LMFDB - Embedded newform 392.2.z.a.37.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(37,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 21, 32]))

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

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

chi := DirichletCharacter("392.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.z (of order $42$, degree $12$, 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:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			37.19
Character	$\chi$	$=$	392.37
Dual form			392.2.z.a.53.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.709961 + 1.22309i) q^{2} +(0.469951 + 0.506487i) q^{3} +(-0.991911 - 1.73670i) q^{4} +(-0.273835 + 0.887753i) q^{5} +(-0.953127 + 0.215208i) q^{6} +(0.528093 - 2.59251i) q^{7} +(2.82836 + 0.0197876i) q^{8} +(0.188515 - 2.51556i) q^{9} +O(q^{10})$	\(q+(-0.709961 + 1.22309i) q^{2} +(0.469951 + 0.506487i) q^{3} +(-0.991911 - 1.73670i) q^{4} +(-0.273835 + 0.887753i) q^{5} +(-0.953127 + 0.215208i) q^{6} +(0.528093 - 2.59251i) q^{7} +(2.82836 + 0.0197876i) q^{8} +(0.188515 - 2.51556i) q^{9} +(-0.891391 - 0.965196i) q^{10} +(2.90057 - 0.217368i) q^{11} +(0.413464 - 1.31855i) q^{12} +(1.19293 - 2.47715i) q^{13} +(2.79596 + 2.48649i) q^{14} +(-0.578324 + 0.278506i) q^{15} +(-2.03223 + 3.44530i) q^{16} +(0.271023 + 0.0408501i) q^{17} +(2.94293 + 2.01652i) q^{18} +(0.864835 + 0.499313i) q^{19} +(1.81338 - 0.405003i) q^{20} +(1.56125 - 0.950882i) q^{21} +(-1.79343 + 3.70199i) q^{22} +(-2.51518 + 0.379103i) q^{23} +(1.31917 + 1.44183i) q^{24} +(3.41808 + 2.33040i) q^{25} +(2.18284 + 3.21774i) q^{26} +(2.98326 - 2.37907i) q^{27} +(-5.02623 + 1.65440i) q^{28} +(6.85394 + 5.46583i) q^{29} +(0.0699487 - 0.905073i) q^{30} +(-4.98617 - 8.63630i) q^{31} +(-2.77111 - 4.93163i) q^{32} +(1.47322 + 1.36695i) q^{33} +(-0.242379 + 0.302484i) q^{34} +(2.15690 + 1.17874i) q^{35} +(-4.55576 + 2.16782i) q^{36} +(-6.06557 + 2.38056i) q^{37} +(-1.22471 + 0.703281i) q^{38} +(1.81526 - 0.559934i) q^{39} +(-0.792071 + 2.50546i) q^{40} +(0.608266 + 2.66499i) q^{41} +(0.0545889 + 2.58464i) q^{42} +(7.65784 + 1.74785i) q^{43} +(-3.25461 - 4.82180i) q^{44} +(2.18158 + 0.856205i) q^{45} +(1.32200 - 3.34545i) q^{46} +(5.47460 - 3.73252i) q^{47} +(-2.70004 + 0.589825i) q^{48} +(-6.44224 - 2.73818i) q^{49} +(-5.27700 + 2.52613i) q^{50} +(0.106678 + 0.156467i) q^{51} +(-5.48533 + 0.385350i) q^{52} +(3.42053 + 1.34246i) q^{53} +(0.791826 + 5.33786i) q^{54} +(-0.601310 + 2.63451i) q^{55} +(1.54494 - 7.32210i) q^{56} +(0.153535 + 0.672680i) q^{57} +(-11.5512 + 4.50247i) q^{58} +(0.968189 + 3.13879i) q^{59} +(1.05733 + 0.728120i) q^{60} +(-14.2533 + 5.59401i) q^{61} +(14.1030 + 0.0328884i) q^{62} +(-6.42207 - 1.81718i) q^{63} +(7.99922 + 0.111933i) q^{64} +(1.87243 + 1.73736i) q^{65} +(-2.71783 + 0.831405i) q^{66} +(2.13348 - 1.23176i) q^{67} +(-0.197886 - 0.511204i) q^{68} +(-1.37402 - 1.09575i) q^{69} +(-2.97302 + 1.80123i) q^{70} +(-4.71309 - 5.91003i) q^{71} +(0.582966 - 7.11118i) q^{72} +(11.0283 + 7.51897i) q^{73} +(1.39467 - 9.10886i) q^{74} +(0.426009 + 2.82639i) q^{75} +(0.00931520 - 1.99723i) q^{76} +(0.968243 - 7.63455i) q^{77} +(-0.603914 + 2.61776i) q^{78} +(4.13722 - 7.16587i) q^{79} +(-2.50207 - 2.74756i) q^{80} +(-4.87637 - 0.734994i) q^{81} +(-3.69137 - 1.14807i) q^{82} +(-7.05258 - 14.6448i) q^{83} +(-3.20001 - 1.76823i) q^{84} +(-0.110481 + 0.229415i) q^{85} +(-7.57455 + 8.12534i) q^{86} +(0.452643 + 6.04010i) q^{87} +(8.20815 - 0.557398i) q^{88} +(-0.674018 + 8.99415i) q^{89} +(-2.59605 + 2.06040i) q^{90} +(-5.79205 - 4.40085i) q^{91} +(3.15323 + 3.99207i) q^{92} +(2.03092 - 6.58407i) q^{93} +(0.678463 + 9.34588i) q^{94} +(-0.680089 + 0.631030i) q^{95} +(1.19552 - 3.72116i) q^{96} -2.79586 q^{97} +(7.92278 - 5.93545i) q^{98} -7.33754i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{16}{21}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.709961	+	1.22309i	−0.502018	+	0.864857i
$2$	−0.709961	+	1.22309i	−0.502018	+	0.864857i
$3$	0.469951	+	0.506487i	0.271326	+	0.292420i	0.853986	−	0.520296i	$-0.174178\pi$
$3$	0.469951	+	0.506487i	0.271326	+	0.292420i	−0.582660	+	0.812716i	$0.697988\pi$
$4$	−0.991911	−	1.73670i	−0.495955	−	0.868348i
$5$	−0.273835	+	0.887753i	−0.122463	+	0.397015i	−0.995958	−	0.0898175i	$-0.971372\pi$
$5$	−0.273835	+	0.887753i	−0.122463	+	0.397015i	0.873495	+	0.486833i	$0.161848\pi$
$6$	−0.953127	+	0.215208i	−0.389113	+	0.0878582i
$7$	0.528093	−	2.59251i	0.199600	−	0.979877i
$7$	0.528093	−	2.59251i	0.199600	−	0.979877i
$8$	2.82836	+	0.0197876i	0.999976	+	0.00699599i
$9$	0.188515	−	2.51556i	0.0628385	−	0.838521i
$10$	−0.891391	−	0.965196i	−0.281883	−	0.305222i
$11$	2.90057	−	0.217368i	0.874555	−	0.0655388i	0.370115	−	0.928986i	$-0.379318\pi$
$11$	2.90057	−	0.217368i	0.874555	−	0.0655388i	0.504440	+	0.863447i	$0.331699\pi$
$12$	0.413464	−	1.31855i	0.119357	−	0.380633i
$13$	1.19293	−	2.47715i	0.330859	−	0.687037i	−0.667481	−	0.744627i	$-0.732627\pi$
$13$	1.19293	−	2.47715i	0.330859	−	0.687037i	0.998340	+	0.0575903i	$0.0183417\pi$
$14$	2.79596	+	2.48649i	0.747251	+	0.664542i
$15$	−0.578324	+	0.278506i	−0.149323	+	0.0719100i
$16$	−2.03223	+	3.44530i	−0.508056	+	0.861324i
$17$	0.271023	+	0.0408501i	0.0657327	+	0.00990762i	0.181826	−	0.983331i	$-0.441799\pi$
$17$	0.271023	+	0.0408501i	0.0657327	+	0.00990762i	−0.116094	+	0.993238i	$0.537037\pi$
$18$	2.94293	+	2.01652i	0.693655	+	0.475299i
$19$	0.864835	+	0.499313i	0.198407	+	0.114550i	0.595912	−	0.803050i	$-0.296791\pi$
$19$	0.864835	+	0.499313i	0.198407	+	0.114550i	−0.397505	+	0.917600i	$0.630124\pi$
$20$	1.81338	−	0.405003i	0.405483	−	0.0905613i
$21$	1.56125	−	0.950882i	0.340693	−	0.207499i
$22$	−1.79343	+	3.70199i	−0.382361	+	0.789267i
$23$	−2.51518	+	0.379103i	−0.524452	+	0.0790485i	−0.405932	−	0.913903i	$-0.633053\pi$
$23$	−2.51518	+	0.379103i	−0.524452	+	0.0790485i	−0.118520	+	0.992952i	$0.537815\pi$
$24$	1.31917	+	1.44183i	0.269274	+	0.294311i
$25$	3.41808	+	2.33040i	0.683615	+	0.466081i
$26$	2.18284	+	3.21774i	0.428091	+	0.631051i
$27$	2.98326	−	2.37907i	0.574129	−	0.457853i
$28$	−5.02623	+	1.65440i	−0.949867	+	0.312653i
$29$	6.85394	+	5.46583i	1.27274	+	1.01498i	0.998579	+	0.0532967i	$0.0169729\pi$
$29$	6.85394	+	5.46583i	1.27274	+	1.01498i	0.274165	+	0.961683i	$0.411599\pi$
$30$	0.0699487	−	0.905073i	0.0127708	−	0.165243i
$31$	−4.98617	−	8.63630i	−0.895542	−	1.55113i	−0.833132	−	0.553075i	$-0.813454\pi$
$31$	−4.98617	−	8.63630i	−0.895542	−	1.55113i	−0.0624107	−	0.998051i	$-0.519879\pi$
$32$	−2.77111	−	4.93163i	−0.489868	−	0.871796i
$33$	1.47322	+	1.36695i	0.256455	+	0.237955i
$34$	−0.242379	+	0.302484i	−0.0415677	+	0.0518756i
$35$	2.15690	+	1.17874i	0.364582	+	0.199243i
$36$	−4.55576	+	2.16782i	−0.759293	+	0.361303i
$37$	−6.06557	+	2.38056i	−0.997174	+	0.391362i	−0.807105	−	0.590409i	$-0.798967\pi$
$37$	−6.06557	+	2.38056i	−0.997174	+	0.391362i	−0.190070	+	0.981771i	$0.560871\pi$
$38$	−1.22471	+	0.703281i	−0.198673	+	0.114087i
$39$	1.81526	−	0.559934i	0.290674	−	0.0896612i
$40$	−0.792071	+	2.50546i	−0.125237	+	0.396149i
$41$	0.608266	+	2.66499i	0.0949952	+	0.416201i	0.999957	−	0.00929193i	$-0.00295776\pi$
$41$	0.608266	+	2.66499i	0.0949952	+	0.416201i	−0.904962	+	0.425493i	$0.860101\pi$
$42$	0.0545889	+	2.58464i	0.00842324	+	0.398819i
$43$	7.65784	+	1.74785i	1.16781	+	0.266545i	0.762102	−	0.647458i	$-0.224168\pi$
$43$	7.65784	+	1.74785i	1.16781	+	0.266545i	0.405708	+	0.914003i	$0.367025\pi$
$44$	−3.25461	−	4.82180i	−0.490651	−	0.726914i
$45$	2.18158	+	0.856205i	0.325210	+	0.127636i
$46$	1.32200	−	3.34545i	0.194919	−	0.493260i
$47$	5.47460	−	3.73252i	0.798552	−	0.544443i	−0.0939024	−	0.995581i	$-0.529934\pi$
$47$	5.47460	−	3.73252i	0.798552	−	0.544443i	0.892454	+	0.451138i	$0.148982\pi$
$48$	−2.70004	+	0.589825i	−0.389718	+	0.0851339i
$49$	−6.44224	−	2.73818i	−0.920319	−	0.391168i
$50$	−5.27700	+	2.52613i	−0.746280	+	0.357248i
$51$	0.106678	+	0.156467i	0.0149378	+	0.0219098i
$52$	−5.48533	+	0.385350i	−0.760678	+	0.0534384i
$53$	3.42053	+	1.34246i	0.469846	+	0.184401i	0.588438	−	0.808542i	$-0.299743\pi$
$53$	3.42053	+	1.34246i	0.469846	+	0.184401i	−0.118593	+	0.992943i	$0.537838\pi$
$54$	0.791826	+	5.33786i	0.107754	+	0.726390i
$55$	−0.601310	+	2.63451i	−0.0810806	+	0.355237i
$56$	1.54494	−	7.32210i	0.206451	−	0.978457i
$57$	0.153535	+	0.672680i	0.0203362	+	0.0890987i
$58$	−11.5512	+	4.50247i	−1.51675	+	0.591203i
$59$	0.968189	+	3.13879i	0.126048	+	0.408636i	0.996498	−	0.0836206i	$-0.0266484\pi$
$59$	0.968189	+	3.13879i	0.126048	+	0.408636i	−0.870450	+	0.492257i	$0.836172\pi$
$60$	1.05733	+	0.728120i	0.136500	+	0.0939999i
$61$	−14.2533	+	5.59401i	−1.82495	+	0.716240i	−0.840197	+	0.542281i	$0.817561\pi$
$61$	−14.2533	+	5.59401i	−1.82495	+	0.716240i	−0.984753	+	0.173959i	$0.944344\pi$
$62$	14.1030	+	0.0328884i	1.79108	+	0.00417683i
$63$	−6.42207	−	1.81718i	−0.809105	−	0.228943i
$64$	7.99922	+	0.111933i	0.999902	+	0.0139916i
$65$	1.87243	+	1.73736i	0.232246	+	0.215493i
$66$	−2.71783	+	0.831405i	−0.334542	+	0.102339i
$67$	2.13348	−	1.23176i	0.260645	−	0.150484i	−0.363983	−	0.931405i	$-0.618584\pi$
$67$	2.13348	−	1.23176i	0.260645	−	0.150484i	0.624629	+	0.780922i	$0.285250\pi$
$68$	−0.197886	−	0.511204i	−0.0239972	−	0.0619926i
$69$	−1.37402	−	1.09575i	−0.165413	−	0.131913i
$70$	−2.97302	+	1.80123i	−0.355344	+	0.215288i
$71$	−4.71309	−	5.91003i	−0.559341	−	0.701391i	0.419095	−	0.907942i	$-0.362347\pi$
