LMFDB - Embedded newform 552.2.x.a.35.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(35,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 11, 20]))

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

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

chi := DirichletCharacter("552.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.x (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$920$
Relative dimension:	$92$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			35.18
Character	$\chi$	$=$	552.35
Dual form			552.2.x.a.347.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20136 + 0.746150i) q^{2} +(-0.910347 + 1.47352i) q^{3} +(0.886521 - 1.79279i) q^{4} +(-3.47534 + 1.02045i) q^{5} +(-0.00581645 - 2.44948i) q^{6} +(-3.08702 + 2.67492i) q^{7} +(0.272658 + 2.81525i) q^{8} +(-1.34254 - 2.68283i) q^{9} +O(q^{10})$	\(q+(-1.20136 + 0.746150i) q^{2} +(-0.910347 + 1.47352i) q^{3} +(0.886521 - 1.79279i) q^{4} +(-3.47534 + 1.02045i) q^{5} +(-0.00581645 - 2.44948i) q^{6} +(-3.08702 + 2.67492i) q^{7} +(0.272658 + 2.81525i) q^{8} +(-1.34254 - 2.68283i) q^{9} +(3.41372 - 3.81905i) q^{10} +(-3.11829 + 4.85215i) q^{11} +(1.83467 + 2.93837i) q^{12} +(3.13718 + 2.71838i) q^{13} +(1.71273 - 5.51692i) q^{14} +(1.66011 - 6.04996i) q^{15} +(-2.42816 - 3.17868i) q^{16} +(0.187820 - 0.0857744i) q^{17} +(3.61466 + 2.22131i) q^{18} +(-0.0995334 + 0.217948i) q^{19} +(-1.25151 + 7.13520i) q^{20} +(-1.13129 - 6.98390i) q^{21} +(0.125748 - 8.15588i) q^{22} +(2.87802 - 3.83628i) q^{23} +(-4.39655 - 2.16109i) q^{24} +(6.83041 - 4.38964i) q^{25} +(-5.79720 - 0.924943i) q^{26} +(5.17539 + 0.464048i) q^{27} +(2.05885 + 7.90574i) q^{28} +(-1.06462 - 2.33120i) q^{29} +(2.51980 + 8.50686i) q^{30} +(-7.48287 + 1.07587i) q^{31} +(5.28886 + 2.00697i) q^{32} +(-4.31103 - 9.01201i) q^{33} +(-0.161638 + 0.243187i) q^{34} +(7.99883 - 12.4464i) q^{35} +(-5.99993 + 0.0284946i) q^{36} +(1.24263 - 4.23200i) q^{37} +(-0.0430464 - 0.336100i) q^{38} +(-6.86152 + 2.14804i) q^{39} +(-3.82041 - 9.50574i) q^{40} +(1.14875 + 3.91228i) q^{41} +(6.57013 + 7.54605i) q^{42} +(-1.10955 + 7.71709i) q^{43} +(5.93444 + 9.89196i) q^{44} +(7.40348 + 7.95377i) q^{45} +(-0.595090 + 6.75617i) q^{46} +0.440853 q^{47} +(6.89433 - 0.684245i) q^{48} +(1.37831 - 9.58634i) q^{49} +(-4.93044 + 10.3700i) q^{50} +(-0.0445905 + 0.354841i) q^{51} +(7.65465 - 3.21439i) q^{52} +(1.39554 + 1.61054i) q^{53} +(-6.56374 + 3.30413i) q^{54} +(5.88573 - 20.0450i) q^{55} +(-8.37228 - 7.96142i) q^{56} +(-0.230541 - 0.345073i) q^{57} +(3.01842 + 2.00624i) q^{58} +(3.90630 + 3.38483i) q^{59} +(-9.37456 - 8.33963i) q^{60} +(-5.95381 + 0.856029i) q^{61} +(8.18684 - 6.87585i) q^{62} +(11.3208 + 4.69079i) q^{63} +(-7.85132 + 1.53520i) q^{64} +(-13.6768 - 6.24597i) q^{65} +(11.9034 + 7.60997i) q^{66} +(4.46017 - 2.86638i) q^{67} +(0.0127310 - 0.412761i) q^{68} +(3.03285 + 7.73316i) q^{69} +(-0.322562 + 20.9209i) q^{70} +(5.47698 - 3.51984i) q^{71} +(7.18680 - 4.51108i) q^{72} +(1.34371 - 2.94232i) q^{73} +(1.66487 + 6.01133i) q^{74} +(0.250190 + 14.0609i) q^{75} +(0.302495 + 0.371657i) q^{76} +(-3.35289 - 23.3199i) q^{77} +(6.64038 - 7.70028i) q^{78} +(5.31766 + 4.60778i) q^{79} +(11.6824 + 8.56919i) q^{80} +(-5.39518 + 7.20361i) q^{81} +(-4.29920 - 3.84291i) q^{82} +(-3.12115 + 10.6297i) q^{83} +(-13.5236 - 4.16321i) q^{84} +(-0.565209 + 0.489756i) q^{85} +(-4.42514 - 10.0989i) q^{86} +(4.40425 + 0.553453i) q^{87} +(-14.5103 - 7.45580i) q^{88} +(4.58957 + 0.659881i) q^{89} +(-14.8289 - 4.03121i) q^{90} -16.9560 q^{91} +(-4.32620 - 8.56061i) q^{92} +(5.22668 - 12.0056i) q^{93} +(-0.529622 + 0.328942i) q^{94} +(0.123507 - 0.859012i) q^{95} +(-7.77201 + 5.96623i) q^{96} +(-12.9092 + 3.79049i) q^{97} +(5.49700 + 12.5450i) q^{98} +(17.2039 + 1.85165i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9}+O(q^{10}) $ 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9	$ 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9} - 14 q^{10} - 6 q^{12} - 30 q^{16} - 16 q^{18} - 52 q^{19} - 32 q^{22} - 26 q^{24} - 112 q^{25} - 30 q^{27} - 34 q^{28} + 11 q^{30} - 30 q^{33} - 88 q^{34} - 18 q^{36} + 124 q^{40} - 3 q^{42} - 36 q^{43} - 110 q^{46} + 32 q^{49} - 30 q^{51} + 90 q^{52} - 39 q^{54} - 6 q^{57} - 68 q^{58} + 13 q^{60} + 28 q^{64} - 46 q^{66} - 100 q^{67} - 92 q^{70} + 29 q^{72} - 36 q^{73} + 14 q^{75} - 50 q^{76} - 86 q^{78} - 2 q^{81} - 12 q^{82} - 151 q^{84} - 42 q^{88} - 196 q^{90} - 136 q^{91} - 68 q^{94} - 175 q^{96} - 36 q^{97} - 54 q^{99}+O(q^{100}) $ 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9 - 14 * q^10 - 6 * q^12 - 30 * q^16 - 16 * q^18 - 52 * q^19 - 32 * q^22 - 26 * q^24 - 112 * q^25 - 30 * q^27 - 34 * q^28 + 11 * q^30 - 30 * q^33 - 88 * q^34 - 18 * q^36 + 124 * q^40 - 3 * q^42 - 36 * q^43 - 110 * q^46 + 32 * q^49 - 30 * q^51 + 90 * q^52 - 39 * q^54 - 6 * q^57 - 68 * q^58 + 13 * q^60 + 28 * q^64 - 46 * q^66 - 100 * q^67 - 92 * q^70 + 29 * q^72 - 36 * q^73 + 14 * q^75 - 50 * q^76 - 86 * q^78 - 2 * q^81 - 12 * q^82 - 151 * q^84 - 42 * q^88 - 196 * q^90 - 136 * q^91 - 68 * q^94 - 175 * q^96 - 36 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−1.20136	+	0.746150i	−0.849488	+	0.527608i
$2$	−1.20136	+	0.746150i	−0.849488	+	0.527608i
$3$	−0.910347	+	1.47352i	−0.525589	+	0.850739i
$3$	−0.910347	+	1.47352i	−0.525589	+	0.850739i
$4$	0.886521	−	1.79279i	0.443261	−	0.896393i
$5$	−3.47534	+	1.02045i	−1.55422	+	0.456360i	−0.942359	−	0.334604i	$-0.891397\pi$
$5$	−3.47534	+	1.02045i	−1.55422	+	0.456360i	−0.611862	+	0.790965i	$0.709579\pi$
$6$	−0.00581645	−	2.44948i	−0.00237455	−	0.999997i
$7$	−3.08702	+	2.67492i	−1.16679	+	1.01103i	−0.167100	+	0.985940i	$0.553440\pi$
$7$	−3.08702	+	2.67492i	−1.16679	+	1.01103i	−0.999685	+	0.0250851i	$0.992014\pi$
$8$	0.272658	+	2.81525i	0.0963990	+	0.995343i
$9$	−1.34254	−	2.68283i	−0.447513	−	0.894278i
$10$	3.41372	−	3.81905i	1.07951	−	1.20769i
$11$	−3.11829	+	4.85215i	−0.940200	+	1.46298i	−0.0546114	+	0.998508i	$0.517392\pi$
$11$	−3.11829	+	4.85215i	−0.940200	+	1.46298i	−0.885588	+	0.464471i	$0.846244\pi$
$12$	1.83467	+	2.93837i	0.529623	+	0.848233i
$13$	3.13718	+	2.71838i	0.870097	+	0.753944i	0.970525	−	0.241001i	$-0.0774756\pi$
$13$	3.13718	+	2.71838i	0.870097	+	0.753944i	−0.100428	+	0.994944i	$0.532021\pi$
$14$	1.71273	−	5.51692i	0.457746	−	1.47446i
$15$	1.66011	−	6.04996i	0.428638	−	1.56209i
$16$	−2.42816	−	3.17868i	−0.607040	−	0.794671i
$17$	0.187820	−	0.0857744i	0.0455530	−	0.0208033i	−0.392508	−	0.919748i	$-0.628393\pi$
$17$	0.187820	−	0.0857744i	0.0455530	−	0.0208033i	0.438061	+	0.898945i	$0.355665\pi$
$18$	3.61466	+	2.22131i	0.851984	+	0.523567i
$19$	−0.0995334	+	0.217948i	−0.0228345	+	0.0500007i	−0.920706	−	0.390258i	$-0.872386\pi$
$19$	−0.0995334	+	0.217948i	−0.0228345	+	0.0500007i	0.897871	+	0.440258i	$0.145113\pi$
$20$	−1.25151	+	7.13520i	−0.279846	+	1.59548i
$21$	−1.13129	−	6.98390i	−0.246869	−	1.52401i
$22$	0.125748	−	8.15588i	0.0268096	−	1.73884i
$23$	2.87802	−	3.83628i	0.600108	−	0.799919i
$23$	2.87802	−	3.83628i	0.600108	−	0.799919i
$24$	−4.39655	−	2.16109i	−0.897443	−	0.441131i
$25$	6.83041	−	4.38964i	1.36608	−	0.877928i
$26$	−5.79720	−	0.924943i	−1.13692	−	0.181396i
$27$	5.17539	+	0.464048i	0.996004	+	0.0893061i
$28$	2.05885	+	7.90574i	0.389086	+	1.49405i
$29$	−1.06462	−	2.33120i	−0.197695	−	0.432893i	0.784657	−	0.619930i	$-0.212839\pi$
$29$	−1.06462	−	2.33120i	−0.197695	−	0.432893i	−0.982353	+	0.187037i	$0.940112\pi$
$30$	2.51980	+	8.50686i	0.460050	+	1.55313i
$31$	−7.48287	+	1.07587i	−1.34396	+	0.193233i	−0.776474	−	0.630149i	$-0.782994\pi$
$31$	−7.48287	+	1.07587i	−1.34396	+	0.193233i	−0.567488	+	0.823381i	$0.692085\pi$
$32$	5.28886	+	2.00697i	0.934948	+	0.354785i
$33$	−4.31103	−	9.01201i	−0.750454	−	1.56879i
$34$	−0.161638	+	0.243187i	−0.0277207	+	0.0417063i
$35$	7.99883	−	12.4464i	1.35205	−	2.10383i
$36$	−5.99993	+	0.0284946i	−0.999989	+	0.00474909i
$37$	1.24263	−	4.23200i	0.204287	−	0.695736i	−0.792068	−	0.610432i	$-0.790996\pi$
$37$	1.24263	−	4.23200i	0.204287	−	0.695736i	0.996355	−	0.0853039i	$-0.0271861\pi$
$38$	−0.0430464	−	0.336100i	−0.00698306	−	0.0545226i
$39$	−6.86152	+	2.14804i	−1.09872	+	0.343961i
$40$	−3.82041	−	9.50574i	−0.604060	−	1.50299i
$41$	1.14875	+	3.91228i	0.179404	+	0.610995i	0.999261	+	0.0384268i	$0.0122346\pi$
$41$	1.14875	+	3.91228i	0.179404	+	0.610995i	−0.819857	+	0.572568i	$0.805947\pi$
$42$	6.57013	+	7.54605i	1.01379	+	1.16438i
$43$	−1.10955	+	7.71709i	−0.169205	+	1.17685i	0.711328	+	0.702860i	$0.248094\pi$
$43$	−1.10955	+	7.71709i	−0.169205	+	1.17685i	−0.880533	+	0.473985i	$0.842815\pi$
$44$	5.93444	+	9.89196i	0.894651	+	1.49127i
$45$	7.40348	+	7.95377i	1.10365	+	1.18568i
$46$	−0.595090	+	6.75617i	−0.0877412	+	0.996143i
$47$	0.440853			0.0643050			0.0321525	−	0.999483i	$-0.489764\pi$
$47$	0.440853			0.0643050			0.0321525	+	0.999483i	$0.489764\pi$
$48$	6.89433	−	0.684245i	0.995111	−	0.0987623i
$49$	1.37831	−	9.58634i	0.196901	−	1.36948i
$50$	−4.93044	+	10.3700i	−0.697270	+	1.46655i
$51$	−0.0445905	+	0.354841i	−0.00624392	+	0.0496877i
$52$	7.65465	−	3.21439i	1.06151	−	0.445756i
$53$	1.39554	+	1.61054i	0.191693	+	0.221225i	0.843457	−	0.537196i	$-0.180516\pi$
$53$	1.39554	+	1.61054i	0.191693	+	0.221225i	−0.651765	+	0.758421i	$0.725971\pi$
$54$	−6.56374	+	3.30413i	−0.893212	+	0.449635i
$55$	5.88573	−	20.0450i	0.793632	−	2.70286i
$56$	−8.37228	−	7.96142i	−1.11879	−	1.06389i
$57$	−0.230541	−	0.345073i	−0.0305359	−	0.0457060i
$58$	3.01842	+	2.00624i	0.396337	+	0.263432i
$59$	3.90630	+	3.38483i	0.508557	+	0.440667i	0.870960	−	0.491355i	$-0.163498\pi$
$59$	3.90630	+	3.38483i	0.508557	+	0.440667i	−0.362403	+	0.932022i	$0.618044\pi$
$60$	−9.37456	−	8.33963i	−1.21025	−	1.07664i
