LMFDB - Embedded newform 429.2.bq.a.29.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(29,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 21, 10]))

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

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

chi := DirichletCharacter("429.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bq (of order $30$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			29.15
Character	$\chi$	$=$	429.29
Dual form			429.2.bq.a.74.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.144098 + 1.37101i) q^{2} +(0.143318 + 1.72611i) q^{3} +(0.0974043 + 0.0207039i) q^{4} +(0.756574 + 1.04133i) q^{5} +(-2.38716 - 0.0522407i) q^{6} +(0.619507 - 2.91455i) q^{7} +(-0.894416 + 2.75273i) q^{8} +(-2.95892 + 0.494764i) q^{9} +O(q^{10})$	\(q+(-0.144098 + 1.37101i) q^{2} +(0.143318 + 1.72611i) q^{3} +(0.0974043 + 0.0207039i) q^{4} +(0.756574 + 1.04133i) q^{5} +(-2.38716 - 0.0522407i) q^{6} +(0.619507 - 2.91455i) q^{7} +(-0.894416 + 2.75273i) q^{8} +(-2.95892 + 0.494764i) q^{9} +(-1.53670 + 0.887212i) q^{10} +(-3.26965 + 0.556210i) q^{11} +(-0.0217775 + 0.171098i) q^{12} +(2.32342 + 2.75712i) q^{13} +(3.90660 + 1.26933i) q^{14} +(-1.68903 + 1.45517i) q^{15} +(-3.46318 - 1.54191i) q^{16} +(0.336659 + 3.20309i) q^{17} +(-0.251949 - 4.12799i) q^{18} +(-5.57769 + 5.02217i) q^{19} +(0.0521338 + 0.117095i) q^{20} +(5.11963 + 0.651632i) q^{21} +(-0.291414 - 4.56286i) q^{22} +(4.15433 - 2.39850i) q^{23} +(-4.87970 - 1.14935i) q^{24} +(1.03311 - 3.17959i) q^{25} +(-4.11483 + 2.78812i) q^{26} +(-1.27808 - 5.03652i) q^{27} +(0.120685 - 0.271064i) q^{28} +(2.30471 - 2.55964i) q^{29} +(-1.75166 - 2.52535i) q^{30} +(7.42043 + 5.39125i) q^{31} +(-0.281390 + 0.487381i) q^{32} +(-1.42868 - 5.56407i) q^{33} -4.43997 q^{34} +(3.50373 - 1.55996i) q^{35} +(-0.298455 - 0.0130691i) q^{36} +(4.32855 - 4.80735i) q^{37} +(-6.08169 - 8.37073i) q^{38} +(-4.42612 + 4.40562i) q^{39} +(-3.54320 + 1.15126i) q^{40} +(0.578319 - 0.122925i) q^{41} +(-1.63112 + 6.92514i) q^{42} +(-4.63258 - 2.67462i) q^{43} +(-0.329994 - 0.0135174i) q^{44} +(-2.75386 - 2.70690i) q^{45} +(2.68973 + 6.04122i) q^{46} +(1.22128 + 0.396818i) q^{47} +(2.16517 - 6.19882i) q^{48} +(-1.71601 - 0.764016i) q^{49} +(4.21036 + 1.87458i) q^{50} +(-5.48064 + 1.04017i) q^{51} +(0.169228 + 0.316660i) q^{52} +(-1.75263 + 2.41229i) q^{53} +(7.08926 - 1.02651i) q^{54} +(-3.05293 - 2.98399i) q^{55} +(7.46888 + 4.31216i) q^{56} +(-9.46821 - 8.90794i) q^{57} +(3.17717 + 3.52861i) q^{58} +(2.07339 - 9.75455i) q^{59} +(-0.194646 + 0.106771i) q^{60} +(9.53549 - 1.00222i) q^{61} +(-8.46071 + 9.39657i) q^{62} +(-0.391055 + 8.93044i) q^{63} +(-6.76150 - 4.91251i) q^{64} +(-1.11325 + 4.50542i) q^{65} +(7.83424 - 1.15695i) q^{66} +(0.968586 + 1.67764i) q^{67} +(-0.0335246 + 0.318965i) q^{68} +(4.73547 + 6.82708i) q^{69} +(1.63383 + 5.02842i) q^{70} +(9.58411 - 1.00733i) q^{71} +(1.28455 - 8.58763i) q^{72} +(10.3172 - 3.35227i) q^{73} +(5.96716 + 6.62720i) q^{74} +(5.63639 + 1.32757i) q^{75} +(-0.647270 + 0.373701i) q^{76} +(-0.404472 + 9.87415i) q^{77} +(-5.40233 - 6.70307i) q^{78} +(5.73393 - 7.89207i) q^{79} +(-1.01451 - 4.77290i) q^{80} +(8.51042 - 2.92794i) q^{81} +(0.0851966 + 0.810592i) q^{82} +(-14.4296 + 10.4837i) q^{83} +(0.485183 + 0.169468i) q^{84} +(-3.08078 + 2.77395i) q^{85} +(4.33447 - 5.96588i) q^{86} +(4.74852 + 3.61134i) q^{87} +(1.39334 - 9.49795i) q^{88} +(-7.17794 + 4.14419i) q^{89} +(4.10800 - 3.38549i) q^{90} +(9.47516 - 5.06366i) q^{91} +(0.454308 - 0.147614i) q^{92} +(-8.24243 + 13.5811i) q^{93} +(-0.720024 + 1.61720i) q^{94} +(-9.44969 - 2.00859i) q^{95} +(-0.881602 - 0.415859i) q^{96} +(-7.08104 + 3.15268i) q^{97} +(1.29474 - 2.24256i) q^{98} +(9.39945 - 3.26349i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) $ 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9	$ 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9} - 52 q^{12} - 20 q^{13} - 3 q^{15} + 30 q^{16} - 20 q^{18} - 10 q^{19} + 4 q^{22} + 5 q^{24} + 60 q^{25} - 24 q^{27} - 10 q^{28} - 65 q^{30} - 8 q^{31} + 49 q^{33} - 24 q^{34} + 3 q^{36} - 6 q^{37} - 35 q^{39} - 120 q^{40} - 13 q^{42} - 32 q^{45} - 30 q^{46} - 33 q^{48} - 26 q^{49} - 100 q^{51} - 60 q^{52} - 42 q^{55} - 20 q^{57} - 34 q^{58} + 32 q^{60} - 30 q^{61} - 45 q^{63} + 40 q^{64} + 42 q^{66} + 32 q^{67} - 33 q^{69} - 268 q^{70} + 55 q^{72} - 40 q^{73} + 9 q^{75} - 32 q^{78} - 37 q^{81} + 28 q^{82} - 180 q^{84} - 10 q^{85} - 142 q^{88} - 30 q^{90} + 8 q^{91} - 26 q^{93} - 90 q^{94} + 330 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) $ 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9 - 52 * q^12 - 20 * q^13 - 3 * q^15 + 30 * q^16 - 20 * q^18 - 10 * q^19 + 4 * q^22 + 5 * q^24 + 60 * q^25 - 24 * q^27 - 10 * q^28 - 65 * q^30 - 8 * q^31 + 49 * q^33 - 24 * q^34 + 3 * q^36 - 6 * q^37 - 35 * q^39 - 120 * q^40 - 13 * q^42 - 32 * q^45 - 30 * q^46 - 33 * q^48 - 26 * q^49 - 100 * q^51 - 60 * q^52 - 42 * q^55 - 20 * q^57 - 34 * q^58 + 32 * q^60 - 30 * q^61 - 45 * q^63 + 40 * q^64 + 42 * q^66 + 32 * q^67 - 33 * q^69 - 268 * q^70 + 55 * q^72 - 40 * q^73 + 9 * q^75 - 32 * q^78 - 37 * q^81 + 28 * q^82 - 180 * q^84 - 10 * q^85 - 142 * q^88 - 30 * q^90 + 8 * q^91 - 26 * q^93 - 90 * q^94 + 330 * q^96 - 14 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−0.144098	+	1.37101i	−0.101893	+	0.969447i	0.817453	+	0.575996i	$0.195386\pi$
$2$	−0.144098	+	1.37101i	−0.101893	+	0.969447i	−0.919346	+	0.393451i	$0.871281\pi$
$3$	0.143318	+	1.72611i	0.0827445	+	0.996571i
$3$	0.143318	+	1.72611i	0.0827445	+	0.996571i
$4$	0.0974043	+	0.0207039i	0.0487022	+	0.0103520i
$5$	0.756574	+	1.04133i	0.338350	+	0.465699i	0.943959	−	0.330064i	$-0.107070\pi$
$5$	0.756574	+	1.04133i	0.338350	+	0.465699i	−0.605609	+	0.795763i	$0.707070\pi$
$6$	−2.38716	−	0.0522407i	−0.974554	−	0.0213272i
$7$	0.619507	−	2.91455i	0.234152	−	1.10160i	−0.691252	−	0.722614i	$-0.742940\pi$
$7$	0.619507	−	2.91455i	0.234152	−	1.10160i	0.925404	−	0.378983i	$-0.123726\pi$
$8$	−0.894416	+	2.75273i	−0.316224	+	0.973237i
$9$	−2.95892	+	0.494764i	−0.986307	+	0.164921i
$10$	−1.53670	+	0.887212i	−0.485946	+	0.280561i
$11$	−3.26965	+	0.556210i	−0.985837	+	0.167703i
$11$	−3.26965	+	0.556210i	−0.985837	+	0.167703i
$12$	−0.0217775	+	0.171098i	−0.00628663	+	0.0493917i
$13$	2.32342	+	2.75712i	0.644400	+	0.764689i
$13$	2.32342	+	2.75712i	0.644400	+	0.764689i
$14$	3.90660	+	1.26933i	1.04408	+	0.339243i
$15$	−1.68903	+	1.45517i	−0.436105	+	0.375724i
$16$	−3.46318	−	1.54191i	−0.865795	−	0.385477i
$17$	0.336659	+	3.20309i	0.0816517	+	0.776864i	0.956355	+	0.292206i	$0.0943893\pi$
$17$	0.336659	+	3.20309i	0.0816517	+	0.776864i	−0.874704	+	0.484658i	$0.838944\pi$
$18$	−0.251949	−	4.12799i	−0.0593849	−	0.972976i
$19$	−5.57769	+	5.02217i	−1.27961	+	1.15217i	−0.299416	+	0.954123i	$0.596792\pi$
$19$	−5.57769	+	5.02217i	−1.27961	+	1.15217i	−0.980193	+	0.198043i	$0.936541\pi$
$20$	0.0521338	+	0.117095i	0.0116575	+	0.0261831i
$21$	5.11963	+	0.651632i	1.11719	+	0.142198i
$22$	−0.291414	−	4.56286i	−0.0621297	−	0.972805i
$23$	4.15433	−	2.39850i	0.866237	−	0.500122i	0.000141147	−	1.00000i	$-0.499955\pi$
$23$	4.15433	−	2.39850i	0.866237	−	0.500122i	0.866096	+	0.499878i	$0.166622\pi$
$24$	−4.87970	−	1.14935i	−0.996065	−	0.234609i
$25$	1.03311	−	3.17959i	0.206622	−	0.635918i
$26$	−4.11483	+	2.78812i	−0.806985	+	0.546795i
$27$	−1.27808	−	5.03652i	−0.245967	−	0.969278i
$28$	0.120685	−	0.271064i	0.0228074	−	0.0512262i
$29$	2.30471	−	2.55964i	0.427973	−	0.475313i	−0.490132	−	0.871648i	$-0.663052\pi$
$29$	2.30471	−	2.55964i	0.427973	−	0.475313i	0.918106	+	0.396335i	$0.129718\pi$
$30$	−1.75166	−	2.52535i	−0.319808	−	0.461065i
$31$	7.42043	+	5.39125i	1.33275	+	0.968298i	0.999677	+	0.0253959i	$0.00808465\pi$
$31$	7.42043	+	5.39125i	1.33275	+	0.968298i	0.333070	+	0.942902i	$0.391915\pi$
$32$	−0.281390	+	0.487381i	−0.0497431	+	0.0861576i
$33$	−1.42868	−	5.56407i	−0.248701	−	0.968580i
$34$	−4.43997			−0.761448
$35$	3.50373	−	1.55996i	0.592238	−	0.263681i
$36$	−0.298455	−	0.0130691i	−0.0497425	−	0.00217818i
$37$	4.32855	−	4.80735i	0.711610	−	0.790323i	−0.273569	−	0.961852i	$-0.588204\pi$
$37$	4.32855	−	4.80735i	0.711610	−	0.790323i	0.985179	+	0.171529i	$0.0548709\pi$
$38$	−6.08169	−	8.37073i	−0.986580	−	1.35791i
$39$	−4.42612	+	4.40562i	−0.708746	+	0.705464i
$40$	−3.54320	+	1.15126i	−0.560230	+	0.182030i
$41$	0.578319	−	0.122925i	0.0903182	−	0.0191977i	−0.162531	−	0.986703i	$-0.551966\pi$
$41$	0.578319	−	0.122925i	0.0903182	−	0.0191977i	0.252849	+	0.967506i	$0.418632\pi$
$42$	−1.63112	+	6.92514i	−0.251687	+	1.06857i
$43$	−4.63258	−	2.67462i	−0.706461	−	0.407876i	0.103288	−	0.994651i	$-0.467064\pi$
$43$	−4.63258	−	2.67462i	−0.706461	−	0.407876i	−0.809749	+	0.586776i	$0.800397\pi$
$44$	−0.329994	−	0.0135174i	−0.0497485	−	0.00203783i
$45$	−2.75386	−	2.70690i	−0.410521	−	0.403521i
$46$	2.68973	+	6.04122i	0.396579	+	0.890730i
$47$	1.22128	+	0.396818i	0.178142	+	0.0578818i	0.396730	−	0.917935i	$-0.370145\pi$
$47$	1.22128	+	0.396818i	0.178142	+	0.0578818i	−0.218588	+	0.975817i	$0.570145\pi$
$48$	2.16517	−	6.19882i	0.312515	−	0.894722i
$49$	−1.71601	−	0.764016i	−0.245144	−	0.109145i
$50$	4.21036	+	1.87458i	0.595436	+	0.265105i
$51$	−5.48064	+	1.04017i	−0.767444	+	0.145653i
$52$	0.169228	+	0.316660i	0.0234676	+	0.0439128i
$53$	−1.75263	+	2.41229i	−0.240742	+	0.331353i	−0.912242	−	0.409651i	$-0.865650\pi$
$53$	−1.75263	+	2.41229i	−0.240742	+	0.331353i	0.671500	+	0.741005i	$0.265650\pi$
$54$	7.08926	−	1.02651i	0.964726	−	0.139690i
$55$	−3.05293	−	2.98399i	−0.411657	−	0.402361i
$56$	7.46888	+	4.31216i	0.998071	+	0.576236i
$57$	−9.46821	−	8.90794i	−1.25410	−	1.17989i
$58$	3.17717	+	3.52861i	0.417183	+	0.463329i
$59$	2.07339	−	9.75455i	0.269933	−	1.26993i	−0.609069	−	0.793117i	$-0.708457\pi$
