LMFDB - Embedded newform 385.2.bg.a.291.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(16,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 10, 12]))

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

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

chi := DirichletCharacter("385.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			291.13
Character	$\chi$	$=$	385.291
Dual form			385.2.bg.a.86.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18747 - 1.31881i) q^{2} +(-2.83596 + 1.26265i) q^{3} +(-0.120139 - 1.14305i) q^{4} +(0.978148 - 0.207912i) q^{5} +(-1.70240 + 5.23946i) q^{6} +(-2.35120 - 1.21320i) q^{7} +(1.22130 + 0.887324i) q^{8} +(4.44100 - 4.93223i) q^{9} +O(q^{10})$	\(q+(1.18747 - 1.31881i) q^{2} +(-2.83596 + 1.26265i) q^{3} +(-0.120139 - 1.14305i) q^{4} +(0.978148 - 0.207912i) q^{5} +(-1.70240 + 5.23946i) q^{6} +(-2.35120 - 1.21320i) q^{7} +(1.22130 + 0.887324i) q^{8} +(4.44100 - 4.93223i) q^{9} +(0.887320 - 1.53688i) q^{10} +(2.89302 + 1.62185i) q^{11} +(1.78398 + 3.08995i) q^{12} +(1.56545 + 4.81797i) q^{13} +(-4.39196 + 1.66016i) q^{14} +(-2.51147 + 1.82469i) q^{15} +(4.86892 - 1.03492i) q^{16} +(4.54211 + 5.04453i) q^{17} +(-1.23116 - 11.7137i) q^{18} +(0.470588 - 4.47735i) q^{19} +(-0.355167 - 1.09309i) q^{20} +(8.19976 + 0.471853i) q^{21} +(5.57429 - 1.88947i) q^{22} +(1.37086 + 2.37440i) q^{23} +(-4.58393 - 0.974344i) q^{24} +(0.913545 - 0.406737i) q^{25} +(8.21293 + 3.65663i) q^{26} +(-3.48892 + 10.7378i) q^{27} +(-1.10428 + 2.83329i) q^{28} +(1.53934 - 1.11840i) q^{29} +(-0.575857 + 5.47892i) q^{30} +(-2.48116 - 0.527387i) q^{31} +(2.90720 - 5.03542i) q^{32} +(-10.2523 - 0.946631i) q^{33} +12.0464 q^{34} +(-2.55206 - 0.697850i) q^{35} +(-6.17131 - 4.48372i) q^{36} +(-1.98819 - 0.885198i) q^{37} +(-5.34598 - 5.93732i) q^{38} +(-10.5230 - 11.6870i) q^{39} +(1.37909 + 0.614012i) q^{40} +(-7.04414 - 5.11787i) q^{41} +(10.3592 - 10.2537i) q^{42} -4.20393 q^{43} +(1.50629 - 3.50172i) q^{44} +(3.31848 - 5.74778i) q^{45} +(4.75924 + 1.01161i) q^{46} +(-0.284103 + 2.70306i) q^{47} +(-12.5013 + 9.08275i) q^{48} +(4.05627 + 5.70497i) q^{49} +(0.548394 - 1.68778i) q^{50} +(-19.2507 - 8.57098i) q^{51} +(5.31911 - 2.36822i) q^{52} +(1.42109 + 0.302061i) q^{53} +(10.0182 + 17.3520i) q^{54} +(3.16701 + 0.984918i) q^{55} +(-1.79501 - 3.56796i) q^{56} +(4.31876 + 13.2918i) q^{57} +(0.352957 - 3.35816i) q^{58} +(0.957850 + 9.11333i) q^{59} +(2.38743 + 2.65151i) q^{60} +(6.57524 - 1.39761i) q^{61} +(-3.64182 + 2.64594i) q^{62} +(-16.4255 + 6.20881i) q^{63} +(-0.112198 - 0.345310i) q^{64} +(2.53296 + 4.38721i) q^{65} +(-13.4227 + 12.3968i) q^{66} +(4.25698 - 7.37331i) q^{67} +(5.22046 - 5.79790i) q^{68} +(-6.88574 - 5.00279i) q^{69} +(-3.95082 + 2.53702i) q^{70} +(-0.762500 + 2.34674i) q^{71} +(9.80025 - 2.08311i) q^{72} +(-0.0333187 - 0.317007i) q^{73} +(-3.52832 + 1.57091i) q^{74} +(-2.07721 + 2.30698i) q^{75} -5.17437 q^{76} +(-4.83444 - 7.32313i) q^{77} -27.9086 q^{78} +(-3.26857 + 3.63011i) q^{79} +(4.54735 - 2.02461i) q^{80} +(-1.58239 - 15.0555i) q^{81} +(-15.1142 + 3.21262i) q^{82} +(5.48455 - 16.8797i) q^{83} +(-0.445762 - 9.42942i) q^{84} +(5.49167 + 3.98993i) q^{85} +(-4.99202 + 5.54420i) q^{86} +(-2.95337 + 5.11538i) q^{87} +(2.09413 + 4.54781i) q^{88} +(-0.447447 - 0.775001i) q^{89} +(-3.63967 - 11.2018i) q^{90} +(2.16449 - 13.2272i) q^{91} +(2.54936 - 1.85222i) q^{92} +(7.70238 - 1.63719i) q^{93} +(3.22748 + 3.58447i) q^{94} +(-0.470588 - 4.47735i) q^{95} +(-1.88673 + 17.9510i) q^{96} +(-1.39215 - 4.28461i) q^{97} +(12.3405 + 1.42498i) q^{98} +(20.8473 - 7.06641i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 3 q^{3} + 20 q^{4} - 16 q^{5} - 6 q^{7} + 20 q^{8} + 13 q^{9}+O(q^{10}) $ 128 * q + 3 * q^3 + 20 * q^4 - 16 * q^5 - 6 * q^7 + 20 * q^8 + 13 * q^9	\( 128 q + 3 q^{3} + 20 q^{4} - 16 q^{5} - 6 q^{7} + 20 q^{8} + 13 q^{9} - 10 q^{10} + 4 q^{11} + 6 q^{12} + 14 q^{13} + 13 q^{14} + 6 q^{15} + 22 q^{16} + 23 q^{17} - 33 q^{18} - 2 q^{19} + 30 q^{20} - 16 q^{21} - 2 q^{22} + 8 q^{23} + 30 q^{24} + 16 q^{25} + 16 q^{26} - 42 q^{27} + 27 q^{28} - 16 q^{29} - 8 q^{31} + 80 q^{32} - 4 q^{33} - 96 q^{34} + 2 q^{35} - 68 q^{36} - 2 q^{37} - 15 q^{38} - 44 q^{39} + 10 q^{40} - 8 q^{41} + 120 q^{42} - 252 q^{43} + 5 q^{44} + 62 q^{45} - 15 q^{46} - 18 q^{47} - 222 q^{48} + 24 q^{49} - 56 q^{51} + 26 q^{52} - 8 q^{53} + 66 q^{54} - 2 q^{55} - 70 q^{56} + 36 q^{57} + 17 q^{58} - 34 q^{59} + 29 q^{60} - 36 q^{61} + 44 q^{62} - 39 q^{63} + 44 q^{64} + 12 q^{65} - 60 q^{66} + 10 q^{67} + 78 q^{68} + 108 q^{69} - 13 q^{70} - 39 q^{72} - 3 q^{73} - 13 q^{74} - 2 q^{75} + 36 q^{76} + 13 q^{77} + 40 q^{78} - 69 q^{79} - 7 q^{80} + 71 q^{81} - 6 q^{82} + 48 q^{83} + 2 q^{84} - 4 q^{85} - 29 q^{86} - 122 q^{87} - 17 q^{88} + 24 q^{90} - 47 q^{91} + 28 q^{92} + 33 q^{93} - 21 q^{94} + 2 q^{95} + 15 q^{96} - 58 q^{97} - 90 q^{98} + 100 q^{99}+O(q^{100}) \) 128 * q + 3 * q^3 + 20 * q^4 - 16 * q^5 - 6 * q^7 + 20 * q^8 + 13 * q^9 - 10 * q^10 + 4 * q^11 + 6 * q^12 + 14 * q^13 + 13 * q^14 + 6 * q^15 + 22 * q^16 + 23 * q^17 - 33 * q^18 - 2 * q^19 + 30 * q^20 - 16 * q^21 - 2 * q^22 + 8 * q^23 + 30 * q^24 + 16 * q^25 + 16 * q^26 - 42 * q^27 + 27 * q^28 - 16 * q^29 - 8 * q^31 + 80 * q^32 - 4 * q^33 - 96 * q^34 + 2 * q^35 - 68 * q^36 - 2 * q^37 - 15 * q^38 - 44 * q^39 + 10 * q^40 - 8 * q^41 + 120 * q^42 - 252 * q^43 + 5 * q^44 + 62 * q^45 - 15 * q^46 - 18 * q^47 - 222 * q^48 + 24 * q^49 - 56 * q^51 + 26 * q^52 - 8 * q^53 + 66 * q^54 - 2 * q^55 - 70 * q^56 + 36 * q^57 + 17 * q^58 - 34 * q^59 + 29 * q^60 - 36 * q^61 + 44 * q^62 - 39 * q^63 + 44 * q^64 + 12 * q^65 - 60 * q^66 + 10 * q^67 + 78 * q^68 + 108 * q^69 - 13 * q^70 - 39 * q^72 - 3 * q^73 - 13 * q^74 - 2 * q^75 + 36 * q^76 + 13 * q^77 + 40 * q^78 - 69 * q^79 - 7 * q^80 + 71 * q^81 - 6 * q^82 + 48 * q^83 + 2 * q^84 - 4 * q^85 - 29 * q^86 - 122 * q^87 - 17 * q^88 + 24 * q^90 - 47 * q^91 + 28 * q^92 + 33 * q^93 - 21 * q^94 + 2 * q^95 + 15 * q^96 - 58 * q^97 - 90 * q^98 + 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.18747	−	1.31881i	0.839665	−	0.932542i	−0.158834	−	0.987305i	$-0.550774\pi$
$2$	1.18747	−	1.31881i	0.839665	−	0.932542i	0.998499	+	0.0547628i	$0.0174403\pi$
$3$	−2.83596	+	1.26265i	−1.63734	+	0.728992i	−0.999163	−	0.0408955i	$-0.986979\pi$
$3$	−2.83596	+	1.26265i	−1.63734	+	0.728992i	−0.638180	+	0.769888i	$0.720312\pi$
$4$	−0.120139	−	1.14305i	−0.0600696	−	0.571525i
$5$	0.978148	−	0.207912i	0.437441	−	0.0929809i
$5$	0.978148	−	0.207912i	0.437441	−	0.0929809i
$6$	−1.70240	+	5.23946i	−0.695004	+	2.13900i
$7$	−2.35120	−	1.21320i	−0.888670	−	0.458548i
$7$	−2.35120	−	1.21320i	−0.888670	−	0.458548i
$8$	1.22130	+	0.887324i	0.431794	+	0.313716i
$9$	4.44100	−	4.93223i	1.48033	−	1.64408i
$10$	0.887320	−	1.53688i	0.280595	−	0.486005i
$11$	2.89302	+	1.62185i	0.872280	+	0.489007i
$11$	2.89302	+	1.62185i	0.872280	+	0.489007i
$12$	1.78398	+	3.08995i	0.514991	+	0.891991i
$13$	1.56545	+	4.81797i	0.434179	+	1.33627i	0.893926	+	0.448215i	$0.147940\pi$
$13$	1.56545	+	4.81797i	0.434179	+	1.33627i	−0.459747	+	0.888050i	$0.652060\pi$
$14$	−4.39196	+	1.66016i	−1.17380	+	0.443696i
$15$	−2.51147	+	1.82469i	−0.648458	+	0.471133i
$16$	4.86892	−	1.03492i	1.21723	−	0.258730i
$17$	4.54211	+	5.04453i	1.10162	+	1.22348i	0.972760	+	0.231815i	$0.0744665\pi$
$17$	4.54211	+	5.04453i	1.10162	+	1.22348i	0.128864	+	0.991662i	$0.458867\pi$
$18$	−1.23116	−	11.7137i	−0.290187	−	2.76094i
$19$	0.470588	−	4.47735i	0.107960	−	1.02717i	−0.797666	−	0.603099i	$-0.793932\pi$
$19$	0.470588	−	4.47735i	0.107960	−	1.02717i	0.905627	−	0.424076i	$-0.139401\pi$
$20$	−0.355167	−	1.09309i	−0.0794178	−	0.244423i
$21$	8.19976	+	0.471853i	1.78933	+	0.102967i
$22$	5.57429	−	1.88947i	1.18844	−	0.402836i
$23$	1.37086	+	2.37440i	0.285844	+	0.495096i	0.972814	−	0.231590i	$-0.0743927\pi$
$23$	1.37086	+	2.37440i	0.285844	+	0.495096i	−0.686969	+	0.726686i	$0.741059\pi$
$24$	−4.58393	−	0.974344i	−0.935691	−	0.198887i
$25$	0.913545	−	0.406737i	0.182709	−	0.0813473i
$26$	8.21293	+	3.65663i	1.61069	+	0.717125i
$27$	−3.48892	+	10.7378i	−0.671444	+	2.06649i
$28$	−1.10428	+	2.83329i	−0.208689	+	0.535441i
$29$	1.53934	−	1.11840i	0.285849	−	0.207681i	−0.435616	−	0.900133i	$-0.643469\pi$
$29$	1.53934	−	1.11840i	0.285849	−	0.207681i	0.721464	+	0.692452i	$0.243469\pi$
$30$	−0.575857	+	5.47892i	−0.105137	+	1.00031i
$31$	−2.48116	−	0.527387i	−0.445630	−	0.0947215i	−0.0203693	−	0.999793i	$-0.506484\pi$
$31$	−2.48116	−	0.527387i	−0.445630	−	0.0947215i	−0.425261	+	0.905071i	$0.639818\pi$
$32$	2.90720	−	5.03542i	0.513926	−	0.890145i
$33$	−10.2523	−	0.946631i	−1.78470	−	0.164787i
$34$	12.0464			2.06594
$35$	−2.55206	−	0.697850i	−0.431377	−	0.117958i
$36$	−6.17131	−	4.48372i	−1.02855	−	0.747287i
$37$	−1.98819	−	0.885198i	−0.326856	−	0.145526i	0.236747	−	0.971571i	$-0.423919\pi$
$37$	−1.98819	−	0.885198i	−0.326856	−	0.145526i	−0.563603	+	0.826046i	$0.690585\pi$
$38$	−5.34598	−	5.93732i	−0.867233	−	0.963160i
$39$	−10.5230	−	11.6870i	−1.68503	−	1.87141i
$40$	1.37909	+	0.614012i	0.218054	+	0.0970838i
$41$	−7.04414	−	5.11787i	−1.10011	−	0.799277i	−0.119032	−	0.992890i	$-0.537979\pi$
$41$	−7.04414	−	5.11787i	−1.10011	−	0.799277i	−0.981078	+	0.193614i	$0.937979\pi$
$42$	10.3592	−	10.2537i	1.59846	−	1.58217i
$43$	−4.20393			−0.641093			−0.320546	−	0.947233i	$-0.603867\pi$
$43$	−4.20393			−0.641093			−0.320546	+	0.947233i	$0.603867\pi$
$44$	1.50629	−	3.50172i	0.227082	−	0.527904i
$45$	3.31848	−	5.74778i	0.494690	−	0.856828i
$46$	4.75924	+	1.01161i	0.701712	+	0.149153i
$47$	−0.284103	+	2.70306i	−0.0414407	+	0.394282i	0.954066	+	0.299595i	$0.0968517\pi$
$47$	−0.284103	+	2.70306i	−0.0414407	+	0.394282i	−0.995507	+	0.0946870i	$0.969815\pi$
$48$	−12.5013	+	9.08275i	−1.80441	+	1.31098i
$49$	4.05627	+	5.70497i	0.579468	+	0.814995i
