LMFDB - Embedded newform 150.2.l.a.23.7

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			23.7
Character	$\chi$	$=$	150.23
Dual form			150.2.l.a.137.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.987688 + 0.156434i) q^{2} +(-0.428879 - 1.67811i) q^{3} +(0.951057 + 0.309017i) q^{4} +(0.334535 + 2.21090i) q^{5} +(-0.161084 - 1.72454i) q^{6} +(2.78015 - 2.78015i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.63213 + 1.43942i) q^{9} +O(q^{10})$	\(q+(0.987688 + 0.156434i) q^{2} +(-0.428879 - 1.67811i) q^{3} +(0.951057 + 0.309017i) q^{4} +(0.334535 + 2.21090i) q^{5} +(-0.161084 - 1.72454i) q^{6} +(2.78015 - 2.78015i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.63213 + 1.43942i) q^{9} +(-0.0154450 + 2.23601i) q^{10} +(-2.08133 - 2.86470i) q^{11} +(0.110677 - 1.72851i) q^{12} +(0.331962 + 2.09592i) q^{13} +(3.18083 - 2.31101i) q^{14} +(3.56667 - 1.50960i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-0.476073 + 0.934346i) q^{17} +(-2.82489 + 1.00994i) q^{18} +(-4.71987 + 1.53358i) q^{19} +(-0.365045 + 2.20607i) q^{20} +(-5.85775 - 3.47305i) 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} +(3.54437 + 3.79967i) q^{27} +(3.50319 - 1.78496i) q^{28} +(0.858514 - 2.64223i) q^{29} +(3.75891 - 0.933062i) q^{30} +(0.458925 + 1.41243i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.91465 + 4.72131i) q^{33} +(-0.616376 + 0.848368i) q^{34} +(7.07669 + 5.21658i) q^{35} +(-2.94810 + 0.555594i) q^{36} +(-1.07161 + 0.169727i) q^{37} +(-4.90167 + 0.776348i) q^{38} +(3.37482 - 1.45597i) q^{39} +(-0.705656 + 2.12180i) q^{40} +(0.691749 - 0.952111i) q^{41} +(-5.24232 - 4.34665i) q^{42} +(-8.25027 - 8.25027i) q^{43} +(-1.09422 - 3.36766i) q^{44} +(-4.06294 - 5.33784i) q^{45} +(-2.41124 + 7.42105i) q^{46} +(10.2948 - 5.24545i) q^{47} +(0.639399 - 1.60971i) 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} +(2.90633 + 4.30735i) q^{54} +(5.63730 - 5.55995i) q^{55} +(3.73929 - 1.21497i) q^{56} +(4.59778 + 7.26276i) q^{57} +(1.26128 - 2.47540i) q^{58} +(-5.11067 - 3.71312i) q^{59} +(3.85859 - 0.333552i) q^{60} +(1.09310 - 0.794185i) q^{61} +(0.232323 + 1.46683i) q^{62} +(-3.31591 + 11.3195i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-4.52283 + 1.43509i) q^{65} +(-4.60503 + 4.05080i) q^{66} +(8.29150 + 4.22473i) q^{67} +(-0.741501 + 0.741501i) q^{68} +(13.4565 - 1.25693i) q^{69} +(6.17351 + 6.25939i) q^{70} +(2.47790 + 0.805120i) q^{71} +(-2.99872 + 0.0875690i) q^{72} +(8.82492 + 1.39773i) q^{73} -1.08497 q^{74} +(4.53075 + 7.38054i) q^{75} -4.96277 q^{76} +(-13.7507 - 2.17789i) q^{77} +(3.56104 - 0.910103i) q^{78} +(-14.4405 - 4.69199i) q^{79} +(-1.02889 + 1.98529i) q^{80} +(4.85616 - 7.57744i) q^{81} +(0.832175 - 0.832175i) q^{82} +(9.56823 + 4.87526i) q^{83} +(-4.49782 - 5.11321i) q^{84} +(-2.22501 - 0.739979i) q^{85} +(-6.85807 - 9.43932i) q^{86} +(-4.80216 - 0.307484i) q^{87} +(-0.553929 - 3.49737i) q^{88} +(2.14121 - 1.55568i) q^{89} +(-3.17790 - 5.90770i) q^{90} +(6.74988 + 4.90407i) q^{91} +(-3.54247 + 6.95248i) q^{92} +(2.17339 - 1.37589i) q^{93} +(10.9886 - 3.57041i) q^{94} +(-4.96956 - 9.92214i) q^{95} +(0.883341 - 1.48987i) 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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{11}{20}\right)$

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
$3$	−0.428879	−	1.67811i	−0.247614	−	0.968859i
$3$	−0.428879	−	1.67811i	−0.247614	−	0.968859i
$4$	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
$6$	−0.161084	−	1.72454i	−0.0657624	−	0.704042i
$7$	2.78015	−	2.78015i	1.05080	−	1.05080i	0.0521581	−	0.998639i	$-0.483390\pi$
$7$	2.78015	−	2.78015i	1.05080	−	1.05080i	0.998639	−	0.0521581i	$-0.0166100\pi$
$8$	0.891007	+	0.453990i	0.315018	+	0.160510i
$9$	−2.63213	+	1.43942i	−0.877375	+	0.479805i
$10$	−0.0154450	+	2.23601i	−0.00488414	+	0.707090i
$11$	−2.08133	−	2.86470i	−0.627544	−	0.863740i	0.370331	−	0.928900i	$-0.379244\pi$
$11$	−2.08133	−	2.86470i	−0.627544	−	0.863740i	−0.997875	+	0.0651600i	$0.979244\pi$
$12$	0.110677	−	1.72851i	0.0319497	−	0.498978i
$13$	0.331962	+	2.09592i	0.0920696	+	0.581304i	0.989989	+	0.141144i	$0.0450782\pi$
$13$	0.331962	+	2.09592i	0.0920696	+	0.581304i	−0.897919	+	0.440160i	$0.854922\pi$
$14$	3.18083	−	2.31101i	0.850113	−	0.617643i
$15$	3.56667	−	1.50960i	0.920910	−	0.389776i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−0.476073	+	0.934346i	−0.115465	+	0.226612i	−0.941505	−	0.336999i	$-0.890588\pi$
$17$	−0.476073	+	0.934346i	−0.115465	+	0.226612i	0.826040	+	0.563611i	$0.190588\pi$
$18$	−2.82489	+	1.00994i	−0.665834	+	0.238045i
$19$	−4.71987	+	1.53358i	−1.08281	+	0.351827i	−0.795465	−	0.605999i	$-0.792774\pi$
$19$	−4.71987	+	1.53358i	−1.08281	+	0.351827i	−0.287348	+	0.957826i	$0.592774\pi$
$20$	−0.365045	+	2.20607i	−0.0816265	+	0.493292i
$21$	−5.85775	−	3.47305i	−1.27827	−	0.757882i
$22$	−1.60756	−	3.15502i	−0.342734	−	0.672653i
$23$	−1.22065	+	7.70688i	−0.254523	+	1.60700i	0.447124	+	0.894472i	$0.352448\pi$
$23$	−1.22065	+	7.70688i	−0.254523	+	1.60700i	−0.701647	+	0.712524i	$0.747552\pi$
$24$	0.379713	−	1.68992i	0.0775086	−	0.344953i
$25$	−4.77617	+	1.47925i	−0.955235	+	0.295850i
$26$			2.12205i			0.416168i
$27$	3.54437	+	3.79967i	0.682114	+	0.731246i
$28$	3.50319	−	1.78496i	0.662041	−	0.337327i
$29$	0.858514	−	2.64223i	0.159422	−	0.490650i	−0.839160	−	0.543885i	$-0.816953\pi$
$29$	0.858514	−	2.64223i	0.159422	−	0.490650i	0.998582	+	0.0532341i	$0.0169530\pi$
$30$	3.75891	−	0.933062i	0.686280	−	0.170353i
$31$	0.458925	+	1.41243i	0.0824253	+	0.253679i	0.983773	−	0.179417i	$-0.0574211\pi$
$31$	0.458925	+	1.41243i	0.0824253	+	0.253679i	−0.901348	+	0.433096i	$0.857421\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−3.91465	+	4.72131i	−0.681454	+	0.821875i
$34$	−0.616376	+	0.848368i	−0.105708	+	0.145494i
$35$	7.07669	+	5.21658i	1.19618	+	0.881762i
$36$	−2.94810	+	0.555594i	−0.491351	+	0.0925991i
$37$	−1.07161	+	0.169727i	−0.176172	+	0.0279030i	−0.243897	−	0.969801i	$-0.578426\pi$
$37$	−1.07161	+	0.169727i	−0.176172	+	0.0279030i	0.0677249	+	0.997704i	$0.478426\pi$
$38$	−4.90167	+	0.776348i	−0.795156	+	0.125940i
$39$	3.37482	−	1.45597i	0.540404	−	0.233141i
$40$	−0.705656	+	2.12180i	−0.111574	+	0.335487i
$41$	0.691749	−	0.952111i	0.108033	−	0.148695i	−0.751577	−	0.659645i	$-0.770707\pi$
$41$	0.691749	−	0.952111i	0.108033	−	0.148695i	0.859610	+	0.510951i	$0.170707\pi$
$42$	−5.24232	−	4.34665i	−0.808908	−	0.670702i
$43$	−8.25027	−	8.25027i	−1.25815	−	1.25815i	−0.951973	−	0.306181i	$-0.900949\pi$
$43$	−8.25027	−	8.25027i	−1.25815	−	1.25815i	−0.306181	−	0.951973i	$-0.599051\pi$
$44$	−1.09422	−	3.36766i	−0.164960	−	0.507694i
$45$	−4.06294	−	5.33784i	−0.605668	−	0.795717i
$46$	−2.41124	+	7.42105i	−0.355519	+	1.09417i
$47$	10.2948	−	5.24545i	1.50165	−	0.765127i	0.506380	−	0.862311i	$-0.330983\pi$
$47$	10.2948	−	5.24545i	1.50165	−	0.765127i	0.995266	+	0.0971836i	$0.0309834\pi$
$48$	0.639399	−	1.60971i	0.0922893	−	0.232342i
$49$		−	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	$-0.244551\pi$
$53$	−1.93475	−	3.79716i	−0.265759	−	0.521581i	−0.984866	+	0.173318i	$0.944551\pi$
$54$	2.90633	+	4.30735i	0.395501	+	0.586156i
$55$	5.63730	−	5.55995i	0.760133	−	0.749704i
$56$	3.73929	−	1.21497i	0.499684	−	0.162357i
$57$	4.59778	+	7.26276i	0.608990	+	0.961976i
$58$	1.26128	−	2.47540i	0.165614	−	0.325036i
$59$	−5.11067	−	3.71312i	−0.665353	−	0.483407i	0.203113	−	0.979155i	$-0.434894\pi$
$59$	−5.11067	−	3.71312i	−0.665353	−	0.483407i	−0.868466	+	0.495748i	$0.834894\pi$
$60$	3.85859	−	0.333552i	0.498142	−	0.0430613i
$61$	1.09310	−	0.794185i	0.139957	−	0.101685i	−0.515604	−	0.856827i	$-0.672432\pi$
$61$	1.09310	−	0.794185i	0.139957	−	0.101685i	0.655561	+	0.755142i	$0.272432\pi$
$62$	0.232323	+	1.46683i	0.0295050	+	0.186287i
$63$	−3.31591	+	11.3195i	−0.417765	+	1.42612i
$64$	0.587785	+	0.809017i	0.0734732	+	0.101127i
$65$	−4.52283	+	1.43509i	−0.560988	+	0.178001i
$66$	−4.60503	+	4.05080i	−0.566840	+	0.498619i
$67$	8.29150	+	4.22473i	1.01297	+	0.516133i	0.879993	−	0.474987i	$-0.157547\pi$
$67$	8.29150	+	4.22473i	1.01297	+	0.516133i	0.132974	+	0.991119i	$0.457547\pi$
$68$	−0.741501	+	0.741501i	−0.0899202	+	0.0899202i
$69$	13.4565	−	1.25693i	1.61998	−	0.151317i
$70$	6.17351	+	6.25939i	0.737876	+	0.748140i
$71$	2.47790	+	0.805120i	0.294073	+	0.0955501i	0.452338	−	0.891847i	$-0.350590\pi$
$71$	2.47790	+	0.805120i	0.294073	+	0.0955501i	−0.158265	+	0.987397i	$0.550590\pi$
$72$	−2.99872	+	0.0875690i	−0.353403	+	0.0103201i
$73$	8.82492	+	1.39773i	1.03288	+	0.163592i	0.649785	−	0.760118i	$-0.274859\pi$
$73$	8.82492	+	1.39773i	1.03288	+	0.163592i	0.383093	+	0.923710i	$0.374859\pi$
$74$	−1.08497			−0.126126
$75$	4.53075	+	7.38054i	0.523165	+	0.852231i
$76$	−4.96277			−0.569269
$77$	−13.7507	−	2.17789i	−1.56704	−	0.248194i