$59$	2.07339	−	9.75455i	0.269933	−	1.26993i	0.879002	−	0.476817i	$-0.158210\pi$
$60$	−0.194646	+	0.106771i	−0.0251288	+	0.0137840i
$61$	9.53549	−	1.00222i	1.22090	−	0.128321i	0.527927	−	0.849290i	$-0.322969\pi$
$61$	9.53549	−	1.00222i	1.22090	−	0.128321i	0.692968	+	0.720968i	$0.256303\pi$
$62$	−8.46071	+	9.39657i	−1.07451	+	1.19337i
$63$	−0.391055	+	8.93044i	−0.0492683	+	1.12513i
$64$	−6.76150	−	4.91251i	−0.845187	−	0.614064i
$65$	−1.11325	+	4.50542i	−0.138082	+	0.558829i
$66$	7.83424	−	1.15695i	0.964328	−	0.142411i
$67$	0.968586	+	1.67764i	0.118332	+	0.204956i	0.919107	−	0.394009i	$-0.128912\pi$
$67$	0.968586	+	1.67764i	0.118332	+	0.204956i	−0.800775	+	0.598965i	$0.795579\pi$
$68$	−0.0335246	+	0.318965i	−0.00406545	+	0.0386802i
$69$	4.73547	+	6.82708i	0.570084	+	0.821884i
$70$	1.63383	+	5.02842i	0.195280	+	0.601011i
$71$	9.58411	−	1.00733i	1.13742	−	0.119548i	0.482961	−	0.875642i	$-0.339561\pi$
$71$	9.58411	−	1.00733i	1.13742	−	0.119548i	0.654463	+	0.756094i	$0.272895\pi$
$72$	1.28455	−	8.58763i	0.151386	−	1.01206i
$73$	10.3172	−	3.35227i	1.20754	−	0.392353i	0.365010	−	0.931004i	$-0.381066\pi$
$73$	10.3172	−	3.35227i	1.20754	−	0.392353i	0.842529	+	0.538650i	$0.181066\pi$
$74$	5.96716	+	6.62720i	0.693668	+	0.770397i
$75$	5.63639	+	1.32757i	0.650834	+	0.153295i
$76$	−0.647270	+	0.373701i	−0.0742469	+	0.0428665i
$77$	−0.404472	+	9.87415i	−0.0460939	+	1.12526i
$78$	−5.40233	−	6.70307i	−0.611694	−	0.758973i
$79$	5.73393	−	7.89207i	0.645117	−	0.887927i	−0.353759	−	0.935337i	$-0.615097\pi$
$79$	5.73393	−	7.89207i	0.645117	−	0.887927i	0.998876	+	0.0474094i	$0.0150965\pi$
$80$	−1.01451	−	4.77290i	−0.113426	−	0.533626i
$81$	8.51042	−	2.92794i	0.945602	−	0.325326i
$82$	0.0851966	+	0.810592i	0.00940839	+	0.0895149i
$83$	−14.4296	+	10.4837i	−1.58385	+	1.15074i	−0.671750	+	0.740778i	$0.734457\pi$
$83$	−14.4296	+	10.4837i	−1.58385	+	1.15074i	−0.912104	+	0.409959i	$0.865543\pi$
$84$	0.485183	+	0.169468i	0.0529378	+	0.0184905i
$85$	−3.08078	+	2.77395i	−0.334158	+	0.300877i
$86$	4.33447	−	5.96588i	0.467397	−	0.643317i
$87$	4.74852	+	3.61134i	0.509095	+	0.387176i
$88$	1.39334	−	9.49795i	0.148530	−	1.01249i
$89$	−7.17794	+	4.14419i	−0.760860	+	0.439283i	−0.829605	−	0.558351i	$-0.811434\pi$
$89$	−7.17794	+	4.14419i	−0.760860	+	0.439283i	0.0687442	+	0.997634i	$0.478101\pi$
$90$	4.10800	−	3.38549i	0.433021	−	0.356862i
$91$	9.47516	−	5.06366i	0.993266	−	0.530816i
$92$	0.454308	−	0.147614i	0.0473649	−	0.0153898i
$93$	−8.24243	+	13.5811i	−0.854700	+	1.40830i
$94$	−0.720024	+	1.61720i	−0.0742648	+	0.166801i
$95$	−9.44969	−	2.00859i	−0.969518	−	0.206077i
$96$	−0.881602	−	0.415859i	−0.0899781	−	0.0424435i
$97$	−7.08104	+	3.15268i	−0.718971	+	0.320106i	−0.733407	−	0.679789i	$-0.762071\pi$
$97$	−7.08104	+	3.15268i	−0.718971	+	0.320106i	0.0144366	+	0.999896i	$0.495405\pi$
$98$	1.29474	−	2.24256i	0.130789	−	0.226533i
$99$	9.39945	−	3.26349i	0.944680	−	0.327993i
$100$	0.166460	−	0.288316i	0.0166460	−	0.0288316i
$101$	−0.829555	+	7.89269i	−0.0825438	+	0.785352i	0.872445	+	0.488712i	$0.162533\pi$
$101$	−0.829555	+	7.89269i	−0.0825438	+	0.785352i	−0.954989	+	0.296641i	$0.904134\pi$
$102$	−0.636326	−	7.66388i	−0.0630056	−	0.758837i
$103$	0.516518	+	1.58968i	0.0508940	+	0.156636i	0.973273	−	0.229650i	$-0.0737580\pi$
$103$	0.516518	+	1.58968i	0.0508940	+	0.156636i	−0.922379	+	0.386285i	$0.873758\pi$
$104$	−9.66772	+	3.92972i	−0.947998	+	0.385341i
$105$	3.19481	+	5.82425i	0.311782	+	0.568389i
$106$	−3.05471	−	2.75047i	−0.296700	−	0.267149i
$107$	1.13712	−	0.241703i	0.109930	−	0.0233663i	−0.152618	−	0.988285i	$-0.548770\pi$
$107$	1.13712	−	0.241703i	0.109930	−	0.0233663i	0.262548	+	0.964919i	$0.415437\pi$
$108$	−0.0202152	−	0.517040i	−0.00194521	−	0.0497522i
$109$			8.13278i			0.778979i	0.921031	+	0.389490i	$0.127349\pi$
$109$			8.13278i			0.778979i	−0.921031	+	0.389490i	$0.872651\pi$
$110$	4.53099	−	3.75560i	0.432013	−	0.358082i
$111$	8.91837	+	6.78259i	0.846495	+	0.643775i
$112$	−6.63944	+	9.13840i	−0.627368	+	0.863498i
$113$	12.1027	−	10.8973i	1.13853	−	1.02513i	0.139135	−	0.990273i	$-0.455568\pi$
$113$	12.1027	−	10.8973i	1.13853	−	1.02513i	0.999392	−	0.0348607i	$-0.0110988\pi$
$114$	13.5772	−	11.6973i	1.27162	−	1.09556i
$115$	5.64070	+	2.51140i	0.525998	+	0.234189i
$116$	0.277483	−	0.201603i	0.0257636	−	0.0187184i
$117$	−8.23893	−	7.00857i	−0.761690	−	0.647942i
$118$	13.0748	+	4.24825i	1.20363	+	0.391083i
$119$	9.54414	+	1.00313i	0.874910	+	0.0919568i
$120$	−2.49500	−	5.95097i	−0.227761	−	0.543247i
$121$	10.3813	−	3.63722i	0.943751	−	0.330657i
$122$			13.2176i			1.19667i
$123$	0.295066	+	0.980625i	0.0266052	+	0.0884200i
$124$	0.611161	+	0.678764i	0.0548839	+	0.0609548i
$125$	10.2135	−	3.31855i	0.913519	−	0.296820i
$126$	−12.1873	−	1.82300i	−1.08573	−	0.162406i
$127$	4.10113	−	9.21130i	0.363917	−	0.817371i	−0.635074	−	0.772451i	$-0.719030\pi$
$127$	4.10113	−	9.21130i	0.363917	−	0.817371i	0.998991	−	0.0449191i	$-0.0143030\pi$
$128$	6.95626	−	7.72571i	0.614852	−	0.682863i
$129$	3.95276	−	8.37966i	0.348021	−	0.737788i
$130$	−6.01654	−	2.17550i	−0.527685	−	0.190804i
$131$	−9.27864			−0.810679			−0.405339	−	0.914166i	$-0.632847\pi$
$131$	−9.27864			−0.810679			−0.405339	+	0.914166i	$0.632847\pi$
$132$	−0.0239614	−	0.571544i	−0.00208557	−	0.0497465i
$133$	11.1820	+	19.3677i	0.969600	+	1.67940i
$134$	−2.43962	+	1.08619i	−0.210751	+	0.0938326i
$135$	4.27773	−	5.14141i	0.368169	−	0.442502i
$136$	−9.11836	−	1.93817i	−0.781893	−	0.166196i
$137$	−5.77536	+	0.607015i	−0.493423	+	0.0518608i	−0.347972	−	0.937505i	$-0.613130\pi$
$137$	−5.77536	+	0.607015i	−0.493423	+	0.0518608i	−0.145450	+	0.989366i	$0.546463\pi$
$138$	−10.0423	+	5.50858i	−0.854861	+	0.468922i
$139$	0.744559	−	3.50288i	0.0631527	−	0.297110i	−0.935225	−	0.354055i	$-0.884803\pi$
$139$	0.744559	−	3.50288i	0.0631527	−	0.297110i	0.998377	+	0.0569448i	$0.0181359\pi$
$140$	0.373575	−	0.0794059i	0.0315729	−	0.00671102i
$141$	−0.509921	+	2.16494i	−0.0429431	+	0.182320i
$142$			13.2850i			1.11485i
$143$	−9.13031	−	7.72253i	−0.763515	−	0.645791i
$144$	11.0102	+	2.84892i	0.917513	+	0.237410i
$145$	4.40912	+	0.463417i	0.366157	+	0.0384847i
$146$	3.10928	+	14.6280i	0.257326	+	1.21062i
$147$	1.07284	−	3.07152i	0.0884866	−	0.253335i
$148$	0.521151	−	0.378638i	0.0428383	−	0.0311239i
$149$	1.29914	+	12.3605i	0.106430	+	1.01261i	0.909211	+	0.416336i	$0.136686\pi$
$149$	1.29914	+	12.3605i	0.106430	+	1.01261i	−0.802781	+	0.596274i	$0.796647\pi$
$150$	−2.63231	+	7.53622i	−0.214927	+	0.615330i
$151$	−18.5124	−	6.01504i	−1.50652	−	0.489497i	−0.564606	−	0.825361i	$-0.690972\pi$
$151$	−18.5124	−	6.01504i	−1.50652	−	0.489497i	−0.941911	+	0.335864i	$0.890972\pi$
$152$	−8.83591	−	19.8458i	−0.716687	−	1.60971i
$153$	−2.58092	−	9.31113i	−0.208655	−	0.752760i
$154$	−13.4792	−	1.97738i	−1.08619	−	0.159342i
$155$			11.8060i			0.948283i
$156$	−0.522337	+	0.337489i	−0.0418204	+	0.0270207i
$157$	−3.03310	+	9.33494i	−0.242068	+	0.745009i	0.754037	+	0.656832i	$0.228104\pi$
$157$	−3.03310	+	9.33494i	−0.242068	+	0.745009i	−0.996105	+	0.0881768i	$0.971896\pi$
$158$	9.99382	+	8.99848i	0.795066	+	0.715880i
$159$	−4.41506	−	2.67951i	−0.350137	−	0.212499i
$160$	−0.720419	+	0.0757190i	−0.0569541	+	0.00598612i
$161$	−4.41692	−	13.5939i	−0.348102	−	1.07135i
$162$	2.78788	+	12.0897i	0.219036	+	0.949859i
$163$	−21.1541	+	9.41839i	−1.65691	+	0.737705i	−0.999870	−	0.0161470i	$-0.994860\pi$
$163$	−21.1541	+	9.41839i	−1.65691	+	0.737705i	−0.657044	+	0.753852i	$0.728193\pi$
$164$	0.0588758			0.00459743
$165$	4.71316	−	5.69736i	0.366919	−	0.443539i
$166$	−12.2939	−	21.2937i	−0.954195	−	1.65271i
$167$	1.96829	−	18.7270i	0.152311	−	1.44914i	−0.605073	−	0.796170i	$-0.706856\pi$
$167$	1.96829	−	18.7270i	0.152311	−	1.44914i	0.757384	−	0.652970i	$-0.226477\pi$
$168$	−6.37284	+	13.5101i	−0.491676	+	1.04233i
$169$	−2.20347	+	12.8119i	−0.169498	+	0.985531i
$170$	−3.35916	−	4.62349i	−0.257636	−	0.354606i
$171$	14.0191	−	17.6199i	1.07207	−	1.34742i
$172$	−0.395858	−	0.356432i	−0.0301839	−	0.0271777i
$173$	−2.19430	−	2.43701i	−0.166829	−	0.185283i	0.653933	−	0.756552i	$-0.273118\pi$
$173$	−2.19430	−	2.43701i	−0.166829	−	0.185283i	−0.820763	+	0.571270i	$0.806451\pi$
$174$	−5.63542	+	5.98986i	−0.427220	+	0.454090i
$175$	−8.62706	−	4.98084i	−0.652145	−	0.376516i
$176$	12.1810	+	3.11525i	0.918179	+	0.234821i
$177$	17.1346	+	2.18091i	1.28791	+	0.163927i
$178$	−4.64737	−	10.4382i	−0.348335	−	0.782374i
$179$	0.0471443	+	0.221796i	0.00352373	+	0.0165778i	0.979874	−	0.199615i	$-0.0639692\pi$
$179$	0.0471443	+	0.221796i	0.00352373	+	0.0165778i	−0.976351	+	0.216193i	$0.930636\pi$
$180$	−0.212194	−	0.320679i	−0.0158160	−	0.0239020i
$181$	7.11993	−	5.17293i	0.529220	−	0.384501i	−0.290846	−	0.956770i	$-0.593937\pi$
$181$	7.11993	−	5.17293i	0.529220	−	0.384501i	0.820066	+	0.572269i	$0.193937\pi$
$182$	5.57695	+	13.7202i	0.413391	+	1.01701i
$183$	3.09655	+	16.3157i	0.228904	+	1.20609i
$184$	2.88673	+	13.5810i	0.212813	+	1.00120i
$185$	8.28093	+	0.870360i	0.608826	+	0.0639902i
$186$	−17.4321	−	13.2574i	−1.27818	−	0.972082i
$187$	−2.88235	−	10.2857i	−0.210778	−	0.752168i
$188$	0.110742	+	0.0639371i	0.00807671	+	0.00466309i
$189$	−15.4710	+	0.604884i	−1.12535	+	0.0439989i
$190$	4.11548	−	12.6661i	0.298568	−	0.918899i
$191$	3.06475	−	14.4185i	0.221757	−	1.04329i	−0.716564	−	0.697522i	$-0.754286\pi$
$191$	3.06475	−	14.4185i	0.221757	−	1.04329i	0.938321	−	0.345765i	$-0.112381\pi$
$192$	7.51050	−	12.3751i	0.542024	−	0.893099i
$193$	−5.38824	+	12.1022i	−0.387854	+	0.871134i	0.609096	+	0.793096i	$0.291532\pi$
$193$	−5.38824	+	12.1022i	−0.387854	+	0.871134i	−0.996950	+	0.0780382i	$0.975134\pi$
$194$	−3.30198	−	10.1624i	−0.237068	−	0.729621i
$195$	−7.93641	−	1.27589i	−0.568338	−	0.0913684i
$196$	−0.151329	−	0.109947i	−0.0108092	−	0.00785333i
$197$	−11.6663	−	20.2066i	−0.831188	−	1.43966i	−0.897097	−	0.441833i	$-0.854328\pi$
