LMFDB - Embedded newform 152.2.t.a.101.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,2,Mod(5,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 16]))

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

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

chi := DirichletCharacter("152.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.t (of order $18$, degree $6$, 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:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.12
Character	$\chi$	$=$	152.101
Dual form			152.2.t.a.149.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.303525 + 1.38126i) q^{2} +(-0.256004 + 0.703365i) q^{3} +(-1.81574 + 0.838493i) q^{4} +(-2.14263 + 0.377803i) q^{5} +(-1.04923 - 0.140118i) q^{6} +(-0.852529 + 1.47662i) q^{7} +(-1.70930 - 2.25351i) q^{8} +(1.86895 + 1.56823i) q^{9} +O(q^{10})$	\(q+(0.303525 + 1.38126i) q^{2} +(-0.256004 + 0.703365i) q^{3} +(-1.81574 + 0.838493i) q^{4} +(-2.14263 + 0.377803i) q^{5} +(-1.04923 - 0.140118i) q^{6} +(-0.852529 + 1.47662i) q^{7} +(-1.70930 - 2.25351i) q^{8} +(1.86895 + 1.56823i) q^{9} +(-1.17218 - 2.84485i) q^{10} +(-1.53231 + 0.884678i) q^{11} +(-0.124929 - 1.49179i) q^{12} +(0.842256 + 2.31408i) q^{13} +(-2.29836 - 0.729369i) q^{14} +(0.282787 - 1.60377i) q^{15} +(2.59386 - 3.04498i) q^{16} +(4.93464 - 4.14065i) q^{17} +(-1.59886 + 3.05750i) q^{18} +(2.87718 + 3.27442i) q^{19} +(3.57368 - 2.48257i) q^{20} +(-0.820354 - 0.977660i) q^{21} +(-1.68706 - 1.84799i) q^{22} +(-0.437651 + 2.48204i) q^{23} +(2.02262 - 0.625354i) q^{24} +(-0.250347 + 0.0911189i) q^{25} +(-2.94070 + 1.86575i) q^{26} +(-3.52617 + 2.03584i) q^{27} +(0.309836 - 3.39601i) q^{28} +(4.76000 - 5.67275i) q^{29} +(2.30105 - 0.0961815i) q^{30} +(-3.22845 + 5.59184i) q^{31} +(4.99320 + 2.65856i) q^{32} +(-0.229975 - 1.30425i) q^{33} +(7.21710 + 5.55922i) q^{34} +(1.26878 - 3.48594i) q^{35} +(-4.70849 - 1.28041i) q^{36} -1.77042i q^{37} +(-3.64952 + 4.96800i) q^{38} -1.84326 q^{39} +(4.51377 + 4.18265i) q^{40} +(3.26449 + 1.18818i) q^{41} +(1.10140 - 1.42986i) q^{42} +(7.28735 - 1.28496i) q^{43} +(2.04048 - 2.89118i) q^{44} +(-4.59695 - 2.65405i) q^{45} +(-3.56118 + 0.148854i) q^{46} +(-6.49519 - 5.45011i) q^{47} +(1.47769 + 2.60395i) q^{48} +(2.04639 + 3.54445i) q^{49} +(-0.201845 - 0.318137i) q^{50} +(1.64910 + 4.53087i) q^{51} +(-3.46966 - 3.49555i) q^{52} +(1.97670 + 0.348545i) q^{53} +(-3.88230 - 4.25262i) q^{54} +(2.94893 - 2.47444i) q^{55} +(4.78481 - 0.602811i) q^{56} +(-3.03968 + 1.18545i) q^{57} +(9.28031 + 4.85297i) q^{58} +(-1.57580 - 1.87796i) q^{59} +(0.831278 + 3.14915i) q^{60} +(-0.728234 - 0.128407i) q^{61} +(-8.70368 - 2.76206i) q^{62} +(-3.90902 + 1.42277i) q^{63} +(-2.15659 + 7.70384i) q^{64} +(-2.67891 - 4.64000i) q^{65} +(1.73170 - 0.713527i) q^{66} +(2.24658 - 2.67737i) q^{67} +(-5.48814 + 11.6560i) q^{68} +(-1.63374 - 0.943240i) q^{69} +(5.20009 + 0.694439i) q^{70} +(-1.73545 - 9.84225i) q^{71} +(0.339435 - 6.89227i) q^{72} +(-14.9953 - 5.45784i) q^{73} +(2.44541 - 0.537367i) q^{74} -0.199412i q^{75} +(-7.96981 - 3.53301i) q^{76} -3.01685i q^{77} +(-0.559477 - 2.54602i) q^{78} +(9.21773 + 3.35498i) q^{79} +(-4.40727 + 7.50422i) q^{80} +(0.741748 + 4.20666i) q^{81} +(-0.650323 + 4.86974i) q^{82} +(-10.5599 - 6.09674i) q^{83} +(2.30931 + 1.08732i) q^{84} +(-9.00874 + 10.7362i) q^{85} +(3.98675 + 9.67569i) q^{86} +(2.77143 + 4.80026i) q^{87} +(4.61280 + 1.94089i) q^{88} +(-0.460676 + 0.167672i) q^{89} +(2.27063 - 7.15514i) q^{90} +(-4.13507 - 0.729125i) q^{91} +(-1.28651 - 4.87372i) q^{92} +(-3.10661 - 3.70231i) q^{93} +(5.55656 - 10.6258i) q^{94} +(-7.40182 - 5.92885i) q^{95} +(-3.14821 + 2.83144i) q^{96} +(5.74523 - 4.82082i) q^{97} +(-4.27467 + 3.90242i) q^{98} +(-4.25119 - 0.749599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9	$ 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 9 q^{10} - 3 q^{12} - 9 q^{14} - 12 q^{15} - 12 q^{17} - 12 q^{18} - 42 q^{20} - 12 q^{22} - 12 q^{23} - 36 q^{24} - 12 q^{25} + 21 q^{26} + 24 q^{28} - 48 q^{30} + 30 q^{31} + 39 q^{32} - 30 q^{33} - 60 q^{34} + 69 q^{36} - 42 q^{38} - 24 q^{39} + 36 q^{40} - 24 q^{41} - 81 q^{42} + 45 q^{44} - 18 q^{46} - 48 q^{47} - 21 q^{48} - 24 q^{49} - 12 q^{50} + 3 q^{52} + 63 q^{54} - 42 q^{55} + 30 q^{56} - 12 q^{57} - 84 q^{58} + 30 q^{60} - 6 q^{62} + 30 q^{63} + 3 q^{64} - 6 q^{65} + 54 q^{66} + 36 q^{68} + 123 q^{70} - 12 q^{71} + 150 q^{72} + 12 q^{73} + 75 q^{74} + 42 q^{76} + 39 q^{78} - 12 q^{79} + 51 q^{80} - 18 q^{81} + 99 q^{82} + 75 q^{84} - 48 q^{86} - 6 q^{87} - 27 q^{88} - 12 q^{89} + 66 q^{90} - 48 q^{92} + 54 q^{94} - 72 q^{95} + 42 q^{96} - 12 q^{97} + 93 q^{98}+O(q^{100}) $ 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 9 * q^10 - 3 * q^12 - 9 * q^14 - 12 * q^15 - 12 * q^17 - 12 * q^18 - 42 * q^20 - 12 * q^22 - 12 * q^23 - 36 * q^24 - 12 * q^25 + 21 * q^26 + 24 * q^28 - 48 * q^30 + 30 * q^31 + 39 * q^32 - 30 * q^33 - 60 * q^34 + 69 * q^36 - 42 * q^38 - 24 * q^39 + 36 * q^40 - 24 * q^41 - 81 * q^42 + 45 * q^44 - 18 * q^46 - 48 * q^47 - 21 * q^48 - 24 * q^49 - 12 * q^50 + 3 * q^52 + 63 * q^54 - 42 * q^55 + 30 * q^56 - 12 * q^57 - 84 * q^58 + 30 * q^60 - 6 * q^62 + 30 * q^63 + 3 * q^64 - 6 * q^65 + 54 * q^66 + 36 * q^68 + 123 * q^70 - 12 * q^71 + 150 * q^72 + 12 * q^73 + 75 * q^74 + 42 * q^76 + 39 * q^78 - 12 * q^79 + 51 * q^80 - 18 * q^81 + 99 * q^82 + 75 * q^84 - 48 * q^86 - 6 * q^87 - 27 * q^88 - 12 * q^89 + 66 * q^90 - 48 * q^92 + 54 * q^94 - 72 * q^95 + 42 * q^96 - 12 * q^97 + 93 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.303525	+	1.38126i	0.214625	+	0.976697i
$2$	0.303525	+	1.38126i	0.214625	+	0.976697i
$3$	−0.256004	+	0.703365i	−0.147804	+	0.406088i	−0.991396	−	0.130897i	$-0.958214\pi$
$3$	−0.256004	+	0.703365i	−0.147804	+	0.406088i	0.843592	+	0.536984i	$0.180437\pi$
$4$	−1.81574	+	0.838493i	−0.907872	+	0.419247i
$5$	−2.14263	+	0.377803i	−0.958212	+	0.168959i	−0.630819	−	0.775930i	$-0.717281\pi$
$5$	−2.14263	+	0.377803i	−0.958212	+	0.168959i	−0.327393	+	0.944888i	$0.606170\pi$
$6$	−1.04923	−	0.140118i	−0.428347	−	0.0572030i
$7$	−0.852529	+	1.47662i	−0.322226	+	0.558111i	−0.980947	−	0.194276i	$-0.937764\pi$
$7$	−0.852529	+	1.47662i	−0.322226	+	0.558111i	0.658721	+	0.752387i	$0.271098\pi$
$8$	−1.70930	−	2.25351i	−0.604329	−	0.796735i
$9$	1.86895	+	1.56823i	0.622983	+	0.522745i
$10$	−1.17218	−	2.84485i	−0.370677	−	0.899620i
$11$	−1.53231	+	0.884678i	−0.462008	+	0.266740i	−0.712888	−	0.701278i	$-0.752613\pi$
$11$	−1.53231	+	0.884678i	−0.462008	+	0.266740i	0.250880	+	0.968018i	$0.419280\pi$
$12$	−0.124929	−	1.49179i	−0.0360638	−	0.430642i
$13$	0.842256	+	2.31408i	0.233600	+	0.641810i	1.00000		0.000553234i	$-0.000176100\pi$
$13$	0.842256	+	2.31408i	0.233600	+	0.641810i	−0.766400	+	0.642364i	$0.777954\pi$
$14$	−2.29836	−	0.729369i	−0.614263	−	0.194932i
$15$	0.282787	−	1.60377i	0.0730154	−	0.414091i
$16$	2.59386	−	3.04498i	0.648465	−	0.761245i
$17$	4.93464	−	4.14065i	1.19683	−	1.00426i	0.197111	−	0.980381i	$-0.436844\pi$
$17$	4.93464	−	4.14065i	1.19683	−	1.00426i	0.999715	−	0.0238751i	$-0.00760042\pi$
$18$	−1.59886	+	3.05750i	−0.376856	+	0.720660i
$19$	2.87718	+	3.27442i	0.660071	+	0.751203i
$19$	2.87718	+	3.27442i	0.660071	+	0.751203i
$20$	3.57368	−	2.48257i	0.799099	−	0.555120i
$21$	−0.820354	−	0.977660i	−0.179016	−	0.213343i
$22$	−1.68706	−	1.84799i	−0.359683	−	0.393992i
$23$	−0.437651	+	2.48204i	−0.0912565	+	0.517541i	0.904574	+	0.426317i	$0.140189\pi$
$23$	−0.437651	+	2.48204i	−0.0912565	+	0.517541i	−0.995830	+	0.0912244i	$0.970922\pi$
$24$	2.02262	−	0.625354i	0.412866	−	0.127650i
$25$	−0.250347	+	0.0911189i	−0.0500694	+	0.0182238i
$26$	−2.94070	+	1.86575i	−0.576718	+	0.365905i
$27$	−3.52617	+	2.03584i	−0.678612	+	0.391797i
$28$	0.309836	−	3.39601i	0.0585536	−	0.641786i
$29$	4.76000	−	5.67275i	0.883910	−	1.05340i	−0.114291	−	0.993447i	$-0.536460\pi$
$29$	4.76000	−	5.67275i	0.883910	−	1.05340i	0.998201	−	0.0599557i	$-0.0190960\pi$
$30$	2.30105	−	0.0961815i	0.420112	−	0.0175603i
$31$	−3.22845	+	5.59184i	−0.579846	+	1.00432i	0.415650	+	0.909525i	$0.363554\pi$
$31$	−3.22845	+	5.59184i	−0.579846	+	1.00432i	−0.995496	+	0.0947989i	$0.969779\pi$
$32$	4.99320	+	2.65856i	0.882682	+	0.469971i
$33$	−0.229975	−	1.30425i	−0.0400334	−	0.227041i
$34$	7.21710	+	5.55922i	1.23772	+	0.953398i
$35$	1.26878	−	3.48594i	0.214463	−	0.589231i
$36$	−4.70849	−	1.28041i	−0.784748	−	0.213402i
$37$		−	1.77042i		−	0.291055i	−0.989354	−	0.145528i	$-0.953512\pi$
$37$		−	1.77042i		−	0.291055i	0.989354	−	0.145528i	$-0.0464880\pi$
$38$	−3.64952	+	4.96800i	−0.592030	+	0.805916i
$39$	−1.84326			−0.295158
$40$	4.51377	+	4.18265i	0.713690	+	0.661335i
$41$	3.26449	+	1.18818i	0.509827	+	0.185562i	0.584109	−	0.811675i	$-0.301444\pi$
$41$	3.26449	+	1.18818i	0.509827	+	0.185562i	−0.0742815	+	0.997237i	$0.523666\pi$
$42$	1.10140	−	1.42986i	0.169950	−	0.220633i
$43$	7.28735	−	1.28496i	1.11131	−	0.195954i	0.412288	−	0.911054i	$-0.364730\pi$
$43$	7.28735	−	1.28496i	1.11131	−	0.195954i	0.699023	+	0.715100i	$0.253619\pi$
$44$	2.04048	−	2.89118i	0.307614	−	0.435861i
$45$	−4.59695	−	2.65405i	−0.685272	−	0.395642i
$46$	−3.56118	+	0.148854i	−0.525067	+	0.0219473i
$47$	−6.49519	−	5.45011i	−0.947421	−	0.794981i	0.0314403	−	0.999506i	$-0.489991\pi$
$47$	−6.49519	−	5.45011i	−0.947421	−	0.794981i	−0.978861	+	0.204525i	$0.934435\pi$
$48$	1.47769	+	2.60395i	0.213287	+	0.375848i
$49$	2.04639	+	3.54445i	0.292341	+	0.506350i
$50$	−0.201845	−	0.318137i	−0.0285452	−	0.0449913i
$51$	1.64910	+	4.53087i	0.230921	+	0.634449i
$52$	−3.46966	−	3.49555i	−0.481156	−	0.484746i
$53$	1.97670	+	0.348545i	0.271520	+	0.0478763i	0.307750	−	0.951467i	$-0.400424\pi$
$53$	1.97670	+	0.348545i	0.271520	+	0.0478763i	−0.0362302	+	0.999343i	$0.511535\pi$
