329$	1.68648	−	5.19046i	0.0929787	−	0.286159i
$330$	−2.98073	−	9.17374i	−0.164084	−	0.504998i
$331$	6.86887	−	4.99052i	0.377547	−	0.274304i	−0.382786	−	0.923837i	$-0.625036\pi$
$331$	6.86887	−	4.99052i	0.377547	−	0.274304i	0.760334	+	0.649533i	$0.225036\pi$
$332$	5.79799	+	6.43932i	0.318206	+	0.353404i
$333$	48.0786	−	10.2194i	2.63469	−	0.560021i
$334$	10.1560	−	17.5908i	0.555714	−	0.962525i
$335$	−4.89206	−	8.47330i	−0.267282	−	0.462946i
$336$	0.522358	+	0.580138i	0.0284970	+	0.0316491i
$337$	−3.32221	−	31.6088i	−0.180973	−	1.72184i	−0.588373	−	0.808590i	$-0.700231\pi$
$337$	−3.32221	−	31.6088i	−0.180973	−	1.72184i	0.407401	−	0.913250i	$-0.366435\pi$
$338$	11.2870	+	2.39913i	0.613933	+	0.130496i
$339$	0.845078	−	8.04038i	0.0458983	−	0.436693i
$340$	−2.15026	−	3.72437i	−0.116614	−	0.201982i
$341$	−19.0322	−	4.04541i	−1.03065	−	0.219071i
$342$	5.09514	−	5.65872i	0.275513	−	0.305989i
$343$	−6.35971	−	4.62060i	−0.343392	−	0.249489i
$344$	5.82578	+	6.47019i	0.314105	+	0.348849i
$345$	25.5085	+	28.3301i	1.37333	+	1.52524i
$346$	17.4341	−	12.6666i	0.937262	−	0.680961i
$347$	20.1281	+	8.96160i	1.08053	+	0.481084i	0.868251	−	0.496125i	$-0.165244\pi$
$347$	20.1281	+	8.96160i	1.08053	+	0.481084i	0.212281	+	0.977209i	$0.431911\pi$
$348$	−7.88332	+	13.6543i	−0.422590	+	0.731948i
$349$	11.4186	−	5.08391i	0.611226	−	0.272135i	−0.0776888	−	0.996978i	$-0.524754\pi$
$349$	11.4186	−	5.08391i	0.611226	−	0.272135i	0.688915	+	0.724842i	$0.258087\pi$
$350$	−0.134522	+	1.27989i	−0.00719050	+	0.0684130i
$351$	0.724562	+	6.89375i	0.0386743	+	0.367961i
$352$	9.40003	−	6.82952i	0.501023	−	0.364015i
$353$	22.4338	+	9.98817i	1.19403	+	0.531617i	0.904880	−	0.425667i	$-0.139960\pi$
$353$	22.4338	+	9.98817i	1.19403	+	0.531617i	0.289151	+	0.957284i	$0.406627\pi$
$354$	−2.03966	+	19.4061i	−0.108407	+	1.03142i
$355$	3.29654	−	2.39508i	0.174962	−	0.127117i
$356$	0.471805	−	0.100285i	0.0250056	−	0.00531511i
$357$	3.70572	−	1.64989i	0.196127	−	0.0873215i
$358$	3.07558	−	3.41577i	0.162549	−	0.180529i
$359$	−10.2882	−	7.47480i	−0.542990	−	0.394505i	0.282204	−	0.959354i	$-0.408934\pi$
$359$	−10.2882	−	7.47480i	−0.542990	−	0.394505i	−0.825194	+	0.564849i	$0.808934\pi$
$360$	−25.5994	−	11.3976i	−1.34921	−	0.600705i
$361$	−17.1181			−0.900954
$362$	−6.14989	+	18.9274i	−0.323231	+	0.994803i
$363$	2.00004	+	19.0291i	0.104975	+	0.998769i
$364$	−0.341041	−	0.378764i	−0.0178754	−	0.0198526i
$365$	20.4598	+	9.10928i	1.07091	+	0.476802i
$366$	−7.23641			−0.378253
$367$	−2.49994	+	7.69404i	−0.130496	+	0.401625i	−0.994862	−	0.101237i	$-0.967720\pi$
$367$	−2.49994	+	7.69404i	−0.130496	+	0.401625i	0.864366	+	0.502863i	$0.167720\pi$
$368$	1.79196	−	3.10377i	0.0934124	−	0.161795i
$369$	21.6091	−	66.5058i	1.12492	−	3.46216i
$370$	−3.82713	+	11.7787i	−0.198963	+	0.612345i
$371$	−0.781746	+	7.43782i	−0.0405862	+	0.386152i
$372$	−24.8530	+	18.0568i	−1.28857	+	0.936201i
$373$	18.2583	+	3.88092i	0.945380	+	0.200947i	0.654713	−	0.755878i	$-0.272790\pi$
$373$	18.2583	+	3.88092i	0.945380	+	0.200947i	0.290667	+	0.956824i	$0.406123\pi$
$374$	1.45610	+	4.48142i	0.0752932	+	0.231728i
$375$	−11.0348	−	33.9617i	−0.569836	−	1.75378i
$376$	25.2959	−	11.2624i	1.30453	−	0.580816i
$377$	−1.82082	+	3.15375i	−0.0937769	+	0.162426i
$378$	2.37205	−	4.10851i	0.122005	−	0.211319i
$379$	−18.8016	+	8.37100i	−0.965772	+	0.429989i	−0.828157	−	0.560497i	$-0.810610\pi$
$379$	−18.8016	+	8.37100i	−0.965772	+	0.429989i	−0.137615	+	0.990486i	$0.543944\pi$
$380$	−0.773596	−	2.38088i	−0.0396847	−	0.122137i
$381$	0.804775	+	2.47684i	0.0412299	+	0.126893i
$382$	−11.1288	−	2.36551i	−0.569401	−	0.121030i
$383$	1.30834	−	0.950563i	0.0668529	−	0.0485715i	−0.553857	−	0.832612i	$-0.686845\pi$
$383$	1.30834	−	0.950563i	0.0668529	−	0.0485715i	0.620710	+	0.784040i	$0.286845\pi$
$384$	1.65319	−	15.7290i	0.0843638	−	0.802668i
$385$	0.614803	−	1.89217i	0.0313333	−	0.0964339i
$386$	−6.49909	+	20.0021i	−0.330795	+	1.01808i
$387$	8.89016	−	15.3982i	0.451912	−	0.782735i
$388$	3.75819	−	11.5665i	0.190793	−	0.587202i
$389$	−0.342145			−0.0173474			−0.00867372	−	0.999962i	$-0.502761\pi$
$389$	−0.342145			−0.0173474			−0.00867372	+	0.999962i	$0.502761\pi$
$390$	−3.21341	−	1.43070i	−0.162717	−	0.0724463i
$391$	−12.4610	−	13.8394i	−0.630182	−	0.699888i
$392$	−2.03408	−	19.3529i	−0.102736	−	0.977471i
$393$	0.660596	−	2.03311i	0.0333227	−	0.102557i
$394$	13.6998			0.690187
$395$	−1.23739	−	0.550922i	−0.0622600	−	0.0277199i
$396$	−11.7159	−	8.51207i	−0.588744	−	0.427747i
$397$	12.5494	−	13.9375i	0.629835	−	0.699503i	−0.340779	−	0.940143i	$-0.610691\pi$
$397$	12.5494	−	13.9375i	0.629835	−	0.699503i	0.970614	+	0.240640i	$0.0773575\pi$
$398$	10.8658	−	4.83779i	0.544656	−	0.242496i
$399$	2.30971	−	0.490943i	0.115630	−	0.0245779i
$400$	−0.881425	+	0.640392i	−0.0440712	+	0.0320196i
$401$	2.49101	−	23.7003i	0.124395	−	1.18354i	−0.737104	−	0.675779i	$-0.763807\pi$
$401$	2.49101	−	23.7003i	0.124395	−	1.18354i	0.861499	−	0.507759i	$-0.169526\pi$
$402$	15.4624	+	6.88431i	0.771195	+	0.343358i
$403$	−5.74033	+	4.17059i	−0.285946	+	0.207752i
$404$	0.480171	+	4.56853i	0.0238894	+	0.227293i
$405$	−1.45390	+	13.8329i	−0.0722448	+	0.687363i
$406$	2.27687	−	1.01373i	0.112999	−	0.0503105i
$407$	−8.85304	+	15.3339i	−0.438829	+	0.760074i
$408$	18.8015	+	8.37096i	0.930812	+	0.414424i
$409$	−8.43569	+	6.12889i	−0.417118	+	0.303054i	−0.776477	−	0.630145i	$-0.782995\pi$
$409$	−8.43569	+	6.12889i	−0.417118	+	0.303054i	0.359359	+	0.933199i	$0.382995\pi$
$410$	11.7898	+	13.0939i	0.582257	+	0.646662i
$411$	−12.5979	−	13.9913i	−0.621406	−	0.690141i
$412$	10.4979	+	7.62720i	0.517196	+	0.375765i
$413$	−2.69308	+	2.99096i	−0.132518	+	0.147176i
$414$	−42.9053	−	9.11979i	−2.10868	−	0.448213i
$415$	6.16724	+	10.6820i	0.302738	+	0.524357i
$416$	0.442896	−	4.21387i	0.0217147	−	0.206602i
$417$	−37.2034	−	7.90782i	−1.82186	−	0.387248i
$418$	0.286717	+	2.72793i	0.0140238	+	0.133428i
$419$	1.22958	+	1.36559i	0.0600690	+	0.0667134i	0.772430	−	0.635100i	$-0.219041\pi$
$419$	1.22958	+	1.36559i	0.0600690	+	0.0667134i	−0.712361	+	0.701813i	$0.752374\pi$
$420$	−1.57059	−	2.72034i	−0.0766368	−	0.132739i
$421$	10.5232	−	18.2267i	0.512868	−	0.888314i	−0.487020	−	0.873391i	$-0.661916\pi$
