LMFDB - Embedded newform 110.2.k.a.7.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,2,Mod(7,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 14]))

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

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

chi := DirichletCharacter("110.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.k (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.6
Character	$\chi$	$=$	110.7
Dual form			110.2.k.a.63.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.987688 - 0.156434i) q^{2} +(1.18907 + 2.33368i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.05320 - 1.97251i) q^{5} +(1.53950 + 2.11894i) q^{6} +(-2.88379 - 1.46937i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-2.26883 + 3.12278i) q^{9} +O(q^{10})$	\(q+(0.987688 - 0.156434i) q^{2} +(1.18907 + 2.33368i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.05320 - 1.97251i) q^{5} +(1.53950 + 2.11894i) q^{6} +(-2.88379 - 1.46937i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-2.26883 + 3.12278i) q^{9} +(-1.34880 - 1.78346i) q^{10} +(-0.0951565 + 3.31526i) q^{11} +(1.85202 + 1.85202i) q^{12} +(-0.250222 - 1.57984i) q^{13} +(-3.07815 - 1.00015i) q^{14} +(3.35088 - 4.80328i) q^{15} +(0.809017 - 0.587785i) q^{16} +(0.892905 - 5.63758i) q^{17} +(-1.75239 + 3.43925i) q^{18} +(-1.49489 + 4.60081i) q^{19} +(-1.61119 - 1.55051i) q^{20} -8.47704i q^{21} +(0.424636 + 3.28933i) q^{22} +(1.82681 - 1.82681i) q^{23} +(2.11894 + 1.53950i) q^{24} +(-2.78155 + 4.15487i) q^{25} +(-0.494282 - 1.52124i) q^{26} +(-2.22465 - 0.352350i) q^{27} +(-3.19671 - 0.506309i) q^{28} +(-0.0395318 - 0.121666i) q^{29} +(2.55822 - 5.26833i) q^{30} +(2.90969 + 2.11401i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-7.84991 + 3.72001i) q^{33} -5.70785i q^{34} +(0.138868 + 7.23583i) q^{35} +(-1.19279 + 3.67105i) q^{36} +(-5.00499 + 9.82285i) q^{37} +(-0.756764 + 4.77802i) q^{38} +(3.38931 - 2.46248i) q^{39} +(-1.83390 - 1.27937i) q^{40} +(3.82966 + 1.24433i) q^{41} +(-1.32610 - 8.37267i) q^{42} +(-7.57778 - 7.57778i) q^{43} +(0.933972 + 3.18240i) q^{44} +(8.54922 + 1.18638i) q^{45} +(1.51854 - 2.09010i) q^{46} +(4.18546 - 2.13260i) q^{47} +(2.33368 + 1.18907i) q^{48} +(2.04273 + 2.81157i) q^{49} +(-2.09734 + 4.53885i) q^{50} +(14.2181 - 4.61972i) q^{51} +(-0.726172 - 1.42519i) q^{52} +(0.932926 - 0.147761i) q^{53} -2.25238 q^{54} +(6.63959 - 3.30392i) q^{55} -3.23656 q^{56} +(-12.5144 + 1.98208i) q^{57} +(-0.0580780 - 0.113984i) q^{58} +(6.38909 - 2.07594i) q^{59} +(1.70258 - 5.60366i) q^{60} +(-1.16546 - 1.60412i) q^{61} +(3.20457 + 1.63281i) q^{62} +(11.1313 - 5.67170i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-2.85271 + 2.15744i) q^{65} +(-7.17133 + 4.90221i) q^{66} +(6.46330 + 6.46330i) q^{67} +(-0.892905 - 5.63758i) q^{68} +(6.43541 + 2.09099i) q^{69} +(1.26909 + 7.12502i) q^{70} +(-10.1913 + 7.40438i) q^{71} +(-0.603832 + 3.81244i) q^{72} +(-1.95589 + 3.83865i) q^{73} +(-3.40674 + 10.4849i) q^{74} +(-13.0036 - 1.55083i) q^{75} +4.83758i q^{76} +(5.14574 - 9.42070i) q^{77} +(2.96237 - 2.96237i) q^{78} +(-4.04236 - 2.93695i) q^{79} +(-2.01146 - 0.976737i) q^{80} +(1.75539 + 5.40254i) q^{81} +(3.97717 + 0.629921i) q^{82} +(9.20374 + 1.45773i) q^{83} +(-2.61955 - 8.06214i) q^{84} +(-12.0606 + 4.17622i) q^{85} +(-8.66991 - 6.29906i) q^{86} +(0.236925 - 0.236925i) q^{87} +(1.42031 + 2.99712i) q^{88} -8.27747i q^{89} +(8.62956 - 0.165617i) q^{90} +(-1.59977 + 4.92359i) q^{91} +(1.17289 - 2.30192i) q^{92} +(-1.47361 + 9.30399i) q^{93} +(3.80032 - 2.76109i) q^{94} +(10.6495 - 1.89687i) q^{95} +(2.49096 + 0.809363i) q^{96} +(-1.20488 - 7.60733i) q^{97} +(2.45740 + 2.45740i) q^{98} +(-10.1369 - 7.81892i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7}+O(q^{10}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36} + 20 q^{37} - 36 q^{38} - 20 q^{41} - 20 q^{42} + 16 q^{45} + 40 q^{46} + 40 q^{47} + 4 q^{48} + 40 q^{50} + 40 q^{51} + 40 q^{52} + 96 q^{55} - 8 q^{56} + 48 q^{58} + 20 q^{60} + 80 q^{61} + 40 q^{62} + 100 q^{63} + 24 q^{66} + 20 q^{68} - 56 q^{70} - 56 q^{71} - 20 q^{73} - 76 q^{75} - 96 q^{77} + 16 q^{78} - 12 q^{80} - 68 q^{81} - 80 q^{85} - 56 q^{86} - 4 q^{88} - 80 q^{90} - 68 q^{91} - 12 q^{92} + 76 q^{93} + 20 q^{95} + 72 q^{97}+O(q^{100}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.987688	−	0.156434i	0.698401	−	0.110616i
$2$	0.987688	−	0.156434i	0.698401	−	0.110616i
$3$	1.18907	+	2.33368i	0.686510	+	1.34735i	0.926396	+	0.376551i	$0.122890\pi$
$3$	1.18907	+	2.33368i	0.686510	+	1.34735i	−0.239885	+	0.970801i	$0.577110\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	−1.05320	−	1.97251i	−0.471004	−	0.882131i
$5$	−1.05320	−	1.97251i	−0.471004	−	0.882131i
$6$	1.53950	+	2.11894i	0.628498	+	0.865054i
$7$	−2.88379	−	1.46937i	−1.08997	−	0.555368i	−0.185821	−	0.982584i	$-0.559495\pi$
$7$	−2.88379	−	1.46937i	−1.08997	−	0.555368i	−0.904150	+	0.427216i	$0.859495\pi$
$8$	0.891007	−	0.453990i	0.315018	−	0.160510i
$9$	−2.26883	+	3.12278i	−0.756277	+	1.04093i
$10$	−1.34880	−	1.78346i	−0.426527	−	0.563981i
$11$	−0.0951565	+	3.31526i	−0.0286908	+	0.999588i
$11$	−0.0951565	+	3.31526i	−0.0286908	+	0.999588i
$12$	1.85202	+	1.85202i	0.534632	+	0.534632i
$13$	−0.250222	−	1.57984i	−0.0693991	−	0.438168i	−0.997783	−	0.0665467i	$-0.978802\pi$
$13$	−0.250222	−	1.57984i	−0.0693991	−	0.438168i	0.928384	−	0.371622i	$-0.121198\pi$
$14$	−3.07815	−	1.00015i	−0.822669	−	0.267302i
$15$	3.35088	−	4.80328i	0.865193	−	1.24020i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	0.892905	−	5.63758i	0.216561	−	1.36731i	−0.604560	−	0.796560i	$-0.706651\pi$
$17$	0.892905	−	5.63758i	0.216561	−	1.36731i	0.821121	−	0.570754i	$-0.193349\pi$
$18$	−1.75239	+	3.43925i	−0.413042	+	0.810640i
$19$	−1.49489	+	4.60081i	−0.342952	+	1.05550i	0.619719	+	0.784824i	$0.287247\pi$
$19$	−1.49489	+	4.60081i	−0.342952	+	1.05550i	−0.962671	+	0.270674i	$0.912753\pi$
$20$	−1.61119	−	1.55051i	−0.360272	−	0.346704i
$21$		−	8.47704i		−	1.84984i
$22$	0.424636	+	3.28933i	0.0905327	+	0.701287i
$23$	1.82681	−	1.82681i	0.380917	−	0.380917i	−0.490516	−	0.871432i	$-0.663192\pi$
$23$	1.82681	−	1.82681i	0.380917	−	0.380917i	0.871432	+	0.490516i	$0.163192\pi$
$24$	2.11894	+	1.53950i	0.432527	+	0.314249i
$25$	−2.78155	+	4.15487i	−0.556311	+	0.830974i
$26$	−0.494282	−	1.52124i	−0.0969368	−	0.298341i
$27$	−2.22465	−	0.352350i	−0.428134	−	0.0678098i
$28$	−3.19671	−	0.506309i	−0.604121	−	0.0956834i
$29$	−0.0395318	−	0.121666i	−0.00734088	−	0.0225929i	0.947319	−	0.320292i	$-0.103781\pi$
$29$	−0.0395318	−	0.121666i	−0.00734088	−	0.0225929i	−0.954660	+	0.297699i	$0.903781\pi$
$30$	2.55822	−	5.26833i	0.467066	−	0.961861i
$31$	2.90969	+	2.11401i	0.522595	+	0.379687i	0.817581	−	0.575814i	$-0.195315\pi$
$31$	2.90969	+	2.11401i	0.522595	+	0.379687i	−0.294986	+	0.955502i	$0.595315\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−7.84991	+	3.72001i	−1.36649	+	0.647571i
$34$		−	5.70785i		−	0.978889i
$35$	0.138868	+	7.23583i	0.0234731	+	1.22308i
$36$	−1.19279	+	3.67105i	−0.198799	+	0.611841i
$37$	−5.00499	+	9.82285i	−0.822815	+	1.61487i	−0.0346525	+	0.999399i	$0.511032\pi$
$37$	−5.00499	+	9.82285i	−0.822815	+	1.61487i	−0.788163	+	0.615467i	$0.788968\pi$
$38$	−0.756764	+	4.77802i	−0.122763	+	0.775097i
$39$	3.38931	−	2.46248i	0.542724	−	0.394312i
$40$	−1.83390	−	1.27937i	−0.289966	−	0.202287i
$41$	3.82966	+	1.24433i	0.598092	+	0.194332i	0.592389	−	0.805652i	$-0.298185\pi$
$41$	3.82966	+	1.24433i	0.598092	+	0.194332i	0.00570285	+	0.999984i	$0.498185\pi$
$42$	−1.32610	−	8.37267i	−0.204622	−	1.29193i
$43$	−7.57778	−	7.57778i	−1.15560	−	1.15560i	−0.985411	−	0.170190i	$-0.945562\pi$
$43$	−7.57778	−	7.57778i	−1.15560	−	1.15560i	−0.170190	−	0.985411i	$-0.554438\pi$
$44$	0.933972	+	3.18240i	0.140802	+	0.479765i
$45$	8.54922	+	1.18638i	1.27444	+	0.176855i
$46$	1.51854	−	2.09010i	0.223897	−	0.308168i
$47$	4.18546	−	2.13260i	0.610512	−	0.311072i	−0.121260	−	0.992621i	$-0.538693\pi$
$47$	4.18546	−	2.13260i	0.610512	−	0.311072i	0.731772	+	0.681549i	$0.238693\pi$
$48$	2.33368	+	1.18907i	0.336838	+	0.171628i
$49$	2.04273	+	2.81157i	0.291818	+	0.401653i
$50$	−2.09734	+	4.53885i	−0.296609	+	0.641890i
$51$	14.2181	−	4.61972i	1.99093	−	0.646891i
$52$	−0.726172	−	1.42519i	−0.100702	−	0.197639i
$53$	0.932926	−	0.147761i	0.128147	−	0.0202965i	−0.0920313	−	0.995756i	$-0.529336\pi$
$53$	0.932926	−	0.147761i	0.128147	−	0.0202965i	0.220179	+	0.975460i	$0.429336\pi$
$54$	−2.25238			−0.306510
$55$	6.63959	−	3.30392i	0.895282	−	0.445501i
$56$	−3.23656			−0.432503
$57$	−12.5144	+	1.98208i	−1.65757	+	0.262533i
$58$	−0.0580780	−	0.113984i	−0.00762601	−	0.0149669i
$59$	6.38909	−	2.07594i	0.831789	−	0.270265i	0.137990	−	0.990434i	$-0.455936\pi$
$59$	6.38909	−	2.07594i	0.831789	−	0.270265i	0.693799	+	0.720169i	$0.255936\pi$
$60$	1.70258	−	5.60366i	0.219802	−	0.723430i
$61$	−1.16546	−	1.60412i	−0.149222	−	0.205386i	0.727862	−	0.685724i	$-0.240514\pi$
$61$	−1.16546	−	1.60412i	−0.149222	−	0.205386i	−0.877084	+	0.480338i	$0.840514\pi$
$62$	3.20457	+	1.63281i	0.406980	+	0.207367i
$63$	11.1313	−	5.67170i	1.40242	−	0.714567i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	−2.85271	+	2.15744i	−0.353835	+	0.267598i
$66$	−7.17133	+	4.90221i	−0.882730	+	0.603420i
$67$	6.46330	+	6.46330i	0.789618	+	0.789618i	0.981431	−	0.191814i	$-0.0614370\pi$
$67$	6.46330	+	6.46330i	0.789618	+	0.789618i	−0.191814	+	0.981431i	$0.561437\pi$
$68$	−0.892905	−	5.63758i	−0.108281	−	0.683657i