$50$	0.548394	−	1.68778i	0.0775546	−	0.238688i
$51$	−19.2507	−	8.57098i	−2.69564	−	1.20018i
$52$	5.31911	−	2.36822i	0.737627	−	0.328413i
$53$	1.42109	+	0.302061i	0.195201	+	0.0414913i	0.304475	−	0.952520i	$-0.401519\pi$
$53$	1.42109	+	0.302061i	0.195201	+	0.0414913i	−0.109273	+	0.994012i	$0.534852\pi$
$54$	10.0182	+	17.3520i	1.36330	+	2.36131i
$55$	3.16701	+	0.984918i	0.427039	+	0.132806i
$56$	−1.79501	−	3.56796i	−0.239868	−	0.476788i
$57$	4.31876	+	13.2918i	0.572034	+	1.76054i
$58$	0.352957	−	3.35816i	0.0463456	−	0.440949i
$59$	0.957850	+	9.11333i	0.124701	+	1.18645i	0.860571	+	0.509331i	$0.170107\pi$
$59$	0.957850	+	9.11333i	0.124701	+	1.18645i	−0.735869	+	0.677124i	$0.763226\pi$
$60$	2.38743	+	2.65151i	0.308217	+	0.342309i
$61$	6.57524	−	1.39761i	0.841873	−	0.178946i	0.233261	−	0.972414i	$-0.425060\pi$
$61$	6.57524	−	1.39761i	0.841873	−	0.178946i	0.608611	+	0.793469i	$0.291727\pi$
$62$	−3.64182	+	2.64594i	−0.462512	+	0.336034i
$63$	−16.4255	+	6.20881i	−2.06941	+	0.782237i
$64$	−0.112198	−	0.345310i	−0.0140247	−	0.0431637i
$65$	2.53296	+	4.38721i	0.314175	+	0.544167i
$66$	−13.4227	+	12.3968i	−1.65222	+	1.52595i
$67$	4.25698	−	7.37331i	0.520073	−	0.900793i	−0.479654	−	0.877457i	$-0.659238\pi$
$67$	4.25698	−	7.37331i	0.520073	−	0.900793i	0.999728	−	0.0233358i	$-0.00742869\pi$
$68$	5.22046	−	5.79790i	0.633073	−	0.703099i
$69$	−6.88574	−	5.00279i	−0.828946	−	0.602265i
$70$	−3.95082	+	2.53702i	−0.472213	+	0.303232i
$71$	−0.762500	+	2.34674i	−0.0904922	+	0.278506i	−0.986053	−	0.166433i	$-0.946775\pi$
$71$	−0.762500	+	2.34674i	−0.0904922	+	0.278506i	0.895561	+	0.444940i	$0.146775\pi$
$72$	9.80025	−	2.08311i	1.15497	−	0.245497i
$73$	−0.0333187	−	0.317007i	−0.00389966	−	0.0371028i	0.992399	−	0.123062i	$-0.0392713\pi$
$73$	−0.0333187	−	0.317007i	−0.00389966	−	0.0371028i	−0.996299	+	0.0859589i	$0.972605\pi$
$74$	−3.52832	+	1.57091i	−0.410159	+	0.182614i
$75$	−2.07721	+	2.30698i	−0.239856	+	0.266387i
$76$	−5.17437			−0.593541
$77$	−4.83444	−	7.32313i	−0.550936	−	0.834548i
$78$	−27.9086			−3.16003
$79$	−3.26857	+	3.63011i	−0.367742	+	0.408419i	−0.898408	−	0.439162i	$-0.855275\pi$
$79$	−3.26857	+	3.63011i	−0.367742	+	0.408419i	0.530665	+	0.847581i	$0.321942\pi$
$80$	4.54735	−	2.02461i	0.508409	−	0.226358i
$81$	−1.58239	−	15.0555i	−0.175822	−	1.67283i
$82$	−15.1142	+	3.21262i	−1.66908	+	0.354775i
$83$	5.48455	−	16.8797i	0.602008	−	1.85279i	0.0858262	−	0.996310i	$-0.472647\pi$
$83$	5.48455	−	16.8797i	0.602008	−	1.85279i	0.516182	−	0.856479i	$-0.327353\pi$
$84$	−0.445762	−	9.42942i	−0.0486366	−	1.02883i
$85$	5.49167	+	3.98993i	0.595656	+	0.432769i
$86$	−4.99202	+	5.54420i	−0.538303	+	0.597846i
$87$	−2.95337	+	5.11538i	−0.316634	+	0.548427i
$88$	2.09413	+	4.54781i	0.223235	+	0.484799i
$89$	−0.447447	−	0.775001i	−0.0474293	−	0.0821499i	0.841336	−	0.540512i	$-0.181770\pi$
$89$	−0.447447	−	0.775001i	−0.0474293	−	0.0821499i	−0.888765	+	0.458362i	$0.848436\pi$
$90$	−3.63967	−	11.2018i	−0.383655	−	1.18077i
$91$	2.16449	−	13.2272i	0.226900	−	1.38659i
$92$	2.54936	−	1.85222i	0.265789	−	0.193107i
$93$	7.70238	−	1.63719i	0.798700	−	0.169769i
$94$	3.22748	+	3.58447i	0.332889	+	0.369710i
$95$	−0.470588	−	4.47735i	−0.0482814	−	0.459366i
$96$	−1.88673	+	17.9510i	−0.192564	+	1.83212i
$97$	−1.39215	−	4.28461i	−0.141352	−	0.435036i	0.855172	−	0.518344i	$-0.173451\pi$
$97$	−1.39215	−	4.28461i	−0.141352	−	0.435036i	−0.996524	+	0.0833083i	$0.973451\pi$
$98$	12.3405	+	1.42498i	1.24658	+	0.143945i
$99$	20.8473	−	7.06641i	2.09523	−	0.710201i
$100$	−0.574673	−	0.995362i	−0.0574673	−	0.0995362i
$101$	9.29231	+	1.97514i	0.924620	+	0.196534i	0.645533	−	0.763732i	$-0.276635\pi$
$101$	9.29231	+	1.97514i	0.924620	+	0.196534i	0.279086	+	0.960266i	$0.409968\pi$
$102$	−34.1631	+	15.2104i	−3.38265	+	1.50605i
$103$	−12.6923	−	5.65097i	−1.25061	−	0.556807i	−0.328780	−	0.944406i	$-0.606638\pi$
$103$	−12.6923	−	5.65097i	−1.25061	−	0.556807i	−0.921828	+	0.387600i	$0.873304\pi$
$104$	−2.36322	+	7.27324i	−0.231733	+	0.713200i
$105$	8.11868	−	1.24328i	0.792302	−	0.121332i
$106$	2.08585	−	1.51546i	0.202596	−	0.147195i
$107$	0.126096	−	1.19972i	0.0121902	−	0.115982i	−0.986735	−	0.162341i	$-0.948095\pi$
$107$	0.126096	−	1.19972i	0.0121902	−	0.115982i	0.998925	+	0.0463597i	$0.0147621\pi$
$108$	12.6930	+	2.69798i	1.22138	+	0.259613i
$109$	−5.82590	+	10.0907i	−0.558020	+	0.966518i	0.439642	+	0.898173i	$0.355105\pi$
$109$	−5.82590	+	10.0907i	−0.558020	+	0.966518i	−0.997662	+	0.0683453i	$0.978228\pi$
$110$	5.05964	−	3.00714i	0.482417	−	0.286719i
$111$	6.75612			0.641263
$112$	−12.7034	−	3.47369i	−1.20036	−	0.328233i
$113$	−7.59431	−	5.51759i	−0.714413	−	0.519051i	0.170182	−	0.985413i	$-0.445565\pi$
$113$	−7.59431	−	5.51759i	−0.714413	−	0.519051i	−0.884594	+	0.466362i	$0.845565\pi$
$114$	22.6578	+	10.0879i	2.12209	+	0.944817i
$115$	1.83457	+	2.03749i	0.171074	+	0.189997i
$116$	−1.46332	−	1.62518i	−0.135866	−	0.150894i
$117$	30.7155	+	13.6754i	2.83965	+	1.26429i
$118$	13.1562	+	9.55854i	1.21113	+	0.879935i
$119$	−4.55937	−	17.3712i	−0.417957	−	1.59241i
$120$	−4.68634			−0.427802
$121$	5.73919	+	9.38412i	0.521744	+	0.853102i
$122$	5.96468	−	10.3311i	0.540017	−	0.935336i
$123$	26.4390	+	5.61978i	2.38392	+	0.506719i
$124$	−0.304744	+	2.89945i	−0.0273669	+	0.260378i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	−11.3164	+	29.0349i	−1.00814	+	2.58663i
$127$	−4.16059	+	12.8050i	−0.369192	+	1.13626i	0.578122	+	0.815951i	$0.303786\pi$
$127$	−4.16059	+	12.8050i	−0.369192	+	1.13626i	−0.947314	+	0.320307i	$0.896214\pi$
$128$	10.0348	+	4.46779i	0.886961	+	0.394900i
$129$	11.9222	−	5.30809i	1.04969	−	0.467352i
$130$	8.79372	+	1.86916i	0.771260	+	0.163936i
$131$	−7.20147	−	12.4733i	−0.629195	−	1.08980i	−0.987714	−	0.156276i	$-0.950051\pi$
$131$	−7.20147	−	12.4733i	−0.629195	−	1.08980i	0.358518	−	0.933523i	$-0.383282\pi$
$132$	0.149663	+	11.8327i	0.0130265	+	1.02990i
$133$	−6.53838	+	9.95622i	−0.566950	+	0.863314i
$134$	−4.66901	−	14.3697i	−0.403341	−	1.24135i
$135$	−1.18017	+	11.2285i	−0.101573	+	0.966399i
$136$	1.07114	+	10.1912i	0.0918492	+	0.873887i
$137$	−13.3389	−	14.8143i	−1.13962	−	1.26567i	−0.959401	−	0.282046i	$-0.908987\pi$
$137$	−13.3389	−	14.8143i	−1.13962	−	1.26567i	−0.180216	−	0.983627i	$-0.557680\pi$
$138$	−14.7743	+	3.14038i	−1.25767	+	0.267327i
$139$	−3.27537	+	2.37970i	−0.277813	+	0.201843i	−0.717963	−	0.696081i	$-0.754925\pi$
$139$	−3.27537	+	2.37970i	−0.277813	+	0.201843i	0.440150	+	0.897924i	$0.354925\pi$
$140$	−0.491075	+	3.00097i	−0.0415034	+	0.253628i
$141$	−2.60732	−	8.02451i	−0.219576	−	0.675785i
$142$	2.18946	+	3.79226i	0.183736	+	0.318240i
$143$	−3.28515	+	16.4775i	−0.274718	+	1.37791i
$144$	16.5184	−	28.6107i	1.37653	−	2.38422i
$145$	1.27318	−	1.41401i	0.105731	−	0.117427i
$146$	−0.457638	−	0.332493i	−0.0378744	−	0.0275173i
$147$	−18.7068	−	11.0574i	−1.54291	−	0.911999i
$148$	−0.772966	+	2.37894i	−0.0635374	+	0.195548i
$149$	−5.94566	+	1.26379i	−0.487087	+	0.103534i	−0.444908	−	0.895576i	$-0.646764\pi$
$149$	−5.94566	+	1.26379i	−0.487087	+	0.103534i	−0.0421796	+	0.999110i	$0.513430\pi$
$150$	0.575857	+	5.47892i	0.0470185	+	0.447352i
$151$	14.9400	−	6.65173i	1.21580	−	0.541310i	0.304289	−	0.952580i	$-0.401581\pi$
$151$	14.9400	−	6.65173i	1.21580	−	0.541310i	0.911514	+	0.411270i	$0.134914\pi$
$152$	4.54759	−	5.05061i	0.368858	−	0.409658i
$153$	45.0522			3.64226
$154$	−15.3986	−	2.32023i	−1.24085	−	0.186970i
$155$	−2.53659			−0.203744
$156$	−12.0945	+	13.4324i	−0.968339	+	1.07545i
$157$	6.69234	−	2.97962i	0.534107	−	0.237800i	−0.121917	−	0.992540i	$-0.538904\pi$
$157$	6.69234	−	2.97962i	0.534107	−	0.237800i	0.656023	+	0.754741i	$0.272237\pi$
$158$	0.906131	+	8.62126i	0.0720879	+	0.685871i
$159$	−4.41155	+	0.937703i	−0.349858	+	0.0743647i
$160$	1.79675	−	5.52983i	0.142046	−	0.437171i
$161$	−0.342535	−	7.24582i	−0.0269956	−	0.571050i
$162$	−21.7344	−	15.7910i	−1.70762	−	1.24066i
$163$	−5.41952	+	6.01899i	−0.424490	+	0.471444i	−0.917014	−	0.398855i	$-0.869408\pi$
$163$	−5.41952	+	6.01899i	−0.424490	+	0.471444i	0.492524	+	0.870299i	$0.336074\pi$
$164$	−5.00370	+	8.66666i	−0.390723	+	0.676752i
$165$	−10.2251	+	1.20564i	−0.796024	+	0.0938587i
$166$	−15.7485	−	27.2772i	−1.22232	−	2.11712i
$167$	6.19697	+	19.0723i	0.479536	+	1.47586i	0.839741	+	0.542987i	$0.182707\pi$
$167$	6.19697	+	19.0723i	0.479536	+	1.47586i	−0.360205	+	0.932873i	$0.617293\pi$
$168$	9.59565	+	7.85212i	0.740321	+	0.605804i
$169$	−10.2450	+	7.44342i	−0.788076	+	0.572571i
$170$	11.7832	−	2.50459i	0.903727	−	0.192093i
$171$	−19.9934	−	22.2049i	−1.52893	−	1.69805i
$172$	0.505057	+	4.80529i	0.0385102	+	0.366400i
$173$	1.81426	−	17.2615i	0.137935	−	1.31237i	−0.678359	−	0.734731i	$-0.737308\pi$
$173$	1.81426	−	17.2615i	0.137935	−	1.31237i	0.816294	−	0.577636i	$-0.196025\pi$
$174$	3.23922	+	9.96929i	0.245564	+	0.755770i
$175$	−2.64138	−	0.151998i	−0.199670	−	0.0114899i
$176$	15.7644	+	4.90262i	1.18829	+	0.369549i
$177$	−14.2234	−	24.6356i	−1.06909	−	1.85173i
$178$	−1.55341	−	0.330188i	−0.116433	−	0.0247486i
$179$	5.13144	−	2.28467i	0.383542	−	0.170764i	−0.205903	−	0.978572i	$-0.566013\pi$
$179$	5.13144	−	2.28467i	0.383542	−	0.170764i	0.589445	+	0.807808i	$0.299346\pi$
$180$	−6.96867	−	3.10265i	−0.519414	−	0.231258i
$181$	7.46759	−	22.9829i	0.555062	−	1.70830i	−0.140719	−	0.990050i	$-0.544941\pi$
$181$	7.46759	−	22.9829i	0.555062	−	1.70830i	0.695780	−	0.718255i	$-0.255059\pi$
$182$	−14.8740	−	18.5614i	−1.10253	−	1.37586i
$183$	−16.8824	+	12.2658i	−1.24798	+	0.906714i
$184$	−0.432634	+	4.11624i	−0.0318942	+	0.303453i
$185$	−2.12878	−	0.452487i	−0.156511	−	0.0332675i
$186$	6.98716	−	12.1021i	0.512324	−	0.887371i
$187$	4.95896	+	21.9606i	0.362635	+	1.60592i
$188$	3.12387			0.227831
$189$	21.2303	−	21.0139i	1.54428	−	1.52854i
$190$	−6.46360	−	4.69608i	−0.468919	−	0.340689i
