LMFDB - Embedded newform 392.2.z.a.37.4

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			37.4
Character	$\chi$	$=$	392.37
Dual form			392.2.z.a.53.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39792 + 0.214038i) q^{2} +(-0.469951 - 0.506487i) q^{3} +(1.90838 - 0.598418i) q^{4} +(0.273835 - 0.887753i) q^{5} +(0.765363 + 0.607442i) q^{6} +(0.528093 - 2.59251i) q^{7} +(-2.53968 + 1.24501i) q^{8} +(0.188515 - 2.51556i) q^{9} +O(q^{10})$	\(q+(-1.39792 + 0.214038i) q^{2} +(-0.469951 - 0.506487i) q^{3} +(1.90838 - 0.598418i) q^{4} +(0.273835 - 0.887753i) q^{5} +(0.765363 + 0.607442i) q^{6} +(0.528093 - 2.59251i) q^{7} +(-2.53968 + 1.24501i) q^{8} +(0.188515 - 2.51556i) q^{9} +(-0.192788 + 1.29962i) q^{10} +(-2.90057 + 0.217368i) q^{11} +(-1.19993 - 0.685340i) q^{12} +(-1.19293 + 2.47715i) q^{13} +(-0.183337 + 3.73716i) q^{14} +(-0.578324 + 0.278506i) q^{15} +(3.28379 - 2.28401i) q^{16} +(0.271023 + 0.0408501i) q^{17} +(0.274897 + 3.55691i) q^{18} +(-0.864835 - 0.499313i) q^{19} +(-0.00866598 - 1.85803i) q^{20} +(-1.56125 + 0.950882i) q^{21} +(4.00825 - 0.924696i) q^{22} +(-2.51518 + 0.379103i) q^{23} +(1.82410 + 0.701221i) q^{24} +(3.41808 + 2.33040i) q^{25} +(1.13742 - 3.71819i) q^{26} +(-2.98326 + 2.37907i) q^{27} +(-0.543605 - 5.26351i) q^{28} +(-6.85394 - 5.46583i) q^{29} +(0.748842 - 0.513114i) q^{30} +(-4.98617 - 8.63630i) q^{31} +(-4.10162 + 3.89573i) q^{32} +(1.47322 + 1.36695i) q^{33} +(-0.387613 + 0.000903920i) q^{34} +(-2.15690 - 1.17874i) q^{35} +(-1.14560 - 4.91345i) q^{36} +(6.06557 - 2.38056i) q^{37} +(1.31584 + 0.512893i) q^{38} +(1.81526 - 0.559934i) q^{39} +(0.409804 + 2.59553i) q^{40} +(0.608266 + 2.66499i) q^{41} +(1.97898 - 1.66343i) q^{42} +(-7.65784 - 1.74785i) q^{43} +(-5.40530 + 2.15057i) q^{44} +(-2.18158 - 0.856205i) q^{45} +(3.43489 - 1.06830i) 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} +(-0.794192 + 5.44119i) q^{52} +(-3.42053 - 1.34246i) q^{53} +(3.66116 - 3.96429i) q^{54} +(-0.601310 + 2.63451i) q^{55} +(1.88651 + 7.24162i) q^{56} +(0.153535 + 0.672680i) q^{57} +(10.7512 + 6.17381i) q^{58} +(-0.968189 - 3.13879i) q^{59} +(-0.936997 + 0.877574i) q^{60} +(14.2533 - 5.59401i) q^{61} +(8.81878 + 11.0056i) q^{62} +(-6.42207 - 1.81718i) q^{63} +(4.89992 - 6.32383i) q^{64} +(1.87243 + 1.73736i) q^{65} +(-2.35203 - 1.59556i) q^{66} +(-2.13348 + 1.23176i) q^{67} +(0.541659 - 0.0842275i) q^{68} +(1.37402 + 1.09575i) q^{69} +(3.26747 + 1.18613i) q^{70} +(-4.71309 - 5.91003i) q^{71} +(2.65312 + 6.62342i) q^{72} +(11.0283 + 7.51897i) q^{73} +(-7.96967 + 4.62611i) q^{74} +(-0.426009 - 2.82639i) q^{75} +(-1.94923 - 0.435344i) q^{76} +(-0.968243 + 7.63455i) q^{77} +(-2.41775 + 1.17128i) q^{78} +(4.13722 - 7.16587i) q^{79} +(-1.12842 - 3.54064i) q^{80} +(-4.87637 - 0.734994i) q^{81} +(-1.42072 - 3.59526i) q^{82} +(7.05258 + 14.6448i) q^{83} +(-2.41043 + 2.74892i) q^{84} +(0.110481 - 0.229415i) q^{85} +(11.0792 + 0.804292i) q^{86} +(0.452643 + 6.04010i) q^{87} +(7.09589 - 4.16327i) q^{88} +(-0.674018 + 8.99415i) q^{89} +(3.23293 + 0.729968i) q^{90} +(5.79205 + 4.40085i) q^{91} +(-4.57305 + 2.22860i) q^{92} +(-2.03092 + 6.58407i) q^{93} +(-6.85416 + 6.38954i) q^{94} +(-0.680089 + 0.631030i) q^{95} +(3.90070 + 0.246617i) q^{96} -2.79586 q^{97} +(9.59182 + 2.44887i) 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 $

$2$	−1.39792	+	0.214038i	−0.988481	+	0.151348i
$2$	−1.39792	+	0.214038i	−0.988481	+	0.151348i
$3$	−0.469951	−	0.506487i	−0.271326	−	0.292420i	0.582660	−	0.812716i	$-0.302012\pi$
$3$	−0.469951	−	0.506487i	−0.271326	−	0.292420i	−0.853986	+	0.520296i	$0.825822\pi$
$4$	1.90838	−	0.598418i	0.954188	−	0.299209i
$5$	0.273835	−	0.887753i	0.122463	−	0.397015i	−0.873495	−	0.486833i	$-0.838152\pi$
$5$	0.273835	−	0.887753i	0.122463	−	0.397015i	0.995958	+	0.0898175i	$0.0286284\pi$
$6$	0.765363	+	0.607442i	0.312458	+	0.247987i
$7$	0.528093	−	2.59251i	0.199600	−	0.979877i
$7$	0.528093	−	2.59251i	0.199600	−	0.979877i
$8$	−2.53968	+	1.24501i	−0.897911	+	0.440176i
$9$	0.188515	−	2.51556i	0.0628385	−	0.838521i
$10$	−0.192788	+	1.29962i	−0.0609648	+	0.410976i
$11$	−2.90057	+	0.217368i	−0.874555	+	0.0655388i	−0.504440	−	0.863447i	$-0.668301\pi$
$11$	−2.90057	+	0.217368i	−0.874555	+	0.0655388i	−0.370115	+	0.928986i	$0.620682\pi$
$12$	−1.19993	−	0.685340i	−0.346391	−	0.197841i
$13$	−1.19293	+	2.47715i	−0.330859	+	0.687037i	−0.998340	−	0.0575903i	$-0.981658\pi$
$13$	−1.19293	+	2.47715i	−0.330859	+	0.687037i	0.667481	+	0.744627i	$0.267373\pi$
$14$	−0.183337	+	3.73716i	−0.0489989	+	0.998799i
$15$	−0.578324	+	0.278506i	−0.149323	+	0.0719100i
$16$	3.28379	−	2.28401i	0.820948	−	0.571003i
$17$	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	$0.537037\pi$
$18$	0.274897	+	3.55691i	0.0647937	+	0.838372i
$19$	−0.864835	−	0.499313i	−0.198407	−	0.114550i	0.397505	−	0.917600i	$-0.369876\pi$
$19$	−0.864835	−	0.499313i	−0.198407	−	0.114550i	−0.595912	+	0.803050i	$0.703209\pi$
$20$	−0.00866598	−	1.85803i	−0.00193777	−	0.415469i
$21$	−1.56125	+	0.950882i	−0.340693	+	0.207499i
$22$	4.00825	−	0.924696i	0.854561	−	0.197146i
$23$	−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	$0.537815\pi$
$24$	1.82410	+	0.701221i	0.372344	+	0.143136i
$25$	3.41808	+	2.33040i	0.683615	+	0.466081i
$26$	1.13742	−	3.71819i	0.223067	−	0.729197i
$27$	−2.98326	+	2.37907i	−0.574129	+	0.457853i
$28$	−0.543605	−	5.26351i	−0.102732	−	0.994709i
$29$	−6.85394	−	5.46583i	−1.27274	−	1.01498i	−0.998579	−	0.0532967i	$-0.983027\pi$
$29$	−6.85394	−	5.46583i	−1.27274	−	1.01498i	−0.274165	−	0.961683i	$-0.588401\pi$
$30$	0.748842	−	0.513114i	0.136719	−	0.0936813i
$31$	−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	$-0.519879\pi$
$32$	−4.10162	+	3.89573i	−0.725071	+	0.688674i
$33$	1.47322	+	1.36695i	0.256455	+	0.237955i
$34$	−0.387613		0.000903920i	−0.0664750		0.000155021i
$35$	−2.15690	−	1.17874i	−0.364582	−	0.199243i
$36$	−1.14560	−	4.91345i	−0.190933	−	0.818908i
$37$	6.06557	−	2.38056i	0.997174	−	0.391362i	0.190070	−	0.981771i	$-0.439129\pi$
$37$	6.06557	−	2.38056i	0.997174	−	0.391362i	0.807105	+	0.590409i	$0.201033\pi$
$38$	1.31584	+	0.512893i	0.213458	+	0.0832022i
$39$	1.81526	−	0.559934i	0.290674	−	0.0896612i
$40$	0.409804	+	2.59553i	0.0647957	+	0.410390i
$41$	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	$0.860101\pi$
$42$	1.97898	−	1.66343i	0.305364	−	0.256672i
$43$	−7.65784	−	1.74785i	−1.16781	−	0.266545i	−0.405708	−	0.914003i	$-0.632975\pi$
$43$	−7.65784	−	1.74785i	−1.16781	−	0.266545i	−0.762102	+	0.647458i	$0.775832\pi$
$44$	−5.40530	+	2.15057i	−0.814880	+	0.324211i
$45$	−2.18158	−	0.856205i	−0.325210	−	0.127636i
$46$	3.43489	−	1.06830i	0.506447	−	0.157513i
$47$	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
$52$	−0.794192	+	5.44119i	−0.110135	+	0.754558i
$53$	−3.42053	−	1.34246i	−0.469846	−	0.184401i	0.118593	−	0.992943i	$-0.462162\pi$
$53$	−3.42053	−	1.34246i	−0.469846	−	0.184401i	−0.588438	+	0.808542i	$0.700257\pi$
$54$	3.66116	−	3.96429i	0.498221	−	0.539472i
$55$	−0.601310	+	2.63451i	−0.0810806	+	0.355237i
$56$	1.88651	+	7.24162i	0.252095	+	0.967702i
$57$	0.153535	+	0.672680i	0.0203362	+	0.0890987i
$58$	10.7512	+	6.17381i	1.41170	+	0.810660i
$59$	−0.968189	−	3.13879i	−0.126048	−	0.408636i	0.870450	−	0.492257i	$-0.163828\pi$
$59$	−0.968189	−	3.13879i	−0.126048	−	0.408636i	−0.996498	+	0.0836206i	$0.973352\pi$
$60$	−0.936997	+	0.877574i	−0.120966	+	0.113294i
$61$	14.2533	−	5.59401i	1.82495	−	0.716240i	0.840197	−	0.542281i	$-0.182439\pi$
$61$	14.2533	−	5.59401i	1.82495	−	0.716240i	0.984753	−	0.173959i	$-0.0556560\pi$
$62$	8.81878	+	11.0056i	1.11999	+	1.39772i
$63$	−6.42207	−	1.81718i	−0.809105	−	0.228943i
$64$	4.89992	−	6.32383i	0.612490	−	0.790479i
$65$	1.87243	+	1.73736i	0.232246	+	0.215493i
$66$	−2.35203	−	1.59556i	−0.289515	−	0.196400i
$67$	−2.13348	+	1.23176i	−0.260645	+	0.150484i	−0.624629	−	0.780922i	$-0.714750\pi$
$67$	−2.13348	+	1.23176i	−0.260645	+	0.150484i	0.363983	+	0.931405i	$0.381416\pi$
$68$	0.541659	−	0.0842275i	0.0656858	−	0.0102141i
$69$	1.37402	+	1.09575i	0.165413	+	0.131913i
$70$	3.26747	+	1.18613i	0.390538	+	0.141769i
$71$	−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	$0.933776\pi$
