LMFDB - Embedded newform 150.2.l.a.137.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			137.4
Character	$\chi$	$=$	150.137
Dual form			150.2.l.a.23.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 + 0.156434i) q^{2} +(1.10553 - 1.33334i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-0.334535 + 2.21090i) q^{5} +(-0.883341 + 1.48987i) q^{6} +(2.78015 + 2.78015i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.555594 - 2.94810i) q^{9} +O(q^{10})$	\(q+(-0.987688 + 0.156434i) q^{2} +(1.10553 - 1.33334i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-0.334535 + 2.21090i) q^{5} +(-0.883341 + 1.48987i) q^{6} +(2.78015 + 2.78015i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.555594 - 2.94810i) q^{9} +(-0.0154450 - 2.23601i) q^{10} +(2.08133 - 2.86470i) q^{11} +(0.639399 - 1.60971i) q^{12} +(0.331962 - 2.09592i) q^{13} +(-3.18083 - 2.31101i) q^{14} +(2.57805 + 2.89027i) q^{15} +(0.809017 - 0.587785i) q^{16} +(0.476073 + 0.934346i) q^{17} +(1.00994 + 2.82489i) q^{18} +(-4.71987 - 1.53358i) q^{19} +(0.365045 + 2.20607i) q^{20} +(6.78043 - 0.633339i) q^{21} +(-1.60756 + 3.15502i) q^{22} +(1.22065 + 7.70688i) q^{23} +(-0.379713 + 1.68992i) q^{24} +(-4.77617 - 1.47925i) q^{25} +2.12205i q^{26} +(-4.54505 - 2.51843i) q^{27} +(3.50319 + 1.78496i) q^{28} +(-0.858514 - 2.64223i) q^{29} +(-2.99844 - 2.45139i) q^{30} +(0.458925 - 1.41243i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.51865 - 5.94214i) q^{33} +(-0.616376 - 0.848368i) q^{34} +(-7.07669 + 5.21658i) q^{35} +(-1.43942 - 2.63213i) q^{36} +(-1.07161 - 0.169727i) q^{37} +(4.90167 + 0.776348i) q^{38} +(-2.42758 - 2.75973i) q^{39} +(-0.705656 - 2.12180i) q^{40} +(-0.691749 - 0.952111i) q^{41} +(-6.59787 + 1.68623i) q^{42} +(-8.25027 + 8.25027i) q^{43} +(1.09422 - 3.36766i) q^{44} +(6.70383 - 0.242121i) q^{45} +(-2.41124 - 7.42105i) q^{46} +(-10.2948 - 5.24545i) q^{47} +(0.110677 - 1.72851i) q^{48} +8.45844i q^{49} +(4.94878 + 0.713878i) q^{50} +(1.77212 + 0.398183i) q^{51} +(-0.331962 - 2.09592i) q^{52} +(1.93475 - 3.79716i) q^{53} +(4.88307 + 1.77642i) q^{54} +(5.63730 + 5.55995i) q^{55} +(-3.73929 - 1.21497i) q^{56} +(-7.26276 + 4.59778i) q^{57} +(1.26128 + 2.47540i) q^{58} +(5.11067 - 3.71312i) q^{59} +(3.34501 + 1.95215i) q^{60} +(1.09310 + 0.794185i) q^{61} +(-0.232323 + 1.46683i) q^{62} +(6.65153 - 9.74080i) q^{63} +(0.587785 - 0.809017i) q^{64} +(4.52283 + 1.43509i) q^{65} +(2.42950 + 5.63141i) q^{66} +(8.29150 - 4.22473i) q^{67} +(0.741501 + 0.741501i) q^{68} +(11.6254 + 6.89267i) q^{69} +(6.17351 - 6.25939i) q^{70} +(-2.47790 + 0.805120i) q^{71} +(1.83345 + 2.37455i) q^{72} +(8.82492 - 1.39773i) q^{73} +1.08497 q^{74} +(-7.25256 + 4.73291i) q^{75} -4.96277 q^{76} +(13.7507 - 2.17789i) q^{77} +(2.82941 + 2.34599i) q^{78} +(-14.4405 + 4.69199i) q^{79} +(1.02889 + 1.98529i) q^{80} +(-8.38263 + 3.27590i) q^{81} +(0.832175 + 0.832175i) q^{82} +(-9.56823 + 4.87526i) q^{83} +(6.25286 - 2.69761i) q^{84} +(-2.22501 + 0.739979i) q^{85} +(6.85807 - 9.43932i) q^{86} +(-4.47211 - 1.77638i) q^{87} +(-0.553929 + 3.49737i) q^{88} +(-2.14121 - 1.55568i) q^{89} +(-6.58342 + 1.28785i) q^{90} +(6.74988 - 4.90407i) q^{91} +(3.54247 + 6.95248i) q^{92} +(-1.37589 - 2.17339i) q^{93} +(10.9886 + 3.57041i) q^{94} +(4.96956 - 9.92214i) q^{95} +(0.161084 + 1.72454i) q^{96} +(7.23583 - 14.2011i) q^{97} +(-1.32319 - 8.35430i) q^{98} +(-9.60181 - 4.54436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{9}{20}\right)$

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
$3$	1.10553	−	1.33334i	0.638280	−	0.769805i
$3$	1.10553	−	1.33334i	0.638280	−	0.769805i
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	−0.334535	+	2.21090i	−0.149609	+	0.988745i
$5$	−0.334535	+	2.21090i	−0.149609	+	0.988745i
$6$	−0.883341	+	1.48987i	−0.360623	+	0.608236i
$7$	2.78015	+	2.78015i	1.05080	+	1.05080i	0.998639	+	0.0521581i	$0.0166100\pi$
$7$	2.78015	+	2.78015i	1.05080	+	1.05080i	0.0521581	+	0.998639i	$0.483390\pi$
$8$	−0.891007	+	0.453990i	−0.315018	+	0.160510i
$9$	−0.555594	−	2.94810i	−0.185198	−	0.982701i
$10$	−0.0154450	−	2.23601i	−0.00488414	−	0.707090i
$11$	2.08133	−	2.86470i	0.627544	−	0.863740i	−0.370331	−	0.928900i	$-0.620756\pi$
$11$	2.08133	−	2.86470i	0.627544	−	0.863740i	0.997875	+	0.0651600i	$0.0207558\pi$
$12$	0.639399	−	1.60971i	0.184579	−	0.464683i
$13$	0.331962	−	2.09592i	0.0920696	−	0.581304i	−0.897919	−	0.440160i	$-0.854922\pi$
$13$	0.331962	−	2.09592i	0.0920696	−	0.581304i	0.989989	−	0.141144i	$-0.0450782\pi$
$14$	−3.18083	−	2.31101i	−0.850113	−	0.617643i
$15$	2.57805	+	2.89027i	0.665649	+	0.746265i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	0.476073	+	0.934346i	0.115465	+	0.226612i	0.941505	−	0.336999i	$-0.109412\pi$
$17$	0.476073	+	0.934346i	0.115465	+	0.226612i	−0.826040	+	0.563611i	$0.809412\pi$
$18$	1.00994	+	2.82489i	0.238045	+	0.665834i
$19$	−4.71987	−	1.53358i	−1.08281	−	0.351827i	−0.287348	−	0.957826i	$-0.592774\pi$
$19$	−4.71987	−	1.53358i	−1.08281	−	0.351827i	−0.795465	+	0.605999i	$0.792774\pi$
$20$	0.365045	+	2.20607i	0.0816265	+	0.493292i
$21$	6.78043	−	0.633339i	1.47961	−	0.138206i
$22$	−1.60756	+	3.15502i	−0.342734	+	0.672653i
$23$	1.22065	+	7.70688i	0.254523	+	1.60700i	0.701647	+	0.712524i	$0.252448\pi$
$23$	1.22065	+	7.70688i	0.254523	+	1.60700i	−0.447124	+	0.894472i	$0.647552\pi$
$24$	−0.379713	+	1.68992i	−0.0775086	+	0.344953i
$25$	−4.77617	−	1.47925i	−0.955235	−	0.295850i
$26$			2.12205i			0.416168i
$27$	−4.54505	−	2.51843i	−0.874696	−	0.484672i
$28$	3.50319	+	1.78496i	0.662041	+	0.337327i
$29$	−0.858514	−	2.64223i	−0.159422	−	0.490650i	0.839160	−	0.543885i	$-0.183047\pi$
$29$	−0.858514	−	2.64223i	−0.159422	−	0.490650i	−0.998582	+	0.0532341i	$0.983047\pi$
$30$	−2.99844	−	2.45139i	−0.547438	−	0.447561i
$31$	0.458925	−	1.41243i	0.0824253	−	0.253679i	−0.901348	−	0.433096i	$-0.857421\pi$
$31$	0.458925	−	1.41243i	0.0824253	−	0.253679i	0.983773	+	0.179417i	$0.0574211\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−1.51865	−	5.94214i	−0.264362	−	1.03439i
$34$	−0.616376	−	0.848368i	−0.105708	−	0.145494i
$35$	−7.07669	+	5.21658i	−1.19618	+	0.881762i
$36$	−1.43942	−	2.63213i	−0.239903	−	0.438688i
$37$	−1.07161	−	0.169727i	−0.176172	−	0.0279030i	0.0677249	−	0.997704i	$-0.478426\pi$
$37$	−1.07161	−	0.169727i	−0.176172	−	0.0279030i	−0.243897	+	0.969801i	$0.578426\pi$
$38$	4.90167	+	0.776348i	0.795156	+	0.125940i
$39$	−2.42758	−	2.75973i	−0.388725	−	0.441910i
$40$	−0.705656	−	2.12180i	−0.111574	−	0.335487i
$41$	−0.691749	−	0.952111i	−0.108033	−	0.148695i	0.751577	−	0.659645i	$-0.229293\pi$
$41$	−0.691749	−	0.952111i	−0.108033	−	0.148695i	−0.859610	+	0.510951i	$0.829293\pi$
$42$	−6.59787	+	1.68623i	−1.01807	+	0.260192i
$43$	−8.25027	+	8.25027i	−1.25815	+	1.25815i	−0.306181	+	0.951973i	$0.599051\pi$
$43$	−8.25027	+	8.25027i	−1.25815	+	1.25815i	−0.951973	+	0.306181i	$0.900949\pi$
$44$	1.09422	−	3.36766i	0.164960	−	0.507694i
$45$	6.70383	−	0.242121i	0.999348	−	0.0360933i
$46$	−2.41124	−	7.42105i	−0.355519	−	1.09417i
$47$	−10.2948	−	5.24545i	−1.50165	−	0.765127i	−0.506380	−	0.862311i	$-0.669017\pi$
$47$	−10.2948	−	5.24545i	−1.50165	−	0.765127i	−0.995266	+	0.0971836i	$0.969017\pi$
$48$	0.110677	−	1.72851i	0.0159748	−	0.249489i
$49$			8.45844i			1.20835i
$50$	4.94878	+	0.713878i	0.699863	+	0.100958i
$51$	1.77212	+	0.398183i	0.248146	+	0.0557567i
$52$	−0.331962	−	2.09592i	−0.0460348	−	0.290652i
$53$	1.93475	−	3.79716i	0.265759	−	0.521581i	−0.719107	−	0.694899i	$-0.755449\pi$
$53$	1.93475	−	3.79716i	0.265759	−	0.521581i	0.984866	+	0.173318i	$0.0554490\pi$
$54$	4.88307	+	1.77642i	0.664501	+	0.241740i
$55$	5.63730	+	5.55995i	0.760133	+	0.749704i
$56$	−3.73929	−	1.21497i	−0.499684	−	0.162357i
$57$	−7.26276	+	4.59778i	−0.961976	+	0.608990i
$58$	1.26128	+	2.47540i	0.165614	+	0.325036i
$59$	5.11067	−	3.71312i	0.665353	−	0.483407i	−0.203113	−	0.979155i	$-0.565106\pi$
$59$	5.11067	−	3.71312i	0.665353	−	0.483407i	0.868466	+	0.495748i	$0.165106\pi$
$60$	3.34501	+	1.95215i	0.431839	+	0.252022i
$61$	1.09310	+	0.794185i	0.139957	+	0.101685i	0.655561	−	0.755142i	$-0.272432\pi$
$61$	1.09310	+	0.794185i	0.139957	+	0.101685i	−0.515604	+	0.856827i	$0.672432\pi$
$62$	−0.232323	+	1.46683i	−0.0295050	+	0.186287i
$63$	6.65153	−	9.74080i	0.838014	−	1.22723i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	4.52283	+	1.43509i	0.560988	+	0.178001i
$66$	2.42950	+	5.63141i	0.299051	+	0.693179i
$67$	8.29150	−	4.22473i	1.01297	−	0.516133i	0.132974	−	0.991119i	$-0.457547\pi$
$67$	8.29150	−	4.22473i	1.01297	−	0.516133i	0.879993	+	0.474987i	$0.157547\pi$
$68$	0.741501	+	0.741501i	0.0899202	+	0.0899202i
$69$	11.6254	+	6.89267i	1.39953	+	0.829780i
$70$	6.17351	−	6.25939i	0.737876	−	0.748140i
$71$	−2.47790	+	0.805120i	−0.294073	+	0.0955501i	−0.452338	−	0.891847i	$-0.649410\pi$
$71$	−2.47790	+	0.805120i	−0.294073	+	0.0955501i	0.158265	+	0.987397i	$0.449410\pi$
$72$	1.83345	+	2.37455i	0.216074	+	0.279843i
$73$	8.82492	−	1.39773i	1.03288	−	0.163592i	0.383093	−	0.923710i	$-0.374859\pi$
$73$	8.82492	−	1.39773i	1.03288	−	0.163592i	0.649785	+	0.760118i	$0.274859\pi$
$74$	1.08497			0.126126
$75$	−7.25256	+	4.73291i	−0.837453	+	0.546509i
$76$	−4.96277			−0.569269
$77$	13.7507	−	2.17789i	1.56704	−	0.248194i
$78$	2.82941	+	2.34599i	0.320368	+	0.265632i
$79$	−14.4405	+	4.69199i	−1.62468	+	0.527891i	−0.973040	−	0.230637i	$-0.925919\pi$