$191$	−3.18952	−	1.42007i	−0.230786	−	0.102752i	0.288086	−	0.957605i	$-0.406981\pi$
$191$	−3.18952	−	1.42007i	−0.230786	−	0.102752i	−0.518872	+	0.854852i	$0.673648\pi$
$192$	0.754195	+	0.837618i	0.0544293	+	0.0604499i
$193$	−5.52175	−	6.13252i	−0.397464	−	0.441429i	0.510880	−	0.859652i	$-0.329320\pi$
$193$	−5.52175	−	6.13252i	−0.397464	−	0.441429i	−0.908344	+	0.418223i	$0.862653\pi$
$194$	−7.30373	−	3.25183i	−0.524378	−	0.233468i
$195$	−12.7229	−	9.24372i	−0.911105	−	0.661957i
$196$	6.03374	−	5.32191i	0.430981	−	0.380137i
$197$	−15.5842			−1.11033			−0.555165	−	0.831740i	$-0.687345\pi$
$197$	−15.5842			−1.11033			−0.555165	+	0.831740i	$0.687345\pi$
$198$	15.4361	−	35.8848i	1.09700	−	2.55022i
$199$	1.44028	−	2.49464i	0.102099	−	0.176840i	−0.810450	−	0.585807i	$-0.800778\pi$
$199$	1.44028	−	2.49464i	0.102099	−	0.176840i	0.912549	+	0.408967i	$0.134111\pi$
$200$	1.47662	+	0.313865i	0.104413	+	0.0221936i
$201$	−2.76272	+	26.2855i	−0.194867	+	1.85404i
$202$	13.6391	−	9.90942i	0.959647	−	0.697224i
$203$	−4.97614	+	0.762040i	−0.349257	+	0.0534847i
$204$	−7.48428	+	23.0342i	−0.524004	+	1.61272i
$205$	−7.95428	−	3.54147i	−0.555551	−	0.247347i
$206$	−22.5242	+	10.0284i	−1.56934	+	0.698714i
$207$	17.7991	+	3.78331i	1.23712	+	0.262958i
$208$	12.6083	+	21.8382i	0.874228	+	1.51421i
$209$	8.62303	−	12.1899i	0.596467	−	0.843190i
$210$	8.00099	−	12.1834i	0.552121	−	0.840734i
$211$	0.961524	+	2.95927i	0.0661940	+	0.203724i	0.978683	−	0.205377i	$-0.0658422\pi$
$211$	0.961524	+	2.95927i	0.0661940	+	0.203724i	−0.912489	+	0.409102i	$0.865842\pi$
$212$	0.174543	−	1.66066i	0.0119876	−	0.114055i
$213$	−0.800686	−	7.61802i	−0.0548621	−	0.521978i
$214$	−1.43248	−	1.59093i	−0.0979223	−	0.108754i
$215$	−4.11206	+	0.874045i	−0.280440	+	0.0596094i
$216$	−13.7889	+	10.0182i	−0.938217	+	0.681655i
$217$	5.19388	+	4.25015i	0.352583	+	0.288519i
$218$	6.38977	+	19.6657i	0.432770	+	1.33193i
$219$	0.494759	+	0.856948i	0.0334327	+	0.0579072i
$220$	0.745328	−	3.73837i	0.0502500	−	0.252041i
$221$	−17.1939	+	29.7807i	−1.15659	+	2.00327i
$222$	8.02266	−	8.91007i	0.538446	−	0.598005i
$223$	−10.5968	−	7.69900i	−0.709612	−	0.515563i	0.173436	−	0.984845i	$-0.444513\pi$
$223$	−10.5968	−	7.69900i	−0.709612	−	0.515563i	−0.883049	+	0.469282i	$0.844513\pi$
$224$	−12.9444	+	8.31225i	−0.864884	+	0.555386i
$225$	2.05093	−	6.31213i	0.136729	−	0.420809i
$226$	−16.2947	+	3.46354i	−1.08390	+	0.230391i
$227$	−0.840588	−	7.99766i	−0.0557918	−	0.530824i	−0.986348	−	0.164674i	$-0.947343\pi$
$227$	−0.840588	−	7.99766i	−0.0557918	−	0.530824i	0.930556	−	0.366149i	$-0.119324\pi$
$228$	14.6743	−	6.53342i	0.971829	−	0.432686i
$229$	3.55256	−	3.94552i	0.234760	−	0.260727i	−0.614241	−	0.789118i	$-0.710538\pi$
$229$	3.55256	−	3.94552i	0.234760	−	0.260727i	0.849001	+	0.528391i	$0.177205\pi$
$230$	4.86556			0.320826
$231$	22.9568	+	14.6639i	1.51045	+	0.964813i
$232$	2.87237			0.188581
$233$	13.2734	−	14.7416i	0.869572	−	0.965757i	−0.130097	−	0.991501i	$-0.541529\pi$
$233$	13.2734	−	14.7416i	0.869572	−	0.965757i	0.999669	+	0.0257439i	$0.00819546\pi$
$234$	54.5089	−	24.2689i	3.56336	−	1.58651i
$235$	0.284103	+	2.70306i	0.0185329	+	0.176328i
$236$	10.3019	−	2.18974i	0.670597	−	0.142540i
$237$	4.68596	−	14.4219i	0.304386	−	0.936804i
$238$	−28.3235	−	14.6147i	−1.83594	−	0.947332i
$239$	21.6491	+	15.7290i	1.40036	+	1.01742i	0.994637	+	0.103429i	$0.0329814\pi$
$239$	21.6491	+	15.7290i	1.40036	+	1.01742i	0.405726	+	0.913995i	$0.367019\pi$
$240$	−10.3397	+	11.4834i	−0.667427	+	0.741253i
$241$	−12.7135	+	22.0205i	−0.818951	+	1.41846i	0.0875047	+	0.996164i	$0.472111\pi$
$241$	−12.7135	+	22.0205i	−0.818951	+	1.41846i	−0.906456	+	0.422301i	$0.861223\pi$
$242$	19.1910	+	3.57440i	1.23364	+	0.229771i
$243$	6.56183	+	11.3654i	0.420941	+	0.729092i
$244$	−2.38748	−	7.34791i	−0.152843	−	0.470402i
$245$	5.15376	+	4.73695i	0.329262	+	0.302633i
$246$	38.8068	−	28.1948i	2.47423	−	1.79764i
$247$	22.3084	−	4.74180i	1.41945	−	0.301714i
$248$	−2.56227	−	2.84569i	−0.162704	−	0.180702i
$249$	5.75922	+	54.7953i	0.364976	+	3.47251i
$250$	0.185500	−	1.76492i	0.0117321	−	0.111623i
$251$	−6.44829	−	19.8458i	−0.407012	−	1.25266i	−0.919203	−	0.393784i	$-0.871166\pi$
$251$	−6.44829	−	19.8458i	−0.407012	−	1.25266i	0.512191	−	0.858872i	$-0.328834\pi$
$252$	9.07032	+	18.0292i	0.571376	+	1.13573i
$253$	0.115005	+	9.09253i	0.00723033	+	0.571642i
$254$	11.9468	+	20.6925i	0.749610	+	1.29836i
$255$	−20.6121	−	4.38123i	−1.29078	−	0.274363i
$256$	18.4716	−	8.22407i	1.15447	−	0.514004i
$257$	−22.6131	−	10.0680i	−1.41057	−	0.628026i	−0.446768	−	0.894650i	$-0.647425\pi$
$257$	−22.6131	−	10.0680i	−1.41057	−	0.628026i	−0.963801	+	0.266624i	$0.914092\pi$
$258$	7.15678	−	22.0263i	0.445562	−	1.37130i
$259$	3.60070	+	4.49335i	0.223737	+	0.279203i
$260$	4.71049	−	3.42237i	0.292132	−	0.212246i
$261$	1.32002	−	12.5592i	0.0817074	−	0.777394i
$262$	−25.0015	−	5.31423i	−1.54460	−	0.328314i
$263$	−0.606062	+	1.04973i	−0.0373714	+	0.0647291i	−0.884106	−	0.467286i	$-0.845232\pi$
$263$	−0.606062	+	1.04973i	−0.0373714	+	0.0647291i	0.846735	+	0.532015i	$0.178565\pi$
$264$	−11.6812	−	10.2533i	−0.718927	−	0.631045i
$265$	1.45283			0.0892469
$266$	5.36630	+	20.4456i	0.329029	+	1.25360i
$267$	2.24750	+	1.63290i	0.137545	+	0.0999321i
$268$	−8.93949	−	3.98012i	−0.546066	−	0.243124i
$269$	−13.0849	−	14.5322i	−0.797798	−	0.886044i	0.197755	−	0.980251i	$-0.436635\pi$
$269$	−13.0849	−	14.5322i	−0.797798	−	0.886044i	−0.995553	+	0.0942075i	$0.969968\pi$
$270$	13.4070	+	14.8899i	0.815921	+	0.906172i
$271$	18.7348	+	8.34128i	1.13806	+	0.506697i	0.887227	−	0.461334i	$-0.152629\pi$
$271$	18.7348	+	8.34128i	1.13806	+	0.506697i	0.250832	+	0.968031i	$0.419296\pi$
$272$	27.3359	+	19.8607i	1.65748	+	1.20423i
$273$	10.5630	+	40.2449i	0.639300	+	2.43573i
$274$	−35.3768			−2.13719
$275$	3.30258	+	0.304937i	0.199153	+	0.0183884i
$276$	−4.89118	+	8.47177i	−0.294414	+	0.509941i
$277$	−18.7397	−	3.98325i	−1.12596	−	0.239330i	−0.392958	−	0.919556i	$-0.628548\pi$
$277$	−18.7397	−	3.98325i	−1.12596	−	0.239330i	−0.733002	+	0.680226i	$0.761882\pi$
$278$	−0.751013	+	7.14541i	−0.0450428	+	0.428553i
$279$	−13.6200	+	9.89552i	−0.815409	+	0.592430i
$280$	−2.49760	−	3.11678i	−0.149260	−	0.186264i
$281$	−2.59071	+	7.97340i	−0.154549	+	0.475653i	−0.998115	−	0.0613727i	$-0.980452\pi$
$281$	−2.59071	+	7.97340i	−0.154549	+	0.475653i	0.843566	+	0.537026i	$0.180452\pi$
$282$	−13.6789	−	6.09025i	−0.814569	−	0.362669i
$283$	−21.6078	+	9.62041i	−1.28445	+	0.571874i	−0.931491	−	0.363765i	$-0.881491\pi$
$283$	−21.6078	+	9.62041i	−1.28445	+	0.571874i	−0.352959	+	0.935639i	$0.614824\pi$
$284$	2.77404	+	0.589640i	0.164609	+	0.0349887i
$285$	6.98790	+	12.1034i	0.413928	+	0.716944i
$286$	17.8297	+	23.8989i	1.05429	+	1.41317i
$287$	10.3532	+	20.5791i	0.611128	+	1.21475i
$288$	−11.9250	−	36.7013i	−0.702685	−	2.16264i
$289$	−3.03948	+	28.9187i	−0.178793	+	1.70110i
$290$	−0.352957	−	3.35816i	−0.0207264	−	0.197198i
$291$	9.35806	+	10.3932i	0.548579	+	0.609259i
$292$	−0.358351	+	0.0761699i	−0.0209709	+	0.00445751i
$293$	7.84755	−	5.70158i	0.458459	−	0.333090i	−0.334467	−	0.942407i	$-0.608556\pi$
$293$	7.84755	−	5.70158i	0.458459	−	0.333090i	0.792926	+	0.609317i	$0.208556\pi$
$294$	−36.7964	+	11.5405i	−2.14601	+	0.673058i
$295$	2.83169	+	8.71503i	0.164867	+	0.507409i
$296$	−1.64271	−	2.84526i	−0.0954806	−	0.165377i
$297$	−27.5087	+	25.4062i	−1.59622	+	1.47422i
$298$	−5.39356	+	9.34192i	−0.312441	+	0.541163i
$299$	−9.29377	+	10.3218i	−0.537473	+	0.596924i
$300$	2.88654	+	2.09720i	0.166655	+	0.121082i
$301$	9.88427	+	5.10022i	0.569720	+	0.293972i
$302$	8.96838	−	27.6018i	0.516072	−	1.58831i
$303$	−28.8466	+	6.13152i	−1.65719	+	0.352247i
$304$	−2.34245	−	22.2869i	−0.134348	−	1.27824i
$305$	6.14097	−	2.73414i	0.351631	−	0.156556i
$306$	53.4980	−	59.4155i	3.05828	−	3.39656i
$307$	14.1322			0.806567			0.403284	−	0.915075i	$-0.367869\pi$
$307$	14.1322			0.806567			0.403284	+	0.915075i	$0.367869\pi$
$308$	−7.78989	+	6.40580i	−0.443870	+	0.365004i
$309$	43.1300			2.45358
$310$	−3.01212	+	3.34529i	−0.171077	+	0.190000i
$311$	11.8296	−	5.26687i	0.670794	−	0.298657i	−0.0429360	−	0.999078i	$-0.513671\pi$
$311$	11.8296	−	5.26687i	0.670794	−	0.298657i	0.713730	+	0.700421i	$0.247004\pi$
$312$	−2.48157	−	23.6105i	−0.140491	−	1.33668i
$313$	−5.71941	+	1.21570i	−0.323280	+	0.0687153i	−0.366693	−	0.930342i	$-0.619510\pi$
$313$	−5.71941	+	1.21570i	−0.323280	+	0.0687153i	0.0434132	+	0.999057i	$0.486177\pi$
$314$	4.01735	−	12.3641i	0.226712	−	0.697749i
$315$	−14.7756	+	9.48818i	−0.832513	+	0.534598i
$316$	4.54208	+	3.30001i	0.255512	+	0.185640i
$317$	8.60024	−	9.55153i	0.483038	−	0.536468i	−0.451529	−	0.892257i	$-0.649121\pi$
$317$	8.60024	−	9.55153i	0.483038	−	0.536468i	0.934566	+	0.355789i	$0.115788\pi$
$318$	−4.00190	+	6.93150i	−0.224416	+	0.388699i
$319$	6.26723	−	0.738965i	0.350898	−	0.0413741i
$320$	−0.181540	−	0.314437i	−0.0101484	−	0.0175775i
$321$	1.15723	+	3.56159i	0.0645903	+	0.198788i
$322$	−9.96263	−	8.15242i	−0.555196	−	0.454316i
$323$	24.7236	−	17.9627i	1.37566	−	0.999473i
$324$	−17.0190	+	3.61751i	−0.945502	+	0.200973i
$325$	3.38976	+	3.76471i	0.188030	+	0.208829i
$326$	1.50243	+	14.2947i	0.0832120	+	0.791709i
$327$	3.78092	−	35.9730i	0.209085	−	1.98931i
$328$	−4.06178	−	12.5009i	−0.224274	−	0.690245i
$329$	3.94735	−	6.01077i	0.217624	−	0.331384i
$330$	−10.5520	+	14.9167i	−0.580867	+	0.821136i
$331$	0.343495	+	0.594950i	0.0188802	+	0.0327014i	0.875311	−	0.483560i	$-0.160657\pi$
$331$	0.343495	+	0.594950i	0.0188802	+	0.0327014i	−0.856431	+	0.516262i	$0.827323\pi$
$332$	−19.9533	−	4.24119i	−1.09508	−	0.232766i
$333$	−13.1955	+	5.87503i	−0.723111	+	0.321950i
$334$	32.5115	+	14.4751i	1.77895	+	0.792040i
$335$	2.63096	−	8.09726i	0.143745	−	0.442401i
$336$	40.4123	−	6.18869i	2.20467	−	0.337621i
$337$	3.55457	−	2.58254i	0.193630	−	0.140680i	−0.486747	−	0.873543i	$-0.661816\pi$