$197$	−11.6663	−	20.2066i	−0.831188	−	1.43966i	0.0659096	−	0.997826i	$-0.479005\pi$
$198$	3.11981	+	13.3570i	0.221715	+	0.949238i
$199$	−0.149049	+	0.258160i	−0.0105658	+	0.0183004i	−0.871260	−	0.490822i	$-0.836697\pi$
$199$	−0.149049	+	0.258160i	−0.0105658	+	0.0183004i	0.860694	+	0.509122i	$0.170030\pi$
$200$	7.82852	+	5.68775i	0.553560	+	0.402185i
$201$	−2.75698	+	1.91232i	−0.194462	+	0.134885i
$202$	−10.7014	−	2.27465i	−0.752947	−	0.160044i
$203$	−6.03241	−	8.30290i	−0.423392	−	0.582750i
$204$	−0.555374	−	0.0121538i	−0.0388840	−	0.000850938i
$205$	0.565547	+	0.509221i	0.0394995	+	0.0355655i
$206$	−2.25389	+	0.479078i	−0.157036	+	0.0333790i
$207$	−11.1056	+	9.15239i	−0.771895	+	0.636135i
$208$	−3.79518	−	13.1309i	−0.263149	−	0.910465i
$209$	15.4437	−	19.5231i	1.06826	−	1.35044i
$210$	−8.44545	+	3.54084i	−0.582791	+	0.244341i
$211$	−6.98062	−	0.733692i	−0.480565	−	0.0505095i	−0.138851	−	0.990313i	$-0.544341\pi$
$211$	−6.98062	−	0.733692i	−0.480565	−	0.0505095i	−0.341714	+	0.939804i	$0.611008\pi$
$212$	−0.220658	+	0.198681i	−0.0151548	+	0.0136455i
$213$	3.11234	+	16.3989i	0.213254	+	1.12363i
$214$	0.167518	+	1.59383i	0.0114513	+	0.108952i
$215$	−0.719713	−	6.84761i	−0.0490840	−	0.467003i
$216$	15.0073	+	0.986522i	1.02112	+	0.0671243i
$217$	20.3101	−	18.2873i	1.37874	−	1.24142i
$218$	−11.1501	−	1.17192i	−0.755179	−	0.0793725i
$219$	7.26503	+	17.3282i	0.490925	+	1.17093i
$220$	−0.235589	−	0.353861i	−0.0158834	−	0.0238573i
$221$	−8.04912	+	8.37033i	−0.541443	+	0.563049i
$222$	−10.5841	+	11.2498i	−0.710357	+	0.755035i
$223$	−1.45057	+	0.308328i	−0.0971374	+	0.0206472i	−0.256224	−	0.966617i	$-0.582478\pi$
$223$	−1.45057	+	0.308328i	−0.0971374	+	0.0206472i	0.159087	+	0.987265i	$0.449145\pi$
$224$	1.24617	+	1.12206i	0.0832636	+	0.0749708i
$225$	−1.48375	+	9.91930i	−0.0989164	+	0.661287i
$226$	13.1963	+	18.1632i	0.877805	+	1.20820i
$227$	−18.5674	−	3.94663i	−1.23236	−	0.261947i	−0.454710	−	0.890639i	$-0.650257\pi$
$227$	−18.5674	−	3.94663i	−1.23236	−	0.261947i	−0.777654	+	0.628692i	$0.783591\pi$
$228$	−0.737815	−	1.06370i	−0.0488630	−	0.0704454i
$229$	9.54673	+	6.93611i	0.630866	+	0.458351i	0.856700	−	0.515815i	$-0.172511\pi$
$229$	9.54673	+	6.93611i	0.630866	+	0.458351i	−0.225834	+	0.974166i	$0.572511\pi$
$230$	−4.25596	+	7.37154i	−0.280630	+	0.486065i
$231$	−17.1019	+	0.716977i	−1.12522	+	0.0471736i
$232$	4.98462	+	8.63362i	0.327256	+	0.566825i
$233$	2.21313	+	1.60793i	0.144987	+	0.105339i	0.657914	−	0.753093i	$-0.271439\pi$
$233$	2.21313	+	1.60793i	0.144987	+	0.105339i	−0.512927	+	0.858432i	$0.671439\pi$
$234$	10.7960	−	10.2857i	0.705756	−	0.672397i
$235$	0.510768	+	1.57198i	0.0333188	+	0.102545i
$236$	0.403915	−	0.907208i	0.0262926	−	0.0590542i
$237$	14.4444	+	8.76632i	0.938262	+	0.569434i
$238$	−2.75059	+	12.9405i	−0.178294	+	0.838809i
$239$	4.65096	−	14.3142i	0.300846	−	0.925907i	−0.680349	−	0.732888i	$-0.738172\pi$
$239$	4.65096	−	14.3142i	0.300846	−	0.925907i	0.981195	−	0.193019i	$-0.0618280\pi$
$240$	8.09315	−	2.43520i	0.522411	−	0.157191i
$241$	3.16993	+	1.83016i	0.204193	+	0.117891i	0.598610	−	0.801041i	$-0.295720\pi$
$241$	3.16993	+	1.83016i	0.204193	+	0.117891i	−0.394417	+	0.918932i	$0.629053\pi$
$242$	3.49073	+	14.7569i	0.224393	+	0.948608i
$243$	6.27364	+	14.2703i	0.402454	+	0.915440i
$244$	0.949548	+	0.0998016i	0.0607886	+	0.00638914i
$245$	−0.502691	−	2.36497i	−0.0321157	−	0.151093i
$246$	−1.38696	+	0.263231i	−0.0884294	+	0.0167830i
$247$	−26.8061	−	3.70978i	−1.70563	−	0.236048i
$248$	−21.4776	+	15.6044i	−1.36383	+	0.990880i
$249$	−20.1641	−	23.4046i	−1.27785	−	1.48321i
$250$	3.07801	+	14.4809i	0.194670	+	0.915852i
$251$	−8.02523	−	18.0250i	−0.506548	−	1.13773i	−0.968089	−	0.250606i	$-0.919370\pi$
$251$	−8.02523	−	18.0250i	−0.506548	−	1.13773i	0.461541	−	0.887119i	$-0.347297\pi$
$252$	−0.222986	+	0.861767i	−0.0140468	+	0.0542862i
$253$	−12.2491	+	10.1529i	−0.770097	+	0.638310i
$254$	12.0378	+	6.95001i	0.755317	+	0.436082i
$255$	−5.22968	−	4.92022i	−0.327495	−	0.308116i
$256$	−1.59514	−	1.77159i	−0.0996965	−	0.110724i
$257$	−1.19982	−	1.08032i	−0.0748424	−	0.0673884i	0.630861	−	0.775896i	$-0.282702\pi$
$257$	−1.19982	−	1.08032i	−0.0748424	−	0.0673884i	−0.705703	+	0.708508i	$0.749369\pi$
$258$	10.9190	+	6.62675i	0.679786	+	0.412564i
$259$	−11.3297	−	15.5940i	−0.703993	−	0.968963i
$260$	−0.201716	+	0.415799i	−0.0125099	+	0.0257868i
$261$	−5.55303	+	8.71405i	−0.343724	+	0.539386i
$262$	1.33704	−	12.7211i	0.0826025	−	0.785910i
$263$	6.20524	+	10.7478i	0.382632	+	0.662738i	0.991438	−	0.130582i	$-0.0416845\pi$
$263$	6.20524	+	10.7478i	0.382632	+	0.662738i	−0.608806	+	0.793319i	$0.708351\pi$
$264$	16.5942	+	1.04383i	1.02130	+	0.0642432i
$265$	−3.83799			−0.235766
$266$	−28.1646	+	12.5397i	−1.72688	+	0.768857i
$267$	−8.18205	−	11.7960i	−0.500734	−	0.721903i
$268$	0.0596107	+	0.183463i	0.00364130	+	0.0112068i
$269$	−0.627690	+	0.0659728i	−0.0382709	+	0.00402244i	−0.123645	−	0.992327i	$-0.539458\pi$
$269$	−0.627690	+	0.0659728i	−0.0382709	+	0.00402244i	0.0853737	+	0.996349i	$0.472792\pi$
$270$	6.43248	+	6.60566i	0.391468	+	0.402008i
$271$	8.83125	+	7.95170i	0.536460	+	0.483031i	0.892254	−	0.451533i	$-0.149123\pi$
$271$	8.83125	+	7.95170i	0.536460	+	0.483031i	−0.355794	+	0.934564i	$0.615789\pi$
$272$	3.77296	−	11.6120i	0.228769	−	0.704080i
$273$	10.0984	+	15.6295i	0.611183	+	0.945938i
$274$		−	8.00552i		−	0.483631i
$275$	−1.60940	+	10.9708i	−0.0970503	+	0.661563i
$276$	0.319908	+	0.763030i	0.0192562	+	0.0459290i
$277$	−5.62349	−	12.6306i	−0.337882	−	0.758897i	−0.999955	−	0.00945697i	$-0.996990\pi$
$277$	−5.62349	−	12.6306i	−0.337882	−	0.758897i	0.662073	−	0.749440i	$-0.269677\pi$
$278$	4.69517	+	1.52555i	0.281598	+	0.0914966i
$279$	−24.6238	−	12.2809i	−1.47419	−	0.735240i
$280$	1.16036	+	11.0401i	0.0693446	+	0.659770i
$281$	−3.17229	+	2.30480i	−0.189243	+	0.137493i	−0.678373	−	0.734718i	$-0.737314\pi$
$281$	−3.17229	+	2.30480i	−0.189243	+	0.137493i	0.489130	+	0.872211i	$0.337314\pi$
$282$	−2.89466	−	1.01107i	−0.172374	−	0.0602082i
$283$	−2.61258	−	12.2912i	−0.155302	−	0.730638i	−0.985018	−	0.172452i	$-0.944831\pi$
$283$	−2.61258	−	12.2912i	−0.155302	−	0.730638i	0.829716	−	0.558186i	$-0.188502\pi$
$284$	0.954389	+	0.100310i	0.0566326	+	0.00595233i
$285$	2.11275	−	16.5991i	0.125148	−	0.983245i
$286$	11.9033	−	11.4049i	0.703857	−	0.674385i
$287$		−	1.76169i		−	0.103990i
$288$	0.591470	−	1.58134i	0.0348527	−	0.0931815i
$289$	6.48205	−	1.37780i	0.381297	−	0.0810472i
$290$	−1.27069	+	5.97815i	−0.0746177	+	0.351049i
$291$	−6.45672	−	11.7708i	−0.378500	−	0.690018i
$292$	1.07435	−	0.112918i	0.0628714	−	0.00660805i
$293$	−7.85597	−	1.66984i	−0.458950	−	0.0975529i	−0.0273660	−	0.999625i	$-0.508712\pi$
$293$	−7.85597	−	1.66984i	−0.458950	−	0.0975529i	−0.431584	+	0.902073i	$0.642045\pi$
$294$	4.05647	+	1.91347i	0.236578	+	0.111596i
$295$	11.7264	−	5.22094i	0.682739	−	0.303975i
$296$	9.36180	+	16.2151i	0.544143	+	0.942484i
$297$	6.98025	+	15.7568i	0.405035	+	0.914301i
$298$	−17.1335			−0.992516
$299$	16.2652	+	5.88128i	0.940641	+	0.340123i
$300$	0.521523	+	0.246007i	0.0301101	+	0.0142032i
$301$	−10.6652	+	11.8449i	−0.614734	+	0.682731i
$302$	10.9143	−	24.5138i	0.628045	−	1.41061i
$303$	−13.7426	−	0.300743i	−0.789489	−	0.0172772i
$304$	27.0603	−	8.79241i	1.55201	−	0.504279i
$305$	8.25795	+	9.17138i	0.472849	+	0.525152i
$306$	13.1375	−	2.19674i	0.751021	−	0.125579i
$307$			12.1887i			0.695647i	0.937560	+	0.347823i	$0.113079\pi$
$307$			12.1887i			0.695647i	−0.937560	+	0.347823i	$0.886921\pi$
$308$	−0.243831	+	0.953411i	−0.0138936	+	0.0543256i
$309$	−2.66993	+	1.11940i	−0.151887	+	0.0636802i
$310$	−16.1861	−	1.70123i	−0.919310	−	0.0966234i
$311$	29.9409	+	9.72838i	1.69779	+	0.551646i	0.988227	−	0.152995i	$-0.0488917\pi$
$311$	29.9409	+	9.72838i	1.69779	+	0.551646i	0.709564	+	0.704641i	$0.248892\pi$
$312$	−8.16869	−	16.1244i	−0.462461	−	0.912862i
$313$	−18.8300	+	13.6808i	−1.06434	+	0.773286i	−0.974886	−	0.222705i	$-0.928511\pi$
$313$	−18.8300	+	13.6808i	−1.06434	+	0.773286i	−0.0894509	+	0.995991i	$0.528511\pi$
$314$	−12.3612	−	5.50355i	−0.697582	−	0.310583i
$315$	−9.59543	+	6.34932i	−0.540641	+	0.357743i
$316$	0.721906	−	0.650007i	0.0406104	−	0.0365658i
$317$	8.10648	−	11.1576i	0.455305	−	0.626674i	−0.518222	−	0.855246i	$-0.673406\pi$
$317$	8.10648	−	11.1576i	0.455305	−	0.626674i	0.973527	+	0.228573i	$0.0734058\pi$
$318$	4.30983	−	5.66696i	0.241683	−	0.317787i
$319$	−6.11190	+	9.65102i	−0.342201	+	0.540354i
$320$		−	10.7577i		−	0.601371i
$321$	0.580176	+	1.92816i	0.0323823	+	0.107619i
$322$	19.2738	−	4.09677i	1.07409	−	0.228304i
$323$	−17.9643	−	16.1751i	−0.999558	−	0.900006i
$324$	0.889571	−	0.108995i	0.0494206	−	0.00605526i
$325$	11.1669	−	4.53910i	0.619427	−	0.251784i
$326$	−9.86440	−	30.3595i	−0.546338	−	1.68146i
$327$	−14.0381	+	1.16557i	−0.776308	+	0.0644563i
$328$	−0.178877	+	1.70190i	−0.00987684	+	0.0939718i
$329$	1.91314	−	3.31365i	0.105475	−	0.182688i
$330$	7.13195	+	7.28274i	0.392601	+	0.400902i
$331$	2.50135	−	4.33246i	0.137487	−	0.238134i	−0.789058	−	0.614319i	$-0.789431\pi$
$331$	2.50135	−	4.33246i	0.137487	−	0.238134i	0.926545	+	0.376185i	$0.122764\pi$
$332$	−1.62256	+	0.722410i	−0.0890495	+	0.0396474i
$333$	−10.4293	+	16.3662i	−0.571524	+	0.896861i
$334$	25.3912	+	5.39707i	1.38934	+	0.295314i
$335$	−1.01418	+	2.27788i	−0.0554104	+	0.124454i
$336$	−16.7254	−	10.1507i	−0.912448	−	0.553767i
$337$	6.65281	−	2.16163i	0.362401	−	0.117751i	−0.122156	−	0.992511i	$-0.538981\pi$
$337$	6.65281	−	2.16163i	0.362401	−	0.117751i	0.484557	+	0.874760i	$0.338981\pi$
$338$	−17.2477	−	4.86714i	−0.938149	−	0.264738i
$339$	20.5445	+	19.3288i	1.11583	+	1.04980i
$340$	−0.357513	+	0.206410i	−0.0193889	+	0.0111942i
$341$	−27.2609	−	13.5002i	−1.47626	−	0.731078i
$342$	22.1368	+	21.7593i	1.19702	+	1.17661i