$79$	−14.4405	+	4.69199i	−1.62468	+	0.527891i	−0.651641	+	0.758528i	$0.725919\pi$
$80$	1.02889	+	1.98529i	0.115034	+	0.221962i
$81$	−8.38263	+	3.27590i	−0.931403	+	0.363989i
$82$	0.832175	+	0.832175i	0.0918984	+	0.0918984i
$83$	−9.56823	+	4.87526i	−1.05025	+	0.535129i	−0.891890	−	0.452252i	$-0.850621\pi$
$83$	−9.56823	+	4.87526i	−1.05025	+	0.535129i	−0.158360	+	0.987381i	$0.550621\pi$
$84$	6.25286	−	2.69761i	0.682243	−	0.294333i
$85$	−2.22501	+	0.739979i	−0.241336	+	0.0802620i
$86$	6.85807	−	9.43932i	0.739525	−	1.01787i
$87$	−4.47211	−	1.77638i	−0.479461	−	0.190448i
$88$	−0.553929	+	3.49737i	−0.0590490	+	0.372821i
$89$	−2.14121	−	1.55568i	−0.226968	−	0.164902i	0.468490	−	0.883469i	$-0.344798\pi$
$89$	−2.14121	−	1.55568i	−0.226968	−	0.164902i	−0.695458	+	0.718567i	$0.744798\pi$
$90$	−6.58342	+	1.28785i	−0.693954	+	0.135751i
$91$	6.74988	−	4.90407i	0.707579	−	0.514086i
$92$	3.54247	+	6.95248i	0.369328	+	0.724846i
$93$	−1.37589	−	2.17339i	−0.142673	−	0.225370i
$94$	10.9886	+	3.57041i	1.13339	+	0.368260i
$95$	4.96956	−	9.92214i	0.509866	−	1.01799i
$96$	0.161084	+	1.72454i	0.0164406	+	0.176011i
$97$	7.23583	−	14.2011i	0.734687	−	1.44190i	−0.156222	−	0.987722i	$-0.549932\pi$
$97$	7.23583	−	14.2011i	0.734687	−	1.44190i	0.890909	−	0.454182i	$-0.150068\pi$
$98$	−1.32319	−	8.35430i	−0.133663	−	0.843912i
$99$	−9.60181	−	4.54436i	−0.965018	−	0.456725i
$100$	−4.99952	+	0.0690705i	−0.499952	+	0.00690705i
$101$			2.78509i			0.277127i	0.990354	+	0.138564i	$0.0442485\pi$
$101$			2.78509i			0.277127i	−0.990354	+	0.138564i	$0.955751\pi$
$102$	−1.81259	−	0.116060i	−0.179473	−	0.0114917i
$103$	9.98017	+	5.08515i	0.983376	+	0.501055i	0.870295	−	0.492531i	$-0.163928\pi$
$103$	9.98017	+	5.08515i	0.983376	+	0.501055i	0.113081	+	0.993586i	$0.463928\pi$
$104$	0.655749	+	2.01819i	0.0643015	+	0.197900i
$105$	−0.868039	+	15.2027i	−0.0847119	+	1.48363i
$106$	−1.31692	+	4.05308i	−0.127911	+	0.393670i
$107$	3.58302	−	3.58302i	0.346384	−	0.346384i	−0.512377	−	0.858761i	$-0.671235\pi$
$107$	3.58302	−	3.58302i	0.346384	−	0.346384i	0.858761	+	0.512377i	$0.171235\pi$
$108$	−5.10084	−	0.990669i	−0.490829	−	0.0953272i
$109$	−5.92254	−	8.15168i	−0.567277	−	0.780789i	0.424952	−	0.905216i	$-0.360291\pi$
$109$	−5.92254	−	8.15168i	−0.567277	−	0.780789i	−0.992229	+	0.124427i	$0.960291\pi$
$110$	−6.43766	−	4.60963i	−0.613807	−	0.439511i
$111$	−1.41101	+	1.24119i	−0.133927	+	0.117808i
$112$	3.88332	+	0.615057i	0.366939	+	0.0581174i
$113$	−3.71655	−	0.588643i	−0.349623	−	0.0553749i	−0.0208469	−	0.999783i	$-0.506636\pi$
$113$	−3.71655	−	0.588643i	−0.349623	−	0.0553749i	−0.328776	+	0.944408i	$0.606636\pi$
$114$	6.45409	−	5.67732i	0.604481	−	0.531729i
$115$	−17.4475	+	0.120517i	−1.62699	+	0.0112382i
$116$	−1.63299	−	2.24762i	−0.151619	−	0.208686i
$117$	−6.36343	+	0.185826i	−0.588300	+	0.0171796i
$118$	−4.46689	+	4.46689i	−0.411211	+	0.411211i
$119$	−1.27407	+	3.92117i	−0.116793	+	0.359453i
$120$	−3.60921	−	1.40484i	−0.329474	−	0.128244i
$121$	−0.475402	−	1.46314i	−0.0432184	−	0.133012i
$122$	−1.20388	−	0.613408i	−0.108994	−	0.0555354i
$123$	−2.03424	−	0.130253i	−0.183421	−	0.0117445i
$124$		−	1.48511i		−	0.133367i
$125$	4.86827	−	10.0648i	0.435431	−	0.900222i
$126$	−5.04584	+	10.6614i	−0.449519	+	0.949793i
$127$	2.99916	+	18.9360i	0.266133	+	1.68030i	0.652373	+	0.757898i	$0.273773\pi$
$127$	2.99916	+	18.9360i	0.266133	+	1.68030i	−0.386241	+	0.922398i	$0.626227\pi$
$128$	−0.453990	+	0.891007i	−0.0401275	+	0.0787546i
$129$	1.87948	+	20.1214i	0.165479	+	1.77159i
$130$	−4.69164	−	0.709899i	−0.411484	−	0.0622623i
$131$	11.4171	+	3.70965i	0.997519	+	0.324113i	0.761874	−	0.647726i	$-0.224280\pi$
$131$	11.4171	+	3.70965i	0.997519	+	0.324113i	0.235645	+	0.971839i	$0.424280\pi$
$132$	−3.28054	−	5.18202i	−0.285534	−	0.451037i
$133$	−8.85836	−	17.3855i	−0.768118	−	1.50752i
$134$	−7.52852	+	5.46979i	−0.650365	+	0.472518i
$135$	7.08848	−	9.20617i	0.610079	−	0.792341i
$136$	−0.848368	−	0.616376i	−0.0727470	−	0.0528538i
$137$	1.31496	−	8.30230i	0.112344	−	0.709314i	−0.865645	−	0.500658i	$-0.833091\pi$
$137$	1.31496	−	8.30230i	0.112344	−	0.709314i	0.977989	−	0.208655i	$-0.0669087\pi$
$138$	−12.5605	−	4.98920i	−1.06922	−	0.424709i
$139$	1.56608	−	2.15552i	0.132833	−	0.182829i	−0.737419	−	0.675435i	$-0.763956\pi$
$139$	1.56608	−	2.15552i	0.132833	−	0.182829i	0.870252	+	0.492607i	$0.163956\pi$
$140$	−5.11832	+	7.14808i	−0.432577	+	0.604123i
$141$	−18.3752	+	7.92742i	−1.54747	+	0.667609i
$142$	2.32145	−	1.18284i	0.194812	−	0.0992615i
$143$	−5.31327	−	5.31327i	−0.444318	−	0.444318i
$144$	−2.18234	−	2.05850i	−0.181861	−	0.171541i
$145$	6.12892	−	1.01417i	0.508979	−	0.0842222i
$146$	−8.49762	+	2.76104i	−0.703268	+	0.228506i
$147$	11.2780	+	9.35108i	0.930192	+	0.771264i
$148$	−1.07161	+	0.169727i	−0.0880862	+	0.0139515i
$149$	15.1777			1.24340			0.621701	−	0.783254i	$-0.286442\pi$
$149$	15.1777			1.24340			0.621701	+	0.783254i	$0.286442\pi$
$150$	6.42288	−	5.80919i	0.524426	−	0.474318i
$151$	13.0979			1.06590			0.532948	−	0.846148i	$-0.321084\pi$
$151$	13.0979			1.06590			0.532948	+	0.846148i	$0.321084\pi$
$152$	4.90167	−	0.776348i	0.397578	−	0.0629701i
$153$	2.49005	−	1.92263i	0.201308	−	0.155435i
$154$	−13.2407	+	4.30216i	−1.06697	+	0.346678i
$155$	2.96921	+	1.48714i	0.238492	+	0.119450i
$156$	−3.16157	−	1.87449i	−0.253128	−	0.150080i
$157$	−6.13050	−	6.13050i	−0.489267	−	0.489267i	0.418808	−	0.908075i	$-0.362448\pi$
$157$	−6.13050	−	6.13050i	−0.489267	−	0.489267i	−0.908075	+	0.418808i	$0.862448\pi$
$158$	13.5287	−	6.89322i	1.07629	−	0.548395i
$159$	−2.92398	−	6.77757i	−0.231887	−	0.537497i
$160$	−1.32679	−	1.79990i	−0.104892	−	0.142294i
$161$	−18.0327	+	24.8199i	−1.42117	+	1.95608i
$162$	7.76696	−	4.54690i	0.610230	−	0.357238i
$163$	−0.771116	+	4.86864i	−0.0603985	+	0.381341i	0.938910	+	0.344162i	$0.111837\pi$
$163$	−0.771116	+	4.86864i	−0.0603985	+	0.381341i	−0.999309	+	0.0371787i	$0.988163\pi$
$164$	−0.952111	−	0.691749i	−0.0743473	−	0.0540165i
$165$	13.6455	−	1.36973i	1.06230	−	0.106633i
$166$	8.68777	−	6.31204i	0.674302	−	0.489909i
$167$	3.73760	+	7.33545i	0.289224	+	0.567634i	0.989207	−	0.146525i	$-0.0468090\pi$
$167$	3.73760	+	7.33545i	0.289224	+	0.567634i	−0.699983	+	0.714160i	$0.746809\pi$
$168$	−5.75388	+	3.64256i	−0.443921	+	0.281030i
$169$	8.08104	+	2.62569i	0.621619	+	0.201976i
$170$	2.08186	−	1.07894i	0.159671	−	0.0827507i
$171$	−1.89882	+	14.7667i	−0.145206	+	1.12924i
$172$	−5.29700	+	10.3959i	−0.403892	+	0.792684i
$173$	−0.713712	−	4.50620i	−0.0542625	−	0.342600i	−0.999851	−	0.0172364i	$-0.994513\pi$
$173$	−0.713712	−	4.50620i	−0.0542625	−	0.342600i	0.945589	−	0.325364i	$-0.105487\pi$
$174$	4.69494	+	1.05492i	0.355923	+	0.0799734i
$175$	−9.16594	−	17.3910i	−0.692880	−	1.31464i
$176$		−	3.54097i		−	0.266910i
$177$	0.699162	−	10.9192i	0.0525522	−	0.820741i
$178$	2.35821	+	1.20157i	0.176755	+	0.0900614i
$179$	3.51637	+	10.8223i	0.262826	+	0.808894i	0.992186	+	0.124765i	$0.0398177\pi$
$179$	3.51637	+	10.8223i	0.262826	+	0.808894i	−0.729361	+	0.684129i	$0.760182\pi$
$180$	6.30090	−	2.30187i	0.469642	−	0.171571i
$181$	2.01769	−	6.20982i	0.149974	−	0.461572i	−0.847643	−	0.530567i	$-0.821979\pi$
$181$	2.01769	−	6.20982i	0.149974	−	0.461572i	0.997617	+	0.0689945i	$0.0219791\pi$
$182$	−5.89961	+	5.89961i	−0.437308	+	0.437308i
$183$	2.26738	−	0.579479i	0.167609	−	0.0428364i
$184$	−4.58646	−	6.31272i	−0.338118	−	0.465380i
$185$	0.733743	−	2.31246i	0.0539458	−	0.170015i
$186$	1.69894	+	1.93139i	0.124572	+	0.141616i
$187$	3.66749	+	0.580873i	0.268193	+	0.0424776i
$188$	−11.4118	−	1.80746i	−0.832294	−	0.131822i
$189$	−5.63432	−	19.6375i	−0.409836	−	1.42842i
$190$	−3.35621	+	10.5774i	−0.243485	+	0.767365i
$191$	−0.349868	−	0.481552i	−0.0253155	−	0.0348439i	0.796172	−	0.605071i	$-0.206855\pi$
$191$	−0.349868	−	0.481552i	−0.0253155	−	0.0348439i	−0.821487	+	0.570227i	$0.806855\pi$
$192$	−0.428879	−	1.67811i	−0.0309517	−	0.121107i
$193$	−15.5790	+	15.5790i	−1.12140	+	1.12140i	−0.129866	+	0.991532i	$0.541455\pi$
$193$	−15.5790	+	15.5790i	−1.12140	+	1.12140i	−0.991532	+	0.129866i	$0.958545\pi$
$194$	−4.92520	+	15.1582i	−0.353609	+	1.08830i
$195$	6.91360	−	4.44392i	0.495093	−	0.318236i
$196$	2.61380	+	8.04445i	0.186700	+	0.574604i
$197$	2.51349	+	1.28069i	0.179079	+	0.0912453i	0.541232	−	0.840873i	$-0.317958\pi$
$197$	2.51349	+	1.28069i	0.179079	+	0.0912453i	−0.362153	+	0.932119i	$0.617958\pi$
$198$	10.1945	+	2.98635i	0.724491	+	0.212231i
$199$			10.4829i			0.743113i	0.928410	+	0.371556i	$0.121176\pi$
$199$			10.4829i			0.743113i	−0.928410	+	0.371556i	$0.878824\pi$
$200$	4.92717	−	0.850318i	0.348403	−	0.0601266i
$201$	3.53352	−	15.7260i	0.249235	−	1.10922i
$202$	−0.435685	−	2.75080i	−0.0306547	−	0.193546i
$203$	4.95900	−	9.73259i	0.348054	−	0.683094i
$204$	1.80843	−	0.168920i	0.126615	−	0.0118267i
$205$	2.33644	−	1.21087i	0.163184	−	0.0845711i
$206$	−10.6528	−	3.46130i	−0.742215	−	0.241160i
$207$	22.0425	−	7.88050i	1.53206	−	0.547733i
$208$	−0.963390	−	1.89076i	−0.0667991	−	0.131101i
$209$	−14.2168	+	10.3291i	−0.983400	+	0.714482i
$210$	−1.52088	−	15.1514i	−0.104951	−	1.04554i
$211$	1.70957	+	1.24207i	0.117692	+	0.0855079i	0.645074	−	0.764120i	$-0.276827\pi$
$211$	1.70957	+	1.24207i	0.117692	+	0.0855079i	−0.527382	+	0.849628i	$0.676827\pi$
$212$	0.666670	−	4.20919i	0.0457871	−	0.289088i