$337$	3.55457	−	2.58254i	0.193630	−	0.140680i	0.680376	+	0.732863i	$0.261816\pi$
$338$	−2.34908	+	22.3500i	−0.127773	+	1.21568i
$339$	28.5040	+	6.05870i	1.54812	+	0.329064i
$340$	3.90092	−	6.75660i	0.211557	−	0.366428i
$341$	−6.32272	−	5.54982i	−0.342394	−	0.300540i
$342$	−53.0257			−2.86730
$343$	−2.61583	−	18.3346i	−0.141241	−	0.989975i
$344$	−5.13424	−	3.73024i	−0.276820	−	0.201121i
$345$	−7.77541	−	3.46184i	−0.418614	−	0.186379i
$346$	−20.6103	−	22.8901i	−1.10802	−	1.23058i
$347$	7.70308	+	8.55513i	0.413523	+	0.459264i	0.913538	−	0.406753i	$-0.133339\pi$
$347$	7.70308	+	8.55513i	0.413523	+	0.459264i	−0.500015	+	0.866017i	$0.666672\pi$
$348$	6.20195	+	2.76129i	0.332459	+	0.148020i
$349$	1.58463	+	1.15130i	0.0848232	+	0.0616277i	0.629389	−	0.777091i	$-0.283305\pi$
$349$	1.58463	+	1.15130i	0.0848232	+	0.0616277i	−0.544565	+	0.838718i	$0.683305\pi$
$350$	−3.33701	+	3.30300i	−0.178370	+	0.176553i
$351$	−57.1962			−3.05291
$352$	16.5773	−	9.85255i	0.883574	−	0.525142i
$353$	−2.42114	+	4.19353i	−0.128864	+	0.223199i	−0.923237	−	0.384232i	$-0.874466\pi$
$353$	−2.42114	+	4.19353i	−0.128864	+	0.223199i	0.794373	+	0.607431i	$0.207800\pi$
$354$	−49.3796	−	10.4960i	−2.62450	−	0.557854i
$355$	−0.257924	+	2.45399i	−0.0136892	+	0.130244i
$356$	−0.832108	+	0.604562i	−0.0441016	+	0.0320417i
$357$	34.8640	+	43.5071i	1.84520	+	2.30264i
$358$	3.08036	−	9.48038i	0.162802	−	0.501054i
$359$	−21.0250	−	9.36095i	−1.10966	−	0.494052i	−0.231700	−	0.972787i	$-0.574429\pi$
$359$	−21.0250	−	9.36095i	−1.10966	−	0.494052i	−0.877959	+	0.478735i	$0.841095\pi$
$360$	9.15299	−	4.07517i	0.482405	−	0.214781i
$361$	−1.24040	−	0.263656i	−0.0652844	−	0.0138766i
$362$	−21.4426	−	37.1397i	−1.12700	−	1.95202i
$363$	−28.1250	−	19.3664i	−1.47618	−	1.01647i
$364$	−15.3794	−	0.885004i	−0.806100	−	0.0463868i
$365$	−0.0985000	−	0.303152i	−0.00515573	−	0.0158677i
$366$	−3.87099	+	36.8300i	−0.202340	+	1.92513i
$367$	0.440953	+	4.19538i	0.0230175	+	0.218997i	0.999984	+	0.00560565i	$0.00178434\pi$
$367$	0.440953	+	4.19538i	0.0230175	+	0.218997i	−0.976967	+	0.213392i	$0.931549\pi$
$368$	9.13192	+	10.1420i	0.476034	+	0.528690i
$369$	−56.5255	+	12.0149i	−2.94260	+	0.625469i
$370$	−3.12460	+	2.27016i	−0.162440	+	0.118020i
$371$	−2.97480	−	2.43427i	−0.154444	−	0.126381i
$372$	−2.79675	−	8.60751i	−0.145005	−	0.446279i
$373$	−0.985818	−	1.70749i	−0.0510437	−	0.0884103i	0.839375	−	0.543553i	$-0.182921\pi$
$373$	−0.985818	−	1.70749i	−0.0510437	−	0.0884103i	−0.890418	+	0.455143i	$0.849588\pi$
$374$	34.8505	+	19.5375i	1.80208	+	1.01026i
$375$	−1.55217	+	2.68844i	−0.0801539	+	0.138831i
$376$	−2.74547	+	3.04915i	−0.141587	+	0.157248i
$377$	7.79818	+	5.66571i	0.401627	+	0.291799i
$378$	−2.50324	−	52.9521i	−0.128753	−	2.72356i
$379$	−1.69511	+	5.21701i	−0.0870719	+	0.267980i	−0.985107	−	0.171945i	$-0.944995\pi$
$379$	−1.69511	+	5.21701i	−0.0870719	+	0.267980i	0.898035	+	0.439925i	$0.144995\pi$
$380$	−5.06129	+	1.07581i	−0.259639	+	0.0551880i
$381$	−4.36895	−	41.5678i	−0.223828	−	2.12958i
$382$	−5.66025	+	2.52011i	−0.289604	+	0.128940i
$383$	0.473774	−	0.526179i	0.0242087	−	0.0268865i	−0.730919	−	0.682464i	$-0.760908\pi$
$383$	0.473774	−	0.526179i	0.0242087	−	0.0268865i	0.755128	+	0.655578i	$0.227575\pi$
$384$	−34.0996			−1.74014
$385$	−6.25136	−	6.15796i	−0.318599	−	0.313839i
$386$	−14.6445			−0.745387
$387$	−18.6696	+	20.7347i	−0.949030	+	1.05400i
$388$	−4.73026	+	2.10605i	−0.240143	+	0.106918i
$389$	0.739922	+	7.03989i	0.0375156	+	0.356937i	0.997135	+	0.0756367i	$0.0240989\pi$
$389$	0.739922	+	7.03989i	0.0375156	+	0.356937i	−0.959620	+	0.281300i	$0.909234\pi$
$390$	−27.2987	+	5.80253i	−1.38233	+	0.293822i
$391$	−5.75112	+	17.7001i	−0.290847	+	0.895134i
$392$	−0.108238	+	10.5667i	−0.00546685	+	0.533698i
$393$	36.1725	+	26.2809i	1.82466	+	1.32570i
$394$	−18.5057	+	20.5527i	−0.932305	+	1.03543i
$395$	−2.44240	+	4.23036i	−0.122890	+	0.212852i
$396$	−10.5818	−	22.9805i	−0.531757	−	1.15481i
$397$	12.2412	+	21.2023i	0.614367	+	1.06411i	0.990495	+	0.137547i	$0.0439217\pi$
$397$	12.2412	+	21.2023i	0.614367	+	1.06411i	−0.376129	+	0.926567i	$0.622745\pi$
$398$	−1.57968	−	4.86176i	−0.0791823	−	0.243698i
$399$	5.97137	−	36.4912i	0.298942	−	1.82684i
$400$	4.02704	−	2.92582i	0.201352	−	0.146291i
$401$	−25.4717	+	5.41417i	−1.27199	+	0.270371i	−0.793960	−	0.607971i	$-0.791984\pi$
$401$	−25.4717	+	5.41417i	−1.27199	+	0.270371i	−0.478034	+	0.878341i	$0.658651\pi$
$402$	31.3851	+	34.8566i	1.56534	+	1.73849i
$403$	−1.34321	−	12.7798i	−0.0669100	−	0.636606i
$404$	1.14131	−	10.8589i	0.0567824	−	0.540249i
$405$	−4.67802	−	14.3975i	−0.232453	−	0.715416i
$406$	−4.90401	+	7.46750i	−0.243382	+	0.370606i
$407$	−4.31622	−	5.78545i	−0.213947	−	0.286774i
$408$	−15.9056	−	27.5493i	−0.787445	−	1.36390i
$409$	−3.05588	−	0.649547i	−0.151103	−	0.0321180i	0.131739	−	0.991284i	$-0.457944\pi$
$409$	−3.05588	−	0.649547i	−0.151103	−	0.0321180i	−0.282842	+	0.959166i	$0.591277\pi$
$410$	−14.1160	+	6.28484i	−0.697138	+	0.310386i
$411$	56.5339	+	25.1705i	2.78861	+	1.24157i
$412$	−4.93449	+	15.1868i	−0.243105	+	0.748200i
$413$	8.80423	−	22.5893i	0.433228	−	1.11155i
$414$	26.1252	−	18.9811i	1.28399	−	0.932870i
$415$	1.85521	−	17.6512i	0.0910687	−	0.866461i
$416$	28.8116	+	6.12410i	1.41261	+	0.300259i
$417$	6.28410	−	10.8844i	0.307734	−	0.533010i
$418$	−5.83661	−	25.8472i	−0.285478	−	1.26423i
$419$	−38.5698			−1.88426			−0.942129	−	0.335251i	$-0.891179\pi$
$419$	−38.5698			−1.88426			−0.942129	+	0.335251i	$0.891179\pi$
$420$	−2.39651	−	9.13068i	−0.116938	−	0.445532i
$421$	−25.1179	−	18.2493i	−1.22417	−	0.889414i	−0.227734	−	0.973723i	$-0.573132\pi$
$421$	−25.1179	−	18.2493i	−1.22417	−	0.889414i	−0.996440	+	0.0843090i	$0.973132\pi$
$422$	5.04450	+	2.24596i	0.245562	+	0.109331i
$423$	12.0704	+	13.4056i	0.586884	+	0.651800i
$424$	1.46754	+	1.62987i	0.0712702	+	0.0791535i
$425$	6.20122	+	2.76096i	0.300803	+	0.133926i
$426$	−10.9975	−	7.99018i	−0.532833	−	0.387126i
$427$	−17.1553	−	4.69104i	−0.830202	−	0.227015i
$428$	−1.38649			−0.0670187
$429$	−11.4887	−	50.8774i	−0.554681	−	2.45638i
$430$	−3.73023	+	6.46094i	−0.179888	+	0.311574i
$431$	−6.27424	−	1.33363i	−0.302219	−	0.0642387i	0.0543061	−	0.998524i	$-0.482705\pi$
$431$	−6.27424	−	1.33363i	−0.302219	−	0.0642387i	−0.356525	+	0.934286i	$0.616039\pi$
$432$	−5.87452	+	55.8923i	−0.282638	+	2.68912i
$433$	−20.4139	+	14.8316i	−0.981030	+	0.712760i	−0.957939	−	0.286973i	$-0.907351\pi$
$433$	−20.4139	+	14.8316i	−0.981030	+	0.712760i	−0.0230917	+	0.999733i	$0.507351\pi$
$434$	11.7727	−	1.80286i	0.565108	−	0.0865399i
$435$	−1.82528	+	5.61764i	−0.0875156	+	0.269345i
$436$	12.2341	+	5.44699i	0.585909	+	0.260863i
$437$	11.2761	−	5.02045i	0.539410	−	0.240161i
$438$	1.71767	+	0.365101i	0.0820732	+	0.0174452i
$439$	8.28369	+	14.3478i	0.395359	+	0.684782i	0.993147	−	0.116872i	$-0.0372868\pi$
$439$	8.28369	+	14.3478i	0.395359	+	0.684782i	−0.597788	+	0.801654i	$0.703953\pi$
$440$	2.99391	+	4.01304i	0.142729	+	0.191314i
$441$	46.1521	+	5.32927i	2.19772	+	0.253775i
$442$	18.8581	+	58.0392i	0.896987	+	2.76064i
$443$	0.237812	−	2.26263i	0.0112988	−	0.107501i	−0.987419	−	0.158126i	$-0.949455\pi$
$443$	0.237812	−	2.26263i	0.0112988	−	0.107501i	0.998718	+	0.0506253i	$0.0161214\pi$
$444$	−0.811676	−	7.72258i	−0.0385204	−	0.366497i
$445$	−0.598801	−	0.665036i	−0.0283859	−	0.0315257i
$446$	−22.7369	+	4.83287i	−1.07662	+	0.228843i
$447$	15.2659	−	11.0913i	0.722054	−	0.524603i
$448$	−0.155131	+	0.948011i	−0.00732926	+	0.0447893i
$449$	−2.02276	−	6.22541i	−0.0954598	−	0.293795i	0.891913	−	0.452206i	$-0.149363\pi$
$449$	−2.02276	−	6.22541i	−0.0954598	−	0.293795i	−0.987373	+	0.158411i	$0.949363\pi$
$450$	−5.88911	−	10.2002i	−0.277615	−	0.480844i
$451$	−12.0784	−	26.2307i	−0.568752	−	1.23515i
$452$	−5.39450	+	9.34355i	−0.253736	+	0.439484i
$453$	−33.9705	+	37.7281i	−1.59608	+	1.77262i
$454$	−11.5456	−	8.38837i	−0.541862	−	0.393686i
$455$	−0.632908	−	13.3882i	−0.0296712	−	0.627649i
$456$	−6.51963	+	20.0653i	−0.305309	+	0.939646i
$457$	1.89129	−	0.402005i	0.0884707	−	0.0188050i	−0.163464	−	0.986549i	$-0.552267\pi$
$457$	1.89129	−	0.402005i	0.0884707	−	0.0188050i	0.251934	+	0.967744i	$0.418933\pi$
$458$	−0.984861	−	9.37033i	−0.0460196	−	0.437847i
$459$	−70.0142	+	31.1723i	−3.26798	+	1.45500i
$460$	2.10855	−	2.34178i	0.0983118	−	0.109186i
$461$	−1.51843			−0.0707202			−0.0353601	−	0.999375i	$-0.511258\pi$
$461$	−1.51843			−0.0707202			−0.0353601	+	0.999375i	$0.511258\pi$
$462$	46.5994	−	12.8629i	2.16800	−	0.598438i
$463$	−2.44389			−0.113577			−0.0567886	−	0.998386i	$-0.518086\pi$
$463$	−2.44389			−0.113577			−0.0567886	+	0.998386i	$0.518086\pi$
$464$	6.33748	−	7.03849i	0.294210	−	0.326754i
$465$	7.19368	−	3.20283i	0.333599	−	0.148528i
$466$	−3.67974	−	35.0104i	−0.170461	−	1.62183i
$467$	19.3556	−	4.11417i	0.895672	−	0.190381i	0.262995	−	0.964797i	$-0.415290\pi$
$467$	19.3556	−	4.11417i	0.895672	−	0.190381i	0.632677	+	0.774416i	$0.281956\pi$
$468$	11.9415	−	36.7523i	0.551998	−	1.69887i
$469$	−18.9543	+	12.1715i	−0.875230	+	0.562029i
$470$	3.90220	+	2.83512i	0.179995	+	0.130774i
$471$	−15.2170	+	16.9002i	−0.701162	+	0.778719i
$472$	−6.91666	+	11.9800i	−0.318365	+	0.551424i
$473$	−12.1621	−	6.81815i	−0.559212	−	0.313499i
$474$	−13.4554	−	23.3054i	−0.618027	−	1.07045i
$475$	−1.39120	−	4.28167i	−0.0638326	−	0.196456i
$476$	−19.3084	+	7.29855i	−0.884998	+	0.334528i
$477$	7.80088	−	5.66767i	0.357178	−	0.259505i
$478$	46.4512	−	9.87350i	2.12463	−	0.451603i
$479$	8.76683	+	9.73655i	0.400567	+	0.444874i	0.909357	−	0.416016i	$-0.136574\pi$
$479$	8.76683	+	9.73655i	0.400567	+	0.444874i	−0.508791	+	0.860890i	$0.669907\pi$
$480$	1.88673	+	17.9510i	0.0861171	+	0.819349i
$481$	1.15244	−	10.9648i	0.0525469	−	0.499951i
$482$	13.9441	+	42.9154i	0.635134	+	1.95474i
$483$	10.1204	+	20.1164i	0.460492	+	0.915326i