$69$	6.43541	+	2.09099i	0.774732	+	0.251726i
$70$	1.26909	+	7.12502i	0.151685	+	0.851602i
$71$	−10.1913	+	7.40438i	−1.20948	+	0.878739i	−0.995183	−	0.0980300i	$-0.968746\pi$
$71$	−10.1913	+	7.40438i	−1.20948	+	0.878739i	−0.214297	+	0.976769i	$0.568746\pi$
$72$	−0.603832	+	3.81244i	−0.0711622	+	0.449301i
$73$	−1.95589	+	3.83865i	−0.228920	+	0.449281i	−0.976683	−	0.214685i	$-0.931128\pi$
$73$	−1.95589	+	3.83865i	−0.228920	+	0.449281i	0.747764	+	0.663965i	$0.231128\pi$
$74$	−3.40674	+	10.4849i	−0.396025	+	1.21884i
$75$	−13.0036	−	1.55083i	−1.50153	−	0.179074i
$76$			4.83758i			0.554908i
$77$	5.14574	−	9.42070i	0.586411	−	1.07359i
$78$	2.96237	−	2.96237i	0.335422	−	0.335422i
$79$	−4.04236	−	2.93695i	−0.454801	−	0.330433i	0.336687	−	0.941617i	$-0.390694\pi$
$79$	−4.04236	−	2.93695i	−0.454801	−	0.330433i	−0.791489	+	0.611184i	$0.790694\pi$
$80$	−2.01146	−	0.976737i	−0.224888	−	0.109203i
$81$	1.75539	+	5.40254i	0.195043	+	0.600282i
$82$	3.97717	+	0.629921i	0.439204	+	0.0695632i
$83$	9.20374	+	1.45773i	1.01024	+	0.160006i	0.639550	−	0.768750i	$-0.279121\pi$
$83$	9.20374	+	1.45773i	1.01024	+	0.160006i	0.370691	+	0.928756i	$0.379121\pi$
$84$	−2.61955	−	8.06214i	−0.285816	−	0.879652i
$85$	−12.0606	+	4.17622i	−1.30815	+	0.452975i
$86$	−8.66991	−	6.29906i	−0.934901	−	0.679245i
$87$	0.236925	−	0.236925i	0.0254010	−	0.0254010i
$88$	1.42031	+	2.99712i	0.151406	+	0.319494i
$89$		−	8.27747i		−	0.877410i	−0.898631	−	0.438705i	$-0.855437\pi$
$89$		−	8.27747i		−	0.877410i	0.898631	−	0.438705i	$-0.144563\pi$
$90$	8.62956	−	0.165617i	0.909635	−	0.0174575i
$91$	−1.59977	+	4.92359i	−0.167702	+	0.516133i
$92$	1.17289	−	2.30192i	0.122282	−	0.239991i
$93$	−1.47361	+	9.30399i	−0.152806	+	0.964779i
$94$	3.80032	−	2.76109i	0.391973	−	0.284785i
$95$	10.6495	−	1.89687i	1.09262	−	0.194615i
$96$	2.49096	+	0.809363i	0.254233	+	0.0826053i
$97$	−1.20488	−	7.60733i	−0.122337	−	0.772407i	−0.970220	−	0.242224i	$-0.922123\pi$
$97$	−1.20488	−	7.60733i	−0.122337	−	0.772407i	0.847883	−	0.530183i	$-0.177877\pi$
$98$	2.45740	+	2.45740i	0.248235	+	0.248235i
$99$	−10.1369	−	7.81892i	−1.01880	−	0.785831i
$100$	−1.36149	+	4.81106i	−0.136149	+	0.481106i
$101$	8.64907	−	11.9044i	0.860615	−	1.18453i	−0.120808	−	0.992676i	$-0.538548\pi$
$101$	8.64907	−	11.9044i	0.860615	−	1.18453i	0.981423	−	0.191859i	$-0.0614515\pi$
$102$	13.3203	−	6.78704i	1.31891	−	0.672017i
$103$	−11.0628	−	5.63679i	−1.09005	−	0.555409i	−0.185877	−	0.982573i	$-0.559513\pi$
$103$	−11.0628	−	5.63679i	−1.09005	−	0.555409i	−0.904174	+	0.427164i	$0.859513\pi$
$104$	−0.940181	−	1.29405i	−0.0921923	−	0.126892i
$105$	−16.7210	+	8.92798i	−1.63180	+	0.871282i
$106$	0.898325	−	0.291884i	0.0872531	−	0.0283502i
$107$	2.07128	+	4.06511i	0.200238	+	0.392989i	0.969189	−	0.246319i	$-0.0792210\pi$
$107$	2.07128	+	4.06511i	0.200238	+	0.392989i	−0.768951	+	0.639308i	$0.779221\pi$
$108$	−2.22465	+	0.352350i	−0.214067	+	0.0339049i
$109$	4.56201			0.436961			0.218481	−	0.975841i	$-0.429890\pi$
$109$	4.56201			0.436961			0.218481	+	0.975841i	$0.429890\pi$
$110$	6.04099	−	4.30191i	0.575986	−	0.410171i
$111$	−28.8747			−2.74067
$112$	−3.19671	+	0.506309i	−0.302061	+	0.0478417i
$113$	−6.18906	−	12.1467i	−0.582218	−	1.14267i	−0.974827	−	0.222961i	$-0.928428\pi$
$113$	−6.18906	−	12.1467i	−0.582218	−	1.14267i	0.392609	−	0.919705i	$-0.371572\pi$
$114$	−12.0502	+	3.91536i	−1.12861	+	0.366707i
$115$	−5.52739	−	1.67940i	−0.515432	−	0.156605i
$116$	−0.0751940	−	0.103496i	−0.00698159	−	0.00960933i
$117$	5.50120	+	2.80300i	0.508586	+	0.259137i
$118$	5.98568	−	3.04986i	0.551027	−	0.280762i
$119$	−10.8586	+	14.9456i	−0.995408	+	1.37006i
$120$	0.805012	−	5.80102i	0.0734872	−	0.529558i
$121$	−10.9819	−	0.630937i	−0.998354	−	0.0573579i
$122$	−1.40205	−	1.40205i	−0.126936	−	0.126936i
$123$	1.64986	+	10.4168i	0.148763	+	0.939252i
$124$	3.42054	+	1.11140i	0.307174	+	0.0998067i
$125$	11.1250	+	1.11074i	0.995053	+	0.0993472i
$126$	10.1070	−	7.34320i	0.900407	−	0.654184i
$127$	0.183933	−	1.16130i	0.0163214	−	0.103049i	−0.978183	−	0.207746i	$-0.933387\pi$
$127$	0.183933	−	1.16130i	0.0163214	−	0.103049i	0.994504	+	0.104697i	$0.0333872\pi$
$128$	0.453990	−	0.891007i	0.0401275	−	0.0787546i
$129$	8.67362	−	26.6947i	0.763670	−	2.35033i
$130$	−2.48009	+	2.57714i	−0.217518	+	0.226031i
$131$		−	6.27310i		−	0.548084i	−0.961718	−	0.274042i	$-0.911639\pi$
$131$		−	6.27310i		−	0.548084i	0.961718	−	0.274042i	$-0.0883607\pi$
$132$	−6.31616	+	5.96370i	−0.549751	+	0.519073i
$133$	11.0712	−	11.0712i	0.959998	−	0.959998i
$134$	7.39481	+	5.37264i	0.638814	+	0.464126i
$135$	1.64798	+	4.75923i	0.141836	+	0.409609i
$136$	−1.76382	−	5.42849i	−0.151247	−	0.465489i
$137$	−0.915400	−	0.144985i	−0.0782079	−	0.0123869i	0.117208	−	0.993107i	$-0.462606\pi$
$137$	−0.915400	−	0.144985i	−0.0782079	−	0.0123869i	−0.195416	+	0.980720i	$0.562606\pi$
$138$	6.68328	+	1.05853i	0.568919	+	0.0901079i
$139$	2.50982	+	7.72444i	0.212880	+	0.655178i	0.999297	+	0.0374822i	$0.0119337\pi$
$139$	2.50982	+	7.72444i	0.212880	+	0.655178i	−0.786417	+	0.617696i	$0.788066\pi$
$140$	2.36806	+	6.83877i	0.200138	+	0.577981i
$141$	9.95362	+	7.23173i	0.838246	+	0.609022i
$142$	−8.90749	+	8.90749i	−0.747500	+	0.747500i
$143$	5.26138	−	0.679218i	0.439979	−	0.0567991i
$144$			3.85997i			0.321664i
$145$	−0.198353	+	0.206115i	−0.0164723	+	0.0171170i
$146$	−1.33131	+	4.09736i	−0.110180	+	0.339100i
$147$	−4.13237	+	8.11023i	−0.340832	+	0.668920i
$148$	−1.72460	+	10.8887i	−0.141761	+	0.895046i
$149$	−5.53773	+	4.02340i	−0.453669	+	0.329610i	−0.791043	−	0.611761i	$-0.790461\pi$
$149$	−5.53773	+	4.02340i	−0.453669	+	0.329610i	0.337374	+	0.941371i	$0.390461\pi$
$150$	−13.0861	+	0.502477i	−1.06848	+	0.0410271i
$151$	−3.22296	−	1.04720i	−0.262281	−	0.0852202i	0.174925	−	0.984582i	$-0.444032\pi$
$151$	−3.22296	−	1.04720i	−0.262281	−	0.0852202i	−0.437206	+	0.899362i	$0.644032\pi$
$152$	0.756764	+	4.77802i	0.0613817	+	0.387549i
$153$	15.5791	+	15.5791i	1.25949	+	1.25949i
$154$	3.60866	−	10.1097i	0.290794	−	0.814662i
$155$	1.10543	−	7.96584i	0.0887899	−	0.639831i
$156$	2.46248	−	3.38931i	0.197156	−	0.271362i
$157$	−9.88267	+	5.03547i	−0.788723	+	0.401874i	−0.801463	−	0.598045i	$-0.795945\pi$
$157$	−9.88267	+	5.03547i	−0.788723	+	0.401874i	0.0127402	+	0.999919i	$0.495945\pi$
$158$	−4.45204	−	2.26843i	−0.354185	−	0.180466i
$159$	1.45414	+	2.00146i	0.115321	+	0.158726i
$160$	−2.13949	−	0.650050i	−0.169142	−	0.0513909i
$161$	−7.95240	+	2.58389i	−0.626737	+	0.203639i
$162$	2.57892	+	5.06142i	0.202619	+	0.397663i
$163$	17.1901	−	2.72265i	1.34643	−	0.213254i	0.558752	−	0.829335i	$-0.311281\pi$
$163$	17.1901	−	2.72265i	1.34643	−	0.213254i	0.787683	+	0.616081i	$0.211281\pi$
$164$	4.02674			0.314436
$165$	15.6052	+	11.5661i	1.21487	+	0.900419i
$166$	9.31846			0.723253
$167$	−6.67411	+	1.05708i	−0.516458	+	0.0817990i	−0.409223	−	0.912435i	$-0.634200\pi$
$167$	−6.67411	+	1.05708i	−0.516458	+	0.0817990i	−0.107236	+	0.994234i	$0.534200\pi$
$168$	−3.84849	−	7.55309i	−0.296918	−	0.582734i
$169$	9.93046	−	3.22660i	0.763881	−	0.248200i
$170$	−11.2588	+	6.01149i	−0.863508	+	0.461060i
$171$	−10.9756	−	15.1067i	−0.839329	−	1.15524i
$172$	−9.54856	−	4.86524i	−0.728071	−	0.370971i
$173$	−4.79362	+	2.44247i	−0.364452	+	0.185698i	−0.626621	−	0.779324i	$-0.715562\pi$
$173$	−4.79362	+	2.44247i	−0.364452	+	0.185698i	0.262168	+	0.965022i	$0.415562\pi$
$174$	0.196945	−	0.271071i	0.0149303	−	0.0205498i
$175$	14.1264	−	7.89466i	1.06786	−	0.596781i
$176$	1.87168	+	2.73803i	0.141083	+	0.206387i
$177$	12.4417	+	12.4417i	0.935173	+	0.935173i
$178$	−1.29488	−	8.17556i	−0.0970555	−	0.612784i
$179$	−13.1183	−	4.26240i	−0.980509	−	0.318587i	−0.225458	−	0.974253i	$-0.572388\pi$
$179$	−13.1183	−	4.26240i	−0.980509	−	0.318587i	−0.755051	+	0.655666i	$0.772388\pi$
$180$	8.49740	−	1.51354i	0.633359	−	0.112812i
$181$	14.9372	−	10.8525i	1.11028	−	0.806663i	0.127569	−	0.991830i	$-0.459283\pi$
$181$	14.9372	−	10.8525i	1.11028	−	0.806663i	0.982707	+	0.185167i	$0.0592826\pi$
$182$	−0.809857	+	5.11324i	−0.0600306	+	0.379018i
$183$	2.35768	−	4.62722i	0.174285	−	0.342054i
$184$	0.798346	−	2.45706i	0.0588548	−	0.181137i
$185$	24.6469	−	0.473017i	1.81207	−	0.0347769i
$186$			9.41997i			0.690705i
$187$	18.6051	+	3.49666i	1.36054	+	0.255701i
$188$	3.32160	−	3.32160i	0.242253	−	0.242253i
$189$	5.89770	+	4.28493i	0.428995	+	0.311683i
$190$	10.2217	−	3.53947i	0.741559	−	0.256780i
$191$	−0.693984	−	2.13586i	−0.0502149	−	0.154546i	0.922805	−	0.385268i	$-0.125891\pi$
$191$	−0.693984	−	2.13586i	−0.0502149	−	0.154546i	−0.973020	+	0.230723i	$0.925891\pi$
$192$	2.58691	+	0.409726i	0.186694	+	0.0295694i
$193$	−5.94097	−	0.940958i	−0.427641	−	0.0677316i	−0.0610956	−	0.998132i	$-0.519459\pi$
$193$	−5.94097	−	0.940958i	−0.427641	−	0.0677316i	−0.366545	+	0.930400i	$0.619459\pi$
$194$	−2.38010	−	7.32518i	−0.170881	−	0.525917i
$195$	−8.42686	−	4.09196i	−0.603460	−	0.293031i
$196$	2.81157	+	2.04273i	0.200826	+	0.145909i
$197$	4.61334	−	4.61334i	0.328687	−	0.328687i	−0.523400	−	0.852087i	$-0.675337\pi$
$197$	4.61334	−	4.61334i	0.328687	−	0.328687i	0.852087	+	0.523400i	$0.175337\pi$
$198$	−11.2353	−	6.13689i	−0.798456	−	0.436130i
$199$			18.8628i			1.33715i	0.743644	+	0.668576i	$0.233096\pi$
$199$			18.8628i			1.33715i	−0.743644	+	0.668576i	$0.766904\pi$
$200$	−0.592111	+	4.96482i	−0.0418686	+	0.351066i
$201$	−7.39797	+	22.7686i	−0.521813	+	1.60597i
$202$	6.68032	−	13.1109i	0.470026	−	0.922478i
$203$	−0.0647709	+	0.408948i	−0.00454603	+	0.0287025i