$213$	−1.66590	+	4.19398i	−0.114146	+	0.287366i
$214$	−2.97840	+	4.09941i	−0.203599	+	0.280230i
$215$	−15.4805	−	21.0005i	−1.05576	−	1.43222i
$216$	5.19302	+	0.180525i	0.353340	+	0.0122832i
$217$	5.20263	−	2.65087i	0.353177	−	0.179953i
$218$	7.12483	+	7.12483i	0.482554	+	0.482554i
$219$	7.89259	−	13.3119i	0.533332	−	0.899532i
$220$	7.07951	+	3.54581i	0.477300	+	0.239058i
$221$	2.11635	−	0.687645i	0.142361	−	0.0462560i
$222$	1.19947	−	1.44664i	0.0805034	−	0.0970920i
$223$	−10.5167	+	1.66568i	−0.704248	+	0.111542i	−0.498279	−	0.867017i	$-0.666034\pi$
$223$	−10.5167	+	1.66568i	−0.704248	+	0.111542i	−0.205969	+	0.978559i	$0.566034\pi$
$224$	−3.93172			−0.262699
$225$	−1.70736	+	14.9025i	−0.113824	+	0.993501i
$226$	3.76287			0.250303
$227$	−1.36230	+	0.215768i	−0.0904192	+	0.0143210i	−0.201480	−	0.979493i	$-0.564575\pi$
$227$	−1.36230	+	0.215768i	−0.0904192	+	0.0143210i	0.111061	+	0.993814i	$0.464575\pi$
$228$	−5.48650	+	6.61706i	−0.363353	+	0.438226i
$229$	15.7865	−	5.12935i	1.04320	−	0.338957i	0.263205	−	0.964740i	$-0.415220\pi$
$229$	15.7865	−	5.12935i	1.04320	−	0.338957i	0.779997	+	0.625783i	$0.215220\pi$
$230$	17.2138	−	2.84842i	1.13505	−	0.187820i
$231$	12.2980	−	20.7421i	0.809146	−	1.36473i
$232$	1.96449	+	1.96449i	0.128975	+	0.128975i
$233$	−22.1187	+	11.2700i	−1.44904	+	0.738324i	−0.988769	−	0.149453i	$-0.952249\pi$
$233$	−22.1187	+	11.2700i	−1.44904	+	0.738324i	−0.460274	+	0.887777i	$0.652249\pi$
$234$	6.25602	−	1.17900i	0.408969	−	0.0770735i
$235$	15.0411	−	21.0059i	0.981175	−	1.37028i
$236$	3.71312	−	5.11067i	0.241704	−	0.332677i
$237$	−9.70839	+	24.4412i	−0.630628	+	1.58763i
$238$	0.644974	−	4.07220i	0.0418074	−	0.263962i
$239$	19.2197	+	13.9639i	1.24322	+	0.903249i	0.997808	−	0.0661704i	$-0.0210781\pi$
$239$	19.2197	+	13.9639i	1.24322	+	0.903249i	0.245408	+	0.969420i	$0.421078\pi$
$240$	3.78454	+	0.822943i	0.244291	+	0.0531207i
$241$	−5.11077	+	3.71319i	−0.329214	+	0.239188i	−0.740097	−	0.672500i	$-0.765220\pi$
$241$	−5.11077	+	3.71319i	−0.329214	+	0.239188i	0.410883	+	0.911688i	$0.365220\pi$
$242$	0.698434	+	1.37075i	0.0448970	+	0.0881154i
$243$	−4.89938	+	14.7985i	−0.314296	+	0.949325i
$244$	1.28502	+	0.417528i	0.0822649	+	0.0267295i
$245$	−18.7008	−	2.82964i	−1.19475	−	0.180779i
$246$	2.02957	−	0.189576i	0.129401	−	0.0120869i
$247$	−4.78108	+	9.38340i	−0.304213	+	0.597051i
$248$	0.232323	+	1.46683i	0.0147525	+	0.0931436i
$249$	−4.07762	+	18.1475i	−0.258408	+	1.15005i
$250$	−3.23385	+	10.7024i	−0.204527	+	0.676882i
$251$		−	13.8304i		−	0.872966i	−0.899712	−	0.436483i	$-0.856224\pi$
$251$		−	13.8304i		−	0.872966i	0.899712	−	0.436483i	$-0.143776\pi$
$252$	3.31591	−	11.3195i	0.208883	−	0.713060i
$253$	24.6185	+	12.5437i	1.54775	+	0.788619i
$254$	−5.92448	−	18.2337i	−0.371735	−	1.14408i
$255$	−1.47318	+	3.78477i	−0.0922539	+	0.237011i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−12.9955	+	12.9955i	−0.810638	+	0.810638i	−0.984730	−	0.174091i	$-0.944301\pi$
$257$	−12.9955	+	12.9955i	−0.810638	+	0.810638i	0.174091	+	0.984730i	$0.444301\pi$
$258$	−5.00401	−	19.5796i	−0.311536	−	1.21897i
$259$	−2.50738	−	3.45111i	−0.155801	−	0.214442i
$260$	4.74493	−	0.0327750i	0.294268	−	0.00203262i
$261$	−7.31259	+	3.99900i	−0.452638	+	0.247532i
$262$	−11.8569	−	1.87794i	−0.732520	−	0.116020i
$263$	8.70800	+	1.37921i	0.536958	+	0.0850458i	0.419023	−	0.907976i	$-0.362373\pi$
$263$	8.70800	+	1.37921i	0.536958	+	0.0850458i	0.117935	+	0.993021i	$0.462373\pi$
$264$	4.05080	+	4.60503i	0.249309	+	0.283420i
$265$	7.74792	+	5.54783i	0.475951	+	0.340801i
$266$	11.4690	+	15.7857i	0.703209	+	0.967885i
$267$	−4.44143	+	1.13511i	−0.271811	+	0.0694675i
$268$	6.58017	−	6.58017i	0.401948	−	0.401948i
$269$	−0.0471754	+	0.145191i	−0.00287634	+	0.00885245i	−0.952484	−	0.304587i	$-0.901481\pi$
$269$	−0.0471754	+	0.145191i	−0.00287634	+	0.00885245i	0.949608	+	0.313440i	$0.101481\pi$
$270$	−5.56105	+	10.2017i	−0.338434	+	0.620856i
$271$	−3.79892	−	11.6919i	−0.230768	−	0.710230i	−0.997655	−	0.0684477i	$-0.978195\pi$
$271$	−3.79892	−	11.6919i	−0.230768	−	0.710230i	0.766887	−	0.641782i	$-0.221805\pi$
$272$	0.934346	+	0.476073i	0.0566530	+	0.0288662i
$273$	0.923411	−	14.4215i	0.0558874	−	0.872829i
$274$			8.40579i			0.507813i
$275$	−14.1784	+	10.6035i	−0.854988	+	0.639416i
$276$	13.1863	+	2.96288i	0.793724	+	0.178345i
$277$	0.680977	+	4.29952i	0.0409160	+	0.258333i	0.999664	−	0.0259243i	$-0.00825290\pi$
$277$	0.680977	+	4.29952i	0.0409160	+	0.258333i	−0.958748	+	0.284258i	$0.908253\pi$
$278$	−1.20960	+	2.37397i	−0.0725468	+	0.142381i
$279$	−4.41895	−	0.568222i	−0.264556	−	0.0340186i
$280$	3.93710	−	7.86075i	0.235287	−	0.469770i
$281$	21.0452	+	6.83801i	1.25545	+	0.407922i	0.859872	−	0.510509i	$-0.170543\pi$
$281$	21.0452	+	6.83801i	1.25545	+	0.407922i	0.395582	+	0.918431i	$0.370543\pi$
$282$	16.9088	−	10.7043i	1.00691	−	0.637434i
$283$	3.54907	+	6.96545i	0.210970	+	0.414053i	0.972107	−	0.234539i	$-0.0753581\pi$
$283$	3.54907	+	6.96545i	0.210970	+	0.414053i	−0.761136	+	0.648592i	$0.775358\pi$
$284$	−2.10783	+	1.53143i	−0.125077	+	0.0908736i
$285$	−7.73558	−	17.5954i	−0.458216	−	1.04226i
$286$	6.07903	+	4.41668i	0.359461	+	0.261164i
$287$	0.723844	−	4.57017i	0.0427272	−	0.269769i
$288$	2.47749	+	1.69176i	0.145987	+	0.0996879i
$289$	9.34599	−	12.8637i	0.549764	−	0.756686i
$290$	−5.89481	+	1.96046i	−0.346155	+	0.115122i
$291$	−10.9355	−	25.3476i	−0.641049	−	1.48590i
$292$	7.96107	−	4.05637i	0.465887	−	0.237381i
$293$	5.69369	+	5.69369i	0.332629	+	0.332629i	0.853584	−	0.520955i	$-0.174424\pi$
$293$	5.69369	+	5.69369i	0.332629	+	0.332629i	−0.520955	+	0.853584i	$0.674424\pi$
$294$	−12.6020	−	7.47169i	−0.734961	−	0.435758i
$295$	6.49965	+	12.5414i	0.378424	+	0.730187i
$296$	1.03187	−	0.335275i	0.0599762	−	0.0194875i
$297$	−16.6743	+	7.77855i	−0.967540	+	0.451357i
$298$	−14.9908	+	2.37431i	−0.868394	+	0.137540i
$299$	16.5582			0.957588
$300$	−5.43504	+	6.74243i	−0.313792	+	0.389274i
$301$	−45.8739			−2.64413
$302$	−12.9367	+	2.04897i	−0.744422	+	0.117905i
$303$	3.71348	+	3.07901i	0.213334	+	0.176885i
$304$	−4.71987	+	1.53358i	−0.270703	+	0.0879568i
$305$	−2.12155	+	2.15106i	−0.121479	+	0.123169i
$306$	−2.15862	+	2.28849i	−0.123400	+	0.130824i
$307$	−6.57841	−	6.57841i	−0.375450	−	0.375450i	0.494008	−	0.869458i	$-0.335531\pi$
$307$	−6.57841	−	6.57841i	−0.375450	−	0.375450i	−0.869458	+	0.494008i	$0.835531\pi$
$308$	12.4047	−	6.32050i	0.706822	−	0.360144i
$309$	17.8137	−	7.68517i	1.01338	−	0.437194i
$310$	−3.16529	−	1.00435i	−0.179776	−	0.0570431i
$311$	−6.69564	+	9.21576i	−0.379675	+	0.522578i	−0.955498	−	0.294996i	$-0.904682\pi$
$311$	−6.69564	+	9.21576i	−0.379675	+	0.522578i	0.575823	+	0.817574i	$0.304682\pi$
$312$	3.41588	+	1.35684i	0.193386	+	0.0768157i
$313$	3.74388	−	23.6379i	0.211617	−	1.33610i	−0.621681	−	0.783271i	$-0.713550\pi$
$313$	3.74388	−	23.6379i	0.211617	−	1.33610i	0.833297	−	0.552825i	$-0.186450\pi$
$314$	7.01404	+	5.09600i	0.395825	+	0.287584i
$315$	19.3108	+	17.9645i	1.08804	+	1.01219i
$316$	−12.2838	+	8.92470i	−0.691018	+	0.502054i
$317$	−6.09176	−	11.9558i	−0.342147	−	0.671502i	0.654253	−	0.756276i	$-0.272983\pi$
$317$	−6.09176	−	11.9558i	−0.342147	−	0.671502i	−0.996400	+	0.0847737i	$0.972983\pi$
$318$	3.94823	+	6.23672i	0.221406	+	0.349738i
$319$	−9.35606	−	3.03997i	−0.523839	−	0.170205i
$320$	1.59202	+	1.57018i	0.0889968	+	0.0877757i
$321$	−0.816240	−	8.73853i	−0.0455581	−	0.487737i
$322$	13.9280	−	27.3352i	0.776176	−	1.52333i
$323$	−0.814110	−	5.14009i	−0.0452983	−	0.286002i
$324$	−6.96005	+	5.70594i	−0.386669	+	0.316997i
$325$	−4.68589	+	9.51943i	−0.259927	+	0.528043i
$326$		−	4.92933i		−	0.273010i
$327$	−17.4165	−	1.11518i	−0.963136	−	0.0616698i
$328$	1.04860	+	0.534289i	0.0578994	+	0.0295012i
$329$	−14.0379	−	43.2041i	−0.773932	−	2.38192i
$330$	−13.2633	+	3.48749i	−0.730118	+	0.191980i
$331$	−2.24416	+	6.90681i	−0.123350	+	0.379633i	−0.993597	−	0.112983i	$-0.963959\pi$
$331$	−2.24416	+	6.90681i	−0.123350	+	0.379633i	0.870247	+	0.492616i	$0.163959\pi$
$332$	−7.59339	+	7.59339i	−0.416742	+	0.416742i
$333$	0.0950100	+	3.25353i	0.00520652	+	0.178292i
$334$	−4.83910	−	6.66045i	−0.264784	−	0.364444i
$335$	6.56666	+	19.7450i	0.358775	+	1.07878i
$336$	5.11321	−	4.49782i	0.278949	−	0.245376i
$337$	−25.1497	−	3.98332i	−1.36999	−	0.216985i	−0.572297	−	0.820046i	$-0.693948\pi$
$337$	−25.1497	−	3.98332i	−1.36999	−	0.216985i	−0.797695	+	0.603061i	$0.793948\pi$
$338$	−8.39230	−	1.32921i	−0.456481	−	0.0722995i
$339$	−4.89363	+	4.30466i	−0.265785	+	0.233797i
$340$	−1.88744	+	1.39133i	−0.102361	+	0.0754554i
$341$	−3.09100	−	4.25440i	−0.167387	−	0.230389i
$342$	−0.434585	−	14.8820i	−0.0234997	−	0.804724i
$343$	−4.05468	+	4.05468i	−0.218932	+	0.218932i
$344$	3.60550	−	11.0966i	0.194396	−	0.598288i
$345$	−19.1281	+	23.3967i	−1.02982	+	1.25964i
$346$	1.40985	+	4.33907i	0.0757940	+	0.233270i
$347$	4.08726	+	2.08256i	0.219416	+	0.111798i	0.560244	−	0.828328i	$-0.310707\pi$
$347$	4.08726	+	2.08256i	0.219416	+	0.111798i	−0.340828	+	0.940126i	$0.610707\pi$
$348$	−4.80216	−	0.307484i	−0.257423	−	0.0164828i
$349$		−	10.1416i		−	0.542867i	−0.962457	−	0.271434i	$-0.912502\pi$
$349$		−	10.1416i		−	0.542867i	0.962457	−	0.271434i	$-0.0874978\pi$
$350$	11.7736	+	15.7430i	0.629328	+	0.841499i
$351$	−6.78721	+	8.69006i	−0.362275	+	0.463841i
$352$	0.553929	+	3.49737i	0.0295245	+	0.186410i