$484$	10.0370	−	7.68757i	0.456228	−	0.349435i
$485$	−2.25255	−	3.90153i	−0.102283	−	0.177159i
$486$	22.7808	+	4.84221i	1.03336	+	0.219647i
$487$	24.1113	−	10.7351i	1.09259	−	0.486452i	0.220295	−	0.975433i	$-0.429298\pi$
$487$	24.1113	−	10.7351i	1.09259	−	0.486452i	0.872294	+	0.488981i	$0.162631\pi$
$488$	9.27045	+	4.12747i	0.419653	+	0.186842i
$489$	7.76967	−	23.9126i	0.351357	−	1.08136i
$490$	12.3671	−	1.17189i	0.558688	−	0.0529406i
$491$	5.54091	−	4.02571i	0.250058	−	0.181678i	−0.455695	−	0.890136i	$-0.650609\pi$
$491$	5.54091	−	4.02571i	0.250058	−	0.181678i	0.705752	+	0.708459i	$0.250609\pi$
$492$	3.24732	−	30.8962i	0.146401	−	1.39291i
$493$	12.6337	+	2.68537i	0.568991	+	0.120943i
$494$	20.2369	−	35.0514i	0.910503	−	1.57704i
$495$	18.9225	−	11.2464i	0.850503	−	0.505487i
$496$	−12.6264			−0.566941
$497$	4.63986	−	4.59257i	0.208126	−	0.206005i
$498$	79.1037	+	57.4722i	3.54472	+	2.57539i
$499$	−3.04529	−	1.35585i	−0.136326	−	0.0606961i	0.337440	−	0.941347i	$-0.390439\pi$
$499$	−3.04529	−	1.35585i	−0.136326	−	0.0606961i	−0.473766	+	0.880651i	$0.657106\pi$
$500$	−0.769062	−	0.854130i	−0.0343935	−	0.0381979i
$501$	−41.6561	−	46.2637i	−1.86106	−	2.06691i
$502$	−33.8300	−	15.0621i	−1.50991	−	0.672254i
$503$	34.4038	+	24.9959i	1.53399	+	1.11451i	0.953967	+	0.299911i	$0.0969570\pi$
$503$	34.4038	+	24.9959i	1.53399	+	1.11451i	0.580024	+	0.814599i	$0.303043\pi$
$504$	−25.5696	−	6.99190i	−1.13896	−	0.311444i
$505$	9.49991			0.422740
$506$	12.1279	+	10.6454i	0.539152	+	0.473245i
$507$	19.6560	−	34.0451i	0.872952	−	1.51200i
$508$	15.1366	+	3.21737i	0.671576	+	0.142748i
$509$	2.57843	−	24.5321i	0.114287	−	1.08737i	−0.775613	−	0.631209i	$-0.782559\pi$
$509$	2.57843	−	24.5321i	0.114287	−	1.08737i	0.889899	−	0.456157i	$-0.150774\pi$
$510$	−30.2541	+	21.9809i	−1.33968	+	0.973332i
$511$	−0.306254	+	0.785768i	−0.0135479	+	0.0347603i
$512$	4.29955	−	13.2326i	0.190015	−	0.584806i
$513$	46.4351	+	20.6742i	2.05016	+	0.912789i
$514$	−40.1302	+	17.8671i	−1.77007	+	0.788084i
$515$	−13.5898	−	2.88861i	−0.598840	−	0.127287i
$516$	−7.49973	−	12.9899i	−0.330157	−	0.571849i
$517$	−5.20589	+	7.35926i	−0.228955	+	0.323660i
$518$	10.2016	+	0.587049i	0.448233	+	0.0257935i
$519$	16.6501	+	51.2437i	0.730858	+	2.24935i
$520$	−0.799385	+	7.60564i	−0.0350554	+	0.333529i
$521$	0.718123	+	6.83248i	0.0314615	+	0.299337i	0.998926	+	0.0463303i	$0.0147527\pi$
$521$	0.718123	+	6.83248i	0.0314615	+	0.299337i	−0.967465	+	0.253006i	$0.918581\pi$
$522$	−14.9957	−	16.6545i	−0.656346	−	0.728946i
$523$	1.70912	−	0.363285i	0.0747348	−	0.0158854i	−0.170393	−	0.985376i	$-0.554504\pi$
$523$	1.70912	−	0.363285i	0.0747348	−	0.0158854i	0.245127	+	0.969491i	$0.421170\pi$
$524$	−13.3924	+	9.73017i	−0.585051	+	0.425064i
$525$	7.68278	−	2.90408i	0.335304	−	0.126745i
$526$	0.664721	+	2.04580i	0.0289832	+	0.0892012i
$527$	−8.60930	−	14.9117i	−0.375027	−	0.649566i
$528$	−50.8975	+	6.00129i	−2.21503	+	0.261173i
$529$	7.74149	−	13.4086i	0.336586	−	0.582985i
$530$	1.72519	−	1.91602i	0.0749375	−	0.0832266i
$531$	49.2028	+	35.7479i	2.13522	+	1.55133i
$532$	12.1660	+	6.27756i	0.527462	+	0.272167i
$533$	13.6305	−	41.9503i	0.590401	−	1.81707i
$534$	4.82232	−	1.02502i	0.208682	−	0.0443568i
$535$	−0.126096	−	1.19972i	−0.00545161	−	0.0518686i
$536$	11.7416	−	5.22768i	0.507158	−	0.225801i
$537$	−11.6678	+	12.9585i	−0.503504	+	0.559198i
$538$	−34.7031			−1.49616
$539$	2.48229	+	23.0833i	0.106920	+	0.994268i
$540$	12.9766			0.558422
$541$	18.5547	−	20.6071i	0.797729	−	0.885968i	−0.197817	−	0.980239i	$-0.563385\pi$
$541$	18.5547	−	20.6071i	0.797729	−	0.885968i	0.995547	+	0.0942708i	$0.0300520\pi$
$542$	33.2475	−	14.8028i	1.42810	−	0.635833i
$543$	7.84157	+	74.6075i	0.336514	+	3.20172i
$544$	38.6062	−	8.20599i	1.65523	−	0.351829i
$545$	−3.60060	+	11.0815i	−0.154233	+	0.474680i
$546$	65.6187	+	33.8588i	2.80822	+	1.44902i
$547$	−19.9098	−	14.4654i	−0.851284	−	0.618494i	0.0742160	−	0.997242i	$-0.476355\pi$
$547$	−19.9098	−	14.4654i	−0.851284	−	0.618494i	−0.925500	+	0.378748i	$0.876355\pi$
$548$	−15.3310	+	17.0268i	−0.654907	+	0.727348i
$549$	22.3073	−	38.6373i	0.952051	−	1.64900i
$550$	4.32385	−	3.99338i	0.184370	−	0.170278i
$551$	−4.28306	−	7.41848i	−0.182464	−	0.316038i
$552$	−3.97044	−	12.2198i	−0.168993	−	0.520108i
$553$	12.0891	−	4.56968i	0.514081	−	0.194322i
$554$	−27.5059	+	19.9842i	−1.16862	+	0.849049i
$555$	6.60848	−	1.40468i	0.280515	−	0.0596252i
$556$	3.11361	+	3.45802i	0.132047	+	0.146653i
$557$	0.227181	+	2.16148i	0.00962597	+	0.0915850i	0.998280	−	0.0586251i	$-0.0186717\pi$
$557$	0.227181	+	2.16148i	0.00962597	+	0.0915850i	−0.988654	+	0.150210i	$0.952005\pi$
$558$	−3.12295	+	29.7129i	−0.132205	+	1.25785i
$559$	−6.58105	−	20.2544i	−0.278349	−	0.856670i
$560$	−13.1480	−	0.756598i	−0.555604	−	0.0319721i
$561$	−41.7920	−	56.0179i	−1.76446	−	2.36508i
$562$	7.43904	+	12.8848i	0.313797	+	0.543513i
$563$	−0.266334	−	0.0566110i	−0.0112246	−	0.00238587i	0.202296	−	0.979324i	$-0.435160\pi$
$563$	−0.266334	−	0.0566110i	−0.0112246	−	0.00238587i	−0.213521	+	0.976939i	$0.568493\pi$
$564$	−8.85916	+	3.94435i	−0.373038	+	0.166087i
$565$	−8.57553	−	3.81807i	−0.360775	−	0.160627i
$566$	−12.9710	+	39.9206i	−0.545211	+	1.67799i
$567$	−14.5448	+	37.3182i	−0.610825	+	1.56722i
$568$	−3.01355	+	2.18947i	−0.126446	+	0.0918683i
$569$	−4.10192	+	39.0271i	−0.171961	+	1.63610i	0.479586	+	0.877495i	$0.340787\pi$
$569$	−4.10192	+	39.0271i	−0.171961	+	1.63610i	−0.651547	+	0.758608i	$0.725880\pi$
$570$	24.2600	+	5.15663i	1.01614	+	0.215987i
$571$	10.2209	−	17.7031i	0.427732	−	0.740853i	−0.568939	−	0.822379i	$-0.692646\pi$
$571$	10.2209	−	17.7031i	0.427732	−	0.740853i	0.996671	+	0.0815263i	$0.0259795\pi$
$572$	19.2292	+	1.77549i	0.804014	+	0.0742371i
$573$	10.8384			0.452781
$574$	39.4340	+	10.7831i	1.64595	+	0.450077i
$575$	2.21810	+	1.61154i	0.0925011	+	0.0672060i
$576$	−2.20142	−	0.980134i	−0.0917257	−	0.0408389i
$577$	9.75839	+	10.8378i	0.406247	+	0.451183i	0.911200	−	0.411964i	$-0.135157\pi$
$577$	9.75839	+	10.8378i	0.406247	+	0.451183i	−0.504953	+	0.863147i	$0.668490\pi$
$578$	34.5292	+	38.3485i	1.43622	+	1.59509i
$579$	23.4027	+	10.4196i	0.972583	+	0.433022i
$580$	−1.76924	−	1.28542i	−0.0734635	−	0.0533744i
$581$	−33.3738	+	33.0337i	−1.38458	+	1.37047i
$582$	24.8190			1.02878
$583$	3.62134	+	3.17867i	0.149981	+	0.131647i
$584$	0.240595	−	0.416723i	0.00995591	−	0.0172441i
$585$	32.8876	+	6.99047i	1.35973	+	0.289020i
$586$	1.79937	−	17.1199i	0.0743314	−	0.707216i
$587$	−28.2748	+	20.5428i	−1.16703	+	0.847893i	−0.990650	−	0.136429i	$-0.956437\pi$
$587$	−28.2748	+	20.5428i	−1.16703	+	0.847893i	−0.176375	+	0.984323i	$0.556437\pi$
$588$	−10.3917	+	22.7112i	−0.428548	+	0.936596i
$589$	−3.52890	+	10.8608i	−0.145406	+	0.447513i
$590$	14.8560	+	6.61434i	0.611614	+	0.272308i
$591$	44.1963	−	19.6774i	1.81799	−	0.809422i
$592$	−10.5964	−	2.25234i	−0.435511	−	0.0925707i
$593$	−5.20010	−	9.00684i	−0.213543	−	0.369867i	0.739278	−	0.673400i	$-0.235167\pi$
$593$	−5.20010	−	9.00684i	−0.213543	−	0.369867i	−0.952821	+	0.303534i	$0.901834\pi$
$594$	0.840455	+	66.4478i	0.0344843	+	2.72639i
$595$	−8.07141	−	16.0436i	−0.330896	−	0.657725i
$596$	2.15888	+	6.64435i	0.0884311	+	0.272163i
$597$	−0.934721	+	8.89327i	−0.0382556	+	0.363977i
$598$	2.57647	+	24.5135i	0.105360	+	1.00243i
$599$	−16.1437	−	17.9294i	−0.659615	−	0.732577i	0.316797	−	0.948493i	$-0.397393\pi$
$599$	−16.1437	−	17.9294i	−0.659615	−	0.732577i	−0.976412	+	0.215917i	$0.930726\pi$
$600$	−4.58393	+	0.974344i	−0.187138	+	0.0397774i
$601$	−4.79090	+	3.48079i	−0.195425	+	0.141985i	−0.681195	−	0.732102i	$-0.738539\pi$
$601$	−4.79090	+	3.48079i	−0.195425	+	0.141985i	0.485770	+	0.874087i	$0.338539\pi$
$602$	18.4635	−	6.97918i	0.752515	−	0.284450i
$603$	−17.4616	−	53.7412i	−0.711091	−	2.18851i
$604$	−9.39814	−	16.2781i	−0.382405	−	0.662345i
$605$	7.56484	+	7.98581i	0.307554	+	0.324669i
$606$	−26.1680	+	45.3242i	−1.06300	+	1.84117i
$607$	14.9314	−	16.5830i	0.606046	−	0.673083i	−0.359551	−	0.933126i	$-0.617070\pi$
$607$	14.9314	−	16.5830i	0.606046	−	0.673083i	0.965597	+	0.260043i	$0.0837367\pi$
$608$	−21.1773	−	15.3862i	−0.858851	−	0.623992i
$609$	13.1500	−	8.44425i	0.532863	−	0.342178i
$610$	3.68637	−	11.3455i	0.149257	−	0.459366i
$611$	−13.4680	+	2.86272i	−0.544858	+	0.115813i
$612$	−5.41255	−	51.4969i	−0.218789	−	2.08164i
$613$	5.99054	−	2.66716i	0.241956	−	0.107726i	−0.282177	−	0.959362i	$-0.591056\pi$
$613$	5.99054	−	2.66716i	0.241956	−	0.107726i	0.524132	+	0.851637i	$0.324390\pi$
$614$	16.7815	−	18.6377i	0.677246	−	0.752158i
$615$	27.0297			1.08994
$616$	0.593701	−	13.2334i	0.0239209	−	0.533190i
$617$	−10.0477			−0.404504			−0.202252	−	0.979334i	$-0.564826\pi$
$617$	−10.0477			−0.404504			−0.202252	+	0.979334i	$0.564826\pi$
$618$	51.2154	−	56.8805i	2.06019	−	2.28807i
$619$	−33.4157	+	14.8776i	−1.34309	+	0.597983i	−0.947297	−	0.320356i	$-0.896197\pi$
$619$	−33.4157	+	14.8776i	−1.34309	+	0.597983i	−0.395794	+	0.918339i	$0.629531\pi$
$620$	0.304744	+	2.89945i	0.0122388	+	0.116445i
$621$	−30.2787	+	6.43593i	−1.21504	+	0.258265i
$622$	7.10120	−	21.8552i	0.284732	−	0.876315i
$623$	0.111803	+	2.36503i	0.00447930	+	0.0947528i
$624$	−63.3307	−	46.0124i	−2.53526	−	1.84197i
$625$	0.669131	−	0.743145i	0.0267652	−	0.0297258i
$626$	−5.18832	+	8.98643i	−0.207367	+	0.359170i
$627$	−9.06303	+	45.4578i	−0.361943	+	1.81541i
$628$	−4.20986	−	7.29170i	−0.167992	−	0.290970i
$629$	−4.56517	−	14.0501i	−0.182025	−	0.560216i
$630$	−5.03242	+	30.7532i	−0.200496	+	1.22524i
$631$	36.8350	−	26.7622i	1.46638	−	1.06539i	0.484735	−	0.874661i	$-0.338916\pi$
$631$	36.8350	−	26.7622i	1.46638	−	1.06539i	0.981644	−	0.190725i	$-0.0610838\pi$
$632$	−7.21297	+	1.53316i	−0.286917	+	0.0609860i
$633$	−6.46337	−	7.17829i	−0.256896	−	0.285312i
$634$	−2.38421	−	22.6842i	−0.0946891	−	0.900906i
$635$	−1.40736	+	13.3902i	−0.0558496	+	0.531373i