$78$	3.56104	−	0.910103i	0.403208	−	0.103049i
$79$	−14.4405	−	4.69199i	−1.62468	−	0.527891i	−0.651641	−	0.758528i	$-0.725919\pi$
$79$	−14.4405	−	4.69199i	−1.62468	−	0.527891i	−0.973040	+	0.230637i	$0.925919\pi$
$80$	−1.02889	+	1.98529i	−0.115034	+	0.221962i
$81$	4.85616	−	7.57744i	0.539574	−	0.841938i
$82$	0.832175	−	0.832175i	0.0918984	−	0.0918984i
$83$	9.56823	+	4.87526i	1.05025	+	0.535129i	0.891890	−	0.452252i	$-0.149379\pi$
$83$	9.56823	+	4.87526i	1.05025	+	0.535129i	0.158360	+	0.987381i	$0.449379\pi$
$84$	−4.49782	−	5.11321i	−0.490752	−	0.557897i
$85$	−2.22501	−	0.739979i	−0.241336	−	0.0802620i
$86$	−6.85807	−	9.43932i	−0.739525	−	1.01787i
$87$	−4.80216	−	0.307484i	−0.514846	−	0.0329657i
$88$	−0.553929	−	3.49737i	−0.0590490	−	0.372821i
$89$	2.14121	−	1.55568i	0.226968	−	0.164902i	−0.468490	−	0.883469i	$-0.655202\pi$
$89$	2.14121	−	1.55568i	0.226968	−	0.164902i	0.695458	+	0.718567i	$0.255202\pi$
$90$	−3.17790	−	5.90770i	−0.334980	−	0.622726i
$91$	6.74988	+	4.90407i	0.707579	+	0.514086i
$92$	−3.54247	+	6.95248i	−0.369328	+	0.724846i
$93$	2.17339	−	1.37589i	0.225370	−	0.142673i
$94$	10.9886	−	3.57041i	1.13339	−	0.368260i
$95$	−4.96956	−	9.92214i	−0.509866	−	1.01799i
$96$	0.883341	−	1.48987i	0.0901557	−	0.152059i
$97$	7.23583	+	14.2011i	0.734687	+	1.44190i	0.890909	+	0.454182i	$0.150068\pi$
$97$	7.23583	+	14.2011i	0.734687	+	1.44190i	−0.156222	+	0.987722i	$0.549932\pi$
$98$	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	$0.955751\pi$
$102$	1.68801	+	0.670500i	0.167138	+	0.0663894i
$103$	9.98017	−	5.08515i	0.983376	−	0.501055i	0.113081	−	0.993586i	$-0.463928\pi$
$103$	9.98017	−	5.08515i	0.983376	−	0.501055i	0.870295	+	0.492531i	$0.163928\pi$
$104$	−0.655749	+	2.01819i	−0.0643015	+	0.197900i
$105$	5.71896	−	14.1128i	0.558113	−	1.37726i
$106$	−1.31692	−	4.05308i	−0.127911	−	0.393670i
$107$	−3.58302	−	3.58302i	−0.346384	−	0.346384i	0.512377	−	0.858761i	$-0.328765\pi$
$107$	−3.58302	−	3.58302i	−0.346384	−	0.346384i	−0.858761	+	0.512377i	$0.828765\pi$
$108$	2.19673	+	4.70897i	0.211381	+	0.453121i
$109$	−5.92254	+	8.15168i	−0.567277	+	0.780789i	−0.992229	−	0.124427i	$-0.960291\pi$
$109$	−5.92254	+	8.15168i	−0.567277	+	0.780789i	0.424952	+	0.905216i	$0.360291\pi$
$110$	6.43766	−	4.60963i	0.613807	−	0.439511i
$111$	0.744415	+	1.72550i	0.0706567	+	0.163777i
$112$	3.88332	−	0.615057i	0.366939	−	0.0581174i
$113$	3.71655	−	0.588643i	0.349623	−	0.0553749i	0.0208469	−	0.999783i	$-0.493364\pi$
$113$	3.71655	−	0.588643i	0.349623	−	0.0553749i	0.328776	+	0.944408i	$0.393364\pi$
$114$	3.40502	+	7.89259i	0.318910	+	0.739209i
$115$	−17.4475	−	0.120517i	−1.62699	−	0.0112382i
$116$	1.63299	−	2.24762i	0.151619	−	0.208686i
$117$	−3.89067	−	5.03890i	−0.359692	−	0.465846i
$118$	−4.46689	−	4.46689i	−0.411211	−	0.411211i
$119$	1.27407	+	3.92117i	0.116793	+	0.359453i
$120$	3.86327	+	0.274172i	0.352666	+	0.0250284i
$121$	−0.475402	+	1.46314i	−0.0432184	+	0.133012i
$122$	1.20388	−	0.613408i	0.108994	−	0.0555354i
$123$	−1.89443	−	0.752492i	−0.170815	−	0.0678499i
$124$			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	−0.386241	−	0.922398i	$-0.626227\pi$
$127$	2.99916	−	18.9360i	0.266133	−	1.68030i	0.652373	−	0.757898i	$-0.273773\pi$
$128$	0.453990	+	0.891007i	0.0401275	+	0.0787546i
$129$	−10.3065	+	17.3833i	−0.907438	+	1.53051i
$130$	−4.69164	+	0.709899i	−0.411484	+	0.0622623i
$131$	−11.4171	+	3.70965i	−0.997519	+	0.324113i	−0.761874	−	0.647726i	$-0.775720\pi$
$131$	−11.4171	+	3.70965i	−0.997519	+	0.324113i	−0.235645	+	0.971839i	$0.575720\pi$
$132$	−5.18202	+	3.28054i	−0.451037	+	0.285534i
$133$	−8.85836	+	17.3855i	−0.768118	+	1.50752i
$134$	7.52852	+	5.46979i	0.650365	+	0.472518i
$135$	−7.21498	+	9.10737i	−0.620966	+	0.783837i
$136$	−0.848368	+	0.616376i	−0.0727470	+	0.0528538i
$137$	−1.31496	−	8.30230i	−0.112344	−	0.709314i	−0.977989	−	0.208655i	$-0.933091\pi$
$137$	−1.31496	−	8.30230i	−0.112344	−	0.709314i	0.865645	−	0.500658i	$-0.166909\pi$
$138$	13.4875	+	0.863606i	1.14813	+	0.0735151i
$139$	1.56608	+	2.15552i	0.132833	+	0.182829i	0.870252	−	0.492607i	$-0.163956\pi$
$139$	1.56608	+	2.15552i	0.132833	+	0.182829i	−0.737419	+	0.675435i	$0.763956\pi$
$140$	5.11832	+	7.14808i	0.432577	+	0.604123i
$141$	−13.2177	−	15.0261i	−1.11313	−	1.26543i
$142$	2.32145	+	1.18284i	0.194812	+	0.0992615i
$143$	5.31327	−	5.31327i	0.444318	−	0.444318i
$144$	−2.97550	−	0.382612i	−0.247958	−	0.0318844i
$145$	6.12892	+	1.01417i	0.508979	+	0.0842222i
$146$	8.49762	+	2.76104i	0.703268	+	0.228506i
$147$	−14.1942	+	3.62765i	−1.17072	+	0.299203i
$148$	−1.07161	−	0.169727i	−0.0880862	−	0.0139515i
$149$	−15.1777			−1.24340			−0.621701	−	0.783254i	$-0.713558\pi$
$149$	−15.1777			−1.24340			−0.621701	+	0.783254i	$0.713558\pi$
$150$	3.32039	+	7.99844i	0.271109	+	0.653070i
$151$	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
$153$	−0.0918285	−	3.14458i	−0.00742389	−	0.254224i
$154$	−13.2407	−	4.30216i	−1.06697	−	0.346678i
$155$	−2.96921	+	1.48714i	−0.238492	+	0.119450i
$156$	3.65957	−	0.341829i	0.293000	−	0.0273682i
$157$	−6.13050	+	6.13050i	−0.489267	+	0.489267i	−0.908075	−	0.418808i	$-0.862448\pi$
$157$	−6.13050	+	6.13050i	−0.489267	+	0.489267i	0.418808	+	0.908075i	$0.362448\pi$
$158$	−13.5287	−	6.89322i	−1.07629	−	0.548395i
$159$	−5.54230	+	4.87526i	−0.439533	+	0.386633i
$160$	−1.32679	+	1.79990i	−0.104892	+	0.142294i
$161$	18.0327	+	24.8199i	1.42117	+	1.95608i
$162$	5.98175	−	6.72448i	0.469971	−	0.528325i
$163$	−0.771116	−	4.86864i	−0.0603985	−	0.381341i	−0.999309	−	0.0371787i	$-0.988163\pi$
$163$	−0.771116	−	4.86864i	−0.0603985	−	0.381341i	0.938910	−	0.344162i	$-0.111837\pi$
$164$	0.952111	−	0.691749i	0.0743473	−	0.0540165i
$165$	−11.7479	−	7.07547i	−0.914576	−	0.550825i
$166$	8.68777	+	6.31204i	0.674302	+	0.489909i
$167$	−3.73760	+	7.33545i	−0.289224	+	0.567634i	−0.989207	−	0.146525i	$-0.953191\pi$
$167$	−3.73760	+	7.33545i	−0.289224	+	0.567634i	0.699983	+	0.714160i	$0.253191\pi$
$168$	−3.64256	−	5.75388i	−0.281030	−	0.443921i
$169$	8.08104	−	2.62569i	0.621619	−	0.201976i
$170$	−2.08186	−	1.07894i	−0.159671	−	0.0827507i
$171$	10.2158	−	10.8304i	0.781225	−	0.828224i
$172$	−5.29700	−	10.3959i	−0.403892	−	0.792684i
$173$	0.713712	−	4.50620i	0.0542625	−	0.342600i	−0.945589	−	0.325364i	$-0.894513\pi$
$173$	0.713712	−	4.50620i	0.0542625	−	0.342600i	0.999851	−	0.0172364i	$-0.00548677\pi$
$174$	−4.69494	−	1.05492i	−0.355923	−	0.0799734i
$175$	−9.16594	+	17.3910i	−0.692880	+	1.31464i
$176$		−	3.54097i		−	0.266910i
$177$	−4.03918	+	10.1688i	−0.303603	+	0.764332i
$178$	2.35821	−	1.20157i	0.176755	−	0.0900614i
$179$	−3.51637	+	10.8223i	−0.262826	+	0.808894i	0.729361	+	0.684129i	$0.239818\pi$
$179$	−3.51637	+	10.8223i	−0.262826	+	0.808894i	−0.992186	+	0.124765i	$0.960182\pi$
$180$	−2.21461	−	6.33210i	−0.165067	−	0.471967i
$181$	2.01769	+	6.20982i	0.149974	+	0.461572i	0.997617	−	0.0689945i	$-0.0219791\pi$
$181$	2.01769	+	6.20982i	0.149974	+	0.461572i	−0.847643	+	0.530567i	$0.821979\pi$
$182$	5.89961	+	5.89961i	0.437308	+	0.437308i
$183$	−1.80154	−	1.49374i	−0.133174	−	0.110420i
$184$	−4.58646	+	6.31272i	−0.338118	+	0.465380i
$185$	−0.733743	−	2.31246i	−0.0539458	−	0.170015i
$186$	2.36186	−	1.01896i	0.173180	−	0.0747135i
$187$	3.66749	−	0.580873i	0.268193	−	0.0424776i
$188$	11.4118	−	1.80746i	0.832294	−	0.131822i
$189$	20.4175	+	0.709775i	1.48515	+	0.0516285i
$190$	−3.35621	−	10.5774i	−0.243485	−	0.767365i
$191$	0.349868	−	0.481552i	0.0253155	−	0.0348439i	−0.796172	−	0.605071i	$-0.793145\pi$
$191$	0.349868	−	0.481552i	0.0253155	−	0.0348439i	0.821487	+	0.570227i	$0.193145\pi$
$192$	1.10553	−	1.33334i	0.0797850	−	0.0962256i
$193$	−15.5790	−	15.5790i	−1.12140	−	1.12140i	−0.991532	−	0.129866i	$-0.958545\pi$
$193$	−15.5790	−	15.5790i	−1.12140	−	1.12140i	−0.129866	−	0.991532i	$-0.541455\pi$
$194$	4.92520	+	15.1582i	0.353609	+	1.08830i
$195$	4.34800	+	6.97433i	0.311366	+	0.499442i
$196$	2.61380	−	8.04445i	0.186700	−	0.574604i
$197$	−2.51349	+	1.28069i	−0.179079	+	0.0912453i	−0.541232	−	0.840873i	$-0.682042\pi$
$197$	−2.51349	+	1.28069i	−0.179079	+	0.0912453i	0.362153	+	0.932119i	$0.382042\pi$
$198$	8.77270	+	5.99046i	0.623449	+	0.425724i
$199$		−	10.4829i		−	0.743113i	−0.928410	−	0.371556i	$-0.878824\pi$
$199$		−	10.4829i		−	0.743113i	0.928410	−	0.371556i	$-0.121176\pi$
$200$	−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
$204$	1.56234	+	0.926308i	0.109385	+	0.0648545i
$205$	2.33644	+	1.21087i	0.163184	+	0.0845711i
$206$	10.6528	−	3.46130i	0.742215	−	0.241160i
$207$	−7.88050	−	22.0425i	−0.547733	−	1.53206i
$208$	−0.963390	+	1.89076i	−0.0667991	+	0.131101i
$209$	14.2168	+	10.3291i	0.983400	+	0.714482i
$210$	7.85627	−	13.0444i	0.542134	−	0.900147i
$211$	1.70957	−	1.24207i	0.117692	−	0.0855079i	−0.527382	−	0.849628i	$-0.676827\pi$