$343$	8.96998	−	12.3461i	0.484333	−	0.666628i
$344$	11.5060	−	10.3600i	0.620360	−	0.558574i
$345$	−3.52654	+	10.0964i	−0.189863	+	0.543572i
$346$	3.65735	−	2.65722i	0.196621	−	0.142853i
$347$	2.41437	+	22.9712i	0.129610	+	1.23316i	0.845128	+	0.534563i	$0.179524\pi$
$347$	2.41437	+	22.9712i	0.129610	+	1.23316i	−0.715518	+	0.698594i	$0.753809\pi$
$348$	0.387758	+	0.450073i	0.0207860	+	0.0241265i
$349$	−5.26900	−	24.7887i	−0.282043	−	1.32691i	−0.859771	−	0.510679i	$-0.829394\pi$
$349$	−5.26900	−	24.7887i	−0.282043	−	1.32691i	0.577728	−	0.816229i	$-0.303939\pi$
$350$	8.07190	−	11.1100i	0.431461	−	0.593855i
$351$	10.9168	−	15.2258i	0.582695	−	0.812691i
$352$	0.648960	−	1.75008i	0.0345897	−	0.0932795i
$353$	16.6906	−	9.63632i	0.888350	−	0.512889i	0.0149478	−	0.999888i	$-0.495242\pi$
$353$	16.6906	−	9.63632i	0.888350	−	0.512889i	0.873403	+	0.486999i	$0.161908\pi$
$354$	−5.45911	+	23.1774i	−0.290148	+	1.23186i
$355$	8.30005	+	9.21814i	0.440521	+	0.489248i
$356$	−0.784964	+	0.255050i	−0.0416030	+	0.0135176i
$357$	−0.363669	+	16.6180i	−0.0192474	+	0.879519i
$358$	−0.310877	+	0.0326745i	−0.0164304	+	0.00172690i
$359$	−1.13273	−	3.48620i	−0.0597834	−	0.183994i	0.916705	−	0.399565i	$-0.130839\pi$
$359$	−1.13273	−	3.48620i	−0.0597834	−	0.183994i	−0.976488	+	0.215571i	$0.930839\pi$
$360$	9.91446	−	5.15953i	0.522538	−	0.271931i
$361$	3.90234	−	37.1283i	0.205386	−	1.95412i
$362$	6.06615	+	10.5069i	0.318830	+	0.552229i
$363$	7.76607	+	17.3979i	0.407613	+	0.913155i
$364$	1.02776	−	0.297050i	0.0538692	−	0.0155696i
$365$	11.2966	+	8.20744i	0.591289	+	0.429597i
$366$	−22.8151	+	1.89432i	−1.19256	+	0.0990177i
$367$	0.840927	−	0.933944i	0.0438960	−	0.0487515i	−0.720797	−	0.693146i	$-0.756224\pi$
$367$	0.840927	−	0.933944i	0.0438960	−	0.0487515i	0.764693	+	0.644395i	$0.222891\pi$
$368$	−18.0855	+	1.90086i	−0.942769	+	0.0990891i
$369$	−1.65038	+	0.649858i	−0.0859154	+	0.0338303i
$370$	−2.38654	+	11.2278i	−0.124070	+	0.583704i
$371$	5.94498	+	6.60256i	0.308648	+	0.342788i
$372$	−1.08403	+	1.15221i	−0.0562044	+	0.0597394i
$373$	11.6700	+	6.73768i	0.604250	+	0.348864i	0.770712	−	0.637184i	$-0.219901\pi$
$373$	11.6700	+	6.73768i	0.604250	+	0.348864i	−0.166462	+	0.986048i	$0.553234\pi$
$374$	14.5172	−	2.46955i	0.750664	−	0.127698i
$375$	7.19196	+	17.1539i	0.371391	+	0.885826i
$376$	−2.18466	+	3.00693i	−0.112665	+	0.155071i
$377$	12.4120	+	0.407261i	0.639252	+	0.0209750i
$378$	1.40004	−	21.2980i	0.0720105	−	1.09545i
$379$	20.6489	+	9.19346i	1.06066	+	0.472237i	0.861514	−	0.507733i	$-0.169516\pi$
$379$	20.6489	+	9.19346i	1.06066	+	0.472237i	0.199146	+	0.979970i	$0.436183\pi$
$380$	−0.878855	−	0.391292i	−0.0450843	−	0.0200728i
$381$	16.4875	+	5.75887i	0.844680	+	0.295036i
$382$	19.3262	+	6.27947i	0.988816	+	0.321286i
$383$	−2.69213	−	6.04662i	−0.137561	−	0.308968i	0.831608	−	0.555363i	$-0.187421\pi$
$383$	−2.69213	−	6.04662i	−0.137561	−	0.308968i	−0.969169	+	0.246395i	$0.920754\pi$
$384$	14.3324	+	10.9000i	0.731397	+	0.556241i
$385$	−10.5883	+	7.04933i	−0.539630	+	0.359267i
$386$	−15.8157	−	9.13121i	−0.804999	−	0.464766i
$387$	15.0307	+	5.62195i	0.764055	+	0.285780i
$388$	−0.754997	+	0.160480i	−0.0383292	+	0.00814712i
$389$	−5.43040	+	1.76444i	−0.275332	+	0.0894609i	−0.443429	−	0.896310i	$-0.646238\pi$
$389$	−5.43040	+	1.76444i	−0.275332	+	0.0894609i	0.168096	+	0.985771i	$0.446238\pi$
$390$	2.89288	−	10.6970i	0.146486	−	0.541664i
$391$	9.08121	+	12.4992i	0.459257	+	0.632113i
$392$	3.63796	−	4.04036i	0.183745	−	0.204069i
$393$	−1.32979	−	16.0160i	−0.0670792	−	0.807899i
$394$	29.3844	−	13.0828i	1.48037	−	0.659101i
$395$	12.5564			0.631782
$396$	0.983114	−	0.123272i	0.0494033	−	0.00619467i
$397$	15.0482	−	26.0642i	0.755247	−	1.30813i	−0.190004	−	0.981783i	$-0.560850\pi$
$397$	15.0482	−	26.0642i	0.755247	−	1.30813i	0.945251	−	0.326343i	$-0.105817\pi$
$398$	−0.332460	−	0.241547i	−0.0166647	−	0.0121076i
$399$	−31.8283	+	22.0771i	−1.59341	+	1.10524i
$400$	−8.48048	+	9.41853i	−0.424024	+	0.470927i
$401$	−12.5249	+	28.1313i	−0.625461	+	1.40481i	0.271387	+	0.962470i	$0.412518\pi$
$401$	−12.5249	+	28.1313i	−0.625461	+	1.40481i	−0.896848	+	0.442339i	$0.854149\pi$
$402$	−2.22453	−	4.05539i	−0.110949	−	0.202265i
$403$	2.37638	+	32.9852i	0.118376	+	1.64311i
$404$	−0.244212	+	0.751607i	−0.0121500	+	0.0373939i
$405$	9.48772	+	6.64699i	0.471449	+	0.330292i
$406$	12.2526	−	7.07403i	0.608086	−	0.351078i
$407$	−11.4790	+	18.1259i	−0.568992	+	0.898469i
$408$	2.03867	−	16.0171i	0.100929	−	0.792963i
$409$	8.73662	+	19.6228i	0.431998	+	0.970284i	0.990081	+	0.140499i	$0.0448705\pi$
$409$	8.73662	+	19.6228i	0.431998	+	0.970284i	−0.558083	+	0.829785i	$0.688463\pi$
$410$	−0.779639	+	0.701990i	−0.0385036	+	0.0346688i
$411$	−1.87549	−	9.88192i	−0.0925110	−	0.487439i
$412$	0.0173985	+	0.165535i	0.000857161	+	0.00815535i
$413$	−27.1457	−	12.0860i	−1.33575	−	0.594715i
$414$	−10.9477	−	16.5447i	−0.538049	−	0.813129i
$415$	−21.8341	−	7.09433i	−1.07179	−	0.348247i
$416$	−1.99756	+	0.356563i	−0.0979382	+	0.0174820i
$417$	6.15306	+	0.783168i	0.301317	+	0.0383519i
$418$	24.5409	+	23.9867i	1.20033	+	1.17323i
$419$	20.1200	−	11.6163i	0.982928	−	0.567493i	0.0797748	−	0.996813i	$-0.474580\pi$
$419$	20.1200	−	11.6163i	0.982928	−	0.567493i	0.903153	+	0.429319i	$0.141247\pi$
$420$	0.190603	+	0.633452i	0.00930049	+	0.0309093i
$421$	2.97212	−	9.14725i	0.144852	−	0.445810i	−0.852140	−	0.523315i	$-0.824695\pi$
$421$	2.97212	−	9.14725i	0.144852	−	0.445810i	0.996992	+	0.0775047i	$0.0246953\pi$
$422$	2.01179	−	9.46474i	0.0979325	−	0.460736i
$423$	−3.81000	−	0.569907i	−0.185249	−	0.0277098i
$424$	−5.07280	−	6.98211i	−0.246357	−	0.339081i
$425$	10.5323	+	2.23871i	0.510893	+	0.108594i
$426$	−22.9314	+	1.90398i	−1.11103	+	0.0922480i
$427$	2.98628	−	28.4126i	0.144516	−	1.37498i
$428$	0.115765			0.00559571
$429$	12.0214	−	16.8667i	0.580399	−	0.814332i
$430$	9.49182			0.457736
$431$	2.97184	−	28.2752i	0.143148	−	1.36197i	−0.653226	−	0.757163i	$-0.726585\pi$
$431$	2.97184	−	28.2752i	0.143148	−	1.36197i	0.796375	−	0.604803i	$-0.206748\pi$
$432$	−3.33961	+	19.4131i	−0.160677	+	0.934011i
$433$	−8.12468	−	1.72695i	−0.390447	−	0.0829921i	0.00850498	−	0.999964i	$-0.497293\pi$
$433$	−8.12468	−	1.72695i	−0.390447	−	0.0829921i	−0.398952	+	0.916972i	$0.630626\pi$
$434$	22.1453	+	30.4804i	1.06301	+	1.46311i
$435$	−0.168005	+	7.67704i	−0.00805521	+	0.368086i
$436$	−0.168381	+	0.792168i	−0.00806397	+	0.0379380i
$437$	−11.1259	+	34.2418i	−0.532222	+	1.63801i
$438$	−24.8040	+	7.46342i	−1.18518	+	0.356616i
$439$	−22.5837	+	13.0387i	−1.07786	+	0.622305i	−0.930319	−	0.366751i	$-0.880470\pi$
$439$	−22.5837	+	13.0387i	−1.07786	+	0.622305i	−0.147544	+	0.989056i	$0.547137\pi$
$440$	10.9447	−	5.73497i	0.521768	−	0.273404i
$441$	5.45554	+	1.41164i	0.259788	+	0.0672211i
$442$	−10.3159	−	12.2415i	−0.490677	−	0.582271i
$443$	−33.7115	−	10.9535i	−1.60168	−	0.520419i	−0.634161	−	0.773201i	$-0.718654\pi$
$443$	−33.7115	−	10.9535i	−1.60168	−	0.520419i	−0.967523	+	0.252783i	$0.918654\pi$
$444$	0.728262	+	0.845299i	0.0345618	+	0.0401161i
$445$	−9.74613	−	4.33926i	−0.462011	−	0.205700i
$446$	−0.213695	−	2.03317i	−0.0101187	−	0.0962734i
$447$	−21.1494	+	4.01393i	−1.00033	+	0.189853i
$448$	−18.5066	+	16.6634i	−0.874354	+	0.787272i
$449$	−9.54183	−	21.4313i	−0.450307	−	1.01141i	−0.985962	−	0.166969i	$-0.946602\pi$
$449$	−9.54183	−	21.4313i	−0.450307	−	1.01141i	0.535656	−	0.844437i	$-0.320065\pi$
$450$	−13.3856	−	3.46358i	−0.631004	−	0.163275i
$451$	−1.82253	+	0.723590i	−0.0858196	+	0.0340725i
$452$	1.40447	−	0.810873i	0.0660609	−	0.0381403i
$453$	7.72947	−	32.8165i	0.363162	−	1.54185i
$454$	8.08639	−	24.8874i	0.379513	−	1.16802i
$455$	12.4416	+	6.03577i	0.583272	+	0.282961i
$456$	32.9897	−	18.0960i	1.54488	−	0.847424i
$457$	0.587544	−	1.31964i	0.0274841	−	0.0617304i	−0.899282	−	0.437370i	$-0.855910\pi$
$457$	0.587544	−	1.31964i	0.0274841	−	0.0617304i	0.926766	+	0.375639i	$0.122577\pi$
$458$	−10.8851	+	12.0891i	−0.508628	+	0.564888i
$459$	15.7021	−	5.78941i	0.732914	−	0.270226i
$460$	0.497432	+	0.361406i	0.0231929	+	0.0168506i
$461$	−9.46212	+	16.3889i	−0.440695	+	0.763306i	−0.997741	−	0.0671757i	$-0.978601\pi$
$461$	−9.46212	+	16.3889i	−0.440695	+	0.763306i	0.557046	+	0.830481i	$0.311935\pi$
$462$	1.48137	−	23.5500i	0.0689196	−	1.09565i
$463$	−33.5188			−1.55775			−0.778875	−	0.627179i	$-0.784209\pi$
$463$	−33.5188			−1.55775			−0.778875	+	0.627179i	$0.784209\pi$
$464$	−11.9283	+	5.31084i	−0.553759	+	0.246549i
$465$	−20.3785	+	1.69201i	−0.945031	+	0.0784652i
$466$	−2.52339	+	2.80251i	−0.116894	+	0.129824i
$467$	−4.63385	−	6.37794i	−0.214429	−	0.295136i	0.688230	−	0.725492i	$-0.258388\pi$
$467$	−4.63385	−	6.37794i	−0.214429	−	0.295136i	−0.902659	+	0.430356i	$0.858388\pi$
$468$	−0.657403	−	0.853243i	−0.0303885	−	0.0394412i
$469$	5.48962	−	1.78368i	0.253487	−	0.0823629i
$470$	−2.22880	+	0.473745i	−0.102807	+	0.0218523i
$471$	−16.5478	−	3.89761i	−0.762484	−	0.179593i
$472$	24.9972	+	14.4321i	1.15059	+	0.664292i
$473$	16.6346	+	6.16840i	0.764858	+	0.283623i
$474$	−14.1001	+	18.5401i	−0.647638	+	0.851574i
$475$	10.2061	+	22.9232i	0.468287	+	1.05179i
$476$	0.908872	+	0.295310i	0.0416581	+	0.0135355i
$477$	3.99238	−	8.00491i	0.182798	−	0.366520i
$478$	18.9546	+	8.43914i	0.866964	+	0.385997i
$479$	17.5996	+	7.83585i	0.804147	+	0.358029i	0.767297	−	0.641292i	$-0.221601\pi$
$479$	17.5996	+	7.83585i	0.804147	+	0.358029i	0.0368494	+	0.999321i	$0.488268\pi$
$480$	−0.233948	−	1.23267i	−0.0106782	−	0.0562635i
$481$	23.3115	+	0.764892i	1.06291	+	0.0348761i
$482$	−2.96594	+	4.08227i	−0.135095	+	0.185942i
$483$	22.8316	−	9.57235i	1.03887	−	0.435557i
$484$	1.08648	−	0.139348i	0.0493857	−	0.00633402i
$485$	−8.64033	−	4.98849i	−0.392337	−	0.226516i
$486$	−20.4687	+	6.54486i	−0.928478	+	0.296881i
$487$	−10.9137	−	12.1208i	−0.494545	−	0.549248i	0.443268	−	0.896389i	$-0.353819\pi$