$204$	12.0946	−	8.78724i	0.846791	−	0.615230i
$205$	−1.57893	−	8.86455i	−0.110277	−	0.619127i
$206$	−11.8084	−	3.83678i	−0.822730	−	0.267321i
$207$	1.56000	+	9.84945i	0.108428	+	0.684584i
$208$	−1.13104	−	1.13104i	−0.0784235	−	0.0784235i
$209$	−15.1106	−	5.39376i	−1.04522	−	0.373094i
$210$	−15.1185	+	11.4338i	−1.04327	+	0.789008i
$211$	0.893982	−	1.23046i	0.0615443	−	0.0847084i	−0.777135	−	0.629333i	$-0.783328\pi$
$211$	0.893982	−	1.23046i	0.0615443	−	0.0847084i	0.838680	+	0.544625i	$0.183328\pi$
$212$	0.841605	−	0.428819i	0.0578017	−	0.0294514i
$213$	−29.3976	−	14.9788i	−2.01429	−	1.02633i
$214$	2.68170	+	3.69104i	0.183317	+	0.252315i
$215$	−6.96632	+	22.9281i	−0.475099	+	1.56368i
$216$	−2.14214	+	0.696024i	−0.145754	+	0.0473585i
$217$	−5.28467	−	10.3718i	−0.358747	−	0.704081i
$218$	4.50585	−	0.713656i	0.305174	−	0.0483349i
$219$	−11.2839			−0.762495
$220$	5.29365	−	5.19396i	0.356898	−	0.350177i
$221$	−9.12989			−0.614143
$222$	−28.5192	+	4.51700i	−1.91408	+	0.303161i
$223$	−3.32183	−	6.51946i	−0.222446	−	0.436575i	0.752631	−	0.658443i	$-0.228785\pi$
$223$	−3.32183	−	6.51946i	−0.222446	−	0.436575i	−0.975077	+	0.221868i	$0.928785\pi$
$224$	−3.07815	+	1.00015i	−0.205667	+	0.0668254i
$225$	−6.66386	−	18.1129i	−0.444258	−	1.20753i
$226$	−8.01303	−	11.0290i	−0.533019	−	0.733637i
$227$	−22.5641	−	11.4970i	−1.49763	−	0.763081i	−0.502778	−	0.864416i	$-0.667689\pi$
$227$	−22.5641	−	11.4970i	−1.49763	−	0.763081i	−0.994852	+	0.101335i	$0.967689\pi$
$228$	−11.2894	+	5.75222i	−0.747657	+	0.380950i
$229$	6.03216	−	8.30255i	0.398616	−	0.548648i	−0.561780	−	0.827287i	$-0.689883\pi$
$229$	6.03216	−	8.30255i	0.398616	−	0.548648i	0.960396	+	0.278639i	$0.0898832\pi$
$230$	−5.72205	−	0.794054i	−0.377301	−	0.0523584i
$231$	28.1036	+	0.806645i	1.84908	+	0.0530733i
$232$	−0.0904585	−	0.0904585i	−0.00593889	−	0.00593889i
$233$	3.39829	+	21.4560i	0.222630	+	1.40563i	0.805275	+	0.592902i	$0.202018\pi$
$233$	3.39829	+	21.4560i	0.222630	+	1.40563i	−0.582645	+	0.812727i	$0.697982\pi$
$234$	5.87195	+	1.90791i	0.383862	+	0.124724i
$235$	−8.61468	−	6.00980i	−0.561960	−	0.392036i
$236$	5.43488	−	3.94867i	0.353781	−	0.257037i
$237$	2.04725	−	12.9258i	0.132983	−	0.839623i
$238$	−8.38692	+	16.4603i	−0.543643	+	1.06696i
$239$	−6.78047	+	20.8681i	−0.438592	+	1.34985i	0.450768	+	0.892641i	$0.351150\pi$
$239$	−6.78047	+	20.8681i	−0.438592	+	1.34985i	−0.889360	+	0.457207i	$0.848850\pi$
$240$	−0.112378	−	5.85553i	−0.00725397	−	0.377973i
$241$			13.1393i			0.846379i	0.906041	+	0.423190i	$0.139090\pi$
$241$			13.1393i			0.846379i	−0.906041	+	0.423190i	$0.860910\pi$
$242$	−10.9454	+	1.09478i	−0.703596	+	0.0703749i
$243$	−15.2985	+	15.2985i	−0.981402	+	0.981402i
$244$	−1.60412	−	1.16546i	−0.102693	−	0.0746108i
$245$	3.39445	−	6.99042i	0.216863	−	0.446602i
$246$	3.25910	+	10.0305i	0.207792	+	0.639519i
$247$	7.64259	+	1.21047i	0.486287	+	0.0770202i
$248$	3.55229	+	0.562627i	0.225571	+	0.0357269i
$249$	7.54202	+	23.2119i	0.477956	+	1.47100i
$250$	11.1618	−	0.643278i	0.705935	−	0.0406845i
$251$	7.99452	+	5.80836i	0.504610	+	0.366621i	0.810775	−	0.585358i	$-0.199046\pi$
$251$	7.99452	+	5.80836i	0.504610	+	0.366621i	−0.306165	+	0.951978i	$0.599046\pi$
$252$	8.83388	−	8.83388i	0.556482	−	0.556482i
$253$	5.88252	+	6.23019i	0.369831	+	0.391689i
$254$		−	1.17578i		−	0.0737750i
$255$	−24.0868	−	23.1797i	−1.50838	−	1.45157i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	13.1555	−	25.8192i	0.820620	−	1.61056i	0.0289711	−	0.999580i	$-0.490777\pi$
$257$	13.1555	−	25.8192i	0.820620	−	1.61056i	0.791649	−	0.610977i	$-0.209223\pi$
$258$	4.39087	−	27.7229i	0.273364	−	1.72595i
$259$	28.8667	−	20.9729i	1.79369	−	1.30319i
$260$	−2.04640	+	2.93339i	−0.126912	+	0.181921i
$261$	0.469628	+	0.152592i	0.0290693	+	0.00944518i
$262$	−0.981330	−	6.19587i	−0.0606267	−	0.382782i
$263$	−5.19181	−	5.19181i	−0.320141	−	0.320141i	0.528680	−	0.848821i	$-0.322687\pi$
$263$	−5.19181	−	5.19181i	−0.320141	−	0.320141i	−0.848821	+	0.528680i	$0.822687\pi$
$264$	−5.30547	+	6.87834i	−0.326529	+	0.423333i
$265$	−1.27401	−	1.68458i	−0.0782620	−	0.103483i
$266$	9.20301	−	12.6669i	0.564273	−	0.776655i
$267$	19.3170	−	9.84250i	1.18218	−	0.602351i
$268$	8.14423	+	4.14969i	0.497488	+	0.253483i
$269$	6.06936	+	8.35375i	0.370055	+	0.509337i	0.952916	−	0.303235i	$-0.0980667\pi$
$269$	6.06936	+	8.35375i	0.370055	+	0.509337i	−0.582861	+	0.812572i	$0.698067\pi$
$270$	2.37220	+	4.44284i	0.144368	+	0.270382i
$271$	2.16113	−	0.702195i	0.131279	−	0.0426553i	−0.242640	−	0.970116i	$-0.578014\pi$
$271$	2.16113	−	0.702195i	0.131279	−	0.0426553i	0.373920	+	0.927461i	$0.378014\pi$
$272$	−2.59131	−	5.08573i	−0.157121	−	0.308368i
$273$	−13.3923	+	2.12114i	−0.810542	+	0.128377i
$274$	−0.926811			−0.0559907
$275$	−13.5098	−	9.61694i	−0.814671	−	0.579923i
$276$	6.76659			0.407301
$277$	24.8100	−	3.92951i	1.49069	−	0.236102i	0.642700	−	0.766118i	$-0.277814\pi$
$277$	24.8100	−	3.92951i	1.49069	−	0.236102i	0.847987	+	0.530016i	$0.177814\pi$
$278$	3.68729	+	7.23671i	0.221149	+	0.434029i
$279$	−13.2032	+	4.28997i	−0.790453	+	0.256834i
$280$	3.40873	+	6.38412i	0.203711	+	0.381524i
$281$	0.689825	+	0.949463i	0.0411515	+	0.0566402i	0.829097	−	0.559105i	$-0.188855\pi$
$281$	0.689825	+	0.949463i	0.0411515	+	0.0566402i	−0.787945	+	0.615745i	$0.788855\pi$
$282$	10.9624	+	5.58561i	0.652800	+	0.332618i
$283$	−15.3084	+	7.80000i	−0.909987	+	0.463662i	−0.845329	−	0.534246i	$-0.820596\pi$
$283$	−15.3084	+	7.80000i	−0.909987	+	0.463662i	−0.0646582	+	0.997907i	$0.520596\pi$
$284$	−7.40438	+	10.1913i	−0.439369	+	0.604740i
$285$	17.0898	+	22.5971i	1.01231	+	1.33854i
$286$	5.09036	−	1.49392i	0.300999	−	0.0883372i
$287$	−9.21556	−	9.21556i	−0.543977	−	0.543977i
$288$	0.603832	+	3.81244i	0.0355811	+	0.224650i
$289$	−14.8171	−	4.81436i	−0.871592	−	0.283197i
$290$	−0.163667	+	0.234607i	−0.00961088	+	0.0137766i
$291$	16.3204	−	11.8575i	0.956719	−	0.695097i
$292$	−0.673955	+	4.25518i	−0.0394402	+	0.249016i
$293$	−7.33718	+	14.4000i	−0.428643	+	0.841259i	0.571149	+	0.820846i	$0.306498\pi$
$293$	−7.33718	+	14.4000i	−0.428643	+	0.841259i	−0.999792	+	0.0204121i	$0.993502\pi$
$294$	−2.81277	+	8.65682i	−0.164044	+	0.504876i
$295$	−10.8238	−	10.4161i	−0.630184	−	0.606451i
$296$			11.0244i			0.640782i
$297$	1.37982	−	7.34177i	0.0800654	−	0.426013i
$298$	−4.84015	+	4.84015i	−0.280383	+	0.280383i
$299$	−3.34318	−	2.42896i	−0.193341	−	0.140470i
$300$	−12.8464	+	2.54341i	−0.741688	+	0.146844i
$301$	10.7182	+	32.9873i	0.617788	+	1.90136i
$302$	−3.34710	−	0.530128i	−0.192604	−	0.0305055i
$303$	38.0655	+	6.02899i	2.18681	+	0.346356i
$304$	1.49489	+	4.60081i	0.0857381	+	0.263875i
$305$	−1.93667	+	3.98832i	−0.110893	+	0.228371i
$306$	17.8244	+	12.9502i	1.01895	+	0.740311i
$307$	−16.0667	+	16.0667i	−0.916974	+	0.916974i	−0.996808	−	0.0798344i	$-0.974561\pi$
$307$	−16.0667	+	16.0667i	−0.916974	+	0.916974i	0.0798344	+	0.996808i	$0.474561\pi$
$308$	1.98273	−	10.5497i	0.112977	−	0.601127i
$309$		−	32.5196i		−	1.84998i
$310$	−0.154315	−	8.04069i	−0.00876452	−	0.456681i
$311$	2.46376	−	7.58267i	0.139707	−	0.429974i	−0.856586	−	0.516005i	$-0.827419\pi$
$311$	2.46376	−	7.58267i	0.139707	−	0.429974i	0.996292	+	0.0860315i	$0.0274186\pi$
$312$	1.90196	−	3.73280i	0.107677	−	0.211328i
$313$	−0.844278	+	5.33056i	−0.0477214	+	0.301301i	−0.999992	−	0.00395342i	$-0.998742\pi$
$313$	−0.844278	+	5.33056i	−0.0477214	+	0.301301i	0.952271	+	0.305255i	$0.0987416\pi$
$314$	−8.97327	+	6.51946i	−0.506391	+	0.367915i
$315$	−22.9109	−	15.9832i	−1.29089	−	0.900552i
$316$	−4.75208	−	1.54405i	−0.267326	−	0.0868594i
$317$	2.33714	+	14.7561i	0.131267	+	0.828785i	0.962186	+	0.272392i	$0.0878149\pi$
$317$	2.33714	+	14.7561i	0.131267	+	0.828785i	−0.830920	+	0.556392i	$0.812185\pi$
$318$	1.74934	+	1.74934i	0.0980979	+	0.0980979i
$319$	0.407118	−	0.119481i	0.0227942	−	0.00668965i
$320$	−2.21484	−	0.307356i	−0.123814	−	0.0171817i
$321$	−7.02379	+	9.66741i	−0.392029	+	0.539582i
$322$	−7.45028	+	3.79611i	−0.415188	+	0.211549i
$323$	24.6026	+	12.5357i	1.36893	+	0.697503i
$324$	3.33895	+	4.59567i	0.185497	+	0.255315i
$325$	7.26003	+	3.35477i	0.402714	+	0.186089i
$326$	16.5526	−	5.37826i	0.916762	−	0.297874i
$327$	5.42456	+	10.6463i	0.299979	+	0.588741i
$328$	3.97717	−	0.629921i	0.219602	−	0.0347816i
$329$	−15.2036			−0.838200
$330$	17.2225	+	8.98249i	0.948065	+	0.494470i
$331$	−10.8055			−0.593926			−0.296963	−	0.954889i	$-0.595974\pi$
$331$	−10.8055			−0.593926			−0.296963	+	0.954889i	$0.595974\pi$
$332$	9.20374	−	1.45773i	0.505121	−	0.0800032i
$333$	−19.3191	−	37.9159i	−1.05868	−	2.07778i
$334$	−6.42658	+	2.08812i	−0.351647	+	0.114257i
$335$	5.94177	−	19.5560i	0.324633	−	1.06846i
$336$	−4.98268	−	6.85807i	−0.271827	−	0.374138i
$337$	5.16619	+	2.63231i	0.281421	+	0.143391i	0.589004	−	0.808130i	$-0.299520\pi$
$337$	5.16619	+	2.63231i	0.281421	+	0.143391i	−0.307583	+	0.951521i	$0.599520\pi$
$338$	9.30344	−	4.74034i	0.506041	−	0.257841i
$339$	20.9873	−	28.8866i	1.13988	−	1.56891i
$340$	−10.1798	+	7.69874i	−0.552075	+	0.417523i
$341$	−7.28537	+	9.44520i	−0.394525	+	0.511486i
$342$	−13.2037	−	13.2037i	−0.713976	−	0.713976i
$343$	1.78459	+	11.2675i	0.0963589	+	0.608386i
$344$	−10.1921	−	3.31161i	−0.549521	−	0.178550i
$345$	−2.65326	−	14.8961i	−0.142847	−	0.801979i
$346$	−4.35252	+	3.16229i	−0.233993	+	0.170006i
$347$	−4.26838	+	26.9495i	−0.229138	+	1.44672i	0.557946	+	0.829878i	$0.311590\pi$
$347$	−4.26838	+	26.9495i	−0.229138	+	1.44672i	−0.787084	+	0.616846i	$0.788410\pi$