$61$	−5.95381	+	0.856029i	−0.762307	+	0.109603i	−0.512494	−	0.858691i	$-0.671278\pi$
$61$	−5.95381	+	0.856029i	−0.762307	+	0.109603i	−0.249813	+	0.968294i	$0.580369\pi$
$62$	8.18684	−	6.87585i	1.03973	−	0.873234i
$63$	11.3208	+	4.69079i	1.42629	+	0.590983i
$64$	−7.85132	+	1.53520i	−0.981414	+	0.191900i
$65$	−13.6768	−	6.24597i	−1.69639	−	0.774717i
$66$	11.9034	+	7.60997i	1.46521	+	0.936723i
$67$	4.46017	−	2.86638i	0.544897	−	0.350184i	−0.239055	−	0.971006i	$-0.576838\pi$
$67$	4.46017	−	2.86638i	0.544897	−	0.350184i	0.783951	+	0.620822i	$0.213201\pi$
$68$	0.0127310	−	0.412761i	0.00154386	−	0.0500546i
$69$	3.03285	+	7.73316i	0.365112	+	0.930964i
$70$	−0.322562	+	20.9209i	−0.0385535	+	2.50053i
$71$	5.47698	−	3.51984i	0.649998	−	0.417728i	−0.173668	−	0.984804i	$-0.555562\pi$
$71$	5.47698	−	3.51984i	0.649998	−	0.417728i	0.823665	+	0.567076i	$0.191925\pi$
$72$	7.18680	−	4.51108i	0.846973	−	0.531636i
$73$	1.34371	−	2.94232i	0.157269	−	0.344372i	−0.814552	−	0.580091i	$-0.803017\pi$
$73$	1.34371	−	2.94232i	0.157269	−	0.344372i	0.971821	+	0.235719i	$0.0757444\pi$
$74$	1.66487	+	6.01133i	0.193537	+	0.698803i
$75$	0.250190	+	14.0609i	0.0288894	+	1.62361i
$76$	0.302495	+	0.371657i	0.0346986	+	0.0426320i
$77$	−3.35289	−	23.3199i	−0.382098	−	2.65755i
$78$	6.64038	−	7.70028i	0.751875	−	0.871885i
$79$	5.31766	+	4.60778i	0.598283	+	0.518415i	0.900518	−	0.434818i	$-0.143187\pi$
$79$	5.31766	+	4.60778i	0.598283	+	0.518415i	−0.302235	+	0.953233i	$0.597733\pi$
$80$	11.6824	+	8.56919i	1.30613	+	0.958065i
$81$	−5.39518	+	7.20361i	−0.599465	+	0.800401i
$82$	−4.29920	−	3.84291i	−0.474767	−	0.424378i
$83$	−3.12115	+	10.6297i	−0.342590	+	1.16676i	0.590477	+	0.807054i	$0.298940\pi$
$83$	−3.12115	+	10.6297i	−0.342590	+	1.16676i	−0.933067	+	0.359701i	$0.882879\pi$
$84$	−13.5236	−	4.16321i	−1.47554	−	0.454243i
$85$	−0.565209	+	0.489756i	−0.0613055	+	0.0531215i
$86$	−4.42514	−	10.0989i	−0.477175	−	1.08899i
$87$	4.40425	+	0.553453i	0.472185	+	0.0593364i
$88$	−14.5103	−	7.45580i	−1.54680	−	0.794791i
$89$	4.58957	+	0.659881i	0.486494	+	0.0699472i	0.381197	−	0.924494i	$-0.375512\pi$
$89$	4.58957	+	0.659881i	0.486494	+	0.0699472i	0.105296	+	0.994441i	$0.466421\pi$
$90$	−14.8289	−	4.03121i	−1.56311	−	0.424927i
$91$	−16.9560			−1.77747
$92$	−4.32620	−	8.56061i	−0.451038	−	0.892505i
$93$	5.22668	−	12.0056i	0.541981	−	1.24492i
$94$	−0.529622	+	0.328942i	−0.0546264	+	0.0339278i
$95$	0.123507	−	0.859012i	0.0126716	−	0.0881328i
$96$	−7.77201	+	5.96623i	−0.793227	+	0.608925i
$97$	−12.9092	+	3.79049i	−1.31073	+	0.384866i	−0.861141	−	0.508367i	$-0.830249\pi$
$97$	−12.9092	+	3.79049i	−1.31073	+	0.384866i	−0.449594	+	0.893233i	$0.648431\pi$
$98$	5.49700	+	12.5450i	0.555281	+	1.26724i
$99$	17.2039	+	1.85165i	1.72906	+	0.186098i
$100$	−1.81438	−	16.1370i	−0.181438	−	1.61370i
$101$	0.186531	+	0.0547705i	0.0185606	+	0.00544987i	0.291000	−	0.956723i	$-0.406012\pi$
$101$	0.186531	+	0.0547705i	0.0185606	+	0.00544987i	−0.272439	+	0.962173i	$0.587830\pi$
$102$	−0.211195	−	0.459562i	−0.0209114	−	0.0455034i
$103$	3.37262	−	5.24790i	0.332314	−	0.517091i	−0.634381	−	0.773020i	$-0.718745\pi$
$103$	3.37262	−	5.24790i	0.332314	−	0.517091i	0.966696	+	0.255929i	$0.0823814\pi$
$104$	−6.79756	+	9.57315i	−0.666556	+	0.938725i
$105$	11.0584	+	23.1170i	1.07919	+	2.25599i
$106$	−2.87825	−	0.893554i	−0.279561	−	0.0867897i
$107$	−6.97629	+	1.00304i	−0.674424	+	0.0969675i	−0.471013	−	0.882126i	$-0.656112\pi$
$107$	−6.97629	+	1.00304i	−0.674424	+	0.0969675i	−0.203410	+	0.979094i	$0.565203\pi$
$108$	5.42003	−	8.86698i	0.521543	−	0.853225i
$109$	−7.77100	+	3.54890i	−0.744327	+	0.339923i	−0.751219	−	0.660053i	$-0.770534\pi$
$109$	−7.77100	+	3.54890i	−0.744327	+	0.339923i	0.00689143	+	0.999976i	$0.497806\pi$
$110$	7.88567	+	28.4728i	0.751869	+	2.71478i
$111$	5.10472	+	5.68362i	0.484519	+	0.539466i
$112$	15.9985	+	3.31753i	1.51172	+	0.313478i
$113$	−0.769294	−	1.19704i	−0.0723691	−	0.112609i	0.803183	−	0.595733i	$-0.203138\pi$
$113$	−0.769294	−	1.19704i	−0.0723691	−	0.112609i	−0.875552	+	0.483124i	$0.839502\pi$
$114$	0.534438	+	0.242538i	0.0500547	+	0.0227157i
$115$	−6.08735	+	16.2693i	−0.567649	+	1.51712i
$116$	−5.12315	−	0.158016i	−0.475673	−	0.0146714i
$117$	3.08118	−	12.0661i	0.284855	−	1.11551i
$118$	−7.21845	−	1.15170i	−0.664512	−	0.106023i
$119$	−0.350364	+	0.767190i	−0.0321178	+	0.0703282i
$120$	17.4848	+	3.02405i	1.59614	+	0.276057i
$121$	−9.25009	−	20.2549i	−0.840918	−	1.84135i
$122$	6.51393	−	5.47083i	0.589744	−	0.495306i
$123$	−6.81059	−	1.86882i	−0.614090	−	0.168506i
$124$	−4.70491	+	14.3690i	−0.422513	+	1.29037i
$125$	−7.39888	+	8.53876i	−0.661776	+	0.763730i
$126$	−17.1004	+	2.81171i	−1.52342	+	0.250487i
$127$	−7.83949	+	12.1985i	−0.695642	+	1.08244i	0.296220	+	0.955120i	$0.404274\pi$
$127$	−7.83949	+	12.1985i	−0.695642	+	1.08244i	−0.991862	+	0.127320i	$0.959362\pi$
$128$	8.28675	−	7.70258i	0.732452	−	0.680819i
$129$	−10.3612	−	8.66018i	−0.912256	−	0.762486i
$130$	21.0911	−	2.70127i	1.84981	−	0.236917i
$131$	−0.867861	+	0.752005i	−0.0758253	+	0.0657030i	−0.691949	−	0.721947i	$-0.743248\pi$
$131$	−0.867861	+	0.752005i	−0.0758253	+	0.0657030i	0.616124	+	0.787650i	$0.288702\pi$
$132$	−19.9784	−	0.260580i	−1.73890	−	0.0226806i
$133$	−0.275731	−	0.939054i	−0.0239089	−	0.0814263i
$134$	−3.21951	+	6.77150i	−0.278124	+	0.584968i
$135$	−18.4598	+	3.66851i	−1.58877	+	0.315735i
$136$	0.292687	+	0.505373i	0.0250977	+	0.0433354i
$137$		−	16.2191i		−	1.38569i	−0.721086	−	0.692846i	$-0.756357\pi$
$137$		−	16.2191i		−	1.38569i	0.721086	−	0.692846i	$-0.243643\pi$
$138$	−9.41364	−	7.02734i	−0.801342	−	0.598207i
$139$	−21.0704			−1.78717			−0.893585	−	0.448894i	$-0.851818\pi$
$139$	−21.0704			−1.78717			−0.893585	+	0.448894i	$0.851818\pi$
$140$	−15.2226	−	25.3742i	−1.28655	−	2.14451i
$141$	−0.401329	+	0.649607i	−0.0337980	+	0.0547068i
$142$	−3.95348	+	8.31523i	−0.331769	+	0.697799i
$143$	−22.9726	+	6.74538i	−1.92107	+	0.564077i
$144$	−5.26798	+	10.7819i	−0.438998	+	0.898488i
$145$	6.07881	+	7.01532i	0.504817	+	0.582590i
$146$	0.581131	+	4.53739i	0.0480948	+	0.375517i
$147$	12.8709	+	10.7579i	1.06158	+	0.887293i
$148$	−6.48545	−	5.97952i	−0.533101	−	0.491513i
$149$	−13.0815	−	8.40696i	−1.07168	−	0.688725i	−0.119057	−	0.992887i	$-0.537987\pi$
$149$	−13.0815	−	8.40696i	−1.07168	−	0.688725i	−0.952620	+	0.304163i	$0.901623\pi$
$150$	−10.7921	−	16.7055i	−0.881170	−	1.36399i
$151$	6.48544	+	5.61967i	0.527778	+	0.457322i	0.877531	−	0.479520i	$-0.159189\pi$
$151$	6.48544	+	5.61967i	0.527778	+	0.457322i	−0.349753	+	0.936842i	$0.613735\pi$
$152$	−0.640717	−	0.220787i	−0.0519690	−	0.0179082i
$153$	−0.482273	−	0.388733i	−0.0389895	−	0.0314272i
$154$	21.4282	+	25.5138i	1.72673	+	2.05596i
$155$	24.9076	−	11.3749i	2.00063	−	0.913657i
$156$	−2.23191	+	14.2055i	−0.178696	+	1.13735i
$157$	10.9191	+	4.98660i	0.871441	+	0.397974i	0.800376	−	0.599498i	$-0.204633\pi$
$157$	10.9191	+	4.98660i	0.871441	+	0.397974i	0.0710650	+	0.997472i	$0.477360\pi$
$158$	−9.82650	−	1.56782i	−0.781754	−	0.124729i
$159$	−3.64360	+	0.590212i	−0.288956	+	0.0468069i
$160$	−20.4286	−	1.57786i	−1.61502	−	0.124741i
$161$	1.37724	+	19.5411i	0.108541	+	1.54006i
$162$	1.10658	−	12.6797i	0.0869408	−	0.996213i
$163$	16.2967	−	10.4733i	1.27646	−	0.820328i	0.286010	−	0.958227i	$-0.407671\pi$
$163$	16.2967	−	10.4733i	1.27646	−	0.820328i	0.990446	+	0.137898i	$0.0440347\pi$
$164$	8.03226	+	1.40886i	0.627214	+	0.110013i
$165$	24.1786	+	26.9206i	1.88230	+	2.09577i
$166$	−4.18170	−	15.0989i	−0.324563	−	1.17190i
$167$	6.49808	+	14.2288i	0.502837	+	1.10106i	0.975537	+	0.219836i	$0.0705521\pi$
$167$	6.49808	+	14.2288i	0.502837	+	1.10106i	−0.472700	+	0.881223i	$0.656721\pi$
$168$	19.3530	−	5.08910i	1.49312	−	0.392632i
$169$	0.602206	+	4.18843i	0.0463235	+	0.322187i
$170$	0.313587	−	1.01010i	0.0240510	−	0.0774714i
$171$	0.718345	−	0.0255716i	0.0549332	−	0.00195551i
$172$	12.8515	+	8.83055i	0.979914	+	0.673323i
$173$	0.0100661	+	0.00646908i	0.000765311	+	0.000491835i	0.541023	−	0.841008i	$-0.318037\pi$
$173$	0.0100661	+	0.00646908i	0.000765311	+	0.000491835i	−0.540258	+	0.841499i	$0.681673\pi$
$174$	−5.70404	+	2.62133i	−0.432422	+	0.198723i
$175$	−9.34371	+	31.8217i	−0.706318	+	2.40550i
$176$	22.9952	−	1.86975i	1.73333	−	0.140938i
$177$	−8.54370	+	2.67465i	−0.642184	+	0.201039i
$178$	−6.00609	+	2.63176i	−0.450175	+	0.197258i
$179$	−2.74285	−	9.34128i	−0.205010	−	0.698200i	−0.996236	−	0.0866767i	$-0.972375\pi$
$179$	−2.74285	−	9.34128i	−0.205010	−	0.698200i	0.791227	−	0.611523i	$-0.209443\pi$
$180$	20.8227	−	6.22168i	1.55204	−	0.463736i
$181$	1.65203	+	0.237527i	0.122795	+	0.0176552i	0.203438	−	0.979088i	$-0.434788\pi$
$181$	1.65203	+	0.237527i	0.122795	+	0.0176552i	−0.0806434	+	0.996743i	$0.525698\pi$
$182$	20.3702	−	12.6517i	1.50994	−	0.937808i
$183$	4.15865	−	9.55236i	0.307417	−	0.706130i
$184$	11.5848	+	7.05636i	0.854044	+	0.520202i
$185$			15.9757i			1.17456i
$186$	2.67886	+	18.3229i	0.196423	+	1.34350i
$187$	−0.169486	+	1.17880i	−0.0123940	+	0.0862023i
$188$	0.390825	−	0.790355i	0.0285039	−	0.0576426i
$189$	−17.2178	+	12.4112i	−1.25241	+	0.902784i
$190$	0.492575	+	1.12414i	0.0357352	+	0.0815534i
$191$	−13.6434	−	15.7454i	−0.987205	−	1.13930i	−0.990250	−	0.139300i	$-0.955515\pi$
$191$	−13.6434	−	15.7454i	−0.987205	−	1.13930i	0.00304484	−	0.999995i	$-0.499031\pi$
$192$	4.88527	−	12.9667i	0.352564	−	0.935788i
$193$	6.86301	+	2.01516i	0.494010	+	0.145054i	0.519242	−	0.854627i	$-0.326214\pi$
$193$	6.86301	+	2.01516i	0.494010	+	0.145054i	−0.0252321	+	0.999682i	$0.508032\pi$
$194$	12.6803	−	14.1860i	0.910395	−	1.01849i
$195$	21.6542	−	14.4670i	1.55069	−	1.03600i
$196$	−15.9643	−	10.9695i	−1.14031	−	0.783536i
$197$	−2.95043	+	3.40498i	−0.210209	+	0.242594i	−0.851057	−	0.525074i	$-0.824038\pi$