$72$	2.65312	+	6.62342i	0.312674	+	0.780578i
$73$	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	$0.405130\pi$
$74$	−7.96967	+	4.62611i	−0.926455	+	0.537774i
$75$	−0.426009	−	2.82639i	−0.0491913	−	0.326363i
$76$	−1.94923	−	0.435344i	−0.223592	−	0.0499374i
$77$	−0.968243	+	7.63455i	−0.110342	+	0.870038i
$78$	−2.41775	+	1.17128i	−0.273756	+	0.132621i
$79$	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	$0.0125507\pi$
$80$	−1.12842	−	3.54064i	−0.126161	−	0.395855i
$81$	−4.87637	−	0.734994i	−0.541819	−	0.0816660i
$82$	−1.42072	−	3.59526i	−0.156892	−	0.397030i
$83$	7.05258	+	14.6448i	0.774121	+	1.60748i	0.794182	+	0.607681i	$0.207900\pi$
$83$	7.05258	+	14.6448i	0.774121	+	1.60748i	−0.0200603	+	0.999799i	$0.506386\pi$
$84$	−2.41043	+	2.74892i	−0.262999	+	0.299932i
$85$	0.110481	−	0.229415i	0.0119833	−	0.0248836i
$86$	11.0792	+	0.804292i	1.19470	+	0.0867291i
$87$	0.452643	+	6.04010i	0.0485284	+	0.647567i
$88$	7.09589	−	4.16327i	0.756424	−	0.443806i
$89$	−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	$0.865162\pi$
$90$	3.23293	+	0.729968i	0.340781	+	0.0769454i
$91$	5.79205	+	4.40085i	0.607172	+	0.461334i
$92$	−4.57305	+	2.22860i	−0.476774	+	0.232348i
$93$	−2.03092	+	6.58407i	−0.210596	+	0.682736i
$94$	−6.85416	+	6.38954i	−0.706953	+	0.659031i
$95$	−0.680089	+	0.631030i	−0.0697756	+	0.0647423i
$96$	3.90070	+	0.246617i	0.398113	+	0.0251702i
$97$	−2.79586			−0.283877			−0.141939	−	0.989875i	$-0.545334\pi$
$97$	−2.79586			−0.283877			−0.141939	+	0.989875i	$0.545334\pi$
$98$	9.59182	+	2.44887i	0.968920	+	0.247374i
$99$			7.33754i			0.737451i
$100$	7.91753	+	2.40185i	0.791753	+	0.240185i
$101$	5.47702	+	5.90282i	0.544984	+	0.587353i	0.944146	−	0.329527i	$-0.106889\pi$
$101$	5.47702	+	5.90282i	0.544984	+	0.587353i	−0.399162	+	0.916880i	$0.630699\pi$
$102$	0.182617	+	0.195896i	0.0180818	+	0.0193966i
$103$	−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	$0.650447\pi$
$104$	−0.0544046	−	7.77636i	−0.00533481	−	0.762534i
$105$	0.416622	+	1.64639i	0.0406581	+	0.160671i
$106$	5.06897	+	1.14453i	0.492342	+	0.111167i
$107$	3.55111	+	0.266119i	0.343299	+	0.0257267i	0.245264	−	0.969456i	$-0.421125\pi$
$107$	3.55111	+	0.266119i	0.343299	+	0.0257267i	0.0980346	+	0.995183i	$0.468744\pi$
$108$	−4.26951	+	6.32540i	−0.410834	+	0.608662i
$109$	2.11851	−	0.158760i	0.202916	−	0.0152065i	0.0271158	−	0.999632i	$-0.491368\pi$
$109$	2.11851	−	0.158760i	0.202916	−	0.0152065i	0.175800	+	0.984426i	$0.443749\pi$
$110$	0.276699	−	3.81155i	0.0263822	−	0.363417i
$111$	−4.05625	−	1.95339i	−0.385002	−	0.185407i
$112$	−4.18718	−	9.71944i	−0.395651	−	0.918401i
$113$	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	$0.211668\pi$
$114$	−0.358609	−	0.907493i	−0.0335868	−	0.0849945i
$115$	−0.352197	+	2.33667i	−0.0328425	+	0.217896i
$116$	−16.3507	−	6.32934i	−1.51813	−	0.587665i
$117$	6.00653	+	3.46787i	0.555304	+	0.320605i
$118$	2.02528	+	4.18056i	0.186442	+	0.384852i
$119$	0.249030	−	0.681058i	0.0228285	−	0.0624325i
$120$	1.12201	−	1.42733i	0.102425	−	0.130297i
$121$	−2.51108	+	0.378484i	−0.228280	+	0.0344077i
$122$	−18.7277	+	10.8708i	−1.69553	+	0.984192i
$123$	1.06393	−	1.56049i	0.0959310	−	0.140705i
$124$	−14.6836	−	13.4975i	−1.31863	−	1.21211i
$125$	6.63652	−	5.29245i	0.593589	−	0.473371i
$126$	9.36651	+	1.16571i	0.834435	+	0.103850i
$127$	−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	$0.240002\pi$
$128$	−5.49616	+	9.88899i	−0.485797	+	0.874072i
$129$	2.71355	+	4.70000i	0.238915	+	0.413812i
$130$	−2.98937	−	2.02792i	−0.262185	−	0.177860i
$131$	5.23563	−	5.64267i	0.457439	−	0.493002i	−0.461644	−	0.887065i	$-0.652740\pi$
$131$	5.23563	−	5.64267i	0.457439	−	0.493002i	0.919083	+	0.394063i	$0.128931\pi$
$132$	3.62946	+	1.72705i	0.315904	+	0.150320i
$133$	−1.75119	+	1.97841i	−0.151847	+	0.171550i
$134$	2.71879	−	2.17855i	0.234868	−	0.188198i
$135$	1.29511	+	3.29987i	0.111465	+	0.284008i
$136$	−0.739170	+	0.233679i	−0.0633833	+	0.0200378i
$137$	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	$0.286818\pi$
$138$	−2.15531	−	1.23768i	−0.183472	−	0.105358i
$139$	13.4095	−	3.06063i	1.13738	−	0.259599i	0.387948	−	0.921681i	$-0.373184\pi$
$139$	13.4095	−	3.06063i	1.13738	−	0.259599i	0.749431	+	0.662082i	$0.230327\pi$
$140$	−4.82155	−	0.958748i	−0.407495	−	0.0810290i
$141$	−4.46326	−	1.01871i	−0.375875	−	0.0857909i
$142$	7.85350	+	7.25298i	0.659051	+	0.608656i
$143$	2.92173	−	7.44444i	0.244327	−	0.622535i
$144$	−5.12653	−	8.69116i	−0.427211	−	0.724263i
$145$	−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	$-0.895536\pi$
$149$	−10.9960	−	16.1282i	−0.900829	−	1.32127i	0.0458012	−	0.998951i	$-0.485416\pi$
$150$	1.20048	+	3.85989i	0.0980190	+	0.315158i
$151$	−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	$0.953465\pi$
$152$	2.81805	+	0.191368i	0.228574	+	0.0155220i
$153$	0.153853	−	0.674075i	0.0124383	−	0.0544957i
$154$	−0.280557	−	10.8798i	−0.0226079	−	0.876716i
$155$	−9.03229	+	2.06156i	−0.725491	+	0.165589i
$156$	3.12912	−	2.15485i	0.250530	−	0.172526i
$157$	−3.27324	−	10.6116i	−0.261233	−	0.846896i	−0.987244	−	0.159213i	$-0.949104\pi$
$157$	−3.27324	−	10.6116i	−0.261233	−	0.846896i	0.726011	−	0.687683i	$-0.241372\pi$
$158$	−4.24974	+	10.9029i	−0.338091	+	0.867385i
$159$	0.927544	+	2.36334i	0.0735590	+	0.187425i
$160$	2.33527	+	4.70801i	0.184619	+	0.372201i
$161$	−0.345423	+	6.72085i	−0.0272231	+	0.529677i
$162$	6.97410	−	0.0162637i	0.547937	−	0.00127780i
$163$	5.94201	−	6.40396i	0.465414	−	0.501597i	−0.456107	−	0.889925i	$-0.650757\pi$
$163$	5.94201	−	6.40396i	0.465414	−	0.501597i	0.921521	+	0.388328i	$0.126947\pi$
$164$	2.75558	+	4.72180i	0.215174	+	0.368711i
$165$	1.61693	−	0.933536i	0.125878	−	0.0726757i
$166$	−12.9935	−	18.9628i	−1.00849	−	1.47180i
$167$	−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	$0.991495\pi$
$168$	2.78122	−	4.35870i	0.214576	−	0.336281i
$169$	3.39220	+	4.25368i	0.260938	+	0.327206i
$170$	−0.105340	+	0.344352i	−0.00807918	+	0.0264106i
$171$	−1.41909	+	2.08142i	−0.108520	+	0.159170i
$172$	−15.6600	+	1.24703i	−1.19406	+	0.0950850i
$173$	−1.83839	−	12.1969i	−0.139770	−	0.927313i	−0.943274	−	0.332014i	$-0.892272\pi$
$173$	−1.83839	−	12.1969i	−0.139770	−	0.927313i	0.803504	−	0.595299i	$-0.202966\pi$
$174$	−1.92557	−	8.34671i	−0.145977	−	0.632763i
$175$	7.84666	−	7.63073i	0.593152	−	0.576829i
$176$	−9.02840	+	7.33872i	−0.680541	+	0.553177i
$177$	−1.13476	+	1.96545i	−0.0852935	+	0.147733i
$178$	−0.982865	−	12.7174i	−0.0736689	−	0.953209i
$179$	3.75478	−	24.9113i	0.280645	−	1.86196i	−0.192939	−	0.981211i	$-0.561802\pi$
$179$	3.75478	−	24.9113i	0.280645	−	1.86196i	0.473584	−	0.880749i	$-0.342960\pi$
$180$	−4.67563	−	0.328468i	−0.348501	−	0.0244826i
$181$	5.25171	+	10.9053i	0.390356	+	0.810583i	0.999842	+	0.0177859i	$0.00566174\pi$
$181$	5.25171	+	10.9053i	0.390356	+	0.810583i	−0.609486	+	0.792797i	$0.708624\pi$
$182$	−9.03879	−	4.91233i	−0.670000	−	0.364126i
$183$	−9.53166	−	4.59020i	−0.704600	−	0.339318i
$184$	5.91577	−	4.09422i	0.436116	−	0.301830i
$185$	−0.452381	−	6.03661i	−0.0332597	−	0.443820i
$186$	1.42982	−	9.63871i	0.104840	−	0.706745i
$187$	−0.795001	−	0.0595771i	−0.0581362	−	0.00435671i
$188$	8.21398	−	10.3991i	0.599066	−	0.758435i
$189$	4.59233	+	8.99052i	0.334043	+	0.653964i
$190$	0.815647	−	1.02770i	0.0591732	−	0.0745569i
$191$	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	$0.356900\pi$
$192$	−5.50566	+	0.490147i	−0.397337	+	0.0353733i
$193$	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	$0.219618\pi$
$194$	3.90840	−	0.598422i	0.280607	−	0.0429642i
$195$		−	1.76483i		−	0.126382i
$196$	−13.9328	−	1.37032i	−0.995198	−	0.0978800i
$197$			6.64325i			0.473312i	0.971593	+	0.236656i	$0.0760515\pi$
$197$			6.64325i			0.473312i	−0.971593	+	0.236656i	$0.923949\pi$
$198$	−1.57051	−	10.2573i	−0.111612	−	0.728956i
$199$	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	$0.158028\pi$
$200$	−11.5822	−	1.66295i	−0.818983	−	0.117588i
$201$	1.62650	+	0.501709i	0.114725	+	0.0353878i
$202$	−8.91988	−	7.07940i	−0.627601	−	0.498105i
$203$	−17.7897	+	14.8824i	−1.24860	+	1.04454i
$204$	−0.297213	−	0.234760i	−0.0208091	−	0.0164365i
$205$	2.53242	+	0.189778i	0.176872	+	0.0132547i
$206$	4.90022	+	0.726906i	0.341414	+	0.0506459i