$421$	10.5232	−	18.2267i	0.512868	−	0.888314i	0.999889	−	0.0149234i	$-0.00475044\pi$
$422$	4.86689	−	1.03449i	0.236917	−	0.0503582i
$423$	−37.8379	−	42.0232i	−1.83974	−	2.04324i
$424$	−30.6979	+	22.3033i	−1.49082	+	1.08315i
$425$	1.74942	+	5.38417i	0.0848594	+	0.261170i
$426$	−2.17825	+	6.70398i	−0.105537	+	0.324809i
$427$	−1.20752	−	0.877316i	−0.0584361	−	0.0424563i
$428$	−1.43320	−	13.6360i	−0.0692762	−	0.659119i
$429$	−4.06841	−	2.95587i	−0.196425	−	0.142711i
$430$	2.24002	+	3.87983i	0.108023	+	0.187102i
$431$	4.04835	+	38.5175i	0.195002	+	1.85532i	0.455995	+	0.889982i	$0.349283\pi$
$431$	4.04835	+	38.5175i	0.195002	+	1.85532i	−0.260993	+	0.965341i	$0.584050\pi$
$432$	3.92850	−	0.835028i	0.189010	−	0.0401753i
$433$	−3.38899	−	10.4302i	−0.162864	−	0.501245i	0.836008	−	0.548717i	$-0.184884\pi$
$433$	−3.38899	−	10.4302i	−0.162864	−	0.501245i	−0.998873	+	0.0474720i	$0.984884\pi$
$434$	4.85614			0.233102
$435$	−15.0177	+	16.6789i	−0.720045	+	0.799691i
$436$	4.10074	−	0.871640i	0.196390	−	0.0417440i
$437$	−5.42030	−	9.38824i	−0.259288	−	0.449100i
$438$	−37.8966	+	8.05518i	−1.81077	+	0.384891i
$439$	12.3299	+	2.62080i	0.588473	+	0.125084i	0.492519	−	0.870302i	$-0.336076\pi$
$439$	12.3299	+	2.62080i	0.588473	+	0.125084i	0.0959547	+	0.995386i	$0.469410\pi$
$440$	9.22155	−	4.10570i	0.439620	−	0.195732i
$441$	−36.3044	+	16.1638i	−1.72878	+	0.769703i
$442$	1.56976	+	0.698904i	0.0746661	+	0.0332435i
$443$	0.686828	+	0.145990i	0.0326322	+	0.00693619i	0.224199	−	0.974543i	$-0.428023\pi$
$443$	0.686828	+	0.145990i	0.0326322	+	0.00693619i	−0.191567	+	0.981480i	$0.561357\pi$
$444$	8.63859	+	26.5868i	0.409969	+	1.26176i
$445$	0.686613			0.0325486
$446$	−9.59680	+	10.6583i	−0.454421	+	0.504686i
$447$	−4.40780	+	41.9374i	−0.208482	+	1.98357i
$448$	−2.28943	+	2.54267i	−0.108166	+	0.120130i
$449$	−2.34165	+	4.05586i	−0.110509	+	0.191408i	−0.915976	−	0.401234i	$-0.868582\pi$
$449$	−2.34165	+	4.05586i	−0.110509	+	0.191408i	0.805466	+	0.592642i	$0.201915\pi$
$450$	10.7878	+	7.83779i	0.508541	+	0.369477i
$451$	12.5950	+	21.8152i	0.593075	+	1.02724i
$452$	3.05831			0.143851
$453$	−6.39702	−	36.2193i	−0.300558	−	1.70173i
$454$	9.57692			0.449467
$455$	−0.362760	−	0.628319i	−0.0170064	−	0.0294560i
$456$	9.69237	+	7.04192i	0.453887	+	0.329768i
$457$	−14.1643	+	24.5333i	−0.662579	+	1.14762i	0.317357	+	0.948306i	$0.397205\pi$
$457$	−14.1643	+	24.5333i	−0.662579	+	1.14762i	−0.979936	+	0.199314i	$0.936129\pi$
$458$	0.887127	−	0.985255i	0.0414527	−	0.0460379i
$459$	2.18143	−	20.7549i	0.101820	−	0.968757i
$460$	−9.64949	+	10.7168i	−0.449910	+	0.499675i
$461$	−17.0518			−0.794182			−0.397091	−	0.917779i	$-0.629980\pi$
$461$	−17.0518			−0.794182			−0.397091	+	0.917779i	$0.629980\pi$
$462$	1.06356	+	3.27330i	0.0494813	+	0.152288i
$463$	18.6521	+	3.96463i	0.866837	+	0.184252i	0.619805	−	0.784756i	$-0.287212\pi$
$463$	18.6521	+	3.96463i	0.866837	+	0.184252i	0.247032	+	0.969007i	$0.420545\pi$
$464$	1.92756	+	0.858204i	0.0894847	+	0.0398411i
$465$	−39.9490	+	17.7864i	−1.85259	+	0.824827i
$466$	0.799483	−	0.355953i	0.0370353	−	0.0164892i
$467$	−37.8980	−	8.05547i	−1.75371	−	0.372763i	−0.784718	−	0.619853i	$-0.787192\pi$
$467$	−37.8980	−	8.05547i	−1.75371	−	0.372763i	−0.968992	+	0.247091i	$0.920525\pi$
$468$	−5.16554	+	1.09797i	−0.238777	+	0.0507537i
$469$	1.74554	+	3.02337i	0.0806018	+	0.139606i
$470$	13.9368	−	2.96236i	0.642856	−	0.136643i
$471$	−41.9803	+	46.6239i	−1.93435	+	2.14831i
$472$	−20.4201			−0.939911
$473$	1.97923	+	6.09145i	0.0910051	+	0.280085i
$474$	2.29196	−	0.487171i	0.105273	−	0.0223765i
$475$	0.344474	+	3.27746i	0.0158056	+	0.150380i
$476$	0.767239	+	1.32890i	0.0351664	+	0.0609099i
$477$	62.6910	+	45.5477i	2.87042	+	2.08548i
$478$	0.401837	+	3.82323i	0.0183796	+	0.174870i
$479$	1.61667	+	1.17458i	0.0738673	+	0.0536678i	0.624106	−	0.781340i	$-0.285463\pi$
$479$	1.61667	+	1.17458i	0.0738673	+	0.0536678i	−0.550239	+	0.835007i	$0.685463\pi$
$480$	8.06949	−	24.8353i	0.368320	−	1.13357i
$481$	1.99526	+	6.14078i	0.0909761	+	0.279996i
$482$	−19.9061	+	14.4626i	−0.906699	+	0.658755i
$483$	−9.10174	−	10.1085i	−0.414144	−	0.459953i
$484$	−7.07990	+	1.50488i	−0.321814	+	0.0684036i
$485$	8.65607	−	14.9928i	0.393052	−	0.680786i
$486$	0.343197	+	0.594435i	0.0155677	+	0.0269641i
$487$	−10.7151	−	11.9003i	−0.485547	−	0.539254i	0.449733	−	0.893163i	$-0.351519\pi$
$487$	−10.7151	−	11.9003i	−0.485547	−	0.539254i	−0.935280	+	0.353908i	$0.884852\pi$
$488$	−0.791574	−	7.53133i	−0.0358329	−	0.340927i
$489$	4.39279	+	0.933717i	0.198649	+	0.0422241i
$490$	1.04666	−	9.95832i	0.0472833	−	0.449871i
$491$	−20.8831	−	36.1706i	−0.942442	−	1.63236i	−0.760793	−	0.648995i	$-0.775190\pi$
$491$	−20.8831	−	36.1706i	−0.942442	−	1.63236i	−0.181650	−	0.983363i	$-0.558144\pi$
$492$	38.9019	+	8.26885i	1.75383	+	0.372788i
$493$	7.33623	−	8.14771i	0.330407	−	0.366954i
$494$	0.809230	+	0.587940i	0.0364090	+	0.0264527i
$495$	−13.7937	−	15.3195i	−0.619981	−	0.688559i
$496$	2.75088	+	3.05516i	0.123518	+	0.137181i
$497$	−1.17624	+	0.854592i	−0.0527618	+	0.0383337i
$498$	−19.4929	−	8.67879i	−0.873497	−	0.388906i
$499$	3.83000	−	6.63376i	0.171455	−	0.296968i	−0.767474	−	0.641080i	$-0.778487\pi$
$499$	3.83000	−	6.63376i	0.171455	−	0.296968i	0.938929	+	0.344112i	$0.111820\pi$
$500$	12.3405	−	5.49434i	0.551884	−	0.245714i
$501$	6.82202	−	64.9072i	0.304785	−	2.89984i
$502$	0.0606998	+	0.577520i	0.00270916	+	0.0257760i
$503$	16.1436	−	11.7290i	0.719808	−	0.522971i	−0.166515	−	0.986039i	$-0.553251\pi$
$503$	16.1436	−	11.7290i	0.719808	−	0.522971i	0.886323	+	0.463068i	$0.153251\pi$
$504$	9.13417	+	4.06679i	0.406868	+	0.181149i
$505$	−0.683518	+	6.50324i	−0.0304162	+	0.289391i
$506$	12.7832	−	9.28751i	0.568281	−	0.412880i
$507$	36.2663	−	7.70865i	1.61064	−	0.342353i
$508$	−0.899997	+	0.400705i	−0.0399309	+	0.0177784i
$509$	−5.75629	+	6.39300i	−0.255143	+	0.283365i	−0.857085	−	0.515175i	$-0.827727\pi$
$509$	−5.75629	+	6.39300i	−0.255143	+	0.283365i	0.601942	+	0.798540i	$0.294394\pi$
$510$	8.56759	+	6.22472i	0.379379	+	0.275635i
$511$	−7.30029	−	3.25030i	−0.322946	−	0.143785i
$512$	−5.10156			−0.225459