$353$	−5.55052	+	10.8935i	−0.295424	+	0.579803i	−0.990238	−	0.139387i	$-0.955487\pi$
$353$	−5.55052	+	10.8935i	−0.295424	+	0.579803i	0.694814	+	0.719190i	$0.255487\pi$
$354$	1.01759	+	10.8942i	0.0540845	+	0.579020i
$355$	−0.951095	−	5.74774i	−0.0504789	−	0.305058i
$356$	−2.51715	−	0.817870i	−0.133408	−	0.0433470i
$357$	3.81974	+	6.03375i	0.202162	+	0.319340i
$358$	−5.16605	−	10.1389i	−0.273034	−	0.535860i
$359$	−27.4018	+	19.9085i	−1.44621	+	1.05073i	−0.459511	+	0.888172i	$0.651975\pi$
$359$	−27.4018	+	19.9085i	−1.44621	+	1.05073i	−0.986699	+	0.162561i	$0.948025\pi$
$360$	−5.86324	+	3.25921i	−0.309020	+	0.171775i
$361$	4.55401	+	3.30868i	0.239685	+	0.174141i
$362$	−1.02142	+	6.44900i	−0.0536847	+	0.338952i
$363$	−2.47643	−	0.983673i	−0.129979	−	0.0516295i
$364$	4.90407	−	6.74988i	0.257043	−	0.353790i
$365$	0.138000	+	19.9786i	0.00722324	+	1.04573i
$366$	−2.14881	+	0.927041i	−0.112320	+	0.0484572i
$367$	−4.23542	+	2.15805i	−0.221087	+	0.112649i	−0.561026	−	0.827798i	$-0.689593\pi$
$367$	−4.23542	+	2.15805i	−0.221087	+	0.112649i	0.339939	+	0.940447i	$0.389593\pi$
$368$	5.51752	+	5.51752i	0.287621	+	0.287621i
$369$	−2.42259	+	2.56833i	−0.126115	+	0.133702i
$370$	−0.362961	+	2.39877i	−0.0188695	+	0.124706i
$371$	15.9356	−	5.17778i	0.827334	−	0.268817i
$372$	−1.98016	−	1.64184i	−0.102667	−	0.0851254i
$373$	37.1540	−	5.88461i	1.92376	−	0.304693i	0.926352	−	0.376660i	$-0.122927\pi$
$373$	37.1540	−	5.88461i	1.92376	−	0.304693i	0.997407	+	0.0719662i	$0.0229274\pi$
$374$	−3.71320			−0.192005
$375$	−8.03776	−	17.6180i	−0.415068	−	0.909790i
$376$	11.5541			0.595857
$377$	−5.82291	+	0.922258i	−0.299895	+	0.0474987i
$378$	8.63693	+	18.5144i	0.444236	+	0.952275i
$379$	15.4663	−	5.02532i	0.794453	−	0.258133i	0.116454	−	0.993196i	$-0.462847\pi$
$379$	15.4663	−	5.02532i	0.794453	−	0.258133i	0.677999	+	0.735063i	$0.262847\pi$
$380$	1.66022	−	10.9722i	0.0851674	−	0.562862i
$381$	28.5638	+	16.9354i	1.46337	+	0.867629i
$382$	0.420892	+	0.420892i	0.0215347	+	0.0215347i
$383$	28.2694	−	14.4040i	1.44450	−	0.736009i	0.456393	−	0.889779i	$-0.349141\pi$
$383$	28.2694	−	14.4040i	1.44450	−	0.736009i	0.988107	+	0.153769i	$0.0491413\pi$
$384$	0.686114	+	1.59036i	0.0350131	+	0.0811578i
$385$	0.215027	+	31.1300i	0.0109588	+	1.58653i
$386$	12.9501	−	17.8242i	0.659141	−	0.907230i
$387$	28.9065	+	19.7388i	1.46940	+	1.00338i
$388$	2.49330	−	15.7420i	0.126578	−	0.799181i
$389$	−8.93091	−	6.48869i	−0.452815	−	0.328989i	0.337891	−	0.941185i	$-0.390286\pi$
$389$	−8.93091	−	6.48869i	−0.452815	−	0.328989i	−0.790706	+	0.612196i	$0.790286\pi$
$390$	−6.13330	+	5.47074i	−0.310572	+	0.277022i
$391$	−6.61978	+	4.80955i	−0.334776	+	0.243229i
$392$	−3.84005	−	7.53652i	−0.193952	−	0.380652i
$393$	17.5682	−	11.1218i	0.886200	−	0.561019i
$394$	−2.68289	−	0.871725i	−0.135162	−	0.0439169i
$395$	−5.54270	−	33.4961i	−0.278883	−	1.68537i
$396$	−10.5361	−	1.35482i	−0.529461	−	0.0680821i
$397$	−6.77912	+	13.3048i	−0.340234	+	0.667748i	−0.996205	−	0.0870388i	$-0.972260\pi$
$397$	−6.77912	+	13.3048i	−0.340234	+	0.667748i	0.655970	+	0.754787i	$0.272260\pi$
$398$	−1.63989	−	10.3538i	−0.0822000	−	0.518991i
$399$	−32.9740	−	7.40905i	−1.65077	−	0.370916i
$400$	−4.73348	+	1.61063i	−0.236674	+	0.0805314i
$401$		−	12.7473i		−	0.636570i	−0.947995	−	0.318285i	$-0.896893\pi$
$401$		−	12.7473i		−	0.636570i	0.947995	−	0.318285i	$-0.103107\pi$
$402$	−1.02993	+	16.0851i	−0.0513684	+	0.802253i
$403$	−2.80799	−	1.43074i	−0.139876	−	0.0712703i
$404$	0.860641	+	2.64878i	0.0428185	+	0.131782i
$405$	−4.43841	−	19.6291i	−0.220546	−	0.975376i
$406$	−3.37544	+	10.3885i	−0.167520	+	0.515574i
$407$	−2.71660	+	2.71660i	−0.134657	+	0.134657i
$408$	−1.75974	+	0.449740i	−0.0871200	+	0.0222655i
$409$	15.8203	+	21.7748i	0.782264	+	1.07669i	0.995028	+	0.0995907i	$0.0317533\pi$
$409$	15.8203	+	21.7748i	0.782264	+	1.07669i	−0.212764	+	0.977104i	$0.568247\pi$
$410$	−2.11825	+	1.56147i	−0.104613	+	0.0771153i
$411$	−9.61607	−	10.9318i	−0.474326	−	0.539224i
$412$	11.0631	+	1.75222i	0.545040	+	0.0863259i
$413$	24.5315	+	3.88540i	1.20711	+	0.191188i
$414$	−20.5383	+	11.2317i	−1.00940	+	0.552007i
$415$	−7.57781	−	22.7854i	−0.371980	−	1.11849i
$416$	1.24731	+	1.71677i	0.0611543	+	0.0841717i
$417$	−1.14269	−	4.47111i	−0.0559579	−	0.218951i
$418$	12.4260	−	12.4260i	0.607775	−	0.607775i
$419$	5.97052	−	18.3754i	0.291679	−	0.897696i	−0.692638	−	0.721286i	$-0.743551\pi$
$419$	5.97052	−	18.3754i	0.291679	−	0.897696i	0.984317	−	0.176410i	$-0.0564485\pi$
$420$	3.87235	+	14.7269i	0.188951	+	0.718599i
$421$	2.15745	+	6.63995i	0.105148	+	0.323611i	0.989765	−	0.142706i	$-0.0455804\pi$
$421$	2.15745	+	6.63995i	0.105148	+	0.323611i	−0.884617	+	0.466318i	$0.845580\pi$
$422$	−1.88282	−	0.959347i	−0.0916545	−	0.0467003i
$423$	−9.74440	+	33.2644i	−0.473789	+	1.61737i
$424$			4.26166i			0.206964i
$425$	−0.891678	−	5.16683i	−0.0432527	−	0.250628i
$426$	0.989313	−	4.40295i	0.0479324	−	0.213323i
$427$	0.831033	+	5.24693i	0.0402165	+	0.253917i
$428$	2.30044	−	4.51487i	0.111196	−	0.218234i
$429$	−12.9584	+	1.21040i	−0.625637	+	0.0584389i
$430$	18.5752	+	18.3203i	0.895773	+	0.883483i
$431$	11.4753	+	3.72856i	0.552747	+	0.179598i	0.572055	−	0.820215i	$-0.306146\pi$
$431$	11.4753	+	3.72856i	0.552747	+	0.179598i	−0.0193080	+	0.999814i	$0.506146\pi$
$432$	−5.15732	+	0.634064i	−0.248132	+	0.0305064i
$433$	−11.0750	−	21.7358i	−0.532228	−	1.04456i	−0.987999	−	0.154460i	$-0.950636\pi$
$433$	−11.0750	−	21.7358i	−0.532228	−	1.04456i	0.455771	−	0.890097i	$-0.349364\pi$
$434$	−4.72389	+	3.43211i	−0.226754	+	0.164746i
$435$	5.42349	−	9.29314i	0.260036	−	0.445572i
$436$	−8.15168	−	5.92254i	−0.390395	−	0.283638i
$437$	6.05780	−	38.2475i	0.289784	−	1.82962i
$438$	−5.71298	+	14.3826i	−0.272977	+	0.687229i
$439$	−4.35738	+	5.99742i	−0.207966	+	0.286241i	−0.900240	−	0.435394i	$-0.856609\pi$
$439$	−4.35738	+	5.99742i	−0.207966	+	0.286241i	0.692274	+	0.721635i	$0.256609\pi$
$440$	−7.54703	−	2.39467i	−0.359791	−	0.114162i
$441$	24.9364	−	4.69946i	1.18745	−	0.223784i
$442$	−1.98273	+	1.01025i	−0.0943087	+	0.0480527i
$443$	0.514362	+	0.514362i	0.0244381	+	0.0244381i	0.719220	−	0.694782i	$-0.244499\pi$
$443$	0.514362	+	0.514362i	0.0244381	+	0.0244381i	−0.694782	+	0.719220i	$0.744499\pi$
$444$	−0.958401	+	1.61647i	−0.0454837	+	0.0767141i
$445$	4.15577	−	4.21358i	0.197002	−	0.199743i
$446$	10.1266	−	3.29034i	0.479509	−	0.155802i
$447$	16.7794	−	20.2370i	0.793639	−	0.957177i
$448$	3.88332	−	0.615057i	0.183469	−	0.0290587i
$449$	29.6955			1.40142			0.700709	−	0.713447i	$-0.252867\pi$
$449$	29.6955			1.40142			0.700709	+	0.713447i	$0.252867\pi$
$450$	−0.644927	−	14.9861i	−0.0304021	−	0.706453i
$451$	−4.16727			−0.196229
$452$	−3.71655	+	0.588643i	−0.174812	+	0.0276874i
$453$	14.4802	−	17.4640i	0.680339	−	0.820531i
$454$	1.31178	−	0.426222i	0.0615648	−	0.0200036i
$455$	8.58435	+	16.5639i	0.402441	+	0.776527i
$456$	4.38382	−	7.39387i	0.205291	−	0.346250i
$457$	−2.68309	−	2.68309i	−0.125510	−	0.125510i	0.641562	−	0.767071i	$-0.278287\pi$
$457$	−2.68309	−	2.68309i	−0.125510	−	0.125510i	−0.767071	+	0.641562i	$0.778287\pi$
$458$	−14.7898	+	7.53576i	−0.691080	+	0.352123i
$459$	0.189306	−	5.44561i	0.00883605	−	0.254179i
$460$	−16.5563	+	5.50620i	−0.771943	+	0.256728i
$461$	6.68161	−	9.19644i	0.311193	−	0.428321i	−0.624560	−	0.780977i	$-0.714721\pi$
$461$	6.68161	−	9.19644i	0.311193	−	0.428321i	0.935753	+	0.352656i	$0.114721\pi$
$462$	−8.90177	+	22.4105i	−0.414148	+	1.04263i
$463$	−2.20029	+	13.8921i	−0.102256	+	0.645619i	0.882318	+	0.470653i	$0.155982\pi$
$463$	−2.20029	+	13.8921i	−0.102256	+	0.645619i	−0.984574	+	0.174966i	$0.944018\pi$
$464$	−2.24762	−	1.63299i	−0.104343	−	0.0758097i
$465$	5.26542	−	2.31488i	0.244178	−	0.107350i
$466$	20.0833	−	14.5914i	0.930343	−	0.675934i
$467$	2.03239	+	3.98879i	0.0940479	+	0.184579i	0.933238	−	0.359259i	$-0.116970\pi$
$467$	2.03239	+	3.98879i	0.0940479	+	0.184579i	−0.839190	+	0.543838i	$0.816970\pi$
$468$	−5.99456	+	2.14314i	−0.277099	+	0.0990667i
$469$	34.7969	+	11.3062i	1.60677	+	0.522072i
$470$	−11.5699	+	23.1003i	−0.533679	+	1.06554i
$471$	−14.9515	+	1.39657i	−0.688929	+	0.0643508i
$472$	−2.86792	+	5.62861i	−0.132007	+	0.259078i
$473$	6.46305	+	40.8061i	0.297171	+	1.87627i
$474$	5.76542	−	25.6590i	0.264814	−	1.17856i
$475$	20.2744	+	14.3065i	0.930253	+	0.656427i
$476$			4.12296i			0.188976i
$477$	−12.2694	−	3.59417i	−0.561776	−	0.164566i
$478$	−21.1675	−	10.7854i	−0.968177	−	0.493311i
$479$	−9.35922	−	28.8047i	−0.427634	−	1.31612i	−0.900450	−	0.434960i	$-0.856763\pi$
$479$	−9.35922	−	28.8047i	−0.427634	−	1.31612i	0.472816	−	0.881161i	$-0.343237\pi$
$480$	−3.86669	−	0.220778i	−0.176489	−	0.0100771i
$481$	−0.711470	+	2.18968i	−0.0324402	+	0.0998408i
$482$	4.46698	−	4.46698i	0.203465	−	0.203465i
$483$	13.1576	+	51.4829i	0.598692	+	2.34255i
$484$	−0.904268	−	1.24462i	−0.0411031	−	0.0565736i
$485$	28.9766	+	20.7485i	1.31576	+	0.942139i
$486$	2.52407	−	15.3828i	0.114494	−	0.697776i
$487$	−0.548721	−	0.0869089i	−0.0248649	−	0.00393822i	0.143990	−	0.989579i	$-0.454007\pi$
$487$	−0.548721	−	0.0869089i	−0.0248649	−	0.00393822i	−0.168855	+	0.985641i	$0.554007\pi$
$488$	−1.33451	−	0.211366i	−0.0604106	−	0.00956809i
$489$	5.63906	+	6.41060i	0.255007	+	0.289897i
$490$	18.9132	−	0.130641i	0.854411	−	0.00590174i
$491$	−3.72379	−	5.12536i	−0.168052	−	0.231304i	0.716682	−	0.697400i	$-0.245660\pi$