$211$	1.70957	−	1.24207i	0.117692	−	0.0855079i	0.645074	+	0.764120i	$0.276827\pi$
$212$	−0.666670	−	4.20919i	−0.0457871	−	0.289088i
$213$	0.288360	−	4.50350i	0.0197581	−	0.308575i
$214$	−2.97840	−	4.09941i	−0.203599	−	0.280230i
$215$	15.4805	−	21.0005i	1.05576	−	1.43222i
$216$	1.43304	+	4.99464i	0.0975061	+	0.339842i
$217$	5.20263	+	2.65087i	0.353177	+	0.179953i
$218$	−7.12483	+	7.12483i	−0.482554	+	0.482554i
$219$	−1.43928	−	15.4087i	−0.0972573	−	1.04122i
$220$	7.07951	−	3.54581i	0.477300	−	0.239058i
$221$	−2.11635	−	0.687645i	−0.142361	−	0.0462560i
$222$	0.465322	+	1.82071i	0.0312304	+	0.122198i
$223$	−10.5167	−	1.66568i	−0.704248	−	0.111542i	−0.205969	−	0.978559i	$-0.566034\pi$
$223$	−10.5167	−	1.66568i	−0.704248	−	0.111542i	−0.498279	+	0.867017i	$0.666034\pi$
$224$	3.93172			0.262699
$225$	10.4422	−	10.7685i	0.696149	−	0.717898i
$226$	3.76287			0.250303
$227$	1.36230	+	0.215768i	0.0904192	+	0.0143210i	0.201480	−	0.979493i	$-0.435425\pi$
$227$	1.36230	+	0.215768i	0.0904192	+	0.0143210i	−0.111061	+	0.993814i	$0.535425\pi$
$228$	2.12843	+	8.32808i	0.140959	+	0.551541i
$229$	15.7865	+	5.12935i	1.04320	+	0.338957i	0.779997	−	0.625783i	$-0.215220\pi$
$229$	15.7865	+	5.12935i	1.04320	+	0.338957i	0.263205	+	0.964740i	$0.415220\pi$
$230$	−17.2138	−	2.84842i	−1.13505	−	0.187820i
$231$	2.24263	+	24.0093i	0.147554	+	1.57969i
$232$	1.96449	−	1.96449i	0.128975	−	0.128975i
$233$	22.1187	+	11.2700i	1.44904	+	0.738324i	0.988769	−	0.149453i	$-0.0477511\pi$
$233$	22.1187	+	11.2700i	1.44904	+	0.738324i	0.460274	+	0.887777i	$0.347751\pi$
$234$	−3.05451	−	5.58550i	−0.199680	−	0.365135i
$235$	15.0411	+	21.0059i	0.981175	+	1.37028i
$236$	−3.71312	−	5.11067i	−0.241704	−	0.332677i
$237$	−1.68048	+	26.2450i	−0.109159	+	1.70480i
$238$	0.644974	+	4.07220i	0.0418074	+	0.263962i
$239$	−19.2197	+	13.9639i	−1.24322	+	0.903249i	−0.997808	−	0.0661704i	$-0.978922\pi$
$239$	−19.2197	+	13.9639i	−1.24322	+	0.903249i	−0.245408	+	0.969420i	$0.578922\pi$
$240$	3.77281	+	0.875145i	0.243534	+	0.0564903i
$241$	−5.11077	−	3.71319i	−0.329214	−	0.239188i	0.410883	−	0.911688i	$-0.365220\pi$
$241$	−5.11077	−	3.71319i	−0.329214	−	0.239188i	−0.740097	+	0.672500i	$0.765220\pi$
$242$	−0.698434	+	1.37075i	−0.0448970	+	0.0881154i
$243$	−14.7985	−	4.89938i	−0.949325	−	0.314296i
$244$	1.28502	−	0.417528i	0.0822649	−	0.0267295i
$245$	18.7008	−	2.82964i	1.19475	−	0.180779i
$246$	−1.75339	−	1.03958i	−0.111792	−	0.0662813i
$247$	−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	$-0.143776\pi$
$252$	−6.65153	+	9.74080i	−0.419007	+	0.613613i
$253$	24.6185	−	12.5437i	1.54775	−	0.788619i
$254$	5.92448	−	18.2337i	0.371735	−	1.14408i
$255$	−0.287508	+	4.05118i	−0.0180044	+	0.253695i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	12.9955	+	12.9955i	0.810638	+	0.810638i	0.984730	−	0.174091i	$-0.0556987\pi$
$257$	12.9955	+	12.9955i	0.810638	+	0.810638i	−0.174091	+	0.984730i	$0.555699\pi$
$258$	−12.8990	+	15.5569i	−0.803054	+	0.968533i
$259$	−2.50738	+	3.45111i	−0.155801	+	0.214442i
$260$	−4.74493	−	0.0327750i	−0.294268	−	0.00203262i
$261$	1.54356	+	8.19045i	0.0955438	+	0.506976i
$262$	−11.8569	+	1.87794i	−0.732520	+	0.116020i
$263$	−8.70800	+	1.37921i	−0.536958	+	0.0850458i	−0.419023	−	0.907976i	$-0.637627\pi$
$263$	−8.70800	+	1.37921i	−0.536958	+	0.0850458i	−0.117935	+	0.993021i	$0.537627\pi$
$264$	−5.63141	+	2.42950i	−0.346589	+	0.149526i
$265$	7.74792	−	5.54783i	0.475951	−	0.340801i
$266$	−11.4690	+	15.7857i	−0.703209	+	0.967885i
$267$	−3.52893	−	2.92600i	−0.215967	−	0.179068i
$268$	6.58017	+	6.58017i	0.401948	+	0.401948i
$269$	0.0471754	+	0.145191i	0.00287634	+	0.00885245i	0.952484	−	0.304587i	$-0.0985186\pi$
$269$	0.0471754	+	0.145191i	0.00287634	+	0.00885245i	−0.949608	+	0.313440i	$0.898519\pi$
$270$	−8.55085	+	7.86657i	−0.520388	+	0.478744i
$271$	−3.79892	+	11.6919i	−0.230768	+	0.710230i	0.766887	+	0.641782i	$0.221805\pi$
$271$	−3.79892	+	11.6919i	−0.230768	+	0.710230i	−0.997655	+	0.0684477i	$0.978195\pi$
$272$	−0.934346	+	0.476073i	−0.0566530	+	0.0288662i
$273$	5.33470	−	13.4303i	0.322871	−	0.812839i
$274$		−	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	−0.958748	−	0.284258i	$-0.908253\pi$
$277$	0.680977	−	4.29952i	0.0409160	−	0.258333i	0.999664	+	0.0259243i	$0.00825290\pi$
$278$	1.20960	+	2.37397i	0.0725468	+	0.142381i
$279$	−3.24101	−	3.05710i	−0.194034	−	0.183024i
$280$	3.93710	+	7.86075i	0.235287	+	0.469770i
$281$	−21.0452	+	6.83801i	−1.25545	+	0.407922i	−0.859872	−	0.510509i	$-0.829457\pi$
$281$	−21.0452	+	6.83801i	−1.25545	+	0.407922i	−0.395582	+	0.918431i	$0.629457\pi$
$282$	−10.7043	−	16.9088i	−0.637434	−	1.00691i
$283$	3.54907	−	6.96545i	0.210970	−	0.414053i	−0.761136	−	0.648592i	$-0.775358\pi$
$283$	3.54907	−	6.96545i	0.210970	−	0.414053i	0.972107	+	0.234539i	$0.0753581\pi$
$284$	2.10783	+	1.53143i	0.125077	+	0.0908736i
$285$	−14.5191	+	12.5949i	−0.860039	+	0.746056i
$286$	6.07903	−	4.41668i	0.359461	−	0.261164i
$287$	−0.723844	−	4.57017i	−0.0427272	−	0.269769i
$288$	−2.87901	−	0.843373i	−0.169648	−	0.0496962i
$289$	9.34599	+	12.8637i	0.549764	+	0.756686i
$290$	5.89481	+	1.96046i	0.346155	+	0.115122i
$291$	20.7278	−	18.2331i	1.21508	−	1.06884i
$292$	7.96107	+	4.05637i	0.465887	+	0.237381i
$293$	−5.69369	+	5.69369i	−0.332629	+	0.332629i	−0.853584	−	0.520955i	$-0.825576\pi$
$293$	−5.69369	+	5.69369i	−0.332629	+	0.332629i	0.520955	+	0.853584i	$0.325576\pi$
$294$	−14.5869	+	1.36252i	−0.850728	+	0.0794639i
$295$	6.49965	−	12.5414i	0.378424	−	0.730187i
$296$	−1.03187	−	0.335275i	−0.0599762	−	0.0194875i
$297$	3.50793	−	18.0619i	0.203550	−	1.04806i
$298$	−14.9908	−	2.37431i	−0.868394	−	0.137540i
$299$	−16.5582			−0.957588
$300$	2.02828	+	8.41939i	0.117103	+	0.486093i
$301$	−45.8739			−2.64413
$302$	12.9367	+	2.04897i	0.744422	+	0.117905i
$303$	4.67370	−	1.19447i	0.268497	−	0.0686205i
$304$	−4.71987	−	1.53358i	−0.270703	−	0.0879568i
$305$	2.12155	+	2.15106i	0.121479	+	0.123169i
$306$	0.401223	−	3.12023i	0.0229364	−	0.178372i
$307$	−6.57841	+	6.57841i	−0.375450	+	0.375450i	−0.869458	−	0.494008i	$-0.835531\pi$
$307$	−6.57841	+	6.57841i	−0.375450	+	0.375450i	0.494008	+	0.869458i	$0.335531\pi$
$308$	−12.4047	−	6.32050i	−0.706822	−	0.360144i
$309$	−12.8138	−	14.5669i	−0.728949	−	0.828684i
$310$	−3.16529	+	1.00435i	−0.179776	+	0.0570431i
$311$	6.69564	+	9.21576i	0.379675	+	0.522578i	0.955498	−	0.294996i	$-0.0953184\pi$
$311$	6.69564	+	9.21576i	0.379675	+	0.522578i	−0.575823	+	0.817574i	$0.695318\pi$
$312$	3.66798	+	0.234862i	0.207659	+	0.0132964i
$313$	3.74388	+	23.6379i	0.211617	+	1.33610i	0.833297	+	0.552825i	$0.186450\pi$
$313$	3.74388	+	23.6379i	0.211617	+	1.33610i	−0.621681	+	0.783271i	$0.713550\pi$
$314$	−7.01404	+	5.09600i	−0.395825	+	0.287584i
$315$	−26.1356	−	3.54438i	−1.47257	−	0.199703i
$316$	−12.2838	−	8.92470i	−0.691018	−	0.502054i
$317$	6.09176	−	11.9558i	0.342147	−	0.671502i	−0.654253	−	0.756276i	$-0.727017\pi$
$317$	6.09176	−	11.9558i	0.342147	−	0.671502i	0.996400	+	0.0847737i	$0.0270167\pi$
$318$	−6.23672	+	3.94823i	−0.349738	+	0.221406i
$319$	−9.35606	+	3.03997i	−0.523839	+	0.170205i
$320$	−1.59202	+	1.57018i	−0.0889968	+	0.0877757i
$321$	−4.47603	+	7.54939i	−0.249828	+	0.421366i
$322$	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
$327$	16.2195	+	6.44261i	0.896940	+	0.356277i
$328$	1.04860	−	0.534289i	0.0578994	−	0.0295012i
$329$	14.0379	−	43.2041i	0.773932	−	2.38192i
$330$	−10.4965	−	8.82614i	−0.577811	−	0.485863i
$331$	−2.24416	−	6.90681i	−0.123350	−	0.379633i	0.870247	−	0.492616i	$-0.163959\pi$
$331$	−2.24416	−	6.90681i	−0.123350	−	0.379633i	−0.993597	+	0.112983i	$0.963959\pi$
$332$	7.59339	+	7.59339i	0.416742	+	0.416742i
$333$	2.57632	−	1.98924i	0.141181	−	0.109010i
$334$	−4.83910	+	6.66045i	−0.264784	+	0.364444i
$335$	−6.56666	+	19.7450i	−0.358775	+	1.07878i
$336$	−2.69761	−	6.25286i	−0.147167	−	0.341121i
$337$	−25.1497	+	3.98332i	−1.36999	+	0.216985i	−0.797695	−	0.603061i	$-0.793948\pi$
$337$	−25.1497	+	3.98332i	−1.36999	+	0.216985i	−0.572297	+	0.820046i	$0.693948\pi$
$338$	8.39230	−	1.32921i	0.456481	−	0.0722995i
$339$	−2.58176	−	5.98433i	−0.140222	−	0.325024i
$340$	−1.88744	−	1.39133i	−0.102361	−	0.0754554i
$341$	3.09100	−	4.25440i	0.167387	−	0.230389i
$342$	11.7843	−	9.09898i	0.637223	−	0.492017i
$343$	−4.05468	−	4.05468i	−0.218932	−	0.218932i
$344$	−3.60550	−	11.0966i	−0.194396	−	0.598288i
$345$	7.28064	+	29.3306i	0.391976	+	1.57911i
$346$	1.40985	−	4.33907i	0.0757940	−	0.233270i
$347$	−4.08726	+	2.08256i	−0.219416	+	0.111798i	−0.560244	−	0.828328i	$-0.689293\pi$
$347$	−4.08726	+	2.08256i	−0.219416	+	0.111798i	0.340828	+	0.940126i	$0.389293\pi$
$348$	−4.47211	−	1.77638i	−0.239730	−	0.0952242i
$349$			10.1416i			0.542867i	0.962457	+	0.271434i	$0.0874978\pi$
$349$			10.1416i			0.542867i	−0.962457	+	0.271434i	$0.912502\pi$