$207$	0.479507	+	6.39857i	0.0333280	+	0.444732i
$208$	1.74049	+	10.8591i	0.120681	+	0.752943i
$209$	2.61705	+	1.26030i	0.181025	+	0.0871771i
$210$	−0.934795	−	2.21235i	−0.0645070	−	0.152667i
$211$	−3.89327	−	8.08445i	−0.268024	−	0.556557i	0.722905	−	0.690948i	$-0.242807\pi$
$211$	−3.89327	−	8.08445i	−0.268024	−	0.556557i	−0.990928	+	0.134391i	$0.957092\pi$
$212$	−7.33100	−	0.515010i	−0.503495	−	0.0353711i
$213$	−0.778429	+	5.16454i	−0.0533371	+	0.353869i
$214$	−5.02113	+	0.388059i	−0.343238	+	0.0265272i
$215$	−3.64865	+	6.31965i	−0.248836	+	0.430996i
$216$	4.61456	−	9.75626i	0.313981	−	0.663829i
$217$	−25.0229	+	8.36593i	−1.69866	+	0.567917i
$218$	−2.92753	+	0.675376i	−0.198277	+	0.0457422i
$219$	−1.37450	−	9.11924i	−0.0928804	−	0.616221i
$220$	0.429013	+	5.38747i	0.0289240	+	0.363223i
$221$	−0.424503	+	0.622632i	−0.0285552	+	0.0418828i
$222$	6.08842	+	1.86249i	0.408628	+	0.125002i
$223$	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	$0.729213\pi$
$224$	7.93368	+	12.6908i	0.530091	+	0.847941i
$225$	6.50664	−	8.15907i	0.433776	−	0.543938i
$226$	−10.9449	+	7.49954i	−0.728043	+	0.498862i
$227$	−6.31928	+	3.64844i	−0.419426	+	0.242156i	−0.694832	−	0.719173i	$-0.744521\pi$
$227$	−6.31928	+	3.64844i	−0.419426	+	0.242156i	0.275406	+	0.961328i	$0.411188\pi$
$228$	0.695546	+	1.19185i	0.0460637	+	0.0789321i
$229$	6.36010	−	6.85456i	0.420287	−	0.452962i	−0.487045	−	0.873377i	$-0.661925\pi$
$229$	6.36010	−	6.85456i	0.420287	−	0.452962i	0.907332	+	0.420415i	$0.138116\pi$
$230$	−0.00779331	−	3.34187i	−0.000513875	−	0.220357i
$231$	4.32183	−	3.09746i	0.284355	−	0.203798i
$232$	24.2118	+	5.34825i	1.58958	+	0.351130i
$233$	−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	$-0.369869\pi$
$234$	−9.13892	−	3.56219i	−0.597430	−	0.232868i
$235$	−1.81441	−	5.88218i	−0.118359	−	0.383711i
$236$	−3.72598	−	5.41061i	−0.242540	−	0.352201i
$237$	−5.57371	+	1.27216i	−0.362052	+	0.0826359i
$238$	−0.202352	+	1.00537i	−0.0131165	+	0.0651683i
$239$	−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	$0.0721287\pi$
$240$	−1.26299	+	2.23546i	−0.0815254	+	0.144298i
$241$	−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	$0.966698\pi$
$242$	3.42929	−	1.06656i	0.220443	−	0.0685610i
$243$	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
$248$	23.4155	+	15.7256i	1.48689	+	0.998576i
$249$	4.10305	−	10.4544i	0.260020	−	0.662520i
$250$	−8.14456	+	8.81891i	−0.515107	+	0.557757i
$251$	18.3670	+	4.19215i	1.15932	+	0.264606i	0.758576	−	0.651585i	$-0.225896\pi$
$251$	18.3670	+	4.19215i	1.15932	+	0.264606i	0.400741	+	0.916191i	$0.368753\pi$
$252$	−13.3432	+	0.375220i	−0.840540	+	0.0236366i
$253$	7.21306	−	1.64634i	0.453482	−	0.103504i
$254$	1.28100	−	2.23076i	0.0803772	−	0.139970i
$255$	−0.168116	+	0.0518570i	−0.0105278	+	0.00324741i
$256$	5.56659	−	15.0004i	0.347912	−	0.937527i
$257$	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	$0.838042\pi$
$258$	−4.79931	−	5.98944i	−0.298792	−	0.372886i
$259$	−2.96845	−	16.9822i	−0.184450	−	1.05522i
$260$	4.61296	+	2.19504i	0.286083	+	0.136130i
$261$	−15.0417	+	16.2111i	−0.931059	+	1.00344i
$262$	−6.11126	+	9.00864i	−0.377555	+	0.556556i
$263$	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	$0.650812\pi$
$264$	−5.44336	−	1.63744i	−0.335016	−	0.100777i
$265$	−2.12843	+	2.66897i	−0.130749	+	0.163954i
$266$	2.02457	−	3.14049i	0.124134	−	0.192556i
$267$	4.87217	−	3.88543i	0.298172	−	0.237784i
$268$	−3.33436	+	3.62737i	−0.203679	+	0.221577i
$269$	10.8059	−	15.8493i	0.658845	−	0.966349i	−0.340811	−	0.940132i	$-0.610702\pi$
$269$	10.8059	−	15.8493i	0.658845	−	0.966349i	0.999656	−	0.0262167i	$-0.00834599\pi$
$270$	−2.51676	−	4.33577i	−0.153165	−	0.263866i
$271$	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	$0.343162\pi$
$272$	0.983286	−	0.484876i	0.0596204	−	0.0293999i
$273$	−0.493008	−	5.00178i	−0.0298382	−	0.302722i
$274$	−10.7887	+	5.22659i	−0.651768	+	0.315750i
$275$	−10.4209	−	6.01652i	−0.628405	−	0.362810i
$276$	3.27787	+	1.26886i	0.197305	+	0.0763763i
$277$	−0.710237	+	4.71212i	−0.0426740	+	0.283124i	−0.999982	−	0.00594523i	$-0.998108\pi$
$277$	−0.710237	+	4.71212i	−0.0426740	+	0.283124i	0.957308	+	0.289069i	$0.0933457\pi$
$278$	−18.0904	+	7.14867i	−1.08499	+	0.428749i
$279$	−22.6651	+	10.9149i	−1.35693	+	0.653461i
$280$	6.94536	+	0.308260i	0.415065	+	0.0184220i
$281$	−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	$0.707913\pi$
$282$	6.45734	+	0.468770i	0.384529	+	0.0279149i
$283$	10.0683	−	0.754512i	0.598496	−	0.0448511i	0.227962	−	0.973670i	$-0.426794\pi$
$283$	10.0683	−	0.754512i	0.598496	−	0.0448511i	0.370534	+	0.928819i	$0.379175\pi$
$284$	−12.5310	−	8.45815i	−0.743578	−	0.501899i
$285$	0.639217	+	0.0479027i	0.0378639	+	0.00283751i
$286$	−2.49095	+	11.0321i	−0.147293	+	0.652342i
$287$	7.23024	−	0.169575i	0.426787	−	0.0100097i
$288$	9.02673	+	11.0523i	0.531905	+	0.651263i
$289$	−16.1730	−	4.98870i	−0.951350	−	0.293453i
$290$	8.42486	−	7.85377i	0.494725	−	0.461189i
$291$	1.31392	+	1.41607i	0.0770233	+	0.0830114i
$292$	25.5456	+	7.74949i	1.49494	+	0.453504i
$293$		−	15.1150i		−	0.883026i	−0.897255	−	0.441513i	$-0.854442\pi$
$293$		−	15.1150i		−	0.883026i	0.897255	−	0.441513i	$-0.145558\pi$
$294$	−3.26736	−	6.00898i	−0.190557	−	0.350451i
$295$	−3.05160			−0.177671
$296$	−12.4408	+	13.5975i	−0.723106	+	0.790341i
$297$	8.13603	−	7.54913i	0.472100	−	0.438045i
$298$	18.8236	+	20.1924i	1.09042	+	1.16971i
$299$	2.06135	−	6.68272i	0.119211	−	0.386472i
$300$	−2.50434	−	5.13887i	−0.144588	−	0.296693i
$301$	−8.57538	+	18.9300i	−0.494277	+	1.09111i
$302$	3.80487	−	16.8513i	0.218946	−	0.969683i
$303$	0.415771	−	5.54808i	0.0238854	−	0.318729i
$304$	−3.98038	+	0.335653i	−0.228290	+	0.0192510i
$305$	−1.06304	−	14.1853i	−0.0608694	−	0.812245i
$306$	−0.0707971	+	0.975235i	−0.00404720	+	0.0557505i
$307$	−14.1687	+	29.4215i	−0.808648	+	1.67917i	−0.0774628	+	0.996995i	$0.524682\pi$
$307$	−14.1687	+	29.4215i	−0.808648	+	1.67917i	−0.731185	+	0.682179i	$0.761032\pi$
$308$	2.72088	+	15.1490i	0.155037	+	0.863195i
$309$	1.05011	+	2.18057i	0.0597385	+	0.124048i
$310$	12.1852	−	4.81516i	0.692072	−	0.273482i
$311$	−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	$0.628794\pi$
$312$	−3.91305	+	3.68206i	−0.221533	+	0.208456i
$313$	−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	$0.975426\pi$
$314$	6.84702	+	14.1336i	0.386400	+	0.797603i
$315$	−3.37180	+	5.20360i	−0.189979	+	0.293190i
$316$	3.60718	−	16.1510i	0.202920	−	0.908563i
$317$	−0.901413	−	5.98048i	−0.0506284	−	0.335897i	−0.999778	−	0.0210719i	$-0.993292\pi$
$317$	−0.901413	−	5.98048i	−0.0506284	−	0.335897i	0.949150	−	0.314825i	$-0.101946\pi$
$318$	−1.80248	−	3.10524i	−0.101078	−	0.174133i
$319$	21.0684	+	14.3642i	1.17960	+	0.804241i
$320$	−4.27222	−	6.08160i	−0.238825	−	0.339972i
$321$	−1.53406	−	1.92365i	−0.0856230	−	0.107368i
$322$	−0.955644	−	9.46916i	−0.0532559	−	0.527696i
$323$	−0.213993	−	0.170654i	−0.0119069	−	0.00949544i
$324$	−9.74577	+	1.51546i	−0.541432	+	0.0841922i
$325$	−9.85028	+	5.68706i	−0.546395	+	0.315461i
$326$	−6.93578	+	10.2241i	−0.384137	+	0.566258i
$327$	−1.07601	−	0.998387i	−0.0595032	−	0.0552109i
$328$	−4.86273	−	6.01092i	−0.268499	−	0.331897i
$329$	−6.78550	−	16.1641i	−0.374096	−	0.891154i
$330$	−2.06053	+	1.65110i	−0.113429	+	0.0908899i
$331$	7.83959	−	3.07681i	0.430903	−	0.169117i	−0.139969	−	0.990156i	$-0.544700\pi$
$331$	7.83959	−	3.07681i	0.430903	−	0.169117i	0.570872	+	0.821039i	$0.306605\pi$
$332$	22.2227	+	23.7275i	1.21963	+	1.30221i
$333$	−4.84500	−	15.7071i	−0.265504	−	0.860744i
$334$	11.7248	−	20.4177i	0.641552	−	1.11721i
$335$	0.509279	+	2.23130i	0.0278249	+	0.121909i
$336$	−2.95500	+	6.68841i	−0.161209	+	0.364883i
$337$	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	$-0.116804\pi$
$338$	−5.65248	−	5.22026i	−0.307455	−	0.283945i
$339$	−6.03403	−	2.36818i	−0.327723	−	0.128622i
$340$	0.0735522	−	0.503924i	0.00398893	−	0.0273291i
$341$	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
$346$	5.18052	+	16.6568i	0.278507	+	0.895477i
$347$	24.0091	+	9.42290i	1.28888	+	0.505848i	0.908075	−	0.418808i	$-0.137552\pi$
$347$	24.0091	+	9.42290i	1.28888	+	0.505848i	0.380804	+	0.924656i	$0.375647\pi$