$491$	−3.72379	−	5.12536i	−0.168052	−	0.231304i	−0.884734	+	0.466096i	$0.845660\pi$
$492$	−1.97493	+	0.504737i	−0.0890366	+	0.0227553i
$493$	2.06004	−	2.06004i	0.0927797	−	0.0927797i
$494$	3.25433	−	10.0158i	0.146419	−	0.450632i
$495$	13.2593	−	19.7084i	0.595960	−	0.885827i
$496$	−0.458925	−	1.41243i	−0.0206063	−	0.0634198i
$497$	−9.12729	−	4.65059i	−0.409415	−	0.208607i
$498$	1.18852	−	18.5619i	0.0532590	−	0.831780i
$499$		−	26.3004i		−	1.17737i	−0.808363	−	0.588684i	$-0.799646\pi$
$499$		−	26.3004i		−	1.17737i	0.808363	−	0.588684i	$-0.200354\pi$
$500$	1.51981	−	11.0766i	0.0679678	−	0.495359i
$501$	13.9127	+	3.12609i	0.621573	+	0.139663i
$502$	2.16355	+	13.6601i	0.0965639	+	0.609681i
$503$	2.72953	−	5.35700i	0.121704	−	0.238857i	−0.822115	−	0.569322i	$-0.807206\pi$
$503$	2.72953	−	5.35700i	0.121704	−	0.238857i	0.943818	+	0.330465i	$0.107206\pi$
$504$	−1.50433	+	11.6988i	−0.0670080	+	0.521108i
$505$	−6.15757	−	0.931711i	−0.274008	−	0.0414606i
$506$	−26.2777	−	8.53813i	−1.16818	−	0.379566i
$507$	12.4348	−	7.87200i	0.552249	−	0.349608i
$508$	8.70391	+	17.0824i	0.386174	+	0.757908i
$509$	1.71448	−	1.24564i	0.0759931	−	0.0552122i	−0.549140	−	0.835730i	$-0.685045\pi$
$509$	1.71448	−	1.24564i	0.0759931	−	0.0552122i	0.625133	+	0.780518i	$0.285045\pi$
$510$	0.862972	−	3.96863i	0.0382130	−	0.175734i
$511$	28.4205	+	20.6487i	1.25725	+	0.913444i
$512$	−0.156434	+	0.987688i	−0.00691349	+	0.0436501i
$513$	17.5899	+	18.8569i	0.776612	+	0.832551i
$514$	10.8026	−	14.8685i	0.476481	−	0.655820i
$515$	−14.5815	+	20.3640i	−0.642537	+	0.897346i
$516$	8.00533	+	18.5558i	0.352415	+	0.816872i
$517$	−36.4534	+	18.5739i	−1.60322	+	0.816881i
$518$	3.01638	+	3.01638i	0.132532	+	0.132532i
$519$	−6.79733	−	4.03013i	−0.298370	−	0.176903i
$520$	−4.68139	+	0.774642i	−0.205292	+	0.0339703i
$521$	−7.20132	+	2.33985i	−0.315496	+	0.102511i	−0.462484	−	0.886627i	$-0.653042\pi$
$521$	−7.20132	+	2.33985i	−0.315496	+	0.102511i	0.146989	+	0.989138i	$0.453042\pi$
$522$	6.59698	−	5.09370i	0.288742	−	0.222945i
$523$	−19.0191	+	3.01233i	−0.831649	+	0.131720i	−0.557719	−	0.830030i	$-0.688323\pi$
$523$	−19.0191	+	3.01233i	−0.831649	+	0.131720i	−0.273929	+	0.961750i	$0.588323\pi$
$524$	12.0047			0.524427
$525$	−33.3214	−	7.00499i	−1.45426	−	0.305723i
$526$	−8.81654			−0.384420
$527$	1.53818	−	0.243623i	0.0670040	−	0.0106124i
$528$	−4.72131	−	3.91465i	−0.205469	−	0.170363i
$529$	−36.0318	+	11.7074i	−1.56660	+	0.509019i
$530$	−8.52040	−	4.26749i	−0.370102	−	0.185368i
$531$	−13.7861	−	13.0038i	−0.598267	−	0.564317i
$532$	−13.7972	−	13.7972i	−0.598186	−	0.598186i
$533$	−2.22518	+	1.13379i	−0.0963834	+	0.0491098i
$534$	4.20918	−	1.81593i	0.182149	−	0.0785828i
$535$	6.72306	+	9.12035i	0.290663	+	0.394307i
$536$	−5.46979	+	7.52852i	−0.236259	+	0.325183i
$537$	18.3172	+	7.27586i	0.790447	+	0.313976i
$538$	0.0238817	−	0.150783i	0.00102961	−	0.00650073i
$539$	24.2309	+	17.6048i	1.04370	+	0.758291i
$540$	3.89668	−	10.9460i	0.167686	−	0.471043i
$541$	−5.35372	+	3.88970i	−0.230174	+	0.167231i	−0.696895	−	0.717174i	$-0.745435\pi$
$541$	−5.35372	+	3.88970i	−0.230174	+	0.167231i	0.466720	+	0.884405i	$0.345435\pi$
$542$	5.58115	+	10.9536i	0.239731	+	0.470499i
$543$	−6.04918	−	9.55543i	−0.259595	−	0.410063i
$544$	−0.997317	−	0.324048i	−0.0427596	−	0.0138934i
$545$	20.0039	−	10.3671i	0.856871	−	0.444079i
$546$	1.34398	+	14.3884i	0.0575169	+	0.615766i
$547$	−1.05652	+	2.07353i	−0.0451734	+	0.0886577i	−0.912490	−	0.409099i	$-0.865843\pi$
$547$	−1.05652	+	2.07353i	−0.0451734	+	0.0886577i	0.867316	+	0.497757i	$0.165843\pi$
$548$	−1.31496	−	8.30230i	−0.0561721	−	0.354657i
$549$	1.73402	−	3.66382i	0.0740061	−	0.156368i
$550$	12.3451	−	12.6909i	0.526395	−	0.541144i
$551$			13.7876i			0.587372i
$552$	−13.4875	−	0.863606i	−0.574066	−	0.0367575i
$553$	−53.1911	−	27.1022i	−2.26192	−	1.15250i
$554$	−1.34519	−	4.14006i	−0.0571515	−	0.175894i
$555$	−2.27211	−	3.53482i	−0.0964459	−	0.150045i
$556$	0.823335	−	2.53396i	0.0349172	−	0.107464i
$557$	0.0556738	−	0.0556738i	0.00235897	−	0.00235897i	−0.705926	−	0.708285i	$-0.749469\pi$
$557$	0.0556738	−	0.0556738i	0.00235897	−	0.00235897i	0.708285	+	0.705926i	$0.249469\pi$
$558$	4.45344	−	0.130050i	0.188529	−	0.00550545i
$559$	14.5532	+	20.0307i	0.615533	+	0.847208i
$560$	−2.65894	+	8.37987i	−0.112361	+	0.354114i
$561$	4.82903	−	4.24783i	0.203882	−	0.179344i
$562$	−21.8558	−	3.46162i	−0.921933	−	0.146020i
$563$	−38.0847	−	6.03203i	−1.60508	−	0.254220i	−0.711355	−	0.702833i	$-0.751918\pi$
$563$	−38.0847	−	6.03203i	−1.60508	−	0.254220i	−0.893726	+	0.448613i	$0.851918\pi$
$564$	−15.0261	+	13.2177i	−0.632714	+	0.556564i
$565$	2.54475	−	8.02000i	0.107058	−	0.337404i
$566$	−4.59501	−	6.32449i	−0.193143	−	0.265838i
$567$	−32.4124	−	14.1975i	−1.36119	−	0.596237i
$568$	1.84231	−	1.84231i	0.0773017	−	0.0773017i
$569$	−2.48906	+	7.66055i	−0.104347	+	0.321147i	−0.989577	−	0.144007i	$-0.954001\pi$
$569$	−2.48906	+	7.66055i	−0.104347	+	0.321147i	0.885230	+	0.465154i	$0.154001\pi$
$570$	10.3929	+	16.1686i	0.435309	+	0.677229i
$571$	−6.28765	−	19.3514i	−0.263130	−	0.809831i	−0.992118	−	0.125305i	$-0.960009\pi$
$571$	−6.28765	−	19.3514i	−0.263130	−	0.809831i	0.728988	−	0.684526i	$-0.239991\pi$
$572$	−6.69511	−	3.41133i	−0.279937	−	0.142635i
$573$	−1.02886	−	0.0658783i	−0.0429814	−	0.00275210i
$574$			4.62714i			0.193133i
$575$	5.57035	−	38.6150i	0.232300	−	1.61036i
$576$	−2.71164	−	1.28337i	−0.112985	−	0.0534736i
$577$	−5.77419	−	36.4568i	−0.240383	−	1.51772i	−0.752380	−	0.658729i	$-0.771094\pi$
$577$	−5.77419	−	36.4568i	−0.240383	−	1.51772i	0.511997	−	0.858987i	$-0.328906\pi$
$578$	−7.21861	+	14.1673i	−0.300255	+	0.589283i
$579$	3.54901	+	37.9951i	0.147492	+	1.57902i
$580$	5.51555	−	2.85847i	0.229021	−	0.118692i
$581$	−40.1550	−	13.0472i	−1.66591	−	0.541287i
$582$	14.7661	+	23.3249i	0.612074	+	0.966846i
$583$	−6.85089	−	13.4456i	−0.283735	−	0.556861i
$584$	−7.22850	+	5.25182i	−0.299118	+	0.217322i
$585$	1.71795	−	14.1311i	0.0710284	−	0.584249i
$586$	−6.51428	−	4.73290i	−0.269102	−	0.195514i
$587$	−4.84574	+	30.5948i	−0.200005	+	1.26278i	0.659520	+	0.751687i	$0.270760\pi$
$587$	−4.84574	+	30.5948i	−0.200005	+	1.26278i	−0.859525	+	0.511094i	$0.829240\pi$
$588$	13.6156	+	5.40832i	0.561500	+	0.223035i
$589$	−4.33213	+	5.96267i	−0.178502	+	0.245688i
$590$	−8.38153	−	11.3702i	−0.345062	−	0.468103i
$591$	4.48635	−	1.93550i	0.184544	−	0.0796158i
$592$	−0.966718	+	0.492567i	−0.0397319	+	0.0202444i
$593$	−21.6044	−	21.6044i	−0.887186	−	0.887186i	0.107066	−	0.994252i	$-0.465854\pi$
$593$	−21.6044	−	21.6044i	−0.887186	−	0.887186i	−0.994252	+	0.107066i	$0.965854\pi$
$594$	15.2522	−	10.2912i	0.625804	−	0.422254i
$595$	−8.24311	−	4.12860i	−0.337934	−	0.169256i
$596$	14.4348	−	4.69016i	0.591273	−	0.192116i
$597$	13.9773	+	11.5892i	0.572051	+	0.474314i
$598$	−16.3544	+	2.59028i	−0.668780	+	0.105924i
$599$	−32.5862			−1.33144			−0.665718	−	0.746204i	$-0.731874\pi$
$599$	−32.5862			−1.33144			−0.665718	+	0.746204i	$0.731874\pi$
$600$	4.31338	−	7.50964i	0.176093	−	0.306580i
$601$	25.6991			1.04829			0.524144	−	0.851630i	$-0.324386\pi$
$601$	25.6991			1.04829			0.524144	+	0.851630i	$0.324386\pi$
$602$	45.3092	−	7.17626i	1.84666	−	0.292483i
$603$	−17.0616	−	22.0970i	−0.694804	−	0.899857i
$604$	12.4569	−	4.04749i	0.506863	−	0.164690i
$605$	3.39389	−	0.561597i	0.137981	−	0.0228322i
$606$	−4.14942	−	2.46019i	−0.168559	−	0.0999383i
$607$	6.64949	+	6.64949i	0.269894	+	0.269894i	0.829058	−	0.559163i	$-0.188877\pi$
$607$	6.64949	+	6.64949i	0.269894	+	0.269894i	−0.559163	+	0.829058i	$0.688877\pi$
$608$	4.42186	−	2.25305i	0.179330	−	0.0913732i
$609$	−7.49452	−	17.3717i	−0.303693	−	0.703939i
$610$	1.75893	−	2.45646i	0.0712168	−	0.0994591i
$611$	−14.4115	+	19.8357i	−0.583027	+	0.802469i
$612$	1.77405	−	2.59800i	0.0717117	−	0.105018i
$613$	−4.00713	+	25.3000i	−0.161846	+	1.02186i	0.764346	+	0.644807i	$0.223062\pi$
$613$	−4.00713	+	25.3000i	−0.161846	+	1.02186i	−0.926192	+	0.377052i	$0.876938\pi$
$614$	7.52651	+	5.46833i	0.303745	+	0.220684i
$615$	0.968500	−	4.45393i	0.0390537	−	0.179600i
$616$	−11.2632	+	8.18320i	−0.453808	+	0.329711i
$617$	20.5976	+	40.4250i	0.829227	+	1.62745i	0.777580	+	0.628785i	$0.216447\pi$
$617$	20.5976	+	40.4250i	0.829227	+	1.62745i	0.0516476	+	0.998665i	$0.483553\pi$
$618$	−16.3921	+	10.3772i	−0.659387	+	0.417433i
$619$	−42.4716	−	13.7999i	−1.70708	−	0.554663i	−0.717235	−	0.696831i	$-0.754593\pi$
$619$	−42.4716	−	13.7999i	−1.70708	−	0.554663i	−0.989843	+	0.142168i	$0.954593\pi$
$620$	3.28344	+	0.496822i	0.131866	+	0.0199528i
$621$	13.8613	−	38.1023i	0.556235	−	1.52899i
$622$	5.17155	−	10.1497i	0.207360	−	0.406967i
$623$	−1.62786	−	10.2779i	−0.0652189	−	0.411776i
$624$	−3.58608	−	0.805769i	−0.143558	−	0.0322566i
$625$	20.6237	+	14.1303i	0.824946	+	0.565211i
$626$			23.9326i			0.956539i
$627$	−1.94492	+	30.3751i	−0.0776728	+	1.21306i
$628$	−7.72488	−	3.93602i	−0.308256	−	0.157064i
$629$	−0.351583	−	1.08206i	−0.0140185	−	0.0431446i
$630$	−21.8833	−	14.7225i	−0.871851	−	0.586557i
$631$	−12.3680	+	38.0648i	−0.492363	+	1.51534i	0.328664	+	0.944447i	$0.393402\pi$
$631$	−12.3680	+	38.0648i	−0.492363	+	1.51534i	−0.821027	+	0.570890i	$0.806598\pi$
$632$	10.7364	−	10.7364i	0.427073	−	0.427073i
$633$	3.54609	−	0.906283i	0.140945	−	0.0360215i
$634$	7.88706	+	10.8556i	0.313235	+	0.431131i
$635$	−42.8689	+	0.296112i	−1.70120	+	0.0117508i