$350$	−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	$-0.0445132\pi$
$353$	5.55052	+	10.8935i	0.295424	+	0.579803i	−0.694814	+	0.719190i	$0.744513\pi$
$354$	−5.58019	+	9.41171i	−0.296584	+	0.500227i
$355$	−0.951095	+	5.74774i	−0.0504789	+	0.305058i
$356$	2.51715	−	0.817870i	0.133408	−	0.0433470i
$357$	6.03375	−	3.81974i	0.319340	−	0.202162i
$358$	−5.16605	+	10.1389i	−0.273034	+	0.535860i
$359$	27.4018	+	19.9085i	1.44621	+	1.05073i	0.986699	+	0.162561i	$0.0519753\pi$
$359$	27.4018	+	19.9085i	1.44621	+	1.05073i	0.459511	+	0.888172i	$0.348025\pi$
$360$	−1.19678	−	6.60058i	−0.0630760	−	0.347881i
$361$	4.55401	−	3.30868i	0.239685	−	0.174141i
$362$	1.02142	+	6.44900i	0.0536847	+	0.338952i
$363$	2.65920	+	0.170269i	0.139572	+	0.00893681i
$364$	4.90407	+	6.74988i	0.257043	+	0.353790i
$365$	−0.138000	+	19.9786i	−0.00722324	+	1.04573i
$366$	−1.54569	−	1.75717i	−0.0807944	−	0.0918488i
$367$	−4.23542	−	2.15805i	−0.221087	−	0.112649i	0.339939	−	0.940447i	$-0.389593\pi$
$367$	−4.23542	−	2.15805i	−0.221087	−	0.112649i	−0.561026	+	0.827798i	$0.689593\pi$
$368$	−5.51752	+	5.51752i	−0.287621	+	0.287621i
$369$	−0.450286	+	3.50179i	−0.0234410	+	0.182296i
$370$	−0.362961	−	2.39877i	−0.0188695	−	0.124706i
$371$	−15.9356	−	5.17778i	−0.827334	−	0.268817i
$372$	2.49219	−	0.636934i	0.129214	−	0.0330235i
$373$	37.1540	+	5.88461i	1.92376	+	0.304693i	0.997407	−	0.0719662i	$-0.0229274\pi$
$373$	37.1540	+	5.88461i	1.92376	+	0.304693i	0.926352	+	0.376660i	$0.122927\pi$
$374$	3.71320			0.192005
$375$	−14.8020	+	12.4861i	−0.764369	+	0.644778i
$376$	11.5541			0.595857
$377$	5.82291	+	0.922258i	0.299895	+	0.0474987i
$378$	20.0551	+	3.89504i	1.03152	+	0.200339i
$379$	15.4663	+	5.02532i	0.794453	+	0.258133i	0.677999	−	0.735063i	$-0.262847\pi$
$379$	15.4663	+	5.02532i	0.794453	+	0.258133i	0.116454	+	0.993196i	$0.462847\pi$
$380$	−1.66022	−	10.9722i	−0.0851674	−	0.562862i
$381$	−33.0630	+	3.08831i	−1.69387	+	0.158219i
$382$	0.420892	−	0.420892i	0.0215347	−	0.0215347i
$383$	−28.2694	−	14.4040i	−1.44450	−	0.736009i	−0.456393	−	0.889779i	$-0.650859\pi$
$383$	−28.2694	−	14.4040i	−1.44450	−	0.736009i	−0.988107	+	0.153769i	$0.950859\pi$
$384$	1.30050	−	1.14398i	0.0663660	−	0.0583786i
$385$	0.215027	−	31.1300i	0.0109588	−	1.58653i
$386$	−12.9501	−	17.8242i	−0.659141	−	0.907230i
$387$	33.5913	+	9.84017i	1.70754	+	0.500204i
$388$	2.49330	+	15.7420i	0.126578	+	0.799181i
$389$	8.93091	−	6.48869i	0.452815	−	0.328989i	−0.337891	−	0.941185i	$-0.609714\pi$
$389$	8.93091	−	6.48869i	0.452815	−	0.328989i	0.790706	+	0.612196i	$0.209714\pi$
$390$	3.20344	+	7.56864i	0.162212	+	0.383253i
$391$	−6.61978	−	4.80955i	−0.334776	−	0.243229i
$392$	3.84005	−	7.53652i	0.193952	−	0.380652i
$393$	11.1218	+	17.5682i	0.561019	+	0.886200i
$394$	−2.68289	+	0.871725i	−0.135162	+	0.0439169i
$395$	5.54270	−	33.4961i	0.278883	−	1.68537i
$396$	7.72758	+	7.28906i	0.388325	+	0.366289i
$397$	−6.77912	−	13.3048i	−0.340234	−	0.667748i	0.655970	−	0.754787i	$-0.272260\pi$
$397$	−6.77912	−	13.3048i	−0.340234	−	0.667748i	−0.996205	+	0.0870388i	$0.972260\pi$
$398$	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	$-0.103107\pi$
$402$	5.95010	−	14.9796i	0.296764	−	0.747114i
$403$	−2.80799	+	1.43074i	−0.139876	+	0.0712703i
$404$	−0.860641	+	2.64878i	−0.0428185	+	0.131782i
$405$	18.3775	+	8.20158i	0.913187	+	0.407540i
$406$	−3.37544	−	10.3885i	−0.167520	−	0.515574i
$407$	2.71660	+	2.71660i	0.134657	+	0.134657i
$408$	1.39820	+	1.15931i	0.0692210	+	0.0573942i
$409$	15.8203	−	21.7748i	0.782264	−	1.07669i	−0.212764	−	0.977104i	$-0.568247\pi$
$409$	15.8203	−	21.7748i	0.782264	−	1.07669i	0.995028	−	0.0995907i	$-0.0317533\pi$
$410$	2.11825	+	1.56147i	0.104613	+	0.0771153i
$411$	−13.3682	+	5.76733i	−0.659407	+	0.284481i
$412$	11.0631	−	1.75222i	0.545040	−	0.0863259i
$413$	−24.5315	+	3.88540i	−1.20711	+	0.191188i
$414$	−4.33527	−	23.0039i	−0.213067	−	1.13058i
$415$	−7.57781	+	22.7854i	−0.371980	+	1.11849i
$416$	−1.24731	+	1.71677i	−0.0611543	+	0.0841717i
$417$	2.94555	−	3.55251i	0.144244	−	0.173967i
$418$	12.4260	+	12.4260i	0.607775	+	0.607775i
$419$	−5.97052	−	18.3754i	−0.291679	−	0.897696i	−0.984317	−	0.176410i	$-0.943551\pi$
$419$	−5.97052	−	18.3754i	−0.291679	−	0.897696i	0.692638	−	0.721286i	$-0.256449\pi$
$420$	9.80014	−	11.6548i	0.478198	−	0.568695i
$421$	2.15745	−	6.63995i	0.105148	−	0.323611i	−0.884617	−	0.466318i	$-0.845580\pi$
$421$	2.15745	−	6.63995i	0.105148	−	0.323611i	0.989765	+	0.142706i	$0.0455804\pi$
$422$	1.88282	−	0.959347i	0.0916545	−	0.0467003i
$423$	−19.5467	+	28.6251i	−0.950395	+	1.39180i
$424$		−	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
$429$	−11.1950	−	6.63752i	−0.540501	−	0.320462i
$430$	18.5752	−	18.3203i	0.895773	−	0.883483i
$431$	−11.4753	+	3.72856i	−0.552747	+	0.179598i	−0.572055	−	0.820215i	$-0.693854\pi$
$431$	−11.4753	+	3.72856i	−0.552747	+	0.179598i	0.0193080	+	0.999814i	$0.493854\pi$
$432$	0.634064	+	5.15732i	0.0305064	+	0.248132i
$433$	−11.0750	+	21.7358i	−0.532228	+	1.04456i	0.455771	+	0.890097i	$0.349364\pi$
$433$	−11.0750	+	21.7358i	−0.532228	+	1.04456i	−0.987999	+	0.154460i	$0.950636\pi$
$434$	4.72389	+	3.43211i	0.226754	+	0.164746i
$435$	−0.926676	−	10.7200i	−0.0444307	−	0.513984i
$436$	−8.15168	+	5.92254i	−0.390395	+	0.283638i
$437$	−6.05780	−	38.2475i	−0.289784	−	1.82962i
$438$	0.988889	−	15.4441i	0.0472510	−	0.737948i
$439$	−4.35738	−	5.99742i	−0.207966	−	0.286241i	0.692274	−	0.721635i	$-0.256609\pi$
$439$	−4.35738	−	5.99742i	−0.207966	−	0.286241i	−0.900240	+	0.435394i	$0.856609\pi$
$440$	7.54703	−	2.39467i	0.359791	−	0.114162i
$441$	12.1752	+	22.2637i	0.579772	+	1.06017i
$442$	−1.98273	−	1.01025i	−0.0943087	−	0.0480527i
$443$	−0.514362	+	0.514362i	−0.0244381	+	0.0244381i	−0.719220	−	0.694782i	$-0.755501\pi$
$443$	−0.514362	+	0.514362i	−0.0244381	+	0.0244381i	0.694782	+	0.719220i	$0.255501\pi$
$444$	0.174772	+	1.87108i	0.00829432	+	0.0887977i
$445$	4.15577	+	4.21358i	0.197002	+	0.199743i
$446$	−10.1266	−	3.29034i	−0.479509	−	0.155802i
$447$	6.50939	+	25.4698i	0.307883	+	1.20468i
$448$	3.88332	+	0.615057i	0.183469	+	0.0290587i
$449$	−29.6955			−1.40142			−0.700709	−	0.713447i	$-0.747133\pi$
$449$	−29.6955			−1.40142			−0.700709	+	0.713447i	$0.747133\pi$
$450$	11.9982	−	9.00236i	0.565602	−	0.424375i
$451$	−4.16727			−0.196229
$452$	3.71655	+	0.588643i	0.174812	+	0.0276874i
$453$	−5.61743	−	21.9798i	−0.263930	−	1.03270i
$454$	1.31178	+	0.426222i	0.0615648	+	0.0200036i
$455$	−8.58435	+	16.5639i	−0.402441	+	0.776527i
$456$	0.799425	+	8.55851i	0.0374365	+	0.400789i
$457$	−2.68309	+	2.68309i	−0.125510	+	0.125510i	−0.767071	−	0.641562i	$-0.778287\pi$
$457$	−2.68309	+	2.68309i	−0.125510	+	0.125510i	0.641562	+	0.767071i	$0.278287\pi$
$458$	14.7898	+	7.53576i	0.691080	+	0.352123i
$459$	−5.23758	+	1.50274i	−0.244469	+	0.0701421i
$460$	−16.5563	−	5.50620i	−0.771943	−	0.256728i
$461$	−6.68161	−	9.19644i	−0.311193	−	0.428321i	0.624560	−	0.780977i	$-0.285279\pi$
$461$	−6.68161	−	9.19644i	−0.311193	−	0.428321i	−0.935753	+	0.352656i	$0.885279\pi$
$462$	−1.54085	+	24.0645i	−0.0716870	+	1.11958i
$463$	−2.20029	−	13.8921i	−0.102256	−	0.645619i	−0.984574	−	0.174966i	$-0.944018\pi$
$463$	−2.20029	−	13.8921i	−0.102256	−	0.645619i	0.882318	−	0.470653i	$-0.155982\pi$
$464$	2.24762	−	1.63299i	0.104343	−	0.0758097i
$465$	3.76903	+	4.34486i	0.174784	+	0.201488i
$466$	20.0833	+	14.5914i	0.930343	+	0.675934i
$467$	−2.03239	+	3.98879i	−0.0940479	+	0.184579i	−0.933238	−	0.359259i	$-0.883030\pi$
$467$	−2.03239	+	3.98879i	−0.0940479	+	0.184579i	0.839190	+	0.543838i	$0.183030\pi$
$468$	−2.14314	−	5.99456i	−0.0990667	−	0.277099i
$469$	34.7969	−	11.3062i	1.60677	−	0.522072i
$470$	11.5699	+	23.1003i	0.533679	+	1.06554i
$471$	12.9169	+	7.65842i	0.595180	+	0.352881i
$472$	−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
$477$	10.5582	+	7.20970i	0.483427	+	0.330109i
$478$	−21.1675	+	10.7854i	−0.968177	+	0.493311i
$479$	9.35922	−	28.8047i	0.427634	−	1.31612i	−0.472816	−	0.881161i	$-0.656763\pi$
$479$	9.35922	−	28.8047i	0.427634	−	1.31612i	0.900450	−	0.434960i	$-0.143237\pi$
$480$	3.58946	+	1.45457i	0.163836	+	0.0663916i
$481$	−0.711470	−	2.18968i	−0.0324402	−	0.0998408i
$482$	−4.46698	−	4.46698i	−0.203465	−	0.203465i
$483$	33.9167	−	40.9056i	1.54326	−	1.86127i
$484$	−0.904268	+	1.24462i	−0.0411031	+	0.0565736i
$485$	−28.9766	+	20.7485i	−1.31576	+	0.942139i
$486$	−13.8499	−	7.15406i	−0.628244	−	0.324515i
$487$	−0.548721	+	0.0869089i	−0.0248649	+	0.00393822i	−0.168855	−	0.985641i	$-0.554007\pi$
$487$	−0.548721	+	0.0869089i	−0.0248649	+	0.00393822i	0.143990	+	0.989579i	$0.454007\pi$
$488$	1.33451	−	0.211366i	0.0604106	−	0.00956809i
$489$	−7.83941	+	3.38208i	−0.354510	+	0.152943i
$490$	18.9132	+	0.130641i	0.854411	+	0.00590174i