$513$	3.75404	−	11.5538i	0.165745	−	0.510111i
$514$	−0.546277	−	5.19748i	−0.0240952	−	0.229251i
$515$	12.3598	+	13.7269i	0.544637	+	0.604881i
$516$	9.23810	+	4.11307i	0.406685	+	0.181068i
$517$	20.3700			0.895870
$518$	1.36556	−	4.20277i	0.0599994	−	0.184659i
$519$	34.6207	−	59.9647i	1.51968	−	2.63216i
$520$	1.13750	−	3.50087i	0.0498827	−	0.153523i
$521$	8.86750	−	27.2914i	0.388492	−	1.19566i	−0.545423	−	0.838161i	$-0.683631\pi$
$521$	8.86750	−	27.2914i	0.388492	−	1.19566i	0.933915	−	0.357495i	$-0.116369\pi$
$522$	2.69935	−	25.6826i	0.118147	−	1.12410i
$523$	−34.6640	+	25.1849i	−1.51575	+	1.10126i	−0.552206	+	0.833708i	$0.686214\pi$
$523$	−34.6640	+	25.1849i	−1.51575	+	1.10126i	−0.963544	+	0.267549i	$0.913786\pi$
$524$	0.791000	+	0.168132i	0.0345550	+	0.00734490i
$525$	1.27781	+	3.93268i	0.0557680	+	0.171636i
$526$	−5.65298	−	17.3981i	−0.246482	−	0.758593i
$527$	19.5153	−	8.68876i	0.850099	−	0.378488i
$528$	−1.45686	+	2.52336i	−0.0634018	+	0.109815i
$529$	−19.7237	+	34.1625i	−0.857553	+	1.48533i
$530$	−17.8369	+	7.94152i	−0.774787	+	0.344957i
$531$	12.8865	+	39.6607i	0.559228	+	1.72113i
$532$	0.276028	+	0.849528i	0.0119673	+	0.0368317i
$533$	8.98520	+	1.90986i	0.389192	+	0.0827253i
$534$	−0.960938	+	0.698162i	−0.0415838	+	0.0302124i
$535$	2.04014	−	19.4106i	0.0882029	−	0.839194i
$536$	−5.47348	+	16.8456i	−0.236418	+	0.727620i
$537$	4.56375	−	14.0458i	0.196940	−	0.606120i
$538$	3.13893	−	5.43679i	0.135329	−	0.234397i
$539$	4.42370	−	13.6148i	0.190542	−	0.586429i
$540$	−16.1606			−0.695440
$541$	−22.2389	−	9.90140i	−0.956125	−	0.425694i	−0.131464	−	0.991321i	$-0.541968\pi$
$541$	−22.2389	−	9.90140i	−0.956125	−	0.425694i	−0.824661	+	0.565627i	$0.808634\pi$
$542$	2.57585	+	2.86077i	0.110642	+	0.122881i
$543$	6.68411	+	63.5951i	0.286843	+	2.72913i
$544$	−3.94198	+	12.1322i	−0.169011	+	0.520163i
$545$	5.96777			0.255631
$546$	1.14658	+	0.510491i	0.0490691	+	0.0218470i
$547$	13.9571	+	10.1404i	0.596762	+	0.433573i	0.844728	−	0.535196i	$-0.179762\pi$
$547$	13.9571	+	10.1404i	0.596762	+	0.433573i	−0.247966	+	0.968769i	$0.579762\pi$
$548$	4.76558	−	5.29271i	0.203575	−	0.226093i
$549$	−14.1281	+	6.29023i	−0.602973	+	0.268461i
$550$	−4.69844	+	0.998684i	−0.200342	+	0.0425840i
$551$	5.16333	−	3.75138i	0.219965	−	0.159814i
$552$	7.21387	−	68.6354i	0.307043	−	2.92132i
$553$	0.441516	+	0.196576i	0.0187752	+	0.00835925i
$554$	11.1589	−	8.10740i	0.474095	−	0.344450i
$555$	4.15957	+	39.5757i	0.176564	+	1.67990i
$556$	1.50394	−	14.3091i	0.0637814	−	0.606839i
$557$	−5.14277	+	2.28971i	−0.217906	+	0.0970181i	−0.512787	−	0.858516i	$-0.671387\pi$
$557$	−5.14277	+	2.28971i	−0.217906	+	0.0970181i	0.294880	+	0.955534i	$0.404720\pi$
$558$	25.1581	−	43.5751i	1.06503	−	1.84468i
$559$	2.13373	+	0.949998i	0.0902472	+	0.0401806i
$560$	−0.340085	+	0.247086i	−0.0143712	+	0.0104413i
$561$	10.1308	+	11.2514i	0.427723	+	0.475034i
$562$	10.2575	+	11.3921i	0.432687	+	0.480548i
$563$	−18.9200	−	13.7462i	−0.797385	−	0.579334i	0.112761	−	0.993622i	$-0.464031\pi$
$563$	−18.9200	−	13.7462i	−0.797385	−	0.579334i	−0.910146	+	0.414288i	$0.864031\pi$
$564$	21.5198	−	23.9002i	0.906149	−	1.00638i
$565$	4.25833	+	0.905136i	0.179149	+	0.0380794i
$566$	−5.49931	−	9.52509i	−0.231153	−	0.400369i
$567$	0.518768	−	4.93575i	0.0217862	−	0.207282i
$568$	−7.21547	−	1.53369i	−0.302754	−	0.0643524i
$569$	2.81291	+	26.7631i	0.117924	+	1.12197i	0.880163	+	0.474672i	$0.157433\pi$
$569$	2.81291	+	26.7631i	0.117924	+	1.12197i	−0.762239	+	0.647295i	$0.775900\pi$
$570$	4.12498	+	4.58126i	0.172777	+	0.191888i
$571$	12.6705	+	21.9459i	0.530243	+	0.918408i	0.999377	+	0.0352810i	$0.0112326\pi$
$571$	12.6705	+	21.9459i	0.530243	+	0.918408i	−0.469134	+	0.883127i	$0.655434\pi$
$572$	0.951165	−	1.64747i	0.0397702	−	0.0688841i
$573$	−35.7581	+	7.60062i	−1.49382	+	0.317520i
$574$	−4.20674	−	4.67206i	−0.175586	−	0.195008i
$575$	15.3582	−	11.1584i	0.640483	−	0.465338i
$576$	10.9551	+	33.7163i	0.456462	+	1.40485i
$577$	−7.75036	+	23.8532i	−0.322652	+	0.993020i	0.649838	+	0.760073i	$0.274837\pi$
$577$	−7.75036	+	23.8532i	−0.322652	+	0.993020i	−0.972489	+	0.232947i	$0.925163\pi$
$578$	8.62633	+	6.26740i	0.358808	+	0.260689i
$579$	7.06364	+	67.2061i	0.293555	+	2.79299i
$580$	−6.86862	−	4.99035i	−0.285204	−	0.207213i
$581$	−2.20054	−	3.81145i	−0.0912939	−	0.158126i
$582$	3.13048	+	29.7845i	0.129763	+	1.23461i
$583$	−27.3040	+	5.80364i	−1.13082	+	0.240362i
$584$	−12.5289	−	38.5600i	−0.518449	−	1.59562i
$585$	−7.51736			−0.310805
$586$	2.44123	−	2.71126i	0.100846	−	0.112001i
$587$	5.47725	−	1.16422i	0.226070	−	0.0480527i	−0.0934837	−	0.995621i	$-0.529800\pi$
$587$	5.47725	−	1.16422i	0.226070	−	0.0480527i	0.319554	+	0.947568i	$0.396467\pi$
$588$	−11.3009	−	19.5737i	−0.466040	−	0.807205i
$589$	12.1635	−	2.58544i	0.501189	−	0.106531i
$590$	−10.2778	−	2.18462i	−0.423131	−	0.0899393i
$591$	40.2132	−	17.9041i	1.65415	−	0.736476i
$592$	3.41766	−	1.52164i	0.140465	−	0.0625390i
$593$	−10.4137	−	4.63648i	−0.427640	−	0.190398i	0.181619	−	0.983369i	$-0.441866\pi$
$593$	−10.4137	−	4.63648i	−0.427640	−	0.190398i	−0.609259	+	0.792971i	$0.708533\pi$
$594$	17.3200	+	3.68148i	0.710649	+	0.151053i
$595$	0.674990	+	2.07741i	0.0276719	+	0.0851653i
$596$	−15.9517			−0.653406
$597$	25.5722	−	28.4008i	1.04660	−	1.16237i
$598$	0.602297	−	5.73047i	0.0246297	−	0.234336i
$599$	2.25376	−	2.50305i	0.0920862	−	0.102272i	−0.695340	−	0.718681i	$-0.744746\pi$
$599$	2.25376	−	2.50305i	0.0920862	−	0.102272i	0.787426	+	0.616409i	$0.211413\pi$
$600$	−10.4899	+	18.1691i	−0.428250	+	0.741750i
$601$	24.1168	+	17.5219i	0.983743	+	0.714731i	0.958542	−	0.284951i	$-0.0919774\pi$
$601$	24.1168	+	17.5219i	0.983743	+	0.714731i	0.0252012	+	0.999682i	$0.491977\pi$
$602$	−0.799266	−	1.38437i	−0.0325757	−	0.0564227i
$603$	36.1724			1.47305
$604$	13.3732	−	3.83881i	0.544148	−	0.156199i
$605$	−10.3033			−0.418889
$606$	−5.65602	−	9.79652i	−0.229760	−	0.397956i
$607$	25.8239	+	18.7621i	1.04816	+	0.761532i	0.971862	−	0.235553i	$-0.0756901\pi$
$607$	25.8239	+	18.7621i	1.04816	+	0.761532i	0.0762976	+	0.997085i	$0.475690\pi$
$608$	−3.71290	+	6.43093i	−0.150578	+	0.260808i
$609$	5.35850	−	5.95122i	0.217137	−	0.241156i