$54$	−3.88230	−	4.25262i	−0.528314	−	0.578709i
$55$	2.94893	−	2.47444i	0.397633	−	0.333654i
$56$	4.78481	−	0.602811i	0.639397	−	0.0805540i
$57$	−3.03968	+	1.18545i	−0.402615	+	0.157016i
$58$	9.28031	+	4.85297i	1.21856	+	0.637226i
$59$	−1.57580	−	1.87796i	−0.205151	−	0.244490i	0.653652	−	0.756795i	$-0.273236\pi$
$59$	−1.57580	−	1.87796i	−0.205151	−	0.244490i	−0.858803	+	0.512306i	$0.828792\pi$
$60$	0.831278	+	3.14915i	0.107318	+	0.406553i
$61$	−0.728234	−	0.128407i	−0.0932408	−	0.0164409i	0.126833	−	0.991924i	$-0.459519\pi$
$61$	−0.728234	−	0.128407i	−0.0932408	−	0.0164409i	−0.220074	+	0.975483i	$0.570630\pi$
$62$	−8.70368	−	2.76206i	−1.10537	−	0.350781i
$63$	−3.90902	+	1.42277i	−0.492491	+	0.179252i
$64$	−2.15659	+	7.70384i	−0.269574	+	0.962980i
$65$	−2.67891	−	4.64000i	−0.332278	−	0.575522i
$66$	1.73170	−	0.713527i	0.213158	−	0.0878291i
$67$	2.24658	−	2.67737i	0.274463	−	0.327093i	−0.611151	−	0.791514i	$-0.709293\pi$
$67$	2.24658	−	2.67737i	0.274463	−	0.327093i	0.885614	+	0.464421i	$0.153738\pi$
$68$	−5.48814	+	11.6560i	−0.665534	+	1.41350i
$69$	−1.63374	−	0.943240i	−0.196679	−	0.113553i
$70$	5.20009	+	0.694439i	0.621529	+	0.0830013i
$71$	−1.73545	−	9.84225i	−0.205960	−	1.16806i	−0.895921	−	0.444213i	$-0.853483\pi$
$71$	−1.73545	−	9.84225i	−0.205960	−	1.16806i	0.689961	−	0.723847i	$-0.257628\pi$
$72$	0.339435	−	6.89227i	0.0400028	−	0.812262i
$73$	−14.9953	−	5.45784i	−1.75506	−	0.638791i	−0.755204	−	0.655490i	$-0.772462\pi$
$73$	−14.9953	−	5.45784i	−1.75506	−	0.638791i	−0.999861	+	0.0166985i	$0.994684\pi$
$74$	2.44541	−	0.537367i	0.284273	−	0.0624677i
$75$		−	0.199412i		−	0.0230261i
$76$	−7.96981	−	3.53301i	−0.914200	−	0.405264i
$77$		−	3.01685i		−	0.343802i
$78$	−0.559477	−	2.54602i	−0.0633483	−	0.288280i
$79$	9.21773	+	3.35498i	1.03708	+	0.377464i	0.803771	−	0.594939i	$-0.202824\pi$
$79$	9.21773	+	3.35498i	1.03708	+	0.377464i	0.233304	+	0.972404i	$0.425046\pi$
$80$	−4.40727	+	7.50422i	−0.492748	+	0.838998i
$81$	0.741748	+	4.20666i	0.0824164	+	0.467407i
$82$	−0.650323	+	4.86974i	−0.0718162	+	0.537773i
$83$	−10.5599	−	6.09674i	−1.15910	−	0.669204i	−0.208008	−	0.978127i	$-0.566698\pi$
$83$	−10.5599	−	6.09674i	−1.15910	−	0.669204i	−0.951087	+	0.308923i	$0.900031\pi$
$84$	2.30931	+	1.08732i	0.251967	+	0.118636i
$85$	−9.00874	+	10.7362i	−0.977135	+	1.16450i
$86$	3.98675	+	9.67569i	0.429902	+	1.04336i
$87$	2.77143	+	4.80026i	0.297129	+	0.514642i
$88$	4.61280	+	1.94089i	0.491726	+	0.206899i
$89$	−0.460676	+	0.167672i	−0.0488316	+	0.0177732i	−0.366320	−	0.930489i	$-0.619383\pi$
$89$	−0.460676	+	0.167672i	−0.0488316	+	0.0177732i	0.317489	+	0.948262i	$0.397160\pi$
$90$	2.27063	−	7.15514i	0.239346	−	0.754218i
$91$	−4.13507	−	0.729125i	−0.433473	−	0.0764330i
$92$	−1.28651	−	4.87372i	−0.134128	−	0.508120i
$93$	−3.10661	−	3.70231i	−0.322140	−	0.383911i
$94$	5.55656	−	10.6258i	0.573115	−	1.09597i
$95$	−7.40182	−	5.92885i	−0.759410	−	0.608287i
$96$	−3.14821	+	2.83144i	−0.321313	+	0.288983i
$97$	5.74523	−	4.82082i	0.583340	−	0.489480i	−0.302702	−	0.953085i	$-0.597889\pi$
$97$	5.74523	−	4.82082i	0.583340	−	0.489480i	0.886042	+	0.463605i	$0.153444\pi$
$98$	−4.27467	+	3.90242i	−0.431807	+	0.394204i
$99$	−4.25119	−	0.749599i	−0.427260	−	0.0753375i
$100$	0.378164	−	0.375363i	0.0378164	−	0.0375363i
$101$	4.55094	+	12.5036i	0.452835	+	1.24416i	0.930720	+	0.365732i	$0.119181\pi$
$101$	4.55094	+	12.5036i	0.452835	+	1.24416i	−0.477885	+	0.878423i	$0.658596\pi$
$102$	−5.75776	+	3.65307i	−0.570103	+	0.361708i
$103$	2.35224	+	4.07420i	0.231773	+	0.401443i	0.958330	−	0.285663i	$-0.0922139\pi$
$103$	2.35224	+	4.07420i	0.231773	+	0.401443i	−0.726557	+	0.687106i	$0.758881\pi$
$104$	3.77513	−	5.85349i	0.370182	−	0.573982i
$105$	2.12707	+	1.78483i	0.207581	+	0.174181i
$106$	0.118547	+	2.83612i	0.0115143	+	0.275468i
$107$	5.84123	+	3.37244i	0.564693	+	0.326026i	0.755027	−	0.655694i	$-0.227624\pi$
$107$	5.84123	+	3.37244i	0.564693	+	0.326026i	−0.190334	+	0.981719i	$0.560957\pi$
$108$	4.69559	−	6.65323i	0.451834	−	0.640207i
$109$	19.3418	−	3.41048i	1.85261	−	0.326664i	0.867343	−	0.497710i	$-0.165826\pi$
$109$	19.3418	−	3.41048i	1.85261	−	0.326664i	0.985263	+	0.171046i	$0.0547146\pi$
$110$	4.31292	+	3.32217i	0.411221	+	0.316757i
$111$	1.24525	+	0.453234i	0.118194	+	0.0430191i
$112$	2.28495	+	6.42608i	0.215907	+	0.607208i
$113$	−10.4597			−0.983964			−0.491982	−	0.870605i	$-0.663727\pi$
$113$	−10.4597			−0.983964			−0.491982	+	0.870605i	$0.663727\pi$
$114$	−2.56003	−	3.83877i	−0.239768	−	0.359534i
$115$		−	5.48343i		−	0.511333i
$116$	−3.88639	+	14.2915i	−0.360842	+	1.32693i
$117$	−2.05489	+	5.64576i	−0.189974	+	0.521950i
$118$	2.11565	−	2.74659i	0.194762	−	0.252844i
$119$	1.90726	+	10.8166i	0.174839	+	0.991559i
$120$	−4.09747	+	2.10405i	−0.374046	+	0.192073i
$121$	−3.93469	+	6.81509i	−0.357699	+	0.619553i
$122$	−0.0436738	−	1.04485i	−0.00395404	−	0.0945966i
$123$	−1.67144	+	1.99195i	−0.150709	+	0.179608i
$124$	1.17332	−	12.8604i	0.105367	−	1.15490i
$125$	9.92295	−	5.72902i	0.887536	−	0.512419i
$126$	−3.15170	−	4.96752i	−0.280776	−	0.442542i
$127$	13.2793	−	4.83326i	1.17835	−	0.428883i	0.322728	−	0.946492i	$-0.395400\pi$
$127$	13.2793	−	4.83326i	1.17835	−	0.428883i	0.855617	+	0.517609i	$0.173178\pi$
$128$	−11.2956	−	0.640500i	−0.998396	−	0.0566127i
$129$	−0.961796	+	5.45462i	−0.0846814	+	0.480252i
$130$	5.59593	−	5.10862i	0.490795	−	0.448056i
$131$	7.59486	+	9.05121i	0.663566	+	0.790808i	0.987893	−	0.155138i	$-0.0495821\pi$
$131$	7.59486	+	9.05121i	0.663566	+	0.790808i	−0.324326	+	0.945945i	$0.605138\pi$
$132$	1.51118	+	2.17535i	0.131531	+	0.189340i
$133$	−7.28796	+	1.45698i	−0.631946	+	0.126336i
$134$	4.38003	+	2.29046i	0.378377	+	0.197865i
$135$	6.78613	−	5.69424i	0.584057	−	0.490082i
$136$	−17.7658	−	4.04263i	−1.52340	−	0.346653i
$137$	0.444110	−	2.51867i	0.0379428	−	0.215185i	−0.959941	−	0.280201i	$-0.909599\pi$
$137$	0.444110	−	2.51867i	0.0379428	−	0.215185i	0.997884	+	0.0650164i	$0.0207100\pi$
$138$	0.806976	−	2.54291i	0.0686944	−	0.216467i
$139$	−4.46380	−	12.2642i	−0.378614	−	1.04023i	−0.971931	−	0.235265i	$-0.924404\pi$
$139$	−4.46380	−	12.2642i	−0.378614	−	1.04023i	0.593317	−	0.804969i	$-0.297818\pi$
$140$	0.619159	+	7.39344i	0.0523285	+	0.624860i
$141$	5.49621	−	3.17324i	0.462864	−	0.267235i
$142$	13.0679	−	5.38448i	1.09664	−	0.451855i
$143$	−3.33781	−	2.80076i	−0.279122	−	0.234211i
$144$	9.62303	−	1.62313i	0.801919	−	0.135261i
$145$	−8.05573	+	13.9529i	−0.668992	+	1.15873i
$146$	2.98723	−	22.3689i	0.247225	−	1.85127i
$147$	−3.01693	+	0.531965i	−0.248832	+	0.0438758i
$148$	1.48448	+	3.21463i	0.122024	+	0.264241i
$149$	−3.68846	+	10.1340i	−0.302171	+	0.830207i	0.691951	+	0.721944i	$0.256751\pi$
$149$	−3.68846	+	10.1340i	−0.302171	+	0.830207i	−0.994122	+	0.108263i	$0.965471\pi$
$150$	0.275439	−	0.0605266i	0.0224895	−	0.00494197i
$151$	22.9437			1.86713			0.933564	−	0.358410i	$-0.116681\pi$
$151$	22.9437			1.86713			0.933564	+	0.358410i	$0.116681\pi$
$152$	2.46096	−	12.0807i	0.199610	−	0.979875i
$153$	15.7161			1.27057
$154$	4.16705	−	0.915691i	0.335790	−	0.0737885i
$155$	4.80475	−	13.2009i	0.385927	−	1.06032i
$156$	3.34690	−	1.54556i	0.267966	−	0.123744i
$157$	4.13263	−	0.728695i	0.329820	−	0.0581562i	−0.00628627	−	0.999980i	$-0.502001\pi$
$157$	4.13263	−	0.728695i	0.329820	−	0.0581562i	0.336106	+	0.941824i	$0.390890\pi$
$158$	−1.83628	+	13.7504i	−0.146086	+	1.09392i
$159$	−0.751196	+	1.30111i	−0.0595737	+	0.103185i
$160$	−11.7030	−	3.80985i	−0.925202	−	0.301195i
$161$	−3.29193	−	2.76226i	−0.259440	−	0.217696i
$162$	−5.58534	+	2.30137i	−0.438826	+	0.180813i
$163$	−6.90931	+	3.98909i	−0.541179	+	0.312450i	−0.745557	−	0.666442i	$-0.767816\pi$
$163$	−6.90931	+	3.98909i	−0.541179	+	0.312450i	0.204378	+	0.978892i	$0.434483\pi$
$164$	−6.92376	+	0.579825i	−0.540654	+	0.0452767i
$165$	0.985500	+	2.70764i	0.0767210	+	0.210789i
$166$	5.21598	−	16.4364i	0.404839	−	1.27571i
$167$	0.862580	−	4.89193i	0.0667484	−	0.378549i	−0.933074	−	0.359685i	$-0.882884\pi$
$167$	0.862580	−	4.89193i	0.0667484	−	0.378549i	0.999822	−	0.0188638i	$-0.00600489\pi$
$168$	−0.800933	+	3.51979i	−0.0617933	+	0.271557i
$169$	5.31300	−	4.45814i	0.408693	−	0.342934i
$170$	−17.5638	−	9.18469i	−1.34709	−	0.704433i
$171$	0.242254	+	10.6318i	0.0185257	+	0.813036i
$172$	−12.1545	+	8.44355i	−0.926775	+	0.643814i
$173$	−3.78001	−	4.50484i	−0.287389	−	0.342497i	0.602963	−	0.797769i	$-0.293987\pi$
$173$	−3.78001	−	4.50484i	−0.287389	−	0.342497i	−0.890352	+	0.455272i	$0.849542\pi$
$174$	−5.78920	+	5.28506i	−0.438878	+	0.400660i
$175$	0.0788798	−	0.447350i	0.00596275	−	0.0338165i
$176$	−1.28076	+	6.96057i	−0.0965411	+	0.524673i
$177$	1.72430	−	0.627594i	0.129606	−	0.0471729i
$178$	−0.371426	−	0.585420i	−0.0278395	−	0.0438791i
$179$	11.9078	−	6.87500i	0.890034	−	0.513861i	0.0160803	−	0.999871i	$-0.494881\pi$
$179$	11.9078	−	6.87500i	0.890034	−	0.513861i	0.873954	+	0.486009i	$0.161548\pi$
$180$	10.5723	+	0.964567i	0.788011	+	0.0718946i
$181$	−14.8464	+	17.6933i	−1.10353	+	1.31513i	−0.158785	+	0.987313i	$0.550758\pi$
$181$	−14.8464	+	17.6933i	−1.10353	+	1.31513i	−0.944741	+	0.327818i	$0.893687\pi$
$182$	−0.247990	−	5.93291i	−0.0183822	−	0.439776i
$183$	0.276748	−	0.479341i	0.0204578	−	0.0354339i
$184$	6.34137	−	3.25630i	0.467492	−	0.240058i
$185$	0.668870	+	3.79335i	0.0491763	+	0.278893i
$186$	4.17091	−	5.41477i	0.305826	−	0.397030i
$187$	−3.89824	+	10.7103i	−0.285067	+	0.783216i
$188$	16.3635	+	4.44984i	1.19343	+	0.324538i
$189$		−	6.94244i		−	0.504988i
$190$	5.94263	−	12.0234i	0.431124	−	0.872267i
$191$	17.9794			1.30094			0.650471	−	0.759531i	$-0.274571\pi$
$191$	17.9794			1.30094			0.650471	+	0.759531i	$0.274571\pi$
$192$	−4.86651	−	3.48908i	−0.351210	−	0.251803i
$193$	−4.81916	−	1.75403i	−0.346891	−	0.126258i	0.162698	−	0.986676i	$-0.447980\pi$