$348$	4.47832	+	11.2559i	0.240063	+	0.603380i
$349$	−7.65664	−	1.74758i	−0.409850	−	0.0935457i	0.0126245	−	0.999920i	$-0.495981\pi$
$349$	−7.65664	−	1.74758i	−0.409850	−	0.0935457i	−0.422475	+	0.906375i	$0.638839\pi$
$350$	−9.33576	+	12.3467i	−0.499017	+	0.659956i
$351$	−2.33448	−	10.2280i	−0.124606	−	0.545933i
$352$	11.0502	−	12.1914i	0.588980	−	0.649803i
$353$	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	$0.202193\pi$
$354$	1.16562	−	2.99043i	0.0619519	−	0.158940i
$355$	−6.53725	+	2.56568i	−0.346961	+	0.136172i
$356$	4.09598	+	17.5676i	0.217086	+	0.931079i
$357$	−0.461979	+	0.193933i	−0.0244505	+	0.0102640i
$358$	0.0830846	+	35.6278i	0.00439116	+	1.88299i
$359$	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	$0.514225\pi$
$360$	6.60648	−	0.541591i	0.348192	−	0.0285444i
$361$	−9.00137	−	15.5908i	−0.473756	−	0.820570i
$362$	−9.67562	−	14.1207i	−0.508540	−	0.742166i
$363$	1.37178	+	1.09396i	0.0719999	+	0.0574180i
$364$	13.6870	+	4.93241i	0.717391	+	0.258528i
$365$	9.69493	−	7.73145i	0.507456	−	0.404682i
$366$	14.3070	+	4.37661i	0.747839	+	0.228769i
$367$	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	$0.536749\pi$
$368$	−7.39347	+	6.98960i	−0.385411	+	0.364358i
$369$	6.81862	−	1.02774i	0.354963	−	0.0535021i
$370$	1.92446	+	8.34189i	0.100048	+	0.433674i
$371$	−5.28670	+	8.15882i	−0.274472	+	0.423585i
$372$	0.0642718	+	13.7802i	0.00333234	+	0.714471i
$373$	−10.2033	−	5.89088i	−0.528307	−	0.305018i	0.212020	−	0.977265i	$-0.431996\pi$
$373$	−10.2033	−	5.89088i	−0.528307	−	0.305018i	−0.740327	+	0.672247i	$0.765329\pi$
$374$	1.12410	−	0.0868764i	0.0581259	−	0.00449227i
$375$	−5.79940	−	0.874119i	−0.299480	−	0.0451393i
$376$	−9.25670	+	16.2953i	−0.477378	+	0.840366i
$377$	21.7159	−	10.4578i	1.11843	−	0.538606i
$378$	−8.34404	−	11.5851i	−0.429171	−	0.595874i
$379$	−9.53647	+	19.8027i	−0.489856	+	1.01720i	0.498761	+	0.866739i	$0.333788\pi$
$379$	−9.53647	+	19.8027i	−0.489856	+	1.01720i	−0.988617	+	0.150456i	$0.951926\pi$
$380$	−0.920245	+	1.61122i	−0.0472076	+	0.0826538i
$381$	1.25326	−	0.0939189i	0.0642065	−	0.00481161i
$382$	−26.3215	−	3.90458i	−1.34673	−	0.199776i
$383$	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	$-0.0904771\pi$
$384$	7.59157	−	1.86361i	0.387406	−	0.0951019i
$385$	6.51245	+	2.95017i	0.331905	+	0.150355i
$386$	−3.23561	+	4.07679i	−0.164688	+	0.207503i
$387$	−5.84045	+	18.9343i	−0.296887	+	0.962484i
$388$	−5.33556	+	1.67309i	−0.270872	+	0.0849385i
$389$	−10.5549	−	11.3755i	−0.535156	−	0.576761i	0.406367	−	0.913710i	$-0.366796\pi$
$389$	−10.5549	−	11.3755i	−0.535156	−	0.576761i	−0.941523	+	0.336949i	$0.890605\pi$
$390$	0.377741	+	2.46710i	0.0191277	+	0.124926i
$391$	−0.697159			−0.0352569
$392$	19.7702	−	1.06654i	0.998548	−	0.0538686i
$393$	−5.31843			−0.268279
$394$	−1.42191	−	9.28676i	−0.0716348	−	0.467860i
$395$	−5.22861	−	5.63510i	−0.263080	−	0.283532i
$396$	4.39092	+	14.0028i	0.220652	+	0.703667i
$397$	−11.7107	+	37.9651i	−0.587743	+	1.90542i	−0.219934	+	0.975515i	$0.570584\pi$
$397$	−11.7107	+	37.9651i	−0.587743	+	1.90542i	−0.367809	+	0.929901i	$0.619892\pi$
$398$	−7.95168	+	10.0189i	−0.398582	+	0.502204i
$399$	1.82501	−	0.0428032i	0.0913649	−	0.00214284i
$400$	16.5469	−	0.154355i	0.827346	−	0.00771775i
$401$	−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	$0.994400\pi$
$402$	−2.38111	−	0.353217i	−0.118759	−	0.0176169i
$403$	27.3415	−	2.04896i	1.36198	−	0.102066i
$404$	13.9846	+	7.98726i	0.695758	+	0.397381i
$405$	−1.98781	+	4.12774i	−0.0987753	+	0.205109i
$406$	21.6833	−	24.6122i	1.07612	−	1.22148i
$407$	−17.0762	+	8.22345i	−0.846434	+	0.407621i
$408$	0.465729	+	0.264562i	0.0230570	+	0.0130978i
$409$	−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	$0.697575\pi$
$410$	−3.58074	+	0.276738i	−0.176840	+	0.0136671i
$411$	−5.07221	−	2.92844i	−0.250194	−	0.144449i
$412$	−7.00571	+	0.0326751i	−0.345147	+	0.00160979i
$413$	−8.64865	+	0.852467i	−0.425572	+	0.0419472i
$414$	−2.03985	−	8.84208i	−0.100253	−	0.434564i
$415$	14.9322	−	2.25067i	0.732995	−	0.110481i
$416$	−4.75733	−	14.8076i	−0.233247	−	0.726005i
$417$	−7.85198	−	5.35339i	−0.384513	−	0.262157i
$418$	−3.92819	−	1.20166i	−0.192134	−	0.0587751i
$419$	27.2972	−	21.7688i	1.33355	−	1.06347i	0.341208	−	0.939988i	$-0.389164\pi$
$419$	27.2972	−	21.7688i	1.33355	−	1.06347i	0.992346	−	0.123486i	$-0.0394076\pi$
$420$	1.78030	+	2.89262i	0.0868697	+	0.141145i
$421$	−16.6545	−	13.2815i	−0.811691	−	0.647302i	0.127061	−	0.991895i	$-0.459445\pi$
$421$	−16.6545	−	13.2815i	−0.811691	−	0.647302i	−0.938752	+	0.344593i	$0.888017\pi$
$422$	7.17287	+	10.4681i	0.349170	+	0.509581i
$423$	−8.35733	−	14.4753i	−0.406348	−	0.703815i
$424$	10.3584	−	0.849169i	0.503049	−	0.0412393i
$425$	0.831180	+	0.771222i	0.0403181	+	0.0374098i
$426$	−0.0172249	−	7.38624i	−0.000834547	−	0.357865i
$427$	−6.97547	−	39.9060i	−0.337567	−	1.93119i
$428$	6.93610	−	1.61719i	0.335269	−	0.0781699i
$429$	−5.14358	+	2.01871i	−0.248334	+	0.0974641i
$430$	3.74788	−	9.61532i	0.180739	−	0.463692i
$431$	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	$0.329561\pi$
$432$	−4.36259	+	14.6262i	−0.209895	+	0.703703i
$433$	−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	$-0.437435\pi$
$434$	33.1894	−	17.0508i	1.59314	−	0.818463i
$435$	5.48607	+	1.25216i	0.263037	+	0.0600364i
$436$	3.94790	−	1.57073i	0.189070	−	0.0752241i
$437$	2.36451	+	0.928002i	0.113110	+	0.0443924i
$438$	3.87332	+	12.4538i	0.185074	+	0.595065i
$439$	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	$-0.879898\pi$
$443$	−19.6367	−	28.8018i	−0.932970	−	1.36842i	−0.00331110	−	0.999995i	$-0.501054\pi$
$444$	−8.90978	−	1.30046i	−0.422840	−	0.0617173i
$445$	7.80001	+	3.06128i	0.369756	+	0.145118i
$446$	−5.47887	−	5.05993i	−0.259432	−	0.239595i
$447$	−3.00113	+	13.1488i	−0.141948	+	0.621917i
$448$	−13.8070	−	16.0427i	−0.652319	−	0.757945i
$449$	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	$0.765960\pi$
$450$	−7.34943	+	12.7984i	−0.346455	+	0.603323i
$451$	−2.34360	−	7.59777i	−0.110356	−	0.357765i
$452$	13.6949	−	12.8264i	0.644154	−	0.603303i
$453$	7.85670	−	3.08353i	0.369140	−	0.144877i
$454$	8.05297	−	6.45281i	0.377944	−	0.302845i
$455$	5.49293	−	3.93680i	0.257513	−	0.184560i
$456$	−1.22742	−	1.51724i	−0.0574792	−	0.0710512i
$457$	−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	$-0.637006\pi$
$458$	−7.42379	+	10.9434i	−0.346891	+	0.511354i
$459$	−0.905719	+	0.522917i	−0.0422753	+	0.0244077i
$460$	0.726183	+	4.67001i	0.0338584	+	0.217740i
$461$	4.15552	+	3.31392i	0.193542	+	0.154345i	0.715466	−	0.698647i	$-0.246214\pi$
$461$	4.15552	+	3.31392i	0.193542	+	0.154345i	−0.521924	+	0.852992i	$0.674786\pi$
$462$	−5.37861	+	5.25505i	−0.250235	+	0.244487i
$463$	−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	$0.949808\pi$
$464$	−34.9909	−	2.29420i	−1.62441	−	0.106505i
$465$	5.28889	+	3.60590i	0.245266	+	0.167220i
$466$	15.3654	+	26.4710i	0.711791	+	1.22624i
$467$	−1.36128	−	9.03152i	−0.0629926	−	0.417929i	−0.997995	−	0.0632881i	$-0.979841\pi$
$467$	−1.36128	−	9.03152i	−0.0629926	−	0.417929i	0.935003	−	0.354641i	$-0.115397\pi$
$468$	13.5380	+	3.02359i	0.625792	+	0.139765i
$469$	2.06669	+	6.18155i	0.0954307	+	0.285437i
$470$	3.79542	+	7.83448i	0.175070	+	0.361378i
$471$	−3.83636	+	6.64478i	−0.176770	+	0.306175i
$472$	6.36671	+	6.76612i	0.293051	+	0.311436i
$473$	22.5920	+	3.40520i	1.03878	+	0.156571i
$474$	7.51933	−	2.97137i	0.345374	−	0.136480i
$475$	−1.79247	−	3.72210i	−0.0822442	−	0.170782i
$476$	0.0676856	−	1.44874i	0.00310237	−	0.0664028i
$477$	−4.02186	+	8.35148i	−0.184148	+	0.382388i
$478$	0.00696336	−	0.0959208i	0.000318497	−	0.00438731i
$479$	−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	$-0.240725\pi$
$480$	1.28708	−	3.39532i	0.0587471	−	0.154975i
$481$	−1.33881	+	17.8652i	−0.0610444	+	0.814581i
$482$	4.45393	−	19.7259i	0.202871	−	0.898489i
$483$	3.56635	−	2.98352i	0.162275	−	0.135755i
$484$	−4.56559	+	2.22496i	−0.207527	+	0.101135i
$485$	−0.765607	+	2.48204i	−0.0347644	+	0.112703i
$486$	−14.3245	−	15.3662i	−0.649775	−	0.697024i
$487$	−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	$0.347124\pi$
$488$	−29.2342	+	31.9525i	−1.32337	+	1.44642i
$489$	−6.03598			−0.272956