$610$	0.407315	−	3.87535i	0.0164917	−	0.156908i
$611$	4.97046	−	5.52025i	0.201083	−	0.223325i
$612$	15.8993			0.642690
$613$	−3.01715	−	9.28583i	−0.121862	−	0.375051i	0.871455	−	0.490476i	$-0.163177\pi$
$613$	−3.01715	−	9.28583i	−0.121862	−	0.375051i	−0.993316	+	0.115425i	$0.963177\pi$
$614$	15.3917	+	3.27161i	0.621158	+	0.132031i
$615$	51.7190	+	23.0268i	2.08551	+	0.928530i
$616$	−3.29036	+	1.46496i	−0.132572	+	0.0590250i
$617$	−38.6383	+	17.2029i	−1.55552	+	0.692563i	−0.991124	−	0.132941i	$-0.957558\pi$
$617$	−38.6383	+	17.2029i	−1.55552	+	0.692563i	−0.564397	+	0.825503i	$0.690891\pi$
$618$	−31.2558	−	6.64362i	−1.25729	−	0.267245i
$619$	−16.4566	+	3.49797i	−0.661449	+	0.140595i	−0.526391	−	0.850243i	$-0.676455\pi$
$619$	−16.4566	+	3.49797i	−0.661449	+	0.140595i	−0.135057	+	0.990838i	$0.543122\pi$
$620$	−8.27113	−	14.3260i	−0.332176	−	0.575347i
$621$	−68.4515	+	14.5498i	−2.74686	+	0.583864i
$622$	4.85309	−	5.38990i	0.194591	−	0.216115i
$623$	−0.244992			−0.00981538
$624$	0.328342	+	1.01053i	0.0131442	+	0.0404536i
$625$	7.05979	−	1.50060i	0.282391	−	0.0600241i
$626$	−3.04149	−	28.9378i	−0.121562	−	1.15659i
$627$	4.40670	+	7.63262i	0.175987	+	0.304818i
$628$	−19.2004	−	13.9499i	−0.766181	−	0.556663i
$629$	−2.03197	−	19.3329i	−0.0810200	−	0.770854i
$630$	4.16232	+	3.02410i	0.165831	+	0.120483i
$631$	−0.383178	+	1.17930i	−0.0152541	+	0.0469472i	−0.958394	−	0.285449i	$-0.907857\pi$
$631$	−0.383178	+	1.17930i	−0.0152541	+	0.0469472i	0.943140	+	0.332396i	$0.107857\pi$
$632$	0.757737	+	2.33208i	0.0301412	+	0.0927650i
$633$	12.9339	−	9.39702i	0.514076	−	0.373498i
$634$	8.68518	+	9.64587i	0.344932	+	0.383086i
$635$	−1.37173	+	0.291571i	−0.0544355	+	0.0115706i
$636$	−22.0359	+	38.1672i	−0.873779	+	1.51343i
$637$	−2.61017	−	4.52095i	−0.103419	−	0.179126i
$638$	6.22458	+	6.91310i	0.246434	+	0.273692i
$639$	1.57467	+	14.9820i	0.0622932	+	0.592680i
$640$	8.33037	+	1.77067i	0.329287	+	0.0699921i
$641$	2.90453	−	27.6348i	0.114722	−	1.09151i	−0.774039	−	0.633138i	$-0.781767\pi$
$641$	2.90453	−	27.6348i	0.114722	−	1.09151i	0.888761	−	0.458370i	$-0.151567\pi$
$642$	16.8819	+	29.2403i	0.666274	+	1.15402i
$643$	−39.8631	−	8.47317i	−1.57205	−	0.334149i	−0.662278	−	0.749259i	$-0.730410\pi$
$643$	−39.8631	−	8.47317i	−1.57205	−	0.334149i	−0.909772	+	0.415109i	$0.863743\pi$
$644$	3.44305	−	3.82389i	0.135675	−	0.150683i
$645$	11.6457	+	8.46106i	0.458547	+	0.333154i
$646$	−2.01507	−	2.23797i	−0.0792820	−	0.0880516i
$647$	23.2625	+	25.8356i	0.914543	+	1.01570i	0.999813	+	0.0193451i	$0.00615812\pi$
$647$	23.2625	+	25.8356i	0.914543	+	1.01570i	−0.0852698	+	0.996358i	$0.527175\pi$
$648$	20.3712	−	14.8005i	0.800256	−	0.581420i
$649$	−13.7233	−	6.11001i	−0.538687	−	0.239839i
$650$	−0.875820	+	1.51696i	−0.0343525	+	0.0595002i
$651$	14.2543	−	6.34641i	0.558669	−	0.248736i
$652$	−0.177578	+	1.68954i	−0.00695450	+	0.0661677i
$653$	0.723875	+	6.88721i	0.0283274	+	0.269517i	0.999513	+	0.0311943i	$0.00993106\pi$
$653$	0.723875	+	6.88721i	0.0283274	+	0.269517i	−0.971186	+	0.238323i	$0.923402\pi$
$654$	−8.35209	+	6.06815i	−0.326592	+	0.237283i
$655$	1.05161	+	0.468209i	0.0410900	+	0.0182944i
$656$	0.556338	−	5.29320i	0.0217213	−	0.206665i
$657$	−66.9860	+	48.6682i	−2.61337	+	1.89873i
$658$	−4.97281	+	1.05700i	−0.193860	+	0.0412063i
$659$	−3.74702	+	1.66828i	−0.145963	+	0.0649870i	−0.478418	−	0.878132i	$-0.658790\pi$
$659$	−3.74702	+	1.66828i	−0.145963	+	0.0649870i	0.332455	+	0.943119i	$0.392123\pi$
$660$	7.84502	−	8.71277i	0.305367	−	0.339144i
$661$	−7.39191	−	5.37054i	−0.287512	−	0.208890i	0.434675	−	0.900587i	$-0.356863\pi$
$661$	−7.39191	−	5.37054i	−0.287512	−	0.208890i	−0.722187	+	0.691698i	$0.756863\pi$
$662$	−7.22530	−	3.21691i	−0.280819	−	0.125029i
$663$	5.52113			0.214423
$664$	6.90021	−	21.2367i	0.267780	−	0.824142i
$665$	0.132911	+	1.26456i	0.00515405	+	0.0490375i
$666$	−30.6377	−	34.0267i	−1.18719	−	1.31851i
$667$	−33.5864	−	14.9536i	−1.30047	−	0.579007i
$668$	24.6886			0.955232
$669$	−14.2404	+	43.8274i	−0.550565	+	1.69446i
$670$	−4.55711	+	7.89315i	−0.176057	+	0.304939i
$671$	1.72151	−	5.29827i	0.0664583	−	0.204538i
$672$	−2.87929	+	8.86154i	−0.111071	+	0.341841i
$673$	2.79285	−	26.5722i	0.107656	−	1.02428i	−0.798689	−	0.601744i	$-0.794473\pi$
$673$	2.79285	−	26.5722i	0.107656	−	1.02428i	0.906345	−	0.422538i	$-0.138861\pi$
$674$	−23.9524	+	17.4024i	−0.922612	+	0.670317i
$675$	20.8090	+	4.42309i	0.800940	+	0.170245i
$676$	4.33411	+	13.3390i	0.166697	+	0.513040i
$677$	2.92730	+	9.00932i	0.112505	+	0.346256i	0.991419	−	0.130726i	$-0.0417307\pi$
$677$	2.92730	+	9.00932i	0.112505	+	0.346256i	−0.878913	+	0.476982i	$0.841731\pi$
$678$	−6.88003	+	3.06319i	−0.264226	+	0.117641i
$679$	−3.08859	+	5.34959i	−0.118529	+	0.205299i
$680$	−5.54121	+	9.59766i	−0.212496	+	0.368054i
$681$	28.1112	−	12.5159i	1.07723	−	0.479611i
$682$	5.60098	+	17.2381i	0.214473	+	0.660079i
$683$	−9.01227	−	27.7369i	−0.344845	−	1.06132i	−0.961667	−	0.274221i	$-0.911580\pi$
$683$	−9.01227	−	27.7369i	−0.344845	−	1.06132i	0.616822	−	0.787103i	$-0.288420\pi$
$684$	9.05299	+	1.92427i	0.346150	+	0.0735764i
$685$	8.20193	−	5.95905i	0.313380	−	0.227684i
$686$	−0.765442	+	7.28269i	−0.0292247	+	0.278055i
$687$	1.31638	−	4.05140i	0.0502230	−	0.154571i
$688$	0.418189	−	1.28705i	0.0159433	−	0.0490685i
$689$	−5.08964	+	8.81552i	−0.193900	+	0.335844i
$690$	10.9737	−	33.7737i	0.417763	−	1.28574i
$691$	5.92932			0.225562			0.112781	−	0.993620i	$-0.464024\pi$
$691$	5.92932			0.225562			0.112781	+	0.993620i	$0.464024\pi$
$692$	23.9284	+	10.6536i	0.909623	+	0.404990i
$693$	4.92176	+	5.46617i	0.186962	+	0.207643i
$694$	−2.14538	−	20.4120i	−0.0814377	−	0.774827i
$695$	6.32897	−	19.4786i	0.240071	−	0.738864i
$696$	40.6305			1.54010
$697$	−25.2650	−	11.2487i	−0.956979	−	0.426075i
$698$	−9.41977	−	6.84386i	−0.356543	−	0.259044i
$699$	1.88154	−	2.08966i	0.0711665	−	0.0790384i
$700$	−1.42900	+	0.636231i	−0.0540110	+	0.0240473i
$701$	27.9911	−	5.94968i	1.05721	−	0.224716i	0.353667	−	0.935371i	$-0.384935\pi$
$701$	27.9911	−	5.94968i	1.05721	−	0.224716i	0.703541	+	0.710655i	$0.251601\pi$
$702$	5.22393	−	3.79540i	0.197164	−	0.143248i
$703$	1.18285	−	11.2540i	0.0446119	−	0.424454i