$193$	−4.81916	−	1.75403i	−0.346891	−	0.126258i	−0.509589	+	0.860418i	$0.670203\pi$
$194$	8.40261	+	6.47240i	0.603273	+	0.464691i
$195$	3.94943	−	0.696390i	0.282824	−	0.0498695i
$196$	−6.68772	−	4.71994i	−0.477694	−	0.337138i
$197$	−17.6944	−	10.2158i	−1.26067	−	0.727848i	−0.287466	−	0.957791i	$-0.592813\pi$
$197$	−17.6944	−	10.2158i	−1.26067	−	0.727848i	−0.973204	+	0.229942i	$0.926146\pi$
$198$	−0.254953	−	6.09950i	−0.0181187	−	0.433473i
$199$	−11.8505	−	9.94375i	−0.840060	−	0.704894i	0.117517	−	0.993071i	$-0.462506\pi$
$199$	−11.8505	−	9.94375i	−0.840060	−	0.704894i	−0.957577	+	0.288177i	$0.906951\pi$
$200$	0.633255	+	0.408410i	0.0447779	+	0.0288789i
$201$	1.30803	+	2.26558i	0.0922616	+	0.159802i
$202$	−15.8894	+	10.0812i	−1.11797	+	0.709309i
$203$	4.31847	+	11.8649i	0.303097	+	0.832753i
$204$	−6.79346	−	6.84415i	−0.475637	−	0.479186i
$205$	−7.44348	−	1.31249i	−0.519875	−	0.0916680i
$206$	−4.91356	+	4.48568i	−0.342344	+	0.312532i
$207$	−4.71037	+	3.95247i	−0.327393	+	0.274716i
$208$	9.23102	+	3.43775i	0.640056	+	0.238365i
$209$	−7.30553	−	2.47203i	−0.505334	−	0.170994i
$210$	−1.81969	+	3.47978i	−0.125570	+	0.240128i
$211$	−13.7494	−	16.3859i	−0.946549	−	1.12805i	−0.991636	−	0.129070i	$-0.958801\pi$
$211$	−13.7494	−	16.3859i	−0.946549	−	1.12805i	0.0450870	−	0.998983i	$-0.485643\pi$
$212$	−3.88143	+	1.02458i	−0.266578	+	0.0703683i
$213$	7.36697	+	1.29900i	0.504776	+	0.0890057i
$214$	−2.88524	+	9.09187i	−0.197231	+	0.621507i
$215$	−15.1286	+	5.50637i	−1.03176	+	0.375531i
$216$	10.6151	+	4.46640i	0.722263	+	0.303900i
$217$	−5.50469	−	9.53440i	−0.373683	−	0.647237i
$218$	10.5815	+	25.6808i	0.716667	+	1.73932i
$219$	7.67770	−	9.14992i	0.518811	−	0.618294i
$220$	−3.27970	+	6.96561i	−0.221117	+	0.469622i
$221$	13.7380	+	7.93166i	0.924121	+	0.533541i
$222$	−0.248068	+	1.85758i	−0.0166492	+	0.124673i
$223$	2.72511	+	15.4549i	0.182487	+	1.03494i	0.929142	+	0.369723i	$0.120548\pi$
$223$	2.72511	+	15.4549i	0.182487	+	1.03494i	−0.746655	+	0.665212i	$0.768341\pi$
$224$	−8.18254	+	5.10658i	−0.546719	+	0.341198i
$225$	−0.610782	−	0.222306i	−0.0407188	−	0.0148204i
$226$	−3.17478	−	14.4475i	−0.211183	−	0.961035i
$227$			26.4134i			1.75312i	0.481297	+	0.876558i	$0.340166\pi$
$227$			26.4134i			1.75312i	−0.481297	+	0.876558i	$0.659834\pi$
$228$	4.52529	−	4.70122i	0.299695	−	0.311346i
$229$			3.36924i			0.222646i	0.993784	+	0.111323i	$0.0355087\pi$
$229$			3.36924i			0.222646i	−0.993784	+	0.111323i	$0.964491\pi$
$230$	7.57403	−	1.66436i	0.499417	−	0.109745i
$231$	2.12195	+	0.772325i	0.139614	+	0.0508153i
$232$	−20.9198	−	1.03027i	−1.37346	−	0.0676408i
$233$	1.78573	+	10.1274i	0.116987	+	0.663465i	0.985747	+	0.168233i	$0.0538060\pi$
$233$	1.78573	+	10.1274i	0.116987	+	0.663465i	−0.868760	+	0.495232i	$0.835083\pi$
$234$	−8.42195	−	1.12470i	−0.550560	−	0.0735239i
$235$	15.9758	+	9.22366i	1.04215	+	0.601685i
$236$	4.43590	+	2.08860i	0.288753	+	0.135956i
$237$	−4.71955	+	5.62454i	−0.306567	+	0.365353i
$238$	−14.3616	+	5.91754i	−0.930927	+	0.383577i
$239$	−1.47648	−	2.55734i	−0.0955056	−	0.165421i	0.814314	−	0.580425i	$-0.197113\pi$
$239$	−1.47648	−	2.55734i	−0.0955056	−	0.165421i	−0.909820	+	0.415004i	$0.863780\pi$
$240$	−4.14993	−	5.02103i	−0.267877	−	0.324106i
$241$	−6.52198	+	2.37381i	−0.420118	+	0.152910i	−0.543424	−	0.839458i	$-0.682872\pi$
$241$	−6.52198	+	2.37381i	−0.420118	+	0.152910i	0.123306	+	0.992369i	$0.460650\pi$
$242$	−10.6077	−	3.36627i	−0.681887	−	0.216392i
$243$	−15.1781	−	2.67632i	−0.973679	−	0.171686i
$244$	1.42996	−	0.377464i	0.0915435	−	0.0241647i
$245$	−5.72375	−	6.82131i	−0.365677	−	0.435797i
$246$	−3.25872	−	1.70409i	−0.207768	−	0.108649i
$247$	−5.15394	+	9.41593i	−0.327937	+	0.599122i
$248$	18.1196	−	2.28279i	1.15060	−	0.144957i
$249$	6.99159	−	5.86664i	0.443074	−	0.371783i
$250$	10.9251	+	11.9672i	0.690965	+	0.756875i
$251$	−18.8074	−	3.31625i	−1.18711	−	0.209320i	−0.454992	−	0.890496i	$-0.650358\pi$
$251$	−18.8074	−	3.31625i	−1.18711	−	0.209320i	−0.732120	+	0.681176i	$0.761469\pi$
$252$	5.90481	−	5.86107i	0.371968	−	0.369213i
$253$	−1.52519	−	4.19043i	−0.0958879	−	0.263450i
$254$	10.7066	+	16.8751i	0.671790	+	1.05884i
$255$	−5.24519	−	9.08494i	−0.328467	−	0.568921i
$256$	−2.54379	−	15.7965i	−0.158987	−	0.987281i
$257$	18.8813	+	15.8433i	1.17778	+	0.988275i	0.999991	+	0.00420666i	$0.00133903\pi$
$257$	18.8813	+	15.8433i	1.17778	+	0.988275i	0.177789	+	0.984069i	$0.443105\pi$
$258$	−7.82616	+	0.327126i	−0.487236	+	0.0203660i
$259$	2.61424	+	1.50933i	0.162441	+	0.0937854i
$260$	8.75483	+	6.17882i	0.542951	+	0.383194i
$261$	17.7924	−	3.13728i	1.10132	−	0.194193i
$262$	−10.1968	+	13.2377i	−0.629961	+	0.817830i
$263$	−26.3560	−	9.59279i	−1.62518	−	0.591517i	−0.640820	−	0.767691i	$-0.721406\pi$
$263$	−26.3560	−	9.59279i	−1.62518	−	0.591517i	−0.984359	+	0.176174i	$0.943628\pi$
$264$	−2.54604	+	2.74760i	−0.156698	+	0.169103i
$265$	−4.36700			−0.268263
$266$	−4.22455	−	9.62432i	−0.259023	−	0.590105i
$267$		−	0.366948i		−	0.0224569i
$268$	−1.83426	+	6.74516i	−0.112045	+	0.412026i
$269$	9.66436	−	26.5526i	0.589246	−	1.61894i	−0.182640	−	0.983180i	$-0.558464\pi$
$269$	9.66436	−	26.5526i	0.589246	−	1.61894i	0.771886	−	0.635761i	$-0.219314\pi$
$270$	9.92497	+	7.64504i	0.604014	+	0.465263i
$271$	−1.10529	−	6.26841i	−0.0671416	−	0.380779i	−0.999800	−	0.0200173i	$-0.993628\pi$
$271$	−1.10529	−	6.26841i	−0.0671416	−	0.380779i	0.932658	−	0.360762i	$-0.117483\pi$
$272$	0.191553	−	25.7661i	0.0116146	−	1.56230i
$273$	1.57143	−	2.72180i	0.0951076	−	0.164731i
$274$	3.61373	−	0.151050i	0.218314	−	0.00912529i
$275$	0.302998	−	0.361098i	0.0182714	−	0.0217751i
$276$	3.75735	+	0.342804i	0.226166	+	0.0206344i
$277$	3.45402	−	1.99418i	0.207532	−	0.119819i	−0.392632	−	0.919696i	$-0.628435\pi$
$277$	3.45402	−	1.99418i	0.207532	−	0.119819i	0.600164	+	0.799877i	$0.295102\pi$
$278$	15.5851	−	9.88814i	0.934733	−	0.593051i
$279$	−14.8031	+	5.38790i	−0.886240	+	0.322565i
$280$	−10.0243	+	3.09931i	−0.599067	+	0.185219i
$281$	3.48646	−	19.7727i	0.207985	−	1.17954i	−0.684688	−	0.728836i	$-0.740061\pi$
$281$	3.48646	−	19.7727i	0.207985	−	1.17954i	0.892673	−	0.450705i	$-0.148827\pi$
$282$	6.05130	+	6.62852i	0.360350	+	0.394723i
$283$	−11.9306	−	14.2183i	−0.709200	−	0.845192i	0.284334	−	0.958725i	$-0.408227\pi$
$283$	−11.9306	−	14.2183i	−0.709200	−	0.845192i	−0.993534	+	0.113534i	$0.963783\pi$
$284$	11.4038	+	16.4158i	0.676691	+	0.974101i
$285$	6.06504	−	3.68837i	0.359262	−	0.218480i
$286$	2.85545	−	5.46048i	0.168847	−	0.322885i
$287$	−4.53756	+	3.80746i	−0.267844	+	0.224747i
$288$	5.16280	+	12.7992i	0.304221	+	0.754202i
$289$	4.25363	−	24.1236i	0.250214	−	1.41903i
$290$	−21.7177	−	6.89197i	−1.27531	−	0.404710i
$291$	1.91999	+	5.27514i	0.112552	+	0.309234i
$292$	31.8040	−	2.66340i	1.86119	−	0.155864i
$293$	−1.75054	+	1.01068i	−0.102268	+	0.0590443i	−0.550262	−	0.834992i	$-0.685472\pi$
$293$	−1.75054	+	1.01068i	−0.102268	+	0.0590443i	0.447994	+	0.894037i	$0.352139\pi$
$294$	−1.65049	−	4.00569i	−0.0962588	−	0.233616i
$295$	4.08584	+	3.42843i	0.237887	+	0.199611i
$296$	−3.98965	+	3.02618i	−0.231894	+	0.175893i
$297$	3.60212	−	6.23905i	0.209016	−	0.362026i
$298$	−15.1172	−	2.01880i	−0.875714	−	0.116946i
$299$	−6.11226	+	1.07776i	−0.353481	+	0.0623282i
$300$	0.167206	+	0.362081i	0.00965362	+	0.0209048i
$301$	−4.31528	+	11.8561i	−0.248729	+	0.683376i
$302$	6.96398	+	31.6911i	0.400732	+	1.82362i
$303$	−9.95965			−0.572167
$304$	17.4335	−	0.267585i	0.999882	−	0.0153471i
$305$	1.60885			0.0921223
$306$	4.77024	+	21.7080i	0.272696	+	1.24096i
$307$	8.48113	−	23.3017i	0.484043	−	1.32990i	−0.421955	−	0.906617i	$-0.638656\pi$
$307$	8.48113	−	23.3017i	0.484043	−	1.32990i	0.905998	−	0.423282i	$-0.139122\pi$
$308$	2.52961	+	5.47783i	0.144138	+	0.312128i
$309$	−3.46783	+	0.611473i	−0.197278	+	0.0347855i
$310$	19.6923	+	2.62978i	1.11845	+	0.149361i
$311$	13.1395	−	22.7583i	0.745073	−	1.29050i	−0.205088	−	0.978744i	$-0.565748\pi$
$311$	13.1395	−	22.7583i	0.745073	−	1.29050i	0.950161	−	0.311761i	$-0.100919\pi$
$312$	3.15069	+	4.15381i	0.178373	+	0.235163i
$313$	−8.24899	−	6.92172i	−0.466260	−	0.391239i	0.379168	−	0.925328i	$-0.376210\pi$
$313$	−8.24899	−	6.92172i	−0.466260	−	0.391239i	−0.845428	+	0.534089i	$0.820655\pi$
$314$	2.26087	+	5.48705i	0.127588	+	0.309652i
$315$	7.83806	−	4.52530i	0.441624	−	0.254972i
$316$	−19.5502	+	1.63722i	−1.09978	+	0.0921006i
$317$	−7.46724	−	20.5161i	−0.419402	−	1.15230i	−0.952045	−	0.305958i	$-0.901023\pi$
$317$	−7.46724	−	20.5161i	−0.419402	−	1.15230i	0.532643	−	0.846340i	$-0.321199\pi$
$318$	−2.02517	−	0.642675i	−0.113566	−	0.0360394i
$319$	−2.27523	+	12.9035i	−0.127388	+	0.722455i
$320$	1.71024	−	17.3212i	0.0956053	−	0.968286i
$321$	−3.86743	+	3.24516i	−0.215859	+	0.181127i
$322$	2.81620	−	5.38542i	0.156941	−	0.300117i
$323$	27.7561	+	4.24465i	1.54439	+	0.236179i
$324$	−4.87408	−	7.01627i	−0.270782	−	0.389793i
$325$	−0.421713	−	0.502578i	−0.0233924	−	0.0278780i
$326$	−7.60711	−	8.33275i	−0.421319	−	0.461508i
$327$	−2.55276	+	14.4774i	−0.141168	+	0.800603i
$328$	−2.90242	−	9.38750i	−0.160259	−	0.518338i
$329$	13.5851	−	4.94457i	0.748971	−	0.272603i
$330$	−3.44082	+	2.18307i	−0.189411	+	0.120174i
$331$	−2.56195	+	1.47914i	−0.140818	+	0.0813011i	−0.568754	−	0.822508i	$-0.692574\pi$
$331$	−2.56195	+	1.47914i	−0.140818	+	0.0813011i	0.427936	+	0.903809i	$0.359241\pi$
$332$	24.2861	+	2.21575i	1.33287	+	0.121605i
$333$	2.77643	−	3.30883i	0.152148	−	0.181323i
$334$	7.01884	−	0.293380i	0.384054	−	0.0160531i
$335$	−3.80206	+	6.58537i	−0.207729	+	0.359797i
$336$	−5.10483	−	0.0379509i	−0.278492	−	0.00207039i
$337$	−0.722576	−	4.09793i	−0.0393612	−	0.223229i	0.958782	−	0.284144i	$-0.0917092\pi$
$337$	−0.722576	−	4.09793i	−0.0393612	−	0.223229i	−0.998143	+	0.0609150i	$0.980598\pi$