$490$	4.80057	−	7.84457i	0.216868	−	0.354382i
$491$			32.4718i			1.46543i	0.680536	+	0.732715i	$0.261747\pi$
$491$			32.4718i			1.46543i	−0.680536	+	0.732715i	$0.738253\pi$
$492$	1.09654	−	3.61468i	0.0494360	−	0.162962i
$493$	−1.63429	−	1.76135i	−0.0736049	−	0.0793272i
$494$	−2.84022	+	2.64769i	−0.127788	+	0.119125i
$495$	6.51392	+	2.00928i	0.292779	+	0.0903104i
$496$	−36.0989	−	16.9714i	−1.62089	−	0.762036i
$497$	−17.8108	+	9.09769i	−0.798922	+	0.408087i
$498$	−3.49810	+	15.4926i	−0.156754	+	0.694242i
$499$	−18.6922	−	1.40078i	−0.836776	−	0.0627077i	−0.350554	−	0.936543i	$-0.614007\pi$
$499$	−18.6922	−	1.40078i	−0.836776	−	0.0627077i	−0.486223	+	0.873835i	$0.661626\pi$
$500$	9.49788	−	14.0714i	0.424758	−	0.629292i
$501$	11.4709	−	0.859623i	0.512481	−	0.0384051i
$502$	−26.5730	−	1.92906i	−1.18601	−	0.0860983i
$503$	−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	$0.659944\pi$
$504$	18.5724	−	3.38047i	0.827280	−	0.150578i
$505$	6.74005	−	3.24584i	0.299928	−	0.144438i
$506$	−9.73093	+	3.84532i	−0.432593	+	0.170945i
$507$	0.560267	−	3.71713i	0.0248823	−	0.165083i
$508$	−1.31327	+	3.39261i	−0.0582671	+	0.150523i
$509$	−30.4006	−	17.5518i	−1.34748	−	0.777969i	−0.359590	−	0.933110i	$-0.617084\pi$
$509$	−30.4006	−	17.5518i	−1.34748	−	0.777969i	−0.987892	+	0.155141i	$0.950417\pi$
$510$	0.223914	−	0.108475i	0.00991508	−	0.00480337i
$511$	25.3170	−	24.6203i	1.11996	−	1.08914i
$512$	−4.57100	+	22.1609i	−0.202012	+	0.979383i
$513$	3.76793	−	0.567925i	0.166358	−	0.0250745i
$514$	−3.05932	−	5.27048i	−0.134941	−	0.232471i
$515$	−1.83320	+	2.68881i	−0.0807805	+	0.118483i
$516$	7.99103	+	7.34553i	0.351786	+	0.323369i
$517$	−15.0681	+	12.0164i	−0.662695	+	0.528482i
$518$	7.78451	+	23.1045i	0.342032	+	1.01515i
$519$	−5.31362	+	6.66307i	−0.233242	+	0.292476i
$520$	−6.91838	−	2.08114i	−0.303391	−	0.0912642i
$521$	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	$0.566606\pi$
$522$	17.5574	−	25.8814i	0.768465	−	1.13280i
$523$	−19.9375	+	21.4875i	−0.871807	+	0.939584i	−0.998629	−	0.0523410i	$-0.983332\pi$
$523$	−19.9375	+	21.4875i	−0.871807	+	0.939584i	0.126822	+	0.991925i	$0.459522\pi$
$524$	6.61488	−	13.9014i	0.288972	−	0.607286i
$525$	−7.55241	−	0.388161i	−0.329614	−	0.0169408i
$526$	−15.5603	−	19.4189i	−0.678459	−	0.846703i
$527$	−0.998573	−	2.54432i	−0.0434985	−	0.110832i
$528$	7.95988	+	1.12393i	0.346409	+	0.0489126i
$529$	−15.7957	+	4.87234i	−0.686771	+	0.211841i
$530$	2.40412	−	4.18658i	0.104428	−	0.181853i
$531$	−8.07835	+	1.84383i	−0.350571	+	0.0800154i
$532$	−2.15801	+	4.82349i	−0.0935615	+	0.209125i
$533$	−7.32719	−	1.67238i	−0.317376	−	0.0724389i
$534$	−5.97929	+	6.47436i	−0.258749	+	0.280173i
$535$	1.20867	−	3.07963i	0.0522552	−	0.133144i
$536$	3.88479	−	5.78447i	0.167797	−	0.249851i
$537$	−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	0.965952	−	0.258722i	$-0.0833015\pi$
$541$	8.65743	+	12.6981i	0.372212	+	0.545935i	−0.593740	+	0.804657i	$0.702349\pi$
$542$	−14.9579	+	4.65213i	−0.642496	+	0.199826i
$543$	3.05534	−	7.78487i	0.131117	−	0.334081i
$544$	−1.27078	+	0.888280i	−0.0544840	+	0.0380847i
$545$	0.439183	−	1.92418i	0.0188125	−	0.0824230i
$546$	1.75976	+	6.88658i	0.0753108	+	0.294719i
$547$	17.8806	−	4.08114i	0.764521	−	0.174497i	0.177558	−	0.984110i	$-0.443180\pi$
$547$	17.8806	−	4.08114i	0.764521	−	0.174497i	0.586963	+	0.809613i	$0.300323\pi$
$548$	13.9631	−	9.61556i	0.596472	−	0.410756i
$549$	−11.3851	−	36.9097i	−0.485905	−	1.57527i
$550$	15.8554	+	6.18016i	0.676077	+	0.263523i
$551$	3.19836	+	8.14930i	0.136255	+	0.347172i
$552$	−4.85379	−	1.07218i	−0.206591	−	0.0456349i
$553$	−16.3928	−	14.5100i	−0.697092	−	0.617030i
$554$	−0.0157159	−	6.73919i	−0.000667705	−	0.286321i
$555$	−2.84487	+	3.06604i	−0.120758	+	0.130146i
$556$	23.7588	−	13.8653i	1.00760	−	0.588020i
$557$	1.62022	−	0.935435i	0.0686509	−	0.0396356i	−0.465282	−	0.885163i	$-0.654047\pi$
$557$	1.62022	−	0.935435i	0.0686509	−	0.0396356i	0.533933	+	0.845527i	$0.320714\pi$
$558$	29.3479	−	20.1095i	1.24239	−	0.851301i
$559$	13.4650	−	16.8845i	0.569507	−	0.714139i
$560$	−9.77506	+	1.05565i	−0.413072	+	0.0446093i
$561$	0.343437	+	0.430656i	0.0144999	+	0.0181823i
$562$	9.20199	+	2.81495i	0.388163	+	0.118742i
$563$	11.0149	−	16.1558i	0.464221	−	0.680887i	−0.520730	−	0.853721i	$-0.674340\pi$
$563$	11.0149	−	16.1558i	0.464221	−	0.680887i	0.984951	+	0.172834i	$0.0552925\pi$
$564$	−9.12720	+	0.726813i	−0.384324	+	0.0306043i
$565$	−1.29903	−	8.61853i	−0.0546508	−	0.362584i
$566$	−13.9132	+	3.20974i	−0.584814	+	0.134916i
$567$	−4.48066	+	12.2539i	−0.188170	+	0.514615i
$568$	19.3277	+	9.14173i	0.810974	+	0.383579i
$569$	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	$-0.0427823\pi$
$570$	−0.903829	+	0.0698526i	−0.0378572	+	0.00292580i
$571$	−1.88722	+	12.5209i	−0.0789776	+	0.523982i	0.914003	+	0.405707i	$0.132975\pi$
$571$	−1.88722	+	12.5209i	−0.0789776	+	0.523982i	−0.992981	+	0.118275i	$0.962263\pi$
$572$	1.12087	−	15.9552i	0.0468659	−	0.667120i
$573$	−5.64066	−	11.7129i	−0.235642	−	0.489315i
$574$	−10.0710	+	1.78460i	−0.420356	+	0.0744877i
$575$	−9.48055	−	4.56559i	−0.395366	−	0.190398i
$576$	−14.9843	−	13.5182i	−0.624345	−	0.563258i
$577$	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	$0.816365\pi$
$578$	23.6763	+	3.51218i	0.984805	+	0.146087i
$579$	−2.53572	−	0.190026i	−0.105381	−	0.00789722i
$580$	−10.0963	+	12.7822i	−0.419226	+	0.530752i
$581$	41.6913	−	10.5501i	1.72965	−	0.437690i
$582$	−2.13985	−	1.69833i	−0.0886997	−	0.0703979i
$583$	10.2133	+	3.15038i	0.422991	+	0.130476i
$584$	−37.3695	−	5.36544i	−1.54636	−	0.222024i
$585$	4.72341	−	4.38269i	0.195289	−	0.181202i
$586$	3.23518	+	21.1296i	0.133644	+	0.872854i
$587$		−	29.5253i		−	1.21864i	−0.792925	−	0.609320i	$-0.791443\pi$
$587$		−	29.5253i		−	1.21864i	0.792925	−	0.609320i	$-0.208557\pi$
$588$	5.85367	+	7.70075i	0.241401	+	0.317574i
$589$			9.95863i			0.410338i
$590$	4.26589	−	0.653158i	0.175624	−	0.0268901i
$591$	3.36472	−	3.12201i	0.138406	−	0.128422i
$592$	14.4809	−	21.6711i	0.595160	−	0.890677i
$593$	−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	$0.642324\pi$
$594$	−9.75774	+	12.2945i	−0.400365	+	0.504451i
$595$	−0.536418	−	0.407575i	−0.0219910	−	0.0167089i
$596$	−30.6359	−	24.1984i	−1.25490	−	0.991207i
$597$	−6.23168	−	0.467000i	−0.255046	−	0.0191130i
$598$	−1.45125	+	9.78314i	−0.0593459	+	0.400062i
$599$	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	$0.748397\pi$
$600$	4.60080	+	6.64772i	0.187827	+	0.271392i
$601$	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	$0.525950\pi$
$602$	7.93598	−	28.2982i	0.323446	−	1.15335i
$603$	2.69638	+	5.59910i	0.109805	+	0.228013i
$604$	−1.71210	+	24.3712i	−0.0696644	+	0.991650i
$605$	−0.351622	+	2.33286i	−0.0142955	+	0.0948442i
$606$	0.606285	+	7.84478i	0.0246286	+	0.318672i
$607$	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	$0.000432955\pi$
$608$	5.49241	−	1.32117i	0.222747	−	0.0535805i
$609$	15.8981	+	2.01625i	0.644222	+	0.0817027i
$610$	4.52223	+	19.6024i	0.183100	+	0.793676i
$611$	2.71517	+	18.0140i	0.109844	+	0.728769i
$612$	−0.109769	−	1.37846i	−0.00443713	−	0.0557208i
$613$	−23.9848	+	35.1793i	−0.968738	+	1.42088i	−0.0625306	+	0.998043i	$0.519917\pi$
$613$	−23.9848	+	35.1793i	−0.968738	+	1.42088i	−0.906207	+	0.422834i	$0.861035\pi$
$614$	13.5094	−	44.1616i	0.545193	−	1.78222i
$615$	−1.09399	−	1.37182i	−0.0441140	−	0.0553172i
$616$	−7.04604	−	20.5948i	−0.283893	−	0.829787i
$617$	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	$0.0565710\pi$
$618$	−1.93469	−	2.82351i	−0.0778248	−	0.113578i
$619$	−15.2944	+	8.83025i	−0.614735	+	0.354918i	−0.774817	−	0.632186i	$-0.782158\pi$
$619$	−15.2944	+	8.83025i	−0.614735	+	0.354918i	0.160081	+	0.987104i	$0.448824\pi$
$620$	−16.0033	+	9.33931i	−0.642709	+	0.375076i
$621$	6.60154	−	7.11477i	0.264911	−	0.285506i
$622$	12.5828	−	0.0293433i	0.504525	−	0.00117656i
$623$	22.9615	+	6.49715i	0.919933	+	0.260303i
$624$	4.68205	−	5.98478i	0.187432	−	0.239583i
$625$	4.67584	+	11.9139i	0.187034	+	0.476554i
$626$	10.2733	−	26.3564i	0.410602	−	1.05341i
$627$	−0.591558	−	1.91778i	−0.0236245	−	0.0765889i
$628$	−12.5967	−	18.2921i	−0.502664	−	0.729935i
$629$	1.74116	−	0.397408i	0.0694245	−	0.0158457i