$197$	−2.95043	+	3.40498i	−0.210209	+	0.242594i	0.640847	+	0.767668i	$0.278583\pi$
$198$	−22.0497	+	10.6122i	−1.56700	+	0.754177i
$199$	5.65117	−	0.812516i	0.400601	−	0.0575977i	0.0609300	−	0.998142i	$-0.480593\pi$
$199$	5.65117	−	0.812516i	0.400601	−	0.0575977i	0.339671	+	0.940544i	$0.389684\pi$
$200$	14.2203	+	18.0325i	1.00553	+	1.27509i
$201$	0.163371	+	9.18156i	0.0115233	+	0.647617i
$202$	−0.264958	+	0.0733813i	−0.0186424	+	0.00516309i
$203$	9.52229	+	4.34868i	0.668334	+	0.305218i
$204$	0.596623	+	0.394515i	0.0417720	+	0.0276216i
$205$	−7.98459	−	12.4243i	−0.557668	−	0.867748i
$206$	−0.136005	+	8.82109i	−0.00947590	+	0.614595i
$207$	−14.1559	−	2.57089i	−0.983906	−	0.178689i
$208$	1.02330	−	16.5728i	0.0709532	−	1.14912i
$209$	−0.747142	−	1.16258i	−0.0516809	−	0.0804170i
$210$	−30.5338	−	19.5206i	−2.10703	−	1.34705i
$211$	7.40132	−	16.2066i	0.509528	−	1.11571i	−0.463726	−	0.885978i	$-0.653488\pi$
$211$	7.40132	−	16.2066i	0.509528	−	1.11571i	0.973254	−	0.229732i	$-0.0737848\pi$
$212$	4.12454	−	1.07413i	0.283274	−	0.0737716i
$213$	0.200615	+	11.2747i	0.0137459	+	0.772531i
$214$	7.63261	−	6.41037i	0.521754	−	0.438204i
$215$	−4.01886	−	27.9518i	−0.274084	−	1.90630i
$216$	0.104695	+	14.6966i	0.00712361	+	0.999975i
$217$	20.2219	−	23.3373i	1.37275	−	1.58424i
$218$	6.68775	−	10.0618i	0.452951	−	0.681473i
$219$	3.11233	+	4.65852i	0.210312	+	0.314793i
$220$	−30.7185	−	28.3221i	−2.07104	−	1.90948i
$221$	0.822392	+	0.241476i	0.0553201	+	0.0162434i
$222$	−10.3734	−	3.01918i	−0.696219	−	0.202634i
$223$	19.5638	−	16.9521i	1.31009	−	1.13520i	0.328434	−	0.944527i	$-0.393479\pi$
$223$	19.5638	−	16.9521i	1.31009	−	1.13520i	0.981654	−	0.190671i	$-0.0610664\pi$
$224$	−21.6953	+	7.95174i	−1.44958	+	0.531298i
$225$	−20.9468	−	12.4316i	−1.39645	−	0.828773i
$226$	1.81737	+	0.864071i	0.120890	+	0.0574771i
$227$	−26.0747	−	3.74897i	−1.73064	−	0.248828i	−0.796220	−	0.605007i	$-0.793170\pi$
$227$	−26.0747	−	3.74897i	−1.73064	−	0.248828i	−0.934418	+	0.356179i	$0.884079\pi$
$228$	−0.823021	+	0.107396i	−0.0545059	+	0.00711250i
$229$		−	20.4089i		−	1.34866i	−0.738430	−	0.674330i	$-0.764432\pi$
$229$		−	20.4089i		−	1.34866i	0.738430	−	0.674330i	$-0.235568\pi$
$230$	−4.82621	−	24.0873i	−0.318231	−	1.58827i
$231$	37.4147	+	16.2886i	2.46170	+	1.07171i
$232$	6.27264	−	3.63280i	0.411819	−	0.238505i
$233$	−14.2939	−	2.05516i	−0.936427	−	0.134638i	−0.342827	−	0.939398i	$-0.611385\pi$
$233$	−14.2939	−	2.05516i	−0.936427	−	0.134638i	−0.593599	+	0.804761i	$0.702294\pi$
$234$	5.30149	+	16.7947i	0.346569	+	1.09790i
$235$	−1.53212	+	0.449870i	−0.0999442	+	0.0293463i
$236$	9.53128	−	4.00243i	0.620434	−	0.260536i
$237$	−11.6306	+	3.64101i	−0.755487	+	0.236509i
$238$	−0.151526	−	1.18309i	−0.00982199	−	0.0766886i
$239$	8.79579	+	2.58268i	0.568953	+	0.167060i	0.553541	−	0.832822i	$-0.313276\pi$
$239$	8.79579	+	2.58268i	0.568953	+	0.167060i	0.0154113	+	0.999881i	$0.495094\pi$
$240$	−23.2619	+	9.41332i	−1.50155	+	0.607627i
$241$	16.6161	+	10.6785i	1.07034	+	0.687863i	0.952305	−	0.305147i	$-0.0987057\pi$
$241$	16.6161	+	10.6785i	1.07034	+	0.687863i	0.118030	+	0.993010i	$0.462342\pi$
$242$	26.2258	+	17.4314i	1.68586	+	1.12053i
$243$	−5.70319	−	14.5077i	−0.365860	−	0.930670i
$244$	−3.74350	+	11.4328i	−0.239653	+	0.731910i
$245$	4.99231	+	34.7223i	0.318947	+	2.21833i
$246$	9.57637	−	2.83659i	0.610567	−	0.180855i
$247$	−0.904720	+	0.413172i	−0.0575659	+	0.0262895i
$248$	−5.06912	−	20.7728i	−0.321889	−	1.31908i
$249$	−12.8217	−	14.2757i	−0.812543	−	0.904689i
$250$	2.51751	−	15.7788i	0.159221	−	0.997938i
$251$	−8.91638	−	13.8742i	−0.562797	−	0.875729i	0.436921	−	0.899500i	$-0.356069\pi$
$251$	−8.91638	−	13.8742i	−0.562797	−	0.875729i	−0.999717	+	0.0237711i	$0.992433\pi$
$252$	18.4457	−	16.1373i	1.16197	−	1.01655i
$253$	9.63972	+	25.9272i	0.606044	+	1.63003i
$254$	0.316136	−	20.5042i	0.0198361	−	1.28655i
$255$	−0.207131	−	1.27870i	−0.0129710	−	0.0800751i
$256$	−4.20807	+	15.4367i	−0.263004	+	0.964795i
$257$	0.647913	+	0.295892i	0.0404157	+	0.0184572i	0.435520	−	0.900179i	$-0.356564\pi$
$257$	0.647913	+	0.295892i	0.0404157	+	0.0184572i	−0.395105	+	0.918636i	$0.629292\pi$
$258$	18.9093	+	2.67294i	1.17724	+	0.166410i
$259$	7.48424	+	16.3882i	0.465048	+	1.01831i
$260$	−23.3224	+	18.9823i	−1.44639	+	1.17723i
$261$	−4.82492	+	5.98593i	−0.298655	+	0.370520i
$262$	0.481502	−	1.55098i	0.0297473	−	0.0958200i
$263$	−7.03072	+	8.11389i	−0.433533	+	0.500324i	−0.929912	−	0.367782i	$-0.880117\pi$
$263$	−7.03072	+	8.11389i	−0.433533	+	0.500324i	0.496379	+	0.868106i	$0.334663\pi$
$264$	24.1957	−	14.5938i	1.48914	−	0.898189i
$265$	−6.49348	−	4.17310i	−0.398891	−	0.256352i
$266$	1.03193	+	0.922403i	0.0632715	+	0.0565562i
$267$	−5.15045	+	6.16212i	−0.315203	+	0.377116i
$268$	−1.18477	−	10.5372i	−0.0723711	−	0.643664i
$269$	10.3951	+	11.9966i	0.633802	+	0.731446i	0.978266	−	0.207353i	$-0.0664849\pi$
$269$	10.3951	+	11.9966i	0.633802	+	0.731446i	−0.344464	+	0.938799i	$0.611939\pi$
$270$	19.4396	−	18.1810i	1.18305	−	1.10646i
$271$	−5.74473	−	19.5648i	−0.348968	−	1.18848i	−0.927815	−	0.373039i	$-0.878316\pi$
$271$	−5.74473	−	19.5648i	−0.348968	−	1.18848i	0.578848	−	0.815436i	$-0.303503\pi$
$272$	−0.728706	−	0.388745i	−0.0441843	−	0.0235712i
$273$	15.4358	−	24.9851i	0.934220	−	1.51216i
$274$	12.1019	+	19.4849i	0.731101	+	1.17713i
$275$			46.8304i			2.82398i
$276$	16.5526	+	1.41837i	0.996349	+	0.0853755i
$277$			3.85488i			0.231617i	0.993272	+	0.115809i	$0.0369459\pi$
$277$			3.85488i			0.231617i	−0.993272	+	0.115809i	$0.963054\pi$
$278$	25.3131	−	15.7217i	1.51818	−	0.942925i
$279$	12.9324	+	18.6309i	0.774244	+	1.11540i
$280$	37.2208	+	19.1251i	2.22437	+	1.14295i
$281$	0.951974	+	3.24213i	0.0567900	+	0.193409i	0.983002	−	0.183593i	$-0.0587730\pi$
$281$	0.951974	+	3.24213i	0.0567900	+	0.193409i	−0.926212	+	0.377003i	$0.876955\pi$
$282$	−0.00256420	−	1.07986i	−0.000152696	−	0.0643048i
$283$	−4.84016	−	5.58584i	−0.287718	−	0.332044i	0.593430	−	0.804886i	$-0.297774\pi$
$283$	−4.84016	−	5.58584i	−0.287718	−	0.332044i	−0.881147	+	0.472842i	$0.843228\pi$
$284$	−1.45486	−	12.9395i	−0.0863302	−	0.767816i
$285$	1.15334	+	0.963990i	0.0683179	+	0.0571018i
$286$	22.5653	−	25.2446i	1.33431	−	1.49275i
$287$	−14.0112	−	9.00448i	−0.827057	−	0.531518i
$288$	−1.71615	−	16.8836i	−0.101125	−	0.994874i
$289$	−11.1047	+	12.8155i	−0.653218	+	0.753854i
$290$	−12.5373	−	3.89221i	−0.736215	−	0.228558i
$291$	6.16650	−	22.4727i	0.361487	−	1.31737i
$292$	−4.08372	−	5.01741i	−0.238981	−	0.293622i
$293$	3.15399	+	6.90627i	0.184258	+	0.403469i	0.979109	−	0.203336i	$-0.0651783\pi$
$293$	3.15399	+	6.90627i	0.184258	+	0.403469i	−0.794851	+	0.606805i	$0.792451\pi$
$294$	−23.4896	−	3.32038i	−1.36994	−	0.193649i
$295$	−17.0298	−	7.77724i	−0.991512	−	0.452808i
$296$	12.2530	+	2.34442i	0.712189	+	0.136267i
$297$	−18.3900	+	23.6647i	−1.06710	+	1.37317i
$298$	21.9884	+	0.339020i	1.27375	+	0.0196389i
$299$	19.4573	−	4.21155i	1.12525	−	0.243560i
$300$	25.4299	+	12.0167i	1.46820	+	0.693785i
$301$	−17.2174	−	26.7908i	−0.992395	−	1.54420i
$302$	−11.9844	−	1.91212i	−0.689627	−	0.110030i
$303$	−0.250514	+	0.224998i	−0.0143916	+	0.0129258i
$304$	0.934470	−	0.212827i	0.0535956	−	0.0122065i
$305$	19.8180	−	9.05057i	1.13477	−	0.518234i
$306$	0.869436	+	0.107160i	0.0497024	+	0.00612592i
$307$	1.71162	+	11.9046i	0.0976875	+	0.679432i	0.978542	+	0.206045i	$0.0660594\pi$
$307$	1.71162	+	11.9046i	0.0976875	+	0.679432i	−0.880855	+	0.473386i	$0.843031\pi$
$308$	−44.7800	−	14.6626i	−2.55158	−	0.835476i
$309$	4.66265	+	9.74705i	0.265249	+	0.554490i
$310$	−21.4356	+	32.2502i	−1.21746	+	1.83169i
$311$	−0.788195	−	0.506542i	−0.0446945	−	0.0287234i	0.518103	−	0.855318i	$-0.326638\pi$
$311$	−0.788195	−	0.506542i	−0.0446945	−	0.0287234i	−0.562797	+	0.826595i	$0.690275\pi$
$312$	−7.91811	−	18.7312i	−0.448275	−	1.06045i
$313$	31.8658	+	9.35663i	1.80116	+	0.528868i	0.997780	−	0.0665999i	$-0.0212151\pi$
$313$	31.8658	+	9.35663i	1.80116	+	0.528868i	0.803379	+	0.595468i	$0.203033\pi$
$314$	−16.8385	+	2.15662i	−0.950253	+	0.121705i
$315$	−44.1304	−	4.74973i	−2.48647	−	0.267617i
$316$	12.9750	−	5.44853i	0.729899	−	0.306504i
$317$	5.95793	−	1.74941i	0.334631	−	0.0982565i	−0.110101	−	0.993920i	$-0.535117\pi$
$317$	5.95793	−	1.74941i	0.334631	−	0.0982565i	0.444731	+	0.895664i	$0.353299\pi$
$318$	3.93688	−	3.42773i	0.220769	−	0.192217i
$319$	14.6311	+	2.10364i	0.819186	+	0.117781i
$320$	25.7194	−	13.3472i	1.43776	−	0.746134i
$321$	4.87284	−	11.1928i	0.271976	−	0.624723i
$322$	−16.2352	−	22.4483i	−0.904751	−	1.25099i
$323$			0.0494723i			0.00275271i
$324$	8.13158	+	16.0586i	0.451755	+	0.892142i
$325$	33.3610	+	4.79658i	1.85053	+	0.266067i
$326$	−11.7636	+	24.7419i	−0.651523	+	1.37033i
$327$	1.84493	−	14.6815i	0.102025	−	0.811888i
$328$	−10.7008	+	4.30073i	−0.590855	+	0.237468i
$329$	−1.36092	+	1.17925i	−0.0750301	+	0.0650140i
$330$	−49.1340	−	14.3004i	−2.70474	−	0.787211i
$331$	−21.6288	−	6.35079i	−1.18883	−	0.349071i	−0.373256	−	0.927728i	$-0.621759\pi$
$331$	−21.6288	−	6.35079i	−1.18883	−	0.349071i	−0.815571	+	0.578657i	$0.803577\pi$
$332$	16.2897	+	15.0190i	0.894015	+	0.824272i
$333$	−13.0220	+	2.34786i	−0.713602	+	0.128662i
$334$	−18.4234	−	12.2454i	−1.00808	−	0.670036i
$335$	−12.5756	+	14.5130i	−0.687079	+	0.792932i
$336$	−19.4527	+	20.5541i	−1.06123	+	1.12132i
$337$	−0.369978	−	2.57326i	−0.0201540	−	0.140174i	0.977260	−	0.212045i	$-0.0680123\pi$
$337$	−0.369978	−	2.57326i	−0.0201540	−	0.140174i	−0.997414	+	0.0718705i	$0.977103\pi$
$338$	−3.84866	−	4.58247i	−0.209340	−	0.249254i
$339$	2.46420	−	0.0438463i	0.133837	−	0.00238140i
$340$	0.376959	+	1.44748i	0.0204434	+	0.0785005i
$341$	18.1134	−	39.6629i	0.980898	−	2.14787i
$342$	−0.843909	+	0.566714i	−0.0456334	+	0.0306444i