$338$	7.77047	+	5.98547i	0.422658	+	0.325567i
$339$	2.67772	−	7.35697i	0.145434	−	0.399576i
$340$	7.35535	−	27.0480i	0.398900	−	1.46688i
$341$		−	11.4245i		−	0.618674i
$342$	−14.6118	+	3.56164i	−0.790113	+	0.192592i
$343$	−18.9138			−1.02125
$344$	−15.3519	−	14.2257i	−0.827720	−	0.767000i
$345$	3.85685	+	1.40378i	0.207646	+	0.0755770i
$346$	5.07502	−	6.58851i	0.272835	−	0.354200i
$347$	20.8493	−	3.67629i	1.11925	−	0.197354i	0.416738	−	0.909027i	$-0.363173\pi$
$347$	20.8493	−	3.67629i	1.11925	−	0.197354i	0.702511	+	0.711673i	$0.252062\pi$
$348$	−9.05720	−	6.39222i	−0.485517	−	0.342659i
$349$	−11.0912	−	6.40353i	−0.593701	−	0.342773i	0.172859	−	0.984947i	$-0.444700\pi$
$349$	−11.0912	−	6.40353i	−0.593701	−	0.342773i	−0.766559	+	0.642173i	$0.778033\pi$
$350$	0.641847	−	0.0268286i	0.0343082	−	0.00143405i
$351$	−7.68103	−	6.44515i	−0.409983	−	0.344017i
$352$	−10.0031	+	0.343646i	−0.533166	+	0.0183164i
$353$	3.38528	+	5.86348i	0.180180	+	0.312081i	0.941942	−	0.335776i	$-0.108999\pi$
$353$	3.38528	+	5.86348i	0.180180	+	0.312081i	−0.761762	+	0.647857i	$0.775665\pi$
$354$	1.39024	+	2.19121i	0.0738903	+	0.116462i
$355$	7.43686	+	20.4326i	0.394708	+	1.08445i
$356$	0.695878	−	0.690724i	0.0368815	−	0.0366083i
$357$	−8.09630	−	1.42760i	−0.428502	−	0.0755564i
$358$	13.1105	+	14.3611i	0.692910	+	0.759006i
$359$	−0.812114	+	0.681445i	−0.0428618	+	0.0359653i	−0.663967	−	0.747762i	$-0.731128\pi$
$359$	−0.812114	+	0.681445i	−0.0428618	+	0.0359653i	0.621105	+	0.783727i	$0.286684\pi$
$360$	1.87664	+	14.8958i	0.0989076	+	0.785078i
$361$	−2.44363	+	18.8422i	−0.128612	+	0.991695i
$362$	−28.9452	−	15.1364i	−1.52133	−	0.795550i
$363$	−3.78619	−	4.51221i	−0.198724	−	0.236830i
$364$	8.11960	−	2.14332i	0.425583	−	0.112341i
$365$	34.1913	+	6.02884i	1.78965	+	0.315564i
$366$	0.746094	+	0.236768i	0.0389989	+	0.0123761i
$367$	−3.39343	+	1.23511i	−0.177135	+	0.0644720i	−0.429065	−	0.903273i	$-0.641157\pi$
$367$	−3.39343	+	1.23511i	−0.177135	+	0.0644720i	0.251930	+	0.967745i	$0.418935\pi$
$368$	6.42256	+	7.77070i	0.334799	+	0.405076i
$369$	4.23782	+	7.34013i	0.220612	+	0.382112i
$370$	−5.03657	+	2.07526i	−0.261839	+	0.107888i
$371$	−2.19986	+	2.62169i	−0.114211	+	0.136111i
$372$	8.74516	+	4.11758i	0.453416	+	0.213487i
$373$	−1.12544	−	0.649775i	−0.0582733	−	0.0336441i	0.470580	−	0.882357i	$-0.344045\pi$
$373$	−1.12544	−	0.649775i	−0.0582733	−	0.0336441i	−0.528854	+	0.848713i	$0.677378\pi$
$374$	−15.9769	−	2.13362i	−0.826147	−	0.110327i
$375$	1.48928	+	8.44610i	0.0769059	+	0.436155i
$376$	−1.17964	+	23.9528i	−0.0608355	+	1.23527i
$377$	17.1363	+	6.23712i	0.882566	+	0.321228i
$378$	9.58929	−	2.10720i	0.493220	−	0.108383i
$379$			31.0537i			1.59512i	0.603238	+	0.797561i	$0.293877\pi$
$379$			31.0537i			1.59512i	−0.603238	+	0.797561i	$0.706123\pi$
$380$	18.4111	+	4.55890i	0.944470	+	0.233867i
$381$			10.5775i			0.541902i
$382$	5.45720	+	24.8342i	0.279214	+	1.27063i
$383$	−2.39576	−	0.871984i	−0.122417	−	0.0445563i	0.280085	−	0.959975i	$-0.409637\pi$
$383$	−2.39576	−	0.871984i	−0.122417	−	0.0445563i	−0.402503	+	0.915419i	$0.631860\pi$
$384$	3.34221	−	7.78093i	0.170557	−	0.397069i
$385$	1.13978	+	6.46399i	0.0580883	+	0.329435i
$386$	0.960032	−	7.18889i	0.0488643	−	0.365905i
$387$	15.6348	+	9.02676i	0.794762	+	0.458856i
$388$	−6.38965	+	13.5707i	−0.324385	+	0.688948i
$389$	−22.6985	+	27.0510i	−1.15086	+	1.37154i	−0.234046	+	0.972226i	$0.575197\pi$
$389$	−22.6985	+	27.0510i	−1.15086	+	1.37154i	−0.916814	+	0.399315i	$0.869248\pi$
$390$	2.16064	+	5.24380i	0.109409	+	0.265530i
$391$	8.11762	+	14.0601i	0.410526	+	0.711052i
$392$	4.48955	−	10.6701i	0.226757	−	0.538921i
$393$	−8.31061	+	3.02482i	−0.419215	+	0.152582i
$394$	8.74002	−	27.5412i	0.440316	−	1.38751i
$395$	−21.0177	−	3.70598i	−1.05751	−	0.186468i
$396$	8.34760	−	2.20351i	0.419483	−	0.110731i
$397$	−1.10383	−	1.31549i	−0.0553995	−	0.0660225i	0.737633	−	0.675202i	$-0.235943\pi$
$397$	−1.10383	−	1.31549i	−0.0553995	−	0.0660225i	−0.793033	+	0.609179i	$0.791499\pi$
$398$	10.1380	−	19.3868i	0.508170	−	0.971771i
$399$	0.840958	−	5.49909i	0.0421005	−	0.275299i
$400$	−0.371910	+	0.998651i	−0.0185955	+	0.0499326i
$401$	−0.632622	+	0.530833i	−0.0315916	+	0.0265085i	−0.658447	−	0.752627i	$-0.728786\pi$
$401$	−0.632622	+	0.530833i	−0.0315916	+	0.0265085i	0.626855	+	0.779136i	$0.284342\pi$
$402$	−2.73233	+	2.49439i	−0.136276	+	0.124409i
$403$	−15.6591	−	2.76113i	−0.780037	−	0.137542i
$404$	−18.7475	−	18.8874i	−0.932724	−	0.939684i
$405$	−3.17858	−	8.73307i	−0.157945	−	0.433950i
$406$	−15.0777	+	9.56622i	−0.748295	+	0.474764i
$407$	1.56625	+	2.71283i	0.0776362	+	0.134470i
$408$	7.39155	−	11.4609i	0.365936	−	0.567398i
$409$	−1.96552	−	1.64927i	−0.0971889	−	0.0815512i	0.592899	−	0.805277i	$-0.297984\pi$
$409$	−1.96552	−	1.64927i	−0.0971889	−	0.0815512i	−0.690087	+	0.723726i	$0.742428\pi$
$410$	−0.446402	−	10.6797i	−0.0220462	−	0.527434i
$411$	1.65785	+	0.957160i	0.0817757	+	0.0472132i
$412$	−7.68726	−	5.42537i	−0.378724	−	0.267289i
$413$	4.11645	−	0.725841i	0.202557	−	0.0357163i
$414$	−6.88909	−	5.30656i	−0.338581	−	0.260803i
$415$	24.9292	+	9.07349i	1.22373	+	0.445400i
$416$	−1.94656	+	13.7939i	−0.0954381	+	0.676300i
$417$	9.76894			0.478387
$418$	1.19710	−	10.8411i	0.0585521	−	0.530258i
$419$			1.93815i			0.0946850i	0.998879	+	0.0473425i	$0.0150752\pi$
$419$			1.93815i			0.0946850i	−0.998879	+	0.0473425i	$0.984925\pi$
$420$	−5.35879	−	1.45725i	−0.261482	−	0.0711067i
$421$	−0.690910	+	1.89826i	−0.0336729	+	0.0925155i	−0.955390	−	0.295348i	$-0.904564\pi$
$421$	−0.690910	+	1.89826i	−0.0336729	+	0.0925155i	0.921717	+	0.387863i	$0.126787\pi$
$422$	18.4599	−	23.9650i	0.898612	−	1.16660i
$423$	−3.59213	−	20.3720i	−0.174655	−	0.990519i
$424$	−2.59332	−	5.05027i	−0.125943	−	0.245263i
$425$	−0.858081	+	1.48624i	−0.0416230	+	0.0720932i
$426$	0.441814	+	10.5700i	0.0214060	+	0.512116i
$427$	0.810450	−	0.965856i	0.0392204	−	0.0467411i
$428$	−13.4340	−	1.22565i	−0.649355	−	0.0592442i
$429$	2.82444	−	1.63069i	0.136365	−	0.0787306i
$430$	−12.1976	−	19.2252i	−0.588222	−	0.927121i
$431$	3.80320	−	1.38425i	0.183194	−	0.0666771i	−0.248794	−	0.968556i	$-0.580034\pi$
$431$	3.80320	−	1.38425i	0.183194	−	0.0666771i	0.431988	+	0.901879i	$0.357812\pi$
$432$	−2.94731	+	16.0178i	−0.141803	+	0.770656i
$433$	2.58648	−	14.6687i	0.124298	−	0.704931i	−0.857424	−	0.514611i	$-0.827936\pi$
$433$	2.58648	−	14.6687i	0.124298	−	0.704931i	0.981722	−	0.190320i	$-0.0609526\pi$
$434$	11.4987	−	10.4973i	0.551953	−	0.503888i
$435$	−7.75170	−	9.23812i	−0.371666	−	0.442934i
$436$	−32.2601	+	22.4105i	−1.54498	+	1.07327i
$437$	−9.38644	+	5.70824i	−0.449014	+	0.273062i
$438$	14.9688	+	7.82764i	0.715236	+	0.374019i
$439$	13.6546	−	11.4576i	0.651698	−	0.546839i	−0.255888	−	0.966706i	$-0.582368\pi$
$439$	13.6546	−	11.4576i	0.651698	−	0.546839i	0.907586	+	0.419867i	$0.137923\pi$
$440$	−10.6168	−	2.41586i	−0.506135	−	0.115172i
$441$	−1.73393	+	9.83362i	−0.0825682	+	0.468268i
$442$	−6.78583	+	21.3832i	−0.322769	+	1.01710i
$443$	−4.31118	−	11.8449i	−0.204830	−	0.562766i	0.794159	−	0.607709i	$-0.207911\pi$
$443$	−4.31118	−	11.8449i	−0.204830	−	0.562766i	−0.998990	+	0.0449434i	$0.985689\pi$
$444$	−2.64109	+	0.221176i	−0.125341	+	0.0104966i
$445$	0.923710	−	0.533304i	0.0437881	−	0.0252811i
$446$	−20.5200	+	8.45503i	−0.971651	+	0.400357i
$447$	−6.18362	−	5.18867i	−0.292475	−	0.245416i
$448$	−9.53711	−	9.75222i	−0.450586	−	0.460749i
$449$	11.6452	−	20.1700i	0.549570	−	0.951883i	−0.448734	−	0.893665i	$-0.648125\pi$
$449$	11.6452	−	20.1700i	0.549570	−	0.951883i	0.998304	−	0.0582176i	$-0.0185417\pi$
$450$	0.121675	−	0.911123i	0.00573580	−	0.0429507i
$451$	−6.05335	+	1.06737i	−0.285041	+	0.0502604i
$452$	18.9921	−	8.77037i	0.893314	−	0.412524i
$453$	−5.87366	+	16.1378i	−0.275969	+	0.758218i
$454$	−36.4836	+	8.01712i	−1.71226	+	0.376262i
$455$	9.13538			0.428273
$456$	7.86713	+	4.82366i	0.368412	+	0.225889i
$457$	−19.0384			−0.890580			−0.445290	−	0.895386i	$-0.646899\pi$
$457$	−19.0384			−0.890580			−0.445290	+	0.895386i	$0.646899\pi$
$458$	−4.65379	+	1.02265i	−0.217457	+	0.0477853i
$459$	−8.97069	+	24.6468i	−0.418716	+	1.15041i
$460$	4.59782	+	9.95652i	0.214375	+	0.464225i
$461$	−17.3243	+	3.05474i	−0.806873	+	0.142273i	−0.561845	−	0.827243i	$-0.689908\pi$
$461$	−17.3243	+	3.05474i	−0.806873	+	0.142273i	−0.245028	+	0.969516i	$0.578797\pi$
$462$	−0.422716	+	3.16538i	−0.0196665	+	0.147267i
$463$	10.9631	−	18.9887i	0.509499	−	0.882478i	−0.490441	−	0.871475i	$-0.663164\pi$
$463$	10.9631	−	18.9887i	0.509499	−	0.882478i	0.999939	−	0.0110034i	$-0.00350256\pi$
$464$	−4.92663	−	29.2084i	−0.228713	−	1.35597i
$465$	8.05504	+	6.75898i	0.373544	+	0.313440i
$466$	−13.4465	+	5.54046i	−0.622896	+	0.256657i
$467$	−31.4592	+	18.1630i	−1.45576	+	0.840484i	−0.998799	−	0.0490026i	$-0.984396\pi$
$467$	−31.4592	+	18.1630i	−1.45576	+	0.840484i	−0.456962	+	0.889486i	$0.651062\pi$
$468$	−1.00278	−	11.9743i	−0.0463534	−	0.553510i
$469$	2.03819	+	5.59988i	0.0941149	+	0.258579i
$470$	−7.89117	+	24.8664i	−0.363993	+	1.14700i
$471$	−0.545431	+	3.09330i	−0.0251322	+	0.142532i
$472$	−1.53849	+	6.76106i	−0.0708148	+	0.311203i
$473$	−10.0297	+	8.41590i	−0.461165	+	0.386964i
$474$	−9.20143	−	4.81172i	−0.422636	−	0.221010i
$475$	−1.01866	−	0.557575i	−0.0467391	−	0.0255833i
$476$	−12.5328	−	18.0410i	−0.574439	−	0.826908i
$477$	3.14775	+	3.75134i	0.144125	+	0.171762i
$478$	3.08420	−	2.81562i	0.141068	−	0.128783i
$479$	−3.06028	+	17.3557i	−0.139828	+	0.793002i	0.831548	+	0.555453i	$0.187455\pi$
$479$	−3.06028	+	17.3557i	−0.139828	+	0.793002i	−0.971376	+	0.237549i	$0.923656\pi$
$480$	5.67572	−	7.25613i	0.259060	−	0.331195i
$481$	4.09689	−	1.49115i	0.186802	−	0.0679905i
$482$	−5.25843	−	8.28803i	−0.239515	−	0.377509i
$483$	2.78562	−	1.60828i	0.126750	−	0.0731792i