$71$	−4.71309	−	5.91003i	−0.559341	−	0.701391i	−0.978436	+	0.206551i	$0.933776\pi$
$72$	0.582966	−	7.11118i	0.0687032	−	0.838061i
$73$	11.0283	+	7.51897i	1.29077	+	0.880029i	0.997117	−	0.0758844i	$-0.0241780\pi$
$73$	11.0283	+	7.51897i	1.29077	+	0.880029i	0.293649	+	0.955913i	$0.405130\pi$
$74$	1.39467	−	9.10886i	0.162127	−	1.05888i
$75$	0.426009	+	2.82639i	0.0491913	+	0.326363i
$76$	0.00931520	−	1.99723i	0.00106853	−	0.229098i
$77$	0.968243	−	7.63455i	0.110342	−	0.870038i
$78$	−0.603914	+	2.61776i	−0.0683797	+	0.296403i
$79$	4.13722	−	7.16587i	0.465474	−	0.806224i	−0.533749	−	0.845643i	$-0.679217\pi$
$79$	4.13722	−	7.16587i	0.465474	−	0.806224i	0.999223	+	0.0394190i	$0.0125507\pi$
$80$	−2.50207	−	2.74756i	−0.279740	−	0.307186i
$81$	−4.87637	−	0.734994i	−0.541819	−	0.0816660i
$82$	−3.69137	−	1.14807i	−0.407644	−	0.126783i
$83$	−7.05258	−	14.6448i	−0.774121	−	1.60748i	−0.794182	−	0.607681i	$-0.792100\pi$
$83$	−7.05258	−	14.6448i	−0.774121	−	1.60748i	0.0200603	−	0.999799i	$-0.493614\pi$
$84$	−3.20001	−	1.76823i	−0.349150	−	0.192930i
$85$	−0.110481	+	0.229415i	−0.0119833	+	0.0248836i
$86$	−7.57455	+	8.12534i	−0.816785	+	0.876178i
$87$	0.452643	+	6.04010i	0.0485284	+	0.647567i
$88$	8.20815	−	0.557398i	0.874992	−	0.0594188i
$89$	−0.674018	+	8.99415i	−0.0714458	+	0.953378i	0.840167	+	0.542328i	$0.182457\pi$
$89$	−0.674018	+	8.99415i	−0.0714458	+	0.953378i	−0.911613	+	0.411050i	$0.865162\pi$
$90$	−2.59605	+	2.06040i	−0.273648	+	0.217185i
$91$	−5.79205	−	4.40085i	−0.607172	−	0.461334i
$92$	3.15323	+	3.99207i	0.328746	+	0.416203i
$93$	2.03092	−	6.58407i	0.210596	−	0.682736i
$94$	0.678463	+	9.34588i	0.0699782	+	0.963954i
$95$	−0.680089	+	0.631030i	−0.0697756	+	0.0647423i
$96$	1.19552	−	3.72116i	0.122017	−	0.379789i
$97$	−2.79586			−0.283877			−0.141939	−	0.989875i	$-0.545334\pi$
$97$	−2.79586			−0.283877			−0.141939	+	0.989875i	$0.545334\pi$
$98$	7.92278	−	5.93545i	0.800321	−	0.599571i
$99$		−	7.33754i		−	0.737451i
$100$	0.656778	−	8.24771i	0.0656778	−	0.824771i
$101$	−5.47702	−	5.90282i	−0.544984	−	0.587353i	0.399162	−	0.916880i	$-0.369301\pi$
$101$	−5.47702	−	5.90282i	−0.544984	−	0.587353i	−0.944146	+	0.329527i	$0.893111\pi$
$102$	−0.267111	+	0.0193909i	−0.0264479	+	0.00191998i
$103$	−3.34727	−	1.03250i	−0.329816	−	0.101735i	0.125425	−	0.992103i	$-0.459971\pi$
$103$	−3.34727	−	1.03250i	−0.329816	−	0.101735i	−0.455241	+	0.890368i	$0.650447\pi$
$104$	3.42305	−	6.98265i	0.335658	−	0.684705i
$105$	0.416622	+	1.64639i	0.0406581	+	0.160671i
$106$	−4.07039	+	3.23053i	−0.395351	+	0.313777i
$107$	−3.55111	−	0.266119i	−0.343299	−	0.0257267i	−0.0980346	−	0.995183i	$-0.531256\pi$
$107$	−3.55111	−	0.266119i	−0.343299	−	0.0257267i	−0.245264	+	0.969456i	$0.578875\pi$
$108$	−7.09086	−	2.82119i	−0.682318	−	0.271469i
$109$	−2.11851	+	0.158760i	−0.202916	+	0.0152065i	−0.175800	−	0.984426i	$-0.556251\pi$
$109$	−2.11851	+	0.158760i	−0.202916	+	0.0152065i	−0.0271158	+	0.999632i	$0.508632\pi$
$110$	−2.79534	−	2.60586i	−0.266526	−	0.248459i
$111$	−4.05625	−	1.95339i	−0.385002	−	0.185407i
$112$	7.85876	+	7.08801i	0.742583	+	0.669754i
$113$	8.45264	−	4.07058i	0.795158	−	0.382928i	0.00822479	−	0.999966i	$-0.497382\pi$
$113$	8.45264	−	4.07058i	0.795158	−	0.382928i	0.786933	+	0.617038i	$0.211668\pi$
$114$	−0.931754	−	0.289789i	−0.0872668	−	0.0271413i
$115$	0.352197	−	2.33667i	0.0328425	−	0.217896i
$116$	2.69399	−	17.3248i	0.250131	−	1.60857i
$117$	−6.00653	−	3.46787i	−0.555304	−	0.320605i
$118$	−4.52641	−	1.04424i	−0.416690	−	0.0961296i
$119$	0.249030	−	0.681058i	0.0228285	−	0.0624325i
$120$	−1.64122	+	0.776272i	−0.149822	+	0.0708636i
$121$	−2.51108	+	0.378484i	−0.228280	+	0.0344077i
$122$	3.27730	−	21.4047i	0.296713	−	1.93789i
$123$	−1.06393	+	1.56049i	−0.0959310	+	0.140705i
$124$	−10.0528	+	17.2259i	−0.902767	+	1.54693i
$125$	−6.63652	+	5.29245i	−0.593589	+	0.473371i
$126$	6.78200	−	6.56466i	0.604189	−	0.584827i
$127$	−1.13410	+	1.42212i	−0.100636	+	0.126193i	−0.829599	−	0.558360i	$-0.811431\pi$
$127$	−1.13410	+	1.42212i	−0.100636	+	0.126193i	0.728964	+	0.684553i	$0.240002\pi$
$128$	−5.81604	+	9.70431i	−0.514070	+	0.857748i
$129$	2.71355	+	4.70000i	0.238915	+	0.413812i
$130$	−3.45430	+	1.05669i	−0.302962	+	0.0926782i
$131$	−5.23563	+	5.64267i	−0.457439	+	0.493002i	−0.919083	−	0.394063i	$-0.871069\pi$
$131$	−5.23563	+	5.64267i	−0.457439	+	0.493002i	0.461644	+	0.887065i	$0.347260\pi$
$132$	0.912671	−	3.91443i	0.0794378	−	0.340707i
$133$	1.75119	−	1.97841i	0.151847	−	0.171550i
$134$	−0.00812462	+	3.48394i	−0.000701860	+	0.300967i
$135$	1.29511	+	3.29987i	0.111465	+	0.284008i
$136$	0.765742	+	0.120902i	0.0656618	+	0.0103672i
$137$	8.10022	−	2.49859i	0.692049	−	0.213469i	0.0712728	−	0.997457i	$-0.477294\pi$
$137$	8.10022	−	2.49859i	0.692049	−	0.213469i	0.620776	+	0.783988i	$0.286818\pi$
$138$	2.31571	−	0.902621i	0.197126	−	0.0768362i
$139$	−13.4095	+	3.06063i	−1.13738	+	0.259599i	−0.749431	−	0.662082i	$-0.769673\pi$
$139$	−13.4095	+	3.06063i	−1.13738	+	0.259599i	−0.387948	+	0.921681i	$0.626816\pi$
$140$	−0.0923421	−	4.91508i	−0.00780433	−	0.415400i
$141$	4.46326	+	1.01871i	0.375875	+	0.0857909i
$142$	10.5746	−	1.56866i	0.887402	−	0.131639i
$143$	2.92173	−	7.44444i	0.244327	−	0.622535i
$144$	8.28375	+	5.76168i	0.690313	+	0.480140i
$145$	−6.72916	+	4.58786i	−0.558826	+	0.381001i
$146$	−17.0261	+	8.15046i	−1.40909	+	0.674537i
$147$	−1.64069	−	4.54972i	−0.135321	−	0.375254i
$148$	10.1508	+	8.17275i	0.834392	+	0.671796i
$149$	10.9960	+	16.1282i	0.900829	+	1.32127i	0.946630	+	0.322322i	$0.104464\pi$
$149$	10.9960	+	16.1282i	0.900829	+	1.32127i	−0.0458012	+	0.998951i	$0.514584\pi$
$150$	−3.75938	−	1.48558i	−0.306952	−	0.121297i
$151$	−4.46287	+	11.3712i	−0.363183	+	0.925376i	0.626150	+	0.779703i	$0.284630\pi$
$151$	−4.46287	+	11.3712i	−0.363183	+	0.925376i	−0.989333	+	0.145673i	$0.953465\pi$
$152$	2.43618	+	1.42935i	0.197601	+	0.115935i
$153$	0.153853	−	0.674075i	0.0124383	−	0.0544957i
$154$	8.65035	+	6.60449i	0.697065	+	0.532205i
$155$	9.03229	−	2.06156i	0.725491	−	0.165589i
$156$	−2.77301	−	2.59715i	−0.222019	−	0.207939i
$157$	3.27324	+	10.6116i	0.261233	+	0.846896i	0.987244	+	0.159213i	$0.0508958\pi$
$157$	3.27324	+	10.6116i	0.261233	+	0.846896i	−0.726011	+	0.687683i	$0.758628\pi$
$158$	5.82726	+	10.1477i	0.463592	+	0.807307i
$159$	0.927544	+	2.36334i	0.0735590	+	0.187425i
$160$	5.13689	−	1.10961i	0.406107	−	0.0877223i
$161$	−0.345423	+	6.72085i	−0.0272231	+	0.529677i
$162$	4.36100	−	5.44243i	0.342632	−	0.427598i
$163$	−5.94201	+	6.40396i	−0.465414	+	0.501597i	−0.921521	−	0.388328i	$-0.873053\pi$
$163$	−5.94201	+	6.40396i	−0.465414	+	0.501597i	0.456107	+	0.889925i	$0.349243\pi$
$164$	4.02493	−	3.69980i	0.314294	−	0.288906i
$165$	−1.61693	+	0.933536i	−0.125878	+	0.0726757i
$166$	22.9190	+	1.77130i	1.77886	+	0.137480i
$167$	−10.3803	+	13.0164i	−0.803248	+	1.00724i	0.196395	+	0.980525i	$0.437077\pi$
$167$	−10.3803	+	13.0164i	−0.803248	+	1.00724i	−0.999643	+	0.0267168i	$0.991495\pi$
$168$	4.43459	−	2.65854i	0.342136	−	0.205111i
$169$	3.39220	+	4.25368i	0.260938	+	0.327206i
$170$	−0.202159	−	0.298004i	−0.0155049	−	0.0228558i
$171$	1.41909	−	2.08142i	0.108520	−	0.159170i
$172$	−4.56041	−	15.0331i	−0.347728	−	1.14626i
$173$	1.83839	+	12.1969i	0.139770	+	0.927313i	0.943274	+	0.332014i	$0.107728\pi$
$173$	1.83839	+	12.1969i	0.139770	+	0.927313i	−0.803504	+	0.595299i	$0.797034\pi$
$174$	−7.70896	−	3.73461i	−0.584415	−	0.283120i
$175$	7.84666	−	7.63073i	0.593152	−	0.576829i
$176$	−5.14572	+	10.4351i	−0.387873	+	0.786572i
$177$	−1.13476	+	1.96545i	−0.0852935	+	0.147733i
$178$	−10.5221	−	7.20988i	−0.788668	−	0.540403i
$179$	−3.75478	+	24.9113i	−0.280645	+	1.86196i	0.192939	+	0.981211i	$0.438198\pi$
$179$	−3.75478	+	24.9113i	−0.280645	+	1.86196i	−0.473584	+	0.880749i	$0.657040\pi$
$180$	−0.676960	−	4.63801i	−0.0504576	−	0.345697i
$181$	−5.25171	−	10.9053i	−0.390356	−	0.810583i	−0.999842	−	0.0177859i	$-0.994338\pi$
$181$	−5.25171	−	10.9053i	−0.390356	−	0.810583i	0.609486	−	0.792797i	$-0.291376\pi$
$182$	9.49478	−	3.95978i	0.703800	−	0.293519i
$183$	−9.53166	−	4.59020i	−0.704600	−	0.339318i
$184$	−7.12134	+	1.02247i	−0.524992	+	0.0753775i
$185$	−0.452381	−	6.03661i	−0.0332597	−	0.443820i
$186$	6.61105	+	7.15843i	0.484746	+	0.524882i
$187$	0.795001	+	0.0595771i	0.0581362	+	0.00435671i
$188$	−11.9126	−	5.80539i	−0.868812	−	0.423401i
$189$	−4.59233	−	8.99052i	−0.334043	−	0.653964i
$190$	−0.288972	−	1.27982i	−0.0209642	−	0.0928478i
$191$	17.9799	+	5.54606i	1.30098	+	0.401299i	0.866407	−	0.499339i	$-0.166424\pi$
$191$	17.9799	+	5.54606i	1.30098	+	0.401299i	0.434571	+	0.900637i	$0.356900\pi$
$192$	3.70255	+	4.10410i	0.267208	+	0.296188i
$193$	2.69786	−	2.50325i	0.194196	−	0.180188i	−0.577081	−	0.816687i	$-0.695808\pi$
$193$	2.69786	−	2.50325i	0.194196	−	0.180188i	0.771278	+	0.636499i	$0.219618\pi$
$194$	1.98495	−	3.41960i	0.142511	−	0.245513i
$195$			1.76483i			0.126382i
$196$	1.63474	+	13.9042i	0.116767	+	0.993159i
$197$		−	6.64325i		−	0.473312i	−0.971593	−	0.236656i	$-0.923949\pi$
$197$		−	6.64325i		−	0.473312i	0.971593	−	0.236656i	$-0.0760515\pi$
$198$	8.97450	+	5.20937i	0.637790	+	0.370214i
$199$	6.63013	−	6.15186i	0.469998	−	0.436094i	−0.409276	−	0.912410i	$-0.634219\pi$
$199$	6.63013	−	6.15186i	0.469998	−	0.436094i	0.879274	+	0.476316i	$0.158028\pi$
$200$	9.62143	+	6.65885i	0.680338	+	0.470852i
$201$	1.62650	+	0.501709i	0.114725	+	0.0353878i
$202$	11.1082	−	2.50813i	0.781568	−	0.176471i
$203$	17.7897	−	14.8824i	1.24860	−	1.04454i