$343$	5.92927	+	9.22613i	0.320151	+	0.498164i
$344$	−22.0281	−	1.01954i	−1.18768	−	0.0549701i
$345$	−18.4315	−	23.7805i	−0.992319	−	1.28030i
$346$	−0.0169199		0.000260873i	−0.000909618		1.40246e-5i
$347$	−13.2939	−	20.6858i	−0.713656	−	1.11047i	−0.988826	−	0.149075i	$-0.952370\pi$
$347$	−13.2939	−	20.6858i	−0.713656	−	1.11047i	0.275170	−	0.961396i	$-0.411266\pi$
$348$	4.89668	−	7.40523i	0.262490	−	0.396962i
$349$	−13.4699	−	6.15151i	−0.721029	−	0.329283i	0.0208814	−	0.999782i	$-0.493353\pi$
$349$	−13.4699	−	6.15151i	−0.721029	−	0.329283i	−0.741910	+	0.670499i	$0.766080\pi$
$350$	−12.5187	−	45.2011i	−0.669150	−	2.41610i
$351$	14.9747	+	15.5245i	0.799289	+	0.828636i
$352$	−26.2303	+	19.4041i	−1.39808	+	1.03424i
$353$	35.5478	−	5.11100i	1.89202	−	0.272031i	0.904136	−	0.427245i	$-0.140516\pi$
$353$	35.5478	−	5.11100i	1.89202	−	0.272031i	0.987881	+	0.155214i	$0.0496068\pi$
$354$	8.26835	−	9.58810i	0.439458	−	0.509602i
$355$	−15.4425	+	17.8216i	−0.819605	+	0.945875i
$356$	5.25178	−	7.64312i	0.278344	−	0.405085i
$357$	−0.811519	−	1.21468i	−0.0429502	−	0.0642876i
$358$	10.2651	+	9.17564i	0.542529	+	0.484948i
$359$	−25.3103	−	7.43176i	−1.33582	−	0.392233i	−0.465646	−	0.884971i	$-0.654178\pi$
$359$	−25.3103	−	7.43176i	−1.33582	−	0.392233i	−0.870178	+	0.492738i	$0.835996\pi$
$360$	−20.3733	+	23.0113i	−1.07377	+	1.21280i
$361$	12.4048	+	14.3159i	0.652882	+	0.753466i
$362$	−2.16191	+	0.947310i	−0.113628	+	0.0497895i
$363$	38.2668	+	4.80874i	2.00849	+	0.252393i
$364$	−15.0319	+	30.3985i	−0.787883	+	1.59331i
$365$	−1.66736	+	11.5968i	−0.0872737	+	0.607002i
$366$	2.13146	+	14.5788i	0.111413	+	0.762045i
$367$			25.9536i			1.35477i	0.735630	+	0.677384i	$0.236886\pi$
$367$			25.9536i			1.35477i	−0.735630	+	0.677384i	$0.763114\pi$
$368$	−19.1826	+	0.166793i	−0.999962	+	0.00869468i
$369$	8.95375	−	8.33428i	0.466113	−	0.433865i
$370$	−11.9203	−	19.1925i	−0.619704	−	0.997771i
$371$	−8.61615	−	1.23882i	−0.447328	−	0.0643161i
$372$	−16.8899	−	20.0135i	−0.875700	−	1.03765i
$373$	8.29335	+	28.2446i	0.429413	+	1.46245i	0.835946	+	0.548812i	$0.184920\pi$
$373$	8.29335	+	28.2446i	0.429413	+	1.46245i	−0.406532	+	0.913636i	$0.633262\pi$
$374$	−0.675948	−	1.54262i	−0.0349524	−	0.0797670i
$375$	−5.84651	−	18.6757i	−0.301913	−	0.964407i
$376$	0.120202	+	1.24111i	0.00619894	+	0.0640055i
$377$	2.99718	−	10.2074i	0.154362	−	0.525710i
$378$	11.4242	−	27.7574i	0.587595	−	1.42769i
$379$	10.0636	+	6.46748i	0.516932	+	0.332212i	0.772957	−	0.634458i	$-0.218777\pi$
$379$	10.0636	+	6.46748i	0.516932	+	0.332212i	−0.256025	+	0.966670i	$0.582413\pi$
$380$	−1.43053	−	0.982955i	−0.0733848	−	0.0504245i
$381$	−10.8381	−	22.6565i	−0.555252	−	1.16073i
$382$	28.1391	+	8.73578i	1.43972	+	0.446961i
$383$	2.98738	+	20.7777i	0.152648	+	1.06169i	0.911758	+	0.410728i	$0.134726\pi$
$383$	2.98738	+	20.7777i	0.152648	+	1.06169i	−0.759110	+	0.650963i	$0.774365\pi$
$384$	3.80612	+	19.2227i	0.194230	+	0.980956i
$385$	35.4493	+	77.6231i	1.80666	+	3.95604i
$386$	−9.74854	+	2.69990i	−0.496187	+	0.137421i
$387$	22.1933	−	7.38375i	1.12815	−	0.375337i
$388$	−4.64877	+	26.5038i	−0.236005	+	1.34553i
$389$	2.91255	−	1.87178i	0.147672	−	0.0949032i	−0.464718	−	0.885459i	$-0.653844\pi$
$389$	2.91255	−	1.87178i	0.147672	−	0.0949032i	0.612391	+	0.790555i	$0.290208\pi$
$390$	−15.2198	+	33.5373i	−0.770686	+	1.69823i
$391$	0.211494	−	0.967388i	0.0106957	−	0.0489229i
$392$	27.3638	+	1.26650i	1.38208	+	0.0639678i
$393$	−0.318043	−	1.96340i	−0.0160431	−	0.0990403i
$394$	1.00390	−	6.29206i	0.0505757	−	0.316989i
$395$	−23.1827	−	10.5872i	−1.16645	−	0.532699i
$396$	18.5713	−	29.2014i	0.933241	−	1.46743i
$397$	−17.4042	+	7.94823i	−0.873491	+	0.398910i	−0.801145	−	0.598470i	$-0.795776\pi$
$397$	−17.4042	+	7.94823i	−0.873491	+	0.398910i	−0.0723455	+	0.997380i	$0.523048\pi$
$398$	−6.18282	+	5.19274i	−0.309917	+	0.260289i
$399$	1.63473	+	0.448569i	0.0818388	+	0.0224565i
$400$	−30.5386	−	11.0530i	−1.52693	−	0.552649i
$401$	−11.6978	−	10.1362i	−0.584161	−	0.506178i	0.311897	−	0.950116i	$-0.399036\pi$
$401$	−11.6978	−	10.1362i	−0.584161	−	0.506178i	−0.896058	+	0.443938i	$0.853581\pi$
$402$	−7.04708	−	10.9084i	−0.351477	−	0.544063i
$403$	−26.3997	−	16.9661i	−1.31506	−	0.845141i
$404$	0.263556	−	0.285855i	0.0131124	−	0.0142218i
$405$	11.3992	−	30.5405i	0.566429	−	1.51757i
$406$	−14.6844	+	1.88073i	−0.728777	+	0.0933390i
$407$	16.6594	+	19.2260i	0.825777	+	0.952998i
$408$	−1.01113	−	0.0287836i	−0.0500582	−	0.00142500i
$409$	−0.196125	+	0.0575876i	−0.00969778	+	0.00284752i	−0.286578	−	0.958057i	$-0.592518\pi$
$409$	−0.196125	+	0.0575876i	−0.00969778	+	0.00284752i	0.276880	+	0.960904i	$0.410700\pi$
$410$	18.8627	+	8.96828i	0.931562	+	0.442912i
$411$	23.8992	+	14.7650i	1.17886	+	0.728304i
$412$	−6.41847	−	10.6988i	−0.316215	−	0.527090i
$413$	−21.1130			−1.03890
$414$	18.9246	−	7.47389i	0.930094	−	0.367322i
$415$		−	40.1267i		−	1.96974i
$416$	11.1364	+	20.6734i	0.546008	+	1.01360i
$417$	19.1814	−	31.0478i	0.939317	−	1.52041i
$418$	1.76504	+	0.839189i	0.0863309	+	0.0410461i
$419$	3.46768	+	11.8098i	0.169407	+	0.576948i	0.999804	+	0.0197760i	$0.00629532\pi$
$419$	3.46768	+	11.8098i	0.169407	+	0.576948i	−0.830397	+	0.557172i	$0.811886\pi$
$420$	51.2474	+	0.668424i	2.50062	+	0.0326157i
$421$	19.7591	−	17.1213i	0.962997	−	0.834442i	−0.0232479	−	0.999730i	$-0.507401\pi$
$421$	19.7591	−	17.1213i	0.962997	−	0.834442i	0.986245	+	0.165288i	$0.0528552\pi$
$422$	3.20094	+	24.9924i	0.155819	+	1.21661i
$423$	−0.591862	−	1.18273i	−0.0287773	−	0.0575065i
$424$	−4.15358	+	4.36794i	−0.201716	+	0.212126i
$425$	0.906367	−	1.41034i	0.0439653	−	0.0684113i
$426$	−8.65364	−	13.3953i	−0.419270	−	0.649004i
$427$	16.0897	−	18.5686i	0.778637	−	0.898595i
$428$	−4.38640	+	13.3962i	−0.212024	+	0.647530i
$429$	10.9736	−	39.9913i	0.529811	−	1.93080i
$430$	25.6843	+	30.5814i	1.23861	+	1.47477i
$431$	2.29877	+	5.03361i	0.110728	+	0.242460i	0.956881	−	0.290479i	$-0.0938146\pi$
$431$	2.29877	+	5.03361i	0.110728	+	0.242460i	−0.846153	+	0.532939i	$0.821087\pi$
$432$	−11.0916	−	17.5777i	−0.533646	−	0.845708i
$433$	3.58638	−	7.85307i	0.172350	−	0.377394i	−0.803670	−	0.595076i	$-0.797122\pi$
$433$	3.58638	−	7.85307i	0.172350	−	0.377394i	0.976020	+	0.217681i	$0.0698494\pi$
$434$	−6.88061	+	43.1251i	−0.330280	+	2.07007i
$435$	−15.8710	+	2.57089i	−0.760959	+	0.123265i
$436$	−0.526744	+	17.0779i	−0.0252265	+	0.817884i
$437$	0.549649	+	1.00910i	0.0262933	+	0.0482716i
$438$	−7.21497	−	3.27428i	−0.344745	−	0.156451i
$439$	9.98828	+	15.5421i	0.476715	+	0.741782i	0.993438	−	0.114370i	$-0.0364849\pi$
$439$	9.98828	+	15.5421i	0.476715	+	0.741782i	−0.516724	+	0.856152i	$0.672849\pi$
$440$	58.0364	+	11.1044i	2.76678	+	0.529382i
$441$	−27.5690	+	9.17225i	−1.31281	+	0.436774i
$442$	−1.16816	+	0.323528i	−0.0555639	+	0.0153887i
$443$	14.8415	−	6.77789i	0.705141	−	0.322027i	−0.0303710	−	0.999539i	$-0.509669\pi$
$443$	14.8415	−	6.77789i	0.705141	−	0.322027i	0.735512	+	0.677511i	$0.236942\pi$
$444$	14.7150	−	4.11302i	0.698341	−	0.195195i
$445$	−16.6237	+	2.39013i	−0.788040	+	0.113303i
$446$	−10.8543	+	34.9631i	−0.513966	+	1.65555i
$447$	24.2965	−	11.6226i	1.14919	−	0.549731i
$448$	20.1307	−	25.7409i	0.951084	−	1.21614i
$449$	−14.4309	+	22.4549i	−0.681037	+	1.05971i	0.312902	+	0.949785i	$0.398699\pi$
$449$	−14.4309	+	22.4549i	−0.681037	+	1.05971i	−0.993939	+	0.109929i	$0.964938\pi$
$450$	34.4404	−	0.694620i	1.62354	−	0.0327447i
$451$	−22.5651	−	6.62571i	−1.06255	−	0.311992i
$452$	−2.82804	+	0.317974i	−0.133020	+	0.0149562i
$453$	−14.1847	+	4.44060i	−0.666456	+	0.208638i
$454$	34.1223	−	14.9518i	1.60144	−	0.701721i
$455$	58.9279	−	17.3028i	2.76258	−	0.811168i
$456$	0.908609	−	0.743119i	0.0425495	−	0.0347997i
$457$	−1.91586	+	13.3251i	−0.0896203	+	0.623323i	0.894665	+	0.446738i	$0.147414\pi$
$457$	−1.91586	+	13.3251i	−0.0896203	+	0.623323i	−0.984285	+	0.176585i	$0.943495\pi$
$458$	15.2281	+	24.5184i	0.711563	+	1.14567i
$459$	1.01184	−	0.356758i	0.0472288	−	0.0166521i
$460$	23.7707	+	25.3364i	1.10832	+	1.18131i
$461$	−19.0779			−0.888545			−0.444272	−	0.895892i	$-0.646538\pi$
$461$	−19.0779			−0.888545			−0.444272	+	0.895892i	$0.646538\pi$
$462$	−57.1022	+	8.34849i	−2.65663	+	0.388407i
$463$	−25.3851	−	3.64982i	−1.17974	−	0.169622i	−0.475589	−	0.879668i	$-0.657765\pi$
$463$	−25.3851	−	3.64982i	−1.17974	−	0.169622i	−0.704155	+	0.710046i	$0.748674\pi$
$464$	−4.82507	+	9.04462i	−0.223998	+	0.419886i
$465$	−5.91336	+	47.0571i	−0.274226	+	2.18222i
$466$	18.7056	−	8.19644i	0.866519	−	0.379693i
$467$	10.3221	−	8.94416i	0.477651	−	0.413887i	−0.382477	−	0.923965i	$-0.624929\pi$
$467$	10.3221	−	8.94416i	0.477651	−	0.413887i	0.860128	+	0.510078i	$0.170384\pi$
$468$	−18.9003	−	16.2207i	−0.873668	−	0.749803i
$469$	−6.10132	+	20.7792i	−0.281733	+	0.959493i
$470$	1.50495	−	1.68364i	0.0694181	−	0.0776606i
$471$	−17.2881	+	11.5501i	−0.796592	+	0.532198i
$472$	−8.46406	+	11.9201i	−0.389590	+	0.548668i
$473$	−33.9846	−	29.4478i	−1.56261	−	1.35401i
$474$	11.2557	−	13.0523i	0.516993	−	0.599512i
$475$	0.276858	+	1.92559i	0.0127031	+	0.0883521i
$476$	1.06480	+	1.30826i	0.0488051	+	0.0599639i
$477$	2.44725	−	5.90623i	0.112052	−	0.270428i
$478$	−12.4940	+	3.46026i	−0.571460	+	0.158269i
$479$	−10.1392	+	22.2017i	−0.463272	+	1.01442i	0.523458	+	0.852051i	$0.324642\pi$
$479$	−10.1392	+	22.2017i	−0.463272	+	1.01442i	−0.986730	+	0.162372i	$0.948086\pi$
$480$	20.9221	−	28.6657i	0.954961	−	1.30840i
$481$	15.4025	−	9.89861i	0.702295	−	0.451338i
$482$	−27.9296	−	0.430622i	−1.27216	−	0.0196143i
$483$	−30.0481	−	15.7598i	−1.36723	−	0.717097i
$484$	−44.5131	−	1.37294i	−2.02332	−	0.0624065i
$485$	40.9960	−	26.3465i	1.86153	−	1.19633i
$486$	17.6765	+	13.1735i	0.801822	+	0.597563i