$487$	−10.9137	−	12.1208i	−0.494545	−	0.549248i	−0.937813	+	0.347141i	$0.887152\pi$
$488$	−5.76986	+	27.1450i	−0.261189	+	1.22880i
$489$	−19.2889	−	35.1644i	−0.872276	−	1.59019i
$490$	3.31483	−	0.348403i	0.149749	−	0.0157392i
$491$	16.4955	−	18.3201i	0.744431	−	0.826774i	−0.245340	−	0.969437i	$-0.578900\pi$
$491$	16.4955	−	18.3201i	0.744431	−	0.826774i	0.989771	+	0.142663i	$0.0455664\pi$
$492$	0.00843794	+	0.101626i	0.000380412	+	0.00458166i
$493$	8.97465	+	6.52047i	0.404198	+	0.293667i
$494$	8.94884	−	36.2167i	0.402627	−	1.62946i
$495$	10.5098	+	7.31890i	0.472378	+	0.328960i
$496$	−17.3855	−	30.1125i	−0.780630	−	1.35209i
$497$	3.00151	−	28.5574i	0.134636	−	1.28098i
$498$	34.9934	−	24.2725i	1.56809	−	1.08768i
$499$	8.81505	+	27.1299i	0.394616	+	1.21450i	0.929260	+	0.369426i	$0.120446\pi$
$499$	8.81505	+	27.1299i	0.394616	+	1.21450i	−0.534644	+	0.845077i	$0.679554\pi$
$500$	1.06354	−	0.111783i	0.0475630	−	0.00499907i
$501$	32.6070	+	0.713573i	1.45677	+	0.0318801i
$502$	25.8687	−	8.40526i	1.15458	−	0.375145i
$503$	8.62422	+	9.57817i	0.384535	+	0.427070i	0.904073	−	0.427378i	$-0.140563\pi$
$503$	8.62422	+	9.57817i	0.384535	+	0.427070i	−0.519538	+	0.854447i	$0.673896\pi$
$504$	−24.2333	−	9.06400i	−1.07944	−	0.403743i
$505$	−8.84655	+	5.10756i	−0.393666	+	0.227283i
$506$	−12.1547	−	18.2567i	−0.540341	−	0.811607i
$507$	−22.4306	−	1.96726i	−0.996176	−	0.0873691i
$508$	0.590178	−	0.812311i	0.0261849	−	0.0360405i
$509$	−3.68370	−	17.3304i	−0.163277	−	0.768158i	−0.981225	−	0.192866i	$-0.938222\pi$
$509$	−3.68370	−	17.3304i	−0.163277	−	0.768158i	0.817948	−	0.575292i	$-0.195112\pi$
$510$	7.49923	−	6.46092i	0.332072	−	0.286094i
$511$	−3.37877	−	32.1468i	−0.149468	−	1.42209i
$512$	19.4797	−	14.1529i	0.860891	−	0.625474i
$513$	32.4230	+	21.6734i	1.43151	+	0.956902i
$514$	1.65401	−	1.48928i	0.0729554	−	0.0656894i
$515$	−1.26460	+	1.74058i	−0.0557250	+	0.0766989i
$516$	0.558508	−	0.734378i	0.0245869	−	0.0323292i
$517$	−4.21388	−	0.618169i	−0.185326	−	0.0271871i
$518$	23.0120	−	13.2860i	1.01109	−	0.583753i
$519$	3.89208	−	4.13687i	0.170843	−	0.181588i
$520$	−11.4065	−	7.09420i	−0.500208	−	0.311101i
$521$	14.1052	−	4.58307i	0.617961	−	0.200788i	0.0167264	−	0.999860i	$-0.494676\pi$
$521$	14.1052	−	4.58307i	0.617961	−	0.200788i	0.601235	+	0.799072i	$0.294676\pi$
$522$	−11.1468	−	8.86891i	−0.487883	−	0.388182i
$523$	−14.0797	+	31.6236i	−0.615664	+	1.38280i	0.289269	+	0.957248i	$0.406588\pi$
$523$	−14.0797	+	31.6236i	−0.615664	+	1.38280i	−0.904932	+	0.425555i	$0.860079\pi$
$524$	−0.903780	−	0.192104i	−0.0394818	−	0.00839212i
$525$	7.36107	−	15.6051i	0.321263	−	0.681063i
$526$	−15.6295	+	6.95868i	−0.681476	+	0.303413i
$527$	−14.7705	+	25.5833i	−0.643415	+	1.11443i
$528$	−3.63151	+	21.4723i	−0.158041	+	0.934461i
$529$	0.00562334	−	0.00973992i	0.000244493	−	0.000423475i
$530$	0.553049	−	5.26191i	0.0240229	−	0.228563i
$531$	−1.30880	+	29.8888i	−0.0567971	+	1.29706i
$532$	0.688184	+	2.11801i	0.0298366	+	0.0918275i
$533$	1.68260	+	1.30889i	0.0728814	+	0.0566943i
$534$	17.3514	−	9.51785i	0.750868	−	0.411878i
$535$	1.11201	+	1.00126i	0.0480764	+	0.0432882i
$536$	−5.48441	+	1.16575i	−0.236890	+	0.0503526i
$537$	−0.376088	+	0.113164i	−0.0162294	+	0.00488337i
$538$		−	0.870072i		−	0.0375115i
$539$	6.03571	+	1.54361i	0.259976	+	0.0664879i
$540$	0.523117	−	0.412230i	0.0225114	−	0.0177395i
$541$	−0.194049	+	0.267085i	−0.00834281	+	0.0114829i	−0.813168	−	0.582029i	$-0.802259\pi$
$541$	−0.194049	+	0.267085i	−0.00834281	+	0.0114829i	0.804825	+	0.593512i	$0.202259\pi$
$542$	−12.1744	+	10.9619i	−0.522935	+	0.470852i
$543$	9.94947	+	11.5484i	0.426973	+	0.495590i
$544$	−1.65586	−	0.737236i	−0.0709944	−	0.0316087i
$545$	−8.46895	+	6.15305i	−0.362770	+	0.263568i
$546$	−22.8832	+	11.5928i	−0.979312	+	0.496125i
$547$	−28.3594	−	9.21454i	−1.21256	−	0.393985i	−0.368194	−	0.929749i	$-0.620024\pi$
$547$	−28.3594	−	9.21454i	−1.21256	−	0.393985i	−0.844368	+	0.535764i	$0.820024\pi$
$548$	−0.575113	−	0.0604468i	−0.0245676	−	0.00258216i
$549$	−27.7189	+	7.68332i	−1.18301	+	0.327916i
$550$	−14.8091	−	3.78737i	−0.631462	−	0.161494i
$551$			25.8515i			1.10131i
$552$	−23.0286	+	6.92922i	−0.980162	+	0.294927i
$553$	−19.4496	−	21.6010i	−0.827083	−	0.918569i
$554$	18.1269	−	5.88978i	0.770138	−	0.250233i
$555$	−0.315536	+	14.4185i	−0.0133937	+	0.612033i
$556$	0.145047	−	0.325780i	0.00615135	−	0.0138162i
$557$	−26.5741	+	29.5135i	−1.12598	+	1.25053i	−0.161356	+	0.986896i	$0.551587\pi$
$557$	−26.5741	+	29.5135i	−1.12598	+	1.25053i	−0.964624	+	0.263631i	$0.915080\pi$
$558$	20.3855	−	31.9898i	0.862986	−	1.35423i
$559$	−3.38915	−	18.9868i	−0.143346	−	0.803058i
$560$	−14.5394			−0.614400
$561$	17.3413	−	6.44938i	0.732148	−	0.272293i
$562$	−2.70277	−	4.68134i	−0.114010	−	0.197470i
$563$	−8.32213	+	3.70525i	−0.350736	+	0.156158i	−0.574540	−	0.818476i	$-0.694819\pi$
$563$	−8.32213	+	3.70525i	−0.350736	+	0.156158i	0.223804	+	0.974634i	$0.428152\pi$
$564$	−0.0944912	+	0.200317i	−0.00397880	+	0.00843486i
$565$	20.5043	+	4.35833i	0.862624	+	0.183356i
$566$	17.2278	−	1.81072i	0.724139	−	0.0761101i
$567$	−3.26136	−	26.6179i	−0.136964	−	1.11785i
$568$	−5.79927	+	27.2834i	−0.243332	+	1.14479i
$569$	−10.1391	+	2.15514i	−0.425055	+	0.0903482i	−0.415472	−	0.909606i	$-0.636384\pi$
$569$	−10.1391	+	2.15514i	−0.425055	+	0.0903482i	−0.00958265	+	0.999954i	$0.503050\pi$
$570$	22.4530	+	5.28849i	0.940452	+	0.221511i
$571$			6.25204i			0.261640i	0.991406	+	0.130820i	$0.0417609\pi$
$571$			6.25204i			0.261640i	−0.991406	+	0.130820i	$0.958239\pi$
$572$	−0.729445	−	0.941241i	−0.0304996	−	0.0393553i
$573$	25.3272	+	3.22367i	1.05806	+	0.134671i
$574$	2.41529	+	0.253857i	0.100812	+	0.0105958i
$575$	−3.33437	−	15.6870i	−0.139053	−	0.654192i
$576$	22.4373	+	11.1904i	0.934886	+	0.466266i
$577$	−1.58850	+	1.15411i	−0.0661302	+	0.0480464i	−0.620359	−	0.784318i	$-0.713013\pi$
$577$	−1.58850	+	1.15411i	−0.0661302	+	0.0480464i	0.554229	+	0.832364i	$0.313013\pi$
$578$	0.954921	+	9.08546i	0.0397195	+	0.377905i
$579$	−21.6619	−	7.56625i	−0.900240	−	0.314442i
$580$	0.419873	+	0.136425i	0.0174343	+	0.00566474i
$581$	21.6161	+	48.5505i	0.896787	+	2.01422i
$582$	17.0683	−	7.15604i	0.707503	−	0.296627i
$583$	4.38876	−	8.86218i	0.181764	−	0.367034i
$584$			31.3988i			1.29929i
$585$	1.06490	−	13.8820i	0.0440283	−	0.573949i
$586$	3.42139	−	10.5299i	0.141336	−	0.434988i
$587$	−20.3738	−	18.3447i	−0.840918	−	0.757166i	0.131275	−	0.991346i	$-0.458093\pi$
$587$	−20.3738	−	18.3447i	−0.840918	−	0.757166i	−0.972193	+	0.234180i	$0.924760\pi$
$588$	0.168092	−	0.276967i	0.00693200	−	0.0114219i
$589$	−68.4646	+	7.19592i	−2.82104	+	0.296503i
$590$	5.46818	+	16.8293i	0.225121	+	0.692852i
$591$	33.2068	−	23.0332i	1.36595	−	0.947461i
$592$	−22.4030	+	9.97448i	−0.920760	+	0.409949i
$593$	18.3812			0.754824			0.377412	−	0.926045i	$-0.376814\pi$
$593$	18.3812			0.754824			0.377412	+	0.926045i	$0.376814\pi$
$594$	−22.6085	+	7.29943i	−0.927637	+	0.299499i
$595$	6.17625	+	10.6976i	0.253202	+	0.438558i
$596$	−0.129369	+	1.23086i	−0.00529915	+	0.0504181i
$597$	−0.466973	−	0.220275i	−0.0191120	−	0.00901528i
$598$	−10.4071	+	21.4522i	−0.425576	+	0.877245i
$599$	8.86894	+	12.2070i	0.362375	+	0.498766i	0.950808	−	0.309779i	$-0.100255\pi$
$599$	8.86894	+	12.2070i	0.362375	+	0.498766i	−0.588434	+	0.808546i	$0.700255\pi$
$600$	−8.69573	+	14.3281i	−0.355002	+	0.584940i
$601$	−6.06056	−	5.45696i	−0.247216	−	0.222594i	0.536202	−	0.844090i	$-0.319859\pi$
$601$	−6.06056	−	5.45696i	−0.247216	−	0.222594i	−0.783417	+	0.621496i	$0.786525\pi$
$602$	−14.7026	−	16.3289i	−0.599235	−	0.665518i
$603$	−3.69600	−	4.48478i	−0.150513	−	0.182634i
$604$	−1.67865	−	0.969170i	−0.0683034	−	0.0394350i
$605$	11.6418	+	8.05854i	0.473305	+	0.327626i
$606$	2.39260	−	18.7978i	0.0971927	−	0.763607i
$607$	−16.8899	−	37.9353i	−0.685540	−	1.53975i	−0.834562	−	0.550913i	$-0.814279\pi$
$607$	−16.8899	−	37.9353i	−0.685540	−	1.53975i	0.149023	−	0.988834i	$-0.452387\pi$
$608$	−0.878209	−	4.13165i	−0.0356161	−	0.167560i
$609$	13.4672	−	11.6026i	0.545718	−	0.470160i
$610$	−13.7640	+	10.0001i	−0.557287	+	0.404893i
$611$	1.74347	+	4.28919i	0.0705331	+	0.173522i
$612$	−0.0586161	−	0.960379i	−0.00236941	−	0.0388210i
$613$	3.34763	+	15.7494i	0.135209	+	0.636110i	0.992599	+	0.121442i	$0.0387517\pi$
$613$	3.34763	+	15.7494i	0.135209	+	0.636110i	−0.857389	+	0.514669i	$0.827915\pi$
$614$	−16.7108	−	1.75638i	−0.674393	−	0.0708815i
$615$	−0.797919	+	1.04918i	−0.0321752	+	0.0423069i
$616$	−26.8191	−	9.94500i	−1.08057	−	0.400696i
$617$	−27.0471	−	15.6157i	−1.08888	−	0.628663i	−0.155599	−	0.987820i	$-0.549731\pi$
$617$	−27.0471	−	15.6157i	−1.08888	−	0.628663i	−0.933277	+	0.359158i	$0.883064\pi$
$618$	−1.14996	−	3.82180i	−0.0462583	−	0.153735i
$619$	−7.48110	+	23.0245i	−0.300691	+	0.925432i	0.680559	+	0.732693i	$0.261737\pi$
$619$	−7.48110	+	23.0245i	−0.300691	+	0.925432i	−0.981250	+	0.192739i	$0.938263\pi$
$620$	−0.244431	+	1.14996i	−0.00981659	+	0.0461834i
$621$	−17.3897	−	17.8579i	−0.697824	−	0.716611i
$622$	−17.6521	+	39.6473i	−0.707785	+	1.58971i
$623$	7.63166	+	23.4878i	0.305756	+	0.941021i
$624$	22.1215	−	8.43280i	0.885569	−	0.337582i
$625$	−2.34065	−	1.70059i	−0.0936262	−	0.0680234i
$626$	−16.0431	−	27.7875i	−0.641211	−	1.11061i
$627$	35.9124	+	23.8596i	1.43421	+	0.952860i
$628$	−0.488707	+	0.846466i	−0.0195015	+	0.0337777i
$629$	16.8556	+	12.2463i	0.672077	+	0.488293i
$630$	−7.32226	−	14.0703i	−0.291726	−	0.560575i
$631$	−39.6432	−	8.42643i	−1.57817	−	0.335451i	−0.666223	−	0.745753i	$-0.732090\pi$
$631$	−39.6432	−	8.42643i	−1.57817	−	0.335451i	−0.911950	+	0.410302i	$0.865423\pi$
$632$	16.5962	+	22.8427i	0.660162	+	0.908636i
$633$	0.265989	−	12.1545i	0.0105721	−	0.483097i
$634$	14.1290	+	12.7218i	0.561135	+	0.505248i
$635$	12.6949	−	2.69837i	0.503780	−	0.107082i