$348$	0.152115	−	0.298543i	0.00815423	−	0.0160036i
$349$	−3.82556	+	11.7739i	−0.204777	+	0.630240i	0.794945	+	0.606681i	$0.207500\pi$
$349$	−3.82556	+	11.7739i	−0.204777	+	0.630240i	−0.999722	+	0.0235584i	$0.992500\pi$
$350$	12.7175	−	10.0073i	0.679781	−	0.534914i
$351$			3.60276i			0.192301i
$352$	2.27696	+	2.41153i	0.121362	+	0.128535i
$353$	−6.40125	+	6.40125i	−0.340704	+	0.340704i	−0.856632	−	0.515928i	$-0.827447\pi$
$353$	−6.40125	+	6.40125i	−0.340704	+	0.340704i	0.515928	+	0.856632i	$0.327447\pi$
$354$	14.2348	+	10.3422i	0.756571	+	0.549681i
$355$	25.3386	+	12.3040i	1.34483	+	0.653031i
$356$	−2.55788	−	7.87234i	−0.135567	−	0.417233i
$357$	−47.7900	−	7.56919i	−2.52931	−	0.400604i
$358$	−13.6236	−	2.15777i	−0.720030	−	0.114041i
$359$	5.66855	+	17.4460i	0.299175	+	0.920766i	0.981787	+	0.189985i	$0.0608439\pi$
$359$	5.66855	+	17.4460i	0.299175	+	0.920766i	−0.682612	+	0.730781i	$0.739156\pi$
$360$	8.15602	−	2.82419i	0.429860	−	0.148848i
$361$	−3.56143	−	2.58753i	−0.187444	−	0.136186i
$362$	13.0556	−	13.0556i	0.686188	−	0.686188i
$363$	−11.5858	−	26.3785i	−0.608099	−	1.38451i
$364$			5.17697i			0.271347i
$365$	9.63171	−	0.184850i	0.504147	−	0.00967547i
$366$	1.60480	−	4.93907i	0.0838843	−	0.258169i
$367$	−3.84253	+	7.54139i	−0.200579	+	0.393658i	−0.969284	−	0.245946i	$-0.920901\pi$
$367$	−3.84253	+	7.54139i	−0.200579	+	0.393658i	0.768705	+	0.639603i	$0.220901\pi$
$368$	0.404149	−	2.55169i	0.0210677	−	0.133016i
$369$	−12.5746	+	9.13600i	−0.654609	+	0.475601i
$370$	24.2694	−	4.32281i	1.26171	−	0.224732i
$371$	−2.90748	−	0.944698i	−0.150949	−	0.0490463i
$372$	1.47361	+	9.30399i	0.0764030	+	0.482389i
$373$	6.13803	+	6.13803i	0.317815	+	0.317815i	0.847928	−	0.530112i	$-0.177850\pi$
$373$	6.13803	+	6.13803i	0.317815	+	0.317815i	−0.530112	+	0.847928i	$0.677850\pi$
$374$	18.9230	+	0.543139i	0.978486	+	0.0280851i
$375$	10.6363	+	27.2830i	0.549258	+	1.40889i
$376$	2.76109	−	3.80032i	0.142393	−	0.195987i
$377$	−0.182322	+	0.0928975i	−0.00939004	+	0.00478447i
$378$	6.49540	+	3.30957i	0.334087	+	0.170226i
$379$	−3.24623	−	4.46805i	−0.166747	−	0.229508i	0.717463	−	0.696596i	$-0.245303\pi$
$379$	−3.24623	−	4.46805i	−0.166747	−	0.229508i	−0.884211	+	0.467088i	$0.845303\pi$
$380$	9.54215	−	5.09492i	0.489502	−	0.261364i
$381$	2.92883	−	0.951633i	0.150048	−	0.0487536i
$382$	−1.01956	−	2.00100i	−0.0521653	−	0.102380i
$383$	−19.3184	+	3.05974i	−0.987126	+	0.156345i	−0.629065	−	0.777353i	$-0.716562\pi$
$383$	−19.3184	+	3.05974i	−0.987126	+	0.156345i	−0.358061	+	0.933698i	$0.616562\pi$
$384$	2.61915			0.133658
$385$	−24.0019	−	0.228151i	−1.22325	−	0.0116276i
$386$	−6.01503			−0.306157
$387$	40.8564	−	6.47102i	2.07685	−	0.328941i
$388$	−3.49670	−	6.86267i	−0.177518	−	0.348399i
$389$	1.75370	−	0.569811i	0.0889160	−	0.0288906i	−0.264221	−	0.964462i	$-0.585115\pi$
$389$	1.75370	−	0.569811i	0.0889160	−	0.0288906i	0.353137	+	0.935572i	$0.385115\pi$
$390$	−8.96324	−	2.72333i	−0.453871	−	0.137901i
$391$	−8.66763	−	11.9300i	−0.438341	−	0.603324i
$392$	3.09651	+	1.57775i	0.156397	+	0.0796884i
$393$	14.6394	−	7.45916i	0.738462	−	0.376265i
$394$	3.83485	−	5.27822i	0.193197	−	0.265913i
$395$	−1.53574	+	11.0668i	−0.0772717	+	0.556830i
$396$	−12.0570	−	4.30375i	−0.605885	−	0.216272i
$397$	1.60774	+	1.60774i	0.0806902	+	0.0806902i	0.746300	−	0.665610i	$-0.231828\pi$
$397$	1.60774	+	1.60774i	0.0806902	+	0.0806902i	−0.665610	+	0.746300i	$0.731828\pi$
$398$	2.95080	+	18.6306i	0.147910	+	0.933868i
$399$	39.0012	+	12.6723i	1.95250	+	0.634407i
$400$	0.191847	+	4.99632i	0.00959236	+	0.249816i
$401$	20.4567	−	14.8626i	1.02156	−	0.742204i	0.0549551	−	0.998489i	$-0.482498\pi$
$401$	20.4567	−	14.8626i	1.02156	−	0.742204i	0.966601	+	0.256285i	$0.0824984\pi$
$402$	−3.74509	+	23.6456i	−0.186788	+	1.17933i
$403$	2.61173	−	5.12580i	0.130099	−	0.255335i
$404$	4.54709	−	13.9945i	0.226226	−	0.696252i
$405$	8.80776	−	9.15245i	0.437661	−	0.454789i
$406$			0.414045i			0.0205487i
$407$	−32.0890	−	17.5275i	−1.59059	−	0.868808i
$408$	10.5711	−	10.5711i	0.523346	−	0.523346i
$409$	−29.0630	−	21.1155i	−1.43707	−	1.04409i	−0.988644	−	0.150275i	$-0.951984\pi$
$409$	−29.0630	−	21.1155i	−1.43707	−	1.04409i	−0.448428	−	0.893819i	$-0.648016\pi$
$410$	−2.94621	−	8.50841i	−0.145503	−	0.420200i
$411$	−0.750127	−	2.30865i	−0.0370010	−	0.113877i
$412$	−12.2632	−	1.94230i	−0.604166	−	0.0956904i
$413$	−21.4751	−	3.40133i	−1.05672	−	0.167368i
$414$	3.08159	+	9.48415i	0.151452	+	0.466121i
$415$	−6.81796	−	19.6897i	−0.334681	−	0.966529i
$416$	−1.29405	−	0.940181i	−0.0634459	−	0.0460962i
$417$	−15.0420	+	15.0420i	−0.736611	+	0.736611i
$418$	−15.7684	−	2.96353i	−0.771256	−	0.144951i
$419$		−	6.83916i		−	0.334115i	−0.985947	−	0.167057i	$-0.946574\pi$
$419$		−	6.83916i		−	0.334115i	0.985947	−	0.167057i	$-0.0534265\pi$
$420$	−13.1437	+	13.6581i	−0.641348	+	0.666447i
$421$	12.0450	−	37.0708i	0.587039	−	1.80672i	−0.00388275	−	0.999992i	$-0.501236\pi$
$421$	12.0450	−	37.0708i	0.587039	−	1.80672i	0.590922	−	0.806729i	$-0.298764\pi$
$422$	0.690489	−	1.35516i	0.0336125	−	0.0659682i
$423$	−2.83647	+	17.9088i	−0.137914	+	0.870755i
$424$	0.764161	−	0.555196i	0.0371109	−	0.0269627i
$425$	20.9398	+	19.3911i	1.01573	+	0.940608i
$426$	−31.3789	−	10.1956i	−1.52031	−	0.493979i
$427$	1.00391	+	6.33842i	0.0485825	+	0.306738i
$428$	3.22609	+	3.22609i	0.155939	+	0.155939i
$429$	7.84124	+	11.4708i	0.378579	+	0.553814i
$430$	−3.29381	+	23.7356i	−0.158842	+	1.14463i
$431$	−11.6062	+	15.9746i	−0.559053	+	0.769471i	−0.991206	−	0.132330i	$-0.957754\pi$
$431$	−11.6062	+	15.9746i	−0.559053	+	0.769471i	0.432153	+	0.901801i	$0.357754\pi$
$432$	−2.00689	+	1.02256i	−0.0965564	+	0.0491979i
$433$	−0.909451	−	0.463389i	−0.0437054	−	0.0222690i	0.432001	−	0.901873i	$-0.357808\pi$
$433$	−0.909451	−	0.463389i	−0.0437054	−	0.0222690i	−0.475707	+	0.879604i	$0.657808\pi$
$434$	−6.84211	−	9.41736i	−0.328432	−	0.452048i
$435$	−0.716864	−	0.217807i	−0.0343710	−	0.0104431i
$436$	4.33873	−	1.40974i	0.207788	−	0.0675143i
$437$	5.67393	+	11.1357i	0.271421	+	0.532693i
$438$	−11.1450	+	1.76519i	−0.532527	+	0.0843441i
$439$	19.3109			0.921658			0.460829	−	0.887489i	$-0.347552\pi$
$439$	19.3109			0.921658			0.460829	+	0.887489i	$0.347552\pi$
$440$	4.41596	−	5.95813i	0.210523	−	0.284042i
$441$	−13.4145			−0.638786
$442$	−9.01749	+	1.42823i	−0.428918	+	0.0679339i
$443$	14.9363	+	29.3141i	0.709645	+	1.39276i	0.910655	+	0.413167i	$0.135577\pi$
$443$	14.9363	+	29.3141i	0.709645	+	1.39276i	−0.201011	+	0.979589i	$0.564423\pi$
$444$	−27.4615	+	8.92277i	−1.30326	+	0.423456i
$445$	−16.3274	+	8.71780i	−0.773991	+	0.413263i
$446$	−4.30080	−	5.91954i	−0.203649	−	0.280298i
$447$	−15.9741	−	8.13920i	−0.755548	−	0.384971i
$448$	−2.88379	+	1.46937i	−0.136246	+	0.0694210i
$449$	−7.46214	+	10.2708i	−0.352160	+	0.484707i	−0.947944	−	0.318438i	$-0.896842\pi$
$449$	−7.46214	+	10.2708i	−0.352160	+	0.484707i	0.595783	+	0.803145i	$0.296842\pi$
$450$	−9.41530	−	16.8474i	−0.443841	−	0.794195i
$451$	−4.48970	+	12.5779i	−0.211412	+	0.592271i
$452$	−9.63969	−	9.63969i	−0.453413	−	0.453413i
$453$	−1.38849	−	8.76657i	−0.0652368	−	0.411889i
$454$	−24.0848	−	7.82562i	−1.13036	−	0.367275i
$455$	11.3967	−	2.02995i	0.534285	−	0.0951656i
$456$	−10.2505	+	7.44745i	−0.480025	+	0.348759i
$457$	−1.89960	+	11.9936i	−0.0888595	+	0.561037i	0.902585	+	0.430511i	$0.141667\pi$
$457$	−1.89960	+	11.9936i	−0.0888595	+	0.561037i	−0.991445	+	0.130526i	$0.958333\pi$
$458$	4.65908	−	9.14397i	0.217705	−	0.427270i
$459$	−3.97280	+	12.2270i	−0.185435	+	0.570709i
$460$	−5.77582	+	0.110848i	−0.269299	+	0.00516833i
$461$		−	32.1562i		−	1.49766i	−0.662761	−	0.748831i	$-0.730615\pi$
$461$		−	32.1562i		−	1.49766i	0.662761	−	0.748831i	$-0.269385\pi$
$462$	27.8838	−	3.59965i	1.29727	−	0.167471i
$463$	25.6290	−	25.6290i	1.19108	−	1.19108i	0.214318	−	0.976764i	$-0.431247\pi$
$463$	25.6290	−	25.6290i	1.19108	−	1.19108i	0.976764	−	0.214318i	$-0.0687528\pi$
$464$	−0.103496	−	0.0751940i	−0.00480467	−	0.00349079i
$465$	19.9042	−	6.89223i	0.923034	−	0.319620i
$466$	6.71291	+	20.6602i	0.310970	+	0.957066i
$467$	8.33160	+	1.31960i	0.385540	+	0.0610636i	0.346196	−	0.938162i	$-0.387473\pi$
$467$	8.33160	+	1.31960i	0.385540	+	0.0610636i	0.0393442	+	0.999226i	$0.487473\pi$
$468$	6.09812	+	0.965848i	0.281886	+	0.0446463i
$469$	−9.14186	−	28.1358i	−0.422132	−	1.29919i
$470$	−9.44876	−	4.58818i	−0.435839	−	0.211637i
$471$	−23.5024	−	17.0755i	−1.08293	−	0.786796i
$472$	4.75026	−	4.75026i	0.218649	−	0.218649i
$473$	25.8434	−	24.4012i	1.18828	−	1.12197i
$474$		−	13.0870i		−	0.601104i
$475$	−14.9576	−	19.0085i	−0.686304	−	0.872170i
$476$	−5.70871	+	17.5696i	−0.261658	+	0.805302i
$477$	−1.65523	+	3.24857i	−0.0757876	+	0.148742i
$478$	−3.43249	+	21.6719i	−0.156999	+	0.991251i
$479$	15.1553	−	11.0110i	0.692463	−	0.503104i	−0.185006	−	0.982737i	$-0.559230\pi$
$479$	15.1553	−	11.0110i	0.692463	−	0.503104i	0.877469	+	0.479634i	$0.159230\pi$
$480$	−1.02700	−	5.76586i	−0.0468760	−	0.263174i
$481$	16.7709	+	5.44919i	0.764686	+	0.248462i
$482$	2.05545	+	12.9776i	0.0936230	+	0.591112i
$483$	−15.4859	−	15.4859i	−0.704635	−	0.704635i
$484$	−10.6394	+	2.79353i	−0.483608	+	0.126979i
$485$	−13.7365	+	10.3886i	−0.623743	+	0.471724i
$486$	−12.7170	+	17.5034i	−0.576854	+	0.793971i
$487$	−13.0107	+	6.62928i	−0.589571	+	0.300401i	−0.723209	−	0.690629i	$-0.757334\pi$
$487$	−13.0107	+	6.62928i	−0.589571	+	0.300401i	0.133639	+	0.991030i	$0.457334\pi$
$488$	−1.76668	−	0.900171i	−0.0799740	−	0.0407488i