$204$	0.165921	−	0.340468i	0.0116168	−	0.0238375i
$205$	−2.53242	−	0.189778i	−0.176872	−	0.0132547i
$206$	3.63927	−	3.36099i	0.253560	−	0.234171i
$207$	0.479507	+	6.39857i	0.0333280	+	0.444732i
$208$	6.11019	+	9.14412i	0.423666	+	0.634030i
$209$	2.61705	+	1.26030i	0.181025	+	0.0871771i
$210$	−2.30947	−	0.659306i	−0.159369	−	0.0454964i
$211$	3.89327	+	8.08445i	0.268024	+	0.556557i	0.990928	−	0.134391i	$-0.0429078\pi$
$211$	3.89327	+	8.08445i	0.268024	+	0.556557i	−0.722905	+	0.690948i	$0.757193\pi$
$212$	−1.06142	−	7.27202i	−0.0728984	−	0.499444i
$213$	0.778429	−	5.16454i	0.0533371	−	0.353869i
$214$	2.84664	−	4.15440i	0.194592	−	0.283989i
$215$	−3.64865	+	6.31965i	−0.248836	+	0.430996i
$216$	8.48481	−	6.66984i	0.577318	−	0.453825i
$217$	−25.0229	+	8.36593i	−1.69866	+	0.567917i
$218$	1.30988	−	2.70384i	0.0887162	−	0.183127i
$219$	1.37450	+	9.11924i	0.0928804	+	0.616221i
$220$	5.17179	−	1.56891i	0.348682	−	0.105776i
$221$	0.424503	−	0.622632i	0.0285552	−	0.0418828i
$222$	5.26895	−	3.57434i	0.353629	−	0.239894i
$223$	3.28801	+	4.12304i	0.220182	+	0.276099i	0.879638	−	0.475644i	$-0.157785\pi$
$223$	3.28801	+	4.12304i	0.220182	+	0.276099i	−0.659456	+	0.751743i	$0.729213\pi$
$224$	−14.2487	+	4.57979i	−0.952032	+	0.306000i
$225$	6.50664	−	8.15907i	0.433776	−	0.543938i
$226$	−1.02235	+	13.2283i	−0.0680059	+	0.879935i
$227$	6.31928	−	3.64844i	0.419426	−	0.242156i	−0.275406	−	0.961328i	$-0.588812\pi$
$227$	6.31928	−	3.64844i	0.419426	−	0.242156i	0.694832	+	0.719173i	$0.255479\pi$
$228$	1.01595	−	0.933882i	0.0672828	−	0.0618479i
$229$	−6.36010	+	6.85456i	−0.420287	+	0.452962i	−0.907332	−	0.420415i	$-0.861884\pi$
$229$	−6.36010	+	6.85456i	−0.420287	+	0.452962i	0.487045	+	0.873377i	$0.338075\pi$
$230$	2.60792	+	2.08972i	0.171961	+	0.137792i
$231$	4.32183	−	3.09746i	0.284355	−	0.203798i
$232$	19.2772	+	15.5949i	1.26561	+	1.02386i
$233$	−7.90695	−	20.1466i	−0.518002	−	1.31985i	−0.915527	−	0.402256i	$-0.868226\pi$
$233$	−7.90695	−	20.1466i	−0.518002	−	1.31985i	0.397526	−	0.917591i	$-0.369869\pi$
$234$	8.50593	−	4.88449i	0.556050	−	0.319309i
$235$	1.81441	+	5.88218i	0.118359	+	0.383711i
$236$	4.49077	−	4.79485i	0.292324	−	0.312118i
$237$	5.57371	−	1.27216i	0.362052	−	0.0826359i
$238$	0.656195	+	0.788111i	0.0425348	+	0.0510856i
$239$	−0.0151325	+	0.0662997i	−0.000978838	+	0.00428857i	−0.975415	−	0.220376i	$-0.929272\pi$
$239$	−0.0151325	+	0.0662997i	−0.000978838	+	0.00428857i	0.974436	+	0.224665i	$0.0721287\pi$
$240$	0.215749	−	2.55849i	0.0139266	−	0.165150i
$241$	−5.22417	+	13.3110i	−0.336518	+	0.857435i	0.658014	+	0.753006i	$0.271397\pi$
$241$	−5.22417	+	13.3110i	−0.336518	+	0.857435i	−0.994532	+	0.104429i	$0.966698\pi$
$242$	1.31985	−	3.33999i	0.0848430	−	0.214703i
$243$	−8.36783	−	12.2734i	−0.536797	−	0.787336i
$244$	23.8531	+	19.2049i	1.52704	+	1.22947i
$245$	4.19493	−	4.96930i	0.268005	−	0.317477i
$246$	−1.15328	−	2.40917i	−0.0735306	−	0.153603i
$247$	2.26856	−	1.54668i	0.144345	−	0.0984127i
$248$	−13.9318	−	24.5252i	−0.884669	−	1.55735i
$249$	4.10305	−	10.4544i	0.260020	−	0.662520i
$250$	−1.76148	−	11.8745i	−0.111406	−	0.751010i
$251$	−18.3670	−	4.19215i	−1.15932	−	0.264606i	−0.400741	−	0.916191i	$-0.631247\pi$
$251$	−18.3670	−	4.19215i	−1.15932	−	0.264606i	−0.758576	+	0.651585i	$0.774104\pi$
$252$	3.21423	+	12.9557i	0.202478	+	0.816130i
$253$	−7.21306	+	1.64634i	−0.453482	+	0.103504i
$254$	−0.934217	−	2.39677i	−0.0586180	−	0.150387i
$255$	−0.168116	+	0.0518570i	−0.0105278	+	0.00324741i
$256$	−7.74012	−	14.0032i	−0.483757	−	0.875202i
$257$	1.57431	+	4.01127i	0.0982025	+	0.250216i	0.971530	−	0.236918i	$-0.0761374\pi$
$257$	1.57431	+	4.01127i	0.0982025	+	0.250216i	−0.873327	+	0.487134i	$0.838042\pi$
$258$	−7.67505	−	0.0178984i	−0.477828	−	0.00111430i
$259$	2.96845	+	16.9822i	0.184450	+	1.05522i
$260$	1.15998	−	4.97514i	0.0719390	−	0.308545i
$261$	15.0417	−	16.2111i	0.931059	−	1.00344i
$262$	−3.18441	−	10.4097i	−0.196734	−	0.643116i
$263$	8.79783	+	15.2383i	0.542497	+	0.939633i	0.998760	+	0.0497876i	$0.0158544\pi$
$263$	8.79783	+	15.2383i	0.542497	+	0.939633i	−0.456263	+	0.889845i	$0.650812\pi$
$264$	4.13975	+	3.89537i	0.254784	+	0.239744i
$265$	−2.12843	+	2.66897i	−0.130749	+	0.163954i
$266$	1.17651	+	3.54646i	0.0721362	+	0.217447i
$267$	−4.87217	+	3.88543i	−0.298172	+	0.237784i
$268$	−4.25541	−	2.48340i	−0.259941	−	0.151698i
$269$	−10.8059	+	15.8493i	−0.658845	+	0.966349i	0.340811	+	0.940132i	$0.389298\pi$
$269$	−10.8059	+	15.8493i	−0.658845	+	0.966349i	−0.999656	+	0.0262167i	$0.991654\pi$
$270$	−4.95553	−	0.758748i	−0.301584	−	0.0461760i
$271$	10.9529	−	1.65088i	0.665338	−	0.100284i	0.192315	−	0.981333i	$-0.438401\pi$
$271$	10.9529	−	1.65088i	0.665338	−	0.100284i	0.473024	+	0.881050i	$0.343162\pi$
$272$	−0.691521	+	0.850738i	−0.0419296	+	0.0515835i
$273$	−0.493008	−	5.00178i	−0.0298382	−	0.302722i
$274$	−2.69484	+	11.6812i	−0.162801	+	0.705688i
$275$	10.4209	+	6.01652i	0.628405	+	0.362810i
$276$	−0.540071	+	3.47315i	−0.0325085	+	0.209059i
$277$	0.710237	−	4.71212i	0.0426740	−	0.283124i	−0.957308	−	0.289069i	$-0.906654\pi$
$277$	0.710237	−	4.71212i	0.0426740	−	0.283124i	0.999982	+	0.00594523i	$0.00189244\pi$
$278$	5.77679	−	18.5740i	0.346469	−	1.11399i
$279$	−22.6651	+	10.9149i	−1.35693	+	0.653461i
$280$	6.07716	+	3.37657i	0.363180	+	0.201789i
$281$	−6.13058	−	2.95233i	−0.365720	−	0.176121i	0.241993	−	0.970278i	$-0.422199\pi$
$281$	−6.13058	−	2.95233i	−0.365720	−	0.176121i	−0.607713	+	0.794156i	$0.707913\pi$
$282$	−4.41472	+	4.73574i	−0.262893	+	0.282009i
$283$	−10.0683	+	0.754512i	−0.598496	+	0.0448511i	−0.370534	−	0.928819i	$-0.620825\pi$
$283$	−10.0683	+	0.754512i	−0.598496	+	0.0448511i	−0.227962	+	0.973670i	$0.573206\pi$
$284$	−5.58896	+	14.0474i	−0.331643	+	0.833561i
$285$	−0.639217	−	0.0479027i	−0.0378639	−	0.00283751i
$286$	7.03093	+	8.85880i	0.415747	+	0.523832i
$287$	7.23024	−	0.169575i	0.426787	−	0.0100097i
$288$	−12.9282	+	6.04122i	−0.761802	+	0.355983i
$289$	−16.1730	−	4.98870i	−0.951350	−	0.293453i
$290$	−0.833940	−	11.4876i	−0.0489707	−	0.674574i
$291$	−1.31392	−	1.41607i	−0.0770233	−	0.0830114i
$292$	2.11907	−	26.6110i	0.124009	−	1.55729i
$293$			15.1150i			0.883026i	0.897255	+	0.441513i	$0.145558\pi$
$293$			15.1150i			0.883026i	−0.897255	+	0.441513i	$0.854442\pi$
$294$	6.72955	+	1.22341i	0.392475	+	0.0713507i
$295$	−3.05160			−0.177671
$296$	−17.2027	+	6.61306i	−0.999888	+	0.384376i
$297$	8.13603	−	7.54913i	0.472100	−	0.438045i
$298$	−27.5330	+	1.99876i	−1.59494	+	0.115785i
$299$	−2.06135	+	6.68272i	−0.119211	+	0.386472i
$300$	4.48601	−	3.54337i	0.259000	−	0.204577i
$301$	8.57538	−	18.9300i	0.494277	−	1.09111i
$302$	−10.7396	−	13.5316i	−0.617993	−	0.778657i
$303$	0.415771	−	5.54808i	0.0238854	−	0.318729i
$304$	−3.47782	+	1.96490i	−0.199467	+	0.112695i
$305$	−1.06304	−	14.1853i	−0.0608694	−	0.812245i
$306$	0.715226	+	0.666743i	0.0408867	+	0.0381152i
$307$	14.1687	−	29.4215i	0.808648	−	1.67917i	0.0774628	−	0.996995i	$-0.475318\pi$
$307$	14.1687	−	29.4215i	0.808648	−	1.67917i	0.731185	−	0.682179i	$-0.238968\pi$
$308$	−14.2193	+	5.89125i	−0.810220	+	0.335685i
$309$	−1.05011	−	2.18057i	−0.0597385	−	0.124048i
$310$	−3.89109	+	12.5109i	−0.220999	+	0.710574i
$311$	−8.79804	−	1.32609i	−0.498891	−	0.0751957i	−0.105223	−	0.994449i	$-0.533556\pi$
$311$	−8.79804	−	1.32609i	−0.498891	−	0.0751957i	−0.393668	+	0.919253i	$0.628794\pi$
$312$	5.14529	−	1.54777i	0.291295	−	0.0876254i
$313$	−10.0012	+	17.3227i	−0.565304	+	0.979135i	0.431718	+	0.902009i	$0.357908\pi$
$313$	−10.0012	+	17.3227i	−0.565304	+	0.979135i	−0.997021	+	0.0771259i	$0.975426\pi$
$314$	−15.3028	−	3.53033i	−0.863588	−	0.199228i
$315$	3.37180	−	5.20360i	0.189979	−	0.293190i
$316$	−16.5487	−	0.0771842i	−0.930937	−	0.00434195i
$317$	0.901413	+	5.98048i	0.0506284	+	0.335897i	0.999778	+	0.0210719i	$0.00670790\pi$
$317$	0.901413	+	5.98048i	0.0506284	+	0.335897i	−0.949150	+	0.314825i	$0.898054\pi$
$318$	−3.54911	−	0.543409i	−0.199024	−	0.0304729i
$319$	21.0684	+	14.3642i	1.17960	+	0.804241i
$320$	−2.28984	+	7.07067i	−0.128006	+	0.395263i
$321$	−1.53406	−	1.92365i	−0.0856230	−	0.107368i
$322$	−7.97498	−	5.19402i	−0.444428	−	0.289452i
$323$	0.213993	+	0.170654i	0.0119069	+	0.00949544i
$324$	3.56046	+	9.19781i	0.197803	+	0.510990i
$325$	9.85028	−	5.68706i	0.546395	−	0.315461i
$326$	−3.61405	−	11.8142i	−0.200163	−	0.654328i
$327$	−1.07601	−	0.998387i	−0.0595032	−	0.0552109i
$328$	1.66766	+	7.54958i	0.0920812	+	0.416856i
$329$	−6.78550	−	16.1641i	−0.374096	−	0.891154i
$330$	0.00615754	−	2.64043i	0.000338961	−	0.145351i
$331$	−7.83959	+	3.07681i	−0.430903	+	0.169117i	−0.570872	−	0.821039i	$-0.693395\pi$
$331$	−7.83959	+	3.07681i	−0.430903	+	0.169117i	0.139969	+	0.990156i	$0.455300\pi$
$332$	−18.4381	+	26.7746i	−1.01192	+	1.46944i
$333$	4.84500	+	15.7071i	0.265504	+	0.860744i
$334$	−8.55072	−	21.9372i	−0.467875	−	1.20035i
$335$	0.509279	+	2.23130i	0.0278249	+	0.121909i
$336$	0.103253	+	7.31138i	0.00563290	+	0.398868i
$337$	4.55456	−	19.9549i	0.248103	−	1.08701i	−0.685323	−	0.728239i	$-0.740339\pi$
$337$	4.55456	−	19.9549i	0.248103	−	1.08701i	0.933426	−	0.358771i	$-0.116804\pi$
$338$	−7.61098	+	1.12902i	−0.413983	+	0.0614108i
$339$	6.03403	+	2.36818i	0.327723	+	0.128622i
$340$	0.508011	−	0.0356883i	0.0275508	−	0.00193547i
$341$	−16.3400	−	23.9664i	−0.884860	−	1.29785i
$342$	1.53827	+	3.21340i	0.0831802	+	0.173761i
$343$	−10.5009	+	15.2556i	−0.566993	+	0.823723i
$344$	21.6245	+	5.09508i	1.16592	+	0.274708i