$636$	−0.374570	−	0.352405i	−0.0148527	−	0.0139738i
$637$	−1.88052	−	6.50638i	−0.0745088	−	0.257792i
$638$	−12.3509	−	9.77014i	−0.488976	−	0.386804i
$639$	−27.8602	+	7.72249i	−1.10213	+	0.305497i
$640$	13.3080	+	1.39872i	0.526044	+	0.0552894i
$641$	−22.6797	+	20.4209i	−0.895794	+	0.806577i	−0.981839	−	0.189715i	$-0.939244\pi$
$641$	−22.6797	+	20.4209i	−0.895794	+	0.806577i	0.0860452	+	0.996291i	$0.472577\pi$
$642$	−2.72712	+	0.517580i	−0.107631	+	0.0204272i
$643$	−1.92531	−	18.3181i	−0.0759270	−	0.722397i	−0.964575	−	0.263808i	$-0.915022\pi$
$643$	−1.92531	−	18.3181i	−0.0759270	−	0.722397i	0.888648	−	0.458589i	$-0.151645\pi$
$644$	−0.148780	−	1.41555i	−0.00586277	−	0.0557806i
$645$	11.7166	−	2.22369i	0.461340	−	0.0875576i
$646$	24.7648	−	22.2983i	0.974356	−	0.877314i
$647$	12.2972	+	1.29249i	0.483453	+	0.0508130i	0.343120	−	0.939291i	$-0.388516\pi$
$647$	12.2972	+	1.29249i	0.483453	+	0.0508130i	0.140333	+	0.990104i	$0.455183\pi$
$648$	0.447966	+	26.0457i	0.0175978	+	1.02317i
$649$	−1.35370	+	33.0472i	−0.0531375	+	1.29722i
$650$	4.61400	+	15.9639i	0.180976	+	0.626156i
$651$	34.4767	+	32.4366i	1.35125	+	1.27129i
$652$	−2.25549	+	0.479420i	−0.0883320	+	0.0187755i
$653$	0.428418	+	0.385749i	0.0167653	+	0.0150955i	0.677471	−	0.735550i	$-0.263076\pi$
$653$	0.428418	+	0.385749i	0.0167653	+	0.0150955i	−0.660705	+	0.750645i	$0.729743\pi$
$654$	0.424862	−	19.4143i	0.0166134	−	0.759157i
$655$	−7.01998	−	9.66217i	−0.274293	−	0.377532i
$656$	−2.19236	−	0.466001i	−0.0855974	−	0.0181943i
$657$	−28.8692	+	15.0237i	−1.12630	+	0.586130i
$658$	4.26735	+	3.10041i	0.166359	+	0.120867i
$659$	−2.19509	+	3.80201i	−0.0855086	+	0.148105i	−0.905608	−	0.424116i	$-0.860585\pi$
$659$	−2.19509	+	3.80201i	−0.0855086	+	0.148105i	0.820099	+	0.572221i	$0.193918\pi$
$660$	0.577040	−	0.457367i	0.0224612	−	0.0178030i
$661$	−0.739392	−	1.28066i	−0.0287590	−	0.0498121i	0.851288	−	0.524699i	$-0.175822\pi$
$661$	−0.739392	−	1.28066i	−0.0287590	−	0.0498121i	−0.880047	+	0.474887i	$0.842489\pi$
$662$	5.57939	+	4.05366i	0.216849	+	0.157550i
$663$	−15.6017	−	12.6941i	−0.605920	−	0.492997i
$664$	−15.9528	−	49.0976i	−0.619088	−	1.90536i
$665$	−11.7083	+	26.2973i	−0.454029	+	1.01977i
$666$	−20.9353	−	16.6570i	−0.811224	−	0.645446i
$667$	3.43521	−	16.1614i	0.133012	−	0.625772i
$668$	0.579442	−	1.78334i	0.0224193	−	0.0689995i
$669$	−0.740101	−	2.45966i	−0.0286140	−	0.0950959i
$670$	−2.97684	−	1.71868i	−0.115006	−	0.0663985i
$671$	−30.6203	+	8.58065i	−1.18208	+	0.331252i
$672$	−1.75820	+	2.31185i	−0.0678242	+	0.0891815i
$673$	−7.10050	−	0.746293i	−0.273704	−	0.0287675i	−0.0333181	−	0.999445i	$-0.510607\pi$
$673$	−7.10050	−	0.746293i	−0.273704	−	0.0287675i	−0.240386	+	0.970677i	$0.577274\pi$
$674$	2.00494	+	9.43252i	0.0772275	+	0.363327i
$675$	−17.3345	−	1.13950i	−0.667204	−	0.0438594i
$676$	−0.479884	+	1.20231i	−0.0184571	+	0.0462428i
$677$	32.9612	−	23.9477i	1.26680	−	0.920385i	0.267731	−	0.963494i	$-0.413726\pi$
$677$	32.9612	−	23.9477i	1.26680	−	0.920385i	0.999070	+	0.0431083i	$0.0137260\pi$
$678$	−29.4604	+	25.3814i	−1.13142	+	0.974767i
$679$	4.80190	+	22.5912i	0.184280	+	0.866970i
$680$	−4.88043	−	10.9616i	−0.187156	−	0.420359i
$681$	4.15128	−	32.6151i	0.159078	−	1.24981i
$682$	22.4371	−	35.4295i	0.859162	−	1.35666i
$683$	−23.1003	−	13.3369i	−0.883907	−	0.510324i	−0.0119627	−	0.999928i	$-0.503808\pi$
$683$	−23.1003	−	13.3369i	−0.883907	−	0.510324i	−0.871945	+	0.489604i	$0.837141\pi$
$684$	1.73033	−	1.42600i	0.0661606	−	0.0545244i
$685$	−5.00159	−	5.55483i	−0.191101	−	0.212239i
$686$	15.6340	+	14.0769i	0.596910	+	0.537460i
$687$	−10.6043	+	17.4728i	−0.404578	+	0.666628i
$688$	11.9194	+	16.4057i	0.454424	+	0.625461i
$689$	−10.7231	+	0.772533i	−0.408516	+	0.0294311i
$690$	−13.3340	−	6.28979i	−0.507618	−	0.239448i
$691$	−3.43916	+	32.7214i	−0.130832	+	1.24478i	0.710280	+	0.703919i	$0.248568\pi$
$691$	−3.43916	+	32.7214i	−0.130832	+	1.24478i	−0.841112	+	0.540861i	$0.818098\pi$
$692$	−0.163278	−	0.282806i	−0.00620691	−	0.0107507i
$693$	−3.68858	−	29.4169i	−0.140118	−	1.11746i
$694$	−31.8415			−1.20869
$695$	4.21098	−	1.87485i	0.159732	−	0.0711171i
$696$	−14.1882	+	9.84136i	−0.537802	+	0.373036i
$697$	0.588438	+	1.81102i	0.0222887	+	0.0685975i
$698$	34.7447	−	3.65181i	1.31511	−	0.138223i
$699$	−2.45829	+	4.05055i	−0.0929810	+	0.153206i
$700$	−0.737190	−	0.663769i	−0.0278632	−	0.0250881i
$701$	−5.33731	+	16.4266i	−0.201588	+	0.620423i	0.798249	+	0.602328i	$0.205760\pi$
$701$	−5.33731	+	16.4266i	−0.201588	+	0.620423i	−0.999836	+	0.0180947i	$0.994240\pi$
$702$	19.3015	+	17.1610i	0.728489	+	0.647699i
$703$			48.5526i			1.83120i
$704$	24.8401	+	12.3014i	0.936198	+	0.463627i
$705$	−2.64021	+	1.10694i	−0.0994362	+	0.0416896i
$706$	10.8064	+	24.2715i	0.406702	+	0.913468i
$707$	22.4897	+	7.30736i	0.845814	+	0.274822i
$708$	1.62383	+	0.567183i	0.0610273	+	0.0213161i
$709$	2.89652	+	27.5586i	0.108781	+	1.03498i	0.903670	+	0.428229i	$0.140862\pi$
$709$	2.89652	+	27.5586i	0.108781	+	1.03498i	−0.794889	+	0.606755i	$0.792471\pi$
$710$	−13.8341	+	10.0511i	−0.519186	+	0.377211i
$711$	−13.0615	+	26.1890i	−0.489845	+	0.982162i
$712$	−4.98776	−	23.4656i	−0.186924	−	0.879409i
$713$	43.7578	+	4.59913i	1.63874	+	0.172239i
$714$	−22.7310	−	2.89322i	−0.850686	−	0.108276i
$715$	1.13399	−	15.3504i	0.0424088	−	0.574071i
$716$			0.0225800i			0.000843854i
$717$	25.3744	+	5.97660i	0.947625	+	0.223200i
$718$	4.94282	−	1.05063i	0.184464	−	0.0392091i
$719$	−7.34102	+	34.5368i	−0.273774	+	1.28800i	0.599343	+	0.800493i	$0.295429\pi$
$719$	−7.34102	+	34.5368i	−0.273774	+	1.28800i	−0.873116	+	0.487512i	$0.837905\pi$
$720$	5.36331	+	13.6207i	0.199879	+	0.507612i
$721$	4.95319	−	0.520601i	0.184466	−	0.0193882i
$722$	50.3408	+	10.7003i	1.87349	+	0.398223i
$723$	−2.70475	+	5.73395i	−0.100591	+	0.213248i
$724$	0.800612	−	0.356456i	0.0297545	−	0.0132476i
$725$	−5.75758	−	9.97241i	−0.213831	−	0.370366i
$726$	−24.9717	+	8.14031i	−0.926788	+	0.302115i
$727$	−4.25440			−0.157787			−0.0788934	−	0.996883i	$-0.525139\pi$
$727$	−4.25440			−0.157787			−0.0788934	+	0.996883i	$0.525139\pi$
$728$	5.46416	+	30.6116i	0.202515	+	1.13454i
$729$	−23.7330	+	12.8742i	−0.879000	+	0.476822i
$730$	−12.8803	+	14.3050i	−0.476720	+	0.529451i
$731$	7.00746	−	15.7390i	0.259180	−	0.582128i
$732$	−0.0361815	+	1.65333i	−0.00133731	+	0.0611088i
$733$	31.4942	−	10.2331i	1.16326	−	0.377968i	0.337140	−	0.941455i	$-0.390541\pi$
$733$	31.4942	−	10.2331i	1.16326	−	0.377968i	0.826125	+	0.563487i	$0.190541\pi$
$734$	1.15927	+	1.28750i	0.0427893	+	0.0475223i
$735$	4.01016	−	1.20664i	0.147917	−	0.0445077i
$736$			2.69965i			0.0995106i
$737$	−4.10006	−	4.94656i	−0.151028	−	0.182209i
$738$	−0.653142	−	2.35632i	−0.0240425	−	0.0867375i
$739$	47.0909	+	4.94945i	1.73227	+	0.182069i	0.917504	−	0.397726i	$-0.130200\pi$
$739$	47.0909	+	4.94945i	1.73227	+	0.182069i	0.814763	+	0.579794i	$0.196867\pi$
$740$	0.788578	+	0.256225i	0.0289887	+	0.00941900i
$741$	2.56171	−	46.8019i	0.0941067	−	1.71931i
$742$	−9.90881	+	7.19917i	−0.363764	+	0.264290i
$743$	24.4530	+	10.8872i	0.897092	+	0.399411i	0.802880	−	0.596141i	$-0.203300\pi$
$743$	24.4530	+	10.8872i	0.897092	+	0.399411i	0.0942123	+	0.995552i	$0.469967\pi$
$744$	−30.0131	−	34.8364i	−1.10033	−	1.27716i
$745$	−11.8885	+	10.7045i	−0.435561	+	0.392181i
$746$	−10.9190	+	15.0288i	−0.399774	+	0.550242i
$747$	37.5090	−	38.1597i	1.37238	−	1.39619i
$748$	−0.0677977	−	1.06155i	−0.00247893	−	0.0388142i
$749$		−	3.46394i		−	0.126570i
$750$	−24.5545	+	7.38835i	−0.896604	+	0.269785i
$751$	−12.6389	+	2.68648i	−0.461199	+	0.0980309i	−0.432651	−	0.901562i	$-0.642422\pi$
$751$	−12.6389	+	2.68648i	−0.461199	+	0.0980309i	−0.0285481	+	0.999592i	$0.509088\pi$
$752$	−3.61766	−	3.25735i	−0.131922	−	0.118783i
$753$	29.9629	−	16.4357i	1.09191	−	0.598951i
$754$	−2.34691	+	16.9583i	−0.0854695	+	0.617584i
$755$	−7.74232	−	23.8284i	−0.281772	−	0.867204i
$756$	−1.51946	−	0.261392i	−0.0552624	−	0.00950672i
$757$	1.14091	−	10.8551i	0.0414672	−	0.394534i	−0.954028	−	0.299719i	$-0.903107\pi$
$757$	1.14091	−	10.8551i	0.0414672	−	0.394534i	0.995495	−	0.0948156i	$-0.0302261\pi$
$758$	−15.5798	+	26.9849i	−0.565882	+	0.980137i
$759$	−19.2806	−	19.6883i	−0.699843	−	0.714639i
$760$	13.9811	−	24.2159i	0.507147	−	0.878404i
$761$	27.3601	−	12.1815i	0.991802	−	0.441579i	0.154306	−	0.988023i	$-0.450686\pi$
$761$	27.3601	−	12.1815i	0.991802	−	0.441579i	0.837495	+	0.546445i	$0.184019\pi$
$762$	−10.2713	+	21.7746i	−0.372089	+	0.788810i
$763$	23.7034	+	5.03832i	0.858122	+	0.182399i
$764$	0.597040	−	1.34097i	0.0216001	−	0.0485147i
$765$	7.74334	−	9.73216i	0.279961	−	0.351867i
$766$	8.67787	−	2.81961i	0.313544	−	0.101877i
$767$	31.7119	−	16.9473i	1.14505	−	0.611931i
$768$	2.82935	−	3.00730i	0.102095	−	0.108516i
$769$	−0.179782	+	0.103797i	−0.00648312	+	0.00374303i	−0.503238	−	0.864148i	$-0.667858\pi$
$769$	−0.179782	+	0.103797i	−0.00648312	+	0.00374303i	0.496755	+	0.867891i	$0.334525\pi$
$770$	−8.13891	−	15.5324i	−0.293306	−	0.559750i
$771$	1.69280	−	2.22584i	0.0609645	−	0.0801618i
$772$	−0.775401	+	1.06725i	−0.0279073	+	0.0384111i
$773$	−3.53408	+	3.18210i	−0.127112	+	0.114452i	−0.730235	−	0.683196i	$-0.760589\pi$
$773$	−3.53408	+	3.18210i	−0.127112	+	0.114452i	0.603123	+	0.797648i	$0.293923\pi$
$774$	−9.87363	+	19.7971i	−0.354900	+	0.711592i
$775$	24.8081	−	18.0241i	0.891134	−	0.647446i
$776$	−2.34509	−	22.3120i	−0.0841837	−	0.800954i
$777$	25.2932	−	21.7912i	0.907389	−	0.781755i
$778$	−1.63655	−	7.69936i	−0.0586732	−	0.276036i
$779$	−2.60833	+	3.59006i	−0.0934531	+	0.128627i
$780$	−0.746625	−	0.288592i	−0.0267334	−	0.0103333i
$781$	−30.7764	+	8.62439i	−1.10127	+	0.308605i
$782$	−18.4451	+	10.6493i	−0.659595	+	0.380817i
$783$	−15.8373	−	8.33627i	−0.565978	−	0.297914i
$784$	4.76481	+	5.29185i	0.170172	+	0.188995i
$785$	−12.0156	+	3.90409i	−0.428854	+	0.139343i