$630$	3.59974	−	7.99593i	0.143417	−	0.318565i
$631$	−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	$0.138815\pi$
$632$	−1.58564	+	23.3499i	−0.0630734	+	0.928808i
$633$	−2.26502	+	5.77119i	−0.0900266	+	0.229384i
$634$	2.54016	+	8.16732i	0.100883	+	0.324366i
$635$	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
$640$	7.27393	+	7.58719i	0.287527	+	0.299910i
$641$	−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	$0.881163\pi$
$642$	2.55623	+	2.36077i	0.100887	+	0.0931722i
$643$	−42.9975	−	9.81389i	−1.69566	−	0.387022i	−0.737968	−	0.674835i	$-0.764215\pi$
$643$	−42.9975	−	9.81389i	−1.69566	−	0.387022i	−0.957687	+	0.287813i	$0.907072\pi$
$644$	3.36268	+	13.0326i	0.132508	+	0.513557i
$645$	4.91550	−	1.12193i	0.193548	−	0.0441760i
$646$	0.335672	+	0.192758i	0.0132069	+	0.00758397i
$647$	−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	$0.699660\pi$
$648$	13.2995	−	4.20446i	0.522452	−	0.165167i
$649$	3.49057	+	8.89384i	0.137017	+	0.349114i
$650$	12.5527	−	10.0584i	0.492356	−	0.394523i
$651$	15.9968	+	8.74218i	0.626963	+	0.342633i
$652$	7.50734	−	15.7770i	0.294010	−	0.617874i
$653$	−8.81553	+	9.50088i	−0.344978	+	0.371798i	−0.881578	−	0.472039i	$-0.843518\pi$
$653$	−8.81553	+	9.50088i	−0.344978	+	0.371798i	0.536599	+	0.843837i	$0.319709\pi$
$654$	1.71786	+	1.16536i	0.0671738	+	0.0455692i
$655$	−3.57559	−	6.19311i	−0.139710	−	0.241985i
$656$	8.08428	+	7.36198i	0.315638	+	0.287437i
$657$	20.9935	−	26.3250i	0.819033	−	1.02703i
$658$	12.9453	+	21.1438i	0.504661	+	0.824270i
$659$	−15.6060	+	12.4454i	−0.607924	+	0.484803i	−0.878402	−	0.477923i	$-0.841390\pi$
$659$	−15.6060	+	12.4454i	−0.607924	+	0.484803i	0.270478	+	0.962726i	$0.412818\pi$
$660$	2.52707	−	2.74914i	0.0983660	−	0.107010i
$661$	26.9637	−	39.5484i	1.04876	−	1.53826i	0.222533	−	0.974925i	$-0.428568\pi$
$661$	26.9637	−	39.5484i	1.04876	−	1.53826i	0.826232	−	0.563330i	$-0.190480\pi$
$662$	−10.3006	+	5.97911i	−0.400343	+	0.232385i
$663$	0.514851	−	0.0776013i	0.0199952	−	0.00301378i
$664$	−36.1442	−	28.4126i	−1.40267	−	1.10262i
$665$	1.27680	+	2.09638i	0.0495123	+	0.0812942i
$666$	10.1349	+	20.9203i	0.392718	+	0.810645i
$667$	19.3110	+	11.1492i	0.747726	+	0.431700i
$668$	−12.0202	+	31.0520i	−0.465074	+	1.20144i
$669$	0.543059	−	3.60296i	0.0209959	−	0.139299i
$670$	−1.18952	−	3.01018i	−0.0459550	−	0.116293i
$671$	−40.1268	+	19.3240i	−1.54908	+	0.745996i
$672$	2.69929	−	9.98237i	0.104127	−	0.385078i
$673$	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	$0.487060\pi$
$674$	−2.09583	+	28.8702i	−0.0807283	+	1.11204i
$675$	−15.7412	+	1.17964i	−0.605880	+	0.0454044i
$676$	9.01907	+	6.08767i	0.346887	+	0.234141i
$677$	11.2592	+	0.843762i	0.432727	+	0.0324284i	0.289313	−	0.957234i	$-0.406573\pi$
$677$	11.2592	+	0.843762i	0.432727	+	0.0324284i	0.143414	+	0.989663i	$0.454192\pi$
$678$	8.94198	+	2.01902i	0.343415	+	0.0775400i
$679$	−1.47648	+	7.24831i	−0.0566620	+	0.278165i
$680$	0.00503856	+	0.720189i	0.000193220	+	0.0276180i
$681$	4.81764	+	1.48605i	0.184612	+	0.0569454i
$682$	−27.9718	−	30.0057i	−1.07109	−	1.14898i
$683$	−1.08081	−	1.16484i	−0.0413561	−	0.0445713i	0.712035	−	0.702144i	$-0.247774\pi$
$683$	−1.08081	−	1.16484i	−0.0413561	−	0.0445713i	−0.753391	+	0.657573i	$0.771583\pi$
$684$	−1.46259	+	4.82134i	−0.0559237	+	0.184348i
$685$		−	7.87519i		−	0.300896i
$686$	11.4141	−	23.5737i	0.435793	−	0.900047i
$687$	−6.46068			−0.246490
$688$	−29.1389	+	11.7510i	−1.11091	+	0.448003i
$689$	7.40592	−	6.87169i	0.282143	−	0.261790i
$690$	−1.68895	+	1.57446i	−0.0642973	+	0.0599388i
$691$	−1.20532	+	3.90757i	−0.0458527	+	0.148651i	−0.975604	−	0.219537i	$-0.929545\pi$
$691$	−1.20532	+	3.90757i	−0.0458527	+	0.148651i	0.929752	+	0.368188i	$0.120022\pi$
$692$	−10.8072	−	22.1761i	−0.410827	−	0.843010i
$693$	19.0227	+	3.87491i	0.722612	+	0.147196i
$694$	−35.5798	−	8.03361i	−1.35059	−	0.304952i
$695$	0.954913	−	12.7424i	0.0362219	−	0.483348i
$696$	−8.66953	−	14.7764i	−0.328618	−	0.560097i
$697$	0.0559890	+	0.747121i	0.00212073	+	0.0282992i
$698$	11.0774	+	0.804166i	0.419287	+	0.0304381i
$699$	−6.48810	+	13.4727i	−0.245402	+	0.509584i
$700$	10.4080	−	19.2579i	0.393386	−	0.727879i
$701$	1.49683	+	3.10821i	0.0565346	+	0.117395i	0.927322	−	0.374264i	$-0.122105\pi$
$701$	1.49683	+	3.10821i	0.0565346	+	0.117395i	−0.870787	+	0.491660i	$0.836390\pi$
$702$	5.45262	+	13.7983i	0.205796	+	0.520785i
$703$	−6.43437	−	0.969825i	−0.242677	−	0.0365776i
$704$	−12.8380	+	19.4078i	−0.483849	+	0.731459i
$705$	−2.12656	+	3.68331i	−0.0800910	+	0.138722i
$706$	−28.4220	+	13.7691i	−1.06968	+	0.518205i
$707$	18.1955	−	11.0820i	0.684313	−	0.416782i
$708$	−0.989377	+	4.42988i	−0.0371831	+	0.166485i
$709$	4.14138	+	27.4763i	0.155533	+	1.03189i	0.921322	+	0.388801i	$0.127111\pi$
$709$	4.14138	+	27.4763i	0.155533	+	1.03189i	−0.765789	+	0.643092i	$0.777651\pi$
$710$	8.58942	−	4.98585i	0.322355	−	0.187115i
$711$	−17.2463	−	11.7583i	−0.646786	−	0.440971i
$712$	−9.48598	−	23.6814i	−0.355502	−	0.887497i
$713$	15.8152	+	19.8316i	0.592283	+	0.742700i
$714$	0.604301	−	0.369985i	0.0226154	−	0.0138463i
$715$	−5.80875	−	4.63232i	−0.217235	−	0.173239i
$716$	−7.74185	−	49.7871i	−0.289326	−	1.86063i
$717$	0.0406915	−	0.0234932i	0.00151965	−	0.000877370i
$718$	−28.6827	−	19.4577i	−1.07043	−	0.726155i
$719$	−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	$-0.661966\pi$
$720$	−9.11942	+	2.17114i	−0.339861	+	0.0809136i
$721$	−4.44443	+	8.13258i	−0.165519	+	0.302873i
$722$	15.9203	+	19.8681i	0.592491	+	0.739416i
$723$	9.19693	−	3.60953i	0.342038	−	0.134240i
$724$	16.5481	+	17.6687i	0.615007	+	0.656650i
$725$	−10.6897	−	34.6551i	−0.397004	−	1.28706i
$726$	−2.15179	−	1.23566i	−0.0798606	−	0.0458596i
$727$	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	$0.892941\pi$
$728$	−20.1890	−	3.96560i	−0.748255	−	0.146975i
$729$	−1.00823	+	4.41734i	−0.0373418	+	0.163605i
$730$	−11.8979	+	12.8830i	−0.440362	+	0.476823i
$731$	−2.00405	−	0.786532i	−0.0741225	−	0.0290909i
$732$	−20.9368	−	3.05592i	−0.773848	−	0.112950i
$733$	24.2699	+	35.5974i	0.896429	+	1.31482i	0.948697	+	0.316187i	$0.102403\pi$
$733$	24.2699	+	35.5974i	0.896429	+	1.31482i	−0.0522677	+	0.998633i	$0.516645\pi$
$734$	−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
$738$	−9.31192	+	2.89615i	−0.342777	+	0.106609i
$739$	36.1733	+	14.1970i	1.33066	+	0.522244i	0.920846	−	0.389926i	$-0.127500\pi$
$739$	36.1733	+	14.1970i	1.33066	+	0.522244i	0.409811	+	0.912171i	$0.365595\pi$
$740$	−4.47573	−	11.2494i	−0.164531	−	0.413536i
$741$	−1.84948	−	0.422133i	−0.0679425	−	0.0155074i
$742$	5.64409	−	12.5369i	0.207201	−	0.460246i
$743$	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	$0.674145\pi$
$744$	−3.03934	−	19.2499i	−0.111428	−	0.705736i
$745$	−17.3289	+	5.34527i	−0.634883	+	0.195836i
$746$	15.5243	+	6.05110i	0.568385	+	0.221547i
$747$	38.1695	−	14.9804i	1.39655	−	0.548105i
$748$	−1.55281	+	0.362047i	−0.0567764	+	0.0132377i
$749$	2.56523	−	9.06576i	0.0937315	−	0.331255i
$750$	8.29421	−	0.0193422i	0.302862	−	0.000706279i
$751$	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	$0.665872\pi$
$752$	9.45233	−	24.7608i	0.344691	−	0.902935i
$753$	−6.50833	−	11.2728i	−0.237177	−	0.410802i
$754$	−28.1188	+	19.2673i	−1.02403	+	0.701673i
$755$	8.87272	+	7.07576i	0.322912	+	0.257513i
$756$	14.1440	+	14.4091i	0.514412	+	0.524056i
$757$	27.4783	−	21.9132i	0.998715	−	0.796449i	0.0196109	−	0.999808i	$-0.493757\pi$
$757$	27.4783	−	21.9132i	0.998715	−	0.796449i	0.979104	+	0.203359i	$0.0651858\pi$
$758$	9.09272	−	29.7238i	0.330262	−	1.07962i
$759$	−4.22364	−	2.87963i	−0.153308	−	0.104524i
$760$	0.941569	−	2.44933i	0.0341543	−	0.0888464i
$761$	−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	$0.495715\pi$
$762$	−1.73186	+	0.399537i	−0.0627386	+	0.0144737i
$763$	0.707182	−	5.57610i	0.0256017	−	0.201868i
$764$	37.6312	−	0.175514i	1.36145	−	0.00634988i
$765$	−0.556281	−	0.321169i	−0.0201124	−	0.0116119i
$766$	1.49872	+	19.3921i	0.0541511	+	0.700666i
$767$	8.93023	+	1.34602i	0.322452	+	0.0486018i
$768$	−10.2136	+	4.23007i	−0.368550	+	0.152639i
$769$	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	$0.351246\pi$
$770$	−9.73536	−	2.73020i	−0.350838	−	0.0983895i
$771$	1.29181	−	2.68247i	0.0465233	−	0.0966066i