$345$	1.34901	−	0.919739i	0.0726282	−	0.0495171i
$346$	−16.2231	−	6.41081i	−0.872160	−	0.344647i
$347$	−24.0091	−	9.42290i	−1.28888	−	0.505848i	−0.380804	−	0.924656i	$-0.624353\pi$
$347$	−24.0091	−	9.42290i	−1.28888	−	0.505848i	−0.908075	+	0.418808i	$0.862448\pi$
$348$	10.0408	−	6.77735i	0.538245	−	0.363304i
$349$	7.65664	+	1.74758i	0.409850	+	0.0935457i	0.422475	−	0.906375i	$-0.361161\pi$
$349$	7.65664	+	1.74758i	0.409850	+	0.0935457i	−0.0126245	+	0.999920i	$0.504019\pi$
$350$	3.76226	+	15.0147i	0.201102	+	0.802570i
$351$	−2.33448	−	10.2280i	−0.124606	−	0.545933i
$352$	−9.10979	−	13.7022i	−0.485553	−	0.730328i
$353$	21.3394	−	6.58234i	1.13578	−	0.350343i	0.330836	−	0.943688i	$-0.392669\pi$
$353$	21.3394	−	6.58234i	1.13578	−	0.350343i	0.804948	+	0.593346i	$0.202193\pi$
$354$	−1.59830	−	2.78331i	−0.0849487	−	0.147931i
$355$	6.53725	−	2.56568i	0.346961	−	0.136172i
$356$	16.2887	−	7.75083i	0.863298	−	0.410793i
$357$	0.461979	−	0.193933i	0.0244505	−	0.0102640i
$358$	−27.8031	−	22.2785i	−1.46944	−	1.17746i
$359$	17.9658	+	16.6698i	0.948196	+	0.879797i	0.992870	−	0.119204i	$-0.0380343\pi$
$359$	17.9658	+	16.6698i	0.948196	+	0.879797i	−0.0446737	+	0.999002i	$0.514225\pi$
$360$	6.15333	+	2.46482i	0.324309	+	0.129908i
$361$	−9.00137	−	15.5908i	−0.473756	−	0.820570i
$362$	17.0667	+	1.31900i	0.897004	+	0.0693251i
$363$	−1.37178	−	1.09396i	−0.0719999	−	0.0574180i
$364$	−1.89774	+	14.4243i	−0.0994686	+	0.756038i
$365$	−9.69493	+	7.73145i	−0.507456	+	0.404682i
$366$	12.3813	−	8.39923i	0.647183	−	0.439035i
$367$	14.7012	+	10.0231i	0.767395	+	0.523201i	0.882591	−	0.470141i	$-0.155797\pi$
$367$	14.7012	+	10.0231i	0.767395	+	0.523201i	−0.115196	+	0.993343i	$0.536749\pi$
$368$	3.80530	−	9.43598i	0.198365	−	0.491884i
$369$	6.81862	−	1.02774i	0.354963	−	0.0535021i
$370$	7.70451	+	3.73245i	0.400538	+	0.194041i
$371$	5.28670	−	8.15882i	0.274472	−	0.423585i
$372$	−13.4490	+	3.00372i	−0.697299	+	0.155736i
$373$	10.2033	+	5.89088i	0.528307	+	0.305018i	0.740327	−	0.672247i	$-0.234671\pi$
$373$	10.2033	+	5.89088i	0.528307	+	0.305018i	−0.212020	+	0.977265i	$0.568004\pi$
$374$	−0.637288	+	0.930062i	−0.0329534	+	0.0480924i
$375$	−5.79940	−	0.874119i	−0.299480	−	0.0451393i
$376$	15.5580	−	10.4486i	0.802341	−	0.538843i
$377$	21.7159	−	10.4578i	1.11843	−	0.538606i
$378$	14.2566	+	0.766067i	0.733281	+	0.0394022i
$379$	9.53647	−	19.8027i	0.489856	−	1.01720i	−0.498761	−	0.866739i	$-0.666212\pi$
$379$	9.53647	−	19.8027i	0.489856	−	1.01720i	0.988617	−	0.150456i	$-0.0480742\pi$
$380$	1.77049	+	0.555182i	0.0908245	+	0.0284802i
$381$	−1.25326	+	0.0939189i	−0.0642065	+	0.00481161i
$382$	−19.5483	+	18.0536i	−1.00018	+	0.923701i
$383$	1.02778	−	13.7147i	0.0525170	−	0.700790i	−0.907357	−	0.420360i	$-0.861904\pi$
$383$	1.02778	−	13.7147i	0.0525170	−	0.700790i	0.959874	−	0.280430i	$-0.0904771\pi$
$384$	−7.64836	+	1.61481i	−0.390304	+	0.0824053i
$385$	6.51245	+	2.95017i	0.331905	+	0.150355i
$386$	1.14633	+	5.07694i	0.0583466	+	0.258409i
$387$	5.84045	−	18.9343i	0.296887	−	0.962484i
$388$	2.77325	+	4.85557i	0.140790	+	0.246504i
$389$	10.5549	+	11.3755i	0.535156	+	0.576761i	0.941523	−	0.336949i	$-0.109395\pi$
$389$	10.5549	+	11.3755i	0.535156	+	0.576761i	−0.406367	+	0.913710i	$0.633204\pi$
$390$	−2.15855	−	1.25296i	−0.109303	−	0.0634462i
$391$	−0.697159			−0.0352569
$392$	−18.1668	−	7.87202i	−0.917560	−	0.397597i
$393$	−5.31843			−0.268279
$394$	8.12531	+	4.71645i	0.409347	+	0.237611i
$395$	5.22861	+	5.63510i	0.263080	+	0.283532i
$396$	−12.7431	+	7.27819i	−0.640364	+	0.365743i
$397$	11.7107	−	37.9651i	0.587743	−	1.90542i	0.219934	−	0.975515i	$-0.429416\pi$
$397$	11.7107	−	37.9651i	0.587743	−	1.90542i	0.367809	−	0.929901i	$-0.380108\pi$
$398$	2.81716	+	12.4768i	0.141212	+	0.625408i
$399$	1.82501	−	0.0428032i	0.0913649	−	0.00214284i
$400$	−14.9752	+	7.04037i	−0.748762	+	0.352018i
$401$	−0.276133	+	3.68474i	−0.0137894	+	0.184007i	0.986056	+	0.166415i	$0.0532191\pi$
$401$	−0.276133	+	3.68474i	−0.0137894	+	0.184007i	−0.999845	+	0.0175922i	$0.994400\pi$
$402$	−1.76839	+	1.63317i	−0.0881992	+	0.0814550i
$403$	−27.3415	+	2.04896i	−1.36198	+	0.102066i
$404$	−4.81870	+	15.3670i	−0.239739	+	0.764537i
$405$	1.98781	−	4.12774i	0.0987753	−	0.205109i
$406$	5.57258	+	32.3245i	0.276562	+	1.60424i
$407$	−17.0762	+	8.22345i	−0.846434	+	0.407621i
$408$	0.298626	+	0.444656i	0.0147842	+	0.0220138i
$409$	−18.1528	−	2.73609i	−0.897596	−	0.135291i	−0.315991	−	0.948762i	$-0.602337\pi$
$409$	−18.1528	−	2.73609i	−0.897596	−	0.135291i	−0.581605	+	0.813471i	$0.697575\pi$
$410$	2.03003	−	2.96264i	0.100256	−	0.146315i
$411$	5.07221	+	2.92844i	0.250194	+	0.144449i
$412$	1.52706	+	6.83733i	0.0752329	+	0.336851i
$413$	8.64865	−	0.852467i	0.425572	−	0.0419472i
$414$	−8.16648	−	3.95626i	−0.401360	−	0.194439i
$415$	14.9322	−	2.25067i	0.732995	−	0.110481i
$416$	−15.5221	+	0.981366i	−0.761034	+	0.0481154i
$417$	−7.85198	−	5.35339i	−0.384513	−	0.262157i
$418$	−3.39947	+	2.30613i	−0.166274	+	0.112796i
$419$	−27.2972	+	21.7688i	−1.33355	+	1.06347i	−0.341208	+	0.939988i	$0.610836\pi$
$419$	−27.2972	+	21.7688i	−1.33355	+	1.06347i	−0.992346	+	0.123486i	$0.960592\pi$
$420$	2.44603	−	2.35662i	0.119354	−	0.114991i
$421$	16.6545	+	13.2815i	0.811691	+	0.647302i	0.938752	−	0.344593i	$-0.111983\pi$
$421$	16.6545	+	13.2815i	0.811691	+	0.647302i	−0.127061	+	0.991895i	$0.540555\pi$
$422$	−12.6521	−	0.977820i	−0.615895	−	0.0475995i
$423$	−8.35733	−	14.4753i	−0.406348	−	0.703815i
$424$	9.64791	+	3.86464i	0.468544	+	0.187683i
$425$	0.831180	+	0.771222i	0.0403181	+	0.0374098i
$426$	5.76406	+	4.61871i	0.279270	+	0.223777i
$427$	6.97547	+	39.9060i	0.337567	+	1.93119i
$428$	3.06022	+	6.43116i	0.147921	+	0.310862i
$429$	5.14358	−	2.01871i	0.248334	−	0.0974641i
$430$	−5.13911	−	8.94934i	−0.247830	−	0.431575i
$431$	9.28656	−	2.86453i	0.447318	−	0.137979i	−0.0629087	−	0.998019i	$-0.520038\pi$
$431$	9.28656	−	2.86453i	0.447318	−	0.137979i	0.510227	+	0.860040i	$0.329561\pi$
$432$	2.13394	+	15.1130i	0.102669	+	0.727126i
$433$	−8.45226	−	37.0318i	−0.406190	−	1.77963i	−0.601481	−	0.798887i	$-0.705422\pi$
$433$	−8.45226	−	37.0318i	−0.406190	−	1.77963i	0.195291	−	0.980745i	$-0.437435\pi$
$434$	7.53295	−	36.5448i	0.361593	−	1.75421i
$435$	−5.48607	−	1.25216i	−0.263037	−	0.0600364i
$436$	2.37709	+	3.52173i	0.113842	+	0.168660i
$437$	−2.36451	−	0.928002i	−0.113110	−	0.0443924i
$438$	−12.1295	−	4.79316i	−0.579571	−	0.229026i
$439$	1.16125	−	0.791729i	0.0554236	−	0.0377871i	−0.535291	−	0.844667i	$-0.679798\pi$
$439$	1.16125	−	0.791729i	0.0554236	−	0.0377871i	0.590715	+	0.806880i	$0.298846\pi$
$440$	−1.75285	+	7.43944i	−0.0835639	+	0.354662i
$441$	−8.10251	+	15.6897i	−0.385834	+	0.747127i
$442$	0.460156	+	0.961251i	0.0218874	+	0.0457221i
$443$	19.6367	+	28.8018i	0.932970	+	1.36842i	0.929659	+	0.368421i	$0.120102\pi$
$443$	19.6367	+	28.8018i	0.932970	+	1.36842i	0.00331110	+	0.999995i	$0.498946\pi$
$444$	0.630998	+	8.98205i	0.0299459	+	0.426269i
$445$	−7.80001	−	3.06128i	−0.369756	−	0.145118i
$446$	−7.37722	+	1.09435i	−0.349321	+	0.0518189i
$447$	−3.00113	+	13.1488i	−0.141948	+	0.621917i
$448$	4.51452	−	20.6790i	0.213291	−	0.976989i
$449$	4.61070	+	20.2008i	0.217592	+	0.953335i	0.959251	+	0.282557i	$0.0911825\pi$
$449$	4.61070	+	20.2008i	0.217592	+	0.953335i	−0.741658	+	0.670778i	$0.765960\pi$
$450$	5.35983	+	13.7508i	0.252665	+	0.648221i
$451$	2.34360	+	7.59777i	0.110356	+	0.357765i
$452$	−15.4536	−	10.6420i	−0.726878	−	0.500559i
$453$	−7.85670	+	3.08353i	−0.369140	+	0.144877i
$454$	−0.0240648	+	10.3193i	−0.00112942	+	0.484310i
$455$	5.49293	−	3.93680i	0.257513	−	0.184560i
$456$	0.420941	+	1.90562i	0.0197124	+	0.0892388i
$457$	−28.9598	−	26.8708i	−1.35468	−	1.25696i	−0.937432	−	0.348169i	$-0.886803\pi$
$457$	−28.9598	−	26.8708i	−1.35468	−	1.25696i	−0.417250	−	0.908792i	$-0.637006\pi$
$458$	−3.86834	−	12.6455i	−0.180755	−	0.590884i
$459$	0.905719	−	0.522917i	0.0422753	−	0.0244077i
$460$	−4.40744	+	1.70611i	−0.205498	+	0.0795479i
$461$	−4.15552	−	3.31392i	−0.193542	−	0.154345i	0.521924	−	0.852992i	$-0.325214\pi$
$461$	−4.15552	−	3.31392i	−0.193542	−	0.154345i	−0.715466	+	0.698647i	$0.753786\pi$
$462$	0.720157	+	7.48507i	0.0335047	+	0.348237i
$463$	−13.2276	−	16.5869i	−0.614739	−	0.770858i	0.372855	−	0.927890i	$-0.378379\pi$
$463$	−13.2276	−	16.5869i	−0.614739	−	0.770858i	−0.987594	+	0.157031i	$0.949808\pi$
$464$	−32.7601	+	12.5060i	−1.52085	+	0.580578i
$465$	5.28889	+	3.60590i	0.245266	+	0.167220i
$466$	30.2548	+	4.63236i	1.40153	+	0.214590i
$467$	1.36128	+	9.03152i	0.0629926	+	0.417929i	0.997995	+	0.0632881i	$0.0201587\pi$
$467$	1.36128	+	9.03152i	0.0629926	+	0.417929i	−0.935003	+	0.354641i	$0.884603\pi$
$468$	−0.0646968	+	13.8713i	−0.00299061	+	0.641203i
$469$	−2.06669	−	6.18155i	−0.0954307	−	0.285437i
$470$	−8.48261	−	1.95692i	−0.391274	−	0.0902662i
$471$	−3.83636	+	6.64478i	−0.176770	+	0.306175i
$472$	2.67628	+	8.89679i	0.123186	+	0.409508i
$473$	22.5920	+	3.40520i	1.03878	+	0.156571i
$474$	−2.40114	+	7.72035i	−0.110288	+	0.354608i
$475$	1.79247	+	3.72210i	0.0822442	+	0.170782i
$476$	−1.42981	+	0.243059i	−0.0655350	+	0.0111406i
$477$	4.02186	−	8.35148i	0.184148	−	0.382388i
$478$	−0.0703472	−	0.0655786i	−0.00321761	−	0.00299950i
$479$	−2.06055	−	27.4961i	−0.0941489	−	1.25633i	−0.821557	−	0.570126i	$-0.806894\pi$
$479$	−2.06055	−	27.4961i	−0.0941489	−	1.25633i	0.727409	−	0.686205i	$-0.240725\pi$
$480$	2.97609	+	2.08031i	0.135839	+	0.0949525i
$481$	−1.33881	+	17.8652i	−0.0610444	+	0.814581i