$704$	−11.6664	−	5.19423i	−0.439695	−	0.195765i
$705$	37.0373	−	26.9092i	1.39491	−	1.01346i
$706$	−2.39114	−	22.7502i	−0.0899918	−	0.856215i
$707$	0.243887	−	2.32043i	0.00917233	−	0.0872689i
$708$	−21.6669	+	9.64673i	−0.814292	+	0.362546i
$709$	−8.37861	+	14.5122i	−0.314665	+	0.545016i	−0.979366	−	0.202093i	$-0.935226\pi$
$709$	−8.37861	+	14.5122i	−0.314665	+	0.545016i	0.664701	+	0.747109i	$0.268559\pi$
$710$	−3.46760	−	1.54388i	−0.130137	−	0.0579406i
$711$	4.05126	−	2.94341i	0.151934	−	0.110387i
$712$	−0.831730	−	0.923730i	−0.0311704	−	0.0346182i
$713$	−47.9322	−	53.2341i	−1.79507	−	1.99363i
$714$	−3.05702	−	2.22105i	−0.114406	−	0.0831208i
$715$	1.81197	−	2.01240i	0.0677638	−	0.0752594i
$716$	5.46466	+	1.16155i	0.204224	+	0.0434091i
$717$	6.17603	+	10.6972i	0.230648	+	0.399494i
$718$	−1.23827	+	11.7813i	−0.0462117	+	0.439675i
$719$	−24.8372	−	5.27932i	−0.926273	−	0.196885i	−0.280007	−	0.959998i	$-0.590337\pi$
$719$	−24.8372	−	5.27932i	−0.926273	−	0.196885i	−0.646266	+	0.763112i	$0.723670\pi$
$720$	0.455283	+	4.33173i	0.0169674	+	0.161434i
$721$	−4.41012	−	4.89793i	−0.164241	−	0.182409i
$722$	7.97305	+	13.8097i	0.296726	+	0.513945i
$723$	−39.5296	+	68.4674i	−1.47012	+	2.54633i
$724$	−23.6610	+	5.02929i	−0.879352	+	0.186912i
$725$	7.47848	+	8.30569i	0.277744	+	0.308466i
$726$	14.4198	−	10.4766i	0.535170	−	0.388824i
$727$	2.63915	+	8.12246i	0.0978806	+	0.301245i	0.987994	−	0.154494i	$-0.0493748\pi$
$727$	2.63915	+	8.12246i	0.0978806	+	0.301245i	−0.890113	+	0.455740i	$0.849375\pi$
$728$	−0.405874	+	1.24915i	−0.0150427	+	0.0462966i
$729$	22.7294	+	16.5139i	0.841830	+	0.611625i
$730$	−2.18074	−	20.7483i	−0.0807128	−	0.767931i
$731$	−5.68896	−	4.13327i	−0.210414	−	0.152874i
$732$	−4.39781	−	7.61723i	−0.162548	−	0.281541i
$733$	−3.15225	−	29.9916i	−0.116431	−	1.10777i	−0.884222	−	0.467066i	$-0.845311\pi$
$733$	−3.15225	−	29.9916i	−0.116431	−	1.10777i	0.767791	−	0.640700i	$-0.221356\pi$
$734$	7.37141	−	1.56684i	0.272084	−	0.0578332i
$735$	−9.94210	−	30.5986i	−0.366720	−	1.12865i
$736$	42.7764			1.57676
$737$	−8.71892	+	9.68334i	−0.321165	+	0.356690i
$738$	−63.7171	+	13.5435i	−2.34546	+	0.498543i
$739$	20.0643	+	34.7524i	0.738077	+	1.27839i	0.953360	+	0.301836i	$0.0975994\pi$
$739$	20.0643	+	34.7524i	0.738077	+	1.27839i	−0.215283	+	0.976552i	$0.569067\pi$
$740$	−14.7244	+	3.12977i	−0.541280	+	0.115053i
$741$	3.14371	+	0.668217i	0.115487	+	0.0245476i
$742$	6.36443	−	2.83363i	0.233646	−	0.104026i
$743$	25.3469	−	11.2852i	0.929888	−	0.414013i	0.114825	−	0.993386i	$-0.463369\pi$
$743$	25.3469	−	11.2852i	0.929888	−	0.414013i	0.815063	+	0.579373i	$0.196703\pi$
$744$	72.3211	+	32.1994i	2.65142	+	1.18049i
$745$	−22.2108	−	4.72106i	−0.813742	−	0.172966i
$746$	−5.37325	−	16.5372i	−0.196729	−	0.605468i
$747$	−45.6012			−1.66846
$748$	−3.83233	+	4.25623i	−0.140124	+	0.155623i
$749$	−0.727946	+	6.92594i	−0.0265986	+	0.253068i
$750$	−22.2583	+	24.7204i	−0.812759	+	0.902661i
$751$	−6.42492	+	11.1283i	−0.234449	+	0.406077i	−0.959112	−	0.283026i	$-0.908662\pi$
$751$	−6.42492	+	11.1283i	−0.234449	+	0.406077i	0.724664	+	0.689103i	$0.241995\pi$
$752$	−3.48196	−	2.52979i	−0.126974	−	0.0922521i
$753$	0.932924	+	1.61587i	0.0339977	+	0.0588857i
$754$	3.39230			0.123540
$755$	19.7568	−	1.38715i	0.719022	−	0.0504835i
$756$	5.76628			0.209718
$757$	8.73861	+	15.1357i	0.317610	+	0.550117i	0.979989	−	0.199052i	$-0.0637863\pi$
$757$	8.73861	+	15.1357i	0.317610	+	0.550117i	−0.662379	+	0.749169i	$0.730453\pi$
$758$	15.5103	+	11.2689i	0.563359	+	0.409304i
$759$	25.3848	−	43.9678i	0.921411	−	1.59593i
$760$	−4.31674	+	4.79423i	−0.156585	+	0.173905i
$761$	−2.08596	+	19.8466i	−0.0756160	+	0.719438i	0.889379	+	0.457170i	$0.151137\pi$
$761$	−2.08596	+	19.8466i	−0.0756160	+	0.719438i	−0.964995	+	0.262268i	$0.915530\pi$
$762$	1.62331	−	1.80287i	0.0588063	−	0.0653110i
$763$	−2.12937			−0.0770884
$764$	−4.27338	−	13.1521i	−0.154605	−	0.475826i
$765$	22.1379	+	4.70555i	0.800396	+	0.170129i
$766$	−1.37623	−	0.612737i	−0.0497252	−	0.0221391i
$767$	−5.00442	+	2.22811i	−0.180699	+	0.0804525i
$768$	−45.9952	+	20.4784i	−1.65971	+	0.738950i
$769$	33.3328	+	7.08510i	1.20201	+	0.255495i	0.765042	−	0.643981i	$-0.222718\pi$
$769$	33.3328	+	7.08510i	1.20201	+	0.255495i	0.436970	+	0.899476i	$0.356052\pi$
$770$	−1.81283	+	0.385328i	−0.0653298	+	0.0138863i
$771$	−8.39600	−	14.5423i	−0.302374	−	0.523728i
$772$	−25.0044	+	5.31486i	−0.899930	+	0.191286i
$773$	−2.06428	+	2.29262i	−0.0742472	+	0.0824598i	−0.779124	−	0.626870i	$-0.784336\pi$
$773$	−2.06428	+	2.29262i	−0.0742472	+	0.0824598i	0.704877	+	0.709330i	$0.251002\pi$
$774$	−16.5630			−0.595343
$775$	6.72926	+	20.7105i	0.241722	+	0.743945i
$776$	−30.6559	+	6.51612i	−1.10048	+	0.233915i
$777$	−1.48419	−	14.1211i	−0.0532449	−	0.506591i
$778$	0.159360	+	0.276019i	0.00571332	+	0.00989576i
$779$	−13.0244	−	9.46276i	−0.466646	−	0.339039i
$780$	−0.446903	−	4.25199i	−0.0160017	−	0.152246i
$781$	−4.39024	−	3.18970i	−0.157095	−	0.114136i
$782$	−5.36073	+	16.4986i	−0.191699	+	0.589990i
$783$	−12.7315	−	39.1835i	−0.454987	−	1.40030i
$784$	−2.44702	+	1.77786i	−0.0873936	+	0.0634951i
$785$	−22.6057	−	25.1062i	−0.806833	−	0.896079i
$786$	−1.94785	+	0.414029i	−0.0694776	+	0.0147679i
$787$	5.37960	−	9.31774i	0.191762	−	0.332141i	−0.754072	−	0.656791i	$-0.771913\pi$
$787$	5.37960	−	9.31774i	0.191762	−	0.332141i	0.945834	+	0.324650i	$0.105247\pi$
$788$	8.32584	+	14.4208i	0.296596	+	0.513719i
$789$	−39.3305	−	43.6810i	−1.40020	−	1.55508i
$790$	0.131889	+	1.25484i	0.00469241	+	0.0446453i
$791$	−1.51942	−	0.322963i	−0.0540244	−	0.0114832i
$792$	−3.90089	+	37.1145i	−0.138612	+	1.31881i
$793$	−1.01577	−	1.75936i	−0.0360709	−	0.0624766i
$794$	−17.0889	−	3.63236i	−0.606462	−	0.128908i
$795$	−41.9783	+	46.6216i	−1.48882	+	1.65350i
$796$	11.6959	+	8.49757i	0.414550	+	0.301188i
$797$	5.59732	+	6.21646i	0.198267	+	0.220198i	0.834077	−	0.551647i	$-0.186001\pi$
$797$	5.59732	+	6.21646i	0.198267	+	0.220198i	−0.635810	+	0.771845i	$0.719334\pi$
$798$	−1.47184	−	1.63465i	−0.0521027	−	0.0578659i
$799$	−18.0929	+	13.1453i	−0.640081	+	0.465046i
$800$	−11.8796	−	5.28915i	−0.420009	−	0.187000i
$801$	−1.26922	+	2.19836i	−0.0448458	+	0.0776751i