$489$	26.7941	+	36.8789i	1.21167	+	1.66772i
$490$	2.25911	−	7.43537i	0.102056	−	0.335896i
$491$	14.6579	−	4.76263i	0.661500	−	0.214934i	0.0410222	−	0.999158i	$-0.486939\pi$
$491$	14.6579	−	4.76263i	0.661500	−	0.214934i	0.620478	+	0.784224i	$0.286939\pi$
$492$	4.78808	+	9.39714i	0.215863	+	0.423656i
$493$	−0.721203	+	0.114227i	−0.0324813	+	0.00514454i
$494$	7.73786			0.348143
$495$	−4.74668	+	28.2300i	−0.213347	+	1.26884i
$496$	3.59657			0.161491
$497$	40.2692	−	6.37802i	1.80632	−	0.286093i
$498$	11.0803	+	21.7463i	0.496521	+	0.974477i
$499$	−22.7215	+	7.38268i	−1.01716	+	0.330494i	−0.769700	−	0.638405i	$-0.779594\pi$
$499$	−22.7215	+	7.38268i	−1.01716	+	0.330494i	−0.247455	+	0.968899i	$0.579594\pi$
$500$	10.9238	−	2.38145i	0.488526	−	0.106502i
$501$	−10.4029	−	14.3183i	−0.464766	−	0.639696i
$502$	8.80473	+	4.48623i	0.392974	+	0.200230i
$503$	−2.00522	+	1.02171i	−0.0894081	+	0.0455557i	−0.498123	−	0.867106i	$-0.665977\pi$
$503$	−2.00522	+	1.02171i	−0.0894081	+	0.0455557i	0.408715	+	0.912662i	$0.365977\pi$
$504$	7.34320	−	10.1070i	0.327092	−	0.450204i
$505$	−32.5907	−	4.52264i	−1.45027	−	0.201255i
$506$	6.78471	+	5.23325i	0.301617	+	0.232647i
$507$	19.3379	+	19.3379i	0.858825	+	0.858825i
$508$	−0.183933	−	1.16130i	−0.00816069	−	0.0515246i
$509$	−8.34206	−	2.71050i	−0.369755	−	0.120141i	0.118245	−	0.992984i	$-0.462273\pi$
$509$	−8.34206	−	2.71050i	−0.369755	−	0.120141i	−0.488000	+	0.872844i	$0.662273\pi$
$510$	−27.4164	−	19.1263i	−1.21402	−	0.846927i
$511$	11.2808	−	8.19596i	0.499032	−	0.362568i
$512$	0.156434	−	0.987688i	0.00691349	−	0.0436501i
$513$	4.94671	−	9.70847i	0.218403	−	0.428640i
$514$	8.95456	−	27.5593i	0.394969	−	1.21559i
$515$	0.532728	+	27.7581i	0.0234748	+	1.22317i
$516$		−	28.0684i		−	1.23564i
$517$	6.67185	+	14.0788i	0.293428	+	0.619186i
$518$	25.2304	−	25.2304i	1.10856	−	1.10856i
$519$	−11.3999	−	8.28252i	−0.500401	−	0.363562i
$520$	−1.56232	+	3.21740i	−0.0685123	+	0.141092i
$521$	−3.59644	−	11.0687i	−0.157563	−	0.484928i	0.840849	−	0.541270i	$-0.182056\pi$
$521$	−3.59644	−	11.0687i	−0.157563	−	0.484928i	−0.998412	+	0.0563418i	$0.982056\pi$
$522$	0.487717	+	0.0772468i	0.0213468	+	0.00338100i
$523$	24.0007	+	3.80134i	1.04948	+	0.166221i	0.657270	−	0.753655i	$-0.271711\pi$
$523$	24.0007	+	3.80134i	1.04948	+	0.166221i	0.392209	+	0.919876i	$0.371711\pi$
$524$	−1.93850	−	5.96608i	−0.0846836	−	0.260629i
$525$	35.2210	+	23.5793i	1.53717	+	1.02909i
$526$	−5.94007	−	4.31571i	−0.258999	−	0.188174i
$527$	14.5160	−	14.5160i	0.632326	−	0.632326i
$528$	−4.16414	+	7.62362i	−0.181221	+	0.331775i
$529$			16.3255i			0.709805i
$530$	−1.52186	−	1.46454i	−0.0661052	−	0.0636156i
$531$	−8.01306	+	24.6617i	−0.347737	+	1.07023i
$532$	7.10817	−	13.9506i	0.308178	−	0.604834i
$533$	1.00758	−	6.36160i	0.0436431	−	0.275552i
$534$	17.5395	−	12.7432i	0.759007	−	0.551451i
$535$	5.83699	−	8.36697i	0.252355	−	0.361736i
$536$	8.69312	+	2.82456i	0.375485	+	0.122003i
$537$	−5.65152	−	35.6823i	−0.243881	−	1.53981i
$538$	7.30145	+	7.30145i	0.314788	+	0.314788i
$539$	−9.51546	+	6.50462i	−0.409860	+	0.280174i
$540$	3.03801	+	4.01704i	0.130735	+	0.172866i
$541$	−21.6471	+	29.7947i	−0.930681	+	1.28097i	0.0289124	+	0.999582i	$0.490796\pi$
$541$	−21.6471	+	29.7947i	−0.930681	+	1.28097i	−0.959593	+	0.281390i	$0.909204\pi$
$542$	2.02468	−	1.03163i	0.0869674	−	0.0443121i
$543$	43.0878	+	21.9543i	1.84908	+	0.942151i
$544$	−3.35499	−	4.61775i	−0.143844	−	0.197984i
$545$	−4.80469	−	8.99859i	−0.205811	−	0.385457i
$546$	−12.8956	+	4.19005i	−0.551883	+	0.179318i
$547$	−8.92433	−	17.5150i	−0.381577	−	0.748887i	0.617719	−	0.786399i	$-0.288057\pi$
$547$	−8.92433	−	17.5150i	−0.381577	−	0.748887i	−0.999296	+	0.0375120i	$0.988057\pi$
$548$	−0.915400	+	0.144985i	−0.0391040	+	0.00619346i
$549$	7.65352			0.326644
$550$	−14.8479	−	7.38514i	−0.633116	−	0.314903i
$551$	0.618860			0.0263643
$552$	6.68328	−	1.05853i	0.284459	−	0.0450539i
$553$	7.34189	+	14.4093i	0.312209	+	0.612744i
$554$	23.8898	−	7.76227i	1.01498	−	0.329787i
$555$	30.4107	+	56.9555i	1.29086	+	2.41763i
$556$	4.77396	+	6.57080i	0.202461	+	0.278664i
$557$	−33.2318	−	16.9324i	−1.40807	−	0.717450i	−0.425786	−	0.904824i	$-0.640002\pi$
$557$	−33.2318	−	16.9324i	−1.40807	−	0.717450i	−0.982289	+	0.187374i	$0.940002\pi$
$558$	−12.3695	+	6.30258i	−0.523643	+	0.266810i
$559$	−10.0755	+	13.8678i	−0.426150	+	0.586546i
$560$	4.36546	+	5.77228i	0.184474	+	0.243923i
$561$	13.9626	+	47.5761i	0.589503	+	2.00867i
$562$	0.829861	+	0.829861i	0.0350056	+	0.0350056i
$563$	−5.81527	−	36.7162i	−0.245084	−	1.54740i	−0.736476	−	0.676463i	$-0.763512\pi$
$563$	−5.81527	−	36.7162i	−0.245084	−	1.54740i	0.491392	−	0.870939i	$-0.336488\pi$
$564$	11.7012	+	3.80195i	0.492709	+	0.160091i
$565$	−17.4412	+	25.0008i	−0.733755	+	1.05179i
$566$	−13.8997	+	10.0987i	−0.584248	+	0.424481i
$567$	2.87612	−	18.1591i	0.120786	−	0.762611i
$568$	−5.71896	+	11.2241i	−0.239962	+	0.470952i
$569$	13.9935	−	43.0676i	0.586638	−	1.80549i	−0.00595291	−	0.999982i	$-0.501895\pi$
$569$	13.9935	−	43.0676i	0.586638	−	1.80549i	0.592591	−	0.805504i	$-0.298105\pi$
$570$	20.4143	+	19.6455i	0.855062	+	0.822860i
$571$			31.9380i			1.33656i	0.743909	+	0.668281i	$0.232970\pi$
$571$			31.9380i			1.33656i	−0.743909	+	0.668281i	$0.767030\pi$
$572$	4.79398	−	2.27183i	0.200447	−	0.0949901i
$573$	4.15923	−	4.15923i	0.173754	−	0.173754i
$574$	−10.5437	−	7.66047i	−0.440087	−	0.319742i
$575$	2.50879	+	12.6715i	0.104624	+	0.528440i
$576$	1.19279	+	3.67105i	0.0496998	+	0.152960i
$577$	14.2295	+	2.25373i	0.592381	+	0.0938240i	0.445425	−	0.895319i	$-0.353052\pi$
$577$	14.2295	+	2.25373i	0.592381	+	0.0938240i	0.146956	+	0.989143i	$0.453052\pi$
$578$	−15.3878	−	2.43718i	−0.640047	−	0.101373i
$579$	−4.86834	−	14.9832i	−0.202321	−	0.622681i
$580$	−0.124952	+	0.257322i	−0.00518834	+	0.0106847i
$581$	−24.3997	−	17.7274i	−1.01227	−	0.735458i
$582$	14.2645	−	14.2645i	0.591285	−	0.591285i
$583$	0.401092	+	3.10695i	0.0166115	+	0.128677i
$584$			4.30822i			0.178276i
$585$	−0.264909	−	13.8032i	−0.0109526	−	0.570694i
$586$	−4.99419	+	15.3705i	−0.206308	+	0.634951i
$587$	2.11966	−	4.16006i	0.0874876	−	0.171704i	−0.843117	−	0.537730i	$-0.819282\pi$
$587$	2.11966	−	4.16006i	0.0874876	−	0.171704i	0.930605	+	0.366026i	$0.119282\pi$
$588$	−1.42392	+	8.99026i	−0.0587213	+	0.370752i
$589$	−14.0758	+	10.2267i	−0.579985	+	0.421383i
$590$	−12.3200	−	8.59469i	−0.507205	−	0.353838i
$591$	16.2516	+	5.28048i	0.668503	+	0.217210i
$592$	1.72460	+	10.8887i	0.0708807	+	0.447523i
$593$	−8.01116	−	8.01116i	−0.328979	−	0.328979i	0.523219	−	0.852198i	$-0.324731\pi$
$593$	−8.01116	−	8.01116i	−0.328979	−	0.328979i	−0.852198	+	0.523219i	$0.824731\pi$
$594$	0.214329	−	7.46723i	0.00879402	−	0.306384i
$595$	40.9165	+	5.67802i	1.67741	+	0.232776i
$596$	−4.02340	+	5.53773i	−0.164805	+	0.226834i
$597$	−44.0199	+	22.4293i	−1.80161	+	0.917968i
$598$	−3.68199	−	1.87607i	−0.150568	−	0.0767181i
$599$	−23.4305	−	32.2493i	−0.957344	−	1.31767i	−0.948187	−	0.317712i	$-0.897085\pi$
$599$	−23.4305	−	32.2493i	−0.957344	−	1.31767i	−0.00915634	−	0.999958i	$-0.502915\pi$
$600$	−12.2904	+	4.52172i	−0.501752	+	0.184598i
$601$	−16.0018	+	5.19929i	−0.652726	+	0.212084i	−0.616616	−	0.787264i	$-0.711497\pi$
$601$	−16.0018	+	5.19929i	−0.652726	+	0.212084i	−0.0361105	+	0.999348i	$0.511497\pi$
$602$	15.7466	+	30.9045i	0.641784	+	1.25957i
$603$	−34.8476	+	5.51931i	−1.41910	+	0.224764i
$604$	−3.38882			−0.137889
$605$	10.3216	+	22.3263i	0.419631	+	0.907695i
$606$	38.5400			1.56558
$607$	−5.79891	+	0.918457i	−0.235371	+	0.0372790i	−0.273005	−	0.962013i	$-0.588018\pi$
$607$	−5.79891	+	0.918457i	−0.235371	+	0.0372790i	0.0376348	+	0.999292i	$0.488018\pi$
$608$	2.19621	+	4.31031i	0.0890683	+	0.174806i
$609$	−1.03137	+	0.335113i	−0.0417933	+	0.0135795i
$610$	−1.28892	+	4.24218i	−0.0521867	+	0.171761i
$611$	−4.41646	−	6.07873i	−0.178671	−	0.245919i
$612$	19.6308	+	10.0024i	0.793526	+	0.404322i
$613$	13.8788	−	7.07161i	0.560560	−	0.285620i	−0.150664	−	0.988585i	$-0.548141\pi$
$613$	13.8788	−	7.07161i	0.560560	−	0.285620i	0.711224	+	0.702965i	$0.248141\pi$
$614$	−13.3555	+	18.3823i	−0.538984	+	0.741847i
$615$	18.8096	−	14.2253i	0.758476	−	0.573620i
$616$	0.307979	−	10.7300i	0.0124088	−	0.432325i
$617$	17.6157	+	17.6157i	0.709182	+	0.709182i	0.966363	−	0.257182i	$-0.0827938\pi$
$617$	17.6157	+	17.6157i	0.709182	+	0.709182i	−0.257182	+	0.966363i	$0.582794\pi$
$618$	−5.08719	−	32.1193i	−0.204637	−	1.29203i
$619$	3.12719	+	1.01609i	0.125693	+	0.0408400i	0.371188	−	0.928558i	$-0.378951\pi$
$619$	3.12719	+	1.01609i	0.125693	+	0.0408400i	−0.245495	+	0.969398i	$0.578951\pi$
$620$	−1.41026	−	7.91756i	−0.0566373	−	0.317977i
$621$	−4.70770	+	3.42034i	−0.188913	+	0.137254i
$622$	1.24723	−	7.87473i	0.0500095	−	0.315748i
$623$	−12.1626	+	23.8705i	−0.487285	+	0.956351i
$624$	1.29460	−	3.98437i	0.0518255	−	0.159503i
$625$	−9.52591	−	23.1140i	−0.381036	−	0.924560i
$626$			5.39701i			0.215708i
$627$	−5.38029	−	41.6770i	−0.214868	−	1.66442i
$628$	−7.84293	+	7.84293i	−0.312967	+	0.312967i
$629$	50.9081	+	36.9869i	2.02984	+	1.47476i
$630$	−25.1292	−	12.2024i	−1.00117	−	0.486154i
$631$	−13.7076	−	42.1877i	−0.545692	−	1.67947i	−0.719340	−	0.694658i	$-0.755556\pi$
$631$	−13.7076	−	42.1877i	−0.545692	−	1.67947i	0.173648	−	0.984808i	$-0.444444\pi$
$632$	−4.93512	−	0.781646i	−0.196309	−	0.0310922i
$633$	3.93451	+	0.623166i	0.156383	+	0.0247686i
$634$	4.61672	+	14.2088i	0.183354	+	0.564304i
$635$	−2.48440	+	0.860274i	−0.0985903	+	0.0341389i