$772$	3.65054	−	6.39158i	0.131386	−	0.230038i
$773$	12.2028	−	0.914473i	0.438904	−	0.0328913i	0.146554	−	0.989203i	$-0.453182\pi$
$773$	12.2028	−	0.914473i	0.438904	−	0.0328913i	0.292350	+	0.956311i	$0.405563\pi$
$774$	4.11184	−	27.7188i	0.147797	−	0.996330i
$775$	3.08297	−	41.1393i	0.110743	−	1.47777i
$776$	7.10059	−	3.48087i	0.254896	−	0.124956i
$777$	−7.20625	+	9.48430i	−0.258523	+	0.340247i
$778$	17.1898	+	13.6429i	0.616283	+	0.489122i
$779$	0.804613	−	2.60849i	0.0288283	−	0.0934589i
$780$	−1.05611	−	3.36796i	−0.0378147	−	0.120592i
$781$	14.9553	+	16.1180i	0.535143	+	0.576746i
$782$	0.974575	−	0.149219i	0.0348507	−	0.00533605i
$783$	33.4507			1.19543
$784$	−27.4090	+	5.72253i	−0.978892	+	0.204376i
$785$	−10.3168			−0.368222
$786$	7.43475	−	1.13835i	0.265189	−	0.0406035i
$787$	−19.4950	−	21.0106i	−0.694923	−	0.748948i	0.282724	−	0.959201i	$-0.408762\pi$
$787$	−19.4950	−	21.0106i	−0.694923	−	0.748948i	−0.977647	+	0.210253i	$0.932571\pi$
$788$	3.97544	+	12.6778i	0.141619	+	0.451629i
$789$	3.58344	−	11.6172i	0.127574	−	0.413584i
$790$	8.51531	+	6.75831i	0.302961	+	0.240450i
$791$	−6.08924	−	24.0632i	−0.216508	−	0.855590i
$792$	−9.13529	−	18.6350i	−0.324608	−	0.662166i
$793$	−3.14603	+	41.9808i	−0.111719	+	1.49078i
$794$	8.24466	−	55.5789i	0.292592	−	1.97242i
$795$	2.35206	−	0.176262i	0.0834189	−	0.00625138i
$796$	8.97140	−	15.7077i	0.317983	−	0.556743i
$797$	−2.03932	+	4.23468i	−0.0722363	+	0.150000i	−0.933960	−	0.357378i	$-0.883671\pi$
$797$	−2.03932	+	4.23468i	−0.0722363	+	0.150000i	0.861724	+	0.507378i	$0.169385\pi$
$798$	−2.54206	+	0.450458i	−0.0899881	+	0.0159460i
$799$	1.63622	−	0.787960i	0.0578851	−	0.0278760i
$800$	−23.0983	+	3.75745i	−0.816647	+	0.132846i
$801$	22.4983	+	3.39107i	0.794938	+	0.119818i
$802$	−0.402662	−	5.21008i	−0.0142185	−	0.183974i
$803$	−33.6228	−	19.4121i	−1.18652	−	0.685038i
$804$	3.40421	−	0.0158774i	0.120057	−	0.000559954i
$805$	5.87186	+	2.14706i	0.206956	+	0.0756738i
$806$	−37.7828	+	8.71642i	−1.33084	+	0.307023i
$807$	−13.1057	+	1.97536i	−0.461342	+	0.0695361i
$808$	−21.2589	−	8.17234i	−0.747886	−	0.287502i
$809$	−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	$0.723465\pi$
$810$	1.89532	−	6.19573i	0.0665947	−	0.217696i
$811$	−24.1618	+	19.2684i	−0.848434	+	0.676604i	−0.947945	−	0.318433i	$-0.896844\pi$
$811$	−24.1618	+	19.2684i	−0.848434	+	0.676604i	0.0995112	+	0.995036i	$0.468272\pi$
$812$	−25.0436	+	39.0470i	−0.878858	+	1.37028i
$813$	−5.98345	−	4.77164i	−0.209849	−	0.167349i
$814$	22.1110	−	15.1507i	0.774991	−	0.531032i
$815$	−4.05800	−	7.02867i	−0.142146	−	0.246203i
$816$	−0.707680	−	0.270153i	−0.0247737	−	0.00945726i
$817$	5.75005	+	5.33526i	0.201169	+	0.186657i
$818$	25.9618	−	0.0605433i	0.907732	−	0.00211685i
$819$	12.1625	−	13.7406i	0.424992	−	0.480137i
$820$	4.94637	−	1.15327i	0.172735	−	0.0402741i
$821$	19.5869	−	7.68729i	0.683587	−	0.268288i	0.00197112	−	0.999998i	$-0.499373\pi$
$821$	19.5869	−	7.68729i	0.683587	−	0.268288i	0.681616	+	0.731710i	$0.261277\pi$
$822$	7.71735	+	3.00809i	0.269174	+	0.104919i
$823$	−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	$0.425282\pi$
$824$	9.78645	−	1.54517i	0.340927	−	0.0538284i
$825$	1.85003	+	8.10553i	0.0644099	+	0.282198i
$826$	11.9077	−	3.04282i	0.414321	−	0.105873i
$827$	14.3157	+	3.26746i	0.497805	+	0.113621i	0.464049	−	0.885809i	$-0.346396\pi$
$827$	14.3157	+	3.26746i	0.497805	+	0.113621i	0.0337559	+	0.999430i	$0.489253\pi$
$828$	4.74410	+	11.9239i	0.164869	+	0.414385i
$829$	30.8810	+	12.1199i	1.07254	+	0.420942i	0.834895	−	0.550409i	$-0.185528\pi$
$829$	30.8810	+	12.1199i	1.07254	+	0.420942i	0.237648	+	0.971351i	$0.423624\pi$
$830$	−20.3924	+	6.34233i	−0.707830	+	0.220146i
$831$	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
$836$	5.74850	+	0.839046i	0.198816	+	0.0290190i
$837$	35.4214	+	13.9019i	1.22434	+	0.480520i
$838$	−33.5000	+	36.2737i	−1.15724	+	1.25305i
$839$	−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	$0.107692\pi$
$840$	−3.10785	−	3.66260i	−0.107231	−	0.126372i
$841$	10.6480	+	46.6520i	0.367173	+	1.60869i
$842$	26.1245	+	15.0018i	0.900308	+	0.516998i
$843$	1.38576	+	4.49251i	0.0477280	+	0.154730i
$844$	−12.2677	−	13.0984i	−0.422271	−	0.450865i
$845$	4.70512	−	1.84662i	0.161861	−	0.0635258i
$846$	14.7812	+	18.4466i	0.508187	+	0.634207i
$847$	−0.344859	+	6.70988i	−0.0118495	+	0.230554i
$848$	−14.2985	+	3.40417i	−0.491012	+	0.116900i
$849$	−5.11374	−	4.74486i	−0.175503	−	0.162843i
$850$	−1.32700	−	0.900205i	−0.0455156	−	0.0308768i
$851$	−14.3536	+	8.28703i	−0.492034	+	0.284076i
$852$	1.60502	+	10.3217i	0.0549870	+	0.353616i
$853$	−14.9535	−	11.9250i	−0.511999	−	0.408305i	0.333120	−	0.942885i	$-0.391899\pi$
$853$	−14.9535	−	11.9250i	−0.511999	−	0.408305i	−0.845118	+	0.534579i	$0.820470\pi$
$854$	18.2926	+	54.2926i	0.625959	+	1.85785i
$855$	1.45919	+	1.82977i	0.0499032	+	0.0625766i
$856$	−9.34999	+	3.74530i	−0.319576	+	0.128012i
$857$	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	$0.563813\pi$
$858$	6.75825	−	3.92292i	0.230723	−	0.133926i
$859$	−0.717681	−	4.76151i	−0.0244870	−	0.162460i	0.973245	−	0.229769i	$-0.0737970\pi$
$859$	−0.717681	−	4.76151i	−0.0244870	−	0.162460i	−0.997732	+	0.0673083i	$0.978559\pi$
$860$	−3.18120	+	14.2437i	−0.108478	+	0.485705i
$861$	−3.48375	−	3.58233i	−0.118726	−	0.122085i
$862$	−12.3688	+	5.99206i	−0.421282	+	0.204090i
$863$	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	$0.0379251\pi$
$864$	2.96800	−	21.3800i	0.100973	−	0.727364i
$865$	−11.3312	−	1.70791i	−0.385274	−	0.0580707i
$866$	19.7418	+	49.9584i	0.670854	+	1.69766i
$867$	5.07379	+	10.5358i	0.172315	+	0.357816i
$868$	−42.7467	+	30.9395i	−1.45092	+	1.05015i
$869$	−10.4427	+	21.6844i	−0.354243	+	0.735594i
$870$	−7.93710	−	0.576194i	−0.269093	−	0.0195348i
$871$	−0.506168	−	6.75434i	−0.0171508	−	0.228862i
$872$	−5.18267	+	3.04076i	−0.175507	+	0.102973i
$873$	−0.527064	+	7.03317i	−0.0178384	+	0.238037i
$874$	−3.50403	−	0.791180i	−0.118526	−	0.0267621i
$875$	−10.2160	−	20.0002i	−0.345365	−	0.676129i
$876$	−8.08018	−	16.5804i	−0.273004	−	0.560200i
$877$	−3.51092	+	11.3821i	−0.118555	+	0.384347i	−0.995327	−	0.0965598i	$-0.969216\pi$
$877$	−3.51092	+	11.3821i	−0.118555	+	0.384347i	0.876772	+	0.480906i	$0.159692\pi$
$878$	−1.45388	+	1.35533i	−0.0490661	+	0.0457401i
$879$	−7.65553	+	7.10330i	−0.258215	+	0.239588i
$880$	4.04267	+	10.0246i	0.136279	+	0.337929i
$881$	−13.8783			−0.467571			−0.233785	−	0.972288i	$-0.575111\pi$
$881$	−13.8783			−0.467571			−0.233785	+	0.972288i	$0.575111\pi$
$882$	7.96850	−	23.6672i	0.268313	−	0.796915i
$883$		−	5.05676i		−	0.170173i	−0.996374	−	0.0850867i	$-0.972883\pi$
$883$		−	5.05676i		−	0.170173i	0.996374	−	0.0850867i	$-0.0271167\pi$
$884$	−0.437518	+	1.44225i	−0.0147153	+	0.0485080i
$885$	1.43410	+	1.54559i	0.0482068	+	0.0519546i
$886$	33.6153	+	36.0597i	1.12933	+	1.21145i
$887$	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	$0.503137\pi$
$888$	12.7335	−	0.0890858i	0.427309	−	0.00298952i
$889$	3.08796	+	3.69119i	0.103567	+	0.123799i
$890$	−11.5590	−	2.60993i	−0.387460	−	0.0874850i
$891$	14.3040	+	1.07194i	0.479202	+	0.0359112i
$892$	8.74206	+	5.90070i	0.292706	+	0.197570i
$893$	−6.59832	+	0.494475i	−0.220804	+	0.0165470i
$894$	1.38100	−	19.0234i	0.0461875	−	0.636236i
$895$	−21.0869	−	10.1549i	−0.704857	−	0.339441i
$896$	22.7348	+	19.4712i	0.759518	+	0.650487i
$897$	−4.35344	+	2.09651i	−0.145357	+	0.0700004i
$898$	−10.7691	−	27.2523i	−0.359371	−	0.909421i
$899$	−13.0297	+	86.4462i	−0.434564	+	2.88314i
$900$	7.53458	−	19.4642i	0.251153	−	0.648808i
$901$	−0.872202	−	0.503566i	−0.0290573	−	0.0167762i
$902$	4.90239	+	10.1195i	0.163232	+	0.336942i
$903$	13.6178	−	4.55287i	0.453173	−	0.151510i
$904$	−16.3991	+	20.8616i	−0.545426	+	0.693845i
$905$	11.1193	−	1.67596i	0.369618	−	0.0557109i
$906$	−10.3231	+	5.99216i	−0.342961	+	0.199076i
$907$	−24.9042	+	36.5278i	−0.826931	+	1.21288i	0.147693	+	0.989033i	$0.452815\pi$
$907$	−24.9042	+	36.5278i	−0.826931	+	1.21288i	−0.974623	+	0.223851i	$0.928137\pi$
$908$	−9.87628	+	10.7442i	−0.327756	+	0.356558i
$909$	15.8814	−	12.6650i	0.526754	−	0.420072i
$910$	−6.83607	+	6.67904i	−0.226614	+	0.221408i