$802$	−20.2800	+	9.02925i	−0.716113	+	0.318834i
$803$	3.11771	−	29.6630i	0.110022	−	1.04679i
$804$	2.15043	+	20.4599i	0.0758397	+	0.721566i
$805$	5.92576	−	4.30532i	0.208856	−	0.151742i
$806$	6.03820	+	2.68838i	0.212686	+	0.0946941i
$807$	2.10849	−	20.0609i	0.0742222	−	0.706177i
$808$	9.57707	−	6.95815i	0.336920	−	0.244787i
$809$	3.88797	−	0.826413i	0.136694	−	0.0290551i	−0.139057	−	0.990284i	$-0.544407\pi$
$809$	3.88797	−	0.826413i	0.136694	−	0.0290551i	0.275750	+	0.961229i	$0.411074\pi$
$810$	11.8366	−	5.27000i	0.415897	−	0.185169i
$811$	−14.4437	+	16.0414i	−0.507188	+	0.563290i	−0.941301	−	0.337569i	$-0.890395\pi$
$811$	−14.4437	+	16.0414i	−0.507188	+	0.563290i	0.434113	+	0.900859i	$0.357062\pi$
$812$	2.45081	+	1.78061i	0.0860064	+	0.0624873i
$813$	11.2996	+	5.03092i	0.396295	+	0.176442i
$814$	16.4938			0.578107
$815$	−0.747294	+	2.29993i	−0.0261766	+	0.0805632i
$816$	−0.334383	−	3.18144i	−0.0117057	−	0.111373i
$817$	−2.73903	−	3.04200i	−0.0958264	−	0.106426i
$818$	8.87342	+	3.95070i	0.310252	+	0.138133i
$819$	2.68228			0.0937266
$820$	−6.61791	+	20.3678i	−0.231108	+	0.711276i
$821$	4.29725	−	7.44306i	0.149975	−	0.259765i	−0.781243	−	0.624227i	$-0.785414\pi$
$821$	4.29725	−	7.44306i	0.149975	−	0.259765i	0.931218	+	0.364463i	$0.118747\pi$
$822$	−5.41959	+	16.6798i	−0.189030	+	0.581774i
$823$	13.9832	−	43.0359i	0.487424	−	1.50014i	−0.341014	−	0.940058i	$-0.610770\pi$
$823$	13.9832	−	43.0359i	0.487424	−	1.50014i	0.828439	−	0.560080i	$-0.189230\pi$
$824$	3.49538	−	33.2563i	0.121767	−	1.15854i
$825$	−12.4862	+	9.07177i	−0.434714	+	0.315838i
$826$	3.66725	+	0.779498i	0.127600	+	0.0271222i
$827$	2.58736	+	7.96308i	0.0899714	+	0.276903i	0.985911	−	0.167273i	$-0.0534962\pi$
$827$	2.58736	+	7.96308i	0.0899714	+	0.276903i	−0.895939	+	0.444177i	$0.853496\pi$
$828$	−16.4752	−	50.7055i	−0.572553	−	1.76214i
$829$	−16.7968	+	7.47843i	−0.583378	+	0.259736i	−0.677135	−	0.735859i	$-0.736779\pi$
$829$	−16.7968	+	7.47843i	−0.583378	+	0.259736i	0.0937576	+	0.995595i	$0.470112\pi$
$830$	5.74498	−	9.95060i	0.199411	−	0.345390i
$831$	22.1593	−	38.3811i	0.768699	−	1.33143i
$832$	−4.25435	+	1.89416i	−0.147493	+	0.0656682i
$833$	4.85676	+	14.9476i	0.168277	+	0.517903i
$834$	10.9486	+	33.6963i	0.379119	+	1.16681i
$835$	34.3760	+	7.30685i	1.18963	+	0.252864i
$836$	−2.69724	+	1.95966i	−0.0932860	+	0.0677763i
$837$	8.39101	−	79.8351i	0.290036	−	2.75951i
$838$	0.528965	−	1.62799i	0.0182728	−	0.0562379i
$839$	4.49389	−	13.8308i	0.155146	−	0.477491i	−0.843029	−	0.537867i	$-0.819230\pi$
$839$	4.49389	−	13.8308i	0.155146	−	0.477491i	0.998176	+	0.0603764i	$0.0192301\pi$
$840$	−4.04739	+	7.01029i	−0.139648	+	0.241878i
$841$	−2.27290	+	6.99527i	−0.0783759	+	0.241216i
$842$	−19.6054			−0.675646
$843$	44.9972	+	20.0340i	1.54979	+	0.690009i
$844$	4.04670	+	4.49432i	0.139293	+	0.154701i
$845$	2.08692	+	19.8558i	0.0717923	+	0.683059i
$846$	−16.2778	+	50.0980i	−0.559643	+	1.72240i
$847$	3.67634			0.126321
$848$	5.38801	+	2.39890i	0.185025	+	0.0823784i
$849$	−28.5904	−	20.7721i	−0.981219	−	0.712898i
$850$	3.52875	−	3.91908i	0.121035	−	0.134423i
$851$	−59.5504	+	26.5136i	−2.04136	+	0.908873i
$852$	−8.38057	+	1.78134i	−0.287113	+	0.0610279i
$853$	36.3767	−	26.4292i	1.24551	−	0.904919i	0.247562	−	0.968872i	$-0.420371\pi$
$853$	36.3767	−	26.4292i	1.24551	−	0.904919i	0.997953	+	0.0639528i	$0.0203707\pi$
$854$	−0.145335	+	1.38277i	−0.00497326	+	0.0473174i
$855$	12.0357	+	5.35864i	0.411613	+	0.183262i
$856$	−28.5852	+	20.7684i	−0.977024	+	0.709849i
$857$	−4.48200	−	42.6434i	−0.153102	−	1.45667i	−0.753753	−	0.657158i	$-0.771758\pi$
$857$	−4.48200	−	42.6434i	−0.153102	−	1.45667i	0.600650	−	0.799512i	$-0.294908\pi$
$858$	−0.489666	+	4.65886i	−0.0167169	+	0.159051i
$859$	22.7266	−	10.1185i	0.775422	−	0.345240i	0.0194217	−	0.999811i	$-0.493817\pi$
$859$	22.7266	−	10.1185i	0.775422	−	0.345240i	0.756000	+	0.654571i	$0.227151\pi$
$860$	−2.72267	+	4.71580i	−0.0928423	+	0.160808i
$861$	−18.4539	−	8.21623i	−0.628909	−	0.280008i
$862$	29.1877	−	21.2061i	0.994136	−	0.722282i
$863$	35.0240	+	38.8980i	1.19223	+	1.32410i	0.933681	+	0.358106i	$0.116577\pi$
$863$	35.0240	+	38.8980i	1.19223	+	1.32410i	0.258548	+	0.965998i	$0.416756\pi$
$864$	32.0759	+	35.6239i	1.09124	+	1.21195i
$865$	30.1645	+	21.9158i	1.02562	+	0.745159i
$866$	−6.83591	+	7.59205i	−0.232294	+	0.257988i
$867$	33.5117	+	7.12314i	1.13812	+	0.241914i
$868$	2.95124	+	5.11169i	0.100171	+	0.173502i
$869$	−0.188557	+	1.79400i	−0.00639634	+	0.0608571i
$870$	20.4501	+	4.34681i	0.693324	+	0.147371i
$871$	0.496686	+	4.72565i	0.0168296	+	0.160122i
$872$	−7.22906	−	8.02869i	−0.244807	−	0.271886i
$873$	32.0019	+	55.4290i	1.08310	+	1.87599i
$874$	−5.04919	+	8.74545i	−0.170791	+	0.295819i
$875$	−6.71119	+	1.42651i	−0.226880	+	0.0482248i
$876$	−31.5101	−	34.9955i	−1.06463	−	1.18239i
$877$	−11.8967	+	8.64349i	−0.401724	+	0.291870i	−0.770243	−	0.637751i	$-0.779865\pi$
$877$	−11.8967	+	8.64349i	−0.401724	+	0.291870i	0.368519	+	0.929620i	$0.379865\pi$
$878$	−3.62857	−	11.1676i	−0.122458	−	0.376888i
$879$	3.62246	−	11.1488i	0.122182	−	0.376039i
$880$	−1.26934	−	0.922231i	−0.0427895	−	0.0310884i
$881$	2.54476	+	24.2118i	0.0857353	+	0.815717i	0.949910	+	0.312524i	$0.101175\pi$
$881$	2.54476	+	24.2118i	0.0857353	+	0.815717i	−0.864174	+	0.503192i	$0.832159\pi$
$882$	29.9492	+	21.7593i	1.00844	+	0.732675i
$883$	−20.2719	−	35.1120i	−0.682205	−	1.18161i	−0.974306	−	0.225227i	$-0.927688\pi$
$883$	−20.2719	−	35.1120i	−0.682205	−	1.18161i	0.292101	−	0.956387i	$-0.405646\pi$
$884$	0.218314	+	2.07712i	0.00734269	+	0.0698611i
$885$	−33.0237	+	7.01939i	−1.11008	+	0.235954i
$886$	−0.202127	−	0.622083i	−0.00679059	−	0.0208993i
$887$	13.2229			0.443980			0.221990	−	0.975049i	$-0.428745\pi$
$887$	13.2229			0.443980			0.221990	+	0.975049i	$0.428745\pi$
$888$	48.2042	−	53.5361i	1.61763	−	1.79656i
$889$	0.489450	−	0.104036i	0.0164156	−	0.00348925i
$890$	−0.319801	−	0.553912i	−0.0107198	−	0.0185672i
$891$	18.1190	−	3.85131i	0.607009	−	0.129024i
$892$	−17.0515	−	3.62441i	−0.570926	−	0.121354i
$893$	−11.8930	+	5.29511i	−0.397984	+	0.177194i
$894$	35.8852	−	15.9771i	1.20018	−	0.534356i
$895$	7.26511	+	3.23464i	0.242846	+	0.108122i