$484$	1.42999	−	15.6737i	0.0649997	−	0.712439i
$485$	−10.4886	+	12.4998i	−0.476261	+	0.567586i
$486$	−0.910268	−	21.7773i	−0.0412906	−	0.987837i
$487$	0.337754	−	0.585007i	0.0153051	−	0.0265092i	−0.858271	−	0.513196i	$-0.828461\pi$
$487$	0.337754	−	0.585007i	0.0153051	−	0.0265092i	0.873577	+	0.486687i	$0.161795\pi$
$488$	0.955403	+	1.86057i	0.0432491	+	0.0842239i
$489$	−1.03698	−	5.88099i	−0.0468937	−	0.265947i
$490$	7.68468	−	9.97642i	0.347158	−	0.450689i
$491$	−3.15446	+	8.66680i	−0.142359	+	0.391127i	−0.990297	−	0.138968i	$-0.955622\pi$
$491$	−3.15446	+	8.66680i	−0.142359	+	0.391127i	0.847938	+	0.530095i	$0.177844\pi$
$492$	1.36468	−	5.01836i	0.0615245	−	0.226245i
$493$		−	47.7025i		−	2.14841i
$494$	−14.5702	−	4.26095i	−0.655543	−	0.191709i
$495$	9.39191			0.422135
$496$	8.65289	+	24.3350i	0.388526	+	1.09267i
$497$	16.0128	+	5.82819i	0.718273	+	0.261430i
$498$	10.2255	+	7.87652i	0.458214	+	0.352955i
$499$	−0.649382	+	0.114504i	−0.0290703	+	0.00512588i	−0.188164	−	0.982138i	$-0.560254\pi$
$499$	−0.649382	+	0.114504i	−0.0290703	+	0.00512588i	0.159094	+	0.987263i	$0.449143\pi$
$500$	−13.2138	+	18.7228i	−0.590939	+	0.837307i
$501$	3.21999	+	1.85906i	0.143859	+	0.0830568i
$502$	−1.12792	−	26.9844i	−0.0503416	−	1.20437i
$503$	15.8352	+	13.2873i	0.706057	+	0.592452i	0.923490	−	0.383623i	$-0.125324\pi$
$503$	15.8352	+	13.2873i	0.706057	+	0.592452i	−0.217433	+	0.976075i	$0.569768\pi$
$504$	9.88791	+	6.37708i	0.440443	+	0.284058i
$505$	−14.4749	−	25.0712i	−0.644123	−	1.11565i
$506$	5.32512	−	3.37858i	0.236731	−	0.150196i
$507$	1.77555	+	4.87828i	0.0788549	+	0.216652i
$508$	−20.0591	+	19.9106i	−0.889980	+	0.883388i
$509$	16.2108	+	2.85840i	0.718532	+	0.126697i	0.520947	−	0.853589i	$-0.325579\pi$
$509$	16.2108	+	2.85840i	0.718532	+	0.126697i	0.197585	+	0.980286i	$0.436690\pi$
$510$	10.9566	−	10.0025i	0.485166	−	0.442917i
$511$	20.8431	−	17.4894i	0.922043	−	0.773686i
$512$	21.0469	−	8.30827i	0.930151	−	0.367177i
$513$	−16.8116	−	5.68869i	−0.742251	−	0.251162i
$514$	−16.1527	+	30.8887i	−0.712464	+	1.36244i
$515$	−6.57922	−	7.84081i	−0.289915	−	0.345508i
$516$	−2.82728	−	10.7107i	−0.124464	−	0.471510i
$517$	14.7742	+	2.60509i	0.649769	+	0.114572i
$518$	−1.29129	+	4.06906i	−0.0567360	+	0.178784i
$519$	4.13625	−	1.50547i	0.181561	−	0.0660828i
$520$	−5.87723	+	13.9681i	−0.257734	+	0.612542i
$521$	16.9994	+	29.4439i	0.744758	+	1.28996i	0.950308	+	0.311312i	$0.100768\pi$
$521$	16.9994	+	29.4439i	0.744758	+	1.28996i	−0.205550	+	0.978647i	$0.565898\pi$
$522$	9.73384	+	23.6237i	0.426038	+	1.03398i
$523$	25.6134	−	30.5249i	1.12000	−	1.33476i	0.183929	−	0.982939i	$-0.441118\pi$
$523$	25.6134	−	30.5249i	1.12000	−	1.33476i	0.936067	−	0.351821i	$-0.114437\pi$
$524$	−21.3797	−	10.0664i	−0.933977	−	0.439755i
$525$	0.294456	+	0.170004i	0.0128511	+	0.00741960i
$526$	5.25041	−	39.3161i	0.228929	−	1.71426i
$527$	7.22263	+	40.9616i	0.314623	+	1.78432i
$528$	−4.56794	−	2.68277i	−0.198794	−	0.116753i
$529$	15.6439	+	5.69393i	0.680171	+	0.247562i
$530$	−1.32550	−	6.03196i	−0.0575759	−	0.262012i
$531$		−	5.98103i		−	0.259555i
$532$	12.0114	−	8.75641i	0.520761	−	0.379639i
$533$			8.55504i			0.370560i
$534$	0.506850	−	0.111378i	0.0219335	−	0.00481980i
$535$	−13.7897	−	5.01904i	−0.596181	−	0.216992i
$536$	−9.87355	−	0.486258i	−0.426472	−	0.0210032i
$537$	1.78718	+	10.1356i	0.0771223	+	0.437383i
$538$	39.6094	+	5.28958i	1.70768	+	0.228050i
$539$	−6.27139	−	3.62079i	−0.270128	−	0.155958i
$540$	−7.54730	+	16.0294i	−0.324784	+	0.689796i
$541$	−14.1195	+	16.8270i	−0.607044	+	0.723447i	−0.978785	−	0.204889i	$-0.934317\pi$
$541$	−14.1195	+	16.8270i	−0.607044	+	0.723447i	0.371741	+	0.928337i	$0.378761\pi$
$542$	8.32281	−	3.42931i	0.357495	−	0.147302i
$543$	−8.64409	−	14.9720i	−0.370953	−	0.642510i
$544$	35.6478	−	7.55609i	1.52839	−	0.323965i
$545$	−40.1537	+	14.6148i	−1.72000	+	0.626028i
$546$	4.23648	+	1.34442i	0.181305	+	0.0575358i
$547$	35.7118	+	6.29695i	1.52692	+	0.269238i	0.873150	−	0.487451i	$-0.162073\pi$
$547$	35.7118	+	6.29695i	1.52692	+	0.269238i	0.653775	+	0.756689i	$0.273184\pi$
$548$	1.30550	+	4.94565i	0.0557681	+	0.211268i
$549$	−1.15966	−	1.38203i	−0.0494931	−	0.0589835i
$550$	0.590737	+	0.308915i	0.0251891	+	0.0131722i
$551$	32.2704	−	0.735305i	1.37476	−	0.0313251i
$552$	0.666951	+	5.29392i	0.0283873	+	0.225324i
$553$	−12.8124	+	10.7509i	−0.544839	+	0.457174i
$554$	3.80285	+	4.16560i	0.161568	+	0.176980i
$555$	−2.83934	−	0.500652i	−0.120523	−	0.0212515i
$556$	18.3885	+	18.5258i	0.779848	+	0.785667i
$557$	15.4935	+	42.5681i	0.656482	+	1.80367i	0.592280	+	0.805733i	$0.298228\pi$
$557$	15.4935	+	42.5681i	0.656482	+	1.80367i	0.0642025	+	0.997937i	$0.479550\pi$
$558$	−11.9352	−	18.8116i	−0.505257	−	0.796357i
$559$	9.11131	+	15.7813i	0.385367	+	0.667476i
$560$	−7.32358	−	12.9054i	−0.309478	−	0.545354i
$561$	−6.53529	−	5.48376i	−0.275920	−	0.231525i
$562$	28.3695	−	1.18581i	1.19669	−	0.0500206i
$563$	−0.501085	−	0.289301i	−0.0211182	−	0.0121926i	0.489404	−	0.872057i	$-0.337214\pi$
$563$	−0.501085	−	0.289301i	−0.0211182	−	0.0121926i	−0.510522	+	0.859865i	$0.670548\pi$
$564$	−7.31898	+	10.3703i	−0.308185	+	0.436669i
$565$	22.4112	−	3.95170i	0.942846	−	0.166249i
$566$	16.0179	−	20.7948i	0.673284	−	0.874072i
$567$	−6.84401	−	2.49102i	−0.287421	−	0.104613i
$568$	−19.2132	+	20.7342i	−0.806167	+	0.869988i
$569$	−37.7888			−1.58419			−0.792095	−	0.610398i	$-0.791010\pi$
$569$	−37.7888			−1.58419			−0.792095	+	0.610398i	$0.791010\pi$
$570$	6.93548	+	7.25786i	0.290495	+	0.303998i
$571$		−	38.9276i		−	1.62907i	−0.580114	−	0.814535i	$-0.696992\pi$
$571$		−	38.9276i		−	1.62907i	0.580114	−	0.814535i	$-0.303008\pi$
$572$	8.40903	+	2.28673i	0.351599	+	0.0956128i
$573$	−4.60279	+	12.6461i	−0.192284	+	0.528297i
$574$	−6.63635	−	5.11188i	−0.276996	−	0.213366i
$575$	−0.116596	−	0.661250i	−0.00486240	−	0.0275760i
$576$	−16.1120	+	11.0160i	−0.671333	+	0.459002i
$577$	13.4685	−	23.3282i	0.560703	−	0.971166i	−0.436732	−	0.899592i	$-0.643864\pi$
$577$	13.4685	−	23.3282i	0.560703	−	0.971166i	0.997435	−	0.0715745i	$-0.0228024\pi$
$578$	34.6119	−	1.44674i	1.43967	−	0.0601766i
$579$	2.46745	−	2.94059i	0.102544	−	0.122207i
$580$	2.92771	−	32.0896i	0.121567	−	1.33245i
$581$	18.0052	−	10.3953i	0.746980	−	0.431269i
$582$	−6.70356	+	4.25314i	−0.277871	+	0.176298i
$583$	−3.33725	+	1.21466i	−0.138215	+	0.0503061i
$584$	13.3321	+	43.1210i	0.551688	+	1.78436i
$585$	2.26987	−	12.8731i	0.0938477	−	0.532237i
$586$	−1.92734	−	2.11118i	−0.0796175	−	0.0872121i
$587$	2.61102	+	3.11170i	0.107769	+	0.128434i	0.817232	−	0.576308i	$-0.195507\pi$
$587$	2.61102	+	3.11170i	0.107769	+	0.128434i	−0.709464	+	0.704742i	$0.751063\pi$
$588$	5.03192	−	3.49558i	0.207513	−	0.144155i
$589$	−27.5989	+	5.51745i	−1.13719	+	0.227343i
$590$	−3.49539	+	6.68422i	−0.143903	+	0.275185i
$591$	11.7153	−	9.83029i	0.481902	−	0.404364i
$592$	−5.39089	−	4.59222i	−0.221564	−	0.188739i
$593$	−1.27991	+	7.25871i	−0.0525595	+	0.298079i	−0.999744	−	0.0226084i	$-0.992803\pi$
$593$	−1.27991	+	7.25871i	−0.0525595	+	0.298079i	0.947185	+	0.320688i	$0.103914\pi$
$594$	9.71107	+	3.08174i	0.398450	+	0.126445i
$595$	−8.17311	−	22.4554i	−0.335065	−	0.920583i
$596$	−1.79996	−	21.4935i	−0.0737291	−	0.880407i
$597$	10.0279	−	5.78959i	0.410413	−	0.236952i
$598$	−3.34388	−	8.11547i	−0.136742	−	0.331866i
$599$	−18.6862	−	15.6796i	−0.763497	−	0.640650i	0.175537	−	0.984473i	$-0.443834\pi$
$599$	−18.6862	−	15.6796i	−0.763497	−	0.640650i	−0.939035	+	0.343823i	$0.888278\pi$
$600$	−0.449377	+	0.340855i	−0.0183457	+	0.0139153i
$601$	−20.5466	+	35.5878i	−0.838114	+	1.45166i	0.0533558	+	0.998576i	$0.483008\pi$
$601$	−20.5466	+	35.5878i	−0.838114	+	1.45166i	−0.891470	+	0.453080i	$0.850325\pi$
$602$	−17.6862	−	2.36188i	−0.720834	−	0.0962629i
$603$	8.39748	−	1.48070i	0.341972	−	0.0602989i
$604$	−41.6598	+	19.2381i	−1.69511	+	0.782787i
$605$	5.85582	−	16.0887i	0.238073	−	0.654100i
$606$	−3.02301	−	13.7568i	−0.122801	−	0.558833i
$607$	−24.4797			−0.993599			−0.496799	−	0.867865i	$-0.665491\pi$
$607$	−24.4797			−0.993599			−0.496799	+	0.867865i	$0.665491\pi$
$608$	5.66112	+	23.9990i	0.229589	+	0.973288i
$609$	−9.45090			−0.382970
$610$	0.488326	+	2.22223i	0.0197717	+	0.0899755i
$611$	7.14138	−	19.6208i	0.288909	−	0.793772i
$612$	−28.5365	+	13.1779i	−1.15352	+	0.532683i
$613$	31.0679	−	5.47811i	1.25482	−	0.221259i	0.493564	−	0.869710i	$-0.335694\pi$
$613$	31.0679	−	5.47811i	1.25482	−	0.221259i	0.761256	+	0.648451i	$0.224583\pi$
$614$	34.7599	+	4.64197i	1.40280	+	0.187334i
$615$	2.82871	−	4.89948i	0.114065	−	0.197566i
$616$	−6.79850	+	5.15670i	−0.273919	+	0.207769i
$617$	4.58334	+	3.84588i	0.184518	+	0.154829i	0.730368	−	0.683054i	$-0.239349\pi$
$617$	4.58334	+	3.84588i	0.184518	+	0.154829i	−0.545850	+	0.837883i	$0.683793\pi$
$618$	−1.89718	−	4.60437i	−0.0763156	−	0.185215i
$619$	6.96767	−	4.02279i	0.280054	−	0.161689i	−0.353394	−	0.935475i	$-0.614972\pi$
$619$	6.96767	−	4.02279i	0.280054	−	0.161689i	0.633448	+	0.773785i	$0.281639\pi$
$620$	2.34470	+	27.9983i	0.0941653	+	1.12444i
$621$	−3.50980	−	9.64309i	−0.140843	−	0.386964i
$622$	35.4232	+	11.2413i	1.42034	+	0.450736i
$623$	0.145151	−	0.823191i	0.00581534	−	0.0329804i
$624$	−4.78116	+	5.61270i	−0.191400	+	0.224688i
$625$	−18.0763	+	15.1678i	−0.723053	+	0.606713i
$626$	7.05690	−	13.4949i	0.282051	−	0.539364i
$627$	3.60898	−	4.50560i	0.144129	−	0.179936i
$628$	−6.89280	+	4.78831i	−0.275053	+	0.191074i
$629$	−7.33070	−	8.73639i	−0.292294	−	0.348343i
$630$	8.62966	+	9.45283i	0.343814	+	0.376610i
$631$	6.41066	−	36.3567i	0.255204	−	1.44734i	−0.540343	−	0.841445i	$-0.681706\pi$
$631$	6.41066	−	36.3567i	0.255204	−	1.44734i	0.795548	−	0.605891i	$-0.207183\pi$
$632$	−8.19538	−	26.5069i	−0.325995	−	1.05439i
$633$	15.0452	−	5.47599i	0.597992	−	0.217651i