$786$	22.1496	+	0.484723i	0.790050	+	0.0172895i
$787$	24.8130	−	2.60795i	0.884487	−	0.0929633i	0.348618	−	0.937265i	$-0.386651\pi$
$787$	24.8130	−	2.60795i	0.884487	−	0.0929633i	0.535868	+	0.844301i	$0.319984\pi$
$788$	−0.717990	−	2.20975i	−0.0255773	−	0.0787189i
$789$	−17.6626	+	12.2513i	−0.628804	+	0.436157i
$790$	−1.80936	+	17.2149i	−0.0643742	+	0.612479i
$791$	−24.2631	−	42.0249i	−0.862697	−	1.49424i
$792$	0.576481	+	28.7931i	0.0204844	+	1.02312i
$793$	24.9182	+	23.9620i	0.884870	+	0.850914i
$794$	33.5658	+	24.3870i	1.19121	+	0.865461i
$795$	−0.550052	−	6.62480i	−0.0195083	−	0.234958i
$796$	−0.0198629	+	0.0220600i	−0.000704021	+	0.000781895i
$797$	0.553053	−	0.0581282i	0.0195901	−	0.00205901i	−0.0947283	−	0.995503i	$-0.530198\pi$
$797$	0.553053	−	0.0581282i	0.0195901	−	0.00205901i	0.114318	+	0.993444i	$0.463532\pi$
$798$	−25.6814	−	46.8180i	−0.909110	−	1.65734i
$799$	−0.859890	+	4.04546i	−0.0304207	+	0.143118i
$800$	1.25897	+	1.39822i	0.0445111	+	0.0494346i
$801$	19.1886	−	15.8137i	0.677994	−	0.558750i
$802$	−36.7633	−	21.2253i	−1.29816	−	0.749492i
$803$	−31.8692	+	16.6993i	−1.12464	+	0.589305i
$804$	−0.308134	+	0.129188i	−0.0108671	+	0.00455612i
$805$	10.8141	−	14.8843i	0.381146	−	0.524602i
$806$	−45.5653	−	1.49508i	−1.60497	−	0.0526619i
$807$	−0.203835	−	1.07401i	−0.00717535	−	0.0378068i
$808$	−20.9845	−	9.34289i	−0.738231	−	0.328682i
$809$	−10.2268	−	4.55325i	−0.359554	−	0.160084i	0.219006	−	0.975724i	$-0.429719\pi$
$809$	−10.2268	−	4.55325i	−0.359554	−	0.160084i	−0.578560	+	0.815640i	$0.696385\pi$
$810$	−10.4802	+	12.0499i	−0.368237	+	0.423390i
$811$	−3.61480	−	1.17452i	−0.126933	−	0.0412430i	0.244862	−	0.969558i	$-0.421257\pi$
$811$	−3.61480	−	1.17452i	−0.126933	−	0.0412430i	−0.371795	+	0.928315i	$0.621257\pi$
$812$	−0.415680	−	0.933633i	−0.0145875	−	0.0327641i
$813$	−12.4598	+	16.3833i	−0.436986	+	0.574589i
$814$	−23.1967	−	18.3497i	−0.813042	−	0.643155i
$815$	−25.8123	−	14.9027i	−0.904165	−	0.522020i
$816$	20.5843	+	4.84835i	0.720595	+	0.169726i
$817$	39.2715	−	8.34741i	1.37394	−	0.292039i
$818$	−28.1619	+	9.15034i	−0.984657	+	0.319934i
$819$	−25.5309	+	19.6709i	−0.892122	+	0.687358i
$820$	0.0445439	+	0.0613094i	0.00155554	+	0.00214102i
$821$	1.92173	−	2.13430i	0.0670689	−	0.0744876i	−0.708677	−	0.705534i	$-0.750707\pi$
$821$	1.92173	−	2.13430i	0.0670689	−	0.0744876i	0.775745	+	0.631046i	$0.217374\pi$
$822$	13.8184	−	1.14733i	0.481973	−	0.0400178i
$823$	−1.82131	+	0.810899i	−0.0634868	+	0.0282662i	−0.438234	−	0.898861i	$-0.644396\pi$
$823$	−1.82131	+	0.810899i	−0.0634868	+	0.0282662i	0.374748	+	0.927127i	$0.377729\pi$
$824$	−4.83793			−0.168537
$825$	−19.1674	−	1.20569i	−0.667325	−	0.0419768i
$826$	20.4817	−	35.4753i	0.712648	−	1.23434i
$827$	−11.8790	−	8.63063i	−0.413075	−	0.300117i	0.361771	−	0.932267i	$-0.382172\pi$
$827$	−11.8790	−	8.63063i	−0.413075	−	0.300117i	−0.774846	+	0.632151i	$0.782172\pi$
$828$	−1.27123	+	0.661552i	−0.0441782	+	0.0229905i
$829$	−5.58856	+	6.20672i	−0.194099	+	0.215568i	−0.832336	−	0.554271i	$-0.812997\pi$
$829$	−5.58856	+	6.20672i	−0.194099	+	0.215568i	0.638238	+	0.769840i	$0.279664\pi$
$830$	12.8726	−	28.9124i	0.446815	−	1.00356i
$831$	20.9958	−	11.5169i	0.728336	−	0.399518i
$832$	−2.16536	−	30.0561i	−0.0750704	−	1.04201i
$833$	1.86951	−	5.75375i	0.0647745	−	0.199356i
$834$	−1.96037	+	8.32303i	−0.0678822	+	0.288203i
$835$	20.9902	−	12.1187i	0.726397	−	0.419386i
$836$	1.90849	−	1.58189i	0.0660065	−	0.0547109i
$837$	17.6692	−	44.2636i	0.610737	−	1.52997i
$838$	13.0267	+	29.2586i	0.450001	+	1.01072i
$839$	2.98684	−	2.68936i	0.103117	−	0.0928472i	−0.615960	−	0.787778i	$-0.711232\pi$
$839$	2.98684	−	2.68936i	0.103117	−	0.0928472i	0.719077	+	0.694931i	$0.244565\pi$
$840$	−18.8901	+	3.58514i	−0.651770	+	0.123699i
$841$	1.79126	+	17.0427i	0.0617676	+	0.587680i
$842$	12.1127	+	5.39290i	0.417430	+	0.185852i
$843$	−4.43299	−	5.14540i	−0.152680	−	0.177217i
$844$	−0.664752	−	0.215991i	−0.0228817	−	0.00743472i
$845$	−15.0086	+	7.39860i	−0.516310	+	0.254519i
$846$	1.33036	−	5.14141i	0.0457387	−	0.176765i
$847$	−4.16961	−	32.5100i	−0.143270	−	1.11706i
$848$	9.78920	−	5.65180i	0.336163	−	0.194084i
$849$	20.8416	−	6.27116i	0.715282	−	0.215226i
$850$	−4.58698	+	14.1173i	−0.157332	+	0.484219i
$851$	6.45180	−	30.3533i	0.221165	−	1.04050i
$852$	−0.0363660	+	1.66176i	−0.00124588	+	0.0569309i
$853$	−2.23975	−	3.08275i	−0.0766875	−	0.105551i	0.768950	−	0.639309i	$-0.220779\pi$
$853$	−2.23975	−	3.08275i	−0.0766875	−	0.105551i	−0.845638	+	0.533758i	$0.820779\pi$
$854$	38.5235	+	8.18842i	1.31825	+	0.280202i
$855$	28.9547	+	1.26790i	0.990229	+	0.0433612i
$856$	−0.351718	+	3.34638i	−0.0120215	+	0.114377i
$857$	−11.9133			−0.406949			−0.203474	−	0.979080i	$-0.565223\pi$
$857$	−11.9133			−0.406949			−0.203474	+	0.979080i	$0.565223\pi$
$858$	21.3921	+	18.9119i	0.730313	+	0.645641i
$859$	3.98531			0.135977			0.0679884	−	0.997686i	$-0.478342\pi$
$859$	3.98531			0.135977			0.0679884	+	0.997686i	$0.478342\pi$
$860$	0.0716693	−	0.681888i	0.00244390	−	0.0232522i
$861$	3.04088	−	0.252482i	0.103633	−	0.00860456i
$862$	38.3371	+	8.14881i	1.30577	+	0.277550i
$863$	−19.6871	−	27.0969i	−0.670156	−	0.922391i	0.329608	−	0.944118i	$-0.393083\pi$
$863$	−19.6871	−	27.0969i	−0.670156	−	0.922391i	−0.999764	+	0.0217273i	$0.993083\pi$
$864$	2.81434	+	0.794309i	0.0957459	+	0.0270230i
$865$	0.877599	−	4.12878i	0.0298393	−	0.140383i
$866$	3.53842	−	10.8901i	0.120240	−	0.370062i
$867$	3.30723	+	10.9913i	0.112319	+	0.373283i
$868$	2.35691	−	1.36076i	0.0799988	−	0.0461873i
$869$	−14.3583	+	28.9936i	−0.487072	+	0.983541i
$870$	−10.5011	−	1.33659i	−0.356019	−	0.0453145i
$871$	−2.37503	+	6.56837i	−0.0804749	+	0.222561i
$872$	−22.3874	−	7.27409i	−0.758132	−	0.246332i
$873$	19.3924	−	12.8320i	0.656333	−	0.434297i
$874$	−45.3425	−	20.1878i	−1.53373	−	0.682862i
$875$	−3.34479	−	31.8235i	−0.113074	−	1.07583i
$876$	0.348883	+	1.83826i	0.0117877	+	0.0621090i
$877$	32.7813	−	29.5164i	1.10695	−	0.996698i	0.106949	−	0.994265i	$-0.465892\pi$
$877$	32.7813	−	29.5164i	1.10695	−	0.996698i	0.999997	−	0.00243378i	$-0.000774698\pi$
$878$	−14.6219	−	32.8413i	−0.493465	−	1.10834i
$879$	1.75643	−	13.7996i	0.0592428	−	0.465449i
$880$	5.97183	+	15.0414i	0.201310	+	0.507047i
$881$	12.9334	−	7.46709i	0.435737	−	0.251573i	−0.266051	−	0.963959i	$-0.585719\pi$
$881$	12.9334	−	7.46709i	0.435737	−	0.251573i	0.701788	+	0.712386i	$0.252386\pi$
$882$	−2.72151	+	7.27616i	−0.0916379	+	0.245001i
$883$	−0.159738	+	0.491624i	−0.00537562	+	0.0165445i	−0.953708	−	0.300733i	$-0.902769\pi$
$883$	−0.159738	+	0.491624i	−0.00537562	+	0.0165445i	0.948333	+	0.317278i	$0.102769\pi$
$884$	−0.957318	+	0.648658i	−0.0321981	+	0.0218167i
$885$	10.6925	+	19.4929i	0.359425	+	0.655245i
$886$	19.8751	−	44.6403i	0.667719	−	1.49972i
$887$	1.02712	−	1.14073i	0.0344873	−	0.0383021i	−0.725654	−	0.688059i	$-0.758463\pi$
$887$	1.02712	−	1.14073i	0.0344873	−	0.0383021i	0.760142	+	0.649757i	$0.225129\pi$
$888$	−26.6474	+	18.4834i	−0.894227	+	0.620263i
$889$	−24.3061	−	17.6594i	−0.815201	−	0.592279i
$890$	7.35354	−	12.7367i	0.246491	−	0.426935i
$891$	−26.1976	+	14.3069i	−0.877651	+	0.479300i
$892$	−0.147675			−0.00494454
$893$	−8.80481	+	3.92015i	−0.294642	+	0.131183i
$894$	−2.45553	−	29.5743i	−0.0821253	−	0.989113i
$895$	−0.195296	+	0.216898i	−0.00652802	+	0.00725011i
$896$	−18.2075	−	25.0605i	−0.608271	−	0.837213i
$897$	−7.82065	+	28.9184i	−0.261124	+	0.965559i
$898$	30.7574	−	9.99368i	1.02639	−	0.333493i
$899$	30.9016	−	6.56833i	1.03062	−	0.219066i
$900$	−0.349892	+	0.935463i	−0.0116631	+	0.0311821i
$901$	−8.31682	−	4.80172i	−0.277073	−	0.159968i
$902$	−0.729422	−	2.60297i	−0.0242871	−	0.0866693i
$903$	−21.9742	−	16.7118i	−0.731256	−	0.556134i
$904$	19.1725	+	43.0622i	0.637669	+	1.43223i
$905$	10.7735	+	3.50052i	0.358124	+	0.116361i
$906$	43.8778	+	15.3260i	1.45774	+	0.509171i
$907$	20.5889	+	9.16678i	0.683644	+	0.304378i	0.719013	−	0.694996i	$-0.244594\pi$
$907$	20.5889	+	9.16678i	0.683644	+	0.304378i	−0.0353690	+	0.999374i	$0.511261\pi$
$908$	−1.72684	−	0.768838i	−0.0573072	−	0.0255148i
$909$	−1.45044	−	23.7643i	−0.0481079	−	0.788211i
$910$	−10.0679	+	16.1878i	−0.333747	+	0.536620i
$911$	−14.4177	+	19.8442i	−0.477678	+	0.657468i	−0.978057	−	0.208339i	$-0.933194\pi$
$911$	−14.4177	+	19.8442i	−0.477678	+	0.657468i	0.500378	+	0.865807i	$0.333194\pi$
$912$	19.0549	+	45.4489i	0.630971	+	1.50496i
$913$	41.3486	−	42.3040i	1.36844	−	1.40006i
$914$	1.72458	+	0.995684i	0.0570439	+	0.0329343i
$915$	−14.6473	+	15.5686i	−0.484225	+	0.514681i
$916$	0.786288	+	0.873262i	0.0259797	+	0.0288534i
$917$	−5.74819	+	27.0431i	−0.189822	+	0.893041i
$918$	5.67465	+	22.3620i	0.187291	+	0.738055i
$919$	−18.2109	+	1.91404i	−0.600722	+	0.0631384i	−0.400008	−	0.916512i	$-0.630993\pi$
$919$	−18.2109	+	1.91404i	−0.600722	+	0.0631384i	−0.200714	+	0.979650i	$0.564326\pi$
$920$	−11.9583	+	13.2811i	−0.394255	+	0.437864i
$921$	−21.0391	+	1.74686i	−0.693261	+	0.0575610i
$922$	−21.1057	−	15.3342i	−0.695081	−	0.505006i
$923$	25.0452	+	24.0841i	0.824373	+	0.792739i
$924$	−1.68064	−	0.284239i	−0.0552890	−	0.00935077i
$925$	−10.8135	−	18.7296i	−0.355546	−	0.615824i
$926$	4.83000	−	45.9544i	0.158724	−	1.51016i
$927$	−2.31485	−	4.44817i	−0.0760297	−	0.146097i
$928$	0.598998	+	1.84353i	0.0196631	+	0.0605167i
$929$	16.9219	−	1.77856i	0.555188	−	0.0583526i	0.177220	−	0.984171i	$-0.443290\pi$
$929$	16.9219	−	1.77856i	0.555188	−	0.0583526i	0.377968	+	0.925819i	$0.376623\pi$
$930$	0.616755	−	28.1829i	0.0202242	−	0.924153i
$931$	13.4084	−	4.35665i	0.439442	−	0.142783i
$932$	0.182278	+	0.202440i	0.00597070	+	0.00663114i
$933$	−12.5012	+	53.0755i	−0.409271	+	1.73762i
$934$	9.41192	−	5.43398i	0.307968	−	0.177805i
$935$	8.53019	−	10.7834i	0.278967	−	0.352655i
$936$	26.6617	−	16.4110i	0.871466	−	0.536410i
$937$	−22.5225	+	30.9996i	−0.735778	+	1.01271i	0.263072	+	0.964776i	$0.415264\pi$