$896$	−2.97237	−	0.631797i	−0.0993000	−	0.0211069i
$897$	−5.72113	−	17.6078i	−0.191023	−	0.587909i
$898$	4.36265			0.145584
$899$	28.2193	−	31.3407i	0.941166	−	1.04527i
$900$	−1.69415	+	16.1188i	−0.0564717	+	0.537293i
$901$	20.5066	−	22.7749i	0.683174	−	0.758742i
$902$	11.7326	−	20.3215i	0.390654	−	0.676633i
$903$	−4.15531	−	3.01901i	−0.138280	−	0.100466i
$904$	−3.94062	−	6.82535i	−0.131063	−	0.227008i
$905$	−34.4336			−1.14461
$906$	−26.2397	+	22.0304i	−0.871757	+	0.731912i
$907$	−12.7747			−0.424175			−0.212088	−	0.977251i	$-0.568026\pi$
$907$	−12.7747			−0.424175			−0.212088	+	0.977251i	$0.568026\pi$
$908$	5.82021	+	10.0809i	0.193150	+	0.334546i
$909$	−19.5582	−	14.2099i	−0.648705	−	0.471311i
$910$	−0.337923	+	0.585299i	−0.0112020	+	0.0194025i
$911$	22.2102	−	24.6669i	0.735855	−	0.817250i	−0.252790	−	0.967521i	$-0.581348\pi$
$911$	22.2102	−	24.6669i	0.735855	−	0.817250i	0.988645	+	0.150271i	$0.0480147\pi$
$912$	0.194650	−	1.85197i	0.00644550	−	0.0613248i
$913$	10.9916	−	12.2074i	0.363769	−	0.404007i
$914$	26.3890			0.872872
$915$	−3.86903	−	11.9077i	−0.127906	−	0.393655i
$916$	1.57624	+	0.335040i	0.0520804	+	0.0110700i
$917$	−0.375228	−	0.167062i	−0.0123911	−	0.00551689i
$918$	−17.7597	+	7.90712i	−0.586157	+	0.260974i
$919$	7.81058	−	3.47749i	0.257647	−	0.114712i	−0.273849	−	0.961773i	$-0.588297\pi$
$919$	7.81058	−	3.47749i	0.257647	−	0.114712i	0.531496	+	0.847061i	$0.321630\pi$
$920$	36.3505	+	7.72655i	1.19844	+	0.254737i
$921$	49.4550	−	10.5120i	1.62960	−	0.346382i
$922$	7.94216	+	13.7562i	0.261561	+	0.453037i
$923$	−1.93567	+	0.411439i	−0.0637132	+	0.0135427i
$924$	−2.79919	+	3.10882i	−0.0920867	+	0.102273i
$925$	19.8163			0.651558
$926$	−5.48914	−	16.8938i	−0.180384	−	0.555166i
$927$	−66.7975	+	14.1982i	−2.19392	+	0.466332i
$928$	2.63243	+	25.0459i	0.0864139	+	0.822173i
$929$	−8.85911	−	15.3444i	−0.290658	−	0.503434i	0.683307	−	0.730131i	$-0.260541\pi$
$929$	−8.85911	−	15.3444i	−0.290658	−	0.503434i	−0.973966	+	0.226696i	$0.927208\pi$
$930$	32.9558	+	23.9438i	1.08066	+	0.785148i
$931$	0.956333	+	9.09890i	0.0313426	+	0.298205i
$932$	0.860557	+	0.625231i	0.0281885	+	0.0204801i
$933$	7.20135	−	22.1635i	0.235762	−	0.725599i
$934$	11.1530	+	34.3255i	0.364938	+	1.12316i
$935$	−6.59574	+	4.79208i	−0.215704	+	0.156718i
$936$	9.10617	+	10.1134i	0.297644	+	0.330568i
$937$	−18.3042	+	3.89067i	−0.597971	+	0.127103i	−0.496946	−	0.867781i	$-0.665545\pi$
$937$	−18.3042	+	3.89067i	−0.597971	+	0.127103i	−0.101025	+	0.994884i	$0.532212\pi$
$938$	1.62603	−	2.81637i	0.0530918	−	0.0919578i
$939$	−46.7461	−	80.9667i	−1.52550	−	2.64225i
$940$	11.5881	+	12.8699i	0.377962	+	0.419769i
$941$	4.57398	+	43.5185i	0.149107	+	1.41866i	0.771636	+	0.636065i	$0.219439\pi$
$941$	4.57398	+	43.5185i	0.149107	+	1.41866i	−0.622529	+	0.782597i	$0.713895\pi$
$942$	57.1659	+	12.1510i	1.86257	+	0.395901i
$943$	−9.69382	+	92.2305i	−0.315674	+	3.00344i
$944$	1.58699	+	2.74875i	0.0516522	+	0.0894643i
$945$	8.02887	+	1.70659i	0.261179	+	0.0555153i
$946$	3.99230	−	4.43390i	0.129801	−	0.144158i
$947$	−24.1813	−	17.5687i	−0.785786	−	0.570907i	0.120924	−	0.992662i	$-0.461414\pi$
$947$	−24.1813	−	17.5687i	−0.785786	−	0.570907i	−0.906710	+	0.421755i	$0.861414\pi$
$948$	1.90571	+	2.11650i	0.0618945	+	0.0687408i
$949$	−7.27792	−	8.08295i	−0.236251	−	0.262384i
$950$	2.48358	−	1.80443i	0.0805780	−	0.0585433i
$951$	38.0997	+	16.9631i	1.23547	+	0.550066i
$952$	1.97717	−	3.42456i	0.0640805	−	0.110991i
$953$	11.9389	−	5.31552i	0.386738	−	0.172187i	−0.204152	−	0.978939i	$-0.565444\pi$
$953$	11.9389	−	5.31552i	0.386738	−	0.172187i	0.590889	+	0.806753i	$0.298777\pi$
$954$	7.54536	−	71.7893i	0.244290	−	2.32427i
$955$	−2.05768	−	19.5775i	−0.0665849	−	0.633513i
$956$	−3.78021	+	2.74648i	−0.122261	+	0.0888276i
$957$	27.3057	+	12.1573i	0.882668	+	0.392989i
$958$	0.194579	−	1.85129i	0.00628655	−	0.0598125i
$959$	−2.92654	+	2.12626i	−0.0945031	+	0.0686605i
$960$	−28.0740	+	5.96732i	−0.906085	+	0.192594i
$961$	46.7469	−	20.8130i	1.50796	−	0.671389i
$962$	4.02464	−	4.46981i	0.129759	−	0.144112i
$963$	58.3765	+	42.4130i	1.88116	+	1.36674i
$964$	−27.3213	−	12.1642i	−0.879961	−	0.391784i
$965$	−36.3887			−1.17139
$966$	−3.91556	+	12.0509i	−0.125981	+	0.387730i
$967$	3.63938	+	34.6264i	0.117035	+	1.11351i	0.882591	+	0.470141i	$0.155797\pi$
$967$	3.63938	+	34.6264i	0.117035	+	1.11351i	−0.765557	+	0.643368i	$0.777536\pi$
$968$	12.4809	+	13.8615i	0.401152	+	0.445525i
$969$	−8.83963	−	3.93566i	−0.283970	−	0.126432i
$970$	−16.1268			−0.517801
$971$	7.99405	−	24.6032i	0.256541	−	0.789553i	−0.736981	−	0.675914i	$-0.763749\pi$
$971$	7.99405	−	24.6032i	0.256541	−	0.789553i	0.993522	−	0.113639i	$-0.0362509\pi$
$972$	−0.417145	+	0.722516i	−0.0133799	+	0.0231747i
$973$	−2.25825	+	6.95018i	−0.0723962	+	0.222813i
$974$	−4.60962	+	14.1870i	−0.147702	+	0.454579i
$975$	−0.588306	+	5.59736i	−0.0188409	+	0.179259i
$976$	−0.952274	+	0.691868i	−0.0304816	+	0.0221461i
$977$	31.5134	+	6.69838i	1.00820	+	0.214300i	0.682276	−	0.731095i	$-0.260990\pi$
$977$	31.5134	+	6.69838i	1.00820	+	0.214300i	0.325927	+	0.945395i	$0.394324\pi$
$978$	−1.29276	−	3.97870i	−0.0413378	−	0.127225i
$979$	−0.282569	−	0.869658i	−0.00903094	−	0.0277944i
$980$	11.1185	−	4.95026i	0.355166	−	0.158130i
$981$	−11.0316	+	19.1072i	−0.352211	+	0.610048i
$982$	−19.4533	+	33.6941i	−0.620780	+	1.07522i
$983$	17.7792	−	7.91580i	0.567068	−	0.252475i	−0.103117	−	0.994669i	$-0.532882\pi$
$983$	17.7792	−	7.91580i	0.567068	−	0.252475i	0.670185	+	0.742194i	$0.266215\pi$
$984$	−31.6710	−	97.4733i	−1.00963	−	3.10733i
$985$	7.32477	+	22.5433i	0.233387	+	0.718290i
$986$	−9.98998	−	2.12344i	−0.318146	−	0.0676240i
$987$	−13.2154	+	9.60152i	−0.420650	+	0.305620i
$988$	−0.127084	+	1.20913i	−0.00404309	+	0.0384674i
$989$	−7.28667	+	22.4261i	−0.231703	+	0.713107i
$990$	−5.93404	+	18.2631i	−0.188596	+	0.580440i
$991$	17.0959	−	29.6110i	0.543069	−	0.940623i	−0.455657	−	0.890156i	$-0.650596\pi$
$991$	17.0959	−	29.6110i	0.543069	−	0.940623i	0.998726	−	0.0504675i	$-0.0160711\pi$
$992$	−15.1631	+	46.6672i	−0.481429	+	1.48169i
$993$	−25.4126			−0.806445
$994$	1.23728	+	0.550873i	0.0392442	+	0.0174726i
$995$	13.7702	+	15.2934i	0.436545	+	0.484833i