$491$	3.72379	−	5.12536i	0.168052	−	0.231304i	−0.716682	−	0.697400i	$-0.754340\pi$
$491$	3.72379	−	5.12536i	0.168052	−	0.231304i	0.884734	+	0.466096i	$0.154340\pi$
$492$	−1.56917	−	1.30107i	−0.0707438	−	0.0586569i
$493$	2.06004	+	2.06004i	0.0927797	+	0.0927797i
$494$	−3.25433	−	10.0158i	−0.146419	−	0.450632i
$495$	−6.83498	+	22.7489i	−0.307210	+	1.02249i
$496$	−0.458925	+	1.41243i	−0.0206063	+	0.0634198i
$497$	9.12729	−	4.65059i	0.409415	−	0.208607i
$498$	6.86630	−	17.2862i	0.307686	−	0.774612i
$499$			26.3004i			1.17737i	0.808363	+	0.588684i	$0.200354\pi$
$499$			26.3004i			1.17737i	−0.808363	+	0.588684i	$0.799646\pi$
$500$	−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	$-0.192794\pi$
$503$	−2.72953	−	5.35700i	−0.121704	−	0.238857i	−0.943818	+	0.330465i	$0.892794\pi$
$504$	−8.09343	+	8.58034i	−0.360510	+	0.382199i
$505$	−6.15757	+	0.931711i	−0.274008	+	0.0414606i
$506$	26.2777	−	8.53813i	1.16818	−	0.379566i
$507$	−7.87200	−	12.4348i	−0.349608	−	0.552249i
$508$	8.70391	−	17.0824i	0.386174	−	0.757908i
$509$	−1.71448	−	1.24564i	−0.0759931	−	0.0552122i	0.549140	−	0.835730i	$-0.314955\pi$
$509$	−1.71448	−	1.24564i	−0.0759931	−	0.0552122i	−0.625133	+	0.780518i	$0.714955\pi$
$510$	−0.917712	+	3.95633i	−0.0406370	+	0.175189i
$511$	28.4205	−	20.6487i	1.25725	−	0.913444i
$512$	0.156434	+	0.987688i	0.00691349	+	0.0436501i
$513$	−22.5560	−	12.4984i	−0.995874	−	0.551817i
$514$	10.8026	+	14.8685i	0.476481	+	0.655820i
$515$	14.5815	+	20.3640i	0.642537	+	0.897346i
$516$	−15.1738	+	13.3476i	−0.667989	+	0.587594i
$517$	−36.4534	−	18.5739i	−1.60322	−	0.816881i
$518$	−3.01638	+	3.01638i	−0.132532	+	0.132532i
$519$	−7.86801	+	0.734927i	−0.345367	+	0.0322597i
$520$	−4.68139	−	0.774642i	−0.205292	−	0.0339703i
$521$	7.20132	+	2.33985i	0.315496	+	0.102511i	0.462484	−	0.886627i	$-0.346958\pi$
$521$	7.20132	+	2.33985i	0.315496	+	0.102511i	−0.146989	+	0.989138i	$0.546958\pi$
$522$	0.243285	+	8.33107i	0.0106483	+	0.364641i
$523$	−19.0191	−	3.01233i	−0.831649	−	0.131720i	−0.273929	−	0.961750i	$-0.588323\pi$
$523$	−19.0191	−	3.01233i	−0.831649	−	0.131720i	−0.557719	+	0.830030i	$0.688323\pi$
$524$	−12.0047			−0.524427
$525$	33.1151	+	7.92284i	1.44526	+	0.345781i
$526$	−8.81654			−0.384420
$527$	−1.53818	−	0.243623i	−0.0670040	−	0.0106124i
$528$	−5.94214	+	1.51865i	−0.258598	+	0.0660906i
$529$	−36.0318	−	11.7074i	−1.56660	−	0.509019i
$530$	8.52040	−	4.26749i	0.370102	−	0.185368i
$531$	18.7967	+	2.41702i	0.815706	+	0.104890i
$532$	−13.7972	+	13.7972i	−0.598186	+	0.598186i
$533$	2.22518	+	1.13379i	0.0963834	+	0.0491098i
$534$	−3.02776	−	3.44202i	−0.131024	−	0.148951i
$535$	6.72306	−	9.12035i	0.290663	−	0.394307i
$536$	5.46979	+	7.52852i	0.236259	+	0.325183i
$537$	19.6691	+	1.25942i	0.848784	+	0.0543478i
$538$	0.0238817	+	0.150783i	0.00102961	+	0.00650073i
$539$	−24.2309	+	17.6048i	−1.04370	+	0.758291i
$540$	−9.67618	+	6.43207i	−0.416397	+	0.276792i
$541$	−5.35372	−	3.88970i	−0.230174	−	0.167231i	0.466720	−	0.884405i	$-0.345435\pi$
$541$	−5.35372	−	3.88970i	−0.230174	−	0.167231i	−0.696895	+	0.717174i	$0.745435\pi$
$542$	−5.58115	+	10.9536i	−0.239731	+	0.470499i
$543$	9.55543	−	6.04918i	0.410063	−	0.259595i
$544$	−0.997317	+	0.324048i	−0.0427596	+	0.0138934i
$545$	−20.0039	−	10.3671i	−0.856871	−	0.444079i
$546$	7.36999	−	12.4304i	0.315406	−	0.531973i
$547$	−1.05652	−	2.07353i	−0.0451734	−	0.0886577i	0.867316	−	0.497757i	$-0.165843\pi$
$547$	−1.05652	−	2.07353i	−0.0451734	−	0.0886577i	−0.912490	+	0.409099i	$0.865843\pi$
$548$	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
$552$	12.5605	+	4.98920i	0.534610	+	0.212354i
$553$	−53.1911	+	27.1022i	−2.26192	+	1.15250i
$554$	1.34519	−	4.14006i	0.0571515	−	0.175894i
$555$	−3.56587	+	2.22307i	−0.151363	+	0.0943640i
$556$	0.823335	+	2.53396i	0.0349172	+	0.107464i
$557$	−0.0556738	−	0.0556738i	−0.00235897	−	0.00235897i	0.705926	−	0.708285i	$-0.250531\pi$
$557$	−0.0556738	−	0.0556738i	−0.00235897	−	0.00235897i	−0.708285	+	0.705926i	$0.750531\pi$
$558$	−2.72288	−	3.52646i	−0.115269	−	0.149287i
$559$	14.5532	−	20.0307i	0.615533	−	0.847208i
$560$	2.65894	+	8.37987i	0.112361	+	0.354114i
$561$	−2.54768	−	5.90533i	−0.107563	−	0.249323i
$562$	−21.8558	+	3.46162i	−0.921933	+	0.146020i
$563$	38.0847	−	6.03203i	1.60508	−	0.254220i	0.711355	−	0.702833i	$-0.248082\pi$
$563$	38.0847	−	6.03203i	1.60508	−	0.254220i	0.893726	+	0.448613i	$0.148082\pi$
$564$	−7.92742	−	18.3752i	−0.333805	−	0.773734i
$565$	2.54475	+	8.02000i	0.107058	+	0.337404i
$566$	4.59501	−	6.32449i	0.193143	−	0.265838i
$567$	−7.56556	−	34.5673i	−0.317724	−	1.45169i
$568$	1.84231	+	1.84231i	0.0773017	+	0.0773017i
$569$	2.48906	+	7.66055i	0.104347	+	0.321147i	0.989577	−	0.144007i	$-0.0459988\pi$
$569$	2.48906	+	7.66055i	0.104347	+	0.321147i	−0.885230	+	0.465154i	$0.845999\pi$
$570$	−16.3106	+	10.1685i	−0.683178	+	0.425912i
$571$	−6.28765	+	19.3514i	−0.263130	+	0.809831i	0.728988	+	0.684526i	$0.239991\pi$
$571$	−6.28765	+	19.3514i	−0.263130	+	0.809831i	−0.992118	+	0.125305i	$0.960009\pi$
$572$	6.69511	−	3.41133i	0.279937	−	0.142635i
$573$	−0.958149	−	0.380590i	−0.0400273	−	0.0158994i
$574$		−	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	0.511997	+	0.858987i	$0.328906\pi$
$577$	−5.77419	+	36.4568i	−0.240383	+	1.51772i	−0.752380	+	0.658729i	$0.771094\pi$
$578$	7.21861	+	14.1673i	0.300255	+	0.589283i
$579$	−19.4617	+	32.8247i	−0.808803	+	1.36415i
$580$	5.51555	+	2.85847i	0.229021	+	0.118692i
$581$	40.1550	−	13.0472i	1.66591	−	0.541287i
$582$	23.3249	−	14.7661i	0.966846	−	0.612074i
$583$	−6.85089	+	13.4456i	−0.283735	+	0.556861i
$584$	7.22850	+	5.25182i	0.299118	+	0.217322i
$585$	9.83895	−	10.2876i	0.406790	−	0.425339i
$586$	−6.51428	+	4.73290i	−0.269102	+	0.195514i
$587$	4.84574	+	30.5948i	0.200005	+	1.26278i	0.859525	+	0.511094i	$0.170760\pi$
$587$	4.84574	+	30.5948i	0.200005	+	1.26278i	−0.659520	+	0.751687i	$0.729240\pi$
$588$	−14.6205	−	0.936154i	−0.602940	−	0.0386063i
$589$	−4.33213	−	5.96267i	−0.178502	−	0.245688i
$590$	8.38153	−	11.3702i	0.345062	−	0.468103i
$591$	3.22713	+	3.66867i	0.132746	+	0.150909i
$592$	−0.966718	−	0.492567i	−0.0397319	−	0.0202444i
$593$	21.6044	−	21.6044i	0.887186	−	0.887186i	−0.107066	−	0.994252i	$-0.534146\pi$
$593$	21.6044	−	21.6044i	0.887186	−	0.887186i	0.994252	+	0.107066i	$0.0341455\pi$
$594$	6.29024	−	17.2908i	0.258092	−	0.709449i
$595$	−8.24311	+	4.12860i	−0.337934	+	0.169256i
$596$	−14.4348	−	4.69016i	−0.591273	−	0.192116i
$597$	−17.5915	+	4.49590i	−0.719971	+	0.184005i
$598$	−16.3544	−	2.59028i	−0.668780	−	0.105924i
$599$	32.5862			1.33144			0.665718	−	0.746204i	$-0.268126\pi$
$599$	32.5862			1.33144			0.665718	+	0.746204i	$0.268126\pi$
$600$	0.686230	+	8.63302i	0.0280152	+	0.352442i
$601$	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
$603$	−27.9054	+	0.814897i	−1.13640	+	0.0331852i
$604$	12.4569	+	4.04749i	0.506863	+	0.164690i
$605$	−3.39389	−	0.561597i	−0.137981	−	0.0228322i
$606$	4.80302	−	0.448635i	0.195109	−	0.0182246i
$607$	6.64949	−	6.64949i	0.269894	−	0.269894i	−0.559163	−	0.829058i	$-0.688877\pi$
$607$	6.64949	−	6.64949i	0.269894	−	0.269894i	0.829058	+	0.559163i	$0.188877\pi$
$608$	−4.42186	−	2.25305i	−0.179330	−	0.0913732i
$609$	−14.2056	+	12.4959i	−0.575639	+	0.506358i
$610$	1.75893	+	2.45646i	0.0712168	+	0.0994591i
$611$	14.4115	+	19.8357i	0.583027	+	0.802469i
$612$	0.884395	−	3.01905i	0.0357496	−	0.122038i
$613$	−4.00713	−	25.3000i	−0.161846	−	1.02186i	−0.926192	−	0.377052i	$-0.876938\pi$
$613$	−4.00713	−	25.3000i	−0.161846	−	1.02186i	0.764346	−	0.644807i	$-0.223062\pi$
$614$	−7.52651	+	5.46833i	−0.303745	+	0.220684i
$615$	1.02993	−	4.44012i	0.0415310	−	0.179043i
$616$	−11.2632	−	8.18320i	−0.453808	−	0.329711i
$617$	−20.5976	+	40.4250i	−0.829227	+	1.62745i	−0.0516476	+	0.998665i	$0.516447\pi$
$617$	−20.5976	+	40.4250i	−0.829227	+	1.62745i	−0.777580	+	0.628785i	$0.783553\pi$
$618$	−10.3772	−	16.3921i	−0.417433	−	0.659387i
$619$	−42.4716	+	13.7999i	−1.70708	+	0.554663i	−0.989843	−	0.142168i	$-0.954593\pi$
$619$	−42.4716	+	13.7999i	−1.70708	+	0.554663i	−0.717235	+	0.696831i	$0.754593\pi$
$620$	−3.28344	+	0.496822i	−0.131866	+	0.0199528i
$621$	−33.6100	+	22.6779i	−1.34872	+	0.910035i
$622$	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
$627$	11.2362	−	28.2874i	0.448729	−	1.12969i
$628$	−7.72488	+	3.93602i	−0.308256	+	0.157064i
$629$	0.351583	−	1.08206i	0.0140185	−	0.0431446i
$630$	−25.2593	−	7.58925i	−1.00636	−	0.302363i
$631$	−12.3680	−	38.0648i	−0.492363	−	1.51534i	−0.821027	−	0.570890i	$-0.806598\pi$
$631$	−12.3680	−	38.0648i	−0.492363	−	1.51534i	0.328664	−	0.944447i	$-0.393402\pi$
$632$	−10.7364	−	10.7364i	−0.427073	−	0.427073i
$633$	−2.81754	−	2.33615i	−0.111987	−	0.0928536i
$634$	7.88706	−	10.8556i	0.313235	−	0.431131i
$635$	42.8689	+	0.296112i	1.70120	+	0.0117508i