$937$	−22.5225	+	30.9996i	−0.735778	+	1.01271i	−0.998850	+	0.0479357i	$0.984736\pi$
$938$	1.65440	+	7.78332i	0.0540179	+	0.254134i
$939$	−26.3133	−	30.5420i	−0.858702	−	0.996702i
$940$	0.0172048	+	0.163693i	0.000561159	+	0.00533907i
$941$	22.6208	−	16.4349i	0.737416	−	0.535764i	−0.154485	−	0.987995i	$-0.549372\pi$
$941$	22.6208	−	16.4349i	0.737416	−	0.535764i	0.891901	+	0.452231i	$0.149372\pi$
$942$	7.72817	−	22.1255i	0.251797	−	0.720889i
$943$	2.10769	−	1.89777i	0.0686358	−	0.0618000i
$944$	−22.2212	+	30.5848i	−0.723237	+	0.995450i
$945$	−12.3348	−	15.6528i	−0.401252	−	0.509186i
$946$	−10.8539	+	21.9172i	−0.352891	+	0.712590i
$947$	33.8468	−	19.5415i	1.09987	−	0.635013i	0.163687	−	0.986512i	$-0.447661\pi$
$947$	33.8468	−	19.5415i	1.09987	−	0.635013i	0.936188	+	0.351499i	$0.114328\pi$
$948$	1.22545	+	1.15293i	0.0398007	+	0.0374455i
$949$	33.2138	+	20.6571i	1.07817	+	0.670559i
$950$	−32.8985	+	10.6894i	−1.06737	+	0.346809i
$951$	20.4211	+	12.3936i	0.662199	+	0.401890i
$952$	−11.2978	+	25.3752i	−0.366163	+	0.822416i
$953$	15.2845	+	3.24882i	0.495113	+	0.105239i	0.448699	−	0.893683i	$-0.351887\pi$
$953$	15.2845	+	3.24882i	0.495113	+	0.105239i	0.0464136	+	0.998922i	$0.485221\pi$
$954$	10.3995	+	6.62707i	0.336695	+	0.214559i
$955$	17.3332	−	7.71724i	0.560889	−	0.249724i
$956$	0.749383	−	1.29797i	0.0242368	−	0.0419793i
$957$	−17.5347	−	9.16665i	−0.566816	−	0.296316i
$958$	−13.2791	+	23.0000i	−0.429027	+	0.743097i
$959$	−1.80870	+	17.2086i	−0.0584060	+	0.555696i
$960$	18.5689	−	1.54176i	0.599309	−	0.0497602i
$961$	16.4176	+	50.5281i	0.529599	+	1.62994i
$962$	−4.40782	+	31.8499i	−0.142114	+	1.02688i
$963$	−3.24507	+	1.27779i	−0.104571	+	0.0411761i
$964$	0.270873	+	0.243896i	0.00872424	+	0.00785535i
$965$	−16.6790	+	3.54524i	−0.536917	+	0.114125i
$966$	9.83375	+	32.6815i	0.316396	+	1.05151i
$967$		−	10.4182i		−	0.335026i	−0.985870	−	0.167513i	$-0.946426\pi$
$967$		−	10.4182i		−	0.335026i	0.985870	−	0.167513i	$-0.0535737\pi$
$968$	0.727128	+	31.8300i	0.0233708	+	1.02305i
$969$	25.3454	−	33.3265i	0.814212	−	1.07060i
$970$	8.08431	−	11.1271i	0.259572	−	0.357270i
$971$	21.4291	−	19.2948i	0.687693	−	0.619201i	−0.249351	−	0.968413i	$-0.580217\pi$
$971$	21.4291	−	19.2948i	0.687693	−	0.619201i	0.937044	+	0.349212i	$0.113551\pi$
$972$	0.315628	+	1.51988i	0.0101238	+	0.0487501i
$973$	−9.74806	−	4.34012i	−0.312508	−	0.139138i
$974$	18.1904	−	13.2161i	0.582857	−	0.423471i
$975$	9.43540	+	18.6247i	0.302175	+	0.596469i
$976$	−34.5685	−	11.2320i	−1.10651	−	0.359527i
$977$	6.10000	+	0.641136i	0.195156	+	0.0205117i	0.201602	−	0.979467i	$-0.435385\pi$
$977$	6.10000	+	0.641136i	0.195156	+	0.0205117i	−0.00644598	+	0.999979i	$0.502052\pi$
$978$	50.9901	−	21.3781i	1.63048	−	0.683596i
$979$	21.1643	−	17.5425i	0.676415	−	0.560661i
$980$		−	0.240766i		−	0.00769100i
$981$	−4.02381	−	24.0643i	−0.128470	−	0.768313i
$982$	22.7400	+	25.2553i	0.725662	+	0.805929i
$983$	−5.43524	+	1.76602i	−0.173357	+	0.0563272i	−0.394410	−	0.918935i	$-0.629051\pi$
$983$	−5.43524	+	1.76602i	−0.173357	+	0.0563272i	0.221052	+	0.975262i	$0.429051\pi$
$984$	−2.96331	−	0.0648492i	−0.0944668	−	0.00206732i
$985$	12.2154	−	27.4363i	0.389215	−	0.874192i
$986$	−10.2328	+	11.3647i	−0.325880	+	0.361926i
$987$	5.99392	+	2.82738i	0.190789	+	0.0899966i
$988$	−2.53422	−	0.916339i	−0.0806242	−	0.0291526i
$989$	−25.6603			−0.815951
$990$	−11.5487	+	13.3543i	−0.367041	+	0.424427i
$991$	3.62842	+	6.28461i	0.115261	+	0.199637i	0.917884	−	0.396849i	$-0.129896\pi$
$991$	3.62842	+	6.28461i	0.115261	+	0.199637i	−0.802623	+	0.596486i	$0.796563\pi$
$992$	−4.71563	+	2.09953i	−0.149721	+	0.0666602i
$993$	7.83680	+	3.69669i	0.248693	+	0.117311i
$994$	38.7199	+	8.23017i	1.22812	+	0.261045i
$995$	−0.381597	+	0.0401074i	−0.0120974	+	0.00127149i
$996$	−1.47950	−	2.69718i	−0.0468798	−	0.0854635i
$997$	−4.33406	+	20.3902i	−0.137261	+	0.645763i	0.854690	+	0.519139i	$0.173747\pi$
$997$	−4.33406	+	20.3902i	−0.137261	+	0.645763i	−0.991951	+	0.126624i	$0.959586\pi$
$998$	−38.4655	+	8.17610i	−1.21760	+	0.258810i
$999$	−29.7445	−	15.6566i	−0.941075	−	0.495354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bq.a.29.15	✓	416
3.2	odd	2	inner	429.2.bq.a.29.38	yes	416
11.8	odd	10	inner	429.2.bq.a.107.15	yes	416
13.9	even	3	inner	429.2.bq.a.425.38	yes	416
33.8	even	10	inner	429.2.bq.a.107.38	yes	416
39.35	odd	6	inner	429.2.bq.a.425.15	yes	416
143.74	odd	30	inner	429.2.bq.a.74.38	yes	416
429.74	even	30	inner	429.2.bq.a.74.15	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bq.a.29.15	✓	416	1.1	even	1	trivial
429.2.bq.a.29.38	yes	416	3.2	odd	2	inner
429.2.bq.a.74.15	yes	416	429.74	even	30	inner
429.2.bq.a.74.38	yes	416	143.74	odd	30	inner
429.2.bq.a.107.15	yes	416	11.8	odd	10	inner
429.2.bq.a.107.38	yes	416	33.8	even	10	inner
429.2.bq.a.425.15	yes	416	39.35	odd	6	inner
429.2.bq.a.425.38	yes	416	13.9	even	3	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bq (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.144098 + 1.37101i) q^{2} +(0.143318 + 1.72611i) q^{3} +(0.0974043 + 0.0207039i) q^{4} +(0.756574 + 1.04133i) q^{5} +(-2.38716 - 0.0522407i) q^{6} +(0.619507 - 2.91455i) q^{7} +(-0.894416 + 2.75273i) q^{8} +(-2.95892 + 0.494764i) q^{9} +O(q^{10})\)	\(q+(-0.144098 + 1.37101i) q^{2} +(0.143318 + 1.72611i) q^{3} +(0.0974043 + 0.0207039i) q^{4} +(0.756574 + 1.04133i) q^{5} +(-2.38716 - 0.0522407i) q^{6} +(0.619507 - 2.91455i) q^{7} +(-0.894416 + 2.75273i) q^{8} +(-2.95892 + 0.494764i) q^{9} +(-1.53670 + 0.887212i) q^{10} +(-3.26965 + 0.556210i) q^{11} +(-0.0217775 + 0.171098i) q^{12} +(2.32342 + 2.75712i) q^{13} +(3.90660 + 1.26933i) q^{14} +(-1.68903 + 1.45517i) q^{15} +(-3.46318 - 1.54191i) q^{16} +(0.336659 + 3.20309i) q^{17} +(-0.251949 - 4.12799i) q^{18} +(-5.57769 + 5.02217i) q^{19} +(0.0521338 + 0.117095i) q^{20} +(5.11963 + 0.651632i) q^{21} +(-0.291414 - 4.56286i) q^{22} +(4.15433 - 2.39850i) q^{23} +(-4.87970 - 1.14935i) q^{24} +(1.03311 - 3.17959i) q^{25} +(-4.11483 + 2.78812i) q^{26} +(-1.27808 - 5.03652i) q^{27} +(0.120685 - 0.271064i) q^{28} +(2.30471 - 2.55964i) q^{29} +(-1.75166 - 2.52535i) q^{30} +(7.42043 + 5.39125i) q^{31} +(-0.281390 + 0.487381i) q^{32} +(-1.42868 - 5.56407i) q^{33} -4.43997 q^{34} +(3.50373 - 1.55996i) q^{35} +(-0.298455 - 0.0130691i) q^{36} +(4.32855 - 4.80735i) q^{37} +(-6.08169 - 8.37073i) q^{38} +(-4.42612 + 4.40562i) q^{39} +(-3.54320 + 1.15126i) q^{40} +(0.578319 - 0.122925i) q^{41} +(-1.63112 + 6.92514i) q^{42} +(-4.63258 - 2.67462i) q^{43} +(-0.329994 - 0.0135174i) q^{44} +(-2.75386 - 2.70690i) q^{45} +(2.68973 + 6.04122i) q^{46} +(1.22128 + 0.396818i) q^{47} +(2.16517 - 6.19882i) q^{48} +(-1.71601 - 0.764016i) q^{49} +(4.21036 + 1.87458i) q^{50} +(-5.48064 + 1.04017i) q^{51} +(0.169228 + 0.316660i) q^{52} +(-1.75263 + 2.41229i) q^{53} +(7.08926 - 1.02651i) q^{54} +(-3.05293 - 2.98399i) q^{55} +(7.46888 + 4.31216i) q^{56} +(-9.46821 - 8.90794i) q^{57} +(3.17717 + 3.52861i) q^{58} +(2.07339 - 9.75455i) q^{59} +(-0.194646 + 0.106771i) q^{60} +(9.53549 - 1.00222i) q^{61} +(-8.46071 + 9.39657i) q^{62} +(-0.391055 + 8.93044i) q^{63} +(-6.76150 - 4.91251i) q^{64} +(-1.11325 + 4.50542i) q^{65} +(7.83424 - 1.15695i) q^{66} +(0.968586 + 1.67764i) q^{67} +(-0.0335246 + 0.318965i) q^{68} +(4.73547 + 6.82708i) q^{69} +(1.63383 + 5.02842i) q^{70} +(9.58411 - 1.00733i) q^{71} +(1.28455 - 8.58763i) q^{72} +(10.3172 - 3.35227i) q^{73} +(5.96716 + 6.62720i) q^{74} +(5.63639 + 1.32757i) q^{75} +(-0.647270 + 0.373701i) q^{76} +(-0.404472 + 9.87415i) q^{77} +(-5.40233 - 6.70307i) q^{78} +(5.73393 - 7.89207i) q^{79} +(-1.01451 - 4.77290i) q^{80} +(8.51042 - 2.92794i) q^{81} +(0.0851966 + 0.810592i) q^{82} +(-14.4296 + 10.4837i) q^{83} +(0.485183 + 0.169468i) q^{84} +(-3.08078 + 2.77395i) q^{85} +(4.33447 - 5.96588i) q^{86} +(4.74852 + 3.61134i) q^{87} +(1.39334 - 9.49795i) q^{88} +(-7.17794 + 4.14419i) q^{89} +(4.10800 - 3.38549i) q^{90} +(9.47516 - 5.06366i) q^{91} +(0.454308 - 0.147614i) q^{92} +(-8.24243 + 13.5811i) q^{93} +(-0.720024 + 1.61720i) q^{94} +(-9.44969 - 2.00859i) q^{95} +(-0.881602 - 0.415859i) q^{96} +(-7.08104 + 3.15268i) q^{97} +(1.29474 - 2.24256i) q^{98} +(9.39945 - 3.26349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) \) 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9	\( 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9} - 52 q^{12} - 20 q^{13} - 3 q^{15} + 30 q^{16} - 20 q^{18} - 10 q^{19} + 4 q^{22} + 5 q^{24} + 60 q^{25} - 24 q^{27} - 10 q^{28} - 65 q^{30} - 8 q^{31} + 49 q^{33} - 24 q^{34} + 3 q^{36} - 6 q^{37} - 35 q^{39} - 120 q^{40} - 13 q^{42} - 32 q^{45} - 30 q^{46} - 33 q^{48} - 26 q^{49} - 100 q^{51} - 60 q^{52} - 42 q^{55} - 20 q^{57} - 34 q^{58} + 32 q^{60} - 30 q^{61} - 45 q^{63} + 40 q^{64} + 42 q^{66} + 32 q^{67} - 33 q^{69} - 268 q^{70} + 55 q^{72} - 40 q^{73} + 9 q^{75} - 32 q^{78} - 37 q^{81} + 28 q^{82} - 180 q^{84} - 10 q^{85} - 142 q^{88} - 30 q^{90} + 8 q^{91} - 26 q^{93} - 90 q^{94} + 330 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) \) 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9 - 52 * q^12 - 20 * q^13 - 3 * q^15 + 30 * q^16 - 20 * q^18 - 10 * q^19 + 4 * q^22 + 5 * q^24 + 60 * q^25 - 24 * q^27 - 10 * q^28 - 65 * q^30 - 8 * q^31 + 49 * q^33 - 24 * q^34 + 3 * q^36 - 6 * q^37 - 35 * q^39 - 120 * q^40 - 13 * q^42 - 32 * q^45 - 30 * q^46 - 33 * q^48 - 26 * q^49 - 100 * q^51 - 60 * q^52 - 42 * q^55 - 20 * q^57 - 34 * q^58 + 32 * q^60 - 30 * q^61 - 45 * q^63 + 40 * q^64 + 42 * q^66 + 32 * q^67 - 33 * q^69 - 268 * q^70 + 55 * q^72 - 40 * q^73 + 9 * q^75 - 32 * q^78 - 37 * q^81 + 28 * q^82 - 180 * q^84 - 10 * q^85 - 142 * q^88 - 30 * q^90 + 8 * q^91 - 26 * q^93 - 90 * q^94 + 330 * q^96 - 14 * q^97 - 4 * q^99

Introduction

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