$636$	−4.87526	−	5.54230i	−0.193317	−	0.219766i
$637$	17.7282	+	2.80788i	0.702418	+	0.111252i
$638$	9.71642	+	1.53893i	0.384677	+	0.0609268i
$639$	3.75029	+	6.85780i	0.148359	+	0.271290i
$640$	−1.81805	−	1.30180i	−0.0718648	−	0.0514582i
$641$	−8.86726	−	12.2047i	−0.350236	−	0.482058i	0.597160	−	0.802122i	$-0.296296\pi$
$641$	−8.86726	−	12.2047i	−0.350236	−	0.482058i	−0.947396	+	0.320064i	$0.896296\pi$
$642$	2.17320	+	8.50326i	0.0857693	+	0.335597i
$643$	28.2993	−	28.2993i	1.11602	−	1.11602i	0.123696	−	0.992320i	$-0.460525\pi$
$643$	28.2993	−	28.2993i	1.11602	−	1.11602i	0.992320	−	0.123696i	$-0.0394747\pi$
$644$	−9.48034	+	29.1775i	−0.373578	+	1.14975i
$645$	−45.1151	−	2.57596i	−1.77641	−	0.101428i
$646$	1.60817	+	4.94945i	0.0632728	+	0.194734i
$647$	16.2495	+	8.27955i	0.638835	+	0.325503i	0.743233	−	0.669033i	$-0.233291\pi$
$647$	16.2495	+	8.27955i	0.638835	+	0.325503i	−0.104398	+	0.994536i	$0.533291\pi$
$648$	5.98175	−	6.72448i	0.234985	−	0.264163i
$649$		−	22.3688i		−	0.878051i
$650$	3.13903	−	10.1353i	0.123123	−	0.397538i
$651$	2.21716	−	9.86750i	0.0868974	−	0.386738i
$652$	0.771116	+	4.86864i	0.0301992	+	0.190671i
$653$	−11.3587	+	22.2926i	−0.444499	+	0.872379i	0.554688	+	0.832059i	$0.312838\pi$
$653$	−11.3587	+	22.2926i	−0.444499	+	0.872379i	−0.999187	+	0.0403201i	$0.987162\pi$
$654$	17.3766	−	1.62309i	0.679477	−	0.0634679i
$655$	−12.0211	+	24.0011i	−0.469703	+	0.937802i
$656$	−1.11927	−	0.363674i	−0.0437003	−	0.0141991i
$657$	−9.02373	−	25.2402i	−0.352049	−	0.984714i
$658$	20.6236	+	40.4762i	0.803993	+	1.57793i
$659$	−20.1677	+	14.6527i	−0.785623	+	0.570789i	−0.906661	−	0.421859i	$-0.861378\pi$
$659$	−20.1677	+	14.6527i	−0.785623	+	0.570789i	0.121038	+	0.992648i	$0.461378\pi$
$660$	12.5544	−	5.51939i	0.488679	−	0.214842i
$661$	−17.0562	−	12.3921i	−0.663411	−	0.481996i	0.204402	−	0.978887i	$-0.434475\pi$
$661$	−17.0562	−	12.3921i	−0.663411	−	0.481996i	−0.867813	+	0.496891i	$0.834475\pi$
$662$	1.13607	−	7.17284i	0.0441545	−	0.278780i
$663$	1.42283	−	3.58204i	0.0552583	−	0.139115i
$664$	6.31204	−	8.68777i	0.244955	−	0.337151i
$665$	41.4011	−	13.7689i	1.60547	−	0.533935i
$666$	−0.602805	−	3.19861i	−0.0233582	−	0.123944i
$667$	19.3154	−	9.84171i	0.747897	−	0.381072i
$668$	5.82145	+	5.82145i	0.225239	+	0.225239i
$669$	−9.40560	+	15.8637i	−0.363641	+	0.613328i
$670$	−9.57462	−	18.4747i	−0.369900	−	0.713738i
$671$	4.55020	−	1.47845i	0.175659	−	0.0570750i
$672$	−4.34665	+	5.24232i	−0.167676	+	0.202227i
$673$	11.5267	−	1.82565i	0.444321	−	0.0703736i	0.0697348	−	0.997566i	$-0.477785\pi$
$673$	11.5267	−	1.82565i	0.444321	−	0.0703736i	0.374586	+	0.927192i	$0.377785\pi$
$674$	25.4632			0.980806
$675$	17.9826	+	18.7517i	0.692150	+	0.721754i
$676$	8.49691			0.326804
$677$	23.2090	−	3.67594i	0.891993	−	0.141278i	0.306419	−	0.951897i	$-0.400869\pi$
$677$	23.2090	−	3.67594i	0.891993	−	0.141278i	0.585574	+	0.810619i	$0.300869\pi$
$678$	4.15998	−	5.01719i	0.159763	−	0.192684i
$679$	59.5978	−	19.3645i	2.28715	−	0.743142i
$680$	1.64655	−	1.66946i	0.0631425	−	0.0640209i
$681$	−1.21838	+	2.05495i	−0.0466884	+	0.0787459i
$682$	3.71848	+	3.71848i	0.142388	+	0.142388i
$683$	−15.4895	+	7.89232i	−0.592691	+	0.301991i	−0.724490	−	0.689285i	$-0.757925\pi$
$683$	−15.4895	+	7.89232i	−0.592691	+	0.301991i	0.131799	+	0.991276i	$0.457925\pi$
$684$	2.75729	+	14.6308i	0.105427	+	0.559421i
$685$	17.9157	+	5.68465i	0.684523	+	0.217199i
$686$	3.37046	−	4.63905i	0.128685	−	0.177120i
$687$	10.6133	−	26.7195i	0.404924	−	1.01941i
$688$	−1.82522	+	11.5240i	−0.0695859	+	0.439348i
$689$	−7.31630	−	5.31560i	−0.278729	−	0.202508i
$690$	15.2326	−	26.1010i	0.579893	−	0.993646i
$691$	3.69930	−	2.68770i	0.140728	−	0.102245i	−0.515194	−	0.857074i	$-0.672280\pi$
$691$	3.69930	−	2.68770i	0.140728	−	0.102245i	0.655922	+	0.754829i	$0.272280\pi$
$692$	−2.07127	−	4.06510i	−0.0787380	−	0.154532i
$693$	−14.0605	−	39.3284i	−0.534113	−	1.49396i
$694$	−4.36272	−	1.41754i	−0.165607	−	0.0538089i
$695$	4.24173	+	4.18354i	0.160898	+	0.158691i
$696$	4.79114	−	0.447526i	0.181608	−	0.0169634i
$697$	0.560278	−	1.09961i	0.0212220	−	0.0416506i
$698$	1.58650	+	10.0167i	0.0600498	+	0.379139i
$699$	−9.42614	+	41.9511i	−0.356529	+	1.58674i
$700$	−14.0914	−	13.7074i	−0.532606	−	0.518090i
$701$			44.4087i			1.67729i	0.544676	+	0.838646i	$0.316652\pi$
$701$			44.4087i			1.67729i	−0.544676	+	0.838646i	$0.683348\pi$
$702$	5.34423	−	9.64482i	0.201705	−	0.364020i
$703$	4.79760	+	2.44450i	0.180945	+	0.0921960i
$704$	−1.09422	−	3.36766i	−0.0412399	−	0.126923i
$705$	−11.3796	−	43.2777i	−0.428581	−	1.62993i
$706$	3.77806	−	11.6277i	0.142189	−	0.437614i
$707$	−7.74297	+	7.74297i	−0.291204	+	0.291204i
$708$	−2.70929	−	10.6009i	−0.101821	−	0.398405i
$709$	−10.6950	−	14.7204i	−0.401659	−	0.552836i	0.559500	−	0.828830i	$-0.310993\pi$
$709$	−10.6950	−	14.7204i	−0.401659	−	0.552836i	−0.961159	+	0.275994i	$0.910993\pi$
$710$	1.83853	+	5.52819i	0.0689988	+	0.207469i
$711$	21.8555	+	39.9652i	0.819647	+	1.49881i
$712$	2.61410	+	0.414033i	0.0979675	+	0.0155165i
$713$	11.4456	+	1.81280i	0.428640	+	0.0678900i
$714$	−4.71660	−	5.36193i	−0.176514	−	0.200665i
$715$	13.5246	−	9.96964i	0.505791	−	0.372844i
$716$	6.68853	+	9.20597i	0.249962	+	0.344043i
$717$	39.8666	−	10.1888i	1.48885	−	0.380508i
$718$	23.9500	−	23.9500i	0.893807	−	0.893807i
$719$	−7.53117	+	23.1785i	−0.280865	+	0.864414i	0.706743	+	0.707471i	$0.250164\pi$
$719$	−7.53117	+	23.1785i	−0.280865	+	0.864414i	−0.987608	+	0.156943i	$0.949836\pi$
$720$	5.28120	−	4.13629i	0.196819	−	0.154151i
$721$	13.6089	+	41.8838i	0.506821	+	1.55984i
$722$	−5.01554	−	2.55554i	−0.186659	−	0.0951075i
$723$	−0.699175	+	10.9195i	−0.0260026	+	0.406099i
$724$		−	6.52939i		−	0.242663i
$725$	0.191892	+	13.8897i	0.00712670	+	0.515851i
$726$	2.59982	+	0.584163i	0.0964885	+	0.0216803i
$727$	−7.37431	−	46.5595i	−0.273498	−	1.72680i	−0.616405	−	0.787429i	$-0.711412\pi$
$727$	−7.37431	−	46.5595i	−0.273498	−	1.72680i	0.342907	−	0.939369i	$-0.388588\pi$
$728$	−3.78778	+	7.43394i	−0.140385	+	0.275520i
$729$	14.3150	+	22.8928i	0.530186	+	0.847881i
$730$	−3.26164	−	19.7111i	−0.120719	−	0.729539i
$731$	−11.6363	−	3.78088i	−0.430385	−	0.139841i
$732$	1.97734	−	1.25178i	0.0730845	−	0.0462670i
$733$	21.4583	+	42.1144i	0.792582	+	1.55553i	0.831003	+	0.556268i	$0.187767\pi$
$733$	21.4583	+	42.1144i	0.792582	+	1.55553i	−0.0384204	+	0.999262i	$0.512233\pi$
$734$	3.84568	−	2.79405i	0.141947	−	0.103130i
$735$	−24.4472	+	21.8062i	−0.901749	+	0.804335i
$736$	−6.31272	−	4.58646i	−0.232690	−	0.169059i
$737$	5.15473	−	32.5457i	0.189877	−	1.19884i
$738$	1.99099	−	2.91569i	0.0732892	−	0.107328i
$739$	−14.8135	+	20.3891i	−0.544925	+	0.750025i	−0.989313	−	0.145810i	$-0.953421\pi$
$739$	−14.8135	+	20.3891i	−0.544925	+	0.750025i	0.444388	+	0.895835i	$0.353421\pi$
$740$	−0.0167574	−	2.42601i	−0.000616015	−	0.0891821i
$741$	7.22562	+	16.7485i	0.265440	+	0.615270i
$742$	−14.9294	+	7.60691i	−0.548075	+	0.279258i
$743$	−35.5509	−	35.5509i	−1.30424	−	1.30424i	−0.925507	−	0.378730i	$-0.876361\pi$
$743$	−35.5509	−	35.5509i	−1.30424	−	1.30424i	−0.378730	−	0.925507i	$-0.623639\pi$
$744$	2.21262	+	1.31186i	0.0811186	+	0.0480952i
$745$	−5.07746	+	33.5563i	−0.186024	+	1.22941i
$746$	−35.7760	+	11.6243i	−1.30985	+	0.425597i
$747$	19.6888	+	25.4995i	0.720376	+	0.932977i
$748$	3.66749	−	0.580873i	0.134097	−	0.0212388i
$749$	19.9226			0.727958
$750$	10.6949	+	16.1437i	0.390521	+	0.589485i
$751$	13.6190			0.496964			0.248482	−	0.968636i	$-0.420068\pi$
$751$	13.6190			0.496964			0.248482	+	0.968636i	$0.420068\pi$
$752$	−11.4118	+	1.80746i	−0.416147	+	0.0659112i
$753$	−18.4406	−	15.2899i	−0.672013	−	0.557197i
$754$	5.60695	−	1.82181i	0.204193	−	0.0663463i
$755$	−4.38172	+	28.9583i	−0.159467	+	1.05390i
$756$	−11.4269	−	16.9353i	−0.415592	−	0.615931i
$757$	18.1299	+	18.1299i	0.658942	+	0.658942i	0.955130	−	0.296188i	$-0.0957154\pi$
$757$	18.1299	+	18.1299i	0.658942	+	0.658942i	−0.296188	+	0.955130i	$0.595715\pi$
$758$	−14.4898	+	7.38292i	−0.526293	+	0.268160i
$759$	43.9416	−	18.9573i	1.59498	−	0.688107i
$760$	0.0766500	+	11.0968i	0.00278039	+	0.402524i
$761$	20.5807	−	28.3270i	0.746052	−	1.02685i	−0.252196	−	0.967676i	$-0.581153\pi$
$761$	20.5807	−	28.3270i	0.746052	−	1.02685i	0.998248	−	0.0591757i	$-0.0188472\pi$
$762$	−30.8614	−	12.2586i	−1.11799	−	0.444081i
$763$	6.19733	−	39.1284i	0.224358	−	1.41654i
$764$	−0.481552	−	0.349868i	−0.0174219	−	0.0126578i
$765$	3.41774	+	6.14843i	0.123569	+	0.222297i
$766$	−25.6681	+	18.6490i	−0.927426	+	0.673814i
$767$	−6.08587	−	11.9442i	−0.219748	−	0.431280i
$768$	−0.926454	−	1.46345i	−0.0334305	−	0.0528077i
$769$	−23.9043	−	7.76696i	−0.862010	−	0.280084i	−0.155542	−	0.987829i	$-0.549712\pi$
$769$	−23.9043	−	7.76696i	−0.862010	−	0.280084i	−0.706468	+	0.707745i	$0.749712\pi$
$770$	−5.08218	−	30.7131i	−0.183149	−	1.10682i
$771$	2.96048	+	31.6944i	0.106619	+	1.14145i
$772$	−10.0023	+	19.6306i	−0.359991	+	0.706522i
$773$	−4.41320	−	27.8639i	−0.158732	−	1.00219i	−0.930501	−	0.366290i	$-0.880628\pi$
$773$	−4.41320	−	27.8639i	−0.158732	−	1.00219i	0.771769	−	0.635903i	$-0.219372\pi$
$774$	−31.6384	−	14.9739i	−1.13722	−	0.538224i
$775$	−4.28123	+	6.06712i	−0.153786	+	0.217938i
$776$			15.9383i			0.572151i
$777$	−7.37350	−	0.472127i	−0.264523	−	0.0169375i
$778$	9.83601	+	5.01170i	0.352638	+	0.179678i
$779$	1.80483	+	5.55469i	0.0646647	+	0.199018i