$482$	−12.5716	−	15.8399i	−0.572620	−	0.721488i
$483$	−3.56635	+	2.98352i	−0.162275	+	0.135755i
$484$	3.14808	+	3.98556i	0.143095	+	0.181162i
$485$	0.765607	−	2.48204i	0.0347644	−	0.112703i
$486$	20.9523	−	1.52103i	0.950415	−	0.0689953i
$487$	−8.55884	+	7.94145i	−0.387838	+	0.359861i	−0.849861	−	0.527007i	$-0.823314\pi$
$487$	−8.55884	+	7.94145i	−0.387838	+	0.359861i	0.462023	+	0.886868i	$0.347124\pi$
$488$	−40.4242	+	15.5398i	−1.82992	+	0.703455i
$489$	−6.03598			−0.272956
$490$	3.09968	+	8.65880i	0.140029	+	0.391165i
$491$		−	32.4718i		−	1.46543i	−0.680536	−	0.732715i	$-0.738253\pi$
$491$		−	32.4718i		−	1.46543i	0.680536	−	0.732715i	$-0.261747\pi$
$492$	3.76542	+	0.299846i	0.169758	+	0.0135181i
$493$	1.63429	+	1.76135i	0.0736049	+	0.0793272i
$494$	0.281141	+	3.87274i	0.0126491	+	0.174243i
$495$	6.51392	+	2.00928i	0.292779	+	0.0903104i
$496$	39.8876	+	0.372085i	1.79101	+	0.0167071i
$497$	−17.8108	+	9.09769i	−0.798922	+	0.408087i
$498$	9.87369	+	12.4406i	0.442451	+	0.557478i
$499$	18.6922	+	1.40078i	0.836776	+	0.0627077i	0.486223	−	0.873835i	$-0.338374\pi$
$499$	18.6922	+	1.40078i	0.836776	+	0.0627077i	0.350554	+	0.936543i	$0.385993\pi$
$500$	15.7742	+	6.27598i	0.705444	+	0.280671i
$501$	−11.4709	+	0.859623i	−0.512481	+	0.0384051i
$502$	18.1673	−	19.4883i	0.810845	−	0.869806i
$503$	−2.16828	−	1.04419i	−0.0966789	−	0.0465581i	0.384919	−	0.922950i	$-0.374229\pi$
$503$	−2.16828	−	1.04419i	−0.0966789	−	0.0465581i	−0.481598	+	0.876392i	$0.659944\pi$
$504$	−18.1280	−	5.26671i	−0.807484	−	0.234598i
$505$	6.74005	−	3.24584i	0.299928	−	0.144438i
$506$	3.10737	−	9.99108i	0.138140	−	0.444158i
$507$	−0.560267	+	3.71713i	−0.0248823	+	0.165083i
$508$	3.59473	+	0.558977i	0.159490	+	0.0248006i
$509$	30.4006	+	17.5518i	1.34748	+	0.777969i	0.987892	−	0.155141i	$-0.0495831\pi$
$509$	30.4006	+	17.5518i	1.34748	+	0.777969i	0.359590	+	0.933110i	$0.382916\pi$
$510$	0.0559301	−	0.242438i	0.00247662	−	0.0107353i
$511$	25.3170	−	24.6203i	1.11996	−	1.08914i
$512$	22.6224	+	0.474872i	0.999780	+	0.0209866i
$513$	3.76793	−	0.567925i	0.166358	−	0.0250745i
$514$	−6.02385	−	0.922321i	−0.265700	−	0.0406818i
$515$	1.83320	−	2.68881i	0.0807805	−	0.118483i
$516$	5.47088	−	9.37459i	0.240842	−	0.412693i
$517$	15.0681	−	12.0164i	0.662695	−	0.528482i
$518$	−22.8783	−	8.42603i	−1.00522	−	0.370219i
$519$	−5.31362	+	6.66307i	−0.233242	+	0.292476i
$520$	5.26151	+	4.95092i	0.230733	+	0.217112i
$521$	16.9655	+	29.3851i	0.743271	+	1.28738i	0.950998	+	0.309197i	$0.100060\pi$
$521$	16.9655	+	29.3851i	0.743271	+	1.28738i	−0.207727	+	0.978187i	$0.566606\pi$
$522$	9.14866	+	29.9067i	0.400426	+	1.30898i
$523$	19.9375	−	21.4875i	0.871807	−	0.939584i	−0.126822	−	0.991925i	$-0.540478\pi$
$523$	19.9375	−	21.4875i	0.871807	−	0.939584i	0.998629	+	0.0523410i	$0.0166683\pi$
$524$	14.9929	+	3.49568i	0.654967	+	0.152709i
$525$	7.55241	+	0.388161i	0.329614	+	0.0169408i
$526$	−24.8839	−	0.0580298i	−1.08499	−	0.00253022i
$527$	−0.998573	−	2.54432i	−0.0434985	−	0.110832i
$528$	−7.70346	+	2.29773i	−0.335250	+	0.0999959i
$529$	−15.7957	+	4.87234i	−0.686771	+	0.211841i
$530$	−1.75329	−	4.49813i	−0.0761582	−	0.195386i
$531$	8.07835	−	1.84383i	0.350571	−	0.0800154i
$532$	−5.17292	−	1.07887i	−0.224275	−	0.0467751i
$533$	7.32719	+	1.67238i	0.317376	+	0.0724389i
$534$	−1.29319	−	8.71762i	−0.0559616	−	0.377248i
$535$	1.20867	−	3.07963i	0.0522552	−	0.133144i
$536$	6.05861	−	3.44165i	0.261692	−	0.148657i
$537$	−14.3818	+	9.80536i	−0.620621	+	0.423132i
$538$	−11.7134	−	24.4690i	−0.505001	−	1.05493i
$539$	−19.2813	−	6.54194i	−0.830506	−	0.281781i
$540$	4.44625	−	5.52238i	0.191336	−	0.237646i
$541$	−8.65743	−	12.6981i	−0.372212	−	0.545935i	0.593740	−	0.804657i	$-0.297651\pi$
$541$	−8.65743	−	12.6981i	−0.372212	−	0.545935i	−0.965952	+	0.258722i	$0.916698\pi$
$542$	−5.75692	+	14.5684i	−0.247281	+	0.625767i
$543$	3.05534	−	7.78487i	0.131117	−	0.334081i
$544$	−0.549578	−	1.44978i	−0.0235630	−	0.0621590i
$545$	0.439183	−	1.92418i	0.0188125	−	0.0824230i
$546$	6.46766	+	2.94808i	0.276790	+	0.126166i
$547$	−17.8806	+	4.08114i	−0.764521	+	0.174497i	−0.586963	−	0.809613i	$-0.699677\pi$
$547$	−17.8806	+	4.08114i	−0.764521	+	0.174497i	−0.177558	+	0.984110i	$0.556820\pi$
$548$	−12.3740	−	11.5892i	−0.528590	−	0.495068i
$549$	11.3851	+	36.9097i	0.485905	+	1.57527i
$550$	−14.7572	+	8.47426i	−0.629250	+	0.361343i
$551$	3.19836	+	8.14930i	0.136255	+	0.347172i
$552$	−3.86455	−	3.12636i	−0.164486	−	0.133067i
$553$	−16.3928	−	14.5100i	−0.697092	−	0.617030i
$554$	5.25911	+	4.21410i	0.223438	+	0.179040i
$555$	2.84487	−	3.06604i	0.120758	−	0.130146i
$556$	18.6164	+	20.2524i	0.789512	+	0.858891i
$557$	−1.62022	+	0.935435i	−0.0686509	+	0.0396356i	−0.533933	−	0.845527i	$-0.679286\pi$
$557$	−1.62022	+	0.935435i	−0.0686509	+	0.0396356i	0.465282	+	0.885163i	$0.345953\pi$
$558$	2.74136	−	35.4707i	0.116051	−	1.50160i
$559$	13.4650	−	16.8845i	0.569507	−	0.714139i
$560$	−8.44440	+	5.03569i	−0.356841	+	0.212797i
$561$	0.343437	+	0.430656i	0.0144999	+	0.0181823i
$562$	7.96345	−	5.40223i	0.335918	−	0.227879i
$563$	−11.0149	+	16.1558i	−0.464221	+	0.680887i	−0.984951	−	0.172834i	$-0.944707\pi$
$563$	−11.0149	+	16.1558i	−0.464221	+	0.680887i	0.520730	+	0.853721i	$0.325660\pi$
$564$	−2.65797	−	8.76180i	−0.111921	−	0.368938i
$565$	1.29903	+	8.61853i	0.0546508	+	0.362584i
$566$	6.22524	−	12.8501i	0.261666	−	0.540130i
$567$	−4.48066	+	12.2539i	−0.188170	+	0.514615i
$568$	−13.2134	−	16.8089i	−0.554420	−	0.705287i
$569$	14.5875	−	25.2662i	0.611538	−	1.05922i	−0.379443	−	0.925215i	$-0.623884\pi$
$569$	14.5875	−	25.2662i	0.611538	−	1.05922i	0.990981	−	0.134000i	$-0.0427823\pi$
$570$	0.512409	−	0.747812i	0.0214624	−	0.0313224i
$571$	1.88722	−	12.5209i	0.0789776	−	0.523982i	−0.914003	−	0.405707i	$-0.867025\pi$
$571$	1.88722	−	12.5209i	0.0789776	−	0.523982i	0.992981	−	0.118275i	$-0.0377365\pi$
$572$	−15.8268	+	2.31007i	−0.661753	+	0.0965888i
$573$	5.64066	+	11.7129i	0.235642	+	0.489315i
$574$	−4.92578	+	8.96364i	−0.205598	+	0.374135i
$575$	−9.48055	−	4.56559i	−0.395366	−	0.190398i
$576$	1.78955	−	20.1014i	0.0745646	−	0.837560i
$577$	1.72785	+	23.0565i	0.0719313	+	0.959856i	0.910085	+	0.414422i	$0.136016\pi$
$577$	1.72785	+	23.0565i	0.0719313	+	0.959856i	−0.838154	+	0.545434i	$0.816365\pi$
$578$	17.5838	−	16.2392i	0.731390	−	0.675463i
$579$	2.53572	+	0.190026i	0.105381	+	0.00789722i
$580$	14.6424	+	7.13575i	0.607994	+	0.296296i
$581$	−41.6913	+	10.5501i	−1.72965	+	0.437690i
$582$	2.66481	−	0.601692i	0.110460	−	0.0249409i
$583$	10.2133	+	3.15038i	0.422991	+	0.130476i
$584$	31.0432	+	21.4846i	1.28458	+	0.889038i
$585$	4.72341	−	4.38269i	0.195289	−	0.181202i
$586$	−18.4870	−	10.7310i	−0.763691	−	0.443295i
$587$			29.5253i			1.21864i	0.792925	+	0.609320i	$0.208557\pi$
$587$			29.5253i			1.21864i	−0.792925	+	0.609320i	$0.791443\pi$
$588$	−6.27406	+	7.36229i	−0.258738	+	0.303616i
$589$		−	9.95863i		−	0.410338i
$590$	2.16651	−	3.73238i	0.0891940	−	0.153660i
$591$	3.36472	−	3.12201i	0.138406	−	0.128422i
$592$	4.12488	−	25.7355i	0.169531	−	1.05772i
$593$	−6.85920	−	2.11578i	−0.281674	−	0.0868848i	0.150699	−	0.988580i	$-0.451847\pi$
$593$	−6.85920	−	2.11578i	−0.281674	−	0.0868848i	−0.432373	+	0.901695i	$0.642324\pi$
$594$	3.45702	+	15.3107i	0.141843	+	0.628206i
$595$	0.536418	+	0.407575i	0.0219910	+	0.0167089i
$596$	17.1027	−	35.0945i	0.700554	−	1.43753i
$597$	6.23168	+	0.467000i	0.255046	+	0.0191130i
$598$	−6.71011	−	7.26569i	−0.274397	−	0.297116i
$599$	2.39997	+	32.0254i	0.0980602	+	1.30852i	0.801598	+	0.597864i	$0.203984\pi$
$599$	2.39997	+	32.0254i	0.0980602	+	1.30852i	−0.703537	+	0.710658i	$0.748397\pi$
$600$	1.14898	+	8.00246i	0.0469069	+	0.326699i
$601$	15.8621	+	7.63879i	0.647029	+	0.311593i	0.728462	−	0.685086i	$-0.240235\pi$
$601$	15.8621	+	7.63879i	0.647029	+	0.311593i	−0.0814333	+	0.996679i	$0.525950\pi$
$602$	17.0650	+	23.9281i	0.695517	+	0.975235i
$603$	−2.69638	−	5.59910i	−0.109805	−	0.228013i
$604$	24.1751	−	3.52857i	0.983671	−	0.143576i
$605$	0.351622	−	2.33286i	0.0142955	−	0.0948442i
$606$	6.49063	+	4.44745i	0.263664	+	0.180665i
$607$	12.2897	−	21.2863i	0.498822	−	0.863984i	−0.501177	−	0.865345i	$-0.667100\pi$
$607$	12.2897	−	21.2863i	0.498822	−	0.863984i	0.999999	+	0.00136017i	$0.000432955\pi$
$608$	0.0658672	−	5.64870i	0.00267127	−	0.229085i
$609$	15.8981	+	2.01625i	0.644222	+	0.0817027i
$610$	18.1046	+	8.77078i	0.733034	+	0.355119i
$611$	−2.71517	−	18.0140i	−0.109844	−	0.728769i
$612$	−1.32327	+	0.401426i	−0.0534901	+	0.0162267i
$613$	23.9848	−	35.1793i	0.968738	−	1.42088i	0.0625306	−	0.998043i	$-0.480083\pi$
$613$	23.9848	−	35.1793i	0.968738	−	1.42088i	0.906207	−	0.422834i	$-0.138965\pi$
$614$	25.9260	+	38.2177i	1.04629	+	1.54234i
$615$	−1.09399	−	1.37182i	−0.0441140	−	0.0553172i
$616$	2.88961	−	21.5741i	0.116426	−	0.869245i
$617$	14.7267	−	18.4668i	0.592876	−	0.743444i	−0.391372	−	0.920232i	$-0.628000\pi$
$617$	14.7267	−	18.4668i	0.592876	−	0.743444i	0.984249	+	0.176789i	$0.0565710\pi$
$618$	3.41258	+	0.263741i	0.137274	+	0.0106092i
$619$	15.2944	−	8.83025i	0.614735	−	0.354918i	−0.160081	−	0.987104i	$-0.551176\pi$
$619$	15.2944	−	8.83025i	0.614735	−	0.354918i	0.774817	+	0.632186i	$0.217842\pi$
$620$	−12.5395	−	13.6415i	−0.503599	−	0.547854i
$621$	−6.60154	+	7.11477i	−0.264911	+	0.285506i
$622$	7.86819	−	9.81934i	0.315486	−	0.393720i
$623$	22.9615	+	6.49715i	0.919933	+	0.260303i
$624$	−1.75988	+	7.39202i	−0.0704517	+	0.295918i