$636$	1.60184	+	4.92996i	0.0635171	+	0.195486i
$637$	−21.1365	+	28.4739i	−0.837457	+	1.12818i
$638$	6.46756	−	9.14281i	0.256053	−	0.361967i
$639$	8.18837	+	14.1827i	0.323927	+	0.561058i
$640$	10.7444	+	2.28380i	0.424711	+	0.0902751i
$641$	−17.4145	+	7.75343i	−0.687831	+	0.306242i	−0.720729	−	0.693216i	$-0.756193\pi$
$641$	−17.4145	+	7.75343i	−0.687831	+	0.306242i	0.0328981	+	0.999459i	$0.489526\pi$
$642$	6.07124	+	2.70309i	0.239613	+	0.106683i
$643$	−3.15114	+	9.69822i	−0.124269	+	0.382460i	−0.993767	−	0.111476i	$-0.964442\pi$
$643$	−3.15114	+	9.69822i	−0.124269	+	0.382460i	0.869498	+	0.493936i	$0.164442\pi$
$644$	−8.24117	+	1.26204i	−0.324748	+	0.0497314i
$645$	10.5580	−	7.67086i	0.415722	−	0.302040i
$646$	5.66889	−	53.9359i	0.223040	−	2.12208i
$647$	3.33249	+	0.708342i	0.131014	+	0.0278478i	0.272952	−	0.962028i	$-0.412000\pi$
$647$	3.33249	+	0.708342i	0.131014	+	0.0278478i	−0.141938	+	0.989876i	$0.545333\pi$
$648$	11.4265	−	19.7913i	0.448876	−	0.777475i
$649$	−12.0094	+	27.9186i	−0.471410	+	1.09590i
$650$	8.99017			0.352624
$651$	−20.0961	−	5.49519i	−0.787628	−	0.215374i
$652$	7.53110	+	5.47166i	0.294941	+	0.214287i
$653$	−43.8106	−	19.5057i	−1.71444	−	0.763318i	−0.997830	−	0.0658453i	$-0.979026\pi$
$653$	−43.8106	−	19.5057i	−1.71444	−	0.763318i	−0.716611	−	0.697473i	$-0.754308\pi$
$654$	−42.9521	−	47.7031i	−1.67956	−	1.86534i
$655$	−9.63745	−	10.7035i	−0.376566	−	0.418219i
$656$	−39.5940	−	17.6284i	−1.54588	−	0.688272i
$657$	−1.71152	−	1.24349i	−0.0667726	−	0.0485131i
$658$	−3.23974	−	12.3434i	−0.126298	−	0.481196i
$659$	−3.97487			−0.154839			−0.0774194	−	0.996999i	$-0.524668\pi$
$659$	−3.97487			−0.154839			−0.0774194	+	0.996999i	$0.524668\pi$
$660$	2.60654	+	11.5430i	0.101459	+	0.449309i
$661$	4.81490	−	8.33965i	0.187278	−	0.324375i	−0.757064	−	0.653341i	$-0.773367\pi$
$661$	4.81490	−	8.33965i	0.187278	−	0.324375i	0.944342	+	0.328966i	$0.106700\pi$
$662$	1.19252	+	0.253477i	0.0463485	+	0.00985168i
$663$	11.1586	−	106.167i	0.433364	−	4.12318i
$664$	21.6760	−	15.7486i	0.841193	−	0.611163i
$665$	−4.32549	+	11.0981i	−0.167735	+	0.430364i
$666$	−7.92117	+	24.3789i	−0.306939	+	0.944661i
$667$	4.76574	+	2.12185i	0.184530	+	0.0821582i
$668$	21.0561	−	9.37478i	0.814685	−	0.362721i
$669$	39.7732	+	8.45405i	1.53772	+	0.326853i
$670$	−7.55461	−	13.0850i	−0.291860	−	0.505516i
$671$	21.2890	+	6.62075i	0.821854	+	0.255591i
$672$	26.2143	−	39.9175i	1.01124	−	1.53985i
$673$	3.95392	+	12.1689i	0.152412	+	0.469077i	0.997890	−	0.0649346i	$-0.0206839\pi$
$673$	3.95392	+	12.1689i	0.152412	+	0.469077i	−0.845477	+	0.534012i	$0.820684\pi$
$674$	0.815030	−	7.75449i	0.0313938	−	0.298692i
$675$	1.18017	+	11.2285i	0.0454247	+	0.432187i
$676$	9.73902	+	10.8163i	0.374578	+	0.416011i
$677$	40.6220	−	8.63447i	1.56123	−	0.331850i	0.655330	−	0.755343i	$-0.272530\pi$
$677$	40.6220	−	8.63447i	1.56123	−	0.331850i	0.905899	+	0.423493i	$0.139196\pi$
$678$	41.8378	−	30.3969i	1.60677	−	1.16739i
$679$	−1.92487	+	11.7629i	−0.0738697	+	0.451420i
$680$	3.16660	+	9.74578i	0.121433	+	0.373734i
$681$	12.4821	+	21.6197i	0.478317	+	0.828469i
$682$	−14.8272	+	1.74826i	−0.567763	+	0.0669445i
$683$	16.1167	−	27.9149i	0.616687	−	1.06813i	−0.373399	−	0.927671i	$-0.621808\pi$
$683$	16.1167	−	27.9149i	0.616687	−	1.06813i	0.990086	−	0.140463i	$-0.0448590\pi$
$684$	−22.9793	+	25.5211i	−0.878637	+	0.975825i
$685$	−16.1275	−	11.7173i	−0.616199	−	0.447694i
$686$	−27.2861	−	18.3219i	−1.04179	−	0.699534i
$687$	−5.09311	+	15.6750i	−0.194314	+	0.598038i
$688$	−20.4686	+	4.35073i	−0.780358	+	0.165870i
$689$	0.769323	+	7.31962i	0.0293089	+	0.278855i
$690$	−13.7986	+	6.14351i	−0.525302	+	0.233879i
$691$	−23.2025	+	25.7690i	−0.882666	+	0.980299i	−0.999918	−	0.0128027i	$-0.995925\pi$
$691$	−23.2025	+	25.7690i	−0.882666	+	0.980299i	0.117252	+	0.993102i	$0.462591\pi$
$692$	−19.9487			−0.758336
$693$	−57.5890	−	8.67743i	−2.18763	−	0.329628i
$694$	20.4298			0.775503
$695$	−2.70903	+	3.00868i	−0.102759	+	0.114126i
$696$	−8.14594	+	3.62681i	−0.308771	+	0.137474i
$697$	−6.17806	−	58.7803i	−0.234011	−	2.22646i
$698$	3.40004	−	0.722702i	0.128694	−	0.0273547i
$699$	−19.0294	+	58.5665i	−0.719758	+	2.21519i
$700$	0.143593	+	3.03749i	0.00542730	+	0.114806i
$701$	6.63056	+	4.81738i	0.250433	+	0.181950i	0.705919	−	0.708293i	$-0.250534\pi$
$701$	6.63056	+	4.81738i	0.250433	+	0.181950i	−0.455486	+	0.890243i	$0.650534\pi$
$702$	−67.9185	+	75.4312i	−2.56342	+	2.84697i
$703$	−4.89896	+	8.48525i	−0.184768	+	0.320027i
$704$	0.235450	−	1.18096i	0.00887387	−	0.0445090i
$705$	−4.21873	−	7.30706i	−0.158887	−	0.275200i
$706$	2.65547	+	8.17271i	0.0999400	+	0.307584i
$707$	−19.4518	−	15.9174i	−0.731561	−	0.598636i
$708$	−26.4509	+	19.2177i	−0.994087	+	0.722247i
$709$	33.5378	−	7.12867i	1.25954	−	0.267723i	0.470682	−	0.882303i	$-0.344008\pi$
$709$	33.5378	−	7.12867i	1.25954	−	0.267723i	0.788855	+	0.614580i	$0.210674\pi$
$710$	2.93008	+	3.25418i	0.109964	+	0.122127i
$711$	3.38884	+	32.2426i	0.127091	+	1.20919i
$712$	0.141211	−	1.34354i	0.00529212	−	0.0503512i
$713$	−2.14910	−	6.61424i	−0.0804843	−	0.247705i
$714$	98.7776	+	5.68413i	3.69666	+	0.212723i
$715$	0.212497	+	16.8004i	0.00794694	+	0.628299i
$716$	−3.22797	−	5.59101i	−0.120635	−	0.208946i
$717$	−81.2562	−	17.2715i	−3.03457	−	0.645017i
$718$	−37.3119	+	16.6123i	−1.39247	+	0.619966i
$719$	−4.46905	−	1.98975i	−0.166667	−	0.0742051i	0.321707	−	0.946839i	$-0.395743\pi$
$719$	−4.46905	−	1.98975i	−0.166667	−	0.0742051i	−0.488375	+	0.872634i	$0.662410\pi$
$720$	10.2089	−	31.4199i	0.380464	−	1.17095i
$721$	22.9863	+	28.6849i	0.856055	+	1.06828i
$722$	−1.82065	+	1.32278i	−0.0677575	+	0.0492287i
$723$	8.25090	−	78.5020i	0.306854	−	2.91952i
$724$	−27.1677	−	5.77468i	−1.00968	−	0.214614i
$725$	0.951366	−	1.64781i	0.0353328	−	0.0611983i
$726$	−58.9382	+	14.0947i	−2.18740	+	0.523102i
$727$	39.1461			1.45185			0.725924	−	0.687775i	$-0.241413\pi$
$727$	39.1461			1.45185			0.725924	+	0.687775i	$0.241413\pi$
$728$	14.3803	−	14.2338i	0.532970	−	0.527538i
$729$	3.78204	+	2.74781i	0.140075	+	0.101771i
$730$	−0.516766	−	0.230079i	−0.0191264	−	0.00851561i
$731$	−19.0947	−	21.2068i	−0.706243	−	0.784363i
$732$	16.0486	+	17.8238i	0.593175	+	0.658788i
$733$	28.2759	+	12.5892i	1.04439	+	0.464994i	0.855933	−	0.517086i	$-0.172983\pi$
$733$	28.2759	+	12.5892i	1.04439	+	0.464994i	0.188461	+	0.982081i	$0.439650\pi$
$734$	6.05655	+	4.40034i	0.223551	+	0.162419i
$735$	−20.5970	−	6.92640i	−0.759732	−	0.255484i
$736$	15.9415			0.587610
$737$	24.2740	−	14.4270i	0.894144	−	0.531424i
$738$	−51.2767	+	88.8139i	−1.88752	+	3.26928i
$739$	51.7562	+	11.0011i	1.90388	+	0.404683i	0.999746	−	0.0225572i	$-0.00718080\pi$
$739$	51.7562	+	11.0011i	1.90388	+	0.404683i	0.904138	+	0.427240i	$0.140514\pi$
$740$	−0.261464	+	2.48767i	−0.00961162	+	0.0914484i
$741$	−57.2786	+	41.6153i	−2.10418	+	1.52878i
$742$	−6.74282	+	1.03259i	−0.247537	+	0.0379075i
$743$	−1.57632	+	4.85142i	−0.0578296	+	0.177981i	−0.975799	−	0.218671i	$-0.929828\pi$
$743$	−1.57632	+	4.85142i	−0.0578296	+	0.177981i	0.917969	+	0.396652i	$0.129828\pi$
$744$	10.8596	+	4.83501i	0.398133	+	0.177260i
$745$	−5.55297	+	2.47234i	−0.203445	+	0.0905797i
$746$	−3.42248	−	0.727471i	−0.125306	−	0.0266346i
$747$	−58.8977	−	102.014i	−2.15495	−	3.73249i
$748$	24.5063	−	8.30667i	0.896037	−	0.303722i
$749$	−1.75199	+	2.66781i	−0.0640162	+	0.0974797i
$750$	1.70240	+	5.23946i	0.0621630	+	0.191318i
$751$	2.44606	−	23.2727i	0.0892580	−	0.849233i	−0.854690	−	0.519139i	$-0.826253\pi$
$751$	2.44606	−	23.2727i	0.0892580	−	0.849233i	0.943948	−	0.330094i	$-0.107081\pi$
$752$	1.41418	+	13.4550i	0.0515699	+	0.490654i
$753$	43.3454	+	48.1400i	1.57959	+	1.75432i
$754$	16.7321	−	3.55651i	0.609347	−	0.129521i
$755$	13.2306	−	9.61258i	0.481510	−	0.349838i
$756$	−26.5706	−	21.7427i	−0.966362	−	0.790773i
$757$	−8.08137	−	24.8719i	−0.293722	−	0.903984i	−0.983648	−	0.180104i	$-0.942357\pi$
$757$	−8.08137	−	24.8719i	−0.293722	−	0.903984i	0.689925	−	0.723880i	$-0.257643\pi$
$758$	4.86738	+	8.43056i	0.176791	+	0.306212i
$759$	−11.8068	−	25.6408i	−0.428561	−	0.930704i
$760$	3.39813	−	5.88574i	0.123263	−	0.213498i
$761$	22.4284	−	24.9092i	0.813027	−	0.902958i	−0.183767	−	0.982970i	$-0.558829\pi$
$761$	22.4284	−	24.9092i	0.813027	−	0.902958i	0.996794	+	0.0800116i	$0.0254957\pi$
$762$	−60.0081	−	43.5985i	−2.17386	−	1.57941i
$763$	25.9400	−	16.6574i	0.939090	−	0.603037i
$764$	−1.24002	+	3.81639i	−0.0448623	+	0.138072i
$765$	44.0677	−	9.36689i	1.59327	−	0.338661i
$766$	−0.131342	−	1.24964i	−0.00474559	−	0.0451513i
$767$	−42.4083	+	18.8814i	−1.53128	+	0.681768i
$768$	−42.0005	+	46.6463i	−1.51556	+	1.68320i
$769$	17.9944			0.648896			0.324448	−	0.945904i	$-0.394821\pi$
$769$	17.9944			0.648896			0.324448	+	0.945904i	$0.394821\pi$
$770$	−15.5445	+	0.932012i	−0.560184	+	0.0335874i
$771$	76.8424			2.76741
$772$	−6.34639	+	7.04838i	−0.228412	+	0.253677i
$773$	17.1177	−	7.62131i	0.615683	−	0.274120i	−0.0751069	−	0.997175i	$-0.523930\pi$
$773$	17.1177	−	7.62131i	0.615683	−	0.274120i	0.690790	+	0.723056i	$0.257263\pi$
$774$	5.17570	+	49.2435i	0.186037	+	1.77002i
$775$	−2.48116	+	0.527387i	−0.0891260	+	0.0189443i
$776$	2.10160	−	6.46807i	0.0754431	−	0.232190i
$777$	−15.8850	−	8.19655i	−0.569871	−	0.294050i
$778$	10.1629	+	7.38381i	0.364359	+	0.264722i
$779$	−26.2294	+	29.1307i	−0.939765	+	1.04371i
$780$	−9.03751	+	15.6534i	−0.323595	+	0.560482i
$781$	−6.01199	+	5.55250i	−0.215126	+	0.198684i
$782$	16.5139	+	28.6029i	0.590537	+	1.02284i
$783$	6.63849	+	20.4312i	0.237240	+	0.730150i
$784$	25.6539	+	23.5791i	0.916210	+	0.842111i
$785$	5.92659	−	4.30592i	0.211529	−	0.153685i
$786$	77.6132	−	16.4972i	2.76837	−	0.588436i
$787$	26.2996	+	29.2087i	0.937480	+	1.04118i	0.999072	+	0.0430757i	$0.0137157\pi$
$787$	26.2996	+	29.2087i	0.937480	+	1.04118i	−0.0615917	+	0.998101i	$0.519618\pi$