$487$	−15.1302	−	6.90974i	−0.685616	−	0.313110i	0.0419778	−	0.999119i	$-0.486634\pi$
$487$	−15.1302	−	6.90974i	−0.685616	−	0.313110i	−0.727594	+	0.686008i	$0.759361\pi$
$488$	−4.03329	−	16.5281i	−0.182578	−	0.748191i
$489$	0.596928	+	33.5478i	0.0269940	+	1.51709i
$490$	−31.9056	−	37.9889i	−1.44135	−	1.71616i
$491$	−33.9941	+	4.88761i	−1.53413	+	0.220575i	−0.857011	−	0.515299i	$-0.827681\pi$
$491$	−33.9941	+	4.88761i	−1.53413	+	0.220575i	−0.677119	+	0.735873i	$0.736772\pi$
$492$	−9.38813	+	10.5532i	−0.423249	+	0.475774i
$493$	−0.399914	−	0.346528i	−0.0180112	−	0.0156068i
$494$	0.778604	−	1.17142i	0.0350311	−	0.0527048i
$495$	−61.6791	+	11.1207i	−2.77227	+	0.499837i
$496$	21.5895	+	21.1733i	0.969396	+	0.950708i
$497$	−7.49226	+	25.5163i	−0.336074	+	1.14456i
$498$	26.0553	+	7.58337i	1.16757	+	0.339819i
$499$	−27.3166	−	31.5250i	−1.22286	−	1.41125i	−0.882074	−	0.471112i	$-0.843853\pi$
$499$	−27.3166	−	31.5250i	−1.22286	−	1.41125i	−0.340784	−	0.940142i	$-0.610693\pi$
$500$	8.74891	+	20.8344i	0.391263	+	0.931743i
$501$	−26.8820	−	3.37808i	−1.20100	−	0.150922i
$502$	21.0640	+	10.0149i	0.940131	+	0.446986i
$503$	−2.44688	+	17.0184i	−0.109101	+	0.758815i	0.859669	+	0.510852i	$0.170670\pi$
$503$	−2.44688	+	17.0184i	−0.109101	+	0.758815i	−0.968770	+	0.247962i	$0.920239\pi$
$504$	−10.1190	+	33.1499i	−0.450738	+	1.47662i
$505$	−0.704151			−0.0313343
$506$	−30.9263	−	23.9552i	−1.37484	−	1.06494i
$507$	−6.71997	−	2.92556i	−0.298444	−	0.129929i
$508$	14.9194	+	24.8687i	0.661941	+	1.10337i
$509$	0.251510	−	1.74929i	0.0111480	−	0.0775361i	−0.983488	−	0.180974i	$-0.942075\pi$
$509$	0.251510	−	1.74929i	0.0111480	−	0.0775361i	0.994636	+	0.103438i	$0.0329842\pi$
$510$	1.20294	+	1.38162i	0.0532670	+	0.0611792i
$511$	3.72240	+	12.6773i	0.164669	+	0.560812i
$512$	−6.46270	−	21.6849i	−0.285614	−	0.958345i
$513$	−0.616263	+	1.08178i	−0.0272087	+	0.0477616i
$514$	−0.999155	+	0.127968i	−0.0440709	+	0.00564443i
$515$	−6.36578	+	21.6799i	−0.280510	+	0.955329i
$516$	−24.7113	+	10.8980i	−1.08785	+	0.479760i
$517$	−1.37471	+	2.13909i	−0.0604596	+	0.0940769i
$518$	−21.2193	−	14.1037i	−0.932323	−	0.619682i
$519$	−0.0186960	+	0.00894350i	−0.000820662	+	0.000392576i
$520$	13.8549	−	40.2066i	0.607578	−	1.76317i
$521$	5.10504	−	0.733994i	0.223656	−	0.0321569i	−0.0295757	−	0.999563i	$-0.509416\pi$
$521$	5.10504	−	0.733994i	0.223656	−	0.0321569i	0.253232	+	0.967406i	$0.418507\pi$
$522$	1.33006	−	10.7914i	0.0582150	−	0.472325i
$523$	11.4222	+	25.0112i	0.499459	+	1.09366i	0.976645	+	0.214861i	$0.0689298\pi$
$523$	11.4222	+	25.0112i	0.499459	+	1.09366i	−0.477185	+	0.878803i	$0.658343\pi$
$524$	0.578808	+	2.22256i	0.0252853	+	0.0970928i
$525$	−38.3840	−	42.7370i	−1.67522	−	1.86519i
$526$	2.39224	−	14.9937i	0.104307	−	0.653754i
$527$	−1.31315	+	0.843908i	−0.0572016	+	0.0367612i
$528$	−18.1785	+	35.5860i	−0.791116	+	1.54868i
$529$	−6.43405	−	22.0817i	−0.279741	−	0.960075i
$530$	10.9147	+	0.168285i	0.474106	+	0.00730983i
$531$	3.83657	−	15.0242i	0.166493	−	0.651995i
$532$	−1.92796	−	0.338164i	−0.0835878	−	0.0146613i
$533$	−7.03123	+	15.3963i	−0.304557	+	0.666886i
$534$	1.58967	−	11.2459i	0.0687918	−	0.486659i
$535$	23.2215	−	10.6049i	1.00395	−	0.458489i
$536$	9.28568	+	11.7750i	0.401080	+	0.508601i
$537$	16.2615	+	4.46215i	0.701737	+	0.192556i
$538$	−21.4395	−	6.65590i	−0.924324	−	0.286956i
$539$	42.2164	+	36.5807i	1.81839	+	1.57564i
$540$	−9.78814	+	36.3467i	−0.421214	+	1.56411i
$541$	9.15055	−	14.2385i	0.393413	−	0.612163i	−0.586889	−	0.809668i	$-0.699647\pi$
$541$	9.15055	−	14.2385i	0.393413	−	0.612163i	0.980302	+	0.197505i	$0.0632838\pi$
$542$	21.4997	+	19.2179i	0.923492	+	0.825478i
$543$	−1.85392	+	2.21808i	−0.0795595	+	0.0951868i
$544$	1.16550	−	0.0767014i	0.0499704	−	0.00328854i
$545$	23.3854	−	20.2636i	1.00172	−	0.867996i
$546$	0.0986237	+	41.5335i	0.00422070	+	1.77747i
$547$	18.9987	−	5.57851i	0.812325	−	0.238520i	0.150917	−	0.988546i	$-0.451777\pi$
$547$	18.9987	−	5.57851i	0.812325	−	0.238520i	0.661408	+	0.750026i	$0.269959\pi$
$548$	−29.0774	−	14.3786i	−1.24212	−	0.614222i
$549$	10.2898	+	14.8238i	0.439158	+	0.632665i
$550$	−34.9425	−	56.2600i	−1.48995	−	2.39894i
$551$	0.614045			0.0261592
$552$	−20.9439	+	10.6467i	−0.891431	+	0.453156i
$553$	−28.7412			−1.22220
$554$	−2.87632	−	4.63109i	−0.122203	−	0.196756i
$555$	−23.5405	−	14.5434i	−0.999240	−	0.617333i
$556$	−18.6794	+	37.7748i	−0.792182	+	1.60201i
$557$	−15.8694	+	4.65968i	−0.672409	+	0.197437i	−0.600075	−	0.799943i	$-0.704863\pi$
$557$	−15.8694	+	4.65968i	−0.672409	+	0.197437i	−0.0723334	+	0.997381i	$0.523045\pi$
$558$	−29.4379	−	12.7328i	−1.24621	−	0.539024i
$559$	−24.4589	+	21.1937i	−1.03450	+	0.896399i
$560$	−58.9857	+	4.79616i	−2.49260	+	0.202675i
$561$	−1.58270	−	1.32286i	−0.0668215	−	0.0558511i
$562$	−3.56277	−	3.18464i	−0.150287	−	0.134336i
$563$	12.2616	−	19.0794i	0.516765	−	0.804102i	−0.480578	−	0.876952i	$-0.659573\pi$
$563$	12.2616	−	19.0794i	0.516765	−	0.804102i	0.997343	+	0.0728503i	$0.0232095\pi$
$564$	0.808819	+	1.29539i	0.0340574	+	0.0545456i
$565$	3.89509	+	3.37511i	0.163868	+	0.141992i
$566$	9.98264	+	3.09911i	0.419601	+	0.130265i
$567$	−2.61402	−	36.6694i	−0.109779	−	1.53997i
$568$	11.4026	+	14.4594i	0.478442	+	0.606702i
$569$	19.6484	−	8.97314i	0.823705	−	0.376174i	0.0414570	−	0.999140i	$-0.486800\pi$
$569$	19.6484	−	8.97314i	0.823705	−	0.376174i	0.782248	+	0.622967i	$0.214073\pi$
$570$	−2.10485	−	0.297533i	−0.0881627	−	0.0124623i
$571$	14.3810	−	31.4900i	0.601825	−	1.31781i	−0.326202	−	0.945300i	$-0.605769\pi$
$571$	14.3810	−	31.4900i	0.601825	−	1.31781i	0.928027	−	0.372513i	$-0.121504\pi$
$572$	−8.27272	+	47.1649i	−0.345900	+	1.97207i
$573$	35.6214	−	5.77018i	1.48811	−	0.241053i
$574$	23.5512	+	0.363115i	0.983008	+	0.0151561i
$575$	2.81816	−	38.8368i	0.117526	−	1.61961i
$576$	14.6594	+	19.0027i	0.610807	+	0.791779i
$577$	−30.7202	+	19.7427i	−1.27890	+	0.821898i	−0.990752	−	0.135689i	$-0.956675\pi$
$577$	−30.7202	+	19.7427i	−1.27890	+	0.821898i	−0.288146	+	0.957586i	$0.593039\pi$
$578$	3.77843	−	23.6818i	0.157162	−	0.985033i
$579$	−9.21710	+	8.27830i	−0.383050	+	0.344034i
$580$	17.9659	−	4.67877i	0.745995	−	0.194275i
$581$	−18.7984	−	41.1628i	−0.779890	−	1.70772i
$582$	9.35984	+	31.5989i	0.387978	+	1.30982i
$583$	−12.1663	+	1.74925i	−0.503877	+	0.0724466i
$584$	8.64974	+	2.98064i	0.357929	+	0.123340i
$585$	1.60468	+	45.0779i	0.0663454	+	1.86374i
$586$	−8.94218	−	5.94356i	−0.369398	−	0.245526i
$587$	−12.8427	+	19.9836i	−0.530073	+	0.824810i	−0.998269	−	0.0588150i	$-0.981268\pi$
$587$	−12.8427	+	19.9836i	−0.530073	+	0.824810i	0.468196	+	0.883625i	$0.344904\pi$
$588$	30.6969	−	13.5378i	1.26592	−	0.558289i
$589$	0.510311	−	1.73796i	0.0210270	−	0.0716114i
$590$	26.2618	−	3.36352i	1.08118	−	0.138474i
$591$	−2.33140	−	7.44723i	−0.0959008	−	0.306338i
$592$	−16.4695	+	6.32605i	−0.676892	+	0.259999i
$593$	−5.98792	−	20.3930i	−0.245894	−	0.837439i	−0.986255	−	0.165230i	$-0.947163\pi$
$593$	−5.98792	−	20.3930i	−0.245894	−	0.837439i	0.740361	−	0.672210i	$-0.234655\pi$
$594$	4.43552	−	42.1515i	0.181992	−	1.72950i
$595$	0.434754	−	3.02378i	0.0178232	−	0.123963i
$596$	−26.6689	+	15.9993i	−1.09240	+	0.655359i
$597$	−3.94727	+	9.06680i	−0.161551	+	0.371079i
$598$	−20.2328	+	19.5777i	−0.827379	+	0.800590i
$599$	27.3866			1.11899			0.559493	−	0.828835i	$-0.310996\pi$
$599$	27.3866			1.11899			0.559493	+	0.828835i	$0.310996\pi$
$600$	−39.5167	+	4.53815i	−1.61326	+	0.185269i
$601$	0.959269	−	6.67186i	0.0391294	−	0.272151i	−0.960859	−	0.277039i	$-0.910647\pi$
$601$	0.959269	−	6.67186i	0.0391294	−	0.272151i	0.999988	+	0.00488810i	$0.00155594\pi$
$602$	40.6742	+	19.3386i	1.65776	+	0.788182i
$603$	−13.6780	−	8.11767i	−0.557010	−	0.330577i
$604$	15.8243	−	6.64505i	0.643883	−	0.270383i
$605$	52.8164	+	60.9534i	2.14729	+	2.47811i
$606$	0.133075	−	0.457224i	0.00540578	−	0.0185735i
$607$	0.125869	−	0.428671i	0.00510887	−	0.0173992i	−0.956899	−	0.290421i	$-0.906205\pi$
$607$	0.125869	−	0.428671i	0.00510887	−	0.0173992i	0.962008	+	0.273021i	$0.0880230\pi$
$608$	−0.963833	+	0.952936i	−0.0390886	+	0.0386467i
$609$	−15.0765	+	10.0725i	−0.610929	+	0.408158i
$610$	−17.0554	+	25.6602i	−0.690554	+	1.03895i
$611$	1.38304	+	1.19841i	0.0559516	+	0.0484824i
$612$	−1.12446	+	0.519992i	−0.0454536	+	0.0210194i
$613$	−22.5695	+	3.24500i	−0.911572	+	0.131064i	−0.582115	−	0.813107i	$-0.697775\pi$
$613$	−22.5695	+	3.24500i	−0.911572	+	0.131064i	−0.329457	+	0.944171i	$0.606866\pi$
$614$	−10.9389	−	13.0246i	−0.441458	−	0.525628i
$615$	25.5762	−	0.455085i	1.03133	−	0.0183508i
$616$	64.7372	−	15.7976i	2.60834	−	0.636503i
$617$	30.3931	+	13.8800i	1.22358	+	0.558790i	0.919211	−	0.393765i	$-0.128828\pi$
$617$	30.3931	+	13.8800i	1.22358	+	0.558790i	0.304367	+	0.952555i	$0.401555\pi$
$618$	−12.8743	−	8.23066i	−0.517879	−	0.331086i
$619$	−21.4719	+	13.7991i	−0.863027	+	0.554634i	−0.895612	−	0.444835i	$-0.853262\pi$
$619$	−21.4719	+	13.7991i	−0.863027	+	0.554634i	0.0325854	+	0.999469i	$0.489626\pi$
$620$	1.68832	−	54.7382i	0.0678046	−	2.19834i
$621$	16.6751	−	18.5187i	0.669148	−	0.743129i
$622$	1.32486	+	0.0204269i	0.0531221	+	0.000819043i
$623$	−15.9332	+	10.2397i	−0.638352	+	0.410244i
$624$	23.4888	+	16.5948i	0.940305	+	0.664325i
$625$	0.135783	−	0.297324i	0.00543133	−	0.0118930i
$626$	−45.2636	+	12.5360i	−1.80910	+	0.501038i
$627$	2.39324	−	0.0425837i	0.0955768	−	0.00170063i
$628$	18.6199	−	15.1549i	0.743017	−	0.604748i
$629$	−0.129607	−	0.901438i	−0.00516778	−	0.0359427i
$630$	56.5604	−	27.2218i	2.25342	−	1.08454i
$631$	−29.7307	−	25.7618i	−1.18356	−	1.02556i	−0.999087	−	0.0427235i	$-0.986397\pi$
$631$	−29.7307	−	25.7618i	−1.18356	−	1.02556i	−0.184474	−	0.982837i	$-0.559058\pi$
$632$	−11.5222	+	16.2269i	−0.458327	+	0.645472i