$625$	4.67584	+	11.9139i	0.187034	+	0.476554i
$626$	−14.0867	−	24.5309i	−0.563019	−	0.980450i
$627$	0.591558	+	1.91778i	0.0236245	+	0.0765889i
$628$	15.1823	−	16.2104i	0.605841	−	0.646864i
$629$	−1.74116	+	0.397408i	−0.0694245	+	0.0158457i
$630$	3.97064	+	7.81838i	0.158194	+	0.311492i
$631$	−2.34904	+	10.2918i	−0.0935139	+	0.409711i	−0.999919	−	0.0126974i	$-0.995958\pi$
$631$	−2.34904	+	10.2918i	−0.0935139	+	0.409711i	0.906405	+	0.422409i	$0.138815\pi$
$632$	11.8433	−	20.1858i	0.471102	−	0.802948i
$633$	−2.26502	+	5.77119i	−0.0900266	+	0.229384i
$634$	−7.95465	−	3.14340i	−0.315920	−	0.124840i
$635$	−0.951935	−	1.39623i	−0.0377764	−	0.0554078i
$636$	3.18437	−	3.95509i	0.126268	−	0.156829i
$637$	−14.4680	+	12.6919i	−0.573243	+	0.502871i
$638$	−32.5265	+	15.5706i	−1.28774	+	0.616446i
$639$	−15.7555	+	10.7419i	−0.623279	+	0.424945i
$640$	−7.02239	−	7.82059i	−0.277584	−	0.309136i
$641$	−12.5738	+	32.0376i	−0.496636	+	1.26541i	0.434479	+	0.900682i	$0.356933\pi$
$641$	−12.5738	+	32.0376i	−0.496636	+	1.26541i	−0.931115	+	0.364726i	$0.881163\pi$
$642$	3.44193	−	0.510581i	0.135842	−	0.0201510i
$643$	42.9975	+	9.81389i	1.69566	+	0.387022i	0.957687	−	0.287813i	$-0.0929282\pi$
$643$	42.9975	+	9.81389i	1.69566	+	0.387022i	0.737968	+	0.674835i	$0.235785\pi$
$644$	12.0147	−	6.06659i	0.473445	−	0.239057i
$645$	−4.91550	+	1.12193i	−0.193548	+	0.0441760i
$646$	−0.360652	+	0.140576i	−0.0141897	+	0.00553089i
$647$	−38.8652	+	11.9883i	−1.52795	+	0.471309i	−0.941026	−	0.338335i	$-0.890136\pi$
$647$	−38.8652	+	11.9883i	−1.52795	+	0.471309i	−0.586921	+	0.809644i	$0.699660\pi$
$648$	−13.7776	−	2.17532i	−0.541234	−	0.0854546i
$649$	3.49057	+	8.89384i	0.137017	+	0.349114i
$650$	−0.0375114	+	16.0854i	−0.00147132	+	0.630921i
$651$	−15.9968	−	8.74218i	−0.626963	−	0.342633i
$652$	17.0157	+	3.96730i	0.666386	+	0.155372i
$653$	8.81553	−	9.50088i	0.344978	−	0.371798i	−0.536599	−	0.843837i	$-0.680291\pi$
$653$	8.81553	−	9.50088i	0.344978	−	0.371798i	0.881578	+	0.472039i	$0.156482\pi$
$654$	1.98504	−	0.607238i	0.0776212	−	0.0237449i
$655$	−3.57559	−	6.19311i	−0.139710	−	0.241985i
$656$	−10.4178	−	3.32020i	−0.406747	−	0.129632i
$657$	20.9935	−	26.3250i	0.819033	−	1.02703i
$658$	24.5876	+	3.17657i	0.958524	+	0.123836i
$659$	15.6060	−	12.4454i	0.607924	−	0.484803i	−0.270478	−	0.962726i	$-0.587182\pi$
$659$	15.6060	−	12.4454i	0.607924	−	0.484803i	0.878402	+	0.477923i	$0.158610\pi$
$660$	3.22512	+	1.88213i	0.125538	+	0.0732620i
$661$	−26.9637	+	39.5484i	−1.04876	+	1.53826i	−0.222533	+	0.974925i	$0.571432\pi$
$661$	−26.9637	+	39.5484i	−1.04876	+	1.53826i	−0.826232	+	0.563330i	$0.809520\pi$
$662$	1.80258	−	11.7730i	0.0700591	−	0.457569i
$663$	0.514851	−	0.0776013i	0.0199952	−	0.00301378i
$664$	−19.6574	−	41.5604i	−0.762856	−	1.61286i
$665$	1.27680	+	2.09638i	0.0495123	+	0.0812942i
$666$	−22.6510	−	5.22555i	−0.877709	−	0.202486i
$667$	−19.3110	−	11.1492i	−0.747726	−	0.431700i
$668$	32.9019	+	5.11621i	1.27301	+	0.197952i
$669$	−0.543059	+	3.60296i	−0.0209959	+	0.139299i
$670$	−3.09065	−	0.961239i	−0.119402	−	0.0371359i
$671$	−40.1268	+	19.3240i	−1.54908	+	0.745996i
$672$	−9.01580	−	5.06451i	−0.347792	−	0.195368i
$673$	21.9773	+	10.5837i	0.847165	+	0.407973i	0.806524	−	0.591201i	$-0.201346\pi$
$673$	21.9773	+	10.5837i	0.847165	+	0.407973i	0.0406402	+	0.999174i	$0.487060\pi$
$674$	21.1731	+	19.7378i	0.815556	+	0.760272i
$675$	15.7412	−	1.17964i	0.605880	−	0.0454044i
$676$	4.02260	−	10.1105i	0.154715	−	0.388865i
$677$	−11.2592	−	0.843762i	−0.432727	−	0.0324284i	−0.143414	−	0.989663i	$-0.545808\pi$
$677$	−11.2592	−	0.843762i	−0.432727	−	0.0324284i	−0.289313	+	0.957234i	$0.593427\pi$
$678$	−7.18043	+	5.69886i	−0.275763	+	0.218863i
$679$	−1.47648	+	7.24831i	−0.0566620	+	0.278165i
$680$	−0.317018	+	0.646682i	−0.0121571	+	0.0247991i
$681$	4.81764	+	1.48605i	0.184612	+	0.0569454i
$682$	40.9138	−	2.97014i	1.56667	−	0.113732i
$683$	1.08081	+	1.16484i	0.0413561	+	0.0445713i	0.753391	−	0.657573i	$-0.228417\pi$
$683$	1.08081	+	1.16484i	0.0413561	+	0.0445713i	−0.712035	+	0.702144i	$0.752226\pi$
$684$	−5.02240	−	0.399942i	−0.192036	−	0.0152921i
$685$			7.87519i			0.300896i
$686$	−11.2038	−	23.6744i	−0.427762	−	0.903892i
$687$	−6.46068			−0.246490
$688$	−21.5843	+	22.8315i	−0.822895	+	0.870443i
$689$	7.40592	−	6.87169i	0.282143	−	0.261790i
$690$	0.167182	+	2.30294i	0.00636451	+	0.0876715i
$691$	1.20532	−	3.90757i	0.0458527	−	0.148651i	−0.929752	−	0.368188i	$-0.879978\pi$
$691$	1.20532	−	3.90757i	0.0458527	−	0.148651i	0.975604	+	0.219537i	$0.0704546\pi$
$692$	19.3588	−	15.2910i	0.735911	−	0.581275i
$693$	−19.0227	−	3.87491i	−0.722612	−	0.147196i
$694$	28.5706	−	22.6755i	1.08453	−	0.860751i
$695$	0.954913	−	12.7424i	0.0362219	−	0.483348i
$696$	1.16072	+	17.0925i	0.0439969	+	0.647891i
$697$	0.0559890	+	0.747121i	0.00212073	+	0.0282992i
$698$	−7.57336	+	8.12406i	−0.286656	+	0.307500i
$699$	6.48810	−	13.4727i	0.245402	−	0.509584i
$700$	−21.0354	−	6.05826i	−0.795065	−	0.228981i
$701$	−1.49683	−	3.10821i	−0.0565346	−	0.117395i	0.870787	−	0.491660i	$-0.163610\pi$
$701$	−1.49683	−	3.10821i	−0.0565346	−	0.117395i	−0.927322	+	0.374264i	$0.877895\pi$
$702$	14.1672	+	4.40622i	0.534708	+	0.166302i
$703$	−6.43437	−	0.969825i	−0.242677	−	0.0365776i
$704$	23.2266	−	1.41410i	0.875386	−	0.0532960i
$705$	−2.12656	+	3.68331i	−0.0800910	+	0.138722i
$706$	−7.09935	+	30.7733i	−0.267188	+	1.15817i
$707$	−18.1955	+	11.0820i	−0.684313	+	0.416782i
$708$	4.53897	+	0.0211701i	0.170585	+	0.000795619i
$709$	−4.14138	−	27.4763i	−0.155533	−	1.03189i	−0.921322	−	0.388801i	$-0.872889\pi$
$709$	−4.14138	−	27.4763i	−0.155533	−	1.03189i	0.765789	−	0.643092i	$-0.222349\pi$
$710$	−1.50313	+	9.81720i	−0.0564113	+	0.368433i
$711$	−17.2463	−	11.7583i	−0.646786	−	0.440971i
$712$	−2.08434	+	25.4253i	−0.0781139	+	0.952855i
$713$	15.8152	+	19.8316i	0.592283	+	0.742700i
$714$	−0.0907882	+	0.702728i	−0.00339766	+	0.0262989i
$715$	5.80875	+	4.63232i	0.217235	+	0.173239i
$716$	46.9878	−	18.1889i	1.75602	−	0.679751i
$717$	−0.0406915	+	0.0234932i	−0.00151965	+	0.000877370i
$718$	−33.1437	+	10.1389i	−1.23691	+	0.378380i
$719$	−37.3906	−	34.6934i	−1.39444	−	1.29385i	−0.907277	−	0.420533i	$-0.861843\pi$
$719$	−37.3906	−	34.6934i	−1.39444	−	1.29385i	−0.487158	−	0.873314i	$-0.661966\pi$
$720$	−7.38333	+	5.77617i	−0.275161	+	0.215265i
$721$	−4.44443	+	8.13258i	−0.165519	+	0.302873i
$722$	25.4597	+	0.0593724i	0.947510	+	0.00220961i
$723$	−9.19693	+	3.60953i	−0.342038	+	0.134240i
$724$	−13.7299	+	19.9377i	−0.510269	+	0.740978i
$725$	10.6897	+	34.6551i	0.397004	+	1.28706i
$726$	2.31193	−	0.901148i	0.0858036	−	0.0334447i
$727$	1.34039	+	5.87265i	0.0497125	+	0.217805i	0.993683	−	0.112226i	$-0.0357981\pi$
$727$	1.34039	+	5.87265i	0.0497125	+	0.217805i	−0.943970	+	0.330031i	$0.892941\pi$
$728$	−16.2949	−	12.5618i	−0.603930	−	0.465571i
$729$	−1.00823	+	4.41734i	−0.0373418	+	0.163605i
$730$	−2.57325	−	17.3468i	−0.0952404	−	0.642034i
$731$	2.00405	+	0.786532i	0.0741225	+	0.0290909i
$732$	1.48276	+	21.1067i	0.0548046	+	0.780125i
$733$	−24.2699	−	35.5974i	−0.896429	−	1.31482i	−0.948697	−	0.316187i	$-0.897597\pi$
$733$	−24.2699	−	35.5974i	−0.896429	−	1.31482i	0.0522677	−	0.998633i	$-0.483355\pi$
$734$	−22.6964	+	10.8649i	−0.837741	+	0.401031i
$735$	4.48830	−	0.210650i	0.165553	−	0.00776993i
$736$	8.83946	+	11.3534i	0.325827	+	0.418492i
$737$	5.92055	−	4.03656i	0.218086	−	0.148689i
$738$	−3.58393	+	9.06945i	−0.131926	+	0.333851i
$739$	−36.1733	−	14.1970i	−1.33066	−	0.522244i	−0.409811	−	0.912171i	$-0.634405\pi$
$739$	−36.1733	−	14.1970i	−1.33066	−	0.522244i	−0.920846	+	0.389926i	$0.872500\pi$
$740$	−10.0350	+	6.77343i	−0.368895	+	0.248996i
$741$	1.84948	+	0.422133i	0.0679425	+	0.0155074i
$742$	6.22564	+	12.2586i	0.228550	+	0.450026i
$743$	8.69634	+	38.1012i	0.319038	+	1.39780i	0.839244	+	0.543756i	$0.182998\pi$
$743$	8.69634	+	38.1012i	0.319038	+	1.39780i	−0.520206	+	0.854041i	$0.674145\pi$
$744$	5.87444	−	18.5819i	0.215367	−	0.681246i
$745$	−17.3289	+	5.34527i	−0.634883	+	0.195836i
$746$	−14.4490	+	8.29729i	−0.529017	+	0.303785i
$747$	−38.1695	+	14.9804i	−1.39655	+	0.548105i
$748$	−0.685103	−	1.43977i	−0.0250498	−	0.0526432i
$749$	−2.56523	+	9.06576i	−0.0937315	+	0.331255i
$750$	5.18647	−	6.47261i	0.189383	−	0.236346i
$751$	9.03817	+	8.38619i	0.329807	+	0.306017i	0.827643	−	0.561255i	$-0.189681\pi$
$751$	9.03817	+	8.38619i	0.329807	+	0.306017i	−0.497836	+	0.867271i	$0.665872\pi$
$752$	1.73400	+	26.4469i	0.0632326	+	0.964420i
$753$	−6.50833	−	11.2728i	−0.237177	−	0.410802i
$754$	−2.62656	+	33.9852i	−0.0956535	+	1.23767i
$755$	−8.87272	−	7.07576i	−0.322912	−	0.257513i
$756$	−11.0586	+	16.8933i	−0.402198	+	0.614403i
$757$	−27.4783	+	21.9132i	−0.998715	+	0.796449i	−0.979104	−	0.203359i	$-0.934814\pi$
$757$	−27.4783	+	21.9132i	−0.998715	+	0.796449i	−0.0196109	+	0.999808i	$0.506243\pi$
$758$	17.4500	+	25.7231i	0.633812	+	0.934306i
$759$	−4.22364	−	2.87963i	−0.153308	−	0.104524i
$760$	−1.93602	+	1.77132i	−0.0702269	+	0.0642526i
$761$	−7.40428	+	1.11601i	−0.268405	+	0.0404555i	−0.281866	−	0.959454i	$-0.590953\pi$
$761$	−7.40428	+	1.11601i	−0.268405	+	0.0404555i	0.0134609	+	0.999909i	$0.495715\pi$
$762$	0.774894	−	1.59953i	0.0280715	−	0.0579449i
$763$	−0.707182	+	5.57610i	−0.0256017	+	0.201868i
$764$	−8.20262	−	36.7268i	−0.296760	−	1.32873i
$765$	0.556281	+	0.321169i	0.0201124	+	0.0116119i
$766$	16.0447	+	10.9940i	0.579719	+	0.397229i
$767$	8.93023	+	1.34602i	0.322452	+	0.0486018i
$768$	3.45498	−	10.5011i	0.124671	−	0.378926i