$634$	26.0715	−	16.5413i	1.03543	−	0.656940i
$635$	−26.6265	+	15.3728i	−1.05664	+	0.610052i
$636$	0.273009	−	2.99236i	0.0108255	−	0.118655i
$637$	−6.47856	+	7.72085i	−0.256690	+	0.305911i
$638$	−18.5136	+	0.773849i	−0.732960	+	0.0306370i
$639$	12.1915	−	21.1163i	0.482287	−	0.835346i
$640$	24.4442	−	2.89514i	0.966240	−	0.114441i
$641$	−1.14508	−	6.49405i	−0.0452278	−	0.256500i	0.953807	−	0.300419i	$-0.0971266\pi$
$641$	−1.14508	−	6.49405i	−0.0452278	−	0.256500i	−0.999035	+	0.0439196i	$0.986015\pi$
$642$	−5.65626	−	4.35693i	−0.223235	−	0.171954i
$643$	−3.70932	+	10.1913i	−0.146281	+	0.401905i	−0.991095	−	0.133156i	$-0.957489\pi$
$643$	−3.70932	+	10.1913i	−0.146281	+	0.401905i	0.844814	+	0.535060i	$0.179711\pi$
$644$	8.29343	+	2.25529i	0.326807	+	0.0888710i
$645$		−	12.0506i		−	0.474491i
$646$	2.56172	+	39.6267i	0.100790	+	1.55909i
$647$	−9.29005			−0.365230			−0.182615	−	0.983185i	$-0.558456\pi$
$647$	−9.29005			−0.365230			−0.182615	+	0.983185i	$0.558456\pi$
$648$	8.21187	−	8.86197i	0.322593	−	0.348131i
$649$	4.07599	+	1.48354i	0.159997	+	0.0582340i
$650$	0.566189	−	0.735039i	0.0222078	−	0.0288306i
$651$	8.11538	−	1.43096i	0.318067	−	0.0560838i
$652$	9.20072	−	13.0366i	0.360328	−	0.510552i
$653$	−15.2943	−	8.83018i	−0.598513	−	0.345552i	0.169943	−	0.985454i	$-0.445642\pi$
$653$	−15.2943	−	8.83018i	−0.598513	−	0.345552i	−0.768456	+	0.639902i	$0.778975\pi$
$654$	−20.7719	+	0.868244i	−0.812244	+	0.0339510i
$655$	−19.6925	−	16.5240i	−0.769451	−	0.645646i
$656$	12.0856	−	6.85834i	0.471863	−	0.267773i
$657$	−19.4663	−	33.7165i	−0.759451	−	1.31541i
$658$	10.9531	+	17.2637i	0.426998	+	0.673010i
$659$	−5.10305	−	14.0205i	−0.198786	−	0.546161i	0.799745	−	0.600340i	$-0.204968\pi$
$659$	−5.10305	−	14.0205i	−0.198786	−	0.546161i	−0.998531	+	0.0541788i	$0.982746\pi$
$660$	−4.05975	−	4.09005i	−0.158026	−	0.159205i
$661$	14.1252	+	2.49066i	0.549408	+	0.0968754i	0.441460	−	0.897281i	$-0.354461\pi$
$661$	14.1252	+	2.49066i	0.549408	+	0.0968754i	0.107948	+	0.994157i	$0.465572\pi$
$662$	−2.82070	−	3.08976i	−0.109630	−	0.120087i
$663$	−9.09584	+	7.63232i	−0.353253	+	0.296415i
$664$	4.31092	+	34.2179i	0.167296	+	1.32791i
$665$	15.0649	−	5.87518i	0.584193	−	0.227830i
$666$	5.41306	+	2.83066i	0.209752	+	0.109686i
$667$	11.9968	+	14.2972i	0.464517	+	0.553590i
$668$	2.53563	+	9.60577i	0.0981064	+	0.371658i
$669$	−11.5681	−	2.03976i	−0.447247	−	0.0788617i
$670$	−10.2501	−	3.25280i	−0.395996	−	0.125667i
$671$	1.22948	−	0.447493i	0.0474634	−	0.0172753i
$672$	−1.49703	−	7.06261i	−0.0577490	−	0.272446i
$673$	0.830347	+	1.43820i	0.0320075	+	0.0554386i	0.881585	−	0.472024i	$-0.156477\pi$
$673$	0.830347	+	1.43820i	0.0320075	+	0.0554386i	−0.849578	+	0.527463i	$0.823143\pi$
$674$	5.44098	−	2.24189i	0.209579	−	0.0863544i
$675$	0.697264	−	0.830966i	0.0268377	−	0.0319839i
$676$	−5.90894	+	12.5498i	−0.227267	+	0.482683i
$677$	−26.8644	−	15.5102i	−1.03248	−	0.596104i	−0.114787	−	0.993390i	$-0.536619\pi$
$677$	−26.8644	−	15.5102i	−1.03248	−	0.596104i	−0.917695	+	0.397286i	$0.869952\pi$
$678$	10.9746	+	1.46559i	0.421478	+	0.0562857i
$679$	2.22056	+	12.5934i	0.0852173	+	0.483291i
$680$	39.5927	+	1.94989i	1.51831	+	0.0747748i
$681$	−18.5782	−	6.76192i	−0.711919	−	0.259117i
$682$	15.7802	−	3.46764i	0.604256	−	0.132783i
$683$			11.2171i			0.429209i	0.976701	+	0.214605i	$0.0688463\pi$
$683$			11.2171i			0.429209i	−0.976701	+	0.214605i	$0.931154\pi$
$684$	−9.35458	−	19.1015i	−0.357681	−	0.730366i
$685$			5.56436i			0.212603i
$686$	−5.74082	−	26.1249i	−0.219186	−	0.997452i
$687$	−2.36980	−	0.862538i	−0.0904136	−	0.0329079i
$688$	14.9897	−	25.5228i	0.571477	−	0.973049i
$689$	0.858324	+	4.86780i	0.0326995	+	0.185448i
$690$	−0.768329	+	5.75339i	−0.0292498	+	0.219028i
$691$	−9.91035	−	5.72174i	−0.377007	−	0.217665i	0.299508	−	0.954094i	$-0.403177\pi$
$691$	−9.91035	−	5.72174i	−0.377007	−	0.217665i	−0.676515	+	0.736428i	$0.736511\pi$
$692$	10.6408	+	5.01013i	0.404503	+	0.190457i
$693$	4.73113	−	5.63834i	0.179721	−	0.214183i
$694$	11.4062	+	27.6824i	0.432973	+	1.05081i
$695$	14.1977	+	24.5911i	0.538549	+	0.932795i
$696$	6.08022	−	14.4505i	0.230470	−	0.547746i
$697$	21.0289	−	7.65390i	0.796527	−	0.289912i
$698$	5.47845	−	17.2635i	0.207363	−	0.653433i
$699$	−7.58038	−	1.33663i	−0.286716	−	0.0505558i
$700$	0.231874	+	0.878413i	0.00876401	+	0.0332009i
$701$	18.4889	+	22.0342i	0.698315	+	0.832219i	0.992335	−	0.123580i	$-0.0394376\pi$
$701$	18.4889	+	22.0342i	0.698315	+	0.832219i	−0.294020	+	0.955799i	$0.594993\pi$
$702$	6.57103	−	12.5657i	0.248007	−	0.474264i
$703$	5.79710	−	5.09382i	0.218642	−	0.192117i
$704$	−3.51085	−	13.7125i	−0.132320	−	0.516810i
$705$	−10.5775	+	8.87555i	−0.398371	+	0.334273i
$706$	−7.07145	+	6.45566i	−0.266138	+	0.242962i
$707$	−22.3429	−	3.93966i	−0.840292	−	0.148166i
$708$	−2.60466	+	2.58537i	−0.0978890	+	0.0971640i
$709$	10.6030	+	29.1316i	0.398205	+	1.09406i	0.963158	+	0.268936i	$0.0866722\pi$
$709$	10.6030	+	29.1316i	0.398205	+	1.09406i	−0.564953	+	0.825123i	$0.691106\pi$
$710$	−25.9654	+	16.4740i	−0.974465	+	0.618259i
$711$	11.9661	+	20.7258i	0.448763	+	0.777280i
$712$	1.16528	+	0.751535i	0.0436709	+	0.0281650i
$713$	−12.4662	−	10.4604i	−0.466864	−	0.391745i
$714$	−0.485554	−	11.6164i	−0.0181714	−	0.434732i
$715$	8.20982	+	4.73994i	0.307030	+	0.177264i
$716$	−15.8570	+	22.4679i	−0.592603	+	0.839664i
$717$	2.17673	−	0.383816i	0.0812914	−	0.0143339i
$718$	−1.18775	−	0.914904i	−0.0443264	−	0.0341439i
$719$	−13.6987	−	4.98590i	−0.510874	−	0.185943i	0.0737047	−	0.997280i	$-0.476518\pi$
$719$	−13.6987	−	4.98590i	−0.510874	−	0.185943i	−0.584578	+	0.811337i	$0.698740\pi$
$720$	−20.0053	+	7.11338i	−0.745555	+	0.265100i
$721$	−8.02142			−0.298733
$722$	−26.7676	+	2.34380i	−0.996188	+	0.0872274i
$723$		−	5.19504i		−	0.193205i
$724$	12.1216	−	44.5751i	0.450497	−	1.65662i
$725$	−0.674758	+	1.85388i	−0.0250599	+	0.0688514i
$726$	5.08332	−	6.59928i	0.188660	−	0.244922i
$727$	−2.29239	−	13.0008i	−0.0850201	−	0.482173i	−0.997352	−	0.0727220i	$-0.976831\pi$
$727$	−2.29239	−	13.0008i	−0.0850201	−	0.482173i	0.912332	−	0.409451i	$-0.134280\pi$
$728$	5.42499	+	10.5647i	0.201063	+	0.391554i
$729$	−0.639240	+	1.10720i	−0.0236756	+	0.0410073i
$730$	2.05053	+	49.0569i	0.0758935	+	1.81568i
$731$	30.6399	−	36.5152i	1.13326	−	1.35056i
$732$	−0.100579	+	1.10241i	−0.00371751	+	0.0407463i
$733$	−0.562220	+	0.324598i	−0.0207661	+	0.0119893i	−0.510347	−	0.859969i	$-0.670483\pi$
$733$	−0.562220	+	0.324598i	−0.0207661	+	0.0119893i	0.489581	+	0.871958i	$0.337150\pi$
$734$	−2.73599	−	4.31231i	−0.100987	−	0.159170i
$735$	6.26317	−	2.27961i	0.231020	−	0.0840846i
$736$	−8.78393	+	11.2298i	−0.323780	+	0.413936i
$737$	−1.07384	+	6.09005i	−0.0395554	+	0.224330i
$738$	−8.85232	+	8.08144i	−0.325858	+	0.297482i
$739$	27.1907	+	32.4046i	1.00023	+	1.19202i	0.981356	+	0.192200i	$0.0615623\pi$
$739$	27.1907	+	32.4046i	1.00023	+	1.19202i	0.0188698	+	0.999822i	$0.493993\pi$
$740$	−4.39519	−	6.32691i	−0.161571	−	0.232582i
$741$	−5.30341	−	6.03561i	−0.194826	−	0.221724i
$742$	−4.28894	−	2.24282i	−0.157452	−	0.0823366i
$743$	−35.7421	+	29.9912i	−1.31125	+	1.10027i	−0.323169	+	0.946341i	$0.604748\pi$
$743$	−35.7421	+	29.9912i	−1.31125	+	1.10027i	−0.988082	+	0.153929i	$0.950807\pi$
$744$	−3.03306	+	13.3291i	−0.111197	+	0.488669i
$745$	4.07436	−	23.1068i	0.149273	−	0.846569i
$746$	0.555907	−	1.75175i	0.0203532	−	0.0641362i
$747$	−10.1747	−	27.9548i	−0.372274	−	1.02281i
$748$	−1.90232	−	22.7158i	−0.0695558	−	0.830574i
$749$	−9.95964	+	5.75020i	−0.363917	+	0.210108i
$750$	−11.2142	+	4.62068i	−0.409485	+	0.168723i
$751$	7.48574	+	6.28128i	0.273158	+	0.229207i	0.769068	−	0.639167i	$-0.220721\pi$
$751$	7.48574	+	6.28128i	0.273158	+	0.229207i	−0.495909	+	0.868374i	$0.665165\pi$
$752$	−33.4431	+	5.64090i	−1.21954	+	0.205702i
$753$	7.14729	−	12.3795i	0.260462	−	0.451133i
$754$	−3.41375	+	25.5628i	−0.124322	+	0.930943i
$755$	−49.1597	+	8.66818i	−1.78911	+	0.315468i
$756$	5.82118	+	12.6057i	0.211714	+	0.458465i
$757$	16.8979	−	46.4265i	0.614164	−	1.68740i	−0.106672	−	0.994294i	$-0.534019\pi$
$757$	16.8979	−	46.4265i	0.614164	−	1.68740i	0.720835	−	0.693106i	$-0.243758\pi$
$758$	−42.8932	+	9.42559i	−1.55795	+	0.342353i
$759$	3.33785			0.121156
$760$	−0.708785	+	26.8142i	−0.0257103	+	0.972654i
$761$	−6.41656			−0.232600			−0.116300	−	0.993214i	$-0.537103\pi$
$761$	−6.41656			−0.232600			−0.116300	+	0.993214i	$0.537103\pi$
$762$	−14.6103	+	3.21054i	−0.529274	+	0.116306i
$763$	−11.4534	+	31.4680i	−0.414642	+	1.13922i
$764$	−32.6460	+	15.0756i	−1.18109	+	0.545416i
$765$	−33.6738	+	5.93759i	−1.21748	+	0.214674i
$766$	0.477262	−	3.57383i	0.0172442	−	0.129128i
$767$	3.01853	−	5.22824i	0.108993	−	0.188781i
$768$	11.7619	+	2.25475i	0.424421	+	0.0813612i
$769$	19.3441	+	16.2316i	0.697567	+	0.585328i	0.921080	−	0.389373i	$-0.127308\pi$
$769$	19.3441	+	16.2316i	0.697567	+	0.585328i	−0.223513	+	0.974701i	$0.571753\pi$
$770$	−8.58248	+	3.53631i	−0.309291	+	0.127440i
$771$	−15.9773	+	9.22448i	−0.575407	+	0.332211i
$772$	10.2211	−	0.855960i	0.367866	−	0.0308067i
$773$	−7.95249	−	21.8493i	−0.286031	−	0.785865i	−0.996612	−	0.0822487i	$-0.973790\pi$
$773$	−7.95249	−	21.8493i	−0.286031	−	0.785865i	0.710581	−	0.703616i	$-0.248432\pi$
$774$	−7.72272	+	24.3355i	−0.277587	+	0.874723i
$775$	0.298711	−	1.69407i	0.0107300	−	0.0608529i
$776$	−20.6841	−	4.70669i	−0.742515	−	0.168960i
$777$	−1.73087	+	1.45237i	−0.0620945	+	0.0521035i
$778$	−44.2540	−	23.1418i	−1.58658	−	0.829674i
$779$	5.50195	+	14.1079i	0.197128	+	0.505468i
$780$	−6.58723	+	4.57603i	−0.235861	+	0.163848i
$781$	11.3665	+	13.5460i	0.406724	+	0.484715i
$782$	−16.9568	+	15.4801i	−0.606373	+	0.553569i
$783$	−5.23580	+	29.6937i	−0.187112	+	1.06117i
$784$	16.1008	+	2.96259i	0.575029	+	0.105807i
$785$	−8.57939	+	3.12264i	−0.306211	+	0.111452i