$636$	−6.77757	+	2.92398i	−0.268748	+	0.115943i
$637$	17.7282	−	2.80788i	0.702418	−	0.111252i
$638$	−9.71642	+	1.53893i	−0.384677	+	0.0609268i
$639$	−7.68105	+	1.44756i	−0.303858	+	0.0572645i
$640$	−1.81805	+	1.30180i	−0.0718648	+	0.0514582i
$641$	8.86726	−	12.2047i	0.350236	−	0.482058i	−0.597160	−	0.802122i	$-0.703704\pi$
$641$	8.86726	−	12.2047i	0.350236	−	0.482058i	0.947396	+	0.320064i	$0.103704\pi$
$642$	−5.60191	+	6.75624i	−0.221090	+	0.266648i
$643$	28.2993	+	28.2993i	1.11602	+	1.11602i	0.992320	+	0.123696i	$0.0394747\pi$
$643$	28.2993	+	28.2993i	1.11602	+	1.11602i	0.123696	+	0.992320i	$0.460525\pi$
$644$	9.48034	+	29.1775i	0.373578	+	1.14975i
$645$	−41.8806	−	16.9714i	−1.64905	−	0.668248i
$646$	1.60817	−	4.94945i	0.0632728	−	0.194734i
$647$	−16.2495	+	8.27955i	−0.638835	+	0.325503i	−0.743233	−	0.669033i	$-0.766709\pi$
$647$	−16.2495	+	8.27955i	−0.638835	+	0.325503i	0.104398	+	0.994536i	$0.466709\pi$
$648$	7.76696	−	4.54690i	0.305115	−	0.178619i
$649$			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	0.999187	+	0.0403201i	$0.0128378\pi$
$653$	11.3587	+	22.2926i	0.444499	+	0.872379i	−0.554688	+	0.832059i	$0.687162\pi$
$654$	15.0120	+	8.90057i	0.587014	+	0.348040i
$655$	−12.0211	−	24.0011i	−0.469703	−	0.937802i
$656$	1.11927	−	0.363674i	0.0437003	−	0.0141991i
$657$	−25.2402	+	9.02373i	−0.984714	+	0.352049i
$658$	20.6236	−	40.4762i	0.803993	−	1.57793i
$659$	20.1677	+	14.6527i	0.785623	+	0.570789i	0.906661	−	0.421859i	$-0.138622\pi$
$659$	20.1677	+	14.6527i	0.785623	+	0.570789i	−0.121038	+	0.992648i	$0.538622\pi$
$660$	−8.98652	−	10.3595i	−0.349800	−	0.403242i
$661$	−17.0562	+	12.3921i	−0.663411	+	0.481996i	−0.867813	−	0.496891i	$-0.834475\pi$
$661$	−17.0562	+	12.3921i	−0.663411	+	0.481996i	0.204402	+	0.978887i	$0.434475\pi$
$662$	−1.13607	−	7.17284i	−0.0441545	−	0.278780i
$663$	−0.246286	+	3.84640i	−0.00956494	+	0.149382i
$664$	6.31204	+	8.68777i	0.244955	+	0.337151i
$665$	−41.4011	−	13.7689i	−1.60547	−	0.533935i
$666$	2.85578	−	1.56173i	0.110659	−	0.0605157i
$667$	19.3154	+	9.84171i	0.747897	+	0.381072i
$668$	−5.82145	+	5.82145i	−0.225239	+	0.225239i
$669$	1.71519	+	18.3625i	0.0663129	+	0.709936i
$670$	−9.57462	+	18.4747i	−0.369900	+	0.713738i
$671$	−4.55020	−	1.47845i	−0.175659	−	0.0570750i
$672$	−1.68623	−	6.59787i	−0.0650479	−	0.254518i
$673$	11.5267	+	1.82565i	0.444321	+	0.0703736i	0.374586	−	0.927192i	$-0.377785\pi$
$673$	11.5267	+	1.82565i	0.444321	+	0.0703736i	0.0697348	+	0.997566i	$0.477785\pi$
$674$	−25.4632			−0.980806
$675$	−22.5492	−	12.9049i	−0.867917	−	0.496709i
$676$	8.49691			0.326804
$677$	−23.2090	−	3.67594i	−0.891993	−	0.141278i	−0.306419	−	0.951897i	$-0.599131\pi$
$677$	−23.2090	−	3.67594i	−0.891993	−	0.141278i	−0.585574	+	0.810619i	$0.699131\pi$
$678$	−1.61382	−	6.31453i	−0.0619783	−	0.242508i
$679$	59.5978	+	19.3645i	2.28715	+	0.743142i
$680$	−1.64655	−	1.66946i	−0.0631425	−	0.0640209i
$681$	−0.222181	−	2.37864i	−0.00851400	−	0.0911495i
$682$	3.71848	−	3.71848i	0.142388	−	0.142388i
$683$	15.4895	+	7.89232i	0.592691	+	0.301991i	0.724490	−	0.689285i	$-0.242075\pi$
$683$	15.4895	+	7.89232i	0.592691	+	0.301991i	−0.131799	+	0.991276i	$0.542075\pi$
$684$	13.0626	−	7.14349i	0.499462	−	0.273138i
$685$	17.9157	−	5.68465i	0.684523	−	0.217199i
$686$	−3.37046	−	4.63905i	−0.128685	−	0.177120i
$687$	1.83712	−	28.6914i	0.0700904	−	1.09465i
$688$	−1.82522	−	11.5240i	−0.0695859	−	0.439348i
$689$	7.31630	−	5.31560i	0.278729	−	0.202508i
$690$	2.60269	+	30.1084i	0.0990826	+	1.14621i
$691$	3.69930	+	2.68770i	0.140728	+	0.102245i	0.655922	−	0.754829i	$-0.272280\pi$
$691$	3.69930	+	2.68770i	0.140728	+	0.102245i	−0.515194	+	0.857074i	$0.672280\pi$
$692$	2.07127	−	4.06510i	0.0787380	−	0.154532i
$693$	39.3284	−	14.0605i	1.49396	−	0.534113i
$694$	−4.36272	+	1.41754i	−0.165607	+	0.0538089i
$695$	−4.24173	+	4.18354i	−0.160898	+	0.158691i
$696$	−4.13917	−	2.45411i	−0.156895	−	0.0930227i
$697$	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	$0.683348\pi$
$702$	−8.06308	+	7.52132i	−0.304321	+	0.283874i
$703$	4.79760	−	2.44450i	0.180945	−	0.0921960i
$704$	1.09422	−	3.36766i	0.0412399	−	0.126923i
$705$	28.7995	−	34.2497i	1.08465	−	1.28992i
$706$	3.77806	+	11.6277i	0.142189	+	0.437614i
$707$	7.74297	+	7.74297i	0.291204	+	0.291204i
$708$	−6.98381	+	8.42290i	−0.262468	+	0.316552i
$709$	−10.6950	+	14.7204i	−0.401659	+	0.552836i	−0.961159	−	0.275994i	$-0.910993\pi$
$709$	−10.6950	+	14.7204i	−0.401659	+	0.552836i	0.559500	+	0.828830i	$0.310993\pi$
$710$	−1.83853	+	5.52819i	−0.0689988	+	0.207469i
$711$	44.7629	−	8.43593i	1.67874	−	0.316372i
$712$	2.61410	−	0.414033i	0.0979675	−	0.0155165i
$713$	−11.4456	+	1.81280i	−0.428640	+	0.0678900i
$714$	6.55700	−	2.82882i	0.245390	−	0.105866i
$715$	13.5246	+	9.96964i	0.505791	+	0.372844i
$716$	−6.68853	+	9.20597i	−0.249962	+	0.344043i
$717$	31.6759	+	26.2639i	1.18296	+	0.980844i
$718$	23.9500	+	23.9500i	0.893807	+	0.893807i
$719$	7.53117	+	23.1785i	0.280865	+	0.864414i	0.987608	+	0.156943i	$0.0501639\pi$
$719$	7.53117	+	23.1785i	0.280865	+	0.864414i	−0.706743	+	0.707471i	$0.749836\pi$
$720$	−0.149490	−	6.70654i	−0.00557118	−	0.249938i
$721$	13.6089	−	41.8838i	0.506821	−	1.55984i
$722$	5.01554	−	2.55554i	0.186659	−	0.0951075i
$723$	−4.03925	+	10.1690i	−0.150221	+	0.378188i
$724$			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	0.342907	+	0.939369i	$0.388588\pi$
$727$	−7.37431	+	46.5595i	−0.273498	+	1.72680i	−0.616405	+	0.787429i	$0.711412\pi$
$728$	3.78778	+	7.43394i	0.140385	+	0.275520i
$729$	−1.87494	+	26.9348i	−0.0694422	+	0.997586i
$730$	−3.26164	+	19.7111i	−0.120719	+	0.729539i
$731$	11.6363	−	3.78088i	0.430385	−	0.139841i
$732$	−1.25178	−	1.97734i	−0.0462670	−	0.0730845i
$733$	21.4583	−	42.1144i	0.792582	−	1.55553i	−0.0384204	−	0.999262i	$-0.512233\pi$
$733$	21.4583	−	42.1144i	0.792582	−	1.55553i	0.831003	−	0.556268i	$-0.187767\pi$
$734$	−3.84568	−	2.79405i	−0.141947	−	0.103130i
$735$	−12.7688	−	30.1684i	−0.470986	−	1.11278i
$736$	−6.31272	+	4.58646i	−0.232690	+	0.169059i
$737$	−5.15473	−	32.5457i	−0.189877	−	1.19884i
$738$	−0.992543	+	3.38823i	−0.0365360	+	0.124723i
$739$	−14.8135	−	20.3891i	−0.544925	−	0.750025i	0.444388	−	0.895835i	$-0.353421\pi$
$739$	−14.8135	−	20.3891i	−0.544925	−	0.750025i	−0.989313	+	0.145810i	$0.953421\pi$
$740$	0.0167574	−	2.42601i	0.000616015	−	0.0891821i
$741$	−13.6959	+	12.0475i	−0.503131	+	0.442577i
$742$	−14.9294	−	7.60691i	−0.548075	−	0.279258i
$743$	35.5509	−	35.5509i	1.30424	−	1.30424i	0.378730	−	0.925507i	$-0.376361\pi$
$743$	35.5509	−	35.5509i	1.30424	−	1.30424i	0.925507	−	0.378730i	$-0.123639\pi$
$744$	2.56114	−	0.239228i	0.0938960	−	0.00877054i
$745$	−5.07746	−	33.5563i	−0.186024	−	1.22941i
$746$	35.7760	+	11.6243i	1.30985	+	0.425597i
$747$	−32.2023	+	0.940376i	−1.17822	+	0.0344066i
$748$	3.66749	+	0.580873i	0.134097	+	0.0212388i
$749$	−19.9226			−0.727958
$750$	−16.5730	+	10.0168i	−0.605159	+	0.365763i
$751$	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
$753$	−23.2089	+	5.93157i	−0.845781	+	0.216158i
$754$	5.60695	+	1.82181i	0.204193	+	0.0663463i
$755$	4.38172	+	28.9583i	0.159467	+	1.05390i
$756$	19.1989	+	6.98439i	0.698256	+	0.254020i
$757$	18.1299	−	18.1299i	0.658942	−	0.658942i	−0.296188	−	0.955130i	$-0.595715\pi$
$757$	18.1299	−	18.1299i	0.658942	−	0.658942i	0.955130	+	0.296188i	$0.0957154\pi$
$758$	14.4898	+	7.38292i	0.526293	+	0.268160i
$759$	−31.6082	−	35.9328i	−1.14730	−	1.30428i
$760$	0.0766500	−	11.0968i	0.00278039	−	0.402524i
$761$	−20.5807	−	28.3270i	−0.746052	−	1.02685i	−0.998248	−	0.0591757i	$-0.981153\pi$
$761$	−20.5807	−	28.3270i	−0.746052	−	1.02685i	0.252196	−	0.967676i	$-0.418847\pi$
$762$	−33.1390	−	2.12190i	−1.20050	−	0.0768683i
$763$	6.19733	+	39.1284i	0.224358	+	1.41654i
$764$	0.481552	−	0.349868i	0.0174219	−	0.0126578i
$765$	6.92164	−	1.25500i	0.250253	−	0.0453745i
$766$	−25.6681	−	18.6490i	−0.927426	−	0.673814i
$767$	6.08587	−	11.9442i	0.219748	−	0.431280i
$768$	1.46345	−	0.926454i	0.0528077	−	0.0334305i
$769$	−23.9043	+	7.76696i	−0.862010	+	0.280084i	−0.706468	−	0.707745i	$-0.749712\pi$
$769$	−23.9043	+	7.76696i	−0.862010	+	0.280084i	−0.155542	+	0.987829i	$0.549712\pi$
$770$	5.08218	−	30.7131i	0.183149	−	1.10682i
$771$	16.2344	−	27.3815i	0.584669	−	0.986119i
$772$	−10.0023	−	19.6306i	−0.359991	−	0.706522i
$773$	4.41320	−	27.8639i	0.158732	−	1.00219i	−0.771769	−	0.635903i	$-0.780628\pi$
$773$	4.41320	−	27.8639i	0.158732	−	1.00219i	0.930501	−	0.366290i	$-0.119372\pi$
$774$	31.6384	+	14.9739i	1.13722	+	0.538224i
$775$	−4.28123	−	6.06712i	−0.153786	−	0.217938i
$776$			15.9383i			0.572151i
$777$	6.86672	+	2.72756i	0.246342	+	0.0978506i
$778$	9.83601	−	5.01170i	0.352638	−	0.179678i
$779$	−1.80483	+	5.55469i	−0.0646647	+	0.199018i
$780$	1.98000	+	7.97659i	0.0708955	+	0.285608i