$769$	0.925590	−	0.445741i	0.0333776	−	0.0160738i	−0.417120	−	0.908851i	$-0.636961\pi$
$769$	0.925590	−	0.445741i	0.0333776	−	0.0160738i	0.450498	+	0.892777i	$0.351246\pi$
$770$	−8.23192	+	5.87083i	−0.296658	+	0.211570i
$771$	−1.29181	+	2.68247i	−0.0465233	+	0.0966066i
$772$	−7.02341	−	2.20236i	−0.252778	−	0.0792648i
$773$	−12.2028	+	0.914473i	−0.438904	+	0.0328913i	−0.292350	−	0.956311i	$-0.594437\pi$
$773$	−12.2028	+	0.914473i	−0.438904	+	0.0328913i	−0.146554	+	0.989203i	$0.546818\pi$
$774$	19.0119	+	20.5860i	0.683368	+	0.739949i
$775$	3.08297	−	41.1393i	0.110743	−	1.47777i
$776$	−7.90771	−	0.0553235i	−0.283870	−	0.00198600i
$777$	−7.20625	+	9.48430i	−0.258523	+	0.340247i
$778$	−21.4069	+	4.83349i	−0.767474	+	0.173289i
$779$	−0.804613	+	2.60849i	−0.0288283	+	0.0934589i
$780$	3.06498	−	1.75056i	0.109744	−	0.0626800i
$781$	−14.9553	−	16.1180i	−0.535143	−	0.576746i
$782$	0.494956	−	0.852690i	0.0176996	−	0.0304921i
$783$	33.4507			1.19543
$784$	22.5259	−	16.6308i	0.804496	−	0.593958i
$785$	−10.3168			−0.368222
$786$	3.77588	−	6.50493i	0.134681	−	0.232023i
$787$	19.4950	+	21.0106i	0.694923	+	0.748948i	0.977647	−	0.210253i	$-0.0674287\pi$
$787$	19.4950	+	21.0106i	0.694923	+	0.748948i	−0.282724	+	0.959201i	$0.591238\pi$
$788$	−11.5373	+	6.58952i	−0.411000	+	0.234742i
$789$	−3.58344	+	11.6172i	−0.127574	+	0.413584i
$790$	−10.6044	+	2.39437i	−0.377286	+	0.0851879i
$791$	−6.08924	−	24.0632i	−0.216508	−	0.855590i
$792$	0.145193	−	20.7532i	0.00515920	−	0.737433i
$793$	−3.14603	+	41.9808i	−0.111719	+	1.49078i
$794$	38.1208	+	41.2770i	1.35285	+	1.46487i
$795$	−2.35206	+	0.176262i	−0.0834189	+	0.00625138i
$796$	−17.2604	−	5.41242i	−0.611779	−	0.191838i
$797$	2.03932	−	4.23468i	0.0722363	−	0.150000i	−0.861724	−	0.507378i	$-0.830615\pi$
$797$	2.03932	−	4.23468i	0.0722363	−	0.150000i	0.933960	+	0.357378i	$0.116329\pi$
$798$	−1.24334	+	2.26255i	−0.0440136	+	0.0800933i
$799$	1.63622	−	0.787960i	0.0578851	−	0.0278760i
$800$	2.02081	−	23.3145i	0.0714463	−	0.824291i
$801$	22.4983	+	3.39107i	0.794938	+	0.119818i
$802$	−4.31073	−	2.95376i	−0.152217	−	0.104301i
$803$	33.6228	+	19.4121i	1.18652	+	0.685038i
$804$	−0.742028	−	3.32239i	−0.0261693	−	0.117172i
$805$	−5.87186	−	2.14706i	−0.206956	−	0.0756738i
$806$	16.9053	−	34.8959i	0.595465	−	1.22916i
$807$	−13.1057	+	1.97536i	−0.461342	+	0.0695361i
$808$	−15.3742	−	16.8037i	−0.540862	−	0.591151i
$809$	−4.86243	−	3.31515i	−0.170954	−	0.116554i	0.474821	−	0.880083i	$-0.342513\pi$
$809$	−4.86243	−	3.31515i	−0.170954	−	0.116554i	−0.645774	+	0.763528i	$0.723465\pi$
$810$	3.63734	+	5.36182i	0.127803	+	0.188395i
$811$	24.1618	−	19.2684i	0.848434	−	0.676604i	−0.0995112	−	0.995036i	$-0.531728\pi$
$811$	24.1618	−	19.2684i	0.848434	−	0.676604i	0.947945	+	0.318433i	$0.103156\pi$
$812$	−43.4921	−	16.1333i	−1.52627	−	0.566169i
$813$	5.98345	+	4.77164i	0.209849	+	0.167349i
$814$	2.06537	−	26.7241i	0.0723913	−	0.936678i
$815$	−4.05800	−	7.02867i	−0.142146	−	0.246203i
$816$	−0.755868	+	0.0495589i	−0.0264607	+	0.00173491i
$817$	5.75005	+	5.33526i	0.201169	+	0.186657i
$818$	16.2342	−	20.2600i	0.567617	−	0.708374i
$819$	−12.1625	+	13.7406i	−0.424992	+	0.480137i
$820$	2.18234	+	4.58628i	0.0762107	+	0.160160i
$821$	−19.5869	+	7.68729i	−0.683587	+	0.268288i	−0.681616	−	0.731710i	$-0.738723\pi$
$821$	−19.5869	+	7.68729i	−0.683587	+	0.268288i	−0.00197112	+	0.999998i	$0.500627\pi$
$822$	−7.18283	+	4.12470i	−0.250530	+	0.143866i
$823$	−3.53206	+	1.08950i	−0.123120	+	0.0379775i	−0.355703	−	0.934599i	$-0.615759\pi$
$823$	−3.53206	+	1.08950i	−0.123120	+	0.0379775i	0.232583	+	0.972577i	$0.425282\pi$
$824$	−9.44685	−	2.98650i	−0.329096	−	0.104040i
$825$	1.85003	+	8.10553i	0.0644099	+	0.282198i
$826$	−5.09756	+	11.1833i	−0.177367	+	0.389117i
$827$	−14.3157	−	3.26746i	−0.497805	−	0.113621i	−0.0337559	−	0.999430i	$-0.510747\pi$
$827$	−14.3157	−	3.26746i	−0.497805	−	0.113621i	−0.464049	+	0.885809i	$0.653604\pi$
$828$	10.6367	−	7.17957i	0.369653	−	0.249507i
$829$	−30.8810	−	12.1199i	−1.07254	−	0.420942i	−0.237648	−	0.971351i	$-0.576376\pi$
$829$	−30.8810	−	12.1199i	−1.07254	−	0.420942i	−0.834895	+	0.550409i	$0.814472\pi$
$830$	−7.84852	+	19.8614i	−0.272426	+	0.689399i
$831$	2.72040	−	1.85474i	0.0943697	−	0.0643402i
$832$	9.81978	−	19.6817i	0.340440	−	0.682340i
$833$	−1.63414	−	1.00527i	−0.0566196	−	0.0348307i
$834$	12.1223	−	5.80300i	0.419761	−	0.200941i
$835$	−8.71289	−	12.7795i	−0.301522	−	0.442251i
$836$	−0.407114	−	5.79513i	−0.0140803	−	0.200429i
$837$	−35.4214	−	13.9019i	−1.22434	−	0.480520i
$838$	−7.24529	−	48.8420i	−0.250285	−	1.68722i
$839$	−1.46540	+	6.42034i	−0.0505913	+	0.221655i	−0.993904	−	0.110251i	$-0.964834\pi$
$839$	−1.46540	+	6.42034i	−0.0505913	+	0.221655i	0.943313	+	0.331906i	$0.107692\pi$
$840$	1.14578	+	4.66482i	0.0395331	+	0.160952i
$841$	10.6480	+	46.6520i	0.367173	+	1.60869i
$842$	−28.0686	+	10.9406i	−0.967307	+	0.377039i
$843$	−1.38576	−	4.49251i	−0.0477280	−	0.154730i
$844$	10.1785	−	14.7805i	0.350357	−	0.508765i
$845$	−4.70512	+	1.84662i	−0.161861	+	0.0635258i
$846$	23.6380	+	0.0551244i	0.812693	+	0.00189521i
$847$	−0.344859	+	6.70988i	−0.0118495	+	0.230554i
$848$	−11.5765	+	9.05655i	−0.397537	+	0.311003i
$849$	−5.11374	−	4.74486i	−0.175503	−	0.162843i
$850$	−1.53338	+	0.469072i	−0.0525945	+	0.0160890i
$851$	14.3536	−	8.28703i	0.492034	−	0.284076i
$852$	−9.74137	+	3.77087i	−0.333734	+	0.129188i
$853$	14.9535	+	11.9250i	0.511999	+	0.408305i	0.845118	−	0.534579i	$-0.179530\pi$
$853$	14.9535	+	11.9250i	0.511999	+	0.408305i	−0.333120	+	0.942885i	$0.608101\pi$
$854$	−53.7611	−	19.8001i	−1.83967	−	0.677545i
$855$	1.45919	+	1.82977i	0.0499032	+	0.0625766i
$856$	−10.0385	−	0.822947i	−0.343110	−	0.0281278i
$857$	18.7458	+	12.7806i	0.640343	+	0.436578i	0.839478	−	0.543394i	$-0.182861\pi$
$857$	18.7458	+	12.7806i	0.640343	+	0.436578i	−0.199135	+	0.979972i	$0.563813\pi$
$858$	−1.18268	+	7.72428i	−0.0403759	+	0.263702i
$859$	0.717681	+	4.76151i	0.0244870	+	0.162460i	0.997732	−	0.0673083i	$-0.0214411\pi$
$859$	0.717681	+	4.76151i	0.0244870	+	0.162460i	−0.973245	+	0.229769i	$0.926203\pi$
$860$	14.5944	+	0.0680694i	0.497666	+	0.00232115i
$861$	3.48375	+	3.58233i	0.118726	+	0.122085i
$862$	−3.08952	+	13.3920i	−0.105229	+	0.456134i
$863$	11.5603	−	20.0230i	0.393517	−	0.681591i	−0.599394	−	0.800454i	$-0.704592\pi$
$863$	11.5603	−	20.0230i	0.393517	−	0.681591i	0.992911	+	0.118863i	$0.0379251\pi$
$864$	−19.9997	−	8.11965i	−0.680402	−	0.276236i
$865$	−11.3312	−	1.70791i	−0.385274	−	0.0580707i
$866$	51.2940	+	15.9532i	1.74304	+	0.542112i
$867$	−5.07379	−	10.5358i	−0.172315	−	0.357816i
$868$	39.3495	+	35.1589i	1.33561	+	1.19337i
$869$	10.4427	−	21.6844i	0.354243	−	0.735594i
$870$	5.42640	−	5.82098i	0.183972	−	0.197350i
$871$	−0.506168	−	6.75434i	−0.0171508	−	0.228862i
$872$	−5.99504	+	0.407110i	−0.203018	+	0.0137865i
$873$	−0.527064	+	7.03317i	−0.0178384	+	0.238037i
$874$	2.81374	−	2.23317i	0.0951763	−	0.0755381i
$875$	10.2160	+	20.0002i	0.345365	+	0.676129i
$876$	14.4740	−	11.4326i	0.489030	−	0.386271i
$877$	3.51092	−	11.3821i	0.118555	−	0.384347i	−0.876772	−	0.480906i	$-0.840308\pi$
$877$	3.51092	−	11.3821i	0.118555	−	0.384347i	0.995327	+	0.0965598i	$0.0307839\pi$
$878$	0.143913	+	1.98242i	0.00485684	+	0.0669033i
$879$	−7.65553	+	7.10330i	−0.258215	+	0.239588i
$880$	−7.85467	−	7.42561i	−0.264781	−	0.250317i
$881$	−13.8783			−0.467571			−0.233785	−	0.972288i	$-0.575111\pi$
$881$	−13.8783			−0.467571			−0.233785	+	0.972288i	$0.575111\pi$
$882$	−13.4374	−	21.0492i	−0.452462	−	0.708762i
$883$			5.05676i			0.170173i	0.996374	+	0.0850867i	$0.0271167\pi$
$883$			5.05676i			0.170173i	−0.996374	+	0.0850867i	$0.972883\pi$
$884$	−1.50239	−	0.119638i	−0.0505309	−	0.00402385i
$885$	−1.43410	−	1.54559i	−0.0482068	−	0.0519546i
$886$	−49.1686	+	3.56939i	−1.65185	+	0.119916i
$887$	16.2403	+	5.00946i	0.545295	+	0.168201i	0.555150	−	0.831750i	$-0.312661\pi$
$887$	16.2403	+	5.00946i	0.545295	+	0.168201i	−0.00985484	+	0.999951i	$0.503137\pi$
$888$	−11.4339	−	5.60514i	−0.383695	−	0.188096i
$889$	3.08796	+	3.69119i	0.103567	+	0.123799i
$890$	9.28193	−	7.36674i	0.311131	−	0.246934i
$891$	−14.3040	−	1.07194i	−0.479202	−	0.0359112i
$892$	3.89905	−	9.79996i	0.130550	−	0.328127i
$893$	6.59832	−	0.494475i	0.220804	−	0.0165470i
$894$	−13.9515	−	13.0058i	−0.466609	−	0.434979i
$895$	−21.0869	−	10.1549i	−0.704857	−	0.339441i
$896$	22.0871	+	20.2029i	0.737880	+	0.674932i
$897$	−4.35344	+	2.09651i	−0.145357	+	0.0700004i
$898$	−27.9809	−	8.70247i	−0.933734	−	0.290405i
$899$	13.0297	−	86.4462i	0.434564	−	2.88314i
$900$	−20.6238	−	3.20699i	−0.687461	−	0.106900i
$901$	0.872202	+	0.503566i	0.0290573	+	0.0167762i
$902$	−10.9566	−	2.52768i	−0.364816	−	0.0841625i
$903$	13.6178	−	4.55287i	0.453173	−	0.151510i
$904$	23.9877	−	11.3458i	0.797817	−	0.377356i
$905$	11.1193	−	1.67596i	0.369618	−	0.0557109i
$906$	1.80651	−	11.7987i	0.0600173	−	0.391984i
$907$	24.9042	−	36.5278i	0.826931	−	1.21288i	−0.147693	−	0.989033i	$-0.547185\pi$
$907$	24.9042	−	36.5278i	0.826931	−	1.21288i	0.974623	−	0.223851i	$-0.0718630\pi$
$908$	−12.6044	−	7.35575i	−0.418292	−	0.244109i
$909$	−15.8814	+	12.6650i	−0.526754	+	0.420072i
$910$	0.915301	+	9.51334i	0.0303419	+	0.315364i
$911$	15.1905	−	19.0483i	0.503285	−	0.631099i	−0.463682	−	0.886002i	$-0.653472\pi$
$911$	15.1905	−	19.0483i	0.503285	−	0.631099i	0.966967	+	0.254902i	$0.0820434\pi$
$912$	−2.62960	−	0.838065i	−0.0870748	−	0.0277511i
$913$	−23.6398	−	40.9454i	−0.782364	−	1.35509i