$633$	17.1431	+	25.6597i	0.681376	+	1.01988i
$634$	−5.85229	+	6.54717i	−0.232424	+	0.260021i
$635$	14.7969	−	50.3937i	0.587198	−	1.99981i
$636$	−2.17200	+	7.05543i	−0.0861256	+	0.279766i
$637$	30.3833	−	26.3273i	1.20383	−	1.04313i
$638$	−19.1469	+	8.38979i	−0.758031	+	0.332155i
$639$	−16.7962	−	9.96830i	−0.664447	−	0.394340i
$640$	−20.9392	+	35.2254i	−0.827693	+	1.39240i
$641$	10.2462	+	1.47318i	0.404700	+	0.0581871i	0.341659	−	0.939824i	$-0.389011\pi$
$641$	10.2462	+	1.47318i	0.404700	+	0.0581871i	0.0630407	+	0.998011i	$0.479920\pi$
$642$	2.49751	+	17.0825i	0.0985687	+	0.674192i
$643$	−37.3914			−1.47457			−0.737287	−	0.675580i	$-0.763893\pi$
$643$	−37.3914			−1.47457			−0.737287	+	0.675580i	$0.763893\pi$
$644$	36.2540	+	14.8545i	1.42861	+	0.585351i
$645$	44.8461	+	19.5239i	1.76582	+	0.768754i
$646$	−0.0369137	−	0.0594339i	−0.00145235	−	0.00233840i
$647$	6.32777	−	44.0106i	0.248770	−	1.73024i	−0.356569	−	0.934269i	$-0.616053\pi$
$647$	6.32777	−	44.0106i	0.248770	−	1.73024i	0.605339	−	0.795968i	$-0.293037\pi$
$648$	−21.7510	−	13.2247i	−0.854461	−	0.519515i
$649$	−28.6047	+	8.39908i	−1.12283	+	0.329693i
$650$	−43.6574	+	19.1299i	−1.71239	+	0.750335i
$651$	15.9791	+	51.0425i	0.626272	+	2.00051i
$652$	−4.32893	−	38.5012i	−0.169534	−	1.50783i
$653$	13.0660	+	3.83654i	0.511314	+	0.150135i	0.527204	−	0.849738i	$-0.323240\pi$
$653$	13.0660	+	3.83654i	0.511314	+	0.150135i	−0.0158907	+	0.999874i	$0.505058\pi$
$654$	8.73817	+	19.0143i	0.341689	+	0.743518i
$655$	2.24873	−	3.49909i	0.0878650	−	0.136721i
$656$	9.64655	−	13.1511i	0.376634	−	0.513466i
$657$	−9.69773	+	0.345219i	−0.378344	+	0.0134683i
$658$	0.755061	−	2.43215i	0.0294354	−	0.0948151i
$659$	−3.59131	+	0.516353i	−0.139898	+	0.0201142i	−0.211908	−	0.977290i	$-0.567968\pi$
$659$	−3.59131	+	0.516353i	−0.139898	+	0.0201142i	0.0720102	+	0.997404i	$0.477059\pi$
$660$	69.6978	−	19.4814i	2.71298	−	0.758314i
$661$	1.04957	−	0.479323i	0.0408236	−	0.0186435i	−0.394899	−	0.918725i	$-0.629220\pi$
$661$	1.04957	−	0.479323i	0.0408236	−	0.0186435i	0.435722	+	0.900081i	$0.356493\pi$
$662$	30.7226	−	8.50876i	1.19407	−	0.330702i
$663$	−1.10448	+	0.991986i	−0.0428945	+	0.0385255i
$664$	−30.7762	−	5.88857i	−1.19435	−	0.228521i
$665$	1.91652	+	2.98216i	0.0743195	+	0.115643i
$666$	13.8922	−	12.5370i	0.538314	−	0.485799i
$667$	−12.0071	−	2.62504i	−0.464918	−	0.101642i
$668$	31.2699	+	0.964476i	1.20987	+	0.0373167i
$669$	7.16950	+	44.2600i	0.277189	+	1.71119i
$670$	4.27892	−	26.8186i	0.165309	−	1.03609i
$671$	14.4121	−	31.5581i	0.556374	−	1.21829i
$672$	8.03319	−	39.2074i	0.309887	−	1.51246i
$673$	−13.2273	−	28.9637i	−0.509875	−	1.11647i	−0.973132	−	0.230246i	$-0.926047\pi$
$673$	−13.2273	−	28.9637i	−0.509875	−	1.11647i	0.463258	−	0.886224i	$-0.346680\pi$
$674$	2.36451	+	2.81534i	0.0910776	+	0.108443i
$675$	37.3871	−	19.5485i	1.43903	−	0.752421i
$676$	8.04283	+	2.63351i	0.309340	+	0.101289i
$677$	−1.56796	+	1.80953i	−0.0602618	+	0.0695458i	−0.785080	−	0.619394i	$-0.787378\pi$
$677$	−1.56796	+	1.80953i	−0.0602618	+	0.0695458i	0.724818	+	0.688940i	$0.241924\pi$
$678$	−2.92767	+	1.89133i	−0.112436	+	0.0726363i
$679$	29.7118	−	46.2325i	1.14024	−	1.77424i
$680$	−1.53290	−	1.45767i	−0.0587839	−	0.0558991i
$681$	29.2612	−	35.0088i	1.12129	−	1.34154i
$682$	7.83374	+	61.1647i	0.299969	+	2.34212i
$683$	−30.9887	+	26.8518i	−1.18575	+	1.02746i	−0.186764	+	0.982405i	$0.559800\pi$
$683$	−30.9887	+	26.8518i	−1.18575	+	1.02746i	−0.998985	+	0.0450526i	$0.985654\pi$
$684$	0.590984	−	1.31051i	0.0225968	−	0.0501085i
$685$	16.5508	+	56.3669i	0.632374	+	2.15367i
$686$	−14.0073	−	6.65976i	−0.534799	−	0.254271i
$687$	30.0730	+	18.5792i	1.14736	+	0.708841i
$688$	27.2244	−	15.2114i	1.03792	−	0.579930i
$689$			8.84619i			0.337013i
$690$	39.8867	+	14.8162i	1.51846	+	0.564044i
$691$	−5.55683			−0.211392			−0.105696	−	0.994399i	$-0.533707\pi$
$691$	−5.55683			−0.211392			−0.105696	+	0.994399i	$0.533707\pi$
$692$	0.0205215	−	0.0123114i	0.000780110	−	0.000468008i
$693$	−58.0620	+	40.3031i	−2.20559	+	1.53099i
$694$	31.4055	+	14.9317i	1.19214	+	0.566801i
$695$	73.2270	−	21.5014i	2.77766	−	0.815594i
$696$	−0.357260	+	12.5500i	−0.0135419	+	0.475706i
$697$	0.551330	+	0.636269i	0.0208831	+	0.0241004i
$698$	20.7722	−	2.66042i	0.786238	−	0.100698i
$699$	16.0408	−	19.1915i	0.606717	−	0.725890i
$700$	48.7662	+	44.9619i	1.84319	+	1.69940i
$701$	−28.6439	−	18.4083i	−1.08187	−	0.695272i	−0.126878	−	0.991918i	$-0.540496\pi$
$701$	−28.6439	−	18.4083i	−1.08187	−	0.695272i	−0.954988	+	0.296646i	$0.904132\pi$
$702$	−29.5735	−	7.47712i	−1.11618	−	0.282206i
$703$	0.798672	+	0.692053i	0.0301225	+	0.0261013i
$704$	17.0336	−	42.8830i	0.641980	−	1.61621i
$705$	0.731863	−	2.66714i	0.0275636	−	0.100450i
$706$	−38.8920	+	32.6641i	−1.46372	+	1.22933i
$707$	−0.722334	+	0.329879i	−0.0271661	+	0.0124064i
$708$	−2.77909	+	17.6882i	−0.104445	+	0.664762i
$709$	−38.0391	−	17.3719i	−1.42859	−	0.652415i	−0.457082	−	0.889424i	$-0.651106\pi$
$709$	−38.0391	−	17.3719i	−1.42859	−	0.652415i	−0.971507	+	0.237009i	$0.923833\pi$
$710$	5.25440	−	32.9326i	0.197194	−	1.23594i
$711$	5.22274	−	20.4525i	0.195868	−	0.767029i
$712$	−0.606351	+	13.1007i	−0.0227240	+	0.490971i
$713$	−17.4085	+	31.8027i	−0.651952	+	1.19102i
$714$	1.88126	+	0.853748i	0.0704043	+	0.0319507i
$715$	72.9545	−	46.8850i	2.72834	−	1.75340i
$716$	−19.1785	−	3.36390i	−0.716734	−	0.125715i
$717$	−11.8129	+	10.6097i	−0.441159	+	0.396225i
$718$	35.9519	−	9.95704i	1.34171	−	0.371593i
$719$	−10.8754	−	23.8138i	−0.405584	−	0.888104i	−0.996673	−	0.0814986i	$-0.974029\pi$
$719$	−10.8754	−	23.8138i	−0.405584	−	0.888104i	0.591090	−	0.806606i	$-0.298698\pi$
$720$	7.30567	−	42.8464i	0.272266	−	1.59679i
$721$	3.62636	+	25.2219i	0.135053	+	0.939313i
$722$	−25.5843	−	7.94266i	−0.952150	−	0.295595i
$723$	−30.8614	+	14.7630i	−1.14775	+	0.549043i
$724$	1.89040	−	2.75117i	0.0702560	−	0.102246i
$725$	−17.5049	−	11.2497i	−0.650117	−	0.417805i
$726$	−49.5602	+	22.7758i	−1.83935	+	0.845288i
$727$	5.12224	−	17.4448i	0.189973	−	0.646990i	−0.808328	−	0.588732i	$-0.799627\pi$
$727$	5.12224	−	17.4448i	0.189973	−	0.646990i	0.998302	−	0.0582579i	$-0.0185546\pi$
$728$	−4.62318	−	47.7355i	−0.171347	−	1.76919i
$729$	26.5693	+	4.80326i	0.984049	+	0.177899i
$730$	−6.64982	−	15.1760i	−0.246121	−	0.561687i
$731$	0.453533	+	1.54459i	0.0167745	+	0.0571288i
$732$	−13.4386	−	15.9239i	−0.496705	−	0.588566i
$733$	24.6057	+	3.53776i	0.908831	+	0.130670i	0.580847	−	0.814013i	$-0.302721\pi$
$733$	24.6057	+	3.53776i	0.908831	+	0.130670i	0.327985	+	0.944683i	$0.393631\pi$
$734$	−19.3653	−	31.1796i	−0.714786	−	1.15086i
$735$	−55.7088	−	24.2530i	−2.05485	−	0.894587i
$736$	22.9207	−	14.5135i	0.844869	−	0.534974i
$737$			30.5796i			1.12641i
$738$	−4.53803	+	16.6933i	−0.167047	+	0.614488i
$739$	−4.61600	+	32.1050i	−0.169802	+	1.18100i	0.709489	+	0.704716i	$0.248926\pi$
$739$	−4.61600	+	32.1050i	−0.169802	+	1.18100i	−0.879291	+	0.476284i	$0.841983\pi$
$740$	28.6410	+	14.1628i	1.05286	+	0.520634i
$741$	0.214791	−	1.70925i	0.00789054	−	0.0627910i
$742$	11.2754	−	4.94068i	0.413934	−	0.181378i
$743$	23.9973	+	27.6944i	0.880377	+	1.01601i	0.999732	+	0.0231578i	$0.00737203\pi$
$743$	23.9973	+	27.6944i	0.880377	+	1.01601i	−0.119355	+	0.992852i	$0.538083\pi$
$744$	35.2239	+	11.4410i	1.29137	+	0.419448i
$745$	54.0415	+	15.8680i	1.97993	+	0.581360i
$746$	−31.0380	−	27.7437i	−1.13638	−	1.01577i
$747$	32.7078	−	5.89719i	1.19672	−	0.215767i
$748$	1.96308	+	1.34888i	0.0717774	+	0.0493200i
$749$	18.8529	−	21.7574i	0.688871	−	0.795000i
$750$	20.9586	+	18.0738i	0.765299	+	0.659961i
$751$	−16.4450	+	2.36443i	−0.600086	+	0.0862794i	−0.435662	−	0.900110i	$-0.643486\pi$
$751$	−16.4450	+	2.36443i	−0.600086	+	0.0862794i	−0.164424	+	0.986390i	$0.552577\pi$
$752$	−1.07046	−	1.40133i	−0.0390357	−	0.0511013i
$753$	28.5609	−	0.508193i	1.04082	−	0.0185196i
$754$	4.01560	+	14.4991i	0.146240	+	0.528027i
$755$	−28.2737	−	12.9122i	−1.02899	−	0.469922i
$756$	6.98670	+	41.8707i	0.254104	+	1.52282i
$757$	−9.05855	−	14.0954i	−0.329239	−	0.512305i	0.636688	−	0.771122i	$-0.280304\pi$
$757$	−9.05855	−	14.0954i	−0.329239	−	0.512305i	−0.965927	+	0.258816i	$0.916668\pi$
$758$	−16.9157	−	0.260808i	−0.614405	−	0.00947298i
$759$	−46.9798	−	9.39840i	−1.70526	−	0.341140i
$760$	2.45201	+	0.113488i	0.0889439	+	0.00411665i
$761$	7.33957	+	11.4206i	0.266059	+	0.413996i	0.948419	−	0.317020i	$-0.102682\pi$
$761$	7.33957	+	11.4206i	0.266059	+	0.413996i	−0.682359	+	0.731017i	$0.739046\pi$
$762$	29.9256	+	19.1317i	1.08409	+	0.693070i
$763$	14.4962	−	31.7424i	0.524799	−	1.14915i
$764$	−40.3233	+	10.5012i	−1.45885	+	0.379919i
$765$	2.07275	+	0.858845i	0.0749404	+	0.0310516i
$766$	−19.0922	−	22.7324i	−0.689829	−	0.821356i
$767$	3.05351	+	21.2376i	0.110256	+	0.766846i
$768$	−18.9155	−	20.2534i	−0.682556	−	0.730833i
$769$	8.59790	−	9.92251i	0.310048	−	0.357815i	−0.579244	−	0.815154i	$-0.696652\pi$
$769$	8.59790	−	9.92251i	0.310048	−	0.357815i	0.889292	+	0.457339i	$0.151198\pi$
$770$	−100.506	−	66.8027i	−3.62198	−	2.40740i
$771$	−1.02583	+	0.685350i	−0.0369443	+	0.0246823i
$772$	9.69695	−	10.5174i	0.349001	−	0.378530i
$773$	7.28846	+	2.14008i	0.262148	+	0.0769735i	0.410165	−	0.912011i	$-0.365471\pi$
$773$	7.28846	+	2.14008i	0.262148	+	0.0769735i	−0.148018	+	0.988985i	$0.547289\pi$
$774$	−21.1527	+	25.4300i	−0.760318	+	0.914064i
$775$	−46.3884	+	40.1958i	−1.66632	+	1.44387i
$776$	−14.1910	−	35.3093i	−0.509427	−	1.26753i
$777$	−30.9616	−	3.89075i	−1.11074	−	0.139580i
$778$	−2.10239	+	4.42188i	−0.0753742	+	0.158532i
$779$	−0.967011	−	0.139035i	−0.0346468	−	0.00498145i
$780$	−6.73939	−	51.6466i	−0.241309	−	1.84924i
$781$			37.5510i			1.34368i
$782$	0.467737	+	1.31999i	0.0167262	+	0.0472026i
$783$	−4.42805	−	12.5589i	−0.158246	−	0.448818i