$780$	5.20198	−	6.36284i	0.186261	−	0.227826i
$781$	−2.85090	+	8.77417i	−0.102013	+	0.313964i
$782$	5.78590	−	5.78590i	0.206903	−	0.206903i
$783$	−2.75229	+	14.1712i	−0.0983587	+	0.506437i
$784$	4.97175	+	6.84302i	0.177562	+	0.244394i
$785$	15.6048	−	11.5031i	0.556959	−	0.410562i
$786$	−15.6121	+	13.7331i	−0.556865	+	0.489844i
$787$	1.75927	+	0.278640i	0.0627111	+	0.00993245i	0.187711	−	0.982224i	$-0.439893\pi$
$787$	1.75927	+	0.278640i	0.0627111	+	0.00993245i	−0.125000	+	0.992157i	$0.539893\pi$
$788$	2.78623	+	0.441295i	0.0992553	+	0.0157205i
$789$	11.4659	−	10.0860i	0.408198	−	0.359070i
$790$	10.7144	+	32.2166i	0.381201	+	1.14622i
$791$	−8.69603	−	11.9691i	−0.309195	−	0.425571i
$792$	10.6184	−	0.310079i	0.377307	−	0.0110182i
$793$	2.02742	−	2.02742i	0.0719957	−	0.0719957i
$794$	4.61434	−	14.2015i	0.163757	−	0.503991i
$795$	15.9627	−	4.19730i	0.566139	−	0.148863i
$796$	3.23939	+	9.96982i	0.114817	+	0.353371i
$797$	−36.0903	−	18.3889i	−1.27839	−	0.651370i	−0.322907	−	0.946431i	$-0.604660\pi$
$797$	−36.0903	−	18.3889i	−1.27839	−	0.651370i	−0.955478	+	0.295061i	$0.904660\pi$
$798$	33.7271	+	2.15955i	1.19393	+	0.0764473i
$799$		−	12.1161i		−	0.428636i
$800$	4.42325	−	2.33128i	0.156386	−	0.0824231i
$801$	−3.39667	+	7.17684i	−0.120015	+	0.253581i
$802$	1.99412	+	12.5904i	0.0704147	+	0.444581i
$803$	14.3635	−	28.1899i	0.506876	−	0.994799i
$804$	−1.49901	−	16.0482i	−0.0528661	−	0.565976i
$805$	−48.8417	−	48.1716i	−1.72144	−	1.69783i
$806$	2.99723	+	0.973861i	0.105573	+	0.0343028i
$807$	0.141435	+	0.223414i	0.00497875	+	0.00786456i
$808$	−1.26441	−	2.48154i	−0.0444816	−	0.0873001i
$809$	9.80668	−	7.12497i	0.344784	−	0.250501i	−0.401893	−	0.915686i	$-0.631648\pi$
$809$	9.80668	−	7.12497i	0.344784	−	0.250501i	0.746678	+	0.665186i	$0.231648\pi$
$810$	7.45443	+	18.6931i	0.261922	+	0.656808i
$811$	−34.3371	−	24.9474i	−1.20574	−	0.876020i	−0.210902	−	0.977507i	$-0.567640\pi$
$811$	−34.3371	−	24.9474i	−1.20574	−	0.876020i	−0.994837	+	0.101487i	$0.967640\pi$
$812$	1.70876	−	10.7887i	0.0599656	−	0.378608i
$813$	−19.7891	−	7.86049i	−0.694032	−	0.275679i
$814$	2.25818	−	3.10812i	0.0791493	−	0.108940i
$815$	−10.5061	−	3.33359i	−0.368013	−	0.116771i
$816$	1.66772	−	0.719487i	0.0583818	−	0.0251871i
$817$	51.5927	−	26.2878i	1.80500	−	0.919693i
$818$	−19.0319	−	19.0319i	−0.665434	−	0.665434i
$819$	−18.2079	−	17.1747i	−0.636236	−	0.600131i
$820$	1.84790	−	1.87361i	0.0645316	−	0.0654293i
$821$	−32.4922	+	10.5573i	−1.13398	+	0.368454i	−0.815089	−	0.579336i	$-0.803312\pi$
$821$	−32.4922	+	10.5573i	−1.13398	+	0.368454i	−0.318896	+	0.947790i	$0.603312\pi$
$822$	11.2078	+	9.29288i	0.390916	+	0.324126i
$823$	−0.223643	+	0.0354216i	−0.00779572	+	0.00123472i	−0.160331	−	0.987063i	$-0.551256\pi$
$823$	−0.223643	+	0.0354216i	−0.00779572	+	0.00123472i	0.152535	+	0.988298i	$0.451256\pi$
$824$	−11.2010			−0.390206
$825$	−1.53658	+	30.6271i	−0.0534967	+	1.06630i
$826$	−24.8372			−0.864198
$827$	6.61308	−	1.04741i	0.229959	−	0.0364220i	−0.0403912	−	0.999184i	$-0.512860\pi$
$827$	6.61308	−	1.04741i	0.229959	−	0.0364220i	0.270351	+	0.962762i	$0.412860\pi$
$828$	18.5285	−	14.3063i	0.643908	−	0.497179i
$829$	33.2782	−	10.8127i	1.15580	−	0.375542i	0.332475	−	0.943112i	$-0.392116\pi$
$829$	33.2782	−	10.8127i	1.15580	−	0.375542i	0.823325	+	0.567570i	$0.192116\pi$
$830$	11.0489	+	21.3194i	0.383514	+	0.740008i
$831$	6.48557	+	3.84529i	0.224982	+	0.133392i
$832$	−1.50051	−	1.50051i	−0.0520210	−	0.0520210i
$833$	−7.90311	+	4.02683i	−0.273826	+	0.139522i
$834$	1.82806	+	4.23731i	0.0633005	+	0.146726i
$835$	−17.4683	+	5.80950i	−0.604516	+	0.201046i
$836$	−10.3291	+	14.2168i	−0.357241	+	0.491700i
$837$	−5.64293	+	5.26378i	−0.195048	+	0.181943i
$838$	−3.02247	+	19.0831i	−0.104410	+	0.659216i
$839$	27.8283	+	20.2184i	0.960739	+	0.698018i	0.953322	−	0.301955i	$-0.0976392\pi$
$839$	27.8283	+	20.2184i	0.960739	+	0.698018i	0.00741655	+	0.999972i	$0.497639\pi$
$840$	−6.12847	−	13.9398i	−0.211452	−	0.480969i
$841$	17.2171	−	12.5090i	0.593695	−	0.431344i
$842$	−3.16961	−	6.22070i	−0.109232	−	0.214380i
$843$	32.3836	−	20.5008i	1.11535	−	0.706086i
$844$	2.00972	+	0.652997i	0.0691774	+	0.0224771i
$845$	−8.50853	+	16.9880i	−0.292702	+	0.584405i
$846$	4.42074	−	34.3792i	0.151988	−	1.18198i
$847$	2.74605	−	5.38942i	0.0943554	−	0.185183i
$848$	−0.666670	−	4.20919i	−0.0228935	−	0.144544i
$849$	13.2109	+	2.96841i	0.453398	+	0.101875i
$850$	1.68897	+	4.96373i	0.0579312	+	0.170254i
$851$		−	8.46599i		−	0.290210i
$852$	−0.288360	+	4.50350i	−0.00987905	+	0.154287i
$853$	−26.7503	−	13.6300i	−0.915914	−	0.466682i	−0.0685222	−	0.997650i	$-0.521828\pi$
$853$	−26.7503	−	13.6300i	−0.915914	−	0.466682i	−0.847392	+	0.530968i	$0.821828\pi$
$854$	−1.64160	−	5.05233i	−0.0561745	−	0.172887i
$855$	−32.0126	−	9.13808i	−1.09481	−	0.312516i
$856$	−1.56584	+	4.81915i	−0.0535192	+	0.164715i
$857$	4.67908	−	4.67908i	0.159834	−	0.159834i	−0.622659	−	0.782493i	$-0.713948\pi$
$857$	4.67908	−	4.67908i	0.159834	−	0.159834i	0.782493	+	0.622659i	$0.213948\pi$
$858$	12.6095	−	3.22264i	0.430481	−	0.110019i
$859$	10.4601	+	14.3971i	0.356895	+	0.491224i	0.949280	−	0.314431i	$-0.101814\pi$
$859$	10.4601	+	14.3971i	0.356895	+	0.491224i	−0.592385	+	0.805655i	$0.701814\pi$
$860$	−21.2124	−	15.1890i	−0.723336	−	0.517939i
$861$	−5.29336	−	6.01760i	−0.180397	−	0.205079i
$862$	−11.9173	−	1.88752i	−0.405906	−	0.0642892i
$863$	39.7649	+	6.29813i	1.35361	+	0.214391i	0.790739	−	0.612153i	$-0.209696\pi$
$863$	39.7649	+	6.29813i	1.35361	+	0.214391i	0.562872	+	0.826544i	$0.309696\pi$
$864$	4.99464	−	1.43304i	0.169921	−	0.0487530i
$865$	10.2015	−	0.0704659i	0.346862	−	0.00239591i
$866$	14.3388	+	19.7357i	0.487254	+	0.670647i
$867$	−6.81933	−	26.6826i	−0.231597	−	0.906188i
$868$	4.12883	−	4.12883i	0.140142	−	0.140142i
$869$	−16.6142	+	51.1332i	−0.563598	+	1.73458i
$870$	−3.90295	+	10.0271i	−0.132322	+	0.339952i
$871$	−6.10224	−	18.7808i	−0.206767	−	0.636362i
$872$	8.97781	+	4.57442i	0.304027	+	0.154909i
$873$	−45.8865	−	13.4419i	−1.55302	−	0.454940i
$874$			38.7242i			1.30987i
$875$	41.5161	−	14.4471i	1.40350	−	0.488401i
$876$	3.39271	−	15.0993i	0.114629	−	0.510157i
$877$	5.43919	+	34.3417i	0.183668	+	1.15964i	0.891421	+	0.453176i	$0.149709\pi$
$877$	5.43919	+	34.3417i	0.183668	+	1.15964i	−0.707753	+	0.706460i	$0.750291\pi$
$878$	3.36553	−	6.60523i	0.113581	−	0.222916i
$879$	13.8862	−	1.29707i	0.468370	−	0.0437490i
$880$	7.82873	+	1.18458i	0.263906	+	0.0399321i
$881$	23.3423	+	7.58438i	0.786423	+	0.255524i	0.674580	−	0.738202i	$-0.264325\pi$
$881$	23.3423	+	7.58438i	0.786423	+	0.255524i	0.111843	+	0.993726i	$0.464325\pi$
$882$	−23.8942	+	8.54251i	−0.804559	+	0.287641i
$883$	−10.4732	−	20.5549i	−0.352452	−	0.691726i	0.644914	−	0.764255i	$-0.276893\pi$
$883$	−10.4732	−	20.5549i	−0.352452	−	0.691726i	−0.997366	+	0.0725286i	$0.976893\pi$
$884$	1.80028	−	1.30798i	0.0605499	−	0.0439921i
$885$	23.9075	+	5.19865i	0.803642	+	0.174751i
$886$	−0.588493	−	0.427565i	−0.0197708	−	0.0143643i
$887$	−8.06436	+	50.9164i	−0.270775	+	1.70960i	0.359428	+	0.933173i	$0.382972\pi$
$887$	−8.06436	+	50.9164i	−0.270775	+	1.70960i	−0.630202	+	0.776431i	$0.717028\pi$
$888$	0.693731	−	1.74649i	0.0232801	−	0.0586084i
$889$	−44.3067	+	60.9829i	−1.48600	+	2.04530i
$890$	−3.44546	+	4.81181i	−0.115492	+	0.161292i
$891$	−8.06252	+	30.8319i	−0.270105	+	1.03291i
$892$	−9.48721	+	4.83398i	−0.317655	+	0.161854i
$893$	40.5457	+	40.5457i	1.35681	+	1.35681i
$894$	−13.4071	+	22.6127i	−0.448399	+	0.756283i
$895$	−25.1033	+	4.15392i	−0.839112	+	0.138850i
$896$	−3.73929	+	1.21497i	−0.124921	+	0.0405893i
$897$	18.3057	−	22.0778i	0.611209	−	0.737155i
$898$	−29.3299	+	4.64540i	−0.978752	+	0.155019i
$899$	−4.12595			−0.137608
$900$	2.98133	+	14.7007i	0.0993778	+	0.490025i
$901$	4.46895			0.148882
$902$	4.11596	−	0.651904i	0.137047	−	0.0217060i
$903$	−50.7151	+	61.1656i	−1.68769	+	2.03546i
$904$	3.57871	−	1.16279i	0.119026	−	0.0386739i
$905$	13.0543	+	6.53832i	0.433940	+	0.217341i
$906$	−11.5700	+	19.5142i	−0.384386	+	0.648316i
$907$	−34.2493	−	34.2493i	−1.13723	−	1.13723i	−0.988945	−	0.148284i	$-0.952625\pi$
$907$	−34.2493	−	34.2493i	−1.13723	−	1.13723i	−0.148284	−	0.988945i	$-0.547375\pi$
$908$	−1.22895	+	0.626182i	−0.0407842	+	0.0207806i
$909$	8.21074	−	1.54738i	0.272333	−	0.0513234i
$910$	−11.0698	−	15.0171i	−0.366961	−	0.497811i
$911$	28.4251	−	39.1238i	0.941766	−	1.29623i	−0.0133232	−	0.999911i	$-0.504241\pi$
$911$	28.4251	−	39.1238i	0.941766	−	1.29623i	0.955089	−	0.296318i	$-0.0957590\pi$
$912$	−3.17319	+	7.98862i	−0.105075	+	0.264530i
$913$	−5.94847	+	37.5571i	−0.196865	+	1.24296i
$914$	3.06979	+	2.23033i	0.101540	+	0.0737728i
$915$	0.522655	+	5.20681i	0.0172784	+	0.172132i
$916$	13.4288	−	9.75661i	0.443701	−	0.322367i
$917$	21.4279	+	42.0547i	0.707612	+	1.38877i
$918$	0.664905	+	5.40818i	0.0219452	+	0.178496i
$919$	2.05593	+	0.668012i	0.0678189	+	0.0220357i	0.342730	−	0.939434i	$-0.388648\pi$
$919$	2.05593	+	0.668012i	0.0678189	+	0.0220357i	−0.274911	+	0.961470i	$0.588648\pi$
$920$	15.4911	−	8.02839i	0.510728	−	0.264688i
$921$	−16.0439	+	1.49861i	−0.528665	+	0.0493810i
$922$	−5.16070	+	10.1285i	−0.169959	+	0.333563i
$923$	0.864900	+	5.46076i	0.0284685	+	0.179743i
$924$	5.28640	−	23.5272i	0.173910	−	0.773987i
$925$	4.86715	+	2.39583i	0.160031	+	0.0787744i
$926$		−	14.0652i		−	0.462212i