$914$	53.4257	−	16.3433i	1.76717	−	0.540589i
$915$	6.68507	−	7.20479i	0.221002	−	0.238183i
$916$	18.2129	+	4.24645i	0.601772	+	0.140307i
$917$	11.8638	+	16.5533i	0.391777	+	0.546638i
$918$	−0.00344912	+	1.47903i	−0.000113838	+	0.0488152i
$919$	−0.478397	−	1.21893i	−0.0157808	−	0.0402089i	0.922766	−	0.385360i	$-0.125923\pi$
$919$	−0.478397	−	1.21893i	−0.0157808	−	0.0402089i	−0.938547	+	0.345151i	$0.887828\pi$
$920$	1.04238	−	6.60198i	0.0343661	−	0.217661i
$921$	21.5602	−	6.65044i	0.710432	−	0.219139i
$922$	7.00349	−	2.72984i	0.230648	−	0.0899023i
$923$	−20.2624	+	4.62476i	−0.666945	+	0.152226i
$924$	−9.66622	−	4.43329i	−0.317995	−	0.145845i
$925$	−26.2803	−	5.99830i	−0.864090	−	0.197223i
$926$	29.6784	−	4.40254i	0.975292	−	0.144676i
$927$	−3.22832	+	8.22563i	−0.106032	+	0.270165i
$928$	7.96240	−	48.9475i	0.261378	−	1.60678i
$929$	0.578786	−	0.394610i	0.0189894	−	0.0129467i	−0.553788	−	0.832658i	$-0.686818\pi$
$929$	0.578786	−	0.394610i	0.0189894	−	0.0129467i	0.572778	+	0.819711i	$0.305866\pi$
$930$	−8.16525	+	3.90875i	−0.267749	+	0.128173i
$931$	−4.20427	−	5.58476i	−0.137789	−	0.183033i
$932$	−27.1455	+	33.7156i	−0.889181	+	1.10439i
$933$	−3.46300	−	5.07929i	−0.113374	−	0.166288i
$934$	−12.0128	−	4.74705i	−0.393072	−	0.155328i
$935$	−0.270589	+	0.689450i	−0.00884921	+	0.0225474i
$936$	−16.9200	−	9.92724i	−0.553047	−	0.324482i
$937$	−6.73531	+	29.5093i	−0.220033	+	0.964028i	0.737419	+	0.675436i	$0.236044\pi$
$937$	−6.73531	+	29.5093i	−0.220033	+	0.964028i	−0.957452	+	0.288592i	$0.906813\pi$
$938$	9.02787	+	1.86091i	0.294770	+	0.0607608i
$939$	−13.4738	+	3.07531i	−0.439701	+	0.100359i
$940$	8.41583	−	8.98568i	0.274494	−	0.293081i
$941$	−9.74289	−	31.5857i	−0.317609	−	1.02966i	−0.963831	−	0.266514i	$-0.914128\pi$
$941$	−9.74289	−	31.5857i	−0.317609	−	1.02966i	0.646222	−	0.763149i	$-0.276348\pi$
$942$	−5.40351	−	9.40976i	−0.176056	−	0.306587i
$943$	−2.54021	−	6.47234i	−0.0827205	−	0.210769i
$944$	−12.7816	−	3.04304i	−0.416007	−	0.0990424i
$945$	9.23890	−	1.61493i	0.300541	−	0.0525338i
$946$	−20.2043	+	25.2146i	−0.656900	+	0.819797i
$947$	−28.0838	+	30.2671i	−0.912601	+	0.983550i	−0.999920	−	0.0126307i	$-0.995979\pi$
$947$	−28.0838	+	30.2671i	−0.912601	+	0.983550i	0.0873195	+	0.996180i	$0.472170\pi$
$948$	−7.73799	−	8.41797i	−0.251318	−	0.273403i
$949$	31.7816	−	18.3491i	1.03167	−	0.595637i
$950$	−5.82506	−	0.450191i	−0.188990	−	0.0146061i
$951$	−2.60542	+	3.26709i	−0.0844864	+	0.105943i
$952$	0.717822	−	1.92135i	0.0232648	−	0.0622712i
$953$	31.7452	+	39.8072i	1.02833	+	1.28948i	0.956396	+	0.292072i	$0.0943446\pi$
$953$	31.7452	+	39.8072i	1.02833	+	1.28948i	0.0719306	+	0.997410i	$0.477084\pi$
$954$	7.35927	+	10.8483i	0.238265	+	0.351228i
$955$	−9.84705	+	14.4430i	−0.318643	+	0.467364i
$956$	0.130152	−	0.0394829i	0.00420943	−	0.00127697i
$957$	2.62585	+	17.4214i	0.0848815	+	0.563152i
$958$	35.0932	+	17.0009i	1.13381	+	0.549275i
$959$	−2.19995	−	22.3194i	−0.0710400	−	0.720731i
$960$	−4.65732	+	2.16310i	−0.150314	+	0.0698137i
$961$	−34.2238	+	59.2773i	−1.10399	+	1.91217i
$962$	−20.9002	−	14.3210i	−0.673851	−	0.461729i
$963$	−1.33888	+	8.88287i	−0.0431447	+	0.286246i
$964$	28.2990	−	4.13050i	0.911450	−	0.133034i
$965$	1.48349	+	3.08051i	0.0477554	+	0.0991651i
$966$	−1.11715	−	6.48016i	−0.0359436	−	0.208496i
$967$	−28.2821	−	13.6200i	−0.909492	−	0.437988i	−0.0801843	−	0.996780i	$-0.525551\pi$
$967$	−28.2821	−	13.6200i	−0.909492	−	0.437988i	−0.829308	+	0.558792i	$0.811265\pi$
$968$	−7.10972	+	1.02080i	−0.228515	+	0.0328098i
$969$	0.0141324	+	0.188584i	0.000453998	+	0.00605818i
$970$	2.49221	+	2.69856i	0.0800200	+	0.0866454i
$971$	16.1151	+	1.20766i	0.517159	+	0.0387557i	0.330753	−	0.943717i	$-0.392697\pi$
$971$	16.1151	+	1.20766i	0.517159	+	0.0387557i	0.186405	+	0.982473i	$0.440316\pi$
$972$	−13.0149	+	26.7065i	−0.417455	+	0.856610i
$973$	0.853257	+	36.3806i	0.0273542	+	1.16631i
$974$	−3.63668	−	16.1064i	−0.116527	−	0.516082i
$975$	7.50957	+	2.31640i	0.240499	+	0.0741840i
$976$	9.69293	−	60.4752i	0.310263	−	1.93576i
$977$	9.55169	−	8.86268i	0.305586	−	0.283542i	−0.512441	−	0.858723i	$-0.671259\pi$
$977$	9.55169	−	8.86268i	0.305586	−	0.283542i	0.818027	+	0.575180i	$0.195068\pi$
$978$	4.28531	−	7.38256i	0.137029	−	0.236068i
$979$			26.2347i			0.838464i
$980$	−12.7912	−	2.35622i	−0.408599	−	0.0752667i
$981$			5.35917i			0.171105i
$982$	39.7160	+	23.0537i	1.26739	+	0.735672i
$983$	6.49091	−	6.02269i	0.207028	−	0.192094i	−0.569843	−	0.821753i	$-0.692996\pi$
$983$	6.49091	−	6.02269i	0.207028	−	0.192094i	0.776871	+	0.629660i	$0.216806\pi$
$984$	−3.04004	+	4.39258i	−0.0969130	+	0.140030i
$985$	5.89757	+	1.81916i	0.187912	+	0.0579632i
$986$	−3.31458	+	0.748403i	−0.105558	+	0.0238340i
$987$	4.99804	−	11.0331i	0.159089	−	0.351187i
$988$	−4.93632	−	2.40563i	−0.157045	−	0.0765333i
$989$	−19.9235	−	1.49306i	−0.633531	−	0.0474766i
$990$	−7.08217	+	6.54062i	−0.225086	+	0.207875i
$991$	−1.53057	−	20.4240i	−0.0486200	−	0.648789i	−0.967275	−	0.253729i	$-0.918343\pi$
$991$	−1.53057	−	20.4240i	−0.0486200	−	0.648789i	0.918655	−	0.395060i	$-0.129276\pi$
$992$	−28.7737	+	48.5221i	−0.913567	+	1.54058i
$993$	−5.24259	−	2.52470i	−0.166368	−	0.0801188i
$994$	1.51763	−	28.2432i	0.0481361	−	0.895821i
$995$	3.64577	+	7.57052i	0.115579	+	0.240001i
$996$	−22.2260	+	3.24408i	−0.704257	+	0.102793i
$997$	4.25915	−	28.2576i	0.134889	−	0.894929i	−0.814350	−	0.580373i	$-0.802907\pi$
$997$	4.25915	−	28.2576i	0.134889	−	0.894929i	0.949239	−	0.314555i	$-0.101855\pi$
$998$	−14.9840	+	21.8677i	−0.474310	+	0.692211i
$999$	−12.4317	+	21.5323i	−0.393321	+	0.681251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.z.a.37.19	yes	648
8.5	even	2	inner	392.2.z.a.37.4	✓	648
49.4	even	21	inner	392.2.z.a.53.4	yes	648
392.53	even	42	inner	392.2.z.a.53.19	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.z.a.37.4	✓	648	8.5	even	2	inner
392.2.z.a.37.19	yes	648	1.1	even	1	trivial
392.2.z.a.53.4	yes	648	49.4	even	21	inner
392.2.z.a.53.19	yes	648	392.53	even	42	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.z (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.709961 + 1.22309i) q^{2} +(0.469951 + 0.506487i) q^{3} +(-0.991911 - 1.73670i) q^{4} +(-0.273835 + 0.887753i) q^{5} +(-0.953127 + 0.215208i) q^{6} +(0.528093 - 2.59251i) q^{7} +(2.82836 + 0.0197876i) q^{8} +(0.188515 - 2.51556i) q^{9} +O(q^{10})\)	\(q+(-0.709961 + 1.22309i) q^{2} +(0.469951 + 0.506487i) q^{3} +(-0.991911 - 1.73670i) q^{4} +(-0.273835 + 0.887753i) q^{5} +(-0.953127 + 0.215208i) q^{6} +(0.528093 - 2.59251i) q^{7} +(2.82836 + 0.0197876i) q^{8} +(0.188515 - 2.51556i) q^{9} +(-0.891391 - 0.965196i) q^{10} +(2.90057 - 0.217368i) q^{11} +(0.413464 - 1.31855i) q^{12} +(1.19293 - 2.47715i) q^{13} +(2.79596 + 2.48649i) q^{14} +(-0.578324 + 0.278506i) q^{15} +(-2.03223 + 3.44530i) q^{16} +(0.271023 + 0.0408501i) q^{17} +(2.94293 + 2.01652i) q^{18} +(0.864835 + 0.499313i) q^{19} +(1.81338 - 0.405003i) q^{20} +(1.56125 - 0.950882i) q^{21} +(-1.79343 + 3.70199i) q^{22} +(-2.51518 + 0.379103i) q^{23} +(1.31917 + 1.44183i) q^{24} +(3.41808 + 2.33040i) q^{25} +(2.18284 + 3.21774i) q^{26} +(2.98326 - 2.37907i) q^{27} +(-5.02623 + 1.65440i) q^{28} +(6.85394 + 5.46583i) q^{29} +(0.0699487 - 0.905073i) q^{30} +(-4.98617 - 8.63630i) q^{31} +(-2.77111 - 4.93163i) q^{32} +(1.47322 + 1.36695i) q^{33} +(-0.242379 + 0.302484i) q^{34} +(2.15690 + 1.17874i) q^{35} +(-4.55576 + 2.16782i) q^{36} +(-6.06557 + 2.38056i) q^{37} +(-1.22471 + 0.703281i) q^{38} +(1.81526 - 0.559934i) q^{39} +(-0.792071 + 2.50546i) q^{40} +(0.608266 + 2.66499i) q^{41} +(0.0545889 + 2.58464i) q^{42} +(7.65784 + 1.74785i) q^{43} +(-3.25461 - 4.82180i) q^{44} +(2.18158 + 0.856205i) q^{45} +(1.32200 - 3.34545i) q^{46} +(5.47460 - 3.73252i) q^{47} +(-2.70004 + 0.589825i) q^{48} +(-6.44224 - 2.73818i) q^{49} +(-5.27700 + 2.52613i) q^{50} +(0.106678 + 0.156467i) q^{51} +(-5.48533 + 0.385350i) q^{52} +(3.42053 + 1.34246i) q^{53} +(0.791826 + 5.33786i) q^{54} +(-0.601310 + 2.63451i) q^{55} +(1.54494 - 7.32210i) q^{56} +(0.153535 + 0.672680i) q^{57} +(-11.5512 + 4.50247i) q^{58} +(0.968189 + 3.13879i) q^{59} +(1.05733 + 0.728120i) q^{60} +(-14.2533 + 5.59401i) q^{61} +(14.1030 + 0.0328884i) q^{62} +(-6.42207 - 1.81718i) q^{63} +(7.99922 + 0.111933i) q^{64} +(1.87243 + 1.73736i) q^{65} +(-2.71783 + 0.831405i) q^{66} +(2.13348 - 1.23176i) q^{67} +(-0.197886 - 0.511204i) q^{68} +(-1.37402 - 1.09575i) q^{69} +(-2.97302 + 1.80123i) q^{70} +(-4.71309 - 5.91003i) q^{71} +(0.582966 - 7.11118i) q^{72} +(11.0283 + 7.51897i) q^{73} +(1.39467 - 9.10886i) q^{74} +(0.426009 + 2.82639i) q^{75} +(0.00931520 - 1.99723i) q^{76} +(0.968243 - 7.63455i) q^{77} +(-0.603914 + 2.61776i) q^{78} +(4.13722 - 7.16587i) q^{79} +(-2.50207 - 2.74756i) q^{80} +(-4.87637 - 0.734994i) q^{81} +(-3.69137 - 1.14807i) q^{82} +(-7.05258 - 14.6448i) q^{83} +(-3.20001 - 1.76823i) q^{84} +(-0.110481 + 0.229415i) q^{85} +(-7.57455 + 8.12534i) q^{86} +(0.452643 + 6.04010i) q^{87} +(8.20815 - 0.557398i) q^{88} +(-0.674018 + 8.99415i) q^{89} +(-2.59605 + 2.06040i) q^{90} +(-5.79205 - 4.40085i) q^{91} +(3.15323 + 3.99207i) q^{92} +(2.03092 - 6.58407i) q^{93} +(0.678463 + 9.34588i) q^{94} +(-0.680089 + 0.631030i) q^{95} +(1.19552 - 3.72116i) q^{96} -2.79586 q^{97} +(7.92278 - 5.93545i) q^{98} -7.33754i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Introduction

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