$911$	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	$0.0820434\pi$
$912$	2.04059	+	1.85827i	0.0675705	+	0.0615334i
$913$	−23.6398	−	40.9454i	−0.782364	−	1.35509i
$914$	46.2349	+	31.3647i	1.52931	+	1.03745i
$915$	−6.68507	+	7.20479i	−0.221002	+	0.238183i
$916$	8.03557	−	16.8871i	0.265503	−	0.557964i
$917$	−11.8638	−	16.5533i	−0.391777	−	0.546638i
$918$	1.15420	−	0.924856i	0.0380943	−	0.0305248i
$919$	−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	$0.887828\pi$
$920$	−2.01471	−	6.37288i	−0.0664229	−	0.210108i
$921$	21.5602	−	6.65044i	0.710432	−	0.219139i
$922$	−6.51840	−	3.74316i	−0.214672	−	0.123274i
$923$	20.2624	−	4.62476i	0.666945	−	0.152226i
$924$	6.39409	−	8.49738i	0.210350	−	0.279543i
$925$	26.2803	+	5.99830i	0.864090	+	0.197223i
$926$	22.0414	+	20.3560i	0.724325	+	0.668939i
$927$	−3.22832	+	8.22563i	−0.106032	+	0.270165i
$928$	49.4056	−	4.28228i	1.62182	−	0.140573i
$929$	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
$934$	3.83606	+	12.3340i	0.125520	+	0.403581i
$935$	−0.270589	+	0.689450i	−0.00884921	+	0.0225474i
$936$	−19.5722	−	1.32910i	−0.639736	−	0.0434431i
$937$	−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	$0.906813\pi$
$938$	−4.21215	−	8.19897i	−0.137532	−	0.267706i
$939$	13.4738	−	3.07531i	0.439701	−	0.100359i
$940$	−6.98258	−	10.1396i	−0.227747	−	0.330718i
$941$	9.74289	+	31.5857i	0.317609	+	1.02966i	0.963831	+	0.266514i	$0.0858718\pi$
$941$	9.74289	+	31.5857i	0.317609	+	1.02966i	−0.646222	+	0.763149i	$0.723652\pi$
$942$	3.94070	−	10.1100i	0.128395	−	0.329402i
$943$	−2.54021	−	6.47234i	−0.0827205	−	0.210769i
$944$	−10.3484	−	8.09579i	−0.336811	−	0.263496i
$945$	9.23890	−	1.61493i	0.300541	−	0.0525338i
$946$	−32.3108	+	0.0753493i	−1.05051	+	0.00244982i
$947$	28.0838	−	30.2671i	0.912601	−	0.983550i	−0.0873195	−	0.996180i	$-0.527830\pi$
$947$	28.0838	−	30.2671i	0.912601	−	0.983550i	0.999920	+	0.0126307i	$0.00402059\pi$
$948$	−9.87545	+	5.76317i	−0.320740	+	0.187179i
$949$	−31.7816	+	18.3491i	−1.03167	+	0.595637i
$950$	3.30241	+	4.81956i	0.107144	+	0.156367i
$951$	−2.60542	+	3.26709i	−0.0844864	+	0.105943i
$952$	0.215466	+	2.03971i	0.00698329	+	0.0661074i
$953$	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	$0.477084\pi$
$954$	3.83471	−	12.5356i	0.124153	−	0.405854i
$955$	9.84705	−	14.4430i	0.318643	−	0.467364i
$956$	0.0107965	+	0.135580i	0.000349183	+	0.00438498i
$957$	−2.62585	−	17.4214i	−0.0848815	−	0.563152i
$958$	8.76571	+	37.9964i	0.283207	+	1.22761i
$959$	−2.19995	−	22.3194i	−0.0710400	−	0.720731i
$960$	−1.07252	+	5.02188i	−0.0346153	+	0.162081i
$961$	−34.2238	+	59.2773i	−1.10399	+	1.91217i
$962$	−1.95227	−	25.2607i	−0.0629438	−	0.814436i
$963$	1.33888	−	8.88287i	0.0431447	−	0.286246i
$964$	−2.00416	+	28.5286i	−0.0645496	+	0.918843i
$965$	−1.48349	−	3.08051i	−0.0477554	−	0.0991651i
$966$	−4.34690	+	4.93406i	−0.139859	+	0.158751i
$967$	−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	$0.811265\pi$
$968$	5.90612	−	4.08754i	0.189830	−	0.131378i
$969$	0.0141324	+	0.188584i	0.000453998	+	0.00605818i
$970$	0.539009	−	3.63356i	0.0173065	−	0.116667i
$971$	−16.1151	−	1.20766i	−0.517159	−	0.0387557i	−0.186405	−	0.982473i	$-0.559684\pi$
$971$	−16.1151	−	1.20766i	−0.517159	−	0.0387557i	−0.330753	+	0.943717i	$0.607303\pi$
$972$	23.3136	+	18.4147i	0.747783	+	0.590652i
$973$	−0.853257	−	36.3806i	−0.0273542	−	1.16631i
$974$	10.2648	−	12.9334i	0.328906	−	0.414414i
$975$	7.50957	+	2.31640i	0.240499	+	0.0741840i
$976$	34.0281	−	50.9243i	1.08921	−	1.63005i
$977$	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	$0.195068\pi$
$978$	8.43783	−	1.29193i	0.269812	−	0.0413114i
$979$		−	26.2347i		−	0.838464i
$980$	−5.03179	+	11.9936i	−0.160735	+	0.383122i
$981$		−	5.35917i		−	0.171105i
$982$	−6.95019	−	45.3930i	−0.221790	−	1.44855i
$983$	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	$0.216806\pi$
$984$	−0.759205	+	5.28774i	−0.0242026	+	0.168567i
$985$	5.89757	+	1.81916i	0.187912	+	0.0579632i
$986$	2.66161	+	2.11243i	0.0847630	+	0.0672735i
$987$	−4.99804	+	11.0331i	−0.159089	+	0.351187i
$988$	3.40370	−	4.30919i	0.108286	−	0.137093i
$989$	19.9235	+	1.49306i	0.633531	+	0.0474766i
$990$	−9.53602	−	1.41459i	−0.303075	−	0.0449586i
$991$	−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	$-0.129276\pi$
$992$	54.0961	+	15.9981i	1.71755	+	0.507940i
$993$	−5.24259	−	2.52470i	−0.166368	−	0.0801188i
$994$	22.9508	−	16.5301i	0.727956	−	0.524302i
$995$	−3.64577	−	7.57052i	−0.115579	−	0.240001i
$996$	1.57406	−	22.4062i	0.0498761	−	0.709969i
$997$	−4.25915	+	28.2576i	−0.134889	+	0.894929i	0.814350	+	0.580373i	$0.197093\pi$
$997$	−4.25915	+	28.2576i	−0.134889	+	0.894929i	−0.949239	+	0.314555i	$0.898145\pi$
$998$	26.4300	−	2.04265i	0.836628	−	0.0646589i
$999$	−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.37.4	✓	648
8.5	even	2	inner	392.2.z.a.37.19	yes	648
49.4	even	21	inner	392.2.z.a.53.19	yes	648
392.53	even	42	inner	392.2.z.a.53.4	yes	648

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

\(f(q)\)	\(=\)	\(q+(-1.39792 + 0.214038i) q^{2} +(-0.469951 - 0.506487i) q^{3} +(1.90838 - 0.598418i) q^{4} +(0.273835 - 0.887753i) q^{5} +(0.765363 + 0.607442i) q^{6} +(0.528093 - 2.59251i) q^{7} +(-2.53968 + 1.24501i) q^{8} +(0.188515 - 2.51556i) q^{9} +O(q^{10})\)	\(q+(-1.39792 + 0.214038i) q^{2} +(-0.469951 - 0.506487i) q^{3} +(1.90838 - 0.598418i) q^{4} +(0.273835 - 0.887753i) q^{5} +(0.765363 + 0.607442i) q^{6} +(0.528093 - 2.59251i) q^{7} +(-2.53968 + 1.24501i) q^{8} +(0.188515 - 2.51556i) q^{9} +(-0.192788 + 1.29962i) q^{10} +(-2.90057 + 0.217368i) q^{11} +(-1.19993 - 0.685340i) q^{12} +(-1.19293 + 2.47715i) q^{13} +(-0.183337 + 3.73716i) q^{14} +(-0.578324 + 0.278506i) q^{15} +(3.28379 - 2.28401i) q^{16} +(0.271023 + 0.0408501i) q^{17} +(0.274897 + 3.55691i) q^{18} +(-0.864835 - 0.499313i) q^{19} +(-0.00866598 - 1.85803i) q^{20} +(-1.56125 + 0.950882i) q^{21} +(4.00825 - 0.924696i) q^{22} +(-2.51518 + 0.379103i) q^{23} +(1.82410 + 0.701221i) q^{24} +(3.41808 + 2.33040i) q^{25} +(1.13742 - 3.71819i) q^{26} +(-2.98326 + 2.37907i) q^{27} +(-0.543605 - 5.26351i) q^{28} +(-6.85394 - 5.46583i) q^{29} +(0.748842 - 0.513114i) q^{30} +(-4.98617 - 8.63630i) q^{31} +(-4.10162 + 3.89573i) q^{32} +(1.47322 + 1.36695i) q^{33} +(-0.387613 + 0.000903920i) q^{34} +(-2.15690 - 1.17874i) q^{35} +(-1.14560 - 4.91345i) q^{36} +(6.06557 - 2.38056i) q^{37} +(1.31584 + 0.512893i) q^{38} +(1.81526 - 0.559934i) q^{39} +(0.409804 + 2.59553i) q^{40} +(0.608266 + 2.66499i) q^{41} +(1.97898 - 1.66343i) q^{42} +(-7.65784 - 1.74785i) q^{43} +(-5.40530 + 2.15057i) q^{44} +(-2.18158 - 0.856205i) q^{45} +(3.43489 - 1.06830i) 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} +(-0.794192 + 5.44119i) q^{52} +(-3.42053 - 1.34246i) q^{53} +(3.66116 - 3.96429i) q^{54} +(-0.601310 + 2.63451i) q^{55} +(1.88651 + 7.24162i) q^{56} +(0.153535 + 0.672680i) q^{57} +(10.7512 + 6.17381i) q^{58} +(-0.968189 - 3.13879i) q^{59} +(-0.936997 + 0.877574i) q^{60} +(14.2533 - 5.59401i) q^{61} +(8.81878 + 11.0056i) q^{62} +(-6.42207 - 1.81718i) q^{63} +(4.89992 - 6.32383i) q^{64} +(1.87243 + 1.73736i) q^{65} +(-2.35203 - 1.59556i) q^{66} +(-2.13348 + 1.23176i) q^{67} +(0.541659 - 0.0842275i) q^{68} +(1.37402 + 1.09575i) q^{69} +(3.26747 + 1.18613i) q^{70} +(-4.71309 - 5.91003i) q^{71} +(2.65312 + 6.62342i) q^{72} +(11.0283 + 7.51897i) q^{73} +(-7.96967 + 4.62611i) q^{74} +(-0.426009 - 2.82639i) q^{75} +(-1.94923 - 0.435344i) q^{76} +(-0.968243 + 7.63455i) q^{77} +(-2.41775 + 1.17128i) q^{78} +(4.13722 - 7.16587i) q^{79} +(-1.12842 - 3.54064i) q^{80} +(-4.87637 - 0.734994i) q^{81} +(-1.42072 - 3.59526i) q^{82} +(7.05258 + 14.6448i) q^{83} +(-2.41043 + 2.74892i) q^{84} +(0.110481 - 0.229415i) q^{85} +(11.0792 + 0.804292i) q^{86} +(0.452643 + 6.04010i) q^{87} +(7.09589 - 4.16327i) q^{88} +(-0.674018 + 8.99415i) q^{89} +(3.23293 + 0.729968i) q^{90} +(5.79205 + 4.40085i) q^{91} +(-4.57305 + 2.22860i) q^{92} +(-2.03092 + 6.58407i) q^{93} +(-6.85416 + 6.38954i) q^{94} +(-0.680089 + 0.631030i) q^{95} +(3.90070 + 0.246617i) q^{96} -2.79586 q^{97} +(9.59182 + 2.44887i) 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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