$788$	1.87228	+	17.8135i	0.0666971	+	0.634581i
$789$	0.393325	−	3.74224i	0.0140027	−	0.133227i
$790$	2.67879	+	8.24447i	0.0953071	+	0.293325i
$791$	11.1618	+	22.1864i	0.396867	+	0.788857i
$792$	31.7309	+	9.86809i	1.12751	+	0.350647i
$793$	17.0269	+	29.4914i	0.604642	+	1.04727i
$794$	42.4979	+	9.03321i	1.50819	+	0.320576i
$795$	−4.12018	+	1.83442i	−0.146128	+	0.0650603i
$796$	−3.02453	−	1.34661i	−0.107202	−	0.0477292i
$797$	−10.9786	+	33.7888i	−0.388883	+	1.19686i	0.544740	+	0.838605i	$0.316628\pi$
$797$	−10.9786	+	33.7888i	−0.388883	+	1.19686i	−0.933624	+	0.358255i	$0.883372\pi$
$798$	−41.0343	−	51.2071i	−1.45260	−	1.81271i
$799$	−14.9261	+	10.8445i	−0.528048	+	0.383649i
$800$	0.607771	−	5.78255i	0.0214879	−	0.204444i
$801$	−5.80959	−	1.23487i	−0.205272	−	0.0436319i
$802$	−23.1064	+	40.0215i	−0.815917	+	1.41321i
$803$	0.417746	−	0.971146i	0.0147419	−	0.0342710i
$804$	30.3775			1.07133
$805$	−1.84154	−	7.01626i	−0.0649058	−	0.247291i
$806$	−18.4492	−	13.4041i	−0.649844	−	0.472139i
$807$	55.4572	+	24.6912i	1.95219	+	0.869170i
$808$	9.59608	+	10.6575i	0.337589	+	0.374930i
$809$	−3.62507	−	4.02604i	−0.127451	−	0.141548i	0.676042	−	0.736863i	$-0.263694\pi$
$809$	−3.62507	−	4.02604i	−0.127451	−	0.141548i	−0.803492	+	0.595315i	$0.797027\pi$
$810$	−24.5426	−	10.9271i	−0.862339	−	0.383938i
$811$	31.8095	+	23.1109i	1.11698	+	0.811534i	0.983749	−	0.179550i	$-0.0574643\pi$
$811$	31.8095	+	23.1109i	1.11698	+	0.811534i	0.133233	+	0.991085i	$0.457464\pi$
$812$	1.46888	+	5.59642i	0.0515476	+	0.196396i
$813$	−63.6633			−2.23277
$814$	−12.7553	−	1.17774i	−0.447073	−	0.0412796i
$815$	−4.04967	+	7.01424i	−0.141854	+	0.245698i
$816$	−102.601	−	21.8084i	−3.59174	−	0.763448i
$817$	−1.97832	+	18.8224i	−0.0692126	+	0.658514i
$818$	−4.48538	+	3.25882i	−0.156828	+	0.113942i
$819$	−55.6272	−	69.4178i	−1.94377	−	2.42565i
$820$	−3.09245	+	9.51760i	−0.107993	+	0.332369i
$821$	−6.40563	−	2.85197i	−0.223558	−	0.0995345i	0.291901	−	0.956448i	$-0.405712\pi$
$821$	−6.40563	−	2.85197i	−0.223558	−	0.0995345i	−0.515459	+	0.856914i	$0.672379\pi$
$822$	100.327	−	44.6686i	3.49931	−	1.55799i
$823$	31.9667	+	6.79472i	1.11429	+	0.236849i	0.728032	−	0.685543i	$-0.240435\pi$
$823$	31.9667	+	6.79472i	1.11429	+	0.236849i	0.386255	+	0.922392i	$0.373768\pi$
$824$	−10.4868	−	18.1637i	−0.365325	−	0.632762i
$825$	−9.75101	+	3.30521i	−0.339487	+	0.115073i
$826$	−19.3364	−	38.4352i	−0.672799	−	1.33733i
$827$	3.84517	+	11.8342i	0.133710	+	0.411516i	0.995387	−	0.0959403i	$-0.0305858\pi$
$827$	3.84517	+	11.8342i	0.133710	+	0.411516i	−0.861677	+	0.507457i	$0.830586\pi$
$828$	2.18614	−	20.7997i	0.0759735	−	0.722840i
$829$	2.72260	+	25.9038i	0.0945600	+	0.899678i	0.934252	+	0.356614i	$0.116069\pi$
$829$	2.72260	+	25.9038i	0.0945600	+	0.899678i	−0.839692	+	0.543063i	$0.817264\pi$
$830$	−21.0756	−	23.4068i	−0.731544	−	0.812462i
$831$	58.1746	−	12.3654i	2.01805	−	0.428951i
$832$	1.48805	−	1.08113i	0.0515889	−	0.0374816i
$833$	−10.3548	+	46.3746i	−0.358772	+	1.60678i
$834$	−6.89232	−	21.2124i	−0.238662	−	0.734525i
$835$	10.0269	+	17.3671i	0.346995	+	0.601014i
$836$	−14.9696	−	8.39206i	−0.517733	−	0.290246i
$837$	14.3196	−	24.8022i	0.494957	−	0.857290i
$838$	−45.8003	+	50.8664i	−1.58214	+	1.75715i
$839$	−0.353306	−	0.256692i	−0.0121975	−	0.00886200i	0.581670	−	0.813425i	$-0.302400\pi$
$839$	−0.353306	−	0.256692i	−0.0121975	−	0.00886200i	−0.593867	+	0.804563i	$0.702400\pi$
$840$	11.0185	+	5.68548i	0.380175	+	0.196168i
$841$	−7.84273	+	24.1374i	−0.270439	+	0.832326i
$842$	−53.8941	+	11.4555i	−1.85731	+	0.394784i
$843$	−2.72046	−	25.8834i	−0.0936975	−	0.891472i
$844$	3.26707	−	1.45459i	0.112457	−	0.0500692i
$845$	−8.47354	+	9.41082i	−0.291499	+	0.323742i
$846$	32.0126			1.10062
$847$	−2.10912	−	29.0267i	−0.0724701	−	0.997371i
$848$	7.23177			0.248340
$849$	49.1316	−	54.5662i	1.68619	−	1.87271i
$850$	11.0049	−	4.89971i	0.377466	−	0.168059i
$851$	−0.623713	−	5.93423i	−0.0213806	−	0.203423i
$852$	−8.61158	+	1.83045i	−0.295028	+	0.0627101i
$853$	10.3316	−	31.7973i	0.353746	−	1.08872i	−0.602987	−	0.797751i	$-0.706023\pi$
$853$	10.3316	−	31.7973i	0.353746	−	1.08872i	0.956733	−	0.290968i	$-0.0939773\pi$
$854$	−26.5579	+	17.0542i	−0.908793	+	0.583582i
$855$	−24.1732	−	17.5628i	−0.826705	−	0.600637i
$856$	1.21855	−	1.35333i	0.0416490	−	0.0462559i
$857$	12.2090	−	21.1466i	0.417052	−	0.722355i	−0.578589	−	0.815619i	$-0.696397\pi$
$857$	12.2090	−	21.1466i	0.417052	−	0.722355i	0.995641	+	0.0932636i	$0.0297299\pi$
$858$	−80.7403	−	45.2637i	−2.75643	−	1.54528i
$859$	−14.9936	−	25.9696i	−0.511574	−	0.886073i	−0.999910	−	0.0134168i	$-0.995729\pi$
$859$	−14.9936	−	25.9696i	−0.511574	−	0.886073i	0.488336	−	0.872656i	$-0.337604\pi$
$860$	1.49310	+	4.59528i	0.0509142	+	0.156698i
$861$	−55.3454	−	45.2891i	−1.88617	−	1.54345i
$862$	−9.20925	+	6.69091i	−0.313668	+	0.227893i
$863$	−43.6604	+	9.28030i	−1.48622	+	0.315905i	−0.878305	−	0.478100i	$-0.841326\pi$
$863$	−43.6604	+	9.28030i	−1.48622	+	0.315905i	−0.607911	+	0.794005i	$0.707992\pi$
$864$	43.9264	+	48.7852i	1.49441	+	1.65971i
$865$	−1.81426	−	17.2615i	−0.0616866	−	0.586908i
$866$	−4.68073	+	44.5342i	−0.159058	+	1.51333i
$867$	−27.8944	−	85.8502i	−0.947345	−	2.91563i
$868$	4.23414	−	6.44747i	0.143716	−	0.218841i
$869$	−15.3436	+	5.20087i	−0.520494	+	0.176427i
$870$	5.24116	+	9.07796i	0.177692	+	0.307772i
$871$	42.1885	+	8.96745i	1.42950	+	0.303850i
$872$	−16.0689	+	7.15434i	−0.544162	+	0.242276i
$873$	−27.3152	−	12.1615i	−0.924479	−	0.411605i
$874$	6.76896	−	20.8327i	0.228964	−	0.704678i
$875$	−2.61526	+	0.400498i	−0.0884120	+	0.0135393i
$876$	0.920094	−	0.668487i	0.0310871	−	0.0225861i
$877$	−3.35708	+	31.9405i	−0.113360	+	1.07855i	0.778936	+	0.627103i	$0.215760\pi$
$877$	−3.35708	+	31.9405i	−0.113360	+	1.07855i	−0.892297	+	0.451449i	$0.850907\pi$
$878$	28.7587	+	6.11284i	0.970558	+	0.206298i
$879$	−15.0563	+	26.0782i	−0.507835	+	0.879596i
$880$	16.4392	+	1.51789i	0.554166	+	0.0511679i
$881$	−48.4335			−1.63177			−0.815883	−	0.578217i	$-0.803749\pi$
$881$	−48.4335			−1.63177			−0.815883	+	0.578217i	$0.803749\pi$
$882$	61.8323	−	54.5377i	2.08200	−	1.83638i
$883$	18.2006	+	13.2235i	0.612497	+	0.445005i	0.850293	−	0.526310i	$-0.176425\pi$
$883$	18.2006	+	13.2235i	0.612497	+	0.445005i	−0.237795	+	0.971315i	$0.576425\pi$
$884$	36.1065	+	16.0757i	1.21439	+	0.540683i
$885$	−19.0346	−	21.1401i	−0.639841	−	0.710616i
$886$	−2.70159	−	3.00042i	−0.0907618	−	0.100801i
$887$	−8.90455	−	3.96456i	−0.298986	−	0.133117i	0.251761	−	0.967789i	$-0.418990\pi$
$887$	−8.90455	−	3.96456i	−0.298986	−	0.133117i	−0.550747	+	0.834672i	$0.685657\pi$
$888$	8.25123	+	5.99487i	0.276893	+	0.201175i
$889$	25.3174	−	25.0594i	0.849118	−	0.840465i
$890$	−1.58811			−0.0532337
$891$	19.8399	−	46.1223i	0.664660	−	1.54515i
$892$	−7.52725	+	13.0376i	−0.252031	+	0.436530i
$893$	11.9689	+	2.54406i	0.400523	+	0.0851337i
$894$	3.50034	−	33.3035i	0.117069	−	1.11384i
$895$	4.54430	−	3.30163i	0.151899	−	0.110361i
$896$	−18.1735	−	22.6789i	−0.607134	−	0.757650i
$897$	13.3240	−	41.0070i	0.444874	−	1.36918i
$898$	−10.6121	−	4.72481i	−0.354131	−	0.157669i
$899$	−4.40919	+	1.96310i	−0.147055	+	0.0654729i
$900$	−7.46147	−	1.58598i	−0.248716	−	0.0528661i
$901$	4.93098	+	8.54071i	0.164275	+	0.284532i
$902$	−48.9361	−	15.2188i	−1.62940	−	0.506731i
$903$	−34.4712	−	1.98364i	−1.14713	−	0.0660113i
$904$	−4.37902	−	13.4772i	−0.145644	−	0.448246i
$905$	2.52600	−	24.0333i	0.0839670	−	0.798892i
$906$	9.41751	+	89.6017i	0.312876	+	2.97682i
$907$	4.08574	+	4.53767i	0.135665	+	0.150671i	0.807149	−	0.590348i	$-0.201009\pi$
$907$	4.08574	+	4.53767i	0.135665	+	0.150671i	−0.671484	+	0.741019i	$0.734343\pi$
$908$	−9.04073	+	1.92167i	−0.300027	+	0.0637728i
$909$	51.0090	−	37.0602i	1.69186	−	1.22921i
$910$	−18.4081	−	15.0633i	−0.610223	−	0.499345i
$911$	−12.1048	−	37.2546i	−0.401048	−	1.23430i	−0.924150	−	0.382030i	$-0.875225\pi$
$911$	−12.1048	−	37.2546i	−0.401048	−	1.23430i	0.523102	−	0.852270i	$-0.324775\pi$
$912$	34.7837	+	60.2471i	1.15180	+	1.99498i
$913$	43.2434	−	39.9383i	1.43115	−	1.32176i
$914$	1.71567	−	2.97162i	0.0567492	−	0.0982926i
$915$	−13.9633	+	15.5078i	−0.461612	+	0.512672i
$916$	−4.93672	−	3.58674i	−0.163114	−	0.118509i
$917$	1.79942	+	38.0641i	0.0594222	+	1.25699i
$918$	−42.0290	+	129.352i	−1.38716	+	4.26925i
$919$	−20.1481	+	4.28260i	−0.664623	+	0.141270i	−0.527857	−	0.849333i	$-0.677004\pi$
$919$	−20.1481	+	4.28260i	−0.664623	+	0.141270i	−0.136766	+	0.990603i	$0.543671\pi$
$920$	0.432634	+	4.11624i	0.0142635	+	0.135708i
$921$	−40.0784	+	17.8440i	−1.32063	+	0.587981i
$922$	−1.80308	+	2.00252i	−0.0593812	+	0.0659495i
$923$	−12.5002			−0.411448
$924$	14.0035	−	28.0025i	0.460682	−	0.921215i
$925$	−2.17634			−0.0715577
$926$	−2.90204	+	3.22304i	−0.0953668	+	0.105916i
$927$	−84.2382	+	37.5053i	−2.76675	+	1.23184i
$928$	−1.15642	−	11.0026i	−0.0379615	−	0.361180i
$929$	25.2034	−	5.35715i	0.826897	−	0.175762i	0.225023	−	0.974353i	$-0.427754\pi$
$929$	25.2034	−	5.35715i	0.826897	−	0.175762i	0.601874	+	0.798591i	$0.294421\pi$
$930$	4.31830	−	13.2904i	0.141603	−	0.435809i
$931$	27.4520	−	15.4767i	0.899702	−	0.507227i
$932$	−18.4451	−	13.4011i	−0.604189	−	0.438969i
$933$	−26.8980	+	29.8733i	−0.880601	+	0.978007i
$934$	17.5583	−	30.4119i	0.574526	−	0.995108i
$935$	9.41646	+	20.4497i	0.307951	+	0.668775i
$936$	25.3782	+	43.9563i	0.829513	+	1.43676i
$937$	1.00152	+	3.08237i	0.0327183	+	0.100697i	0.966082	−	0.258235i	$-0.0831410\pi$
$937$	1.00152	+	3.08237i	0.0327183	+	0.100697i	−0.933364	+	0.358932i	$0.883141\pi$
$938$	−6.45563	+	39.4505i	−0.210784	+	1.28811i
$939$	14.6850	−	10.6693i	0.479227	−	0.348179i
$940$	3.05560	−	0.649488i	0.0996627	−	0.0211840i
$941$	2.91852	+	3.24135i	0.0951411	+	0.105665i	0.788835	−	0.614605i	$-0.210685\pi$
$941$	2.91852	+	3.24135i	0.0951411	+	0.105665i	−0.693694	+	0.720270i	$0.744018\pi$