$786$	−6.70053	−	10.5610i	−0.239000	−	0.376698i
$787$	−14.5878	+	8.42229i	−0.520000	+	0.300222i	−0.736935	−	0.675964i	$-0.763728\pi$
$787$	−14.5878	+	8.42229i	−0.520000	+	0.300222i	0.216935	+	0.976186i	$0.430394\pi$
$788$	40.6943	+	3.71277i	1.44968	+	0.132262i
$789$	13.4945	−	16.0821i	0.480416	−	0.572537i
$790$	−1.26048	−	30.1557i	−0.0448458	−	1.07289i
$791$	8.91718	−	15.4450i	0.317058	−	0.549161i
$792$	5.57732	+	10.8614i	0.198181	+	0.385942i
$793$	−0.316215	−	1.79334i	−0.0112291	−	0.0636835i
$794$	1.48199	−	1.92395i	0.0525939	−	0.0682785i
$795$	1.11797	−	3.07160i	0.0396503	−	0.108938i
$796$	29.8553	+	8.11875i	1.05819	+	0.287762i
$797$			25.8382i			0.915236i	0.889149	+	0.457618i	$0.151297\pi$
$797$			25.8382i			0.915236i	−0.889149	+	0.457618i	$0.848703\pi$
$798$	7.85091	−	0.507533i	0.277919	−	0.0179665i
$799$	−54.6185			−1.93226
$800$	−1.49228	−	0.210588i	−0.0527600	−	0.00744539i
$801$	−1.12393	−	0.409077i	−0.0397121	−	0.0144540i
$802$	−0.925233	−	0.712692i	−0.0326711	−	0.0251660i
$803$	27.8058	−	4.90291i	0.981245	−	0.173020i
$804$	−4.27473	−	3.01694i	−0.150758	−	0.106399i
$805$	8.09696	+	4.67478i	0.285380	+	0.164764i
$806$	−0.939114	−	22.4674i	−0.0330789	−	0.791380i
$807$	16.2020	+	13.5951i	0.570339	+	0.478571i
$808$	20.3980	−	31.6280i	0.717601	−	1.11267i
$809$	8.06314	+	13.9658i	0.283485	+	0.491010i	0.972241	−	0.233983i	$-0.0751761\pi$
$809$	8.06314	+	13.9658i	0.283485	+	0.491010i	−0.688756	+	0.724993i	$0.741843\pi$
$810$	11.0978	−	7.04114i	0.389938	−	0.247400i
$811$	9.65274	+	26.5207i	0.338954	+	0.931267i	0.985692	+	0.168556i	$0.0539103\pi$
$811$	9.65274	+	26.5207i	0.338954	+	0.931267i	−0.646739	+	0.762712i	$0.723868\pi$
$812$	−17.7899	−	17.9226i	−0.624303	−	0.628961i
$813$	4.69194	+	0.827315i	0.164553	+	0.0290152i
$814$	−3.27171	+	2.98681i	−0.114674	+	0.104688i
$815$	13.2970	−	11.1575i	0.465773	−	0.390830i
$816$	18.0740	+	6.73096i	0.632715	+	0.235631i
$817$	25.1745	+	20.1648i	0.880745	+	0.705476i
$818$	1.68148	−	3.21549i	0.0587916	−	0.112427i
$819$	−6.58480	−	7.84746i	−0.230092	−	0.274213i
$820$	14.6160	−	3.85816i	0.510412	−	0.134733i
$821$	−20.8238	−	3.67179i	−0.726755	−	0.128146i	−0.201982	−	0.979389i	$-0.564738\pi$
$821$	−20.8238	−	3.67179i	−0.726755	−	0.128146i	−0.524772	+	0.851243i	$0.675850\pi$
$822$	−0.818885	+	2.58044i	−0.0285619	+	0.0900032i
$823$	8.88714	−	3.23466i	0.309786	−	0.112753i	−0.182449	−	0.983215i	$-0.558402\pi$
$823$	8.88714	−	3.23466i	0.309786	−	0.112753i	0.492235	+	0.870462i	$0.336180\pi$
$824$	5.16056	−	12.2648i	0.179777	−	0.427266i
$825$	0.176415	+	0.305560i	0.00614199	+	0.0106382i
$826$	2.25202	+	5.46557i	0.0783578	+	0.190171i
$827$	−4.99117	+	5.94825i	−0.173560	+	0.206841i	−0.845811	−	0.533482i	$-0.820883\pi$
$827$	−4.99117	+	5.94825i	−0.173560	+	0.206841i	0.672251	+	0.740323i	$0.265328\pi$
$828$	5.23871	−	11.1263i	0.182058	−	0.386665i
$829$	1.84492	+	1.06517i	0.0640768	+	0.0369947i	0.531696	−	0.846935i	$-0.321555\pi$
$829$	1.84492	+	1.06517i	0.0640768	+	0.0369947i	−0.467619	+	0.883930i	$0.654888\pi$
$830$	−4.96618	+	37.1877i	−0.172379	+	1.29080i
$831$	0.518393	+	2.93995i	0.0179828	+	0.101986i
$832$	−19.6437	+	1.49808i	−0.681023	+	0.0519365i
$833$	24.7745	+	9.01720i	0.858387	+	0.312427i
$834$	2.96512	+	13.4934i	0.102674	+	0.467239i
$835$			10.8075i			0.374008i
$836$	15.3378	−	1.63706i	0.530468	−	0.0566188i
$837$		−	26.2904i		−	0.908728i
$838$	−2.67709	+	0.588278i	−0.0924785	+	0.0203217i
$839$	22.2127	+	8.08475i	0.766867	+	0.279117i	0.695685	−	0.718347i	$-0.255101\pi$
$839$	22.2127	+	8.08475i	0.766867	+	0.279117i	0.0711815	+	0.997463i	$0.477323\pi$
$840$	0.386315	−	7.84418i	0.0133291	−	0.270650i
$841$	−4.48667	−	25.4452i	−0.154713	−	0.877419i
$842$	−2.83169	−	0.378155i	−0.0975866	−	0.0130321i
$843$	13.0149	+	7.51415i	0.448256	+	0.258801i
$844$	38.7049	+	18.2238i	1.33228	+	0.627291i
$845$	−9.69949	+	11.5594i	−0.333673	+	0.397656i
$846$	27.0486	−	11.1451i	0.929951	−	0.383175i
$847$	−6.70887	−	11.6201i	−0.230520	−	0.399272i
$848$	6.18858	−	5.11492i	0.212517	−	0.175647i
$849$	13.0549	−	4.75161i	0.448044	−	0.163075i
$850$	−2.31333	−	0.734119i	−0.0793465	−	0.0251801i
$851$	4.39425	+	0.774826i	0.150633	+	0.0265607i
$852$	−14.4657	+	3.81851i	−0.495588	+	0.130820i
$853$	−8.36486	−	9.96886i	−0.286408	−	0.341327i	0.603588	−	0.797296i	$-0.293737\pi$
$853$	−8.36486	−	9.96886i	−0.286408	−	0.341327i	−0.889996	+	0.455969i	$0.849293\pi$
$854$	1.58009	+	0.826278i	0.0540695	+	0.0282746i
$855$	−4.53579	−	22.6885i	−0.155121	−	0.775931i
$856$	−2.38460	−	18.9278i	−0.0815040	−	0.646938i
$857$	27.9742	−	23.4731i	0.955580	−	0.801827i	−0.0246480	−	0.999696i	$-0.507847\pi$
$857$	27.9742	−	23.4731i	0.955580	−	0.801827i	0.980228	+	0.197869i	$0.0634021\pi$
$858$	3.10970	+	3.40633i	0.106163	+	0.116290i
$859$	−16.8682	−	2.97432i	−0.575535	−	0.101482i	−0.121698	−	0.992567i	$-0.538834\pi$
$859$	−16.8682	−	2.97432i	−0.575535	−	0.101482i	−0.453837	+	0.891085i	$0.649945\pi$
$860$	22.8527	−	22.6834i	0.779269	−	0.773497i
$861$	−1.51640	−	4.16628i	−0.0516789	−	0.141987i
$862$	3.06638	+	4.83305i	0.104441	+	0.164614i
$863$	−3.15825	−	5.47025i	−0.107508	−	0.186210i	0.807252	−	0.590207i	$-0.200954\pi$
$863$	−3.15825	−	5.47025i	−0.107508	−	0.186210i	−0.914760	+	0.403997i	$0.867621\pi$
$864$	−23.0193	+	0.790805i	−0.783132	+	0.0269037i
$865$	9.80110	+	8.22410i	0.333248	+	0.279628i
$866$	21.0463	−	0.879713i	0.715182	−	0.0298939i
$867$	15.8787	+	9.16758i	0.539269	+	0.311347i
$868$	17.9896	+	12.6964i	0.610608	+	0.430944i
$869$	−17.0925	+	3.01386i	−0.579822	+	0.102238i
$870$	10.4074	−	13.5111i	0.352843	−	0.458069i
$871$	8.08784	+	2.94373i	0.274046	+	0.0997446i
$872$	−40.7464	−	37.7573i	−1.37985	−	1.27862i
$873$	18.2977			0.619284
$874$	−10.7336	−	11.2325i	−0.363068	−	0.379945i
$875$			19.5366i			0.660458i
$876$	−6.26859	+	23.0516i	−0.211796	+	0.778842i
$877$	−10.5095	+	28.8745i	−0.354879	+	0.975022i	0.625901	+	0.779903i	$0.284732\pi$
$877$	−10.5095	+	28.8745i	−0.354879	+	0.975022i	−0.980780	+	0.195119i	$0.937491\pi$
$878$	19.9703	+	15.3828i	0.673966	+	0.519146i
$879$	−0.262728	−	1.49001i	−0.00886160	−	0.0502566i
$880$	0.114472	−	15.3978i	0.00385884	−	0.519059i
$881$	−18.8960	+	32.7289i	−0.636624	+	1.10266i	0.349545	+	0.936920i	$0.386336\pi$
$881$	−18.8960	+	32.7289i	−0.636624	+	1.10266i	−0.986169	+	0.165745i	$0.946997\pi$
$882$	−14.1091	+	0.589744i	−0.475077	+	0.0198577i
$883$	26.3755	−	31.4331i	0.887607	−	1.05781i	−0.110348	−	0.993893i	$-0.535197\pi$
$883$	26.3755	−	31.4331i	0.887607	−	1.05781i	0.997955	−	0.0639160i	$-0.0203590\pi$
$884$	−31.5954	−	2.88262i	−1.06267	−	0.0969531i
$885$	−3.45743	+	1.99615i	−0.116220	+	0.0670997i
$886$	15.0522	−	9.55006i	0.505690	−	0.320840i
$887$	−12.3474	+	4.49409i	−0.414585	+	0.150897i	−0.540887	−	0.841095i	$-0.681911\pi$
$887$	−12.3474	+	4.49409i	−0.414585	+	0.150897i	0.126302	+	0.991992i	$0.459689\pi$
$888$	−1.10714	−	3.58089i	−0.0371532	−	0.120167i
$889$	−4.18406	+	23.7290i	−0.140329	+	0.795845i
$890$	1.01700	+	1.11401i	0.0340899	+	0.0373417i
$891$	−4.85812	−	5.78968i	−0.162753	−	0.193962i
$892$	−17.9069	−	25.7771i	−0.599568	−	0.863082i
$893$	−0.841911	−	36.9489i	−0.0281735	−	1.23645i
$894$	5.29001	−	10.1161i	0.176924	−	0.338332i
$895$	−22.9167	+	19.2294i	−0.766020	+	0.642767i
$896$	10.5756	−	16.1332i	0.353305	−	0.538974i
$897$	0.806705	−	4.57505i	0.0269351	−	0.152757i
$898$	31.3946	+	9.96287i	1.04765	+	0.332465i
$899$	16.3537	+	44.9313i	0.545425	+	1.49854i
$900$	1.29543	−	0.108485i	0.0431809	−	0.00361615i
$901$	11.1975	−	6.46487i	0.373042	−	0.215376i
$902$	−3.31166	−	8.03726i	−0.110266	−	0.267612i
$903$	−7.23446	−	6.07043i	−0.240748	−	0.202011i
$904$	17.8787	+	23.5710i	0.594638	+	0.783959i
$905$	25.1258	−	43.5191i	0.835209	−	1.44662i
$906$	−24.0732	−	3.21483i	−0.799779	−	0.106805i
$907$	−3.84659	+	0.678257i	−0.127724	+	0.0225212i	−0.237145	−	0.971474i	$-0.576212\pi$
$907$	−3.84659	+	0.678257i	−0.127724	+	0.0225212i	0.109421	+	0.993996i	$0.465100\pi$
$908$	−22.1474	−	47.9599i	−0.734988	−	1.59161i
$909$	−11.1031	+	30.5055i	−0.368267	+	1.01181i
$910$	2.77282	+	12.6183i	0.0919181	+	0.418293i
$911$	15.4475			0.511799			0.255900	−	0.966703i	$-0.417628\pi$
$911$	15.4475			0.511799			0.255900	+	0.966703i	$0.417628\pi$
$912$	−4.27484	+	12.3306i	−0.141554	+	0.408308i
$913$	21.5746			0.714015
$914$	−5.77864	−	26.2970i	−0.191140	−	0.869826i
$915$	−0.411871	+	1.13161i	−0.0136160	+	0.0374097i
$916$	−2.82508	−	6.11768i	−0.0933434	−	0.202134i
$917$	−19.8401	+	3.49834i	−0.655176	+	0.115525i
$918$	−36.7664	−	4.90992i	−1.21347	−	0.162051i
$919$	−18.1357	+	31.4120i	−0.598242	+	1.03619i	0.394839	+	0.918750i	$0.370800\pi$
$919$	−18.1357	+	31.4120i	−0.598242	+	1.03619i	−0.993081	+	0.117435i	$0.962533\pi$
$920$	−12.3570	+	9.37283i	−0.407397	+	0.309013i
$921$	14.2184	+	11.9306i	0.468512	+	0.393128i
$922$	−9.47774	−	23.0021i	−0.312133	−	0.757535i
$923$	21.3141	−	12.3057i	0.701561	−	0.405046i
$924$	−4.50050	+	0.376892i	−0.148056	+	0.0123988i
$925$	0.161319	+	0.443219i	0.00530413	+	0.0145730i
$926$	29.5558	+	9.37934i	0.971264	+	0.308224i
$927$	−1.99309	+	11.3033i	−0.0654615	+	0.371251i
$928$	38.8490	−	15.6704i	1.27528	−	0.514407i
$929$	0.892298	−	0.748727i	0.0292753	−	0.0245649i	−0.628033	−	0.778187i	$-0.716140\pi$
$929$	0.892298	−	0.748727i	0.0292753	−	0.0245649i	0.657308	+	0.753622i	$0.271695\pi$
$930$	−6.89099	+	13.1776i	−0.225964	+	0.432111i
$931$	−5.71818	+	16.8988i	−0.187406	+	0.553835i
$932$	−11.7341	−	16.8914i	−0.384365	−	0.553295i
$933$	12.6436	+	15.0681i	0.413933	+	0.493307i
$934$	−34.6365	−	37.9404i	−1.13334	−	1.24145i
$935$	4.30608	−	24.4210i	0.140824	−	0.798651i
$936$	16.2352	−	5.01958i	0.530663	−	0.164070i
$937$	40.8373	−	14.8635i	1.33410	−	0.485571i	0.426147	−	0.904654i	$-0.359871\pi$
$937$	40.8373	−	14.8635i	1.33410	−	0.485571i	0.907948	+	0.419083i	$0.137648\pi$