$636$	2.00146	+	1.45414i	0.0793629	+	0.0576605i
$637$	3.93069	−	3.93069i	0.155740	−	0.155740i
$638$	0.383414	−	0.181697i	0.0151795	−	0.00719346i
$639$		−	48.6243i		−	1.92355i
$640$	−2.23566	+	0.0429062i	−0.0883721	+	0.00169602i
$641$	4.66993	−	14.3726i	0.184451	−	0.567682i	−0.815487	−	0.578775i	$-0.803531\pi$
$641$	4.66993	−	14.3726i	0.184451	−	0.567682i	0.999938	+	0.0110930i	$0.00353107\pi$
$642$	−5.42499	+	10.6472i	−0.214107	+	0.420210i
$643$	4.44964	−	28.0939i	0.175477	−	1.10792i	−0.729978	−	0.683471i	$-0.760470\pi$
$643$	4.44964	−	28.0939i	0.175477	−	1.10792i	0.905454	−	0.424444i	$-0.139530\pi$
$644$	−6.76471	+	4.91485i	−0.266567	+	0.193672i
$645$	−61.7904	+	11.0060i	−2.43299	+	0.433359i
$646$	26.2608	+	8.53264i	1.03322	+	0.335712i
$647$	−0.587106	−	3.70684i	−0.0230815	−	0.145731i	0.973456	−	0.228874i	$-0.0735043\pi$
$647$	−0.587106	−	3.70684i	−0.0230815	−	0.145731i	−0.996538	+	0.0831427i	$0.973504\pi$
$648$	4.01676	+	4.01676i	0.157793	+	0.157793i
$649$	6.27432	+	21.3790i	0.246289	+	0.839200i
$650$	7.69545	+	2.17775i	0.301840	+	0.0854182i
$651$	17.9205	−	24.6655i	0.702361	−	0.966717i
$652$	15.5074	−	7.90143i	0.607318	−	0.309444i
$653$	−34.8065	−	17.7348i	−1.36209	−	0.694017i	−0.388310	−	0.921529i	$-0.626941\pi$
$653$	−34.8065	−	17.7348i	−1.36209	−	0.694017i	−0.973775	+	0.227512i	$0.926941\pi$
$654$	7.02322	+	9.66663i	0.274629	+	0.377995i
$655$	−12.3737	+	6.60681i	−0.483482	+	0.258149i
$656$	3.82966	−	1.24433i	0.149523	−	0.0485830i
$657$	−7.54968	−	14.8171i	−0.294541	−	0.578069i
$658$	−15.0164	+	2.37836i	−0.585400	+	0.0927182i
$659$	18.8202			0.733133			0.366566	−	0.930392i	$-0.380533\pi$
$659$	18.8202			0.733133			0.366566	+	0.930392i	$0.380533\pi$
$660$	18.4156	+	6.17772i	0.716826	+	0.240467i
$661$	−20.2793			−0.788774			−0.394387	−	0.918944i	$-0.629043\pi$
$661$	−20.2793			−0.788774			−0.394387	+	0.918944i	$0.629043\pi$
$662$	−10.6725	+	1.69036i	−0.414799	+	0.0656977i
$663$	−10.8561	−	21.3063i	−0.421615	−	0.827467i
$664$	8.86238	−	2.87956i	0.343927	−	0.111749i
$665$	−33.4983	−	10.1779i	−1.29901	−	0.394681i
$666$	−25.0126	−	34.4269i	−0.969218	−	1.33401i
$667$	−0.294479	−	0.150045i	−0.0114023	−	0.00580975i
$668$	−6.02080	+	3.06775i	−0.232952	+	0.118695i
$669$	11.2645	−	15.5042i	0.435509	−	0.599427i
$670$	2.80938	−	20.2447i	0.108536	−	0.782123i
$671$	5.42896	−	3.71115i	0.209583	−	0.143268i
$672$	−5.99417	−	5.99417i	−0.231230	−	0.231230i
$673$	5.08142	+	32.0828i	0.195874	+	1.23670i	0.868113	+	0.496367i	$0.165333\pi$
$673$	5.08142	+	32.0828i	0.195874	+	1.23670i	−0.672239	+	0.740335i	$0.734667\pi$
$674$	5.51437	+	1.79173i	0.212406	+	0.0690148i
$675$	7.65196	−	8.26306i	0.294524	−	0.318045i
$676$	8.44735	−	6.13736i	0.324898	−	0.236052i
$677$	−6.36796	+	40.2057i	−0.244740	+	1.54523i	0.492930	+	0.870069i	$0.335926\pi$
$677$	−6.36796	+	40.2057i	−0.244740	+	1.54523i	−0.737670	+	0.675161i	$0.764074\pi$
$678$	16.2101	−	31.8141i	0.622545	−	1.22181i
$679$	−7.70331	+	23.7084i	−0.295626	+	0.909843i
$680$	−8.85007	+	9.19642i	−0.339385	+	0.352667i
$681$		−	66.3281i		−	2.54170i
$682$	−5.71812	+	10.4686i	−0.218958	+	0.400863i
$683$	−3.51088	+	3.51088i	−0.134340	+	0.134340i	−0.771079	−	0.636739i	$-0.780283\pi$
$683$	−3.51088	+	3.51088i	−0.134340	+	0.134340i	0.636739	+	0.771079i	$0.280283\pi$
$684$	−15.1067	−	10.9756i	−0.577619	−	0.419664i
$685$	0.678112	+	1.95833i	0.0259093	+	0.0748240i
$686$	3.52524	+	10.8496i	0.134594	+	0.414239i
$687$	26.5482	+	4.20482i	1.01288	+	0.160424i
$688$	−10.5847	−	1.67645i	−0.403537	−	0.0639139i
$689$	−0.466877	−	1.43690i	−0.0177866	−	0.0547415i
$690$	−4.95086	−	14.2976i	−0.188476	−	0.544302i
$691$	−14.6693	−	10.6579i	−0.558046	−	0.405444i	0.272697	−	0.962100i	$-0.412084\pi$
$691$	−14.6693	−	10.6579i	−0.558046	−	0.405444i	−0.830743	+	0.556656i	$0.812084\pi$
$692$	−3.80424	+	3.80424i	−0.144616	+	0.144616i
$693$	17.7439	+	37.4430i	0.674036	+	1.42234i
$694$			27.2854i			1.03574i
$695$	12.5932	−	13.0860i	0.477686	−	0.496380i
$696$	0.103540	−	0.318663i	0.00392467	−	0.0120789i
$697$	10.4345	−	20.4789i	0.395236	−	0.775695i
$698$	−1.93662	+	12.2273i	−0.0733022	+	0.462812i
$699$	−46.0307	+	33.4432i	−1.74104	+	1.26494i
$700$	10.9955	−	11.8736i	0.415590	−	0.448779i
$701$	21.4667	+	6.97496i	0.810786	+	0.263440i	0.684931	−	0.728608i	$-0.259832\pi$
$701$	21.4667	+	6.97496i	0.810786	+	0.263440i	0.125856	+	0.992049i	$0.459832\pi$
$702$	0.563595	+	3.55840i	0.0212715	+	0.134303i
$703$	−37.7111	−	37.7111i	−1.42230	−	1.42230i
$704$	2.62617	+	2.02564i	0.0989775	+	0.0763443i
$705$	3.78151	−	27.2500i	0.142420	−	1.02629i
$706$	−5.32107	+	7.32382i	−0.200261	+	0.275636i
$707$	−42.4341	+	21.6212i	−1.59590	+	0.813150i
$708$	15.6774	+	7.98804i	0.589193	+	0.300209i
$709$	15.6188	+	21.4974i	0.586575	+	0.807352i	0.994397	−	0.105710i	$-0.0337115\pi$
$709$	15.6188	+	21.4974i	0.586575	+	0.807352i	−0.407822	+	0.913062i	$0.633712\pi$
$710$	26.9514	+	8.18873i	1.01147	+	0.307318i
$711$	18.3429	−	5.95996i	0.687912	−	0.223516i
$712$	−3.75789	−	7.37528i	−0.140833	−	0.276400i
$713$	9.17735	−	1.45355i	0.343694	−	0.0544358i
$714$	−48.3857			−1.81079
$715$	−6.88103	−	9.66276i	−0.257336	−	0.361367i
$716$	−13.7934			−0.515484
$717$	−56.7621	+	8.99023i	−2.11982	+	0.335746i
$718$	8.32792	+	16.3445i	0.310795	+	0.609970i
$719$	32.8487	−	10.6732i	1.22505	−	0.398043i	0.376132	−	0.926566i	$-0.377254\pi$
$719$	32.8487	−	10.6732i	1.22505	−	0.398043i	0.848919	+	0.528523i	$0.177254\pi$
$720$	7.61380	−	4.06530i	0.283750	−	0.151505i
$721$	23.6204	+	32.5106i	0.879668	+	1.21076i
$722$	−3.92236	−	1.99854i	−0.145975	−	0.0743781i
$723$	−30.6630	+	15.6236i	−1.14037	+	0.581048i
$724$	10.8525	−	14.9372i	0.403331	−	0.555138i
$725$	0.615469	+	0.174172i	0.0228579	+	0.00646859i
$726$	−15.5697	−	24.2413i	−0.577846	−	0.899679i
$727$	−15.7382	−	15.7382i	−0.583698	−	0.583698i	0.352219	−	0.935918i	$-0.385427\pi$
$727$	−15.7382	−	15.7382i	−0.583698	−	0.583698i	−0.935918	+	0.352219i	$0.885427\pi$
$728$	0.809857	+	5.11324i	0.0300153	+	0.189509i
$729$	−37.6854	−	12.2447i	−1.39576	−	0.453509i
$730$	9.48421	−	1.68930i	0.351026	−	0.0625240i
$731$	−49.4866	+	35.9541i	−1.83033	+	1.32981i
$732$	0.812403	−	5.12931i	0.0300273	−	0.189585i
$733$	15.3054	−	30.0385i	0.565317	−	1.10950i	−0.414583	−	0.910011i	$-0.636073\pi$
$733$	15.3054	−	30.0385i	0.565317	−	1.10950i	0.979901	−	0.199486i	$-0.0639273\pi$
$734$	−2.61549	+	8.04965i	−0.0965395	+	0.297118i
$735$	20.3497	−	0.390547i	0.750609	−	0.0144055i
$736$		−	2.58350i		−	0.0952291i
$737$	−22.0425	+	20.8125i	−0.811947	+	0.766638i
$738$	−10.9906	+	10.9906i	−0.404570	+	0.404570i
$739$	33.7503	+	24.5210i	1.24153	+	0.902021i	0.997699	−	0.0677976i	$-0.0215972\pi$
$739$	33.7503	+	24.5210i	1.24153	+	0.902021i	0.243827	+	0.969819i	$0.421597\pi$
$740$	23.2944	−	8.06616i	0.856319	−	0.296518i
$741$	6.26274	+	19.2747i	0.230067	+	0.708075i
$742$	−3.01947	−	0.478237i	−0.110848	−	0.0175566i
$743$	−20.1145	−	3.18583i	−0.737931	−	0.116877i	−0.223856	−	0.974622i	$-0.571865\pi$
$743$	−20.1145	−	3.18583i	−0.737931	−	0.116877i	−0.514075	+	0.857745i	$0.671865\pi$
$744$	2.91093	+	8.95892i	0.106720	+	0.328450i
$745$	13.7685	+	6.68578i	0.504439	+	0.244948i
$746$	7.02267	+	5.10227i	0.257118	+	0.186807i
$747$	−25.4339	+	25.4339i	−0.930577	+	0.930577i
$748$	18.7750	−	2.42376i	0.686482	−	0.0886214i
$749$		−	14.7664i		−	0.539553i
$750$	14.7734	+	25.2832i	0.539448	+	0.923213i
$751$	−0.612465	+	1.88497i	−0.0223492	+	0.0687836i	−0.961609	−	0.274423i	$-0.911513\pi$
$751$	−0.612465	+	1.88497i	−0.0223492	+	0.0687836i	0.939260	+	0.343207i	$0.111513\pi$
$752$	2.13260	−	4.18546i	0.0777679	−	0.152628i
$753$	−4.04882	+	25.5632i	−0.147547	+	0.931576i
$754$	−0.165545	+	0.120275i	−0.00602878	+	0.00438016i
$755$	1.32880	+	7.46022i	0.0483598	+	0.271505i
$756$	6.93316	+	2.25272i	0.252157	+	0.0819307i
$757$	0.401874	+	2.53733i	0.0146064	+	0.0922209i	0.993915	−	0.110153i	$-0.0351342\pi$
$757$	0.401874	+	2.53733i	0.0146064	+	0.0922209i	−0.979308	+	0.202374i	$0.935134\pi$
$758$	−3.90522	−	3.90522i	−0.141844	−	0.141844i
$759$	−7.54455	+	21.1361i	−0.273850	+	0.767191i
$760$	8.62765	−	6.52492i	0.312958	−	0.236684i
$761$	7.71934	−	10.6248i	0.279826	−	0.385147i	−0.645850	−	0.763464i	$-0.723497\pi$
$761$	7.71934	−	10.6248i	0.279826	−	0.385147i	0.925676	+	0.378317i	$0.123497\pi$
$762$	2.74390	−	1.39809i	0.0994010	−	0.0506473i
$763$	−13.1559	−	6.70326i	−0.476275	−	0.242674i
$764$	−1.32004	−	1.81687i	−0.0477572	−	0.0657322i
$765$	14.3220	−	47.1376i	0.517812	−	1.70426i
$766$	−18.6019	+	6.04414i	−0.672116	+	0.218384i
$767$	−4.87834	−	9.57428i	−0.176147	−	0.345707i
$768$	2.58691	−	0.409726i	0.0933470	−	0.0147847i
$769$	47.5711			1.71546			0.857729	−	0.514103i	$-0.171875\pi$
$769$	47.5711			1.71546			0.857729	+	0.514103i	$0.171875\pi$
$770$	−23.7420	+	3.52938i	−0.855604	+	0.127190i
$771$	75.8967			2.73335
$772$	−5.94097	+	0.940958i	−0.213820	+	0.0338658i
$773$	17.6947	+	34.7279i	0.636436	+	1.24908i	0.953706	+	0.300741i	$0.0972338\pi$
$773$	17.6947	+	34.7279i	0.636436	+	1.24908i	−0.317270	+	0.948335i	$0.602766\pi$
$774$	39.3411	−	12.7827i	1.41409	−	0.459465i
$775$	−16.8769	+	6.20913i	−0.606236	+	0.223039i
$776$	−4.52721	−	6.23117i	−0.162517	−	0.223686i
$777$	83.2686	+	42.4275i	2.98725	+	1.52208i
$778$	1.64297	−	0.837134i	0.0589033	−	0.0300127i
$779$	−11.4499	+	15.7594i	−0.410234	+	0.564639i
$780$	−9.27891	−	1.28764i	−0.332238	−	0.0461050i
$781$	−23.5777	−	34.4912i	−0.843676	−	1.23419i
$782$	−10.4272	−	10.4272i	−0.372875	−	0.372875i