$781$	−2.85090	−	8.77417i	−0.102013	−	0.313964i
$782$	−5.78590	−	5.78590i	−0.206903	−	0.206903i
$783$	13.0825	−	6.10298i	0.467530	−	0.218103i
$784$	4.97175	−	6.84302i	0.177562	−	0.244394i
$785$	−15.6048	−	11.5031i	−0.556959	−	0.410562i
$786$	8.23657	+	19.0918i	0.293789	+	0.680981i
$787$	1.75927	−	0.278640i	0.0627111	−	0.00993245i	−0.125000	−	0.992157i	$-0.539893\pi$
$787$	1.75927	−	0.278640i	0.0627111	−	0.00993245i	0.187711	+	0.982224i	$0.439893\pi$
$788$	−2.78623	+	0.441295i	−0.0992553	+	0.0157205i
$789$	6.04915	+	14.0215i	0.215356	+	0.499178i
$790$	10.7144	−	32.2166i	0.381201	−	1.14622i
$791$	8.69603	−	11.9691i	0.309195	−	0.425571i
$792$	6.49218	+	8.40818i	0.230690	+	0.298772i
$793$	2.02742	+	2.02742i	0.0719957	+	0.0719957i
$794$	−4.61434	−	14.2015i	−0.163757	−	0.503991i
$795$	−12.6328	−	10.6225i	−0.448039	−	0.376742i
$796$	3.23939	−	9.96982i	0.114817	−	0.353371i
$797$	36.0903	−	18.3889i	1.27839	−	0.651370i	0.322907	−	0.946431i	$-0.395340\pi$
$797$	36.0903	−	18.3889i	1.27839	−	0.651370i	0.955478	+	0.295061i	$0.0953400\pi$
$798$	31.4090	+	12.4761i	1.11187	+	0.441649i
$799$			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
$804$	8.22017	−	13.8644i	0.289903	−	0.488958i
$805$	−48.8417	+	48.1716i	−1.72144	+	1.69783i
$806$	−2.99723	+	0.973861i	−0.105573	+	0.0343028i
$807$	0.223414	−	0.141435i	0.00786456	−	0.00497875i
$808$	−1.26441	+	2.48154i	−0.0444816	+	0.0873001i
$809$	−9.80668	−	7.12497i	−0.344784	−	0.250501i	0.401893	−	0.915686i	$-0.368352\pi$
$809$	−9.80668	−	7.12497i	−0.344784	−	0.250501i	−0.746678	+	0.665186i	$0.768352\pi$
$810$	16.8683	+	10.9755i	0.592691	+	0.385639i
$811$	−34.3371	+	24.9474i	−1.20574	+	0.876020i	−0.994837	−	0.101487i	$-0.967640\pi$
$811$	−34.3371	+	24.9474i	−1.20574	+	0.876020i	−0.210902	+	0.977507i	$0.567640\pi$
$812$	−1.70876	−	10.7887i	−0.0599656	−	0.378608i
$813$	21.2495	+	1.36061i	0.745254	+	0.0477187i
$814$	2.25818	+	3.10812i	0.0791493	+	0.108940i
$815$	10.5061	−	3.33359i	0.368013	−	0.116771i
$816$	1.19963	+	1.36376i	0.0419953	+	0.0477411i
$817$	51.5927	+	26.2878i	1.80500	+	0.919693i
$818$	19.0319	−	19.0319i	0.665434	−	0.665434i
$819$	−24.8255	−	3.19225i	−0.867474	−	0.111546i
$820$	1.84790	+	1.87361i	0.0645316	+	0.0654293i
$821$	32.4922	+	10.5573i	1.13398	+	0.368454i	0.815089	−	0.579336i	$-0.196688\pi$
$821$	32.4922	+	10.5573i	1.13398	+	0.368454i	0.318896	+	0.947790i	$0.396688\pi$
$822$	−14.1059	+	3.60507i	−0.491999	+	0.125741i
$823$	−0.223643	−	0.0354216i	−0.00779572	−	0.00123472i	0.152535	−	0.988298i	$-0.451256\pi$
$823$	−0.223643	−	0.0354216i	−0.00779572	−	0.00123472i	−0.160331	+	0.987063i	$0.551256\pi$
$824$	11.2010			0.390206
$825$	11.7131	−	28.3405i	0.407797	−	0.986691i
$826$	−24.8372			−0.864198
$827$	−6.61308	−	1.04741i	−0.229959	−	0.0364220i	0.0403912	−	0.999184i	$-0.487140\pi$
$827$	−6.61308	−	1.04741i	−0.229959	−	0.0364220i	−0.270351	+	0.962762i	$0.587140\pi$
$828$	−0.683297	−	23.3989i	−0.0237462	−	0.813167i
$829$	33.2782	+	10.8127i	1.15580	+	0.375542i	0.823325	−	0.567570i	$-0.192116\pi$
$829$	33.2782	+	10.8127i	1.15580	+	0.375542i	0.332475	+	0.943112i	$0.392116\pi$
$830$	−11.0489	+	21.3194i	−0.383514	+	0.740008i
$831$	−7.50714	+	0.701219i	−0.260420	+	0.0243250i
$832$	−1.50051	+	1.50051i	−0.0520210	+	0.0520210i
$833$	7.90311	+	4.02683i	0.273826	+	0.139522i
$834$	3.46502	−	3.04799i	0.119984	−	0.105543i
$835$	−17.4683	−	5.80950i	−0.604516	−	0.201046i
$836$	10.3291	+	14.2168i	0.357241	+	0.491700i
$837$	−3.74015	+	6.74991i	−0.129278	+	0.233311i
$838$	−3.02247	−	19.0831i	−0.104410	−	0.659216i
$839$	−27.8283	+	20.2184i	−0.960739	+	0.698018i	−0.953322	−	0.301955i	$-0.902361\pi$
$839$	−27.8283	+	20.2184i	−0.960739	+	0.698018i	−0.00741655	+	0.999972i	$0.502361\pi$
$840$	11.5027	−	9.97821i	0.396880	−	0.344281i
$841$	17.2171	+	12.5090i	0.593695	+	0.431344i
$842$	3.16961	−	6.22070i	0.109232	−	0.214380i
$843$	20.5008	+	32.3836i	0.706086	+	1.11535i
$844$	2.00972	−	0.652997i	0.0691774	−	0.0224771i
$845$	8.50853	+	16.9880i	0.292702	+	0.584405i
$846$	−23.7840	+	25.2149i	−0.817712	+	0.866907i
$847$	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
$852$	1.66590	−	4.19398i	0.0570730	−	0.143683i
$853$	−26.7503	+	13.6300i	−0.915914	+	0.466682i	−0.847392	−	0.530968i	$-0.821828\pi$
$853$	−26.7503	+	13.6300i	−0.915914	+	0.466682i	−0.0685222	+	0.997650i	$0.521828\pi$
$854$	1.64160	−	5.05233i	0.0561745	−	0.172887i
$855$	27.3626	+	18.9631i	0.935780	+	0.648523i
$856$	−1.56584	−	4.81915i	−0.0535192	−	0.164715i
$857$	−4.67908	−	4.67908i	−0.159834	−	0.159834i	0.622659	−	0.782493i	$-0.286052\pi$
$857$	−4.67908	−	4.67908i	−0.159834	−	0.159834i	−0.782493	+	0.622659i	$0.786052\pi$
$858$	−10.0189	−	8.30708i	−0.342038	−	0.283599i
$859$	10.4601	−	14.3971i	0.356895	−	0.491224i	−0.592385	−	0.805655i	$-0.701814\pi$
$859$	10.4601	−	14.3971i	0.356895	−	0.491224i	0.949280	+	0.314431i	$0.101814\pi$
$860$	21.2124	−	15.1890i	0.723336	−	0.517939i
$861$	−7.35882	+	3.17474i	−0.250788	+	0.108195i
$862$	−11.9173	+	1.88752i	−0.405906	+	0.0642892i
$863$	−39.7649	+	6.29813i	−1.35361	+	0.214391i	−0.790739	−	0.612153i	$-0.790304\pi$
$863$	−39.7649	+	6.29813i	−1.35361	+	0.214391i	−0.562872	+	0.826544i	$0.690304\pi$
$864$	−0.180525	+	5.19302i	−0.00614159	+	0.176670i
$865$	10.2015	+	0.0704659i	0.346862	+	0.00239591i
$866$	−14.3388	+	19.7357i	−0.487254	+	0.670647i
$867$	17.5784	−	21.2006i	0.596992	−	0.720010i
$868$	4.12883	+	4.12883i	0.140142	+	0.140142i
$869$	16.6142	+	51.1332i	0.563598	+	1.73458i
$870$	0.761707	−	10.7330i	0.0258243	−	0.363881i
$871$	−6.10224	+	18.7808i	−0.206767	+	0.636362i
$872$	−8.97781	+	4.57442i	−0.304027	+	0.154909i
$873$	−39.4869	−	26.9637i	−1.33643	−	0.912584i
$874$		−	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	−0.707753	−	0.706460i	$-0.750291\pi$
$877$	5.43919	−	34.3417i	0.183668	−	1.15964i	0.891421	−	0.453176i	$-0.149709\pi$
$878$	−3.36553	−	6.60523i	−0.113581	−	0.222916i
$879$	11.9966	+	7.11275i	0.404634	+	0.239907i
$880$	7.82873	−	1.18458i	0.263906	−	0.0399321i
$881$	−23.3423	+	7.58438i	−0.786423	+	0.255524i	−0.674580	−	0.738202i	$-0.735675\pi$
$881$	−23.3423	+	7.58438i	−0.786423	+	0.255524i	−0.111843	+	0.993726i	$0.535675\pi$
$882$	8.54251	+	23.8942i	0.287641	+	0.804559i
$883$	−10.4732	+	20.5549i	−0.352452	+	0.691726i	−0.997366	−	0.0725286i	$-0.976893\pi$
$883$	−10.4732	+	20.5549i	−0.352452	+	0.691726i	0.644914	+	0.764255i	$0.276893\pi$
$884$	−1.80028	−	1.30798i	−0.0605499	−	0.0439921i
$885$	−23.8334	−	5.52841i	−0.801151	−	0.185836i
$886$	−0.588493	+	0.427565i	−0.0197708	+	0.0143643i
$887$	8.06436	+	50.9164i	0.270775	+	1.70960i	0.630202	+	0.776431i	$0.282972\pi$
$887$	8.06436	+	50.9164i	0.270775	+	1.70960i	−0.359428	+	0.933173i	$0.617028\pi$
$888$	−0.120081	+	1.87539i	−0.00402967	+	0.0629339i
$889$	−44.3067	−	60.9829i	−1.48600	−	2.04530i
$890$	3.44546	+	4.81181i	0.115492	+	0.161292i
$891$	−31.8144	+	1.85968i	−1.06582	+	0.0623016i
$892$	−9.48721	−	4.83398i	−0.317655	−	0.161854i
$893$	−40.5457	+	40.5457i	−1.35681	+	1.35681i
$894$	2.44489	+	26.1745i	0.0817692	+	0.875408i
$895$	−25.1033	−	4.15392i	−0.839112	−	0.138850i
$896$	3.73929	+	1.21497i	0.124921	+	0.0405893i
$897$	7.10149	+	27.7866i	0.237112	+	0.927767i
$898$	−29.3299	−	4.64540i	−0.978752	−	0.155019i
$899$	4.12595			0.137608
$900$	13.2588	−	7.01459i	0.441960	−	0.233820i
$901$	4.46895			0.148882
$902$	−4.11596	−	0.651904i	−0.137047	−	0.0217060i
$903$	19.6744	+	76.9816i	0.654722	+	2.56179i
$904$	3.57871	+	1.16279i	0.119026	+	0.0386739i
$905$	−13.0543	+	6.53832i	−0.433940	+	0.217341i
$906$	−2.10987	−	22.5880i	−0.0700959	−	0.750435i
$907$	−34.2493	+	34.2493i	−1.13723	+	1.13723i	−0.148284	+	0.988945i	$0.547375\pi$
$907$	−34.2493	+	34.2493i	−1.13723	+	1.13723i	−0.988945	+	0.148284i	$0.952625\pi$
$908$	1.22895	+	0.626182i	0.0407842	+	0.0207806i
$909$	−4.00891	−	7.33071i	−0.132967	−	0.243144i
$910$	−11.0698	+	15.0171i	−0.366961	+	0.497811i
$911$	−28.4251	−	39.1238i	−0.941766	−	1.29623i	−0.955089	−	0.296318i	$-0.904241\pi$
$911$	−28.4251	−	39.1238i	−0.941766	−	1.29623i	0.0133232	−	0.999911i	$-0.495759\pi$
$912$	−0.549264	+	8.57820i	−0.0181879	+	0.284053i
$913$	−5.94847	−	37.5571i	−0.196865	−	1.24296i
$914$	−3.06979	+	2.23033i	−0.101540	+	0.0737728i
$915$	2.69983	−	4.48274i	0.0892537	−	0.148195i
$916$	13.4288	+	9.75661i	0.443701	+	0.322367i
$917$	−21.4279	+	42.0547i	−0.707612	+	1.38877i
$918$	−5.40818	+	0.664905i	−0.178496	+	0.0219452i
$919$	2.05593	−	0.668012i	0.0678189	−	0.0220357i	−0.274911	−	0.961470i	$-0.588648\pi$
$919$	2.05593	−	0.668012i	0.0678189	−	0.0220357i	0.342730	+	0.939434i	$0.388648\pi$
$920$	−15.4911	−	8.02839i	−0.510728	−	0.264688i
$921$	13.8607	+	8.21797i	0.456724	+	0.270791i
$922$	−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
$927$	−18.9494	+	27.7504i	−0.622381	+	0.911442i
$928$	2.47540	−	1.26128i	0.0812591	−	0.0414036i