$938$	−7.11624	+	4.51497i	−0.232353	+	0.147419i
$939$	6.98026	−	4.03006i	0.227792	−	0.131516i
$940$	−36.7420	−	3.35217i	−1.19839	−	0.109336i
$941$	−1.66255	+	1.98135i	−0.0541977	+	0.0645903i	−0.792462	−	0.609921i	$-0.791201\pi$
$941$	−1.66255	+	1.98135i	−0.0541977	+	0.0645903i	0.738265	+	0.674511i	$0.235646\pi$
$942$	−4.43819	+	0.185512i	−0.144604	+	0.00604431i
$943$	−4.37781	+	7.58259i	−0.142561	+	0.246923i
$944$	−9.80574	−	0.0728989i	−0.319150	−	0.00237266i
$945$	2.62287	+	14.8751i	0.0853221	+	0.483885i
$946$	−14.6688	−	11.2991i	−0.476924	−	0.367367i
$947$	18.5494	−	50.9642i	0.602776	−	1.65611i	−0.142847	−	0.989745i	$-0.545626\pi$
$947$	18.5494	−	50.9642i	0.602776	−	1.65611i	0.745623	−	0.666368i	$-0.232152\pi$
$948$	3.85336	−	14.1700i	0.125151	−	0.460221i
$949$		−	39.2972i		−	1.27564i
$950$	0.460967	−	1.57626i	0.0149558	−	0.0511408i
$951$	16.3419			0.529923
$952$	21.1153	−	22.7869i	0.684350	−	0.738527i
$953$	10.2109	+	3.71647i	0.330764	+	0.120388i	0.502064	−	0.864831i	$-0.332574\pi$
$953$	10.2109	+	3.71647i	0.330764	+	0.120388i	−0.171299	+	0.985219i	$0.554797\pi$
$954$	−4.22614	+	5.48647i	−0.136826	+	0.177631i
$955$	−38.5231	+	6.79266i	−1.24658	+	0.219805i
$956$	4.82523	+	3.40546i	0.156059	+	0.110140i
$957$	−8.49337	−	4.90365i	−0.274552	−	0.158512i
$958$	−24.9015	+	1.04086i	−0.804532	+	0.0336287i
$959$	3.34051	+	2.80302i	0.107871	+	0.0905143i
$960$	11.7453	+	5.63722i	0.379078	+	0.181940i
$961$	−5.34576	−	9.25913i	−0.172444	−	0.298682i
$962$	3.30317	+	5.20627i	0.106498	+	0.167857i
$963$	5.62820	+	15.4633i	0.181366	+	0.498299i
$964$	9.85184	−	9.77887i	0.317306	−	0.314956i
$965$	10.9883	+	1.93754i	0.353727	+	0.0623717i
$966$	3.06695	+	3.35950i	0.0986776	+	0.108090i
$967$	−34.1884	+	28.6875i	−1.09943	+	0.922528i	−0.997386	−	0.0722525i	$-0.976981\pi$
$967$	−34.1884	+	28.6875i	−1.09943	+	0.922528i	−0.102040	+	0.994780i	$0.532537\pi$
$968$	22.0834	−	2.78216i	0.709788	−	0.0894221i
$969$	−10.0912	+	18.4360i	−0.324176	+	0.592250i
$970$	−20.4490	−	10.6934i	−0.656577	−	0.343345i
$971$	22.6598	+	27.0049i	0.727187	+	0.866628i	0.995308	−	0.0967571i	$-0.0308470\pi$
$971$	22.6598	+	27.0049i	0.727187	+	0.866628i	−0.268121	+	0.963385i	$0.586403\pi$
$972$	29.8037	−	7.86726i	0.955955	−	0.252343i
$973$	21.9151	+	3.86422i	0.702565	+	0.123881i
$974$	0.910563	+	0.288961i	0.0291763	+	0.00925891i
$975$	0.461456	−	0.167956i	0.0147784	−	0.00537890i
$976$	−2.27993	+	1.88439i	−0.0729789	+	0.0603178i
$977$	−25.2280	−	43.6962i	−0.807115	−	1.39796i	−0.914854	−	0.403786i	$-0.867694\pi$
$977$	−25.2280	−	43.6962i	−0.807115	−	1.39796i	0.107738	−	0.994179i	$-0.465639\pi$
$978$	7.80841	−	3.21736i	0.249685	−	0.102880i
$979$	0.557561	−	0.664476i	0.0178197	−	0.0212367i
$980$	16.1125	+	7.58642i	0.514695	+	0.242339i
$981$	41.4972	+	23.9584i	1.32490	+	0.764934i
$982$	−12.9285	−	1.72652i	−0.412566	−	0.0550956i
$983$	0.873927	+	4.95628i	0.0278739	+	0.158081i	0.995568	−	0.0940475i	$-0.0299806\pi$
$983$	0.873927	+	4.95628i	0.0278739	+	0.158081i	−0.967694	+	0.252128i	$0.918869\pi$
$984$	7.34587	+	0.361774i	0.234178	+	0.0115329i
$985$	41.7720	+	15.2038i	1.33097	+	0.484432i
$986$	65.8894	−	14.4789i	2.09835	−	0.461103i
$987$			10.8211i			0.344440i
$988$	1.46305	−	21.4185i	0.0465457	−	0.681413i
$989$			18.6499i			0.593031i
$990$	2.85068	+	12.9726i	0.0906006	+	0.412298i
$991$	−50.4247	−	18.3531i	−1.60179	−	0.583005i	−0.622000	−	0.783017i	$-0.713680\pi$
$991$	−50.4247	−	18.3531i	−1.60179	−	0.583005i	−0.979794	+	0.200012i	$0.935902\pi$
$992$	−30.9865	+	19.3381i	−0.983823	+	0.613987i
$993$	−0.384508	−	2.18065i	−0.0122020	−	0.0692010i
$994$	−3.18993	+	23.8868i	−0.101179	+	0.757644i
$995$	29.1480	+	16.8286i	0.924054	+	0.533503i
$996$	−7.77581	+	16.5147i	−0.246386	+	0.523289i
$997$	34.4204	−	41.0206i	1.09010	−	1.29914i	0.138990	−	0.990294i	$-0.455614\pi$
$997$	34.4204	−	41.0206i	1.09010	−	1.29914i	0.951113	−	0.308842i	$-0.0999413\pi$
$998$	−0.355263	−	0.862209i	−0.0112456	−	0.0272928i
$999$	3.60429	+	6.24281i	0.114035	+	0.197514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.t.a.101.12	yes	108
4.3	odd	2		608.2.bf.a.177.11		108
8.3	odd	2		608.2.bf.a.177.8		108
8.5	even	2	inner	152.2.t.a.101.3	✓	108
19.16	even	9	inner	152.2.t.a.149.3	yes	108
76.35	odd	18		608.2.bf.a.529.8		108
152.35	odd	18		608.2.bf.a.529.11		108
152.149	even	18	inner	152.2.t.a.149.12	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.t.a.101.3	✓	108	8.5	even	2	inner
152.2.t.a.101.12	yes	108	1.1	even	1	trivial
152.2.t.a.149.3	yes	108	19.16	even	9	inner
152.2.t.a.149.12	yes	108	152.149	even	18	inner
608.2.bf.a.177.8		108	8.3	odd	2
608.2.bf.a.177.11		108	4.3	odd	2
608.2.bf.a.529.8		108	76.35	odd	18
608.2.bf.a.529.11		108	152.35	odd	18

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.303525 + 1.38126i) q^{2} +(-0.256004 + 0.703365i) q^{3} +(-1.81574 + 0.838493i) q^{4} +(-2.14263 + 0.377803i) q^{5} +(-1.04923 - 0.140118i) q^{6} +(-0.852529 + 1.47662i) q^{7} +(-1.70930 - 2.25351i) q^{8} +(1.86895 + 1.56823i) q^{9} +O(q^{10})\)	\(q+(0.303525 + 1.38126i) q^{2} +(-0.256004 + 0.703365i) q^{3} +(-1.81574 + 0.838493i) q^{4} +(-2.14263 + 0.377803i) q^{5} +(-1.04923 - 0.140118i) q^{6} +(-0.852529 + 1.47662i) q^{7} +(-1.70930 - 2.25351i) q^{8} +(1.86895 + 1.56823i) q^{9} +(-1.17218 - 2.84485i) q^{10} +(-1.53231 + 0.884678i) q^{11} +(-0.124929 - 1.49179i) q^{12} +(0.842256 + 2.31408i) q^{13} +(-2.29836 - 0.729369i) q^{14} +(0.282787 - 1.60377i) q^{15} +(2.59386 - 3.04498i) q^{16} +(4.93464 - 4.14065i) q^{17} +(-1.59886 + 3.05750i) q^{18} +(2.87718 + 3.27442i) q^{19} +(3.57368 - 2.48257i) q^{20} +(-0.820354 - 0.977660i) q^{21} +(-1.68706 - 1.84799i) q^{22} +(-0.437651 + 2.48204i) q^{23} +(2.02262 - 0.625354i) q^{24} +(-0.250347 + 0.0911189i) q^{25} +(-2.94070 + 1.86575i) q^{26} +(-3.52617 + 2.03584i) q^{27} +(0.309836 - 3.39601i) q^{28} +(4.76000 - 5.67275i) q^{29} +(2.30105 - 0.0961815i) q^{30} +(-3.22845 + 5.59184i) q^{31} +(4.99320 + 2.65856i) q^{32} +(-0.229975 - 1.30425i) q^{33} +(7.21710 + 5.55922i) q^{34} +(1.26878 - 3.48594i) q^{35} +(-4.70849 - 1.28041i) q^{36} -1.77042i q^{37} +(-3.64952 + 4.96800i) q^{38} -1.84326 q^{39} +(4.51377 + 4.18265i) q^{40} +(3.26449 + 1.18818i) q^{41} +(1.10140 - 1.42986i) q^{42} +(7.28735 - 1.28496i) q^{43} +(2.04048 - 2.89118i) q^{44} +(-4.59695 - 2.65405i) q^{45} +(-3.56118 + 0.148854i) q^{46} +(-6.49519 - 5.45011i) q^{47} +(1.47769 + 2.60395i) q^{48} +(2.04639 + 3.54445i) q^{49} +(-0.201845 - 0.318137i) q^{50} +(1.64910 + 4.53087i) q^{51} +(-3.46966 - 3.49555i) q^{52} +(1.97670 + 0.348545i) q^{53} +(-3.88230 - 4.25262i) q^{54} +(2.94893 - 2.47444i) q^{55} +(4.78481 - 0.602811i) q^{56} +(-3.03968 + 1.18545i) q^{57} +(9.28031 + 4.85297i) q^{58} +(-1.57580 - 1.87796i) q^{59} +(0.831278 + 3.14915i) q^{60} +(-0.728234 - 0.128407i) q^{61} +(-8.70368 - 2.76206i) q^{62} +(-3.90902 + 1.42277i) q^{63} +(-2.15659 + 7.70384i) q^{64} +(-2.67891 - 4.64000i) q^{65} +(1.73170 - 0.713527i) q^{66} +(2.24658 - 2.67737i) q^{67} +(-5.48814 + 11.6560i) q^{68} +(-1.63374 - 0.943240i) q^{69} +(5.20009 + 0.694439i) q^{70} +(-1.73545 - 9.84225i) q^{71} +(0.339435 - 6.89227i) q^{72} +(-14.9953 - 5.45784i) q^{73} +(2.44541 - 0.537367i) q^{74} -0.199412i q^{75} +(-7.96981 - 3.53301i) q^{76} -3.01685i q^{77} +(-0.559477 - 2.54602i) q^{78} +(9.21773 + 3.35498i) q^{79} +(-4.40727 + 7.50422i) q^{80} +(0.741748 + 4.20666i) q^{81} +(-0.650323 + 4.86974i) q^{82} +(-10.5599 - 6.09674i) q^{83} +(2.30931 + 1.08732i) q^{84} +(-9.00874 + 10.7362i) q^{85} +(3.98675 + 9.67569i) q^{86} +(2.77143 + 4.80026i) q^{87} +(4.61280 + 1.94089i) q^{88} +(-0.460676 + 0.167672i) q^{89} +(2.27063 - 7.15514i) q^{90} +(-4.13507 - 0.729125i) q^{91} +(-1.28651 - 4.87372i) q^{92} +(-3.10661 - 3.70231i) q^{93} +(5.55656 - 10.6258i) q^{94} +(-7.40182 - 5.92885i) q^{95} +(-3.14821 + 2.83144i) q^{96} +(5.74523 - 4.82082i) q^{97} +(-4.27467 + 3.90242i) q^{98} +(-4.25119 - 0.749599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9	\( 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 9 q^{10} - 3 q^{12} - 9 q^{14} - 12 q^{15} - 12 q^{17} - 12 q^{18} - 42 q^{20} - 12 q^{22} - 12 q^{23} - 36 q^{24} - 12 q^{25} + 21 q^{26} + 24 q^{28} - 48 q^{30} + 30 q^{31} + 39 q^{32} - 30 q^{33} - 60 q^{34} + 69 q^{36} - 42 q^{38} - 24 q^{39} + 36 q^{40} - 24 q^{41} - 81 q^{42} + 45 q^{44} - 18 q^{46} - 48 q^{47} - 21 q^{48} - 24 q^{49} - 12 q^{50} + 3 q^{52} + 63 q^{54} - 42 q^{55} + 30 q^{56} - 12 q^{57} - 84 q^{58} + 30 q^{60} - 6 q^{62} + 30 q^{63} + 3 q^{64} - 6 q^{65} + 54 q^{66} + 36 q^{68} + 123 q^{70} - 12 q^{71} + 150 q^{72} + 12 q^{73} + 75 q^{74} + 42 q^{76} + 39 q^{78} - 12 q^{79} + 51 q^{80} - 18 q^{81} + 99 q^{82} + 75 q^{84} - 48 q^{86} - 6 q^{87} - 27 q^{88} - 12 q^{89} + 66 q^{90} - 48 q^{92} + 54 q^{94} - 72 q^{95} + 42 q^{96} - 12 q^{97} + 93 q^{98}+O(q^{100}) \) 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 9 * q^10 - 3 * q^12 - 9 * q^14 - 12 * q^15 - 12 * q^17 - 12 * q^18 - 42 * q^20 - 12 * q^22 - 12 * q^23 - 36 * q^24 - 12 * q^25 + 21 * q^26 + 24 * q^28 - 48 * q^30 + 30 * q^31 + 39 * q^32 - 30 * q^33 - 60 * q^34 + 69 * q^36 - 42 * q^38 - 24 * q^39 + 36 * q^40 - 24 * q^41 - 81 * q^42 + 45 * q^44 - 18 * q^46 - 48 * q^47 - 21 * q^48 - 24 * q^49 - 12 * q^50 + 3 * q^52 + 63 * q^54 - 42 * q^55 + 30 * q^56 - 12 * q^57 - 84 * q^58 + 30 * q^60 - 6 * q^62 + 30 * q^63 + 3 * q^64 - 6 * q^65 + 54 * q^66 + 36 * q^68 + 123 * q^70 - 12 * q^71 + 150 * q^72 + 12 * q^73 + 75 * q^74 + 42 * q^76 + 39 * q^78 - 12 * q^79 + 51 * q^80 - 18 * q^81 + 99 * q^82 + 75 * q^84 - 48 * q^86 - 6 * q^87 - 27 * q^88 - 12 * q^89 + 66 * q^90 - 48 * q^92 + 54 * q^94 - 72 * q^95 + 42 * q^96 - 12 * q^97 + 93 * q^98

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