$783$	0.0450753	+	0.284595i	0.00161086	+	0.0101706i
$784$	3.30520	+	1.07392i	0.118043	+	0.0383544i
$785$	20.3409	+	14.1903i	0.725997	+	0.506473i
$786$	13.2923	−	9.65744i	0.474122	−	0.344470i
$787$	2.98950	−	18.8749i	0.106564	−	0.672819i	−0.875350	−	0.483490i	$-0.839369\pi$
$787$	2.98950	−	18.8749i	0.106564	−	0.672819i	0.981914	−	0.189329i	$-0.0606312\pi$
$788$	2.96194	−	5.81314i	0.105515	−	0.207085i
$789$	5.94261	−	18.2895i	0.211562	−	0.651122i
$790$	0.214387	+	11.1708i	0.00762754	+	0.397438i
$791$			44.1226i			1.56882i
$792$	−12.5818	−	2.36464i	−0.447074	−	0.0840237i
$793$	−2.24262	+	2.24262i	−0.0796378	+	0.0796378i
$794$	1.83945	+	1.33644i	0.0652797	+	0.0474285i
$795$	2.41638	−	4.97623i	0.0857003	−	0.176489i
$796$	5.82894	+	17.9396i	0.206601	+	0.635853i
$797$	5.73859	+	0.908904i	0.203271	+	0.0321950i	0.257240	−	0.966348i	$-0.417187\pi$
$797$	5.73859	+	0.908904i	0.203271	+	0.0321950i	−0.0539683	+	0.998543i	$0.517187\pi$
$798$	40.5035	+	6.41512i	1.43381	+	0.227093i
$799$	−8.28548	−	25.5001i	−0.293119	−	0.902128i
$800$	0.971082	+	4.90479i	0.0343329	+	0.173411i
$801$	25.8487	+	18.7802i	0.913319	+	0.663565i
$802$	17.8798	−	17.8798i	0.631357	−	0.631357i
$803$	−12.5400	−	6.84956i	−0.442528	−	0.241716i
$804$			23.9403i			0.844310i
$805$	13.4722	+	12.9648i	0.474832	+	0.456949i
$806$	1.77772	−	5.47126i	0.0626175	−	0.192717i
$807$	−12.2781	+	24.0972i	−0.432210	+	0.848260i
$808$	2.30188	−	14.5335i	0.0809800	−	0.511287i
$809$	2.85986	−	2.07781i	0.100547	−	0.0730518i	−0.536376	−	0.843979i	$-0.680207\pi$
$809$	2.85986	−	2.07781i	0.100547	−	0.0730518i	0.636923	+	0.770928i	$0.280207\pi$
$810$	7.26756	−	10.4176i	0.255356	−	0.366037i
$811$	3.95891	+	1.28633i	0.139016	+	0.0451691i	0.377699	−	0.925929i	$-0.376716\pi$
$811$	3.95891	+	1.28633i	0.139016	+	0.0451691i	−0.238682	+	0.971098i	$0.576716\pi$
$812$	0.0647709	+	0.408948i	0.00227301	+	0.0143512i
$813$	4.20844	+	4.20844i	0.147596	+	0.147596i
$814$	−34.4359	−	12.2919i	−1.20698	−	0.430832i
$815$	−23.4750	−	31.0401i	−0.822294	−	1.08729i
$816$	8.78724	−	12.0946i	0.307615	−	0.423396i
$817$	46.1919	−	23.5360i	1.61605	−	0.823419i
$818$	−32.0084	−	16.3091i	−1.11915	−	0.570233i
$819$	−11.7457	−	16.1665i	−0.410427	−	0.564904i
$820$	−4.24095	−	7.94277i	−0.148100	−	0.277374i
$821$	27.3481	−	8.88592i	0.954454	−	0.310121i	0.209930	−	0.977716i	$-0.432676\pi$
$821$	27.3481	−	8.88592i	0.954454	−	0.310121i	0.744524	+	0.667596i	$0.232676\pi$
$822$	−1.10204	−	2.16288i	−0.0384382	−	0.0754392i
$823$	−11.3562	+	1.79865i	−0.395853	+	0.0626970i	−0.351188	−	0.936305i	$-0.614222\pi$
$823$	−11.3562	+	1.79865i	−0.395853	+	0.0626970i	−0.0446653	+	0.999002i	$0.514222\pi$
$824$	−12.4161			−0.432535
$825$	6.37878	−	42.9628i	0.222081	−	1.49577i
$826$	−21.7428			−0.756529
$827$	21.5720	−	3.41667i	0.750132	−	0.118809i	0.230349	−	0.973108i	$-0.426013\pi$
$827$	21.5720	−	3.41667i	0.750132	−	0.118809i	0.519782	+	0.854299i	$0.326013\pi$
$828$	4.52730	+	8.88532i	0.157334	+	0.308786i
$829$	−47.1901	+	15.3330i	−1.63898	+	0.532537i	−0.976311	−	0.216374i	$-0.930577\pi$
$829$	−47.1901	+	15.3330i	−1.63898	+	0.532537i	−0.662670	+	0.748911i	$0.730577\pi$
$830$	−9.81417	−	18.3807i	−0.340655	−	0.638004i
$831$	38.6711	+	53.2262i	1.34148	+	1.84639i
$832$	−1.42519	−	0.726172i	−0.0494097	−	0.0251755i
$833$	17.6744	−	9.00556i	0.612382	−	0.312024i
$834$	−12.5037	+	17.2099i	−0.432969	+	0.595931i
$835$	9.11424	+	12.0514i	0.315411	+	0.417056i
$836$	−16.0378	−	0.460327i	−0.554680	−	0.0159207i
$837$	−5.72816	−	5.72816i	−0.197994	−	0.197994i
$838$	−1.06988	−	6.75495i	−0.0369584	−	0.233346i
$839$	11.2885	+	3.66786i	0.389722	+	0.126629i	0.497322	−	0.867566i	$-0.334317\pi$
$839$	11.2885	+	3.66786i	0.389722	+	0.126629i	−0.107600	+	0.994194i	$0.534317\pi$
$840$	−10.8453	+	15.5461i	−0.374198	+	0.536390i
$841$	23.4483	−	17.0362i	0.808560	−	0.587454i
$842$	6.09759	−	38.4987i	0.210137	−	1.32675i
$843$	−1.39549	+	2.73881i	−0.0480634	+	0.0943297i
$844$	0.469994	−	1.44649i	0.0161779	−	0.0497904i
$845$	−16.8232	−	16.1896i	−0.578736	−	0.556940i
$846$			18.1320i			0.623391i
$847$	30.7424	+	17.9559i	1.05632	+	0.616972i
$848$	0.667901	−	0.667901i	0.0229358	−	0.0229358i
$849$	−36.4054	−	26.4501i	−1.24943	−	0.907765i
$850$	23.7154	+	15.8767i	0.813431	+	0.544566i
$851$	8.80132	+	27.0877i	0.301705	+	0.928553i
$852$	−32.5875	−	5.16135i	−1.11643	−	0.176825i
$853$	44.5555	+	7.05690i	1.52555	+	0.241624i	0.862155	−	0.506644i	$-0.169114\pi$
$853$	44.5555	+	7.05690i	1.52555	+	0.241624i	0.663397	+	0.748268i	$0.269114\pi$
$854$	1.98309	+	6.10334i	0.0678601	+	0.208852i
$855$	−18.2385	+	37.5598i	−0.623744	+	1.28452i
$856$	3.69104	+	2.68170i	0.126157	+	0.0916586i
$857$	−13.0859	+	13.0859i	−0.447006	+	0.447006i	−0.894358	−	0.447352i	$-0.852367\pi$
$857$	−13.0859	+	13.0859i	−0.447006	+	0.447006i	0.447352	+	0.894358i	$0.352367\pi$
$858$	9.53912	+	10.1029i	0.325660	+	0.344907i
$859$			3.40430i			0.116153i	0.998312	+	0.0580767i	$0.0184968\pi$
$859$			3.40430i			0.116153i	−0.998312	+	0.0580767i	$0.981503\pi$
$860$	0.459809	+	23.9586i	0.0156794	+	0.816983i
$861$	10.5482	−	32.4642i	0.359483	−	1.10638i
$862$	−8.96437	+	17.5936i	−0.305328	+	0.599239i
$863$	3.69767	−	23.3461i	0.125870	−	0.794712i	−0.841298	−	0.540572i	$-0.818208\pi$
$863$	3.69767	−	23.3461i	0.125870	−	0.794712i	0.967168	−	0.254140i	$-0.0817923\pi$
$864$	−1.82222	+	1.32392i	−0.0619930	+	0.0450406i
$865$	9.86642	+	6.88304i	0.335468	+	0.234030i
$866$	−0.970744	−	0.315414i	−0.0329872	−	0.0107182i
$867$	−6.38336	−	40.3029i	−0.216790	−	1.36876i
$868$	−8.23107	−	8.23107i	−0.279381	−	0.279381i
$869$	10.1214	−	13.1220i	0.343345	−	0.445134i
$870$	−0.742111	−	0.102983i	−0.0251599	−	0.00349146i
$871$	8.59371	−	11.8282i	0.291187	−	0.400784i
$872$	4.06478	−	2.07111i	0.137651	−	0.0701366i
$873$	26.4897	+	13.4972i	0.896539	+	0.456810i
$874$	7.34608	+	10.1110i	0.248485	+	0.342010i
$875$	−30.4502	−	19.5499i	−1.02940	−	0.660906i
$876$	−10.7316	+	3.48692i	−0.362588	+	0.117812i
$877$	−13.8039	−	27.0917i	−0.466126	−	0.914823i	−0.997698	−	0.0678103i	$-0.978399\pi$
$877$	−13.8039	−	27.0917i	−0.466126	−	0.914823i	0.531573	−	0.847013i	$-0.321601\pi$
$878$	19.0731	−	3.02089i	0.643687	−	0.101950i
$879$	−42.3295			−1.42774
$880$	3.42954	−	6.57558i	0.115610	−	0.221663i
$881$	13.1634			0.443486			0.221743	−	0.975105i	$-0.428825\pi$
$881$	13.1634			0.443486			0.221743	+	0.975105i	$0.428825\pi$
$882$	−13.2494	+	2.09849i	−0.446129	+	0.0706599i
$883$	13.4156	+	26.3296i	0.451471	+	0.886061i	0.998792	+	0.0491387i	$0.0156476\pi$
$883$	13.4156	+	26.3296i	0.451471	+	0.886061i	−0.547321	+	0.836923i	$0.684352\pi$
$884$	−8.68304	+	2.82129i	−0.292042	+	0.0948903i
$885$	11.4377	−	37.6448i	0.384475	−	1.26542i
$886$	19.3381	+	26.6167i	0.649678	+	0.894204i
$887$	23.7370	+	12.0946i	0.797010	+	0.406097i	0.804557	−	0.593875i	$-0.202403\pi$
$887$	23.7370	+	12.0946i	0.797010	+	0.406097i	−0.00754780	+	0.999972i	$0.502403\pi$
$888$	−25.7275	+	13.1088i	−0.863360	+	0.439904i
$889$	−2.23680	+	3.07870i	−0.0750200	+	0.103256i
$890$	−14.7626	+	11.1646i	−0.494843	+	0.374239i
$891$	−18.0778	+	5.30549i	−0.605631	+	0.177741i
$892$	−5.17387	−	5.17387i	−0.173234	−	0.173234i
$893$	3.55486	+	22.4445i	0.118959	+	0.751078i
$894$	−17.0507	−	5.54010i	−0.570260	−	0.185289i
$895$	5.40856	+	30.3651i	0.180788	+	1.01499i
$896$	−2.61843	+	1.90240i	−0.0874756	+	0.0635547i
$897$	1.69315	−	10.6901i	0.0565326	−	0.356933i
$898$	−5.76357	+	11.3116i	−0.192333	+	0.377474i
$899$	0.142179	−	0.437582i	0.00474193	−	0.0145942i
$900$	−11.9349	−	15.1671i	−0.397830	−	0.505571i
$901$		−	5.39138i		−	0.179613i
$902$	−2.46681	+	13.1254i	−0.0821356	+	0.437028i
$903$	−64.2371	+	64.2371i	−2.13768	+	2.13768i
$904$	−11.0290	−	8.01303i	−0.366819	−	0.266509i
$905$	−37.1385	−	18.0339i	−1.23453	−	0.599468i
$906$	−2.74279	−	8.44143i	−0.0911230	−	0.280448i
$907$	−16.8839	−	2.67415i	−0.560622	−	0.0887937i	−0.130309	−	0.991473i	$-0.541597\pi$
$907$	−16.8839	−	2.67415i	−0.560622	−	0.0887937i	−0.430313	+	0.902680i	$0.641597\pi$
$908$	−25.0125	−	3.96159i	−0.830068	−	0.131470i
$909$	17.5516	+	54.0183i	0.582150	+	1.79167i
$910$	10.9388	−	3.78779i	0.362618	−	0.125564i
$911$	12.2331	+	8.88787i	0.405301	+	0.294468i	0.771697	−	0.635991i	$-0.219408\pi$
$911$	12.2331	+	8.88787i	0.405301	+	0.294468i	−0.366396	+	0.930459i	$0.619408\pi$
$912$	−8.95930	+	8.95930i	−0.296672	+	0.296672i
$913$	−5.70854	+	30.3741i	−0.188925	+	1.00523i
$914$			12.1431i			0.401658i
$915$	−11.6103	+	0.222823i	−0.383825	+	0.00736629i
$916$	3.17129	−	9.76023i	0.104782	−	0.322487i
$917$	−9.21748	+	18.0903i	−0.304388	+	0.597395i
$918$	−2.01116	+	12.6980i	−0.0663783	+	0.419096i
$919$	23.9620	−	17.4094i	0.790433	−	0.574283i	−0.117659	−	0.993054i	$-0.537539\pi$
$919$	23.9620	−	17.4094i	0.790433	−	0.574283i	0.908092	+	0.418771i	$0.137539\pi$
$920$	−5.68737	+	1.01302i	−0.187507	+	0.0333983i
$921$	−56.5990	−	18.3901i	−1.86500	−	0.605975i
$922$	−5.03033	−	31.7603i	−0.165665	−	1.04597i
$923$	14.2478	+	14.2478i	0.468972	+	0.468972i
$924$	26.9774	−	7.91732i	0.887490	−	0.260461i
$925$	−26.8910	−	48.1179i	−0.884171	−	1.58211i
$926$	21.3042	−	29.3227i	0.700100	−	0.963605i
$927$	42.7021	−	21.7578i	1.40252	−	0.714620i
$928$	−0.113984	−	0.0580780i	−0.00374172	−	0.00190650i
$929$	−9.57984	−	13.1855i	−0.314304	−	0.432603i	0.622413	−	0.782689i	$-0.286152\pi$
$929$	−9.57984	−	13.1855i	−0.314304	−	0.432603i	−0.936718	+	0.350086i	$0.886152\pi$
$930$	18.5809	−	9.92107i	0.609293	−	0.325325i
$931$	−15.9892	+	5.19519i	−0.524024	+	0.170266i
$932$	9.86223	+	19.3557i	0.323048	+	0.634018i