$996$	−2.71096	−	25.7931i	−0.0859001	−	0.817285i
$997$	3.71341	−	11.4287i	0.117605	−	0.361951i	−0.874876	−	0.484346i	$-0.839058\pi$
$997$	3.71341	−	11.4287i	0.117605	−	0.361951i	0.992481	+	0.122395i	$0.0390576\pi$
$998$	−7.13555			−0.225872
$999$	−66.7342	−	29.7120i	−2.11138	−	0.940045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.g.a.76.5	yes	96
151.2	even	15	inner	151.2.g.a.2.5	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.g.a.2.5	✓	96	151.2	even	15	inner
151.2.g.a.76.5	yes	96	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.465766 - 0.806731i) q^{2} +(-2.42147 - 1.75930i) q^{3} +(0.566123 - 0.980554i) q^{4} +(1.07846 - 1.19776i) q^{5} +(-0.291444 + 2.77290i) q^{6} +(-0.384809 + 0.427373i) q^{7} -2.91779 q^{8} +(1.84134 + 5.66705i) q^{9} +O(q^{10})\)	\(q+(-0.465766 - 0.806731i) q^{2} +(-2.42147 - 1.75930i) q^{3} +(0.566123 - 0.980554i) q^{4} +(1.07846 - 1.19776i) q^{5} +(-0.291444 + 2.77290i) q^{6} +(-0.384809 + 0.427373i) q^{7} -2.91779 q^{8} +(1.84134 + 5.66705i) q^{9} +(-1.46858 - 0.312156i) q^{10} +(-1.96090 - 0.873048i) q^{11} +(-3.09595 + 1.37840i) q^{12} +(-0.715073 + 0.318371i) q^{13} +(0.524007 + 0.111381i) q^{14} +(-4.71869 + 1.00299i) q^{15} +(0.226763 + 0.392764i) q^{16} +(2.30510 - 0.489965i) q^{17} +(3.71415 - 4.12498i) q^{18} +1.37182 q^{19} +(-0.563921 - 1.73557i) q^{20} +(1.68368 - 0.357878i) q^{21} +(0.209005 + 1.98855i) q^{22} +(-3.95119 - 6.84365i) q^{23} +(7.06535 + 5.13328i) q^{24} +(0.251108 + 2.38913i) q^{25} +(0.589897 + 0.428585i) q^{26} +(2.73655 - 8.42223i) q^{27} +(0.201214 + 0.619272i) q^{28} +(3.76386 - 2.73461i) q^{29} +(3.00695 + 3.33956i) q^{30} +(8.86672 - 1.88468i) q^{31} +(-2.70655 + 4.68789i) q^{32} +(3.21231 + 5.56388i) q^{33} +(-1.46891 - 1.63139i) q^{34} +(0.0968866 + 0.921814i) q^{35} +(6.59927 + 1.40272i) q^{36} +(0.862247 - 8.20374i) q^{37} +(-0.638946 - 1.10669i) q^{38} +(2.29164 + 0.487104i) q^{39} +(-3.14673 + 3.49480i) q^{40} +(-9.49425 - 6.89797i) q^{41} +(-1.07292 - 1.19159i) q^{42} +(-1.99664 - 2.21750i) q^{43} +(-1.96618 + 1.42851i) q^{44} +(8.77355 + 3.90624i) q^{45} +(-3.68066 + 6.37509i) q^{46} +(-8.66953 + 3.85992i) q^{47} +(0.141892 - 1.35001i) q^{48} +(0.697129 + 6.63274i) q^{49} +(1.81043 - 1.31536i) q^{50} +(-6.44374 - 2.86894i) q^{51} +(-0.0926394 + 0.881405i) q^{52} +(10.5209 - 7.64391i) q^{53} +(-8.06907 + 1.71513i) q^{54} +(-3.16046 + 1.40713i) q^{55} +(1.12279 - 1.24699i) q^{56} +(-3.32182 - 2.41344i) q^{57} +(-3.95917 - 1.76274i) q^{58} +6.99848 q^{59} +(-1.68788 + 5.19475i) q^{60} +(0.271292 + 2.58117i) q^{61} +(-5.65025 - 6.27524i) q^{62} +(-3.13051 - 1.39379i) q^{63} +5.94954 q^{64} +(-0.389850 + 1.19983i) q^{65} +(2.99237 - 5.18294i) q^{66} +(1.87590 - 5.77342i) q^{67} +(0.824535 - 2.53766i) q^{68} +(-2.47237 + 23.5231i) q^{69} +(0.698530 - 0.507512i) q^{70} +(2.47292 + 0.525636i) q^{71} +(-5.37263 - 16.5353i) q^{72} +(4.29396 + 13.2155i) q^{73} +(-7.01981 + 3.12542i) q^{74} +(3.59516 - 6.22700i) q^{75} +(0.776617 - 1.34514i) q^{76} +(1.12769 - 0.502079i) q^{77} +(-0.674408 - 2.07562i) q^{78} +(-0.259696 - 0.799261i) q^{79} +(0.714991 + 0.151976i) q^{80} +(-6.98172 + 5.07251i) q^{81} +(-1.14271 + 10.8722i) q^{82} +(-2.36487 + 7.27833i) q^{83} +(0.602254 - 1.85355i) q^{84} +(1.89911 - 3.28936i) q^{85} +(-0.858954 + 2.64359i) q^{86} -13.9251 q^{87} +(5.72149 + 2.54737i) q^{88} +(0.285055 + 0.316585i) q^{89} +(-0.935143 - 8.89729i) q^{90} +(0.139103 - 0.428115i) q^{91} -8.94743 q^{92} +(-24.7863 - 11.0356i) q^{93} +(7.15189 + 5.19615i) q^{94} +(1.47946 - 1.64310i) q^{95} +(14.8013 - 6.58995i) q^{96} +(10.5066 - 2.23324i) q^{97} +(5.02614 - 3.65170i) q^{98} +(1.33693 - 12.7201i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) \) 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9	\( 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9} + 11 q^{10} - 7 q^{11} + 7 q^{12} - 8 q^{13} + 5 q^{14} + 10 q^{15} - 47 q^{16} - 26 q^{17} - 40 q^{18} - 20 q^{19} + 23 q^{20} - 2 q^{21} - 32 q^{22} - q^{23} + 95 q^{24} - 51 q^{25} + 41 q^{26} + 5 q^{27} - 2 q^{28} + 13 q^{29} + 19 q^{30} - 24 q^{31} - 60 q^{32} + 39 q^{33} + 47 q^{34} - 54 q^{35} + 11 q^{36} + 5 q^{37} + 8 q^{38} - 13 q^{39} - 74 q^{40} + 8 q^{41} + 166 q^{42} - 8 q^{43} + 18 q^{44} - 33 q^{45} + 21 q^{46} - 5 q^{47} + 8 q^{48} + 21 q^{49} - 72 q^{50} - 6 q^{51} + 96 q^{52} + 41 q^{53} - 60 q^{54} - 116 q^{55} - 85 q^{56} - 8 q^{57} - 58 q^{58} + 32 q^{59} - 6 q^{60} - 18 q^{61} + 38 q^{62} - 129 q^{63} + 160 q^{64} + 53 q^{65} + 43 q^{66} + 4 q^{67} + 10 q^{68} + 81 q^{69} + 33 q^{70} - 41 q^{71} - 40 q^{72} - 58 q^{73} - 20 q^{74} + 32 q^{75} - q^{76} - 22 q^{77} - 10 q^{78} + 32 q^{79} + 71 q^{80} - 66 q^{81} - 10 q^{82} + 80 q^{83} - 58 q^{84} - 2 q^{85} - 72 q^{86} + 72 q^{87} + 89 q^{88} + 9 q^{89} + 121 q^{90} - 138 q^{91} - 72 q^{92} - 85 q^{93} + 11 q^{94} - 47 q^{95} - 201 q^{96} + 54 q^{97} - 92 q^{98} - 21 q^{99}+O(q^{100}) \) 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9 + 11 * q^10 - 7 * q^11 + 7 * q^12 - 8 * q^13 + 5 * q^14 + 10 * q^15 - 47 * q^16 - 26 * q^17 - 40 * q^18 - 20 * q^19 + 23 * q^20 - 2 * q^21 - 32 * q^22 - q^23 + 95 * q^24 - 51 * q^25 + 41 * q^26 + 5 * q^27 - 2 * q^28 + 13 * q^29 + 19 * q^30 - 24 * q^31 - 60 * q^32 + 39 * q^33 + 47 * q^34 - 54 * q^35 + 11 * q^36 + 5 * q^37 + 8 * q^38 - 13 * q^39 - 74 * q^40 + 8 * q^41 + 166 * q^42 - 8 * q^43 + 18 * q^44 - 33 * q^45 + 21 * q^46 - 5 * q^47 + 8 * q^48 + 21 * q^49 - 72 * q^50 - 6 * q^51 + 96 * q^52 + 41 * q^53 - 60 * q^54 - 116 * q^55 - 85 * q^56 - 8 * q^57 - 58 * q^58 + 32 * q^59 - 6 * q^60 - 18 * q^61 + 38 * q^62 - 129 * q^63 + 160 * q^64 + 53 * q^65 + 43 * q^66 + 4 * q^67 + 10 * q^68 + 81 * q^69 + 33 * q^70 - 41 * q^71 - 40 * q^72 - 58 * q^73 - 20 * q^74 + 32 * q^75 - q^76 - 22 * q^77 - 10 * q^78 + 32 * q^79 + 71 * q^80 - 66 * q^81 - 10 * q^82 + 80 * q^83 - 58 * q^84 - 2 * q^85 - 72 * q^86 + 72 * q^87 + 89 * q^88 + 9 * q^89 + 121 * q^90 - 138 * q^91 - 72 * q^92 - 85 * q^93 + 11 * q^94 - 47 * q^95 - 201 * q^96 + 54 * q^97 - 92 * q^98 - 21 * q^99

Introduction

L-functions

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