$942$	4.21854	+	40.1368i	0.137448	+	1.30773i
$943$	2.49533	−	23.7415i	0.0812591	−	0.773129i
$944$	14.0953	+	43.3808i	0.458762	+	1.41192i
$945$	16.3973	−	24.9688i	0.533405	−	0.812234i
$946$	−23.4339	+	7.94318i	−0.761902	+	0.258255i
$947$	9.45357	+	16.3741i	0.307200	+	0.532086i	0.977749	−	0.209780i	$-0.0672747\pi$
$947$	9.45357	+	16.3741i	0.307200	+	0.532086i	−0.670549	+	0.741865i	$0.733941\pi$
$948$	−17.0479	−	3.62365i	−0.553691	−	0.117691i
$949$	1.47517	−	0.656788i	0.0478860	−	0.0213202i
$950$	−7.29872	−	3.24960i	−0.236802	−	0.105431i
$951$	−12.3297	+	37.9469i	−0.399818	+	1.23051i
$952$	9.84553	−	25.2610i	0.319095	−	0.818714i
$953$	−42.3439	+	30.7647i	−1.37165	+	0.996565i	−0.374049	+	0.927409i	$0.622031\pi$
$953$	−42.3439	+	30.7647i	−1.37165	+	0.996565i	−0.997606	+	0.0691562i	$0.977969\pi$
$954$	1.78867	−	17.0181i	0.0579104	−	0.550980i
$955$	−3.41507	−	0.725896i	−0.110509	−	0.0234894i
$956$	15.3781	−	26.6356i	0.497363	−	0.861458i
$957$	−16.8406	+	10.0090i	−0.544378	+	0.323545i
$958$	23.2510			0.751206
$959$	13.3896	+	51.0142i	0.432372	+	1.64733i
$960$	0.911864	+	0.662508i	0.0294303	+	0.0213824i
$961$	−22.4419	−	9.99177i	−0.723932	−	0.322315i
$962$	−13.0920	−	14.5402i	−0.422103	−	0.468793i
$963$	−5.35732	−	5.94991i	−0.172637	−	0.191733i
$964$	26.6979	+	11.8867i	0.859882	+	0.382844i
$965$	−6.67611	−	4.85048i	−0.214911	−	0.156142i
$966$	38.5473	+	10.5406i	1.24024	+	0.339138i
$967$	33.0924			1.06418			0.532090	−	0.846688i	$-0.321407\pi$
$967$	33.0924			1.06418			0.532090	+	0.846688i	$0.321407\pi$
$968$	−1.31751	+	16.5533i	−0.0423463	+	0.532044i
$969$	−47.4344	+	82.1589i	−1.52381	+	2.63932i
$970$	−7.82022	−	1.66224i	−0.251092	−	0.0533713i
$971$	−0.754614	+	7.17967i	−0.0242167	+	0.230407i	0.975719	+	0.219028i	$0.0702886\pi$
$971$	−0.754614	+	7.17967i	−0.0242167	+	0.230407i	−0.999935	+	0.0113785i	$0.996378\pi$
$972$	12.2029	−	8.86592i	0.391408	−	0.284375i
$973$	10.5881	−	1.62145i	0.339439	−	0.0519813i
$974$	14.4738	−	44.5459i	0.463772	−	1.42734i
$975$	−14.3667	−	6.39649i	−0.460104	−	0.204851i
$976$	30.5679	−	13.6097i	0.978454	−	0.435636i
$977$	19.9901	+	4.24904i	0.639541	+	0.135939i	0.516258	−	0.856433i	$-0.327324\pi$
$977$	19.9901	+	4.24904i	0.639541	+	0.135939i	0.123283	+	0.992372i	$0.460658\pi$
$978$	−22.3100	−	38.6421i	−0.713397	−	1.23564i
$979$	−0.0375376	−	2.96779i	−0.00119971	−	0.0948510i
$980$	4.79540	−	6.46010i	0.153183	−	0.206360i
$981$	23.8971	+	73.5476i	0.762975	+	2.34819i
$982$	1.27048	−	12.0878i	0.0405427	−	0.385738i
$983$	−2.83262	−	26.9506i	−0.0903467	−	0.859591i	−0.942029	−	0.335532i	$-0.891084\pi$
$983$	−2.83262	−	26.9506i	−0.0903467	−	0.859591i	0.851682	−	0.524059i	$-0.175583\pi$
$984$	27.3033	+	30.3234i	0.870397	+	0.966674i
$985$	−15.2437	+	3.24014i	−0.485704	+	0.103240i
$986$	18.5435	−	13.4727i	0.590546	−	0.429057i
$987$	−3.60503	+	22.0304i	−0.114749	+	0.701236i
$988$	−8.10023	−	24.9300i	−0.257703	−	0.793128i
$989$	−5.76299	−	9.98180i	−0.183253	−	0.317403i
$990$	7.63794	−	38.3100i	0.242750	−	1.21757i
$991$	−7.72355	+	13.3776i	−0.245347	+	0.424953i	−0.962229	−	0.272241i	$-0.912235\pi$
$991$	−7.72355	+	13.3776i	−0.245347	+	0.424953i	0.716882	+	0.697194i	$0.245568\pi$
$992$	−9.86886	+	10.9605i	−0.313337	+	0.347995i
$993$	−1.72535	−	1.25354i	−0.0547524	−	0.0397800i
$994$	−0.547079	−	11.5726i	−0.0173523	−	0.367062i
$995$	0.890142	−	2.73958i	0.0282194	−	0.0868504i
$996$	61.9418	−	13.1661i	1.96270	−	0.417185i
$997$	5.28991	+	50.3302i	0.167533	+	1.59397i	0.678651	+	0.734461i	$0.262565\pi$
$997$	5.28991	+	50.3302i	0.167533	+	1.59397i	−0.511118	+	0.859511i	$0.670768\pi$
$998$	−5.40429	+	2.40614i	−0.171070	+	0.0761651i
$999$	16.4417	−	18.2604i	0.520193	−	0.577733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.bg.a.291.13	yes	128
7.2	even	3	inner	385.2.bg.a.16.4	✓	128
11.9	even	5	inner	385.2.bg.a.361.4	yes	128
77.9	even	15	inner	385.2.bg.a.86.13	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.bg.a.16.4	✓	128	7.2	even	3	inner
385.2.bg.a.86.13	yes	128	77.9	even	15	inner
385.2.bg.a.291.13	yes	128	1.1	even	1	trivial
385.2.bg.a.361.4	yes	128	11.9	even	5	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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18747 - 1.31881i) q^{2} +(-2.83596 + 1.26265i) q^{3} +(-0.120139 - 1.14305i) q^{4} +(0.978148 - 0.207912i) q^{5} +(-1.70240 + 5.23946i) q^{6} +(-2.35120 - 1.21320i) q^{7} +(1.22130 + 0.887324i) q^{8} +(4.44100 - 4.93223i) q^{9} +O(q^{10})\)	\(q+(1.18747 - 1.31881i) q^{2} +(-2.83596 + 1.26265i) q^{3} +(-0.120139 - 1.14305i) q^{4} +(0.978148 - 0.207912i) q^{5} +(-1.70240 + 5.23946i) q^{6} +(-2.35120 - 1.21320i) q^{7} +(1.22130 + 0.887324i) q^{8} +(4.44100 - 4.93223i) q^{9} +(0.887320 - 1.53688i) q^{10} +(2.89302 + 1.62185i) q^{11} +(1.78398 + 3.08995i) q^{12} +(1.56545 + 4.81797i) q^{13} +(-4.39196 + 1.66016i) q^{14} +(-2.51147 + 1.82469i) q^{15} +(4.86892 - 1.03492i) q^{16} +(4.54211 + 5.04453i) q^{17} +(-1.23116 - 11.7137i) q^{18} +(0.470588 - 4.47735i) q^{19} +(-0.355167 - 1.09309i) q^{20} +(8.19976 + 0.471853i) q^{21} +(5.57429 - 1.88947i) q^{22} +(1.37086 + 2.37440i) q^{23} +(-4.58393 - 0.974344i) q^{24} +(0.913545 - 0.406737i) q^{25} +(8.21293 + 3.65663i) q^{26} +(-3.48892 + 10.7378i) q^{27} +(-1.10428 + 2.83329i) q^{28} +(1.53934 - 1.11840i) q^{29} +(-0.575857 + 5.47892i) q^{30} +(-2.48116 - 0.527387i) q^{31} +(2.90720 - 5.03542i) q^{32} +(-10.2523 - 0.946631i) q^{33} +12.0464 q^{34} +(-2.55206 - 0.697850i) q^{35} +(-6.17131 - 4.48372i) q^{36} +(-1.98819 - 0.885198i) q^{37} +(-5.34598 - 5.93732i) q^{38} +(-10.5230 - 11.6870i) q^{39} +(1.37909 + 0.614012i) q^{40} +(-7.04414 - 5.11787i) q^{41} +(10.3592 - 10.2537i) q^{42} -4.20393 q^{43} +(1.50629 - 3.50172i) q^{44} +(3.31848 - 5.74778i) q^{45} +(4.75924 + 1.01161i) q^{46} +(-0.284103 + 2.70306i) q^{47} +(-12.5013 + 9.08275i) q^{48} +(4.05627 + 5.70497i) q^{49} +(0.548394 - 1.68778i) q^{50} +(-19.2507 - 8.57098i) q^{51} +(5.31911 - 2.36822i) q^{52} +(1.42109 + 0.302061i) q^{53} +(10.0182 + 17.3520i) q^{54} +(3.16701 + 0.984918i) q^{55} +(-1.79501 - 3.56796i) q^{56} +(4.31876 + 13.2918i) q^{57} +(0.352957 - 3.35816i) q^{58} +(0.957850 + 9.11333i) q^{59} +(2.38743 + 2.65151i) q^{60} +(6.57524 - 1.39761i) q^{61} +(-3.64182 + 2.64594i) q^{62} +(-16.4255 + 6.20881i) q^{63} +(-0.112198 - 0.345310i) q^{64} +(2.53296 + 4.38721i) q^{65} +(-13.4227 + 12.3968i) q^{66} +(4.25698 - 7.37331i) q^{67} +(5.22046 - 5.79790i) q^{68} +(-6.88574 - 5.00279i) q^{69} +(-3.95082 + 2.53702i) q^{70} +(-0.762500 + 2.34674i) q^{71} +(9.80025 - 2.08311i) q^{72} +(-0.0333187 - 0.317007i) q^{73} +(-3.52832 + 1.57091i) q^{74} +(-2.07721 + 2.30698i) q^{75} -5.17437 q^{76} +(-4.83444 - 7.32313i) q^{77} -27.9086 q^{78} +(-3.26857 + 3.63011i) q^{79} +(4.54735 - 2.02461i) q^{80} +(-1.58239 - 15.0555i) q^{81} +(-15.1142 + 3.21262i) q^{82} +(5.48455 - 16.8797i) q^{83} +(-0.445762 - 9.42942i) q^{84} +(5.49167 + 3.98993i) q^{85} +(-4.99202 + 5.54420i) q^{86} +(-2.95337 + 5.11538i) q^{87} +(2.09413 + 4.54781i) q^{88} +(-0.447447 - 0.775001i) q^{89} +(-3.63967 - 11.2018i) q^{90} +(2.16449 - 13.2272i) q^{91} +(2.54936 - 1.85222i) q^{92} +(7.70238 - 1.63719i) q^{93} +(3.22748 + 3.58447i) q^{94} +(-0.470588 - 4.47735i) q^{95} +(-1.88673 + 17.9510i) q^{96} +(-1.39215 - 4.28461i) q^{97} +(12.3405 + 1.42498i) q^{98} +(20.8473 - 7.06641i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 3 q^{3} + 20 q^{4} - 16 q^{5} - 6 q^{7} + 20 q^{8} + 13 q^{9}+O(q^{10}) \) 128 * q + 3 * q^3 + 20 * q^4 - 16 * q^5 - 6 * q^7 + 20 * q^8 + 13 * q^9	\( 128 q + 3 q^{3} + 20 q^{4} - 16 q^{5} - 6 q^{7} + 20 q^{8} + 13 q^{9} - 10 q^{10} + 4 q^{11} + 6 q^{12} + 14 q^{13} + 13 q^{14} + 6 q^{15} + 22 q^{16} + 23 q^{17} - 33 q^{18} - 2 q^{19} + 30 q^{20} - 16 q^{21} - 2 q^{22} + 8 q^{23} + 30 q^{24} + 16 q^{25} + 16 q^{26} - 42 q^{27} + 27 q^{28} - 16 q^{29} - 8 q^{31} + 80 q^{32} - 4 q^{33} - 96 q^{34} + 2 q^{35} - 68 q^{36} - 2 q^{37} - 15 q^{38} - 44 q^{39} + 10 q^{40} - 8 q^{41} + 120 q^{42} - 252 q^{43} + 5 q^{44} + 62 q^{45} - 15 q^{46} - 18 q^{47} - 222 q^{48} + 24 q^{49} - 56 q^{51} + 26 q^{52} - 8 q^{53} + 66 q^{54} - 2 q^{55} - 70 q^{56} + 36 q^{57} + 17 q^{58} - 34 q^{59} + 29 q^{60} - 36 q^{61} + 44 q^{62} - 39 q^{63} + 44 q^{64} + 12 q^{65} - 60 q^{66} + 10 q^{67} + 78 q^{68} + 108 q^{69} - 13 q^{70} - 39 q^{72} - 3 q^{73} - 13 q^{74} - 2 q^{75} + 36 q^{76} + 13 q^{77} + 40 q^{78} - 69 q^{79} - 7 q^{80} + 71 q^{81} - 6 q^{82} + 48 q^{83} + 2 q^{84} - 4 q^{85} - 29 q^{86} - 122 q^{87} - 17 q^{88} + 24 q^{90} - 47 q^{91} + 28 q^{92} + 33 q^{93} - 21 q^{94} + 2 q^{95} + 15 q^{96} - 58 q^{97} - 90 q^{98} + 100 q^{99}+O(q^{100}) \) 128 * q + 3 * q^3 + 20 * q^4 - 16 * q^5 - 6 * q^7 + 20 * q^8 + 13 * q^9 - 10 * q^10 + 4 * q^11 + 6 * q^12 + 14 * q^13 + 13 * q^14 + 6 * q^15 + 22 * q^16 + 23 * q^17 - 33 * q^18 - 2 * q^19 + 30 * q^20 - 16 * q^21 - 2 * q^22 + 8 * q^23 + 30 * q^24 + 16 * q^25 + 16 * q^26 - 42 * q^27 + 27 * q^28 - 16 * q^29 - 8 * q^31 + 80 * q^32 - 4 * q^33 - 96 * q^34 + 2 * q^35 - 68 * q^36 - 2 * q^37 - 15 * q^38 - 44 * q^39 + 10 * q^40 - 8 * q^41 + 120 * q^42 - 252 * q^43 + 5 * q^44 + 62 * q^45 - 15 * q^46 - 18 * q^47 - 222 * q^48 + 24 * q^49 - 56 * q^51 + 26 * q^52 - 8 * q^53 + 66 * q^54 - 2 * q^55 - 70 * q^56 + 36 * q^57 + 17 * q^58 - 34 * q^59 + 29 * q^60 - 36 * q^61 + 44 * q^62 - 39 * q^63 + 44 * q^64 + 12 * q^65 - 60 * q^66 + 10 * q^67 + 78 * q^68 + 108 * q^69 - 13 * q^70 - 39 * q^72 - 3 * q^73 - 13 * q^74 - 2 * q^75 + 36 * q^76 + 13 * q^77 + 40 * q^78 - 69 * q^79 - 7 * q^80 + 71 * q^81 - 6 * q^82 + 48 * q^83 + 2 * q^84 - 4 * q^85 - 29 * q^86 - 122 * q^87 - 17 * q^88 + 24 * q^90 - 47 * q^91 + 28 * q^92 + 33 * q^93 - 21 * q^94 + 2 * q^95 + 15 * q^96 - 58 * q^97 - 90 * q^98 + 100 * q^99

Introduction

L-functions

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