$933$	20.6251	−	3.26670i	0.675236	−	0.106947i
$934$	8.43545			0.276016
$935$	−12.6976	−	40.3813i	−0.415256	−	1.32061i
$936$	6.17414			0.201808
$937$	5.22379	−	0.827367i	0.170654	−	0.0270289i	−0.0705228	−	0.997510i	$-0.522467\pi$
$937$	5.22379	−	0.827367i	0.170654	−	0.0270289i	0.241176	+	0.970481i	$0.422467\pi$
$938$	−13.4307	−	26.3593i	−0.438528	−	0.860660i
$939$	−13.4438	+	4.36814i	−0.438720	+	0.142549i
$940$	−10.0502	−	3.05358i	−0.327801	−	0.0995967i
$941$	14.0871	+	19.3893i	0.459227	+	0.632072i	0.974348	−	0.225046i	$-0.0722531\pi$
$941$	14.0871	+	19.3893i	0.459227	+	0.632072i	−0.515121	+	0.857117i	$0.672253\pi$
$942$	−25.8842	−	13.1887i	−0.843353	−	0.429710i
$943$	9.26923	−	4.72291i	0.301848	−	0.153799i
$944$	3.94867	−	5.43488i	0.128518	−	0.176890i
$945$	2.24061	−	16.1461i	0.0728871	−	0.525233i
$946$	21.7080	−	28.1436i	0.705789	−	0.915028i
$947$	16.0373	+	16.0373i	0.521142	+	0.521142i	0.917916	−	0.396774i	$-0.129870\pi$
$947$	16.0373	+	16.0373i	0.521142	+	0.521142i	−0.396774	+	0.917916i	$0.629870\pi$
$948$	−2.04725	−	12.9258i	−0.0664916	−	0.419812i
$949$	6.55386	+	2.12948i	0.212747	+	0.0691258i
$950$	−17.7471	−	16.4346i	−0.575791	−	0.533208i
$951$	−31.6570	+	23.0002i	−1.02655	+	0.745832i
$952$	−2.88994	+	18.2463i	−0.0936634	+	0.591367i
$953$	19.1804	−	37.6437i	0.621315	−	1.21940i	−0.339080	−	0.940758i	$-0.610116\pi$
$953$	19.1804	−	37.6437i	0.621315	−	1.21940i	0.960395	−	0.278642i	$-0.0898843\pi$
$954$	−1.12666	+	3.46751i	−0.0364770	+	0.112265i
$955$	−3.48210	+	3.61837i	−0.112678	+	0.117088i
$956$			21.9421i			0.709657i
$957$	0.762922	+	0.808012i	0.0246618	+	0.0261193i
$958$	13.2462	−	13.2462i	0.427966	−	0.427966i
$959$	2.42679	+	1.76317i	0.0783651	+	0.0569356i
$960$	−1.91634	−	5.53421i	−0.0618495	−	0.178616i
$961$	−5.58230	−	17.1805i	−0.180074	−	0.554211i
$962$	17.4168	+	2.75856i	0.561541	+	0.0889394i
$963$	−17.3938	−	2.75491i	−0.560508	−	0.0887757i
$964$	4.06028	+	12.4963i	0.130773	+	0.402477i
$965$	4.40097	+	12.7096i	0.141672	+	0.409137i
$966$	−17.7178	−	12.8728i	−0.570062	−	0.414174i
$967$	10.8438	−	10.8438i	0.348712	−	0.348712i	−0.510918	−	0.859629i	$-0.670694\pi$
$967$	10.8438	−	10.8438i	0.348712	−	0.348712i	0.859629	+	0.510918i	$0.170694\pi$
$968$	−10.0714	+	4.42351i	−0.323706	+	0.142177i
$969$			72.3206i			2.32327i
$970$	−11.9423	+	12.4096i	−0.383443	+	0.398448i
$971$	3.48625	−	10.7296i	0.111879	−	0.344328i	−0.879404	−	0.476076i	$-0.842059\pi$
$971$	3.48625	−	10.7296i	0.111879	−	0.344328i	0.991283	+	0.131748i	$0.0420588\pi$
$972$	−9.82227	+	19.2773i	−0.315049	+	0.618319i
$973$	4.11222	−	25.9635i	0.131832	−	0.832352i
$974$	−11.8135	+	8.58298i	−0.378528	+	0.275016i
$975$	0.803728	+	20.9317i	0.0257399	+	0.670350i
$976$	−1.88575	−	0.612718i	−0.0603614	−	0.0196126i
$977$	−4.25976	−	26.8951i	−0.136282	−	0.860449i	−0.957205	−	0.289411i	$-0.906541\pi$
$977$	−4.25976	−	26.8951i	−0.136282	−	0.860449i	0.820923	−	0.571039i	$-0.193459\pi$
$978$	32.2333	+	32.2333i	1.03071	+	1.03071i
$979$	27.4420	+	0.787655i	0.877049	+	0.0251736i
$980$	1.06815	−	7.69723i	0.0341208	−	0.245879i
$981$	−10.3504	+	14.2461i	−0.330464	+	0.454845i
$982$	13.7324	−	6.99699i	0.438217	−	0.223283i
$983$	−12.1590	−	6.19532i	−0.387812	−	0.197600i	0.249204	−	0.968451i	$-0.419831\pi$
$983$	−12.1590	−	6.19532i	−0.387812	−	0.197600i	−0.637015	+	0.770851i	$0.719831\pi$
$984$	6.19917	+	8.53242i	0.197622	+	0.272004i
$985$	−13.9586	−	4.24108i	−0.444757	−	0.135132i
$986$	−0.694454	+	0.225642i	−0.0221159	+	0.00718590i
$987$	−18.0781	−	35.4803i	−0.575433	−	1.12935i
$988$	7.64259	−	1.21047i	0.243143	−	0.0385101i
$989$	−27.6864			−0.880375
$990$	−0.272096	+	28.6250i	−0.00864778	+	0.909762i
$991$	−30.2514			−0.960967			−0.480483	−	0.877004i	$-0.659539\pi$
$991$	−30.2514			−0.960967			−0.480483	+	0.877004i	$0.659539\pi$
$992$	3.55229	−	0.562627i	0.112785	−	0.0178634i
$993$	−12.8486	−	25.2167i	−0.407736	−	0.800228i
$994$	38.7757	−	12.5990i	1.22989	−	0.399616i
$995$	37.2071	−	19.8663i	1.17954	−	0.629803i
$996$	14.3458	+	19.7453i	0.454563	+	0.625652i
$997$	−10.4017	−	5.29994i	−0.329426	−	0.167851i	0.281453	−	0.959575i	$-0.409184\pi$
$997$	−10.4017	−	5.29994i	−0.329426	−	0.167851i	−0.610879	+	0.791724i	$0.709184\pi$
$998$	−21.2869	+	10.8462i	−0.673825	+	0.343331i
$999$	14.5954	−	20.0889i	0.461779	−	0.635585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.k.a.7.6	✓	48
3.2	odd	2		990.2.bh.c.667.2		48
4.3	odd	2		880.2.cm.c.337.1		48
5.2	odd	4		550.2.bh.b.293.6		48
5.3	odd	4	inner	110.2.k.a.73.1	yes	48
5.4	even	2		550.2.bh.b.7.1		48
11.8	odd	10	inner	110.2.k.a.107.1	yes	48
15.8	even	4		990.2.bh.c.73.4		48
20.3	even	4		880.2.cm.c.513.6		48
33.8	even	10		990.2.bh.c.217.4		48
44.19	even	10		880.2.cm.c.657.6		48
55.8	even	20	inner	110.2.k.a.63.6	yes	48
55.19	odd	10		550.2.bh.b.107.6		48
55.52	even	20		550.2.bh.b.393.1		48
165.8	odd	20		990.2.bh.c.613.2		48
220.63	odd	20		880.2.cm.c.833.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.7.6	✓	48	1.1	even	1	trivial
110.2.k.a.63.6	yes	48	55.8	even	20	inner
110.2.k.a.73.1	yes	48	5.3	odd	4	inner
110.2.k.a.107.1	yes	48	11.8	odd	10	inner
550.2.bh.b.7.1		48	5.4	even	2
550.2.bh.b.107.6		48	55.19	odd	10
550.2.bh.b.293.6		48	5.2	odd	4
550.2.bh.b.393.1		48	55.52	even	20
880.2.cm.c.337.1		48	4.3	odd	2
880.2.cm.c.513.6		48	20.3	even	4
880.2.cm.c.657.6		48	44.19	even	10
880.2.cm.c.833.1		48	220.63	odd	20
990.2.bh.c.73.4		48	15.8	even	4
990.2.bh.c.217.4		48	33.8	even	10
990.2.bh.c.613.2		48	165.8	odd	20
990.2.bh.c.667.2		48	3.2	odd	2

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.987688 - 0.156434i) q^{2} +(1.18907 + 2.33368i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.05320 - 1.97251i) q^{5} +(1.53950 + 2.11894i) q^{6} +(-2.88379 - 1.46937i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-2.26883 + 3.12278i) q^{9} +O(q^{10})\)	\(q+(0.987688 - 0.156434i) q^{2} +(1.18907 + 2.33368i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.05320 - 1.97251i) q^{5} +(1.53950 + 2.11894i) q^{6} +(-2.88379 - 1.46937i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-2.26883 + 3.12278i) q^{9} +(-1.34880 - 1.78346i) q^{10} +(-0.0951565 + 3.31526i) q^{11} +(1.85202 + 1.85202i) q^{12} +(-0.250222 - 1.57984i) q^{13} +(-3.07815 - 1.00015i) q^{14} +(3.35088 - 4.80328i) q^{15} +(0.809017 - 0.587785i) q^{16} +(0.892905 - 5.63758i) q^{17} +(-1.75239 + 3.43925i) q^{18} +(-1.49489 + 4.60081i) q^{19} +(-1.61119 - 1.55051i) q^{20} -8.47704i q^{21} +(0.424636 + 3.28933i) q^{22} +(1.82681 - 1.82681i) q^{23} +(2.11894 + 1.53950i) q^{24} +(-2.78155 + 4.15487i) q^{25} +(-0.494282 - 1.52124i) q^{26} +(-2.22465 - 0.352350i) q^{27} +(-3.19671 - 0.506309i) q^{28} +(-0.0395318 - 0.121666i) q^{29} +(2.55822 - 5.26833i) q^{30} +(2.90969 + 2.11401i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-7.84991 + 3.72001i) q^{33} -5.70785i q^{34} +(0.138868 + 7.23583i) q^{35} +(-1.19279 + 3.67105i) q^{36} +(-5.00499 + 9.82285i) q^{37} +(-0.756764 + 4.77802i) q^{38} +(3.38931 - 2.46248i) q^{39} +(-1.83390 - 1.27937i) q^{40} +(3.82966 + 1.24433i) q^{41} +(-1.32610 - 8.37267i) q^{42} +(-7.57778 - 7.57778i) q^{43} +(0.933972 + 3.18240i) q^{44} +(8.54922 + 1.18638i) q^{45} +(1.51854 - 2.09010i) q^{46} +(4.18546 - 2.13260i) q^{47} +(2.33368 + 1.18907i) q^{48} +(2.04273 + 2.81157i) q^{49} +(-2.09734 + 4.53885i) q^{50} +(14.2181 - 4.61972i) q^{51} +(-0.726172 - 1.42519i) q^{52} +(0.932926 - 0.147761i) q^{53} -2.25238 q^{54} +(6.63959 - 3.30392i) q^{55} -3.23656 q^{56} +(-12.5144 + 1.98208i) q^{57} +(-0.0580780 - 0.113984i) q^{58} +(6.38909 - 2.07594i) q^{59} +(1.70258 - 5.60366i) q^{60} +(-1.16546 - 1.60412i) q^{61} +(3.20457 + 1.63281i) q^{62} +(11.1313 - 5.67170i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-2.85271 + 2.15744i) q^{65} +(-7.17133 + 4.90221i) q^{66} +(6.46330 + 6.46330i) q^{67} +(-0.892905 - 5.63758i) q^{68} +(6.43541 + 2.09099i) q^{69} +(1.26909 + 7.12502i) q^{70} +(-10.1913 + 7.40438i) q^{71} +(-0.603832 + 3.81244i) q^{72} +(-1.95589 + 3.83865i) q^{73} +(-3.40674 + 10.4849i) q^{74} +(-13.0036 - 1.55083i) q^{75} +4.83758i q^{76} +(5.14574 - 9.42070i) q^{77} +(2.96237 - 2.96237i) q^{78} +(-4.04236 - 2.93695i) q^{79} +(-2.01146 - 0.976737i) q^{80} +(1.75539 + 5.40254i) q^{81} +(3.97717 + 0.629921i) q^{82} +(9.20374 + 1.45773i) q^{83} +(-2.61955 - 8.06214i) q^{84} +(-12.0606 + 4.17622i) q^{85} +(-8.66991 - 6.29906i) q^{86} +(0.236925 - 0.236925i) q^{87} +(1.42031 + 2.99712i) q^{88} -8.27747i q^{89} +(8.62956 - 0.165617i) q^{90} +(-1.59977 + 4.92359i) q^{91} +(1.17289 - 2.30192i) q^{92} +(-1.47361 + 9.30399i) q^{93} +(3.80032 - 2.76109i) q^{94} +(10.6495 - 1.89687i) q^{95} +(2.49096 + 0.809363i) q^{96} +(-1.20488 - 7.60733i) q^{97} +(2.45740 + 2.45740i) q^{98} +(-10.1369 - 7.81892i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7}+O(q^{10}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36} + 20 q^{37} - 36 q^{38} - 20 q^{41} - 20 q^{42} + 16 q^{45} + 40 q^{46} + 40 q^{47} + 4 q^{48} + 40 q^{50} + 40 q^{51} + 40 q^{52} + 96 q^{55} - 8 q^{56} + 48 q^{58} + 20 q^{60} + 80 q^{61} + 40 q^{62} + 100 q^{63} + 24 q^{66} + 20 q^{68} - 56 q^{70} - 56 q^{71} - 20 q^{73} - 76 q^{75} - 96 q^{77} + 16 q^{78} - 12 q^{80} - 68 q^{81} - 80 q^{85} - 56 q^{86} - 4 q^{88} - 80 q^{90} - 68 q^{91} - 12 q^{92} + 76 q^{93} + 20 q^{95} + 72 q^{97}+O(q^{100}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Introduction

L-functions

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