$927$	9.44663	−	32.2479i	0.310268	−	1.05916i
$928$	2.47540	+	1.26128i	0.0812591	+	0.0414036i
$929$	−0.0671055	−	0.206530i	−0.00220166	−	0.00677602i	0.949950	−	0.312403i	$-0.101134\pi$
$929$	−0.0671055	−	0.206530i	−0.00220166	−	0.00677602i	−0.952151	+	0.305627i	$0.901134\pi$
$930$	−4.83847	+	3.11007i	−0.158660	+	0.101983i
$931$	12.9717	−	39.9228i	0.425130	−	1.30842i
$932$	−17.5535	+	17.5535i	−0.574984	+	0.574984i
$933$	4.88550	+	19.1159i	0.159944	+	0.625826i
$934$	−2.63135	−	3.62175i	−0.0861006	−	0.118507i
$935$	−2.51115	+	7.91413i	−0.0821235	+	0.258820i
$936$	5.58550	−	3.05451i	0.182568	−	0.0998398i
$937$	−14.9705	−	2.37109i	−0.489065	−	0.0774603i	−0.0929682	−	0.995669i	$-0.529635\pi$
$937$	−14.9705	−	2.37109i	−0.489065	−	0.0774603i	−0.396097	+	0.918209i	$0.629635\pi$
$938$	−36.1372	−	5.72357i	−1.17992	−	0.186881i
$939$	−27.3784	−	31.1244i	−0.893462	−	1.01571i
$940$	7.81377	−	24.6258i	0.254857	−	0.803205i
$941$	−17.7384	−	24.4148i	−0.578256	−	0.795901i	0.415247	−	0.909709i	$-0.363695\pi$
$941$	−17.7384	−	24.4148i	−0.578256	−	0.795901i	−0.993503	+	0.113808i	$0.963695\pi$
$942$	14.5490	−	3.71831i	0.474031	−	0.121149i
$943$	6.49342	−	6.49342i	0.211455	−	0.211455i
$944$	1.95210	−	6.00796i	0.0635356	−	0.195542i
$945$	45.3015	−	5.88748i	1.47366	−	0.191520i
$946$	−12.7670	−	39.2926i	−0.415089	−	1.27751i
$947$	−15.9210	−	8.11213i	−0.517362	−	0.263609i	0.175756	−	0.984434i	$-0.443763\pi$
$947$	−15.9210	−	8.11213i	−0.517362	−	0.263609i	−0.693117	+	0.720825i	$0.743763\pi$
$948$	−1.68048	+	26.2450i	−0.0545793	+	0.852399i
$949$		−	18.9603i		−	0.615479i
$950$	−22.2628	−	10.9588i	−0.722301	−	0.355549i
$951$	−22.6757	−	5.09509i	−0.735311	−	0.165220i
$952$	−0.644974	−	4.07220i	−0.0209037	−	0.131981i
$953$	15.1784	−	29.7892i	0.491676	−	0.964968i	−0.503230	−	0.864153i	$-0.667855\pi$
$953$	15.1784	−	29.7892i	0.491676	−	0.964968i	0.994905	−	0.100815i	$-0.0321450\pi$
$954$	12.6806	+	1.63056i	0.410549	+	0.0527914i
$955$	1.18171	−	0.612427i	0.0382391	−	0.0198177i
$956$	22.5941	+	7.34126i	0.730744	+	0.237433i
$957$	−14.3967	+	9.11403i	−0.465380	+	0.294615i
$958$	13.7500	+	26.9860i	0.444244	+	0.871877i
$959$	26.7374	−	19.4259i	0.863396	−	0.627294i
$960$	3.85362	−	0.386823i	0.124375	−	0.0124846i
$961$	23.2952	+	16.9249i	0.751458	+	0.545966i
$962$	0.360169	−	2.27402i	0.0116123	−	0.0733173i
$963$	−12.5538	−	8.57241i	−0.404541	−	0.276242i
$964$	−3.71319	+	5.11077i	−0.119594	+	0.164607i
$965$	−29.2318	−	39.6552i	−0.941006	−	1.27655i
$966$	−21.0493	−	48.7907i	−0.677250	−	1.56982i
$967$	−24.4672	+	12.4667i	−0.786814	+	0.400902i	−0.800748	−	0.599001i	$-0.795564\pi$
$967$	−24.4672	+	12.4667i	−0.786814	+	0.400902i	0.0139344	+	0.999903i	$0.495564\pi$
$968$	1.08784	+	1.08784i	0.0349644	+	0.0349644i
$969$	−7.75352	−	4.59705i	−0.249079	−	0.147679i
$970$	−31.8656	−	15.9601i	−1.02314	−	0.512447i
$971$	53.0240	−	17.2285i	1.70162	−	0.552890i	0.712718	−	0.701450i	$-0.247464\pi$
$971$	53.0240	−	17.2285i	1.70162	−	0.552890i	0.988903	+	0.148560i	$0.0474637\pi$
$972$	−0.0865973	+	15.5882i	−0.00277761	+	0.499992i
$973$	10.3466	−	1.63874i	0.331696	−	0.0525355i
$974$	0.555561			0.0178013
$975$	7.51224	+	16.7719i	0.240584	+	0.537132i
$976$	1.35115			0.0432492
$977$	41.8568	−	6.62946i	1.33912	−	0.212095i	0.554556	−	0.832147i	$-0.312888\pi$
$977$	41.8568	−	6.62946i	1.33912	−	0.212095i	0.784561	+	0.620051i	$0.212888\pi$
$978$	−6.57247	−	5.44953i	−0.210164	−	0.174257i
$979$	−8.91312	+	2.89605i	−0.284865	+	0.0925582i
$980$	−18.6599	+	3.08771i	−0.596069	+	0.0986332i
$981$	−20.7415	+	21.9893i	−0.662224	+	0.702064i
$982$	4.47973	+	4.47973i	0.142954	+	0.142954i
$983$	36.2358	−	18.4631i	1.15574	−	0.588880i	0.232310	−	0.972642i	$-0.425372\pi$
$983$	36.2358	−	18.4631i	1.15574	−	0.588880i	0.923432	+	0.383761i	$0.125372\pi$
$984$	1.87165	−	0.807469i	0.0596661	−	0.0257412i
$985$	−3.67233	+	5.12865i	−0.117010	+	0.163412i
$986$	−1.71242	+	2.35694i	−0.0545346	+	0.0750604i
$987$	−73.1251	−	29.0463i	−2.32760	−	0.924554i
$988$	−1.64745	+	10.4016i	−0.0524123	+	0.330918i
$989$	−73.6546	−	53.5132i	−2.34208	−	1.70162i
$990$	−10.0129	+	21.5400i	−0.318232	+	0.684585i
$991$	8.75570	−	6.36139i	0.278134	−	0.202076i	−0.439969	−	0.898013i	$-0.645011\pi$
$991$	8.75570	−	6.36139i	0.278134	−	0.202076i	0.718103	+	0.695937i	$0.245011\pi$
$992$	0.674227	+	1.32324i	0.0214067	+	0.0420130i
$993$	6.72814	+	10.6279i	0.213511	+	0.337267i
$994$	9.74243	+	3.16551i	0.309011	+	0.100404i
$995$	−23.1766	−	3.50689i	−0.734749	−	0.111176i
$996$	1.72983	+	18.5193i	0.0548119	+	0.586807i
$997$	1.54339	−	3.02908i	0.0488797	−	0.0959319i	−0.865275	−	0.501298i	$-0.832856\pi$
$997$	1.54339	−	3.02908i	0.0488797	−	0.0959319i	0.914154	+	0.405366i	$0.132856\pi$
$998$	4.11429	+	25.9766i	0.130236	+	0.822275i
$999$	4.44310	+	3.47020i	0.140574	+	0.109792i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.137.4	yes	80
3.2	odd	2	inner	150.2.l.a.137.7	yes	80
5.2	odd	4		750.2.l.a.293.1		80
5.3	odd	4		750.2.l.c.293.10		80
5.4	even	2		750.2.l.b.707.7		80
15.2	even	4		750.2.l.a.293.10		80
15.8	even	4		750.2.l.c.293.1		80
15.14	odd	2		750.2.l.b.707.4		80
25.2	odd	20		750.2.l.b.593.4		80
25.11	even	5		750.2.l.c.407.1		80
25.14	even	10		750.2.l.a.407.10		80
25.23	odd	20	inner	150.2.l.a.23.7	yes	80
75.2	even	20		750.2.l.b.593.7		80
75.11	odd	10		750.2.l.c.407.10		80
75.14	odd	10		750.2.l.a.407.1		80
75.23	even	20	inner	150.2.l.a.23.4	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.23.4	✓	80	75.23	even	20	inner
150.2.l.a.23.7	yes	80	25.23	odd	20	inner
150.2.l.a.137.4	yes	80	1.1	even	1	trivial
150.2.l.a.137.7	yes	80	3.2	odd	2	inner
750.2.l.a.293.1		80	5.2	odd	4
750.2.l.a.293.10		80	15.2	even	4
750.2.l.a.407.1		80	75.14	odd	10
750.2.l.a.407.10		80	25.14	even	10
750.2.l.b.593.4		80	25.2	odd	20
750.2.l.b.593.7		80	75.2	even	20
750.2.l.b.707.4		80	15.14	odd	2
750.2.l.b.707.7		80	5.4	even	2
750.2.l.c.293.1		80	15.8	even	4
750.2.l.c.293.10		80	5.3	odd	4
750.2.l.c.407.1		80	25.11	even	5
750.2.l.c.407.10		80	75.11	odd	10

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 + 0.156434i) q^{2} +(1.10553 - 1.33334i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-0.334535 + 2.21090i) q^{5} +(-0.883341 + 1.48987i) q^{6} +(2.78015 + 2.78015i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.555594 - 2.94810i) q^{9} +O(q^{10})\)	\(q+(-0.987688 + 0.156434i) q^{2} +(1.10553 - 1.33334i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-0.334535 + 2.21090i) q^{5} +(-0.883341 + 1.48987i) q^{6} +(2.78015 + 2.78015i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.555594 - 2.94810i) q^{9} +(-0.0154450 - 2.23601i) q^{10} +(2.08133 - 2.86470i) q^{11} +(0.639399 - 1.60971i) q^{12} +(0.331962 - 2.09592i) q^{13} +(-3.18083 - 2.31101i) q^{14} +(2.57805 + 2.89027i) q^{15} +(0.809017 - 0.587785i) q^{16} +(0.476073 + 0.934346i) q^{17} +(1.00994 + 2.82489i) q^{18} +(-4.71987 - 1.53358i) q^{19} +(0.365045 + 2.20607i) q^{20} +(6.78043 - 0.633339i) q^{21} +(-1.60756 + 3.15502i) q^{22} +(1.22065 + 7.70688i) q^{23} +(-0.379713 + 1.68992i) q^{24} +(-4.77617 - 1.47925i) q^{25} +2.12205i q^{26} +(-4.54505 - 2.51843i) q^{27} +(3.50319 + 1.78496i) q^{28} +(-0.858514 - 2.64223i) q^{29} +(-2.99844 - 2.45139i) q^{30} +(0.458925 - 1.41243i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.51865 - 5.94214i) q^{33} +(-0.616376 - 0.848368i) q^{34} +(-7.07669 + 5.21658i) q^{35} +(-1.43942 - 2.63213i) q^{36} +(-1.07161 - 0.169727i) q^{37} +(4.90167 + 0.776348i) q^{38} +(-2.42758 - 2.75973i) q^{39} +(-0.705656 - 2.12180i) q^{40} +(-0.691749 - 0.952111i) q^{41} +(-6.59787 + 1.68623i) q^{42} +(-8.25027 + 8.25027i) q^{43} +(1.09422 - 3.36766i) q^{44} +(6.70383 - 0.242121i) q^{45} +(-2.41124 - 7.42105i) q^{46} +(-10.2948 - 5.24545i) q^{47} +(0.110677 - 1.72851i) q^{48} +8.45844i q^{49} +(4.94878 + 0.713878i) q^{50} +(1.77212 + 0.398183i) q^{51} +(-0.331962 - 2.09592i) q^{52} +(1.93475 - 3.79716i) q^{53} +(4.88307 + 1.77642i) q^{54} +(5.63730 + 5.55995i) q^{55} +(-3.73929 - 1.21497i) q^{56} +(-7.26276 + 4.59778i) q^{57} +(1.26128 + 2.47540i) q^{58} +(5.11067 - 3.71312i) q^{59} +(3.34501 + 1.95215i) q^{60} +(1.09310 + 0.794185i) q^{61} +(-0.232323 + 1.46683i) q^{62} +(6.65153 - 9.74080i) q^{63} +(0.587785 - 0.809017i) q^{64} +(4.52283 + 1.43509i) q^{65} +(2.42950 + 5.63141i) q^{66} +(8.29150 - 4.22473i) q^{67} +(0.741501 + 0.741501i) q^{68} +(11.6254 + 6.89267i) q^{69} +(6.17351 - 6.25939i) q^{70} +(-2.47790 + 0.805120i) q^{71} +(1.83345 + 2.37455i) q^{72} +(8.82492 - 1.39773i) q^{73} +1.08497 q^{74} +(-7.25256 + 4.73291i) q^{75} -4.96277 q^{76} +(13.7507 - 2.17789i) q^{77} +(2.82941 + 2.34599i) q^{78} +(-14.4405 + 4.69199i) q^{79} +(1.02889 + 1.98529i) q^{80} +(-8.38263 + 3.27590i) q^{81} +(0.832175 + 0.832175i) q^{82} +(-9.56823 + 4.87526i) q^{83} +(6.25286 - 2.69761i) q^{84} +(-2.22501 + 0.739979i) q^{85} +(6.85807 - 9.43932i) q^{86} +(-4.47211 - 1.77638i) q^{87} +(-0.553929 + 3.49737i) q^{88} +(-2.14121 - 1.55568i) q^{89} +(-6.58342 + 1.28785i) q^{90} +(6.74988 - 4.90407i) q^{91} +(3.54247 + 6.95248i) q^{92} +(-1.37589 - 2.17339i) q^{93} +(10.9886 + 3.57041i) q^{94} +(4.96956 - 9.92214i) q^{95} +(0.161084 + 1.72454i) q^{96} +(7.23583 - 14.2011i) q^{97} +(-1.32319 - 8.35430i) q^{98} +(-9.60181 - 4.54436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

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