$929$	0.0671055	−	0.206530i	0.00220166	−	0.00677602i	−0.949950	−	0.312403i	$-0.898866\pi$
$929$	0.0671055	−	0.206530i	0.00220166	−	0.00677602i	0.952151	+	0.305627i	$0.0988661\pi$
$930$	3.04294	+	4.88097i	0.0997818	+	0.160053i
$931$	12.9717	+	39.9228i	0.425130	+	1.30842i
$932$	17.5535	+	17.5535i	0.574984	+	0.574984i
$933$	12.5935	−	15.1885i	0.412291	−	0.497249i
$934$	−2.63135	+	3.62175i	−0.0861006	+	0.118507i
$935$	2.51115	+	7.91413i	0.0821235	+	0.258820i
$936$	−1.17900	−	6.25602i	−0.0385368	−	0.204484i
$937$	−14.9705	+	2.37109i	−0.489065	+	0.0774603i	−0.396097	−	0.918209i	$-0.629635\pi$
$937$	−14.9705	+	2.37109i	−0.489065	+	0.0774603i	−0.0929682	+	0.995669i	$0.529635\pi$
$938$	36.1372	−	5.72357i	1.17992	−	0.186881i
$939$	38.0615	−	16.4205i	1.24209	−	0.535862i
$940$	7.81377	+	24.6258i	0.254857	+	0.803205i
$941$	17.7384	−	24.4148i	0.578256	−	0.795901i	−0.415247	−	0.909709i	$-0.636305\pi$
$941$	17.7384	−	24.4148i	0.578256	−	0.795901i	0.993503	+	0.113808i	$0.0363048\pi$
$942$	11.5598	+	9.58478i	0.376640	+	0.312289i
$943$	6.49342	+	6.49342i	0.211455	+	0.211455i
$944$	−1.95210	−	6.00796i	−0.0635356	−	0.195542i
$945$	5.26112	+	45.3785i	0.171144	+	1.47616i
$946$	−12.7670	+	39.2926i	−0.415089	+	1.27751i
$947$	15.9210	−	8.11213i	0.517362	−	0.263609i	−0.175756	−	0.984434i	$-0.556237\pi$
$947$	15.9210	−	8.11213i	0.517362	−	0.263609i	0.693117	+	0.720825i	$0.256237\pi$
$948$	−9.70839	+	24.4412i	−0.315314	+	0.793814i
$949$			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	−0.994905	−	0.100815i	$-0.967855\pi$
$953$	−15.1784	−	29.7892i	−0.491676	−	0.964968i	0.503230	−	0.864153i	$-0.332145\pi$
$954$	9.30037	+	8.77260i	0.301111	+	0.284024i
$955$	1.18171	+	0.612427i	0.0382391	+	0.0198177i
$956$	−22.5941	+	7.34126i	−0.730744	+	0.237433i
$957$	9.11403	+	14.3967i	0.294615	+	0.465380i
$958$	13.7500	−	26.9860i	0.444244	−	0.871877i
$959$	−26.7374	−	19.4259i	−0.863396	−	0.627294i
$960$	3.31772	+	1.99818i	0.107079	+	0.0644908i
$961$	23.2952	−	16.9249i	0.751458	−	0.545966i
$962$	−0.360169	−	2.27402i	−0.0116123	−	0.0733173i
$963$	14.5884	+	4.27350i	0.470105	+	0.137712i
$964$	−3.71319	−	5.11077i	−0.119594	−	0.164607i
$965$	29.2318	−	39.6552i	0.941006	−	1.27655i
$966$	39.8982	−	35.0962i	1.28370	−	1.12920i
$967$	−24.4672	−	12.4667i	−0.786814	−	0.400902i	0.0139344	−	0.999903i	$-0.495564\pi$
$967$	−24.4672	−	12.4667i	−0.786814	−	0.400902i	−0.800748	+	0.599001i	$0.795564\pi$
$968$	−1.08784	+	1.08784i	−0.0349644	+	0.0349644i
$969$	−8.97481	+	0.838309i	−0.288312	+	0.0269304i
$970$	−31.8656	+	15.9601i	−1.02314	+	0.512447i
$971$	−53.0240	−	17.2285i	−1.70162	−	0.552890i	−0.712718	−	0.701450i	$-0.752536\pi$
$971$	−53.0240	−	17.2285i	−1.70162	−	0.552890i	−0.988903	+	0.148560i	$0.952536\pi$
$972$	−12.5602	−	9.23258i	−0.402870	−	0.296135i
$973$	10.3466	+	1.63874i	0.331696	+	0.0525355i
$974$	−0.555561			−0.0178013
$975$	−13.9650	+	11.9461i	−0.447238	+	0.382583i
$976$	1.35115			0.0432492
$977$	−41.8568	−	6.62946i	−1.33912	−	0.212095i	−0.554556	−	0.832147i	$-0.687112\pi$
$977$	−41.8568	−	6.62946i	−1.33912	−	0.212095i	−0.784561	+	0.620051i	$0.787112\pi$
$978$	−8.27196	+	2.11409i	−0.264508	+	0.0676010i
$979$	−8.91312	−	2.89605i	−0.284865	−	0.0925582i
$980$	18.6599	+	3.08771i	0.596069	+	0.0986332i
$981$	3.85521	−	29.9812i	0.123088	−	0.957227i
$982$	4.47973	−	4.47973i	0.142954	−	0.142954i
$983$	−36.2358	−	18.4631i	−1.15574	−	0.588880i	−0.232310	−	0.972642i	$-0.574628\pi$
$983$	−36.2358	−	18.4631i	−1.15574	−	0.588880i	−0.923432	+	0.383761i	$0.874628\pi$
$984$	−1.34632	−	1.53053i	−0.0429192	−	0.0487914i
$985$	−3.67233	−	5.12865i	−0.117010	−	0.163412i
$986$	1.71242	+	2.35694i	0.0545346	+	0.0750604i
$987$	−78.5219	−	5.02777i	−2.49938	−	0.160036i
$988$	−1.64745	−	10.4016i	−0.0524123	−	0.330918i
$989$	73.6546	−	53.5132i	2.34208	−	1.70162i
$990$	−10.3095	+	21.3996i	−0.327659	+	0.680124i
$991$	8.75570	+	6.36139i	0.278134	+	0.202076i	0.718103	−	0.695937i	$-0.245011\pi$
$991$	8.75570	+	6.36139i	0.278134	+	0.202076i	−0.439969	+	0.898013i	$0.645011\pi$
$992$	−0.674227	+	1.32324i	−0.0214067	+	0.0420130i
$993$	−10.6279	+	6.72814i	−0.337267	+	0.213511i
$994$	9.74243	−	3.16551i	0.309011	−	0.100404i
$995$	23.1766	−	3.50689i	0.734749	−	0.111176i
$996$	9.48592	−	15.9992i	0.300573	−	0.506955i
$997$	1.54339	+	3.02908i	0.0488797	+	0.0959319i	0.914154	−	0.405366i	$-0.132856\pi$
$997$	1.54339	+	3.02908i	0.0488797	+	0.0959319i	−0.865275	+	0.501298i	$0.832856\pi$
$998$	−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.23.7	yes	80
3.2	odd	2	inner	150.2.l.a.23.4	✓	80
5.2	odd	4		750.2.l.c.407.1		80
5.3	odd	4		750.2.l.a.407.10		80
5.4	even	2		750.2.l.b.593.4		80
15.2	even	4		750.2.l.c.407.10		80
15.8	even	4		750.2.l.a.407.1		80
15.14	odd	2		750.2.l.b.593.7		80
25.9	even	10		750.2.l.a.293.1		80
25.12	odd	20	inner	150.2.l.a.137.4	yes	80
25.13	odd	20		750.2.l.b.707.7		80
25.16	even	5		750.2.l.c.293.10		80
75.38	even	20		750.2.l.b.707.4		80
75.41	odd	10		750.2.l.c.293.1		80
75.59	odd	10		750.2.l.a.293.10		80
75.62	even	20	inner	150.2.l.a.137.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.23.4	✓	80	3.2	odd	2	inner
150.2.l.a.23.7	yes	80	1.1	even	1	trivial
150.2.l.a.137.4	yes	80	25.12	odd	20	inner
150.2.l.a.137.7	yes	80	75.62	even	20	inner
750.2.l.a.293.1		80	25.9	even	10
750.2.l.a.293.10		80	75.59	odd	10
750.2.l.a.407.1		80	15.8	even	4
750.2.l.a.407.10		80	5.3	odd	4
750.2.l.b.593.4		80	5.4	even	2
750.2.l.b.593.7		80	15.14	odd	2
750.2.l.b.707.4		80	75.38	even	20
750.2.l.b.707.7		80	25.13	odd	20
750.2.l.c.293.1		80	75.41	odd	10
750.2.l.c.293.10		80	25.16	even	5
750.2.l.c.407.1		80	5.2	odd	4
750.2.l.c.407.10		80	15.2	even	4

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)

\(f(q)\)	\(=\)	\(q+(0.987688 + 0.156434i) q^{2} +(-0.428879 - 1.67811i) q^{3} +(0.951057 + 0.309017i) q^{4} +(0.334535 + 2.21090i) q^{5} +(-0.161084 - 1.72454i) q^{6} +(2.78015 - 2.78015i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.63213 + 1.43942i) q^{9} +O(q^{10})\)	\(q+(0.987688 + 0.156434i) q^{2} +(-0.428879 - 1.67811i) q^{3} +(0.951057 + 0.309017i) q^{4} +(0.334535 + 2.21090i) q^{5} +(-0.161084 - 1.72454i) q^{6} +(2.78015 - 2.78015i) q^{7} +(0.891007 + 0.453990i) q^{8} +(-2.63213 + 1.43942i) q^{9} +(-0.0154450 + 2.23601i) q^{10} +(-2.08133 - 2.86470i) q^{11} +(0.110677 - 1.72851i) q^{12} +(0.331962 + 2.09592i) q^{13} +(3.18083 - 2.31101i) q^{14} +(3.56667 - 1.50960i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-0.476073 + 0.934346i) q^{17} +(-2.82489 + 1.00994i) q^{18} +(-4.71987 + 1.53358i) q^{19} +(-0.365045 + 2.20607i) q^{20} +(-5.85775 - 3.47305i) 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} +(3.54437 + 3.79967i) q^{27} +(3.50319 - 1.78496i) q^{28} +(0.858514 - 2.64223i) q^{29} +(3.75891 - 0.933062i) q^{30} +(0.458925 + 1.41243i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.91465 + 4.72131i) q^{33} +(-0.616376 + 0.848368i) q^{34} +(7.07669 + 5.21658i) q^{35} +(-2.94810 + 0.555594i) q^{36} +(-1.07161 + 0.169727i) q^{37} +(-4.90167 + 0.776348i) q^{38} +(3.37482 - 1.45597i) q^{39} +(-0.705656 + 2.12180i) q^{40} +(0.691749 - 0.952111i) q^{41} +(-5.24232 - 4.34665i) q^{42} +(-8.25027 - 8.25027i) q^{43} +(-1.09422 - 3.36766i) q^{44} +(-4.06294 - 5.33784i) q^{45} +(-2.41124 + 7.42105i) q^{46} +(10.2948 - 5.24545i) q^{47} +(0.639399 - 1.60971i) 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} +(2.90633 + 4.30735i) q^{54} +(5.63730 - 5.55995i) q^{55} +(3.73929 - 1.21497i) q^{56} +(4.59778 + 7.26276i) q^{57} +(1.26128 - 2.47540i) q^{58} +(-5.11067 - 3.71312i) q^{59} +(3.85859 - 0.333552i) q^{60} +(1.09310 - 0.794185i) q^{61} +(0.232323 + 1.46683i) q^{62} +(-3.31591 + 11.3195i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-4.52283 + 1.43509i) q^{65} +(-4.60503 + 4.05080i) q^{66} +(8.29150 + 4.22473i) q^{67} +(-0.741501 + 0.741501i) q^{68} +(13.4565 - 1.25693i) q^{69} +(6.17351 + 6.25939i) q^{70} +(2.47790 + 0.805120i) q^{71} +(-2.99872 + 0.0875690i) q^{72} +(8.82492 + 1.39773i) q^{73} -1.08497 q^{74} +(4.53075 + 7.38054i) q^{75} -4.96277 q^{76} +(-13.7507 - 2.17789i) q^{77} +(3.56104 - 0.910103i) q^{78} +(-14.4405 - 4.69199i) q^{79} +(-1.02889 + 1.98529i) q^{80} +(4.85616 - 7.57744i) q^{81} +(0.832175 - 0.832175i) q^{82} +(9.56823 + 4.87526i) q^{83} +(-4.49782 - 5.11321i) q^{84} +(-2.22501 - 0.739979i) q^{85} +(-6.85807 - 9.43932i) q^{86} +(-4.80216 - 0.307484i) q^{87} +(-0.553929 - 3.49737i) q^{88} +(2.14121 - 1.55568i) q^{89} +(-3.17790 - 5.90770i) q^{90} +(6.74988 + 4.90407i) q^{91} +(-3.54247 + 6.95248i) q^{92} +(2.17339 - 1.37589i) q^{93} +(10.9886 - 3.57041i) q^{94} +(-4.96956 - 9.92214i) q^{95} +(0.883341 - 1.48987i) 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

Modular forms

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