$784$	−33.8187	+	18.8960i	−1.20781	+	0.674856i
$785$	−43.0363	−	6.18769i	−1.53603	−	0.220848i
$786$	1.84707	+	2.12144i	0.0658829	+	0.0756691i
$787$	34.3137	−	10.0754i	1.22315	−	0.359149i	0.394490	−	0.918900i	$-0.370921\pi$
$787$	34.3137	−	10.0754i	1.22315	−	0.359149i	0.828661	+	0.559751i	$0.189103\pi$
$788$	3.48877	+	8.30807i	0.124282	+	0.295963i
$789$	−5.55560	−	17.7464i	−0.197785	−	0.631788i
$790$	35.7503	−	4.57877i	1.27194	−	0.162905i
$791$	5.57683	+	1.63750i	0.198289	+	0.0582230i
$792$	−0.522084	+	48.9383i	−0.0185514	+	1.73895i
$793$	−21.0052	−	13.4992i	−0.745916	−	0.479371i
$794$	14.9781	−	22.5348i	0.531552	−	0.799730i
$795$	12.0605	−	5.76931i	0.427741	−	0.204616i
$796$	3.55322	−	10.8517i	0.125940	−	0.384627i
$797$	2.22808	+	15.4966i	0.0789225	+	0.548918i	0.990471	+	0.137725i	$0.0439789\pi$
$797$	2.22808	+	15.4966i	0.0789225	+	0.548918i	−0.911548	+	0.411194i	$0.865112\pi$
$798$	−2.29859	+	0.680861i	−0.0813693	+	0.0241022i
$799$	0.0828009	−	0.0378139i	0.00292928	−	0.00133776i
$800$	44.9350	−	9.50781i	1.58869	−	0.336152i
$801$	−4.39132	−	13.1990i	−0.155160	−	0.466363i
$802$	21.6164	+	3.44890i	0.763301	+	0.121785i
$803$	10.0865	+	15.6949i	0.355945	+	0.553861i
$804$	16.6054	+	7.84676i	0.585627	+	0.276734i
$805$	−24.7272	−	66.5068i	−0.871518	−	2.34406i
$806$	44.3748	+	0.684176i	1.56303	+	0.0240991i
$807$	−27.1404	+	4.39637i	−0.955389	+	0.154760i
$808$	−0.103334	+	0.540067i	−0.00363527	+	0.0189995i
$809$	19.1811	+	8.75973i	0.674372	+	0.307976i	0.723007	−	0.690841i	$-0.242760\pi$
$809$	19.1811	+	8.75973i	0.674372	+	0.307976i	−0.0486342	+	0.998817i	$0.515487\pi$
$810$	9.09333	+	45.1956i	0.319507	+	1.58801i
$811$	−8.93023	−	19.5545i	−0.313583	−	0.686651i	0.685561	−	0.728015i	$-0.259557\pi$
$811$	−8.93023	−	19.5545i	−0.313583	−	0.686651i	−0.999144	+	0.0413643i	$0.986830\pi$
$812$	16.2380	−	13.2162i	0.569841	−	0.463798i
$813$	34.0588	+	9.34573i	1.19450	+	0.327769i
$814$	−34.3594	−	10.6669i	−1.20430	−	0.373874i
$815$	−45.9492	+	53.0281i	−1.60953	+	1.85749i
$816$	1.23620	−	0.719872i	0.0432757	−	0.0252005i
$817$	−1.57149	−	1.00993i	−0.0549793	−	0.0353331i
$818$	0.192648	−	0.215522i	0.00673577	−	0.00753556i
$819$	22.7641	+	45.4901i	0.795441	+	1.58955i
$820$	−29.3525	+	3.30028i	−1.02503	+	0.115251i
$821$	15.2209	+	17.5658i	0.531213	+	0.613052i	0.956402	−	0.292052i	$-0.0943381\pi$
$821$	15.2209	+	17.5658i	0.531213	+	0.613052i	−0.425190	+	0.905104i	$0.639793\pi$
$822$	−39.7284	+	0.0943375i	−1.38569	+	0.00329040i
$823$	5.75395	+	19.5962i	0.200570	+	0.683079i	0.996933	+	0.0782602i	$0.0249365\pi$
$823$	5.75395	+	19.5962i	0.200570	+	0.683079i	−0.796363	+	0.604819i	$0.793245\pi$
$824$	15.6938	+	8.06391i	0.546718	+	0.280920i
$825$	−69.0056	−	42.6319i	−2.40247	−	1.48425i
$826$	25.3642	−	15.7534i	0.882535	−	0.548132i
$827$		−	47.2674i		−	1.64365i	−0.569740	−	0.821825i	$-0.692956\pi$
$827$		−	47.2674i		−	1.64365i	0.569740	−	0.821825i	$-0.307044\pi$
$828$	−17.1586	+	23.0994i	−0.596302	+	0.802760i
$829$		−	5.79740i		−	0.201352i	−0.994919	−	0.100676i	$-0.967899\pi$
$829$		−	5.79740i		−	0.201352i	0.994919	−	0.100676i	$-0.0321005\pi$
$830$	29.9405	+	48.2065i	1.03925	+	1.67327i
$831$	−5.68025	−	3.50927i	−0.197046	−	0.121735i
$832$	−28.8043	−	16.5267i	−0.998608	−	0.572959i
$833$	−0.563389	−	1.91873i	−0.0195203	−	0.0664799i
$834$	0.122555	+	51.6116i	0.00424373	+	1.78717i
$835$	−37.1029	−	42.8190i	−1.28400	−	1.48181i
$836$	−2.74661	+	0.308818i	−0.0949934	+	0.0106807i
$837$	−39.2260	+	2.09565i	−1.35585	+	0.0724364i
$838$	−12.9778	−	11.6004i	−0.448311	−	0.400730i
$839$	24.3435	+	15.6446i	0.840431	+	0.540112i	0.888577	−	0.458728i	$-0.151695\pi$
$839$	24.3435	+	15.6446i	0.840431	+	0.540112i	−0.0481455	+	0.998840i	$0.515331\pi$
$840$	−62.0652	+	37.4352i	−2.14145	+	1.29164i
$841$	14.6899	−	16.9530i	0.506548	−	0.584588i
$842$	−10.9626	+	35.3120i	−0.377797	+	1.21693i
$843$	−5.64397	−	1.54870i	−0.194389	−	0.0533402i
$844$	−22.4936	−	27.6365i	−0.774261	−	0.951287i
$845$	−6.36697	−	13.9417i	−0.219030	−	0.479610i
$846$	1.59354	+	0.979270i	0.0547869	+	0.0336680i
$847$	82.7354	+	37.7840i	2.84282	+	1.29827i
$848$	1.73080	−	8.34665i	0.0594361	−	0.286625i
$849$	12.6371	−	2.04703i	0.433704	−	0.0702539i
$850$	−0.0365503	+	2.37060i	−0.00125366	+	0.0813110i
$851$	−12.6588	−	16.9468i	−0.433939	−	0.580930i
$852$	20.3910	+	9.63562i	0.698585	+	0.330111i
$853$	6.49283	+	10.1030i	0.222310	+	0.345921i	0.934436	−	0.356130i	$-0.115904\pi$
$853$	6.49283	+	10.1030i	0.222310	+	0.345921i	−0.712126	+	0.702051i	$0.752268\pi$
$854$	−5.47462	+	34.3128i	−0.187337	+	1.17416i
$855$	−2.47040	+	0.821907i	−0.0844859	+	0.0281086i
$856$	−4.72595	−	19.3666i	−0.161530	−	0.661935i
$857$	−37.1239	+	16.9539i	−1.26813	+	0.579135i	−0.931924	−	0.362653i	$-0.881871\pi$
$857$	−37.1239	+	16.9539i	−1.26813	+	0.579135i	−0.336205	+	0.941789i	$0.609144\pi$
$858$	16.6563	+	56.2319i	0.568637	+	1.91972i
$859$	8.07856	+	56.1876i	0.275637	+	1.91710i	0.384663	+	0.923057i	$0.374318\pi$
$859$	8.07856	+	56.1876i	0.275637	+	1.91710i	−0.109026	+	0.994039i	$0.534773\pi$
$860$	−53.6744	−	17.5749i	−1.83028	−	0.599299i
$861$	26.0234	−	12.4487i	0.886875	−	0.424250i
$862$	−6.51747	−	4.33194i	−0.221986	−	0.147546i
$863$	1.61501	+	1.03790i	0.0549756	+	0.0353307i	0.567840	−	0.823139i	$-0.307779\pi$
$863$	1.61501	+	1.03790i	0.0549756	+	0.0353307i	−0.512864	+	0.858470i	$0.671416\pi$
$864$	26.4406	+	12.8411i	0.899528	+	0.436864i
$865$	−0.0415845	−	0.0122103i	−0.00141392	−	0.000415163i
$866$	1.55104	+	12.1103i	0.0527066	+	0.411525i
$867$	−8.77482	−	28.0296i	−0.298009	−	0.951936i
$868$	−23.9117	−	56.9426i	−0.811615	−	1.93276i
$869$	−38.9396	+	11.4337i	−1.32094	+	0.387862i
$870$	17.1485	−	14.9307i	0.581390	−	0.506199i
$871$	21.7843	+	3.13210i	0.738132	+	0.106127i
$872$	−12.1099	−	20.9097i	−0.410092	−	0.708093i
$873$	27.5004	+	29.5444i	0.930748	+	0.999928i
$874$	−1.41326	−	0.802164i	−0.0478043	−	0.0271336i
$875$		−	46.1508i		−	1.56018i
$876$	11.1109	−	1.44986i	0.375401	−	0.0489863i
$877$	−25.9003	−	3.72390i	−0.874591	−	0.125747i	−0.309623	−	0.950860i	$-0.600203\pi$
$877$	−25.9003	−	3.72390i	−0.874591	−	0.125747i	−0.564969	+	0.825112i	$0.691112\pi$
$878$	−23.5962	−	11.2188i	−0.796334	−	0.378617i
$879$	−13.0478	−	1.63963i	−0.440090	−	0.0553033i
$880$	−78.0081	+	29.9635i	−2.62965	+	1.01007i
$881$	25.8675	−	22.4143i	0.871498	−	0.755157i	−0.0992999	−	0.995058i	$-0.531660\pi$
$881$	25.8675	−	22.4143i	0.871498	−	0.755157i	0.970797	+	0.239901i	$0.0771149\pi$
$882$	26.2763	−	31.5897i	0.884770	−	1.06368i
$883$	16.6627	+	4.89262i	0.560746	+	0.164650i	0.549809	−	0.835290i	$-0.314700\pi$
$883$	16.6627	+	4.89262i	0.560746	+	0.164650i	0.0109369	+	0.999940i	$0.496519\pi$
$884$	1.16198	−	1.26030i	0.0390817	−	0.0423884i
$885$	26.9629	−	18.0138i	0.906349	−	0.605526i
$886$	−12.7726	+	19.2167i	−0.429105	+	0.645596i
$887$	−15.9739	+	18.4348i	−0.536350	+	0.618980i	−0.957648	−	0.287942i	$-0.907029\pi$
$887$	−15.9739	+	18.4348i	−0.536350	+	0.618980i	0.421298	+	0.906922i	$0.361575\pi$
$888$	−14.6090	+	15.9208i	−0.490246	+	0.534266i
$889$	−8.42929	−	58.6270i	−0.282709	−	1.96629i
$890$	18.1876	−	15.2752i	0.609651	−	0.512025i
$891$	−18.1293	−	48.6412i	−0.607353	−	1.62954i
$892$	−13.0478	−	50.1021i	−0.436873	−	1.67754i
$893$	−0.0438796	+	0.0960829i	−0.00146838	+	0.00321529i
$894$	−20.5166	+	32.0918i	−0.686178	+	1.07331i
$895$	19.0647	+	29.6652i	0.637261	+	0.991598i
$896$	−4.97759	+	45.9445i	−0.166290	+	1.53490i
$897$	−11.5071	+	32.5048i	−0.384211	+	1.08530i
$898$	0.581943	−	37.7441i	0.0194197	−	1.25954i
$899$	10.4745	+	16.2986i	0.349344	+	0.543590i
$900$	−40.8569	+	26.5322i	−1.36190	+	0.884406i
$901$	0.400254	+	0.182790i	0.0133344	+	0.00608961i
$902$	32.0525	−	8.87709i	1.06723	−	0.295575i
$903$	55.1507	−	0.981314i	1.83530	−	0.0326561i
$904$	3.16023	−	2.49214i	0.105108	−	0.0828874i
$905$	−5.98377	+	0.860336i	−0.198907	+	0.0285985i
$906$	13.7276	−	15.9187i	0.456067	−	0.528862i
$907$	−11.2820	+	13.0201i	−0.374611	+	0.432325i	−0.911482	−	0.411340i	$-0.865061\pi$
$907$	−11.2820	+	13.0201i	−0.374611	+	0.432325i	0.536871	+	0.843665i	$0.319606\pi$
$908$	−29.8369	+	43.4228i	−0.990171	+	1.44104i
$909$	−0.103485	−	0.573964i	−0.00343239	−	0.0190372i
$910$	−57.8831	+	64.7559i	−1.91880	+	2.14664i
$911$	−25.9514	−	7.62003i	−0.859810	−	0.252463i	−0.178034	−	0.984024i	$-0.556974\pi$
$911$	−25.9514	−	7.62003i	−0.859810	−	0.252463i	−0.681776	+	0.731561i	$0.738792\pi$
$912$	−0.537087	+	1.57071i	−0.0177847	+	0.0520114i
$913$	−41.8441	−	48.2906i	−1.38484	−	1.59819i
$914$	−7.64090	−	17.4378i	−0.252739	−	0.576790i
$915$	−4.70502	+	37.4414i	−0.155543	+	1.23778i
$916$	−36.5888	−	18.0930i	−1.20893	−	0.597808i
$917$	0.667551	−	4.64292i	0.0220445	−	0.153323i
$918$	−0.949391	+	1.18358i	−0.0313346	+	0.0390640i
$919$			30.5019i			1.00616i	0.864238	+	0.503082i	$0.167801\pi$
$919$			30.5019i			1.00616i	−0.864238	+	0.503082i	$0.832199\pi$
$920$	−47.4619	−	12.7015i	−1.56477	−	0.418756i
$921$	−19.0999	−	8.31520i	−0.629362	−	0.273995i
$922$	22.9193	−	14.2349i	0.754809	−	0.468803i
$923$	26.7505	+	3.84615i	0.880505	+	0.126597i
$924$	62.3709	−	52.6363i	2.05185	−	1.73161i
$925$	−10.0893	−	34.3610i	−0.331734	−	1.12978i
$926$	33.2199	−	14.5563i	1.09167	−	0.478350i
$927$	−18.6071	−	2.00268i	−0.611138	−	0.0657765i
$928$	−0.952010	−	14.4661i	−0.0312513	−	0.474871i
$929$	2.21603	−	7.54710i	0.0727055	−	0.247612i	−0.915119	−	0.403183i	$-0.867904\pi$
$929$	2.21603	−	7.54710i	0.0727055	−	0.247612i	0.987825	+	0.155571i	$0.0497218\pi$
$930$	−28.0076	−	60.9447i	−0.918405	−	1.99846i
$931$	1.95213	+	1.25456i	0.0639786	+	0.0411165i
$932$	−16.3563	+	23.8040i	−0.535769	+	0.779727i
$933$	1.46393	−	0.700294i	0.0479270	−	0.0229266i
$934$	−5.72687	+	18.4470i	−0.187389	+	0.603604i
$935$	−0.613888	−	4.26968i	−0.0200763	−	0.139634i
$936$	34.8091	+	5.38441i	1.13777	+	0.175995i
$937$	−1.16692	−	2.55520i	−0.0381216	−	0.0834747i	0.889613	−	0.456715i	$-0.150974\pi$
$937$	−1.16692	−	2.55520i	−0.0381216	−	0.0834747i	−0.927735	+	0.373240i	$0.878247\pi$
$938$	−8.17451	−	29.5157i	−0.266907	−	0.963722i
$939$	−42.7961	+	38.4371i	−1.39660	+	1.25435i
$940$	−0.551733	+	3.14557i	−0.0179955	+	0.102597i
$941$	43.9943	−	28.2734i	1.43417	−	0.921687i	0.434393	−	0.900723i	$-0.356963\pi$
$941$	43.9943	−	28.2734i	1.43417	−	0.921687i	0.999780	−	0.0209637i	$-0.00667346\pi$
$942$	12.1511	−	26.7752i	0.395904	−	0.872384i
$943$	18.3147	+	6.85268i	0.596408	+	0.223154i
$944$	1.27418	−	20.6358i	0.0414709	−	0.671638i
$945$	47.1728	−	60.7033i	1.53453	−	1.97468i
$946$	62.8002	+	10.0198i	2.04181	+	0.325771i
$947$	−0.621582	−	0.283867i	−0.0201987	−	0.00922443i	0.405290	−	0.914188i	$-0.367171\pi$
$947$	−0.621582	−	0.283867i	−0.0201987	−	0.00922443i	−0.425489	+	0.904964i	$0.639898\pi$
$948$	−3.78319	+	24.0790i	−0.122872	+	0.782048i
$949$	12.2138	−	5.57786i	0.396477	−	0.181065i
$950$	−1.76938	−	2.10674i	−0.0574064	−	0.0683518i
$951$	−2.84599	+	10.3717i	−0.0922876	+	0.336326i
$952$	−2.25537	−	0.777184i	−0.0730968	−	0.0251887i
$953$	−42.0698	−	36.4537i	−1.36278	−	1.18085i	−0.964654	−	0.263519i	$-0.915117\pi$
$953$	−42.0698	−	36.4537i	−1.36278	−	1.18085i	−0.398122	−	0.917333i	$-0.630338\pi$
$954$	1.46691	+	8.92150i	0.0474929	+	0.288844i
$955$	63.4831	+	40.7981i	2.05426	+	1.32020i
$956$	12.4278	−	13.4794i	0.401945	−	0.435954i
$957$	−16.4192	+	19.6443i	−0.530756	+	0.635009i
$958$	−4.38502	−	34.2376i	−0.141674	−	1.10617i
$959$	43.3848	+	50.0687i	1.40097	+	1.61680i
$960$	−3.74611	+	50.0488i	−0.120905	+	1.61532i
$961$	25.0915	−	7.36753i	0.809404	−	0.237662i
$962$	−11.1181	+	23.3844i	−0.358462	+	0.753942i
$963$	12.0569	+	17.3696i	0.388529	+	0.559728i
$964$	33.8748	−	20.3223i	1.09103	−	0.654538i
$965$	−25.9077			−0.833997
$966$	47.8577	−	3.48717i	1.53980	−	0.112198i
$967$		−	25.4311i		−	0.817809i	−0.912577	−	0.408905i	$-0.865911\pi$
$967$		−	25.4311i		−	0.817809i	0.912577	−	0.408905i	$-0.134089\pi$
$968$	54.5005	−	31.5640i	1.75171	−	1.01451i
$969$	−0.0728985	−	0.0450369i	−0.00234184	−	0.00144680i
$970$	−29.5924	+	62.2408i	−0.950155	+	1.99843i
$971$	15.8565	+	54.0022i	0.508858	+	1.73301i	0.666489	+	0.745515i	$0.267796\pi$
$971$	15.8565	+	54.0022i	0.508858	+	1.73301i	−0.157631	+	0.987498i	$0.550386\pi$
$972$	−31.0652	−	2.63679i	−0.996417	−	0.0845750i
$973$	65.0449	−	56.3617i	2.08524	−	1.80687i
$974$	23.3325	−	2.98834i	0.747622	−	0.0957526i
$975$	−37.4379	+	44.7916i	−1.19897	+	1.43448i
$976$	17.1779	+	16.8467i	0.549850	+	0.539250i
$977$	4.70247	−	7.31719i	0.150445	−	0.234098i	−0.757848	−	0.652431i	$-0.773749\pi$
$977$	4.70247	−	7.31719i	0.150445	−	0.234098i	0.908294	+	0.418333i	$0.137386\pi$
$978$	−25.7488	−	39.8576i	−0.823357	−	1.27450i
$979$	−17.5135	+	20.2116i	−0.559733	+	0.645966i
$980$	66.6754	+	21.8319i	2.12987	+	0.697395i
$981$	19.9540	+	16.0838i	0.637081	+	0.513515i
$982$	37.1921	−	31.2364i	1.18685	−	0.996794i
$983$	4.38170	+	9.59459i	0.139755	+	0.306020i	0.966548	−	0.256486i	$-0.0825647\pi$
$983$	4.38170	+	9.59459i	0.139755	+	0.306020i	−0.826793	+	0.562506i	$0.809837\pi$
$984$	3.40425	−	19.6831i	0.108524	−	0.627474i
$985$	6.77913	−	14.8442i	0.216001	−	0.472976i
$986$	0.739001	+	0.117908i	0.0235346	+	0.00375495i
$987$	−0.498735	−	3.07888i	−0.0158749	−	0.0980017i
$988$	−0.0613249	+	1.98825i	−0.00195100	+	0.0632548i
$989$	26.4116	+	26.4665i	0.839840	+	0.841584i
$990$	65.8010	−	59.3818i	2.09129	−	1.88728i
$991$	−4.41472	−	6.86944i	−0.140238	−	0.218215i	0.764029	−	0.645182i	$-0.223218\pi$
$991$	−4.41472	−	6.86944i	−0.140238	−	0.218215i	−0.904267	+	0.426967i	$0.859582\pi$
$992$	−41.7351	−	9.32771i	−1.32509	−	0.296155i
$993$	29.0477	−	26.0891i	0.921802	−	0.827913i
$994$	−10.0381	−	36.2446i	−0.318389	−	1.14961i
$995$	−18.8106	+	8.59052i	−0.596337	+	0.272338i
$996$	−36.9601	+	10.3308i	−1.17112	+	0.327344i
$997$	−4.78096	+	0.687398i	−0.151414	+	0.0217701i	−0.217605	−	0.976037i	$-0.569825\pi$
$997$	−4.78096	+	0.687398i	−0.151414	+	0.0217701i	0.0661907	+	0.997807i	$0.478915\pi$
$998$	56.3394	+	17.4906i	1.78339	+	0.553654i
$999$	8.39493	−	21.3256i	0.265604	−	0.674712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.x.a.35.18	✓	920
3.2	odd	2	inner	552.2.x.a.35.75	yes	920
8.3	odd	2	inner	552.2.x.a.35.74	yes	920
23.2	even	11	inner	552.2.x.a.347.19	yes	920
24.11	even	2	inner	552.2.x.a.35.19	yes	920
69.2	odd	22	inner	552.2.x.a.347.74	yes	920
184.163	odd	22	inner	552.2.x.a.347.75	yes	920
552.347	even	22	inner	552.2.x.a.347.18	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.x.a.35.18	✓	920	1.1	even	1	trivial
552.2.x.a.35.19	yes	920	24.11	even	2	inner
552.2.x.a.35.74	yes	920	8.3	odd	2	inner
552.2.x.a.35.75	yes	920	3.2	odd	2	inner
552.2.x.a.347.18	yes	920	552.347	even	22	inner
552.2.x.a.347.19	yes	920	23.2	even	11	inner
552.2.x.a.347.74	yes	920	69.2	odd	22	inner
552.2.x.a.347.75	yes	920	184.163	odd	22	inner

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.x (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20136 + 0.746150i) q^{2} +(-0.910347 + 1.47352i) q^{3} +(0.886521 - 1.79279i) q^{4} +(-3.47534 + 1.02045i) q^{5} +(-0.00581645 - 2.44948i) q^{6} +(-3.08702 + 2.67492i) q^{7} +(0.272658 + 2.81525i) q^{8} +(-1.34254 - 2.68283i) q^{9} +O(q^{10})\)	\(q+(-1.20136 + 0.746150i) q^{2} +(-0.910347 + 1.47352i) q^{3} +(0.886521 - 1.79279i) q^{4} +(-3.47534 + 1.02045i) q^{5} +(-0.00581645 - 2.44948i) q^{6} +(-3.08702 + 2.67492i) q^{7} +(0.272658 + 2.81525i) q^{8} +(-1.34254 - 2.68283i) q^{9} +(3.41372 - 3.81905i) q^{10} +(-3.11829 + 4.85215i) q^{11} +(1.83467 + 2.93837i) q^{12} +(3.13718 + 2.71838i) q^{13} +(1.71273 - 5.51692i) q^{14} +(1.66011 - 6.04996i) q^{15} +(-2.42816 - 3.17868i) q^{16} +(0.187820 - 0.0857744i) q^{17} +(3.61466 + 2.22131i) q^{18} +(-0.0995334 + 0.217948i) q^{19} +(-1.25151 + 7.13520i) q^{20} +(-1.13129 - 6.98390i) q^{21} +(0.125748 - 8.15588i) q^{22} +(2.87802 - 3.83628i) q^{23} +(-4.39655 - 2.16109i) q^{24} +(6.83041 - 4.38964i) q^{25} +(-5.79720 - 0.924943i) q^{26} +(5.17539 + 0.464048i) q^{27} +(2.05885 + 7.90574i) q^{28} +(-1.06462 - 2.33120i) q^{29} +(2.51980 + 8.50686i) q^{30} +(-7.48287 + 1.07587i) q^{31} +(5.28886 + 2.00697i) q^{32} +(-4.31103 - 9.01201i) q^{33} +(-0.161638 + 0.243187i) q^{34} +(7.99883 - 12.4464i) q^{35} +(-5.99993 + 0.0284946i) q^{36} +(1.24263 - 4.23200i) q^{37} +(-0.0430464 - 0.336100i) q^{38} +(-6.86152 + 2.14804i) q^{39} +(-3.82041 - 9.50574i) q^{40} +(1.14875 + 3.91228i) q^{41} +(6.57013 + 7.54605i) q^{42} +(-1.10955 + 7.71709i) q^{43} +(5.93444 + 9.89196i) q^{44} +(7.40348 + 7.95377i) q^{45} +(-0.595090 + 6.75617i) q^{46} +0.440853 q^{47} +(6.89433 - 0.684245i) q^{48} +(1.37831 - 9.58634i) q^{49} +(-4.93044 + 10.3700i) q^{50} +(-0.0445905 + 0.354841i) q^{51} +(7.65465 - 3.21439i) q^{52} +(1.39554 + 1.61054i) q^{53} +(-6.56374 + 3.30413i) q^{54} +(5.88573 - 20.0450i) q^{55} +(-8.37228 - 7.96142i) q^{56} +(-0.230541 - 0.345073i) q^{57} +(3.01842 + 2.00624i) q^{58} +(3.90630 + 3.38483i) q^{59} +(-9.37456 - 8.33963i) q^{60} +(-5.95381 + 0.856029i) q^{61} +(8.18684 - 6.87585i) q^{62} +(11.3208 + 4.69079i) q^{63} +(-7.85132 + 1.53520i) q^{64} +(-13.6768 - 6.24597i) q^{65} +(11.9034 + 7.60997i) q^{66} +(4.46017 - 2.86638i) q^{67} +(0.0127310 - 0.412761i) q^{68} +(3.03285 + 7.73316i) q^{69} +(-0.322562 + 20.9209i) q^{70} +(5.47698 - 3.51984i) q^{71} +(7.18680 - 4.51108i) q^{72} +(1.34371 - 2.94232i) q^{73} +(1.66487 + 6.01133i) q^{74} +(0.250190 + 14.0609i) q^{75} +(0.302495 + 0.371657i) q^{76} +(-3.35289 - 23.3199i) q^{77} +(6.64038 - 7.70028i) q^{78} +(5.31766 + 4.60778i) q^{79} +(11.6824 + 8.56919i) q^{80} +(-5.39518 + 7.20361i) q^{81} +(-4.29920 - 3.84291i) q^{82} +(-3.12115 + 10.6297i) q^{83} +(-13.5236 - 4.16321i) q^{84} +(-0.565209 + 0.489756i) q^{85} +(-4.42514 - 10.0989i) q^{86} +(4.40425 + 0.553453i) q^{87} +(-14.5103 - 7.45580i) q^{88} +(4.58957 + 0.659881i) q^{89} +(-14.8289 - 4.03121i) q^{90} -16.9560 q^{91} +(-4.32620 - 8.56061i) q^{92} +(5.22668 - 12.0056i) q^{93} +(-0.529622 + 0.328942i) q^{94} +(0.123507 - 0.859012i) q^{95} +(-7.77201 + 5.96623i) q^{96} +(-12.9092 + 3.79049i) q^{97} +(5.49700 + 12.5450i) q^{98} +(17.2039 + 1.85165i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9}+O(q^{10}) \) 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9	\( 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9} - 14 q^{10} - 6 q^{12} - 30 q^{16} - 16 q^{18} - 52 q^{19} - 32 q^{22} - 26 q^{24} - 112 q^{25} - 30 q^{27} - 34 q^{28} + 11 q^{30} - 30 q^{33} - 88 q^{34} - 18 q^{36} + 124 q^{40} - 3 q^{42} - 36 q^{43} - 110 q^{46} + 32 q^{49} - 30 q^{51} + 90 q^{52} - 39 q^{54} - 6 q^{57} - 68 q^{58} + 13 q^{60} + 28 q^{64} - 46 q^{66} - 100 q^{67} - 92 q^{70} + 29 q^{72} - 36 q^{73} + 14 q^{75} - 50 q^{76} - 86 q^{78} - 2 q^{81} - 12 q^{82} - 151 q^{84} - 42 q^{88} - 196 q^{90} - 136 q^{91} - 68 q^{94} - 175 q^{96} - 36 q^{97} - 54 q^{99}+O(q^{100}) \) 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9 - 14 * q^10 - 6 * q^12 - 30 * q^16 - 16 * q^18 - 52 * q^19 - 32 * q^22 - 26 * q^24 - 112 * q^25 - 30 * q^27 - 34 * q^28 + 11 * q^30 - 30 * q^33 - 88 * q^34 - 18 * q^36 + 124 * q^40 - 3 * q^42 - 36 * q^43 - 110 * q^46 + 32 * q^49 - 30 * q^51 + 90 * q^52 - 39 * q^54 - 6 * q^57 - 68 * q^58 + 13 * q^60 + 28 * q^64 - 46 * q^66 - 100 * q^67 - 92 * q^70 + 29 * q^72 - 36 * q^73 + 14 * q^75 - 50 * q^76 - 86 * q^78 - 2 * q^81 - 12 * q^82 - 151 * q^84 - 42 * q^88 - 196 * q^90 - 136 * q^91 - 68 * q^94 - 175 * q^96 - 36 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

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